LMFDB - Embedded newform 4010.2.a.h.1.2

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 8x^{7} + 16x^{6} + 17x^{5} - 36x^{4} - 4x^{3} + 17x^{2} - 2 $ x^9 - 2x^8 - 8x^7 + 16x^6 + 17x^5 - 36x^4 - 4x^3 + 17*x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.589646$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.18512 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.18512 q^{6} -0.791922 q^{7} +1.00000 q^{8} +1.77477 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.18512 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.18512 q^{6} -0.791922 q^{7} +1.00000 q^{8} +1.77477 q^{9} +1.00000 q^{10} +0.552253 q^{11} -2.18512 q^{12} +2.18175 q^{13} -0.791922 q^{14} -2.18512 q^{15} +1.00000 q^{16} -6.40120 q^{17} +1.77477 q^{18} +1.60755 q^{19} +1.00000 q^{20} +1.73045 q^{21} +0.552253 q^{22} -0.116032 q^{23} -2.18512 q^{24} +1.00000 q^{25} +2.18175 q^{26} +2.67728 q^{27} -0.791922 q^{28} -7.26885 q^{29} -2.18512 q^{30} -9.20173 q^{31} +1.00000 q^{32} -1.20674 q^{33} -6.40120 q^{34} -0.791922 q^{35} +1.77477 q^{36} +3.45269 q^{37} +1.60755 q^{38} -4.76739 q^{39} +1.00000 q^{40} +6.88184 q^{41} +1.73045 q^{42} +3.48205 q^{43} +0.552253 q^{44} +1.77477 q^{45} -0.116032 q^{46} +4.60163 q^{47} -2.18512 q^{48} -6.37286 q^{49} +1.00000 q^{50} +13.9874 q^{51} +2.18175 q^{52} -5.31887 q^{53} +2.67728 q^{54} +0.552253 q^{55} -0.791922 q^{56} -3.51269 q^{57} -7.26885 q^{58} -3.25952 q^{59} -2.18512 q^{60} -10.9186 q^{61} -9.20173 q^{62} -1.40548 q^{63} +1.00000 q^{64} +2.18175 q^{65} -1.20674 q^{66} -3.76760 q^{67} -6.40120 q^{68} +0.253545 q^{69} -0.791922 q^{70} +0.154848 q^{71} +1.77477 q^{72} -1.03107 q^{73} +3.45269 q^{74} -2.18512 q^{75} +1.60755 q^{76} -0.437342 q^{77} -4.76739 q^{78} +9.86274 q^{79} +1.00000 q^{80} -11.1745 q^{81} +6.88184 q^{82} -1.29394 q^{83} +1.73045 q^{84} -6.40120 q^{85} +3.48205 q^{86} +15.8833 q^{87} +0.552253 q^{88} +13.6416 q^{89} +1.77477 q^{90} -1.72778 q^{91} -0.116032 q^{92} +20.1069 q^{93} +4.60163 q^{94} +1.60755 q^{95} -2.18512 q^{96} -1.27934 q^{97} -6.37286 q^{98} +0.980123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * 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
$3$	−2.18512	−1.26158	−0.630791	−	0.775953i	$-0.717270\pi$
$3$	−2.18512	−1.26158	−0.630791	+	0.775953i	$0.717270\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.18512	−0.892073
$7$	−0.791922	−0.299318	−0.149659	−	0.988738i	$-0.547818\pi$
$7$	−0.791922	−0.299318	−0.149659	+	0.988738i	$0.547818\pi$
$8$	1.00000	0.353553
$9$	1.77477	0.591590
$10$	1.00000	0.316228
$11$	0.552253	0.166511	0.0832553	−	0.996528i	$-0.473468\pi$
$11$	0.552253	0.166511	0.0832553	+	0.996528i	$0.473468\pi$
$12$	−2.18512	−0.630791
$13$	2.18175	0.605108	0.302554	−	0.953132i	$-0.402161\pi$
$13$	2.18175	0.605108	0.302554	+	0.953132i	$0.402161\pi$
$14$	−0.791922	−0.211650
$15$	−2.18512	−0.564197
$16$	1.00000	0.250000
$17$	−6.40120	−1.55252	−0.776259	−	0.630414i	$-0.782885\pi$
$17$	−6.40120	−1.55252	−0.776259	+	0.630414i	$0.782885\pi$
$18$	1.77477	0.418317
$19$	1.60755	0.368796	0.184398	−	0.982852i	$-0.440966\pi$
$19$	1.60755	0.368796	0.184398	+	0.982852i	$0.440966\pi$
$20$	1.00000	0.223607
$21$	1.73045	0.377615
$22$	0.552253	0.117741
$23$	−0.116032	−0.0241944	−0.0120972	−	0.999927i	$-0.503851\pi$
$23$	−0.116032	−0.0241944	−0.0120972	+	0.999927i	$0.503851\pi$
$24$	−2.18512	−0.446037
$25$	1.00000	0.200000
$26$	2.18175	0.427876
$27$	2.67728	0.515243
$28$	−0.791922	−0.149659
$29$	−7.26885	−1.34979	−0.674896	−	0.737913i	$-0.735811\pi$
$29$	−7.26885	−1.34979	−0.674896	+	0.737913i	$0.735811\pi$
$30$	−2.18512	−0.398947
$31$	−9.20173	−1.65268	−0.826340	−	0.563172i	$-0.809581\pi$
$31$	−9.20173	−1.65268	−0.826340	+	0.563172i	$0.809581\pi$
$32$	1.00000	0.176777
$33$	−1.20674	−0.210067
$34$	−6.40120	−1.09780
$35$	−0.791922	−0.133859
$36$	1.77477	0.295795
$37$	3.45269	0.567619	0.283810	−	0.958881i	$-0.408402\pi$
$37$	3.45269	0.567619	0.283810	+	0.958881i	$0.408402\pi$
$38$	1.60755	0.260779
$39$	−4.76739	−0.763394
$40$	1.00000	0.158114
$41$	6.88184	1.07476	0.537381	−	0.843340i	$-0.319414\pi$
$41$	6.88184	1.07476	0.537381	+	0.843340i	$0.319414\pi$
$42$	1.73045	0.267014
$43$	3.48205	0.531008	0.265504	−	0.964110i	$-0.414462\pi$
$43$	3.48205	0.531008	0.265504	+	0.964110i	$0.414462\pi$
$44$	0.552253	0.0832553
$45$	1.77477	0.264567
$46$	−0.116032	−0.0171080
$47$	4.60163	0.671216	0.335608	−	0.942002i	$-0.391058\pi$
$47$	4.60163	0.671216	0.335608	+	0.942002i	$0.391058\pi$
$48$	−2.18512	−0.315396
$49$	−6.37286	−0.910408
$50$	1.00000	0.141421
$51$	13.9874	1.95863
$52$	2.18175	0.302554
$53$	−5.31887	−0.730603	−0.365301	−	0.930889i	$-0.619034\pi$
$53$	−5.31887	−0.730603	−0.365301	+	0.930889i	$0.619034\pi$
$54$	2.67728	0.364332
$55$	0.552253	0.0744658
$56$	−0.791922	−0.105825
$57$	−3.51269	−0.465267
$58$	−7.26885	−0.954447
$59$	−3.25952	−0.424354	−0.212177	−	0.977231i	$-0.568055\pi$
$59$	−3.25952	−0.424354	−0.212177	+	0.977231i	$0.568055\pi$
$60$	−2.18512	−0.282098
$61$	−10.9186	−1.39798	−0.698990	−	0.715132i	$-0.746367\pi$
$61$	−10.9186	−1.39798	−0.698990	+	0.715132i	$0.746367\pi$
$62$	−9.20173	−1.16862
$63$	−1.40548	−0.177074
$64$	1.00000	0.125000
$65$	2.18175	0.270613
$66$	−1.20674	−0.148540
$67$	−3.76760	−0.460286	−0.230143	−	0.973157i	$-0.573919\pi$
$67$	−3.76760	−0.460286	−0.230143	+	0.973157i	$0.573919\pi$
$68$	−6.40120	−0.776259
$69$	0.253545	0.0305232
$70$	−0.791922	−0.0946528
$71$	0.154848	0.0183771	0.00918855	−	0.999958i	$-0.497075\pi$
$71$	0.154848	0.0183771	0.00918855	+	0.999958i	$0.497075\pi$
$72$	1.77477	0.209159
