LMFDB - Embedded newform 4010.2.a.l.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.51896$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.51896 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51896 q^{6} +1.25913 q^{7} -1.00000 q^{8} -0.692760 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.51896 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51896 q^{6} +1.25913 q^{7} -1.00000 q^{8} -0.692760 q^{9} +1.00000 q^{10} -4.69102 q^{11} +1.51896 q^{12} +3.82177 q^{13} -1.25913 q^{14} -1.51896 q^{15} +1.00000 q^{16} -0.345292 q^{17} +0.692760 q^{18} +5.84430 q^{19} -1.00000 q^{20} +1.91258 q^{21} +4.69102 q^{22} +4.93160 q^{23} -1.51896 q^{24} +1.00000 q^{25} -3.82177 q^{26} -5.60916 q^{27} +1.25913 q^{28} +7.80731 q^{29} +1.51896 q^{30} -1.46743 q^{31} -1.00000 q^{32} -7.12548 q^{33} +0.345292 q^{34} -1.25913 q^{35} -0.692760 q^{36} +0.209085 q^{37} -5.84430 q^{38} +5.80511 q^{39} +1.00000 q^{40} -0.370194 q^{41} -1.91258 q^{42} -8.41418 q^{43} -4.69102 q^{44} +0.692760 q^{45} -4.93160 q^{46} +4.61677 q^{47} +1.51896 q^{48} -5.41458 q^{49} -1.00000 q^{50} -0.524485 q^{51} +3.82177 q^{52} -10.3472 q^{53} +5.60916 q^{54} +4.69102 q^{55} -1.25913 q^{56} +8.87726 q^{57} -7.80731 q^{58} +0.967177 q^{59} -1.51896 q^{60} +6.90282 q^{61} +1.46743 q^{62} -0.872278 q^{63} +1.00000 q^{64} -3.82177 q^{65} +7.12548 q^{66} -10.0442 q^{67} -0.345292 q^{68} +7.49091 q^{69} +1.25913 q^{70} +6.14803 q^{71} +0.692760 q^{72} +6.53058 q^{73} -0.209085 q^{74} +1.51896 q^{75} +5.84430 q^{76} -5.90663 q^{77} -5.80511 q^{78} +15.3956 q^{79} -1.00000 q^{80} -6.44180 q^{81} +0.370194 q^{82} +7.49903 q^{83} +1.91258 q^{84} +0.345292 q^{85} +8.41418 q^{86} +11.8590 q^{87} +4.69102 q^{88} -12.6239 q^{89} -0.692760 q^{90} +4.81212 q^{91} +4.93160 q^{92} -2.22897 q^{93} -4.61677 q^{94} -5.84430 q^{95} -1.51896 q^{96} +17.7870 q^{97} +5.41458 q^{98} +3.24975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.51896	0.876972	0.438486	−	0.898738i	$-0.355515\pi$
$3$	1.51896	0.876972	0.438486	+	0.898738i	$0.355515\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.51896	−0.620113
$7$	1.25913	0.475908	0.237954	−	0.971276i	$-0.423523\pi$
$7$	1.25913	0.475908	0.237954	+	0.971276i	$0.423523\pi$
$8$	−1.00000	−0.353553
$9$	−0.692760	−0.230920
$10$	1.00000	0.316228
$11$	−4.69102	−1.41440	−0.707199	−	0.707015i	$-0.750041\pi$
$11$	−4.69102	−1.41440	−0.707199	+	0.707015i	$0.750041\pi$
$12$	1.51896	0.438486
$13$	3.82177	1.05997	0.529984	−	0.848008i	$-0.322198\pi$
$13$	3.82177	1.05997	0.529984	+	0.848008i	$0.322198\pi$
$14$	−1.25913	−0.336518
$15$	−1.51896	−0.392194
$16$	1.00000	0.250000
$17$	−0.345292	−0.0837457	−0.0418729	−	0.999123i	$-0.513332\pi$
$17$	−0.345292	−0.0837457	−0.0418729	+	0.999123i	$0.513332\pi$
$18$	0.692760	0.163285
$19$	5.84430	1.34077	0.670387	−	0.742012i	$-0.266128\pi$
$19$	5.84430	1.34077	0.670387	+	0.742012i	$0.266128\pi$
$20$	−1.00000	−0.223607
$21$	1.91258	0.417358
$22$	4.69102	1.00013
$23$	4.93160	1.02831	0.514155	−	0.857697i	$-0.328106\pi$
$23$	4.93160	1.02831	0.514155	+	0.857697i	$0.328106\pi$
$24$	−1.51896	−0.310056
$25$	1.00000	0.200000
$26$	−3.82177	−0.749510
$27$	−5.60916	−1.07948
$28$	1.25913	0.237954
$29$	7.80731	1.44978	0.724890	−	0.688864i	$-0.241890\pi$
$29$	7.80731	1.44978	0.724890	+	0.688864i	$0.241890\pi$
$30$	1.51896	0.277323
$31$	−1.46743	−0.263558	−0.131779	−	0.991279i	$-0.542069\pi$
$31$	−1.46743	−0.263558	−0.131779	+	0.991279i	$0.542069\pi$
$32$	−1.00000	−0.176777
$33$	−7.12548	−1.24039
$34$	0.345292	0.0592172
$35$	−1.25913	−0.212833
$36$	−0.692760	−0.115460
$37$	0.209085	0.0343734	0.0171867	−	0.999852i	$-0.494529\pi$
$37$	0.209085	0.0343734	0.0171867	+	0.999852i	$0.494529\pi$
$38$	−5.84430	−0.948070
$39$	5.80511	0.929562
$40$	1.00000	0.158114
$41$	−0.370194	−0.0578147	−0.0289073	−	0.999582i	$-0.509203\pi$
$41$	−0.370194	−0.0578147	−0.0289073	+	0.999582i	$0.509203\pi$
$42$	−1.91258	−0.295117
$43$	−8.41418	−1.28315	−0.641576	−	0.767060i	$-0.721719\pi$
$43$	−8.41418	−1.28315	−0.641576	+	0.767060i	$0.721719\pi$
$44$	−4.69102	−0.707199
$45$	0.692760	0.103271
$46$	−4.93160	−0.727125
$47$	4.61677	0.673425	0.336713	−	0.941607i	$-0.390685\pi$
$47$	4.61677	0.673425	0.336713	+	0.941607i	$0.390685\pi$
$48$	1.51896	0.219243
$49$	−5.41458	−0.773511
$50$	−1.00000	−0.141421
$51$	−0.524485	−0.0734426
$52$	3.82177	0.529984
$53$	−10.3472	−1.42130	−0.710652	−	0.703544i	$-0.751600\pi$
$53$	−10.3472	−1.42130	−0.710652	+	0.703544i	$0.751600\pi$
$54$	5.60916	0.763309
$55$	4.69102	0.632538
$56$	−1.25913	−0.168259
$57$	8.87726	1.17582
$58$	−7.80731	−1.02515
$59$	0.967177	0.125916	0.0629579	−	0.998016i	$-0.479947\pi$
$59$	0.967177	0.125916	0.0629579	+	0.998016i	$0.479947\pi$
$60$	−1.51896	−0.196097
$61$	6.90282	0.883815	0.441908	−	0.897061i	$-0.354302\pi$
$61$	6.90282	0.883815	0.441908	+	0.897061i	$0.354302\pi$
$62$	1.46743	0.186364
$63$	−0.872278	−0.109897
$64$	1.00000	0.125000
$65$	−3.82177	−0.474032
$66$	7.12548	0.877086
$67$	−10.0442	−1.22709	−0.613546	−	0.789659i	$-0.710257\pi$
$67$	−10.0442	−1.22709	−0.613546	+	0.789659i	$0.710257\pi$
$68$	−0.345292	−0.0418729
$69$	7.49091	0.901799
$70$	1.25913	0.150495
$71$	6.14803	0.729637	0.364819	−	0.931079i	$-0.381131\pi$
$71$	6.14803	0.729637	0.364819	+	0.931079i	$0.381131\pi$
$72$	0.692760	0.0816425
$73$	6.53058	0.764347	0.382174	−	0.924091i	$-0.375176\pi$
$73$	6.53058	0.764347	0.382174	+	0.924091i	$0.375176\pi$
$74$	−0.209085	−0.0243057
$75$	1.51896	0.175394
$76$	5.84430	0.670387
$77$	−5.90663	−0.673123
$78$	−5.80511	−0.657300
