LMFDB - Embedded newform 4033.2.a.d.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54579 q^{2} -2.84288 q^{3} +0.389475 q^{4} -4.15668 q^{5} +4.39450 q^{6} -1.08781 q^{7} +2.48954 q^{8} +5.08197 q^{9} +O(q^{10})$	\(q-1.54579 q^{2} -2.84288 q^{3} +0.389475 q^{4} -4.15668 q^{5} +4.39450 q^{6} -1.08781 q^{7} +2.48954 q^{8} +5.08197 q^{9} +6.42537 q^{10} +5.27627 q^{11} -1.10723 q^{12} -3.68764 q^{13} +1.68152 q^{14} +11.8169 q^{15} -4.62726 q^{16} -5.74510 q^{17} -7.85567 q^{18} -7.16189 q^{19} -1.61892 q^{20} +3.09250 q^{21} -8.15601 q^{22} -9.35188 q^{23} -7.07746 q^{24} +12.2780 q^{25} +5.70033 q^{26} -5.91880 q^{27} -0.423673 q^{28} +0.900862 q^{29} -18.2666 q^{30} +0.930630 q^{31} +2.17371 q^{32} -14.9998 q^{33} +8.88073 q^{34} +4.52166 q^{35} +1.97930 q^{36} -1.00000 q^{37} +11.0708 q^{38} +10.4835 q^{39} -10.3482 q^{40} +9.06663 q^{41} -4.78037 q^{42} -0.794928 q^{43} +2.05497 q^{44} -21.1241 q^{45} +14.4561 q^{46} -9.18462 q^{47} +13.1547 q^{48} -5.81668 q^{49} -18.9792 q^{50} +16.3326 q^{51} -1.43624 q^{52} -0.585765 q^{53} +9.14923 q^{54} -21.9318 q^{55} -2.70813 q^{56} +20.3604 q^{57} -1.39255 q^{58} +8.45828 q^{59} +4.60240 q^{60} +9.66321 q^{61} -1.43856 q^{62} -5.52820 q^{63} +5.89442 q^{64} +15.3283 q^{65} +23.1866 q^{66} +5.81221 q^{67} -2.23757 q^{68} +26.5863 q^{69} -6.98955 q^{70} +0.925457 q^{71} +12.6518 q^{72} -6.77773 q^{73} +1.54579 q^{74} -34.9049 q^{75} -2.78937 q^{76} -5.73955 q^{77} -16.2054 q^{78} +2.60905 q^{79} +19.2340 q^{80} +1.58052 q^{81} -14.0151 q^{82} +11.7543 q^{83} +1.20445 q^{84} +23.8805 q^{85} +1.22879 q^{86} -2.56104 q^{87} +13.1355 q^{88} -6.13277 q^{89} +32.6535 q^{90} +4.01144 q^{91} -3.64232 q^{92} -2.64567 q^{93} +14.1975 q^{94} +29.7697 q^{95} -6.17959 q^{96} -0.963032 q^{97} +8.99138 q^{98} +26.8138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.54579	−1.09304	−0.546520	−	0.837446i	$-0.684048\pi$
$2$	−1.54579	−1.09304	−0.546520	+	0.837446i	$0.684048\pi$
$3$	−2.84288	−1.64134	−0.820669	−	0.571404i	$-0.806399\pi$
$3$	−2.84288	−1.64134	−0.820669	+	0.571404i	$0.806399\pi$
$4$	0.389475	0.194737
$5$	−4.15668	−1.85892	−0.929462	−	0.368918i	$-0.879728\pi$
$5$	−4.15668	−1.85892	−0.929462	+	0.368918i	$0.879728\pi$
$6$	4.39450	1.79405
$7$	−1.08781	−0.411152	−0.205576	−	0.978641i	$-0.565907\pi$
$7$	−1.08781	−0.411152	−0.205576	+	0.978641i	$0.565907\pi$
$8$	2.48954	0.880185
$9$	5.08197	1.69399
$10$	6.42537	2.03188
$11$	5.27627	1.59085	0.795427	−	0.606049i	$-0.207247\pi$
$11$	5.27627	1.59085	0.795427	+	0.606049i	$0.207247\pi$
$12$	−1.10723	−0.319630
$13$	−3.68764	−1.02277	−0.511384	−	0.859352i	$-0.670867\pi$
$13$	−3.68764	−1.02277	−0.511384	+	0.859352i	$0.670867\pi$
$14$	1.68152	0.449406
$15$	11.8169	3.05112
$16$	−4.62726	−1.15681
$17$	−5.74510	−1.39339	−0.696696	−	0.717367i	$-0.745347\pi$
$17$	−5.74510	−1.39339	−0.696696	+	0.717367i	$0.745347\pi$
$18$	−7.85567	−1.85160
$19$	−7.16189	−1.64305	−0.821525	−	0.570173i	$-0.806876\pi$
$19$	−7.16189	−1.64305	−0.821525	+	0.570173i	$0.806876\pi$
$20$	−1.61892	−0.362002
$21$	3.09250	0.674839
$22$	−8.15601	−1.73887
$23$	−9.35188	−1.95000	−0.975001	−	0.222200i	$-0.928676\pi$
$23$	−9.35188	−1.95000	−0.975001	+	0.222200i	$0.928676\pi$
$24$	−7.07746	−1.44468
$25$	12.2780	2.45560
$26$	5.70033	1.11793
$27$	−5.91880	−1.13907
$28$	−0.423673	−0.0800666
$29$	0.900862	0.167286	0.0836429	−	0.996496i	$-0.473344\pi$
$29$	0.900862	0.167286	0.0836429	+	0.996496i	$0.473344\pi$
$30$	−18.2666	−3.33500
$31$	0.930630	0.167146	0.0835730	−	0.996502i	$-0.473367\pi$
$31$	0.930630	0.167146	0.0835730	+	0.996502i	$0.473367\pi$
$32$	2.17371	0.384260
$33$	−14.9998	−2.61113
$34$	8.88073	1.52303
$35$	4.52166	0.764300
$36$	1.97930	0.329883
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	11.0708	1.79592
$39$	10.4835	1.67871
$40$	−10.3482	−1.63620
$41$	9.06663	1.41597	0.707985	−	0.706227i	$-0.249604\pi$
$41$	9.06663	1.41597	0.707985	+	0.706227i	$0.249604\pi$
$42$	−4.78037	−0.737627
$43$	−0.794928	−0.121225	−0.0606127	−	0.998161i	$-0.519305\pi$
$43$	−0.794928	−0.121225	−0.0606127	+	0.998161i	$0.519305\pi$
$44$	2.05497	0.309799
$45$	−21.1241	−3.14900
$46$	14.4561	2.13143
$47$	−9.18462	−1.33971	−0.669857	−	0.742490i	$-0.733645\pi$
$47$	−9.18462	−1.33971	−0.669857	+	0.742490i	$0.733645\pi$
$48$	13.1547	1.89872
$49$	−5.81668	−0.830954
$50$	−18.9792	−2.68407
$51$	16.3326	2.28703
$52$	−1.43624	−0.199171
$53$	−0.585765	−0.0804609	−0.0402305	−	0.999190i	$-0.512809\pi$
$53$	−0.585765	−0.0804609	−0.0402305	+	0.999190i	$0.512809\pi$
$54$	9.14923	1.24505
$55$	−21.9318	−2.95728
$56$	−2.70813	−0.361890
$57$	20.3604	2.69680
$58$	−1.39255	−0.182850
$59$	8.45828	1.10117	0.550587	−	0.834778i	$-0.314404\pi$
$59$	8.45828	1.10117	0.550587	+	0.834778i	$0.314404\pi$
$60$	4.60240	0.594167
$61$	9.66321	1.23725	0.618624	−	0.785687i	$-0.287691\pi$
$61$	9.66321	1.23725	0.618624	+	0.785687i	$0.287691\pi$
$62$	−1.43856	−0.182697
$63$	−5.52820	−0.696488
$64$	5.89442	0.736802
$65$	15.3283	1.90125
$66$	23.1866	2.85407
$67$	5.81221	0.710075	0.355037	−	0.934852i	$-0.384468\pi$
$67$	5.81221	0.710075	0.355037	+	0.934852i	$0.384468\pi$
$68$	−2.23757	−0.271345
$69$	26.5863	3.20061
$70$	−6.98955	−0.835411
$71$	0.925457	0.109831	0.0549157	−	0.998491i	$-0.482511\pi$
$71$	0.925457	0.109831	0.0549157	+	0.998491i	$0.482511\pi$
$72$	12.6518	1.49102
$73$	−6.77773	−0.793273	−0.396637	−	0.917976i	$-0.629823\pi$
$73$	−6.77773	−0.793273	−0.396637	+	0.917976i	$0.629823\pi$
$74$	1.54579	0.179695
$75$	−34.9049	−4.03047
