LMFDB - Embedded newform 8034.2.a.v.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 $ x^11 - 5x^10 - 31x^9 + 168x^8 + 300x^7 - 1928x^6 - 736x^5 + 8532x^4 - 2065x^3 - 10494x^2 + 4024x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$4.01421$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.01421 q^{5} +1.00000 q^{6} +2.23635 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.01421 q^{5} +1.00000 q^{6} +2.23635 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.01421 q^{10} -5.19311 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.23635 q^{14} +4.01421 q^{15} +1.00000 q^{16} +7.80246 q^{17} +1.00000 q^{18} +1.23635 q^{19} +4.01421 q^{20} +2.23635 q^{21} -5.19311 q^{22} -2.23388 q^{23} +1.00000 q^{24} +11.1139 q^{25} +1.00000 q^{26} +1.00000 q^{27} +2.23635 q^{28} -0.116304 q^{29} +4.01421 q^{30} -1.23635 q^{31} +1.00000 q^{32} -5.19311 q^{33} +7.80246 q^{34} +8.97718 q^{35} +1.00000 q^{36} -4.93641 q^{37} +1.23635 q^{38} +1.00000 q^{39} +4.01421 q^{40} +3.24372 q^{41} +2.23635 q^{42} +9.31683 q^{43} -5.19311 q^{44} +4.01421 q^{45} -2.23388 q^{46} +1.50695 q^{47} +1.00000 q^{48} -1.99873 q^{49} +11.1139 q^{50} +7.80246 q^{51} +1.00000 q^{52} -2.85574 q^{53} +1.00000 q^{54} -20.8462 q^{55} +2.23635 q^{56} +1.23635 q^{57} -0.116304 q^{58} -9.33959 q^{59} +4.01421 q^{60} -1.08106 q^{61} -1.23635 q^{62} +2.23635 q^{63} +1.00000 q^{64} +4.01421 q^{65} -5.19311 q^{66} -5.69974 q^{67} +7.80246 q^{68} -2.23388 q^{69} +8.97718 q^{70} -14.5022 q^{71} +1.00000 q^{72} -14.6250 q^{73} -4.93641 q^{74} +11.1139 q^{75} +1.23635 q^{76} -11.6136 q^{77} +1.00000 q^{78} +0.0792320 q^{79} +4.01421 q^{80} +1.00000 q^{81} +3.24372 q^{82} -9.59784 q^{83} +2.23635 q^{84} +31.3207 q^{85} +9.31683 q^{86} -0.116304 q^{87} -5.19311 q^{88} +16.0505 q^{89} +4.01421 q^{90} +2.23635 q^{91} -2.23388 q^{92} -1.23635 q^{93} +1.50695 q^{94} +4.96297 q^{95} +1.00000 q^{96} -3.88521 q^{97} -1.99873 q^{98} -5.19311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * 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
$5$	4.01421	1.79521	0.897604	−	0.440802i	$-0.145306\pi$
$5$	4.01421	1.79521	0.897604	+	0.440802i	$0.145306\pi$
$6$	1.00000	0.408248
$7$	2.23635	0.845261	0.422631	−	0.906302i	$-0.361107\pi$
$7$	2.23635	0.845261	0.422631	+	0.906302i	$0.361107\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.01421	1.26940
$11$	−5.19311	−1.56578	−0.782890	−	0.622160i	$-0.786255\pi$
$11$	−5.19311	−1.56578	−0.782890	+	0.622160i	$0.786255\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.23635	0.597690
$15$	4.01421	1.03646
$16$	1.00000	0.250000
$17$	7.80246	1.89237	0.946187	−	0.323621i	$-0.104900\pi$
$17$	7.80246	1.89237	0.946187	+	0.323621i	$0.104900\pi$
$18$	1.00000	0.235702
$19$	1.23635	0.283638	0.141819	−	0.989893i	$-0.454705\pi$
$19$	1.23635	0.283638	0.141819	+	0.989893i	$0.454705\pi$
$20$	4.01421	0.897604
$21$	2.23635	0.488012
$22$	−5.19311	−1.10717
$23$	−2.23388	−0.465795	−0.232898	−	0.972501i	$-0.574821\pi$
$23$	−2.23388	−0.465795	−0.232898	+	0.972501i	$0.574821\pi$
$24$	1.00000	0.204124
$25$	11.1139	2.22277
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	2.23635	0.422631
$29$	−0.116304	−0.0215971	−0.0107986	−	0.999942i	$-0.503437\pi$
$29$	−0.116304	−0.0215971	−0.0107986	+	0.999942i	$0.503437\pi$
$30$	4.01421	0.732891
$31$	−1.23635	−0.222055	−0.111028	−	0.993817i	$-0.535414\pi$
$31$	−1.23635	−0.222055	−0.111028	+	0.993817i	$0.535414\pi$
$32$	1.00000	0.176777
$33$	−5.19311	−0.904004
$34$	7.80246	1.33811
$35$	8.97718	1.51742
$36$	1.00000	0.166667
$37$	−4.93641	−0.811541	−0.405770	−	0.913975i	$-0.632997\pi$
$37$	−4.93641	−0.811541	−0.405770	+	0.913975i	$0.632997\pi$
$38$	1.23635	0.200563
$39$	1.00000	0.160128
$40$	4.01421	0.634702
$41$	3.24372	0.506584	0.253292	−	0.967390i	$-0.418487\pi$
$41$	3.24372	0.506584	0.253292	+	0.967390i	$0.418487\pi$
$42$	2.23635	0.345076
$43$	9.31683	1.42080	0.710402	−	0.703796i	$-0.248513\pi$
$43$	9.31683	1.42080	0.710402	+	0.703796i	$0.248513\pi$
$44$	−5.19311	−0.782890
$45$	4.01421	0.598403
$46$	−2.23388	−0.329367
$47$	1.50695	0.219812	0.109906	−	0.993942i	$-0.464945\pi$
$47$	1.50695	0.219812	0.109906	+	0.993942i	$0.464945\pi$
$48$	1.00000	0.144338
$49$	−1.99873	−0.285534
$50$	11.1139	1.57174
$51$	7.80246	1.09256
$52$	1.00000	0.138675
$53$	−2.85574	−0.392267	−0.196133	−	0.980577i	$-0.562839\pi$
$53$	−2.85574	−0.392267	−0.196133	+	0.980577i	$0.562839\pi$
$54$	1.00000	0.136083
$55$	−20.8462	−2.81090
$56$	2.23635	0.298845
$57$	1.23635	0.163759
$58$	−0.116304	−0.0152715
$59$	−9.33959	−1.21591	−0.607956	−	0.793971i	$-0.708010\pi$
$59$	−9.33959	−1.21591	−0.607956	+	0.793971i	$0.708010\pi$
$60$	4.01421	0.518232
$61$	−1.08106	−0.138416	−0.0692080	−	0.997602i	$-0.522047\pi$
$61$	−1.08106	−0.138416	−0.0692080	+	0.997602i	$0.522047\pi$
$62$	−1.23635	−0.157017
$63$	2.23635	0.281754
$64$	1.00000	0.125000
$65$	4.01421	0.497901
$66$	−5.19311	−0.639227
$67$	−5.69974	−0.696334	−0.348167	−	0.937433i	$-0.613196\pi$
$67$	−5.69974	−0.696334	−0.348167	+	0.937433i	$0.613196\pi$
$68$	7.80246	0.946187
$69$	−2.23388	−0.268927
$70$	8.97718	1.07298
$71$	−14.5022	−1.72110	−0.860550	−	0.509367i	$-0.829880\pi$
$71$	−14.5022	−1.72110	−0.860550	+	0.509367i	$0.829880\pi$
$72$	1.00000	0.117851
$73$	−14.6250	−1.71173	−0.855863	−	0.517202i	$-0.826973\pi$
$73$	−14.6250	−1.71173	−0.855863	+	0.517202i	$0.826973\pi$
$74$	−4.93641	−0.573846
$75$	11.1139	1.28332
$76$	1.23635	0.141819
$77$	−11.6136	−1.32349
$78$	1.00000	0.113228
