LMFDB - Embedded newform 2005.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69709 q^{2} -2.81518 q^{3} +5.27428 q^{4} -1.00000 q^{5} +7.59279 q^{6} -1.69501 q^{7} -8.83103 q^{8} +4.92525 q^{9} +O(q^{10})$	\(q-2.69709 q^{2} -2.81518 q^{3} +5.27428 q^{4} -1.00000 q^{5} +7.59279 q^{6} -1.69501 q^{7} -8.83103 q^{8} +4.92525 q^{9} +2.69709 q^{10} +3.99475 q^{11} -14.8481 q^{12} +0.417191 q^{13} +4.57159 q^{14} +2.81518 q^{15} +13.2695 q^{16} +3.25467 q^{17} -13.2838 q^{18} -5.00259 q^{19} -5.27428 q^{20} +4.77176 q^{21} -10.7742 q^{22} +9.05864 q^{23} +24.8610 q^{24} +1.00000 q^{25} -1.12520 q^{26} -5.41992 q^{27} -8.93997 q^{28} +0.120938 q^{29} -7.59279 q^{30} +1.05743 q^{31} -18.1270 q^{32} -11.2459 q^{33} -8.77813 q^{34} +1.69501 q^{35} +25.9772 q^{36} -1.90238 q^{37} +13.4924 q^{38} -1.17447 q^{39} +8.83103 q^{40} -0.542340 q^{41} -12.8699 q^{42} +11.1424 q^{43} +21.0695 q^{44} -4.92525 q^{45} -24.4320 q^{46} +5.31919 q^{47} -37.3561 q^{48} -4.12694 q^{49} -2.69709 q^{50} -9.16249 q^{51} +2.20039 q^{52} -5.09266 q^{53} +14.6180 q^{54} -3.99475 q^{55} +14.9687 q^{56} +14.0832 q^{57} -0.326181 q^{58} +10.2722 q^{59} +14.8481 q^{60} +10.9389 q^{61} -2.85198 q^{62} -8.34834 q^{63} +22.3510 q^{64} -0.417191 q^{65} +30.3313 q^{66} -14.3735 q^{67} +17.1661 q^{68} -25.5017 q^{69} -4.57159 q^{70} -11.4397 q^{71} -43.4950 q^{72} -12.7976 q^{73} +5.13088 q^{74} -2.81518 q^{75} -26.3851 q^{76} -6.77114 q^{77} +3.16765 q^{78} -7.86078 q^{79} -13.2695 q^{80} +0.482318 q^{81} +1.46274 q^{82} +1.88060 q^{83} +25.1676 q^{84} -3.25467 q^{85} -30.0519 q^{86} -0.340463 q^{87} -35.2778 q^{88} -7.72178 q^{89} +13.2838 q^{90} -0.707144 q^{91} +47.7779 q^{92} -2.97686 q^{93} -14.3463 q^{94} +5.00259 q^{95} +51.0307 q^{96} -4.83462 q^{97} +11.1307 q^{98} +19.6751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) $ 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * 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 $

$2$	−2.69709	−1.90713	−0.953565	−	0.301188i	$-0.902617\pi$
$2$	−2.69709	−1.90713	−0.953565	+	0.301188i	$0.902617\pi$
$3$	−2.81518	−1.62535	−0.812673	−	0.582720i	$-0.801988\pi$
$3$	−2.81518	−1.62535	−0.812673	+	0.582720i	$0.801988\pi$
$4$	5.27428	2.63714
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.59279	3.09974
$7$	−1.69501	−0.640654	−0.320327	−	0.947307i	$-0.603793\pi$
$7$	−1.69501	−0.640654	−0.320327	+	0.947307i	$0.603793\pi$
$8$	−8.83103	−3.12224
$9$	4.92525	1.64175
$10$	2.69709	0.852894
$11$	3.99475	1.20446	0.602231	−	0.798322i	$-0.294278\pi$
$11$	3.99475	1.20446	0.602231	+	0.798322i	$0.294278\pi$
$12$	−14.8481	−4.28627
$13$	0.417191	0.115708	0.0578540	−	0.998325i	$-0.481574\pi$
$13$	0.417191	0.115708	0.0578540	+	0.998325i	$0.481574\pi$
$14$	4.57159	1.22181
$15$	2.81518	0.726877
$16$	13.2695	3.31738
$17$	3.25467	0.789374	0.394687	−	0.918816i	$-0.370853\pi$
$17$	3.25467	0.789374	0.394687	+	0.918816i	$0.370853\pi$
$18$	−13.2838	−3.13103
$19$	−5.00259	−1.14767	−0.573837	−	0.818970i	$-0.694546\pi$
$19$	−5.00259	−1.14767	−0.573837	+	0.818970i	$0.694546\pi$
$20$	−5.27428	−1.17937
$21$	4.77176	1.04128
$22$	−10.7742	−2.29707
$23$	9.05864	1.88886	0.944429	−	0.328716i	$-0.106616\pi$
$23$	9.05864	1.88886	0.944429	+	0.328716i	$0.106616\pi$
$24$	24.8610	5.07472
$25$	1.00000	0.200000
$26$	−1.12520	−0.220670
$27$	−5.41992	−1.04306
$28$	−8.93997	−1.68949
$29$	0.120938	0.0224577	0.0112288	−	0.999937i	$-0.496426\pi$
$29$	0.120938	0.0224577	0.0112288	+	0.999937i	$0.496426\pi$
$30$	−7.59279	−1.38625
$31$	1.05743	0.189920	0.0949600	−	0.995481i	$-0.469728\pi$
$31$	1.05743	0.189920	0.0949600	+	0.995481i	$0.469728\pi$
$32$	−18.1270	−3.20442
$33$	−11.2459	−1.95767
$34$	−8.77813	−1.50544
$35$	1.69501	0.286509
$36$	25.9772	4.32953
$37$	−1.90238	−0.312749	−0.156375	−	0.987698i	$-0.549981\pi$
$37$	−1.90238	−0.312749	−0.156375	+	0.987698i	$0.549981\pi$
$38$	13.4924	2.18876
$39$	−1.17447	−0.188066
$40$	8.83103	1.39631
$41$	−0.542340	−0.0846993	−0.0423496	−	0.999103i	$-0.513484\pi$
$41$	−0.542340	−0.0846993	−0.0423496	+	0.999103i	$0.513484\pi$
$42$	−12.8699	−1.98586
$43$	11.1424	1.69919	0.849597	−	0.527433i	$-0.176845\pi$
$43$	11.1424	1.69919	0.849597	+	0.527433i	$0.176845\pi$
$44$	21.0695	3.17634
$45$	−4.92525	−0.734212
$46$	−24.4320	−3.60230
$47$	5.31919	0.775883	0.387941	−	0.921684i	$-0.373186\pi$
$47$	5.31919	0.775883	0.387941	+	0.921684i	$0.373186\pi$
$48$	−37.3561	−5.39188
$49$	−4.12694	−0.589563
$50$	−2.69709	−0.381426
$51$	−9.16249	−1.28300
$52$	2.20039	0.305139
$53$	−5.09266	−0.699531	−0.349766	−	0.936837i	$-0.613739\pi$
$53$	−5.09266	−0.699531	−0.349766	+	0.936837i	$0.613739\pi$
$54$	14.6180	1.98926
$55$	−3.99475	−0.538652
$56$	14.9687	2.00028
$57$	14.0832	1.86537
$58$	−0.326181	−0.0428297
$59$	10.2722	1.33733	0.668665	−	0.743564i	$-0.266866\pi$
$59$	10.2722	1.33733	0.668665	+	0.743564i	$0.266866\pi$
$60$	14.8481	1.91688
$61$	10.9389	1.40058	0.700289	−	0.713860i	$-0.253055\pi$
$61$	10.9389	1.40058	0.700289	+	0.713860i	$0.253055\pi$
$62$	−2.85198	−0.362202
$63$	−8.34834	−1.05179
$64$	22.3510	2.79387
$65$	−0.417191	−0.0517462
$66$	30.3313	3.73353
$67$	−14.3735	−1.75600	−0.878000	−	0.478660i	$-0.841123\pi$
$67$	−14.3735	−1.75600	−0.878000	+	0.478660i	$0.841123\pi$
$68$	17.1661	2.08169
$69$	−25.5017	−3.07005
$70$	−4.57159	−0.546410
$71$	−11.4397	−1.35764	−0.678819	−	0.734306i	$-0.737508\pi$
$71$	−11.4397	−1.35764	−0.678819	+	0.734306i	$0.737508\pi$
$72$	−43.4950	−5.12594
$73$	−12.7976	−1.49785	−0.748926	−	0.662654i	$-0.769430\pi$