$76$	−2.78937	−0.319963
$77$	−5.73955	−0.654083
$78$	−16.2054	−1.83489
$79$	2.60905	0.293541	0.146770	−	0.989171i	$-0.453112\pi$
$79$	2.60905	0.293541	0.146770	+	0.989171i	$0.453112\pi$
$80$	19.2340	2.15043
$81$	1.58052	0.175614
$82$	−14.0151	−1.54771
$83$	11.7543	1.29020	0.645100	−	0.764098i	$-0.276816\pi$
$83$	11.7543	1.29020	0.645100	+	0.764098i	$0.276816\pi$
$84$	1.20445	0.131416
$85$	23.8805	2.59021
$86$	1.22879	0.132504
$87$	−2.56104	−0.274573
$88$	13.1355	1.40025
$89$	−6.13277	−0.650072	−0.325036	−	0.945702i	$-0.605376\pi$
$89$	−6.13277	−0.650072	−0.325036	+	0.945702i	$0.605376\pi$
$90$	32.6535	3.44198
$91$	4.01144	0.420513
$92$	−3.64232	−0.379738
$93$	−2.64567	−0.274343
$94$	14.1975	1.46436
$95$	29.7697	3.05430
$96$	−6.17959	−0.630701
$97$	−0.963032	−0.0977811	−0.0488906	−	0.998804i	$-0.515569\pi$
$97$	−0.963032	−0.0977811	−0.0488906	+	0.998804i	$0.515569\pi$
$98$	8.99138	0.908266
$99$	26.8138	2.69489
$100$	4.78197	0.478197
$101$	−1.28159	−0.127523	−0.0637616	−	0.997965i	$-0.520310\pi$
$101$	−1.28159	−0.127523	−0.0637616	+	0.997965i	$0.520310\pi$
$102$	−25.2469	−2.49981
$103$	17.0677	1.68173	0.840865	−	0.541244i	$-0.182047\pi$
$103$	17.0677	1.68173	0.840865	+	0.541244i	$0.182047\pi$
$104$	−9.18052	−0.900224
$105$	−12.8545	−1.25448
$106$	0.905470	0.0879471
$107$	−14.7232	−1.42334	−0.711672	−	0.702512i	$-0.752062\pi$
$107$	−14.7232	−1.42334	−0.711672	+	0.702512i	$0.752062\pi$
$108$	−2.30522	−0.221820
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	33.9019	3.23242
$111$	2.84288	0.269834
$112$	5.03356	0.475627
$113$	17.0760	1.60637	0.803186	−	0.595728i	$-0.203136\pi$
$113$	17.0760	1.60637	0.803186	+	0.595728i	$0.203136\pi$
$114$	−31.4729	−2.94771
$115$	38.8728	3.62491
$116$	0.350863	0.0325768
$117$	−18.7405	−1.73256
$118$	−13.0747	−1.20363
$119$	6.24955	0.572895
$120$	29.4187	2.68555
$121$	16.8390	1.53082
$122$	−14.9373	−1.35236
$123$	−25.7754	−2.32409
$124$	0.362457	0.0325496
$125$	−30.2523	−2.70585
$126$	8.54545	0.761289
$127$	18.9888	1.68498	0.842492	−	0.538709i	$-0.181088\pi$
$127$	18.9888	1.68498	0.842492	+	0.538709i	$0.181088\pi$
$128$	−13.4590	−1.18962
$129$	2.25989	0.198972
$130$	−23.6944	−2.07814
$131$	8.12207	0.709628	0.354814	−	0.934937i	$-0.384544\pi$
$131$	8.12207	0.709628	0.354814	+	0.934937i	$0.384544\pi$
$132$	−5.84204	−0.508484
$133$	7.79074	0.675543
$134$	−8.98447	−0.776140
$135$	24.6026	2.11745
$136$	−14.3026	−1.22644
$137$	−5.10373	−0.436041	−0.218020	−	0.975944i	$-0.569960\pi$
$137$	−5.10373	−0.436041	−0.218020	+	0.975944i	$0.569960\pi$
$138$	−41.0969	−3.49840
$139$	−13.4615	−1.14179	−0.570894	−	0.821024i	$-0.693403\pi$
$139$	−13.4615	−1.14179	−0.570894	+	0.821024i	$0.693403\pi$
$140$	1.76107	0.148838
$141$	26.1108	2.19892
$142$	−1.43056	−0.120050
$143$	−19.4570	−1.62707
$144$	−23.5156	−1.95963
$145$	−3.74459	−0.310972
$146$	10.4770	0.867080
$147$	16.5361	1.36388
$148$	−0.389475	−0.0320146
$149$	0.923382	0.0756464	0.0378232	−	0.999284i	$-0.487958\pi$
$149$	0.923382	0.0756464	0.0378232	+	0.999284i	$0.487958\pi$
$150$	53.9557	4.40546
$151$	14.0561	1.14387	0.571934	−	0.820300i	$-0.306193\pi$
$151$	14.0561	1.14387	0.571934	+	0.820300i	$0.306193\pi$
$152$	−17.8298	−1.44619
$153$	−29.1964	−2.36039
$154$	8.87216	0.714939
$155$	−3.86833	−0.310712
$156$	4.08306	0.326907
$157$	−0.116475	−0.00929570	−0.00464785	−	0.999989i	$-0.501479\pi$
$157$	−0.116475	−0.00929570	−0.00464785	+	0.999989i	$0.501479\pi$
$158$	−4.03305	−0.320852
$159$	1.66526	0.132064
$160$	−9.03540	−0.714311
$161$	10.1730	0.801747
$162$	−2.44316	−0.191953
$163$	16.2364	1.27174	0.635868	−	0.771798i	$-0.280642\pi$
$163$	16.2364	1.27174	0.635868	+	0.771798i	$0.280642\pi$
$164$	3.53122	0.275742
$165$	62.3494	4.85389
$166$	−18.1697	−1.41024
$167$	−15.3735	−1.18963	−0.594817	−	0.803861i	$-0.702775\pi$
$167$	−15.3735	−1.18963	−0.594817	+	0.803861i	$0.702775\pi$
$168$	7.69890	0.593983
$169$	0.598691	0.0460532
$170$	−36.9144	−2.83120
$171$	−36.3965	−2.78331
$172$	−0.309604	−0.0236071
$173$	−14.1227	−1.07373	−0.536866	−	0.843667i	$-0.680392\pi$
$173$	−14.1227	−1.07373	−0.536866	+	0.843667i	$0.680392\pi$
$174$	3.95884	0.300119
$175$	−13.3561	−1.00962
$176$	−24.4146	−1.84032
$177$	−24.0459	−1.80740
$178$	9.47999	0.710555
$179$	−2.42402	−0.181180	−0.0905900	−	0.995888i	$-0.528875\pi$
$179$	−2.42402	−0.181180	−0.0905900	+	0.995888i	$0.528875\pi$
$180$	−8.22731	−0.613228
$181$	−1.72587	−0.128283	−0.0641414	−	0.997941i	$-0.520431\pi$
$181$	−1.72587	−0.128283	−0.0641414	+	0.997941i	$0.520431\pi$
$182$	−6.20085	−0.459638
$183$	−27.4714	−2.03074
$184$	−23.2819	−1.71636
$185$	4.15668	0.305605
$186$	4.08966	0.299868
$187$	−30.3127	−2.21668
$188$	−3.57717	−0.260892
$189$	6.43850	0.468332
$190$	−46.0178	−3.33848
$191$	−7.39643	−0.535187	−0.267593	−	0.963532i	$-0.586228\pi$
$191$	−7.39643	−0.535187	−0.267593	+	0.963532i	$0.586228\pi$
$192$	−16.7571	−1.20934
$193$	7.13304	0.513448	0.256724	−	0.966485i	$-0.417357\pi$
$193$	7.13304	0.513448	0.256724	+	0.966485i	$0.417357\pi$
$194$	1.48865	0.106879
$195$	−43.5767	−3.12059
$196$	−2.26545	−0.161818
$197$	24.6192	1.75404	0.877022	−	0.480450i	$-0.159527\pi$
$197$	24.6192	1.75404	0.877022	+	0.480450i	$0.159527\pi$
$198$	−41.4486	−2.94563
$199$	−3.58390	−0.254056	−0.127028	−	0.991899i	$-0.540544\pi$
$199$	−3.58390	−0.254056	−0.127028	+	0.991899i	$0.540544\pi$
$200$	30.5665	2.16138
$201$	−16.5234	−1.16547
$202$	1.98108	0.139388
$203$	−0.979962	−0.0687799
$204$	6.36114	0.445369
$205$	−37.6871	−2.63218
$206$	−26.3831	−1.83820
