LMFDB - Embedded newform 4018.2.a.bi.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.113481.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 3x + 12 $ x^4 - 2x^3 - 9x^2 + 3*x + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.31920$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.07936 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.07936 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -4.07936 q^{10} -1.94052 q^{11} -1.00000 q^{12} -4.70068 q^{13} -4.07936 q^{15} +1.00000 q^{16} -0.440968 q^{17} +2.00000 q^{18} -4.01707 q^{19} +4.07936 q^{20} +1.94052 q^{22} +4.39856 q^{23} +1.00000 q^{24} +11.6412 q^{25} +4.70068 q^{26} +5.00000 q^{27} -4.37868 q^{29} +4.07936 q^{30} +6.06229 q^{31} -1.00000 q^{32} +1.94052 q^{33} +0.440968 q^{34} -2.00000 q^{36} +5.95759 q^{37} +4.01707 q^{38} +4.70068 q^{39} -4.07936 q^{40} +1.00000 q^{41} -3.45804 q^{43} -1.94052 q^{44} -8.15873 q^{45} -4.39856 q^{46} +1.69788 q^{47} -1.00000 q^{48} -11.6412 q^{50} +0.440968 q^{51} -4.70068 q^{52} +3.31920 q^{53} -5.00000 q^{54} -7.91608 q^{55} +4.01707 q^{57} +4.37868 q^{58} -9.41564 q^{59} -4.07936 q^{60} -10.8423 q^{61} -6.06229 q^{62} +1.00000 q^{64} -19.1758 q^{65} -1.94052 q^{66} -4.01988 q^{67} -0.440968 q^{68} -4.39856 q^{69} -3.12087 q^{71} +2.00000 q^{72} +9.01707 q^{73} -5.95759 q^{74} -11.6412 q^{75} -4.01707 q^{76} -4.70068 q^{78} -16.7800 q^{79} +4.07936 q^{80} +1.00000 q^{81} -1.00000 q^{82} +2.43726 q^{83} -1.79887 q^{85} +3.45804 q^{86} +4.37868 q^{87} +1.94052 q^{88} -5.01707 q^{89} +8.15873 q^{90} +4.39856 q^{92} -6.06229 q^{93} -1.69788 q^{94} -16.3871 q^{95} +1.00000 q^{96} -15.5402 q^{97} +3.88104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9} + 3 q^{10} - 4 q^{12} + q^{13} + 3 q^{15} + 4 q^{16} + 3 q^{17} + 8 q^{18} - 2 q^{19} - 3 q^{20} - 9 q^{23} + 4 q^{24} + 19 q^{25} - q^{26} + 20 q^{27} - 18 q^{29} - 3 q^{30} + 19 q^{31} - 4 q^{32} - 3 q^{34} - 8 q^{36} + 2 q^{37} + 2 q^{38} - q^{39} + 3 q^{40} + 4 q^{41} + 5 q^{43} + 6 q^{45} + 9 q^{46} - 4 q^{48} - 19 q^{50} - 3 q^{51} + q^{52} + 6 q^{53} - 20 q^{54} + 6 q^{55} + 2 q^{57} + 18 q^{58} + 3 q^{59} + 3 q^{60} + q^{61} - 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{71} + 8 q^{72} + 22 q^{73} - 2 q^{74} - 19 q^{75} - 2 q^{76} + q^{78} - 28 q^{79} - 3 q^{80} + 4 q^{81} - 4 q^{82} + 12 q^{83} - 24 q^{85} - 5 q^{86} + 18 q^{87} - 6 q^{89} - 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} + 4 q^{96} - 11 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9 + 3 * q^10 - 4 * q^12 + q^13 + 3 * q^15 + 4 * q^16 + 3 * q^17 + 8 * q^18 - 2 * q^19 - 3 * q^20 - 9 * q^23 + 4 * q^24 + 19 * q^25 - q^26 + 20 * q^27 - 18 * q^29 - 3 * q^30 + 19 * q^31 - 4 * q^32 - 3 * q^34 - 8 * q^36 + 2 * q^37 + 2 * q^38 - q^39 + 3 * q^40 + 4 * q^41 + 5 * q^43 + 6 * q^45 + 9 * q^46 - 4 * q^48 - 19 * q^50 - 3 * q^51 + q^52 + 6 * q^53 - 20 * q^54 + 6 * q^55 + 2 * q^57 + 18 * q^58 + 3 * q^59 + 3 * q^60 + q^61 - 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^71 + 8 * q^72 + 22 * q^73 - 2 * q^74 - 19 * q^75 - 2 * q^76 + q^78 - 28 * q^79 - 3 * q^80 + 4 * q^81 - 4 * q^82 + 12 * q^83 - 24 * q^85 - 5 * q^86 + 18 * q^87 - 6 * q^89 - 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 + 4 * q^96 - 11 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	4.07936	1.82435	0.912173	−	0.409805i	$-0.134403\pi$
$5$	4.07936	1.82435	0.912173	+	0.409805i	$0.134403\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−4.07936	−1.29001
$11$	−1.94052	−0.585089	−0.292544	−	0.956252i	$-0.594502\pi$
$11$	−1.94052	−0.585089	−0.292544	+	0.956252i	$0.594502\pi$
$12$	−1.00000	−0.288675
$13$	−4.70068	−1.30374	−0.651868	−	0.758333i	$-0.726014\pi$
$13$	−4.70068	−1.30374	−0.651868	+	0.758333i	$0.726014\pi$
$14$	0	0
$15$	−4.07936	−1.05329
$16$	1.00000	0.250000
$17$	−0.440968	−0.106950	−0.0534752	−	0.998569i	$-0.517030\pi$
$17$	−0.440968	−0.106950	−0.0534752	+	0.998569i	$0.517030\pi$
$18$	2.00000	0.471405
$19$	−4.01707	−0.921580	−0.460790	−	0.887509i	$-0.652434\pi$
$19$	−4.01707	−0.921580	−0.460790	+	0.887509i	$0.652434\pi$
$20$	4.07936	0.912173
$21$	0	0
$22$	1.94052	0.413720
$23$	4.39856	0.917163	0.458582	−	0.888652i	$-0.348358\pi$
$23$	4.39856	0.917163	0.458582	+	0.888652i	$0.348358\pi$
$24$	1.00000	0.204124
$25$	11.6412	2.32824
$26$	4.70068	0.921880
$27$	5.00000	0.962250
$28$	0	0
$29$	−4.37868	−0.813100	−0.406550	−	0.913628i	$-0.633268\pi$
$29$	−4.37868	−0.813100	−0.406550	+	0.913628i	$0.633268\pi$
$30$	4.07936	0.744786
$31$	6.06229	1.08882	0.544410	−	0.838819i	$-0.316754\pi$
$31$	6.06229	1.08882	0.544410	+	0.838819i	$0.316754\pi$
$32$	−1.00000	−0.176777
$33$	1.94052	0.337801
$34$	0.440968	0.0756253
$35$	0	0
$36$	−2.00000	−0.333333
$37$	5.95759	0.979422	0.489711	−	0.871885i	$-0.337102\pi$
$37$	5.95759	0.979422	0.489711	+	0.871885i	$0.337102\pi$
$38$	4.01707	0.651655
$39$	4.70068	0.752712
$40$	−4.07936	−0.645004
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−3.45804	−0.527346	−0.263673	−	0.964612i	$-0.584934\pi$
$43$	−3.45804	−0.527346	−0.263673	+	0.964612i	$0.584934\pi$
$44$	−1.94052	−0.292544
$45$	−8.15873	−1.21623
$46$	−4.39856	−0.648532
$47$	1.69788	0.247661	0.123830	−	0.992303i	$-0.460482\pi$
$47$	1.69788	0.247661	0.123830	+	0.992303i	$0.460482\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−11.6412	−1.64631
$51$	0.440968	0.0617478
$52$	−4.70068	−0.651868
$53$	3.31920	0.455927	0.227963	−	0.973670i	$-0.426793\pi$
$53$	3.31920	0.455927	0.227963	+	0.973670i	$0.426793\pi$
$54$	−5.00000	−0.680414
$55$	−7.91608	−1.06740
$56$	0	0
$57$	4.01707	0.532074
$58$	4.37868	0.574949
