LMFDB - Embedded newform 4015.2.a.g.1.3

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:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.62713 q^{2} -1.17329 q^{3} +4.90182 q^{4} -1.00000 q^{5} +3.08238 q^{6} +3.02645 q^{7} -7.62347 q^{8} -1.62339 q^{9} +O(q^{10})$	\(q-2.62713 q^{2} -1.17329 q^{3} +4.90182 q^{4} -1.00000 q^{5} +3.08238 q^{6} +3.02645 q^{7} -7.62347 q^{8} -1.62339 q^{9} +2.62713 q^{10} -1.00000 q^{11} -5.75125 q^{12} +2.13851 q^{13} -7.95089 q^{14} +1.17329 q^{15} +10.2242 q^{16} -3.09577 q^{17} +4.26487 q^{18} -1.70981 q^{19} -4.90182 q^{20} -3.55090 q^{21} +2.62713 q^{22} -4.01359 q^{23} +8.94453 q^{24} +1.00000 q^{25} -5.61815 q^{26} +5.42457 q^{27} +14.8351 q^{28} +2.76361 q^{29} -3.08238 q^{30} +10.1598 q^{31} -11.6134 q^{32} +1.17329 q^{33} +8.13300 q^{34} -3.02645 q^{35} -7.95760 q^{36} +2.15376 q^{37} +4.49190 q^{38} -2.50909 q^{39} +7.62347 q^{40} -0.398697 q^{41} +9.32869 q^{42} -5.72977 q^{43} -4.90182 q^{44} +1.62339 q^{45} +10.5442 q^{46} -4.40266 q^{47} -11.9960 q^{48} +2.15942 q^{49} -2.62713 q^{50} +3.63223 q^{51} +10.4826 q^{52} -10.8706 q^{53} -14.2511 q^{54} +1.00000 q^{55} -23.0721 q^{56} +2.00610 q^{57} -7.26038 q^{58} +3.66342 q^{59} +5.75125 q^{60} +6.08499 q^{61} -26.6911 q^{62} -4.91313 q^{63} +10.0616 q^{64} -2.13851 q^{65} -3.08238 q^{66} -8.55834 q^{67} -15.1749 q^{68} +4.70910 q^{69} +7.95089 q^{70} +13.1147 q^{71} +12.3759 q^{72} -1.00000 q^{73} -5.65821 q^{74} -1.17329 q^{75} -8.38120 q^{76} -3.02645 q^{77} +6.59171 q^{78} -10.7983 q^{79} -10.2242 q^{80} -1.49440 q^{81} +1.04743 q^{82} +9.67818 q^{83} -17.4059 q^{84} +3.09577 q^{85} +15.0529 q^{86} -3.24252 q^{87} +7.62347 q^{88} +12.0632 q^{89} -4.26487 q^{90} +6.47210 q^{91} -19.6739 q^{92} -11.9204 q^{93} +11.5664 q^{94} +1.70981 q^{95} +13.6259 q^{96} -0.620523 q^{97} -5.67308 q^{98} +1.62339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−2.62713	−1.85766	−0.928831	−	0.370502i	$-0.879185\pi$
$2$	−2.62713	−1.85766	−0.928831	+	0.370502i	$0.879185\pi$
$3$	−1.17329	−0.677398	−0.338699	−	0.940895i	$-0.609987\pi$
$3$	−1.17329	−0.677398	−0.338699	+	0.940895i	$0.609987\pi$
$4$	4.90182	2.45091
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.08238	1.25838
$7$	3.02645	1.14389	0.571946	−	0.820291i	$-0.306189\pi$
$7$	3.02645	1.14389	0.571946	+	0.820291i	$0.306189\pi$
$8$	−7.62347	−2.69530
$9$	−1.62339	−0.541132
$10$	2.62713	0.830772
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.75125	−1.66024
$13$	2.13851	0.593116	0.296558	−	0.955015i	$-0.404161\pi$
$13$	2.13851	0.593116	0.296558	+	0.955015i	$0.404161\pi$
$14$	−7.95089	−2.12497
$15$	1.17329	0.302942
$16$	10.2242	2.55606
$17$	−3.09577	−0.750835	−0.375417	−	0.926856i	$-0.622501\pi$
$17$	−3.09577	−0.750835	−0.375417	+	0.926856i	$0.622501\pi$
$18$	4.26487	1.00524
$19$	−1.70981	−0.392258	−0.196129	−	0.980578i	$-0.562837\pi$
$19$	−1.70981	−0.392258	−0.196129	+	0.980578i	$0.562837\pi$
$20$	−4.90182	−1.09608
$21$	−3.55090	−0.774870
$22$	2.62713	0.560106
$23$	−4.01359	−0.836891	−0.418445	−	0.908242i	$-0.637425\pi$
$23$	−4.01359	−0.836891	−0.418445	+	0.908242i	$0.637425\pi$
$24$	8.94453	1.82579
$25$	1.00000	0.200000
$26$	−5.61815	−1.10181
$27$	5.42457	1.04396
$28$	14.8351	2.80358
$29$	2.76361	0.513190	0.256595	−	0.966519i	$-0.417399\pi$
$29$	2.76361	0.513190	0.256595	+	0.966519i	$0.417399\pi$
$30$	−3.08238	−0.562764
$31$	10.1598	1.82475	0.912377	−	0.409350i	$-0.134245\pi$
$31$	10.1598	1.82475	0.912377	+	0.409350i	$0.134245\pi$
$32$	−11.6134	−2.05299
$33$	1.17329	0.204243
$34$	8.13300	1.39480
$35$	−3.02645	−0.511564
$36$	−7.95760	−1.32627
$37$	2.15376	0.354076	0.177038	−	0.984204i	$-0.443349\pi$
$37$	2.15376	0.354076	0.177038	+	0.984204i	$0.443349\pi$
$38$	4.49190	0.728683
$39$	−2.50909	−0.401776
$40$	7.62347	1.20538
$41$	−0.398697	−0.0622661	−0.0311330	−	0.999515i	$-0.509912\pi$
$41$	−0.398697	−0.0622661	−0.0311330	+	0.999515i	$0.509912\pi$
$42$	9.32869	1.43945
$43$	−5.72977	−0.873782	−0.436891	−	0.899514i	$-0.643921\pi$
$43$	−5.72977	−0.873782	−0.436891	+	0.899514i	$0.643921\pi$
$44$	−4.90182	−0.738978
$45$	1.62339	0.242001
$46$	10.5442	1.55466
$47$	−4.40266	−0.642194	−0.321097	−	0.947046i	$-0.604052\pi$
$47$	−4.40266	−0.642194	−0.321097	+	0.947046i	$0.604052\pi$
$48$	−11.9960	−1.73147
$49$	2.15942	0.308488
$50$	−2.62713	−0.371533
$51$	3.63223	0.508614
$52$	10.4826	1.45367
$53$	−10.8706	−1.49319	−0.746597	−	0.665276i	$-0.768314\pi$
$53$	−10.8706	−1.49319	−0.746597	+	0.665276i	$0.768314\pi$
$54$	−14.2511	−1.93933
$55$	1.00000	0.134840
$56$	−23.0721	−3.08314
$57$	2.00610	0.265715
$58$	−7.26038	−0.953335
$59$	3.66342	0.476937	0.238468	−	0.971150i	$-0.423355\pi$
$59$	3.66342	0.476937	0.238468	+	0.971150i	$0.423355\pi$
$60$	5.75125	0.742483
$61$	6.08499	0.779103	0.389552	−	0.921005i	$-0.372630\pi$
$61$	6.08499	0.779103	0.389552	+	0.921005i	$0.372630\pi$
$62$	−26.6911	−3.38978
$63$	−4.91313	−0.618996
$64$	10.0616	1.25770
$65$	−2.13851	−0.265250
$66$	−3.08238	−0.379415
$67$	−8.55834	−1.04557	−0.522784	−	0.852465i	$-0.675107\pi$
$67$	−8.55834	−1.04557	−0.522784	+	0.852465i	$0.675107\pi$
$68$	−15.1749	−1.84023
$69$	4.70910	0.566908
$70$	7.95089	0.950313
$71$	13.1147	1.55643	0.778214	−	0.627999i	$-0.216126\pi$
$71$	13.1147	1.55643	0.778214	+	0.627999i	$0.216126\pi$
$72$	12.3759	1.45851
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−5.65821	−0.657753
$75$	−1.17329	−0.135480
$76$	−8.38120	−0.961390
$77$	−3.02645	−0.344896
$78$	6.59171	0.746364
