LMFDB - Embedded newform 619.2.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +O(q^{10})$	\(q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +0.0784807 q^{10} +0.333322 q^{11} -11.8134 q^{12} -1.65481 q^{13} +8.20170 q^{14} +0.0977777 q^{15} +3.42599 q^{16} -1.50147 q^{17} -14.9719 q^{18} -5.02748 q^{19} -0.126069 q^{20} +10.2184 q^{21} -0.809826 q^{22} -5.35036 q^{23} +13.9931 q^{24} -4.99896 q^{25} +4.02046 q^{26} -9.57238 q^{27} -13.1749 q^{28} +3.38998 q^{29} -0.237557 q^{30} -5.45120 q^{31} +0.922070 q^{32} -1.00895 q^{33} +3.64791 q^{34} +0.109047 q^{35} +24.0503 q^{36} -4.83972 q^{37} +12.2145 q^{38} +5.00902 q^{39} +0.149330 q^{40} +0.0826437 q^{41} -24.8261 q^{42} +1.78583 q^{43} +1.30087 q^{44} -0.199060 q^{45} +12.9990 q^{46} +7.93095 q^{47} -10.3703 q^{48} +4.39602 q^{49} +12.1453 q^{50} +4.54487 q^{51} -6.45832 q^{52} +11.6068 q^{53} +23.2567 q^{54} -0.0107671 q^{55} +15.6058 q^{56} +15.2179 q^{57} -8.23615 q^{58} -12.7123 q^{59} +0.381602 q^{60} -1.27687 q^{61} +13.2440 q^{62} -20.8030 q^{63} -9.09220 q^{64} +0.0534544 q^{65} +2.45130 q^{66} +11.1702 q^{67} -5.85987 q^{68} +16.1952 q^{69} -0.264935 q^{70} +9.44501 q^{71} -28.4879 q^{72} +16.0226 q^{73} +11.7584 q^{74} +15.1316 q^{75} -19.6210 q^{76} -1.12523 q^{77} -12.1697 q^{78} +2.17453 q^{79} -0.110668 q^{80} +10.4879 q^{81} -0.200788 q^{82} +0.893308 q^{83} +39.8797 q^{84} +0.0485011 q^{85} -4.33878 q^{86} -10.2613 q^{87} -1.54090 q^{88} +11.3541 q^{89} +0.483629 q^{90} +5.58631 q^{91} -20.8811 q^{92} +16.5005 q^{93} -19.2687 q^{94} +0.162400 q^{95} -2.79105 q^{96} -8.98396 q^{97} -10.6804 q^{98} +2.05406 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42956	−1.71796	−0.858979	−	0.512011i	$-0.828901\pi$
$2$	−2.42956	−1.71796	−0.858979	+	0.512011i	$0.828901\pi$
$3$	−3.02694	−1.74761	−0.873804	−	0.486279i	$-0.838354\pi$
$3$	−3.02694	−1.74761	−0.873804	+	0.486279i	$0.838354\pi$
$4$	3.90276	1.95138
$5$	−0.0323024	−0.0144461	−0.00722304	−	0.999974i	$-0.502299\pi$
$5$	−0.0323024	−0.0144461	−0.00722304	+	0.999974i	$0.502299\pi$
$6$	7.35414	3.00231
$7$	−3.37580	−1.27593	−0.637966	−	0.770064i	$-0.720224\pi$
$7$	−3.37580	−1.27593	−0.637966	+	0.770064i	$0.720224\pi$
$8$	−4.62286	−1.63443
$9$	6.16239	2.05413
$10$	0.0784807	0.0248178
$11$	0.333322	0.100500	0.0502502	−	0.998737i	$-0.483998\pi$
$11$	0.333322	0.100500	0.0502502	+	0.998737i	$0.483998\pi$
$12$	−11.8134	−3.41024
$13$	−1.65481	−0.458962	−0.229481	−	0.973313i	$-0.573703\pi$
$13$	−1.65481	−0.458962	−0.229481	+	0.973313i	$0.573703\pi$
$14$	8.20170	2.19200
$15$	0.0977777	0.0252461
$16$	3.42599	0.856497
$17$	−1.50147	−0.364160	−0.182080	−	0.983284i	$-0.558283\pi$
$17$	−1.50147	−0.364160	−0.182080	+	0.983284i	$0.558283\pi$
$18$	−14.9719	−3.52891
$19$	−5.02748	−1.15338	−0.576691	−	0.816962i	$-0.695656\pi$
$19$	−5.02748	−1.15338	−0.576691	+	0.816962i	$0.695656\pi$
$20$	−0.126069	−0.0281898
$21$	10.2184	2.22983
$22$	−0.809826	−0.172655
$23$	−5.35036	−1.11563	−0.557814	−	0.829966i	$-0.688360\pi$
$23$	−5.35036	−1.11563	−0.557814	+	0.829966i	$0.688360\pi$
$24$	13.9931	2.85634
$25$	−4.99896	−0.999791
$26$	4.02046	0.788477
$27$	−9.57238	−1.84221
$28$	−13.1749	−2.48983
$29$	3.38998	0.629503	0.314752	−	0.949174i	$-0.398079\pi$
$29$	3.38998	0.629503	0.314752	+	0.949174i	$0.398079\pi$
$30$	−0.237557	−0.0433717
$31$	−5.45120	−0.979065	−0.489532	−	0.871985i	$-0.662832\pi$
$31$	−5.45120	−0.979065	−0.489532	+	0.871985i	$0.662832\pi$
$32$	0.922070	0.163000
$33$	−1.00895	−0.175635
$34$	3.64791	0.625611
$35$	0.109047	0.0184322
$36$	24.0503	4.00838
$37$	−4.83972	−0.795644	−0.397822	−	0.917463i	$-0.630234\pi$
$37$	−4.83972	−0.795644	−0.397822	+	0.917463i	$0.630234\pi$
$38$	12.2145	1.98146
$39$	5.00902	0.802085
$40$	0.149330	0.0236111
$41$	0.0826437	0.0129068	0.00645339	−	0.999979i	$-0.497946\pi$
$41$	0.0826437	0.0129068	0.00645339	+	0.999979i	$0.497946\pi$
$42$	−24.8261	−3.83075
$43$	1.78583	0.272337	0.136168	−	0.990686i	$-0.456521\pi$
$43$	1.78583	0.272337	0.136168	+	0.990686i	$0.456521\pi$
$44$	1.30087	0.196114
$45$	−0.199060	−0.0296742
$46$	12.9990	1.91660
$47$	7.93095	1.15685	0.578424	−	0.815736i	$-0.303668\pi$
$47$	7.93095	1.15685	0.578424	+	0.815736i	$0.303668\pi$
$48$	−10.3703	−1.49682
$49$	4.39602	0.628003
$50$	12.1453	1.71760
$51$	4.54487	0.636409
$52$	−6.45832	−0.895608
$53$	11.6068	1.59432	0.797161	−	0.603767i	$-0.206334\pi$
$53$	11.6068	1.59432	0.797161	+	0.603767i	$0.206334\pi$
$54$	23.2567	3.16483
$55$	−0.0107671	−0.00145184
$56$	15.6058	2.08542
$57$	15.2179	2.01566
$58$	−8.23615	−1.08146
$59$	−12.7123	−1.65501	−0.827503	−	0.561461i	$-0.810240\pi$
$59$	−12.7123	−1.65501	−0.827503	+	0.561461i	$0.810240\pi$
$60$	0.381602	0.0492647
$61$	−1.27687	−0.163486	−0.0817432	−	0.996653i	$-0.526049\pi$
$61$	−1.27687	−0.163486	−0.0817432	+	0.996653i	$0.526049\pi$
$62$	13.2440	1.68199
$63$	−20.8030	−2.62093
$64$	−9.09220	−1.13653
$65$	0.0534544	0.00663020
$66$	2.45130	0.301734
$67$	11.1702	1.36466	0.682329	−	0.731045i	$-0.260967\pi$
$67$	11.1702	1.36466	0.682329	+	0.731045i	$0.260967\pi$
$68$	−5.85987	−0.710614
$69$	16.1952	1.94968
$70$	−0.264935	−0.0316658
$71$	9.44501	1.12092	0.560458	−	0.828183i	$-0.310625\pi$
$71$	9.44501	1.12092	0.560458	+	0.828183i	$0.310625\pi$
$72$	−28.4879	−3.35733
$73$	16.0226	1.87530	0.937651	−	0.347579i	$-0.112996\pi$
$73$	16.0226	1.87530	0.937651	+	0.347579i	$0.112996\pi$
$74$	11.7584	1.36688
$75$	15.1316	1.74724
$76$	−19.6210	−2.25068
$77$	−1.12523	−0.128232
$78$	−12.1697	−1.37795
$79$	2.17453	0.244654	0.122327	−	0.992490i	$-0.460964\pi$