$59$	−9.41564	−1.22581	−0.612906	−	0.790156i	$-0.709999\pi$
$59$	−9.41564	−1.22581	−0.612906	+	0.790156i	$0.709999\pi$
$60$	−4.07936	−0.526644
$61$	−10.8423	−1.38822	−0.694110	−	0.719869i	$-0.744202\pi$
$61$	−10.8423	−1.38822	−0.694110	+	0.719869i	$0.744202\pi$
$62$	−6.06229	−0.769911
$63$	0	0
$64$	1.00000	0.125000
$65$	−19.1758	−2.37847
$66$	−1.94052	−0.238861
$67$	−4.01988	−0.491107	−0.245553	−	0.969383i	$-0.578970\pi$
$67$	−4.01988	−0.491107	−0.245553	+	0.969383i	$0.578970\pi$
$68$	−0.440968	−0.0534752
$69$	−4.39856	−0.529525
$70$	0	0
$71$	−3.12087	−0.370380	−0.185190	−	0.982703i	$-0.559290\pi$
$71$	−3.12087	−0.370380	−0.185190	+	0.982703i	$0.559290\pi$
$72$	2.00000	0.235702
$73$	9.01707	1.05537	0.527684	−	0.849441i	$-0.323060\pi$
$73$	9.01707	1.05537	0.527684	+	0.849441i	$0.323060\pi$
$74$	−5.95759	−0.692556
$75$	−11.6412	−1.34421
$76$	−4.01707	−0.460790
$77$	0	0
$78$	−4.70068	−0.532248
$79$	−16.7800	−1.88790	−0.943951	−	0.330084i	$-0.892923\pi$
$79$	−16.7800	−1.88790	−0.943951	+	0.330084i	$0.892923\pi$
$80$	4.07936	0.456087
$81$	1.00000	0.111111
$82$	−1.00000	−0.110432
$83$	2.43726	0.267524	0.133762	−	0.991013i	$-0.457294\pi$
$83$	2.43726	0.267524	0.133762	+	0.991013i	$0.457294\pi$
$84$	0	0
$85$	−1.79887	−0.195115
$86$	3.45804	0.372890
$87$	4.37868	0.469444
$88$	1.94052	0.206860
$89$	−5.01707	−0.531809	−0.265904	−	0.963999i	$-0.585671\pi$
$89$	−5.01707	−0.531809	−0.265904	+	0.963999i	$0.585671\pi$
$90$	8.15873	0.860005
$91$	0	0
$92$	4.39856	0.458582
$93$	−6.06229	−0.628630
$94$	−1.69788	−0.175123
$95$	−16.3871	−1.68128
$96$	1.00000	0.102062
$97$	−15.5402	−1.57787	−0.788935	−	0.614477i	$-0.789367\pi$
$97$	−15.5402	−1.57787	−0.788935	+	0.614477i	$0.789367\pi$
$98$	0	0
$99$	3.88104	0.390059
$100$	11.6412	1.16412
$101$	13.7178	1.36497	0.682484	−	0.730901i	$-0.260900\pi$
$101$	13.7178	1.36497	0.682484	+	0.730901i	$0.260900\pi$
$102$	−0.440968	−0.0436623
$103$	−18.9803	−1.87018	−0.935092	−	0.354406i	$-0.884683\pi$
$103$	−18.9803	−1.87018	−0.935092	+	0.354406i	$0.884683\pi$
$104$	4.70068	0.460940
$105$	0	0
$106$	−3.31920	−0.322389
$107$	−7.25691	−0.701552	−0.350776	−	0.936459i	$-0.614082\pi$
$107$	−7.25691	−0.701552	−0.350776	+	0.936459i	$0.614082\pi$
$108$	5.00000	0.481125
$109$	2.53740	0.243039	0.121520	−	0.992589i	$-0.461223\pi$
$109$	2.53740	0.243039	0.121520	+	0.992589i	$0.461223\pi$
$110$	7.91608	0.754769
$111$	−5.95759	−0.565470
$112$	0	0
$113$	−5.68080	−0.534405	−0.267202	−	0.963640i	$-0.586099\pi$
$113$	−5.68080	−0.534405	−0.267202	+	0.963640i	$0.586099\pi$
$114$	−4.01707	−0.376233
$115$	17.9433	1.67322
$116$	−4.37868	−0.406550
$117$	9.40137	0.869157
$118$	9.41564	0.866779
$119$	0	0
$120$	4.07936	0.372393
$121$	−7.23438	−0.657671
$122$	10.8423	0.981619
$123$	−1.00000	−0.0901670
$124$	6.06229	0.544410
$125$	27.0919	2.42317
$126$	0	0
$127$	−14.3986	−1.27767	−0.638833	−	0.769346i	$-0.720582\pi$
$127$	−14.3986	−1.27767	−0.638833	+	0.769346i	$0.720582\pi$
$128$	−1.00000	−0.0883883
$129$	3.45804	0.304464
$130$	19.1758	1.68183
$131$	10.3419	0.903575	0.451788	−	0.892126i	$-0.350787\pi$
$131$	10.3419	0.903575	0.451788	+	0.892126i	$0.350787\pi$
$132$	1.94052	0.168901
$133$	0	0
$134$	4.01988	0.347265
$135$	20.3968	1.75548
$136$	0.440968	0.0378127
$137$	−1.33346	−0.113925	−0.0569627	−	0.998376i	$-0.518142\pi$
$137$	−1.33346	−0.113925	−0.0569627	+	0.998376i	$0.518142\pi$
$138$	4.39856	0.374430
$139$	2.24545	0.190457	0.0952284	−	0.995455i	$-0.469642\pi$
$139$	2.24545	0.190457	0.0952284	+	0.995455i	$0.469642\pi$
$140$	0	0
$141$	−1.69788	−0.142987
$142$	3.12087	0.261898
$143$	9.12177	0.762801
$144$	−2.00000	−0.166667
$145$	−17.8622	−1.48338
$146$	−9.01707	−0.746258
$147$	0	0
$148$	5.95759	0.489711
$149$	−12.4165	−1.01720	−0.508601	−	0.861002i	$-0.669837\pi$
$149$	−12.4165	−1.01720	−0.508601	+	0.861002i	$0.669837\pi$
$150$	11.6412	0.950500
$151$	−11.9613	−0.973397	−0.486698	−	0.873570i	$-0.661799\pi$
$151$	−11.9613	−0.973397	−0.486698	+	0.873570i	$0.661799\pi$
$152$	4.01707	0.325828
$153$	0.881935	0.0713002
$154$	0	0
$155$	24.7303	1.98638
$156$	4.70068	0.376356
$157$	−8.56184	−0.683309	−0.341655	−	0.939826i	$-0.610987\pi$
$157$	−8.56184	−0.683309	−0.341655	+	0.939826i	$0.610987\pi$
$158$	16.7800	1.33495
$159$	−3.31920	−0.263230
$160$	−4.07936	−0.322502
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−20.1200	−1.57592	−0.787961	−	0.615725i	$-0.788863\pi$
$163$	−20.1200	−1.57592	−0.787961	+	0.615725i	$0.788863\pi$
$164$	1.00000	0.0780869
$165$	7.91608	0.616266
$166$	−2.43726	−0.189168
$167$	−19.0794	−1.47641	−0.738203	−	0.674579i	$-0.764325\pi$
$167$	−19.0794	−1.47641	−0.738203	+	0.674579i	$0.764325\pi$
$168$	0	0
$169$	9.09644	0.699726
$170$	1.79887	0.137967
$171$	8.03415	0.614387
$172$	−3.45804	−0.263673
$173$	23.6838	1.80064	0.900322	−	0.435224i	$-0.143331\pi$
$173$	23.6838	1.80064	0.900322	+	0.435224i	$0.143331\pi$
$174$	−4.37868	−0.331947
$175$	0	0
$176$	−1.94052	−0.146272
$177$	9.41564	0.707722
$178$	5.01707	0.376046
$179$	−10.7178	−0.801083	−0.400541	−	0.916279i	$-0.631178\pi$
$179$	−10.7178	−0.801083	−0.400541	+	0.916279i	$0.631178\pi$
$180$	−8.15873	−0.608116
$181$	19.2381	1.42996	0.714978	−	0.699147i	$-0.246437\pi$
$181$	19.2381	1.42996	0.714978	+	0.699147i	$0.246437\pi$
$182$	0	0
$183$	10.8423	0.801489
$184$	−4.39856	−0.324266
$185$	24.3032	1.78681
$186$	6.06229	0.444509
$187$	0.855706	0.0625754
$188$	1.69788	0.123830
$189$	0	0
$190$	16.3871	1.18885
$191$	−2.13884	−0.154761	−0.0773807	−	0.997002i	$-0.524656\pi$
$191$	−2.13884	−0.154761	−0.0773807	+	0.997002i	$0.524656\pi$
$192$	−1.00000	−0.0721688
