LMFDB - Embedded newform 6762.2.a.cm.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.42048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 13x^{2} + 8x + 34 $ x^4 - 2x^3 - 13x^2 + 8*x + 34
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.35854$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82843 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82843 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.82843 q^{10} -5.10824 q^{11} -1.00000 q^{12} -0.0556701 q^{13} -3.82843 q^{15} +1.00000 q^{16} +6.77276 q^{17} +1.00000 q^{18} -4.16391 q^{19} +3.82843 q^{20} -5.10824 q^{22} +1.00000 q^{23} -1.00000 q^{24} +9.65685 q^{25} -0.0556701 q^{26} -1.00000 q^{27} +2.94433 q^{29} -3.82843 q^{30} +3.21958 q^{31} +1.00000 q^{32} +5.10824 q^{33} +6.77276 q^{34} +1.00000 q^{36} -8.05257 q^{37} -4.16391 q^{38} +0.0556701 q^{39} +3.82843 q^{40} +4.16391 q^{41} +12.5596 q^{43} -5.10824 q^{44} +3.82843 q^{45} +1.00000 q^{46} -11.9969 q^{47} -1.00000 q^{48} +9.65685 q^{50} -6.77276 q^{51} -0.0556701 q^{52} +5.71709 q^{53} -1.00000 q^{54} -19.5565 q^{55} +4.16391 q^{57} +2.94433 q^{58} -8.60118 q^{59} -3.82843 q^{60} +5.77732 q^{61} +3.21958 q^{62} +1.00000 q^{64} -0.213129 q^{65} +5.10824 q^{66} +12.1544 q^{67} +6.77276 q^{68} -1.00000 q^{69} +11.9443 q^{71} +1.00000 q^{72} +2.21958 q^{73} -8.05257 q^{74} -9.65685 q^{75} -4.16391 q^{76} +0.0556701 q^{78} -2.94433 q^{79} +3.82843 q^{80} +1.00000 q^{81} +4.16391 q^{82} +14.7651 q^{83} +25.9290 q^{85} +12.5596 q^{86} -2.94433 q^{87} -5.10824 q^{88} -2.39572 q^{89} +3.82843 q^{90} +1.00000 q^{92} -3.21958 q^{93} -11.9969 q^{94} -15.9412 q^{95} -1.00000 q^{96} -4.60118 q^{97} -5.10824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{15} + 4 q^{16} + 10 q^{17} + 4 q^{18} + 4 q^{19} + 4 q^{20} + 6 q^{22} + 4 q^{23} - 4 q^{24} + 16 q^{25} - 6 q^{26} - 4 q^{27} + 6 q^{29} - 4 q^{30} - 2 q^{31} + 4 q^{32} - 6 q^{33} + 10 q^{34} + 4 q^{36} + 4 q^{38} + 6 q^{39} + 4 q^{40} - 4 q^{41} + 20 q^{43} + 6 q^{44} + 4 q^{45} + 4 q^{46} - 10 q^{47} - 4 q^{48} + 16 q^{50} - 10 q^{51} - 6 q^{52} - 4 q^{54} - 10 q^{55} - 4 q^{57} + 6 q^{58} - 6 q^{59} - 4 q^{60} - 2 q^{62} + 4 q^{64} - 14 q^{65} - 6 q^{66} + 18 q^{67} + 10 q^{68} - 4 q^{69} + 42 q^{71} + 4 q^{72} - 6 q^{73} - 16 q^{75} + 4 q^{76} + 6 q^{78} - 6 q^{79} + 4 q^{80} + 4 q^{81} - 4 q^{82} + 10 q^{83} + 34 q^{85} + 20 q^{86} - 6 q^{87} + 6 q^{88} + 4 q^{90} + 4 q^{92} + 2 q^{93} - 10 q^{94} - 20 q^{95} - 4 q^{96} + 10 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^15 + 4 * q^16 + 10 * q^17 + 4 * q^18 + 4 * q^19 + 4 * q^20 + 6 * q^22 + 4 * q^23 - 4 * q^24 + 16 * q^25 - 6 * q^26 - 4 * q^27 + 6 * q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 - 6 * q^33 + 10 * q^34 + 4 * q^36 + 4 * q^38 + 6 * q^39 + 4 * q^40 - 4 * q^41 + 20 * q^43 + 6 * q^44 + 4 * q^45 + 4 * q^46 - 10 * q^47 - 4 * q^48 + 16 * q^50 - 10 * q^51 - 6 * q^52 - 4 * q^54 - 10 * q^55 - 4 * q^57 + 6 * q^58 - 6 * q^59 - 4 * q^60 - 2 * q^62 + 4 * q^64 - 14 * q^65 - 6 * q^66 + 18 * q^67 + 10 * q^68 - 4 * q^69 + 42 * q^71 + 4 * q^72 - 6 * q^73 - 16 * q^75 + 4 * q^76 + 6 * q^78 - 6 * q^79 + 4 * q^80 + 4 * q^81 - 4 * q^82 + 10 * q^83 + 34 * q^85 + 20 * q^86 - 6 * q^87 + 6 * q^88 + 4 * q^90 + 4 * q^92 + 2 * q^93 - 10 * q^94 - 20 * q^95 - 4 * q^96 + 10 * q^97 + 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.82843	1.71212	0.856062	−	0.516873i	$-0.172904\pi$
$5$	3.82843	1.71212	0.856062	+	0.516873i	$0.172904\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.82843	1.21065
$11$	−5.10824	−1.54019	−0.770096	−	0.637928i	$-0.779792\pi$
$11$	−5.10824	−1.54019	−0.770096	+	0.637928i	$0.779792\pi$
$12$	−1.00000	−0.288675
$13$	−0.0556701	−0.0154401	−0.00772006	−	0.999970i	$-0.502457\pi$
$13$	−0.0556701	−0.0154401	−0.00772006	+	0.999970i	$0.502457\pi$
$14$	0	0
$15$	−3.82843	−0.988496
$16$	1.00000	0.250000
$17$	6.77276	1.64263	0.821317	−	0.570471i	$-0.193239\pi$
$17$	6.77276	1.64263	0.821317	+	0.570471i	$0.193239\pi$
$18$	1.00000	0.235702
$19$	−4.16391	−0.955267	−0.477633	−	0.878559i	$-0.658505\pi$
$19$	−4.16391	−0.955267	−0.477633	+	0.878559i	$0.658505\pi$
$20$	3.82843	0.856062
$21$	0	0
$22$	−5.10824	−1.08908
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	9.65685	1.93137
$26$	−0.0556701	−0.0109178
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.94433	0.546748	0.273374	−	0.961908i	$-0.411860\pi$
$29$	2.94433	0.546748	0.273374	+	0.961908i	$0.411860\pi$
$30$	−3.82843	−0.698972
$31$	3.21958	0.578254	0.289127	−	0.957291i	$-0.406635\pi$
$31$	3.21958	0.578254	0.289127	+	0.957291i	$0.406635\pi$
$32$	1.00000	0.176777
$33$	5.10824	0.889231
$34$	6.77276	1.16152
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.05257	−1.32383	−0.661917	−	0.749577i	$-0.730257\pi$
$37$	−8.05257	−1.32383	−0.661917	+	0.749577i	$0.730257\pi$
$38$	−4.16391	−0.675476
$39$	0.0556701	0.00891436
$40$	3.82843	0.605327
$41$	4.16391	0.650294	0.325147	−	0.945664i	$-0.394586\pi$
$41$	4.16391	0.650294	0.325147	+	0.945664i	$0.394586\pi$
$42$	0	0
$43$	12.5596	1.91533	0.957663	−	0.287893i	$-0.0929547\pi$
$43$	12.5596	1.91533	0.957663	+	0.287893i	$0.0929547\pi$
$44$	−5.10824	−0.770096
$45$	3.82843	0.570708
$46$	1.00000	0.147442
$47$	−11.9969	−1.74993	−0.874964	−	0.484188i	$-0.839115\pi$
$47$	−11.9969	−1.74993	−0.874964	+	0.484188i	$0.839115\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	9.65685	1.36569
$51$	−6.77276	−0.948376
$52$	−0.0556701	−0.00772006
$53$	5.71709	0.785302	0.392651	−	0.919687i	$-0.371558\pi$
$53$	5.71709	0.785302	0.392651	+	0.919687i	$0.371558\pi$
$54$	−1.00000	−0.136083
$55$	−19.5565	−2.63700
$56$	0	0
