LMFDB - Embedded newform 4011.2.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47855 q^{2} +1.00000 q^{3} +0.186109 q^{4} +3.98947 q^{5} -1.47855 q^{6} -1.00000 q^{7} +2.68193 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.47855 q^{2} +1.00000 q^{3} +0.186109 q^{4} +3.98947 q^{5} -1.47855 q^{6} -1.00000 q^{7} +2.68193 q^{8} +1.00000 q^{9} -5.89863 q^{10} +4.84256 q^{11} +0.186109 q^{12} +1.76323 q^{13} +1.47855 q^{14} +3.98947 q^{15} -4.33758 q^{16} -4.24111 q^{17} -1.47855 q^{18} -3.33056 q^{19} +0.742476 q^{20} -1.00000 q^{21} -7.15997 q^{22} -6.65389 q^{23} +2.68193 q^{24} +10.9159 q^{25} -2.60703 q^{26} +1.00000 q^{27} -0.186109 q^{28} -5.64359 q^{29} -5.89863 q^{30} +9.97798 q^{31} +1.04947 q^{32} +4.84256 q^{33} +6.27069 q^{34} -3.98947 q^{35} +0.186109 q^{36} +8.75182 q^{37} +4.92440 q^{38} +1.76323 q^{39} +10.6995 q^{40} +6.47053 q^{41} +1.47855 q^{42} -8.81890 q^{43} +0.901243 q^{44} +3.98947 q^{45} +9.83811 q^{46} +8.40411 q^{47} -4.33758 q^{48} +1.00000 q^{49} -16.1397 q^{50} -4.24111 q^{51} +0.328153 q^{52} +0.147185 q^{53} -1.47855 q^{54} +19.3193 q^{55} -2.68193 q^{56} -3.33056 q^{57} +8.34433 q^{58} +2.19993 q^{59} +0.742476 q^{60} +15.1650 q^{61} -14.7529 q^{62} -1.00000 q^{63} +7.12347 q^{64} +7.03437 q^{65} -7.15997 q^{66} -8.76442 q^{67} -0.789308 q^{68} -6.65389 q^{69} +5.89863 q^{70} +7.02500 q^{71} +2.68193 q^{72} +1.50018 q^{73} -12.9400 q^{74} +10.9159 q^{75} -0.619847 q^{76} -4.84256 q^{77} -2.60703 q^{78} -2.89105 q^{79} -17.3047 q^{80} +1.00000 q^{81} -9.56700 q^{82} +2.65450 q^{83} -0.186109 q^{84} -16.9198 q^{85} +13.0392 q^{86} -5.64359 q^{87} +12.9874 q^{88} +8.87297 q^{89} -5.89863 q^{90} -1.76323 q^{91} -1.23835 q^{92} +9.97798 q^{93} -12.4259 q^{94} -13.2872 q^{95} +1.04947 q^{96} -4.53365 q^{97} -1.47855 q^{98} +4.84256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−1.47855	−1.04549	−0.522746	−	0.852488i	$-0.675092\pi$
$2$	−1.47855	−1.04549	−0.522746	+	0.852488i	$0.675092\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.186109	0.0930544
$5$	3.98947	1.78415	0.892073	−	0.451891i	$-0.149250\pi$
$5$	3.98947	1.78415	0.892073	+	0.451891i	$0.149250\pi$
$6$	−1.47855	−0.603615
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.68193	0.948205
$9$	1.00000	0.333333
$10$	−5.89863	−1.86531
$11$	4.84256	1.46009	0.730044	−	0.683400i	$-0.239500\pi$
$11$	4.84256	1.46009	0.730044	+	0.683400i	$0.239500\pi$
$12$	0.186109	0.0537250
$13$	1.76323	0.489033	0.244516	−	0.969645i	$-0.421371\pi$
$13$	1.76323	0.489033	0.244516	+	0.969645i	$0.421371\pi$
$14$	1.47855	0.395159
$15$	3.98947	1.03008
$16$	−4.33758	−1.08440
$17$	−4.24111	−1.02862	−0.514310	−	0.857604i	$-0.671952\pi$
$17$	−4.24111	−1.02862	−0.514310	+	0.857604i	$0.671952\pi$
$18$	−1.47855	−0.348497
$19$	−3.33056	−0.764083	−0.382042	−	0.924145i	$-0.624779\pi$
$19$	−3.33056	−0.764083	−0.382042	+	0.924145i	$0.624779\pi$
$20$	0.742476	0.166023
$21$	−1.00000	−0.218218
$22$	−7.15997	−1.52651
$23$	−6.65389	−1.38743	−0.693716	−	0.720249i	$-0.744028\pi$
$23$	−6.65389	−1.38743	−0.693716	+	0.720249i	$0.744028\pi$
$24$	2.68193	0.547446
$25$	10.9159	2.18318
$26$	−2.60703	−0.511280
$27$	1.00000	0.192450
$28$	−0.186109	−0.0351712
$29$	−5.64359	−1.04799	−0.523995	−	0.851722i	$-0.675559\pi$
$29$	−5.64359	−1.04799	−0.523995	+	0.851722i	$0.675559\pi$
$30$	−5.89863	−1.07694
$31$	9.97798	1.79210	0.896049	−	0.443955i	$-0.146425\pi$
$31$	9.97798	1.79210	0.896049	+	0.443955i	$0.146425\pi$
$32$	1.04947	0.185522
$33$	4.84256	0.842982
$34$	6.27069	1.07542
$35$	−3.98947	−0.674344
$36$	0.186109	0.0310181
$37$	8.75182	1.43879	0.719395	−	0.694601i	$-0.244419\pi$
$37$	8.75182	1.43879	0.719395	+	0.694601i	$0.244419\pi$
$38$	4.92440	0.798843
$39$	1.76323	0.282343
$40$	10.6995	1.69174
$41$	6.47053	1.01053	0.505264	−	0.862965i	$-0.331395\pi$
$41$	6.47053	1.01053	0.505264	+	0.862965i	$0.331395\pi$
$42$	1.47855	0.228145
$43$	−8.81890	−1.34487	−0.672435	−	0.740156i	$-0.734752\pi$
$43$	−8.81890	−1.34487	−0.672435	+	0.740156i	$0.734752\pi$
$44$	0.901243	0.135868
$45$	3.98947	0.594716
$46$	9.83811	1.45055
$47$	8.40411	1.22587	0.612933	−	0.790135i	$-0.289990\pi$
$47$	8.40411	1.22587	0.612933	+	0.790135i	$0.289990\pi$
$48$	−4.33758	−0.626076
$49$	1.00000	0.142857
$50$	−16.1397	−2.28250
$51$	−4.24111	−0.593875
$52$	0.328153	0.0455066
$53$	0.147185	0.0202174	0.0101087	−	0.999949i	$-0.496782\pi$
$53$	0.147185	0.0202174	0.0101087	+	0.999949i	$0.496782\pi$
$54$	−1.47855	−0.201205
$55$	19.3193	2.60501
$56$	−2.68193	−0.358388
$57$	−3.33056	−0.441144
$58$	8.34433	1.09566
$59$	2.19993	0.286407	0.143203	−	0.989693i	$-0.454260\pi$
$59$	2.19993	0.286407	0.143203	+	0.989693i	$0.454260\pi$
$60$	0.742476	0.0958532
$61$	15.1650	1.94168	0.970838	−	0.239737i	$-0.0770612\pi$
$61$	15.1650	1.94168	0.970838	+	0.239737i	$0.0770612\pi$
$62$	−14.7529	−1.87362
$63$	−1.00000	−0.125988
$64$	7.12347	0.890433
$65$	7.03437	0.872506
$66$	−7.15997	−0.881331
$67$	−8.76442	−1.07074	−0.535372	−	0.844616i	$-0.679829\pi$
$67$	−8.76442	−1.07074	−0.535372	+	0.844616i	$0.679829\pi$
$68$	−0.789308	−0.0957177
$69$	−6.65389	−0.801034
$70$	5.89863	0.705022
$71$	7.02500	0.833714	0.416857	−	0.908972i	$-0.363132\pi$
$71$	7.02500	0.833714	0.416857	+	0.908972i	$0.363132\pi$
$72$	2.68193	0.316068
$73$	1.50018	0.175583	0.0877914	−	0.996139i	$-0.472019\pi$
$73$	1.50018	0.175583	0.0877914	+	0.996139i	$0.472019\pi$
$74$	−12.9400	−1.50424
$75$	10.9159	1.26046
$76$	−0.619847	−0.0711013
$77$	−4.84256	−0.551861
$78$	−2.60703	−0.295188
