LMFDB - Embedded newform 5610.2.a.ck.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.19985813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 23x^{3} + 28x^{2} + 40x - 24 $ x^5 - 2x^4 - 23x^3 + 28x^2 + 40x - 24
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.18590$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.13795 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.13795 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.43005 q^{13} -1.13795 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +6.43005 q^{19} +1.00000 q^{20} -1.13795 q^{21} -1.00000 q^{22} +5.50974 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.43005 q^{26} +1.00000 q^{27} -1.13795 q^{28} -1.29211 q^{29} +1.00000 q^{30} -4.33328 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -1.13795 q^{35} +1.00000 q^{36} +7.25359 q^{37} +6.43005 q^{38} -2.43005 q^{39} +1.00000 q^{40} -2.37179 q^{41} -1.13795 q^{42} +12.7633 q^{43} -1.00000 q^{44} +1.00000 q^{45} +5.50974 q^{46} +2.37179 q^{47} +1.00000 q^{48} -5.70507 q^{49} +1.00000 q^{50} -1.00000 q^{51} -2.43005 q^{52} +7.09943 q^{53} +1.00000 q^{54} -1.00000 q^{55} -1.13795 q^{56} +6.43005 q^{57} -1.29211 q^{58} -0.823536 q^{59} +1.00000 q^{60} +3.23472 q^{61} -4.33328 q^{62} -1.13795 q^{63} +1.00000 q^{64} -2.43005 q^{65} -1.00000 q^{66} +0.977695 q^{67} -1.00000 q^{68} +5.50974 q^{69} -1.13795 q^{70} +9.68365 q^{71} +1.00000 q^{72} +13.8430 q^{73} +7.25359 q^{74} +1.00000 q^{75} +6.43005 q^{76} +1.13795 q^{77} -2.43005 q^{78} -10.0554 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.37179 q^{82} +1.23472 q^{83} -1.13795 q^{84} -1.00000 q^{85} +12.7633 q^{86} -1.29211 q^{87} -1.00000 q^{88} -8.58421 q^{89} +1.00000 q^{90} +2.76528 q^{91} +5.50974 q^{92} -4.33328 q^{93} +2.37179 q^{94} +6.43005 q^{95} +1.00000 q^{96} -13.1934 q^{97} -5.70507 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} - 5 q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} + 11 q^{19} + 5 q^{20} + 2 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{24} + 5 q^{25} + 9 q^{26} + 5 q^{27} + 2 q^{28} + 7 q^{29} + 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + 7 q^{37} + 11 q^{38} + 9 q^{39} + 5 q^{40} + 4 q^{41} + 2 q^{42} + 11 q^{43} - 5 q^{44} + 5 q^{45} + 4 q^{46} - 4 q^{47} + 5 q^{48} + 19 q^{49} + 5 q^{50} - 5 q^{51} + 9 q^{52} + 12 q^{53} + 5 q^{54} - 5 q^{55} + 2 q^{56} + 11 q^{57} + 7 q^{58} + 4 q^{59} + 5 q^{60} + 19 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} - 5 q^{68} + 4 q^{69} + 2 q^{70} - 2 q^{71} + 5 q^{72} + 14 q^{73} + 7 q^{74} + 5 q^{75} + 11 q^{76} - 2 q^{77} + 9 q^{78} + 16 q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} + 9 q^{83} + 2 q^{84} - 5 q^{85} + 11 q^{86} + 7 q^{87} - 5 q^{88} - 16 q^{89} + 5 q^{90} + 11 q^{91} + 4 q^{92} + 10 q^{93} - 4 q^{94} + 11 q^{95} + 5 q^{96} + 8 q^{97} + 19 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 - 5 * q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 + 11 * q^19 + 5 * q^20 + 2 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^24 + 5 * q^25 + 9 * q^26 + 5 * q^27 + 2 * q^28 + 7 * q^29 + 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + 7 * q^37 + 11 * q^38 + 9 * q^39 + 5 * q^40 + 4 * q^41 + 2 * q^42 + 11 * q^43 - 5 * q^44 + 5 * q^45 + 4 * q^46 - 4 * q^47 + 5 * q^48 + 19 * q^49 + 5 * q^50 - 5 * q^51 + 9 * q^52 + 12 * q^53 + 5 * q^54 - 5 * q^55 + 2 * q^56 + 11 * q^57 + 7 * q^58 + 4 * q^59 + 5 * q^60 + 19 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 - 5 * q^68 + 4 * q^69 + 2 * q^70 - 2 * q^71 + 5 * q^72 + 14 * q^73 + 7 * q^74 + 5 * q^75 + 11 * q^76 - 2 * q^77 + 9 * q^78 + 16 * q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 + 9 * q^83 + 2 * q^84 - 5 * q^85 + 11 * q^86 + 7 * q^87 - 5 * q^88 - 16 * q^89 + 5 * q^90 + 11 * q^91 + 4 * q^92 + 10 * q^93 - 4 * q^94 + 11 * q^95 + 5 * q^96 + 8 * q^97 + 19 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−1.13795	−0.430104	−0.215052	−	0.976603i	$-0.568992\pi$
$7$	−1.13795	−0.430104	−0.215052	+	0.976603i	$0.568992\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−2.43005	−0.673976	−0.336988	−	0.941509i	$-0.609408\pi$
$13$	−2.43005	−0.673976	−0.336988	+	0.941509i	$0.609408\pi$
$14$	−1.13795	−0.304129
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	6.43005	1.47516	0.737578	−	0.675262i	$-0.235969\pi$
$19$	6.43005	1.47516	0.737578	+	0.675262i	$0.235969\pi$
$20$	1.00000	0.223607
$21$	−1.13795	−0.248321
$22$	−1.00000	−0.213201
$23$	5.50974	1.14886	0.574430	−	0.818553i	$-0.305224\pi$
$23$	5.50974	1.14886	0.574430	+	0.818553i	$0.305224\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.43005	−0.476573
$27$	1.00000	0.192450
$28$	−1.13795	−0.215052
$29$	−1.29211	−0.239938	−0.119969	−	0.992778i	$-0.538280\pi$
$29$	−1.29211	−0.239938	−0.119969	+	0.992778i	$0.538280\pi$
$30$	1.00000	0.182574
$31$	−4.33328	−0.778280	−0.389140	−	0.921179i	$-0.627228\pi$
$31$	−4.33328	−0.778280	−0.389140	+	0.921179i	$0.627228\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−1.13795	−0.192348
$36$	1.00000	0.166667
$37$	7.25359	1.19248	0.596242	−	0.802805i	$-0.296660\pi$
$37$	7.25359	1.19248	0.596242	+	0.802805i	$0.296660\pi$
$38$	6.43005	1.04309
$39$	−2.43005	−0.389120
$40$	1.00000	0.158114
$41$	−2.37179	−0.370412	−0.185206	−	0.982700i	$-0.559295\pi$
$41$	−2.37179	−0.370412	−0.185206	+	0.982700i	$0.559295\pi$
$42$	−1.13795	−0.175589
$43$	12.7633	1.94639	0.973195	−	0.229981i	$-0.0738664\pi$
$43$	12.7633	1.94639	0.973195	+	0.229981i	$0.0738664\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	5.50974	0.812367
$47$	2.37179	0.345962	0.172981	−	0.984925i	$-0.444660\pi$
$47$	2.37179	0.345962	0.172981	+	0.984925i	$0.444660\pi$
$48$	1.00000	0.144338
$49$	−5.70507	−0.815011
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−2.43005	−0.336988
$53$	7.09943	0.975182	0.487591	−	0.873072i	$-0.337876\pi$
$53$	7.09943	0.975182	0.487591	+	0.873072i	$0.337876\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	−1.13795	−0.152065