$57$	4.16391	0.551524
$58$	2.94433	0.386609
$59$	−8.60118	−1.11978	−0.559889	−	0.828567i	$-0.689156\pi$
$59$	−8.60118	−1.11978	−0.559889	+	0.828567i	$0.689156\pi$
$60$	−3.82843	−0.494248
$61$	5.77732	0.739710	0.369855	−	0.929089i	$-0.379407\pi$
$61$	5.77732	0.739710	0.369855	+	0.929089i	$0.379407\pi$
$62$	3.21958	0.408887
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.213129	−0.0264354
$66$	5.10824	0.628781
$67$	12.1544	1.48489	0.742446	−	0.669906i	$-0.233666\pi$
$67$	12.1544	1.48489	0.742446	+	0.669906i	$0.233666\pi$
$68$	6.77276	0.821317
$69$	−1.00000	−0.120386
$70$	0	0
$71$	11.9443	1.41753	0.708766	−	0.705444i	$-0.249252\pi$
$71$	11.9443	1.41753	0.708766	+	0.705444i	$0.249252\pi$
$72$	1.00000	0.117851
$73$	2.21958	0.259782	0.129891	−	0.991528i	$-0.458537\pi$
$73$	2.21958	0.259782	0.129891	+	0.991528i	$0.458537\pi$
$74$	−8.05257	−0.936092
$75$	−9.65685	−1.11508
$76$	−4.16391	−0.477633
$77$	0	0
$78$	0.0556701	0.00630340
$79$	−2.94433	−0.331263	−0.165631	−	0.986188i	$-0.552966\pi$
$79$	−2.94433	−0.331263	−0.165631	+	0.986188i	$0.552966\pi$
$80$	3.82843	0.428031
$81$	1.00000	0.111111
$82$	4.16391	0.459827
$83$	14.7651	1.62068	0.810340	−	0.585960i	$-0.199282\pi$
$83$	14.7651	1.62068	0.810340	+	0.585960i	$0.199282\pi$
$84$	0	0
$85$	25.9290	2.81240
$86$	12.5596	1.35434
$87$	−2.94433	−0.315665
$88$	−5.10824	−0.544540
$89$	−2.39572	−0.253945	−0.126973	−	0.991906i	$-0.540526\pi$
$89$	−2.39572	−0.253945	−0.126973	+	0.991906i	$0.540526\pi$
$90$	3.82843	0.403552
$91$	0	0
$92$	1.00000	0.104257
$93$	−3.21958	−0.333855
$94$	−11.9969	−1.23739
$95$	−15.9412	−1.63554
$96$	−1.00000	−0.102062
$97$	−4.60118	−0.467179	−0.233590	−	0.972335i	$-0.575047\pi$
$97$	−4.60118	−0.467179	−0.233590	+	0.972335i	$0.575047\pi$
$98$	0	0
$99$	−5.10824	−0.513398
$100$	9.65685	0.965685
$101$	14.8875	1.48136	0.740678	−	0.671860i	$-0.234504\pi$
$101$	14.8875	1.48136	0.740678	+	0.671860i	$0.234504\pi$
$102$	−6.77276	−0.670603
$103$	−6.15436	−0.606407	−0.303204	−	0.952926i	$-0.598056\pi$
$103$	−6.15436	−0.606407	−0.303204	+	0.952926i	$0.598056\pi$
$104$	−0.0556701	−0.00545891
$105$	0	0
$106$	5.71709	0.555293
$107$	4.12236	0.398523	0.199262	−	0.979946i	$-0.436146\pi$
$107$	4.12236	0.398523	0.199262	+	0.979946i	$0.436146\pi$
$108$	−1.00000	−0.0962250
$109$	20.0960	1.92485	0.962425	−	0.271549i	$-0.0875358\pi$
$109$	20.0960	1.92485	0.962425	+	0.271549i	$0.0875358\pi$
$110$	−19.5565	−1.86464
$111$	8.05257	0.764316
$112$	0	0
$113$	−5.33238	−0.501629	−0.250814	−	0.968035i	$-0.580698\pi$
$113$	−5.33238	−0.501629	−0.250814	+	0.968035i	$0.580698\pi$
$114$	4.16391	0.389986
$115$	3.82843	0.357003
$116$	2.94433	0.273374
$117$	−0.0556701	−0.00514671
$118$	−8.60118	−0.791803
$119$	0	0
$120$	−3.82843	−0.349486
$121$	15.0941	1.37219
$122$	5.77732	0.523054
$123$	−4.16391	−0.375447
$124$	3.21958	0.289127
$125$	17.8284	1.59462
$126$	0	0
$127$	8.54861	0.758567	0.379283	−	0.925281i	$-0.376171\pi$
$127$	8.54861	0.758567	0.379283	+	0.925281i	$0.376171\pi$
$128$	1.00000	0.0883883
$129$	−12.5596	−1.10581
$130$	−0.213129	−0.0186927
$131$	6.94123	0.606458	0.303229	−	0.952918i	$-0.401935\pi$
$131$	6.94123	0.606458	0.303229	+	0.952918i	$0.401935\pi$
$132$	5.10824	0.444615
$133$	0	0
$134$	12.1544	1.04998
$135$	−3.82843	−0.329499
$136$	6.77276	0.580759
$137$	5.27981	0.451085	0.225542	−	0.974233i	$-0.427585\pi$
$137$	5.27981	0.451085	0.225542	+	0.974233i	$0.427585\pi$
$138$	−1.00000	−0.0851257
$139$	−9.31371	−0.789978	−0.394989	−	0.918686i	$-0.629252\pi$
$139$	−9.31371	−0.789978	−0.394989	+	0.918686i	$0.629252\pi$
$140$	0	0
$141$	11.9969	1.01032
$142$	11.9443	1.00235
$143$	0.284376	0.0237808
$144$	1.00000	0.0833333
$145$	11.2722	0.936101
$146$	2.21958	0.183694
$147$	0	0
$148$	−8.05257	−0.661917
$149$	−11.7190	−0.960056	−0.480028	−	0.877253i	$-0.659374\pi$
$149$	−11.7190	−0.960056	−0.480028	+	0.877253i	$0.659374\pi$
$150$	−9.65685	−0.788479
$151$	17.5565	1.42873	0.714365	−	0.699773i	$-0.246716\pi$
$151$	17.5565	1.42873	0.714365	+	0.699773i	$0.246716\pi$
$152$	−4.16391	−0.337738
$153$	6.77276	0.547545
$154$	0	0
$155$	12.3259	0.990043
$156$	0.0556701	0.00445718
$157$	9.15892	0.730962	0.365481	−	0.930819i	$-0.380905\pi$
$157$	9.15892	0.730962	0.365481	+	0.930819i	$0.380905\pi$
$158$	−2.94433	−0.234238
$159$	−5.71709	−0.453394
$160$	3.82843	0.302664
$161$	0	0
$162$	1.00000	0.0785674
$163$	−12.1730	−0.953466	−0.476733	−	0.879048i	$-0.658179\pi$
$163$	−12.1730	−0.953466	−0.476733	+	0.879048i	$0.658179\pi$
$164$	4.16391	0.325147
$165$	19.5565	1.52247
$166$	14.7651	1.14599
$167$	−21.0788	−1.63113	−0.815563	−	0.578668i	$-0.803573\pi$
$167$	−21.0788	−1.63113	−0.815563	+	0.578668i	$0.803573\pi$
$168$	0	0
$169$	−12.9969	−0.999762
$170$	25.9290	1.98866
$171$	−4.16391	−0.318422
$172$	12.5596	0.957663
$173$	−13.4250	−1.02069	−0.510344	−	0.859970i	$-0.670482\pi$
$173$	−13.4250	−1.02069	−0.510344	+	0.859970i	$0.670482\pi$
$174$	−2.94433	−0.223209
$175$	0	0
$176$	−5.10824	−0.385048
$177$	8.60118	0.646505
$178$	−2.39572	−0.179567
$179$	1.99690	0.149255	0.0746277	−	0.997211i	$-0.476223\pi$
$179$	1.99690	0.149255	0.0746277	+	0.997211i	$0.476223\pi$
$180$	3.82843	0.285354
$181$	−20.5443	−1.52705	−0.763523	−	0.645781i	$-0.776532\pi$
$181$	−20.5443	−1.52705	−0.763523	+	0.645781i	$0.776532\pi$
$182$	0	0
$183$	−5.77732	−0.427072
$184$	1.00000	0.0737210
$185$	−30.8287	−2.26657
$186$	−3.21958	−0.236071
$187$	−34.5969	−2.52997
$188$	−11.9969	−0.874964
$189$	0	0
$190$	−15.9412	−1.15650
$191$	−1.94743	−0.140911	−0.0704555	−	0.997515i	$-0.522445\pi$
$191$	−1.94743	−0.140911	−0.0704555	+	0.997515i	$0.522445\pi$
$192$	−1.00000	−0.0721688