$79$	2.17453	0.244654	0.122327	+	0.992490i	$0.460964\pi$
$80$	−0.110668	−0.0123730
$81$	10.4879	1.16532
$82$	−0.200788	−0.0221733
$83$	0.893308	0.0980533	0.0490266	−	0.998797i	$-0.484388\pi$
$83$	0.893308	0.0980533	0.0490266	+	0.998797i	$0.484388\pi$
$84$	39.8797	4.35124
$85$	0.0485011	0.00526069
$86$	−4.33878	−0.467863
$87$	−10.2613	−1.10012
$88$	−1.54090	−0.164260
$89$	11.3541	1.20353	0.601767	−	0.798672i	$-0.294464\pi$
$89$	11.3541	1.20353	0.601767	+	0.798672i	$0.294464\pi$
$90$	0.483629	0.0509789
$91$	5.58631	0.585604
$92$	−20.8811	−2.17701
$93$	16.5005	1.71102
$94$	−19.2687	−1.98742
$95$	0.162400	0.0166619
$96$	−2.79105	−0.284861
$97$	−8.98396	−0.912183	−0.456091	−	0.889933i	$-0.650751\pi$
$97$	−8.98396	−0.912183	−0.456091	+	0.889933i	$0.650751\pi$
$98$	−10.6804	−1.07888
$99$	2.05406	0.206441
$100$	−19.5097	−1.95097
$101$	−19.1212	−1.90263	−0.951315	−	0.308221i	$-0.900266\pi$
$101$	−19.1212	−1.90263	−0.951315	+	0.308221i	$0.900266\pi$
$102$	−11.0420	−1.09332
$103$	−19.7952	−1.95048	−0.975241	−	0.221143i	$-0.929021\pi$
$103$	−19.7952	−1.95048	−0.975241	+	0.221143i	$0.929021\pi$
$104$	7.64995	0.750139
$105$	−0.330078	−0.0322123
$106$	−28.1995	−2.73898
$107$	−0.880564	−0.0851273	−0.0425637	−	0.999094i	$-0.513553\pi$
$107$	−0.880564	−0.0851273	−0.0425637	+	0.999094i	$0.513553\pi$
$108$	−37.3587	−3.59484
$109$	10.0304	0.960736	0.480368	−	0.877067i	$-0.340503\pi$
$109$	10.0304	0.960736	0.480368	+	0.877067i	$0.340503\pi$
$110$	0.0261593	0.00249420
$111$	14.6495	1.39047
$112$	−11.5655	−1.09283
$113$	7.05601	0.663774	0.331887	−	0.943319i	$-0.392315\pi$
$113$	7.05601	0.663774	0.331887	+	0.943319i	$0.392315\pi$
$114$	−36.9727	−3.46282
$115$	0.172830	0.0161165
$116$	13.2303	1.22840
$117$	−10.1976	−0.942767
$118$	30.8854	2.84323
$119$	5.06866	0.464644
$120$	−0.452012	−0.0412629
$121$	−10.8889	−0.989900
$122$	3.10223	0.280863
$123$	−0.250158	−0.0225560
$124$	−21.2747	−1.91052
$125$	0.322991	0.0288892
$126$	50.5421	4.50265
$127$	−3.23199	−0.286793	−0.143396	−	0.989665i	$-0.545802\pi$
$127$	−3.23199	−0.286793	−0.143396	+	0.989665i	$0.545802\pi$
$128$	20.2459	1.78950
$129$	−5.40561	−0.475938
$130$	−0.129871	−0.0113904
$131$	10.2444	0.895054	0.447527	−	0.894270i	$-0.352305\pi$
$131$	10.2444	0.895054	0.447527	+	0.894270i	$0.352305\pi$
$132$	−3.93767	−0.342731
$133$	16.9717	1.47164
$134$	−27.1387	−2.34442
$135$	0.309211	0.0266127
$136$	6.94108	0.595193
$137$	−3.81470	−0.325912	−0.162956	−	0.986633i	$-0.552103\pi$
$137$	−3.81470	−0.325912	−0.162956	+	0.986633i	$0.552103\pi$
$138$	−39.3473	−3.34946
$139$	14.8581	1.26025	0.630123	−	0.776496i	$-0.283005\pi$
$139$	14.8581	1.26025	0.630123	+	0.776496i	$0.283005\pi$
$140$	0.425582	0.0359682
$141$	−24.0065	−2.02172
$142$	−22.9472	−1.92569
$143$	−0.551585	−0.0461258
$144$	21.1123	1.75936
$145$	−0.109505	−0.00909386
$146$	−38.9278	−3.22169
$147$	−13.3065	−1.09750
$148$	−18.8882	−1.55260
$149$	−4.00235	−0.327885	−0.163943	−	0.986470i	$-0.552421\pi$
$149$	−4.00235	−0.327885	−0.163943	+	0.986470i	$0.552421\pi$
$150$	−36.7630	−3.00169
$151$	4.75933	0.387309	0.193654	−	0.981070i	$-0.437966\pi$
$151$	4.75933	0.387309	0.193654	+	0.981070i	$0.437966\pi$
$152$	23.2413	1.88512
$153$	−9.25265	−0.748032
$154$	2.73381	0.220297
$155$	0.176087	0.0141437
$156$	19.5490	1.56517
$157$	19.7896	1.57938	0.789690	−	0.613506i	$-0.210241\pi$
$157$	19.7896	1.57938	0.789690	+	0.613506i	$0.210241\pi$
$158$	−5.28315	−0.420305
$159$	−35.1333	−2.78625
$160$	−0.0297851	−0.00235472
$161$	18.0617	1.42346
$162$	−25.4810	−2.00197
$163$	−6.82013	−0.534194	−0.267097	−	0.963670i	$-0.586064\pi$
$163$	−6.82013	−0.534194	−0.267097	+	0.963670i	$0.586064\pi$
$164$	0.322538	0.0251860
$165$	0.0325915	0.00253724
$166$	−2.17034	−0.168451
$167$	13.2644	1.02643	0.513215	−	0.858260i	$-0.328454\pi$
$167$	13.2644	1.02643	0.513215	+	0.858260i	$0.328454\pi$
$168$	−47.2380	−3.64449
$169$	−10.2616	−0.789354
$170$	−0.117836	−0.00903764
$171$	−30.9813	−2.36920
$172$	6.96966	0.531432
$173$	14.2557	1.08384	0.541921	−	0.840429i	$-0.317697\pi$
$173$	14.2557	1.08384	0.541921	+	0.840429i	$0.317697\pi$
$174$	24.9304	1.88997
$175$	16.8755	1.27567
$176$	1.14196	0.0860783
$177$	38.4796	2.89230
$178$	−27.5855	−2.06762
$179$	12.2721	0.917260	0.458630	−	0.888627i	$-0.348340\pi$
$179$	12.2721	0.917260	0.458630	+	0.888627i	$0.348340\pi$
$180$	−0.776884	−0.0579055
$181$	5.03653	0.374362	0.187181	−	0.982325i	$-0.440065\pi$
$181$	5.03653	0.374362	0.187181	+	0.982325i	$0.440065\pi$
$182$	−13.5723	−1.00604
$183$	3.86501	0.285710
$184$	24.7339	1.82341
$185$	0.156335	0.0114939
$186$	−40.0889	−2.93946
$187$	−0.500473	−0.0365982
$188$	30.9526	2.25745
$189$	32.3144	2.35053
$190$	−0.394560	−0.0286244
$191$	6.68323	0.483581	0.241791	−	0.970328i	$-0.422265\pi$
$191$	6.68323	0.483581	0.241791	+	0.970328i	$0.422265\pi$
$192$	27.5216	1.98620
$193$	−9.66090	−0.695407	−0.347703	−	0.937605i	$-0.613038\pi$
$193$	−9.66090	−0.695407	−0.347703	+	0.937605i	$0.613038\pi$
$194$	21.8271	1.56709
$195$	−0.161804	−0.0115870
$196$	17.1566	1.22547
$197$	22.6726	1.61536	0.807678	−	0.589624i	$-0.200724\pi$
$197$	22.6726	1.61536	0.807678	+	0.589624i	$0.200724\pi$
$198$	−4.99046	−0.354657
$199$	−10.8711	−0.770633	−0.385316	−	0.922785i	$-0.625908\pi$
$199$	−10.8711	−0.770633	−0.385316	+	0.922785i	$0.625908\pi$
$200$	23.1095	1.63409
$201$	−33.8116	−2.38489
$202$	46.4561	3.26864
$203$	−11.4439	−0.803203
$204$	17.7375	1.24187
$205$	−0.00266959	−0.000186452 0
$206$	48.0937	3.35085
$207$	−32.9710	−2.29164
$208$	−5.66936	−0.393100
$209$	−1.67577	−0.115915