$79$	0.0792320	0.00891429	0.00445715	−	0.999990i	$-0.498581\pi$
$79$	0.0792320	0.00891429	0.00445715	+	0.999990i	$0.498581\pi$
$80$	4.01421	0.448802
$81$	1.00000	0.111111
$82$	3.24372	0.358209
$83$	−9.59784	−1.05350	−0.526750	−	0.850020i	$-0.676590\pi$
$83$	−9.59784	−1.05350	−0.526750	+	0.850020i	$0.676590\pi$
$84$	2.23635	0.244006
$85$	31.3207	3.39721
$86$	9.31683	1.00466
$87$	−0.116304	−0.0124691
$88$	−5.19311	−0.553587
$89$	16.0505	1.70135	0.850675	−	0.525692i	$-0.176194\pi$
$89$	16.0505	1.70135	0.850675	+	0.525692i	$0.176194\pi$
$90$	4.01421	0.423135
$91$	2.23635	0.234433
$92$	−2.23388	−0.232898
$93$	−1.23635	−0.128204
$94$	1.50695	0.155430
$95$	4.96297	0.509190
$96$	1.00000	0.102062
$97$	−3.88521	−0.394483	−0.197241	−	0.980355i	$-0.563198\pi$
$97$	−3.88521	−0.394483	−0.197241	+	0.980355i	$0.563198\pi$
$98$	−1.99873	−0.201903
$99$	−5.19311	−0.521927
$100$	11.1139	1.11139
$101$	−5.89235	−0.586311	−0.293155	−	0.956065i	$-0.594705\pi$
$101$	−5.89235	−0.586311	−0.293155	+	0.956065i	$0.594705\pi$
$102$	7.80246	0.772558
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	8.97718	0.876083
$106$	−2.85574	−0.277374
$107$	12.3430	1.19324	0.596620	−	0.802524i	$-0.296510\pi$
$107$	12.3430	1.19324	0.596620	+	0.802524i	$0.296510\pi$
$108$	1.00000	0.0962250
$109$	−3.93305	−0.376718	−0.188359	−	0.982100i	$-0.560317\pi$
$109$	−3.93305	−0.376718	−0.188359	+	0.982100i	$0.560317\pi$
$110$	−20.8462	−1.98761
$111$	−4.93641	−0.468543
$112$	2.23635	0.211315
$113$	11.7686	1.10710	0.553549	−	0.832817i	$-0.313273\pi$
$113$	11.7686	1.10710	0.553549	+	0.832817i	$0.313273\pi$
$114$	1.23635	0.115795
$115$	−8.96725	−0.836200
$116$	−0.116304	−0.0107986
$117$	1.00000	0.0924500
$118$	−9.33959	−0.859779
$119$	17.4490	1.59955
$120$	4.01421	0.366445
$121$	15.9684	1.45167
$122$	−1.08106	−0.0978749
$123$	3.24372	0.292476
$124$	−1.23635	−0.111028
$125$	24.5424	2.19514
$126$	2.23635	0.199230
$127$	−9.74264	−0.864520	−0.432260	−	0.901749i	$-0.642284\pi$
$127$	−9.74264	−0.864520	−0.432260	+	0.901749i	$0.642284\pi$
$128$	1.00000	0.0883883
$129$	9.31683	0.820301
$130$	4.01421	0.352069
$131$	8.54155	0.746279	0.373139	−	0.927775i	$-0.378281\pi$
$131$	8.54155	0.746279	0.373139	+	0.927775i	$0.378281\pi$
$132$	−5.19311	−0.452002
$133$	2.76491	0.239748
$134$	−5.69974	−0.492382
$135$	4.01421	0.345488
$136$	7.80246	0.669055
$137$	14.5616	1.24408	0.622039	−	0.782986i	$-0.286305\pi$
$137$	14.5616	1.24408	0.622039	+	0.782986i	$0.286305\pi$
$138$	−2.23388	−0.190160
$139$	15.4474	1.31023	0.655117	−	0.755527i	$-0.272619\pi$
$139$	15.4474	1.31023	0.655117	+	0.755527i	$0.272619\pi$
$140$	8.97718	0.758710
$141$	1.50695	0.126908
$142$	−14.5022	−1.21700
$143$	−5.19311	−0.434269
$144$	1.00000	0.0833333
$145$	−0.466869	−0.0387714
$146$	−14.6250	−1.21037
$147$	−1.99873	−0.164853
$148$	−4.93641	−0.405770
$149$	−22.4485	−1.83905	−0.919526	−	0.393030i	$-0.871427\pi$
$149$	−22.4485	−1.83905	−0.919526	+	0.393030i	$0.871427\pi$
$150$	11.1139	0.907444
$151$	−12.4597	−1.01396	−0.506978	−	0.861959i	$-0.669237\pi$
$151$	−12.4597	−1.01396	−0.506978	+	0.861959i	$0.669237\pi$
$152$	1.23635	0.100281
$153$	7.80246	0.630791
$154$	−11.6136	−0.935851
$155$	−4.96297	−0.398635
$156$	1.00000	0.0800641
$157$	−6.79618	−0.542394	−0.271197	−	0.962524i	$-0.587419\pi$
$157$	−6.79618	−0.542394	−0.271197	+	0.962524i	$0.587419\pi$
$158$	0.0792320	0.00630336
$159$	−2.85574	−0.226475
$160$	4.01421	0.317351
$161$	−4.99573	−0.393719
$162$	1.00000	0.0785674
$163$	16.7029	1.30827	0.654136	−	0.756377i	$-0.273033\pi$
$163$	16.7029	1.30827	0.654136	+	0.756377i	$0.273033\pi$
$164$	3.24372	0.253292
$165$	−20.8462	−1.62288
$166$	−9.59784	−0.744937
$167$	5.56949	0.430980	0.215490	−	0.976506i	$-0.430865\pi$
$167$	5.56949	0.430980	0.215490	+	0.976506i	$0.430865\pi$
$168$	2.23635	0.172538
$169$	1.00000	0.0769231
$170$	31.3207	2.40219
$171$	1.23635	0.0945461
$172$	9.31683	0.710402
$173$	5.15030	0.391570	0.195785	−	0.980647i	$-0.437274\pi$
$173$	5.15030	0.391570	0.195785	+	0.980647i	$0.437274\pi$
$174$	−0.116304	−0.00881699
$175$	24.8545	1.87883
$176$	−5.19311	−0.391445
$177$	−9.33959	−0.702007
$178$	16.0505	1.20304
$179$	4.92521	0.368128	0.184064	−	0.982914i	$-0.441075\pi$
$179$	4.92521	0.368128	0.184064	+	0.982914i	$0.441075\pi$
$180$	4.01421	0.299201
$181$	1.01041	0.0751028	0.0375514	−	0.999295i	$-0.488044\pi$
$181$	1.01041	0.0751028	0.0375514	+	0.999295i	$0.488044\pi$
$182$	2.23635	0.165769
$183$	−1.08106	−0.0799145
$184$	−2.23388	−0.164684
$185$	−19.8158	−1.45689
$186$	−1.23635	−0.0906536
$187$	−40.5190	−2.96304
$188$	1.50695	0.109906
$189$	2.23635	0.162671
$190$	4.96297	0.360052
$191$	−2.82982	−0.204759	−0.102379	−	0.994745i	$-0.532646\pi$
$191$	−2.82982	−0.204759	−0.102379	+	0.994745i	$0.532646\pi$
$192$	1.00000	0.0721688
$193$	−3.23167	−0.232621	−0.116310	−	0.993213i	$-0.537107\pi$
$193$	−3.23167	−0.232621	−0.116310	+	0.993213i	$0.537107\pi$
$194$	−3.88521	−0.278941
$195$	4.01421	0.287463
$196$	−1.99873	−0.142767
$197$	−14.0395	−1.00028	−0.500138	−	0.865946i	$-0.666717\pi$
$197$	−14.0395	−1.00028	−0.500138	+	0.865946i	$0.666717\pi$
$198$	−5.19311	−0.369058
$199$	−9.17267	−0.650233	−0.325117	−	0.945674i	$-0.605404\pi$
$199$	−9.17267	−0.650233	−0.325117	+	0.945674i	$0.605404\pi$
$200$	11.1139	0.785870
$201$	−5.69974	−0.402028
$202$	−5.89235	−0.414584
$203$	−0.260097	−0.0182552
$204$	7.80246	0.546281
$205$	13.0210	0.909424
$206$	−1.00000	−0.0696733
$207$	−2.23388	−0.155265
$208$	1.00000	0.0693375
$209$	−6.42050	−0.444115
$210$	8.97718	0.619484
