LMFDB - Embedded newform 242.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,2,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("242.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.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:	$1.93237972891$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} -1.23607 q^{5} +2.61803 q^{6} -2.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} -1.23607 q^{10} +2.61803 q^{12} -3.23607 q^{13} -2.00000 q^{14} -3.23607 q^{15} +1.00000 q^{16} +1.61803 q^{17} +3.85410 q^{18} +0.854102 q^{19} -1.23607 q^{20} -5.23607 q^{21} -3.23607 q^{23} +2.61803 q^{24} -3.47214 q^{25} -3.23607 q^{26} +2.23607 q^{27} -2.00000 q^{28} -4.47214 q^{29} -3.23607 q^{30} +2.00000 q^{31} +1.00000 q^{32} +1.61803 q^{34} +2.47214 q^{35} +3.85410 q^{36} +9.70820 q^{37} +0.854102 q^{38} -8.47214 q^{39} -1.23607 q^{40} +3.38197 q^{41} -5.23607 q^{42} +11.5623 q^{43} -4.76393 q^{45} -3.23607 q^{46} +2.47214 q^{47} +2.61803 q^{48} -3.00000 q^{49} -3.47214 q^{50} +4.23607 q^{51} -3.23607 q^{52} -10.4721 q^{53} +2.23607 q^{54} -2.00000 q^{56} +2.23607 q^{57} -4.47214 q^{58} -6.38197 q^{59} -3.23607 q^{60} +6.47214 q^{61} +2.00000 q^{62} -7.70820 q^{63} +1.00000 q^{64} +4.00000 q^{65} -0.0901699 q^{67} +1.61803 q^{68} -8.47214 q^{69} +2.47214 q^{70} -0.763932 q^{71} +3.85410 q^{72} +12.6180 q^{73} +9.70820 q^{74} -9.09017 q^{75} +0.854102 q^{76} -8.47214 q^{78} -13.4164 q^{79} -1.23607 q^{80} -5.70820 q^{81} +3.38197 q^{82} -6.32624 q^{83} -5.23607 q^{84} -2.00000 q^{85} +11.5623 q^{86} -11.7082 q^{87} +3.09017 q^{89} -4.76393 q^{90} +6.47214 q^{91} -3.23607 q^{92} +5.23607 q^{93} +2.47214 q^{94} -1.05573 q^{95} +2.61803 q^{96} +13.8541 q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{6} - 4 q^{7} + 2 q^{8} + q^{9} + 2 q^{10} + 3 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} + q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^6 - 4 * q^7 + 2 * q^8 + q^9 + 2 * q^10 + 3 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 + q^17 + q^18 - 5 * q^19 + 2 * q^20 - 6 * q^21 - 2 * q^23 + 3 * q^24 + 2 * q^25 - 2 * q^26 - 4 * q^28 - 2 * q^30 + 4 * q^31 + 2 * q^32 + q^34 - 4 * q^35 + q^36 + 6 * q^37 - 5 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^41 - 6 * q^42 + 3 * q^43 - 14 * q^45 - 2 * q^46 - 4 * q^47 + 3 * q^48 - 6 * q^49 + 2 * q^50 + 4 * q^51 - 2 * q^52 - 12 * q^53 - 4 * q^56 - 15 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 + 8 * q^65 + 11 * q^67 + q^68 - 8 * q^69 - 4 * q^70 - 6 * q^71 + q^72 + 23 * q^73 + 6 * q^74 - 7 * q^75 - 5 * q^76 - 8 * q^78 + 2 * q^80 + 2 * q^81 + 9 * q^82 + 3 * q^83 - 6 * q^84 - 4 * q^85 + 3 * q^86 - 10 * q^87 - 5 * q^89 - 14 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 - 4 * q^94 - 20 * q^95 + 3 * q^96 + 21 * q^97 - 6 * q^98

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	1.00000	0.500000
$5$	−1.23607	−0.552786	−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607	−0.552786	−0.276393	+	0.961045i	$0.589139\pi$
$6$	2.61803	1.06881
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	3.85410	1.28470
$10$	−1.23607	−0.390879
$11$	0	0
$11$	0	0
$12$	2.61803	0.755761
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	−2.00000	−0.534522
$15$	−3.23607	−0.835549
$16$	1.00000	0.250000
$17$	1.61803	0.392431	0.196215	−	0.980561i	$-0.437135\pi$
$17$	1.61803	0.392431	0.196215	+	0.980561i	$0.437135\pi$
$18$	3.85410	0.908421
$19$	0.854102	0.195944	0.0979722	−	0.995189i	$-0.468764\pi$
$19$	0.854102	0.195944	0.0979722	+	0.995189i	$0.468764\pi$
$20$	−1.23607	−0.276393
$21$	−5.23607	−1.14260
$22$	0	0
$23$	−3.23607	−0.674767	−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607	−0.674767	−0.337383	+	0.941367i	$0.609542\pi$
$24$	2.61803	0.534404
$25$	−3.47214	−0.694427
$26$	−3.23607	−0.634645
$27$	2.23607	0.430331
$28$	−2.00000	−0.377964
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	−3.23607	−0.590822
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.61803	0.277491
$35$	2.47214	0.417867
$36$	3.85410	0.642350
$37$	9.70820	1.59602	0.798009	−	0.602645i	$-0.205886\pi$
$37$	9.70820	1.59602	0.798009	+	0.602645i	$0.205886\pi$
$38$	0.854102	0.138554
$39$	−8.47214	−1.35663
$40$	−1.23607	−0.195440
$41$	3.38197	0.528174	0.264087	−	0.964499i	$-0.414929\pi$
$41$	3.38197	0.528174	0.264087	+	0.964499i	$0.414929\pi$
$42$	−5.23607	−0.807943
$43$	11.5623	1.76324	0.881618	−	0.471964i	$-0.156455\pi$
$43$	11.5623	1.76324	0.881618	+	0.471964i	$0.156455\pi$
$44$	0	0
$45$	−4.76393	−0.710165
$46$	−3.23607	−0.477132
$47$	2.47214	0.360598	0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214	0.360598	0.180299	+	0.983612i	$0.442293\pi$
$48$	2.61803	0.377881
$49$	−3.00000	−0.428571
$50$	−3.47214	−0.491034
$51$	4.23607	0.593168
$52$	−3.23607	−0.448762
$53$	−10.4721	−1.43846	−0.719229	−	0.694773i	$-0.755505\pi$
$53$	−10.4721	−1.43846	−0.719229	+	0.694773i	$0.755505\pi$
$54$	2.23607	0.304290
$55$	0	0
$56$	−2.00000	−0.267261
$57$	2.23607	0.296174
$58$	−4.47214	−0.587220
$59$	−6.38197	−0.830861	−0.415431	−	0.909625i	$-0.636369\pi$
$59$	−6.38197	−0.830861	−0.415431	+	0.909625i	$0.636369\pi$
$60$	−3.23607	−0.417775
$61$	6.47214	0.828672	0.414336	−	0.910124i	$-0.364014\pi$
$61$	6.47214	0.828672	0.414336	+	0.910124i	$0.364014\pi$
$62$	2.00000	0.254000
$63$	−7.70820	−0.971142
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	−0.0901699	−0.0110160	−0.00550801	−	0.999985i	$-0.501753\pi$
$67$	−0.0901699	−0.0110160	−0.00550801	+	0.999985i	$0.501753\pi$
$68$	1.61803	0.196215
$69$	−8.47214	−1.01993
$70$	2.47214	0.295477
$71$	−0.763932	−0.0906621	−0.0453310	−	0.998972i	$-0.514434\pi$
$71$	−0.763932	−0.0906621	−0.0453310	+	0.998972i	$0.514434\pi$
$72$	3.85410	0.454210