$79$	15.3956	1.73214	0.866071	−	0.499922i	$-0.166638\pi$
$79$	15.3956	1.73214	0.866071	+	0.499922i	$0.166638\pi$
$80$	−1.00000	−0.111803
$81$	−6.44180	−0.715756
$82$	0.370194	0.0408811
$83$	7.49903	0.823126	0.411563	−	0.911381i	$-0.364983\pi$
$83$	7.49903	0.823126	0.411563	+	0.911381i	$0.364983\pi$
$84$	1.91258	0.208679
$85$	0.345292	0.0374522
$86$	8.41418	0.907325
$87$	11.8590	1.27142
$88$	4.69102	0.500065
$89$	−12.6239	−1.33813	−0.669066	−	0.743203i	$-0.733306\pi$
$89$	−12.6239	−1.33813	−0.669066	+	0.743203i	$0.733306\pi$
$90$	−0.692760	−0.0730233
$91$	4.81212	0.504447
$92$	4.93160	0.514155
$93$	−2.22897	−0.231133
$94$	−4.61677	−0.476183
$95$	−5.84430	−0.599612
$96$	−1.51896	−0.155028
$97$	17.7870	1.80600	0.902998	−	0.429644i	$-0.141361\pi$
$97$	17.7870	1.80600	0.902998	+	0.429644i	$0.141361\pi$
$98$	5.41458	0.546955
$99$	3.24975	0.326613
$100$	1.00000	0.100000
$101$	−2.12324	−0.211270	−0.105635	−	0.994405i	$-0.533688\pi$
$101$	−2.12324	−0.211270	−0.105635	+	0.994405i	$0.533688\pi$
$102$	0.524485	0.0519318
$103$	6.53211	0.643627	0.321814	−	0.946803i	$-0.395708\pi$
$103$	6.53211	0.643627	0.321814	+	0.946803i	$0.395708\pi$
$104$	−3.82177	−0.374755
$105$	−1.91258	−0.186648
$106$	10.3472	1.00501
$107$	6.16612	0.596101	0.298050	−	0.954550i	$-0.403664\pi$
$107$	6.16612	0.596101	0.298050	+	0.954550i	$0.403664\pi$
$108$	−5.60916	−0.539741
$109$	18.4925	1.77126	0.885631	−	0.464389i	$-0.153726\pi$
$109$	18.4925	1.77126	0.885631	+	0.464389i	$0.153726\pi$
$110$	−4.69102	−0.447272
$111$	0.317593	0.0301445
$112$	1.25913	0.118977
$113$	−2.64275	−0.248609	−0.124304	−	0.992244i	$-0.539670\pi$
$113$	−2.64275	−0.248609	−0.124304	+	0.992244i	$0.539670\pi$
$114$	−8.87726	−0.831431
$115$	−4.93160	−0.459874
$116$	7.80731	0.724890
$117$	−2.64757	−0.244768
$118$	−0.967177	−0.0890359
$119$	−0.434770	−0.0398553
$120$	1.51896	0.138661
$121$	11.0057	1.00052
$122$	−6.90282	−0.624952
$123$	−0.562311	−0.0507018
$124$	−1.46743	−0.131779
$125$	−1.00000	−0.0894427
$126$	0.872278	0.0777087
$127$	13.2289	1.17387	0.586937	−	0.809633i	$-0.300334\pi$
$127$	13.2289	1.17387	0.586937	+	0.809633i	$0.300334\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7808	−1.12529
$130$	3.82177	0.335191
$131$	16.9310	1.47926	0.739632	−	0.673011i	$-0.234999\pi$
$131$	16.9310	1.47926	0.739632	+	0.673011i	$0.234999\pi$
$132$	−7.12548	−0.620193
$133$	7.35876	0.638085
$134$	10.0442	0.867684
$135$	5.60916	0.482759
$136$	0.345292	0.0296086
$137$	−18.1747	−1.55277	−0.776385	−	0.630258i	$-0.782949\pi$
$137$	−18.1747	−1.55277	−0.776385	+	0.630258i	$0.782949\pi$
$138$	−7.49091	−0.637668
$139$	9.93501	0.842676	0.421338	−	0.906904i	$-0.361561\pi$
$139$	9.93501	0.842676	0.421338	+	0.906904i	$0.361561\pi$
$140$	−1.25913	−0.106416
$141$	7.01269	0.590575
$142$	−6.14803	−0.515931
$143$	−17.9280	−1.49922
$144$	−0.692760	−0.0577300
$145$	−7.80731	−0.648362
$146$	−6.53058	−0.540475
$147$	−8.22453	−0.678348
$148$	0.209085	0.0171867
$149$	18.6558	1.52834	0.764169	−	0.645016i	$-0.223149\pi$
$149$	18.6558	1.52834	0.764169	+	0.645016i	$0.223149\pi$
$150$	−1.51896	−0.124023
$151$	−12.7211	−1.03523	−0.517616	−	0.855613i	$-0.673180\pi$
$151$	−12.7211	−1.03523	−0.517616	+	0.855613i	$0.673180\pi$
$152$	−5.84430	−0.474035
$153$	0.239205	0.0193386
$154$	5.90663	0.475970
$155$	1.46743	0.117867
$156$	5.80511	0.464781
$157$	18.8540	1.50471	0.752357	−	0.658756i	$-0.228917\pi$
$157$	18.8540	1.50471	0.752357	+	0.658756i	$0.228917\pi$
$158$	−15.3956	−1.22481
$159$	−15.7171	−1.24644
$160$	1.00000	0.0790569
$161$	6.20955	0.489381
$162$	6.44180	0.506116
$163$	4.84629	0.379591	0.189796	−	0.981824i	$-0.439217\pi$
$163$	4.84629	0.379591	0.189796	+	0.981824i	$0.439217\pi$
$164$	−0.370194	−0.0289073
$165$	7.12548	0.554718
$166$	−7.49903	−0.582038
$167$	1.99947	0.154724	0.0773618	−	0.997003i	$-0.475350\pi$
$167$	1.99947	0.154724	0.0773618	+	0.997003i	$0.475350\pi$
$168$	−1.91258	−0.147558
$169$	1.60591	0.123532
$170$	−0.345292	−0.0264827
$171$	−4.04870	−0.309612
$172$	−8.41418	−0.641576
$173$	−1.57471	−0.119723	−0.0598615	−	0.998207i	$-0.519066\pi$
$173$	−1.57471	−0.119723	−0.0598615	+	0.998207i	$0.519066\pi$
$174$	−11.8590	−0.899028
$175$	1.25913	0.0951816
$176$	−4.69102	−0.353599
$177$	1.46910	0.110425
$178$	12.6239	0.946203
$179$	11.3895	0.851293	0.425646	−	0.904890i	$-0.360047\pi$
$179$	11.3895	0.851293	0.425646	+	0.904890i	$0.360047\pi$
$180$	0.692760	0.0516353
$181$	10.2341	0.760698	0.380349	−	0.924843i	$-0.375804\pi$
$181$	10.2341	0.760698	0.380349	+	0.924843i	$0.375804\pi$
$182$	−4.81212	−0.356698
$183$	10.4851	0.775081
$184$	−4.93160	−0.363562
$185$	−0.209085	−0.0153723
$186$	2.22897	0.163436
$187$	1.61978	0.118450
$188$	4.61677	0.336713
$189$	−7.06268	−0.513734
$190$	5.84430	0.423990
$191$	−18.9442	−1.37076	−0.685378	−	0.728187i	$-0.740363\pi$
$191$	−18.9442	−1.37076	−0.685378	+	0.728187i	$0.740363\pi$
$192$	1.51896	0.109622
$193$	16.0099	1.15242	0.576210	−	0.817301i	$-0.304531\pi$
$193$	16.0099	1.15242	0.576210	+	0.817301i	$0.304531\pi$
$194$	−17.7870	−1.27703
$195$	−5.80511	−0.415713
$196$	−5.41458	−0.386756
$197$	15.0976	1.07566	0.537831	−	0.843052i	$-0.319244\pi$
$197$	15.0976	1.07566	0.537831	+	0.843052i	$0.319244\pi$
$198$	−3.24975	−0.230950
$199$	−0.411731	−0.0291868	−0.0145934	−	0.999894i	$-0.504645\pi$
$199$	−0.411731	−0.0291868	−0.0145934	+	0.999894i	$0.504645\pi$
$200$	−1.00000	−0.0707107
$201$	−15.2567	−1.07612
$202$	2.12324	0.149391
$203$	9.83045	0.689962
$204$	−0.524485	−0.0367213
$205$	0.370194	0.0258555
$206$	−6.53211	−0.455113
