LMFDB - Embedded newform 3009.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3009,2,Mod(1,3009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3009 = 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3009.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:	$24.0269859682$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 13 x^{14} + 65 x^{13} + 49 x^{12} - 403 x^{11} + 11 x^{10} + 1205 x^{9} - 452 x^{8} + \cdots - 4 $ x^16 - 4x^15 - 13x^14 + 65x^13 + 49x^12 - 403x^11 + 11x^10 + 1205x^9 - 452x^8 - 1783x^7 + 946x^6 + 1190x^5 - 645x^4 - 299x^3 + 119x^2 + 16*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.18288$ of defining polynomial
Character	$\chi$	$=$	3009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18288 q^{2} -1.00000 q^{3} -0.600803 q^{4} -0.208439 q^{5} +1.18288 q^{6} +1.11694 q^{7} +3.07643 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.18288 q^{2} -1.00000 q^{3} -0.600803 q^{4} -0.208439 q^{5} +1.18288 q^{6} +1.11694 q^{7} +3.07643 q^{8} +1.00000 q^{9} +0.246558 q^{10} +3.82494 q^{11} +0.600803 q^{12} -4.99287 q^{13} -1.32120 q^{14} +0.208439 q^{15} -2.43743 q^{16} +1.00000 q^{17} -1.18288 q^{18} +0.558018 q^{19} +0.125231 q^{20} -1.11694 q^{21} -4.52443 q^{22} -3.52996 q^{23} -3.07643 q^{24} -4.95655 q^{25} +5.90594 q^{26} -1.00000 q^{27} -0.671063 q^{28} -2.80488 q^{29} -0.246558 q^{30} +2.09043 q^{31} -3.26968 q^{32} -3.82494 q^{33} -1.18288 q^{34} -0.232814 q^{35} -0.600803 q^{36} -2.31724 q^{37} -0.660066 q^{38} +4.99287 q^{39} -0.641248 q^{40} +5.17506 q^{41} +1.32120 q^{42} +8.47438 q^{43} -2.29803 q^{44} -0.208439 q^{45} +4.17551 q^{46} -4.91490 q^{47} +2.43743 q^{48} -5.75244 q^{49} +5.86299 q^{50} -1.00000 q^{51} +2.99973 q^{52} +8.74794 q^{53} +1.18288 q^{54} -0.797266 q^{55} +3.43619 q^{56} -0.558018 q^{57} +3.31783 q^{58} +1.00000 q^{59} -0.125231 q^{60} -3.87902 q^{61} -2.47271 q^{62} +1.11694 q^{63} +8.74249 q^{64} +1.04071 q^{65} +4.52443 q^{66} +0.184405 q^{67} -0.600803 q^{68} +3.52996 q^{69} +0.275391 q^{70} -15.3952 q^{71} +3.07643 q^{72} +7.92631 q^{73} +2.74100 q^{74} +4.95655 q^{75} -0.335259 q^{76} +4.27223 q^{77} -5.90594 q^{78} +11.1720 q^{79} +0.508056 q^{80} +1.00000 q^{81} -6.12146 q^{82} +15.0081 q^{83} +0.671063 q^{84} -0.208439 q^{85} -10.0241 q^{86} +2.80488 q^{87} +11.7671 q^{88} -13.5764 q^{89} +0.246558 q^{90} -5.57674 q^{91} +2.12081 q^{92} -2.09043 q^{93} +5.81372 q^{94} -0.116313 q^{95} +3.26968 q^{96} +7.09518 q^{97} +6.80443 q^{98} +3.82494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9} - 7 q^{11} - 10 q^{12} + 7 q^{13} - 13 q^{14} + 3 q^{15} + 2 q^{16} + 16 q^{17} - 4 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} + 23 q^{22} - 16 q^{23} + 9 q^{24} + 5 q^{25} - 11 q^{26} - 16 q^{27} + 8 q^{28} + 4 q^{29} - 15 q^{31} - 22 q^{32} + 7 q^{33} - 4 q^{34} - 23 q^{35} + 10 q^{36} + 20 q^{37} - 17 q^{38} - 7 q^{39} + 21 q^{40} - 4 q^{41} + 13 q^{42} - 12 q^{43} - 19 q^{44} - 3 q^{45} + 24 q^{46} - 36 q^{47} - 2 q^{48} - 11 q^{49} + 9 q^{50} - 16 q^{51} + 6 q^{52} - 32 q^{53} + 4 q^{54} - 29 q^{55} - 11 q^{56} + 19 q^{57} - 33 q^{58} + 16 q^{59} + 17 q^{60} + 11 q^{62} - 3 q^{63} + 9 q^{64} - 5 q^{65} - 23 q^{66} - 30 q^{67} + 10 q^{68} + 16 q^{69} + 16 q^{70} - 70 q^{71} - 9 q^{72} + 21 q^{73} - 29 q^{74} - 5 q^{75} - 8 q^{76} - 13 q^{77} + 11 q^{78} - 25 q^{79} - 9 q^{80} + 16 q^{81} + 22 q^{82} - 23 q^{83} - 8 q^{84} - 3 q^{85} - 58 q^{86} - 4 q^{87} + 41 q^{88} - 31 q^{89} - 36 q^{91} - 26 q^{92} + 15 q^{93} + 9 q^{94} - 10 q^{95} + 22 q^{96} + 52 q^{97} - 36 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9 - 7 * q^11 - 10 * q^12 + 7 * q^13 - 13 * q^14 + 3 * q^15 + 2 * q^16 + 16 * q^17 - 4 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 + 23 * q^22 - 16 * q^23 + 9 * q^24 + 5 * q^25 - 11 * q^26 - 16 * q^27 + 8 * q^28 + 4 * q^29 - 15 * q^31 - 22 * q^32 + 7 * q^33 - 4 * q^34 - 23 * q^35 + 10 * q^36 + 20 * q^37 - 17 * q^38 - 7 * q^39 + 21 * q^40 - 4 * q^41 + 13 * q^42 - 12 * q^43 - 19 * q^44 - 3 * q^45 + 24 * q^46 - 36 * q^47 - 2 * q^48 - 11 * q^49 + 9 * q^50 - 16 * q^51 + 6 * q^52 - 32 * q^53 + 4 * q^54 - 29 * q^55 - 11 * q^56 + 19 * q^57 - 33 * q^58 + 16 * q^59 + 17 * q^60 + 11 * q^62 - 3 * q^63 + 9 * q^64 - 5 * q^65 - 23 * q^66 - 30 * q^67 + 10 * q^68 + 16 * q^69 + 16 * q^70 - 70 * q^71 - 9 * q^72 + 21 * q^73 - 29 * q^74 - 5 * q^75 - 8 * q^76 - 13 * q^77 + 11 * q^78 - 25 * q^79 - 9 * q^80 + 16 * q^81 + 22 * q^82 - 23 * q^83 - 8 * q^84 - 3 * q^85 - 58 * q^86 - 4 * q^87 + 41 * q^88 - 31 * q^89 - 36 * q^91 - 26 * q^92 + 15 * q^93 + 9 * q^94 - 10 * q^95 + 22 * q^96 + 52 * q^97 - 36 * q^98 - 7 * 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 $

$2$	−1.18288	−0.836420	−0.418210	−	0.908350i	$-0.637342\pi$
$2$	−1.18288	−0.836420	−0.418210	+	0.908350i	$0.637342\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.600803	−0.300402
$5$	−0.208439	−0.0932168	−0.0466084	−	0.998913i	$-0.514841\pi$
$5$	−0.208439	−0.0932168	−0.0466084	+	0.998913i	$0.514841\pi$
$6$	1.18288	0.482907
$7$	1.11694	0.422164	0.211082	−	0.977468i	$-0.432301\pi$
$7$	1.11694	0.422164	0.211082	+	0.977468i	$0.432301\pi$
$8$	3.07643	1.08768
$9$	1.00000	0.333333
$10$	0.246558	0.0779684
$11$	3.82494	1.15326	0.576631	−	0.817005i	$-0.304367\pi$
$11$	3.82494	1.15326	0.576631	+	0.817005i	$0.304367\pi$
$12$	0.600803	0.173437
$13$	−4.99287	−1.38477	−0.692386	−	0.721527i	$-0.743441\pi$
$13$	−4.99287	−1.38477	−0.692386	+	0.721527i	$0.743441\pi$
$14$	−1.32120	−0.353107
$15$	0.208439	0.0538188
$16$	−2.43743	−0.609357
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.18288	−0.278807
$19$	0.558018	0.128018	0.0640090	−	0.997949i	$-0.479611\pi$
$19$	0.558018	0.128018	0.0640090	+	0.997949i	$0.479611\pi$
$20$	0.125231	0.0280025
$21$	−1.11694	−0.243737
$22$	−4.52443	−0.964611
$23$	−3.52996	−0.736048	−0.368024	−	0.929816i	$-0.619966\pi$
$23$	−3.52996	−0.736048	−0.368024	+	0.929816i	$0.619966\pi$
$24$	−3.07643	−0.627973
$25$	−4.95655	−0.991311
$26$	5.90594	1.15825
$27$	−1.00000	−0.192450
$28$	−0.671063	−0.126819
$29$	−2.80488	−0.520853	−0.260427	−	0.965494i	$-0.583863\pi$
$29$	−2.80488	−0.520853	−0.260427	+	0.965494i	$0.583863\pi$
$30$	−0.246558	−0.0450151
