LMFDB - Embedded newform 8470.2.a.db.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:	$1$
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	$-0.579530\pi$
$13$	−1.78301	−0.494517	−0.247259	+	0.968950i	$0.579530\pi$
$14$	−1.00000	−0.267261
$15$	1.84175	0.475539
$16$	1.00000	0.250000
$17$	−7.29256	−1.76870	−0.884352	−	0.466820i	$-0.845400\pi$
$17$	−7.29256	−1.76870	−0.884352	+	0.466820i	$0.845400\pi$
$18$	0.392057	0.0924087
$19$	−3.17287	−0.727907	−0.363954	−	0.931417i	$-0.618573\pi$
$19$	−3.17287	−0.727907	−0.363954	+	0.931417i	$0.618573\pi$
$20$	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	$-0.362302\pi$
$29$	4.51518	0.838449	0.419224	+	0.907883i	$0.362302\pi$
$30$	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	$-0.394405\pi$
$41$	4.17080	0.651369	0.325684	+	0.945479i	$0.394405\pi$
$42$	−1.84175	−0.284189
$43$	−11.6531	−1.77709	−0.888544	−	0.458791i	$-0.848283\pi$
$43$	−11.6531	−1.77709	−0.888544	+	0.458791i	$0.848283\pi$
$44$	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	$-0.715937\pi$
$61$	−9.80246	−1.25508	−0.627538	+	0.778586i	$0.715937\pi$
$62$	−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	$-0.384776\pi$
$73$	6.05144	0.708268	0.354134	+	0.935195i	$0.384776\pi$
$74$	−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	$-0.822200\pi$
$79$	−15.0746	−1.69602	−0.848010	+	0.529980i	$0.822200\pi$
$80$	1.00000	0.111803
$81$	−10.0225	−1.11361
$82$	4.17080	0.460587
$83$	−17.5840	−1.93010	−0.965049	−	0.262071i	$-0.915594\pi$
$83$	−17.5840	−1.93010	−0.965049	+	0.262071i	$0.915594\pi$
$84$	−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	$-0.645430\pi$
$101$	−8.86707	−0.882306	−0.441153	+	0.897432i	$0.645430\pi$
$102$	−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	$-0.454123\pi$
$107$	2.97142	0.287258	0.143629	+	0.989632i	$0.454123\pi$
$108$	−4.80319	−0.462187
$109$	12.2500	1.17334	0.586668	−	0.809827i	$-0.300439\pi$
$109$	12.2500	1.17334	0.586668	+	0.809827i	$0.300439\pi$
$110$	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	$-0.600810\pi$
$127$	−7.01945	−0.622875	−0.311438	+	0.950267i	$0.600810\pi$
$128$	1.00000	0.0883883
$129$	−21.4622	−1.88964
$130$	−1.78301	−0.156380
$131$	21.3705	1.86715	0.933573	−	0.358386i	$-0.116673\pi$
$131$	21.3705	1.86715	0.933573	+	0.358386i	$0.116673\pi$
$132$	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	$-0.426677\pi$
$139$	5.38369	0.456638	0.228319	+	0.973586i	$0.426677\pi$
$140$	−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	$-0.472724\pi$
$149$	2.08940	0.171170	0.0855851	+	0.996331i	$0.472724\pi$
$150$	1.84175	0.150379
$151$	−8.31004	−0.676262	−0.338131	−	0.941099i	$-0.609795\pi$
$151$	−8.31004	−0.676262	−0.338131	+	0.941099i	$0.609795\pi$
$152$	−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	$-0.492674\pi$
$167$	0.594823	0.0460288	0.0230144	+	0.999735i	$0.492674\pi$
$168$	−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	$-0.513892\pi$
$173$	−1.14769	−0.0872571	−0.0436285	+	0.999048i	$0.513892\pi$
$174$	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	$-0.550180\pi$
$193$	−4.36205	−0.313987	−0.156993	+	0.987600i	$0.550180\pi$
$194$	5.08081	0.364781
$195$	−3.28386	−0.235162
$196$	1.00000	0.0714286
$197$	−21.7781	−1.55162	−0.775812	−	0.630964i	$-0.782659\pi$
$197$	−21.7781	−1.55162	−0.775812	+	0.630964i	$0.782659\pi$
$198$	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	$-0.534696\pi$
$211$	−3.16035	−0.217567	−0.108784	+	0.994065i	$0.534696\pi$
$212$	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	$-0.316552\pi$
$227$	16.4207	1.08988	0.544941	+	0.838474i	$0.316552\pi$
$228$	−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	$-0.563230\pi$
$233$	−6.02448	−0.394677	−0.197338	+	0.980335i	$0.563230\pi$
$234$	−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	$-0.323653\pi$
$239$	16.2666	1.05220	0.526101	+	0.850422i	$0.323653\pi$
$240$	1.84175	0.118885
$241$	28.6835	1.84767	0.923834	−	0.382793i	$-0.125038\pi$
$241$	28.6835	1.84767	0.923834	+	0.382793i	$0.125038\pi$
$242$	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	$-0.518740\pi$
$263$	−1.90841	−0.117678	−0.0588389	+	0.998267i	$0.518740\pi$
