LMFDB - Embedded newform 8670.2.a.ci.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, 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("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.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:	$69.2302985525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.30652992.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} + 63x^{2} - 73 $ x^6 - 15x^4 + 63x^2 - 73
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.95952$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.60256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.60256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.49161 q^{11} +1.00000 q^{12} -2.98735 q^{13} -1.60256 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +2.37513 q^{19} +1.00000 q^{20} -1.60256 q^{21} -3.49161 q^{22} -0.784395 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.98735 q^{26} +1.00000 q^{27} -1.60256 q^{28} +10.1220 q^{29} +1.00000 q^{30} +6.28115 q^{31} +1.00000 q^{32} -3.49161 q^{33} -1.60256 q^{35} +1.00000 q^{36} +11.6103 q^{37} +2.37513 q^{38} -2.98735 q^{39} +1.00000 q^{40} +4.85491 q^{41} -1.60256 q^{42} -5.92125 q^{43} -3.49161 q^{44} +1.00000 q^{45} -0.784395 q^{46} +1.44121 q^{47} +1.00000 q^{48} -4.43180 q^{49} +1.00000 q^{50} -2.98735 q^{52} -6.25743 q^{53} +1.00000 q^{54} -3.49161 q^{55} -1.60256 q^{56} +2.37513 q^{57} +10.1220 q^{58} +3.25038 q^{59} +1.00000 q^{60} -6.21702 q^{61} +6.28115 q^{62} -1.60256 q^{63} +1.00000 q^{64} -2.98735 q^{65} -3.49161 q^{66} +7.98876 q^{67} -0.784395 q^{69} -1.60256 q^{70} +2.35891 q^{71} +1.00000 q^{72} +3.79290 q^{73} +11.6103 q^{74} +1.00000 q^{75} +2.37513 q^{76} +5.59552 q^{77} -2.98735 q^{78} -4.37179 q^{79} +1.00000 q^{80} +1.00000 q^{81} +4.85491 q^{82} +12.0259 q^{83} -1.60256 q^{84} -5.92125 q^{86} +10.1220 q^{87} -3.49161 q^{88} -2.14774 q^{89} +1.00000 q^{90} +4.78741 q^{91} -0.784395 q^{92} +6.28115 q^{93} +1.44121 q^{94} +2.37513 q^{95} +1.00000 q^{96} -0.268171 q^{97} -4.43180 q^{98} -3.49161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} + 6 q^{18} + 6 q^{19} + 6 q^{20} + 6 q^{21} + 6 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 6 q^{27} + 6 q^{28} + 12 q^{29} + 6 q^{30} + 6 q^{31} + 6 q^{32} + 6 q^{33} + 6 q^{35} + 6 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 6 q^{42} + 18 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} + 6 q^{48} + 18 q^{49} + 6 q^{50} + 6 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} - 30 q^{59} + 6 q^{60} - 24 q^{61} + 6 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 6 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 6 q^{73} + 6 q^{74} + 6 q^{75} + 6 q^{76} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 18 q^{83} + 6 q^{84} + 18 q^{86} + 12 q^{87} + 6 q^{88} - 12 q^{89} + 6 q^{90} + 6 q^{91} + 6 q^{92} + 6 q^{93} - 6 q^{94} + 6 q^{95} + 6 q^{96} + 18 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 + 6 * q^18 + 6 * q^19 + 6 * q^20 + 6 * q^21 + 6 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 6 * q^27 + 6 * q^28 + 12 * q^29 + 6 * q^30 + 6 * q^31 + 6 * q^32 + 6 * q^33 + 6 * q^35 + 6 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 6 * q^42 + 18 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 + 6 * q^48 + 18 * q^49 + 6 * q^50 + 6 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 - 30 * q^59 + 6 * q^60 - 24 * q^61 + 6 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 6 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 6 * q^73 + 6 * q^74 + 6 * q^75 + 6 * q^76 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 18 * q^83 + 6 * q^84 + 18 * q^86 + 12 * q^87 + 6 * q^88 - 12 * q^89 + 6 * q^90 + 6 * q^91 + 6 * q^92 + 6 * q^93 - 6 * q^94 + 6 * q^95 + 6 * q^96 + 18 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−1.60256	−0.605711	−0.302855	−	0.953037i	$-0.597940\pi$
$7$	−1.60256	−0.605711	−0.302855	+	0.953037i	$0.597940\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−3.49161	−1.05276	−0.526380	−	0.850249i	$-0.676451\pi$
$11$	−3.49161	−1.05276	−0.526380	+	0.850249i	$0.676451\pi$
$12$	1.00000	0.288675
$13$	−2.98735	−0.828543	−0.414271	−	0.910153i	$-0.635964\pi$
$13$	−2.98735	−0.828543	−0.414271	+	0.910153i	$0.635964\pi$
$14$	−1.60256	−0.428302
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	2.37513	0.544892	0.272446	−	0.962171i	$-0.412167\pi$
$19$	2.37513	0.544892	0.272446	+	0.962171i	$0.412167\pi$
$20$	1.00000	0.223607
$21$	−1.60256	−0.349707
$22$	−3.49161	−0.744414
$23$	−0.784395	−0.163558	−0.0817788	−	0.996651i	$-0.526060\pi$
$23$	−0.784395	−0.163558	−0.0817788	+	0.996651i	$0.526060\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.98735	−0.585868
$27$	1.00000	0.192450
$28$	−1.60256	−0.302855
$29$	10.1220	1.87961	0.939804	−	0.341713i	$-0.111007\pi$
$29$	10.1220	1.87961	0.939804	+	0.341713i	$0.111007\pi$
$30$	1.00000	0.182574
$31$	6.28115	1.12813	0.564064	−	0.825731i	$-0.309237\pi$
$31$	6.28115	1.12813	0.564064	+	0.825731i	$0.309237\pi$
$32$	1.00000	0.176777
$33$	−3.49161	−0.607811
$34$	0	0
$35$	−1.60256	−0.270882
$36$	1.00000	0.166667
$37$	11.6103	1.90871	0.954357	−	0.298668i	$-0.0965422\pi$
$37$	11.6103	1.90871	0.954357	+	0.298668i	$0.0965422\pi$
$38$	2.37513	0.385297
$39$	−2.98735	−0.478359
$40$	1.00000	0.158114
$41$	4.85491	0.758210	0.379105	−	0.925354i	$-0.376232\pi$
$41$	4.85491	0.758210	0.379105	+	0.925354i	$0.376232\pi$
$42$	−1.60256	−0.247280
$43$	−5.92125	−0.902982	−0.451491	−	0.892276i	$-0.649108\pi$
$43$	−5.92125	−0.902982	−0.451491	+	0.892276i	$0.649108\pi$
$44$	−3.49161	−0.526380
$45$	1.00000	0.149071
$46$	−0.784395	−0.115653
$47$	1.44121	0.210222	0.105111	−	0.994461i	$-0.466480\pi$
$47$	1.44121	0.210222	0.105111	+	0.994461i	$0.466480\pi$
$48$	1.00000	0.144338
$49$	−4.43180	−0.633115
$50$	1.00000	0.141421
$51$	0	0
