LMFDB - Embedded newform 4018.2.a.z.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} +3.41421 q^{11} -2.41421 q^{12} +2.24264 q^{13} -2.41421 q^{15} +1.00000 q^{16} -7.82843 q^{17} +2.82843 q^{18} -2.82843 q^{19} +1.00000 q^{20} +3.41421 q^{22} -4.00000 q^{23} -2.41421 q^{24} -4.00000 q^{25} +2.24264 q^{26} +0.414214 q^{27} -1.82843 q^{29} -2.41421 q^{30} -5.58579 q^{31} +1.00000 q^{32} -8.24264 q^{33} -7.82843 q^{34} +2.82843 q^{36} +1.41421 q^{37} -2.82843 q^{38} -5.41421 q^{39} +1.00000 q^{40} +1.00000 q^{41} +8.07107 q^{43} +3.41421 q^{44} +2.82843 q^{45} -4.00000 q^{46} -11.4142 q^{47} -2.41421 q^{48} -4.00000 q^{50} +18.8995 q^{51} +2.24264 q^{52} -2.65685 q^{53} +0.414214 q^{54} +3.41421 q^{55} +6.82843 q^{57} -1.82843 q^{58} -0.828427 q^{59} -2.41421 q^{60} +8.65685 q^{61} -5.58579 q^{62} +1.00000 q^{64} +2.24264 q^{65} -8.24264 q^{66} +8.82843 q^{67} -7.82843 q^{68} +9.65685 q^{69} -7.24264 q^{71} +2.82843 q^{72} -4.00000 q^{73} +1.41421 q^{74} +9.65685 q^{75} -2.82843 q^{76} -5.41421 q^{78} +5.24264 q^{79} +1.00000 q^{80} -9.48528 q^{81} +1.00000 q^{82} +13.0711 q^{83} -7.82843 q^{85} +8.07107 q^{86} +4.41421 q^{87} +3.41421 q^{88} -2.17157 q^{89} +2.82843 q^{90} -4.00000 q^{92} +13.4853 q^{93} -11.4142 q^{94} -2.82843 q^{95} -2.41421 q^{96} -17.8284 q^{97} +9.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{15} + 2 q^{16} - 10 q^{17} + 2 q^{20} + 4 q^{22} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 2 q^{27} + 2 q^{29} - 2 q^{30} - 14 q^{31} + 2 q^{32} - 8 q^{33} - 10 q^{34} - 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 8 q^{46} - 20 q^{47} - 2 q^{48} - 8 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 2 q^{54} + 4 q^{55} + 8 q^{57} + 2 q^{58} + 4 q^{59} - 2 q^{60} + 6 q^{61} - 14 q^{62} + 2 q^{64} - 4 q^{65} - 8 q^{66} + 12 q^{67} - 10 q^{68} + 8 q^{69} - 6 q^{71} - 8 q^{73} + 8 q^{75} - 8 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + 12 q^{83} - 10 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} - 10 q^{89} - 8 q^{92} + 10 q^{93} - 20 q^{94} - 2 q^{96} - 30 q^{97} + 8 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 - 2 * q^15 + 2 * q^16 - 10 * q^17 + 2 * q^20 + 4 * q^22 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 2 * q^27 + 2 * q^29 - 2 * q^30 - 14 * q^31 + 2 * q^32 - 8 * q^33 - 10 * q^34 - 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 8 * q^46 - 20 * q^47 - 2 * q^48 - 8 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 2 * q^54 + 4 * q^55 + 8 * q^57 + 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 - 14 * q^62 + 2 * q^64 - 4 * q^65 - 8 * q^66 + 12 * q^67 - 10 * q^68 + 8 * q^69 - 6 * q^71 - 8 * q^73 + 8 * q^75 - 8 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + 12 * q^83 - 10 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 - 10 * q^89 - 8 * q^92 + 10 * q^93 - 20 * q^94 - 2 * q^96 - 30 * q^97 + 8 * 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	$-0.745448\pi$
$3$	−2.41421	−1.39385	−0.696923	+	0.717146i	$0.745448\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−2.41421	−0.985599
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.82843	0.942809
$10$	1.00000	0.316228
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	−2.41421	−0.696923
$13$	2.24264	0.621997	0.310998	−	0.950410i	$-0.399337\pi$
$13$	2.24264	0.621997	0.310998	+	0.950410i	$0.399337\pi$
$14$	0	0
$15$	−2.41421	−0.623347
$16$	1.00000	0.250000
$17$	−7.82843	−1.89867	−0.949336	−	0.314262i	$-0.898243\pi$
$17$	−7.82843	−1.89867	−0.949336	+	0.314262i	$0.898243\pi$
$18$	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	$0.605177\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	3.41421	0.727913
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−2.41421	−0.492799
$25$	−4.00000	−0.800000
$26$	2.24264	0.439818
$27$	0.414214	0.0797154
$28$	0	0
$29$	−1.82843	−0.339530	−0.169765	−	0.985485i	$-0.554301\pi$
$29$	−1.82843	−0.339530	−0.169765	+	0.985485i	$0.554301\pi$
$30$	−2.41421	−0.440773
$31$	−5.58579	−1.00324	−0.501618	−	0.865089i	$-0.667262\pi$
$31$	−5.58579	−1.00324	−0.501618	+	0.865089i	$0.667262\pi$
$32$	1.00000	0.176777
$33$	−8.24264	−1.43486
$34$	−7.82843	−1.34256
$35$	0	0
$36$	2.82843	0.471405
$37$	1.41421	0.232495	0.116248	−	0.993220i	$-0.462913\pi$
$37$	1.41421	0.232495	0.116248	+	0.993220i	$0.462913\pi$
$38$	−2.82843	−0.458831
$39$	−5.41421	−0.866968
$40$	1.00000	0.158114
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	8.07107	1.23083	0.615413	−	0.788205i	$-0.288989\pi$
$43$	8.07107	1.23083	0.615413	+	0.788205i	$0.288989\pi$
$44$	3.41421	0.514712
$45$	2.82843	0.421637
$46$	−4.00000	−0.589768
$47$	−11.4142	−1.66493	−0.832467	−	0.554075i	$-0.813072\pi$
$47$	−11.4142	−1.66493	−0.832467	+	0.554075i	$0.813072\pi$
$48$	−2.41421	−0.348462
$49$	0	0
$50$	−4.00000	−0.565685
$51$	18.8995	2.64646
$52$	2.24264	0.310998
$53$	−2.65685	−0.364947	−0.182473	−	0.983211i	$-0.558410\pi$
$53$	−2.65685	−0.364947	−0.182473	+	0.983211i	$0.558410\pi$
$54$	0.414214	0.0563673
$55$	3.41421	0.460372
$56$	0	0
$57$	6.82843	0.904447
$58$	−1.82843	−0.240084
$59$	−0.828427	−0.107852	−0.0539260	−	0.998545i	$-0.517174\pi$
$59$	−0.828427	−0.107852	−0.0539260	+	0.998545i	$0.517174\pi$
$60$	−2.41421	−0.311674
$61$	8.65685	1.10840	0.554198	−	0.832385i	$-0.313025\pi$
$61$	8.65685	1.10840	0.554198	+	0.832385i	$0.313025\pi$
$62$	−5.58579	−0.709396
$63$	0	0
$64$	1.00000	0.125000
$65$	2.24264	0.278165
