LMFDB - Embedded newform 8015.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27050 q^{2} -2.16931 q^{3} +3.15517 q^{4} -1.00000 q^{5} +4.92541 q^{6} +1.00000 q^{7} -2.62281 q^{8} +1.70590 q^{9} +O(q^{10})$	\(q-2.27050 q^{2} -2.16931 q^{3} +3.15517 q^{4} -1.00000 q^{5} +4.92541 q^{6} +1.00000 q^{7} -2.62281 q^{8} +1.70590 q^{9} +2.27050 q^{10} -5.39963 q^{11} -6.84453 q^{12} +0.581257 q^{13} -2.27050 q^{14} +2.16931 q^{15} -0.355248 q^{16} -5.79806 q^{17} -3.87324 q^{18} +7.35353 q^{19} -3.15517 q^{20} -2.16931 q^{21} +12.2599 q^{22} +8.30753 q^{23} +5.68968 q^{24} +1.00000 q^{25} -1.31974 q^{26} +2.80731 q^{27} +3.15517 q^{28} -9.77778 q^{29} -4.92541 q^{30} +9.81460 q^{31} +6.05221 q^{32} +11.7135 q^{33} +13.1645 q^{34} -1.00000 q^{35} +5.38239 q^{36} -8.59532 q^{37} -16.6962 q^{38} -1.26092 q^{39} +2.62281 q^{40} -6.68811 q^{41} +4.92541 q^{42} -3.21682 q^{43} -17.0367 q^{44} -1.70590 q^{45} -18.8622 q^{46} +8.71478 q^{47} +0.770642 q^{48} +1.00000 q^{49} -2.27050 q^{50} +12.5778 q^{51} +1.83396 q^{52} +1.22929 q^{53} -6.37399 q^{54} +5.39963 q^{55} -2.62281 q^{56} -15.9521 q^{57} +22.2004 q^{58} -0.757184 q^{59} +6.84453 q^{60} +1.11818 q^{61} -22.2841 q^{62} +1.70590 q^{63} -13.0310 q^{64} -0.581257 q^{65} -26.5954 q^{66} -6.59119 q^{67} -18.2938 q^{68} -18.0216 q^{69} +2.27050 q^{70} +6.12847 q^{71} -4.47424 q^{72} +6.78348 q^{73} +19.5157 q^{74} -2.16931 q^{75} +23.2016 q^{76} -5.39963 q^{77} +2.86293 q^{78} -5.86626 q^{79} +0.355248 q^{80} -11.2076 q^{81} +15.1854 q^{82} -10.8544 q^{83} -6.84453 q^{84} +5.79806 q^{85} +7.30379 q^{86} +21.2110 q^{87} +14.1622 q^{88} -16.9852 q^{89} +3.87324 q^{90} +0.581257 q^{91} +26.2117 q^{92} -21.2909 q^{93} -19.7869 q^{94} -7.35353 q^{95} -13.1291 q^{96} +12.3135 q^{97} -2.27050 q^{98} -9.21121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.27050	−1.60549	−0.802743	−	0.596325i	$-0.796627\pi$
$2$	−2.27050	−1.60549	−0.802743	+	0.596325i	$0.796627\pi$
$3$	−2.16931	−1.25245	−0.626225	−	0.779642i	$-0.715401\pi$
$3$	−2.16931	−1.25245	−0.626225	+	0.779642i	$0.715401\pi$
$4$	3.15517	1.57758
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.92541	2.01079
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.62281	−0.927303
$9$	1.70590	0.568632
$10$	2.27050	0.717995
$11$	−5.39963	−1.62805	−0.814025	−	0.580830i	$-0.802728\pi$
$11$	−5.39963	−1.62805	−0.814025	+	0.580830i	$0.802728\pi$
$12$	−6.84453	−1.97585
$13$	0.581257	0.161212	0.0806058	−	0.996746i	$-0.474315\pi$
$13$	0.581257	0.161212	0.0806058	+	0.996746i	$0.474315\pi$
$14$	−2.27050	−0.606817
$15$	2.16931	0.560113
$16$	−0.355248	−0.0888119
$17$	−5.79806	−1.40624	−0.703118	−	0.711073i	$-0.748209\pi$
$17$	−5.79806	−1.40624	−0.703118	+	0.711073i	$0.748209\pi$
$18$	−3.87324	−0.912931
$19$	7.35353	1.68702	0.843508	−	0.537117i	$-0.180487\pi$
$19$	7.35353	1.68702	0.843508	+	0.537117i	$0.180487\pi$
$20$	−3.15517	−0.705517
$21$	−2.16931	−0.473382
$22$	12.2599	2.61381
$23$	8.30753	1.73224	0.866120	−	0.499837i	$-0.166607\pi$
$23$	8.30753	1.73224	0.866120	+	0.499837i	$0.166607\pi$
$24$	5.68968	1.16140
$25$	1.00000	0.200000
$26$	−1.31974	−0.258823
$27$	2.80731	0.540267
$28$	3.15517	0.596271
$29$	−9.77778	−1.81569	−0.907844	−	0.419308i	$-0.862273\pi$
$29$	−9.77778	−1.81569	−0.907844	+	0.419308i	$0.862273\pi$
$30$	−4.92541	−0.899253
$31$	9.81460	1.76276	0.881378	−	0.472413i	$-0.156617\pi$
$31$	9.81460	1.76276	0.881378	+	0.472413i	$0.156617\pi$
$32$	6.05221	1.06989
$33$	11.7135	2.03905
$34$	13.1645	2.25769
$35$	−1.00000	−0.169031
$36$	5.38239	0.897066
$37$	−8.59532	−1.41306	−0.706531	−	0.707682i	$-0.749741\pi$
$37$	−8.59532	−1.41306	−0.706531	+	0.707682i	$0.749741\pi$
$38$	−16.6962	−2.70848
$39$	−1.26092	−0.201910
$40$	2.62281	0.414703
$41$	−6.68811	−1.04451	−0.522254	−	0.852790i	$-0.674909\pi$
$41$	−6.68811	−1.04451	−0.522254	+	0.852790i	$0.674909\pi$
$42$	4.92541	0.760008
$43$	−3.21682	−0.490561	−0.245280	−	0.969452i	$-0.578880\pi$
$43$	−3.21682	−0.490561	−0.245280	+	0.969452i	$0.578880\pi$
$44$	−17.0367	−2.56839
$45$	−1.70590	−0.254300
$46$	−18.8622	−2.78109
$47$	8.71478	1.27118	0.635591	−	0.772026i	$-0.280757\pi$
$47$	8.71478	1.27118	0.635591	+	0.772026i	$0.280757\pi$
$48$	0.770642	0.111233
$49$	1.00000	0.142857
$50$	−2.27050	−0.321097
$51$	12.5778	1.76124
$52$	1.83396	0.254325
$53$	1.22929	0.168856	0.0844279	−	0.996430i	$-0.473094\pi$
$53$	1.22929	0.168856	0.0844279	+	0.996430i	$0.473094\pi$
$54$	−6.37399	−0.867390
$55$	5.39963	0.728086
$56$	−2.62281	−0.350488
$57$	−15.9521	−2.11290
$58$	22.2004	2.91506
$59$	−0.757184	−0.0985769	−0.0492885	−	0.998785i	$-0.515695\pi$
$59$	−0.757184	−0.0985769	−0.0492885	+	0.998785i	$0.515695\pi$
$60$	6.84453	0.883625
$61$	1.11818	0.143168	0.0715840	−	0.997435i	$-0.477195\pi$
$61$	1.11818	0.143168	0.0715840	+	0.997435i	$0.477195\pi$
$62$	−22.2841	−2.83008
$63$	1.70590	0.214923
$64$	−13.0310	−1.62888
$65$	−0.581257	−0.0720960
$66$	−26.5954	−3.27367
$67$	−6.59119	−0.805242	−0.402621	−	0.915367i	$-0.631901\pi$
$67$	−6.59119	−0.805242	−0.402621	+	0.915367i	$0.631901\pi$
$68$	−18.2938	−2.21846
$69$	−18.0216	−2.16954
$70$	2.27050	0.271377
$71$	6.12847	0.727315	0.363658	−	0.931533i	$-0.381528\pi$
$71$	6.12847	0.727315	0.363658	+	0.931533i	$0.381528\pi$
$72$	−4.47424	−0.527295
$73$	6.78348	0.793946	0.396973	−	0.917830i	$-0.370061\pi$
$73$	6.78348	0.793946	0.396973	+	0.917830i	$0.370061\pi$
$74$	19.5157	2.26865
$75$	−2.16931	−0.250490
$76$	23.2016	2.66141
$77$	−5.39963	−0.615345