$211$	11.2117	0.771846	0.385923	−	0.922531i	$-0.373883\pi$
$211$	11.2117	0.771846	0.385923	+	0.922531i	$0.373883\pi$
$212$	−2.85574	−0.196133
$213$	−14.5022	−0.993677
$214$	12.3430	0.843747
$215$	37.3997	2.55064
$216$	1.00000	0.0680414
$217$	−2.76491	−0.187695
$218$	−3.93305	−0.266380
$219$	−14.6250	−0.988266
$220$	−20.8462	−1.40545
$221$	7.80246	0.524850
$222$	−4.93641	−0.331310
$223$	−12.8222	−0.858636	−0.429318	−	0.903153i	$-0.641246\pi$
$223$	−12.8222	−0.858636	−0.429318	+	0.903153i	$0.641246\pi$
$224$	2.23635	0.149422
$225$	11.1139	0.740925
$226$	11.7686	0.782836
$227$	−19.3462	−1.28405	−0.642027	−	0.766682i	$-0.721906\pi$
$227$	−19.3462	−1.28405	−0.642027	+	0.766682i	$0.721906\pi$
$228$	1.23635	0.0818793
$229$	4.22990	0.279520	0.139760	−	0.990185i	$-0.455367\pi$
$229$	4.22990	0.279520	0.139760	+	0.990185i	$0.455367\pi$
$230$	−8.96725	−0.591283
$231$	−11.6136	−0.764119
$232$	−0.116304	−0.00763574
$233$	8.27641	0.542206	0.271103	−	0.962550i	$-0.412612\pi$
$233$	8.27641	0.542206	0.271103	+	0.962550i	$0.412612\pi$
$234$	1.00000	0.0653720
$235$	6.04922	0.394608
$236$	−9.33959	−0.607956
$237$	0.0792320	0.00514667
$238$	17.4490	1.13105
$239$	−18.6795	−1.20828	−0.604138	−	0.796880i	$-0.706482\pi$
$239$	−18.6795	−1.20828	−0.604138	+	0.796880i	$0.706482\pi$
$240$	4.01421	0.259116
$241$	0.516718	0.0332848	0.0166424	−	0.999862i	$-0.494702\pi$
$241$	0.516718	0.0332848	0.0166424	+	0.999862i	$0.494702\pi$
$242$	15.9684	1.02648
$243$	1.00000	0.0641500
$244$	−1.08106	−0.0692080
$245$	−8.02334	−0.512592
$246$	3.24372	0.206812
$247$	1.23635	0.0786671
$248$	−1.23635	−0.0785084
$249$	−9.59784	−0.608239
$250$	24.5424	1.55220
$251$	30.1537	1.90329	0.951643	−	0.307206i	$-0.0993941\pi$
$251$	30.1537	1.90329	0.951643	+	0.307206i	$0.0993941\pi$
$252$	2.23635	0.140877
$253$	11.6008	0.729333
$254$	−9.74264	−0.611308
$255$	31.3207	1.96138
$256$	1.00000	0.0625000
$257$	22.2068	1.38522	0.692610	−	0.721312i	$-0.256461\pi$
$257$	22.2068	1.38522	0.692610	+	0.721312i	$0.256461\pi$
$258$	9.31683	0.580041
$259$	−11.0395	−0.685964
$260$	4.01421	0.248951
$261$	−0.116304	−0.00719905
$262$	8.54155	0.527699
$263$	−11.1287	−0.686225	−0.343113	−	0.939294i	$-0.611481\pi$
$263$	−11.1287	−0.686225	−0.343113	+	0.939294i	$0.611481\pi$
$264$	−5.19311	−0.319614
$265$	−11.4636	−0.704200
$266$	2.76491	0.169528
$267$	16.0505	0.982275
$268$	−5.69974	−0.348167
$269$	−4.08454	−0.249039	−0.124520	−	0.992217i	$-0.539739\pi$
$269$	−4.08454	−0.249039	−0.124520	+	0.992217i	$0.539739\pi$
$270$	4.01421	0.244297
$271$	−19.9905	−1.21434	−0.607168	−	0.794573i	$-0.707695\pi$
$271$	−19.9905	−1.21434	−0.607168	+	0.794573i	$0.707695\pi$
$272$	7.80246	0.473093
$273$	2.23635	0.135350
$274$	14.5616	0.879696
$275$	−57.7155	−3.48038
$276$	−2.23388	−0.134464
$277$	12.2724	0.737379	0.368689	−	0.929553i	$-0.379807\pi$
$277$	12.2724	0.737379	0.368689	+	0.929553i	$0.379807\pi$
$278$	15.4474	0.926475
$279$	−1.23635	−0.0740184
$280$	8.97718	0.536489
$281$	−3.17235	−0.189247	−0.0946234	−	0.995513i	$-0.530165\pi$
$281$	−3.17235	−0.189247	−0.0946234	+	0.995513i	$0.530165\pi$
$282$	1.50695	0.0897377
$283$	−20.6819	−1.22941	−0.614705	−	0.788757i	$-0.710725\pi$
$283$	−20.6819	−1.22941	−0.614705	+	0.788757i	$0.710725\pi$
$284$	−14.5022	−0.860550
$285$	4.96297	0.293981
$286$	−5.19311	−0.307075
$287$	7.25409	0.428196
$288$	1.00000	0.0589256
$289$	43.8783	2.58108
$290$	−0.466869	−0.0274155
$291$	−3.88521	−0.227755
$292$	−14.6250	−0.855863
$293$	24.6718	1.44134	0.720670	−	0.693279i	$-0.243835\pi$
$293$	24.6718	1.44134	0.720670	+	0.693279i	$0.243835\pi$
$294$	−1.99873	−0.116569
$295$	−37.4911	−2.18281
$296$	−4.93641	−0.286923
$297$	−5.19311	−0.301335
$298$	−22.4485	−1.30041
$299$	−2.23388	−0.129188
$300$	11.1139	0.641660
$301$	20.8357	1.20095
$302$	−12.4597	−0.716975
$303$	−5.89235	−0.338507
$304$	1.23635	0.0709096
$305$	−4.33962	−0.248486
$306$	7.80246	0.446037
$307$	12.9064	0.736607	0.368303	−	0.929706i	$-0.379939\pi$
$307$	12.9064	0.736607	0.368303	+	0.929706i	$0.379939\pi$
$308$	−11.6136	−0.661747
$309$	−1.00000	−0.0568880
$310$	−4.96297	−0.281878
$311$	−20.6245	−1.16951	−0.584754	−	0.811211i	$-0.698809\pi$
$311$	−20.6245	−1.16951	−0.584754	+	0.811211i	$0.698809\pi$
$312$	1.00000	0.0566139
$313$	23.2827	1.31602	0.658008	−	0.753011i	$-0.271399\pi$
$313$	23.2827	1.31602	0.658008	+	0.753011i	$0.271399\pi$
$314$	−6.79618	−0.383530
$315$	8.97718	0.505807
$316$	0.0792320	0.00445715
$317$	6.19787	0.348107	0.174054	−	0.984736i	$-0.444313\pi$
$317$	6.19787	0.348107	0.174054	+	0.984736i	$0.444313\pi$
$318$	−2.85574	−0.160142
$319$	0.603980	0.0338164
$320$	4.01421	0.224401
$321$	12.3430	0.688917
$322$	−4.99573	−0.278401
$323$	9.64657	0.536750
$324$	1.00000	0.0555556
$325$	11.1139	0.616487
$326$	16.7029	0.925087
$327$	−3.93305	−0.217498
$328$	3.24372	0.179104
$329$	3.37008	0.185798
$330$	−20.8462	−1.14755
$331$	25.5869	1.40638	0.703192	−	0.711000i	$-0.251757\pi$
$331$	25.5869	1.40638	0.703192	+	0.711000i	$0.251757\pi$
$332$	−9.59784	−0.526750
$333$	−4.93641	−0.270514
$334$	5.56949	0.304749
$335$	−22.8799	−1.25006
$336$	2.23635	0.122003
$337$	22.0186	1.19943	0.599715	−	0.800214i	$-0.295281\pi$
$337$	22.0186	1.19943	0.599715	+	0.800214i	$0.295281\pi$
$338$	1.00000	0.0543928
$339$	11.7686	0.639183
$340$	31.3207	1.69860
$341$	6.42050	0.347690
$342$	1.23635	0.0668542
$343$	−20.1243	−1.08661
$344$	9.31683	0.502330
$345$	−8.96725	−0.482780
$346$	5.15030	0.276882
$347$	−18.6025	−0.998636	−0.499318	−	0.866419i	$-0.666416\pi$
