LMFDB - Embedded newform 3549.2.a.be.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 $ x^9 - x^8 - 11x^7 + 8x^6 + 37x^5 - 18x^4 - 41x^3 + 12x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.43930$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} +2.86638 q^{5} +1.43930 q^{6} +1.00000 q^{7} +2.77556 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} +2.86638 q^{5} +1.43930 q^{6} +1.00000 q^{7} +2.77556 q^{8} +1.00000 q^{9} -4.12559 q^{10} +0.920607 q^{11} -0.0715948 q^{12} -1.43930 q^{14} -2.86638 q^{15} -4.13806 q^{16} +2.98468 q^{17} -1.43930 q^{18} +7.98255 q^{19} +0.205218 q^{20} -1.00000 q^{21} -1.32503 q^{22} -4.01590 q^{23} -2.77556 q^{24} +3.21612 q^{25} -1.00000 q^{27} +0.0715948 q^{28} +1.05024 q^{29} +4.12559 q^{30} +3.15556 q^{31} +0.404809 q^{32} -0.920607 q^{33} -4.29586 q^{34} +2.86638 q^{35} +0.0715948 q^{36} +1.61715 q^{37} -11.4893 q^{38} +7.95580 q^{40} +6.54652 q^{41} +1.43930 q^{42} +11.4441 q^{43} +0.0659107 q^{44} +2.86638 q^{45} +5.78010 q^{46} +4.63900 q^{47} +4.13806 q^{48} +1.00000 q^{49} -4.62897 q^{50} -2.98468 q^{51} +6.68041 q^{53} +1.43930 q^{54} +2.63881 q^{55} +2.77556 q^{56} -7.98255 q^{57} -1.51162 q^{58} -9.98868 q^{59} -0.205218 q^{60} -8.95997 q^{61} -4.54181 q^{62} +1.00000 q^{63} +7.69348 q^{64} +1.32503 q^{66} -11.2659 q^{67} +0.213687 q^{68} +4.01590 q^{69} -4.12559 q^{70} +9.09996 q^{71} +2.77556 q^{72} -7.52599 q^{73} -2.32758 q^{74} -3.21612 q^{75} +0.571509 q^{76} +0.920607 q^{77} +6.24310 q^{79} -11.8613 q^{80} +1.00000 q^{81} -9.42243 q^{82} -9.66531 q^{83} -0.0715948 q^{84} +8.55521 q^{85} -16.4715 q^{86} -1.05024 q^{87} +2.55520 q^{88} -6.52667 q^{89} -4.12559 q^{90} -0.287518 q^{92} -3.15556 q^{93} -6.67693 q^{94} +22.8810 q^{95} -0.404809 q^{96} +0.561935 q^{97} -1.43930 q^{98} +0.920607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9	$ 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9} + q^{10} - q^{11} - 5 q^{12} - q^{14} - 9 q^{15} + 5 q^{16} + 11 q^{17} - q^{18} + 7 q^{19} + 23 q^{20} - 9 q^{21} - 3 q^{22} + 22 q^{23} + 6 q^{24} - 8 q^{25} - 9 q^{27} + 5 q^{28} + 11 q^{29} - q^{30} + 7 q^{31} - 18 q^{32} + q^{33} - 6 q^{34} + 9 q^{35} + 5 q^{36} - q^{37} - 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 32 q^{43} + 18 q^{44} + 9 q^{45} - 9 q^{46} - 12 q^{47} - 5 q^{48} + 9 q^{49} + 10 q^{50} - 11 q^{51} + 13 q^{53} + q^{54} + 9 q^{55} - 6 q^{56} - 7 q^{57} + 4 q^{58} + 29 q^{59} - 23 q^{60} - 12 q^{61} + 30 q^{62} + 9 q^{63} + 6 q^{64} + 3 q^{66} - 20 q^{67} + 34 q^{68} - 22 q^{69} + q^{70} - 2 q^{71} - 6 q^{72} + q^{73} + 43 q^{74} + 8 q^{75} + 13 q^{76} - q^{77} + 3 q^{79} - 39 q^{80} + 9 q^{81} - 19 q^{82} + 24 q^{83} - 5 q^{84} + 15 q^{85} - 28 q^{86} - 11 q^{87} - 19 q^{88} + 11 q^{89} + q^{90} + 73 q^{92} - 7 q^{93} + 15 q^{94} + 39 q^{95} + 18 q^{96} + 20 q^{97} - q^{98} - q^{99}+O(q^{100}) $ 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9 + q^10 - q^11 - 5 * q^12 - q^14 - 9 * q^15 + 5 * q^16 + 11 * q^17 - q^18 + 7 * q^19 + 23 * q^20 - 9 * q^21 - 3 * q^22 + 22 * q^23 + 6 * q^24 - 8 * q^25 - 9 * q^27 + 5 * q^28 + 11 * q^29 - q^30 + 7 * q^31 - 18 * q^32 + q^33 - 6 * q^34 + 9 * q^35 + 5 * q^36 - q^37 - 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 32 * q^43 + 18 * q^44 + 9 * q^45 - 9 * q^46 - 12 * q^47 - 5 * q^48 + 9 * q^49 + 10 * q^50 - 11 * q^51 + 13 * q^53 + q^54 + 9 * q^55 - 6 * q^56 - 7 * q^57 + 4 * q^58 + 29 * q^59 - 23 * q^60 - 12 * q^61 + 30 * q^62 + 9 * q^63 + 6 * q^64 + 3 * q^66 - 20 * q^67 + 34 * q^68 - 22 * q^69 + q^70 - 2 * q^71 - 6 * q^72 + q^73 + 43 * q^74 + 8 * q^75 + 13 * q^76 - q^77 + 3 * q^79 - 39 * q^80 + 9 * q^81 - 19 * q^82 + 24 * q^83 - 5 * q^84 + 15 * q^85 - 28 * q^86 - 11 * q^87 - 19 * q^88 + 11 * q^89 + q^90 + 73 * q^92 - 7 * q^93 + 15 * q^94 + 39 * q^95 + 18 * q^96 + 20 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.43930	−1.01774	−0.508871	−	0.860843i	$-0.669937\pi$