$207$	−3.41642	−0.237457
$208$	3.82177	0.264992
$209$	−27.4158	−1.89639
$210$	1.91258	0.131980
$211$	−8.39733	−0.578096	−0.289048	−	0.957315i	$-0.593339\pi$
$211$	−8.39733	−0.578096	−0.289048	+	0.957315i	$0.593339\pi$
$212$	−10.3472	−0.710652
$213$	9.33862	0.639872
$214$	−6.16612	−0.421507
$215$	8.41418	0.573843
$216$	5.60916	0.381655
$217$	−1.84769	−0.125430
$218$	−18.4925	−1.25247
$219$	9.91970	0.670311
$220$	4.69102	0.316269
$221$	−1.31963	−0.0887678
$222$	−0.317593	−0.0213154
$223$	22.6910	1.51950	0.759751	−	0.650214i	$-0.225321\pi$
$223$	22.6910	1.51950	0.759751	+	0.650214i	$0.225321\pi$
$224$	−1.25913	−0.0841295
$225$	−0.692760	−0.0461840
$226$	2.64275	0.175793
$227$	3.38241	0.224499	0.112249	−	0.993680i	$-0.464194\pi$
$227$	3.38241	0.224499	0.112249	+	0.993680i	$0.464194\pi$
$228$	8.87726	0.587911
$229$	6.73268	0.444908	0.222454	−	0.974943i	$-0.428593\pi$
$229$	6.73268	0.444908	0.222454	+	0.974943i	$0.428593\pi$
$230$	4.93160	0.325180
$231$	−8.97194	−0.590310
$232$	−7.80731	−0.512575
$233$	−2.37660	−0.155696	−0.0778480	−	0.996965i	$-0.524805\pi$
$233$	−2.37660	−0.155696	−0.0778480	+	0.996965i	$0.524805\pi$
$234$	2.64757	0.173077
$235$	−4.61677	−0.301165
$236$	0.967177	0.0629579
$237$	23.3853	1.51904
$238$	0.434770	0.0281819
$239$	−17.0416	−1.10233	−0.551166	−	0.834395i	$-0.685817\pi$
$239$	−17.0416	−1.10233	−0.551166	+	0.834395i	$0.685817\pi$
$240$	−1.51896	−0.0980485
$241$	20.5102	1.32118	0.660588	−	0.750749i	$-0.270307\pi$
$241$	20.5102	1.32118	0.660588	+	0.750749i	$0.270307\pi$
$242$	−11.0057	−0.707474
$243$	7.04262	0.451784
$244$	6.90282	0.441908
$245$	5.41458	0.345925
$246$	0.562311	0.0358516
$247$	22.3356	1.42118
$248$	1.46743	0.0931819
$249$	11.3907	0.721858
$250$	1.00000	0.0632456
$251$	−29.8922	−1.88678	−0.943388	−	0.331691i	$-0.892381\pi$
$251$	−29.8922	−1.88678	−0.943388	+	0.331691i	$0.892381\pi$
$252$	−0.872278	−0.0549483
$253$	−23.1343	−1.45444
$254$	−13.2289	−0.830054
$255$	0.524485	0.0328446
$256$	1.00000	0.0625000
$257$	11.2873	0.704085	0.352043	−	0.935984i	$-0.385487\pi$
$257$	11.2873	0.704085	0.352043	+	0.935984i	$0.385487\pi$
$258$	12.7808	0.795699
$259$	0.263267	0.0163586
$260$	−3.82177	−0.237016
$261$	−5.40859	−0.334783
$262$	−16.9310	−1.04600
$263$	11.6872	0.720666	0.360333	−	0.932824i	$-0.382663\pi$
$263$	11.6872	0.720666	0.360333	+	0.932824i	$0.382663\pi$
$264$	7.12548	0.438543
$265$	10.3472	0.635626
$266$	−7.35876	−0.451194
$267$	−19.1752	−1.17350
$268$	−10.0442	−0.613546
$269$	−20.6427	−1.25861	−0.629304	−	0.777159i	$-0.716660\pi$
$269$	−20.6427	−1.25861	−0.629304	+	0.777159i	$0.716660\pi$
$270$	−5.60916	−0.341362
$271$	25.0690	1.52283	0.761417	−	0.648263i	$-0.224504\pi$
$271$	25.0690	1.52283	0.761417	+	0.648263i	$0.224504\pi$
$272$	−0.345292	−0.0209364
$273$	7.30942	0.442386
$274$	18.1747	1.09797
$275$	−4.69102	−0.282879
$276$	7.49091	0.450900
$277$	−9.90362	−0.595051	−0.297526	−	0.954714i	$-0.596161\pi$
$277$	−9.90362	−0.595051	−0.297526	+	0.954714i	$0.596161\pi$
$278$	−9.93501	−0.595862
$279$	1.01658	0.0608609
$280$	1.25913	0.0752477
$281$	−24.0812	−1.43656	−0.718281	−	0.695753i	$-0.755071\pi$
$281$	−24.0812	−1.43656	−0.718281	+	0.695753i	$0.755071\pi$
$282$	−7.01269	−0.417600
$283$	−12.2596	−0.728758	−0.364379	−	0.931251i	$-0.618719\pi$
$283$	−12.2596	−0.728758	−0.364379	+	0.931251i	$0.618719\pi$
$284$	6.14803	0.364819
$285$	−8.87726	−0.525843
$286$	17.9280	1.06011
$287$	−0.466125	−0.0275145
$288$	0.692760	0.0408213
$289$	−16.8808	−0.992987
$290$	7.80731	0.458461
$291$	27.0178	1.58381
$292$	6.53058	0.382174
$293$	16.9317	0.989161	0.494580	−	0.869132i	$-0.335322\pi$
$293$	16.9317	0.989161	0.494580	+	0.869132i	$0.335322\pi$
$294$	8.22453	0.479664
$295$	−0.967177	−0.0563112
$296$	−0.209085	−0.0121528
$297$	26.3127	1.52682
$298$	−18.6558	−1.08070
$299$	18.8474	1.08998
$300$	1.51896	0.0876972
$301$	−10.5946	−0.610662
$302$	12.7211	0.732020
$303$	−3.22511	−0.185278
$304$	5.84430	0.335194
$305$	−6.90282	−0.395254
$306$	−0.239205	−0.0136744
$307$	−28.2098	−1.61002	−0.805009	−	0.593263i	$-0.797839\pi$
$307$	−28.2098	−1.61002	−0.805009	+	0.593263i	$0.797839\pi$
$308$	−5.90663	−0.336562
$309$	9.92201	0.564443
$310$	−1.46743	−0.0833444
$311$	8.53611	0.484038	0.242019	−	0.970271i	$-0.422190\pi$
$311$	8.53611	0.484038	0.242019	+	0.970271i	$0.422190\pi$
$312$	−5.80511	−0.328650
$313$	8.25032	0.466335	0.233168	−	0.972437i	$-0.425091\pi$
$313$	8.25032	0.466335	0.233168	+	0.972437i	$0.425091\pi$
$314$	−18.8540	−1.06399
$315$	0.872278	0.0491473
$316$	15.3956	0.866071
$317$	24.7740	1.39145	0.695723	−	0.718310i	$-0.255084\pi$
$317$	24.7740	1.39145	0.695723	+	0.718310i	$0.255084\pi$
$318$	15.7171	0.881369
$319$	−36.6243	−2.05057
$320$	−1.00000	−0.0559017
$321$	9.36608	0.522764
$322$	−6.20955	−0.346045
$323$	−2.01799	−0.112284
$324$	−6.44180	−0.357878
$325$	3.82177	0.211994
$326$	−4.84629	−0.268411
$327$	28.0894	1.55335
$328$	0.370194	0.0204406
$329$	5.81314	0.320489
$330$	−7.12548	−0.392245
$331$	8.41271	0.462405	0.231202	−	0.972906i	$-0.425734\pi$
$331$	8.41271	0.462405	0.231202	+	0.972906i	$0.425734\pi$
$332$	7.49903	0.411563
$333$	−0.144846	−0.00793751
$334$	−1.99947	−0.109406
$335$	10.0442	0.548772
$336$	1.91258	0.104340
$337$	−19.9410	−1.08626	−0.543128	−	0.839650i	$-0.682760\pi$
$337$	−19.9410	−1.08626	−0.543128	+	0.839650i	$0.682760\pi$
$338$	−1.60591	−0.0873502
$339$	−4.01423	−0.218023
$340$	0.345292	0.0187261
$341$	6.88375	0.372776
$342$	4.04870	0.218928
$343$	−15.6316	−0.844029
$344$	8.41418	0.453662
$345$	−7.49091	−0.403297
$346$	1.57471	0.0846569