$207$	−47.5260	−3.30329
$208$	17.0637	1.18315
$209$	−37.7880	−2.61385
$210$	19.8705	1.37119
$211$	10.8092	0.744134	0.372067	−	0.928206i	$-0.378649\pi$
$211$	10.8092	0.744134	0.372067	+	0.928206i	$0.378649\pi$
$212$	−0.228140	−0.0156687
$213$	−2.63096	−0.180271
$214$	22.7590	1.55577
$215$	3.30426	0.225349
$216$	−14.7351	−1.00259
$217$	−1.01234	−0.0687224
$218$	1.54579	0.104694
$219$	19.2683	1.30203
$220$	−8.54186	−0.575892
$221$	21.1859	1.42511
$222$	−4.39450	−0.294940
$223$	27.8851	1.86732	0.933662	−	0.358156i	$-0.116594\pi$
$223$	27.8851	1.86732	0.933662	+	0.358156i	$0.116594\pi$
$224$	−2.36457	−0.157989
$225$	62.3964	4.15976
$226$	−26.3959	−1.75583
$227$	10.5347	0.699214	0.349607	−	0.936896i	$-0.386315\pi$
$227$	10.5347	0.699214	0.349607	+	0.936896i	$0.386315\pi$
$228$	7.92985	0.525167
$229$	−7.52789	−0.497457	−0.248728	−	0.968573i	$-0.580013\pi$
$229$	−7.52789	−0.497457	−0.248728	+	0.968573i	$0.580013\pi$
$230$	−60.0893	−3.96217
$231$	16.3169	1.07357
$232$	2.24273	0.147242
$233$	−14.7528	−0.966485	−0.483243	−	0.875487i	$-0.660541\pi$
$233$	−14.7528	−0.966485	−0.483243	+	0.875487i	$0.660541\pi$
$234$	28.9689	1.89376
$235$	38.1775	2.49043
$236$	3.29428	0.214440
$237$	−7.41721	−0.481800
$238$	−9.66051	−0.626198
$239$	−15.4130	−0.996987	−0.498494	−	0.866893i	$-0.666113\pi$
$239$	−15.4130	−0.996987	−0.498494	+	0.866893i	$0.666113\pi$
$240$	−54.6801	−3.52958
$241$	−16.2956	−1.04969	−0.524845	−	0.851198i	$-0.675877\pi$
$241$	−16.2956	−1.04969	−0.524845	+	0.851198i	$0.675877\pi$
$242$	−26.0296	−1.67324
$243$	13.2632	0.850832
$244$	3.76357	0.240938
$245$	24.1781	1.54468
$246$	39.8434	2.54032
$247$	26.4105	1.68046
$248$	2.31684	0.147119
$249$	−33.4160	−2.11765
$250$	46.7638	2.95760
$251$	13.0648	0.824642	0.412321	−	0.911039i	$-0.364718\pi$
$251$	13.0648	0.824642	0.412321	+	0.911039i	$0.364718\pi$
$252$	−2.15309	−0.135632
$253$	−49.3430	−3.10217
$254$	−29.3527	−1.84176
$255$	−67.8895	−4.25141
$256$	9.01592	0.563495
$257$	27.3432	1.70562	0.852812	−	0.522218i	$-0.174895\pi$
$257$	27.3432	1.70562	0.852812	+	0.522218i	$0.174895\pi$
$258$	−3.49331	−0.217484
$259$	1.08781	0.0675930
$260$	5.97000	0.370244
$261$	4.57815	0.283381
$262$	−12.5550	−0.775652
$263$	6.17318	0.380655	0.190327	−	0.981721i	$-0.439045\pi$
$263$	6.17318	0.380655	0.190327	+	0.981721i	$0.439045\pi$
$264$	−37.3426	−2.29828
$265$	2.43484	0.149571
$266$	−12.0429	−0.738396
$267$	17.4347	1.06699
$268$	2.26371	0.138278
$269$	24.0311	1.46520	0.732600	−	0.680659i	$-0.238307\pi$
$269$	24.0311	1.46520	0.732600	+	0.680659i	$0.238307\pi$
$270$	−38.0304	−2.31446
$271$	−5.71698	−0.347282	−0.173641	−	0.984809i	$-0.555553\pi$
$271$	−5.71698	−0.347282	−0.173641	+	0.984809i	$0.555553\pi$
$272$	26.5841	1.61190
$273$	−11.4040	−0.690204
$274$	7.88931	0.476610
$275$	64.7820	3.90650
$276$	10.3547	0.623279
$277$	7.20235	0.432747	0.216374	−	0.976311i	$-0.430577\pi$
$277$	7.20235	0.432747	0.216374	+	0.976311i	$0.430577\pi$
$278$	20.8087	1.24802
$279$	4.72943	0.283144
$280$	11.2568	0.672725
$281$	−0.330399	−0.0197100	−0.00985498	−	0.999951i	$-0.503137\pi$
$281$	−0.330399	−0.0197100	−0.00985498	+	0.999951i	$0.503137\pi$
$282$	−40.3618	−2.40351
$283$	2.61087	0.155200	0.0776002	−	0.996985i	$-0.475274\pi$
$283$	2.61087	0.155200	0.0776002	+	0.996985i	$0.475274\pi$
$284$	0.360442	0.0213883
$285$	−84.6317	−5.01315
$286$	30.0764	1.77846
$287$	−9.86274	−0.582179
$288$	11.0467	0.650934
$289$	16.0062	0.941539
$290$	5.78837	0.339904
$291$	2.73779	0.160492
$292$	−2.63975	−0.154480
$293$	14.2972	0.835253	0.417626	−	0.908619i	$-0.362862\pi$
$293$	14.2972	0.835253	0.417626	+	0.908619i	$0.362862\pi$
$294$	−25.5614	−1.49077
$295$	−35.1584	−2.04700
$296$	−2.48954	−0.144701
$297$	−31.2292	−1.81210
$298$	−1.42736	−0.0826845
$299$	34.4864	1.99440
$300$	−13.5946	−0.784882
$301$	0.864727	0.0498421
$302$	−21.7278	−1.25029
$303$	3.64342	0.209309
$304$	33.1399	1.90070
$305$	−40.1669	−2.29995
$306$	45.1316	2.58000
$307$	−8.43285	−0.481288	−0.240644	−	0.970613i	$-0.577359\pi$
$307$	−8.43285	−0.481288	−0.240644	+	0.970613i	$0.577359\pi$
$308$	−2.23541	−0.127374
$309$	−48.5215	−2.76029
$310$	5.97964	0.339620
$311$	−13.4027	−0.759999	−0.379999	−	0.924987i	$-0.624076\pi$
$311$	−13.4027	−0.759999	−0.379999	+	0.924987i	$0.624076\pi$
$312$	26.0991	1.47757
$313$	11.5526	0.652991	0.326496	−	0.945199i	$-0.394132\pi$
$313$	11.5526	0.652991	0.326496	+	0.945199i	$0.394132\pi$
$314$	0.180046	0.0101606
$315$	22.9790	1.29472
$316$	1.01616	0.0571633
$317$	−18.4849	−1.03821	−0.519107	−	0.854709i	$-0.673735\pi$
$317$	−18.4849	−1.03821	−0.519107	+	0.854709i	$0.673735\pi$
$318$	−2.57414	−0.144351
$319$	4.75319	0.266127
$320$	−24.5012	−1.36966
$321$	41.8563	2.33619
$322$	−15.7254	−0.876342
$323$	41.1458	2.28941
$324$	0.615573	0.0341985
$325$	−45.2768	−2.51151
$326$	−25.0982	−1.39006
$327$	2.84288	0.157212
$328$	22.5717	1.24632
$329$	9.99108	0.550826
$330$	−96.3792	−5.30550
$331$	2.81347	0.154642	0.0773212	−	0.997006i	$-0.475363\pi$
$331$	2.81347	0.154642	0.0773212	+	0.997006i	$0.475363\pi$
$332$	4.57799	0.251250
$333$	−5.08197	−0.278490
$334$	23.7642	1.30032
$335$	−24.1595	−1.31997
$336$	−14.3098	−0.780664
$337$	−15.1507	−0.825310	−0.412655	−	0.910887i	$-0.635398\pi$
$337$	−15.1507	−0.825310	−0.412655	+	0.910887i	$0.635398\pi$
$338$	−0.925452	−0.0503380
$339$	−48.5449	−2.63660
$340$	9.30086	0.504410
$341$	4.91025	0.265905
$342$	56.2615	3.04227
$343$	13.9421	0.752800
$344$	−1.97900	−0.106701
$345$	−110.511	−5.94970
$346$	21.8308	1.17363