$193$	14.9217	1.07409	0.537044	−	0.843554i	$-0.319541\pi$
$193$	14.9217	1.07409	0.537044	+	0.843554i	$0.319541\pi$
$194$	15.5402	1.11572
$195$	19.1758	1.37321
$196$	0	0
$197$	−22.2524	−1.58541	−0.792707	−	0.609602i	$-0.791329\pi$
$197$	−22.2524	−1.58541	−0.792707	+	0.609602i	$0.791329\pi$
$198$	−3.88104	−0.275813
$199$	−1.48248	−0.105090	−0.0525450	−	0.998619i	$-0.516733\pi$
$199$	−1.48248	−0.105090	−0.0525450	+	0.998619i	$0.516733\pi$
$200$	−11.6412	−0.823157
$201$	4.01988	0.283541
$202$	−13.7178	−0.965178
$203$	0	0
$204$	0.440968	0.0308739
$205$	4.07936	0.284915
$206$	18.9803	1.32242
$207$	−8.79712	−0.611442
$208$	−4.70068	−0.325934
$209$	7.79521	0.539206
$210$	0	0
$211$	−23.8226	−1.64002	−0.820008	−	0.572351i	$-0.806031\pi$
$211$	−23.8226	−1.64002	−0.820008	+	0.572351i	$0.806031\pi$
$212$	3.31920	0.227963
$213$	3.12087	0.213839
$214$	7.25691	0.496072
$215$	−14.1066	−0.962063
$216$	−5.00000	−0.340207
$217$	0	0
$218$	−2.53740	−0.171855
$219$	−9.01707	−0.609317
$220$	−7.91608	−0.533702
$221$	2.07285	0.139435
$222$	5.95759	0.399847
$223$	−6.91608	−0.463135	−0.231568	−	0.972819i	$-0.574385\pi$
$223$	−6.91608	−0.463135	−0.231568	+	0.972819i	$0.574385\pi$
$224$	0	0
$225$	−23.2824	−1.55216
$226$	5.68080	0.377881
$227$	−21.1606	−1.40448	−0.702240	−	0.711940i	$-0.747817\pi$
$227$	−21.1606	−1.40448	−0.702240	+	0.711940i	$0.747817\pi$
$228$	4.01707	0.266037
$229$	17.8709	1.18094	0.590470	−	0.807060i	$-0.298942\pi$
$229$	17.8709	1.18094	0.590470	+	0.807060i	$0.298942\pi$
$230$	−17.9433	−1.18315
$231$	0	0
$232$	4.37868	0.287474
$233$	−19.8847	−1.30269	−0.651346	−	0.758780i	$-0.725796\pi$
$233$	−19.8847	−1.30269	−0.651346	+	0.758780i	$0.725796\pi$
$234$	−9.40137	−0.614587
$235$	6.92625	0.451819
$236$	−9.41564	−0.612906
$237$	16.7800	1.08998
$238$	0	0
$239$	−9.61396	−0.621875	−0.310938	−	0.950430i	$-0.600643\pi$
$239$	−9.61396	−0.621875	−0.310938	+	0.950430i	$0.600643\pi$
$240$	−4.07936	−0.263322
$241$	12.1587	0.783212	0.391606	−	0.920133i	$-0.371920\pi$
$241$	12.1587	0.783212	0.391606	+	0.920133i	$0.371920\pi$
$242$	7.23438	0.465044
$243$	−16.0000	−1.02640
$244$	−10.8423	−0.694110
$245$	0	0
$246$	1.00000	0.0637577
$247$	18.8830	1.20150
$248$	−6.06229	−0.384956
$249$	−2.43726	−0.154455
$250$	−27.0919	−1.71344
$251$	21.7234	1.37117	0.685584	−	0.727994i	$-0.259547\pi$
$251$	21.7234	1.37117	0.685584	+	0.727994i	$0.259547\pi$
$252$	0	0
$253$	−8.53549	−0.536622
$254$	14.3986	0.903446
$255$	1.79887	0.112649
$256$	1.00000	0.0625000
$257$	−25.4697	−1.58875	−0.794377	−	0.607425i	$-0.792203\pi$
$257$	−25.4697	−1.58875	−0.794377	+	0.607425i	$0.792203\pi$
$258$	−3.45804	−0.215288
$259$	0	0
$260$	−19.1758	−1.18923
$261$	8.75736	0.542067
$262$	−10.3419	−0.638924
$263$	0.982926	0.0606098	0.0303049	−	0.999541i	$-0.490352\pi$
$263$	0.982926	0.0606098	0.0303049	+	0.999541i	$0.490352\pi$
$264$	−1.94052	−0.119431
$265$	13.5402	0.831769
$266$	0	0
$267$	5.01707	0.307040
$268$	−4.01988	−0.245553
$269$	16.5800	1.01090	0.505450	−	0.862856i	$-0.331327\pi$
$269$	16.5800	1.01090	0.505450	+	0.862856i	$0.331327\pi$
$270$	−20.3968	−1.24131
$271$	−0.900754	−0.0547169	−0.0273585	−	0.999626i	$-0.508710\pi$
$271$	−0.900754	−0.0547169	−0.0273585	+	0.999626i	$0.508710\pi$
$272$	−0.440968	−0.0267376
$273$	0	0
$274$	1.33346	0.0805575
$275$	−22.5900	−1.36223
$276$	−4.39856	−0.264762
$277$	22.7811	1.36878	0.684392	−	0.729114i	$-0.260068\pi$
$277$	22.7811	1.36878	0.684392	+	0.729114i	$0.260068\pi$
$278$	−2.24545	−0.134673
$279$	−12.1246	−0.725880
$280$	0	0
$281$	22.3940	1.33591	0.667957	−	0.744200i	$-0.267169\pi$
$281$	22.3940	1.33591	0.667957	+	0.744200i	$0.267169\pi$
$282$	1.69788	0.101107
$283$	8.25601	0.490769	0.245384	−	0.969426i	$-0.421086\pi$
$283$	8.25601	0.490769	0.245384	+	0.969426i	$0.421086\pi$
$284$	−3.12087	−0.185190
$285$	16.3871	0.970688
$286$	−9.12177	−0.539382
$287$	0	0
$288$	2.00000	0.117851
$289$	−16.8055	−0.988562
$290$	17.8622	1.04891
$291$	15.5402	0.910983
$292$	9.01707	0.527684
$293$	−22.0938	−1.29073	−0.645367	−	0.763873i	$-0.723295\pi$
$293$	−22.0938	−1.29073	−0.645367	+	0.763873i	$0.723295\pi$
$294$	0	0
$295$	−38.4098	−2.23630
$296$	−5.95759	−0.346278
$297$	−9.70260	−0.563002
$298$	12.4165	0.719270
$299$	−20.6762	−1.19574
$300$	−11.6412	−0.672105
$301$	0	0
$302$	11.9613	0.688295
$303$	−13.7178	−0.788065
$304$	−4.01707	−0.230395
$305$	−44.2298	−2.53259
$306$	−0.881935	−0.0504169
$307$	−14.3382	−0.818323	−0.409162	−	0.912462i	$-0.634179\pi$
$307$	−14.3382	−0.818323	−0.409162	+	0.912462i	$0.634179\pi$
$308$	0	0
$309$	18.9803	1.07975
$310$	−24.7303	−1.40459
$311$	11.3049	0.641044	0.320522	−	0.947241i	$-0.396142\pi$
$311$	11.3049	0.641044	0.320522	+	0.947241i	$0.396142\pi$
$312$	−4.70068	−0.266124
$313$	18.6196	1.05244	0.526220	−	0.850348i	$-0.323609\pi$
$313$	18.6196	1.05244	0.526220	+	0.850348i	$0.323609\pi$
$314$	8.56184	0.483173
$315$	0	0
$316$	−16.7800	−0.943951
$317$	−5.65547	−0.317643	−0.158821	−	0.987307i	$-0.550769\pi$
$317$	−5.65547	−0.317643	−0.158821	+	0.987307i	$0.550769\pi$
$318$	3.31920	0.186131
$319$	8.49691	0.475736
$320$	4.07936	0.228043
$321$	7.25691	0.405041
$322$	0	0
$323$	1.77140	0.0985633
$324$	1.00000	0.0555556
$325$	−54.7216	−3.03541
$326$	20.1200	1.11435
$327$	−2.53740	−0.140319
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−7.91608	−0.435766
$331$	29.4448	1.61843	0.809217	−	0.587509i	$-0.199891\pi$
$331$	29.4448	1.61843	0.809217	+	0.587509i	$0.199891\pi$
$332$	2.43726	0.133762
$333$	−11.9152	−0.652948
$334$	19.0794	1.04398
$335$	−16.3986	−0.895949
$336$	0	0
$337$	−25.2266	−1.37418	−0.687091	−	0.726571i	$-0.741113\pi$
