LMFDB - Embedded newform 1617.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +2.23607 q^{5} +0.381966 q^{6} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +2.23607 q^{5} +0.381966 q^{6} +1.47214 q^{8} +1.00000 q^{9} -0.854102 q^{10} -1.00000 q^{11} +1.85410 q^{12} -5.47214 q^{13} -2.23607 q^{15} +3.14590 q^{16} +6.00000 q^{17} -0.381966 q^{18} +0.236068 q^{19} -4.14590 q^{20} +0.381966 q^{22} +6.47214 q^{23} -1.47214 q^{24} +2.09017 q^{26} -1.00000 q^{27} -5.76393 q^{29} +0.854102 q^{30} -0.472136 q^{31} -4.14590 q^{32} +1.00000 q^{33} -2.29180 q^{34} -1.85410 q^{36} -9.47214 q^{37} -0.0901699 q^{38} +5.47214 q^{39} +3.29180 q^{40} +6.00000 q^{41} +8.47214 q^{43} +1.85410 q^{44} +2.23607 q^{45} -2.47214 q^{46} +2.52786 q^{47} -3.14590 q^{48} -6.00000 q^{51} +10.1459 q^{52} +4.94427 q^{53} +0.381966 q^{54} -2.23607 q^{55} -0.236068 q^{57} +2.20163 q^{58} +5.94427 q^{59} +4.14590 q^{60} +10.9443 q^{61} +0.180340 q^{62} -4.70820 q^{64} -12.2361 q^{65} -0.381966 q^{66} -12.7082 q^{67} -11.1246 q^{68} -6.47214 q^{69} -4.47214 q^{71} +1.47214 q^{72} -1.00000 q^{73} +3.61803 q^{74} -0.437694 q^{76} -2.09017 q^{78} +6.47214 q^{79} +7.03444 q^{80} +1.00000 q^{81} -2.29180 q^{82} +3.52786 q^{83} +13.4164 q^{85} -3.23607 q^{86} +5.76393 q^{87} -1.47214 q^{88} +13.4164 q^{89} -0.854102 q^{90} -12.0000 q^{92} +0.472136 q^{93} -0.965558 q^{94} +0.527864 q^{95} +4.14590 q^{96} +10.9443 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{8} + 2 q^{9} + 5 q^{10} - 2 q^{11} - 3 q^{12} - 2 q^{13} + 13 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} - 15 q^{20} + 3 q^{22} + 4 q^{23} + 6 q^{24} - 7 q^{26} - 2 q^{27} - 16 q^{29} - 5 q^{30} + 8 q^{31} - 15 q^{32} + 2 q^{33} - 18 q^{34} + 3 q^{36} - 10 q^{37} + 11 q^{38} + 2 q^{39} + 20 q^{40} + 12 q^{41} + 8 q^{43} - 3 q^{44} + 4 q^{46} + 14 q^{47} - 13 q^{48} - 12 q^{51} + 27 q^{52} - 8 q^{53} + 3 q^{54} + 4 q^{57} + 29 q^{58} - 6 q^{59} + 15 q^{60} + 4 q^{61} - 22 q^{62} + 4 q^{64} - 20 q^{65} - 3 q^{66} - 12 q^{67} + 18 q^{68} - 4 q^{69} - 6 q^{72} - 2 q^{73} + 5 q^{74} - 21 q^{76} + 7 q^{78} + 4 q^{79} - 15 q^{80} + 2 q^{81} - 18 q^{82} + 16 q^{83} - 2 q^{86} + 16 q^{87} + 6 q^{88} + 5 q^{90} - 24 q^{92} - 8 q^{93} - 31 q^{94} + 10 q^{95} + 15 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^8 + 2 * q^9 + 5 * q^10 - 2 * q^11 - 3 * q^12 - 2 * q^13 + 13 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 - 15 * q^20 + 3 * q^22 + 4 * q^23 + 6 * q^24 - 7 * q^26 - 2 * q^27 - 16 * q^29 - 5 * q^30 + 8 * q^31 - 15 * q^32 + 2 * q^33 - 18 * q^34 + 3 * q^36 - 10 * q^37 + 11 * q^38 + 2 * q^39 + 20 * q^40 + 12 * q^41 + 8 * q^43 - 3 * q^44 + 4 * q^46 + 14 * q^47 - 13 * q^48 - 12 * q^51 + 27 * q^52 - 8 * q^53 + 3 * q^54 + 4 * q^57 + 29 * q^58 - 6 * q^59 + 15 * q^60 + 4 * q^61 - 22 * q^62 + 4 * q^64 - 20 * q^65 - 3 * q^66 - 12 * q^67 + 18 * q^68 - 4 * q^69 - 6 * q^72 - 2 * q^73 + 5 * q^74 - 21 * q^76 + 7 * q^78 + 4 * q^79 - 15 * q^80 + 2 * q^81 - 18 * q^82 + 16 * q^83 - 2 * q^86 + 16 * q^87 + 6 * q^88 + 5 * q^90 - 24 * q^92 - 8 * q^93 - 31 * q^94 + 10 * q^95 + 15 * q^96 + 4 * q^97 - 2 * 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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.85410	−0.927051
$5$	2.23607	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	0.381966	0.155937
$7$	0	0
$7$	0	0
$8$	1.47214	0.520479
$9$	1.00000	0.333333
$10$	−0.854102	−0.270091
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.85410	0.535233
$13$	−5.47214	−1.51770	−0.758849	−	0.651267i	$-0.774238\pi$
$13$	−5.47214	−1.51770	−0.758849	+	0.651267i	$0.774238\pi$
$14$	0	0
$15$	−2.23607	−0.577350
$16$	3.14590	0.786475
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−0.381966	−0.0900303
$19$	0.236068	0.0541577	0.0270789	−	0.999633i	$-0.491379\pi$
$19$	0.236068	0.0541577	0.0270789	+	0.999633i	$0.491379\pi$
$20$	−4.14590	−0.927051
$21$	0	0
$22$	0.381966	0.0814354
$23$	6.47214	1.34953	0.674767	−	0.738031i	$-0.264244\pi$
$23$	6.47214	1.34953	0.674767	+	0.738031i	$0.264244\pi$
$24$	−1.47214	−0.300498
$25$	0	0
$26$	2.09017	0.409916
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−5.76393	−1.07034	−0.535168	−	0.844746i	$-0.679752\pi$
$29$	−5.76393	−1.07034	−0.535168	+	0.844746i	$0.679752\pi$
$30$	0.854102	0.155937
$31$	−0.472136	−0.0847981	−0.0423991	−	0.999101i	$-0.513500\pi$
$31$	−0.472136	−0.0847981	−0.0423991	+	0.999101i	$0.513500\pi$
$32$	−4.14590	−0.732898
$33$	1.00000	0.174078
$34$	−2.29180	−0.393040
$35$	0	0
$36$	−1.85410	−0.309017
$37$	−9.47214	−1.55721	−0.778605	−	0.627515i	$-0.784072\pi$
$37$	−9.47214	−1.55721	−0.778605	+	0.627515i	$0.784072\pi$
$38$	−0.0901699	−0.0146275
$39$	5.47214	0.876243
$40$	3.29180	0.520479
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	8.47214	1.29199	0.645994	−	0.763342i	$-0.276443\pi$
$43$	8.47214	1.29199	0.645994	+	0.763342i	$0.276443\pi$
$44$	1.85410	0.279516
$45$	2.23607	0.333333
$46$	−2.47214	−0.364497
$47$	2.52786	0.368727	0.184363	−	0.982858i	$-0.440978\pi$
$47$	2.52786	0.368727	0.184363	+	0.982858i	$0.440978\pi$
$48$	−3.14590	−0.454071
$49$	0	0
$50$	0	0
$51$	−6.00000	−0.840168
$52$	10.1459	1.40698
$53$	4.94427	0.679148	0.339574	−	0.940579i	$-0.389717\pi$
$53$	4.94427	0.679148	0.339574	+	0.940579i	$0.389717\pi$
$54$	0.381966	0.0519790
$55$	−2.23607	−0.301511
$56$	0	0
$57$	−0.236068	−0.0312680
$58$	2.20163	0.289088
$59$	5.94427	0.773878	0.386939	−	0.922105i	$-0.373532\pi$
