LMFDB - Embedded newform 357.2.a.g.1.3

Error: no document with id 271722290 found in table mf_hecke_traces.

Error: no document with id 265646810 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(1,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,1,3,3,2,1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
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			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	357.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -1.34292 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} -3.14637 q^{10} -0.489289 q^{11} +3.48929 q^{12} -3.63565 q^{13} +2.34292 q^{14} -1.34292 q^{15} +1.19656 q^{16} +1.00000 q^{17} +2.34292 q^{18} -3.34292 q^{19} -4.68585 q^{20} +1.00000 q^{21} -1.14637 q^{22} +4.48929 q^{23} +3.48929 q^{24} -3.19656 q^{25} -8.51806 q^{26} +1.00000 q^{27} +3.48929 q^{28} +6.97858 q^{29} -3.14637 q^{30} -5.14637 q^{31} -4.17513 q^{32} -0.489289 q^{33} +2.34292 q^{34} -1.34292 q^{35} +3.48929 q^{36} +4.12494 q^{37} -7.83221 q^{38} -3.63565 q^{39} -4.68585 q^{40} +2.65708 q^{41} +2.34292 q^{42} -4.88240 q^{43} -1.70727 q^{44} -1.34292 q^{45} +10.5181 q^{46} -8.22533 q^{47} +1.19656 q^{48} +1.00000 q^{49} -7.48929 q^{50} +1.00000 q^{51} -12.6858 q^{52} -3.73183 q^{53} +2.34292 q^{54} +0.657077 q^{55} +3.48929 q^{56} -3.34292 q^{57} +16.3503 q^{58} +8.81079 q^{59} -4.68585 q^{60} -2.56090 q^{61} -12.0575 q^{62} +1.00000 q^{63} -12.1751 q^{64} +4.88240 q^{65} -1.14637 q^{66} +16.0575 q^{67} +3.48929 q^{68} +4.48929 q^{69} -3.14637 q^{70} +2.10038 q^{71} +3.48929 q^{72} +1.66442 q^{73} +9.66442 q^{74} -3.19656 q^{75} -11.6644 q^{76} -0.489289 q^{77} -8.51806 q^{78} -3.83221 q^{79} -1.60688 q^{80} +1.00000 q^{81} +6.22533 q^{82} +12.9786 q^{83} +3.48929 q^{84} -1.34292 q^{85} -11.4391 q^{86} +6.97858 q^{87} -1.70727 q^{88} -9.27131 q^{89} -3.14637 q^{90} -3.63565 q^{91} +15.6644 q^{92} -5.14637 q^{93} -19.2713 q^{94} +4.48929 q^{95} -4.17513 q^{96} -6.97858 q^{97} +2.34292 q^{98} -0.489289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} + 6 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} + 3 q^{17} + q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21}+ \cdots + 6 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 + 6 * q^11 + 3 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 + 3 * q^17 + q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 - 2 * q^22 + 6 * q^23 + 3 * q^24 - 5 * q^25 + 3 * q^27 + 3 * q^28 + 6 * q^29 - 8 * q^30 - 14 * q^31 + 7 * q^32 + 6 * q^33 + q^34 + 2 * q^35 + 3 * q^36 - 4 * q^37 - 10 * q^38 - 2 * q^39 - 2 * q^40 + 14 * q^41 + q^42 + 2 * q^43 - 8 * q^44 + 2 * q^45 + 6 * q^46 - 2 * q^47 - q^48 + 3 * q^49 - 15 * q^50 + 3 * q^51 - 26 * q^52 - 4 * q^53 + q^54 + 8 * q^55 + 3 * q^56 - 4 * q^57 + 10 * q^58 - 2 * q^59 - 2 * q^60 - 12 * q^61 + 3 * q^63 - 17 * q^64 - 2 * q^65 - 2 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 8 * q^70 + 3 * q^72 - 22 * q^73 + 2 * q^74 - 5 * q^75 - 8 * q^76 + 6 * q^77 + 2 * q^79 - 14 * q^80 + 3 * q^81 - 4 * q^82 + 24 * q^83 + 3 * q^84 + 2 * q^85 - 30 * q^86 + 6 * q^87 - 8 * q^88 - 10 * q^89 - 8 * q^90 - 2 * q^91 + 20 * q^92 - 14 * q^93 - 40 * q^94 + 6 * q^95 + 7 * q^96 - 6 * q^97 + q^98 + 6 * q^99

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 $

$2$	2.34292	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$2$	2.34292	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.48929	1.74464
$5$	−1.34292	−0.600573	−0.300287	−	0.953849i	$-0.597082\pi$
$5$	−1.34292	−0.600573	−0.300287	+	0.953849i	$0.597082\pi$
$6$	2.34292	0.956494
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.48929	1.23365
$9$	1.00000	0.333333
$10$	−3.14637	−0.994968
$11$	−0.489289	−0.147526	−0.0737630	−	0.997276i	$-0.523501\pi$
$11$	−0.489289	−0.147526	−0.0737630	+	0.997276i	$0.523501\pi$
$12$	3.48929	1.00727
$13$	−3.63565	−1.00835	−0.504175	−	0.863602i	$-0.668203\pi$
$13$	−3.63565	−1.00835	−0.504175	+	0.863602i	$0.668203\pi$
$14$	2.34292	0.626173
$15$	−1.34292	−0.346741
$16$	1.19656	0.299139
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.34292	0.552232
$19$	−3.34292	−0.766919	−0.383460	−	0.923558i	$-0.625267\pi$
$19$	−3.34292	−0.766919	−0.383460	+	0.923558i	$0.625267\pi$
$20$	−4.68585	−1.04779
$21$	1.00000	0.218218
$22$	−1.14637	−0.244406
$23$	4.48929	0.936081	0.468041	−	0.883707i	$-0.344960\pi$
$23$	4.48929	0.936081	0.468041	+	0.883707i	$0.344960\pi$
$24$	3.48929	0.712248
$25$	−3.19656	−0.639312
$26$	−8.51806	−1.67053
$27$	1.00000	0.192450
$28$	3.48929	0.659414
$29$	6.97858	1.29589	0.647945	−	0.761687i	$-0.275629\pi$
$29$	6.97858	1.29589	0.647945	+	0.761687i	$0.275629\pi$
$30$	−3.14637	−0.574445
$31$	−5.14637	−0.924315	−0.462157	−	0.886798i	$-0.652924\pi$
$31$	−5.14637	−0.924315	−0.462157	+	0.886798i	$0.652924\pi$
$32$	−4.17513	−0.738067
$33$	−0.489289	−0.0851742
$34$	2.34292	0.401808
$35$	−1.34292	−0.226995
$36$	3.48929	0.581548
$37$	4.12494	0.678136	0.339068	−	0.940762i	$-0.389888\pi$
$37$	4.12494	0.678136	0.339068	+	0.940762i	$0.389888\pi$
$38$	−7.83221	−1.27055
$39$	−3.63565	−0.582171
$40$	−4.68585	−0.740897
$41$	2.65708	0.414966	0.207483	−	0.978239i	$-0.433473\pi$
$41$	2.65708	0.414966	0.207483	+	0.978239i	$0.433473\pi$
$42$	2.34292	0.361521
$43$	−4.88240	−0.744560	−0.372280	−	0.928121i	$-0.621424\pi$
$43$	−4.88240	−0.744560	−0.372280	+	0.928121i	$0.621424\pi$
$44$	−1.70727	−0.257380
$45$	−1.34292	−0.200191
$46$	10.5181	1.55080
$47$	−8.22533	−1.19979	−0.599894	−	0.800080i	$-0.704790\pi$
$47$	−8.22533	−1.19979	−0.599894	+	0.800080i	$0.704790\pi$
$48$	1.19656	0.172708
$49$	1.00000	0.142857
$50$	−7.48929	−1.05915
$51$	1.00000	0.140028
$52$	−12.6858	−1.75921
$53$	−3.73183	−0.512606	−0.256303	−	0.966596i	$-0.582504\pi$
$53$	−3.73183	−0.512606	−0.256303	+	0.966596i	$0.582504\pi$
$54$	2.34292	0.318831
$55$	0.657077	0.0886002
