LMFDB - Embedded newform 4018.2.a.bc.1.2

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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} +3.82843 q^{5} +2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} +3.82843 q^{5} +2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +3.82843 q^{10} +2.24264 q^{11} +2.41421 q^{12} +3.41421 q^{13} +9.24264 q^{15} +1.00000 q^{16} -1.82843 q^{17} +2.82843 q^{18} -2.82843 q^{19} +3.82843 q^{20} +2.24264 q^{22} -5.65685 q^{23} +2.41421 q^{24} +9.65685 q^{25} +3.41421 q^{26} -0.414214 q^{27} -5.00000 q^{29} +9.24264 q^{30} -8.41421 q^{31} +1.00000 q^{32} +5.41421 q^{33} -1.82843 q^{34} +2.82843 q^{36} +9.41421 q^{37} -2.82843 q^{38} +8.24264 q^{39} +3.82843 q^{40} -1.00000 q^{41} -7.24264 q^{43} +2.24264 q^{44} +10.8284 q^{45} -5.65685 q^{46} +1.75736 q^{47} +2.41421 q^{48} +9.65685 q^{50} -4.41421 q^{51} +3.41421 q^{52} +9.48528 q^{53} -0.414214 q^{54} +8.58579 q^{55} -6.82843 q^{57} -5.00000 q^{58} -6.48528 q^{59} +9.24264 q^{60} -5.48528 q^{61} -8.41421 q^{62} +1.00000 q^{64} +13.0711 q^{65} +5.41421 q^{66} -12.8284 q^{67} -1.82843 q^{68} -13.6569 q^{69} -10.8995 q^{71} +2.82843 q^{72} +9.41421 q^{74} +23.3137 q^{75} -2.82843 q^{76} +8.24264 q^{78} -0.757359 q^{79} +3.82843 q^{80} -9.48528 q^{81} -1.00000 q^{82} +5.75736 q^{83} -7.00000 q^{85} -7.24264 q^{86} -12.0711 q^{87} +2.24264 q^{88} -1.82843 q^{89} +10.8284 q^{90} -5.65685 q^{92} -20.3137 q^{93} +1.75736 q^{94} -10.8284 q^{95} +2.41421 q^{96} +5.82843 q^{97} +6.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{13} + 10 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{20} - 4 q^{22} + 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} - 10 q^{29} + 10 q^{30} - 14 q^{31} + 2 q^{32} + 8 q^{33} + 2 q^{34} + 16 q^{37} + 8 q^{39} + 2 q^{40} - 2 q^{41} - 6 q^{43} - 4 q^{44} + 16 q^{45} + 12 q^{47} + 2 q^{48} + 8 q^{50} - 6 q^{51} + 4 q^{52} + 2 q^{53} + 2 q^{54} + 20 q^{55} - 8 q^{57} - 10 q^{58} + 4 q^{59} + 10 q^{60} + 6 q^{61} - 14 q^{62} + 2 q^{64} + 12 q^{65} + 8 q^{66} - 20 q^{67} + 2 q^{68} - 16 q^{69} - 2 q^{71} + 16 q^{74} + 24 q^{75} + 8 q^{78} - 10 q^{79} + 2 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} - 14 q^{85} - 6 q^{86} - 10 q^{87} - 4 q^{88} + 2 q^{89} + 16 q^{90} - 18 q^{93} + 12 q^{94} - 16 q^{95} + 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^13 + 10 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^20 - 4 * q^22 + 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 - 10 * q^29 + 10 * q^30 - 14 * q^31 + 2 * q^32 + 8 * q^33 + 2 * q^34 + 16 * q^37 + 8 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^43 - 4 * q^44 + 16 * q^45 + 12 * q^47 + 2 * q^48 + 8 * q^50 - 6 * q^51 + 4 * q^52 + 2 * q^53 + 2 * q^54 + 20 * q^55 - 8 * q^57 - 10 * q^58 + 4 * q^59 + 10 * q^60 + 6 * q^61 - 14 * q^62 + 2 * q^64 + 12 * q^65 + 8 * q^66 - 20 * q^67 + 2 * q^68 - 16 * q^69 - 2 * q^71 + 16 * q^74 + 24 * q^75 + 8 * q^78 - 10 * q^79 + 2 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 - 14 * q^85 - 6 * q^86 - 10 * q^87 - 4 * q^88 + 2 * q^89 + 16 * q^90 - 18 * q^93 + 12 * q^94 - 16 * q^95 + 2 * q^96 + 6 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.41421	1.39385	0.696923	−	0.717146i	$-0.254552\pi$
$3$	2.41421	1.39385	0.696923	+	0.717146i	$0.254552\pi$
$4$	1.00000	0.500000
$5$	3.82843	1.71212	0.856062	−	0.516873i	$-0.172904\pi$
$5$	3.82843	1.71212	0.856062	+	0.516873i	$0.172904\pi$
$6$	2.41421	0.985599
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.82843	0.942809
$10$	3.82843	1.21065
$11$	2.24264	0.676182	0.338091	−	0.941113i	$-0.390219\pi$
$11$	2.24264	0.676182	0.338091	+	0.941113i	$0.390219\pi$
$12$	2.41421	0.696923
$13$	3.41421	0.946932	0.473466	−	0.880812i	$-0.343003\pi$
$13$	3.41421	0.946932	0.473466	+	0.880812i	$0.343003\pi$
$14$	0	0
$15$	9.24264	2.38644
$16$	1.00000	0.250000
$17$	−1.82843	−0.443459	−0.221729	−	0.975108i	$-0.571170\pi$
$17$	−1.82843	−0.443459	−0.221729	+	0.975108i	$0.571170\pi$
$18$	2.82843	0.666667
$19$	−2.82843	−0.648886	−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843	−0.648886	−0.324443	+	0.945905i	$0.605177\pi$
$20$	3.82843	0.856062
$21$	0	0
$22$	2.24264	0.478133
$23$	−5.65685	−1.17954	−0.589768	−	0.807573i	$-0.700781\pi$
$23$	−5.65685	−1.17954	−0.589768	+	0.807573i	$0.700781\pi$
$24$	2.41421	0.492799
$25$	9.65685	1.93137
$26$	3.41421	0.669582
$27$	−0.414214	−0.0797154
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	9.24264	1.68747
$31$	−8.41421	−1.51124	−0.755619	−	0.655012i	$-0.772664\pi$
$31$	−8.41421	−1.51124	−0.755619	+	0.655012i	$0.772664\pi$
$32$	1.00000	0.176777
$33$	5.41421	0.942494
$34$	−1.82843	−0.313573
$35$	0	0
$36$	2.82843	0.471405
$37$	9.41421	1.54769	0.773844	−	0.633377i	$-0.218332\pi$
$37$	9.41421	1.54769	0.773844	+	0.633377i	$0.218332\pi$
$38$	−2.82843	−0.458831
$39$	8.24264	1.31988
$40$	3.82843	0.605327
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−7.24264	−1.10449	−0.552246	−	0.833681i	$-0.686229\pi$
$43$	−7.24264	−1.10449	−0.552246	+	0.833681i	$0.686229\pi$
$44$	2.24264	0.338091
$45$	10.8284	1.61421
$46$	−5.65685	−0.834058
$47$	1.75736	0.256337	0.128169	−	0.991752i	$-0.459090\pi$
$47$	1.75736	0.256337	0.128169	+	0.991752i	$0.459090\pi$
$48$	2.41421	0.348462
$49$	0	0
$50$	9.65685	1.36569
$51$	−4.41421	−0.618114
$52$	3.41421	0.473466
$53$	9.48528	1.30290	0.651452	−	0.758690i	$-0.274160\pi$
$53$	9.48528	1.30290	0.651452	+	0.758690i	$0.274160\pi$
$54$	−0.414214	−0.0563673
$55$	8.58579	1.15771
$56$	0	0