$52$	−2.98735	−0.414271
$53$	−6.25743	−0.859523	−0.429762	−	0.902942i	$-0.641402\pi$
$53$	−6.25743	−0.859523	−0.429762	+	0.902942i	$0.641402\pi$
$54$	1.00000	0.136083
$55$	−3.49161	−0.470809
$56$	−1.60256	−0.214151
$57$	2.37513	0.314593
$58$	10.1220	1.32908
$59$	3.25038	0.423164	0.211582	−	0.977360i	$-0.432139\pi$
$59$	3.25038	0.423164	0.211582	+	0.977360i	$0.432139\pi$
$60$	1.00000	0.129099
$61$	−6.21702	−0.796007	−0.398004	−	0.917384i	$-0.630297\pi$
$61$	−6.21702	−0.796007	−0.398004	+	0.917384i	$0.630297\pi$
$62$	6.28115	0.797707
$63$	−1.60256	−0.201904
$64$	1.00000	0.125000
$65$	−2.98735	−0.370536
$66$	−3.49161	−0.429788
$67$	7.98876	0.975983	0.487991	−	0.872848i	$-0.337730\pi$
$67$	7.98876	0.975983	0.487991	+	0.872848i	$0.337730\pi$
$68$	0	0
$69$	−0.784395	−0.0944301
$70$	−1.60256	−0.191543
$71$	2.35891	0.279951	0.139975	−	0.990155i	$-0.455298\pi$
$71$	2.35891	0.279951	0.139975	+	0.990155i	$0.455298\pi$
$72$	1.00000	0.117851
$73$	3.79290	0.443925	0.221962	−	0.975055i	$-0.428754\pi$
$73$	3.79290	0.443925	0.221962	+	0.975055i	$0.428754\pi$
$74$	11.6103	1.34966
$75$	1.00000	0.115470
$76$	2.37513	0.272446
$77$	5.59552	0.637668
$78$	−2.98735	−0.338251
$79$	−4.37179	−0.491865	−0.245932	−	0.969287i	$-0.579094\pi$
$79$	−4.37179	−0.491865	−0.245932	+	0.969287i	$0.579094\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	4.85491	0.536135
$83$	12.0259	1.32001	0.660005	−	0.751261i	$-0.270554\pi$
$83$	12.0259	1.32001	0.660005	+	0.751261i	$0.270554\pi$
$84$	−1.60256	−0.174854
$85$	0	0
$86$	−5.92125	−0.638505
$87$	10.1220	1.08519
$88$	−3.49161	−0.372207
$89$	−2.14774	−0.227660	−0.113830	−	0.993500i	$-0.536312\pi$
$89$	−2.14774	−0.227660	−0.113830	+	0.993500i	$0.536312\pi$
$90$	1.00000	0.105409
$91$	4.78741	0.501857
$92$	−0.784395	−0.0817788
$93$	6.28115	0.651325
$94$	1.44121	0.148649
$95$	2.37513	0.243683
$96$	1.00000	0.102062
$97$	−0.268171	−0.0272287	−0.0136143	−	0.999907i	$-0.504334\pi$
$97$	−0.268171	−0.0272287	−0.0136143	+	0.999907i	$0.504334\pi$
$98$	−4.43180	−0.447680
$99$	−3.49161	−0.350920
$100$	1.00000	0.100000
$101$	−10.8530	−1.07991	−0.539955	−	0.841694i	$-0.681559\pi$
$101$	−10.8530	−1.07991	−0.539955	+	0.841694i	$0.681559\pi$
$102$	0	0
$103$	14.2589	1.40497	0.702484	−	0.711699i	$-0.252074\pi$
$103$	14.2589	1.40497	0.702484	+	0.711699i	$0.252074\pi$
$104$	−2.98735	−0.292934
$105$	−1.60256	−0.156394
$106$	−6.25743	−0.607775
$107$	−5.66263	−0.547427	−0.273714	−	0.961811i	$-0.588252\pi$
$107$	−5.66263	−0.547427	−0.273714	+	0.961811i	$0.588252\pi$
$108$	1.00000	0.0962250
$109$	8.56433	0.820314	0.410157	−	0.912015i	$-0.365474\pi$
$109$	8.56433	0.820314	0.410157	+	0.912015i	$0.365474\pi$
$110$	−3.49161	−0.332912
$111$	11.6103	1.10200
$112$	−1.60256	−0.151428
$113$	−4.95883	−0.466488	−0.233244	−	0.972418i	$-0.574934\pi$
$113$	−4.95883	−0.466488	−0.233244	+	0.972418i	$0.574934\pi$
$114$	2.37513	0.222451
$115$	−0.784395	−0.0731452
$116$	10.1220	0.939804
$117$	−2.98735	−0.276181
$118$	3.25038	0.299222
$119$	0	0
$120$	1.00000	0.0912871
$121$	1.19135	0.108304
$122$	−6.21702	−0.562862
$123$	4.85491	0.437753
$124$	6.28115	0.564064
$125$	1.00000	0.0894427
$126$	−1.60256	−0.142767
$127$	15.8640	1.40770	0.703851	−	0.710348i	$-0.251462\pi$
$127$	15.8640	1.40770	0.703851	+	0.710348i	$0.251462\pi$
$128$	1.00000	0.0883883
$129$	−5.92125	−0.521337
$130$	−2.98735	−0.262008
$131$	18.0373	1.57593	0.787963	−	0.615723i	$-0.211136\pi$
$131$	18.0373	1.57593	0.787963	+	0.615723i	$0.211136\pi$
$132$	−3.49161	−0.303906
$133$	−3.80628	−0.330047
$134$	7.98876	0.690124
$135$	1.00000	0.0860663
$136$	0	0
$137$	16.2963	1.39229	0.696145	−	0.717901i	$-0.254897\pi$
$137$	16.2963	1.39229	0.696145	+	0.717901i	$0.254897\pi$
$138$	−0.784395	−0.0667721
$139$	2.04580	0.173522	0.0867611	−	0.996229i	$-0.472348\pi$
$139$	2.04580	0.173522	0.0867611	+	0.996229i	$0.472348\pi$
$140$	−1.60256	−0.135441
$141$	1.44121	0.121371
$142$	2.35891	0.197955
$143$	10.4307	0.872257
$144$	1.00000	0.0833333
$145$	10.1220	0.840587
$146$	3.79290	0.313902
$147$	−4.43180	−0.365529
$148$	11.6103	0.954357
$149$	−14.9980	−1.22868	−0.614341	−	0.789040i	$-0.710578\pi$
$149$	−14.9980	−1.22868	−0.614341	+	0.789040i	$0.710578\pi$
$150$	1.00000	0.0816497
$151$	0.264269	0.0215059	0.0107530	−	0.999942i	$-0.496577\pi$
$151$	0.264269	0.0215059	0.0107530	+	0.999942i	$0.496577\pi$
$152$	2.37513	0.192648
$153$	0	0
$154$	5.59552	0.450900
$155$	6.28115	0.504514
$156$	−2.98735	−0.239180
$157$	−3.05453	−0.243778	−0.121889	−	0.992544i	$-0.538895\pi$
$157$	−3.05453	−0.243778	−0.121889	+	0.992544i	$0.538895\pi$
$158$	−4.37179	−0.347801
$159$	−6.25743	−0.496246
$160$	1.00000	0.0790569
$161$	1.25704	0.0990687
$162$	1.00000	0.0785674
$163$	17.5727	1.37640	0.688199	−	0.725522i	$-0.258402\pi$
$163$	17.5727	1.37640	0.688199	+	0.725522i	$0.258402\pi$
$164$	4.85491	0.379105
$165$	−3.49161	−0.271822
$166$	12.0259	0.933388
$167$	23.8440	1.84510	0.922550	−	0.385877i	$-0.126101\pi$
$167$	23.8440	1.84510	0.922550	+	0.385877i	$0.126101\pi$
$168$	−1.60256	−0.123640
$169$	−4.07572	−0.313517
$170$	0	0
$171$	2.37513	0.181631
$172$	−5.92125	−0.451491
$173$	10.8188	0.822542	0.411271	−	0.911513i	$-0.365085\pi$
$173$	10.8188	0.822542	0.411271	+	0.911513i	$0.365085\pi$
$174$	10.1220	0.767347
$175$	−1.60256	−0.121142
$176$	−3.49161	−0.263190
$177$	3.25038	0.244314
$178$	−2.14774	−0.160980
$179$	12.8670	0.961721	0.480861	−	0.876797i	$-0.340324\pi$
$179$	12.8670	0.961721	0.480861	+	0.876797i	$0.340324\pi$
$180$	1.00000	0.0745356
$181$	3.15419	0.234449	0.117225	−	0.993105i	$-0.462600\pi$
$181$	3.15419	0.234449	0.117225	+	0.993105i	$0.462600\pi$
$182$	4.78741	0.354867
$183$	−6.21702	−0.459575
$184$	−0.784395	−0.0578264
$185$	11.6103	0.853603
$186$	6.28115	0.460556
$187$	0	0
$188$	1.44121	0.105111
$189$	−1.60256	−0.116569
$190$	2.37513	0.172310