$210$	0.801943	0.0553394
$211$	22.4482	1.54540	0.772699	−	0.634773i	$-0.218906\pi$
$211$	22.4482	1.54540	0.772699	+	0.634773i	$0.218906\pi$
$212$	45.2987	3.11112
$213$	−28.5895	−1.95892
$214$	2.13938	0.146245
$215$	−0.0576867	−0.00393420
$216$	44.2518	3.01095
$217$	18.4022	1.24922
$218$	−24.3694	−1.65050
$219$	−48.4995	−3.27729
$220$	−0.0420214	−0.00283308
$221$	2.48465	0.167136
$222$	−35.5919	−2.38877
$223$	9.86150	0.660375	0.330187	−	0.943915i	$-0.392888\pi$
$223$	9.86150	0.660375	0.330187	+	0.943915i	$0.392888\pi$
$224$	−3.11272	−0.207978
$225$	−30.8055	−2.05370
$226$	−17.1430	−1.14034
$227$	−9.95777	−0.660920	−0.330460	−	0.943820i	$-0.607204\pi$
$227$	−9.95777	−0.660920	−0.330460	+	0.943820i	$0.607204\pi$
$228$	59.3917	3.93331
$229$	12.5539	0.829585	0.414792	−	0.909916i	$-0.363854\pi$
$229$	12.5539	0.829585	0.414792	+	0.909916i	$0.363854\pi$
$230$	−0.419900	−0.0276874
$231$	3.40600	0.224099
$232$	−15.6714	−1.02888
$233$	−6.22700	−0.407944	−0.203972	−	0.978977i	$-0.565385\pi$
$233$	−6.22700	−0.407944	−0.203972	+	0.978977i	$0.565385\pi$
$234$	24.7756	1.61963
$235$	−0.256189	−0.0167119
$236$	−49.6132	−3.22954
$237$	−6.58218	−0.427559
$238$	−12.3146	−0.798238
$239$	2.13865	0.138338	0.0691688	−	0.997605i	$-0.477965\pi$
$239$	2.13865	0.138338	0.0691688	+	0.997605i	$0.477965\pi$
$240$	0.334985	0.0216232
$241$	23.6818	1.52548	0.762739	−	0.646706i	$-0.223854\pi$
$241$	23.6818	1.52548	0.762739	+	0.646706i	$0.223854\pi$
$242$	26.4552	1.70061
$243$	−3.02913	−0.194319
$244$	−4.98331	−0.319024
$245$	−0.142002	−0.00907219
$246$	0.607773	0.0387502
$247$	8.31952	0.529358
$248$	25.2001	1.60021
$249$	−2.70399	−0.171359
$250$	−0.784725	−0.0496304
$251$	−20.3919	−1.28713	−0.643563	−	0.765393i	$-0.722545\pi$
$251$	−20.3919	−1.28713	−0.643563	+	0.765393i	$0.722545\pi$
$252$	−81.1890	−5.11443
$253$	−1.78339	−0.112121
$254$	7.85231	0.492698
$255$	−0.146810	−0.00919362
$256$	−31.0042	−1.93776
$257$	−30.6145	−1.90968	−0.954839	−	0.297125i	$-0.903972\pi$
$257$	−30.6145	−1.90968	−0.954839	+	0.297125i	$0.903972\pi$
$258$	13.1333	0.817641
$259$	16.3379	1.01519
$260$	0.208619	0.0129380
$261$	20.8904	1.29308
$262$	−24.8893	−1.53766
$263$	−24.3347	−1.50054	−0.750270	−	0.661132i	$-0.770076\pi$
$263$	−24.3347	−1.50054	−0.750270	+	0.661132i	$0.770076\pi$
$264$	4.66422	0.287063
$265$	−0.374929	−0.0230317
$266$	−41.2339	−2.52821
$267$	−34.3683	−2.10331
$268$	43.5946	2.66296
$269$	12.3260	0.751528	0.375764	−	0.926715i	$-0.377380\pi$
$269$	12.3260	0.751528	0.375764	+	0.926715i	$0.377380\pi$
$270$	−0.751247	−0.0457194
$271$	−13.9583	−0.847906	−0.423953	−	0.905684i	$-0.639358\pi$
$271$	−13.9583	−0.847906	−0.423953	+	0.905684i	$0.639358\pi$
$272$	−5.14402	−0.311902
$273$	−16.9094	−1.02341
$274$	9.26804	0.559903
$275$	−1.66626	−0.100479
$276$	63.2061	3.80456
$277$	1.93138	0.116046	0.0580228	−	0.998315i	$-0.481520\pi$
$277$	1.93138	0.116046	0.0580228	+	0.998315i	$0.481520\pi$
$278$	−36.0986	−2.16505
$279$	−33.5924	−2.01113
$280$	−0.504107	−0.0301261
$281$	16.4329	0.980304	0.490152	−	0.871637i	$-0.336941\pi$
$281$	16.4329	0.980304	0.490152	+	0.871637i	$0.336941\pi$
$282$	58.3253	3.47322
$283$	−29.2492	−1.73868	−0.869342	−	0.494210i	$-0.835457\pi$
$283$	−29.2492	−1.73868	−0.869342	+	0.494210i	$0.835457\pi$
$284$	36.8615	2.18733
$285$	−0.491575	−0.0291184
$286$	1.34011	0.0792422
$287$	−0.278988	−0.0164682
$288$	5.68215	0.334824
$289$	−14.7456	−0.867387
$290$	0.266048	0.0156229
$291$	27.1939	1.59414
$292$	62.5322	3.65942
$293$	9.62737	0.562437	0.281218	−	0.959644i	$-0.409261\pi$
$293$	9.62737	0.562437	0.281218	+	0.959644i	$0.409261\pi$
$294$	32.3290	1.88546
$295$	0.410640	0.0239084
$296$	22.3733	1.30042
$297$	−3.19069	−0.185142
$298$	9.72394	0.563293
$299$	8.85383	0.512030
$300$	59.0548	3.40953
$301$	−6.02861	−0.347483
$302$	−11.5631	−0.665380
$303$	57.8788	3.32505
$304$	−17.2241	−0.987869
$305$	0.0412460	0.00236174
$306$	22.4799	1.28509
$307$	31.4085	1.79258	0.896288	−	0.443473i	$-0.146254\pi$
$307$	31.4085	1.79258	0.896288	+	0.443473i	$0.146254\pi$
$308$	−4.39149	−0.250228
$309$	59.9191	3.40868
$310$	−0.427814	−0.0242982
$311$	−9.93124	−0.563149	−0.281575	−	0.959539i	$-0.590857\pi$
$311$	−9.93124	−0.563149	−0.281575	+	0.959539i	$0.590857\pi$
$312$	−23.1560	−1.31095
$313$	−17.6550	−0.997917	−0.498959	−	0.866626i	$-0.666284\pi$
$313$	−17.6550	−0.997917	−0.498959	+	0.866626i	$0.666284\pi$
$314$	−48.0800	−2.71331
$315$	0.671988	0.0378622
$316$	8.48666	0.477412
$317$	−22.9524	−1.28914	−0.644568	−	0.764547i	$-0.722963\pi$
$317$	−22.9524	−1.28914	−0.644568	+	0.764547i	$0.722963\pi$
$318$	85.3583	4.78666
$319$	1.12995	0.0632653
$320$	0.293700	0.0164183
$321$	2.66542	0.148769
$322$	−43.8821	−2.44545
$323$	7.54860	0.420016
$324$	40.9317	2.27398
$325$	8.27232	0.458866
$326$	16.5699	0.917723
$327$	−30.3614	−1.67899
$328$	−0.382050	−0.0210952
$329$	−26.7733	−1.47606
$330$	−0.0791829	−0.00435887
$331$	12.6516	0.695396	0.347698	−	0.937606i	$-0.386963\pi$
$331$	12.6516	0.695396	0.347698	+	0.937606i	$0.386963\pi$
$332$	3.48636	0.191339
$333$	−29.8242	−1.63436
$334$	−32.2266	−1.76336
$335$	−0.360825	−0.0197140
$336$	35.0080	1.90984
$337$	3.30965	0.180288	0.0901440	−	0.995929i	$-0.471267\pi$
$337$	3.30965	0.180288	0.0901440	+	0.995929i	$0.471267\pi$
$338$	24.9312	1.35608
$339$	−21.3582	−1.16002
$340$	0.189288	0.0102656
$341$	−1.81701	−0.0983964
$342$	75.2708	4.07018
$343$	8.79051	0.474643
$344$	−8.25564	−0.445114
$345$	−0.523146	−0.0281652
$346$	−34.6351	−1.86199
$347$	17.1461	0.920450	0.460225	−	0.887802i	$-0.347769\pi$