$57$	−6.82843	−0.904447
$58$	−5.00000	−0.656532
$59$	−6.48528	−0.844312	−0.422156	−	0.906523i	$-0.638727\pi$
$59$	−6.48528	−0.844312	−0.422156	+	0.906523i	$0.638727\pi$
$60$	9.24264	1.19322
$61$	−5.48528	−0.702318	−0.351159	−	0.936316i	$-0.614212\pi$
$61$	−5.48528	−0.702318	−0.351159	+	0.936316i	$0.614212\pi$
$62$	−8.41421	−1.06861
$63$	0	0
$64$	1.00000	0.125000
$65$	13.0711	1.62127
$66$	5.41421	0.666444
$67$	−12.8284	−1.56724	−0.783621	−	0.621239i	$-0.786629\pi$
$67$	−12.8284	−1.56724	−0.783621	+	0.621239i	$0.786629\pi$
$68$	−1.82843	−0.221729
$69$	−13.6569	−1.64409
$70$	0	0
$71$	−10.8995	−1.29353	−0.646766	−	0.762688i	$-0.723879\pi$
$71$	−10.8995	−1.29353	−0.646766	+	0.762688i	$0.723879\pi$
$72$	2.82843	0.333333
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	9.41421	1.09438
$75$	23.3137	2.69204
$76$	−2.82843	−0.324443
$77$	0	0
$78$	8.24264	0.933295
$79$	−0.757359	−0.0852096	−0.0426048	−	0.999092i	$-0.513566\pi$
$79$	−0.757359	−0.0852096	−0.0426048	+	0.999092i	$0.513566\pi$
$80$	3.82843	0.428031
$81$	−9.48528	−1.05392
$82$	−1.00000	−0.110432
$83$	5.75736	0.631952	0.315976	−	0.948767i	$-0.397668\pi$
$83$	5.75736	0.631952	0.315976	+	0.948767i	$0.397668\pi$
$84$	0	0
$85$	−7.00000	−0.759257
$86$	−7.24264	−0.780994
$87$	−12.0711	−1.29415
$88$	2.24264	0.239066
$89$	−1.82843	−0.193813	−0.0969064	−	0.995293i	$-0.530895\pi$
$89$	−1.82843	−0.193813	−0.0969064	+	0.995293i	$0.530895\pi$
$90$	10.8284	1.14142
$91$	0	0
$92$	−5.65685	−0.589768
$93$	−20.3137	−2.10643
$94$	1.75736	0.181258
$95$	−10.8284	−1.11097
$96$	2.41421	0.246400
$97$	5.82843	0.591787	0.295894	−	0.955221i	$-0.404383\pi$
$97$	5.82843	0.591787	0.295894	+	0.955221i	$0.404383\pi$
$98$	0	0
$99$	6.34315	0.637510
$100$	9.65685	0.965685
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−4.41421	−0.437072
$103$	−13.5858	−1.33865	−0.669324	−	0.742971i	$-0.733416\pi$
$103$	−13.5858	−1.33865	−0.669324	+	0.742971i	$0.733416\pi$
$104$	3.41421	0.334791
$105$	0	0
$106$	9.48528	0.921292
$107$	−10.8995	−1.05369	−0.526847	−	0.849960i	$-0.676626\pi$
$107$	−10.8995	−1.05369	−0.526847	+	0.849960i	$0.676626\pi$
$108$	−0.414214	−0.0398577
$109$	5.17157	0.495347	0.247673	−	0.968844i	$-0.420334\pi$
$109$	5.17157	0.495347	0.247673	+	0.968844i	$0.420334\pi$
$110$	8.58579	0.818623
$111$	22.7279	2.15724
$112$	0	0
$113$	11.0000	1.03479	0.517396	−	0.855746i	$-0.326901\pi$
$113$	11.0000	1.03479	0.517396	+	0.855746i	$0.326901\pi$
$114$	−6.82843	−0.639541
$115$	−21.6569	−2.01951
$116$	−5.00000	−0.464238
$117$	9.65685	0.892776
$118$	−6.48528	−0.597019
$119$	0	0
$120$	9.24264	0.843734
$121$	−5.97056	−0.542778
$122$	−5.48528	−0.496614
$123$	−2.41421	−0.217682
$124$	−8.41421	−0.755619
$125$	17.8284	1.59462
$126$	0	0
$127$	5.07107	0.449985	0.224992	−	0.974361i	$-0.427764\pi$
$127$	5.07107	0.449985	0.224992	+	0.974361i	$0.427764\pi$
$128$	1.00000	0.0883883
$129$	−17.4853	−1.53949
$130$	13.0711	1.14641
$131$	20.7279	1.81101	0.905503	−	0.424339i	$-0.139493\pi$
$131$	20.7279	1.81101	0.905503	+	0.424339i	$0.139493\pi$
$132$	5.41421	0.471247
$133$	0	0
$134$	−12.8284	−1.10821
$135$	−1.58579	−0.136483
$136$	−1.82843	−0.156786
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	−13.6569	−1.16255
$139$	22.4853	1.90718	0.953588	−	0.301113i	$-0.0973583\pi$
$139$	22.4853	1.90718	0.953588	+	0.301113i	$0.0973583\pi$
$140$	0	0
$141$	4.24264	0.357295
$142$	−10.8995	−0.914665
$143$	7.65685	0.640298
$144$	2.82843	0.235702
$145$	−19.1421	−1.58967
$146$	0	0
$147$	0	0
$148$	9.41421	0.773844
$149$	−11.4853	−0.940911	−0.470455	−	0.882424i	$-0.655910\pi$
$149$	−11.4853	−0.940911	−0.470455	+	0.882424i	$0.655910\pi$
$150$	23.3137	1.90356
$151$	11.2426	0.914913	0.457457	−	0.889232i	$-0.348761\pi$
$151$	11.2426	0.914913	0.457457	+	0.889232i	$0.348761\pi$
$152$	−2.82843	−0.229416
$153$	−5.17157	−0.418097
$154$	0	0
$155$	−32.2132	−2.58743
$156$	8.24264	0.659939
$157$	15.3137	1.22217	0.611083	−	0.791566i	$-0.290734\pi$
$157$	15.3137	1.22217	0.611083	+	0.791566i	$0.290734\pi$
$158$	−0.757359	−0.0602523
$159$	22.8995	1.81605
$160$	3.82843	0.302664
$161$	0	0
$162$	−9.48528	−0.745234
$163$	−9.31371	−0.729506	−0.364753	−	0.931104i	$-0.618847\pi$
$163$	−9.31371	−0.729506	−0.364753	+	0.931104i	$0.618847\pi$
$164$	−1.00000	−0.0780869
$165$	20.7279	1.61367
$166$	5.75736	0.446858
$167$	−1.65685	−0.128211	−0.0641056	−	0.997943i	$-0.520419\pi$
$167$	−1.65685	−0.128211	−0.0641056	+	0.997943i	$0.520419\pi$
$168$	0	0
$169$	−1.34315	−0.103319
$170$	−7.00000	−0.536875
$171$	−8.00000	−0.611775
$172$	−7.24264	−0.552246
$173$	18.3137	1.39237	0.696183	−	0.717865i	$-0.254880\pi$
$173$	18.3137	1.39237	0.696183	+	0.717865i	$0.254880\pi$
$174$	−12.0711	−0.915105
$175$	0	0
$176$	2.24264	0.169045
$177$	−15.6569	−1.17684
$178$	−1.82843	−0.137046
$179$	21.2132	1.58555	0.792775	−	0.609515i	$-0.208636\pi$
$179$	21.2132	1.58555	0.792775	+	0.609515i	$0.208636\pi$
$180$	10.8284	0.807103
$181$	2.10051	0.156129	0.0780647	−	0.996948i	$-0.475126\pi$
$181$	2.10051	0.156129	0.0780647	+	0.996948i	$0.475126\pi$
$182$	0	0
$183$	−13.2426	−0.978924
$184$	−5.65685	−0.417029
$185$	36.0416	2.64983
$186$	−20.3137	−1.48947
$187$	−4.10051	−0.299859
$188$	1.75736	0.128169
$189$	0	0
$190$	−10.8284	−0.785577
$191$	3.92893	0.284288	0.142144	−	0.989846i	$-0.454600\pi$
$191$	3.92893	0.284288	0.142144	+	0.989846i	$0.454600\pi$
$192$	2.41421	0.174231
$193$	−7.41421	−0.533687	−0.266843	−	0.963740i	$-0.585981\pi$
$193$	−7.41421	−0.533687	−0.266843	+	0.963740i	$0.585981\pi$
$194$	5.82843	0.418457