$78$	2.86293	0.324163
$79$	−5.86626	−0.660006	−0.330003	−	0.943980i	$-0.607050\pi$
$79$	−5.86626	−0.660006	−0.330003	+	0.943980i	$0.607050\pi$
$80$	0.355248	0.0397179
$81$	−11.2076	−1.24529
$82$	15.1854	1.67694
$83$	−10.8544	−1.19142	−0.595710	−	0.803200i	$-0.703129\pi$
$83$	−10.8544	−1.19142	−0.595710	+	0.803200i	$0.703129\pi$
$84$	−6.84453	−0.746800
$85$	5.79806	0.628888
$86$	7.30379	0.787588
$87$	21.2110	2.27406
$88$	14.1622	1.50970
$89$	−16.9852	−1.80043	−0.900215	−	0.435445i	$-0.856591\pi$
$89$	−16.9852	−1.80043	−0.900215	+	0.435445i	$0.856591\pi$
$90$	3.87324	0.408275
$91$	0.581257	0.0609322
$92$	26.2117	2.73275
$93$	−21.2909	−2.20776
$94$	−19.7869	−2.04086
$95$	−7.35353	−0.754456
$96$	−13.1291	−1.33998
$97$	12.3135	1.25024	0.625121	−	0.780528i	$-0.285049\pi$
$97$	12.3135	1.25024	0.625121	+	0.780528i	$0.285049\pi$
$98$	−2.27050	−0.229355
$99$	−9.21121	−0.925762
$100$	3.15517	0.315517
$101$	5.24249	0.521647	0.260824	−	0.965386i	$-0.416006\pi$
$101$	5.24249	0.521647	0.260824	+	0.965386i	$0.416006\pi$
$102$	−28.5578	−2.82765
$103$	9.71232	0.956983	0.478492	−	0.878092i	$-0.341184\pi$
$103$	9.71232	0.956983	0.478492	+	0.878092i	$0.341184\pi$
$104$	−1.52453	−0.149492
$105$	2.16931	0.211703
$106$	−2.79110	−0.271095
$107$	13.9090	1.34463	0.672316	−	0.740265i	$-0.265300\pi$
$107$	13.9090	1.34463	0.672316	+	0.740265i	$0.265300\pi$
$108$	8.85753	0.852316
$109$	5.88357	0.563544	0.281772	−	0.959481i	$-0.409078\pi$
$109$	5.88357	0.563544	0.281772	+	0.959481i	$0.409078\pi$
$110$	−12.2599	−1.16893
$111$	18.6459	1.76979
$112$	−0.355248	−0.0335678
$113$	1.87545	0.176427	0.0882137	−	0.996102i	$-0.471884\pi$
$113$	1.87545	0.176427	0.0882137	+	0.996102i	$0.471884\pi$
$114$	36.2192	3.39224
$115$	−8.30753	−0.774681
$116$	−30.8505	−2.86440
$117$	0.991564	0.0916701
$118$	1.71919	0.158264
$119$	−5.79806	−0.531507
$120$	−5.68968	−0.519395
$121$	18.1560	1.65055
$122$	−2.53882	−0.229854
$123$	14.5086	1.30819
$124$	30.9667	2.78089
$125$	−1.00000	−0.0894427
$126$	−3.87324	−0.345056
$127$	−4.27308	−0.379175	−0.189587	−	0.981864i	$-0.560715\pi$
$127$	−4.27308	−0.379175	−0.189587	+	0.981864i	$0.560715\pi$
$128$	17.4826	1.54526
$129$	6.97828	0.614403
$130$	1.31974	0.115749
$131$	−8.80299	−0.769121	−0.384561	−	0.923100i	$-0.625647\pi$
$131$	−8.80299	−0.769121	−0.384561	+	0.923100i	$0.625647\pi$
$132$	36.9579	3.21678
$133$	7.35353	0.637632
$134$	14.9653	1.29280
$135$	−2.80731	−0.241615
$136$	15.2072	1.30401
$137$	4.27602	0.365325	0.182663	−	0.983176i	$-0.441528\pi$
$137$	4.27602	0.365325	0.182663	+	0.983176i	$0.441528\pi$
$138$	40.9180	3.48317
$139$	2.93836	0.249229	0.124614	−	0.992205i	$-0.460231\pi$
$139$	2.93836	0.249229	0.124614	+	0.992205i	$0.460231\pi$
$140$	−3.15517	−0.266660
$141$	−18.9050	−1.59209
$142$	−13.9147	−1.16769
$143$	−3.13857	−0.262460
$144$	−0.606016	−0.0505013
$145$	9.77778	0.812001
$146$	−15.4019	−1.27467
$147$	−2.16931	−0.178922
$148$	−27.1197	−2.22922
$149$	−21.6233	−1.77145	−0.885726	−	0.464208i	$-0.846339\pi$
$149$	−21.6233	−1.77145	−0.885726	+	0.464208i	$0.846339\pi$
$150$	4.92541	0.402158
$151$	−0.525383	−0.0427551	−0.0213775	−	0.999771i	$-0.506805\pi$
$151$	−0.525383	−0.0427551	−0.0213775	+	0.999771i	$0.506805\pi$
$152$	−19.2869	−1.56437
$153$	−9.89089	−0.799631
$154$	12.2599	0.987927
$155$	−9.81460	−0.788328
$156$	−3.97843	−0.318529
$157$	−5.82825	−0.465145	−0.232572	−	0.972579i	$-0.574714\pi$
$157$	−5.82825	−0.465145	−0.232572	+	0.972579i	$0.574714\pi$
$158$	13.3193	1.05963
$159$	−2.66670	−0.211483
$160$	−6.05221	−0.478469
$161$	8.30753	0.654725
$162$	25.4469	1.99929
$163$	4.75865	0.372726	0.186363	−	0.982481i	$-0.440330\pi$
$163$	4.75865	0.372726	0.186363	+	0.982481i	$0.440330\pi$
$164$	−21.1021	−1.64780
$165$	−11.7135	−0.911892
$166$	24.6448	1.91281
$167$	−5.90152	−0.456673	−0.228337	−	0.973582i	$-0.573329\pi$
$167$	−5.90152	−0.456673	−0.228337	+	0.973582i	$0.573329\pi$
$168$	5.68968	0.438969
$169$	−12.6621	−0.974011
$170$	−13.1645	−1.00967
$171$	12.5444	0.959292
$172$	−10.1496	−0.773901
$173$	14.7627	1.12239	0.561195	−	0.827684i	$-0.310342\pi$
$173$	14.7627	1.12239	0.561195	+	0.827684i	$0.310342\pi$
$174$	−48.1596	−3.65097
$175$	1.00000	0.0755929
$176$	1.91821	0.144590
$177$	1.64256	0.123463
$178$	38.5650	2.89057
$179$	11.3450	0.847967	0.423984	−	0.905670i	$-0.360631\pi$
$179$	11.3450	0.847967	0.423984	+	0.905670i	$0.360631\pi$
$180$	−5.38239	−0.401180
$181$	−16.3749	−1.21714	−0.608568	−	0.793502i	$-0.708256\pi$
$181$	−16.3749	−1.21714	−0.608568	+	0.793502i	$0.708256\pi$
$182$	−1.31974	−0.0978259
$183$	−2.42567	−0.179311
$184$	−21.7891	−1.60631
$185$	8.59532	0.631940
$186$	48.3410	3.54453
$187$	31.3074	2.28942
$188$	27.4966	2.00540
$189$	2.80731	0.204202
$190$	16.6962	1.21127
$191$	7.01050	0.507262	0.253631	−	0.967301i	$-0.418375\pi$
$191$	7.01050	0.507262	0.253631	+	0.967301i	$0.418375\pi$
$192$	28.2684	2.04009
$193$	0.623572	0.0448857	0.0224428	−	0.999748i	$-0.492856\pi$
$193$	0.623572	0.0448857	0.0224428	+	0.999748i	$0.492856\pi$
$194$	−27.9577	−2.00725
$195$	1.26092	0.0902967
$196$	3.15517	0.225369
$197$	0.883459	0.0629438	0.0314719	−	0.999505i	$-0.489981\pi$
$197$	0.883459	0.0629438	0.0314719	+	0.999505i	$0.489981\pi$
$198$	20.9141	1.48630
$199$	−6.68463	−0.473861	−0.236930	−	0.971527i	$-0.576141\pi$
$199$	−6.68463	−0.473861	−0.236930	+	0.971527i	$0.576141\pi$
$200$	−2.62281	−0.185461
$201$	14.2983	1.00853
$202$	−11.9031	−0.837497
$203$	−9.77778	−0.686266
$204$	39.6850	2.77851
$205$	6.68811	0.467118
