LMFDB - Embedded newform 8470.2.a.cv.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.4642000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14x^2 - 9x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.84175$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.84175 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.84175 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.392057 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.84175 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.84175 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.392057 q^{9} -1.00000 q^{10} +1.84175 q^{12} +1.78301 q^{13} -1.00000 q^{14} +1.84175 q^{15} +1.00000 q^{16} +7.29256 q^{17} -0.392057 q^{18} +3.17287 q^{19} +1.00000 q^{20} +1.84175 q^{21} -4.72397 q^{23} -1.84175 q^{24} +1.00000 q^{25} -1.78301 q^{26} -4.80319 q^{27} +1.00000 q^{28} -4.51518 q^{29} -1.84175 q^{30} -4.99011 q^{31} -1.00000 q^{32} -7.29256 q^{34} +1.00000 q^{35} +0.392057 q^{36} -4.73296 q^{37} -3.17287 q^{38} +3.28386 q^{39} -1.00000 q^{40} -4.17080 q^{41} -1.84175 q^{42} +11.6531 q^{43} +0.392057 q^{45} +4.72397 q^{46} +3.74365 q^{47} +1.84175 q^{48} +1.00000 q^{49} -1.00000 q^{50} +13.4311 q^{51} +1.78301 q^{52} +1.32043 q^{53} +4.80319 q^{54} -1.00000 q^{56} +5.84365 q^{57} +4.51518 q^{58} +9.71495 q^{59} +1.84175 q^{60} +9.80246 q^{61} +4.99011 q^{62} +0.392057 q^{63} +1.00000 q^{64} +1.78301 q^{65} -6.96181 q^{67} +7.29256 q^{68} -8.70039 q^{69} -1.00000 q^{70} +16.7995 q^{71} -0.392057 q^{72} -6.05144 q^{73} +4.73296 q^{74} +1.84175 q^{75} +3.17287 q^{76} -3.28386 q^{78} +15.0746 q^{79} +1.00000 q^{80} -10.0225 q^{81} +4.17080 q^{82} +17.5840 q^{83} +1.84175 q^{84} +7.29256 q^{85} -11.6531 q^{86} -8.31586 q^{87} +14.3054 q^{89} -0.392057 q^{90} +1.78301 q^{91} -4.72397 q^{92} -9.19056 q^{93} -3.74365 q^{94} +3.17287 q^{95} -1.84175 q^{96} +5.08081 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 - q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} - q^{9} - 6 q^{10} - q^{12} + 6 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} + 21 q^{17} + q^{18} - 3 q^{19} + 6 q^{20} - q^{21} - 10 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 6 q^{28} + 10 q^{29} + q^{30} - 4 q^{31} - 6 q^{32} - 21 q^{34} + 6 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} + 26 q^{39} - 6 q^{40} + 7 q^{41} + q^{42} + 19 q^{43} - q^{45} + 10 q^{46} + 10 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 4 q^{51} + 6 q^{52} - 16 q^{53} + 4 q^{54} - 6 q^{56} + 16 q^{57} - 10 q^{58} - 3 q^{59} - q^{60} - 8 q^{61} + 4 q^{62} - q^{63} + 6 q^{64} + 6 q^{65} - 27 q^{67} + 21 q^{68} + 4 q^{69} - 6 q^{70} + 4 q^{71} + q^{72} + 13 q^{73} + 2 q^{74} - q^{75} - 3 q^{76} - 26 q^{78} + 14 q^{79} + 6 q^{80} - 14 q^{81} - 7 q^{82} + 51 q^{83} - q^{84} + 21 q^{85} - 19 q^{86} + 8 q^{87} + q^{89} + q^{90} + 6 q^{91} - 10 q^{92} + 4 q^{93} - 10 q^{94} - 3 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 - q^9 - 6 * q^10 - q^12 + 6 * q^13 - 6 * q^14 - q^15 + 6 * q^16 + 21 * q^17 + q^18 - 3 * q^19 + 6 * q^20 - q^21 - 10 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 6 * q^28 + 10 * q^29 + q^30 - 4 * q^31 - 6 * q^32 - 21 * q^34 + 6 * q^35 - q^36 - 2 * q^37 + 3 * q^38 + 26 * q^39 - 6 * q^40 + 7 * q^41 + q^42 + 19 * q^43 - q^45 + 10 * q^46 + 10 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 4 * q^51 + 6 * q^52 - 16 * q^53 + 4 * q^54 - 6 * q^56 + 16 * q^57 - 10 * q^58 - 3 * q^59 - q^60 - 8 * q^61 + 4 * q^62 - q^63 + 6 * q^64 + 6 * q^65 - 27 * q^67 + 21 * q^68 + 4 * q^69 - 6 * q^70 + 4 * q^71 + q^72 + 13 * q^73 + 2 * q^74 - q^75 - 3 * q^76 - 26 * q^78 + 14 * q^79 + 6 * q^80 - 14 * q^81 - 7 * q^82 + 51 * q^83 - q^84 + 21 * q^85 - 19 * q^86 + 8 * q^87 + q^89 + q^90 + 6 * q^91 - 10 * q^92 + 4 * q^93 - 10 * q^94 - 3 * q^95 + q^96 + 7 * q^97 - 6 * q^98

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
$3$	1.84175	1.06334	0.531669	−	0.846953i	$-0.321565\pi$
$3$	1.84175	1.06334	0.531669	+	0.846953i	$0.321565\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.84175	−0.751893
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0.392057	0.130686
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	1.84175	0.531669
$13$	1.78301	0.494517	0.247259	−	0.968950i	$-0.420470\pi$
$13$	1.78301	0.494517	0.247259	+	0.968950i	$0.420470\pi$
$14$	−1.00000	−0.267261
$15$	1.84175	0.475539
$16$	1.00000	0.250000
$17$	7.29256	1.76870	0.884352	−	0.466820i	$-0.154600\pi$
$17$	7.29256	1.76870	0.884352	+	0.466820i	$0.154600\pi$
$18$	−0.392057	−0.0924087
$19$	3.17287	0.727907	0.363954	−	0.931417i	$-0.381427\pi$
$19$	3.17287	0.727907	0.363954	+	0.931417i	$0.381427\pi$
$20$	1.00000	0.223607
$21$	1.84175	0.401904
$22$	0	0
$23$	−4.72397	−0.985016	−0.492508	−	0.870308i	$-0.663920\pi$
$23$	−4.72397	−0.985016	−0.492508	+	0.870308i	$0.663920\pi$
$24$	−1.84175	−0.375946
$25$	1.00000	0.200000
$26$	−1.78301	−0.349677
$27$	−4.80319	−0.924374
$28$	1.00000	0.188982
$29$	−4.51518	−0.838449	−0.419224	−	0.907883i	$-0.637698\pi$
$29$	−4.51518	−0.838449	−0.419224	+	0.907883i	$0.637698\pi$
$30$	−1.84175	−0.336257
$31$	−4.99011	−0.896250	−0.448125	−	0.893971i	$-0.647908\pi$
$31$	−4.99011	−0.896250	−0.448125	+	0.893971i	$0.647908\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.29256	−1.25066
$35$	1.00000	0.169031
$36$	0.392057	0.0653428
$37$	−4.73296	−0.778093	−0.389047	−	0.921218i	$-0.627196\pi$
$37$	−4.73296	−0.778093	−0.389047	+	0.921218i	$0.627196\pi$
$38$	−3.17287	−0.514708
$39$	3.28386	0.525839
$40$	−1.00000	−0.158114
$41$	−4.17080	−0.651369	−0.325684	−	0.945479i	$-0.605595\pi$
$41$	−4.17080	−0.651369	−0.325684	+	0.945479i	$0.605595\pi$
$42$	−1.84175	−0.284189
$43$	11.6531	1.77709	0.888544	−	0.458791i	$-0.151717\pi$
$43$	11.6531	1.77709	0.888544	+	0.458791i	$0.151717\pi$
$44$	0	0
$45$	0.392057	0.0584444