$347$	17.1461	0.920450	0.460225	+	0.887802i	$0.347769\pi$
$348$	−40.0473	−2.14676
$349$	−13.5765	−0.726734	−0.363367	−	0.931646i	$-0.618373\pi$
$349$	−13.5765	−0.726734	−0.363367	+	0.931646i	$0.618373\pi$
$350$	−41.0000	−2.19154
$351$	15.8405	0.845502
$352$	0.307346	0.0163816
$353$	−35.8042	−1.90566	−0.952832	−	0.303499i	$-0.901845\pi$
$353$	−35.8042	−1.90566	−0.952832	+	0.303499i	$0.901845\pi$
$354$	−93.4884	−4.96885
$355$	−0.305097	−0.0161929
$356$	44.3124	2.34855
$357$	−15.3426	−0.812014
$358$	−29.8158	−1.57581
$359$	31.2324	1.64838	0.824191	−	0.566312i	$-0.191630\pi$
$359$	31.2324	1.64838	0.824191	+	0.566312i	$0.191630\pi$
$360$	0.920227	0.0485002
$361$	6.27551	0.330290
$362$	−12.2365	−0.643138
$363$	32.9601	1.72996
$364$	21.8020	1.14273
$365$	−0.517568	−0.0270908
$366$	−9.39027	−0.490837
$367$	32.6644	1.70507	0.852534	−	0.522672i	$-0.175065\pi$
$367$	32.6644	1.70507	0.852534	+	0.522672i	$0.175065\pi$
$368$	−18.3303	−0.955532
$369$	0.509283	0.0265122
$370$	−0.379824	−0.0197461
$371$	−39.1824	−2.03425
$372$	64.3973	3.33885
$373$	19.1389	0.990975	0.495487	−	0.868615i	$-0.334989\pi$
$373$	19.1389	0.990975	0.495487	+	0.868615i	$0.334989\pi$
$374$	1.21593	0.0628742
$375$	−0.977675	−0.0504869
$376$	−36.6636	−1.89078
$377$	−5.60977	−0.288918
$378$	−78.5098	−4.03811
$379$	22.0104	1.13060	0.565299	−	0.824886i	$-0.308761\pi$
$379$	22.0104	1.13060	0.565299	+	0.824886i	$0.308761\pi$
$380$	0.633806	0.0325136
$381$	9.78306	0.501201
$382$	−16.2373	−0.830772
$383$	−12.3848	−0.632833	−0.316416	−	0.948620i	$-0.602480\pi$
$383$	−12.3848	−0.632833	−0.316416	+	0.948620i	$0.602480\pi$
$384$	−61.2832	−3.12735
$385$	0.0363476	0.00185245
$386$	23.4717	1.19468
$387$	11.0050	0.559415
$388$	−35.0622	−1.78001
$389$	16.1516	0.818919	0.409460	−	0.912328i	$-0.365717\pi$
$389$	16.1516	0.818919	0.409460	+	0.912328i	$0.365717\pi$
$390$	0.393111	0.0199060
$391$	8.03341	0.406267
$392$	−20.3222	−1.02642
$393$	−31.0091	−1.56420
$394$	−55.0844	−2.77511
$395$	−0.0702426	−0.00353429
$396$	8.01650	0.402844
$397$	−23.0393	−1.15631	−0.578155	−	0.815927i	$-0.696227\pi$
$397$	−23.0393	−1.15631	−0.578155	+	0.815927i	$0.696227\pi$
$398$	26.4120	1.32391
$399$	−51.3725	−2.57184
$400$	−17.1264	−0.856319
$401$	−6.98825	−0.348977	−0.174488	−	0.984659i	$-0.555827\pi$
$401$	−6.98825	−0.348977	−0.174488	+	0.984659i	$0.555827\pi$
$402$	82.1472	4.09713
$403$	9.02070	0.449353
$404$	−74.6253	−3.71275
$405$	−0.338785	−0.0168343
$406$	27.8036	1.37987
$407$	−1.61318	−0.0799626
$408$	−21.0103	−1.04016
$409$	−16.6359	−0.822591	−0.411296	−	0.911502i	$-0.634924\pi$
$409$	−16.6359	−0.822591	−0.411296	+	0.911502i	$0.634924\pi$
$410$	0.00648593	0.000320317 0
$411$	11.5469	0.569566
$412$	−77.2560	−3.80613
$413$	42.9143	2.11168
$414$	80.1050	3.93695
$415$	−0.0288560	−0.00141649
$416$	−1.52585	−0.0748110
$417$	−44.9746	−2.20241
$418$	4.07138	0.199138
$419$	16.2490	0.793815	0.396907	−	0.917859i	$-0.370083\pi$
$419$	16.2490	0.793815	0.396907	+	0.917859i	$0.370083\pi$
$420$	−1.28821	−0.0628584
$421$	−21.2631	−1.03630	−0.518150	−	0.855290i	$-0.673379\pi$
$421$	−21.2631	−1.03630	−0.518150	+	0.855290i	$0.673379\pi$
$422$	−54.5392	−2.65493
$423$	48.8736	2.37632
$424$	−53.6568	−2.60580
$425$	7.50578	0.364084
$426$	69.4599	3.36534
$427$	4.31045	0.208598
$428$	−3.43663	−0.166116
$429$	1.66962	0.0806098
$430$	0.140153	0.00675879
$431$	−12.5978	−0.606814	−0.303407	−	0.952861i	$-0.598124\pi$
$431$	−12.5978	−0.606814	−0.303407	+	0.952861i	$0.598124\pi$
$432$	−32.7949	−1.57784
$433$	9.83400	0.472592	0.236296	−	0.971681i	$-0.424067\pi$
$433$	9.83400	0.472592	0.236296	+	0.971681i	$0.424067\pi$
$434$	−44.7091	−2.14611
$435$	0.331464	0.0158925
$436$	39.1461	1.87476
$437$	26.8988	1.28674
$438$	117.832	5.63024
$439$	−10.9426	−0.522259	−0.261130	−	0.965304i	$-0.584095\pi$
$439$	−10.9426	−0.522259	−0.261130	+	0.965304i	$0.584095\pi$
$440$	0.0497748	0.00237292
$441$	27.0900	1.29000
$442$	−6.03660	−0.287132
$443$	−9.86639	−0.468766	−0.234383	−	0.972144i	$-0.575307\pi$
$443$	−9.86639	−0.468766	−0.234383	+	0.972144i	$0.575307\pi$
$444$	57.1736	2.71334
$445$	−0.366766	−0.0173864
$446$	−23.9591	−1.13450
$447$	12.1149	0.573015
$448$	30.6934	1.45013
$449$	35.9120	1.69479	0.847397	−	0.530961i	$-0.178169\pi$
$449$	35.9120	1.69479	0.847397	+	0.530961i	$0.178169\pi$
$450$	74.8438	3.52817
$451$	0.0275470	0.00129714
$452$	27.5379	1.29527
$453$	−14.4062	−0.676864
$454$	24.1930	1.13543
$455$	−0.180451	−0.00845969
$456$	−70.3501	−3.29445
$457$	−24.8431	−1.16211	−0.581056	−	0.813864i	$-0.697360\pi$
$457$	−24.8431	−1.16211	−0.581056	+	0.813864i	$0.697360\pi$
$458$	−30.5004	−1.42519
$459$	14.3726	0.670858
$460$	0.674512	0.0314493
$461$	32.2525	1.50215	0.751073	−	0.660219i	$-0.229536\pi$
$461$	32.2525	1.50215	0.751073	+	0.660219i	$0.229536\pi$
$462$	−8.27509	−0.384992
$463$	−10.2424	−0.476005	−0.238002	−	0.971265i	$-0.576493\pi$
$463$	−10.2424	−0.476005	−0.238002	+	0.971265i	$0.576493\pi$
$464$	11.6140	0.539168
$465$	−0.533006	−0.0247176
$466$	15.1289	0.700830
$467$	−12.5826	−0.582253	−0.291127	−	0.956685i	$-0.594030\pi$
$467$	−12.5826	−0.582253	−0.291127	+	0.956685i	$0.594030\pi$
$468$	−39.7987	−1.83970
$469$	−37.7084	−1.74121
$470$	0.622426	0.0287104
$471$	−59.9020	−2.76014
$472$	58.7674	2.70499
$473$	0.595257	0.0273700
$474$	15.9918	0.734528
$475$	25.1321	1.15314
$476$	19.7817	0.906695
$477$	71.5259	3.27495
$478$	−5.19597	−0.237658
$479$	−5.02267	−0.229492	−0.114746	−	0.993395i	$-0.536605\pi$
$479$	−5.02267	−0.229492	−0.114746	+	0.993395i	$0.536605\pi$
$480$	0.0901578	0.00411512
