LMFDB - Embedded newform 4015.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.615983 q^{2} -0.785692 q^{3} -1.62056 q^{4} +1.00000 q^{5} -0.483973 q^{6} +2.63763 q^{7} -2.23021 q^{8} -2.38269 q^{9} +O(q^{10})$	\(q+0.615983 q^{2} -0.785692 q^{3} -1.62056 q^{4} +1.00000 q^{5} -0.483973 q^{6} +2.63763 q^{7} -2.23021 q^{8} -2.38269 q^{9} +0.615983 q^{10} -1.00000 q^{11} +1.27326 q^{12} -2.47288 q^{13} +1.62473 q^{14} -0.785692 q^{15} +1.86736 q^{16} +3.43844 q^{17} -1.46770 q^{18} +1.08483 q^{19} -1.62056 q^{20} -2.07236 q^{21} -0.615983 q^{22} -0.371795 q^{23} +1.75225 q^{24} +1.00000 q^{25} -1.52325 q^{26} +4.22913 q^{27} -4.27445 q^{28} -7.27060 q^{29} -0.483973 q^{30} +9.04017 q^{31} +5.61068 q^{32} +0.785692 q^{33} +2.11802 q^{34} +2.63763 q^{35} +3.86130 q^{36} +0.207031 q^{37} +0.668235 q^{38} +1.94292 q^{39} -2.23021 q^{40} -4.81231 q^{41} -1.27654 q^{42} -0.935615 q^{43} +1.62056 q^{44} -2.38269 q^{45} -0.229020 q^{46} -11.8266 q^{47} -1.46717 q^{48} -0.0429124 q^{49} +0.615983 q^{50} -2.70156 q^{51} +4.00747 q^{52} -1.34937 q^{53} +2.60507 q^{54} -1.00000 q^{55} -5.88246 q^{56} -0.852340 q^{57} -4.47856 q^{58} -1.99743 q^{59} +1.27326 q^{60} +12.3282 q^{61} +5.56859 q^{62} -6.28465 q^{63} -0.278641 q^{64} -2.47288 q^{65} +0.483973 q^{66} +0.726488 q^{67} -5.57222 q^{68} +0.292117 q^{69} +1.62473 q^{70} -14.0406 q^{71} +5.31389 q^{72} +1.00000 q^{73} +0.127528 q^{74} -0.785692 q^{75} -1.75803 q^{76} -2.63763 q^{77} +1.19681 q^{78} -5.33450 q^{79} +1.86736 q^{80} +3.82527 q^{81} -2.96430 q^{82} -15.2944 q^{83} +3.35840 q^{84} +3.43844 q^{85} -0.576323 q^{86} +5.71245 q^{87} +2.23021 q^{88} +1.00219 q^{89} -1.46770 q^{90} -6.52255 q^{91} +0.602519 q^{92} -7.10278 q^{93} -7.28496 q^{94} +1.08483 q^{95} -4.40826 q^{96} +6.65230 q^{97} -0.0264333 q^{98} +2.38269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.615983	0.435566	0.217783	−	0.975997i	$-0.430118\pi$
$2$	0.615983	0.435566	0.217783	+	0.975997i	$0.430118\pi$
$3$	−0.785692	−0.453619	−0.226810	−	0.973939i	$-0.572830\pi$
$3$	−0.785692	−0.453619	−0.226810	+	0.973939i	$0.572830\pi$
$4$	−1.62056	−0.810282
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.483973	−0.197581
$7$	2.63763	0.996930	0.498465	−	0.866910i	$-0.333897\pi$
$7$	2.63763	0.996930	0.498465	+	0.866910i	$0.333897\pi$
$8$	−2.23021	−0.788497
$9$	−2.38269	−0.794230
$10$	0.615983	0.194791
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.27326	0.367560
$13$	−2.47288	−0.685854	−0.342927	−	0.939362i	$-0.611418\pi$
$13$	−2.47288	−0.685854	−0.342927	+	0.939362i	$0.611418\pi$
$14$	1.62473	0.434229
$15$	−0.785692	−0.202865
$16$	1.86736	0.466840
$17$	3.43844	0.833945	0.416972	−	0.908919i	$-0.363091\pi$
$17$	3.43844	0.833945	0.416972	+	0.908919i	$0.363091\pi$
$18$	−1.46770	−0.345939
$19$	1.08483	0.248876	0.124438	−	0.992227i	$-0.460287\pi$
$19$	1.08483	0.248876	0.124438	+	0.992227i	$0.460287\pi$
$20$	−1.62056	−0.362369
$21$	−2.07236	−0.452227
$22$	−0.615983	−0.131328
$23$	−0.371795	−0.0775247	−0.0387623	−	0.999248i	$-0.512342\pi$
$23$	−0.371795	−0.0775247	−0.0387623	+	0.999248i	$0.512342\pi$
$24$	1.75225	0.357677
$25$	1.00000	0.200000
$26$	−1.52325	−0.298735
$27$	4.22913	0.813897
$28$	−4.27445	−0.807795
$29$	−7.27060	−1.35012	−0.675058	−	0.737765i	$-0.735881\pi$
$29$	−7.27060	−1.35012	−0.675058	+	0.737765i	$0.735881\pi$
$30$	−0.483973	−0.0883609
$31$	9.04017	1.62366	0.811831	−	0.583892i	$-0.198471\pi$
$31$	9.04017	1.62366	0.811831	+	0.583892i	$0.198471\pi$
$32$	5.61068	0.991837
$33$	0.785692	0.136771
$34$	2.11802	0.363238
$35$	2.63763	0.445841
$36$	3.86130	0.643550
$37$	0.207031	0.0340357	0.0170178	−	0.999855i	$-0.494583\pi$
$37$	0.207031	0.0340357	0.0170178	+	0.999855i	$0.494583\pi$
$38$	0.668235	0.108402
$39$	1.94292	0.311117
$40$	−2.23021	−0.352627
$41$	−4.81231	−0.751556	−0.375778	−	0.926710i	$-0.622624\pi$
$41$	−4.81231	−0.751556	−0.375778	+	0.926710i	$0.622624\pi$
$42$	−1.27654	−0.196974
$43$	−0.935615	−0.142680	−0.0713400	−	0.997452i	$-0.522728\pi$
$43$	−0.935615	−0.142680	−0.0713400	+	0.997452i	$0.522728\pi$
$44$	1.62056	0.244309
$45$	−2.38269	−0.355190
$46$	−0.229020	−0.0337671
$47$	−11.8266	−1.72508	−0.862541	−	0.505987i	$-0.831128\pi$
$47$	−11.8266	−1.72508	−0.862541	+	0.505987i	$0.831128\pi$
$48$	−1.46717	−0.211768
$49$	−0.0429124	−0.00613034
$50$	0.615983	0.0871131
$51$	−2.70156	−0.378293
$52$	4.00747	0.555735
$53$	−1.34937	−0.185351	−0.0926755	−	0.995696i	$-0.529542\pi$
$53$	−1.34937	−0.185351	−0.0926755	+	0.995696i	$0.529542\pi$
$54$	2.60507	0.354506
$55$	−1.00000	−0.134840
$56$	−5.88246	−0.786076
$57$	−0.852340	−0.112895
$58$	−4.47856	−0.588064
$59$	−1.99743	−0.260043	−0.130021	−	0.991511i	$-0.541505\pi$
$59$	−1.99743	−0.260043	−0.130021	+	0.991511i	$0.541505\pi$
$60$	1.27326	0.164378
$61$	12.3282	1.57847	0.789233	−	0.614093i	$-0.210478\pi$
$61$	12.3282	1.57847	0.789233	+	0.614093i	$0.210478\pi$
$62$	5.56859	0.707212
$63$	−6.28465	−0.791791
$64$	−0.278641	−0.0348301
$65$	−2.47288	−0.306723
$66$	0.483973	0.0595729
$67$	0.726488	0.0887546	0.0443773	−	0.999015i	$-0.485870\pi$
$67$	0.726488	0.0887546	0.0443773	+	0.999015i	$0.485870\pi$
$68$	−5.57222	−0.675731
$69$	0.292117	0.0351667
$70$	1.62473	0.194193
$71$	−14.0406	−1.66632	−0.833158	−	0.553035i	$-0.813470\pi$
$71$	−14.0406	−1.66632	−0.833158	+	0.553035i	$0.813470\pi$
$72$	5.31389	0.626248
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	0.127528	0.0148248
$75$	−0.785692	−0.0907239
$76$	−1.75803	−0.201660
$77$	−2.63763	−0.300586
$78$	1.19681	0.135512
$79$	−5.33450	−0.600178	−0.300089	−	0.953911i	$-0.597016\pi$
