LMFDB - Embedded newform 8470.2.a.de.1.2

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:	6.6.13298000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 3x^{3} + 26x^{2} + 13x - 1 $ x^6 - x^5 - 10x^4 + 3x^3 + 26x^2 + 13x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
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			1.2
Root			$2.79700$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.64424 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.64424 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.99201 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.64424 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.64424 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.99201 q^{9} +1.00000 q^{10} -2.64424 q^{12} +3.06037 q^{13} +1.00000 q^{14} -2.64424 q^{15} +1.00000 q^{16} -0.0683587 q^{17} +3.99201 q^{18} +2.77079 q^{19} +1.00000 q^{20} -2.64424 q^{21} +1.83120 q^{23} -2.64424 q^{24} +1.00000 q^{25} +3.06037 q^{26} -2.62310 q^{27} +1.00000 q^{28} +3.30937 q^{29} -2.64424 q^{30} +4.12571 q^{31} +1.00000 q^{32} -0.0683587 q^{34} +1.00000 q^{35} +3.99201 q^{36} -5.63448 q^{37} +2.77079 q^{38} -8.09234 q^{39} +1.00000 q^{40} -5.13257 q^{41} -2.64424 q^{42} +2.84053 q^{43} +3.99201 q^{45} +1.83120 q^{46} +11.9195 q^{47} -2.64424 q^{48} +1.00000 q^{49} +1.00000 q^{50} +0.180757 q^{51} +3.06037 q^{52} +0.123629 q^{53} -2.62310 q^{54} +1.00000 q^{56} -7.32664 q^{57} +3.30937 q^{58} -11.1929 q^{59} -2.64424 q^{60} +2.53653 q^{61} +4.12571 q^{62} +3.99201 q^{63} +1.00000 q^{64} +3.06037 q^{65} -2.20818 q^{67} -0.0683587 q^{68} -4.84213 q^{69} +1.00000 q^{70} +13.7247 q^{71} +3.99201 q^{72} +6.98905 q^{73} -5.63448 q^{74} -2.64424 q^{75} +2.77079 q^{76} -8.09234 q^{78} -12.4142 q^{79} +1.00000 q^{80} -5.03990 q^{81} -5.13257 q^{82} -3.05366 q^{83} -2.64424 q^{84} -0.0683587 q^{85} +2.84053 q^{86} -8.75076 q^{87} +13.5707 q^{89} +3.99201 q^{90} +3.06037 q^{91} +1.83120 q^{92} -10.9094 q^{93} +11.9195 q^{94} +2.77079 q^{95} -2.64424 q^{96} -2.74477 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 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 + 15 * q^9	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9} + 6 q^{10} + q^{12} + 2 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 7 q^{17} + 15 q^{18} + 11 q^{19} + 6 q^{20} + q^{21} - 6 q^{23} + q^{24} + 6 q^{25} + 2 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + q^{30} + 6 q^{32} + 7 q^{34} + 6 q^{35} + 15 q^{36} - 14 q^{37} + 11 q^{38} + 20 q^{39} + 6 q^{40} + 13 q^{41} + q^{42} + 19 q^{43} + 15 q^{45} - 6 q^{46} + 22 q^{47} + q^{48} + 6 q^{49} + 6 q^{50} - 14 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 6 q^{56} + 32 q^{57} + 2 q^{58} - 7 q^{59} + q^{60} + 22 q^{61} + 15 q^{63} + 6 q^{64} + 2 q^{65} + 5 q^{67} + 7 q^{68} - 36 q^{69} + 6 q^{70} + 8 q^{71} + 15 q^{72} + 13 q^{73} - 14 q^{74} + q^{75} + 11 q^{76} + 20 q^{78} - 16 q^{79} + 6 q^{80} + 18 q^{81} + 13 q^{82} - 5 q^{83} + q^{84} + 7 q^{85} + 19 q^{86} + 14 q^{87} + q^{89} + 15 q^{90} + 2 q^{91} - 6 q^{92} - 42 q^{93} + 22 q^{94} + 11 q^{95} + q^{96} - 3 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 + 15 * q^9 + 6 * q^10 + q^12 + 2 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 7 * q^17 + 15 * q^18 + 11 * q^19 + 6 * q^20 + q^21 - 6 * q^23 + q^24 + 6 * q^25 + 2 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + q^30 + 6 * q^32 + 7 * q^34 + 6 * q^35 + 15 * q^36 - 14 * q^37 + 11 * q^38 + 20 * q^39 + 6 * q^40 + 13 * q^41 + q^42 + 19 * q^43 + 15 * q^45 - 6 * q^46 + 22 * q^47 + q^48 + 6 * q^49 + 6 * q^50 - 14 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 6 * q^56 + 32 * q^57 + 2 * q^58 - 7 * q^59 + q^60 + 22 * q^61 + 15 * q^63 + 6 * q^64 + 2 * q^65 + 5 * q^67 + 7 * q^68 - 36 * q^69 + 6 * q^70 + 8 * q^71 + 15 * q^72 + 13 * q^73 - 14 * q^74 + q^75 + 11 * q^76 + 20 * q^78 - 16 * q^79 + 6 * q^80 + 18 * q^81 + 13 * q^82 - 5 * q^83 + q^84 + 7 * q^85 + 19 * q^86 + 14 * q^87 + q^89 + 15 * q^90 + 2 * q^91 - 6 * q^92 - 42 * q^93 + 22 * q^94 + 11 * q^95 + q^96 - 3 * 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
$3$	−2.64424	−1.52665	−0.763326	−	0.646013i	$-0.776435\pi$
$3$	−2.64424	−1.52665	−0.763326	+	0.646013i	$0.776435\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.64424	−1.07951
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.99201	1.33067
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−2.64424	−0.763326
$13$	3.06037	0.848793	0.424396	−	0.905477i	$-0.360486\pi$
$13$	3.06037	0.848793	0.424396	+	0.905477i	$0.360486\pi$
$14$	1.00000	0.267261
$15$	−2.64424	−0.682740
$16$	1.00000	0.250000
$17$	−0.0683587	−0.0165794	−0.00828971	−	0.999966i	$-0.502639\pi$
$17$	−0.0683587	−0.0165794	−0.00828971	+	0.999966i	$0.502639\pi$
$18$	3.99201	0.940925
$19$	2.77079	0.635664	0.317832	−	0.948147i	$-0.397045\pi$
$19$	2.77079	0.635664	0.317832	+	0.948147i	$0.397045\pi$
$20$	1.00000	0.223607
$21$	−2.64424	−0.577021
$22$	0	0
$23$	1.83120	0.381831	0.190916	−	0.981606i	$-0.438854\pi$
$23$	1.83120	0.381831	0.190916	+	0.981606i	$0.438854\pi$
$24$	−2.64424	−0.539753
$25$	1.00000	0.200000
$26$	3.06037	0.600187
$27$	−2.62310	−0.504817
$28$	1.00000	0.188982
$29$	3.30937	0.614534	0.307267	−	0.951623i	$-0.400586\pi$
$29$	3.30937	0.614534	0.307267	+	0.951623i	$0.400586\pi$
$30$	−2.64424	−0.482770
$31$	4.12571	0.741000	0.370500	−	0.928833i	$-0.379186\pi$
$31$	4.12571	0.741000	0.370500	+	0.928833i	$0.379186\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.0683587	−0.0117234
$35$	1.00000	0.169031
$36$	3.99201	0.665334
$37$	−5.63448	−0.926303	−0.463151	−	0.886279i	$-0.653281\pi$
$37$	−5.63448	−0.926303	−0.463151	+	0.886279i	$0.653281\pi$
$38$	2.77079	0.449482
$39$	−8.09234	−1.29581
$40$	1.00000	0.158114
$41$	−5.13257	−0.801573	−0.400787	−	0.916171i	$-0.631263\pi$
$41$	−5.13257	−0.801573	−0.400787	+	0.916171i	$0.631263\pi$