$56$	3.48929	0.466276
$57$	−3.34292	−0.442781
$58$	16.3503	2.14690
$59$	8.81079	1.14707	0.573533	−	0.819182i	$-0.305572\pi$
$59$	8.81079	1.14707	0.573533	+	0.819182i	$0.305572\pi$
$60$	−4.68585	−0.604940
$61$	−2.56090	−0.327890	−0.163945	−	0.986469i	$-0.552422\pi$
$61$	−2.56090	−0.327890	−0.163945	+	0.986469i	$0.552422\pi$
$62$	−12.0575	−1.53131
$63$	1.00000	0.125988
$64$	−12.1751	−1.52189
$65$	4.88240	0.605588
$66$	−1.14637	−0.141108
$67$	16.0575	1.96174	0.980870	−	0.194663i	$-0.0623612\pi$
$67$	16.0575	1.96174	0.980870	+	0.194663i	$0.0623612\pi$
$68$	3.48929	0.423138
$69$	4.48929	0.540447
$70$	−3.14637	−0.376063
$71$	2.10038	0.249270	0.124635	−	0.992203i	$-0.460224\pi$
$71$	2.10038	0.249270	0.124635	+	0.992203i	$0.460224\pi$
$72$	3.48929	0.411217
$73$	1.66442	0.194806	0.0974030	−	0.995245i	$-0.468946\pi$
$73$	1.66442	0.194806	0.0974030	+	0.995245i	$0.468946\pi$
$74$	9.66442	1.12347
$75$	−3.19656	−0.369107
$76$	−11.6644	−1.33800
$77$	−0.489289	−0.0557596
$78$	−8.51806	−0.964480
$79$	−3.83221	−0.431157	−0.215579	−	0.976486i	$-0.569164\pi$
$79$	−3.83221	−0.431157	−0.215579	+	0.976486i	$0.569164\pi$
$80$	−1.60688	−0.179655
$81$	1.00000	0.111111
$82$	6.22533	0.687472
$83$	12.9786	1.42458	0.712292	−	0.701883i	$-0.247657\pi$
$83$	12.9786	1.42458	0.712292	+	0.701883i	$0.247657\pi$
$84$	3.48929	0.380713
$85$	−1.34292	−0.145660
$86$	−11.4391	−1.23351
$87$	6.97858	0.748182
$88$	−1.70727	−0.181995
$89$	−9.27131	−0.982757	−0.491378	−	0.870946i	$-0.663507\pi$
$89$	−9.27131	−0.982757	−0.491378	+	0.870946i	$0.663507\pi$
$90$	−3.14637	−0.331656
$91$	−3.63565	−0.381120
$92$	15.6644	1.63313
$93$	−5.14637	−0.533653
$94$	−19.2713	−1.98768
$95$	4.48929	0.460591
$96$	−4.17513	−0.426123
$97$	−6.97858	−0.708567	−0.354284	−	0.935138i	$-0.615275\pi$
$97$	−6.97858	−0.708567	−0.354284	+	0.935138i	$0.615275\pi$
$98$	2.34292	0.236671
$99$	−0.489289	−0.0491754
$100$	−11.1537	−1.11537
$101$	16.1825	1.61022	0.805109	−	0.593128i	$-0.202107\pi$
$101$	16.1825	1.61022	0.805109	+	0.593128i	$0.202107\pi$
$102$	2.34292	0.231984
$103$	2.61423	0.257588	0.128794	−	0.991671i	$-0.458889\pi$
$103$	2.61423	0.257588	0.128794	+	0.991671i	$0.458889\pi$
$104$	−12.6858	−1.24395
$105$	−1.34292	−0.131056
$106$	−8.74338	−0.849233
$107$	−4.88240	−0.472000	−0.236000	−	0.971753i	$-0.575837\pi$
$107$	−4.88240	−0.472000	−0.236000	+	0.971753i	$0.575837\pi$
$108$	3.48929	0.335757
$109$	9.49663	0.909613	0.454806	−	0.890590i	$-0.349708\pi$
$109$	9.49663	0.909613	0.454806	+	0.890590i	$0.349708\pi$
$110$	1.53948	0.146784
$111$	4.12494	0.391522
$112$	1.19656	0.113064
$113$	8.58967	0.808048	0.404024	−	0.914748i	$-0.367611\pi$
$113$	8.58967	0.808048	0.404024	+	0.914748i	$0.367611\pi$
$114$	−7.83221	−0.733554
$115$	−6.02877	−0.562186
$116$	24.3503	2.26087
$117$	−3.63565	−0.336116
$118$	20.6430	1.90034
$119$	1.00000	0.0916698
$120$	−4.68585	−0.427757
$121$	−10.7606	−0.978236
$122$	−6.00000	−0.543214
$123$	2.65708	0.239581
$124$	−17.9572	−1.61260
$125$	11.0073	0.984527
$126$	2.34292	0.208724
$127$	−14.2541	−1.26485	−0.632423	−	0.774623i	$-0.717940\pi$
$127$	−14.2541	−1.26485	−0.632423	+	0.774623i	$0.717940\pi$
$128$	−20.1751	−1.78325
$129$	−4.88240	−0.429872
$130$	11.4391	1.00328
$131$	−0.0716150	−0.00625703	−0.00312851	−	0.999995i	$-0.500996\pi$
$131$	−0.0716150	−0.00625703	−0.00312851	+	0.999995i	$0.500996\pi$
$132$	−1.70727	−0.148599
$133$	−3.34292	−0.289868
$134$	37.6216	3.25001
$135$	−1.34292	−0.115580
$136$	3.48929	0.299204
$137$	11.3963	0.973647	0.486824	−	0.873500i	$-0.338155\pi$
$137$	11.3963	0.973647	0.486824	+	0.873500i	$0.338155\pi$
$138$	10.5181	0.895357
$139$	21.4292	1.81760	0.908802	−	0.417228i	$-0.136998\pi$
$139$	21.4292	1.81760	0.908802	+	0.417228i	$0.136998\pi$
$140$	−4.68585	−0.396026
$141$	−8.22533	−0.692697
$142$	4.92104	0.412964
$143$	1.77888	0.148758
$144$	1.19656	0.0997131
$145$	−9.37169	−0.778277
$146$	3.89962	0.322734
$147$	1.00000	0.0824786
$148$	14.3931	1.18311
$149$	0.292731	0.0239815	0.0119907	−	0.999928i	$-0.496183\pi$
$149$	0.292731	0.0239815	0.0119907	+	0.999928i	$0.496183\pi$
$150$	−7.48929	−0.611498
$151$	−16.3074	−1.32708	−0.663540	−	0.748141i	$-0.730947\pi$
$151$	−16.3074	−1.32708	−0.663540	+	0.748141i	$0.730947\pi$
$152$	−11.6644	−0.946110
$153$	1.00000	0.0808452
$154$	−1.14637	−0.0923768
$155$	6.91117	0.555119
$156$	−12.6858	−1.01568
$157$	−3.44331	−0.274806	−0.137403	−	0.990515i	$-0.543876\pi$
$157$	−3.44331	−0.274806	−0.137403	+	0.990515i	$0.543876\pi$
$158$	−8.97858	−0.714297
$159$	−3.73183	−0.295953
$160$	5.60688	0.443263
$161$	4.48929	0.353806
$162$	2.34292	0.184077
$163$	8.39312	0.657400	0.328700	−	0.944434i	$-0.393390\pi$
$163$	8.39312	0.657400	0.328700	+	0.944434i	$0.393390\pi$
$164$	9.27131	0.723968
$165$	0.657077	0.0511534
$166$	30.4078	2.36010
$167$	5.05019	0.390796	0.195398	−	0.980724i	$-0.437400\pi$
$167$	5.05019	0.390796	0.195398	+	0.980724i	$0.437400\pi$
$168$	3.48929	0.269204
$169$	0.217980	0.0167677
$170$	−3.14637	−0.241315
$171$	−3.34292	−0.255640
$172$	−17.0361	−1.29899
$173$	−13.9284	−1.05896	−0.529478	−	0.848324i	$-0.677612\pi$
$173$	−13.9284	−1.05896	−0.529478	+	0.848324i	$0.677612\pi$
$174$	16.3503	1.23951
$175$	−3.19656	−0.241637
$176$	−0.585462	−0.0441309
$177$	8.81079	0.662259
$178$	−21.7220	−1.62813
$179$	18.6858	1.39665	0.698323	−	0.715783i	$-0.253930\pi$
$179$	18.6858	1.39665	0.698323	+	0.715783i	$0.253930\pi$
$180$	−4.68585	−0.349262
$181$	−19.6216	−1.45846	−0.729230	−	0.684268i	$-0.760122\pi$
$181$	−19.6216	−1.45846	−0.729230	+	0.684268i	$0.760122\pi$
$182$	−8.51806	−0.631400
$183$	−2.56090	−0.189307
$184$	15.6644	1.15480
$185$	−5.53948	−0.407271
$186$	−12.0575	−0.884102
$187$	−0.489289	−0.0357803
$188$	−28.7005	−2.09320
$189$	1.00000	0.0727393
$190$	10.5181	0.763060
$191$	−24.3074	−1.75882	−0.879412	−	0.476062i	$-0.842064\pi$