$2$	−1.43930	−1.01774	−0.508871	+	0.860843i	$0.669937\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0715948	0.0357974
$5$	2.86638	1.28188	0.640941	−	0.767590i	$-0.278544\pi$
$5$	2.86638	1.28188	0.640941	+	0.767590i	$0.278544\pi$
$6$	1.43930	0.587593
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.77556	0.981309
$9$	1.00000	0.333333
$10$	−4.12559	−1.30463
$11$	0.920607	0.277573	0.138787	−	0.990322i	$-0.455680\pi$
$11$	0.920607	0.277573	0.138787	+	0.990322i	$0.455680\pi$
$12$	−0.0715948	−0.0206676
$13$	0	0
$13$	0	0
$14$	−1.43930	−0.384670
$15$	−2.86638	−0.740095
$16$	−4.13806	−1.03452
$17$	2.98468	0.723890	0.361945	−	0.932199i	$-0.382113\pi$
$17$	2.98468	0.723890	0.361945	+	0.932199i	$0.382113\pi$
$18$	−1.43930	−0.339247
$19$	7.98255	1.83132	0.915661	−	0.401951i	$-0.131668\pi$
$19$	7.98255	1.83132	0.915661	+	0.401951i	$0.131668\pi$
$20$	0.205218	0.0458881
$21$	−1.00000	−0.218218
$22$	−1.32503	−0.282498
$23$	−4.01590	−0.837373	−0.418687	−	0.908131i	$-0.637509\pi$
$23$	−4.01590	−0.837373	−0.418687	+	0.908131i	$0.637509\pi$
$24$	−2.77556	−0.566559
$25$	3.21612	0.643223
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.0715948	0.0135302
$29$	1.05024	0.195025	0.0975126	−	0.995234i	$-0.468911\pi$
$29$	1.05024	0.195025	0.0975126	+	0.995234i	$0.468911\pi$
$30$	4.12559	0.753226
$31$	3.15556	0.566756	0.283378	−	0.959008i	$-0.408545\pi$
$31$	3.15556	0.566756	0.283378	+	0.959008i	$0.408545\pi$
$32$	0.404809	0.0715608
$33$	−0.920607	−0.160257
$34$	−4.29586	−0.736733
$35$	2.86638	0.484506
$36$	0.0715948	0.0119325
$37$	1.61715	0.265859	0.132929	−	0.991126i	$-0.457562\pi$
$37$	1.61715	0.265859	0.132929	+	0.991126i	$0.457562\pi$
$38$	−11.4893	−1.86381
$39$	0	0
$40$	7.95580	1.25792
$41$	6.54652	1.02239	0.511197	−	0.859463i	$-0.329202\pi$
$41$	6.54652	1.02239	0.511197	+	0.859463i	$0.329202\pi$
$42$	1.43930	0.222089
$43$	11.4441	1.74521	0.872604	−	0.488429i	$-0.162430\pi$
$43$	11.4441	1.74521	0.872604	+	0.488429i	$0.162430\pi$
$44$	0.0659107	0.00993641
$45$	2.86638	0.427294
$46$	5.78010	0.852229
$47$	4.63900	0.676667	0.338334	−	0.941026i	$-0.390137\pi$
$47$	4.63900	0.676667	0.338334	+	0.941026i	$0.390137\pi$
$48$	4.13806	0.597278
$49$	1.00000	0.142857
$50$	−4.62897	−0.654635
$51$	−2.98468	−0.417938
$52$	0	0
$53$	6.68041	0.917625	0.458813	−	0.888533i	$-0.348275\pi$
$53$	6.68041	0.917625	0.458813	+	0.888533i	$0.348275\pi$
$54$	1.43930	0.195864
$55$	2.63881	0.355817
$56$	2.77556	0.370900
$57$	−7.98255	−1.05731
$58$	−1.51162	−0.198485
$59$	−9.98868	−1.30042	−0.650208	−	0.759756i	$-0.725318\pi$
$59$	−9.98868	−1.30042	−0.650208	+	0.759756i	$0.725318\pi$
$60$	−0.205218	−0.0264935
$61$	−8.95997	−1.14721	−0.573603	−	0.819133i	$-0.694455\pi$
$61$	−8.95997	−1.14721	−0.573603	+	0.819133i	$0.694455\pi$
$62$	−4.54181	−0.576811
$63$	1.00000	0.125988
$64$	7.69348	0.961686
$65$	0	0
$66$	1.32503	0.163100
$67$	−11.2659	−1.37635	−0.688173	−	0.725547i	$-0.741587\pi$
$67$	−11.2659	−1.37635	−0.688173	+	0.725547i	$0.741587\pi$
$68$	0.213687	0.0259134
$69$	4.01590	0.483458
$70$	−4.12559	−0.493102
$71$	9.09996	1.07997	0.539983	−	0.841676i	$-0.318431\pi$
$71$	9.09996	1.07997	0.539983	+	0.841676i	$0.318431\pi$