$347$	17.6036	0.945013	0.472506	−	0.881327i	$-0.343349\pi$
$347$	17.6036	0.945013	0.472506	+	0.881327i	$0.343349\pi$
$348$	11.8590	0.635709
$349$	−23.8660	−1.27752	−0.638759	−	0.769407i	$-0.720552\pi$
$349$	−23.8660	−1.27752	−0.638759	+	0.769407i	$0.720552\pi$
$350$	−1.25913	−0.0673036
$351$	−21.4369	−1.14422
$352$	4.69102	0.250032
$353$	−16.2405	−0.864396	−0.432198	−	0.901779i	$-0.642262\pi$
$353$	−16.2405	−0.864396	−0.432198	+	0.901779i	$0.642262\pi$
$354$	−1.46910	−0.0780820
$355$	−6.14803	−0.326304
$356$	−12.6239	−0.669066
$357$	−0.660398	−0.0349520
$358$	−11.3895	−0.601955
$359$	27.8019	1.46733	0.733665	−	0.679511i	$-0.237808\pi$
$359$	27.8019	1.46733	0.733665	+	0.679511i	$0.237808\pi$
$360$	−0.692760	−0.0365117
$361$	15.1558	0.797675
$362$	−10.2341	−0.537895
$363$	16.7172	0.877428
$364$	4.81212	0.252224
$365$	−6.53058	−0.341826
$366$	−10.4851	−0.548065
$367$	31.2201	1.62967	0.814837	−	0.579689i	$-0.196826\pi$
$367$	31.2201	1.62967	0.814837	+	0.579689i	$0.196826\pi$
$368$	4.93160	0.257077
$369$	0.256456	0.0133506
$370$	0.209085	0.0108698
$371$	−13.0286	−0.676410
$372$	−2.22897	−0.115567
$373$	−28.7982	−1.49111	−0.745557	−	0.666442i	$-0.767816\pi$
$373$	−28.7982	−1.49111	−0.745557	+	0.666442i	$0.767816\pi$
$374$	−1.61978	−0.0837566
$375$	−1.51896	−0.0784388
$376$	−4.61677	−0.238092
$377$	29.8377	1.53672
$378$	7.06268	0.363265
$379$	−8.06997	−0.414527	−0.207263	−	0.978285i	$-0.566456\pi$
$379$	−8.06997	−0.414527	−0.207263	+	0.978285i	$0.566456\pi$
$380$	−5.84430	−0.299806
$381$	20.0942	1.02945
$382$	18.9442	0.969271
$383$	−18.5721	−0.948989	−0.474494	−	0.880258i	$-0.657369\pi$
$383$	−18.5721	−0.948989	−0.474494	+	0.880258i	$0.657369\pi$
$384$	−1.51896	−0.0775141
$385$	5.90663	0.301030
$386$	−16.0099	−0.814885
$387$	5.82901	0.296305
$388$	17.7870	0.902998
$389$	−29.2175	−1.48138	−0.740692	−	0.671844i	$-0.765502\pi$
$389$	−29.2175	−1.48138	−0.740692	+	0.671844i	$0.765502\pi$
$390$	5.80511	0.293953
$391$	−1.70284	−0.0861165
$392$	5.41458	0.273478
$393$	25.7175	1.29727
$394$	−15.0976	−0.760609
$395$	−15.3956	−0.774637
$396$	3.24975	0.163306
$397$	−5.06991	−0.254452	−0.127226	−	0.991874i	$-0.540607\pi$
$397$	−5.06991	−0.254452	−0.127226	+	0.991874i	$0.540607\pi$
$398$	0.411731	0.0206382
$399$	11.1777	0.559583
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	15.2567	0.760935
$403$	−5.60818	−0.279363
$404$	−2.12324	−0.105635
$405$	6.44180	0.320096
$406$	−9.83045	−0.487877
$407$	−0.980825	−0.0486177
$408$	0.524485	0.0259659
$409$	−20.1684	−0.997262	−0.498631	−	0.866814i	$-0.666164\pi$
$409$	−20.1684	−0.997262	−0.498631	+	0.866814i	$0.666164\pi$
$410$	−0.370194	−0.0182826
$411$	−27.6067	−1.36174
$412$	6.53211	0.321814
$413$	1.21781	0.0599243
$414$	3.41642	0.167908
$415$	−7.49903	−0.368113
$416$	−3.82177	−0.187378
$417$	15.0909	0.739004
$418$	27.4158	1.34095
$419$	−18.9327	−0.924923	−0.462462	−	0.886639i	$-0.653034\pi$
$419$	−18.9327	−0.924923	−0.462462	+	0.886639i	$0.653034\pi$
$420$	−1.91258	−0.0933241
$421$	−2.97184	−0.144838	−0.0724192	−	0.997374i	$-0.523072\pi$
$421$	−2.97184	−0.144838	−0.0724192	+	0.997374i	$0.523072\pi$
$422$	8.39733	0.408775
$423$	−3.19831	−0.155507
$424$	10.3472	0.502507
$425$	−0.345292	−0.0167491
$426$	−9.33862	−0.452458
$427$	8.69158	0.420615
$428$	6.16612	0.298050
$429$	−27.2319	−1.31477
$430$	−8.41418	−0.405768
$431$	18.0029	0.867168	0.433584	−	0.901113i	$-0.357249\pi$
$431$	18.0029	0.867168	0.433584	+	0.901113i	$0.357249\pi$
$432$	−5.60916	−0.269871
$433$	4.35510	0.209293	0.104646	−	0.994510i	$-0.466629\pi$
$433$	4.35510	0.209293	0.104646	+	0.994510i	$0.466629\pi$
$434$	1.84769	0.0886921
$435$	−11.8590	−0.568595
$436$	18.4925	0.885631
$437$	28.8218	1.37873
$438$	−9.91970	−0.473982
$439$	−22.2495	−1.06191	−0.530954	−	0.847400i	$-0.678166\pi$
$439$	−22.2495	−1.06191	−0.530954	+	0.847400i	$0.678166\pi$
$440$	−4.69102	−0.223636
$441$	3.75100	0.178619
$442$	1.31963	0.0627683
$443$	−22.9055	−1.08827	−0.544137	−	0.838996i	$-0.683143\pi$
$443$	−22.9055	−1.08827	−0.544137	+	0.838996i	$0.683143\pi$
$444$	0.317593	0.0150723
$445$	12.6239	0.598431
$446$	−22.6910	−1.07445
$447$	28.3373	1.34031
$448$	1.25913	0.0594885
$449$	−31.5363	−1.48829	−0.744146	−	0.668017i	$-0.767143\pi$
$449$	−31.5363	−1.48829	−0.744146	+	0.668017i	$0.767143\pi$
$450$	0.692760	0.0326570
$451$	1.73659	0.0817729
$452$	−2.64275	−0.124304
$453$	−19.3229	−0.907870
$454$	−3.38241	−0.158744
$455$	−4.81212	−0.225596
$456$	−8.87726	−0.415716
$457$	39.3675	1.84153	0.920766	−	0.390115i	$-0.127565\pi$
$457$	39.3675	1.84153	0.920766	+	0.390115i	$0.127565\pi$
$458$	−6.73268	−0.314597
$459$	1.93680	0.0904020
$460$	−4.93160	−0.229937
$461$	33.8004	1.57424	0.787120	−	0.616800i	$-0.211571\pi$
$461$	33.8004	1.57424	0.787120	+	0.616800i	$0.211571\pi$
$462$	8.97194	0.417412
$463$	−8.52464	−0.396173	−0.198087	−	0.980185i	$-0.563473\pi$
$463$	−8.52464	−0.396173	−0.198087	+	0.980185i	$0.563473\pi$
$464$	7.80731	0.362445
$465$	2.22897	0.103366
$466$	2.37660	0.110094
$467$	−21.8957	−1.01321	−0.506607	−	0.862177i	$-0.669100\pi$
$467$	−21.8957	−1.01321	−0.506607	+	0.862177i	$0.669100\pi$
$468$	−2.64757	−0.122384
$469$	−12.6470	−0.583983
$470$	4.61677	0.212956
$471$	28.6385	1.31959
$472$	−0.967177	−0.0445179
$473$	39.4711	1.81489
$474$	−23.3853	−1.07412
$475$	5.84430	0.268155
$476$	−0.434770	−0.0199276
$477$	7.16816	0.328207
$478$	17.0416	0.779467
$479$	−29.6469	−1.35460	−0.677300	−	0.735707i	$-0.736850\pi$
$479$	−29.6469	−1.35460	−0.677300	+	0.735707i	$0.736850\pi$
$480$	1.51896	0.0693307
$481$	0.799076	0.0364347
