LMFDB - Embedded newform 4114.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4114,2,Mod(1,4114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4114, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4114.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4114 = 2 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4114.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:	$32.8504553916$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	4114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +0.618034 q^{5} +0.618034 q^{6} -3.85410 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +0.618034 q^{5} +0.618034 q^{6} -3.85410 q^{7} -1.00000 q^{8} -2.61803 q^{9} -0.618034 q^{10} -0.618034 q^{12} +2.23607 q^{13} +3.85410 q^{14} -0.381966 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.61803 q^{18} +6.47214 q^{19} +0.618034 q^{20} +2.38197 q^{21} -6.23607 q^{23} +0.618034 q^{24} -4.61803 q^{25} -2.23607 q^{26} +3.47214 q^{27} -3.85410 q^{28} +9.23607 q^{29} +0.381966 q^{30} -7.47214 q^{31} -1.00000 q^{32} -1.00000 q^{34} -2.38197 q^{35} -2.61803 q^{36} +7.47214 q^{37} -6.47214 q^{38} -1.38197 q^{39} -0.618034 q^{40} +9.70820 q^{41} -2.38197 q^{42} +4.38197 q^{43} -1.61803 q^{45} +6.23607 q^{46} +6.32624 q^{47} -0.618034 q^{48} +7.85410 q^{49} +4.61803 q^{50} -0.618034 q^{51} +2.23607 q^{52} -6.61803 q^{53} -3.47214 q^{54} +3.85410 q^{56} -4.00000 q^{57} -9.23607 q^{58} -7.76393 q^{59} -0.381966 q^{60} -13.9443 q^{61} +7.47214 q^{62} +10.0902 q^{63} +1.00000 q^{64} +1.38197 q^{65} +13.0902 q^{67} +1.00000 q^{68} +3.85410 q^{69} +2.38197 q^{70} -15.5623 q^{71} +2.61803 q^{72} +7.61803 q^{73} -7.47214 q^{74} +2.85410 q^{75} +6.47214 q^{76} +1.38197 q^{78} -10.2361 q^{79} +0.618034 q^{80} +5.70820 q^{81} -9.70820 q^{82} +1.09017 q^{83} +2.38197 q^{84} +0.618034 q^{85} -4.38197 q^{86} -5.70820 q^{87} +14.4164 q^{89} +1.61803 q^{90} -8.61803 q^{91} -6.23607 q^{92} +4.61803 q^{93} -6.32624 q^{94} +4.00000 q^{95} +0.618034 q^{96} +5.47214 q^{97} -7.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + q^{10} + q^{12} + q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 3 q^{18} + 4 q^{19} - q^{20} + 7 q^{21} - 8 q^{23} - q^{24} - 7 q^{25} - 2 q^{27} - q^{28} + 14 q^{29} + 3 q^{30} - 6 q^{31} - 2 q^{32} - 2 q^{34} - 7 q^{35} - 3 q^{36} + 6 q^{37} - 4 q^{38} - 5 q^{39} + q^{40} + 6 q^{41} - 7 q^{42} + 11 q^{43} - q^{45} + 8 q^{46} - 3 q^{47} + q^{48} + 9 q^{49} + 7 q^{50} + q^{51} - 11 q^{53} + 2 q^{54} + q^{56} - 8 q^{57} - 14 q^{58} - 20 q^{59} - 3 q^{60} - 10 q^{61} + 6 q^{62} + 9 q^{63} + 2 q^{64} + 5 q^{65} + 15 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} - 11 q^{71} + 3 q^{72} + 13 q^{73} - 6 q^{74} - q^{75} + 4 q^{76} + 5 q^{78} - 16 q^{79} - q^{80} - 2 q^{81} - 6 q^{82} - 9 q^{83} + 7 q^{84} - q^{85} - 11 q^{86} + 2 q^{87} + 2 q^{89} + q^{90} - 15 q^{91} - 8 q^{92} + 7 q^{93} + 3 q^{94} + 8 q^{95} - q^{96} + 2 q^{97} - 9 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 - 3 * q^9 + q^10 + q^12 + q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 3 * q^18 + 4 * q^19 - q^20 + 7 * q^21 - 8 * q^23 - q^24 - 7 * q^25 - 2 * q^27 - q^28 + 14 * q^29 + 3 * q^30 - 6 * q^31 - 2 * q^32 - 2 * q^34 - 7 * q^35 - 3 * q^36 + 6 * q^37 - 4 * q^38 - 5 * q^39 + q^40 + 6 * q^41 - 7 * q^42 + 11 * q^43 - q^45 + 8 * q^46 - 3 * q^47 + q^48 + 9 * q^49 + 7 * q^50 + q^51 - 11 * q^53 + 2 * q^54 + q^56 - 8 * q^57 - 14 * q^58 - 20 * q^59 - 3 * q^60 - 10 * q^61 + 6 * q^62 + 9 * q^63 + 2 * q^64 + 5 * q^65 + 15 * q^67 + 2 * q^68 + q^69 + 7 * q^70 - 11 * q^71 + 3 * q^72 + 13 * q^73 - 6 * q^74 - q^75 + 4 * q^76 + 5 * q^78 - 16 * q^79 - q^80 - 2 * q^81 - 6 * q^82 - 9 * q^83 + 7 * q^84 - q^85 - 11 * q^86 + 2 * q^87 + 2 * q^89 + q^90 - 15 * q^91 - 8 * q^92 + 7 * q^93 + 3 * q^94 + 8 * q^95 - q^96 + 2 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	0.618034	0.252311
$7$	−3.85410	−1.45671	−0.728357	−	0.685198i	$-0.759716\pi$
$7$	−3.85410	−1.45671	−0.728357	+	0.685198i	$0.759716\pi$
$8$	−1.00000	−0.353553
$9$	−2.61803	−0.872678
$10$	−0.618034	−0.195440
$11$	0	0
$11$	0	0
$12$	−0.618034	−0.178411
$13$	2.23607	0.620174	0.310087	−	0.950708i	$-0.399642\pi$
$13$	2.23607	0.620174	0.310087	+	0.950708i	$0.399642\pi$
$14$	3.85410	1.03005
$15$	−0.381966	−0.0986232
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.61803	0.617077
$19$	6.47214	1.48481	0.742405	−	0.669951i	$-0.233685\pi$
$19$	6.47214	1.48481	0.742405	+	0.669951i	$0.233685\pi$
$20$	0.618034	0.138197
$21$	2.38197	0.519788
$22$	0	0
$23$	−6.23607	−1.30031	−0.650155	−	0.759802i	$-0.725296\pi$
$23$	−6.23607	−1.30031	−0.650155	+	0.759802i	$0.725296\pi$
$24$	0.618034	0.126156
$25$	−4.61803	−0.923607
$26$	−2.23607	−0.438529
$27$	3.47214	0.668213
$28$	−3.85410	−0.728357
$29$	9.23607	1.71509	0.857547	−	0.514405i	$-0.171987\pi$
$29$	9.23607	1.71509	0.857547	+	0.514405i	$0.171987\pi$
$30$	0.381966	0.0697371
$31$	−7.47214	−1.34204	−0.671018	−	0.741441i	$-0.734143\pi$
$31$	−7.47214	−1.34204	−0.671018	+	0.741441i	$0.734143\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.00000	−0.171499
$35$	−2.38197	−0.402626
$36$	−2.61803	−0.436339
$37$	7.47214	1.22841	0.614206	−	0.789146i	$-0.289476\pi$
$37$	7.47214	1.22841	0.614206	+	0.789146i	$0.289476\pi$
$38$	−6.47214	−1.04992
$39$	−1.38197	−0.221292
$40$	−0.618034	−0.0977198
$41$	9.70820	1.51617	0.758083	−	0.652158i	$-0.226136\pi$
$41$	9.70820	1.51617	0.758083	+	0.652158i	$0.226136\pi$
$42$	−2.38197	−0.367545
$43$	4.38197	0.668244	0.334122	−	0.942530i	$-0.391560\pi$
$43$	4.38197	0.668244	0.334122	+	0.942530i	$0.391560\pi$
$44$	0	0
$45$	−1.61803	−0.241202
$46$	6.23607	0.919458
$47$	6.32624	0.922777	0.461388	−	0.887198i	$-0.347352\pi$
$47$	6.32624	0.922777	0.461388	+	0.887198i	$0.347352\pi$
$48$	−0.618034	−0.0892055
