LMFDB - Embedded newform 619.2.a.b.1.30

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			1.30
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)

$f(q)$	$=$	$q+2.81795 q^{2} +1.69440 q^{3} +5.94086 q^{4} -2.73112 q^{5} +4.77473 q^{6} -1.24727 q^{7} +11.1052 q^{8} -0.129016 q^{9} +O(q^{10})$	\(q+2.81795 q^{2} +1.69440 q^{3} +5.94086 q^{4} -2.73112 q^{5} +4.77473 q^{6} -1.24727 q^{7} +11.1052 q^{8} -0.129016 q^{9} -7.69618 q^{10} -0.667171 q^{11} +10.0662 q^{12} +0.636485 q^{13} -3.51474 q^{14} -4.62761 q^{15} +19.4121 q^{16} -1.78533 q^{17} -0.363560 q^{18} -5.81505 q^{19} -16.2252 q^{20} -2.11337 q^{21} -1.88006 q^{22} -1.72433 q^{23} +18.8166 q^{24} +2.45904 q^{25} +1.79358 q^{26} -5.30180 q^{27} -7.40985 q^{28} +5.11991 q^{29} -13.0404 q^{30} +2.93123 q^{31} +32.4921 q^{32} -1.13045 q^{33} -5.03098 q^{34} +3.40644 q^{35} -0.766464 q^{36} -2.26845 q^{37} -16.3865 q^{38} +1.07846 q^{39} -30.3296 q^{40} +12.5582 q^{41} -5.95537 q^{42} -0.542861 q^{43} -3.96357 q^{44} +0.352358 q^{45} -4.85908 q^{46} -7.59303 q^{47} +32.8918 q^{48} -5.44432 q^{49} +6.92946 q^{50} -3.02506 q^{51} +3.78127 q^{52} -10.6477 q^{53} -14.9402 q^{54} +1.82213 q^{55} -13.8511 q^{56} -9.85300 q^{57} +14.4277 q^{58} +5.40784 q^{59} -27.4920 q^{60} +7.79382 q^{61} +8.26008 q^{62} +0.160917 q^{63} +52.7370 q^{64} -1.73832 q^{65} -3.18556 q^{66} +10.9382 q^{67} -10.6064 q^{68} -2.92170 q^{69} +9.59920 q^{70} +15.3861 q^{71} -1.43274 q^{72} -14.7792 q^{73} -6.39237 q^{74} +4.16659 q^{75} -34.5464 q^{76} +0.832141 q^{77} +3.03905 q^{78} -2.62015 q^{79} -53.0169 q^{80} -8.59631 q^{81} +35.3884 q^{82} -13.2306 q^{83} -12.5552 q^{84} +4.87596 q^{85} -1.52976 q^{86} +8.67516 q^{87} -7.40904 q^{88} -0.970941 q^{89} +0.992928 q^{90} -0.793867 q^{91} -10.2440 q^{92} +4.96668 q^{93} -21.3968 q^{94} +15.8816 q^{95} +55.0545 q^{96} -6.09460 q^{97} -15.3418 q^{98} +0.0860755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.81795	1.99259	0.996297	−	0.0859787i	$-0.0274017\pi$
$2$	2.81795	1.99259	0.996297	+	0.0859787i	$0.0274017\pi$
$3$	1.69440	0.978261	0.489131	−	0.872211i	$-0.337314\pi$
$3$	1.69440	0.978261	0.489131	+	0.872211i	$0.337314\pi$
$4$	5.94086	2.97043
$5$	−2.73112	−1.22140	−0.610698	−	0.791864i	$-0.709111\pi$
$5$	−2.73112	−1.22140	−0.610698	+	0.791864i	$0.709111\pi$
$6$	4.77473	1.94928
$7$	−1.24727	−0.471423	−0.235712	−	0.971823i	$-0.575742\pi$
$7$	−1.24727	−0.471423	−0.235712	+	0.971823i	$0.575742\pi$
$8$	11.1052	3.92627
$9$	−0.129016	−0.0430052
$10$	−7.69618	−2.43375
$11$	−0.667171	−0.201160	−0.100580	−	0.994929i	$-0.532070\pi$
$11$	−0.667171	−0.201160	−0.100580	+	0.994929i	$0.532070\pi$
$12$	10.0662	2.90586
$13$	0.636485	0.176529	0.0882646	−	0.996097i	$-0.471868\pi$
$13$	0.636485	0.176529	0.0882646	+	0.996097i	$0.471868\pi$
$14$	−3.51474	−0.939355
$15$	−4.62761	−1.19484
$16$	19.4121	4.85303
$17$	−1.78533	−0.433007	−0.216503	−	0.976282i	$-0.569465\pi$
$17$	−1.78533	−0.433007	−0.216503	+	0.976282i	$0.569465\pi$
$18$	−0.363560	−0.0856919
$19$	−5.81505	−1.33406	−0.667032	−	0.745030i	$-0.732435\pi$
$19$	−5.81505	−1.33406	−0.667032	+	0.745030i	$0.732435\pi$
$20$	−16.2252	−3.62807
$21$	−2.11337	−0.461175
$22$	−1.88006	−0.400829
$23$	−1.72433	−0.359547	−0.179774	−	0.983708i	$-0.557537\pi$
$23$	−1.72433	−0.359547	−0.179774	+	0.983708i	$0.557537\pi$
$24$	18.8166	3.84092
$25$	2.45904	0.491808
$26$	1.79358	0.351751
$27$	−5.30180	−1.02033
$28$	−7.40985	−1.40033
$29$	5.11991	0.950743	0.475371	−	0.879785i	$-0.342314\pi$
$29$	5.11991	0.950743	0.475371	+	0.879785i	$0.342314\pi$
$30$	−13.0404	−2.38084
$31$	2.93123	0.526465	0.263233	−	0.964732i	$-0.415211\pi$
$31$	2.93123	0.526465	0.263233	+	0.964732i	$0.415211\pi$
$32$	32.4921	5.74384
$33$	−1.13045	−0.196787
$34$	−5.03098	−0.862806
$35$	3.40644	0.575794
$36$	−0.766464	−0.127744
$37$	−2.26845	−0.372930	−0.186465	−	0.982462i	$-0.559703\pi$
$37$	−2.26845	−0.372930	−0.186465	+	0.982462i	$0.559703\pi$
$38$	−16.3865	−2.65825
$39$	1.07846	0.172692
$40$	−30.3296	−4.79553
$41$	12.5582	1.96126	0.980630	−	0.195867i	$-0.0627522\pi$
$41$	12.5582	1.96126	0.980630	+	0.195867i	$0.0627522\pi$
$42$	−5.95537	−0.918934
$43$	−0.542861	−0.0827855	−0.0413927	−	0.999143i	$-0.513179\pi$
$43$	−0.542861	−0.0827855	−0.0413927	+	0.999143i	$0.513179\pi$
$44$	−3.96357	−0.597531
$45$	0.352358	0.0525264
$46$	−4.85908	−0.716432
$47$	−7.59303	−1.10756	−0.553779	−	0.832664i	$-0.686815\pi$
$47$	−7.59303	−1.10756	−0.553779	+	0.832664i	$0.686815\pi$
$48$	32.8918	4.74753
$49$	−5.44432	−0.777760
$50$	6.92946	0.979974
$51$	−3.02506	−0.423594
$52$	3.78127	0.524367
$53$	−10.6477	−1.46257	−0.731287	−	0.682070i	$-0.761080\pi$
$53$	−10.6477	−1.46257	−0.731287	+	0.682070i	$0.761080\pi$
$54$	−14.9402	−2.03311
$55$	1.82213	0.245696
$56$	−13.8511	−1.85093
$57$	−9.85300	−1.30506
$58$	14.4277	1.89444
$59$	5.40784	0.704041	0.352020	−	0.935992i	$-0.385495\pi$
$59$	5.40784	0.704041	0.352020	+	0.935992i	$0.385495\pi$
$60$	−27.4920	−3.54920
$61$	7.79382	0.997896	0.498948	−	0.866632i	$-0.333720\pi$
$61$	7.79382	0.997896	0.498948	+	0.866632i	$0.333720\pi$
$62$	8.26008	1.04903
$63$	0.160917	0.0202736
$64$	52.7370	6.59212
$65$	−1.73832	−0.215612
$66$	−3.18556	−0.392116
$67$	10.9382	1.33631	0.668154	−	0.744023i	$-0.267085\pi$
$67$	10.9382	1.33631	0.668154	+	0.744023i	$0.267085\pi$
$68$	−10.6064	−1.28622
$69$	−2.92170	−0.351731
$70$	9.59920	1.14732
$71$	15.3861	1.82600	0.913000	−	0.407960i	$-0.133760\pi$
$71$	15.3861	1.82600	0.913000	+	0.407960i	$0.133760\pi$
$72$	−1.43274	−0.168850
$73$	−14.7792	−1.72978	−0.864888	−	0.501964i	$-0.832611\pi$