$42$	−2.64424	−0.408015
$43$	2.84053	0.433177	0.216589	−	0.976263i	$-0.430507\pi$
$43$	2.84053	0.433177	0.216589	+	0.976263i	$0.430507\pi$
$44$	0	0
$45$	3.99201	0.595093
$46$	1.83120	0.269996
$47$	11.9195	1.73864	0.869322	−	0.494247i	$-0.164556\pi$
$47$	11.9195	1.73864	0.869322	+	0.494247i	$0.164556\pi$
$48$	−2.64424	−0.381663
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0.180757	0.0253110
$52$	3.06037	0.424396
$53$	0.123629	0.0169818	0.00849088	−	0.999964i	$-0.497297\pi$
$53$	0.123629	0.0169818	0.00849088	+	0.999964i	$0.497297\pi$
$54$	−2.62310	−0.356959
$55$	0	0
$56$	1.00000	0.133631
$57$	−7.32664	−0.970438
$58$	3.30937	0.434541
$59$	−11.1929	−1.45720	−0.728598	−	0.684941i	$-0.759828\pi$
$59$	−11.1929	−1.45720	−0.728598	+	0.684941i	$0.759828\pi$
$60$	−2.64424	−0.341370
$61$	2.53653	0.324770	0.162385	−	0.986728i	$-0.448081\pi$
$61$	2.53653	0.324770	0.162385	+	0.986728i	$0.448081\pi$
$62$	4.12571	0.523966
$63$	3.99201	0.502946
$64$	1.00000	0.125000
$65$	3.06037	0.379592
$66$	0	0
$67$	−2.20818	−0.269773	−0.134886	−	0.990861i	$-0.543067\pi$
$67$	−2.20818	−0.269773	−0.134886	+	0.990861i	$0.543067\pi$
$68$	−0.0683587	−0.00828971
$69$	−4.84213	−0.582924
$70$	1.00000	0.119523
$71$	13.7247	1.62883	0.814413	−	0.580285i	$-0.197059\pi$
$71$	13.7247	1.62883	0.814413	+	0.580285i	$0.197059\pi$
$72$	3.99201	0.470462
$73$	6.98905	0.818007	0.409003	−	0.912533i	$-0.365876\pi$
$73$	6.98905	0.818007	0.409003	+	0.912533i	$0.365876\pi$
$74$	−5.63448	−0.654995
$75$	−2.64424	−0.305331
$76$	2.77079	0.317832
$77$	0	0
$78$	−8.09234	−0.916277
$79$	−12.4142	−1.39671	−0.698354	−	0.715752i	$-0.746084\pi$
$79$	−12.4142	−1.39671	−0.698354	+	0.715752i	$0.746084\pi$
$80$	1.00000	0.111803
$81$	−5.03990	−0.559989
$82$	−5.13257	−0.566798
$83$	−3.05366	−0.335183	−0.167591	−	0.985857i	$-0.553599\pi$
$83$	−3.05366	−0.335183	−0.167591	+	0.985857i	$0.553599\pi$
$84$	−2.64424	−0.288510
$85$	−0.0683587	−0.00741454
$86$	2.84053	0.306303
$87$	−8.75076	−0.938180
$88$	0	0
$89$	13.5707	1.43849	0.719246	−	0.694756i	$-0.244487\pi$
$89$	13.5707	1.43849	0.719246	+	0.694756i	$0.244487\pi$
$90$	3.99201	0.420794
$91$	3.06037	0.320813
$92$	1.83120	0.190916
$93$	−10.9094	−1.13125
$94$	11.9195	1.22941
$95$	2.77079	0.284277
$96$	−2.64424	−0.269877
$97$	−2.74477	−0.278689	−0.139345	−	0.990244i	$-0.544500\pi$
$97$	−2.74477	−0.278689	−0.139345	+	0.990244i	$0.544500\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−5.53961	−0.551212	−0.275606	−	0.961271i	$-0.588879\pi$
$101$	−5.53961	−0.551212	−0.275606	+	0.961271i	$0.588879\pi$
$102$	0.180757	0.0178976
$103$	−3.61697	−0.356390	−0.178195	−	0.983995i	$-0.557026\pi$
$103$	−3.61697	−0.356390	−0.178195	+	0.983995i	$0.557026\pi$
$104$	3.06037	0.300094
$105$	−2.64424	−0.258051
$106$	0.123629	0.0120079
$107$	6.58182	0.636288	0.318144	−	0.948042i	$-0.396940\pi$
$107$	6.58182	0.636288	0.318144	+	0.948042i	$0.396940\pi$
$108$	−2.62310	−0.252408
$109$	1.14986	0.110137	0.0550683	−	0.998483i	$-0.482462\pi$
$109$	1.14986	0.110137	0.0550683	+	0.998483i	$0.482462\pi$
$110$	0	0
$111$	14.8989	1.41414
$112$	1.00000	0.0944911
$113$	−12.1536	−1.14332	−0.571658	−	0.820492i	$-0.693700\pi$
$113$	−12.1536	−1.14332	−0.571658	+	0.820492i	$0.693700\pi$
$114$	−7.32664	−0.686203
$115$	1.83120	0.170760
$116$	3.30937	0.307267
$117$	12.2170	1.12946
$118$	−11.1929	−1.03039
$119$	−0.0683587	−0.00626643
$120$	−2.64424	−0.241385
$121$	0	0
$122$	2.53653	0.229647
$123$	13.5718	1.22372
$124$	4.12571	0.370500
$125$	1.00000	0.0894427
$126$	3.99201	0.355636
$127$	13.7815	1.22291	0.611457	−	0.791278i	$-0.290584\pi$
$127$	13.7815	1.22291	0.611457	+	0.791278i	$0.290584\pi$
$128$	1.00000	0.0883883
$129$	−7.51106	−0.661312
$130$	3.06037	0.268412
$131$	4.89161	0.427382	0.213691	−	0.976901i	$-0.431452\pi$
$131$	4.89161	0.427382	0.213691	+	0.976901i	$0.431452\pi$
$132$	0	0
$133$	2.77079	0.240258
$134$	−2.20818	−0.190758
$135$	−2.62310	−0.225761
$136$	−0.0683587	−0.00586171
$137$	−19.0559	−1.62805	−0.814026	−	0.580829i	$-0.802729\pi$
$137$	−19.0559	−1.62805	−0.814026	+	0.580829i	$0.802729\pi$
$138$	−4.84213	−0.412190
$139$	7.65318	0.649135	0.324567	−	0.945863i	$-0.394781\pi$
$139$	7.65318	0.649135	0.324567	+	0.945863i	$0.394781\pi$
$140$	1.00000	0.0845154
$141$	−31.5181	−2.65430
$142$	13.7247	1.15175
$143$	0	0
$144$	3.99201	0.332667
$145$	3.30937	0.274828
$146$	6.98905	0.578418
$147$	−2.64424	−0.218093
$148$	−5.63448	−0.463151
$149$	−14.6774	−1.20242	−0.601208	−	0.799092i	$-0.705314\pi$
$149$	−14.6774	−1.20242	−0.601208	+	0.799092i	$0.705314\pi$
$150$	−2.64424	−0.215901
$151$	−11.0935	−0.902774	−0.451387	−	0.892328i	$-0.649071\pi$
$151$	−11.0935	−0.902774	−0.451387	+	0.892328i	$0.649071\pi$
$152$	2.77079	0.224741
$153$	−0.272888	−0.0220617
$154$	0	0
$155$	4.12571	0.331385
$156$	−8.09234	−0.647906
$157$	13.1941	1.05300	0.526502	−	0.850174i	$-0.323503\pi$
$157$	13.1941	1.05300	0.526502	+	0.850174i	$0.323503\pi$
$158$	−12.4142	−0.987622
$159$	−0.326905	−0.0259253
$160$	1.00000	0.0790569
$161$	1.83120	0.144319
$162$	−5.03990	−0.395972
$163$	−3.70882	−0.290497	−0.145248	−	0.989395i	$-0.546398\pi$
$163$	−3.70882	−0.290497	−0.145248	+	0.989395i	$0.546398\pi$
$164$	−5.13257	−0.400787
$165$	0	0
$166$	−3.05366	−0.237010
$167$	−8.75429	−0.677428	−0.338714	−	0.940889i	$-0.609992\pi$
$167$	−8.75429	−0.677428	−0.338714	+	0.940889i	$0.609992\pi$
$168$	−2.64424	−0.204008
$169$	−3.63416	−0.279551
$170$	−0.0683587	−0.00524287
$171$	11.0610	0.845858
$172$	2.84053	0.216589
$173$	−3.03876	−0.231033	−0.115516	−	0.993306i	$-0.536852\pi$
$173$	−3.03876	−0.231033	−0.115516	+	0.993306i	$0.536852\pi$
$174$	−8.75076	−0.663393
$175$	1.00000	0.0755929
$176$	0	0
$177$	29.5968	2.22463
$178$	13.5707	1.01717
$179$	−7.29987	−0.545618	−0.272809	−	0.962068i	$-0.587953\pi$
$179$	−7.29987	−0.545618	−0.272809	+	0.962068i	$0.587953\pi$
$180$	3.99201	0.297547
$181$	10.9351	0.812800	0.406400	−	0.913695i	$-0.366784\pi$