$481$	8.00881	0.365170
$482$	−57.5363	−2.62071
$483$	−54.6719	−2.48766
$484$	−42.4967	−1.93167
$485$	0.290204	0.0131775
$486$	7.35945	0.333831
$487$	14.1461	0.641019	0.320510	−	0.947245i	$-0.396146\pi$
$487$	14.1461	0.641019	0.320510	+	0.947245i	$0.396146\pi$
$488$	5.90278	0.267206
$489$	20.6442	0.933561
$490$	0.345003	0.0155856
$491$	−2.94129	−0.132739	−0.0663693	−	0.997795i	$-0.521142\pi$
$491$	−2.94129	−0.132739	−0.0663693	+	0.997795i	$0.521142\pi$
$492$	−0.976305	−0.0440152
$493$	−5.08995	−0.229240
$494$	−20.2128	−0.909415
$495$	−0.0663512	−0.00298226
$496$	−18.6758	−0.838566
$497$	−31.8844	−1.43021
$498$	6.56951	0.294387
$499$	26.8514	1.20204	0.601018	−	0.799236i	$-0.294762\pi$
$499$	26.8514	1.20204	0.601018	+	0.799236i	$0.294762\pi$
$500$	1.26055	0.0563737
$501$	−40.1506	−1.79380
$502$	49.5434	2.21123
$503$	−22.6589	−1.01031	−0.505155	−	0.863029i	$-0.668565\pi$
$503$	−22.6589	−1.01031	−0.505155	+	0.863029i	$0.668565\pi$
$504$	96.1693	4.28372
$505$	0.617661	0.0274856
$506$	4.33286	0.192619
$507$	31.0613	1.37948
$508$	−12.6137	−0.559641
$509$	4.59675	0.203747	0.101874	−	0.994797i	$-0.467516\pi$
$509$	4.59675	0.203747	0.101874	+	0.994797i	$0.467516\pi$
$510$	0.356684	0.0157942
$511$	−54.0890	−2.39276
$512$	34.8347	1.53949
$513$	48.1249	2.12477
$514$	74.3796	3.28074
$515$	0.639434	0.0281768
$516$	−21.0968	−0.928734
$517$	2.64356	0.116264
$518$	−39.6939	−1.74405
$519$	−43.1513	−1.89413
$520$	−0.247112	−0.0108366
$521$	−20.6840	−0.906182	−0.453091	−	0.891464i	$-0.649679\pi$
$521$	−20.6840	−0.906182	−0.453091	+	0.891464i	$0.649679\pi$
$522$	−50.7544	−2.22146
$523$	−33.1967	−1.45159	−0.725794	−	0.687912i	$-0.758528\pi$
$523$	−33.1967	−1.45159	−0.725794	+	0.687912i	$0.758528\pi$
$524$	39.9812	1.74659
$525$	−51.0811	−2.22936
$526$	59.1225	2.57786
$527$	8.18482	0.356536
$528$	−3.45664	−0.150431
$529$	5.62636	0.244624
$530$	0.910913	0.0395675
$531$	−78.3385	−3.39960
$532$	66.2366	2.87172
$533$	−0.136760	−0.00592372
$534$	83.4998	3.61339
$535$	0.0284444	0.00122976
$536$	−51.6382	−2.23043
$537$	−37.1470	−1.60301
$538$	−29.9467	−1.29109
$539$	1.46529	0.0631146
$540$	1.20678	0.0519314
$541$	32.4624	1.39567	0.697833	−	0.716261i	$-0.254148\pi$
$541$	32.4624	1.39567	0.697833	+	0.716261i	$0.254148\pi$
$542$	33.9125	1.45667
$543$	−15.2453	−0.654238
$544$	−1.38446	−0.0593582
$545$	−0.324006	−0.0138789
$546$	41.0825	1.75817
$547$	7.64787	0.326999	0.163500	−	0.986543i	$-0.447722\pi$
$547$	7.64787	0.326999	0.163500	+	0.986543i	$0.447722\pi$
$548$	−14.8879	−0.635977
$549$	−7.86857	−0.335822
$550$	4.04828	0.172619
$551$	−17.0430	−0.726058
$552$	−74.8683	−3.18661
$553$	−7.34078	−0.312162
$554$	−4.69241	−0.199361
$555$	−0.473216	−0.0200869
$556$	57.9874	2.45921
$557$	11.5304	0.488559	0.244279	−	0.969705i	$-0.421449\pi$
$557$	11.5304	0.488559	0.244279	+	0.969705i	$0.421449\pi$
$558$	81.6148	3.45503
$559$	−2.95521	−0.124992
$560$	0.373592	0.0157872
$561$	1.51490	0.0639593
$562$	−39.9247	−1.68412
$563$	−15.3958	−0.648858	−0.324429	−	0.945910i	$-0.605172\pi$
$563$	−15.3958	−0.648858	−0.324429	+	0.945910i	$0.605172\pi$
$564$	−93.6917	−3.94513
$565$	−0.227926	−0.00958894
$566$	71.0627	2.98699
$567$	−35.4050	−1.48687
$568$	−43.6629	−1.83205
$569$	−44.9142	−1.88290	−0.941450	−	0.337153i	$-0.890536\pi$
$569$	−44.9142	−1.88290	−0.941450	+	0.337153i	$0.890536\pi$
$570$	1.19431	0.0500241
$571$	−13.6202	−0.569988	−0.284994	−	0.958529i	$-0.591992\pi$
$571$	−13.6202	−0.569988	−0.284994	+	0.958529i	$0.591992\pi$
$572$	−2.15270	−0.0900089
$573$	−20.2298	−0.845110
$574$	0.677819	0.0282916
$575$	26.7462	1.11539
$576$	−56.0297	−2.33457
$577$	25.4563	1.05976	0.529879	−	0.848073i	$-0.322237\pi$
$577$	25.4563	1.05976	0.529879	+	0.848073i	$0.322237\pi$
$578$	35.8253	1.49013
$579$	29.2430	1.21530
$580$	−0.427370	−0.0177456
$581$	−3.01563	−0.125109
$582$	−66.0693	−2.73866
$583$	3.86882	0.160230
$584$	−74.0701	−3.06504
$585$	0.329407	0.0136193
$586$	−23.3903	−0.966242
$587$	−0.0745162	−0.00307561	−0.00153781	−	0.999999i	$-0.500489\pi$
$587$	−0.0745162	−0.00307561	−0.00153781	+	0.999999i	$0.500489\pi$
$588$	−51.9321	−2.14164
$589$	27.4058	1.12924
$590$	−0.997674	−0.0410736
$591$	−68.6287	−2.82301
$592$	−16.5808	−0.681467
$593$	18.1883	0.746903	0.373452	−	0.927650i	$-0.378174\pi$
$593$	18.1883	0.746903	0.373452	+	0.927650i	$0.378174\pi$
$594$	7.75196	0.318067
$595$	−0.163730	−0.00671228
$596$	−15.6202	−0.639828
$597$	32.9062	1.34676
$598$	−21.5109	−0.879646
$599$	10.8427	0.443021	0.221510	−	0.975158i	$-0.428901\pi$
$599$	10.8427	0.443021	0.221510	+	0.975158i	$0.428901\pi$
$600$	−69.9510	−2.85574
$601$	−10.7179	−0.437193	−0.218597	−	0.975815i	$-0.570148\pi$
$601$	−10.7179	−0.437193	−0.218597	+	0.975815i	$0.570148\pi$
$602$	14.6469	0.596961
$603$	68.8352	2.80318
$604$	18.5745	0.755786
$605$	0.351738	0.0143002
$606$	−140.620	−5.71229
$607$	40.9798	1.66332	0.831660	−	0.555285i	$-0.187391\pi$
$607$	40.9798	1.66332	0.831660	+	0.555285i	$0.187391\pi$
$608$	−4.63568	−0.188002
$609$	34.6400	1.40368
$610$	−0.100210	−0.00405737
$611$	−13.1242	−0.530949
$612$	−36.1108	−1.45969
$613$	−33.5595	−1.35546	−0.677728	−	0.735313i	$-0.737035\pi$
$613$	−33.5595	−1.35546	−0.677728	+	0.735313i	$0.737035\pi$
$614$	−76.3087	−3.07957
$615$	0.00808071	0.000325846 0
$616$	5.20177	0.209585
$617$	37.5593	1.51208	0.756040	−	0.654526i	$-0.227132\pi$
$617$	37.5593	1.51208	0.756040	+	0.654526i	$0.227132\pi$
$618$	−145.577	−5.85596
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	0.687225	0.0275996
$621$	51.2157	2.05522
$622$	24.1285	0.967466