$79$	−2.89105	−0.325269	−0.162634	−	0.986686i	$-0.551999\pi$
$79$	−2.89105	−0.325269	−0.162634	+	0.986686i	$0.551999\pi$
$80$	−17.3047	−1.93472
$81$	1.00000	0.111111
$82$	−9.56700	−1.05650
$83$	2.65450	0.291369	0.145685	−	0.989331i	$-0.453462\pi$
$83$	2.65450	0.291369	0.145685	+	0.989331i	$0.453462\pi$
$84$	−0.186109	−0.0203061
$85$	−16.9198	−1.83521
$86$	13.0392	1.40605
$87$	−5.64359	−0.605057
$88$	12.9874	1.38446
$89$	8.87297	0.940533	0.470267	−	0.882524i	$-0.344158\pi$
$89$	8.87297	0.940533	0.470267	+	0.882524i	$0.344158\pi$
$90$	−5.89863	−0.621771
$91$	−1.76323	−0.184837
$92$	−1.23835	−0.129107
$93$	9.97798	1.03467
$94$	−12.4259	−1.28163
$95$	−13.2872	−1.36324
$96$	1.04947	0.107111
$97$	−4.53365	−0.460323	−0.230161	−	0.973152i	$-0.573925\pi$
$97$	−4.53365	−0.460323	−0.230161	+	0.973152i	$0.573925\pi$
$98$	−1.47855	−0.149356
$99$	4.84256	0.486696
$100$	2.03154	0.203154
$101$	−10.4950	−1.04429	−0.522147	−	0.852856i	$-0.674869\pi$
$101$	−10.4950	−1.04429	−0.522147	+	0.852856i	$0.674869\pi$
$102$	6.27069	0.620891
$103$	−10.3040	−1.01528	−0.507642	−	0.861568i	$-0.669483\pi$
$103$	−10.3040	−1.01528	−0.507642	+	0.861568i	$0.669483\pi$
$104$	4.72886	0.463703
$105$	−3.98947	−0.389333
$106$	−0.217620	−0.0211372
$107$	4.64248	0.448805	0.224403	−	0.974497i	$-0.427957\pi$
$107$	4.64248	0.448805	0.224403	+	0.974497i	$0.427957\pi$
$108$	0.186109	0.0179083
$109$	10.3378	0.990184	0.495092	−	0.868841i	$-0.335134\pi$
$109$	10.3378	0.990184	0.495092	+	0.868841i	$0.335134\pi$
$110$	−28.5645	−2.72352
$111$	8.75182	0.830686
$112$	4.33758	0.409863
$113$	−1.97650	−0.185934	−0.0929668	−	0.995669i	$-0.529635\pi$
$113$	−1.97650	−0.185934	−0.0929668	+	0.995669i	$0.529635\pi$
$114$	4.92440	0.461212
$115$	−26.5455	−2.47538
$116$	−1.05032	−0.0975199
$117$	1.76323	0.163011
$118$	−3.25271	−0.299436
$119$	4.24111	0.388782
$120$	10.6995	0.976724
$121$	12.4504	1.13186
$122$	−22.4222	−2.03001
$123$	6.47053	0.583428
$124$	1.85699	0.166763
$125$	23.6013	2.11097
$126$	1.47855	0.131720
$127$	−5.45154	−0.483746	−0.241873	−	0.970308i	$-0.577762\pi$
$127$	−5.45154	−0.483746	−0.241873	+	0.970308i	$0.577762\pi$
$128$	−12.6313	−1.11646
$129$	−8.81890	−0.776461
$130$	−10.4007	−0.912199
$131$	−6.42493	−0.561349	−0.280674	−	0.959803i	$-0.590558\pi$
$131$	−6.42493	−0.561349	−0.280674	+	0.959803i	$0.590558\pi$
$132$	0.901243	0.0784432
$133$	3.33056	0.288796
$134$	12.9586	1.11946
$135$	3.98947	0.343359
$136$	−11.3744	−0.975343
$137$	13.0480	1.11477	0.557384	−	0.830255i	$-0.311805\pi$
$137$	13.0480	1.11477	0.557384	+	0.830255i	$0.311805\pi$
$138$	9.83811	0.837475
$139$	15.1530	1.28526	0.642628	−	0.766178i	$-0.277844\pi$
$139$	15.1530	1.28526	0.642628	+	0.766178i	$0.277844\pi$
$140$	−0.742476	−0.0627507
$141$	8.40411	0.707754
$142$	−10.3868	−0.871641
$143$	8.53857	0.714031
$144$	−4.33758	−0.361465
$145$	−22.5150	−1.86977
$146$	−2.21809	−0.183571
$147$	1.00000	0.0824786
$148$	1.62879	0.133886
$149$	−5.46924	−0.448058	−0.224029	−	0.974583i	$-0.571921\pi$
$149$	−5.46924	−0.448058	−0.224029	+	0.974583i	$0.571921\pi$
$150$	−16.1397	−1.31780
$151$	−11.1754	−0.909443	−0.454722	−	0.890634i	$-0.650261\pi$
$151$	−11.1754	−0.909443	−0.454722	+	0.890634i	$0.650261\pi$
$152$	−8.93233	−0.724507
$153$	−4.24111	−0.342874
$154$	7.15997	0.576967
$155$	39.8069	3.19737
$156$	0.328153	0.0262733
$157$	12.7976	1.02136	0.510680	−	0.859771i	$-0.329394\pi$
$157$	12.7976	1.02136	0.510680	+	0.859771i	$0.329394\pi$
$158$	4.27456	0.340066
$159$	0.147185	0.0116725
$160$	4.18684	0.330999
$161$	6.65389	0.524400
$162$	−1.47855	−0.116166
$163$	9.33890	0.731479	0.365740	−	0.930717i	$-0.380816\pi$
$163$	9.33890	0.731479	0.365740	+	0.930717i	$0.380816\pi$
$164$	1.20422	0.0940340
$165$	19.3193	1.50400
$166$	−3.92481	−0.304624
$167$	7.53656	0.583197	0.291598	−	0.956541i	$-0.405813\pi$
$167$	7.53656	0.583197	0.291598	+	0.956541i	$0.405813\pi$
$168$	−2.68193	−0.206915
$169$	−9.89101	−0.760847
$170$	25.0168	1.91870
$171$	−3.33056	−0.254694
$172$	−1.64128	−0.125146
$173$	−0.927193	−0.0704932	−0.0352466	−	0.999379i	$-0.511222\pi$
$173$	−0.927193	−0.0704932	−0.0352466	+	0.999379i	$0.511222\pi$
$174$	8.34433	0.632582
$175$	−10.9159	−0.825164
$176$	−21.0050	−1.58331
$177$	2.19993	0.165357
$178$	−13.1191	−0.983320
$179$	11.5492	0.863231	0.431615	−	0.902058i	$-0.357944\pi$
$179$	11.5492	0.863231	0.431615	+	0.902058i	$0.357944\pi$
$180$	0.742476	0.0553409
$181$	4.37885	0.325478	0.162739	−	0.986669i	$-0.447967\pi$
$181$	4.37885	0.325478	0.162739	+	0.986669i	$0.447967\pi$
$182$	2.60703	0.193246
$183$	15.1650	1.12103
$184$	−17.8453	−1.31557
$185$	34.9152	2.56701
$186$	−14.7529	−1.08174
$187$	−20.5379	−1.50188
$188$	1.56408	0.114072
$189$	−1.00000	−0.0727393
$190$	19.6458	1.42525
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	7.12347	0.514092
$193$	6.32621	0.455371	0.227685	−	0.973735i	$-0.426884\pi$
$193$	6.32621	0.455371	0.227685	+	0.973735i	$0.426884\pi$
$194$	6.70323	0.481264
$195$	7.03437	0.503742
$196$	0.186109	0.0132935
$197$	−21.4893	−1.53105	−0.765523	−	0.643409i	$-0.777520\pi$
$197$	−21.4893	−1.53105	−0.765523	+	0.643409i	$0.777520\pi$
$198$	−7.15997	−0.508837
$199$	−13.8446	−0.981415	−0.490708	−	0.871324i	$-0.663262\pi$
$199$	−13.8446	−0.981415	−0.490708	+	0.871324i	$0.663262\pi$
$200$	29.2756	2.07010
$201$	−8.76442	−0.618195
$202$	15.5174	1.09180
$203$	5.64359	0.396103
$204$	−0.789308	−0.0552626
$205$	25.8140	1.80293
$206$	15.2350	1.06147
$207$	−6.65389	−0.462477
$208$	−7.64817	−0.530305
$209$	−16.1285	−1.11563
$210$	5.89863	0.407044