$79$	−5.33450	−0.600178	−0.300089	+	0.953911i	$0.597016\pi$
$80$	1.86736	0.208777
$81$	3.82527	0.425030
$82$	−2.96430	−0.327352
$83$	−15.2944	−1.67877	−0.839387	−	0.543535i	$-0.817086\pi$
$83$	−15.2944	−1.67877	−0.839387	+	0.543535i	$0.817086\pi$
$84$	3.35840	0.366431
$85$	3.43844	0.372951
$86$	−0.576323	−0.0621465
$87$	5.71245	0.612439
$88$	2.23021	0.237741
$89$	1.00219	0.106231	0.0531157	−	0.998588i	$-0.483085\pi$
$89$	1.00219	0.106231	0.0531157	+	0.998588i	$0.483085\pi$
$90$	−1.46770	−0.154709
$91$	−6.52255	−0.683749
$92$	0.602519	0.0628169
$93$	−7.10278	−0.736524
$94$	−7.28496	−0.751387
$95$	1.08483	0.111301
$96$	−4.40826	−0.449916
$97$	6.65230	0.675439	0.337719	−	0.941247i	$-0.390345\pi$
$97$	6.65230	0.675439	0.337719	+	0.941247i	$0.390345\pi$
$98$	−0.0264333	−0.00267017
$99$	2.38269	0.239469
$100$	−1.62056	−0.162056
$101$	3.16362	0.314792	0.157396	−	0.987536i	$-0.449690\pi$
$101$	3.16362	0.314792	0.157396	+	0.987536i	$0.449690\pi$
$102$	−1.66411	−0.164772
$103$	−7.88779	−0.777207	−0.388604	−	0.921405i	$-0.627042\pi$
$103$	−7.88779	−0.777207	−0.388604	+	0.921405i	$0.627042\pi$
$104$	5.51504	0.540794
$105$	−2.07236	−0.202242
$106$	−0.831192	−0.0807325
$107$	1.78872	0.172922	0.0864609	−	0.996255i	$-0.472444\pi$
$107$	1.78872	0.172922	0.0864609	+	0.996255i	$0.472444\pi$
$108$	−6.85359	−0.659487
$109$	−1.84339	−0.176565	−0.0882826	−	0.996095i	$-0.528138\pi$
$109$	−1.84339	−0.176565	−0.0882826	+	0.996095i	$0.528138\pi$
$110$	−0.615983	−0.0587317
$111$	−0.162663	−0.0154392
$112$	4.92541	0.465407
$113$	−9.84801	−0.926423	−0.463211	−	0.886248i	$-0.653303\pi$
$113$	−9.84801	−0.926423	−0.463211	+	0.886248i	$0.653303\pi$
$114$	−0.525027	−0.0491733
$115$	−0.371795	−0.0346701
$116$	11.7825	1.09398
$117$	5.89211	0.544725
$118$	−1.23038	−0.113266
$119$	9.06934	0.831385
$120$	1.75225	0.159958
$121$	1.00000	0.0909091
$122$	7.59397	0.687526
$123$	3.78099	0.340920
$124$	−14.6502	−1.31562
$125$	1.00000	0.0894427
$126$	−3.87124	−0.344877
$127$	−8.17387	−0.725314	−0.362657	−	0.931923i	$-0.618130\pi$
$127$	−8.17387	−0.725314	−0.362657	+	0.931923i	$0.618130\pi$
$128$	−11.3930	−1.00701
$129$	0.735105	0.0647224
$130$	−1.52325	−0.133598
$131$	13.9626	1.21992	0.609959	−	0.792433i	$-0.291186\pi$
$131$	13.9626	1.21992	0.609959	+	0.792433i	$0.291186\pi$
$132$	−1.27326	−0.110823
$133$	2.86137	0.248112
$134$	0.447504	0.0386585
$135$	4.22913	0.363986
$136$	−7.66844	−0.657563
$137$	8.60873	0.735494	0.367747	−	0.929926i	$-0.380129\pi$
$137$	8.60873	0.735494	0.367747	+	0.929926i	$0.380129\pi$
$138$	0.179939	0.0153174
$139$	−20.3800	−1.72861	−0.864304	−	0.502970i	$-0.832241\pi$
$139$	−20.3800	−1.72861	−0.864304	+	0.502970i	$0.832241\pi$
$140$	−4.27445	−0.361257
$141$	9.29204	0.782531
$142$	−8.64879	−0.725790
$143$	2.47288	0.206793
$144$	−4.44934	−0.370778
$145$	−7.27060	−0.603790
$146$	0.615983	0.0509791
$147$	0.0337159	0.00278084
$148$	−0.335507	−0.0275785
$149$	13.0632	1.07018	0.535091	−	0.844794i	$-0.320277\pi$
$149$	13.0632	1.07018	0.535091	+	0.844794i	$0.320277\pi$
$150$	−0.483973	−0.0395162
$151$	5.24140	0.426539	0.213270	−	0.976993i	$-0.431589\pi$
$151$	5.24140	0.426539	0.213270	+	0.976993i	$0.431589\pi$
$152$	−2.41939	−0.196238
$153$	−8.19274	−0.662344
$154$	−1.62473	−0.130925
$155$	9.04017	0.726124
$156$	−3.14863	−0.252092
$157$	−19.7629	−1.57725	−0.788626	−	0.614874i	$-0.789207\pi$
$157$	−19.7629	−1.57725	−0.788626	+	0.614874i	$0.789207\pi$
$158$	−3.28596	−0.261417
$159$	1.06019	0.0840787
$160$	5.61068	0.443563
$161$	−0.980658	−0.0772867
$162$	2.35630	0.185129
$163$	−9.61981	−0.753481	−0.376741	−	0.926319i	$-0.622955\pi$
$163$	−9.61981	−0.753481	−0.376741	+	0.926319i	$0.622955\pi$
$164$	7.79866	0.608973
$165$	0.785692	0.0611660
$166$	−9.42106	−0.731216
$167$	−11.5320	−0.892374	−0.446187	−	0.894940i	$-0.647218\pi$
$167$	−11.5320	−0.892374	−0.446187	+	0.894940i	$0.647218\pi$
$168$	4.62180	0.356579
$169$	−6.88486	−0.529604
$170$	2.11802	0.162445
$171$	−2.58481	−0.197665
$172$	1.51623	0.115611
$173$	−2.42970	−0.184727	−0.0923635	−	0.995725i	$-0.529442\pi$
$173$	−2.42970	−0.184727	−0.0923635	+	0.995725i	$0.529442\pi$
$174$	3.51877	0.266757
$175$	2.63763	0.199386
$176$	−1.86736	−0.140758
$177$	1.56936	0.117960
$178$	0.617329	0.0462708
$179$	−24.3364	−1.81898	−0.909492	−	0.415721i	$-0.863529\pi$
$179$	−24.3364	−1.81898	−0.909492	+	0.415721i	$0.863529\pi$
$180$	3.86130	0.287804
$181$	−12.8701	−0.956625	−0.478312	−	0.878190i	$-0.658751\pi$
$181$	−12.8701	−0.956625	−0.478312	+	0.878190i	$0.658751\pi$
$182$	−4.01778	−0.297817
$183$	−9.68618	−0.716023
$184$	0.829180	0.0611280
$185$	0.207031	0.0152212
$186$	−4.37519	−0.320805
$187$	−3.43844	−0.251444
$188$	19.1657	1.39780
$189$	11.1549	0.811399
$190$	0.668235	0.0484789
$191$	−24.1811	−1.74968	−0.874842	−	0.484408i	$-0.839035\pi$
$191$	−24.1811	−1.74968	−0.874842	+	0.484408i	$0.839035\pi$
$192$	0.218926	0.0157996
$193$	1.48391	0.106814	0.0534071	−	0.998573i	$-0.482992\pi$
$193$	1.48391	0.106814	0.0534071	+	0.998573i	$0.482992\pi$
$194$	4.09770	0.294198
$195$	1.94292	0.139136
$196$	0.0695423	0.00496731
$197$	−17.7363	−1.26366	−0.631829	−	0.775108i	$-0.717696\pi$
$197$	−17.7363	−1.26366	−0.631829	+	0.775108i	$0.717696\pi$
$198$	1.46770	0.104305
$199$	−1.22002	−0.0864847	−0.0432424	−	0.999065i	$-0.513769\pi$
$199$	−1.22002	−0.0864847	−0.0432424	+	0.999065i	$0.513769\pi$
$200$	−2.23021	−0.157699
$201$	−0.570796	−0.0402608
$202$	1.94874	0.137113
$203$	−19.1771	−1.34597
$204$	4.37805	0.306525
$205$	−4.81231	−0.336106
$206$	−4.85875	−0.338525
$207$	0.885873	0.0615724
$208$	−4.61776	−0.320184