$73$	−14.7792	−1.72978	−0.864888	+	0.501964i	$0.832611\pi$
$74$	−6.39237	−0.743098
$75$	4.16659	0.481117
$76$	−34.5464	−3.96274
$77$	0.832141	0.0948313
$78$	3.03905	0.344104
$79$	−2.62015	−0.294789	−0.147395	−	0.989078i	$-0.547089\pi$
$79$	−2.62015	−0.294789	−0.147395	+	0.989078i	$0.547089\pi$
$80$	−53.0169	−5.92747
$81$	−8.59631	−0.955145
$82$	35.3884	3.90800
$83$	−13.2306	−1.45225	−0.726123	−	0.687565i	$-0.758680\pi$
$83$	−13.2306	−1.45225	−0.726123	+	0.687565i	$0.758680\pi$
$84$	−12.5552	−1.36989
$85$	4.87596	0.528873
$86$	−1.52976	−0.164958
$87$	8.67516	0.930074
$88$	−7.40904	−0.789807
$89$	−0.970941	−0.102920	−0.0514598	−	0.998675i	$-0.516387\pi$
$89$	−0.970941	−0.102920	−0.0514598	+	0.998675i	$0.516387\pi$
$90$	0.992928	0.104664
$91$	−0.793867	−0.0832199
$92$	−10.2440	−1.06801
$93$	4.96668	0.515020
$94$	−21.3968	−2.20691
$95$	15.8816	1.62942
$96$	55.0545	5.61898
$97$	−6.09460	−0.618813	−0.309406	−	0.950930i	$-0.600130\pi$
$97$	−6.09460	−0.618813	−0.309406	+	0.950930i	$0.600130\pi$
$98$	−15.3418	−1.54976
$99$	0.0860755	0.00865091
$100$	14.6088	1.46088
$101$	6.29536	0.626412	0.313206	−	0.949685i	$-0.398597\pi$
$101$	6.29536	0.626412	0.313206	+	0.949685i	$0.398597\pi$
$102$	−8.52449	−0.844050
$103$	5.39253	0.531342	0.265671	−	0.964064i	$-0.414407\pi$
$103$	5.39253	0.531342	0.265671	+	0.964064i	$0.414407\pi$
$104$	7.06827	0.693101
$105$	5.77187	0.563277
$106$	−30.0047	−2.91432
$107$	13.7409	1.32838	0.664192	−	0.747562i	$-0.268776\pi$
$107$	13.7409	1.32838	0.664192	+	0.747562i	$0.268776\pi$
$108$	−31.4972	−3.03082
$109$	17.9679	1.72101	0.860507	−	0.509438i	$-0.170147\pi$
$109$	17.9679	1.72101	0.860507	+	0.509438i	$0.170147\pi$
$110$	5.13467	0.489571
$111$	−3.84365	−0.364823
$112$	−24.2121	−2.28783
$113$	11.2845	1.06156	0.530780	−	0.847510i	$-0.321899\pi$
$113$	11.2845	1.06156	0.530780	+	0.847510i	$0.321899\pi$
$114$	−27.7653	−2.60046
$115$	4.70936	0.439150
$116$	30.4166	2.82411
$117$	−0.0821165	−0.00759167
$118$	15.2390	1.40287
$119$	2.22679	0.204129
$120$	−51.3904	−4.69128
$121$	−10.5549	−0.959535
$122$	21.9626	1.98840
$123$	21.2786	1.91863
$124$	17.4141	1.56383
$125$	6.93968	0.620704
$126$	0.453457	0.0403971
$127$	−10.5821	−0.939009	−0.469504	−	0.882930i	$-0.655567\pi$
$127$	−10.5821	−0.939009	−0.469504	+	0.882930i	$0.655567\pi$
$128$	83.6262	7.39158
$129$	−0.919822	−0.0809858
$130$	−4.89850	−0.429627
$131$	−10.6897	−0.933967	−0.466984	−	0.884266i	$-0.654659\pi$
$131$	−10.6897	−0.933967	−0.466984	+	0.884266i	$0.654659\pi$
$132$	−6.71587	−0.584541
$133$	7.25292	0.628908
$134$	30.8232	2.66272
$135$	14.4799	1.24623
$136$	−19.8264	−1.70010
$137$	12.4722	1.06557	0.532785	−	0.846250i	$-0.321145\pi$
$137$	12.4722	1.06557	0.532785	+	0.846250i	$0.321145\pi$
$138$	−8.23321	−0.700858
$139$	−6.40633	−0.543377	−0.271689	−	0.962385i	$-0.587582\pi$
$139$	−6.40633	−0.543377	−0.271689	+	0.962385i	$0.587582\pi$
$140$	20.2372	1.71036
$141$	−12.8656	−1.08348
$142$	43.3574	3.63848
$143$	−0.424644	−0.0355105
$144$	−2.50447	−0.208705
$145$	−13.9831	−1.16123
$146$	−41.6472	−3.44674
$147$	−9.22485	−0.760853
$148$	−13.4765	−1.10776
$149$	−0.472671	−0.0387227	−0.0193613	−	0.999813i	$-0.506163\pi$
$149$	−0.472671	−0.0387227	−0.0193613	+	0.999813i	$0.506163\pi$
$150$	11.7413	0.958670
$151$	−14.2433	−1.15910	−0.579550	−	0.814936i	$-0.696772\pi$
$151$	−14.2433	−1.15910	−0.579550	+	0.814936i	$0.696772\pi$
$152$	−64.5770	−5.23789
$153$	0.230336	0.0186215
$154$	2.34493	0.188960
$155$	−8.00556	−0.643022
$156$	6.40697	0.512968
$157$	−2.28948	−0.182721	−0.0913603	−	0.995818i	$-0.529121\pi$
$157$	−2.28948	−0.182721	−0.0913603	+	0.995818i	$0.529121\pi$
$158$	−7.38345	−0.587396
$159$	−18.0414	−1.43078
$160$	−88.7399	−7.01551
$161$	2.15070	0.169499
$162$	−24.2240	−1.90322
$163$	11.1904	0.876498	0.438249	−	0.898854i	$-0.355599\pi$
$163$	11.1904	0.876498	0.438249	+	0.898854i	$0.355599\pi$
$164$	74.6065	5.82579
$165$	3.08741	0.240354
$166$	−37.2832	−2.89374
$167$	22.7194	1.75808	0.879042	−	0.476745i	$-0.158183\pi$
$167$	22.7194	1.75808	0.879042	+	0.476745i	$0.158183\pi$
$168$	−23.4693	−1.81070
$169$	−12.5949	−0.968837
$170$	13.7402	1.05383
$171$	0.750232	0.0573717
$172$	−3.22506	−0.245909
$173$	−0.481260	−0.0365895	−0.0182948	−	0.999833i	$-0.505824\pi$
$173$	−0.481260	−0.0365895	−0.0182948	+	0.999833i	$0.505824\pi$
$174$	24.4462	1.85326
$175$	−3.06708	−0.231850
$176$	−12.9512	−0.976233
$177$	9.16303	0.688736
$178$	−2.73607	−0.205077
$179$	−5.06894	−0.378870	−0.189435	−	0.981893i	$-0.560666\pi$
$179$	−5.06894	−0.378870	−0.189435	+	0.981893i	$0.560666\pi$
$180$	2.09331	0.156026
$181$	13.8451	1.02910	0.514549	−	0.857461i	$-0.327959\pi$
$181$	13.8451	1.02910	0.514549	+	0.857461i	$0.327959\pi$
$182$	−2.23708	−0.165823
$183$	13.2058	0.976203
$184$	−19.1490	−1.41168
$185$	6.19541	0.455495
$186$	13.9959	1.02623
$187$	1.19112	0.0871034
$188$	−45.1091	−3.28992
$189$	6.61276	0.481008
$190$	44.7536	3.24677
$191$	12.6000	0.911705	0.455853	−	0.890055i	$-0.349334\pi$
$191$	12.6000	0.911705	0.455853	+	0.890055i	$0.349334\pi$
$192$	89.3574	6.44882
$193$	−4.28724	−0.308602	−0.154301	−	0.988024i	$-0.549313\pi$
$193$	−4.28724	−0.308602	−0.154301	+	0.988024i	$0.549313\pi$
$194$	−17.1743	−1.23304
$195$	−2.94540	−0.210925
$196$	−32.3440	−2.31028
$197$	−22.9055	−1.63195	−0.815975	−	0.578087i	$-0.803799\pi$
$197$	−22.9055	−1.63195	−0.815975	+	0.578087i	$0.803799\pi$
$198$	0.242557	0.0172378
$199$	7.57911	0.537269	0.268634	−	0.963242i	$-0.413428\pi$
$199$	7.57911	0.537269	0.268634	+	0.963242i	$0.413428\pi$
$200$	27.3080	1.93097