$211$	10.0748	0.693580	0.346790	−	0.937943i	$-0.387272\pi$
$211$	10.0748	0.693580	0.346790	+	0.937943i	$0.387272\pi$
$212$	0.0273924	0.00188132
$213$	7.02500	0.481345
$214$	−6.86413	−0.469222
$215$	−35.1828	−2.39945
$216$	2.68193	0.182482
$217$	−9.97798	−0.677349
$218$	−15.2850	−1.03523
$219$	1.50018	0.101373
$220$	3.59549	0.242408
$221$	−7.47807	−0.503029
$222$	−12.9400	−0.868476
$223$	−24.5942	−1.64695	−0.823475	−	0.567352i	$-0.807968\pi$
$223$	−24.5942	−1.64695	−0.823475	+	0.567352i	$0.807968\pi$
$224$	−1.04947	−0.0701208
$225$	10.9159	0.727726
$226$	2.92236	0.194392
$227$	16.8081	1.11559	0.557795	−	0.829978i	$-0.311647\pi$
$227$	16.8081	1.11559	0.557795	+	0.829978i	$0.311647\pi$
$228$	−0.619847	−0.0410503
$229$	5.48139	0.362220	0.181110	−	0.983463i	$-0.442031\pi$
$229$	5.48139	0.362220	0.181110	+	0.983463i	$0.442031\pi$
$230$	39.2489	2.58799
$231$	−4.84256	−0.318617
$232$	−15.1357	−0.993708
$233$	−10.8965	−0.713854	−0.356927	−	0.934132i	$-0.616176\pi$
$233$	−10.8965	−0.713854	−0.356927	+	0.934132i	$0.616176\pi$
$234$	−2.60703	−0.170427
$235$	33.5280	2.18712
$236$	0.409426	0.0266514
$237$	−2.89105	−0.187794
$238$	−6.27069	−0.406469
$239$	−8.00105	−0.517545	−0.258773	−	0.965938i	$-0.583318\pi$
$239$	−8.00105	−0.517545	−0.258773	+	0.965938i	$0.583318\pi$
$240$	−17.3047	−1.11701
$241$	−17.8186	−1.14780	−0.573899	−	0.818926i	$-0.694570\pi$
$241$	−17.8186	−1.14780	−0.573899	+	0.818926i	$0.694570\pi$
$242$	−18.4086	−1.18335
$243$	1.00000	0.0641500
$244$	2.82233	0.180681
$245$	3.98947	0.254878
$246$	−9.56700	−0.609970
$247$	−5.87256	−0.373662
$248$	26.7602	1.69928
$249$	2.65450	0.168222
$250$	−34.8957	−2.20700
$251$	29.2549	1.84655	0.923276	−	0.384138i	$-0.125501\pi$
$251$	29.2549	1.84655	0.923276	+	0.384138i	$0.125501\pi$
$252$	−0.186109	−0.0117237
$253$	−32.2219	−2.02577
$254$	8.06037	0.505753
$255$	−16.9198	−1.05956
$256$	4.42913	0.276821
$257$	23.8269	1.48628	0.743139	−	0.669137i	$-0.233336\pi$
$257$	23.8269	1.48628	0.743139	+	0.669137i	$0.233336\pi$
$258$	13.0392	0.811784
$259$	−8.75182	−0.543812
$260$	1.30916	0.0811905
$261$	−5.64359	−0.349330
$262$	9.49957	0.586886
$263$	−31.6959	−1.95445	−0.977227	−	0.212197i	$-0.931938\pi$
$263$	−31.6959	−1.95445	−0.977227	+	0.212197i	$0.931938\pi$
$264$	12.9874	0.799320
$265$	0.587191	0.0360708
$266$	−4.92440	−0.301934
$267$	8.87297	0.543017
$268$	−1.63114	−0.0996375
$269$	−5.47852	−0.334031	−0.167016	−	0.985954i	$-0.553413\pi$
$269$	−5.47852	−0.334031	−0.167016	+	0.985954i	$0.553413\pi$
$270$	−5.89863	−0.358979
$271$	−4.30444	−0.261476	−0.130738	−	0.991417i	$-0.541735\pi$
$271$	−4.30444	−0.261476	−0.130738	+	0.991417i	$0.541735\pi$
$272$	18.3962	1.11543
$273$	−1.76323	−0.106716
$274$	−19.2921	−1.16548
$275$	52.8609	3.18763
$276$	−1.23835	−0.0745397
$277$	−28.0893	−1.68772	−0.843862	−	0.536560i	$-0.819724\pi$
$277$	−28.0893	−1.68772	−0.843862	+	0.536560i	$0.819724\pi$
$278$	−22.4044	−1.34373
$279$	9.97798	0.597366
$280$	−10.6995	−0.639416
$281$	−0.192727	−0.0114971	−0.00574857	−	0.999983i	$-0.501830\pi$
$281$	−0.192727	−0.0114971	−0.00574857	+	0.999983i	$0.501830\pi$
$282$	−12.4259	−0.739951
$283$	−31.0087	−1.84328	−0.921639	−	0.388048i	$-0.873149\pi$
$283$	−31.0087	−1.84328	−0.921639	+	0.388048i	$0.873149\pi$
$284$	1.30741	0.0775807
$285$	−13.2872	−0.787065
$286$	−12.6247	−0.746514
$287$	−6.47053	−0.381943
$288$	1.04947	0.0618407
$289$	0.987035	0.0580609
$290$	33.2895	1.95483
$291$	−4.53365	−0.265767
$292$	0.279197	0.0163388
$293$	13.9127	0.812789	0.406395	−	0.913698i	$-0.366786\pi$
$293$	13.9127	0.812789	0.406395	+	0.913698i	$0.366786\pi$
$294$	−1.47855	−0.0862308
$295$	8.77656	0.510991
$296$	23.4718	1.36427
$297$	4.84256	0.280994
$298$	8.08654	0.468441
$299$	−11.7324	−0.678500
$300$	2.03154	0.117291
$301$	8.81890	0.508313
$302$	16.5234	0.950816
$303$	−10.4950	−0.602923
$304$	14.4466	0.828568
$305$	60.5003	3.46423
$306$	6.27069	0.358472
$307$	23.2464	1.32674	0.663372	−	0.748289i	$-0.269125\pi$
$307$	23.2464	1.32674	0.663372	+	0.748289i	$0.269125\pi$
$308$	−0.901243	−0.0513531
$309$	−10.3040	−0.586175
$310$	−58.8564	−3.34282
$311$	−3.87839	−0.219923	−0.109962	−	0.993936i	$-0.535073\pi$
$311$	−3.87839	−0.219923	−0.109962	+	0.993936i	$0.535073\pi$
$312$	4.72886	0.267719
$313$	5.56261	0.314418	0.157209	−	0.987565i	$-0.449750\pi$
$313$	5.56261	0.314418	0.157209	+	0.987565i	$0.449750\pi$
$314$	−18.9219	−1.06782
$315$	−3.98947	−0.224781
$316$	−0.538050	−0.0302677
$317$	−12.4690	−0.700329	−0.350164	−	0.936688i	$-0.613874\pi$
$317$	−12.4690	−0.700329	−0.350164	+	0.936688i	$0.613874\pi$
$318$	−0.217620	−0.0122035
$319$	−27.3295	−1.53016
$320$	28.4189	1.58866
$321$	4.64248	0.259118
$322$	−9.83811	−0.548256
$323$	14.1253	0.785952
$324$	0.186109	0.0103394
$325$	19.2473	1.06765
$326$	−13.8080	−0.764756
$327$	10.3378	0.571683
$328$	17.3535	0.958187
$329$	−8.40411	−0.463334
$330$	−28.5645	−1.57242
$331$	20.9137	1.14952	0.574759	−	0.818322i	$-0.305096\pi$
$331$	20.9137	1.14952	0.574759	+	0.818322i	$0.305096\pi$
$332$	0.494026	0.0271132
$333$	8.75182	0.479597
$334$	−11.1432	−0.609728
$335$	−34.9654	−1.91037
$336$	4.33758	0.236634
$337$	35.7571	1.94782	0.973908	−	0.226945i	$-0.0728738\pi$
$337$	35.7571	1.94782	0.973908	+	0.226945i	$0.0728738\pi$
$338$	14.6243	0.795460
$339$	−1.97650	−0.107349
$340$	−3.14892	−0.170774
$341$	48.3190	2.61662
$342$	4.92440	0.266281
$343$	−1.00000	−0.0539949
$344$	−23.6517	−1.27521
$345$	−26.5455	−1.42916
$346$	1.37090	0.0737001
$347$	−19.2163	−1.03159	−0.515793	−	0.856713i	$-0.672503\pi$