$66$	−8.24264	−1.01460
$67$	8.82843	1.07856	0.539282	−	0.842125i	$-0.318696\pi$
$67$	8.82843	1.07856	0.539282	+	0.842125i	$0.318696\pi$
$68$	−7.82843	−0.949336
$69$	9.65685	1.16255
$70$	0	0
$71$	−7.24264	−0.859543	−0.429772	−	0.902938i	$-0.641406\pi$
$71$	−7.24264	−0.859543	−0.429772	+	0.902938i	$0.641406\pi$
$72$	2.82843	0.333333
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	1.41421	0.164399
$75$	9.65685	1.11508
$76$	−2.82843	−0.324443
$77$	0	0
$78$	−5.41421	−0.613039
$79$	5.24264	0.589843	0.294922	−	0.955521i	$-0.404706\pi$
$79$	5.24264	0.589843	0.294922	+	0.955521i	$0.404706\pi$
$80$	1.00000	0.111803
$81$	−9.48528	−1.05392
$82$	1.00000	0.110432
$83$	13.0711	1.43474	0.717368	−	0.696694i	$-0.245347\pi$
$83$	13.0711	1.43474	0.717368	+	0.696694i	$0.245347\pi$
$84$	0	0
$85$	−7.82843	−0.849112
$86$	8.07107	0.870326
$87$	4.41421	0.473253
$88$	3.41421	0.363956
$89$	−2.17157	−0.230186	−0.115093	−	0.993355i	$-0.536717\pi$
$89$	−2.17157	−0.230186	−0.115093	+	0.993355i	$0.536717\pi$
$90$	2.82843	0.298142
$91$	0	0
$92$	−4.00000	−0.417029
$93$	13.4853	1.39836
$94$	−11.4142	−1.17729
$95$	−2.82843	−0.290191
$96$	−2.41421	−0.246400
$97$	−17.8284	−1.81020	−0.905101	−	0.425196i	$-0.860205\pi$
$97$	−17.8284	−1.81020	−0.905101	+	0.425196i	$0.860205\pi$
$98$	0	0
$99$	9.65685	0.970550
$100$	−4.00000	−0.400000
$101$	−11.6569	−1.15990	−0.579950	−	0.814652i	$-0.696928\pi$
$101$	−11.6569	−1.15990	−0.579950	+	0.814652i	$0.696928\pi$
$102$	18.8995	1.87133
$103$	10.8995	1.07396	0.536980	−	0.843595i	$-0.319565\pi$
$103$	10.8995	1.07396	0.536980	+	0.843595i	$0.319565\pi$
$104$	2.24264	0.219909
$105$	0	0
$106$	−2.65685	−0.258056
$107$	−6.89949	−0.666999	−0.333500	−	0.942750i	$-0.608230\pi$
$107$	−6.89949	−0.666999	−0.333500	+	0.942750i	$0.608230\pi$
$108$	0.414214	0.0398577
$109$	−14.1421	−1.35457	−0.677285	−	0.735720i	$-0.736844\pi$
$109$	−14.1421	−1.35457	−0.677285	+	0.735720i	$0.736844\pi$
$110$	3.41421	0.325532
$111$	−3.41421	−0.324063
$112$	0	0
$113$	−5.00000	−0.470360	−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000	−0.470360	−0.235180	+	0.971952i	$0.575568\pi$
$114$	6.82843	0.639541
$115$	−4.00000	−0.373002
$116$	−1.82843	−0.169765
$117$	6.34315	0.586424
$118$	−0.828427	−0.0762629
$119$	0	0
$120$	−2.41421	−0.220387
$121$	0.656854	0.0597140
$122$	8.65685	0.783755
$123$	−2.41421	−0.217682
$124$	−5.58579	−0.501618
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−14.2426	−1.26383	−0.631915	−	0.775038i	$-0.717731\pi$
$127$	−14.2426	−1.26383	−0.631915	+	0.775038i	$0.717731\pi$
$128$	1.00000	0.0883883
$129$	−19.4853	−1.71558
$130$	2.24264	0.196693
$131$	−8.24264	−0.720163	−0.360081	−	0.932921i	$-0.617251\pi$
$131$	−8.24264	−0.720163	−0.360081	+	0.932921i	$0.617251\pi$
$132$	−8.24264	−0.717430
$133$	0	0
$134$	8.82843	0.762660
$135$	0.414214	0.0356498
$136$	−7.82843	−0.671282
$137$	−9.65685	−0.825041	−0.412520	−	0.910948i	$-0.635351\pi$
$137$	−9.65685	−0.825041	−0.412520	+	0.910948i	$0.635351\pi$
$138$	9.65685	0.822046
$139$	−18.4853	−1.56790	−0.783951	−	0.620823i	$-0.786798\pi$
$139$	−18.4853	−1.56790	−0.783951	+	0.620823i	$0.786798\pi$
$140$	0	0
$141$	27.5563	2.32066
$142$	−7.24264	−0.607789
$143$	7.65685	0.640298
$144$	2.82843	0.235702
$145$	−1.82843	−0.151843
$146$	−4.00000	−0.331042
$147$	0	0
$148$	1.41421	0.116248
$149$	9.34315	0.765420	0.382710	−	0.923868i	$-0.374991\pi$
$149$	9.34315	0.765420	0.382710	+	0.923868i	$0.374991\pi$
$150$	9.65685	0.788479
$151$	5.92893	0.482490	0.241245	−	0.970464i	$-0.422444\pi$
$151$	5.92893	0.482490	0.241245	+	0.970464i	$0.422444\pi$
$152$	−2.82843	−0.229416
$153$	−22.1421	−1.79009
$154$	0	0
$155$	−5.58579	−0.448661
$156$	−5.41421	−0.433484
$157$	2.34315	0.187003	0.0935017	−	0.995619i	$-0.470194\pi$
$157$	2.34315	0.187003	0.0935017	+	0.995619i	$0.470194\pi$
$158$	5.24264	0.417082
$159$	6.41421	0.508680
$160$	1.00000	0.0790569
$161$	0	0
$162$	−9.48528	−0.745234
$163$	−2.68629	−0.210407	−0.105203	−	0.994451i	$-0.533549\pi$
$163$	−2.68629	−0.210407	−0.105203	+	0.994451i	$0.533549\pi$
$164$	1.00000	0.0780869
$165$	−8.24264	−0.641689
$166$	13.0711	1.01451
$167$	8.97056	0.694163	0.347081	−	0.937835i	$-0.387173\pi$
$167$	8.97056	0.694163	0.347081	+	0.937835i	$0.387173\pi$
$168$	0	0
$169$	−7.97056	−0.613120
$170$	−7.82843	−0.600413
$171$	−8.00000	−0.611775
$172$	8.07107	0.615413
$173$	4.17157	0.317159	0.158579	−	0.987346i	$-0.449309\pi$
$173$	4.17157	0.317159	0.158579	+	0.987346i	$0.449309\pi$
$174$	4.41421	0.334641
$175$	0	0
$176$	3.41421	0.257356
$177$	2.00000	0.150329
$178$	−2.17157	−0.162766
$179$	−4.24264	−0.317110	−0.158555	−	0.987350i	$-0.550683\pi$
$179$	−4.24264	−0.317110	−0.158555	+	0.987350i	$0.550683\pi$
$180$	2.82843	0.210819
$181$	9.89949	0.735824	0.367912	−	0.929861i	$-0.380073\pi$
$181$	9.89949	0.735824	0.367912	+	0.929861i	$0.380073\pi$
$182$	0	0
$183$	−20.8995	−1.54494
$184$	−4.00000	−0.294884
$185$	1.41421	0.103975
$186$	13.4853	0.988789
$187$	−26.7279	−1.95454
$188$	−11.4142	−0.832467
$189$	0	0
$190$	−2.82843	−0.205196
$191$	5.24264	0.379344	0.189672	−	0.981847i	$-0.439258\pi$
$191$	5.24264	0.379344	0.189672	+	0.981847i	$0.439258\pi$
$192$	−2.41421	−0.174231
$193$	−11.8995	−0.856544	−0.428272	−	0.903650i	$-0.640878\pi$
$193$	−11.8995	−0.856544	−0.428272	+	0.903650i	$0.640878\pi$
$194$	−17.8284	−1.28001
$195$	−5.41421	−0.387720
$196$	0	0
$197$	0.686292	0.0488962	0.0244481	−	0.999701i	$-0.492217\pi$