$79$	−10.7983	−1.21491	−0.607453	−	0.794355i	$-0.707809\pi$
$79$	−10.7983	−1.21491	−0.607453	+	0.794355i	$0.707809\pi$
$80$	−10.2242	−1.14310
$81$	−1.49440	−0.166045
$82$	1.04743	0.115669
$83$	9.67818	1.06232	0.531159	−	0.847272i	$-0.321757\pi$
$83$	9.67818	1.06232	0.531159	+	0.847272i	$0.321757\pi$
$84$	−17.4059	−1.89914
$85$	3.09577	0.335784
$86$	15.0529	1.62319
$87$	−3.24252	−0.347634
$88$	7.62347	0.812665
$89$	12.0632	1.27870	0.639348	−	0.768917i	$-0.279204\pi$
$89$	12.0632	1.27870	0.639348	+	0.768917i	$0.279204\pi$
$90$	−4.26487	−0.449557
$91$	6.47210	0.678460
$92$	−19.6739	−2.05115
$93$	−11.9204	−1.23609
$94$	11.5664	1.19298
$95$	1.70981	0.175423
$96$	13.6259	1.39069
$97$	−0.620523	−0.0630046	−0.0315023	−	0.999504i	$-0.510029\pi$
$97$	−0.620523	−0.0630046	−0.0315023	+	0.999504i	$0.510029\pi$
$98$	−5.67308	−0.573067
$99$	1.62339	0.163157
$100$	4.90182	0.490182
$101$	−4.81863	−0.479472	−0.239736	−	0.970838i	$-0.577061\pi$
$101$	−4.81863	−0.479472	−0.239736	+	0.970838i	$0.577061\pi$
$102$	−9.54235	−0.944834
$103$	−4.07639	−0.401659	−0.200830	−	0.979626i	$-0.564364\pi$
$103$	−4.07639	−0.401659	−0.200830	+	0.979626i	$0.564364\pi$
$104$	−16.3029	−1.59863
$105$	3.55090	0.346532
$106$	28.5586	2.77385
$107$	−15.5620	−1.50443	−0.752216	−	0.658916i	$-0.771015\pi$
$107$	−15.5620	−1.50443	−0.752216	+	0.658916i	$0.771015\pi$
$108$	26.5903	2.55865
$109$	5.77229	0.552885	0.276442	−	0.961030i	$-0.410844\pi$
$109$	5.77229	0.552885	0.276442	+	0.961030i	$0.410844\pi$
$110$	−2.62713	−0.250487
$111$	−2.52698	−0.239850
$112$	30.9431	2.92385
$113$	−13.0505	−1.22769	−0.613845	−	0.789427i	$-0.710378\pi$
$113$	−13.0505	−1.22769	−0.613845	+	0.789427i	$0.710378\pi$
$114$	−5.27030	−0.493609
$115$	4.01359	0.374269
$116$	13.5468	1.25778
$117$	−3.47165	−0.320954
$118$	−9.62429	−0.885988
$119$	−9.36921	−0.858874
$120$	−8.94453	−0.816520
$121$	1.00000	0.0909091
$122$	−15.9861	−1.44731
$123$	0.467787	0.0421789
$124$	49.8016	4.47231
$125$	−1.00000	−0.0894427
$126$	12.9074	1.14989
$127$	−13.2548	−1.17617	−0.588087	−	0.808798i	$-0.700119\pi$
$127$	−13.2548	−1.17617	−0.588087	+	0.808798i	$0.700119\pi$
$128$	−3.20627	−0.283397
$129$	6.72268	0.591899
$130$	5.61815	0.492744
$131$	11.9115	1.04071	0.520354	−	0.853950i	$-0.325800\pi$
$131$	11.9115	1.04071	0.520354	+	0.853950i	$0.325800\pi$
$132$	5.75125	0.500582
$133$	−5.17467	−0.448701
$134$	22.4839	1.94231
$135$	−5.42457	−0.466873
$136$	23.6005	2.02373
$137$	−1.34104	−0.114573	−0.0572864	−	0.998358i	$-0.518245\pi$
$137$	−1.34104	−0.114573	−0.0572864	+	0.998358i	$0.518245\pi$
$138$	−12.3714	−1.05312
$139$	−20.2581	−1.71827	−0.859136	−	0.511747i	$-0.828999\pi$
$139$	−20.2581	−1.71827	−0.859136	+	0.511747i	$0.828999\pi$
$140$	−14.8351	−1.25380
$141$	5.16559	0.435021
$142$	−34.4540	−2.89132
$143$	−2.13851	−0.178831
$144$	−16.5980	−1.38316
$145$	−2.76361	−0.229506
$146$	2.62713	0.217423
$147$	−2.53362	−0.208969
$148$	10.5573	0.867808
$149$	16.1149	1.32019	0.660093	−	0.751184i	$-0.270517\pi$
$149$	16.1149	1.32019	0.660093	+	0.751184i	$0.270517\pi$
$150$	3.08238	0.251676
$151$	−4.61140	−0.375270	−0.187635	−	0.982239i	$-0.560082\pi$
$151$	−4.61140	−0.375270	−0.187635	+	0.982239i	$0.560082\pi$
$152$	13.0347	1.05725
$153$	5.02566	0.406300
$154$	7.95089	0.640701
$155$	−10.1598	−0.816055
$156$	−12.2991	−0.984717
$157$	13.6668	1.09073	0.545364	−	0.838199i	$-0.316391\pi$
$157$	13.6668	1.09073	0.545364	+	0.838199i	$0.316391\pi$
$158$	28.3686	2.25689
$159$	12.7544	1.01149
$160$	11.6134	0.918123
$161$	−12.1469	−0.957313
$162$	3.92600	0.308455
$163$	−5.84744	−0.458007	−0.229003	−	0.973426i	$-0.573547\pi$
$163$	−5.84744	−0.458007	−0.229003	+	0.973426i	$0.573547\pi$
$164$	−1.95434	−0.152609
$165$	−1.17329	−0.0913404
$166$	−25.4259	−1.97343
$167$	21.9844	1.70120	0.850601	−	0.525811i	$-0.176238\pi$
$167$	21.9844	1.70120	0.850601	+	0.525811i	$0.176238\pi$
$168$	27.0702	2.08851
$169$	−8.42677	−0.648213
$170$	−8.13300	−0.623773
$171$	2.77570	0.212263
$172$	−28.0863	−2.14156
$173$	20.4683	1.55618	0.778088	−	0.628155i	$-0.216190\pi$
$173$	20.4683	1.55618	0.778088	+	0.628155i	$0.216190\pi$
$174$	8.51852	0.645787
$175$	3.02645	0.228778
$176$	−10.2242	−0.770680
$177$	−4.29825	−0.323076
$178$	−31.6916	−2.37539
$179$	15.6578	1.17032	0.585160	−	0.810918i	$-0.301032\pi$
$179$	15.6578	1.17032	0.585160	+	0.810918i	$0.301032\pi$
$180$	7.95760	0.593124
$181$	−20.2375	−1.50424	−0.752122	−	0.659024i	$-0.770969\pi$
$181$	−20.2375	−1.50424	−0.752122	+	0.659024i	$0.770969\pi$
$182$	−17.0031	−1.26035
$183$	−7.13945	−0.527763
$184$	30.5975	2.25568
$185$	−2.15376	−0.158347
$186$	31.3164	2.29623
$187$	3.09577	0.226385
$188$	−21.5811	−1.57396
$189$	16.4172	1.19418
$190$	−4.49190	−0.325877
$191$	−11.5038	−0.832385	−0.416192	−	0.909277i	$-0.636636\pi$
$191$	−11.5038	−0.832385	−0.416192	+	0.909277i	$0.636636\pi$
$192$	−11.8052	−0.851964
$193$	13.5083	0.972351	0.486176	−	0.873861i	$-0.338392\pi$
$193$	13.5083	0.972351	0.486176	+	0.873861i	$0.338392\pi$
$194$	1.63020	0.117041
$195$	2.50909	0.179680
$196$	10.5851	0.756077
$197$	−5.23629	−0.373070	−0.186535	−	0.982448i	$-0.559726\pi$
$197$	−5.23629	−0.373070	−0.186535	+	0.982448i	$0.559726\pi$
$198$	−4.26487	−0.303091
$199$	3.96257	0.280899	0.140449	−	0.990088i	$-0.455145\pi$
$199$	3.96257	0.280899	0.140449	+	0.990088i	$0.455145\pi$
$200$	−7.62347	−0.539061
$201$	10.0414	0.708266
$202$	12.6592	0.890698
$203$	8.36395	0.587034
$204$	17.8046	1.24657
$205$	0.398697	0.0278462
$206$	10.7092	0.746147
$207$	6.51564	0.452868