$72$	2.77556	0.327103
$73$	−7.52599	−0.880851	−0.440425	−	0.897789i	$-0.645172\pi$
$73$	−7.52599	−0.880851	−0.440425	+	0.897789i	$0.645172\pi$
$74$	−2.32758	−0.270575
$75$	−3.21612	−0.371365
$76$	0.571509	0.0655566
$77$	0.920607	0.104913
$78$	0	0
$79$	6.24310	0.702404	0.351202	−	0.936300i	$-0.385773\pi$
$79$	6.24310	0.702404	0.351202	+	0.936300i	$0.385773\pi$
$80$	−11.8613	−1.32613
$81$	1.00000	0.111111
$82$	−9.42243	−1.04053
$83$	−9.66531	−1.06091	−0.530453	−	0.847714i	$-0.677978\pi$
$83$	−9.66531	−1.06091	−0.530453	+	0.847714i	$0.677978\pi$
$84$	−0.0715948	−0.00781164
$85$	8.55521	0.927943
$86$	−16.4715	−1.77617
$87$	−1.05024	−0.112598
$88$	2.55520	0.272385
$89$	−6.52667	−0.691826	−0.345913	−	0.938267i	$-0.612431\pi$
$89$	−6.52667	−0.691826	−0.345913	+	0.938267i	$0.612431\pi$
$90$	−4.12559	−0.434875
$91$	0	0
$92$	−0.287518	−0.0299758
$93$	−3.15556	−0.327217
$94$	−6.67693	−0.688672
$95$	22.8810	2.34754
$96$	−0.404809	−0.0413157
$97$	0.561935	0.0570559	0.0285279	−	0.999593i	$-0.490918\pi$
$97$	0.561935	0.0570559	0.0285279	+	0.999593i	$0.490918\pi$
$98$	−1.43930	−0.145392
$99$	0.920607	0.0925245
$100$	0.230257	0.0230257
$101$	−2.92723	−0.291271	−0.145635	−	0.989338i	$-0.546523\pi$
$101$	−2.92723	−0.291271	−0.145635	+	0.989338i	$0.546523\pi$
$102$	4.29586	0.425353
$103$	15.0401	1.48195	0.740974	−	0.671533i	$-0.234364\pi$
$103$	15.0401	1.48195	0.740974	+	0.671533i	$0.234364\pi$
$104$	0	0
$105$	−2.86638	−0.279730
$106$	−9.61514	−0.933905
$107$	12.1569	1.17525	0.587624	−	0.809134i	$-0.300064\pi$
$107$	12.1569	1.17525	0.587624	+	0.809134i	$0.300064\pi$
$108$	−0.0715948	−0.00688922
$109$	10.3967	0.995823	0.497911	−	0.867228i	$-0.334101\pi$
$109$	10.3967	0.995823	0.497911	+	0.867228i	$0.334101\pi$
$110$	−3.79804	−0.362129
$111$	−1.61715	−0.153494
$112$	−4.13806	−0.391010
$113$	−15.2958	−1.43891	−0.719455	−	0.694540i	$-0.755608\pi$
$113$	−15.2958	−1.43891	−0.719455	+	0.694540i	$0.755608\pi$
$114$	11.4893	1.07607
$115$	−11.5111	−1.07341
$116$	0.0751920	0.00698140
$117$	0	0
$118$	14.3767	1.32349
$119$	2.98468	0.273605
$120$	−7.95580	−0.726262
$121$	−10.1525	−0.922953
$122$	12.8961	1.16756
$123$	−6.54652	−0.590280
$124$	0.225922	0.0202884
$125$	−5.11328	−0.457346
$126$	−1.43930	−0.128223
$127$	−7.30215	−0.647961	−0.323981	−	0.946064i	$-0.605021\pi$
$127$	−7.30215	−0.647961	−0.323981	+	0.946064i	$0.605021\pi$
$128$	−11.8829	−1.05031
$129$	−11.4441	−1.00760
$130$	0	0
$131$	20.5301	1.79372	0.896861	−	0.442313i	$-0.145842\pi$
$131$	20.5301	1.79372	0.896861	+	0.442313i	$0.145842\pi$
$132$	−0.0659107	−0.00573679
$133$	7.98255	0.692175
$134$	16.2150	1.40076
$135$	−2.86638	−0.246698
$136$	8.28415	0.710360
$137$	−14.8963	−1.27268	−0.636340	−	0.771409i	$-0.719552\pi$
$137$	−14.8963	−1.27268	−0.636340	+	0.771409i	$0.719552\pi$
$138$	−5.78010	−0.492035
$139$	−20.5500	−1.74303	−0.871514	−	0.490371i	$-0.836861\pi$
$139$	−20.5500	−1.74303	−0.871514	+	0.490371i	$0.836861\pi$
$140$	0.205218	0.0173441
$141$	−4.63900	−0.390674
$142$	−13.0976	−1.09913
$143$	0	0
$144$	−4.13806	−0.344839
$145$	3.01039	0.250000
$146$	10.8322	0.896478
$147$	−1.00000	−0.0824786
$148$	0.115780	0.00951705
$149$	12.9977	1.06482	0.532408	−	0.846488i	$-0.321287\pi$
$149$	12.9977	1.06482	0.532408	+	0.846488i	$0.321287\pi$
$150$	4.62897	0.377954
$151$	−18.6960	−1.52146	−0.760728	−	0.649071i	$-0.775158\pi$
$151$	−18.6960	−1.52146	−0.760728	+	0.649071i	$0.775158\pi$
$152$	22.1561	1.79709
$153$	2.98468	0.241297
$154$	−1.32503	−0.106774
$155$	9.04503	0.726514
$156$	0	0
$157$	−15.0687	−1.20262	−0.601308	−	0.799017i	$-0.705354\pi$