$73$	−12.7976	−1.49785	−0.748926	+	0.662654i	$0.769430\pi$
$74$	5.13088	0.596453
$75$	−2.81518	−0.325069
$76$	−26.3851	−3.02658
$77$	−6.77114	−0.771644
$78$	3.16765	0.358665
$79$	−7.86078	−0.884407	−0.442204	−	0.896915i	$-0.645803\pi$
$79$	−7.86078	−0.884407	−0.442204	+	0.896915i	$0.645803\pi$
$80$	−13.2695	−1.48358
$81$	0.482318	0.0535908
$82$	1.46274	0.161533
$83$	1.88060	0.206423	0.103211	−	0.994659i	$-0.467088\pi$
$83$	1.88060	0.206423	0.103211	+	0.994659i	$0.467088\pi$
$84$	25.1676	2.74601
$85$	−3.25467	−0.353019
$86$	−30.0519	−3.24058
$87$	−0.340463	−0.0365015
$88$	−35.2778	−3.76062
$89$	−7.72178	−0.818507	−0.409253	−	0.912421i	$-0.634211\pi$
$89$	−7.72178	−0.818507	−0.409253	+	0.912421i	$0.634211\pi$
$90$	13.2838	1.40024
$91$	−0.707144	−0.0741288
$92$	47.7779	4.98119
$93$	−2.97686	−0.308686
$94$	−14.3463	−1.47971
$95$	5.00259	0.513255
$96$	51.0307	5.20830
$97$	−4.83462	−0.490881	−0.245441	−	0.969412i	$-0.578933\pi$
$97$	−4.83462	−0.490881	−0.245441	+	0.969412i	$0.578933\pi$
$98$	11.1307	1.12437
$99$	19.6751	1.97743
$100$	5.27428	0.527428
$101$	−10.4291	−1.03773	−0.518866	−	0.854855i	$-0.673646\pi$
$101$	−10.4291	−1.03773	−0.518866	+	0.854855i	$0.673646\pi$
$102$	24.7120	2.44686
$103$	−5.03885	−0.496493	−0.248247	−	0.968697i	$-0.579854\pi$
$103$	−5.03885	−0.496493	−0.248247	+	0.968697i	$0.579854\pi$
$104$	−3.68423	−0.361268
$105$	−4.77176	−0.465676
$106$	13.7354	1.33410
$107$	17.7389	1.71488	0.857440	−	0.514584i	$-0.172054\pi$
$107$	17.7389	1.71488	0.857440	+	0.514584i	$0.172054\pi$
$108$	−28.5862	−2.75071
$109$	12.9830	1.24354	0.621772	−	0.783199i	$-0.286413\pi$
$109$	12.9830	1.24354	0.621772	+	0.783199i	$0.286413\pi$
$110$	10.7742	1.02728
$111$	5.35554	0.508326
$112$	−22.4919	−2.12529
$113$	13.4963	1.26962	0.634810	−	0.772668i	$-0.281078\pi$
$113$	13.4963	1.26962	0.634810	+	0.772668i	$0.281078\pi$
$114$	−37.9836	−3.55749
$115$	−9.05864	−0.844723
$116$	0.637863	0.0592241
$117$	2.05477	0.189964
$118$	−27.7051	−2.55046
$119$	−5.51670	−0.505715
$120$	−24.8610	−2.26948
$121$	4.95803	0.450730
$122$	−29.5031	−2.67108
$123$	1.52679	0.137666
$124$	5.57718	0.500846
$125$	−1.00000	−0.0894427
$126$	22.5162	2.00590
$127$	−11.9175	−1.05751	−0.528754	−	0.848775i	$-0.677341\pi$
$127$	−11.9175	−1.05751	−0.528754	+	0.848775i	$0.677341\pi$
$128$	−24.0287	−2.12386
$129$	−31.3678	−2.76178
$130$	1.12520	0.0986867
$131$	−1.75053	−0.152944	−0.0764722	−	0.997072i	$-0.524366\pi$
$131$	−1.75053	−0.152944	−0.0764722	+	0.997072i	$0.524366\pi$
$132$	−59.3143	−5.16265
$133$	8.47945	0.735261
$134$	38.7666	3.34892
$135$	5.41992	0.466472
$136$	−28.7421	−2.46461
$137$	−0.878098	−0.0750210	−0.0375105	−	0.999296i	$-0.511943\pi$
$137$	−0.878098	−0.0750210	−0.0375105	+	0.999296i	$0.511943\pi$
$138$	68.7804	5.85498
$139$	4.45047	0.377484	0.188742	−	0.982027i	$-0.439559\pi$
$139$	4.45047	0.377484	0.188742	+	0.982027i	$0.439559\pi$
$140$	8.93997	0.755565
$141$	−14.9745	−1.26108
$142$	30.8538	2.58919
$143$	1.66658	0.139366
$144$	65.3556	5.44630
$145$	−0.120938	−0.0100434
$146$	34.5164	2.85660
$147$	11.6181	0.958243
$148$	−10.0337	−0.824764
$149$	−5.37882	−0.440650	−0.220325	−	0.975426i	$-0.570712\pi$
$149$	−5.37882	−0.440650	−0.220325	+	0.975426i	$0.570712\pi$
$150$	7.59279	0.619949
$151$	−8.63384	−0.702612	−0.351306	−	0.936261i	$-0.614262\pi$
$151$	−8.63384	−0.702612	−0.351306	+	0.936261i	$0.614262\pi$
$152$	44.1781	3.58331
$153$	16.0301	1.29595
$154$	18.2624	1.47162
$155$	−1.05743	−0.0849348
$156$	−6.19448	−0.495956
$157$	−0.453244	−0.0361728	−0.0180864	−	0.999836i	$-0.505757\pi$
$157$	−0.453244	−0.0361728	−0.0180864	+	0.999836i	$0.505757\pi$
$158$	21.2012	1.68668
$159$	14.3368	1.13698
$160$	18.1270	1.43306
$161$	−15.3545	−1.21010
$162$	−1.30085	−0.102205
$163$	22.1626	1.73591	0.867955	−	0.496643i	$-0.165434\pi$
$163$	22.1626	1.73591	0.867955	+	0.496643i	$0.165434\pi$
$164$	−2.86046	−0.223364
$165$	11.2459	0.875496
$166$	−5.07215	−0.393675
$167$	6.88461	0.532747	0.266374	−	0.963870i	$-0.414175\pi$
$167$	6.88461	0.532747	0.266374	+	0.963870i	$0.414175\pi$
$168$	−42.1396	−3.25114
$169$	−12.8260	−0.986612
$170$	8.77813	0.673252
$171$	−24.6390	−1.88419
$172$	58.7680	4.48101
$173$	15.0562	1.14470	0.572350	−	0.820009i	$-0.306032\pi$
$173$	15.0562	1.14470	0.572350	+	0.820009i	$0.306032\pi$
$174$	0.918260	0.0696131
$175$	−1.69501	−0.128131
$176$	53.0084	3.99566
$177$	−28.9182	−2.17362
$178$	20.8263	1.56100
$179$	15.9193	1.18986	0.594931	−	0.803777i	$-0.297179\pi$
$179$	15.9193	1.18986	0.594931	+	0.803777i	$0.297179\pi$
$180$	−25.9772	−1.93622
$181$	5.30651	0.394430	0.197215	−	0.980360i	$-0.436810\pi$
$181$	5.30651	0.394430	0.197215	+	0.980360i	$0.436810\pi$
$182$	1.90723	0.141373
$183$	−30.7949	−2.27642
$184$	−79.9972	−5.89747
$185$	1.90238	0.139866
$186$	8.02884	0.588703
$187$	13.0016	0.950771
$188$	28.0549	2.04611
$189$	9.18682	0.668243
$190$	−13.4924	−0.978844
$191$	23.7034	1.71512	0.857559	−	0.514386i	$-0.171980\pi$
$191$	23.7034	1.71512	0.857559	+	0.514386i	$0.171980\pi$
$192$	−62.9221	−4.54101
$193$	−7.66345	−0.551628	−0.275814	−	0.961211i	$-0.588947\pi$
$193$	−7.66345	−0.551628	−0.275814	+	0.961211i	$0.588947\pi$
$194$	13.0394	0.936174
$195$	1.17447	0.0841055
$196$	−21.7667	−1.55476
$197$	1.58986	0.113273	0.0566363	−	0.998395i	$-0.481962\pi$
$197$	1.58986	0.113273	0.0566363	+	0.998395i	$0.481962\pi$
$198$	−53.0656	−3.77121
$199$	9.58357	0.679362	0.339681	−	0.940541i	$-0.389681\pi$
$199$	9.58357	0.679362	0.339681	+	0.940541i	$0.389681\pi$