$191$	−7.21412	−0.521995	−0.260998	−	0.965339i	$-0.584051\pi$
$191$	−7.21412	−0.521995	−0.260998	+	0.965339i	$0.584051\pi$
$192$	1.00000	0.0721688
$193$	26.2136	1.88689	0.943447	−	0.331525i	$-0.107563\pi$
$193$	26.2136	1.88689	0.943447	+	0.331525i	$0.107563\pi$
$194$	−0.268171	−0.0192536
$195$	−2.98735	−0.213929
$196$	−4.43180	−0.316557
$197$	1.72607	0.122977	0.0614885	−	0.998108i	$-0.480415\pi$
$197$	1.72607	0.122977	0.0614885	+	0.998108i	$0.480415\pi$
$198$	−3.49161	−0.248138
$199$	−18.5956	−1.31821	−0.659105	−	0.752051i	$-0.729065\pi$
$199$	−18.5956	−1.31821	−0.659105	+	0.752051i	$0.729065\pi$
$200$	1.00000	0.0707107
$201$	7.98876	0.563484
$202$	−10.8530	−0.763611
$203$	−16.2211	−1.13850
$204$	0	0
$205$	4.85491	0.339082
$206$	14.2589	0.993463
$207$	−0.784395	−0.0545192
$208$	−2.98735	−0.207136
$209$	−8.29302	−0.573640
$210$	−1.60256	−0.110587
$211$	20.9409	1.44163	0.720815	−	0.693127i	$-0.243768\pi$
$211$	20.9409	1.44163	0.720815	+	0.693127i	$0.243768\pi$
$212$	−6.25743	−0.429762
$213$	2.35891	0.161630
$214$	−5.66263	−0.387089
$215$	−5.92125	−0.403826
$216$	1.00000	0.0680414
$217$	−10.0659	−0.683319
$218$	8.56433	0.580049
$219$	3.79290	0.256300
$220$	−3.49161	−0.235404
$221$	0	0
$222$	11.6103	0.779229
$223$	−4.09278	−0.274073	−0.137036	−	0.990566i	$-0.543758\pi$
$223$	−4.09278	−0.274073	−0.137036	+	0.990566i	$0.543758\pi$
$224$	−1.60256	−0.107076
$225$	1.00000	0.0666667
$226$	−4.95883	−0.329857
$227$	10.3530	0.687152	0.343576	−	0.939125i	$-0.388362\pi$
$227$	10.3530	0.687152	0.343576	+	0.939125i	$0.388362\pi$
$228$	2.37513	0.157297
$229$	−23.2062	−1.53351	−0.766753	−	0.641942i	$-0.778129\pi$
$229$	−23.2062	−1.53351	−0.766753	+	0.641942i	$0.778129\pi$
$230$	−0.784395	−0.0517215
$231$	5.59552	0.368158
$232$	10.1220	0.664542
$233$	−17.8458	−1.16912	−0.584558	−	0.811352i	$-0.698732\pi$
$233$	−17.8458	−1.16912	−0.584558	+	0.811352i	$0.698732\pi$
$234$	−2.98735	−0.195289
$235$	1.44121	0.0940139
$236$	3.25038	0.211582
$237$	−4.37179	−0.283978
$238$	0	0
$239$	4.58848	0.296804	0.148402	−	0.988927i	$-0.452587\pi$
$239$	4.58848	0.296804	0.148402	+	0.988927i	$0.452587\pi$
$240$	1.00000	0.0645497
$241$	−15.1749	−0.977502	−0.488751	−	0.872423i	$-0.662547\pi$
$241$	−15.1749	−0.977502	−0.488751	+	0.872423i	$0.662547\pi$
$242$	1.19135	0.0765827
$243$	1.00000	0.0641500
$244$	−6.21702	−0.398004
$245$	−4.43180	−0.283137
$246$	4.85491	0.309538
$247$	−7.09534	−0.451466
$248$	6.28115	0.398853
$249$	12.0259	0.762108
$250$	1.00000	0.0632456
$251$	−15.1932	−0.958987	−0.479494	−	0.877545i	$-0.659180\pi$
$251$	−15.1932	−0.958987	−0.479494	+	0.877545i	$0.659180\pi$
$252$	−1.60256	−0.100952
$253$	2.73880	0.172187
$254$	15.8640	0.995396
$255$	0	0
$256$	1.00000	0.0625000
$257$	−19.9381	−1.24371	−0.621853	−	0.783134i	$-0.713620\pi$
$257$	−19.9381	−1.24371	−0.621853	+	0.783134i	$0.713620\pi$
$258$	−5.92125	−0.368641
$259$	−18.6061	−1.15613
$260$	−2.98735	−0.185268
$261$	10.1220	0.626536
$262$	18.0373	1.11435
$263$	−13.0708	−0.805978	−0.402989	−	0.915205i	$-0.632029\pi$
$263$	−13.0708	−0.805978	−0.402989	+	0.915205i	$0.632029\pi$
$264$	−3.49161	−0.214894
$265$	−6.25743	−0.384391
$266$	−3.80628	−0.233378
$267$	−2.14774	−0.131440
$268$	7.98876	0.487991
$269$	18.8300	1.14809	0.574044	−	0.818825i	$-0.305374\pi$
$269$	18.8300	1.14809	0.574044	+	0.818825i	$0.305374\pi$
$270$	1.00000	0.0608581
$271$	−7.45834	−0.453062	−0.226531	−	0.974004i	$-0.572738\pi$
$271$	−7.45834	−0.453062	−0.226531	+	0.974004i	$0.572738\pi$
$272$	0	0
$273$	4.78741	0.289747
$274$	16.2963	0.984498
$275$	−3.49161	−0.210552
$276$	−0.784395	−0.0472150
$277$	−20.0283	−1.20339	−0.601693	−	0.798727i	$-0.705507\pi$
$277$	−20.0283	−1.20339	−0.601693	+	0.798727i	$0.705507\pi$
$278$	2.04580	0.122699
$279$	6.28115	0.376043
$280$	−1.60256	−0.0957713
$281$	−8.96767	−0.534966	−0.267483	−	0.963563i	$-0.586192\pi$
$281$	−8.96767	−0.534966	−0.267483	+	0.963563i	$0.586192\pi$
$282$	1.44121	0.0858226
$283$	−30.3038	−1.80137	−0.900686	−	0.434470i	$-0.856936\pi$
$283$	−30.3038	−1.80137	−0.900686	+	0.434470i	$0.856936\pi$
$284$	2.35891	0.139975
$285$	2.37513	0.140690
$286$	10.4307	0.616779
$287$	−7.78029	−0.459256
$288$	1.00000	0.0589256
$289$	0	0
$290$	10.1220	0.594384
$291$	−0.268171	−0.0157205
$292$	3.79290	0.221962
$293$	−13.2296	−0.772879	−0.386440	−	0.922315i	$-0.626295\pi$
$293$	−13.2296	−0.772879	−0.386440	+	0.922315i	$0.626295\pi$
$294$	−4.43180	−0.258468
$295$	3.25038	0.189245
$296$	11.6103	0.674832
$297$	−3.49161	−0.202604
$298$	−14.9980	−0.868810
$299$	2.34327	0.135515
$300$	1.00000	0.0577350
$301$	9.48916	0.546946
$302$	0.264269	0.0152070
$303$	−10.8530	−0.623486
$304$	2.37513	0.136223
$305$	−6.21702	−0.355985
$306$	0	0
$307$	19.2521	1.09878	0.549388	−	0.835568i	$-0.314861\pi$
$307$	19.2521	1.09878	0.549388	+	0.835568i	$0.314861\pi$
$308$	5.59552	0.318834
$309$	14.2589	0.811159
$310$	6.28115	0.356745
$311$	10.9497	0.620903	0.310451	−	0.950589i	$-0.399520\pi$
$311$	10.9497	0.620903	0.310451	+	0.950589i	$0.399520\pi$
$312$	−2.98735	−0.169126
$313$	21.0626	1.19053	0.595265	−	0.803529i	$-0.297047\pi$
$313$	21.0626	1.19053	0.595265	+	0.803529i	$0.297047\pi$
$314$	−3.05453	−0.172377
$315$	−1.60256	−0.0902940
$316$	−4.37179	−0.245932
$317$	−22.6107	−1.26995	−0.634973	−	0.772535i	$-0.718989\pi$
$317$	−22.6107	−1.26995	−0.634973	+	0.772535i	$0.718989\pi$
$318$	−6.25743	−0.350899
$319$	−35.3421	−1.97878
$320$	1.00000	0.0559017
$321$	−5.66263	−0.316057
$322$	1.25704	0.0700521
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.98735	−0.165709
$326$	17.5727	0.973260
$327$	8.56433	0.473608
$328$	4.85491	0.268068
$329$	−2.30962	−0.127333
$330$	−3.49161	−0.192207
$331$	13.8364	0.760519	0.380260	−	0.924880i	$-0.375835\pi$
$331$	13.8364	0.760519	0.380260	+	0.924880i	$0.375835\pi$
$332$	12.0259	0.660005
$333$	11.6103	0.636238
$334$	23.8440	1.30468