$208$	21.8646	1.51604
$209$	1.70981	0.118270
$210$	−9.32869	−0.643741
$211$	10.9958	0.756983	0.378491	−	0.925605i	$-0.376443\pi$
$211$	10.9958	0.756983	0.378491	+	0.925605i	$0.376443\pi$
$212$	−53.2859	−3.65969
$213$	−15.3873	−1.05432
$214$	40.8834	2.79473
$215$	5.72977	0.390767
$216$	−41.3541	−2.81379
$217$	30.7482	2.08732
$218$	−15.1646	−1.02707
$219$	1.17329	0.0792835
$220$	4.90182	0.330481
$221$	−6.62034	−0.445332
$222$	6.63871	0.445561
$223$	21.0333	1.40850	0.704248	−	0.709955i	$-0.251285\pi$
$223$	21.0333	1.40850	0.704248	+	0.709955i	$0.251285\pi$
$224$	−35.1475	−2.34839
$225$	−1.62339	−0.108226
$226$	34.2854	2.28063
$227$	8.82895	0.585998	0.292999	−	0.956113i	$-0.405347\pi$
$227$	8.82895	0.585998	0.292999	+	0.956113i	$0.405347\pi$
$228$	9.83356	0.651244
$229$	0.822856	0.0543758	0.0271879	−	0.999630i	$-0.491345\pi$
$229$	0.822856	0.0543758	0.0271879	+	0.999630i	$0.491345\pi$
$230$	−10.5442	−0.695266
$231$	3.55090	0.233632
$232$	−21.0683	−1.38320
$233$	−8.42316	−0.551819	−0.275910	−	0.961184i	$-0.588979\pi$
$233$	−8.42316	−0.551819	−0.275910	+	0.961184i	$0.588979\pi$
$234$	9.12047	0.596224
$235$	4.40266	0.287198
$236$	17.9574	1.16893
$237$	12.6695	0.822976
$238$	24.6141	1.59550
$239$	−20.7460	−1.34195	−0.670975	−	0.741480i	$-0.734124\pi$
$239$	−20.7460	−1.34195	−0.670975	+	0.741480i	$0.734124\pi$
$240$	11.9960	0.774336
$241$	17.1379	1.10395	0.551975	−	0.833861i	$-0.313874\pi$
$241$	17.1379	1.10395	0.551975	+	0.833861i	$0.313874\pi$
$242$	−2.62713	−0.168878
$243$	−14.5204	−0.931481
$244$	29.8275	1.90951
$245$	−2.15942	−0.137960
$246$	−1.22894	−0.0783542
$247$	−3.65645	−0.232654
$248$	−77.4530	−4.91827
$249$	−11.3553	−0.719612
$250$	2.62713	0.166154
$251$	−3.01807	−0.190499	−0.0952493	−	0.995453i	$-0.530365\pi$
$251$	−3.01807	−0.190499	−0.0952493	+	0.995453i	$0.530365\pi$
$252$	−24.0833	−1.51710
$253$	4.01359	0.252332
$254$	34.8221	2.18493
$255$	−3.63223	−0.227459
$256$	−11.6999	−0.731245
$257$	−21.0021	−1.31008	−0.655038	−	0.755596i	$-0.727348\pi$
$257$	−21.0021	−1.31008	−0.655038	+	0.755596i	$0.727348\pi$
$258$	−17.6614	−1.09955
$259$	6.51825	0.405024
$260$	−10.4826	−0.650103
$261$	−4.48644	−0.277704
$262$	−31.2930	−1.93329
$263$	6.75688	0.416647	0.208323	−	0.978060i	$-0.433199\pi$
$263$	6.75688	0.416647	0.208323	+	0.978060i	$0.433199\pi$
$264$	−8.94453	−0.550498
$265$	10.8706	0.667777
$266$	13.5945	0.833534
$267$	−14.1536	−0.866186
$268$	−41.9515	−2.56259
$269$	−3.41145	−0.208000	−0.104000	−	0.994577i	$-0.533164\pi$
$269$	−3.41145	−0.208000	−0.104000	+	0.994577i	$0.533164\pi$
$270$	14.2511	0.867293
$271$	−11.3469	−0.689275	−0.344637	−	0.938736i	$-0.611998\pi$
$271$	−11.3469	−0.689275	−0.344637	+	0.938736i	$0.611998\pi$
$272$	−31.6519	−1.91918
$273$	−7.59364	−0.459588
$274$	3.52309	0.212838
$275$	−1.00000	−0.0603023
$276$	23.0832	1.38944
$277$	19.7874	1.18891	0.594456	−	0.804128i	$-0.297367\pi$
$277$	19.7874	1.18891	0.594456	+	0.804128i	$0.297367\pi$
$278$	53.2208	3.19197
$279$	−16.4934	−0.987432
$280$	23.0721	1.37882
$281$	−7.65339	−0.456563	−0.228281	−	0.973595i	$-0.573311\pi$
$281$	−7.65339	−0.456563	−0.228281	+	0.973595i	$0.573311\pi$
$282$	−13.5707	−0.808123
$283$	−9.50764	−0.565171	−0.282585	−	0.959242i	$-0.591192\pi$
$283$	−9.50764	−0.565171	−0.282585	+	0.959242i	$0.591192\pi$
$284$	64.2859	3.81467
$285$	−2.00610	−0.118831
$286$	5.61815	0.332208
$287$	−1.20664	−0.0712256
$288$	18.8532	1.11094
$289$	−7.41620	−0.436247
$290$	7.26038	0.426344
$291$	0.728053	0.0426792
$292$	−4.90182	−0.286858
$293$	−22.3422	−1.30524	−0.652622	−	0.757684i	$-0.726331\pi$
$293$	−22.3422	−1.30524	−0.652622	+	0.757684i	$0.726331\pi$
$294$	6.65615	0.388195
$295$	−3.66342	−0.213293
$296$	−16.4191	−0.954342
$297$	−5.42457	−0.314766
$298$	−42.3360	−2.45246
$299$	−8.58310	−0.496373
$300$	−5.75125	−0.332049
$301$	−17.3409	−0.999512
$302$	12.1148	0.697126
$303$	5.65365	0.324794
$304$	−17.4815	−1.00263
$305$	−6.08499	−0.348426
$306$	−13.2031	−0.754769
$307$	16.6573	0.950683	0.475342	−	0.879801i	$-0.342324\pi$
$307$	16.6573	0.950683	0.475342	+	0.879801i	$0.342324\pi$
$308$	−14.8351	−0.845310
$309$	4.78278	0.272083
$310$	26.6911	1.51596
$311$	17.9534	1.01804	0.509022	−	0.860754i	$-0.330007\pi$
$311$	17.9534	1.01804	0.509022	+	0.860754i	$0.330007\pi$
$312$	19.1280	1.08291
$313$	7.64537	0.432142	0.216071	−	0.976378i	$-0.430676\pi$
$313$	7.64537	0.432142	0.216071	+	0.976378i	$0.430676\pi$
$314$	−35.9045	−2.02621
$315$	4.91313	0.276823
$316$	−52.9315	−2.97763
$317$	5.16783	0.290254	0.145127	−	0.989413i	$-0.453641\pi$
$317$	5.16783	0.290254	0.145127	+	0.989413i	$0.453641\pi$
$318$	−33.5074	−1.87900
$319$	−2.76361	−0.154733
$320$	−10.0616	−0.562461
$321$	18.2587	1.01910
$322$	31.9116	1.77836
$323$	5.29319	0.294521
$324$	−7.32530	−0.406961
$325$	2.13851	0.118623
$326$	15.3620	0.850822
$327$	−6.77256	−0.374523
$328$	3.03946	0.167826
$329$	−13.3244	−0.734601
$330$	3.08238	0.169680
$331$	−18.3054	−1.00615	−0.503077	−	0.864241i	$-0.667799\pi$
$331$	−18.3054	−1.00615	−0.503077	+	0.864241i	$0.667799\pi$
$332$	47.4407	2.60365
$333$	−3.49640	−0.191602
$334$	−57.7559	−3.16026
$335$	8.55834	0.467592
$336$	−36.3052	−1.98061
$337$	12.4880	0.680262	0.340131	−	0.940378i	$-0.389529\pi$
$337$	12.4880	0.680262	0.340131	+	0.940378i	$0.389529\pi$
$338$	22.1382	1.20416
$339$	15.3120	0.831635
$340$	15.1749	0.822976
$341$	−10.1598	−0.550184
$342$	−7.29213	−0.394313
$343$	−14.6498	−0.791015
$344$	43.6808	2.35511
$345$	−4.70910	−0.253529
$346$	−53.7729	−2.89085
