LMFDB - Embedded newform 4003.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} +O(q^{10})$	\(q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} -2.86577 q^{10} -0.0380846 q^{11} +7.64589 q^{12} -4.40285 q^{13} +9.62596 q^{14} +2.35564 q^{15} +3.10429 q^{16} +7.19381 q^{17} -2.29842 q^{18} +1.70361 q^{19} +4.55912 q^{20} -7.91249 q^{21} +0.0920891 q^{22} +2.13708 q^{23} -8.87581 q^{24} -3.59537 q^{25} +10.6462 q^{26} -4.07350 q^{27} -15.3139 q^{28} -1.31015 q^{29} -5.69599 q^{30} +1.94251 q^{31} +1.42498 q^{32} -0.0756967 q^{33} -17.3948 q^{34} -4.71809 q^{35} +3.65654 q^{36} -3.58057 q^{37} -4.11936 q^{38} -8.75110 q^{39} -5.29250 q^{40} +9.66585 q^{41} +19.1325 q^{42} +6.38812 q^{43} -0.146504 q^{44} +1.12655 q^{45} -5.16748 q^{46} -9.04545 q^{47} +6.17007 q^{48} +8.84782 q^{49} +8.69366 q^{50} +14.2984 q^{51} -16.9369 q^{52} -8.91888 q^{53} +9.84979 q^{54} -0.0451368 q^{55} +17.7772 q^{56} +3.38609 q^{57} +3.16795 q^{58} +14.0599 q^{59} +9.06170 q^{60} +3.91881 q^{61} -4.69703 q^{62} -3.78404 q^{63} -9.65421 q^{64} -5.21814 q^{65} +0.183036 q^{66} +5.52385 q^{67} +27.6732 q^{68} +4.24764 q^{69} +11.4084 q^{70} -9.15115 q^{71} -4.24473 q^{72} -1.82962 q^{73} +8.65788 q^{74} -7.14614 q^{75} +6.55346 q^{76} +0.151612 q^{77} +21.1603 q^{78} -11.8647 q^{79} +3.67911 q^{80} -10.9481 q^{81} -23.3722 q^{82} -7.24574 q^{83} -30.4378 q^{84} +8.52591 q^{85} -15.4466 q^{86} -2.60404 q^{87} +0.170070 q^{88} +2.78275 q^{89} -2.72402 q^{90} +17.5275 q^{91} +8.22091 q^{92} +3.86094 q^{93} +21.8720 q^{94} +2.01907 q^{95} +2.83229 q^{96} -8.45647 q^{97} -21.3942 q^{98} -0.0362009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.41802	−1.70980	−0.854898	−	0.518796i	$-0.826380\pi$
$2$	−2.41802	−1.70980	−0.854898	+	0.518796i	$0.826380\pi$
$3$	1.98760	1.14754	0.573770	−	0.819017i	$-0.305480\pi$
$3$	1.98760	1.14754	0.573770	+	0.819017i	$0.305480\pi$
$4$	3.84680	1.92340
$5$	1.18517	0.530025	0.265013	−	0.964245i	$-0.414624\pi$
$5$	1.18517	0.530025	0.265013	+	0.964245i	$0.414624\pi$
$6$	−4.80604	−1.96206
$7$	−3.98093	−1.50465	−0.752326	−	0.658792i	$-0.771068\pi$
$7$	−3.98093	−1.50465	−0.752326	+	0.658792i	$0.771068\pi$
$8$	−4.46560	−1.57883
$9$	0.950540	0.316847
$10$	−2.86577	−0.906235
$11$	−0.0380846	−0.0114829	−0.00574146	−	0.999984i	$-0.501828\pi$
$11$	−0.0380846	−0.0114829	−0.00574146	+	0.999984i	$0.501828\pi$
$12$	7.64589	2.20718
$13$	−4.40285	−1.22113	−0.610566	−	0.791965i	$-0.709058\pi$
$13$	−4.40285	−1.22113	−0.610566	+	0.791965i	$0.709058\pi$
$14$	9.62596	2.57265
$15$	2.35564	0.608225
$16$	3.10429	0.776072
$17$	7.19381	1.74476	0.872378	−	0.488832i	$-0.162577\pi$
$17$	7.19381	1.74476	0.872378	+	0.488832i	$0.162577\pi$
$18$	−2.29842	−0.541743
$19$	1.70361	0.390835	0.195418	−	0.980720i	$-0.437394\pi$
$19$	1.70361	0.390835	0.195418	+	0.980720i	$0.437394\pi$
$20$	4.55912	1.01945
$21$	−7.91249	−1.72665
$22$	0.0920891	0.0196335
$23$	2.13708	0.445611	0.222805	−	0.974863i	$-0.428479\pi$
$23$	2.13708	0.445611	0.222805	+	0.974863i	$0.428479\pi$
$24$	−8.87581	−1.81177
$25$	−3.59537	−0.719073
$26$	10.6462	2.08789
$27$	−4.07350	−0.783945
$28$	−15.3139	−2.89405
$29$	−1.31015	−0.243288	−0.121644	−	0.992574i	$-0.538817\pi$
$29$	−1.31015	−0.243288	−0.121644	+	0.992574i	$0.538817\pi$
$30$	−5.69599	−1.03994
$31$	1.94251	0.348886	0.174443	−	0.984667i	$-0.444188\pi$
$31$	1.94251	0.348886	0.174443	+	0.984667i	$0.444188\pi$
$32$	1.42498	0.251904
$33$	−0.0756967	−0.0131771
$34$	−17.3948	−2.98318
$35$	−4.71809	−0.797503
$36$	3.65654	0.609423
$37$	−3.58057	−0.588642	−0.294321	−	0.955707i	$-0.595093\pi$
$37$	−3.58057	−0.588642	−0.294321	+	0.955707i	$0.595093\pi$
$38$	−4.11936	−0.668249
$39$	−8.75110	−1.40130
$40$	−5.29250	−0.836818
$41$	9.66585	1.50955	0.754776	−	0.655983i	$-0.227746\pi$
$41$	9.66585	1.50955	0.754776	+	0.655983i	$0.227746\pi$
$42$	19.1325	2.95221
$43$	6.38812	0.974178	0.487089	−	0.873352i	$-0.338059\pi$
$43$	6.38812	0.974178	0.487089	+	0.873352i	$0.338059\pi$
$44$	−0.146504	−0.0220863
$45$	1.12655	0.167937
$46$	−5.16748	−0.761904
$47$	−9.04545	−1.31941	−0.659707	−	0.751523i	$-0.729320\pi$
$47$	−9.04545	−1.31941	−0.659707	+	0.751523i	$0.729320\pi$
$48$	6.17007	0.890573
$49$	8.84782	1.26397
$50$	8.69366	1.22947
$51$	14.2984	2.00218
$52$	−16.9369	−2.34873
$53$	−8.91888	−1.22510	−0.612552	−	0.790431i	$-0.709857\pi$
$53$	−8.91888	−1.22510	−0.612552	+	0.790431i	$0.709857\pi$
$54$	9.84979	1.34039
$55$	−0.0451368	−0.00608624
$56$	17.7772	2.37558
$57$	3.38609	0.448499
$58$	3.16795	0.415973
$59$	14.0599	1.83045	0.915223	−	0.402948i	$-0.132014\pi$
$59$	14.0599	1.83045	0.915223	+	0.402948i	$0.132014\pi$
$60$	9.06170	1.16986
$61$	3.91881	0.501753	0.250876	−	0.968019i	$-0.419281\pi$
$61$	3.91881	0.501753	0.250876	+	0.968019i	$0.419281\pi$
$62$	−4.69703	−0.596524
$63$	−3.78404	−0.476744
$64$	−9.65421	−1.20678
$65$	−5.21814	−0.647230
$66$	0.183036	0.0225302
$67$	5.52385	0.674846	0.337423	−	0.941353i	$-0.390445\pi$
$67$	5.52385	0.674846	0.337423	+	0.941353i	$0.390445\pi$
$68$	27.6732	3.35587
$69$	4.24764	0.511356
$70$	11.4084	1.36357
$71$	−9.15115	−1.08604	−0.543021	−	0.839719i	$-0.682720\pi$
$71$	−9.15115	−1.08604	−0.543021	+	0.839719i	$0.682720\pi$
$72$	−4.24473	−0.500246
$73$	−1.82962	−0.214140	−0.107070	−	0.994251i	$-0.534147\pi$
$73$	−1.82962	−0.214140	−0.107070	+	0.994251i	$0.534147\pi$
$74$	8.65788	1.00646
$75$	−7.14614	−0.825165
$76$	6.55346	0.751733
$77$	0.151612	0.0172778
$78$	21.1603	2.39593