$206$	−22.0518	−1.53642
$207$	14.1718	0.985007
$208$	−0.206490	−0.0143175
$209$	−39.7063	−2.74654
$210$	−4.92541	−0.339886
$211$	−27.8333	−1.91612	−0.958061	−	0.286565i	$-0.907487\pi$
$211$	−27.8333	−1.91612	−0.958061	+	0.286565i	$0.907487\pi$
$212$	3.87861	0.266384
$213$	−13.2945	−0.910927
$214$	−31.5803	−2.15879
$215$	3.21682	0.219385
$216$	−7.36303	−0.500991
$217$	9.81460	0.666259
$218$	−13.3586	−0.904761
$219$	−14.7155	−0.994378
$220$	17.0367	1.14862
$221$	−3.37016	−0.226701
$222$	−42.3355	−2.84137
$223$	24.7433	1.65693	0.828467	−	0.560037i	$-0.189213\pi$
$223$	24.7433	1.65693	0.828467	+	0.560037i	$0.189213\pi$
$224$	6.05221	0.404380
$225$	1.70590	0.113726
$226$	−4.25820	−0.283252
$227$	−8.93233	−0.592860	−0.296430	−	0.955055i	$-0.595796\pi$
$227$	−8.93233	−0.592860	−0.296430	+	0.955055i	$0.595796\pi$
$228$	−50.3315	−3.33328
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	18.8622	1.24374
$231$	11.7135	0.770689
$232$	25.6453	1.68369
$233$	−12.3763	−0.810800	−0.405400	−	0.914139i	$-0.632868\pi$
$233$	−12.3763	−0.810800	−0.405400	+	0.914139i	$0.632868\pi$
$234$	−2.25135	−0.147175
$235$	−8.71478	−0.568489
$236$	−2.38904	−0.155513
$237$	12.7257	0.826625
$238$	13.1645	0.853327
$239$	−29.1989	−1.88872	−0.944359	−	0.328917i	$-0.893316\pi$
$239$	−29.1989	−1.88872	−0.944359	+	0.328917i	$0.893316\pi$
$240$	−0.770642	−0.0497447
$241$	−17.0569	−1.09873	−0.549365	−	0.835582i	$-0.685130\pi$
$241$	−17.0569	−1.09873	−0.549365	+	0.835582i	$0.685130\pi$
$242$	−41.2232	−2.64993
$243$	15.8908	1.01940
$244$	3.52804	0.225860
$245$	−1.00000	−0.0638877
$246$	−32.9417	−2.10029
$247$	4.27429	0.271966
$248$	−25.7418	−1.63461
$249$	23.5464	1.49219
$250$	2.27050	0.143599
$251$	24.9772	1.57654	0.788272	−	0.615327i	$-0.210976\pi$
$251$	24.9772	1.57654	0.788272	+	0.615327i	$0.210976\pi$
$252$	5.38239	0.339059
$253$	−44.8576	−2.82017
$254$	9.70203	0.608760
$255$	−12.5778	−0.787651
$256$	−13.6321	−0.852004
$257$	−8.07369	−0.503623	−0.251811	−	0.967776i	$-0.581026\pi$
$257$	−8.07369	−0.503623	−0.251811	+	0.967776i	$0.581026\pi$
$258$	−15.8442	−0.986415
$259$	−8.59532	−0.534087
$260$	−1.83396	−0.113738
$261$	−16.6799	−1.03246
$262$	19.9872	1.23481
$263$	26.3048	1.62202	0.811012	−	0.585029i	$-0.198917\pi$
$263$	26.3048	1.62202	0.811012	+	0.585029i	$0.198917\pi$
$264$	−30.7222	−1.89082
$265$	−1.22929	−0.0755146
$266$	−16.6962	−1.02371
$267$	36.8462	2.25495
$268$	−20.7963	−1.27034
$269$	−12.7509	−0.777434	−0.388717	−	0.921357i	$-0.627082\pi$
$269$	−12.7509	−0.777434	−0.388717	+	0.921357i	$0.627082\pi$
$270$	6.37399	0.387909
$271$	−28.2762	−1.71766	−0.858829	−	0.512262i	$-0.828808\pi$
$271$	−28.2762	−1.71766	−0.858829	+	0.512262i	$0.828808\pi$
$272$	2.05975	0.124890
$273$	−1.26092	−0.0763146
$274$	−9.70871	−0.586525
$275$	−5.39963	−0.325610
$276$	−56.8611	−3.42264
$277$	−24.6714	−1.48236	−0.741180	−	0.671306i	$-0.765734\pi$
$277$	−24.6714	−1.48236	−0.741180	+	0.671306i	$0.765734\pi$
$278$	−6.67156	−0.400133
$279$	16.7427	1.00236
$280$	2.62281	0.156743
$281$	−18.5854	−1.10871	−0.554355	−	0.832280i	$-0.687035\pi$
$281$	−18.5854	−1.10871	−0.554355	+	0.832280i	$0.687035\pi$
$282$	42.9239	2.55608
$283$	−27.4384	−1.63105	−0.815523	−	0.578724i	$-0.803551\pi$
$283$	−27.4384	−1.63105	−0.815523	+	0.578724i	$0.803551\pi$
$284$	19.3364	1.14740
$285$	15.9521	0.944919
$286$	7.12612	0.421376
$287$	−6.68811	−0.394787
$288$	10.3244	0.608374
$289$	16.6175	0.977498
$290$	−22.2004	−1.30366
$291$	−26.7117	−1.56587
$292$	21.4030	1.25252
$293$	−14.6462	−0.855642	−0.427821	−	0.903864i	$-0.640719\pi$
$293$	−14.6462	−0.855642	−0.427821	+	0.903864i	$0.640719\pi$
$294$	4.92541	0.287256
$295$	0.757184	0.0440849
$296$	22.5439	1.31034
$297$	−15.1584	−0.879581
$298$	49.0958	2.84404
$299$	4.82881	0.279257
$300$	−6.84453	−0.395169
$301$	−3.21682	−0.185415
$302$	1.19288	0.0686427
$303$	−11.3726	−0.653337
$304$	−2.61232	−0.149827
$305$	−1.11818	−0.0640267
$306$	22.4573	1.28380
$307$	−11.6064	−0.662410	−0.331205	−	0.943559i	$-0.607455\pi$
$307$	−11.6064	−0.662410	−0.331205	+	0.943559i	$0.607455\pi$
$308$	−17.0367	−0.970758
$309$	−21.0690	−1.19857
$310$	22.2841	1.26565
$311$	−30.4610	−1.72728	−0.863641	−	0.504107i	$-0.831822\pi$
$311$	−30.4610	−1.72728	−0.863641	+	0.504107i	$0.831822\pi$
$312$	3.30717	0.187231
$313$	30.2728	1.71112	0.855560	−	0.517704i	$-0.173213\pi$
$313$	30.2728	1.71112	0.855560	+	0.517704i	$0.173213\pi$
$314$	13.2330	0.746784
$315$	−1.70590	−0.0961164
$316$	−18.5090	−1.04122
$317$	19.9862	1.12254	0.561268	−	0.827634i	$-0.310314\pi$
$317$	19.9862	1.12254	0.561268	+	0.827634i	$0.310314\pi$
$318$	6.05475	0.339534
$319$	52.7964	2.95603
$320$	13.0310	0.728458
$321$	−30.1728	−1.68408
$322$	−18.8622	−1.05115
$323$	−42.6362	−2.37234
$324$	−35.3619	−1.96455
$325$	0.581257	0.0322423
$326$	−10.8045	−0.598406
$327$	−12.7633	−0.705811
$328$	17.5416	0.968575
$329$	8.71478	0.480461
$330$	26.5954	1.46403
$331$	20.6846	1.13693	0.568463	−	0.822709i	$-0.307538\pi$
$331$	20.6846	1.13693	0.568463	+	0.822709i	$0.307538\pi$
$332$	−34.2473	−1.87957
$333$	−14.6627	−0.803513
$334$	13.3994	0.733182
$335$	6.59119	0.360115
$336$	0.770642	0.0420419
$337$	−2.07787	−0.113189	−0.0565943	−	0.998397i	$-0.518024\pi$
$337$	−2.07787	−0.113189	−0.0565943	+	0.998397i	$0.518024\pi$
$338$	28.7494	1.56376
$339$	−4.06842	−0.220966
$340$	18.2938	0.992123
$341$	−52.9952	−2.86985
$342$	−28.4820	−1.54013
$343$	1.00000	0.0539949
$344$	8.43711	0.454899
$345$	18.0216	0.970250
$346$	−33.5188	−1.80198
