LMFDB - Embedded newform 4018.2.a.y.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:	$1$
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.82843 q^{5} +0.414214 q^{6} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.82843 q^{5} +0.414214 q^{6} +1.00000 q^{8} -2.82843 q^{9} +1.82843 q^{10} -6.24264 q^{11} +0.414214 q^{12} -0.585786 q^{13} +0.757359 q^{15} +1.00000 q^{16} -3.82843 q^{17} -2.82843 q^{18} -2.82843 q^{19} +1.82843 q^{20} -6.24264 q^{22} +5.65685 q^{23} +0.414214 q^{24} -1.65685 q^{25} -0.585786 q^{26} -2.41421 q^{27} -5.00000 q^{29} +0.757359 q^{30} +5.58579 q^{31} +1.00000 q^{32} -2.58579 q^{33} -3.82843 q^{34} -2.82843 q^{36} +6.58579 q^{37} -2.82843 q^{38} -0.242641 q^{39} +1.82843 q^{40} +1.00000 q^{41} +1.24264 q^{43} -6.24264 q^{44} -5.17157 q^{45} +5.65685 q^{46} -10.2426 q^{47} +0.414214 q^{48} -1.65685 q^{50} -1.58579 q^{51} -0.585786 q^{52} -7.48528 q^{53} -2.41421 q^{54} -11.4142 q^{55} -1.17157 q^{57} -5.00000 q^{58} -10.4853 q^{59} +0.757359 q^{60} -11.4853 q^{61} +5.58579 q^{62} +1.00000 q^{64} -1.07107 q^{65} -2.58579 q^{66} -7.17157 q^{67} -3.82843 q^{68} +2.34315 q^{69} +8.89949 q^{71} -2.82843 q^{72} +6.58579 q^{74} -0.686292 q^{75} -2.82843 q^{76} -0.242641 q^{78} -9.24264 q^{79} +1.82843 q^{80} +7.48528 q^{81} +1.00000 q^{82} -14.2426 q^{83} -7.00000 q^{85} +1.24264 q^{86} -2.07107 q^{87} -6.24264 q^{88} -3.82843 q^{89} -5.17157 q^{90} +5.65685 q^{92} +2.31371 q^{93} -10.2426 q^{94} -5.17157 q^{95} +0.414214 q^{96} -0.171573 q^{97} +17.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.414214	0.239146	0.119573	−	0.992825i	$-0.461847\pi$
$3$	0.414214	0.239146	0.119573	+	0.992825i	$0.461847\pi$
$4$	1.00000	0.500000
$5$	1.82843	0.817697	0.408849	−	0.912602i	$-0.365930\pi$
$5$	1.82843	0.817697	0.408849	+	0.912602i	$0.365930\pi$
$6$	0.414214	0.169102
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.82843	−0.942809
$10$	1.82843	0.578199
$11$	−6.24264	−1.88223	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−6.24264	−1.88223	−0.941113	+	0.338091i	$0.890219\pi$
$12$	0.414214	0.119573
$13$	−0.585786	−0.162468	−0.0812340	−	0.996695i	$-0.525886\pi$
$13$	−0.585786	−0.162468	−0.0812340	+	0.996695i	$0.525886\pi$
$14$	0	0
$15$	0.757359	0.195549
$16$	1.00000	0.250000
$17$	−3.82843	−0.928530	−0.464265	−	0.885696i	$-0.653681\pi$
$17$	−3.82843	−0.928530	−0.464265	+	0.885696i	$0.653681\pi$
$18$	−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	$0.605177\pi$
$20$	1.82843	0.408849
$21$	0	0
$22$	−6.24264	−1.33094
$23$	5.65685	1.17954	0.589768	−	0.807573i	$-0.299219\pi$
$23$	5.65685	1.17954	0.589768	+	0.807573i	$0.299219\pi$
$24$	0.414214	0.0845510
$25$	−1.65685	−0.331371
$26$	−0.585786	−0.114882
$27$	−2.41421	−0.464616
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0.757359	0.138274
$31$	5.58579	1.00324	0.501618	−	0.865089i	$-0.332738\pi$
$31$	5.58579	1.00324	0.501618	+	0.865089i	$0.332738\pi$
$32$	1.00000	0.176777
$33$	−2.58579	−0.450128
$34$	−3.82843	−0.656570
$35$	0	0
$36$	−2.82843	−0.471405
$37$	6.58579	1.08270	0.541348	−	0.840798i	$-0.317914\pi$
$37$	6.58579	1.08270	0.541348	+	0.840798i	$0.317914\pi$
$38$	−2.82843	−0.458831
$39$	−0.242641	−0.0388536
$40$	1.82843	0.289100
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.24264	0.189501	0.0947505	−	0.995501i	$-0.469795\pi$
$43$	1.24264	0.189501	0.0947505	+	0.995501i	$0.469795\pi$
$44$	−6.24264	−0.941113
$45$	−5.17157	−0.770933
$46$	5.65685	0.834058
$47$	−10.2426	−1.49404	−0.747021	−	0.664800i	$-0.768517\pi$
$47$	−10.2426	−1.49404	−0.747021	+	0.664800i	$0.768517\pi$
$48$	0.414214	0.0597866
$49$	0	0
$50$	−1.65685	−0.234315
$51$	−1.58579	−0.222055
$52$	−0.585786	−0.0812340
$53$	−7.48528	−1.02818	−0.514091	−	0.857736i	$-0.671871\pi$
$53$	−7.48528	−1.02818	−0.514091	+	0.857736i	$0.671871\pi$
$54$	−2.41421	−0.328533
$55$	−11.4142	−1.53909
$56$	0	0
$57$	−1.17157	−0.155179
$58$	−5.00000	−0.656532
$59$	−10.4853	−1.36507	−0.682534	−	0.730854i	$-0.739122\pi$
$59$	−10.4853	−1.36507	−0.682534	+	0.730854i	$0.739122\pi$
$60$	0.757359	0.0977747
$61$	−11.4853	−1.47054	−0.735270	−	0.677775i	$-0.762945\pi$
$61$	−11.4853	−1.47054	−0.735270	+	0.677775i	$0.762945\pi$
$62$	5.58579	0.709396
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.07107	−0.132850
$66$	−2.58579	−0.318288
$67$	−7.17157	−0.876147	−0.438074	−	0.898939i	$-0.644339\pi$
$67$	−7.17157	−0.876147	−0.438074	+	0.898939i	$0.644339\pi$
$68$	−3.82843	−0.464265
$69$	2.34315	0.282082
$70$	0	0
$71$	8.89949	1.05618	0.528088	−	0.849190i	$-0.322909\pi$
$71$	8.89949	1.05618	0.528088	+	0.849190i	$0.322909\pi$
$72$	−2.82843	−0.333333
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	6.58579	0.765582
$75$	−0.686292	−0.0792461
$76$	−2.82843	−0.324443
$77$	0	0
$78$	−0.242641	−0.0274736
$79$	−9.24264	−1.03988	−0.519939	−	0.854203i	$-0.674045\pi$
$79$	−9.24264	−1.03988	−0.519939	+	0.854203i	$0.674045\pi$
$80$	1.82843	0.204424
$81$	7.48528	0.831698
$82$	1.00000	0.110432
$83$	−14.2426	−1.56333	−0.781666	−	0.623697i	$-0.785630\pi$
$83$	−14.2426	−1.56333	−0.781666	+	0.623697i	$0.785630\pi$
$84$	0	0
$85$	−7.00000	−0.759257