$31$	2.09043	0.375451	0.187726	−	0.982221i	$-0.439888\pi$
$31$	2.09043	0.375451	0.187726	+	0.982221i	$0.439888\pi$
$32$	−3.26968	−0.578004
$33$	−3.82494	−0.665836
$34$	−1.18288	−0.202862
$35$	−0.232814	−0.0393528
$36$	−0.600803	−0.100134
$37$	−2.31724	−0.380951	−0.190476	−	0.981692i	$-0.561003\pi$
$37$	−2.31724	−0.380951	−0.190476	+	0.981692i	$0.561003\pi$
$38$	−0.660066	−0.107077
$39$	4.99287	0.799499
$40$	−0.641248	−0.101390
$41$	5.17506	0.808209	0.404104	−	0.914713i	$-0.367583\pi$
$41$	5.17506	0.808209	0.404104	+	0.914713i	$0.367583\pi$
$42$	1.32120	0.203866
$43$	8.47438	1.29233	0.646165	−	0.763197i	$-0.276372\pi$
$43$	8.47438	1.29233	0.646165	+	0.763197i	$0.276372\pi$
$44$	−2.29803	−0.346442
$45$	−0.208439	−0.0310723
$46$	4.17551	0.615646
$47$	−4.91490	−0.716912	−0.358456	−	0.933547i	$-0.616697\pi$
$47$	−4.91490	−0.716912	−0.358456	+	0.933547i	$0.616697\pi$
$48$	2.43743	0.351812
$49$	−5.75244	−0.821777
$50$	5.86299	0.829152
$51$	−1.00000	−0.140028
$52$	2.99973	0.415988
$53$	8.74794	1.20162	0.600811	−	0.799391i	$-0.294844\pi$
$53$	8.74794	1.20162	0.600811	+	0.799391i	$0.294844\pi$
$54$	1.18288	0.160969
$55$	−0.797266	−0.107503
$56$	3.43619	0.459181
$57$	−0.558018	−0.0739113
$58$	3.31783	0.435652
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.125231	−0.0161673
$61$	−3.87902	−0.496658	−0.248329	−	0.968676i	$-0.579881\pi$
$61$	−3.87902	−0.496658	−0.248329	+	0.968676i	$0.579881\pi$
$62$	−2.47271	−0.314035
$63$	1.11694	0.140721
$64$	8.74249	1.09281
$65$	1.04071	0.129084
$66$	4.52443	0.556918
$67$	0.184405	0.0225286	0.0112643	−	0.999937i	$-0.496414\pi$
$67$	0.184405	0.0225286	0.0112643	+	0.999937i	$0.496414\pi$
$68$	−0.600803	−0.0728581
$69$	3.52996	0.424958
$70$	0.275391	0.0329155
$71$	−15.3952	−1.82707	−0.913535	−	0.406761i	$-0.866658\pi$
$71$	−15.3952	−1.82707	−0.913535	+	0.406761i	$0.866658\pi$
$72$	3.07643	0.362561
$73$	7.92631	0.927705	0.463852	−	0.885912i	$-0.346467\pi$
$73$	7.92631	0.927705	0.463852	+	0.885912i	$0.346467\pi$
$74$	2.74100	0.318635
$75$	4.95655	0.572333
$76$	−0.335259	−0.0384569
$77$	4.27223	0.486866
$78$	−5.90594	−0.668717
$79$	11.1720	1.25695	0.628475	−	0.777830i	$-0.283680\pi$
$79$	11.1720	1.25695	0.628475	+	0.777830i	$0.283680\pi$
$80$	0.508056	0.0568023
$81$	1.00000	0.111111
$82$	−6.12146	−0.676002
$83$	15.0081	1.64735	0.823675	−	0.567062i	$-0.191920\pi$
$83$	15.0081	1.64735	0.823675	+	0.567062i	$0.191920\pi$
$84$	0.671063	0.0732189
$85$	−0.208439	−0.0226084
$86$	−10.0241	−1.08093
$87$	2.80488	0.300715
$88$	11.7671	1.25438
$89$	−13.5764	−1.43910	−0.719549	−	0.694442i	$-0.755651\pi$
$89$	−13.5764	−1.43910	−0.719549	+	0.694442i	$0.755651\pi$
$90$	0.246558	0.0259895
$91$	−5.57674	−0.584602
$92$	2.12081	0.221110
$93$	−2.09043	−0.216767
$94$	5.81372	0.599639
$95$	−0.116313	−0.0119334
$96$	3.26968	0.333710
$97$	7.09518	0.720407	0.360203	−	0.932874i	$-0.382707\pi$
$97$	7.09518	0.720407	0.360203	+	0.932874i	$0.382707\pi$
$98$	6.80443	0.687351
$99$	3.82494	0.384420
$100$	2.97791	0.297791
$101$	−9.51350	−0.946629	−0.473314	−	0.880894i	$-0.656943\pi$
$101$	−9.51350	−0.946629	−0.473314	+	0.880894i	$0.656943\pi$
$102$	1.18288	0.117122
$103$	5.22813	0.515143	0.257571	−	0.966259i	$-0.417078\pi$
$103$	5.22813	0.515143	0.257571	+	0.966259i	$0.417078\pi$
$104$	−15.3602	−1.50619
$105$	0.232814	0.0227204
$106$	−10.3477	−1.00506
$107$	−17.8995	−1.73041	−0.865203	−	0.501421i	$-0.832811\pi$
$107$	−17.8995	−1.73041	−0.865203	+	0.501421i	$0.832811\pi$
$108$	0.600803	0.0578123
$109$	−19.0758	−1.82713	−0.913564	−	0.406695i	$-0.866681\pi$
$109$	−19.0758	−1.82713	−0.913564	+	0.406695i	$0.866681\pi$
$110$	0.943068	0.0899180
$111$	2.31724	0.219942
$112$	−2.72247	−0.257249
$113$	7.71295	0.725574	0.362787	−	0.931872i	$-0.381825\pi$
$113$	7.71295	0.725574	0.362787	+	0.931872i	$0.381825\pi$
$114$	0.660066	0.0618209
$115$	0.735783	0.0686121
$116$	1.68518	0.156465
$117$	−4.99287	−0.461591
$118$	−1.18288	−0.108893
$119$	1.11694	0.102390
$120$	0.641248	0.0585377
$121$	3.63013	0.330012
$122$	4.58840	0.415414
$123$	−5.17506	−0.466619
$124$	−1.25593	−0.112786
$125$	2.07534	0.185624
$126$	−1.32120	−0.117702
$127$	0.670511	0.0594982	0.0297491	−	0.999557i	$-0.490529\pi$
$127$	0.670511	0.0594982	0.0297491	+	0.999557i	$0.490529\pi$
$128$	−3.80192	−0.336045
$129$	−8.47438	−0.746127
$130$	−1.23103	−0.107969
$131$	−1.33427	−0.116575	−0.0582877	−	0.998300i	$-0.518564\pi$
$131$	−1.33427	−0.116575	−0.0582877	+	0.998300i	$0.518564\pi$
$132$	2.29803	0.200018
$133$	0.623274	0.0540447
$134$	−0.218128	−0.0188434
$135$	0.208439	0.0179396
$136$	3.07643	0.263802
$137$	2.27661	0.194504	0.0972521	−	0.995260i	$-0.468995\pi$
$137$	2.27661	0.194504	0.0972521	+	0.995260i	$0.468995\pi$
$138$	−4.17551	−0.355443
$139$	16.4573	1.39589	0.697945	−	0.716151i	$-0.254098\pi$
$139$	16.4573	1.39589	0.697945	+	0.716151i	$0.254098\pi$
$140$	0.139876	0.0118217
$141$	4.91490	0.413909
$142$	18.2106	1.52820
$143$	−19.0974	−1.59700
$144$	−2.43743	−0.203119
$145$	0.584647	0.0485523
$146$	−9.37585	−0.775951
$147$	5.75244	0.474453
$148$	1.39220	0.114438
$149$	−18.8442	−1.54378	−0.771889	−	0.635757i	$-0.780688\pi$
$149$	−18.8442	−1.54378	−0.771889	+	0.635757i	$0.780688\pi$
$150$	−5.86299	−0.478711
$151$	−3.11855	−0.253784	−0.126892	−	0.991917i	$-0.540500\pi$
$151$	−3.11855	−0.253784	−0.126892	+	0.991917i	$0.540500\pi$
$152$	1.71670	0.139243
$153$	1.00000	0.0808452
$154$	−5.05352	−0.407224
$155$	−0.435727	−0.0349984
$156$	−2.99973	−0.240171
$157$	−4.35179	−0.347311	−0.173655	−	0.984806i	$-0.555558\pi$
$157$	−4.35179	−0.347311	−0.173655	+	0.984806i	$0.555558\pi$
$158$	−13.2151	−1.05134
$159$	−8.74794	−0.693757
$160$	0.681530	0.0538797
$161$	−3.94277	−0.310733
$162$	−1.18288	−0.0929355
$163$	18.8303	1.47491	0.737453	−	0.675399i	$-0.236029\pi$
$163$	18.8303	1.47491	0.737453	+	0.675399i	$0.236029\pi$
$164$	−3.10919	−0.242787
$165$	0.797266	0.0620671
$166$	−17.7527	−1.37788
$167$	−17.9349	−1.38785	−0.693923	−	0.720050i	$-0.744119\pi$
$167$	−17.9349	−1.38785	−0.693923	+	0.720050i	$0.744119\pi$
$168$	−3.43619	−0.265108
$169$	11.9287	0.917594
$170$	0.246558	0.0189101
$171$	0.558018	0.0426727
$172$	−5.09144	−0.388218
$173$	−2.14827	−0.163330	−0.0816651	−	0.996660i	$-0.526024\pi$
