LMFDB - Embedded newform 5819.2.a.o.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [18,2,-2,18,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 25 x^{16} + 48 x^{15} + 251 x^{14} - 460 x^{13} - 1295 x^{12} + 2248 x^{11} + \cdots - 39 $ x^18 - 2x^17 - 25x^16 + 48x^15 + 251x^14 - 460x^13 - 1295x^12 + 2248x^11 + 3649x^10 - 5930x^9 - 5548x^8 + 8236x^7 + 4387x^6 - 5508x^5 - 1902x^4 + 1554x^3 + 468x^2 - 132*x - 39
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.11676$ of defining polynomial
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.11676 q^{2} -0.0440645 q^{3} -0.752841 q^{4} -0.262759 q^{5} -0.0492096 q^{6} -1.32879 q^{7} -3.07427 q^{8} -2.99806 q^{9} -0.293440 q^{10} -1.00000 q^{11} +0.0331736 q^{12} -2.67442 q^{13} -1.48394 q^{14} +0.0115784 q^{15} -1.92755 q^{16} +0.0811822 q^{17} -3.34812 q^{18} -8.19886 q^{19} +0.197816 q^{20} +0.0585523 q^{21} -1.11676 q^{22} +0.135466 q^{24} -4.93096 q^{25} -2.98669 q^{26} +0.264301 q^{27} +1.00037 q^{28} +4.62889 q^{29} +0.0129303 q^{30} +4.03031 q^{31} +3.99593 q^{32} +0.0440645 q^{33} +0.0906612 q^{34} +0.349151 q^{35} +2.25706 q^{36} -3.78201 q^{37} -9.15618 q^{38} +0.117847 q^{39} +0.807793 q^{40} -2.12797 q^{41} +0.0653890 q^{42} +9.45988 q^{43} +0.752841 q^{44} +0.787768 q^{45} +10.9428 q^{47} +0.0849364 q^{48} -5.23433 q^{49} -5.50671 q^{50} -0.00357725 q^{51} +2.01341 q^{52} +5.72549 q^{53} +0.295162 q^{54} +0.262759 q^{55} +4.08505 q^{56} +0.361278 q^{57} +5.16937 q^{58} -9.25403 q^{59} -0.00871666 q^{60} -2.95777 q^{61} +4.50090 q^{62} +3.98378 q^{63} +8.31760 q^{64} +0.702728 q^{65} +0.0492096 q^{66} +4.10232 q^{67} -0.0611173 q^{68} +0.389919 q^{70} -13.9892 q^{71} +9.21684 q^{72} -10.2763 q^{73} -4.22361 q^{74} +0.217280 q^{75} +6.17244 q^{76} +1.32879 q^{77} +0.131607 q^{78} +9.53548 q^{79} +0.506481 q^{80} +8.98253 q^{81} -2.37644 q^{82} +14.3372 q^{83} -0.0440806 q^{84} -0.0213314 q^{85} +10.5644 q^{86} -0.203969 q^{87} +3.07427 q^{88} +5.34322 q^{89} +0.879750 q^{90} +3.55373 q^{91} -0.177594 q^{93} +12.2205 q^{94} +2.15433 q^{95} -0.176078 q^{96} +7.59324 q^{97} -5.84550 q^{98} +2.99806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 2 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} + 10 q^{7} + 6 q^{8} + 16 q^{9} + 12 q^{10} - 18 q^{11} + 10 q^{12} + 28 q^{14} + 8 q^{15} + 26 q^{16} - 20 q^{18} + 16 q^{19} + 40 q^{20} + 12 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) $ 18 * q + 2 * q^2 - 2 * q^3 + 18 * q^4 + 8 * q^5 - 6 * q^6 + 10 * q^7 + 6 * q^8 + 16 * q^9 + 12 * q^10 - 18 * q^11 + 10 * q^12 + 28 * q^14 + 8 * q^15 + 26 * q^16 - 20 * q^18 + 16 * q^19 + 40 * q^20 + 12 * q^21 - 2 * q^22 + 26 * q^24 + 6 * q^25 - 20 * q^26 - 14 * q^27 + 32 * q^28 - 12 * q^29 + 14 * q^30 + 24 * q^32 + 2 * q^33 + 24 * q^34 + 2 * q^35 - 12 * q^36 + 36 * q^37 - 8 * q^38 - 10 * q^39 + 22 * q^40 + 6 * q^41 - 4 * q^42 + 20 * q^43 - 18 * q^44 - 16 * q^45 - 36 * q^47 + 28 * q^48 + 4 * q^49 + 52 * q^50 + 44 * q^51 - 16 * q^52 + 20 * q^53 - 8 * q^54 - 8 * q^55 + 40 * q^56 + 44 * q^57 + 2 * q^58 - 32 * q^59 + 88 * q^60 + 20 * q^61 + 2 * q^63 + 10 * q^64 - 40 * q^65 + 6 * q^66 - 12 * q^68 + 14 * q^70 - 28 * q^71 - 38 * q^72 - 16 * q^73 + 40 * q^74 + 16 * q^75 + 34 * q^76 - 10 * q^77 - 72 * q^78 + 40 * q^79 + 28 * q^80 + 18 * q^81 + 24 * q^82 + 32 * q^83 - 74 * q^84 - 12 * q^85 - 20 * q^86 + 46 * q^87 - 6 * q^88 + 88 * q^89 + 32 * q^90 - 32 * q^91 - 24 * q^93 - 22 * q^94 + 58 * q^95 + 10 * q^96 + 52 * q^97 + 82 * q^98 - 16 * 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 $

$2$	1.11676	0.789670	0.394835	−	0.918752i	$-0.370802\pi$
$2$	1.11676	0.789670	0.394835	+	0.918752i	$0.370802\pi$
$3$	−0.0440645	−0.0254406	−0.0127203	−	0.999919i	$-0.504049\pi$
$3$	−0.0440645	−0.0254406	−0.0127203	+	0.999919i	$0.504049\pi$
$4$	−0.752841	−0.376421
$5$	−0.262759	−0.117510	−0.0587548	−	0.998272i	$-0.518713\pi$
$5$	−0.262759	−0.117510	−0.0587548	+	0.998272i	$0.518713\pi$
$6$	−0.0492096	−0.0200897
$7$	−1.32879	−0.502234	−0.251117	−	0.967957i	$-0.580798\pi$
$7$	−1.32879	−0.502234	−0.251117	+	0.967957i	$0.580798\pi$
$8$	−3.07427	−1.08692
$9$	−2.99806	−0.999353
$10$	−0.293440	−0.0927938
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.0331736	0.00957638
$13$	−2.67442	−0.741750	−0.370875	−	0.928683i	$-0.620942\pi$
$13$	−2.67442	−0.741750	−0.370875	+	0.928683i	$0.620942\pi$
$14$	−1.48394	−0.396599
$15$	0.0115784	0.00298952
$16$	−1.92755	−0.481887
$17$	0.0811822	0.0196896	0.00984479	−	0.999952i	$-0.496866\pi$
$17$	0.0811822	0.0196896	0.00984479	+	0.999952i	$0.496866\pi$
$18$	−3.34812	−0.789159
$19$	−8.19886	−1.88095	−0.940473	−	0.339867i	$-0.889618\pi$
$19$	−8.19886	−1.88095	−0.940473	+	0.339867i	$0.889618\pi$
$20$	0.197816	0.0442330
$21$	0.0585523	0.0127772
$22$	−1.11676	−0.238095
$23$	0	0
$23$	0	0
$24$	0.135466	0.0276519
$25$	−4.93096	−0.986192
$26$	−2.98669	−0.585738
$27$	0.264301	0.0508648
$28$	1.00037	0.189051
$29$	4.62889	0.859562	0.429781	−	0.902933i	$-0.358591\pi$
$29$	4.62889	0.859562	0.429781	+	0.902933i	$0.358591\pi$
$30$	0.0129303	0.00236073
$31$	4.03031	0.723865	0.361933	−	0.932204i	$-0.382117\pi$
$31$	4.03031	0.723865	0.361933	+	0.932204i	$0.382117\pi$
$32$	3.99593	0.706387
$33$	0.0440645	0.00767064
$34$	0.0906612	0.0155483
$35$	0.349151	0.0590173
$36$	2.25706	0.376177
$37$	−3.78201	−0.621759	−0.310879	−	0.950449i	$-0.600624\pi$
$37$	−3.78201	−0.621759	−0.310879	+	0.950449i	$0.600624\pi$
$38$	−9.15618	−1.48533
$39$	0.117847	0.0188706
$40$	0.807793	0.127723
$41$	−2.12797	−0.332334	−0.166167	−	0.986098i	$-0.553139\pi$
$41$	−2.12797	−0.332334	−0.166167	+	0.986098i	$0.553139\pi$
$42$	0.0653890	0.0100897
$43$	9.45988	1.44262	0.721309	−	0.692613i	$-0.243541\pi$
$43$	9.45988	1.44262	0.721309	+	0.692613i	$0.243541\pi$
$44$	0.752841	0.113495
$45$	0.787768	0.117434
$46$	0	0
$47$	10.9428	1.59617	0.798086	−	0.602543i	$-0.205846\pi$
$47$	10.9428	1.59617	0.798086	+	0.602543i	$0.205846\pi$