$201$	18.5336	1.30726
$202$	17.7400	1.24818
$203$	−6.38589	−0.448202
$204$	−17.9715	−1.25826
$205$	−34.2980	−2.39548
$206$	15.1959	1.05875
$207$	0.222465	0.0154624
$208$	12.3555	0.856701
$209$	3.87963	0.268360
$210$	16.2649	1.12238
$211$	−11.5046	−0.792011	−0.396005	−	0.918248i	$-0.629604\pi$
$211$	−11.5046	−0.792011	−0.396005	+	0.918248i	$0.629604\pi$
$212$	−63.2565	−4.34447
$213$	26.0703	1.78630
$214$	38.7212	2.64693
$215$	1.48262	0.101114
$216$	−58.8773	−4.00609
$217$	−3.65603	−0.248188
$218$	50.6328	3.42928
$219$	−25.0419	−1.69217
$220$	10.8250	0.729822
$221$	−1.13634	−0.0764383
$222$	−10.8312	−0.726944
$223$	−1.18122	−0.0791002	−0.0395501	−	0.999218i	$-0.512592\pi$
$223$	−1.18122	−0.0791002	−0.0395501	+	0.999218i	$0.512592\pi$
$224$	−40.5264	−2.70778
$225$	−0.317255	−0.0211503
$226$	31.7993	2.11526
$227$	−12.2514	−0.813153	−0.406576	−	0.913617i	$-0.633277\pi$
$227$	−12.2514	−0.813153	−0.406576	+	0.913617i	$0.633277\pi$
$228$	−58.5353	−3.87660
$229$	−25.2192	−1.66653	−0.833264	−	0.552875i	$-0.813531\pi$
$229$	−25.2192	−1.66653	−0.833264	+	0.552875i	$0.813531\pi$
$230$	13.2707	0.875047
$231$	1.40998	0.0927698
$232$	56.8574	3.73287
$233$	−2.99553	−0.196244	−0.0981219	−	0.995174i	$-0.531284\pi$
$233$	−2.99553	−0.196244	−0.0981219	+	0.995174i	$0.531284\pi$
$234$	−0.231400	−0.0151271
$235$	20.7375	1.35277
$236$	32.1272	2.09130
$237$	−4.43957	−0.288381
$238$	6.27498	0.406747
$239$	−13.6110	−0.880420	−0.440210	−	0.897895i	$-0.645096\pi$
$239$	−13.6110	−0.880420	−0.440210	+	0.897895i	$0.645096\pi$
$240$	−89.8317	−5.79861
$241$	−5.37746	−0.346393	−0.173196	−	0.984887i	$-0.555409\pi$
$241$	−5.37746	−0.346393	−0.173196	+	0.984887i	$0.555409\pi$
$242$	−29.7432	−1.91196
$243$	1.33983	0.0859499
$244$	46.3020	2.96418
$245$	14.8691	0.949953
$246$	59.9621	3.82304
$247$	−3.70119	−0.235501
$248$	32.5518	2.06704
$249$	−22.4179	−1.42068
$250$	19.5557	1.23681
$251$	15.4784	0.976989	0.488494	−	0.872567i	$-0.337546\pi$
$251$	15.4784	0.976989	0.488494	+	0.872567i	$0.337546\pi$
$252$	0.955986	0.0602215
$253$	1.15042	0.0723264
$254$	−29.8198	−1.87106
$255$	8.26182	0.517375
$256$	130.181	8.13629
$257$	−0.717584	−0.0447616	−0.0223808	−	0.999750i	$-0.507125\pi$
$257$	−0.717584	−0.0447616	−0.0223808	+	0.999750i	$0.507125\pi$
$258$	−2.59202	−0.161372
$259$	2.82936	0.175808
$260$	−10.3271	−0.640460
$261$	−0.660548	−0.0408869
$262$	−30.1232	−1.86102
$263$	−6.84952	−0.422360	−0.211180	−	0.977447i	$-0.567731\pi$
$263$	−6.84952	−0.422360	−0.211180	+	0.977447i	$0.567731\pi$
$264$	−12.5539	−0.772637
$265$	29.0802	1.78638
$266$	20.4384	1.25316
$267$	−1.64516	−0.100682
$268$	64.9820	3.96941
$269$	0.925786	0.0564462	0.0282231	−	0.999602i	$-0.491015\pi$
$269$	0.925786	0.0564462	0.0282231	+	0.999602i	$0.491015\pi$
$270$	40.8036	2.48323
$271$	−6.85417	−0.416361	−0.208181	−	0.978090i	$-0.566754\pi$
$271$	−6.85417	−0.416361	−0.208181	+	0.978090i	$0.566754\pi$
$272$	−34.6571	−2.10139
$273$	−1.34513	−0.0814108
$274$	35.1460	2.12325
$275$	−1.64060	−0.0989319
$276$	−17.3574	−1.04479
$277$	22.5550	1.35520	0.677599	−	0.735432i	$-0.263021\pi$
$277$	22.5550	1.35520	0.677599	+	0.735432i	$0.263021\pi$
$278$	−18.0527	−1.08273
$279$	−0.378175	−0.0226407
$280$	37.8291	2.26072
$281$	18.2474	1.08855	0.544273	−	0.838908i	$-0.316805\pi$
$281$	18.2474	1.08855	0.544273	+	0.838908i	$0.316805\pi$
$282$	−36.2547	−2.15894
$283$	−14.8559	−0.883094	−0.441547	−	0.897238i	$-0.645570\pi$
$283$	−14.8559	−0.883094	−0.441547	+	0.897238i	$0.645570\pi$
$284$	91.4070	5.42401
$285$	26.9098	1.59400
$286$	−1.19663	−0.0707581
$287$	−15.6634	−0.924584
$288$	−4.19199	−0.247015
$289$	−13.8126	−0.812505
$290$	−39.4037	−2.31387
$291$	−10.3267	−0.605360
$292$	−87.8013	−5.13818
$293$	10.3252	0.603206	0.301603	−	0.953434i	$-0.402478\pi$
$293$	10.3252	0.603206	0.301603	+	0.953434i	$0.402478\pi$
$294$	−25.9952	−1.51607
$295$	−14.7695	−0.859913
$296$	−25.1915	−1.46422
$297$	3.53721	0.205249
$298$	−1.33196	−0.0771586
$299$	−1.09751	−0.0634706
$300$	24.7532	1.42912
$301$	0.677093	0.0390270
$302$	−40.1369	−2.30962
$303$	10.6668	0.612794
$304$	−112.882	−6.47424
$305$	−21.2859	−1.21883
$306$	0.649075	0.0371052
$307$	−9.77636	−0.557966	−0.278983	−	0.960296i	$-0.589997\pi$
$307$	−9.77636	−0.557966	−0.278983	+	0.960296i	$0.589997\pi$
$308$	4.94364	0.281690
$309$	9.13709	0.519791
$310$	−22.5593	−1.28128
$311$	−3.43417	−0.194734	−0.0973669	−	0.995249i	$-0.531042\pi$
$311$	−3.43417	−0.194734	−0.0973669	+	0.995249i	$0.531042\pi$
$312$	11.9765	0.678033
$313$	−24.4971	−1.38466	−0.692328	−	0.721583i	$-0.743415\pi$
$313$	−24.4971	−1.38466	−0.692328	+	0.721583i	$0.743415\pi$
$314$	−6.45166	−0.364088
$315$	−0.439485	−0.0247622
$316$	−15.5659	−0.875652
$317$	−10.7686	−0.604825	−0.302412	−	0.953177i	$-0.597792\pi$
$317$	−10.7686	−0.604825	−0.302412	+	0.953177i	$0.597792\pi$
$318$	−50.8399	−2.85096
$319$	−3.41585	−0.191251
$320$	−144.031	−8.05159
$321$	23.2826	1.29951
$322$	6.06057	0.337743
$323$	10.3818	0.577658
$324$	−51.0695	−2.83719
$325$	1.56514	0.0868184
$326$	31.5340	1.74651
$327$	30.4448	1.68360
$328$	139.461	7.70044
$329$	9.47054	0.522128
$330$	8.70017	0.478929
$331$	5.24152	0.288100	0.144050	−	0.989570i	$-0.453987\pi$
$331$	5.24152	0.288100	0.144050	+	0.989570i	$0.453987\pi$
$332$	−78.6011	−4.31380
$333$	0.292665	0.0160379
$334$	64.0224	3.50315
$335$	−29.8735	−1.63216
$336$	−41.0249	−2.23809
$337$	−1.40912	−0.0767597	−0.0383799	−	0.999263i	$-0.512220\pi$
$337$	−1.40912	−0.0767597	−0.0383799	+	0.999263i	$0.512220\pi$
$338$	−35.4918	−1.93050
$339$	19.1205	1.03848