$181$	10.9351	0.812800	0.406400	+	0.913695i	$0.366784\pi$
$182$	3.06037	0.226849
$183$	−6.70720	−0.495811
$184$	1.83120	0.134998
$185$	−5.63448	−0.414255
$186$	−10.9094	−0.799914
$187$	0	0
$188$	11.9195	0.869322
$189$	−2.62310	−0.190803
$190$	2.77079	0.201014
$191$	22.6520	1.63904	0.819519	−	0.573051i	$-0.194241\pi$
$191$	22.6520	1.63904	0.819519	+	0.573051i	$0.194241\pi$
$192$	−2.64424	−0.190832
$193$	−16.9764	−1.22199	−0.610994	−	0.791635i	$-0.709230\pi$
$193$	−16.9764	−1.22199	−0.610994	+	0.791635i	$0.709230\pi$
$194$	−2.74477	−0.197063
$195$	−8.09234	−0.579505
$196$	1.00000	0.0714286
$197$	26.3241	1.87551	0.937757	−	0.347293i	$-0.112899\pi$
$197$	26.3241	1.87551	0.937757	+	0.347293i	$0.112899\pi$
$198$	0	0
$199$	16.9127	1.19891	0.599456	−	0.800408i	$-0.295384\pi$
$199$	16.9127	1.19891	0.599456	+	0.800408i	$0.295384\pi$
$200$	1.00000	0.0707107
$201$	5.83897	0.411849
$202$	−5.53961	−0.389766
$203$	3.30937	0.232272
$204$	0.180757	0.0126555
$205$	−5.13257	−0.358474
$206$	−3.61697	−0.252006
$207$	7.31016	0.508091
$208$	3.06037	0.212198
$209$	0	0
$210$	−2.64424	−0.182470
$211$	−16.4483	−1.13235	−0.566173	−	0.824286i	$-0.691577\pi$
$211$	−16.4483	−1.13235	−0.566173	+	0.824286i	$0.691577\pi$
$212$	0.123629	0.00849088
$213$	−36.2915	−2.48665
$214$	6.58182	0.449924
$215$	2.84053	0.193723
$216$	−2.62310	−0.178480
$217$	4.12571	0.280072
$218$	1.14986	0.0778784
$219$	−18.4807	−1.24881
$220$	0	0
$221$	−0.209203	−0.0140725
$222$	14.8989	0.999950
$223$	20.4675	1.37060	0.685302	−	0.728259i	$-0.259670\pi$
$223$	20.4675	1.37060	0.685302	+	0.728259i	$0.259670\pi$
$224$	1.00000	0.0668153
$225$	3.99201	0.266134
$226$	−12.1536	−0.808447
$227$	23.7041	1.57329	0.786647	−	0.617403i	$-0.211815\pi$
$227$	23.7041	1.57329	0.786647	+	0.617403i	$0.211815\pi$
$228$	−7.32664	−0.485219
$229$	−26.6368	−1.76021	−0.880106	−	0.474778i	$-0.842528\pi$
$229$	−26.6368	−1.76021	−0.880106	+	0.474778i	$0.842528\pi$
$230$	1.83120	0.120746
$231$	0	0
$232$	3.30937	0.217271
$233$	30.3368	1.98743	0.993714	−	0.111950i	$-0.0357097\pi$
$233$	30.3368	1.98743	0.993714	+	0.111950i	$0.0357097\pi$
$234$	12.2170	0.798650
$235$	11.9195	0.777545
$236$	−11.1929	−0.728598
$237$	32.8262	2.13229
$238$	−0.0683587	−0.00443104
$239$	−9.95180	−0.643728	−0.321864	−	0.946786i	$-0.604309\pi$
$239$	−9.95180	−0.643728	−0.321864	+	0.946786i	$0.604309\pi$
$240$	−2.64424	−0.170685
$241$	−30.1849	−1.94438	−0.972191	−	0.234189i	$-0.924757\pi$
$241$	−30.1849	−1.94438	−0.972191	+	0.234189i	$0.924757\pi$
$242$	0	0
$243$	21.1960	1.35973
$244$	2.53653	0.162385
$245$	1.00000	0.0638877
$246$	13.5718	0.865303
$247$	8.47964	0.539547
$248$	4.12571	0.261983
$249$	8.07461	0.511707
$250$	1.00000	0.0632456
$251$	−1.16998	−0.0738485	−0.0369242	−	0.999318i	$-0.511756\pi$
$251$	−1.16998	−0.0738485	−0.0369242	+	0.999318i	$0.511756\pi$
$252$	3.99201	0.251473
$253$	0	0
$254$	13.7815	0.864730
$255$	0.180757	0.0113194
$256$	1.00000	0.0625000
$257$	−0.980916	−0.0611879	−0.0305939	−	0.999532i	$-0.509740\pi$
$257$	−0.980916	−0.0611879	−0.0305939	+	0.999532i	$0.509740\pi$
$258$	−7.51106	−0.467618
$259$	−5.63448	−0.350110
$260$	3.06037	0.189796
$261$	13.2110	0.817741
$262$	4.89161	0.302204
$263$	−15.9923	−0.986125	−0.493063	−	0.869994i	$-0.664123\pi$
$263$	−15.9923	−0.986125	−0.493063	+	0.869994i	$0.664123\pi$
$264$	0	0
$265$	0.123629	0.00759448
$266$	2.77079	0.169888
$267$	−35.8842	−2.19608
$268$	−2.20818	−0.134886
$269$	15.1048	0.920953	0.460476	−	0.887672i	$-0.347679\pi$
$269$	15.1048	0.920953	0.460476	+	0.887672i	$0.347679\pi$
$270$	−2.62310	−0.159637
$271$	−0.499548	−0.0303454	−0.0151727	−	0.999885i	$-0.504830\pi$
$271$	−0.499548	−0.0303454	−0.0151727	+	0.999885i	$0.504830\pi$
$272$	−0.0683587	−0.00414486
$273$	−8.09234	−0.489771
$274$	−19.0559	−1.15121
$275$	0	0
$276$	−4.84213	−0.291462
$277$	−11.1061	−0.667302	−0.333651	−	0.942697i	$-0.608281\pi$
$277$	−11.1061	−0.667302	−0.333651	+	0.942697i	$0.608281\pi$
$278$	7.65318	0.459007
$279$	16.4699	0.986025
$280$	1.00000	0.0597614
$281$	15.4512	0.921742	0.460871	−	0.887467i	$-0.347537\pi$
$281$	15.4512	0.921742	0.460871	+	0.887467i	$0.347537\pi$
$282$	−31.5181	−1.87688
$283$	14.3139	0.850876	0.425438	−	0.904988i	$-0.360120\pi$
$283$	14.3139	0.850876	0.425438	+	0.904988i	$0.360120\pi$
$284$	13.7247	0.814413
$285$	−7.32664	−0.433993
$286$	0	0
$287$	−5.13257	−0.302966
$288$	3.99201	0.235231
$289$	−16.9953	−0.999725
$290$	3.30937	0.194333
$291$	7.25783	0.425462
$292$	6.98905	0.409003
$293$	−17.5749	−1.02673	−0.513367	−	0.858169i	$-0.671602\pi$
$293$	−17.5749	−1.02673	−0.513367	+	0.858169i	$0.671602\pi$
$294$	−2.64424	−0.154215
$295$	−11.1929	−0.651678
$296$	−5.63448	−0.327498
$297$	0	0
$298$	−14.6774	−0.850237
$299$	5.60414	0.324096
$300$	−2.64424	−0.152665
$301$	2.84053	0.163726
$302$	−11.0935	−0.638358
$303$	14.6481	0.841509
$304$	2.77079	0.158916
$305$	2.53653	0.145241
$306$	−0.272888	−0.0156000
$307$	5.38032	0.307071	0.153536	−	0.988143i	$-0.450934\pi$
$307$	5.38032	0.307071	0.153536	+	0.988143i	$0.450934\pi$
$308$	0	0
$309$	9.56413	0.544084
$310$	4.12571	0.234325
$311$	16.9028	0.958470	0.479235	−	0.877687i	$-0.340914\pi$
$311$	16.9028	0.958470	0.479235	+	0.877687i	$0.340914\pi$
$312$	−8.09234	−0.458139
$313$	−1.35523	−0.0766020	−0.0383010	−	0.999266i	$-0.512195\pi$
$313$	−1.35523	−0.0766020	−0.0383010	+	0.999266i	$0.512195\pi$
$314$	13.1941	0.744587
$315$	3.99201	0.224924
$316$	−12.4142	−0.698354
$317$	29.3217	1.64687	0.823434	−	0.567412i	$-0.192055\pi$
$317$	29.3217	1.64687	0.823434	+	0.567412i	$0.192055\pi$
$318$	−0.326905	−0.0183319
$319$	0	0
$320$	1.00000	0.0559017
$321$	−17.4039	−0.971391
$322$	1.83120	0.102049
$323$	−0.189408	−0.0105389
$324$	−5.03990	−0.279995
$325$	3.06037	0.169759
$326$	−3.70882	−0.205412
$327$	−3.04051	−0.168140
$328$	−5.13257	−0.283399
$329$	11.9195	0.657145
$330$	0	0