$347$	−8.74915	−0.469679	−0.234839	−	0.972034i	$-0.575456\pi$
$347$	−8.74915	−0.469679	−0.234839	+	0.972034i	$0.575456\pi$
$348$	−15.8942	−0.852021
$349$	−20.4586	−1.09512	−0.547561	−	0.836766i	$-0.684444\pi$
$349$	−20.4586	−1.09512	−0.547561	+	0.836766i	$0.684444\pi$
$350$	−7.95089	−0.424993
$351$	11.6005	0.619189
$352$	11.6134	0.618999
$353$	−22.5096	−1.19806	−0.599032	−	0.800725i	$-0.704448\pi$
$353$	−22.5096	−1.19806	−0.599032	+	0.800725i	$0.704448\pi$
$354$	11.2921	0.600167
$355$	−13.1147	−0.696056
$356$	59.1317	3.13397
$357$	10.9928	0.581800
$358$	−41.1351	−2.17406
$359$	−12.5815	−0.664028	−0.332014	−	0.943274i	$-0.607728\pi$
$359$	−12.5815	−0.664028	−0.332014	+	0.943274i	$0.607728\pi$
$360$	−12.3759	−0.652268
$361$	−16.0765	−0.846134
$362$	53.1667	2.79438
$363$	−1.17329	−0.0615817
$364$	31.7251	1.66285
$365$	1.00000	0.0523424
$366$	18.7563	0.980406
$367$	−27.2121	−1.42046	−0.710230	−	0.703969i	$-0.751409\pi$
$367$	−27.2121	−1.42046	−0.710230	+	0.703969i	$0.751409\pi$
$368$	−41.0358	−2.13914
$369$	0.647243	0.0336941
$370$	5.65821	0.294156
$371$	−32.8994	−1.70805
$372$	−58.4316	−3.02954
$373$	−7.34518	−0.380319	−0.190160	−	0.981753i	$-0.560901\pi$
$373$	−7.34518	−0.380319	−0.190160	+	0.981753i	$0.560901\pi$
$374$	−8.13300	−0.420547
$375$	1.17329	0.0605883
$376$	33.5636	1.73091
$377$	5.91002	0.304381
$378$	−43.1302	−2.21838
$379$	−18.8271	−0.967082	−0.483541	−	0.875322i	$-0.660650\pi$
$379$	−18.8271	−0.967082	−0.483541	+	0.875322i	$0.660650\pi$
$380$	8.38120	0.429946
$381$	15.5517	0.796738
$382$	30.2220	1.54629
$383$	−31.2815	−1.59841	−0.799205	−	0.601058i	$-0.794746\pi$
$383$	−31.2815	−1.59841	−0.799205	+	0.601058i	$0.794746\pi$
$384$	3.76188	0.191972
$385$	3.02645	0.154242
$386$	−35.4882	−1.80630
$387$	9.30169	0.472831
$388$	−3.04170	−0.154419
$389$	14.9072	0.755826	0.377913	−	0.925841i	$-0.376642\pi$
$389$	14.9072	0.755826	0.377913	+	0.925841i	$0.376642\pi$
$390$	−6.59171	−0.333784
$391$	12.4252	0.628367
$392$	−16.4623	−0.831470
$393$	−13.9756	−0.704974
$394$	13.7564	0.693039
$395$	10.7983	0.543323
$396$	7.95760	0.399884
$397$	−27.0220	−1.35619	−0.678097	−	0.734972i	$-0.737195\pi$
$397$	−27.0220	−1.35619	−0.678097	+	0.734972i	$0.737195\pi$
$398$	−10.4102	−0.521815
$399$	6.07138	0.303949
$400$	10.2242	0.511211
$401$	−11.7165	−0.585094	−0.292547	−	0.956251i	$-0.594503\pi$
$401$	−11.7165	−0.585094	−0.292547	+	0.956251i	$0.594503\pi$
$402$	−26.3801	−1.31572
$403$	21.7268	1.08229
$404$	−23.6201	−1.17514
$405$	1.49440	0.0742575
$406$	−21.9732	−1.09051
$407$	−2.15376	−0.106758
$408$	−27.6902	−1.37087
$409$	−2.00655	−0.0992176	−0.0496088	−	0.998769i	$-0.515797\pi$
$409$	−2.00655	−0.0992176	−0.0496088	+	0.998769i	$0.515797\pi$
$410$	−1.04743	−0.0517289
$411$	1.57343	0.0776114
$412$	−19.9818	−0.984431
$413$	11.0872	0.545564
$414$	−17.1174	−0.841276
$415$	−9.67818	−0.475083
$416$	−24.8355	−1.21766
$417$	23.7686	1.16396
$418$	−4.49190	−0.219706
$419$	−22.0754	−1.07845	−0.539226	−	0.842161i	$-0.681283\pi$
$419$	−22.0754	−1.07845	−0.539226	+	0.842161i	$0.681283\pi$
$420$	17.4059	0.849321
$421$	−12.7145	−0.619669	−0.309834	−	0.950791i	$-0.600274\pi$
$421$	−12.7145	−0.619669	−0.309834	+	0.950791i	$0.600274\pi$
$422$	−28.8874	−1.40622
$423$	7.14726	0.347512
$424$	82.8719	4.02461
$425$	−3.09577	−0.150167
$426$	40.4245	1.95857
$427$	18.4159	0.891210
$428$	−76.2820	−3.68723
$429$	2.50909	0.121140
$430$	−15.0529	−0.725914
$431$	−28.6114	−1.37816	−0.689081	−	0.724684i	$-0.741986\pi$
$431$	−28.6114	−1.37816	−0.689081	+	0.724684i	$0.741986\pi$
$432$	55.4621	2.66842
$433$	−13.8933	−0.667670	−0.333835	−	0.942631i	$-0.608343\pi$
$433$	−13.8933	−0.667670	−0.333835	+	0.942631i	$0.608343\pi$
$434$	−80.7795	−3.87754
$435$	3.24252	0.155467
$436$	28.2947	1.35507
$437$	6.86248	0.328277
$438$	−3.08238	−0.147282
$439$	−0.832645	−0.0397400	−0.0198700	−	0.999803i	$-0.506325\pi$
$439$	−0.832645	−0.0397400	−0.0198700	+	0.999803i	$0.506325\pi$
$440$	−7.62347	−0.363435
$441$	−3.50559	−0.166933
$442$	17.3925	0.827277
$443$	−34.2981	−1.62955	−0.814776	−	0.579777i	$-0.803140\pi$
$443$	−34.2981	−1.62955	−0.814776	+	0.579777i	$0.803140\pi$
$444$	−12.3868	−0.587852
$445$	−12.0632	−0.571850
$446$	−55.2573	−2.61651
$447$	−18.9074	−0.894291
$448$	30.4510	1.43867
$449$	−34.8062	−1.64261	−0.821304	−	0.570491i	$-0.806753\pi$
$449$	−34.8062	−1.64261	−0.821304	+	0.570491i	$0.806753\pi$
$450$	4.26487	0.201048
$451$	0.398697	0.0187739
$452$	−63.9713	−3.00896
$453$	5.41050	0.254207
$454$	−23.1948	−1.08859
$455$	−6.47210	−0.303417
$456$	−15.2935	−0.716182
$457$	−11.7220	−0.548333	−0.274167	−	0.961682i	$-0.588402\pi$
$457$	−11.7220	−0.548333	−0.274167	+	0.961682i	$0.588402\pi$
$458$	−2.16175	−0.101012
$459$	−16.7932	−0.783841
$460$	19.6739	0.917300
$461$	−11.4273	−0.532223	−0.266111	−	0.963942i	$-0.585739\pi$
$461$	−11.4273	−0.532223	−0.266111	+	0.963942i	$0.585739\pi$
$462$	−9.32869	−0.434010
$463$	−19.8878	−0.924266	−0.462133	−	0.886811i	$-0.652916\pi$
$463$	−19.8878	−0.924266	−0.462133	+	0.886811i	$0.652916\pi$
$464$	28.2558	1.31174
$465$	11.9204	0.552794
$466$	22.1287	1.02509
$467$	36.2365	1.67683	0.838413	−	0.545035i	$-0.183484\pi$
$467$	36.2365	1.67683	0.838413	+	0.545035i	$0.183484\pi$
$468$	−17.0174	−0.786629
$469$	−25.9014	−1.19602
$470$	−11.5664	−0.533517
$471$	−16.0351	−0.738857
$472$	−27.9280	−1.28549
$473$	5.72977	0.263455
$474$	−33.2846	−1.52881
$475$	−1.70981	−0.0784516
$476$	−45.9262	−2.10502
$477$	17.6473	0.808015
$478$	54.5026	2.49289
