LMFDB - Embedded newform 4010.2.a.k.1.9

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} + \cdots - 512 $ x^15 - 7x^14 - 7x^13 + 133x^12 - 99x^11 - 941x^10 + 1290x^9 + 3031x^8 - 5452x^7 - 4098x^6 + 9986x^5 + 850x^4 - 7216x^3 + 1688x^2 + 1441x - 512
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.79590$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +1.00000 q^{10} -3.07208 q^{11} -0.154802 q^{12} +6.08938 q^{13} +4.41535 q^{14} +0.154802 q^{15} +1.00000 q^{16} +6.99132 q^{17} +2.97604 q^{18} -0.745971 q^{19} -1.00000 q^{20} +0.683507 q^{21} +3.07208 q^{22} -2.22179 q^{23} +0.154802 q^{24} +1.00000 q^{25} -6.08938 q^{26} +0.925104 q^{27} -4.41535 q^{28} +2.48268 q^{29} -0.154802 q^{30} +2.52786 q^{31} -1.00000 q^{32} +0.475565 q^{33} -6.99132 q^{34} +4.41535 q^{35} -2.97604 q^{36} -3.01023 q^{37} +0.745971 q^{38} -0.942651 q^{39} +1.00000 q^{40} +6.07906 q^{41} -0.683507 q^{42} +1.67837 q^{43} -3.07208 q^{44} +2.97604 q^{45} +2.22179 q^{46} +2.53479 q^{47} -0.154802 q^{48} +12.4953 q^{49} -1.00000 q^{50} -1.08227 q^{51} +6.08938 q^{52} -0.745448 q^{53} -0.925104 q^{54} +3.07208 q^{55} +4.41535 q^{56} +0.115478 q^{57} -2.48268 q^{58} -3.79594 q^{59} +0.154802 q^{60} +4.16103 q^{61} -2.52786 q^{62} +13.1402 q^{63} +1.00000 q^{64} -6.08938 q^{65} -0.475565 q^{66} -13.0017 q^{67} +6.99132 q^{68} +0.343938 q^{69} -4.41535 q^{70} +8.13964 q^{71} +2.97604 q^{72} +1.02853 q^{73} +3.01023 q^{74} -0.154802 q^{75} -0.745971 q^{76} +13.5643 q^{77} +0.942651 q^{78} -7.95012 q^{79} -1.00000 q^{80} +8.78490 q^{81} -6.07906 q^{82} -6.71915 q^{83} +0.683507 q^{84} -6.99132 q^{85} -1.67837 q^{86} -0.384325 q^{87} +3.07208 q^{88} +8.62004 q^{89} -2.97604 q^{90} -26.8868 q^{91} -2.22179 q^{92} -0.391319 q^{93} -2.53479 q^{94} +0.745971 q^{95} +0.154802 q^{96} -16.4913 q^{97} -12.4953 q^{98} +9.14262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * 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
$3$	−0.154802	−0.0893752	−0.0446876	−	0.999001i	$-0.514229\pi$
$3$	−0.154802	−0.0893752	−0.0446876	+	0.999001i	$0.514229\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.154802	0.0631978
$7$	−4.41535	−1.66885	−0.834423	−	0.551125i	$-0.814199\pi$
$7$	−4.41535	−1.66885	−0.834423	+	0.551125i	$0.814199\pi$
$8$	−1.00000	−0.353553
$9$	−2.97604	−0.992012
$10$	1.00000	0.316228
$11$	−3.07208	−0.926267	−0.463133	−	0.886289i	$-0.653275\pi$
$11$	−3.07208	−0.926267	−0.463133	+	0.886289i	$0.653275\pi$
$12$	−0.154802	−0.0446876
$13$	6.08938	1.68889	0.844446	−	0.535641i	$-0.179930\pi$
$13$	6.08938	1.68889	0.844446	+	0.535641i	$0.179930\pi$
$14$	4.41535	1.18005
$15$	0.154802	0.0399698
$16$	1.00000	0.250000
$17$	6.99132	1.69565	0.847823	−	0.530280i	$-0.177913\pi$
$17$	6.99132	1.69565	0.847823	+	0.530280i	$0.177913\pi$
$18$	2.97604	0.701458
$19$	−0.745971	−0.171138	−0.0855688	−	0.996332i	$-0.527271\pi$
$19$	−0.745971	−0.171138	−0.0855688	+	0.996332i	$0.527271\pi$
$20$	−1.00000	−0.223607
$21$	0.683507	0.149153
$22$	3.07208	0.654969
$23$	−2.22179	−0.463274	−0.231637	−	0.972802i	$-0.574408\pi$
$23$	−2.22179	−0.463274	−0.231637	+	0.972802i	$0.574408\pi$
$24$	0.154802	0.0315989
$25$	1.00000	0.200000
$26$	−6.08938	−1.19423
$27$	0.925104	0.178036
$28$	−4.41535	−0.834423
$29$	2.48268	0.461023	0.230511	−	0.973070i	$-0.425960\pi$
$29$	2.48268	0.461023	0.230511	+	0.973070i	$0.425960\pi$
$30$	−0.154802	−0.0282629
$31$	2.52786	0.454017	0.227009	−	0.973893i	$-0.427105\pi$
$31$	2.52786	0.454017	0.227009	+	0.973893i	$0.427105\pi$
$32$	−1.00000	−0.176777
$33$	0.475565	0.0827852
$34$	−6.99132	−1.19900
$35$	4.41535	0.746330
$36$	−2.97604	−0.496006
$37$	−3.01023	−0.494878	−0.247439	−	0.968903i	$-0.579589\pi$
$37$	−3.01023	−0.494878	−0.247439	+	0.968903i	$0.579589\pi$
$38$	0.745971	0.121013
$39$	−0.942651	−0.150945
$40$	1.00000	0.158114
$41$	6.07906	0.949389	0.474694	−	0.880151i	$-0.342559\pi$
$41$	6.07906	0.949389	0.474694	+	0.880151i	$0.342559\pi$
$42$	−0.683507	−0.105467
$43$	1.67837	0.255948	0.127974	−	0.991777i	$-0.459153\pi$
$43$	1.67837	0.255948	0.127974	+	0.991777i	$0.459153\pi$
$44$	−3.07208	−0.463133
$45$	2.97604	0.443641
$46$	2.22179	0.327584
$47$	2.53479	0.369737	0.184868	−	0.982763i	$-0.440814\pi$
$47$	2.53479	0.369737	0.184868	+	0.982763i	$0.440814\pi$
$48$	−0.154802	−0.0223438
$49$	12.4953	1.78504
$50$	−1.00000	−0.141421
$51$	−1.08227	−0.151549
$52$	6.08938	0.844446
$53$	−0.745448	−0.102395	−0.0511976	−	0.998689i	$-0.516304\pi$
$53$	−0.745448	−0.102395	−0.0511976	+	0.998689i	$0.516304\pi$
$54$	−0.925104	−0.125891
$55$	3.07208	0.414239
$56$	4.41535	0.590026
$57$	0.115478	0.0152954
$58$	−2.48268	−0.325992
$59$	−3.79594	−0.494189	−0.247095	−	0.968991i	$-0.579476\pi$
$59$	−3.79594	−0.494189	−0.247095	+	0.968991i	$0.579476\pi$
$60$	0.154802	0.0199849
$61$	4.16103	0.532766	0.266383	−	0.963867i	$-0.414171\pi$
$61$	4.16103	0.532766	0.266383	+	0.963867i	$0.414171\pi$
$62$	−2.52786	−0.321039
$63$	13.1402	1.65551
$64$	1.00000	0.125000
$65$	−6.08938	−0.755295
$66$	−0.475565	−0.0585380
$67$	−13.0017	−1.58841	−0.794203	−	0.607653i	$-0.792111\pi$
$67$	−13.0017	−1.58841	−0.794203	+	0.607653i	$0.792111\pi$
$68$	6.99132	0.847823
$69$	0.343938	0.0414052
$70$	−4.41535	−0.527735
$71$	8.13964	0.965998	0.482999	−	0.875621i	$-0.339548\pi$
$71$	8.13964	0.965998	0.482999	+	0.875621i	$0.339548\pi$
$72$	2.97604	0.350729
$73$	1.02853	0.120380	0.0601902	−	0.998187i	$-0.480829\pi$
$73$	1.02853	0.120380	0.0601902	+	0.998187i	$0.480829\pi$
$74$	3.01023	0.349932
$75$	−0.154802	−0.0178750
$76$	−0.745971	−0.0855688