$200$	−8.83103	−0.624448
$201$	40.4640	2.85411
$202$	28.1281	1.97909
$203$	−0.204992	−0.0143876
$204$	−48.3256	−3.38347
$205$	0.542340	0.0378787
$206$	13.5902	0.946876
$207$	44.6161	3.10103
$208$	5.53592	0.383847
$209$	−19.9841	−1.38233
$210$	12.8699	0.888105
$211$	28.7155	1.97686	0.988428	−	0.151690i	$-0.0484715\pi$
$211$	28.7155	1.97686	0.988428	+	0.151690i	$0.0484715\pi$
$212$	−26.8602	−1.84476
$213$	32.2047	2.20663
$214$	−47.8433	−3.27050
$215$	−11.1424	−0.759902
$216$	47.8635	3.25670
$217$	−1.79235	−0.121673
$218$	−35.0162	−2.37160
$219$	36.0277	2.43453
$220$	−21.0695	−1.42050
$221$	1.35782	0.0913369
$222$	−14.4444	−0.969443
$223$	−11.1054	−0.743673	−0.371836	−	0.928298i	$-0.621272\pi$
$223$	−11.1054	−0.743673	−0.371836	+	0.928298i	$0.621272\pi$
$224$	30.7254	2.05293
$225$	4.92525	0.328350
$226$	−36.4006	−2.42133
$227$	−5.05824	−0.335727	−0.167864	−	0.985810i	$-0.553687\pi$
$227$	−5.05824	−0.335727	−0.167864	+	0.985810i	$0.553687\pi$
$228$	74.2788	4.91924
$229$	−15.7021	−1.03762	−0.518812	−	0.854888i	$-0.673626\pi$
$229$	−15.7021	−1.03762	−0.518812	+	0.854888i	$0.673626\pi$
$230$	24.4320	1.61100
$231$	19.0620	1.25419
$232$	−1.06801	−0.0701183
$233$	−5.16000	−0.338043	−0.169022	−	0.985612i	$-0.554061\pi$
$233$	−5.16000	−0.338043	−0.169022	+	0.985612i	$0.554061\pi$
$234$	−5.54190	−0.362285
$235$	−5.31919	−0.346985
$236$	54.1787	3.52673
$237$	22.1295	1.43747
$238$	14.8790	0.964464
$239$	29.1152	1.88331	0.941653	−	0.336585i	$-0.109272\pi$
$239$	29.1152	1.88331	0.941653	+	0.336585i	$0.109272\pi$
$240$	37.3561	2.41132
$241$	22.5126	1.45016	0.725081	−	0.688664i	$-0.241802\pi$
$241$	22.5126	1.45016	0.725081	+	0.688664i	$0.241802\pi$
$242$	−13.3723	−0.859601
$243$	14.9019	0.955960
$244$	57.6947	3.69352
$245$	4.12694	0.263661
$246$	−4.11788	−0.262546
$247$	−2.08704	−0.132795
$248$	−9.33820	−0.592976
$249$	−5.29424	−0.335509
$250$	2.69709	0.170579
$251$	−13.7493	−0.867849	−0.433924	−	0.900949i	$-0.642871\pi$
$251$	−13.7493	−0.867849	−0.433924	+	0.900949i	$0.642871\pi$
$252$	−44.0315	−2.77373
$253$	36.1870	2.27506
$254$	32.1426	2.01681
$255$	9.16249	0.573777
$256$	20.1055	1.25659
$257$	−22.4347	−1.39944	−0.699719	−	0.714418i	$-0.746692\pi$
$257$	−22.4347	−1.39944	−0.699719	+	0.714418i	$0.746692\pi$
$258$	84.6016	5.26707
$259$	3.22455	0.200364
$260$	−2.20039	−0.136462
$261$	0.595651	0.0368699
$262$	4.72133	0.291685
$263$	9.55138	0.588964	0.294482	−	0.955657i	$-0.404853\pi$
$263$	9.55138	0.588964	0.294482	+	0.955657i	$0.404853\pi$
$264$	99.3133	6.11231
$265$	5.09266	0.312840
$266$	−22.8698	−1.40224
$267$	21.7382	1.33036
$268$	−75.8098	−4.63082
$269$	−7.37461	−0.449638	−0.224819	−	0.974401i	$-0.572179\pi$
$269$	−7.37461	−0.449638	−0.224819	+	0.974401i	$0.572179\pi$
$270$	−14.6180	−0.889623
$271$	7.60156	0.461762	0.230881	−	0.972982i	$-0.425839\pi$
$271$	7.60156	0.461762	0.230881	+	0.972982i	$0.425839\pi$
$272$	43.1879	2.61865
$273$	1.99074	0.120485
$274$	2.36831	0.143075
$275$	3.99475	0.240893
$276$	−134.503	−8.09615
$277$	11.2458	0.675695	0.337847	−	0.941201i	$-0.390301\pi$
$277$	11.2458	0.675695	0.337847	+	0.941201i	$0.390301\pi$
$278$	−12.0033	−0.719911
$279$	5.20810	0.311801
$280$	−14.9687	−0.894550
$281$	15.0866	0.899992	0.449996	−	0.893031i	$-0.351425\pi$
$281$	15.0866	0.899992	0.449996	+	0.893031i	$0.351425\pi$
$282$	40.3875	2.40504
$283$	−11.5453	−0.686298	−0.343149	−	0.939281i	$-0.611494\pi$
$283$	−11.5453	−0.686298	−0.343149	+	0.939281i	$0.611494\pi$
$284$	−60.3360	−3.58028
$285$	−14.0832	−0.834217
$286$	−4.49490	−0.265789
$287$	0.919272	0.0542629
$288$	−89.2798	−5.26086
$289$	−6.40712	−0.376889
$290$	0.326181	0.0191540
$291$	13.6103	0.797852
$292$	−67.4984	−3.95005
$293$	−7.54297	−0.440665	−0.220332	−	0.975425i	$-0.570714\pi$
$293$	−7.54297	−0.440665	−0.220332	+	0.975425i	$0.570714\pi$
$294$	−31.3350	−1.82749
$295$	−10.2722	−0.598072
$296$	16.8000	0.976479
$297$	−21.6512	−1.25633
$298$	14.5072	0.840377
$299$	3.77919	0.218556
$300$	−14.8481	−0.857254
$301$	−18.8864	−1.08859
$302$	23.2862	1.33997
$303$	29.3598	1.68667
$304$	−66.3819	−3.80726
$305$	−10.9389	−0.626357
$306$	−43.2345	−2.47155
$307$	19.2031	1.09598	0.547988	−	0.836486i	$-0.315394\pi$
$307$	19.2031	1.09598	0.547988	+	0.836486i	$0.315394\pi$
$308$	−35.7129	−2.03493
$309$	14.1853	0.806973
$310$	2.85198	0.161982
$311$	1.68359	0.0954675	0.0477338	−	0.998860i	$-0.484800\pi$
$311$	1.68359	0.0954675	0.0477338	+	0.998860i	$0.484800\pi$
$312$	10.3718	0.587186
$313$	−2.62495	−0.148371	−0.0741853	−	0.997244i	$-0.523636\pi$
$313$	−2.62495	−0.148371	−0.0741853	+	0.997244i	$0.523636\pi$
$314$	1.22244	0.0689863
$315$	8.34834	0.470376
$316$	−41.4600	−2.33231
$317$	−22.6289	−1.27096	−0.635482	−	0.772116i	$-0.719199\pi$
$317$	−22.6289	−1.27096	−0.635482	+	0.772116i	$0.719199\pi$
$318$	−38.6675	−2.16837
$319$	0.483119	0.0270494
$320$	−22.3510	−1.24946
$321$	−49.9381	−2.78727
$322$	41.4124	2.30782
$323$	−16.2818	−0.905943
$324$	2.54388	0.141327
$325$	0.417191	0.0231416
$326$	−59.7745	−3.31060
$327$	−36.5494	−2.02119
$328$	4.78942	0.264452
$329$	−9.01607	−0.497072
$330$	−30.3313	−1.66968
$331$	19.6782	1.08161	0.540806	−	0.841147i	$-0.318119\pi$
$331$	19.6782	1.08161	0.540806	+	0.841147i	$0.318119\pi$
$332$	9.91883	0.544367
$333$	−9.36969	−0.513456
$334$	−18.5684	−1.01602
$335$	14.3735	0.785307
$336$	63.3189	3.45433
$337$	18.6680	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$337$	18.6680	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$338$	34.5927	1.88160