$479$	30.2173	1.38066	0.690332	−	0.723493i	$-0.257464\pi$
$479$	30.2173	1.38066	0.690332	+	0.723493i	$0.257464\pi$
$480$	−13.6259	−0.621935
$481$	4.60583	0.210008
$482$	−45.0236	−2.05077
$483$	14.2519	0.648482
$484$	4.90182	0.222810
$485$	0.620523	0.0281765
$486$	38.1469	1.73038
$487$	−30.1886	−1.36797	−0.683987	−	0.729494i	$-0.739756\pi$
$487$	−30.1886	−1.36797	−0.683987	+	0.729494i	$0.739756\pi$
$488$	−46.3888	−2.09992
$489$	6.86073	0.310253
$490$	5.67308	0.256283
$491$	11.6473	0.525634	0.262817	−	0.964846i	$-0.415348\pi$
$491$	11.6473	0.525634	0.262817	+	0.964846i	$0.415348\pi$
$492$	2.29301	0.103377
$493$	−8.55552	−0.385321
$494$	9.60598	0.432194
$495$	−1.62339	−0.0729662
$496$	103.876	4.66417
$497$	39.6910	1.78039
$498$	29.8318	1.33680
$499$	18.9121	0.846622	0.423311	−	0.905985i	$-0.360868\pi$
$499$	18.9121	0.846622	0.423311	+	0.905985i	$0.360868\pi$
$500$	−4.90182	−0.219216
$501$	−25.7940	−1.15239
$502$	7.92886	0.353882
$503$	−1.51293	−0.0674584	−0.0337292	−	0.999431i	$-0.510738\pi$
$503$	−1.51293	−0.0674584	−0.0337292	+	0.999431i	$0.510738\pi$
$504$	37.4551	1.66838
$505$	4.81863	0.214426
$506$	−10.5442	−0.468748
$507$	9.88703	0.439099
$508$	−64.9727	−2.88270
$509$	−16.1892	−0.717574	−0.358787	−	0.933420i	$-0.616810\pi$
$509$	−16.1892	−0.717574	−0.358787	+	0.933420i	$0.616810\pi$
$510$	9.54235	0.422542
$511$	−3.02645	−0.133882
$512$	37.1498	1.64180
$513$	−9.27501	−0.409502
$514$	55.1754	2.43368
$515$	4.07639	0.179627
$516$	32.9534	1.45069
$517$	4.40266	0.193629
$518$	−17.1243	−0.752398
$519$	−24.0152	−1.05415
$520$	16.3029	0.714928
$521$	19.6932	0.862775	0.431387	−	0.902167i	$-0.358024\pi$
$521$	19.6932	0.862775	0.431387	+	0.902167i	$0.358024\pi$
$522$	11.7865	0.515880
$523$	−15.8202	−0.691768	−0.345884	−	0.938277i	$-0.612421\pi$
$523$	−15.8202	−0.691768	−0.345884	+	0.938277i	$0.612421\pi$
$524$	58.3879	2.55069
$525$	−3.55090	−0.154974
$526$	−17.7512	−0.773989
$527$	−31.4524	−1.37009
$528$	11.9960	0.522057
$529$	−6.89111	−0.299614
$530$	−28.5586	−1.24050
$531$	−5.94718	−0.258086
$532$	−25.3653	−1.09973
$533$	−0.852618	−0.0369310
$534$	37.1834	1.60908
$535$	15.5620	0.672803
$536$	65.2443	2.81812
$537$	−18.3711	−0.792772
$538$	8.96232	0.386393
$539$	−2.15942	−0.0930127
$540$	−26.5903	−1.14426
$541$	26.4396	1.13673	0.568364	−	0.822777i	$-0.307576\pi$
$541$	26.4396	1.13673	0.568364	+	0.822777i	$0.307576\pi$
$542$	29.8098	1.28044
$543$	23.7444	1.01897
$544$	35.9526	1.54145
$545$	−5.77229	−0.247258
$546$	19.9495	0.853759
$547$	19.9442	0.852752	0.426376	−	0.904546i	$-0.359790\pi$
$547$	19.9442	0.852752	0.426376	+	0.904546i	$0.359790\pi$
$548$	−6.57354	−0.280808
$549$	−9.87834	−0.421597
$550$	2.62713	0.112021
$551$	−4.72526	−0.201303
$552$	−35.8997	−1.52799
$553$	−32.6806	−1.38972
$554$	−51.9842	−2.20860
$555$	2.52698	0.107264
$556$	−99.3018	−4.21134
$557$	−17.6443	−0.747611	−0.373806	−	0.927507i	$-0.621947\pi$
$557$	−17.6443	−0.747611	−0.373806	+	0.927507i	$0.621947\pi$
$558$	43.3303	1.83432
$559$	−12.2532	−0.518254
$560$	−30.9431	−1.30759
$561$	−3.63223	−0.153353
$562$	20.1065	0.848140
$563$	8.43471	0.355480	0.177740	−	0.984077i	$-0.443121\pi$
$563$	8.43471	0.355480	0.177740	+	0.984077i	$0.443121\pi$
$564$	25.3208	1.06620
$565$	13.0505	0.549039
$566$	24.9778	1.04990
$567$	−4.52274	−0.189937
$568$	−99.9795	−4.19505
$569$	−26.1415	−1.09591	−0.547955	−	0.836508i	$-0.684594\pi$
$569$	−26.1415	−1.09591	−0.547955	+	0.836508i	$0.684594\pi$
$570$	5.27030	0.220748
$571$	12.9129	0.540389	0.270195	−	0.962806i	$-0.412912\pi$
$571$	12.9129	0.540389	0.270195	+	0.962806i	$0.412912\pi$
$572$	−10.4826	−0.438299
$573$	13.4973	0.563856
$574$	3.17000	0.132313
$575$	−4.01359	−0.167378
$576$	−16.3340	−0.680581
$577$	17.9291	0.746397	0.373199	−	0.927751i	$-0.378261\pi$
$577$	17.9291	0.746397	0.373199	+	0.927751i	$0.378261\pi$
$578$	19.4833	0.810400
$579$	−15.8492	−0.658669
$580$	−13.5468	−0.562498
$581$	29.2905	1.21518
$582$	−1.91269	−0.0792836
$583$	10.8706	0.450215
$584$	7.62347	0.315462
$585$	3.47165	0.143535
$586$	58.6958	2.42470
$587$	11.4390	0.472137	0.236069	−	0.971736i	$-0.424141\pi$
$587$	11.4390	0.472137	0.236069	+	0.971736i	$0.424141\pi$
$588$	−12.4194	−0.512165
$589$	−17.3714	−0.715774
$590$	9.62429	0.396226
$591$	6.14368	0.252717
$592$	22.0205	0.905037
$593$	−0.638621	−0.0262250	−0.0131125	−	0.999914i	$-0.504174\pi$
$593$	−0.638621	−0.0262250	−0.0131125	+	0.999914i	$0.504174\pi$
$594$	14.2511	0.584729
$595$	9.36921	0.384100
$596$	78.9925	3.23566
$597$	−4.64923	−0.190280
$598$	22.5489	0.922095
$599$	10.3175	0.421560	0.210780	−	0.977533i	$-0.432400\pi$
$599$	10.3175	0.421560	0.210780	+	0.977533i	$0.432400\pi$
$600$	8.94453	0.365159
$601$	19.0158	0.775669	0.387835	−	0.921729i	$-0.373223\pi$
$601$	19.0158	0.775669	0.387835	+	0.921729i	$0.373223\pi$
$602$	45.5568	1.85676
$603$	13.8936	0.565790
$604$	−22.6043	−0.919754
$605$	−1.00000	−0.0406558
$606$	−14.8529	−0.603357
$607$	12.9106	0.524025	0.262013	−	0.965064i	$-0.415614\pi$
$607$	12.9106	0.524025	0.262013	+	0.965064i	$0.415614\pi$
$608$	19.8568	0.805300
$609$	−9.81332	−0.397656
$610$	15.9861	0.647257
$611$	−9.41514	−0.380896
$612$	24.6349	0.995807
$613$	47.7304	1.92781	0.963906	−	0.266243i	$-0.0857823\pi$
$613$	47.7304	1.92781	0.963906	+	0.266243i	$0.0857823\pi$
$614$	−43.7610	−1.76605
$615$	−0.467787	−0.0188630
$616$	23.0721	0.929601
$617$	4.21968	0.169878	0.0849389	−	0.996386i	$-0.472930\pi$
$617$	4.21968	0.169878	0.0849389	+	0.996386i	$0.472930\pi$
$618$	−12.5650	−0.505439