$623$	−38.3292	−1.53563
$624$	17.1608	0.686984
$625$	24.9843	0.999374
$626$	42.8938	1.71438
$627$	5.07246	0.202574
$628$	77.2339	3.08197
$629$	7.26669	0.289742
$630$	−1.63263	−0.0650457
$631$	−33.2887	−1.32520	−0.662601	−	0.748973i	$-0.730547\pi$
$631$	−33.2887	−1.32520	−0.662601	+	0.748973i	$0.730547\pi$
$632$	−10.0525	−0.399869
$633$	−67.9494	−2.70075
$634$	55.7642	2.21468
$635$	0.104401	0.00414304
$636$	−137.117	−5.43702
$637$	−7.27458	−0.288229
$638$	−2.74529	−0.108687
$639$	58.2038	2.30251
$640$	−0.653992	−0.0258513
$641$	−43.8778	−1.73307	−0.866535	−	0.499116i	$-0.833658\pi$
$641$	−43.8778	−1.73307	−0.866535	+	0.499116i	$0.833658\pi$
$642$	−6.47579	−0.255579
$643$	−16.4937	−0.650448	−0.325224	−	0.945637i	$-0.605440\pi$
$643$	−16.4937	−0.650448	−0.325224	+	0.945637i	$0.605440\pi$
$644$	70.4906	2.77772
$645$	0.174614	0.00687544
$646$	−18.3398	−0.721569
$647$	16.1560	0.635160	0.317580	−	0.948232i	$-0.397130\pi$
$647$	16.1560	0.635160	0.317580	+	0.948232i	$0.397130\pi$
$648$	−48.4840	−1.90463
$649$	−4.23731	−0.166329
$650$	−20.0981	−0.788312
$651$	−55.7023	−2.18315
$652$	−26.6173	−1.04241
$653$	−14.2100	−0.556079	−0.278039	−	0.960570i	$-0.589685\pi$
$653$	−14.2100	−0.556079	−0.278039	+	0.960570i	$0.589685\pi$
$654$	73.7648	2.88443
$655$	−0.330918	−0.0129300
$656$	0.283136	0.0110546
$657$	98.7374	3.85211
$658$	65.0473	2.53581
$659$	23.0308	0.897152	0.448576	−	0.893745i	$-0.351931\pi$
$659$	23.0308	0.897152	0.448576	+	0.893745i	$0.351931\pi$
$660$	0.127197	0.00495112
$661$	−30.3656	−1.18109	−0.590543	−	0.807006i	$-0.701087\pi$
$661$	−30.3656	−1.18109	−0.590543	+	0.807006i	$0.701087\pi$
$662$	−30.7379	−1.19466
$663$	−7.52089	−0.292087
$664$	−4.12963	−0.160261
$665$	−0.548229	−0.0212594
$666$	72.4597	2.80776
$667$	−18.1376	−0.702291
$668$	51.7677	2.00295
$669$	−29.8502	−1.15408
$670$	0.876645	0.0338678
$671$	−0.425609	−0.0164304
$672$	9.42204	0.363463
$673$	−10.7264	−0.413474	−0.206737	−	0.978397i	$-0.566284\pi$
$673$	−10.7264	−0.413474	−0.206737	+	0.978397i	$0.566284\pi$
$674$	−8.04099	−0.309727
$675$	47.8519	1.84182
$676$	−40.0485	−1.54033
$677$	39.4288	1.51537	0.757687	−	0.652618i	$-0.226329\pi$
$677$	39.4288	1.51537	0.757687	+	0.652618i	$0.226329\pi$
$678$	51.8909	1.99286
$679$	30.3280	1.16388
$680$	−0.224214	−0.00859821
$681$	30.1416	1.15503
$682$	4.41452	0.169041
$683$	13.3888	0.512308	0.256154	−	0.966636i	$-0.417545\pi$
$683$	13.3888	0.512308	0.256154	+	0.966636i	$0.417545\pi$
$684$	−120.912	−4.62320
$685$	0.123224	0.00470815
$686$	−21.3571	−0.815416
$687$	−38.0000	−1.44979
$688$	6.11824	0.233256
$689$	−19.2071	−0.731733
$690$	1.27101	0.0483867
$691$	−10.3514	−0.393787	−0.196893	−	0.980425i	$-0.563085\pi$
$691$	−10.3514	−0.393787	−0.196893	+	0.980425i	$0.563085\pi$
$692$	55.6366	2.11499
$693$	−6.93410	−0.263405
$694$	−41.6574	−1.58129
$695$	−0.479952	−0.0182056
$696$	47.4364	1.79807
$697$	−0.124087	−0.00470013
$698$	32.9849	1.24850
$699$	18.8488	0.712926
$700$	65.8609	2.48931
$701$	1.46168	0.0552070	0.0276035	−	0.999619i	$-0.491212\pi$
$701$	1.46168	0.0552070	0.0276035	+	0.999619i	$0.491212\pi$
$702$	−38.4854	−1.45254
$703$	24.3315	0.917682
$704$	−3.03063	−0.114221
$705$	0.775470	0.0292059
$706$	86.9883	3.27385
$707$	64.5493	2.42763
$708$	150.176	5.64397
$709$	−2.10668	−0.0791180	−0.0395590	−	0.999217i	$-0.512595\pi$
$709$	−2.10668	−0.0791180	−0.0395590	+	0.999217i	$0.512595\pi$
$710$	0.741250	0.0278186
$711$	13.4003	0.502551
$712$	−52.4885	−1.96709
$713$	29.1659	1.09227
$714$	37.2756	1.39501
$715$	0.0178175	0.000666338 0
$716$	47.8950	1.78992
$717$	−6.47356	−0.241760
$718$	−75.8809	−2.83185
$719$	−21.1806	−0.789903	−0.394952	−	0.918702i	$-0.629239\pi$
$719$	−21.1806	−0.789903	−0.394952	+	0.918702i	$0.629239\pi$
$720$	−0.681978	−0.0254158
$721$	66.8248	2.48868
$722$	−15.2467	−0.567424
$723$	−71.6835	−2.66594
$724$	19.6563	0.730522
$725$	−16.9464	−0.629372
$726$	−80.0785	−2.97199
$727$	39.1371	1.45151	0.725757	−	0.687951i	$-0.241489\pi$
$727$	39.1371	1.45151	0.725757	+	0.687951i	$0.241489\pi$
$728$	−25.8247	−0.957127
$729$	−22.2947	−0.825729
$730$	1.25746	0.0465408
$731$	−2.68137	−0.0991742
$732$	15.0842	0.557528
$733$	−19.7887	−0.730914	−0.365457	−	0.930828i	$-0.619087\pi$
$733$	−19.7887	−0.730914	−0.365457	+	0.930828i	$0.619087\pi$
$734$	−79.3601	−2.92923
$735$	0.429833	0.0158546
$736$	−4.93341	−0.181848
$737$	3.72328	0.137149
$738$	−1.23733	−0.0455468
$739$	34.3551	1.26377	0.631886	−	0.775061i	$-0.282281\pi$
$739$	34.3551	1.26377	0.631886	+	0.775061i	$0.282281\pi$
$740$	0.610136	0.0224290
$741$	−25.1827	−0.925110
$742$	95.1959	3.49475
$743$	8.25712	0.302924	0.151462	−	0.988463i	$-0.451602\pi$
$743$	8.25712	0.302924	0.151462	+	0.988463i	$0.451602\pi$
$744$	−76.2794	−2.79654
$745$	0.129286	0.00473666
$746$	−46.4991	−1.70245
$747$	5.50491	0.201414
$748$	−1.95322	−0.0714170
$749$	2.97261	0.108617
$750$	2.37532	0.0867344
$751$	12.9342	0.471975	0.235988	−	0.971756i	$-0.424167\pi$
$751$	12.9342	0.471975	0.235988	+	0.971756i	$0.424167\pi$
$752$	27.1713	0.990837
$753$	61.7252	2.24939
$754$	13.6293	0.496349
$755$	−0.153738	−0.00559510
$756$	126.115	4.58677
$757$	−9.35561	−0.340035	−0.170018	−	0.985441i	$-0.554382\pi$
$757$	−9.35561	−0.340035	−0.170018	+	0.985441i	$0.554382\pi$
$758$	−53.4756	−1.94232
$759$	5.39823	0.195943
$760$	−0.750750	−0.0272326
$761$	−33.5186	−1.21505	−0.607524	−	0.794301i	$-0.707837\pi$
$761$	−33.5186	−1.21505	−0.607524	+	0.794301i	$0.707837\pi$
$762$	−23.7685	−0.861042
$763$	−33.8606	−1.22583
$764$	26.0830	0.943650
$765$	0.298883	0.0108061