$337$	−25.2266	−1.37418	−0.687091	+	0.726571i	$0.741113\pi$
$338$	−9.09644	−0.494781
$339$	5.68080	0.308539
$340$	−1.79887	−0.0975573
$341$	−11.7640	−0.637056
$342$	−8.03415	−0.434437
$343$	0	0
$344$	3.45804	0.186445
$345$	−17.9433	−0.966036
$346$	−23.6838	−1.27325
$347$	25.6113	1.37489	0.687444	−	0.726238i	$-0.258733\pi$
$347$	25.6113	1.37489	0.687444	+	0.726238i	$0.258733\pi$
$348$	4.37868	0.234722
$349$	8.25601	0.441934	0.220967	−	0.975281i	$-0.429079\pi$
$349$	8.25601	0.441934	0.220967	+	0.975281i	$0.429079\pi$
$350$	0	0
$351$	−23.5034	−1.25452
$352$	1.94052	0.103430
$353$	−26.8423	−1.42867	−0.714337	−	0.699802i	$-0.753271\pi$
$353$	−26.8423	−1.42867	−0.714337	+	0.699802i	$0.753271\pi$
$354$	−9.41564	−0.500435
$355$	−12.7312	−0.675701
$356$	−5.01707	−0.265904
$357$	0	0
$358$	10.7178	0.566451
$359$	0.384295	0.0202823	0.0101412	−	0.999949i	$-0.496772\pi$
$359$	0.384295	0.0202823	0.0101412	+	0.999949i	$0.496772\pi$
$360$	8.15873	0.430003
$361$	−2.86312	−0.150690
$362$	−19.2381	−1.01113
$363$	7.23438	0.379707
$364$	0	0
$365$	36.7839	1.92536
$366$	−10.8423	−0.566738
$367$	−13.1841	−0.688202	−0.344101	−	0.938933i	$-0.611816\pi$
$367$	−13.1841	−0.688202	−0.344101	+	0.938933i	$0.611816\pi$
$368$	4.39856	0.229291
$369$	−2.00000	−0.104116
$370$	−24.3032	−1.26346
$371$	0	0
$372$	−6.06229	−0.314315
$373$	22.7718	1.17908	0.589539	−	0.807740i	$-0.299309\pi$
$373$	22.7718	1.17908	0.589539	+	0.807740i	$0.299309\pi$
$374$	−0.855706	−0.0442475
$375$	−27.0919	−1.39902
$376$	−1.69788	−0.0875613
$377$	20.5828	1.06007
$378$	0	0
$379$	31.1870	1.60197	0.800985	−	0.598684i	$-0.204310\pi$
$379$	31.1870	1.60197	0.800985	+	0.598684i	$0.204310\pi$
$380$	−16.3871	−0.840641
$381$	14.3986	0.737661
$382$	2.13884	0.109433
$383$	26.4933	1.35374	0.676871	−	0.736102i	$-0.263335\pi$
$383$	26.4933	1.35374	0.676871	+	0.736102i	$0.263335\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−14.9217	−0.759495
$387$	6.91608	0.351564
$388$	−15.5402	−0.788935
$389$	−25.3741	−1.28652	−0.643260	−	0.765648i	$-0.722418\pi$
$389$	−25.3741	−1.28652	−0.643260	+	0.765648i	$0.722418\pi$
$390$	−19.1758	−0.971004
$391$	−1.93962	−0.0980909
$392$	0	0
$393$	−10.3419	−0.521679
$394$	22.2524	1.12106
$395$	−68.4519	−3.44419
$396$	3.88104	0.195030
$397$	20.2409	1.01586	0.507931	−	0.861398i	$-0.330411\pi$
$397$	20.2409	1.01586	0.507931	+	0.861398i	$0.330411\pi$
$398$	1.48248	0.0743099
$399$	0	0
$400$	11.6412	0.582060
$401$	24.1769	1.20733	0.603667	−	0.797236i	$-0.293705\pi$
$401$	24.1769	1.20733	0.603667	+	0.797236i	$0.293705\pi$
$402$	−4.01988	−0.200494
$403$	−28.4969	−1.41953
$404$	13.7178	0.682484
$405$	4.07936	0.202705
$406$	0	0
$407$	−11.5608	−0.573049
$408$	−0.440968	−0.0218311
$409$	0.369133	0.0182525	0.00912624	−	0.999958i	$-0.497095\pi$
$409$	0.369133	0.0182525	0.00912624	+	0.999958i	$0.497095\pi$
$410$	−4.07936	−0.201465
$411$	1.33346	0.0657749
$412$	−18.9803	−0.935092
$413$	0	0
$414$	8.79712	0.432355
$415$	9.94248	0.488057
$416$	4.70068	0.230470
$417$	−2.24545	−0.109960
$418$	−7.79521	−0.381276
$419$	−23.1427	−1.13060	−0.565298	−	0.824887i	$-0.691239\pi$
$419$	−23.1427	−1.13060	−0.565298	+	0.824887i	$0.691239\pi$
$420$	0	0
$421$	3.35790	0.163654	0.0818270	−	0.996647i	$-0.473925\pi$
$421$	3.35790	0.163654	0.0818270	+	0.996647i	$0.473925\pi$
$422$	23.8226	1.15967
$423$	−3.39575	−0.165107
$424$	−3.31920	−0.161194
$425$	−5.13339	−0.249006
$426$	−3.12087	−0.151207
$427$	0	0
$428$	−7.25691	−0.350776
$429$	−9.12177	−0.440403
$430$	14.1066	0.680281
$431$	−14.4267	−0.694910	−0.347455	−	0.937697i	$-0.612954\pi$
$431$	−14.4267	−0.694910	−0.347455	+	0.937697i	$0.612954\pi$
$432$	5.00000	0.240563
$433$	17.0172	0.817796	0.408898	−	0.912580i	$-0.365913\pi$
$433$	17.0172	0.817796	0.408898	+	0.912580i	$0.365913\pi$
$434$	0	0
$435$	17.8622	0.856428
$436$	2.53740	0.121520
$437$	−17.6693	−0.845239
$438$	9.01707	0.430852
$439$	−6.95198	−0.331800	−0.165900	−	0.986143i	$-0.553053\pi$
$439$	−6.95198	−0.331800	−0.165900	+	0.986143i	$0.553053\pi$
$440$	7.91608	0.377384
$441$	0	0
$442$	−2.07285	−0.0985954
$443$	−6.93861	−0.329663	−0.164832	−	0.986322i	$-0.552708\pi$
$443$	−6.93861	−0.329663	−0.164832	+	0.986322i	$0.552708\pi$
$444$	−5.95759	−0.282735
$445$	−20.4665	−0.970204
$446$	6.91608	0.327486
$447$	12.4165	0.587282
$448$	0	0
$449$	−6.34363	−0.299375	−0.149687	−	0.988733i	$-0.547827\pi$
$449$	−6.34363	−0.299375	−0.149687	+	0.988733i	$0.547827\pi$
$450$	23.2824	1.09754
$451$	−1.94052	−0.0913755
$452$	−5.68080	−0.267202
$453$	11.9613	0.561991
$454$	21.1606	0.993118
$455$	0	0
$456$	−4.01707	−0.188117
$457$	−0.102054	−0.00477390	−0.00238695	−	0.999997i	$-0.500760\pi$
$457$	−0.102054	−0.00477390	−0.00238695	+	0.999997i	$0.500760\pi$
$458$	−17.8709	−0.835051
$459$	−2.20484	−0.102913
$460$	17.9433	0.836612
$461$	−32.0692	−1.49361	−0.746806	−	0.665042i	$-0.768413\pi$
$461$	−32.0692	−1.49361	−0.746806	+	0.665042i	$0.768413\pi$
$462$	0	0
$463$	−30.6907	−1.42632	−0.713158	−	0.701003i	$-0.752736\pi$
$463$	−30.6907	−1.42632	−0.713158	+	0.701003i	$0.752736\pi$
$464$	−4.37868	−0.203275
$465$	−24.7303	−1.14684
$466$	19.8847	0.921143
$467$	−16.2852	−0.753590	−0.376795	−	0.926297i	$-0.622974\pi$
$467$	−16.2852	−0.753590	−0.376795	+	0.926297i	$0.622974\pi$
$468$	9.40137	0.434578
$469$	0	0
$470$	−6.92625	−0.319484
$471$	8.56184	0.394509
$472$	9.41564	0.433390
$473$	6.71040	0.308544
$474$	−16.7800	−0.770733
$475$	−46.7636	−2.14566
$476$	0	0
$477$	−6.63840	−0.303951
$478$	9.61396	0.439732
$479$	18.9208	0.864514	0.432257	−	0.901751i	$-0.357717\pi$
$479$	18.9208	0.864514	0.432257	+	0.901751i	$0.357717\pi$
$480$	4.07936	0.186197
$481$	−28.0048	−1.27691