$339$	−37.9944	−2.06357
$340$	−17.1661	−0.930960
$341$	4.22417	0.228752
$342$	66.4536	3.59340
$343$	18.8603	1.01836
$344$	−98.3985	−5.30529
$345$	25.5017	1.37297
$346$	−40.6079	−2.18309
$347$	−13.1864	−0.707885	−0.353943	−	0.935267i	$-0.615159\pi$
$347$	−13.1864	−0.707885	−0.353943	+	0.935267i	$0.615159\pi$
$348$	−1.79570	−0.0962596
$349$	28.8075	1.54203	0.771016	−	0.636816i	$-0.219749\pi$
$349$	28.8075	1.54203	0.771016	+	0.636816i	$0.219749\pi$
$350$	4.57159	0.244362
$351$	−2.26114	−0.120691
$352$	−72.4127	−3.85961
$353$	14.2005	0.755814	0.377907	−	0.925843i	$-0.376644\pi$
$353$	14.2005	0.755814	0.377907	+	0.925843i	$0.376644\pi$
$354$	77.9949	4.14538
$355$	11.4397	0.607154
$356$	−40.7269	−2.15852
$357$	15.5305	0.821962
$358$	−42.9357	−2.26922
$359$	−15.4652	−0.816223	−0.408112	−	0.912932i	$-0.633813\pi$
$359$	−15.4652	−0.816223	−0.408112	+	0.912932i	$0.633813\pi$
$360$	43.4950	2.29239
$361$	6.02592	0.317154
$362$	−14.3121	−0.752229
$363$	−13.9578	−0.732593
$364$	−3.72968	−0.195488
$365$	12.7976	0.669860
$366$	83.0565	4.34143
$367$	−27.4018	−1.43036	−0.715181	−	0.698939i	$-0.753656\pi$
$367$	−27.4018	−1.43036	−0.715181	+	0.698939i	$0.753656\pi$
$368$	120.204	6.26605
$369$	−2.67116	−0.139055
$370$	−5.13088	−0.266742
$371$	8.63212	0.448157
$372$	−15.7008	−0.814048
$373$	27.2475	1.41082	0.705411	−	0.708799i	$-0.250762\pi$
$373$	27.2475	1.41082	0.705411	+	0.708799i	$0.250762\pi$
$374$	−35.0665	−1.81324
$375$	2.81518	0.145375
$376$	−46.9739	−2.42249
$377$	0.0504544	0.00259853
$378$	−24.7777	−1.27443
$379$	−24.5113	−1.25906	−0.629531	−	0.776975i	$-0.716753\pi$
$379$	−24.5113	−1.25906	−0.629531	+	0.776975i	$0.716753\pi$
$380$	26.3851	1.35353
$381$	33.5500	1.71882
$382$	−63.9301	−3.27095
$383$	16.9286	0.865009	0.432504	−	0.901632i	$-0.357630\pi$
$383$	16.9286	0.865009	0.432504	+	0.901632i	$0.357630\pi$
$384$	67.6451	3.45200
$385$	6.77114	0.345089
$386$	20.6690	1.05202
$387$	54.8789	2.78965
$388$	−25.4992	−1.29452
$389$	−7.80178	−0.395566	−0.197783	−	0.980246i	$-0.563374\pi$
$389$	−7.80178	−0.395566	−0.197783	+	0.980246i	$0.563374\pi$
$390$	−3.16765	−0.160400
$391$	29.4829	1.49101
$392$	36.4451	1.84076
$393$	4.92806	0.248588
$394$	−4.28798	−0.216025
$395$	7.86078	0.395519
$396$	103.772	5.21475
$397$	−32.2308	−1.61762	−0.808808	−	0.588073i	$-0.799887\pi$
$397$	−32.2308	−1.61762	−0.808808	+	0.588073i	$0.799887\pi$
$398$	−25.8477	−1.29563
$399$	−23.8712	−1.19505
$400$	13.2695	0.663475
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−109.135	−5.44315
$403$	0.441150	0.0219753
$404$	−55.0059	−2.73665
$405$	−0.482318	−0.0239666
$406$	0.552881	0.0274390
$407$	−7.59953	−0.376695
$408$	80.9142	4.00585
$409$	−32.5850	−1.61123	−0.805613	−	0.592441i	$-0.798164\pi$
$409$	−32.5850	−1.61123	−0.805613	+	0.592441i	$0.798164\pi$
$410$	−1.46274	−0.0722395
$411$	2.47201	0.121935
$412$	−26.5763	−1.30932
$413$	−17.4115	−0.856766
$414$	−120.333	−5.91407
$415$	−1.88060	−0.0923151
$416$	−7.56241	−0.370778
$417$	−12.5289	−0.613542
$418$	53.8989	2.63628
$419$	9.31285	0.454963	0.227481	−	0.973782i	$-0.426951\pi$
$419$	9.31285	0.454963	0.227481	+	0.973782i	$0.426951\pi$
$420$	−25.1676	−1.22805
$421$	4.14739	0.202131	0.101066	−	0.994880i	$-0.467775\pi$
$421$	4.14739	0.202131	0.101066	+	0.994880i	$0.467775\pi$
$422$	−77.4482	−3.77012
$423$	26.1983	1.27381
$424$	44.9735	2.18411
$425$	3.25467	0.157875
$426$	−86.8590	−4.20833
$427$	−18.5415	−0.897285
$428$	93.5598	4.52238
$429$	−4.69171	−0.226518
$430$	30.0519	1.44923
$431$	15.9877	0.770099	0.385050	−	0.922896i	$-0.374184\pi$
$431$	15.9877	0.770099	0.385050	+	0.922896i	$0.374184\pi$
$432$	−71.9197	−3.46024
$433$	9.44890	0.454085	0.227043	−	0.973885i	$-0.427094\pi$
$433$	9.44890	0.454085	0.227043	+	0.973885i	$0.427094\pi$
$434$	4.83414	0.232046
$435$	0.340463	0.0163240
$436$	68.4759	3.27940
$437$	−45.3167	−2.16779
$438$	−97.1699	−4.64296
$439$	36.8541	1.75895	0.879475	−	0.475945i	$-0.157894\pi$
$439$	36.8541	1.75895	0.879475	+	0.475945i	$0.157894\pi$
$440$	35.2778	1.68180
$441$	−20.3262	−0.967914
$442$	−3.66216	−0.174191
$443$	−16.8294	−0.799591	−0.399795	−	0.916604i	$-0.630919\pi$
$443$	−16.8294	−0.799591	−0.399795	+	0.916604i	$0.630919\pi$
$444$	28.2467	1.34053
$445$	7.72178	0.366047
$446$	29.9523	1.41828
$447$	15.1424	0.716209
$448$	−37.8852	−1.78991
$449$	−26.5192	−1.25152	−0.625759	−	0.780017i	$-0.715210\pi$
$449$	−26.5192	−1.25152	−0.625759	+	0.780017i	$0.715210\pi$
$450$	−13.2838	−0.626206
$451$	−2.16651	−0.102017
$452$	71.1831	3.34817
$453$	24.3058	1.14199
$454$	13.6425	0.640275
$455$	0.707144	0.0331514
$456$	−124.369	−5.82412
$457$	7.21106	0.337319	0.168660	−	0.985674i	$-0.446056\pi$
$457$	7.21106	0.337319	0.168660	+	0.985674i	$0.446056\pi$
$458$	42.3500	1.97888
$459$	−17.6401	−0.823367
$460$	−47.7779	−2.22765
$461$	34.3910	1.60175	0.800874	−	0.598833i	$-0.204369\pi$
$461$	34.3910	1.60175	0.800874	+	0.598833i	$0.204369\pi$
$462$	−51.4119	−2.39190
$463$	8.45471	0.392924	0.196462	−	0.980511i	$-0.437055\pi$
$463$	8.45471	0.392924	0.196462	+	0.980511i	$0.437055\pi$
$464$	1.60479	0.0745006
$465$	2.97686	0.138048
$466$	13.9170	0.644692
$467$	−32.3849	−1.49860	−0.749298	−	0.662234i	$-0.769609\pi$
$467$	−32.3849	−1.49860	−0.749298	+	0.662234i	$0.769609\pi$
$468$	10.8374	0.500961
$469$	24.3632	1.12499
$470$	14.3463	0.661746
$471$	1.27597	0.0587934
$472$	−90.7144	−4.17547
$473$	44.5109	2.04662
$474$	−59.6853	−2.74144
$475$	−5.00259	−0.229535
$476$	−29.0966	−1.33364
$477$	−25.0826	−1.14845
$478$	−78.5263	−3.59171