$191$	−24.3074	−1.75882	−0.879412	+	0.476062i	$0.842064\pi$
$192$	−12.1751	−0.878665
$193$	4.51806	0.325217	0.162608	−	0.986691i	$-0.448009\pi$
$193$	4.51806	0.325217	0.162608	+	0.986691i	$0.448009\pi$
$194$	−16.3503	−1.17388
$195$	4.88240	0.349636
$196$	3.48929	0.249235
$197$	−17.2327	−1.22778	−0.613889	−	0.789393i	$-0.710396\pi$
$197$	−17.2327	−1.22778	−0.613889	+	0.789393i	$0.710396\pi$
$198$	−1.14637	−0.0814686
$199$	−3.04598	−0.215924	−0.107962	−	0.994155i	$-0.534432\pi$
$199$	−3.04598	−0.215924	−0.107962	+	0.994155i	$0.534432\pi$
$200$	−11.1537	−0.788687
$201$	16.0575	1.13261
$202$	37.9143	2.66764
$203$	6.97858	0.489800
$204$	3.48929	0.244299
$205$	−3.56825	−0.249217
$206$	6.12494	0.426745
$207$	4.48929	0.312027
$208$	−4.35027	−0.301637
$209$	1.63565	0.113141
$210$	−3.14637	−0.217120
$211$	16.6184	1.14406	0.572030	−	0.820232i	$-0.306156\pi$
$211$	16.6184	1.14406	0.572030	+	0.820232i	$0.306156\pi$
$212$	−13.0214	−0.894315
$213$	2.10038	0.143916
$214$	−11.4391	−0.781961
$215$	6.55669	0.447163
$216$	3.48929	0.237416
$217$	−5.14637	−0.349358
$218$	22.2499	1.50695
$219$	1.66442	0.112471
$220$	2.29273	0.154576
$221$	−3.63565	−0.244561
$222$	9.66442	0.648634
$223$	27.2572	1.82528	0.912640	−	0.408765i	$-0.134040\pi$
$223$	27.2572	1.82528	0.912640	+	0.408765i	$0.134040\pi$
$224$	−4.17513	−0.278963
$225$	−3.19656	−0.213104
$226$	20.1249	1.33869
$227$	26.0288	1.72759	0.863795	−	0.503843i	$-0.168081\pi$
$227$	26.0288	1.72759	0.863795	+	0.503843i	$0.168081\pi$
$228$	−11.6644	−0.772495
$229$	−3.64973	−0.241181	−0.120590	−	0.992702i	$-0.538479\pi$
$229$	−3.64973	−0.241181	−0.120590	+	0.992702i	$0.538479\pi$
$230$	−14.1249	−0.931371
$231$	−0.489289	−0.0321928
$232$	24.3503	1.59867
$233$	−13.2327	−0.866901	−0.433451	−	0.901177i	$-0.642704\pi$
$233$	−13.2327	−0.866901	−0.433451	+	0.901177i	$0.642704\pi$
$234$	−8.51806	−0.556843
$235$	11.0460	0.720560
$236$	30.7434	2.00122
$237$	−3.83221	−0.248929
$238$	2.34292	0.151869
$239$	−15.4391	−0.998672	−0.499336	−	0.866408i	$-0.666423\pi$
$239$	−15.4391	−0.998672	−0.499336	+	0.866408i	$0.666423\pi$
$240$	−1.60688	−0.103724
$241$	−5.02142	−0.323458	−0.161729	−	0.986835i	$-0.551707\pi$
$241$	−5.02142	−0.323458	−0.161729	+	0.986835i	$0.551707\pi$
$242$	−25.2113	−1.62064
$243$	1.00000	0.0641500
$244$	−8.93573	−0.572052
$245$	−1.34292	−0.0857962
$246$	6.22533	0.396912
$247$	12.1537	0.773322
$248$	−17.9572	−1.14028
$249$	12.9786	0.822484
$250$	25.7894	1.63106
$251$	−4.75325	−0.300022	−0.150011	−	0.988684i	$-0.547931\pi$
$251$	−4.75325	−0.300022	−0.150011	+	0.988684i	$0.547931\pi$
$252$	3.48929	0.219805
$253$	−2.19656	−0.138096
$254$	−33.3963	−2.09547
$255$	−1.34292	−0.0840971
$256$	−22.9185	−1.43241
$257$	−4.26817	−0.266241	−0.133121	−	0.991100i	$-0.542500\pi$
$257$	−4.26817	−0.266241	−0.133121	+	0.991100i	$0.542500\pi$
$258$	−11.4391	−0.712167
$259$	4.12494	0.256311
$260$	17.0361	1.05654
$261$	6.97858	0.431963
$262$	−0.167788	−0.0103660
$263$	−9.12181	−0.562475	−0.281237	−	0.959638i	$-0.590745\pi$
$263$	−9.12181	−0.562475	−0.281237	+	0.959638i	$0.590745\pi$
$264$	−1.70727	−0.105075
$265$	5.01156	0.307858
$266$	−7.83221	−0.480224
$267$	−9.27131	−0.567395
$268$	56.0294	3.42254
$269$	−13.9284	−0.849229	−0.424614	−	0.905374i	$-0.639590\pi$
$269$	−13.9284	−0.849229	−0.424614	+	0.905374i	$0.639590\pi$
$270$	−3.14637	−0.191482
$271$	16.7722	1.01884	0.509418	−	0.860519i	$-0.329861\pi$
$271$	16.7722	1.01884	0.509418	+	0.860519i	$0.329861\pi$
$272$	1.19656	0.0725520
$273$	−3.63565	−0.220040
$274$	26.7005	1.61304
$275$	1.56404	0.0943151
$276$	15.6644	0.942887
$277$	−26.8353	−1.61238	−0.806190	−	0.591657i	$-0.798474\pi$
$277$	−26.8353	−1.61238	−0.806190	+	0.591657i	$0.798474\pi$
$278$	50.2070	3.01122
$279$	−5.14637	−0.308105
$280$	−4.68585	−0.280033
$281$	24.0147	1.43260	0.716298	−	0.697794i	$-0.245835\pi$
$281$	24.0147	1.43260	0.716298	+	0.697794i	$0.245835\pi$
$282$	−19.2713	−1.14759
$283$	30.5181	1.81411	0.907055	−	0.421012i	$-0.138325\pi$
$283$	30.5181	1.81411	0.907055	+	0.421012i	$0.138325\pi$
$284$	7.32885	0.434887
$285$	4.48929	0.265923
$286$	4.16779	0.246446
$287$	2.65708	0.156842
$288$	−4.17513	−0.246022
$289$	1.00000	0.0588235
$290$	−21.9572	−1.28937
$291$	−6.97858	−0.409091
$292$	5.80765	0.339867
$293$	23.0937	1.34915	0.674573	−	0.738208i	$-0.264328\pi$
$293$	23.0937	1.34915	0.674573	+	0.738208i	$0.264328\pi$
$294$	2.34292	0.136642
$295$	−11.8322	−0.688898
$296$	14.3931	0.836583
$297$	−0.489289	−0.0283914
$298$	0.685846	0.0397300
$299$	−16.3215	−0.943897
$300$	−11.1537	−0.643960
$301$	−4.88240	−0.281417
$302$	−38.2070	−2.19857
$303$	16.1825	0.929659
$304$	−4.00000	−0.229416
$305$	3.43910	0.196922
$306$	2.34292	0.133936
$307$	−26.6577	−1.52143	−0.760717	−	0.649083i	$-0.775153\pi$
$307$	−26.6577	−1.52143	−0.760717	+	0.649083i	$0.775153\pi$
$308$	−1.70727	−0.0972807
$309$	2.61423	0.148718
$310$	16.1923	0.919663
$311$	1.17092	0.0663970	0.0331985	−	0.999449i	$-0.489431\pi$
$311$	1.17092	0.0663970	0.0331985	+	0.999449i	$0.489431\pi$
$312$	−12.6858	−0.718195
$313$	−23.3963	−1.32243	−0.661217	−	0.750195i	$-0.729960\pi$
$313$	−23.3963	−1.32243	−0.661217	+	0.750195i	$0.729960\pi$
$314$	−8.06740	−0.455270
$315$	−1.34292	−0.0756651
$316$	−13.3717	−0.752216
$317$	−24.1579	−1.35684	−0.678422	−	0.734672i	$-0.737336\pi$
$317$	−24.1579	−1.35684	−0.678422	+	0.734672i	$0.737336\pi$
$318$	−8.74338	−0.490305
$319$	−3.41454	−0.191177
$320$	16.3503	0.914008
$321$	−4.88240	−0.272509
$322$	10.5181	0.586148
$323$	−3.34292	−0.186005
$324$	3.48929	0.193849
$325$	11.6216	0.644649
$326$	19.6644	1.08911
$327$	9.49663	0.525165
$328$	9.27131	0.511922
$329$	−8.22533	−0.453477
$330$	1.53948	0.0847456
$331$	−30.5040	−1.67665	−0.838325	−	0.545170i	$-0.816465\pi$
$331$	−30.5040	−1.67665	−0.838325	+	0.545170i	$0.816465\pi$
$332$	45.2860	2.48539
$333$	4.12494	0.226045
$334$	11.8322	0.647430