$77$	13.5643	1.54580
$78$	0.942651	0.106734
$79$	−7.95012	−0.894459	−0.447229	−	0.894419i	$-0.647589\pi$
$79$	−7.95012	−0.894459	−0.447229	+	0.894419i	$0.647589\pi$
$80$	−1.00000	−0.111803
$81$	8.78490	0.976100
$82$	−6.07906	−0.671319
$83$	−6.71915	−0.737522	−0.368761	−	0.929524i	$-0.620218\pi$
$83$	−6.71915	−0.737522	−0.368761	+	0.929524i	$0.620218\pi$
$84$	0.683507	0.0745767
$85$	−6.99132	−0.758316
$86$	−1.67837	−0.180983
$87$	−0.384325	−0.0412040
$88$	3.07208	0.327485
$89$	8.62004	0.913722	0.456861	−	0.889538i	$-0.348974\pi$
$89$	8.62004	0.913722	0.456861	+	0.889538i	$0.348974\pi$
$90$	−2.97604	−0.313702
$91$	−26.8868	−2.81850
$92$	−2.22179	−0.231637
$93$	−0.391319	−0.0405779
$94$	−2.53479	−0.261443
$95$	0.745971	0.0765350
$96$	0.154802	0.0157994
$97$	−16.4913	−1.67444	−0.837218	−	0.546870i	$-0.815819\pi$
$97$	−16.4913	−1.67444	−0.837218	+	0.546870i	$0.815819\pi$
$98$	−12.4953	−1.26222
$99$	9.14262	0.918868
$100$	1.00000	0.100000
$101$	−11.6975	−1.16394	−0.581970	−	0.813210i	$-0.697718\pi$
$101$	−11.6975	−1.16394	−0.581970	+	0.813210i	$0.697718\pi$
$102$	1.08227	0.107161
$103$	2.10592	0.207503	0.103751	−	0.994603i	$-0.466915\pi$
$103$	2.10592	0.207503	0.103751	+	0.994603i	$0.466915\pi$
$104$	−6.08938	−0.597113
$105$	−0.683507	−0.0667034
$106$	0.745448	0.0724043
$107$	−11.0502	−1.06826	−0.534130	−	0.845402i	$-0.679361\pi$
$107$	−11.0502	−1.06826	−0.534130	+	0.845402i	$0.679361\pi$
$108$	0.925104	0.0890182
$109$	−3.08659	−0.295642	−0.147821	−	0.989014i	$-0.547226\pi$
$109$	−3.08659	−0.295642	−0.147821	+	0.989014i	$0.547226\pi$
$110$	−3.07208	−0.292911
$111$	0.465990	0.0442299
$112$	−4.41535	−0.417211
$113$	12.8891	1.21250	0.606250	−	0.795274i	$-0.292673\pi$
$113$	12.8891	1.21250	0.606250	+	0.795274i	$0.292673\pi$
$114$	−0.115478	−0.0108155
$115$	2.22179	0.207183
$116$	2.48268	0.230511
$117$	−18.1222	−1.67540
$118$	3.79594	0.349444
$119$	−30.8691	−2.82977
$120$	−0.154802	−0.0141315
$121$	−1.56233	−0.142030
$122$	−4.16103	−0.376722
$123$	−0.941052	−0.0848518
$124$	2.52786	0.227009
$125$	−1.00000	−0.0894427
$126$	−13.1402	−1.17063
$127$	−11.2095	−0.994681	−0.497340	−	0.867556i	$-0.665690\pi$
$127$	−11.2095	−0.994681	−0.497340	+	0.867556i	$0.665690\pi$
$128$	−1.00000	−0.0883883
$129$	−0.259815	−0.0228754
$130$	6.08938	0.534074
$131$	6.16032	0.538230	0.269115	−	0.963108i	$-0.413269\pi$
$131$	6.16032	0.538230	0.269115	+	0.963108i	$0.413269\pi$
$132$	0.475565	0.0413926
$133$	3.29372	0.285602
$134$	13.0017	1.12317
$135$	−0.925104	−0.0796203
$136$	−6.99132	−0.599501
$137$	−16.4405	−1.40460	−0.702302	−	0.711879i	$-0.747844\pi$
$137$	−16.4405	−1.40460	−0.702302	+	0.711879i	$0.747844\pi$
$138$	−0.343938	−0.0292779
$139$	5.10643	0.433122	0.216561	−	0.976269i	$-0.430516\pi$
$139$	5.10643	0.433122	0.216561	+	0.976269i	$0.430516\pi$
$140$	4.41535	0.373165
$141$	−0.392391	−0.0330453
$142$	−8.13964	−0.683063
$143$	−18.7071	−1.56436
$144$	−2.97604	−0.248003
$145$	−2.48268	−0.206176
$146$	−1.02853	−0.0851217
$147$	−1.93430	−0.159539
$148$	−3.01023	−0.247439
$149$	8.47553	0.694342	0.347171	−	0.937802i	$-0.387142\pi$
$149$	8.47553	0.694342	0.347171	+	0.937802i	$0.387142\pi$
$150$	0.154802	0.0126396
$151$	−20.8152	−1.69391	−0.846957	−	0.531661i	$-0.821568\pi$
$151$	−20.8152	−1.69391	−0.846957	+	0.531661i	$0.821568\pi$
$152$	0.745971	0.0605063
$153$	−20.8064	−1.68210
$154$	−13.5643	−1.09304
$155$	−2.52786	−0.203043
$156$	−0.942651	−0.0754725
$157$	6.57637	0.524851	0.262426	−	0.964952i	$-0.415478\pi$
$157$	6.57637	0.524851	0.262426	+	0.964952i	$0.415478\pi$
$158$	7.95012	0.632478
$159$	0.115397	0.00915159
$160$	1.00000	0.0790569
$161$	9.80996	0.773133
$162$	−8.78490	−0.690207
$163$	−7.48490	−0.586263	−0.293131	−	0.956072i	$-0.594697\pi$
$163$	−7.48490	−0.586263	−0.293131	+	0.956072i	$0.594697\pi$
$164$	6.07906	0.474694
$165$	−0.475565	−0.0370227
$166$	6.71915	0.521507
$167$	−8.85429	−0.685166	−0.342583	−	0.939488i	$-0.611302\pi$
$167$	−8.85429	−0.685166	−0.342583	+	0.939488i	$0.611302\pi$
$168$	−0.683507	−0.0527337
$169$	24.0806	1.85235
$170$	6.99132	0.536210
$171$	2.22004	0.169770
$172$	1.67837	0.127974
$173$	−12.4239	−0.944571	−0.472285	−	0.881446i	$-0.656571\pi$
$173$	−12.4239	−0.944571	−0.472285	+	0.881446i	$0.656571\pi$
$174$	0.384325	0.0291356
$175$	−4.41535	−0.333769
$176$	−3.07208	−0.231567
$177$	0.587620	0.0441682
$178$	−8.62004	−0.646099
$179$	4.44563	0.332282	0.166141	−	0.986102i	$-0.446869\pi$
$179$	4.44563	0.332282	0.166141	+	0.986102i	$0.446869\pi$
$180$	2.97604	0.221821
$181$	−16.4715	−1.22431	−0.612157	−	0.790736i	$-0.709698\pi$
$181$	−16.4715	−1.22431	−0.612157	+	0.790736i	$0.709698\pi$
$182$	26.8868	1.99298
$183$	−0.644138	−0.0476160
$184$	2.22179	0.163792
$185$	3.01023	0.221316
$186$	0.391319	0.0286929
$187$	−21.4779	−1.57062
$188$	2.53479	0.184868
$189$	−4.08466	−0.297115
$190$	−0.745971	−0.0541184
$191$	5.80047	0.419707	0.209853	−	0.977733i	$-0.432701\pi$
$191$	5.80047	0.419707	0.209853	+	0.977733i	$0.432701\pi$
$192$	−0.154802	−0.0111719
$193$	17.6844	1.27295	0.636475	−	0.771297i	$-0.280392\pi$
$193$	17.6844	1.27295	0.636475	+	0.771297i	$0.280392\pi$
$194$	16.4913	1.18400
$195$	0.942651	0.0675046
$196$	12.4953	0.892522
$197$	0.207977	0.0148178	0.00740888	−	0.999973i	$-0.497642\pi$
$197$	0.207977	0.0148178	0.00740888	+	0.999973i	$0.497642\pi$
$198$	−9.14262	−0.649738
$199$	20.8974	1.48138	0.740688	−	0.671849i	$-0.234500\pi$
$199$	20.8974	1.48138	0.740688	+	0.671849i	$0.234500\pi$
$200$	−1.00000	−0.0707107
$201$	2.01269	0.141964
$202$	11.6975	0.823030