$49$	7.85410	1.12201
$50$	4.61803	0.653089
$51$	−0.618034	−0.0865421
$52$	2.23607	0.310087
$53$	−6.61803	−0.909057	−0.454528	−	0.890732i	$-0.650192\pi$
$53$	−6.61803	−0.909057	−0.454528	+	0.890732i	$0.650192\pi$
$54$	−3.47214	−0.472498
$55$	0	0
$56$	3.85410	0.515026
$57$	−4.00000	−0.529813
$58$	−9.23607	−1.21276
$59$	−7.76393	−1.01078	−0.505389	−	0.862892i	$-0.668651\pi$
$59$	−7.76393	−1.01078	−0.505389	+	0.862892i	$0.668651\pi$
$60$	−0.381966	−0.0493116
$61$	−13.9443	−1.78538	−0.892691	−	0.450670i	$-0.851185\pi$
$61$	−13.9443	−1.78538	−0.892691	+	0.450670i	$0.851185\pi$
$62$	7.47214	0.948962
$63$	10.0902	1.27124
$64$	1.00000	0.125000
$65$	1.38197	0.171412
$66$	0	0
$67$	13.0902	1.59922	0.799609	−	0.600520i	$-0.205040\pi$
$67$	13.0902	1.59922	0.799609	+	0.600520i	$0.205040\pi$
$68$	1.00000	0.121268
$69$	3.85410	0.463979
$70$	2.38197	0.284699
$71$	−15.5623	−1.84691	−0.923453	−	0.383712i	$-0.874646\pi$
$71$	−15.5623	−1.84691	−0.923453	+	0.383712i	$0.874646\pi$
$72$	2.61803	0.308538
$73$	7.61803	0.891623	0.445812	−	0.895127i	$-0.352915\pi$
$73$	7.61803	0.891623	0.445812	+	0.895127i	$0.352915\pi$
$74$	−7.47214	−0.868618
$75$	2.85410	0.329563
$76$	6.47214	0.742405
$77$	0	0
$78$	1.38197	0.156477
$79$	−10.2361	−1.15165	−0.575824	−	0.817574i	$-0.695319\pi$
$79$	−10.2361	−1.15165	−0.575824	+	0.817574i	$0.695319\pi$
$80$	0.618034	0.0690983
$81$	5.70820	0.634245
$82$	−9.70820	−1.07209
$83$	1.09017	0.119662	0.0598308	−	0.998209i	$-0.480944\pi$
$83$	1.09017	0.119662	0.0598308	+	0.998209i	$0.480944\pi$
$84$	2.38197	0.259894
$85$	0.618034	0.0670352
$86$	−4.38197	−0.472520
$87$	−5.70820	−0.611984
$88$	0	0
$89$	14.4164	1.52814	0.764068	−	0.645136i	$-0.223199\pi$
$89$	14.4164	1.52814	0.764068	+	0.645136i	$0.223199\pi$
$90$	1.61803	0.170556
$91$	−8.61803	−0.903415
$92$	−6.23607	−0.650155
$93$	4.61803	0.478868
$94$	−6.32624	−0.652502
$95$	4.00000	0.410391
$96$	0.618034	0.0630778
$97$	5.47214	0.555611	0.277806	−	0.960637i	$-0.410393\pi$
$97$	5.47214	0.555611	0.277806	+	0.960637i	$0.410393\pi$
$98$	−7.85410	−0.793384
$99$	0	0
$100$	−4.61803	−0.461803
$101$	−13.4721	−1.34053	−0.670264	−	0.742123i	$-0.733819\pi$
$101$	−13.4721	−1.34053	−0.670264	+	0.742123i	$0.733819\pi$
$102$	0.618034	0.0611945
$103$	−11.4721	−1.13038	−0.565192	−	0.824960i	$-0.691198\pi$
$103$	−11.4721	−1.13038	−0.565192	+	0.824960i	$0.691198\pi$
$104$	−2.23607	−0.219265
$105$	1.47214	0.143666
$106$	6.61803	0.642800
$107$	−2.70820	−0.261812	−0.130906	−	0.991395i	$-0.541789\pi$
$107$	−2.70820	−0.261812	−0.130906	+	0.991395i	$0.541789\pi$
$108$	3.47214	0.334106
$109$	−14.3820	−1.37754	−0.688771	−	0.724979i	$-0.741850\pi$
$109$	−14.3820	−1.37754	−0.688771	+	0.724979i	$0.741850\pi$
$110$	0	0
$111$	−4.61803	−0.438324
$112$	−3.85410	−0.364178
$113$	−7.94427	−0.747334	−0.373667	−	0.927563i	$-0.621900\pi$
$113$	−7.94427	−0.747334	−0.373667	+	0.927563i	$0.621900\pi$
$114$	4.00000	0.374634
$115$	−3.85410	−0.359397
$116$	9.23607	0.857547
$117$	−5.85410	−0.541212
$118$	7.76393	0.714728
$119$	−3.85410	−0.353305
$120$	0.381966	0.0348686
$121$	0	0
$122$	13.9443	1.26246
$123$	−6.00000	−0.541002
$124$	−7.47214	−0.671018
$125$	−5.94427	−0.531672
$126$	−10.0902	−0.898904
$127$	8.32624	0.738834	0.369417	−	0.929264i	$-0.379557\pi$
$127$	8.32624	0.738834	0.369417	+	0.929264i	$0.379557\pi$
$128$	−1.00000	−0.0883883
$129$	−2.70820	−0.238444
$130$	−1.38197	−0.121206
$131$	−7.23607	−0.632218	−0.316109	−	0.948723i	$-0.602377\pi$
$131$	−7.23607	−0.632218	−0.316109	+	0.948723i	$0.602377\pi$
$132$	0	0
$133$	−24.9443	−2.16294
$134$	−13.0902	−1.13082
$135$	2.14590	0.184689
$136$	−1.00000	−0.0857493
$137$	7.18034	0.613458	0.306729	−	0.951797i	$-0.400765\pi$
$137$	7.18034	0.613458	0.306729	+	0.951797i	$0.400765\pi$
$138$	−3.85410	−0.328083
$139$	1.29180	0.109569	0.0547844	−	0.998498i	$-0.482553\pi$
$139$	1.29180	0.109569	0.0547844	+	0.998498i	$0.482553\pi$
$140$	−2.38197	−0.201313
$141$	−3.90983	−0.329267
$142$	15.5623	1.30596
$143$	0	0
$144$	−2.61803	−0.218169
$145$	5.70820	0.474041
$146$	−7.61803	−0.630473
$147$	−4.85410	−0.400360
$148$	7.47214	0.614206
$149$	−20.0344	−1.64129	−0.820643	−	0.571442i	$-0.806384\pi$
$149$	−20.0344	−1.64129	−0.820643	+	0.571442i	$0.806384\pi$
$150$	−2.85410	−0.233036
$151$	−14.8885	−1.21161	−0.605806	−	0.795612i	$-0.707149\pi$
$151$	−14.8885	−1.21161	−0.605806	+	0.795612i	$0.707149\pi$
$152$	−6.47214	−0.524960
$153$	−2.61803	−0.211656
$154$	0	0
$155$	−4.61803	−0.370929
$156$	−1.38197	−0.110646
$157$	−16.0902	−1.28414	−0.642068	−	0.766648i	$-0.721923\pi$
$157$	−16.0902	−1.28414	−0.642068	+	0.766648i	$0.721923\pi$
$158$	10.2361	0.814338
$159$	4.09017	0.324372
$160$	−0.618034	−0.0488599
$161$	24.0344	1.89418
$162$	−5.70820	−0.448479
$163$	−6.47214	−0.506937	−0.253468	−	0.967344i	$-0.581571\pi$
$163$	−6.47214	−0.506937	−0.253468	+	0.967344i	$0.581571\pi$
$164$	9.70820	0.758083
$165$	0	0
$166$	−1.09017	−0.0846136
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	−2.38197	−0.183773
$169$	−8.00000	−0.615385
$170$	−0.618034	−0.0474010
$171$	−16.9443	−1.29576
$172$	4.38197	0.334122
$173$	13.2361	1.00632	0.503160	−	0.864193i	$-0.332171\pi$
$173$	13.2361	1.00632	0.503160	+	0.864193i	$0.332171\pi$
$174$	5.70820	0.432738
$175$	17.7984	1.34543
$176$	0	0
$177$	4.79837	0.360668
$178$	−14.4164	−1.08056
$179$	−3.29180	−0.246040	−0.123020	−	0.992404i	$-0.539258\pi$
$179$	−3.29180	−0.246040	−0.123020	+	0.992404i	$0.539258\pi$
$180$	−1.61803	−0.120601
$181$	2.23607	0.166206	0.0831028	−	0.996541i	$-0.473517\pi$
$181$	2.23607	0.166206	0.0831028	+	0.996541i	$0.473517\pi$
$182$	8.61803	0.638811
$183$	8.61803	0.637063
$184$	6.23607	0.459729
$185$	4.61803	0.339525
$186$	−4.61803	−0.338611
$187$	0	0
$188$	6.32624	0.461388
$189$	−13.3820	−0.973395
$190$	−4.00000	−0.290191