$195$	31.5563	2.25980
$196$	0	0
$197$	−23.3137	−1.66103	−0.830516	−	0.556994i	$-0.811955\pi$
$197$	−23.3137	−1.66103	−0.830516	+	0.556994i	$0.811955\pi$
$198$	6.34315	0.450788
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	9.65685	0.682843
$201$	−30.9706	−2.18450
$202$	10.0000	0.703598
$203$	0	0
$204$	−4.41421	−0.309057
$205$	−3.82843	−0.267389
$206$	−13.5858	−0.946567
$207$	−16.0000	−1.11208
$208$	3.41421	0.236733
$209$	−6.34315	−0.438765
$210$	0	0
$211$	17.6569	1.21555	0.607774	−	0.794110i	$-0.292063\pi$
$211$	17.6569	1.21555	0.607774	+	0.794110i	$0.292063\pi$
$212$	9.48528	0.651452
$213$	−26.3137	−1.80299
$214$	−10.8995	−0.745074
$215$	−27.7279	−1.89103
$216$	−0.414214	−0.0281837
$217$	0	0
$218$	5.17157	0.350263
$219$	0	0
$220$	8.58579	0.578854
$221$	−6.24264	−0.419925
$222$	22.7279	1.52540
$223$	8.55635	0.572976	0.286488	−	0.958084i	$-0.407512\pi$
$223$	8.55635	0.572976	0.286488	+	0.958084i	$0.407512\pi$
$224$	0	0
$225$	27.3137	1.82091
$226$	11.0000	0.731709
$227$	1.72792	0.114686	0.0573431	−	0.998355i	$-0.481737\pi$
$227$	1.72792	0.114686	0.0573431	+	0.998355i	$0.481737\pi$
$228$	−6.82843	−0.452224
$229$	−1.07107	−0.0707782	−0.0353891	−	0.999374i	$-0.511267\pi$
$229$	−1.07107	−0.0707782	−0.0353891	+	0.999374i	$0.511267\pi$
$230$	−21.6569	−1.42801
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−25.8995	−1.69673	−0.848366	−	0.529410i	$-0.822413\pi$
$233$	−25.8995	−1.69673	−0.848366	+	0.529410i	$0.822413\pi$
$234$	9.65685	0.631288
$235$	6.72792	0.438881
$236$	−6.48528	−0.422156
$237$	−1.82843	−0.118769
$238$	0	0
$239$	28.4853	1.84256	0.921280	−	0.388900i	$-0.127145\pi$
$239$	28.4853	1.84256	0.921280	+	0.388900i	$0.127145\pi$
$240$	9.24264	0.596610
$241$	11.5563	0.744410	0.372205	−	0.928151i	$-0.378602\pi$
$241$	11.5563	0.744410	0.372205	+	0.928151i	$0.378602\pi$
$242$	−5.97056	−0.383802
$243$	−21.6569	−1.38929
$244$	−5.48528	−0.351159
$245$	0	0
$246$	−2.41421	−0.153925
$247$	−9.65685	−0.614451
$248$	−8.41421	−0.534303
$249$	13.8995	0.880845
$250$	17.8284	1.12757
$251$	−4.24264	−0.267793	−0.133897	−	0.990995i	$-0.542749\pi$
$251$	−4.24264	−0.267793	−0.133897	+	0.990995i	$0.542749\pi$
$252$	0	0
$253$	−12.6863	−0.797580
$254$	5.07107	0.318187
$255$	−16.8995	−1.05829
$256$	1.00000	0.0625000
$257$	11.1421	0.695027	0.347514	−	0.937675i	$-0.387026\pi$
$257$	11.1421	0.695027	0.347514	+	0.937675i	$0.387026\pi$
$258$	−17.4853	−1.08859
$259$	0	0
$260$	13.0711	0.810633
$261$	−14.1421	−0.875376
$262$	20.7279	1.28058
$263$	−3.31371	−0.204332	−0.102166	−	0.994767i	$-0.532577\pi$
$263$	−3.31371	−0.204332	−0.102166	+	0.994767i	$0.532577\pi$
$264$	5.41421	0.333222
$265$	36.3137	2.23073
$266$	0	0
$267$	−4.41421	−0.270145
$268$	−12.8284	−0.783621
$269$	−16.6274	−1.01379	−0.506896	−	0.862007i	$-0.669207\pi$
$269$	−16.6274	−1.01379	−0.506896	+	0.862007i	$0.669207\pi$
$270$	−1.58579	−0.0965079
$271$	−6.00000	−0.364474	−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000	−0.364474	−0.182237	+	0.983255i	$0.558334\pi$
$272$	−1.82843	−0.110865
$273$	0	0
$274$	−4.00000	−0.241649
$275$	21.6569	1.30596
$276$	−13.6569	−0.822046
$277$	18.9706	1.13983	0.569915	−	0.821703i	$-0.306976\pi$
$277$	18.9706	1.13983	0.569915	+	0.821703i	$0.306976\pi$
$278$	22.4853	1.34858
$279$	−23.7990	−1.42481
$280$	0	0
$281$	10.9706	0.654449	0.327224	−	0.944947i	$-0.393887\pi$
$281$	10.9706	0.654449	0.327224	+	0.944947i	$0.393887\pi$
$282$	4.24264	0.252646
$283$	9.51472	0.565591	0.282796	−	0.959180i	$-0.408738\pi$
$283$	9.51472	0.565591	0.282796	+	0.959180i	$0.408738\pi$
$284$	−10.8995	−0.646766
$285$	−26.1421	−1.54853
$286$	7.65685	0.452759
$287$	0	0
$288$	2.82843	0.166667
$289$	−13.6569	−0.803344
$290$	−19.1421	−1.12406
$291$	14.0711	0.824861
$292$	0	0
$293$	0.343146	0.0200468	0.0100234	−	0.999950i	$-0.496809\pi$
$293$	0.343146	0.0200468	0.0100234	+	0.999950i	$0.496809\pi$
$294$	0	0
$295$	−24.8284	−1.44557
$296$	9.41421	0.547190
$297$	−0.928932	−0.0539021
$298$	−11.4853	−0.665324
$299$	−19.3137	−1.11694
$300$	23.3137	1.34602
$301$	0	0
$302$	11.2426	0.646941
$303$	24.1421	1.38693
$304$	−2.82843	−0.162221
$305$	−21.0000	−1.20246
$306$	−5.17157	−0.295639
$307$	8.97056	0.511977	0.255989	−	0.966680i	$-0.417599\pi$
$307$	8.97056	0.511977	0.255989	+	0.966680i	$0.417599\pi$
$308$	0	0
$309$	−32.7990	−1.86587
$310$	−32.2132	−1.82959
$311$	−8.14214	−0.461698	−0.230849	−	0.972990i	$-0.574150\pi$
$311$	−8.14214	−0.461698	−0.230849	+	0.972990i	$0.574150\pi$
$312$	8.24264	0.466648
$313$	−8.68629	−0.490978	−0.245489	−	0.969399i	$-0.578949\pi$
$313$	−8.68629	−0.490978	−0.245489	+	0.969399i	$0.578949\pi$
$314$	15.3137	0.864203
$315$	0	0
$316$	−0.757359	−0.0426048
$317$	−30.6274	−1.72021	−0.860104	−	0.510119i	$-0.829601\pi$
$317$	−30.6274	−1.72021	−0.860104	+	0.510119i	$0.829601\pi$
$318$	22.8995	1.28414
$319$	−11.2132	−0.627819
$320$	3.82843	0.214016
$321$	−26.3137	−1.46869
$322$	0	0
$323$	5.17157	0.287754
$324$	−9.48528	−0.526960
$325$	32.9706	1.82888
$326$	−9.31371	−0.515839
$327$	12.4853	0.690438
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	20.7279	1.14103
$331$	−28.0416	−1.54131	−0.770654	−	0.637254i	$-0.780070\pi$
$331$	−28.0416	−1.54131	−0.770654	+	0.637254i	$0.780070\pi$
$332$	5.75736	0.315976
$333$	26.6274	1.45917
$334$	−1.65685	−0.0906590
$335$	−49.1127	−2.68331
$336$	0	0
$337$	34.6569	1.88788	0.943940	−	0.330118i	$-0.107089\pi$
$337$	34.6569	1.88788	0.943940	+	0.330118i	$0.107089\pi$
$338$	−1.34315	−0.0730575
$339$	26.5563	1.44234
$340$	−7.00000	−0.379628