$73$	12.6180	1.47683	0.738415	−	0.674347i	$-0.235575\pi$
$73$	12.6180	1.47683	0.738415	+	0.674347i	$0.235575\pi$
$74$	9.70820	1.12856
$75$	−9.09017	−1.04964
$76$	0.854102	0.0979722
$77$	0	0
$78$	−8.47214	−0.959280
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	−1.23607	−0.138197
$81$	−5.70820	−0.634245
$82$	3.38197	0.373476
$83$	−6.32624	−0.694395	−0.347197	−	0.937792i	$-0.612867\pi$
$83$	−6.32624	−0.694395	−0.347197	+	0.937792i	$0.612867\pi$
$84$	−5.23607	−0.571302
$85$	−2.00000	−0.216930
$86$	11.5623	1.24680
$87$	−11.7082	−1.25525
$88$	0	0
$89$	3.09017	0.327557	0.163779	−	0.986497i	$-0.447632\pi$
$89$	3.09017	0.327557	0.163779	+	0.986497i	$0.447632\pi$
$90$	−4.76393	−0.502163
$91$	6.47214	0.678464
$92$	−3.23607	−0.337383
$93$	5.23607	0.542955
$94$	2.47214	0.254981
$95$	−1.05573	−0.108315
$96$	2.61803	0.267202
$97$	13.8541	1.40667	0.703335	−	0.710858i	$-0.251693\pi$
$97$	13.8541	1.40667	0.703335	+	0.710858i	$0.251693\pi$
$98$	−3.00000	−0.303046
$99$	0	0
$100$	−3.47214	−0.347214
$101$	18.1803	1.80901	0.904506	−	0.426461i	$-0.140240\pi$
$101$	18.1803	1.80901	0.904506	+	0.426461i	$0.140240\pi$
$102$	4.23607	0.419433
$103$	2.29180	0.225817	0.112909	−	0.993605i	$-0.463983\pi$
$103$	2.29180	0.225817	0.112909	+	0.993605i	$0.463983\pi$
$104$	−3.23607	−0.317323
$105$	6.47214	0.631616
$106$	−10.4721	−1.01714
$107$	−7.85410	−0.759285	−0.379642	−	0.925133i	$-0.623953\pi$
$107$	−7.85410	−0.759285	−0.379642	+	0.925133i	$0.623953\pi$
$108$	2.23607	0.215166
$109$	1.05573	0.101120	0.0505602	−	0.998721i	$-0.483899\pi$
$109$	1.05573	0.101120	0.0505602	+	0.998721i	$0.483899\pi$
$110$	0	0
$111$	25.4164	2.41242
$112$	−2.00000	−0.188982
$113$	4.85410	0.456636	0.228318	−	0.973587i	$-0.426677\pi$
$113$	4.85410	0.456636	0.228318	+	0.973587i	$0.426677\pi$
$114$	2.23607	0.209427
$115$	4.00000	0.373002
$116$	−4.47214	−0.415227
$117$	−12.4721	−1.15305
$118$	−6.38197	−0.587508
$119$	−3.23607	−0.296650
$120$	−3.23607	−0.295411
$121$	0	0
$122$	6.47214	0.585960
$123$	8.85410	0.798347
$124$	2.00000	0.179605
$125$	10.4721	0.936656
$126$	−7.70820	−0.686701
$127$	6.94427	0.616204	0.308102	−	0.951353i	$-0.400306\pi$
$127$	6.94427	0.616204	0.308102	+	0.951353i	$0.400306\pi$
$128$	1.00000	0.0883883
$129$	30.2705	2.66517
$130$	4.00000	0.350823
$131$	−17.7984	−1.55505	−0.777526	−	0.628851i	$-0.783525\pi$
$131$	−17.7984	−1.55505	−0.777526	+	0.628851i	$0.783525\pi$
$132$	0	0
$133$	−1.70820	−0.148120
$134$	−0.0901699	−0.00778950
$135$	−2.76393	−0.237881
$136$	1.61803	0.138745
$137$	4.90983	0.419475	0.209738	−	0.977758i	$-0.432739\pi$
$137$	4.90983	0.419475	0.209738	+	0.977758i	$0.432739\pi$
$138$	−8.47214	−0.721196
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	2.47214	0.208934
$141$	6.47214	0.545052
$142$	−0.763932	−0.0641078
$143$	0	0
$144$	3.85410	0.321175
$145$	5.52786	0.459064
$146$	12.6180	1.04428
$147$	−7.85410	−0.647795
$148$	9.70820	0.798009
$149$	16.1803	1.32555	0.662773	−	0.748821i	$-0.269380\pi$
$149$	16.1803	1.32555	0.662773	+	0.748821i	$0.269380\pi$
$150$	−9.09017	−0.742209
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0.854102	0.0692768
$153$	6.23607	0.504156
$154$	0	0
$155$	−2.47214	−0.198567
$156$	−8.47214	−0.678314
$157$	−3.70820	−0.295947	−0.147973	−	0.988991i	$-0.547275\pi$
$157$	−3.70820	−0.295947	−0.147973	+	0.988991i	$0.547275\pi$
$158$	−13.4164	−1.06735
$159$	−27.4164	−2.17426
$160$	−1.23607	−0.0977198
$161$	6.47214	0.510076
$162$	−5.70820	−0.448479
$163$	12.0902	0.946975	0.473488	−	0.880800i	$-0.342995\pi$
$163$	12.0902	0.946975	0.473488	+	0.880800i	$0.342995\pi$
$164$	3.38197	0.264087
$165$	0	0
$166$	−6.32624	−0.491011
$167$	−19.2361	−1.48853	−0.744266	−	0.667884i	$-0.767200\pi$
$167$	−19.2361	−1.48853	−0.744266	+	0.667884i	$0.767200\pi$
$168$	−5.23607	−0.403971
$169$	−2.52786	−0.194451
$170$	−2.00000	−0.153393
$171$	3.29180	0.251730
$172$	11.5623	0.881618
$173$	−13.8885	−1.05593	−0.527963	−	0.849267i	$-0.677044\pi$
$173$	−13.8885	−1.05593	−0.527963	+	0.849267i	$0.677044\pi$
$174$	−11.7082	−0.887597
$175$	6.94427	0.524938
$176$	0	0
$177$	−16.7082	−1.25587
$178$	3.09017	0.231618
$179$	−6.38197	−0.477011	−0.238505	−	0.971141i	$-0.576657\pi$
$179$	−6.38197	−0.477011	−0.238505	+	0.971141i	$0.576657\pi$
$180$	−4.76393	−0.355083
$181$	18.1803	1.35133	0.675667	−	0.737207i	$-0.263856\pi$
$181$	18.1803	1.35133	0.675667	+	0.737207i	$0.263856\pi$
$182$	6.47214	0.479747
$183$	16.9443	1.25256
$184$	−3.23607	−0.238566
$185$	−12.0000	−0.882258
$186$	5.23607	0.383927
$187$	0	0
$188$	2.47214	0.180299
$189$	−4.47214	−0.325300
$190$	−1.05573	−0.0765906
$191$	9.23607	0.668298	0.334149	−	0.942520i	$-0.391551\pi$
$191$	9.23607	0.668298	0.334149	+	0.942520i	$0.391551\pi$
$192$	2.61803	0.188940
$193$	−9.41641	−0.677808	−0.338904	−	0.940821i	$-0.610056\pi$
$193$	−9.41641	−0.677808	−0.338904	+	0.940821i	$0.610056\pi$
$194$	13.8541	0.994667
$195$	10.4721	0.749925
$196$	−3.00000	−0.214286
$197$	−3.05573	−0.217712	−0.108856	−	0.994058i	$-0.534719\pi$
$197$	−3.05573	−0.217712	−0.108856	+	0.994058i	$0.534719\pi$
$198$	0	0
$199$	−1.05573	−0.0748386	−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573	−0.0748386	−0.0374193	+	0.999300i	$0.511914\pi$
$200$	−3.47214	−0.245517
$201$	−0.236068	−0.0166510
$202$	18.1803	1.27916
$203$	8.94427	0.627765
$204$	4.23607	0.296584
$205$	−4.18034	−0.291968
$206$	2.29180	0.159677
$207$	−12.4721	−0.866873
$208$	−3.23607	−0.224381
$209$	0	0
$210$	6.47214	0.446620
$211$	5.09017	0.350422	0.175211	−	0.984531i	$-0.443939\pi$
$211$	5.09017	0.350422	0.175211	+	0.984531i	$0.443939\pi$
$212$	−10.4721	−0.719229
$213$	−2.00000	−0.137038
$214$	−7.85410	−0.536895
$215$	−14.2918	−0.974692
$216$	2.23607	0.152145
$217$	−4.00000	−0.271538
$218$	1.05573	0.0715029
