LMFDB - Embedded newform 4018.2.a.bq.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:	$0$
Dimension:	$6$
Coefficient field:	6.6.5163008.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 5x^2 - 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.78566$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.71387 q^{3} +1.00000 q^{4} +3.56002 q^{5} -2.71387 q^{6} +1.00000 q^{8} +4.36512 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.71387 q^{3} +1.00000 q^{4} +3.56002 q^{5} -2.71387 q^{6} +1.00000 q^{8} +4.36512 q^{9} +3.56002 q^{10} -3.83167 q^{11} -2.71387 q^{12} -1.23459 q^{13} -9.66144 q^{15} +1.00000 q^{16} +7.36103 q^{17} +4.36512 q^{18} +1.14256 q^{19} +3.56002 q^{20} -3.83167 q^{22} -4.15301 q^{23} -2.71387 q^{24} +7.67373 q^{25} -1.23459 q^{26} -3.70476 q^{27} -4.30139 q^{29} -9.66144 q^{30} +3.42454 q^{31} +1.00000 q^{32} +10.3987 q^{33} +7.36103 q^{34} +4.36512 q^{36} +0.0352494 q^{37} +1.14256 q^{38} +3.35052 q^{39} +3.56002 q^{40} -1.00000 q^{41} +3.45066 q^{43} -3.83167 q^{44} +15.5399 q^{45} -4.15301 q^{46} -0.688821 q^{47} -2.71387 q^{48} +7.67373 q^{50} -19.9769 q^{51} -1.23459 q^{52} +13.0771 q^{53} -3.70476 q^{54} -13.6408 q^{55} -3.10076 q^{57} -4.30139 q^{58} +10.4785 q^{59} -9.66144 q^{60} +12.2915 q^{61} +3.42454 q^{62} +1.00000 q^{64} -4.39515 q^{65} +10.3987 q^{66} -7.18016 q^{67} +7.36103 q^{68} +11.2708 q^{69} +5.49156 q^{71} +4.36512 q^{72} +7.25221 q^{73} +0.0352494 q^{74} -20.8255 q^{75} +1.14256 q^{76} +3.35052 q^{78} -6.96382 q^{79} +3.56002 q^{80} -3.04110 q^{81} -1.00000 q^{82} -9.63576 q^{83} +26.2054 q^{85} +3.45066 q^{86} +11.6734 q^{87} -3.83167 q^{88} +13.6462 q^{89} +15.5399 q^{90} -4.15301 q^{92} -9.29377 q^{93} -0.688821 q^{94} +4.06753 q^{95} -2.71387 q^{96} -17.7499 q^{97} -16.7257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9} + 12 q^{10} + 4 q^{12} + 8 q^{13} - 4 q^{15} + 6 q^{16} + 16 q^{17} + 18 q^{18} + 12 q^{19} + 12 q^{20} + 12 q^{23} + 4 q^{24} + 14 q^{25} + 8 q^{26} + 28 q^{27} - 4 q^{30} - 4 q^{31} + 6 q^{32} - 20 q^{33} + 16 q^{34} + 18 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} - 6 q^{41} + 4 q^{43} + 28 q^{45} + 12 q^{46} - 16 q^{47} + 4 q^{48} + 14 q^{50} - 16 q^{51} + 8 q^{52} - 16 q^{53} + 28 q^{54} - 12 q^{55} - 28 q^{57} + 16 q^{59} - 4 q^{60} + 32 q^{61} - 4 q^{62} + 6 q^{64} - 4 q^{65} - 20 q^{66} - 20 q^{67} + 16 q^{68} + 56 q^{69} + 12 q^{71} + 18 q^{72} + 16 q^{73} - 24 q^{74} - 4 q^{75} + 12 q^{76} + 4 q^{78} + 12 q^{80} + 42 q^{81} - 6 q^{82} + 32 q^{83} + 48 q^{85} + 4 q^{86} + 20 q^{87} + 8 q^{89} + 28 q^{90} + 12 q^{92} - 12 q^{93} - 16 q^{94} + 28 q^{95} + 4 q^{96} + 8 q^{97} - 76 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9 + 12 * q^10 + 4 * q^12 + 8 * q^13 - 4 * q^15 + 6 * q^16 + 16 * q^17 + 18 * q^18 + 12 * q^19 + 12 * q^20 + 12 * q^23 + 4 * q^24 + 14 * q^25 + 8 * q^26 + 28 * q^27 - 4 * q^30 - 4 * q^31 + 6 * q^32 - 20 * q^33 + 16 * q^34 + 18 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 - 6 * q^41 + 4 * q^43 + 28 * q^45 + 12 * q^46 - 16 * q^47 + 4 * q^48 + 14 * q^50 - 16 * q^51 + 8 * q^52 - 16 * q^53 + 28 * q^54 - 12 * q^55 - 28 * q^57 + 16 * q^59 - 4 * q^60 + 32 * q^61 - 4 * q^62 + 6 * q^64 - 4 * q^65 - 20 * q^66 - 20 * q^67 + 16 * q^68 + 56 * q^69 + 12 * q^71 + 18 * q^72 + 16 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 + 4 * q^78 + 12 * q^80 + 42 * q^81 - 6 * q^82 + 32 * q^83 + 48 * q^85 + 4 * q^86 + 20 * q^87 + 8 * q^89 + 28 * q^90 + 12 * q^92 - 12 * q^93 - 16 * q^94 + 28 * q^95 + 4 * q^96 + 8 * q^97 - 76 * 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
$3$	−2.71387	−1.56686	−0.783428	−	0.621482i	$-0.786531\pi$
$3$	−2.71387	−1.56686	−0.783428	+	0.621482i	$0.786531\pi$
$4$	1.00000	0.500000
$5$	3.56002	1.59209	0.796044	−	0.605239i	$-0.206922\pi$
$5$	3.56002	1.59209	0.796044	+	0.605239i	$0.206922\pi$
$6$	−2.71387	−1.10793
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	4.36512	1.45504
$10$	3.56002	1.12578
$11$	−3.83167	−1.15529	−0.577646	−	0.816287i	$-0.696029\pi$
$11$	−3.83167	−1.15529	−0.577646	+	0.816287i	$0.696029\pi$
$12$	−2.71387	−0.783428
$13$	−1.23459	−0.342413	−0.171207	−	0.985235i	$-0.554767\pi$
$13$	−1.23459	−0.342413	−0.171207	+	0.985235i	$0.554767\pi$
$14$	0	0
$15$	−9.66144	−2.49457
$16$	1.00000	0.250000
$17$	7.36103	1.78531	0.892656	−	0.450739i	$-0.148839\pi$
$17$	7.36103	1.78531	0.892656	+	0.450739i	$0.148839\pi$
$18$	4.36512	1.02887
$19$	1.14256	0.262121	0.131061	−	0.991374i	$-0.458162\pi$
$19$	1.14256	0.262121	0.131061	+	0.991374i	$0.458162\pi$
$20$	3.56002	0.796044
$21$	0	0
$22$	−3.83167	−0.816915
$23$	−4.15301	−0.865963	−0.432982	−	0.901403i	$-0.642538\pi$
$23$	−4.15301	−0.865963	−0.432982	+	0.901403i	$0.642538\pi$
$24$	−2.71387	−0.553967
$25$	7.67373	1.53475
$26$	−1.23459	−0.242123
$27$	−3.70476	−0.712981
$28$	0	0
$29$	−4.30139	−0.798748	−0.399374	−	0.916788i	$-0.630772\pi$
$29$	−4.30139	−0.798748	−0.399374	+	0.916788i	$0.630772\pi$
$30$	−9.66144	−1.76393
$31$	3.42454	0.615065	0.307533	−	0.951538i	$-0.400497\pi$
$31$	3.42454	0.615065	0.307533	+	0.951538i	$0.400497\pi$
$32$	1.00000	0.176777
$33$	10.3987	1.81018
$34$	7.36103	1.26241
$35$	0	0
$36$	4.36512	0.727520
$37$	0.0352494	0.00579496	0.00289748	−	0.999996i	$-0.499078\pi$
$37$	0.0352494	0.00579496	0.00289748	+	0.999996i	$0.499078\pi$
$38$	1.14256	0.185348
$39$	3.35052	0.536512
$40$	3.56002	0.562888
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	3.45066	0.526220	0.263110	−	0.964766i	$-0.415252\pi$
$43$	3.45066	0.526220	0.263110	+	0.964766i	$0.415252\pi$
$44$	−3.83167	−0.577646
$45$	15.5399	2.31655
$46$	−4.15301	−0.612328