$193$	4.44037	0.319625	0.159812	−	0.987147i	$-0.448911\pi$
$193$	4.44037	0.319625	0.159812	+	0.987147i	$0.448911\pi$
$194$	−4.60118	−0.330346
$195$	0.213129	0.0152625
$196$	0	0
$197$	−15.7620	−1.12300	−0.561498	−	0.827478i	$-0.689775\pi$
$197$	−15.7620	−1.12300	−0.561498	+	0.827478i	$0.689775\pi$
$198$	−5.10824	−0.363027
$199$	−19.8733	−1.40878	−0.704392	−	0.709811i	$-0.748780\pi$
$199$	−19.8733	−1.40878	−0.704392	+	0.709811i	$0.748780\pi$
$200$	9.65685	0.682843
$201$	−12.1544	−0.857302
$202$	14.8875	1.04748
$203$	0	0
$204$	−6.77276	−0.474188
$205$	15.9412	1.11338
$206$	−6.15436	−0.428795
$207$	1.00000	0.0695048
$208$	−0.0556701	−0.00386003
$209$	21.2703	1.47129
$210$	0	0
$211$	−10.6427	−0.732676	−0.366338	−	0.930482i	$-0.619389\pi$
$211$	−10.6427	−0.732676	−0.366338	+	0.930482i	$0.619389\pi$
$212$	5.71709	0.392651
$213$	−11.9443	−0.818412
$214$	4.12236	0.281798
$215$	48.0836	3.27928
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	20.0960	1.36107
$219$	−2.21958	−0.149985
$220$	−19.5565	−1.31850
$221$	−0.377040	−0.0253625
$222$	8.05257	0.540453
$223$	28.5424	1.91134	0.955671	−	0.294438i	$-0.0951323\pi$
$223$	28.5424	1.91134	0.955671	+	0.294438i	$0.0951323\pi$
$224$	0	0
$225$	9.65685	0.643790
$226$	−5.33238	−0.354705
$227$	3.68319	0.244462	0.122231	−	0.992502i	$-0.460995\pi$
$227$	3.68319	0.244462	0.122231	+	0.992502i	$0.460995\pi$
$228$	4.16391	0.275762
$229$	12.1639	0.803814	0.401907	−	0.915681i	$-0.368348\pi$
$229$	12.1639	0.803814	0.401907	+	0.915681i	$0.368348\pi$
$230$	3.82843	0.252439
$231$	0	0
$232$	2.94433	0.193305
$233$	−1.49294	−0.0978059	−0.0489030	−	0.998804i	$-0.515573\pi$
$233$	−1.49294	−0.0978059	−0.0489030	+	0.998804i	$0.515573\pi$
$234$	−0.0556701	−0.00363927
$235$	−45.9293	−2.99609
$236$	−8.60118	−0.559889
$237$	2.94433	0.191255
$238$	0	0
$239$	25.1193	1.62483	0.812415	−	0.583080i	$-0.198153\pi$
$239$	25.1193	1.62483	0.812415	+	0.583080i	$0.198153\pi$
$240$	−3.82843	−0.247124
$241$	−11.8471	−0.763139	−0.381570	−	0.924340i	$-0.624616\pi$
$241$	−11.8471	−0.763139	−0.381570	+	0.924340i	$0.624616\pi$
$242$	15.0941	0.970287
$243$	−1.00000	−0.0641500
$244$	5.77732	0.369855
$245$	0	0
$246$	−4.16391	−0.265481
$247$	0.231805	0.0147494
$248$	3.21958	0.204444
$249$	−14.7651	−0.935700
$250$	17.8284	1.12757
$251$	−8.09413	−0.510897	−0.255448	−	0.966823i	$-0.582223\pi$
$251$	−8.09413	−0.510897	−0.255448	+	0.966823i	$0.582223\pi$
$252$	0	0
$253$	−5.10824	−0.321152
$254$	8.54861	0.536388
$255$	−25.9290	−1.62374
$256$	1.00000	0.0625000
$257$	−1.94123	−0.121091	−0.0605453	−	0.998165i	$-0.519284\pi$
$257$	−1.94123	−0.121091	−0.0605453	+	0.998165i	$0.519284\pi$
$258$	−12.5596	−0.781928
$259$	0	0
$260$	−0.213129	−0.0132177
$261$	2.94433	0.182249
$262$	6.94123	0.428831
$263$	−29.3075	−1.80718	−0.903589	−	0.428400i	$-0.859077\pi$
$263$	−29.3075	−1.80718	−0.903589	+	0.428400i	$0.859077\pi$
$264$	5.10824	0.314391
$265$	21.8875	1.34454
$266$	0	0
$267$	2.39572	0.146615
$268$	12.1544	0.742446
$269$	−2.62941	−0.160318	−0.0801590	−	0.996782i	$-0.525543\pi$
$269$	−2.62941	−0.160318	−0.0801590	+	0.996782i	$0.525543\pi$
$270$	−3.82843	−0.232991
$271$	−3.21958	−0.195576	−0.0977878	−	0.995207i	$-0.531177\pi$
$271$	−3.21958	−0.195576	−0.0977878	+	0.995207i	$0.531177\pi$
$272$	6.77276	0.410659
$273$	0	0
$274$	5.27981	0.318965
$275$	−49.3295	−2.97468
$276$	−1.00000	−0.0601929
$277$	14.7701	0.887448	0.443724	−	0.896163i	$-0.353657\pi$
$277$	14.7701	0.887448	0.443724	+	0.896163i	$0.353657\pi$
$278$	−9.31371	−0.558599
$279$	3.21958	0.192751
$280$	0	0
$281$	3.44992	0.205805	0.102903	−	0.994691i	$-0.467187\pi$
$281$	3.44992	0.205805	0.102903	+	0.994691i	$0.467187\pi$
$282$	11.9969	0.714405
$283$	−0.951992	−0.0565900	−0.0282950	−	0.999600i	$-0.509008\pi$
$283$	−0.951992	−0.0565900	−0.0282950	+	0.999600i	$0.509008\pi$
$284$	11.9443	0.708766
$285$	15.9412	0.944277
$286$	0.284376	0.0168155
$287$	0	0
$288$	1.00000	0.0589256
$289$	28.8702	1.69825
$290$	11.2722	0.661924
$291$	4.60118	0.269726
$292$	2.21958	0.129891
$293$	14.5147	0.847959	0.423979	−	0.905672i	$-0.360633\pi$
$293$	14.5147	0.847959	0.423979	+	0.905672i	$0.360633\pi$
$294$	0	0
$295$	−32.9290	−1.91720
$296$	−8.05257	−0.468046
$297$	5.10824	0.296410
$298$	−11.7190	−0.678862
$299$	−0.0556701	−0.00321949
$300$	−9.65685	−0.557539
$301$	0	0
$302$	17.5565	1.01026
$303$	−14.8875	−0.855262
$304$	−4.16391	−0.238817
$305$	22.1180	1.26648
$306$	6.77276	0.387173
$307$	−17.2611	−0.985145	−0.492573	−	0.870271i	$-0.663943\pi$
$307$	−17.2611	−0.985145	−0.492573	+	0.870271i	$0.663943\pi$
$308$	0	0
$309$	6.15436	0.350109
$310$	12.3259	0.700066
$311$	−2.37059	−0.134424	−0.0672119	−	0.997739i	$-0.521410\pi$
$311$	−2.37059	−0.134424	−0.0672119	+	0.997739i	$0.521410\pi$
$312$	0.0556701	0.00315170
$313$	5.83798	0.329982	0.164991	−	0.986295i	$-0.447240\pi$
$313$	5.83798	0.329982	0.164991	+	0.986295i	$0.447240\pi$
$314$	9.15892	0.516868
$315$	0	0
$316$	−2.94433	−0.165631
$317$	0.629412	0.0353513	0.0176757	−	0.999844i	$-0.494373\pi$
$317$	0.629412	0.0353513	0.0176757	+	0.999844i	$0.494373\pi$
$318$	−5.71709	−0.320598
$319$	−15.0403	−0.842098
$320$	3.82843	0.214016
$321$	−4.12236	−0.230087
$322$	0	0
$323$	−28.2012	−1.56915
$324$	1.00000	0.0555556
$325$	−0.537598	−0.0298206
$326$	−12.1730	−0.674202
$327$	−20.0960	−1.11131
$328$	4.16391	0.229914
$329$	0	0
$330$	19.5565	1.07655
$331$	13.7003	0.753037	0.376518	−	0.926409i	$-0.377121\pi$
$331$	13.7003	0.753037	0.376518	+	0.926409i	$0.377121\pi$
$332$	14.7651	0.810340
$333$	−8.05257	−0.441278
$334$	−21.0788	−1.15338
$335$	46.5321	2.54232
$336$	0	0
$337$	−19.8318	−1.08031	−0.540153	−	0.841567i	$-0.681634\pi$