$479$	−37.9086	−1.73209	−0.866043	−	0.499969i	$-0.833345\pi$
$479$	−37.9086	−1.73209	−0.866043	+	0.499969i	$0.833345\pi$
$480$	−51.0307	−2.32922
$481$	−0.793656	−0.0361876
$482$	−60.7184	−2.76565
$483$	43.2257	1.96684
$484$	26.1501	1.18864
$485$	4.83462	0.219529
$486$	−40.1919	−1.82314
$487$	−25.8592	−1.17179	−0.585897	−	0.810386i	$-0.699258\pi$
$487$	−25.8592	−1.17179	−0.585897	+	0.810386i	$0.699258\pi$
$488$	−96.6014	−4.37294
$489$	−62.3918	−2.82145
$490$	−11.1307	−0.502835
$491$	−4.98324	−0.224890	−0.112445	−	0.993658i	$-0.535868\pi$
$491$	−4.98324	−0.224890	−0.112445	+	0.993658i	$0.535868\pi$
$492$	8.05270	0.363044
$493$	0.393614	0.0177275
$494$	5.62892	0.253257
$495$	−19.6751	−0.884332
$496$	14.0316	0.630036
$497$	19.3903	0.869776
$498$	14.2790	0.639858
$499$	17.0653	0.763946	0.381973	−	0.924174i	$-0.375245\pi$
$499$	17.0653	0.763946	0.381973	+	0.924174i	$0.375245\pi$
$500$	−5.27428	−0.235873
$501$	−19.3814	−0.865898
$502$	37.0831	1.65510
$503$	8.61725	0.384224	0.192112	−	0.981373i	$-0.438466\pi$
$503$	8.61725	0.384224	0.192112	+	0.981373i	$0.438466\pi$
$504$	73.7245	3.28395
$505$	10.4291	0.464088
$506$	−97.5996	−4.33883
$507$	36.1074	1.60359
$508$	−62.8564	−2.78880
$509$	21.1246	0.936331	0.468166	−	0.883641i	$-0.344915\pi$
$509$	21.1246	0.936331	0.468166	+	0.883641i	$0.344915\pi$
$510$	−24.7120	−1.09427
$511$	21.6921	0.959604
$512$	−6.16890	−0.272630
$513$	27.1136	1.19710
$514$	60.5084	2.66891
$515$	5.03885	0.222038
$516$	−165.442	−7.28320
$517$	21.2488	0.934522
$518$	−8.69690	−0.382120
$519$	−42.3859	−1.86053
$520$	3.68423	0.161564
$521$	32.8196	1.43785	0.718927	−	0.695086i	$-0.244634\pi$
$521$	32.8196	1.43785	0.718927	+	0.695086i	$0.244634\pi$
$522$	−1.60652	−0.0703156
$523$	6.53305	0.285670	0.142835	−	0.989746i	$-0.454378\pi$
$523$	6.53305	0.285670	0.142835	+	0.989746i	$0.454378\pi$
$524$	−9.23279	−0.403336
$525$	4.77176	0.208257
$526$	−25.7609	−1.12323
$527$	3.44159	0.149918
$528$	−149.228	−6.49432
$529$	59.0590	2.56778
$530$	−13.7354	−0.596626
$531$	50.5933	2.19556
$532$	44.7230	1.93899
$533$	−0.226260	−0.00980039
$534$	−58.6299	−2.53716
$535$	−17.7389	−0.766918
$536$	126.933	5.48266
$537$	−44.8156	−1.93394
$538$	19.8900	0.857518
$539$	−16.4861	−0.710106
$540$	28.5862	1.23015
$541$	25.5520	1.09857	0.549284	−	0.835636i	$-0.314901\pi$
$541$	25.5520	1.09857	0.549284	+	0.835636i	$0.314901\pi$
$542$	−20.5021	−0.880639
$543$	−14.9388	−0.641085
$544$	−58.9973	−2.52949
$545$	−12.9830	−0.556130
$546$	−5.36919	−0.229780
$547$	−9.94484	−0.425211	−0.212605	−	0.977138i	$-0.568195\pi$
$547$	−9.94484	−0.425211	−0.212605	+	0.977138i	$0.568195\pi$
$548$	−4.63134	−0.197841
$549$	53.8766	2.29940
$550$	−10.7742	−0.459413
$551$	−0.605005	−0.0257741
$552$	225.207	9.58543
$553$	13.3241	0.566599
$554$	−30.3309	−1.28864
$555$	−5.35554	−0.227330
$556$	23.4731	0.995479
$557$	−1.96779	−0.0833780	−0.0416890	−	0.999131i	$-0.513274\pi$
$557$	−1.96779	−0.0833780	−0.0416890	+	0.999131i	$0.513274\pi$
$558$	−14.0467	−0.594645
$559$	4.64849	0.196610
$560$	22.4919	0.950458
$561$	−36.6019	−1.54533
$562$	−40.6899	−1.71640
$563$	−18.4133	−0.776029	−0.388014	−	0.921653i	$-0.626839\pi$
$563$	−18.4133	−0.776029	−0.388014	+	0.921653i	$0.626839\pi$
$564$	−78.9796	−3.32564
$565$	−13.4963	−0.567792
$566$	31.1388	1.30886
$567$	−0.817533	−0.0343332
$568$	101.024	4.23887
$569$	19.1931	0.804617	0.402309	−	0.915504i	$-0.368208\pi$
$569$	19.1931	0.804617	0.402309	+	0.915504i	$0.368208\pi$
$570$	37.9836	1.59096
$571$	11.4916	0.480909	0.240455	−	0.970660i	$-0.422704\pi$
$571$	11.4916	0.480909	0.240455	+	0.970660i	$0.422704\pi$
$572$	8.78999	0.367528
$573$	−66.7294	−2.78766
$574$	−2.47936	−0.103486
$575$	9.05864	0.377772
$576$	110.084	4.58684
$577$	38.2846	1.59381	0.796904	−	0.604106i	$-0.206470\pi$
$577$	38.2846	1.59381	0.796904	+	0.604106i	$0.206470\pi$
$578$	17.2806	0.718777
$579$	21.5740	0.896585
$580$	−0.637863	−0.0264858
$581$	−3.18764	−0.132246
$582$	−36.7083	−1.52161
$583$	−20.3439	−0.842559
$584$	113.016	4.67665
$585$	−2.05477	−0.0849543
$586$	20.3440	0.840405
$587$	−30.5652	−1.26156	−0.630780	−	0.775962i	$-0.717265\pi$
$587$	−30.5652	−1.26156	−0.630780	+	0.775962i	$0.717265\pi$
$588$	61.2771	2.52702
$589$	−5.28989	−0.217966
$590$	27.7051	1.14060
$591$	−4.47573	−0.184107
$592$	−25.2436	−1.03751
$593$	−14.1355	−0.580477	−0.290238	−	0.956954i	$-0.593735\pi$
$593$	−14.1355	−0.580477	−0.290238	+	0.956954i	$0.593735\pi$
$594$	58.3953	2.39599
$595$	5.51670	0.226163
$596$	−28.3694	−1.16206
$597$	−26.9795	−1.10420
$598$	−10.1928	−0.416815
$599$	18.2625	0.746187	0.373093	−	0.927794i	$-0.378297\pi$
$599$	18.2625	0.746187	0.373093	+	0.927794i	$0.378297\pi$
$600$	24.8610	1.01494
$601$	−16.8321	−0.686597	−0.343298	−	0.939226i	$-0.611544\pi$
$601$	−16.8321	−0.686597	−0.343298	+	0.939226i	$0.611544\pi$
$602$	50.9383	2.07609
$603$	−70.7930	−2.88291
$604$	−45.5373	−1.85289
$605$	−4.95803	−0.201573
$606$	−79.1858	−3.21671
$607$	−12.4273	−0.504407	−0.252204	−	0.967674i	$-0.581155\pi$
$607$	−12.4273	−0.504407	−0.252204	+	0.967674i	$0.581155\pi$
$608$	90.6818	3.67763
$609$	0.577089	0.0233848
$610$	29.5031	1.19454
$611$	2.21912	0.0897759
$612$	84.5471	3.41761
$613$	16.5358	0.667874	0.333937	−	0.942595i	$-0.391623\pi$
$613$	16.5358	0.667874	0.333937	+	0.942595i	$0.391623\pi$
$614$	−51.7924	−2.09017
$615$	−1.52679	−0.0615659
$616$	59.7962	2.40926
$617$	25.2913	1.01819	0.509095	−	0.860710i	$-0.329980\pi$
$617$	25.2913	1.01819	0.509095	+	0.860710i	$0.329980\pi$
$618$	−38.2590	−1.53900