$47$	−0.688821	−0.100475	−0.0502375	−	0.998737i	$-0.515998\pi$
$47$	−0.688821	−0.100475	−0.0502375	+	0.998737i	$0.515998\pi$
$48$	−2.71387	−0.391714
$49$	0	0
$50$	7.67373	1.08523
$51$	−19.9769	−2.79733
$52$	−1.23459	−0.171207
$53$	13.0771	1.79628	0.898138	−	0.439714i	$-0.144920\pi$
$53$	13.0771	1.79628	0.898138	+	0.439714i	$0.144920\pi$
$54$	−3.70476	−0.504154
$55$	−13.6408	−1.83933
$56$	0	0
$57$	−3.10076	−0.410706
$58$	−4.30139	−0.564800
$59$	10.4785	1.36419	0.682094	−	0.731265i	$-0.261070\pi$
$59$	10.4785	1.36419	0.682094	+	0.731265i	$0.261070\pi$
$60$	−9.66144	−1.24729
$61$	12.2915	1.57377	0.786884	−	0.617101i	$-0.211693\pi$
$61$	12.2915	1.57377	0.786884	+	0.617101i	$0.211693\pi$
$62$	3.42454	0.434917
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.39515	−0.545152
$66$	10.3987	1.27999
$67$	−7.18016	−0.877196	−0.438598	−	0.898683i	$-0.644525\pi$
$67$	−7.18016	−0.877196	−0.438598	+	0.898683i	$0.644525\pi$
$68$	7.36103	0.892656
$69$	11.2708	1.35684
$70$	0	0
$71$	5.49156	0.651728	0.325864	−	0.945417i	$-0.394345\pi$
$71$	5.49156	0.651728	0.325864	+	0.945417i	$0.394345\pi$
$72$	4.36512	0.514434
$73$	7.25221	0.848807	0.424404	−	0.905473i	$-0.360484\pi$
$73$	7.25221	0.848807	0.424404	+	0.905473i	$0.360484\pi$
$74$	0.0352494	0.00409765
$75$	−20.8255	−2.40473
$76$	1.14256	0.131061
$77$	0	0
$78$	3.35052	0.379371
$79$	−6.96382	−0.783491	−0.391745	−	0.920074i	$-0.628129\pi$
$79$	−6.96382	−0.783491	−0.391745	+	0.920074i	$0.628129\pi$
$80$	3.56002	0.398022
$81$	−3.04110	−0.337900
$82$	−1.00000	−0.110432
$83$	−9.63576	−1.05766	−0.528831	−	0.848727i	$-0.677369\pi$
$83$	−9.63576	−1.05766	−0.528831	+	0.848727i	$0.677369\pi$
$84$	0	0
$85$	26.2054	2.84237
$86$	3.45066	0.372094
$87$	11.6734	1.25152
$88$	−3.83167	−0.408458
$89$	13.6462	1.44650	0.723248	−	0.690588i	$-0.242648\pi$
$89$	13.6462	1.44650	0.723248	+	0.690588i	$0.242648\pi$
$90$	15.5399	1.63805
$91$	0	0
$92$	−4.15301	−0.432982
$93$	−9.29377	−0.963719
$94$	−0.688821	−0.0710465
$95$	4.06753	0.417320
$96$	−2.71387	−0.276984
$97$	−17.7499	−1.80223	−0.901117	−	0.433576i	$-0.857252\pi$
$97$	−17.7499	−1.80223	−0.901117	+	0.433576i	$0.857252\pi$
$98$	0	0
$99$	−16.7257	−1.68100
$100$	7.67373	0.767373
$101$	−6.17156	−0.614093	−0.307047	−	0.951694i	$-0.599341\pi$
$101$	−6.17156	−0.614093	−0.307047	+	0.951694i	$0.599341\pi$
$102$	−19.9769	−1.97801
$103$	−3.99182	−0.393326	−0.196663	−	0.980471i	$-0.563010\pi$
$103$	−3.99182	−0.393326	−0.196663	+	0.980471i	$0.563010\pi$
$104$	−1.23459	−0.121061
$105$	0	0
$106$	13.0771	1.27016
$107$	7.85165	0.759047	0.379524	−	0.925182i	$-0.376088\pi$
$107$	7.85165	0.759047	0.379524	+	0.925182i	$0.376088\pi$
$108$	−3.70476	−0.356490
$109$	−5.27452	−0.505207	−0.252604	−	0.967570i	$-0.581287\pi$
$109$	−5.27452	−0.505207	−0.252604	+	0.967570i	$0.581287\pi$
$110$	−13.6408	−1.30060
$111$	−0.0956623	−0.00907987
$112$	0	0
$113$	−18.8171	−1.77016	−0.885082	−	0.465434i	$-0.845898\pi$
$113$	−18.8171	−1.77016	−0.885082	+	0.465434i	$0.845898\pi$
$114$	−3.10076	−0.290413
$115$	−14.7848	−1.37869
$116$	−4.30139	−0.399374
$117$	−5.38912	−0.498224
$118$	10.4785	0.964627
$119$	0	0
$120$	−9.66144	−0.881965
$121$	3.68171	0.334701
$122$	12.2915	1.11282
$123$	2.71387	0.244702
$124$	3.42454	0.307533
$125$	9.51851	0.851362
$126$	0	0
$127$	16.2190	1.43920	0.719600	−	0.694388i	$-0.244325\pi$
$127$	16.2190	1.43920	0.719600	+	0.694388i	$0.244325\pi$
$128$	1.00000	0.0883883
$129$	−9.36465	−0.824511
$130$	−4.39515	−0.385480
$131$	17.6372	1.54097	0.770484	−	0.637460i	$-0.220015\pi$
$131$	17.6372	1.54097	0.770484	+	0.637460i	$0.220015\pi$
$132$	10.3987	0.905089
$133$	0	0
$134$	−7.18016	−0.620271
$135$	−13.1890	−1.13513
$136$	7.36103	0.631203
$137$	11.8720	1.01429	0.507147	−	0.861860i	$-0.330700\pi$
$137$	11.8720	1.01429	0.507147	+	0.861860i	$0.330700\pi$
$138$	11.2708	0.959431
$139$	7.15180	0.606608	0.303304	−	0.952894i	$-0.401910\pi$
$139$	7.15180	0.606608	0.303304	+	0.952894i	$0.401910\pi$
$140$	0	0
$141$	1.86937	0.157430
$142$	5.49156	0.460841
$143$	4.73053	0.395587
$144$	4.36512	0.363760
$145$	−15.3130	−1.27168
$146$	7.25221	0.600197
$147$	0	0
$148$	0.0352494	0.00289748
$149$	−7.67136	−0.628462	−0.314231	−	0.949347i	$-0.601747\pi$
$149$	−7.67136	−0.628462	−0.314231	+	0.949347i	$0.601747\pi$
$150$	−20.8255	−1.70040
$151$	13.2311	1.07673	0.538365	−	0.842712i	$-0.319042\pi$
$151$	13.2311	1.07673	0.538365	+	0.842712i	$0.319042\pi$
$152$	1.14256	0.0926738
$153$	32.1318	2.59770
$154$	0	0
$155$	12.1914	0.979238
$156$	3.35052	0.268256
$157$	−12.9502	−1.03354	−0.516771	−	0.856124i	$-0.672866\pi$
$157$	−12.9502	−1.03354	−0.516771	+	0.856124i	$0.672866\pi$
$158$	−6.96382	−0.554011
$159$	−35.4896	−2.81451
$160$	3.56002	0.281444
$161$	0	0
$162$	−3.04110	−0.238932
$163$	19.4728	1.52523	0.762613	−	0.646855i	$-0.223916\pi$
$163$	19.4728	1.52523	0.762613	+	0.646855i	$0.223916\pi$
$164$	−1.00000	−0.0780869
$165$	37.0195	2.88196
$166$	−9.63576	−0.747880
$167$	−5.04041	−0.390038	−0.195019	−	0.980799i	$-0.562477\pi$
$167$	−5.04041	−0.390038	−0.195019	+	0.980799i	$0.562477\pi$
$168$	0	0
$169$	−11.4758	−0.882753
$170$	26.2054	2.00986
$171$	4.98741	0.381396
$172$	3.45066	0.263110
$173$	17.1628	1.30487	0.652433	−	0.757846i	$-0.273748\pi$
$173$	17.1628	1.30487	0.652433	+	0.757846i	$0.273748\pi$
$174$	11.6734	0.884960
$175$	0	0
$176$	−3.83167	−0.288823
$177$	−28.4374	−2.13749
$178$	13.6462	1.02283
$179$	−3.31103	−0.247478	−0.123739	−	0.992315i	$-0.539489\pi$
$179$	−3.31103	−0.247478	−0.123739	+	0.992315i	$0.539489\pi$
$180$	15.5399	1.15828
$181$	10.1830	0.756899	0.378449	−	0.925622i	$-0.376457\pi$
$181$	10.1830	0.756899	0.378449	+	0.925622i	$0.376457\pi$
$182$	0	0
$183$	−33.3576	−2.46587