$619$	−24.3096	−0.977087	−0.488543	−	0.872540i	$-0.662472\pi$
$619$	−24.3096	−0.977087	−0.488543	+	0.872540i	$0.662472\pi$
$620$	−49.8016	−2.00008
$621$	−21.7720	−0.873681
$622$	−47.1659	−1.89118
$623$	36.5087	1.46269
$624$	−25.6535	−1.02696
$625$	1.00000	0.0400000
$626$	−20.0854	−0.802774
$627$	−2.00610	−0.0801160
$628$	66.9922	2.67328
$629$	−6.66754	−0.265852
$630$	−12.9074	−0.514245
$631$	−3.89815	−0.155183	−0.0775915	−	0.996985i	$-0.524723\pi$
$631$	−3.89815	−0.155183	−0.0775915	+	0.996985i	$0.524723\pi$
$632$	82.3208	3.27454
$633$	−12.9012	−0.512779
$634$	−13.5766	−0.539194
$635$	13.2548	0.526001
$636$	62.5197	2.47907
$637$	4.61794	0.182969
$638$	7.26038	0.287441
$639$	−21.2903	−0.842232
$640$	3.20627	0.126739
$641$	25.9592	1.02533	0.512663	−	0.858590i	$-0.328659\pi$
$641$	25.9592	1.02533	0.512663	+	0.858590i	$0.328659\pi$
$642$	−47.9680	−1.89314
$643$	19.6526	0.775023	0.387511	−	0.921865i	$-0.373335\pi$
$643$	19.6526	0.775023	0.387511	+	0.921865i	$0.373335\pi$
$644$	−59.5421	−2.34629
$645$	−6.72268	−0.264705
$646$	−13.9059	−0.547121
$647$	−36.1823	−1.42247	−0.711236	−	0.702953i	$-0.751864\pi$
$647$	−36.1823	−1.42247	−0.711236	+	0.702953i	$0.751864\pi$
$648$	11.3925	0.447542
$649$	−3.66342	−0.143802
$650$	−5.61815	−0.220362
$651$	−36.0765	−1.41395
$652$	−28.6631	−1.12253
$653$	−22.7845	−0.891628	−0.445814	−	0.895126i	$-0.647086\pi$
$653$	−22.7845	−0.891628	−0.445814	+	0.895126i	$0.647086\pi$
$654$	17.7924	0.695738
$655$	−11.9115	−0.465419
$656$	−4.07637	−0.159156
$657$	1.62339	0.0633347
$658$	35.0051	1.36464
$659$	18.0428	0.702847	0.351423	−	0.936217i	$-0.385698\pi$
$659$	18.0428	0.702847	0.351423	+	0.936217i	$0.385698\pi$
$660$	−5.75125	−0.223867
$661$	−6.96335	−0.270843	−0.135421	−	0.990788i	$-0.543239\pi$
$661$	−6.96335	−0.270843	−0.135421	+	0.990788i	$0.543239\pi$
$662$	48.0907	1.86910
$663$	7.76756	0.301667
$664$	−73.7813	−2.86327
$665$	5.17467	0.200665
$666$	9.18551	0.355931
$667$	−11.0920	−0.429484
$668$	107.764	4.16950
$669$	−24.6781	−0.954112
$670$	−22.4839	−0.868628
$671$	−6.08499	−0.234908
$672$	41.2382	1.59080
$673$	−31.0832	−1.19817	−0.599085	−	0.800685i	$-0.704469\pi$
$673$	−31.0832	−1.19817	−0.599085	+	0.800685i	$0.704469\pi$
$674$	−32.8075	−1.26370
$675$	5.42457	0.208792
$676$	−41.3066	−1.58871
$677$	−20.7117	−0.796015	−0.398007	−	0.917382i	$-0.630298\pi$
$677$	−20.7117	−0.796015	−0.398007	+	0.917382i	$0.630298\pi$
$678$	−40.2267	−1.54490
$679$	−1.87798	−0.0720704
$680$	−23.6005	−0.905039
$681$	−10.3589	−0.396954
$682$	26.6911	1.02206
$683$	−21.5358	−0.824045	−0.412023	−	0.911174i	$-0.635178\pi$
$683$	−21.5358	−0.824045	−0.412023	+	0.911174i	$0.635178\pi$
$684$	13.6060	0.520238
$685$	1.34104	0.0512385
$686$	38.4869	1.46944
$687$	−0.965447	−0.0368341
$688$	−58.5825	−2.23344
$689$	−23.2469	−0.885638
$690$	12.3714	0.470972
$691$	11.4273	0.434715	0.217358	−	0.976092i	$-0.430256\pi$
$691$	11.4273	0.434715	0.217358	+	0.976092i	$0.430256\pi$
$692$	100.332	3.81405
$693$	4.91313	0.186634
$694$	22.9852	0.872505
$695$	20.2581	0.768435
$696$	24.7192	0.936980
$697$	1.23428	0.0467515
$698$	53.7474	2.03437
$699$	9.88279	0.373801
$700$	14.8351	0.560715
$701$	−18.1417	−0.685204	−0.342602	−	0.939481i	$-0.611308\pi$
$701$	−18.1417	−0.685204	−0.342602	+	0.939481i	$0.611308\pi$
$702$	−30.4761	−1.15024
$703$	−3.68252	−0.138889
$704$	−10.0616	−0.379211
$705$	−5.16559	−0.194547
$706$	59.1356	2.22560
$707$	−14.5834	−0.548464
$708$	−21.0693	−0.791831
$709$	−41.0110	−1.54020	−0.770101	−	0.637922i	$-0.779794\pi$
$709$	−41.0110	−1.54020	−0.770101	+	0.637922i	$0.779794\pi$
$710$	34.4540	1.29304
$711$	17.5300	0.657424
$712$	−91.9634	−3.44648
$713$	−40.7773	−1.52712
$714$	−28.8795	−1.08079
$715$	2.13851	0.0799757
$716$	76.7518	2.86835
$717$	24.3411	0.909034
$718$	33.0534	1.23354
$719$	−11.2892	−0.421017	−0.210509	−	0.977592i	$-0.567512\pi$
$719$	−11.2892	−0.421017	−0.210509	+	0.977592i	$0.567512\pi$
$720$	16.5980	0.618569
$721$	−12.3370	−0.459454
$722$	42.2352	1.57183
$723$	−20.1077	−0.747814
$724$	−99.2008	−3.68677
$725$	2.76361	0.102638
$726$	3.08238	0.114398
$727$	−15.1328	−0.561244	−0.280622	−	0.959818i	$-0.590541\pi$
$727$	−15.1328	−0.561244	−0.280622	+	0.959818i	$0.590541\pi$
$728$	−49.3399	−1.82866
$729$	21.5198	0.797029
$730$	−2.62713	−0.0972345
$731$	17.7381	0.656066
$732$	−34.9963	−1.29350
$733$	−17.8482	−0.659238	−0.329619	−	0.944114i	$-0.606920\pi$
$733$	−17.8482	−0.659238	−0.329619	+	0.944114i	$0.606920\pi$
$734$	71.4898	2.63874
$735$	2.53362	0.0934539
$736$	46.6116	1.71813
$737$	8.55834	0.315251
$738$	−1.70039	−0.0625923
$739$	14.5309	0.534529	0.267265	−	0.963623i	$-0.413880\pi$
$739$	14.5309	0.534529	0.267265	+	0.963623i	$0.413880\pi$
$740$	−10.5573	−0.388096
$741$	4.29007	0.157600
$742$	86.4311	3.17299
$743$	−39.7810	−1.45942	−0.729711	−	0.683756i	$-0.760345\pi$
$743$	−39.7810	−1.45942	−0.729711	+	0.683756i	$0.760345\pi$
$744$	90.8747	3.33163
$745$	−16.1149	−0.590405
$746$	19.2968	0.706505
$747$	−15.7115	−0.574854
$748$	15.1749	0.554850
$749$	−47.0976	−1.72091
$750$	−3.08238	−0.112553
$751$	−3.87710	−0.141477	−0.0707387	−	0.997495i	$-0.522536\pi$
$751$	−3.87710	−0.141477	−0.0707387	+	0.997495i	$0.522536\pi$
$752$	−45.0138	−1.64148
$753$	3.54106	0.129043
$754$	−15.5264	−0.565438
$755$	4.61140	0.167826
$756$	80.4743	2.92682
$757$	−31.7171	−1.15278	−0.576390	−	0.817175i	$-0.695539\pi$
$757$	−31.7171	−1.15278	−0.576390	+	0.817175i	$0.695539\pi$
$758$	49.4612	1.79651
$759$	−4.70910	−0.170929
$760$	−13.0347	−0.472819