$209$	−1.08483	−0.0750391
$210$	−1.27654	−0.0880897
$211$	0.268573	0.0184894	0.00924468	−	0.999957i	$-0.497057\pi$
$211$	0.268573	0.0184894	0.00924468	+	0.999957i	$0.497057\pi$
$212$	2.18675	0.150187
$213$	11.0316	0.755873
$214$	1.10182	0.0753188
$215$	−0.935615	−0.0638084
$216$	−9.43184	−0.641755
$217$	23.8446	1.61868
$218$	−1.13550	−0.0769057
$219$	−0.785692	−0.0530921
$220$	1.62056	0.109258
$221$	−8.50286	−0.571964
$222$	−0.100197	−0.00672481
$223$	28.8838	1.93420	0.967100	−	0.254396i	$-0.0818768\pi$
$223$	28.8838	1.93420	0.967100	+	0.254396i	$0.0818768\pi$
$224$	14.7989	0.988792
$225$	−2.38269	−0.158846
$226$	−6.06621	−0.403518
$227$	−2.78695	−0.184976	−0.0924880	−	0.995714i	$-0.529482\pi$
$227$	−2.78695	−0.184976	−0.0924880	+	0.995714i	$0.529482\pi$
$228$	1.38127	0.0914770
$229$	21.2125	1.40176	0.700880	−	0.713279i	$-0.252791\pi$
$229$	21.2125	1.40176	0.700880	+	0.713279i	$0.252791\pi$
$230$	−0.229020	−0.0151011
$231$	2.07236	0.136351
$232$	16.2149	1.06456
$233$	−11.0637	−0.724806	−0.362403	−	0.932021i	$-0.618044\pi$
$233$	−11.0637	−0.724806	−0.362403	+	0.932021i	$0.618044\pi$
$234$	3.62944	0.237264
$235$	−11.8266	−0.771480
$236$	3.23696	0.210708
$237$	4.19127	0.272252
$238$	5.58656	0.362123
$239$	−9.49139	−0.613947	−0.306973	−	0.951718i	$-0.599316\pi$
$239$	−9.49139	−0.613947	−0.306973	+	0.951718i	$0.599316\pi$
$240$	−1.46717	−0.0947054
$241$	−14.0409	−0.904454	−0.452227	−	0.891903i	$-0.649370\pi$
$241$	−14.0409	−0.904454	−0.452227	+	0.891903i	$0.649370\pi$
$242$	0.615983	0.0395969
$243$	−15.6929	−1.00670
$244$	−19.9787	−1.27900
$245$	−0.0429124	−0.00274157
$246$	2.32903	0.148493
$247$	−2.68265	−0.170693
$248$	−20.1614	−1.28025
$249$	12.0166	0.761524
$250$	0.615983	0.0389582
$251$	18.2711	1.15326	0.576632	−	0.817004i	$-0.304367\pi$
$251$	18.2711	1.15326	0.576632	+	0.817004i	$0.304367\pi$
$252$	10.1847	0.641575
$253$	0.371795	0.0233746
$254$	−5.03497	−0.315922
$255$	−2.70156	−0.169178
$256$	−6.46061	−0.403788
$257$	0.963081	0.0600753	0.0300377	−	0.999549i	$-0.490437\pi$
$257$	0.963081	0.0600753	0.0300377	+	0.999549i	$0.490437\pi$
$258$	0.452812	0.0281909
$259$	0.546071	0.0339312
$260$	4.00747	0.248532
$261$	17.3236	1.07230
$262$	8.60072	0.531354
$263$	−4.53391	−0.279573	−0.139787	−	0.990182i	$-0.544642\pi$
$263$	−4.53391	−0.279573	−0.139787	+	0.990182i	$0.544642\pi$
$264$	−1.75225	−0.107844
$265$	−1.34937	−0.0828914
$266$	1.76256	0.108069
$267$	−0.787409	−0.0481886
$268$	−1.17732	−0.0719163
$269$	31.1523	1.89939	0.949695	−	0.313178i	$-0.101394\pi$
$269$	31.1523	1.89939	0.949695	+	0.313178i	$0.101394\pi$
$270$	2.60507	0.158540
$271$	4.43239	0.269248	0.134624	−	0.990897i	$-0.457017\pi$
$271$	4.43239	0.269248	0.134624	+	0.990897i	$0.457017\pi$
$272$	6.42081	0.389319
$273$	5.12471	0.310162
$274$	5.30283	0.320356
$275$	−1.00000	−0.0603023
$276$	−0.473394	−0.0284950
$277$	5.84921	0.351445	0.175722	−	0.984440i	$-0.443774\pi$
$277$	5.84921	0.351445	0.175722	+	0.984440i	$0.443774\pi$
$278$	−12.5537	−0.752923
$279$	−21.5399	−1.28956
$280$	−5.88246	−0.351544
$281$	−28.5589	−1.70368	−0.851840	−	0.523803i	$-0.824513\pi$
$281$	−28.5589	−1.70368	−0.851840	+	0.523803i	$0.824513\pi$
$282$	5.72374	0.340844
$283$	31.1072	1.84913	0.924567	−	0.381020i	$-0.124427\pi$
$283$	31.1072	1.84913	0.924567	+	0.381020i	$0.124427\pi$
$284$	22.7538	1.35019
$285$	−0.852340	−0.0504883
$286$	1.52325	0.0900718
$287$	−12.6931	−0.749249
$288$	−13.3685	−0.787746
$289$	−5.17712	−0.304536
$290$	−4.47856	−0.262990
$291$	−5.22666	−0.306392
$292$	−1.62056	−0.0948364
$293$	−24.4249	−1.42692	−0.713458	−	0.700698i	$-0.752872\pi$
$293$	−24.4249	−1.42692	−0.713458	+	0.700698i	$0.752872\pi$
$294$	0.0207684	0.00121124
$295$	−1.99743	−0.116295
$296$	−0.461722	−0.0268370
$297$	−4.22913	−0.245399
$298$	8.04674	0.466135
$299$	0.919406	0.0531706
$300$	1.27326	0.0735120
$301$	−2.46781	−0.142242
$302$	3.22861	0.185786
$303$	−2.48563	−0.142796
$304$	2.02576	0.116186
$305$	12.3282	0.705912
$306$	−5.04659	−0.288494
$307$	−4.51256	−0.257545	−0.128773	−	0.991674i	$-0.541104\pi$
$307$	−4.51256	−0.257545	−0.128773	+	0.991674i	$0.541104\pi$
$308$	4.27445	0.243559
$309$	6.19737	0.352556
$310$	5.56859	0.316275
$311$	9.38328	0.532077	0.266038	−	0.963962i	$-0.414285\pi$
$311$	9.38328	0.532077	0.266038	+	0.963962i	$0.414285\pi$
$312$	−4.33312	−0.245315
$313$	11.4881	0.649345	0.324673	−	0.945826i	$-0.394746\pi$
$313$	11.4881	0.649345	0.324673	+	0.945826i	$0.394746\pi$
$314$	−12.1736	−0.686997
$315$	−6.28465	−0.354100
$316$	8.64490	0.486314
$317$	−34.1036	−1.91545	−0.957723	−	0.287692i	$-0.907112\pi$
$317$	−34.1036	−1.91545	−0.957723	+	0.287692i	$0.907112\pi$
$318$	0.653061	0.0366218
$319$	7.27060	0.407075
$320$	−0.278641	−0.0155765
$321$	−1.40538	−0.0784406
$322$	−0.604069	−0.0336634
$323$	3.73012	0.207549
$324$	−6.19910	−0.344394
$325$	−2.47288	−0.137171
$326$	−5.92564	−0.328191
$327$	1.44834	0.0800934
$328$	10.7324	0.592600
$329$	−31.1941	−1.71979
$330$	0.483973	0.0266418
$331$	−24.7994	−1.36310	−0.681548	−	0.731773i	$-0.738693\pi$
$331$	−24.7994	−1.36310	−0.681548	+	0.731773i	$0.738693\pi$
$332$	24.7855	1.36028
$333$	−0.493290	−0.0270322
$334$	−7.10353	−0.388688
$335$	0.726488	0.0396923
$336$	−3.86985	−0.211118
$337$	−32.0340	−1.74500	−0.872501	−	0.488612i	$-0.837504\pi$
$337$	−32.0340	−1.74500	−0.872501	+	0.488612i	$0.837504\pi$
$338$	−4.24095	−0.230677
$339$	7.73750	0.420243
$340$	−5.57222	−0.302196
$341$	−9.04017	−0.489553
$342$	−1.59220	−0.0860961
$343$	−18.5766	−1.00304
$344$	2.08662	0.112503
$345$	0.292117	0.0157270
$346$	−1.49666	−0.0804608