$57$	6.43005	0.851682
$58$	−1.29211	−0.169662
$59$	−0.823536	−0.107215	−0.0536076	−	0.998562i	$-0.517072\pi$
$59$	−0.823536	−0.107215	−0.0536076	+	0.998562i	$0.517072\pi$
$60$	1.00000	0.129099
$61$	3.23472	0.414164	0.207082	−	0.978324i	$-0.433603\pi$
$61$	3.23472	0.414164	0.207082	+	0.978324i	$0.433603\pi$
$62$	−4.33328	−0.550327
$63$	−1.13795	−0.143368
$64$	1.00000	0.125000
$65$	−2.43005	−0.301411
$66$	−1.00000	−0.123091
$67$	0.977695	0.119444	0.0597222	−	0.998215i	$-0.480979\pi$
$67$	0.977695	0.119444	0.0597222	+	0.998215i	$0.480979\pi$
$68$	−1.00000	−0.121268
$69$	5.50974	0.663295
$70$	−1.13795	−0.136011
$71$	9.68365	1.14924	0.574619	−	0.818421i	$-0.305150\pi$
$71$	9.68365	1.14924	0.574619	+	0.818421i	$0.305150\pi$
$72$	1.00000	0.117851
$73$	13.8430	1.62020	0.810102	−	0.586290i	$-0.199412\pi$
$73$	13.8430	1.62020	0.810102	+	0.586290i	$0.199412\pi$
$74$	7.25359	0.843213
$75$	1.00000	0.115470
$76$	6.43005	0.737578
$77$	1.13795	0.129681
$78$	−2.43005	−0.275150
$79$	−10.0554	−1.13133	−0.565663	−	0.824637i	$-0.691380\pi$
$79$	−10.0554	−1.13133	−0.565663	+	0.824637i	$0.691380\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−2.37179	−0.261921
$83$	1.23472	0.135529	0.0677643	−	0.997701i	$-0.478413\pi$
$83$	1.23472	0.135529	0.0677643	+	0.997701i	$0.478413\pi$
$84$	−1.13795	−0.124160
$85$	−1.00000	−0.108465
$86$	12.7633	1.37631
$87$	−1.29211	−0.138528
$88$	−1.00000	−0.106600
$89$	−8.58421	−0.909925	−0.454962	−	0.890511i	$-0.650347\pi$
$89$	−8.58421	−0.909925	−0.454962	+	0.890511i	$0.650347\pi$
$90$	1.00000	0.105409
$91$	2.76528	0.289880
$92$	5.50974	0.574430
$93$	−4.33328	−0.449340
$94$	2.37179	0.244632
$95$	6.43005	0.659710
$96$	1.00000	0.102062
$97$	−13.1934	−1.33959	−0.669793	−	0.742548i	$-0.733617\pi$
$97$	−13.1934	−1.33959	−0.669793	+	0.742548i	$0.733617\pi$
$98$	−5.70507	−0.576300
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	0.212419	0.0211364	0.0105682	−	0.999944i	$-0.496636\pi$
$101$	0.212419	0.0211364	0.0105682	+	0.999944i	$0.496636\pi$
$102$	−1.00000	−0.0990148
$103$	−10.8216	−1.06628	−0.533142	−	0.846026i	$-0.678989\pi$
$103$	−10.8216	−1.06628	−0.533142	+	0.846026i	$0.678989\pi$
$104$	−2.43005	−0.238286
$105$	−1.13795	−0.111052
$106$	7.09943	0.689558
$107$	10.2157	0.987588	0.493794	−	0.869579i	$-0.335610\pi$
$107$	10.2157	0.987588	0.493794	+	0.869579i	$0.335610\pi$
$108$	1.00000	0.0962250
$109$	15.9013	1.52307	0.761533	−	0.648126i	$-0.224447\pi$
$109$	15.9013	1.52307	0.761533	+	0.648126i	$0.224447\pi$
$110$	−1.00000	−0.0953463
$111$	7.25359	0.688480
$112$	−1.13795	−0.107526
$113$	3.19533	0.300591	0.150296	−	0.988641i	$-0.451977\pi$
$113$	3.19533	0.300591	0.150296	+	0.988641i	$0.451977\pi$
$114$	6.43005	0.602230
$115$	5.50974	0.513786
$116$	−1.29211	−0.119969
$117$	−2.43005	−0.224659
$118$	−0.823536	−0.0758126
$119$	1.13795	0.104316
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	3.23472	0.292858
$123$	−2.37179	−0.213858
$124$	−4.33328	−0.389140
$125$	1.00000	0.0894427
$126$	−1.13795	−0.101376
$127$	4.64769	0.412416	0.206208	−	0.978508i	$-0.433888\pi$
$127$	4.64769	0.412416	0.206208	+	0.978508i	$0.433888\pi$
$128$	1.00000	0.0883883
$129$	12.7633	1.12375
$130$	−2.43005	−0.213130
$131$	5.97831	0.522328	0.261164	−	0.965294i	$-0.415894\pi$
$131$	5.97831	0.522328	0.261164	+	0.965294i	$0.415894\pi$
$132$	−1.00000	−0.0870388
$133$	−7.31707	−0.634470
$134$	0.977695	0.0844600
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	−12.8216	−1.09542	−0.547711	−	0.836667i	$-0.684501\pi$
$137$	−12.8216	−1.09542	−0.547711	+	0.836667i	$0.684501\pi$
$138$	5.50974	0.469020
$139$	20.7999	1.76423	0.882113	−	0.471039i	$-0.156121\pi$
$139$	20.7999	1.76423	0.882113	+	0.471039i	$0.156121\pi$
$140$	−1.13795	−0.0961742
$141$	2.37179	0.199741
$142$	9.68365	0.812634
$143$	2.43005	0.203211
$144$	1.00000	0.0833333
$145$	−1.29211	−0.107304
$146$	13.8430	1.14566
$147$	−5.70507	−0.470547
$148$	7.25359	0.596242
$149$	5.25359	0.430391	0.215195	−	0.976571i	$-0.430961\pi$
$149$	5.25359	0.430391	0.215195	+	0.976571i	$0.430961\pi$
$150$	1.00000	0.0816497
$151$	−0.393481	−0.0320211	−0.0160105	−	0.999872i	$-0.505097\pi$
$151$	−0.393481	−0.0320211	−0.0160105	+	0.999872i	$0.505097\pi$
$152$	6.43005	0.521546
$153$	−1.00000	−0.0808452
$154$	1.13795	0.0916985
$155$	−4.33328	−0.348057
$156$	−2.43005	−0.194560
$157$	−13.0725	−1.04330	−0.521651	−	0.853159i	$-0.674684\pi$
$157$	−13.0725	−1.04330	−0.521651	+	0.853159i	$0.674684\pi$
$158$	−10.0554	−0.799968
$159$	7.09943	0.563022
$160$	1.00000	0.0790569
$161$	−6.26980	−0.494130
$162$	1.00000	0.0785674
$163$	−10.5240	−0.824304	−0.412152	−	0.911115i	$-0.635223\pi$
$163$	−10.5240	−0.824304	−0.412152	+	0.911115i	$0.635223\pi$
$164$	−2.37179	−0.185206
$165$	−1.00000	−0.0778499
$166$	1.23472	0.0958331
$167$	−8.64769	−0.669178	−0.334589	−	0.942364i	$-0.608598\pi$
$167$	−8.64769	−0.669178	−0.334589	+	0.942364i	$0.608598\pi$
$168$	−1.13795	−0.0877946
$169$	−7.09483	−0.545756
$170$	−1.00000	−0.0766965
$171$	6.43005	0.491719
$172$	12.7633	0.973195
$173$	10.1583	0.772322	0.386161	−	0.922431i	$-0.373801\pi$
$173$	10.1583	0.772322	0.386161	+	0.922431i	$0.373801\pi$
$174$	−1.29211	−0.0979544
$175$	−1.13795	−0.0860208
$176$	−1.00000	−0.0753778
$177$	−0.823536	−0.0619008
$178$	−8.58421	−0.643414
$179$	2.05826	0.153842	0.0769208	−	0.997037i	$-0.475491\pi$
$179$	2.05826	0.153842	0.0769208	+	0.997037i	$0.475491\pi$
$180$	1.00000	0.0745356
$181$	9.95867	0.740222	0.370111	−	0.928988i	$-0.379320\pi$
$181$	9.95867	0.740222	0.370111	+	0.928988i	$0.379320\pi$
$182$	2.76528	0.204976
$183$	3.23472	0.239118
$184$	5.50974	0.406184
$185$	7.25359	0.533295
$186$	−4.33328	−0.317731
$187$	1.00000	0.0731272
$188$	2.37179	0.172981
$189$	−1.13795	−0.0827735
$190$	6.43005	0.466485
$191$	−4.70789	−0.340651	−0.170326	−	0.985388i	$-0.554482\pi$
$191$	−4.70789	−0.340651	−0.170326	+	0.985388i	$0.554482\pi$
$192$	1.00000	0.0721688