$184$	−4.15301	−0.306164
$185$	0.125488	0.00922609
$186$	−9.29377	−0.681452
$187$	−28.2050	−2.06256
$188$	−0.688821	−0.0502375
$189$	0	0
$190$	4.06753	0.295090
$191$	−4.21763	−0.305177	−0.152589	−	0.988290i	$-0.548761\pi$
$191$	−4.21763	−0.305177	−0.152589	+	0.988290i	$0.548761\pi$
$192$	−2.71387	−0.195857
$193$	25.2425	1.81699	0.908497	−	0.417892i	$-0.137231\pi$
$193$	25.2425	1.81699	0.908497	+	0.417892i	$0.137231\pi$
$194$	−17.7499	−1.27437
$195$	11.9279	0.854175
$196$	0	0
$197$	16.4881	1.17473	0.587366	−	0.809322i	$-0.300165\pi$
$197$	16.4881	1.17473	0.587366	+	0.809322i	$0.300165\pi$
$198$	−16.7257	−1.18864
$199$	−18.4538	−1.30816	−0.654078	−	0.756427i	$-0.726943\pi$
$199$	−18.4538	−1.30816	−0.654078	+	0.756427i	$0.726943\pi$
$200$	7.67373	0.542614
$201$	19.4861	1.37444
$202$	−6.17156	−0.434229
$203$	0	0
$204$	−19.9769	−1.39866
$205$	−3.56002	−0.248642
$206$	−3.99182	−0.278124
$207$	−18.1284	−1.26001
$208$	−1.23459	−0.0856033
$209$	−4.37791	−0.302827
$210$	0	0
$211$	16.7313	1.15183	0.575915	−	0.817510i	$-0.304646\pi$
$211$	16.7313	1.15183	0.575915	+	0.817510i	$0.304646\pi$
$212$	13.0771	0.898138
$213$	−14.9034	−1.02116
$214$	7.85165	0.536728
$215$	12.2844	0.837789
$216$	−3.70476	−0.252077
$217$	0	0
$218$	−5.27452	−0.357235
$219$	−19.6816	−1.32996
$220$	−13.6408	−0.919664
$221$	−9.08784	−0.611314
$222$	−0.0956623	−0.00642044
$223$	12.9000	0.863848	0.431924	−	0.901910i	$-0.357835\pi$
$223$	12.9000	0.863848	0.431924	+	0.901910i	$0.357835\pi$
$224$	0	0
$225$	33.4967	2.23311
$226$	−18.8171	−1.25170
$227$	10.6843	0.709140	0.354570	−	0.935029i	$-0.384627\pi$
$227$	10.6843	0.709140	0.354570	+	0.935029i	$0.384627\pi$
$228$	−3.10076	−0.205353
$229$	27.5895	1.82317	0.911583	−	0.411116i	$-0.134861\pi$
$229$	27.5895	1.82317	0.911583	+	0.411116i	$0.134861\pi$
$230$	−14.7848	−0.974881
$231$	0	0
$232$	−4.30139	−0.282400
$233$	4.04806	0.265197	0.132599	−	0.991170i	$-0.457668\pi$
$233$	4.04806	0.265197	0.132599	+	0.991170i	$0.457668\pi$
$234$	−5.38912	−0.352298
$235$	−2.45222	−0.159965
$236$	10.4785	0.682094
$237$	18.8989	1.22762
$238$	0	0
$239$	−9.79701	−0.633716	−0.316858	−	0.948473i	$-0.602628\pi$
$239$	−9.79701	−0.633716	−0.316858	+	0.948473i	$0.602628\pi$
$240$	−9.66144	−0.623643
$241$	9.92602	0.639391	0.319696	−	0.947520i	$-0.396419\pi$
$241$	9.92602	0.639391	0.319696	+	0.947520i	$0.396419\pi$
$242$	3.68171	0.236669
$243$	19.3674	1.24242
$244$	12.2915	0.786884
$245$	0	0
$246$	2.71387	0.173030
$247$	−1.41059	−0.0897537
$248$	3.42454	0.217458
$249$	26.1502	1.65720
$250$	9.51851	0.602004
$251$	29.3003	1.84942	0.924711	−	0.380671i	$-0.124307\pi$
$251$	29.3003	1.84942	0.924711	+	0.380671i	$0.124307\pi$
$252$	0	0
$253$	15.9130	1.00044
$254$	16.2190	1.01767
$255$	−71.1182	−4.45359
$256$	1.00000	0.0625000
$257$	−12.5703	−0.784114	−0.392057	−	0.919941i	$-0.628236\pi$
$257$	−12.5703	−0.784114	−0.392057	+	0.919941i	$0.628236\pi$
$258$	−9.36465	−0.583018
$259$	0	0
$260$	−4.39515	−0.272576
$261$	−18.7761	−1.16221
$262$	17.6372	1.08963
$263$	−26.2262	−1.61717	−0.808587	−	0.588377i	$-0.799767\pi$
$263$	−26.2262	−1.61717	−0.808587	+	0.588377i	$0.799767\pi$
$264$	10.3987	0.639994
$265$	46.5547	2.85983
$266$	0	0
$267$	−37.0341	−2.26645
$268$	−7.18016	−0.438598
$269$	12.9457	0.789315	0.394658	−	0.918828i	$-0.370863\pi$
$269$	12.9457	0.789315	0.394658	+	0.918828i	$0.370863\pi$
$270$	−13.1890	−0.802657
$271$	−25.8345	−1.56934	−0.784668	−	0.619916i	$-0.787167\pi$
$271$	−25.8345	−1.56934	−0.784668	+	0.619916i	$0.787167\pi$
$272$	7.36103	0.446328
$273$	0	0
$274$	11.8720	0.717214
$275$	−29.4032	−1.77308
$276$	11.2708	0.678420
$277$	−7.18420	−0.431657	−0.215828	−	0.976431i	$-0.569245\pi$
$277$	−7.18420	−0.431657	−0.215828	+	0.976431i	$0.569245\pi$
$278$	7.15180	0.428936
$279$	14.9485	0.894944
$280$	0	0
$281$	−15.5879	−0.929899	−0.464949	−	0.885337i	$-0.653928\pi$
$281$	−15.5879	−0.929899	−0.464949	+	0.885337i	$0.653928\pi$
$282$	1.86937	0.111320
$283$	20.5883	1.22385	0.611925	−	0.790916i	$-0.290395\pi$
$283$	20.5883	1.22385	0.611925	+	0.790916i	$0.290395\pi$
$284$	5.49156	0.325864
$285$	−11.0388	−0.653880
$286$	4.73053	0.279722
$287$	0	0
$288$	4.36512	0.257217
$289$	37.1847	2.18734
$290$	−15.3130	−0.899211
$291$	48.1711	2.82384
$292$	7.25221	0.424404
$293$	−30.0542	−1.75579	−0.877894	−	0.478855i	$-0.841052\pi$
$293$	−30.0542	−1.75579	−0.877894	+	0.478855i	$0.841052\pi$
$294$	0	0
$295$	37.3037	2.17191
$296$	0.0352494	0.00204883
$297$	14.1954	0.823702
$298$	−7.67136	−0.444390
$299$	5.12726	0.296517
$300$	−20.8255	−1.20236
$301$	0	0
$302$	13.2311	0.761363
$303$	16.7488	0.962196
$304$	1.14256	0.0655303
$305$	43.7580	2.50558
$306$	32.1318	1.83685
$307$	14.0044	0.799273	0.399636	−	0.916674i	$-0.369136\pi$
$307$	14.0044	0.799273	0.399636	+	0.916674i	$0.369136\pi$
$308$	0	0
$309$	10.8333	0.616285
$310$	12.1914	0.692426
$311$	2.38735	0.135374	0.0676871	−	0.997707i	$-0.478438\pi$
$311$	2.38735	0.135374	0.0676871	+	0.997707i	$0.478438\pi$
$312$	3.35052	0.189686
$313$	20.5955	1.16413	0.582064	−	0.813143i	$-0.302245\pi$
$313$	20.5955	1.16413	0.582064	+	0.813143i	$0.302245\pi$
$314$	−12.9502	−0.730824
$315$	0	0
$316$	−6.96382	−0.391745
$317$	24.6696	1.38558	0.692792	−	0.721137i	$-0.256380\pi$
$317$	24.6696	1.38558	0.692792	+	0.721137i	$0.256380\pi$
$318$	−35.4896	−1.99016
$319$	16.4815	0.922787
$320$	3.56002	0.199011
$321$	−21.3084	−1.18932
$322$	0	0
$323$	8.41041	0.467968
$324$	−3.04110	−0.168950
$325$	−9.47389	−0.525517
$326$	19.4728	1.07850
$327$	14.3144	0.791587
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	37.0195	2.03786
$331$	4.43922	0.244001	0.122001	−	0.992530i	$-0.461069\pi$
$331$	4.43922	0.244001	0.122001	+	0.992530i	$0.461069\pi$