$347$	−18.6025	−0.998636	−0.499318	+	0.866419i	$0.666416\pi$
$348$	−0.116304	−0.00623456
$349$	−21.2016	−1.13490	−0.567448	−	0.823409i	$-0.692069\pi$
$349$	−21.2016	−1.13490	−0.567448	+	0.823409i	$0.692069\pi$
$350$	24.8545	1.32853
$351$	1.00000	0.0533761
$352$	−5.19311	−0.276793
$353$	29.2088	1.55463	0.777313	−	0.629114i	$-0.216582\pi$
$353$	29.2088	1.55463	0.777313	+	0.629114i	$0.216582\pi$
$354$	−9.33959	−0.496394
$355$	−58.2150	−3.08973
$356$	16.0505	0.850675
$357$	17.4490	0.923501
$358$	4.92521	0.260306
$359$	−17.7302	−0.935764	−0.467882	−	0.883791i	$-0.654983\pi$
$359$	−17.7302	−0.935764	−0.467882	+	0.883791i	$0.654983\pi$
$360$	4.01421	0.211567
$361$	−17.4714	−0.919549
$362$	1.01041	0.0531057
$363$	15.9684	0.838121
$364$	2.23635	0.117217
$365$	−58.7078	−3.07291
$366$	−1.08106	−0.0565081
$367$	−17.9769	−0.938389	−0.469194	−	0.883095i	$-0.655456\pi$
$367$	−17.9769	−0.938389	−0.469194	+	0.883095i	$0.655456\pi$
$368$	−2.23388	−0.116449
$369$	3.24372	0.168861
$370$	−19.8158	−1.03017
$371$	−6.38645	−0.331568
$372$	−1.23635	−0.0641018
$373$	1.98299	0.102675	0.0513377	−	0.998681i	$-0.483652\pi$
$373$	1.98299	0.102675	0.0513377	+	0.998681i	$0.483652\pi$
$374$	−40.5190	−2.09519
$375$	24.5424	1.26736
$376$	1.50695	0.0777152
$377$	−0.116304	−0.00598997
$378$	2.23635	0.115025
$379$	−20.2152	−1.03839	−0.519193	−	0.854657i	$-0.673767\pi$
$379$	−20.2152	−1.03839	−0.519193	+	0.854657i	$0.673767\pi$
$380$	4.96297	0.254595
$381$	−9.74264	−0.499131
$382$	−2.82982	−0.144786
$383$	−23.9519	−1.22388	−0.611941	−	0.790903i	$-0.709611\pi$
$383$	−23.9519	−1.22388	−0.611941	+	0.790903i	$0.709611\pi$
$384$	1.00000	0.0510310
$385$	−46.6194	−2.37595
$386$	−3.23167	−0.164488
$387$	9.31683	0.473601
$388$	−3.88521	−0.197241
$389$	1.47466	0.0747682	0.0373841	−	0.999301i	$-0.488097\pi$
$389$	1.47466	0.0747682	0.0373841	+	0.999301i	$0.488097\pi$
$390$	4.01421	0.203267
$391$	−17.4297	−0.881459
$392$	−1.99873	−0.100951
$393$	8.54155	0.430864
$394$	−14.0395	−0.707302
$395$	0.318054	0.0160030
$396$	−5.19311	−0.260963
$397$	−31.1587	−1.56381	−0.781906	−	0.623396i	$-0.785752\pi$
$397$	−31.1587	−1.56381	−0.781906	+	0.623396i	$0.785752\pi$
$398$	−9.17267	−0.459784
$399$	2.76491	0.138419
$400$	11.1139	0.555694
$401$	−22.9265	−1.14489	−0.572446	−	0.819942i	$-0.694006\pi$
$401$	−22.9265	−1.14489	−0.572446	+	0.819942i	$0.694006\pi$
$402$	−5.69974	−0.284277
$403$	−1.23635	−0.0615870
$404$	−5.89235	−0.293155
$405$	4.01421	0.199468
$406$	−0.260097	−0.0129084
$407$	25.6353	1.27069
$408$	7.80246	0.386279
$409$	−26.9192	−1.33107	−0.665535	−	0.746367i	$-0.731796\pi$
$409$	−26.9192	−1.33107	−0.665535	+	0.746367i	$0.731796\pi$
$410$	13.0210	0.643060
$411$	14.5616	0.718269
$412$	−1.00000	−0.0492665
$413$	−20.8866	−1.02776
$414$	−2.23388	−0.109789
$415$	−38.5277	−1.89125
$416$	1.00000	0.0490290
$417$	15.4474	0.756464
$418$	−6.42050	−0.314037
$419$	10.9923	0.537008	0.268504	−	0.963279i	$-0.413471\pi$
$419$	10.9923	0.537008	0.268504	+	0.963279i	$0.413471\pi$
$420$	8.97718	0.438042
$421$	−2.16806	−0.105665	−0.0528323	−	0.998603i	$-0.516825\pi$
$421$	−2.16806	−0.105665	−0.0528323	+	0.998603i	$0.516825\pi$
$422$	11.2117	0.545777
$423$	1.50695	0.0732706
$424$	−2.85574	−0.138687
$425$	86.7155	4.20632
$426$	−14.5022	−0.702636
$427$	−2.41764	−0.116998
$428$	12.3430	0.596620
$429$	−5.19311	−0.250726
$430$	37.3997	1.80357
$431$	−9.15493	−0.440978	−0.220489	−	0.975390i	$-0.570765\pi$
$431$	−9.15493	−0.440978	−0.220489	+	0.975390i	$0.570765\pi$
$432$	1.00000	0.0481125
$433$	26.6172	1.27914	0.639571	−	0.768732i	$-0.279112\pi$
$433$	26.6172	1.27914	0.639571	+	0.768732i	$0.279112\pi$
$434$	−2.76491	−0.132720
$435$	−0.466869	−0.0223847
$436$	−3.93305	−0.188359
$437$	−2.76185	−0.132117
$438$	−14.6250	−0.698809
$439$	18.3242	0.874567	0.437284	−	0.899324i	$-0.355941\pi$
$439$	18.3242	0.874567	0.437284	+	0.899324i	$0.355941\pi$
$440$	−20.8462	−0.993804
$441$	−1.99873	−0.0951778
$442$	7.80246	0.371125
$443$	−26.4783	−1.25802	−0.629011	−	0.777396i	$-0.716540\pi$
$443$	−26.4783	−1.25802	−0.629011	+	0.777396i	$0.716540\pi$
$444$	−4.93641	−0.234272
$445$	64.4301	3.05428
$446$	−12.8222	−0.607147
$447$	−22.4485	−1.06178
$448$	2.23635	0.105658
$449$	6.13210	0.289392	0.144696	−	0.989476i	$-0.453780\pi$
$449$	6.13210	0.289392	0.144696	+	0.989476i	$0.453780\pi$
$450$	11.1139	0.523913
$451$	−16.8450	−0.793199
$452$	11.7686	0.553549
$453$	−12.4597	−0.585408
$454$	−19.3462	−0.907963
$455$	8.97718	0.420857
$456$	1.23635	0.0578974
$457$	13.7988	0.645483	0.322741	−	0.946487i	$-0.395396\pi$
$457$	13.7988	0.645483	0.322741	+	0.946487i	$0.395396\pi$
$458$	4.22990	0.197650
$459$	7.80246	0.364188
$460$	−8.96725	−0.418100
$461$	11.2673	0.524769	0.262385	−	0.964963i	$-0.415491\pi$
$461$	11.2673	0.524769	0.262385	+	0.964963i	$0.415491\pi$
$462$	−11.6136	−0.540314
$463$	29.5170	1.37177	0.685887	−	0.727708i	$-0.259415\pi$
$463$	29.5170	1.37177	0.685887	+	0.727708i	$0.259415\pi$
$464$	−0.116304	−0.00539928
$465$	−4.96297	−0.230152
$466$	8.27641	0.383397
$467$	27.2511	1.26103	0.630515	−	0.776177i	$-0.282844\pi$
$467$	27.2511	1.26103	0.630515	+	0.776177i	$0.282844\pi$
$468$	1.00000	0.0462250
$469$	−12.7466	−0.588584
$470$	6.04922	0.279030
$471$	−6.79618	−0.313151
$472$	−9.33959	−0.429890
$473$	−48.3833	−2.22467
$474$	0.0792320	0.00363925
$475$	13.7406	0.630464
$476$	17.4490	0.799775
$477$	−2.85574	−0.130756
$478$	−18.6795	−0.854380
$479$	16.4484	0.751547	0.375773	−	0.926712i	$-0.377377\pi$
$479$	16.4484	0.751547	0.375773	+	0.926712i	$0.377377\pi$