$193$	−10.2679	−0.739097	−0.369548	−	0.929212i	$-0.620488\pi$
$193$	−10.2679	−0.739097	−0.369548	+	0.929212i	$0.620488\pi$
$194$	−13.1934	−0.947230
$195$	−2.43005	−0.174020
$196$	−5.70507	−0.407505
$197$	13.8378	0.985903	0.492951	−	0.870057i	$-0.335918\pi$
$197$	13.8378	0.985903	0.492951	+	0.870057i	$0.335918\pi$
$198$	−1.00000	−0.0710669
$199$	18.9738	1.34502	0.672509	−	0.740089i	$-0.265217\pi$
$199$	18.9738	1.34502	0.672509	+	0.740089i	$0.265217\pi$
$200$	1.00000	0.0707107
$201$	0.977695	0.0689613
$202$	0.212419	0.0149457
$203$	1.47035	0.103198
$204$	−1.00000	−0.0700140
$205$	−2.37179	−0.165653
$206$	−10.8216	−0.753976
$207$	5.50974	0.382954
$208$	−2.43005	−0.168494
$209$	−6.43005	−0.444776
$210$	−1.13795	−0.0785259
$211$	7.31097	0.503308	0.251654	−	0.967817i	$-0.419025\pi$
$211$	7.31097	0.503308	0.251654	+	0.967817i	$0.419025\pi$
$212$	7.09943	0.487591
$213$	9.68365	0.663512
$214$	10.2157	0.698330
$215$	12.7633	0.870452
$216$	1.00000	0.0680414
$217$	4.93105	0.334741
$218$	15.9013	1.07697
$219$	13.8430	0.935425
$220$	−1.00000	−0.0674200
$221$	2.43005	0.163463
$222$	7.25359	0.486829
$223$	−24.0005	−1.60719	−0.803595	−	0.595177i	$-0.797082\pi$
$223$	−24.0005	−1.60719	−0.803595	+	0.595177i	$0.797082\pi$
$224$	−1.13795	−0.0760324
$225$	1.00000	0.0666667
$226$	3.19533	0.212550
$227$	−17.5435	−1.16440	−0.582201	−	0.813045i	$-0.697808\pi$
$227$	−17.5435	−1.16440	−0.582201	+	0.813045i	$0.697808\pi$
$228$	6.43005	0.425841
$229$	17.5050	1.15676	0.578381	−	0.815767i	$-0.303685\pi$
$229$	17.5050	1.15676	0.578381	+	0.815767i	$0.303685\pi$
$230$	5.50974	0.363302
$231$	1.13795	0.0748715
$232$	−1.29211	−0.0848310
$233$	−27.6600	−1.81207	−0.906034	−	0.423205i	$-0.860905\pi$
$233$	−27.6600	−1.81207	−0.906034	+	0.423205i	$0.860905\pi$
$234$	−2.43005	−0.158858
$235$	2.37179	0.154719
$236$	−0.823536	−0.0536076
$237$	−10.0554	−0.653171
$238$	1.13795	0.0737622
$239$	6.82769	0.441646	0.220823	−	0.975314i	$-0.429126\pi$
$239$	6.82769	0.441646	0.220823	+	0.975314i	$0.429126\pi$
$240$	1.00000	0.0645497
$241$	−16.6011	−1.06937	−0.534687	−	0.845050i	$-0.679570\pi$
$241$	−16.6011	−1.06937	−0.534687	+	0.845050i	$0.679570\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	3.23472	0.207082
$245$	−5.70507	−0.364484
$246$	−2.37179	−0.151220
$247$	−15.6254	−0.994219
$248$	−4.33328	−0.275164
$249$	1.23472	0.0782474
$250$	1.00000	0.0632456
$251$	−30.7980	−1.94395	−0.971975	−	0.235084i	$-0.924464\pi$
$251$	−30.7980	−1.94395	−0.971975	+	0.235084i	$0.924464\pi$
$252$	−1.13795	−0.0716840
$253$	−5.50974	−0.346395
$254$	4.64769	0.291622
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	9.38801	0.585608	0.292804	−	0.956173i	$-0.405412\pi$
$257$	9.38801	0.585608	0.292804	+	0.956173i	$0.405412\pi$
$258$	12.7633	0.794610
$259$	−8.25421	−0.512892
$260$	−2.43005	−0.150706
$261$	−1.29211	−0.0799794
$262$	5.97831	0.369341
$263$	4.23738	0.261288	0.130644	−	0.991429i	$-0.458295\pi$
$263$	4.23738	0.261288	0.130644	+	0.991429i	$0.458295\pi$
$264$	−1.00000	−0.0615457
$265$	7.09943	0.436115
$266$	−7.31707	−0.448638
$267$	−8.58421	−0.525345
$268$	0.977695	0.0597222
$269$	−18.3690	−1.11998	−0.559988	−	0.828501i	$-0.689194\pi$
$269$	−18.3690	−1.11998	−0.559988	+	0.828501i	$0.689194\pi$
$270$	1.00000	0.0608581
$271$	−18.2346	−1.10767	−0.553835	−	0.832626i	$-0.686836\pi$
$271$	−18.2346	−1.10767	−0.553835	+	0.832626i	$0.686836\pi$
$272$	−1.00000	−0.0606339
$273$	2.76528	0.167362
$274$	−12.8216	−0.774581
$275$	−1.00000	−0.0603023
$276$	5.50974	0.331648
$277$	−0.469448	−0.0282064	−0.0141032	−	0.999901i	$-0.504489\pi$
$277$	−0.469448	−0.0282064	−0.0141032	+	0.999901i	$0.504489\pi$
$278$	20.7999	1.24750
$279$	−4.33328	−0.259427
$280$	−1.13795	−0.0680054
$281$	15.1082	0.901281	0.450641	−	0.892705i	$-0.351196\pi$
$281$	15.1082	0.901281	0.450641	+	0.892705i	$0.351196\pi$
$282$	2.37179	0.141238
$283$	−17.4889	−1.03961	−0.519805	−	0.854285i	$-0.673995\pi$
$283$	−17.4889	−1.03961	−0.519805	+	0.854285i	$0.673995\pi$
$284$	9.68365	0.574619
$285$	6.43005	0.380884
$286$	2.43005	0.143692
$287$	2.69898	0.159316
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−1.29211	−0.0758751
$291$	−13.1934	−0.773410
$292$	13.8430	0.810102
$293$	16.7675	0.979567	0.489784	−	0.871844i	$-0.337076\pi$
$293$	16.7675	0.979567	0.489784	+	0.871844i	$0.337076\pi$
$294$	−5.70507	−0.332727
$295$	−0.823536	−0.0479481
$296$	7.25359	0.421606
$297$	−1.00000	−0.0580259
$298$	5.25359	0.304332
$299$	−13.3890	−0.774305
$300$	1.00000	0.0577350
$301$	−14.5240	−0.837150
$302$	−0.393481	−0.0226423
$303$	0.212419	0.0122031
$304$	6.43005	0.368789
$305$	3.23472	0.185220
$306$	−1.00000	−0.0571662
$307$	−26.9020	−1.53538	−0.767689	−	0.640823i	$-0.778593\pi$
$307$	−26.9020	−1.53538	−0.767689	+	0.640823i	$0.778593\pi$
$308$	1.13795	0.0648406
$309$	−10.8216	−0.615619
$310$	−4.33328	−0.246114
$311$	−31.2103	−1.76977	−0.884887	−	0.465805i	$-0.845765\pi$
$311$	−31.2103	−1.76977	−0.884887	+	0.465805i	$0.845765\pi$
$312$	−2.43005	−0.137575
$313$	−20.5646	−1.16238	−0.581189	−	0.813769i	$-0.697412\pi$
$313$	−20.5646	−1.16238	−0.581189	+	0.813769i	$0.697412\pi$
$314$	−13.0725	−0.737725
$315$	−1.13795	−0.0641161
$316$	−10.0554	−0.565663
$317$	−14.7229	−0.826919	−0.413460	−	0.910522i	$-0.635680\pi$
$317$	−14.7229	−0.826919	−0.413460	+	0.910522i	$0.635680\pi$
$318$	7.09943	0.398116
$319$	1.29211	0.0723441
$320$	1.00000	0.0559017
$321$	10.2157	0.570184
$322$	−6.26980	−0.349402
$323$	−6.43005	−0.357778
$324$	1.00000	0.0555556
$325$	−2.43005	−0.134795
$326$	−10.5240	−0.582871
$327$	15.9013	0.879343
$328$	−2.37179	−0.130960
$329$	−2.69898	−0.148800
$330$	−1.00000	−0.0550482
$331$	16.7229	0.919172	0.459586	−	0.888133i	$-0.347998\pi$
$331$	16.7229	0.919172	0.459586	+	0.888133i	$0.347998\pi$
$332$	1.23472	0.0677643
$333$	7.25359	0.397494
$334$	−8.64769	−0.473181
$335$	0.977695	0.0534172
$336$	−1.13795	−0.0620802
$337$	18.5866	1.01248	0.506239	−	0.862393i	$-0.331035\pi$
$337$	18.5866	1.01248	0.506239	+	0.862393i	$0.331035\pi$