$73$	−1.03107	−0.120678	−0.0603390	−	0.998178i	$-0.519218\pi$
$73$	−1.03107	−0.120678	−0.0603390	+	0.998178i	$0.519218\pi$
$74$	3.45269	0.401367
$75$	−2.18512	−0.252316
$76$	1.60755	0.184398
$77$	−0.437342	−0.0498397
$78$	−4.76739	−0.539801
$79$	9.86274	1.10965	0.554823	−	0.831969i	$-0.312786\pi$
$79$	9.86274	1.10965	0.554823	+	0.831969i	$0.312786\pi$
$80$	1.00000	0.111803
$81$	−11.1745	−1.24161
$82$	6.88184	0.759972
$83$	−1.29394	−0.142028	−0.0710140	−	0.997475i	$-0.522624\pi$
$83$	−1.29394	−0.142028	−0.0710140	+	0.997475i	$0.522624\pi$
$84$	1.73045	0.188807
$85$	−6.40120	−0.694308
$86$	3.48205	0.375479
$87$	15.8833	1.70287
$88$	0.552253	0.0588704
$89$	13.6416	1.44601	0.723005	−	0.690843i	$-0.242760\pi$
$89$	13.6416	1.44601	0.723005	+	0.690843i	$0.242760\pi$
$90$	1.77477	0.187077
$91$	−1.72778	−0.181120
$92$	−0.116032	−0.0120972
$93$	20.1069	2.08499
$94$	4.60163	0.474622
$95$	1.60755	0.164931
$96$	−2.18512	−0.223018
$97$	−1.27934	−0.129898	−0.0649488	−	0.997889i	$-0.520688\pi$
$97$	−1.27934	−0.129898	−0.0649488	+	0.997889i	$0.520688\pi$
$98$	−6.37286	−0.643756
$99$	0.980123	0.0985061
$100$	1.00000	0.100000
$101$	−9.39250	−0.934588	−0.467294	−	0.884102i	$-0.654771\pi$
$101$	−9.39250	−0.934588	−0.467294	+	0.884102i	$0.654771\pi$
$102$	13.9874	1.38496
$103$	3.21981	0.317257	0.158629	−	0.987338i	$-0.449293\pi$
$103$	3.21981	0.317257	0.158629	+	0.987338i	$0.449293\pi$
$104$	2.18175	0.213938
$105$	1.73045	0.168874
$106$	−5.31887	−0.516614
$107$	−8.26771	−0.799270	−0.399635	−	0.916674i	$-0.630863\pi$
$107$	−8.26771	−0.799270	−0.399635	+	0.916674i	$0.630863\pi$
$108$	2.67728	0.257621
$109$	−17.2551	−1.65274	−0.826371	−	0.563126i	$-0.809599\pi$
$109$	−17.2551	−1.65274	−0.826371	+	0.563126i	$0.809599\pi$
$110$	0.552253	0.0526553
$111$	−7.54456	−0.716098
$112$	−0.791922	−0.0748296
$113$	−6.27580	−0.590378	−0.295189	−	0.955439i	$-0.595383\pi$
$113$	−6.27580	−0.590378	−0.295189	+	0.955439i	$0.595383\pi$
$114$	−3.51269	−0.328994
$115$	−0.116032	−0.0108200
$116$	−7.26885	−0.674896
$117$	3.87210	0.357976
$118$	−3.25952	−0.300064
$119$	5.06925	0.464697
$120$	−2.18512	−0.199474
$121$	−10.6950	−0.972274
$122$	−10.9186	−0.988521
$123$	−15.0377	−1.35590
$124$	−9.20173	−0.826340
$125$	1.00000	0.0894427
$126$	−1.40548	−0.125210
$127$	−4.17481	−0.370454	−0.185227	−	0.982696i	$-0.559302\pi$
$127$	−4.17481	−0.370454	−0.185227	+	0.982696i	$0.559302\pi$
$128$	1.00000	0.0883883
$129$	−7.60872	−0.669910
$130$	2.18175	0.191352
$131$	−6.73510	−0.588448	−0.294224	−	0.955736i	$-0.595061\pi$
$131$	−6.73510	−0.588448	−0.294224	+	0.955736i	$0.595061\pi$
$132$	−1.20674	−0.105033
$133$	−1.27305	−0.110388
$134$	−3.76760	−0.325471
$135$	2.67728	0.230424
$136$	−6.40120	−0.548898
$137$	11.6906	0.998795	0.499397	−	0.866373i	$-0.333555\pi$
$137$	11.6906	0.998795	0.499397	+	0.866373i	$0.333555\pi$
$138$	0.253545	0.0215831
$139$	8.44968	0.716692	0.358346	−	0.933589i	$-0.383341\pi$
$139$	8.44968	0.716692	0.358346	+	0.933589i	$0.383341\pi$
$140$	−0.791922	−0.0669296
$141$	−10.0551	−0.846795
$142$	0.154848	0.0129946
$143$	1.20488	0.100757
$144$	1.77477	0.147898
$145$	−7.26885	−0.603645
$146$	−1.03107	−0.0853323
$147$	13.9255	1.14856
$148$	3.45269	0.283810
$149$	−20.5878	−1.68662	−0.843309	−	0.537429i	$-0.819396\pi$
$149$	−20.5878	−1.68662	−0.843309	+	0.537429i	$0.819396\pi$
$150$	−2.18512	−0.178415
$151$	−19.4233	−1.58065	−0.790323	−	0.612691i	$-0.790087\pi$
$151$	−19.4233	−1.58065	−0.790323	+	0.612691i	$0.790087\pi$
$152$	1.60755	0.130389
$153$	−11.3607	−0.918455
$154$	−0.437342	−0.0352420
$155$	−9.20173	−0.739101
$156$	−4.76739	−0.381697
$157$	−13.0162	−1.03881	−0.519403	−	0.854529i	$-0.673846\pi$
$157$	−13.0162	−1.03881	−0.519403	+	0.854529i	$0.673846\pi$
$158$	9.86274	0.784638
$159$	11.6224	0.921715
$160$	1.00000	0.0790569
$161$	0.0918884	0.00724182
$162$	−11.1745	−0.877952
$163$	9.47828	0.742396	0.371198	−	0.928554i	$-0.378947\pi$
$163$	9.47828	0.742396	0.371198	+	0.928554i	$0.378947\pi$
$164$	6.88184	0.537381
$165$	−1.20674	−0.0939448
$166$	−1.29394	−0.100429
$167$	18.2779	1.41439	0.707193	−	0.707021i	$-0.249961\pi$
$167$	18.2779	1.41439	0.707193	+	0.707021i	$0.249961\pi$
$168$	1.73045	0.133507
$169$	−8.23997	−0.633844
$170$	−6.40120	−0.490950
$171$	2.85303	0.218176
$172$	3.48205	0.265504
$173$	15.6546	1.19020	0.595100	−	0.803652i	$-0.297112\pi$
$173$	15.6546	1.19020	0.595100	+	0.803652i	$0.297112\pi$
$174$	15.8833	1.20411
$175$	−0.791922	−0.0598637
$176$	0.552253	0.0416277
$177$	7.12247	0.535358
$178$	13.6416	1.02248
$179$	−5.47553	−0.409260	−0.204630	−	0.978839i	$-0.565599\pi$
$179$	−5.47553	−0.409260	−0.204630	+	0.978839i	$0.565599\pi$
$180$	1.77477	0.132284
$181$	−2.34206	−0.174084	−0.0870419	−	0.996205i	$-0.527741\pi$
$181$	−2.34206	−0.174084	−0.0870419	+	0.996205i	$0.527741\pi$
$182$	−1.72778	−0.128071
$183$	23.8584	1.76367
$184$	−0.116032	−0.00855400
$185$	3.45269	0.253847
$186$	20.1069	1.47431
$187$	−3.53508	−0.258511
$188$	4.60163	0.335608
$189$	−2.12020	−0.154222
$190$	1.60755	0.116624
$191$	−4.64508	−0.336106	−0.168053	−	0.985778i	$-0.553748\pi$
$191$	−4.64508	−0.336106	−0.168053	+	0.985778i	$0.553748\pi$
$192$	−2.18512	−0.157698
$193$	−7.69377	−0.553809	−0.276905	−	0.960897i	$-0.589309\pi$
$193$	−7.69377	−0.553809	−0.276905	+	0.960897i	$0.589309\pi$
$194$	−1.27934	−0.0918515
$195$	−4.76739	−0.341400
$196$	−6.37286	−0.455204
$197$	−25.1394	−1.79111	−0.895553	−	0.444955i	$-0.853220\pi$
$197$	−25.1394	−1.79111	−0.895553	+	0.444955i	$0.853220\pi$
$198$	0.980123	0.0696543
$199$	−4.58464	−0.324996	−0.162498	−	0.986709i	$-0.551955\pi$