$203$	−10.9619	−0.769375
$204$	−1.08227	−0.0757743
$205$	−6.07906	−0.424580
$206$	−2.10592	−0.146727
$207$	6.61212	0.459574
$208$	6.08938	0.422223
$209$	2.29168	0.158519
$210$	0.683507	0.0471664
$211$	18.2355	1.25538	0.627691	−	0.778463i	$-0.284000\pi$
$211$	18.2355	1.25538	0.627691	+	0.778463i	$0.284000\pi$
$212$	−0.745448	−0.0511976
$213$	−1.26004	−0.0863362
$214$	11.0502	0.755374
$215$	−1.67837	−0.114464
$216$	−0.925104	−0.0629454
$217$	−11.1614	−0.757685
$218$	3.08659	0.209050
$219$	−0.159219	−0.0107590
$220$	3.07208	0.207120
$221$	42.5729	2.86376
$222$	−0.465990	−0.0312752
$223$	−0.115780	−0.00775320	−0.00387660	−	0.999992i	$-0.501234\pi$
$223$	−0.115780	−0.00775320	−0.00387660	+	0.999992i	$0.501234\pi$
$224$	4.41535	0.295013
$225$	−2.97604	−0.198402
$226$	−12.8891	−0.857367
$227$	−29.4485	−1.95457	−0.977284	−	0.211935i	$-0.932024\pi$
$227$	−29.4485	−1.95457	−0.977284	+	0.211935i	$0.932024\pi$
$228$	0.115478	0.00764772
$229$	−6.16106	−0.407134	−0.203567	−	0.979061i	$-0.565254\pi$
$229$	−6.16106	−0.407134	−0.203567	+	0.979061i	$0.565254\pi$
$230$	−2.22179	−0.146500
$231$	−2.09979	−0.138156
$232$	−2.48268	−0.162996
$233$	8.87040	0.581119	0.290560	−	0.956857i	$-0.406159\pi$
$233$	8.87040	0.581119	0.290560	+	0.956857i	$0.406159\pi$
$234$	18.1222	1.18469
$235$	−2.53479	−0.165351
$236$	−3.79594	−0.247095
$237$	1.23070	0.0799424
$238$	30.8691	2.00095
$239$	7.53613	0.487472	0.243736	−	0.969842i	$-0.421627\pi$
$239$	7.53613	0.487472	0.243736	+	0.969842i	$0.421627\pi$
$240$	0.154802	0.00999245
$241$	−25.3180	−1.63088	−0.815439	−	0.578844i	$-0.803504\pi$
$241$	−25.3180	−1.63088	−0.815439	+	0.578844i	$0.803504\pi$
$242$	1.56233	0.100430
$243$	−4.13524	−0.265276
$244$	4.16103	0.266383
$245$	−12.4953	−0.798296
$246$	0.941052	0.0599993
$247$	−4.54251	−0.289033
$248$	−2.52786	−0.160519
$249$	1.04014	0.0659162
$250$	1.00000	0.0632456
$251$	18.4613	1.16527	0.582633	−	0.812735i	$-0.302022\pi$
$251$	18.4613	1.16527	0.582633	+	0.812735i	$0.302022\pi$
$252$	13.1402	0.827757
$253$	6.82550	0.429116
$254$	11.2095	0.703345
$255$	1.08227	0.0677746
$256$	1.00000	0.0625000
$257$	−28.3938	−1.77116	−0.885578	−	0.464491i	$-0.846237\pi$
$257$	−28.3938	−1.77116	−0.885578	+	0.464491i	$0.846237\pi$
$258$	0.259815	0.0161754
$259$	13.2912	0.825876
$260$	−6.08938	−0.377648
$261$	−7.38855	−0.457340
$262$	−6.16032	−0.380586
$263$	15.6425	0.964559	0.482280	−	0.876017i	$-0.339809\pi$
$263$	15.6425	0.964559	0.482280	+	0.876017i	$0.339809\pi$
$264$	−0.475565	−0.0292690
$265$	0.745448	0.0457925
$266$	−3.29372	−0.201951
$267$	−1.33440	−0.0816641
$268$	−13.0017	−0.794203
$269$	12.6077	0.768704	0.384352	−	0.923187i	$-0.374425\pi$
$269$	12.6077	0.768704	0.384352	+	0.923187i	$0.374425\pi$
$270$	0.925104	0.0563001
$271$	−25.6235	−1.55651	−0.778257	−	0.627946i	$-0.783896\pi$
$271$	−25.6235	−1.55651	−0.778257	+	0.627946i	$0.783896\pi$
$272$	6.99132	0.423911
$273$	4.16213	0.251904
$274$	16.4405	0.993205
$275$	−3.07208	−0.185253
$276$	0.343938	0.0207026
$277$	29.5108	1.77313	0.886565	−	0.462604i	$-0.153085\pi$
$277$	29.5108	1.77313	0.886565	+	0.462604i	$0.153085\pi$
$278$	−5.10643	−0.306263
$279$	−7.52301	−0.450391
$280$	−4.41535	−0.263868
$281$	−11.9491	−0.712824	−0.356412	−	0.934329i	$-0.616000\pi$
$281$	−11.9491	−0.712824	−0.356412	+	0.934329i	$0.616000\pi$
$282$	0.392391	0.0233666
$283$	−29.0019	−1.72398	−0.861991	−	0.506923i	$-0.830783\pi$
$283$	−29.0019	−1.72398	−0.861991	+	0.506923i	$0.830783\pi$
$284$	8.13964	0.482999
$285$	−0.115478	−0.00684033
$286$	18.7071	1.10617
$287$	−26.8412	−1.58438
$288$	2.97604	0.175365
$289$	31.8786	1.87521
$290$	2.48268	0.145788
$291$	2.55289	0.149653
$292$	1.02853	0.0601902
$293$	−7.99449	−0.467043	−0.233521	−	0.972352i	$-0.575025\pi$
$293$	−7.99449	−0.467043	−0.233521	+	0.972352i	$0.575025\pi$
$294$	1.93430	0.112811
$295$	3.79594	0.221008
$296$	3.01023	0.174966
$297$	−2.84199	−0.164909
$298$	−8.47553	−0.490974
$299$	−13.5293	−0.782420
$300$	−0.154802	−0.00893752
$301$	−7.41058	−0.427138
$302$	20.8152	1.19778
$303$	1.81079	0.104027
$304$	−0.745971	−0.0427844
$305$	−4.16103	−0.238260
$306$	20.8064	1.18942
$307$	24.2347	1.38315	0.691574	−	0.722306i	$-0.256918\pi$
$307$	24.2347	1.38315	0.691574	+	0.722306i	$0.256918\pi$
$308$	13.5643	0.772898
$309$	−0.326002	−0.0185456
$310$	2.52786	0.143573
$311$	25.0016	1.41771	0.708854	−	0.705355i	$-0.249212\pi$
$311$	25.0016	1.41771	0.708854	+	0.705355i	$0.249212\pi$
$312$	0.942651	0.0533671
$313$	−22.7439	−1.28556	−0.642780	−	0.766051i	$-0.722219\pi$
$313$	−22.7439	−1.28556	−0.642780	+	0.766051i	$0.722219\pi$
$314$	−6.57637	−0.371126
$315$	−13.1402	−0.740369
$316$	−7.95012	−0.447229
$317$	−5.43701	−0.305373	−0.152686	−	0.988275i	$-0.548792\pi$
$317$	−5.43701	−0.305373	−0.152686	+	0.988275i	$0.548792\pi$
$318$	−0.115397	−0.00647115
$319$	−7.62700	−0.427030
$320$	−1.00000	−0.0559017
$321$	1.71059	0.0954760
$322$	−9.80996	−0.546688
$323$	−5.21533	−0.290188
$324$	8.78490	0.488050
$325$	6.08938	0.337778
$326$	7.48490	0.414551
$327$	0.477811	0.0264230
$328$	−6.07906	−0.335660
$329$	−11.1920	−0.617034
$330$	0.475565	0.0261790
$331$	19.8682	1.09206	0.546028	−	0.837767i	$-0.316139\pi$
$331$	19.8682	1.09206	0.546028	+	0.837767i	$0.316139\pi$
$332$	−6.71915	−0.368761
$333$	8.95855	0.490925
$334$	8.85429	0.484485
$335$	13.0017	0.710356
$336$	0.683507	0.0372883
$337$	−9.36919	−0.510372	−0.255186	−	0.966892i	$-0.582137\pi$
$337$	−9.36919	−0.510372	−0.255186	+	0.966892i	$0.582137\pi$
$338$	−24.0806	−1.30981
$339$	−1.99526	−0.108367
$340$	−6.99132	−0.379158