$173$	−2.14827	−0.163330	−0.0816651	+	0.996660i	$0.526024\pi$
$174$	−3.31783	−0.251524
$175$	−5.53618	−0.418496
$176$	−9.32301	−0.702748
$177$	−1.00000	−0.0751646
$178$	16.0592	1.20369
$179$	−7.92771	−0.592545	−0.296272	−	0.955103i	$-0.595744\pi$
$179$	−7.92771	−0.592545	−0.296272	+	0.955103i	$0.595744\pi$
$180$	0.125231	0.00933417
$181$	−22.1978	−1.64995	−0.824973	−	0.565172i	$-0.808810\pi$
$181$	−22.1978	−1.64995	−0.824973	+	0.565172i	$0.808810\pi$
$182$	6.59660	0.488972
$183$	3.87902	0.286745
$184$	−10.8597	−0.800587
$185$	0.483003	0.0355111
$186$	2.47271	0.181308
$187$	3.82494	0.279707
$188$	2.95289	0.215361
$189$	−1.11694	−0.0812456
$190$	0.137584	0.00998137
$191$	0.894875	0.0647509	0.0323755	−	0.999476i	$-0.489693\pi$
$191$	0.894875	0.0647509	0.0323755	+	0.999476i	$0.489693\pi$
$192$	−8.74249	−0.630935
$193$	−19.8061	−1.42568	−0.712838	−	0.701329i	$-0.752590\pi$
$193$	−19.8061	−1.42568	−0.712838	+	0.701329i	$0.752590\pi$
$194$	−8.39272	−0.602563
$195$	−1.04071	−0.0745267
$196$	3.45609	0.246863
$197$	−14.0055	−0.997847	−0.498924	−	0.866646i	$-0.666271\pi$
$197$	−14.0055	−0.997847	−0.498924	+	0.866646i	$0.666271\pi$
$198$	−4.52443	−0.321537
$199$	6.02904	0.427388	0.213694	−	0.976901i	$-0.431451\pi$
$199$	6.02904	0.427388	0.213694	+	0.976901i	$0.431451\pi$
$200$	−15.2485	−1.07823
$201$	−0.184405	−0.0130069
$202$	11.2533	0.791779
$203$	−3.13289	−0.219886
$204$	0.600803	0.0420647
$205$	−1.07869	−0.0753387
$206$	−6.18423	−0.430876
$207$	−3.52996	−0.245349
$208$	12.1698	0.843821
$209$	2.13438	0.147638
$210$	−0.275391	−0.0190038
$211$	−22.1812	−1.52701	−0.763507	−	0.645800i	$-0.776524\pi$
$211$	−22.1812	−1.52701	−0.763507	+	0.645800i	$0.776524\pi$
$212$	−5.25579	−0.360969
$213$	15.3952	1.05486
$214$	21.1729	1.44735
$215$	−1.76639	−0.120467
$216$	−3.07643	−0.209324
$217$	2.33488	0.158502
$218$	22.5643	1.52825
$219$	−7.92631	−0.535611
$220$	0.479000	0.0322942
$221$	−4.99287	−0.335857
$222$	−2.74100	−0.183964
$223$	−17.7400	−1.18796	−0.593978	−	0.804482i	$-0.702443\pi$
$223$	−17.7400	−1.18796	−0.593978	+	0.804482i	$0.702443\pi$
$224$	−3.65204	−0.244012
$225$	−4.95655	−0.330437
$226$	−9.12347	−0.606884
$227$	−20.7886	−1.37979	−0.689895	−	0.723910i	$-0.742343\pi$
$227$	−20.7886	−1.37979	−0.689895	+	0.723910i	$0.742343\pi$
$228$	0.335259	0.0222031
$229$	12.2864	0.811911	0.405955	−	0.913893i	$-0.366939\pi$
$229$	12.2864	0.811911	0.405955	+	0.913893i	$0.366939\pi$
$230$	−0.870340	−0.0573885
$231$	−4.27223	−0.281092
$232$	−8.62902	−0.566523
$233$	−17.3327	−1.13550	−0.567751	−	0.823200i	$-0.692186\pi$
$233$	−17.3327	−1.13550	−0.567751	+	0.823200i	$0.692186\pi$
$234$	5.90594	0.386084
$235$	1.02446	0.0668282
$236$	−0.600803	−0.0391090
$237$	−11.1720	−0.725700
$238$	−1.32120	−0.0856410
$239$	29.1917	1.88825	0.944127	−	0.329583i	$-0.106908\pi$
$239$	29.1917	1.88825	0.944127	+	0.329583i	$0.106908\pi$
$240$	−0.508056	−0.0327948
$241$	−8.93133	−0.575318	−0.287659	−	0.957733i	$-0.592877\pi$
$241$	−8.93133	−0.575318	−0.287659	+	0.957733i	$0.592877\pi$
$242$	−4.29400	−0.276028
$243$	−1.00000	−0.0641500
$244$	2.33053	0.149197
$245$	1.19903	0.0766035
$246$	6.12146	0.390290
$247$	−2.78611	−0.177276
$248$	6.43104	0.408372
$249$	−15.0081	−0.951098
$250$	−2.45487	−0.155259
$251$	−28.7635	−1.81554	−0.907768	−	0.419473i	$-0.862215\pi$
$251$	−28.7635	−1.81554	−0.907768	+	0.419473i	$0.862215\pi$
$252$	−0.671063	−0.0422730
$253$	−13.5019	−0.848856
$254$	−0.793131	−0.0497655
$255$	0.208439	0.0130530
$256$	−12.9878	−0.811736
$257$	16.1986	1.01044	0.505219	−	0.862991i	$-0.331412\pi$
$257$	16.1986	1.01044	0.505219	+	0.862991i	$0.331412\pi$
$258$	10.0241	0.624076
$259$	−2.58822	−0.160824
$260$	−0.625262	−0.0387771
$261$	−2.80488	−0.173618
$262$	1.57827	0.0975061
$263$	30.1816	1.86107	0.930537	−	0.366197i	$-0.119340\pi$
$263$	30.1816	1.86107	0.930537	+	0.366197i	$0.119340\pi$
$264$	−11.7671	−0.724218
$265$	−1.82341	−0.112011
$266$	−0.737256	−0.0452040
$267$	13.5764	0.830863
$268$	−0.110791	−0.00676764
$269$	11.2358	0.685061	0.342530	−	0.939507i	$-0.388716\pi$
$269$	11.2358	0.685061	0.342530	+	0.939507i	$0.388716\pi$
$270$	−0.246558	−0.0150050
$271$	−2.19143	−0.133120	−0.0665599	−	0.997782i	$-0.521202\pi$
$271$	−2.19143	−0.133120	−0.0665599	+	0.997782i	$0.521202\pi$
$272$	−2.43743	−0.147791
$273$	5.57674	0.337520
$274$	−2.69295	−0.162687
$275$	−18.9585	−1.14324
$276$	−2.12081	−0.127658
$277$	26.1791	1.57295	0.786476	−	0.617621i	$-0.211904\pi$
$277$	26.1791	1.57295	0.786476	+	0.617621i	$0.211904\pi$
$278$	−19.4670	−1.16755
$279$	2.09043	0.125150
$280$	−0.716237	−0.0428034
$281$	1.46406	0.0873387	0.0436693	−	0.999046i	$-0.486095\pi$
$281$	1.46406	0.0873387	0.0436693	+	0.999046i	$0.486095\pi$
$282$	−5.81372	−0.346202
$283$	27.5046	1.63498	0.817490	−	0.575942i	$-0.195365\pi$
$283$	27.5046	1.63498	0.817490	+	0.575942i	$0.195365\pi$
$284$	9.24946	0.548855
$285$	0.116313	0.00688977
$286$	22.5899	1.33577
$287$	5.78024	0.341197
$288$	−3.26968	−0.192668
$289$	1.00000	0.0588235
$290$	−0.691565	−0.0406101
$291$	−7.09518	−0.415927
$292$	−4.76216	−0.278684
$293$	−30.9123	−1.80592	−0.902958	−	0.429729i	$-0.858609\pi$
$293$	−30.9123	−1.80592	−0.902958	+	0.429729i	$0.858609\pi$
$294$	−6.80443	−0.396842
$295$	−0.208439	−0.0121358
$296$	−7.12881	−0.414354
$297$	−3.82494	−0.221945
$298$	22.2904	1.29125
$299$	17.6246	1.01926
$300$	−2.97791	−0.171930
$301$	9.46539	0.545576
$302$	3.68886	0.212270
$303$	9.51350	0.546536
$304$	−1.36013	−0.0780087
$305$	0.808540	0.0462968
$306$	−1.18288	−0.0676205
$307$	−23.0406	−1.31499	−0.657497	−	0.753457i	$-0.728385\pi$
$307$	−23.0406	−1.31499	−0.657497	+	0.753457i	$0.728385\pi$
$308$	−2.56677	−0.146255
$309$	−5.22813	−0.297418
$310$	0.515411	0.0292734
$311$	−32.4305	−1.83897	−0.919484	−	0.393128i	$-0.871393\pi$
$311$	−32.4305	−1.83897	−0.919484	+	0.393128i	$0.871393\pi$
$312$	15.3602	0.869600
$313$	−11.0908	−0.626888	−0.313444	−	0.949607i	$-0.601483\pi$
$313$	−11.0908	−0.626888	−0.313444	+	0.949607i	$0.601483\pi$
$314$	5.14763	0.290498
$315$	−0.232814	−0.0131176
$316$	−6.71218	−0.377590
$317$	−1.78423	−0.100212	−0.0501062	−	0.998744i	$-0.515956\pi$
$317$	−1.78423	−0.100212	−0.0501062	+	0.998744i	$0.515956\pi$