$347$	3.91026	0.209914	0.104957	−	0.994477i	$-0.466530\pi$
$347$	3.91026	0.209914	0.104957	+	0.994477i	$0.466530\pi$
$348$	66.9243	3.58752
$349$	14.2894	0.764892	0.382446	−	0.923978i	$-0.375082\pi$
$349$	14.2894	0.764892	0.382446	+	0.923978i	$0.375082\pi$
$350$	−2.27050	−0.121363
$351$	1.63177	0.0870972
$352$	−32.6797	−1.74183
$353$	13.6889	0.728586	0.364293	−	0.931284i	$-0.381311\pi$
$353$	13.6889	0.728586	0.364293	+	0.931284i	$0.381311\pi$
$354$	−3.72944	−0.198218
$355$	−6.12847	−0.325265
$356$	−53.5913	−2.84033
$357$	12.5778	0.665686
$358$	−25.7589	−1.36140
$359$	20.3010	1.07145	0.535724	−	0.844393i	$-0.320039\pi$
$359$	20.3010	1.07145	0.535724	+	0.844393i	$0.320039\pi$
$360$	4.47424	0.235813
$361$	35.0744	1.84602
$362$	37.1792	1.95409
$363$	−39.3859	−2.06723
$364$	1.83396	0.0961258
$365$	−6.78348	−0.355064
$366$	5.50749	0.287881
$367$	15.6201	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$367$	15.6201	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$368$	−2.95123	−0.153843
$369$	−11.4092	−0.593941
$370$	−19.5157	−1.01457
$371$	1.22929	0.0638215
$372$	−67.1764	−3.48293
$373$	−2.58997	−0.134103	−0.0670517	−	0.997750i	$-0.521359\pi$
$373$	−2.58997	−0.134103	−0.0670517	+	0.997750i	$0.521359\pi$
$374$	−71.0833	−3.67563
$375$	2.16931	0.112023
$376$	−22.8572	−1.17877
$377$	−5.68340	−0.292710
$378$	−6.37399	−0.327843
$379$	−26.6067	−1.36669	−0.683347	−	0.730094i	$-0.739476\pi$
$379$	−26.6067	−1.36669	−0.683347	+	0.730094i	$0.739476\pi$
$380$	−23.2016	−1.19022
$381$	9.26963	0.474898
$382$	−15.9173	−0.814401
$383$	−9.86799	−0.504231	−0.252115	−	0.967697i	$-0.581126\pi$
$383$	−9.86799	−0.504231	−0.252115	+	0.967697i	$0.581126\pi$
$384$	−37.9251	−1.93536
$385$	5.39963	0.275191
$386$	−1.41582	−0.0720633
$387$	−5.48757	−0.278949
$388$	38.8511	1.97236
$389$	29.6778	1.50473	0.752363	−	0.658749i	$-0.228914\pi$
$389$	29.6778	1.50473	0.752363	+	0.658749i	$0.228914\pi$
$390$	−2.86293	−0.144970
$391$	−48.1675	−2.43594
$392$	−2.62281	−0.132472
$393$	19.0964	0.963286
$394$	−2.00589	−0.101055
$395$	5.86626	0.295164
$396$	−29.0629	−1.46047
$397$	−14.0076	−0.703020	−0.351510	−	0.936184i	$-0.614332\pi$
$397$	−14.0076	−0.703020	−0.351510	+	0.936184i	$0.614332\pi$
$398$	15.1775	0.760777
$399$	−15.9521	−0.798602
$400$	−0.355248	−0.0177624
$401$	−21.1724	−1.05730	−0.528651	−	0.848840i	$-0.677302\pi$
$401$	−21.1724	−1.05730	−0.528651	+	0.848840i	$0.677302\pi$
$402$	−32.4643	−1.61917
$403$	5.70480	0.284177
$404$	16.5409	0.822942
$405$	11.2076	0.556910
$406$	22.2004	1.10179
$407$	46.4115	2.30053
$408$	−32.9891	−1.63320
$409$	17.9006	0.885127	0.442564	−	0.896737i	$-0.354069\pi$
$409$	17.9006	0.885127	0.442564	+	0.896737i	$0.354069\pi$
$410$	−15.1854	−0.749951
$411$	−9.27601	−0.457552
$412$	30.6440	1.50972
$413$	−0.757184	−0.0372586
$414$	−32.1770	−1.58142
$415$	10.8544	0.532819
$416$	3.51789	0.172479
$417$	−6.37422	−0.312147
$418$	90.1532	4.40954
$419$	1.17821	0.0575594	0.0287797	−	0.999586i	$-0.490838\pi$
$419$	1.17821	0.0575594	0.0287797	+	0.999586i	$0.490838\pi$
$420$	6.84453	0.333979
$421$	33.8858	1.65149	0.825746	−	0.564041i	$-0.190754\pi$
$421$	33.8858	1.65149	0.825746	+	0.564041i	$0.190754\pi$
$422$	63.1954	3.07631
$423$	14.8665	0.722835
$424$	−3.22419	−0.156580
$425$	−5.79806	−0.281247
$426$	30.1852	1.46248
$427$	1.11818	0.0541124
$428$	43.8852	2.12127
$429$	6.80853	0.328719
$430$	−7.30379	−0.352220
$431$	34.3697	1.65553	0.827766	−	0.561074i	$-0.189612\pi$
$431$	34.3697	1.65553	0.827766	+	0.561074i	$0.189612\pi$
$432$	−0.997289	−0.0479821
$433$	−34.4268	−1.65444	−0.827222	−	0.561875i	$-0.810080\pi$
$433$	−34.4268	−1.65444	−0.827222	+	0.561875i	$0.810080\pi$
$434$	−22.2841	−1.06967
$435$	−21.2110	−1.01699
$436$	18.5637	0.889038
$437$	61.0896	2.92231
$438$	33.4114	1.59646
$439$	−34.4949	−1.64635	−0.823176	−	0.567787i	$-0.807800\pi$
$439$	−34.4949	−1.64635	−0.823176	+	0.567787i	$0.807800\pi$
$440$	−14.1622	−0.675157
$441$	1.70590	0.0812332
$442$	7.65195	0.363966
$443$	−7.43296	−0.353150	−0.176575	−	0.984287i	$-0.556502\pi$
$443$	−7.43296	−0.353150	−0.176575	+	0.984287i	$0.556502\pi$
$444$	58.8309	2.79199
$445$	16.9852	0.805177
$446$	−56.1797	−2.66019
$447$	46.9077	2.21866
$448$	−13.0310	−0.615659
$449$	8.01725	0.378357	0.189179	−	0.981943i	$-0.439417\pi$
$449$	8.01725	0.378357	0.189179	+	0.981943i	$0.439417\pi$
$450$	−3.87324	−0.182586
$451$	36.1133	1.70051
$452$	5.91735	0.278329
$453$	1.13972	0.0535486
$454$	20.2809	0.951828
$455$	−0.581257	−0.0272497
$456$	41.8392	1.95930
$457$	16.6685	0.779719	0.389860	−	0.920874i	$-0.372524\pi$
$457$	16.6685	0.779719	0.389860	+	0.920874i	$0.372524\pi$
$458$	2.27050	0.106093
$459$	−16.2769	−0.759742
$460$	−26.2117	−1.22212
$461$	21.0886	0.982192	0.491096	−	0.871105i	$-0.336596\pi$
$461$	21.0886	0.982192	0.491096	+	0.871105i	$0.336596\pi$
$462$	−26.5954	−1.23733
$463$	9.60780	0.446512	0.223256	−	0.974760i	$-0.428331\pi$
$463$	9.60780	0.446512	0.223256	+	0.974760i	$0.428331\pi$
$464$	3.47353	0.161255
$465$	21.2909	0.987342
$466$	28.1004	1.30173
$467$	2.20731	0.102142	0.0510712	−	0.998695i	$-0.483736\pi$
$467$	2.20731	0.102142	0.0510712	+	0.998695i	$0.483736\pi$
$468$	3.12855	0.144617
$469$	−6.59119	−0.304353
$470$	19.7869	0.912702
$471$	12.6433	0.582571
$472$	1.98595	0.0914107
$473$	17.3696	0.798657
$474$	−28.8938	−1.32713
$475$	7.35353	0.337403
$476$	−18.2938	−0.838497
$477$	2.09704	0.0960168
$478$	66.2960	3.03231
$479$	18.5010	0.845330	0.422665	−	0.906286i	$-0.361095\pi$