$335$	7.98876	0.436473
$336$	−1.60256	−0.0874268
$337$	8.81167	0.480002	0.240001	−	0.970773i	$-0.422852\pi$
$337$	8.81167	0.480002	0.240001	+	0.970773i	$0.422852\pi$
$338$	−4.07572	−0.221690
$339$	−4.95883	−0.269327
$340$	0	0
$341$	−21.9313	−1.18765
$342$	2.37513	0.128432
$343$	18.3201	0.989195
$344$	−5.92125	−0.319252
$345$	−0.784395	−0.0422304
$346$	10.8188	0.581625
$347$	−14.7497	−0.791808	−0.395904	−	0.918292i	$-0.629569\pi$
$347$	−14.7497	−0.791808	−0.395904	+	0.918292i	$0.629569\pi$
$348$	10.1220	0.542596
$349$	−2.76211	−0.147852	−0.0739261	−	0.997264i	$-0.523553\pi$
$349$	−2.76211	−0.147852	−0.0739261	+	0.997264i	$0.523553\pi$
$350$	−1.60256	−0.0856604
$351$	−2.98735	−0.159453
$352$	−3.49161	−0.186103
$353$	15.9669	0.849830	0.424915	−	0.905233i	$-0.360304\pi$
$353$	15.9669	0.849830	0.424915	+	0.905233i	$0.360304\pi$
$354$	3.25038	0.172756
$355$	2.35891	0.125198
$356$	−2.14774	−0.113830
$357$	0	0
$358$	12.8670	0.680040
$359$	24.2038	1.27743	0.638713	−	0.769445i	$-0.279467\pi$
$359$	24.2038	1.27743	0.638713	+	0.769445i	$0.279467\pi$
$360$	1.00000	0.0527046
$361$	−13.3588	−0.703093
$362$	3.15419	0.165780
$363$	1.19135	0.0625295
$364$	4.78741	0.250929
$365$	3.79290	0.198529
$366$	−6.21702	−0.324969
$367$	−19.2945	−1.00716	−0.503581	−	0.863948i	$-0.667985\pi$
$367$	−19.2945	−1.00716	−0.503581	+	0.863948i	$0.667985\pi$
$368$	−0.784395	−0.0408894
$369$	4.85491	0.252737
$370$	11.6103	0.603588
$371$	10.0279	0.520623
$372$	6.28115	0.325662
$373$	10.6498	0.551424	0.275712	−	0.961240i	$-0.411086\pi$
$373$	10.6498	0.551424	0.275712	+	0.961240i	$0.411086\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	1.44121	0.0743245
$377$	−30.2380	−1.55734
$378$	−1.60256	−0.0824268
$379$	−20.1097	−1.03297	−0.516483	−	0.856298i	$-0.672759\pi$
$379$	−20.1097	−1.03297	−0.516483	+	0.856298i	$0.672759\pi$
$380$	2.37513	0.121841
$381$	15.8640	0.812737
$382$	−7.21412	−0.369106
$383$	−16.7143	−0.854062	−0.427031	−	0.904237i	$-0.640441\pi$
$383$	−16.7143	−0.854062	−0.427031	+	0.904237i	$0.640441\pi$
$384$	1.00000	0.0510310
$385$	5.59552	0.285174
$386$	26.2136	1.33423
$387$	−5.92125	−0.300994
$388$	−0.268171	−0.0136143
$389$	28.2413	1.43189	0.715945	−	0.698156i	$-0.245996\pi$
$389$	28.2413	1.43189	0.715945	+	0.698156i	$0.245996\pi$
$390$	−2.98735	−0.151271
$391$	0	0
$392$	−4.43180	−0.223840
$393$	18.0373	0.909861
$394$	1.72607	0.0869579
$395$	−4.37179	−0.219969
$396$	−3.49161	−0.175460
$397$	−6.39291	−0.320851	−0.160426	−	0.987048i	$-0.551287\pi$
$397$	−6.39291	−0.320851	−0.160426	+	0.987048i	$0.551287\pi$
$398$	−18.5956	−0.932115
$399$	−3.80628	−0.190553
$400$	1.00000	0.0500000
$401$	14.7469	0.736425	0.368213	−	0.929742i	$-0.379970\pi$
$401$	14.7469	0.736425	0.368213	+	0.929742i	$0.379970\pi$
$402$	7.98876	0.398443
$403$	−18.7640	−0.934702
$404$	−10.8530	−0.539955
$405$	1.00000	0.0496904
$406$	−16.2211	−0.805040
$407$	−40.5385	−2.00942
$408$	0	0
$409$	28.6543	1.41686	0.708431	−	0.705780i	$-0.249403\pi$
$409$	28.6543	1.41686	0.708431	+	0.705780i	$0.249403\pi$
$410$	4.85491	0.239767
$411$	16.2963	0.803839
$412$	14.2589	0.702484
$413$	−5.20893	−0.256315
$414$	−0.784395	−0.0385509
$415$	12.0259	0.590326
$416$	−2.98735	−0.146467
$417$	2.04580	0.100183
$418$	−8.29302	−0.405625
$419$	−2.96336	−0.144770	−0.0723849	−	0.997377i	$-0.523061\pi$
$419$	−2.96336	−0.144770	−0.0723849	+	0.997377i	$0.523061\pi$
$420$	−1.60256	−0.0781969
$421$	−13.2392	−0.645237	−0.322618	−	0.946529i	$-0.604563\pi$
$421$	−13.2392	−0.645237	−0.322618	+	0.946529i	$0.604563\pi$
$422$	20.9409	1.01939
$423$	1.44121	0.0700739
$424$	−6.25743	−0.303887
$425$	0	0
$426$	2.35891	0.114289
$427$	9.96314	0.482150
$428$	−5.66263	−0.273714
$429$	10.4307	0.503598
$430$	−5.92125	−0.285548
$431$	−19.5788	−0.943078	−0.471539	−	0.881845i	$-0.656301\pi$
$431$	−19.5788	−0.943078	−0.471539	+	0.881845i	$0.656301\pi$
$432$	1.00000	0.0481125
$433$	−23.5618	−1.13231	−0.566154	−	0.824300i	$-0.691569\pi$
$433$	−23.5618	−1.13231	−0.566154	+	0.824300i	$0.691569\pi$
$434$	−10.0659	−0.483180
$435$	10.1220	0.485313
$436$	8.56433	0.410157
$437$	−1.86304	−0.0891212
$438$	3.79290	0.181232
$439$	−14.6091	−0.697254	−0.348627	−	0.937262i	$-0.613352\pi$
$439$	−14.6091	−0.697254	−0.348627	+	0.937262i	$0.613352\pi$
$440$	−3.49161	−0.166456
$441$	−4.43180	−0.211038
$442$	0	0
$443$	13.3797	0.635691	0.317846	−	0.948143i	$-0.397041\pi$
$443$	13.3797	0.635691	0.317846	+	0.948143i	$0.397041\pi$
$444$	11.6103	0.550998
$445$	−2.14774	−0.101813
$446$	−4.09278	−0.193799
$447$	−14.9980	−0.709380
$448$	−1.60256	−0.0757138
$449$	−9.39590	−0.443420	−0.221710	−	0.975113i	$-0.571164\pi$
$449$	−9.39590	−0.443420	−0.221710	+	0.975113i	$0.571164\pi$
$450$	1.00000	0.0471405
$451$	−16.9515	−0.798213
$452$	−4.95883	−0.233244
$453$	0.264269	0.0124164
$454$	10.3530	0.485890
$455$	4.78741	0.224437
$456$	2.37513	0.111226
$457$	25.3449	1.18558	0.592791	−	0.805356i	$-0.298026\pi$
$457$	25.3449	1.18558	0.592791	+	0.805356i	$0.298026\pi$
$458$	−23.2062	−1.08435
$459$	0	0
$460$	−0.784395	−0.0365726
$461$	−35.5596	−1.65617	−0.828087	−	0.560599i	$-0.810571\pi$
$461$	−35.5596	−1.65617	−0.828087	+	0.560599i	$0.810571\pi$
$462$	5.59552	0.260327
$463$	31.2121	1.45055	0.725275	−	0.688460i	$-0.241713\pi$
$463$	31.2121	1.45055	0.725275	+	0.688460i	$0.241713\pi$
$464$	10.1220	0.469902
$465$	6.28115	0.291281
$466$	−17.8458	−0.826690
$467$	1.38878	0.0642650	0.0321325	−	0.999484i	$-0.489770\pi$
$467$	1.38878	0.0642650	0.0321325	+	0.999484i	$0.489770\pi$
$468$	−2.98735	−0.138090
$469$	−12.8025	−0.591163
$470$	1.44121	0.0664779
$471$	−3.05453	−0.140745
$472$	3.25038	0.149611
$473$	20.6747	0.950624
$474$	−4.37179	−0.200803
$475$	2.37513	0.108978
$476$	0	0
$477$	−6.25743	−0.286508
$478$	4.58848	0.209872
$479$	28.1331	1.28543	0.642716	−	0.766104i	$-0.277807\pi$
$479$	28.1331	1.28543	0.642716	+	0.766104i	$0.277807\pi$