$338$	−7.09483	−0.385908
$339$	3.19533	0.173547
$340$	−1.00000	−0.0542326
$341$	4.33328	0.234660
$342$	6.43005	0.347698
$343$	14.4577	0.780643
$344$	12.7633	0.688153
$345$	5.50974	0.296635
$346$	10.1583	0.546114
$347$	5.33875	0.286599	0.143300	−	0.989679i	$-0.454229\pi$
$347$	5.33875	0.286599	0.143300	+	0.989679i	$0.454229\pi$
$348$	−1.29211	−0.0692642
$349$	3.61174	0.193332	0.0966659	−	0.995317i	$-0.469182\pi$
$349$	3.61174	0.193332	0.0966659	+	0.995317i	$0.469182\pi$
$350$	−1.13795	−0.0608259
$351$	−2.43005	−0.129707
$352$	−1.00000	−0.0533002
$353$	1.20694	0.0642391	0.0321195	−	0.999484i	$-0.489774\pi$
$353$	1.20694	0.0642391	0.0321195	+	0.999484i	$0.489774\pi$
$354$	−0.823536	−0.0437704
$355$	9.68365	0.513955
$356$	−8.58421	−0.454962
$357$	1.13795	0.0602266
$358$	2.05826	0.108782
$359$	19.0572	1.00580	0.502901	−	0.864344i	$-0.332266\pi$
$359$	19.0572	1.00580	0.502901	+	0.864344i	$0.332266\pi$
$360$	1.00000	0.0527046
$361$	22.3456	1.17608
$362$	9.95867	0.523416
$363$	1.00000	0.0524864
$364$	2.76528	0.144940
$365$	13.8430	0.724577
$366$	3.23472	0.169082
$367$	6.11652	0.319280	0.159640	−	0.987175i	$-0.448967\pi$
$367$	6.11652	0.319280	0.159640	+	0.987175i	$0.448967\pi$
$368$	5.50974	0.287215
$369$	−2.37179	−0.123471
$370$	7.25359	0.377096
$371$	−8.07879	−0.419430
$372$	−4.33328	−0.224670
$373$	−0.655728	−0.0339523	−0.0169762	−	0.999856i	$-0.505404\pi$
$373$	−0.655728	−0.0339523	−0.0169762	+	0.999856i	$0.505404\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	2.37179	0.122316
$377$	3.13989	0.161713
$378$	−1.13795	−0.0585297
$379$	20.2937	1.04242	0.521209	−	0.853429i	$-0.325481\pi$
$379$	20.2937	1.04242	0.521209	+	0.853429i	$0.325481\pi$
$380$	6.43005	0.329855
$381$	4.64769	0.238108
$382$	−4.70789	−0.240877
$383$	−14.9236	−0.762560	−0.381280	−	0.924460i	$-0.624517\pi$
$383$	−14.9236	−0.762560	−0.381280	+	0.924460i	$0.624517\pi$
$384$	1.00000	0.0510310
$385$	1.13795	0.0579952
$386$	−10.2679	−0.522620
$387$	12.7633	0.648797
$388$	−13.1934	−0.669793
$389$	−5.94067	−0.301204	−0.150602	−	0.988594i	$-0.548121\pi$
$389$	−5.94067	−0.301204	−0.150602	+	0.988594i	$0.548121\pi$
$390$	−2.43005	−0.123051
$391$	−5.50974	−0.278640
$392$	−5.70507	−0.288150
$393$	5.97831	0.301566
$394$	13.8378	0.697139
$395$	−10.0554	−0.505944
$396$	−1.00000	−0.0502519
$397$	3.19293	0.160249	0.0801243	−	0.996785i	$-0.474468\pi$
$397$	3.19293	0.160249	0.0801243	+	0.996785i	$0.474468\pi$
$398$	18.9738	0.951071
$399$	−7.31707	−0.366312
$400$	1.00000	0.0500000
$401$	23.6841	1.18273	0.591364	−	0.806405i	$-0.298590\pi$
$401$	23.6841	1.18273	0.591364	+	0.806405i	$0.298590\pi$
$402$	0.977695	0.0487630
$403$	10.5301	0.524542
$404$	0.212419	0.0105682
$405$	1.00000	0.0496904
$406$	1.47035	0.0729723
$407$	−7.25359	−0.359547
$408$	−1.00000	−0.0495074
$409$	−17.8796	−0.884089	−0.442045	−	0.896993i	$-0.645747\pi$
$409$	−17.8796	−0.884089	−0.442045	+	0.896993i	$0.645747\pi$
$410$	−2.37179	−0.117135
$411$	−12.8216	−0.632443
$412$	−10.8216	−0.533142
$413$	0.937141	0.0461137
$414$	5.50974	0.270789
$415$	1.23472	0.0606102
$416$	−2.43005	−0.119143
$417$	20.7999	1.01858
$418$	−6.43005	−0.314504
$419$	−10.7714	−0.526216	−0.263108	−	0.964766i	$-0.584748\pi$
$419$	−10.7714	−0.526216	−0.263108	+	0.964766i	$0.584748\pi$
$420$	−1.13795	−0.0555262
$421$	17.9459	0.874629	0.437315	−	0.899309i	$-0.355930\pi$
$421$	17.9459	0.874629	0.437315	+	0.899309i	$0.355930\pi$
$422$	7.31097	0.355893
$423$	2.37179	0.115321
$424$	7.09943	0.344779
$425$	−1.00000	−0.0485071
$426$	9.68365	0.469174
$427$	−3.68095	−0.178134
$428$	10.2157	0.493794
$429$	2.43005	0.117324
$430$	12.7633	0.615503
$431$	−15.2786	−0.735942	−0.367971	−	0.929837i	$-0.619947\pi$
$431$	−15.2786	−0.735942	−0.367971	+	0.929837i	$0.619947\pi$
$432$	1.00000	0.0481125
$433$	5.13601	0.246821	0.123410	−	0.992356i	$-0.460617\pi$
$433$	5.13601	0.246821	0.123410	+	0.992356i	$0.460617\pi$
$434$	4.93105	0.236698
$435$	−1.29211	−0.0619518
$436$	15.9013	0.761533
$437$	35.4280	1.69475
$438$	13.8430	0.661445
$439$	−8.02302	−0.382918	−0.191459	−	0.981501i	$-0.561322\pi$
$439$	−8.02302	−0.382918	−0.191459	+	0.981501i	$0.561322\pi$
$440$	−1.00000	−0.0476731
$441$	−5.70507	−0.271670
$442$	2.43005	0.115586
$443$	−31.9628	−1.51860	−0.759300	−	0.650741i	$-0.774458\pi$
$443$	−31.9628	−1.51860	−0.759300	+	0.650741i	$0.774458\pi$
$444$	7.25359	0.344240
$445$	−8.58421	−0.406931
$446$	−24.0005	−1.13645
$447$	5.25359	0.248486
$448$	−1.13795	−0.0537630
$449$	−12.6685	−0.597864	−0.298932	−	0.954274i	$-0.596630\pi$
$449$	−12.6685	−0.597864	−0.298932	+	0.954274i	$0.596630\pi$
$450$	1.00000	0.0471405
$451$	2.37179	0.111683
$452$	3.19533	0.150296
$453$	−0.393481	−0.0184874
$454$	−17.5435	−0.823357
$455$	2.76528	0.129638
$456$	6.43005	0.301115
$457$	31.0373	1.45186	0.725932	−	0.687767i	$-0.241409\pi$
$457$	31.0373	1.45186	0.725932	+	0.687767i	$0.241409\pi$
$458$	17.5050	0.817954
$459$	−1.00000	−0.0466760
$460$	5.50974	0.256893
$461$	−11.1171	−0.517777	−0.258888	−	0.965907i	$-0.583356\pi$
$461$	−11.1171	−0.517777	−0.258888	+	0.965907i	$0.583356\pi$
$462$	1.13795	0.0529421
$463$	−34.6844	−1.61192	−0.805959	−	0.591971i	$-0.798350\pi$
$463$	−34.6844	−1.61192	−0.805959	+	0.591971i	$0.798350\pi$
$464$	−1.29211	−0.0599846
$465$	−4.33328	−0.200951
$466$	−27.6600	−1.28133
$467$	8.52489	0.394485	0.197242	−	0.980355i	$-0.436801\pi$
$467$	8.52489	0.394485	0.197242	+	0.980355i	$0.436801\pi$
$468$	−2.43005	−0.112329
$469$	−1.11257	−0.0513735
$470$	2.37179	0.109403
$471$	−13.0725	−0.602350
$472$	−0.823536	−0.0379063
$473$	−12.7633	−0.586859
$474$	−10.0554	−0.461862
$475$	6.43005	0.295031
$476$	1.13795	0.0521578
$477$	7.09943	0.325061
$478$	6.82769	0.312291
$479$	29.5652	1.35087	0.675434	−	0.737421i	$-0.263956\pi$
$479$	29.5652	1.35087	0.675434	+	0.737421i	$0.263956\pi$
$480$	1.00000	0.0456435
$481$	−17.6266	−0.803705
$482$	−16.6011	−0.756161
$483$	−6.26980	−0.285286
$484$	1.00000	0.0454545