$199$	−4.58464	−0.324996	−0.162498	+	0.986709i	$0.551955\pi$
$200$	1.00000	0.0707107
$201$	8.23268	0.580688
$202$	−9.39250	−0.660854
$203$	5.75636	0.404017
$204$	13.9874	0.979315
$205$	6.88184	0.480648
$206$	3.21981	0.224335
$207$	−0.205930	−0.0143131
$208$	2.18175	0.151277
$209$	0.887773	0.0614086
$210$	1.73045	0.119412
$211$	−11.5742	−0.796799	−0.398400	−	0.917212i	$-0.630434\pi$
$211$	−11.5742	−0.796799	−0.398400	+	0.917212i	$0.630434\pi$
$212$	−5.31887	−0.365301
$213$	−0.338362	−0.0231842
$214$	−8.26771	−0.565169
$215$	3.48205	0.237474
$216$	2.67728	0.182166
$217$	7.28705	0.494677
$218$	−17.2551	−1.16867
$219$	2.25303	0.152245
$220$	0.552253	0.0372329
$221$	−13.9658	−0.939442
$222$	−7.54456	−0.506358
$223$	−24.1055	−1.61422	−0.807111	−	0.590400i	$-0.798970\pi$
$223$	−24.1055	−1.61422	−0.807111	+	0.590400i	$0.798970\pi$
$224$	−0.791922	−0.0529125
$225$	1.77477	0.118318
$226$	−6.27580	−0.417460
$227$	−1.79868	−0.119383	−0.0596914	−	0.998217i	$-0.519012\pi$
$227$	−1.79868	−0.119383	−0.0596914	+	0.998217i	$0.519012\pi$
$228$	−3.51269	−0.232634
$229$	−16.6193	−1.09824	−0.549118	−	0.835745i	$-0.685036\pi$
$229$	−16.6193	−1.09824	−0.549118	+	0.835745i	$0.685036\pi$
$230$	−0.116032	−0.00765093
$231$	0.955646	0.0628769
$232$	−7.26885	−0.477223
$233$	19.6043	1.28432	0.642160	−	0.766571i	$-0.278039\pi$
$233$	19.6043	1.28432	0.642160	+	0.766571i	$0.278039\pi$
$234$	3.87210	0.253127
$235$	4.60163	0.300177
$236$	−3.25952	−0.212177
$237$	−21.5513	−1.39991
$238$	5.06925	0.328591
$239$	−26.7120	−1.72786	−0.863928	−	0.503615i	$-0.832003\pi$
$239$	−26.7120	−1.72786	−0.863928	+	0.503615i	$0.832003\pi$
$240$	−2.18512	−0.141049
$241$	−2.20295	−0.141905	−0.0709523	−	0.997480i	$-0.522604\pi$
$241$	−2.20295	−0.141905	−0.0709523	+	0.997480i	$0.522604\pi$
$242$	−10.6950	−0.687502
$243$	16.3858	1.05115
$244$	−10.9186	−0.698990
$245$	−6.37286	−0.407147
$246$	−15.0377	−0.958767
$247$	3.50726	0.223162
$248$	−9.20173	−0.584310
$249$	2.82741	0.179180
$250$	1.00000	0.0632456
$251$	20.0687	1.26673	0.633363	−	0.773855i	$-0.281674\pi$
$251$	20.0687	1.26673	0.633363	+	0.773855i	$0.281674\pi$
$252$	−1.40548	−0.0885369
$253$	−0.0640791	−0.00402862
$254$	−4.17481	−0.261951
$255$	13.9874	0.875926
$256$	1.00000	0.0625000
$257$	−23.4564	−1.46317	−0.731584	−	0.681751i	$-0.761219\pi$
$257$	−23.4564	−1.46317	−0.731584	+	0.681751i	$0.761219\pi$
$258$	−7.60872	−0.473698
$259$	−2.73426	−0.169899
$260$	2.18175	0.135306
$261$	−12.9005	−0.798523
$262$	−6.73510	−0.416096
$263$	12.5075	0.771242	0.385621	−	0.922657i	$-0.373987\pi$
$263$	12.5075	0.771242	0.385621	+	0.922657i	$0.373987\pi$
$264$	−1.20674	−0.0742699
$265$	−5.31887	−0.326735
$266$	−1.27305	−0.0780558
$267$	−29.8087	−1.82426
$268$	−3.76760	−0.230143
$269$	17.5075	1.06745	0.533726	−	0.845658i	$-0.320791\pi$
$269$	17.5075	1.06745	0.533726	+	0.845658i	$0.320791\pi$
$270$	2.67728	0.162934
$271$	−7.18008	−0.436159	−0.218080	−	0.975931i	$-0.569979\pi$
$271$	−7.18008	−0.436159	−0.218080	+	0.975931i	$0.569979\pi$
$272$	−6.40120	−0.388130
$273$	3.77540	0.228498
$274$	11.6906	0.706255
$275$	0.552253	0.0333021
$276$	0.253545	0.0152616
$277$	−17.9333	−1.07751	−0.538754	−	0.842463i	$-0.681105\pi$
$277$	−17.9333	−1.07751	−0.538754	+	0.842463i	$0.681105\pi$
$278$	8.44968	0.506778
$279$	−16.3310	−0.977709
$280$	−0.791922	−0.0473264
$281$	25.0268	1.49297	0.746486	−	0.665401i	$-0.231740\pi$
$281$	25.0268	1.49297	0.746486	+	0.665401i	$0.231740\pi$
$282$	−10.0551	−0.598774
$283$	26.7008	1.58720	0.793598	−	0.608442i	$-0.208205\pi$
$283$	26.7008	1.58720	0.793598	+	0.608442i	$0.208205\pi$
$284$	0.154848	0.00918855
$285$	−3.51269	−0.208074
$286$	1.20488	0.0712460
$287$	−5.44988	−0.321696
$288$	1.77477	0.104579
$289$	23.9754	1.41031
$290$	−7.26885	−0.426842
$291$	2.79553	0.163877
$292$	−1.03107	−0.0603390
$293$	−15.1930	−0.887584	−0.443792	−	0.896130i	$-0.646367\pi$
$293$	−15.1930	−0.887584	−0.443792	+	0.896130i	$0.646367\pi$
$294$	13.9255	0.812151
$295$	−3.25952	−0.189777
$296$	3.45269	0.200684
$297$	1.47854	0.0857934
$298$	−20.5878	−1.19262
$299$	−0.253153	−0.0146402
$300$	−2.18512	−0.126158
$301$	−2.75751	−0.158940
$302$	−19.4233	−1.11769
$303$	20.5238	1.17906
$304$	1.60755	0.0921991
$305$	−10.9186	−0.625196
$306$	−11.3607	−0.649446
$307$	−9.39457	−0.536177	−0.268088	−	0.963394i	$-0.586392\pi$
$307$	−9.39457	−0.536177	−0.268088	+	0.963394i	$0.586392\pi$
$308$	−0.437342	−0.0249199
$309$	−7.03568	−0.400246
$310$	−9.20173	−0.522623
$311$	−18.7923	−1.06561	−0.532807	−	0.846237i	$-0.678863\pi$
$311$	−18.7923	−1.06561	−0.532807	+	0.846237i	$0.678863\pi$
$312$	−4.76739	−0.269901
$313$	−2.13516	−0.120687	−0.0603433	−	0.998178i	$-0.519220\pi$
$313$	−2.13516	−0.120687	−0.0603433	+	0.998178i	$0.519220\pi$
$314$	−13.0162	−0.734547
$315$	−1.40548	−0.0791898
$316$	9.86274	0.554823
$317$	−3.84740	−0.216092	−0.108046	−	0.994146i	$-0.534459\pi$
$317$	−3.84740	−0.216092	−0.108046	+	0.994146i	$0.534459\pi$
$318$	11.6224	0.651751
$319$	−4.01425	−0.224755
$320$	1.00000	0.0559017
$321$	18.0660	1.00834
$322$	0.0918884	0.00512074
$323$	−10.2902	−0.572564
$324$	−11.1745	−0.620806
$325$	2.18175	0.121022
$326$	9.47828	0.524953
$327$	37.7046	2.08507
$328$	6.88184	0.379986
$329$	−3.64413	−0.200907
$330$	−1.20674	−0.0664290
$331$	−25.0532	−1.37705	−0.688524	−	0.725213i	$-0.741741\pi$
$331$	−25.0532	−1.37705	−0.688524	+	0.725213i	$0.741741\pi$
$332$	−1.29394	−0.0710140
$333$	6.12774	0.335798
$334$	18.2779	1.00012
$335$	−3.76760	−0.205846
$336$	1.73045	0.0944037
$337$	3.47669	0.189387	0.0946936	−	0.995506i	$-0.469813\pi$
$337$	3.47669	0.189387	0.0946936	+	0.995506i	$0.469813\pi$