$347$	3.38097	0.181500	0.0907499	−	0.995874i	$-0.471074\pi$
$347$	3.38097	0.181500	0.0907499	+	0.995874i	$0.471074\pi$
$348$	−9.25739	−0.496248
$349$	3.87855	0.207614	0.103807	−	0.994597i	$-0.466898\pi$
$349$	3.87855	0.207614	0.103807	+	0.994597i	$0.466898\pi$
$350$	1.62473	0.0868457
$351$	−10.4581	−0.558215
$352$	−5.61068	−0.299050
$353$	−16.2291	−0.863787	−0.431893	−	0.901925i	$-0.642154\pi$
$353$	−16.2291	−0.863787	−0.431893	+	0.901925i	$0.642154\pi$
$354$	0.966700	0.0513795
$355$	−14.0406	−0.745199
$356$	−1.62411	−0.0860775
$357$	−7.12570	−0.377132
$358$	−14.9908	−0.792287
$359$	−10.0041	−0.527998	−0.263999	−	0.964523i	$-0.585042\pi$
$359$	−10.0041	−0.527998	−0.263999	+	0.964523i	$0.585042\pi$
$360$	5.31389	0.280066
$361$	−17.8231	−0.938061
$362$	−7.92774	−0.416673
$363$	−0.785692	−0.0412381
$364$	10.5702	0.554029
$365$	1.00000	0.0523424
$366$	−5.96652	−0.311875
$367$	24.6638	1.28744	0.643720	−	0.765261i	$-0.277390\pi$
$367$	24.6638	1.28744	0.643720	+	0.765261i	$0.277390\pi$
$368$	−0.694276	−0.0361916
$369$	11.4662	0.596908
$370$	0.127528	0.00662984
$371$	−3.55915	−0.184782
$372$	11.5105	0.596793
$373$	−17.7031	−0.916631	−0.458316	−	0.888790i	$-0.651547\pi$
$373$	−17.7031	−0.916631	−0.458316	+	0.888790i	$0.651547\pi$
$374$	−2.11802	−0.109520
$375$	−0.785692	−0.0405729
$376$	26.3757	1.36022
$377$	17.9793	0.925983
$378$	6.87122	0.353417
$379$	24.3913	1.25290	0.626449	−	0.779462i	$-0.284508\pi$
$379$	24.3913	1.25290	0.626449	+	0.779462i	$0.284508\pi$
$380$	−1.75803	−0.0901852
$381$	6.42214	0.329016
$382$	−14.8952	−0.762103
$383$	24.9110	1.27289	0.636446	−	0.771321i	$-0.280404\pi$
$383$	24.9110	1.27289	0.636446	+	0.771321i	$0.280404\pi$
$384$	8.95138	0.456798
$385$	−2.63763	−0.134426
$386$	0.914064	0.0465246
$387$	2.22928	0.113321
$388$	−10.7805	−0.547296
$389$	0.545741	0.0276702	0.0138351	−	0.999904i	$-0.495596\pi$
$389$	0.545741	0.0276702	0.0138351	+	0.999904i	$0.495596\pi$
$390$	1.19681	0.0606027
$391$	−1.27840	−0.0646513
$392$	0.0957035	0.00483376
$393$	−10.9703	−0.553378
$394$	−10.9253	−0.550406
$395$	−5.33450	−0.268408
$396$	−3.86130	−0.194038
$397$	11.7188	0.588151	0.294076	−	0.955782i	$-0.404988\pi$
$397$	11.7188	0.588151	0.294076	+	0.955782i	$0.404988\pi$
$398$	−0.751510	−0.0376698
$399$	−2.24816	−0.112549
$400$	1.86736	0.0933680
$401$	−1.52808	−0.0763084	−0.0381542	−	0.999272i	$-0.512148\pi$
$401$	−1.52808	−0.0763084	−0.0381542	+	0.999272i	$0.512148\pi$
$402$	−0.351600	−0.0175362
$403$	−22.3553	−1.11360
$404$	−5.12685	−0.255071
$405$	3.82527	0.190079
$406$	−11.8128	−0.586259
$407$	−0.207031	−0.0102621
$408$	6.02503	0.298283
$409$	−29.7684	−1.47195	−0.735977	−	0.677006i	$-0.763277\pi$
$409$	−29.7684	−1.47195	−0.735977	+	0.677006i	$0.763277\pi$
$410$	−2.96430	−0.146396
$411$	−6.76381	−0.333634
$412$	12.7827	0.629757
$413$	−5.26847	−0.259244
$414$	0.545682	0.0268188
$415$	−15.2944	−0.750770
$416$	−13.8745	−0.680255
$417$	16.0124	0.784130
$418$	−0.668235	−0.0326844
$419$	19.9213	0.973217	0.486608	−	0.873620i	$-0.338234\pi$
$419$	19.9213	0.973217	0.486608	+	0.873620i	$0.338234\pi$
$420$	3.35840	0.163873
$421$	−29.3484	−1.43035	−0.715177	−	0.698943i	$-0.753654\pi$
$421$	−29.3484	−1.43035	−0.715177	+	0.698943i	$0.753654\pi$
$422$	0.165437	0.00805333
$423$	28.1790	1.37011
$424$	3.00938	0.146149
$425$	3.43844	0.166789
$426$	6.79528	0.329232
$427$	32.5173	1.57362
$428$	−2.89873	−0.140115
$429$	−1.94292	−0.0938052
$430$	−0.576323	−0.0277928
$431$	25.5953	1.23288	0.616441	−	0.787401i	$-0.288574\pi$
$431$	25.5953	1.23288	0.616441	+	0.787401i	$0.288574\pi$
$432$	7.89732	0.379960
$433$	−8.98075	−0.431587	−0.215794	−	0.976439i	$-0.569234\pi$
$433$	−8.98075	−0.431587	−0.215794	+	0.976439i	$0.569234\pi$
$434$	14.6879	0.705041
$435$	5.71245	0.273891
$436$	2.98734	0.143068
$437$	−0.403334	−0.0192941
$438$	−0.483973	−0.0231251
$439$	11.7395	0.560298	0.280149	−	0.959957i	$-0.409616\pi$
$439$	11.7395	0.560298	0.280149	+	0.959957i	$0.409616\pi$
$440$	2.23021	0.106321
$441$	0.102247	0.00486890
$442$	−5.23762	−0.249128
$443$	26.3787	1.25329	0.626644	−	0.779306i	$-0.284428\pi$
$443$	26.3787	1.25329	0.626644	+	0.779306i	$0.284428\pi$
$444$	0.263605	0.0125102
$445$	1.00219	0.0475081
$446$	17.7919	0.842471
$447$	−10.2637	−0.485456
$448$	−0.734951	−0.0347232
$449$	24.4811	1.15533	0.577667	−	0.816273i	$-0.303963\pi$
$449$	24.4811	1.15533	0.577667	+	0.816273i	$0.303963\pi$
$450$	−1.46770	−0.0691878
$451$	4.81231	0.226603
$452$	15.9593	0.750664
$453$	−4.11813	−0.193486
$454$	−1.71671	−0.0805692
$455$	−6.52255	−0.305782
$456$	1.90089	0.0890175
$457$	3.39311	0.158723	0.0793614	−	0.996846i	$-0.474712\pi$
$457$	3.39311	0.158723	0.0793614	+	0.996846i	$0.474712\pi$
$458$	13.0665	0.610559
$459$	14.5416	0.678745
$460$	0.602519	0.0280926
$461$	−9.36835	−0.436328	−0.218164	−	0.975912i	$-0.570007\pi$
$461$	−9.36835	−0.436328	−0.218164	+	0.975912i	$0.570007\pi$
$462$	1.27654	0.0593900
$463$	34.6802	1.61172	0.805862	−	0.592104i	$-0.201702\pi$
$463$	34.6802	1.61172	0.805862	+	0.592104i	$0.201702\pi$
$464$	−13.5768	−0.630289
$465$	−7.10278	−0.329384
$466$	−6.81504	−0.315701
$467$	−4.56793	−0.211378	−0.105689	−	0.994399i	$-0.533705\pi$
$467$	−4.56793	−0.211378	−0.105689	+	0.994399i	$0.533705\pi$
$468$	−9.54854	−0.441382
$469$	1.91621	0.0884822
$470$	−7.28496	−0.336030
$471$	15.5275	0.715472
$472$	4.45467	0.205043
$473$	0.935615	0.0430196
$474$	2.58175	0.118584
$475$	1.08483	0.0497753
$476$	−14.6974	−0.673656
$477$	3.21514	0.147211
$478$	−5.84653	−0.267414
$479$	5.19230	0.237242	0.118621	−	0.992940i	$-0.462153\pi$