$191$	14.2705	1.03258	0.516289	−	0.856414i	$-0.327313\pi$
$191$	14.2705	1.03258	0.516289	+	0.856414i	$0.327313\pi$
$192$	−0.618034	−0.0446028
$193$	17.6525	1.27065	0.635327	−	0.772244i	$-0.280866\pi$
$193$	17.6525	1.27065	0.635327	+	0.772244i	$0.280866\pi$
$194$	−5.47214	−0.392876
$195$	−0.854102	−0.0611635
$196$	7.85410	0.561007
$197$	12.0344	0.857418	0.428709	−	0.903443i	$-0.358968\pi$
$197$	12.0344	0.857418	0.428709	+	0.903443i	$0.358968\pi$
$198$	0	0
$199$	−8.03444	−0.569546	−0.284773	−	0.958595i	$-0.591918\pi$
$199$	−8.03444	−0.569546	−0.284773	+	0.958595i	$0.591918\pi$
$200$	4.61803	0.326544
$201$	−8.09017	−0.570637
$202$	13.4721	0.947896
$203$	−35.5967	−2.49840
$204$	−0.618034	−0.0432710
$205$	6.00000	0.419058
$206$	11.4721	0.799302
$207$	16.3262	1.13475
$208$	2.23607	0.155043
$209$	0	0
$210$	−1.47214	−0.101587
$211$	10.2705	0.707051	0.353526	−	0.935425i	$-0.384983\pi$
$211$	10.2705	0.707051	0.353526	+	0.935425i	$0.384983\pi$
$212$	−6.61803	−0.454528
$213$	9.61803	0.659017
$214$	2.70820	0.185129
$215$	2.70820	0.184698
$216$	−3.47214	−0.236249
$217$	28.7984	1.95496
$218$	14.3820	0.974070
$219$	−4.70820	−0.318151
$220$	0	0
$221$	2.23607	0.150414
$222$	4.61803	0.309942
$223$	27.7082	1.85548	0.927739	−	0.373229i	$-0.121749\pi$
$223$	27.7082	1.85548	0.927739	+	0.373229i	$0.121749\pi$
$224$	3.85410	0.257513
$225$	12.0902	0.806011
$226$	7.94427	0.528445
$227$	−2.23607	−0.148413	−0.0742065	−	0.997243i	$-0.523642\pi$
$227$	−2.23607	−0.148413	−0.0742065	+	0.997243i	$0.523642\pi$
$228$	−4.00000	−0.264906
$229$	−17.5623	−1.16055	−0.580275	−	0.814421i	$-0.697055\pi$
$229$	−17.5623	−1.16055	−0.580275	+	0.814421i	$0.697055\pi$
$230$	3.85410	0.254132
$231$	0	0
$232$	−9.23607	−0.606378
$233$	−17.1803	−1.12552	−0.562761	−	0.826620i	$-0.690261\pi$
$233$	−17.1803	−1.12552	−0.562761	+	0.826620i	$0.690261\pi$
$234$	5.85410	0.382695
$235$	3.90983	0.255049
$236$	−7.76393	−0.505389
$237$	6.32624	0.410933
$238$	3.85410	0.249824
$239$	21.1803	1.37004	0.685021	−	0.728523i	$-0.259793\pi$
$239$	21.1803	1.37004	0.685021	+	0.728523i	$0.259793\pi$
$240$	−0.381966	−0.0246558
$241$	−13.9443	−0.898230	−0.449115	−	0.893474i	$-0.648261\pi$
$241$	−13.9443	−0.898230	−0.449115	+	0.893474i	$0.648261\pi$
$242$	0	0
$243$	−13.9443	−0.894525
$244$	−13.9443	−0.892691
$245$	4.85410	0.310117
$246$	6.00000	0.382546
$247$	14.4721	0.920840
$248$	7.47214	0.474481
$249$	−0.673762	−0.0426979
$250$	5.94427	0.375949
$251$	−16.4721	−1.03971	−0.519856	−	0.854254i	$-0.674014\pi$
$251$	−16.4721	−1.03971	−0.519856	+	0.854254i	$0.674014\pi$
$252$	10.0902	0.635621
$253$	0	0
$254$	−8.32624	−0.522435
$255$	−0.381966	−0.0239196
$256$	1.00000	0.0625000
$257$	−15.4164	−0.961649	−0.480825	−	0.876817i	$-0.659663\pi$
$257$	−15.4164	−0.961649	−0.480825	+	0.876817i	$0.659663\pi$
$258$	2.70820	0.168605
$259$	−28.7984	−1.78944
$260$	1.38197	0.0857059
$261$	−24.1803	−1.49673
$262$	7.23607	0.447046
$263$	−8.14590	−0.502298	−0.251149	−	0.967948i	$-0.580808\pi$
$263$	−8.14590	−0.502298	−0.251149	+	0.967948i	$0.580808\pi$
$264$	0	0
$265$	−4.09017	−0.251257
$266$	24.9443	1.52943
$267$	−8.90983	−0.545273
$268$	13.0902	0.799609
$269$	9.88854	0.602915	0.301458	−	0.953480i	$-0.402527\pi$
$269$	9.88854	0.602915	0.301458	+	0.953480i	$0.402527\pi$
$270$	−2.14590	−0.130595
$271$	−5.85410	−0.355611	−0.177806	−	0.984066i	$-0.556900\pi$
$271$	−5.85410	−0.355611	−0.177806	+	0.984066i	$0.556900\pi$
$272$	1.00000	0.0606339
$273$	5.32624	0.322359
$274$	−7.18034	−0.433780
$275$	0	0
$276$	3.85410	0.231990
$277$	20.1246	1.20917	0.604585	−	0.796540i	$-0.293339\pi$
$277$	20.1246	1.20917	0.604585	+	0.796540i	$0.293339\pi$
$278$	−1.29180	−0.0774768
$279$	19.5623	1.17116
$280$	2.38197	0.142350
$281$	−18.4721	−1.10196	−0.550978	−	0.834520i	$-0.685745\pi$
$281$	−18.4721	−1.10196	−0.550978	+	0.834520i	$0.685745\pi$
$282$	3.90983	0.232827
$283$	−9.27051	−0.551075	−0.275537	−	0.961290i	$-0.588856\pi$
$283$	−9.27051	−0.551075	−0.275537	+	0.961290i	$0.588856\pi$
$284$	−15.5623	−0.923453
$285$	−2.47214	−0.146437
$286$	0	0
$287$	−37.4164	−2.20862
$288$	2.61803	0.154269
$289$	1.00000	0.0588235
$290$	−5.70820	−0.335197
$291$	−3.38197	−0.198254
$292$	7.61803	0.445812
$293$	8.88854	0.519274	0.259637	−	0.965706i	$-0.416397\pi$
$293$	8.88854	0.519274	0.259637	+	0.965706i	$0.416397\pi$
$294$	4.85410	0.283097
$295$	−4.79837	−0.279372
$296$	−7.47214	−0.434309
$297$	0	0
$298$	20.0344	1.16056
$299$	−13.9443	−0.806418
$300$	2.85410	0.164782
$301$	−16.8885	−0.973439
$302$	14.8885	0.856739
$303$	8.32624	0.478330
$304$	6.47214	0.371202
$305$	−8.61803	−0.493467
$306$	2.61803	0.149663
$307$	−8.94427	−0.510477	−0.255238	−	0.966878i	$-0.582154\pi$
$307$	−8.94427	−0.510477	−0.255238	+	0.966878i	$0.582154\pi$
$308$	0	0
$309$	7.09017	0.403346
$310$	4.61803	0.262287
$311$	−4.27051	−0.242158	−0.121079	−	0.992643i	$-0.538636\pi$
$311$	−4.27051	−0.242158	−0.121079	+	0.992643i	$0.538636\pi$
$312$	1.38197	0.0782384
$313$	8.14590	0.460433	0.230217	−	0.973139i	$-0.426057\pi$
$313$	8.14590	0.460433	0.230217	+	0.973139i	$0.426057\pi$
$314$	16.0902	0.908021
$315$	6.23607	0.351363
$316$	−10.2361	−0.575824
$317$	−14.1803	−0.796447	−0.398224	−	0.917288i	$-0.630373\pi$
$317$	−14.1803	−0.796447	−0.398224	+	0.917288i	$0.630373\pi$
$318$	−4.09017	−0.229365
$319$	0	0
$320$	0.618034	0.0345492
$321$	1.67376	0.0934203
$322$	−24.0344	−1.33939
$323$	6.47214	0.360119
$324$	5.70820	0.317122
$325$	−10.3262	−0.572797
$326$	6.47214	0.358458
$327$	8.88854	0.491538
$328$	−9.70820	−0.536046
$329$	−24.3820	−1.34422
$330$	0	0
$331$	−13.7426	−0.755364	−0.377682	−	0.925935i	$-0.623279\pi$
$331$	−13.7426	−0.755364	−0.377682	+	0.925935i	$0.623279\pi$
$332$	1.09017	0.0598308
$333$	−19.5623	−1.07201
$334$	12.0000	0.656611
$335$	8.09017	0.442013
$336$	2.38197	0.129947