$347$	−19.2163	−1.03159	−0.515793	+	0.856713i	$0.672503\pi$
$348$	−1.05032	−0.0563032
$349$	27.9775	1.49760	0.748800	−	0.662796i	$-0.230630\pi$
$349$	27.9775	1.49760	0.748800	+	0.662796i	$0.230630\pi$
$350$	16.1397	0.862703
$351$	1.76323	0.0941144
$352$	5.08214	0.270879
$353$	−1.30871	−0.0696558	−0.0348279	−	0.999393i	$-0.511088\pi$
$353$	−1.30871	−0.0696558	−0.0348279	+	0.999393i	$0.511088\pi$
$354$	−3.25271	−0.172879
$355$	28.0260	1.48747
$356$	1.65134	0.0875207
$357$	4.24111	0.224463
$358$	−17.0761	−0.902501
$359$	15.8109	0.834467	0.417233	−	0.908799i	$-0.363000\pi$
$359$	15.8109	0.834467	0.417233	+	0.908799i	$0.363000\pi$
$360$	10.6995	0.563912
$361$	−7.90736	−0.416177
$362$	−6.47435	−0.340284
$363$	12.4504	0.653478
$364$	−0.328153	−0.0171999
$365$	5.98493	0.313266
$366$	−22.4222	−1.17203
$367$	0.412286	0.0215212	0.0107606	−	0.999942i	$-0.496575\pi$
$367$	0.412286	0.0215212	0.0107606	+	0.999942i	$0.496575\pi$
$368$	28.8618	1.50452
$369$	6.47053	0.336842
$370$	−51.6238	−2.68379
$371$	−0.147185	−0.00764147
$372$	1.85699	0.0962804
$373$	9.51920	0.492886	0.246443	−	0.969157i	$-0.420738\pi$
$373$	9.51920	0.492886	0.246443	+	0.969157i	$0.420738\pi$
$374$	30.3662	1.57020
$375$	23.6013	1.21877
$376$	22.5392	1.16237
$377$	−9.95097	−0.512501
$378$	1.47855	0.0760484
$379$	−29.1830	−1.49903	−0.749515	−	0.661987i	$-0.769713\pi$
$379$	−29.1830	−1.49903	−0.749515	+	0.661987i	$0.769713\pi$
$380$	−2.47286	−0.126855
$381$	−5.45154	−0.279291
$382$	1.47855	0.0756492
$383$	−18.7917	−0.960213	−0.480106	−	0.877210i	$-0.659402\pi$
$383$	−18.7917	−0.960213	−0.480106	+	0.877210i	$0.659402\pi$
$384$	−12.6313	−0.644590
$385$	−19.3193	−0.984602
$386$	−9.35362	−0.476087
$387$	−8.81890	−0.448290
$388$	−0.843753	−0.0428350
$389$	−25.7602	−1.30610	−0.653048	−	0.757317i	$-0.726510\pi$
$389$	−25.7602	−1.30610	−0.653048	+	0.757317i	$0.726510\pi$
$390$	−10.4007	−0.526658
$391$	28.2199	1.42714
$392$	2.68193	0.135458
$393$	−6.42493	−0.324095
$394$	31.7729	1.60070
$395$	−11.5338	−0.580327
$396$	0.901243	0.0452892
$397$	−9.54401	−0.479000	−0.239500	−	0.970896i	$-0.576984\pi$
$397$	−9.54401	−0.479000	−0.239500	+	0.970896i	$0.576984\pi$
$398$	20.4699	1.02606
$399$	3.33056	0.166737
$400$	−47.3486	−2.36743
$401$	7.77406	0.388218	0.194109	−	0.980980i	$-0.437818\pi$
$401$	7.77406	0.388218	0.194109	+	0.980980i	$0.437818\pi$
$402$	12.9586	0.646318
$403$	17.5935	0.876395
$404$	−1.95322	−0.0971761
$405$	3.98947	0.198239
$406$	−8.34433	−0.414122
$407$	42.3813	2.10076
$408$	−11.3744	−0.563115
$409$	−31.8156	−1.57318	−0.786590	−	0.617476i	$-0.788155\pi$
$409$	−31.8156	−1.57318	−0.786590	+	0.617476i	$0.788155\pi$
$410$	−38.1673	−1.88495
$411$	13.0480	0.643611
$412$	−1.91767	−0.0944766
$413$	−2.19993	−0.108252
$414$	9.83811	0.483517
$415$	10.5901	0.519846
$416$	1.85046	0.0907265
$417$	15.1530	0.742043
$418$	23.8467	1.16638
$419$	−28.9314	−1.41339	−0.706697	−	0.707517i	$-0.749815\pi$
$419$	−28.9314	−1.41339	−0.706697	+	0.707517i	$0.749815\pi$
$420$	−0.742476	−0.0362291
$421$	21.7369	1.05939	0.529695	−	0.848188i	$-0.322306\pi$
$421$	21.7369	1.05939	0.529695	+	0.848188i	$0.322306\pi$
$422$	−14.8961	−0.725133
$423$	8.40411	0.408622
$424$	0.394740	0.0191703
$425$	−46.2955	−2.24566
$426$	−10.3868	−0.503242
$427$	−15.1650	−0.733884
$428$	0.864005	0.0417633
$429$	8.53857	0.412246
$430$	52.0195	2.50860
$431$	23.6544	1.13939	0.569695	−	0.821856i	$-0.307061\pi$
$431$	23.6544	1.13939	0.569695	+	0.821856i	$0.307061\pi$
$432$	−4.33758	−0.208692
$433$	19.4228	0.933399	0.466700	−	0.884416i	$-0.345443\pi$
$433$	19.4228	0.933399	0.466700	+	0.884416i	$0.345443\pi$
$434$	14.7529	0.708164
$435$	−22.5150	−1.07951
$436$	1.92396	0.0921409
$437$	22.1612	1.06011
$438$	−2.21809	−0.105985
$439$	35.7598	1.70672	0.853362	−	0.521319i	$-0.174560\pi$
$439$	35.7598	1.70672	0.853362	+	0.521319i	$0.174560\pi$
$440$	51.8129	2.47008
$441$	1.00000	0.0476190
$442$	11.0567	0.525913
$443$	37.0311	1.75940	0.879701	−	0.475527i	$-0.157743\pi$
$443$	37.0311	1.75940	0.879701	+	0.475527i	$0.157743\pi$
$444$	1.62879	0.0772990
$445$	35.3985	1.67805
$446$	36.3638	1.72187
$447$	−5.46924	−0.258686
$448$	−7.12347	−0.336552
$449$	−32.6820	−1.54236	−0.771180	−	0.636618i	$-0.780333\pi$
$449$	−32.6820	−1.54236	−0.771180	+	0.636618i	$0.780333\pi$
$450$	−16.1397	−0.760832
$451$	31.3340	1.47546
$452$	−0.367844	−0.0173019
$453$	−11.1754	−0.525067
$454$	−24.8516	−1.16634
$455$	−7.03437	−0.329776
$456$	−8.93233	−0.418295
$457$	1.28688	0.0601979	0.0300990	−	0.999547i	$-0.490418\pi$
$457$	1.28688	0.0601979	0.0300990	+	0.999547i	$0.490418\pi$
$458$	−8.10451	−0.378699
$459$	−4.24111	−0.197958
$460$	−4.94035	−0.230345
$461$	−29.2367	−1.36169	−0.680845	−	0.732427i	$-0.738387\pi$
$461$	−29.2367	−1.36169	−0.680845	+	0.732427i	$0.738387\pi$
$462$	7.15997	0.333112
$463$	3.74030	0.173827	0.0869133	−	0.996216i	$-0.472300\pi$
$463$	3.74030	0.173827	0.0869133	+	0.996216i	$0.472300\pi$
$464$	24.4795	1.13643
$465$	39.8069	1.84600
$466$	16.1110	0.746329
$467$	20.0729	0.928864	0.464432	−	0.885609i	$-0.346258\pi$
$467$	20.0729	0.928864	0.464432	+	0.885609i	$0.346258\pi$
$468$	0.328153	0.0151689
$469$	8.76442	0.404703
$470$	−49.5728	−2.28662
$471$	12.7976	0.589682
$472$	5.90006	0.271572
$473$	−42.7061	−1.96363
$474$	4.27456	0.196337
$475$	−36.3561	−1.66813
$476$	0.789308	0.0361779
$477$	0.147185	0.00673914
$478$	11.8300	0.541090
$479$	24.4234	1.11593	0.557967	−	0.829863i	$-0.311582\pi$
$479$	24.4234	1.11593	0.557967	+	0.829863i	$0.311582\pi$
$480$	4.18684	0.191102