$48$	0.0849364	0.0122595
$49$	−5.23433	−0.747761
$50$	−5.50671	−0.778766
$51$	−0.00357725	−0.000500915 0
$52$	2.01341	0.279210
$53$	5.72549	0.786456	0.393228	−	0.919441i	$-0.371358\pi$
$53$	5.72549	0.786456	0.393228	+	0.919441i	$0.371358\pi$
$54$	0.295162	0.0401664
$55$	0.262759	0.0354305
$56$	4.08505	0.545888
$57$	0.361278	0.0478525
$58$	5.16937	0.678771
$59$	−9.25403	−1.20477	−0.602386	−	0.798205i	$-0.705783\pi$
$59$	−9.25403	−1.20477	−0.602386	+	0.798205i	$0.705783\pi$
$60$	−0.00871666	−0.00112532
$61$	−2.95777	−0.378703	−0.189352	−	0.981909i	$-0.560639\pi$
$61$	−2.95777	−0.378703	−0.189352	+	0.981909i	$0.560639\pi$
$62$	4.50090	0.571615
$63$	3.98378	0.501909
$64$	8.31760	1.03970
$65$	0.702728	0.0871627
$66$	0.0492096	0.00605728
$67$	4.10232	0.501178	0.250589	−	0.968094i	$-0.419376\pi$
$67$	4.10232	0.501178	0.250589	+	0.968094i	$0.419376\pi$
$68$	−0.0611173	−0.00741156
$69$	0	0
$70$	0.389919	0.0466042
$71$	−13.9892	−1.66022	−0.830108	−	0.557603i	$-0.811721\pi$
$71$	−13.9892	−1.66022	−0.830108	+	0.557603i	$0.811721\pi$
$72$	9.21684	1.08622
$73$	−10.2763	−1.20275	−0.601377	−	0.798965i	$-0.705381\pi$
$73$	−10.2763	−1.20275	−0.601377	+	0.798965i	$0.705381\pi$
$74$	−4.22361	−0.490985
$75$	0.217280	0.0250893
$76$	6.17244	0.708027
$77$	1.32879	0.151429
$78$	0.131607	0.0149016
$79$	9.53548	1.07283	0.536413	−	0.843956i	$-0.319779\pi$
$79$	9.53548	1.07283	0.536413	+	0.843956i	$0.319779\pi$
$80$	0.506481	0.0566263
$81$	8.98253	0.998059
$82$	−2.37644	−0.262434
$83$	14.3372	1.57372	0.786858	−	0.617134i	$-0.211707\pi$
$83$	14.3372	1.57372	0.786858	+	0.617134i	$0.211707\pi$
$84$	−0.0440806	−0.00480959
$85$	−0.0213314	−0.00231371
$86$	10.5644	1.13919
$87$	−0.203969	−0.0218678
$88$	3.07427	0.327718
$89$	5.34322	0.566380	0.283190	−	0.959064i	$-0.408607\pi$
$89$	5.34322	0.566380	0.283190	+	0.959064i	$0.408607\pi$
$90$	0.879750	0.0927338
$91$	3.55373	0.372532
$92$	0	0
$93$	−0.177594	−0.0184156
$94$	12.2205	1.26045
$95$	2.15433	0.221029
$96$	−0.176078	−0.0179709
$97$	7.59324	0.770976	0.385488	−	0.922713i	$-0.374033\pi$
$97$	7.59324	0.770976	0.385488	+	0.922713i	$0.374033\pi$
$98$	−5.84550	−0.590485
$99$	2.99806	0.301316
$100$	3.71223	0.371223
$101$	−1.72990	−0.172132	−0.0860659	−	0.996289i	$-0.527430\pi$
$101$	−1.72990	−0.172132	−0.0860659	+	0.996289i	$0.527430\pi$
$102$	−0.00399494	−0.000395558 0
$103$	3.85283	0.379631	0.189815	−	0.981820i	$-0.439211\pi$
$103$	3.85283	0.379631	0.189815	+	0.981820i	$0.439211\pi$
$104$	8.22188	0.806222
$105$	−0.0153852	−0.00150144
$106$	6.39401	0.621041
$107$	4.58455	0.443205	0.221603	−	0.975137i	$-0.428871\pi$
$107$	4.58455	0.443205	0.221603	+	0.975137i	$0.428871\pi$
$108$	−0.198977	−0.0191466
$109$	−10.7870	−1.03321	−0.516604	−	0.856224i	$-0.672804\pi$
$109$	−10.7870	−1.03321	−0.516604	+	0.856224i	$0.672804\pi$
$110$	0.293440	0.0279784
$111$	0.166652	0.0158179
$112$	2.56130	0.242020
$113$	16.0804	1.51271	0.756357	−	0.654160i	$-0.226978\pi$
$113$	16.0804	1.51271	0.756357	+	0.654160i	$0.226978\pi$
$114$	0.403462	0.0377877
$115$	0	0
$116$	−3.48482	−0.323557
$117$	8.01806	0.741270
$118$	−10.3346	−0.951373
$119$	−0.107874	−0.00988878
$120$	−0.0355950	−0.00324936
$121$	1.00000	0.0909091
$122$	−3.30313	−0.299051
$123$	0.0937681	0.00845479
$124$	−3.03418	−0.272478
$125$	2.60945	0.233396
$126$	4.44894	0.396343
$127$	−14.5780	−1.29359	−0.646793	−	0.762666i	$-0.723890\pi$
$127$	−14.5780	−1.29359	−0.646793	+	0.762666i	$0.723890\pi$
$128$	1.29693	0.114633
$129$	−0.416845	−0.0367011
$130$	0.784781	0.0688298
$131$	4.61363	0.403095	0.201547	−	0.979479i	$-0.435403\pi$
$131$	4.61363	0.403095	0.201547	+	0.979479i	$0.435403\pi$
$132$	−0.0331736	−0.00288739
$133$	10.8945	0.944676
$134$	4.58132	0.395766
$135$	−0.0694477	−0.00597710
$136$	−0.249576	−0.0214010
$137$	0.124793	0.0106618	0.00533088	−	0.999986i	$-0.498303\pi$
$137$	0.124793	0.0106618	0.00533088	+	0.999986i	$0.498303\pi$
$138$	0	0
$139$	−6.83298	−0.579566	−0.289783	−	0.957092i	$-0.593583\pi$
$139$	−6.83298	−0.579566	−0.289783	+	0.957092i	$0.593583\pi$
$140$	−0.262855	−0.0222153
$141$	−0.482189	−0.0406077
$142$	−15.6226	−1.31102
$143$	2.67442	0.223646
$144$	5.77890	0.481575
$145$	−1.21628	−0.101007
$146$	−11.4762	−0.949780
$147$	0.230648	0.0190235
$148$	2.84725	0.234043
$149$	−12.3157	−1.00894	−0.504469	−	0.863430i	$-0.668312\pi$
$149$	−12.3157	−1.00894	−0.504469	+	0.863430i	$0.668312\pi$
$150$	0.242650	0.0198123
$151$	−8.78885	−0.715226	−0.357613	−	0.933870i	$-0.616409\pi$
$151$	−8.78885	−0.715226	−0.357613	+	0.933870i	$0.616409\pi$
$152$	25.2055	2.04444
$153$	−0.243389	−0.0196768
$154$	1.48394	0.119579
$155$	−1.05900	−0.0850611
$156$	−0.0887200	−0.00710328
$157$	−23.5294	−1.87785	−0.938924	−	0.344124i	$-0.888176\pi$
$157$	−23.5294	−1.87785	−0.938924	+	0.344124i	$0.888176\pi$
$158$	10.6489	0.847179
$159$	−0.252291	−0.0200080
$160$	−1.04997	−0.0830072
$161$	0	0
$162$	10.0314	0.788137
$163$	16.1005	1.26109	0.630544	−	0.776154i	$-0.282832\pi$
$163$	16.1005	1.26109	0.630544	+	0.776154i	$0.282832\pi$
$164$	1.60203	0.125097
$165$	−0.0115784	−0.000901374 0
$166$	16.0113	1.24272
$167$	12.0537	0.932747	0.466373	−	0.884588i	$-0.345560\pi$
$167$	12.0537	0.932747	0.466373	+	0.884588i	$0.345560\pi$
$168$	−0.180006	−0.0138877
$169$	−5.84749	−0.449807
$170$	−0.0238221	−0.00182707
$171$	24.5807	1.87973
$172$	−7.12179	−0.543031
$173$	23.0882	1.75536	0.877681	−	0.479246i	$-0.159090\pi$
$173$	23.0882	1.75536	0.877681	+	0.479246i	$0.159090\pi$
$174$	−0.227786	−0.0172684
$175$	6.55219	0.495299
$176$	1.92755	0.145294
$177$	0.407774	0.0306502
$178$	5.96710	0.447253
$179$	−17.4438	−1.30381	−0.651907	−	0.758299i	$-0.726031\pi$
$179$	−17.4438	−1.30381	−0.651907	+	0.758299i	$0.726031\pi$
$180$	−0.593064	−0.0442044
$181$	4.99121	0.370994	0.185497	−	0.982645i	$-0.440611\pi$
$181$	4.99121	0.370994	0.185497	+	0.982645i	$0.440611\pi$
$182$	3.96867	0.294178
$183$	0.130333	0.00963446
$184$	0	0
$185$	0.993759	0.0730626
$186$	−0.198330	−0.0145422