$46$	4.72397	0.696512
$47$	3.74365	0.546067	0.273034	−	0.962004i	$-0.411973\pi$
$47$	3.74365	0.546067	0.273034	+	0.962004i	$0.411973\pi$
$48$	1.84175	0.265834
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	13.4311	1.88073
$52$	1.78301	0.247259
$53$	1.32043	0.181375	0.0906875	−	0.995879i	$-0.471094\pi$
$53$	1.32043	0.181375	0.0906875	+	0.995879i	$0.471094\pi$
$54$	4.80319	0.653631
$55$	0	0
$56$	−1.00000	−0.133631
$57$	5.84365	0.774011
$58$	4.51518	0.592873
$59$	9.71495	1.26478	0.632389	−	0.774651i	$-0.282074\pi$
$59$	9.71495	1.26478	0.632389	+	0.774651i	$0.282074\pi$
$60$	1.84175	0.237769
$61$	9.80246	1.25508	0.627538	−	0.778586i	$-0.284063\pi$
$61$	9.80246	1.25508	0.627538	+	0.778586i	$0.284063\pi$
$62$	4.99011	0.633745
$63$	0.392057	0.0493945
$64$	1.00000	0.125000
$65$	1.78301	0.221155
$66$	0	0
$67$	−6.96181	−0.850520	−0.425260	−	0.905071i	$-0.639817\pi$
$67$	−6.96181	−0.850520	−0.425260	+	0.905071i	$0.639817\pi$
$68$	7.29256	0.884352
$69$	−8.70039	−1.04740
$70$	−1.00000	−0.119523
$71$	16.7995	1.99373	0.996867	−	0.0791011i	$-0.0252050\pi$
$71$	16.7995	1.99373	0.996867	+	0.0791011i	$0.0252050\pi$
$72$	−0.392057	−0.0462043
$73$	−6.05144	−0.708268	−0.354134	−	0.935195i	$-0.615224\pi$
$73$	−6.05144	−0.708268	−0.354134	+	0.935195i	$0.615224\pi$
$74$	4.73296	0.550195
$75$	1.84175	0.212667
$76$	3.17287	0.363954
$77$	0	0
$78$	−3.28386	−0.371824
$79$	15.0746	1.69602	0.848010	−	0.529980i	$-0.177800\pi$
$79$	15.0746	1.69602	0.848010	+	0.529980i	$0.177800\pi$
$80$	1.00000	0.111803
$81$	−10.0225	−1.11361
$82$	4.17080	0.460587
$83$	17.5840	1.93010	0.965049	−	0.262071i	$-0.0844055\pi$
$83$	17.5840	1.93010	0.965049	+	0.262071i	$0.0844055\pi$
$84$	1.84175	0.200952
$85$	7.29256	0.790989
$86$	−11.6531	−1.25659
$87$	−8.31586	−0.891554
$88$	0	0
$89$	14.3054	1.51637	0.758186	−	0.652038i	$-0.226086\pi$
$89$	14.3054	1.51637	0.758186	+	0.652038i	$0.226086\pi$
$90$	−0.392057	−0.0413264
$91$	1.78301	0.186910
$92$	−4.72397	−0.492508
$93$	−9.19056	−0.953016
$94$	−3.74365	−0.386128
$95$	3.17287	0.325530
$96$	−1.84175	−0.187973
$97$	5.08081	0.515878	0.257939	−	0.966161i	$-0.416957\pi$
$97$	5.08081	0.515878	0.257939	+	0.966161i	$0.416957\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	8.86707	0.882306	0.441153	−	0.897432i	$-0.354570\pi$
$101$	8.86707	0.882306	0.441153	+	0.897432i	$0.354570\pi$
$102$	−13.4311	−1.32988
$103$	−12.5767	−1.23922	−0.619609	−	0.784911i	$-0.712709\pi$
$103$	−12.5767	−1.23922	−0.619609	+	0.784911i	$0.712709\pi$
$104$	−1.78301	−0.174838
$105$	1.84175	0.179737
$106$	−1.32043	−0.128251
$107$	−2.97142	−0.287258	−0.143629	−	0.989632i	$-0.545877\pi$
$107$	−2.97142	−0.287258	−0.143629	+	0.989632i	$0.545877\pi$
$108$	−4.80319	−0.462187
$109$	−12.2500	−1.17334	−0.586668	−	0.809827i	$-0.699561\pi$
$109$	−12.2500	−1.17334	−0.586668	+	0.809827i	$0.699561\pi$
$110$	0	0
$111$	−8.71694	−0.827375
$112$	1.00000	0.0944911
$113$	−7.00620	−0.659088	−0.329544	−	0.944140i	$-0.606895\pi$
$113$	−7.00620	−0.659088	−0.329544	+	0.944140i	$0.606895\pi$
$114$	−5.84365	−0.547308
$115$	−4.72397	−0.440513
$116$	−4.51518	−0.419224
$117$	0.699040	0.0646263
$118$	−9.71495	−0.894333
$119$	7.29256	0.668508
$120$	−1.84175	−0.168128
$121$	0	0
$122$	−9.80246	−0.887473
$123$	−7.68158	−0.692625
$124$	−4.99011	−0.448125
$125$	1.00000	0.0894427
$126$	−0.392057	−0.0349272
$127$	7.01945	0.622875	0.311438	−	0.950267i	$-0.399190\pi$
$127$	7.01945	0.622875	0.311438	+	0.950267i	$0.399190\pi$
$128$	−1.00000	−0.0883883
$129$	21.4622	1.88964
$130$	−1.78301	−0.156380
$131$	−21.3705	−1.86715	−0.933573	−	0.358386i	$-0.883327\pi$
$131$	−21.3705	−1.86715	−0.933573	+	0.358386i	$0.883327\pi$
$132$	0	0
$133$	3.17287	0.275123
$134$	6.96181	0.601409
$135$	−4.80319	−0.413393
$136$	−7.29256	−0.625332
$137$	−2.98330	−0.254881	−0.127440	−	0.991846i	$-0.540676\pi$
$137$	−2.98330	−0.254881	−0.127440	+	0.991846i	$0.540676\pi$
$138$	8.70039	0.740627
$139$	−5.38369	−0.456638	−0.228319	−	0.973586i	$-0.573323\pi$
$139$	−5.38369	−0.456638	−0.228319	+	0.973586i	$0.573323\pi$
$140$	1.00000	0.0845154
$141$	6.89488	0.580654
$142$	−16.7995	−1.40978
$143$	0	0
$144$	0.392057	0.0326714
$145$	−4.51518	−0.374966
$146$	6.05144	0.500821
$147$	1.84175	0.151905
$148$	−4.73296	−0.389047
$149$	−2.08940	−0.171170	−0.0855851	−	0.996331i	$-0.527276\pi$
$149$	−2.08940	−0.171170	−0.0855851	+	0.996331i	$0.527276\pi$
$150$	−1.84175	−0.150379
$151$	8.31004	0.676262	0.338131	−	0.941099i	$-0.390205\pi$
$151$	8.31004	0.676262	0.338131	+	0.941099i	$0.390205\pi$
$152$	−3.17287	−0.257354
$153$	2.85910	0.231144
$154$	0	0
$155$	−4.99011	−0.400815
$156$	3.28386	0.262919
$157$	21.6516	1.72799	0.863994	−	0.503502i	$-0.167955\pi$
$157$	21.6516	1.72799	0.863994	+	0.503502i	$0.167955\pi$
$158$	−15.0746	−1.19927
$159$	2.43191	0.192863
$160$	−1.00000	−0.0790569
$161$	−4.72397	−0.372301
$162$	10.0225	0.787439
$163$	−18.5513	−1.45305	−0.726524	−	0.687141i	$-0.758865\pi$
$163$	−18.5513	−1.45305	−0.726524	+	0.687141i	$0.758865\pi$
$164$	−4.17080	−0.325684
$165$	0	0
$166$	−17.5840	−1.36478
$167$	−0.594823	−0.0460288	−0.0230144	−	0.999735i	$-0.507326\pi$
$167$	−0.594823	−0.0460288	−0.0230144	+	0.999735i	$0.507326\pi$
$168$	−1.84175	−0.142094
$169$	−9.82088	−0.755453
$170$	−7.29256	−0.559314
$171$	1.24395	0.0951270
$172$	11.6531	0.888544
$173$	1.14769	0.0872571	0.0436285	−	0.999048i	$-0.486108\pi$
$173$	1.14769	0.0872571	0.0436285	+	0.999048i	$0.486108\pi$
$174$	8.31586	0.630424
$175$	1.00000	0.0755929
$176$	0	0
$177$	17.8925	1.34489
$178$	−14.3054	−1.07224
$179$	11.8128	0.882927	0.441463	−	0.897279i	$-0.354460\pi$
$179$	11.8128	0.882927	0.441463	+	0.897279i	$0.354460\pi$
$180$	0.392057	0.0292222
$181$	13.5133	1.00444	0.502218	−	0.864741i	$-0.332518\pi$
$181$	13.5133	1.00444	0.502218	+	0.864741i	$0.332518\pi$
$182$	−1.78301	−0.132165
$183$	18.0537	1.33457
$184$	4.72397	0.348256