$482$	−20.5102	−0.934213
$483$	9.43206	0.429174
$484$	11.0057	0.500260
$485$	−17.7870	−0.807666
$486$	−7.04262	−0.319460
$487$	−39.7890	−1.80301	−0.901507	−	0.432765i	$-0.857538\pi$
$487$	−39.7890	−1.80301	−0.901507	+	0.432765i	$0.857538\pi$
$488$	−6.90282	−0.312476
$489$	7.36133	0.332891
$490$	−5.41458	−0.244606
$491$	23.8029	1.07421	0.537105	−	0.843515i	$-0.319518\pi$
$491$	23.8029	1.07421	0.537105	+	0.843515i	$0.319518\pi$
$492$	−0.562311	−0.0253509
$493$	−2.69580	−0.121413
$494$	−22.3356	−1.00492
$495$	−3.24975	−0.146066
$496$	−1.46743	−0.0658896
$497$	7.74120	0.347240
$498$	−11.3907	−0.510431
$499$	−0.441097	−0.0197462	−0.00987311	−	0.999951i	$-0.503143\pi$
$499$	−0.441097	−0.0197462	−0.00987311	+	0.999951i	$0.503143\pi$
$500$	−1.00000	−0.0447214
$501$	3.03712	0.135688
$502$	29.8922	1.33415
$503$	34.2380	1.52660	0.763299	−	0.646046i	$-0.223578\pi$
$503$	34.2380	1.52660	0.763299	+	0.646046i	$0.223578\pi$
$504$	0.872278	0.0388543
$505$	2.12324	0.0944829
$506$	23.1343	1.02844
$507$	2.43932	0.108334
$508$	13.2289	0.586937
$509$	−4.65264	−0.206224	−0.103112	−	0.994670i	$-0.532880\pi$
$509$	−4.65264	−0.206224	−0.103112	+	0.994670i	$0.532880\pi$
$510$	−0.524485	−0.0232246
$511$	8.22289	0.363759
$512$	−1.00000	−0.0441942
$513$	−32.7816	−1.44734
$514$	−11.2873	−0.497864
$515$	−6.53211	−0.287839
$516$	−12.7808	−0.562644
$517$	−21.6574	−0.952491
$518$	−0.263267	−0.0115673
$519$	−2.39192	−0.104994
$520$	3.82177	0.167596
$521$	33.4331	1.46473	0.732366	−	0.680911i	$-0.238416\pi$
$521$	33.4331	1.46473	0.732366	+	0.680911i	$0.238416\pi$
$522$	5.40859	0.236728
$523$	2.37593	0.103892	0.0519462	−	0.998650i	$-0.483458\pi$
$523$	2.37593	0.103892	0.0519462	+	0.998650i	$0.483458\pi$
$524$	16.9310	0.739632
$525$	1.91258	0.0834716
$526$	−11.6872	−0.509588
$527$	0.506692	0.0220719
$528$	−7.12548	−0.310097
$529$	1.32069	0.0574212
$530$	−10.3472	−0.449456
$531$	−0.670022	−0.0290765
$532$	7.35876	0.319043
$533$	−1.41480	−0.0612817
$534$	19.1752	0.829793
$535$	−6.16612	−0.266584
$536$	10.0442	0.433842
$537$	17.3002	0.746560
$538$	20.6427	0.889971
$539$	25.3999	1.09405
$540$	5.60916	0.241380
$541$	−24.2374	−1.04205	−0.521024	−	0.853542i	$-0.674450\pi$
$541$	−24.2374	−1.04205	−0.521024	+	0.853542i	$0.674450\pi$
$542$	−25.0690	−1.07681
$543$	15.5453	0.667111
$544$	0.345292	0.0148043
$545$	−18.4925	−0.792133
$546$	−7.30942	−0.312814
$547$	11.0374	0.471927	0.235963	−	0.971762i	$-0.424175\pi$
$547$	11.0374	0.471927	0.235963	+	0.971762i	$0.424175\pi$
$548$	−18.1747	−0.776385
$549$	−4.78200	−0.204091
$550$	4.69102	0.200026
$551$	45.6282	1.94383
$552$	−7.49091	−0.318834
$553$	19.3851	0.824340
$554$	9.90362	0.420765
$555$	−0.317593	−0.0134811
$556$	9.93501	0.421338
$557$	35.7645	1.51539	0.757695	−	0.652609i	$-0.226326\pi$
$557$	35.7645	1.51539	0.757695	+	0.652609i	$0.226326\pi$
$558$	−1.01658	−0.0430351
$559$	−32.1571	−1.36010
$560$	−1.25913	−0.0532081
$561$	2.46037	0.103877
$562$	24.0812	1.01580
$563$	−6.69740	−0.282262	−0.141131	−	0.989991i	$-0.545074\pi$
$563$	−6.69740	−0.282262	−0.141131	+	0.989991i	$0.545074\pi$
$564$	7.01269	0.295288
$565$	2.64275	0.111181
$566$	12.2596	0.515310
$567$	−8.11110	−0.340634
$568$	−6.14803	−0.257966
$569$	25.3270	1.06176	0.530882	−	0.847446i	$-0.321861\pi$
$569$	25.3270	1.06176	0.530882	+	0.847446i	$0.321861\pi$
$570$	8.87726	0.371827
$571$	−3.67510	−0.153798	−0.0768990	−	0.997039i	$-0.524502\pi$
$571$	−3.67510	−0.153798	−0.0768990	+	0.997039i	$0.524502\pi$
$572$	−17.9280	−0.749608
$573$	−28.7755	−1.20212
$574$	0.466125	0.0194557
$575$	4.93160	0.205662
$576$	−0.692760	−0.0288650
$577$	12.5390	0.522005	0.261002	−	0.965338i	$-0.415947\pi$
$577$	12.5390	0.522005	0.261002	+	0.965338i	$0.415947\pi$
$578$	16.8808	0.702148
$579$	24.3185	1.01064
$580$	−7.80731	−0.324181
$581$	9.44229	0.391732
$582$	−27.0178	−1.11992
$583$	48.5392	2.01029
$584$	−6.53058	−0.270238
$585$	2.64757	0.109463
$586$	−16.9317	−0.699442
$587$	−34.4475	−1.42180	−0.710900	−	0.703293i	$-0.751712\pi$
$587$	−34.4475	−1.42180	−0.710900	+	0.703293i	$0.751712\pi$
$588$	−8.22453	−0.339174
$589$	−8.57610	−0.353372
$590$	0.967177	0.0398181
$591$	22.9327	0.943326
$592$	0.209085	0.00859336
$593$	2.97066	0.121990	0.0609951	−	0.998138i	$-0.480573\pi$
$593$	2.97066	0.121990	0.0609951	+	0.998138i	$0.480573\pi$
$594$	−26.3127	−1.07962
$595$	0.434770	0.0178238
$596$	18.6558	0.764169
$597$	−0.625402	−0.0255960
$598$	−18.8474	−0.770729
$599$	−46.0341	−1.88090	−0.940451	−	0.339930i	$-0.889596\pi$
$599$	−46.0341	−1.88090	−0.940451	+	0.339930i	$0.889596\pi$
$600$	−1.51896	−0.0620113
$601$	−9.69943	−0.395648	−0.197824	−	0.980238i	$-0.563387\pi$
$601$	−9.69943	−0.395648	−0.197824	+	0.980238i	$0.563387\pi$
$602$	10.5946	0.431803
$603$	6.95820	0.283360
$604$	−12.7211	−0.517616
$605$	−11.0057	−0.447446
$606$	3.22511	0.131011
$607$	−30.4928	−1.23767	−0.618833	−	0.785523i	$-0.712394\pi$
$607$	−30.4928	−1.23767	−0.618833	+	0.785523i	$0.712394\pi$
$608$	−5.84430	−0.237018
$609$	14.9321	0.605078
$610$	6.90282	0.279487
$611$	17.6442	0.713809
$612$	0.239205	0.00966928
$613$	42.5217	1.71743	0.858717	−	0.512450i	$-0.171262\pi$
$613$	42.5217	1.71743	0.858717	+	0.512450i	$0.171262\pi$
$614$	28.2098	1.13845
$615$	0.562311	0.0226746
$616$	5.90663	0.237985
$617$	−0.0424548	−0.00170917	−0.000854584	−	1.00000i	$-0.500272\pi$
$617$	−0.0424548	−0.00170917	−0.000854584		1.00000i	$0.500272\pi$
$618$	−9.92201	−0.399122
$619$	31.7320	1.27542	0.637708	−	0.770278i	$-0.279883\pi$
$619$	31.7320	1.27542	0.637708	+	0.770278i	$0.279883\pi$