$479$	18.5010	0.845330	0.422665	+	0.906286i	$0.361095\pi$
$480$	13.1291	0.599259
$481$	−4.99608	−0.227802
$482$	38.7276	1.76400
$483$	−18.0216	−0.820011
$484$	57.2852	2.60387
$485$	−12.3135	−0.559126
$486$	−36.0801	−1.63663
$487$	11.8436	0.536686	0.268343	−	0.963323i	$-0.413524\pi$
$487$	11.8436	0.536686	0.268343	+	0.963323i	$0.413524\pi$
$488$	−2.93277	−0.132760
$489$	−10.3230	−0.466821
$490$	2.27050	0.102571
$491$	8.20527	0.370299	0.185149	−	0.982710i	$-0.440723\pi$
$491$	8.20527	0.370299	0.185149	+	0.982710i	$0.440723\pi$
$492$	45.7770	2.06379
$493$	56.6921	2.55329
$494$	−9.70477	−0.436638
$495$	9.21121	0.414013
$496$	−3.48662	−0.156554
$497$	6.12847	0.274899
$498$	−53.4622	−2.39570
$499$	−20.7318	−0.928082	−0.464041	−	0.885814i	$-0.653601\pi$
$499$	−20.7318	−0.928082	−0.464041	+	0.885814i	$0.653601\pi$
$500$	−3.15517	−0.141103
$501$	12.8022	0.571960
$502$	−56.7106	−2.53112
$503$	−25.7982	−1.15028	−0.575142	−	0.818054i	$-0.695053\pi$
$503$	−25.7982	−1.15028	−0.575142	+	0.818054i	$0.695053\pi$
$504$	−4.47424	−0.199299
$505$	−5.24249	−0.233288
$506$	101.849	4.52774
$507$	27.4681	1.21990
$508$	−13.4823	−0.598180
$509$	15.0188	0.665697	0.332848	−	0.942980i	$-0.391990\pi$
$509$	15.0188	0.665697	0.332848	+	0.942980i	$0.391990\pi$
$510$	28.5578	1.26456
$511$	6.78348	0.300083
$512$	−4.01353	−0.177375
$513$	20.6436	0.911438
$514$	18.3313	0.808559
$515$	−9.71232	−0.427976
$516$	22.0176	0.969273
$517$	−47.0566	−2.06955
$518$	19.5157	0.857469
$519$	−32.0249	−1.40574
$520$	1.52453	0.0668549
$521$	5.60314	0.245478	0.122739	−	0.992439i	$-0.460832\pi$
$521$	5.60314	0.245478	0.122739	+	0.992439i	$0.460832\pi$
$522$	37.8717	1.65760
$523$	−16.1077	−0.704339	−0.352170	−	0.935936i	$-0.614556\pi$
$523$	−16.1077	−0.704339	−0.352170	+	0.935936i	$0.614556\pi$
$524$	−27.7749	−1.21335
$525$	−2.16931	−0.0946764
$526$	−59.7251	−2.60414
$527$	−56.9056	−2.47885
$528$	−4.16118	−0.181092
$529$	46.0150	2.00065
$530$	2.79110	0.121238
$531$	−1.29168	−0.0560540
$532$	23.2016	1.00592
$533$	−3.88751	−0.168387
$534$	−83.6593	−3.62029
$535$	−13.9090	−0.601337
$536$	17.2874	0.746703
$537$	−24.6109	−1.06204
$538$	28.9508	1.24816
$539$	−5.39963	−0.232578
$540$	−8.85753	−0.381167
$541$	10.8463	0.466319	0.233160	−	0.972438i	$-0.425094\pi$
$541$	10.8463	0.466319	0.233160	+	0.972438i	$0.425094\pi$
$542$	64.2012	2.75768
$543$	35.5222	1.52440
$544$	−35.0911	−1.50452
$545$	−5.88357	−0.252024
$546$	2.86293	0.122522
$547$	−6.84945	−0.292862	−0.146431	−	0.989221i	$-0.546779\pi$
$547$	−6.84945	−0.292862	−0.146431	+	0.989221i	$0.546779\pi$
$548$	13.4916	0.576332
$549$	1.90750	0.0814100
$550$	12.2599	0.522762
$551$	−71.9012	−3.06309
$552$	47.2672	2.01183
$553$	−5.86626	−0.249459
$554$	56.0164	2.37991
$555$	−18.6459	−0.791474
$556$	9.27104	0.393180
$557$	−38.1906	−1.61819	−0.809095	−	0.587678i	$-0.800042\pi$
$557$	−38.1906	−1.61819	−0.809095	+	0.587678i	$0.800042\pi$
$558$	−38.0143	−1.60927
$559$	−1.86980	−0.0790841
$560$	0.355248	0.0150120
$561$	−67.9153	−2.86739
$562$	42.1981	1.78002
$563$	2.60088	0.109614	0.0548071	−	0.998497i	$-0.482546\pi$
$563$	2.60088	0.109614	0.0548071	+	0.998497i	$0.482546\pi$
$564$	−59.6486	−2.51166
$565$	−1.87545	−0.0789007
$566$	62.2990	2.61862
$567$	−11.2076	−0.470675
$568$	−16.0738	−0.674442
$569$	6.51815	0.273255	0.136628	−	0.990622i	$-0.456374\pi$
$569$	6.51815	0.273255	0.136628	+	0.990622i	$0.456374\pi$
$570$	−36.2192	−1.51705
$571$	−40.6820	−1.70249	−0.851244	−	0.524769i	$-0.824152\pi$
$571$	−40.6820	−1.70249	−0.851244	+	0.524769i	$0.824152\pi$
$572$	−9.90272	−0.414053
$573$	−15.2079	−0.635320
$574$	15.1854	0.633824
$575$	8.30753	0.346448
$576$	−22.2296	−0.926234
$577$	2.03040	0.0845268	0.0422634	−	0.999107i	$-0.486543\pi$
$577$	2.03040	0.0845268	0.0422634	+	0.999107i	$0.486543\pi$
$578$	−37.7300	−1.56936
$579$	−1.35272	−0.0562171
$580$	30.8505	1.28100
$581$	−10.8544	−0.450315
$582$	60.6489	2.51398
$583$	−6.63770	−0.274905
$584$	−17.7918	−0.736229
$585$	−0.991564	−0.0409961
$586$	33.2543	1.37372
$587$	0.872039	0.0359929	0.0179964	−	0.999838i	$-0.494271\pi$
$587$	0.872039	0.0359929	0.0179964	+	0.999838i	$0.494271\pi$
$588$	−6.84453	−0.282264
$589$	72.1720	2.97379
$590$	−1.71919	−0.0707777
$591$	−1.91649	−0.0788341
$592$	3.05347	0.125497
$593$	16.5312	0.678855	0.339427	−	0.940632i	$-0.389767\pi$
$593$	16.5312	0.678855	0.339427	+	0.940632i	$0.389767\pi$
$594$	34.4172	1.41215
$595$	5.79806	0.237697
$596$	−68.2253	−2.79462
$597$	14.5010	0.593487
$598$	−10.9638	−0.448343
$599$	15.4431	0.630988	0.315494	−	0.948928i	$-0.397830\pi$
$599$	15.4431	0.630988	0.315494	+	0.948928i	$0.397830\pi$
$600$	5.68968	0.232280
$601$	−16.8758	−0.688380	−0.344190	−	0.938900i	$-0.611846\pi$
$601$	−16.8758	−0.688380	−0.344190	+	0.938900i	$0.611846\pi$
$602$	7.30379	0.297680
$603$	−11.2439	−0.457887
$604$	−1.65767	−0.0674498
$605$	−18.1560	−0.738146
$606$	25.8214	1.04892
$607$	−0.147435	−0.00598422	−0.00299211	−	0.999996i	$-0.500952\pi$
$607$	−0.147435	−0.00598422	−0.00299211	+	0.999996i	$0.500952\pi$
$608$	44.5051	1.80492
$609$	21.2110	0.859514
$610$	2.53882	0.102794
$611$	5.06552	0.204929
$612$	−31.2074	−1.26149
$613$	−13.2662	−0.535816	−0.267908	−	0.963445i	$-0.586332\pi$
$613$	−13.2662	−0.535816	−0.267908	+	0.963445i	$0.586332\pi$
$614$	26.3523	1.06349
$615$	−14.5086	−0.585042
$616$	14.1622	0.570611
$617$	−46.0094	−1.85227	−0.926134	−	0.377194i	$-0.876889\pi$
$617$	−46.0094	−1.85227	−0.926134	+	0.377194i	$0.876889\pi$
$618$	47.8372	1.92429