$185$	−4.73296	−0.347974
$186$	9.19056	0.673884
$187$	0	0
$188$	3.74365	0.273034
$189$	−4.80319	−0.349381
$190$	−3.17287	−0.230185
$191$	17.2066	1.24503	0.622515	−	0.782608i	$-0.286111\pi$
$191$	17.2066	1.24503	0.622515	+	0.782608i	$0.286111\pi$
$192$	1.84175	0.132917
$193$	4.36205	0.313987	0.156993	−	0.987600i	$-0.449820\pi$
$193$	4.36205	0.313987	0.156993	+	0.987600i	$0.449820\pi$
$194$	−5.08081	−0.364781
$195$	3.28386	0.235162
$196$	1.00000	0.0714286
$197$	21.7781	1.55162	0.775812	−	0.630964i	$-0.217341\pi$
$197$	21.7781	1.55162	0.775812	+	0.630964i	$0.217341\pi$
$198$	0	0
$199$	−22.3518	−1.58448	−0.792239	−	0.610211i	$-0.791085\pi$
$199$	−22.3518	−1.58448	−0.792239	+	0.610211i	$0.791085\pi$
$200$	−1.00000	−0.0707107
$201$	−12.8219	−0.904389
$202$	−8.86707	−0.623885
$203$	−4.51518	−0.316904
$204$	13.4311	0.940365
$205$	−4.17080	−0.291301
$206$	12.5767	0.876259
$207$	−1.85207	−0.128727
$208$	1.78301	0.123629
$209$	0	0
$210$	−1.84175	−0.127093
$211$	3.16035	0.217567	0.108784	−	0.994065i	$-0.465304\pi$
$211$	3.16035	0.217567	0.108784	+	0.994065i	$0.465304\pi$
$212$	1.32043	0.0906875
$213$	30.9405	2.12001
$214$	2.97142	0.203122
$215$	11.6531	0.794738
$216$	4.80319	0.326816
$217$	−4.99011	−0.338751
$218$	12.2500	0.829674
$219$	−11.1453	−0.753127
$220$	0	0
$221$	13.0027	0.874655
$222$	8.71694	0.585043
$223$	2.65283	0.177646	0.0888232	−	0.996047i	$-0.471689\pi$
$223$	2.65283	0.177646	0.0888232	+	0.996047i	$0.471689\pi$
$224$	−1.00000	−0.0668153
$225$	0.392057	0.0261371
$226$	7.00620	0.466046
$227$	−16.4207	−1.08988	−0.544941	−	0.838474i	$-0.683448\pi$
$227$	−16.4207	−1.08988	−0.544941	+	0.838474i	$0.683448\pi$
$228$	5.84365	0.387005
$229$	10.9499	0.723589	0.361795	−	0.932258i	$-0.382164\pi$
$229$	10.9499	0.723589	0.361795	+	0.932258i	$0.382164\pi$
$230$	4.72397	0.311490
$231$	0	0
$232$	4.51518	0.296436
$233$	6.02448	0.394677	0.197338	−	0.980335i	$-0.436770\pi$
$233$	6.02448	0.394677	0.197338	+	0.980335i	$0.436770\pi$
$234$	−0.699040	−0.0456977
$235$	3.74365	0.244209
$236$	9.71495	0.632389
$237$	27.7636	1.80344
$238$	−7.29256	−0.472706
$239$	−16.2666	−1.05220	−0.526101	−	0.850422i	$-0.676347\pi$
$239$	−16.2666	−1.05220	−0.526101	+	0.850422i	$0.676347\pi$
$240$	1.84175	0.118885
$241$	−28.6835	−1.84767	−0.923834	−	0.382793i	$-0.874962\pi$
$241$	−28.6835	−1.84767	−0.923834	+	0.382793i	$0.874962\pi$
$242$	0	0
$243$	−4.04934	−0.259765
$244$	9.80246	0.627538
$245$	1.00000	0.0638877
$246$	7.68158	0.489760
$247$	5.65726	0.359963
$248$	4.99011	0.316872
$249$	32.3854	2.05234
$250$	−1.00000	−0.0632456
$251$	−7.45336	−0.470452	−0.235226	−	0.971941i	$-0.575583\pi$
$251$	−7.45336	−0.470452	−0.235226	+	0.971941i	$0.575583\pi$
$252$	0.392057	0.0246973
$253$	0	0
$254$	−7.01945	−0.440439
$255$	13.4311	0.841088
$256$	1.00000	0.0625000
$257$	−0.517538	−0.0322831	−0.0161416	−	0.999870i	$-0.505138\pi$
$257$	−0.517538	−0.0322831	−0.0161416	+	0.999870i	$0.505138\pi$
$258$	−21.4622	−1.33618
$259$	−4.73296	−0.294092
$260$	1.78301	0.110577
$261$	−1.77021	−0.109573
$262$	21.3705	1.32027
$263$	1.90841	0.117678	0.0588389	−	0.998267i	$-0.481260\pi$
$263$	1.90841	0.117678	0.0588389	+	0.998267i	$0.481260\pi$
$264$	0	0
$265$	1.32043	0.0811133
$266$	−3.17287	−0.194541
$267$	26.3471	1.61242
$268$	−6.96181	−0.425260
$269$	−5.90413	−0.359981	−0.179991	−	0.983668i	$-0.557607\pi$
$269$	−5.90413	−0.359981	−0.179991	+	0.983668i	$0.557607\pi$
$270$	4.80319	0.292313
$271$	12.0446	0.731655	0.365828	−	0.930683i	$-0.380786\pi$
$271$	12.0446	0.731655	0.365828	+	0.930683i	$0.380786\pi$
$272$	7.29256	0.442176
$273$	3.28386	0.198748
$274$	2.98330	0.180228
$275$	0	0
$276$	−8.70039	−0.523702
$277$	−0.317418	−0.0190718	−0.00953591	−	0.999955i	$-0.503035\pi$
$277$	−0.317418	−0.0190718	−0.00953591	+	0.999955i	$0.503035\pi$
$278$	5.38369	0.322892
$279$	−1.95641	−0.117127
$280$	−1.00000	−0.0597614
$281$	15.1034	0.900996	0.450498	−	0.892777i	$-0.351246\pi$
$281$	15.1034	0.900996	0.450498	+	0.892777i	$0.351246\pi$
$282$	−6.89488	−0.410584
$283$	−11.7700	−0.699653	−0.349826	−	0.936815i	$-0.613759\pi$
$283$	−11.7700	−0.699653	−0.349826	+	0.936815i	$0.613759\pi$
$284$	16.7995	0.996867
$285$	5.84365	0.346148
$286$	0	0
$287$	−4.17080	−0.246194
$288$	−0.392057	−0.0231022
$289$	36.1814	2.12832
$290$	4.51518	0.265141
$291$	9.35761	0.548553
$292$	−6.05144	−0.354134
$293$	20.6978	1.20918	0.604590	−	0.796537i	$-0.293337\pi$
$293$	20.6978	1.20918	0.604590	+	0.796537i	$0.293337\pi$
$294$	−1.84175	−0.107413
$295$	9.71495	0.565626
$296$	4.73296	0.275098
$297$	0	0
$298$	2.08940	0.121036
$299$	−8.42288	−0.487108
$300$	1.84175	0.106334
$301$	11.6531	0.671676
$302$	−8.31004	−0.478189
$303$	16.3310	0.938189
$304$	3.17287	0.181977
$305$	9.80246	0.561287
$306$	−2.85910	−0.163444
$307$	−16.9774	−0.968949	−0.484475	−	0.874805i	$-0.660989\pi$
$307$	−16.9774	−0.968949	−0.484475	+	0.874805i	$0.660989\pi$
$308$	0	0
$309$	−23.1631	−1.31771
$310$	4.99011	0.283419
$311$	−1.47641	−0.0837197	−0.0418599	−	0.999123i	$-0.513328\pi$
$311$	−1.47641	−0.0837197	−0.0418599	+	0.999123i	$0.513328\pi$
$312$	−3.28386	−0.185912
$313$	−0.173082	−0.00978315	−0.00489157	−	0.999988i	$-0.501557\pi$
$313$	−0.173082	−0.00978315	−0.00489157	+	0.999988i	$0.501557\pi$
$314$	−21.6516	−1.22187
$315$	0.392057	0.0220899
$316$	15.0746	0.848010
$317$	2.70667	0.152022	0.0760109	−	0.997107i	$-0.475782\pi$
$317$	2.70667	0.152022	0.0760109	+	0.997107i	$0.475782\pi$
$318$	−2.43191	−0.136375
$319$	0	0
$320$	1.00000	0.0559017
$321$	−5.47262	−0.305452
$322$	4.72397	0.263257
$323$	23.1384	1.28745
$324$	−10.0225	−0.556803
$325$	1.78301	0.0989035
$326$	18.5513	1.02746
$327$	−22.5615	−1.24765
$328$	4.17080	0.230294
$329$	3.74365	0.206394
$330$	0	0
$331$	−2.85293	−0.156811	−0.0784055	−	0.996922i	$-0.524983\pi$
$331$	−2.85293	−0.156811	−0.0784055	+	0.996922i	$0.524983\pi$
$332$	17.5840	0.965049