$480$	1.00000	0.0456435
$481$	−34.6839	−1.58145
$482$	−15.1749	−0.691198
$483$	1.25704	0.0571973
$484$	1.19135	0.0541521
$485$	−0.268171	−0.0121770
$486$	1.00000	0.0453609
$487$	16.2135	0.734704	0.367352	−	0.930082i	$-0.380264\pi$
$487$	16.2135	0.734704	0.367352	+	0.930082i	$0.380264\pi$
$488$	−6.21702	−0.281431
$489$	17.5727	0.794664
$490$	−4.43180	−0.200208
$491$	−2.91554	−0.131577	−0.0657883	−	0.997834i	$-0.520956\pi$
$491$	−2.91554	−0.131577	−0.0657883	+	0.997834i	$0.520956\pi$
$492$	4.85491	0.218876
$493$	0	0
$494$	−7.09534	−0.319235
$495$	−3.49161	−0.156936
$496$	6.28115	0.282032
$497$	−3.78029	−0.169569
$498$	12.0259	0.538892
$499$	−8.55741	−0.383082	−0.191541	−	0.981485i	$-0.561349\pi$
$499$	−8.55741	−0.383082	−0.191541	+	0.981485i	$0.561349\pi$
$500$	1.00000	0.0447214
$501$	23.8440	1.06527
$502$	−15.1932	−0.678106
$503$	35.3912	1.57801	0.789007	−	0.614384i	$-0.210595\pi$
$503$	35.3912	1.57801	0.789007	+	0.614384i	$0.210595\pi$
$504$	−1.60256	−0.0713837
$505$	−10.8530	−0.482950
$506$	2.73880	0.121755
$507$	−4.07572	−0.181009
$508$	15.8640	0.703851
$509$	−35.8058	−1.58707	−0.793533	−	0.608527i	$-0.791761\pi$
$509$	−35.8058	−1.58707	−0.793533	+	0.608527i	$0.791761\pi$
$510$	0	0
$511$	−6.07834	−0.268890
$512$	1.00000	0.0441942
$513$	2.37513	0.104864
$514$	−19.9381	−0.879433
$515$	14.2589	0.628321
$516$	−5.92125	−0.260669
$517$	−5.03213	−0.221313
$518$	−18.6061	−0.817506
$519$	10.8188	0.474895
$520$	−2.98735	−0.131004
$521$	29.8860	1.30933	0.654665	−	0.755919i	$-0.272810\pi$
$521$	29.8860	1.30933	0.654665	+	0.755919i	$0.272810\pi$
$522$	10.1220	0.443028
$523$	−25.9973	−1.13678	−0.568391	−	0.822759i	$-0.692434\pi$
$523$	−25.9973	−1.13678	−0.568391	+	0.822759i	$0.692434\pi$
$524$	18.0373	0.787963
$525$	−1.60256	−0.0699415
$526$	−13.0708	−0.569913
$527$	0	0
$528$	−3.49161	−0.151953
$529$	−22.3847	−0.973249
$530$	−6.25743	−0.271805
$531$	3.25038	0.141055
$532$	−3.80628	−0.165023
$533$	−14.5033	−0.628209
$534$	−2.14774	−0.0929418
$535$	−5.66263	−0.244817
$536$	7.98876	0.345062
$537$	12.8670	0.555250
$538$	18.8300	0.811821
$539$	15.4741	0.666518
$540$	1.00000	0.0430331
$541$	−39.9426	−1.71726	−0.858632	−	0.512592i	$-0.828685\pi$
$541$	−39.9426	−1.71726	−0.858632	+	0.512592i	$0.828685\pi$
$542$	−7.45834	−0.320363
$543$	3.15419	0.135359
$544$	0	0
$545$	8.56433	0.366855
$546$	4.78741	0.204882
$547$	−5.84806	−0.250045	−0.125023	−	0.992154i	$-0.539900\pi$
$547$	−5.84806	−0.250045	−0.125023	+	0.992154i	$0.539900\pi$
$548$	16.2963	0.696145
$549$	−6.21702	−0.265336
$550$	−3.49161	−0.148883
$551$	24.0410	1.02418
$552$	−0.784395	−0.0333861
$553$	7.00606	0.297928
$554$	−20.0283	−0.850923
$555$	11.6103	0.492828
$556$	2.04580	0.0867611
$557$	−31.0270	−1.31466	−0.657328	−	0.753604i	$-0.728313\pi$
$557$	−31.0270	−1.31466	−0.657328	+	0.753604i	$0.728313\pi$
$558$	6.28115	0.265902
$559$	17.6889	0.748159
$560$	−1.60256	−0.0677205
$561$	0	0
$562$	−8.96767	−0.378278
$563$	2.26510	0.0954628	0.0477314	−	0.998860i	$-0.484801\pi$
$563$	2.26510	0.0954628	0.0477314	+	0.998860i	$0.484801\pi$
$564$	1.44121	0.0606857
$565$	−4.95883	−0.208620
$566$	−30.3038	−1.27376
$567$	−1.60256	−0.0673012
$568$	2.35891	0.0989776
$569$	−9.84648	−0.412786	−0.206393	−	0.978469i	$-0.566173\pi$
$569$	−9.84648	−0.412786	−0.206393	+	0.978469i	$0.566173\pi$
$570$	2.37513	0.0994831
$571$	−27.6269	−1.15615	−0.578074	−	0.815984i	$-0.696195\pi$
$571$	−27.6269	−1.15615	−0.578074	+	0.815984i	$0.696195\pi$
$572$	10.4307	0.436128
$573$	−7.21412	−0.301374
$574$	−7.78029	−0.324743
$575$	−0.784395	−0.0327115
$576$	1.00000	0.0416667
$577$	17.6830	0.736151	0.368076	−	0.929796i	$-0.380017\pi$
$577$	17.6830	0.736151	0.368076	+	0.929796i	$0.380017\pi$
$578$	0	0
$579$	26.2136	1.08940
$580$	10.1220	0.420293
$581$	−19.2722	−0.799544
$582$	−0.268171	−0.0111161
$583$	21.8485	0.904872
$584$	3.79290	0.156951
$585$	−2.98735	−0.123512
$586$	−13.2296	−0.546508
$587$	−18.6767	−0.770869	−0.385435	−	0.922735i	$-0.625948\pi$
$587$	−18.6767	−0.770869	−0.385435	+	0.922735i	$0.625948\pi$
$588$	−4.43180	−0.182764
$589$	14.9185	0.614707
$590$	3.25038	0.133816
$591$	1.72607	0.0710008
$592$	11.6103	0.477179
$593$	−8.33270	−0.342183	−0.171091	−	0.985255i	$-0.554729\pi$
$593$	−8.33270	−0.342183	−0.171091	+	0.985255i	$0.554729\pi$
$594$	−3.49161	−0.143263
$595$	0	0
$596$	−14.9980	−0.614341
$597$	−18.5956	−0.761069
$598$	2.34327	0.0958232
$599$	−34.5160	−1.41028	−0.705142	−	0.709066i	$-0.749117\pi$
$599$	−34.5160	−1.41028	−0.705142	+	0.709066i	$0.749117\pi$
$600$	1.00000	0.0408248
$601$	37.9355	1.54742	0.773711	−	0.633539i	$-0.218398\pi$
$601$	37.9355	1.54742	0.773711	+	0.633539i	$0.218398\pi$
$602$	9.48916	0.386749
$603$	7.98876	0.325328
$604$	0.264269	0.0107530
$605$	1.19135	0.0484351
$606$	−10.8530	−0.440871
$607$	−43.2144	−1.75402	−0.877010	−	0.480472i	$-0.840465\pi$
$607$	−43.2144	−1.75402	−0.877010	+	0.480472i	$0.840465\pi$
$608$	2.37513	0.0963241
$609$	−16.2211	−0.657313
$610$	−6.21702	−0.251720
$611$	−4.30539	−0.174178
$612$	0	0
$613$	16.1410	0.651928	0.325964	−	0.945382i	$-0.394311\pi$
$613$	16.1410	0.651928	0.325964	+	0.945382i	$0.394311\pi$
$614$	19.2521	0.776951
$615$	4.85491	0.195769
$616$	5.59552	0.225450
$617$	−35.7713	−1.44010	−0.720049	−	0.693923i	$-0.755881\pi$
$617$	−35.7713	−1.44010	−0.720049	+	0.693923i	$0.755881\pi$
$618$	14.2589	0.573576
$619$	8.07288	0.324477	0.162238	−	0.986752i	$-0.448129\pi$
$619$	8.07288	0.324477	0.162238	+	0.986752i	$0.448129\pi$
$620$	6.28115	0.252257
$621$	−0.784395	−0.0314767
$622$	10.9497	0.439045
$623$	3.44188	0.137896
$624$	−2.98735	−0.119590
$625$	1.00000	0.0400000
$626$	21.0626	0.841832
$627$	−8.29302	−0.331191
$628$	−3.05453	−0.121889
$629$	0	0
$630$	−1.60256	−0.0638475
$631$	−38.8194	−1.54537	−0.772687	−	0.634787i	$-0.781088\pi$