$187$	−0.0811822	−0.00593663
$188$	−8.23820	−0.600832
$189$	−0.351200	−0.0255461
$190$	2.40587	0.174540
$191$	12.9393	0.936257	0.468128	−	0.883660i	$-0.344928\pi$
$191$	12.9393	0.936257	0.468128	+	0.883660i	$0.344928\pi$
$192$	−0.366511	−0.0264506
$193$	−16.1428	−1.16199	−0.580993	−	0.813908i	$-0.697336\pi$
$193$	−16.1428	−1.16199	−0.580993	+	0.813908i	$0.697336\pi$
$194$	8.47984	0.608817
$195$	−0.0309654	−0.00221748
$196$	3.94062	0.281473
$197$	−5.55486	−0.395767	−0.197884	−	0.980226i	$-0.563407\pi$
$197$	−5.55486	−0.395767	−0.197884	+	0.980226i	$0.563407\pi$
$198$	3.34812	0.237940
$199$	−20.7314	−1.46961	−0.734806	−	0.678277i	$-0.762727\pi$
$199$	−20.7314	−1.46961	−0.734806	+	0.678277i	$0.762727\pi$
$200$	15.1591	1.07191
$201$	−0.180767	−0.0127503
$202$	−1.93189	−0.135927
$203$	−6.15080	−0.431702
$204$	0.00269310	0.000188555 0
$205$	0.559145	0.0390524
$206$	4.30270	0.299783
$207$	0	0
$208$	5.15507	0.357440
$209$	8.19886	0.567127
$210$	−0.0171816	−0.00118564
$211$	−20.5192	−1.41260	−0.706300	−	0.707913i	$-0.749637\pi$
$211$	−20.5192	−1.41260	−0.706300	+	0.707913i	$0.749637\pi$
$212$	−4.31038	−0.296038
$213$	0.616428	0.0422369
$214$	5.11986	0.349986
$215$	−2.48567	−0.169521
$216$	−0.812534	−0.0552859
$217$	−5.35542	−0.363550
$218$	−12.0465	−0.815895
$219$	0.452822	0.0305988
$220$	−0.197816	−0.0133368
$221$	−0.217115	−0.0146047
$222$	0.186111	0.0124910
$223$	0.230557	0.0154392	0.00771961	−	0.999970i	$-0.497543\pi$
$223$	0.230557	0.0154392	0.00771961	+	0.999970i	$0.497543\pi$
$224$	−5.30973	−0.354772
$225$	14.7833	0.985553
$226$	17.9579	1.19454
$227$	20.3403	1.35004	0.675018	−	0.737801i	$-0.264136\pi$
$227$	20.3403	1.35004	0.675018	+	0.737801i	$0.264136\pi$
$228$	−0.271985	−0.0180127
$229$	1.27110	0.0839966	0.0419983	−	0.999118i	$-0.486628\pi$
$229$	1.27110	0.0839966	0.0419983	+	0.999118i	$0.486628\pi$
$230$	0	0
$231$	−0.0585523	−0.00385246
$232$	−14.2304	−0.934274
$233$	12.2822	0.804633	0.402317	−	0.915501i	$-0.368205\pi$
$233$	12.2822	0.804633	0.402317	+	0.915501i	$0.368205\pi$
$234$	8.95427	0.585359
$235$	−2.87533	−0.187566
$236$	6.96681	0.453501
$237$	−0.420176	−0.0272934
$238$	−0.120469	−0.00780887
$239$	−12.9587	−0.838227	−0.419113	−	0.907934i	$-0.637659\pi$
$239$	−12.9587	−0.838227	−0.419113	+	0.907934i	$0.637659\pi$
$240$	−0.0223178	−0.00144061
$241$	24.0336	1.54814	0.774069	−	0.633102i	$-0.218218\pi$
$241$	24.0336	1.54814	0.774069	+	0.633102i	$0.218218\pi$
$242$	1.11676	0.0717882
$243$	−1.18871	−0.0762561
$244$	2.22673	0.142552
$245$	1.37537	0.0878690
$246$	0.104717	0.00667649
$247$	21.9272	1.39519
$248$	−12.3903	−0.786782
$249$	−0.631763	−0.0400363
$250$	2.91414	0.184306
$251$	−16.9027	−1.06689	−0.533445	−	0.845835i	$-0.679103\pi$
$251$	−16.9027	−1.06689	−0.533445	+	0.845835i	$0.679103\pi$
$252$	−2.99915	−0.188929
$253$	0	0
$254$	−16.2801	−1.02151
$255$	0.000939956 0	5.88623e−5 0
$256$	−15.1868	−0.949177
$257$	−0.200323	−0.0124958	−0.00624789	−	0.999980i	$-0.501989\pi$
$257$	−0.200323	−0.0124958	−0.00624789	+	0.999980i	$0.501989\pi$
$258$	−0.465517	−0.0289818
$259$	5.02549	0.312269
$260$	−0.529043	−0.0328098
$261$	−13.8777	−0.859006
$262$	5.15233	0.318312
$263$	7.48713	0.461676	0.230838	−	0.972992i	$-0.425853\pi$
$263$	7.48713	0.461676	0.230838	+	0.972992i	$0.425853\pi$
$264$	−0.135466	−0.00833737
$265$	−1.50443	−0.0924161
$266$	12.1666	0.745983
$267$	−0.235446	−0.0144091
$268$	−3.08840	−0.188654
$269$	8.80913	0.537102	0.268551	−	0.963265i	$-0.413455\pi$
$269$	8.80913	0.537102	0.268551	+	0.963265i	$0.413455\pi$
$270$	−0.0775566	−0.00471994
$271$	24.9118	1.51328	0.756641	−	0.653831i	$-0.226839\pi$
$271$	24.9118	1.51328	0.756641	+	0.653831i	$0.226839\pi$
$272$	−0.156483	−0.00948815
$273$	−0.156593	−0.00947746
$274$	0.139364	0.00841928
$275$	4.93096	0.297348
$276$	0	0
$277$	23.6530	1.42117	0.710586	−	0.703610i	$-0.248430\pi$
$277$	23.6530	1.42117	0.710586	+	0.703610i	$0.248430\pi$
$278$	−7.63082	−0.457666
$279$	−12.0831	−0.723397
$280$	−1.07339	−0.0641470
$281$	19.4381	1.15958	0.579789	−	0.814766i	$-0.303135\pi$
$281$	19.4381	1.15958	0.579789	+	0.814766i	$0.303135\pi$
$282$	−0.538491	−0.0320667
$283$	21.3780	1.27079	0.635396	−	0.772187i	$-0.280837\pi$
$283$	21.3780	1.27079	0.635396	+	0.772187i	$0.280837\pi$
$284$	10.5317	0.624939
$285$	−0.0949293	−0.00562313
$286$	2.98669	0.176607
$287$	2.82762	0.166909
$288$	−11.9800	−0.705930
$289$	−16.9934	−0.999612
$290$	−1.35830	−0.0797621
$291$	−0.334592	−0.0196141
$292$	7.73645	0.452742
$293$	6.79202	0.396794	0.198397	−	0.980122i	$-0.436426\pi$
$293$	6.79202	0.396794	0.198397	+	0.980122i	$0.436426\pi$
$294$	0.257579	0.0150223
$295$	2.43158	0.141572
$296$	11.6269	0.675801
$297$	−0.264301	−0.0153363
$298$	−13.7537	−0.796729
$299$	0	0
$300$	−0.163577	−0.00944415
$301$	−12.5702	−0.724532
$302$	−9.81506	−0.564793
$303$	0.0762273	0.00437915
$304$	15.8037	0.906404
$305$	0.777181	0.0445013
$306$	−0.271808	−0.0155382
$307$	−3.25128	−0.185560	−0.0927801	−	0.995687i	$-0.529575\pi$
$307$	−3.25128	−0.185560	−0.0927801	+	0.995687i	$0.529575\pi$
$308$	−1.00037	−0.0570011
$309$	−0.169773	−0.00965805
$310$	−1.18265	−0.0671702
$311$	12.4062	0.703490	0.351745	−	0.936096i	$-0.385588\pi$
$311$	12.4062	0.703490	0.351745	+	0.936096i	$0.385588\pi$
$312$	−0.362293	−0.0205108
$313$	−10.7697	−0.608740	−0.304370	−	0.952554i	$-0.598446\pi$
$313$	−10.7697	−0.608740	−0.304370	+	0.952554i	$0.598446\pi$
$314$	−26.2767	−1.48288
$315$	−1.04678	−0.0589791
$316$	−7.17870	−0.403834
$317$	20.1758	1.13319	0.566593	−	0.823998i	$-0.308261\pi$
$317$	20.1758	1.13319	0.566593	+	0.823998i	$0.308261\pi$
$318$	−0.281749	−0.0157997
$319$	−4.62889	−0.259168
$320$	−2.18553	−0.122175
$321$	−0.202016	−0.0112754
$322$	0	0
$323$	−0.665601	−0.0370350
$324$	−6.76242	−0.375690
$325$	13.1874	0.731508
$326$	17.9804	0.995844
$327$	0.475324	0.0262855
$328$	6.54197	0.361220
$329$	−14.5407	−0.801652
$330$	−0.0129303	−0.000711788 0
$331$	−3.05803	−0.168085	−0.0840424	−	0.996462i	$-0.526783\pi$