$333$	−1.85559	−0.101686
$334$	0.594823	0.0325473
$335$	−6.96181	−0.380364
$336$	1.84175	0.100476
$337$	11.5719	0.630363	0.315182	−	0.949031i	$-0.397935\pi$
$337$	11.5719	0.630363	0.315182	+	0.949031i	$0.397935\pi$
$338$	9.82088	0.534186
$339$	−12.9037	−0.700833
$340$	7.29256	0.395494
$341$	0	0
$342$	−1.24395	−0.0672650
$343$	1.00000	0.0539949
$344$	−11.6531	−0.628296
$345$	−8.70039	−0.468413
$346$	−1.14769	−0.0617001
$347$	−29.9288	−1.60666	−0.803332	−	0.595532i	$-0.796941\pi$
$347$	−29.9288	−1.60666	−0.803332	+	0.595532i	$0.796941\pi$
$348$	−8.31586	−0.445777
$349$	−20.3624	−1.08997	−0.544987	−	0.838444i	$-0.683465\pi$
$349$	−20.3624	−1.08997	−0.544987	+	0.838444i	$0.683465\pi$
$350$	−1.00000	−0.0534522
$351$	−8.56412	−0.457119
$352$	0	0
$353$	−12.1572	−0.647063	−0.323532	−	0.946217i	$-0.604870\pi$
$353$	−12.1572	−0.647063	−0.323532	+	0.946217i	$0.604870\pi$
$354$	−17.8925	−0.950978
$355$	16.7995	0.891625
$356$	14.3054	0.758186
$357$	13.4311	0.710849
$358$	−11.8128	−0.624324
$359$	11.5130	0.607631	0.303815	−	0.952731i	$-0.401739\pi$
$359$	11.5130	0.607631	0.303815	+	0.952731i	$0.401739\pi$
$360$	−0.392057	−0.0206632
$361$	−8.93287	−0.470151
$362$	−13.5133	−0.710243
$363$	0	0
$364$	1.78301	0.0934550
$365$	−6.05144	−0.316747
$366$	−18.0537	−0.943683
$367$	−34.3478	−1.79294	−0.896471	−	0.443102i	$-0.853878\pi$
$367$	−34.3478	−1.79294	−0.896471	+	0.443102i	$0.853878\pi$
$368$	−4.72397	−0.246254
$369$	−1.63519	−0.0851245
$370$	4.73296	0.246055
$371$	1.32043	0.0685533
$372$	−9.19056	−0.476508
$373$	9.63189	0.498720	0.249360	−	0.968411i	$-0.419780\pi$
$373$	9.63189	0.498720	0.249360	+	0.968411i	$0.419780\pi$
$374$	0	0
$375$	1.84175	0.0951078
$376$	−3.74365	−0.193064
$377$	−8.05061	−0.414627
$378$	4.80319	0.247049
$379$	−2.68332	−0.137833	−0.0689164	−	0.997622i	$-0.521954\pi$
$379$	−2.68332	−0.137833	−0.0689164	+	0.997622i	$0.521954\pi$
$380$	3.17287	0.162765
$381$	12.9281	0.662326
$382$	−17.2066	−0.880369
$383$	22.2924	1.13909	0.569544	−	0.821961i	$-0.307120\pi$
$383$	22.2924	1.13909	0.569544	+	0.821961i	$0.307120\pi$
$384$	−1.84175	−0.0939866
$385$	0	0
$386$	−4.36205	−0.222022
$387$	4.56870	0.232240
$388$	5.08081	0.257939
$389$	−6.33260	−0.321076	−0.160538	−	0.987030i	$-0.551323\pi$
$389$	−6.33260	−0.321076	−0.160538	+	0.987030i	$0.551323\pi$
$390$	−3.28386	−0.166285
$391$	−34.4498	−1.74220
$392$	−1.00000	−0.0505076
$393$	−39.3591	−1.98541
$394$	−21.7781	−1.09716
$395$	15.0746	0.758484
$396$	0	0
$397$	−3.02619	−0.151880	−0.0759401	−	0.997112i	$-0.524196\pi$
$397$	−3.02619	−0.151880	−0.0759401	+	0.997112i	$0.524196\pi$
$398$	22.3518	1.12040
$399$	5.84365	0.292549
$400$	1.00000	0.0500000
$401$	−29.2629	−1.46132	−0.730660	−	0.682741i	$-0.760788\pi$
$401$	−29.2629	−1.46132	−0.730660	+	0.682741i	$0.760788\pi$
$402$	12.8219	0.639500
$403$	−8.89741	−0.443211
$404$	8.86707	0.441153
$405$	−10.0225	−0.498020
$406$	4.51518	0.224085
$407$	0	0
$408$	−13.4311	−0.664938
$409$	4.14523	0.204969	0.102484	−	0.994735i	$-0.467321\pi$
$409$	4.14523	0.204969	0.102484	+	0.994735i	$0.467321\pi$
$410$	4.17080	0.205981
$411$	−5.49451	−0.271024
$412$	−12.5767	−0.619609
$413$	9.71495	0.478041
$414$	1.85207	0.0910240
$415$	17.5840	0.863166
$416$	−1.78301	−0.0874191
$417$	−9.91543	−0.485561
$418$	0	0
$419$	−20.4108	−0.997134	−0.498567	−	0.866851i	$-0.666140\pi$
$419$	−20.4108	−0.997134	−0.498567	+	0.866851i	$0.666140\pi$
$420$	1.84175	0.0898684
$421$	16.8699	0.822190	0.411095	−	0.911592i	$-0.365146\pi$
$421$	16.8699	0.822190	0.411095	+	0.911592i	$0.365146\pi$
$422$	−3.16035	−0.153843
$423$	1.46772	0.0713631
$424$	−1.32043	−0.0641257
$425$	7.29256	0.353741
$426$	−30.9405	−1.49907
$427$	9.80246	0.474374
$428$	−2.97142	−0.143629
$429$	0	0
$430$	−11.6531	−0.561965
$431$	23.7694	1.14493	0.572466	−	0.819929i	$-0.305987\pi$
$431$	23.7694	1.14493	0.572466	+	0.819929i	$0.305987\pi$
$432$	−4.80319	−0.231094
$433$	−13.0237	−0.625881	−0.312940	−	0.949773i	$-0.601314\pi$
$433$	−13.0237	−0.625881	−0.312940	+	0.949773i	$0.601314\pi$
$434$	4.99011	0.239533
$435$	−8.31586	−0.398715
$436$	−12.2500	−0.586668
$437$	−14.9886	−0.717001
$438$	11.1453	0.532541
$439$	7.91759	0.377886	0.188943	−	0.981988i	$-0.439494\pi$
$439$	7.91759	0.377886	0.188943	+	0.981988i	$0.439494\pi$
$440$	0	0
$441$	0.392057	0.0186694
$442$	−13.0027	−0.618475
$443$	−24.7797	−1.17732	−0.588659	−	0.808382i	$-0.700344\pi$
$443$	−24.7797	−1.17732	−0.588659	+	0.808382i	$0.700344\pi$
$444$	−8.71694	−0.413688
$445$	14.3054	0.678143
$446$	−2.65283	−0.125615
$447$	−3.84816	−0.182012
$448$	1.00000	0.0472456
$449$	0.775504	0.0365983	0.0182991	−	0.999833i	$-0.494175\pi$
$449$	0.775504	0.0365983	0.0182991	+	0.999833i	$0.494175\pi$
$450$	−0.392057	−0.0184817
$451$	0	0
$452$	−7.00620	−0.329544
$453$	15.3051	0.719094
$454$	16.4207	0.770663
$455$	1.78301	0.0835887
$456$	−5.84365	−0.273654
$457$	30.6660	1.43449	0.717247	−	0.696819i	$-0.245402\pi$
$457$	30.6660	1.43449	0.717247	+	0.696819i	$0.245402\pi$
$458$	−10.9499	−0.511655
$459$	−35.0275	−1.63495
$460$	−4.72397	−0.220256
$461$	9.43899	0.439618	0.219809	−	0.975543i	$-0.429457\pi$
$461$	9.43899	0.439618	0.219809	+	0.975543i	$0.429457\pi$
$462$	0	0
$463$	36.7925	1.70989	0.854947	−	0.518715i	$-0.173590\pi$
$463$	36.7925	1.70989	0.854947	+	0.518715i	$0.173590\pi$
$464$	−4.51518	−0.209612
$465$	−9.19056	−0.426202
$466$	−6.02448	−0.279079
$467$	2.52468	0.116828	0.0584141	−	0.998292i	$-0.481396\pi$
$467$	2.52468	0.116828	0.0584141	+	0.998292i	$0.481396\pi$
$468$	0.699040	0.0323131
$469$	−6.96181	−0.321466
$470$	−3.74365	−0.172682
$471$	39.8770	1.83743
$472$	−9.71495	−0.447167
$473$	0	0
$474$	−27.7636	−1.27523
$475$	3.17287	0.145581
$476$	7.29256	0.334254
$477$	0.517683	0.0237031
$478$	16.2666	0.744019
$479$	24.6789	1.12761	0.563805	−	0.825908i	$-0.309337\pi$
$479$	24.6789	1.12761	0.563805	+	0.825908i	$0.309337\pi$