$331$	7.10546	0.390551	0.195276	−	0.980748i	$-0.437440\pi$
$331$	7.10546	0.390551	0.195276	+	0.980748i	$0.437440\pi$
$332$	−3.05366	−0.167591
$333$	−22.4929	−1.23260
$334$	−8.75429	−0.479014
$335$	−2.20818	−0.120646
$336$	−2.64424	−0.144255
$337$	28.7650	1.56693	0.783463	−	0.621438i	$-0.213451\pi$
$337$	28.7650	1.56693	0.783463	+	0.621438i	$0.213451\pi$
$338$	−3.63416	−0.197672
$339$	32.1371	1.74545
$340$	−0.0683587	−0.00370727
$341$	0	0
$342$	11.0610	0.598112
$343$	1.00000	0.0539949
$344$	2.84053	0.153151
$345$	−4.84213	−0.260692
$346$	−3.03876	−0.163365
$347$	−25.7893	−1.38444	−0.692222	−	0.721685i	$-0.743368\pi$
$347$	−25.7893	−1.38444	−0.692222	+	0.721685i	$0.743368\pi$
$348$	−8.75076	−0.469090
$349$	36.6973	1.96436	0.982180	−	0.187942i	$-0.0601818\pi$
$349$	36.6973	1.96436	0.982180	+	0.187942i	$0.0601818\pi$
$350$	1.00000	0.0534522
$351$	−8.02766	−0.428485
$352$	0	0
$353$	16.9704	0.903241	0.451620	−	0.892210i	$-0.350846\pi$
$353$	16.9704	0.903241	0.451620	+	0.892210i	$0.350846\pi$
$354$	29.5968	1.57305
$355$	13.7247	0.728434
$356$	13.5707	0.719246
$357$	0.180757	0.00956667
$358$	−7.29987	−0.385810
$359$	21.1819	1.11794	0.558969	−	0.829189i	$-0.311197\pi$
$359$	21.1819	1.11794	0.558969	+	0.829189i	$0.311197\pi$
$360$	3.99201	0.210397
$361$	−11.3227	−0.595932
$362$	10.9351	0.574736
$363$	0	0
$364$	3.06037	0.160407
$365$	6.98905	0.365824
$366$	−6.70720	−0.350591
$367$	36.4966	1.90511	0.952554	−	0.304371i	$-0.0984461\pi$
$367$	36.4966	1.90511	0.952554	+	0.304371i	$0.0984461\pi$
$368$	1.83120	0.0954579
$369$	−20.4893	−1.06663
$370$	−5.63448	−0.292923
$371$	0.123629	0.00641850
$372$	−10.9094	−0.565625
$373$	−6.23055	−0.322606	−0.161303	−	0.986905i	$-0.551570\pi$
$373$	−6.23055	−0.322606	−0.161303	+	0.986905i	$0.551570\pi$
$374$	0	0
$375$	−2.64424	−0.136548
$376$	11.9195	0.614703
$377$	10.1279	0.521612
$378$	−2.62310	−0.134918
$379$	0.463665	0.0238169	0.0119084	−	0.999929i	$-0.496209\pi$
$379$	0.463665	0.0238169	0.0119084	+	0.999929i	$0.496209\pi$
$380$	2.77079	0.142139
$381$	−36.4417	−1.86696
$382$	22.6520	1.15898
$383$	30.4947	1.55821	0.779103	−	0.626896i	$-0.215675\pi$
$383$	30.4947	1.55821	0.779103	+	0.626896i	$0.215675\pi$
$384$	−2.64424	−0.134938
$385$	0	0
$386$	−16.9764	−0.864076
$387$	11.3394	0.576416
$388$	−2.74477	−0.139345
$389$	−13.9789	−0.708758	−0.354379	−	0.935102i	$-0.615308\pi$
$389$	−13.9789	−0.708758	−0.354379	+	0.935102i	$0.615308\pi$
$390$	−8.09234	−0.409772
$391$	−0.125178	−0.00633054
$392$	1.00000	0.0505076
$393$	−12.9346	−0.652463
$394$	26.3241	1.32619
$395$	−12.4142	−0.624627
$396$	0	0
$397$	−11.9510	−0.599801	−0.299901	−	0.953970i	$-0.596953\pi$
$397$	−11.9510	−0.599801	−0.299901	+	0.953970i	$0.596953\pi$
$398$	16.9127	0.847759
$399$	−7.32664	−0.366791
$400$	1.00000	0.0500000
$401$	−14.4578	−0.721990	−0.360995	−	0.932568i	$-0.617563\pi$
$401$	−14.4578	−0.721990	−0.360995	+	0.932568i	$0.617563\pi$
$402$	5.83897	0.291221
$403$	12.6262	0.628955
$404$	−5.53961	−0.275606
$405$	−5.03990	−0.250435
$406$	3.30937	0.164241
$407$	0	0
$408$	0.180757	0.00894880
$409$	−3.54419	−0.175249	−0.0876246	−	0.996154i	$-0.527928\pi$
$409$	−3.54419	−0.175249	−0.0876246	+	0.996154i	$0.527928\pi$
$410$	−5.13257	−0.253480
$411$	50.3882	2.48547
$412$	−3.61697	−0.178195
$413$	−11.1929	−0.550768
$414$	7.31016	0.359275
$415$	−3.05366	−0.149898
$416$	3.06037	0.150047
$417$	−20.2369	−0.991003
$418$	0	0
$419$	−35.5085	−1.73471	−0.867353	−	0.497694i	$-0.834180\pi$
$419$	−35.5085	−1.73471	−0.867353	+	0.497694i	$0.834180\pi$
$420$	−2.64424	−0.129026
$421$	−26.6190	−1.29733	−0.648665	−	0.761074i	$-0.724672\pi$
$421$	−26.6190	−1.29733	−0.648665	+	0.761074i	$0.724672\pi$
$422$	−16.4483	−0.800690
$423$	47.5829	2.31356
$424$	0.123629	0.00600396
$425$	−0.0683587	−0.00331588
$426$	−36.2915	−1.75833
$427$	2.53653	0.122751
$428$	6.58182	0.318144
$429$	0	0
$430$	2.84053	0.136983
$431$	26.0439	1.25449	0.627244	−	0.778823i	$-0.284183\pi$
$431$	26.0439	1.25449	0.627244	+	0.778823i	$0.284183\pi$
$432$	−2.62310	−0.126204
$433$	1.69218	0.0813208	0.0406604	−	0.999173i	$-0.487054\pi$
$433$	1.69218	0.0813208	0.0406604	+	0.999173i	$0.487054\pi$
$434$	4.12571	0.198040
$435$	−8.75076	−0.419567
$436$	1.14986	0.0550683
$437$	5.07387	0.242716
$438$	−18.4807	−0.883044
$439$	12.8065	0.611223	0.305611	−	0.952156i	$-0.401139\pi$
$439$	12.8065	0.611223	0.305611	+	0.952156i	$0.401139\pi$
$440$	0	0
$441$	3.99201	0.190096
$442$	−0.209203	−0.00995075
$443$	0.704398	0.0334670	0.0167335	−	0.999860i	$-0.494673\pi$
$443$	0.704398	0.0334670	0.0167335	+	0.999860i	$0.494673\pi$
$444$	14.8989	0.707071
$445$	13.5707	0.643313
$446$	20.4675	0.969163
$447$	38.8105	1.83567
$448$	1.00000	0.0472456
$449$	−18.4066	−0.868660	−0.434330	−	0.900754i	$-0.643015\pi$
$449$	−18.4066	−0.868660	−0.434330	+	0.900754i	$0.643015\pi$
$450$	3.99201	0.188185
$451$	0	0
$452$	−12.1536	−0.571658
$453$	29.3338	1.37822
$454$	23.7041	1.11249
$455$	3.06037	0.143472
$456$	−7.32664	−0.343101
$457$	16.9955	0.795016	0.397508	−	0.917599i	$-0.369875\pi$
$457$	16.9955	0.795016	0.397508	+	0.917599i	$0.369875\pi$
$458$	−26.6368	−1.24466
$459$	0.179312	0.00836957
$460$	1.83120	0.0853801
$461$	13.3276	0.620729	0.310364	−	0.950618i	$-0.399549\pi$
$461$	13.3276	0.620729	0.310364	+	0.950618i	$0.399549\pi$
$462$	0	0
$463$	−34.9814	−1.62572	−0.812861	−	0.582457i	$-0.802091\pi$
$463$	−34.9814	−1.62572	−0.812861	+	0.582457i	$0.802091\pi$
$464$	3.30937	0.153634
$465$	−10.9094	−0.505910
$466$	30.3368	1.40532
$467$	−3.57861	−0.165599	−0.0827993	−	0.996566i	$-0.526386\pi$
$467$	−3.57861	−0.165599	−0.0827993	+	0.996566i	$0.526386\pi$
$468$	12.2170	0.564731
$469$	−2.20818	−0.101964
$470$	11.9195	0.549807
$471$	−34.8884	−1.60757
$472$	−11.1929	−0.515197
$473$	0	0
$474$	32.8262	1.50776
$475$	2.77079	0.127133
$476$	−0.0683587	−0.00313322
$477$	0.493528	0.0225971
$478$	−9.95180	−0.455185
$479$	18.3300	0.837518	0.418759	−	0.908097i	$-0.362465\pi$