$157$	−15.0687	−1.20262	−0.601308	+	0.799017i	$0.705354\pi$
$158$	−8.98572	−0.714865
$159$	−6.68041	−0.529791
$160$	1.16034	0.0917326
$161$	−4.01590	−0.316497
$162$	−1.43930	−0.113082
$163$	−9.07260	−0.710621	−0.355311	−	0.934748i	$-0.615625\pi$
$163$	−9.07260	−0.710621	−0.355311	+	0.934748i	$0.615625\pi$
$164$	0.468697	0.0365991
$165$	−2.63881	−0.205431
$166$	13.9113	1.07973
$167$	−5.92599	−0.458567	−0.229283	−	0.973360i	$-0.573638\pi$
$167$	−5.92599	−0.458567	−0.229283	+	0.973360i	$0.573638\pi$
$168$	−2.77556	−0.214139
$169$	0	0
$170$	−12.3135	−0.944406
$171$	7.98255	0.610441
$172$	0.819338	0.0624739
$173$	−5.39610	−0.410258	−0.205129	−	0.978735i	$-0.565761\pi$
$173$	−5.39610	−0.410258	−0.205129	+	0.978735i	$0.565761\pi$
$174$	1.51162	0.114596
$175$	3.21612	0.243116
$176$	−3.80953	−0.287154
$177$	9.98868	0.750795
$178$	9.39387	0.704100
$179$	12.7671	0.954258	0.477129	−	0.878833i	$-0.341677\pi$
$179$	12.7671	0.954258	0.477129	+	0.878833i	$0.341677\pi$
$180$	0.205218	0.0152960
$181$	−3.96815	−0.294950	−0.147475	−	0.989066i	$-0.547115\pi$
$181$	−3.96815	−0.294950	−0.147475	+	0.989066i	$0.547115\pi$
$182$	0	0
$183$	8.95997	0.662340
$184$	−11.1464	−0.821722
$185$	4.63538	0.340800
$186$	4.54181	0.333022
$187$	2.74771	0.200933
$188$	0.332128	0.0242229
$189$	−1.00000	−0.0727393
$190$	−32.9327	−2.38919
$191$	21.9168	1.58585	0.792923	−	0.609322i	$-0.208558\pi$
$191$	21.9168	1.58585	0.792923	+	0.609322i	$0.208558\pi$
$192$	−7.69348	−0.555229
$193$	−10.2802	−0.739983	−0.369991	−	0.929035i	$-0.620639\pi$
$193$	−10.2802	−0.739983	−0.369991	+	0.929035i	$0.620639\pi$
$194$	−0.808795	−0.0580681
$195$	0	0
$196$	0.0715948	0.00511392
$197$	13.2140	0.941458	0.470729	−	0.882278i	$-0.343991\pi$
$197$	13.2140	0.941458	0.470729	+	0.882278i	$0.343991\pi$
$198$	−1.32503	−0.0941660
$199$	−20.3660	−1.44371	−0.721855	−	0.692045i	$-0.756710\pi$
$199$	−20.3660	−1.44371	−0.721855	+	0.692045i	$0.756710\pi$
$200$	8.92653	0.631201
$201$	11.2659	0.794634
$202$	4.21318	0.296438
$203$	1.05024	0.0737126
$204$	−0.213687	−0.0149611
$205$	18.7648	1.31059
$206$	−21.6473	−1.50824
$207$	−4.01590	−0.279124
$208$	0	0
$209$	7.34879	0.508327
$210$	4.12559	0.284693
$211$	3.82094	0.263044	0.131522	−	0.991313i	$-0.458014\pi$
$211$	3.82094	0.263044	0.131522	+	0.991313i	$0.458014\pi$
$212$	0.478283	0.0328486
$213$	−9.09996	−0.623519
$214$	−17.4974	−1.19610
$215$	32.8031	2.23715
$216$	−2.77556	−0.188853
$217$	3.15556	0.214213
$218$	−14.9640	−1.01349
$219$	7.52599	0.508559
$220$	0.188925	0.0127373
$221$	0	0
$222$	2.32758	0.156217
$223$	26.9148	1.80235	0.901175	−	0.433456i	$-0.142706\pi$
$223$	26.9148	1.80235	0.901175	+	0.433456i	$0.142706\pi$
$224$	0.404809	0.0270475
$225$	3.21612	0.214408
$226$	22.0153	1.46444
$227$	27.2647	1.80962	0.904810	−	0.425814i	$-0.140012\pi$
$227$	27.2647	1.80962	0.904810	+	0.425814i	$0.140012\pi$
$228$	−0.571509	−0.0378491
$229$	−5.09112	−0.336431	−0.168215	−	0.985750i	$-0.553800\pi$
$229$	−5.09112	−0.336431	−0.168215	+	0.985750i	$0.553800\pi$
$230$	16.5679	1.09246
$231$	−0.920607	−0.0605715
$232$	2.91501	0.191380
$233$	8.58247	0.562257	0.281128	−	0.959670i	$-0.409291\pi$
$233$	8.58247	0.562257	0.281128	+	0.959670i	$0.409291\pi$
$234$	0	0
$235$	13.2971	0.867408
$236$	−0.715138	−0.0465515
$237$	−6.24310	−0.405533
$238$	−4.29586	−0.278459
$239$	−4.40895	−0.285191	−0.142596	−	0.989781i	$-0.545545\pi$
$239$	−4.40895	−0.285191	−0.142596	+	0.989781i	$0.545545\pi$
$240$	11.8613	0.765640
$241$	4.62930	0.298199	0.149100	−	0.988822i	$-0.452362\pi$
$241$	4.62930	0.298199	0.149100	+	0.988822i	$0.452362\pi$