$219$	33.0344	2.23226
$220$	0	0
$221$	−5.23607	−0.352216
$222$	25.4164	1.70584
$223$	12.2918	0.823120	0.411560	−	0.911383i	$-0.364984\pi$
$223$	12.2918	0.823120	0.411560	+	0.911383i	$0.364984\pi$
$224$	−2.00000	−0.133631
$225$	−13.3820	−0.892131
$226$	4.85410	0.322890
$227$	−23.5066	−1.56019	−0.780093	−	0.625663i	$-0.784828\pi$
$227$	−23.5066	−1.56019	−0.780093	+	0.625663i	$0.784828\pi$
$228$	2.23607	0.148087
$229$	−11.7082	−0.773700	−0.386850	−	0.922143i	$-0.626437\pi$
$229$	−11.7082	−0.773700	−0.386850	+	0.922143i	$0.626437\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	−4.47214	−0.293610
$233$	−7.38197	−0.483609	−0.241804	−	0.970325i	$-0.577739\pi$
$233$	−7.38197	−0.483609	−0.241804	+	0.970325i	$0.577739\pi$
$234$	−12.4721	−0.815329
$235$	−3.05573	−0.199334
$236$	−6.38197	−0.415431
$237$	−35.1246	−2.28159
$238$	−3.23607	−0.209763
$239$	−8.29180	−0.536352	−0.268176	−	0.963370i	$-0.586421\pi$
$239$	−8.29180	−0.536352	−0.268176	+	0.963370i	$0.586421\pi$
$240$	−3.23607	−0.208887
$241$	0.0901699	0.00580836	0.00290418	−	0.999996i	$-0.499076\pi$
$241$	0.0901699	0.00580836	0.00290418	+	0.999996i	$0.499076\pi$
$242$	0	0
$243$	−21.6525	−1.38901
$244$	6.47214	0.414336
$245$	3.70820	0.236908
$246$	8.85410	0.564517
$247$	−2.76393	−0.175865
$248$	2.00000	0.127000
$249$	−16.5623	−1.04959
$250$	10.4721	0.662316
$251$	3.05573	0.192876	0.0964379	−	0.995339i	$-0.469255\pi$
$251$	3.05573	0.192876	0.0964379	+	0.995339i	$0.469255\pi$
$252$	−7.70820	−0.485571
$253$	0	0
$254$	6.94427	0.435722
$255$	−5.23607	−0.327895
$256$	1.00000	0.0625000
$257$	−3.38197	−0.210961	−0.105481	−	0.994421i	$-0.533638\pi$
$257$	−3.38197	−0.210961	−0.105481	+	0.994421i	$0.533638\pi$
$258$	30.2705	1.88456
$259$	−19.4164	−1.20648
$260$	4.00000	0.248069
$261$	−17.2361	−1.06689
$262$	−17.7984	−1.09959
$263$	−18.7639	−1.15703	−0.578517	−	0.815670i	$-0.696368\pi$
$263$	−18.7639	−1.15703	−0.578517	+	0.815670i	$0.696368\pi$
$264$	0	0
$265$	12.9443	0.795160
$266$	−1.70820	−0.104737
$267$	8.09017	0.495110
$268$	−0.0901699	−0.00550801
$269$	−16.1803	−0.986533	−0.493266	−	0.869878i	$-0.664197\pi$
$269$	−16.1803	−0.986533	−0.493266	+	0.869878i	$0.664197\pi$
$270$	−2.76393	−0.168208
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	1.61803	0.0981077
$273$	16.9443	1.02551
$274$	4.90983	0.296614
$275$	0	0
$276$	−8.47214	−0.509963
$277$	−10.2918	−0.618374	−0.309187	−	0.951001i	$-0.600057\pi$
$277$	−10.2918	−0.618374	−0.309187	+	0.951001i	$0.600057\pi$
$278$	0	0
$279$	7.70820	0.461478
$280$	2.47214	0.147738
$281$	−4.90983	−0.292896	−0.146448	−	0.989218i	$-0.546784\pi$
$281$	−4.90983	−0.292896	−0.146448	+	0.989218i	$0.546784\pi$
$282$	6.47214	0.385410
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−0.763932	−0.0453310
$285$	−2.76393	−0.163721
$286$	0	0
$287$	−6.76393	−0.399262
$288$	3.85410	0.227105
$289$	−14.3820	−0.845998
$290$	5.52786	0.324607
$291$	36.2705	2.12621
$292$	12.6180	0.738415
$293$	16.3607	0.955801	0.477901	−	0.878414i	$-0.341398\pi$
$293$	16.3607	0.955801	0.477901	+	0.878414i	$0.341398\pi$
$294$	−7.85410	−0.458061
$295$	7.88854	0.459289
$296$	9.70820	0.564278
$297$	0	0
$298$	16.1803	0.937302
$299$	10.4721	0.605619
$300$	−9.09017	−0.524821
$301$	−23.1246	−1.33288
$302$	−8.00000	−0.460348
$303$	47.5967	2.73436
$304$	0.854102	0.0489861
$305$	−8.00000	−0.458079
$306$	6.23607	0.356492
$307$	3.20163	0.182726	0.0913632	−	0.995818i	$-0.470878\pi$
$307$	3.20163	0.182726	0.0913632	+	0.995818i	$0.470878\pi$
$308$	0	0
$309$	6.00000	0.341328
$310$	−2.47214	−0.140408
$311$	−32.0689	−1.81846	−0.909230	−	0.416295i	$-0.863328\pi$
$311$	−32.0689	−1.81846	−0.909230	+	0.416295i	$0.863328\pi$
$312$	−8.47214	−0.479640
$313$	−11.3262	−0.640197	−0.320098	−	0.947384i	$-0.603716\pi$
$313$	−11.3262	−0.640197	−0.320098	+	0.947384i	$0.603716\pi$
$314$	−3.70820	−0.209266
$315$	9.52786	0.536834
$316$	−13.4164	−0.754732
$317$	9.70820	0.545267	0.272634	−	0.962118i	$-0.412105\pi$
$317$	9.70820	0.545267	0.272634	+	0.962118i	$0.412105\pi$
$318$	−27.4164	−1.53744
$319$	0	0
$320$	−1.23607	−0.0690983
$321$	−20.5623	−1.14768
$322$	6.47214	0.360678
$323$	1.38197	0.0768946
$324$	−5.70820	−0.317122
$325$	11.2361	0.623265
$326$	12.0902	0.669613
$327$	2.76393	0.152846
$328$	3.38197	0.186738
$329$	−4.94427	−0.272587
$330$	0	0
$331$	−27.2705	−1.49892	−0.749461	−	0.662048i	$-0.769687\pi$
$331$	−27.2705	−1.49892	−0.749461	+	0.662048i	$0.769687\pi$
$332$	−6.32624	−0.347197
$333$	37.4164	2.05041
$334$	−19.2361	−1.05255
$335$	0.111456	0.00608950
$336$	−5.23607	−0.285651
$337$	−2.20163	−0.119930	−0.0599651	−	0.998200i	$-0.519099\pi$
$337$	−2.20163	−0.119930	−0.0599651	+	0.998200i	$0.519099\pi$
$338$	−2.52786	−0.137498
$339$	12.7082	0.690215
$340$	−2.00000	−0.108465
$341$	0	0
$342$	3.29180	0.178000
$343$	20.0000	1.07990
$344$	11.5623	0.623398
$345$	10.4721	0.563801
$346$	−13.8885	−0.746653
$347$	14.3820	0.772064	0.386032	−	0.922485i	$-0.373845\pi$
$347$	14.3820	0.772064	0.386032	+	0.922485i	$0.373845\pi$
$348$	−11.7082	−0.627626
$349$	29.5967	1.58428	0.792139	−	0.610341i	$-0.208968\pi$
$349$	29.5967	1.58428	0.792139	+	0.610341i	$0.208968\pi$
$350$	6.94427	0.371187
$351$	−7.23607	−0.386233
$352$	0	0
$353$	30.3820	1.61707	0.808534	−	0.588449i	$-0.200261\pi$
$353$	30.3820	1.61707	0.808534	+	0.588449i	$0.200261\pi$
$354$	−16.7082	−0.888031
$355$	0.944272	0.0501167
$356$	3.09017	0.163779
$357$	−8.47214	−0.448393
$358$	−6.38197	−0.337297
$359$	−35.1246	−1.85381	−0.926903	−	0.375301i	$-0.877539\pi$
$359$	−35.1246	−1.85381	−0.926903	+	0.375301i	$0.877539\pi$
$360$	−4.76393	−0.251081
$361$	−18.2705	−0.961606
$362$	18.1803	0.955537
$363$	0	0
$364$	6.47214	0.339232
$365$	−15.5967	−0.816371
$366$	16.9443	0.885691
$367$	6.29180	0.328429	0.164215	−	0.986425i	$-0.447491\pi$