$479$	18.3300	0.837518	0.418759	+	0.908097i	$0.362465\pi$
$480$	−2.64424	−0.120693
$481$	−17.2436	−0.786239
$482$	−30.1849	−1.37489
$483$	−4.84213	−0.220325
$484$	0	0
$485$	−2.74477	−0.124634
$486$	21.1960	0.961471
$487$	0.487041	0.0220699	0.0110350	−	0.999939i	$-0.496487\pi$
$487$	0.487041	0.0220699	0.0110350	+	0.999939i	$0.496487\pi$
$488$	2.53653	0.114823
$489$	9.80700	0.443488
$490$	1.00000	0.0451754
$491$	6.09167	0.274913	0.137457	−	0.990508i	$-0.456107\pi$
$491$	6.09167	0.274913	0.137457	+	0.990508i	$0.456107\pi$
$492$	13.5718	0.611862
$493$	−0.226224	−0.0101886
$494$	8.47964	0.381517
$495$	0	0
$496$	4.12571	0.185250
$497$	13.7247	0.615639
$498$	8.07461	0.361832
$499$	42.3141	1.89424	0.947120	−	0.320879i	$-0.103978\pi$
$499$	42.3141	1.89424	0.947120	+	0.320879i	$0.103978\pi$
$500$	1.00000	0.0447214
$501$	23.1485	1.03420
$502$	−1.16998	−0.0522188
$503$	32.3677	1.44320	0.721602	−	0.692308i	$-0.243406\pi$
$503$	32.3677	1.44320	0.721602	+	0.692308i	$0.243406\pi$
$504$	3.99201	0.177818
$505$	−5.53961	−0.246510
$506$	0	0
$507$	9.60960	0.426777
$508$	13.7815	0.611457
$509$	23.7319	1.05190	0.525950	−	0.850516i	$-0.323710\pi$
$509$	23.7319	1.05190	0.525950	+	0.850516i	$0.323710\pi$
$510$	0.180757	0.00800405
$511$	6.98905	0.309178
$512$	1.00000	0.0441942
$513$	−7.26808	−0.320893
$514$	−0.980916	−0.0432664
$515$	−3.61697	−0.159383
$516$	−7.51106	−0.330656
$517$	0	0
$518$	−5.63448	−0.247565
$519$	8.03522	0.352707
$520$	3.06037	0.134206
$521$	−30.8219	−1.35033	−0.675167	−	0.737665i	$-0.735928\pi$
$521$	−30.8219	−1.35033	−0.675167	+	0.737665i	$0.735928\pi$
$522$	13.2110	0.578230
$523$	37.6079	1.64448	0.822240	−	0.569141i	$-0.192724\pi$
$523$	37.6079	1.64448	0.822240	+	0.569141i	$0.192724\pi$
$524$	4.89161	0.213691
$525$	−2.64424	−0.115404
$526$	−15.9923	−0.697296
$527$	−0.282028	−0.0122853
$528$	0	0
$529$	−19.6467	−0.854205
$530$	0.123629	0.00537011
$531$	−44.6823	−1.93905
$532$	2.77079	0.120129
$533$	−15.7075	−0.680369
$534$	−35.8842	−1.55286
$535$	6.58182	0.284557
$536$	−2.20818	−0.0953790
$537$	19.3026	0.832969
$538$	15.1048	0.651212
$539$	0	0
$540$	−2.62310	−0.112880
$541$	−7.18833	−0.309050	−0.154525	−	0.987989i	$-0.549385\pi$
$541$	−7.18833	−0.309050	−0.154525	+	0.987989i	$0.549385\pi$
$542$	−0.499548	−0.0214574
$543$	−28.9150	−1.24086
$544$	−0.0683587	−0.00293086
$545$	1.14986	0.0492546
$546$	−8.09234	−0.346320
$547$	17.0757	0.730103	0.365052	−	0.930987i	$-0.381051\pi$
$547$	17.0757	0.730103	0.365052	+	0.930987i	$0.381051\pi$
$548$	−19.0559	−0.814026
$549$	10.1259	0.432161
$550$	0	0
$551$	9.16957	0.390637
$552$	−4.84213	−0.206095
$553$	−12.4142	−0.527906
$554$	−11.1061	−0.471854
$555$	14.8989	0.632424
$556$	7.65318	0.324567
$557$	35.7390	1.51431	0.757156	−	0.653234i	$-0.226588\pi$
$557$	35.7390	1.51431	0.757156	+	0.653234i	$0.226588\pi$
$558$	16.4699	0.697225
$559$	8.69307	0.367678
$560$	1.00000	0.0422577
$561$	0	0
$562$	15.4512	0.651770
$563$	−18.6595	−0.786404	−0.393202	−	0.919452i	$-0.628633\pi$
$563$	−18.6595	−0.786404	−0.393202	+	0.919452i	$0.628633\pi$
$564$	−31.5181	−1.32715
$565$	−12.1536	−0.511307
$566$	14.3139	0.601660
$567$	−5.03990	−0.211656
$568$	13.7247	0.575877
$569$	39.7394	1.66596	0.832981	−	0.553301i	$-0.186632\pi$
$569$	39.7394	1.66596	0.832981	+	0.553301i	$0.186632\pi$
$570$	−7.32664	−0.306879
$571$	13.3763	0.559779	0.279890	−	0.960032i	$-0.409702\pi$
$571$	13.3763	0.559779	0.279890	+	0.960032i	$0.409702\pi$
$572$	0	0
$573$	−59.8972	−2.50224
$574$	−5.13257	−0.214229
$575$	1.83120	0.0763663
$576$	3.99201	0.166334
$577$	19.8754	0.827422	0.413711	−	0.910408i	$-0.364232\pi$
$577$	19.8754	0.827422	0.413711	+	0.910408i	$0.364232\pi$
$578$	−16.9953	−0.706912
$579$	44.8897	1.86555
$580$	3.30937	0.137414
$581$	−3.05366	−0.126687
$582$	7.25783	0.300847
$583$	0	0
$584$	6.98905	0.289209
$585$	12.2170	0.505111
$586$	−17.5749	−0.726010
$587$	5.68609	0.234690	0.117345	−	0.993091i	$-0.462562\pi$
$587$	5.68609	0.234690	0.117345	+	0.993091i	$0.462562\pi$
$588$	−2.64424	−0.109047
$589$	11.4315	0.471026
$590$	−11.1929	−0.460806
$591$	−69.6072	−2.86326
$592$	−5.63448	−0.231576
$593$	28.1824	1.15731	0.578656	−	0.815571i	$-0.303577\pi$
$593$	28.1824	1.15731	0.578656	+	0.815571i	$0.303577\pi$
$594$	0	0
$595$	−0.0683587	−0.00280243
$596$	−14.6774	−0.601208
$597$	−44.7214	−1.83032
$598$	5.60414	0.229170
$599$	36.2189	1.47987	0.739933	−	0.672681i	$-0.234857\pi$
$599$	36.2189	1.47987	0.739933	+	0.672681i	$0.234857\pi$
$600$	−2.64424	−0.107951
$601$	−14.3423	−0.585034	−0.292517	−	0.956260i	$-0.594493\pi$
$601$	−14.3423	−0.585034	−0.292517	+	0.956260i	$0.594493\pi$
$602$	2.84053	0.115772
$603$	−8.81509	−0.358978
$604$	−11.0935	−0.451387
$605$	0	0
$606$	14.6481	0.595037
$607$	−3.54637	−0.143943	−0.0719714	−	0.997407i	$-0.522929\pi$
$607$	−3.54637	−0.143943	−0.0719714	+	0.997407i	$0.522929\pi$
$608$	2.77079	0.112370
$609$	−8.75076	−0.354599
$610$	2.53653	0.102701
$611$	36.4781	1.47575
$612$	−0.272888	−0.0110309
$613$	−20.4324	−0.825259	−0.412629	−	0.910899i	$-0.635390\pi$
$613$	−20.4324	−0.825259	−0.412629	+	0.910899i	$0.635390\pi$
$614$	5.38032	0.217132
$615$	13.5718	0.547266
$616$	0	0
$617$	19.3755	0.780028	0.390014	−	0.920809i	$-0.372470\pi$
$617$	19.3755	0.780028	0.390014	+	0.920809i	$0.372470\pi$
$618$	9.56413	0.384726
$619$	−6.00523	−0.241371	−0.120685	−	0.992691i	$-0.538509\pi$
$619$	−6.00523	−0.241371	−0.120685	+	0.992691i	$0.538509\pi$
$620$	4.12571	0.165693
$621$	−4.80343	−0.192755
$622$	16.9028	0.677741
$623$	13.5707	0.543699
$624$	−8.09234	−0.323953
$625$	1.00000	0.0400000
$626$	−1.35523	−0.0541658
$627$	0	0
$628$	13.1941	0.526502
$629$	0.385166	0.0153576
$630$	3.99201	0.159045
$631$	21.7929	0.867562	0.433781	−	0.901018i	$-0.357179\pi$
$631$	21.7929	0.867562	0.433781	+	0.901018i	$0.357179\pi$
$632$	−12.4142	−0.493811
$633$	43.4932	1.72870
$634$	29.3217	1.16451
$635$	13.7815	0.546903