$479$	5.19230	0.237242	0.118621	+	0.992940i	$0.462153\pi$
$480$	−4.40826	−0.201209
$481$	−0.511963	−0.0233435
$482$	−8.64895	−0.393949
$483$	0.770495	0.0350587
$484$	−1.62056	−0.0736620
$485$	6.65230	0.302065
$486$	−9.66655	−0.438484
$487$	−12.4624	−0.564725	−0.282362	−	0.959308i	$-0.591118\pi$
$487$	−12.4624	−0.564725	−0.282362	+	0.959308i	$0.591118\pi$
$488$	−27.4945	−1.24462
$489$	7.55820	0.341794
$490$	−0.0264333	−0.00119414
$491$	6.08004	0.274388	0.137194	−	0.990544i	$-0.456192\pi$
$491$	6.08004	0.274388	0.137194	+	0.990544i	$0.456192\pi$
$492$	−6.12734	−0.276242
$493$	−24.9995	−1.12592
$494$	−1.65247	−0.0743480
$495$	2.38269	0.107094
$496$	16.8813	0.757991
$497$	−37.0340	−1.66120
$498$	7.40205	0.331694
$499$	−14.1937	−0.635396	−0.317698	−	0.948192i	$-0.602910\pi$
$499$	−14.1937	−0.635396	−0.317698	+	0.948192i	$0.602910\pi$
$500$	−1.62056	−0.0724739
$501$	9.06061	0.404798
$502$	11.2547	0.502322
$503$	−2.26393	−0.100944	−0.0504718	−	0.998725i	$-0.516073\pi$
$503$	−2.26393	−0.100944	−0.0504718	+	0.998725i	$0.516073\pi$
$504$	14.0161	0.624325
$505$	3.16362	0.140779
$506$	0.229020	0.0101812
$507$	5.40937	0.240239
$508$	13.2463	0.587709
$509$	35.9305	1.59259	0.796297	−	0.604906i	$-0.206789\pi$
$509$	35.9305	1.59259	0.796297	+	0.604906i	$0.206789\pi$
$510$	−1.66411	−0.0736881
$511$	2.63763	0.116682
$512$	18.8064	0.831131
$513$	4.58788	0.202560
$514$	0.593241	0.0261668
$515$	−7.88779	−0.347578
$516$	−1.19129	−0.0524434
$517$	11.8266	0.520132
$518$	0.336370	0.0147793
$519$	1.90900	0.0837957
$520$	5.51504	0.241850
$521$	−16.7027	−0.731759	−0.365879	−	0.930662i	$-0.619232\pi$
$521$	−16.7027	−0.731759	−0.365879	+	0.930662i	$0.619232\pi$
$522$	10.6710	0.467058
$523$	42.1763	1.84424	0.922120	−	0.386905i	$-0.126456\pi$
$523$	42.1763	1.84424	0.922120	+	0.386905i	$0.126456\pi$
$524$	−22.6273	−0.988477
$525$	−2.07236	−0.0904454
$526$	−2.79281	−0.121772
$527$	31.0841	1.35404
$528$	1.46717	0.0638504
$529$	−22.8618	−0.993990
$530$	−0.831192	−0.0361047
$531$	4.75925	0.206534
$532$	−4.63704	−0.201041
$533$	11.9003	0.515458
$534$	−0.485030	−0.0209893
$535$	1.78872	0.0773329
$536$	−1.62022	−0.0699828
$537$	19.1209	0.825127
$538$	19.1893	0.827309
$539$	0.0429124	0.00184837
$540$	−6.85359	−0.294931
$541$	22.7192	0.976774	0.488387	−	0.872627i	$-0.337585\pi$
$541$	22.7192	0.976774	0.488387	+	0.872627i	$0.337585\pi$
$542$	2.73028	0.117275
$543$	10.1119	0.433943
$544$	19.2920	0.827137
$545$	−1.84339	−0.0789623
$546$	3.15673	0.135096
$547$	28.4153	1.21495	0.607474	−	0.794339i	$-0.292183\pi$
$547$	28.4153	1.21495	0.607474	+	0.794339i	$0.292183\pi$
$548$	−13.9510	−0.595958
$549$	−29.3743	−1.25366
$550$	−0.615983	−0.0262656
$551$	−7.88734	−0.336012
$552$	−0.651480	−0.0277288
$553$	−14.0704	−0.598335
$554$	3.60301	0.153077
$555$	−0.162663	−0.00690464
$556$	33.0271	1.40066
$557$	2.30377	0.0976139	0.0488070	−	0.998808i	$-0.484458\pi$
$557$	2.30377	0.0976139	0.0488070	+	0.998808i	$0.484458\pi$
$558$	−13.2682	−0.561688
$559$	2.31367	0.0978576
$560$	4.92541	0.208136
$561$	2.70156	0.114060
$562$	−17.5918	−0.742064
$563$	5.23325	0.220555	0.110278	−	0.993901i	$-0.464826\pi$
$563$	5.23325	0.220555	0.110278	+	0.993901i	$0.464826\pi$
$564$	−15.0583	−0.634071
$565$	−9.84801	−0.414309
$566$	19.1615	0.805419
$567$	10.0896	0.423725
$568$	31.3135	1.31389
$569$	−11.9254	−0.499941	−0.249970	−	0.968254i	$-0.580421\pi$
$569$	−11.9254	−0.499941	−0.249970	+	0.968254i	$0.580421\pi$
$570$	−0.525027	−0.0219910
$571$	−16.7216	−0.699777	−0.349888	−	0.936791i	$-0.613780\pi$
$571$	−16.7216	−0.699777	−0.349888	+	0.936791i	$0.613780\pi$
$572$	−4.00747	−0.167561
$573$	18.9989	0.793691
$574$	−7.81872	−0.326347
$575$	−0.371795	−0.0155049
$576$	0.663915	0.0276631
$577$	−13.8757	−0.577654	−0.288827	−	0.957381i	$-0.593265\pi$
$577$	−13.8757	−0.577654	−0.288827	+	0.957381i	$0.593265\pi$
$578$	−3.18901	−0.132646
$579$	−1.16590	−0.0484530
$580$	11.7825	0.489241
$581$	−40.3408	−1.67362
$582$	−3.21953	−0.133454
$583$	1.34937	0.0558854
$584$	−2.23021	−0.0922866
$585$	5.89211	0.243609
$586$	−15.0453	−0.621515
$587$	35.1107	1.44917	0.724586	−	0.689184i	$-0.242031\pi$
$587$	35.1107	1.44917	0.724586	+	0.689184i	$0.242031\pi$
$588$	−0.0546388	−0.00225327
$589$	9.80702	0.404091
$590$	−1.23038	−0.0506540
$591$	13.9353	0.573220
$592$	0.386602	0.0158892
$593$	22.6632	0.930666	0.465333	−	0.885136i	$-0.345935\pi$
$593$	22.6632	0.930666	0.465333	+	0.885136i	$0.345935\pi$
$594$	−2.60507	−0.106887
$595$	9.06934	0.371807
$596$	−21.1698	−0.867151
$597$	0.958557	0.0392311
$598$	0.566338	0.0231593
$599$	−20.2396	−0.826969	−0.413484	−	0.910511i	$-0.635688\pi$
$599$	−20.2396	−0.826969	−0.413484	+	0.910511i	$0.635688\pi$
$600$	1.75225	0.0715355
$601$	−11.2299	−0.458079	−0.229039	−	0.973417i	$-0.573558\pi$
$601$	−11.2299	−0.458079	−0.229039	+	0.973417i	$0.573558\pi$
$602$	−1.52013	−0.0619557
$603$	−1.73099	−0.0704916
$604$	−8.49403	−0.345617
$605$	1.00000	0.0406558
$606$	−1.53111	−0.0621970
$607$	−39.4528	−1.60134	−0.800669	−	0.599107i	$-0.795522\pi$
$607$	−39.4528	−1.60134	−0.800669	+	0.599107i	$0.795522\pi$
$608$	6.08661	0.246845
$609$	15.0673	0.610559
$610$	7.59397	0.307471
$611$	29.2457	1.18315
$612$	13.2769	0.536685
$613$	28.7459	1.16104	0.580518	−	0.814248i	$-0.302850\pi$
$613$	28.7459	1.16104	0.580518	+	0.814248i	$0.302850\pi$
$614$	−2.77966	−0.112178
$615$	3.78099	0.152464
$616$	5.88246	0.237011
$617$	11.5380	0.464502	0.232251	−	0.972656i	$-0.425391\pi$
$617$	11.5380	0.464502	0.232251	+	0.972656i	$0.425391\pi$
$618$	3.81748	0.153561
$619$	0.573386	0.0230463	0.0115232	−	0.999934i	$-0.496332\pi$