$86$	1.24264	0.133997
$87$	−2.07107	−0.222042
$88$	−6.24264	−0.665468
$89$	−3.82843	−0.405812	−0.202906	−	0.979198i	$-0.565039\pi$
$89$	−3.82843	−0.405812	−0.202906	+	0.979198i	$0.565039\pi$
$90$	−5.17157	−0.545132
$91$	0	0
$92$	5.65685	0.589768
$93$	2.31371	0.239920
$94$	−10.2426	−1.05645
$95$	−5.17157	−0.530592
$96$	0.414214	0.0422755
$97$	−0.171573	−0.0174206	−0.00871029	−	0.999962i	$-0.502773\pi$
$97$	−0.171573	−0.0174206	−0.00871029	+	0.999962i	$0.502773\pi$
$98$	0	0
$99$	17.6569	1.77458
$100$	−1.65685	−0.165685
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	−1.58579	−0.157016
$103$	16.4142	1.61734	0.808670	−	0.588262i	$-0.200188\pi$
$103$	16.4142	1.61734	0.808670	+	0.588262i	$0.200188\pi$
$104$	−0.585786	−0.0574411
$105$	0	0
$106$	−7.48528	−0.727035
$107$	8.89949	0.860347	0.430173	−	0.902746i	$-0.358452\pi$
$107$	8.89949	0.860347	0.430173	+	0.902746i	$0.358452\pi$
$108$	−2.41421	−0.232308
$109$	10.8284	1.03718	0.518588	−	0.855024i	$-0.326458\pi$
$109$	10.8284	1.03718	0.518588	+	0.855024i	$0.326458\pi$
$110$	−11.4142	−1.08830
$111$	2.72792	0.258923
$112$	0	0
$113$	11.0000	1.03479	0.517396	−	0.855746i	$-0.326901\pi$
$113$	11.0000	1.03479	0.517396	+	0.855746i	$0.326901\pi$
$114$	−1.17157	−0.109728
$115$	10.3431	0.964503
$116$	−5.00000	−0.464238
$117$	1.65685	0.153176
$118$	−10.4853	−0.965248
$119$	0	0
$120$	0.757359	0.0691371
$121$	27.9706	2.54278
$122$	−11.4853	−1.03983
$123$	0.414214	0.0373484
$124$	5.58579	0.501618
$125$	−12.1716	−1.08866
$126$	0	0
$127$	−9.07107	−0.804927	−0.402464	−	0.915436i	$-0.631846\pi$
$127$	−9.07107	−0.804927	−0.402464	+	0.915436i	$0.631846\pi$
$128$	1.00000	0.0883883
$129$	0.514719	0.0453184
$130$	−1.07107	−0.0939389
$131$	4.72792	0.413080	0.206540	−	0.978438i	$-0.433780\pi$
$131$	4.72792	0.413080	0.206540	+	0.978438i	$0.433780\pi$
$132$	−2.58579	−0.225064
$133$	0	0
$134$	−7.17157	−0.619530
$135$	−4.41421	−0.379915
$136$	−3.82843	−0.328285
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	2.34315	0.199462
$139$	−5.51472	−0.467752	−0.233876	−	0.972266i	$-0.575141\pi$
$139$	−5.51472	−0.467752	−0.233876	+	0.972266i	$0.575141\pi$
$140$	0	0
$141$	−4.24264	−0.357295
$142$	8.89949	0.746829
$143$	3.65685	0.305802
$144$	−2.82843	−0.235702
$145$	−9.14214	−0.759213
$146$	0	0
$147$	0	0
$148$	6.58579	0.541348
$149$	5.48528	0.449372	0.224686	−	0.974431i	$-0.427864\pi$
$149$	5.48528	0.449372	0.224686	+	0.974431i	$0.427864\pi$
$150$	−0.686292	−0.0560355
$151$	2.75736	0.224391	0.112195	−	0.993686i	$-0.464212\pi$
$151$	2.75736	0.224391	0.112195	+	0.993686i	$0.464212\pi$
$152$	−2.82843	−0.229416
$153$	10.8284	0.875426
$154$	0	0
$155$	10.2132	0.820344
$156$	−0.242641	−0.0194268
$157$	7.31371	0.583697	0.291849	−	0.956464i	$-0.405730\pi$
$157$	7.31371	0.583697	0.291849	+	0.956464i	$0.405730\pi$
$158$	−9.24264	−0.735305
$159$	−3.10051	−0.245886
$160$	1.82843	0.144550
$161$	0	0
$162$	7.48528	0.588099
$163$	13.3137	1.04281	0.521405	−	0.853309i	$-0.325408\pi$
$163$	13.3137	1.04281	0.521405	+	0.853309i	$0.325408\pi$
$164$	1.00000	0.0780869
$165$	−4.72792	−0.368068
$166$	−14.2426	−1.10544
$167$	−9.65685	−0.747270	−0.373635	−	0.927576i	$-0.621889\pi$
$167$	−9.65685	−0.747270	−0.373635	+	0.927576i	$0.621889\pi$
$168$	0	0
$169$	−12.6569	−0.973604
$170$	−7.00000	−0.536875
$171$	8.00000	0.611775
$172$	1.24264	0.0947505
$173$	4.31371	0.327965	0.163983	−	0.986463i	$-0.447566\pi$
$173$	4.31371	0.327965	0.163983	+	0.986463i	$0.447566\pi$
$174$	−2.07107	−0.157007
$175$	0	0
$176$	−6.24264	−0.470557
$177$	−4.34315	−0.326451
$178$	−3.82843	−0.286953
$179$	−21.2132	−1.58555	−0.792775	−	0.609515i	$-0.791364\pi$
$179$	−21.2132	−1.58555	−0.792775	+	0.609515i	$0.791364\pi$
$180$	−5.17157	−0.385466
$181$	−21.8995	−1.62778	−0.813888	−	0.581021i	$-0.802653\pi$
$181$	−21.8995	−1.62778	−0.813888	+	0.581021i	$0.802653\pi$
$182$	0	0
$183$	−4.75736	−0.351674
$184$	5.65685	0.417029
$185$	12.0416	0.885318
$186$	2.31371	0.169649
$187$	23.8995	1.74770
$188$	−10.2426	−0.747021
$189$	0	0
$190$	−5.17157	−0.375185
$191$	18.0711	1.30758	0.653788	−	0.756678i	$-0.273179\pi$
$191$	18.0711	1.30758	0.653788	+	0.756678i	$0.273179\pi$
$192$	0.414214	0.0298933
$193$	−4.58579	−0.330092	−0.165046	−	0.986286i	$-0.552777\pi$
$193$	−4.58579	−0.330092	−0.165046	+	0.986286i	$0.552777\pi$
$194$	−0.171573	−0.0123182
$195$	−0.443651	−0.0317705
$196$	0	0
$197$	−0.686292	−0.0488962	−0.0244481	−	0.999701i	$-0.507783\pi$
$197$	−0.686292	−0.0488962	−0.0244481	+	0.999701i	$0.507783\pi$
$198$	17.6569	1.25482
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.65685	−0.117157
$201$	−2.97056	−0.209527
$202$	−10.0000	−0.703598
$203$	0	0
$204$	−1.58579	−0.111027
$205$	1.82843	0.127703
$206$	16.4142	1.14363
$207$	−16.0000	−1.11208
$208$	−0.585786	−0.0406170
$209$	17.6569	1.22135
$210$	0	0
$211$	6.34315	0.436680	0.218340	−	0.975873i	$-0.429936\pi$
$211$	6.34315	0.436680	0.218340	+	0.975873i	$0.429936\pi$
$212$	−7.48528	−0.514091
$213$	3.68629	0.252581
$214$	8.89949	0.608357
$215$	2.27208	0.154954
$216$	−2.41421	−0.164266
$217$	0	0
$218$	10.8284	0.733394
$219$	0	0
$220$	−11.4142	−0.769546