$761$	35.1416	1.27388	0.636941	−	0.770913i	$-0.280200\pi$
$761$	35.1416	1.27388	0.636941	+	0.770913i	$0.280200\pi$
$762$	−40.8564	−1.48007
$763$	17.4696	0.632440
$764$	−56.3895	−2.04010
$765$	−5.02566	−0.181703
$766$	82.1807	2.96931
$767$	7.83426	0.282879
$768$	13.7274	0.495344
$769$	−12.4527	−0.449057	−0.224529	−	0.974468i	$-0.572084\pi$
$769$	−12.4527	−0.449057	−0.224529	+	0.974468i	$0.572084\pi$
$770$	−7.95089	−0.286530
$771$	24.6415	0.887444
$772$	66.2155	2.38315
$773$	−43.0988	−1.55016	−0.775079	−	0.631865i	$-0.782290\pi$
$773$	−43.0988	−1.55016	−0.775079	+	0.631865i	$0.782290\pi$
$774$	−24.4368	−0.878361
$775$	10.1598	0.364951
$776$	4.73054	0.169817
$777$	−7.64778	−0.274363
$778$	−39.1632	−1.40407
$779$	0.681698	0.0244244
$780$	12.2991	0.440379
$781$	−13.1147	−0.469281
$782$	−32.6425	−1.16729
$783$	14.9914	0.535750
$784$	22.0784	0.788513
$785$	−13.6668	−0.487789
$786$	36.7157	1.30960
$787$	−13.1906	−0.470195	−0.235098	−	0.971972i	$-0.575541\pi$
$787$	−13.1906	−0.470195	−0.235098	+	0.971972i	$0.575541\pi$
$788$	−25.6674	−0.914363
$789$	−7.92776	−0.282236
$790$	−28.3686	−1.00931
$791$	−39.4968	−1.40434
$792$	−12.3759	−0.439759
$793$	13.0128	0.462099
$794$	70.9903	2.51935
$795$	−12.7544	−0.452351
$796$	19.4238	0.688458
$797$	7.61361	0.269688	0.134844	−	0.990867i	$-0.456947\pi$
$797$	7.61361	0.269688	0.134844	+	0.990867i	$0.456947\pi$
$798$	−15.9503	−0.564635
$799$	13.6296	0.482182
$800$	−11.6134	−0.410597
$801$	−19.5833	−0.691943
$802$	30.7808	1.08691
$803$	1.00000	0.0352892
$804$	49.2212	1.73590
$805$	12.1469	0.428123
$806$	−57.0793	−2.01053
$807$	4.00261	0.140899
$808$	36.7347	1.29232
$809$	−1.84738	−0.0649505	−0.0324752	−	0.999473i	$-0.510339\pi$
$809$	−1.84738	−0.0649505	−0.0324752	+	0.999473i	$0.510339\pi$
$810$	−3.92600	−0.137945
$811$	36.3527	1.27652	0.638258	−	0.769822i	$-0.279655\pi$
$811$	36.3527	1.27652	0.638258	+	0.769822i	$0.279655\pi$
$812$	40.9986	1.43877
$813$	13.3132	0.466914
$814$	5.65821	0.198320
$815$	5.84744	0.204827
$816$	37.1368	1.30005
$817$	9.79684	0.342748
$818$	5.27148	0.184313
$819$	−10.5068	−0.367136
$820$	1.95434	0.0682486
$821$	−27.4633	−0.958476	−0.479238	−	0.877685i	$-0.659087\pi$
$821$	−27.4633	−0.958476	−0.479238	+	0.877685i	$0.659087\pi$
$822$	−4.13360	−0.144176
$823$	12.6271	0.440153	0.220077	−	0.975483i	$-0.429369\pi$
$823$	12.6271	0.440153	0.220077	+	0.975483i	$0.429369\pi$
$824$	31.0763	1.08259
$825$	1.17329	0.0408486
$826$	−29.1275	−1.01347
$827$	27.3984	0.952734	0.476367	−	0.879246i	$-0.341953\pi$
$827$	27.3984	0.952734	0.476367	+	0.879246i	$0.341953\pi$
$828$	31.9385	1.10994
$829$	−34.1432	−1.18584	−0.592922	−	0.805260i	$-0.702026\pi$
$829$	−34.1432	−1.18584	−0.592922	+	0.805260i	$0.702026\pi$
$830$	25.4259	0.882544
$831$	−23.2164	−0.805367
$832$	21.5168	0.745962
$833$	−6.68506	−0.231624
$834$	−62.4433	−2.16224
$835$	−21.9844	−0.760801
$836$	8.38120	0.289870
$837$	55.1126	1.90497
$838$	57.9949	2.00340
$839$	0.865168	0.0298689	0.0149345	−	0.999888i	$-0.495246\pi$
$839$	0.865168	0.0298689	0.0149345	+	0.999888i	$0.495246\pi$
$840$	−27.0702	−0.934011
$841$	−21.3624	−0.736636
$842$	33.4028	1.15114
$843$	8.97963	0.309275
$844$	53.8995	1.85530
$845$	8.42677	0.289890
$846$	−18.7768	−0.645560
$847$	3.02645	0.103990
$848$	−111.144	−3.81669
$849$	11.1552	0.382846
$850$	8.13300	0.278960
$851$	−8.64430	−0.296323
$852$	−75.4259	−2.58405
$853$	−45.0493	−1.54246	−0.771230	−	0.636557i	$-0.780358\pi$
$853$	−45.0493	−1.54246	−0.771230	+	0.636557i	$0.780358\pi$
$854$	−48.3811	−1.65557
$855$	−2.77570	−0.0949270
$856$	118.636	4.05490
$857$	−4.52253	−0.154487	−0.0772434	−	0.997012i	$-0.524612\pi$
$857$	−4.52253	−0.154487	−0.0772434	+	0.997012i	$0.524612\pi$
$858$	−6.59171	−0.225037
$859$	4.47389	0.152647	0.0763235	−	0.997083i	$-0.475682\pi$
$859$	4.47389	0.152647	0.0763235	+	0.997083i	$0.475682\pi$
$860$	28.0863	0.957736
$861$	1.41573	0.0482481
$862$	75.1659	2.56016
$863$	−47.3545	−1.61197	−0.805983	−	0.591939i	$-0.798363\pi$
$863$	−47.3545	−1.61197	−0.805983	+	0.591939i	$0.798363\pi$
$864$	−62.9980	−2.14324
$865$	−20.4683	−0.695943
$866$	36.4996	1.24031
$867$	8.70134	0.295513
$868$	150.722	5.11584
$869$	10.7983	0.366308
$870$	−8.51852	−0.288805
$871$	−18.3021	−0.620143
$872$	−44.0049	−1.49019
$873$	1.00735	0.0340938
$874$	−18.0287	−0.609828
$875$	−3.02645	−0.102313
$876$	5.75125	0.194317
$877$	−9.60841	−0.324453	−0.162226	−	0.986754i	$-0.551868\pi$
$877$	−9.60841	−0.324453	−0.162226	+	0.986754i	$0.551868\pi$
$878$	2.18747	0.0738235
$879$	26.2138	0.884170
$880$	10.2242	0.344659
$881$	6.80933	0.229412	0.114706	−	0.993399i	$-0.463407\pi$
$881$	6.80933	0.229412	0.114706	+	0.993399i	$0.463407\pi$
$882$	9.20964	0.310105
$883$	−43.1853	−1.45330	−0.726651	−	0.687007i	$-0.758924\pi$
$883$	−43.1853	−1.45330	−0.726651	+	0.687007i	$0.758924\pi$
$884$	−32.4517	−1.09147
$885$	4.29825	0.144484
$886$	90.1056	3.02716
$887$	−1.22538	−0.0411442	−0.0205721	−	0.999788i	$-0.506549\pi$
$887$	−1.22538	−0.0411442	−0.0205721	+	0.999788i	$0.506549\pi$
$888$	19.2644	0.646469
$889$	−40.1150	−1.34542
$890$	31.6916	1.06231
$891$	1.49440	0.0500644
$892$	103.102	3.45210
$893$	7.52773	0.251906
$894$	49.6723	1.66129
$895$	−15.6578	−0.523383
$896$	−9.70362	−0.324175
$897$	10.0704	0.336242
$898$	91.4406	3.05141
$899$	28.0778	0.936446
$900$	−7.95760	−0.265253
$901$	33.6530	1.12114
$902$	−1.04743	−0.0348756
$903$	20.3459	0.677068
$904$	99.4903	3.30900
$905$	20.2375	0.672718
$906$	−14.2141	−0.472232
$907$	5.72095	0.189961	0.0949805	−	0.995479i	$-0.469721\pi$