$619$	−4.19559	−0.168635	−0.0843174	−	0.996439i	$-0.526871\pi$
$619$	−4.19559	−0.168635	−0.0843174	+	0.996439i	$0.526871\pi$
$620$	−30.9667	−1.24365
$621$	23.3218	0.935871
$622$	69.1616	2.77313
$623$	−16.9852	−0.680499
$624$	0.447941	0.0179320
$625$	1.00000	0.0400000
$626$	−68.7344	−2.74718
$627$	86.1353	3.43991
$628$	−18.3891	−0.733805
$629$	49.8361	1.98710
$630$	3.87324	0.154314
$631$	9.97023	0.396908	0.198454	−	0.980110i	$-0.436408\pi$
$631$	9.97023	0.396908	0.198454	+	0.980110i	$0.436408\pi$
$632$	15.3861	0.612026
$633$	60.3789	2.39985
$634$	−45.3786	−1.80221
$635$	4.27308	0.169572
$636$	−8.41390	−0.333633
$637$	0.581257	0.0230302
$638$	−119.874	−4.74586
$639$	10.4545	0.413575
$640$	−17.4826	−0.691059
$641$	13.0008	0.513502	0.256751	−	0.966478i	$-0.417348\pi$
$641$	13.0008	0.513502	0.256751	+	0.966478i	$0.417348\pi$
$642$	68.5074	2.70377
$643$	−34.4112	−1.35705	−0.678524	−	0.734579i	$-0.737380\pi$
$643$	−34.4112	−1.35705	−0.678524	+	0.734579i	$0.737380\pi$
$644$	26.2117	1.03288
$645$	−6.97828	−0.274769
$646$	96.8054	3.80876
$647$	7.26904	0.285775	0.142888	−	0.989739i	$-0.454361\pi$
$647$	7.26904	0.285775	0.142888	+	0.989739i	$0.454361\pi$
$648$	29.3954	1.15476
$649$	4.08851	0.160488
$650$	−1.31974	−0.0517646
$651$	−21.2909	−0.834456
$652$	15.0143	0.588007
$653$	32.5981	1.27566	0.637832	−	0.770176i	$-0.279832\pi$
$653$	32.5981	1.27566	0.637832	+	0.770176i	$0.279832\pi$
$654$	28.9790	1.13317
$655$	8.80299	0.343961
$656$	2.37594	0.0927647
$657$	11.5719	0.451464
$658$	−19.7869	−0.771374
$659$	2.72047	0.105974	0.0529872	−	0.998595i	$-0.483126\pi$
$659$	2.72047	0.105974	0.0529872	+	0.998595i	$0.483126\pi$
$660$	−36.9579	−1.43859
$661$	18.0496	0.702047	0.351023	−	0.936367i	$-0.385834\pi$
$661$	18.0496	0.702047	0.351023	+	0.936367i	$0.385834\pi$
$662$	−46.9643	−1.82532
$663$	7.31091	0.283932
$664$	28.4689	1.10481
$665$	−7.35353	−0.285158
$666$	33.2917	1.29003
$667$	−81.2292	−3.14521
$668$	−18.6203	−0.720440
$669$	−53.6759	−2.07523
$670$	−14.9653	−0.578160
$671$	−6.03775	−0.233085
$672$	−13.1291	−0.506466
$673$	−13.2977	−0.512589	−0.256295	−	0.966599i	$-0.582502\pi$
$673$	−13.2977	−0.512589	−0.256295	+	0.966599i	$0.582502\pi$
$674$	4.71779	0.181723
$675$	2.80731	0.108053
$676$	−39.9512	−1.53658
$677$	40.6833	1.56359	0.781793	−	0.623538i	$-0.214305\pi$
$677$	40.6833	1.56359	0.781793	+	0.623538i	$0.214305\pi$
$678$	9.23736	0.354759
$679$	12.3135	0.472547
$680$	−15.2072	−0.583170
$681$	19.3770	0.742528
$682$	120.326	4.60751
$683$	−12.6248	−0.483075	−0.241537	−	0.970392i	$-0.577652\pi$
$683$	−12.6248	−0.483075	−0.241537	+	0.970392i	$0.577652\pi$
$684$	39.5796	1.51336
$685$	−4.27602	−0.163379
$686$	−2.27050	−0.0866881
$687$	2.16931	0.0827643
$688$	1.14277	0.0435676
$689$	0.714532	0.0272215
$690$	−40.9180	−1.55772
$691$	−17.1003	−0.650526	−0.325263	−	0.945624i	$-0.605453\pi$
$691$	−17.1003	−0.650526	−0.325263	+	0.945624i	$0.605453\pi$
$692$	46.5789	1.77067
$693$	−9.21121	−0.349905
$694$	−8.87825	−0.337014
$695$	−2.93836	−0.111459
$696$	−55.6325	−2.10874
$697$	38.7781	1.46882
$698$	−32.4440	−1.22802
$699$	26.8481	1.01549
$700$	3.15517	0.119254
$701$	32.7541	1.23711	0.618553	−	0.785743i	$-0.287719\pi$
$701$	32.7541	1.23711	0.618553	+	0.785743i	$0.287719\pi$
$702$	−3.70492	−0.139833
$703$	−63.2059	−2.38386
$704$	70.3628	2.65190
$705$	18.9050	0.712005
$706$	−31.0806	−1.16973
$707$	5.24249	0.197164
$708$	5.18257	0.194773
$709$	2.04029	0.0766247	0.0383124	−	0.999266i	$-0.487802\pi$
$709$	2.04029	0.0766247	0.0383124	+	0.999266i	$0.487802\pi$
$710$	13.9147	0.522209
$711$	−10.0072	−0.375301
$712$	44.5490	1.66955
$713$	81.5351	3.05351
$714$	−28.5578	−1.06875
$715$	3.13857	0.117376
$716$	35.7955	1.33774
$717$	63.3413	2.36553
$718$	−46.0935	−1.72019
$719$	34.5687	1.28919	0.644597	−	0.764522i	$-0.277025\pi$
$719$	34.5687	1.28919	0.644597	+	0.764522i	$0.277025\pi$
$720$	0.606016	0.0225849
$721$	9.71232	0.361706
$722$	−79.6364	−2.96376
$723$	37.0016	1.37611
$724$	−51.6655	−1.92013
$725$	−9.77778	−0.363138
$726$	89.4258	3.31890
$727$	41.3445	1.53338	0.766692	−	0.642015i	$-0.221901\pi$
$727$	41.3445	1.53338	0.766692	+	0.642015i	$0.221901\pi$
$728$	−1.52453	−0.0565027
$729$	−0.849283	−0.0314549
$730$	15.4019	0.570049
$731$	18.6513	0.689844
$732$	−7.65341	−0.282878
$733$	−15.2449	−0.563082	−0.281541	−	0.959549i	$-0.590846\pi$
$733$	−15.2449	−0.563082	−0.281541	+	0.959549i	$0.590846\pi$
$734$	−35.4655	−1.30905
$735$	2.16931	0.0800161
$736$	50.2789	1.85330
$737$	35.5900	1.31097
$738$	25.9047	0.953564
$739$	26.0149	0.956975	0.478487	−	0.878094i	$-0.341185\pi$
$739$	26.0149	0.956975	0.478487	+	0.878094i	$0.341185\pi$
$740$	27.1197	0.996939
$741$	−9.27225	−0.340624
$742$	−2.79110	−0.102464
$743$	38.3110	1.40549	0.702746	−	0.711441i	$-0.251957\pi$
$743$	38.3110	1.40549	0.702746	+	0.711441i	$0.251957\pi$
$744$	55.8420	2.04727
$745$	21.6233	0.792218
$746$	5.88052	0.215301
$747$	−18.5164	−0.677480
$748$	98.7800	3.61175
$749$	13.9090	0.508223
$750$	−4.92541	−0.179851
$751$	43.2600	1.57858	0.789289	−	0.614022i	$-0.210449\pi$
$751$	43.2600	1.57858	0.789289	+	0.614022i	$0.210449\pi$
$752$	−3.09591	−0.112896
$753$	−54.1831	−1.97454
$754$	12.9042	0.469942
$755$	0.525383	0.0191207
$756$	8.85753	0.322145
$757$	−45.8829	−1.66764	−0.833820	−	0.552036i	$-0.813851\pi$
$757$	−45.8829	−1.66764	−0.833820	+	0.552036i	$0.813851\pi$
$758$	60.4105	2.19421
$759$	97.3099	3.53212
$760$	19.2869	0.699610
$761$	−32.1926	−1.16698	−0.583491	−	0.812120i	$-0.698314\pi$