$340$	28.9674	1.57098
$341$	−1.95563	−0.105904
$342$	2.11412	0.114318
$343$	15.5214	0.838077
$344$	−6.02856	−0.325038
$345$	7.97952	0.429603
$346$	−1.35617	−0.0729080
$347$	−31.9358	−1.71440	−0.857202	−	0.514980i	$-0.827799\pi$
$347$	−31.9358	−1.71440	−0.857202	+	0.514980i	$0.827799\pi$
$348$	51.5379	2.76272
$349$	10.9469	0.585973	0.292986	−	0.956117i	$-0.405351\pi$
$349$	10.9469	0.585973	0.292986	+	0.956117i	$0.405351\pi$
$350$	−8.64290	−0.461982
$351$	−3.37451	−0.180118
$352$	−21.6778	−1.15543
$353$	25.2258	1.34263	0.671317	−	0.741170i	$-0.265729\pi$
$353$	25.2258	1.34263	0.671317	+	0.741170i	$0.265729\pi$
$354$	25.8210	1.37237
$355$	−42.0215	−2.23027
$356$	−5.76823	−0.305715
$357$	3.77306	0.199692
$358$	−14.2840	−0.754934
$359$	−7.62285	−0.402318	−0.201159	−	0.979559i	$-0.564471\pi$
$359$	−7.62285	−0.402318	−0.201159	+	0.979559i	$0.564471\pi$
$360$	3.91299	0.206233
$361$	14.8148	0.779724
$362$	39.0148	2.05057
$363$	−17.8842	−0.938676
$364$	−4.71625	−0.247199
$365$	40.3639	2.11274
$366$	37.2134	1.94518
$367$	34.8115	1.81715	0.908573	−	0.417727i	$-0.137173\pi$
$367$	34.8115	1.81715	0.908573	+	0.417727i	$0.137173\pi$
$368$	−33.4729	−1.74489
$369$	−1.62020	−0.0843444
$370$	17.4584	0.907617
$371$	13.2805	0.689491
$372$	29.5063	1.52983
$373$	31.4203	1.62688	0.813440	−	0.581649i	$-0.197592\pi$
$373$	31.4203	1.62688	0.813440	+	0.581649i	$0.197592\pi$
$374$	3.35653	0.173562
$375$	11.7586	0.607210
$376$	−84.3218	−4.34857
$377$	3.25874	0.167834
$378$	18.6345	0.958453
$379$	−18.1670	−0.933177	−0.466588	−	0.884475i	$-0.654517\pi$
$379$	−18.1670	−0.933177	−0.466588	+	0.884475i	$0.654517\pi$
$380$	94.3505	4.84008
$381$	−17.9303	−0.918596
$382$	35.5063	1.81666
$383$	−27.9732	−1.42936	−0.714682	−	0.699449i	$-0.753429\pi$
$383$	−27.9732	−1.42936	−0.714682	+	0.699449i	$0.753429\pi$
$384$	141.696	7.23090
$385$	−2.27268	−0.115827
$386$	−12.0812	−0.614919
$387$	0.0700375	0.00356021
$388$	−36.2072	−1.83814
$389$	18.2199	0.923785	0.461892	−	0.886936i	$-0.347171\pi$
$389$	18.2199	0.923785	0.461892	+	0.886936i	$0.347171\pi$
$390$	−8.30001	−0.420287
$391$	3.07850	0.155686
$392$	−60.4601	−3.05370
$393$	−18.1127	−0.913664
$394$	−64.5466	−3.25181
$395$	7.15594	0.360055
$396$	0.511362	0.0256969
$397$	6.47785	0.325114	0.162557	−	0.986699i	$-0.448026\pi$
$397$	6.47785	0.325114	0.162557	+	0.986699i	$0.448026\pi$
$398$	21.3576	1.07056
$399$	12.2893	0.615236
$400$	47.7352	2.38676
$401$	−1.72309	−0.0860470	−0.0430235	−	0.999074i	$-0.513699\pi$
$401$	−1.72309	−0.0860470	−0.0430235	+	0.999074i	$0.513699\pi$
$402$	52.2268	2.60483
$403$	1.86569	0.0929364
$404$	37.3999	1.86071
$405$	23.4776	1.16661
$406$	−17.9952	−0.893085
$407$	1.51344	0.0750185
$408$	−33.5938	−1.66314
$409$	−20.9508	−1.03595	−0.517976	−	0.855395i	$-0.673314\pi$
$409$	−20.9508	−1.03595	−0.517976	+	0.855395i	$0.673314\pi$
$410$	−96.6502	−4.77321
$411$	21.1328	1.04241
$412$	32.0363	1.57831
$413$	−6.74503	−0.331901
$414$	0.626897	0.0308103
$415$	36.1344	1.77377
$416$	20.6807	1.01396
$417$	−10.8549	−0.531565
$418$	10.9326	0.534732
$419$	16.5607	0.809044	0.404522	−	0.914528i	$-0.367438\pi$
$419$	16.5607	0.809044	0.404522	+	0.914528i	$0.367438\pi$
$420$	34.2899	1.67318
$421$	0.597840	0.0291369	0.0145685	−	0.999894i	$-0.495363\pi$
$421$	0.597840	0.0291369	0.0145685	+	0.999894i	$0.495363\pi$
$422$	−32.4195	−1.57816
$423$	0.979619	0.0476307
$424$	−118.244	−5.74246
$425$	−4.39020	−0.212956
$426$	73.4648	3.55938
$427$	−9.72098	−0.470431
$428$	81.6328	3.94587
$429$	−0.719516	−0.0347386
$430$	4.17795	0.201479
$431$	15.9241	0.767038	0.383519	−	0.923533i	$-0.374712\pi$
$431$	15.9241	0.767038	0.383519	+	0.923533i	$0.374712\pi$
$432$	−102.919	−4.95170
$433$	−15.2644	−0.733561	−0.366780	−	0.930308i	$-0.619540\pi$
$433$	−15.2644	−0.733561	−0.366780	+	0.930308i	$0.619540\pi$
$434$	−10.3025	−0.494537
$435$	−23.6929	−1.13599
$436$	106.745	5.11215
$437$	10.0271	0.479659
$438$	−70.5669	−3.37181
$439$	25.5542	1.21964	0.609819	−	0.792541i	$-0.291242\pi$
$439$	25.5542	1.21964	0.609819	+	0.792541i	$0.291242\pi$
$440$	20.2350	0.964667
$441$	0.702403	0.0334477
$442$	−3.20214	−0.152310
$443$	−31.9483	−1.51791	−0.758955	−	0.651143i	$-0.774290\pi$
$443$	−31.9483	−1.51791	−0.758955	+	0.651143i	$0.774290\pi$
$444$	−22.8346	−1.08368
$445$	2.65176	0.125706
$446$	−3.32862	−0.157615
$447$	−0.800892	−0.0378809
$448$	−65.7772	−3.10768
$449$	36.1380	1.70546	0.852729	−	0.522354i	$-0.174946\pi$
$449$	36.1380	1.70546	0.852729	+	0.522354i	$0.174946\pi$
$450$	−0.894009	−0.0421440
$451$	−8.37846	−0.394526
$452$	67.0399	3.15329
$453$	−24.1338	−1.13390
$454$	−34.5238	−1.62028
$455$	2.16815	0.101644
$456$	−109.419	−5.12402
$457$	−1.22612	−0.0573554	−0.0286777	−	0.999589i	$-0.509130\pi$
$457$	−1.22612	−0.0573554	−0.0286777	+	0.999589i	$0.509130\pi$
$458$	−71.0664	−3.32071
$459$	9.46547	0.441810
$460$	27.9776	1.30446
$461$	30.0644	1.40024	0.700119	−	0.714027i	$-0.253130\pi$
$461$	30.0644	1.40024	0.700119	+	0.714027i	$0.253130\pi$
$462$	3.97325	0.184852
$463$	−10.2211	−0.475017	−0.237508	−	0.971385i	$-0.576331\pi$
$463$	−10.2211	−0.475017	−0.237508	+	0.971385i	$0.576331\pi$
$464$	99.3882	4.61398
$465$	−13.5646	−0.629044
$466$	−8.44127	−0.391034
$467$	−30.3465	−1.40427	−0.702133	−	0.712045i	$-0.747769\pi$
$467$	−30.3465	−1.40427	−0.702133	+	0.712045i	$0.747769\pi$
$468$	−0.487843	−0.0225505
$469$	−13.6428	−0.629966
$470$	58.4373	2.69551
$471$	−3.87929	−0.178748
$472$	60.0550	2.76425
$473$	0.362181	0.0166531
$474$	−12.5105	−0.574626
$475$	−14.2994	−0.656103
$476$	13.2290	0.606352
$477$	1.37372	0.0628983