$59$	5.94427	0.773878	0.386939	+	0.922105i	$0.373532\pi$
$60$	4.14590	0.535233
$61$	10.9443	1.40127	0.700635	−	0.713520i	$-0.252900\pi$
$61$	10.9443	1.40127	0.700635	+	0.713520i	$0.252900\pi$
$62$	0.180340	0.0229032
$63$	0	0
$64$	−4.70820	−0.588525
$65$	−12.2361	−1.51770
$66$	−0.381966	−0.0470168
$67$	−12.7082	−1.55255	−0.776277	−	0.630392i	$-0.782894\pi$
$67$	−12.7082	−1.55255	−0.776277	+	0.630392i	$0.782894\pi$
$68$	−11.1246	−1.34906
$69$	−6.47214	−0.779154
$70$	0	0
$71$	−4.47214	−0.530745	−0.265372	−	0.964146i	$-0.585495\pi$
$71$	−4.47214	−0.530745	−0.265372	+	0.964146i	$0.585495\pi$
$72$	1.47214	0.173493
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	3.61803	0.420588
$75$	0	0
$76$	−0.437694	−0.0502070
$77$	0	0
$78$	−2.09017	−0.236665
$79$	6.47214	0.728172	0.364086	−	0.931365i	$-0.381381\pi$
$79$	6.47214	0.728172	0.364086	+	0.931365i	$0.381381\pi$
$80$	7.03444	0.786475
$81$	1.00000	0.111111
$82$	−2.29180	−0.253087
$83$	3.52786	0.387233	0.193617	−	0.981077i	$-0.437978\pi$
$83$	3.52786	0.387233	0.193617	+	0.981077i	$0.437978\pi$
$84$	0	0
$85$	13.4164	1.45521
$86$	−3.23607	−0.348954
$87$	5.76393	0.617958
$88$	−1.47214	−0.156930
$89$	13.4164	1.42214	0.711068	−	0.703123i	$-0.248212\pi$
$89$	13.4164	1.42214	0.711068	+	0.703123i	$0.248212\pi$
$90$	−0.854102	−0.0900303
$91$	0	0
$92$	−12.0000	−1.25109
$93$	0.472136	0.0489582
$94$	−0.965558	−0.0995897
$95$	0.527864	0.0541577
$96$	4.14590	0.423139
$97$	10.9443	1.11122	0.555611	−	0.831442i	$-0.312484\pi$
$97$	10.9443	1.11122	0.555611	+	0.831442i	$0.312484\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	0	0
$101$	12.4721	1.24102	0.620512	−	0.784197i	$-0.286925\pi$
$101$	12.4721	1.24102	0.620512	+	0.784197i	$0.286925\pi$
$102$	2.29180	0.226922
$103$	19.4164	1.91316	0.956578	−	0.291477i	$-0.0941468\pi$
$103$	19.4164	1.91316	0.956578	+	0.291477i	$0.0941468\pi$
$104$	−8.05573	−0.789929
$105$	0	0
$106$	−1.88854	−0.183432
$107$	2.05573	0.198735	0.0993674	−	0.995051i	$-0.468318\pi$
$107$	2.05573	0.198735	0.0993674	+	0.995051i	$0.468318\pi$
$108$	1.85410	0.178411
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0.854102	0.0814354
$111$	9.47214	0.899055
$112$	0	0
$113$	−2.47214	−0.232559	−0.116279	−	0.993217i	$-0.537097\pi$
$113$	−2.47214	−0.232559	−0.116279	+	0.993217i	$0.537097\pi$
$114$	0.0901699	0.00844519
$115$	14.4721	1.34953
$116$	10.6869	0.992255
$117$	−5.47214	−0.505899
$118$	−2.27051	−0.209017
$119$	0	0
$120$	−3.29180	−0.300498
$121$	1.00000	0.0909091
$122$	−4.18034	−0.378470
$123$	−6.00000	−0.541002
$124$	0.875388	0.0786122
$125$	−11.1803	−1.00000
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	10.0902	0.891853
$129$	−8.47214	−0.745930
$130$	4.67376	0.409916
$131$	4.47214	0.390732	0.195366	−	0.980730i	$-0.437410\pi$
$131$	4.47214	0.390732	0.195366	+	0.980730i	$0.437410\pi$
$132$	−1.85410	−0.161379
$133$	0	0
$134$	4.85410	0.419331
$135$	−2.23607	−0.192450
$136$	8.83282	0.757408
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	2.47214	0.210442
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	−2.52786	−0.212885
$142$	1.70820	0.143349
$143$	5.47214	0.457603
$144$	3.14590	0.262158
$145$	−12.8885	−1.07034
$146$	0.381966	0.0316117
$147$	0	0
$148$	17.5623	1.44361
$149$	−15.6525	−1.28230	−0.641150	−	0.767415i	$-0.721543\pi$
$149$	−15.6525	−1.28230	−0.641150	+	0.767415i	$0.721543\pi$
$150$	0	0
$151$	10.9443	0.890632	0.445316	−	0.895373i	$-0.353091\pi$
$151$	10.9443	0.890632	0.445316	+	0.895373i	$0.353091\pi$
$152$	0.347524	0.0281879
$153$	6.00000	0.485071
$154$	0	0
$155$	−1.05573	−0.0847981
$156$	−10.1459	−0.812322
$157$	−23.4164	−1.86883	−0.934416	−	0.356183i	$-0.884078\pi$
$157$	−23.4164	−1.86883	−0.934416	+	0.356183i	$0.884078\pi$
$158$	−2.47214	−0.196673
$159$	−4.94427	−0.392106
$160$	−9.27051	−0.732898
$161$	0	0
$162$	−0.381966	−0.0300101
$163$	22.1246	1.73293	0.866467	−	0.499235i	$-0.166386\pi$
$163$	22.1246	1.73293	0.866467	+	0.499235i	$0.166386\pi$
$164$	−11.1246	−0.868686
$165$	2.23607	0.174078
$166$	−1.34752	−0.104588
$167$	9.52786	0.737288	0.368644	−	0.929571i	$-0.379822\pi$
$167$	9.52786	0.737288	0.368644	+	0.929571i	$0.379822\pi$
$168$	0	0
$169$	16.9443	1.30341
$170$	−5.12461	−0.393040
$171$	0.236068	0.0180526
$172$	−15.7082	−1.19774
$173$	14.4721	1.10030	0.550148	−	0.835067i	$-0.314571\pi$
$173$	14.4721	1.10030	0.550148	+	0.835067i	$0.314571\pi$
$174$	−2.20163	−0.166905
$175$	0	0
$176$	−3.14590	−0.237131
$177$	−5.94427	−0.446799
$178$	−5.12461	−0.384106
$179$	−14.4721	−1.08170	−0.540849	−	0.841120i	$-0.681897\pi$
$179$	−14.4721	−1.08170	−0.540849	+	0.841120i	$0.681897\pi$
$180$	−4.14590	−0.309017
$181$	−8.47214	−0.629729	−0.314864	−	0.949137i	$-0.601959\pi$
$181$	−8.47214	−0.629729	−0.314864	+	0.949137i	$0.601959\pi$
$182$	0	0
$183$	−10.9443	−0.809024
$184$	9.52786	0.702403
$185$	−21.1803	−1.55721
$186$	−0.180340	−0.0132232
$187$	−6.00000	−0.438763
$188$	−4.68692	−0.341829
$189$	0	0
$190$	−0.201626	−0.0146275
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	4.70820	0.339785
$193$	−9.88854	−0.711793	−0.355896	−	0.934525i	$-0.615824\pi$
$193$	−9.88854	−0.711793	−0.355896	+	0.934525i	$0.615824\pi$
$194$	−4.18034	−0.300131
$195$	12.2361	0.876243
$196$	0	0
$197$	0.472136	0.0336383	0.0168191	−	0.999859i	$-0.494646\pi$
$197$	0.472136	0.0336383	0.0168191	+	0.999859i	$0.494646\pi$
$198$	0.381966	0.0271451
$199$	15.5279	1.10074	0.550371	−	0.834921i	$-0.314486\pi$