$332$	−9.63576	−0.528831
$333$	0.153868	0.00843189
$334$	−5.04041	−0.275799
$335$	−25.5615	−1.39657
$336$	0	0
$337$	−11.0501	−0.601935	−0.300968	−	0.953634i	$-0.597310\pi$
$337$	−11.0501	−0.601935	−0.300968	+	0.953634i	$0.597310\pi$
$338$	−11.4758	−0.624201
$339$	51.0673	2.77359
$340$	26.2054	1.42119
$341$	−13.1217	−0.710580
$342$	4.98741	0.269688
$343$	0	0
$344$	3.45066	0.186047
$345$	40.1241	2.16021
$346$	17.1628	0.922679
$347$	−21.8704	−1.17406	−0.587032	−	0.809564i	$-0.699704\pi$
$347$	−21.8704	−1.17406	−0.587032	+	0.809564i	$0.699704\pi$
$348$	11.6734	0.625761
$349$	−22.4910	−1.20391	−0.601957	−	0.798528i	$-0.705612\pi$
$349$	−22.4910	−1.20391	−0.601957	+	0.798528i	$0.705612\pi$
$350$	0	0
$351$	4.57385	0.244134
$352$	−3.83167	−0.204229
$353$	−2.29627	−0.122218	−0.0611090	−	0.998131i	$-0.519464\pi$
$353$	−2.29627	−0.122218	−0.0611090	+	0.998131i	$0.519464\pi$
$354$	−28.4374	−1.51143
$355$	19.5500	1.03761
$356$	13.6462	0.723248
$357$	0	0
$358$	−3.31103	−0.174993
$359$	−25.4500	−1.34320	−0.671599	−	0.740915i	$-0.734392\pi$
$359$	−25.4500	−1.34320	−0.671599	+	0.740915i	$0.734392\pi$
$360$	15.5399	0.819024
$361$	−17.6946	−0.931293
$362$	10.1830	0.535208
$363$	−9.99170	−0.524428
$364$	0	0
$365$	25.8180	1.35138
$366$	−33.3576	−1.74363
$367$	−13.6434	−0.712181	−0.356090	−	0.934452i	$-0.615890\pi$
$367$	−13.6434	−0.712181	−0.356090	+	0.934452i	$0.615890\pi$
$368$	−4.15301	−0.216491
$369$	−4.36512	−0.227239
$370$	0.125488	0.00652383
$371$	0	0
$372$	−9.29377	−0.481859
$373$	4.33954	0.224693	0.112346	−	0.993669i	$-0.464163\pi$
$373$	4.33954	0.224693	0.112346	+	0.993669i	$0.464163\pi$
$374$	−28.2050	−1.45845
$375$	−25.8321	−1.33396
$376$	−0.688821	−0.0355232
$377$	5.31044	0.273502
$378$	0	0
$379$	15.0524	0.773189	0.386595	−	0.922250i	$-0.373651\pi$
$379$	15.0524	0.773189	0.386595	+	0.922250i	$0.373651\pi$
$380$	4.06753	0.208660
$381$	−44.0163	−2.25502
$382$	−4.21763	−0.215793
$383$	24.4341	1.24853	0.624263	−	0.781214i	$-0.285399\pi$
$383$	24.4341	1.24853	0.624263	+	0.781214i	$0.285399\pi$
$384$	−2.71387	−0.138492
$385$	0	0
$386$	25.2425	1.28481
$387$	15.0625	0.765671
$388$	−17.7499	−0.901117
$389$	5.30198	0.268821	0.134411	−	0.990926i	$-0.457086\pi$
$389$	5.30198	0.268821	0.134411	+	0.990926i	$0.457086\pi$
$390$	11.9279	0.603993
$391$	−30.5705	−1.54601
$392$	0	0
$393$	−47.8651	−2.41448
$394$	16.4881	0.830660
$395$	−24.7913	−1.24739
$396$	−16.7257	−0.840498
$397$	−24.5508	−1.23217	−0.616085	−	0.787680i	$-0.711282\pi$
$397$	−24.5508	−1.23217	−0.616085	+	0.787680i	$0.711282\pi$
$398$	−18.4538	−0.925006
$399$	0	0
$400$	7.67373	0.383686
$401$	28.7496	1.43569	0.717844	−	0.696204i	$-0.245129\pi$
$401$	28.7496	1.43569	0.717844	+	0.696204i	$0.245129\pi$
$402$	19.4861	0.971876
$403$	−4.22789	−0.210606
$404$	−6.17156	−0.307047
$405$	−10.8264	−0.537967
$406$	0	0
$407$	−0.135064	−0.00669487
$408$	−19.9769	−0.989005
$409$	−20.1016	−0.993962	−0.496981	−	0.867762i	$-0.665558\pi$
$409$	−20.1016	−0.993962	−0.496981	+	0.867762i	$0.665558\pi$
$410$	−3.56002	−0.175817
$411$	−32.2191	−1.58925
$412$	−3.99182	−0.196663
$413$	0	0
$414$	−18.1284	−0.890962
$415$	−34.3035	−1.68389
$416$	−1.23459	−0.0605306
$417$	−19.4091	−0.950467
$418$	−4.37791	−0.214131
$419$	−38.6571	−1.88852	−0.944261	−	0.329198i	$-0.893222\pi$
$419$	−38.6571	−1.88852	−0.944261	+	0.329198i	$0.893222\pi$
$420$	0	0
$421$	10.7092	0.521936	0.260968	−	0.965347i	$-0.415958\pi$
$421$	10.7092	0.521936	0.260968	+	0.965347i	$0.415958\pi$
$422$	16.7313	0.814467
$423$	−3.00679	−0.146195
$424$	13.0771	0.635079
$425$	56.4865	2.74000
$426$	−14.9034	−0.722072
$427$	0	0
$428$	7.85165	0.379524
$429$	−12.8381	−0.619828
$430$	12.2844	0.592406
$431$	6.92758	0.333690	0.166845	−	0.985983i	$-0.446642\pi$
$431$	6.92758	0.333690	0.166845	+	0.985983i	$0.446642\pi$
$432$	−3.70476	−0.178245
$433$	−8.87201	−0.426362	−0.213181	−	0.977013i	$-0.568382\pi$
$433$	−8.87201	−0.426362	−0.213181	+	0.977013i	$0.568382\pi$
$434$	0	0
$435$	41.5576	1.99253
$436$	−5.27452	−0.252604
$437$	−4.74506	−0.226987
$438$	−19.6816	−0.940423
$439$	7.90044	0.377068	0.188534	−	0.982067i	$-0.439626\pi$
$439$	7.90044	0.377068	0.188534	+	0.982067i	$0.439626\pi$
$440$	−13.6408	−0.650301
$441$	0	0
$442$	−9.08784	−0.432264
$443$	22.8242	1.08441	0.542204	−	0.840247i	$-0.317590\pi$
$443$	22.8242	1.08441	0.542204	+	0.840247i	$0.317590\pi$
$444$	−0.0956623	−0.00453993
$445$	48.5808	2.30295
$446$	12.9000	0.610833
$447$	20.8191	0.984710
$448$	0	0
$449$	−32.5904	−1.53803	−0.769017	−	0.639228i	$-0.779254\pi$
$449$	−32.5904	−1.53803	−0.769017	+	0.639228i	$0.779254\pi$
$450$	33.4967	1.57905
$451$	3.83167	0.180426
$452$	−18.8171	−0.885082
$453$	−35.9075	−1.68708
$454$	10.6843	0.501438
$455$	0	0
$456$	−3.10076	−0.145207
$457$	−19.2750	−0.901648	−0.450824	−	0.892613i	$-0.648870\pi$
$457$	−19.2750	−0.901648	−0.450824	+	0.892613i	$0.648870\pi$
$458$	27.5895	1.28917
$459$	−27.2708	−1.27289
$460$	−14.7848	−0.689345
$461$	−17.9008	−0.833725	−0.416862	−	0.908970i	$-0.636870\pi$
$461$	−17.9008	−0.833725	−0.416862	+	0.908970i	$0.636870\pi$
$462$	0	0
$463$	−27.5304	−1.27944	−0.639722	−	0.768606i	$-0.720951\pi$
$463$	−27.5304	−1.27944	−0.639722	+	0.768606i	$0.720951\pi$
$464$	−4.30139	−0.199687
$465$	−33.0860	−1.53433
$466$	4.04806	0.187523
$467$	−28.1291	−1.30166	−0.650831	−	0.759223i	$-0.725579\pi$
$467$	−28.1291	−1.30166	−0.650831	+	0.759223i	$0.725579\pi$
$468$	−5.38912	−0.249112
$469$	0	0
$470$	−2.45222	−0.113112
$471$	35.1453	1.61941
$472$	10.4785	0.482313
$473$	−13.2218	−0.607938
$474$	18.8989	0.868056
$475$	8.76769	0.402289
$476$	0	0
$477$	57.0830	2.61365
$478$	−9.79701	−0.448105