$221$	2.24264	0.150856
$222$	2.72792	0.183086
$223$	22.5563	1.51048	0.755242	−	0.655446i	$-0.227519\pi$
$223$	22.5563	1.51048	0.755242	+	0.655446i	$0.227519\pi$
$224$	0	0
$225$	4.68629	0.312419
$226$	11.0000	0.731709
$227$	23.7279	1.57488	0.787439	−	0.616393i	$-0.211407\pi$
$227$	23.7279	1.57488	0.787439	+	0.616393i	$0.211407\pi$
$228$	−1.17157	−0.0775893
$229$	−13.0711	−0.863760	−0.431880	−	0.901931i	$-0.642150\pi$
$229$	−13.0711	−0.863760	−0.431880	+	0.901931i	$0.642150\pi$
$230$	10.3431	0.682007
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−6.10051	−0.399657	−0.199829	−	0.979831i	$-0.564039\pi$
$233$	−6.10051	−0.399657	−0.199829	+	0.979831i	$0.564039\pi$
$234$	1.65685	0.108312
$235$	−18.7279	−1.22167
$236$	−10.4853	−0.682534
$237$	−3.82843	−0.248683
$238$	0	0
$239$	11.5147	0.744825	0.372413	−	0.928067i	$-0.378531\pi$
$239$	11.5147	0.744825	0.372413	+	0.928067i	$0.378531\pi$
$240$	0.757359	0.0488873
$241$	19.5563	1.25974	0.629868	−	0.776703i	$-0.283109\pi$
$241$	19.5563	1.25974	0.629868	+	0.776703i	$0.283109\pi$
$242$	27.9706	1.79802
$243$	10.3431	0.663513
$244$	−11.4853	−0.735270
$245$	0	0
$246$	0.414214	0.0264093
$247$	1.65685	0.105423
$248$	5.58579	0.354698
$249$	−5.89949	−0.373865
$250$	−12.1716	−0.769798
$251$	−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
$253$	−35.3137	−2.22015
$254$	−9.07107	−0.569169
$255$	−2.89949	−0.181573
$256$	1.00000	0.0625000
$257$	17.1421	1.06930	0.534649	−	0.845075i	$-0.320444\pi$
$257$	17.1421	1.06930	0.534649	+	0.845075i	$0.320444\pi$
$258$	0.514719	0.0320450
$259$	0	0
$260$	−1.07107	−0.0664248
$261$	14.1421	0.875376
$262$	4.72792	0.292092
$263$	19.3137	1.19093	0.595467	−	0.803380i	$-0.296967\pi$
$263$	19.3137	1.19093	0.595467	+	0.803380i	$0.296967\pi$
$264$	−2.58579	−0.159144
$265$	−13.6863	−0.840742
$266$	0	0
$267$	−1.58579	−0.0970486
$268$	−7.17157	−0.438074
$269$	−28.6274	−1.74544	−0.872722	−	0.488217i	$-0.837647\pi$
$269$	−28.6274	−1.74544	−0.872722	+	0.488217i	$0.837647\pi$
$270$	−4.41421	−0.268640
$271$	6.00000	0.364474	0.182237	−	0.983255i	$-0.441666\pi$
$271$	6.00000	0.364474	0.182237	+	0.983255i	$0.441666\pi$
$272$	−3.82843	−0.232132
$273$	0	0
$274$	−4.00000	−0.241649
$275$	10.3431	0.623715
$276$	2.34315	0.141041
$277$	−14.9706	−0.899494	−0.449747	−	0.893156i	$-0.648486\pi$
$277$	−14.9706	−0.899494	−0.449747	+	0.893156i	$0.648486\pi$
$278$	−5.51472	−0.330751
$279$	−15.7990	−0.945861
$280$	0	0
$281$	−22.9706	−1.37031	−0.685154	−	0.728398i	$-0.740265\pi$
$281$	−22.9706	−1.37031	−0.685154	+	0.728398i	$0.740265\pi$
$282$	−4.24264	−0.252646
$283$	−26.4853	−1.57439	−0.787193	−	0.616706i	$-0.788467\pi$
$283$	−26.4853	−1.57439	−0.787193	+	0.616706i	$0.788467\pi$
$284$	8.89949	0.528088
$285$	−2.14214	−0.126889
$286$	3.65685	0.216234
$287$	0	0
$288$	−2.82843	−0.166667
$289$	−2.34315	−0.137832
$290$	−9.14214	−0.536845
$291$	−0.0710678	−0.00416607
$292$	0	0
$293$	−11.6569	−0.681001	−0.340500	−	0.940244i	$-0.610596\pi$
$293$	−11.6569	−0.681001	−0.340500	+	0.940244i	$0.610596\pi$
$294$	0	0
$295$	−19.1716	−1.11621
$296$	6.58579	0.382791
$297$	15.0711	0.874512
$298$	5.48528	0.317754
$299$	−3.31371	−0.191637
$300$	−0.686292	−0.0396231
$301$	0	0
$302$	2.75736	0.158668
$303$	−4.14214	−0.237959
$304$	−2.82843	−0.162221
$305$	−21.0000	−1.20246
$306$	10.8284	0.619020
$307$	24.9706	1.42515	0.712573	−	0.701598i	$-0.247530\pi$
$307$	24.9706	1.42515	0.712573	+	0.701598i	$0.247530\pi$
$308$	0	0
$309$	6.79899	0.386781
$310$	10.2132	0.580071
$311$	−20.1421	−1.14216	−0.571078	−	0.820896i	$-0.693475\pi$
$311$	−20.1421	−1.14216	−0.571078	+	0.820896i	$0.693475\pi$
$312$	−0.242641	−0.0137368
$313$	31.3137	1.76996	0.884978	−	0.465633i	$-0.154173\pi$
$313$	31.3137	1.76996	0.884978	+	0.465633i	$0.154173\pi$
$314$	7.31371	0.412736
$315$	0	0
$316$	−9.24264	−0.519939
$317$	14.6274	0.821558	0.410779	−	0.911735i	$-0.365257\pi$
$317$	14.6274	0.821558	0.410779	+	0.911735i	$0.365257\pi$
$318$	−3.10051	−0.173868
$319$	31.2132	1.74760
$320$	1.82843	0.102212
$321$	3.68629	0.205749
$322$	0	0
$323$	10.8284	0.602510
$324$	7.48528	0.415849
$325$	0.970563	0.0538371
$326$	13.3137	0.737378
$327$	4.48528	0.248037
$328$	1.00000	0.0552158
$329$	0	0
$330$	−4.72792	−0.260264
$331$	20.0416	1.10159	0.550794	−	0.834641i	$-0.314325\pi$
$331$	20.0416	1.10159	0.550794	+	0.834641i	$0.314325\pi$
$332$	−14.2426	−0.781666
$333$	−18.6274	−1.02078
$334$	−9.65685	−0.528400
$335$	−13.1127	−0.716423
$336$	0	0
$337$	23.3431	1.27158	0.635791	−	0.771861i	$-0.280674\pi$
$337$	23.3431	1.27158	0.635791	+	0.771861i	$0.280674\pi$
$338$	−12.6569	−0.688442
$339$	4.55635	0.247467
$340$	−7.00000	−0.379628
$341$	−34.8701	−1.88832
$342$	8.00000	0.432590
$343$	0	0
$344$	1.24264	0.0669987
$345$	4.28427	0.230657
$346$	4.31371	0.231906
$347$	28.2843	1.51838	0.759190	−	0.650870i	$-0.225596\pi$
$347$	28.2843	1.51838	0.759190	+	0.650870i	$0.225596\pi$
$348$	−2.07107	−0.111021
$349$	−7.51472	−0.402254	−0.201127	−	0.979565i	$-0.564460\pi$
$349$	−7.51472	−0.402254	−0.201127	+	0.979565i	$0.564460\pi$
$350$	0	0
$351$	1.41421	0.0754851
$352$	−6.24264	−0.332734