$335$	−21.5640	−1.17817
$336$	1.19656	0.0652776
$337$	−29.2186	−1.59164	−0.795819	−	0.605534i	$-0.792959\pi$
$337$	−29.2186	−1.59164	−0.795819	+	0.605534i	$0.792959\pi$
$338$	0.510711	0.0277790
$339$	8.58967	0.466527
$340$	−4.68585	−0.254126
$341$	2.51806	0.136360
$342$	−7.83221	−0.423518
$343$	1.00000	0.0539949
$344$	−17.0361	−0.918526
$345$	−6.02877	−0.324578
$346$	−32.6331	−1.75437
$347$	−30.2646	−1.62469	−0.812344	−	0.583179i	$-0.801809\pi$
$347$	−30.2646	−1.62469	−0.812344	+	0.583179i	$0.801809\pi$
$348$	24.3503	1.30531
$349$	−10.4647	−0.560164	−0.280082	−	0.959976i	$-0.590362\pi$
$349$	−10.4647	−0.560164	−0.280082	+	0.959976i	$0.590362\pi$
$350$	−7.48929	−0.400319
$351$	−3.63565	−0.194057
$352$	2.04285	0.108884
$353$	−27.9044	−1.48520	−0.742602	−	0.669733i	$-0.766408\pi$
$353$	−27.9044	−1.48520	−0.742602	+	0.669733i	$0.766408\pi$
$354$	20.6430	1.09716
$355$	−2.82065	−0.149705
$356$	−32.3503	−1.71456
$357$	1.00000	0.0529256
$358$	43.7795	2.31382
$359$	−9.01156	−0.475612	−0.237806	−	0.971313i	$-0.576428\pi$
$359$	−9.01156	−0.475612	−0.237806	+	0.971313i	$0.576428\pi$
$360$	−4.68585	−0.246966
$361$	−7.82487	−0.411835
$362$	−45.9718	−2.41623
$363$	−10.7606	−0.564785
$364$	−12.6858	−0.664919
$365$	−2.23519	−0.116995
$366$	−6.00000	−0.313625
$367$	4.58546	0.239359	0.119680	−	0.992813i	$-0.461813\pi$
$367$	4.58546	0.239359	0.119680	+	0.992813i	$0.461813\pi$
$368$	5.37169	0.280019
$369$	2.65708	0.138322
$370$	−12.9786	−0.674724
$371$	−3.73183	−0.193747
$372$	−17.9572	−0.931035
$373$	−1.85677	−0.0961399	−0.0480700	−	0.998844i	$-0.515307\pi$
$373$	−1.85677	−0.0961399	−0.0480700	+	0.998844i	$0.515307\pi$
$374$	−1.14637	−0.0592771
$375$	11.0073	0.568417
$376$	−28.7005	−1.48012
$377$	−25.3717	−1.30671
$378$	2.34292	0.120507
$379$	23.1281	1.18801	0.594005	−	0.804462i	$-0.297546\pi$
$379$	23.1281	1.18801	0.594005	+	0.804462i	$0.297546\pi$
$380$	15.6644	0.803568
$381$	−14.2541	−0.730259
$382$	−56.9504	−2.91384
$383$	4.50337	0.230111	0.115056	−	0.993359i	$-0.463295\pi$
$383$	4.50337	0.230111	0.115056	+	0.993359i	$0.463295\pi$
$384$	−20.1751	−1.02956
$385$	0.657077	0.0334877
$386$	10.5855	0.538786
$387$	−4.88240	−0.248187
$388$	−24.3503	−1.23620
$389$	−33.1856	−1.68258	−0.841289	−	0.540586i	$-0.818203\pi$
$389$	−33.1856	−1.68258	−0.841289	+	0.540586i	$0.818203\pi$
$390$	11.4391	0.579241
$391$	4.48929	0.227033
$392$	3.48929	0.176236
$393$	−0.0716150	−0.00361250
$394$	−40.3748	−2.03405
$395$	5.14637	0.258942
$396$	−1.70727	−0.0857935
$397$	−9.77467	−0.490577	−0.245288	−	0.969450i	$-0.578883\pi$
$397$	−9.77467	−0.490577	−0.245288	+	0.969450i	$0.578883\pi$
$398$	−7.13650	−0.357720
$399$	−3.34292	−0.167355
$400$	−3.82487	−0.191243
$401$	32.4464	1.62030	0.810149	−	0.586224i	$-0.199386\pi$
$401$	32.4464	1.62030	0.810149	+	0.586224i	$0.199386\pi$
$402$	37.6216	1.87639
$403$	18.7104	0.932032
$404$	56.4653	2.80926
$405$	−1.34292	−0.0667304
$406$	16.3503	0.811450
$407$	−2.01829	−0.100043
$408$	3.48929	0.172746
$409$	−26.9070	−1.33046	−0.665232	−	0.746637i	$-0.731667\pi$
$409$	−26.9070	−1.33046	−0.665232	+	0.746637i	$0.731667\pi$
$410$	−8.36014	−0.412878
$411$	11.3963	0.562136
$412$	9.12181	0.449399
$413$	8.81079	0.433551
$414$	10.5181	0.516934
$415$	−17.4292	−0.855567
$416$	15.1793	0.744229
$417$	21.4292	1.04939
$418$	3.83221	0.187440
$419$	25.2285	1.23249	0.616246	−	0.787554i	$-0.288653\pi$
$419$	25.2285	1.23249	0.616246	+	0.787554i	$0.288653\pi$
$420$	−4.68585	−0.228646
$421$	−24.0617	−1.17270	−0.586349	−	0.810059i	$-0.699435\pi$
$421$	−24.0617	−1.17270	−0.586349	+	0.810059i	$0.699435\pi$
$422$	38.9357	1.89536
$423$	−8.22533	−0.399929
$424$	−13.0214	−0.632376
$425$	−3.19656	−0.155056
$426$	4.92104	0.238425
$427$	−2.56090	−0.123931
$428$	−17.0361	−0.823472
$429$	1.77888	0.0858853
$430$	15.3618	0.740813
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	1.19656	0.0575694
$433$	−5.15058	−0.247521	−0.123760	−	0.992312i	$-0.539495\pi$
$433$	−5.15058	−0.247521	−0.123760	+	0.992312i	$0.539495\pi$
$434$	−12.0575	−0.578780
$435$	−9.37169	−0.449338
$436$	33.1365	1.58695
$437$	−15.0073	−0.717899
$438$	3.89962	0.186331
$439$	−23.6974	−1.13102	−0.565508	−	0.824743i	$-0.691320\pi$
$439$	−23.6974	−1.13102	−0.565508	+	0.824743i	$0.691320\pi$
$440$	2.29273	0.109302
$441$	1.00000	0.0476190
$442$	−8.51806	−0.405163
$443$	−1.67429	−0.0795479	−0.0397739	−	0.999209i	$-0.512664\pi$
$443$	−1.67429	−0.0795479	−0.0397739	+	0.999209i	$0.512664\pi$
$444$	14.3931	0.683067
$445$	12.4507	0.590218
$446$	63.8616	3.02393
$447$	0.292731	0.0138457
$448$	−12.1751	−0.575221
$449$	9.85677	0.465170	0.232585	−	0.972576i	$-0.425282\pi$
$449$	9.85677	0.465170	0.232585	+	0.972576i	$0.425282\pi$
$450$	−7.48929	−0.353048
$451$	−1.30008	−0.0612183
$452$	29.9718	1.40976
$453$	−16.3074	−0.766190
$454$	60.9834	2.86209
$455$	4.88240	0.228891
$456$	−11.6644	−0.546237
$457$	35.1898	1.64611	0.823055	−	0.567961i	$-0.192268\pi$
$457$	35.1898	1.64611	0.823055	+	0.567961i	$0.192268\pi$
$458$	−8.55104	−0.399564
$459$	1.00000	0.0466760
$460$	−21.0361	−0.980814
$461$	12.1249	0.564715	0.282357	−	0.959309i	$-0.408884\pi$
$461$	12.1249	0.564715	0.282357	+	0.959309i	$0.408884\pi$
$462$	−1.14637	−0.0533337
$463$	17.7648	0.825601	0.412800	−	0.910822i	$-0.364551\pi$
$463$	17.7648	0.825601	0.412800	+	0.910822i	$0.364551\pi$
$464$	8.35027	0.387652
$465$	6.91117	0.320498
$466$	−31.0031	−1.43619
$467$	−39.7711	−1.84039	−0.920193	−	0.391465i	$-0.871968\pi$
$467$	−39.7711	−1.84039	−0.920193	+	0.391465i	$0.871968\pi$
$468$	−12.6858	−0.586403
$469$	16.0575	0.741468
$470$	25.8799	1.19375
$471$	−3.44331	−0.158659
$472$	30.7434	1.41508
$473$	2.38890	0.109842
$474$	−8.97858	−0.412400
$475$	10.6858	0.490300
$476$	3.48929	0.159931
$477$	−3.73183	−0.170869
$478$	−36.1726	−1.65450
$479$	8.46473	0.386763	0.193382	−	0.981124i	$-0.438054\pi$