$480$	−1.84175	−0.0840642
$481$	−8.43890	−0.384781
$482$	28.6835	1.30650
$483$	−8.70039	−0.395882
$484$	0	0
$485$	5.08081	0.230708
$486$	4.04934	0.183682
$487$	29.7180	1.34665	0.673326	−	0.739346i	$-0.264865\pi$
$487$	29.7180	1.34665	0.673326	+	0.739346i	$0.264865\pi$
$488$	−9.80246	−0.443737
$489$	−34.1669	−1.54508
$490$	−1.00000	−0.0451754
$491$	30.8565	1.39253	0.696267	−	0.717783i	$-0.254843\pi$
$491$	30.8565	1.39253	0.696267	+	0.717783i	$0.254843\pi$
$492$	−7.68158	−0.346312
$493$	−32.9272	−1.48297
$494$	−5.65726	−0.254532
$495$	0	0
$496$	−4.99011	−0.224063
$497$	16.7995	0.753560
$498$	−32.3854	−1.45123
$499$	19.9890	0.894829	0.447415	−	0.894327i	$-0.352345\pi$
$499$	19.9890	0.894829	0.447415	+	0.894327i	$0.352345\pi$
$500$	1.00000	0.0447214
$501$	−1.09552	−0.0489441
$502$	7.45336	0.332660
$503$	29.9393	1.33493	0.667464	−	0.744642i	$-0.267380\pi$
$503$	29.9393	1.33493	0.667464	+	0.744642i	$0.267380\pi$
$504$	−0.392057	−0.0174636
$505$	8.86707	0.394579
$506$	0	0
$507$	−18.0876	−0.803301
$508$	7.01945	0.311438
$509$	−7.80426	−0.345918	−0.172959	−	0.984929i	$-0.555333\pi$
$509$	−7.80426	−0.345918	−0.172959	+	0.984929i	$0.555333\pi$
$510$	−13.4311	−0.594739
$511$	−6.05144	−0.267700
$512$	−1.00000	−0.0441942
$513$	−15.2399	−0.672859
$514$	0.517538	0.0228276
$515$	−12.5767	−0.554195
$516$	21.4622	0.944822
$517$	0	0
$518$	4.73296	0.207954
$519$	2.11376	0.0927837
$520$	−1.78301	−0.0781901
$521$	26.3914	1.15623	0.578115	−	0.815955i	$-0.303789\pi$
$521$	26.3914	1.15623	0.578115	+	0.815955i	$0.303789\pi$
$522$	1.77021	0.0774799
$523$	20.7173	0.905905	0.452952	−	0.891535i	$-0.350371\pi$
$523$	20.7173	0.905905	0.452952	+	0.891535i	$0.350371\pi$
$524$	−21.3705	−0.933573
$525$	1.84175	0.0803807
$526$	−1.90841	−0.0832107
$527$	−36.3907	−1.58520
$528$	0	0
$529$	−0.684086	−0.0297429
$530$	−1.32043	−0.0573558
$531$	3.80881	0.165288
$532$	3.17287	0.137562
$533$	−7.43656	−0.322113
$534$	−26.3471	−1.14015
$535$	−2.97142	−0.128465
$536$	6.96181	0.300704
$537$	21.7562	0.938849
$538$	5.90413	0.254545
$539$	0	0
$540$	−4.80319	−0.206696
$541$	−10.7306	−0.461346	−0.230673	−	0.973031i	$-0.574093\pi$
$541$	−10.7306	−0.461346	−0.230673	+	0.973031i	$0.574093\pi$
$542$	−12.0446	−0.517359
$543$	24.8882	1.06805
$544$	−7.29256	−0.312666
$545$	−12.2500	−0.524732
$546$	−3.28386	−0.140536
$547$	10.6113	0.453704	0.226852	−	0.973929i	$-0.427157\pi$
$547$	10.6113	0.453704	0.226852	+	0.973929i	$0.427157\pi$
$548$	−2.98330	−0.127440
$549$	3.84312	0.164020
$550$	0	0
$551$	−14.3261	−0.610313
$552$	8.70039	0.370313
$553$	15.0746	0.641036
$554$	0.317418	0.0134858
$555$	−8.71694	−0.370014
$556$	−5.38369	−0.228319
$557$	−31.7039	−1.34334	−0.671669	−	0.740852i	$-0.734422\pi$
$557$	−31.7039	−1.34334	−0.671669	+	0.740852i	$0.734422\pi$
$558$	1.95641	0.0828213
$559$	20.7777	0.878801
$560$	1.00000	0.0422577
$561$	0	0
$562$	−15.1034	−0.637100
$563$	9.50273	0.400492	0.200246	−	0.979746i	$-0.435826\pi$
$563$	9.50273	0.400492	0.200246	+	0.979746i	$0.435826\pi$
$564$	6.89488	0.290327
$565$	−7.00620	−0.294753
$566$	11.7700	0.494729
$567$	−10.0225	−0.420904
$568$	−16.7995	−0.704891
$569$	−38.6738	−1.62129	−0.810645	−	0.585538i	$-0.800883\pi$
$569$	−38.6738	−1.62129	−0.810645	+	0.585538i	$0.800883\pi$
$570$	−5.84365	−0.244764
$571$	7.44900	0.311731	0.155865	−	0.987778i	$-0.450183\pi$
$571$	7.44900	0.311731	0.155865	+	0.987778i	$0.450183\pi$
$572$	0	0
$573$	31.6904	1.32389
$574$	4.17080	0.174086
$575$	−4.72397	−0.197003
$576$	0.392057	0.0163357
$577$	3.69803	0.153951	0.0769754	−	0.997033i	$-0.475474\pi$
$577$	3.69803	0.153951	0.0769754	+	0.997033i	$0.475474\pi$
$578$	−36.1814	−1.50495
$579$	8.03381	0.333874
$580$	−4.51518	−0.187483
$581$	17.5840	0.729508
$582$	−9.35761	−0.387885
$583$	0	0
$584$	6.05144	0.250410
$585$	0.699040	0.0289018
$586$	−20.6978	−0.855020
$587$	42.4946	1.75394	0.876970	−	0.480546i	$-0.159561\pi$
$587$	42.4946	1.75394	0.876970	+	0.480546i	$0.159561\pi$
$588$	1.84175	0.0759526
$589$	−15.8330	−0.652387
$590$	−9.71495	−0.399958
$591$	40.1098	1.64990
$592$	−4.73296	−0.194523
$593$	−1.64274	−0.0674592	−0.0337296	−	0.999431i	$-0.510738\pi$
$593$	−1.64274	−0.0674592	−0.0337296	+	0.999431i	$0.510738\pi$
$594$	0	0
$595$	7.29256	0.298966
$596$	−2.08940	−0.0855851
$597$	−41.1665	−1.68483
$598$	8.42288	0.344437
$599$	−25.8198	−1.05497	−0.527484	−	0.849565i	$-0.676865\pi$
$599$	−25.8198	−1.05497	−0.527484	+	0.849565i	$0.676865\pi$
$600$	−1.84175	−0.0751893
$601$	14.5340	0.592853	0.296426	−	0.955056i	$-0.404205\pi$
$601$	14.5340	0.592853	0.296426	+	0.955056i	$0.404205\pi$
$602$	−11.6531	−0.474947
$603$	−2.72942	−0.111151
$604$	8.31004	0.338131
$605$	0	0
$606$	−16.3310	−0.663400
$607$	−13.2886	−0.539366	−0.269683	−	0.962949i	$-0.586919\pi$
$607$	−13.2886	−0.539366	−0.269683	+	0.962949i	$0.586919\pi$
$608$	−3.17287	−0.128677
$609$	−8.31586	−0.336976
$610$	−9.80246	−0.396890
$611$	6.67495	0.270040
$612$	2.85910	0.115572
$613$	11.2979	0.456316	0.228158	−	0.973624i	$-0.426730\pi$
$613$	11.2979	0.456316	0.228158	+	0.973624i	$0.426730\pi$
$614$	16.9774	0.685151
$615$	−7.68158	−0.309751
$616$	0	0
$617$	−20.2865	−0.816705	−0.408352	−	0.912824i	$-0.633897\pi$
$617$	−20.2865	−0.816705	−0.408352	+	0.912824i	$0.633897\pi$
$618$	23.1631	0.931758
$619$	−26.8474	−1.07909	−0.539544	−	0.841958i	$-0.681403\pi$
$619$	−26.8474	−1.07909	−0.539544	+	0.841958i	$0.681403\pi$
$620$	−4.99011	−0.200408
$621$	22.6901	0.910524
$622$	1.47641	0.0591988
$623$	14.3054	0.573135
$624$	3.28386	0.131460
$625$	1.00000	0.0400000
$626$	0.173082	0.00691773
$627$	0	0
$628$	21.6516	0.863994
$629$	−34.5154	−1.37622
$630$	−0.392057	−0.0156199
$631$	44.6357	1.77692	0.888459	−	0.458956i	$-0.151776\pi$
$631$	44.6357	1.77692	0.888459	+	0.458956i	$0.151776\pi$
$632$	−15.0746	−0.599634
$633$	5.82058	0.231347
$634$	−2.70667	−0.107496