$337$	−5.56231	−0.302998	−0.151499	−	0.988457i	$-0.548410\pi$
$337$	−5.56231	−0.302998	−0.151499	+	0.988457i	$0.548410\pi$
$338$	8.00000	0.435143
$339$	4.90983	0.266665
$340$	0.618034	0.0335176
$341$	0	0
$342$	16.9443	0.916241
$343$	−3.29180	−0.177740
$344$	−4.38197	−0.236260
$345$	2.38197	0.128241
$346$	−13.2361	−0.711575
$347$	−14.8541	−0.797410	−0.398705	−	0.917079i	$-0.630540\pi$
$347$	−14.8541	−0.797410	−0.398705	+	0.917079i	$0.630540\pi$
$348$	−5.70820	−0.305992
$349$	12.5279	0.670601	0.335301	−	0.942111i	$-0.391162\pi$
$349$	12.5279	0.670601	0.335301	+	0.942111i	$0.391162\pi$
$350$	−17.7984	−0.951363
$351$	7.76393	0.414408
$352$	0	0
$353$	−1.96556	−0.104616	−0.0523081	−	0.998631i	$-0.516658\pi$
$353$	−1.96556	−0.104616	−0.0523081	+	0.998631i	$0.516658\pi$
$354$	−4.79837	−0.255031
$355$	−9.61803	−0.510472
$356$	14.4164	0.764068
$357$	2.38197	0.126067
$358$	3.29180	0.173977
$359$	9.70820	0.512379	0.256190	−	0.966627i	$-0.417533\pi$
$359$	9.70820	0.512379	0.256190	+	0.966627i	$0.417533\pi$
$360$	1.61803	0.0852779
$361$	22.8885	1.20466
$362$	−2.23607	−0.117525
$363$	0	0
$364$	−8.61803	−0.451708
$365$	4.70820	0.246439
$366$	−8.61803	−0.450472
$367$	−21.7082	−1.13316	−0.566580	−	0.824007i	$-0.691734\pi$
$367$	−21.7082	−1.13316	−0.566580	+	0.824007i	$0.691734\pi$
$368$	−6.23607	−0.325078
$369$	−25.4164	−1.32313
$370$	−4.61803	−0.240080
$371$	25.5066	1.32424
$372$	4.61803	0.239434
$373$	22.3607	1.15779	0.578896	−	0.815401i	$-0.303484\pi$
$373$	22.3607	1.15779	0.578896	+	0.815401i	$0.303484\pi$
$374$	0	0
$375$	3.67376	0.189712
$376$	−6.32624	−0.326251
$377$	20.6525	1.06366
$378$	13.3820	0.688294
$379$	7.29180	0.374554	0.187277	−	0.982307i	$-0.440034\pi$
$379$	7.29180	0.374554	0.187277	+	0.982307i	$0.440034\pi$
$380$	4.00000	0.205196
$381$	−5.14590	−0.263632
$382$	−14.2705	−0.730143
$383$	−14.5066	−0.741251	−0.370626	−	0.928782i	$-0.620857\pi$
$383$	−14.5066	−0.741251	−0.370626	+	0.928782i	$0.620857\pi$
$384$	0.618034	0.0315389
$385$	0	0
$386$	−17.6525	−0.898487
$387$	−11.4721	−0.583161
$388$	5.47214	0.277806
$389$	−30.4164	−1.54217	−0.771087	−	0.636730i	$-0.780286\pi$
$389$	−30.4164	−1.54217	−0.771087	+	0.636730i	$0.780286\pi$
$390$	0.854102	0.0432491
$391$	−6.23607	−0.315372
$392$	−7.85410	−0.396692
$393$	4.47214	0.225589
$394$	−12.0344	−0.606286
$395$	−6.32624	−0.318308
$396$	0	0
$397$	−28.9787	−1.45440	−0.727200	−	0.686426i	$-0.759179\pi$
$397$	−28.9787	−1.45440	−0.727200	+	0.686426i	$0.759179\pi$
$398$	8.03444	0.402730
$399$	15.4164	0.771786
$400$	−4.61803	−0.230902
$401$	−8.32624	−0.415792	−0.207896	−	0.978151i	$-0.566662\pi$
$401$	−8.32624	−0.415792	−0.207896	+	0.978151i	$0.566662\pi$
$402$	8.09017	0.403501
$403$	−16.7082	−0.832295
$404$	−13.4721	−0.670264
$405$	3.52786	0.175301
$406$	35.5967	1.76664
$407$	0	0
$408$	0.618034	0.0305972
$409$	−10.8885	−0.538404	−0.269202	−	0.963084i	$-0.586760\pi$
$409$	−10.8885	−0.538404	−0.269202	+	0.963084i	$0.586760\pi$
$410$	−6.00000	−0.296319
$411$	−4.43769	−0.218895
$412$	−11.4721	−0.565192
$413$	29.9230	1.47241
$414$	−16.3262	−0.802391
$415$	0.673762	0.0330737
$416$	−2.23607	−0.109632
$417$	−0.798374	−0.0390965
$418$	0	0
$419$	−29.1803	−1.42555	−0.712776	−	0.701391i	$-0.752563\pi$
$419$	−29.1803	−1.42555	−0.712776	+	0.701391i	$0.752563\pi$
$420$	1.47214	0.0718329
$421$	1.79837	0.0876474	0.0438237	−	0.999039i	$-0.486046\pi$
$421$	1.79837	0.0876474	0.0438237	+	0.999039i	$0.486046\pi$
$422$	−10.2705	−0.499961
$423$	−16.5623	−0.805287
$424$	6.61803	0.321400
$425$	−4.61803	−0.224008
$426$	−9.61803	−0.465995
$427$	53.7426	2.60079
$428$	−2.70820	−0.130906
$429$	0	0
$430$	−2.70820	−0.130601
$431$	−12.9443	−0.623504	−0.311752	−	0.950164i	$-0.600916\pi$
$431$	−12.9443	−0.623504	−0.311752	+	0.950164i	$0.600916\pi$
$432$	3.47214	0.167053
$433$	3.85410	0.185216	0.0926082	−	0.995703i	$-0.470480\pi$
$433$	3.85410	0.185216	0.0926082	+	0.995703i	$0.470480\pi$
$434$	−28.7984	−1.38237
$435$	−3.52786	−0.169148
$436$	−14.3820	−0.688771
$437$	−40.3607	−1.93071
$438$	4.70820	0.224967
$439$	−30.0902	−1.43613	−0.718063	−	0.695978i	$-0.754971\pi$
$439$	−30.0902	−1.43613	−0.718063	+	0.695978i	$0.754971\pi$
$440$	0	0
$441$	−20.5623	−0.979157
$442$	−2.23607	−0.106359
$443$	−22.4164	−1.06504	−0.532518	−	0.846419i	$-0.678754\pi$
$443$	−22.4164	−1.06504	−0.532518	+	0.846419i	$0.678754\pi$
$444$	−4.61803	−0.219162
$445$	8.90983	0.422366
$446$	−27.7082	−1.31202
$447$	12.3820	0.585647
$448$	−3.85410	−0.182089
$449$	−10.6738	−0.503726	−0.251863	−	0.967763i	$-0.581043\pi$
$449$	−10.6738	−0.503726	−0.251863	+	0.967763i	$0.581043\pi$
$450$	−12.0902	−0.569936
$451$	0	0
$452$	−7.94427	−0.373667
$453$	9.20163	0.432330
$454$	2.23607	0.104944
$455$	−5.32624	−0.249698
$456$	4.00000	0.187317
$457$	18.0689	0.845227	0.422613	−	0.906310i	$-0.361113\pi$
$457$	18.0689	0.845227	0.422613	+	0.906310i	$0.361113\pi$
$458$	17.5623	0.820633
$459$	3.47214	0.162065
$460$	−3.85410	−0.179698
$461$	20.5967	0.959286	0.479643	−	0.877464i	$-0.340766\pi$
$461$	20.5967	0.959286	0.479643	+	0.877464i	$0.340766\pi$
$462$	0	0
$463$	31.4508	1.46164	0.730822	−	0.682568i	$-0.239137\pi$
$463$	31.4508	1.46164	0.730822	+	0.682568i	$0.239137\pi$
$464$	9.23607	0.428774
$465$	2.85410	0.132356
$466$	17.1803	0.795864
$467$	1.61803	0.0748737	0.0374368	−	0.999299i	$-0.488081\pi$
$467$	1.61803	0.0748737	0.0374368	+	0.999299i	$0.488081\pi$
$468$	−5.85410	−0.270606
$469$	−50.4508	−2.32960
$470$	−3.90983	−0.180347
$471$	9.94427	0.458208
$472$	7.76393	0.357364
$473$	0	0
$474$	−6.32624	−0.290574
$475$	−29.8885	−1.37138
$476$	−3.85410	−0.176652
$477$	17.3262	0.793314
$478$	−21.1803	−0.968766
$479$	−14.5967	−0.666942	−0.333471	−	0.942760i	$-0.608220\pi$
$479$	−14.5967	−0.666942	−0.333471	+	0.942760i	$0.608220\pi$
$480$	0.381966	0.0174343