$331$	−3.05803	−0.168085	−0.0840424	+	0.996462i	$0.526783\pi$
$332$	−10.7937	−0.592379
$333$	11.3387	0.621357
$334$	13.4612	0.736563
$335$	−1.07792	−0.0588932
$336$	−0.112862	−0.00615715
$337$	2.81357	0.153265	0.0766325	−	0.997059i	$-0.475583\pi$
$337$	2.81357	0.153265	0.0766325	+	0.997059i	$0.475583\pi$
$338$	−6.53026	−0.355199
$339$	−0.708573	−0.0384844
$340$	0.0160591	0.000870929 0
$341$	−4.03031	−0.218254
$342$	27.4508	1.48437
$343$	16.2568	0.877785
$344$	−29.0822	−1.56801
$345$	0	0
$346$	25.7840	1.38616
$347$	4.12654	0.221524	0.110762	−	0.993847i	$-0.464671\pi$
$347$	4.12654	0.221524	0.110762	+	0.993847i	$0.464671\pi$
$348$	0.153557	0.00823150
$349$	11.4667	0.613798	0.306899	−	0.951742i	$-0.400709\pi$
$349$	11.4667	0.613798	0.306899	+	0.951742i	$0.400709\pi$
$350$	7.31724	0.391123
$351$	−0.706852	−0.0377290
$352$	−3.99593	−0.212984
$353$	−0.262450	−0.0139688	−0.00698439	−	0.999976i	$-0.502223\pi$
$353$	−0.262450	−0.0139688	−0.00698439	+	0.999976i	$0.502223\pi$
$354$	0.455387	0.0242035
$355$	3.67580	0.195091
$356$	−4.02259	−0.213197
$357$	0.00475340	0.000251577 0
$358$	−19.4806	−1.02958
$359$	1.39009	0.0733661	0.0366830	−	0.999327i	$-0.488321\pi$
$359$	1.39009	0.0733661	0.0366830	+	0.999327i	$0.488321\pi$
$360$	−2.42181	−0.127641
$361$	48.2213	2.53796
$362$	5.57400	0.292963
$363$	−0.0440645	−0.00231279
$364$	−2.67539	−0.140229
$365$	2.70020	0.141335
$366$	0.145551	0.00760805
$367$	−12.3611	−0.645243	−0.322621	−	0.946528i	$-0.604564\pi$
$367$	−12.3611	−0.645243	−0.322621	+	0.946528i	$0.604564\pi$
$368$	0	0
$369$	6.37979	0.332119
$370$	1.10979	0.0576954
$371$	−7.60795	−0.394985
$372$	0.133700	0.00693201
$373$	−13.9136	−0.720421	−0.360211	−	0.932871i	$-0.617295\pi$
$373$	−13.9136	−0.720421	−0.360211	+	0.932871i	$0.617295\pi$
$374$	−0.0906612	−0.00468798
$375$	−0.114984	−0.00593776
$376$	−33.6412	−1.73491
$377$	−12.3796	−0.637580
$378$	−0.392207	−0.0201730
$379$	16.3533	0.840014	0.420007	−	0.907521i	$-0.362028\pi$
$379$	16.3533	0.840014	0.420007	+	0.907521i	$0.362028\pi$
$380$	−1.62187	−0.0832000
$381$	0.642371	0.0329097
$382$	14.4502	0.739334
$383$	−13.0099	−0.664776	−0.332388	−	0.943143i	$-0.607854\pi$
$383$	−13.0099	−0.664776	−0.332388	+	0.943143i	$0.607854\pi$
$384$	−0.0571485	−0.00291635
$385$	−0.349151	−0.0177944
$386$	−18.0277	−0.917587
$387$	−28.3613	−1.44168
$388$	−5.71650	−0.290211
$389$	34.2589	1.73700	0.868498	−	0.495692i	$-0.165086\pi$
$389$	34.2589	1.73700	0.868498	+	0.495692i	$0.165086\pi$
$390$	−0.0345810	−0.00175108
$391$	0	0
$392$	16.0917	0.812755
$393$	−0.203297	−0.0102550
$394$	−6.20346	−0.312526
$395$	−2.50554	−0.126067
$396$	−2.25706	−0.113422
$397$	−17.3976	−0.873160	−0.436580	−	0.899665i	$-0.643810\pi$
$397$	−17.3976	−0.873160	−0.436580	+	0.899665i	$0.643810\pi$
$398$	−23.1521	−1.16051
$399$	−0.480062	−0.0240332
$400$	9.50466	0.475233
$401$	−24.3204	−1.21450	−0.607250	−	0.794511i	$-0.707727\pi$
$401$	−24.3204	−1.21450	−0.607250	+	0.794511i	$0.707727\pi$
$402$	−0.201873	−0.0100685
$403$	−10.7787	−0.536927
$404$	1.30234	0.0647940
$405$	−2.36024	−0.117281
$406$	−6.86899	−0.340902
$407$	3.78201	0.187467
$408$	0.0109974	0.000544454 0
$409$	−27.3654	−1.35313	−0.676567	−	0.736381i	$-0.736533\pi$
$409$	−27.3654	−1.35313	−0.676567	+	0.736381i	$0.736533\pi$
$410$	0.624433	0.0308385
$411$	−0.00549893	−0.000271242 0
$412$	−2.90057	−0.142901
$413$	12.2966	0.605078
$414$	0	0
$415$	−3.76724	−0.184927
$416$	−10.6868	−0.523962
$417$	0.301092	0.0147445
$418$	9.15618	0.447843
$419$	−23.7978	−1.16260	−0.581298	−	0.813690i	$-0.697455\pi$
$419$	−23.7978	−1.16260	−0.581298	+	0.813690i	$0.697455\pi$
$420$	0.0115826	0.000565172 0
$421$	−2.32520	−0.113323	−0.0566615	−	0.998393i	$-0.518046\pi$
$421$	−2.32520	−0.113323	−0.0566615	+	0.998393i	$0.518046\pi$
$422$	−22.9151	−1.11549
$423$	−32.8072	−1.59514
$424$	−17.6017	−0.854814
$425$	−0.400306	−0.0194177
$426$	0.688404	0.0333533
$427$	3.93024	0.190198
$428$	−3.45144	−0.166832
$429$	−0.117847	−0.00568970
$430$	−2.77591	−0.133866
$431$	−13.3904	−0.644995	−0.322498	−	0.946570i	$-0.604522\pi$
$431$	−13.3904	−0.644995	−0.322498	+	0.946570i	$0.604522\pi$
$432$	−0.509454	−0.0245111
$433$	17.8105	0.855919	0.427959	−	0.903798i	$-0.359233\pi$
$433$	17.8105	0.855919	0.427959	+	0.903798i	$0.359233\pi$
$434$	−5.98074	−0.287084
$435$	0.0535949	0.00256968
$436$	8.12091	0.388921
$437$	0	0
$438$	0.505694	0.0241630
$439$	−10.9988	−0.524942	−0.262471	−	0.964940i	$-0.584537\pi$
$439$	−10.9988	−0.524942	−0.262471	+	0.964940i	$0.584537\pi$
$440$	−0.807793	−0.0385100
$441$	15.6928	0.747277
$442$	−0.242466	−0.0115329
$443$	11.5122	0.546960	0.273480	−	0.961878i	$-0.411825\pi$
$443$	11.5122	0.546960	0.273480	+	0.961878i	$0.411825\pi$
$444$	−0.125463	−0.00595420
$445$	−1.40398	−0.0665550
$446$	0.257477	0.0121919
$447$	0.542683	0.0256680
$448$	−11.0523	−0.522173
$449$	2.11085	0.0996170	0.0498085	−	0.998759i	$-0.484139\pi$
$449$	2.11085	0.0996170	0.0498085	+	0.998759i	$0.484139\pi$
$450$	16.5094	0.778262
$451$	2.12797	0.100202
$452$	−12.1060	−0.569416
$453$	0.387276	0.0181958
$454$	22.7153	1.06608
$455$	−0.933776	−0.0437761
$456$	−1.11067	−0.0520118
$457$	7.10870	0.332531	0.166265	−	0.986081i	$-0.446829\pi$
$457$	7.10870	0.332531	0.166265	+	0.986081i	$0.446829\pi$
$458$	1.41952	0.0663296
$459$	0.0214566	0.00100151
$460$	0	0
$461$	−17.5100	−0.815522	−0.407761	−	0.913089i	$-0.633690\pi$
$461$	−17.5100	−0.815522	−0.407761	+	0.913089i	$0.633690\pi$
$462$	−0.0653890	−0.00304217
$463$	−2.11009	−0.0980640	−0.0490320	−	0.998797i	$-0.515614\pi$
$463$	−2.11009	−0.0980640	−0.0490320	+	0.998797i	$0.515614\pi$
$464$	−8.92240	−0.414212
$465$	0.0466644	0.00216401
$466$	13.7163	0.635395
$467$	14.5714	0.674286	0.337143	−	0.941453i	$-0.390539\pi$
$467$	14.5714	0.674286	0.337143	+	0.941453i	$0.390539\pi$
$468$	−6.03633	−0.279029
$469$	−5.45111	−0.251709
$470$	−3.21106	−0.148115
$471$	1.03681	0.0477737
$472$	28.4494	1.30949