$338$	−8.23997	−0.448195
$339$	13.7134	0.744810
$340$	−6.40120	−0.347154
$341$	−5.08169	−0.275189
$342$	2.85303	0.154274
$343$	10.5903	0.571820
$344$	3.48205	0.187740
$345$	0.253545	0.0136504
$346$	15.6546	0.841599
$347$	25.1403	1.34960	0.674800	−	0.738001i	$-0.264230\pi$
$347$	25.1403	1.34960	0.674800	+	0.738001i	$0.264230\pi$
$348$	15.8833	0.851437
$349$	33.0834	1.77092	0.885458	−	0.464719i	$-0.153845\pi$
$349$	33.0834	1.77092	0.885458	+	0.464719i	$0.153845\pi$
$350$	−0.791922	−0.0423300
$351$	5.84115	0.311778
$352$	0.552253	0.0294352
$353$	−15.0366	−0.800319	−0.400160	−	0.916445i	$-0.631045\pi$
$353$	−15.0366	−0.800319	−0.400160	+	0.916445i	$0.631045\pi$
$354$	7.12247	0.378555
$355$	0.154848	0.00821849
$356$	13.6416	0.723005
$357$	−11.0769	−0.586254
$358$	−5.47553	−0.289391
$359$	13.0347	0.687946	0.343973	−	0.938980i	$-0.388227\pi$
$359$	13.0347	0.687946	0.343973	+	0.938980i	$0.388227\pi$
$360$	1.77477	0.0935386
$361$	−16.4158	−0.863989
$362$	−2.34206	−0.123096
$363$	23.3699	1.22660
$364$	−1.72778	−0.0905600
$365$	−1.03107	−0.0539689
$366$	23.8584	1.24710
$367$	−27.4090	−1.43074	−0.715369	−	0.698747i	$-0.753741\pi$
$367$	−27.4090	−1.43074	−0.715369	+	0.698747i	$0.753741\pi$
$368$	−0.116032	−0.00604859
$369$	12.2137	0.635819
$370$	3.45269	0.179497
$371$	4.21213	0.218683
$372$	20.1069	1.04250
$373$	16.0454	0.830800	0.415400	−	0.909639i	$-0.363642\pi$
$373$	16.0454	0.830800	0.415400	+	0.909639i	$0.363642\pi$
$374$	−3.53508	−0.182795
$375$	−2.18512	−0.112839
$376$	4.60163	0.237311
$377$	−15.8588	−0.816770
$378$	−2.12020	−0.109051
$379$	37.1261	1.90704	0.953519	−	0.301332i	$-0.0974314\pi$
$379$	37.1261	1.90704	0.953519	+	0.301332i	$0.0974314\pi$
$380$	1.60755	0.0824654
$381$	9.12248	0.467359
$382$	−4.64508	−0.237663
$383$	27.6528	1.41299	0.706496	−	0.707717i	$-0.250275\pi$
$383$	27.6528	1.41299	0.706496	+	0.707717i	$0.250275\pi$
$384$	−2.18512	−0.111509
$385$	−0.437342	−0.0222890
$386$	−7.69377	−0.391602
$387$	6.17984	0.314139
$388$	−1.27934	−0.0649488
$389$	−20.5359	−1.04121	−0.520605	−	0.853798i	$-0.674294\pi$
$389$	−20.5359	−1.04121	−0.520605	+	0.853798i	$0.674294\pi$
$390$	−4.76739	−0.241406
$391$	0.742744	0.0375622
$392$	−6.37286	−0.321878
$393$	14.7170	0.742376
$394$	−25.1394	−1.26650
$395$	9.86274	0.496248
$396$	0.980123	0.0492530
$397$	2.75215	0.138127	0.0690633	−	0.997612i	$-0.477999\pi$
$397$	2.75215	0.138127	0.0690633	+	0.997612i	$0.477999\pi$
$398$	−4.58464	−0.229807
$399$	2.78178	0.139263
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	8.23268	0.410609
$403$	−20.0759	−1.00005
$404$	−9.39250	−0.467294
$405$	−11.1745	−0.555265
$406$	5.75636	0.285683
$407$	1.90676	0.0945146
$408$	13.9874	0.692480
$409$	10.1257	0.500685	0.250343	−	0.968157i	$-0.419457\pi$
$409$	10.1257	0.500685	0.250343	+	0.968157i	$0.419457\pi$
$410$	6.88184	0.339870
$411$	−25.5454	−1.26006
$412$	3.21981	0.158629
$413$	2.58129	0.127017
$414$	−0.205930	−0.0101209
$415$	−1.29394	−0.0635169
$416$	2.18175	0.106969
$417$	−18.4636	−0.904166
$418$	0.887773	0.0434224
$419$	5.57855	0.272530	0.136265	−	0.990672i	$-0.456490\pi$
$419$	5.57855	0.272530	0.136265	+	0.990672i	$0.456490\pi$
$420$	1.73045	0.0844372
$421$	−9.73804	−0.474603	−0.237302	−	0.971436i	$-0.576263\pi$
$421$	−9.73804	−0.474603	−0.237302	+	0.971436i	$0.576263\pi$
$422$	−11.5742	−0.563422
$423$	8.16683	0.397085
$424$	−5.31887	−0.258307
$425$	−6.40120	−0.310504
$426$	−0.338362	−0.0163937
$427$	8.64666	0.418441
$428$	−8.26771	−0.399635
$429$	−2.63281	−0.127113
$430$	3.48205	0.167919
$431$	−8.27952	−0.398811	−0.199405	−	0.979917i	$-0.563901\pi$
$431$	−8.27952	−0.398811	−0.199405	+	0.979917i	$0.563901\pi$
$432$	2.67728	0.128811
$433$	15.3197	0.736217	0.368108	−	0.929783i	$-0.380006\pi$
$433$	15.3197	0.736217	0.368108	+	0.929783i	$0.380006\pi$
$434$	7.28705	0.349790
$435$	15.8833	0.761548
$436$	−17.2551	−0.826371
$437$	−0.186527	−0.00892279
$438$	2.25303	0.107654
$439$	31.9765	1.52615	0.763077	−	0.646307i	$-0.223688\pi$
$439$	31.9765	1.52615	0.763077	+	0.646307i	$0.223688\pi$
$440$	0.552253	0.0263276
$441$	−11.3104	−0.538589
$442$	−13.9658	−0.664286
$443$	21.3391	1.01385	0.506926	−	0.861990i	$-0.330782\pi$
$443$	21.3391	1.01385	0.506926	+	0.861990i	$0.330782\pi$
$444$	−7.54456	−0.358049
$445$	13.6416	0.646675
$446$	−24.1055	−1.14143
$447$	44.9869	2.12781
$448$	−0.791922	−0.0374148
$449$	−28.6038	−1.34990	−0.674948	−	0.737865i	$-0.735834\pi$
$449$	−28.6038	−1.34990	−0.674948	+	0.737865i	$0.735834\pi$
$450$	1.77477	0.0836635
$451$	3.80052	0.178959
$452$	−6.27580	−0.295189
$453$	42.4423	1.99411
$454$	−1.79868	−0.0844164
$455$	−1.72778	−0.0809993
$456$	−3.51269	−0.164497
$457$	−30.1010	−1.40807	−0.704033	−	0.710167i	$-0.748619\pi$
$457$	−30.1010	−1.40807	−0.704033	+	0.710167i	$0.748619\pi$
$458$	−16.6193	−0.776570
$459$	−17.1378	−0.799924
$460$	−0.116032	−0.00541002
$461$	−20.6615	−0.962301	−0.481150	−	0.876638i	$-0.659781\pi$
$461$	−20.6615	−0.962301	−0.481150	+	0.876638i	$0.659781\pi$
$462$	0.955646	0.0444607
$463$	31.8871	1.48192	0.740959	−	0.671550i	$-0.234371\pi$
$463$	31.8871	1.48192	0.740959	+	0.671550i	$0.234371\pi$
$464$	−7.26885	−0.337448
$465$	20.1069	0.932436
$466$	19.6043	0.908151
$467$	−25.9443	−1.20056	−0.600279	−	0.799791i	$-0.704944\pi$
$467$	−25.9443	−1.20056	−0.600279	+	0.799791i	$0.704944\pi$
$468$	3.87210	0.178988
$469$	2.98365	0.137772
$470$	4.60163	0.212257
$471$	28.4420	1.31054
$472$	−3.25952	−0.150032
$473$	1.92297	0.0884185
$474$	−21.5513	−0.989885
$475$	1.60755	0.0737593
$476$	5.06925	0.232349
$477$	−9.43977	−0.432217