$79$	−11.8647	−1.33488	−0.667441	−	0.744663i	$-0.732610\pi$
$79$	−11.8647	−1.33488	−0.667441	+	0.744663i	$0.732610\pi$
$80$	3.67911	0.411337
$81$	−10.9481	−1.21645
$82$	−23.3722	−2.58103
$83$	−7.24574	−0.795324	−0.397662	−	0.917532i	$-0.630178\pi$
$83$	−7.24574	−0.795324	−0.397662	+	0.917532i	$0.630178\pi$
$84$	−30.4378	−3.32103
$85$	8.52591	0.924765
$86$	−15.4466	−1.66565
$87$	−2.60404	−0.279183
$88$	0.170070	0.0181296
$89$	2.78275	0.294971	0.147486	−	0.989064i	$-0.452882\pi$
$89$	2.78275	0.294971	0.147486	+	0.989064i	$0.452882\pi$
$90$	−2.72402	−0.287137
$91$	17.5275	1.83738
$92$	8.22091	0.857089
$93$	3.86094	0.400360
$94$	21.8720	2.25593
$95$	2.01907	0.207152
$96$	2.83229	0.289070
$97$	−8.45647	−0.858624	−0.429312	−	0.903156i	$-0.641244\pi$
$97$	−8.45647	−0.858624	−0.429312	+	0.903156i	$0.641244\pi$
$98$	−21.3942	−2.16114
$99$	−0.0362009	−0.00363833
$100$	−13.8307	−1.38307
$101$	1.57357	0.156576	0.0782879	−	0.996931i	$-0.475055\pi$
$101$	1.57357	0.156576	0.0782879	+	0.996931i	$0.475055\pi$
$102$	−34.5738	−3.42331
$103$	−5.21843	−0.514187	−0.257093	−	0.966387i	$-0.582765\pi$
$103$	−5.21843	−0.514187	−0.257093	+	0.966387i	$0.582765\pi$
$104$	19.6614	1.92796
$105$	−9.37766	−0.915166
$106$	21.5660	2.09468
$107$	−2.01408	−0.194709	−0.0973544	−	0.995250i	$-0.531038\pi$
$107$	−2.01408	−0.194709	−0.0973544	+	0.995250i	$0.531038\pi$
$108$	−15.6699	−1.50784
$109$	−9.79023	−0.937734	−0.468867	−	0.883269i	$-0.655338\pi$
$109$	−9.79023	−0.937734	−0.468867	+	0.883269i	$0.655338\pi$
$110$	0.109141	0.0104062
$111$	−7.11673	−0.675490
$112$	−12.3580	−1.16772
$113$	−8.42747	−0.792789	−0.396395	−	0.918080i	$-0.629739\pi$
$113$	−8.42747	−0.792789	−0.396395	+	0.918080i	$0.629739\pi$
$114$	−8.18763	−0.766841
$115$	2.53280	0.236185
$116$	−5.03987	−0.467940
$117$	−4.18509	−0.386912
$118$	−33.9971	−3.12969
$119$	−28.6381	−2.62525
$120$	−10.5194	−0.960282
$121$	−10.9985	−0.999868
$122$	−9.47576	−0.857895
$123$	19.2118	1.73227
$124$	7.47247	0.671048
$125$	−10.1870	−0.911152
$126$	9.14986	0.815134
$127$	−19.4601	−1.72681	−0.863403	−	0.504515i	$-0.831671\pi$
$127$	−19.4601	−1.72681	−0.863403	+	0.504515i	$0.831671\pi$
$128$	20.4941	1.81144
$129$	12.6970	1.11791
$130$	12.6175	1.10663
$131$	−2.40274	−0.209928	−0.104964	−	0.994476i	$-0.533473\pi$
$131$	−2.40274	−0.209928	−0.104964	+	0.994476i	$0.533473\pi$
$132$	−0.291190	−0.0253449
$133$	−6.78196	−0.588071
$134$	−13.3568	−1.15385
$135$	−4.82780	−0.415511
$136$	−32.1247	−2.75467
$137$	−2.09096	−0.178642	−0.0893212	−	0.996003i	$-0.528470\pi$
$137$	−2.09096	−0.178642	−0.0893212	+	0.996003i	$0.528470\pi$
$138$	−10.2709	−0.874315
$139$	3.51975	0.298541	0.149271	−	0.988796i	$-0.452307\pi$
$139$	3.51975	0.298541	0.149271	+	0.988796i	$0.452307\pi$
$140$	−18.1496	−1.53392
$141$	−17.9787	−1.51408
$142$	22.1276	1.85691
$143$	0.167681	0.0140222
$144$	2.95075	0.245896
$145$	−1.55275	−0.128949
$146$	4.42404	0.366136
$147$	17.5859	1.45046
$148$	−13.7737	−1.13219
$149$	−12.9329	−1.05950	−0.529752	−	0.848153i	$-0.677715\pi$
$149$	−12.9329	−1.05950	−0.529752	+	0.848153i	$0.677715\pi$
$150$	17.2795	1.41086
$151$	5.82111	0.473715	0.236858	−	0.971544i	$-0.423882\pi$
$151$	5.82111	0.473715	0.236858	+	0.971544i	$0.423882\pi$
$152$	−7.60765	−0.617062
$153$	6.83801	0.552820
$154$	−0.366600	−0.0295415
$155$	2.30221	0.184918
$156$	−33.6637	−2.69526
$157$	−18.3839	−1.46720	−0.733599	−	0.679582i	$-0.762161\pi$
$157$	−18.3839	−1.46720	−0.733599	+	0.679582i	$0.762161\pi$
$158$	28.6890	2.28238
$159$	−17.7271	−1.40585
$160$	1.68885	0.133515
$161$	−8.50755	−0.670489
$162$	26.4727	2.07989
$163$	4.44173	0.347903	0.173952	−	0.984754i	$-0.444346\pi$
$163$	4.44173	0.347903	0.173952	+	0.984754i	$0.444346\pi$
$164$	37.1826	2.90347
$165$	−0.0897137	−0.00698420
$166$	17.5203	1.35984
$167$	−18.7029	−1.44728	−0.723639	−	0.690179i	$-0.757532\pi$
$167$	−18.7029	−1.44728	−0.723639	+	0.690179i	$0.757532\pi$
$168$	35.3340	2.72608
$169$	6.38512	0.491163
$170$	−20.6158	−1.58116
$171$	1.61935	0.123835
$172$	24.5738	1.87374
$173$	1.92716	0.146519	0.0732596	−	0.997313i	$-0.476660\pi$
$173$	1.92716	0.146519	0.0732596	+	0.997313i	$0.476660\pi$
$174$	6.29661	0.477345
$175$	14.3129	1.08195
$176$	−0.118225	−0.00891157
$177$	27.9454	2.10051
$178$	−6.72875	−0.504341
$179$	−23.8105	−1.77968	−0.889841	−	0.456271i	$-0.849185\pi$
$179$	−23.8105	−1.77968	−0.889841	+	0.456271i	$0.849185\pi$
$180$	4.33363	0.323010
$181$	−13.1009	−0.973780	−0.486890	−	0.873463i	$-0.661869\pi$
$181$	−13.1009	−0.973780	−0.486890	+	0.873463i	$0.661869\pi$
$182$	−42.3817	−3.14154
$183$	7.78902	0.575781
$184$	−9.54332	−0.703543
$185$	−4.24359	−0.311995
$186$	−9.33580	−0.684534
$187$	−0.273973	−0.0200349
$188$	−34.7961	−2.53776
$189$	16.2163	1.17956
$190$	−4.88215	−0.354188
$191$	2.97286	0.215108	0.107554	−	0.994199i	$-0.465698\pi$
$191$	2.97286	0.215108	0.107554	+	0.994199i	$0.465698\pi$
$192$	−19.1887	−1.38482
$193$	17.6884	1.27324	0.636619	−	0.771178i	$-0.280332\pi$
$193$	17.6884	1.27324	0.636619	+	0.771178i	$0.280332\pi$
$194$	20.4479	1.46807
$195$	−10.3716	−0.742722
$196$	34.0358	2.43113
$197$	3.95275	0.281622	0.140811	−	0.990037i	$-0.455029\pi$
$197$	3.95275	0.281622	0.140811	+	0.990037i	$0.455029\pi$
$198$	0.0875344	0.00622080
$199$	−25.4381	−1.80326	−0.901629	−	0.432511i	$-0.857628\pi$
$199$	−25.4381	−1.80326	−0.901629	+	0.432511i	$0.857628\pi$
$200$	16.0555	1.13529
$201$	10.9792	0.774413
$202$	−3.80491	−0.267713
$203$	5.21560	0.366064
$204$	55.0031	3.85099
$205$	11.4557	0.800100