$341$	−18.8701	−1.02187
$342$	−8.00000	−0.432590
$343$	0	0
$344$	−7.24264	−0.390497
$345$	−52.2843	−2.81489
$346$	18.3137	0.984551
$347$	−28.2843	−1.51838	−0.759190	−	0.650870i	$-0.774404\pi$
$347$	−28.2843	−1.51838	−0.759190	+	0.650870i	$0.774404\pi$
$348$	−12.0711	−0.647077
$349$	24.4853	1.31067	0.655334	−	0.755340i	$-0.272528\pi$
$349$	24.4853	1.31067	0.655334	+	0.755340i	$0.272528\pi$
$350$	0	0
$351$	−1.41421	−0.0754851
$352$	2.24264	0.119533
$353$	28.0000	1.49029	0.745145	−	0.666903i	$-0.232380\pi$
$353$	28.0000	1.49029	0.745145	+	0.666903i	$0.232380\pi$
$354$	−15.6569	−0.832152
$355$	−41.7279	−2.21469
$356$	−1.82843	−0.0969064
$357$	0	0
$358$	21.2132	1.12115
$359$	34.8701	1.84037	0.920186	−	0.391482i	$-0.128038\pi$
$359$	34.8701	1.84037	0.920186	+	0.391482i	$0.128038\pi$
$360$	10.8284	0.570708
$361$	−11.0000	−0.578947
$362$	2.10051	0.110400
$363$	−14.4142	−0.756550
$364$	0	0
$365$	0	0
$366$	−13.2426	−0.692204
$367$	−15.9289	−0.831483	−0.415742	−	0.909483i	$-0.636478\pi$
$367$	−15.9289	−0.831483	−0.415742	+	0.909483i	$0.636478\pi$
$368$	−5.65685	−0.294884
$369$	−2.82843	−0.147242
$370$	36.0416	1.87372
$371$	0	0
$372$	−20.3137	−1.05322
$373$	13.4142	0.694562	0.347281	−	0.937761i	$-0.387105\pi$
$373$	13.4142	0.694562	0.347281	+	0.937761i	$0.387105\pi$
$374$	−4.10051	−0.212032
$375$	43.0416	2.22266
$376$	1.75736	0.0906289
$377$	−17.0711	−0.879205
$378$	0	0
$379$	31.7279	1.62975	0.814877	−	0.579634i	$-0.196804\pi$
$379$	31.7279	1.62975	0.814877	+	0.579634i	$0.196804\pi$
$380$	−10.8284	−0.555487
$381$	12.2426	0.627209
$382$	3.92893	0.201022
$383$	−10.7279	−0.548171	−0.274086	−	0.961705i	$-0.588375\pi$
$383$	−10.7279	−0.548171	−0.274086	+	0.961705i	$0.588375\pi$
$384$	2.41421	0.123200
$385$	0	0
$386$	−7.41421	−0.377374
$387$	−20.4853	−1.04133
$388$	5.82843	0.295894
$389$	38.9706	1.97589	0.987943	−	0.154818i	$-0.0494792\pi$
$389$	38.9706	1.97589	0.987943	+	0.154818i	$0.0494792\pi$
$390$	31.5563	1.59792
$391$	10.3431	0.523075
$392$	0	0
$393$	50.0416	2.52427
$394$	−23.3137	−1.17453
$395$	−2.89949	−0.145889
$396$	6.34315	0.318755
$397$	34.7279	1.74294	0.871472	−	0.490445i	$-0.163166\pi$
$397$	34.7279	1.74294	0.871472	+	0.490445i	$0.163166\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	9.65685	0.482843
$401$	−17.6274	−0.880271	−0.440136	−	0.897931i	$-0.645070\pi$
$401$	−17.6274	−0.880271	−0.440136	+	0.897931i	$0.645070\pi$
$402$	−30.9706	−1.54467
$403$	−28.7279	−1.43104
$404$	10.0000	0.497519
$405$	−36.3137	−1.80444
$406$	0	0
$407$	21.1127	1.04652
$408$	−4.41421	−0.218536
$409$	37.8995	1.87401	0.937005	−	0.349317i	$-0.113586\pi$
$409$	37.8995	1.87401	0.937005	+	0.349317i	$0.113586\pi$
$410$	−3.82843	−0.189073
$411$	−9.65685	−0.476337
$412$	−13.5858	−0.669324
$413$	0	0
$414$	−16.0000	−0.786357
$415$	22.0416	1.08198
$416$	3.41421	0.167396
$417$	54.2843	2.65831
$418$	−6.34315	−0.310253
$419$	24.0416	1.17451	0.587255	−	0.809402i	$-0.300208\pi$
$419$	24.0416	1.17451	0.587255	+	0.809402i	$0.300208\pi$
$420$	0	0
$421$	15.9706	0.778358	0.389179	−	0.921162i	$-0.372759\pi$
$421$	15.9706	0.778358	0.389179	+	0.921162i	$0.372759\pi$
$422$	17.6569	0.859522
$423$	4.97056	0.241677
$424$	9.48528	0.460646
$425$	−17.6569	−0.856483
$426$	−26.3137	−1.27490
$427$	0	0
$428$	−10.8995	−0.526847
$429$	18.4853	0.892478
$430$	−27.7279	−1.33716
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−0.414214	−0.0199289
$433$	−30.6274	−1.47186	−0.735930	−	0.677058i	$-0.763255\pi$
$433$	−30.6274	−1.47186	−0.735930	+	0.677058i	$0.763255\pi$
$434$	0	0
$435$	−46.2132	−2.21575
$436$	5.17157	0.247673
$437$	16.0000	0.765384
$438$	0	0
$439$	−16.1421	−0.770422	−0.385211	−	0.922829i	$-0.625871\pi$
$439$	−16.1421	−0.770422	−0.385211	+	0.922829i	$0.625871\pi$
$440$	8.58579	0.409311
$441$	0	0
$442$	−6.24264	−0.296932
$443$	−24.8995	−1.18301	−0.591505	−	0.806301i	$-0.701466\pi$
$443$	−24.8995	−1.18301	−0.591505	+	0.806301i	$0.701466\pi$
$444$	22.7279	1.07862
$445$	−7.00000	−0.331832
$446$	8.55635	0.405155
$447$	−27.7279	−1.31149
$448$	0	0
$449$	19.8284	0.935761	0.467881	−	0.883792i	$-0.345018\pi$
$449$	19.8284	0.935761	0.467881	+	0.883792i	$0.345018\pi$
$450$	27.3137	1.28758
$451$	−2.24264	−0.105602
$452$	11.0000	0.517396
$453$	27.1421	1.27525
$454$	1.72792	0.0810954
$455$	0	0
$456$	−6.82843	−0.319770
$457$	−13.4142	−0.627490	−0.313745	−	0.949507i	$-0.601584\pi$
$457$	−13.4142	−0.627490	−0.313745	+	0.949507i	$0.601584\pi$
$458$	−1.07107	−0.0500477
$459$	0.757359	0.0353505
$460$	−21.6569	−1.00976
$461$	−10.4558	−0.486977	−0.243489	−	0.969904i	$-0.578292\pi$
$461$	−10.4558	−0.486977	−0.243489	+	0.969904i	$0.578292\pi$
$462$	0	0
$463$	35.3137	1.64117	0.820584	−	0.571527i	$-0.193649\pi$
$463$	35.3137	1.64117	0.820584	+	0.571527i	$0.193649\pi$
$464$	−5.00000	−0.232119
$465$	−77.7696	−3.60648
$466$	−25.8995	−1.19977
$467$	20.8284	0.963825	0.481912	−	0.876219i	$-0.339942\pi$
$467$	20.8284	0.963825	0.481912	+	0.876219i	$0.339942\pi$
$468$	9.65685	0.446388
$469$	0	0
$470$	6.72792	0.310336
$471$	36.9706	1.70351
$472$	−6.48528	−0.298509
$473$	−16.2426	−0.746837
$474$	−1.82843	−0.0839824
$475$	−27.3137	−1.25324
$476$	0	0
$477$	26.8284	1.22839
$478$	28.4853	1.30289
$479$	−6.24264	−0.285234	−0.142617	−	0.989778i	$-0.545552\pi$
$479$	−6.24264	−0.285234	−0.142617	+	0.989778i	$0.545552\pi$
$480$	9.24264	0.421867
$481$	32.1421	1.46556
$482$	11.5563	0.526377
$483$	0	0
$484$	−5.97056	−0.271389
$485$	22.3137	1.01321
$486$	−21.6569	−0.982375
$487$	7.55635	0.342411	0.171205	−	0.985235i	$-0.445234\pi$