$478$	−38.3551	−1.75432
$479$	−27.3071	−1.24769	−0.623847	−	0.781547i	$-0.714431\pi$
$479$	−27.3071	−1.24769	−0.623847	+	0.781547i	$0.714431\pi$
$480$	−150.361	−6.86300
$481$	−1.44383	−0.0658330
$482$	−15.1534	−0.690220
$483$	3.64414	0.165814
$484$	−62.7051	−2.85023
$485$	16.6451	0.755815
$486$	3.77557	0.171263
$487$	9.70226	0.439652	0.219826	−	0.975539i	$-0.429451\pi$
$487$	9.70226	0.439652	0.219826	+	0.975539i	$0.429451\pi$
$488$	86.5516	3.91801
$489$	18.9610	0.857444
$490$	41.9005	1.89287
$491$	−16.9254	−0.763834	−0.381917	−	0.924197i	$-0.624736\pi$
$491$	−16.9254	−0.763834	−0.381917	+	0.924197i	$0.624736\pi$
$492$	126.413	5.69914
$493$	−9.14073	−0.411678
$494$	−10.4298	−0.469258
$495$	−0.235083	−0.0105662
$496$	56.9014	2.55495
$497$	−19.1907	−0.860818
$498$	−63.1726	−2.83083
$499$	−2.46708	−0.110442	−0.0552209	−	0.998474i	$-0.517586\pi$
$499$	−2.46708	−0.110442	−0.0552209	+	0.998474i	$0.517586\pi$
$500$	41.2277	1.84376
$501$	38.4958	1.71987
$502$	43.6175	1.94674
$503$	−5.80054	−0.258633	−0.129317	−	0.991603i	$-0.541278\pi$
$503$	−5.80054	−0.258633	−0.129317	+	0.991603i	$0.541278\pi$
$504$	1.78701	0.0795998
$505$	−17.1934	−0.765097
$506$	3.24184	0.144117
$507$	−21.3408	−0.947776
$508$	−62.8667	−2.78926
$509$	16.6225	0.736780	0.368390	−	0.929671i	$-0.379909\pi$
$509$	16.6225	0.736780	0.368390	+	0.929671i	$0.379909\pi$
$510$	23.2814	1.03092
$511$	18.4337	0.815457
$512$	199.591	8.82075
$513$	30.8302	1.36119
$514$	−2.02212	−0.0891918
$515$	−14.7277	−0.648979
$516$	−5.46454	−0.240563
$517$	5.06585	0.222796
$518$	7.97301	0.350314
$519$	−0.815446	−0.0357941
$520$	−19.3043	−0.846550
$521$	−30.2162	−1.32379	−0.661897	−	0.749595i	$-0.730249\pi$
$521$	−30.2162	−1.32379	−0.661897	+	0.749595i	$0.730249\pi$
$522$	−1.86139	−0.0814709
$523$	−15.6072	−0.682456	−0.341228	−	0.939981i	$-0.610843\pi$
$523$	−15.6072	−0.682456	−0.341228	+	0.939981i	$0.610843\pi$
$524$	−63.5063	−2.77428
$525$	−5.19686	−0.226810
$526$	−19.3016	−0.841591
$527$	−5.23322	−0.227963
$528$	−21.9445	−0.955011
$529$	−20.0267	−0.870726
$530$	81.9466	3.55953
$531$	−0.697696	−0.0302774
$532$	43.0886	1.86813
$533$	7.99310	0.346220
$534$	−4.63599	−0.200619
$535$	−37.5281	−1.62248
$536$	121.470	5.24670
$537$	−8.58880	−0.370634
$538$	2.60882	0.112474
$539$	3.63229	0.156454
$540$	86.0229	3.70184
$541$	−12.0703	−0.518944	−0.259472	−	0.965751i	$-0.583549\pi$
$541$	−12.0703	−0.518944	−0.259472	+	0.965751i	$0.583549\pi$
$542$	−19.3147	−0.829639
$543$	23.4591	1.00673
$544$	−58.0092	−2.48712
$545$	−49.0726	−2.10204
$546$	−3.79051	−0.162219
$547$	−40.9002	−1.74877	−0.874384	−	0.485234i	$-0.838734\pi$
$547$	−40.9002	−1.74877	−0.874384	+	0.485234i	$0.838734\pi$
$548$	74.0955	3.16520
$549$	−1.00552	−0.0429147
$550$	−4.62314	−0.197131
$551$	−29.7725	−1.26835
$552$	−32.4459	−1.38099
$553$	3.26802	0.138971
$554$	63.5589	2.70036
$555$	10.4975	0.445593
$556$	−38.0591	−1.61407
$557$	18.1298	0.768182	0.384091	−	0.923295i	$-0.374515\pi$
$557$	18.1298	0.768182	0.384091	+	0.923295i	$0.374515\pi$
$558$	−1.06568	−0.0451138
$559$	−0.345523	−0.0146140
$560$	66.1263	2.79435
$561$	2.01823	0.0852099
$562$	51.4202	2.16903
$563$	37.2310	1.56910	0.784549	−	0.620067i	$-0.212895\pi$
$563$	37.2310	1.56910	0.784549	+	0.620067i	$0.212895\pi$
$564$	−76.4328	−3.21840
$565$	−30.8195	−1.29659
$566$	−41.8634	−1.75965
$567$	10.7219	0.450278
$568$	170.866	7.16936
$569$	−13.1301	−0.550442	−0.275221	−	0.961381i	$-0.588751\pi$
$569$	−13.1301	−0.550442	−0.275221	+	0.961381i	$0.588751\pi$
$570$	75.8305	3.17619
$571$	−3.29523	−0.137901	−0.0689505	−	0.997620i	$-0.521965\pi$
$571$	−3.29523	−0.137901	−0.0689505	+	0.997620i	$0.521965\pi$
$572$	−2.52275	−0.105482
$573$	21.3494	0.891886
$574$	−44.1388	−1.84232
$575$	−4.24019	−0.176828
$576$	−6.80390	−0.283496
$577$	−26.3419	−1.09663	−0.548314	−	0.836272i	$-0.684730\pi$
$577$	−26.3419	−1.09663	−0.548314	+	0.836272i	$0.684730\pi$
$578$	−38.9232	−1.61899
$579$	−7.26429	−0.301893
$580$	−83.0716	−3.44936
$581$	16.5021	0.684622
$582$	−29.1001	−1.20624
$583$	7.10384	0.294211
$584$	−164.126	−6.79157
$585$	0.224270	0.00927244
$586$	29.0960	1.20194
$587$	29.3658	1.21205	0.606027	−	0.795444i	$-0.292762\pi$
$587$	29.3658	1.21205	0.606027	+	0.795444i	$0.292762\pi$
$588$	−54.8035	−2.26006
$589$	−17.0453	−0.702338
$590$	−41.6197	−1.71346
$591$	−38.8110	−1.59647
$592$	−44.0353	−1.80984
$593$	3.30771	0.135831	0.0679156	−	0.997691i	$-0.478365\pi$
$593$	3.30771	0.135831	0.0679156	+	0.997691i	$0.478365\pi$
$594$	9.96768	0.408979
$595$	−6.08163	−0.249323
$596$	−2.80807	−0.115023
$597$	12.8420	0.525589
$598$	−3.09273	−0.126471
$599$	−36.9715	−1.51061	−0.755307	−	0.655371i	$-0.772512\pi$
$599$	−36.9715	−1.51061	−0.755307	+	0.655371i	$0.772512\pi$
$600$	46.2707	1.88899
$601$	38.7949	1.58248	0.791239	−	0.611508i	$-0.209437\pi$
$601$	38.7949	1.58248	0.791239	+	0.611508i	$0.209437\pi$
$602$	1.90802	0.0777649
$603$	−1.41119	−0.0574682
$604$	−84.6173	−3.44303
$605$	28.8267	1.17197
$606$	30.0587	1.22105
$607$	−37.2775	−1.51305	−0.756523	−	0.653967i	$-0.773104\pi$
$607$	−37.2775	−1.51305	−0.756523	+	0.653967i	$0.773104\pi$
$608$	−188.943	−7.66265
$609$	−10.8202	−0.438459
$610$	−59.9826	−2.42862
$611$	−4.83285	−0.195516
$612$	1.36839	0.0553140
$613$	32.0225	1.29338	0.646689	−	0.762754i	$-0.276153\pi$
$613$	32.0225	1.29338	0.646689	+	0.762754i	$0.276153\pi$
$614$	−27.5493	−1.11180
$615$	−58.1145	−2.34340
$616$	9.24106	0.372333
$617$	34.6730	1.39588	0.697941	−	0.716156i	$-0.254100\pi$
$617$	34.6730	1.39588	0.697941	+	0.716156i	$0.254100\pi$
$618$	25.7479	1.03573