$485$	−13.1934	−0.599081
$486$	1.00000	0.0453609
$487$	16.1555	0.732075	0.366038	−	0.930600i	$-0.380714\pi$
$487$	16.1555	0.732075	0.366038	+	0.930600i	$0.380714\pi$
$488$	3.23472	0.146429
$489$	−10.5240	−0.475912
$490$	−5.70507	−0.257729
$491$	−38.3337	−1.72998	−0.864989	−	0.501791i	$-0.832674\pi$
$491$	−38.3337	−1.72998	−0.864989	+	0.501791i	$0.832674\pi$
$492$	−2.37179	−0.106929
$493$	1.29211	0.0581936
$494$	−15.6254	−0.703019
$495$	−1.00000	−0.0449467
$496$	−4.33328	−0.194570
$497$	−11.0195	−0.494292
$498$	1.23472	0.0553293
$499$	35.2074	1.57610	0.788050	−	0.615611i	$-0.211091\pi$
$499$	35.2074	1.57610	0.788050	+	0.615611i	$0.211091\pi$
$500$	1.00000	0.0447214
$501$	−8.64769	−0.386350
$502$	−30.7980	−1.37458
$503$	−24.4541	−1.09036	−0.545178	−	0.838320i	$-0.683538\pi$
$503$	−24.4541	−1.09036	−0.545178	+	0.838320i	$0.683538\pi$
$504$	−1.13795	−0.0506882
$505$	0.212419	0.00945250
$506$	−5.50974	−0.244938
$507$	−7.09483	−0.315093
$508$	4.64769	0.206208
$509$	14.2490	0.631575	0.315788	−	0.948830i	$-0.397731\pi$
$509$	14.2490	0.631575	0.315788	+	0.948830i	$0.397731\pi$
$510$	−1.00000	−0.0442807
$511$	−15.7526	−0.696856
$512$	1.00000	0.0441942
$513$	6.43005	0.283894
$514$	9.38801	0.414087
$515$	−10.8216	−0.476856
$516$	12.7633	0.561874
$517$	−2.37179	−0.104311
$518$	−8.25421	−0.362669
$519$	10.1583	0.445900
$520$	−2.43005	−0.106565
$521$	3.93786	0.172521	0.0862603	−	0.996273i	$-0.472508\pi$
$521$	3.93786	0.172521	0.0862603	+	0.996273i	$0.472508\pi$
$522$	−1.29211	−0.0565540
$523$	31.7058	1.38640	0.693199	−	0.720747i	$-0.256201\pi$
$523$	31.7058	1.38640	0.693199	+	0.720747i	$0.256201\pi$
$524$	5.97831	0.261164
$525$	−1.13795	−0.0496641
$526$	4.23738	0.184759
$527$	4.33328	0.188761
$528$	−1.00000	−0.0435194
$529$	7.35727	0.319881
$530$	7.09943	0.308380
$531$	−0.823536	−0.0357384
$532$	−7.31707	−0.317235
$533$	5.76359	0.249649
$534$	−8.58421	−0.371475
$535$	10.2157	0.441663
$536$	0.977695	0.0422300
$537$	2.05826	0.0888205
$538$	−18.3690	−0.791943
$539$	5.70507	0.245735
$540$	1.00000	0.0430331
$541$	34.9832	1.50404	0.752022	−	0.659138i	$-0.229079\pi$
$541$	34.9832	1.50404	0.752022	+	0.659138i	$0.229079\pi$
$542$	−18.2346	−0.783241
$543$	9.95867	0.427367
$544$	−1.00000	−0.0428746
$545$	15.9013	0.681136
$546$	2.76528	0.118343
$547$	−36.2486	−1.54988	−0.774939	−	0.632037i	$-0.782219\pi$
$547$	−36.2486	−1.54988	−0.774939	+	0.632037i	$0.782219\pi$
$548$	−12.8216	−0.547711
$549$	3.23472	0.138055
$550$	−1.00000	−0.0426401
$551$	−8.30832	−0.353946
$552$	5.50974	0.234510
$553$	11.4426	0.486588
$554$	−0.469448	−0.0199449
$555$	7.25359	0.307898
$556$	20.7999	0.882113
$557$	8.33610	0.353212	0.176606	−	0.984282i	$-0.443488\pi$
$557$	8.33610	0.353212	0.176606	+	0.984282i	$0.443488\pi$
$558$	−4.33328	−0.183442
$559$	−31.0156	−1.31182
$560$	−1.13795	−0.0480871
$561$	1.00000	0.0422200
$562$	15.1082	0.637302
$563$	−13.7865	−0.581032	−0.290516	−	0.956870i	$-0.593827\pi$
$563$	−13.7865	−0.581032	−0.290516	+	0.956870i	$0.593827\pi$
$564$	2.37179	0.0998706
$565$	3.19533	0.134429
$566$	−17.4889	−0.735115
$567$	−1.13795	−0.0477893
$568$	9.68365	0.406317
$569$	−13.7523	−0.576528	−0.288264	−	0.957551i	$-0.593078\pi$
$569$	−13.7523	−0.576528	−0.288264	+	0.957551i	$0.593078\pi$
$570$	6.43005	0.269325
$571$	5.10572	0.213668	0.106834	−	0.994277i	$-0.465929\pi$
$571$	5.10572	0.213668	0.106834	+	0.994277i	$0.465929\pi$
$572$	2.43005	0.101606
$573$	−4.70789	−0.196675
$574$	2.69898	0.112653
$575$	5.50974	0.229772
$576$	1.00000	0.0416667
$577$	−20.4638	−0.851920	−0.425960	−	0.904742i	$-0.640063\pi$
$577$	−20.4638	−0.851920	−0.425960	+	0.904742i	$0.640063\pi$
$578$	1.00000	0.0415945
$579$	−10.2679	−0.426718
$580$	−1.29211	−0.0536518
$581$	−1.40505	−0.0582914
$582$	−13.1934	−0.546884
$583$	−7.09943	−0.294028
$584$	13.8430	0.572828
$585$	−2.43005	−0.100470
$586$	16.7675	0.692658
$587$	−4.14806	−0.171209	−0.0856045	−	0.996329i	$-0.527282\pi$
$587$	−4.14806	−0.171209	−0.0856045	+	0.996329i	$0.527282\pi$
$588$	−5.70507	−0.235273
$589$	−27.8632	−1.14808
$590$	−0.823536	−0.0339044
$591$	13.8378	0.569211
$592$	7.25359	0.298121
$593$	−20.1989	−0.829468	−0.414734	−	0.909943i	$-0.636125\pi$
$593$	−20.1989	−0.829468	−0.414734	+	0.909943i	$0.636125\pi$
$594$	−1.00000	−0.0410305
$595$	1.13795	0.0466513
$596$	5.25359	0.215195
$597$	18.9738	0.776546
$598$	−13.3890	−0.547516
$599$	−7.97504	−0.325851	−0.162926	−	0.986638i	$-0.552093\pi$
$599$	−7.97504	−0.325851	−0.162926	+	0.986638i	$0.552093\pi$
$600$	1.00000	0.0408248
$601$	17.7688	0.724805	0.362402	−	0.932022i	$-0.381957\pi$
$601$	17.7688	0.724805	0.362402	+	0.932022i	$0.381957\pi$
$602$	−14.5240	−0.591955
$603$	0.977695	0.0398148
$604$	−0.393481	−0.0160105
$605$	1.00000	0.0406558
$606$	0.212419	0.00862891
$607$	−23.3415	−0.947400	−0.473700	−	0.880686i	$-0.657082\pi$
$607$	−23.3415	−0.947400	−0.473700	+	0.880686i	$0.657082\pi$
$608$	6.43005	0.260773
$609$	1.47035	0.0595816
$610$	3.23472	0.130970
$611$	−5.76359	−0.233170
$612$	−1.00000	−0.0404226
$613$	−23.5444	−0.950948	−0.475474	−	0.879730i	$-0.657723\pi$
$613$	−23.5444	−0.950948	−0.475474	+	0.879730i	$0.657723\pi$
$614$	−26.9020	−1.08568
$615$	−2.37179	−0.0956400
$616$	1.13795	0.0458492
$617$	−46.0191	−1.85266	−0.926330	−	0.376712i	$-0.877055\pi$
$617$	−46.0191	−1.85266	−0.926330	+	0.376712i	$0.877055\pi$
$618$	−10.8216	−0.435308
$619$	31.4318	1.26335	0.631676	−	0.775232i	$-0.282367\pi$
$619$	31.4318	1.26335	0.631676	+	0.775232i	$0.282367\pi$
$620$	−4.33328	−0.174029
$621$	5.50974	0.221098
$622$	−31.2103	−1.25142
$623$	9.76839	0.391362
$624$	−2.43005	−0.0972800
$625$	1.00000	0.0400000
$626$	−20.5646	−0.821925
$627$	−6.43005	−0.256792
$628$	−13.0725	−0.521651
$629$	−7.25359	−0.289220
$630$	−1.13795	−0.0453369
$631$	−27.1304	−1.08004	−0.540021	−	0.841651i	$-0.681584\pi$
$631$	−27.1304	−1.08004	−0.540021	+	0.841651i	$0.681584\pi$
$632$	−10.0554	−0.399984
$633$	7.31097	0.290585
$634$	−14.7229	−0.584720
$635$	4.64769	0.184438