$242$	14.6125	0.939327
$243$	−1.00000	−0.0641500
$244$	−0.641487	−0.0410670
$245$	2.86638	0.183126
$246$	9.42243	0.600752
$247$	0	0
$248$	8.75845	0.556162
$249$	9.66531	0.612514
$250$	7.35956	0.465460
$251$	−16.4973	−1.04130	−0.520650	−	0.853770i	$-0.674310\pi$
$251$	−16.4973	−1.04130	−0.520650	+	0.853770i	$0.674310\pi$
$252$	0.0715948	0.00451005
$253$	−3.69707	−0.232433
$254$	10.5100	0.659457
$255$	−8.55521	−0.535748
$256$	1.71610	0.107256
$257$	15.8475	0.988540	0.494270	−	0.869308i	$-0.335435\pi$
$257$	15.8475	0.988540	0.494270	+	0.869308i	$0.335435\pi$
$258$	16.4715	1.02547
$259$	1.61715	0.100485
$260$	0	0
$261$	1.05024	0.0650084
$262$	−29.5490	−1.82554
$263$	8.50599	0.524502	0.262251	−	0.965000i	$-0.415535\pi$
$263$	8.50599	0.524502	0.262251	+	0.965000i	$0.415535\pi$
$264$	−2.55520	−0.157262
$265$	19.1486	1.17629
$266$	−11.4893	−0.704455
$267$	6.52667	0.399426
$268$	−0.806579	−0.0492696
$269$	2.14357	0.130696	0.0653479	−	0.997863i	$-0.479184\pi$
$269$	2.14357	0.130696	0.0653479	+	0.997863i	$0.479184\pi$
$270$	4.12559	0.251075
$271$	24.4875	1.48751	0.743754	−	0.668453i	$-0.233043\pi$
$271$	24.4875	1.48751	0.743754	+	0.668453i	$0.233043\pi$
$272$	−12.3508	−0.748876
$273$	0	0
$274$	21.4404	1.29526
$275$	2.96078	0.178542
$276$	0.287518	0.0173065
$277$	19.4563	1.16902	0.584508	−	0.811388i	$-0.301288\pi$
$277$	19.4563	1.16902	0.584508	+	0.811388i	$0.301288\pi$
$278$	29.5777	1.77395
$279$	3.15556	0.188919
$280$	7.95580	0.475450
$281$	15.2398	0.909130	0.454565	−	0.890714i	$-0.349795\pi$
$281$	15.2398	0.909130	0.454565	+	0.890714i	$0.349795\pi$
$282$	6.67693	0.397605
$283$	−9.39124	−0.558251	−0.279126	−	0.960255i	$-0.590045\pi$
$283$	−9.39124	−0.558251	−0.279126	+	0.960255i	$0.590045\pi$
$284$	0.651510	0.0386600
$285$	−22.8810	−1.35535
$286$	0	0
$287$	6.54652	0.386429
$288$	0.404809	0.0238536
$289$	−8.09171	−0.475983
$290$	−4.33287	−0.254435
$291$	−0.561935	−0.0329412
$292$	−0.538822	−0.0315322
$293$	13.1364	0.767436	0.383718	−	0.923450i	$-0.374643\pi$
$293$	13.1364	0.767436	0.383718	+	0.923450i	$0.374643\pi$
$294$	1.43930	0.0839419
$295$	−28.6313	−1.66698
$296$	4.48851	0.260889
$297$	−0.920607	−0.0534190
$298$	−18.7077	−1.08371
$299$	0	0
$300$	−0.230257	−0.0132939
$301$	11.4441	0.659626
$302$	26.9092	1.54845
$303$	2.92723	0.168165
$304$	−33.0323	−1.89453
$305$	−25.6826	−1.47058
$306$	−4.29586	−0.245578
$307$	−19.4366	−1.10930	−0.554652	−	0.832082i	$-0.687149\pi$
$307$	−19.4366	−1.10930	−0.554652	+	0.832082i	$0.687149\pi$
$308$	0.0659107	0.00375561
$309$	−15.0401	−0.855604
$310$	−13.0185	−0.739404
$311$	28.1906	1.59854	0.799270	−	0.600972i	$-0.205220\pi$
$311$	28.1906	1.59854	0.799270	+	0.600972i	$0.205220\pi$
$312$	0	0
$313$	−13.3965	−0.757217	−0.378608	−	0.925557i	$-0.623597\pi$
$313$	−13.3965	−0.757217	−0.378608	+	0.925557i	$0.623597\pi$
$314$	21.6885	1.22395
$315$	2.86638	0.161502
$316$	0.446974	0.0251442
$317$	−27.5802	−1.54906	−0.774529	−	0.632539i	$-0.782013\pi$
$317$	−27.5802	−1.54906	−0.774529	+	0.632539i	$0.782013\pi$
$318$	9.61514	0.539191
$319$	0.966861	0.0541338
$320$	22.0524	1.23277
$321$	−12.1569	−0.678529
$322$	5.78010	0.322112
$323$	23.8253	1.32568
$324$	0.0715948	0.00397749
$325$	0	0
$326$	13.0582	0.723228
$327$	−10.3967	−0.574938
$328$	18.1703	1.00328
$329$	4.63900	0.255756
$330$	3.79804	0.209075
$331$	−19.8272	−1.08980	−0.544901	−	0.838500i	$-0.683433\pi$
$331$	−19.8272	−1.08980	−0.544901	+	0.838500i	$0.683433\pi$
$332$	−0.691986	−0.0379777
$333$	1.61715	0.0886195
$334$	8.52930	0.466703
$335$	−32.2923	−1.76431