$473$	−9.45988	−0.434966
$474$	−0.469237	−0.0215528
$475$	40.4282	1.85497
$476$	0.0812118	0.00372234
$477$	−17.1653	−0.785947
$478$	−14.4718	−0.661923
$479$	1.82354	0.0833196	0.0416598	−	0.999132i	$-0.486735\pi$
$479$	1.82354	0.0833196	0.0416598	+	0.999132i	$0.486735\pi$
$480$	0.0462663	0.00211176
$481$	10.1147	0.461190
$482$	26.8398	1.22252
$483$	0	0
$484$	−0.752841	−0.0342201
$485$	−1.99519	−0.0905971
$486$	−1.32751	−0.0602172
$487$	−20.8231	−0.943583	−0.471792	−	0.881710i	$-0.656393\pi$
$487$	−20.8231	−0.943583	−0.471792	+	0.881710i	$0.656393\pi$
$488$	9.09298	0.411620
$489$	−0.709460	−0.0320829
$490$	1.53596	0.0693876
$491$	−4.09067	−0.184609	−0.0923046	−	0.995731i	$-0.529423\pi$
$491$	−4.09067	−0.184609	−0.0923046	+	0.995731i	$0.529423\pi$
$492$	−0.0705925	−0.00318256
$493$	0.375783	0.0169244
$494$	24.4874	1.10174
$495$	−0.787768	−0.0354075
$496$	−7.76862	−0.348821
$497$	18.5887	0.833817
$498$	−0.705529	−0.0316155
$499$	−26.8805	−1.20334	−0.601668	−	0.798746i	$-0.705497\pi$
$499$	−26.8805	−1.20334	−0.601668	+	0.798746i	$0.705497\pi$
$500$	−1.96450	−0.0878552
$501$	−0.531142	−0.0237297
$502$	−18.8763	−0.842491
$503$	−13.8646	−0.618190	−0.309095	−	0.951031i	$-0.600026\pi$
$503$	−13.8646	−0.618190	−0.309095	+	0.951031i	$0.600026\pi$
$504$	−12.2472	−0.545534
$505$	0.454548	0.0202271
$506$	0	0
$507$	0.257667	0.0114434
$508$	10.9749	0.486932
$509$	9.52468	0.422174	0.211087	−	0.977467i	$-0.432300\pi$
$509$	9.52468	0.422174	0.211087	+	0.977467i	$0.432300\pi$
$510$	0.00104971	4.64819e−5 0
$511$	13.6551	0.604064
$512$	−19.5539	−0.864171
$513$	−2.16697	−0.0956740
$514$	−0.223713	−0.00986755
$515$	−1.01237	−0.0446103
$516$	0.313818	0.0138151
$517$	−10.9428	−0.481264
$518$	5.61228	0.246589
$519$	−1.01737	−0.0446575
$520$	−2.16038	−0.0947388
$521$	−1.16536	−0.0510553	−0.0255276	−	0.999674i	$-0.508127\pi$
$521$	−1.16536	−0.0510553	−0.0255276	+	0.999674i	$0.508127\pi$
$522$	−15.4981	−0.678332
$523$	−37.2747	−1.62991	−0.814954	−	0.579526i	$-0.803238\pi$
$523$	−37.2747	−1.62991	−0.814954	+	0.579526i	$0.803238\pi$
$524$	−3.47333	−0.151733
$525$	−0.288719	−0.0126007
$526$	8.36135	0.364572
$527$	0.327189	0.0142526
$528$	−0.0849364	−0.00369638
$529$	0	0
$530$	−1.68009	−0.0729783
$531$	27.7441	1.20399
$532$	−8.20185	−0.355595
$533$	5.69109	0.246509
$534$	−0.262937	−0.0113784
$535$	−1.20463	−0.0520809
$536$	−12.6116	−0.544740
$537$	0.768653	0.0331698
$538$	9.83771	0.424134
$539$	5.23433	0.225458
$540$	0.0522831	0.00224990
$541$	−21.1598	−0.909729	−0.454865	−	0.890561i	$-0.650312\pi$
$541$	−21.1598	−0.909729	−0.454865	+	0.890561i	$0.650312\pi$
$542$	27.8205	1.19499
$543$	−0.219935	−0.00943832
$544$	0.324398	0.0139085
$545$	2.83439	0.121412
$546$	−0.174878	−0.00748407
$547$	35.2148	1.50567	0.752837	−	0.658207i	$-0.228685\pi$
$547$	35.2148	1.50567	0.752837	+	0.658207i	$0.228685\pi$
$548$	−0.0939491	−0.00401331
$549$	8.86756	0.378458
$550$	5.50671	0.234807
$551$	−37.9516	−1.61679
$552$	0	0
$553$	−12.6706	−0.538810
$554$	26.4148	1.12226
$555$	−0.0437895	−0.00185876
$556$	5.14415	0.218161
$557$	−32.3811	−1.37203	−0.686015	−	0.727587i	$-0.740642\pi$
$557$	−32.3811	−1.37203	−0.686015	+	0.727587i	$0.740642\pi$
$558$	−13.4940	−0.571245
$559$	−25.2997	−1.07006
$560$	−0.673006	−0.0284397
$561$	0.00357725	0.000151032 0
$562$	21.7077	0.915685
$563$	15.1392	0.638042	0.319021	−	0.947748i	$-0.396646\pi$
$563$	15.1392	0.638042	0.319021	+	0.947748i	$0.396646\pi$
$564$	0.363012	0.0152856
$565$	−4.22527	−0.177758
$566$	23.8742	1.00351
$567$	−11.9359	−0.501259
$568$	43.0066	1.80452
$569$	32.0770	1.34474	0.672370	−	0.740216i	$-0.265277\pi$
$569$	32.0770	1.34474	0.672370	+	0.740216i	$0.265277\pi$
$570$	−0.106013	−0.00444042
$571$	31.2100	1.30610	0.653050	−	0.757315i	$-0.273489\pi$
$571$	31.2100	1.30610	0.653050	+	0.757315i	$0.273489\pi$
$572$	−2.01341	−0.0841850
$573$	−0.570165	−0.0238190
$574$	3.15779	0.131803
$575$	0	0
$576$	−24.9366	−1.03903
$577$	26.5671	1.10600	0.553001	−	0.833181i	$-0.313483\pi$
$577$	26.5671	1.10600	0.553001	+	0.833181i	$0.313483\pi$
$578$	−18.9776	−0.789364
$579$	0.711326	0.0295617
$580$	0.915668	0.0380210
$581$	−19.0511	−0.790374
$582$	−0.373660	−0.0154887
$583$	−5.72549	−0.237125
$584$	31.5922	1.30730
$585$	−2.10682	−0.0871063
$586$	7.58508	0.313337
$587$	−6.53031	−0.269535	−0.134767	−	0.990877i	$-0.543029\pi$
$587$	−6.53031	−0.269535	−0.134767	+	0.990877i	$0.543029\pi$
$588$	−0.173641	−0.00716084
$589$	−33.0439	−1.36155
$590$	2.71550	0.111795
$591$	0.244772	0.0100686
$592$	7.29001	0.299618
$593$	47.0459	1.93194	0.965971	−	0.258651i	$-0.0832781\pi$
$593$	47.0459	1.93194	0.965971	+	0.258651i	$0.0832781\pi$
$594$	−0.295162	−0.0121106
$595$	0.0283449	0.00116203
$596$	9.27174	0.379785
$597$	0.913520	0.0373879
$598$	0	0
$599$	−30.6852	−1.25376	−0.626882	−	0.779114i	$-0.715669\pi$
$599$	−30.6852	−1.25376	−0.626882	+	0.779114i	$0.715669\pi$
$600$	−0.667978	−0.0272701
$601$	−10.8112	−0.440996	−0.220498	−	0.975387i	$-0.570768\pi$
$601$	−10.8112	−0.440996	−0.220498	+	0.975387i	$0.570768\pi$
$602$	−14.0379	−0.572142
$603$	−12.2990	−0.500854
$604$	6.61661	0.269226
$605$	−0.262759	−0.0106827
$606$	0.0851278	0.00345808
$607$	−9.12543	−0.370390	−0.185195	−	0.982702i	$-0.559292\pi$
$607$	−9.12543	−0.370390	−0.185195	+	0.982702i	$0.559292\pi$
$608$	−32.7620	−1.32868
$609$	0.271032	0.0109828
$610$	0.867927	0.0351413
$611$	−29.2656	−1.18396
$612$	0.183233	0.00740676
$613$	−5.02740	−0.203055	−0.101527	−	0.994833i	$-0.532373\pi$
$613$	−5.02740	−0.203055	−0.101527	+	0.994833i	$0.532373\pi$
$614$	−3.63090	−0.146531
$615$	−0.0246385	−0.000993518 0
$616$	−4.08505	−0.164591
$617$	39.7035	1.59840	0.799201	−	0.601063i	$-0.205256\pi$
$617$	39.7035	1.59840	0.799201	+	0.601063i	$0.205256\pi$
$618$	−0.189596	−0.00762668
$619$	11.9841	0.481683	0.240841	−	0.970564i	$-0.422577\pi$
$619$	11.9841	0.481683	0.240841	+	0.970564i	$0.422577\pi$
$620$	0.797260	0.0320187
$621$	0	0
$622$	13.8548	0.555525
$623$	−7.09999	−0.284455