$199$	15.5279	1.10074	0.550371	+	0.834921i	$0.314486\pi$
$200$	0	0
$201$	12.7082	0.896368
$202$	−4.76393	−0.335189
$203$	0	0
$204$	11.1246	0.778879
$205$	13.4164	0.937043
$206$	−7.41641	−0.516726
$207$	6.47214	0.449845
$208$	−17.2148	−1.19363
$209$	−0.236068	−0.0163292
$210$	0	0
$211$	1.05573	0.0726793	0.0363397	−	0.999339i	$-0.488430\pi$
$211$	1.05573	0.0726793	0.0363397	+	0.999339i	$0.488430\pi$
$212$	−9.16718	−0.629605
$213$	4.47214	0.306426
$214$	−0.785218	−0.0536764
$215$	18.9443	1.29199
$216$	−1.47214	−0.100166
$217$	0	0
$218$	−2.29180	−0.155220
$219$	1.00000	0.0675737
$220$	4.14590	0.279516
$221$	−32.8328	−2.20857
$222$	−3.61803	−0.242827
$223$	18.0000	1.20537	0.602685	−	0.797980i	$-0.294098\pi$
$223$	18.0000	1.20537	0.602685	+	0.797980i	$0.294098\pi$
$224$	0	0
$225$	0	0
$226$	0.944272	0.0628120
$227$	−26.8328	−1.78096	−0.890478	−	0.455026i	$-0.849630\pi$
$227$	−26.8328	−1.78096	−0.890478	+	0.455026i	$0.849630\pi$
$228$	0.437694	0.0289870
$229$	−11.4164	−0.754417	−0.377209	−	0.926128i	$-0.623116\pi$
$229$	−11.4164	−0.754417	−0.377209	+	0.926128i	$0.623116\pi$
$230$	−5.52786	−0.364497
$231$	0	0
$232$	−8.48529	−0.557087
$233$	−13.4164	−0.878938	−0.439469	−	0.898258i	$-0.644833\pi$
$233$	−13.4164	−0.878938	−0.439469	+	0.898258i	$0.644833\pi$
$234$	2.09017	0.136639
$235$	5.65248	0.368727
$236$	−11.0213	−0.717425
$237$	−6.47214	−0.420410
$238$	0	0
$239$	−27.3607	−1.76982	−0.884908	−	0.465767i	$-0.845779\pi$
$239$	−27.3607	−1.76982	−0.884908	+	0.465767i	$0.845779\pi$
$240$	−7.03444	−0.454071
$241$	−19.0000	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$241$	−19.0000	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$242$	−0.381966	−0.0245537
$243$	−1.00000	−0.0641500
$244$	−20.2918	−1.29905
$245$	0	0
$246$	2.29180	0.146120
$247$	−1.29180	−0.0821950
$248$	−0.695048	−0.0441356
$249$	−3.52786	−0.223569
$250$	4.27051	0.270091
$251$	−13.9443	−0.880155	−0.440077	−	0.897960i	$-0.645049\pi$
$251$	−13.9443	−0.880155	−0.440077	+	0.897960i	$0.645049\pi$
$252$	0	0
$253$	−6.47214	−0.406900
$254$	−6.11146	−0.383467
$255$	−13.4164	−0.840168
$256$	5.56231	0.347644
$257$	−12.2361	−0.763265	−0.381632	−	0.924314i	$-0.624638\pi$
$257$	−12.2361	−0.763265	−0.381632	+	0.924314i	$0.624638\pi$
$258$	3.23607	0.201469
$259$	0	0
$260$	22.6869	1.40698
$261$	−5.76393	−0.356778
$262$	−1.70820	−0.105533
$263$	22.4164	1.38225	0.691127	−	0.722733i	$-0.257114\pi$
$263$	22.4164	1.38225	0.691127	+	0.722733i	$0.257114\pi$
$264$	1.47214	0.0906037
$265$	11.0557	0.679148
$266$	0	0
$267$	−13.4164	−0.821071
$268$	23.5623	1.43930
$269$	−7.52786	−0.458982	−0.229491	−	0.973311i	$-0.573706\pi$
$269$	−7.52786	−0.458982	−0.229491	+	0.973311i	$0.573706\pi$
$270$	0.854102	0.0519790
$271$	18.7082	1.13644	0.568221	−	0.822876i	$-0.307632\pi$
$271$	18.7082	1.13644	0.568221	+	0.822876i	$0.307632\pi$
$272$	18.8754	1.14449
$273$	0	0
$274$	−2.29180	−0.138452
$275$	0	0
$276$	12.0000	0.722315
$277$	−1.05573	−0.0634326	−0.0317163	−	0.999497i	$-0.510097\pi$
$277$	−1.05573	−0.0634326	−0.0317163	+	0.999497i	$0.510097\pi$
$278$	−3.05573	−0.183270
$279$	−0.472136	−0.0282660
$280$	0	0
$281$	−17.1803	−1.02489	−0.512447	−	0.858719i	$-0.671261\pi$
$281$	−17.1803	−1.02489	−0.512447	+	0.858719i	$0.671261\pi$
$282$	0.965558	0.0574982
$283$	−8.70820	−0.517649	−0.258824	−	0.965924i	$-0.583335\pi$
$283$	−8.70820	−0.517649	−0.258824	+	0.965924i	$0.583335\pi$
$284$	8.29180	0.492028
$285$	−0.527864	−0.0312680
$286$	−2.09017	−0.123594
$287$	0	0
$288$	−4.14590	−0.244299
$289$	19.0000	1.11765
$290$	4.92299	0.289088
$291$	−10.9443	−0.641565
$292$	1.85410	0.108503
$293$	25.8885	1.51242	0.756212	−	0.654326i	$-0.227048\pi$
$293$	25.8885	1.51242	0.756212	+	0.654326i	$0.227048\pi$
$294$	0	0
$295$	13.2918	0.773878
$296$	−13.9443	−0.810494
$297$	1.00000	0.0580259
$298$	5.97871	0.346338
$299$	−35.4164	−2.04818
$300$	0	0
$301$	0	0
$302$	−4.18034	−0.240552
$303$	−12.4721	−0.716505
$304$	0.742646	0.0425937
$305$	24.4721	1.40127
$306$	−2.29180	−0.131013
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	−19.4164	−1.10456
$310$	0.403252	0.0229032
$311$	4.94427	0.280364	0.140182	−	0.990126i	$-0.455231\pi$
$311$	4.94427	0.280364	0.140182	+	0.990126i	$0.455231\pi$
$312$	8.05573	0.456066
$313$	−18.3607	−1.03781	−0.518903	−	0.854833i	$-0.673660\pi$
$313$	−18.3607	−1.03781	−0.518903	+	0.854833i	$0.673660\pi$
$314$	8.94427	0.504754
$315$	0	0
$316$	−12.0000	−0.675053
$317$	9.05573	0.508620	0.254310	−	0.967123i	$-0.418152\pi$
$317$	9.05573	0.508620	0.254310	+	0.967123i	$0.418152\pi$
$318$	1.88854	0.105904
$319$	5.76393	0.322718
$320$	−10.5279	−0.588525
$321$	−2.05573	−0.114740
$322$	0	0
$323$	1.41641	0.0788110
$324$	−1.85410	−0.103006
$325$	0	0
$326$	−8.45085	−0.468049
$327$	−6.00000	−0.331801
$328$	8.83282	0.487711
$329$	0	0
$330$	−0.854102	−0.0470168
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	−6.54102	−0.358985
$333$	−9.47214	−0.519070
$334$	−3.63932	−0.199135
$335$	−28.4164	−1.55255
$336$	0	0
$337$	−15.4164	−0.839785	−0.419893	−	0.907574i	$-0.637932\pi$
$337$	−15.4164	−0.839785	−0.419893	+	0.907574i	$0.637932\pi$
$338$	−6.47214	−0.352038
$339$	2.47214	0.134268
$340$	−24.8754	−1.34906
$341$	0.472136	0.0255676
$342$	−0.0901699	−0.00487583
$343$	0	0
$344$	12.4721	0.672453
$345$	−14.4721	−0.779154
$346$	−5.52786	−0.297180
$347$	−16.9443	−0.909616	−0.454808	−	0.890589i	$-0.650292\pi$
$347$	−16.9443	−0.909616	−0.454808	+	0.890589i	$0.650292\pi$