$206$	12.6182	0.879155
$207$	2.03138	0.141190
$208$	−13.6677	−0.947686
$209$	−0.0648813	−0.00448793
$210$	22.6753	1.56475
$211$	1.61604	0.111253	0.0556265	−	0.998452i	$-0.482284\pi$
$211$	1.61604	0.111253	0.0556265	+	0.998452i	$0.482284\pi$
$212$	−34.3092	−2.35636
$213$	−18.1888	−1.24628
$214$	4.87008	0.332912
$215$	7.57102	0.516339
$216$	18.1906	1.23771
$217$	−7.73302	−0.524952
$218$	23.6729	1.60333
$219$	−3.63654	−0.245734
$220$	−0.173632	−0.0117063
$221$	−31.6733	−2.13058
$222$	17.2084	1.15495
$223$	16.3278	1.09339	0.546696	−	0.837331i	$-0.315885\pi$
$223$	16.3278	1.09339	0.546696	+	0.837331i	$0.315885\pi$
$224$	−5.67276	−0.379028
$225$	−3.41754	−0.227836
$226$	20.3778	1.35551
$227$	15.8393	1.05129	0.525645	−	0.850704i	$-0.323824\pi$
$227$	15.8393	1.05129	0.525645	+	0.850704i	$0.323824\pi$
$228$	13.0256	0.862643
$229$	23.6857	1.56520	0.782598	−	0.622527i	$-0.213894\pi$
$229$	23.6857	1.56520	0.782598	+	0.622527i	$0.213894\pi$
$230$	−6.12436	−0.403828
$231$	0.301344	0.0198270
$232$	5.85059	0.384110
$233$	−2.04580	−0.134025	−0.0670125	−	0.997752i	$-0.521347\pi$
$233$	−2.04580	−0.134025	−0.0670125	+	0.997752i	$0.521347\pi$
$234$	10.1196	0.661540
$235$	−10.7204	−0.699323
$236$	54.0857	3.52068
$237$	−23.5822	−1.53183
$238$	69.2474	4.48864
$239$	−8.98564	−0.581232	−0.290616	−	0.956840i	$-0.593860\pi$
$239$	−8.98564	−0.581232	−0.290616	+	0.956840i	$0.593860\pi$
$240$	7.31259	0.472026
$241$	−2.76429	−0.178063	−0.0890317	−	0.996029i	$-0.528377\pi$
$241$	−2.76429	−0.178063	−0.0890317	+	0.996029i	$0.528377\pi$
$242$	26.5947	1.70957
$243$	−9.53990	−0.611985
$244$	15.0749	0.965072
$245$	10.4862	0.669938
$246$	−46.4545	−2.96183
$247$	−7.50075	−0.477261
$248$	−8.67449	−0.550831
$249$	−14.4016	−0.912665
$250$	24.6323	1.55788
$251$	−20.1402	−1.27124	−0.635619	−	0.772003i	$-0.719255\pi$
$251$	−20.1402	−1.27124	−0.635619	+	0.772003i	$0.719255\pi$
$252$	−14.5564	−0.916970
$253$	−0.0813896	−0.00511692
$254$	47.0549	2.95249
$255$	16.9461	1.06120
$256$	−30.2466	−1.89041
$257$	−20.4148	−1.27344	−0.636721	−	0.771094i	$-0.719710\pi$
$257$	−20.4148	−1.27344	−0.636721	+	0.771094i	$0.719710\pi$
$258$	−30.7015	−1.91139
$259$	14.2540	0.885701
$260$	−20.0731	−1.24488
$261$	−1.24535	−0.0770850
$262$	5.80986	0.358935
$263$	−28.8916	−1.78153	−0.890766	−	0.454462i	$-0.849832\pi$
$263$	−28.8916	−1.78153	−0.890766	+	0.454462i	$0.849832\pi$
$264$	0.338031	0.0208044
$265$	−10.5704	−0.649335
$266$	16.3989	1.00548
$267$	5.53099	0.338491
$268$	21.2492	1.29800
$269$	26.7773	1.63264	0.816321	−	0.577599i	$-0.196010\pi$
$269$	26.7773	1.63264	0.816321	+	0.577599i	$0.196010\pi$
$270$	11.6737	0.710438
$271$	23.0889	1.40255	0.701275	−	0.712891i	$-0.252615\pi$
$271$	23.0889	1.40255	0.701275	+	0.712891i	$0.252615\pi$
$272$	22.3317	1.35406
$273$	34.8375	2.10846
$274$	5.05596	0.305442
$275$	0.136928	0.00825707
$276$	16.3398	0.983543
$277$	9.19091	0.552229	0.276114	−	0.961125i	$-0.410953\pi$
$277$	9.19091	0.552229	0.276114	+	0.961125i	$0.410953\pi$
$278$	−8.51081	−0.510444
$279$	1.84644	0.110543
$280$	21.0691	1.25912
$281$	−15.4595	−0.922237	−0.461119	−	0.887338i	$-0.652552\pi$
$281$	−15.4595	−0.922237	−0.461119	+	0.887338i	$0.652552\pi$
$282$	43.4728	2.58877
$283$	13.9620	0.829952	0.414976	−	0.909832i	$-0.363790\pi$
$283$	13.9620	0.829952	0.414976	+	0.909832i	$0.363790\pi$
$284$	−35.2027	−2.08889
$285$	4.01310	0.237716
$286$	−0.405455	−0.0239750
$287$	−38.4791	−2.27135
$288$	1.35450	0.0798149
$289$	34.7510	2.04417
$290$	3.75457	0.220476
$291$	−16.8080	−0.985305
$292$	−7.03817	−0.411878
$293$	−10.1841	−0.594963	−0.297482	−	0.954728i	$-0.596147\pi$
$293$	−10.1841	−0.594963	−0.297482	+	0.954728i	$0.596147\pi$
$294$	−42.5230	−2.47999
$295$	16.6634	0.970182
$296$	15.9894	0.929364
$297$	0.155137	0.00900199
$298$	31.2719	1.81153
$299$	−9.40923	−0.544150
$300$	−27.4898	−1.58712
$301$	−25.4307	−1.46580
$302$	−14.0755	−0.809957
$303$	3.12762	0.179677
$304$	5.28850	0.303316
$305$	4.64447	0.265941
$306$	−16.5344	−0.945210
$307$	−0.715150	−0.0408158	−0.0204079	−	0.999792i	$-0.506496\pi$
$307$	−0.715150	−0.0408158	−0.0204079	+	0.999792i	$0.506496\pi$
$308$	0.583222	0.0332321
$309$	−10.3721	−0.590050
$310$	−5.56679	−0.316172
$311$	−19.8097	−1.12330	−0.561652	−	0.827373i	$-0.689834\pi$
$311$	−19.8097	−1.12330	−0.561652	+	0.827373i	$0.689834\pi$
$312$	39.0789	2.21241
$313$	−24.6558	−1.39363	−0.696815	−	0.717251i	$-0.745400\pi$
$313$	−24.6558	−1.39363	−0.696815	+	0.717251i	$0.745400\pi$
$314$	44.4527	2.50861
$315$	−4.48473	−0.252686
$316$	−45.6411	−2.56751
$317$	15.7692	0.885689	0.442845	−	0.896598i	$-0.353969\pi$
$317$	15.7692	0.885689	0.442845	+	0.896598i	$0.353969\pi$
$318$	42.8645	2.40372
$319$	0.0498963	0.00279366
$320$	−11.4419	−0.639621
$321$	−4.00318	−0.223436
$322$	20.5714	1.14640
$323$	12.2555	0.681912
$324$	−42.1152	−2.33973
$325$	15.8299	0.878083
$326$	−10.7402	−0.594843
$327$	−19.4590	−1.07609
$328$	−43.1638	−2.38332
$329$	36.0093	1.98526
$330$	0.216929	0.0119416
$331$	21.9236	1.20503	0.602515	−	0.798108i	$-0.294165\pi$
$331$	21.9236	1.20503	0.602515	+	0.798108i	$0.294165\pi$
$332$	−27.8729	−1.52973
$333$	−3.40348	−0.186509
$334$	45.2240	2.47455
$335$	6.54672	0.357685
$336$	−24.5626	−1.34000
$337$	12.2221	0.665779	0.332889	−	0.942966i	$-0.391976\pi$
$337$	12.2221	0.665779	0.332889	+	0.942966i	$0.391976\pi$
$338$	−15.4393	−0.839788
$339$	−16.7504	−0.909757
$340$	32.7975	1.77869
$341$	−0.0739798	−0.00400623
$342$	−3.91562	−0.211732
$343$	−7.35606	−0.397190