$624$	−0.227155	−0.00909350
$625$	23.9691	0.958765
$626$	−12.0272	−0.480704
$627$	−0.361278	−0.0144281
$628$	17.7139	0.706861
$629$	−0.307032	−0.0122422
$630$	−1.16900	−0.0465741
$631$	32.1027	1.27799	0.638994	−	0.769211i	$-0.279351\pi$
$631$	32.1027	1.27799	0.638994	+	0.769211i	$0.279351\pi$
$632$	−29.3146	−1.16607
$633$	0.904168	0.0359374
$634$	22.5316	0.894843
$635$	3.83050	0.152009
$636$	0.189935	0.00753140
$637$	13.9988	0.554652
$638$	−5.16937	−0.204657
$639$	41.9405	1.65914
$640$	−0.340780	−0.0134705
$641$	−2.21045	−0.0873077	−0.0436538	−	0.999047i	$-0.513900\pi$
$641$	−2.21045	−0.0873077	−0.0436538	+	0.999047i	$0.513900\pi$
$642$	−0.225604	−0.00890387
$643$	−38.2964	−1.51026	−0.755131	−	0.655574i	$-0.772427\pi$
$643$	−38.2964	−1.51026	−0.755131	+	0.655574i	$0.772427\pi$
$644$	0	0
$645$	0.109530	0.00431273
$646$	−0.743318	−0.0292455
$647$	20.7722	0.816639	0.408320	−	0.912839i	$-0.366115\pi$
$647$	20.7722	0.816639	0.408320	+	0.912839i	$0.366115\pi$
$648$	−27.6147	−1.08481
$649$	9.25403	0.363252
$650$	14.7272	0.577650
$651$	0.235984	0.00924894
$652$	−12.1211	−0.474699
$653$	−44.9713	−1.75986	−0.879932	−	0.475100i	$-0.842412\pi$
$653$	−44.9713	−1.75986	−0.879932	+	0.475100i	$0.842412\pi$
$654$	0.530825	0.0207569
$655$	−1.21227	−0.0473675
$656$	4.10177	0.160147
$657$	30.8091	1.20198
$658$	−16.2385	−0.633041
$659$	20.0386	0.780592	0.390296	−	0.920690i	$-0.372373\pi$
$659$	20.0386	0.780592	0.390296	+	0.920690i	$0.372373\pi$
$660$	0.00871666	0.000339296 0
$661$	9.50497	0.369701	0.184850	−	0.982767i	$-0.440820\pi$
$661$	9.50497	0.369701	0.184850	+	0.982767i	$0.440820\pi$
$662$	−3.41510	−0.132732
$663$	0.00956706	0.000371554 0
$664$	−44.0765	−1.71050
$665$	−2.86264	−0.111008
$666$	12.6626	0.490667
$667$	0	0
$668$	−9.07456	−0.351105
$669$	−0.0101594	−0.000392784 0
$670$	−1.20378	−0.0465062
$671$	2.95777	0.114183
$672$	0.233971	0.00902562
$673$	8.59001	0.331120	0.165560	−	0.986200i	$-0.447057\pi$
$673$	8.59001	0.331120	0.165560	+	0.986200i	$0.447057\pi$
$674$	3.14209	0.121029
$675$	−1.30326	−0.0501625
$676$	4.40223	0.169317
$677$	−13.3716	−0.513914	−0.256957	−	0.966423i	$-0.582720\pi$
$677$	−13.3716	−0.513914	−0.256957	+	0.966423i	$0.582720\pi$
$678$	−0.791308	−0.0303900
$679$	−10.0898	−0.387211
$680$	0.0655784	0.00251482
$681$	−0.896287	−0.0343458
$682$	−4.50090	−0.172348
$683$	24.8017	0.949011	0.474505	−	0.880253i	$-0.342627\pi$
$683$	24.8017	0.949011	0.474505	+	0.880253i	$0.342627\pi$
$684$	−18.5053	−0.707569
$685$	−0.0327905	−0.00125286
$686$	18.1550	0.693161
$687$	−0.0560103	−0.00213693
$688$	−18.2344	−0.695179
$689$	−15.3123	−0.583354
$690$	0	0
$691$	38.8702	1.47869	0.739345	−	0.673326i	$-0.235135\pi$
$691$	38.8702	1.47869	0.739345	+	0.673326i	$0.235135\pi$
$692$	−17.3817	−0.660754
$693$	−3.98378	−0.151331
$694$	4.60837	0.174931
$695$	1.79543	0.0681046
$696$	0.627057	0.0237685
$697$	−0.172754	−0.00654351
$698$	12.8056	0.484698
$699$	−0.541209	−0.0204704
$700$	−4.93276	−0.186441
$701$	39.5309	1.49306	0.746531	−	0.665351i	$-0.231718\pi$
$701$	39.5309	1.49306	0.746531	+	0.665351i	$0.231718\pi$
$702$	−0.789386	−0.0297935
$703$	31.0082	1.16950
$704$	−8.31760	−0.313481
$705$	0.126700	0.00477179
$706$	−0.293094	−0.0110307
$707$	2.29867	0.0864505
$708$	−0.306989	−0.0115374
$709$	39.8304	1.49586	0.747931	−	0.663776i	$-0.231047\pi$
$709$	39.8304	1.49586	0.747931	+	0.663776i	$0.231047\pi$
$710$	4.10500	0.154058
$711$	−28.5879	−1.07213
$712$	−16.4265	−0.615609
$713$	0	0
$714$	0.00530842	0.000198663 0
$715$	−0.702728	−0.0262805
$716$	13.1324	0.490782
$717$	0.571017	0.0213250
$718$	1.55240	0.0579350
$719$	−51.3075	−1.91345	−0.956723	−	0.291001i	$-0.906012\pi$
$719$	−51.3075	−1.91345	−0.956723	+	0.291001i	$0.906012\pi$
$720$	−1.51846	−0.0565897
$721$	−5.11959	−0.190664
$722$	53.8517	2.00415
$723$	−1.05903	−0.0393856
$724$	−3.75759	−0.139650
$725$	−22.8248	−0.847693
$726$	−0.0492096	−0.00182634
$727$	−47.1718	−1.74950	−0.874752	−	0.484571i	$-0.838976\pi$
$727$	−47.1718	−1.74950	−0.874752	+	0.484571i	$0.838976\pi$
$728$	−10.9251	−0.404912
$729$	−26.8952	−0.996119
$730$	3.01549	0.111608
$731$	0.767974	0.0284045
$732$	−0.0981197	−0.00362661
$733$	−11.6137	−0.428961	−0.214481	−	0.976728i	$-0.568806\pi$
$733$	−11.6137	−0.428961	−0.214481	+	0.976728i	$0.568806\pi$
$734$	−13.8044	−0.509529
$735$	−0.0606049	−0.00223545
$736$	0	0
$737$	−4.10232	−0.151111
$738$	7.12471	0.262264
$739$	−22.3209	−0.821086	−0.410543	−	0.911841i	$-0.634661\pi$
$739$	−22.3209	−0.821086	−0.410543	+	0.911841i	$0.634661\pi$
$740$	−0.748143	−0.0275023
$741$	−0.966209	−0.0354946
$742$	−8.49628	−0.311908
$743$	−7.11611	−0.261065	−0.130532	−	0.991444i	$-0.541669\pi$
$743$	−7.11611	−0.261065	−0.130532	+	0.991444i	$0.541669\pi$
$744$	0.545971	0.0200163
$745$	3.23606	0.118560
$746$	−15.5382	−0.568896
$747$	−42.9839	−1.57270
$748$	0.0611173	0.00223467
$749$	−6.09189	−0.222593
$750$	−0.128410	−0.00468887
$751$	46.7731	1.70677	0.853387	−	0.521278i	$-0.174545\pi$
$751$	46.7731	1.70677	0.853387	+	0.521278i	$0.174545\pi$
$752$	−21.0928	−0.769175
$753$	0.744809	0.0271424
$754$	−13.8250	−0.503478
$755$	2.30935	0.0840459
$756$	0.264398	0.00961606
$757$	−20.7933	−0.755746	−0.377873	−	0.925858i	$-0.623344\pi$
$757$	−20.7933	−0.755746	−0.377873	+	0.925858i	$0.623344\pi$
$758$	18.2628	0.663334
$759$	0	0
$760$	−6.62298	−0.240241
$761$	30.1482	1.09287	0.546436	−	0.837501i	$-0.315984\pi$
$761$	30.1482	1.09287	0.546436	+	0.837501i	$0.315984\pi$
$762$	0.717376	0.0259878
$763$	14.3336	0.518913
$764$	−9.74126	−0.352426
$765$	0.0639527	0.00231222
$766$	−14.5290	−0.524954
$767$	24.7491	0.893639
$768$	0.669200	0.0241477
$769$	−15.3741	−0.554406	−0.277203	−	0.960811i	$-0.589407\pi$
$769$	−15.3741	−0.554406	−0.277203	+	0.960811i	$0.589407\pi$
$770$	−0.389919	−0.0140517
$771$	0.00882712	0.000317901 0
$772$	12.1530	0.437396
$773$	47.1711	1.69663	0.848313	−	0.529495i	$-0.177619\pi$
$773$	47.1711	1.69663	0.848313	+	0.529495i	$0.177619\pi$