$348$	−10.6869	−0.572879
$349$	24.4164	1.30698	0.653490	−	0.756935i	$-0.273304\pi$
$349$	24.4164	1.30698	0.653490	+	0.756935i	$0.273304\pi$
$350$	0	0
$351$	5.47214	0.292081
$352$	4.14590	0.220977
$353$	0.236068	0.0125646	0.00628232	−	0.999980i	$-0.498000\pi$
$353$	0.236068	0.0125646	0.00628232	+	0.999980i	$0.498000\pi$
$354$	2.27051	0.120676
$355$	−10.0000	−0.530745
$356$	−24.8754	−1.31839
$357$	0	0
$358$	5.52786	0.292157
$359$	−3.05573	−0.161275	−0.0806376	−	0.996743i	$-0.525696\pi$
$359$	−3.05573	−0.161275	−0.0806376	+	0.996743i	$0.525696\pi$
$360$	3.29180	0.173493
$361$	−18.9443	−0.997067
$362$	3.23607	0.170084
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−2.23607	−0.117041
$366$	4.18034	0.218510
$367$	1.41641	0.0739359	0.0369679	−	0.999316i	$-0.488230\pi$
$367$	1.41641	0.0739359	0.0369679	+	0.999316i	$0.488230\pi$
$368$	20.3607	1.06137
$369$	6.00000	0.312348
$370$	8.09017	0.420588
$371$	0	0
$372$	−0.875388	−0.0453868
$373$	0.944272	0.0488925	0.0244463	−	0.999701i	$-0.492218\pi$
$373$	0.944272	0.0488925	0.0244463	+	0.999701i	$0.492218\pi$
$374$	2.29180	0.118506
$375$	11.1803	0.577350
$376$	3.72136	0.191914
$377$	31.5410	1.62445
$378$	0	0
$379$	5.65248	0.290348	0.145174	−	0.989406i	$-0.453626\pi$
$379$	5.65248	0.290348	0.145174	+	0.989406i	$0.453626\pi$
$380$	−0.978714	−0.0502070
$381$	−16.0000	−0.819705
$382$	−4.58359	−0.234517
$383$	−8.94427	−0.457031	−0.228515	−	0.973540i	$-0.573387\pi$
$383$	−8.94427	−0.457031	−0.228515	+	0.973540i	$0.573387\pi$
$384$	−10.0902	−0.514912
$385$	0	0
$386$	3.77709	0.192249
$387$	8.47214	0.430663
$388$	−20.2918	−1.03016
$389$	−32.8328	−1.66469	−0.832345	−	0.554258i	$-0.813002\pi$
$389$	−32.8328	−1.66469	−0.832345	+	0.554258i	$0.813002\pi$
$390$	−4.67376	−0.236665
$391$	38.8328	1.96386
$392$	0	0
$393$	−4.47214	−0.225589
$394$	−0.180340	−0.00908539
$395$	14.4721	0.728172
$396$	1.85410	0.0931721
$397$	−17.4164	−0.874104	−0.437052	−	0.899436i	$-0.643978\pi$
$397$	−17.4164	−0.874104	−0.437052	+	0.899436i	$0.643978\pi$
$398$	−5.93112	−0.297300
$399$	0	0
$400$	0	0
$401$	0.472136	0.0235773	0.0117887	−	0.999931i	$-0.496247\pi$
$401$	0.472136	0.0235773	0.0117887	+	0.999931i	$0.496247\pi$
$402$	−4.85410	−0.242101
$403$	2.58359	0.128698
$404$	−23.1246	−1.15049
$405$	2.23607	0.111111
$406$	0	0
$407$	9.47214	0.469516
$408$	−8.83282	−0.437290
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−5.12461	−0.253087
$411$	−6.00000	−0.295958
$412$	−36.0000	−1.77359
$413$	0	0
$414$	−2.47214	−0.121499
$415$	7.88854	0.387233
$416$	22.6869	1.11232
$417$	−8.00000	−0.391762
$418$	0.0901699	0.00441036
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	20.5279	1.00047	0.500233	−	0.865891i	$-0.333248\pi$
$421$	20.5279	1.00047	0.500233	+	0.865891i	$0.333248\pi$
$422$	−0.403252	−0.0196300
$423$	2.52786	0.122909
$424$	7.27864	0.353482
$425$	0	0
$426$	−1.70820	−0.0827628
$427$	0	0
$428$	−3.81153	−0.184237
$429$	−5.47214	−0.264197
$430$	−7.23607	−0.348954
$431$	27.3607	1.31792	0.658959	−	0.752179i	$-0.270997\pi$
$431$	27.3607	1.31792	0.658959	+	0.752179i	$0.270997\pi$
$432$	−3.14590	−0.151357
$433$	−39.4164	−1.89423	−0.947116	−	0.320892i	$-0.896017\pi$
$433$	−39.4164	−1.89423	−0.947116	+	0.320892i	$0.896017\pi$
$434$	0	0
$435$	12.8885	0.617958
$436$	−11.1246	−0.532772
$437$	1.52786	0.0730876
$438$	−0.381966	−0.0182510
$439$	−32.1246	−1.53322	−0.766612	−	0.642111i	$-0.778059\pi$
$439$	−32.1246	−1.53322	−0.766612	+	0.642111i	$0.778059\pi$
$440$	−3.29180	−0.156930
$441$	0	0
$442$	12.5410	0.596515
$443$	26.9443	1.28016	0.640080	−	0.768308i	$-0.278901\pi$
$443$	26.9443	1.28016	0.640080	+	0.768308i	$0.278901\pi$
$444$	−17.5623	−0.833470
$445$	30.0000	1.42214
$446$	−6.87539	−0.325559
$447$	15.6525	0.740337
$448$	0	0
$449$	1.41641	0.0668444	0.0334222	−	0.999441i	$-0.489359\pi$
$449$	1.41641	0.0668444	0.0334222	+	0.999441i	$0.489359\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	4.58359	0.215594
$453$	−10.9443	−0.514207
$454$	10.2492	0.481020
$455$	0	0
$456$	−0.347524	−0.0162743
$457$	15.4164	0.721149	0.360575	−	0.932730i	$-0.382581\pi$
$457$	15.4164	0.721149	0.360575	+	0.932730i	$0.382581\pi$
$458$	4.36068	0.203761
$459$	−6.00000	−0.280056
$460$	−26.8328	−1.25109
$461$	7.52786	0.350608	0.175304	−	0.984514i	$-0.443909\pi$
$461$	7.52786	0.350608	0.175304	+	0.984514i	$0.443909\pi$
$462$	0	0
$463$	10.7082	0.497652	0.248826	−	0.968548i	$-0.419955\pi$
$463$	10.7082	0.497652	0.248826	+	0.968548i	$0.419955\pi$
$464$	−18.1327	−0.841791
$465$	1.05573	0.0489582
$466$	5.12461	0.237393
$467$	−29.8328	−1.38050	−0.690249	−	0.723572i	$-0.742499\pi$
$467$	−29.8328	−1.38050	−0.690249	+	0.723572i	$0.742499\pi$
$468$	10.1459	0.468994
$469$	0	0
$470$	−2.15905	−0.0995897
$471$	23.4164	1.07897
$472$	8.75078	0.402787
$473$	−8.47214	−0.389549
$474$	2.47214	0.113549
$475$	0	0
$476$	0	0
$477$	4.94427	0.226383
$478$	10.4508	0.478011
$479$	−13.8885	−0.634584	−0.317292	−	0.948328i	$-0.602773\pi$
$479$	−13.8885	−0.634584	−0.317292	+	0.948328i	$0.602773\pi$
$480$	9.27051	0.423139
$481$	51.8328	2.36337
$482$	7.25735	0.330563
$483$	0	0
$484$	−1.85410	−0.0842774
$485$	24.4721	1.11122
$486$	0.381966	0.0173263
$487$	13.8885	0.629350	0.314675	−	0.949199i	$-0.398104\pi$
$487$	13.8885	0.629350	0.314675	+	0.949199i	$0.398104\pi$
$488$	16.1115	0.729331
$489$	−22.1246	−1.00051
$490$	0	0
$491$	24.8885	1.12320	0.561602	−	0.827407i	$-0.310185\pi$
$491$	24.8885	1.12320	0.561602	+	0.827407i	$0.310185\pi$