$636$	7.09943	0.281511
$637$	13.8636	0.549298
$638$	1.29211	0.0511550
$639$	9.68365	0.383079
$640$	1.00000	0.0395285
$641$	24.6771	0.974687	0.487344	−	0.873210i	$-0.337966\pi$
$641$	24.6771	0.974687	0.487344	+	0.873210i	$0.337966\pi$
$642$	10.2157	0.403181
$643$	21.4665	0.846555	0.423277	−	0.906000i	$-0.360880\pi$
$643$	21.4665	0.846555	0.423277	+	0.906000i	$0.360880\pi$
$644$	−6.26980	−0.247065
$645$	12.7633	0.502556
$646$	−6.43005	−0.252987
$647$	14.4113	0.566566	0.283283	−	0.959036i	$-0.408576\pi$
$647$	14.4113	0.566566	0.283283	+	0.959036i	$0.408576\pi$
$648$	1.00000	0.0392837
$649$	0.823536	0.0323266
$650$	−2.43005	−0.0953146
$651$	4.93105	0.193263
$652$	−10.5240	−0.412152
$653$	−22.9203	−0.896941	−0.448471	−	0.893798i	$-0.648031\pi$
$653$	−22.9203	−0.896941	−0.448471	+	0.893798i	$0.648031\pi$
$654$	15.9013	0.621789
$655$	5.97831	0.233592
$656$	−2.37179	−0.0926030
$657$	13.8430	0.540068
$658$	−2.69898	−0.105217
$659$	−22.1483	−0.862777	−0.431388	−	0.902166i	$-0.641976\pi$
$659$	−22.1483	−0.862777	−0.431388	+	0.902166i	$0.641976\pi$
$660$	−1.00000	−0.0389249
$661$	15.3578	0.597349	0.298674	−	0.954355i	$-0.403456\pi$
$661$	15.3578	0.597349	0.298674	+	0.954355i	$0.403456\pi$
$662$	16.7229	0.649953
$663$	2.43005	0.0943755
$664$	1.23472	0.0479166
$665$	−7.31707	−0.283744
$666$	7.25359	0.281071
$667$	−7.11918	−0.275656
$668$	−8.64769	−0.334589
$669$	−24.0005	−0.927911
$670$	0.977695	0.0377716
$671$	−3.23472	−0.124875
$672$	−1.13795	−0.0438973
$673$	−7.55669	−0.291289	−0.145645	−	0.989337i	$-0.546526\pi$
$673$	−7.55669	−0.291289	−0.145645	+	0.989337i	$0.546526\pi$
$674$	18.5866	0.715930
$675$	1.00000	0.0384900
$676$	−7.09483	−0.272878
$677$	−5.78370	−0.222286	−0.111143	−	0.993804i	$-0.535451\pi$
$677$	−5.78370	−0.222286	−0.111143	+	0.993804i	$0.535451\pi$
$678$	3.19533	0.122716
$679$	15.0134	0.576161
$680$	−1.00000	−0.0383482
$681$	−17.5435	−0.672268
$682$	4.33328	0.165930
$683$	−45.1857	−1.72898	−0.864492	−	0.502647i	$-0.832359\pi$
$683$	−45.1857	−1.72898	−0.864492	+	0.502647i	$0.832359\pi$
$684$	6.43005	0.245859
$685$	−12.8216	−0.489888
$686$	14.4577	0.551998
$687$	17.5050	0.667857
$688$	12.7633	0.486598
$689$	−17.2520	−0.657249
$690$	5.50974	0.209752
$691$	19.6985	0.749368	0.374684	−	0.927153i	$-0.377751\pi$
$691$	19.6985	0.749368	0.374684	+	0.927153i	$0.377751\pi$
$692$	10.1583	0.386161
$693$	1.13795	0.0432271
$694$	5.33875	0.202656
$695$	20.7999	0.788985
$696$	−1.29211	−0.0489772
$697$	2.37179	0.0898381
$698$	3.61174	0.136706
$699$	−27.6600	−1.04620
$700$	−1.13795	−0.0430104
$701$	−17.6265	−0.665742	−0.332871	−	0.942972i	$-0.608017\pi$
$701$	−17.6265	−0.665742	−0.332871	+	0.942972i	$0.608017\pi$
$702$	−2.43005	−0.0917165
$703$	46.6410	1.75910
$704$	−1.00000	−0.0376889
$705$	2.37179	0.0893270
$706$	1.20694	0.0454239
$707$	−0.241721	−0.00909086
$708$	−0.823536	−0.0309504
$709$	31.0791	1.16720	0.583600	−	0.812042i	$-0.301644\pi$
$709$	31.0791	1.16720	0.583600	+	0.812042i	$0.301644\pi$
$710$	9.68365	0.363421
$711$	−10.0554	−0.377108
$712$	−8.58421	−0.321707
$713$	−23.8753	−0.894135
$714$	1.13795	0.0425866
$715$	2.43005	0.0908789
$716$	2.05826	0.0769208
$717$	6.82769	0.254985
$718$	19.0572	0.711209
$719$	34.3463	1.28090	0.640451	−	0.767999i	$-0.278748\pi$
$719$	34.3463	1.28090	0.640451	+	0.767999i	$0.278748\pi$
$720$	1.00000	0.0372678
$721$	12.3144	0.458613
$722$	22.3456	0.831617
$723$	−16.6011	−0.617403
$724$	9.95867	0.370111
$725$	−1.29211	−0.0479876
$726$	1.00000	0.0371135
$727$	−1.97397	−0.0732106	−0.0366053	−	0.999330i	$-0.511654\pi$
$727$	−1.97397	−0.0732106	−0.0366053	+	0.999330i	$0.511654\pi$
$728$	2.76528	0.102488
$729$	1.00000	0.0370370
$730$	13.8430	0.512353
$731$	−12.7633	−0.472069
$732$	3.23472	0.119559
$733$	44.0694	1.62774	0.813869	−	0.581048i	$-0.197357\pi$
$733$	44.0694	1.62774	0.813869	+	0.581048i	$0.197357\pi$
$734$	6.11652	0.225765
$735$	−5.70507	−0.210435
$736$	5.50974	0.203092
$737$	−0.977695	−0.0360139
$738$	−2.37179	−0.0873070
$739$	−41.2521	−1.51748	−0.758742	−	0.651392i	$-0.774185\pi$
$739$	−41.2521	−1.51748	−0.758742	+	0.651392i	$0.774185\pi$
$740$	7.25359	0.266647
$741$	−15.6254	−0.574013
$742$	−8.07879	−0.296582
$743$	−20.4919	−0.751774	−0.375887	−	0.926666i	$-0.622662\pi$
$743$	−20.4919	−0.751774	−0.375887	+	0.926666i	$0.622662\pi$
$744$	−4.33328	−0.158866
$745$	5.25359	0.192477
$746$	−0.655728	−0.0240079
$747$	1.23472	0.0451762
$748$	1.00000	0.0365636
$749$	−11.6249	−0.424766
$750$	1.00000	0.0365148
$751$	−21.8829	−0.798517	−0.399259	−	0.916838i	$-0.630732\pi$
$751$	−21.8829	−0.798517	−0.399259	+	0.916838i	$0.630732\pi$
$752$	2.37179	0.0864905
$753$	−30.7980	−1.12234
$754$	3.13989	0.114348
$755$	−0.393481	−0.0143202
$756$	−1.13795	−0.0413868
$757$	13.7993	0.501544	0.250772	−	0.968046i	$-0.419316\pi$
$757$	13.7993	0.501544	0.250772	+	0.968046i	$0.419316\pi$
$758$	20.2937	0.737100
$759$	−5.50974	−0.199991
$760$	6.43005	0.233243
$761$	32.3037	1.17101	0.585503	−	0.810670i	$-0.300897\pi$
$761$	32.3037	1.17101	0.585503	+	0.810670i	$0.300897\pi$
$762$	4.64769	0.168368
$763$	−18.0948	−0.655077
$764$	−4.70789	−0.170326
$765$	−1.00000	−0.0361551
$766$	−14.9236	−0.539211
$767$	2.00124	0.0722605
$768$	1.00000	0.0360844
$769$	16.0285	0.578004	0.289002	−	0.957329i	$-0.406677\pi$
$769$	16.0285	0.578004	0.289002	+	0.957329i	$0.406677\pi$
$770$	1.13795	0.0410088
$771$	9.38801	0.338101
$772$	−10.2679	−0.369548
$773$	10.1082	0.363566	0.181783	−	0.983339i	$-0.441813\pi$
$773$	10.1082	0.363566	0.181783	+	0.983339i	$0.441813\pi$
$774$	12.7633	0.458769
$775$	−4.33328	−0.155656
$776$	−13.1934	−0.473615
$777$	−8.25421	−0.296118
$778$	−5.94067	−0.212984
$779$	−15.2508	−0.546416
$780$	−2.43005	−0.0870099
$781$	−9.68365	−0.346508
$782$	−5.50974	−0.197028
$783$	−1.29211	−0.0461761
$784$	−5.70507	−0.203753
$785$	−13.0725	−0.466579
$786$	5.97831	0.213239
$787$	−41.9727	−1.49616	−0.748082	−	0.663606i	$-0.769025\pi$
$787$	−41.9727	−1.49616	−0.748082	+	0.663606i	$0.769025\pi$