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−47.5599	−1.91005
$621$	9.14204	0.366858
$622$	−9.67733	−0.388025
$623$	1.21102	0.0485186
$624$	20.9352	0.838077
$625$	−31.2483	−1.24993
$626$	−69.0316	−2.75906
$627$	6.57364	0.262526
$628$	−13.6015	−0.542759
$629$	4.04993	0.161481
$630$	−1.23845	−0.0493409
$631$	−35.0751	−1.39632	−0.698160	−	0.715942i	$-0.745997\pi$
$631$	−35.0751	−1.39632	−0.698160	+	0.715942i	$0.745997\pi$
$632$	−29.0971	−1.15742
$633$	−19.4934	−0.774794
$634$	−30.3454	−1.20517
$635$	28.9010	1.14690
$636$	−107.182	−4.25003
$637$	−3.46523	−0.137297
$638$	−9.62571	−0.381086
$639$	−1.98505	−0.0785275
$640$	−228.394	−9.02805
$641$	36.8354	1.45491	0.727455	−	0.686155i	$-0.240703\pi$
$641$	36.8354	1.45491	0.727455	+	0.686155i	$0.240703\pi$
$642$	65.6092	2.58939
$643$	−40.1327	−1.58268	−0.791340	−	0.611376i	$-0.790616\pi$
$643$	−40.1327	−1.58268	−0.791340	+	0.611376i	$0.790616\pi$
$644$	12.7770	0.503485
$645$	2.51215	0.0989158
$646$	29.2554	1.15104
$647$	6.17440	0.242741	0.121370	−	0.992607i	$-0.461271\pi$
$647$	6.17440	0.242741	0.121370	+	0.992607i	$0.461271\pi$
$648$	−95.4634	−3.75016
$649$	−3.60795	−0.141625
$650$	4.41050	0.172994
$651$	−6.19478	−0.242792
$652$	66.4805	2.60358
$653$	−3.31994	−0.129919	−0.0649597	−	0.997888i	$-0.520692\pi$
$653$	−3.31994	−0.129919	−0.0649597	+	0.997888i	$0.520692\pi$
$654$	85.7920	3.35473
$655$	29.1950	1.14074
$656$	243.781	9.51805
$657$	1.90675	0.0743894
$658$	26.6875	1.04039
$659$	−32.2558	−1.25651	−0.628253	−	0.778009i	$-0.716230\pi$
$659$	−32.2558	−1.25651	−0.628253	+	0.778009i	$0.716230\pi$
$660$	18.3419	0.713956
$661$	1.57682	0.0613314	0.0306657	−	0.999530i	$-0.490237\pi$
$661$	1.57682	0.0613314	0.0306657	+	0.999530i	$0.490237\pi$
$662$	14.7704	0.574067
$663$	−1.92541	−0.0747766
$664$	−146.928	−5.70191
$665$	−19.8086	−0.768146
$666$	0.824716	0.0319571
$667$	−8.82840	−0.341837
$668$	134.973	5.22227
$669$	−2.00145	−0.0773806
$670$	−84.1820	−3.25223
$671$	−5.19981	−0.200736
$672$	−68.6678	−2.64892
$673$	−15.1856	−0.585363	−0.292681	−	0.956210i	$-0.594548\pi$
$673$	−15.1856	−0.585363	−0.292681	+	0.956210i	$0.594548\pi$
$674$	−3.97084	−0.152951
$675$	−13.0373	−0.501807
$676$	−74.8245	−2.87786
$677$	−39.8257	−1.53063	−0.765313	−	0.643658i	$-0.777416\pi$
$677$	−39.8257	−1.53063	−0.765313	+	0.643658i	$0.777416\pi$
$678$	53.8807	2.06927
$679$	7.60160	0.291723
$680$	54.1484	2.07650
$681$	−20.7587	−0.795476
$682$	−5.51088	−0.211023
$683$	−8.46551	−0.323924	−0.161962	−	0.986797i	$-0.551782\pi$
$683$	−8.46551	−0.323924	−0.161962	+	0.986797i	$0.551782\pi$
$684$	4.45702	0.170419
$685$	−34.0631	−1.30148
$686$	43.7386	1.66995
$687$	−42.7313	−1.63030
$688$	−10.5381	−0.401760
$689$	−6.77710	−0.258187
$690$	22.4859	0.856025
$691$	9.66441	0.367651	0.183826	−	0.982959i	$-0.441152\pi$
$691$	9.66441	0.367651	0.183826	+	0.982959i	$0.441152\pi$
$692$	−2.85910	−0.108687
$693$	−0.107359	−0.00407824
$694$	−89.9936	−3.41611
$695$	17.4965	0.663679
$696$	96.3390	3.65172
$697$	−22.4206	−0.849239
$698$	30.8478	1.16761
$699$	−5.07562	−0.191978
$700$	−18.2211	−0.688693
$701$	31.4717	1.18867	0.594335	−	0.804218i	$-0.297415\pi$
$701$	31.4717	1.18867	0.594335	+	0.804218i	$0.297415\pi$
$702$	−9.50922	−0.358902
$703$	13.1911	0.497512
$704$	−35.1846	−1.32607
$705$	35.1376	1.32336
$706$	71.0852	2.67533
$707$	−7.85200	−0.295305
$708$	54.4363	2.04584
$709$	−29.4151	−1.10471	−0.552353	−	0.833610i	$-0.686270\pi$
$709$	−29.4151	−1.10471	−0.552353	+	0.833610i	$0.686270\pi$
$710$	−118.415	−4.44402
$711$	0.338040	0.0126775
$712$	−10.7825	−0.404090
$713$	−5.05441	−0.189289
$714$	10.6323	0.397905
$715$	1.15976	0.0433724
$716$	−30.1139	−1.12541
$717$	−23.0624	−0.861281
$718$	−21.4808	−0.801657
$719$	−41.2623	−1.53882	−0.769412	−	0.638753i	$-0.779451\pi$
$719$	−41.2623	−1.53882	−0.769412	+	0.638753i	$0.779451\pi$
$720$	6.84001	0.254912
$721$	−6.72593	−0.250487
$722$	41.7473	1.55367
$723$	−9.11155	−0.338862
$724$	82.2518	3.05686
$725$	12.5901	0.467583
$726$	−50.3968	−1.87040
$727$	11.3716	0.421750	0.210875	−	0.977513i	$-0.432369\pi$
$727$	11.3716	0.421750	0.210875	+	0.977513i	$0.432369\pi$
$728$	−8.81602	−0.326744
$729$	28.0591	1.03923
$730$	113.744	4.20984
$731$	0.969187	0.0358467
$732$	78.4540	2.89974
$733$	22.3723	0.826341	0.413170	−	0.910654i	$-0.364421\pi$
$733$	22.3723	0.826341	0.413170	+	0.910654i	$0.364421\pi$
$734$	98.0972	3.62083
$735$	25.1942	0.929302
$736$	−56.0271	−2.06518
$737$	−7.29762	−0.268811
$738$	−4.56566	−0.168064
$739$	13.3041	0.489398	0.244699	−	0.969599i	$-0.421311\pi$
$739$	13.3041	0.489398	0.244699	+	0.969599i	$0.421311\pi$
$740$	36.8061	1.35302
$741$	−6.27129	−0.230381
$742$	37.4239	1.37388
$743$	−9.08074	−0.333140	−0.166570	−	0.986030i	$-0.553269\pi$
$743$	−9.08074	−0.333140	−0.166570	+	0.986030i	$0.553269\pi$
$744$	55.1557	2.02211
$745$	1.29092	0.0472957
$746$	88.5409	3.24171
$747$	1.70695	0.0624541
$748$	7.07629	0.258735
$749$	−17.1386	−0.626231
$750$	33.1351	1.20992
$751$	−15.4519	−0.563848	−0.281924	−	0.959437i	$-0.590973\pi$
$751$	−15.4519	−0.563848	−0.281924	+	0.959437i	$0.590973\pi$
$752$	−147.397	−5.37500
$753$	26.2266	0.955750
$754$	9.18298	0.334424
$755$	38.9001	1.41572
$756$	39.2855	1.42880
$757$	9.35179	0.339897	0.169948	−	0.985453i	$-0.445640\pi$
$757$	9.35179	0.339897	0.169948	+	0.985453i	$0.445640\pi$
$758$	−51.1938	−1.85944
$759$	1.94927	0.0707541
$760$	176.368	6.39754
$761$	−4.02548	−0.145924	−0.0729618	−	0.997335i	$-0.523245\pi$
$761$	−4.02548	−0.145924	−0.0729618	+	0.997335i	$0.523245\pi$
$762$	−50.5267	−1.83039
$763$	−22.4108	−0.811326