$337$	−19.8318	−1.08031	−0.540153	+	0.841567i	$0.681634\pi$
$338$	−12.9969	−0.706938
$339$	5.33238	0.289615
$340$	25.9290	1.40620
$341$	−16.4464	−0.890622
$342$	−4.16391	−0.225159
$343$	0	0
$344$	12.5596	0.677170
$345$	−3.82843	−0.206116
$346$	−13.4250	−0.721735
$347$	5.55774	0.298355	0.149178	−	0.988810i	$-0.452337\pi$
$347$	5.55774	0.298355	0.149178	+	0.988810i	$0.452337\pi$
$348$	−2.94433	−0.157833
$349$	15.5027	0.829843	0.414922	−	0.909857i	$-0.363809\pi$
$349$	15.5027	0.829843	0.414922	+	0.909857i	$0.363809\pi$
$350$	0	0
$351$	0.0556701	0.00297145
$352$	−5.10824	−0.272270
$353$	−15.9412	−0.848466	−0.424233	−	0.905553i	$-0.639456\pi$
$353$	−15.9412	−0.848466	−0.424233	+	0.905553i	$0.639456\pi$
$354$	8.60118	0.457148
$355$	45.7280	2.42699
$356$	−2.39572	−0.126973
$357$	0	0
$358$	1.99690	0.105539
$359$	32.4047	1.71026	0.855128	−	0.518416i	$-0.173478\pi$
$359$	32.4047	1.71026	0.855128	+	0.518416i	$0.173478\pi$
$360$	3.82843	0.201776
$361$	−1.66184	−0.0874654
$362$	−20.5443	−1.07978
$363$	−15.0941	−0.792236
$364$	0	0
$365$	8.49751	0.444780
$366$	−5.77732	−0.301985
$367$	−10.8669	−0.567247	−0.283623	−	0.958936i	$-0.591537\pi$
$367$	−10.8669	−0.567247	−0.283623	+	0.958936i	$0.591537\pi$
$368$	1.00000	0.0521286
$369$	4.16391	0.216765
$370$	−30.8287	−1.60271
$371$	0	0
$372$	−3.21958	−0.166928
$373$	−0.216482	−0.0112090	−0.00560451	−	0.999984i	$-0.501784\pi$
$373$	−0.216482	−0.0112090	−0.00560451	+	0.999984i	$0.501784\pi$
$374$	−34.5969	−1.78896
$375$	−17.8284	−0.920656
$376$	−11.9969	−0.618693
$377$	−0.163911	−0.00844186
$378$	0	0
$379$	8.93667	0.459046	0.229523	−	0.973303i	$-0.426283\pi$
$379$	8.93667	0.459046	0.229523	+	0.973303i	$0.426283\pi$
$380$	−15.9412	−0.817768
$381$	−8.54861	−0.437959
$382$	−1.94743	−0.0996391
$383$	−26.8287	−1.37088	−0.685441	−	0.728128i	$-0.740390\pi$
$383$	−26.8287	−1.37088	−0.685441	+	0.728128i	$0.740390\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	4.44037	0.226009
$387$	12.5596	0.638442
$388$	−4.60118	−0.233590
$389$	−3.66598	−0.185873	−0.0929363	−	0.995672i	$-0.529625\pi$
$389$	−3.66598	−0.185873	−0.0929363	+	0.995672i	$0.529625\pi$
$390$	0.213129	0.0107922
$391$	6.77276	0.342513
$392$	0	0
$393$	−6.94123	−0.350139
$394$	−15.7620	−0.794078
$395$	−11.2722	−0.567164
$396$	−5.10824	−0.256699
$397$	−19.9572	−1.00162	−0.500812	−	0.865556i	$-0.666965\pi$
$397$	−19.9572	−1.00162	−0.500812	+	0.865556i	$0.666965\pi$
$398$	−19.8733	−0.996160
$399$	0	0
$400$	9.65685	0.482843
$401$	0.386165	0.0192842	0.00964209	−	0.999954i	$-0.496931\pi$
$401$	0.386165	0.0192842	0.00964209	+	0.999954i	$0.496931\pi$
$402$	−12.1544	−0.606204
$403$	−0.179235	−0.00892831
$404$	14.8875	0.740678
$405$	3.82843	0.190236
$406$	0	0
$407$	41.1345	2.03896
$408$	−6.77276	−0.335301
$409$	15.5314	0.767978	0.383989	−	0.923338i	$-0.374550\pi$
$409$	15.5314	0.767978	0.383989	+	0.923338i	$0.374550\pi$
$410$	15.9412	0.787281
$411$	−5.27981	−0.260434
$412$	−6.15436	−0.303204
$413$	0	0
$414$	1.00000	0.0491473
$415$	56.5271	2.77481
$416$	−0.0556701	−0.00272945
$417$	9.31371	0.456094
$418$	21.2703	1.04036
$419$	−0.559628	−0.0273396	−0.0136698	−	0.999907i	$-0.504351\pi$
$419$	−0.559628	−0.0273396	−0.0136698	+	0.999907i	$0.504351\pi$
$420$	0	0
$421$	17.2024	0.838392	0.419196	−	0.907896i	$-0.362312\pi$
$421$	17.2024	0.838392	0.419196	+	0.907896i	$0.362312\pi$
$422$	−10.6427	−0.518080
$423$	−11.9969	−0.583309
$424$	5.71709	0.277646
$425$	65.4035	3.17254
$426$	−11.9443	−0.578705
$427$	0	0
$428$	4.12236	0.199262
$429$	−0.284376	−0.0137298
$430$	48.0836	2.31880
$431$	18.8501	0.907977	0.453989	−	0.891007i	$-0.350001\pi$
$431$	18.8501	0.907977	0.453989	+	0.891007i	$0.350001\pi$
$432$	−1.00000	−0.0481125
$433$	−0.435383	−0.0209232	−0.0104616	−	0.999945i	$-0.503330\pi$
$433$	−0.435383	−0.0209232	−0.0104616	+	0.999945i	$0.503330\pi$
$434$	0	0
$435$	−11.2722	−0.540458
$436$	20.0960	0.962425
$437$	−4.16391	−0.199187
$438$	−2.21958	−0.106056
$439$	34.0048	1.62296	0.811481	−	0.584379i	$-0.198662\pi$
$439$	34.0048	1.62296	0.811481	+	0.584379i	$0.198662\pi$
$440$	−19.5565	−0.932321
$441$	0	0
$442$	−0.377040	−0.0179340
$443$	16.9412	0.804902	0.402451	−	0.915441i	$-0.368158\pi$
$443$	16.9412	0.804902	0.402451	+	0.915441i	$0.368158\pi$
$444$	8.05257	0.382158
$445$	−9.17183	−0.434786
$446$	28.5424	1.35152
$447$	11.7190	0.554289
$448$	0	0
$449$	5.28937	0.249621	0.124810	−	0.992181i	$-0.460168\pi$
$449$	5.28937	0.249621	0.124810	+	0.992181i	$0.460168\pi$
$450$	9.65685	0.455228
$451$	−21.2703	−1.00158
$452$	−5.33238	−0.250814
$453$	−17.5565	−0.824878
$454$	3.68319	0.172861
$455$	0	0
$456$	4.16391	0.194993
$457$	6.95723	0.325446	0.162723	−	0.986672i	$-0.447972\pi$
$457$	6.95723	0.325446	0.162723	+	0.986672i	$0.447972\pi$
$458$	12.1639	0.568382
$459$	−6.77276	−0.316125
$460$	3.82843	0.178501
$461$	−6.65564	−0.309984	−0.154992	−	0.987916i	$-0.549535\pi$
$461$	−6.65564	−0.309984	−0.154992	+	0.987916i	$0.549535\pi$
$462$	0	0
$463$	19.8604	0.922993	0.461496	−	0.887142i	$-0.347313\pi$
$463$	19.8604	0.922993	0.461496	+	0.887142i	$0.347313\pi$
$464$	2.94433	0.136687
$465$	−12.3259	−0.571601
$466$	−1.49294	−0.0691592
$467$	−18.5443	−0.858128	−0.429064	−	0.903274i	$-0.641157\pi$
$467$	−18.5443	−0.858128	−0.429064	+	0.903274i	$0.641157\pi$
$468$	−0.0556701	−0.00257335
$469$	0	0
$470$	−45.9293	−2.11856
$471$	−9.15892	−0.422021
$472$	−8.60118	−0.395902
$473$	−64.1576	−2.94997
$474$	2.94433	0.135238
$475$	−40.2103	−1.84497
$476$	0	0
$477$	5.71709	0.261767
$478$	25.1193	1.14893
$479$	−9.28317	−0.424159	−0.212079	−	0.977252i	$-0.568024\pi$
$479$	−9.28317	−0.424159	−0.212079	+	0.977252i	$0.568024\pi$