$636$	−0.326905	−0.0129626
$637$	3.06037	0.121256
$638$	0	0
$639$	54.7892	2.16743
$640$	1.00000	0.0395285
$641$	−41.0344	−1.62076	−0.810380	−	0.585904i	$-0.800739\pi$
$641$	−41.0344	−1.62076	−0.810380	+	0.585904i	$0.800739\pi$
$642$	−17.4039	−0.686877
$643$	−24.7624	−0.976534	−0.488267	−	0.872694i	$-0.662371\pi$
$643$	−24.7624	−0.976534	−0.488267	+	0.872694i	$0.662371\pi$
$644$	1.83120	0.0721594
$645$	−7.51106	−0.295748
$646$	−0.189408	−0.00745215
$647$	44.1102	1.73415	0.867076	−	0.498175i	$-0.165996\pi$
$647$	44.1102	1.73415	0.867076	+	0.498175i	$0.165996\pi$
$648$	−5.03990	−0.197986
$649$	0	0
$650$	3.06037	0.120037
$651$	−10.9094	−0.427572
$652$	−3.70882	−0.145248
$653$	−22.0286	−0.862046	−0.431023	−	0.902341i	$-0.641847\pi$
$653$	−22.0286	−0.862046	−0.431023	+	0.902341i	$0.641847\pi$
$654$	−3.04051	−0.118893
$655$	4.89161	0.191131
$656$	−5.13257	−0.200393
$657$	27.9003	1.08850
$658$	11.9195	0.464672
$659$	19.5066	0.759868	0.379934	−	0.925014i	$-0.375947\pi$
$659$	19.5066	0.759868	0.379934	+	0.925014i	$0.375947\pi$
$660$	0	0
$661$	8.75637	0.340583	0.170292	−	0.985394i	$-0.445529\pi$
$661$	8.75637	0.340583	0.170292	+	0.985394i	$0.445529\pi$
$662$	7.10546	0.276161
$663$	0.553182	0.0214838
$664$	−3.05366	−0.118505
$665$	2.77079	0.107447
$666$	−22.4929	−0.871582
$667$	6.06011	0.234648
$668$	−8.75429	−0.338714
$669$	−54.1209	−2.09244
$670$	−2.20818	−0.0853096
$671$	0	0
$672$	−2.64424	−0.102004
$673$	−2.41083	−0.0929306	−0.0464653	−	0.998920i	$-0.514796\pi$
$673$	−2.41083	−0.0929306	−0.0464653	+	0.998920i	$0.514796\pi$
$674$	28.7650	1.10798
$675$	−2.62310	−0.100963
$676$	−3.63416	−0.139776
$677$	2.32293	0.0892776	0.0446388	−	0.999003i	$-0.485786\pi$
$677$	2.32293	0.0892776	0.0446388	+	0.999003i	$0.485786\pi$
$678$	32.1371	1.23422
$679$	−2.74477	−0.105335
$680$	−0.0683587	−0.00262144
$681$	−62.6792	−2.40187
$682$	0	0
$683$	−4.35856	−0.166776	−0.0833879	−	0.996517i	$-0.526574\pi$
$683$	−4.35856	−0.166776	−0.0833879	+	0.996517i	$0.526574\pi$
$684$	11.0610	0.422929
$685$	−19.0559	−0.728087
$686$	1.00000	0.0381802
$687$	70.4342	2.68723
$688$	2.84053	0.108294
$689$	0.378350	0.0144140
$690$	−4.84213	−0.184337
$691$	−20.4837	−0.779236	−0.389618	−	0.920977i	$-0.627393\pi$
$691$	−20.4837	−0.779236	−0.389618	+	0.920977i	$0.627393\pi$
$692$	−3.03876	−0.115516
$693$	0	0
$694$	−25.7893	−0.978950
$695$	7.65318	0.290302
$696$	−8.75076	−0.331697
$697$	0.350856	0.0132896
$698$	36.6973	1.38901
$699$	−80.2177	−3.03411
$700$	1.00000	0.0377964
$701$	−25.5850	−0.966333	−0.483166	−	0.875529i	$-0.660513\pi$
$701$	−25.5850	−0.966333	−0.483166	+	0.875529i	$0.660513\pi$
$702$	−8.02766	−0.302984
$703$	−15.6120	−0.588817
$704$	0	0
$705$	−31.5181	−1.18704
$706$	16.9704	0.638688
$707$	−5.53961	−0.208339
$708$	29.5968	1.11232
$709$	−20.1461	−0.756604	−0.378302	−	0.925682i	$-0.623492\pi$
$709$	−20.1461	−0.756604	−0.378302	+	0.925682i	$0.623492\pi$
$710$	13.7247	0.515080
$711$	−49.5576	−1.85856
$712$	13.5707	0.508584
$713$	7.55500	0.282937
$714$	0.180757	0.00676465
$715$	0	0
$716$	−7.29987	−0.272809
$717$	26.3150	0.982750
$718$	21.1819	0.790501
$719$	−41.3909	−1.54362	−0.771811	−	0.635852i	$-0.780649\pi$
$719$	−41.3909	−1.54362	−0.771811	+	0.635852i	$0.780649\pi$
$720$	3.99201	0.148773
$721$	−3.61697	−0.134703
$722$	−11.3227	−0.421387
$723$	79.8162	2.96840
$724$	10.9351	0.406400
$725$	3.30937	0.122907
$726$	0	0
$727$	−18.3813	−0.681723	−0.340862	−	0.940113i	$-0.610719\pi$
$727$	−18.3813	−0.681723	−0.340862	+	0.940113i	$0.610719\pi$
$728$	3.06037	0.113425
$729$	−40.9277	−1.51584
$730$	6.98905	0.258676
$731$	−0.194175	−0.00718183
$732$	−6.70720	−0.247905
$733$	47.3817	1.75008	0.875042	−	0.484048i	$-0.160834\pi$
$733$	47.3817	1.75008	0.875042	+	0.484048i	$0.160834\pi$
$734$	36.4966	1.34711
$735$	−2.64424	−0.0975343
$736$	1.83120	0.0674989
$737$	0	0
$738$	−20.4893	−0.754220
$739$	−36.4944	−1.34247	−0.671234	−	0.741246i	$-0.734235\pi$
$739$	−36.4944	−1.34247	−0.671234	+	0.741246i	$0.734235\pi$
$740$	−5.63448	−0.207128
$741$	−22.4222	−0.823700
$742$	0.123629	0.00453857
$743$	19.4544	0.713714	0.356857	−	0.934159i	$-0.383848\pi$
$743$	19.4544	0.713714	0.356857	+	0.934159i	$0.383848\pi$
$744$	−10.9094	−0.399957
$745$	−14.6774	−0.537737
$746$	−6.23055	−0.228117
$747$	−12.1902	−0.446017
$748$	0	0
$749$	6.58182	0.240494
$750$	−2.64424	−0.0965540
$751$	−34.0903	−1.24397	−0.621986	−	0.783029i	$-0.713674\pi$
$751$	−34.0903	−1.24397	−0.621986	+	0.783029i	$0.713674\pi$
$752$	11.9195	0.434661
$753$	3.09371	0.112741
$754$	10.1279	0.368835
$755$	−11.0935	−0.403733
$756$	−2.62310	−0.0954014
$757$	−8.47015	−0.307853	−0.153926	−	0.988082i	$-0.549192\pi$
$757$	−8.47015	−0.307853	−0.153926	+	0.988082i	$0.549192\pi$
$758$	0.463665	0.0168411
$759$	0	0
$760$	2.77079	0.100507
$761$	14.8964	0.539993	0.269997	−	0.962861i	$-0.412977\pi$
$761$	14.8964	0.539993	0.269997	+	0.962861i	$0.412977\pi$
$762$	−36.4417	−1.32014
$763$	1.14986	0.0416277
$764$	22.6520	0.819519
$765$	−0.272888	−0.00986630
$766$	30.4947	1.10182
$767$	−34.2545	−1.23686
$768$	−2.64424	−0.0954158
$769$	26.5771	0.958396	0.479198	−	0.877707i	$-0.340928\pi$
$769$	26.5771	0.958396	0.479198	+	0.877707i	$0.340928\pi$
$770$	0	0
$771$	2.59378	0.0934126
$772$	−16.9764	−0.610994
$773$	23.5243	0.846112	0.423056	−	0.906104i	$-0.360957\pi$
$773$	23.5243	0.846112	0.423056	+	0.906104i	$0.360957\pi$
$774$	11.3394	0.407587
$775$	4.12571	0.148200
$776$	−2.74477	−0.0985315
$777$	14.8989	0.534496
$778$	−13.9789	−0.501167
$779$	−14.2213	−0.509531
$780$	−8.09234	−0.289752
$781$	0	0
$782$	−0.125178	−0.00447637
$783$	−8.68081	−0.310227
$784$	1.00000	0.0357143
$785$	13.1941	0.470918
$786$	−12.9346	−0.461361
$787$	9.85816	0.351405	0.175703	−	0.984443i	$-0.443780\pi$
$787$	9.85816	0.351405	0.175703	+	0.984443i	$0.443780\pi$
$788$	26.3241	0.937757
$789$	42.2874	1.50547
$790$	−12.4142	−0.441678
$791$	−12.1536	−0.432133
$792$	0	0