$482$	−12.1587	−0.553815
$483$	0	0
$484$	−7.23438	−0.328836
$485$	−63.3942	−2.87858
$486$	16.0000	0.725775
$487$	−31.0190	−1.40560	−0.702802	−	0.711385i	$-0.748068\pi$
$487$	−31.0190	−1.40560	−0.702802	+	0.711385i	$0.748068\pi$
$488$	10.8423	0.490810
$489$	20.1200	0.909859
$490$	0	0
$491$	−14.5780	−0.657897	−0.328948	−	0.944348i	$-0.606694\pi$
$491$	−14.5780	−0.657897	−0.328948	+	0.944348i	$0.606694\pi$
$492$	−1.00000	−0.0450835
$493$	1.93086	0.0869614
$494$	−18.8830	−0.849586
$495$	15.8322	0.711603
$496$	6.06229	0.272205
$497$	0	0
$498$	2.43726	0.109216
$499$	34.7266	1.55457	0.777287	−	0.629146i	$-0.216595\pi$
$499$	34.7266	1.55457	0.777287	+	0.629146i	$0.216595\pi$
$500$	27.0919	1.21159
$501$	19.0794	0.852403
$502$	−21.7234	−0.969562
$503$	15.5498	0.693329	0.346665	−	0.937989i	$-0.387314\pi$
$503$	15.5498	0.693329	0.346665	+	0.937989i	$0.387314\pi$
$504$	0	0
$505$	55.9597	2.49017
$506$	8.53549	0.379449
$507$	−9.09644	−0.403987
$508$	−14.3986	−0.638833
$509$	28.8793	1.28005	0.640026	−	0.768353i	$-0.278924\pi$
$509$	28.8793	1.28005	0.640026	+	0.768353i	$0.278924\pi$
$510$	−1.79887	−0.0796552
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−20.0854	−0.886791
$514$	25.4697	1.12342
$515$	−77.4275	−3.41186
$516$	3.45804	0.152232
$517$	−3.29476	−0.144903
$518$	0	0
$519$	−23.6838	−1.03960
$520$	19.1758	0.840914
$521$	25.7009	1.12597	0.562987	−	0.826465i	$-0.309652\pi$
$521$	25.7009	1.12597	0.562987	+	0.826465i	$0.309652\pi$
$522$	−8.75736	−0.383299
$523$	25.3391	1.10800	0.554000	−	0.832516i	$-0.313101\pi$
$523$	25.3391	1.10800	0.554000	+	0.832516i	$0.313101\pi$
$524$	10.3419	0.451788
$525$	0	0
$526$	−0.982926	−0.0428576
$527$	−2.67327	−0.116450
$528$	1.94052	0.0844503
$529$	−3.65266	−0.158811
$530$	−13.5402	−0.588149
$531$	18.8313	0.817208
$532$	0	0
$533$	−4.70068	−0.203609
$534$	−5.01707	−0.217110
$535$	−29.6036	−1.27987
$536$	4.01988	0.173632
$537$	10.7178	0.462505
$538$	−16.5800	−0.714814
$539$	0	0
$540$	20.3968	0.877739
$541$	3.62588	0.155889	0.0779443	−	0.996958i	$-0.475164\pi$
$541$	3.62588	0.155889	0.0779443	+	0.996958i	$0.475164\pi$
$542$	0.900754	0.0386907
$543$	−19.2381	−0.825585
$544$	0.440968	0.0189063
$545$	10.3510	0.443388
$546$	0	0
$547$	−25.5979	−1.09449	−0.547245	−	0.836973i	$-0.684323\pi$
$547$	−25.5979	−1.09449	−0.547245	+	0.836973i	$0.684323\pi$
$548$	−1.33346	−0.0569627
$549$	21.6847	0.925479
$550$	22.5900	0.963240
$551$	17.5895	0.749337
$552$	4.39856	0.187215
$553$	0	0
$554$	−22.7811	−0.967877
$555$	−24.3032	−1.03161
$556$	2.24545	0.0952284
$557$	−20.8064	−0.881597	−0.440799	−	0.897606i	$-0.645305\pi$
$557$	−20.8064	−0.881597	−0.440799	+	0.897606i	$0.645305\pi$
$558$	12.1246	0.513274
$559$	16.2552	0.687520
$560$	0	0
$561$	−0.855706	−0.0361279
$562$	−22.3940	−0.944634
$563$	−4.18035	−0.176181	−0.0880905	−	0.996112i	$-0.528076\pi$
$563$	−4.18035	−0.176181	−0.0880905	+	0.996112i	$0.528076\pi$
$564$	−1.69788	−0.0714935
$565$	−23.1741	−0.974940
$566$	−8.25601	−0.347026
$567$	0	0
$568$	3.12087	0.130949
$569$	22.3313	0.936178	0.468089	−	0.883681i	$-0.344943\pi$
$569$	22.3313	0.936178	0.468089	+	0.883681i	$0.344943\pi$
$570$	−16.3871	−0.686380
$571$	0.540213	0.0226072	0.0113036	−	0.999936i	$-0.496402\pi$
$571$	0.540213	0.0226072	0.0113036	+	0.999936i	$0.496402\pi$
$572$	9.12177	0.381400
$573$	2.13884	0.0893515
$574$	0	0
$575$	51.2045	2.13538
$576$	−2.00000	−0.0833333
$577$	34.1976	1.42367	0.711833	−	0.702349i	$-0.247865\pi$
$577$	34.1976	1.42367	0.711833	+	0.702349i	$0.247865\pi$
$578$	16.8055	0.699019
$579$	−14.9217	−0.620125
$580$	−17.8622	−0.741688
$581$	0	0
$582$	−15.5402	−0.644163
$583$	−6.44097	−0.266758
$584$	−9.01707	−0.373129
$585$	38.3516	1.58564
$586$	22.0938	0.912686
$587$	−28.7424	−1.18633	−0.593163	−	0.805082i	$-0.702121\pi$
$587$	−28.7424	−1.18633	−0.593163	+	0.805082i	$0.702121\pi$
$588$	0	0
$589$	−24.3527	−1.00343
$590$	38.4098	1.58131
$591$	22.2524	0.915340
$592$	5.95759	0.244856
$593$	−6.60340	−0.271169	−0.135585	−	0.990766i	$-0.543291\pi$
$593$	−6.60340	−0.271169	−0.135585	+	0.990766i	$0.543291\pi$
$594$	9.70260	0.398102
$595$	0	0
$596$	−12.4165	−0.508601
$597$	1.48248	0.0606738
$598$	20.6762	0.845515
$599$	16.2363	0.663399	0.331700	−	0.943385i	$-0.392378\pi$
$599$	16.2363	0.663399	0.331700	+	0.943385i	$0.392378\pi$
$600$	11.6412	0.475250
$601$	−13.7519	−0.560952	−0.280476	−	0.959861i	$-0.590492\pi$
$601$	−13.7519	−0.560952	−0.280476	+	0.959861i	$0.590492\pi$
$602$	0	0
$603$	8.03977	0.327405
$604$	−11.9613	−0.486698
$605$	−29.5117	−1.19982
$606$	13.7178	0.557246
$607$	39.0984	1.58695	0.793477	−	0.608600i	$-0.208268\pi$
$607$	39.0984	1.58695	0.793477	+	0.608600i	$0.208268\pi$
$608$	4.01707	0.162914
$609$	0	0
$610$	44.2298	1.79081
$611$	−7.98118	−0.322884
$612$	0.881935	0.0356501
$613$	40.8010	1.64794	0.823968	−	0.566636i	$-0.191755\pi$
$613$	40.8010	1.64794	0.823968	+	0.566636i	$0.191755\pi$
$614$	14.3382	0.578642
$615$	−4.07936	−0.164496
$616$	0	0
$617$	3.41929	0.137656	0.0688278	−	0.997629i	$-0.478074\pi$
$617$	3.41929	0.137656	0.0688278	+	0.997629i	$0.478074\pi$
$618$	−18.9803	−0.763499
$619$	7.17686	0.288463	0.144231	−	0.989544i	$-0.453929\pi$
$619$	7.17686	0.288463	0.144231	+	0.989544i	$0.453929\pi$
$620$	24.7303	0.993192
$621$	21.9928	0.882541
$622$	−11.3049	−0.453286
$623$	0	0
$624$	4.70068	0.188178
$625$	52.3116	2.09246
$626$	−18.6196	−0.744188
$627$	−7.79521	−0.311311
$628$	−8.56184	−0.341655
$629$	−2.62711	−0.104750
$630$	0	0
$631$	29.4156	1.17102	0.585509	−	0.810666i	$-0.300895\pi$
$631$	29.4156	1.17102	0.585509	+	0.810666i	$0.300895\pi$
$632$	16.7800	0.667474
$633$	23.8226	0.946864