$353$	−28.0000	−1.49029	−0.745145	−	0.666903i	$-0.767620\pi$
$353$	−28.0000	−1.49029	−0.745145	+	0.666903i	$0.767620\pi$
$354$	−4.34315	−0.230836
$355$	16.2721	0.863632
$356$	−3.82843	−0.202906
$357$	0	0
$358$	−21.2132	−1.12115
$359$	−18.8701	−0.995924	−0.497962	−	0.867199i	$-0.665918\pi$
$359$	−18.8701	−0.995924	−0.497962	+	0.867199i	$0.665918\pi$
$360$	−5.17157	−0.272566
$361$	−11.0000	−0.578947
$362$	−21.8995	−1.15101
$363$	11.5858	0.608096
$364$	0	0
$365$	0	0
$366$	−4.75736	−0.248671
$367$	30.0711	1.56970	0.784848	−	0.619688i	$-0.212741\pi$
$367$	30.0711	1.56970	0.784848	+	0.619688i	$0.212741\pi$
$368$	5.65685	0.294884
$369$	−2.82843	−0.147242
$370$	12.0416	0.626015
$371$	0	0
$372$	2.31371	0.119960
$373$	10.5858	0.548111	0.274056	−	0.961714i	$-0.411635\pi$
$373$	10.5858	0.548111	0.274056	+	0.961714i	$0.411635\pi$
$374$	23.8995	1.23581
$375$	−5.04163	−0.260349
$376$	−10.2426	−0.528224
$377$	2.92893	0.150848
$378$	0	0
$379$	6.27208	0.322175	0.161088	−	0.986940i	$-0.448500\pi$
$379$	6.27208	0.322175	0.161088	+	0.986940i	$0.448500\pi$
$380$	−5.17157	−0.265296
$381$	−3.75736	−0.192495
$382$	18.0711	0.924596
$383$	−14.7279	−0.752562	−0.376281	−	0.926506i	$-0.622797\pi$
$383$	−14.7279	−0.752562	−0.376281	+	0.926506i	$0.622797\pi$
$384$	0.414214	0.0211377
$385$	0	0
$386$	−4.58579	−0.233410
$387$	−3.51472	−0.178663
$388$	−0.171573	−0.00871029
$389$	5.02944	0.255003	0.127501	−	0.991838i	$-0.459304\pi$
$389$	5.02944	0.255003	0.127501	+	0.991838i	$0.459304\pi$
$390$	−0.443651	−0.0224651
$391$	−21.6569	−1.09523
$392$	0	0
$393$	1.95837	0.0987867
$394$	−0.686292	−0.0345749
$395$	−16.8995	−0.850306
$396$	17.6569	0.887290
$397$	−9.27208	−0.465352	−0.232676	−	0.972554i	$-0.574748\pi$
$397$	−9.27208	−0.465352	−0.232676	+	0.972554i	$0.574748\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	−1.65685	−0.0828427
$401$	27.6274	1.37965	0.689824	−	0.723977i	$-0.257688\pi$
$401$	27.6274	1.37965	0.689824	+	0.723977i	$0.257688\pi$
$402$	−2.97056	−0.148158
$403$	−3.27208	−0.162994
$404$	−10.0000	−0.497519
$405$	13.6863	0.680077
$406$	0	0
$407$	−41.1127	−2.03788
$408$	−1.58579	−0.0785081
$409$	−18.1005	−0.895012	−0.447506	−	0.894281i	$-0.647688\pi$
$409$	−18.1005	−0.895012	−0.447506	+	0.894281i	$0.647688\pi$
$410$	1.82843	0.0902996
$411$	−1.65685	−0.0817266
$412$	16.4142	0.808670
$413$	0	0
$414$	−16.0000	−0.786357
$415$	−26.0416	−1.27833
$416$	−0.585786	−0.0287205
$417$	−2.28427	−0.111861
$418$	17.6569	0.863625
$419$	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
$421$	−17.9706	−0.875832	−0.437916	−	0.899016i	$-0.644283\pi$
$421$	−17.9706	−0.875832	−0.437916	+	0.899016i	$0.644283\pi$
$422$	6.34315	0.308780
$423$	28.9706	1.40860
$424$	−7.48528	−0.363517
$425$	6.34315	0.307688
$426$	3.68629	0.178601
$427$	0	0
$428$	8.89949	0.430173
$429$	1.51472	0.0731313
$430$	2.27208	0.109569
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−2.41421	−0.116154
$433$	−14.6274	−0.702949	−0.351474	−	0.936197i	$-0.614320\pi$
$433$	−14.6274	−0.702949	−0.351474	+	0.936197i	$0.614320\pi$
$434$	0	0
$435$	−3.78680	−0.181563
$436$	10.8284	0.518588
$437$	−16.0000	−0.765384
$438$	0	0
$439$	−12.1421	−0.579513	−0.289756	−	0.957100i	$-0.593574\pi$
$439$	−12.1421	−0.579513	−0.289756	+	0.957100i	$0.593574\pi$
$440$	−11.4142	−0.544151
$441$	0	0
$442$	2.24264	0.106672
$443$	−5.10051	−0.242332	−0.121166	−	0.992632i	$-0.538663\pi$
$443$	−5.10051	−0.242332	−0.121166	+	0.992632i	$0.538663\pi$
$444$	2.72792	0.129461
$445$	−7.00000	−0.331832
$446$	22.5563	1.06807
$447$	2.27208	0.107466
$448$	0	0
$449$	14.1716	0.668798	0.334399	−	0.942432i	$-0.391467\pi$
$449$	14.1716	0.668798	0.334399	+	0.942432i	$0.391467\pi$
$450$	4.68629	0.220914
$451$	−6.24264	−0.293954
$452$	11.0000	0.517396
$453$	1.14214	0.0536622
$454$	23.7279	1.11361
$455$	0	0
$456$	−1.17157	−0.0548639
$457$	−10.5858	−0.495182	−0.247591	−	0.968865i	$-0.579639\pi$
$457$	−10.5858	−0.495182	−0.247591	+	0.968865i	$0.579639\pi$
$458$	−13.0711	−0.610771
$459$	9.24264	0.431410
$460$	10.3431	0.482252
$461$	−40.4558	−1.88422	−0.942108	−	0.335309i	$-0.891159\pi$
$461$	−40.4558	−1.88422	−0.942108	+	0.335309i	$0.891159\pi$
$462$	0	0
$463$	12.6863	0.589582	0.294791	−	0.955562i	$-0.404750\pi$
$463$	12.6863	0.589582	0.294791	+	0.955562i	$0.404750\pi$
$464$	−5.00000	−0.232119
$465$	4.23045	0.196182
$466$	−6.10051	−0.282600
$467$	−15.1716	−0.702057	−0.351028	−	0.936365i	$-0.614168\pi$
$467$	−15.1716	−0.702057	−0.351028	+	0.936365i	$0.614168\pi$
$468$	1.65685	0.0765881
$469$	0	0
$470$	−18.7279	−0.863855
$471$	3.02944	0.139589
$472$	−10.4853	−0.482624
$473$	−7.75736	−0.356684
$474$	−3.82843	−0.175845
$475$	4.68629	0.215022
$476$	0	0
$477$	21.1716	0.969380
$478$	11.5147	0.526671
$479$	−2.24264	−0.102469	−0.0512344	−	0.998687i	$-0.516316\pi$
$479$	−2.24264	−0.102469	−0.0512344	+	0.998687i	$0.516316\pi$
$480$	0.757359	0.0345686
$481$	−3.85786	−0.175903
$482$	19.5563	0.890767
$483$	0	0
$484$	27.9706	1.27139
$485$	−0.313708	−0.0142448
$486$	10.3431	0.469175
$487$	−23.5563	−1.06744	−0.533720	−	0.845661i	$-0.679206\pi$
$487$	−23.5563	−1.06744	−0.533720	+	0.845661i	$0.679206\pi$
$488$	−11.4853	−0.519914