$367$	6.29180	0.328429	0.164215	+	0.986425i	$0.447491\pi$
$368$	−3.23607	−0.168692
$369$	13.0344	0.678546
$370$	−12.0000	−0.623850
$371$	20.9443	1.08737
$372$	5.23607	0.271477
$373$	−17.7082	−0.916896	−0.458448	−	0.888721i	$-0.651594\pi$
$373$	−17.7082	−0.916896	−0.458448	+	0.888721i	$0.651594\pi$
$374$	0	0
$375$	27.4164	1.41578
$376$	2.47214	0.127491
$377$	14.4721	0.745353
$378$	−4.47214	−0.230022
$379$	−19.2705	−0.989860	−0.494930	−	0.868933i	$-0.664806\pi$
$379$	−19.2705	−0.989860	−0.494930	+	0.868933i	$0.664806\pi$
$380$	−1.05573	−0.0541577
$381$	18.1803	0.931407
$382$	9.23607	0.472558
$383$	16.3607	0.835992	0.417996	−	0.908449i	$-0.362733\pi$
$383$	16.3607	0.835992	0.417996	+	0.908449i	$0.362733\pi$
$384$	2.61803	0.133601
$385$	0	0
$386$	−9.41641	−0.479283
$387$	44.5623	2.26523
$388$	13.8541	0.703335
$389$	20.6525	1.04712	0.523561	−	0.851988i	$-0.324603\pi$
$389$	20.6525	1.04712	0.523561	+	0.851988i	$0.324603\pi$
$390$	10.4721	0.530277
$391$	−5.23607	−0.264799
$392$	−3.00000	−0.151523
$393$	−46.5967	−2.35049
$394$	−3.05573	−0.153945
$395$	16.5836	0.834411
$396$	0	0
$397$	23.1246	1.16059	0.580295	−	0.814406i	$-0.302937\pi$
$397$	23.1246	1.16059	0.580295	+	0.814406i	$0.302937\pi$
$398$	−1.05573	−0.0529189
$399$	−4.47214	−0.223887
$400$	−3.47214	−0.173607
$401$	6.79837	0.339495	0.169747	−	0.985488i	$-0.445705\pi$
$401$	6.79837	0.339495	0.169747	+	0.985488i	$0.445705\pi$
$402$	−0.236068	−0.0117740
$403$	−6.47214	−0.322400
$404$	18.1803	0.904506
$405$	7.05573	0.350602
$406$	8.94427	0.443897
$407$	0	0
$408$	4.23607	0.209717
$409$	13.4164	0.663399	0.331699	−	0.943385i	$-0.392378\pi$
$409$	13.4164	0.663399	0.331699	+	0.943385i	$0.392378\pi$
$410$	−4.18034	−0.206452
$411$	12.8541	0.634046
$412$	2.29180	0.112909
$413$	12.7639	0.628072
$414$	−12.4721	−0.612972
$415$	7.81966	0.383852
$416$	−3.23607	−0.158661
$417$	0	0
$418$	0	0
$419$	−4.14590	−0.202540	−0.101270	−	0.994859i	$-0.532291\pi$
$419$	−4.14590	−0.202540	−0.101270	+	0.994859i	$0.532291\pi$
$420$	6.47214	0.315808
$421$	−4.58359	−0.223391	−0.111695	−	0.993743i	$-0.535628\pi$
$421$	−4.58359	−0.223391	−0.111695	+	0.993743i	$0.535628\pi$
$422$	5.09017	0.247786
$423$	9.52786	0.463261
$424$	−10.4721	−0.508572
$425$	−5.61803	−0.272515
$426$	−2.00000	−0.0969003
$427$	−12.9443	−0.626417
$428$	−7.85410	−0.379642
$429$	0	0
$430$	−14.2918	−0.689212
$431$	0.944272	0.0454840	0.0227420	−	0.999741i	$-0.492760\pi$
$431$	0.944272	0.0454840	0.0227420	+	0.999741i	$0.492760\pi$
$432$	2.23607	0.107583
$433$	−14.7426	−0.708486	−0.354243	−	0.935153i	$-0.615261\pi$
$433$	−14.7426	−0.708486	−0.354243	+	0.935153i	$0.615261\pi$
$434$	−4.00000	−0.192006
$435$	14.4721	0.693886
$436$	1.05573	0.0505602
$437$	−2.76393	−0.132217
$438$	33.0344	1.57845
$439$	−33.4164	−1.59488	−0.797439	−	0.603399i	$-0.793812\pi$
$439$	−33.4164	−1.59488	−0.797439	+	0.603399i	$0.793812\pi$
$440$	0	0
$441$	−11.5623	−0.550586
$442$	−5.23607	−0.249054
$443$	11.5623	0.549342	0.274671	−	0.961538i	$-0.411431\pi$
$443$	11.5623	0.549342	0.274671	+	0.961538i	$0.411431\pi$
$444$	25.4164	1.20621
$445$	−3.81966	−0.181069
$446$	12.2918	0.582033
$447$	42.3607	2.00359
$448$	−2.00000	−0.0944911
$449$	−24.2705	−1.14540	−0.572698	−	0.819766i	$-0.694103\pi$
$449$	−24.2705	−1.14540	−0.572698	+	0.819766i	$0.694103\pi$
$450$	−13.3820	−0.630832
$451$	0	0
$452$	4.85410	0.228318
$453$	−20.9443	−0.984048
$454$	−23.5066	−1.10322
$455$	−8.00000	−0.375046
$456$	2.23607	0.104713
$457$	−29.5623	−1.38287	−0.691433	−	0.722440i	$-0.743020\pi$
$457$	−29.5623	−1.38287	−0.691433	+	0.722440i	$0.743020\pi$
$458$	−11.7082	−0.547088
$459$	3.61803	0.168875
$460$	4.00000	0.186501
$461$	32.6525	1.52078	0.760389	−	0.649468i	$-0.225008\pi$
$461$	32.6525	1.52078	0.760389	+	0.649468i	$0.225008\pi$
$462$	0	0
$463$	7.41641	0.344670	0.172335	−	0.985038i	$-0.444869\pi$
$463$	7.41641	0.344670	0.172335	+	0.985038i	$0.444869\pi$
$464$	−4.47214	−0.207614
$465$	−6.47214	−0.300138
$466$	−7.38197	−0.341963
$467$	29.3050	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$467$	29.3050	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$468$	−12.4721	−0.576525
$469$	0.180340	0.00832732
$470$	−3.05573	−0.140950
$471$	−9.70820	−0.447330
$472$	−6.38197	−0.293754
$473$	0	0
$474$	−35.1246	−1.61333
$475$	−2.96556	−0.136069
$476$	−3.23607	−0.148325
$477$	−40.3607	−1.84799
$478$	−8.29180	−0.379258
$479$	−25.5279	−1.16640	−0.583199	−	0.812329i	$-0.698199\pi$
$479$	−25.5279	−1.16640	−0.583199	+	0.812329i	$0.698199\pi$
$480$	−3.23607	−0.147706
$481$	−31.4164	−1.43246
$482$	0.0901699	0.00410713
$483$	16.9443	0.770991
$484$	0	0
$485$	−17.1246	−0.777589
$486$	−21.6525	−0.982176
$487$	−32.6525	−1.47962	−0.739812	−	0.672813i	$-0.765086\pi$
$487$	−32.6525	−1.47962	−0.739812	+	0.672813i	$0.765086\pi$
$488$	6.47214	0.292980
$489$	31.6525	1.43137
$490$	3.70820	0.167520
$491$	16.1459	0.728654	0.364327	−	0.931271i	$-0.381299\pi$
$491$	16.1459	0.728654	0.364327	+	0.931271i	$0.381299\pi$
$492$	8.85410	0.399174
$493$	−7.23607	−0.325896
$494$	−2.76393	−0.124355
$495$	0	0
$496$	2.00000	0.0898027
$497$	1.52786	0.0685341
$498$	−16.5623	−0.742175
$499$	−24.1459	−1.08092	−0.540459	−	0.841370i	$-0.681750\pi$
$499$	−24.1459	−1.08092	−0.540459	+	0.841370i	$0.681750\pi$
$500$	10.4721	0.468328
$501$	−50.3607	−2.24995
$502$	3.05573	0.136384
$503$	1.23607	0.0551135	0.0275568	−	0.999620i	$-0.491227\pi$
$503$	1.23607	0.0551135	0.0275568	+	0.999620i	$0.491227\pi$
$504$	−7.70820	−0.343351
$505$	−22.4721	−0.999997
$506$	0	0
$507$	−6.61803	−0.293917
$508$	6.94427	0.308102
$509$	−21.7082	−0.962199	−0.481100	−	0.876666i	$-0.659762\pi$
$509$	−21.7082	−0.962199	−0.481100	+	0.876666i	$0.659762\pi$
$510$	−5.23607	−0.231857