$481$	16.7082	0.761829
$482$	13.9443	0.635144
$483$	−14.8541	−0.675885
$484$	0	0
$485$	3.38197	0.153567
$486$	13.9443	0.632525
$487$	−40.1803	−1.82074	−0.910372	−	0.413790i	$-0.864205\pi$
$487$	−40.1803	−1.82074	−0.910372	+	0.413790i	$0.864205\pi$
$488$	13.9443	0.631228
$489$	4.00000	0.180886
$490$	−4.85410	−0.219286
$491$	−33.9443	−1.53188	−0.765942	−	0.642910i	$-0.777727\pi$
$491$	−33.9443	−1.53188	−0.765942	+	0.642910i	$0.777727\pi$
$492$	−6.00000	−0.270501
$493$	9.23607	0.415972
$494$	−14.4721	−0.651132
$495$	0	0
$496$	−7.47214	−0.335509
$497$	59.9787	2.69041
$498$	0.673762	0.0301920
$499$	−13.3607	−0.598106	−0.299053	−	0.954236i	$-0.596671\pi$
$499$	−13.3607	−0.598106	−0.299053	+	0.954236i	$0.596671\pi$
$500$	−5.94427	−0.265836
$501$	7.41641	0.331341
$502$	16.4721	0.735187
$503$	−25.3262	−1.12924	−0.564621	−	0.825351i	$-0.690977\pi$
$503$	−25.3262	−1.12924	−0.564621	+	0.825351i	$0.690977\pi$
$504$	−10.0902	−0.449452
$505$	−8.32624	−0.370513
$506$	0	0
$507$	4.94427	0.219583
$508$	8.32624	0.369417
$509$	7.58359	0.336137	0.168068	−	0.985775i	$-0.446247\pi$
$509$	7.58359	0.336137	0.168068	+	0.985775i	$0.446247\pi$
$510$	0.381966	0.0169137
$511$	−29.3607	−1.29884
$512$	−1.00000	−0.0441942
$513$	22.4721	0.992169
$514$	15.4164	0.679989
$515$	−7.09017	−0.312430
$516$	−2.70820	−0.119222
$517$	0	0
$518$	28.7984	1.26533
$519$	−8.18034	−0.359077
$520$	−1.38197	−0.0606032
$521$	24.5623	1.07609	0.538047	−	0.842915i	$-0.319162\pi$
$521$	24.5623	1.07609	0.538047	+	0.842915i	$0.319162\pi$
$522$	24.1803	1.05834
$523$	5.05573	0.221072	0.110536	−	0.993872i	$-0.464743\pi$
$523$	5.05573	0.221072	0.110536	+	0.993872i	$0.464743\pi$
$524$	−7.23607	−0.316109
$525$	−11.0000	−0.480079
$526$	8.14590	0.355178
$527$	−7.47214	−0.325491
$528$	0	0
$529$	15.8885	0.690806
$530$	4.09017	0.177666
$531$	20.3262	0.882084
$532$	−24.9443	−1.08147
$533$	21.7082	0.940287
$534$	8.90983	0.385566
$535$	−1.67376	−0.0723630
$536$	−13.0902	−0.565409
$537$	2.03444	0.0877926
$538$	−9.88854	−0.426325
$539$	0	0
$540$	2.14590	0.0923447
$541$	20.9443	0.900465	0.450232	−	0.892911i	$-0.351341\pi$
$541$	20.9443	0.900465	0.450232	+	0.892911i	$0.351341\pi$
$542$	5.85410	0.251455
$543$	−1.38197	−0.0593058
$544$	−1.00000	−0.0428746
$545$	−8.88854	−0.380743
$546$	−5.32624	−0.227942
$547$	−32.1246	−1.37355	−0.686775	−	0.726870i	$-0.740974\pi$
$547$	−32.1246	−1.37355	−0.686775	+	0.726870i	$0.740974\pi$
$548$	7.18034	0.306729
$549$	36.5066	1.55806
$550$	0	0
$551$	59.7771	2.54659
$552$	−3.85410	−0.164041
$553$	39.4508	1.67762
$554$	−20.1246	−0.855013
$555$	−2.85410	−0.121150
$556$	1.29180	0.0547844
$557$	−14.5066	−0.614663	−0.307332	−	0.951602i	$-0.599436\pi$
$557$	−14.5066	−0.614663	−0.307332	+	0.951602i	$0.599436\pi$
$558$	−19.5623	−0.828138
$559$	9.79837	0.414427
$560$	−2.38197	−0.100656
$561$	0	0
$562$	18.4721	0.779200
$563$	19.1803	0.808355	0.404177	−	0.914681i	$-0.367558\pi$
$563$	19.1803	0.808355	0.404177	+	0.914681i	$0.367558\pi$
$564$	−3.90983	−0.164634
$565$	−4.90983	−0.206558
$566$	9.27051	0.389669
$567$	−22.0000	−0.923913
$568$	15.5623	0.652980
$569$	37.7082	1.58081	0.790405	−	0.612585i	$-0.209870\pi$
$569$	37.7082	1.58081	0.790405	+	0.612585i	$0.209870\pi$
$570$	2.47214	0.103546
$571$	36.1803	1.51410	0.757050	−	0.653357i	$-0.226640\pi$
$571$	36.1803	1.51410	0.757050	+	0.653357i	$0.226640\pi$
$572$	0	0
$573$	−8.81966	−0.368447
$574$	37.4164	1.56173
$575$	28.7984	1.20098
$576$	−2.61803	−0.109085
$577$	35.4721	1.47672	0.738362	−	0.674404i	$-0.235600\pi$
$577$	35.4721	1.47672	0.738362	+	0.674404i	$0.235600\pi$
$578$	−1.00000	−0.0415945
$579$	−10.9098	−0.453397
$580$	5.70820	0.237020
$581$	−4.20163	−0.174313
$582$	3.38197	0.140187
$583$	0	0
$584$	−7.61803	−0.315236
$585$	−3.61803	−0.149587
$586$	−8.88854	−0.367182
$587$	−31.6180	−1.30502	−0.652508	−	0.757782i	$-0.726283\pi$
$587$	−31.6180	−1.30502	−0.652508	+	0.757782i	$0.726283\pi$
$588$	−4.85410	−0.200180
$589$	−48.3607	−1.99267
$590$	4.79837	0.197546
$591$	−7.43769	−0.305946
$592$	7.47214	0.307103
$593$	5.74265	0.235822	0.117911	−	0.993024i	$-0.462380\pi$
$593$	5.74265	0.235822	0.117911	+	0.993024i	$0.462380\pi$
$594$	0	0
$595$	−2.38197	−0.0976511
$596$	−20.0344	−0.820643
$597$	4.96556	0.203227
$598$	13.9443	0.570224
$599$	−34.5623	−1.41218	−0.706089	−	0.708123i	$-0.749542\pi$
$599$	−34.5623	−1.41218	−0.706089	+	0.708123i	$0.749542\pi$
$600$	−2.85410	−0.116518
$601$	−13.0000	−0.530281	−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000	−0.530281	−0.265141	+	0.964210i	$0.585418\pi$
$602$	16.8885	0.688326
$603$	−34.2705	−1.39560
$604$	−14.8885	−0.605806
$605$	0	0
$606$	−8.32624	−0.338230
$607$	−39.1591	−1.58942	−0.794708	−	0.606991i	$-0.792376\pi$
$607$	−39.1591	−1.58942	−0.794708	+	0.606991i	$0.792376\pi$
$608$	−6.47214	−0.262480
$609$	22.0000	0.891485
$610$	8.61803	0.348934
$611$	14.1459	0.572282
$612$	−2.61803	−0.105828
$613$	4.27051	0.172484	0.0862421	−	0.996274i	$-0.472514\pi$
$613$	4.27051	0.172484	0.0862421	+	0.996274i	$0.472514\pi$
$614$	8.94427	0.360961
$615$	−3.70820	−0.149529
$616$	0	0
$617$	−24.6180	−0.991085	−0.495542	−	0.868584i	$-0.665031\pi$
$617$	−24.6180	−0.991085	−0.495542	+	0.868584i	$0.665031\pi$
$618$	−7.09017	−0.285208
$619$	−17.7639	−0.713993	−0.356996	−	0.934106i	$-0.616199\pi$
$619$	−17.7639	−0.713993	−0.356996	+	0.934106i	$0.616199\pi$
$620$	−4.61803	−0.185465
$621$	−21.6525	−0.868884
$622$	4.27051	0.171232
$623$	−55.5623	−2.22606
$624$	−1.38197	−0.0553229
$625$	19.4164	0.776656
$626$	−8.14590	−0.325576
$627$	0	0
$628$	−16.0902	−0.642068
$629$	7.47214	0.297934
$630$	−6.23607	−0.248451
$631$	26.0132	1.03557	0.517784	−	0.855512i	$-0.326757\pi$
$631$	26.0132	1.03557	0.517784	+	0.855512i	$0.326757\pi$
$632$	10.2361	0.407169
$633$	−6.34752	−0.252291
$634$	14.1803	0.563173