$489$	5.51472	0.249384
$490$	0	0
$491$	−10.7574	−0.485473	−0.242736	−	0.970092i	$-0.578045\pi$
$491$	−10.7574	−0.485473	−0.242736	+	0.970092i	$0.578045\pi$
$492$	0.414214	0.0186742
$493$	19.1421	0.862118
$494$	1.65685	0.0745454
$495$	32.2843	1.45107
$496$	5.58579	0.250809
$497$	0	0
$498$	−5.89949	−0.264363
$499$	−32.1421	−1.43888	−0.719440	−	0.694555i	$-0.755601\pi$
$499$	−32.1421	−1.43888	−0.719440	+	0.694555i	$0.755601\pi$
$500$	−12.1716	−0.544329
$501$	−4.00000	−0.178707
$502$	−4.24264	−0.189358
$503$	−0.686292	−0.0306002	−0.0153001	−	0.999883i	$-0.504870\pi$
$503$	−0.686292	−0.0306002	−0.0153001	+	0.999883i	$0.504870\pi$
$504$	0	0
$505$	−18.2843	−0.813639
$506$	−35.3137	−1.56989
$507$	−5.24264	−0.232834
$508$	−9.07107	−0.402464
$509$	18.3431	0.813046	0.406523	−	0.913641i	$-0.366741\pi$
$509$	18.3431	0.813046	0.406523	+	0.913641i	$0.366741\pi$
$510$	−2.89949	−0.128392
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.82843	0.301482
$514$	17.1421	0.756107
$515$	30.0122	1.32250
$516$	0.514719	0.0226592
$517$	63.9411	2.81213
$518$	0	0
$519$	1.78680	0.0784317
$520$	−1.07107	−0.0469694
$521$	4.48528	0.196504	0.0982519	−	0.995162i	$-0.468675\pi$
$521$	4.48528	0.196504	0.0982519	+	0.995162i	$0.468675\pi$
$522$	14.1421	0.618984
$523$	−1.65685	−0.0724492	−0.0362246	−	0.999344i	$-0.511533\pi$
$523$	−1.65685	−0.0724492	−0.0362246	+	0.999344i	$0.511533\pi$
$524$	4.72792	0.206540
$525$	0	0
$526$	19.3137	0.842118
$527$	−21.3848	−0.931535
$528$	−2.58579	−0.112532
$529$	9.00000	0.391304
$530$	−13.6863	−0.594495
$531$	29.6569	1.28700
$532$	0	0
$533$	−0.585786	−0.0253732
$534$	−1.58579	−0.0686237
$535$	16.2721	0.703503
$536$	−7.17157	−0.309765
$537$	−8.78680	−0.379178
$538$	−28.6274	−1.23422
$539$	0	0
$540$	−4.41421	−0.189958
$541$	30.9706	1.33153	0.665764	−	0.746162i	$-0.268106\pi$
$541$	30.9706	1.33153	0.665764	+	0.746162i	$0.268106\pi$
$542$	6.00000	0.257722
$543$	−9.07107	−0.389277
$544$	−3.82843	−0.164142
$545$	19.7990	0.848096
$546$	0	0
$547$	36.1421	1.54533	0.772663	−	0.634816i	$-0.218924\pi$
$547$	36.1421	1.54533	0.772663	+	0.634816i	$0.218924\pi$
$548$	−4.00000	−0.170872
$549$	32.4853	1.38644
$550$	10.3431	0.441033
$551$	14.1421	0.602475
$552$	2.34315	0.0997309
$553$	0	0
$554$	−14.9706	−0.636038
$555$	4.98781	0.211721
$556$	−5.51472	−0.233876
$557$	−36.6569	−1.55320	−0.776600	−	0.629994i	$-0.783058\pi$
$557$	−36.6569	−1.55320	−0.776600	+	0.629994i	$0.783058\pi$
$558$	−15.7990	−0.668825
$559$	−0.727922	−0.0307878
$560$	0	0
$561$	9.89949	0.417957
$562$	−22.9706	−0.968955
$563$	4.62742	0.195022	0.0975112	−	0.995234i	$-0.468912\pi$
$563$	4.62742	0.195022	0.0975112	+	0.995234i	$0.468912\pi$
$564$	−4.24264	−0.178647
$565$	20.1127	0.846148
$566$	−26.4853	−1.11326
$567$	0	0
$568$	8.89949	0.373415
$569$	−38.1127	−1.59777	−0.798884	−	0.601486i	$-0.794576\pi$
$569$	−38.1127	−1.59777	−0.798884	+	0.601486i	$0.794576\pi$
$570$	−2.14214	−0.0897242
$571$	−36.9706	−1.54717	−0.773585	−	0.633693i	$-0.781538\pi$
$571$	−36.9706	−1.54717	−0.773585	+	0.633693i	$0.781538\pi$
$572$	3.65685	0.152901
$573$	7.48528	0.312702
$574$	0	0
$575$	−9.37258	−0.390864
$576$	−2.82843	−0.117851
$577$	−32.2843	−1.34401	−0.672006	−	0.740546i	$-0.734567\pi$
$577$	−32.2843	−1.34401	−0.672006	+	0.740546i	$0.734567\pi$
$578$	−2.34315	−0.0974620
$579$	−1.89949	−0.0789403
$580$	−9.14214	−0.379607
$581$	0	0
$582$	−0.0710678	−0.00294586
$583$	46.7279	1.93527
$584$	0	0
$585$	3.02944	0.125252
$586$	−11.6569	−0.481540
$587$	−0.757359	−0.0312596	−0.0156298	−	0.999878i	$-0.504975\pi$
$587$	−0.757359	−0.0312596	−0.0156298	+	0.999878i	$0.504975\pi$
$588$	0	0
$589$	−15.7990	−0.650986
$590$	−19.1716	−0.789281
$591$	−0.284271	−0.0116934
$592$	6.58579	0.270674
$593$	46.6569	1.91597	0.957984	−	0.286823i	$-0.0925991\pi$
$593$	46.6569	1.91597	0.957984	+	0.286823i	$0.0925991\pi$
$594$	15.0711	0.618373
$595$	0	0
$596$	5.48528	0.224686
$597$	1.65685	0.0678105
$598$	−3.31371	−0.135508
$599$	35.7574	1.46101	0.730503	−	0.682909i	$-0.239286\pi$
$599$	35.7574	1.46101	0.730503	+	0.682909i	$0.239286\pi$
$600$	−0.686292	−0.0280177
$601$	−3.68629	−0.150367	−0.0751835	−	0.997170i	$-0.523954\pi$
$601$	−3.68629	−0.150367	−0.0751835	+	0.997170i	$0.523954\pi$
$602$	0	0
$603$	20.2843	0.826039
$604$	2.75736	0.112195
$605$	51.1421	2.07922
$606$	−4.14214	−0.168263
$607$	−11.0416	−0.448166	−0.224083	−	0.974570i	$-0.571939\pi$
$607$	−11.0416	−0.448166	−0.224083	+	0.974570i	$0.571939\pi$
$608$	−2.82843	−0.114708
$609$	0	0
$610$	−21.0000	−0.850265
$611$	6.00000	0.242734
$612$	10.8284	0.437713
$613$	−22.2426	−0.898372	−0.449186	−	0.893438i	$-0.648286\pi$
$613$	−22.2426	−0.898372	−0.449186	+	0.893438i	$0.648286\pi$
$614$	24.9706	1.00773
$615$	0.757359	0.0305397
$616$	0	0
$617$	23.7990	0.958111	0.479056	−	0.877785i	$-0.340979\pi$
$617$	23.7990	0.958111	0.479056	+	0.877785i	$0.340979\pi$
$618$	6.79899	0.273495
$619$	20.9289	0.841205	0.420602	−	0.907245i	$-0.361819\pi$
$619$	20.9289	0.841205	0.420602	+	0.907245i	$0.361819\pi$
$620$	10.2132	0.410172
$621$	−13.6569	−0.548031
$622$	−20.1421	−0.807626
$623$	0	0
$624$	−0.242641	−0.00971340