$619$	0.573386	0.0230463	0.0115232	+	0.999934i	$0.496332\pi$
$620$	−14.6502	−0.588365
$621$	−1.57237	−0.0630971
$622$	5.77994	0.231754
$623$	2.64339	0.105905
$624$	3.62814	0.145242
$625$	1.00000	0.0400000
$626$	7.07647	0.282833
$627$	0.852340	0.0340392
$628$	32.0271	1.27802
$629$	0.711864	0.0283839
$630$	−3.87124	−0.154234
$631$	−1.23731	−0.0492564	−0.0246282	−	0.999697i	$-0.507840\pi$
$631$	−1.23731	−0.0492564	−0.0246282	+	0.999697i	$0.507840\pi$
$632$	11.8970	0.473239
$633$	−0.211016	−0.00838713
$634$	−21.0072	−0.834303
$635$	−8.17387	−0.324370
$636$	−1.71811	−0.0681275
$637$	0.106117	0.00420452
$638$	4.47856	0.177308
$639$	33.4544	1.32344
$640$	−11.3930	−0.450347
$641$	33.7321	1.33234	0.666168	−	0.745802i	$-0.267933\pi$
$641$	33.7321	1.33234	0.666168	+	0.745802i	$0.267933\pi$
$642$	−0.865690	−0.0341661
$643$	−11.1822	−0.440982	−0.220491	−	0.975389i	$-0.570766\pi$
$643$	−11.1822	−0.440982	−0.220491	+	0.975389i	$0.570766\pi$
$644$	1.58922	0.0626241
$645$	0.735105	0.0289447
$646$	2.29769	0.0904013
$647$	13.6278	0.535765	0.267883	−	0.963452i	$-0.413676\pi$
$647$	13.6278	0.535765	0.267883	+	0.963452i	$0.413676\pi$
$648$	−8.53114	−0.335135
$649$	1.99743	0.0784058
$650$	−1.52325	−0.0597469
$651$	−18.7345	−0.734263
$652$	15.5895	0.610533
$653$	33.2972	1.30302	0.651510	−	0.758640i	$-0.274136\pi$
$653$	33.2972	1.30302	0.651510	+	0.758640i	$0.274136\pi$
$654$	0.892153	0.0348859
$655$	13.9626	0.545564
$656$	−8.98631	−0.350857
$657$	−2.38269	−0.0929575
$658$	−19.2150	−0.749080
$659$	30.5489	1.19002	0.595008	−	0.803720i	$-0.297149\pi$
$659$	30.5489	1.19002	0.595008	+	0.803720i	$0.297149\pi$
$660$	−1.27326	−0.0495618
$661$	−0.462126	−0.0179746	−0.00898731	−	0.999960i	$-0.502861\pi$
$661$	−0.462126	−0.0179746	−0.00898731	+	0.999960i	$0.502861\pi$
$662$	−15.2760	−0.593718
$663$	6.68063	0.259454
$664$	34.1096	1.32371
$665$	2.86137	0.110959
$666$	−0.303859	−0.0117743
$667$	2.70317	0.104667
$668$	18.6884	0.723075
$669$	−22.6937	−0.877390
$670$	0.447504	0.0172886
$671$	−12.3282	−0.475926
$672$	−11.6274	−0.448535
$673$	29.8047	1.14889	0.574444	−	0.818544i	$-0.305218\pi$
$673$	29.8047	1.14889	0.574444	+	0.818544i	$0.305218\pi$
$674$	−19.7324	−0.760063
$675$	4.22913	0.162779
$676$	11.1574	0.429129
$677$	6.06308	0.233023	0.116512	−	0.993189i	$-0.462829\pi$
$677$	6.06308	0.233023	0.116512	+	0.993189i	$0.462829\pi$
$678$	4.76617	0.183044
$679$	17.5463	0.673365
$680$	−7.66844	−0.294071
$681$	2.18968	0.0839087
$682$	−5.56859	−0.213232
$683$	21.3509	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$683$	21.3509	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$684$	4.18885	0.160165
$685$	8.60873	0.328923
$686$	−11.4429	−0.436891
$687$	−16.6665	−0.635866
$688$	−1.74713	−0.0666087
$689$	3.33684	0.127124
$690$	0.179939	0.00685015
$691$	−18.8520	−0.717166	−0.358583	−	0.933498i	$-0.616740\pi$
$691$	−18.8520	−0.717166	−0.358583	+	0.933498i	$0.616740\pi$
$692$	3.93749	0.149681
$693$	6.28465	0.238734
$694$	2.08262	0.0790551
$695$	−20.3800	−0.773057
$696$	−12.7399	−0.482906
$697$	−16.5468	−0.626756
$698$	2.38912	0.0904295
$699$	8.69265	0.328786
$700$	−4.27445	−0.161559
$701$	41.0335	1.54981	0.774906	−	0.632076i	$-0.217797\pi$
$701$	41.0335	1.54981	0.774906	+	0.632076i	$0.217797\pi$
$702$	−6.44204	−0.243139
$703$	0.224593	0.00847068
$704$	0.278641	0.0105017
$705$	9.29204	0.349958
$706$	−9.99683	−0.376236
$707$	8.34446	0.313826
$708$	−2.54325	−0.0955813
$709$	−15.6669	−0.588382	−0.294191	−	0.955747i	$-0.595050\pi$
$709$	−15.6669	−0.588382	−0.294191	+	0.955747i	$0.595050\pi$
$710$	−8.64879	−0.324583
$711$	12.7104	0.476679
$712$	−2.23508	−0.0837632
$713$	−3.36109	−0.125874
$714$	−4.38931	−0.164266
$715$	2.47288	0.0924805
$716$	39.4386	1.47389
$717$	7.45730	0.278498
$718$	−6.16238	−0.229978
$719$	−37.3713	−1.39372	−0.696858	−	0.717209i	$-0.745419\pi$
$719$	−37.3713	−1.39372	−0.696858	+	0.717209i	$0.745419\pi$
$720$	−4.44934	−0.165817
$721$	−20.8051	−0.774821
$722$	−10.9788	−0.408587
$723$	11.0318	0.410278
$724$	20.8568	0.775136
$725$	−7.27060	−0.270023
$726$	−0.483973	−0.0179619
$727$	41.5444	1.54080	0.770399	−	0.637562i	$-0.220057\pi$
$727$	41.5444	1.54080	0.770399	+	0.637562i	$0.220057\pi$
$728$	14.5466	0.539134
$729$	0.853957	0.0316280
$730$	0.615983	0.0227986
$731$	−3.21706	−0.118987
$732$	15.6971	0.580181
$733$	19.1933	0.708921	0.354460	−	0.935071i	$-0.384665\pi$
$733$	19.1933	0.708921	0.354460	+	0.935071i	$0.384665\pi$
$734$	15.1925	0.560765
$735$	0.0337159	0.00124363
$736$	−2.08602	−0.0768918
$737$	−0.726488	−0.0267605
$738$	7.06300	0.259993
$739$	−27.2245	−1.00147	−0.500735	−	0.865601i	$-0.666937\pi$
$739$	−27.2245	−1.00147	−0.500735	+	0.865601i	$0.666937\pi$
$740$	−0.335507	−0.0123335
$741$	2.10774	0.0774296
$742$	−2.19238	−0.0804847
$743$	16.7966	0.616207	0.308104	−	0.951353i	$-0.400306\pi$
$743$	16.7966	0.616207	0.308104	+	0.951353i	$0.400306\pi$
$744$	15.8407	0.580747
$745$	13.0632	0.478600
$746$	−10.9048	−0.399253
$747$	36.4417	1.33333
$748$	5.57222	0.203741
$749$	4.71797	0.172391
$750$	−0.483973	−0.0176722
$751$	1.05813	0.0386117	0.0193059	−	0.999814i	$-0.493854\pi$
$751$	1.05813	0.0386117	0.0193059	+	0.999814i	$0.493854\pi$
$752$	−22.0845	−0.805338
$753$	−14.3555	−0.523143
$754$	11.0750	0.403326
$755$	5.24140	0.190754
$756$	−18.0772	−0.657462
$757$	−28.1322	−1.02248	−0.511240	−	0.859438i	$-0.670814\pi$
$757$	−28.1322	−1.02248	−0.511240	+	0.859438i	$0.670814\pi$
$758$	15.0246	0.545720
$759$	−0.292117	−0.0106032
$760$	−2.41939	−0.0877605
$761$	−8.18126	−0.296571	−0.148285	−	0.988945i	$-0.547375\pi$
$761$	−8.18126	−0.296571	−0.148285	+	0.988945i	$0.547375\pi$