$764$	74.8550	2.70816
$765$	−0.629075	−0.0227443
$766$	−78.8272	−2.84814
$767$	3.44201	0.124284
$768$	220.578	7.95942
$769$	13.1595	0.474545	0.237273	−	0.971443i	$-0.423747\pi$
$769$	13.1595	0.474545	0.237273	+	0.971443i	$0.423747\pi$
$770$	−6.40431	−0.230795
$771$	−1.21587	−0.0437886
$772$	−25.4699	−0.916681
$773$	−19.2946	−0.693978	−0.346989	−	0.937869i	$-0.612796\pi$
$773$	−19.2946	−0.693978	−0.346989	+	0.937869i	$0.612796\pi$
$774$	0.197362	0.00709405
$775$	7.20802	0.258920
$776$	−67.6815	−2.42962
$777$	4.79406	0.171986
$778$	51.3428	1.84073
$779$	−73.0265	−2.61645
$780$	−17.4982	−0.626537
$781$	−10.2652	−0.367317
$782$	8.67507	0.310220
$783$	−27.1447	−0.970072
$784$	−105.686	−3.77449
$785$	6.25286	0.223174
$786$	−51.0407	−1.82056
$787$	18.2376	0.650099	0.325050	−	0.945697i	$-0.394619\pi$
$787$	18.2376	0.650099	0.325050	+	0.945697i	$0.394619\pi$
$788$	−136.078	−4.84759
$789$	−11.6058	−0.413178
$790$	20.1651	0.717443
$791$	−14.0748	−0.500444
$792$	0.955882	0.0339658
$793$	4.96064	0.176158
$794$	18.2543	0.647820
$795$	49.2734	1.74755
$796$	45.0264	1.59592
$797$	14.9298	0.528840	0.264420	−	0.964408i	$-0.414819\pi$
$797$	14.9298	0.528840	0.264420	+	0.964408i	$0.414819\pi$
$798$	34.6308	1.22592
$799$	13.5561	0.479580
$800$	79.8994	2.82487
$801$	0.125267	0.00442608
$802$	−4.85558	−0.171457
$803$	9.86027	0.347961
$804$	110.105	3.88312
$805$	−5.87383	−0.207025
$806$	5.25741	0.185185
$807$	1.56865	0.0552191
$808$	69.9110	2.45946
$809$	−30.9136	−1.08686	−0.543432	−	0.839453i	$-0.682875\pi$
$809$	−30.9136	−1.08686	−0.543432	+	0.839453i	$0.682875\pi$
$810$	66.1587	2.32458
$811$	44.8995	1.57664	0.788318	−	0.615268i	$-0.210952\pi$
$811$	44.8995	1.57664	0.788318	+	0.615268i	$0.210952\pi$
$812$	−37.9377	−1.33135
$813$	−11.6137	−0.407310
$814$	4.26481	0.149481
$815$	−30.5623	−1.07055
$816$	−58.7229	−2.05571
$817$	3.15676	0.110441
$818$	−59.0384	−2.06423
$819$	0.102421	0.00357889
$820$	−203.760	−7.11560
$821$	22.7230	0.793038	0.396519	−	0.918026i	$-0.370218\pi$
$821$	22.7230	0.793038	0.396519	+	0.918026i	$0.370218\pi$
$822$	59.5514	2.07709
$823$	−9.66099	−0.336761	−0.168380	−	0.985722i	$-0.553854\pi$
$823$	−9.66099	−0.336761	−0.168380	+	0.985722i	$0.553854\pi$
$824$	59.8849	2.08619
$825$	−2.77983	−0.0967813
$826$	−19.0072	−0.661344
$827$	28.6256	0.995408	0.497704	−	0.867347i	$-0.334177\pi$
$827$	28.6256	0.995408	0.497704	+	0.867347i	$0.334177\pi$
$828$	1.32164	0.0459300
$829$	−1.43739	−0.0499228	−0.0249614	−	0.999688i	$-0.507946\pi$
$829$	−1.43739	−0.0499228	−0.0249614	+	0.999688i	$0.507946\pi$
$830$	101.825	3.53440
$831$	38.2171	1.32574
$832$	33.5663	1.16370
$833$	9.71992	0.336775
$834$	−30.5885	−1.05919
$835$	−62.0496	−2.14732
$836$	23.0483	0.797144
$837$	−15.5408	−0.537169
$838$	46.6673	1.61210
$839$	−24.8847	−0.859115	−0.429558	−	0.903039i	$-0.641331\pi$
$839$	−24.8847	−0.859115	−0.429558	+	0.903039i	$0.641331\pi$
$840$	64.0976	2.21158
$841$	−2.78657	−0.0960887
$842$	1.68468	0.0580580
$843$	30.9183	1.06488
$844$	−68.3474	−2.35261
$845$	34.3982	1.18333
$846$	2.76052	0.0949087
$847$	13.1648	0.452347
$848$	−206.694	−7.09791
$849$	−25.1719	−0.863897
$850$	−12.3714	−0.424335
$851$	3.91155	0.134086
$852$	154.880	5.30609
$853$	53.8865	1.84504	0.922520	−	0.385949i	$-0.126126\pi$
$853$	53.8865	1.84504	0.922520	+	0.385949i	$0.126126\pi$
$854$	−27.3933	−0.937378
$855$	−2.04898	−0.0700735
$856$	152.595	5.21559
$857$	13.4064	0.457954	0.228977	−	0.973432i	$-0.426462\pi$
$857$	13.4064	0.457954	0.228977	+	0.973432i	$0.426462\pi$
$858$	−2.02756	−0.0692199
$859$	17.0470	0.581635	0.290817	−	0.956779i	$-0.406073\pi$
$859$	17.0470	0.581635	0.290817	+	0.956779i	$0.406073\pi$
$860$	8.80804	0.300352
$861$	−26.5401	−0.904484
$862$	44.8735	1.52840
$863$	22.0056	0.749078	0.374539	−	0.927211i	$-0.377801\pi$
$863$	22.0056	0.749078	0.374539	+	0.927211i	$0.377801\pi$
$864$	−172.267	−5.86063
$865$	1.31438	0.0446903
$866$	−43.0144	−1.46169
$867$	−23.4040	−0.794842
$868$	−21.7200	−0.737225
$869$	1.74809	0.0592997
$870$	−66.7656	−2.26357
$871$	6.96197	0.235897
$872$	199.537	6.75716
$873$	0.786299	0.0266122
$874$	28.2558	0.955765
$875$	−8.65564	−0.292614
$876$	−148.770	−5.02648
$877$	−3.18136	−0.107427	−0.0537134	−	0.998556i	$-0.517106\pi$
$877$	−3.18136	−0.107427	−0.0537134	+	0.998556i	$0.517106\pi$
$878$	72.0107	2.43024
$879$	17.4950	0.590093
$880$	35.3713	1.19237
$881$	14.1933	0.478184	0.239092	−	0.970997i	$-0.423150\pi$
$881$	14.1933	0.478184	0.239092	+	0.970997i	$0.423150\pi$
$882$	1.97934	0.0666478
$883$	20.3870	0.686076	0.343038	−	0.939322i	$-0.388544\pi$
$883$	20.3870	0.686076	0.343038	+	0.939322i	$0.388544\pi$
$884$	−6.75082	−0.227055
$885$	−25.0254	−0.841219
$886$	−90.0289	−3.02458
$887$	46.5243	1.56213	0.781066	−	0.624448i	$-0.214676\pi$
$887$	46.5243	1.56213	0.781066	+	0.624448i	$0.214676\pi$
$888$	−42.6844	−1.43239
$889$	13.1987	0.442670
$890$	7.47254	0.250480
$891$	5.73521	0.192137
$892$	−7.01745	−0.234962
$893$	44.1538	1.47755
$894$	−2.25688	−0.0754813
$895$	13.8439	0.462751
$896$	−104.304	−3.48456
$897$	−1.85962	−0.0620908
$898$	101.835	3.39828
$899$	15.0076	0.500533
$900$	−1.88477	−0.0628255
$901$	19.0097	0.633304
$902$	−23.6101	−0.786131
$903$	1.14726	0.0381786
$904$	125.317	4.16797
$905$	−37.8127	−1.25694
$906$	−68.0078	−2.25941
$907$	9.88807	0.328328	0.164164	−	0.986433i	$-0.447507\pi$
$907$	9.88807	0.328328	0.164164	+	0.986433i	$0.447507\pi$
$908$	−72.7837	−2.41541
$909$	−0.812200	−0.0269390
$910$	6.10975	0.202536
$911$	7.90295	0.261836	0.130918	−	0.991393i	$-0.458207\pi$