$318$	10.3477	0.580272
$319$	−10.7285	−0.600680
$320$	−1.82228	−0.101868
$321$	17.8995	0.999051
$322$	4.66380	0.259904
$323$	0.558018	0.0310489
$324$	−0.600803	−0.0333780
$325$	24.7474	1.37274
$326$	−22.2739	−1.23364
$327$	19.0758	1.05489
$328$	15.9207	0.879074
$329$	−5.48966	−0.302655
$330$	−0.943068	−0.0519142
$331$	11.4189	0.627641	0.313821	−	0.949482i	$-0.398391\pi$
$331$	11.4189	0.627641	0.313821	+	0.949482i	$0.398391\pi$
$332$	−9.01691	−0.494867
$333$	−2.31724	−0.126984
$334$	21.2148	1.16082
$335$	−0.0384372	−0.00210005
$336$	2.72247	0.148523
$337$	−0.879251	−0.0478959	−0.0239479	−	0.999713i	$-0.507624\pi$
$337$	−0.879251	−0.0478959	−0.0239479	+	0.999713i	$0.507624\pi$
$338$	−14.1102	−0.767494
$339$	−7.71295	−0.418910
$340$	0.125231	0.00679160
$341$	7.99574	0.432994
$342$	−0.660066	−0.0356923
$343$	−14.2437	−0.769089
$344$	26.0708	1.40564
$345$	−0.735783	−0.0396132
$346$	2.54114	0.136613
$347$	−29.0781	−1.56099	−0.780496	−	0.625160i	$-0.785034\pi$
$347$	−29.0781	−1.56099	−0.780496	+	0.625160i	$0.785034\pi$
$348$	−1.68518	−0.0903352
$349$	−4.17798	−0.223642	−0.111821	−	0.993728i	$-0.535668\pi$
$349$	−4.17798	−0.223642	−0.111821	+	0.993728i	$0.535668\pi$
$350$	6.54862	0.350038
$351$	4.99287	0.266500
$352$	−12.5063	−0.666589
$353$	30.8068	1.63968	0.819840	−	0.572593i	$-0.194062\pi$
$353$	30.8068	1.63968	0.819840	+	0.572593i	$0.194062\pi$
$354$	1.18288	0.0628692
$355$	3.20895	0.170314
$356$	8.15676	0.432307
$357$	−1.11694	−0.0591148
$358$	9.37750	0.495616
$359$	−0.0154740	−0.000816685 0	−0.000408343	−	1.00000i	$-0.500130\pi$
$359$	−0.0154740	−0.000816685 0	−0.000408343		1.00000i	$0.500130\pi$
$360$	−0.641248	−0.0337968
$361$	−18.6886	−0.983611
$362$	26.2572	1.38005
$363$	−3.63013	−0.190532
$364$	3.35053	0.175615
$365$	−1.65215	−0.0864777
$366$	−4.58840	−0.239840
$367$	−20.7526	−1.08328	−0.541639	−	0.840611i	$-0.682196\pi$
$367$	−20.7526	−1.08328	−0.541639	+	0.840611i	$0.682196\pi$
$368$	8.60403	0.448516
$369$	5.17506	0.269403
$370$	−0.571332	−0.0297022
$371$	9.77094	0.507282
$372$	1.25593	0.0651172
$373$	10.3814	0.537529	0.268765	−	0.963206i	$-0.413385\pi$
$373$	10.3814	0.537529	0.268765	+	0.963206i	$0.413385\pi$
$374$	−4.52443	−0.233952
$375$	−2.07534	−0.107170
$376$	−15.1203	−0.779772
$377$	14.0044	0.721263
$378$	1.32120	0.0679554
$379$	23.2491	1.19422	0.597112	−	0.802158i	$-0.296315\pi$
$379$	23.2491	1.19422	0.597112	+	0.802158i	$0.296315\pi$
$380$	0.0698811	0.00358483
$381$	−0.670511	−0.0343513
$382$	−1.05853	−0.0541589
$383$	−17.9881	−0.919147	−0.459573	−	0.888140i	$-0.651998\pi$
$383$	−17.9881	−0.919147	−0.459573	+	0.888140i	$0.651998\pi$
$384$	3.80192	0.194016
$385$	−0.890500	−0.0453841
$386$	23.4282	1.19246
$387$	8.47438	0.430777
$388$	−4.26281	−0.216411
$389$	−29.2771	−1.48441	−0.742203	−	0.670175i	$-0.766219\pi$
$389$	−29.2771	−1.48441	−0.742203	+	0.670175i	$0.766219\pi$
$390$	1.23103	0.0623356
$391$	−3.52996	−0.178518
$392$	−17.6970	−0.893832
$393$	1.33427	0.0673049
$394$	16.5667	0.834619
$395$	−2.32868	−0.117169
$396$	−2.29803	−0.115481
$397$	21.2951	1.06877	0.534386	−	0.845241i	$-0.320543\pi$
$397$	21.2951	1.06877	0.534386	+	0.845241i	$0.320543\pi$
$398$	−7.13161	−0.357476
$399$	−0.623274	−0.0312027
$400$	12.0812	0.604062
$401$	23.8311	1.19007	0.595034	−	0.803701i	$-0.297139\pi$
$401$	23.8311	1.19007	0.595034	+	0.803701i	$0.297139\pi$
$402$	0.218128	0.0108792
$403$	−10.4372	−0.519915
$404$	5.71574	0.284369
$405$	−0.208439	−0.0103574
$406$	3.70582	0.183917
$407$	−8.86328	−0.439336
$408$	−3.07643	−0.152306
$409$	−8.74422	−0.432374	−0.216187	−	0.976352i	$-0.569362\pi$
$409$	−8.74422	−0.432374	−0.216187	+	0.976352i	$0.569362\pi$
$410$	1.27595	0.0630147
$411$	−2.27661	−0.112297
$412$	−3.14108	−0.154750
$413$	1.11694	0.0549611
$414$	4.17551	0.205215
$415$	−3.12827	−0.153561
$416$	16.3251	0.800403
$417$	−16.4573	−0.805918
$418$	−2.52471	−0.123488
$419$	−14.9756	−0.731608	−0.365804	−	0.930692i	$-0.619206\pi$
$419$	−14.9756	−0.731608	−0.365804	+	0.930692i	$0.619206\pi$
$420$	−0.139876	−0.00682524
$421$	29.6616	1.44562	0.722810	−	0.691047i	$-0.242850\pi$
$421$	29.6616	1.44562	0.722810	+	0.691047i	$0.242850\pi$
$422$	26.2376	1.27722
$423$	−4.91490	−0.238971
$424$	26.9124	1.30698
$425$	−4.95655	−0.240428
$426$	−18.2106	−0.882305
$427$	−4.33264	−0.209671
$428$	10.7541	0.519817
$429$	19.0974	0.922031
$430$	2.08942	0.100761
$431$	−12.7576	−0.614511	−0.307255	−	0.951627i	$-0.599411\pi$
$431$	−12.7576	−0.614511	−0.307255	+	0.951627i	$0.599411\pi$
$432$	2.43743	0.117271
$433$	−8.67953	−0.417112	−0.208556	−	0.978010i	$-0.566876\pi$
$433$	−8.67953	−0.417112	−0.208556	+	0.978010i	$0.566876\pi$
$434$	−2.76188	−0.132574
$435$	−0.584647	−0.0280317
$436$	11.4608	0.548872
$437$	−1.96978	−0.0942275
$438$	9.37585	0.447995
$439$	−22.9102	−1.09345	−0.546723	−	0.837314i	$-0.684125\pi$
$439$	−22.9102	−1.09345	−0.546723	+	0.837314i	$0.684125\pi$
$440$	−2.45273	−0.116929
$441$	−5.75244	−0.273926
$442$	5.90594	0.280917
$443$	−19.2084	−0.912617	−0.456309	−	0.889822i	$-0.650829\pi$
$443$	−19.2084	−0.912617	−0.456309	+	0.889822i	$0.650829\pi$
$444$	−1.39220	−0.0660710
$445$	2.82986	0.134148
$446$	20.9842	0.993630
$447$	18.8442	0.891301
$448$	9.76485	0.461346
$449$	−24.4851	−1.15553	−0.577763	−	0.816205i	$-0.696074\pi$
$449$	−24.4851	−1.15553	−0.577763	+	0.816205i	$0.696074\pi$
$450$	5.86299	0.276384
$451$	19.7943	0.932076
$452$	−4.63397	−0.217964
$453$	3.11855	0.146522
$454$	24.5904	1.15408
$455$	1.16241	0.0544947
$456$	−1.71670	−0.0803920
$457$	−29.0196	−1.35748	−0.678741	−	0.734378i	$-0.737474\pi$
$457$	−29.0196	−1.35748	−0.678741	+	0.734378i	$0.737474\pi$
$458$	−14.5333	−0.679098
$459$	−1.00000	−0.0466760
$460$	−0.442061	−0.0206112
$461$	−24.1460	−1.12459	−0.562296	−	0.826936i	$-0.690082\pi$
$461$	−24.1460	−1.12459	−0.562296	+	0.826936i	$0.690082\pi$
$462$	5.05352	0.235111
$463$	−28.8614	−1.34130	−0.670651	−	0.741773i	$-0.733985\pi$
$463$	−28.8614	−1.34130	−0.670651	+	0.741773i	$0.733985\pi$
$464$	6.83669	0.317386
$465$	0.435727	0.0202063
$466$	20.5024	0.949756
$467$	8.41480	0.389391	0.194695	−	0.980864i	$-0.437628\pi$
$467$	8.41480	0.389391	0.194695	+	0.980864i	$0.437628\pi$
$468$	2.99973	0.138663