$480$	−3.82843	−0.174743
$481$	0.448288	0.0204402
$482$	−11.8471	−0.539621
$483$	0	0
$484$	15.0941	0.686097
$485$	−17.6153	−0.799869
$486$	−1.00000	−0.0453609
$487$	9.86232	0.446904	0.223452	−	0.974715i	$-0.428267\pi$
$487$	9.86232	0.446904	0.223452	+	0.974715i	$0.428267\pi$
$488$	5.77732	0.261527
$489$	12.1730	0.550484
$490$	0	0
$491$	−41.3368	−1.86551	−0.932753	−	0.360517i	$-0.882600\pi$
$491$	−41.3368	−1.86551	−0.932753	+	0.360517i	$0.882600\pi$
$492$	−4.16391	−0.187724
$493$	19.9412	0.898108
$494$	0.231805	0.0104294
$495$	−19.5565	−0.879001
$496$	3.21958	0.144563
$497$	0	0
$498$	−14.7651	−0.661640
$499$	−4.45449	−0.199410	−0.0997051	−	0.995017i	$-0.531790\pi$
$499$	−4.45449	−0.199410	−0.0997051	+	0.995017i	$0.531790\pi$
$500$	17.8284	0.797311
$501$	21.0788	0.941732
$502$	−8.09413	−0.361259
$503$	9.67596	0.431430	0.215715	−	0.976456i	$-0.430792\pi$
$503$	9.67596	0.431430	0.215715	+	0.976456i	$0.430792\pi$
$504$	0	0
$505$	56.9955	2.53627
$506$	−5.10824	−0.227089
$507$	12.9969	0.577213
$508$	8.54861	0.379283
$509$	−4.58586	−0.203265	−0.101632	−	0.994822i	$-0.532407\pi$
$509$	−4.58586	−0.203265	−0.101632	+	0.994822i	$0.532407\pi$
$510$	−25.9290	−1.14816
$511$	0	0
$512$	1.00000	0.0441942
$513$	4.16391	0.183841
$514$	−1.94123	−0.0856240
$515$	−23.5615	−1.03824
$516$	−12.5596	−0.552907
$517$	61.2831	2.69523
$518$	0	0
$519$	13.4250	0.589294
$520$	−0.213129	−0.00934633
$521$	22.9305	1.00460	0.502301	−	0.864693i	$-0.332487\pi$
$521$	22.9305	1.00460	0.502301	+	0.864693i	$0.332487\pi$
$522$	2.94433	0.128870
$523$	−3.05713	−0.133679	−0.0668396	−	0.997764i	$-0.521292\pi$
$523$	−3.05713	−0.133679	−0.0668396	+	0.997764i	$0.521292\pi$
$524$	6.94123	0.303229
$525$	0	0
$526$	−29.3075	−1.27787
$527$	21.8054	0.949860
$528$	5.10824	0.222308
$529$	1.00000	0.0434783
$530$	21.8875	0.950730
$531$	−8.60118	−0.373260
$532$	0	0
$533$	−0.231805	−0.0100406
$534$	2.39572	0.103673
$535$	15.7821	0.682321
$536$	12.1544	0.524988
$537$	−1.99690	−0.0861726
$538$	−2.62941	−0.113362
$539$	0	0
$540$	−3.82843	−0.164749
$541$	−39.3350	−1.69114	−0.845571	−	0.533863i	$-0.820740\pi$
$541$	−39.3350	−1.69114	−0.845571	+	0.533863i	$0.820740\pi$
$542$	−3.21958	−0.138293
$543$	20.5443	0.881640
$544$	6.77276	0.290380
$545$	76.9361	3.29558
$546$	0	0
$547$	−12.4019	−0.530268	−0.265134	−	0.964212i	$-0.585416\pi$
$547$	−12.4019	−0.530268	−0.265134	+	0.964212i	$0.585416\pi$
$548$	5.27981	0.225542
$549$	5.77732	0.246570
$550$	−49.3295	−2.10342
$551$	−12.2599	−0.522291
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	14.7701	0.627521
$555$	30.8287	1.30860
$556$	−9.31371	−0.394989
$557$	−31.0838	−1.31706	−0.658531	−	0.752553i	$-0.728822\pi$
$557$	−31.0838	−1.31706	−0.658531	+	0.752553i	$0.728822\pi$
$558$	3.21958	0.136296
$559$	−0.699196	−0.0295728
$560$	0	0
$561$	34.5969	1.46068
$562$	3.44992	0.145526
$563$	34.1901	1.44094	0.720471	−	0.693485i	$-0.243925\pi$
$563$	34.1901	1.44094	0.720471	+	0.693485i	$0.243925\pi$
$564$	11.9969	0.505161
$565$	−20.4146	−0.858851
$566$	−0.951992	−0.0400152
$567$	0	0
$568$	11.9443	0.501173
$569$	−38.4822	−1.61326	−0.806629	−	0.591059i	$-0.798710\pi$
$569$	−38.4822	−1.61326	−0.806629	+	0.591059i	$0.798710\pi$
$570$	15.9412	0.667705
$571$	−27.0815	−1.13332	−0.566662	−	0.823950i	$-0.691766\pi$
$571$	−27.0815	−1.13332	−0.566662	+	0.823950i	$0.691766\pi$
$572$	0.284376	0.0118904
$573$	1.94743	0.0813550
$574$	0	0
$575$	9.65685	0.402719
$576$	1.00000	0.0416667
$577$	8.33884	0.347150	0.173575	−	0.984821i	$-0.444468\pi$
$577$	8.33884	0.347150	0.173575	+	0.984821i	$0.444468\pi$
$578$	28.8702	1.20084
$579$	−4.44037	−0.184536
$580$	11.2722	0.468051
$581$	0	0
$582$	4.60118	0.190725
$583$	−29.2043	−1.20952
$584$	2.21958	0.0918469
$585$	−0.213129	−0.00881180
$586$	14.5147	0.599597
$587$	−40.4714	−1.67043	−0.835217	−	0.549920i	$-0.814658\pi$
$587$	−40.4714	−1.67043	−0.835217	+	0.549920i	$0.814658\pi$
$588$	0	0
$589$	−13.4061	−0.552387
$590$	−32.9290	−1.35567
$591$	15.7620	0.648362
$592$	−8.05257	−0.330959
$593$	30.3369	1.24579	0.622895	−	0.782306i	$-0.285957\pi$
$593$	30.3369	1.24579	0.622895	+	0.782306i	$0.285957\pi$
$594$	5.10824	0.209594
$595$	0	0
$596$	−11.7190	−0.480028
$597$	19.8733	0.813362
$598$	−0.0556701	−0.00227652
$599$	−6.79443	−0.277613	−0.138806	−	0.990320i	$-0.544327\pi$
$599$	−6.79443	−0.277613	−0.138806	+	0.990320i	$0.544327\pi$
$600$	−9.65685	−0.394239
$601$	−21.0251	−0.857633	−0.428816	−	0.903392i	$-0.641069\pi$
$601$	−21.0251	−0.857633	−0.428816	+	0.903392i	$0.641069\pi$
$602$	0	0
$603$	12.1544	0.494964
$604$	17.5565	0.714365
$605$	57.7868	2.34937
$606$	−14.8875	−0.604761
$607$	−2.43727	−0.0989259	−0.0494629	−	0.998776i	$-0.515751\pi$
$607$	−2.43727	−0.0989259	−0.0494629	+	0.998776i	$0.515751\pi$
$608$	−4.16391	−0.168869
$609$	0	0
$610$	22.1180	0.895534
$611$	0.667869	0.0270191
$612$	6.77276	0.273772
$613$	4.30872	0.174028	0.0870138	−	0.996207i	$-0.472268\pi$
$613$	4.30872	0.174028	0.0870138	+	0.996207i	$0.472268\pi$
$614$	−17.2611	−0.696603
$615$	−15.9412	−0.642812
$616$	0	0
$617$	−12.0621	−0.485603	−0.242801	−	0.970076i	$-0.578066\pi$
$617$	−12.0621	−0.485603	−0.242801	+	0.970076i	$0.578066\pi$
$618$	6.15436	0.247565
$619$	−39.0944	−1.57134	−0.785668	−	0.618648i	$-0.787681\pi$
$619$	−39.0944	−1.57134	−0.785668	+	0.618648i	$0.787681\pi$
$620$	12.3259	0.495021
$621$	−1.00000	−0.0401286
$622$	−2.37059	−0.0950519
$623$	0	0
$624$	0.0556701	0.00222859
$625$	19.9706	0.798823
$626$	5.83798	0.233333
$627$	−21.2703	−0.849452
$628$	9.15892	0.365481
$629$	−54.5381	−2.17458
$630$	0	0
$631$	13.1947	0.525273	0.262636	−	0.964895i	$-0.415408\pi$
$631$	13.1947	0.525273	0.262636	+	0.964895i	$0.415408\pi$