$344$	−28.5268	−1.53806
$345$	5.03419	0.271032
$346$	−4.65990	−0.250518
$347$	16.0200	0.860000	0.430000	−	0.902829i	$-0.358514\pi$
$347$	16.0200	0.860000	0.430000	+	0.902829i	$0.358514\pi$
$348$	−10.0172	−0.536980
$349$	21.0489	1.12672	0.563362	−	0.826210i	$-0.309508\pi$
$349$	21.0489	1.12672	0.563362	+	0.826210i	$0.309508\pi$
$350$	−34.6089	−1.84992
$351$	17.9350	0.957301
$352$	−0.0542699	−0.00289259
$353$	−20.1480	−1.07237	−0.536185	−	0.844101i	$-0.680135\pi$
$353$	−20.1480	−1.07237	−0.536185	+	0.844101i	$0.680135\pi$
$354$	−67.5726	−3.59144
$355$	−10.8457	−0.575629
$356$	10.7047	0.567348
$357$	−56.9210	−3.01258
$358$	57.5742	3.04289
$359$	29.8810	1.57706	0.788529	−	0.614998i	$-0.210843\pi$
$359$	29.8810	1.57706	0.788529	+	0.614998i	$0.210843\pi$
$360$	−5.03074	−0.265143
$361$	−16.0977	−0.847248
$362$	31.6781	1.66496
$363$	−21.8607	−1.14739
$364$	67.4247	3.53401
$365$	−2.16841	−0.113500
$366$	−18.8340	−0.984468
$367$	4.29453	0.224173	0.112086	−	0.993698i	$-0.464247\pi$
$367$	4.29453	0.224173	0.112086	+	0.993698i	$0.464247\pi$
$368$	6.63409	0.345826
$369$	9.18778	0.478297
$370$	10.2611	0.533448
$371$	35.5055	1.84335
$372$	14.8523	0.770054
$373$	28.1049	1.45522	0.727608	−	0.685993i	$-0.240632\pi$
$373$	28.1049	1.45522	0.727608	+	0.685993i	$0.240632\pi$
$374$	0.662472	0.0342556
$375$	−20.2476	−1.04558
$376$	40.3933	2.08313
$377$	5.76838	0.297087
$378$	−39.2113	−2.01681
$379$	23.1014	1.18664	0.593321	−	0.804966i	$-0.297817\pi$
$379$	23.1014	1.18664	0.593321	+	0.804966i	$0.297817\pi$
$380$	7.76697	0.398437
$381$	−38.6789	−1.98158
$382$	−7.18842	−0.367791
$383$	18.2406	0.932053	0.466027	−	0.884771i	$-0.345685\pi$
$383$	18.2406	0.932053	0.466027	+	0.884771i	$0.345685\pi$
$384$	40.7339	2.07869
$385$	0.179686	0.00915767
$386$	−42.7708	−2.17698
$387$	6.07216	0.308665
$388$	−32.5304	−1.65148
$389$	21.7415	1.10234	0.551168	−	0.834394i	$-0.314182\pi$
$389$	21.7415	1.10234	0.551168	+	0.834394i	$0.314182\pi$
$390$	25.0786	1.26990
$391$	15.3737	0.777483
$392$	−39.5108	−1.99560
$393$	−4.77568	−0.240901
$394$	−9.55781	−0.481516
$395$	−14.0617	−0.707521
$396$	−0.139258	−0.00699796
$397$	−34.1794	−1.71541	−0.857707	−	0.514139i	$-0.828112\pi$
$397$	−34.1794	−1.71541	−0.857707	+	0.514139i	$0.828112\pi$
$398$	61.5097	3.08320
$399$	−13.4798	−0.674834
$400$	−11.1610	−0.558052
$401$	−10.9417	−0.546404	−0.273202	−	0.961957i	$-0.588083\pi$
$401$	−10.9417	−0.546404	−0.273202	+	0.961957i	$0.588083\pi$
$402$	−26.5479	−1.32409
$403$	−8.55261	−0.426036
$404$	6.05321	0.301158
$405$	−12.9754	−0.644752
$406$	−12.6114	−0.625894
$407$	0.136364	0.00675933
$408$	−63.8509	−3.16109
$409$	−16.6049	−0.821059	−0.410530	−	0.911847i	$-0.634656\pi$
$409$	−16.6049	−0.821059	−0.410530	+	0.911847i	$0.634656\pi$
$410$	−27.7001	−1.36801
$411$	−4.15598	−0.204999
$412$	−20.0743	−0.988988
$413$	−55.9716	−2.75418
$414$	−4.91190	−0.241407
$415$	−8.58745	−0.421542
$416$	−6.27400	−0.307608
$417$	6.99584	0.342588
$418$	0.156884	0.00767345
$419$	−16.5458	−0.808314	−0.404157	−	0.914690i	$-0.632435\pi$
$419$	−16.5458	−0.808314	−0.404157	+	0.914690i	$0.632435\pi$
$420$	−36.0740	−1.76023
$421$	−23.8031	−1.16009	−0.580047	−	0.814583i	$-0.696966\pi$
$421$	−23.8031	−1.16009	−0.580047	+	0.814583i	$0.696966\pi$
$422$	−3.90762	−0.190220
$423$	−8.59806	−0.418052
$424$	39.8282	1.93423
$425$	−25.8644	−1.25461
$426$	43.9808	2.13088
$427$	−15.6005	−0.754963
$428$	−7.74778	−0.374503
$429$	0.333282	0.0160910
$430$	−18.3068	−0.882834
$431$	−30.7888	−1.48304	−0.741521	−	0.670929i	$-0.765895\pi$
$431$	−30.7888	−1.48304	−0.741521	+	0.670929i	$0.765895\pi$
$432$	−12.6453	−0.608398
$433$	−13.4275	−0.645285	−0.322642	−	0.946521i	$-0.604571\pi$
$433$	−13.4275	−0.645285	−0.322642	+	0.946521i	$0.604571\pi$
$434$	18.6986	0.897560
$435$	−3.08624	−0.147974
$436$	−37.6611	−1.80364
$437$	3.64075	0.174161
$438$	8.79321	0.420156
$439$	9.28285	0.443046	0.221523	−	0.975155i	$-0.428897\pi$
$439$	9.28285	0.443046	0.221523	+	0.975155i	$0.428897\pi$
$440$	0.201563	0.00960912
$441$	8.41021	0.400486
$442$	76.5866	3.64285
$443$	−24.9339	−1.18465	−0.592323	−	0.805700i	$-0.701789\pi$
$443$	−24.9339	−1.18465	−0.592323	+	0.805700i	$0.701789\pi$
$444$	−27.3766	−1.29924
$445$	3.29804	0.156342
$446$	−39.4810	−1.86948
$447$	−25.7054	−1.21582
$448$	38.4327	1.81578
$449$	7.49398	0.353663	0.176831	−	0.984241i	$-0.443415\pi$
$449$	7.49398	0.353663	0.176831	+	0.984241i	$0.443415\pi$
$450$	8.26367	0.389553
$451$	−0.368120	−0.0173341
$452$	−32.4188	−1.52485
$453$	11.5700	0.543607
$454$	−38.2996	−1.79749
$455$	20.7731	0.973856
$456$	−15.1209	−0.708103
$457$	−17.7743	−0.831448	−0.415724	−	0.909491i	$-0.636472\pi$
$457$	−17.7743	−0.831448	−0.415724	+	0.909491i	$0.636472\pi$
$458$	−57.2725	−2.67617
$459$	−29.3040	−1.36779
$460$	9.74319	0.454279
$461$	0.0813028	0.00378665	0.00189332	−	0.999998i	$-0.499397\pi$
$461$	0.0813028	0.00378665	0.00189332	+	0.999998i	$0.499397\pi$
$462$	−0.728654	−0.0339000
$463$	16.8166	0.781533	0.390766	−	0.920490i	$-0.372210\pi$
$463$	16.8166	0.781533	0.390766	+	0.920490i	$0.372210\pi$
$464$	−4.06707	−0.188809
$465$	4.57587	0.212201
$466$	4.94678	0.229155
$467$	−11.1678	−0.516783	−0.258392	−	0.966040i	$-0.583192\pi$
$467$	−11.1678	−0.516783	−0.258392	+	0.966040i	$0.583192\pi$
$468$	−16.0992	−0.744186
$469$	−21.9901	−1.01541
$470$	25.9221	1.19570
$471$	−36.5399	−1.68367
$472$	−62.7860	−2.88996
$473$	−0.243289	−0.0111864
$474$	57.0222	2.61912
$475$	−6.12511	−0.281039
$476$	−110.165	−5.04941