$197$	0.686292	0.0488962	0.0244481	+	0.999701i	$0.492217\pi$
$198$	9.65685	0.686283
$199$	11.3137	0.802008	0.401004	−	0.916076i	$-0.368661\pi$
$199$	11.3137	0.802008	0.401004	+	0.916076i	$0.368661\pi$
$200$	−4.00000	−0.282843
$201$	−21.3137	−1.50335
$202$	−11.6569	−0.820173
$203$	0	0
$204$	18.8995	1.32323
$205$	1.00000	0.0698430
$206$	10.8995	0.759404
$207$	−11.3137	−0.786357
$208$	2.24264	0.155499
$209$	−9.65685	−0.667979
$210$	0	0
$211$	9.65685	0.664805	0.332403	−	0.943138i	$-0.392141\pi$
$211$	9.65685	0.664805	0.332403	+	0.943138i	$0.392141\pi$
$212$	−2.65685	−0.182473
$213$	17.4853	1.19807
$214$	−6.89949	−0.471640
$215$	8.07107	0.550442
$216$	0.414214	0.0281837
$217$	0	0
$218$	−14.1421	−0.957826
$219$	9.65685	0.652550
$220$	3.41421	0.230186
$221$	−17.5563	−1.18097
$222$	−3.41421	−0.229147
$223$	−25.8701	−1.73239	−0.866194	−	0.499709i	$-0.833440\pi$
$223$	−25.8701	−1.73239	−0.866194	+	0.499709i	$0.833440\pi$
$224$	0	0
$225$	−11.3137	−0.754247
$226$	−5.00000	−0.332595
$227$	−17.7279	−1.17664	−0.588322	−	0.808627i	$-0.700211\pi$
$227$	−17.7279	−1.17664	−0.588322	+	0.808627i	$0.700211\pi$
$228$	6.82843	0.452224
$229$	−0.585786	−0.0387099	−0.0193549	−	0.999813i	$-0.506161\pi$
$229$	−0.585786	−0.0387099	−0.0193549	+	0.999813i	$0.506161\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−1.82843	−0.120042
$233$	−15.7574	−1.03230	−0.516149	−	0.856499i	$-0.672635\pi$
$233$	−15.7574	−1.03230	−0.516149	+	0.856499i	$0.672635\pi$
$234$	6.34315	0.414664
$235$	−11.4142	−0.744581
$236$	−0.828427	−0.0539260
$237$	−12.6569	−0.822151
$238$	0	0
$239$	20.4853	1.32508	0.662541	−	0.749025i	$-0.269478\pi$
$239$	20.4853	1.32508	0.662541	+	0.749025i	$0.269478\pi$
$240$	−2.41421	−0.155837
$241$	18.5858	1.19722	0.598608	−	0.801042i	$-0.295721\pi$
$241$	18.5858	1.19722	0.598608	+	0.801042i	$0.295721\pi$
$242$	0.656854	0.0422242
$243$	21.6569	1.38929
$244$	8.65685	0.554198
$245$	0	0
$246$	−2.41421	−0.153925
$247$	−6.34315	−0.403605
$248$	−5.58579	−0.354698
$249$	−31.5563	−1.99980
$250$	−9.00000	−0.569210
$251$	27.0711	1.70871	0.854355	−	0.519689i	$-0.173952\pi$
$251$	27.0711	1.70871	0.854355	+	0.519689i	$0.173952\pi$
$252$	0	0
$253$	−13.6569	−0.858599
$254$	−14.2426	−0.893663
$255$	18.8995	1.18353
$256$	1.00000	0.0625000
$257$	−8.51472	−0.531134	−0.265567	−	0.964092i	$-0.585559\pi$
$257$	−8.51472	−0.531134	−0.265567	+	0.964092i	$0.585559\pi$
$258$	−19.4853	−1.21310
$259$	0	0
$260$	2.24264	0.139083
$261$	−5.17157	−0.320112
$262$	−8.24264	−0.509232
$263$	−24.9706	−1.53975	−0.769875	−	0.638194i	$-0.779682\pi$
$263$	−24.9706	−1.53975	−0.769875	+	0.638194i	$0.779682\pi$
$264$	−8.24264	−0.507299
$265$	−2.65685	−0.163209
$266$	0	0
$267$	5.24264	0.320844
$268$	8.82843	0.539282
$269$	25.3137	1.54340	0.771702	−	0.635984i	$-0.219406\pi$
$269$	25.3137	1.54340	0.771702	+	0.635984i	$0.219406\pi$
$270$	0.414214	0.0252082
$271$	−6.00000	−0.364474	−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000	−0.364474	−0.182237	+	0.983255i	$0.558334\pi$
$272$	−7.82843	−0.474668
$273$	0	0
$274$	−9.65685	−0.583392
$275$	−13.6569	−0.823539
$276$	9.65685	0.581274
$277$	−23.6569	−1.42140	−0.710701	−	0.703494i	$-0.751622\pi$
$277$	−23.6569	−1.42140	−0.710701	+	0.703494i	$0.751622\pi$
$278$	−18.4853	−1.10867
$279$	−15.7990	−0.945861
$280$	0	0
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	27.5563	1.64096
$283$	5.51472	0.327816	0.163908	−	0.986476i	$-0.447590\pi$
$283$	5.51472	0.327816	0.163908	+	0.986476i	$0.447590\pi$
$284$	−7.24264	−0.429772
$285$	6.82843	0.404481
$286$	7.65685	0.452759
$287$	0	0
$288$	2.82843	0.166667
$289$	44.2843	2.60496
$290$	−1.82843	−0.107369
$291$	43.0416	2.52315
$292$	−4.00000	−0.234082
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	−0.828427	−0.0482329
$296$	1.41421	0.0821995
$297$	1.41421	0.0820610
$298$	9.34315	0.541234
$299$	−8.97056	−0.518781
$300$	9.65685	0.557539
$301$	0	0
$302$	5.92893	0.341172
$303$	28.1421	1.61672
$304$	−2.82843	−0.162221
$305$	8.65685	0.495690
$306$	−22.1421	−1.26578
$307$	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
$309$	−26.3137	−1.49693
$310$	−5.58579	−0.317251
$311$	−22.4853	−1.27502	−0.637512	−	0.770441i	$-0.720036\pi$
$311$	−22.4853	−1.27502	−0.637512	+	0.770441i	$0.720036\pi$
$312$	−5.41421	−0.306519
$313$	−28.9706	−1.63751	−0.818757	−	0.574141i	$-0.805336\pi$
$313$	−28.9706	−1.63751	−0.818757	+	0.574141i	$0.805336\pi$
$314$	2.34315	0.132231
$315$	0	0
$316$	5.24264	0.294922
$317$	−10.3431	−0.580929	−0.290464	−	0.956886i	$-0.593810\pi$
$317$	−10.3431	−0.580929	−0.290464	+	0.956886i	$0.593810\pi$
$318$	6.41421	0.359691
$319$	−6.24264	−0.349521
$320$	1.00000	0.0559017
$321$	16.6569	0.929695
$322$	0	0
$323$	22.1421	1.23202
$324$	−9.48528	−0.526960
$325$	−8.97056	−0.497597
$326$	−2.68629	−0.148780
$327$	34.1421	1.88806
$328$	1.00000	0.0552158
$329$	0	0
$330$	−8.24264	−0.453742
$331$	32.0416	1.76117	0.880584	−	0.473891i	$-0.157151\pi$
$331$	32.0416	1.76117	0.880584	+	0.473891i	$0.157151\pi$
$332$	13.0711	0.717368
$333$	4.00000	0.219199
$334$	8.97056	0.490847
$335$	8.82843	0.482349
$336$	0	0
$337$	2.65685	0.144728	0.0723640	−	0.997378i	$-0.476946\pi$
$337$	2.65685	0.144728	0.0723640	+	0.997378i	$0.476946\pi$
$338$	−7.97056	−0.433541
$339$	12.0711	0.655610
$340$	−7.82843	−0.424556
$341$	−19.0711	−1.03276
$342$	−8.00000	−0.432590
$343$	0	0
$344$	8.07107	0.435163
$345$	9.65685	0.519908
$346$	4.17157	0.224265