$481$	15.4315	0.703616
$482$	26.3457	1.20001
$483$	6.65389	0.302763
$484$	2.31713	0.105324
$485$	−18.0869	−0.821283
$486$	−1.47855	−0.0670684
$487$	−1.12264	−0.0508719	−0.0254359	−	0.999676i	$-0.508097\pi$
$487$	−1.12264	−0.0508719	−0.0254359	+	0.999676i	$0.508097\pi$
$488$	40.6714	1.84111
$489$	9.33890	0.422320
$490$	−5.89863	−0.266473
$491$	16.4274	0.741359	0.370680	−	0.928761i	$-0.379125\pi$
$491$	16.4274	0.741359	0.370680	+	0.928761i	$0.379125\pi$
$492$	1.20422	0.0542905
$493$	23.9351	1.07798
$494$	8.68287	0.390661
$495$	19.3193	0.868337
$496$	−43.2803	−1.94334
$497$	−7.02500	−0.315114
$498$	−3.92481	−0.175875
$499$	19.6442	0.879396	0.439698	−	0.898146i	$-0.355086\pi$
$499$	19.6442	0.879396	0.439698	+	0.898146i	$0.355086\pi$
$500$	4.39241	0.196435
$501$	7.53656	0.336709
$502$	−43.2548	−1.93056
$503$	18.7013	0.833849	0.416924	−	0.908941i	$-0.363108\pi$
$503$	18.7013	0.833849	0.416924	+	0.908941i	$0.363108\pi$
$504$	−2.68193	−0.119463
$505$	−41.8696	−1.86317
$506$	47.6417	2.11793
$507$	−9.89101	−0.439275
$508$	−1.01458	−0.0450147
$509$	−4.72751	−0.209543	−0.104772	−	0.994496i	$-0.533411\pi$
$509$	−4.72751	−0.209543	−0.104772	+	0.994496i	$0.533411\pi$
$510$	25.0168	1.10776
$511$	−1.50018	−0.0663641
$512$	18.7140	0.827049
$513$	−3.33056	−0.147048
$514$	−35.2292	−1.55389
$515$	−41.1076	−1.81142
$516$	−1.64128	−0.0722531
$517$	40.6974	1.78987
$518$	12.9400	0.568551
$519$	−0.927193	−0.0406993
$520$	18.8657	0.827315
$521$	9.68996	0.424525	0.212262	−	0.977213i	$-0.431917\pi$
$521$	9.68996	0.424525	0.212262	+	0.977213i	$0.431917\pi$
$522$	8.34433	0.365222
$523$	−42.2049	−1.84549	−0.922746	−	0.385409i	$-0.874060\pi$
$523$	−42.2049	−1.84549	−0.922746	+	0.385409i	$0.874060\pi$
$524$	−1.19574	−0.0522359
$525$	−10.9159	−0.476409
$526$	46.8640	2.04337
$527$	−42.3177	−1.84339
$528$	−21.0050	−0.914126
$529$	21.2743	0.924968
$530$	−0.868191	−0.0377118
$531$	2.19993	0.0954689
$532$	0.619847	0.0268738
$533$	11.4091	0.494181
$534$	−13.1191	−0.567720
$535$	18.5210	0.800734
$536$	−23.5056	−1.01529
$537$	11.5492	0.498386
$538$	8.10026	0.349227
$539$	4.84256	0.208584
$540$	0.742476	0.0319511
$541$	28.0283	1.20503	0.602516	−	0.798107i	$-0.294165\pi$
$541$	28.0283	1.20503	0.602516	+	0.798107i	$0.294165\pi$
$542$	6.36432	0.273371
$543$	4.37885	0.187915
$544$	−4.45093	−0.190832
$545$	41.2425	1.76663
$546$	2.60703	0.111570
$547$	−13.3691	−0.571622	−0.285811	−	0.958286i	$-0.592263\pi$
$547$	−13.3691	−0.571622	−0.285811	+	0.958286i	$0.592263\pi$
$548$	2.42835	0.103734
$549$	15.1650	0.647225
$550$	−78.1575	−3.33265
$551$	18.7963	0.800751
$552$	−17.8453	−0.759545
$553$	2.89105	0.122940
$554$	41.5315	1.76450
$555$	34.9152	1.48207
$556$	2.82010	0.119599
$557$	14.2472	0.603675	0.301837	−	0.953359i	$-0.402400\pi$
$557$	14.2472	0.603675	0.301837	+	0.953359i	$0.402400\pi$
$558$	−14.7529	−0.624542
$559$	−15.5498	−0.657686
$560$	17.3047	0.731255
$561$	−20.5379	−0.867109
$562$	0.284957	0.0120202
$563$	−31.5628	−1.33021	−0.665106	−	0.746749i	$-0.731614\pi$
$563$	−31.5628	−1.33021	−0.665106	+	0.746749i	$0.731614\pi$
$564$	1.56408	0.0658596
$565$	−7.88520	−0.331733
$566$	45.8480	1.92713
$567$	−1.00000	−0.0419961
$568$	18.8405	0.790531
$569$	−17.4406	−0.731147	−0.365573	−	0.930782i	$-0.619127\pi$
$569$	−17.4406	−0.731147	−0.365573	+	0.930782i	$0.619127\pi$
$570$	19.6458	0.822871
$571$	−31.4537	−1.31630	−0.658148	−	0.752888i	$-0.728660\pi$
$571$	−31.4537	−1.31630	−0.658148	+	0.752888i	$0.728660\pi$
$572$	1.58910	0.0664437
$573$	−1.00000	−0.0417756
$574$	9.56700	0.399319
$575$	−72.6332	−3.02901
$576$	7.12347	0.296811
$577$	−44.5798	−1.85588	−0.927940	−	0.372729i	$-0.878422\pi$
$577$	−44.5798	−1.85588	−0.927940	+	0.372729i	$0.878422\pi$
$578$	−1.45938	−0.0607022
$579$	6.32621	0.262908
$580$	−4.19023	−0.173990
$581$	−2.65450	−0.110127
$582$	6.70323	0.277858
$583$	0.712753	0.0295192
$584$	4.02338	0.166489
$585$	7.03437	0.290835
$586$	−20.5706	−0.849765
$587$	−19.5156	−0.805495	−0.402747	−	0.915311i	$-0.631945\pi$
$587$	−19.5156	−0.805495	−0.402747	+	0.915311i	$0.631945\pi$
$588$	0.186109	0.00767499
$589$	−33.2323	−1.36931
$590$	−12.9766	−0.534238
$591$	−21.4893	−0.883950
$592$	−37.9617	−1.56022
$593$	26.1523	1.07395	0.536974	−	0.843599i	$-0.319567\pi$
$593$	26.1523	1.07395	0.536974	+	0.843599i	$0.319567\pi$
$594$	−7.15997	−0.293777
$595$	16.9198	0.693644
$596$	−1.01787	−0.0416937
$597$	−13.8446	−0.566620
$598$	17.3469	0.709366
$599$	0.854958	0.0349326	0.0174663	−	0.999847i	$-0.494440\pi$
$599$	0.854958	0.0349326	0.0174663	+	0.999847i	$0.494440\pi$
$600$	29.2756	1.19517
$601$	0.529961	0.0216176	0.0108088	−	0.999942i	$-0.496559\pi$
$601$	0.529961	0.0216176	0.0108088	+	0.999942i	$0.496559\pi$
$602$	−13.0392	−0.531438
$603$	−8.76442	−0.356915
$604$	−2.07984	−0.0846276
$605$	49.6706	2.01940
$606$	15.5174	0.630352
$607$	8.06843	0.327487	0.163744	−	0.986503i	$-0.447643\pi$
$607$	8.06843	0.327487	0.163744	+	0.986503i	$0.447643\pi$
$608$	−3.49533	−0.141754
$609$	5.64359	0.228690
$610$	−89.4526	−3.62183
$611$	14.8184	0.599489
$612$	−0.789308	−0.0319059
$613$	−31.4530	−1.27037	−0.635187	−	0.772358i	$-0.719077\pi$
$613$	−31.4530	−1.27037	−0.635187	+	0.772358i	$0.719077\pi$
$614$	−34.3710	−1.38710
$615$	25.8140	1.04092
$616$	−12.9874	−0.523278
$617$	−17.2339	−0.693812	−0.346906	−	0.937900i	$-0.612768\pi$
$617$	−17.2339	−0.693812	−0.346906	+	0.937900i	$0.612768\pi$
$618$	15.2350	0.612841
$619$	−29.2460	−1.17550	−0.587748	−	0.809044i	$-0.699985\pi$
$619$	−29.2460	−1.17550	−0.587748	+	0.809044i	$0.699985\pi$