$478$	−26.7120	−1.22178
$479$	21.3104	0.973699	0.486850	−	0.873486i	$-0.338146\pi$
$479$	21.3104	0.973699	0.486850	+	0.873486i	$0.338146\pi$
$480$	−2.18512	−0.0997368
$481$	7.53291	0.343471
$482$	−2.20295	−0.100342
$483$	−0.200788	−0.00913615
$484$	−10.6950	−0.486137
$485$	−1.27934	−0.0580920
$486$	16.3858	0.743277
$487$	9.47987	0.429574	0.214787	−	0.976661i	$-0.431094\pi$
$487$	9.47987	0.429574	0.214787	+	0.976661i	$0.431094\pi$
$488$	−10.9186	−0.494260
$489$	−20.7112	−0.936594
$490$	−6.37286	−0.287896
$491$	17.6875	0.798226	0.399113	−	0.916902i	$-0.369318\pi$
$491$	17.6875	0.798226	0.399113	+	0.916902i	$0.369318\pi$
$492$	−15.0377	−0.677951
$493$	46.5294	2.09558
$494$	3.50726	0.157799
$495$	0.980123	0.0440533
$496$	−9.20173	−0.413170
$497$	−0.122628	−0.00550060
$498$	2.82741	0.126699
$499$	6.62155	0.296421	0.148211	−	0.988956i	$-0.452649\pi$
$499$	6.62155	0.296421	0.148211	+	0.988956i	$0.452649\pi$
$500$	1.00000	0.0447214
$501$	−39.9395	−1.78436
$502$	20.0687	0.895711
$503$	8.03099	0.358084	0.179042	−	0.983841i	$-0.442700\pi$
$503$	8.03099	0.358084	0.179042	+	0.983841i	$0.442700\pi$
$504$	−1.40548	−0.0626051
$505$	−9.39250	−0.417961
$506$	−0.0640791	−0.00284866
$507$	18.0054	0.799646
$508$	−4.17481	−0.185227
$509$	5.47434	0.242646	0.121323	−	0.992613i	$-0.461286\pi$
$509$	5.47434	0.242646	0.121323	+	0.992613i	$0.461286\pi$
$510$	13.9874	0.619373
$511$	0.816530	0.0361212
$512$	1.00000	0.0441942
$513$	4.30385	0.190020
$514$	−23.4564	−1.03462
$515$	3.21981	0.141882
$516$	−7.60872	−0.334955
$517$	2.54126	0.111765
$518$	−2.73426	−0.120137
$519$	−34.2073	−1.50154
$520$	2.18175	0.0956760
$521$	−29.6990	−1.30114	−0.650569	−	0.759447i	$-0.725470\pi$
$521$	−29.6990	−1.30114	−0.650569	+	0.759447i	$0.725470\pi$
$522$	−12.9005	−0.564641
$523$	−31.7742	−1.38939	−0.694695	−	0.719305i	$-0.744461\pi$
$523$	−31.7742	−1.38939	−0.694695	+	0.719305i	$0.744461\pi$
$524$	−6.73510	−0.294224
$525$	1.73045	0.0755230
$526$	12.5075	0.545351
$527$	58.9021	2.56582
$528$	−1.20674	−0.0525167
$529$	−22.9865	−0.999415
$530$	−5.31887	−0.231037
$531$	−5.78491	−0.251044
$532$	−1.27305	−0.0551938
$533$	15.0144	0.650348
$534$	−29.8087	−1.28995
$535$	−8.26771	−0.357444
$536$	−3.76760	−0.162736
$537$	11.9647	0.516316
$538$	17.5075	0.754802
$539$	−3.51943	−0.151593
$540$	2.67728	0.115212
$541$	31.6161	1.35928	0.679642	−	0.733544i	$-0.262135\pi$
$541$	31.6161	1.35928	0.679642	+	0.733544i	$0.262135\pi$
$542$	−7.18008	−0.308411
$543$	5.11769	0.219621
$544$	−6.40120	−0.274449
$545$	−17.2551	−0.739129
$546$	3.77540	0.161572
$547$	−2.42682	−0.103763	−0.0518817	−	0.998653i	$-0.516522\pi$
$547$	−2.42682	−0.103763	−0.0518817	+	0.998653i	$0.516522\pi$
$548$	11.6906	0.499397
$549$	−19.3780	−0.827031
$550$	0.552253	0.0235482
$551$	−11.6850	−0.497798
$552$	0.253545	0.0107916
$553$	−7.81052	−0.332137
$554$	−17.9333	−0.761913
$555$	−7.54456	−0.320249
$556$	8.44968	0.358346
$557$	−26.8156	−1.13622	−0.568108	−	0.822954i	$-0.692324\pi$
$557$	−26.8156	−1.13622	−0.568108	+	0.822954i	$0.692324\pi$
$558$	−16.3310	−0.691345
$559$	7.59696	0.321317
$560$	−0.791922	−0.0334648
$561$	7.72460	0.326133
$562$	25.0268	1.05569
$563$	−0.0829354	−0.00349531	−0.00174766	−	0.999998i	$-0.500556\pi$
$563$	−0.0829354	−0.00349531	−0.00174766	+	0.999998i	$0.500556\pi$
$564$	−10.0551	−0.423397
$565$	−6.27580	−0.264025
$566$	26.7008	1.12232
$567$	8.84933	0.371637
$568$	0.154848	0.00649728
$569$	25.4279	1.06599	0.532996	−	0.846118i	$-0.321066\pi$
$569$	25.4279	1.06599	0.532996	+	0.846118i	$0.321066\pi$
$570$	−3.51269	−0.147130
$571$	5.68891	0.238073	0.119037	−	0.992890i	$-0.462019\pi$
$571$	5.68891	0.238073	0.119037	+	0.992890i	$0.462019\pi$
$572$	1.20488	0.0503785
$573$	10.1501	0.424026
$574$	−5.44988	−0.227474
$575$	−0.116032	−0.00483887
$576$	1.77477	0.0739488
$577$	12.7382	0.530298	0.265149	−	0.964208i	$-0.414579\pi$
$577$	12.7382	0.530298	0.265149	+	0.964208i	$0.414579\pi$
$578$	23.9754	0.997243
$579$	16.8118	0.698676
$580$	−7.26885	−0.301823
$581$	1.02470	0.0425116
$582$	2.79553	0.115878
$583$	−2.93736	−0.121653
$584$	−1.03107	−0.0426662
$585$	3.87210	0.160092
$586$	−15.1930	−0.627617
$587$	23.1405	0.955111	0.477555	−	0.878602i	$-0.341523\pi$
$587$	23.1405	0.955111	0.477555	+	0.878602i	$0.341523\pi$
$588$	13.9255	0.574278
$589$	−14.7922	−0.609502
$590$	−3.25952	−0.134193
$591$	54.9327	2.25963
$592$	3.45269	0.141905
$593$	−3.55616	−0.146034	−0.0730169	−	0.997331i	$-0.523263\pi$
$593$	−3.55616	−0.146034	−0.0730169	+	0.997331i	$0.523263\pi$
$594$	1.47854	0.0606651
$595$	5.06925	0.207819
$596$	−20.5878	−0.843309
$597$	10.0180	0.410010
$598$	−0.253153	−0.0103522
$599$	−23.8173	−0.973147	−0.486574	−	0.873640i	$-0.661754\pi$
$599$	−23.8173	−0.973147	−0.486574	+	0.873640i	$0.661754\pi$
$600$	−2.18512	−0.0892073
$601$	7.36844	0.300565	0.150282	−	0.988643i	$-0.451982\pi$
$601$	7.36844	0.300565	0.150282	+	0.988643i	$0.451982\pi$
$602$	−2.75751	−0.112388
$603$	−6.68663	−0.272301
$604$	−19.4233	−0.790323
$605$	−10.6950	−0.434814
$606$	20.5238	0.833721
$607$	−25.8635	−1.04977	−0.524883	−	0.851174i	$-0.675891\pi$
$607$	−25.8635	−1.04977	−0.524883	+	0.851174i	$0.675891\pi$
$608$	1.60755	0.0651946
$609$	−12.5784	−0.509701
$610$	−10.9186	−0.442080
$611$	10.0396	0.406159
$612$	−11.3607	−0.459227
$613$	39.7776	1.60660	0.803301	−	0.595573i	$-0.203075\pi$
$613$	39.7776	1.60660	0.803301	+	0.595573i	$0.203075\pi$
$614$	−9.39457	−0.379134
$615$	−15.0377	−0.606377
$616$	−0.437342	−0.0176210
$617$	14.4978	0.583660	0.291830	−	0.956470i	$-0.405736\pi$
$617$	14.4978	0.583660	0.291830	+	0.956470i	$0.405736\pi$