$479$	−20.4404	−0.933945	−0.466973	−	0.884272i	$-0.654655\pi$
$479$	−20.4404	−0.933945	−0.466973	+	0.884272i	$0.654655\pi$
$480$	−9.66144	−0.440983
$481$	−0.0435184	−0.00198427
$482$	9.92602	0.452118
$483$	0	0
$484$	3.68171	0.167350
$485$	−63.1901	−2.86932
$486$	19.3674	0.878525
$487$	20.7054	0.938250	0.469125	−	0.883132i	$-0.344569\pi$
$487$	20.7054	0.938250	0.469125	+	0.883132i	$0.344569\pi$
$488$	12.2915	0.556411
$489$	−52.8467	−2.38981
$490$	0	0
$491$	2.67971	0.120934	0.0604669	−	0.998170i	$-0.480741\pi$
$491$	2.67971	0.120934	0.0604669	+	0.998170i	$0.480741\pi$
$492$	2.71387	0.122351
$493$	−31.6626	−1.42601
$494$	−1.41059	−0.0634654
$495$	−59.5438	−2.67629
$496$	3.42454	0.153766
$497$	0	0
$498$	26.1502	1.17182
$499$	−28.8589	−1.29190	−0.645951	−	0.763379i	$-0.723539\pi$
$499$	−28.8589	−1.29190	−0.645951	+	0.763379i	$0.723539\pi$
$500$	9.51851	0.425681
$501$	13.6790	0.611134
$502$	29.3003	1.30774
$503$	28.0170	1.24922	0.624608	−	0.780939i	$-0.285259\pi$
$503$	28.0170	1.24922	0.624608	+	0.780939i	$0.285259\pi$
$504$	0	0
$505$	−21.9709	−0.977691
$506$	15.9130	0.707418
$507$	31.1439	1.38315
$508$	16.2190	0.719600
$509$	−36.3628	−1.61175	−0.805877	−	0.592083i	$-0.798306\pi$
$509$	−36.3628	−1.61175	−0.805877	+	0.592083i	$0.798306\pi$
$510$	−71.1182	−3.14917
$511$	0	0
$512$	1.00000	0.0441942
$513$	−4.23291	−0.186887
$514$	−12.5703	−0.554453
$515$	−14.2110	−0.626210
$516$	−9.36465	−0.412256
$517$	2.63934	0.116078
$518$	0	0
$519$	−46.5778	−2.04454
$520$	−4.39515	−0.192740
$521$	26.1211	1.14439	0.572193	−	0.820119i	$-0.306093\pi$
$521$	26.1211	1.14439	0.572193	+	0.820119i	$0.306093\pi$
$522$	−18.7761	−0.821806
$523$	6.24127	0.272912	0.136456	−	0.990646i	$-0.456429\pi$
$523$	6.24127	0.272912	0.136456	+	0.990646i	$0.456429\pi$
$524$	17.6372	0.770484
$525$	0	0
$526$	−26.2262	−1.14351
$527$	25.2081	1.09808
$528$	10.3987	0.452544
$529$	−5.75248	−0.250108
$530$	46.5547	2.02220
$531$	45.7400	1.98495
$532$	0	0
$533$	1.23459	0.0534759
$534$	−37.0341	−1.60262
$535$	27.9520	1.20847
$536$	−7.18016	−0.310136
$537$	8.98572	0.387762
$538$	12.9457	0.558130
$539$	0	0
$540$	−13.1890	−0.567564
$541$	−20.8304	−0.895567	−0.447784	−	0.894142i	$-0.647786\pi$
$541$	−20.8304	−0.895567	−0.447784	+	0.894142i	$0.647786\pi$
$542$	−25.8345	−1.10969
$543$	−27.6355	−1.18595
$544$	7.36103	0.315602
$545$	−18.7774	−0.804334
$546$	0	0
$547$	0.913364	0.0390526	0.0195263	−	0.999809i	$-0.493784\pi$
$547$	0.913364	0.0390526	0.0195263	+	0.999809i	$0.493784\pi$
$548$	11.8720	0.507147
$549$	53.6539	2.28989
$550$	−29.4032	−1.25376
$551$	−4.91459	−0.209369
$552$	11.2708	0.479715
$553$	0	0
$554$	−7.18420	−0.305228
$555$	−0.340560	−0.0144560
$556$	7.15180	0.303304
$557$	17.3109	0.733486	0.366743	−	0.930322i	$-0.380473\pi$
$557$	17.3109	0.733486	0.366743	+	0.930322i	$0.380473\pi$
$558$	14.9485	0.632821
$559$	−4.26014	−0.180185
$560$	0	0
$561$	76.5450	3.23173
$562$	−15.5879	−0.657538
$563$	14.5713	0.614105	0.307053	−	0.951692i	$-0.400657\pi$
$563$	14.5713	0.614105	0.307053	+	0.951692i	$0.400657\pi$
$564$	1.86937	0.0787149
$565$	−66.9892	−2.81826
$566$	20.5883	0.865393
$567$	0	0
$568$	5.49156	0.230421
$569$	−12.2076	−0.511768	−0.255884	−	0.966708i	$-0.582366\pi$
$569$	−12.2076	−0.511768	−0.255884	+	0.966708i	$0.582366\pi$
$570$	−11.0388	−0.462363
$571$	−39.1241	−1.63729	−0.818646	−	0.574299i	$-0.805275\pi$
$571$	−39.1241	−1.63729	−0.818646	+	0.574299i	$0.805275\pi$
$572$	4.73053	0.197794
$573$	11.4461	0.478169
$574$	0	0
$575$	−31.8691	−1.32903
$576$	4.36512	0.181880
$577$	−14.5467	−0.605588	−0.302794	−	0.953056i	$-0.597919\pi$
$577$	−14.5467	−0.605588	−0.302794	+	0.953056i	$0.597919\pi$
$578$	37.1847	1.54668
$579$	−68.5049	−2.84697
$580$	−15.3130	−0.635838
$581$	0	0
$582$	48.1711	1.99676
$583$	−50.1071	−2.07522
$584$	7.25221	0.300099
$585$	−19.1854	−0.793217
$586$	−30.0542	−1.24153
$587$	−7.43333	−0.306806	−0.153403	−	0.988164i	$-0.549023\pi$
$587$	−7.43333	−0.306806	−0.153403	+	0.988164i	$0.549023\pi$
$588$	0	0
$589$	3.91274	0.161222
$590$	37.3037	1.53577
$591$	−44.7467	−1.84063
$592$	0.0352494	0.00144874
$593$	15.4957	0.636333	0.318166	−	0.948035i	$-0.396933\pi$
$593$	15.4957	0.636333	0.318166	+	0.948035i	$0.396933\pi$
$594$	14.1954	0.582445
$595$	0	0
$596$	−7.67136	−0.314231
$597$	50.0813	2.04969
$598$	5.12726	0.209669
$599$	−20.0048	−0.817373	−0.408686	−	0.912675i	$-0.634013\pi$
$599$	−20.0048	−0.817373	−0.408686	+	0.912675i	$0.634013\pi$
$600$	−20.8255	−0.850199
$601$	18.3618	0.748992	0.374496	−	0.927229i	$-0.377816\pi$
$601$	18.3618	0.748992	0.374496	+	0.927229i	$0.377816\pi$
$602$	0	0
$603$	−31.3422	−1.27635
$604$	13.2311	0.538365
$605$	13.1069	0.532873
$606$	16.7488	0.680375
$607$	−21.6638	−0.879309	−0.439654	−	0.898167i	$-0.644899\pi$
$607$	−21.6638	−0.879309	−0.439654	+	0.898167i	$0.644899\pi$
$608$	1.14256	0.0463369
$609$	0	0
$610$	43.7580	1.77171
$611$	0.850410	0.0344039
$612$	32.1318	1.29885
$613$	31.8438	1.28616	0.643079	−	0.765800i	$-0.277657\pi$
$613$	31.8438	1.28616	0.643079	+	0.765800i	$0.277657\pi$
$614$	14.0044	0.565171
$615$	9.66144	0.389587
$616$	0	0
$617$	38.8834	1.56539	0.782694	−	0.622406i	$-0.213845\pi$
$617$	38.8834	1.56539	0.782694	+	0.622406i	$0.213845\pi$
$618$	10.8333	0.435780
$619$	41.1926	1.65567	0.827836	−	0.560970i	$-0.189572\pi$
$619$	41.1926	1.65567	0.827836	+	0.560970i	$0.189572\pi$
$620$	12.1914	0.489619
$621$	15.3859	0.617415
$622$	2.38735	0.0957240
$623$	0	0
$624$	3.35052	0.134128
$625$	−4.48256	−0.179302
$626$	20.5955	0.823163
$627$	11.8811	0.474486
$628$	−12.9502	−0.516771
$629$	0.259472	0.0103458
$630$	0	0
$631$	16.7374	0.666307	0.333154	−	0.942873i	$-0.391887\pi$
$631$	16.7374	0.666307	0.333154	+	0.942873i	$0.391887\pi$