$477$	−8.47776	−0.388170
$478$	21.7274	0.993789
$479$	13.9707	0.638339	0.319170	−	0.947698i	$-0.396596\pi$
$479$	13.9707	0.638339	0.319170	+	0.947698i	$0.396596\pi$
$480$	3.35675	0.153214
$481$	15.7647	0.718809
$482$	6.68409	0.304452
$483$	−16.9096	−0.769413
$484$	−42.3093	−1.92315
$485$	−10.0224	−0.455092
$486$	23.0676	1.04637
$487$	3.31761	0.150335	0.0751677	−	0.997171i	$-0.476051\pi$
$487$	3.31761	0.150335	0.0751677	+	0.997171i	$0.476051\pi$
$488$	−17.4999	−0.792181
$489$	8.82837	0.399233
$490$	−25.3558	−1.14546
$491$	16.1274	0.727817	0.363909	−	0.931435i	$-0.381442\pi$
$491$	16.1274	0.727817	0.363909	+	0.931435i	$0.381442\pi$
$492$	73.9040	3.33185
$493$	−9.42495	−0.424478
$494$	18.1369	0.816019
$495$	−0.0429043	−0.00192840
$496$	6.03012	0.270760
$497$	36.4301	1.63411
$498$	34.8233	1.56047
$499$	8.39383	0.375759	0.187880	−	0.982192i	$-0.439839\pi$
$499$	8.39383	0.375759	0.187880	+	0.982192i	$0.439839\pi$
$500$	−39.1873	−1.75251
$501$	−37.1739	−1.66081
$502$	48.6993	2.17356
$503$	32.2495	1.43793	0.718967	−	0.695044i	$-0.244615\pi$
$503$	32.2495	1.43793	0.718967	+	0.695044i	$0.244615\pi$
$504$	16.8980	0.752696
$505$	1.86495	0.0829891
$506$	0.196801	0.00874889
$507$	12.6910	0.563629
$508$	−74.8592	−3.32134
$509$	14.5939	0.646863	0.323432	−	0.946252i	$-0.395163\pi$
$509$	14.5939	0.646863	0.323432	+	0.946252i	$0.395163\pi$
$510$	−40.9759	−1.81444
$511$	7.28358	0.322206
$512$	32.1486	1.42078
$513$	−6.93966	−0.306394
$514$	49.3634	2.17733
$515$	−6.18473	−0.272532
$516$	48.8428	2.15019
$517$	0.344492	0.0151507
$518$	−34.4664	−1.51437
$519$	3.83042	0.168137
$520$	23.3021	1.02187
$521$	3.80211	0.166574	0.0832868	−	0.996526i	$-0.473458\pi$
$521$	3.80211	0.166574	0.0832868	+	0.996526i	$0.473458\pi$
$522$	3.01127	0.131800
$523$	15.5976	0.682036	0.341018	−	0.940057i	$-0.389228\pi$
$523$	15.5976	0.682036	0.341018	+	0.940057i	$0.389228\pi$
$524$	−9.24287	−0.403777
$525$	28.4483	1.24159
$526$	69.8604	3.04606
$527$	13.9741	0.608721
$528$	−0.234984	−0.0102264
$529$	−18.4329	−0.801431
$530$	25.5594	1.11023
$531$	13.3645	0.579971
$532$	−26.0889	−1.13110
$533$	−42.5573	−1.84336
$534$	−13.3740	−0.578751
$535$	−2.38703	−0.103200
$536$	−24.6673	−1.06547
$537$	−47.3257	−2.04225
$538$	−64.7480	−2.79148
$539$	−0.336965	−0.0145141
$540$	−18.5716	−0.799194
$541$	−27.9575	−1.20199	−0.600994	−	0.799253i	$-0.705229\pi$
$541$	−27.9575	−1.20199	−0.600994	+	0.799253i	$0.705229\pi$
$542$	−55.8293	−2.39807
$543$	−26.0392	−1.11745
$544$	10.2511	0.439511
$545$	−11.6031	−0.497023
$546$	−84.2377	−3.60504
$547$	−39.1298	−1.67307	−0.836534	−	0.547915i	$-0.815422\pi$
$547$	−39.1298	−1.67307	−0.836534	+	0.547915i	$0.815422\pi$
$548$	−8.04349	−0.343601
$549$	3.72499	0.158979
$550$	−0.331094	−0.0141179
$551$	−2.23198	−0.0950855
$552$	−18.9683	−0.807343
$553$	47.2325	2.00853
$554$	−22.2238	−0.944198
$555$	−8.43455	−0.358027
$556$	13.5398	0.574215
$557$	15.8261	0.670573	0.335286	−	0.942116i	$-0.391167\pi$
$557$	15.8261	0.670573	0.335286	+	0.942116i	$0.391167\pi$
$558$	−4.46472	−0.189007
$559$	−28.1259	−1.18960
$560$	−14.6463	−0.618919
$561$	−0.544548	−0.0229908
$562$	37.3814	1.57684
$563$	−18.1927	−0.766731	−0.383366	−	0.923597i	$-0.625235\pi$
$563$	−18.1927	−0.766731	−0.383366	+	0.923597i	$0.625235\pi$
$564$	−69.1605	−2.91218
$565$	−9.98800	−0.420198
$566$	−33.7602	−1.41905
$567$	43.5836	1.83034
$568$	40.8654	1.71467
$569$	13.7968	0.578394	0.289197	−	0.957270i	$-0.406612\pi$
$569$	13.7968	0.578394	0.289197	+	0.957270i	$0.406612\pi$
$570$	−9.70375	−0.406445
$571$	−16.6615	−0.697261	−0.348630	−	0.937260i	$-0.613353\pi$
$571$	−16.6615	−0.697261	−0.348630	+	0.937260i	$0.613353\pi$
$572$	0.645035	0.0269703
$573$	5.90884	0.246845
$574$	93.0431	3.88354
$575$	−7.68357	−0.320427
$576$	−9.17671	−0.382363
$577$	−0.258446	−0.0107592	−0.00537961	−	0.999986i	$-0.501712\pi$
$577$	−0.258446	−0.0107592	−0.00537961	+	0.999986i	$0.501712\pi$
$578$	−84.0284	−3.49512
$579$	35.1574	1.46109
$580$	−5.97312	−0.248020
$581$	28.8448	1.19668
$582$	40.6421	1.68467
$583$	0.339672	0.0140678
$584$	8.17033	0.338091
$585$	−4.96005	−0.205073
$586$	24.6254	1.01727
$587$	−28.0773	−1.15887	−0.579437	−	0.815017i	$-0.696728\pi$
$587$	−28.0773	−1.15887	−0.579437	+	0.815017i	$0.696728\pi$
$588$	67.6495	2.78982
$589$	3.30929	0.136357
$590$	−40.2924	−1.65881
$591$	7.85647	0.323172
$592$	−11.1151	−0.456828
$593$	−16.4295	−0.674677	−0.337339	−	0.941383i	$-0.609527\pi$
$593$	−16.4295	−0.674677	−0.337339	+	0.941383i	$0.609527\pi$
$594$	−0.375125	−0.0153916
$595$	−33.9411	−1.39145
$596$	−49.7503	−2.03785
$597$	−50.5606	−2.06931
$598$	22.7517	0.930385
$599$	36.6459	1.49731	0.748656	−	0.662958i	$-0.230699\pi$
$599$	36.6459	1.49731	0.748656	+	0.662958i	$0.230699\pi$
$600$	31.9118	1.30279
$601$	−8.53950	−0.348334	−0.174167	−	0.984716i	$-0.555723\pi$
$601$	−8.53950	−0.348334	−0.174167	+	0.984716i	$0.555723\pi$
$602$	61.4917	2.50622
$603$	5.25065	0.213823
$604$	22.3927	0.911145
$605$	−13.0352	−0.529955
$606$	−7.56263	−0.307211
$607$	6.19355	0.251388	0.125694	−	0.992069i	$-0.459884\pi$
$607$	6.19355	0.251388	0.125694	+	0.992069i	$0.459884\pi$
$608$	2.42762	0.0984530
$609$	10.3665	0.420072
$610$	−11.2304	−0.454706
$611$	39.8258	1.61118
$612$	26.3045	1.06330
$613$	−16.3029	−0.658467	−0.329234	−	0.944248i	$-0.606790\pi$
$613$	−16.3029	−0.658467	−0.329234	+	0.944248i	$0.606790\pi$
$614$	1.72924	0.0697866
$615$	22.7693	0.918147
$616$	−0.677039	−0.0272787
$617$	−25.9262	−1.04375	−0.521874	−	0.853023i	$-0.674767\pi$