$347$	−8.05188	−0.432248	−0.216124	−	0.976366i	$-0.569341\pi$
$347$	−8.05188	−0.432248	−0.216124	+	0.976366i	$0.569341\pi$
$348$	−0.997461	−0.0534695
$349$	22.4692	1.20275	0.601375	−	0.798967i	$-0.294620\pi$
$349$	22.4692	1.20275	0.601375	+	0.798967i	$0.294620\pi$
$350$	20.6457	1.10356
$351$	21.8264	1.16501
$352$	11.4690	0.611302
$353$	−7.05303	−0.375395	−0.187698	−	0.982227i	$-0.560102\pi$
$353$	−7.05303	−0.375395	−0.187698	+	0.982227i	$0.560102\pi$
$354$	37.1699	1.97556
$355$	−3.84683	−0.204168
$356$	−2.38856	−0.126593
$357$	−17.7667	−0.940315
$358$	3.74704	0.198037
$359$	−16.5364	−0.872759	−0.436380	−	0.899763i	$-0.643740\pi$
$359$	−16.5364	−0.872759	−0.436380	+	0.899763i	$0.643740\pi$
$360$	−52.5893	−2.77170
$361$	32.2926	1.69961
$362$	2.66783	0.140218
$363$	−47.8712	−2.51259
$364$	1.56235	0.0818895
$365$	28.1729	1.47463
$366$	42.4650	2.21968
$367$	−26.7363	−1.39562	−0.697812	−	0.716281i	$-0.745843\pi$
$367$	−26.7363	−1.39562	−0.697812	+	0.716281i	$0.745843\pi$
$368$	43.2736	2.25579
$369$	46.0764	2.39864
$370$	−6.42537	−0.334039
$371$	0.637198	0.0330817
$372$	−1.03042	−0.0534248
$373$	22.6080	1.17060	0.585298	−	0.810818i	$-0.300978\pi$
$373$	22.6080	1.17060	0.585298	+	0.810818i	$0.300978\pi$
$374$	46.8571	2.42292
$375$	86.0037	4.44121
$376$	−22.8655	−1.17920
$377$	−3.32205	−0.171094
$378$	−9.95259	−0.511906
$379$	26.6944	1.37120	0.685601	−	0.727978i	$-0.259540\pi$
$379$	26.6944	1.37120	0.685601	+	0.727978i	$0.259540\pi$
$380$	11.5945	0.594787
$381$	−53.9829	−2.76563
$382$	11.4333	0.584981
$383$	−28.3591	−1.44908	−0.724541	−	0.689232i	$-0.757948\pi$
$383$	−28.3591	−1.44908	−0.724541	+	0.689232i	$0.757948\pi$
$384$	38.2622	1.95256
$385$	23.8575	1.21589
$386$	−11.0262	−0.561219
$387$	−4.03980	−0.205355
$388$	−0.375077	−0.0190416
$389$	−11.9971	−0.608279	−0.304139	−	0.952628i	$-0.598369\pi$
$389$	−11.9971	−0.608279	−0.304139	+	0.952628i	$0.598369\pi$
$390$	67.3605	3.41093
$391$	53.7275	2.71712
$392$	−14.4808	−0.731393
$393$	−23.0901	−1.16474
$394$	−38.0562	−1.91724
$395$	−10.8450	−0.545670
$396$	10.4433	0.524796
$397$	31.2060	1.56618	0.783092	−	0.621906i	$-0.213642\pi$
$397$	31.2060	1.56618	0.783092	+	0.621906i	$0.213642\pi$
$398$	5.53996	0.277693
$399$	−22.1482	−1.10879
$400$	−56.8135	−2.84067
$401$	10.8345	0.541048	0.270524	−	0.962713i	$-0.412803\pi$
$401$	10.8345	0.541048	0.270524	+	0.962713i	$0.412803\pi$
$402$	25.5418	1.27391
$403$	−3.43183	−0.170951
$404$	−0.499148	−0.0248335
$405$	−6.56973	−0.326452
$406$	1.51482	0.0751792
$407$	−5.27627	−0.261535
$408$	40.6607	2.01300
$409$	25.1437	1.24328	0.621638	−	0.783304i	$-0.286467\pi$
$409$	25.1437	1.24328	0.621638	+	0.783304i	$0.286467\pi$
$410$	58.2564	2.87708
$411$	14.5093	0.715691
$412$	6.64744	0.327496
$413$	−9.20097	−0.452750
$414$	73.4653	3.61062
$415$	−48.8588	−2.39838
$416$	−8.01584	−0.393009
$417$	38.2694	1.87406
$418$	58.4125	2.85705
$419$	−22.3879	−1.09372	−0.546861	−	0.837223i	$-0.684177\pi$
$419$	−22.3879	−1.09372	−0.546861	+	0.837223i	$0.684177\pi$
$420$	−5.00652	−0.244293
$421$	0.932557	0.0454500	0.0227250	−	0.999742i	$-0.492766\pi$
$421$	0.932557	0.0454500	0.0227250	+	0.999742i	$0.492766\pi$
$422$	−16.7087	−0.813369
$423$	−46.6760	−2.26946
$424$	−1.45828	−0.0708205
$425$	−70.5383	−3.42161
$426$	4.06692	0.197043
$427$	−10.5117	−0.508697
$428$	−5.73430	−0.277178
$429$	55.3139	2.67058
$430$	−5.10770	−0.246315
$431$	−18.2117	−0.877226	−0.438613	−	0.898676i	$-0.644530\pi$
$431$	−18.2117	−0.877226	−0.438613	+	0.898676i	$0.644530\pi$
$432$	27.3878	1.31770
$433$	9.91615	0.476540	0.238270	−	0.971199i	$-0.423420\pi$
$433$	9.91615	0.476540	0.238270	+	0.971199i	$0.423420\pi$
$434$	1.56487	0.0751164
$435$	10.6454	0.510409
$436$	−0.389475	−0.0186524
$437$	66.9771	3.20395
$438$	−29.7848	−1.42317
$439$	16.6043	0.792478	0.396239	−	0.918147i	$-0.370315\pi$
$439$	16.6043	0.792478	0.396239	+	0.918147i	$0.370315\pi$
$440$	−54.5999	−2.60295
$441$	−29.5602	−1.40763
$442$	−32.7489	−1.55771
$443$	−34.2329	−1.62645	−0.813227	−	0.581946i	$-0.802292\pi$
$443$	−34.2329	−1.62645	−0.813227	+	0.581946i	$0.802292\pi$
$444$	1.10723	0.0525468
$445$	25.4920	1.20843
$446$	−43.1046	−2.04106
$447$	−2.62506	−0.124161
$448$	−6.41198	−0.302938
$449$	−5.12235	−0.241739	−0.120869	−	0.992668i	$-0.538568\pi$
$449$	−5.12235	−0.241739	−0.120869	+	0.992668i	$0.538568\pi$
$450$	−96.4519	−4.54679
$451$	47.8380	2.25260
$452$	6.65065	0.312820
$453$	−39.9598	−1.87747
$454$	−16.2845	−0.764269
$455$	−16.6743	−0.781701
$456$	50.6880	2.37368
$457$	−0.0968236	−0.00452922	−0.00226461	−	0.999997i	$-0.500721\pi$
$457$	−0.0968236	−0.00452922	−0.00226461	+	0.999997i	$0.500721\pi$
$458$	11.6366	0.543740
$459$	34.0041	1.58717
$460$	15.1400	0.705904
$461$	−27.0070	−1.25784	−0.628921	−	0.777470i	$-0.716503\pi$
$461$	−27.0070	−1.25784	−0.628921	+	0.777470i	$0.716503\pi$
$462$	−25.2225	−1.17346
$463$	17.3916	0.808259	0.404129	−	0.914702i	$-0.367575\pi$
$463$	17.3916	0.808259	0.404129	+	0.914702i	$0.367575\pi$
$464$	−4.16852	−0.193519
$465$	10.9972	0.509983
$466$	22.8047	1.05641
$467$	−33.6579	−1.55750	−0.778752	−	0.627332i	$-0.784147\pi$
$467$	−33.6579	−1.55750	−0.778752	+	0.627332i	$0.784147\pi$
$468$	−7.29894	−0.337394
$469$	−6.32256	−0.291949
$470$	−59.0145	−2.72214
$471$	0.331124	0.0152574
$472$	21.0572	0.969237
$473$	−4.19425	−0.192852
$474$	11.4655	0.526626
$475$	−87.9336	−4.03467
$476$	2.43404	0.111564
$477$	−2.97684	−0.136300
$478$	23.8254	1.08975
$479$	−32.7427	−1.49605	−0.748026	−	0.663670i	$-0.768998\pi$