$264$	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	$-0.619214\pi$
$271$	−12.0446	−0.731655	−0.365828	+	0.930683i	$0.619214\pi$
$272$	−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	$-0.496965\pi$
$277$	0.317418	0.0190718	0.00953591	+	0.999955i	$0.496965\pi$
$278$	5.38369	0.322892
$279$	−1.95641	−0.117127
$280$	−1.00000	−0.0597614
$281$	−15.1034	−0.900996	−0.450498	−	0.892777i	$-0.648754\pi$
$281$	−15.1034	−0.900996	−0.450498	+	0.892777i	$0.648754\pi$
$282$	6.89488	0.410584
$283$	11.7700	0.699653	0.349826	−	0.936815i	$-0.386241\pi$
$283$	11.7700	0.699653	0.349826	+	0.936815i	$0.386241\pi$
$284$	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	$-0.706663\pi$
$293$	−20.6978	−1.20918	−0.604590	+	0.796537i	$0.706663\pi$
$294$	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	$-0.339011\pi$
$307$	16.9774	0.968949	0.484475	+	0.874805i	$0.339011\pi$
$308$	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	$-0.602065\pi$
$337$	−11.5719	−0.630363	−0.315182	+	0.949031i	$0.602065\pi$
$338$	−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	$-0.203059\pi$
$347$	29.9288	1.60666	0.803332	+	0.595532i	$0.203059\pi$
$348$	8.31586	0.445777
$349$	20.3624	1.08997	0.544987	−	0.838444i	$-0.316535\pi$
$349$	20.3624	1.08997	0.544987	+	0.838444i	$0.316535\pi$
$350$	−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	$-0.598261\pi$
$359$	−11.5130	−0.607631	−0.303815	+	0.952731i	$0.598261\pi$
$360$	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	$-0.580220\pi$
$373$	−9.63189	−0.498720	−0.249360	+	0.968411i	$0.580220\pi$
$374$	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	$-0.532679\pi$
$409$	−4.14523	−0.204969	−0.102484	+	0.994735i	$0.532679\pi$
$410$	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	$-0.694013\pi$
$431$	−23.7694	−1.14493	−0.572466	+	0.819929i	$0.694013\pi$
$432$	−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	$-0.560506\pi$
$439$	−7.91759	−0.377886	−0.188943	+	0.981988i	$0.560506\pi$
$440$	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	$-0.754598\pi$
$457$	−30.6660	−1.43449	−0.717247	+	0.696819i	$0.754598\pi$
$458$	10.9499	0.511655
$459$	35.0275	1.63495
$460$	−4.72397	−0.220256
$461$	−9.43899	−0.439618	−0.219809	−	0.975543i	$-0.570543\pi$
$461$	−9.43899	−0.439618	−0.219809	+	0.975543i	$0.570543\pi$
$462$	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	$-0.690663\pi$
$479$	−24.6789	−1.12761	−0.563805	+	0.825908i	$0.690663\pi$
$480$	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	$-0.745157\pi$
$491$	−30.8565	−1.39253	−0.696267	+	0.717783i	$0.745157\pi$
$492$	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	$-0.732620\pi$
$503$	−29.9393	−1.33493	−0.667464	+	0.744642i	$0.732620\pi$
$504$	−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	$-0.649629\pi$
$523$	−20.7173	−0.905905	−0.452952	+	0.891535i	$0.649629\pi$
$524$	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	$-0.425907\pi$
$541$	10.7306	0.461346	0.230673	+	0.973031i	$0.425907\pi$
$542$	−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	$-0.572843\pi$
$547$	−10.6113	−0.453704	−0.226852	+	0.973929i	$0.572843\pi$
$548$	−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	$-0.265578\pi$
$557$	31.7039	1.34334	0.671669	+	0.740852i	$0.265578\pi$
$558$	−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	$-0.564174\pi$
$563$	−9.50273	−0.400492	−0.200246	+	0.979746i	$0.564174\pi$
$564$	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	$-0.199117\pi$
$569$	38.6738	1.62129	0.810645	+	0.585538i	$0.199117\pi$
$570$	−5.84365	−0.244764
$571$	−7.44900	−0.311731	−0.155865	−	0.987778i	$-0.549817\pi$
$571$	−7.44900	−0.311731	−0.155865	+	0.987778i	$0.549817\pi$
$572$	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	$-0.489262\pi$
$593$	1.64274	0.0674592	0.0337296	+	0.999431i	$0.489262\pi$
$594$	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	$-0.595795\pi$
$601$	−14.5340	−0.592853	−0.296426	+	0.955056i	$0.595795\pi$
$602$	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	$-0.413081\pi$
$607$	13.2886	0.539366	0.269683	+	0.962949i	$0.413081\pi$
$608$	−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	$-0.573270\pi$