$762$	3.95593	0.143308
$763$	−4.86219	−0.176023
$764$	39.1871	1.41774
$765$	−8.19274	−0.296209
$766$	15.3447	0.554428
$767$	4.93940	0.178351
$768$	5.07604	0.183166
$769$	−4.70831	−0.169786	−0.0848930	−	0.996390i	$-0.527055\pi$
$769$	−4.70831	−0.169786	−0.0848930	+	0.996390i	$0.527055\pi$
$770$	−1.62473	−0.0585514
$771$	−0.756685	−0.0272513
$772$	−2.40477	−0.0865497
$773$	17.9997	0.647406	0.323703	−	0.946159i	$-0.395072\pi$
$773$	17.9997	0.647406	0.323703	+	0.946159i	$0.395072\pi$
$774$	1.37320	0.0493586
$775$	9.04017	0.324732
$776$	−14.8360	−0.532581
$777$	−0.429044	−0.0153919
$778$	0.336167	0.0120522
$779$	−5.22052	−0.187045
$780$	−3.14863	−0.112739
$781$	14.0406	0.502413
$782$	−0.787471	−0.0281599
$783$	−30.7483	−1.09886
$784$	−0.0801329	−0.00286189
$785$	−19.7629	−0.705368
$786$	−6.75751	−0.241032
$787$	53.0712	1.89178	0.945892	−	0.324482i	$-0.105190\pi$
$787$	53.0712	1.89178	0.945892	+	0.324482i	$0.105190\pi$
$788$	28.7428	1.02392
$789$	3.56226	0.126820
$790$	−3.28596	−0.116909
$791$	−25.9754	−0.923579
$792$	−5.31389	−0.188821
$793$	−30.4862	−1.08260
$794$	7.21860	0.256178
$795$	1.06019	0.0376012
$796$	1.97712	0.0700771
$797$	−7.94298	−0.281355	−0.140677	−	0.990055i	$-0.544928\pi$
$797$	−7.94298	−0.281355	−0.140677	+	0.990055i	$0.544928\pi$
$798$	−1.38483	−0.0490223
$799$	−40.6650	−1.43862
$800$	5.61068	0.198367
$801$	−2.38790	−0.0843721
$802$	−0.941269	−0.0332373
$803$	−1.00000	−0.0352892
$804$	0.925011	0.0326226
$805$	−0.980658	−0.0345637
$806$	−13.7705	−0.485044
$807$	−24.4761	−0.861600
$808$	−7.05553	−0.248213
$809$	−23.3185	−0.819834	−0.409917	−	0.912123i	$-0.634442\pi$
$809$	−23.3185	−0.819834	−0.409917	+	0.912123i	$0.634442\pi$
$810$	2.35630	0.0827920
$811$	−17.8700	−0.627499	−0.313750	−	0.949506i	$-0.601585\pi$
$811$	−17.8700	−0.627499	−0.313750	+	0.949506i	$0.601585\pi$
$812$	31.0778	1.09062
$813$	−3.48249	−0.122136
$814$	−0.127528	−0.00446984
$815$	−9.61981	−0.336967
$816$	−5.04478	−0.176603
$817$	−1.01498	−0.0355097
$818$	−18.3369	−0.641133
$819$	15.5412	0.543053
$820$	7.79866	0.272341
$821$	−14.2856	−0.498570	−0.249285	−	0.968430i	$-0.580196\pi$
$821$	−14.2856	−0.498570	−0.249285	+	0.968430i	$0.580196\pi$
$822$	−4.16639	−0.145320
$823$	−19.4104	−0.676604	−0.338302	−	0.941038i	$-0.609853\pi$
$823$	−19.4104	−0.676604	−0.338302	+	0.941038i	$0.609853\pi$
$824$	17.5914	0.612826
$825$	0.785692	0.0273543
$826$	−3.24529	−0.112918
$827$	3.05299	0.106163	0.0530814	−	0.998590i	$-0.483096\pi$
$827$	3.05299	0.106163	0.0530814	+	0.998590i	$0.483096\pi$
$828$	−1.43561	−0.0498910
$829$	13.9163	0.483332	0.241666	−	0.970359i	$-0.422306\pi$
$829$	13.9163	0.483332	0.241666	+	0.970359i	$0.422306\pi$
$830$	−9.42106	−0.327010
$831$	−4.59567	−0.159422
$832$	0.689046	0.0238884
$833$	−0.147552	−0.00511237
$834$	9.86336	0.341540
$835$	−11.5320	−0.399082
$836$	1.75803	0.0608028
$837$	38.2321	1.32149
$838$	12.2712	0.423900
$839$	−2.45538	−0.0847690	−0.0423845	−	0.999101i	$-0.513495\pi$
$839$	−2.45538	−0.0847690	−0.0423845	+	0.999101i	$0.513495\pi$
$840$	4.62180	0.159467
$841$	23.8616	0.822814
$842$	−18.0781	−0.623014
$843$	22.4385	0.772822
$844$	−0.435241	−0.0149816
$845$	−6.88486	−0.236846
$846$	17.3578	0.596774
$847$	2.63763	0.0906300
$848$	−2.51977	−0.0865292
$849$	−24.4407	−0.838803
$850$	2.11802	0.0726476
$851$	−0.0769732	−0.00263861
$852$	−17.8774	−0.612471
$853$	−12.0638	−0.413058	−0.206529	−	0.978440i	$-0.566217\pi$
$853$	−12.0638	−0.413058	−0.206529	+	0.978440i	$0.566217\pi$
$854$	20.0301	0.685415
$855$	−2.58481	−0.0883985
$856$	−3.98921	−0.136348
$857$	15.6304	0.533925	0.266963	−	0.963707i	$-0.413980\pi$
$857$	15.6304	0.533925	0.266963	+	0.963707i	$0.413980\pi$
$858$	−1.19681	−0.0408583
$859$	18.7532	0.639850	0.319925	−	0.947443i	$-0.396342\pi$
$859$	18.7532	0.639850	0.319925	+	0.947443i	$0.396342\pi$
$860$	1.51623	0.0517029
$861$	9.97285	0.339874
$862$	15.7663	0.537001
$863$	−39.2020	−1.33445	−0.667226	−	0.744855i	$-0.732518\pi$
$863$	−39.2020	−1.33445	−0.667226	+	0.744855i	$0.732518\pi$
$864$	23.7283	0.807253
$865$	−2.42970	−0.0826124
$866$	−5.53199	−0.187985
$867$	4.06762	0.138143
$868$	−38.6417	−1.31159
$869$	5.33450	0.180960
$870$	3.51877	0.119298
$871$	−1.79652	−0.0608727
$872$	4.11115	0.139221
$873$	−15.8504	−0.536453
$874$	−0.248447	−0.00840384
$875$	2.63763	0.0891681
$876$	1.27326	0.0430196
$877$	40.4190	1.36485	0.682426	−	0.730955i	$-0.260925\pi$
$877$	40.4190	1.36485	0.682426	+	0.730955i	$0.260925\pi$
$878$	7.23136	0.244047
$879$	19.1904	0.647276
$880$	−1.86736	−0.0629487
$881$	−9.00760	−0.303474	−0.151737	−	0.988421i	$-0.548487\pi$
$881$	−9.00760	−0.303474	−0.151737	+	0.988421i	$0.548487\pi$
$882$	0.0629823	0.00212073
$883$	−10.0059	−0.336726	−0.168363	−	0.985725i	$-0.553848\pi$
$883$	−10.0059	−0.336726	−0.168363	+	0.985725i	$0.553848\pi$
$884$	13.7794	0.463453
$885$	1.56936	0.0527535
$886$	16.2488	0.545889
$887$	−12.3263	−0.413877	−0.206938	−	0.978354i	$-0.566350\pi$
$887$	−12.3263	−0.413877	−0.206938	+	0.978354i	$0.566350\pi$
$888$	0.362771	0.0121738
$889$	−21.5596	−0.723087
$890$	0.617329	0.0206929
$891$	−3.82527	−0.128151
$892$	−46.8080	−1.56725
$893$	−12.8298	−0.429332
$894$	−6.32226	−0.211448
$895$	−24.3364	−0.813475
$896$	−30.0505	−1.00392
$897$	−0.722370	−0.0241192
$898$	15.0799	0.503223
$899$	−65.7274	−2.19213
$900$	3.86130	0.128710
$901$	−4.63975	−0.154572
$902$	2.96430	0.0987004
$903$	1.93893	0.0645237
$904$	21.9631	0.730482
$905$	−12.8701	−0.427815
$906$	−2.53670	−0.0842761
$907$	16.6766	0.553736	0.276868	−	0.960908i	$-0.410704\pi$