$631$	−38.8194	−1.54537	−0.772687	+	0.634787i	$0.781088\pi$
$632$	−4.37179	−0.173901
$633$	20.9409	0.832326
$634$	−22.6107	−0.897987
$635$	15.8640	0.629543
$636$	−6.25743	−0.248123
$637$	13.2394	0.524562
$638$	−35.3421	−1.39921
$639$	2.35891	0.0933170
$640$	1.00000	0.0395285
$641$	−27.1891	−1.07390	−0.536952	−	0.843613i	$-0.680424\pi$
$641$	−27.1891	−1.07390	−0.536952	+	0.843613i	$0.680424\pi$
$642$	−5.66263	−0.223486
$643$	26.3431	1.03887	0.519435	−	0.854510i	$-0.326142\pi$
$643$	26.3431	1.03887	0.519435	+	0.854510i	$0.326142\pi$
$644$	1.25704	0.0495343
$645$	−5.92125	−0.233149
$646$	0	0
$647$	−15.4225	−0.606321	−0.303161	−	0.952939i	$-0.598042\pi$
$647$	−15.4225	−0.606321	−0.303161	+	0.952939i	$0.598042\pi$
$648$	1.00000	0.0392837
$649$	−11.3491	−0.445490
$650$	−2.98735	−0.117174
$651$	−10.0659	−0.394514
$652$	17.5727	0.688199
$653$	38.6536	1.51263	0.756316	−	0.654206i	$-0.226997\pi$
$653$	38.6536	1.51263	0.756316	+	0.654206i	$0.226997\pi$
$654$	8.56433	0.334892
$655$	18.0373	0.704775
$656$	4.85491	0.189552
$657$	3.79290	0.147975
$658$	−2.30962	−0.0900384
$659$	−7.14935	−0.278499	−0.139250	−	0.990257i	$-0.544469\pi$
$659$	−7.14935	−0.278499	−0.139250	+	0.990257i	$0.544469\pi$
$660$	−3.49161	−0.135911
$661$	13.5061	0.525326	0.262663	−	0.964888i	$-0.415399\pi$
$661$	13.5061	0.525326	0.262663	+	0.964888i	$0.415399\pi$
$662$	13.8364	0.537768
$663$	0	0
$664$	12.0259	0.466694
$665$	−3.80628	−0.147601
$666$	11.6103	0.449888
$667$	−7.93965	−0.307424
$668$	23.8440	0.922550
$669$	−4.09278	−0.158236
$670$	7.98876	0.308633
$671$	21.7074	0.838005
$672$	−1.60256	−0.0618201
$673$	−30.0616	−1.15879	−0.579395	−	0.815047i	$-0.696711\pi$
$673$	−30.0616	−1.15879	−0.579395	+	0.815047i	$0.696711\pi$
$674$	8.81167	0.339413
$675$	1.00000	0.0384900
$676$	−4.07572	−0.156758
$677$	31.5274	1.21170	0.605848	−	0.795580i	$-0.292834\pi$
$677$	31.5274	1.21170	0.605848	+	0.795580i	$0.292834\pi$
$678$	−4.95883	−0.190443
$679$	0.429760	0.0164927
$680$	0	0
$681$	10.3530	0.396727
$682$	−21.9313	−0.839794
$683$	−27.5116	−1.05270	−0.526351	−	0.850267i	$-0.676440\pi$
$683$	−27.5116	−1.05270	−0.526351	+	0.850267i	$0.676440\pi$
$684$	2.37513	0.0908153
$685$	16.2963	0.622651
$686$	18.3201	0.699466
$687$	−23.2062	−0.885370
$688$	−5.92125	−0.225746
$689$	18.6931	0.712152
$690$	−0.784395	−0.0298614
$691$	−0.393797	−0.0149807	−0.00749037	−	0.999972i	$-0.502384\pi$
$691$	−0.393797	−0.0149807	−0.00749037	+	0.999972i	$0.502384\pi$
$692$	10.8188	0.411271
$693$	5.59552	0.212556
$694$	−14.7497	−0.559893
$695$	2.04580	0.0776015
$696$	10.1220	0.383673
$697$	0	0
$698$	−2.76211	−0.104547
$699$	−17.8458	−0.674990
$700$	−1.60256	−0.0605711
$701$	−37.7858	−1.42715	−0.713576	−	0.700578i	$-0.752926\pi$
$701$	−37.7858	−1.42715	−0.713576	+	0.700578i	$0.752926\pi$
$702$	−2.98735	−0.112750
$703$	27.5758	1.04004
$704$	−3.49161	−0.131595
$705$	1.44121	0.0542790
$706$	15.9669	0.600921
$707$	17.3925	0.654113
$708$	3.25038	0.122157
$709$	40.3553	1.51557	0.757787	−	0.652502i	$-0.226281\pi$
$709$	40.3553	1.51557	0.757787	+	0.652502i	$0.226281\pi$
$710$	2.35891	0.0885282
$711$	−4.37179	−0.163955
$712$	−2.14774	−0.0804900
$713$	−4.92690	−0.184514
$714$	0	0
$715$	10.4307	0.390085
$716$	12.8670	0.480861
$717$	4.58848	0.171360
$718$	24.2038	0.903277
$719$	30.2202	1.12702	0.563512	−	0.826108i	$-0.309450\pi$
$719$	30.2202	1.12702	0.563512	+	0.826108i	$0.309450\pi$
$720$	1.00000	0.0372678
$721$	−22.8507	−0.851005
$722$	−13.3588	−0.497162
$723$	−15.1749	−0.564361
$724$	3.15419	0.117225
$725$	10.1220	0.375922
$726$	1.19135	0.0442150
$727$	26.8869	0.997181	0.498591	−	0.866838i	$-0.333851\pi$
$727$	26.8869	0.997181	0.498591	+	0.866838i	$0.333851\pi$
$728$	4.78741	0.177433
$729$	1.00000	0.0370370
$730$	3.79290	0.140381
$731$	0	0
$732$	−6.21702	−0.229788
$733$	−3.97906	−0.146970	−0.0734849	−	0.997296i	$-0.523412\pi$
$733$	−3.97906	−0.146970	−0.0734849	+	0.997296i	$0.523412\pi$
$734$	−19.2945	−0.712172
$735$	−4.43180	−0.163469
$736$	−0.784395	−0.0289132
$737$	−27.8937	−1.02748
$738$	4.85491	0.178712
$739$	38.9194	1.43168	0.715838	−	0.698267i	$-0.246045\pi$
$739$	38.9194	1.43168	0.715838	+	0.698267i	$0.246045\pi$
$740$	11.6103	0.426802
$741$	−7.09534	−0.260654
$742$	10.0279	0.368136
$743$	−33.0426	−1.21222	−0.606108	−	0.795382i	$-0.707270\pi$
$743$	−33.0426	−1.21222	−0.606108	+	0.795382i	$0.707270\pi$
$744$	6.28115	0.230278
$745$	−14.9980	−0.549484
$746$	10.6498	0.389916
$747$	12.0259	0.440003
$748$	0	0
$749$	9.07470	0.331582
$750$	1.00000	0.0365148
$751$	26.0644	0.951105	0.475553	−	0.879687i	$-0.342248\pi$
$751$	26.0644	0.951105	0.475553	+	0.879687i	$0.342248\pi$
$752$	1.44121	0.0525554
$753$	−15.1932	−0.553672
$754$	−30.2380	−1.10120
$755$	0.264269	0.00961773
$756$	−1.60256	−0.0582845
$757$	15.1681	0.551295	0.275647	−	0.961259i	$-0.411108\pi$
$757$	15.1681	0.551295	0.275647	+	0.961259i	$0.411108\pi$
$758$	−20.1097	−0.730417
$759$	2.73880	0.0994122
$760$	2.37513	0.0861549
$761$	−2.09358	−0.0758922	−0.0379461	−	0.999280i	$-0.512082\pi$
$761$	−2.09358	−0.0758922	−0.0379461	+	0.999280i	$0.512082\pi$
$762$	15.8640	0.574692
$763$	−13.7248	−0.496873
$764$	−7.21412	−0.260998
$765$	0	0
$766$	−16.7143	−0.603913
$767$	−9.71004	−0.350609
$768$	1.00000	0.0360844
$769$	−5.41975	−0.195441	−0.0977206	−	0.995214i	$-0.531155\pi$
$769$	−5.41975	−0.195441	−0.0977206	+	0.995214i	$0.531155\pi$
$770$	5.59552	0.201648
$771$	−19.9381	−0.718054
$772$	26.2136	0.943447
$773$	−25.1073	−0.903046	−0.451523	−	0.892259i	$-0.649119\pi$
$773$	−25.1073	−0.903046	−0.451523	+	0.892259i	$0.649119\pi$
$774$	−5.92125	−0.212835
$775$	6.28115	0.225626
$776$	−0.268171	−0.00962678
$777$	−18.6061	−0.667491
$778$	28.2413	1.01250
$779$	11.5310	0.413142
$780$	−2.98735	−0.106964
$781$	−8.23639	−0.294721
$782$	0	0
$783$	10.1220	0.361731
$784$	−4.43180	−0.158279
$785$	−3.05453	−0.109021
$786$	18.0373	0.643369