$492$	11.1246	0.501536
$493$	−34.5836	−1.55757
$494$	0.493422	0.0222001
$495$	−2.23607	−0.100504
$496$	−1.48529	−0.0666916
$497$	0	0
$498$	1.34752	0.0603840
$499$	−18.1246	−0.811369	−0.405685	−	0.914013i	$-0.632967\pi$
$499$	−18.1246	−0.811369	−0.405685	+	0.914013i	$0.632967\pi$
$500$	20.7295	0.927051
$501$	−9.52786	−0.425674
$502$	5.32624	0.237722
$503$	37.4164	1.66832	0.834158	−	0.551526i	$-0.185954\pi$
$503$	37.4164	1.66832	0.834158	+	0.551526i	$0.185954\pi$
$504$	0	0
$505$	27.8885	1.24102
$506$	2.47214	0.109900
$507$	−16.9443	−0.752522
$508$	−29.6656	−1.31620
$509$	44.4721	1.97119	0.985596	−	0.169115i	$-0.0540908\pi$
$509$	44.4721	1.97119	0.985596	+	0.169115i	$0.0540908\pi$
$510$	5.12461	0.226922
$511$	0	0
$512$	−22.3050	−0.985749
$513$	−0.236068	−0.0104227
$514$	4.67376	0.206151
$515$	43.4164	1.91316
$516$	15.7082	0.691515
$517$	−2.52786	−0.111175
$518$	0	0
$519$	−14.4721	−0.635256
$520$	−18.0132	−0.789929
$521$	−28.2361	−1.23704	−0.618522	−	0.785767i	$-0.712268\pi$
$521$	−28.2361	−1.23704	−0.618522	+	0.785767i	$0.712268\pi$
$522$	2.20163	0.0963626
$523$	16.7082	0.730599	0.365299	−	0.930890i	$-0.380967\pi$
$523$	16.7082	0.730599	0.365299	+	0.930890i	$0.380967\pi$
$524$	−8.29180	−0.362229
$525$	0	0
$526$	−8.56231	−0.373334
$527$	−2.83282	−0.123399
$528$	3.14590	0.136908
$529$	18.8885	0.821241
$530$	−4.22291	−0.183432
$531$	5.94427	0.257959
$532$	0	0
$533$	−32.8328	−1.42215
$534$	5.12461	0.221764
$535$	4.59675	0.198735
$536$	−18.7082	−0.808071
$537$	14.4721	0.624519
$538$	2.87539	0.123967
$539$	0	0
$540$	4.14590	0.178411
$541$	−5.41641	−0.232870	−0.116435	−	0.993198i	$-0.537147\pi$
$541$	−5.41641	−0.232870	−0.116435	+	0.993198i	$0.537147\pi$
$542$	−7.14590	−0.306943
$543$	8.47214	0.363574
$544$	−24.8754	−1.06652
$545$	13.4164	0.574696
$546$	0	0
$547$	13.4164	0.573644	0.286822	−	0.957984i	$-0.407401\pi$
$547$	13.4164	0.573644	0.286822	+	0.957984i	$0.407401\pi$
$548$	−11.1246	−0.475220
$549$	10.9443	0.467090
$550$	0	0
$551$	−1.36068	−0.0579669
$552$	−9.52786	−0.405533
$553$	0	0
$554$	0.403252	0.0171325
$555$	21.1803	0.899055
$556$	−14.8328	−0.629052
$557$	32.1246	1.36116	0.680582	−	0.732672i	$-0.261727\pi$
$557$	32.1246	1.36116	0.680582	+	0.732672i	$0.261727\pi$
$558$	0.180340	0.00763440
$559$	−46.3607	−1.96085
$560$	0	0
$561$	6.00000	0.253320
$562$	6.56231	0.276814
$563$	4.47214	0.188478	0.0942390	−	0.995550i	$-0.469958\pi$
$563$	4.47214	0.188478	0.0942390	+	0.995550i	$0.469958\pi$
$564$	4.68692	0.197355
$565$	−5.52786	−0.232559
$566$	3.32624	0.139812
$567$	0	0
$568$	−6.58359	−0.276241
$569$	−3.52786	−0.147896	−0.0739479	−	0.997262i	$-0.523560\pi$
$569$	−3.52786	−0.147896	−0.0739479	+	0.997262i	$0.523560\pi$
$570$	0.201626	0.00844519
$571$	−37.4164	−1.56583	−0.782914	−	0.622130i	$-0.786268\pi$
$571$	−37.4164	−1.56583	−0.782914	+	0.622130i	$0.786268\pi$
$572$	−10.1459	−0.424221
$573$	−12.0000	−0.501307
$574$	0	0
$575$	0	0
$576$	−4.70820	−0.196175
$577$	17.0557	0.710039	0.355020	−	0.934859i	$-0.384474\pi$
$577$	17.0557	0.710039	0.355020	+	0.934859i	$0.384474\pi$
$578$	−7.25735	−0.301866
$579$	9.88854	0.410954
$580$	23.8967	0.992255
$581$	0	0
$582$	4.18034	0.173281
$583$	−4.94427	−0.204771
$584$	−1.47214	−0.0609174
$585$	−12.2361	−0.505899
$586$	−9.88854	−0.408492
$587$	31.9443	1.31848	0.659241	−	0.751932i	$-0.270878\pi$
$587$	31.9443	1.31848	0.659241	+	0.751932i	$0.270878\pi$
$588$	0	0
$589$	−0.111456	−0.00459247
$590$	−5.07701	−0.209017
$591$	−0.472136	−0.0194211
$592$	−29.7984	−1.22471
$593$	−10.5836	−0.434616	−0.217308	−	0.976103i	$-0.569728\pi$
$593$	−10.5836	−0.434616	−0.217308	+	0.976103i	$0.569728\pi$
$594$	−0.381966	−0.0156723
$595$	0	0
$596$	29.0213	1.18876
$597$	−15.5279	−0.635513
$598$	13.5279	0.553195
$599$	−37.3050	−1.52424	−0.762120	−	0.647436i	$-0.775841\pi$
$599$	−37.3050	−1.52424	−0.762120	+	0.647436i	$0.775841\pi$
$600$	0	0
$601$	−47.8328	−1.95114	−0.975571	−	0.219686i	$-0.929497\pi$
$601$	−47.8328	−1.95114	−0.975571	+	0.219686i	$0.929497\pi$
$602$	0	0
$603$	−12.7082	−0.517518
$604$	−20.2918	−0.825661
$605$	2.23607	0.0909091
$606$	4.76393	0.193522
$607$	−9.29180	−0.377142	−0.188571	−	0.982060i	$-0.560386\pi$
$607$	−9.29180	−0.377142	−0.188571	+	0.982060i	$0.560386\pi$
$608$	−0.978714	−0.0396921
$609$	0	0
$610$	−9.34752	−0.378470
$611$	−13.8328	−0.559616
$612$	−11.1246	−0.449686
$613$	−7.41641	−0.299546	−0.149773	−	0.988720i	$-0.547854\pi$
$613$	−7.41641	−0.299546	−0.149773	+	0.988720i	$0.547854\pi$
$614$	−6.11146	−0.246638
$615$	−13.4164	−0.541002
$616$	0	0
$617$	40.2492	1.62037	0.810186	−	0.586172i	$-0.199366\pi$
$617$	40.2492	1.62037	0.810186	+	0.586172i	$0.199366\pi$
$618$	7.41641	0.298332
$619$	0.583592	0.0234565	0.0117283	−	0.999931i	$-0.496267\pi$
$619$	0.583592	0.0234565	0.0117283	+	0.999931i	$0.496267\pi$
$620$	1.95743	0.0786122
$621$	−6.47214	−0.259718
$622$	−1.88854	−0.0757237
$623$	0	0
$624$	17.2148	0.689143
$625$	−25.0000	−1.00000
$626$	7.01316	0.280302
$627$	0.236068	0.00942765
$628$	43.4164	1.73250
$629$	−56.8328	−2.26607
$630$	0	0
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	9.52786	0.378998
$633$	−1.05573	−0.0419614
$634$	−3.45898	−0.137374
$635$	35.7771	1.41977
$636$	9.16718	0.363503
$637$	0	0
$638$	−2.20163	−0.0871632
$639$	−4.47214	−0.176915
$640$	22.5623	0.891853
$641$	40.4721	1.59855	0.799277	−	0.600963i	$-0.205216\pi$
$641$	40.4721	1.59855	0.799277	+	0.600963i	$0.205216\pi$
$642$	0.785218	0.0309901