$341$	−7.76579	−0.420541
$342$	−2.22004	−0.120046
$343$	−24.2637	−1.31012
$344$	−1.67837	−0.0904915
$345$	−0.343938	−0.0185170
$346$	12.4239	0.667912
$347$	−8.04989	−0.432141	−0.216070	−	0.976378i	$-0.569324\pi$
$347$	−8.04989	−0.432141	−0.216070	+	0.976378i	$0.569324\pi$
$348$	−0.384325	−0.0206020
$349$	−14.1691	−0.758456	−0.379228	−	0.925303i	$-0.623810\pi$
$349$	−14.1691	−0.758456	−0.379228	+	0.925303i	$0.623810\pi$
$350$	4.41535	0.236010
$351$	5.63332	0.300684
$352$	3.07208	0.163742
$353$	29.1375	1.55083	0.775417	−	0.631449i	$-0.217539\pi$
$353$	29.1375	1.55083	0.775417	+	0.631449i	$0.217539\pi$
$354$	−0.587620	−0.0312317
$355$	−8.13964	−0.432007
$356$	8.62004	0.456861
$357$	4.77862	0.252911
$358$	−4.44563	−0.234959
$359$	−1.74842	−0.0922780	−0.0461390	−	0.998935i	$-0.514692\pi$
$359$	−1.74842	−0.0922780	−0.0461390	+	0.998935i	$0.514692\pi$
$360$	−2.97604	−0.156851
$361$	−18.4435	−0.970712
$362$	16.4715	0.865721
$363$	0.241853	0.0126940
$364$	−26.8868	−1.40925
$365$	−1.02853	−0.0538357
$366$	0.644138	0.0336696
$367$	−13.1991	−0.688986	−0.344493	−	0.938789i	$-0.611949\pi$
$367$	−13.1991	−0.688986	−0.344493	+	0.938789i	$0.611949\pi$
$368$	−2.22179	−0.115819
$369$	−18.0915	−0.941805
$370$	−3.01023	−0.156494
$371$	3.29141	0.170882
$372$	−0.391319	−0.0202889
$373$	−35.7076	−1.84887	−0.924434	−	0.381341i	$-0.875462\pi$
$373$	−35.7076	−1.84887	−0.924434	+	0.381341i	$0.875462\pi$
$374$	21.4779	1.11060
$375$	0.154802	0.00799396
$376$	−2.53479	−0.130722
$377$	15.1180	0.778617
$378$	4.08466	0.210092
$379$	20.2654	1.04096	0.520481	−	0.853873i	$-0.325753\pi$
$379$	20.2654	1.04096	0.520481	+	0.853873i	$0.325753\pi$
$380$	0.745971	0.0382675
$381$	1.73525	0.0888998
$382$	−5.80047	−0.296778
$383$	−35.0482	−1.79088	−0.895439	−	0.445183i	$-0.853139\pi$
$383$	−35.0482	−1.79088	−0.895439	+	0.445183i	$0.853139\pi$
$384$	0.154802	0.00789972
$385$	−13.5643	−0.691301
$386$	−17.6844	−0.900111
$387$	−4.99488	−0.253904
$388$	−16.4913	−0.837218
$389$	−16.6478	−0.844078	−0.422039	−	0.906578i	$-0.638686\pi$
$389$	−16.6478	−0.844078	−0.422039	+	0.906578i	$0.638686\pi$
$390$	−0.942651	−0.0477330
$391$	−15.5332	−0.785549
$392$	−12.4953	−0.631109
$393$	−0.953633	−0.0481044
$394$	−0.207977	−0.0104777
$395$	7.95012	0.400014
$396$	9.14262	0.459434
$397$	3.46731	0.174019	0.0870095	−	0.996207i	$-0.472269\pi$
$397$	3.46731	0.174019	0.0870095	+	0.996207i	$0.472269\pi$
$398$	−20.8974	−1.04749
$399$	−0.509876	−0.0255257
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−2.01269	−0.100384
$403$	15.3931	0.766786
$404$	−11.6975	−0.581970
$405$	−8.78490	−0.436525
$406$	10.9619	0.544031
$407$	9.24766	0.458389
$408$	1.08227	0.0535805
$409$	−39.8306	−1.96949	−0.984747	−	0.173990i	$-0.944334\pi$
$409$	−39.8306	−1.96949	−0.984747	+	0.173990i	$0.944334\pi$
$410$	6.07906	0.300223
$411$	2.54502	0.125537
$412$	2.10592	0.103751
$413$	16.7604	0.824725
$414$	−6.61212	−0.324968
$415$	6.71915	0.329830
$416$	−6.08938	−0.298557
$417$	−0.790487	−0.0387103
$418$	−2.29168	−0.112090
$419$	25.3727	1.23954	0.619768	−	0.784785i	$-0.287227\pi$
$419$	25.3727	1.23954	0.619768	+	0.784785i	$0.287227\pi$
$420$	−0.683507	−0.0333517
$421$	−21.5568	−1.05062	−0.525308	−	0.850912i	$-0.676050\pi$
$421$	−21.5568	−1.05062	−0.525308	+	0.850912i	$0.676050\pi$
$422$	−18.2355	−0.887689
$423$	−7.54362	−0.366783
$424$	0.745448	0.0362022
$425$	6.99132	0.339129
$426$	1.26004	0.0610489
$427$	−18.3724	−0.889103
$428$	−11.0502	−0.534130
$429$	2.89590	0.139815
$430$	1.67837	0.0809380
$431$	−3.17088	−0.152736	−0.0763679	−	0.997080i	$-0.524332\pi$
$431$	−3.17088	−0.152736	−0.0763679	+	0.997080i	$0.524332\pi$
$432$	0.925104	0.0445091
$433$	−13.6613	−0.656520	−0.328260	−	0.944587i	$-0.606462\pi$
$433$	−13.6613	−0.656520	−0.328260	+	0.944587i	$0.606462\pi$
$434$	11.1614	0.535764
$435$	0.384325	0.0184270
$436$	−3.08659	−0.147821
$437$	1.65739	0.0792836
$438$	0.159219	0.00760777
$439$	−12.4747	−0.595386	−0.297693	−	0.954662i	$-0.596217\pi$
$439$	−12.4747	−0.595386	−0.297693	+	0.954662i	$0.596217\pi$
$440$	−3.07208	−0.146456
$441$	−37.1865	−1.77079
$442$	−42.5729	−2.02498
$443$	−14.6634	−0.696677	−0.348338	−	0.937369i	$-0.613254\pi$
$443$	−14.6634	−0.696677	−0.348338	+	0.937369i	$0.613254\pi$
$444$	0.465990	0.0221149
$445$	−8.62004	−0.408629
$446$	0.115780	0.00548234
$447$	−1.31203	−0.0620570
$448$	−4.41535	−0.208606
$449$	−10.8612	−0.512573	−0.256286	−	0.966601i	$-0.582499\pi$
$449$	−10.8612	−0.512573	−0.256286	+	0.966601i	$0.582499\pi$
$450$	2.97604	0.140292
$451$	−18.6753	−0.879387
$452$	12.8891	0.606250
$453$	3.22224	0.151394
$454$	29.4485	1.38209
$455$	26.8868	1.26047
$456$	−0.115478	−0.00540776
$457$	−18.3430	−0.858050	−0.429025	−	0.903293i	$-0.641143\pi$
$457$	−18.3430	−0.858050	−0.429025	+	0.903293i	$0.641143\pi$
$458$	6.16106	0.287888
$459$	6.46770	0.301887
$460$	2.22179	0.103591
$461$	38.6901	1.80198	0.900988	−	0.433844i	$-0.142843\pi$
$461$	38.6901	1.80198	0.900988	+	0.433844i	$0.142843\pi$
$462$	2.09979	0.0976909
$463$	23.1873	1.07760	0.538802	−	0.842433i	$-0.318877\pi$
$463$	23.1873	1.07760	0.538802	+	0.842433i	$0.318877\pi$
$464$	2.48268	0.115256
$465$	0.391319	0.0181470
$466$	−8.87040	−0.410913
$467$	22.1349	1.02428	0.512140	−	0.858902i	$-0.328853\pi$
$467$	22.1349	1.02428	0.512140	+	0.858902i	$0.328853\pi$
$468$	−18.1222	−0.837700
$469$	57.4069	2.65080
$470$	2.53479	0.116921
$471$	−1.01804	−0.0469087
$472$	3.79594	0.174722
$473$	−5.15607	−0.237077
$474$	−1.23070	−0.0565278
$475$	−0.745971	−0.0342275
$476$	−30.8691	−1.41488
$477$	2.21848	0.101577