$619$	9.00876	0.362092	0.181046	−	0.983475i	$-0.442052\pi$
$619$	9.00876	0.362092	0.181046	+	0.983475i	$0.442052\pi$
$620$	−5.57718	−0.223985
$621$	−49.0971	−1.97020
$622$	−4.54079	−0.182069
$623$	13.0885	0.524380
$624$	−15.5846	−0.623884
$625$	1.00000	0.0400000
$626$	7.07971	0.282962
$627$	56.2589	2.24676
$628$	−2.39054	−0.0953929
$629$	−6.19162	−0.246876
$630$	−22.5162	−0.897068
$631$	7.90718	0.314780	0.157390	−	0.987537i	$-0.449692\pi$
$631$	7.90718	0.314780	0.157390	+	0.987537i	$0.449692\pi$
$632$	69.4188	2.76133
$633$	−80.8393	−3.21308
$634$	61.0321	2.42389
$635$	11.9175	0.472932
$636$	75.6162	2.99838
$637$	−1.72172	−0.0682172
$638$	−1.30301	−0.0515868
$639$	−56.3432	−2.22890
$640$	24.0287	0.949817
$641$	−26.8993	−1.06246	−0.531230	−	0.847228i	$-0.678270\pi$
$641$	−26.8993	−1.06246	−0.531230	+	0.847228i	$0.678270\pi$
$642$	134.687	5.31569
$643$	12.5421	0.494610	0.247305	−	0.968938i	$-0.420455\pi$
$643$	12.5421	0.494610	0.247305	+	0.968938i	$0.420455\pi$
$644$	−80.9840	−3.19122
$645$	31.3678	1.23510
$646$	43.9134	1.72775
$647$	20.7524	0.815862	0.407931	−	0.913013i	$-0.366250\pi$
$647$	20.7524	0.815862	0.407931	+	0.913013i	$0.366250\pi$
$648$	−4.25936	−0.167324
$649$	41.0350	1.61076
$650$	−1.12520	−0.0441340
$651$	5.04580	0.197761
$652$	116.892	4.57784
$653$	−7.61116	−0.297848	−0.148924	−	0.988849i	$-0.547581\pi$
$653$	−7.61116	−0.297848	−0.148924	+	0.988849i	$0.547581\pi$
$654$	98.5770	3.85467
$655$	1.75053	0.0683988
$656$	−7.19659	−0.280979
$657$	−63.0316	−2.45910
$658$	24.3171	0.947981
$659$	41.6030	1.62062	0.810311	−	0.586000i	$-0.199298\pi$
$659$	41.6030	1.62062	0.810311	+	0.586000i	$0.199298\pi$
$660$	59.3143	2.30881
$661$	−46.6217	−1.81337	−0.906686	−	0.421805i	$-0.861397\pi$
$661$	−46.6217	−1.81337	−0.906686	+	0.421805i	$0.861397\pi$
$662$	−53.0739	−2.06277
$663$	−3.82251	−0.148454
$664$	−16.6077	−0.644502
$665$	−8.47945	−0.328819
$666$	25.2709	0.979226
$667$	1.09554	0.0424194
$668$	36.3114	1.40493
$669$	31.2637	1.20873
$670$	−38.7666	−1.49768
$671$	43.6980	1.68694
$672$	−86.4975	−3.33671
$673$	22.8593	0.881162	0.440581	−	0.897713i	$-0.354772\pi$
$673$	22.8593	0.881162	0.440581	+	0.897713i	$0.354772\pi$
$674$	−50.3493	−1.93938
$675$	−5.41992	−0.208613
$676$	−67.6477	−2.60184
$677$	−30.1556	−1.15898	−0.579488	−	0.814981i	$-0.696747\pi$
$677$	−30.1556	−1.15898	−0.579488	+	0.814981i	$0.696747\pi$
$678$	102.474	3.93550
$679$	8.19473	0.314485
$680$	28.7421	1.10221
$681$	14.2399	0.545673
$682$	−11.3930	−0.436259
$683$	40.2993	1.54201	0.771004	−	0.636830i	$-0.219755\pi$
$683$	40.2993	1.54201	0.771004	+	0.636830i	$0.219755\pi$
$684$	−129.953	−4.96888
$685$	0.878098	0.0335504
$686$	−50.8678	−1.94214
$687$	44.2043	1.68650
$688$	147.854	5.63686
$689$	−2.12461	−0.0809414
$690$	−68.7804	−2.61843
$691$	38.2270	1.45422	0.727112	−	0.686519i	$-0.240862\pi$
$691$	38.2270	1.45422	0.727112	+	0.686519i	$0.240862\pi$
$692$	79.4106	3.01874
$693$	−33.3496	−1.26684
$694$	35.5650	1.35003
$695$	−4.45047	−0.168816
$696$	3.00664	0.113967
$697$	−1.76514	−0.0668594
$698$	−77.6964	−2.94085
$699$	14.5263	0.549437
$700$	−8.93997	−0.337899
$701$	51.7431	1.95431	0.977155	−	0.212528i	$-0.0681698\pi$
$701$	51.7431	1.95431	0.977155	+	0.212528i	$0.0681698\pi$
$702$	6.09850	0.230173
$703$	9.51683	0.358934
$704$	89.2867	3.36512
$705$	14.9745	0.563971
$706$	−38.2999	−1.44144
$707$	17.6774	0.664827
$708$	−152.523	−5.73216
$709$	−25.2236	−0.947293	−0.473646	−	0.880715i	$-0.657062\pi$
$709$	−25.2236	−0.947293	−0.473646	+	0.880715i	$0.657062\pi$
$710$	−30.8538	−1.15792
$711$	−38.7163	−1.45197
$712$	68.1913	2.55558
$713$	9.57888	0.358732
$714$	−41.8872	−1.56759
$715$	−1.66658	−0.0623264
$716$	83.9627	3.13784
$717$	−81.9646	−3.06102
$718$	41.7111	1.55664
$719$	−14.7565	−0.550323	−0.275162	−	0.961398i	$-0.588731\pi$
$719$	−14.7565	−0.550323	−0.275162	+	0.961398i	$0.588731\pi$
$720$	−65.3556	−2.43566
$721$	8.54091	0.318080
$722$	−16.2524	−0.604854
$723$	−63.3770	−2.35701
$724$	27.9881	1.04017
$725$	0.120938	0.00449154
$726$	37.6453	1.39715
$727$	−30.1456	−1.11804	−0.559019	−	0.829155i	$-0.688822\pi$
$727$	−30.1456	−1.11804	−0.559019	+	0.829155i	$0.688822\pi$
$728$	6.24481	0.231448
$729$	−43.3986	−1.60736
$730$	−34.5164	−1.27751
$731$	36.2647	1.34130
$732$	−162.421	−6.00325
$733$	31.3415	1.15762	0.578812	−	0.815461i	$-0.303516\pi$
$733$	31.3415	1.15762	0.578812	+	0.815461i	$0.303516\pi$
$734$	73.9051	2.72789
$735$	−11.6181	−0.428540
$736$	−164.206	−6.05270
$737$	−57.4185	−2.11504
$738$	7.20435	0.265196
$739$	5.49468	0.202125	0.101063	−	0.994880i	$-0.467776\pi$
$739$	5.49468	0.202125	0.101063	+	0.994880i	$0.467776\pi$
$740$	10.0337	0.368846
$741$	5.87539	0.215838
$742$	−23.2816	−0.854694
$743$	5.24364	0.192371	0.0961853	−	0.995363i	$-0.469336\pi$
$743$	5.24364	0.192371	0.0961853	+	0.995363i	$0.469336\pi$
$744$	26.2887	0.963791
$745$	5.37882	0.197065
$746$	−73.4889	−2.69062
$747$	9.26243	0.338895
$748$	68.5741	2.50732
$749$	−30.0675	−1.09864
$750$	−7.59279	−0.277250
$751$	−32.9151	−1.20109	−0.600544	−	0.799591i	$-0.705049\pi$
$751$	−32.9151	−1.20109	−0.600544	+	0.799591i	$0.705049\pi$
$752$	70.5830	2.57390
$753$	38.7068	1.41055
$754$	−0.136080	−0.00495574
$755$	8.63384	0.314218
$756$	48.4539	1.76225
$757$	−14.1564	−0.514525	−0.257262	−	0.966342i	$-0.582820\pi$
$757$	−14.1564	−0.514525	−0.257262	+	0.966342i	$0.582820\pi$
$758$	66.1092	2.40119
$759$	−101.873	−3.69776
$760$	−44.1781	−1.60251
$761$	−37.8345	−1.37150	−0.685751	−	0.727837i	$-0.740526\pi$