$479$	8.46473	0.386763	0.193382	+	0.981124i	$0.438054\pi$
$480$	5.60688	0.255918
$481$	−14.9969	−0.683798
$482$	−11.7648	−0.535872
$483$	4.48929	0.204270
$484$	−37.5468	−1.70667
$485$	9.37169	0.425547
$486$	2.34292	0.106277
$487$	21.1793	0.959728	0.479864	−	0.877343i	$-0.340686\pi$
$487$	21.1793	0.959728	0.479864	+	0.877343i	$0.340686\pi$
$488$	−8.93573	−0.404502
$489$	8.39312	0.379550
$490$	−3.14637	−0.142138
$491$	−17.1793	−0.775293	−0.387647	−	0.921808i	$-0.626712\pi$
$491$	−17.1793	−0.775293	−0.387647	+	0.921808i	$0.626712\pi$
$492$	9.27131	0.417983
$493$	6.97858	0.314299
$494$	28.4752	1.28116
$495$	0.657077	0.0295334
$496$	−6.15792	−0.276499
$497$	2.10038	0.0942151
$498$	30.4078	1.36261
$499$	2.79610	0.125170	0.0625852	−	0.998040i	$-0.480065\pi$
$499$	2.79610	0.125170	0.0625852	+	0.998040i	$0.480065\pi$
$500$	38.4078	1.71765
$501$	5.05019	0.225626
$502$	−11.1365	−0.497046
$503$	37.5008	1.67208	0.836040	−	0.548668i	$-0.184865\pi$
$503$	37.5008	1.67208	0.836040	+	0.548668i	$0.184865\pi$
$504$	3.48929	0.155425
$505$	−21.7318	−0.967054
$506$	−5.14637	−0.228784
$507$	0.217980	0.00968085
$508$	−49.7367	−2.20671
$509$	−6.39312	−0.283370	−0.141685	−	0.989912i	$-0.545252\pi$
$509$	−6.39312	−0.283370	−0.141685	+	0.989912i	$0.545252\pi$
$510$	−3.14637	−0.139323
$511$	1.66442	0.0736298
$512$	−13.3461	−0.589818
$513$	−3.34292	−0.147594
$514$	−10.0000	−0.441081
$515$	−3.51071	−0.154700
$516$	−17.0361	−0.749973
$517$	4.02456	0.177000
$518$	9.66442	0.424630
$519$	−13.9284	−0.611388
$520$	17.0361	0.747083
$521$	−5.39204	−0.236230	−0.118115	−	0.993000i	$-0.537685\pi$
$521$	−5.39204	−0.236230	−0.118115	+	0.993000i	$0.537685\pi$
$522$	16.3503	0.715632
$523$	41.8223	1.82876	0.914382	−	0.404853i	$-0.132677\pi$
$523$	41.8223	1.82876	0.914382	+	0.404853i	$0.132677\pi$
$524$	−0.249885	−0.0109163
$525$	−3.19656	−0.139509
$526$	−21.3717	−0.931850
$527$	−5.14637	−0.224179
$528$	−0.585462	−0.0254790
$529$	−2.84629	−0.123752
$530$	11.7417	0.510027
$531$	8.81079	0.382356
$532$	−11.6644	−0.505717
$533$	−9.66021	−0.418430
$534$	−21.7220	−0.940001
$535$	6.55669	0.283471
$536$	56.0294	2.42010
$537$	18.6858	0.806354
$538$	−32.6331	−1.40691
$539$	−0.489289	−0.0210752
$540$	−4.68585	−0.201647
$541$	−17.9718	−0.772670	−0.386335	−	0.922359i	$-0.626259\pi$
$541$	−17.9718	−0.772670	−0.386335	+	0.922359i	$0.626259\pi$
$542$	39.2959	1.68790
$543$	−19.6216	−0.842042
$544$	−4.17513	−0.179007
$545$	−12.7533	−0.546289
$546$	−8.51806	−0.364539
$547$	−16.4752	−0.704429	−0.352215	−	0.935919i	$-0.614571\pi$
$547$	−16.4752	−0.704429	−0.352215	+	0.935919i	$0.614571\pi$
$548$	39.7648	1.69867
$549$	−2.56090	−0.109297
$550$	3.66442	0.156252
$551$	−23.3288	−0.993842
$552$	15.6644	0.666722
$553$	−3.83221	−0.162962
$554$	−62.8732	−2.67122
$555$	−5.53948	−0.235138
$556$	74.7728	3.17107
$557$	6.61002	0.280076	0.140038	−	0.990146i	$-0.455278\pi$
$557$	6.61002	0.280076	0.140038	+	0.990146i	$0.455278\pi$
$558$	−12.0575	−0.510436
$559$	17.7507	0.750776
$560$	−1.60688	−0.0679033
$561$	−0.489289	−0.0206578
$562$	56.2646	2.37338
$563$	11.4721	0.483490	0.241745	−	0.970340i	$-0.422280\pi$
$563$	11.4721	0.483490	0.241745	+	0.970340i	$0.422280\pi$
$564$	−28.7005	−1.20851
$565$	−11.5353	−0.485292
$566$	71.5015	3.00543
$567$	1.00000	0.0419961
$568$	7.32885	0.307512
$569$	26.6430	1.11693	0.558466	−	0.829527i	$-0.311390\pi$
$569$	26.6430	1.11693	0.558466	+	0.829527i	$0.311390\pi$
$570$	10.5181	0.440553
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	6.20704	0.259529
$573$	−24.3074	−1.01546
$574$	6.22533	0.259840
$575$	−14.3503	−0.598448
$576$	−12.1751	−0.507297
$577$	22.2640	0.926861	0.463430	−	0.886133i	$-0.346618\pi$
$577$	22.2640	0.926861	0.463430	+	0.886133i	$0.346618\pi$
$578$	2.34292	0.0974528
$579$	4.51806	0.187764
$580$	−32.7005	−1.35782
$581$	12.9786	0.538442
$582$	−16.3503	−0.677740
$583$	1.82594	0.0756227
$584$	5.80765	0.240322
$585$	4.88240	0.201863
$586$	54.1067	2.23513
$587$	−4.08210	−0.168486	−0.0842431	−	0.996445i	$-0.526847\pi$
$587$	−4.08210	−0.168486	−0.0842431	+	0.996445i	$0.526847\pi$
$588$	3.48929	0.143896
$589$	17.2039	0.708875
$590$	−27.7220	−1.14130
$591$	−17.2327	−0.708857
$592$	4.93573	0.202857
$593$	19.8751	0.816171	0.408085	−	0.912944i	$-0.366197\pi$
$593$	19.8751	0.816171	0.408085	+	0.912944i	$0.366197\pi$
$594$	−1.14637	−0.0470359
$595$	−1.34292	−0.0550545
$596$	1.02142	0.0418391
$597$	−3.04598	−0.124664
$598$	−38.2400	−1.56375
$599$	7.13650	0.291589	0.145795	−	0.989315i	$-0.453426\pi$
$599$	7.13650	0.291589	0.145795	+	0.989315i	$0.453426\pi$
$600$	−11.1537	−0.455348
$601$	−5.91790	−0.241396	−0.120698	−	0.992689i	$-0.538513\pi$
$601$	−5.91790	−0.241396	−0.120698	+	0.992689i	$0.538513\pi$
$602$	−11.4391	−0.466223
$603$	16.0575	0.653914
$604$	−56.9013	−2.31528
$605$	14.4507	0.587503
$606$	37.9143	1.54016
$607$	−31.8898	−1.29437	−0.647183	−	0.762335i	$-0.724053\pi$
$607$	−31.8898	−1.29437	−0.647183	+	0.762335i	$0.724053\pi$
$608$	13.9572	0.566037
$609$	6.97858	0.282786
$610$	8.05754	0.326240
$611$	29.9044	1.20980
$612$	3.48929	0.141046
$613$	38.8543	1.56931	0.784654	−	0.619934i	$-0.212841\pi$
$613$	38.8543	1.56931	0.784654	+	0.619934i	$0.212841\pi$
$614$	−62.4569	−2.52056
$615$	−3.56825	−0.143886
$616$	−1.70727	−0.0687878
$617$	−41.4355	−1.66813	−0.834065	−	0.551666i	$-0.813992\pi$
$617$	−41.4355	−1.66813	−0.834065	+	0.551666i	$0.813992\pi$
$618$	6.12494	0.246381
$619$	40.1396	1.61335	0.806674	−	0.590997i	$-0.201265\pi$
$619$	40.1396	1.61335	0.806674	+	0.590997i	$0.201265\pi$
$620$	24.1151	0.968485
$621$	4.48929	0.180149
$622$	2.74338	0.110000
$623$	−9.27131	−0.371447
$624$	−4.35027	−0.174150
$625$	1.20077	0.0480307
$626$	−54.8156	−2.19087
$627$	1.63565	0.0653217
$628$	−12.0147	−0.479438
$629$	4.12494	0.164472
$630$	−3.14637	−0.125354
$631$	25.3331	1.00849	0.504247	−	0.863560i	$-0.331770\pi$