$479$	−32.7427	−1.49605	−0.748026	+	0.663670i	$0.768998\pi$
$480$	25.6866	1.17243
$481$	3.68764	0.168142
$482$	25.1896	1.14735
$483$	−28.9207	−1.31594
$484$	6.55836	0.298107
$485$	4.00302	0.181768
$486$	−20.5021	−0.929994
$487$	−25.1940	−1.14165	−0.570824	−	0.821073i	$-0.693376\pi$
$487$	−25.1940	−1.14165	−0.570824	+	0.821073i	$0.693376\pi$
$488$	24.0569	1.08901
$489$	−46.1583	−2.08735
$490$	−37.3743	−1.68840
$491$	19.9775	0.901572	0.450786	−	0.892632i	$-0.351144\pi$
$491$	19.9775	0.901572	0.450786	+	0.892632i	$0.351144\pi$
$492$	−10.0388	−0.452586
$493$	−5.17554	−0.233095
$494$	−40.8251	−1.83681
$495$	−111.457	−5.00960
$496$	−4.30626	−0.193357
$497$	−1.00672	−0.0451574
$498$	51.6542	2.31468
$499$	−35.3406	−1.58206	−0.791032	−	0.611775i	$-0.790456\pi$
$499$	−35.3406	−1.58206	−0.791032	+	0.611775i	$0.790456\pi$
$500$	−11.7825	−0.526929
$501$	43.7049	1.95259
$502$	−20.1955	−0.901367
$503$	−32.8867	−1.46635	−0.733173	−	0.680042i	$-0.761961\pi$
$503$	−32.8867	−1.46635	−0.733173	+	0.680042i	$0.761961\pi$
$504$	−13.7627	−0.613038
$505$	5.32717	0.237056
$506$	76.2741	3.39080
$507$	−1.70201	−0.0755888
$508$	7.39565	0.328129
$509$	−21.5857	−0.956771	−0.478385	−	0.878150i	$-0.658778\pi$
$509$	−21.5857	−0.956771	−0.478385	+	0.878150i	$0.658778\pi$
$510$	104.943	4.64696
$511$	7.37285	0.326156
$512$	12.9812	0.573692
$513$	42.3898	1.87155
$514$	−42.2670	−1.86432
$515$	−70.9450	−3.12621
$516$	0.880168	0.0387472
$517$	−48.4605	−2.13129
$518$	−1.68152	−0.0738818
$519$	40.1493	1.76236
$520$	38.1605	1.67345
$521$	19.9310	0.873191	0.436596	−	0.899658i	$-0.356184\pi$
$521$	19.9310	0.873191	0.436596	+	0.899658i	$0.356184\pi$
$522$	−7.07687	−0.309746
$523$	34.1139	1.49170	0.745848	−	0.666116i	$-0.232044\pi$
$523$	34.1139	1.49170	0.745848	+	0.666116i	$0.232044\pi$
$524$	3.16334	0.138191
$525$	37.9697	1.65713
$526$	−9.54245	−0.416071
$527$	−5.34656	−0.232900
$528$	69.4079	3.02059
$529$	64.4577	2.80251
$530$	−3.76375	−0.163487
$531$	42.9847	1.86538
$532$	3.03430	0.131553
$533$	−33.4345	−1.44821
$534$	−26.9505	−1.16626
$535$	61.1996	2.64589
$536$	14.4697	0.624997
$537$	6.89121	0.297378
$538$	−37.1471	−1.60152
$539$	−30.6903	−1.32193
$540$	9.58207	0.412347
$541$	−8.05950	−0.346505	−0.173253	−	0.984877i	$-0.555428\pi$
$541$	−8.05950	−0.346505	−0.173253	+	0.984877i	$0.555428\pi$
$542$	8.83726	0.379593
$543$	4.90644	0.210555
$544$	−12.4882	−0.535425
$545$	4.15668	0.178053
$546$	17.6283	0.754421
$547$	41.1175	1.75806	0.879028	−	0.476771i	$-0.158193\pi$
$547$	41.1175	1.75806	0.879028	+	0.476771i	$0.158193\pi$
$548$	−1.98777	−0.0849134
$549$	49.1082	2.09589
$550$	−100.139	−4.26996
$551$	−6.45187	−0.274859
$552$	66.1876	2.81713
$553$	−2.83814	−0.120690
$554$	−11.1333	−0.473010
$555$	−11.8169	−0.501602
$556$	−5.24291	−0.222349
$557$	28.4048	1.20355	0.601776	−	0.798665i	$-0.294460\pi$
$557$	28.4048	1.20355	0.601776	+	0.798665i	$0.294460\pi$
$558$	−7.31072	−0.309488
$559$	2.93141	0.123985
$560$	−20.9229	−0.884154
$561$	86.1753	3.63832
$562$	0.510729	0.0215438
$563$	−0.367902	−0.0155052	−0.00775260	−	0.999970i	$-0.502468\pi$
$563$	−0.367902	−0.0155052	−0.00775260	+	0.999970i	$0.502468\pi$
$564$	10.1695	0.428212
$565$	−70.9793	−2.98612
$566$	−4.03587	−0.169640
$567$	−1.71930	−0.0722039
$568$	2.30396	0.0966720
$569$	4.35683	0.182648	0.0913240	−	0.995821i	$-0.470890\pi$
$569$	4.35683	0.182648	0.0913240	+	0.995821i	$0.470890\pi$
$570$	130.823	5.47957
$571$	−11.8457	−0.495727	−0.247864	−	0.968795i	$-0.579728\pi$
$571$	−11.8457	−0.495727	−0.247864	+	0.968795i	$0.579728\pi$
$572$	−7.57800	−0.316852
$573$	21.0272	0.878423
$574$	15.2457	0.636345
$575$	−114.822	−4.78842
$576$	29.9553	1.24814
$577$	−5.19480	−0.216262	−0.108131	−	0.994137i	$-0.534487\pi$
$577$	−5.19480	−0.216262	−0.108131	+	0.994137i	$0.534487\pi$
$578$	−24.7422	−1.02914
$579$	−20.2784	−0.842741
$580$	−1.45842	−0.0605578
$581$	−12.7864	−0.530468
$582$	−4.23205	−0.175424
$583$	−3.09065	−0.128002
$584$	−16.8734	−0.698227
$585$	77.8982	3.22069
$586$	−22.1005	−0.912965
$587$	−6.75520	−0.278817	−0.139409	−	0.990235i	$-0.544520\pi$
$587$	−6.75520	−0.278817	−0.139409	+	0.990235i	$0.544520\pi$
$588$	6.44040	0.265598
$589$	−6.66506	−0.274629
$590$	54.3475	2.23745
$591$	−69.9894	−2.87898
$592$	4.62726	0.190179
$593$	−0.610130	−0.0250550	−0.0125275	−	0.999922i	$-0.503988\pi$
$593$	−0.610130	−0.0250550	−0.0125275	+	0.999922i	$0.503988\pi$
$594$	48.2738	1.98070
$595$	−25.9774	−1.06497
$596$	0.359634	0.0147312
$597$	10.1886	0.416992
$598$	−53.3088	−2.17996
$599$	−39.3830	−1.60915	−0.804574	−	0.593853i	$-0.797606\pi$
$599$	−39.3830	−1.60915	−0.804574	+	0.593853i	$0.797606\pi$
$600$	−86.8970	−3.54756
$601$	−1.83455	−0.0748330	−0.0374165	−	0.999300i	$-0.511913\pi$
$601$	−1.83455	−0.0748330	−0.0374165	+	0.999300i	$0.511913\pi$
$602$	−1.33669	−0.0544794
$603$	29.5375	1.20286
$604$	5.47449	0.222754
$605$	−69.9943	−2.84567
$606$	−5.63196	−0.228783
$607$	−8.37581	−0.339964	−0.169982	−	0.985447i	$-0.554371\pi$
$607$	−8.37581	−0.339964	−0.169982	+	0.985447i	$0.554371\pi$
$608$	−15.5678	−0.631359
$609$	2.78592	0.112891
$610$	62.0897	2.51394
$611$	33.8696	1.37022
$612$	−11.3713	−0.459656
$613$	−46.2637	−1.86857	−0.934286	−	0.356525i	$-0.883961\pi$
$613$	−46.2637	−1.86857	−0.934286	+	0.356525i	$0.883961\pi$
$614$	13.0354	0.526067
$615$	107.140	4.32030
$616$	−14.2888	−0.575714
$617$	20.2800	0.816443	0.408222	−	0.912883i	$-0.366149\pi$
$617$	20.2800	0.816443	0.408222	+	0.912883i	$0.366149\pi$
$618$	75.0041	3.01711