$634$	5.65547	0.224607
$635$	−58.7370	−2.33091
$636$	−3.31920	−0.131615
$637$	0	0
$638$	−8.49691	−0.336396
$639$	6.24175	0.246920
$640$	−4.07936	−0.161251
$641$	−27.0361	−1.06786	−0.533931	−	0.845528i	$-0.679286\pi$
$641$	−27.0361	−1.06786	−0.533931	+	0.845528i	$0.679286\pi$
$642$	−7.25691	−0.286407
$643$	15.9105	0.627448	0.313724	−	0.949514i	$-0.398423\pi$
$643$	15.9105	0.627448	0.313724	+	0.949514i	$0.398423\pi$
$644$	0	0
$645$	14.1066	0.555447
$646$	−1.77140	−0.0696948
$647$	2.40227	0.0944428	0.0472214	−	0.998884i	$-0.484963\pi$
$647$	2.40227	0.0944428	0.0472214	+	0.998884i	$0.484963\pi$
$648$	−1.00000	−0.0392837
$649$	18.2712	0.717208
$650$	54.7216	2.14636
$651$	0	0
$652$	−20.1200	−0.787961
$653$	18.2297	0.713382	0.356691	−	0.934222i	$-0.383905\pi$
$653$	18.2297	0.713382	0.356691	+	0.934222i	$0.383905\pi$
$654$	2.53740	0.0992204
$655$	42.1883	1.64843
$656$	1.00000	0.0390434
$657$	−18.0341	−0.703579
$658$	0	0
$659$	5.41372	0.210889	0.105444	−	0.994425i	$-0.466374\pi$
$659$	5.41372	0.210889	0.105444	+	0.994425i	$0.466374\pi$
$660$	7.91608	0.308133
$661$	39.6518	1.54228	0.771138	−	0.636668i	$-0.219688\pi$
$661$	39.6518	1.54228	0.771138	+	0.636668i	$0.219688\pi$
$662$	−29.4448	−1.14441
$663$	−2.07285	−0.0805028
$664$	−2.43726	−0.0945841
$665$	0	0
$666$	11.9152	0.461704
$667$	−19.2599	−0.745746
$668$	−19.0794	−0.738203
$669$	6.91608	0.267391
$670$	16.3986	0.633532
$671$	21.0398	0.812231
$672$	0	0
$673$	−3.21450	−0.123910	−0.0619550	−	0.998079i	$-0.519734\pi$
$673$	−3.21450	−0.123910	−0.0619550	+	0.998079i	$0.519734\pi$
$674$	25.2266	0.971694
$675$	58.2060	2.24035
$676$	9.09644	0.349863
$677$	−15.6998	−0.603394	−0.301697	−	0.953404i	$-0.597553\pi$
$677$	−15.6998	−0.603394	−0.301697	+	0.953404i	$0.597553\pi$
$678$	−5.68080	−0.218170
$679$	0	0
$680$	1.79887	0.0689834
$681$	21.1606	0.810877
$682$	11.7640	0.450466
$683$	25.3014	0.968133	0.484066	−	0.875031i	$-0.339159\pi$
$683$	25.3014	0.968133	0.484066	+	0.875031i	$0.339159\pi$
$684$	8.03415	0.307193
$685$	−5.43968	−0.207840
$686$	0	0
$687$	−17.8709	−0.681816
$688$	−3.45804	−0.131837
$689$	−15.6025	−0.594408
$690$	17.9433	0.683091
$691$	−39.1902	−1.49087	−0.745433	−	0.666580i	$-0.767757\pi$
$691$	−39.1902	−1.49087	−0.745433	+	0.666580i	$0.767757\pi$
$692$	23.6838	0.900322
$693$	0	0
$694$	−25.6113	−0.972192
$695$	9.16001	0.347459
$696$	−4.37868	−0.165973
$697$	−0.440968	−0.0167028
$698$	−8.25601	−0.312495
$699$	19.8847	0.752110
$700$	0	0
$701$	10.0748	0.380520	0.190260	−	0.981734i	$-0.439067\pi$
$701$	10.0748	0.380520	0.190260	+	0.981734i	$0.439067\pi$
$702$	23.5034	0.887080
$703$	−23.9321	−0.902616
$704$	−1.94052	−0.0731361
$705$	−6.92625	−0.260858
$706$	26.8423	1.01022
$707$	0	0
$708$	9.41564	0.353861
$709$	−38.4537	−1.44416	−0.722079	−	0.691811i	$-0.756813\pi$
$709$	−38.4537	−1.44416	−0.722079	+	0.691811i	$0.756813\pi$
$710$	12.7312	0.477793
$711$	33.5601	1.25860
$712$	5.01707	0.188023
$713$	26.6653	0.998625
$714$	0	0
$715$	37.2110	1.39161
$716$	−10.7178	−0.400541
$717$	9.61396	0.359040
$718$	−0.384295	−0.0143418
$719$	−2.43637	−0.0908611	−0.0454306	−	0.998967i	$-0.514466\pi$
$719$	−2.43637	−0.0908611	−0.0454306	+	0.998967i	$0.514466\pi$
$720$	−8.15873	−0.304058
$721$	0	0
$722$	2.86312	0.106554
$723$	−12.1587	−0.452188
$724$	19.2381	0.714978
$725$	−50.9731	−1.89309
$726$	−7.23438	−0.268493
$727$	28.8804	1.07111	0.535557	−	0.844499i	$-0.320102\pi$
$727$	28.8804	1.07111	0.535557	+	0.844499i	$0.320102\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−36.7839	−1.36143
$731$	1.52488	0.0563999
$732$	10.8423	0.400744
$733$	51.7612	1.91184	0.955922	−	0.293620i	$-0.0948599\pi$
$733$	51.7612	1.91184	0.955922	+	0.293620i	$0.0948599\pi$
$734$	13.1841	0.486632
$735$	0	0
$736$	−4.39856	−0.162133
$737$	7.80066	0.287341
$738$	2.00000	0.0736210
$739$	22.5951	0.831176	0.415588	−	0.909553i	$-0.363576\pi$
$739$	22.5951	0.831176	0.415588	+	0.909553i	$0.363576\pi$
$740$	24.3032	0.893403
$741$	−18.8830	−0.693684
$742$	0	0
$743$	−25.6291	−0.940241	−0.470121	−	0.882602i	$-0.655790\pi$
$743$	−25.6291	−0.940241	−0.470121	+	0.882602i	$0.655790\pi$
$744$	6.06229	0.222254
$745$	−50.6515	−1.85573
$746$	−22.7718	−0.833734
$747$	−4.87453	−0.178350
$748$	0.855706	0.0312877
$749$	0	0
$750$	27.0919	0.989256
$751$	−18.3751	−0.670518	−0.335259	−	0.942126i	$-0.608824\pi$
$751$	−18.3751	−0.670518	−0.335259	+	0.942126i	$0.608824\pi$
$752$	1.69788	0.0619152
$753$	−21.7234	−0.791644
$754$	−20.5828	−0.749581
$755$	−48.7945	−1.77581
$756$	0	0
$757$	49.8133	1.81050	0.905248	−	0.424883i	$-0.139685\pi$
$757$	49.8133	1.81050	0.905248	+	0.424883i	$0.139685\pi$
$758$	−31.1870	−1.13276
$759$	8.53549	0.309819
$760$	16.3871	0.594423
$761$	−13.8893	−0.503487	−0.251743	−	0.967794i	$-0.581004\pi$
$761$	−13.8893	−0.503487	−0.251743	+	0.967794i	$0.581004\pi$
$762$	−14.3986	−0.521605
$763$	0	0
$764$	−2.13884	−0.0773807
$765$	3.59773	0.130076
$766$	−26.4933	−0.957240
$767$	44.2599	1.59813
$768$	−1.00000	−0.0360844
$769$	7.76562	0.280035	0.140018	−	0.990149i	$-0.455284\pi$
$769$	7.76562	0.280035	0.140018	+	0.990149i	$0.455284\pi$
$770$	0	0
$771$	25.4697	0.917268
$772$	14.9217	0.537044
$773$	−33.3345	−1.19896	−0.599480	−	0.800390i	$-0.704626\pi$
$773$	−33.3345	−1.19896	−0.599480	+	0.800390i	$0.704626\pi$
$774$	−6.91608	−0.248593
$775$	70.5723	2.53503
$776$	15.5402	0.557861
$777$	0	0
$778$	25.3741	0.909706
$779$	−4.01707	−0.143927
$780$	19.1758	0.686604
$781$	6.05612	0.216705
$782$	1.93962	0.0693608
$783$	−21.8934	−0.782406
$784$	0	0
$785$	−34.9269	−1.24659
$786$	10.3419	0.368883
$787$	−23.0605	−0.822020	−0.411010	−	0.911631i	$-0.634824\pi$