$347$	5.65685	0.303676	0.151838	−	0.988405i	$-0.451481\pi$
$347$	5.65685	0.303676	0.151838	+	0.988405i	$0.451481\pi$
$348$	4.41421	0.236627
$349$	19.7990	1.05982	0.529908	−	0.848055i	$-0.322227\pi$
$349$	19.7990	1.05982	0.529908	+	0.848055i	$0.322227\pi$
$350$	0	0
$351$	0.928932	0.0495827
$352$	3.41421	0.181978
$353$	17.6569	0.939780	0.469890	−	0.882725i	$-0.344294\pi$
$353$	17.6569	0.939780	0.469890	+	0.882725i	$0.344294\pi$
$354$	2.00000	0.106299
$355$	−7.24264	−0.384399
$356$	−2.17157	−0.115093
$357$	0	0
$358$	−4.24264	−0.224231
$359$	−18.3848	−0.970311	−0.485156	−	0.874428i	$-0.661237\pi$
$359$	−18.3848	−0.970311	−0.485156	+	0.874428i	$0.661237\pi$
$360$	2.82843	0.149071
$361$	−11.0000	−0.578947
$362$	9.89949	0.520306
$363$	−1.58579	−0.0832322
$364$	0	0
$365$	−4.00000	−0.209370
$366$	−20.8995	−1.09243
$367$	5.24264	0.273664	0.136832	−	0.990594i	$-0.456308\pi$
$367$	5.24264	0.273664	0.136832	+	0.990594i	$0.456308\pi$
$368$	−4.00000	−0.208514
$369$	2.82843	0.147242
$370$	1.41421	0.0735215
$371$	0	0
$372$	13.4853	0.699179
$373$	−20.2426	−1.04812	−0.524062	−	0.851680i	$-0.675584\pi$
$373$	−20.2426	−1.04812	−0.524062	+	0.851680i	$0.675584\pi$
$374$	−26.7279	−1.38207
$375$	21.7279	1.12203
$376$	−11.4142	−0.588643
$377$	−4.10051	−0.211187
$378$	0	0
$379$	9.38478	0.482064	0.241032	−	0.970517i	$-0.422514\pi$
$379$	9.38478	0.482064	0.241032	+	0.970517i	$0.422514\pi$
$380$	−2.82843	−0.145095
$381$	34.3848	1.76159
$382$	5.24264	0.268237
$383$	14.7279	0.752562	0.376281	−	0.926506i	$-0.377203\pi$
$383$	14.7279	0.752562	0.376281	+	0.926506i	$0.377203\pi$
$384$	−2.41421	−0.123200
$385$	0	0
$386$	−11.8995	−0.605668
$387$	22.8284	1.16043
$388$	−17.8284	−0.905101
$389$	−2.00000	−0.101404	−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000	−0.101404	−0.0507020	+	0.998714i	$0.516146\pi$
$390$	−5.41421	−0.274159
$391$	31.3137	1.58360
$392$	0	0
$393$	19.8995	1.00380
$394$	0.686292	0.0345749
$395$	5.24264	0.263786
$396$	9.65685	0.485275
$397$	−11.4142	−0.572863	−0.286431	−	0.958101i	$-0.592469\pi$
$397$	−11.4142	−0.572863	−0.286431	+	0.958101i	$0.592469\pi$
$398$	11.3137	0.567105
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−19.9706	−0.997282	−0.498641	−	0.866809i	$-0.666167\pi$
$401$	−19.9706	−0.997282	−0.498641	+	0.866809i	$0.666167\pi$
$402$	−21.3137	−1.06303
$403$	−12.5269	−0.624010
$404$	−11.6569	−0.579950
$405$	−9.48528	−0.471327
$406$	0	0
$407$	4.82843	0.239336
$408$	18.8995	0.935664
$409$	33.8995	1.67622	0.838111	−	0.545500i	$-0.183660\pi$
$409$	33.8995	1.67622	0.838111	+	0.545500i	$0.183660\pi$
$410$	1.00000	0.0493865
$411$	23.3137	1.14998
$412$	10.8995	0.536980
$413$	0	0
$414$	−11.3137	−0.556038
$415$	13.0711	0.641633
$416$	2.24264	0.109955
$417$	44.6274	2.18541
$418$	−9.65685	−0.472332
$419$	11.7574	0.574385	0.287192	−	0.957873i	$-0.407278\pi$
$419$	11.7574	0.574385	0.287192	+	0.957873i	$0.407278\pi$
$420$	0	0
$421$	−26.1127	−1.27266	−0.636328	−	0.771419i	$-0.719547\pi$
$421$	−26.1127	−1.27266	−0.636328	+	0.771419i	$0.719547\pi$
$422$	9.65685	0.470088
$423$	−32.2843	−1.56971
$424$	−2.65685	−0.129028
$425$	31.3137	1.51894
$426$	17.4853	0.847165
$427$	0	0
$428$	−6.89949	−0.333500
$429$	−18.4853	−0.892478
$430$	8.07107	0.389221
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	0.414214	0.0199289
$433$	8.97056	0.431098	0.215549	−	0.976493i	$-0.430846\pi$
$433$	8.97056	0.431098	0.215549	+	0.976493i	$0.430846\pi$
$434$	0	0
$435$	4.41421	0.211645
$436$	−14.1421	−0.677285
$437$	11.3137	0.541208
$438$	9.65685	0.461422
$439$	26.4853	1.26407	0.632037	−	0.774938i	$-0.282219\pi$
$439$	26.4853	1.26407	0.632037	+	0.774938i	$0.282219\pi$
$440$	3.41421	0.162766
$441$	0	0
$442$	−17.5563	−0.835070
$443$	0.757359	0.0359832	0.0179916	−	0.999838i	$-0.494273\pi$
$443$	0.757359	0.0359832	0.0179916	+	0.999838i	$0.494273\pi$
$444$	−3.41421	−0.162031
$445$	−2.17157	−0.102942
$446$	−25.8701	−1.22498
$447$	−22.5563	−1.06688
$448$	0	0
$449$	19.8284	0.935761	0.467881	−	0.883792i	$-0.345018\pi$
$449$	19.8284	0.935761	0.467881	+	0.883792i	$0.345018\pi$
$450$	−11.3137	−0.533333
$451$	3.41421	0.160769
$452$	−5.00000	−0.235180
$453$	−14.3137	−0.672517
$454$	−17.7279	−0.832013
$455$	0	0
$456$	6.82843	0.319770
$457$	−11.2721	−0.527286	−0.263643	−	0.964620i	$-0.584924\pi$
$457$	−11.2721	−0.527286	−0.263643	+	0.964620i	$0.584924\pi$
$458$	−0.585786	−0.0273720
$459$	−3.24264	−0.151354
$460$	−4.00000	−0.186501
$461$	−1.97056	−0.0917783	−0.0458891	−	0.998947i	$-0.514612\pi$
$461$	−1.97056	−0.0917783	−0.0458891	+	0.998947i	$0.514612\pi$
$462$	0	0
$463$	−5.65685	−0.262896	−0.131448	−	0.991323i	$-0.541963\pi$
$463$	−5.65685	−0.262896	−0.131448	+	0.991323i	$0.541963\pi$
$464$	−1.82843	−0.0848826
$465$	13.4853	0.625365
$466$	−15.7574	−0.729946
$467$	17.5147	0.810485	0.405242	−	0.914209i	$-0.367187\pi$
$467$	17.5147	0.810485	0.405242	+	0.914209i	$0.367187\pi$
$468$	6.34315	0.293212
$469$	0	0
$470$	−11.4142	−0.526498
$471$	−5.65685	−0.260654
$472$	−0.828427	−0.0381314
$473$	27.5563	1.26704
$474$	−12.6569	−0.581349
$475$	11.3137	0.519109
$476$	0	0
$477$	−7.51472	−0.344075
$478$	20.4853	0.936975
$479$	7.21320	0.329580	0.164790	−	0.986329i	$-0.447305\pi$
$479$	7.21320	0.329580	0.164790	+	0.986329i	$0.447305\pi$
$480$	−2.41421	−0.110193
$481$	3.17157	0.144611
$482$	18.5858	0.846559
$483$	0	0
$484$	0.656854	0.0298570
$485$	−17.8284	−0.809547
$486$	21.6569	0.982375
$487$	−21.4142	−0.970371	−0.485185	−	0.874411i	$-0.661248\pi$