$619$	10.0110	0.402375	0.201188	−	0.979553i	$-0.435520\pi$
$619$	10.0110	0.402375	0.201188	+	0.979553i	$0.435520\pi$
$620$	−1.50662	−0.0605072
$621$	55.3519	2.22120
$622$	20.7178	0.830709
$623$	6.67126	0.267278
$624$	−48.5100	−1.94195
$625$	64.3592	2.57437
$626$	−17.8579	−0.713746
$627$	107.427	4.29022
$628$	−0.0453640	−0.00181022
$629$	5.74510	0.229072
$630$	−35.5207	−1.41518
$631$	−29.5998	−1.17835	−0.589175	−	0.808006i	$-0.700547\pi$
$631$	−29.5998	−1.17835	−0.589175	+	0.808006i	$0.700547\pi$
$632$	6.49532	0.258370
$633$	−30.7292	−1.22138
$634$	28.5738	1.13481
$635$	−78.9304	−3.13226
$636$	0.648576	0.0257177
$637$	21.4498	0.849873
$638$	−7.34744	−0.290888
$639$	4.70314	0.186053
$640$	55.9446	2.21140
$641$	−0.699280	−0.0276199	−0.0138100	−	0.999905i	$-0.504396\pi$
$641$	−0.699280	−0.0276199	−0.0138100	+	0.999905i	$0.504396\pi$
$642$	−64.7011	−2.55355
$643$	18.2314	0.718974	0.359487	−	0.933150i	$-0.382952\pi$
$643$	18.2314	0.718974	0.359487	+	0.933150i	$0.382952\pi$
$644$	3.96214	0.156130
$645$	−9.39362	−0.369874
$646$	−63.6028	−2.50242
$647$	−24.8133	−0.975513	−0.487757	−	0.872980i	$-0.662185\pi$
$647$	−24.8133	−0.975513	−0.487757	+	0.872980i	$0.662185\pi$
$648$	3.93477	0.154572
$649$	44.6281	1.75181
$650$	69.9886	2.74518
$651$	2.87797	0.112797
$652$	6.32368	0.247654
$653$	32.6749	1.27867	0.639334	−	0.768930i	$-0.279210\pi$
$653$	32.6749	1.27867	0.639334	+	0.768930i	$0.279210\pi$
$654$	−4.39450	−0.171839
$655$	−33.7608	−1.31914
$656$	−41.9537	−1.63802
$657$	−34.4442	−1.34380
$658$	−15.4441	−0.602075
$659$	8.74221	0.340548	0.170274	−	0.985397i	$-0.445535\pi$
$659$	8.74221	0.340548	0.170274	+	0.985397i	$0.445535\pi$
$660$	24.2835	0.945234
$661$	6.96488	0.270902	0.135451	−	0.990784i	$-0.456752\pi$
$661$	6.96488	0.270902	0.135451	+	0.990784i	$0.456752\pi$
$662$	−4.34904	−0.169030
$663$	−60.2289	−2.33910
$664$	29.2627	1.13561
$665$	−32.3836	−1.25578
$666$	7.85567	0.304401
$667$	−8.42475	−0.326208
$668$	−5.98757	−0.231666
$669$	−79.2740	−3.06491
$670$	37.3456	1.44279
$671$	50.9857	1.96828
$672$	6.72219	0.259314
$673$	−29.9065	−1.15281	−0.576405	−	0.817164i	$-0.695545\pi$
$673$	−29.9065	−1.15281	−0.576405	+	0.817164i	$0.695545\pi$
$674$	23.4198	0.902097
$675$	−72.6710	−2.79711
$676$	0.233175	0.00896827
$677$	23.7982	0.914639	0.457319	−	0.889303i	$-0.348810\pi$
$677$	23.7982	0.914639	0.457319	+	0.889303i	$0.348810\pi$
$678$	75.0404	2.88191
$679$	1.04759	0.0402029
$680$	59.4515	2.27986
$681$	−29.9490	−1.14765
$682$	−7.59023	−0.290645
$683$	17.7591	0.679533	0.339767	−	0.940510i	$-0.389652\pi$
$683$	17.7591	0.679533	0.339767	+	0.940510i	$0.389652\pi$
$684$	−14.1755	−0.542014
$685$	21.2146	0.810567
$686$	−21.5515	−0.822841
$687$	21.4009	0.816495
$688$	3.67834	0.140235
$689$	2.16009	0.0822928
$690$	170.827	6.50326
$691$	23.9380	0.910644	0.455322	−	0.890327i	$-0.349524\pi$
$691$	23.9380	0.910644	0.455322	+	0.890327i	$0.349524\pi$
$692$	−5.50045	−0.209096
$693$	−29.1683	−1.10801
$694$	12.4465	0.472464
$695$	55.9551	2.12250
$696$	−6.37581	−0.241675
$697$	−52.0887	−1.97300
$698$	−34.7327	−1.31465
$699$	41.9403	1.58633
$700$	−5.20185	−0.196611
$701$	−22.2529	−0.840479	−0.420240	−	0.907413i	$-0.638054\pi$
$701$	−22.2529	−0.840479	−0.420240	+	0.907413i	$0.638054\pi$
$702$	−33.7391	−1.27340
$703$	7.16189	0.270116
$704$	31.1005	1.17215
$705$	−108.534	−4.08763
$706$	10.9025	0.410322
$707$	1.39412	0.0524314
$708$	−9.36526	−0.351968
$709$	12.9953	0.488048	0.244024	−	0.969769i	$-0.421532\pi$
$709$	12.9953	0.488048	0.244024	+	0.969769i	$0.421532\pi$
$710$	5.94640	0.223164
$711$	13.2591	0.497255
$712$	−15.2678	−0.572184
$713$	−8.70314	−0.325935
$714$	27.4637	1.02780
$715$	80.8764	3.02461
$716$	−0.944096	−0.0352825
$717$	43.8175	1.63639
$718$	25.5619	0.953961
$719$	45.4823	1.69620	0.848102	−	0.529833i	$-0.177745\pi$
$719$	45.4823	1.69620	0.848102	+	0.529833i	$0.177745\pi$
$720$	97.7468	3.64281
$721$	−18.5663	−0.691447
$722$	−49.9177	−1.85775
$723$	46.3264	1.72290
$724$	−0.672182	−0.0249814
$725$	11.0608	0.410787
$726$	73.9990	2.74636
$727$	−40.1449	−1.48889	−0.744446	−	0.667683i	$-0.767286\pi$
$727$	−40.1449	−1.48889	−0.744446	+	0.667683i	$0.767286\pi$
$728$	9.98663	0.370129
$729$	−42.4471	−1.57212
$730$	−43.5494	−1.61184
$731$	4.56694	0.168914
$732$	−10.6994	−0.395461
$733$	15.2788	0.564334	0.282167	−	0.959365i	$-0.408947\pi$
$733$	15.2788	0.564334	0.282167	+	0.959365i	$0.408947\pi$
$734$	41.3288	1.52547
$735$	−68.7354	−2.53534
$736$	−20.3282	−0.749309
$737$	30.6668	1.12963
$738$	−71.2245	−2.62181
$739$	−6.46561	−0.237841	−0.118921	−	0.992904i	$-0.537943\pi$
$739$	−6.46561	−0.237841	−0.118921	+	0.992904i	$0.537943\pi$
$740$	1.61892	0.0595127
$741$	−75.0818	−2.75820
$742$	−0.984976	−0.0361596
$743$	2.78933	0.102331	0.0511654	−	0.998690i	$-0.483706\pi$
$743$	2.78933	0.102331	0.0511654	+	0.998690i	$0.483706\pi$
$744$	−6.58649	−0.241473
$745$	−3.83820	−0.140621
$746$	−34.9472	−1.27951
$747$	59.7349	2.18559
$748$	−11.8060	−0.431671
$749$	16.0160	0.585211
$750$	−132.944	−4.85442
$751$	−21.6708	−0.790778	−0.395389	−	0.918514i	$-0.629390\pi$
$751$	−21.6708	−0.790778	−0.395389	+	0.918514i	$0.629390\pi$
$752$	42.4996	1.54980
$753$	−37.1416	−1.35352
$754$	5.13521	0.187013
$755$	−58.4266	−2.12636
$756$	2.50763	0.0912017
$757$	−3.27212	−0.118927	−0.0594636	−	0.998230i	$-0.518939\pi$
$757$	−3.27212	−0.118927	−0.0594636	+	0.998230i	$0.518939\pi$
$758$	−41.2641	−1.49878
$759$	140.276	5.09171
$760$	74.1128	2.68835
$761$	−44.4323	−1.61067	−0.805335	−	0.592820i	$-0.798015\pi$