$632$	−2.94433	−0.117119
$633$	10.6427	0.423011
$634$	0.629412	0.0249971
$635$	32.7277	1.29876
$636$	−5.71709	−0.226697
$637$	0	0
$638$	−15.0403	−0.595453
$639$	11.9443	0.472510
$640$	3.82843	0.151332
$641$	44.5194	1.75841	0.879206	−	0.476442i	$-0.158074\pi$
$641$	44.5194	1.75841	0.879206	+	0.476442i	$0.158074\pi$
$642$	−4.12236	−0.162696
$643$	−4.30348	−0.169713	−0.0848563	−	0.996393i	$-0.527043\pi$
$643$	−4.30348	−0.169713	−0.0848563	+	0.996393i	$0.527043\pi$
$644$	0	0
$645$	−48.0836	−1.89329
$646$	−28.2012	−1.10956
$647$	−23.6378	−0.929296	−0.464648	−	0.885496i	$-0.653819\pi$
$647$	−23.6378	−0.929296	−0.464648	+	0.885496i	$0.653819\pi$
$648$	1.00000	0.0392837
$649$	43.9369	1.72468
$650$	−0.537598	−0.0210863
$651$	0	0
$652$	−12.1730	−0.476733
$653$	−17.0403	−0.666840	−0.333420	−	0.942778i	$-0.608203\pi$
$653$	−17.0403	−0.666840	−0.333420	+	0.942778i	$0.608203\pi$
$654$	−20.0960	−0.785816
$655$	26.5740	1.03833
$656$	4.16391	0.162573
$657$	2.21958	0.0865941
$658$	0	0
$659$	0.998791	0.0389074	0.0194537	−	0.999811i	$-0.493807\pi$
$659$	0.998791	0.0389074	0.0194537	+	0.999811i	$0.493807\pi$
$660$	19.5565	0.761237
$661$	−26.3652	−1.02549	−0.512743	−	0.858542i	$-0.671371\pi$
$661$	−26.3652	−1.02549	−0.512743	+	0.858542i	$0.671371\pi$
$662$	13.7003	0.532477
$663$	0.377040	0.0146430
$664$	14.7651	0.572997
$665$	0	0
$666$	−8.05257	−0.312031
$667$	2.94433	0.114005
$668$	−21.0788	−0.815563
$669$	−28.5424	−1.10351
$670$	46.5321	1.79769
$671$	−29.5119	−1.13930
$672$	0	0
$673$	−20.3388	−0.784005	−0.392002	−	0.919964i	$-0.628217\pi$
$673$	−20.3388	−0.784005	−0.392002	+	0.919964i	$0.628217\pi$
$674$	−19.8318	−0.763892
$675$	−9.65685	−0.371692
$676$	−12.9969	−0.499881
$677$	−30.5763	−1.17514	−0.587572	−	0.809172i	$-0.699916\pi$
$677$	−30.5763	−1.17514	−0.587572	+	0.809172i	$0.699916\pi$
$678$	5.33238	0.204789
$679$	0	0
$680$	25.9290	0.994332
$681$	−3.68319	−0.141140
$682$	−16.4464	−0.629765
$683$	40.0360	1.53194	0.765968	−	0.642878i	$-0.222260\pi$
$683$	40.0360	1.53194	0.765968	+	0.642878i	$0.222260\pi$
$684$	−4.16391	−0.159211
$685$	20.2134	0.772314
$686$	0	0
$687$	−12.1639	−0.464082
$688$	12.5596	0.478831
$689$	−0.318271	−0.0121252
$690$	−3.82843	−0.145746
$691$	−20.6862	−0.786940	−0.393470	−	0.919338i	$-0.628725\pi$
$691$	−20.6862	−0.786940	−0.393470	+	0.919338i	$0.628725\pi$
$692$	−13.4250	−0.510344
$693$	0	0
$694$	5.55774	0.210969
$695$	−35.6569	−1.35254
$696$	−2.94433	−0.111605
$697$	28.2012	1.06820
$698$	15.5027	0.586788
$699$	1.49294	0.0564683
$700$	0	0
$701$	−18.5954	−0.702339	−0.351170	−	0.936312i	$-0.614216\pi$
$701$	−18.5954	−0.702339	−0.351170	+	0.936312i	$0.614216\pi$
$702$	0.0556701	0.00210113
$703$	33.5302	1.26462
$704$	−5.10824	−0.192524
$705$	45.9293	1.72980
$706$	−15.9412	−0.599956
$707$	0	0
$708$	8.60118	0.323252
$709$	−19.8886	−0.746930	−0.373465	−	0.927644i	$-0.621830\pi$
$709$	−19.8886	−0.746930	−0.373465	+	0.927644i	$0.621830\pi$
$710$	45.7280	1.71614
$711$	−2.94433	−0.110421
$712$	−2.39572	−0.0897833
$713$	3.21958	0.120574
$714$	0	0
$715$	1.08871	0.0407156
$716$	1.99690	0.0746277
$717$	−25.1193	−0.938096
$718$	32.4047	1.20933
$719$	28.5412	1.06441	0.532204	−	0.846616i	$-0.321364\pi$
$719$	28.5412	1.06441	0.532204	+	0.846616i	$0.321364\pi$
$720$	3.82843	0.142677
$721$	0	0
$722$	−1.66184	−0.0618474
$723$	11.8471	0.440599
$724$	−20.5443	−0.763523
$725$	28.4330	1.05597
$726$	−15.0941	−0.560196
$727$	24.4745	0.907710	0.453855	−	0.891076i	$-0.350048\pi$
$727$	24.4745	0.907710	0.453855	+	0.891076i	$0.350048\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.49751	0.314507
$731$	85.0633	3.14618
$732$	−5.77732	−0.213536
$733$	−29.9168	−1.10500	−0.552501	−	0.833512i	$-0.686326\pi$
$733$	−29.9168	−1.10500	−0.552501	+	0.833512i	$0.686326\pi$
$734$	−10.8669	−0.401104
$735$	0	0
$736$	1.00000	0.0368605
$737$	−62.0874	−2.28702
$738$	4.16391	0.153276
$739$	4.97969	0.183181	0.0915904	−	0.995797i	$-0.470805\pi$
$739$	4.97969	0.183181	0.0915904	+	0.995797i	$0.470805\pi$
$740$	−30.8287	−1.13328
$741$	−0.231805	−0.00851559
$742$	0	0
$743$	34.0502	1.24918	0.624589	−	0.780953i	$-0.285266\pi$
$743$	34.0502	1.24918	0.624589	+	0.780953i	$0.285266\pi$
$744$	−3.21958	−0.118036
$745$	−44.8652	−1.64374
$746$	−0.216482	−0.00792598
$747$	14.7651	0.540227
$748$	−34.5969	−1.26499
$749$	0	0
$750$	−17.8284	−0.651002
$751$	−45.8165	−1.67187	−0.835933	−	0.548831i	$-0.815073\pi$
$751$	−45.8165	−1.67187	−0.835933	+	0.548831i	$0.815073\pi$
$752$	−11.9969	−0.437482
$753$	8.09413	0.294966
$754$	−0.163911	−0.00596929
$755$	67.2139	2.44616
$756$	0	0
$757$	17.0256	0.618804	0.309402	−	0.950931i	$-0.399871\pi$
$757$	17.0256	0.618804	0.309402	+	0.950931i	$0.399871\pi$
$758$	8.93667	0.324594
$759$	5.10824	0.185417
$760$	−15.9412	−0.578249
$761$	45.2961	1.64198	0.820991	−	0.570942i	$-0.193422\pi$
$761$	45.2961	1.64198	0.820991	+	0.570942i	$0.193422\pi$
$762$	−8.54861	−0.309684
$763$	0	0
$764$	−1.94743	−0.0704555
$765$	25.9290	0.937465
$766$	−26.8287	−0.969360
$767$	0.478829	0.0172895
$768$	−1.00000	−0.0360844
$769$	−13.8318	−0.498787	−0.249393	−	0.968402i	$-0.580231\pi$
$769$	−13.8318	−0.498787	−0.249393	+	0.968402i	$0.580231\pi$
$770$	0	0
$771$	1.94123	0.0699117
$772$	4.44037	0.159812
$773$	−7.17467	−0.258055	−0.129028	−	0.991641i	$-0.541186\pi$
$773$	−7.17467	−0.258055	−0.129028	+	0.991641i	$0.541186\pi$
$774$	12.5596	0.451447
$775$	31.0910	1.11682
$776$	−4.60118	−0.165173
$777$	0	0
$778$	−3.66598	−0.131432
$779$	−17.3382	−0.621204
$780$	0.213129	0.00763124
$781$	−61.0145	−2.18327
$782$	6.77276	0.242193
$783$	−2.94433	−0.105222
$784$	0	0
$785$	35.0643	1.25150
$786$	−6.94123	−0.247585