$625$	−13.9706	−0.558823
$626$	31.3137	1.25155
$627$	7.31371	0.292081
$628$	7.31371	0.291849
$629$	−25.2132	−1.00532
$630$	0	0
$631$	−31.4142	−1.25058	−0.625290	−	0.780392i	$-0.715019\pi$
$631$	−31.4142	−1.25058	−0.625290	+	0.780392i	$0.715019\pi$
$632$	−9.24264	−0.367653
$633$	2.62742	0.104430
$634$	14.6274	0.580929
$635$	−16.5858	−0.658187
$636$	−3.10051	−0.122943
$637$	0	0
$638$	31.2132	1.23574
$639$	−25.1716	−0.995772
$640$	1.82843	0.0722749
$641$	46.6690	1.84332	0.921658	−	0.388003i	$-0.126835\pi$
$641$	46.6690	1.84332	0.921658	+	0.388003i	$0.126835\pi$
$642$	3.68629	0.145486
$643$	−5.58579	−0.220282	−0.110141	−	0.993916i	$-0.535130\pi$
$643$	−5.58579	−0.220282	−0.110141	+	0.993916i	$0.535130\pi$
$644$	0	0
$645$	0.941125	0.0370568
$646$	10.8284	0.426039
$647$	41.3848	1.62700	0.813502	−	0.581563i	$-0.197558\pi$
$647$	41.3848	1.62700	0.813502	+	0.581563i	$0.197558\pi$
$648$	7.48528	0.294050
$649$	65.4558	2.56937
$650$	0.970563	0.0380686
$651$	0	0
$652$	13.3137	0.521405
$653$	−17.4853	−0.684252	−0.342126	−	0.939654i	$-0.611147\pi$
$653$	−17.4853	−0.684252	−0.342126	+	0.939654i	$0.611147\pi$
$654$	4.48528	0.175388
$655$	8.64466	0.337775
$656$	1.00000	0.0390434
$657$	0	0
$658$	0	0
$659$	−26.3431	−1.02618	−0.513092	−	0.858334i	$-0.671500\pi$
$659$	−26.3431	−1.02618	−0.513092	+	0.858334i	$0.671500\pi$
$660$	−4.72792	−0.184034
$661$	4.20101	0.163400	0.0817002	−	0.996657i	$-0.473965\pi$
$661$	4.20101	0.163400	0.0817002	+	0.996657i	$0.473965\pi$
$662$	20.0416	0.778940
$663$	0.928932	0.0360767
$664$	−14.2426	−0.552722
$665$	0	0
$666$	−18.6274	−0.721798
$667$	−28.2843	−1.09517
$668$	−9.65685	−0.373635
$669$	9.34315	0.361227
$670$	−13.1127	−0.506588
$671$	71.6985	2.76789
$672$	0	0
$673$	−16.9289	−0.652562	−0.326281	−	0.945273i	$-0.605796\pi$
$673$	−16.9289	−0.652562	−0.326281	+	0.945273i	$0.605796\pi$
$674$	23.3431	0.899144
$675$	4.00000	0.153960
$676$	−12.6569	−0.486802
$677$	−14.1421	−0.543526	−0.271763	−	0.962364i	$-0.587607\pi$
$677$	−14.1421	−0.543526	−0.271763	+	0.962364i	$0.587607\pi$
$678$	4.55635	0.174986
$679$	0	0
$680$	−7.00000	−0.268438
$681$	9.82843	0.376626
$682$	−34.8701	−1.33524
$683$	45.6569	1.74701	0.873505	−	0.486814i	$-0.161841\pi$
$683$	45.6569	1.74701	0.873505	+	0.486814i	$0.161841\pi$
$684$	8.00000	0.305888
$685$	−7.31371	−0.279442
$686$	0	0
$687$	−5.41421	−0.206565
$688$	1.24264	0.0473752
$689$	4.38478	0.167047
$690$	4.28427	0.163099
$691$	20.6985	0.787407	0.393704	−	0.919237i	$-0.371194\pi$
$691$	20.6985	0.787407	0.393704	+	0.919237i	$0.371194\pi$
$692$	4.31371	0.163983
$693$	0	0
$694$	28.2843	1.07366
$695$	−10.0833	−0.382480
$696$	−2.07107	−0.0785036
$697$	−3.82843	−0.145012
$698$	−7.51472	−0.284436
$699$	−2.52691	−0.0955766
$700$	0	0
$701$	−22.3431	−0.843889	−0.421944	−	0.906622i	$-0.638652\pi$
$701$	−22.3431	−0.843889	−0.421944	+	0.906622i	$0.638652\pi$
$702$	1.41421	0.0533761
$703$	−18.6274	−0.702546
$704$	−6.24264	−0.235278
$705$	−7.75736	−0.292159
$706$	−28.0000	−1.05379
$707$	0	0
$708$	−4.34315	−0.163225
$709$	23.6274	0.887346	0.443673	−	0.896189i	$-0.353675\pi$
$709$	23.6274	0.887346	0.443673	+	0.896189i	$0.353675\pi$
$710$	16.2721	0.610680
$711$	26.1421	0.980407
$712$	−3.82843	−0.143476
$713$	31.5980	1.18335
$714$	0	0
$715$	6.68629	0.250053
$716$	−21.2132	−0.792775
$717$	4.76955	0.178122
$718$	−18.8701	−0.704224
$719$	−33.8995	−1.26424	−0.632119	−	0.774871i	$-0.717815\pi$
$719$	−33.8995	−1.26424	−0.632119	+	0.774871i	$0.717815\pi$
$720$	−5.17157	−0.192733
$721$	0	0
$722$	−11.0000	−0.409378
$723$	8.10051	0.301261
$724$	−21.8995	−0.813888
$725$	8.28427	0.307670
$726$	11.5858	0.429989
$727$	−2.58579	−0.0959015	−0.0479508	−	0.998850i	$-0.515269\pi$
$727$	−2.58579	−0.0959015	−0.0479508	+	0.998850i	$0.515269\pi$
$728$	0	0
$729$	−18.1716	−0.673021
$730$	0	0
$731$	−4.75736	−0.175957
$732$	−4.75736	−0.175837
$733$	−42.6569	−1.57557	−0.787783	−	0.615952i	$-0.788771\pi$
$733$	−42.6569	−1.57557	−0.787783	+	0.615952i	$0.788771\pi$
$734$	30.0711	1.10994
$735$	0	0
$736$	5.65685	0.208514
$737$	44.7696	1.64911
$738$	−2.82843	−0.104116
$739$	8.89949	0.327373	0.163687	−	0.986512i	$-0.447661\pi$
$739$	8.89949	0.327373	0.163687	+	0.986512i	$0.447661\pi$
$740$	12.0416	0.442659
$741$	0.686292	0.0252115
$742$	0	0
$743$	0.970563	0.0356065	0.0178032	−	0.999842i	$-0.494333\pi$
$743$	0.970563	0.0356065	0.0178032	+	0.999842i	$0.494333\pi$
$744$	2.31371	0.0848247
$745$	10.0294	0.367450
$746$	10.5858	0.387573
$747$	40.2843	1.47392
$748$	23.8995	0.873852
$749$	0	0
$750$	−5.04163	−0.184094
$751$	−36.3431	−1.32618	−0.663090	−	0.748540i	$-0.730755\pi$
$751$	−36.3431	−1.32618	−0.663090	+	0.748540i	$0.730755\pi$
$752$	−10.2426	−0.373511
$753$	−1.75736	−0.0640417
$754$	2.92893	0.106665
$755$	5.04163	0.183484
$756$	0	0
$757$	34.9411	1.26996	0.634978	−	0.772530i	$-0.281009\pi$
$757$	34.9411	1.26996	0.634978	+	0.772530i	$0.281009\pi$
$758$	6.27208	0.227812
$759$	−14.6274	−0.530942
$760$	−5.17157	−0.187593
$761$	−15.2721	−0.553612	−0.276806	−	0.960926i	$-0.589276\pi$
$761$	−15.2721	−0.553612	−0.276806	+	0.960926i	$0.589276\pi$
$762$	−3.75736	−0.136115
$763$	0	0