$620$	7.40841	0.297529
$621$	−6.65389	−0.267011
$622$	5.73439	0.229928
$623$	−8.87297	−0.355488
$624$	−7.64817	−0.306172
$625$	39.5773	1.58309
$626$	−8.22460	−0.328721
$627$	−16.1285	−0.644109
$628$	2.38174	0.0950420
$629$	−37.1175	−1.47997
$630$	5.89863	0.235007
$631$	−11.9370	−0.475205	−0.237602	−	0.971363i	$-0.576362\pi$
$631$	−11.9370	−0.475205	−0.237602	+	0.971363i	$0.576362\pi$
$632$	−7.75359	−0.308421
$633$	10.0748	0.400439
$634$	18.4360	0.732189
$635$	−21.7488	−0.863074
$636$	0.0273924	0.00108618
$637$	1.76323	0.0698618
$638$	40.4080	1.59977
$639$	7.02500	0.277905
$640$	−50.3924	−1.99193
$641$	−0.347445	−0.0137232	−0.00686162	−	0.999976i	$-0.502184\pi$
$641$	−0.347445	−0.0137232	−0.00686162	+	0.999976i	$0.502184\pi$
$642$	−6.86413	−0.270906
$643$	−43.2227	−1.70454	−0.852268	−	0.523105i	$-0.824774\pi$
$643$	−43.2227	−1.70454	−0.852268	+	0.523105i	$0.824774\pi$
$644$	1.23835	0.0487977
$645$	−35.1828	−1.38532
$646$	−20.8849	−0.821707
$647$	36.4078	1.43134	0.715668	−	0.698440i	$-0.246122\pi$
$647$	36.4078	1.43134	0.715668	+	0.698440i	$0.246122\pi$
$648$	2.68193	0.105356
$649$	10.6533	0.418179
$650$	−28.4580	−1.11622
$651$	−9.97798	−0.391068
$652$	1.73805	0.0680673
$653$	20.2964	0.794261	0.397131	−	0.917762i	$-0.370006\pi$
$653$	20.2964	0.794261	0.397131	+	0.917762i	$0.370006\pi$
$654$	−15.2850	−0.597690
$655$	−25.6321	−1.00153
$656$	−28.0665	−1.09581
$657$	1.50018	0.0585276
$658$	12.4259	0.484412
$659$	−8.81439	−0.343360	−0.171680	−	0.985153i	$-0.554919\pi$
$659$	−8.81439	−0.343360	−0.171680	+	0.985153i	$0.554919\pi$
$660$	3.59549	0.139954
$661$	5.51923	0.214673	0.107337	−	0.994223i	$-0.465768\pi$
$661$	5.51923	0.214673	0.107337	+	0.994223i	$0.465768\pi$
$662$	−30.9219	−1.20181
$663$	−7.47807	−0.290424
$664$	7.11918	0.276278
$665$	13.2872	0.515255
$666$	−12.9400	−0.501415
$667$	37.5519	1.45401
$668$	1.40262	0.0542690
$669$	−24.5942	−0.950867
$670$	51.6981	1.99727
$671$	73.4373	2.83502
$672$	−1.04947	−0.0404843
$673$	1.83985	0.0709210	0.0354605	−	0.999371i	$-0.488710\pi$
$673$	1.83985	0.0709210	0.0354605	+	0.999371i	$0.488710\pi$
$674$	−52.8687	−2.03643
$675$	10.9159	0.420153
$676$	−1.84080	−0.0708001
$677$	−8.35410	−0.321074	−0.160537	−	0.987030i	$-0.551323\pi$
$677$	−8.35410	−0.321074	−0.160537	+	0.987030i	$0.551323\pi$
$678$	2.92236	0.112232
$679$	4.53365	0.173986
$680$	−45.3777	−1.74016
$681$	16.8081	0.644087
$682$	−71.4420	−2.73566
$683$	−16.7970	−0.642718	−0.321359	−	0.946957i	$-0.604140\pi$
$683$	−16.7970	−0.642718	−0.321359	+	0.946957i	$0.604140\pi$
$684$	−0.619847	−0.0237004
$685$	52.0547	1.98891
$686$	1.47855	0.0564513
$687$	5.48139	0.209128
$688$	38.2527	1.45837
$689$	0.259522	0.00988698
$690$	39.2489	1.49418
$691$	13.4164	0.510383	0.255192	−	0.966890i	$-0.417861\pi$
$691$	13.4164	0.510383	0.255192	+	0.966890i	$0.417861\pi$
$692$	−0.172559	−0.00655970
$693$	−4.84256	−0.183954
$694$	28.4123	1.07852
$695$	60.4523	2.29309
$696$	−15.1357	−0.573718
$697$	−27.4423	−1.03945
$698$	−41.3661	−1.56573
$699$	−10.8965	−0.412144
$700$	−2.03154	−0.0767851
$701$	15.6205	0.589980	0.294990	−	0.955500i	$-0.404684\pi$
$701$	15.6205	0.589980	0.294990	+	0.955500i	$0.404684\pi$
$702$	−2.60703	−0.0983959
$703$	−29.1485	−1.09936
$704$	34.4958	1.30011
$705$	33.5280	1.26274
$706$	1.93500	0.0728246
$707$	10.4950	0.394706
$708$	0.409426	0.0153872
$709$	−1.03598	−0.0389069	−0.0194535	−	0.999811i	$-0.506193\pi$
$709$	−1.03598	−0.0389069	−0.0194535	+	0.999811i	$0.506193\pi$
$710$	−41.4379	−1.55514
$711$	−2.89105	−0.108423
$712$	23.7967	0.891818
$713$	−66.3924	−2.48641
$714$	−6.27069	−0.234675
$715$	34.0644	1.27394
$716$	2.14941	0.0803274
$717$	−8.00105	−0.298805
$718$	−23.3772	−0.872428
$719$	−9.75606	−0.363840	−0.181920	−	0.983313i	$-0.558231\pi$
$719$	−9.75606	−0.363840	−0.181920	+	0.983313i	$0.558231\pi$
$720$	−17.3047	−0.644907
$721$	10.3040	0.383741
$722$	11.6914	0.435110
$723$	−17.8186	−0.662682
$724$	0.814943	0.0302871
$725$	−61.6049	−2.28795
$726$	−18.4086	−0.683206
$727$	−25.1124	−0.931369	−0.465685	−	0.884951i	$-0.654192\pi$
$727$	−25.1124	−0.931369	−0.465685	+	0.884951i	$0.654192\pi$
$728$	−4.72886	−0.175263
$729$	1.00000	0.0370370
$730$	−8.84902	−0.327517
$731$	37.4020	1.38336
$732$	2.82233	0.104316
$733$	13.4572	0.497052	0.248526	−	0.968625i	$-0.420054\pi$
$733$	13.4572	0.497052	0.248526	+	0.968625i	$0.420054\pi$
$734$	−0.609586	−0.0225002
$735$	3.98947	0.147154
$736$	−6.98307	−0.257399
$737$	−42.4423	−1.56338
$738$	−9.56700	−0.352166
$739$	−37.6783	−1.38602	−0.693009	−	0.720929i	$-0.743716\pi$
$739$	−37.6783	−1.38602	−0.693009	+	0.720929i	$0.743716\pi$
$740$	6.49802	0.238872
$741$	−5.87256	−0.215734
$742$	0.217620	0.00798910
$743$	29.2441	1.07286	0.536431	−	0.843944i	$-0.319772\pi$
$743$	29.2441	1.07286	0.536431	+	0.843944i	$0.319772\pi$
$744$	26.7602	0.981077
$745$	−21.8194	−0.799400
$746$	−14.0746	−0.515308
$747$	2.65450	0.0971231
$748$	−3.82227	−0.139756
$749$	−4.64248	−0.169632
$750$	−34.8957	−1.27421
$751$	−26.9800	−0.984514	−0.492257	−	0.870450i	$-0.663828\pi$
$751$	−26.9800	−0.984514	−0.492257	+	0.870450i	$0.663828\pi$
$752$	−36.4535	−1.32932
$753$	29.2549	1.06611
$754$	14.7130	0.535816
$755$	−44.5841	−1.62258
$756$	−0.186109	−0.00676871
$757$	−2.76841	−0.100620	−0.0503098	−	0.998734i	$-0.516021\pi$
$757$	−2.76841	−0.100620	−0.0503098	+	0.998734i	$0.516021\pi$
$758$	43.1485	1.56722
$759$	−32.2219	−1.16958
$760$	−35.6353	−1.29263
$761$	22.6616	0.821483	0.410742	−	0.911752i	$-0.365270\pi$
$761$	22.6616	0.821483	0.410742	+	0.911752i	$0.365270\pi$