$635$	7.01945	0.278558
$636$	2.43191	0.0964313
$637$	1.78301	0.0706453
$638$	0	0
$639$	6.58636	0.260552
$640$	−1.00000	−0.0395285
$641$	37.5419	1.48282	0.741408	−	0.671055i	$-0.234158\pi$
$641$	37.5419	1.48282	0.741408	+	0.671055i	$0.234158\pi$
$642$	5.47262	0.215987
$643$	−11.4711	−0.452377	−0.226189	−	0.974084i	$-0.572627\pi$
$643$	−11.4711	−0.452377	−0.226189	+	0.974084i	$0.572627\pi$
$644$	−4.72397	−0.186151
$645$	21.4622	0.845074
$646$	−23.1384	−0.910367
$647$	−3.16972	−0.124615	−0.0623073	−	0.998057i	$-0.519846\pi$
$647$	−3.16972	−0.124615	−0.0623073	+	0.998057i	$0.519846\pi$
$648$	10.0225	0.393719
$649$	0	0
$650$	−1.78301	−0.0699353
$651$	−9.19056	−0.360206
$652$	−18.5513	−0.726524
$653$	8.94978	0.350232	0.175116	−	0.984548i	$-0.443970\pi$
$653$	8.94978	0.350232	0.175116	+	0.984548i	$0.443970\pi$
$654$	22.5615	0.882223
$655$	−21.3705	−0.835013
$656$	−4.17080	−0.162842
$657$	−2.37251	−0.0925604
$658$	−3.74365	−0.145943
$659$	23.4818	0.914720	0.457360	−	0.889282i	$-0.348795\pi$
$659$	23.4818	0.914720	0.457360	+	0.889282i	$0.348795\pi$
$660$	0	0
$661$	−31.4616	−1.22371	−0.611857	−	0.790969i	$-0.709577\pi$
$661$	−31.4616	−1.22371	−0.611857	+	0.790969i	$0.709577\pi$
$662$	2.85293	0.110882
$663$	23.9477	0.930053
$664$	−17.5840	−0.682392
$665$	3.17287	0.123039
$666$	1.85559	0.0719026
$667$	21.3296	0.825886
$668$	−0.594823	−0.0230144
$669$	4.88585	0.188898
$670$	6.96181	0.268958
$671$	0	0
$672$	−1.84175	−0.0710472
$673$	23.4140	0.902545	0.451273	−	0.892386i	$-0.350970\pi$
$673$	23.4140	0.902545	0.451273	+	0.892386i	$0.350970\pi$
$674$	−11.5719	−0.445734
$675$	−4.80319	−0.184875
$676$	−9.82088	−0.377726
$677$	21.9206	0.842478	0.421239	−	0.906950i	$-0.361595\pi$
$677$	21.9206	0.842478	0.421239	+	0.906950i	$0.361595\pi$
$678$	12.9037	0.495564
$679$	5.08081	0.194984
$680$	−7.29256	−0.279657
$681$	−30.2430	−1.15891
$682$	0	0
$683$	32.1014	1.22833	0.614163	−	0.789179i	$-0.289494\pi$
$683$	32.1014	1.22833	0.614163	+	0.789179i	$0.289494\pi$
$684$	1.24395	0.0475635
$685$	−2.98330	−0.113986
$686$	−1.00000	−0.0381802
$687$	20.1670	0.769419
$688$	11.6531	0.444272
$689$	2.35434	0.0896931
$690$	8.70039	0.331218
$691$	−5.98057	−0.227511	−0.113756	−	0.993509i	$-0.536288\pi$
$691$	−5.98057	−0.227511	−0.113756	+	0.993509i	$0.536288\pi$
$692$	1.14769	0.0436285
$693$	0	0
$694$	29.9288	1.13608
$695$	−5.38369	−0.204215
$696$	8.31586	0.315212
$697$	−30.4158	−1.15208
$698$	20.3624	0.770728
$699$	11.0956	0.419675
$700$	1.00000	0.0377964
$701$	26.1070	0.986046	0.493023	−	0.870016i	$-0.335892\pi$
$701$	26.1070	0.986046	0.493023	+	0.870016i	$0.335892\pi$
$702$	8.56412	0.323232
$703$	−15.0171	−0.566380
$704$	0	0
$705$	6.89488	0.259676
$706$	12.1572	0.457543
$707$	8.86707	0.333480
$708$	17.8925	0.672443
$709$	−36.1381	−1.35720	−0.678598	−	0.734510i	$-0.737412\pi$
$709$	−36.1381	−1.35720	−0.678598	+	0.734510i	$0.737412\pi$
$710$	−16.7995	−0.630474
$711$	5.91008	0.221645
$712$	−14.3054	−0.536119
$713$	23.5731	0.882821
$714$	−13.4311	−0.502646
$715$	0	0
$716$	11.8128	0.441463
$717$	−29.9591	−1.11884
$718$	−11.5130	−0.429660
$719$	−39.7918	−1.48398	−0.741992	−	0.670409i	$-0.766119\pi$
$719$	−39.7918	−1.48398	−0.741992	+	0.670409i	$0.766119\pi$
$720$	0.392057	0.0146111
$721$	−12.5767	−0.468380
$722$	8.93287	0.332447
$723$	−52.8280	−1.96469
$724$	13.5133	0.502218
$725$	−4.51518	−0.167690
$726$	0	0
$727$	17.6577	0.654887	0.327443	−	0.944871i	$-0.393813\pi$
$727$	17.6577	0.654887	0.327443	+	0.944871i	$0.393813\pi$
$728$	−1.78301	−0.0660827
$729$	22.6095	0.837389
$730$	6.05144	0.223974
$731$	84.9812	3.14314
$732$	18.0537	0.667285
$733$	10.8120	0.399350	0.199675	−	0.979862i	$-0.436011\pi$
$733$	10.8120	0.399350	0.199675	+	0.979862i	$0.436011\pi$
$734$	34.3478	1.26780
$735$	1.84175	0.0679341
$736$	4.72397	0.174128
$737$	0	0
$738$	1.63519	0.0601921
$739$	−41.9060	−1.54154	−0.770769	−	0.637114i	$-0.780128\pi$
$739$	−41.9060	−1.54154	−0.770769	+	0.637114i	$0.780128\pi$
$740$	−4.73296	−0.173987
$741$	10.4193	0.382762
$742$	−1.32043	−0.0484745
$743$	−49.2037	−1.80511	−0.902555	−	0.430574i	$-0.858311\pi$
$743$	−49.2037	−1.80511	−0.902555	+	0.430574i	$0.858311\pi$
$744$	9.19056	0.336942
$745$	−2.08940	−0.0765496
$746$	−9.63189	−0.352649
$747$	6.89393	0.252236
$748$	0	0
$749$	−2.97142	−0.108573
$750$	−1.84175	−0.0672513
$751$	−23.5299	−0.858616	−0.429308	−	0.903158i	$-0.641243\pi$
$751$	−23.5299	−0.858616	−0.429308	+	0.903158i	$0.641243\pi$
$752$	3.74365	0.136517
$753$	−13.7273	−0.500249
$754$	8.05061	0.293186
$755$	8.31004	0.302433
$756$	−4.80319	−0.174690
$757$	1.06572	0.0387344	0.0193672	−	0.999812i	$-0.493835\pi$
$757$	1.06572	0.0387344	0.0193672	+	0.999812i	$0.493835\pi$
$758$	2.68332	0.0974625
$759$	0	0
$760$	−3.17287	−0.115092
$761$	−47.7288	−1.73017	−0.865085	−	0.501626i	$-0.832735\pi$
$761$	−47.7288	−1.73017	−0.865085	+	0.501626i	$0.832735\pi$
$762$	−12.9281	−0.468335
$763$	−12.2500	−0.443480
$764$	17.2066	0.622515
$765$	2.85910	0.103371
$766$	−22.2924	−0.805457
$767$	17.3218	0.625455
$768$	1.84175	0.0664586
$769$	−19.1610	−0.690963	−0.345481	−	0.938426i	$-0.612284\pi$
$769$	−19.1610	−0.690963	−0.345481	+	0.938426i	$0.612284\pi$
$770$	0	0
$771$	−0.953178	−0.0343279
$772$	4.36205	0.156993
$773$	4.18093	0.150378	0.0751888	−	0.997169i	$-0.476044\pi$
$773$	4.18093	0.150378	0.0751888	+	0.997169i	$0.476044\pi$
$774$	−4.56870	−0.164218
$775$	−4.99011	−0.179250
$776$	−5.08081	−0.182391
$777$	−8.71694	−0.312719
$778$	6.33260	0.227035
$779$	−13.2334	−0.474136
$780$	3.28386	0.117581
$781$	0	0
$782$	34.4498	1.23192
$783$	21.6873	0.775040
$784$	1.00000	0.0357143
$785$	21.6516	0.772780
$786$	39.3591	1.40389
$787$	16.4954	0.587998	0.293999	−	0.955806i	$-0.405014\pi$
$787$	16.4954	0.587998	0.293999	+	0.955806i	$0.405014\pi$
$788$	21.7781	0.775812
$789$	3.51483	0.125131
$790$	−15.0746	−0.536329
$791$	−7.00620	−0.249112