$787$	−23.0605	−0.822020	−0.411010	+	0.911631i	$0.634824\pi$
$788$	−22.2524	−0.792707
$789$	−0.982926	−0.0349931
$790$	68.4519	2.43541
$791$	0	0
$792$	−3.88104	−0.137907
$793$	50.9664	1.80987
$794$	−20.2409	−0.718323
$795$	−13.5402	−0.480222
$796$	−1.48248	−0.0525450
$797$	55.2752	1.95795	0.978974	−	0.203984i	$-0.0653890\pi$
$797$	55.2752	1.95795	0.978974	+	0.203984i	$0.0653890\pi$
$798$	0	0
$799$	−0.748708	−0.0264874
$800$	−11.6412	−0.411579
$801$	10.0341	0.354539
$802$	−24.1769	−0.853715
$803$	−17.4978	−0.617484
$804$	4.01988	0.141770
$805$	0	0
$806$	28.4969	1.00376
$807$	−16.5800	−0.583643
$808$	−13.7178	−0.482589
$809$	27.0605	0.951398	0.475699	−	0.879608i	$-0.342195\pi$
$809$	27.0605	0.951398	0.475699	+	0.879608i	$0.342195\pi$
$810$	−4.07936	−0.143334
$811$	28.0614	0.985370	0.492685	−	0.870208i	$-0.336015\pi$
$811$	28.0614	0.985370	0.492685	+	0.870208i	$0.336015\pi$
$812$	0	0
$813$	0.900754	0.0315908
$814$	11.5608	0.405207
$815$	−82.0769	−2.87503
$816$	0.440968	0.0154370
$817$	13.8912	0.485992
$818$	−0.369133	−0.0129065
$819$	0	0
$820$	4.07936	0.142458
$821$	1.96641	0.0686281	0.0343141	−	0.999411i	$-0.489075\pi$
$821$	1.96641	0.0686281	0.0343141	+	0.999411i	$0.489075\pi$
$822$	−1.33346	−0.0465099
$823$	−23.4278	−0.816641	−0.408320	−	0.912839i	$-0.633885\pi$
$823$	−23.4278	−0.816641	−0.408320	+	0.912839i	$0.633885\pi$
$824$	18.9803	0.661210
$825$	22.5900	0.786482
$826$	0	0
$827$	−35.6449	−1.23949	−0.619747	−	0.784801i	$-0.712765\pi$
$827$	−35.6449	−1.23949	−0.619747	+	0.784801i	$0.712765\pi$
$828$	−8.79712	−0.305721
$829$	−22.0945	−0.767375	−0.383687	−	0.923463i	$-0.625346\pi$
$829$	−22.0945	−0.767375	−0.383687	+	0.923463i	$0.625346\pi$
$830$	−9.94248	−0.345108
$831$	−22.7811	−0.790268
$832$	−4.70068	−0.162967
$833$	0	0
$834$	2.24545	0.0777536
$835$	−77.8317	−2.69348
$836$	7.79521	0.269603
$837$	30.3114	1.04772
$838$	23.1427	0.799452
$839$	−14.2759	−0.492860	−0.246430	−	0.969161i	$-0.579258\pi$
$839$	−14.2759	−0.492860	−0.246430	+	0.969161i	$0.579258\pi$
$840$	0	0
$841$	−9.82718	−0.338868
$842$	−3.35790	−0.115721
$843$	−22.3940	−0.771291
$844$	−23.8226	−0.820008
$845$	37.1077	1.27654
$846$	3.39575	0.116748
$847$	0	0
$848$	3.31920	0.113982
$849$	−8.25601	−0.283346
$850$	5.13339	0.176074
$851$	26.2048	0.898290
$852$	3.12087	0.106919
$853$	−31.3715	−1.07414	−0.537070	−	0.843538i	$-0.680469\pi$
$853$	−31.3715	−1.07414	−0.537070	+	0.843538i	$0.680469\pi$
$854$	0	0
$855$	32.7742	1.12085
$856$	7.25691	0.248036
$857$	−37.9251	−1.29550	−0.647748	−	0.761855i	$-0.724289\pi$
$857$	−37.9251	−1.29550	−0.647748	+	0.761855i	$0.724289\pi$
$858$	9.12177	0.311412
$859$	−37.0493	−1.26411	−0.632053	−	0.774925i	$-0.717788\pi$
$859$	−37.0493	−1.26411	−0.632053	+	0.774925i	$0.717788\pi$
$860$	−14.1066	−0.481031
$861$	0	0
$862$	14.4267	0.491375
$863$	−34.6451	−1.17933	−0.589666	−	0.807647i	$-0.700741\pi$
$863$	−34.6451	−1.17933	−0.589666	+	0.807647i	$0.700741\pi$
$864$	−5.00000	−0.170103
$865$	96.6147	3.28500
$866$	−17.0172	−0.578269
$867$	16.8055	0.570746
$868$	0	0
$869$	32.5620	1.10459
$870$	−17.8622	−0.605586
$871$	18.8962	0.640273
$872$	−2.53740	−0.0859274
$873$	31.0804	1.05191
$874$	17.6693	0.597675
$875$	0	0
$876$	−9.01707	−0.304659
$877$	32.4202	1.09475	0.547376	−	0.836887i	$-0.315627\pi$
$877$	32.4202	1.09475	0.547376	+	0.836887i	$0.315627\pi$
$878$	6.95198	0.234618
$879$	22.0938	0.745205
$880$	−7.91608	−0.266851
$881$	1.96496	0.0662010	0.0331005	−	0.999452i	$-0.489462\pi$
$881$	1.96496	0.0662010	0.0331005	+	0.999452i	$0.489462\pi$
$882$	0	0
$883$	31.8577	1.07210	0.536048	−	0.844188i	$-0.319917\pi$
$883$	31.8577	1.07210	0.536048	+	0.844188i	$0.319917\pi$
$884$	2.07285	0.0697175
$885$	38.4098	1.29113
$886$	6.93861	0.233107
$887$	42.1401	1.41493	0.707463	−	0.706751i	$-0.249840\pi$
$887$	42.1401	1.41493	0.707463	+	0.706751i	$0.249840\pi$
$888$	5.95759	0.199924
$889$	0	0
$890$	20.4665	0.686038
$891$	−1.94052	−0.0650098
$892$	−6.91608	−0.231568
$893$	−6.82049	−0.228239
$894$	−12.4165	−0.415271
$895$	−43.7216	−1.46145
$896$	0	0
$897$	20.6762	0.690360
$898$	6.34363	0.211690
$899$	−26.5448	−0.885319
$900$	−23.2824	−0.776080
$901$	−1.46366	−0.0487615
$902$	1.94052	0.0646122
$903$	0	0
$904$	5.68080	0.188941
$905$	78.4792	2.60874
$906$	−11.9613	−0.397388
$907$	48.2194	1.60110	0.800550	−	0.599266i	$-0.204541\pi$
$907$	48.2194	1.60110	0.800550	+	0.599266i	$0.204541\pi$
$908$	−21.1606	−0.702240
$909$	−27.4355	−0.909979
$910$	0	0
$911$	−11.5650	−0.383167	−0.191583	−	0.981476i	$-0.561362\pi$
$911$	−11.5650	−0.383167	−0.191583	+	0.981476i	$0.561362\pi$
$912$	4.01707	0.133019
$913$	−4.72956	−0.156525
$914$	0.102054	0.00337566
$915$	44.2298	1.46219
$916$	17.8709	0.590470
$917$	0	0
$918$	2.20484	0.0727705
$919$	10.6555	0.351492	0.175746	−	0.984436i	$-0.443766\pi$
$919$	10.6555	0.351492	0.175746	+	0.984436i	$0.443766\pi$
$920$	−17.9433	−0.591574
$921$	14.3382	0.472459
$922$	32.0692	1.05614
$923$	14.6702	0.482877
$924$	0	0
$925$	69.3536	2.28033
$926$	30.6907	1.00856
$927$	37.9606	1.24679
$928$	4.37868	0.143737
$929$	0.941368	0.0308853	0.0154426	−	0.999881i	$-0.495084\pi$
$929$	0.941368	0.0308853	0.0154426	+	0.999881i	$0.495084\pi$
$930$	24.7303	0.810938
$931$	0	0
$932$	−19.8847	−0.651346
$933$	−11.3049	−0.370107
$934$	16.2852	0.532869
$935$	3.49074	0.114159
$936$	−9.40137	−0.307293
$937$	−22.1066	−0.722191	−0.361096	−	0.932529i	$-0.617597\pi$
$937$	−22.1066	−0.722191	−0.361096	+	0.932529i	$0.617597\pi$
$938$	0	0
$939$	−18.6196	−0.607627
$940$	6.92625	0.225909
$941$	3.80359	0.123993	0.0619967	−	0.998076i	$-0.480253\pi$
$941$	3.80359	0.123993	0.0619967	+	0.998076i	$0.480253\pi$