$469$	0.205969	0.00951079
$470$	−1.21181	−0.0558965
$471$	4.35179	0.200520
$472$	3.07643	0.141604
$473$	32.4140	1.49040
$474$	13.2151	0.606990
$475$	−2.76585	−0.126906
$476$	−0.671063	−0.0307581
$477$	8.74794	0.400541
$478$	−34.5302	−1.57937
$479$	−6.05392	−0.276611	−0.138305	−	0.990390i	$-0.544166\pi$
$479$	−6.05392	−0.276611	−0.138305	+	0.990390i	$0.544166\pi$
$480$	−0.681530	−0.0311074
$481$	11.5696	0.527531
$482$	10.5647	0.481207
$483$	3.94277	0.179402
$484$	−2.18100	−0.0991361
$485$	−1.47891	−0.0671540
$486$	1.18288	0.0536564
$487$	−13.8126	−0.625908	−0.312954	−	0.949768i	$-0.601318\pi$
$487$	−13.8126	−0.625908	−0.312954	+	0.949768i	$0.601318\pi$
$488$	−11.9335	−0.540205
$489$	−18.8303	−0.851537
$490$	−1.41831	−0.0640727
$491$	−14.1507	−0.638610	−0.319305	−	0.947652i	$-0.603449\pi$
$491$	−14.1507	−0.638610	−0.319305	+	0.947652i	$0.603449\pi$
$492$	3.10919	0.140173
$493$	−2.80488	−0.126325
$494$	3.29562	0.148277
$495$	−0.797266	−0.0358345
$496$	−5.09526	−0.228784
$497$	−17.1955	−0.771324
$498$	17.7527	0.795518
$499$	−5.69854	−0.255102	−0.127551	−	0.991832i	$-0.540712\pi$
$499$	−5.69854	−0.255102	−0.127551	+	0.991832i	$0.540712\pi$
$500$	−1.24687	−0.0557617
$501$	17.9349	0.801273
$502$	34.0237	1.51855
$503$	−14.9253	−0.665486	−0.332743	−	0.943018i	$-0.607974\pi$
$503$	−14.9253	−0.665486	−0.332743	+	0.943018i	$0.607974\pi$
$504$	3.43619	0.153060
$505$	1.98299	0.0882417
$506$	15.9711	0.710000
$507$	−11.9287	−0.529773
$508$	−0.402845	−0.0178734
$509$	16.0056	0.709435	0.354718	−	0.934974i	$-0.384577\pi$
$509$	16.0056	0.709435	0.354718	+	0.934974i	$0.384577\pi$
$510$	−0.246558	−0.0109178
$511$	8.85323	0.391644
$512$	22.9668	1.01500
$513$	−0.558018	−0.0246371
$514$	−19.1609	−0.845151
$515$	−1.08975	−0.0480200
$516$	5.09144	0.224138
$517$	−18.7992	−0.826786
$518$	3.06154	0.134516
$519$	2.14827	0.0942988
$520$	3.20167	0.140402
$521$	32.3795	1.41857	0.709287	−	0.704920i	$-0.249017\pi$
$521$	32.3795	1.41857	0.709287	+	0.704920i	$0.249017\pi$
$522$	3.31783	0.145217
$523$	22.2295	0.972027	0.486013	−	0.873951i	$-0.338451\pi$
$523$	22.2295	0.972027	0.486013	+	0.873951i	$0.338451\pi$
$524$	0.801633	0.0350195
$525$	5.53618	0.241619
$526$	−35.7011	−1.55664
$527$	2.09043	0.0910604
$528$	9.32301	0.405732
$529$	−10.5394	−0.458233
$530$	2.15687	0.0936885
$531$	1.00000	0.0433963
$532$	−0.374465	−0.0162351
$533$	−25.8384	−1.11918
$534$	−16.0592	−0.694951
$535$	3.73095	0.161303
$536$	0.567308	0.0245040
$537$	7.92771	0.342106
$538$	−13.2906	−0.572998
$539$	−22.0027	−0.947724
$540$	−0.125231	−0.00538908
$541$	−26.7359	−1.14947	−0.574734	−	0.818341i	$-0.694894\pi$
$541$	−26.7359	−1.14947	−0.574734	+	0.818341i	$0.694894\pi$
$542$	2.59219	0.111344
$543$	22.1978	0.952597
$544$	−3.26968	−0.140186
$545$	3.97614	0.170319
$546$	−6.59660	−0.282308
$547$	−25.5135	−1.09088	−0.545439	−	0.838151i	$-0.683637\pi$
$547$	−25.5135	−1.09088	−0.545439	+	0.838151i	$0.683637\pi$
$548$	−1.36780	−0.0584294
$549$	−3.87902	−0.165553
$550$	22.4256	0.956229
$551$	−1.56517	−0.0666786
$552$	10.8597	0.462219
$553$	12.4785	0.530639
$554$	−30.9667	−1.31565
$555$	−0.483003	−0.0205023
$556$	−9.88761	−0.419328
$557$	30.0266	1.27227	0.636134	−	0.771578i	$-0.280532\pi$
$557$	30.0266	1.27227	0.636134	+	0.771578i	$0.280532\pi$
$558$	−2.47271	−0.104678
$559$	−42.3115	−1.78958
$560$	0.567469	0.0239799
$561$	−3.82494	−0.161489
$562$	−1.73181	−0.0730518
$563$	31.6502	1.33390	0.666948	−	0.745104i	$-0.267600\pi$
$563$	31.6502	1.33390	0.666948	+	0.745104i	$0.267600\pi$
$564$	−2.95289	−0.124339
$565$	−1.60768	−0.0676357
$566$	−32.5346	−1.36753
$567$	1.11694	0.0469072
$568$	−47.3621	−1.98727
$569$	−37.3624	−1.56631	−0.783156	−	0.621825i	$-0.786392\pi$
$569$	−37.3624	−1.56631	−0.783156	+	0.621825i	$0.786392\pi$
$570$	−0.137584	−0.00576274
$571$	−5.30179	−0.221873	−0.110937	−	0.993827i	$-0.535385\pi$
$571$	−5.30179	−0.221873	−0.110937	+	0.993827i	$0.535385\pi$
$572$	11.4738	0.479743
$573$	−0.894875	−0.0373840
$574$	−6.83731	−0.285384
$575$	17.4965	0.729653
$576$	8.74249	0.364270
$577$	41.1774	1.71424	0.857119	−	0.515119i	$-0.172252\pi$
$577$	41.1774	1.71424	0.857119	+	0.515119i	$0.172252\pi$
$578$	−1.18288	−0.0492012
$579$	19.8061	0.823114
$580$	−0.351258	−0.0145852
$581$	16.7632	0.695453
$582$	8.39272	0.347890
$583$	33.4603	1.38578
$584$	24.3847	1.00905
$585$	1.04071	0.0430280
$586$	36.5654	1.51050
$587$	−34.1776	−1.41066	−0.705330	−	0.708879i	$-0.749201\pi$
$587$	−34.1776	−1.41066	−0.705330	+	0.708879i	$0.749201\pi$
$588$	−3.45609	−0.142527
$589$	1.16649	0.0480646
$590$	0.246558	0.0101506
$591$	14.0055	0.576107
$592$	5.64810	0.232135
$593$	−0.858968	−0.0352736	−0.0176368	−	0.999844i	$-0.505614\pi$
$593$	−0.858968	−0.0352736	−0.0176368	+	0.999844i	$0.505614\pi$
$594$	4.52443	0.185639
$595$	−0.232814	−0.00954446
$596$	11.3217	0.463754
$597$	−6.02904	−0.246752
$598$	−20.8478	−0.852529
$599$	−23.5391	−0.961783	−0.480892	−	0.876780i	$-0.659687\pi$
$599$	−23.5391	−0.961783	−0.480892	+	0.876780i	$0.659687\pi$
$600$	15.2485	0.622517
$601$	34.7668	1.41817	0.709083	−	0.705125i	$-0.249109\pi$
$601$	34.7668	1.41817	0.709083	+	0.705125i	$0.249109\pi$
$602$	−11.1964	−0.456331
$603$	0.184405	0.00750954
$604$	1.87364	0.0762372
$605$	−0.756661	−0.0307627
$606$	−11.2533	−0.457134
$607$	−28.1414	−1.14222	−0.571112	−	0.820872i	$-0.693488\pi$
$607$	−28.1414	−1.14222	−0.571112	+	0.820872i	$0.693488\pi$
$608$	−1.82454	−0.0739949
$609$	3.13289	0.126951
$610$	−0.956402	−0.0387236
$611$	24.5394	0.992759
$612$	−0.600803	−0.0242860
$613$	31.0610	1.25454	0.627271	−	0.778801i	$-0.284172\pi$
$613$	31.0610	1.25454	0.627271	+	0.778801i	$0.284172\pi$
$614$	27.2541	1.09989
$615$	1.07869	0.0434968
$616$	13.1432	0.529555
$617$	−22.2629	−0.896271	−0.448135	−	0.893966i	$-0.647912\pi$
$617$	−22.2629	−0.896271	−0.448135	+	0.893966i	$0.647912\pi$
$618$	6.18423	0.248766
$619$	48.3669	1.94403	0.972015	−	0.234917i	$-0.0754819\pi$
$619$	48.3669	1.94403	0.972015	+	0.234917i	$0.0754819\pi$
$620$	0.261786	0.0105136
$621$	3.52996	0.141653
$622$	38.3613	1.53815
$623$	−15.1641	−0.607536
$624$	−12.1698	−0.487180
$625$	24.3502	0.974007
$626$	13.1190	0.524342
$627$	−2.13438	−0.0852390
$628$	2.61457	0.104333
$629$	−2.31724	−0.0923942