$620$	1.46743	0.0589334
$621$	−27.6621	−1.11004
$622$	−8.53611	−0.342267
$623$	−15.8952	−0.636828
$624$	5.80511	0.232391
$625$	1.00000	0.0400000
$626$	−8.25032	−0.329749
$627$	−41.6434	−1.66308
$628$	18.8540	0.752357
$629$	−0.0721956	−0.00287863
$630$	−0.872278	−0.0347524
$631$	39.2787	1.56366	0.781829	−	0.623492i	$-0.214287\pi$
$631$	39.2787	1.56366	0.781829	+	0.623492i	$0.214287\pi$
$632$	−15.3956	−0.612404
$633$	−12.7552	−0.506974
$634$	−24.7740	−0.983902
$635$	−13.2289	−0.524973
$636$	−15.7171	−0.623222
$637$	−20.6933	−0.819897
$638$	36.6243	1.44997
$639$	−4.25911	−0.168488
$640$	1.00000	0.0395285
$641$	−1.48979	−0.0588434	−0.0294217	−	0.999567i	$-0.509367\pi$
$641$	−1.48979	−0.0588434	−0.0294217	+	0.999567i	$0.509367\pi$
$642$	−9.36608	−0.369650
$643$	−7.18195	−0.283228	−0.141614	−	0.989922i	$-0.545229\pi$
$643$	−7.18195	−0.283228	−0.141614	+	0.989922i	$0.545229\pi$
$644$	6.20955	0.244691
$645$	12.7808	0.503244
$646$	2.01799	0.0793968
$647$	−11.0633	−0.434944	−0.217472	−	0.976067i	$-0.569781\pi$
$647$	−11.0633	−0.434944	−0.217472	+	0.976067i	$0.569781\pi$
$648$	6.44180	0.253058
$649$	−4.53705	−0.178095
$650$	−3.82177	−0.149902
$651$	−2.80657	−0.109998
$652$	4.84629	0.189796
$653$	2.86486	0.112110	0.0560552	−	0.998428i	$-0.482148\pi$
$653$	2.86486	0.112110	0.0560552	+	0.998428i	$0.482148\pi$
$654$	−28.0894	−1.09838
$655$	−16.9310	−0.661547
$656$	−0.370194	−0.0144537
$657$	−4.52413	−0.176503
$658$	−5.81314	−0.226620
$659$	23.1976	0.903648	0.451824	−	0.892107i	$-0.350773\pi$
$659$	23.1976	0.903648	0.451824	+	0.892107i	$0.350773\pi$
$660$	7.12548	0.277359
$661$	−2.02797	−0.0788787	−0.0394394	−	0.999222i	$-0.512557\pi$
$661$	−2.02797	−0.0788787	−0.0394394	+	0.999222i	$0.512557\pi$
$662$	−8.41271	−0.326969
$663$	−2.00446	−0.0778468
$664$	−7.49903	−0.291019
$665$	−7.35876	−0.285360
$666$	0.144846	0.00561267
$667$	38.5025	1.49082
$668$	1.99947	0.0773618
$669$	34.4667	1.33256
$670$	−10.0442	−0.388040
$671$	−32.3813	−1.25007
$672$	−1.91258	−0.0737792
$673$	−22.3683	−0.862235	−0.431118	−	0.902296i	$-0.641881\pi$
$673$	−22.3683	−0.862235	−0.431118	+	0.902296i	$0.641881\pi$
$674$	19.9410	0.768099
$675$	−5.60916	−0.215896
$676$	1.60591	0.0617659
$677$	32.9818	1.26759	0.633796	−	0.773500i	$-0.281496\pi$
$677$	32.9818	1.26759	0.633796	+	0.773500i	$0.281496\pi$
$678$	4.01423	0.154166
$679$	22.3962	0.859489
$680$	−0.345292	−0.0132414
$681$	5.13775	0.196879
$682$	−6.88375	−0.263592
$683$	−18.8072	−0.719637	−0.359818	−	0.933022i	$-0.617161\pi$
$683$	−18.8072	−0.719637	−0.359818	+	0.933022i	$0.617161\pi$
$684$	−4.04870	−0.154806
$685$	18.1747	0.694420
$686$	15.6316	0.596818
$687$	10.2267	0.390172
$688$	−8.41418	−0.320788
$689$	−39.5448	−1.50654
$690$	7.49091	0.285174
$691$	40.8304	1.55326	0.776630	−	0.629957i	$-0.216927\pi$
$691$	40.8304	1.55326	0.776630	+	0.629957i	$0.216927\pi$
$692$	−1.57471	−0.0598615
$693$	4.09188	0.155438
$694$	−17.6036	−0.668225
$695$	−9.93501	−0.376856
$696$	−11.8590	−0.449514
$697$	0.127825	0.00484173
$698$	23.8660	0.903341
$699$	−3.60996	−0.136541
$700$	1.25913	0.0475908
$701$	−24.3725	−0.920536	−0.460268	−	0.887780i	$-0.652247\pi$
$701$	−24.3725	−0.920536	−0.460268	+	0.887780i	$0.652247\pi$
$702$	21.4369	0.809083
$703$	1.22196	0.0460870
$704$	−4.69102	−0.176800
$705$	−7.01269	−0.264113
$706$	16.2405	0.611220
$707$	−2.67344	−0.100545
$708$	1.46910	0.0552123
$709$	−20.0328	−0.752349	−0.376174	−	0.926549i	$-0.622761\pi$
$709$	−20.0328	−0.752349	−0.376174	+	0.926549i	$0.622761\pi$
$710$	6.14803	0.230732
$711$	−10.6655	−0.399986
$712$	12.6239	0.473101
$713$	−7.23678	−0.271020
$714$	0.660398	0.0247148
$715$	17.9280	0.670470
$716$	11.3895	0.425646
$717$	−25.8856	−0.966715
$718$	−27.8019	−1.03756
$719$	−25.4917	−0.950679	−0.475340	−	0.879802i	$-0.657675\pi$
$719$	−25.4917	−0.950679	−0.475340	+	0.879802i	$0.657675\pi$
$720$	0.692760	0.0258176
$721$	8.22480	0.306308
$722$	−15.1558	−0.564042
$723$	31.1541	1.15863
$724$	10.2341	0.380349
$725$	7.80731	0.289956
$726$	−16.7172	−0.620435
$727$	3.86793	0.143454	0.0717269	−	0.997424i	$-0.477149\pi$
$727$	3.86793	0.143454	0.0717269	+	0.997424i	$0.477149\pi$
$728$	−4.81212	−0.178349
$729$	30.0229	1.11196
$730$	6.53058	0.241708
$731$	2.90535	0.107458
$732$	10.4851	0.387541
$733$	−2.30485	−0.0851316	−0.0425658	−	0.999094i	$-0.513553\pi$
$733$	−2.30485	−0.0851316	−0.0425658	+	0.999094i	$0.513553\pi$
$734$	−31.2201	−1.15235
$735$	8.22453	0.303366
$736$	−4.93160	−0.181781
$737$	47.1175	1.73559
$738$	−0.256456	−0.00944027
$739$	−41.0863	−1.51138	−0.755692	−	0.654928i	$-0.772699\pi$
$739$	−41.0863	−1.51138	−0.755692	+	0.654928i	$0.772699\pi$
$740$	−0.209085	−0.00768614
$741$	33.9268	1.24633
$742$	13.0286	0.478294
$743$	−12.6611	−0.464490	−0.232245	−	0.972657i	$-0.574607\pi$
$743$	−12.6611	−0.464490	−0.232245	+	0.972657i	$0.574607\pi$
$744$	2.22897	0.0817179
$745$	−18.6558	−0.683494
$746$	28.7982	1.05438
$747$	−5.19503	−0.190076
$748$	1.61978	0.0592248
$749$	7.76397	0.283689
$750$	1.51896	0.0554646
$751$	−39.0887	−1.42637	−0.713183	−	0.700978i	$-0.752747\pi$
$751$	−39.0887	−1.42637	−0.713183	+	0.700978i	$0.752747\pi$
$752$	4.61677	0.168356
$753$	−45.4050	−1.65465
$754$	−29.8377	−1.08663
$755$	12.7211	0.462970
$756$	−7.06268	−0.256867
$757$	−30.5966	−1.11205	−0.556025	−	0.831165i	$-0.687674\pi$
$757$	−30.5966	−1.11205	−0.556025	+	0.831165i	$0.687674\pi$
$758$	8.06997	0.293115
$759$	−35.1400	−1.27550
$760$	5.84430	0.211995
$761$	−14.1710	−0.513699	−0.256850	−	0.966451i	$-0.582685\pi$
$761$	−14.1710	−0.513699	−0.256850	+	0.966451i	$0.582685\pi$