$478$	−7.53613	−0.344695
$479$	16.5196	0.754799	0.377399	−	0.926051i	$-0.376818\pi$
$479$	16.5196	0.754799	0.377399	+	0.926051i	$0.376818\pi$
$480$	−0.154802	−0.00706573
$481$	−18.3304	−0.835796
$482$	25.3180	1.15320
$483$	−1.51861	−0.0690989
$484$	−1.56233	−0.0710151
$485$	16.4913	0.748830
$486$	4.13524	0.187578
$487$	29.4405	1.33407	0.667037	−	0.745024i	$-0.267562\pi$
$487$	29.4405	1.33407	0.667037	+	0.745024i	$0.267562\pi$
$488$	−4.16103	−0.188361
$489$	1.15868	0.0523974
$490$	12.4953	0.564481
$491$	17.5779	0.793280	0.396640	−	0.917974i	$-0.370176\pi$
$491$	17.5779	0.793280	0.396640	+	0.917974i	$0.370176\pi$
$492$	−0.941052	−0.0424259
$493$	17.3572	0.781731
$494$	4.54251	0.204377
$495$	−9.14262	−0.410930
$496$	2.52786	0.113504
$497$	−35.9394	−1.61210
$498$	−1.04014	−0.0466098
$499$	−35.8606	−1.60534	−0.802672	−	0.596421i	$-0.796589\pi$
$499$	−35.8606	−1.60534	−0.802672	+	0.596421i	$0.796589\pi$
$500$	−1.00000	−0.0447214
$501$	1.37067	0.0612368
$502$	−18.4613	−0.823968
$503$	−6.35538	−0.283372	−0.141686	−	0.989912i	$-0.545252\pi$
$503$	−6.35538	−0.283372	−0.141686	+	0.989912i	$0.545252\pi$
$504$	−13.1402	−0.585313
$505$	11.6975	0.520530
$506$	−6.82550	−0.303431
$507$	−3.72773	−0.165554
$508$	−11.2095	−0.497340
$509$	−8.02027	−0.355492	−0.177746	−	0.984076i	$-0.556881\pi$
$509$	−8.02027	−0.355492	−0.177746	+	0.984076i	$0.556881\pi$
$510$	−1.08227	−0.0479239
$511$	−4.54132	−0.200896
$512$	−1.00000	−0.0441942
$513$	−0.690101	−0.0304687
$514$	28.3938	1.25240
$515$	−2.10592	−0.0927981
$516$	−0.259815	−0.0114377
$517$	−7.78707	−0.342475
$518$	−13.2912	−0.583982
$519$	1.92325	0.0844212
$520$	6.08938	0.267037
$521$	−33.1875	−1.45397	−0.726986	−	0.686652i	$-0.759080\pi$
$521$	−33.1875	−1.45397	−0.726986	+	0.686652i	$0.759080\pi$
$522$	7.38855	0.323388
$523$	−34.9210	−1.52699	−0.763494	−	0.645815i	$-0.776518\pi$
$523$	−34.9210	−1.52699	−0.763494	+	0.645815i	$0.776518\pi$
$524$	6.16032	0.269115
$525$	0.683507	0.0298307
$526$	−15.6425	−0.682047
$527$	17.6731	0.769852
$528$	0.475565	0.0206963
$529$	−18.0637	−0.785377
$530$	−0.745448	−0.0323802
$531$	11.2969	0.490242
$532$	3.29372	0.142801
$533$	37.0177	1.60341
$534$	1.33440	0.0577452
$535$	11.0502	0.477741
$536$	13.0017	0.561586
$537$	−0.688193	−0.0296977
$538$	−12.6077	−0.543556
$539$	−38.3866	−1.65343
$540$	−0.925104	−0.0398102
$541$	5.86367	0.252099	0.126049	−	0.992024i	$-0.459770\pi$
$541$	5.86367	0.252099	0.126049	+	0.992024i	$0.459770\pi$
$542$	25.6235	1.10062
$543$	2.54982	0.109423
$544$	−6.99132	−0.299751
$545$	3.08659	0.132215
$546$	−4.16213	−0.178123
$547$	11.9297	0.510079	0.255039	−	0.966931i	$-0.417912\pi$
$547$	11.9297	0.510079	0.255039	+	0.966931i	$0.417912\pi$
$548$	−16.4405	−0.702302
$549$	−12.3834	−0.528510
$550$	3.07208	0.130994
$551$	−1.85201	−0.0788983
$552$	−0.343938	−0.0146390
$553$	35.1026	1.49271
$554$	−29.5108	−1.25379
$555$	−0.465990	−0.0197802
$556$	5.10643	0.216561
$557$	22.5121	0.953868	0.476934	−	0.878939i	$-0.341748\pi$
$557$	22.5121	0.953868	0.476934	+	0.878939i	$0.341748\pi$
$558$	7.52301	0.318474
$559$	10.2202	0.432269
$560$	4.41535	0.186583
$561$	3.32483	0.140374
$562$	11.9491	0.504042
$563$	−5.22004	−0.219998	−0.109999	−	0.993932i	$-0.535085\pi$
$563$	−5.22004	−0.219998	−0.109999	+	0.993932i	$0.535085\pi$
$564$	−0.392391	−0.0165226
$565$	−12.8891	−0.542247
$566$	29.0019	1.21904
$567$	−38.7884	−1.62896
$568$	−8.13964	−0.341532
$569$	−14.6065	−0.612335	−0.306168	−	0.951978i	$-0.599047\pi$
$569$	−14.6065	−0.612335	−0.306168	+	0.951978i	$0.599047\pi$
$570$	0.115478	0.00483685
$571$	2.78927	0.116727	0.0583636	−	0.998295i	$-0.481412\pi$
$571$	2.78927	0.116727	0.0583636	+	0.998295i	$0.481412\pi$
$572$	−18.7071	−0.782182
$573$	−0.897926	−0.0375114
$574$	26.8412	1.12033
$575$	−2.22179	−0.0926549
$576$	−2.97604	−0.124002
$577$	−22.3981	−0.932447	−0.466223	−	0.884667i	$-0.654386\pi$
$577$	−22.3981	−0.932447	−0.466223	+	0.884667i	$0.654386\pi$
$578$	−31.8786	−1.32598
$579$	−2.73758	−0.113770
$580$	−2.48268	−0.103088
$581$	29.6674	1.23081
$582$	−2.55289	−0.105821
$583$	2.29008	0.0948452
$584$	−1.02853	−0.0425609
$585$	18.1222	0.749262
$586$	7.99449	0.330249
$587$	17.3786	0.717292	0.358646	−	0.933474i	$-0.383239\pi$
$587$	17.3786	0.717292	0.358646	+	0.933474i	$0.383239\pi$
$588$	−1.93430	−0.0797694
$589$	−1.88571	−0.0776994
$590$	−3.79594	−0.156276
$591$	−0.0321954	−0.00132434
$592$	−3.01023	−0.123720
$593$	30.3699	1.24714	0.623570	−	0.781767i	$-0.285681\pi$
$593$	30.3699	1.24714	0.623570	+	0.781767i	$0.285681\pi$
$594$	2.84199	0.116608
$595$	30.8691	1.26551
$596$	8.47553	0.347171
$597$	−3.23497	−0.132398
$598$	13.5293	0.553255
$599$	38.9697	1.59226	0.796129	−	0.605127i	$-0.206878\pi$
$599$	38.9697	1.59226	0.796129	+	0.605127i	$0.206878\pi$
$600$	0.154802	0.00631978
$601$	−17.3389	−0.707270	−0.353635	−	0.935383i	$-0.615055\pi$
$601$	−17.3389	−0.707270	−0.353635	+	0.935383i	$0.615055\pi$
$602$	7.41058	0.302033
$603$	38.6934	1.57572
$604$	−20.8152	−0.846957
$605$	1.56233	0.0635178
$606$	−1.81079	−0.0735585
$607$	16.2869	0.661066	0.330533	−	0.943794i	$-0.392772\pi$
$607$	16.2869	0.661066	0.330533	+	0.943794i	$0.392772\pi$
$608$	0.745971	0.0302531
$609$	1.69693	0.0687631
$610$	4.16103	0.168475
$611$	15.4353	0.624445
$612$	−20.8064	−0.841050
$613$	8.14183	0.328845	0.164423	−	0.986390i	$-0.447424\pi$
$613$	8.14183	0.328845	0.164423	+	0.986390i	$0.447424\pi$
$614$	−24.2347	−0.978033
$615$	0.941052	0.0379469
$616$	−13.5643	−0.546521
$617$	25.3130	1.01906	0.509531	−	0.860452i	$-0.329819\pi$