$761$	−44.4323	−1.61067	−0.805335	+	0.592820i	$0.798015\pi$
$762$	83.4464	3.02294
$763$	1.08781	0.0393812
$764$	−2.88072	−0.104221
$765$	121.360	4.38779
$766$	43.8373	1.58391
$767$	−31.1911	−1.12625
$768$	−25.6312	−0.924886
$769$	−12.8000	−0.461578	−0.230789	−	0.973004i	$-0.574131\pi$
$769$	−12.8000	−0.461578	−0.230789	+	0.973004i	$0.574131\pi$
$770$	−36.8787	−1.32902
$771$	−77.7335	−2.79950
$772$	2.77814	0.0999874
$773$	−3.61357	−0.129971	−0.0649856	−	0.997886i	$-0.520700\pi$
$773$	−3.61357	−0.129971	−0.0649856	+	0.997886i	$0.520700\pi$
$774$	6.24470	0.224461
$775$	11.4263	0.410444
$776$	−2.39751	−0.0860654
$777$	−3.09250	−0.110943
$778$	18.5451	0.664873
$779$	−64.9342	−2.32651
$780$	−16.9720	−0.607695
$781$	4.88296	0.174726
$782$	−83.0515	−2.96992
$783$	−5.33202	−0.190551
$784$	26.9153	0.961260
$785$	0.484149	0.0172800
$786$	35.6924	1.27311
$787$	24.1340	0.860284	0.430142	−	0.902761i	$-0.358464\pi$
$787$	24.1340	0.860284	0.430142	+	0.902761i	$0.358464\pi$
$788$	9.58855	0.341578
$789$	−17.5496	−0.624783
$790$	16.7641	0.596439
$791$	−18.5753	−0.660463
$792$	66.7541	2.37200
$793$	−35.6344	−1.26542
$794$	−48.2380	−1.71190
$795$	−6.92195	−0.245496
$796$	−1.39584	−0.0494741
$797$	13.5866	0.481263	0.240632	−	0.970617i	$-0.422645\pi$
$797$	13.5866	0.481263	0.240632	+	0.970617i	$0.422645\pi$
$798$	34.2365	1.21196
$799$	52.7665	1.86675
$800$	26.6887	0.943590
$801$	−31.1666	−1.10122
$802$	−16.7479	−0.591388
$803$	−35.7611	−1.26198
$804$	−6.43545	−0.226961
$805$	−42.2860	−1.49039
$806$	5.30489	0.186857
$807$	−68.3175	−2.40489
$808$	−3.19057	−0.112244
$809$	22.8186	0.802259	0.401129	−	0.916021i	$-0.368618\pi$
$809$	22.8186	0.802259	0.401129	+	0.916021i	$0.368618\pi$
$810$	10.1554	0.356826
$811$	−22.1555	−0.777985	−0.388993	−	0.921241i	$-0.627177\pi$
$811$	−22.1555	−0.777985	−0.388993	+	0.921241i	$0.627177\pi$
$812$	−0.381670	−0.0133940
$813$	16.2527	0.570007
$814$	8.15601	0.285868
$815$	−67.4897	−2.36406
$816$	−75.5753	−2.64566
$817$	5.69319	0.199179
$818$	−38.8670	−1.35895
$819$	20.3860	0.712345
$820$	−14.6782	−0.512584
$821$	34.7429	1.21254	0.606268	−	0.795260i	$-0.292666\pi$
$821$	34.7429	1.21254	0.606268	+	0.795260i	$0.292666\pi$
$822$	−22.4284	−0.782279
$823$	3.91182	0.136358	0.0681788	−	0.997673i	$-0.478281\pi$
$823$	3.91182	0.136358	0.0681788	+	0.997673i	$0.478281\pi$
$824$	42.4907	1.48023
$825$	−184.167	−6.41189
$826$	14.2228	0.494874
$827$	−25.7622	−0.895838	−0.447919	−	0.894074i	$-0.647835\pi$
$827$	−25.7622	−0.895838	−0.447919	+	0.894074i	$0.647835\pi$
$828$	−18.5102	−0.643273
$829$	−5.50871	−0.191325	−0.0956627	−	0.995414i	$-0.530497\pi$
$829$	−5.50871	−0.191325	−0.0956627	+	0.995414i	$0.530497\pi$
$830$	75.5255	2.62153
$831$	−20.4754	−0.710285
$832$	−21.7365	−0.753578
$833$	33.4174	1.15784
$834$	−59.1565	−2.04842
$835$	63.9026	2.21144
$836$	−14.7175	−0.509015
$837$	−5.50821	−0.190392
$838$	34.6071	1.19548
$839$	−38.9702	−1.34540	−0.672700	−	0.739916i	$-0.734865\pi$
$839$	−38.9702	−1.34540	−0.672700	+	0.739916i	$0.734865\pi$
$840$	−32.0019	−1.10417
$841$	−28.1884	−0.972015
$842$	−1.44154	−0.0496787
$843$	0.939286	0.0323507
$844$	4.20990	0.144911
$845$	−2.48857	−0.0856093
$846$	72.1514	2.48061
$847$	−18.3176	−0.629398
$848$	2.71048	0.0930784
$849$	−7.42240	−0.254736
$850$	109.038	3.73996
$851$	9.35188	0.320578
$852$	−1.02469	−0.0351054
$853$	−49.3689	−1.69036	−0.845180	−	0.534482i	$-0.820507\pi$
$853$	−49.3689	−1.69036	−0.845180	+	0.534482i	$0.820507\pi$
$854$	16.2489	0.556026
$855$	151.289	5.17396
$856$	−36.6539	−1.25281
$857$	15.6790	0.535585	0.267793	−	0.963477i	$-0.413706\pi$
$857$	15.6790	0.535585	0.267793	+	0.963477i	$0.413706\pi$
$858$	−85.5037	−2.91905
$859$	48.6675	1.66051	0.830257	−	0.557381i	$-0.188194\pi$
$859$	48.6675	1.66051	0.830257	+	0.557381i	$0.188194\pi$
$860$	1.28693	0.0438838
$861$	28.0386	0.955552
$862$	28.1515	0.958843
$863$	14.7316	0.501470	0.250735	−	0.968056i	$-0.419328\pi$
$863$	14.7316	0.501470	0.250735	+	0.968056i	$0.419328\pi$
$864$	−12.8657	−0.437701
$865$	58.7037	1.99599
$866$	−15.3283	−0.520877
$867$	−45.5036	−1.54538
$868$	−0.394282	−0.0133828
$869$	13.7660	0.466981
$870$	−16.4556	−0.557898
$871$	−21.4333	−0.726241
$872$	−2.48954	−0.0843064
$873$	−4.89410	−0.165640
$874$	−103.533	−3.50205
$875$	32.9086	1.11251
$876$	7.50450	0.253554
$877$	−5.94782	−0.200844	−0.100422	−	0.994945i	$-0.532019\pi$
$877$	−5.94782	−0.200844	−0.100422	+	0.994945i	$0.532019\pi$
$878$	−25.6667	−0.866211
$879$	−40.6453	−1.37093
$880$	101.484	3.42102
$881$	−25.7410	−0.867237	−0.433618	−	0.901097i	$-0.642763\pi$
$881$	−25.7410	−0.867237	−0.433618	+	0.901097i	$0.642763\pi$
$882$	45.6939	1.53859
$883$	−28.8263	−0.970082	−0.485041	−	0.874491i	$-0.661195\pi$
$883$	−28.8263	−0.970082	−0.485041	+	0.874491i	$0.661195\pi$
$884$	8.25135	0.277523
$885$	99.9510	3.35982
$886$	52.9170	1.77778
$887$	16.5441	0.555497	0.277748	−	0.960654i	$-0.410412\pi$
$887$	16.5441	0.555497	0.277748	+	0.960654i	$0.410412\pi$
$888$	7.07746	0.237504
$889$	−20.6561	−0.692784
$890$	−39.4053	−1.32087
$891$	8.33926	0.279376
$892$	10.8605	0.363638
$893$	65.7792	2.20122
$894$	4.05780	0.135713
$895$	10.0759	0.336800
$896$	14.6407	0.489113
$897$	−98.0407	−3.27348
$898$	7.91809	0.264230
$899$	0.838368	0.0279612
$900$	24.3018	0.810061
$901$	3.36527	0.112114
$902$	−73.9476	−2.46219
$903$	−2.45832	−0.0818077
$904$	42.5113	1.41390
$905$	7.17388	0.238468
$906$	61.7695	2.05215
$907$	−15.2787	−0.507322	−0.253661	−	0.967293i	$-0.581635\pi$
$907$	−15.2787	−0.507322	−0.253661	+	0.967293i	$0.581635\pi$