$787$	22.4618	0.800676	0.400338	−	0.916368i	$-0.368893\pi$
$787$	22.4618	0.800676	0.400338	+	0.916368i	$0.368893\pi$
$788$	1.72607	0.0614885
$789$	−13.0708	−0.465332
$790$	−4.37179	−0.155541
$791$	7.94682	0.282557
$792$	−3.49161	−0.124069
$793$	18.5724	0.659526
$794$	−6.39291	−0.226876
$795$	−6.25743	−0.221928
$796$	−18.5956	−0.659105
$797$	45.7053	1.61897	0.809483	−	0.587143i	$-0.199748\pi$
$797$	45.7053	1.61897	0.809483	+	0.587143i	$0.199748\pi$
$798$	−3.80628	−0.134741
$799$	0	0
$800$	1.00000	0.0353553
$801$	−2.14774	−0.0758867
$802$	14.7469	0.520731
$803$	−13.2433	−0.467346
$804$	7.98876	0.281742
$805$	1.25704	0.0443048
$806$	−18.7640	−0.660934
$807$	18.8300	0.662849
$808$	−10.8530	−0.381806
$809$	−8.63598	−0.303625	−0.151813	−	0.988409i	$-0.548511\pi$
$809$	−8.63598	−0.303625	−0.151813	+	0.988409i	$0.548511\pi$
$810$	1.00000	0.0351364
$811$	22.7666	0.799445	0.399722	−	0.916636i	$-0.369107\pi$
$811$	22.7666	0.799445	0.399722	+	0.916636i	$0.369107\pi$
$812$	−16.2211	−0.569250
$813$	−7.45834	−0.261575
$814$	−40.5385	−1.42087
$815$	17.5727	0.615544
$816$	0	0
$817$	−14.0637	−0.492027
$818$	28.6543	1.00187
$819$	4.78741	0.167286
$820$	4.85491	0.169541
$821$	−57.0357	−1.99056	−0.995280	−	0.0970485i	$-0.969060\pi$
$821$	−57.0357	−1.99056	−0.995280	+	0.0970485i	$0.969060\pi$
$822$	16.2963	0.568400
$823$	10.7746	0.375579	0.187789	−	0.982209i	$-0.439868\pi$
$823$	10.7746	0.375579	0.187789	+	0.982209i	$0.439868\pi$
$824$	14.2589	0.496731
$825$	−3.49161	−0.121562
$826$	−5.20893	−0.181242
$827$	11.0396	0.383883	0.191942	−	0.981406i	$-0.438522\pi$
$827$	11.0396	0.383883	0.191942	+	0.981406i	$0.438522\pi$
$828$	−0.784395	−0.0272596
$829$	29.4018	1.02117	0.510584	−	0.859828i	$-0.329429\pi$
$829$	29.4018	1.02117	0.510584	+	0.859828i	$0.329429\pi$
$830$	12.0259	0.417424
$831$	−20.0283	−0.694776
$832$	−2.98735	−0.103568
$833$	0	0
$834$	2.04580	0.0708401
$835$	23.8440	0.825154
$836$	−8.29302	−0.286820
$837$	6.28115	0.217108
$838$	−2.96336	−0.102368
$839$	−45.1877	−1.56005	−0.780027	−	0.625746i	$-0.784795\pi$
$839$	−45.1877	−1.56005	−0.780027	+	0.625746i	$0.784795\pi$
$840$	−1.60256	−0.0552936
$841$	73.4549	2.53293
$842$	−13.2392	−0.456251
$843$	−8.96767	−0.308863
$844$	20.9409	0.720815
$845$	−4.07572	−0.140209
$846$	1.44121	0.0495497
$847$	−1.90920	−0.0656010
$848$	−6.25743	−0.214881
$849$	−30.3038	−1.04002
$850$	0	0
$851$	−9.10703	−0.312185
$852$	2.35891	0.0808149
$853$	−1.34644	−0.0461014	−0.0230507	−	0.999734i	$-0.507338\pi$
$853$	−1.34644	−0.0461014	−0.0230507	+	0.999734i	$0.507338\pi$
$854$	9.96314	0.340932
$855$	2.37513	0.0812276
$856$	−5.66263	−0.193545
$857$	−27.3260	−0.933438	−0.466719	−	0.884406i	$-0.654564\pi$
$857$	−27.3260	−0.933438	−0.466719	+	0.884406i	$0.654564\pi$
$858$	10.4307	0.356097
$859$	−12.1819	−0.415640	−0.207820	−	0.978167i	$-0.566637\pi$
$859$	−12.1819	−0.415640	−0.207820	+	0.978167i	$0.566637\pi$
$860$	−5.92125	−0.201913
$861$	−7.78029	−0.265151
$862$	−19.5788	−0.666857
$863$	39.2071	1.33462	0.667312	−	0.744778i	$-0.267445\pi$
$863$	39.2071	1.33462	0.667312	+	0.744778i	$0.267445\pi$
$864$	1.00000	0.0340207
$865$	10.8188	0.367852
$866$	−23.5618	−0.800662
$867$	0	0
$868$	−10.0659	−0.341660
$869$	15.2646	0.517816
$870$	10.1220	0.343168
$871$	−23.8653	−0.808644
$872$	8.56433	0.290025
$873$	−0.268171	−0.00907622
$874$	−1.86304	−0.0630182
$875$	−1.60256	−0.0541764
$876$	3.79290	0.128150
$877$	18.5342	0.625855	0.312928	−	0.949777i	$-0.398690\pi$
$877$	18.5342	0.625855	0.312928	+	0.949777i	$0.398690\pi$
$878$	−14.6091	−0.493033
$879$	−13.2296	−0.446222
$880$	−3.49161	−0.117702
$881$	7.55988	0.254699	0.127349	−	0.991858i	$-0.459353\pi$
$881$	7.55988	0.254699	0.127349	+	0.991858i	$0.459353\pi$
$882$	−4.43180	−0.149227
$883$	−28.2029	−0.949104	−0.474552	−	0.880228i	$-0.657390\pi$
$883$	−28.2029	−0.949104	−0.474552	+	0.880228i	$0.657390\pi$
$884$	0	0
$885$	3.25038	0.109260
$886$	13.3797	0.449501
$887$	6.51004	0.218586	0.109293	−	0.994010i	$-0.465141\pi$
$887$	6.51004	0.218586	0.109293	+	0.994010i	$0.465141\pi$
$888$	11.6103	0.389615
$889$	−25.4230	−0.852660
$890$	−2.14774	−0.0719924
$891$	−3.49161	−0.116973
$892$	−4.09278	−0.137036
$893$	3.42305	0.114548
$894$	−14.9980	−0.501608
$895$	12.8670	0.430095
$896$	−1.60256	−0.0535378
$897$	2.34327	0.0782394
$898$	−9.39590	−0.313545
$899$	63.5778	2.12044
$900$	1.00000	0.0333333
$901$	0	0
$902$	−16.9515	−0.564422
$903$	9.48916	0.315779
$904$	−4.95883	−0.164928
$905$	3.15419	0.104849
$906$	0.264269	0.00877975
$907$	0.791563	0.0262834	0.0131417	−	0.999914i	$-0.495817\pi$
$907$	0.791563	0.0262834	0.0131417	+	0.999914i	$0.495817\pi$
$908$	10.3530	0.343576
$909$	−10.8530	−0.359970
$910$	4.78741	0.158701
$911$	45.6218	1.51152	0.755759	−	0.654850i	$-0.227268\pi$
$911$	45.6218	1.51152	0.755759	+	0.654850i	$0.227268\pi$
$912$	2.37513	0.0786483
$913$	−41.9896	−1.38965
$914$	25.3449	0.838334
$915$	−6.21702	−0.205528
$916$	−23.2062	−0.766753
$917$	−28.9058	−0.954555
$918$	0	0
$919$	6.30968	0.208137	0.104069	−	0.994570i	$-0.466814\pi$
$919$	6.30968	0.208137	0.104069	+	0.994570i	$0.466814\pi$
$920$	−0.784395	−0.0258607
$921$	19.2521	0.634378
$922$	−35.5596	−1.17109
$923$	−7.04689	−0.231951
$924$	5.59552	0.184079
$925$	11.6103	0.381743
$926$	31.2121	1.02569
$927$	14.2589	0.468323
$928$	10.1220	0.332271
$929$	−44.3483	−1.45502	−0.727510	−	0.686097i	$-0.759323\pi$
$929$	−44.3483	−1.45502	−0.727510	+	0.686097i	$0.759323\pi$
$930$	6.28115	0.205967
$931$	−10.5261	−0.344979
$932$	−17.8458	−0.584558
$933$	10.9497	0.358479
$934$	1.38878	0.0454422
$935$	0	0
$936$	−2.98735	−0.0976447
$937$	−21.9771	−0.717961	−0.358980	−	0.933345i	$-0.616876\pi$
$937$	−21.9771	−0.717961	−0.358980	+	0.933345i	$0.616876\pi$
$938$	−12.8025	−0.418016
$939$	21.0626	0.687353
$940$	1.44121	0.0470070
$941$	0.863426	0.0281469	0.0140734	−	0.999901i	$-0.495520\pi$
