LMFDB - Embedded newform 5819.2.a.n.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:	$1$
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	$-0.481287\pi$
$5$	0.262759	0.117510	0.0587548	+	0.998272i	$0.481287\pi$
$6$	−0.0492096	−0.0200897
$7$	1.32879	0.502234	0.251117	−	0.967957i	$-0.419202\pi$
$7$	1.32879	0.502234	0.251117	+	0.967957i	$0.419202\pi$
$8$	−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	$-0.503134\pi$
$17$	−0.0811822	−0.0196896	−0.00984479	+	0.999952i	$0.503134\pi$
$18$	−3.34812	−0.789159
$19$	8.19886	1.88095	0.940473	−	0.339867i	$-0.110382\pi$
$19$	8.19886	1.88095	0.940473	+	0.339867i	$0.110382\pi$
$20$	−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	$-0.399376\pi$
$37$	3.78201	0.621759	0.310879	+	0.950449i	$0.399376\pi$
$38$	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	$-0.756459\pi$
$43$	−9.45988	−1.44262	−0.721309	+	0.692613i	$0.756459\pi$
$44$	−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	$-0.628642\pi$
$53$	−5.72549	−0.786456	−0.393228	+	0.919441i	$0.628642\pi$
$54$	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	$-0.439361\pi$
$61$	2.95777	0.378703	0.189352	+	0.981909i	$0.439361\pi$
$62$	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	$-0.580624\pi$
$67$	−4.10232	−0.501178	−0.250589	+	0.968094i	$0.580624\pi$
$68$	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	$-0.680221\pi$
$79$	−9.53548	−1.07283	−0.536413	+	0.843956i	$0.680221\pi$
$80$	−0.506481	−0.0566263
$81$	8.98253	0.998059
$82$	−2.37644	−0.262434
$83$	−14.3372	−1.57372	−0.786858	−	0.617134i	$-0.788293\pi$
$83$	−14.3372	−1.57372	−0.786858	+	0.617134i	$0.788293\pi$
$84$	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	$-0.591393\pi$
$89$	−5.34322	−0.566380	−0.283190	+	0.959064i	$0.591393\pi$
$90$	−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	$-0.625967\pi$
$97$	−7.59324	−0.770976	−0.385488	+	0.922713i	$0.625967\pi$
$98$	−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	$-0.560789\pi$
$103$	−3.85283	−0.379631	−0.189815	+	0.981820i	$0.560789\pi$
$104$	8.22188	0.806222
$105$	−0.0153852	−0.00150144
$106$	−6.39401	−0.621041
$107$	−4.58455	−0.443205	−0.221603	−	0.975137i	$-0.571129\pi$
$107$	−4.58455	−0.443205	−0.221603	+	0.975137i	$0.571129\pi$
$108$	−0.198977	−0.0191466
$109$	10.7870	1.03321	0.516604	−	0.856224i	$-0.327196\pi$
$109$	10.7870	1.03321	0.516604	+	0.856224i	$0.327196\pi$
$110$	0.293440	0.0279784
$111$	−0.166652	−0.0158179
$112$	−2.56130	−0.242020
$113$	−16.0804	−1.51271	−0.756357	−	0.654160i	$-0.773022\pi$
$113$	−16.0804	−1.51271	−0.756357	+	0.654160i	$0.773022\pi$
$114$	−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	$-0.501697\pi$
$137$	−0.124793	−0.0106618	−0.00533088	+	0.999986i	$0.501697\pi$
$138$	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	$-0.331688\pi$
$149$	12.3157	1.00894	0.504469	+	0.863430i	$0.331688\pi$
$150$	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	$-0.111824\pi$
$157$	23.5294	1.87785	0.938924	+	0.344124i	$0.111824\pi$
$158$	−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	$-0.559389\pi$
$181$	−4.99121	−0.370994	−0.185497	+	0.982645i	$0.559389\pi$
$182$	−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	$-0.655072\pi$
$191$	−12.9393	−0.936257	−0.468128	+	0.883660i	$0.655072\pi$
$192$	−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	$-0.237273\pi$
$199$	20.7314	1.46961	0.734806	+	0.678277i	$0.237273\pi$
$200$	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	$-0.735864\pi$
$227$	−20.3403	−1.35004	−0.675018	+	0.737801i	$0.735864\pi$
$228$	0.271985	0.0180127
$229$	−1.27110	−0.0839966	−0.0419983	−	0.999118i	$-0.513372\pi$
$229$	−1.27110	−0.0839966	−0.0419983	+	0.999118i	$0.513372\pi$
$230$	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	$-0.781782\pi$
$241$	−24.0336	−1.54814	−0.774069	+	0.633102i	$0.781782\pi$
$242$	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	$-0.320897\pi$
$251$	16.9027	1.06689	0.533445	+	0.845835i	$0.320897\pi$
$252$	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	$-0.574147\pi$
$263$	−7.48713	−0.461676	−0.230838	+	0.972992i	$0.574147\pi$
$264$	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	$-0.696865\pi$