$511$	−25.2361	−1.11638
$512$	1.00000	0.0441942
$513$	1.90983	0.0843211
$514$	−3.38197	−0.149172
$515$	−2.83282	−0.124829
$516$	30.2705	1.33258
$517$	0	0
$518$	−19.4164	−0.853108
$519$	−36.3607	−1.59606
$520$	4.00000	0.175412
$521$	9.03444	0.395806	0.197903	−	0.980222i	$-0.436587\pi$
$521$	9.03444	0.395806	0.197903	+	0.980222i	$0.436587\pi$
$522$	−17.2361	−0.754402
$523$	33.7984	1.47790	0.738950	−	0.673760i	$-0.235322\pi$
$523$	33.7984	1.47790	0.738950	+	0.673760i	$0.235322\pi$
$524$	−17.7984	−0.777526
$525$	18.1803	0.793455
$526$	−18.7639	−0.818146
$527$	3.23607	0.140965
$528$	0	0
$529$	−12.5279	−0.544690
$530$	12.9443	0.562263
$531$	−24.5967	−1.06741
$532$	−1.70820	−0.0740600
$533$	−10.9443	−0.474049
$534$	8.09017	0.350096
$535$	9.70820	0.419722
$536$	−0.0901699	−0.00389475
$537$	−16.7082	−0.721012
$538$	−16.1803	−0.697584
$539$	0	0
$540$	−2.76393	−0.118941
$541$	37.1246	1.59611	0.798056	−	0.602583i	$-0.205862\pi$
$541$	37.1246	1.59611	0.798056	+	0.602583i	$0.205862\pi$
$542$	2.00000	0.0859074
$543$	47.5967	2.04257
$544$	1.61803	0.0693726
$545$	−1.30495	−0.0558980
$546$	16.9443	0.725148
$547$	−7.32624	−0.313247	−0.156624	−	0.987658i	$-0.550061\pi$
$547$	−7.32624	−0.313247	−0.156624	+	0.987658i	$0.550061\pi$
$548$	4.90983	0.209738
$549$	24.9443	1.06460
$550$	0	0
$551$	−3.81966	−0.162723
$552$	−8.47214	−0.360598
$553$	26.8328	1.14105
$554$	−10.2918	−0.437257
$555$	−31.4164	−1.33355
$556$	0	0
$557$	30.7639	1.30351	0.651755	−	0.758430i	$-0.274033\pi$
$557$	30.7639	1.30351	0.651755	+	0.758430i	$0.274033\pi$
$558$	7.70820	0.326314
$559$	−37.4164	−1.58255
$560$	2.47214	0.104467
$561$	0	0
$562$	−4.90983	−0.207109
$563$	2.61803	0.110337	0.0551685	−	0.998477i	$-0.482430\pi$
$563$	2.61803	0.110337	0.0551685	+	0.998477i	$0.482430\pi$
$564$	6.47214	0.272526
$565$	−6.00000	−0.252422
$566$	24.0000	1.00880
$567$	11.4164	0.479444
$568$	−0.763932	−0.0320539
$569$	−13.2148	−0.553992	−0.276996	−	0.960871i	$-0.589339\pi$
$569$	−13.2148	−0.553992	−0.276996	+	0.960871i	$0.589339\pi$
$570$	−2.76393	−0.115768
$571$	6.47214	0.270850	0.135425	−	0.990788i	$-0.456760\pi$
$571$	6.47214	0.270850	0.135425	+	0.990788i	$0.456760\pi$
$572$	0	0
$573$	24.1803	1.01015
$574$	−6.76393	−0.282321
$575$	11.2361	0.468576
$576$	3.85410	0.160588
$577$	17.7984	0.740956	0.370478	−	0.928841i	$-0.379194\pi$
$577$	17.7984	0.740956	0.370478	+	0.928841i	$0.379194\pi$
$578$	−14.3820	−0.598211
$579$	−24.6525	−1.02452
$580$	5.52786	0.229532
$581$	12.6525	0.524913
$582$	36.2705	1.50346
$583$	0	0
$584$	12.6180	0.522138
$585$	15.4164	0.637390
$586$	16.3607	0.675853
$587$	28.8541	1.19094	0.595468	−	0.803379i	$-0.296967\pi$
$587$	28.8541	1.19094	0.595468	+	0.803379i	$0.296967\pi$
$588$	−7.85410	−0.323898
$589$	1.70820	0.0703853
$590$	7.88854	0.324766
$591$	−8.00000	−0.329076
$592$	9.70820	0.399005
$593$	31.6869	1.30123	0.650613	−	0.759410i	$-0.274512\pi$
$593$	31.6869	1.30123	0.650613	+	0.759410i	$0.274512\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	16.1803	0.662773
$597$	−2.76393	−0.113120
$598$	10.4721	0.428237
$599$	13.4164	0.548180	0.274090	−	0.961704i	$-0.411623\pi$
$599$	13.4164	0.548180	0.274090	+	0.961704i	$0.411623\pi$
$600$	−9.09017	−0.371105
$601$	−33.8541	−1.38094	−0.690469	−	0.723362i	$-0.742596\pi$
$601$	−33.8541	−1.38094	−0.690469	+	0.723362i	$0.742596\pi$
$602$	−23.1246	−0.942489
$603$	−0.347524	−0.0141523
$604$	−8.00000	−0.325515
$605$	0	0
$606$	47.5967	1.93349
$607$	−17.1246	−0.695067	−0.347533	−	0.937668i	$-0.612981\pi$
$607$	−17.1246	−0.695067	−0.347533	+	0.937668i	$0.612981\pi$
$608$	0.854102	0.0346384
$609$	23.4164	0.948881
$610$	−8.00000	−0.323911
$611$	−8.00000	−0.323645
$612$	6.23607	0.252078
$613$	22.2918	0.900357	0.450179	−	0.892939i	$-0.351360\pi$
$613$	22.2918	0.900357	0.450179	+	0.892939i	$0.351360\pi$
$614$	3.20163	0.129207
$615$	−10.9443	−0.441316
$616$	0	0
$617$	−32.4508	−1.30642	−0.653211	−	0.757176i	$-0.726579\pi$
$617$	−32.4508	−1.30642	−0.653211	+	0.757176i	$0.726579\pi$
$618$	6.00000	0.241355
$619$	29.7984	1.19770	0.598849	−	0.800862i	$-0.295625\pi$
$619$	29.7984	1.19770	0.598849	+	0.800862i	$0.295625\pi$
$620$	−2.47214	−0.0992834
$621$	−7.23607	−0.290373
$622$	−32.0689	−1.28585
$623$	−6.18034	−0.247610
$624$	−8.47214	−0.339157
$625$	4.41641	0.176656
$626$	−11.3262	−0.452688
$627$	0	0
$628$	−3.70820	−0.147973
$629$	15.7082	0.626327
$630$	9.52786	0.379599
$631$	10.2918	0.409710	0.204855	−	0.978792i	$-0.434328\pi$
$631$	10.2918	0.409710	0.204855	+	0.978792i	$0.434328\pi$
$632$	−13.4164	−0.533676
$633$	13.3262	0.529670
$634$	9.70820	0.385562
$635$	−8.58359	−0.340629
$636$	−27.4164	−1.08713
$637$	9.70820	0.384653
$638$	0	0
$639$	−2.94427	−0.116474
$640$	−1.23607	−0.0488599
$641$	32.3262	1.27681	0.638405	−	0.769701i	$-0.279595\pi$
$641$	32.3262	1.27681	0.638405	+	0.769701i	$0.279595\pi$
$642$	−20.5623	−0.811529
$643$	−6.97871	−0.275214	−0.137607	−	0.990487i	$-0.543941\pi$
$643$	−6.97871	−0.275214	−0.137607	+	0.990487i	$0.543941\pi$
$644$	6.47214	0.255038
$645$	−37.4164	−1.47327
$646$	1.38197	0.0543727
$647$	46.9443	1.84557	0.922785	−	0.385316i	$-0.125907\pi$
$647$	46.9443	1.84557	0.922785	+	0.385316i	$0.125907\pi$
$648$	−5.70820	−0.224239
$649$	0	0
$650$	11.2361	0.440715
$651$	−10.4721	−0.410435
$652$	12.0902	0.473488
$653$	−46.6525	−1.82565	−0.912826	−	0.408348i	$-0.866105\pi$
$653$	−46.6525	−1.82565	−0.912826	+	0.408348i	$0.866105\pi$
$654$	2.76393	0.108078
$655$	22.0000	0.859611
$656$	3.38197	0.132044
$657$	48.6312	1.89728
$658$	−4.94427	−0.192748
$659$	−28.0902	−1.09424	−0.547119	−	0.837055i	$-0.684275\pi$
$659$	−28.0902	−1.09424	−0.547119	+	0.837055i	$0.684275\pi$
$660$	0	0
$661$	−12.4721	−0.485110	−0.242555	−	0.970138i	$-0.577985\pi$