$761$	−32.1926	−1.16698	−0.583491	+	0.812120i	$0.698314\pi$
$762$	−21.0467	−0.762441
$763$	5.88357	0.213000
$764$	22.1193	0.800248
$765$	9.89089	0.357606
$766$	22.4053	0.809536
$767$	−0.440118	−0.0158917
$768$	29.5722	1.06709
$769$	25.2747	0.911428	0.455714	−	0.890126i	$-0.349384\pi$
$769$	25.2747	0.911428	0.455714	+	0.890126i	$0.349384\pi$
$770$	−12.2599	−0.441815
$771$	17.5143	0.630763
$772$	1.96747	0.0708109
$773$	−34.7941	−1.25146	−0.625729	−	0.780041i	$-0.715198\pi$
$773$	−34.7941	−1.25146	−0.625729	+	0.780041i	$0.715198\pi$
$774$	12.4595	0.447848
$775$	9.81460	0.352551
$776$	−32.2959	−1.15935
$777$	18.6459	0.668918
$778$	−67.3835	−2.41582
$779$	−49.1812	−1.76210
$780$	3.97843	0.142451
$781$	−33.0915	−1.18411
$782$	109.364	3.91086
$783$	−27.4492	−0.980956
$784$	−0.355248	−0.0126874
$785$	5.82825	0.208019
$786$	−43.3584	−1.54654
$787$	36.6781	1.30743	0.653716	−	0.756740i	$-0.273209\pi$
$787$	36.6781	1.30743	0.653716	+	0.756740i	$0.273209\pi$
$788$	2.78746	0.0992992
$789$	−57.0633	−2.03151
$790$	−13.3193	−0.473881
$791$	1.87545	0.0666833
$792$	24.1593	0.858462
$793$	0.649948	0.0230803
$794$	31.8042	1.12869
$795$	2.66670	0.0945783
$796$	−21.0911	−0.747556
$797$	−40.1620	−1.42261	−0.711305	−	0.702883i	$-0.751896\pi$
$797$	−40.1620	−1.42261	−0.711305	+	0.702883i	$0.751896\pi$
$798$	36.2192	1.28214
$799$	−50.5288	−1.78758
$800$	6.05221	0.213978
$801$	−28.9751	−1.02378
$802$	48.0720	1.69748
$803$	−36.6283	−1.29258
$804$	45.1136	1.59103
$805$	−8.30753	−0.292802
$806$	−12.9528	−0.456241
$807$	27.6606	0.973698
$808$	−13.7501	−0.483725
$809$	22.8720	0.804136	0.402068	−	0.915610i	$-0.368291\pi$
$809$	22.8720	0.804136	0.402068	+	0.915610i	$0.368291\pi$
$810$	−25.4469	−0.894112
$811$	−7.89969	−0.277396	−0.138698	−	0.990335i	$-0.544292\pi$
$811$	−7.89969	−0.277396	−0.138698	+	0.990335i	$0.544292\pi$
$812$	−30.8505	−1.08264
$813$	61.3398	2.15128
$814$	−105.377	−3.69347
$815$	−4.75865	−0.166688
$816$	−4.46822	−0.156419
$817$	−23.6550	−0.827583
$818$	−40.6433	−1.42106
$819$	0.991564	0.0346481
$820$	21.1021	0.736918
$821$	−7.09283	−0.247541	−0.123771	−	0.992311i	$-0.539499\pi$
$821$	−7.09283	−0.247541	−0.123771	+	0.992311i	$0.539499\pi$
$822$	21.0612	0.734593
$823$	22.8142	0.795254	0.397627	−	0.917547i	$-0.369834\pi$
$823$	22.8142	0.795254	0.397627	+	0.917547i	$0.369834\pi$
$824$	−25.4736	−0.887414
$825$	11.7135	0.407810
$826$	1.71919	0.0598181
$827$	−38.3592	−1.33388	−0.666941	−	0.745111i	$-0.732397\pi$
$827$	−38.3592	−1.33388	−0.666941	+	0.745111i	$0.732397\pi$
$828$	44.7144	1.55393
$829$	22.3202	0.775211	0.387606	−	0.921825i	$-0.373302\pi$
$829$	22.3202	0.775211	0.387606	+	0.921825i	$0.373302\pi$
$830$	−24.6448	−0.855434
$831$	53.5199	1.85658
$832$	−7.57438	−0.262594
$833$	−5.79806	−0.200891
$834$	14.4727	0.501147
$835$	5.90152	0.204230
$836$	−125.280	−4.33291
$837$	27.5526	0.952358
$838$	−2.67513	−0.0924107
$839$	32.7952	1.13221	0.566107	−	0.824331i	$-0.308449\pi$
$839$	32.7952	1.13221	0.566107	+	0.824331i	$0.308449\pi$
$840$	−5.68968	−0.196313
$841$	66.6050	2.29672
$842$	−76.9377	−2.65145
$843$	40.3174	1.38860
$844$	−87.8187	−3.02284
$845$	12.6621	0.435591
$846$	−33.7544	−1.16050
$847$	18.1560	0.623847
$848$	−0.436702	−0.0149964
$849$	59.5224	2.04281
$850$	13.1645	0.451538
$851$	−71.4058	−2.44776
$852$	−41.9465	−1.43706
$853$	51.6703	1.76916	0.884578	−	0.466392i	$-0.154446\pi$
$853$	51.6703	1.76916	0.884578	+	0.466392i	$0.154446\pi$
$854$	−2.53882	−0.0868767
$855$	−12.5444	−0.429008
$856$	−36.4806	−1.24688
$857$	−38.0123	−1.29847	−0.649237	−	0.760586i	$-0.724912\pi$
$857$	−38.0123	−1.29847	−0.649237	+	0.760586i	$0.724912\pi$
$858$	−15.4588	−0.527753
$859$	−26.2921	−0.897075	−0.448537	−	0.893764i	$-0.648055\pi$
$859$	−26.2921	−0.897075	−0.448537	+	0.893764i	$0.648055\pi$
$860$	10.1496	0.346099
$861$	14.5086	0.494451
$862$	−78.0365	−2.65793
$863$	32.0822	1.09209	0.546046	−	0.837755i	$-0.316132\pi$
$863$	32.0822	1.09209	0.546046	+	0.837755i	$0.316132\pi$
$864$	16.9904	0.578026
$865$	−14.7627	−0.501948
$866$	78.1660	2.65619
$867$	−36.0484	−1.22427
$868$	30.9667	1.05108
$869$	31.6756	1.07452
$870$	48.1596	1.63276
$871$	−3.83117	−0.129814
$872$	−15.4315	−0.522576
$873$	21.0055	0.710929
$874$	−138.704	−4.69173
$875$	−1.00000	−0.0338062
$876$	−46.4298	−1.56872
$877$	12.9735	0.438083	0.219042	−	0.975715i	$-0.429707\pi$
$877$	12.9735	0.438083	0.219042	+	0.975715i	$0.429707\pi$
$878$	78.3206	2.64319
$879$	31.7722	1.07165
$880$	−1.91821	−0.0646627
$881$	−44.8233	−1.51014	−0.755068	−	0.655647i	$-0.772396\pi$
$881$	−44.8233	−1.51014	−0.755068	+	0.655647i	$0.772396\pi$
$882$	−3.87324	−0.130419
$883$	5.88140	0.197925	0.0989625	−	0.995091i	$-0.468448\pi$
$883$	5.88140	0.197925	0.0989625	+	0.995091i	$0.468448\pi$
$884$	−10.6334	−0.357641
$885$	−1.64256	−0.0552142
$886$	16.8765	0.566978
$887$	36.5898	1.22857	0.614283	−	0.789086i	$-0.289445\pi$
$887$	36.5898	1.22857	0.614283	+	0.789086i	$0.289445\pi$
$888$	−48.9046	−1.64113
$889$	−4.27308	−0.143315
$890$	−38.5650	−1.29270
$891$	60.5169	2.02739
$892$	78.0693	2.61395
$893$	64.0844	2.14450
$894$	−106.504	−3.56202
$895$	−11.3450	−0.379222
$896$	17.4826	0.584052
$897$	−10.4752	−0.349756
$898$	−18.2032	−0.607447
$899$	−95.9651	−3.20061
$900$	5.38239	0.179413
$901$	−7.12748	−0.237451
$902$	−81.9953	−2.73014
$903$	6.97828	0.232223
$904$	−4.91894	−0.163602
$905$	16.3749	0.544320
$906$	−2.58773	−0.0859716
$907$	−5.70755	−0.189516	−0.0947580	−	0.995500i	$-0.530208\pi$