$487$	7.55635	0.342411	0.171205	+	0.985235i	$0.445234\pi$
$488$	−5.48528	−0.248307
$489$	−22.4853	−1.01682
$490$	0	0
$491$	−19.2426	−0.868408	−0.434204	−	0.900815i	$-0.642970\pi$
$491$	−19.2426	−0.868408	−0.434204	+	0.900815i	$0.642970\pi$
$492$	−2.41421	−0.108841
$493$	9.14214	0.411741
$494$	−9.65685	−0.434482
$495$	24.2843	1.09150
$496$	−8.41421	−0.377809
$497$	0	0
$498$	13.8995	0.622851
$499$	−3.85786	−0.172702	−0.0863509	−	0.996265i	$-0.527521\pi$
$499$	−3.85786	−0.172702	−0.0863509	+	0.996265i	$0.527521\pi$
$500$	17.8284	0.797311
$501$	−4.00000	−0.178707
$502$	−4.24264	−0.189358
$503$	23.3137	1.03951	0.519753	−	0.854316i	$-0.326024\pi$
$503$	23.3137	1.03951	0.519753	+	0.854316i	$0.326024\pi$
$504$	0	0
$505$	38.2843	1.70363
$506$	−12.6863	−0.563974
$507$	−3.24264	−0.144011
$508$	5.07107	0.224992
$509$	−29.6569	−1.31452	−0.657258	−	0.753665i	$-0.728284\pi$
$509$	−29.6569	−1.31452	−0.657258	+	0.753665i	$0.728284\pi$
$510$	−16.8995	−0.748322
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.17157	0.0517262
$514$	11.1421	0.491459
$515$	−52.0122	−2.29193
$516$	−17.4853	−0.769747
$517$	3.94113	0.173331
$518$	0	0
$519$	44.2132	1.94074
$520$	13.0711	0.573204
$521$	12.4853	0.546990	0.273495	−	0.961873i	$-0.411820\pi$
$521$	12.4853	0.546990	0.273495	+	0.961873i	$0.411820\pi$
$522$	−14.1421	−0.618984
$523$	−9.65685	−0.422265	−0.211132	−	0.977457i	$-0.567715\pi$
$523$	−9.65685	−0.422265	−0.211132	+	0.977457i	$0.567715\pi$
$524$	20.7279	0.905503
$525$	0	0
$526$	−3.31371	−0.144485
$527$	15.3848	0.670171
$528$	5.41421	0.235623
$529$	9.00000	0.391304
$530$	36.3137	1.57737
$531$	−18.3431	−0.796025
$532$	0	0
$533$	−3.41421	−0.147886
$534$	−4.41421	−0.191022
$535$	−41.7279	−1.80406
$536$	−12.8284	−0.554104
$537$	51.2132	2.21001
$538$	−16.6274	−0.716859
$539$	0	0
$540$	−1.58579	−0.0682414
$541$	−2.97056	−0.127714	−0.0638572	−	0.997959i	$-0.520340\pi$
$541$	−2.97056	−0.127714	−0.0638572	+	0.997959i	$0.520340\pi$
$542$	−6.00000	−0.257722
$543$	5.07107	0.217620
$544$	−1.82843	−0.0783932
$545$	19.7990	0.848096
$546$	0	0
$547$	7.85786	0.335978	0.167989	−	0.985789i	$-0.446273\pi$
$547$	7.85786	0.335978	0.167989	+	0.985789i	$0.446273\pi$
$548$	−4.00000	−0.170872
$549$	−15.5147	−0.662152
$550$	21.6569	0.923451
$551$	14.1421	0.602475
$552$	−13.6569	−0.581274
$553$	0	0
$554$	18.9706	0.805982
$555$	87.0122	3.69346
$556$	22.4853	0.953588
$557$	−25.3431	−1.07382	−0.536912	−	0.843638i	$-0.680409\pi$
$557$	−25.3431	−1.07382	−0.536912	+	0.843638i	$0.680409\pi$
$558$	−23.7990	−1.00749
$559$	−24.7279	−1.04588
$560$	0	0
$561$	−9.89949	−0.417957
$562$	10.9706	0.462765
$563$	40.6274	1.71224	0.856121	−	0.516776i	$-0.172868\pi$
$563$	40.6274	1.71224	0.856121	+	0.516776i	$0.172868\pi$
$564$	4.24264	0.178647
$565$	42.1127	1.77169
$566$	9.51472	0.399933
$567$	0	0
$568$	−10.8995	−0.457333
$569$	24.1127	1.01086	0.505428	−	0.862869i	$-0.331334\pi$
$569$	24.1127	1.01086	0.505428	+	0.862869i	$0.331334\pi$
$570$	−26.1421	−1.09497
$571$	−3.02944	−0.126778	−0.0633890	−	0.997989i	$-0.520191\pi$
$571$	−3.02944	−0.126778	−0.0633890	+	0.997989i	$0.520191\pi$
$572$	7.65685	0.320149
$573$	9.48528	0.396253
$574$	0	0
$575$	−54.6274	−2.27812
$576$	2.82843	0.117851
$577$	−24.2843	−1.01097	−0.505484	−	0.862836i	$-0.668686\pi$
$577$	−24.2843	−1.01097	−0.505484	+	0.862836i	$0.668686\pi$
$578$	−13.6569	−0.568050
$579$	−17.8995	−0.743878
$580$	−19.1421	−0.794834
$581$	0	0
$582$	14.0711	0.583265
$583$	21.2721	0.880999
$584$	0	0
$585$	36.9706	1.52854
$586$	0.343146	0.0141752
$587$	9.24264	0.381485	0.190742	−	0.981640i	$-0.438911\pi$
$587$	9.24264	0.381485	0.190742	+	0.981640i	$0.438911\pi$
$588$	0	0
$589$	23.7990	0.980620
$590$	−24.8284	−1.02217
$591$	−56.2843	−2.31523
$592$	9.41421	0.386922
$593$	−35.3431	−1.45137	−0.725685	−	0.688028i	$-0.758477\pi$
$593$	−35.3431	−1.45137	−0.725685	+	0.688028i	$0.758477\pi$
$594$	−0.928932	−0.0381145
$595$	0	0
$596$	−11.4853	−0.470455
$597$	−9.65685	−0.395229
$598$	−19.3137	−0.789796
$599$	44.2426	1.80771	0.903853	−	0.427844i	$-0.140727\pi$
$599$	44.2426	1.80771	0.903853	+	0.427844i	$0.140727\pi$
$600$	23.3137	0.951778
$601$	26.3137	1.07336	0.536679	−	0.843786i	$-0.319679\pi$
$601$	26.3137	1.07336	0.536679	+	0.843786i	$0.319679\pi$
$602$	0	0
$603$	−36.2843	−1.47761
$604$	11.2426	0.457457
$605$	−22.8579	−0.929304
$606$	24.1421	0.980707
$607$	−37.0416	−1.50347	−0.751737	−	0.659463i	$-0.770784\pi$
$607$	−37.0416	−1.50347	−0.751737	+	0.659463i	$0.770784\pi$
$608$	−2.82843	−0.114708
$609$	0	0
$610$	−21.0000	−0.850265
$611$	6.00000	0.242734
$612$	−5.17157	−0.209048
$613$	−13.7574	−0.555655	−0.277827	−	0.960631i	$-0.589614\pi$
$613$	−13.7574	−0.555655	−0.277827	+	0.960631i	$0.589614\pi$
$614$	8.97056	0.362022
$615$	−9.24264	−0.372699
$616$	0	0
$617$	−15.7990	−0.636043	−0.318022	−	0.948083i	$-0.603018\pi$
$617$	−15.7990	−0.636043	−0.318022	+	0.948083i	$0.603018\pi$
$618$	−32.7990	−1.31937
$619$	−35.0711	−1.40963	−0.704813	−	0.709394i	$-0.748969\pi$
$619$	−35.0711	−1.40963	−0.704813	+	0.709394i	$0.748969\pi$
$620$	−32.2132	−1.29371
$621$	2.34315	0.0940272
$622$	−8.14214	−0.326470
$623$	0	0
$624$	8.24264	0.329970
$625$	19.9706	0.798823
$626$	−8.68629	−0.347174
$627$	−15.3137	−0.611571
$628$	15.3137	0.611083
$629$	−17.2132	−0.686335
$630$	0	0
$631$	−28.5858	−1.13798	−0.568991	−	0.822344i	$-0.692666\pi$
$631$	−28.5858	−1.13798	−0.568991	+	0.822344i	$0.692666\pi$
$632$	−0.757359	−0.0301261
$633$	42.6274	1.69429
$634$	−30.6274	−1.21637
$635$	19.4142	0.770430