$643$	−21.4164	−0.844581	−0.422290	−	0.906461i	$-0.638774\pi$
$643$	−21.4164	−0.844581	−0.422290	+	0.906461i	$0.638774\pi$
$644$	0	0
$645$	−18.9443	−0.745930
$646$	−0.541020	−0.0212861
$647$	22.4164	0.881280	0.440640	−	0.897684i	$-0.354752\pi$
$647$	22.4164	0.881280	0.440640	+	0.897684i	$0.354752\pi$
$648$	1.47214	0.0578310
$649$	−5.94427	−0.233333
$650$	0	0
$651$	0	0
$652$	−41.0213	−1.60652
$653$	−29.8885	−1.16963	−0.584815	−	0.811167i	$-0.698833\pi$
$653$	−29.8885	−1.16963	−0.584815	+	0.811167i	$0.698833\pi$
$654$	2.29180	0.0896163
$655$	10.0000	0.390732
$656$	18.8754	0.736960
$657$	−1.00000	−0.0390137
$658$	0	0
$659$	−2.88854	−0.112522	−0.0562608	−	0.998416i	$-0.517918\pi$
$659$	−2.88854	−0.112522	−0.0562608	+	0.998416i	$0.517918\pi$
$660$	−4.14590	−0.161379
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	6.11146	0.237528
$663$	32.8328	1.27512
$664$	5.19350	0.201547
$665$	0	0
$666$	3.61803	0.140196
$667$	−37.3050	−1.44445
$668$	−17.6656	−0.683504
$669$	−18.0000	−0.695920
$670$	10.8541	0.419331
$671$	−10.9443	−0.422499
$672$	0	0
$673$	−45.4164	−1.75067	−0.875337	−	0.483513i	$-0.839360\pi$
$673$	−45.4164	−1.75067	−0.875337	+	0.483513i	$0.839360\pi$
$674$	5.88854	0.226818
$675$	0	0
$676$	−31.4164	−1.20832
$677$	16.5836	0.637359	0.318680	−	0.947862i	$-0.396761\pi$
$677$	16.5836	0.637359	0.318680	+	0.947862i	$0.396761\pi$
$678$	−0.944272	−0.0362645
$679$	0	0
$680$	19.7508	0.757408
$681$	26.8328	1.02824
$682$	−0.180340	−0.00690557
$683$	18.4721	0.706817	0.353408	−	0.935469i	$-0.385023\pi$
$683$	18.4721	0.706817	0.353408	+	0.935469i	$0.385023\pi$
$684$	−0.437694	−0.0167357
$685$	13.4164	0.512615
$686$	0	0
$687$	11.4164	0.435563
$688$	26.6525	1.01612
$689$	−27.0557	−1.03074
$690$	5.52786	0.210442
$691$	33.4164	1.27122	0.635610	−	0.772010i	$-0.280749\pi$
$691$	33.4164	1.27122	0.635610	+	0.772010i	$0.280749\pi$
$692$	−26.8328	−1.02003
$693$	0	0
$694$	6.47214	0.245679
$695$	17.8885	0.678551
$696$	8.48529	0.321634
$697$	36.0000	1.36360
$698$	−9.32624	−0.353003
$699$	13.4164	0.507455
$700$	0	0
$701$	13.4164	0.506731	0.253365	−	0.967371i	$-0.418463\pi$
$701$	13.4164	0.506731	0.253365	+	0.967371i	$0.418463\pi$
$702$	−2.09017	−0.0788884
$703$	−2.23607	−0.0843349
$704$	4.70820	0.177447
$705$	−5.65248	−0.212885
$706$	−0.0901699	−0.00339359
$707$	0	0
$708$	11.0213	0.414205
$709$	−4.41641	−0.165862	−0.0829308	−	0.996555i	$-0.526428\pi$
$709$	−4.41641	−0.165862	−0.0829308	+	0.996555i	$0.526428\pi$
$710$	3.81966	0.143349
$711$	6.47214	0.242724
$712$	19.7508	0.740192
$713$	−3.05573	−0.114438
$714$	0	0
$715$	12.2361	0.457603
$716$	26.8328	1.00279
$717$	27.3607	1.02180
$718$	1.16718	0.0435589
$719$	−49.3607	−1.84084	−0.920421	−	0.390928i	$-0.872154\pi$
$719$	−49.3607	−1.84084	−0.920421	+	0.390928i	$0.872154\pi$
$720$	7.03444	0.262158
$721$	0	0
$722$	7.23607	0.269299
$723$	19.0000	0.706618
$724$	15.7082	0.583791
$725$	0	0
$726$	0.381966	0.0141761
$727$	31.4164	1.16517	0.582585	−	0.812770i	$-0.302041\pi$
$727$	31.4164	1.16517	0.582585	+	0.812770i	$0.302041\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.854102	0.0316117
$731$	50.8328	1.88012
$732$	20.2918	0.750006
$733$	46.9443	1.73393	0.866963	−	0.498372i	$-0.166069\pi$
$733$	46.9443	1.73393	0.866963	+	0.498372i	$0.166069\pi$
$734$	−0.541020	−0.0199694
$735$	0	0
$736$	−26.8328	−0.989071
$737$	12.7082	0.468113
$738$	−2.29180	−0.0843622
$739$	16.5836	0.610037	0.305019	−	0.952346i	$-0.401337\pi$
$739$	16.5836	0.610037	0.305019	+	0.952346i	$0.401337\pi$
$740$	39.2705	1.44361
$741$	1.29180	0.0474553
$742$	0	0
$743$	−50.3050	−1.84551	−0.922755	−	0.385387i	$-0.874068\pi$
$743$	−50.3050	−1.84551	−0.922755	+	0.385387i	$0.874068\pi$
$744$	0.695048	0.0254817
$745$	−35.0000	−1.28230
$746$	−0.360680	−0.0132054
$747$	3.52786	0.129078
$748$	11.1246	0.406756
$749$	0	0
$750$	−4.27051	−0.155937
$751$	−28.1246	−1.02628	−0.513141	−	0.858304i	$-0.671518\pi$
$751$	−28.1246	−1.02628	−0.513141	+	0.858304i	$0.671518\pi$
$752$	7.95240	0.289994
$753$	13.9443	0.508158
$754$	−12.0476	−0.438748
$755$	24.4721	0.890632
$756$	0	0
$757$	−38.4164	−1.39627	−0.698134	−	0.715967i	$-0.745986\pi$
$757$	−38.4164	−1.39627	−0.698134	+	0.715967i	$0.745986\pi$
$758$	−2.15905	−0.0784204
$759$	6.47214	0.234924
$760$	0.777088	0.0281879
$761$	22.4721	0.814614	0.407307	−	0.913291i	$-0.366468\pi$
$761$	22.4721	0.814614	0.407307	+	0.913291i	$0.366468\pi$
$762$	6.11146	0.221395
$763$	0	0
$764$	−22.2492	−0.804949
$765$	13.4164	0.485071
$766$	3.41641	0.123440
$767$	−32.5279	−1.17451
$768$	−5.56231	−0.200712
$769$	1.00000	0.0360609	0.0180305	−	0.999837i	$-0.494260\pi$
$769$	1.00000	0.0360609	0.0180305	+	0.999837i	$0.494260\pi$
$770$	0	0
$771$	12.2361	0.440671
$772$	18.3344	0.659868
$773$	−51.6525	−1.85781	−0.928905	−	0.370318i	$-0.879249\pi$
$773$	−51.6525	−1.85781	−0.928905	+	0.370318i	$0.879249\pi$
$774$	−3.23607	−0.116318
$775$	0	0
$776$	16.1115	0.578368
$777$	0	0
$778$	12.5410	0.449617
$779$	1.41641	0.0507481
$780$	−22.6869	−0.812322
$781$	4.47214	0.160026
$782$	−14.8328	−0.530420
$783$	5.76393	0.205986
$784$	0	0
$785$	−52.3607	−1.86883
$786$	1.70820	0.0609296
$787$	−2.12461	−0.0757342	−0.0378671	−	0.999283i	$-0.512056\pi$
$787$	−2.12461	−0.0757342	−0.0378671	+	0.999283i	$0.512056\pi$
$788$	−0.875388	−0.0311844
$789$	−22.4164	−0.798045
$790$	−5.52786	−0.196673
$791$	0	0
$792$	−1.47214	−0.0523101
$793$	−59.8885	−2.12670
$794$	6.65248	0.236088
$795$	−11.0557	−0.392106