$635$	5.14590	0.204209
$636$	4.09017	0.162186
$637$	17.5623	0.695844
$638$	0	0
$639$	40.7426	1.61175
$640$	−0.618034	−0.0244299
$641$	−3.97871	−0.157150	−0.0785749	−	0.996908i	$-0.525037\pi$
$641$	−3.97871	−0.157150	−0.0785749	+	0.996908i	$0.525037\pi$
$642$	−1.67376	−0.0660581
$643$	29.6869	1.17074	0.585369	−	0.810767i	$-0.300950\pi$
$643$	29.6869	1.17074	0.585369	+	0.810767i	$0.300950\pi$
$644$	24.0344	0.947090
$645$	−1.67376	−0.0659043
$646$	−6.47214	−0.254643
$647$	−28.3820	−1.11581	−0.557905	−	0.829905i	$-0.688395\pi$
$647$	−28.3820	−1.11581	−0.557905	+	0.829905i	$0.688395\pi$
$648$	−5.70820	−0.224239
$649$	0	0
$650$	10.3262	0.405028
$651$	−17.7984	−0.697573
$652$	−6.47214	−0.253468
$653$	5.76393	0.225560	0.112780	−	0.993620i	$-0.464024\pi$
$653$	5.76393	0.225560	0.112780	+	0.993620i	$0.464024\pi$
$654$	−8.88854	−0.347570
$655$	−4.47214	−0.174741
$656$	9.70820	0.379042
$657$	−19.9443	−0.778100
$658$	24.3820	0.950508
$659$	−9.41641	−0.366811	−0.183406	−	0.983037i	$-0.558712\pi$
$659$	−9.41641	−0.366811	−0.183406	+	0.983037i	$0.558712\pi$
$660$	0	0
$661$	30.5410	1.18791	0.593954	−	0.804499i	$-0.297566\pi$
$661$	30.5410	1.18791	0.593954	+	0.804499i	$0.297566\pi$
$662$	13.7426	0.534123
$663$	−1.38197	−0.0536711
$664$	−1.09017	−0.0423068
$665$	−15.4164	−0.597823
$666$	19.5623	0.758024
$667$	−57.5967	−2.23015
$668$	−12.0000	−0.464294
$669$	−17.1246	−0.662076
$670$	−8.09017	−0.312551
$671$	0	0
$672$	−2.38197	−0.0918863
$673$	−19.5623	−0.754071	−0.377036	−	0.926199i	$-0.623057\pi$
$673$	−19.5623	−0.754071	−0.377036	+	0.926199i	$0.623057\pi$
$674$	5.56231	0.214252
$675$	−16.0344	−0.617166
$676$	−8.00000	−0.307692
$677$	−11.3050	−0.434485	−0.217242	−	0.976118i	$-0.569706\pi$
$677$	−11.3050	−0.434485	−0.217242	+	0.976118i	$0.569706\pi$
$678$	−4.90983	−0.188561
$679$	−21.0902	−0.809366
$680$	−0.618034	−0.0237005
$681$	1.38197	0.0529571
$682$	0	0
$683$	21.6525	0.828509	0.414254	−	0.910161i	$-0.364042\pi$
$683$	21.6525	0.828509	0.414254	+	0.910161i	$0.364042\pi$
$684$	−16.9443	−0.647880
$685$	4.43769	0.169556
$686$	3.29180	0.125681
$687$	10.8541	0.414110
$688$	4.38197	0.167061
$689$	−14.7984	−0.563773
$690$	−2.38197	−0.0906799
$691$	17.5836	0.668911	0.334456	−	0.942411i	$-0.391448\pi$
$691$	17.5836	0.668911	0.334456	+	0.942411i	$0.391448\pi$
$692$	13.2361	0.503160
$693$	0	0
$694$	14.8541	0.563854
$695$	0.798374	0.0302840
$696$	5.70820	0.216369
$697$	9.70820	0.367724
$698$	−12.5279	−0.474187
$699$	10.6180	0.401611
$700$	17.7984	0.672715
$701$	39.1033	1.47691	0.738456	−	0.674302i	$-0.235555\pi$
$701$	39.1033	1.47691	0.738456	+	0.674302i	$0.235555\pi$
$702$	−7.76393	−0.293031
$703$	48.3607	1.82396
$704$	0	0
$705$	−2.41641	−0.0910072
$706$	1.96556	0.0739748
$707$	51.9230	1.95276
$708$	4.79837	0.180334
$709$	8.81966	0.331229	0.165615	−	0.986191i	$-0.447039\pi$
$709$	8.81966	0.331229	0.165615	+	0.986191i	$0.447039\pi$
$710$	9.61803	0.360958
$711$	26.7984	1.00502
$712$	−14.4164	−0.540278
$713$	46.5967	1.74506
$714$	−2.38197	−0.0891428
$715$	0	0
$716$	−3.29180	−0.123020
$717$	−13.0902	−0.488861
$718$	−9.70820	−0.362307
$719$	−15.8197	−0.589974	−0.294987	−	0.955501i	$-0.595315\pi$
$719$	−15.8197	−0.589974	−0.294987	+	0.955501i	$0.595315\pi$
$720$	−1.61803	−0.0603006
$721$	44.2148	1.64664
$722$	−22.8885	−0.851823
$723$	8.61803	0.320508
$724$	2.23607	0.0831028
$725$	−42.6525	−1.58407
$726$	0	0
$727$	28.3607	1.05184	0.525920	−	0.850534i	$-0.323721\pi$
$727$	28.3607	1.05184	0.525920	+	0.850534i	$0.323721\pi$
$728$	8.61803	0.319406
$729$	−8.50658	−0.315058
$730$	−4.70820	−0.174258
$731$	4.38197	0.162073
$732$	8.61803	0.318532
$733$	45.6525	1.68621	0.843106	−	0.537747i	$-0.180724\pi$
$733$	45.6525	1.68621	0.843106	+	0.537747i	$0.180724\pi$
$734$	21.7082	0.801264
$735$	−3.00000	−0.110657
$736$	6.23607	0.229865
$737$	0	0
$738$	25.4164	0.935591
$739$	28.3607	1.04326	0.521632	−	0.853170i	$-0.325323\pi$
$739$	28.3607	1.04326	0.521632	+	0.853170i	$0.325323\pi$
$740$	4.61803	0.169762
$741$	−8.94427	−0.328576
$742$	−25.5066	−0.936376
$743$	10.6180	0.389538	0.194769	−	0.980849i	$-0.437604\pi$
$743$	10.6180	0.389538	0.194769	+	0.980849i	$0.437604\pi$
$744$	−4.61803	−0.169305
$745$	−12.3820	−0.453640
$746$	−22.3607	−0.818683
$747$	−2.85410	−0.104426
$748$	0	0
$749$	10.4377	0.381385
$750$	−3.67376	−0.134147
$751$	19.0000	0.693320	0.346660	−	0.937991i	$-0.387316\pi$
$751$	19.0000	0.693320	0.346660	+	0.937991i	$0.387316\pi$
$752$	6.32624	0.230694
$753$	10.1803	0.370992
$754$	−20.6525	−0.752119
$755$	−9.20163	−0.334881
$756$	−13.3820	−0.486697
$757$	−25.1803	−0.915195	−0.457598	−	0.889159i	$-0.651290\pi$
$757$	−25.1803	−0.915195	−0.457598	+	0.889159i	$0.651290\pi$
$758$	−7.29180	−0.264850
$759$	0	0
$760$	−4.00000	−0.145095
$761$	−5.74265	−0.208171	−0.104085	−	0.994568i	$-0.533192\pi$
$761$	−5.74265	−0.208171	−0.104085	+	0.994568i	$0.533192\pi$
$762$	5.14590	0.186416
$763$	55.4296	2.00668
$764$	14.2705	0.516289
$765$	−1.61803	−0.0585001
$766$	14.5066	0.524144
$767$	−17.3607	−0.626858
$768$	−0.618034	−0.0223014
$769$	−26.8328	−0.967616	−0.483808	−	0.875174i	$-0.660747\pi$
$769$	−26.8328	−0.967616	−0.483808	+	0.875174i	$0.660747\pi$
$770$	0	0
$771$	9.52786	0.343138
$772$	17.6525	0.635327
$773$	3.72949	0.134140	0.0670702	−	0.997748i	$-0.478635\pi$
$773$	3.72949	0.134140	0.0670702	+	0.997748i	$0.478635\pi$
$774$	11.4721	0.412357
$775$	34.5066	1.23951
$776$	−5.47214	−0.196438
$777$	17.7984	0.638513
$778$	30.4164	1.09048
$779$	62.8328	2.25122
$780$	−0.854102	−0.0305818
$781$	0	0
$782$	6.23607	0.223001
$783$	32.0689	1.14605
$784$	7.85410	0.280504
$785$	−9.94427	−0.354926
$786$	−4.47214	−0.159516
$787$	−22.6180	−0.806246	−0.403123	−	0.915146i	$-0.632075\pi$
$787$	−22.6180	−0.806246	−0.403123	+	0.915146i	$0.632075\pi$
$788$	12.0344	0.428709