$336$	4.13806	0.225750
$337$	−5.24434	−0.285678	−0.142839	−	0.989746i	$-0.545623\pi$
$337$	−5.24434	−0.285678	−0.142839	+	0.989746i	$0.545623\pi$
$338$	0	0
$339$	15.2958	0.830754
$340$	0.612509	0.0332179
$341$	2.90503	0.157316
$342$	−11.4893	−0.621271
$343$	1.00000	0.0539949
$344$	31.7638	1.71259
$345$	11.5111	0.619736
$346$	7.76662	0.417536
$347$	9.84401	0.528454	0.264227	−	0.964460i	$-0.414883\pi$
$347$	9.84401	0.528454	0.264227	+	0.964460i	$0.414883\pi$
$348$	−0.0751920	−0.00403071
$349$	16.2789	0.871388	0.435694	−	0.900095i	$-0.356503\pi$
$349$	16.2789	0.871388	0.435694	+	0.900095i	$0.356503\pi$
$350$	−4.62897	−0.247429
$351$	0	0
$352$	0.372670	0.0198634
$353$	17.0572	0.907863	0.453931	−	0.891037i	$-0.350021\pi$
$353$	17.0572	0.907863	0.453931	+	0.891037i	$0.350021\pi$
$354$	−14.3767	−0.764116
$355$	26.0839	1.38439
$356$	−0.467276	−0.0247656
$357$	−2.98468	−0.157966
$358$	−18.3757	−0.971188
$359$	36.7099	1.93748	0.968738	−	0.248085i	$-0.0798011\pi$
$359$	36.7099	1.93748	0.968738	+	0.248085i	$0.0798011\pi$
$360$	7.95580	0.419308
$361$	44.7211	2.35374
$362$	5.71138	0.300183
$363$	10.1525	0.532867
$364$	0	0
$365$	−21.5723	−1.12915
$366$	−12.8961	−0.674091
$367$	−9.74654	−0.508765	−0.254383	−	0.967104i	$-0.581872\pi$
$367$	−9.74654	−0.508765	−0.254383	+	0.967104i	$0.581872\pi$
$368$	16.6180	0.866276
$369$	6.54652	0.340798
$370$	−6.67171	−0.346846
$371$	6.68041	0.346830
$372$	−0.225922	−0.0117135
$373$	0.589925	0.0305452	0.0152726	−	0.999883i	$-0.495138\pi$
$373$	0.589925	0.0305452	0.0152726	+	0.999883i	$0.495138\pi$
$374$	−3.95480	−0.204498
$375$	5.11328	0.264049
$376$	12.8758	0.664020
$377$	0	0
$378$	1.43930	0.0740298
$379$	3.62980	0.186451	0.0932253	−	0.995645i	$-0.470282\pi$
$379$	3.62980	0.186451	0.0932253	+	0.995645i	$0.470282\pi$
$380$	1.63816	0.0840359
$381$	7.30215	0.374101
$382$	−31.5450	−1.61398
$383$	−28.6977	−1.46638	−0.733191	−	0.680022i	$-0.761970\pi$
$383$	−28.6977	−1.46638	−0.733191	+	0.680022i	$0.761970\pi$
$384$	11.8829	0.606396
$385$	2.63881	0.134486
$386$	14.7963	0.753111
$387$	11.4441	0.581736
$388$	0.0402316	0.00204245
$389$	−4.28777	−0.217398	−0.108699	−	0.994075i	$-0.534669\pi$
$389$	−4.28777	−0.217398	−0.108699	+	0.994075i	$0.534669\pi$
$390$	0	0
$391$	−11.9862	−0.606166
$392$	2.77556	0.140187
$393$	−20.5301	−1.03561
$394$	−19.0189	−0.958161
$395$	17.8951	0.900399
$396$	0.0659107	0.00331214
$397$	31.2556	1.56868	0.784338	−	0.620334i	$-0.213003\pi$
$397$	31.2556	1.56868	0.784338	+	0.620334i	$0.213003\pi$
$398$	29.3129	1.46932
$399$	−7.98255	−0.399627
$400$	−13.3085	−0.665425
$401$	−24.4307	−1.22001	−0.610006	−	0.792397i	$-0.708833\pi$
$401$	−24.4307	−1.22001	−0.610006	+	0.792397i	$0.708833\pi$
$402$	−16.2150	−0.808732
$403$	0	0
$404$	−0.209575	−0.0104267
$405$	2.86638	0.142431
$406$	−1.51162	−0.0750204
$407$	1.48876	0.0737953
$408$	−8.28415	−0.410127
$409$	17.3704	0.858909	0.429454	−	0.903089i	$-0.358706\pi$
$409$	17.3704	0.858909	0.429454	+	0.903089i	$0.358706\pi$
$410$	−27.0082	−1.33384
$411$	14.8963	0.734782
$412$	1.07680	0.0530499
$413$	−9.98868	−0.491511
$414$	5.78010	0.284076
$415$	−27.7044	−1.35996
$416$	0	0
$417$	20.5500	1.00634
$418$	−10.5771	−0.517345
$419$	33.2787	1.62577	0.812884	−	0.582425i	$-0.197896\pi$
$419$	33.2787	1.62577	0.812884	+	0.582425i	$0.197896\pi$
$420$	−0.205218	−0.0100136
$421$	−28.8184	−1.40452	−0.702261	−	0.711919i	$-0.747826\pi$
$421$	−28.8184	−1.40452	−0.702261	+	0.711919i	$0.747826\pi$
$422$	−5.49950	−0.267711
$423$	4.63900	0.225556
$424$	18.5419	0.900474
$425$	9.59907	0.465623