$630$	0.275391	0.0109718
$631$	−12.7861	−0.509008	−0.254504	−	0.967072i	$-0.581912\pi$
$631$	−12.7861	−0.509008	−0.254504	+	0.967072i	$0.581912\pi$
$632$	34.3699	1.36716
$633$	22.1812	0.881622
$634$	2.11053	0.0838197
$635$	−0.139761	−0.00554623
$636$	5.25579	0.208406
$637$	28.7212	1.13797
$638$	12.6905	0.502421
$639$	−15.3952	−0.609023
$640$	0.792468	0.0313251
$641$	44.6705	1.76438	0.882189	−	0.470896i	$-0.156069\pi$
$641$	44.6705	1.76438	0.882189	+	0.470896i	$0.156069\pi$
$642$	−21.1729	−0.835626
$643$	19.8149	0.781425	0.390713	−	0.920513i	$-0.372229\pi$
$643$	19.8149	0.781425	0.390713	+	0.920513i	$0.372229\pi$
$644$	2.36883	0.0933449
$645$	1.76639	0.0695516
$646$	−0.660066	−0.0259700
$647$	32.7105	1.28598	0.642991	−	0.765874i	$-0.277693\pi$
$647$	32.7105	1.28598	0.642991	+	0.765874i	$0.277693\pi$
$648$	3.07643	0.120854
$649$	3.82494	0.150142
$650$	−29.2731	−1.14819
$651$	−2.33488	−0.0915113
$652$	−11.3133	−0.443064
$653$	−1.17981	−0.0461694	−0.0230847	−	0.999734i	$-0.507349\pi$
$653$	−1.17981	−0.0461694	−0.0230847	+	0.999734i	$0.507349\pi$
$654$	−22.5643	−0.882333
$655$	0.278114	0.0108668
$656$	−12.6138	−0.492488
$657$	7.92631	0.309235
$658$	6.49358	0.253146
$659$	31.1479	1.21335	0.606674	−	0.794950i	$-0.292503\pi$
$659$	31.1479	1.21335	0.606674	+	0.794950i	$0.292503\pi$
$660$	−0.479000	−0.0186451
$661$	−25.0333	−0.973683	−0.486841	−	0.873490i	$-0.661851\pi$
$661$	−25.0333	−0.973683	−0.486841	+	0.873490i	$0.661851\pi$
$662$	−13.5072	−0.524971
$663$	4.99287	0.193907
$664$	46.1713	1.79179
$665$	−0.129915	−0.00503787
$666$	2.74100	0.106212
$667$	9.90113	0.383373
$668$	10.7754	0.416911
$669$	17.7400	0.685866
$670$	0.0454664	0.00175652
$671$	−14.8370	−0.572776
$672$	3.65204	0.140881
$673$	22.2077	0.856042	0.428021	−	0.903769i	$-0.359211\pi$
$673$	22.2077	0.856042	0.428021	+	0.903769i	$0.359211\pi$
$674$	1.04005	0.0400610
$675$	4.95655	0.190778
$676$	−7.16682	−0.275647
$677$	−5.54701	−0.213189	−0.106594	−	0.994303i	$-0.533995\pi$
$677$	−5.54701	−0.213189	−0.106594	+	0.994303i	$0.533995\pi$
$678$	9.12347	0.350385
$679$	7.92491	0.304130
$680$	−0.641248	−0.0245908
$681$	20.7886	0.796622
$682$	−9.45797	−0.362165
$683$	−31.4461	−1.20325	−0.601627	−	0.798777i	$-0.705480\pi$
$683$	−31.4461	−1.20325	−0.601627	+	0.798777i	$0.705480\pi$
$684$	−0.335259	−0.0128190
$685$	−0.474535	−0.0181311
$686$	16.8486	0.643282
$687$	−12.2864	−0.468757
$688$	−20.6557	−0.787491
$689$	−43.6773	−1.66397
$690$	0.870340	0.0331333
$691$	39.9339	1.51916	0.759578	−	0.650416i	$-0.225406\pi$
$691$	39.9339	1.51916	0.759578	+	0.650416i	$0.225406\pi$
$692$	1.29069	0.0490647
$693$	4.27223	0.162289
$694$	34.3958	1.30565
$695$	−3.43035	−0.130121
$696$	8.62902	0.327082
$697$	5.17506	0.196019
$698$	4.94204	0.187059
$699$	17.3327	0.655582
$700$	3.32616	0.125717
$701$	−32.8614	−1.24116	−0.620578	−	0.784145i	$-0.713102\pi$
$701$	−32.8614	−1.24116	−0.620578	+	0.784145i	$0.713102\pi$
$702$	−5.90594	−0.222906
$703$	−1.29306	−0.0487686
$704$	33.4394	1.26030
$705$	−1.02446	−0.0385833
$706$	−36.4406	−1.37146
$707$	−10.6260	−0.399633
$708$	0.600803	0.0225796
$709$	20.6666	0.776151	0.388075	−	0.921628i	$-0.373140\pi$
$709$	20.6666	0.776151	0.388075	+	0.921628i	$0.373140\pi$
$710$	−3.79580	−0.142454
$711$	11.1720	0.418983
$712$	−41.7669	−1.56528
$713$	−7.37913	−0.276350
$714$	1.32120	0.0494448
$715$	3.98065	0.148868
$716$	4.76299	0.178001
$717$	−29.1917	−1.09018
$718$	0.0183038	0.000683092 0
$719$	−43.8039	−1.63361	−0.816806	−	0.576913i	$-0.804257\pi$
$719$	−43.8039	−1.63361	−0.816806	+	0.576913i	$0.804257\pi$
$720$	0.508056	0.0189341
$721$	5.83952	0.217475
$722$	22.1063	0.822712
$723$	8.93133	0.332160
$724$	13.3365	0.495647
$725$	13.9025	0.516327
$726$	4.29400	0.159365
$727$	−25.3881	−0.941593	−0.470796	−	0.882242i	$-0.656033\pi$
$727$	−25.3881	−0.941593	−0.470796	+	0.882242i	$0.656033\pi$
$728$	−17.1565	−0.635860
$729$	1.00000	0.0370370
$730$	1.95429	0.0723317
$731$	8.47438	0.313436
$732$	−2.33053	−0.0861388
$733$	8.56462	0.316341	0.158171	−	0.987412i	$-0.449440\pi$
$733$	8.56462	0.316341	0.158171	+	0.987412i	$0.449440\pi$
$734$	24.5478	0.906075
$735$	−1.19903	−0.0442270
$736$	11.5419	0.425439
$737$	0.705336	0.0259814
$738$	−6.12146	−0.225334
$739$	−10.1016	−0.371594	−0.185797	−	0.982588i	$-0.559487\pi$
$739$	−10.1016	−0.371594	−0.185797	+	0.982588i	$0.559487\pi$
$740$	−0.290190	−0.0106676
$741$	2.78611	0.102350
$742$	−11.5578	−0.424301
$743$	46.6666	1.71203	0.856015	−	0.516951i	$-0.172933\pi$
$743$	46.6666	1.71203	0.856015	+	0.516951i	$0.172933\pi$
$744$	−6.43104	−0.235774
$745$	3.92787	0.143906
$746$	−12.2799	−0.449600
$747$	15.0081	0.549117
$748$	−2.29803	−0.0840245
$749$	−19.9927	−0.730516
$750$	2.45487	0.0896390
$751$	−13.6821	−0.499267	−0.249633	−	0.968340i	$-0.580310\pi$
$751$	−13.6821	−0.499267	−0.249633	+	0.968340i	$0.580310\pi$
$752$	11.9797	0.436855
$753$	28.7635	1.04820
$754$	−16.5655	−0.603279
$755$	0.650028	0.0236569
$756$	0.671063	0.0244063
$757$	18.9806	0.689862	0.344931	−	0.938628i	$-0.387902\pi$
$757$	18.9806	0.689862	0.344931	+	0.938628i	$0.387902\pi$
$758$	−27.5008	−0.998873
$759$	13.5019	0.490087
$760$	−0.357828	−0.0129798
$761$	−41.4890	−1.50397	−0.751987	−	0.659178i	$-0.770905\pi$
$761$	−41.4890	−1.50397	−0.751987	+	0.659178i	$0.770905\pi$
$762$	0.793131	0.0287321
$763$	−21.3065	−0.771348
$764$	−0.537644	−0.0194513
$765$	−0.208439	−0.00753613
$766$	21.2776	0.768793
$767$	−4.99287	−0.180282
$768$	12.9878	0.468656
$769$	33.9914	1.22576	0.612881	−	0.790175i	$-0.290011\pi$
$769$	33.9914	1.22576	0.612881	+	0.790175i	$0.290011\pi$
$770$	1.05335	0.0379602
$771$	−16.1986	−0.583377
$772$	11.8996	0.428275
$773$	20.2367	0.727864	0.363932	−	0.931425i	$-0.381434\pi$
$773$	20.2367	0.727864	0.363932	+	0.931425i	$0.381434\pi$
$774$	−10.0241	−0.360310
$775$	−10.3613	−0.372189
$776$	21.8278	0.783573
$777$	2.58822	0.0928518
$778$	34.6311	1.24159
$779$	2.88778	0.103465
$780$	0.625262	0.0223880
$781$	−58.8855	−2.10709
$782$	4.17551	0.149316
$783$	2.80488	0.100238
$784$	14.0212	0.500756
$785$	0.907084	0.0323752
$786$	−1.57827	−0.0562951
$787$	−5.36885	−0.191379	−0.0956894	−	0.995411i	$-0.530506\pi$
$787$	−5.36885	−0.191379	−0.0956894	+	0.995411i	$0.530506\pi$