$907$	−5.70755	−0.189516	−0.0947580	+	0.995500i	$0.530208\pi$
$908$	−28.1830	−0.935286
$909$	8.94315	0.296626
$910$	1.31974	0.0437491
$911$	17.9656	0.595228	0.297614	−	0.954686i	$-0.403809\pi$
$911$	17.9656	0.595228	0.297614	+	0.954686i	$0.403809\pi$
$912$	5.66694	0.187651
$913$	58.6095	1.93969
$914$	−37.8458	−1.25183
$915$	2.42567	0.0801903
$916$	−3.15517	−0.104250
$917$	−8.80299	−0.290700
$918$	36.9568	1.21975
$919$	51.0734	1.68476	0.842379	−	0.538886i	$-0.181155\pi$
$919$	51.0734	1.68476	0.842379	+	0.538886i	$0.181155\pi$
$920$	21.7891	0.718364
$921$	25.1778	0.829636
$922$	−47.8816	−1.57690
$923$	3.56221	0.117252
$924$	36.9579	1.21583
$925$	−8.59532	−0.282612
$926$	−21.8145	−0.716869
$927$	16.5682	0.544172
$928$	−59.1772	−1.94259
$929$	−0.685073	−0.0224765	−0.0112383	−	0.999937i	$-0.503577\pi$
$929$	−0.685073	−0.0224765	−0.0112383	+	0.999937i	$0.503577\pi$
$930$	−48.3410	−1.58516
$931$	7.35353	0.241002
$932$	−39.0494	−1.27911
$933$	66.0792	2.16334
$934$	−5.01171	−0.163988
$935$	−31.3074	−1.02386
$936$	−2.60068	−0.0850060
$937$	−15.9446	−0.520886	−0.260443	−	0.965489i	$-0.583869\pi$
$937$	−15.9446	−0.520886	−0.260443	+	0.965489i	$0.583869\pi$
$938$	14.9653	0.488634
$939$	−65.6710	−2.14309
$940$	−27.4966	−0.896840
$941$	−27.1903	−0.886379	−0.443189	−	0.896428i	$-0.646153\pi$
$941$	−27.1903	−0.886379	−0.443189	+	0.896428i	$0.646153\pi$
$942$	−28.7065	−0.935309
$943$	−55.5617	−1.80934
$944$	0.268988	0.00875480
$945$	−2.80731	−0.0913217
$946$	−39.4378	−1.28223
$947$	56.5950	1.83909	0.919545	−	0.392985i	$-0.128558\pi$
$947$	56.5950	1.83909	0.919545	+	0.392985i	$0.128558\pi$
$948$	40.1518	1.30407
$949$	3.94294	0.127993
$950$	−16.6962	−0.541696
$951$	−43.3562	−1.40592
$952$	15.2072	0.492868
$953$	26.4409	0.856506	0.428253	−	0.903659i	$-0.359129\pi$
$953$	26.4409	0.856506	0.428253	+	0.903659i	$0.359129\pi$
$954$	−4.76133	−0.154154
$955$	−7.01050	−0.226854
$956$	−92.1274	−2.97961
$957$	−114.532	−3.70228
$958$	−42.0064	−1.35717
$959$	4.27602	0.138080
$960$	−28.2684	−0.912357
$961$	65.3265	2.10731
$962$	11.3436	0.365733
$963$	23.7273	0.764601
$964$	−53.8173	−1.73334
$965$	−0.623572	−0.0200735
$966$	40.9180	1.31652
$967$	−1.33851	−0.0430436	−0.0215218	−	0.999768i	$-0.506851\pi$
$967$	−1.33851	−0.0430436	−0.0215218	+	0.999768i	$0.506851\pi$
$968$	−47.6197	−1.53056
$969$	92.4910	2.97124
$970$	27.9577	0.897668
$971$	36.0972	1.15841	0.579207	−	0.815180i	$-0.303362\pi$
$971$	36.0972	1.15841	0.579207	+	0.815180i	$0.303362\pi$
$972$	50.1382	1.60818
$973$	2.93836	0.0941996
$974$	−26.8910	−0.861642
$975$	−1.26092	−0.0403819
$976$	−0.397230	−0.0127150
$977$	−25.6477	−0.820543	−0.410271	−	0.911964i	$-0.634566\pi$
$977$	−25.6477	−0.820543	−0.410271	+	0.911964i	$0.634566\pi$
$978$	23.4383	0.749474
$979$	91.7140	2.93119
$980$	−3.15517	−0.100788
$981$	10.0368	0.320449
$982$	−18.6301	−0.594509
$983$	−5.37904	−0.171565	−0.0857824	−	0.996314i	$-0.527339\pi$
$983$	−5.37904	−0.171565	−0.0857824	+	0.996314i	$0.527339\pi$
$984$	−38.0532	−1.21309
$985$	−0.883459	−0.0281493
$986$	−128.719	−4.09926
$987$	−18.9050	−0.601754
$988$	13.4861	0.429050
$989$	−26.7238	−0.849768
$990$	−20.9141	−0.664692
$991$	4.53190	0.143960	0.0719802	−	0.997406i	$-0.477068\pi$
$991$	4.53190	0.143960	0.0719802	+	0.997406i	$0.477068\pi$
$992$	59.4001	1.88595
$993$	−44.8712	−1.42394
$994$	−13.9147	−0.441347
$995$	6.68463	0.211917
$996$	74.2930	2.35406
$997$	34.2165	1.08365	0.541824	−	0.840492i	$-0.317734\pi$
$997$	34.2165	1.08365	0.541824	+	0.840492i	$0.317734\pi$
$998$	47.0715	1.49002
$999$	−24.1297	−0.763430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.9	✓	68	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27050 q^{2} -2.16931 q^{3} +3.15517 q^{4} -1.00000 q^{5} +4.92541 q^{6} +1.00000 q^{7} -2.62281 q^{8} +1.70590 q^{9} +O(q^{10})\)	\(q-2.27050 q^{2} -2.16931 q^{3} +3.15517 q^{4} -1.00000 q^{5} +4.92541 q^{6} +1.00000 q^{7} -2.62281 q^{8} +1.70590 q^{9} +2.27050 q^{10} -5.39963 q^{11} -6.84453 q^{12} +0.581257 q^{13} -2.27050 q^{14} +2.16931 q^{15} -0.355248 q^{16} -5.79806 q^{17} -3.87324 q^{18} +7.35353 q^{19} -3.15517 q^{20} -2.16931 q^{21} +12.2599 q^{22} +8.30753 q^{23} +5.68968 q^{24} +1.00000 q^{25} -1.31974 q^{26} +2.80731 q^{27} +3.15517 q^{28} -9.77778 q^{29} -4.92541 q^{30} +9.81460 q^{31} +6.05221 q^{32} +11.7135 q^{33} +13.1645 q^{34} -1.00000 q^{35} +5.38239 q^{36} -8.59532 q^{37} -16.6962 q^{38} -1.26092 q^{39} +2.62281 q^{40} -6.68811 q^{41} +4.92541 q^{42} -3.21682 q^{43} -17.0367 q^{44} -1.70590 q^{45} -18.8622 q^{46} +8.71478 q^{47} +0.770642 q^{48} +1.00000 q^{49} -2.27050 q^{50} +12.5778 q^{51} +1.83396 q^{52} +1.22929 q^{53} -6.37399 q^{54} +5.39963 q^{55} -2.62281 q^{56} -15.9521 q^{57} +22.2004 q^{58} -0.757184 q^{59} +6.84453 q^{60} +1.11818 q^{61} -22.2841 q^{62} +1.70590 q^{63} -13.0310 q^{64} -0.581257 q^{65} -26.5954 q^{66} -6.59119 q^{67} -18.2938 q^{68} -18.0216 q^{69} +2.27050 q^{70} +6.12847 q^{71} -4.47424 q^{72} +6.78348 q^{73} +19.5157 q^{74} -2.16931 q^{75} +23.2016 q^{76} -5.39963 q^{77} +2.86293 q^{78} -5.86626 q^{79} +0.355248 q^{80} -11.2076 q^{81} +15.1854 q^{82} -10.8544 q^{83} -6.84453 q^{84} +5.79806 q^{85} +7.30379 q^{86} +21.2110 q^{87} +14.1622 q^{88} -16.9852 q^{89} +3.87324 q^{90} +0.581257 q^{91} +26.2117 q^{92} -21.2909 q^{93} -19.7869 q^{94} -7.35353 q^{95} -13.1291 q^{96} +12.3135 q^{97} -2.27050 q^{98} -9.21121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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