$618$	−7.03568	−0.283017
$619$	44.4112	1.78504	0.892518	−	0.451011i	$-0.148936\pi$
$619$	44.4112	1.78504	0.892518	+	0.451011i	$0.148936\pi$
$620$	−9.20173	−0.369550
$621$	−0.310650	−0.0124660
$622$	−18.7923	−0.753503
$623$	−10.8031	−0.432817
$624$	−4.76739	−0.190848
$625$	1.00000	0.0400000
$626$	−2.13516	−0.0853383
$627$	−1.93990	−0.0774719
$628$	−13.0162	−0.519403
$629$	−22.1014	−0.881239
$630$	−1.40548	−0.0559957
$631$	−18.6015	−0.740512	−0.370256	−	0.928930i	$-0.620730\pi$
$631$	−18.6015	−0.740512	−0.370256	+	0.928930i	$0.620730\pi$
$632$	9.86274	0.392319
$633$	25.2910	1.00523
$634$	−3.84740	−0.152800
$635$	−4.17481	−0.165672
$636$	11.6224	0.460858
$637$	−13.9040	−0.550896
$638$	−4.01425	−0.158926
$639$	0.274820	0.0108717
$640$	1.00000	0.0395285
$641$	16.1737	0.638824	0.319412	−	0.947616i	$-0.396515\pi$
$641$	16.1737	0.638824	0.319412	+	0.947616i	$0.396515\pi$
$642$	18.0660	0.713007
$643$	−16.8285	−0.663649	−0.331825	−	0.943341i	$-0.607664\pi$
$643$	−16.8285	−0.663649	−0.331825	+	0.943341i	$0.607664\pi$
$644$	0.0918884	0.00362091
$645$	−7.60872	−0.299593
$646$	−10.2902	−0.404864
$647$	−8.24417	−0.324112	−0.162056	−	0.986782i	$-0.551812\pi$
$647$	−8.24417	−0.324112	−0.162056	+	0.986782i	$0.551812\pi$
$648$	−11.1745	−0.438976
$649$	−1.80008	−0.0706595
$650$	2.18175	0.0855752
$651$	−15.9231	−0.624076
$652$	9.47828	0.371198
$653$	5.56300	0.217697	0.108848	−	0.994058i	$-0.465284\pi$
$653$	5.56300	0.217697	0.108848	+	0.994058i	$0.465284\pi$
$654$	37.7046	1.47437
$655$	−6.73510	−0.263162
$656$	6.88184	0.268691
$657$	−1.82992	−0.0713920
$658$	−3.64413	−0.142063
$659$	23.1142	0.900400	0.450200	−	0.892928i	$-0.351353\pi$
$659$	23.1142	0.900400	0.450200	+	0.892928i	$0.351353\pi$
$660$	−1.20674	−0.0469724
$661$	47.2204	1.83666	0.918330	−	0.395816i	$-0.129538\pi$
$661$	47.2204	1.83666	0.918330	+	0.395816i	$0.129538\pi$
$662$	−25.0532	−0.973720
$663$	30.5170	1.18518
$664$	−1.29394	−0.0502145
$665$	−1.27305	−0.0493668
$666$	6.12774	0.237445
$667$	0.843420	0.0326573
$668$	18.2779	0.707193
$669$	52.6734	2.03647
$670$	−3.76760	−0.145555
$671$	−6.02982	−0.232779
$672$	1.73045	0.0667535
$673$	15.6844	0.604589	0.302294	−	0.953215i	$-0.402247\pi$
$673$	15.6844	0.604589	0.302294	+	0.953215i	$0.402247\pi$
$674$	3.47669	0.133917
$675$	2.67728	0.103049
$676$	−8.23997	−0.316922
$677$	−10.1346	−0.389503	−0.194751	−	0.980853i	$-0.562390\pi$
$677$	−10.1346	−0.389503	−0.194751	+	0.980853i	$0.562390\pi$
$678$	13.7134	0.526660
$679$	1.01314	0.0388808
$680$	−6.40120	−0.245475
$681$	3.93035	0.150611
$682$	−5.08169	−0.194588
$683$	25.2232	0.965139	0.482570	−	0.875858i	$-0.339704\pi$
$683$	25.2232	0.965139	0.482570	+	0.875858i	$0.339704\pi$
$684$	2.85303	0.109088
$685$	11.6906	0.446675
$686$	10.5903	0.404338
$687$	36.3153	1.38552
$688$	3.48205	0.132752
$689$	−11.6044	−0.442094
$690$	0.253545	0.00965228
$691$	46.7905	1.77999	0.889997	−	0.455966i	$-0.150706\pi$
$691$	46.7905	1.77999	0.889997	+	0.455966i	$0.150706\pi$
$692$	15.6546	0.595100
$693$	−0.776181	−0.0294847
$694$	25.1403	0.954311
$695$	8.44968	0.320515
$696$	15.8833	0.602057
$697$	−44.0520	−1.66859
$698$	33.0834	1.25223
$699$	−42.8378	−1.62027
$700$	−0.791922	−0.0299318
$701$	−14.9471	−0.564546	−0.282273	−	0.959334i	$-0.591088\pi$
$701$	−14.9471	−0.564546	−0.282273	+	0.959334i	$0.591088\pi$
$702$	5.84115	0.220460
$703$	5.55036	0.209336
$704$	0.552253	0.0208138
$705$	−10.0551	−0.378698
$706$	−15.0366	−0.565911
$707$	7.43812	0.279739
$708$	7.12247	0.267679
$709$	23.0829	0.866895	0.433447	−	0.901179i	$-0.357297\pi$
$709$	23.0829	0.866895	0.433447	+	0.901179i	$0.357297\pi$
$710$	0.154848	0.00581135
$711$	17.5041	0.656455
$712$	13.6416	0.511242
$713$	1.06770	0.0399855
$714$	−11.0769	−0.414544
$715$	1.20488	0.0450599
$716$	−5.47553	−0.204630
$717$	58.3691	2.17983
$718$	13.0347	0.486451
$719$	−35.2743	−1.31551	−0.657756	−	0.753231i	$-0.728494\pi$
$719$	−35.2743	−1.31551	−0.657756	+	0.753231i	$0.728494\pi$
$720$	1.77477	0.0661418
$721$	−2.54984	−0.0949609
$722$	−16.4158	−0.610933
$723$	4.81372	0.179024
$724$	−2.34206	−0.0870419
$725$	−7.26885	−0.269958
$726$	23.3699	0.867340
$727$	−6.11120	−0.226652	−0.113326	−	0.993558i	$-0.536150\pi$
$727$	−6.11120	−0.226652	−0.113326	+	0.993558i	$0.536150\pi$
$728$	−1.72778	−0.0640356
$729$	−2.28161	−0.0845039
$730$	−1.03107	−0.0381618
$731$	−22.2893	−0.824400
$732$	23.8584	0.881833
$733$	−12.9386	−0.477898	−0.238949	−	0.971032i	$-0.576803\pi$
$733$	−12.9386	−0.477898	−0.238949	+	0.971032i	$0.576803\pi$
$734$	−27.4090	−1.01168
$735$	13.9255	0.513650
$736$	−0.116032	−0.00427700
$737$	−2.08067	−0.0766425
$738$	12.2137	0.449592
$739$	−20.1982	−0.743003	−0.371502	−	0.928432i	$-0.621157\pi$
$739$	−20.1982	−0.743003	−0.371502	+	0.928432i	$0.621157\pi$
$740$	3.45269	0.126923
$741$	−7.66381	−0.281537
$742$	4.21213	0.154632
$743$	23.4237	0.859331	0.429665	−	0.902988i	$-0.358632\pi$
$743$	23.4237	0.859331	0.429665	+	0.902988i	$0.358632\pi$
$744$	20.1069	0.737156
$745$	−20.5878	−0.754278
$746$	16.0454	0.587464
$747$	−2.29644	−0.0840224
$748$	−3.53508	−0.129255
$749$	6.54738	0.239236
$750$	−2.18512	−0.0797895
$751$	−32.2284	−1.17603	−0.588016	−	0.808849i	$-0.700091\pi$
$751$	−32.2284	−1.17603	−0.588016	+	0.808849i	$0.700091\pi$
$752$	4.60163	0.167804
$753$	−43.8527	−1.59808
$754$	−15.8588	−0.577544
$755$	−19.4233	−0.706886
$756$	−2.12020	−0.0771108
$757$	17.3305	0.629888	0.314944	−	0.949110i	$-0.398014\pi$
$757$	17.3305	0.629888	0.314944	+	0.949110i	$0.398014\pi$
$758$	37.1261	1.34848
$759$	0.140021	0.00508243
$760$	1.60755	0.0583118
$761$	−26.4195	−0.957708	−0.478854	−	0.877895i	$-0.658948\pi$