$487$	−21.4142	−0.970371	−0.485185	+	0.874411i	$0.661248\pi$
$488$	8.65685	0.391877
$489$	6.48528	0.293275
$490$	0	0
$491$	−37.8701	−1.70905	−0.854526	−	0.519409i	$-0.826152\pi$
$491$	−37.8701	−1.70905	−0.854526	+	0.519409i	$0.826152\pi$
$492$	−2.41421	−0.108841
$493$	14.3137	0.644657
$494$	−6.34315	−0.285392
$495$	9.65685	0.434043
$496$	−5.58579	−0.250809
$497$	0	0
$498$	−31.5563	−1.41407
$499$	5.51472	0.246873	0.123436	−	0.992352i	$-0.460609\pi$
$499$	5.51472	0.246873	0.123436	+	0.992352i	$0.460609\pi$
$500$	−9.00000	−0.402492
$501$	−21.6569	−0.967557
$502$	27.0711	1.20824
$503$	21.6569	0.965631	0.482816	−	0.875722i	$-0.339614\pi$
$503$	21.6569	0.965631	0.482816	+	0.875722i	$0.339614\pi$
$504$	0	0
$505$	−11.6569	−0.518723
$506$	−13.6569	−0.607121
$507$	19.2426	0.854596
$508$	−14.2426	−0.631915
$509$	−4.68629	−0.207716	−0.103858	−	0.994592i	$-0.533119\pi$
$509$	−4.68629	−0.207716	−0.103858	+	0.994592i	$0.533119\pi$
$510$	18.8995	0.836884
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.17157	−0.0517262
$514$	−8.51472	−0.375568
$515$	10.8995	0.480289
$516$	−19.4853	−0.857792
$517$	−38.9706	−1.71392
$518$	0	0
$519$	−10.0711	−0.442071
$520$	2.24264	0.0983463
$521$	−14.8284	−0.649645	−0.324823	−	0.945775i	$-0.605305\pi$
$521$	−14.8284	−0.649645	−0.324823	+	0.945775i	$0.605305\pi$
$522$	−5.17157	−0.226354
$523$	−7.31371	−0.319806	−0.159903	−	0.987133i	$-0.551118\pi$
$523$	−7.31371	−0.319806	−0.159903	+	0.987133i	$0.551118\pi$
$524$	−8.24264	−0.360081
$525$	0	0
$526$	−24.9706	−1.08877
$527$	43.7279	1.90482
$528$	−8.24264	−0.358715
$529$	−7.00000	−0.304348
$530$	−2.65685	−0.115406
$531$	−2.34315	−0.101684
$532$	0	0
$533$	2.24264	0.0971396
$534$	5.24264	0.226871
$535$	−6.89949	−0.298291
$536$	8.82843	0.381330
$537$	10.2426	0.442003
$538$	25.3137	1.09135
$539$	0	0
$540$	0.414214	0.0178249
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	−6.00000	−0.257722
$543$	−23.8995	−1.02563
$544$	−7.82843	−0.335641
$545$	−14.1421	−0.605783
$546$	0	0
$547$	−17.7990	−0.761030	−0.380515	−	0.924775i	$-0.624253\pi$
$547$	−17.7990	−0.761030	−0.380515	+	0.924775i	$0.624253\pi$
$548$	−9.65685	−0.412520
$549$	24.4853	1.04501
$550$	−13.6569	−0.582330
$551$	5.17157	0.220316
$552$	9.65685	0.411023
$553$	0	0
$554$	−23.6569	−1.00508
$555$	−3.41421	−0.144925
$556$	−18.4853	−0.783951
$557$	38.7990	1.64397	0.821983	−	0.569512i	$-0.192868\pi$
$557$	38.7990	1.64397	0.821983	+	0.569512i	$0.192868\pi$
$558$	−15.7990	−0.668825
$559$	18.1005	0.765570
$560$	0	0
$561$	64.5269	2.72433
$562$	−26.0000	−1.09674
$563$	−35.9411	−1.51474	−0.757369	−	0.652987i	$-0.773516\pi$
$563$	−35.9411	−1.51474	−0.757369	+	0.652987i	$0.773516\pi$
$564$	27.5563	1.16033
$565$	−5.00000	−0.210352
$566$	5.51472	0.231801
$567$	0	0
$568$	−7.24264	−0.303894
$569$	27.8284	1.16663	0.583314	−	0.812247i	$-0.301756\pi$
$569$	27.8284	1.16663	0.583314	+	0.812247i	$0.301756\pi$
$570$	6.82843	0.286011
$571$	45.2548	1.89386	0.946928	−	0.321446i	$-0.104169\pi$
$571$	45.2548	1.89386	0.946928	+	0.321446i	$0.104169\pi$
$572$	7.65685	0.320149
$573$	−12.6569	−0.528748
$574$	0	0
$575$	16.0000	0.667246
$576$	2.82843	0.117851
$577$	17.6569	0.735064	0.367532	−	0.930011i	$-0.380203\pi$
$577$	17.6569	0.735064	0.367532	+	0.930011i	$0.380203\pi$
$578$	44.2843	1.84198
$579$	28.7279	1.19389
$580$	−1.82843	−0.0759213
$581$	0	0
$582$	43.0416	1.78413
$583$	−9.07107	−0.375685
$584$	−4.00000	−0.165521
$585$	6.34315	0.262257
$586$	−14.0000	−0.578335
$587$	−30.8995	−1.27536	−0.637679	−	0.770302i	$-0.720105\pi$
$587$	−30.8995	−1.27536	−0.637679	+	0.770302i	$0.720105\pi$
$588$	0	0
$589$	15.7990	0.650986
$590$	−0.828427	−0.0341058
$591$	−1.65685	−0.0681539
$592$	1.41421	0.0581238
$593$	−27.0000	−1.10876	−0.554379	−	0.832265i	$-0.687044\pi$
$593$	−27.0000	−1.10876	−0.554379	+	0.832265i	$0.687044\pi$
$594$	1.41421	0.0580259
$595$	0	0
$596$	9.34315	0.382710
$597$	−27.3137	−1.11788
$598$	−8.97056	−0.366834
$599$	39.8406	1.62784	0.813922	−	0.580974i	$-0.197328\pi$
$599$	39.8406	1.62784	0.813922	+	0.580974i	$0.197328\pi$
$600$	9.65685	0.394239
$601$	−22.3137	−0.910195	−0.455098	−	0.890442i	$-0.650396\pi$
$601$	−22.3137	−0.910195	−0.455098	+	0.890442i	$0.650396\pi$
$602$	0	0
$603$	24.9706	1.01688
$604$	5.92893	0.241245
$605$	0.656854	0.0267049
$606$	28.1421	1.14320
$607$	29.3848	1.19269	0.596346	−	0.802728i	$-0.296619\pi$
$607$	29.3848	1.19269	0.596346	+	0.802728i	$0.296619\pi$
$608$	−2.82843	−0.114708
$609$	0	0
$610$	8.65685	0.350506
$611$	−25.5980	−1.03558
$612$	−22.1421	−0.895043
$613$	−10.0416	−0.405578	−0.202789	−	0.979222i	$-0.565000\pi$
$613$	−10.0416	−0.405578	−0.202789	+	0.979222i	$0.565000\pi$
$614$	8.97056	0.362022
$615$	−2.41421	−0.0973505
$616$	0	0
$617$	7.79899	0.313976	0.156988	−	0.987601i	$-0.449822\pi$
$617$	7.79899	0.313976	0.156988	+	0.987601i	$0.449822\pi$
$618$	−26.3137	−1.05849
$619$	−3.07107	−0.123437	−0.0617183	−	0.998094i	$-0.519658\pi$
$619$	−3.07107	−0.123437	−0.0617183	+	0.998094i	$0.519658\pi$
$620$	−5.58579	−0.224331
$621$	−1.65685	−0.0664873
$622$	−22.4853	−0.901578
$623$	0	0
$624$	−5.41421	−0.216742
$625$	11.0000	0.440000
$626$	−28.9706	−1.15790
$627$	23.3137	0.931060
$628$	2.34315	0.0935017
$629$	−11.0711	−0.441432
$630$	0	0
$631$	−23.2132	−0.924103	−0.462052	−	0.886853i	$-0.652886\pi$
$631$	−23.2132	−0.924103	−0.462052	+	0.886853i	$0.652886\pi$
$632$	5.24264	0.208541
$633$	−23.3137	−0.926637
$634$	−10.3431	−0.410779