$761$	−37.8345	−1.37150	−0.685751	+	0.727837i	$0.740526\pi$
$762$	−90.4872	−3.27801
$763$	−22.0063	−0.796681
$764$	125.018	4.52301
$765$	−16.0301	−0.579568
$766$	−45.6578	−1.64968
$767$	4.28548	0.154740
$768$	−56.6006	−2.04240
$769$	−21.1661	−0.763267	−0.381634	−	0.924314i	$-0.624638\pi$
$769$	−21.1661	−0.763267	−0.381634	+	0.924314i	$0.624638\pi$
$770$	−18.2624	−0.658130
$771$	63.1578	2.27457
$772$	−40.4192	−1.45472
$773$	−9.61518	−0.345834	−0.172917	−	0.984936i	$-0.555319\pi$
$773$	−9.61518	−0.345834	−0.172917	+	0.984936i	$0.555319\pi$
$774$	−148.013	−5.32022
$775$	1.05743	0.0379840
$776$	42.6947	1.53265
$777$	−9.07770	−0.325661
$778$	21.0421	0.754396
$779$	2.71311	0.0972071
$780$	6.19448	0.221798
$781$	−45.6986	−1.63522
$782$	−79.5180	−2.84356
$783$	−0.655476	−0.0234248
$784$	−54.7624	−1.95580
$785$	0.453244	0.0161770
$786$	−13.2914	−0.474089
$787$	25.2110	0.898677	0.449338	−	0.893362i	$-0.351660\pi$
$787$	25.2110	0.898677	0.449338	+	0.893362i	$0.351660\pi$
$788$	8.38535	0.298716
$789$	−26.8889	−0.957269
$790$	−21.2012	−0.754306
$791$	−22.8763	−0.813387
$792$	−173.752	−6.17400
$793$	4.56360	0.162058
$794$	86.9292	3.08500
$795$	−14.3368	−0.508473
$796$	50.5465	1.79157
$797$	55.4332	1.96354	0.981772	−	0.190064i	$-0.0608697\pi$
$797$	55.4332	1.96354	0.981772	+	0.190064i	$0.0608697\pi$
$798$	64.3827	2.27912
$799$	17.3122	0.612461
$800$	−18.1270	−0.640885
$801$	−38.0317	−1.34378
$802$	−2.69709	−0.0952375
$803$	−51.1234	−1.80411
$804$	213.418	7.52669
$805$	15.3545	0.541175
$806$	−1.18982	−0.0419097
$807$	20.7609	0.730817
$808$	92.0996	3.24005
$809$	32.8736	1.15577	0.577887	−	0.816117i	$-0.303877\pi$
$809$	32.8736	1.15577	0.577887	+	0.816117i	$0.303877\pi$
$810$	1.30085	0.0457073
$811$	−41.3055	−1.45043	−0.725216	−	0.688521i	$-0.758260\pi$
$811$	−41.3055	−1.45043	−0.725216	+	0.688521i	$0.758260\pi$
$812$	−1.08118	−0.0379421
$813$	−21.3998	−0.750523
$814$	20.4966	0.718406
$815$	−22.1626	−0.776322
$816$	−121.582	−4.25621
$817$	−55.7407	−1.95012
$818$	87.8847	3.07282
$819$	−3.48286	−0.121701
$820$	2.86046	0.0998915
$821$	−22.7423	−0.793713	−0.396856	−	0.917881i	$-0.629899\pi$
$821$	−22.7423	−0.793713	−0.396856	+	0.917881i	$0.629899\pi$
$822$	−6.66722	−0.232546
$823$	43.9860	1.53326	0.766628	−	0.642092i	$-0.221933\pi$
$823$	43.9860	1.53326	0.766628	+	0.642092i	$0.221933\pi$
$824$	44.4983	1.55017
$825$	−11.2459	−0.391534
$826$	46.9604	1.63396
$827$	38.8556	1.35114	0.675571	−	0.737295i	$-0.263897\pi$
$827$	38.8556	1.35114	0.675571	+	0.737295i	$0.263897\pi$
$828$	235.318	8.17786
$829$	−43.5807	−1.51362	−0.756810	−	0.653635i	$-0.773243\pi$
$829$	−43.5807	−1.51362	−0.756810	+	0.653635i	$0.773243\pi$
$830$	5.07215	0.176057
$831$	−31.6590	−1.09824
$832$	9.32464	0.323274
$833$	−13.4318	−0.465385
$834$	33.7915	1.17010
$835$	−6.88461	−0.238252
$836$	−105.402	−3.64540
$837$	−5.73118	−0.198099
$838$	−25.1176	−0.867673
$839$	−48.0917	−1.66031	−0.830155	−	0.557532i	$-0.811748\pi$
$839$	−48.0917	−1.66031	−0.830155	+	0.557532i	$0.811748\pi$
$840$	42.1396	1.45395
$841$	−28.9854	−0.999496
$842$	−11.1859	−0.385491
$843$	−42.4716	−1.46280
$844$	151.454	5.21325
$845$	12.8260	0.441226
$846$	−70.6591	−2.42931
$847$	−8.40392	−0.288762
$848$	−67.5771	−2.32061
$849$	32.5022	1.11547
$850$	−8.77813	−0.301087
$851$	−17.2330	−0.590739
$852$	169.857	5.81920
$853$	−15.8061	−0.541191	−0.270596	−	0.962693i	$-0.587221\pi$
$853$	−15.8061	−0.541191	−0.270596	+	0.962693i	$0.587221\pi$
$854$	50.0080	1.71124
$855$	24.6390	0.842636
$856$	−156.652	−5.35427
$857$	−6.20703	−0.212028	−0.106014	−	0.994365i	$-0.533809\pi$
$857$	−6.20703	−0.212028	−0.106014	+	0.994365i	$0.533809\pi$
$858$	12.6540	0.431999
$859$	15.4632	0.527599	0.263799	−	0.964578i	$-0.415024\pi$
$859$	15.4632	0.527599	0.263799	+	0.964578i	$0.415024\pi$
$860$	−58.7680	−2.00397
$861$	−2.58792	−0.0881960
$862$	−43.1202	−1.46868
$863$	53.0028	1.80424	0.902119	−	0.431488i	$-0.142011\pi$
$863$	53.0028	1.80424	0.902119	+	0.431488i	$0.142011\pi$
$864$	98.2467	3.34242
$865$	−15.0562	−0.511926
$866$	−25.4845	−0.865999
$867$	18.0372	0.612576
$868$	−9.45339	−0.320869
$869$	−31.4019	−1.06524
$870$	−0.918260	−0.0311319
$871$	−5.99649	−0.203183
$872$	−114.653	−3.88264
$873$	−23.8117	−0.805904
$874$	122.223	4.13426
$875$	1.69501	0.0573018
$876$	190.020	6.42019
$877$	24.1836	0.816622	0.408311	−	0.912843i	$-0.366118\pi$
$877$	24.1836	0.816622	0.408311	+	0.912843i	$0.366118\pi$
$878$	−99.3987	−3.35454
$879$	21.2348	0.716233
$880$	−53.0084	−1.78691
$881$	51.1311	1.72265	0.861325	−	0.508055i	$-0.169635\pi$
$881$	51.1311	1.72265	0.861325	+	0.508055i	$0.169635\pi$
$882$	54.8215	1.84594
$883$	23.3831	0.786906	0.393453	−	0.919345i	$-0.371280\pi$
$883$	23.3831	0.786906	0.393453	+	0.919345i	$0.371280\pi$
$884$	7.16153	0.240868
$885$	28.9182	0.972074
$886$	45.3905	1.52492
$887$	−37.2151	−1.24956	−0.624780	−	0.780801i	$-0.714811\pi$
$887$	−37.2151	−1.24956	−0.624780	+	0.780801i	$0.714811\pi$
$888$	−47.2950	−1.58712
$889$	20.2003	0.677497
$890$	−20.8263	−0.698100
$891$	1.92674	0.0645482
$892$	−58.5731	−1.96117
$893$	−26.6097	−0.890460
$894$	−40.8403	−1.36590
$895$	−15.9193	−0.532122
$896$	40.7289	1.36066
$897$	−10.6391	−0.355229
$898$	71.5245	2.38680
$899$	0.127884	0.00426516
$900$	25.9772	0.865905
$901$	−16.5749	−0.552191
$902$	5.84328	0.194560
$903$	53.1687	1.76934
$904$	−119.186	−3.96406
$905$	−5.30651	−0.176394
$906$	−65.5549	−2.17792
$907$	51.4958	1.70989	0.854945	−	0.518719i	$-0.173591\pi$
$907$	51.4958	1.70989	0.854945	+	0.518719i	$0.173591\pi$