$789$	5.03444	0.179231
$790$	6.32624	0.225077
$791$	30.6180	1.08865
$792$	0	0
$793$	−31.1803	−1.10725
$794$	28.9787	1.02842
$795$	2.52786	0.0896541
$796$	−8.03444	−0.284773
$797$	−24.8885	−0.881597	−0.440799	−	0.897606i	$-0.645305\pi$
$797$	−24.8885	−0.881597	−0.440799	+	0.897606i	$0.645305\pi$
$798$	−15.4164	−0.545735
$799$	6.32624	0.223806
$800$	4.61803	0.163272
$801$	−37.7426	−1.33357
$802$	8.32624	0.294010
$803$	0	0
$804$	−8.09017	−0.285318
$805$	14.8541	0.523538
$806$	16.7082	0.588521
$807$	−6.11146	−0.215133
$808$	13.4721	0.473948
$809$	26.2016	0.921200	0.460600	−	0.887608i	$-0.347634\pi$
$809$	26.2016	0.921200	0.460600	+	0.887608i	$0.347634\pi$
$810$	−3.52786	−0.123957
$811$	1.47214	0.0516937	0.0258468	−	0.999666i	$-0.491772\pi$
$811$	1.47214	0.0516937	0.0258468	+	0.999666i	$0.491772\pi$
$812$	−35.5967	−1.24920
$813$	3.61803	0.126890
$814$	0	0
$815$	−4.00000	−0.140114
$816$	−0.618034	−0.0216355
$817$	28.3607	0.992215
$818$	10.8885	0.380709
$819$	22.5623	0.788391
$820$	6.00000	0.209529
$821$	2.63932	0.0921129	0.0460565	−	0.998939i	$-0.485335\pi$
$821$	2.63932	0.0921129	0.0460565	+	0.998939i	$0.485335\pi$
$822$	4.43769	0.154782
$823$	21.1459	0.737100	0.368550	−	0.929608i	$-0.379854\pi$
$823$	21.1459	0.737100	0.368550	+	0.929608i	$0.379854\pi$
$824$	11.4721	0.399651
$825$	0	0
$826$	−29.9230	−1.04115
$827$	17.6738	0.614577	0.307288	−	0.951616i	$-0.400578\pi$
$827$	17.6738	0.614577	0.307288	+	0.951616i	$0.400578\pi$
$828$	16.3262	0.567376
$829$	−34.1803	−1.18713	−0.593566	−	0.804785i	$-0.702280\pi$
$829$	−34.1803	−1.18713	−0.593566	+	0.804785i	$0.702280\pi$
$830$	−0.673762	−0.0233866
$831$	−12.4377	−0.431459
$832$	2.23607	0.0775217
$833$	7.85410	0.272129
$834$	0.798374	0.0276454
$835$	−7.41641	−0.256655
$836$	0	0
$837$	−25.9443	−0.896765
$838$	29.1803	1.00802
$839$	6.29180	0.217217	0.108608	−	0.994085i	$-0.465361\pi$
$839$	6.29180	0.217217	0.108608	+	0.994085i	$0.465361\pi$
$840$	−1.47214	−0.0507935
$841$	56.3050	1.94155
$842$	−1.79837	−0.0619761
$843$	11.4164	0.393202
$844$	10.2705	0.353526
$845$	−4.94427	−0.170088
$846$	16.5623	0.569424
$847$	0	0
$848$	−6.61803	−0.227264
$849$	5.72949	0.196636
$850$	4.61803	0.158397
$851$	−46.5967	−1.59732
$852$	9.61803	0.329508
$853$	5.78522	0.198082	0.0990411	−	0.995083i	$-0.468422\pi$
$853$	5.78522	0.198082	0.0990411	+	0.995083i	$0.468422\pi$
$854$	−53.7426	−1.83904
$855$	−10.4721	−0.358139
$856$	2.70820	0.0925645
$857$	−7.09017	−0.242196	−0.121098	−	0.992641i	$-0.538641\pi$
$857$	−7.09017	−0.242196	−0.121098	+	0.992641i	$0.538641\pi$
$858$	0	0
$859$	16.3475	0.557770	0.278885	−	0.960324i	$-0.410035\pi$
$859$	16.3475	0.557770	0.278885	+	0.960324i	$0.410035\pi$
$860$	2.70820	0.0923490
$861$	23.1246	0.788085
$862$	12.9443	0.440884
$863$	−36.2361	−1.23349	−0.616745	−	0.787163i	$-0.711549\pi$
$863$	−36.2361	−1.23349	−0.616745	+	0.787163i	$0.711549\pi$
$864$	−3.47214	−0.118124
$865$	8.18034	0.278140
$866$	−3.85410	−0.130968
$867$	−0.618034	−0.0209895
$868$	28.7984	0.977481
$869$	0	0
$870$	3.52786	0.119606
$871$	29.2705	0.991793
$872$	14.3820	0.487035
$873$	−14.3262	−0.484870
$874$	40.3607	1.36522
$875$	22.9098	0.774494
$876$	−4.70820	−0.159075
$877$	23.5623	0.795643	0.397821	−	0.917463i	$-0.369766\pi$
$877$	23.5623	0.795643	0.397821	+	0.917463i	$0.369766\pi$
$878$	30.0902	1.01549
$879$	−5.49342	−0.185289
$880$	0	0
$881$	−56.8328	−1.91475	−0.957373	−	0.288854i	$-0.906726\pi$
$881$	−56.8328	−1.91475	−0.957373	+	0.288854i	$0.906726\pi$
$882$	20.5623	0.692369
$883$	24.8197	0.835248	0.417624	−	0.908620i	$-0.362863\pi$
$883$	24.8197	0.835248	0.417624	+	0.908620i	$0.362863\pi$
$884$	2.23607	0.0752071
$885$	2.96556	0.0996861
$886$	22.4164	0.753094
$887$	1.14590	0.0384755	0.0192377	−	0.999815i	$-0.493876\pi$
$887$	1.14590	0.0384755	0.0192377	+	0.999815i	$0.493876\pi$
$888$	4.61803	0.154971
$889$	−32.0902	−1.07627
$890$	−8.90983	−0.298658
$891$	0	0
$892$	27.7082	0.927739
$893$	40.9443	1.37015
$894$	−12.3820	−0.414115
$895$	−2.03444	−0.0680039
$896$	3.85410	0.128757
$897$	8.61803	0.287748
$898$	10.6738	0.356188
$899$	−69.0132	−2.30172
$900$	12.0902	0.403006
$901$	−6.61803	−0.220479
$902$	0	0
$903$	10.4377	0.347345
$904$	7.94427	0.264223
$905$	1.38197	0.0459381
$906$	−9.20163	−0.305704
$907$	38.0689	1.26406	0.632028	−	0.774945i	$-0.282223\pi$
$907$	38.0689	1.26406	0.632028	+	0.774945i	$0.282223\pi$
$908$	−2.23607	−0.0742065
$909$	35.2705	1.16985
$910$	5.32624	0.176563
$911$	−16.1115	−0.533796	−0.266898	−	0.963725i	$-0.585999\pi$
$911$	−16.1115	−0.533796	−0.266898	+	0.963725i	$0.585999\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	−18.0689	−0.597666
$915$	5.32624	0.176080
$916$	−17.5623	−0.580275
$917$	27.8885	0.920961
$918$	−3.47214	−0.114598
$919$	37.4508	1.23539	0.617695	−	0.786418i	$-0.288067\pi$
$919$	37.4508	1.23539	0.617695	+	0.786418i	$0.288067\pi$
$920$	3.85410	0.127066
$921$	5.52786	0.182149
$922$	−20.5967	−0.678318
$923$	−34.7984	−1.14540
$924$	0	0
$925$	−34.5066	−1.13457
$926$	−31.4508	−1.03354
$927$	30.0344	0.986460
$928$	−9.23607	−0.303189
$929$	−23.6738	−0.776711	−0.388355	−	0.921510i	$-0.626957\pi$
$929$	−23.6738	−0.776711	−0.388355	+	0.921510i	$0.626957\pi$
$930$	−2.85410	−0.0935897
$931$	50.8328	1.66598
$932$	−17.1803	−0.562761
$933$	2.63932	0.0864075
$934$	−1.61803	−0.0529437
$935$	0	0
$936$	5.85410	0.191347
$937$	25.8885	0.845742	0.422871	−	0.906190i	$-0.361022\pi$
$937$	25.8885	0.845742	0.422871	+	0.906190i	$0.361022\pi$
$938$	50.4508	1.64728
$939$	−5.03444	−0.164293
$940$	3.90983	0.127525
$941$	33.7639	1.10067	0.550336	−	0.834943i	$-0.314499\pi$
$941$	33.7639	1.10067	0.550336	+	0.834943i	$0.314499\pi$
$942$	−9.94427	−0.324002
$943$	−60.5410	−1.97149
$944$	−7.76393	−0.252694
$945$	−8.27051	−0.269040
$946$	0	0
$947$	6.70820	0.217987	0.108994	−	0.994042i	$-0.465237\pi$