$426$	13.0976	0.634581
$427$	−8.95997	−0.433603
$428$	0.870368	0.0420708
$429$	0	0
$430$	−47.2136	−2.27684
$431$	11.9805	0.577081	0.288541	−	0.957468i	$-0.406830\pi$
$431$	11.9805	0.577081	0.288541	+	0.957468i	$0.406830\pi$
$432$	4.13806	0.199093
$433$	−12.9962	−0.624558	−0.312279	−	0.949990i	$-0.601092\pi$
$433$	−12.9962	−0.624558	−0.312279	+	0.949990i	$0.601092\pi$
$434$	−4.54181	−0.218014
$435$	−3.01039	−0.144337
$436$	0.744349	0.0356479
$437$	−32.0571	−1.53350
$438$	−10.8322	−0.517582
$439$	33.1408	1.58172	0.790861	−	0.611996i	$-0.209633\pi$
$439$	33.1408	1.58172	0.790861	+	0.611996i	$0.209633\pi$
$440$	7.32417	0.349166
$441$	1.00000	0.0476190
$442$	0	0
$443$	24.7031	1.17368	0.586841	−	0.809702i	$-0.300371\pi$
$443$	24.7031	1.17368	0.586841	+	0.809702i	$0.300371\pi$
$444$	−0.115780	−0.00549467
$445$	−18.7079	−0.886840
$446$	−38.7386	−1.83433
$447$	−12.9977	−0.614772
$448$	7.69348	0.363483
$449$	−21.9994	−1.03821	−0.519107	−	0.854709i	$-0.673735\pi$
$449$	−21.9994	−1.03821	−0.519107	+	0.854709i	$0.673735\pi$
$450$	−4.62897	−0.218212
$451$	6.02677	0.283790
$452$	−1.09510	−0.0515092
$453$	18.6960	0.878413
$454$	−39.2422	−1.84173
$455$	0	0
$456$	−22.1561	−1.03755
$457$	35.6397	1.66716	0.833578	−	0.552402i	$-0.186289\pi$
$457$	35.6397	1.66716	0.833578	+	0.552402i	$0.186289\pi$
$458$	7.32767	0.342399
$459$	−2.98468	−0.139313
$460$	−0.824134	−0.0384254
$461$	−23.5001	−1.09451	−0.547255	−	0.836966i	$-0.684327\pi$
$461$	−23.5001	−1.09451	−0.547255	+	0.836966i	$0.684327\pi$
$462$	1.32503	0.0616461
$463$	−34.0308	−1.58155	−0.790773	−	0.612109i	$-0.790321\pi$
$463$	−34.0308	−1.58155	−0.790773	+	0.612109i	$0.790321\pi$
$464$	−4.34597	−0.201757
$465$	−9.04503	−0.419453
$466$	−12.3528	−0.572232
$467$	−21.5151	−0.995601	−0.497800	−	0.867292i	$-0.665859\pi$
$467$	−21.5151	−0.995601	−0.497800	+	0.867292i	$0.665859\pi$
$468$	0	0
$469$	−11.2659	−0.520210
$470$	−19.1386	−0.882797
$471$	15.0687	0.694331
$472$	−27.7242	−1.27611
$473$	10.5355	0.484423
$474$	8.98572	0.412728
$475$	25.6728	1.17795
$476$	0.213687	0.00979435
$477$	6.68041	0.305875
$478$	6.34582	0.290251
$479$	−9.91346	−0.452957	−0.226479	−	0.974016i	$-0.572721\pi$
$479$	−9.91346	−0.452957	−0.226479	+	0.974016i	$0.572721\pi$
$480$	−1.16034	−0.0529618
$481$	0	0
$482$	−6.66297	−0.303490
$483$	4.01590	0.182730
$484$	−0.726865	−0.0330393
$485$	1.61072	0.0731389
$486$	1.43930	0.0652881
$487$	11.8078	0.535061	0.267531	−	0.963549i	$-0.413792\pi$
$487$	11.8078	0.535061	0.267531	+	0.963549i	$0.413792\pi$
$488$	−24.8689	−1.12576
$489$	9.07260	0.410277
$490$	−4.12559	−0.186375
$491$	−29.8552	−1.34735	−0.673673	−	0.739030i	$-0.735284\pi$
$491$	−29.8552	−1.34735	−0.673673	+	0.739030i	$0.735284\pi$
$492$	−0.468697	−0.0211305
$493$	3.13464	0.141177
$494$	0	0
$495$	2.63881	0.118606
$496$	−13.0579	−0.586318
$497$	9.09996	0.408189
$498$	−13.9113	−0.623381
$499$	20.6327	0.923645	0.461823	−	0.886972i	$-0.347196\pi$
$499$	20.6327	0.923645	0.461823	+	0.886972i	$0.347196\pi$
$500$	−0.366084	−0.0163718
$501$	5.92599	0.264754
$502$	23.7446	1.05977
$503$	16.6116	0.740677	0.370338	−	0.928897i	$-0.379242\pi$
$503$	16.6116	0.740677	0.370338	+	0.928897i	$0.379242\pi$
$504$	2.77556	0.123633
$505$	−8.39055	−0.373375
$506$	5.32120	0.236556
$507$	0	0
$508$	−0.522796	−0.0231953
$509$	−29.8212	−1.32180	−0.660902	−	0.750473i	$-0.729826\pi$
$509$	−29.8212	−1.32180	−0.660902	+	0.750473i	$0.729826\pi$
$510$	12.3135	0.545253
$511$	−7.52599	−0.332930
$512$	21.2958	0.941149
$513$	−7.98255	−0.352438
$514$	−22.8094	−1.00608
$515$	43.1107	1.89968
$516$	−0.819338	−0.0360693