$796$	−28.7902	−1.02044
$797$	−50.2361	−1.77945	−0.889726	−	0.456494i	$-0.849105\pi$
$797$	−50.2361	−1.77945	−0.889726	+	0.456494i	$0.849105\pi$
$798$	0	0
$799$	15.1672	0.536576
$800$	0	0
$801$	13.4164	0.474045
$802$	−0.180340	−0.00636802
$803$	1.00000	0.0352892
$804$	−23.5623	−0.830978
$805$	0	0
$806$	−0.986844	−0.0347601
$807$	7.52786	0.264993
$808$	18.3607	0.645926
$809$	−37.1803	−1.30719	−0.653596	−	0.756844i	$-0.726740\pi$
$809$	−37.1803	−1.30719	−0.653596	+	0.756844i	$0.726740\pi$
$810$	−0.854102	−0.0300101
$811$	39.5410	1.38847	0.694236	−	0.719747i	$-0.255742\pi$
$811$	39.5410	1.38847	0.694236	+	0.719747i	$0.255742\pi$
$812$	0	0
$813$	−18.7082	−0.656125
$814$	−3.61803	−0.126812
$815$	49.4721	1.73293
$816$	−18.8754	−0.660771
$817$	2.00000	0.0699711
$818$	−5.34752	−0.186972
$819$	0	0
$820$	−24.8754	−0.868686
$821$	33.5410	1.17059	0.585295	−	0.810821i	$-0.300979\pi$
$821$	33.5410	1.17059	0.585295	+	0.810821i	$0.300979\pi$
$822$	2.29180	0.0799356
$823$	21.5410	0.750873	0.375436	−	0.926848i	$-0.377493\pi$
$823$	21.5410	0.750873	0.375436	+	0.926848i	$0.377493\pi$
$824$	28.5836	0.995757
$825$	0	0
$826$	0	0
$827$	53.8328	1.87195	0.935975	−	0.352066i	$-0.114521\pi$
$827$	53.8328	1.87195	0.935975	+	0.352066i	$0.114521\pi$
$828$	−12.0000	−0.417029
$829$	18.8328	0.654091	0.327045	−	0.945009i	$-0.393947\pi$
$829$	18.8328	0.654091	0.327045	+	0.945009i	$0.393947\pi$
$830$	−3.01316	−0.104588
$831$	1.05573	0.0366228
$832$	25.7639	0.893204
$833$	0	0
$834$	3.05573	0.105811
$835$	21.3050	0.737288
$836$	0.437694	0.0151380
$837$	0.472136	0.0163194
$838$	−1.14590	−0.0395844
$839$	−29.4721	−1.01749	−0.508746	−	0.860917i	$-0.669891\pi$
$839$	−29.4721	−1.01749	−0.508746	+	0.860917i	$0.669891\pi$
$840$	0	0
$841$	4.22291	0.145618
$842$	−7.84095	−0.270217
$843$	17.1803	0.591722
$844$	−1.95743	−0.0673774
$845$	37.8885	1.30341
$846$	−0.965558	−0.0331966
$847$	0	0
$848$	15.5542	0.534133
$849$	8.70820	0.298865
$850$	0	0
$851$	−61.3050	−2.10151
$852$	−8.29180	−0.284072
$853$	34.7214	1.18884	0.594418	−	0.804156i	$-0.297382\pi$
$853$	34.7214	1.18884	0.594418	+	0.804156i	$0.297382\pi$
$854$	0	0
$855$	0.527864	0.0180526
$856$	3.02631	0.103437
$857$	38.7214	1.32270	0.661348	−	0.750079i	$-0.269985\pi$
$857$	38.7214	1.32270	0.661348	+	0.750079i	$0.269985\pi$
$858$	2.09017	0.0713572
$859$	−11.4164	−0.389523	−0.194761	−	0.980851i	$-0.562393\pi$
$859$	−11.4164	−0.389523	−0.194761	+	0.980851i	$0.562393\pi$
$860$	−35.1246	−1.19774
$861$	0	0
$862$	−10.4508	−0.355957
$863$	−27.3050	−0.929471	−0.464736	−	0.885449i	$-0.653851\pi$
$863$	−27.3050	−0.929471	−0.464736	+	0.885449i	$0.653851\pi$
$864$	4.14590	0.141046
$865$	32.3607	1.10030
$866$	15.0557	0.511614
$867$	−19.0000	−0.645274
$868$	0	0
$869$	−6.47214	−0.219552
$870$	−4.92299	−0.166905
$871$	69.5410	2.35631
$872$	8.83282	0.299117
$873$	10.9443	0.370407
$874$	−0.583592	−0.0197403
$875$	0	0
$876$	−1.85410	−0.0626443
$877$	13.8885	0.468983	0.234491	−	0.972118i	$-0.424658\pi$
$877$	13.8885	0.468983	0.234491	+	0.972118i	$0.424658\pi$
$878$	12.2705	0.414110
$879$	−25.8885	−0.873199
$880$	−7.03444	−0.237131
$881$	26.5967	0.896067	0.448034	−	0.894017i	$-0.352124\pi$
$881$	26.5967	0.896067	0.448034	+	0.894017i	$0.352124\pi$
$882$	0	0
$883$	−0.236068	−0.00794432	−0.00397216	−	0.999992i	$-0.501264\pi$
$883$	−0.236068	−0.00794432	−0.00397216	+	0.999992i	$0.501264\pi$
$884$	60.8754	2.04746
$885$	−13.2918	−0.446799
$886$	−10.2918	−0.345760
$887$	16.3607	0.549338	0.274669	−	0.961539i	$-0.411432\pi$
$887$	16.3607	0.549338	0.274669	+	0.961539i	$0.411432\pi$
$888$	13.9443	0.467939
$889$	0	0
$890$	−11.4590	−0.384106
$891$	−1.00000	−0.0335013
$892$	−33.3738	−1.11744
$893$	0.596748	0.0199694
$894$	−5.97871	−0.199958
$895$	−32.3607	−1.08170
$896$	0	0
$897$	35.4164	1.18252
$898$	−0.541020	−0.0180541
$899$	2.72136	0.0907624
$900$	0	0
$901$	29.6656	0.988305
$902$	2.29180	0.0763085
$903$	0	0
$904$	−3.63932	−0.121042
$905$	−18.9443	−0.629729
$906$	4.18034	0.138882
$907$	−49.8885	−1.65652	−0.828261	−	0.560343i	$-0.810669\pi$
$907$	−49.8885	−1.65652	−0.828261	+	0.560343i	$0.810669\pi$
$908$	49.7508	1.65104
$909$	12.4721	0.413675
$910$	0	0
$911$	−4.58359	−0.151861	−0.0759306	−	0.997113i	$-0.524193\pi$
$911$	−4.58359	−0.151861	−0.0759306	+	0.997113i	$0.524193\pi$
$912$	−0.742646	−0.0245915
$913$	−3.52786	−0.116755
$914$	−5.88854	−0.194776
$915$	−24.4721	−0.809024
$916$	21.1672	0.699383
$917$	0	0
$918$	2.29180	0.0756405
$919$	−33.8885	−1.11788	−0.558940	−	0.829208i	$-0.688792\pi$
$919$	−33.8885	−1.11788	−0.558940	+	0.829208i	$0.688792\pi$
$920$	21.3050	0.702403
$921$	−16.0000	−0.527218
$922$	−2.87539	−0.0946959
$923$	24.4721	0.805510
$924$	0	0
$925$	0	0
$926$	−4.09017	−0.134411
$927$	19.4164	0.637719
$928$	23.8967	0.784447
$929$	−32.4853	−1.06581	−0.532904	−	0.846176i	$-0.678899\pi$
$929$	−32.4853	−1.06581	−0.532904	+	0.846176i	$0.678899\pi$
$930$	−0.403252	−0.0132232
$931$	0	0
$932$	24.8754	0.814820
$933$	−4.94427	−0.161868
$934$	11.3951	0.372860
$935$	−13.4164	−0.438763
$936$	−8.05573	−0.263310
$937$	−46.7214	−1.52632	−0.763160	−	0.646209i	$-0.776353\pi$
$937$	−46.7214	−1.52632	−0.763160	+	0.646209i	$0.776353\pi$
$938$	0	0
$939$	18.3607	0.599178
$940$	−10.4803	−0.341829
$941$	−47.1935	−1.53846	−0.769232	−	0.638970i	$-0.779361\pi$
$941$	−47.1935	−1.53846	−0.769232	+	0.638970i	$0.779361\pi$
$942$	−8.94427	−0.291420
$943$	38.8328	1.26457
$944$	18.7001	0.608636
$945$	0	0