$762$	8.06037	0.291996
$763$	−10.3378	−0.374254
$764$	−0.186109	−0.00673318
$765$	−16.9198	−0.611737
$766$	27.7845	1.00389
$767$	3.87899	0.140062
$768$	4.42913	0.159823
$769$	−2.69922	−0.0973365	−0.0486682	−	0.998815i	$-0.515498\pi$
$769$	−2.69922	−0.0973365	−0.0486682	+	0.998815i	$0.515498\pi$
$770$	28.5645	1.02939
$771$	23.8269	0.858103
$772$	1.17736	0.0423742
$773$	52.3773	1.88388	0.941941	−	0.335779i	$-0.109000\pi$
$773$	52.3773	1.88388	0.941941	+	0.335779i	$0.109000\pi$
$774$	13.0392	0.468684
$775$	108.919	3.91247
$776$	−12.1589	−0.436480
$777$	−8.75182	−0.313970
$778$	38.0878	1.36551
$779$	−21.5505	−0.772127
$780$	1.30916	0.0468754
$781$	34.0190	1.21730
$782$	−41.7245	−1.49207
$783$	−5.64359	−0.201686
$784$	−4.33758	−0.154914
$785$	51.0557	1.82226
$786$	9.49957	0.338839
$787$	−33.1447	−1.18148	−0.590740	−	0.806862i	$-0.701164\pi$
$787$	−33.1447	−1.18148	−0.590740	+	0.806862i	$0.701164\pi$
$788$	−3.99934	−0.142470
$789$	−31.6959	−1.12840
$790$	17.0533	0.606727
$791$	1.97650	0.0702763
$792$	12.9874	0.461487
$793$	26.7394	0.949543
$794$	14.1113	0.500791
$795$	0.587191	0.0208255
$796$	−2.57659	−0.0913250
$797$	−3.55826	−0.126040	−0.0630201	−	0.998012i	$-0.520073\pi$
$797$	−3.55826	−0.126040	−0.0630201	+	0.998012i	$0.520073\pi$
$798$	−4.92440	−0.174322
$799$	−35.6428	−1.26095
$800$	11.4559	0.405028
$801$	8.87297	0.313511
$802$	−11.4943	−0.405879
$803$	7.26472	0.256366
$804$	−1.63114	−0.0575257
$805$	26.5455	0.935607
$806$	−26.0129	−0.916264
$807$	−5.47852	−0.192853
$808$	−28.1469	−0.990204
$809$	48.5458	1.70678	0.853390	−	0.521274i	$-0.174543\pi$
$809$	48.5458	1.70678	0.853390	+	0.521274i	$0.174543\pi$
$810$	−5.89863	−0.207257
$811$	−56.2943	−1.97676	−0.988379	−	0.152007i	$-0.951427\pi$
$811$	−56.2943	−1.97676	−0.988379	+	0.152007i	$0.951427\pi$
$812$	1.05032	0.0368591
$813$	−4.30444	−0.150963
$814$	−62.6628	−2.19633
$815$	37.2573	1.30507
$816$	18.3962	0.643995
$817$	29.3719	1.02759
$818$	47.0409	1.64475
$819$	−1.76323	−0.0616123
$820$	4.80421	0.167770
$821$	−28.0050	−0.977383	−0.488691	−	0.872457i	$-0.662526\pi$
$821$	−28.0050	−0.977383	−0.488691	+	0.872457i	$0.662526\pi$
$822$	−19.2921	−0.672891
$823$	23.2104	0.809062	0.404531	−	0.914524i	$-0.367435\pi$
$823$	23.2104	0.809062	0.404531	+	0.914524i	$0.367435\pi$
$824$	−27.6346	−0.962698
$825$	52.8609	1.84038
$826$	3.25271	0.113176
$827$	−24.9494	−0.867577	−0.433788	−	0.901015i	$-0.642823\pi$
$827$	−24.9494	−0.867577	−0.433788	+	0.901015i	$0.642823\pi$
$828$	−1.23835	−0.0430355
$829$	−34.2631	−1.19001	−0.595004	−	0.803723i	$-0.702849\pi$
$829$	−34.2631	−1.19001	−0.595004	+	0.803723i	$0.702849\pi$
$830$	−15.6579	−0.543495
$831$	−28.0893	−0.974408
$832$	12.5603	0.435451
$833$	−4.24111	−0.146946
$834$	−22.4044	−0.775800
$835$	30.0669	1.04051
$836$	−3.00165	−0.103814
$837$	9.97798	0.344889
$838$	42.7766	1.47769
$839$	−48.6661	−1.68014	−0.840070	−	0.542478i	$-0.817486\pi$
$839$	−48.6661	−1.68014	−0.840070	+	0.542478i	$0.817486\pi$
$840$	−10.6995	−0.369167
$841$	2.85015	0.0982810
$842$	−32.1390	−1.10758
$843$	−0.192727	−0.00663787
$844$	1.87501	0.0645407
$845$	−39.4599	−1.35746
$846$	−12.4259	−0.427211
$847$	−12.4504	−0.427802
$848$	−0.638427	−0.0219237
$849$	−31.0087	−1.06422
$850$	68.4503	2.34782
$851$	−58.2337	−1.99622
$852$	1.30741	0.0447912
$853$	−5.24314	−0.179522	−0.0897608	−	0.995963i	$-0.528610\pi$
$853$	−5.24314	−0.179522	−0.0897608	+	0.995963i	$0.528610\pi$
$854$	22.4222	0.767271
$855$	−13.2872	−0.454412
$856$	12.4508	0.425559
$857$	29.0723	0.993092	0.496546	−	0.868010i	$-0.334601\pi$
$857$	29.0723	0.993092	0.496546	+	0.868010i	$0.334601\pi$
$858$	−12.6247	−0.431000
$859$	37.4001	1.27607	0.638037	−	0.770005i	$-0.279747\pi$
$859$	37.4001	1.27607	0.638037	+	0.770005i	$0.279747\pi$
$860$	−6.54782	−0.223279
$861$	−6.47053	−0.220515
$862$	−34.9741	−1.19122
$863$	−46.3125	−1.57650	−0.788249	−	0.615357i	$-0.789012\pi$
$863$	−46.3125	−1.57650	−0.788249	+	0.615357i	$0.789012\pi$
$864$	1.04947	0.0357038
$865$	−3.69901	−0.125770
$866$	−28.7175	−0.975862
$867$	0.987035	0.0335215
$868$	−1.85699	−0.0630303
$869$	−14.0001	−0.474921
$870$	33.2895	1.12862
$871$	−15.4537	−0.523629
$872$	27.7253	0.938897
$873$	−4.53365	−0.153441
$874$	−32.7664	−1.10834
$875$	−23.6013	−0.797870
$876$	0.279197	0.00943318
$877$	13.3633	0.451246	0.225623	−	0.974215i	$-0.427558\pi$
$877$	13.3633	0.451246	0.225623	+	0.974215i	$0.427558\pi$
$878$	−52.8727	−1.78437
$879$	13.9127	0.469264
$880$	−83.7989	−2.82486
$881$	49.8592	1.67980	0.839900	−	0.542741i	$-0.182613\pi$
$881$	49.8592	1.67980	0.839900	+	0.542741i	$0.182613\pi$
$882$	−1.47855	−0.0497854
$883$	−31.2333	−1.05108	−0.525542	−	0.850768i	$-0.676137\pi$
$883$	−31.2333	−1.05108	−0.525542	+	0.850768i	$0.676137\pi$
$884$	−1.39173	−0.0468091
$885$	8.77656	0.295021
$886$	−54.7524	−1.83944
$887$	42.3795	1.42296	0.711481	−	0.702705i	$-0.248025\pi$
$887$	42.3795	1.42296	0.711481	+	0.702705i	$0.248025\pi$
$888$	23.4718	0.787661
$889$	5.45154	0.182839
$890$	−52.3384	−1.75439
$891$	4.84256	0.162232
$892$	−4.57720	−0.153256
$893$	−27.9904	−0.936664
$894$	8.08654	0.270454
$895$	46.0754	1.54013
$896$	12.6313	0.421983
$897$	−11.7324	−0.391732
$898$	48.3220	1.61252
$899$	−56.3117	−1.87810
$900$	2.03154	0.0677181
$901$	−0.624228	−0.0207961
$902$	−46.3288	−1.54258
$903$	8.81890	0.293475
$904$	−5.30084	−0.176303
$905$	17.4693	0.580700
$906$	16.5234	0.548954
$907$	17.8764	0.593577	0.296789	−	0.954943i	$-0.404084\pi$
$907$	17.8764	0.593577	0.296789	+	0.954943i	$0.404084\pi$