$761$	−26.4195	−0.957708	−0.478854	+	0.877895i	$0.658948\pi$
$762$	9.12248	0.330472
$763$	13.6647	0.494696
$764$	−4.64508	−0.168053
$765$	−11.3607	−0.410746
$766$	27.6528	0.999136
$767$	−7.11147	−0.256780
$768$	−2.18512	−0.0788489
$769$	−33.6622	−1.21389	−0.606945	−	0.794744i	$-0.707605\pi$
$769$	−33.6622	−1.21389	−0.606945	+	0.794744i	$0.707605\pi$
$770$	−0.437342	−0.0157607
$771$	51.2551	1.84591
$772$	−7.69377	−0.276905
$773$	18.1856	0.654092	0.327046	−	0.945008i	$-0.393947\pi$
$773$	18.1856	0.654092	0.327046	+	0.945008i	$0.393947\pi$
$774$	6.17984	0.222130
$775$	−9.20173	−0.330536
$776$	−1.27934	−0.0459258
$777$	5.97471	0.214341
$778$	−20.5359	−0.736247
$779$	11.0629	0.396369
$780$	−4.76739	−0.170700
$781$	0.0855154	0.00305998
$782$	0.742744	0.0265605
$783$	−19.4607	−0.695470
$784$	−6.37286	−0.227602
$785$	−13.0162	−0.464568
$786$	14.7170	0.524939
$787$	25.2679	0.900702	0.450351	−	0.892852i	$-0.351299\pi$
$787$	25.2679	0.900702	0.450351	+	0.892852i	$0.351299\pi$
$788$	−25.1394	−0.895553
$789$	−27.3303	−0.972986
$790$	9.86274	0.350901
$791$	4.96995	0.176711
$792$	0.980123	0.0348272
$793$	−23.8216	−0.845929
$794$	2.75215	0.0976702
$795$	11.6224	0.412204
$796$	−4.58464	−0.162498
$797$	43.2948	1.53358	0.766790	−	0.641898i	$-0.221853\pi$
$797$	43.2948	1.53358	0.766790	+	0.641898i	$0.221853\pi$
$798$	2.78178	0.0984738
$799$	−29.4559	−1.04208
$800$	1.00000	0.0353553
$801$	24.2108	0.855445
$802$	−1.00000	−0.0353112
$803$	−0.569414	−0.0200942
$804$	8.23268	0.290344
$805$	0.0918884	0.00323864
$806$	−20.0759	−0.707142
$807$	−38.2561	−1.34668
$808$	−9.39250	−0.330427
$809$	6.83309	0.240239	0.120119	−	0.992759i	$-0.461672\pi$
$809$	6.83309	0.240239	0.120119	+	0.992759i	$0.461672\pi$
$810$	−11.1745	−0.392632
$811$	−44.0497	−1.54679	−0.773397	−	0.633922i	$-0.781444\pi$
$811$	−44.0497	−1.54679	−0.773397	+	0.633922i	$0.781444\pi$
$812$	5.75636	0.202009
$813$	15.6894	0.550251
$814$	1.90676	0.0668319
$815$	9.47828	0.332010
$816$	13.9874	0.489658
$817$	5.59756	0.195834
$818$	10.1257	0.354038
$819$	−3.06640	−0.107149
$820$	6.88184	0.240324
$821$	25.6253	0.894328	0.447164	−	0.894452i	$-0.352434\pi$
$821$	25.6253	0.894328	0.447164	+	0.894452i	$0.352434\pi$
$822$	−25.5454	−0.890998
$823$	3.13049	0.109122	0.0545611	−	0.998510i	$-0.482624\pi$
$823$	3.13049	0.109122	0.0545611	+	0.998510i	$0.482624\pi$
$824$	3.21981	0.112167
$825$	−1.20674	−0.0420134
$826$	2.58129	0.0898146
$827$	28.8396	1.00285	0.501425	−	0.865201i	$-0.332809\pi$
$827$	28.8396	1.00285	0.501425	+	0.865201i	$0.332809\pi$
$828$	−0.205930	−0.00715657
$829$	16.1737	0.561737	0.280868	−	0.959746i	$-0.409378\pi$
$829$	16.1737	0.561737	0.280868	+	0.959746i	$0.409378\pi$
$830$	−1.29394	−0.0449132
$831$	39.1865	1.35937
$832$	2.18175	0.0756385
$833$	40.7939	1.41343
$834$	−18.4636	−0.639342
$835$	18.2779	0.632532
$836$	0.887773	0.0307043
$837$	−24.6356	−0.851531
$838$	5.57855	0.192708
$839$	40.3414	1.39274	0.696369	−	0.717684i	$-0.254798\pi$
$839$	40.3414	1.39274	0.696369	+	0.717684i	$0.254798\pi$
$840$	1.73045	0.0597061
$841$	23.8362	0.821937
$842$	−9.73804	−0.335595
$843$	−54.6866	−1.88351
$844$	−11.5742	−0.398400
$845$	−8.23997	−0.283464
$846$	8.16683	0.280782
$847$	8.46962	0.291020
$848$	−5.31887	−0.182651
$849$	−58.3445	−2.00238
$850$	−6.40120	−0.219559
$851$	−0.400623	−0.0137332
$852$	−0.338362	−0.0115921
$853$	6.51602	0.223104	0.111552	−	0.993759i	$-0.464418\pi$
$853$	6.51602	0.223104	0.111552	+	0.993759i	$0.464418\pi$
$854$	8.64666	0.295883
$855$	2.85303	0.0975714
$856$	−8.26771	−0.282585
$857$	−5.35562	−0.182944	−0.0914722	−	0.995808i	$-0.529157\pi$
$857$	−5.35562	−0.182944	−0.0914722	+	0.995808i	$0.529157\pi$
$858$	−2.63281	−0.0898826
$859$	49.0806	1.67461	0.837305	−	0.546736i	$-0.184130\pi$
$859$	49.0806	1.67461	0.837305	+	0.546736i	$0.184130\pi$
$860$	3.48205	0.118737
$861$	11.9087	0.405846
$862$	−8.27952	−0.282002
$863$	12.2189	0.415935	0.207967	−	0.978136i	$-0.433315\pi$
$863$	12.2189	0.415935	0.207967	+	0.978136i	$0.433315\pi$
$864$	2.67728	0.0910829
$865$	15.6546	0.532274
$866$	15.3197	0.520584
$867$	−52.3891	−1.77923
$868$	7.28705	0.247339
$869$	5.44673	0.184768
$870$	15.8833	0.538496
$871$	−8.21996	−0.278523
$872$	−17.2551	−0.584333
$873$	−2.27054	−0.0768462
$874$	−0.186527	−0.00630937
$875$	−0.791922	−0.0267719
$876$	2.25303	0.0761227
$877$	52.0183	1.75653	0.878267	−	0.478170i	$-0.158700\pi$
$877$	52.0183	1.75653	0.878267	+	0.478170i	$0.158700\pi$
$878$	31.9765	1.07915
$879$	33.1986	1.11976
$880$	0.552253	0.0186165
$881$	10.8843	0.366701	0.183350	−	0.983048i	$-0.441306\pi$
$881$	10.8843	0.366701	0.183350	+	0.983048i	$0.441306\pi$
$882$	−11.3104	−0.380840
$883$	5.23167	0.176060	0.0880298	−	0.996118i	$-0.471943\pi$
$883$	5.23167	0.176060	0.0880298	+	0.996118i	$0.471943\pi$
$884$	−13.9658	−0.469721
$885$	7.12247	0.239419
$886$	21.3391	0.716902
$887$	51.2736	1.72160	0.860800	−	0.508944i	$-0.169964\pi$
$887$	51.2736	1.72160	0.860800	+	0.508944i	$0.169964\pi$
$888$	−7.54456	−0.253179
$889$	3.30612	0.110884
$890$	13.6416	0.457269
$891$	−6.17116	−0.206742
$892$	−24.1055	−0.807111
$893$	7.39733	0.247542
$894$	44.9869	1.50459
$895$	−5.47553	−0.183027
$896$	−0.791922	−0.0264563
$897$	0.553171	0.0184698
$898$	−28.6038	−0.954521
$899$	66.8860	2.23077
$900$	1.77477	0.0591590
$901$	34.0471	1.13427
$902$	3.80052	0.126543
$903$	6.02551	0.200516
$904$	−6.27580	−0.208730
$905$	−2.34206	−0.0778527
$906$	42.4423	1.41005
$907$	−36.7532	−1.22037	−0.610185	−	0.792259i	$-0.708905\pi$
$907$	−36.7532	−1.22037	−0.610185	+	0.792259i	$0.708905\pi$