$617$	25.3130	1.01906	0.509531	+	0.860452i	$0.329819\pi$
$618$	0.326002	0.0131137
$619$	27.8255	1.11840	0.559201	−	0.829032i	$-0.311108\pi$
$619$	27.8255	1.11840	0.559201	+	0.829032i	$0.311108\pi$
$620$	−2.52786	−0.101521
$621$	−2.05538	−0.0824797
$622$	−25.0016	−1.00247
$623$	−38.0605	−1.52486
$624$	−0.942651	−0.0377362
$625$	1.00000	0.0400000
$626$	22.7439	0.909028
$627$	−0.354758	−0.0141677
$628$	6.57637	0.262426
$629$	−21.0455	−0.839138
$630$	13.1402	0.523520
$631$	−13.7708	−0.548205	−0.274103	−	0.961700i	$-0.588381\pi$
$631$	−13.7708	−0.548205	−0.274103	+	0.961700i	$0.588381\pi$
$632$	7.95012	0.316239
$633$	−2.82289	−0.112200
$634$	5.43701	0.215931
$635$	11.2095	0.444835
$636$	0.115397	0.00457579
$637$	76.0888	3.01475
$638$	7.62700	0.301956
$639$	−24.2239	−0.958281
$640$	1.00000	0.0395285
$641$	7.82313	0.308995	0.154497	−	0.987993i	$-0.450624\pi$
$641$	7.82313	0.308995	0.154497	+	0.987993i	$0.450624\pi$
$642$	−1.71059	−0.0675117
$643$	−19.4985	−0.768948	−0.384474	−	0.923136i	$-0.625617\pi$
$643$	−19.4985	−0.768948	−0.384474	+	0.923136i	$0.625617\pi$
$644$	9.80996	0.386567
$645$	0.259815	0.0102302
$646$	5.21533	0.205194
$647$	−20.7712	−0.816599	−0.408300	−	0.912848i	$-0.633878\pi$
$647$	−20.7712	−0.816599	−0.408300	+	0.912848i	$0.633878\pi$
$648$	−8.78490	−0.345103
$649$	11.6614	0.457751
$650$	−6.08938	−0.238845
$651$	1.72781	0.0677182
$652$	−7.48490	−0.293131
$653$	−14.9981	−0.586920	−0.293460	−	0.955971i	$-0.594807\pi$
$653$	−14.9981	−0.586920	−0.293460	+	0.955971i	$0.594807\pi$
$654$	−0.477811	−0.0186839
$655$	−6.16032	−0.240704
$656$	6.07906	0.237347
$657$	−3.06094	−0.119419
$658$	11.1920	0.436309
$659$	−48.6747	−1.89610	−0.948048	−	0.318127i	$-0.896946\pi$
$659$	−48.6747	−1.89610	−0.948048	+	0.318127i	$0.896946\pi$
$660$	−0.475565	−0.0185113
$661$	−23.0823	−0.897797	−0.448898	−	0.893583i	$-0.648184\pi$
$661$	−23.0823	−0.897797	−0.448898	+	0.893583i	$0.648184\pi$
$662$	−19.8682	−0.772200
$663$	−6.59038	−0.255949
$664$	6.71915	0.260753
$665$	−3.29372	−0.127725
$666$	−8.95855	−0.347137
$667$	−5.51599	−0.213580
$668$	−8.85429	−0.342583
$669$	0.0179230	0.000692944 0
$670$	−13.0017	−0.502298
$671$	−12.7830	−0.493483
$672$	−0.683507	−0.0263668
$673$	24.1094	0.929349	0.464675	−	0.885482i	$-0.346171\pi$
$673$	24.1094	0.929349	0.464675	+	0.885482i	$0.346171\pi$
$674$	9.36919	0.360888
$675$	0.925104	0.0356073
$676$	24.0806	0.926177
$677$	−32.1416	−1.23530	−0.617651	−	0.786452i	$-0.711916\pi$
$677$	−32.1416	−1.23530	−0.617651	+	0.786452i	$0.711916\pi$
$678$	1.99526	0.0766274
$679$	72.8147	2.79437
$680$	6.99132	0.268105
$681$	4.55870	0.174690
$682$	7.76579	0.297367
$683$	−24.7150	−0.945692	−0.472846	−	0.881145i	$-0.656773\pi$
$683$	−24.7150	−0.945692	−0.472846	+	0.881145i	$0.656773\pi$
$684$	2.22004	0.0848852
$685$	16.4405	0.628158
$686$	24.2637	0.926394
$687$	0.953747	0.0363877
$688$	1.67837	0.0639871
$689$	−4.53932	−0.172934
$690$	0.343938	0.0130935
$691$	8.28709	0.315256	0.157628	−	0.987499i	$-0.449615\pi$
$691$	8.28709	0.315256	0.157628	+	0.987499i	$0.449615\pi$
$692$	−12.4239	−0.472285
$693$	−40.3679	−1.53345
$694$	8.04989	0.305570
$695$	−5.10643	−0.193698
$696$	0.384325	0.0145678
$697$	42.5006	1.60983
$698$	14.1691	0.536309
$699$	−1.37316	−0.0519376
$700$	−4.41535	−0.166885
$701$	−34.6270	−1.30785	−0.653923	−	0.756561i	$-0.726878\pi$
$701$	−34.6270	−1.30785	−0.653923	+	0.756561i	$0.726878\pi$
$702$	−5.63332	−0.212616
$703$	2.24554	0.0846923
$704$	−3.07208	−0.115783
$705$	0.392391	0.0147783
$706$	−29.1375	−1.09661
$707$	51.6484	1.94244
$708$	0.587620	0.0220841
$709$	31.5726	1.18574	0.592868	−	0.805300i	$-0.297996\pi$
$709$	31.5726	1.18574	0.592868	+	0.805300i	$0.297996\pi$
$710$	8.13964	0.305475
$711$	23.6599	0.887314
$712$	−8.62004	−0.323050
$713$	−5.61637	−0.210335
$714$	−4.77862	−0.178835
$715$	18.7071	0.699605
$716$	4.44563	0.166141
$717$	−1.16661	−0.0435679
$718$	1.74842	0.0652504
$719$	−13.7600	−0.513163	−0.256581	−	0.966523i	$-0.582596\pi$
$719$	−13.7600	−0.513163	−0.256581	+	0.966523i	$0.582596\pi$
$720$	2.97604	0.110910
$721$	−9.29839	−0.346290
$722$	18.4435	0.686397
$723$	3.91929	0.145760
$724$	−16.4715	−0.612157
$725$	2.48268	0.0922045
$726$	−0.241853	−0.00897599
$727$	5.15813	0.191304	0.0956522	−	0.995415i	$-0.469506\pi$
$727$	5.15813	0.191304	0.0956522	+	0.995415i	$0.469506\pi$
$728$	26.8868	0.996490
$729$	−25.7146	−0.952391
$730$	1.02853	0.0380676
$731$	11.7340	0.433998
$732$	−0.644138	−0.0238080
$733$	3.56423	0.131648	0.0658239	−	0.997831i	$-0.479032\pi$
$733$	3.56423	0.131648	0.0658239	+	0.997831i	$0.479032\pi$
$734$	13.1991	0.487187
$735$	1.93430	0.0713479
$736$	2.22179	0.0818961
$737$	39.9421	1.47129
$738$	18.0915	0.665957
$739$	−24.8946	−0.915763	−0.457882	−	0.889013i	$-0.651392\pi$
$739$	−24.8946	−0.915763	−0.457882	+	0.889013i	$0.651392\pi$
$740$	3.01023	0.110658
$741$	0.703191	0.0258324
$742$	−3.29141	−0.120832
$743$	2.95294	0.108333	0.0541664	−	0.998532i	$-0.482750\pi$
$743$	2.95294	0.108333	0.0541664	+	0.998532i	$0.482750\pi$
$744$	0.391319	0.0143464
$745$	−8.47553	−0.310519
$746$	35.7076	1.30735
$747$	19.9964	0.731631
$748$	−21.4779	−0.785310
$749$	48.7904	1.78276
$750$	−0.154802	−0.00565258
$751$	−30.8730	−1.12657	−0.563286	−	0.826262i	$-0.690463\pi$
$751$	−30.8730	−1.12657	−0.563286	+	0.826262i	$0.690463\pi$
$752$	2.53479	0.0924342
$753$	−2.85785	−0.104146
$754$	−15.1180	−0.550565
$755$	20.8152	0.757542
$756$	−4.08466	−0.148558
$757$	−16.6834	−0.606368	−0.303184	−	0.952932i	$-0.598050\pi$
$757$	−16.6834	−0.606368	−0.303184	+	0.952932i	$0.598050\pi$