$788$	13.8378	0.492951
$789$	4.23738	0.150855
$790$	−10.0554	−0.357757
$791$	−3.63612	−0.129286
$792$	−1.00000	−0.0355335
$793$	−7.86056	−0.279137
$794$	3.19293	0.113313
$795$	7.09943	0.251791
$796$	18.9738	0.672509
$797$	−39.7014	−1.40630	−0.703149	−	0.711043i	$-0.748223\pi$
$797$	−39.7014	−1.40630	−0.703149	+	0.711043i	$0.748223\pi$
$798$	−7.31707	−0.259021
$799$	−2.37179	−0.0839081
$800$	1.00000	0.0353553
$801$	−8.58421	−0.303308
$802$	23.6841	0.836315
$803$	−13.8430	−0.488510
$804$	0.977695	0.0344806
$805$	−6.26980	−0.220981
$806$	10.5301	0.370907
$807$	−18.3690	−0.646619
$808$	0.212419	0.00747286
$809$	29.0669	1.02194	0.510969	−	0.859599i	$-0.329287\pi$
$809$	29.0669	1.02194	0.510969	+	0.859599i	$0.329287\pi$
$810$	1.00000	0.0351364
$811$	−3.17762	−0.111581	−0.0557907	−	0.998442i	$-0.517768\pi$
$811$	−3.17762	−0.111581	−0.0557907	+	0.998442i	$0.517768\pi$
$812$	1.47035	0.0515992
$813$	−18.2346	−0.639514
$814$	−7.25359	−0.254238
$815$	−10.5240	−0.368640
$816$	−1.00000	−0.0350070
$817$	82.0689	2.87123
$818$	−17.8796	−0.625145
$819$	2.76528	0.0966266
$820$	−2.37179	−0.0828267
$821$	23.8829	0.833518	0.416759	−	0.909017i	$-0.363166\pi$
$821$	23.8829	0.833518	0.416759	+	0.909017i	$0.363166\pi$
$822$	−12.8216	−0.447204
$823$	−14.7436	−0.513929	−0.256965	−	0.966421i	$-0.582722\pi$
$823$	−14.7436	−0.513929	−0.256965	+	0.966421i	$0.582722\pi$
$824$	−10.8216	−0.376988
$825$	−1.00000	−0.0348155
$826$	0.937141	0.0326073
$827$	−4.36852	−0.151908	−0.0759542	−	0.997111i	$-0.524200\pi$
$827$	−4.36852	−0.151908	−0.0759542	+	0.997111i	$0.524200\pi$
$828$	5.50974	0.191477
$829$	14.6829	0.509959	0.254980	−	0.966946i	$-0.417931\pi$
$829$	14.6829	0.509959	0.254980	+	0.966946i	$0.417931\pi$
$830$	1.23472	0.0428579
$831$	−0.469448	−0.0162850
$832$	−2.43005	−0.0842470
$833$	5.70507	0.197669
$834$	20.7999	0.720242
$835$	−8.64769	−0.299266
$836$	−6.43005	−0.222388
$837$	−4.33328	−0.149780
$838$	−10.7714	−0.372091
$839$	19.2142	0.663348	0.331674	−	0.943394i	$-0.392387\pi$
$839$	19.2142	0.663348	0.331674	+	0.943394i	$0.392387\pi$
$840$	−1.13795	−0.0392629
$841$	−27.3305	−0.942430
$842$	17.9459	0.618456
$843$	15.1082	0.520355
$844$	7.31097	0.251654
$845$	−7.09483	−0.244070
$846$	2.37179	0.0815440
$847$	−1.13795	−0.0391004
$848$	7.09943	0.243796
$849$	−17.4889	−0.600219
$850$	−1.00000	−0.0342997
$851$	39.9654	1.37000
$852$	9.68365	0.331756
$853$	31.1581	1.06683	0.533417	−	0.845852i	$-0.320908\pi$
$853$	31.1581	1.06683	0.533417	+	0.845852i	$0.320908\pi$
$854$	−3.68095	−0.125959
$855$	6.43005	0.219903
$856$	10.2157	0.349165
$857$	50.5362	1.72628	0.863141	−	0.504962i	$-0.168494\pi$
$857$	50.5362	1.72628	0.863141	+	0.504962i	$0.168494\pi$
$858$	2.43005	0.0829607
$859$	−51.9303	−1.77184	−0.885919	−	0.463840i	$-0.846471\pi$
$859$	−51.9303	−1.77184	−0.885919	+	0.463840i	$0.846471\pi$
$860$	12.7633	0.435226
$861$	2.69898	0.0919810
$862$	−15.2786	−0.520390
$863$	−26.5260	−0.902957	−0.451479	−	0.892282i	$-0.649103\pi$
$863$	−26.5260	−0.902957	−0.451479	+	0.892282i	$0.649103\pi$
$864$	1.00000	0.0340207
$865$	10.1583	0.345393
$866$	5.13601	0.174529
$867$	1.00000	0.0339618
$868$	4.93105	0.167371
$869$	10.0554	0.341107
$870$	−1.29211	−0.0438065
$871$	−2.37585	−0.0805027
$872$	15.9013	0.538485
$873$	−13.1934	−0.446529
$874$	35.4280	1.19837
$875$	−1.13795	−0.0384697
$876$	13.8430	0.467712
$877$	−12.3200	−0.416018	−0.208009	−	0.978127i	$-0.566698\pi$
$877$	−12.3200	−0.416018	−0.208009	+	0.978127i	$0.566698\pi$
$878$	−8.02302	−0.270764
$879$	16.7675	0.565553
$880$	−1.00000	−0.0337100
$881$	−48.6771	−1.63997	−0.819987	−	0.572383i	$-0.806019\pi$
$881$	−48.6771	−1.63997	−0.819987	+	0.572383i	$0.806019\pi$
$882$	−5.70507	−0.192100
$883$	8.37355	0.281792	0.140896	−	0.990024i	$-0.455002\pi$
$883$	8.37355	0.281792	0.140896	+	0.990024i	$0.455002\pi$
$884$	2.43005	0.0817316
$885$	−0.823536	−0.0276829
$886$	−31.9628	−1.07381
$887$	54.0557	1.81501	0.907507	−	0.420038i	$-0.137983\pi$
$887$	54.0557	1.81501	0.907507	+	0.420038i	$0.137983\pi$
$888$	7.25359	0.243415
$889$	−5.28883	−0.177382
$890$	−8.58421	−0.287743
$891$	−1.00000	−0.0335013
$892$	−24.0005	−0.803595
$893$	15.2508	0.510348
$894$	5.25359	0.175706
$895$	2.05826	0.0688000
$896$	−1.13795	−0.0380162
$897$	−13.3890	−0.447045
$898$	−12.6685	−0.422753
$899$	5.59906	0.186739
$900$	1.00000	0.0333333
$901$	−7.09943	−0.236516
$902$	2.37179	0.0789721
$903$	−14.5240	−0.483329
$904$	3.19533	0.106275
$905$	9.95867	0.331037
$906$	−0.393481	−0.0130725
$907$	33.5934	1.11545	0.557726	−	0.830025i	$-0.311674\pi$
$907$	33.5934	1.11545	0.557726	+	0.830025i	$0.311674\pi$
$908$	−17.5435	−0.582201
$909$	0.212419	0.00704548
$910$	2.76528	0.0916680
$911$	32.8140	1.08718	0.543588	−	0.839352i	$-0.317065\pi$
$911$	32.8140	1.08718	0.543588	+	0.839352i	$0.317065\pi$
$912$	6.43005	0.212920
$913$	−1.23472	−0.0408634
$914$	31.0373	1.02662
$915$	3.23472	0.106937
$916$	17.5050	0.578381
$917$	−6.80301	−0.224655
$918$	−1.00000	−0.0330049
$919$	54.3684	1.79345	0.896723	−	0.442591i	$-0.145941\pi$
$919$	54.3684	1.79345	0.896723	+	0.442591i	$0.145941\pi$
$920$	5.50974	0.181651
$921$	−26.9020	−0.886451
$922$	−11.1171	−0.366123
$923$	−23.5318	−0.774558
$924$	1.13795	0.0374357
$925$	7.25359	0.238497
$926$	−34.6844	−1.13980
$927$	−10.8216	−0.355428
$928$	−1.29211	−0.0424155
$929$	−21.4533	−0.703861	−0.351931	−	0.936026i	$-0.614475\pi$
$929$	−21.4533	−0.703861	−0.351931	+	0.936026i	$0.614475\pi$
$930$	−4.33328	−0.142094
$931$	−36.6839	−1.20227
$932$	−27.6600	−0.906034
$933$	−31.2103	−1.02178
$934$	8.52489	0.278943
$935$	1.00000	0.0327035
$936$	−2.43005	−0.0794288
$937$	0.519671	0.0169769	0.00848845	−	0.999964i	$-0.497298\pi$
$937$	0.519671	0.0169769	0.00848845	+	0.999964i	$0.497298\pi$
$938$	−1.11257	−0.0363266
$939$	−20.5646	−0.671099
$940$	2.37179	0.0773594
$941$	−34.8768	−1.13695	−0.568476	−	0.822700i	$-0.692467\pi$
$941$	−34.8768	−1.13695	−0.568476	+	0.822700i	$0.692467\pi$
$942$	−13.0725	−0.425926