$636$	22.8995	0.908024
$637$	0	0
$638$	−11.2132	−0.443935
$639$	−30.8284	−1.21955
$640$	3.82843	0.151332
$641$	−46.6690	−1.84332	−0.921658	−	0.388003i	$-0.873165\pi$
$641$	−46.6690	−1.84332	−0.921658	+	0.388003i	$0.873165\pi$
$642$	−26.3137	−1.03852
$643$	8.41421	0.331824	0.165912	−	0.986141i	$-0.446943\pi$
$643$	8.41421	0.331824	0.165912	+	0.986141i	$0.446943\pi$
$644$	0	0
$645$	−66.9411	−2.63580
$646$	5.17157	0.203473
$647$	−4.61522	−0.181443	−0.0907216	−	0.995876i	$-0.528917\pi$
$647$	−4.61522	−0.181443	−0.0907216	+	0.995876i	$0.528917\pi$
$648$	−9.48528	−0.372617
$649$	−14.5442	−0.570908
$650$	32.9706	1.29321
$651$	0	0
$652$	−9.31371	−0.364753
$653$	−0.514719	−0.0201425	−0.0100712	−	0.999949i	$-0.503206\pi$
$653$	−0.514719	−0.0201425	−0.0100712	+	0.999949i	$0.503206\pi$
$654$	12.4853	0.488213
$655$	79.3553	3.10067
$656$	−1.00000	−0.0390434
$657$	0	0
$658$	0	0
$659$	−37.6569	−1.46690	−0.733451	−	0.679742i	$-0.762092\pi$
$659$	−37.6569	−1.46690	−0.733451	+	0.679742i	$0.762092\pi$
$660$	20.7279	0.806833
$661$	−43.7990	−1.70358	−0.851792	−	0.523881i	$-0.824484\pi$
$661$	−43.7990	−1.70358	−0.851792	+	0.523881i	$0.824484\pi$
$662$	−28.0416	−1.08987
$663$	−15.0711	−0.585312
$664$	5.75736	0.223429
$665$	0	0
$666$	26.6274	1.03179
$667$	28.2843	1.09517
$668$	−1.65685	−0.0641056
$669$	20.6569	0.798640
$670$	−49.1127	−1.89739
$671$	−12.3015	−0.474895
$672$	0	0
$673$	−31.0711	−1.19770	−0.598851	−	0.800861i	$-0.704376\pi$
$673$	−31.0711	−1.19770	−0.598851	+	0.800861i	$0.704376\pi$
$674$	34.6569	1.33493
$675$	−4.00000	−0.153960
$676$	−1.34315	−0.0516595
$677$	−14.1421	−0.543526	−0.271763	−	0.962364i	$-0.587607\pi$
$677$	−14.1421	−0.543526	−0.271763	+	0.962364i	$0.587607\pi$
$678$	26.5563	1.01989
$679$	0	0
$680$	−7.00000	−0.268438
$681$	4.17157	0.159855
$682$	−18.8701	−0.722572
$683$	34.3431	1.31410	0.657052	−	0.753845i	$-0.271803\pi$
$683$	34.3431	1.31410	0.657052	+	0.753845i	$0.271803\pi$
$684$	−8.00000	−0.305888
$685$	−15.3137	−0.585107
$686$	0	0
$687$	−2.58579	−0.0986539
$688$	−7.24264	−0.276123
$689$	32.3848	1.23376
$690$	−52.2843	−1.99043
$691$	38.6985	1.47216	0.736080	−	0.676895i	$-0.236675\pi$
$691$	38.6985	1.47216	0.736080	+	0.676895i	$0.236675\pi$
$692$	18.3137	0.696183
$693$	0	0
$694$	−28.2843	−1.07366
$695$	86.0833	3.26532
$696$	−12.0711	−0.457553
$697$	1.82843	0.0692566
$698$	24.4853	0.926782
$699$	−62.5269	−2.36499
$700$	0	0
$701$	−33.6569	−1.27120	−0.635601	−	0.772018i	$-0.719248\pi$
$701$	−33.6569	−1.27120	−0.635601	+	0.772018i	$0.719248\pi$
$702$	−1.41421	−0.0533761
$703$	−26.6274	−1.00427
$704$	2.24264	0.0845227
$705$	16.2426	0.611733
$706$	28.0000	1.05379
$707$	0	0
$708$	−15.6569	−0.588421
$709$	−21.6274	−0.812235	−0.406117	−	0.913821i	$-0.633118\pi$
$709$	−21.6274	−0.812235	−0.406117	+	0.913821i	$0.633118\pi$
$710$	−41.7279	−1.56602
$711$	−2.14214	−0.0803364
$712$	−1.82843	−0.0685232
$713$	47.5980	1.78256
$714$	0	0
$715$	29.3137	1.09627
$716$	21.2132	0.792775
$717$	68.7696	2.56825
$718$	34.8701	1.30134
$719$	14.1005	0.525860	0.262930	−	0.964815i	$-0.415311\pi$
$719$	14.1005	0.525860	0.262930	+	0.964815i	$0.415311\pi$
$720$	10.8284	0.403552
$721$	0	0
$722$	−11.0000	−0.409378
$723$	27.8995	1.03759
$724$	2.10051	0.0780647
$725$	−48.2843	−1.79323
$726$	−14.4142	−0.534962
$727$	5.41421	0.200802	0.100401	−	0.994947i	$-0.467987\pi$
$727$	5.41421	0.200802	0.100401	+	0.994947i	$0.467987\pi$
$728$	0	0
$729$	−23.8284	−0.882534
$730$	0	0
$731$	13.2426	0.489797
$732$	−13.2426	−0.489462
$733$	31.3431	1.15769	0.578843	−	0.815439i	$-0.303505\pi$
$733$	31.3431	1.15769	0.578843	+	0.815439i	$0.303505\pi$
$734$	−15.9289	−0.587948
$735$	0	0
$736$	−5.65685	−0.208514
$737$	−28.7696	−1.05974
$738$	−2.82843	−0.104116
$739$	−10.8995	−0.400944	−0.200472	−	0.979699i	$-0.564248\pi$
$739$	−10.8995	−0.400944	−0.200472	+	0.979699i	$0.564248\pi$
$740$	36.0416	1.32492
$741$	−23.3137	−0.856450
$742$	0	0
$743$	−32.9706	−1.20957	−0.604786	−	0.796388i	$-0.706741\pi$
$743$	−32.9706	−1.20957	−0.604786	+	0.796388i	$0.706741\pi$
$744$	−20.3137	−0.744737
$745$	−43.9706	−1.61096
$746$	13.4142	0.491129
$747$	16.2843	0.595810
$748$	−4.10051	−0.149929
$749$	0	0
$750$	43.0416	1.57166
$751$	−47.6569	−1.73902	−0.869512	−	0.493912i	$-0.835566\pi$
$751$	−47.6569	−1.73902	−0.869512	+	0.493912i	$0.835566\pi$
$752$	1.75736	0.0640843
$753$	−10.2426	−0.373263
$754$	−17.0711	−0.621692
$755$	43.0416	1.56645
$756$	0	0
$757$	−32.9411	−1.19727	−0.598633	−	0.801024i	$-0.704289\pi$
$757$	−32.9411	−1.19727	−0.598633	+	0.801024i	$0.704289\pi$
$758$	31.7279	1.15241
$759$	−30.6274	−1.11170
$760$	−10.8284	−0.392788
$761$	40.7279	1.47639	0.738193	−	0.674590i	$-0.235679\pi$
$761$	40.7279	1.47639	0.738193	+	0.674590i	$0.235679\pi$
$762$	12.2426	0.443504
$763$	0	0
$764$	3.92893	0.142144
$765$	−19.7990	−0.715834
$766$	−10.7279	−0.387616
$767$	−22.1421	−0.799506
$768$	2.41421	0.0871154
$769$	9.02944	0.325610	0.162805	−	0.986658i	$-0.447946\pi$
$769$	9.02944	0.325610	0.162805	+	0.986658i	$0.447946\pi$
$770$	0	0
$771$	26.8995	0.968762
$772$	−7.41421	−0.266843
$773$	17.2132	0.619116	0.309558	−	0.950881i	$-0.399819\pi$
$773$	17.2132	0.619116	0.309558	+	0.950881i	$0.399819\pi$
$774$	−20.4853	−0.736328
$775$	−81.2548	−2.91876
$776$	5.82843	0.209228
$777$	0	0
$778$	38.9706	1.39716
$779$	2.82843	0.101339
$780$	31.5563	1.12990
$781$	−24.4437	−0.874663
$782$	10.3431	0.369870
$783$	2.07107	0.0740139
$784$	0	0
$785$	58.6274	2.09250
$786$	50.0416	1.78493
$787$	−8.97056	−0.319766	−0.159883	−	0.987136i	$-0.551112\pi$