$793$	7.76271	0.275662
$794$	−11.9510	−0.424123
$795$	−0.326905	−0.0115941
$796$	16.9127	0.599456
$797$	−38.6360	−1.36856	−0.684279	−	0.729220i	$-0.739883\pi$
$797$	−38.6360	−1.36856	−0.684279	+	0.729220i	$0.739883\pi$
$798$	−7.32664	−0.259360
$799$	−0.814804	−0.0288257
$800$	1.00000	0.0353553
$801$	54.1743	1.91416
$802$	−14.4578	−0.510524
$803$	0	0
$804$	5.83897	0.205925
$805$	1.83120	0.0645413
$806$	12.6262	0.444738
$807$	−39.9406	−1.40598
$808$	−5.53961	−0.194883
$809$	30.9594	1.08847	0.544237	−	0.838932i	$-0.316819\pi$
$809$	30.9594	1.08847	0.544237	+	0.838932i	$0.316819\pi$
$810$	−5.03990	−0.177084
$811$	−49.4329	−1.73582	−0.867912	−	0.496717i	$-0.834539\pi$
$811$	−49.4329	−1.73582	−0.867912	+	0.496717i	$0.834539\pi$
$812$	3.30937	0.116136
$813$	1.32092	0.0463268
$814$	0	0
$815$	−3.70882	−0.129914
$816$	0.180757	0.00632776
$817$	7.87053	0.275355
$818$	−3.54419	−0.123920
$819$	12.2170	0.426896
$820$	−5.13257	−0.179237
$821$	23.1278	0.807167	0.403584	−	0.914943i	$-0.367764\pi$
$821$	23.1278	0.807167	0.403584	+	0.914943i	$0.367764\pi$
$822$	50.3882	1.75749
$823$	−36.0554	−1.25681	−0.628406	−	0.777885i	$-0.716292\pi$
$823$	−36.0554	−1.25681	−0.628406	+	0.777885i	$0.716292\pi$
$824$	−3.61697	−0.126003
$825$	0	0
$826$	−11.1929	−0.389452
$827$	−10.3899	−0.361293	−0.180647	−	0.983548i	$-0.557819\pi$
$827$	−10.3899	−0.361293	−0.180647	+	0.983548i	$0.557819\pi$
$828$	7.31016	0.254046
$829$	37.4379	1.30027	0.650136	−	0.759818i	$-0.274712\pi$
$829$	37.4379	1.30027	0.650136	+	0.759818i	$0.274712\pi$
$830$	−3.05366	−0.105994
$831$	29.3672	1.01874
$832$	3.06037	0.106099
$833$	−0.0683587	−0.00236849
$834$	−20.2369	−0.700745
$835$	−8.75429	−0.302955
$836$	0	0
$837$	−10.8222	−0.374069
$838$	−35.5085	−1.22662
$839$	−32.6640	−1.12769	−0.563843	−	0.825882i	$-0.690678\pi$
$839$	−32.6640	−1.12769	−0.563843	+	0.825882i	$0.690678\pi$
$840$	−2.64424	−0.0912350
$841$	−18.0481	−0.622348
$842$	−26.6190	−0.917351
$843$	−40.8567	−1.40718
$844$	−16.4483	−0.566173
$845$	−3.63416	−0.125019
$846$	47.5829	1.63593
$847$	0	0
$848$	0.123629	0.00424544
$849$	−37.8495	−1.29899
$850$	−0.0683587	−0.00234468
$851$	−10.3179	−0.353692
$852$	−36.2915	−1.24333
$853$	−21.4274	−0.733659	−0.366830	−	0.930288i	$-0.619557\pi$
$853$	−21.4274	−0.733659	−0.366830	+	0.930288i	$0.619557\pi$
$854$	2.53653	0.0867983
$855$	11.0610	0.378279
$856$	6.58182	0.224962
$857$	−46.6805	−1.59457	−0.797287	−	0.603600i	$-0.793732\pi$
$857$	−46.6805	−1.59457	−0.797287	+	0.603600i	$0.793732\pi$
$858$	0	0
$859$	34.0149	1.16057	0.580287	−	0.814412i	$-0.302940\pi$
$859$	34.0149	1.16057	0.580287	+	0.814412i	$0.302940\pi$
$860$	2.84053	0.0968614
$861$	13.5718	0.462524
$862$	26.0439	0.887057
$863$	−5.55865	−0.189219	−0.0946094	−	0.995514i	$-0.530160\pi$
$863$	−5.55865	−0.189219	−0.0946094	+	0.995514i	$0.530160\pi$
$864$	−2.62310	−0.0892398
$865$	−3.03876	−0.103321
$866$	1.69218	0.0575025
$867$	44.9397	1.52623
$868$	4.12571	0.140036
$869$	0	0
$870$	−8.75076	−0.296679
$871$	−6.75785	−0.228981
$872$	1.14986	0.0389392
$873$	−10.9571	−0.370843
$874$	5.07387	0.171626
$875$	1.00000	0.0338062
$876$	−18.4807	−0.624406
$877$	−18.3183	−0.618564	−0.309282	−	0.950970i	$-0.600089\pi$
$877$	−18.3183	−0.618564	−0.309282	+	0.950970i	$0.600089\pi$
$878$	12.8065	0.432200
$879$	46.4721	1.56747
$880$	0	0
$881$	−0.0269589	−0.000908270 0	−0.000454135	−	1.00000i	$-0.500145\pi$
$881$	−0.0269589	−0.000908270 0	−0.000454135		1.00000i	$0.500145\pi$
$882$	3.99201	0.134418
$883$	−5.28336	−0.177799	−0.0888997	−	0.996041i	$-0.528335\pi$
$883$	−5.28336	−0.177799	−0.0888997	+	0.996041i	$0.528335\pi$
$884$	−0.209203	−0.00703625
$885$	29.5968	0.994886
$886$	0.704398	0.0236647
$887$	39.7555	1.33486	0.667430	−	0.744672i	$-0.267394\pi$
$887$	39.7555	1.33486	0.667430	+	0.744672i	$0.267394\pi$
$888$	14.8989	0.499975
$889$	13.7815	0.462218
$890$	13.5707	0.454891
$891$	0	0
$892$	20.4675	0.685302
$893$	33.0266	1.10519
$894$	38.8105	1.29802
$895$	−7.29987	−0.244008
$896$	1.00000	0.0334077
$897$	−14.8187	−0.494782
$898$	−18.4066	−0.614235
$899$	13.6535	0.455369
$900$	3.99201	0.133067
$901$	−0.00845113	−0.000281548 0
$902$	0	0
$903$	−7.51106	−0.249952
$904$	−12.1536	−0.404223
$905$	10.9351	0.363495
$906$	29.3338	0.974551
$907$	−5.61591	−0.186473	−0.0932367	−	0.995644i	$-0.529721\pi$
$907$	−5.61591	−0.186473	−0.0932367	+	0.995644i	$0.529721\pi$
$908$	23.7041	0.786647
$909$	−22.1142	−0.733481
$910$	3.06037	0.101450
$911$	−28.1487	−0.932609	−0.466304	−	0.884624i	$-0.654415\pi$
$911$	−28.1487	−0.932609	−0.466304	+	0.884624i	$0.654415\pi$
$912$	−7.32664	−0.242609
$913$	0	0
$914$	16.9955	0.562161
$915$	−6.70720	−0.221733
$916$	−26.6368	−0.880106
$917$	4.89161	0.161535
$918$	0.179312	0.00591818
$919$	47.6030	1.57028	0.785140	−	0.619319i	$-0.212591\pi$
$919$	47.6030	1.57028	0.785140	+	0.619319i	$0.212591\pi$
$920$	1.83120	0.0603728
$921$	−14.2269	−0.468791
$922$	13.3276	0.438921
$923$	42.0027	1.38254
$924$	0	0
$925$	−5.63448	−0.185261
$926$	−34.9814	−1.14956
$927$	−14.4390	−0.474238
$928$	3.30937	0.108635
$929$	−38.1848	−1.25280	−0.626401	−	0.779501i	$-0.715473\pi$
$929$	−38.1848	−1.25280	−0.626401	+	0.779501i	$0.715473\pi$
$930$	−10.9094	−0.357732
$931$	2.77079	0.0908091
$932$	30.3368	0.993714
$933$	−44.6951	−1.46325
$934$	−3.57861	−0.117096
$935$	0	0
$936$	12.2170	0.399325
$937$	−0.397595	−0.0129889	−0.00649443	−	0.999979i	$-0.502067\pi$
$937$	−0.397595	−0.0129889	−0.00649443	+	0.999979i	$0.502067\pi$
$938$	−2.20818	−0.0720998
$939$	3.58355	0.116945
$940$	11.9195	0.388772
$941$	−6.77789	−0.220953	−0.110477	−	0.993879i	$-0.535238\pi$
$941$	−6.77789	−0.220953	−0.110477	+	0.993879i	$0.535238\pi$
$942$	−34.8884	−1.13673
$943$	−9.39876	−0.306066
$944$	−11.1929	−0.364299
$945$	−2.62310	−0.0853296
$946$	0	0
$947$	−10.5378	−0.342432	−0.171216	−	0.985234i	$-0.554770\pi$
$947$	−10.5378	−0.342432	−0.171216	+	0.985234i	$0.554770\pi$