$480$	4.01421	0.183223
$481$	−4.93641	−0.225081
$482$	0.516718	0.0235359
$483$	−4.99573	−0.227314
$484$	15.9684	0.725834
$485$	−15.5960	−0.708179
$486$	1.00000	0.0453609
$487$	6.46698	0.293047	0.146523	−	0.989207i	$-0.453192\pi$
$487$	6.46698	0.293047	0.146523	+	0.989207i	$0.453192\pi$
$488$	−1.08106	−0.0489375
$489$	16.7029	0.755331
$490$	−8.02334	−0.362458
$491$	−10.2085	−0.460701	−0.230351	−	0.973108i	$-0.573987\pi$
$491$	−10.2085	−0.460701	−0.230351	+	0.973108i	$0.573987\pi$
$492$	3.24372	0.146238
$493$	−0.907458	−0.0408699
$494$	1.23635	0.0556261
$495$	−20.8462	−0.936968
$496$	−1.23635	−0.0555138
$497$	−32.4321	−1.45478
$498$	−9.59784	−0.430090
$499$	−7.91365	−0.354264	−0.177132	−	0.984187i	$-0.556682\pi$
$499$	−7.91365	−0.354264	−0.177132	+	0.984187i	$0.556682\pi$
$500$	24.5424	1.09757
$501$	5.56949	0.248826
$502$	30.1537	1.34583
$503$	23.6265	1.05345	0.526727	−	0.850035i	$-0.323419\pi$
$503$	23.6265	1.05345	0.526727	+	0.850035i	$0.323419\pi$
$504$	2.23635	0.0996150
$505$	−23.6531	−1.05255
$506$	11.6008	0.515716
$507$	1.00000	0.0444116
$508$	−9.74264	−0.432260
$509$	24.5165	1.08667	0.543336	−	0.839515i	$-0.317161\pi$
$509$	24.5165	1.08667	0.543336	+	0.839515i	$0.317161\pi$
$510$	31.3207	1.38690
$511$	−32.7066	−1.44686
$512$	1.00000	0.0441942
$513$	1.23635	0.0545862
$514$	22.2068	0.979499
$515$	−4.01421	−0.176887
$516$	9.31683	0.410151
$517$	−7.82577	−0.344177
$518$	−11.0395	−0.485050
$519$	5.15030	0.226073
$520$	4.01421	0.176035
$521$	−12.1888	−0.533999	−0.266999	−	0.963697i	$-0.586032\pi$
$521$	−12.1888	−0.533999	−0.266999	+	0.963697i	$0.586032\pi$
$522$	−0.116304	−0.00509049
$523$	23.5146	1.02822	0.514111	−	0.857724i	$-0.328122\pi$
$523$	23.5146	1.02822	0.514111	+	0.857724i	$0.328122\pi$
$524$	8.54155	0.373139
$525$	24.8545	1.08474
$526$	−11.1287	−0.485234
$527$	−9.64657	−0.420211
$528$	−5.19311	−0.226001
$529$	−18.0098	−0.783035
$530$	−11.4636	−0.497945
$531$	−9.33959	−0.405304
$532$	2.76491	0.119874
$533$	3.24372	0.140501
$534$	16.0505	0.694573
$535$	49.5472	2.14211
$536$	−5.69974	−0.246191
$537$	4.92521	0.212539
$538$	−4.08454	−0.176097
$539$	10.3796	0.447083
$540$	4.01421	0.172744
$541$	−25.3387	−1.08940	−0.544698	−	0.838632i	$-0.683356\pi$
$541$	−25.3387	−1.08940	−0.544698	+	0.838632i	$0.683356\pi$
$542$	−19.9905	−0.858665
$543$	1.01041	0.0433606
$544$	7.80246	0.334528
$545$	−15.7881	−0.676287
$546$	2.23635	0.0957070
$547$	−32.2208	−1.37766	−0.688830	−	0.724923i	$-0.741876\pi$
$547$	−32.2208	−1.37766	−0.688830	+	0.724923i	$0.741876\pi$
$548$	14.5616	0.622039
$549$	−1.08106	−0.0461387
$550$	−57.7155	−2.46100
$551$	−0.143793	−0.00612578
$552$	−2.23388	−0.0950801
$553$	0.177191	0.00753491
$554$	12.2724	0.521405
$555$	−19.8158	−0.841133
$556$	15.4474	0.655117
$557$	−40.4034	−1.71195	−0.855974	−	0.517019i	$-0.827042\pi$
$557$	−40.4034	−1.71195	−0.855974	+	0.517019i	$0.827042\pi$
$558$	−1.23635	−0.0523389
$559$	9.31683	0.394060
$560$	8.97718	0.379355
$561$	−40.5190	−1.71071
$562$	−3.17235	−0.133818
$563$	−13.5860	−0.572582	−0.286291	−	0.958143i	$-0.592422\pi$
$563$	−13.5860	−0.572582	−0.286291	+	0.958143i	$0.592422\pi$
$564$	1.50695	0.0634542
$565$	47.2416	1.98747
$566$	−20.6819	−0.869325
$567$	2.23635	0.0939179
$568$	−14.5022	−0.608500
$569$	−32.1345	−1.34715	−0.673573	−	0.739121i	$-0.735241\pi$
$569$	−32.1345	−1.34715	−0.673573	+	0.739121i	$0.735241\pi$
$570$	4.96297	0.207876
$571$	5.29242	0.221481	0.110741	−	0.993849i	$-0.464678\pi$
$571$	5.29242	0.221481	0.110741	+	0.993849i	$0.464678\pi$
$572$	−5.19311	−0.217135
$573$	−2.82982	−0.118218
$574$	7.25409	0.302780
$575$	−24.8270	−1.03536
$576$	1.00000	0.0416667
$577$	−17.7231	−0.737821	−0.368910	−	0.929465i	$-0.620269\pi$
$577$	−17.7231	−0.737821	−0.368910	+	0.929465i	$0.620269\pi$
$578$	43.8783	1.82510
$579$	−3.23167	−0.134304
$580$	−0.466869	−0.0193857
$581$	−21.4641	−0.890483
$582$	−3.88521	−0.161047
$583$	14.8302	0.614203
$584$	−14.6250	−0.605187
$585$	4.01421	0.165967
$586$	24.6718	1.01918
$587$	14.0828	0.581260	0.290630	−	0.956836i	$-0.406135\pi$
$587$	14.0828	0.581260	0.290630	+	0.956836i	$0.406135\pi$
$588$	−1.99873	−0.0824264
$589$	−1.52856	−0.0629834
$590$	−37.4911	−1.54348
$591$	−14.0395	−0.577509
$592$	−4.93641	−0.202885
$593$	−26.8020	−1.10063	−0.550313	−	0.834959i	$-0.685492\pi$
$593$	−26.8020	−1.10063	−0.550313	+	0.834959i	$0.685492\pi$
$594$	−5.19311	−0.213076
$595$	70.0441	2.87153
$596$	−22.4485	−0.919526
$597$	−9.17267	−0.375412
$598$	−2.23388	−0.0913500
$599$	27.3195	1.11625	0.558123	−	0.829758i	$-0.311522\pi$
$599$	27.3195	1.11625	0.558123	+	0.829758i	$0.311522\pi$
$600$	11.1139	0.453722
$601$	5.51305	0.224882	0.112441	−	0.993658i	$-0.464133\pi$
$601$	5.51305	0.224882	0.112441	+	0.993658i	$0.464133\pi$
$602$	20.8357	0.849200
$603$	−5.69974	−0.232111
$604$	−12.4597	−0.506978
$605$	64.1003	2.60605
$606$	−5.89235	−0.239360
$607$	−16.3386	−0.663165	−0.331583	−	0.943426i	$-0.607583\pi$
$607$	−16.3386	−0.663165	−0.331583	+	0.943426i	$0.607583\pi$
$608$	1.23635	0.0501406
$609$	−0.260097	−0.0105397
$610$	−4.33962	−0.175706
$611$	1.50695	0.0609648
$612$	7.80246	0.315396
$613$	32.4607	1.31107	0.655537	−	0.755163i	$-0.272442\pi$
$613$	32.4607	1.31107	0.655537	+	0.755163i	$0.272442\pi$
$614$	12.9064	0.520860
$615$	13.0210	0.525056
$616$	−11.6136	−0.467926
$617$	0.311419	0.0125373	0.00626863	−	0.999980i	$-0.498005\pi$
$617$	0.311419	0.0125373	0.00626863	+	0.999980i	$0.498005\pi$
$618$	−1.00000	−0.0402259
$619$	7.31497	0.294013	0.147007	−	0.989135i	$-0.453036\pi$