$787$	7.14025	0.254522	0.127261	−	0.991869i	$-0.459381\pi$
$787$	7.14025	0.254522	0.127261	+	0.991869i	$0.459381\pi$
$788$	−15.7620	−0.561498
$789$	29.3075	1.04337
$790$	−11.2722	−0.401045
$791$	0	0
$792$	−5.10824	−0.181513
$793$	−0.321624	−0.0114212
$794$	−19.9572	−0.708256
$795$	−21.8875	−0.776268
$796$	−19.8733	−0.704392
$797$	−1.94889	−0.0690333	−0.0345167	−	0.999404i	$-0.510989\pi$
$797$	−1.94889	−0.0690333	−0.0345167	+	0.999404i	$0.510989\pi$
$798$	0	0
$799$	−81.2521	−2.87449
$800$	9.65685	0.341421
$801$	−2.39572	−0.0846485
$802$	0.386165	0.0136360
$803$	−11.3382	−0.400115
$804$	−12.1544	−0.428651
$805$	0	0
$806$	−0.179235	−0.00631327
$807$	2.62941	0.0925597
$808$	14.8875	0.523739
$809$	39.9350	1.40404	0.702020	−	0.712157i	$-0.252281\pi$
$809$	39.9350	1.40404	0.702020	+	0.712157i	$0.252281\pi$
$810$	3.82843	0.134517
$811$	39.4035	1.38364	0.691822	−	0.722068i	$-0.256808\pi$
$811$	39.4035	1.38364	0.691822	+	0.722068i	$0.256808\pi$
$812$	0	0
$813$	3.21958	0.112916
$814$	41.1345	1.44176
$815$	−46.6036	−1.63245
$816$	−6.77276	−0.237094
$817$	−52.2972	−1.82965
$818$	15.5314	0.543043
$819$	0	0
$820$	15.9412	0.556692
$821$	−39.4978	−1.37848	−0.689241	−	0.724532i	$-0.742056\pi$
$821$	−39.4978	−1.37848	−0.689241	+	0.724532i	$0.742056\pi$
$822$	−5.27981	−0.184155
$823$	8.81054	0.307116	0.153558	−	0.988140i	$-0.450927\pi$
$823$	8.81054	0.307116	0.153558	+	0.988140i	$0.450927\pi$
$824$	−6.15436	−0.214397
$825$	49.3295	1.71743
$826$	0	0
$827$	26.5271	0.922437	0.461219	−	0.887286i	$-0.347412\pi$
$827$	26.5271	0.922437	0.461219	+	0.887286i	$0.347412\pi$
$828$	1.00000	0.0347524
$829$	17.1070	0.594152	0.297076	−	0.954854i	$-0.403989\pi$
$829$	17.1070	0.594152	0.297076	+	0.954854i	$0.403989\pi$
$830$	56.5271	1.96208
$831$	−14.7701	−0.512369
$832$	−0.0556701	−0.00193001
$833$	0	0
$834$	9.31371	0.322507
$835$	−80.6987	−2.79269
$836$	21.2703	0.735647
$837$	−3.21958	−0.111285
$838$	−0.559628	−0.0193320
$839$	13.4585	0.464640	0.232320	−	0.972639i	$-0.425368\pi$
$839$	13.4585	0.464640	0.232320	+	0.972639i	$0.425368\pi$
$840$	0	0
$841$	−20.3309	−0.701066
$842$	17.2024	0.592833
$843$	−3.44992	−0.118822
$844$	−10.6427	−0.366338
$845$	−49.7577	−1.71172
$846$	−11.9969	−0.412462
$847$	0	0
$848$	5.71709	0.196326
$849$	0.951992	0.0326723
$850$	65.4035	2.24332
$851$	−8.05257	−0.276039
$852$	−11.9443	−0.409206
$853$	−38.3278	−1.31232	−0.656160	−	0.754622i	$-0.727820\pi$
$853$	−38.3278	−1.31232	−0.656160	+	0.754622i	$0.727820\pi$
$854$	0	0
$855$	−15.9412	−0.545179
$856$	4.12236	0.140899
$857$	−45.5957	−1.55752	−0.778759	−	0.627323i	$-0.784151\pi$
$857$	−45.5957	−1.55752	−0.778759	+	0.627323i	$0.784151\pi$
$858$	−0.284376	−0.00970845
$859$	−27.2420	−0.929486	−0.464743	−	0.885446i	$-0.653853\pi$
$859$	−27.2420	−0.929486	−0.464743	+	0.885446i	$0.653853\pi$
$860$	48.0836	1.63964
$861$	0	0
$862$	18.8501	0.642037
$863$	56.4633	1.92203	0.961017	−	0.276489i	$-0.0891709\pi$
$863$	56.4633	1.92203	0.961017	+	0.276489i	$0.0891709\pi$
$864$	−1.00000	−0.0340207
$865$	−51.3968	−1.74754
$866$	−0.435383	−0.0147949
$867$	−28.8702	−0.980485
$868$	0	0
$869$	15.0403	0.510209
$870$	−11.2722	−0.382162
$871$	−0.676635	−0.0229269
$872$	20.0960	0.680537
$873$	−4.60118	−0.155726
$874$	−4.16391	−0.140846
$875$	0	0
$876$	−2.21958	−0.0749927
$877$	15.1902	0.512938	0.256469	−	0.966552i	$-0.417441\pi$
$877$	15.1902	0.512938	0.256469	+	0.966552i	$0.417441\pi$
$878$	34.0048	1.14761
$879$	−14.5147	−0.489569
$880$	−19.5565	−0.659250
$881$	−2.60885	−0.0878942	−0.0439471	−	0.999034i	$-0.513993\pi$
$881$	−2.60885	−0.0878942	−0.0439471	+	0.999034i	$0.513993\pi$
$882$	0	0
$883$	−25.7863	−0.867779	−0.433890	−	0.900966i	$-0.642859\pi$
$883$	−25.7863	−0.867779	−0.433890	+	0.900966i	$0.642859\pi$
$884$	−0.377040	−0.0126812
$885$	32.9290	1.10690
$886$	16.9412	0.569152
$887$	−14.2692	−0.479111	−0.239556	−	0.970883i	$-0.577002\pi$
$887$	−14.2692	−0.479111	−0.239556	+	0.970883i	$0.577002\pi$
$888$	8.05257	0.270227
$889$	0	0
$890$	−9.17183	−0.307440
$891$	−5.10824	−0.171133
$892$	28.5424	0.955671
$893$	49.9540	1.67165
$894$	11.7190	0.391941
$895$	7.64499	0.255544
$896$	0	0
$897$	0.0556701	0.00185877
$898$	5.28937	0.176508
$899$	9.47951	0.316159
$900$	9.65685	0.321895
$901$	38.7204	1.28996
$902$	−21.2703	−0.708222
$903$	0	0
$904$	−5.33238	−0.177352
$905$	−78.6524	−2.61449
$906$	−17.5565	−0.583277
$907$	−41.5206	−1.37867	−0.689335	−	0.724443i	$-0.742097\pi$
$907$	−41.5206	−1.37867	−0.689335	+	0.724443i	$0.742097\pi$
$908$	3.68319	0.122231
$909$	14.8875	0.493786
$910$	0	0
$911$	8.50317	0.281723	0.140861	−	0.990029i	$-0.455013\pi$
$911$	8.50317	0.281723	0.140861	+	0.990029i	$0.455013\pi$
$912$	4.16391	0.137881
$913$	−75.4237	−2.49616
$914$	6.95723	0.230125
$915$	−22.1180	−0.731200
$916$	12.1639	0.401907
$917$	0	0
$918$	−6.77276	−0.223534
$919$	14.5873	0.481191	0.240596	−	0.970625i	$-0.422657\pi$
$919$	14.5873	0.481191	0.240596	+	0.970625i	$0.422657\pi$
$920$	3.82843	0.126220
$921$	17.2611	0.568774
$922$	−6.65564	−0.219192
$923$	−0.664942	−0.0218868
$924$	0	0
$925$	−77.7625	−2.55682
$926$	19.8604	0.652654
$927$	−6.15436	−0.202136
$928$	2.94433	0.0966524
$929$	31.3816	1.02960	0.514798	−	0.857311i	$-0.327867\pi$
$929$	31.3816	1.02960	0.514798	+	0.857311i	$0.327867\pi$
$930$	−12.3259	−0.404183
$931$	0	0
$932$	−1.49294	−0.0489030
$933$	2.37059	0.0776096
$934$	−18.5443	−0.606788
$935$	−132.452	−4.33163
$936$	−0.0556701	−0.00181964
$937$	12.9726	0.423795	0.211897	−	0.977292i	$-0.432036\pi$
$937$	12.9726	0.423795	0.211897	+	0.977292i	$0.432036\pi$
$938$	0	0
$939$	−5.83798	−0.190515
$940$	−45.9293	−1.49805
$941$	−9.88142	−0.322125	−0.161063	−	0.986944i	$-0.551492\pi$