$631$	25.3331	1.00849	0.504247	+	0.863560i	$0.331770\pi$
$632$	−13.3717	−0.531897
$633$	16.6184	0.660524
$634$	−56.6002	−2.24788
$635$	19.1422	0.759633
$636$	−13.0214	−0.516333
$637$	−3.63565	−0.144050
$638$	−8.00000	−0.316723
$639$	2.10038	0.0830899
$640$	27.0937	1.07097
$641$	−10.2969	−0.406705	−0.203352	−	0.979106i	$-0.565184\pi$
$641$	−10.2969	−0.406705	−0.203352	+	0.979106i	$0.565184\pi$
$642$	−11.4391	−0.451465
$643$	−13.5725	−0.535246	−0.267623	−	0.963524i	$-0.586238\pi$
$643$	−13.5725	−0.535246	−0.267623	+	0.963524i	$0.586238\pi$
$644$	15.6644	0.617265
$645$	6.55669	0.258170
$646$	−7.83221	−0.308154
$647$	33.1428	1.30298	0.651488	−	0.758659i	$-0.274145\pi$
$647$	33.1428	1.30298	0.651488	+	0.758659i	$0.274145\pi$
$648$	3.48929	0.137072
$649$	−4.31102	−0.169222
$650$	27.2285	1.06799
$651$	−5.14637	−0.201702
$652$	29.2860	1.14693
$653$	32.1966	1.25995	0.629974	−	0.776616i	$-0.283065\pi$
$653$	32.1966	1.25995	0.629974	+	0.776616i	$0.283065\pi$
$654$	22.2499	0.870039
$655$	0.0961734	0.00375781
$656$	3.17935	0.124133
$657$	1.66442	0.0649353
$658$	−19.2713	−0.751274
$659$	−38.4408	−1.49744	−0.748720	−	0.662886i	$-0.769331\pi$
$659$	−38.4408	−1.49744	−0.748720	+	0.662886i	$0.769331\pi$
$660$	2.29273	0.0892444
$661$	21.1997	0.824572	0.412286	−	0.911054i	$-0.364730\pi$
$661$	21.1997	0.824572	0.412286	+	0.911054i	$0.364730\pi$
$662$	−71.4685	−2.77770
$663$	−3.63565	−0.141197
$664$	45.2860	1.75744
$665$	4.48929	0.174087
$666$	9.66442	0.374489
$667$	31.3288	1.21306
$668$	17.6216	0.681799
$669$	27.2572	1.05383
$670$	−50.5229	−1.95187
$671$	1.25302	0.0483723
$672$	−4.17513	−0.161059
$673$	37.9143	1.46149	0.730745	−	0.682651i	$-0.239173\pi$
$673$	37.9143	1.46149	0.730745	+	0.682651i	$0.239173\pi$
$674$	−68.4569	−2.63686
$675$	−3.19656	−0.123036
$676$	0.760597	0.0292537
$677$	39.6075	1.52224	0.761120	−	0.648611i	$-0.224650\pi$
$677$	39.6075	1.52224	0.761120	+	0.648611i	$0.224650\pi$
$678$	20.1249	0.772894
$679$	−6.97858	−0.267813
$680$	−4.68585	−0.179694
$681$	26.0288	0.997425
$682$	5.89962	0.225908
$683$	0.374212	0.0143188	0.00715940	−	0.999974i	$-0.497721\pi$
$683$	0.374212	0.0143188	0.00715940	+	0.999974i	$0.497721\pi$
$684$	−11.6644	−0.446000
$685$	−15.3043	−0.584747
$686$	2.34292	0.0894532
$687$	−3.64973	−0.139246
$688$	−5.84208	−0.222727
$689$	13.5676	0.516886
$690$	−14.1249	−0.537727
$691$	−41.9044	−1.59412	−0.797060	−	0.603900i	$-0.793613\pi$
$691$	−41.9044	−1.59412	−0.797060	+	0.603900i	$0.793613\pi$
$692$	−48.6002	−1.84750
$693$	−0.489289	−0.0185865
$694$	−70.9076	−2.69161
$695$	−28.7778	−1.09160
$696$	24.3503	0.922995
$697$	2.65708	0.100644
$698$	−24.5181	−0.928022
$699$	−13.2327	−0.500506
$700$	−11.1537	−0.421571
$701$	10.4422	0.394398	0.197199	−	0.980364i	$-0.436816\pi$
$701$	10.4422	0.394398	0.197199	+	0.980364i	$0.436816\pi$
$702$	−8.51806	−0.321493
$703$	−13.7894	−0.520076
$704$	5.95715	0.224519
$705$	11.0460	0.416016
$706$	−65.3780	−2.46053
$707$	16.1825	0.608605
$708$	30.7434	1.15541
$709$	41.9143	1.57412	0.787062	−	0.616873i	$-0.211601\pi$
$709$	41.9143	1.57412	0.787062	+	0.616873i	$0.211601\pi$
$710$	−6.60858	−0.248015
$711$	−3.83221	−0.143719
$712$	−32.3503	−1.21238
$713$	−23.1035	−0.865234
$714$	2.34292	0.0876817
$715$	−2.38890	−0.0893400
$716$	65.2003	2.43665
$717$	−15.4391	−0.576584
$718$	−21.1134	−0.787945
$719$	−40.4366	−1.50803	−0.754015	−	0.656857i	$-0.771885\pi$
$719$	−40.4366	−1.50803	−0.754015	+	0.656857i	$0.771885\pi$
$720$	−1.60688	−0.0598851
$721$	2.61423	0.0973591
$722$	−18.3331	−0.682286
$723$	−5.02142	−0.186749
$724$	−68.4653	−2.54449
$725$	−22.3074	−0.828477
$726$	−25.2113	−0.935677
$727$	6.49350	0.240831	0.120415	−	0.992724i	$-0.461577\pi$
$727$	6.49350	0.240831	0.120415	+	0.992724i	$0.461577\pi$
$728$	−12.6858	−0.470169
$729$	1.00000	0.0370370
$730$	−5.23688	−0.193826
$731$	−4.88240	−0.180582
$732$	−8.93573	−0.330274
$733$	−24.9933	−0.923147	−0.461574	−	0.887102i	$-0.652715\pi$
$733$	−24.9933	−0.923147	−0.461574	+	0.887102i	$0.652715\pi$
$734$	10.7434	0.396546
$735$	−1.34292	−0.0495345
$736$	−18.7434	−0.690890
$737$	−7.85677	−0.289408
$738$	6.22533	0.229157
$739$	8.18186	0.300975	0.150487	−	0.988612i	$-0.451916\pi$
$739$	8.18186	0.300975	0.150487	+	0.988612i	$0.451916\pi$
$740$	−19.3288	−0.710543
$741$	12.1537	0.446478
$742$	−8.74338	−0.320980
$743$	−1.64973	−0.0605227	−0.0302614	−	0.999542i	$-0.509634\pi$
$743$	−1.64973	−0.0605227	−0.0302614	+	0.999542i	$0.509634\pi$
$744$	−17.9572	−0.658341
$745$	−0.393115	−0.0144026
$746$	−4.35027	−0.159275
$747$	12.9786	0.474861
$748$	−1.70727	−0.0624239
$749$	−4.88240	−0.178399
$750$	25.7894	0.941694
$751$	−10.2106	−0.372591	−0.186296	−	0.982494i	$-0.559648\pi$
$751$	−10.2106	−0.372591	−0.186296	+	0.982494i	$0.559648\pi$
$752$	−9.84208	−0.358904
$753$	−4.75325	−0.173218
$754$	−59.4439	−2.16482
$755$	21.8996	0.797009
$756$	3.48929	0.126904
$757$	31.4763	1.14403	0.572013	−	0.820245i	$-0.306163\pi$
$757$	31.4763	1.14403	0.572013	+	0.820245i	$0.306163\pi$
$758$	54.1873	1.96817
$759$	−2.19656	−0.0797300
$760$	15.6644	0.568208
$761$	18.1151	0.656671	0.328336	−	0.944561i	$-0.393512\pi$
$761$	18.1151	0.656671	0.328336	+	0.944561i	$0.393512\pi$
$762$	−33.3963	−1.20982
$763$	9.49663	0.343801
$764$	−84.8156	−3.06852
$765$	−1.34292	−0.0485535
$766$	10.5510	0.381224
$767$	−32.0330	−1.15664
$768$	−22.9185	−0.827001
$769$	−10.1207	−0.364963	−0.182481	−	0.983209i	$-0.558413\pi$
$769$	−10.1207	−0.364963	−0.182481	+	0.983209i	$0.558413\pi$
$770$	1.53948	0.0554790
$771$	−4.26817	−0.153714
$772$	15.7648	0.567388
$773$	−9.05440	−0.325664	−0.162832	−	0.986654i	$-0.552063\pi$
$773$	−9.05440	−0.325664	−0.162832	+	0.986654i	$0.552063\pi$
$774$	−11.4391	−0.411170
$775$	16.4507	0.590925
$776$	−24.3503	−0.874124
$777$	4.12494	0.147981
$778$	−77.7513	−2.78752
$779$	−8.88240	−0.318245
$780$	17.0361	0.609991
$781$	−1.02769	−0.0367738