$787$	−8.97056	−0.319766	−0.159883	+	0.987136i	$0.551112\pi$
$788$	−23.3137	−0.830516
$789$	−8.00000	−0.284808
$790$	−2.89949	−0.103159
$791$	0	0
$792$	6.34315	0.225394
$793$	−18.7279	−0.665048
$794$	34.7279	1.23245
$795$	87.6690	3.10930
$796$	−4.00000	−0.141776
$797$	−51.7696	−1.83377	−0.916886	−	0.399150i	$-0.869305\pi$
$797$	−51.7696	−1.83377	−0.916886	+	0.399150i	$0.869305\pi$
$798$	0	0
$799$	−3.21320	−0.113675
$800$	9.65685	0.341421
$801$	−5.17157	−0.182729
$802$	−17.6274	−0.622446
$803$	0	0
$804$	−30.9706	−1.09225
$805$	0	0
$806$	−28.7279	−1.01190
$807$	−40.1421	−1.41307
$808$	10.0000	0.351799
$809$	−37.6985	−1.32541	−0.662704	−	0.748881i	$-0.730591\pi$
$809$	−37.6985	−1.32541	−0.662704	+	0.748881i	$0.730591\pi$
$810$	−36.3137	−1.27593
$811$	20.7279	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$811$	20.7279	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$812$	0	0
$813$	−14.4853	−0.508021
$814$	21.1127	0.740000
$815$	−35.6569	−1.24901
$816$	−4.41421	−0.154528
$817$	20.4853	0.716689
$818$	37.8995	1.32512
$819$	0	0
$820$	−3.82843	−0.133694
$821$	7.21320	0.251743	0.125871	−	0.992047i	$-0.459827\pi$
$821$	7.21320	0.251743	0.125871	+	0.992047i	$0.459827\pi$
$822$	−9.65685	−0.336821
$823$	51.8701	1.80808	0.904038	−	0.427452i	$-0.140589\pi$
$823$	51.8701	1.80808	0.904038	+	0.427452i	$0.140589\pi$
$824$	−13.5858	−0.473283
$825$	52.2843	1.82030
$826$	0	0
$827$	−25.1127	−0.873254	−0.436627	−	0.899643i	$-0.643827\pi$
$827$	−25.1127	−0.873254	−0.436627	+	0.899643i	$0.643827\pi$
$828$	−16.0000	−0.556038
$829$	15.6863	0.544807	0.272404	−	0.962183i	$-0.412181\pi$
$829$	15.6863	0.544807	0.272404	+	0.962183i	$0.412181\pi$
$830$	22.0416	0.765076
$831$	45.7990	1.58875
$832$	3.41421	0.118367
$833$	0	0
$834$	54.2843	1.87971
$835$	−6.34315	−0.219514
$836$	−6.34315	−0.219382
$837$	3.48528	0.120469
$838$	24.0416	0.830504
$839$	21.1127	0.728891	0.364446	−	0.931225i	$-0.381258\pi$
$839$	21.1127	0.728891	0.364446	+	0.931225i	$0.381258\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	15.9706	0.550382
$843$	26.4853	0.912202
$844$	17.6569	0.607774
$845$	−5.14214	−0.176895
$846$	4.97056	0.170891
$847$	0	0
$848$	9.48528	0.325726
$849$	22.9706	0.788348
$850$	−17.6569	−0.605625
$851$	−53.2548	−1.82555
$852$	−26.3137	−0.901493
$853$	−5.82843	−0.199562	−0.0997808	−	0.995009i	$-0.531814\pi$
$853$	−5.82843	−0.199562	−0.0997808	+	0.995009i	$0.531814\pi$
$854$	0	0
$855$	−30.6274	−1.04744
$856$	−10.8995	−0.372537
$857$	−21.5980	−0.737773	−0.368886	−	0.929474i	$-0.620261\pi$
$857$	−21.5980	−0.737773	−0.368886	+	0.929474i	$0.620261\pi$
$858$	18.4853	0.631077
$859$	−30.3848	−1.03672	−0.518358	−	0.855164i	$-0.673456\pi$
$859$	−30.3848	−1.03672	−0.518358	+	0.855164i	$0.673456\pi$
$860$	−27.7279	−0.945514
$861$	0	0
$862$	−16.0000	−0.544962
$863$	−22.5858	−0.768829	−0.384415	−	0.923161i	$-0.625597\pi$
$863$	−22.5858	−0.768829	−0.384415	+	0.923161i	$0.625597\pi$
$864$	−0.414214	−0.0140918
$865$	70.1127	2.38390
$866$	−30.6274	−1.04076
$867$	−32.9706	−1.11974
$868$	0	0
$869$	−1.69848	−0.0576172
$870$	−46.2132	−1.56677
$871$	−43.7990	−1.48407
$872$	5.17157	0.175132
$873$	16.4853	0.557942
$874$	16.0000	0.541208
$875$	0	0
$876$	0	0
$877$	−10.6274	−0.358862	−0.179431	−	0.983771i	$-0.557426\pi$
$877$	−10.6274	−0.358862	−0.179431	+	0.983771i	$0.557426\pi$
$878$	−16.1421	−0.544771
$879$	0.828427	0.0279422
$880$	8.58579	0.289427
$881$	23.8995	0.805194	0.402597	−	0.915377i	$-0.368108\pi$
$881$	23.8995	0.805194	0.402597	+	0.915377i	$0.368108\pi$
$882$	0	0
$883$	−0.828427	−0.0278788	−0.0139394	−	0.999903i	$-0.504437\pi$
$883$	−0.828427	−0.0278788	−0.0139394	+	0.999903i	$0.504437\pi$
$884$	−6.24264	−0.209963
$885$	−59.9411	−2.01490
$886$	−24.8995	−0.836515
$887$	4.97056	0.166895	0.0834476	−	0.996512i	$-0.473407\pi$
$887$	4.97056	0.166895	0.0834476	+	0.996512i	$0.473407\pi$
$888$	22.7279	0.762699
$889$	0	0
$890$	−7.00000	−0.234641
$891$	−21.2721	−0.712641
$892$	8.55635	0.286488
$893$	−4.97056	−0.166334
$894$	−27.7279	−0.927360
$895$	81.2132	2.71466
$896$	0	0
$897$	−46.6274	−1.55684
$898$	19.8284	0.661683
$899$	42.0711	1.40315
$900$	27.3137	0.910457
$901$	−17.3431	−0.577784
$902$	−2.24264	−0.0746718
$903$	0	0
$904$	11.0000	0.365855
$905$	8.04163	0.267313
$906$	27.1421	0.901737
$907$	−3.92893	−0.130458	−0.0652290	−	0.997870i	$-0.520778\pi$
$907$	−3.92893	−0.130458	−0.0652290	+	0.997870i	$0.520778\pi$
$908$	1.72792	0.0573431
$909$	28.2843	0.938130
$910$	0	0
$911$	20.8284	0.690077	0.345038	−	0.938589i	$-0.387866\pi$
$911$	20.8284	0.690077	0.345038	+	0.938589i	$0.387866\pi$
$912$	−6.82843	−0.226112
$913$	12.9117	0.427315
$914$	−13.4142	−0.443703
$915$	−50.6985	−1.67604
$916$	−1.07107	−0.0353891
$917$	0	0
$918$	0.757359	0.0249966
$919$	−12.7574	−0.420826	−0.210413	−	0.977613i	$-0.567481\pi$
$919$	−12.7574	−0.420826	−0.210413	+	0.977613i	$0.567481\pi$
$920$	−21.6569	−0.714005
$921$	21.6569	0.713618
$922$	−10.4558	−0.344345
$923$	−37.2132	−1.22489
$924$	0	0
$925$	90.9117	2.98916
$926$	35.3137	1.16048
$927$	−38.4264	−1.26209
$928$	−5.00000	−0.164133
$929$	−34.1421	−1.12017	−0.560084	−	0.828436i	$-0.689231\pi$
$929$	−34.1421	−1.12017	−0.560084	+	0.828436i	$0.689231\pi$
$930$	−77.7696	−2.55016
$931$	0	0
$932$	−25.8995	−0.848366
$933$	−19.6569	−0.643537
$934$	20.8284	0.681527
$935$	−15.6985	−0.513395
$936$	9.65685	0.315644
$937$	−33.9706	−1.10977	−0.554885	−	0.831927i	$-0.687238\pi$
$937$	−33.9706	−1.10977	−0.554885	+	0.831927i	$0.687238\pi$
$938$	0	0
$939$	−20.9706	−0.684348