$788$	8.41453	0.299755
$789$	−30.1816	−1.07449
$790$	2.75455	0.0980023
$791$	8.61492	0.306311
$792$	11.7671	0.418127
$793$	19.3674	0.687758
$794$	−25.1895	−0.893942
$795$	1.82341	0.0646698
$796$	−3.62227	−0.128388
$797$	22.2684	0.788786	0.394393	−	0.918942i	$-0.370955\pi$
$797$	22.2684	0.788786	0.394393	+	0.918942i	$0.370955\pi$
$798$	0.737256	0.0260986
$799$	−4.91490	−0.173877
$800$	16.2064	0.572981
$801$	−13.5764	−0.479699
$802$	−28.1892	−0.995396
$803$	30.3176	1.06989
$804$	0.110791	0.00390730
$805$	0.821827	0.0289656
$806$	12.3459	0.434867
$807$	−11.2358	−0.395520
$808$	−29.2676	−1.02963
$809$	−31.9227	−1.12234	−0.561172	−	0.827699i	$-0.689649\pi$
$809$	−31.9227	−1.12234	−0.561172	+	0.827699i	$0.689649\pi$
$810$	0.246558	0.00866316
$811$	−22.8848	−0.803595	−0.401797	−	0.915729i	$-0.631614\pi$
$811$	−22.8848	−0.803595	−0.401797	+	0.915729i	$0.631614\pi$
$812$	1.88225	0.0660540
$813$	2.19143	0.0768567
$814$	10.4842	0.367470
$815$	−3.92498	−0.137486
$816$	2.43743	0.0853271
$817$	4.72885	0.165442
$818$	10.3433	0.361646
$819$	−5.57674	−0.194867
$820$	0.648078	0.0226319
$821$	−17.1107	−0.597167	−0.298583	−	0.954384i	$-0.596514\pi$
$821$	−17.1107	−0.597167	−0.298583	+	0.954384i	$0.596514\pi$
$822$	2.69295	0.0939275
$823$	−52.9183	−1.84462	−0.922308	−	0.386455i	$-0.873699\pi$
$823$	−52.9183	−1.84462	−0.922308	+	0.386455i	$0.873699\pi$
$824$	16.0840	0.560312
$825$	18.9585	0.660050
$826$	−1.32120	−0.0459706
$827$	30.4725	1.05963	0.529817	−	0.848112i	$-0.322261\pi$
$827$	30.4725	1.05963	0.529817	+	0.848112i	$0.322261\pi$
$828$	2.12081	0.0737034
$829$	−23.1718	−0.804789	−0.402394	−	0.915466i	$-0.631822\pi$
$829$	−23.1718	−0.804789	−0.402394	+	0.915466i	$0.631822\pi$
$830$	3.70036	0.128441
$831$	−26.1791	−0.908144
$832$	−43.6501	−1.51329
$833$	−5.75244	−0.199310
$834$	19.4670	0.674086
$835$	3.73834	0.129371
$836$	−1.28234	−0.0443508
$837$	−2.09043	−0.0722557
$838$	17.7143	0.611931
$839$	−30.2229	−1.04341	−0.521705	−	0.853126i	$-0.674704\pi$
$839$	−30.2229	−1.04341	−0.521705	+	0.853126i	$0.674704\pi$
$840$	0.716237	0.0247125
$841$	−21.1326	−0.728712
$842$	−35.0861	−1.20915
$843$	−1.46406	−0.0504250
$844$	13.3265	0.458717
$845$	−2.48641	−0.0855352
$846$	5.81372	0.199880
$847$	4.05465	0.139319
$848$	−21.3225	−0.732217
$849$	−27.5046	−0.943957
$850$	5.86299	0.201099
$851$	8.17976	0.280399
$852$	−9.24946	−0.316881
$853$	2.84716	0.0974850	0.0487425	−	0.998811i	$-0.484479\pi$
$853$	2.84716	0.0974850	0.0487425	+	0.998811i	$0.484479\pi$
$854$	5.12498	0.175373
$855$	−0.116313	−0.00397781
$856$	−55.0664	−1.88213
$857$	13.5533	0.462971	0.231486	−	0.972838i	$-0.425641\pi$
$857$	13.5533	0.462971	0.231486	+	0.972838i	$0.425641\pi$
$858$	−22.5899	−0.771205
$859$	−22.8340	−0.779087	−0.389544	−	0.921008i	$-0.627367\pi$
$859$	−22.8340	−0.779087	−0.389544	+	0.921008i	$0.627367\pi$
$860$	1.06125	0.0361885
$861$	−5.78024	−0.196990
$862$	15.0906	0.513989
$863$	−18.8772	−0.642588	−0.321294	−	0.946979i	$-0.604118\pi$
$863$	−18.8772	−0.642588	−0.321294	+	0.946979i	$0.604118\pi$
$864$	3.26968	0.111237
$865$	0.447784	0.0152251
$866$	10.2668	0.348880
$867$	−1.00000	−0.0339618
$868$	−1.40281	−0.0476143
$869$	42.7322	1.44959
$870$	0.691565	0.0234463
$871$	−0.920709	−0.0311970
$872$	−58.6853	−1.98733
$873$	7.09518	0.240136
$874$	2.33001	0.0788138
$875$	2.31803	0.0783637
$876$	4.76216	0.160898
$877$	30.4097	1.02686	0.513432	−	0.858131i	$-0.328374\pi$
$877$	30.4097	1.02686	0.513432	+	0.858131i	$0.328374\pi$
$878$	27.1000	0.914579
$879$	30.9123	1.04265
$880$	1.94328	0.0655079
$881$	−3.97165	−0.133808	−0.0669041	−	0.997759i	$-0.521312\pi$
$881$	−3.97165	−0.133808	−0.0669041	+	0.997759i	$0.521312\pi$
$882$	6.80443	0.229117
$883$	52.3741	1.76253	0.881264	−	0.472624i	$-0.156693\pi$
$883$	52.3741	1.76253	0.881264	+	0.472624i	$0.156693\pi$
$884$	2.99973	0.100892
$885$	0.208439	0.00700661
$886$	22.7211	0.763331
$887$	−10.9880	−0.368942	−0.184471	−	0.982838i	$-0.559057\pi$
$887$	−10.9880	−0.368942	−0.184471	+	0.982838i	$0.559057\pi$
$888$	7.12881	0.239227
$889$	0.748921	0.0251180
$890$	−3.34737	−0.112204
$891$	3.82494	0.128140
$892$	10.6582	0.356864
$893$	−2.74260	−0.0917776
$894$	−22.2904	−0.745501
$895$	1.65244	0.0552351
$896$	−4.24652	−0.141866
$897$	−17.6246	−0.588470
$898$	28.9629	0.966504
$899$	−5.86339	−0.195555
$900$	2.97791	0.0992638
$901$	8.74794	0.291436
$902$	−23.4142	−0.779607
$903$	−9.46539	−0.314988
$904$	23.7284	0.789193
$905$	4.62688	0.153803
$906$	−3.68886	−0.122554
$907$	42.7996	1.42114	0.710569	−	0.703628i	$-0.248438\pi$
$907$	42.7996	1.42114	0.710569	+	0.703628i	$0.248438\pi$
$908$	12.4899	0.414491
$909$	−9.51350	−0.315543
$910$	−1.37499	−0.0455805
$911$	11.8160	0.391481	0.195740	−	0.980656i	$-0.437289\pi$
$911$	11.8160	0.391481	0.195740	+	0.980656i	$0.437289\pi$
$912$	1.36013	0.0450384
$913$	57.4049	1.89983
$914$	34.3267	1.13542
$915$	−0.808540	−0.0267295
$916$	−7.38174	−0.243899
$917$	−1.49030	−0.0492140
$918$	1.18288	0.0390407
$919$	−3.74026	−0.123380	−0.0616899	−	0.998095i	$-0.519649\pi$
$919$	−3.74026	−0.123380	−0.0616899	+	0.998095i	$0.519649\pi$
$920$	2.26358	0.0746281
$921$	23.0406	0.759213
$922$	28.5618	0.940631
$923$	76.8660	2.53007
$924$	2.56677	0.0844406
$925$	11.4855	0.377641
$926$	34.1394	1.12189
$927$	5.22813	0.171714
$928$	9.17107	0.301055
$929$	1.85618	0.0608992	0.0304496	−	0.999536i	$-0.490306\pi$
$929$	1.85618	0.0608992	0.0304496	+	0.999536i	$0.490306\pi$
$930$	−0.515411	−0.0169010
$931$	−3.20996	−0.105202
$932$	10.4135	0.341107
$933$	32.4305	1.06173
$934$	−9.95367	−0.325694
$935$	−0.797266	−0.0260734
$936$	−15.3602	−0.502064
$937$	16.8616	0.550844	0.275422	−	0.961323i	$-0.411182\pi$
$937$	16.8616	0.550844	0.275422	+	0.961323i	$0.411182\pi$
$938$	−0.243636	−0.00795501
$939$	11.0908	0.361934
$940$	−0.615497	−0.0200753
$941$	50.7271	1.65366	0.826829	−	0.562454i	$-0.190143\pi$
$941$	50.7271	1.65366	0.826829	+	0.562454i	$0.190143\pi$
$942$	−5.14763	−0.167719
$943$	−18.2678	−0.594881
$944$	−2.43743	−0.0793315
$945$	0.232814	0.00757345
$946$	−38.3417	−1.24660
$947$	−50.0810	−1.62741	−0.813706	−	0.581277i	$-0.802553\pi$
$947$	−50.0810	−1.62741	−0.813706	+	0.581277i	$0.802553\pi$
$948$	6.71218	0.218002