$774$	−31.6728	−1.13846
$775$	−19.8733	−0.713870
$776$	−23.3437	−0.837989
$777$	−0.221446	−0.00794431
$778$	38.2591	1.37165
$779$	17.4470	0.625102
$780$	0.0233120	0.000834703 0
$781$	13.9892	0.500574
$782$	0	0
$783$	1.22342	0.0437215
$784$	10.0894	0.360336
$785$	6.18256	0.220665
$786$	−0.227035	−0.00809806
$787$	−0.0705773	−0.00251581	−0.00125790	−	0.999999i	$-0.500400\pi$
$787$	−0.0705773	−0.00251581	−0.00125790	+	0.999999i	$0.500400\pi$
$788$	4.18193	0.148975
$789$	−0.329917	−0.0117453
$790$	−2.79809	−0.0995516
$791$	−21.3674	−0.759736
$792$	−9.21684	−0.327506
$793$	7.91031	0.280903
$794$	−19.4290	−0.689509
$795$	0.0662917	0.00235113
$796$	15.6075	0.553192
$797$	−23.8335	−0.844224	−0.422112	−	0.906544i	$-0.638711\pi$
$797$	−23.8335	−0.844224	−0.422112	+	0.906544i	$0.638711\pi$
$798$	−0.536115	−0.0189783
$799$	0.888361	0.0314280
$800$	−19.7037	−0.696633
$801$	−16.0193	−0.566013
$802$	−27.1601	−0.959055
$803$	10.2763	0.362644
$804$	0.136089	0.00479947
$805$	0	0
$806$	−12.0373	−0.423995
$807$	−0.388170	−0.0136642
$808$	5.31819	0.187093
$809$	34.3206	1.20665	0.603325	−	0.797496i	$-0.293842\pi$
$809$	34.3206	1.20665	0.603325	+	0.797496i	$0.293842\pi$
$810$	−2.63583	−0.0926137
$811$	24.4113	0.857196	0.428598	−	0.903495i	$-0.359008\pi$
$811$	24.4113	0.857196	0.428598	+	0.903495i	$0.359008\pi$
$812$	4.63058	0.162501
$813$	−1.09772	−0.0384989
$814$	4.22361	0.148037
$815$	−4.23055	−0.148190
$816$	0.00689532	0.000241385 0
$817$	−77.5602	−2.71349
$818$	−30.5607	−1.06853
$819$	−10.6543	−0.372291
$820$	−0.420948	−0.0147001
$821$	9.48170	0.330914	0.165457	−	0.986217i	$-0.447090\pi$
$821$	9.48170	0.330914	0.165457	+	0.986217i	$0.447090\pi$
$822$	−0.00614100	−0.000214192 0
$823$	21.3644	0.744715	0.372358	−	0.928089i	$-0.378549\pi$
$823$	21.3644	0.744715	0.372358	+	0.928089i	$0.378549\pi$
$824$	−11.8446	−0.412628
$825$	−0.217280	−0.00756472
$826$	13.7324	0.477812
$827$	37.0040	1.28675	0.643377	−	0.765549i	$-0.277533\pi$
$827$	37.0040	1.28675	0.643377	+	0.765549i	$0.277533\pi$
$828$	0	0
$829$	−28.0334	−0.973639	−0.486820	−	0.873502i	$-0.661843\pi$
$829$	−28.0334	−0.973639	−0.486820	+	0.873502i	$0.661843\pi$
$830$	−4.20711	−0.146031
$831$	−1.04226	−0.0361555
$832$	−22.2447	−0.771197
$833$	−0.424934	−0.0147231
$834$	0.336248	0.0116433
$835$	−3.16723	−0.109607
$836$	−6.17244	−0.213478
$837$	1.06522	0.0368193
$838$	−26.5765	−0.918068
$839$	−31.1731	−1.07622	−0.538108	−	0.842876i	$-0.680861\pi$
$839$	−31.1731	−1.07622	−0.538108	+	0.842876i	$0.680861\pi$
$840$	0.0472982	0.00163194
$841$	−7.57342	−0.261152
$842$	−2.59669	−0.0894879
$843$	−0.856529	−0.0295004
$844$	15.4477	0.531732
$845$	1.53648	0.0528566
$846$	−36.6378	−1.25963
$847$	−1.32879	−0.0456577
$848$	−11.0361	−0.378983
$849$	−0.942012	−0.0323298
$850$	−0.447047	−0.0153336
$851$	0	0
$852$	−0.464072	−0.0158989
$853$	−0.982475	−0.0336393	−0.0168197	−	0.999859i	$-0.505354\pi$
$853$	−0.982475	−0.0336393	−0.0168197	+	0.999859i	$0.505354\pi$
$854$	4.38915	0.150194
$855$	−6.45880	−0.220886
$856$	−14.0941	−0.481728
$857$	−50.9881	−1.74172	−0.870861	−	0.491530i	$-0.836438\pi$
$857$	−50.9881	−1.74172	−0.870861	+	0.491530i	$0.836438\pi$
$858$	−0.131607	−0.00449299
$859$	30.3592	1.03584	0.517922	−	0.855428i	$-0.326706\pi$
$859$	30.3592	1.03584	0.517922	+	0.855428i	$0.326706\pi$
$860$	1.87132	0.0638113
$861$	−0.124598	−0.00424628
$862$	−14.9540	−0.509334
$863$	12.5141	0.425984	0.212992	−	0.977054i	$-0.431679\pi$
$863$	12.5141	0.425984	0.212992	+	0.977054i	$0.431679\pi$
$864$	1.05613	0.0359302
$865$	−6.06664	−0.206272
$866$	19.8901	0.675894
$867$	0.748806	0.0254308
$868$	4.03178	0.136848
$869$	−9.53548	−0.323469
$870$	0.0598528	0.00202920
$871$	−10.9713	−0.371749
$872$	33.1622	1.12301
$873$	−22.7650	−0.770477
$874$	0	0
$875$	−3.46741	−0.117220
$876$	−0.340903	−0.0115180
$877$	13.4628	0.454607	0.227303	−	0.973824i	$-0.427009\pi$
$877$	13.4628	0.454607	0.227303	+	0.973824i	$0.427009\pi$
$878$	−12.2830	−0.414531
$879$	−0.299287	−0.0100947
$880$	−0.506481	−0.0170735
$881$	−0.512545	−0.0172681	−0.00863404	−	0.999963i	$-0.502748\pi$
$881$	−0.512545	−0.0172681	−0.00863404	+	0.999963i	$0.502748\pi$
$882$	17.5251	0.590102
$883$	−4.92816	−0.165846	−0.0829230	−	0.996556i	$-0.526426\pi$
$883$	−4.92816	−0.165846	−0.0829230	+	0.996556i	$0.526426\pi$
$884$	0.163453	0.00549752
$885$	−0.107146	−0.00360169
$886$	12.8564	0.431919
$887$	15.3274	0.514644	0.257322	−	0.966326i	$-0.417160\pi$
$887$	15.3274	0.514644	0.257322	+	0.966326i	$0.417160\pi$
$888$	−0.512335	−0.0171928
$889$	19.3710	0.649683
$890$	−1.56791	−0.0525565
$891$	−8.98253	−0.300926
$892$	−0.173573	−0.00581164
$893$	−89.7185	−3.00232
$894$	0.606049	0.0202693
$895$	4.58353	0.153210
$896$	−1.72334	−0.0575728
$897$	0	0
$898$	2.35731	0.0786646
$899$	18.6558	0.622207
$900$	−11.1295	−0.370983
$901$	0.464807	0.0154850
$902$	2.37644	0.0791269
$903$	0.553898	0.0184326
$904$	−49.4354	−1.64420
$905$	−1.31149	−0.0435953
$906$	0.432495	0.0143687
$907$	3.98154	0.132205	0.0661025	−	0.997813i	$-0.478944\pi$
$907$	3.98154	0.132205	0.0661025	+	0.997813i	$0.478944\pi$
$908$	−15.3130	−0.508181
$909$	5.18635	0.172020
$910$	−1.04281	−0.0345687
$911$	−38.0364	−1.26020	−0.630102	−	0.776512i	$-0.716987\pi$
$911$	−38.0364	−1.26020	−0.630102	+	0.776512i	$0.716987\pi$
$912$	−0.696382	−0.0230595
$913$	−14.3372	−0.474493
$914$	7.93873	0.262590
$915$	−0.0342461	−0.00113214
$916$	−0.956936	−0.0316181
$917$	−6.13053	−0.202448
$918$	0.0239619	0.000790860 0
$919$	17.7269	0.584756	0.292378	−	0.956303i	$-0.405553\pi$
$919$	17.7269	0.584756	0.292378	+	0.956303i	$0.405553\pi$
$920$	0	0
$921$	0.143266	0.00472077
$922$	−19.5545	−0.643994
$923$	37.4130	1.23146
$924$	0.0440806	0.00145014
$925$	18.6489	0.613173
$926$	−2.35647	−0.0774383
$927$	−11.5510	−0.379385
$928$	18.4967	0.607184
$929$	27.1909	0.892104	0.446052	−	0.895007i	$-0.352830\pi$
$929$	27.1909	0.892104	0.446052	+	0.895007i	$0.352830\pi$
$930$	0.0521130	0.00170885