$281$	−19.4381	−1.15958	−0.579789	+	0.814766i	$0.696865\pi$
$282$	−0.538491	−0.0320667
$283$	−21.3780	−1.27079	−0.635396	−	0.772187i	$-0.719163\pi$
$283$	−21.3780	−1.27079	−0.635396	+	0.772187i	$0.719163\pi$
$284$	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	$-0.563574\pi$
$293$	−6.79202	−0.396794	−0.198397	+	0.980122i	$0.563574\pi$
$294$	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	$-0.401554\pi$
$313$	10.7697	0.608740	0.304370	+	0.952554i	$0.401554\pi$
$314$	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	$-0.524417\pi$
$337$	−2.81357	−0.153265	−0.0766325	+	0.997059i	$0.524417\pi$
$338$	−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	$-0.511679\pi$
$359$	−1.39009	−0.0733661	−0.0366830	+	0.999327i	$0.511679\pi$
$360$	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	$-0.395436\pi$
$367$	12.3611	0.645243	0.322621	+	0.946528i	$0.395436\pi$
$368$	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	$-0.382705\pi$
$373$	13.9136	0.720421	0.360211	+	0.932871i	$0.382705\pi$
$374$	−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	$-0.637972\pi$
$379$	−16.3533	−0.840014	−0.420007	+	0.907521i	$0.637972\pi$
$380$	−1.62187	−0.0832000
$381$	0.642371	0.0329097
$382$	−14.4502	−0.739334
$383$	13.0099	0.664776	0.332388	−	0.943143i	$-0.392146\pi$
$383$	13.0099	0.664776	0.332388	+	0.943143i	$0.392146\pi$
$384$	−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	$-0.834914\pi$
$389$	−34.2589	−1.73700	−0.868498	+	0.495692i	$0.834914\pi$
$390$	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	$-0.292273\pi$
$401$	24.3204	1.21450	0.607250	+	0.794511i	$0.292273\pi$
$402$	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	$-0.302545\pi$
$419$	23.7978	1.16260	0.581298	+	0.813690i	$0.302545\pi$
$420$	0.0115826	0.000565172 0
$421$	2.32520	0.113323	0.0566615	−	0.998393i	$-0.481954\pi$
$421$	2.32520	0.113323	0.0566615	+	0.998393i	$0.481954\pi$
$422$	−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	$-0.395478\pi$
$431$	13.3904	0.644995	0.322498	+	0.946570i	$0.395478\pi$
$432$	−0.509454	−0.0245111
$433$	−17.8105	−0.855919	−0.427959	−	0.903798i	$-0.640767\pi$
$433$	−17.8105	−0.855919	−0.427959	+	0.903798i	$0.640767\pi$
$434$	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	$-0.553171\pi$
$457$	−7.10870	−0.332531	−0.166265	+	0.986081i	$0.553171\pi$
$458$	−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	$-0.609461\pi$
$467$	−14.5714	−0.674286	−0.337143	+	0.941453i	$0.609461\pi$
$468$	−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	$-0.513265\pi$
$479$	−1.82354	−0.0833196	−0.0416598	+	0.999132i	$0.513265\pi$
$480$	−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	$-0.399974\pi$
$503$	13.8646	0.618190	0.309095	+	0.951031i	$0.399974\pi$
$504$	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	$-0.491873\pi$
$521$	1.16536	0.0510553	0.0255276	+	0.999674i	$0.491873\pi$
$522$	−15.4981	−0.678332
$523$	37.2747	1.62991	0.814954	−	0.579526i	$-0.196762\pi$
$523$	37.2747	1.62991	0.814954	+	0.579526i	$0.196762\pi$
$524$	−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	$-0.259358\pi$
$557$	32.3811	1.37203	0.686015	+	0.727587i	$0.259358\pi$
$558$	−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	$-0.603354\pi$
$563$	−15.1392	−0.638042	−0.319021	+	0.947748i	$0.603354\pi$
$564$	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	$-0.734723\pi$
$569$	−32.0770	−1.34474	−0.672370	+	0.740216i	$0.734723\pi$
$570$	−0.106013	−0.00444042
$571$	−31.2100	−1.30610	−0.653050	−	0.757315i	$-0.726511\pi$
$571$	−31.2100	−1.30610	−0.653050	+	0.757315i	$0.726511\pi$
$572$	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	$-0.467627\pi$
$613$	5.02740	0.203055	0.101527	+	0.994833i	$0.467627\pi$
$614$	−3.63090	−0.146531
$615$	0.0246385	0.000993518 0
$616$	−4.08505	−0.164591
$617$	−39.7035	−1.59840	−0.799201	−	0.601063i	$-0.794744\pi$
$617$	−39.7035	−1.59840	−0.799201	+	0.601063i	$0.794744\pi$
$618$	0.189596	0.00762668
$619$	−11.9841	−0.481683	−0.240841	−	0.970564i	$-0.577423\pi$
$619$	−11.9841	−0.481683	−0.240841	+	0.970564i	$0.577423\pi$
$620$	−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	$-0.720649\pi$
$631$	−32.1027	−1.27799	−0.638994	+	0.769211i	$0.720649\pi$