$635$	−14.2426	−0.565202
$636$	6.41421	0.254340
$637$	0	0
$638$	−6.24264	−0.247149
$639$	−20.4853	−0.810385
$640$	1.00000	0.0395285
$641$	−34.8701	−1.37728	−0.688642	−	0.725101i	$-0.741793\pi$
$641$	−34.8701	−1.37728	−0.688642	+	0.725101i	$0.741793\pi$
$642$	16.6569	0.657394
$643$	24.5563	0.968408	0.484204	−	0.874955i	$-0.339109\pi$
$643$	24.5563	0.968408	0.484204	+	0.874955i	$0.339109\pi$
$644$	0	0
$645$	−19.4853	−0.767232
$646$	22.1421	0.871171
$647$	−25.3848	−0.997979	−0.498989	−	0.866608i	$-0.666295\pi$
$647$	−25.3848	−0.997979	−0.498989	+	0.866608i	$0.666295\pi$
$648$	−9.48528	−0.372617
$649$	−2.82843	−0.111025
$650$	−8.97056	−0.351854
$651$	0	0
$652$	−2.68629	−0.105203
$653$	19.6274	0.768080	0.384040	−	0.923316i	$-0.374532\pi$
$653$	19.6274	0.768080	0.384040	+	0.923316i	$0.374532\pi$
$654$	34.1421	1.33506
$655$	−8.24264	−0.322067
$656$	1.00000	0.0390434
$657$	−11.3137	−0.441390
$658$	0	0
$659$	46.6274	1.81635	0.908173	−	0.418595i	$-0.137477\pi$
$659$	46.6274	1.81635	0.908173	+	0.418595i	$0.137477\pi$
$660$	−8.24264	−0.320844
$661$	−17.4558	−0.678954	−0.339477	−	0.940614i	$-0.610250\pi$
$661$	−17.4558	−0.678954	−0.339477	+	0.940614i	$0.610250\pi$
$662$	32.0416	1.24533
$663$	42.3848	1.64609
$664$	13.0711	0.507256
$665$	0	0
$666$	4.00000	0.154997
$667$	7.31371	0.283188
$668$	8.97056	0.347081
$669$	62.4558	2.41468
$670$	8.82843	0.341072
$671$	29.5563	1.14101
$672$	0	0
$673$	−15.5563	−0.599653	−0.299827	−	0.953994i	$-0.596929\pi$
$673$	−15.5563	−0.599653	−0.299827	+	0.953994i	$0.596929\pi$
$674$	2.65685	0.102338
$675$	−1.65685	−0.0637723
$676$	−7.97056	−0.306560
$677$	27.7990	1.06840	0.534201	−	0.845358i	$-0.320613\pi$
$677$	27.7990	1.06840	0.534201	+	0.845358i	$0.320613\pi$
$678$	12.0711	0.463587
$679$	0	0
$680$	−7.82843	−0.300206
$681$	42.7990	1.64006
$682$	−19.0711	−0.730269
$683$	−9.65685	−0.369509	−0.184755	−	0.982785i	$-0.559149\pi$
$683$	−9.65685	−0.369509	−0.184755	+	0.982785i	$0.559149\pi$
$684$	−8.00000	−0.305888
$685$	−9.65685	−0.368969
$686$	0	0
$687$	1.41421	0.0539556
$688$	8.07107	0.307707
$689$	−5.95837	−0.226996
$690$	9.65685	0.367630
$691$	−5.72792	−0.217900	−0.108950	−	0.994047i	$-0.534749\pi$
$691$	−5.72792	−0.217900	−0.108950	+	0.994047i	$0.534749\pi$
$692$	4.17157	0.158579
$693$	0	0
$694$	5.65685	0.214731
$695$	−18.4853	−0.701187
$696$	4.41421	0.167320
$697$	−7.82843	−0.296523
$698$	19.7990	0.749403
$699$	38.0416	1.43887
$700$	0	0
$701$	24.9706	0.943125	0.471563	−	0.881833i	$-0.343690\pi$
$701$	24.9706	0.943125	0.471563	+	0.881833i	$0.343690\pi$
$702$	0.928932	0.0350603
$703$	−4.00000	−0.150863
$704$	3.41421	0.128678
$705$	27.5563	1.03783
$706$	17.6569	0.664524
$707$	0	0
$708$	2.00000	0.0751646
$709$	−16.7990	−0.630899	−0.315450	−	0.948942i	$-0.602155\pi$
$709$	−16.7990	−0.630899	−0.315450	+	0.948942i	$0.602155\pi$
$710$	−7.24264	−0.271811
$711$	14.8284	0.556109
$712$	−2.17157	−0.0813831
$713$	22.3431	0.836757
$714$	0	0
$715$	7.65685	0.286350
$716$	−4.24264	−0.158555
$717$	−49.4558	−1.84696
$718$	−18.3848	−0.686114
$719$	−43.3553	−1.61688	−0.808441	−	0.588578i	$-0.799688\pi$
$719$	−43.3553	−1.61688	−0.808441	+	0.588578i	$0.799688\pi$
$720$	2.82843	0.105409
$721$	0	0
$722$	−11.0000	−0.409378
$723$	−44.8701	−1.66874
$724$	9.89949	0.367912
$725$	7.31371	0.271624
$726$	−1.58579	−0.0588541
$727$	28.9289	1.07291	0.536457	−	0.843927i	$-0.319762\pi$
$727$	28.9289	1.07291	0.536457	+	0.843927i	$0.319762\pi$
$728$	0	0
$729$	−23.8284	−0.882534
$730$	−4.00000	−0.148047
$731$	−63.1838	−2.33694
$732$	−20.8995	−0.772468
$733$	18.1716	0.671182	0.335591	−	0.942008i	$-0.391064\pi$
$733$	18.1716	0.671182	0.335591	+	0.942008i	$0.391064\pi$
$734$	5.24264	0.193509
$735$	0	0
$736$	−4.00000	−0.147442
$737$	30.1421	1.11030
$738$	2.82843	0.104116
$739$	−12.5563	−0.461893	−0.230946	−	0.972966i	$-0.574182\pi$
$739$	−12.5563	−0.461893	−0.230946	+	0.972966i	$0.574182\pi$
$740$	1.41421	0.0519875
$741$	15.3137	0.562563
$742$	0	0
$743$	33.9411	1.24518	0.622590	−	0.782549i	$-0.286081\pi$
$743$	33.9411	1.24518	0.622590	+	0.782549i	$0.286081\pi$
$744$	13.4853	0.494394
$745$	9.34315	0.342306
$746$	−20.2426	−0.741136
$747$	36.9706	1.35268
$748$	−26.7279	−0.977270
$749$	0	0
$750$	21.7279	0.793392
$751$	31.6569	1.15518	0.577588	−	0.816329i	$-0.303994\pi$
$751$	31.6569	1.15518	0.577588	+	0.816329i	$0.303994\pi$
$752$	−11.4142	−0.416234
$753$	−65.3553	−2.38168
$754$	−4.10051	−0.149332
$755$	5.92893	0.215776
$756$	0	0
$757$	−46.4558	−1.68847	−0.844233	−	0.535976i	$-0.819944\pi$
$757$	−46.4558	−1.68847	−0.844233	+	0.535976i	$0.819944\pi$
$758$	9.38478	0.340870
$759$	32.9706	1.19676
$760$	−2.82843	−0.102598
$761$	−23.5563	−0.853917	−0.426958	−	0.904271i	$-0.640415\pi$
$761$	−23.5563	−0.853917	−0.426958	+	0.904271i	$0.640415\pi$
$762$	34.3848	1.24563
$763$	0	0
$764$	5.24264	0.189672
$765$	−22.1421	−0.800551
$766$	14.7279	0.532141
$767$	−1.85786	−0.0670836
$768$	−2.41421	−0.0871154
$769$	22.9706	0.828340	0.414170	−	0.910200i	$-0.364072\pi$
$769$	22.9706	0.828340	0.414170	+	0.910200i	$0.364072\pi$
$770$	0	0
$771$	20.5563	0.740319
$772$	−11.8995	−0.428272
$773$	−7.55635	−0.271783	−0.135891	−	0.990724i	$-0.543390\pi$
$773$	−7.55635	−0.271783	−0.135891	+	0.990724i	$0.543390\pi$
$774$	22.8284	0.820551
$775$	22.3431	0.802589
$776$	−17.8284	−0.640003
$777$	0	0
$778$	−2.00000	−0.0717035
$779$	−2.82843	−0.101339
$780$	−5.41421	−0.193860
$781$	−24.7279	−0.884835
$782$	31.3137	1.11978