$762$	−20.0942	−0.727935
$763$	23.2846	0.842958
$764$	−18.9442	−0.685378
$765$	−0.239205	−0.00864847
$766$	18.5721	0.671037
$767$	3.69633	0.133467
$768$	1.51896	0.0548108
$769$	−45.1587	−1.62847	−0.814233	−	0.580539i	$-0.802842\pi$
$769$	−45.1587	−1.62847	−0.814233	+	0.580539i	$0.802842\pi$
$770$	−5.90663	−0.212860
$771$	17.1450	0.617463
$772$	16.0099	0.576210
$773$	−26.6339	−0.957955	−0.478977	−	0.877827i	$-0.658992\pi$
$773$	−26.6339	−0.957955	−0.478977	+	0.877827i	$0.658992\pi$
$774$	−5.82901	−0.209519
$775$	−1.46743	−0.0527116
$776$	−17.7870	−0.638516
$777$	0.399892	0.0143460
$778$	29.2175	1.04750
$779$	−2.16353	−0.0775164
$780$	−5.80511	−0.207856
$781$	−28.8406	−1.03200
$782$	1.70284	0.0608936
$783$	−43.7924	−1.56501
$784$	−5.41458	−0.193378
$785$	−18.8540	−0.672928
$786$	−25.7175	−0.917311
$787$	24.9739	0.890224	0.445112	−	0.895475i	$-0.353164\pi$
$787$	24.9739	0.890224	0.445112	+	0.895475i	$0.353164\pi$
$788$	15.0976	0.537831
$789$	17.7524	0.632004
$790$	15.3956	0.547751
$791$	−3.32758	−0.118315
$792$	−3.24975	−0.115475
$793$	26.3810	0.936816
$794$	5.06991	0.179924
$795$	15.7171	0.557426
$796$	−0.411731	−0.0145934
$797$	23.4613	0.831041	0.415521	−	0.909584i	$-0.363599\pi$
$797$	23.4613	0.831041	0.415521	+	0.909584i	$0.363599\pi$
$798$	−11.1777	−0.395685
$799$	−1.59414	−0.0563965
$800$	−1.00000	−0.0353553
$801$	8.74534	0.309002
$802$	−1.00000	−0.0353112
$803$	−30.6351	−1.08109
$804$	−15.2567	−0.538062
$805$	−6.20955	−0.218858
$806$	5.60818	0.197540
$807$	−31.3555	−1.10376
$808$	2.12324	0.0746953
$809$	−1.61527	−0.0567900	−0.0283950	−	0.999597i	$-0.509040\pi$
$809$	−1.61527	−0.0567900	−0.0283950	+	0.999597i	$0.509040\pi$
$810$	−6.44180	−0.226342
$811$	46.9319	1.64800	0.824002	−	0.566587i	$-0.191737\pi$
$811$	46.9319	1.64800	0.824002	+	0.566587i	$0.191737\pi$
$812$	9.83045	0.344981
$813$	38.0788	1.33548
$814$	0.980825	0.0343779
$815$	−4.84629	−0.169758
$816$	−0.524485	−0.0183607
$817$	−49.1750	−1.72042
$818$	20.1684	0.705170
$819$	−3.33364	−0.116487
$820$	0.370194	0.0129278
$821$	−33.9356	−1.18436	−0.592181	−	0.805805i	$-0.701733\pi$
$821$	−33.9356	−1.18436	−0.592181	+	0.805805i	$0.701733\pi$
$822$	27.6067	0.962893
$823$	27.4145	0.955609	0.477805	−	0.878466i	$-0.341433\pi$
$823$	27.4145	0.955609	0.477805	+	0.878466i	$0.341433\pi$
$824$	−6.53211	−0.227557
$825$	−7.12548	−0.248077
$826$	−1.21781	−0.0423729
$827$	43.4077	1.50943	0.754716	−	0.656051i	$-0.227775\pi$
$827$	43.4077	1.50943	0.754716	+	0.656051i	$0.227775\pi$
$828$	−3.41642	−0.118729
$829$	42.9604	1.49208	0.746038	−	0.665903i	$-0.231954\pi$
$829$	42.9604	1.49208	0.746038	+	0.665903i	$0.231954\pi$
$830$	7.49903	0.260295
$831$	−15.0432	−0.521843
$832$	3.82177	0.132496
$833$	1.86961	0.0647783
$834$	−15.0909	−0.522554
$835$	−1.99947	−0.0691945
$836$	−27.4158	−0.948194
$837$	8.23104	0.284506
$838$	18.9327	0.654020
$839$	41.3153	1.42636	0.713181	−	0.700980i	$-0.247254\pi$
$839$	41.3153	1.42636	0.713181	+	0.700980i	$0.247254\pi$
$840$	1.91258	0.0659901
$841$	31.9540	1.10186
$842$	2.97184	0.102416
$843$	−36.5783	−1.25983
$844$	−8.39733	−0.289048
$845$	−1.60591	−0.0552451
$846$	3.19831	0.109960
$847$	13.8577	0.476155
$848$	−10.3472	−0.355326
$849$	−18.6219	−0.639101
$850$	0.345292	0.0118434
$851$	1.03113	0.0353465
$852$	9.33862	0.319936
$853$	−24.6424	−0.843741	−0.421871	−	0.906656i	$-0.638626\pi$
$853$	−24.6424	−0.843741	−0.421871	+	0.906656i	$0.638626\pi$
$854$	−8.69158	−0.297420
$855$	4.04870	0.138462
$856$	−6.16612	−0.210753
$857$	−1.38145	−0.0471893	−0.0235947	−	0.999722i	$-0.507511\pi$
$857$	−1.38145	−0.0471893	−0.0235947	+	0.999722i	$0.507511\pi$
$858$	27.2319	0.929683
$859$	−25.2013	−0.859858	−0.429929	−	0.902863i	$-0.641461\pi$
$859$	−25.2013	−0.859858	−0.429929	+	0.902863i	$0.641461\pi$
$860$	8.41418	0.286921
$861$	−0.708025	−0.0241294
$862$	−18.0029	−0.613180
$863$	−10.1607	−0.345875	−0.172938	−	0.984933i	$-0.555326\pi$
$863$	−10.1607	−0.345875	−0.172938	+	0.984933i	$0.555326\pi$
$864$	5.60916	0.190827
$865$	1.57471	0.0535417
$866$	−4.35510	−0.147992
$867$	−25.6412	−0.870822
$868$	−1.84769	−0.0627148
$869$	−72.2212	−2.44994
$870$	11.8590	0.402057
$871$	−38.3865	−1.30068
$872$	−18.4925	−0.626236
$873$	−12.3221	−0.417041
$874$	−28.8218	−0.974910
$875$	−1.25913	−0.0425665
$876$	9.91970	0.335156
$877$	−43.6025	−1.47235	−0.736177	−	0.676789i	$-0.763371\pi$
$877$	−43.6025	−1.47235	−0.736177	+	0.676789i	$0.763371\pi$
$878$	22.2495	0.750883
$879$	25.7186	0.867466
$880$	4.69102	0.158134
$881$	31.4963	1.06114	0.530568	−	0.847642i	$-0.321979\pi$
$881$	31.4963	1.06114	0.530568	+	0.847642i	$0.321979\pi$
$882$	−3.75100	−0.126303
$883$	−30.9874	−1.04281	−0.521404	−	0.853310i	$-0.674591\pi$
$883$	−30.9874	−1.04281	−0.521404	+	0.853310i	$0.674591\pi$
$884$	−1.31963	−0.0443839
$885$	−1.46910	−0.0493834
$886$	22.9055	0.769526
$887$	10.8673	0.364890	0.182445	−	0.983216i	$-0.441599\pi$
$887$	10.8673	0.364890	0.182445	+	0.983216i	$0.441599\pi$
$888$	−0.317593	−0.0106577
$889$	16.6570	0.558656
$890$	−12.6239	−0.423155
$891$	30.2187	1.01236
$892$	22.6910	0.759751
$893$	26.9818	0.902911
$894$	−28.3373	−0.947743
$895$	−11.3895	−0.380710
$896$	−1.25913	−0.0420647
$897$	28.6285	0.955878
$898$	31.5363	1.05238
$899$	−11.4567	−0.382102
$900$	−0.692760	−0.0230920
$901$	3.57282	0.119028
$902$	−1.73659	−0.0578222
$903$	−16.0928	−0.535534
$904$	2.64275	0.0878965
$905$	−10.2341	−0.340195
$906$	19.3229	0.641961
$907$	12.1119	0.402169	0.201085	−	0.979574i	$-0.435553\pi$
$907$	12.1119	0.402169	0.201085	+	0.979574i	$0.435553\pi$