$908$	−26.6786	−0.885360
$909$	−51.3658	−1.70370
$910$	−1.90723	−0.0632240
$911$	25.6153	0.848672	0.424336	−	0.905505i	$-0.360507\pi$
$911$	25.6153	0.848672	0.424336	+	0.905505i	$0.360507\pi$
$912$	186.877	6.18812
$913$	7.51254	0.248629
$914$	−19.4489	−0.643311
$915$	30.7949	1.01805
$916$	−82.8174	−2.73636
$917$	2.96716	0.0979844
$918$	47.5768	1.57027
$919$	−41.8328	−1.37994	−0.689968	−	0.723840i	$-0.742375\pi$
$919$	−41.8328	−1.37994	−0.689968	+	0.723840i	$0.742375\pi$
$920$	79.9972	2.63743
$921$	−54.0601	−1.78134
$922$	−92.7555	−3.05474
$923$	−4.77253	−0.157090
$924$	100.538	3.30747
$925$	−1.90238	−0.0625498
$926$	−22.8031	−0.749356
$927$	−24.8176	−0.815117
$928$	−2.19224	−0.0719639
$929$	−29.1366	−0.955941	−0.477971	−	0.878376i	$-0.658627\pi$
$929$	−29.1366	−0.955941	−0.477971	+	0.878376i	$0.658627\pi$
$930$	−8.02884	−0.263276
$931$	20.6454	0.676625
$932$	−27.2153	−0.891468
$933$	−4.73961	−0.155168
$934$	87.3450	2.85801
$935$	−13.0016	−0.425198
$936$	−18.1457	−0.593112
$937$	29.6693	0.969254	0.484627	−	0.874721i	$-0.338955\pi$
$937$	29.6693	0.969254	0.484627	+	0.874721i	$0.338955\pi$
$938$	−65.7097	−2.14550
$939$	7.38970	0.241154
$940$	−28.0549	−0.915050
$941$	2.69421	0.0878287	0.0439143	−	0.999035i	$-0.486017\pi$
$941$	2.69421	0.0878287	0.0439143	+	0.999035i	$0.486017\pi$
$942$	−3.44139	−0.112127
$943$	−4.91287	−0.159985
$944$	136.307	4.43643
$945$	−9.18682	−0.298847
$946$	−120.050	−3.90316
$947$	59.0079	1.91750	0.958750	−	0.284251i	$-0.0917450\pi$
$947$	59.0079	1.91750	0.958750	+	0.284251i	$0.0917450\pi$
$948$	116.717	3.79081
$949$	−5.33907	−0.173313
$950$	13.4924	0.437752
$951$	63.7044	2.06576
$952$	48.7182	1.57896
$953$	51.0711	1.65435	0.827177	−	0.561942i	$-0.189945\pi$
$953$	51.0711	1.65435	0.827177	+	0.561942i	$0.189945\pi$
$954$	67.6500	2.19025
$955$	−23.7034	−0.767024
$956$	153.562	4.96655
$957$	−1.36007	−0.0439647
$958$	102.243	3.30331
$959$	1.48839	0.0480625
$960$	62.9221	2.03080
$961$	−29.8818	−0.963930
$962$	2.14056	0.0690144
$963$	87.3682	2.81540
$964$	118.738	3.82428
$965$	7.66345	0.246695
$966$	−116.583	−3.75101
$967$	−11.6582	−0.374901	−0.187450	−	0.982274i	$-0.560022\pi$
$967$	−11.6582	−0.374901	−0.187450	+	0.982274i	$0.560022\pi$
$968$	−43.7846	−1.40729
$969$	45.8362	1.47247
$970$	−13.0394	−0.418670
$971$	16.4634	0.528335	0.264168	−	0.964477i	$-0.414903\pi$
$971$	16.4634	0.528335	0.264168	+	0.964477i	$0.414903\pi$
$972$	78.5971	2.52100
$973$	−7.54360	−0.241837
$974$	69.7446	2.23476
$975$	−1.17447	−0.0376131
$976$	145.153	4.64624
$977$	33.0541	1.05749	0.528747	−	0.848780i	$-0.322662\pi$
$977$	33.0541	1.05749	0.528747	+	0.848780i	$0.322662\pi$
$978$	168.276	5.38088
$979$	−30.8466	−0.985861
$980$	21.7667	0.695310
$981$	63.9444	2.04159
$982$	13.4402	0.428895
$983$	16.3957	0.522941	0.261471	−	0.965211i	$-0.415793\pi$
$983$	16.3957	0.522941	0.261471	+	0.965211i	$0.415793\pi$
$984$	−13.4831	−0.429825
$985$	−1.58986	−0.0506570
$986$	−1.06161	−0.0338086
$987$	25.3819	0.807914
$988$	−11.0076	−0.350199
$989$	100.935	3.20953
$990$	53.0656	1.68653
$991$	0.576931	0.0183268	0.00916341	−	0.999958i	$-0.497083\pi$
$991$	0.576931	0.0183268	0.00916341	+	0.999958i	$0.497083\pi$
$992$	−19.1680	−0.608584
$993$	−55.3977	−1.75799
$994$	−52.2975	−1.65877
$995$	−9.58357	−0.303820
$996$	−27.9233	−0.884784
$997$	−59.4299	−1.88216	−0.941082	−	0.338180i	$-0.890189\pi$
$997$	−59.4299	−1.88216	−0.941082	+	0.338180i	$0.890189\pi$
$998$	−46.0265	−1.45694
$999$	10.3107	0.326217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.f.1.1	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.f.1.1	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69709 q^{2} -2.81518 q^{3} +5.27428 q^{4} -1.00000 q^{5} +7.59279 q^{6} -1.69501 q^{7} -8.83103 q^{8} +4.92525 q^{9} +O(q^{10})\)	\(q-2.69709 q^{2} -2.81518 q^{3} +5.27428 q^{4} -1.00000 q^{5} +7.59279 q^{6} -1.69501 q^{7} -8.83103 q^{8} +4.92525 q^{9} +2.69709 q^{10} +3.99475 q^{11} -14.8481 q^{12} +0.417191 q^{13} +4.57159 q^{14} +2.81518 q^{15} +13.2695 q^{16} +3.25467 q^{17} -13.2838 q^{18} -5.00259 q^{19} -5.27428 q^{20} +4.77176 q^{21} -10.7742 q^{22} +9.05864 q^{23} +24.8610 q^{24} +1.00000 q^{25} -1.12520 q^{26} -5.41992 q^{27} -8.93997 q^{28} +0.120938 q^{29} -7.59279 q^{30} +1.05743 q^{31} -18.1270 q^{32} -11.2459 q^{33} -8.77813 q^{34} +1.69501 q^{35} +25.9772 q^{36} -1.90238 q^{37} +13.4924 q^{38} -1.17447 q^{39} +8.83103 q^{40} -0.542340 q^{41} -12.8699 q^{42} +11.1424 q^{43} +21.0695 q^{44} -4.92525 q^{45} -24.4320 q^{46} +5.31919 q^{47} -37.3561 q^{48} -4.12694 q^{49} -2.69709 q^{50} -9.16249 q^{51} +2.20039 q^{52} -5.09266 q^{53} +14.6180 q^{54} -3.99475 q^{55} +14.9687 q^{56} +14.0832 q^{57} -0.326181 q^{58} +10.2722 q^{59} +14.8481 q^{60} +10.9389 q^{61} -2.85198 q^{62} -8.34834 q^{63} +22.3510 q^{64} -0.417191 q^{65} +30.3313 q^{66} -14.3735 q^{67} +17.1661 q^{68} -25.5017 q^{69} -4.57159 q^{70} -11.4397 q^{71} -43.4950 q^{72} -12.7976 q^{73} +5.13088 q^{74} -2.81518 q^{75} -26.3851 q^{76} -6.77114 q^{77} +3.16765 q^{78} -7.86078 q^{79} -13.2695 q^{80} +0.482318 q^{81} +1.46274 q^{82} +1.88060 q^{83} +25.1676 q^{84} -3.25467 q^{85} -30.0519 q^{86} -0.340463 q^{87} -35.2778 q^{88} -7.72178 q^{89} +13.2838 q^{90} -0.707144 q^{91} +47.7779 q^{92} -2.97686 q^{93} -14.3463 q^{94} +5.00259 q^{95} +51.0307 q^{96} -4.83462 q^{97} +11.1307 q^{98} +19.6751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

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