$949$	−39.5750	−1.28466
$950$	3.27165	0.106146
$951$	1.78423	0.0578577
$952$	3.43619	0.111368
$953$	−42.2230	−1.36774	−0.683869	−	0.729605i	$-0.739704\pi$
$953$	−42.2230	−1.36774	−0.683869	+	0.729605i	$0.739704\pi$
$954$	−10.3477	−0.335020
$955$	−0.186527	−0.00603587
$956$	−17.5385	−0.567235
$957$	10.7285	0.346803
$958$	7.16104	0.231363
$959$	2.54285	0.0821127
$960$	1.82228	0.0588137
$961$	−26.6301	−0.859036
$962$	−13.6855	−0.441237
$963$	−17.8995	−0.576802
$964$	5.36598	0.172826
$965$	4.12837	0.132897
$966$	−4.66380	−0.150055
$967$	−49.7812	−1.60085	−0.800427	−	0.599430i	$-0.795394\pi$
$967$	−49.7812	−1.60085	−0.800427	+	0.599430i	$0.795394\pi$
$968$	11.1678	0.358948
$969$	−0.558018	−0.0179261
$970$	1.74937	0.0561690
$971$	−23.8520	−0.765448	−0.382724	−	0.923863i	$-0.625014\pi$
$971$	−23.8520	−0.765448	−0.382724	+	0.923863i	$0.625014\pi$
$972$	0.600803	0.0192708
$973$	18.3819	0.589295
$974$	16.3386	0.523522
$975$	−24.7474	−0.792552
$976$	9.45483	0.302642
$977$	6.12940	0.196097	0.0980485	−	0.995182i	$-0.468740\pi$
$977$	6.12940	0.196097	0.0980485	+	0.995182i	$0.468740\pi$
$978$	22.2739	0.712242
$979$	−51.9289	−1.65966
$980$	−0.720384	−0.0230118
$981$	−19.0758	−0.609043
$982$	16.7385	0.534146
$983$	37.9772	1.21128	0.605642	−	0.795737i	$-0.292916\pi$
$983$	37.9772	1.21128	0.605642	+	0.795737i	$0.292916\pi$
$984$	−15.9207	−0.507534
$985$	2.91929	0.0930162
$986$	3.31783	0.105661
$987$	5.48966	0.174738
$988$	1.67390	0.0532540
$989$	−29.9143	−0.951218
$990$	0.943068	0.0299727
$991$	−18.4508	−0.586108	−0.293054	−	0.956096i	$-0.594672\pi$
$991$	−18.4508	−0.586108	−0.293054	+	0.956096i	$0.594672\pi$
$992$	−6.83503	−0.217012
$993$	−11.4189	−0.362369
$994$	20.3401	0.645150
$995$	−1.25669	−0.0398397
$996$	9.01691	0.285712
$997$	14.0568	0.445183	0.222591	−	0.974912i	$-0.428548\pi$
$997$	14.0568	0.445183	0.222591	+	0.974912i	$0.428548\pi$
$998$	6.74067	0.213372
$999$	2.31724	0.0733141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3009.2.a.f.1.6	✓	16
3.2	odd	2		9027.2.a.m.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3009.2.a.f.1.6	✓	16	1.1	even	1	trivial
9027.2.a.m.1.11		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 3009 = 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.18288 q^{2} -1.00000 q^{3} -0.600803 q^{4} -0.208439 q^{5} +1.18288 q^{6} +1.11694 q^{7} +3.07643 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.18288 q^{2} -1.00000 q^{3} -0.600803 q^{4} -0.208439 q^{5} +1.18288 q^{6} +1.11694 q^{7} +3.07643 q^{8} +1.00000 q^{9} +0.246558 q^{10} +3.82494 q^{11} +0.600803 q^{12} -4.99287 q^{13} -1.32120 q^{14} +0.208439 q^{15} -2.43743 q^{16} +1.00000 q^{17} -1.18288 q^{18} +0.558018 q^{19} +0.125231 q^{20} -1.11694 q^{21} -4.52443 q^{22} -3.52996 q^{23} -3.07643 q^{24} -4.95655 q^{25} +5.90594 q^{26} -1.00000 q^{27} -0.671063 q^{28} -2.80488 q^{29} -0.246558 q^{30} +2.09043 q^{31} -3.26968 q^{32} -3.82494 q^{33} -1.18288 q^{34} -0.232814 q^{35} -0.600803 q^{36} -2.31724 q^{37} -0.660066 q^{38} +4.99287 q^{39} -0.641248 q^{40} +5.17506 q^{41} +1.32120 q^{42} +8.47438 q^{43} -2.29803 q^{44} -0.208439 q^{45} +4.17551 q^{46} -4.91490 q^{47} +2.43743 q^{48} -5.75244 q^{49} +5.86299 q^{50} -1.00000 q^{51} +2.99973 q^{52} +8.74794 q^{53} +1.18288 q^{54} -0.797266 q^{55} +3.43619 q^{56} -0.558018 q^{57} +3.31783 q^{58} +1.00000 q^{59} -0.125231 q^{60} -3.87902 q^{61} -2.47271 q^{62} +1.11694 q^{63} +8.74249 q^{64} +1.04071 q^{65} +4.52443 q^{66} +0.184405 q^{67} -0.600803 q^{68} +3.52996 q^{69} +0.275391 q^{70} -15.3952 q^{71} +3.07643 q^{72} +7.92631 q^{73} +2.74100 q^{74} +4.95655 q^{75} -0.335259 q^{76} +4.27223 q^{77} -5.90594 q^{78} +11.1720 q^{79} +0.508056 q^{80} +1.00000 q^{81} -6.12146 q^{82} +15.0081 q^{83} +0.671063 q^{84} -0.208439 q^{85} -10.0241 q^{86} +2.80488 q^{87} +11.7671 q^{88} -13.5764 q^{89} +0.246558 q^{90} -5.57674 q^{91} +2.12081 q^{92} -2.09043 q^{93} +5.81372 q^{94} -0.116313 q^{95} +3.26968 q^{96} +7.09518 q^{97} +6.80443 q^{98} +3.82494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9} - 7 q^{11} - 10 q^{12} + 7 q^{13} - 13 q^{14} + 3 q^{15} + 2 q^{16} + 16 q^{17} - 4 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} + 23 q^{22} - 16 q^{23} + 9 q^{24} + 5 q^{25} - 11 q^{26} - 16 q^{27} + 8 q^{28} + 4 q^{29} - 15 q^{31} - 22 q^{32} + 7 q^{33} - 4 q^{34} - 23 q^{35} + 10 q^{36} + 20 q^{37} - 17 q^{38} - 7 q^{39} + 21 q^{40} - 4 q^{41} + 13 q^{42} - 12 q^{43} - 19 q^{44} - 3 q^{45} + 24 q^{46} - 36 q^{47} - 2 q^{48} - 11 q^{49} + 9 q^{50} - 16 q^{51} + 6 q^{52} - 32 q^{53} + 4 q^{54} - 29 q^{55} - 11 q^{56} + 19 q^{57} - 33 q^{58} + 16 q^{59} + 17 q^{60} + 11 q^{62} - 3 q^{63} + 9 q^{64} - 5 q^{65} - 23 q^{66} - 30 q^{67} + 10 q^{68} + 16 q^{69} + 16 q^{70} - 70 q^{71} - 9 q^{72} + 21 q^{73} - 29 q^{74} - 5 q^{75} - 8 q^{76} - 13 q^{77} + 11 q^{78} - 25 q^{79} - 9 q^{80} + 16 q^{81} + 22 q^{82} - 23 q^{83} - 8 q^{84} - 3 q^{85} - 58 q^{86} - 4 q^{87} + 41 q^{88} - 31 q^{89} - 36 q^{91} - 26 q^{92} + 15 q^{93} + 9 q^{94} - 10 q^{95} + 22 q^{96} + 52 q^{97} - 36 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9 - 7 * q^11 - 10 * q^12 + 7 * q^13 - 13 * q^14 + 3 * q^15 + 2 * q^16 + 16 * q^17 - 4 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 + 23 * q^22 - 16 * q^23 + 9 * q^24 + 5 * q^25 - 11 * q^26 - 16 * q^27 + 8 * q^28 + 4 * q^29 - 15 * q^31 - 22 * q^32 + 7 * q^33 - 4 * q^34 - 23 * q^35 + 10 * q^36 + 20 * q^37 - 17 * q^38 - 7 * q^39 + 21 * q^40 - 4 * q^41 + 13 * q^42 - 12 * q^43 - 19 * q^44 - 3 * q^45 + 24 * q^46 - 36 * q^47 - 2 * q^48 - 11 * q^49 + 9 * q^50 - 16 * q^51 + 6 * q^52 - 32 * q^53 + 4 * q^54 - 29 * q^55 - 11 * q^56 + 19 * q^57 - 33 * q^58 + 16 * q^59 + 17 * q^60 + 11 * q^62 - 3 * q^63 + 9 * q^64 - 5 * q^65 - 23 * q^66 - 30 * q^67 + 10 * q^68 + 16 * q^69 + 16 * q^70 - 70 * q^71 - 9 * q^72 + 21 * q^73 - 29 * q^74 - 5 * q^75 - 8 * q^76 - 13 * q^77 + 11 * q^78 - 25 * q^79 - 9 * q^80 + 16 * q^81 + 22 * q^82 - 23 * q^83 - 8 * q^84 - 3 * q^85 - 58 * q^86 - 4 * q^87 + 41 * q^88 - 31 * q^89 - 36 * q^91 - 26 * q^92 + 15 * q^93 + 9 * q^94 - 10 * q^95 + 22 * q^96 + 52 * q^97 - 36 * q^98 - 7 * q^99

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