$764$	18.0711	0.653788
$765$	19.7990	0.715834
$766$	−14.7279	−0.532141
$767$	6.14214	0.221780
$768$	0.414214	0.0149466
$769$	−42.9706	−1.54956	−0.774779	−	0.632232i	$-0.782139\pi$
$769$	−42.9706	−1.54956	−0.774779	+	0.632232i	$0.782139\pi$
$770$	0	0
$771$	7.10051	0.255718
$772$	−4.58579	−0.165046
$773$	25.2132	0.906856	0.453428	−	0.891293i	$-0.350201\pi$
$773$	25.2132	0.906856	0.453428	+	0.891293i	$0.350201\pi$
$774$	−3.51472	−0.126334
$775$	−9.25483	−0.332443
$776$	−0.171573	−0.00615911
$777$	0	0
$778$	5.02944	0.180314
$779$	−2.82843	−0.101339
$780$	−0.443651	−0.0158852
$781$	−55.5563	−1.98796
$782$	−21.6569	−0.774448
$783$	12.0711	0.431385
$784$	0	0
$785$	13.3726	0.477288
$786$	1.95837	0.0698527
$787$	−24.9706	−0.890104	−0.445052	−	0.895505i	$-0.646815\pi$
$787$	−24.9706	−0.890104	−0.445052	+	0.895505i	$0.646815\pi$
$788$	−0.686292	−0.0244481
$789$	8.00000	0.284808
$790$	−16.8995	−0.601257
$791$	0	0
$792$	17.6569	0.627409
$793$	6.72792	0.238916
$794$	−9.27208	−0.329054
$795$	−5.66905	−0.201060
$796$	4.00000	0.141776
$797$	−21.7696	−0.771117	−0.385559	−	0.922683i	$-0.625991\pi$
$797$	−21.7696	−0.771117	−0.385559	+	0.922683i	$0.625991\pi$
$798$	0	0
$799$	39.2132	1.38726
$800$	−1.65685	−0.0585786
$801$	10.8284	0.382604
$802$	27.6274	0.975558
$803$	0	0
$804$	−2.97056	−0.104764
$805$	0	0
$806$	−3.27208	−0.115254
$807$	−11.8579	−0.417417
$808$	−10.0000	−0.351799
$809$	21.6985	0.762878	0.381439	−	0.924394i	$-0.375429\pi$
$809$	21.6985	0.762878	0.381439	+	0.924394i	$0.375429\pi$
$810$	13.6863	0.480887
$811$	4.72792	0.166020	0.0830099	−	0.996549i	$-0.473547\pi$
$811$	4.72792	0.166020	0.0830099	+	0.996549i	$0.473547\pi$
$812$	0	0
$813$	2.48528	0.0871626
$814$	−41.1127	−1.44100
$815$	24.3431	0.852703
$816$	−1.58579	−0.0555136
$817$	−3.51472	−0.122964
$818$	−18.1005	−0.632869
$819$	0	0
$820$	1.82843	0.0638514
$821$	−35.2132	−1.22895	−0.614475	−	0.788937i	$-0.710632\pi$
$821$	−35.2132	−1.22895	−0.614475	+	0.788937i	$0.710632\pi$
$822$	−1.65685	−0.0577894
$823$	−1.87006	−0.0651861	−0.0325931	−	0.999469i	$-0.510377\pi$
$823$	−1.87006	−0.0651861	−0.0325931	+	0.999469i	$0.510377\pi$
$824$	16.4142	0.571816
$825$	4.28427	0.149159
$826$	0	0
$827$	37.1127	1.29053	0.645267	−	0.763957i	$-0.276746\pi$
$827$	37.1127	1.29053	0.645267	+	0.763957i	$0.276746\pi$
$828$	−16.0000	−0.556038
$829$	−38.3137	−1.33069	−0.665345	−	0.746536i	$-0.731716\pi$
$829$	−38.3137	−1.33069	−0.665345	+	0.746536i	$0.731716\pi$
$830$	−26.0416	−0.903918
$831$	−6.20101	−0.215111
$832$	−0.585786	−0.0203085
$833$	0	0
$834$	−2.28427	−0.0790978
$835$	−17.6569	−0.611041
$836$	17.6569	0.610675
$837$	−13.4853	−0.466120
$838$	24.0416	0.830504
$839$	41.1127	1.41937	0.709684	−	0.704520i	$-0.248838\pi$
$839$	41.1127	1.41937	0.709684	+	0.704520i	$0.248838\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−17.9706	−0.619306
$843$	−9.51472	−0.327704
$844$	6.34315	0.218340
$845$	−23.1421	−0.796114
$846$	28.9706	0.996028
$847$	0	0
$848$	−7.48528	−0.257046
$849$	−10.9706	−0.376509
$850$	6.34315	0.217568
$851$	37.2548	1.27708
$852$	3.68629	0.126290
$853$	0.171573	0.00587454	0.00293727	−	0.999996i	$-0.499065\pi$
$853$	0.171573	0.00587454	0.00293727	+	0.999996i	$0.499065\pi$
$854$	0	0
$855$	14.6274	0.500247
$856$	8.89949	0.304178
$857$	−57.5980	−1.96751	−0.983755	−	0.179518i	$-0.942546\pi$
$857$	−57.5980	−1.96751	−0.983755	+	0.179518i	$0.942546\pi$
$858$	1.51472	0.0517116
$859$	−6.38478	−0.217846	−0.108923	−	0.994050i	$-0.534740\pi$
$859$	−6.38478	−0.217846	−0.108923	+	0.994050i	$0.534740\pi$
$860$	2.27208	0.0774772
$861$	0	0
$862$	−16.0000	−0.544962
$863$	−25.4142	−0.865110	−0.432555	−	0.901608i	$-0.642388\pi$
$863$	−25.4142	−0.865110	−0.432555	+	0.901608i	$0.642388\pi$
$864$	−2.41421	−0.0821332
$865$	7.88730	0.268176
$866$	−14.6274	−0.497060
$867$	−0.970563	−0.0329620
$868$	0	0
$869$	57.6985	1.95729
$870$	−3.78680	−0.128384
$871$	4.20101	0.142346
$872$	10.8284	0.366697
$873$	0.485281	0.0164243
$874$	−16.0000	−0.541208
$875$	0	0
$876$	0	0
$877$	34.6274	1.16928	0.584642	−	0.811291i	$-0.301235\pi$
$877$	34.6274	1.16928	0.584642	+	0.811291i	$0.301235\pi$
$878$	−12.1421	−0.409777
$879$	−4.82843	−0.162859
$880$	−11.4142	−0.384773
$881$	−4.10051	−0.138150	−0.0690748	−	0.997611i	$-0.522005\pi$
$881$	−4.10051	−0.138150	−0.0690748	+	0.997611i	$0.522005\pi$
$882$	0	0
$883$	4.82843	0.162490	0.0812448	−	0.996694i	$-0.474110\pi$
$883$	4.82843	0.162490	0.0812448	+	0.996694i	$0.474110\pi$
$884$	2.24264	0.0754282
$885$	−7.94113	−0.266938
$886$	−5.10051	−0.171355
$887$	28.9706	0.972736	0.486368	−	0.873754i	$-0.338321\pi$
$887$	28.9706	0.972736	0.486368	+	0.873754i	$0.338321\pi$
$888$	2.72792	0.0915431
$889$	0	0
$890$	−7.00000	−0.234641
$891$	−46.7279	−1.56544
$892$	22.5563	0.755242
$893$	28.9706	0.969463
$894$	2.27208	0.0759897
$895$	−38.7868	−1.29650
$896$	0	0
$897$	−1.37258	−0.0458292
$898$	14.1716	0.472912
$899$	−27.9289	−0.931482
$900$	4.68629	0.156210
$901$	28.6569	0.954698
$902$	−6.24264	−0.207857
$903$	0	0
$904$	11.0000	0.365855
$905$	−40.0416	−1.33103
$906$	1.14214	0.0379449
$907$	−18.0711	−0.600040	−0.300020	−	0.953933i	$-0.596993\pi$