$661$	−12.4721	−0.485110	−0.242555	+	0.970138i	$0.577985\pi$
$662$	−27.2705	−1.05990
$663$	−13.7082	−0.532383
$664$	−6.32624	−0.245506
$665$	2.11146	0.0818788
$666$	37.4164	1.44986
$667$	14.4721	0.560363
$668$	−19.2361	−0.744266
$669$	32.1803	1.24416
$670$	0.111456	0.00430593
$671$	0	0
$672$	−5.23607	−0.201986
$673$	3.14590	0.121265	0.0606327	−	0.998160i	$-0.480688\pi$
$673$	3.14590	0.121265	0.0606327	+	0.998160i	$0.480688\pi$
$674$	−2.20163	−0.0848035
$675$	−7.76393	−0.298834
$676$	−2.52786	−0.0972255
$677$	30.3607	1.16686	0.583428	−	0.812165i	$-0.301711\pi$
$677$	30.3607	1.16686	0.583428	+	0.812165i	$0.301711\pi$
$678$	12.7082	0.488056
$679$	−27.7082	−1.06334
$680$	−2.00000	−0.0766965
$681$	−61.5410	−2.35826
$682$	0	0
$683$	9.52786	0.364574	0.182287	−	0.983245i	$-0.441650\pi$
$683$	9.52786	0.364574	0.182287	+	0.983245i	$0.441650\pi$
$684$	3.29180	0.125865
$685$	−6.06888	−0.231880
$686$	20.0000	0.763604
$687$	−30.6525	−1.16946
$688$	11.5623	0.440809
$689$	33.8885	1.29105
$690$	10.4721	0.398667
$691$	25.2148	0.959216	0.479608	−	0.877483i	$-0.340779\pi$
$691$	25.2148	0.959216	0.479608	+	0.877483i	$0.340779\pi$
$692$	−13.8885	−0.527963
$693$	0	0
$694$	14.3820	0.545932
$695$	0	0
$696$	−11.7082	−0.443798
$697$	5.47214	0.207272
$698$	29.5967	1.12025
$699$	−19.3262	−0.730985
$700$	6.94427	0.262469
$701$	38.8328	1.46670	0.733348	−	0.679854i	$-0.237957\pi$
$701$	38.8328	1.46670	0.733348	+	0.679854i	$0.237957\pi$
$702$	−7.23607	−0.273108
$703$	8.29180	0.312731
$704$	0	0
$705$	−8.00000	−0.301297
$706$	30.3820	1.14344
$707$	−36.3607	−1.36748
$708$	−16.7082	−0.627933
$709$	15.5279	0.583161	0.291581	−	0.956546i	$-0.405819\pi$
$709$	15.5279	0.583161	0.291581	+	0.956546i	$0.405819\pi$
$710$	0.944272	0.0354379
$711$	−51.7082	−1.93921
$712$	3.09017	0.115809
$713$	−6.47214	−0.242383
$714$	−8.47214	−0.317062
$715$	0	0
$716$	−6.38197	−0.238505
$717$	−21.7082	−0.810708
$718$	−35.1246	−1.31084
$719$	−26.8328	−1.00070	−0.500348	−	0.865825i	$-0.666794\pi$
$719$	−26.8328	−1.00070	−0.500348	+	0.865825i	$0.666794\pi$
$720$	−4.76393	−0.177541
$721$	−4.58359	−0.170702
$722$	−18.2705	−0.679958
$723$	0.236068	0.00877946
$724$	18.1803	0.675667
$725$	15.5279	0.576690
$726$	0	0
$727$	43.1246	1.59940	0.799702	−	0.600398i	$-0.204991\pi$
$727$	43.1246	1.59940	0.799702	+	0.600398i	$0.204991\pi$
$728$	6.47214	0.239873
$729$	−39.5623	−1.46527
$730$	−15.5967	−0.577262
$731$	18.7082	0.691948
$732$	16.9443	0.626278
$733$	17.4164	0.643290	0.321645	−	0.946860i	$-0.395764\pi$
$733$	17.4164	0.643290	0.321645	+	0.946860i	$0.395764\pi$
$734$	6.29180	0.232234
$735$	9.70820	0.358092
$736$	−3.23607	−0.119283
$737$	0	0
$738$	13.0344	0.479804
$739$	−17.4377	−0.641456	−0.320728	−	0.947171i	$-0.603928\pi$
$739$	−17.4377	−0.641456	−0.320728	+	0.947171i	$0.603928\pi$
$740$	−12.0000	−0.441129
$741$	−7.23607	−0.265824
$742$	20.9443	0.768888
$743$	−13.2361	−0.485584	−0.242792	−	0.970078i	$-0.578063\pi$
$743$	−13.2361	−0.485584	−0.242792	+	0.970078i	$0.578063\pi$
$744$	5.23607	0.191964
$745$	−20.0000	−0.732743
$746$	−17.7082	−0.648343
$747$	−24.3820	−0.892089
$748$	0	0
$749$	15.7082	0.573965
$750$	27.4164	1.00111
$751$	37.7771	1.37851	0.689253	−	0.724521i	$-0.257939\pi$
$751$	37.7771	1.37851	0.689253	+	0.724521i	$0.257939\pi$
$752$	2.47214	0.0901495
$753$	8.00000	0.291536
$754$	14.4721	0.527044
$755$	9.88854	0.359881
$756$	−4.47214	−0.162650
$757$	28.6525	1.04139	0.520696	−	0.853742i	$-0.325673\pi$
$757$	28.6525	1.04139	0.520696	+	0.853742i	$0.325673\pi$
$758$	−19.2705	−0.699936
$759$	0	0
$760$	−1.05573	−0.0382953
$761$	−46.7426	−1.69442	−0.847210	−	0.531258i	$-0.821719\pi$
$761$	−46.7426	−1.69442	−0.847210	+	0.531258i	$0.821719\pi$
$762$	18.1803	0.658604
$763$	−2.11146	−0.0764398
$764$	9.23607	0.334149
$765$	−7.70820	−0.278691
$766$	16.3607	0.591135
$767$	20.6525	0.745718
$768$	2.61803	0.0944702
$769$	−13.4164	−0.483808	−0.241904	−	0.970300i	$-0.577772\pi$
$769$	−13.4164	−0.483808	−0.241904	+	0.970300i	$0.577772\pi$
$770$	0	0
$771$	−8.85410	−0.318873
$772$	−9.41641	−0.338904
$773$	31.8885	1.14695	0.573476	−	0.819223i	$-0.305595\pi$
$773$	31.8885	1.14695	0.573476	+	0.819223i	$0.305595\pi$
$774$	44.5623	1.60176
$775$	−6.94427	−0.249446
$776$	13.8541	0.497333
$777$	−50.8328	−1.82362
$778$	20.6525	0.740427
$779$	2.88854	0.103493
$780$	10.4721	0.374963
$781$	0	0
$782$	−5.23607	−0.187241
$783$	−10.0000	−0.357371
$784$	−3.00000	−0.107143
$785$	4.58359	0.163595
$786$	−46.5967	−1.66205
$787$	−25.2148	−0.898810	−0.449405	−	0.893328i	$-0.648364\pi$
$787$	−25.2148	−0.898810	−0.449405	+	0.893328i	$0.648364\pi$
$788$	−3.05573	−0.108856
$789$	−49.1246	−1.74888
$790$	16.5836	0.590018
$791$	−9.70820	−0.345184
$792$	0	0
$793$	−20.9443	−0.743753
$794$	23.1246	0.820662
$795$	33.8885	1.20190
$796$	−1.05573	−0.0374193
$797$	−29.2361	−1.03559	−0.517797	−	0.855503i	$-0.673248\pi$
$797$	−29.2361	−1.03559	−0.517797	+	0.855503i	$0.673248\pi$
$798$	−4.47214	−0.158312
$799$	4.00000	0.141510
$800$	−3.47214	−0.122759
$801$	11.9098	0.420813
$802$	6.79837	0.240059
$803$	0	0
$804$	−0.236068	−0.00832548
$805$	−8.00000	−0.281963
$806$	−6.47214	−0.227971
$807$	−42.3607	−1.49117
$808$	18.1803	0.639582
$809$	28.0902	0.987598	0.493799	−	0.869576i	$-0.335608\pi$
$809$	28.0902	0.987598	0.493799	+	0.869576i	$0.335608\pi$
$810$	7.05573	0.247913
$811$	10.6180	0.372850	0.186425	−	0.982469i	$-0.440310\pi$
$811$	10.6180	0.372850	0.186425	+	0.982469i	$0.440310\pi$
$812$	8.94427	0.313882
$813$	5.23607	0.183637
$814$	0	0
$815$	−14.9443	−0.523475
$816$	4.23607	0.148292
$817$	9.87539	0.345496
$818$	13.4164	0.469094
$819$	24.9443	0.871623
$820$	−4.18034	−0.145984
$821$	−36.5410	−1.27529	−0.637645	−	0.770330i	$-0.720091\pi$
$821$	−36.5410	−1.27529	−0.637645	+	0.770330i	$0.720091\pi$