$946$	3.23607	0.105214
$947$	35.8885	1.16622	0.583110	−	0.812393i	$-0.301835\pi$
$947$	35.8885	1.16622	0.583110	+	0.812393i	$0.301835\pi$
$948$	12.0000	0.389742
$949$	5.47214	0.177633
$950$	0	0
$951$	−9.05573	−0.293652
$952$	0	0
$953$	56.4853	1.82974	0.914869	−	0.403751i	$-0.132294\pi$
$953$	56.4853	1.82974	0.914869	+	0.403751i	$0.132294\pi$
$954$	−1.88854	−0.0611439
$955$	26.8328	0.868290
$956$	50.7295	1.64071
$957$	−5.76393	−0.186321
$958$	5.30495	0.171395
$959$	0	0
$960$	10.5279	0.339785
$961$	−30.7771	−0.992809
$962$	−19.7984	−0.638325
$963$	2.05573	0.0662449
$964$	35.2279	1.13462
$965$	−22.1115	−0.711793
$966$	0	0
$967$	−34.2492	−1.10138	−0.550690	−	0.834710i	$-0.685635\pi$
$967$	−34.2492	−1.10138	−0.550690	+	0.834710i	$0.685635\pi$
$968$	1.47214	0.0473162
$969$	−1.41641	−0.0455016
$970$	−9.34752	−0.300131
$971$	−10.8885	−0.349430	−0.174715	−	0.984619i	$-0.555900\pi$
$971$	−10.8885	−0.349430	−0.174715	+	0.984619i	$0.555900\pi$
$972$	1.85410	0.0594703
$973$	0	0
$974$	−5.30495	−0.169982
$975$	0	0
$976$	34.4296	1.10206
$977$	−22.4721	−0.718947	−0.359474	−	0.933155i	$-0.617044\pi$
$977$	−22.4721	−0.718947	−0.359474	+	0.933155i	$0.617044\pi$
$978$	8.45085	0.270228
$979$	−13.4164	−0.428790
$980$	0	0
$981$	6.00000	0.191565
$982$	−9.50658	−0.303367
$983$	−14.8328	−0.473093	−0.236547	−	0.971620i	$-0.576016\pi$
$983$	−14.8328	−0.473093	−0.236547	+	0.971620i	$0.576016\pi$
$984$	−8.83282	−0.281580
$985$	1.05573	0.0336383
$986$	13.2098	0.420684
$987$	0	0
$988$	2.39512	0.0761990
$989$	54.8328	1.74358
$990$	0.854102	0.0271451
$991$	26.7082	0.848414	0.424207	−	0.905565i	$-0.360553\pi$
$991$	26.7082	0.848414	0.424207	+	0.905565i	$0.360553\pi$
$992$	1.95743	0.0621484
$993$	16.0000	0.507745
$994$	0	0
$995$	34.7214	1.10074
$996$	6.54102	0.207260
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	6.92299	0.219143
$999$	9.47214	0.299685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.k.1.2	✓	2
3.2	odd	2		4851.2.a.bh.1.1		2
7.6	odd	2		1617.2.a.l.1.2	yes	2
21.20	even	2		4851.2.a.bg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.k.1.2	✓	2	1.1	even	1	trivial
1617.2.a.l.1.2	yes	2	7.6	odd	2
4851.2.a.bg.1.1		2	21.20	even	2
4851.2.a.bh.1.1		2	3.2	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +2.23607 q^{5} +0.381966 q^{6} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} -1.00000 q^{3} -1.85410 q^{4} +2.23607 q^{5} +0.381966 q^{6} +1.47214 q^{8} +1.00000 q^{9} -0.854102 q^{10} -1.00000 q^{11} +1.85410 q^{12} -5.47214 q^{13} -2.23607 q^{15} +3.14590 q^{16} +6.00000 q^{17} -0.381966 q^{18} +0.236068 q^{19} -4.14590 q^{20} +0.381966 q^{22} +6.47214 q^{23} -1.47214 q^{24} +2.09017 q^{26} -1.00000 q^{27} -5.76393 q^{29} +0.854102 q^{30} -0.472136 q^{31} -4.14590 q^{32} +1.00000 q^{33} -2.29180 q^{34} -1.85410 q^{36} -9.47214 q^{37} -0.0901699 q^{38} +5.47214 q^{39} +3.29180 q^{40} +6.00000 q^{41} +8.47214 q^{43} +1.85410 q^{44} +2.23607 q^{45} -2.47214 q^{46} +2.52786 q^{47} -3.14590 q^{48} -6.00000 q^{51} +10.1459 q^{52} +4.94427 q^{53} +0.381966 q^{54} -2.23607 q^{55} -0.236068 q^{57} +2.20163 q^{58} +5.94427 q^{59} +4.14590 q^{60} +10.9443 q^{61} +0.180340 q^{62} -4.70820 q^{64} -12.2361 q^{65} -0.381966 q^{66} -12.7082 q^{67} -11.1246 q^{68} -6.47214 q^{69} -4.47214 q^{71} +1.47214 q^{72} -1.00000 q^{73} +3.61803 q^{74} -0.437694 q^{76} -2.09017 q^{78} +6.47214 q^{79} +7.03444 q^{80} +1.00000 q^{81} -2.29180 q^{82} +3.52786 q^{83} +13.4164 q^{85} -3.23607 q^{86} +5.76393 q^{87} -1.47214 q^{88} +13.4164 q^{89} -0.854102 q^{90} -12.0000 q^{92} +0.472136 q^{93} -0.965558 q^{94} +0.527864 q^{95} +4.14590 q^{96} +10.9443 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 3 q^{6} - 6 q^{8} + 2 q^{9} + 5 q^{10} - 2 q^{11} - 3 q^{12} - 2 q^{13} + 13 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} - 15 q^{20} + 3 q^{22} + 4 q^{23} + 6 q^{24} - 7 q^{26} - 2 q^{27} - 16 q^{29} - 5 q^{30} + 8 q^{31} - 15 q^{32} + 2 q^{33} - 18 q^{34} + 3 q^{36} - 10 q^{37} + 11 q^{38} + 2 q^{39} + 20 q^{40} + 12 q^{41} + 8 q^{43} - 3 q^{44} + 4 q^{46} + 14 q^{47} - 13 q^{48} - 12 q^{51} + 27 q^{52} - 8 q^{53} + 3 q^{54} + 4 q^{57} + 29 q^{58} - 6 q^{59} + 15 q^{60} + 4 q^{61} - 22 q^{62} + 4 q^{64} - 20 q^{65} - 3 q^{66} - 12 q^{67} + 18 q^{68} - 4 q^{69} - 6 q^{72} - 2 q^{73} + 5 q^{74} - 21 q^{76} + 7 q^{78} + 4 q^{79} - 15 q^{80} + 2 q^{81} - 18 q^{82} + 16 q^{83} - 2 q^{86} + 16 q^{87} + 6 q^{88} + 5 q^{90} - 24 q^{92} - 8 q^{93} - 31 q^{94} + 10 q^{95} + 15 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 3 * q^6 - 6 * q^8 + 2 * q^9 + 5 * q^10 - 2 * q^11 - 3 * q^12 - 2 * q^13 + 13 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 - 15 * q^20 + 3 * q^22 + 4 * q^23 + 6 * q^24 - 7 * q^26 - 2 * q^27 - 16 * q^29 - 5 * q^30 + 8 * q^31 - 15 * q^32 + 2 * q^33 - 18 * q^34 + 3 * q^36 - 10 * q^37 + 11 * q^38 + 2 * q^39 + 20 * q^40 + 12 * q^41 + 8 * q^43 - 3 * q^44 + 4 * q^46 + 14 * q^47 - 13 * q^48 - 12 * q^51 + 27 * q^52 - 8 * q^53 + 3 * q^54 + 4 * q^57 + 29 * q^58 - 6 * q^59 + 15 * q^60 + 4 * q^61 - 22 * q^62 + 4 * q^64 - 20 * q^65 - 3 * q^66 - 12 * q^67 + 18 * q^68 - 4 * q^69 - 6 * q^72 - 2 * q^73 + 5 * q^74 - 21 * q^76 + 7 * q^78 + 4 * q^79 - 15 * q^80 + 2 * q^81 - 18 * q^82 + 16 * q^83 - 2 * q^86 + 16 * q^87 + 6 * q^88 + 5 * q^90 - 24 * q^92 - 8 * q^93 - 31 * q^94 + 10 * q^95 + 15 * q^96 + 4 * q^97 - 2 * q^99

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