$783$	−0.757359	−0.0270658
$784$	0	0
$785$	2.34315	0.0836305
$786$	19.8995	0.709791
$787$	−25.6569	−0.914568	−0.457284	−	0.889321i	$-0.651178\pi$
$787$	−25.6569	−0.914568	−0.457284	+	0.889321i	$0.651178\pi$
$788$	0.686292	0.0244481
$789$	60.2843	2.14618
$790$	5.24264	0.186525
$791$	0	0
$792$	9.65685	0.343141
$793$	19.4142	0.689419
$794$	−11.4142	−0.405075
$795$	6.41421	0.227489
$796$	11.3137	0.401004
$797$	−37.6274	−1.33283	−0.666416	−	0.745580i	$-0.732172\pi$
$797$	−37.6274	−1.33283	−0.666416	+	0.745580i	$0.732172\pi$
$798$	0	0
$799$	89.3553	3.16116
$800$	−4.00000	−0.141421
$801$	−6.14214	−0.217022
$802$	−19.9706	−0.705185
$803$	−13.6569	−0.481940
$804$	−21.3137	−0.751677
$805$	0	0
$806$	−12.5269	−0.441242
$807$	−61.1127	−2.15127
$808$	−11.6569	−0.410087
$809$	−4.24264	−0.149163	−0.0745817	−	0.997215i	$-0.523762\pi$
$809$	−4.24264	−0.149163	−0.0745817	+	0.997215i	$0.523762\pi$
$810$	−9.48528	−0.333279
$811$	24.4437	0.858333	0.429166	−	0.903225i	$-0.358807\pi$
$811$	24.4437	0.858333	0.429166	+	0.903225i	$0.358807\pi$
$812$	0	0
$813$	14.4853	0.508021
$814$	4.82843	0.169236
$815$	−2.68629	−0.0940967
$816$	18.8995	0.661615
$817$	−22.8284	−0.798666
$818$	33.8995	1.18527
$819$	0	0
$820$	1.00000	0.0349215
$821$	−1.75736	−0.0613323	−0.0306661	−	0.999530i	$-0.509763\pi$
$821$	−1.75736	−0.0613323	−0.0306661	+	0.999530i	$0.509763\pi$
$822$	23.3137	0.813159
$823$	25.1838	0.877851	0.438925	−	0.898523i	$-0.355359\pi$
$823$	25.1838	0.877851	0.438925	+	0.898523i	$0.355359\pi$
$824$	10.8995	0.379702
$825$	32.9706	1.14789
$826$	0	0
$827$	15.4558	0.537452	0.268726	−	0.963217i	$-0.413397\pi$
$827$	15.4558	0.537452	0.268726	+	0.963217i	$0.413397\pi$
$828$	−11.3137	−0.393179
$829$	−51.1421	−1.77624	−0.888120	−	0.459612i	$-0.847989\pi$
$829$	−51.1421	−1.77624	−0.888120	+	0.459612i	$0.847989\pi$
$830$	13.0711	0.453703
$831$	57.1127	1.98122
$832$	2.24264	0.0777496
$833$	0	0
$834$	44.6274	1.54532
$835$	8.97056	0.310439
$836$	−9.65685	−0.333989
$837$	−2.31371	−0.0799735
$838$	11.7574	0.406151
$839$	31.1716	1.07616	0.538081	−	0.842893i	$-0.319149\pi$
$839$	31.1716	1.07616	0.538081	+	0.842893i	$0.319149\pi$
$840$	0	0
$841$	−25.6569	−0.884719
$842$	−26.1127	−0.899903
$843$	62.7696	2.16190
$844$	9.65685	0.332403
$845$	−7.97056	−0.274196
$846$	−32.2843	−1.10996
$847$	0	0
$848$	−2.65685	−0.0912367
$849$	−13.3137	−0.456925
$850$	31.3137	1.07405
$851$	−5.65685	−0.193914
$852$	17.4853	0.599036
$853$	21.0000	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$853$	21.0000	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$854$	0	0
$855$	−8.00000	−0.273594
$856$	−6.89949	−0.235820
$857$	27.9411	0.954451	0.477225	−	0.878781i	$-0.341643\pi$
$857$	27.9411	0.954451	0.477225	+	0.878781i	$0.341643\pi$
$858$	−18.4853	−0.631077
$859$	45.8995	1.56607	0.783035	−	0.621977i	$-0.213670\pi$
$859$	45.8995	1.56607	0.783035	+	0.621977i	$0.213670\pi$
$860$	8.07107	0.275221
$861$	0	0
$862$	12.0000	0.408722
$863$	−7.55635	−0.257221	−0.128611	−	0.991695i	$-0.541052\pi$
$863$	−7.55635	−0.257221	−0.128611	+	0.991695i	$0.541052\pi$
$864$	0.414214	0.0140918
$865$	4.17157	0.141838
$866$	8.97056	0.304832
$867$	−106.912	−3.63091
$868$	0	0
$869$	17.8995	0.607199
$870$	4.41421	0.149656
$871$	19.7990	0.670863
$872$	−14.1421	−0.478913
$873$	−50.4264	−1.70668
$874$	11.3137	0.382692
$875$	0	0
$876$	9.65685	0.326275
$877$	45.6569	1.54172	0.770861	−	0.637003i	$-0.219826\pi$
$877$	45.6569	1.54172	0.770861	+	0.637003i	$0.219826\pi$
$878$	26.4853	0.893835
$879$	33.7990	1.14001
$880$	3.41421	0.115093
$881$	57.1543	1.92558	0.962789	−	0.270254i	$-0.0871076\pi$
$881$	57.1543	1.92558	0.962789	+	0.270254i	$0.0871076\pi$
$882$	0	0
$883$	15.4558	0.520131	0.260065	−	0.965591i	$-0.416256\pi$
$883$	15.4558	0.520131	0.260065	+	0.965591i	$0.416256\pi$
$884$	−17.5563	−0.590484
$885$	2.00000	0.0672293
$886$	0.757359	0.0254440
$887$	−53.2548	−1.78812	−0.894061	−	0.447945i	$-0.852156\pi$
$887$	−53.2548	−1.78812	−0.894061	+	0.447945i	$0.852156\pi$
$888$	−3.41421	−0.114574
$889$	0	0
$890$	−2.17157	−0.0727913
$891$	−32.3848	−1.08493
$892$	−25.8701	−0.866194
$893$	32.2843	1.08035
$894$	−22.5563	−0.754397
$895$	−4.24264	−0.141816
$896$	0	0
$897$	21.6569	0.723101
$898$	19.8284	0.661683
$899$	10.2132	0.340629
$900$	−11.3137	−0.377124
$901$	20.7990	0.692915
$902$	3.41421	0.113681
$903$	0	0
$904$	−5.00000	−0.166298
$905$	9.89949	0.329070
$906$	−14.3137	−0.475541
$907$	44.7574	1.48614	0.743072	−	0.669212i	$-0.233368\pi$
$907$	44.7574	1.48614	0.743072	+	0.669212i	$0.233368\pi$
$908$	−17.7279	−0.588322
$909$	−32.9706	−1.09356
$910$	0	0
$911$	−54.7696	−1.81460	−0.907298	−	0.420488i	$-0.861859\pi$
$911$	−54.7696	−1.81460	−0.907298	+	0.420488i	$0.861859\pi$
$912$	6.82843	0.226112
$913$	44.6274	1.47695
$914$	−11.2721	−0.372847
$915$	−20.8995	−0.690916
$916$	−0.585786	−0.0193549
$917$	0	0
$918$	−3.24264	−0.107023
$919$	42.2132	1.39249	0.696243	−	0.717807i	$-0.254854\pi$
$919$	42.2132	1.39249	0.696243	+	0.717807i	$0.254854\pi$
$920$	−4.00000	−0.131876
$921$	−21.6569	−0.713618
$922$	−1.97056	−0.0648970
$923$	−16.2426	−0.534633
$924$	0	0
$925$	−5.65685	−0.185996
$926$	−5.65685	−0.185896
$927$	30.8284	1.01254
$928$	−1.82843	−0.0600211
$929$	−30.8284	−1.01145	−0.505724	−	0.862695i	$-0.668775\pi$
$929$	−30.8284	−1.01145	−0.505724	+	0.862695i	$0.668775\pi$
$930$	13.4853	0.442200
$931$	0	0
$932$	−15.7574	−0.516149
$933$	54.2843	1.77719
$934$	17.5147	0.573099