$907$	−18.0711	−0.600040	−0.300020	+	0.953933i	$0.596993\pi$
$908$	23.7279	0.787439
$909$	28.2843	0.938130
$910$	0	0
$911$	15.1716	0.502657	0.251328	−	0.967902i	$-0.419133\pi$
$911$	15.1716	0.502657	0.251328	+	0.967902i	$0.419133\pi$
$912$	−1.17157	−0.0387947
$913$	88.9117	2.94255
$914$	−10.5858	−0.350147
$915$	−8.69848	−0.287563
$916$	−13.0711	−0.431880
$917$	0	0
$918$	9.24264	0.305053
$919$	−21.2426	−0.700730	−0.350365	−	0.936613i	$-0.613942\pi$
$919$	−21.2426	−0.700730	−0.350365	+	0.936613i	$0.613942\pi$
$920$	10.3431	0.341003
$921$	10.3431	0.340818
$922$	−40.4558	−1.33234
$923$	−5.21320	−0.171595
$924$	0	0
$925$	−10.9117	−0.358774
$926$	12.6863	0.416897
$927$	−46.4264	−1.52484
$928$	−5.00000	−0.164133
$929$	5.85786	0.192190	0.0960951	−	0.995372i	$-0.469365\pi$
$929$	5.85786	0.192190	0.0960951	+	0.995372i	$0.469365\pi$
$930$	4.23045	0.138722
$931$	0	0
$932$	−6.10051	−0.199829
$933$	−8.34315	−0.273142
$934$	−15.1716	−0.496429
$935$	43.6985	1.42909
$936$	1.65685	0.0541560
$937$	0.0294373	0.000961673 0	0.000480837	−	1.00000i	$-0.499847\pi$
$937$	0.0294373	0.000961673 0	0.000480837		1.00000i	$0.499847\pi$
$938$	0	0
$939$	12.9706	0.423278
$940$	−18.7279	−0.610837
$941$	−56.9706	−1.85719	−0.928594	−	0.371098i	$-0.878981\pi$
$941$	−56.9706	−1.85719	−0.928594	+	0.371098i	$0.878981\pi$
$942$	3.02944	0.0987044
$943$	5.65685	0.184213
$944$	−10.4853	−0.341267
$945$	0	0
$946$	−7.75736	−0.252214
$947$	−45.4558	−1.47712	−0.738558	−	0.674190i	$-0.764493\pi$
$947$	−45.4558	−1.47712	−0.738558	+	0.674190i	$0.764493\pi$
$948$	−3.82843	−0.124342
$949$	0	0
$950$	4.68629	0.152043
$951$	6.05887	0.196472
$952$	0	0
$953$	22.8284	0.739485	0.369743	−	0.929134i	$-0.379446\pi$
$953$	22.8284	0.739485	0.369743	+	0.929134i	$0.379446\pi$
$954$	21.1716	0.685455
$955$	33.0416	1.06920
$956$	11.5147	0.372413
$957$	12.9289	0.417933
$958$	−2.24264	−0.0724564
$959$	0	0
$960$	0.757359	0.0244437
$961$	0.201010	0.00648420
$962$	−3.85786	−0.124383
$963$	−25.1716	−0.811143
$964$	19.5563	0.629868
$965$	−8.38478	−0.269915
$966$	0	0
$967$	29.5269	0.949521	0.474761	−	0.880115i	$-0.342535\pi$
$967$	29.5269	0.949521	0.474761	+	0.880115i	$0.342535\pi$
$968$	27.9706	0.899008
$969$	4.48528	0.144088
$970$	−0.313708	−0.0100726
$971$	4.12994	0.132536	0.0662681	−	0.997802i	$-0.478891\pi$
$971$	4.12994	0.132536	0.0662681	+	0.997802i	$0.478891\pi$
$972$	10.3431	0.331757
$973$	0	0
$974$	−23.5563	−0.754794
$975$	0.402020	0.0128750
$976$	−11.4853	−0.367635
$977$	−17.3137	−0.553915	−0.276957	−	0.960882i	$-0.589326\pi$
$977$	−17.3137	−0.553915	−0.276957	+	0.960882i	$0.589326\pi$
$978$	5.51472	0.176341
$979$	23.8995	0.763831
$980$	0	0
$981$	−30.6274	−0.977858
$982$	−10.7574	−0.343281
$983$	25.2426	0.805115	0.402558	−	0.915395i	$-0.368121\pi$
$983$	25.2426	0.805115	0.402558	+	0.915395i	$0.368121\pi$
$984$	0.414214	0.0132046
$985$	−1.25483	−0.0399823
$986$	19.1421	0.609610
$987$	0	0
$988$	1.65685	0.0527116
$989$	7.02944	0.223523
$990$	32.2843	1.02606
$991$	10.9706	0.348491	0.174246	−	0.984702i	$-0.444251\pi$
$991$	10.9706	0.348491	0.174246	+	0.984702i	$0.444251\pi$
$992$	5.58579	0.177349
$993$	8.30152	0.263441
$994$	0	0
$995$	7.31371	0.231860
$996$	−5.89949	−0.186933
$997$	17.9411	0.568201	0.284101	−	0.958794i	$-0.408305\pi$
$997$	17.9411	0.568201	0.284101	+	0.958794i	$0.408305\pi$
$998$	−32.1421	−1.01744
$999$	−15.8995	−0.503038

Twists

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

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

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.82843 q^{5} +0.414214 q^{6} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.82843 q^{5} +0.414214 q^{6} +1.00000 q^{8} -2.82843 q^{9} +1.82843 q^{10} -6.24264 q^{11} +0.414214 q^{12} -0.585786 q^{13} +0.757359 q^{15} +1.00000 q^{16} -3.82843 q^{17} -2.82843 q^{18} -2.82843 q^{19} +1.82843 q^{20} -6.24264 q^{22} +5.65685 q^{23} +0.414214 q^{24} -1.65685 q^{25} -0.585786 q^{26} -2.41421 q^{27} -5.00000 q^{29} +0.757359 q^{30} +5.58579 q^{31} +1.00000 q^{32} -2.58579 q^{33} -3.82843 q^{34} -2.82843 q^{36} +6.58579 q^{37} -2.82843 q^{38} -0.242641 q^{39} +1.82843 q^{40} +1.00000 q^{41} +1.24264 q^{43} -6.24264 q^{44} -5.17157 q^{45} +5.65685 q^{46} -10.2426 q^{47} +0.414214 q^{48} -1.65685 q^{50} -1.58579 q^{51} -0.585786 q^{52} -7.48528 q^{53} -2.41421 q^{54} -11.4142 q^{55} -1.17157 q^{57} -5.00000 q^{58} -10.4853 q^{59} +0.757359 q^{60} -11.4853 q^{61} +5.58579 q^{62} +1.00000 q^{64} -1.07107 q^{65} -2.58579 q^{66} -7.17157 q^{67} -3.82843 q^{68} +2.34315 q^{69} +8.89949 q^{71} -2.82843 q^{72} +6.58579 q^{74} -0.686292 q^{75} -2.82843 q^{76} -0.242641 q^{78} -9.24264 q^{79} +1.82843 q^{80} +7.48528 q^{81} +1.00000 q^{82} -14.2426 q^{83} -7.00000 q^{85} +1.24264 q^{86} -2.07107 q^{87} -6.24264 q^{88} -3.82843 q^{89} -5.17157 q^{90} +5.65685 q^{92} +2.31371 q^{93} -10.2426 q^{94} -5.17157 q^{95} +0.414214 q^{96} -0.171573 q^{97} +17.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8}+O(q^{10}) \) 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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