$619$	7.31497	0.294013	0.147007	+	0.989135i	$0.453036\pi$
$620$	−4.96297	−0.199318
$621$	−2.23388	−0.0896424
$622$	−20.6245	−0.826967
$623$	35.8945	1.43808
$624$	1.00000	0.0400320
$625$	42.9488	1.71795
$626$	23.2827	0.930564
$627$	−6.42050	−0.256410
$628$	−6.79618	−0.271197
$629$	−38.5161	−1.53574
$630$	8.97718	0.357659
$631$	3.35488	0.133556	0.0667779	−	0.997768i	$-0.478728\pi$
$631$	3.35488	0.133556	0.0667779	+	0.997768i	$0.478728\pi$
$632$	0.0792320	0.00315168
$633$	11.2117	0.445625
$634$	6.19787	0.246149
$635$	−39.1090	−1.55199
$636$	−2.85574	−0.113238
$637$	−1.99873	−0.0791928
$638$	0.603980	0.0239118
$639$	−14.5022	−0.573700
$640$	4.01421	0.158676
$641$	−28.7634	−1.13609	−0.568043	−	0.822999i	$-0.692299\pi$
$641$	−28.7634	−1.13609	−0.568043	+	0.822999i	$0.692299\pi$
$642$	12.3430	0.487138
$643$	29.1758	1.15058	0.575290	−	0.817949i	$-0.304889\pi$
$643$	29.1758	1.15058	0.575290	+	0.817949i	$0.304889\pi$
$644$	−4.99573	−0.196859
$645$	37.3997	1.47261
$646$	9.64657	0.379539
$647$	−21.0205	−0.826399	−0.413200	−	0.910640i	$-0.635589\pi$
$647$	−21.0205	−0.826399	−0.413200	+	0.910640i	$0.635589\pi$
$648$	1.00000	0.0392837
$649$	48.5015	1.90385
$650$	11.1139	0.435922
$651$	−2.76491	−0.108366
$652$	16.7029	0.654136
$653$	23.2411	0.909496	0.454748	−	0.890620i	$-0.349729\pi$
$653$	23.2411	0.909496	0.454748	+	0.890620i	$0.349729\pi$
$654$	−3.93305	−0.153794
$655$	34.2876	1.33973
$656$	3.24372	0.126646
$657$	−14.6250	−0.570575
$658$	3.37008	0.131379
$659$	−42.9632	−1.67361	−0.836805	−	0.547502i	$-0.815579\pi$
$659$	−42.9632	−1.67361	−0.836805	+	0.547502i	$0.815579\pi$
$660$	−20.8462	−0.811438
$661$	31.9187	1.24149	0.620746	−	0.784012i	$-0.286830\pi$
$661$	31.9187	1.24149	0.620746	+	0.784012i	$0.286830\pi$
$662$	25.5869	0.994464
$663$	7.80246	0.303022
$664$	−9.59784	−0.372468
$665$	11.0989	0.430399
$666$	−4.93641	−0.191282
$667$	0.259809	0.0100598
$668$	5.56949	0.215490
$669$	−12.8222	−0.495734
$670$	−22.8799	−0.883929
$671$	5.61408	0.216729
$672$	2.23635	0.0862691
$673$	27.9334	1.07675	0.538377	−	0.842704i	$-0.319038\pi$
$673$	27.9334	1.07675	0.538377	+	0.842704i	$0.319038\pi$
$674$	22.0186	0.848125
$675$	11.1139	0.427773
$676$	1.00000	0.0384615
$677$	−9.39035	−0.360900	−0.180450	−	0.983584i	$-0.557755\pi$
$677$	−9.39035	−0.360900	−0.180450	+	0.983584i	$0.557755\pi$
$678$	11.7686	0.451971
$679$	−8.68868	−0.333441
$680$	31.3207	1.20109
$681$	−19.3462	−0.741349
$682$	6.42050	0.245854
$683$	38.4458	1.47109	0.735545	−	0.677476i	$-0.236926\pi$
$683$	38.4458	1.47109	0.735545	+	0.677476i	$0.236926\pi$
$684$	1.23635	0.0472731
$685$	58.4531	2.23338
$686$	−20.1243	−0.768350
$687$	4.22990	0.161381
$688$	9.31683	0.355201
$689$	−2.85574	−0.108795
$690$	−8.96725	−0.341377
$691$	−21.3076	−0.810580	−0.405290	−	0.914188i	$-0.632829\pi$
$691$	−21.3076	−0.810580	−0.405290	+	0.914188i	$0.632829\pi$
$692$	5.15030	0.195785
$693$	−11.6136	−0.441164
$694$	−18.6025	−0.706143
$695$	62.0092	2.35214
$696$	−0.116304	−0.00440850
$697$	25.3090	0.958646
$698$	−21.2016	−0.802493
$699$	8.27641	0.313043
$700$	24.8545	0.939413
$701$	31.0938	1.17440	0.587198	−	0.809443i	$-0.300231\pi$
$701$	31.0938	1.17440	0.587198	+	0.809443i	$0.300231\pi$
$702$	1.00000	0.0377426
$703$	−6.10313	−0.230184
$704$	−5.19311	−0.195723
$705$	6.04922	0.227827
$706$	29.2088	1.09929
$707$	−13.1774	−0.495586
$708$	−9.33959	−0.351003
$709$	−9.34353	−0.350904	−0.175452	−	0.984488i	$-0.556139\pi$
$709$	−9.34353	−0.350904	−0.175452	+	0.984488i	$0.556139\pi$
$710$	−58.2150	−2.18477
$711$	0.0792320	0.00297143
$712$	16.0505	0.601518
$713$	2.76185	0.103432
$714$	17.4490	0.653014
$715$	−20.8462	−0.779604
$716$	4.92521	0.184064
$717$	−18.6795	−0.697599
$718$	−17.7302	−0.661685
$719$	−38.1738	−1.42364	−0.711821	−	0.702361i	$-0.752129\pi$
$719$	−38.1738	−1.42364	−0.711821	+	0.702361i	$0.752129\pi$
$720$	4.01421	0.149601
$721$	−2.23635	−0.0832861
$722$	−17.4714	−0.650220
$723$	0.516718	0.0192170
$724$	1.01041	0.0375514
$725$	−1.29259	−0.0480056
$726$	15.9684	0.592641
$727$	25.1504	0.932776	0.466388	−	0.884580i	$-0.345555\pi$
$727$	25.1504	0.932776	0.466388	+	0.884580i	$0.345555\pi$
$728$	2.23635	0.0828847
$729$	1.00000	0.0370370
$730$	−58.7078	−2.17287
$731$	72.6942	2.68869
$732$	−1.08106	−0.0399573
$733$	23.3435	0.862212	0.431106	−	0.902301i	$-0.358124\pi$
$733$	23.3435	0.862212	0.431106	+	0.902301i	$0.358124\pi$
$734$	−17.9769	−0.663541
$735$	−8.02334	−0.295945
$736$	−2.23388	−0.0823418
$737$	29.5993	1.09031
$738$	3.24372	0.119403
$739$	22.2284	0.817686	0.408843	−	0.912605i	$-0.365932\pi$
$739$	22.2284	0.817686	0.408843	+	0.912605i	$0.365932\pi$
$740$	−19.8158	−0.728443
$741$	1.23635	0.0454185
$742$	−6.38645	−0.234454
$743$	11.3691	0.417092	0.208546	−	0.978013i	$-0.433127\pi$
$743$	11.3691	0.417092	0.208546	+	0.978013i	$0.433127\pi$
$744$	−1.23635	−0.0453268
$745$	−90.1129	−3.30148
$746$	1.98299	0.0726025
$747$	−9.59784	−0.351167
$748$	−40.5190	−1.48152
$749$	27.6032	1.00860
$750$	24.5424	0.896161
$751$	−42.3666	−1.54598	−0.772990	−	0.634419i	$-0.781240\pi$
$751$	−42.3666	−1.54598	−0.772990	+	0.634419i	$0.781240\pi$
$752$	1.50695	0.0549529
$753$	30.1537	1.09886
$754$	−0.116304	−0.00423555
$755$	−50.0158	−1.82026
$756$	2.23635	0.0813353
$757$	−43.9294	−1.59664	−0.798320	−	0.602234i	$-0.794278\pi$
$757$	−43.9294	−1.59664	−0.798320	+	0.602234i	$0.794278\pi$
$758$	−20.2152	−0.734249
$759$	11.6008	0.421081
$760$	4.96297	0.180026
$761$	−13.7162	−0.497213	−0.248607	−	0.968605i	$-0.579973\pi$