$822$	12.8541	0.448338
$823$	−25.5967	−0.892247	−0.446123	−	0.894972i	$-0.647196\pi$
$823$	−25.5967	−0.892247	−0.446123	+	0.894972i	$0.647196\pi$
$824$	2.29180	0.0798385
$825$	0	0
$826$	12.7639	0.444114
$827$	41.6180	1.44720	0.723600	−	0.690219i	$-0.242486\pi$
$827$	41.6180	1.44720	0.723600	+	0.690219i	$0.242486\pi$
$828$	−12.4721	−0.433437
$829$	48.9443	1.69990	0.849952	−	0.526859i	$-0.176631\pi$
$829$	48.9443	1.69990	0.849952	+	0.526859i	$0.176631\pi$
$830$	7.81966	0.271424
$831$	−26.9443	−0.934686
$832$	−3.23607	−0.112190
$833$	−4.85410	−0.168185
$834$	0	0
$835$	23.7771	0.822840
$836$	0	0
$837$	4.47214	0.154580
$838$	−4.14590	−0.143218
$839$	47.8885	1.65330	0.826648	−	0.562719i	$-0.190245\pi$
$839$	47.8885	1.65330	0.826648	+	0.562719i	$0.190245\pi$
$840$	6.47214	0.223310
$841$	−9.00000	−0.310345
$842$	−4.58359	−0.157961
$843$	−12.8541	−0.442719
$844$	5.09017	0.175211
$845$	3.12461	0.107490
$846$	9.52786	0.327575
$847$	0	0
$848$	−10.4721	−0.359615
$849$	62.8328	2.15642
$850$	−5.61803	−0.192697
$851$	−31.4164	−1.07694
$852$	−2.00000	−0.0685189
$853$	−21.5279	−0.737100	−0.368550	−	0.929608i	$-0.620146\pi$
$853$	−21.5279	−0.737100	−0.368550	+	0.929608i	$0.620146\pi$
$854$	−12.9443	−0.442944
$855$	−4.06888	−0.139153
$856$	−7.85410	−0.268448
$857$	31.7426	1.08431	0.542154	−	0.840279i	$-0.317609\pi$
$857$	31.7426	1.08431	0.542154	+	0.840279i	$0.317609\pi$
$858$	0	0
$859$	8.49342	0.289792	0.144896	−	0.989447i	$-0.453715\pi$
$859$	8.49342	0.289792	0.144896	+	0.989447i	$0.453715\pi$
$860$	−14.2918	−0.487346
$861$	−17.7082	−0.603494
$862$	0.944272	0.0321620
$863$	−28.7639	−0.979136	−0.489568	−	0.871965i	$-0.662845\pi$
$863$	−28.7639	−0.979136	−0.489568	+	0.871965i	$0.662845\pi$
$864$	2.23607	0.0760726
$865$	17.1672	0.583702
$866$	−14.7426	−0.500975
$867$	−37.6525	−1.27875
$868$	−4.00000	−0.135769
$869$	0	0
$870$	14.4721	0.490651
$871$	0.291796	0.00988713
$872$	1.05573	0.0357515
$873$	53.3951	1.80715
$874$	−2.76393	−0.0934914
$875$	−20.9443	−0.708046
$876$	33.0344	1.11613
$877$	−5.81966	−0.196516	−0.0982580	−	0.995161i	$-0.531327\pi$
$877$	−5.81966	−0.196516	−0.0982580	+	0.995161i	$0.531327\pi$
$878$	−33.4164	−1.12775
$879$	42.8328	1.44472
$880$	0	0
$881$	45.3394	1.52752	0.763761	−	0.645499i	$-0.223350\pi$
$881$	45.3394	1.52752	0.763761	+	0.645499i	$0.223350\pi$
$882$	−11.5623	−0.389323
$883$	−23.5623	−0.792935	−0.396467	−	0.918049i	$-0.629764\pi$
$883$	−23.5623	−0.792935	−0.396467	+	0.918049i	$0.629764\pi$
$884$	−5.23607	−0.176108
$885$	20.6525	0.694225
$886$	11.5623	0.388443
$887$	33.7771	1.13412	0.567062	−	0.823675i	$-0.308080\pi$
$887$	33.7771	1.13412	0.567062	+	0.823675i	$0.308080\pi$
$888$	25.4164	0.852919
$889$	−13.8885	−0.465807
$890$	−3.81966	−0.128035
$891$	0	0
$892$	12.2918	0.411560
$893$	2.11146	0.0706572
$894$	42.3607	1.41675
$895$	7.88854	0.263685
$896$	−2.00000	−0.0668153
$897$	27.4164	0.915407
$898$	−24.2705	−0.809917
$899$	−8.94427	−0.298308
$900$	−13.3820	−0.446066
$901$	−16.9443	−0.564496
$902$	0	0
$903$	−60.5410	−2.01468
$904$	4.85410	0.161445
$905$	−22.4721	−0.746999
$906$	−20.9443	−0.695827
$907$	30.5623	1.01480	0.507402	−	0.861709i	$-0.330606\pi$
$907$	30.5623	1.01480	0.507402	+	0.861709i	$0.330606\pi$
$908$	−23.5066	−0.780093
$909$	70.0689	2.32404
$910$	−8.00000	−0.265197
$911$	−4.18034	−0.138501	−0.0692504	−	0.997599i	$-0.522061\pi$
$911$	−4.18034	−0.138501	−0.0692504	+	0.997599i	$0.522061\pi$
$912$	2.23607	0.0740436
$913$	0	0
$914$	−29.5623	−0.977834
$915$	−20.9443	−0.692396
$916$	−11.7082	−0.386850
$917$	35.5967	1.17551
$918$	3.61803	0.119413
$919$	16.5836	0.547042	0.273521	−	0.961866i	$-0.411812\pi$
$919$	16.5836	0.547042	0.273521	+	0.961866i	$0.411812\pi$
$920$	4.00000	0.131876
$921$	8.38197	0.276195
$922$	32.6525	1.07535
$923$	2.47214	0.0813713
$924$	0	0
$925$	−33.7082	−1.10832
$926$	7.41641	0.243718
$927$	8.83282	0.290108
$928$	−4.47214	−0.146805
$929$	−58.7426	−1.92728	−0.963642	−	0.267197i	$-0.913902\pi$
$929$	−58.7426	−1.92728	−0.963642	+	0.267197i	$0.913902\pi$
$930$	−6.47214	−0.212230
$931$	−2.56231	−0.0839762
$932$	−7.38197	−0.241804
$933$	−83.9574	−2.74864
$934$	29.3050	0.958887
$935$	0	0
$936$	−12.4721	−0.407665
$937$	−31.1459	−1.01749	−0.508746	−	0.860917i	$-0.669891\pi$
$937$	−31.1459	−1.01749	−0.508746	+	0.860917i	$0.669891\pi$
$938$	0.180340	0.00588831
$939$	−29.6525	−0.967672
$940$	−3.05573	−0.0996669
$941$	25.8197	0.841697	0.420848	−	0.907131i	$-0.361732\pi$
$941$	25.8197	0.841697	0.420848	+	0.907131i	$0.361732\pi$
$942$	−9.70820	−0.316310
$943$	−10.9443	−0.356395
$944$	−6.38197	−0.207715
$945$	5.52786	0.179821
$946$	0	0
$947$	21.2148	0.689388	0.344694	−	0.938715i	$-0.387983\pi$
$947$	21.2148	0.689388	0.344694	+	0.938715i	$0.387983\pi$
$948$	−35.1246	−1.14079
$949$	−40.8328	−1.32549
$950$	−2.96556	−0.0962154
$951$	25.4164	0.824183
$952$	−3.23607	−0.104882
$953$	4.32624	0.140141	0.0700703	−	0.997542i	$-0.477678\pi$
$953$	4.32624	0.140141	0.0700703	+	0.997542i	$0.477678\pi$
$954$	−40.3607	−1.30673
$955$	−11.4164	−0.369426
$956$	−8.29180	−0.268176
$957$	0	0
$958$	−25.5279	−0.824768
$959$	−9.81966	−0.317093
$960$	−3.23607	−0.104444
$961$	−27.0000	−0.870968
$962$	−31.4164	−1.01291
$963$	−30.2705	−0.975454
$964$	0.0901699	0.00290418
$965$	11.6393	0.374683
$966$	16.9443	0.545173
$967$	38.0000	1.22200	0.610999	−	0.791632i	$-0.290768\pi$
$967$	38.0000	1.22200	0.610999	+	0.791632i	$0.290768\pi$
$968$	0	0
$969$	3.61803	0.116228
$970$	−17.1246	−0.549838
$971$	−45.8885	−1.47263	−0.736317	−	0.676637i	$-0.763437\pi$
$971$	−45.8885	−1.47263	−0.736317	+	0.676637i	$0.763437\pi$
$972$	−21.6525	−0.694503
$973$	0	0
$974$	−32.6525	−1.04625
$975$	29.4164	0.942079
$976$	6.47214	0.207168
$977$	19.3050	0.617620	0.308810	−	0.951124i	$-0.400069\pi$