$907$	16.6766	0.553736	0.276868	+	0.960908i	$0.410704\pi$
$908$	4.51643	0.149883
$909$	−7.53793	−0.250017
$910$	−4.01778	−0.133188
$911$	−57.6310	−1.90940	−0.954700	−	0.297570i	$-0.903824\pi$
$911$	−57.6310	−1.90940	−0.954700	+	0.297570i	$0.903824\pi$
$912$	−1.59163	−0.0527040
$913$	15.2944	0.506169
$914$	2.09010	0.0691342
$915$	−9.68618	−0.320215
$916$	−34.3762	−1.13582
$917$	36.8281	1.21617
$918$	8.95740	0.295638
$919$	−11.0339	−0.363973	−0.181987	−	0.983301i	$-0.558253\pi$
$919$	−11.0339	−0.363973	−0.181987	+	0.983301i	$0.558253\pi$
$920$	0.829180	0.0273373
$921$	3.54548	0.116828
$922$	−5.77075	−0.190049
$923$	34.7208	1.14285
$924$	−3.35840	−0.110483
$925$	0.207031	0.00680714
$926$	21.3624	0.702011
$927$	18.7942	0.617281
$928$	−40.7930	−1.33909
$929$	4.06976	0.133525	0.0667623	−	0.997769i	$-0.478733\pi$
$929$	4.06976	0.133525	0.0667623	+	0.997769i	$0.478733\pi$
$930$	−4.37519	−0.143468
$931$	−0.0465525	−0.00152570
$932$	17.9294	0.587298
$933$	−7.37236	−0.241360
$934$	−2.81377	−0.0920692
$935$	−3.43844	−0.112449
$936$	−13.1406	−0.429514
$937$	48.0926	1.57112	0.785559	−	0.618787i	$-0.212376\pi$
$937$	48.0926	1.57112	0.785559	+	0.618787i	$0.212376\pi$
$938$	1.18035	0.0385398
$939$	−9.02610	−0.294556
$940$	19.1657	0.625117
$941$	−36.9137	−1.20335	−0.601676	−	0.798740i	$-0.705500\pi$
$941$	−36.9137	−1.20335	−0.601676	+	0.798740i	$0.705500\pi$
$942$	9.56471	0.311635
$943$	1.78919	0.0582642
$944$	−3.72992	−0.121398
$945$	11.1549	0.362868
$946$	0.576323	0.0187379
$947$	−23.3319	−0.758184	−0.379092	−	0.925359i	$-0.623764\pi$
$947$	−23.3319	−0.758184	−0.379092	+	0.925359i	$0.623764\pi$
$948$	−6.79223	−0.220601
$949$	−2.47288	−0.0802731
$950$	0.668235	0.0216804
$951$	26.7949	0.868883
$952$	−20.2265	−0.655544
$953$	7.73317	0.250502	0.125251	−	0.992125i	$-0.460026\pi$
$953$	7.73317	0.250502	0.125251	+	0.992125i	$0.460026\pi$
$954$	1.98047	0.0641201
$955$	−24.1811	−0.782483
$956$	15.3814	0.497470
$957$	−5.71245	−0.184657
$958$	3.19837	0.103335
$959$	22.7066	0.733236
$960$	0.218926	0.00706580
$961$	50.7246	1.63628
$962$	−0.315361	−0.0101676
$963$	−4.26195	−0.137340
$964$	22.7542	0.732863
$965$	1.48391	0.0477688
$966$	0.474612	0.0152704
$967$	28.7785	0.925455	0.462728	−	0.886500i	$-0.346871\pi$
$967$	28.7785	0.925455	0.462728	+	0.886500i	$0.346871\pi$
$968$	−2.23021	−0.0716815
$969$	−2.93072	−0.0941483
$970$	4.09770	0.131569
$971$	−48.7425	−1.56422	−0.782111	−	0.623139i	$-0.785857\pi$
$971$	−48.7425	−1.56422	−0.782111	+	0.623139i	$0.785857\pi$
$972$	25.4313	0.815711
$973$	−53.7549	−1.72330
$974$	−7.67662	−0.245975
$975$	1.94292	0.0622233
$976$	23.0212	0.736892
$977$	−43.7309	−1.39908	−0.699538	−	0.714595i	$-0.746611\pi$
$977$	−43.7309	−1.39908	−0.699538	+	0.714595i	$0.746611\pi$
$978$	4.65572	0.148874
$979$	−1.00219	−0.0320300
$980$	0.0695423	0.00222145
$981$	4.39224	0.140233
$982$	3.74520	0.119514
$983$	24.8926	0.793952	0.396976	−	0.917829i	$-0.370060\pi$
$983$	24.8926	0.793952	0.396976	+	0.917829i	$0.370060\pi$
$984$	−8.43239	−0.268815
$985$	−17.7363	−0.565125
$986$	−15.3993	−0.490413
$987$	24.5089	0.780128
$988$	4.34741	0.138309
$989$	0.347857	0.0110612
$990$	1.46770	0.0466464
$991$	32.4391	1.03046	0.515231	−	0.857051i	$-0.327706\pi$
$991$	32.4391	1.03046	0.515231	+	0.857051i	$0.327706\pi$
$992$	50.7214	1.61041
$993$	19.4847	0.618327
$994$	−22.8123	−0.723562
$995$	−1.22002	−0.0386771
$996$	−19.4738	−0.617049
$997$	−38.2383	−1.21102	−0.605509	−	0.795838i	$-0.707030\pi$
$997$	−38.2383	−1.21102	−0.605509	+	0.795838i	$0.707030\pi$
$998$	−8.74306	−0.276757
$999$	0.875562	0.0277016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.15	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.15	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.615983 q^{2} -0.785692 q^{3} -1.62056 q^{4} +1.00000 q^{5} -0.483973 q^{6} +2.63763 q^{7} -2.23021 q^{8} -2.38269 q^{9} +O(q^{10})\)	\(q+0.615983 q^{2} -0.785692 q^{3} -1.62056 q^{4} +1.00000 q^{5} -0.483973 q^{6} +2.63763 q^{7} -2.23021 q^{8} -2.38269 q^{9} +0.615983 q^{10} -1.00000 q^{11} +1.27326 q^{12} -2.47288 q^{13} +1.62473 q^{14} -0.785692 q^{15} +1.86736 q^{16} +3.43844 q^{17} -1.46770 q^{18} +1.08483 q^{19} -1.62056 q^{20} -2.07236 q^{21} -0.615983 q^{22} -0.371795 q^{23} +1.75225 q^{24} +1.00000 q^{25} -1.52325 q^{26} +4.22913 q^{27} -4.27445 q^{28} -7.27060 q^{29} -0.483973 q^{30} +9.04017 q^{31} +5.61068 q^{32} +0.785692 q^{33} +2.11802 q^{34} +2.63763 q^{35} +3.86130 q^{36} +0.207031 q^{37} +0.668235 q^{38} +1.94292 q^{39} -2.23021 q^{40} -4.81231 q^{41} -1.27654 q^{42} -0.935615 q^{43} +1.62056 q^{44} -2.38269 q^{45} -0.229020 q^{46} -11.8266 q^{47} -1.46717 q^{48} -0.0429124 q^{49} +0.615983 q^{50} -2.70156 q^{51} +4.00747 q^{52} -1.34937 q^{53} +2.60507 q^{54} -1.00000 q^{55} -5.88246 q^{56} -0.852340 q^{57} -4.47856 q^{58} -1.99743 q^{59} +1.27326 q^{60} +12.3282 q^{61} +5.56859 q^{62} -6.28465 q^{63} -0.278641 q^{64} -2.47288 q^{65} +0.483973 q^{66} +0.726488 q^{67} -5.57222 q^{68} +0.292117 q^{69} +1.62473 q^{70} -14.0406 q^{71} +5.31389 q^{72} +1.00000 q^{73} +0.127528 q^{74} -0.785692 q^{75} -1.75803 q^{76} -2.63763 q^{77} +1.19681 q^{78} -5.33450 q^{79} +1.86736 q^{80} +3.82527 q^{81} -2.96430 q^{82} -15.2944 q^{83} +3.35840 q^{84} +3.43844 q^{85} -0.576323 q^{86} +5.71245 q^{87} +2.23021 q^{88} +1.00219 q^{89} -1.46770 q^{90} -6.52255 q^{91} +0.602519 q^{92} -7.10278 q^{93} -7.28496 q^{94} +1.08483 q^{95} -4.40826 q^{96} +6.65230 q^{97} -0.0264333 q^{98} +2.38269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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