$782$	10.5181	0.376125
$783$	6.97858	0.249394
$784$	1.19656	0.0427342
$785$	4.62410	0.165041
$786$	−0.167788	−0.00598481
$787$	17.7402	0.632372	0.316186	−	0.948697i	$-0.397598\pi$
$787$	17.7402	0.632372	0.316186	+	0.948697i	$0.397598\pi$
$788$	−60.1298	−2.14203
$789$	−9.12181	−0.324745
$790$	12.0575	0.428988
$791$	8.58967	0.305414
$792$	−1.70727	−0.0606652
$793$	9.31056	0.330628
$794$	−22.9013	−0.812737
$795$	5.01156	0.177742
$796$	−10.6283	−0.376710
$797$	−9.02142	−0.319555	−0.159778	−	0.987153i	$-0.551078\pi$
$797$	−9.02142	−0.319555	−0.159778	+	0.987153i	$0.551078\pi$
$798$	−7.83221	−0.277257
$799$	−8.22533	−0.290991
$800$	13.3461	0.471854
$801$	−9.27131	−0.327586
$802$	76.0195	2.68434
$803$	−0.814383	−0.0287390
$804$	56.0294	1.97600
$805$	−6.02877	−0.212486
$806$	43.8370	1.54409
$807$	−13.9284	−0.490302
$808$	56.4653	1.98644
$809$	−31.8328	−1.11918	−0.559591	−	0.828769i	$-0.689042\pi$
$809$	−31.8328	−1.11918	−0.559591	+	0.828769i	$0.689042\pi$
$810$	−3.14637	−0.110552
$811$	−39.7220	−1.39483	−0.697413	−	0.716669i	$-0.745666\pi$
$811$	−39.7220	−1.39483	−0.697413	+	0.716669i	$0.745666\pi$
$812$	24.3503	0.854527
$813$	16.7722	0.588225
$814$	−4.72869	−0.165741
$815$	−11.2713	−0.394817
$816$	1.19656	0.0418879
$817$	16.3215	0.571017
$818$	−63.0409	−2.20417
$819$	−3.63565	−0.127040
$820$	−12.4507	−0.434796
$821$	−19.8328	−0.692170	−0.346085	−	0.938203i	$-0.612489\pi$
$821$	−19.8328	−0.692170	−0.346085	+	0.938203i	$0.612489\pi$
$822$	26.7005	0.931288
$823$	6.31729	0.220207	0.110103	−	0.993920i	$-0.464882\pi$
$823$	6.31729	0.220207	0.110103	+	0.993920i	$0.464882\pi$
$824$	9.12181	0.317773
$825$	1.56404	0.0544529
$826$	20.6430	0.718262
$827$	46.8114	1.62779	0.813896	−	0.581011i	$-0.197343\pi$
$827$	46.8114	1.62779	0.813896	+	0.581011i	$0.197343\pi$
$828$	15.6644	0.544376
$829$	−11.1709	−0.387982	−0.193991	−	0.981003i	$-0.562143\pi$
$829$	−11.1709	−0.387982	−0.193991	+	0.981003i	$0.562143\pi$
$830$	−40.8353	−1.41742
$831$	−26.8353	−0.930908
$832$	44.2646	1.53460
$833$	1.00000	0.0346479
$834$	50.2070	1.73853
$835$	−6.78202	−0.234701
$836$	5.70727	0.197390
$837$	−5.14637	−0.177884
$838$	59.1083	2.04186
$839$	−0.849424	−0.0293254	−0.0146627	−	0.999892i	$-0.504667\pi$
$839$	−0.849424	−0.0293254	−0.0146627	+	0.999892i	$0.504667\pi$
$840$	−4.68585	−0.161677
$841$	19.7005	0.679329
$842$	−56.3748	−1.94280
$843$	24.0147	0.827110
$844$	57.9865	1.99598
$845$	−0.292731	−0.0100703
$846$	−19.2713	−0.662561
$847$	−10.7606	−0.369738
$848$	−4.46535	−0.153341
$849$	30.5181	1.04738
$850$	−7.48929	−0.256880
$851$	18.5181	0.634791
$852$	7.32885	0.251082
$853$	−39.4538	−1.35087	−0.675436	−	0.737419i	$-0.736045\pi$
$853$	−39.4538	−1.35087	−0.675436	+	0.737419i	$0.736045\pi$
$854$	−6.00000	−0.205316
$855$	4.48929	0.153530
$856$	−17.0361	−0.582282
$857$	31.4208	1.07331	0.536657	−	0.843800i	$-0.319687\pi$
$857$	31.4208	1.07331	0.536657	+	0.843800i	$0.319687\pi$
$858$	4.16779	0.142286
$859$	13.5065	0.460836	0.230418	−	0.973092i	$-0.425991\pi$
$859$	13.5065	0.460836	0.230418	+	0.973092i	$0.425991\pi$
$860$	22.8782	0.780140
$861$	2.65708	0.0905529
$862$	37.4868	1.27680
$863$	29.7121	1.01141	0.505706	−	0.862706i	$-0.331232\pi$
$863$	29.7121	1.01141	0.505706	+	0.862706i	$0.331232\pi$
$864$	−4.17513	−0.142041
$865$	18.7047	0.635981
$866$	−12.0674	−0.410067
$867$	1.00000	0.0339618
$868$	−17.9572	−0.609506
$869$	1.87506	0.0636070
$870$	−21.9572	−0.744417
$871$	−58.3797	−1.97812
$872$	33.1365	1.12214
$873$	−6.97858	−0.236189
$874$	−35.1611	−1.18934
$875$	11.0073	0.372116
$876$	5.80765	0.196222
$877$	37.1035	1.25290	0.626448	−	0.779463i	$-0.284508\pi$
$877$	37.1035	1.25290	0.626448	+	0.779463i	$0.284508\pi$
$878$	−55.5212	−1.87375
$879$	23.0937	0.778930
$880$	0.786230	0.0265038
$881$	−16.7925	−0.565754	−0.282877	−	0.959156i	$-0.591289\pi$
$881$	−16.7925	−0.565754	−0.282877	+	0.959156i	$0.591289\pi$
$882$	2.34292	0.0788903
$883$	47.8181	1.60921	0.804604	−	0.593812i	$-0.202378\pi$
$883$	47.8181	1.60921	0.804604	+	0.593812i	$0.202378\pi$
$884$	−12.6858	−0.426671
$885$	−11.8322	−0.397735
$886$	−3.92273	−0.131787
$887$	4.85785	0.163110	0.0815552	−	0.996669i	$-0.474011\pi$
$887$	4.85785	0.163110	0.0815552	+	0.996669i	$0.474011\pi$
$888$	14.3931	0.483001
$889$	−14.2541	−0.478067
$890$	29.1709	0.977812
$891$	−0.489289	−0.0163918
$892$	95.1083	3.18446
$893$	27.4966	0.920140
$894$	0.685846	0.0229381
$895$	−25.0937	−0.838788
$896$	−20.1751	−0.674004
$897$	−16.3215	−0.544959
$898$	23.0937	0.770645
$899$	−35.9143	−1.19781
$900$	−11.1537	−0.371790
$901$	−3.73183	−0.124325
$902$	−3.04598	−0.101420
$903$	−4.88240	−0.162476
$904$	29.9718	0.996849
$905$	26.3503	0.875913
$906$	−38.2070	−1.26934
$907$	59.9718	1.99133	0.995666	−	0.0929985i	$-0.0296452\pi$
$907$	59.9718	1.99133	0.995666	+	0.0929985i	$0.0296452\pi$
$908$	90.8219	3.01403
$909$	16.1825	0.536739
$910$	11.4391	0.379202
$911$	−5.49602	−0.182091	−0.0910456	−	0.995847i	$-0.529021\pi$
$911$	−5.49602	−0.182091	−0.0910456	+	0.995847i	$0.529021\pi$
$912$	−4.00000	−0.132453
$913$	−6.35027	−0.210163
$914$	82.4471	2.72711
$915$	3.43910	0.113693
$916$	−12.7350	−0.420775
$917$	−0.0716150	−0.00236493
$918$	2.34292	0.0773280
$919$	−12.6044	−0.415780	−0.207890	−	0.978152i	$-0.566660\pi$
$919$	−12.6044	−0.415780	−0.207890	+	0.978152i	$0.566660\pi$
$920$	−21.0361	−0.693540
$921$	−26.6577	−0.878401
$922$	28.4078	0.935561
$923$	−7.63627	−0.251351
$924$	−1.70727	−0.0561650
$925$	−13.1856	−0.433540
$926$	41.6216	1.36777
$927$	2.61423	0.0858626
$928$	−29.1365	−0.956452
$929$	27.6848	0.908308	0.454154	−	0.890923i	$-0.349942\pi$
$929$	27.6848	0.908308	0.454154	+	0.890923i	$0.349942\pi$
$930$	16.1923	0.530968
$931$	−3.34292	−0.109560
$932$	−46.1726	−1.51243
$933$	1.17092	0.0383343
$934$	−93.1806	−3.04896
$935$	0.657077	0.0214887
$936$	−12.6858	−0.414650
$937$	7.85050	0.256465	0.128232	−	0.991744i	$-0.459070\pi$