$947$	6.70820	0.217987	0.108994	+	0.994042i	$0.465237\pi$
$948$	6.32624	0.205467
$949$	17.0344	0.552961
$950$	29.8885	0.969712
$951$	8.76393	0.284190
$952$	3.85410	0.124912
$953$	−45.7214	−1.48106	−0.740530	−	0.672023i	$-0.765425\pi$
$953$	−45.7214	−1.48106	−0.740530	+	0.672023i	$0.765425\pi$
$954$	−17.3262	−0.560958
$955$	8.81966	0.285397
$956$	21.1803	0.685021
$957$	0	0
$958$	14.5967	0.471600
$959$	−27.6738	−0.893632
$960$	−0.381966	−0.0123279
$961$	24.8328	0.801059
$962$	−16.7082	−0.538694
$963$	7.09017	0.228478
$964$	−13.9443	−0.449115
$965$	10.9098	0.351200
$966$	14.8541	0.477923
$967$	−22.5623	−0.725555	−0.362777	−	0.931876i	$-0.618171\pi$
$967$	−22.5623	−0.725555	−0.362777	+	0.931876i	$0.618171\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	−3.38197	−0.108588
$971$	4.16718	0.133731	0.0668657	−	0.997762i	$-0.478700\pi$
$971$	4.16718	0.133731	0.0668657	+	0.997762i	$0.478700\pi$
$972$	−13.9443	−0.447263
$973$	−4.97871	−0.159610
$974$	40.1803	1.28746
$975$	6.38197	0.204386
$976$	−13.9443	−0.446345
$977$	−33.0000	−1.05576	−0.527882	−	0.849318i	$-0.677014\pi$
$977$	−33.0000	−1.05576	−0.527882	+	0.849318i	$0.677014\pi$
$978$	−4.00000	−0.127906
$979$	0	0
$980$	4.85410	0.155059
$981$	37.6525	1.20215
$982$	33.9443	1.08321
$983$	3.29180	0.104992	0.0524960	−	0.998621i	$-0.483282\pi$
$983$	3.29180	0.104992	0.0524960	+	0.998621i	$0.483282\pi$
$984$	6.00000	0.191273
$985$	7.43769	0.236985
$986$	−9.23607	−0.294136
$987$	15.0689	0.479648
$988$	14.4721	0.460420
$989$	−27.3262	−0.868924
$990$	0	0
$991$	61.4164	1.95096	0.975478	−	0.220096i	$-0.0706370\pi$
$991$	61.4164	1.95096	0.975478	+	0.220096i	$0.0706370\pi$
$992$	7.47214	0.237241
$993$	8.49342	0.269531
$994$	−59.9787	−1.90241
$995$	−4.96556	−0.157419
$996$	−0.673762	−0.0213490
$997$	−37.1803	−1.17751	−0.588757	−	0.808310i	$-0.700382\pi$
$997$	−37.1803	−1.17751	−0.588757	+	0.808310i	$0.700382\pi$
$998$	13.3607	0.422925
$999$	25.9443	0.820840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4114.2.a.h.1.1	✓	2
11.10	odd	2		4114.2.a.m.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4114.2.a.h.1.1	✓	2	1.1	even	1	trivial
4114.2.a.m.1.1	yes	2	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4114 = 2 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4114.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +0.618034 q^{5} +0.618034 q^{6} -3.85410 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +0.618034 q^{5} +0.618034 q^{6} -3.85410 q^{7} -1.00000 q^{8} -2.61803 q^{9} -0.618034 q^{10} -0.618034 q^{12} +2.23607 q^{13} +3.85410 q^{14} -0.381966 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.61803 q^{18} +6.47214 q^{19} +0.618034 q^{20} +2.38197 q^{21} -6.23607 q^{23} +0.618034 q^{24} -4.61803 q^{25} -2.23607 q^{26} +3.47214 q^{27} -3.85410 q^{28} +9.23607 q^{29} +0.381966 q^{30} -7.47214 q^{31} -1.00000 q^{32} -1.00000 q^{34} -2.38197 q^{35} -2.61803 q^{36} +7.47214 q^{37} -6.47214 q^{38} -1.38197 q^{39} -0.618034 q^{40} +9.70820 q^{41} -2.38197 q^{42} +4.38197 q^{43} -1.61803 q^{45} +6.23607 q^{46} +6.32624 q^{47} -0.618034 q^{48} +7.85410 q^{49} +4.61803 q^{50} -0.618034 q^{51} +2.23607 q^{52} -6.61803 q^{53} -3.47214 q^{54} +3.85410 q^{56} -4.00000 q^{57} -9.23607 q^{58} -7.76393 q^{59} -0.381966 q^{60} -13.9443 q^{61} +7.47214 q^{62} +10.0902 q^{63} +1.00000 q^{64} +1.38197 q^{65} +13.0902 q^{67} +1.00000 q^{68} +3.85410 q^{69} +2.38197 q^{70} -15.5623 q^{71} +2.61803 q^{72} +7.61803 q^{73} -7.47214 q^{74} +2.85410 q^{75} +6.47214 q^{76} +1.38197 q^{78} -10.2361 q^{79} +0.618034 q^{80} +5.70820 q^{81} -9.70820 q^{82} +1.09017 q^{83} +2.38197 q^{84} +0.618034 q^{85} -4.38197 q^{86} -5.70820 q^{87} +14.4164 q^{89} +1.61803 q^{90} -8.61803 q^{91} -6.23607 q^{92} +4.61803 q^{93} -6.32624 q^{94} +4.00000 q^{95} +0.618034 q^{96} +5.47214 q^{97} -7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + q^{10} + q^{12} + q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 3 q^{18} + 4 q^{19} - q^{20} + 7 q^{21} - 8 q^{23} - q^{24} - 7 q^{25} - 2 q^{27} - q^{28} + 14 q^{29} + 3 q^{30} - 6 q^{31} - 2 q^{32} - 2 q^{34} - 7 q^{35} - 3 q^{36} + 6 q^{37} - 4 q^{38} - 5 q^{39} + q^{40} + 6 q^{41} - 7 q^{42} + 11 q^{43} - q^{45} + 8 q^{46} - 3 q^{47} + q^{48} + 9 q^{49} + 7 q^{50} + q^{51} - 11 q^{53} + 2 q^{54} + q^{56} - 8 q^{57} - 14 q^{58} - 20 q^{59} - 3 q^{60} - 10 q^{61} + 6 q^{62} + 9 q^{63} + 2 q^{64} + 5 q^{65} + 15 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} - 11 q^{71} + 3 q^{72} + 13 q^{73} - 6 q^{74} - q^{75} + 4 q^{76} + 5 q^{78} - 16 q^{79} - q^{80} - 2 q^{81} - 6 q^{82} - 9 q^{83} + 7 q^{84} - q^{85} - 11 q^{86} + 2 q^{87} + 2 q^{89} + q^{90} - 15 q^{91} - 8 q^{92} + 7 q^{93} + 3 q^{94} + 8 q^{95} - q^{96} + 2 q^{97} - 9 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - q^7 - 2 * q^8 - 3 * q^9 + q^10 + q^12 + q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 3 * q^18 + 4 * q^19 - q^20 + 7 * q^21 - 8 * q^23 - q^24 - 7 * q^25 - 2 * q^27 - q^28 + 14 * q^29 + 3 * q^30 - 6 * q^31 - 2 * q^32 - 2 * q^34 - 7 * q^35 - 3 * q^36 + 6 * q^37 - 4 * q^38 - 5 * q^39 + q^40 + 6 * q^41 - 7 * q^42 + 11 * q^43 - q^45 + 8 * q^46 - 3 * q^47 + q^48 + 9 * q^49 + 7 * q^50 + q^51 - 11 * q^53 + 2 * q^54 + q^56 - 8 * q^57 - 14 * q^58 - 20 * q^59 - 3 * q^60 - 10 * q^61 + 6 * q^62 + 9 * q^63 + 2 * q^64 + 5 * q^65 + 15 * q^67 + 2 * q^68 + q^69 + 7 * q^70 - 11 * q^71 + 3 * q^72 + 13 * q^73 - 6 * q^74 - q^75 + 4 * q^76 + 5 * q^78 - 16 * q^79 - q^80 - 2 * q^81 - 6 * q^82 - 9 * q^83 + 7 * q^84 - q^85 - 11 * q^86 + 2 * q^87 + 2 * q^89 + q^90 - 15 * q^91 - 8 * q^92 + 7 * q^93 + 3 * q^94 + 8 * q^95 - q^96 + 2 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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