$907$	5.72095	0.189961	0.0949805	+	0.995479i	$0.469721\pi$
$908$	43.2779	1.43623
$909$	7.82255	0.259458
$910$	17.0031	0.563646
$911$	6.44708	0.213601	0.106801	−	0.994280i	$-0.465939\pi$
$911$	6.44708	0.213601	0.106801	+	0.994280i	$0.465939\pi$
$912$	20.5108	0.679182
$913$	−9.67818	−0.320301
$914$	30.7953	1.01862
$915$	7.13945	0.236023
$916$	4.03349	0.133270
$917$	36.0495	1.19046
$918$	44.1181	1.45611
$919$	−13.0694	−0.431119	−0.215559	−	0.976491i	$-0.569157\pi$
$919$	−13.0694	−0.431119	−0.215559	+	0.976491i	$0.569157\pi$
$920$	−30.5975	−1.00877
$921$	−19.5438	−0.643991
$922$	30.0210	0.988691
$923$	28.0459	0.923142
$924$	17.4059	0.572612
$925$	2.15376	0.0708151
$926$	52.2479	1.71697
$927$	6.61760	0.217350
$928$	−32.0951	−1.05357
$929$	−24.7898	−0.813326	−0.406663	−	0.913578i	$-0.633308\pi$
$929$	−24.7898	−0.813326	−0.406663	+	0.913578i	$0.633308\pi$
$930$	−31.3164	−1.02691
$931$	−3.69220	−0.121007
$932$	−41.2888	−1.35246
$933$	−21.0645	−0.689621
$934$	−95.1981	−3.11498
$935$	−3.09577	−0.101243
$936$	26.4660	0.865068
$937$	60.5440	1.97789	0.988943	−	0.148294i	$-0.0473783\pi$
$937$	60.5440	1.97789	0.988943	+	0.148294i	$0.0473783\pi$
$938$	68.0464	2.22179
$939$	−8.97022	−0.292732
$940$	21.5811	0.703897
$941$	59.2744	1.93229	0.966146	−	0.257997i	$-0.0830623\pi$
$941$	59.2744	1.93229	0.966146	+	0.257997i	$0.0830623\pi$
$942$	42.1263	1.37255
$943$	1.60021	0.0521099
$944$	37.4556	1.21908
$945$	−16.4172	−0.534052
$946$	−15.0529	−0.489411
$947$	22.6883	0.737272	0.368636	−	0.929574i	$-0.379825\pi$
$947$	22.6883	0.737272	0.368636	+	0.929574i	$0.379825\pi$
$948$	62.1039	2.01704
$949$	−2.13851	−0.0694190
$950$	4.49190	0.145737
$951$	−6.06335	−0.196618
$952$	71.4259	2.31493
$953$	−21.2496	−0.688341	−0.344171	−	0.938907i	$-0.611840\pi$
$953$	−21.2496	−0.688341	−0.344171	+	0.938907i	$0.611840\pi$
$954$	−46.3618	−1.50102
$955$	11.5038	0.372254
$956$	−101.693	−3.28900
$957$	3.24252	0.104816
$958$	−79.3849	−2.56481
$959$	−4.05860	−0.131059
$960$	11.8052	0.381010
$961$	72.2216	2.32973
$962$	−12.1001	−0.390124
$963$	25.2632	0.814096
$964$	84.0070	2.70568
$965$	−13.5083	−0.434849
$966$	−37.4415	−1.20466
$967$	36.7232	1.18094	0.590470	−	0.807060i	$-0.298942\pi$
$967$	36.7232	1.18094	0.590470	+	0.807060i	$0.298942\pi$
$968$	−7.62347	−0.245028
$969$	−6.21044	−0.199508
$970$	−1.63020	−0.0523425
$971$	−52.3491	−1.67996	−0.839982	−	0.542615i	$-0.817434\pi$
$971$	−52.3491	−1.67996	−0.839982	+	0.542615i	$0.817434\pi$
$972$	−71.1762	−2.28298
$973$	−61.3103	−1.96552
$974$	79.3093	2.54123
$975$	−2.50909	−0.0803551
$976$	62.2143	1.99143
$977$	59.1510	1.89241	0.946204	−	0.323571i	$-0.104884\pi$
$977$	59.1510	1.89241	0.946204	+	0.323571i	$0.104884\pi$
$978$	−18.0240	−0.576345
$979$	−12.0632	−0.385541
$980$	−10.5851	−0.338128
$981$	−9.37070	−0.299183
$982$	−30.5989	−0.976452
$983$	43.4192	1.38486	0.692429	−	0.721486i	$-0.256541\pi$
$983$	43.4192	1.38486	0.692429	+	0.721486i	$0.256541\pi$
$984$	−3.56616	−0.113685
$985$	5.23629	0.166842
$986$	22.4765	0.715797
$987$	15.6334	0.497617
$988$	−17.9233	−0.570216
$989$	22.9969	0.731260
$990$	4.26487	0.135547
$991$	−7.94547	−0.252396	−0.126198	−	0.992005i	$-0.540277\pi$
$991$	−7.94547	−0.252396	−0.126198	+	0.992005i	$0.540277\pi$
$992$	−117.990	−3.74620
$993$	21.4775	0.681568
$994$	−104.274	−3.30736
$995$	−3.96257	−0.125622
$996$	−55.6616	−1.76371
$997$	25.4003	0.804434	0.402217	−	0.915544i	$-0.368240\pi$
$997$	25.4003	0.804434	0.402217	+	0.915544i	$0.368240\pi$
$998$	−49.6846	−1.57274
$999$	11.6832	0.369641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.3	✓	32	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)

\(f(q)\)	\(=\)	\(q-2.62713 q^{2} -1.17329 q^{3} +4.90182 q^{4} -1.00000 q^{5} +3.08238 q^{6} +3.02645 q^{7} -7.62347 q^{8} -1.62339 q^{9} +O(q^{10})\)	\(q-2.62713 q^{2} -1.17329 q^{3} +4.90182 q^{4} -1.00000 q^{5} +3.08238 q^{6} +3.02645 q^{7} -7.62347 q^{8} -1.62339 q^{9} +2.62713 q^{10} -1.00000 q^{11} -5.75125 q^{12} +2.13851 q^{13} -7.95089 q^{14} +1.17329 q^{15} +10.2242 q^{16} -3.09577 q^{17} +4.26487 q^{18} -1.70981 q^{19} -4.90182 q^{20} -3.55090 q^{21} +2.62713 q^{22} -4.01359 q^{23} +8.94453 q^{24} +1.00000 q^{25} -5.61815 q^{26} +5.42457 q^{27} +14.8351 q^{28} +2.76361 q^{29} -3.08238 q^{30} +10.1598 q^{31} -11.6134 q^{32} +1.17329 q^{33} +8.13300 q^{34} -3.02645 q^{35} -7.95760 q^{36} +2.15376 q^{37} +4.49190 q^{38} -2.50909 q^{39} +7.62347 q^{40} -0.398697 q^{41} +9.32869 q^{42} -5.72977 q^{43} -4.90182 q^{44} +1.62339 q^{45} +10.5442 q^{46} -4.40266 q^{47} -11.9960 q^{48} +2.15942 q^{49} -2.62713 q^{50} +3.63223 q^{51} +10.4826 q^{52} -10.8706 q^{53} -14.2511 q^{54} +1.00000 q^{55} -23.0721 q^{56} +2.00610 q^{57} -7.26038 q^{58} +3.66342 q^{59} +5.75125 q^{60} +6.08499 q^{61} -26.6911 q^{62} -4.91313 q^{63} +10.0616 q^{64} -2.13851 q^{65} -3.08238 q^{66} -8.55834 q^{67} -15.1749 q^{68} +4.70910 q^{69} +7.95089 q^{70} +13.1147 q^{71} +12.3759 q^{72} -1.00000 q^{73} -5.65821 q^{74} -1.17329 q^{75} -8.38120 q^{76} -3.02645 q^{77} +6.59171 q^{78} -10.7983 q^{79} -10.2242 q^{80} -1.49440 q^{81} +1.04743 q^{82} +9.67818 q^{83} -17.4059 q^{84} +3.09577 q^{85} +15.0529 q^{86} -3.24252 q^{87} +7.62347 q^{88} +12.0632 q^{89} -4.26487 q^{90} +6.47210 q^{91} -19.6739 q^{92} -11.9204 q^{93} +11.5664 q^{94} +1.70981 q^{95} +13.6259 q^{96} -0.620523 q^{97} -5.67308 q^{98} +1.62339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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