$908$	3.38241	0.112249
$909$	1.47089	0.0487865
$910$	4.81212	0.159520
$911$	−42.7555	−1.41655	−0.708276	−	0.705935i	$-0.750527\pi$
$911$	−42.7555	−1.41655	−0.708276	+	0.705935i	$0.750527\pi$
$912$	8.87726	0.293955
$913$	−35.1781	−1.16423
$914$	−39.3675	−1.30216
$915$	−10.4851	−0.346627
$916$	6.73268	0.222454
$917$	21.3184	0.703994
$918$	−1.93680	−0.0639239
$919$	−36.8142	−1.21439	−0.607194	−	0.794554i	$-0.707705\pi$
$919$	−36.8142	−1.21439	−0.607194	+	0.794554i	$0.707705\pi$
$920$	4.93160	0.162590
$921$	−42.8495	−1.41194
$922$	−33.8004	−1.11316
$923$	23.4964	0.773392
$924$	−8.97194	−0.295155
$925$	0.209085	0.00687469
$926$	8.52464	0.280137
$927$	−4.52518	−0.148626
$928$	−7.80731	−0.256287
$929$	0.170390	0.00559031	0.00279516	−	0.999996i	$-0.499110\pi$
$929$	0.170390	0.00559031	0.00279516	+	0.999996i	$0.499110\pi$
$930$	−2.22897	−0.0730907
$931$	−31.6444	−1.03710
$932$	−2.37660	−0.0778480
$933$	12.9660	0.424488
$934$	21.8957	0.716450
$935$	−1.61978	−0.0529723
$936$	2.64757	0.0865385
$937$	−6.11583	−0.199796	−0.0998978	−	0.994998i	$-0.531852\pi$
$937$	−6.11583	−0.199796	−0.0998978	+	0.994998i	$0.531852\pi$
$938$	12.6470	0.412938
$939$	12.5319	0.408963
$940$	−4.61677	−0.150582
$941$	−15.7107	−0.512155	−0.256078	−	0.966656i	$-0.582430\pi$
$941$	−15.7107	−0.512155	−0.256078	+	0.966656i	$0.582430\pi$
$942$	−28.6385	−0.933092
$943$	−1.82565	−0.0594514
$944$	0.967177	0.0314789
$945$	7.06268	0.229749
$946$	−39.4711	−1.28332
$947$	29.8383	0.969614	0.484807	−	0.874621i	$-0.338890\pi$
$947$	29.8383	0.969614	0.484807	+	0.874621i	$0.338890\pi$
$948$	23.3853	0.759520
$949$	24.9584	0.810183
$950$	−5.84430	−0.189614
$951$	37.6307	1.22026
$952$	0.434770	0.0140910
$953$	−36.2748	−1.17505	−0.587527	−	0.809204i	$-0.699899\pi$
$953$	−36.2748	−1.17505	−0.587527	+	0.809204i	$0.699899\pi$
$954$	−7.16816	−0.232078
$955$	18.9442	0.613021
$956$	−17.0416	−0.551166
$957$	−55.6308	−1.79829
$958$	29.6469	0.957847
$959$	−22.8844	−0.738976
$960$	−1.51896	−0.0490242
$961$	−28.8466	−0.930537
$962$	−0.799076	−0.0257633
$963$	−4.27164	−0.137652
$964$	20.5102	0.660588
$965$	−16.0099	−0.515378
$966$	−9.43206	−0.303472
$967$	27.9519	0.898873	0.449437	−	0.893312i	$-0.351625\pi$
$967$	27.9519	0.898873	0.449437	+	0.893312i	$0.351625\pi$
$968$	−11.0057	−0.353737
$969$	−3.06525	−0.0984700
$970$	17.7870	0.571106
$971$	−3.09101	−0.0991951	−0.0495975	−	0.998769i	$-0.515794\pi$
$971$	−3.09101	−0.0991951	−0.0495975	+	0.998769i	$0.515794\pi$
$972$	7.04262	0.225892
$973$	12.5095	0.401037
$974$	39.7890	1.27492
$975$	5.80511	0.185912
$976$	6.90282	0.220954
$977$	−42.1022	−1.34697	−0.673484	−	0.739202i	$-0.735203\pi$
$977$	−42.1022	−1.34697	−0.673484	+	0.739202i	$0.735203\pi$
$978$	−7.36133	−0.235389
$979$	59.2191	1.89265
$980$	5.41458	0.172962
$981$	−12.8109	−0.409020
$982$	−23.8029	−0.759581
$983$	35.7078	1.13890	0.569451	−	0.822025i	$-0.307156\pi$
$983$	35.7078	1.13890	0.569451	+	0.822025i	$0.307156\pi$
$984$	0.562311	0.0179258
$985$	−15.0976	−0.481051
$986$	2.69580	0.0858519
$987$	8.82992	0.281059
$988$	22.3356	0.710589
$989$	−41.4954	−1.31948
$990$	3.24975	0.103284
$991$	12.9774	0.412240	0.206120	−	0.978527i	$-0.433916\pi$
$991$	12.9774	0.412240	0.206120	+	0.978527i	$0.433916\pi$
$992$	1.46743	0.0465910
$993$	12.7786	0.405516
$994$	−7.74120	−0.245536
$995$	0.411731	0.0130527
$996$	11.3907	0.360929
$997$	52.5264	1.66353	0.831764	−	0.555130i	$-0.187331\pi$
$997$	52.5264	1.66353	0.831764	+	0.555130i	$0.187331\pi$
$998$	0.441097	0.0139627
$999$	−1.17279	−0.0371055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.13	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.13	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.51896 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51896 q^{6} +1.25913 q^{7} -1.00000 q^{8} -0.692760 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.51896 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.51896 q^{6} +1.25913 q^{7} -1.00000 q^{8} -0.692760 q^{9} +1.00000 q^{10} -4.69102 q^{11} +1.51896 q^{12} +3.82177 q^{13} -1.25913 q^{14} -1.51896 q^{15} +1.00000 q^{16} -0.345292 q^{17} +0.692760 q^{18} +5.84430 q^{19} -1.00000 q^{20} +1.91258 q^{21} +4.69102 q^{22} +4.93160 q^{23} -1.51896 q^{24} +1.00000 q^{25} -3.82177 q^{26} -5.60916 q^{27} +1.25913 q^{28} +7.80731 q^{29} +1.51896 q^{30} -1.46743 q^{31} -1.00000 q^{32} -7.12548 q^{33} +0.345292 q^{34} -1.25913 q^{35} -0.692760 q^{36} +0.209085 q^{37} -5.84430 q^{38} +5.80511 q^{39} +1.00000 q^{40} -0.370194 q^{41} -1.91258 q^{42} -8.41418 q^{43} -4.69102 q^{44} +0.692760 q^{45} -4.93160 q^{46} +4.61677 q^{47} +1.51896 q^{48} -5.41458 q^{49} -1.00000 q^{50} -0.524485 q^{51} +3.82177 q^{52} -10.3472 q^{53} +5.60916 q^{54} +4.69102 q^{55} -1.25913 q^{56} +8.87726 q^{57} -7.80731 q^{58} +0.967177 q^{59} -1.51896 q^{60} +6.90282 q^{61} +1.46743 q^{62} -0.872278 q^{63} +1.00000 q^{64} -3.82177 q^{65} +7.12548 q^{66} -10.0442 q^{67} -0.345292 q^{68} +7.49091 q^{69} +1.25913 q^{70} +6.14803 q^{71} +0.692760 q^{72} +6.53058 q^{73} -0.209085 q^{74} +1.51896 q^{75} +5.84430 q^{76} -5.90663 q^{77} -5.80511 q^{78} +15.3956 q^{79} -1.00000 q^{80} -6.44180 q^{81} +0.370194 q^{82} +7.49903 q^{83} +1.91258 q^{84} +0.345292 q^{85} +8.41418 q^{86} +11.8590 q^{87} +4.69102 q^{88} -12.6239 q^{89} -0.692760 q^{90} +4.81212 q^{91} +4.93160 q^{92} -2.22897 q^{93} -4.61677 q^{94} -5.84430 q^{95} -1.51896 q^{96} +17.7870 q^{97} +5.41458 q^{98} +3.24975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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