$935$	−26.7279	−0.874097
$936$	6.34315	0.207332
$937$	29.9706	0.979096	0.489548	−	0.871976i	$-0.337162\pi$
$937$	29.9706	0.979096	0.489548	+	0.871976i	$0.337162\pi$
$938$	0	0
$939$	69.9411	2.28244
$940$	−11.4142	−0.372291
$941$	41.9411	1.36724	0.683621	−	0.729837i	$-0.260404\pi$
$941$	41.9411	1.36724	0.683621	+	0.729837i	$0.260404\pi$
$942$	−5.65685	−0.184310
$943$	−4.00000	−0.130258
$944$	−0.828427	−0.0269630
$945$	0	0
$946$	27.5563	0.895934
$947$	−32.7696	−1.06487	−0.532434	−	0.846472i	$-0.678722\pi$
$947$	−32.7696	−1.06487	−0.532434	+	0.846472i	$0.678722\pi$
$948$	−12.6569	−0.411076
$949$	−8.97056	−0.291197
$950$	11.3137	0.367065
$951$	24.9706	0.809726
$952$	0	0
$953$	20.4853	0.663583	0.331792	−	0.943353i	$-0.392347\pi$
$953$	20.4853	0.663583	0.331792	+	0.943353i	$0.392347\pi$
$954$	−7.51472	−0.243298
$955$	5.24264	0.169648
$956$	20.4853	0.662541
$957$	15.0711	0.487178
$958$	7.21320	0.233048
$959$	0	0
$960$	−2.41421	−0.0779184
$961$	0.201010	0.00648420
$962$	3.17157	0.102256
$963$	−19.5147	−0.628853
$964$	18.5858	0.598608
$965$	−11.8995	−0.383058
$966$	0	0
$967$	−33.9289	−1.09108	−0.545540	−	0.838084i	$-0.683676\pi$
$967$	−33.9289	−1.09108	−0.545540	+	0.838084i	$0.683676\pi$
$968$	0.656854	0.0211121
$969$	−53.4558	−1.71725
$970$	−17.8284	−0.572436
$971$	3.24264	0.104061	0.0520306	−	0.998645i	$-0.483431\pi$
$971$	3.24264	0.104061	0.0520306	+	0.998645i	$0.483431\pi$
$972$	21.6569	0.694644
$973$	0	0
$974$	−21.4142	−0.686156
$975$	21.6569	0.693574
$976$	8.65685	0.277099
$977$	50.2843	1.60874	0.804368	−	0.594131i	$-0.202504\pi$
$977$	50.2843	1.60874	0.804368	+	0.594131i	$0.202504\pi$
$978$	6.48528	0.207376
$979$	−7.41421	−0.236959
$980$	0	0
$981$	−40.0000	−1.27710
$982$	−37.8701	−1.20848
$983$	14.7574	0.470687	0.235343	−	0.971912i	$-0.424379\pi$
$983$	14.7574	0.470687	0.235343	+	0.971912i	$0.424379\pi$
$984$	−2.41421	−0.0769623
$985$	0.686292	0.0218671
$986$	14.3137	0.455841
$987$	0	0
$988$	−6.34315	−0.201802
$989$	−32.2843	−1.02658
$990$	9.65685	0.306915
$991$	19.6569	0.624421	0.312210	−	0.950013i	$-0.398931\pi$
$991$	19.6569	0.624421	0.312210	+	0.950013i	$0.398931\pi$
$992$	−5.58579	−0.177349
$993$	−77.3553	−2.45480
$994$	0	0
$995$	11.3137	0.358669
$996$	−31.5563	−0.999901
$997$	20.2843	0.642409	0.321205	−	0.947010i	$-0.395912\pi$
$997$	20.2843	0.642409	0.321205	+	0.947010i	$0.395912\pi$
$998$	5.51472	0.174565
$999$	0.585786	0.0185335

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41421 q^{6} +1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} +3.41421 q^{11} -2.41421 q^{12} +2.24264 q^{13} -2.41421 q^{15} +1.00000 q^{16} -7.82843 q^{17} +2.82843 q^{18} -2.82843 q^{19} +1.00000 q^{20} +3.41421 q^{22} -4.00000 q^{23} -2.41421 q^{24} -4.00000 q^{25} +2.24264 q^{26} +0.414214 q^{27} -1.82843 q^{29} -2.41421 q^{30} -5.58579 q^{31} +1.00000 q^{32} -8.24264 q^{33} -7.82843 q^{34} +2.82843 q^{36} +1.41421 q^{37} -2.82843 q^{38} -5.41421 q^{39} +1.00000 q^{40} +1.00000 q^{41} +8.07107 q^{43} +3.41421 q^{44} +2.82843 q^{45} -4.00000 q^{46} -11.4142 q^{47} -2.41421 q^{48} -4.00000 q^{50} +18.8995 q^{51} +2.24264 q^{52} -2.65685 q^{53} +0.414214 q^{54} +3.41421 q^{55} +6.82843 q^{57} -1.82843 q^{58} -0.828427 q^{59} -2.41421 q^{60} +8.65685 q^{61} -5.58579 q^{62} +1.00000 q^{64} +2.24264 q^{65} -8.24264 q^{66} +8.82843 q^{67} -7.82843 q^{68} +9.65685 q^{69} -7.24264 q^{71} +2.82843 q^{72} -4.00000 q^{73} +1.41421 q^{74} +9.65685 q^{75} -2.82843 q^{76} -5.41421 q^{78} +5.24264 q^{79} +1.00000 q^{80} -9.48528 q^{81} +1.00000 q^{82} +13.0711 q^{83} -7.82843 q^{85} +8.07107 q^{86} +4.41421 q^{87} +3.41421 q^{88} -2.17157 q^{89} +2.82843 q^{90} -4.00000 q^{92} +13.4853 q^{93} -11.4142 q^{94} -2.82843 q^{95} -2.41421 q^{96} -17.8284 q^{97} +9.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{15} + 2 q^{16} - 10 q^{17} + 2 q^{20} + 4 q^{22} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 2 q^{27} + 2 q^{29} - 2 q^{30} - 14 q^{31} + 2 q^{32} - 8 q^{33} - 10 q^{34} - 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 8 q^{46} - 20 q^{47} - 2 q^{48} - 8 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 2 q^{54} + 4 q^{55} + 8 q^{57} + 2 q^{58} + 4 q^{59} - 2 q^{60} + 6 q^{61} - 14 q^{62} + 2 q^{64} - 4 q^{65} - 8 q^{66} + 12 q^{67} - 10 q^{68} + 8 q^{69} - 6 q^{71} - 8 q^{73} + 8 q^{75} - 8 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + 12 q^{83} - 10 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} - 10 q^{89} - 8 q^{92} + 10 q^{93} - 20 q^{94} - 2 q^{96} - 30 q^{97} + 8 q^{99}+O(q^{100}) \) 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 - 2 * q^15 + 2 * q^16 - 10 * q^17 + 2 * q^20 + 4 * q^22 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 2 * q^27 + 2 * q^29 - 2 * q^30 - 14 * q^31 + 2 * q^32 - 8 * q^33 - 10 * q^34 - 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 8 * q^46 - 20 * q^47 - 2 * q^48 - 8 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 2 * q^54 + 4 * q^55 + 8 * q^57 + 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 - 14 * q^62 + 2 * q^64 - 4 * q^65 - 8 * q^66 + 12 * q^67 - 10 * q^68 + 8 * q^69 - 6 * q^71 - 8 * q^73 + 8 * q^75 - 8 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + 12 * q^83 - 10 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 - 10 * q^89 - 8 * q^92 + 10 * q^93 - 20 * q^94 - 2 * q^96 - 30 * q^97 + 8 * q^99

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