$617$	−25.9262	−1.04375	−0.521874	+	0.853023i	$0.674767\pi$
$618$	25.0800	1.00886
$619$	36.7414	1.47676	0.738381	−	0.674384i	$-0.235591\pi$
$619$	36.7414	1.47676	0.738381	+	0.674384i	$0.235591\pi$
$620$	8.85616	0.355672
$621$	−8.70537	−0.349335
$622$	47.9002	1.92062
$623$	−11.0780	−0.443829
$624$	−27.1659	−1.08751
$625$	5.90350	0.236140
$626$	59.6182	2.38282
$627$	−0.128958	−0.00515008
$628$	−70.7194	−2.82201
$629$	−25.7580	−1.02704
$630$	10.8442	0.432042
$631$	46.8575	1.86537	0.932684	−	0.360695i	$-0.117460\pi$
$631$	46.8575	1.86537	0.932684	+	0.360695i	$0.117460\pi$
$632$	52.9829	2.10755
$633$	3.21204	0.127667
$634$	−38.1303	−1.51435
$635$	−23.0636	−0.915251
$636$	−68.1928	−2.70402
$637$	−38.9557	−1.54348
$638$	−0.120650	−0.00477658
$639$	−8.69853	−0.344109
$640$	24.2890	0.960107
$641$	20.8636	0.824062	0.412031	−	0.911170i	$-0.364819\pi$
$641$	20.8636	0.824062	0.412031	+	0.911170i	$0.364819\pi$
$642$	9.67976	0.382030
$643$	−8.77176	−0.345925	−0.172962	−	0.984928i	$-0.555334\pi$
$643$	−8.77176	−0.345925	−0.172962	+	0.984928i	$0.555334\pi$
$644$	−32.7269	−1.28962
$645$	15.0481	0.592519
$646$	−29.6339	−1.16593
$647$	27.5253	1.08213	0.541066	−	0.840980i	$-0.318021\pi$
$647$	27.5253	1.08213	0.541066	+	0.840980i	$0.318021\pi$
$648$	48.8898	1.92057
$649$	−0.535466	−0.0210189
$650$	−38.2769	−1.50134
$651$	−15.3701	−0.602403
$652$	17.0865	0.669157
$653$	−40.0024	−1.56541	−0.782707	−	0.622390i	$-0.786162\pi$
$653$	−40.0024	−1.56541	−0.782707	+	0.622390i	$0.786162\pi$
$654$	47.0523	1.83989
$655$	−2.84766	−0.111267
$656$	30.0056	1.17152
$657$	−1.73912	−0.0678496
$658$	−87.0711	−3.39439
$659$	7.53803	0.293640	0.146820	−	0.989163i	$-0.453096\pi$
$659$	7.53803	0.293640	0.146820	+	0.989163i	$0.453096\pi$
$660$	−0.345111	−0.0134334
$661$	−11.3506	−0.441487	−0.220744	−	0.975332i	$-0.570848\pi$
$661$	−11.3506	−0.441487	−0.220744	+	0.975332i	$0.570848\pi$
$662$	−53.0116	−2.06035
$663$	−62.9538	−2.44492
$664$	32.3566	1.25568
$665$	−8.03779	−0.311692
$666$	8.22966	0.318893
$667$	−2.79988	−0.108412
$668$	−71.9465	−2.78370
$669$	32.4531	1.25471
$670$	−15.8301	−0.611569
$671$	−0.149246	−0.00576159
$672$	−11.2752	−0.434949
$673$	2.26081	0.0871479	0.0435740	−	0.999050i	$-0.486126\pi$
$673$	2.26081	0.0871479	0.0435740	+	0.999050i	$0.486126\pi$
$674$	−29.5532	−1.13835
$675$	14.6457	0.563714
$676$	24.5623	0.944703
$677$	14.0653	0.540572	0.270286	−	0.962780i	$-0.412882\pi$
$677$	14.0653	0.540572	0.270286	+	0.962780i	$0.412882\pi$
$678$	40.5028	1.55550
$679$	33.6646	1.29193
$680$	−38.0733	−1.46004
$681$	31.4821	1.20640
$682$	0.178884	0.00684984
$683$	−23.4525	−0.897384	−0.448692	−	0.893686i	$-0.648110\pi$
$683$	−23.4525	−0.897384	−0.448692	+	0.893686i	$0.648110\pi$
$684$	6.22932	0.238184
$685$	−2.47814	−0.0946849
$686$	17.7871	0.679113
$687$	47.0777	1.79612
$688$	19.8305	0.756032
$689$	39.2685	1.49601
$690$	−12.1727	−0.463409
$691$	18.8679	0.717770	0.358885	−	0.933382i	$-0.383157\pi$
$691$	18.8679	0.717770	0.358885	+	0.933382i	$0.383157\pi$
$692$	7.41340	0.281815
$693$	0.144113	0.00547441
$694$	−38.7367	−1.47042
$695$	4.17151	0.158234
$696$	11.6286	0.440781
$697$	69.5343	2.63380
$698$	−50.8967	−1.92647
$699$	−4.06623	−0.153799
$700$	55.0590	2.08103
$701$	11.0737	0.418248	0.209124	−	0.977889i	$-0.432939\pi$
$701$	11.0737	0.418248	0.209124	+	0.977889i	$0.432939\pi$
$702$	−43.3672	−1.63679
$703$	−6.09990	−0.230062
$704$	0.367676	0.0138573
$705$	−21.3079	−0.802500
$706$	48.7182	1.83353
$707$	−6.26427	−0.235592
$708$	107.501	4.04012
$709$	13.4467	0.505003	0.252501	−	0.967597i	$-0.418747\pi$
$709$	13.4467	0.505003	0.252501	+	0.967597i	$0.418747\pi$
$710$	26.2250	0.984208
$711$	−11.2779	−0.422953
$712$	−12.4267	−0.465709
$713$	4.15130	0.155467
$714$	137.636	5.15089
$715$	0.198731	0.00743210
$716$	−91.5944	−3.42304
$717$	−17.8598	−0.666987
$718$	−72.2527	−2.69645
$719$	23.6692	0.882713	0.441356	−	0.897332i	$-0.354497\pi$
$719$	23.6692	0.882713	0.441356	+	0.897332i	$0.354497\pi$
$720$	3.49714	0.130331
$721$	20.7742	0.773672
$722$	38.9245	1.44862
$723$	−5.49429	−0.204335
$724$	−50.3964	−1.87297
$725$	4.71046	0.174942
$726$	52.8595	1.96180
$727$	−7.57287	−0.280862	−0.140431	−	0.990090i	$-0.544849\pi$
$727$	−7.57287	−0.280862	−0.140431	+	0.990090i	$0.544849\pi$
$728$	−78.2706	−2.90090
$729$	13.8828	0.514178
$730$	5.24325	0.194061
$731$	45.9549	1.69970
$732$	29.9628	1.10746
$733$	−50.4106	−1.86196	−0.930980	−	0.365071i	$-0.881045\pi$
$733$	−50.4106	−1.86196	−0.930980	+	0.365071i	$0.881045\pi$
$734$	−10.3842	−0.383290
$735$	20.8423	0.768780
$736$	3.04530	0.112251
$737$	−0.210374	−0.00774921
$738$	−22.2162	−0.817790
$739$	−24.1820	−0.889550	−0.444775	−	0.895642i	$-0.646716\pi$
$739$	−24.1820	−0.889550	−0.444775	+	0.895642i	$0.646716\pi$
$740$	−16.3243	−0.600092
$741$	−14.9085	−0.547676
$742$	−85.8528	−3.15176
$743$	11.0223	0.404370	0.202185	−	0.979347i	$-0.435196\pi$
$743$	11.0223	0.404370	0.202185	+	0.979347i	$0.435196\pi$
$744$	−17.2414	−0.632100
$745$	−15.3277	−0.561563
$746$	−67.9581	−2.48812
$747$	−6.88737	−0.251996
$748$	−1.05392	−0.0385352
$749$	8.01793	0.292969
$750$	48.9591	1.78773
$751$	23.9784	0.874984	0.437492	−	0.899222i	$-0.355867\pi$
$751$	23.9784	0.874984	0.437492	+	0.899222i	$0.355867\pi$
$752$	−28.0797	−1.02396
$753$	−40.0306	−1.45879
$754$	−13.9480	−0.507958
$755$	6.89902	0.251081
$756$	62.3810	2.26878
$757$	28.3252	1.02950	0.514749	−	0.857341i	$-0.327885\pi$
$757$	28.3252	1.02950	0.514749	+	0.857341i	$0.327885\pi$