$613$	−11.2979	−0.456316	−0.228158	+	0.973624i	$0.573270\pi$
$614$	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	$-0.651205\pi$
$659$	−23.4818	−0.914720	−0.457360	+	0.889282i	$0.651205\pi$
$660$	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	$-0.649030\pi$
$673$	−23.4140	−0.902545	−0.451273	+	0.892386i	$0.649030\pi$
$674$	−11.5719	−0.445734
$675$	−4.80319	−0.184875
$676$	−9.82088	−0.377726
$677$	−21.9206	−0.842478	−0.421239	−	0.906950i	$-0.638405\pi$
$677$	−21.9206	−0.842478	−0.421239	+	0.906950i	$0.638405\pi$
$678$	−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	$-0.664108\pi$
$701$	−26.1070	−0.986046	−0.493023	+	0.870016i	$0.664108\pi$
$702$	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	$-0.563989\pi$
$733$	−10.8120	−0.399350	−0.199675	+	0.979862i	$0.563989\pi$
$734$	−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	$-0.219872\pi$
$739$	41.9060	1.54154	0.770769	+	0.637114i	$0.219872\pi$
$740$	−4.73296	−0.173987
$741$	10.4193	0.382762
$742$	−1.32043	−0.0484745
$743$	49.2037	1.80511	0.902555	−	0.430574i	$-0.141689\pi$
$743$	49.2037	1.80511	0.902555	+	0.430574i	$0.141689\pi$
$744$	−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	$-0.167265\pi$
$761$	47.7288	1.73017	0.865085	+	0.501626i	$0.167265\pi$
$762$	−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	$-0.387716\pi$
$769$	19.1610	0.690963	0.345481	+	0.938426i	$0.387716\pi$
$770$	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	$-0.594986\pi$
$787$	−16.4954	−0.587998	−0.293999	+	0.955806i	$0.594986\pi$
$788$	−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	$-0.336461\pi$
$809$	27.9575	0.982934	0.491467	+	0.870896i	$0.336461\pi$
$810$	−10.0225	−0.352153
$811$	22.1078	0.776311	0.388156	−	0.921594i	$-0.373112\pi$
$811$	22.1078	0.776311	0.388156	+	0.921594i	$0.373112\pi$
$812$	−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	$-0.879509\pi$
$821$	−53.2494	−1.85842	−0.929208	+	0.369558i	$0.879509\pi$
$822$	−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	$-0.599184\pi$
$827$	−17.6329	−0.613156	−0.306578	+	0.951846i	$0.599184\pi$
$828$	−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	$-0.267914\pi$
$853$	38.9150	1.33243	0.666213	+	0.745762i	$0.267914\pi$
$854$	9.80246	0.335433
$855$	−1.24395	−0.0425421
$856$	2.97142	0.101561
$857$	−25.6321	−0.875575	−0.437787	−	0.899079i	$-0.644238\pi$
$857$	−25.6321	−0.875575	−0.437787	+	0.899079i	$0.644238\pi$
$858$	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	$-0.117987\pi$
$877$	55.2059	1.86417	0.932086	+	0.362238i	$0.117987\pi$
$878$	−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	$-0.258542\pi$
$887$	40.9735	1.37576	0.687879	+	0.725826i	$0.258542\pi$
$888$	−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	$-0.359333\pi$
$919$	25.9299	0.855350	0.427675	+	0.903933i	$0.359333\pi$
$920$	−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	$-0.303504\pi$
$937$	35.4374	1.15769	0.578845	+	0.815437i	$0.303504\pi$
$938$	6.96181	0.227311
$939$	−0.318774	−0.0104028
$940$	3.74365	0.122104
$941$	−23.5197	−0.766721	−0.383360	−	0.923599i	$-0.625233\pi$
$941$	−23.5197	−0.766721	−0.383360	+	0.923599i	$0.625233\pi$
$942$	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	$-0.735034\pi$
$953$	−41.5577	−1.34618	−0.673092	+	0.739559i	$0.735034\pi$
$954$	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	$-0.291670\pi$
$967$	37.8603	1.21751	0.608753	+	0.793360i	$0.291670\pi$
$968$	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	$-0.720236\pi$
$997$	−40.2897	−1.27599	−0.637994	+	0.770041i	$0.720236\pi$
$998$	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.db.1.5		6
11.3	even	5		770.2.n.g.141.1	yes	12
11.4	even	5		770.2.n.g.71.1	✓	12
11.10	odd	2		8470.2.a.cv.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.71.1	✓	12	11.4	even	5
770.2.n.g.141.1	yes	12	11.3	even	5
8470.2.a.cv.1.5		6	11.10	odd	2
8470.2.a.db.1.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
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

L-functions

Modular forms

Varieties

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Database

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