$977$	19.3050	0.617620	0.308810	+	0.951124i	$0.400069\pi$
$978$	31.6525	1.01213
$979$	0	0
$980$	3.70820	0.118454
$981$	4.06888	0.129909
$982$	16.1459	0.515236
$983$	−6.00000	−0.191370	−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000	−0.191370	−0.0956851	+	0.995412i	$0.530504\pi$
$984$	8.85410	0.282258
$985$	3.77709	0.120348
$986$	−7.23607	−0.230443
$987$	−12.9443	−0.412021
$988$	−2.76393	−0.0879324
$989$	−37.4164	−1.18977
$990$	0	0
$991$	−36.5410	−1.16076	−0.580382	−	0.814344i	$-0.697097\pi$
$991$	−36.5410	−1.16076	−0.580382	+	0.814344i	$0.697097\pi$
$992$	2.00000	0.0635001
$993$	−71.3951	−2.26566
$994$	1.52786	0.0484609
$995$	1.30495	0.0413697
$996$	−16.5623	−0.524797
$997$	−22.6525	−0.717411	−0.358706	−	0.933451i	$-0.616782\pi$
$997$	−22.6525	−0.717411	−0.358706	+	0.933451i	$0.616782\pi$
$998$	−24.1459	−0.764325
$999$	21.7082	0.686817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.a.f.1.2		2
3.2	odd	2		2178.2.a.p.1.2		2
4.3	odd	2		1936.2.a.o.1.1		2
5.4	even	2		6050.2.a.bs.1.1		2
8.3	odd	2		7744.2.a.cz.1.2		2
8.5	even	2		7744.2.a.bm.1.1		2
11.2	odd	10		242.2.c.d.81.1		4
11.3	even	5		22.2.c.a.9.1	yes	4
11.4	even	5		22.2.c.a.5.1	✓	4
11.5	even	5		242.2.c.a.3.1		4
11.6	odd	10		242.2.c.d.3.1		4
11.7	odd	10		242.2.c.c.27.1		4
11.8	odd	10		242.2.c.c.9.1		4
11.9	even	5		242.2.c.a.81.1		4
11.10	odd	2		242.2.a.d.1.2		2
33.14	odd	10		198.2.f.e.163.1		4
33.26	odd	10		198.2.f.e.181.1		4
33.32	even	2		2178.2.a.x.1.2		2
44.3	odd	10		176.2.m.c.97.1		4
44.15	odd	10		176.2.m.c.49.1		4
44.43	even	2		1936.2.a.n.1.1		2
55.3	odd	20		550.2.ba.c.449.1		8
55.4	even	10		550.2.h.h.401.1		4
55.14	even	10		550.2.h.h.251.1		4
55.37	odd	20		550.2.ba.c.49.1		8
55.47	odd	20		550.2.ba.c.449.2		8
55.48	odd	20		550.2.ba.c.49.2		8
55.54	odd	2		6050.2.a.ci.1.1		2
88.3	odd	10		704.2.m.a.449.1		4
88.21	odd	2		7744.2.a.bn.1.1		2
88.37	even	10		704.2.m.h.577.1		4
88.43	even	2		7744.2.a.cy.1.2		2
88.59	odd	10		704.2.m.a.577.1		4
88.69	even	10		704.2.m.h.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.5.1	✓	4	11.4	even	5
22.2.c.a.9.1	yes	4	11.3	even	5
176.2.m.c.49.1		4	44.15	odd	10
176.2.m.c.97.1		4	44.3	odd	10
198.2.f.e.163.1		4	33.14	odd	10
198.2.f.e.181.1		4	33.26	odd	10
242.2.a.d.1.2		2	11.10	odd	2
242.2.a.f.1.2		2	1.1	even	1	trivial
242.2.c.a.3.1		4	11.5	even	5
242.2.c.a.81.1		4	11.9	even	5
242.2.c.c.9.1		4	11.8	odd	10
242.2.c.c.27.1		4	11.7	odd	10
242.2.c.d.3.1		4	11.6	odd	10
242.2.c.d.81.1		4	11.2	odd	10
550.2.h.h.251.1		4	55.14	even	10
550.2.h.h.401.1		4	55.4	even	10
550.2.ba.c.49.1		8	55.37	odd	20
550.2.ba.c.49.2		8	55.48	odd	20
550.2.ba.c.449.1		8	55.3	odd	20
550.2.ba.c.449.2		8	55.47	odd	20
704.2.m.a.449.1		4	88.3	odd	10
704.2.m.a.577.1		4	88.59	odd	10
704.2.m.h.449.1		4	88.69	even	10
704.2.m.h.577.1		4	88.37	even	10
1936.2.a.n.1.1		2	44.43	even	2
1936.2.a.o.1.1		2	4.3	odd	2
2178.2.a.p.1.2		2	3.2	odd	2
2178.2.a.x.1.2		2	33.32	even	2
6050.2.a.bs.1.1		2	5.4	even	2
6050.2.a.ci.1.1		2	55.54	odd	2
7744.2.a.bm.1.1		2	8.5	even	2
7744.2.a.bn.1.1		2	88.21	odd	2
7744.2.a.cy.1.2		2	88.43	even	2
7744.2.a.cz.1.2		2	8.3	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} -1.23607 q^{5} +2.61803 q^{6} -2.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} -1.23607 q^{10} +2.61803 q^{12} -3.23607 q^{13} -2.00000 q^{14} -3.23607 q^{15} +1.00000 q^{16} +1.61803 q^{17} +3.85410 q^{18} +0.854102 q^{19} -1.23607 q^{20} -5.23607 q^{21} -3.23607 q^{23} +2.61803 q^{24} -3.47214 q^{25} -3.23607 q^{26} +2.23607 q^{27} -2.00000 q^{28} -4.47214 q^{29} -3.23607 q^{30} +2.00000 q^{31} +1.00000 q^{32} +1.61803 q^{34} +2.47214 q^{35} +3.85410 q^{36} +9.70820 q^{37} +0.854102 q^{38} -8.47214 q^{39} -1.23607 q^{40} +3.38197 q^{41} -5.23607 q^{42} +11.5623 q^{43} -4.76393 q^{45} -3.23607 q^{46} +2.47214 q^{47} +2.61803 q^{48} -3.00000 q^{49} -3.47214 q^{50} +4.23607 q^{51} -3.23607 q^{52} -10.4721 q^{53} +2.23607 q^{54} -2.00000 q^{56} +2.23607 q^{57} -4.47214 q^{58} -6.38197 q^{59} -3.23607 q^{60} +6.47214 q^{61} +2.00000 q^{62} -7.70820 q^{63} +1.00000 q^{64} +4.00000 q^{65} -0.0901699 q^{67} +1.61803 q^{68} -8.47214 q^{69} +2.47214 q^{70} -0.763932 q^{71} +3.85410 q^{72} +12.6180 q^{73} +9.70820 q^{74} -9.09017 q^{75} +0.854102 q^{76} -8.47214 q^{78} -13.4164 q^{79} -1.23607 q^{80} -5.70820 q^{81} +3.38197 q^{82} -6.32624 q^{83} -5.23607 q^{84} -2.00000 q^{85} +11.5623 q^{86} -11.7082 q^{87} +3.09017 q^{89} -4.76393 q^{90} +6.47214 q^{91} -3.23607 q^{92} +5.23607 q^{93} +2.47214 q^{94} -1.05573 q^{95} +2.61803 q^{96} +13.8541 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{6} - 4 q^{7} + 2 q^{8} + q^{9} + 2 q^{10} + 3 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} + q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^6 - 4 * q^7 + 2 * q^8 + q^9 + 2 * q^10 + 3 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 + q^17 + q^18 - 5 * q^19 + 2 * q^20 - 6 * q^21 - 2 * q^23 + 3 * q^24 + 2 * q^25 - 2 * q^26 - 4 * q^28 - 2 * q^30 + 4 * q^31 + 2 * q^32 + q^34 - 4 * q^35 + q^36 + 6 * q^37 - 5 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^41 - 6 * q^42 + 3 * q^43 - 14 * q^45 - 2 * q^46 - 4 * q^47 + 3 * q^48 - 6 * q^49 + 2 * q^50 + 4 * q^51 - 2 * q^52 - 12 * q^53 - 4 * q^56 - 15 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 + 8 * q^65 + 11 * q^67 + q^68 - 8 * q^69 - 4 * q^70 - 6 * q^71 + q^72 + 23 * q^73 + 6 * q^74 - 7 * q^75 - 5 * q^76 - 8 * q^78 + 2 * q^80 + 2 * q^81 + 9 * q^82 + 3 * q^83 - 6 * q^84 - 4 * q^85 + 3 * q^86 - 10 * q^87 - 5 * q^89 - 14 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 - 4 * q^94 - 20 * q^95 + 3 * q^96 + 21 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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