$761$	−13.7162	−0.497213	−0.248607	+	0.968605i	$0.579973\pi$
$762$	−9.74264	−0.352939
$763$	−8.79568	−0.318425
$764$	−2.82982	−0.102379
$765$	31.3207	1.13240
$766$	−23.9519	−0.865416
$767$	−9.33959	−0.337233
$768$	1.00000	0.0360844
$769$	−9.37171	−0.337952	−0.168976	−	0.985620i	$-0.554046\pi$
$769$	−9.37171	−0.337952	−0.168976	+	0.985620i	$0.554046\pi$
$770$	−46.6194	−1.68005
$771$	22.2068	0.799758
$772$	−3.23167	−0.116310
$773$	23.6918	0.852133	0.426067	−	0.904692i	$-0.359899\pi$
$773$	23.6918	0.852133	0.426067	+	0.904692i	$0.359899\pi$
$774$	9.31683	0.334887
$775$	−13.7406	−0.493579
$776$	−3.88521	−0.139471
$777$	−11.0395	−0.396041
$778$	1.47466	0.0528691
$779$	4.01037	0.143687
$780$	4.01421	0.143732
$781$	75.3117	2.69486
$782$	−17.4297	−0.623286
$783$	−0.116304	−0.00415637
$784$	−1.99873	−0.0713834
$785$	−27.2813	−0.973710
$786$	8.54155	0.304667
$787$	−9.05780	−0.322876	−0.161438	−	0.986883i	$-0.551613\pi$
$787$	−9.05780	−0.322876	−0.161438	+	0.986883i	$0.551613\pi$
$788$	−14.0395	−0.500138
$789$	−11.1287	−0.396192
$790$	0.318054	0.0113158
$791$	26.3187	0.935786
$792$	−5.19311	−0.184529
$793$	−1.08106	−0.0383897
$794$	−31.1587	−1.10578
$795$	−11.4636	−0.406570
$796$	−9.17267	−0.325117
$797$	43.6515	1.54622	0.773108	−	0.634275i	$-0.218701\pi$
$797$	43.6515	1.54622	0.773108	+	0.634275i	$0.218701\pi$
$798$	2.76491	0.0978769
$799$	11.7579	0.415966
$800$	11.1139	0.392935
$801$	16.0505	0.567117
$802$	−22.9265	−0.809562
$803$	75.9491	2.68019
$804$	−5.69974	−0.201014
$805$	−20.0539	−0.706807
$806$	−1.23635	−0.0435486
$807$	−4.08454	−0.143783
$808$	−5.89235	−0.207292
$809$	21.3913	0.752079	0.376039	−	0.926604i	$-0.377286\pi$
$809$	21.3913	0.752079	0.376039	+	0.926604i	$0.377286\pi$
$810$	4.01421	0.141045
$811$	21.6682	0.760874	0.380437	−	0.924807i	$-0.375774\pi$
$811$	21.6682	0.760874	0.380437	+	0.924807i	$0.375774\pi$
$812$	−0.260097	−0.00912761
$813$	−19.9905	−0.701097
$814$	25.6353	0.898517
$815$	67.0489	2.34862
$816$	7.80246	0.273141
$817$	11.5189	0.402994
$818$	−26.9192	−0.941208
$819$	2.23635	0.0781444
$820$	13.0210	0.454712
$821$	5.07122	0.176987	0.0884934	−	0.996077i	$-0.471795\pi$
$821$	5.07122	0.176987	0.0884934	+	0.996077i	$0.471795\pi$
$822$	14.5616	0.507893
$823$	−54.6693	−1.90565	−0.952825	−	0.303520i	$-0.901838\pi$
$823$	−54.6693	−1.90565	−0.952825	+	0.303520i	$0.901838\pi$
$824$	−1.00000	−0.0348367
$825$	−57.7155	−2.00940
$826$	−20.8866	−0.726738
$827$	39.6918	1.38022	0.690110	−	0.723705i	$-0.257562\pi$
$827$	39.6918	1.38022	0.690110	+	0.723705i	$0.257562\pi$
$828$	−2.23388	−0.0776326
$829$	−5.18387	−0.180043	−0.0900216	−	0.995940i	$-0.528694\pi$
$829$	−5.18387	−0.180043	−0.0900216	+	0.995940i	$0.528694\pi$
$830$	−38.5277	−1.33732
$831$	12.2724	0.425726
$832$	1.00000	0.0346688
$833$	−15.5950	−0.540336
$834$	15.4474	0.534901
$835$	22.3571	0.773699
$836$	−6.42050	−0.222058
$837$	−1.23635	−0.0427345
$838$	10.9923	0.379722
$839$	−0.510751	−0.0176331	−0.00881655	−	0.999961i	$-0.502806\pi$
$839$	−0.510751	−0.0176331	−0.00881655	+	0.999961i	$0.502806\pi$
$840$	8.97718	0.309742
$841$	−28.9865	−0.999534
$842$	−2.16806	−0.0747162
$843$	−3.17235	−0.109262
$844$	11.2117	0.385923
$845$	4.01421	0.138093
$846$	1.50695	0.0518101
$847$	35.7108	1.22704
$848$	−2.85574	−0.0980666
$849$	−20.6819	−0.709801
$850$	86.7155	2.97432
$851$	11.0273	0.378012
$852$	−14.5022	−0.496839
$853$	50.8119	1.73977	0.869884	−	0.493257i	$-0.164194\pi$
$853$	50.8119	1.73977	0.869884	+	0.493257i	$0.164194\pi$
$854$	−2.41764	−0.0827299
$855$	4.96297	0.169730
$856$	12.3430	0.421874
$857$	−14.3372	−0.489751	−0.244876	−	0.969555i	$-0.578747\pi$
$857$	−14.3372	−0.489751	−0.244876	+	0.969555i	$0.578747\pi$
$858$	−5.19311	−0.177290
$859$	3.96274	0.135207	0.0676035	−	0.997712i	$-0.478465\pi$
$859$	3.96274	0.135207	0.0676035	+	0.997712i	$0.478465\pi$
$860$	37.3997	1.27532
$861$	7.25409	0.247219
$862$	−9.15493	−0.311818
$863$	−39.8694	−1.35717	−0.678585	−	0.734522i	$-0.737406\pi$
$863$	−39.8694	−1.35717	−0.678585	+	0.734522i	$0.737406\pi$
$864$	1.00000	0.0340207
$865$	20.6744	0.702950
$866$	26.6172	0.904490
$867$	43.8783	1.49019
$868$	−2.76491	−0.0938473
$869$	−0.411460	−0.0139578
$870$	−0.466869	−0.0158283
$871$	−5.69974	−0.193128
$872$	−3.93305	−0.133190
$873$	−3.88521	−0.131494
$874$	−2.76185	−0.0934211
$875$	54.8853	1.85546
$876$	−14.6250	−0.494133
$877$	4.72388	0.159514	0.0797571	−	0.996814i	$-0.474586\pi$
$877$	4.72388	0.159514	0.0797571	+	0.996814i	$0.474586\pi$
$878$	18.3242	0.618413
$879$	24.6718	0.832158
$880$	−20.8462	−0.702726
$881$	−23.8566	−0.803750	−0.401875	−	0.915694i	$-0.631641\pi$
$881$	−23.8566	−0.803750	−0.401875	+	0.915694i	$0.631641\pi$
$882$	−1.99873	−0.0673009
$883$	−3.65500	−0.123001	−0.0615003	−	0.998107i	$-0.519589\pi$
$883$	−3.65500	−0.123001	−0.0615003	+	0.998107i	$0.519589\pi$
$884$	7.80246	0.262425
$885$	−37.4911	−1.26025
$886$	−26.4783	−0.889556
$887$	34.6764	1.16432	0.582160	−	0.813074i	$-0.302208\pi$
$887$	34.6764	1.16432	0.582160	+	0.813074i	$0.302208\pi$
$888$	−4.93641	−0.165655
$889$	−21.7880	−0.730745
$890$	64.4301	2.15970
$891$	−5.19311	−0.173976
$892$	−12.8222	−0.429318
$893$	1.86312	0.0623470
$894$	−22.4485	−0.750790
$895$	19.7708	0.660866
$896$	2.23635	0.0747112
$897$	−2.23388	−0.0745869
$898$	6.13210	0.204631
$899$	0.143793	0.00479576
$900$	11.1139	0.370462
$901$	−22.2818	−0.742315
$902$	−16.8450	−0.560876
$903$	20.8357	0.693369
$904$	11.7686	0.391418
$905$	4.05598	0.134825
$906$	−12.4597	−0.413946