$758$	−20.2654	−0.736072
$759$	−1.05660	−0.0383523
$760$	−0.745971	−0.0270592
$761$	4.46462	0.161843	0.0809213	−	0.996720i	$-0.474214\pi$
$761$	4.46462	0.161843	0.0809213	+	0.996720i	$0.474214\pi$
$762$	−1.73525	−0.0628616
$763$	13.6284	0.493380
$764$	5.80047	0.209853
$765$	20.8064	0.752258
$766$	35.0482	1.26634
$767$	−23.1149	−0.834632
$768$	−0.154802	−0.00558595
$769$	14.1587	0.510577	0.255289	−	0.966865i	$-0.417830\pi$
$769$	14.1587	0.510577	0.255289	+	0.966865i	$0.417830\pi$
$770$	13.5643	0.488824
$771$	4.39542	0.158297
$772$	17.6844	0.636475
$773$	2.64733	0.0952179	0.0476090	−	0.998866i	$-0.484840\pi$
$773$	2.64733	0.0952179	0.0476090	+	0.998866i	$0.484840\pi$
$774$	4.99488	0.179537
$775$	2.52786	0.0908035
$776$	16.4913	0.592002
$777$	−2.05751	−0.0738128
$778$	16.6478	0.596853
$779$	−4.53480	−0.162476
$780$	0.942651	0.0337523
$781$	−25.0056	−0.894771
$782$	15.5332	0.555467
$783$	2.29674	0.0820788
$784$	12.4953	0.446261
$785$	−6.57637	−0.234721
$786$	0.953633	0.0340149
$787$	−19.8674	−0.708195	−0.354097	−	0.935209i	$-0.615212\pi$
$787$	−19.8674	−0.708195	−0.354097	+	0.935209i	$0.615212\pi$
$788$	0.207977	0.00740888
$789$	−2.42150	−0.0862077
$790$	−7.95012	−0.282853
$791$	−56.9097	−2.02348
$792$	−9.14262	−0.324869
$793$	25.3381	0.899783
$794$	−3.46731	−0.123050
$795$	−0.115397	−0.00409271
$796$	20.8974	0.740688
$797$	−24.9638	−0.884263	−0.442131	−	0.896950i	$-0.645778\pi$
$797$	−24.9638	−0.884263	−0.442131	+	0.896950i	$0.645778\pi$
$798$	0.509876	0.0180494
$799$	17.7215	0.626942
$800$	−1.00000	−0.0353553
$801$	−25.6536	−0.906424
$802$	1.00000	0.0353112
$803$	−3.15973	−0.111504
$804$	2.01269	0.0709820
$805$	−9.80996	−0.345756
$806$	−15.3931	−0.542200
$807$	−1.95170	−0.0687030
$808$	11.6975	0.411515
$809$	36.0771	1.26840	0.634201	−	0.773168i	$-0.281329\pi$
$809$	36.0771	1.26840	0.634201	+	0.773168i	$0.281329\pi$
$810$	8.78490	0.308670
$811$	−9.67711	−0.339809	−0.169905	−	0.985461i	$-0.554346\pi$
$811$	−9.67711	−0.339809	−0.169905	+	0.985461i	$0.554346\pi$
$812$	−10.9619	−0.384688
$813$	3.96657	0.139114
$814$	−9.24766	−0.324130
$815$	7.48490	0.262185
$816$	−1.08227	−0.0378871
$817$	−1.25201	−0.0438024
$818$	39.8306	1.39264
$819$	80.0160	2.79598
$820$	−6.07906	−0.212290
$821$	−54.0490	−1.88632	−0.943161	−	0.332335i	$-0.892163\pi$
$821$	−54.0490	−1.88632	−0.943161	+	0.332335i	$0.892163\pi$
$822$	−2.54502	−0.0887678
$823$	6.13977	0.214019	0.107010	−	0.994258i	$-0.465872\pi$
$823$	6.13977	0.214019	0.107010	+	0.994258i	$0.465872\pi$
$824$	−2.10592	−0.0733633
$825$	0.475565	0.0165570
$826$	−16.7604	−0.583169
$827$	−38.4233	−1.33611	−0.668055	−	0.744112i	$-0.732873\pi$
$827$	−38.4233	−1.33611	−0.668055	+	0.744112i	$0.732873\pi$
$828$	6.61212	0.229787
$829$	−37.4537	−1.30082	−0.650411	−	0.759583i	$-0.725403\pi$
$829$	−37.4537	−1.30082	−0.650411	+	0.759583i	$0.725403\pi$
$830$	−6.71915	−0.233225
$831$	−4.56834	−0.158474
$832$	6.08938	0.211111
$833$	87.3588	3.02680
$834$	0.790487	0.0273723
$835$	8.85429	0.306415
$836$	2.29168	0.0792595
$837$	2.33854	0.0808316
$838$	−25.3727	−0.876485
$839$	0.219915	0.00759230	0.00379615	−	0.999993i	$-0.498792\pi$
$839$	0.219915	0.00759230	0.00379615	+	0.999993i	$0.498792\pi$
$840$	0.683507	0.0235832
$841$	−22.8363	−0.787458
$842$	21.5568	0.742898
$843$	1.84975	0.0637087
$844$	18.2355	0.627691
$845$	−24.0806	−0.828398
$846$	7.54362	0.259355
$847$	6.89824	0.237026
$848$	−0.745448	−0.0255988
$849$	4.48956	0.154081
$850$	−6.99132	−0.239800
$851$	6.68808	0.229265
$852$	−1.26004	−0.0431681
$853$	1.66005	0.0568390	0.0284195	−	0.999596i	$-0.490953\pi$
$853$	1.66005	0.0568390	0.0284195	+	0.999596i	$0.490953\pi$
$854$	18.3724	0.628691
$855$	−2.22004	−0.0759237
$856$	11.0502	0.377687
$857$	24.0659	0.822074	0.411037	−	0.911619i	$-0.365167\pi$
$857$	24.0659	0.822074	0.411037	+	0.911619i	$0.365167\pi$
$858$	−2.89590	−0.0988643
$859$	11.3191	0.386203	0.193102	−	0.981179i	$-0.438145\pi$
$859$	11.3191	0.386203	0.193102	+	0.981179i	$0.438145\pi$
$860$	−1.67837	−0.0572318
$861$	4.15507	0.141605
$862$	3.17088	0.108001
$863$	−20.3884	−0.694029	−0.347015	−	0.937860i	$-0.612805\pi$
$863$	−20.3884	−0.694029	−0.347015	+	0.937860i	$0.612805\pi$
$864$	−0.925104	−0.0314727
$865$	12.4239	0.422425
$866$	13.6613	0.464230
$867$	−4.93488	−0.167597
$868$	−11.1614	−0.378842
$869$	24.4234	0.828507
$870$	−0.384325	−0.0130298
$871$	−79.1721	−2.68264
$872$	3.08659	0.104525
$873$	49.0786	1.66106
$874$	−1.65739	−0.0560620
$875$	4.41535	0.149266
$876$	−0.159219	−0.00537951
$877$	−8.71953	−0.294438	−0.147219	−	0.989104i	$-0.547032\pi$
$877$	−8.71953	−0.294438	−0.147219	+	0.989104i	$0.547032\pi$
$878$	12.4747	0.421001
$879$	1.23757	0.0417421
$880$	3.07208	0.103560
$881$	−22.8663	−0.770386	−0.385193	−	0.922836i	$-0.625865\pi$
$881$	−22.8663	−0.770386	−0.385193	+	0.922836i	$0.625865\pi$
$882$	37.1865	1.25213
$883$	1.05873	0.0356292	0.0178146	−	0.999841i	$-0.494329\pi$
$883$	1.05873	0.0356292	0.0178146	+	0.999841i	$0.494329\pi$
$884$	42.5729	1.43188
$885$	−0.587620	−0.0197526
$886$	14.6634	0.492625
$887$	53.9716	1.81219	0.906094	−	0.423076i	$-0.139050\pi$
$887$	53.9716	1.81219	0.906094	+	0.423076i	$0.139050\pi$
$888$	−0.465990	−0.0156376
$889$	49.4938	1.65997
$890$	8.62004	0.288944
$891$	−26.9879	−0.904129
$892$	−0.115780	−0.00387660
$893$	−1.89088	−0.0632759
$894$	1.31203	0.0438809
$895$	−4.44563	−0.148601
$896$	4.41535	0.147506
$897$	2.09437	0.0699289
$898$	10.8612	0.362444
$899$	6.27588	0.209312
$900$	−2.97604	−0.0992012
$901$	−5.21167	−0.173626
$902$	18.6753	0.621821