$931$	42.9155	1.40650
$932$	−9.24654	−0.302880
$933$	−0.546672	−0.0178972
$934$	16.2729	0.532464
$935$	0.0213314	0.000697611 0
$936$	−24.6497	−0.805700
$937$	24.1656	0.789454	0.394727	−	0.918798i	$-0.370839\pi$
$937$	24.1656	0.789454	0.394727	+	0.918798i	$0.370839\pi$
$938$	−6.08760	−0.198767
$939$	0.474562	0.0154867
$940$	2.16466	0.0706035
$941$	22.9768	0.749022	0.374511	−	0.927222i	$-0.377811\pi$
$941$	22.9768	0.749022	0.374511	+	0.927222i	$0.377811\pi$
$942$	1.15787	0.0377255
$943$	0	0
$944$	17.8376	0.580564
$945$	0.0922811	0.00300191
$946$	−10.5644	−0.343480
$947$	54.3648	1.76662	0.883310	−	0.468789i	$-0.155310\pi$
$947$	54.3648	1.76662	0.883310	+	0.468789i	$0.155310\pi$
$948$	0.316326	0.0102738
$949$	27.4832	0.892143
$950$	45.1487	1.46482
$951$	−0.889036	−0.0288290
$952$	0.331633	0.0107483
$953$	−1.66758	−0.0540182	−0.0270091	−	0.999635i	$-0.508598\pi$
$953$	−1.66758	−0.0540182	−0.0270091	+	0.999635i	$0.508598\pi$
$954$	−19.1696	−0.620639
$955$	−3.39993	−0.110019
$956$	9.75582	0.315526
$957$	0.203969	0.00659340
$958$	2.03646	0.0657950
$959$	−0.165823	−0.00535470
$960$	0.0963041	0.00310820
$961$	−14.7566	−0.476019
$962$	11.2957	0.364188
$963$	−13.7448	−0.442918
$964$	−18.0934	−0.582751
$965$	4.24168	0.136545
$966$	0	0
$967$	38.2229	1.22916	0.614582	−	0.788853i	$-0.289325\pi$
$967$	38.2229	1.22916	0.614582	+	0.788853i	$0.289325\pi$
$968$	−3.07427	−0.0988108
$969$	0.0293294	0.000942195 0
$970$	−2.22816	−0.0715419
$971$	25.7891	0.827612	0.413806	−	0.910365i	$-0.364199\pi$
$971$	25.7891	0.827612	0.413806	+	0.910365i	$0.364199\pi$
$972$	0.894913	0.0287044
$973$	9.07958	0.291078
$974$	−23.2544	−0.745120
$975$	−0.581098	−0.0186100
$976$	5.70124	0.182492
$977$	38.1754	1.22134	0.610670	−	0.791885i	$-0.290900\pi$
$977$	38.1754	1.22134	0.610670	+	0.791885i	$0.290900\pi$
$978$	−0.792298	−0.0253349
$979$	−5.34322	−0.170770
$980$	−1.03543	−0.0330757
$981$	32.3401	1.03254
$982$	−4.56830	−0.145780
$983$	−10.1268	−0.322994	−0.161497	−	0.986873i	$-0.551632\pi$
$983$	−10.1268	−0.322994	−0.161497	+	0.986873i	$0.551632\pi$
$984$	−0.288269	−0.00918966
$985$	1.45959	0.0465064
$986$	0.419660	0.0133647
$987$	0.640727	0.0203946
$988$	−16.5077	−0.525179
$989$	0	0
$990$	−0.879750	−0.0279603
$991$	−17.3994	−0.552710	−0.276355	−	0.961056i	$-0.589126\pi$
$991$	−17.3994	−0.552710	−0.276355	+	0.961056i	$0.589126\pi$
$992$	16.1048	0.511329
$993$	0.134751	0.00427618
$994$	20.7592	0.658440
$995$	5.44738	0.172694
$996$	0.475617	0.0150705
$997$	33.5571	1.06277	0.531383	−	0.847132i	$-0.321673\pi$
$997$	33.5571	1.06277	0.531383	+	0.847132i	$0.321673\pi$
$998$	−30.0191	−0.950239
$999$	−0.999591	−0.0316257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.o.1.13	yes	18
23.22	odd	2		5819.2.a.n.1.13	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5819.2.a.n.1.13	✓	18	23.22	odd	2
5819.2.a.o.1.13	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q+1.11676 q^{2} -0.0440645 q^{3} -0.752841 q^{4} -0.262759 q^{5} -0.0492096 q^{6} -1.32879 q^{7} -3.07427 q^{8} -2.99806 q^{9} -0.293440 q^{10} -1.00000 q^{11} +0.0331736 q^{12} -2.67442 q^{13} -1.48394 q^{14} +0.0115784 q^{15} -1.92755 q^{16} +0.0811822 q^{17} -3.34812 q^{18} -8.19886 q^{19} +0.197816 q^{20} +0.0585523 q^{21} -1.11676 q^{22} +0.135466 q^{24} -4.93096 q^{25} -2.98669 q^{26} +0.264301 q^{27} +1.00037 q^{28} +4.62889 q^{29} +0.0129303 q^{30} +4.03031 q^{31} +3.99593 q^{32} +0.0440645 q^{33} +0.0906612 q^{34} +0.349151 q^{35} +2.25706 q^{36} -3.78201 q^{37} -9.15618 q^{38} +0.117847 q^{39} +0.807793 q^{40} -2.12797 q^{41} +0.0653890 q^{42} +9.45988 q^{43} +0.752841 q^{44} +0.787768 q^{45} +10.9428 q^{47} +0.0849364 q^{48} -5.23433 q^{49} -5.50671 q^{50} -0.00357725 q^{51} +2.01341 q^{52} +5.72549 q^{53} +0.295162 q^{54} +0.262759 q^{55} +4.08505 q^{56} +0.361278 q^{57} +5.16937 q^{58} -9.25403 q^{59} -0.00871666 q^{60} -2.95777 q^{61} +4.50090 q^{62} +3.98378 q^{63} +8.31760 q^{64} +0.702728 q^{65} +0.0492096 q^{66} +4.10232 q^{67} -0.0611173 q^{68} +0.389919 q^{70} -13.9892 q^{71} +9.21684 q^{72} -10.2763 q^{73} -4.22361 q^{74} +0.217280 q^{75} +6.17244 q^{76} +1.32879 q^{77} +0.131607 q^{78} +9.53548 q^{79} +0.506481 q^{80} +8.98253 q^{81} -2.37644 q^{82} +14.3372 q^{83} -0.0440806 q^{84} -0.0213314 q^{85} +10.5644 q^{86} -0.203969 q^{87} +3.07427 q^{88} +5.34322 q^{89} +0.879750 q^{90} +3.55373 q^{91} -0.177594 q^{93} +12.2205 q^{94} +2.15433 q^{95} -0.176078 q^{96} +7.59324 q^{97} -5.84550 q^{98} +2.99806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 2 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} + 10 q^{7} + 6 q^{8} + 16 q^{9} + 12 q^{10} - 18 q^{11} + 10 q^{12} + 28 q^{14} + 8 q^{15} + 26 q^{16} - 20 q^{18} + 16 q^{19} + 40 q^{20} + 12 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) \) 18 * q + 2 * q^2 - 2 * q^3 + 18 * q^4 + 8 * q^5 - 6 * q^6 + 10 * q^7 + 6 * q^8 + 16 * q^9 + 12 * q^10 - 18 * q^11 + 10 * q^12 + 28 * q^14 + 8 * q^15 + 26 * q^16 - 20 * q^18 + 16 * q^19 + 40 * q^20 + 12 * q^21 - 2 * q^22 + 26 * q^24 + 6 * q^25 - 20 * q^26 - 14 * q^27 + 32 * q^28 - 12 * q^29 + 14 * q^30 + 24 * q^32 + 2 * q^33 + 24 * q^34 + 2 * q^35 - 12 * q^36 + 36 * q^37 - 8 * q^38 - 10 * q^39 + 22 * q^40 + 6 * q^41 - 4 * q^42 + 20 * q^43 - 18 * q^44 - 16 * q^45 - 36 * q^47 + 28 * q^48 + 4 * q^49 + 52 * q^50 + 44 * q^51 - 16 * q^52 + 20 * q^53 - 8 * q^54 - 8 * q^55 + 40 * q^56 + 44 * q^57 + 2 * q^58 - 32 * q^59 + 88 * q^60 + 20 * q^61 + 2 * q^63 + 10 * q^64 - 40 * q^65 + 6 * q^66 - 12 * q^68 + 14 * q^70 - 28 * q^71 - 38 * q^72 - 16 * q^73 + 40 * q^74 + 16 * q^75 + 34 * q^76 - 10 * q^77 - 72 * q^78 + 40 * q^79 + 28 * q^80 + 18 * q^81 + 24 * q^82 + 32 * q^83 - 74 * q^84 - 12 * q^85 - 20 * q^86 + 46 * q^87 - 6 * q^88 + 88 * q^89 + 32 * q^90 - 32 * q^91 - 24 * q^93 - 22 * q^94 + 58 * q^95 + 10 * q^96 + 52 * q^97 + 82 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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