$632$	−6.96382	−0.277006
$633$	−45.4066	−1.80475
$634$	24.6696	0.979756
$635$	57.7398	2.29133
$636$	−35.4896	−1.40725
$637$	0	0
$638$	16.4815	0.652509
$639$	23.9713	0.948290
$640$	3.56002	0.140722
$641$	5.65452	0.223340	0.111670	−	0.993745i	$-0.464380\pi$
$641$	5.65452	0.223340	0.111670	+	0.993745i	$0.464380\pi$
$642$	−21.3084	−0.840975
$643$	12.2800	0.484274	0.242137	−	0.970242i	$-0.422152\pi$
$643$	12.2800	0.484274	0.242137	+	0.970242i	$0.422152\pi$
$644$	0	0
$645$	−33.3383	−1.31269
$646$	8.41041	0.330903
$647$	−17.0590	−0.670658	−0.335329	−	0.942101i	$-0.608848\pi$
$647$	−17.0590	−0.670658	−0.335329	+	0.942101i	$0.608848\pi$
$648$	−3.04110	−0.119466
$649$	−40.1503	−1.57604
$650$	−9.47389	−0.371596
$651$	0	0
$652$	19.4728	0.762613
$653$	9.29179	0.363616	0.181808	−	0.983334i	$-0.441805\pi$
$653$	9.29179	0.363616	0.181808	+	0.983334i	$0.441805\pi$
$654$	14.3144	0.559737
$655$	62.7887	2.45336
$656$	−1.00000	−0.0390434
$657$	31.6568	1.23505
$658$	0	0
$659$	−25.4682	−0.992099	−0.496049	−	0.868294i	$-0.665217\pi$
$659$	−25.4682	−0.992099	−0.496049	+	0.868294i	$0.665217\pi$
$660$	37.0195	1.44098
$661$	−2.12104	−0.0824988	−0.0412494	−	0.999149i	$-0.513134\pi$
$661$	−2.12104	−0.0824988	−0.0412494	+	0.999149i	$0.513134\pi$
$662$	4.43922	0.172535
$663$	24.6632	0.957841
$664$	−9.63576	−0.373940
$665$	0	0
$666$	0.153868	0.00596225
$667$	17.8637	0.691686
$668$	−5.04041	−0.195019
$669$	−35.0090	−1.35353
$670$	−25.5615	−0.987527
$671$	−47.0971	−1.81816
$672$	0	0
$673$	−15.4713	−0.596374	−0.298187	−	0.954507i	$-0.596382\pi$
$673$	−15.4713	−0.596374	−0.298187	+	0.954507i	$0.596382\pi$
$674$	−11.0501	−0.425632
$675$	−28.4293	−1.09424
$676$	−11.4758	−0.441377
$677$	−7.37631	−0.283494	−0.141747	−	0.989903i	$-0.545272\pi$
$677$	−7.37631	−0.283494	−0.141747	+	0.989903i	$0.545272\pi$
$678$	51.0673	1.96123
$679$	0	0
$680$	26.2054	1.00493
$681$	−28.9958	−1.11112
$682$	−13.1217	−0.502456
$683$	3.21374	0.122970	0.0614851	−	0.998108i	$-0.480416\pi$
$683$	3.21374	0.122970	0.0614851	+	0.998108i	$0.480416\pi$
$684$	4.98741	0.190698
$685$	42.2645	1.61484
$686$	0	0
$687$	−74.8745	−2.85664
$688$	3.45066	0.131555
$689$	−16.1448	−0.615068
$690$	40.1241	1.52750
$691$	31.4515	1.19647	0.598236	−	0.801320i	$-0.295869\pi$
$691$	31.4515	1.19647	0.598236	+	0.801320i	$0.295869\pi$
$692$	17.1628	0.652433
$693$	0	0
$694$	−21.8704	−0.830188
$695$	25.4605	0.965773
$696$	11.6734	0.442480
$697$	−7.36103	−0.278819
$698$	−22.4910	−0.851296
$699$	−10.9859	−0.415526
$700$	0	0
$701$	−18.0751	−0.682688	−0.341344	−	0.939938i	$-0.610882\pi$
$701$	−18.0751	−0.682688	−0.341344	+	0.939938i	$0.610882\pi$
$702$	4.57385	0.172629
$703$	0.0402745	0.00151898
$704$	−3.83167	−0.144412
$705$	6.65501	0.250642
$706$	−2.29627	−0.0864212
$707$	0	0
$708$	−28.4374	−1.06874
$709$	−23.4180	−0.879482	−0.439741	−	0.898125i	$-0.644930\pi$
$709$	−23.4180	−0.879482	−0.439741	+	0.898125i	$0.644930\pi$
$710$	19.5500	0.733700
$711$	−30.3979	−1.14001
$712$	13.6462	0.511414
$713$	−14.2222	−0.532624
$714$	0	0
$715$	16.8408	0.629810
$716$	−3.31103	−0.123739
$717$	26.5879	0.992942
$718$	−25.4500	−0.949784
$719$	−12.3806	−0.461717	−0.230859	−	0.972987i	$-0.574154\pi$
$719$	−12.3806	−0.461717	−0.230859	+	0.972987i	$0.574154\pi$
$720$	15.5399	0.579138
$721$	0	0
$722$	−17.6946	−0.658523
$723$	−26.9380	−1.00183
$724$	10.1830	0.378449
$725$	−33.0077	−1.22587
$726$	−9.99170	−0.370827
$727$	−30.6052	−1.13508	−0.567542	−	0.823345i	$-0.692106\pi$
$727$	−30.6052	−1.13508	−0.567542	+	0.823345i	$0.692106\pi$
$728$	0	0
$729$	−43.4375	−1.60880
$730$	25.8180	0.955567
$731$	25.4004	0.939467
$732$	−33.3576	−1.23293
$733$	−0.0522878	−0.00193130	−0.000965648	−	1.00000i	$-0.500307\pi$
$733$	−0.0522878	−0.00193130	−0.000965648		1.00000i	$0.500307\pi$
$734$	−13.6434	−0.503588
$735$	0	0
$736$	−4.15301	−0.153082
$737$	27.5120	1.01342
$738$	−4.36512	−0.160682
$739$	−45.1893	−1.66232	−0.831158	−	0.556036i	$-0.812322\pi$
$739$	−45.1893	−1.66232	−0.831158	+	0.556036i	$0.812322\pi$
$740$	0.125488	0.00461304
$741$	3.82816	0.140631
$742$	0	0
$743$	−20.4512	−0.750280	−0.375140	−	0.926968i	$-0.622405\pi$
$743$	−20.4512	−0.750280	−0.375140	+	0.926968i	$0.622405\pi$
$744$	−9.29377	−0.340726
$745$	−27.3102	−1.00057
$746$	4.33954	0.158882
$747$	−42.0612	−1.53894
$748$	−28.2050	−1.03128
$749$	0	0
$750$	−25.8321	−0.943253
$751$	5.16477	0.188465	0.0942326	−	0.995550i	$-0.469960\pi$
$751$	5.16477	0.188465	0.0942326	+	0.995550i	$0.469960\pi$
$752$	−0.688821	−0.0251187
$753$	−79.5175	−2.89778
$754$	5.31044	0.193395
$755$	47.1028	1.71425
$756$	0	0
$757$	−41.9682	−1.52536	−0.762681	−	0.646775i	$-0.776117\pi$
$757$	−41.9682	−1.52536	−0.762681	+	0.646775i	$0.776117\pi$
$758$	15.0524	0.546727
$759$	−43.1859	−1.56755
$760$	4.06753	0.147545
$761$	−0.561818	−0.0203659	−0.0101829	−	0.999948i	$-0.503241\pi$
$761$	−0.561818	−0.0203659	−0.0101829	+	0.999948i	$0.503241\pi$
$762$	−44.0163	−1.59454
$763$	0	0
$764$	−4.21763	−0.152589
$765$	114.390	4.13577
$766$	24.4341	0.882841
$767$	−12.9367	−0.467116
$768$	−2.71387	−0.0979285
$769$	−34.7058	−1.25152	−0.625761	−	0.780015i	$-0.715211\pi$
$769$	−34.7058	−1.25152	−0.625761	+	0.780015i	$0.715211\pi$
$770$	0	0
$771$	34.1142	1.22859
$772$	25.2425	0.908497
$773$	38.7053	1.39213	0.696067	−	0.717977i	$-0.254932\pi$
$773$	38.7053	1.39213	0.696067	+	0.717977i	$0.254932\pi$
$774$	15.0625	0.541411
$775$	26.2790	0.943968
$776$	−17.7499	−0.637186
$777$	0	0
$778$	5.30198	0.190085
$779$	−1.14256	−0.0409364
$780$	11.9279	0.427087
$781$	−21.0418	−0.752937
$782$	−30.5705	−1.09320
$783$	15.9356	0.569492
$784$	0	0
$785$	−46.1031	−1.64549
$786$	−47.8651	−1.70729