$903$	1.14717	0.0381756
$904$	−12.8891	−0.428684
$905$	16.4715	0.547530
$906$	−3.22224	−0.107052
$907$	−42.0614	−1.39662	−0.698312	−	0.715793i	$-0.746065\pi$
$907$	−42.0614	−1.39662	−0.698312	+	0.715793i	$0.746065\pi$
$908$	−29.4485	−0.977284
$909$	34.8120	1.15464
$910$	−26.8868	−0.891287
$911$	17.5017	0.579858	0.289929	−	0.957048i	$-0.406368\pi$
$911$	17.5017	0.579858	0.289929	+	0.957048i	$0.406368\pi$
$912$	0.115478	0.00382386
$913$	20.6417	0.683142
$914$	18.3430	0.606733
$915$	0.644138	0.0212945
$916$	−6.16106	−0.203567
$917$	−27.2000	−0.898223
$918$	−6.46770	−0.213466
$919$	−23.6999	−0.781786	−0.390893	−	0.920436i	$-0.627834\pi$
$919$	−23.6999	−0.781786	−0.390893	+	0.920436i	$0.627834\pi$
$920$	−2.22179	−0.0732501
$921$	−3.75159	−0.123619
$922$	−38.6901	−1.27419
$923$	49.5654	1.63146
$924$	−2.09979	−0.0690779
$925$	−3.01023	−0.0989757
$926$	−23.1873	−0.761981
$927$	−6.26731	−0.205845
$928$	−2.48268	−0.0814980
$929$	21.2366	0.696751	0.348376	−	0.937355i	$-0.386733\pi$
$929$	21.2366	0.696751	0.348376	+	0.937355i	$0.386733\pi$
$930$	−0.391319	−0.0128319
$931$	−9.32114	−0.305488
$932$	8.87040	0.290560
$933$	−3.87030	−0.126708
$934$	−22.1349	−0.724275
$935$	21.4779	0.702402
$936$	18.1222	0.592344
$937$	−38.9094	−1.27112	−0.635558	−	0.772053i	$-0.719230\pi$
$937$	−38.9094	−1.27112	−0.635558	+	0.772053i	$0.719230\pi$
$938$	−57.4069	−1.87440
$939$	3.52081	0.114897
$940$	−2.53479	−0.0826757
$941$	43.8295	1.42880	0.714401	−	0.699737i	$-0.246699\pi$
$941$	43.8295	1.42880	0.714401	+	0.699737i	$0.246699\pi$
$942$	1.01804	0.0331694
$943$	−13.5064	−0.439828
$944$	−3.79594	−0.123547
$945$	4.08466	0.132874
$946$	5.15607	0.167638
$947$	5.64650	0.183487	0.0917433	−	0.995783i	$-0.470756\pi$
$947$	5.64650	0.183487	0.0917433	+	0.995783i	$0.470756\pi$
$948$	1.23070	0.0399712
$949$	6.26311	0.203309
$950$	0.745971	0.0242025
$951$	0.841662	0.0272927
$952$	30.8691	1.00047
$953$	44.5998	1.44473	0.722364	−	0.691513i	$-0.243055\pi$
$953$	44.5998	1.44473	0.722364	+	0.691513i	$0.243055\pi$
$954$	−2.21848	−0.0718260
$955$	−5.80047	−0.187699
$956$	7.53613	0.243736
$957$	1.18068	0.0381659
$958$	−16.5196	−0.533723
$959$	72.5904	2.34407
$960$	0.154802	0.00499622
$961$	−24.6099	−0.793868
$962$	18.3304	0.590997
$963$	32.8857	1.05973
$964$	−25.3180	−0.815439
$965$	−17.6844	−0.569280
$966$	1.51861	0.0488603
$967$	−1.31598	−0.0423192	−0.0211596	−	0.999776i	$-0.506736\pi$
$967$	−1.31598	−0.0423192	−0.0211596	+	0.999776i	$0.506736\pi$
$968$	1.56233	0.0502152
$969$	0.807345	0.0259357
$970$	−16.4913	−0.529503
$971$	6.26871	0.201173	0.100586	−	0.994928i	$-0.467928\pi$
$971$	6.26871	0.201173	0.100586	+	0.994928i	$0.467928\pi$
$972$	−4.13524	−0.132638
$973$	−22.5467	−0.722813
$974$	−29.4405	−0.943333
$975$	−0.942651	−0.0301890
$976$	4.16103	0.133191
$977$	10.8736	0.347878	0.173939	−	0.984756i	$-0.444350\pi$
$977$	10.8736	0.347878	0.173939	+	0.984756i	$0.444350\pi$
$978$	−1.15868	−0.0370505
$979$	−26.4814	−0.846351
$980$	−12.4953	−0.399148
$981$	9.18580	0.293280
$982$	−17.5779	−0.560933
$983$	−22.8613	−0.729162	−0.364581	−	0.931172i	$-0.618788\pi$
$983$	−22.8613	−0.729162	−0.364581	+	0.931172i	$0.618788\pi$
$984$	0.941052	0.0299996
$985$	−0.207977	−0.00662671
$986$	−17.3572	−0.552767
$987$	1.73254	0.0551475
$988$	−4.54251	−0.144516
$989$	−3.72897	−0.118574
$990$	9.14262	0.290571
$991$	−11.4088	−0.362413	−0.181206	−	0.983445i	$-0.558000\pi$
$991$	−11.4088	−0.362413	−0.181206	+	0.983445i	$0.558000\pi$
$992$	−2.52786	−0.0802597
$993$	−3.07565	−0.0976027
$994$	35.9394	1.13993
$995$	−20.8974	−0.662492
$996$	1.04014	0.0329581
$997$	−11.3329	−0.358917	−0.179458	−	0.983766i	$-0.557434\pi$
$997$	−11.3329	−0.358917	−0.179458	+	0.983766i	$0.557434\pi$
$998$	35.8606	1.13515
$999$	−2.78478	−0.0881064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.k.1.9	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.k.1.9	✓	15	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +1.00000 q^{10} -3.07208 q^{11} -0.154802 q^{12} +6.08938 q^{13} +4.41535 q^{14} +0.154802 q^{15} +1.00000 q^{16} +6.99132 q^{17} +2.97604 q^{18} -0.745971 q^{19} -1.00000 q^{20} +0.683507 q^{21} +3.07208 q^{22} -2.22179 q^{23} +0.154802 q^{24} +1.00000 q^{25} -6.08938 q^{26} +0.925104 q^{27} -4.41535 q^{28} +2.48268 q^{29} -0.154802 q^{30} +2.52786 q^{31} -1.00000 q^{32} +0.475565 q^{33} -6.99132 q^{34} +4.41535 q^{35} -2.97604 q^{36} -3.01023 q^{37} +0.745971 q^{38} -0.942651 q^{39} +1.00000 q^{40} +6.07906 q^{41} -0.683507 q^{42} +1.67837 q^{43} -3.07208 q^{44} +2.97604 q^{45} +2.22179 q^{46} +2.53479 q^{47} -0.154802 q^{48} +12.4953 q^{49} -1.00000 q^{50} -1.08227 q^{51} +6.08938 q^{52} -0.745448 q^{53} -0.925104 q^{54} +3.07208 q^{55} +4.41535 q^{56} +0.115478 q^{57} -2.48268 q^{58} -3.79594 q^{59} +0.154802 q^{60} +4.16103 q^{61} -2.52786 q^{62} +13.1402 q^{63} +1.00000 q^{64} -6.08938 q^{65} -0.475565 q^{66} -13.0017 q^{67} +6.99132 q^{68} +0.343938 q^{69} -4.41535 q^{70} +8.13964 q^{71} +2.97604 q^{72} +1.02853 q^{73} +3.01023 q^{74} -0.154802 q^{75} -0.745971 q^{76} +13.5643 q^{77} +0.942651 q^{78} -7.95012 q^{79} -1.00000 q^{80} +8.78490 q^{81} -6.07906 q^{82} -6.71915 q^{83} +0.683507 q^{84} -6.99132 q^{85} -1.67837 q^{86} -0.384325 q^{87} +3.07208 q^{88} +8.62004 q^{89} -2.97604 q^{90} -26.8868 q^{91} -2.22179 q^{92} -0.391319 q^{93} -2.53479 q^{94} +0.745971 q^{95} +0.154802 q^{96} -16.4913 q^{97} -12.4953 q^{98} +9.14262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * q^99

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