$940$	6.72792	0.219441
$941$	23.0294	0.750738	0.375369	−	0.926875i	$-0.377516\pi$
$941$	23.0294	0.750738	0.375369	+	0.926875i	$0.377516\pi$
$942$	36.9706	1.20457
$943$	5.65685	0.184213
$944$	−6.48528	−0.211078
$945$	0	0
$946$	−16.2426	−0.528094
$947$	5.45584	0.177291	0.0886456	−	0.996063i	$-0.471746\pi$
$947$	5.45584	0.177291	0.0886456	+	0.996063i	$0.471746\pi$
$948$	−1.82843	−0.0593846
$949$	0	0
$950$	−27.3137	−0.886174
$951$	−73.9411	−2.39771
$952$	0	0
$953$	17.1716	0.556242	0.278121	−	0.960546i	$-0.410288\pi$
$953$	17.1716	0.556242	0.278121	+	0.960546i	$0.410288\pi$
$954$	26.8284	0.868602
$955$	15.0416	0.486736
$956$	28.4853	0.921280
$957$	−27.0711	−0.875083
$958$	−6.24264	−0.201691
$959$	0	0
$960$	9.24264	0.298305
$961$	39.7990	1.28384
$962$	32.1421	1.03630
$963$	−30.8284	−0.993432
$964$	11.5563	0.372205
$965$	−28.3848	−0.913738
$966$	0	0
$967$	−35.5269	−1.14247	−0.571234	−	0.820787i	$-0.693535\pi$
$967$	−35.5269	−1.14247	−0.571234	+	0.820787i	$0.693535\pi$
$968$	−5.97056	−0.191901
$969$	12.4853	0.401085
$970$	22.3137	0.716450
$971$	−57.8701	−1.85714	−0.928569	−	0.371159i	$-0.878960\pi$
$971$	−57.8701	−1.85714	−0.928569	+	0.371159i	$0.878960\pi$
$972$	−21.6569	−0.694644
$973$	0	0
$974$	7.55635	0.242121
$975$	79.5980	2.54918
$976$	−5.48528	−0.175580
$977$	5.31371	0.170001	0.0850003	−	0.996381i	$-0.472911\pi$
$977$	5.31371	0.170001	0.0850003	+	0.996381i	$0.472911\pi$
$978$	−22.4853	−0.719000
$979$	−4.10051	−0.131053
$980$	0	0
$981$	14.6274	0.467017
$982$	−19.2426	−0.614057
$983$	−16.7574	−0.534477	−0.267238	−	0.963630i	$-0.586111\pi$
$983$	−16.7574	−0.534477	−0.267238	+	0.963630i	$0.586111\pi$
$984$	−2.41421	−0.0769623
$985$	−89.2548	−2.84390
$986$	9.14214	0.291145
$987$	0	0
$988$	−9.65685	−0.307225
$989$	40.9706	1.30279
$990$	24.2843	0.771805
$991$	−22.9706	−0.729684	−0.364842	−	0.931069i	$-0.618877\pi$
$991$	−22.9706	−0.729684	−0.364842	+	0.931069i	$0.618877\pi$
$992$	−8.41421	−0.267152
$993$	−67.6985	−2.14835
$994$	0	0
$995$	−15.3137	−0.485477
$996$	13.8995	0.440422
$997$	49.9411	1.58165	0.790826	−	0.612041i	$-0.209651\pi$
$997$	49.9411	1.58165	0.790826	+	0.612041i	$0.209651\pi$
$998$	−3.85786	−0.122119
$999$	−3.89949	−0.123375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bc.1.2	yes	2
7.6	odd	2		4018.2.a.y.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.y.1.1	✓	2	7.6	odd	2
4018.2.a.bc.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} +3.82843 q^{5} +2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} +3.82843 q^{5} +2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +3.82843 q^{10} +2.24264 q^{11} +2.41421 q^{12} +3.41421 q^{13} +9.24264 q^{15} +1.00000 q^{16} -1.82843 q^{17} +2.82843 q^{18} -2.82843 q^{19} +3.82843 q^{20} +2.24264 q^{22} -5.65685 q^{23} +2.41421 q^{24} +9.65685 q^{25} +3.41421 q^{26} -0.414214 q^{27} -5.00000 q^{29} +9.24264 q^{30} -8.41421 q^{31} +1.00000 q^{32} +5.41421 q^{33} -1.82843 q^{34} +2.82843 q^{36} +9.41421 q^{37} -2.82843 q^{38} +8.24264 q^{39} +3.82843 q^{40} -1.00000 q^{41} -7.24264 q^{43} +2.24264 q^{44} +10.8284 q^{45} -5.65685 q^{46} +1.75736 q^{47} +2.41421 q^{48} +9.65685 q^{50} -4.41421 q^{51} +3.41421 q^{52} +9.48528 q^{53} -0.414214 q^{54} +8.58579 q^{55} -6.82843 q^{57} -5.00000 q^{58} -6.48528 q^{59} +9.24264 q^{60} -5.48528 q^{61} -8.41421 q^{62} +1.00000 q^{64} +13.0711 q^{65} +5.41421 q^{66} -12.8284 q^{67} -1.82843 q^{68} -13.6569 q^{69} -10.8995 q^{71} +2.82843 q^{72} +9.41421 q^{74} +23.3137 q^{75} -2.82843 q^{76} +8.24264 q^{78} -0.757359 q^{79} +3.82843 q^{80} -9.48528 q^{81} -1.00000 q^{82} +5.75736 q^{83} -7.00000 q^{85} -7.24264 q^{86} -12.0711 q^{87} +2.24264 q^{88} -1.82843 q^{89} +10.8284 q^{90} -5.65685 q^{92} -20.3137 q^{93} +1.75736 q^{94} -10.8284 q^{95} +2.41421 q^{96} +5.82843 q^{97} +6.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{13} + 10 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{20} - 4 q^{22} + 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} - 10 q^{29} + 10 q^{30} - 14 q^{31} + 2 q^{32} + 8 q^{33} + 2 q^{34} + 16 q^{37} + 8 q^{39} + 2 q^{40} - 2 q^{41} - 6 q^{43} - 4 q^{44} + 16 q^{45} + 12 q^{47} + 2 q^{48} + 8 q^{50} - 6 q^{51} + 4 q^{52} + 2 q^{53} + 2 q^{54} + 20 q^{55} - 8 q^{57} - 10 q^{58} + 4 q^{59} + 10 q^{60} + 6 q^{61} - 14 q^{62} + 2 q^{64} + 12 q^{65} + 8 q^{66} - 20 q^{67} + 2 q^{68} - 16 q^{69} - 2 q^{71} + 16 q^{74} + 24 q^{75} + 8 q^{78} - 10 q^{79} + 2 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} - 14 q^{85} - 6 q^{86} - 10 q^{87} - 4 q^{88} + 2 q^{89} + 16 q^{90} - 18 q^{93} + 12 q^{94} - 16 q^{95} + 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^13 + 10 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^20 - 4 * q^22 + 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 - 10 * q^29 + 10 * q^30 - 14 * q^31 + 2 * q^32 + 8 * q^33 + 2 * q^34 + 16 * q^37 + 8 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^43 - 4 * q^44 + 16 * q^45 + 12 * q^47 + 2 * q^48 + 8 * q^50 - 6 * q^51 + 4 * q^52 + 2 * q^53 + 2 * q^54 + 20 * q^55 - 8 * q^57 - 10 * q^58 + 4 * q^59 + 10 * q^60 + 6 * q^61 - 14 * q^62 + 2 * q^64 + 12 * q^65 + 8 * q^66 - 20 * q^67 + 2 * q^68 - 16 * q^69 - 2 * q^71 + 16 * q^74 + 24 * q^75 + 8 * q^78 - 10 * q^79 + 2 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 - 14 * q^85 - 6 * q^86 - 10 * q^87 - 4 * q^88 + 2 * q^89 + 16 * q^90 - 18 * q^93 + 12 * q^94 - 16 * q^95 + 2 * q^96 + 6 * q^97 + 24 * q^99

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