$941$	−9.88142	−0.322125	−0.161063	+	0.986944i	$0.551492\pi$
$942$	−9.15892	−0.298414
$943$	4.16391	0.135596
$944$	−8.60118	−0.279945
$945$	0	0
$946$	−64.1576	−2.08594
$947$	26.1607	0.850109	0.425054	−	0.905168i	$-0.360255\pi$
$947$	26.1607	0.850109	0.425054	+	0.905168i	$0.360255\pi$
$948$	2.94433	0.0956274
$949$	−0.123564	−0.00401107
$950$	−40.2103	−1.30459
$951$	−0.629412	−0.0204101
$952$	0	0
$953$	11.8360	0.383405	0.191703	−	0.981453i	$-0.438599\pi$
$953$	11.8360	0.383405	0.191703	+	0.981453i	$0.438599\pi$
$954$	5.71709	0.185098
$955$	−7.45559	−0.241257
$956$	25.1193	0.812415
$957$	15.0403	0.486185
$958$	−9.28317	−0.299926
$959$	0	0
$960$	−3.82843	−0.123562
$961$	−20.6343	−0.665622
$962$	0.448288	0.0144534
$963$	4.12236	0.132841
$964$	−11.8471	−0.381570
$965$	16.9996	0.547238
$966$	0	0
$967$	−23.7730	−0.764488	−0.382244	−	0.924061i	$-0.624849\pi$
$967$	−23.7730	−0.764488	−0.382244	+	0.924061i	$0.624849\pi$
$968$	15.0941	0.485144
$969$	28.2012	0.905952
$970$	−17.6153	−0.565593
$971$	−5.57805	−0.179008	−0.0895041	−	0.995986i	$-0.528528\pi$
$971$	−5.57805	−0.179008	−0.0895041	+	0.995986i	$0.528528\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	9.86232	0.316009
$975$	0.537598	0.0172169
$976$	5.77732	0.184927
$977$	−37.4656	−1.19863	−0.599316	−	0.800512i	$-0.704561\pi$
$977$	−37.4656	−1.19863	−0.599316	+	0.800512i	$0.704561\pi$
$978$	12.1730	0.389251
$979$	12.2379	0.391125
$980$	0	0
$981$	20.0960	0.641616
$982$	−41.3368	−1.31911
$983$	−9.25494	−0.295187	−0.147593	−	0.989048i	$-0.547153\pi$
$983$	−9.25494	−0.295187	−0.147593	+	0.989048i	$0.547153\pi$
$984$	−4.16391	−0.132741
$985$	−60.3437	−1.92271
$986$	19.9412	0.635058
$987$	0	0
$988$	0.231805	0.00737471
$989$	12.5596	0.399373
$990$	−19.5565	−0.621547
$991$	−3.35915	−0.106707	−0.0533535	−	0.998576i	$-0.516991\pi$
$991$	−3.35915	−0.106707	−0.0533535	+	0.998576i	$0.516991\pi$
$992$	3.21958	0.102222
$993$	−13.7003	−0.434766
$994$	0	0
$995$	−76.0836	−2.41201
$996$	−14.7651	−0.467850
$997$	3.35337	0.106202	0.0531012	−	0.998589i	$-0.483089\pi$
$997$	3.35337	0.106202	0.0531012	+	0.998589i	$0.483089\pi$
$998$	−4.45449	−0.141004
$999$	8.05257	0.254772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cm.1.3		4
7.3	odd	6		966.2.i.l.415.4	yes	8
7.5	odd	6		966.2.i.l.277.4	✓	8
7.6	odd	2		6762.2.a.cp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.4	✓	8	7.5	odd	6
966.2.i.l.415.4	yes	8	7.3	odd	6
6762.2.a.cm.1.3		4	1.1	even	1	trivial
6762.2.a.cp.1.1		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82843 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82843 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.82843 q^{10} -5.10824 q^{11} -1.00000 q^{12} -0.0556701 q^{13} -3.82843 q^{15} +1.00000 q^{16} +6.77276 q^{17} +1.00000 q^{18} -4.16391 q^{19} +3.82843 q^{20} -5.10824 q^{22} +1.00000 q^{23} -1.00000 q^{24} +9.65685 q^{25} -0.0556701 q^{26} -1.00000 q^{27} +2.94433 q^{29} -3.82843 q^{30} +3.21958 q^{31} +1.00000 q^{32} +5.10824 q^{33} +6.77276 q^{34} +1.00000 q^{36} -8.05257 q^{37} -4.16391 q^{38} +0.0556701 q^{39} +3.82843 q^{40} +4.16391 q^{41} +12.5596 q^{43} -5.10824 q^{44} +3.82843 q^{45} +1.00000 q^{46} -11.9969 q^{47} -1.00000 q^{48} +9.65685 q^{50} -6.77276 q^{51} -0.0556701 q^{52} +5.71709 q^{53} -1.00000 q^{54} -19.5565 q^{55} +4.16391 q^{57} +2.94433 q^{58} -8.60118 q^{59} -3.82843 q^{60} +5.77732 q^{61} +3.21958 q^{62} +1.00000 q^{64} -0.213129 q^{65} +5.10824 q^{66} +12.1544 q^{67} +6.77276 q^{68} -1.00000 q^{69} +11.9443 q^{71} +1.00000 q^{72} +2.21958 q^{73} -8.05257 q^{74} -9.65685 q^{75} -4.16391 q^{76} +0.0556701 q^{78} -2.94433 q^{79} +3.82843 q^{80} +1.00000 q^{81} +4.16391 q^{82} +14.7651 q^{83} +25.9290 q^{85} +12.5596 q^{86} -2.94433 q^{87} -5.10824 q^{88} -2.39572 q^{89} +3.82843 q^{90} +1.00000 q^{92} -3.21958 q^{93} -11.9969 q^{94} -15.9412 q^{95} -1.00000 q^{96} -4.60118 q^{97} -5.10824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{15} + 4 q^{16} + 10 q^{17} + 4 q^{18} + 4 q^{19} + 4 q^{20} + 6 q^{22} + 4 q^{23} - 4 q^{24} + 16 q^{25} - 6 q^{26} - 4 q^{27} + 6 q^{29} - 4 q^{30} - 2 q^{31} + 4 q^{32} - 6 q^{33} + 10 q^{34} + 4 q^{36} + 4 q^{38} + 6 q^{39} + 4 q^{40} - 4 q^{41} + 20 q^{43} + 6 q^{44} + 4 q^{45} + 4 q^{46} - 10 q^{47} - 4 q^{48} + 16 q^{50} - 10 q^{51} - 6 q^{52} - 4 q^{54} - 10 q^{55} - 4 q^{57} + 6 q^{58} - 6 q^{59} - 4 q^{60} - 2 q^{62} + 4 q^{64} - 14 q^{65} - 6 q^{66} + 18 q^{67} + 10 q^{68} - 4 q^{69} + 42 q^{71} + 4 q^{72} - 6 q^{73} - 16 q^{75} + 4 q^{76} + 6 q^{78} - 6 q^{79} + 4 q^{80} + 4 q^{81} - 4 q^{82} + 10 q^{83} + 34 q^{85} + 20 q^{86} - 6 q^{87} + 6 q^{88} + 4 q^{90} + 4 q^{92} + 2 q^{93} - 10 q^{94} - 20 q^{95} - 4 q^{96} + 10 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^15 + 4 * q^16 + 10 * q^17 + 4 * q^18 + 4 * q^19 + 4 * q^20 + 6 * q^22 + 4 * q^23 - 4 * q^24 + 16 * q^25 - 6 * q^26 - 4 * q^27 + 6 * q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 - 6 * q^33 + 10 * q^34 + 4 * q^36 + 4 * q^38 + 6 * q^39 + 4 * q^40 - 4 * q^41 + 20 * q^43 + 6 * q^44 + 4 * q^45 + 4 * q^46 - 10 * q^47 - 4 * q^48 + 16 * q^50 - 10 * q^51 - 6 * q^52 - 4 * q^54 - 10 * q^55 - 4 * q^57 + 6 * q^58 - 6 * q^59 - 4 * q^60 - 2 * q^62 + 4 * q^64 - 14 * q^65 - 6 * q^66 + 18 * q^67 + 10 * q^68 - 4 * q^69 + 42 * q^71 + 4 * q^72 - 6 * q^73 - 16 * q^75 + 4 * q^76 + 6 * q^78 - 6 * q^79 + 4 * q^80 + 4 * q^81 - 4 * q^82 + 10 * q^83 + 34 * q^85 + 20 * q^86 - 6 * q^87 + 6 * q^88 + 4 * q^90 + 4 * q^92 + 2 * q^93 - 10 * q^94 - 20 * q^95 - 4 * q^96 + 10 * q^97 + 6 * q^99

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