$943$	−13.0680	−0.425552
$944$	−0.823536	−0.0268038
$945$	−1.13795	−0.0370175
$946$	−12.7633	−0.414972
$947$	−50.1516	−1.62971	−0.814854	−	0.579666i	$-0.803183\pi$
$947$	−50.1516	−1.62971	−0.814854	+	0.579666i	$0.803183\pi$
$948$	−10.0554	−0.326586
$949$	−33.6393	−1.09198
$950$	6.43005	0.208619
$951$	−14.7229	−0.477422
$952$	1.13795	0.0368811
$953$	−26.8601	−0.870084	−0.435042	−	0.900410i	$-0.643267\pi$
$953$	−26.8601	−0.870084	−0.435042	+	0.900410i	$0.643267\pi$
$954$	7.09943	0.229853
$955$	−4.70789	−0.152344
$956$	6.82769	0.220823
$957$	1.29211	0.0417679
$958$	29.5652	0.955208
$959$	14.5903	0.471146
$960$	1.00000	0.0322749
$961$	−12.2227	−0.394280
$962$	−17.6266	−0.568305
$963$	10.2157	0.329196
$964$	−16.6011	−0.534687
$965$	−10.2679	−0.330534
$966$	−6.26980	−0.201728
$967$	−8.53117	−0.274344	−0.137172	−	0.990547i	$-0.543801\pi$
$967$	−8.53117	−0.274344	−0.137172	+	0.990547i	$0.543801\pi$
$968$	1.00000	0.0321412
$969$	−6.43005	−0.206563
$970$	−13.1934	−0.423614
$971$	13.5026	0.433319	0.216659	−	0.976247i	$-0.430484\pi$
$971$	13.5026	0.433319	0.216659	+	0.976247i	$0.430484\pi$
$972$	1.00000	0.0320750
$973$	−23.6692	−0.758800
$974$	16.1555	0.517655
$975$	−2.43005	−0.0778240
$976$	3.23472	0.103541
$977$	42.9208	1.37316	0.686579	−	0.727056i	$-0.259112\pi$
$977$	42.9208	1.37316	0.686579	+	0.727056i	$0.259112\pi$
$978$	−10.5240	−0.336521
$979$	8.58421	0.274353
$980$	−5.70507	−0.182242
$981$	15.9013	0.507689
$982$	−38.3337	−1.22328
$983$	−9.99912	−0.318922	−0.159461	−	0.987204i	$-0.550976\pi$
$983$	−9.99912	−0.318922	−0.159461	+	0.987204i	$0.550976\pi$
$984$	−2.37179	−0.0756101
$985$	13.8378	0.440909
$986$	1.29211	0.0411491
$987$	−2.69898	−0.0859095
$988$	−15.6254	−0.497110
$989$	70.3227	2.23613
$990$	−1.00000	−0.0317821
$991$	36.7629	1.16781	0.583906	−	0.811821i	$-0.301524\pi$
$991$	36.7629	1.16781	0.583906	+	0.811821i	$0.301524\pi$
$992$	−4.33328	−0.137582
$993$	16.7229	0.530684
$994$	−11.0195	−0.349517
$995$	18.9738	0.601510
$996$	1.23472	0.0391237
$997$	7.90083	0.250222	0.125111	−	0.992143i	$-0.460071\pi$
$997$	7.90083	0.250222	0.125111	+	0.992143i	$0.460071\pi$
$998$	35.2074	1.11447
$999$	7.25359	0.229493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ck.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ck.1.2	✓	5	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.13795 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.13795 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.43005 q^{13} -1.13795 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +6.43005 q^{19} +1.00000 q^{20} -1.13795 q^{21} -1.00000 q^{22} +5.50974 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.43005 q^{26} +1.00000 q^{27} -1.13795 q^{28} -1.29211 q^{29} +1.00000 q^{30} -4.33328 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -1.13795 q^{35} +1.00000 q^{36} +7.25359 q^{37} +6.43005 q^{38} -2.43005 q^{39} +1.00000 q^{40} -2.37179 q^{41} -1.13795 q^{42} +12.7633 q^{43} -1.00000 q^{44} +1.00000 q^{45} +5.50974 q^{46} +2.37179 q^{47} +1.00000 q^{48} -5.70507 q^{49} +1.00000 q^{50} -1.00000 q^{51} -2.43005 q^{52} +7.09943 q^{53} +1.00000 q^{54} -1.00000 q^{55} -1.13795 q^{56} +6.43005 q^{57} -1.29211 q^{58} -0.823536 q^{59} +1.00000 q^{60} +3.23472 q^{61} -4.33328 q^{62} -1.13795 q^{63} +1.00000 q^{64} -2.43005 q^{65} -1.00000 q^{66} +0.977695 q^{67} -1.00000 q^{68} +5.50974 q^{69} -1.13795 q^{70} +9.68365 q^{71} +1.00000 q^{72} +13.8430 q^{73} +7.25359 q^{74} +1.00000 q^{75} +6.43005 q^{76} +1.13795 q^{77} -2.43005 q^{78} -10.0554 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.37179 q^{82} +1.23472 q^{83} -1.13795 q^{84} -1.00000 q^{85} +12.7633 q^{86} -1.29211 q^{87} -1.00000 q^{88} -8.58421 q^{89} +1.00000 q^{90} +2.76528 q^{91} +5.50974 q^{92} -4.33328 q^{93} +2.37179 q^{94} +6.43005 q^{95} +1.00000 q^{96} -13.1934 q^{97} -5.70507 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} - 5 q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} + 11 q^{19} + 5 q^{20} + 2 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{24} + 5 q^{25} + 9 q^{26} + 5 q^{27} + 2 q^{28} + 7 q^{29} + 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + 7 q^{37} + 11 q^{38} + 9 q^{39} + 5 q^{40} + 4 q^{41} + 2 q^{42} + 11 q^{43} - 5 q^{44} + 5 q^{45} + 4 q^{46} - 4 q^{47} + 5 q^{48} + 19 q^{49} + 5 q^{50} - 5 q^{51} + 9 q^{52} + 12 q^{53} + 5 q^{54} - 5 q^{55} + 2 q^{56} + 11 q^{57} + 7 q^{58} + 4 q^{59} + 5 q^{60} + 19 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} - 5 q^{68} + 4 q^{69} + 2 q^{70} - 2 q^{71} + 5 q^{72} + 14 q^{73} + 7 q^{74} + 5 q^{75} + 11 q^{76} - 2 q^{77} + 9 q^{78} + 16 q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} + 9 q^{83} + 2 q^{84} - 5 q^{85} + 11 q^{86} + 7 q^{87} - 5 q^{88} - 16 q^{89} + 5 q^{90} + 11 q^{91} + 4 q^{92} + 10 q^{93} - 4 q^{94} + 11 q^{95} + 5 q^{96} + 8 q^{97} + 19 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 - 5 * q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 + 11 * q^19 + 5 * q^20 + 2 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^24 + 5 * q^25 + 9 * q^26 + 5 * q^27 + 2 * q^28 + 7 * q^29 + 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + 7 * q^37 + 11 * q^38 + 9 * q^39 + 5 * q^40 + 4 * q^41 + 2 * q^42 + 11 * q^43 - 5 * q^44 + 5 * q^45 + 4 * q^46 - 4 * q^47 + 5 * q^48 + 19 * q^49 + 5 * q^50 - 5 * q^51 + 9 * q^52 + 12 * q^53 + 5 * q^54 - 5 * q^55 + 2 * q^56 + 11 * q^57 + 7 * q^58 + 4 * q^59 + 5 * q^60 + 19 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 - 5 * q^68 + 4 * q^69 + 2 * q^70 - 2 * q^71 + 5 * q^72 + 14 * q^73 + 7 * q^74 + 5 * q^75 + 11 * q^76 - 2 * q^77 + 9 * q^78 + 16 * q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 + 9 * q^83 + 2 * q^84 - 5 * q^85 + 11 * q^86 + 7 * q^87 - 5 * q^88 - 16 * q^89 + 5 * q^90 + 11 * q^91 + 4 * q^92 + 10 * q^93 - 4 * q^94 + 11 * q^95 + 5 * q^96 + 8 * q^97 + 19 * q^98 - 5 * q^99

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