$766$	30.0896	1.08718
$767$	21.0365	0.759585
$768$	93.8480	3.38645
$769$	−11.1247	−0.401166	−0.200583	−	0.979677i	$-0.564284\pi$
$769$	−11.1247	−0.401166	−0.200583	+	0.979677i	$0.564284\pi$
$770$	−0.0883087	−0.00318242
$771$	92.6682	3.33737
$772$	−37.7041	−1.35700
$773$	16.8751	0.606953	0.303477	−	0.952839i	$-0.401853\pi$
$773$	16.8751	0.606953	0.303477	+	0.952839i	$0.401853\pi$
$774$	−26.7373	−0.961052
$775$	27.2503	0.978860
$776$	41.5316	1.49090
$777$	−49.4539	−1.77415
$778$	−39.2413	−1.40687
$779$	−0.415489	−0.0148864
$780$	−0.631480	−0.0226106
$781$	3.14823	0.112652
$782$	−19.5176	−0.697949
$783$	−32.4502	−1.15967
$784$	15.0607	0.537883
$785$	−0.639252	−0.0228159
$786$	75.3385	2.68723
$787$	10.5636	0.376553	0.188277	−	0.982116i	$-0.439710\pi$
$787$	10.5636	0.376553	0.188277	+	0.982116i	$0.439710\pi$
$788$	88.4856	3.15217
$789$	73.6596	2.62235
$790$	0.170659	0.00607176
$791$	−23.8197	−0.846930
$792$	−9.49563	−0.337413
$793$	2.11298	0.0750340
$794$	55.9753	1.98649
$795$	1.13489	0.0402504
$796$	−42.4273	−1.50380
$797$	27.0776	0.959137	0.479568	−	0.877504i	$-0.340793\pi$
$797$	27.0776	0.959137	0.479568	+	0.877504i	$0.340793\pi$
$798$	124.813	4.41832
$799$	−11.9081	−0.421278
$800$	−4.60939	−0.162966
$801$	69.9685	2.47222
$802$	16.9784	0.599527
$803$	5.34068	0.188469
$804$	−131.958	−4.65381
$805$	−0.583438	−0.0205635
$806$	−21.9163	−0.771970
$807$	−37.3100	−1.31338
$808$	88.3945	3.10971
$809$	5.49991	0.193367	0.0966833	−	0.995315i	$-0.469177\pi$
$809$	5.49991	0.193367	0.0966833	+	0.995315i	$0.469177\pi$
$810$	0.823097	0.0289207
$811$	40.2347	1.41283	0.706415	−	0.707798i	$-0.250311\pi$
$811$	40.2347	1.41283	0.706415	+	0.707798i	$0.250311\pi$
$812$	−44.6627	−1.56735
$813$	42.2510	1.48181
$814$	3.91933	0.137372
$815$	0.220307	0.00771701
$816$	15.5707	0.545082
$817$	−8.97822	−0.314108
$818$	40.4179	1.41318
$819$	34.4250	1.20291
$820$	−0.0104188	−0.000363839 0
$821$	22.0387	0.769157	0.384579	−	0.923092i	$-0.374347\pi$
$821$	22.0387	0.769157	0.384579	+	0.923092i	$0.374347\pi$
$822$	−28.0539	−0.978490
$823$	1.67762	0.0584781	0.0292390	−	0.999572i	$-0.490692\pi$
$823$	1.67762	0.0584781	0.0292390	+	0.999572i	$0.490692\pi$
$824$	91.5105	3.18792
$825$	5.04368	0.175599
$826$	−104.263	−3.62777
$827$	−3.15787	−0.109810	−0.0549049	−	0.998492i	$-0.517486\pi$
$827$	−3.15787	−0.109810	−0.0549049	+	0.998492i	$0.517486\pi$
$828$	−128.678	−4.47186
$829$	24.1320	0.838138	0.419069	−	0.907954i	$-0.362357\pi$
$829$	24.1320	0.838138	0.419069	+	0.907954i	$0.362357\pi$
$830$	0.0701074	0.00243346
$831$	−5.84619	−0.202802
$832$	15.0459	0.521622
$833$	−6.60050	−0.228694
$834$	109.268	3.78365
$835$	−0.428472	−0.0148279
$836$	−6.54011	−0.226195
$837$	52.1810	1.80364
$838$	−39.4778	−1.36374
$839$	−54.9414	−1.89679	−0.948394	−	0.317095i	$-0.897293\pi$
$839$	−54.9414	−1.89679	−0.948394	+	0.317095i	$0.897293\pi$
$840$	1.52590	0.0526486
$841$	−17.5080	−0.603726
$842$	51.6599	1.78032
$843$	−49.7414	−1.71319
$844$	87.6098	3.01565
$845$	0.331475	0.0114031
$846$	−118.741	−4.08241
$847$	36.7587	1.26304
$848$	39.7649	1.36553
$849$	88.5357	3.03854
$850$	−18.2357	−0.625481
$851$	25.8942	0.887642
$852$	−111.578	−3.82259
$853$	−50.7022	−1.73601	−0.868006	−	0.496554i	$-0.834598\pi$
$853$	−50.7022	−1.73601	−0.868006	+	0.496554i	$0.834598\pi$
$854$	−10.4725	−0.358362
$855$	1.00077	0.0342256
$856$	4.07072	0.139134
$857$	50.1517	1.71315	0.856575	−	0.516023i	$-0.172588\pi$
$857$	50.1517	1.71315	0.856575	+	0.516023i	$0.172588\pi$
$858$	−4.05643	−0.138484
$859$	−31.2237	−1.06534	−0.532669	−	0.846324i	$-0.678811\pi$
$859$	−31.2237	−1.06534	−0.532669	+	0.846324i	$0.678811\pi$
$860$	−0.225137	−0.00767711
$861$	0.844483	0.0287799
$862$	30.6071	1.04248
$863$	55.4201	1.88652	0.943261	−	0.332053i	$-0.107741\pi$
$863$	55.4201	1.88652	0.943261	+	0.332053i	$0.107741\pi$
$864$	−8.82641	−0.300280
$865$	−0.460495	−0.0156573
$866$	−23.8923	−0.811893
$867$	44.6341	1.51585
$868$	71.8191	2.43770
$869$	0.724819	0.0245878
$870$	−0.805312	−0.0273026
$871$	−18.4846	−0.626326
$872$	−46.3690	−1.57025
$873$	−55.3627	−1.87374
$874$	−65.3522	−2.21057
$875$	−1.09035	−0.0368606
$876$	−189.282	−6.39523
$877$	−49.2248	−1.66220	−0.831102	−	0.556120i	$-0.812289\pi$
$877$	−49.2248	−1.66220	−0.831102	+	0.556120i	$0.812289\pi$
$878$	26.5856	0.897220
$879$	−29.1415	−0.982918
$880$	−0.0368880	−0.00124350
$881$	14.1734	0.477515	0.238758	−	0.971079i	$-0.423260\pi$
$881$	14.1734	0.477515	0.238758	+	0.971079i	$0.423260\pi$
$882$	−65.8168	−2.21617
$883$	−44.5572	−1.49947	−0.749734	−	0.661739i	$-0.769819\pi$
$883$	−44.5572	−1.49947	−0.749734	+	0.661739i	$0.769819\pi$
$884$	9.69697	0.326145
$885$	−1.24298	−0.0417824
$886$	23.9710	0.805321
$887$	43.2413	1.45190	0.725950	−	0.687748i	$-0.241401\pi$
$887$	43.2413	1.45190	0.725950	+	0.687748i	$0.241401\pi$
$888$	−67.7228	−2.27263
$889$	10.9106	0.365928
$890$	0.891079	0.0298690
$891$	3.49585	0.117115
$892$	38.4870	1.28864
$893$	−39.8726	−1.33429
$894$	−29.4338	−0.984415
$895$	−0.396419	−0.0132508
$896$	−68.3461	−2.28328
$897$	−26.8001	−0.894828
$898$	−87.2504	−2.91158
$899$	−18.4795	−0.616324
$900$	−120.226	−4.00755
$901$	−17.4273	−0.580588
$902$	−0.0669270	−0.00222842
$903$	18.2483	0.607264
$904$	−32.6189	−1.08489
$905$	−0.162692	−0.00540807
$906$	35.0008	1.16282
$907$	0.447171	0.0148481	0.00742403	−	0.999972i	$-0.497637\pi$
$907$	0.447171	0.0148481	0.00742403	+	0.999972i	$0.497637\pi$
$908$	−38.8627	−1.28971
$909$	−117.832	−3.90825
$910$	0.438417	0.0145334
$911$	10.6948	0.354335	0.177167	−	0.984181i	$-0.443307\pi$