$758$	−55.8597	−2.02891
$759$	−0.161770	−0.00587187
$760$	−9.01637	−0.327058
$761$	47.1208	1.70813	0.854064	−	0.520168i	$-0.174131\pi$
$761$	47.1208	1.70813	0.854064	+	0.520168i	$0.174131\pi$
$762$	93.5261	3.38809
$763$	38.9743	1.41096
$764$	11.4360	0.413740
$765$	8.10422	0.293009
$766$	−44.1062	−1.59362
$767$	−61.9038	−2.23522
$768$	−60.1180	−2.16932
$769$	−28.4705	−1.02667	−0.513337	−	0.858187i	$-0.671591\pi$
$769$	−28.4705	−1.02667	−0.513337	+	0.858187i	$0.671591\pi$
$770$	−0.434485	−0.0156577
$771$	−40.5765	−1.46133
$772$	68.0438	2.44895
$773$	33.5823	1.20787	0.603936	−	0.797033i	$-0.293598\pi$
$773$	33.5823	1.20787	0.603936	+	0.797033i	$0.293598\pi$
$774$	−14.6826	−0.527755
$775$	−6.98405	−0.250875
$776$	37.7632	1.35562
$777$	28.3312	1.01638
$778$	−52.5712	−1.88477
$779$	16.4669	0.589986
$780$	−39.8973	−1.42855
$781$	0.348517	0.0124709
$782$	−37.1739	−1.32934
$783$	5.33688	0.190724
$784$	27.4662	0.980935
$785$	−21.7881	−0.777652
$786$	11.5477	0.411892
$787$	−10.5391	−0.375677	−0.187838	−	0.982200i	$-0.560148\pi$
$787$	−10.5391	−0.375677	−0.187838	+	0.982200i	$0.560148\pi$
$788$	15.2054	0.541672
$789$	−57.4249	−2.04438
$790$	34.0014	1.20972
$791$	33.5492	1.19287
$792$	0.161659	0.00574429
$793$	−17.2540	−0.612706
$794$	82.6463	2.93301
$795$	−21.0097	−0.745138
$796$	−97.8553	−3.46839
$797$	−27.0168	−0.956984	−0.478492	−	0.878092i	$-0.658816\pi$
$797$	−27.0168	−0.956984	−0.478492	+	0.878092i	$0.658816\pi$
$798$	32.5944	1.15383
$799$	−65.0713	−2.30206
$800$	−5.12334	−0.181137
$801$	2.64512	0.0934607
$802$	26.4573	0.934239
$803$	0.0696801	0.00245896
$804$	42.2348	1.48951
$805$	−10.0829	−0.355376
$806$	20.6803	0.728434
$807$	53.2225	1.87352
$808$	−7.02692	−0.247206
$809$	31.4360	1.10523	0.552615	−	0.833437i	$-0.313630\pi$
$809$	31.4360	1.10523	0.552615	+	0.833437i	$0.313630\pi$
$810$	31.3747	1.10239
$811$	−49.2678	−1.73003	−0.865013	−	0.501749i	$-0.832690\pi$
$811$	−49.2678	−1.73003	−0.865013	+	0.501749i	$0.832690\pi$
$812$	20.0634	0.704087
$813$	45.8914	1.60948
$814$	−0.329731	−0.0115571
$815$	5.26421	0.184397
$816$	44.3863	1.55383
$817$	10.8829	0.380743
$818$	40.1509	1.40384
$819$	16.6606	0.582167
$820$	44.0678	1.53891
$821$	37.4976	1.30868	0.654338	−	0.756202i	$-0.272947\pi$
$821$	37.4976	1.30868	0.654338	+	0.756202i	$0.272947\pi$
$822$	10.0492	0.350507
$823$	8.06303	0.281060	0.140530	−	0.990076i	$-0.455119\pi$
$823$	8.06303	0.281060	0.140530	+	0.990076i	$0.455119\pi$
$824$	23.3034	0.811813
$825$	0.272158	0.00947531
$826$	135.340	4.70909
$827$	−11.8482	−0.412002	−0.206001	−	0.978552i	$-0.566045\pi$
$827$	−11.8482	−0.412002	−0.206001	+	0.978552i	$0.566045\pi$
$828$	7.81430	0.271566
$829$	4.63772	0.161075	0.0805374	−	0.996752i	$-0.474336\pi$
$829$	4.63772	0.161075	0.0805374	+	0.996752i	$0.474336\pi$
$830$	20.7646	0.720750
$831$	18.2678	0.633704
$832$	42.5061	1.47363
$833$	63.6496	2.20533
$834$	−16.9161	−0.585755
$835$	−22.1662	−0.767093
$836$	−0.249586	−0.00863210
$837$	−7.91283	−0.273507
$838$	40.0079	1.38205
$839$	−29.4772	−1.01767	−0.508833	−	0.860865i	$-0.669923\pi$
$839$	−29.4772	−1.01767	−0.508833	+	0.860865i	$0.669923\pi$
$840$	41.8769	1.44489
$841$	−27.2835	−0.940811
$842$	57.5563	1.98352
$843$	−30.7273	−1.05830
$844$	6.21660	0.213984
$845$	7.56746	0.260329
$846$	20.7903	0.714784
$847$	43.7845	1.50445
$848$	−27.6868	−0.950768
$849$	27.7507	0.952402
$850$	62.5406	2.14512
$851$	−7.65195	−0.262305
$852$	−69.9687	−2.39709
$853$	−58.0575	−1.98785	−0.993926	−	0.110051i	$-0.964898\pi$
$853$	−58.0575	−1.98785	−0.993926	+	0.110051i	$0.964898\pi$
$854$	37.7223	1.29083
$855$	1.91921	0.0656356
$856$	8.99409	0.307412
$857$	38.3131	1.30875	0.654376	−	0.756169i	$-0.272931\pi$
$857$	38.3131	1.30875	0.654376	+	0.756169i	$0.272931\pi$
$858$	−0.805880	−0.0275123
$859$	18.9783	0.647531	0.323766	−	0.946137i	$-0.395051\pi$
$859$	18.9783	0.647531	0.323766	+	0.946137i	$0.395051\pi$
$860$	29.1242	0.993127
$861$	−76.4809	−2.60646
$862$	74.4477	2.53570
$863$	−24.9369	−0.848861	−0.424431	−	0.905460i	$-0.639526\pi$
$863$	−24.9369	−0.848861	−0.424431	+	0.905460i	$0.639526\pi$
$864$	−5.80467	−0.197479
$865$	2.28402	0.0776589
$866$	32.4679	1.10330
$867$	69.0709	2.34577
$868$	−29.7474	−1.00969
$869$	0.451861	0.0153284
$870$	7.46257	0.253005
$871$	−24.3207	−0.824076
$872$	43.7193	1.48052
$873$	−8.03821	−0.272052
$874$	−8.80338	−0.297779
$875$	40.5537	1.37097
$876$	−13.9890	−0.472646
$877$	54.2292	1.83119	0.915594	−	0.402104i	$-0.131721\pi$
$877$	54.2292	1.83119	0.915594	+	0.402104i	$0.131721\pi$
$878$	−22.4461	−0.757518
$879$	−20.2419	−0.682744
$880$	−0.140117	−0.00472336
$881$	−6.50103	−0.219025	−0.109513	−	0.993985i	$-0.534929\pi$
$881$	−6.50103	−0.219025	−0.109513	+	0.993985i	$0.534929\pi$
$882$	−20.3360	−0.684750
$883$	45.5897	1.53422	0.767108	−	0.641518i	$-0.221695\pi$
$883$	45.5897	1.53422	0.767108	+	0.641518i	$0.221695\pi$
$884$	−121.841	−4.09796
$885$	33.1202	1.11332
$886$	60.2907	2.02550
$887$	−2.49760	−0.0838613	−0.0419306	−	0.999121i	$-0.513351\pi$
$887$	−2.49760	−0.0838613	−0.0419306	+	0.999121i	$0.513351\pi$
$888$	31.7805	1.06648
$889$	77.4694	2.59824
$890$	−7.97472	−0.267313
$891$	0.416953	0.0139685
$892$	62.8099	2.10303
$893$	−15.4099	−0.515674
$894$	62.1560	2.07881
$895$	−28.2196	−0.943276
$896$	−81.5855	−2.72558
$897$	−18.7018	−0.624433
$898$	−18.1206	−0.604691
$899$	−2.54498	−0.0848798
$900$	−13.1466	−0.438220
$901$	−64.1608	−2.13751
$902$	0.890119	0.0296377
$903$	−50.5459	−1.68206
$904$	37.6337	1.25168