$911$	7.90295	0.261836	0.130918	+	0.991393i	$0.458207\pi$
$912$	−191.268	−6.33350
$913$	8.82707	0.292133
$914$	−3.45514	−0.114286
$915$	−36.0667	−1.19233
$916$	−149.823	−4.95031
$917$	13.3330	0.440294
$918$	26.6733	0.880348
$919$	−1.41959	−0.0468279	−0.0234140	−	0.999726i	$-0.507454\pi$
$919$	−1.41959	−0.0468279	−0.0234140	+	0.999726i	$0.507454\pi$
$920$	52.2982	1.72422
$921$	−16.5650	−0.545837
$922$	84.7200	2.79010
$923$	9.79305	0.322342
$924$	8.37649	0.275566
$925$	−5.57820	−0.183410
$926$	−28.8027	−0.946516
$927$	−0.695721	−0.0228505
$928$	166.356	5.46092
$929$	−13.4297	−0.440614	−0.220307	−	0.975431i	$-0.570706\pi$
$929$	−13.4297	−0.440614	−0.220307	+	0.975431i	$0.570706\pi$
$930$	−38.2244	−1.25343
$931$	31.6590	1.03758
$932$	−17.7960	−0.582929
$933$	−5.81885	−0.190501
$934$	−85.5149	−2.79813
$935$	−3.25310	−0.106388
$936$	−0.911917	−0.0298069
$937$	−51.7062	−1.68917	−0.844583	−	0.535424i	$-0.820152\pi$
$937$	−51.7062	−1.68917	−0.844583	+	0.535424i	$0.820152\pi$
$938$	−38.4448	−1.25527
$939$	−41.5078	−1.35456
$940$	123.199	4.01830
$941$	16.1493	0.526453	0.263227	−	0.964734i	$-0.415213\pi$
$941$	16.1493	0.526453	0.263227	+	0.964734i	$0.415213\pi$
$942$	−10.9317	−0.356173
$943$	−21.6545	−0.705166
$944$	104.978	3.41673
$945$	−18.0603	−0.587501
$946$	1.02061	0.0331829
$947$	−42.6170	−1.38487	−0.692433	−	0.721483i	$-0.743461\pi$
$947$	−42.6170	−1.38487	−0.692433	+	0.721483i	$0.743461\pi$
$948$	−26.3749	−0.856616
$949$	−9.40675	−0.305356
$950$	−40.2951	−1.30735
$951$	−18.2463	−0.591676
$952$	24.7288	0.801466
$953$	−36.8171	−1.19262	−0.596311	−	0.802754i	$-0.703367\pi$
$953$	−36.8171	−1.19262	−0.596311	+	0.802754i	$0.703367\pi$
$954$	3.87108	0.125331
$955$	−34.4122	−1.11355
$956$	−80.8609	−2.61523
$957$	−5.78781	−0.187093
$958$	−76.9501	−2.48615
$959$	−15.5562	−0.502335
$960$	−244.046	−7.87656
$961$	−22.4079	−0.722835
$962$	−4.06865	−0.131178
$963$	−1.77279	−0.0571274
$964$	−31.9467	−1.02893
$965$	11.7090	0.376925
$966$	10.2690	0.330400
$967$	−9.04497	−0.290867	−0.145433	−	0.989368i	$-0.546458\pi$
$967$	−9.04497	−0.290867	−0.145433	+	0.989368i	$0.546458\pi$
$968$	−117.214	−3.76739
$969$	17.5909	0.565100
$970$	46.9051	1.50603
$971$	26.2332	0.841862	0.420931	−	0.907093i	$-0.361703\pi$
$971$	26.2332	0.841862	0.420931	+	0.907093i	$0.361703\pi$
$972$	7.95972	0.255308
$973$	7.99041	0.256161
$974$	27.3405	0.876047
$975$	2.65197	0.0849311
$976$	151.294	4.84282
$977$	30.2760	0.968614	0.484307	−	0.874898i	$-0.339072\pi$
$977$	30.2760	0.968614	0.484307	+	0.874898i	$0.339072\pi$
$978$	53.4311	1.70854
$979$	0.647784	0.0207033
$980$	88.3354	2.82177
$981$	−2.31814	−0.0740126
$982$	−47.6950	−1.52201
$983$	7.11248	0.226853	0.113426	−	0.993546i	$-0.463817\pi$
$983$	7.11248	0.226853	0.113426	+	0.993546i	$0.463817\pi$
$984$	236.302	7.53304
$985$	62.5578	1.99326
$986$	−25.7582	−0.820307
$987$	16.0469	0.510777
$988$	−21.9882	−0.699539
$989$	0.936071	0.0297653
$990$	−0.662452	−0.0210541
$991$	−36.8918	−1.17191	−0.585954	−	0.810345i	$-0.699280\pi$
$991$	−36.8918	−1.17191	−0.585954	+	0.810345i	$0.699280\pi$
$992$	95.2419	3.02393
$993$	8.88123	0.281837
$994$	−54.0784	−1.71526
$995$	−20.6995	−0.656218
$996$	−133.182	−4.22002
$997$	−55.9262	−1.77120	−0.885600	−	0.464450i	$-0.846252\pi$
$997$	−55.9262	−1.77120	−0.885600	+	0.464450i	$0.846252\pi$
$998$	−6.95213	−0.220066
$999$	12.0268	0.380512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.30	✓	30
3.2	odd	2		5571.2.a.g.1.1		30
4.3	odd	2		9904.2.a.n.1.10		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.30	✓	30	1.1	even	1	trivial
5571.2.a.g.1.1		30	3.2	odd	2
9904.2.a.n.1.10		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)

\(f(q)\)	\(=\)	\(q+2.81795 q^{2} +1.69440 q^{3} +5.94086 q^{4} -2.73112 q^{5} +4.77473 q^{6} -1.24727 q^{7} +11.1052 q^{8} -0.129016 q^{9} +O(q^{10})\)	\(q+2.81795 q^{2} +1.69440 q^{3} +5.94086 q^{4} -2.73112 q^{5} +4.77473 q^{6} -1.24727 q^{7} +11.1052 q^{8} -0.129016 q^{9} -7.69618 q^{10} -0.667171 q^{11} +10.0662 q^{12} +0.636485 q^{13} -3.51474 q^{14} -4.62761 q^{15} +19.4121 q^{16} -1.78533 q^{17} -0.363560 q^{18} -5.81505 q^{19} -16.2252 q^{20} -2.11337 q^{21} -1.88006 q^{22} -1.72433 q^{23} +18.8166 q^{24} +2.45904 q^{25} +1.79358 q^{26} -5.30180 q^{27} -7.40985 q^{28} +5.11991 q^{29} -13.0404 q^{30} +2.93123 q^{31} +32.4921 q^{32} -1.13045 q^{33} -5.03098 q^{34} +3.40644 q^{35} -0.766464 q^{36} -2.26845 q^{37} -16.3865 q^{38} +1.07846 q^{39} -30.3296 q^{40} +12.5582 q^{41} -5.95537 q^{42} -0.542861 q^{43} -3.96357 q^{44} +0.352358 q^{45} -4.85908 q^{46} -7.59303 q^{47} +32.8918 q^{48} -5.44432 q^{49} +6.92946 q^{50} -3.02506 q^{51} +3.78127 q^{52} -10.6477 q^{53} -14.9402 q^{54} +1.82213 q^{55} -13.8511 q^{56} -9.85300 q^{57} +14.4277 q^{58} +5.40784 q^{59} -27.4920 q^{60} +7.79382 q^{61} +8.26008 q^{62} +0.160917 q^{63} +52.7370 q^{64} -1.73832 q^{65} -3.18556 q^{66} +10.9382 q^{67} -10.6064 q^{68} -2.92170 q^{69} +9.59920 q^{70} +15.3861 q^{71} -1.43274 q^{72} -14.7792 q^{73} -6.39237 q^{74} +4.16659 q^{75} -34.5464 q^{76} +0.832141 q^{77} +3.03905 q^{78} -2.62015 q^{79} -53.0169 q^{80} -8.59631 q^{81} +35.3884 q^{82} -13.2306 q^{83} -12.5552 q^{84} +4.87596 q^{85} -1.52976 q^{86} +8.67516 q^{87} -7.40904 q^{88} -0.970941 q^{89} +0.992928 q^{90} -0.793867 q^{91} -10.2440 q^{92} +4.96668 q^{93} -21.3968 q^{94} +15.8816 q^{95} +55.0545 q^{96} -6.09460 q^{97} -15.3418 q^{98} +0.0860755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 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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