$937$	7.85050	0.256465	0.128232	+	0.991744i	$0.459070\pi$
$938$	37.6216	1.22839
$939$	−23.3963	−0.763508
$940$	38.5426	1.25712
$941$	−45.1281	−1.47113	−0.735567	−	0.677452i	$-0.763084\pi$
$941$	−45.1281	−1.47113	−0.735567	+	0.677452i	$0.763084\pi$
$942$	−8.06740	−0.262850
$943$	11.9284	0.388442
$944$	10.5426	0.343133
$945$	−1.34292	−0.0436853
$946$	5.59702	0.181975
$947$	28.3074	0.919868	0.459934	−	0.887953i	$-0.347873\pi$
$947$	28.3074	0.919868	0.459934	+	0.887953i	$0.347873\pi$
$948$	−13.3717	−0.434292
$949$	−6.05127	−0.196432
$950$	25.0361	0.812279
$951$	−24.1579	−0.783374
$952$	3.48929	0.113088
$953$	22.6184	0.732683	0.366342	−	0.930480i	$-0.380610\pi$
$953$	22.6184	0.732683	0.366342	+	0.930480i	$0.380610\pi$
$954$	−8.74338	−0.283078
$955$	32.6430	1.05630
$956$	−53.8715	−1.74233
$957$	−3.41454	−0.110376
$958$	19.8322	0.640750
$959$	11.3963	0.368004
$960$	16.3503	0.527703
$961$	−4.51492	−0.145643
$962$	−35.1365	−1.13285
$963$	−4.88240	−0.157333
$964$	−17.5212	−0.564320
$965$	−6.06740	−0.195317
$966$	10.5181	0.338413
$967$	18.5040	0.595048	0.297524	−	0.954714i	$-0.403839\pi$
$967$	18.5040	0.595048	0.297524	+	0.954714i	$0.403839\pi$
$968$	−37.5468	−1.20680
$969$	−3.34292	−0.107390
$970$	21.9572	0.705002
$971$	−28.3074	−0.908428	−0.454214	−	0.890892i	$-0.650080\pi$
$971$	−28.3074	−0.908428	−0.454214	+	0.890892i	$0.650080\pi$
$972$	3.48929	0.111919
$973$	21.4292	0.686990
$974$	49.6216	1.58998
$975$	11.6216	0.372188
$976$	−3.06427	−0.0980848
$977$	−34.3650	−1.09943	−0.549716	−	0.835351i	$-0.685264\pi$
$977$	−34.3650	−1.09943	−0.549716	+	0.835351i	$0.685264\pi$
$978$	19.6644	0.628799
$979$	4.53635	0.144982
$980$	−4.68585	−0.149684
$981$	9.49663	0.303204
$982$	−40.2499	−1.28443
$983$	−11.4286	−0.364516	−0.182258	−	0.983251i	$-0.558341\pi$
$983$	−11.4286	−0.364516	−0.182258	+	0.983251i	$0.558341\pi$
$984$	9.27131	0.295559
$985$	23.1422	0.737370
$986$	16.3503	0.520699
$987$	−8.22533	−0.261815
$988$	42.4078	1.34917
$989$	−21.9185	−0.696968
$990$	1.53948	0.0489279
$991$	53.8715	1.71128	0.855642	−	0.517569i	$-0.173163\pi$
$991$	53.8715	1.71128	0.855642	+	0.517569i	$0.173163\pi$
$992$	21.4868	0.682206
$993$	−30.5040	−0.968015
$994$	4.92104	0.156086
$995$	4.09052	0.129678
$996$	45.2860	1.43494
$997$	−16.5426	−0.523910	−0.261955	−	0.965080i	$-0.584367\pi$
$997$	−16.5426	−0.523910	−0.261955	+	0.965080i	$0.584367\pi$
$998$	6.55104	0.207369
$999$	4.12494	0.130507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.a.g.1.3	✓	3
3.2	odd	2		1071.2.a.h.1.1		3
4.3	odd	2		5712.2.a.bt.1.1		3
5.4	even	2		8925.2.a.bm.1.1		3
7.6	odd	2		2499.2.a.s.1.3		3
17.16	even	2		6069.2.a.r.1.3		3
21.20	even	2		7497.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.a.g.1.3	✓	3	1.1	even	1	trivial
1071.2.a.h.1.1		3	3.2	odd	2
2499.2.a.s.1.3		3	7.6	odd	2
5712.2.a.bt.1.1		3	4.3	odd	2
6069.2.a.r.1.3		3	17.16	even	2
7497.2.a.ba.1.1		3	21.20	even	2
8925.2.a.bm.1.1		3	5.4	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -1.34292 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} -3.14637 q^{10} -0.489289 q^{11} +3.48929 q^{12} -3.63565 q^{13} +2.34292 q^{14} -1.34292 q^{15} +1.19656 q^{16} +1.00000 q^{17} +2.34292 q^{18} -3.34292 q^{19} -4.68585 q^{20} +1.00000 q^{21} -1.14637 q^{22} +4.48929 q^{23} +3.48929 q^{24} -3.19656 q^{25} -8.51806 q^{26} +1.00000 q^{27} +3.48929 q^{28} +6.97858 q^{29} -3.14637 q^{30} -5.14637 q^{31} -4.17513 q^{32} -0.489289 q^{33} +2.34292 q^{34} -1.34292 q^{35} +3.48929 q^{36} +4.12494 q^{37} -7.83221 q^{38} -3.63565 q^{39} -4.68585 q^{40} +2.65708 q^{41} +2.34292 q^{42} -4.88240 q^{43} -1.70727 q^{44} -1.34292 q^{45} +10.5181 q^{46} -8.22533 q^{47} +1.19656 q^{48} +1.00000 q^{49} -7.48929 q^{50} +1.00000 q^{51} -12.6858 q^{52} -3.73183 q^{53} +2.34292 q^{54} +0.657077 q^{55} +3.48929 q^{56} -3.34292 q^{57} +16.3503 q^{58} +8.81079 q^{59} -4.68585 q^{60} -2.56090 q^{61} -12.0575 q^{62} +1.00000 q^{63} -12.1751 q^{64} +4.88240 q^{65} -1.14637 q^{66} +16.0575 q^{67} +3.48929 q^{68} +4.48929 q^{69} -3.14637 q^{70} +2.10038 q^{71} +3.48929 q^{72} +1.66442 q^{73} +9.66442 q^{74} -3.19656 q^{75} -11.6644 q^{76} -0.489289 q^{77} -8.51806 q^{78} -3.83221 q^{79} -1.60688 q^{80} +1.00000 q^{81} +6.22533 q^{82} +12.9786 q^{83} +3.48929 q^{84} -1.34292 q^{85} -11.4391 q^{86} +6.97858 q^{87} -1.70727 q^{88} -9.27131 q^{89} -3.14637 q^{90} -3.63565 q^{91} +15.6644 q^{92} -5.14637 q^{93} -19.2713 q^{94} +4.48929 q^{95} -4.17513 q^{96} -6.97858 q^{97} +2.34292 q^{98} -0.489289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} + 6 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} + 3 q^{17} + q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21}+ \cdots + 6 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 + 6 * q^11 + 3 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 + 3 * q^17 + q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 - 2 * q^22 + 6 * q^23 + 3 * q^24 - 5 * q^25 + 3 * q^27 + 3 * q^28 + 6 * q^29 - 8 * q^30 - 14 * q^31 + 7 * q^32 + 6 * q^33 + q^34 + 2 * q^35 + 3 * q^36 - 4 * q^37 - 10 * q^38 - 2 * q^39 - 2 * q^40 + 14 * q^41 + q^42 + 2 * q^43 - 8 * q^44 + 2 * q^45 + 6 * q^46 - 2 * q^47 - q^48 + 3 * q^49 - 15 * q^50 + 3 * q^51 - 26 * q^52 - 4 * q^53 + q^54 + 8 * q^55 + 3 * q^56 - 4 * q^57 + 10 * q^58 - 2 * q^59 - 2 * q^60 - 12 * q^61 + 3 * q^63 - 17 * q^64 - 2 * q^65 - 2 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 8 * q^70 + 3 * q^72 - 22 * q^73 + 2 * q^74 - 5 * q^75 - 8 * q^76 + 6 * q^77 + 2 * q^79 - 14 * q^80 + 3 * q^81 - 4 * q^82 + 24 * q^83 + 3 * q^84 + 2 * q^85 - 30 * q^86 + 6 * q^87 - 8 * q^88 - 10 * q^89 - 8 * q^90 - 2 * q^91 + 20 * q^92 - 14 * q^93 - 40 * q^94 + 6 * q^95 + 7 * q^96 - 6 * q^97 + q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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