$907$	−26.9845	−0.896005	−0.448003	−	0.894032i	$-0.647864\pi$
$907$	−26.9845	−0.896005	−0.448003	+	0.894032i	$0.647864\pi$
$908$	−19.3462	−0.642027
$909$	−5.89235	−0.195437
$910$	8.97718	0.297591
$911$	−0.613965	−0.0203416	−0.0101708	−	0.999948i	$-0.503238\pi$
$911$	−0.613965	−0.0203416	−0.0101708	+	0.999948i	$0.503238\pi$
$912$	1.23635	0.0409397
$913$	49.8426	1.64955
$914$	13.7988	0.456425
$915$	−4.33962	−0.143463
$916$	4.22990	0.139760
$917$	19.1019	0.630801
$918$	7.80246	0.257519
$919$	−34.5629	−1.14013	−0.570063	−	0.821601i	$-0.693081\pi$
$919$	−34.5629	−1.14013	−0.570063	+	0.821601i	$0.693081\pi$
$920$	−8.96725	−0.295641
$921$	12.9064	0.425280
$922$	11.2673	0.371068
$923$	−14.5022	−0.477347
$924$	−11.6136	−0.382060
$925$	−54.8626	−1.80387
$926$	29.5170	0.969990
$927$	−1.00000	−0.0328443
$928$	−0.116304	−0.00381787
$929$	−4.79952	−0.157467	−0.0787336	−	0.996896i	$-0.525088\pi$
$929$	−4.79952	−0.157467	−0.0787336	+	0.996896i	$0.525088\pi$
$930$	−4.96297	−0.162742
$931$	−2.47114	−0.0809883
$932$	8.27641	0.271103
$933$	−20.6245	−0.675216
$934$	27.2511	0.891683
$935$	−162.652	−5.31928
$936$	1.00000	0.0326860
$937$	−27.9842	−0.914203	−0.457101	−	0.889415i	$-0.651112\pi$
$937$	−27.9842	−0.914203	−0.457101	+	0.889415i	$0.651112\pi$
$938$	−12.7466	−0.416192
$939$	23.2827	0.759803
$940$	6.04922	0.197304
$941$	10.5759	0.344763	0.172382	−	0.985030i	$-0.444854\pi$
$941$	10.5759	0.344763	0.172382	+	0.985030i	$0.444854\pi$
$942$	−6.79618	−0.221431
$943$	−7.24607	−0.235964
$944$	−9.33959	−0.303978
$945$	8.97718	0.292028
$946$	−48.3833	−1.57308
$947$	36.2632	1.17840	0.589198	−	0.807989i	$-0.299444\pi$
$947$	36.2632	1.17840	0.589198	+	0.807989i	$0.299444\pi$
$948$	0.0792320	0.00257334
$949$	−14.6250	−0.474747
$950$	13.7406	0.445805
$951$	6.19787	0.200980
$952$	17.4490	0.565526
$953$	13.7552	0.445576	0.222788	−	0.974867i	$-0.428484\pi$
$953$	13.7552	0.445576	0.222788	+	0.974867i	$0.428484\pi$
$954$	−2.85574	−0.0924581
$955$	−11.3595	−0.367585
$956$	−18.6795	−0.604138
$957$	0.603980	0.0195239
$958$	16.4484	0.531424
$959$	32.5648	1.05157
$960$	4.01421	0.129558
$961$	−29.4714	−0.950692
$962$	−4.93641	−0.159156
$963$	12.3430	0.397746
$964$	0.516718	0.0166424
$965$	−12.9726	−0.417603
$966$	−4.99573	−0.160735
$967$	−54.3821	−1.74881	−0.874406	−	0.485195i	$-0.838749\pi$
$967$	−54.3821	−1.74881	−0.874406	+	0.485195i	$0.838749\pi$
$968$	15.9684	0.513242
$969$	9.64657	0.309893
$970$	−15.5960	−0.500758
$971$	−24.1070	−0.773630	−0.386815	−	0.922157i	$-0.626425\pi$
$971$	−24.1070	−0.773630	−0.386815	+	0.922157i	$0.626425\pi$
$972$	1.00000	0.0320750
$973$	34.5459	1.10749
$974$	6.46698	0.207215
$975$	11.1139	0.355929
$976$	−1.08106	−0.0346040
$977$	25.1581	0.804879	0.402440	−	0.915447i	$-0.368162\pi$
$977$	25.1581	0.804879	0.402440	+	0.915447i	$0.368162\pi$
$978$	16.7029	0.534099
$979$	−83.3520	−2.66394
$980$	−8.02334	−0.256296
$981$	−3.93305	−0.125573
$982$	−10.2085	−0.325765
$983$	39.0255	1.24472	0.622361	−	0.782731i	$-0.286174\pi$
$983$	39.0255	1.24472	0.622361	+	0.782731i	$0.286174\pi$
$984$	3.24372	0.103406
$985$	−56.3576	−1.79570
$986$	−0.907458	−0.0288994
$987$	3.37008	0.107271
$988$	1.23635	0.0393336
$989$	−20.8127	−0.661804
$990$	−20.8462	−0.662536
$991$	−49.6119	−1.57597	−0.787987	−	0.615692i	$-0.788877\pi$
$991$	−49.6119	−1.57597	−0.787987	+	0.615692i	$0.788877\pi$
$992$	−1.23635	−0.0392542
$993$	25.5869	0.811976
$994$	−32.4321	−1.02868
$995$	−36.8210	−1.16730
$996$	−9.59784	−0.304119
$997$	35.6087	1.12774	0.563870	−	0.825864i	$-0.309312\pi$
$997$	35.6087	1.12774	0.563870	+	0.825864i	$0.309312\pi$
$998$	−7.91365	−0.250502
$999$	−4.93641	−0.156181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.v.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.v.1.10	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.01421 q^{5} +1.00000 q^{6} +2.23635 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.01421 q^{5} +1.00000 q^{6} +2.23635 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.01421 q^{10} -5.19311 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.23635 q^{14} +4.01421 q^{15} +1.00000 q^{16} +7.80246 q^{17} +1.00000 q^{18} +1.23635 q^{19} +4.01421 q^{20} +2.23635 q^{21} -5.19311 q^{22} -2.23388 q^{23} +1.00000 q^{24} +11.1139 q^{25} +1.00000 q^{26} +1.00000 q^{27} +2.23635 q^{28} -0.116304 q^{29} +4.01421 q^{30} -1.23635 q^{31} +1.00000 q^{32} -5.19311 q^{33} +7.80246 q^{34} +8.97718 q^{35} +1.00000 q^{36} -4.93641 q^{37} +1.23635 q^{38} +1.00000 q^{39} +4.01421 q^{40} +3.24372 q^{41} +2.23635 q^{42} +9.31683 q^{43} -5.19311 q^{44} +4.01421 q^{45} -2.23388 q^{46} +1.50695 q^{47} +1.00000 q^{48} -1.99873 q^{49} +11.1139 q^{50} +7.80246 q^{51} +1.00000 q^{52} -2.85574 q^{53} +1.00000 q^{54} -20.8462 q^{55} +2.23635 q^{56} +1.23635 q^{57} -0.116304 q^{58} -9.33959 q^{59} +4.01421 q^{60} -1.08106 q^{61} -1.23635 q^{62} +2.23635 q^{63} +1.00000 q^{64} +4.01421 q^{65} -5.19311 q^{66} -5.69974 q^{67} +7.80246 q^{68} -2.23388 q^{69} +8.97718 q^{70} -14.5022 q^{71} +1.00000 q^{72} -14.6250 q^{73} -4.93641 q^{74} +11.1139 q^{75} +1.23635 q^{76} -11.6136 q^{77} +1.00000 q^{78} +0.0792320 q^{79} +4.01421 q^{80} +1.00000 q^{81} +3.24372 q^{82} -9.59784 q^{83} +2.23635 q^{84} +31.3207 q^{85} +9.31683 q^{86} -0.116304 q^{87} -5.19311 q^{88} +16.0505 q^{89} +4.01421 q^{90} +2.23635 q^{91} -2.23388 q^{92} -1.23635 q^{93} +1.50695 q^{94} +4.96297 q^{95} +1.00000 q^{96} -3.88521 q^{97} -1.99873 q^{98} -5.19311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more