$942$	−8.56184	−0.278960
$943$	4.39856	0.143237
$944$	−9.41564	−0.306453
$945$	0	0
$946$	−6.71040	−0.218174
$947$	−32.3212	−1.05030	−0.525148	−	0.851011i	$-0.675990\pi$
$947$	−32.3212	−1.05030	−0.525148	+	0.851011i	$0.675990\pi$
$948$	16.7800	0.544991
$949$	−42.3864	−1.37592
$950$	46.7636	1.51721
$951$	5.65547	0.183391
$952$	0	0
$953$	−52.2882	−1.69378	−0.846890	−	0.531768i	$-0.821528\pi$
$953$	−52.2882	−1.69378	−0.846890	+	0.531768i	$0.821528\pi$
$954$	6.63840	0.214926
$955$	−8.72512	−0.282338
$956$	−9.61396	−0.310938
$957$	−8.49691	−0.274666
$958$	−18.9208	−0.611303
$959$	0	0
$960$	−4.07936	−0.131661
$961$	5.75135	0.185527
$962$	28.0048	0.902910
$963$	14.5138	0.467701
$964$	12.1587	0.391606
$965$	60.8710	1.95951
$966$	0	0
$967$	−27.0071	−0.868489	−0.434244	−	0.900795i	$-0.642985\pi$
$967$	−27.0071	−0.868489	−0.434244	+	0.900795i	$0.642985\pi$
$968$	7.23438	0.232522
$969$	−1.77140	−0.0569056
$970$	63.3942	2.03546
$971$	−43.1053	−1.38331	−0.691657	−	0.722226i	$-0.743119\pi$
$971$	−43.1053	−1.38331	−0.691657	+	0.722226i	$0.743119\pi$
$972$	−16.0000	−0.513200
$973$	0	0
$974$	31.0190	0.993912
$975$	54.7216	1.75249
$976$	−10.8423	−0.347055
$977$	−36.4611	−1.16649	−0.583246	−	0.812295i	$-0.698218\pi$
$977$	−36.4611	−1.16649	−0.583246	+	0.812295i	$0.698218\pi$
$978$	−20.1200	−0.643367
$979$	9.73573	0.311155
$980$	0	0
$981$	−5.07481	−0.162026
$982$	14.5780	0.465203
$983$	45.2441	1.44306	0.721531	−	0.692382i	$-0.243439\pi$
$983$	45.2441	1.44306	0.721531	+	0.692382i	$0.243439\pi$
$984$	1.00000	0.0318788
$985$	−90.7754	−2.89235
$986$	−1.93086	−0.0614910
$987$	0	0
$988$	18.8830	0.600748
$989$	−15.2104	−0.483663
$990$	−15.8322	−0.503179
$991$	5.77314	0.183390	0.0916950	−	0.995787i	$-0.470772\pi$
$991$	5.77314	0.183390	0.0916950	+	0.995787i	$0.470772\pi$
$992$	−6.06229	−0.192478
$993$	−29.4448	−0.934404
$994$	0	0
$995$	−6.04757	−0.191721
$996$	−2.43726	−0.0772276
$997$	1.26253	0.0399846	0.0199923	−	0.999800i	$-0.493636\pi$
$997$	1.26253	0.0399846	0.0199923	+	0.999800i	$0.493636\pi$
$998$	−34.7266	−1.09925
$999$	29.7880	0.942450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bi.1.4		4
7.3	odd	6		574.2.e.f.247.4	yes	8
7.5	odd	6		574.2.e.f.165.4	✓	8
7.6	odd	2		4018.2.a.bk.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.f.165.4	✓	8	7.5	odd	6
574.2.e.f.247.4	yes	8	7.3	odd	6
4018.2.a.bi.1.4		4	1.1	even	1	trivial
4018.2.a.bk.1.1		4	7.6	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.07936 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.07936 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -4.07936 q^{10} -1.94052 q^{11} -1.00000 q^{12} -4.70068 q^{13} -4.07936 q^{15} +1.00000 q^{16} -0.440968 q^{17} +2.00000 q^{18} -4.01707 q^{19} +4.07936 q^{20} +1.94052 q^{22} +4.39856 q^{23} +1.00000 q^{24} +11.6412 q^{25} +4.70068 q^{26} +5.00000 q^{27} -4.37868 q^{29} +4.07936 q^{30} +6.06229 q^{31} -1.00000 q^{32} +1.94052 q^{33} +0.440968 q^{34} -2.00000 q^{36} +5.95759 q^{37} +4.01707 q^{38} +4.70068 q^{39} -4.07936 q^{40} +1.00000 q^{41} -3.45804 q^{43} -1.94052 q^{44} -8.15873 q^{45} -4.39856 q^{46} +1.69788 q^{47} -1.00000 q^{48} -11.6412 q^{50} +0.440968 q^{51} -4.70068 q^{52} +3.31920 q^{53} -5.00000 q^{54} -7.91608 q^{55} +4.01707 q^{57} +4.37868 q^{58} -9.41564 q^{59} -4.07936 q^{60} -10.8423 q^{61} -6.06229 q^{62} +1.00000 q^{64} -19.1758 q^{65} -1.94052 q^{66} -4.01988 q^{67} -0.440968 q^{68} -4.39856 q^{69} -3.12087 q^{71} +2.00000 q^{72} +9.01707 q^{73} -5.95759 q^{74} -11.6412 q^{75} -4.01707 q^{76} -4.70068 q^{78} -16.7800 q^{79} +4.07936 q^{80} +1.00000 q^{81} -1.00000 q^{82} +2.43726 q^{83} -1.79887 q^{85} +3.45804 q^{86} +4.37868 q^{87} +1.94052 q^{88} -5.01707 q^{89} +8.15873 q^{90} +4.39856 q^{92} -6.06229 q^{93} -1.69788 q^{94} -16.3871 q^{95} +1.00000 q^{96} -15.5402 q^{97} +3.88104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 4 q^{8} - 8 q^{9} + 3 q^{10} - 4 q^{12} + q^{13} + 3 q^{15} + 4 q^{16} + 3 q^{17} + 8 q^{18} - 2 q^{19} - 3 q^{20} - 9 q^{23} + 4 q^{24} + 19 q^{25} - q^{26} + 20 q^{27} - 18 q^{29} - 3 q^{30} + 19 q^{31} - 4 q^{32} - 3 q^{34} - 8 q^{36} + 2 q^{37} + 2 q^{38} - q^{39} + 3 q^{40} + 4 q^{41} + 5 q^{43} + 6 q^{45} + 9 q^{46} - 4 q^{48} - 19 q^{50} - 3 q^{51} + q^{52} + 6 q^{53} - 20 q^{54} + 6 q^{55} + 2 q^{57} + 18 q^{58} + 3 q^{59} + 3 q^{60} + q^{61} - 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} + 3 q^{68} + 9 q^{69} - 9 q^{71} + 8 q^{72} + 22 q^{73} - 2 q^{74} - 19 q^{75} - 2 q^{76} + q^{78} - 28 q^{79} - 3 q^{80} + 4 q^{81} - 4 q^{82} + 12 q^{83} - 24 q^{85} - 5 q^{86} + 18 q^{87} - 6 q^{89} - 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} + 4 q^{96} - 11 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 4 * q^8 - 8 * q^9 + 3 * q^10 - 4 * q^12 + q^13 + 3 * q^15 + 4 * q^16 + 3 * q^17 + 8 * q^18 - 2 * q^19 - 3 * q^20 - 9 * q^23 + 4 * q^24 + 19 * q^25 - q^26 + 20 * q^27 - 18 * q^29 - 3 * q^30 + 19 * q^31 - 4 * q^32 - 3 * q^34 - 8 * q^36 + 2 * q^37 + 2 * q^38 - q^39 + 3 * q^40 + 4 * q^41 + 5 * q^43 + 6 * q^45 + 9 * q^46 - 4 * q^48 - 19 * q^50 - 3 * q^51 + q^52 + 6 * q^53 - 20 * q^54 + 6 * q^55 + 2 * q^57 + 18 * q^58 + 3 * q^59 + 3 * q^60 + q^61 - 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 + 3 * q^68 + 9 * q^69 - 9 * q^71 + 8 * q^72 + 22 * q^73 - 2 * q^74 - 19 * q^75 - 2 * q^76 + q^78 - 28 * q^79 - 3 * q^80 + 4 * q^81 - 4 * q^82 + 12 * q^83 - 24 * q^85 - 5 * q^86 + 18 * q^87 - 6 * q^89 - 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 + 4 * q^96 - 11 * q^97

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