$792$	0	0
$793$	17.4779	0.620657
$794$	3.02619	0.107396
$795$	2.43191	0.0862508
$796$	−22.3518	−0.792239
$797$	−10.8490	−0.384291	−0.192145	−	0.981366i	$-0.561545\pi$
$797$	−10.8490	−0.384291	−0.192145	+	0.981366i	$0.561545\pi$
$798$	−5.84365	−0.206863
$799$	27.3008	0.965832
$800$	−1.00000	−0.0353553
$801$	5.60854	0.198168
$802$	29.2629	1.03331
$803$	0	0
$804$	−12.8219	−0.452195
$805$	−4.72397	−0.166498
$806$	8.89741	0.313398
$807$	−10.8740	−0.382782
$808$	−8.86707	−0.311942
$809$	−27.9575	−0.982934	−0.491467	−	0.870896i	$-0.663539\pi$
$809$	−27.9575	−0.982934	−0.491467	+	0.870896i	$0.663539\pi$
$810$	10.0225	0.352153
$811$	−22.1078	−0.776311	−0.388156	−	0.921594i	$-0.626888\pi$
$811$	−22.1078	−0.776311	−0.388156	+	0.921594i	$0.626888\pi$
$812$	−4.51518	−0.158452
$813$	22.1831	0.777996
$814$	0	0
$815$	−18.5513	−0.649822
$816$	13.4311	0.470182
$817$	36.9740	1.29356
$818$	−4.14523	−0.144935
$819$	0.699040	0.0244264
$820$	−4.17080	−0.145651
$821$	53.2494	1.85842	0.929208	−	0.369558i	$-0.120491\pi$
$821$	53.2494	1.85842	0.929208	+	0.369558i	$0.120491\pi$
$822$	5.49451	0.191643
$823$	17.7656	0.619268	0.309634	−	0.950856i	$-0.399793\pi$
$823$	17.7656	0.619268	0.309634	+	0.950856i	$0.399793\pi$
$824$	12.5767	0.438129
$825$	0	0
$826$	−9.71495	−0.338026
$827$	17.6329	0.613156	0.306578	−	0.951846i	$-0.400816\pi$
$827$	17.6329	0.613156	0.306578	+	0.951846i	$0.400816\pi$
$828$	−1.85207	−0.0643637
$829$	5.62500	0.195364	0.0976822	−	0.995218i	$-0.468857\pi$
$829$	5.62500	0.195364	0.0976822	+	0.995218i	$0.468857\pi$
$830$	−17.5840	−0.610350
$831$	−0.584607	−0.0202798
$832$	1.78301	0.0618147
$833$	7.29256	0.252672
$834$	9.91543	0.343343
$835$	−0.594823	−0.0205847
$836$	0	0
$837$	23.9684	0.828471
$838$	20.4108	0.705080
$839$	−37.3725	−1.29024	−0.645120	−	0.764081i	$-0.723193\pi$
$839$	−37.3725	−1.29024	−0.645120	+	0.764081i	$0.723193\pi$
$840$	−1.84175	−0.0635465
$841$	−8.61311	−0.297004
$842$	−16.8699	−0.581376
$843$	27.8168	0.958062
$844$	3.16035	0.108784
$845$	−9.82088	−0.337849
$846$	−1.46772	−0.0504613
$847$	0	0
$848$	1.32043	0.0453437
$849$	−21.6774	−0.743967
$850$	−7.29256	−0.250133
$851$	22.3584	0.766435
$852$	30.9405	1.06001
$853$	−38.9150	−1.33243	−0.666213	−	0.745762i	$-0.732086\pi$
$853$	−38.9150	−1.33243	−0.666213	+	0.745762i	$0.732086\pi$
$854$	−9.80246	−0.335433
$855$	1.24395	0.0425421
$856$	2.97142	0.101561
$857$	25.6321	0.875575	0.437787	−	0.899079i	$-0.355762\pi$
$857$	25.6321	0.875575	0.437787	+	0.899079i	$0.355762\pi$
$858$	0	0
$859$	−53.9880	−1.84205	−0.921024	−	0.389506i	$-0.872646\pi$
$859$	−53.9880	−1.84205	−0.921024	+	0.389506i	$0.872646\pi$
$860$	11.6531	0.397369
$861$	−7.68158	−0.261788
$862$	−23.7694	−0.809589
$863$	−21.8955	−0.745331	−0.372666	−	0.927966i	$-0.621556\pi$
$863$	−21.8955	−0.745331	−0.372666	+	0.927966i	$0.621556\pi$
$864$	4.80319	0.163408
$865$	1.14769	0.0390225
$866$	13.0237	0.442564
$867$	66.6372	2.26312
$868$	−4.99011	−0.169375
$869$	0	0
$870$	8.31586	0.281934
$871$	−12.4130	−0.420597
$872$	12.2500	0.414837
$873$	1.99197	0.0674179
$874$	14.9886	0.506996
$875$	1.00000	0.0338062
$876$	−11.1453	−0.376564
$877$	−55.2059	−1.86417	−0.932086	−	0.362238i	$-0.882013\pi$
$877$	−55.2059	−1.86417	−0.932086	+	0.362238i	$0.882013\pi$
$878$	−7.91759	−0.267206
$879$	38.1203	1.28577
$880$	0	0
$881$	5.26217	0.177287	0.0886435	−	0.996063i	$-0.471747\pi$
$881$	5.26217	0.177287	0.0886435	+	0.996063i	$0.471747\pi$
$882$	−0.392057	−0.0132012
$883$	−40.8216	−1.37376	−0.686878	−	0.726772i	$-0.741020\pi$
$883$	−40.8216	−1.37376	−0.686878	+	0.726772i	$0.741020\pi$
$884$	13.0027	0.437328
$885$	17.8925	0.601451
$886$	24.7797	0.832489
$887$	−40.9735	−1.37576	−0.687879	−	0.725826i	$-0.741458\pi$
$887$	−40.9735	−1.37576	−0.687879	+	0.725826i	$0.741458\pi$
$888$	8.71694	0.292521
$889$	7.01945	0.235425
$890$	−14.3054	−0.479519
$891$	0	0
$892$	2.65283	0.0888232
$893$	11.8781	0.397486
$894$	3.84816	0.128702
$895$	11.8128	0.394857
$896$	−1.00000	−0.0334077
$897$	−15.5129	−0.517960
$898$	−0.775504	−0.0258789
$899$	22.5313	0.751460
$900$	0.392057	0.0130686
$901$	9.62931	0.320799
$902$	0	0
$903$	21.4622	0.714218
$904$	7.00620	0.233023
$905$	13.5133	0.449197
$906$	−15.3051	−0.508476
$907$	−54.4658	−1.80851	−0.904254	−	0.426995i	$-0.859572\pi$
$907$	−54.4658	−1.80851	−0.904254	+	0.426995i	$0.859572\pi$
$908$	−16.4207	−0.544941
$909$	3.47639	0.115305
$910$	−1.78301	−0.0591061
$911$	−13.4055	−0.444144	−0.222072	−	0.975030i	$-0.571282\pi$
$911$	−13.4055	−0.444144	−0.222072	+	0.975030i	$0.571282\pi$
$912$	5.84365	0.193503
$913$	0	0
$914$	−30.6660	−1.01434
$915$	18.0537	0.596838
$916$	10.9499	0.361795
$917$	−21.3705	−0.705715
$918$	35.0275	1.15608
$919$	−25.9299	−0.855350	−0.427675	−	0.903933i	$-0.640667\pi$
$919$	−25.9299	−0.855350	−0.427675	+	0.903933i	$0.640667\pi$
$920$	4.72397	0.155745
$921$	−31.2681	−1.03032
$922$	−9.43899	−0.310857
$923$	29.9536	0.985936
$924$	0	0
$925$	−4.73296	−0.155619
$926$	−36.7925	−1.20908
$927$	−4.93077	−0.161948
$928$	4.51518	0.148218
$929$	12.0103	0.394047	0.197023	−	0.980399i	$-0.436873\pi$
$929$	12.0103	0.394047	0.197023	+	0.980399i	$0.436873\pi$
$930$	9.19056	0.301370
$931$	3.17287	0.103987
$932$	6.02448	0.197338
$933$	−2.71919	−0.0890223
$934$	−2.52468	−0.0826100
$935$	0	0
$936$	−0.699040	−0.0228488
$937$	−35.4374	−1.15769	−0.578845	−	0.815437i	$-0.696496\pi$
$937$	−35.4374	−1.15769	−0.578845	+	0.815437i	$0.696496\pi$
$938$	6.96181	0.227311
$939$	−0.318774	−0.0104028
$940$	3.74365	0.122104
$941$	23.5197	0.766721	0.383360	−	0.923599i	$-0.374767\pi$
$941$	23.5197	0.766721	0.383360	+	0.923599i	$0.374767\pi$
$942$	−39.8770	−1.29926
$943$	19.7027	0.641609
$944$	9.71495	0.316195
$945$	−4.80319	−0.156248
$946$	0	0
$947$	−14.8719	−0.483272	−0.241636	−	0.970367i	$-0.577684\pi$
$947$	−14.8719	−0.483272	−0.241636	+	0.970367i	$0.577684\pi$