$905$	−15.5268	−0.516128
$906$	−27.9765	−0.929457
$907$	−43.5818	−1.44711	−0.723554	−	0.690267i	$-0.757493\pi$
$907$	−43.5818	−1.44711	−0.723554	+	0.690267i	$0.757493\pi$
$908$	60.9305	2.02205
$909$	1.49574	0.0496106
$910$	−50.2296	−1.66509
$911$	24.3188	0.805719	0.402859	−	0.915262i	$-0.368016\pi$
$911$	24.3188	0.805719	0.402859	+	0.915262i	$0.368016\pi$
$912$	10.5114	0.348067
$913$	0.275951	0.00913264
$914$	42.9786	1.42161
$915$	9.23133	0.305178
$916$	91.1143	3.01050
$917$	9.56515	0.315869
$918$	70.8575	2.33865
$919$	34.0017	1.12161	0.560806	−	0.827947i	$-0.310491\pi$
$919$	34.0017	1.12161	0.560806	+	0.827947i	$0.310491\pi$
$920$	−11.3105	−0.372895
$921$	−1.42143	−0.0468377
$922$	−0.196591	−0.00647439
$923$	40.2912	1.32620
$924$	1.15921	0.0381352
$925$	12.8735	0.423277
$926$	−40.6628	−1.33626
$927$	−4.96032	−0.162918
$928$	−1.86694	−0.0612852
$929$	4.80524	0.157655	0.0788274	−	0.996888i	$-0.474882\pi$
$929$	4.80524	0.157655	0.0788274	+	0.996888i	$0.474882\pi$
$930$	−11.0645	−0.362820
$931$	15.0733	0.494006
$932$	−7.86979	−0.257784
$933$	−39.3737	−1.28904
$934$	27.0039	0.883593
$935$	−0.324705	−0.0106190
$936$	18.6889	0.610867
$937$	−40.1814	−1.31267	−0.656335	−	0.754470i	$-0.727894\pi$
$937$	−40.1814	−1.31267	−0.656335	+	0.754470i	$0.727894\pi$
$938$	53.1724	1.73614
$939$	−49.0058	−1.59924
$940$	−41.2393	−1.34508
$941$	−48.6888	−1.58721	−0.793605	−	0.608434i	$-0.791798\pi$
$941$	−48.6888	−1.58721	−0.793605	+	0.608434i	$0.791798\pi$
$942$	88.3540	2.87873
$943$	20.6566	0.672673
$944$	43.6460	1.42056
$945$	19.2191	0.625199
$946$	0.588276	0.0191265
$947$	29.2771	0.951378	0.475689	−	0.879614i	$-0.342199\pi$
$947$	29.2771	0.951378	0.475689	+	0.879614i	$0.342199\pi$
$948$	−90.7161	−2.94632
$949$	8.05553	0.261494
$950$	14.8106	0.480520
$951$	31.3429	1.01636
$952$	127.886	4.14482
$953$	31.2574	1.01253	0.506264	−	0.862379i	$-0.331026\pi$
$953$	31.2574	1.01253	0.506264	+	0.862379i	$0.331026\pi$
$954$	20.4994	0.663691
$955$	3.52335	0.114013
$956$	−34.5660	−1.11794
$957$	0.0991738	0.00320583
$958$	−33.7815	−1.09143
$959$	8.32395	0.268794
$960$	−22.7419	−0.733991
$961$	−27.2266	−0.878279
$962$	−38.1194	−1.22902
$963$	−1.91447	−0.0616928
$964$	−10.6337	−0.342487
$965$	20.9638	0.674848
$966$	40.8876	1.31554
$967$	−2.36055	−0.0759102	−0.0379551	−	0.999279i	$-0.512084\pi$
$967$	−2.36055	−0.0759102	−0.0379551	+	0.999279i	$0.512084\pi$
$968$	49.1151	1.57862
$969$	24.3589	0.782521
$970$	24.2343	0.778115
$971$	−23.2067	−0.744739	−0.372369	−	0.928085i	$-0.621455\pi$
$971$	−23.2067	−0.744739	−0.372369	+	0.928085i	$0.621455\pi$
$972$	−36.6981	−1.17709
$973$	−14.0119	−0.449200
$974$	−8.02204	−0.257043
$975$	31.4634	1.00764
$976$	12.1651	0.389396
$977$	−45.7548	−1.46383	−0.731914	−	0.681398i	$-0.761373\pi$
$977$	−45.7548	−1.46383	−0.731914	+	0.681398i	$0.761373\pi$
$978$	−21.3471	−0.682606
$979$	−0.105980	−0.00338714
$980$	40.3383	1.28856
$981$	−9.30601	−0.297118
$982$	−38.9962	−1.24442
$983$	−40.9871	−1.30729	−0.653643	−	0.756803i	$-0.726760\pi$
$983$	−40.9871	−1.30729	−0.653643	+	0.756803i	$0.726760\pi$
$984$	−85.7922	−2.73496
$985$	4.68469	0.149267
$986$	22.7897	0.725771
$987$	71.5720	2.27816
$988$	−28.8539	−0.917965
$989$	13.6519	0.434105
$990$	0.103743	0.00329718
$991$	3.65932	0.116242	0.0581211	−	0.998310i	$-0.481489\pi$
$991$	3.65932	0.116242	0.0581211	+	0.998310i	$0.481489\pi$
$992$	2.76805	0.0878857
$993$	43.5752	1.38282
$994$	−88.0886	−2.79400
$995$	−30.1485	−0.955771
$996$	−55.4002	−1.75542
$997$	−33.7286	−1.06819	−0.534097	−	0.845423i	$-0.679348\pi$
$997$	−33.7286	−1.06819	−0.534097	+	0.845423i	$0.679348\pi$
$998$	−20.2964	−0.642472
$999$	14.5854	0.461463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.17	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.17	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} +O(q^{10})\)	\(q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} -2.86577 q^{10} -0.0380846 q^{11} +7.64589 q^{12} -4.40285 q^{13} +9.62596 q^{14} +2.35564 q^{15} +3.10429 q^{16} +7.19381 q^{17} -2.29842 q^{18} +1.70361 q^{19} +4.55912 q^{20} -7.91249 q^{21} +0.0920891 q^{22} +2.13708 q^{23} -8.87581 q^{24} -3.59537 q^{25} +10.6462 q^{26} -4.07350 q^{27} -15.3139 q^{28} -1.31015 q^{29} -5.69599 q^{30} +1.94251 q^{31} +1.42498 q^{32} -0.0756967 q^{33} -17.3948 q^{34} -4.71809 q^{35} +3.65654 q^{36} -3.58057 q^{37} -4.11936 q^{38} -8.75110 q^{39} -5.29250 q^{40} +9.66585 q^{41} +19.1325 q^{42} +6.38812 q^{43} -0.146504 q^{44} +1.12655 q^{45} -5.16748 q^{46} -9.04545 q^{47} +6.17007 q^{48} +8.84782 q^{49} +8.69366 q^{50} +14.2984 q^{51} -16.9369 q^{52} -8.91888 q^{53} +9.84979 q^{54} -0.0451368 q^{55} +17.7772 q^{56} +3.38609 q^{57} +3.16795 q^{58} +14.0599 q^{59} +9.06170 q^{60} +3.91881 q^{61} -4.69703 q^{62} -3.78404 q^{63} -9.65421 q^{64} -5.21814 q^{65} +0.183036 q^{66} +5.52385 q^{67} +27.6732 q^{68} +4.24764 q^{69} +11.4084 q^{70} -9.15115 q^{71} -4.24473 q^{72} -1.82962 q^{73} +8.65788 q^{74} -7.14614 q^{75} +6.55346 q^{76} +0.151612 q^{77} +21.1603 q^{78} -11.8647 q^{79} +3.67911 q^{80} -10.9481 q^{81} -23.3722 q^{82} -7.24574 q^{83} -30.4378 q^{84} +8.52591 q^{85} -15.4466 q^{86} -2.60404 q^{87} +0.170070 q^{88} +2.78275 q^{89} -2.72402 q^{90} +17.5275 q^{91} +8.22091 q^{92} +3.86094 q^{93} +21.8720 q^{94} +2.01907 q^{95} +2.83229 q^{96} -8.45647 q^{97} -21.3942 q^{98} -0.0362009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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