$911$	10.6948	0.354335	0.177167	+	0.984181i	$0.443307\pi$
$912$	52.1363	1.72641
$913$	0.297759	0.00985439
$914$	60.3578	1.99646
$915$	−0.124849	−0.00412739
$916$	48.9948	1.61883
$917$	−34.5829	−1.14203
$918$	−34.9192	−1.15251
$919$	30.0350	0.990762	0.495381	−	0.868676i	$-0.335028\pi$
$919$	30.0350	0.990762	0.495381	+	0.868676i	$0.335028\pi$
$920$	−0.798967	−0.0263412
$921$	−95.0716	−3.13272
$922$	−78.3592	−2.58062
$923$	−15.6297	−0.514458
$924$	13.2928	0.437301
$925$	24.1935	0.795478
$926$	24.8845	0.817756
$927$	−121.986	−4.00655
$928$	3.12580	0.102609
$929$	57.2823	1.87937	0.939686	−	0.342038i	$-0.111117\pi$
$929$	57.2823	1.87937	0.939686	+	0.342038i	$0.111117\pi$
$930$	1.29497	0.0424637
$931$	−22.1009	−0.724327
$932$	−24.3024	−0.796053
$933$	30.0613	0.984163
$934$	30.5702	1.00029
$935$	0.0161665	0.000528701 0
$936$	47.1420	1.54088
$937$	1.22719	0.0400907	0.0200453	−	0.999799i	$-0.493619\pi$
$937$	1.22719	0.0400907	0.0200453	+	0.999799i	$0.493619\pi$
$938$	91.6147	2.99133
$939$	53.4406	1.74397
$940$	−0.999843	−0.0326113
$941$	−38.6797	−1.26092	−0.630460	−	0.776221i	$-0.717134\pi$
$941$	−38.6797	−1.26092	−0.630460	+	0.776221i	$0.717134\pi$
$942$	145.535	4.74180
$943$	−0.442173	−0.0143991
$944$	−43.5524	−1.41751
$945$	−1.04384	−0.0339560
$946$	−1.44621	−0.0470204
$947$	26.2148	0.851867	0.425934	−	0.904754i	$-0.359946\pi$
$947$	26.2148	0.851867	0.425934	+	0.904754i	$0.359946\pi$
$948$	−25.6887	−0.834329
$949$	−26.5143	−0.860692
$950$	−61.0600	−1.98105
$951$	69.4757	2.25290
$952$	−23.4317	−0.759426
$953$	−0.823051	−0.0266613	−0.0133306	−	0.999911i	$-0.504243\pi$
$953$	−0.823051	−0.0266613	−0.0133306	+	0.999911i	$0.504243\pi$
$954$	−173.776	−5.62622
$955$	−0.215884	−0.00698586
$956$	8.34661	0.269949
$957$	−3.42031	−0.110563
$958$	12.2029	0.394257
$959$	12.8777	0.415842
$960$	−0.889014	−0.0286928
$961$	−1.28441	−0.0414325
$962$	−19.4579	−0.627347
$963$	−5.42638	−0.174863
$964$	92.4242	2.97678
$965$	0.312071	0.0100459
$966$	132.829	4.27369
$967$	−12.7952	−0.411466	−0.205733	−	0.978608i	$-0.565958\pi$
$967$	−12.7952	−0.411466	−0.205733	+	0.978608i	$0.565958\pi$
$968$	50.3378	1.61792
$969$	−22.8492	−0.734022
$970$	−0.705067	−0.0226383
$971$	−25.3492	−0.813494	−0.406747	−	0.913541i	$-0.633337\pi$
$971$	−25.3492	−0.813494	−0.406747	+	0.913541i	$0.633337\pi$
$972$	−11.8220	−0.379189
$973$	−50.1579	−1.60799
$974$	−34.3687	−1.10124
$975$	−25.0399	−0.801917
$976$	−4.37454	−0.140026
$977$	15.0049	0.480050	0.240025	−	0.970767i	$-0.422844\pi$
$977$	15.0049	0.480050	0.240025	+	0.970767i	$0.422844\pi$
$978$	−50.1562	−1.60382
$979$	3.78458	0.120956
$980$	−0.554200	−0.0177033
$981$	61.8112	1.97348
$982$	7.14604	0.228039
$983$	−12.4298	−0.396451	−0.198225	−	0.980156i	$-0.563518\pi$
$983$	−12.4298	−0.396451	−0.198225	+	0.980156i	$0.563518\pi$
$984$	1.15644	0.0368661
$985$	−0.732380	−0.0233356
$986$	12.3663	0.393824
$987$	81.0413	2.57957
$988$	32.4690	1.03298
$989$	−9.55484	−0.303826
$990$	0.161204	0.00512340
$991$	−26.4538	−0.840331	−0.420166	−	0.907447i	$-0.638028\pi$
$991$	−26.4538	−0.840331	−0.420166	+	0.907447i	$0.638028\pi$
$992$	−5.02639	−0.159588
$993$	−38.2958	−1.21528
$994$	77.4651	2.45704
$995$	0.351163	0.0111326
$996$	−10.5530	−0.334385
$997$	−33.4142	−1.05824	−0.529119	−	0.848547i	$-0.677478\pi$
$997$	−33.4142	−1.05824	−0.529119	+	0.848547i	$0.677478\pi$
$998$	−65.2371	−2.06505
$999$	46.3276	1.46574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.2	✓	30
3.2	odd	2		5571.2.a.g.1.29		30
4.3	odd	2		9904.2.a.n.1.28		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.2	✓	30	1.1	even	1	trivial
5571.2.a.g.1.29		30	3.2	odd	2
9904.2.a.n.1.28		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)

\(f(q)\)	\(=\)	\(q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +O(q^{10})\)	\(q-2.42956 q^{2} -3.02694 q^{3} +3.90276 q^{4} -0.0323024 q^{5} +7.35414 q^{6} -3.37580 q^{7} -4.62286 q^{8} +6.16239 q^{9} +0.0784807 q^{10} +0.333322 q^{11} -11.8134 q^{12} -1.65481 q^{13} +8.20170 q^{14} +0.0977777 q^{15} +3.42599 q^{16} -1.50147 q^{17} -14.9719 q^{18} -5.02748 q^{19} -0.126069 q^{20} +10.2184 q^{21} -0.809826 q^{22} -5.35036 q^{23} +13.9931 q^{24} -4.99896 q^{25} +4.02046 q^{26} -9.57238 q^{27} -13.1749 q^{28} +3.38998 q^{29} -0.237557 q^{30} -5.45120 q^{31} +0.922070 q^{32} -1.00895 q^{33} +3.64791 q^{34} +0.109047 q^{35} +24.0503 q^{36} -4.83972 q^{37} +12.2145 q^{38} +5.00902 q^{39} +0.149330 q^{40} +0.0826437 q^{41} -24.8261 q^{42} +1.78583 q^{43} +1.30087 q^{44} -0.199060 q^{45} +12.9990 q^{46} +7.93095 q^{47} -10.3703 q^{48} +4.39602 q^{49} +12.1453 q^{50} +4.54487 q^{51} -6.45832 q^{52} +11.6068 q^{53} +23.2567 q^{54} -0.0107671 q^{55} +15.6058 q^{56} +15.2179 q^{57} -8.23615 q^{58} -12.7123 q^{59} +0.381602 q^{60} -1.27687 q^{61} +13.2440 q^{62} -20.8030 q^{63} -9.09220 q^{64} +0.0534544 q^{65} +2.45130 q^{66} +11.1702 q^{67} -5.85987 q^{68} +16.1952 q^{69} -0.264935 q^{70} +9.44501 q^{71} -28.4879 q^{72} +16.0226 q^{73} +11.7584 q^{74} +15.1316 q^{75} -19.6210 q^{76} -1.12523 q^{77} -12.1697 q^{78} +2.17453 q^{79} -0.110668 q^{80} +10.4879 q^{81} -0.200788 q^{82} +0.893308 q^{83} +39.8797 q^{84} +0.0485011 q^{85} -4.33878 q^{86} -10.2613 q^{87} -1.54090 q^{88} +11.3541 q^{89} +0.483629 q^{90} +5.58631 q^{91} -20.8811 q^{92} +16.5005 q^{93} -19.2687 q^{94} +0.162400 q^{95} -2.79105 q^{96} -8.98396 q^{97} -10.6804 q^{98} +2.05406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 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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