$941$	0.863426	0.0281469	0.0140734	+	0.999901i	$0.495520\pi$
$942$	−3.05453	−0.0995219
$943$	−3.80817	−0.124011
$944$	3.25038	0.105791
$945$	−1.60256	−0.0521313
$946$	20.6747	0.672193
$947$	14.3981	0.467875	0.233938	−	0.972252i	$-0.424839\pi$
$947$	14.3981	0.467875	0.233938	+	0.972252i	$0.424839\pi$
$948$	−4.37179	−0.141989
$949$	−11.3307	−0.367811
$950$	2.37513	0.0770593
$951$	−22.6107	−0.733203
$952$	0	0
$953$	−56.4564	−1.82880	−0.914400	−	0.404811i	$-0.867337\pi$
$953$	−56.4564	−1.82880	−0.914400	+	0.404811i	$0.867337\pi$
$954$	−6.25743	−0.202592
$955$	−7.21412	−0.233443
$956$	4.58848	0.148402
$957$	−35.3421	−1.14245
$958$	28.1331	0.908938
$959$	−26.1159	−0.843325
$960$	1.00000	0.0322749
$961$	8.45283	0.272672
$962$	−34.6839	−1.11825
$963$	−5.66263	−0.182476
$964$	−15.1749	−0.488751
$965$	26.2136	0.843844
$966$	1.25704	0.0404446
$967$	44.5545	1.43278	0.716388	−	0.697702i	$-0.245794\pi$
$967$	44.5545	1.43278	0.716388	+	0.697702i	$0.245794\pi$
$968$	1.19135	0.0382913
$969$	0	0
$970$	−0.268171	−0.00861046
$971$	−47.3911	−1.52085	−0.760427	−	0.649424i	$-0.775010\pi$
$971$	−47.3911	−1.52085	−0.760427	+	0.649424i	$0.775010\pi$
$972$	1.00000	0.0320750
$973$	−3.27851	−0.105104
$974$	16.2135	0.519514
$975$	−2.98735	−0.0956719
$976$	−6.21702	−0.199002
$977$	−15.9709	−0.510953	−0.255477	−	0.966815i	$-0.582232\pi$
$977$	−15.9709	−0.510953	−0.255477	+	0.966815i	$0.582232\pi$
$978$	17.5727	0.561912
$979$	7.49907	0.239671
$980$	−4.43180	−0.141569
$981$	8.56433	0.273438
$982$	−2.91554	−0.0930387
$983$	−45.1435	−1.43985	−0.719927	−	0.694050i	$-0.755825\pi$
$983$	−45.1435	−1.43985	−0.719927	+	0.694050i	$0.755825\pi$
$984$	4.85491	0.154769
$985$	1.72607	0.0549970
$986$	0	0
$987$	−2.30962	−0.0735160
$988$	−7.09534	−0.225733
$989$	4.64460	0.147690
$990$	−3.49161	−0.110971
$991$	−18.6311	−0.591837	−0.295918	−	0.955213i	$-0.595626\pi$
$991$	−18.6311	−0.591837	−0.295918	+	0.955213i	$0.595626\pi$
$992$	6.28115	0.199427
$993$	13.8364	0.439086
$994$	−3.78029	−0.119904
$995$	−18.5956	−0.589521
$996$	12.0259	0.381054
$997$	−9.39555	−0.297560	−0.148780	−	0.988870i	$-0.547535\pi$
$997$	−9.39555	−0.297560	−0.148780	+	0.988870i	$0.547535\pi$
$998$	−8.55741	−0.270880
$999$	11.6103	0.367332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.ci.1.3	yes	6
17.16	even	2		8670.2.a.cf.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.cf.1.4	✓	6	17.16	even	2
8670.2.a.ci.1.3	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.60256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.60256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.49161 q^{11} +1.00000 q^{12} -2.98735 q^{13} -1.60256 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +2.37513 q^{19} +1.00000 q^{20} -1.60256 q^{21} -3.49161 q^{22} -0.784395 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.98735 q^{26} +1.00000 q^{27} -1.60256 q^{28} +10.1220 q^{29} +1.00000 q^{30} +6.28115 q^{31} +1.00000 q^{32} -3.49161 q^{33} -1.60256 q^{35} +1.00000 q^{36} +11.6103 q^{37} +2.37513 q^{38} -2.98735 q^{39} +1.00000 q^{40} +4.85491 q^{41} -1.60256 q^{42} -5.92125 q^{43} -3.49161 q^{44} +1.00000 q^{45} -0.784395 q^{46} +1.44121 q^{47} +1.00000 q^{48} -4.43180 q^{49} +1.00000 q^{50} -2.98735 q^{52} -6.25743 q^{53} +1.00000 q^{54} -3.49161 q^{55} -1.60256 q^{56} +2.37513 q^{57} +10.1220 q^{58} +3.25038 q^{59} +1.00000 q^{60} -6.21702 q^{61} +6.28115 q^{62} -1.60256 q^{63} +1.00000 q^{64} -2.98735 q^{65} -3.49161 q^{66} +7.98876 q^{67} -0.784395 q^{69} -1.60256 q^{70} +2.35891 q^{71} +1.00000 q^{72} +3.79290 q^{73} +11.6103 q^{74} +1.00000 q^{75} +2.37513 q^{76} +5.59552 q^{77} -2.98735 q^{78} -4.37179 q^{79} +1.00000 q^{80} +1.00000 q^{81} +4.85491 q^{82} +12.0259 q^{83} -1.60256 q^{84} -5.92125 q^{86} +10.1220 q^{87} -3.49161 q^{88} -2.14774 q^{89} +1.00000 q^{90} +4.78741 q^{91} -0.784395 q^{92} +6.28115 q^{93} +1.44121 q^{94} +2.37513 q^{95} +1.00000 q^{96} -0.268171 q^{97} -4.43180 q^{98} -3.49161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} + 6 q^{18} + 6 q^{19} + 6 q^{20} + 6 q^{21} + 6 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 6 q^{27} + 6 q^{28} + 12 q^{29} + 6 q^{30} + 6 q^{31} + 6 q^{32} + 6 q^{33} + 6 q^{35} + 6 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 6 q^{42} + 18 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} + 6 q^{48} + 18 q^{49} + 6 q^{50} + 6 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} - 30 q^{59} + 6 q^{60} - 24 q^{61} + 6 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 6 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 6 q^{73} + 6 q^{74} + 6 q^{75} + 6 q^{76} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 18 q^{83} + 6 q^{84} + 18 q^{86} + 12 q^{87} + 6 q^{88} - 12 q^{89} + 6 q^{90} + 6 q^{91} + 6 q^{92} + 6 q^{93} - 6 q^{94} + 6 q^{95} + 6 q^{96} + 18 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 + 6 * q^18 + 6 * q^19 + 6 * q^20 + 6 * q^21 + 6 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 6 * q^27 + 6 * q^28 + 12 * q^29 + 6 * q^30 + 6 * q^31 + 6 * q^32 + 6 * q^33 + 6 * q^35 + 6 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 6 * q^42 + 18 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 + 6 * q^48 + 18 * q^49 + 6 * q^50 + 6 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 - 30 * q^59 + 6 * q^60 - 24 * q^61 + 6 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 6 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 6 * q^73 + 6 * q^74 + 6 * q^75 + 6 * q^76 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 18 * q^83 + 6 * q^84 + 18 * q^86 + 12 * q^87 + 6 * q^88 - 12 * q^89 + 6 * q^90 + 6 * q^91 + 6 * q^92 + 6 * q^93 - 6 * q^94 + 6 * q^95 + 6 * q^96 + 18 * q^97 + 18 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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