$787$	42.3900	1.51104	0.755520	−	0.655125i	$-0.227384\pi$
$787$	42.3900	1.51104	0.755520	+	0.655125i	$0.227384\pi$
$788$	16.4881	0.587366
$789$	71.1745	2.53388
$790$	−24.7913	−0.882035
$791$	0	0
$792$	−16.7257	−0.594322
$793$	−15.1750	−0.538878
$794$	−24.5508	−0.871276
$795$	−126.344	−4.48094
$796$	−18.4538	−0.654078
$797$	41.2964	1.46279	0.731396	−	0.681953i	$-0.238869\pi$
$797$	41.2964	1.46279	0.731396	+	0.681953i	$0.238869\pi$
$798$	0	0
$799$	−5.07043	−0.179379
$800$	7.67373	0.271307
$801$	59.5673	2.10471
$802$	28.7496	1.01518
$803$	−27.7881	−0.980621
$804$	19.4861	0.687220
$805$	0	0
$806$	−4.22789	−0.148921
$807$	−35.1331	−1.23674
$808$	−6.17156	−0.217115
$809$	−35.1199	−1.23475	−0.617375	−	0.786669i	$-0.711804\pi$
$809$	−35.1199	−1.23475	−0.617375	+	0.786669i	$0.711804\pi$
$810$	−10.8264	−0.380400
$811$	−32.8973	−1.15518	−0.577590	−	0.816327i	$-0.696007\pi$
$811$	−32.8973	−1.15518	−0.577590	+	0.816327i	$0.696007\pi$
$812$	0	0
$813$	70.1117	2.45893
$814$	−0.135064	−0.00473399
$815$	69.3235	2.42829
$816$	−19.9769	−0.699332
$817$	3.94258	0.137933
$818$	−20.1016	−0.702837
$819$	0	0
$820$	−3.56002	−0.124321
$821$	−34.9588	−1.22007	−0.610036	−	0.792374i	$-0.708845\pi$
$821$	−34.9588	−1.22007	−0.610036	+	0.792374i	$0.708845\pi$
$822$	−32.2191	−1.12377
$823$	42.8370	1.49320	0.746602	−	0.665271i	$-0.231684\pi$
$823$	42.8370	1.49320	0.746602	+	0.665271i	$0.231684\pi$
$824$	−3.99182	−0.139062
$825$	79.7966	2.77816
$826$	0	0
$827$	−34.4103	−1.19656	−0.598281	−	0.801286i	$-0.704149\pi$
$827$	−34.4103	−1.19656	−0.598281	+	0.801286i	$0.704149\pi$
$828$	−18.1284	−0.630005
$829$	−43.9882	−1.52777	−0.763886	−	0.645351i	$-0.776711\pi$
$829$	−43.9882	−1.52777	−0.763886	+	0.645351i	$0.776711\pi$
$830$	−34.3035	−1.19069
$831$	19.4970	0.676344
$832$	−1.23459	−0.0428016
$833$	0	0
$834$	−19.4091	−0.672082
$835$	−17.9439	−0.620976
$836$	−4.37791	−0.151413
$837$	−12.6871	−0.438530
$838$	−38.6571	−1.33539
$839$	−20.7157	−0.715187	−0.357593	−	0.933877i	$-0.616403\pi$
$839$	−20.7157	−0.715187	−0.357593	+	0.933877i	$0.616403\pi$
$840$	0	0
$841$	−10.4981	−0.362002
$842$	10.7092	0.369065
$843$	42.3037	1.45702
$844$	16.7313	0.575915
$845$	−40.8540	−1.40542
$846$	−3.00679	−0.103375
$847$	0	0
$848$	13.0771	0.449069
$849$	−55.8742	−1.91760
$850$	56.4865	1.93747
$851$	−0.146391	−0.00501822
$852$	−14.9034	−0.510582
$853$	1.58508	0.0542722	0.0271361	−	0.999632i	$-0.491361\pi$
$853$	1.58508	0.0542722	0.0271361	+	0.999632i	$0.491361\pi$
$854$	0	0
$855$	17.7553	0.607217
$856$	7.85165	0.268364
$857$	−8.05929	−0.275300	−0.137650	−	0.990481i	$-0.543955\pi$
$857$	−8.05929	−0.275300	−0.137650	+	0.990481i	$0.543955\pi$
$858$	−12.8381	−0.438285
$859$	12.8259	0.437612	0.218806	−	0.975768i	$-0.429784\pi$
$859$	12.8259	0.437612	0.218806	+	0.975768i	$0.429784\pi$
$860$	12.2844	0.418894
$861$	0	0
$862$	6.92758	0.235954
$863$	2.00172	0.0681395	0.0340697	−	0.999419i	$-0.489153\pi$
$863$	2.00172	0.0681395	0.0340697	+	0.999419i	$0.489153\pi$
$864$	−3.70476	−0.126038
$865$	61.1000	2.07746
$866$	−8.87201	−0.301483
$867$	−100.915	−3.42724
$868$	0	0
$869$	26.6831	0.905161
$870$	41.5576	1.40893
$871$	8.86454	0.300363
$872$	−5.27452	−0.178618
$873$	−77.4806	−2.62232
$874$	−4.74506	−0.160504
$875$	0	0
$876$	−19.6816	−0.664980
$877$	−14.4098	−0.486584	−0.243292	−	0.969953i	$-0.578227\pi$
$877$	−14.4098	−0.486584	−0.243292	+	0.969953i	$0.578227\pi$
$878$	7.90044	0.266627
$879$	81.5635	2.75107
$880$	−13.6408	−0.459832
$881$	−38.4642	−1.29589	−0.647946	−	0.761686i	$-0.724372\pi$
$881$	−38.4642	−1.29589	−0.647946	+	0.761686i	$0.724372\pi$
$882$	0	0
$883$	−33.7500	−1.13578	−0.567890	−	0.823105i	$-0.692240\pi$
$883$	−33.7500	−1.13578	−0.567890	+	0.823105i	$0.692240\pi$
$884$	−9.08784	−0.305657
$885$	−101.238	−3.40307
$886$	22.8242	0.766793
$887$	−25.3151	−0.849997	−0.424999	−	0.905194i	$-0.639725\pi$
$887$	−25.3151	−0.849997	−0.424999	+	0.905194i	$0.639725\pi$
$888$	−0.0956623	−0.00321022
$889$	0	0
$890$	48.5808	1.62843
$891$	11.6525	0.390374
$892$	12.9000	0.431924
$893$	−0.787019	−0.0263366
$894$	20.8191	0.696295
$895$	−11.7873	−0.394007
$896$	0	0
$897$	−13.9147	−0.464600
$898$	−32.5904	−1.08755
$899$	−14.7303	−0.491282
$900$	33.4967	1.11656
$901$	96.2608	3.20691
$902$	3.83167	0.127581
$903$	0	0
$904$	−18.8171	−0.625848
$905$	36.2518	1.20505
$906$	−35.9075	−1.19295
$907$	−7.91136	−0.262692	−0.131346	−	0.991337i	$-0.541930\pi$
$907$	−7.91136	−0.262692	−0.131346	+	0.991337i	$0.541930\pi$
$908$	10.6843	0.354570
$909$	−26.9396	−0.893530
$910$	0	0
$911$	−33.7773	−1.11909	−0.559547	−	0.828799i	$-0.689025\pi$
$911$	−33.7773	−1.11909	−0.559547	+	0.828799i	$0.689025\pi$
$912$	−3.10076	−0.102677
$913$	36.9211	1.22191
$914$	−19.2750	−0.637561
$915$	−118.754	−3.92588
$916$	27.5895	0.911583
$917$	0	0
$918$	−27.2708	−0.900071
$919$	39.5547	1.30479	0.652394	−	0.757880i	$-0.273765\pi$
$919$	39.5547	1.30479	0.652394	+	0.757880i	$0.273765\pi$
$920$	−14.7848	−0.487440
$921$	−38.0062	−1.25235
$922$	−17.9008	−0.589533
$923$	−6.77981	−0.223160
$924$	0	0
$925$	0.270494	0.00889379
$926$	−27.5304	−0.904704
$927$	−17.4248	−0.572305
$928$	−4.30139	−0.141200
$929$	40.6991	1.33529	0.667647	−	0.744478i	$-0.267302\pi$
$929$	40.6991	1.33529	0.667647	+	0.744478i	$0.267302\pi$
$930$	−33.0860	−1.08493
$931$	0	0
$932$	4.04806	0.132599
$933$	−6.47897	−0.212112
$934$	−28.1291	−0.920413
$935$	−100.410	−3.28377
$936$	−5.38912	−0.176149
$937$	11.7658	0.384373	0.192186	−	0.981358i	$-0.438442\pi$
$937$	11.7658	0.384373	0.192186	+	0.981358i	$0.438442\pi$
$938$	0	0
$939$	−55.8937	−1.82402
$940$	−2.45222	−0.0799825
$941$	−0.583623	−0.0190256	−0.00951278	−	0.999955i	$-0.503028\pi$