$632$	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	$-0.486100\pi$
$641$	2.21045	0.0873077	0.0436538	+	0.999047i	$0.486100\pi$
$642$	0.225604	0.00890387
$643$	38.2964	1.51026	0.755131	−	0.655574i	$-0.227573\pi$
$643$	38.2964	1.51026	0.755131	+	0.655574i	$0.227573\pi$
$644$	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	$-0.627627\pi$
$659$	−20.0386	−0.780592	−0.390296	+	0.920690i	$0.627627\pi$
$660$	0.00871666	0.000339296 0
$661$	−9.50497	−0.369701	−0.184850	−	0.982767i	$-0.559180\pi$
$661$	−9.50497	−0.369701	−0.184850	+	0.982767i	$0.559180\pi$
$662$	−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	$-0.417280\pi$
$677$	13.3716	0.513914	0.256957	+	0.966423i	$0.417280\pi$
$678$	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	$-0.768282\pi$
$701$	−39.5309	−1.49306	−0.746531	+	0.665351i	$0.768282\pi$
$702$	−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	$-0.768953\pi$
$709$	−39.8304	−1.49586	−0.747931	+	0.663776i	$0.768953\pi$
$710$	−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	$-0.161024\pi$
$727$	47.1718	1.74950	0.874752	+	0.484571i	$0.161024\pi$
$728$	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	$-0.431194\pi$
$733$	11.6137	0.428961	0.214481	+	0.976728i	$0.431194\pi$
$734$	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	$-0.458331\pi$
$743$	7.11611	0.261065	0.130532	+	0.991444i	$0.458331\pi$
$744$	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	$-0.825455\pi$
$751$	−46.7731	−1.70677	−0.853387	+	0.521278i	$0.825455\pi$
$752$	−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	$-0.376656\pi$
$757$	20.7933	0.755746	0.377873	+	0.925858i	$0.376656\pi$
$758$	−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	$-0.410593\pi$
$769$	15.3741	0.554406	0.277203	+	0.960811i	$0.410593\pi$
$770$	0.389919	0.0140517
$771$	0.00882712	0.000317901 0
$772$	12.1530	0.437396
$773$	−47.1711	−1.69663	−0.848313	−	0.529495i	$-0.822381\pi$
$773$	−47.1711	−1.69663	−0.848313	+	0.529495i	$0.822381\pi$
$774$	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	$-0.499600\pi$
$787$	0.0705773	0.00251581	0.00125790	+	0.999999i	$0.499600\pi$
$788$	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	$-0.361289\pi$
$797$	23.8335	0.844224	0.422112	+	0.906544i	$0.361289\pi$
$798$	−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	$-0.722467\pi$
$827$	−37.0040	−1.28675	−0.643377	+	0.765549i	$0.722467\pi$
$828$	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	$-0.319139\pi$
$839$	31.1731	1.07622	0.538108	+	0.842876i	$0.319139\pi$
$840$	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	$-0.497252\pi$
$881$	0.512545	0.0172681	0.00863404	+	0.999963i	$0.497252\pi$
$882$	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	$-0.521056\pi$
$907$	−3.98154	−0.132205	−0.0661025	+	0.997813i	$0.521056\pi$
$908$	15.3130	0.508181
$909$	5.18635	0.172020
$910$	−1.04281	−0.0345687
$911$	38.0364	1.26020	0.630102	−	0.776512i	$-0.283013\pi$
$911$	38.0364	1.26020	0.630102	+	0.776512i	$0.283013\pi$
$912$	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	$-0.594447\pi$
$919$	−17.7269	−0.584756	−0.292378	+	0.956303i	$0.594447\pi$
$920$	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	$-0.629161\pi$
$937$	−24.1656	−0.789454	−0.394727	+	0.918798i	$0.629161\pi$
$938$	−6.08760	−0.198767
$939$	−0.474562	−0.0154867
$940$	−2.16466	−0.0706035
$941$	−22.9768	−0.749022	−0.374511	−	0.927222i	$-0.622189\pi$
$941$	−22.9768	−0.749022	−0.374511	+	0.927222i	$0.622189\pi$
$942$	−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	$-0.491402\pi$
$953$	1.66758	0.0540182	0.0270091	+	0.999635i	$0.491402\pi$
$954$	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	$-0.635801\pi$
$971$	−25.7891	−0.827612	−0.413806	+	0.910365i	$0.635801\pi$
$972$	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	$-0.709100\pi$
$977$	−38.1754	−1.22134	−0.610670	+	0.791885i	$0.709100\pi$
$978$	−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	$-0.448368\pi$
$983$	10.1268	0.322994	0.161497	+	0.986873i	$0.448368\pi$
$984$	−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.n.1.13	✓	18
23.22	odd	2		5819.2.a.o.1.13	yes	18

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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