$908$	−1.79868	−0.0596914
$909$	−16.6695	−0.552893
$910$	−1.72778	−0.0572752
$911$	17.3028	0.573266	0.286633	−	0.958040i	$-0.407464\pi$
$911$	17.3028	0.573266	0.286633	+	0.958040i	$0.407464\pi$
$912$	−3.51269	−0.116317
$913$	−0.714581	−0.0236492
$914$	−30.1010	−0.995653
$915$	23.8584	0.788736
$916$	−16.6193	−0.549118
$917$	5.33367	0.176133
$918$	−17.1378	−0.565632
$919$	−35.3728	−1.16684	−0.583420	−	0.812171i	$-0.698286\pi$
$919$	−35.3728	−1.16684	−0.583420	+	0.812171i	$0.698286\pi$
$920$	−0.116032	−0.00382546
$921$	20.5283	0.676431
$922$	−20.6615	−0.680449
$923$	0.337840	0.0111201
$924$	0.955646	0.0314384
$925$	3.45269	0.113524
$926$	31.8871	1.04787
$927$	5.71442	0.187686
$928$	−7.26885	−0.238612
$929$	−6.76743	−0.222032	−0.111016	−	0.993819i	$-0.535411\pi$
$929$	−6.76743	−0.222032	−0.111016	+	0.993819i	$0.535411\pi$
$930$	20.1069	0.659332
$931$	−10.2447	−0.335755
$932$	19.6043	0.642160
$933$	41.0635	1.34436
$934$	−25.9443	−0.848922
$935$	−3.53508	−0.115610
$936$	3.87210	0.126564
$937$	53.2800	1.74058	0.870291	−	0.492537i	$-0.163930\pi$
$937$	53.2800	1.74058	0.870291	+	0.492537i	$0.163930\pi$
$938$	2.98365	0.0974195
$939$	4.66560	0.152256
$940$	4.60163	0.150089
$941$	−13.0068	−0.424008	−0.212004	−	0.977269i	$-0.567999\pi$
$941$	−13.0068	−0.424008	−0.212004	+	0.977269i	$0.567999\pi$
$942$	28.4420	0.926692
$943$	−0.798514	−0.0260032
$944$	−3.25952	−0.106088
$945$	−2.12020	−0.0689700
$946$	1.92297	0.0625213
$947$	−7.87341	−0.255851	−0.127926	−	0.991784i	$-0.540832\pi$
$947$	−7.87341	−0.255851	−0.127926	+	0.991784i	$0.540832\pi$
$948$	−21.5513	−0.699954
$949$	−2.24954	−0.0730233
$950$	1.60755	0.0521557
$951$	8.40706	0.272617
$952$	5.06925	0.164295
$953$	−13.6868	−0.443359	−0.221680	−	0.975120i	$-0.571154\pi$
$953$	−13.6868	−0.443359	−0.221680	+	0.975120i	$0.571154\pi$
$954$	−9.43977	−0.305624
$955$	−4.64508	−0.150311
$956$	−26.7120	−0.863928
$957$	8.77163	0.283547
$958$	21.3104	0.688509
$959$	−9.25804	−0.298958
$960$	−2.18512	−0.0705246
$961$	53.6718	1.73135
$962$	7.53291	0.242871
$963$	−14.6733	−0.472840
$964$	−2.20295	−0.0709523
$965$	−7.69377	−0.247671
$966$	−0.200788	−0.00646023
$967$	−45.3188	−1.45735	−0.728677	−	0.684857i	$-0.759865\pi$
$967$	−45.3188	−1.45735	−0.728677	+	0.684857i	$0.759865\pi$
$968$	−10.6950	−0.343751
$969$	22.4854	0.722336
$970$	−1.27934	−0.0410772
$971$	−49.9392	−1.60263	−0.801313	−	0.598246i	$-0.795865\pi$
$971$	−49.9392	−1.60263	−0.801313	+	0.598246i	$0.795865\pi$
$972$	16.3858	0.525576
$973$	−6.69149	−0.214519
$974$	9.47987	0.303755
$975$	−4.76739	−0.152679
$976$	−10.9186	−0.349495
$977$	3.92008	0.125415	0.0627073	−	0.998032i	$-0.480027\pi$
$977$	3.92008	0.125415	0.0627073	+	0.998032i	$0.480027\pi$
$978$	−20.7112	−0.662272
$979$	7.53364	0.240776
$980$	−6.37286	−0.203574
$981$	−30.6239	−0.977746
$982$	17.6875	0.564431
$983$	−4.31280	−0.137557	−0.0687785	−	0.997632i	$-0.521910\pi$
$983$	−4.31280	−0.137557	−0.0687785	+	0.997632i	$0.521910\pi$
$984$	−15.0377	−0.479383
$985$	−25.1394	−0.801007
$986$	46.5294	1.48180
$987$	7.96288	0.253461
$988$	3.50726	0.111581
$989$	−0.404030	−0.0128474
$990$	0.980123	0.0311504
$991$	−42.4144	−1.34734	−0.673669	−	0.739033i	$-0.735283\pi$
$991$	−42.4144	−1.34734	−0.673669	+	0.739033i	$0.735283\pi$
$992$	−9.20173	−0.292155
$993$	54.7444	1.73726
$994$	−0.122628	−0.00388951
$995$	−4.58464	−0.145343
$996$	2.82741	0.0895901
$997$	27.0549	0.856837	0.428419	−	0.903580i	$-0.359071\pi$
$997$	27.0549	0.856837	0.428419	+	0.903580i	$0.359071\pi$
$998$	6.62155	0.209601
$999$	9.24382	0.292462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.h.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.h.1.2	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.18512 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.18512 q^{6} -0.791922 q^{7} +1.00000 q^{8} +1.77477 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.18512 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.18512 q^{6} -0.791922 q^{7} +1.00000 q^{8} +1.77477 q^{9} +1.00000 q^{10} +0.552253 q^{11} -2.18512 q^{12} +2.18175 q^{13} -0.791922 q^{14} -2.18512 q^{15} +1.00000 q^{16} -6.40120 q^{17} +1.77477 q^{18} +1.60755 q^{19} +1.00000 q^{20} +1.73045 q^{21} +0.552253 q^{22} -0.116032 q^{23} -2.18512 q^{24} +1.00000 q^{25} +2.18175 q^{26} +2.67728 q^{27} -0.791922 q^{28} -7.26885 q^{29} -2.18512 q^{30} -9.20173 q^{31} +1.00000 q^{32} -1.20674 q^{33} -6.40120 q^{34} -0.791922 q^{35} +1.77477 q^{36} +3.45269 q^{37} +1.60755 q^{38} -4.76739 q^{39} +1.00000 q^{40} +6.88184 q^{41} +1.73045 q^{42} +3.48205 q^{43} +0.552253 q^{44} +1.77477 q^{45} -0.116032 q^{46} +4.60163 q^{47} -2.18512 q^{48} -6.37286 q^{49} +1.00000 q^{50} +13.9874 q^{51} +2.18175 q^{52} -5.31887 q^{53} +2.67728 q^{54} +0.552253 q^{55} -0.791922 q^{56} -3.51269 q^{57} -7.26885 q^{58} -3.25952 q^{59} -2.18512 q^{60} -10.9186 q^{61} -9.20173 q^{62} -1.40548 q^{63} +1.00000 q^{64} +2.18175 q^{65} -1.20674 q^{66} -3.76760 q^{67} -6.40120 q^{68} +0.253545 q^{69} -0.791922 q^{70} +0.154848 q^{71} +1.77477 q^{72} -1.03107 q^{73} +3.45269 q^{74} -2.18512 q^{75} +1.60755 q^{76} -0.437342 q^{77} -4.76739 q^{78} +9.86274 q^{79} +1.00000 q^{80} -11.1745 q^{81} +6.88184 q^{82} -1.29394 q^{83} +1.73045 q^{84} -6.40120 q^{85} +3.48205 q^{86} +15.8833 q^{87} +0.552253 q^{88} +13.6416 q^{89} +1.77477 q^{90} -1.72778 q^{91} -0.116032 q^{92} +20.1069 q^{93} +4.60163 q^{94} +1.60755 q^{95} -2.18512 q^{96} -1.27934 q^{97} -6.37286 q^{98} +0.980123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * q^99

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