$908$	3.12813	0.103811
$909$	−10.4950	−0.348098
$910$	10.4007	0.344779
$911$	0.710421	0.0235373	0.0117687	−	0.999931i	$-0.496254\pi$
$911$	0.710421	0.0235373	0.0117687	+	0.999931i	$0.496254\pi$
$912$	14.4466	0.478374
$913$	12.8546	0.425425
$914$	−1.90272	−0.0629365
$915$	60.5003	2.00008
$916$	1.02013	0.0337062
$917$	6.42493	0.212170
$918$	6.27069	0.206964
$919$	−50.1359	−1.65383	−0.826916	−	0.562326i	$-0.809907\pi$
$919$	−50.1359	−1.65383	−0.826916	+	0.562326i	$0.809907\pi$
$920$	−71.1932	−2.34717
$921$	23.2464	0.765997
$922$	43.2280	1.42364
$923$	12.3867	0.407713
$924$	−0.901243	−0.0296487
$925$	95.5340	3.14114
$926$	−5.53022	−0.181734
$927$	−10.3040	−0.338428
$928$	−5.92279	−0.194425
$929$	44.7451	1.46804	0.734020	−	0.679128i	$-0.237642\pi$
$929$	44.7451	1.46804	0.734020	+	0.679128i	$0.237642\pi$
$930$	−58.8564	−1.92998
$931$	−3.33056	−0.109155
$932$	−2.02794	−0.0664273
$933$	−3.87839	−0.126973
$934$	−29.6788	−0.971121
$935$	−81.9352	−2.67957
$936$	4.72886	0.154568
$937$	−9.91368	−0.323866	−0.161933	−	0.986802i	$-0.551773\pi$
$937$	−9.91368	−0.323866	−0.161933	+	0.986802i	$0.551773\pi$
$938$	−12.9586	−0.423114
$939$	5.56261	0.181529
$940$	6.23985	0.203521
$941$	12.8183	0.417865	0.208933	−	0.977930i	$-0.433001\pi$
$941$	12.8183	0.417865	0.208933	+	0.977930i	$0.433001\pi$
$942$	−18.9219	−0.616508
$943$	−43.0542	−1.40204
$944$	−9.54238	−0.310578
$945$	−3.98947	−0.129778
$946$	63.1431	2.05296
$947$	−12.5132	−0.406626	−0.203313	−	0.979114i	$-0.565171\pi$
$947$	−12.5132	−0.406626	−0.203313	+	0.979114i	$0.565171\pi$
$948$	−0.538050	−0.0174750
$949$	2.64517	0.0858658
$950$	53.7542	1.74402
$951$	−12.4690	−0.404335
$952$	11.3744	0.368645
$953$	14.5979	0.472873	0.236437	−	0.971647i	$-0.424020\pi$
$953$	14.5979	0.472873	0.236437	+	0.971647i	$0.424020\pi$
$954$	−0.217620	−0.00704572
$955$	−3.98947	−0.129096
$956$	−1.48907	−0.0481598
$957$	−27.3295	−0.883436
$958$	−36.1112	−1.16670
$959$	−13.0480	−0.421343
$960$	28.4189	0.917215
$961$	68.5600	2.21161
$962$	−22.8162	−0.735625
$963$	4.64248	0.149602
$964$	−3.31620	−0.106808
$965$	25.2383	0.812448
$966$	−9.83811	−0.316536
$967$	−23.0088	−0.739913	−0.369957	−	0.929049i	$-0.620627\pi$
$967$	−23.0088	−0.739913	−0.369957	+	0.929049i	$0.620627\pi$
$968$	33.3911	1.07323
$969$	14.1253	0.453770
$970$	26.7424	0.858646
$971$	−32.6720	−1.04849	−0.524247	−	0.851566i	$-0.675653\pi$
$971$	−32.6720	−1.04849	−0.524247	+	0.851566i	$0.675653\pi$
$972$	0.186109	0.00596944
$973$	−15.1530	−0.485781
$974$	1.65989	0.0531862
$975$	19.2473	0.616406
$976$	−65.7793	−2.10554
$977$	62.0326	1.98460	0.992300	−	0.123859i	$-0.0395270\pi$
$977$	62.0326	1.98460	0.992300	+	0.123859i	$0.0395270\pi$
$978$	−13.8080	−0.441532
$979$	42.9679	1.37326
$980$	0.742476	0.0237175
$981$	10.3378	0.330061
$982$	−24.2888	−0.775085
$983$	−45.6568	−1.45623	−0.728113	−	0.685457i	$-0.759603\pi$
$983$	−45.6568	−1.45623	−0.728113	+	0.685457i	$0.759603\pi$
$984$	17.3535	0.553210
$985$	−85.7308	−2.73161
$986$	−35.3893	−1.12702
$987$	−8.40411	−0.267506
$988$	−1.09293	−0.0347709
$989$	58.6800	1.86592
$990$	−28.5645	−0.907840
$991$	−53.8990	−1.71216	−0.856078	−	0.516846i	$-0.827106\pi$
$991$	−53.8990	−1.71216	−0.856078	+	0.516846i	$0.827106\pi$
$992$	10.4716	0.332474
$993$	20.9137	0.663675
$994$	10.3868	0.329449
$995$	−55.2325	−1.75099
$996$	0.494026	0.0156538
$997$	−46.4113	−1.46986	−0.734931	−	0.678142i	$-0.762785\pi$
$997$	−46.4113	−1.46986	−0.734931	+	0.678142i	$0.762785\pi$
$998$	−29.0449	−0.919402
$999$	8.75182	0.276895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.8	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.8	✓	29	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47855 q^{2} +1.00000 q^{3} +0.186109 q^{4} +3.98947 q^{5} -1.47855 q^{6} -1.00000 q^{7} +2.68193 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.47855 q^{2} +1.00000 q^{3} +0.186109 q^{4} +3.98947 q^{5} -1.47855 q^{6} -1.00000 q^{7} +2.68193 q^{8} +1.00000 q^{9} -5.89863 q^{10} +4.84256 q^{11} +0.186109 q^{12} +1.76323 q^{13} +1.47855 q^{14} +3.98947 q^{15} -4.33758 q^{16} -4.24111 q^{17} -1.47855 q^{18} -3.33056 q^{19} +0.742476 q^{20} -1.00000 q^{21} -7.15997 q^{22} -6.65389 q^{23} +2.68193 q^{24} +10.9159 q^{25} -2.60703 q^{26} +1.00000 q^{27} -0.186109 q^{28} -5.64359 q^{29} -5.89863 q^{30} +9.97798 q^{31} +1.04947 q^{32} +4.84256 q^{33} +6.27069 q^{34} -3.98947 q^{35} +0.186109 q^{36} +8.75182 q^{37} +4.92440 q^{38} +1.76323 q^{39} +10.6995 q^{40} +6.47053 q^{41} +1.47855 q^{42} -8.81890 q^{43} +0.901243 q^{44} +3.98947 q^{45} +9.83811 q^{46} +8.40411 q^{47} -4.33758 q^{48} +1.00000 q^{49} -16.1397 q^{50} -4.24111 q^{51} +0.328153 q^{52} +0.147185 q^{53} -1.47855 q^{54} +19.3193 q^{55} -2.68193 q^{56} -3.33056 q^{57} +8.34433 q^{58} +2.19993 q^{59} +0.742476 q^{60} +15.1650 q^{61} -14.7529 q^{62} -1.00000 q^{63} +7.12347 q^{64} +7.03437 q^{65} -7.15997 q^{66} -8.76442 q^{67} -0.789308 q^{68} -6.65389 q^{69} +5.89863 q^{70} +7.02500 q^{71} +2.68193 q^{72} +1.50018 q^{73} -12.9400 q^{74} +10.9159 q^{75} -0.619847 q^{76} -4.84256 q^{77} -2.60703 q^{78} -2.89105 q^{79} -17.3047 q^{80} +1.00000 q^{81} -9.56700 q^{82} +2.65450 q^{83} -0.186109 q^{84} -16.9198 q^{85} +13.0392 q^{86} -5.64359 q^{87} +12.9874 q^{88} +8.87297 q^{89} -5.89863 q^{90} -1.76323 q^{91} -1.23835 q^{92} +9.97798 q^{93} -12.4259 q^{94} -13.2872 q^{95} +1.04947 q^{96} -4.53365 q^{97} -1.47855 q^{98} +4.84256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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