$941$	−0.583623	−0.0190256	−0.00951278	+	0.999955i	$0.503028\pi$
$942$	35.1453	1.14510
$943$	4.15301	0.135241
$944$	10.4785	0.341047
$945$	0	0
$946$	−13.2218	−0.429877
$947$	−29.0760	−0.944844	−0.472422	−	0.881372i	$-0.656620\pi$
$947$	−29.0760	−0.944844	−0.472422	+	0.881372i	$0.656620\pi$
$948$	18.8989	0.613809
$949$	−8.95349	−0.290643
$950$	8.76769	0.284461
$951$	−66.9503	−2.17101
$952$	0	0
$953$	3.57108	0.115679	0.0578394	−	0.998326i	$-0.481579\pi$
$953$	3.57108	0.115679	0.0578394	+	0.998326i	$0.481579\pi$
$954$	57.0830	1.84813
$955$	−15.0148	−0.485869
$956$	−9.79701	−0.316858
$957$	−44.7287	−1.44587
$958$	−20.4404	−0.660399
$959$	0	0
$960$	−9.66144	−0.311822
$961$	−19.2725	−0.621695
$962$	−0.0435184	−0.00140309
$963$	34.2734	1.10444
$964$	9.92602	0.319696
$965$	89.8637	2.89281
$966$	0	0
$967$	31.2064	1.00353	0.501765	−	0.865004i	$-0.332684\pi$
$967$	31.2064	1.00353	0.501765	+	0.865004i	$0.332684\pi$
$968$	3.68171	0.118335
$969$	−22.8248	−0.733239
$970$	−63.1901	−2.02891
$971$	−15.6379	−0.501844	−0.250922	−	0.968007i	$-0.580734\pi$
$971$	−15.6379	−0.501844	−0.250922	+	0.968007i	$0.580734\pi$
$972$	19.3674	0.621211
$973$	0	0
$974$	20.7054	0.663443
$975$	25.7109	0.823409
$976$	12.2915	0.393442
$977$	44.6398	1.42815	0.714076	−	0.700068i	$-0.246847\pi$
$977$	44.6398	1.42815	0.714076	+	0.700068i	$0.246847\pi$
$978$	−52.8467	−1.68985
$979$	−52.2878	−1.67113
$980$	0	0
$981$	−23.0239	−0.735096
$982$	2.67971	0.0855131
$983$	22.7233	0.724760	0.362380	−	0.932031i	$-0.381964\pi$
$983$	22.7233	0.724760	0.362380	+	0.932031i	$0.381964\pi$
$984$	2.71387	0.0865152
$985$	58.6981	1.87028
$986$	−31.6626	−1.00834
$987$	0	0
$988$	−1.41059	−0.0448768
$989$	−14.3306	−0.455687
$990$	−59.5438	−1.89243
$991$	45.9918	1.46098	0.730490	−	0.682924i	$-0.239292\pi$
$991$	45.9918	1.46098	0.730490	+	0.682924i	$0.239292\pi$
$992$	3.42454	0.108729
$993$	−12.0475	−0.382315
$994$	0	0
$995$	−65.6959	−2.08270
$996$	26.1502	0.828602
$997$	−58.4876	−1.85232	−0.926160	−	0.377130i	$-0.876911\pi$
$997$	−58.4876	−1.85232	−0.926160	+	0.377130i	$0.876911\pi$
$998$	−28.8589	−0.913512
$999$	−0.130590	−0.00413169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bq.1.1	yes	6
7.6	odd	2		4018.2.a.bp.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bp.1.6	✓	6	7.6	odd	2
4018.2.a.bq.1.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.71387 q^{3} +1.00000 q^{4} +3.56002 q^{5} -2.71387 q^{6} +1.00000 q^{8} +4.36512 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.71387 q^{3} +1.00000 q^{4} +3.56002 q^{5} -2.71387 q^{6} +1.00000 q^{8} +4.36512 q^{9} +3.56002 q^{10} -3.83167 q^{11} -2.71387 q^{12} -1.23459 q^{13} -9.66144 q^{15} +1.00000 q^{16} +7.36103 q^{17} +4.36512 q^{18} +1.14256 q^{19} +3.56002 q^{20} -3.83167 q^{22} -4.15301 q^{23} -2.71387 q^{24} +7.67373 q^{25} -1.23459 q^{26} -3.70476 q^{27} -4.30139 q^{29} -9.66144 q^{30} +3.42454 q^{31} +1.00000 q^{32} +10.3987 q^{33} +7.36103 q^{34} +4.36512 q^{36} +0.0352494 q^{37} +1.14256 q^{38} +3.35052 q^{39} +3.56002 q^{40} -1.00000 q^{41} +3.45066 q^{43} -3.83167 q^{44} +15.5399 q^{45} -4.15301 q^{46} -0.688821 q^{47} -2.71387 q^{48} +7.67373 q^{50} -19.9769 q^{51} -1.23459 q^{52} +13.0771 q^{53} -3.70476 q^{54} -13.6408 q^{55} -3.10076 q^{57} -4.30139 q^{58} +10.4785 q^{59} -9.66144 q^{60} +12.2915 q^{61} +3.42454 q^{62} +1.00000 q^{64} -4.39515 q^{65} +10.3987 q^{66} -7.18016 q^{67} +7.36103 q^{68} +11.2708 q^{69} +5.49156 q^{71} +4.36512 q^{72} +7.25221 q^{73} +0.0352494 q^{74} -20.8255 q^{75} +1.14256 q^{76} +3.35052 q^{78} -6.96382 q^{79} +3.56002 q^{80} -3.04110 q^{81} -1.00000 q^{82} -9.63576 q^{83} +26.2054 q^{85} +3.45066 q^{86} +11.6734 q^{87} -3.83167 q^{88} +13.6462 q^{89} +15.5399 q^{90} -4.15301 q^{92} -9.29377 q^{93} -0.688821 q^{94} +4.06753 q^{95} -2.71387 q^{96} -17.7499 q^{97} -16.7257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9} + 12 q^{10} + 4 q^{12} + 8 q^{13} - 4 q^{15} + 6 q^{16} + 16 q^{17} + 18 q^{18} + 12 q^{19} + 12 q^{20} + 12 q^{23} + 4 q^{24} + 14 q^{25} + 8 q^{26} + 28 q^{27} - 4 q^{30} - 4 q^{31} + 6 q^{32} - 20 q^{33} + 16 q^{34} + 18 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} - 6 q^{41} + 4 q^{43} + 28 q^{45} + 12 q^{46} - 16 q^{47} + 4 q^{48} + 14 q^{50} - 16 q^{51} + 8 q^{52} - 16 q^{53} + 28 q^{54} - 12 q^{55} - 28 q^{57} + 16 q^{59} - 4 q^{60} + 32 q^{61} - 4 q^{62} + 6 q^{64} - 4 q^{65} - 20 q^{66} - 20 q^{67} + 16 q^{68} + 56 q^{69} + 12 q^{71} + 18 q^{72} + 16 q^{73} - 24 q^{74} - 4 q^{75} + 12 q^{76} + 4 q^{78} + 12 q^{80} + 42 q^{81} - 6 q^{82} + 32 q^{83} + 48 q^{85} + 4 q^{86} + 20 q^{87} + 8 q^{89} + 28 q^{90} + 12 q^{92} - 12 q^{93} - 16 q^{94} + 28 q^{95} + 4 q^{96} + 8 q^{97} - 76 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9 + 12 * q^10 + 4 * q^12 + 8 * q^13 - 4 * q^15 + 6 * q^16 + 16 * q^17 + 18 * q^18 + 12 * q^19 + 12 * q^20 + 12 * q^23 + 4 * q^24 + 14 * q^25 + 8 * q^26 + 28 * q^27 - 4 * q^30 - 4 * q^31 + 6 * q^32 - 20 * q^33 + 16 * q^34 + 18 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 - 6 * q^41 + 4 * q^43 + 28 * q^45 + 12 * q^46 - 16 * q^47 + 4 * q^48 + 14 * q^50 - 16 * q^51 + 8 * q^52 - 16 * q^53 + 28 * q^54 - 12 * q^55 - 28 * q^57 + 16 * q^59 - 4 * q^60 + 32 * q^61 - 4 * q^62 + 6 * q^64 - 4 * q^65 - 20 * q^66 - 20 * q^67 + 16 * q^68 + 56 * q^69 + 12 * q^71 + 18 * q^72 + 16 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 + 4 * q^78 + 12 * q^80 + 42 * q^81 - 6 * q^82 + 32 * q^83 + 48 * q^85 + 4 * q^86 + 20 * q^87 + 8 * q^89 + 28 * q^90 + 12 * q^92 - 12 * q^93 - 16 * q^94 + 28 * q^95 + 4 * q^96 + 8 * q^97 - 76 * q^99

Introduction

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