$948$	27.7636	0.901721
$949$	−10.7898	−0.350251
$950$	−3.17287	−0.102942
$951$	4.98502	0.161650
$952$	−7.29256	−0.236353
$953$	41.5577	1.34618	0.673092	−	0.739559i	$-0.264966\pi$
$953$	41.5577	1.34618	0.673092	+	0.739559i	$0.264966\pi$
$954$	−0.517683	−0.0167606
$955$	17.2066	0.556794
$956$	−16.2666	−0.526101
$957$	0	0
$958$	−24.6789	−0.797341
$959$	−2.98330	−0.0963358
$960$	1.84175	0.0594423
$961$	−6.09879	−0.196735
$962$	8.43890	0.272081
$963$	−1.16496	−0.0375404
$964$	−28.6835	−0.923834
$965$	4.36205	0.140419
$966$	8.70039	0.279931
$967$	−37.8603	−1.21751	−0.608753	−	0.793360i	$-0.708330\pi$
$967$	−37.8603	−1.21751	−0.608753	+	0.793360i	$0.708330\pi$
$968$	0	0
$969$	42.6152	1.36900
$970$	−5.08081	−0.163135
$971$	−12.6110	−0.404707	−0.202354	−	0.979313i	$-0.564859\pi$
$971$	−12.6110	−0.404707	−0.202354	+	0.979313i	$0.564859\pi$
$972$	−4.04934	−0.129883
$973$	−5.38369	−0.172593
$974$	−29.7180	−0.952227
$975$	3.28386	0.105168
$976$	9.80246	0.313769
$977$	28.7687	0.920393	0.460197	−	0.887817i	$-0.347779\pi$
$977$	28.7687	0.920393	0.460197	+	0.887817i	$0.347779\pi$
$978$	34.1669	1.09254
$979$	0	0
$980$	1.00000	0.0319438
$981$	−4.80269	−0.153338
$982$	−30.8565	−0.984671
$983$	32.9791	1.05187	0.525936	−	0.850524i	$-0.323715\pi$
$983$	32.9791	1.05187	0.525936	+	0.850524i	$0.323715\pi$
$984$	7.68158	0.244880
$985$	21.7781	0.693907
$986$	32.9272	1.04862
$987$	6.89488	0.219466
$988$	5.65726	0.179981
$989$	−55.0491	−1.75046
$990$	0	0
$991$	−32.5491	−1.03396	−0.516979	−	0.855998i	$-0.672943\pi$
$991$	−32.5491	−1.03396	−0.516979	+	0.855998i	$0.672943\pi$
$992$	4.99011	0.158436
$993$	−5.25439	−0.166743
$994$	−16.7995	−0.532848
$995$	−22.3518	−0.708600
$996$	32.3854	1.02617
$997$	40.2897	1.27599	0.637994	−	0.770041i	$-0.279764\pi$
$997$	40.2897	1.27599	0.637994	+	0.770041i	$0.279764\pi$
$998$	−19.9890	−0.632740
$999$	22.7333	0.719249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cv.1.5		6
11.7	odd	10		770.2.n.g.71.1	✓	12
11.8	odd	10		770.2.n.g.141.1	yes	12
11.10	odd	2		8470.2.a.db.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.71.1	✓	12	11.7	odd	10
770.2.n.g.141.1	yes	12	11.8	odd	10
8470.2.a.cv.1.5		6	1.1	even	1	trivial
8470.2.a.db.1.5		6	11.10	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.84175 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.84175 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.392057 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.84175 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.84175 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.392057 q^{9} -1.00000 q^{10} +1.84175 q^{12} +1.78301 q^{13} -1.00000 q^{14} +1.84175 q^{15} +1.00000 q^{16} +7.29256 q^{17} -0.392057 q^{18} +3.17287 q^{19} +1.00000 q^{20} +1.84175 q^{21} -4.72397 q^{23} -1.84175 q^{24} +1.00000 q^{25} -1.78301 q^{26} -4.80319 q^{27} +1.00000 q^{28} -4.51518 q^{29} -1.84175 q^{30} -4.99011 q^{31} -1.00000 q^{32} -7.29256 q^{34} +1.00000 q^{35} +0.392057 q^{36} -4.73296 q^{37} -3.17287 q^{38} +3.28386 q^{39} -1.00000 q^{40} -4.17080 q^{41} -1.84175 q^{42} +11.6531 q^{43} +0.392057 q^{45} +4.72397 q^{46} +3.74365 q^{47} +1.84175 q^{48} +1.00000 q^{49} -1.00000 q^{50} +13.4311 q^{51} +1.78301 q^{52} +1.32043 q^{53} +4.80319 q^{54} -1.00000 q^{56} +5.84365 q^{57} +4.51518 q^{58} +9.71495 q^{59} +1.84175 q^{60} +9.80246 q^{61} +4.99011 q^{62} +0.392057 q^{63} +1.00000 q^{64} +1.78301 q^{65} -6.96181 q^{67} +7.29256 q^{68} -8.70039 q^{69} -1.00000 q^{70} +16.7995 q^{71} -0.392057 q^{72} -6.05144 q^{73} +4.73296 q^{74} +1.84175 q^{75} +3.17287 q^{76} -3.28386 q^{78} +15.0746 q^{79} +1.00000 q^{80} -10.0225 q^{81} +4.17080 q^{82} +17.5840 q^{83} +1.84175 q^{84} +7.29256 q^{85} -11.6531 q^{86} -8.31586 q^{87} +14.3054 q^{89} -0.392057 q^{90} +1.78301 q^{91} -4.72397 q^{92} -9.19056 q^{93} -3.74365 q^{94} +3.17287 q^{95} -1.84175 q^{96} +5.08081 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} - q^{9} - 6 q^{10} - q^{12} + 6 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} + 21 q^{17} + q^{18} - 3 q^{19} + 6 q^{20} - q^{21} - 10 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 6 q^{28} + 10 q^{29} + q^{30} - 4 q^{31} - 6 q^{32} - 21 q^{34} + 6 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} + 26 q^{39} - 6 q^{40} + 7 q^{41} + q^{42} + 19 q^{43} - q^{45} + 10 q^{46} + 10 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 4 q^{51} + 6 q^{52} - 16 q^{53} + 4 q^{54} - 6 q^{56} + 16 q^{57} - 10 q^{58} - 3 q^{59} - q^{60} - 8 q^{61} + 4 q^{62} - q^{63} + 6 q^{64} + 6 q^{65} - 27 q^{67} + 21 q^{68} + 4 q^{69} - 6 q^{70} + 4 q^{71} + q^{72} + 13 q^{73} + 2 q^{74} - q^{75} - 3 q^{76} - 26 q^{78} + 14 q^{79} + 6 q^{80} - 14 q^{81} - 7 q^{82} + 51 q^{83} - q^{84} + 21 q^{85} - 19 q^{86} + 8 q^{87} + q^{89} + q^{90} + 6 q^{91} - 10 q^{92} + 4 q^{93} - 10 q^{94} - 3 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 - q^9 - 6 * q^10 - q^12 + 6 * q^13 - 6 * q^14 - q^15 + 6 * q^16 + 21 * q^17 + q^18 - 3 * q^19 + 6 * q^20 - q^21 - 10 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 6 * q^28 + 10 * q^29 + q^30 - 4 * q^31 - 6 * q^32 - 21 * q^34 + 6 * q^35 - q^36 - 2 * q^37 + 3 * q^38 + 26 * q^39 - 6 * q^40 + 7 * q^41 + q^42 + 19 * q^43 - q^45 + 10 * q^46 + 10 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 4 * q^51 + 6 * q^52 - 16 * q^53 + 4 * q^54 - 6 * q^56 + 16 * q^57 - 10 * q^58 - 3 * q^59 - q^60 - 8 * q^61 + 4 * q^62 - q^63 + 6 * q^64 + 6 * q^65 - 27 * q^67 + 21 * q^68 + 4 * q^69 - 6 * q^70 + 4 * q^71 + q^72 + 13 * q^73 + 2 * q^74 - q^75 - 3 * q^76 - 26 * q^78 + 14 * q^79 + 6 * q^80 - 14 * q^81 - 7 * q^82 + 51 * q^83 - q^84 + 21 * q^85 - 19 * q^86 + 8 * q^87 + q^89 + q^90 + 6 * q^91 - 10 * q^92 + 4 * q^93 - 10 * q^94 - 3 * q^95 + q^96 + 7 * q^97 - 6 * q^98

Introduction

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