$908$	4.10300	0.136163
$909$	−6.51302	−0.216023
$910$	25.7749	0.854431
$911$	19.3452	0.640935	0.320468	−	0.947259i	$-0.396160\pi$
$911$	19.3452	0.640935	0.320468	+	0.947259i	$0.396160\pi$
$912$	−94.2128	−3.11970
$913$	62.0187	2.05252
$914$	0.149669	0.00495062
$915$	114.190	3.77499
$916$	−2.93192	−0.0968734
$917$	−8.83523	−0.291765
$918$	−52.5632	−1.73485
$919$	−51.2636	−1.69103	−0.845514	−	0.533953i	$-0.820706\pi$
$919$	−51.2636	−1.69103	−0.845514	+	0.533953i	$0.820706\pi$
$920$	96.7753	3.19059
$921$	23.9736	0.789956
$922$	41.7472	1.37487
$923$	−3.41275	−0.112332
$924$	6.35500	0.209064
$925$	−12.2780	−0.403698
$926$	−26.8839	−0.883459
$927$	86.7376	2.84884
$928$	1.95821	0.0642813
$929$	49.2942	1.61729	0.808645	−	0.588297i	$-0.200202\pi$
$929$	49.2942	1.61729	0.808645	+	0.588297i	$0.200202\pi$
$930$	−16.9994	−0.557432
$931$	41.6584	1.36530
$932$	−5.74582	−0.188211
$933$	38.1024	1.24742
$934$	52.0282	1.70241
$935$	126.000	4.12064
$936$	−46.6552	−1.52497
$937$	29.0813	0.950044	0.475022	−	0.879974i	$-0.342440\pi$
$937$	29.0813	0.950044	0.475022	+	0.879974i	$0.342440\pi$
$938$	9.77336	0.319112
$939$	−32.8426	−1.07178
$940$	14.8692	0.484979
$941$	7.02565	0.229030	0.114515	−	0.993422i	$-0.463469\pi$
$941$	7.02565	0.229030	0.114515	+	0.993422i	$0.463469\pi$
$942$	−0.511849	−0.0166769
$943$	−84.7901	−2.76115
$944$	−39.1386	−1.27385
$945$	−26.7628	−0.870594
$946$	6.48344	0.210795
$947$	−21.6660	−0.704050	−0.352025	−	0.935991i	$-0.614507\pi$
$947$	−21.6660	−0.704050	−0.352025	+	0.935991i	$0.614507\pi$
$948$	−2.88881	−0.0938243
$949$	24.9938	0.811334
$950$	135.927	4.41006
$951$	52.5503	1.70406
$952$	15.5585	0.504254
$953$	−28.1553	−0.912041	−0.456020	−	0.889969i	$-0.650726\pi$
$953$	−28.1553	−0.912041	−0.456020	+	0.889969i	$0.650726\pi$
$954$	4.60158	0.148982
$955$	30.7446	0.994872
$956$	−6.00299	−0.194151
$957$	−13.5127	−0.436805
$958$	50.6134	1.63524
$959$	5.55187	0.179279
$960$	69.6541	2.24807
$961$	−30.1339	−0.972062
$962$	−5.70033	−0.183786
$963$	−74.8228	−2.41113
$964$	−6.34671	−0.204414
$965$	−29.6498	−0.954460
$966$	44.7054	1.43837
$967$	−2.59902	−0.0835787	−0.0417894	−	0.999126i	$-0.513306\pi$
$967$	−2.59902	−0.0835787	−0.0417894	+	0.999126i	$0.513306\pi$
$968$	41.9213	1.34740
$969$	−116.972	−3.75770
$970$	−6.18783	−0.198679
$971$	−23.0336	−0.739185	−0.369592	−	0.929194i	$-0.620503\pi$
$971$	−23.0336	−0.739185	−0.369592	+	0.929194i	$0.620503\pi$
$972$	5.16566	0.165689
$973$	14.6435	0.469448
$974$	38.9446	1.24787
$975$	128.717	4.12223
$976$	−44.7142	−1.43127
$977$	−61.1182	−1.95534	−0.977672	−	0.210139i	$-0.932608\pi$
$977$	−61.1182	−1.95534	−0.977672	+	0.210139i	$0.932608\pi$
$978$	71.3511	2.28156
$979$	−32.3581	−1.03417
$980$	9.41674	0.300807
$981$	−5.08197	−0.162255
$982$	−30.8811	−0.985454
$983$	−21.4717	−0.684840	−0.342420	−	0.939547i	$-0.611247\pi$
$983$	−21.4717	−0.684840	−0.342420	+	0.939547i	$0.611247\pi$
$984$	−64.1687	−2.04562
$985$	−102.334	−3.26064
$986$	8.00031	0.254782
$987$	−28.4035	−0.904092
$988$	10.2862	0.327248
$989$	7.43407	0.236390
$990$	172.289	5.47569
$991$	22.1513	0.703661	0.351830	−	0.936064i	$-0.385559\pi$
$991$	22.1513	0.703661	0.351830	+	0.936064i	$0.385559\pi$
$992$	2.02291	0.0642276
$993$	−7.99837	−0.253820
$994$	1.55618	0.0493589
$995$	14.8971	0.472271
$996$	−13.0147	−0.412386
$997$	14.0264	0.444221	0.222111	−	0.975021i	$-0.428705\pi$
$997$	14.0264	0.444221	0.222111	+	0.975021i	$0.428705\pi$
$998$	54.6293	1.72926
$999$	5.91880	0.187262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.24	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.24	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54579 q^{2} -2.84288 q^{3} +0.389475 q^{4} -4.15668 q^{5} +4.39450 q^{6} -1.08781 q^{7} +2.48954 q^{8} +5.08197 q^{9} +O(q^{10})\)	\(q-1.54579 q^{2} -2.84288 q^{3} +0.389475 q^{4} -4.15668 q^{5} +4.39450 q^{6} -1.08781 q^{7} +2.48954 q^{8} +5.08197 q^{9} +6.42537 q^{10} +5.27627 q^{11} -1.10723 q^{12} -3.68764 q^{13} +1.68152 q^{14} +11.8169 q^{15} -4.62726 q^{16} -5.74510 q^{17} -7.85567 q^{18} -7.16189 q^{19} -1.61892 q^{20} +3.09250 q^{21} -8.15601 q^{22} -9.35188 q^{23} -7.07746 q^{24} +12.2780 q^{25} +5.70033 q^{26} -5.91880 q^{27} -0.423673 q^{28} +0.900862 q^{29} -18.2666 q^{30} +0.930630 q^{31} +2.17371 q^{32} -14.9998 q^{33} +8.88073 q^{34} +4.52166 q^{35} +1.97930 q^{36} -1.00000 q^{37} +11.0708 q^{38} +10.4835 q^{39} -10.3482 q^{40} +9.06663 q^{41} -4.78037 q^{42} -0.794928 q^{43} +2.05497 q^{44} -21.1241 q^{45} +14.4561 q^{46} -9.18462 q^{47} +13.1547 q^{48} -5.81668 q^{49} -18.9792 q^{50} +16.3326 q^{51} -1.43624 q^{52} -0.585765 q^{53} +9.14923 q^{54} -21.9318 q^{55} -2.70813 q^{56} +20.3604 q^{57} -1.39255 q^{58} +8.45828 q^{59} +4.60240 q^{60} +9.66321 q^{61} -1.43856 q^{62} -5.52820 q^{63} +5.89442 q^{64} +15.3283 q^{65} +23.1866 q^{66} +5.81221 q^{67} -2.23757 q^{68} +26.5863 q^{69} -6.98955 q^{70} +0.925457 q^{71} +12.6518 q^{72} -6.77773 q^{73} +1.54579 q^{74} -34.9049 q^{75} -2.78937 q^{76} -5.73955 q^{77} -16.2054 q^{78} +2.60905 q^{79} +19.2340 q^{80} +1.58052 q^{81} -14.0151 q^{82} +11.7543 q^{83} +1.20445 q^{84} +23.8805 q^{85} +1.22879 q^{86} -2.56104 q^{87} +13.1355 q^{88} -6.13277 q^{89} +32.6535 q^{90} +4.01144 q^{91} -3.64232 q^{92} -2.64567 q^{93} +14.1975 q^{94} +29.7697 q^{95} -6.17959 q^{96} -0.963032 q^{97} +8.99138 q^{98} +26.8138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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