$948$	32.8262	1.06614
$949$	21.3891	0.694318
$950$	2.77079	0.0898964
$951$	−77.5335	−2.51420
$952$	−0.0683587	−0.00221552
$953$	−9.44810	−0.306054	−0.153027	−	0.988222i	$-0.548902\pi$
$953$	−9.44810	−0.306054	−0.153027	+	0.988222i	$0.548902\pi$
$954$	0.493528	0.0159786
$955$	22.6520	0.733000
$956$	−9.95180	−0.321864
$957$	0	0
$958$	18.3300	0.592215
$959$	−19.0559	−0.615346
$960$	−2.64424	−0.0853425
$961$	−13.9785	−0.450920
$962$	−17.2436	−0.555955
$963$	26.2747	0.846689
$964$	−30.1849	−0.972191
$965$	−16.9764	−0.546490
$966$	−4.84213	−0.155793
$967$	47.0752	1.51384	0.756918	−	0.653509i	$-0.226704\pi$
$967$	47.0752	1.51384	0.756918	+	0.653509i	$0.226704\pi$
$968$	0	0
$969$	0.500840	0.0160893
$970$	−2.74477	−0.0881293
$971$	17.2012	0.552012	0.276006	−	0.961156i	$-0.410989\pi$
$971$	17.2012	0.552012	0.276006	+	0.961156i	$0.410989\pi$
$972$	21.1960	0.679863
$973$	7.65318	0.245350
$974$	0.487041	0.0156058
$975$	−8.09234	−0.259162
$976$	2.53653	0.0811924
$977$	−6.75798	−0.216207	−0.108103	−	0.994140i	$-0.534478\pi$
$977$	−6.75798	−0.216207	−0.108103	+	0.994140i	$0.534478\pi$
$978$	9.80700	0.313593
$979$	0	0
$980$	1.00000	0.0319438
$981$	4.59025	0.146555
$982$	6.09167	0.194393
$983$	−45.4819	−1.45065	−0.725323	−	0.688408i	$-0.758310\pi$
$983$	−45.4819	−1.45065	−0.725323	+	0.688408i	$0.758310\pi$
$984$	13.5718	0.432652
$985$	26.3241	0.838755
$986$	−0.226224	−0.00720444
$987$	−31.5181	−1.00323
$988$	8.47964	0.269773
$989$	5.20158	0.165401
$990$	0	0
$991$	−11.7391	−0.372906	−0.186453	−	0.982464i	$-0.559699\pi$
$991$	−11.7391	−0.372906	−0.186453	+	0.982464i	$0.559699\pi$
$992$	4.12571	0.130991
$993$	−18.7885	−0.596236
$994$	13.7247	0.435322
$995$	16.9127	0.536170
$996$	8.07461	0.255854
$997$	−17.1623	−0.543536	−0.271768	−	0.962363i	$-0.587608\pi$
$997$	−17.1623	−0.543536	−0.271768	+	0.962363i	$0.587608\pi$
$998$	42.3141	1.33943
$999$	14.7798	0.467613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.de.1.2		6
11.3	even	5		770.2.n.i.141.3	yes	12
11.4	even	5		770.2.n.i.71.3	✓	12
11.10	odd	2		8470.2.a.cy.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.71.3	✓	12	11.4	even	5
770.2.n.i.141.3	yes	12	11.3	even	5
8470.2.a.cy.1.2		6	11.10	odd	2
8470.2.a.de.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.64424 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.64424 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.99201 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.64424 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.64424 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.99201 q^{9} +1.00000 q^{10} -2.64424 q^{12} +3.06037 q^{13} +1.00000 q^{14} -2.64424 q^{15} +1.00000 q^{16} -0.0683587 q^{17} +3.99201 q^{18} +2.77079 q^{19} +1.00000 q^{20} -2.64424 q^{21} +1.83120 q^{23} -2.64424 q^{24} +1.00000 q^{25} +3.06037 q^{26} -2.62310 q^{27} +1.00000 q^{28} +3.30937 q^{29} -2.64424 q^{30} +4.12571 q^{31} +1.00000 q^{32} -0.0683587 q^{34} +1.00000 q^{35} +3.99201 q^{36} -5.63448 q^{37} +2.77079 q^{38} -8.09234 q^{39} +1.00000 q^{40} -5.13257 q^{41} -2.64424 q^{42} +2.84053 q^{43} +3.99201 q^{45} +1.83120 q^{46} +11.9195 q^{47} -2.64424 q^{48} +1.00000 q^{49} +1.00000 q^{50} +0.180757 q^{51} +3.06037 q^{52} +0.123629 q^{53} -2.62310 q^{54} +1.00000 q^{56} -7.32664 q^{57} +3.30937 q^{58} -11.1929 q^{59} -2.64424 q^{60} +2.53653 q^{61} +4.12571 q^{62} +3.99201 q^{63} +1.00000 q^{64} +3.06037 q^{65} -2.20818 q^{67} -0.0683587 q^{68} -4.84213 q^{69} +1.00000 q^{70} +13.7247 q^{71} +3.99201 q^{72} +6.98905 q^{73} -5.63448 q^{74} -2.64424 q^{75} +2.77079 q^{76} -8.09234 q^{78} -12.4142 q^{79} +1.00000 q^{80} -5.03990 q^{81} -5.13257 q^{82} -3.05366 q^{83} -2.64424 q^{84} -0.0683587 q^{85} +2.84053 q^{86} -8.75076 q^{87} +13.5707 q^{89} +3.99201 q^{90} +3.06037 q^{91} +1.83120 q^{92} -10.9094 q^{93} +11.9195 q^{94} +2.77079 q^{95} -2.64424 q^{96} -2.74477 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 15 q^{9} + 6 q^{10} + q^{12} + 2 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 7 q^{17} + 15 q^{18} + 11 q^{19} + 6 q^{20} + q^{21} - 6 q^{23} + q^{24} + 6 q^{25} + 2 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + q^{30} + 6 q^{32} + 7 q^{34} + 6 q^{35} + 15 q^{36} - 14 q^{37} + 11 q^{38} + 20 q^{39} + 6 q^{40} + 13 q^{41} + q^{42} + 19 q^{43} + 15 q^{45} - 6 q^{46} + 22 q^{47} + q^{48} + 6 q^{49} + 6 q^{50} - 14 q^{51} + 2 q^{52} - 10 q^{53} + 4 q^{54} + 6 q^{56} + 32 q^{57} + 2 q^{58} - 7 q^{59} + q^{60} + 22 q^{61} + 15 q^{63} + 6 q^{64} + 2 q^{65} + 5 q^{67} + 7 q^{68} - 36 q^{69} + 6 q^{70} + 8 q^{71} + 15 q^{72} + 13 q^{73} - 14 q^{74} + q^{75} + 11 q^{76} + 20 q^{78} - 16 q^{79} + 6 q^{80} + 18 q^{81} + 13 q^{82} - 5 q^{83} + q^{84} + 7 q^{85} + 19 q^{86} + 14 q^{87} + q^{89} + 15 q^{90} + 2 q^{91} - 6 q^{92} - 42 q^{93} + 22 q^{94} + 11 q^{95} + q^{96} - 3 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 15 * q^9 + 6 * q^10 + q^12 + 2 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 7 * q^17 + 15 * q^18 + 11 * q^19 + 6 * q^20 + q^21 - 6 * q^23 + q^24 + 6 * q^25 + 2 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + q^30 + 6 * q^32 + 7 * q^34 + 6 * q^35 + 15 * q^36 - 14 * q^37 + 11 * q^38 + 20 * q^39 + 6 * q^40 + 13 * q^41 + q^42 + 19 * q^43 + 15 * q^45 - 6 * q^46 + 22 * q^47 + q^48 + 6 * q^49 + 6 * q^50 - 14 * q^51 + 2 * q^52 - 10 * q^53 + 4 * q^54 + 6 * q^56 + 32 * q^57 + 2 * q^58 - 7 * q^59 + q^60 + 22 * q^61 + 15 * q^63 + 6 * q^64 + 2 * q^65 + 5 * q^67 + 7 * q^68 - 36 * q^69 + 6 * q^70 + 8 * q^71 + 15 * q^72 + 13 * q^73 - 14 * q^74 + q^75 + 11 * q^76 + 20 * q^78 - 16 * q^79 + 6 * q^80 + 18 * q^81 + 13 * q^82 - 5 * q^83 + q^84 + 7 * q^85 + 19 * q^86 + 14 * q^87 + q^89 + 15 * q^90 + 2 * q^91 - 6 * q^92 - 42 * q^93 + 22 * q^94 + 11 * q^95 + q^96 - 3 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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