$517$	4.27069	0.187825
$518$	−2.32758	−0.102268
$519$	5.39610	0.236862
$520$	0	0
$521$	4.98520	0.218406	0.109203	−	0.994019i	$-0.465170\pi$
$521$	4.98520	0.218406	0.109203	+	0.994019i	$0.465170\pi$
$522$	−1.51162	−0.0661618
$523$	16.8858	0.738365	0.369182	−	0.929357i	$-0.379638\pi$
$523$	16.8858	0.738365	0.369182	+	0.929357i	$0.379638\pi$
$524$	1.46985	0.0642106
$525$	−3.21612	−0.140363
$526$	−12.2427	−0.533807
$527$	9.41833	0.410269
$528$	3.80953	0.165789
$529$	−6.87255	−0.298806
$530$	−27.5606	−1.19716
$531$	−9.98868	−0.433472
$532$	0.571509	0.0247781
$533$	0	0
$534$	−9.39387	−0.406512
$535$	34.8461	1.50653
$536$	−31.2691	−1.35062
$537$	−12.7671	−0.550941
$538$	−3.08525	−0.133015
$539$	0.920607	0.0396534
$540$	−0.205218	−0.00883117
$541$	19.5003	0.838383	0.419192	−	0.907898i	$-0.362314\pi$
$541$	19.5003	0.838383	0.419192	+	0.907898i	$0.362314\pi$
$542$	−35.2449	−1.51390
$543$	3.96815	0.170290
$544$	1.20822	0.0518022
$545$	29.8008	1.27653
$546$	0	0
$547$	8.65098	0.369889	0.184945	−	0.982749i	$-0.440789\pi$
$547$	8.65098	0.369889	0.184945	+	0.982749i	$0.440789\pi$
$548$	−1.06650	−0.0455587
$549$	−8.95997	−0.382402
$550$	−4.26146	−0.181709
$551$	8.38362	0.357154
$552$	11.1464	0.474421
$553$	6.24310	0.265484
$554$	−28.0035	−1.18976
$555$	−4.63538	−0.196761
$556$	−1.47127	−0.0623959
$557$	5.34490	0.226471	0.113235	−	0.993568i	$-0.463879\pi$
$557$	5.34490	0.226471	0.113235	+	0.993568i	$0.463879\pi$
$558$	−4.54181	−0.192270
$559$	0	0
$560$	−11.8613	−0.501229
$561$	−2.74771	−0.116009
$562$	−21.9347	−0.925259
$563$	−3.59510	−0.151515	−0.0757576	−	0.997126i	$-0.524138\pi$
$563$	−3.59510	−0.151515	−0.0757576	+	0.997126i	$0.524138\pi$
$564$	−0.332128	−0.0139851
$565$	−43.8436	−1.84451
$566$	13.5168	0.568155
$567$	1.00000	0.0419961
$568$	25.2575	1.05978
$569$	12.3357	0.517141	0.258571	−	0.965992i	$-0.416749\pi$
$569$	12.3357	0.517141	0.258571	+	0.965992i	$0.416749\pi$
$570$	32.9327	1.37940
$571$	40.8083	1.70777	0.853887	−	0.520459i	$-0.174239\pi$
$571$	40.8083	1.70777	0.853887	+	0.520459i	$0.174239\pi$
$572$	0	0
$573$	−21.9168	−0.915589
$574$	−9.42243	−0.393285
$575$	−12.9156	−0.538618
$576$	7.69348	0.320562
$577$	−11.6793	−0.486215	−0.243107	−	0.969999i	$-0.578167\pi$
$577$	−11.6793	−0.486215	−0.243107	+	0.969999i	$0.578167\pi$
$578$	11.6464	0.484427
$579$	10.2802	0.427229
$580$	0.215529	0.00894934
$581$	−9.66531	−0.400985
$582$	0.808795	0.0335256
$583$	6.15004	0.254709
$584$	−20.8888	−0.864387
$585$	0	0
$586$	−18.9073	−0.781052
$587$	−14.1896	−0.585667	−0.292833	−	0.956164i	$-0.594598\pi$
$587$	−14.1896	−0.585667	−0.292833	+	0.956164i	$0.594598\pi$
$588$	−0.0715948	−0.00295252
$589$	25.1894	1.03791
$590$	41.2092	1.69656
$591$	−13.2140	−0.543551
$592$	−6.69189	−0.275035
$593$	0.460952	0.0189290	0.00946451	−	0.999955i	$-0.496987\pi$
$593$	0.460952	0.0189290	0.00946451	+	0.999955i	$0.496987\pi$
$594$	1.32503	0.0543668
$595$	8.55521	0.350729
$596$	0.930571	0.0381177
$597$	20.3660	0.833526
$598$	0	0
$599$	−19.4498	−0.794696	−0.397348	−	0.917668i	$-0.630069\pi$
$599$	−19.4498	−0.794696	−0.397348	+	0.917668i	$0.630069\pi$
$600$	−8.92653	−0.364424
$601$	−13.0585	−0.532667	−0.266333	−	0.963881i	$-0.585812\pi$
$601$	−13.0585	−0.532667	−0.266333	+	0.963881i	$0.585812\pi$
$602$	−16.4715	−0.671329
$603$	−11.2659	−0.458782
$604$	−1.33853	−0.0544642
$605$	−29.1008	−1.18312
$606$	−4.21318	−0.171149
$607$	−0.787345	−0.0319574	−0.0159787	−	0.999872i	$-0.505086\pi$
$607$	−0.787345	−0.0319574	−0.0159787	+	0.999872i	$0.505086\pi$
$608$	3.23141	0.131051
$609$	−1.05024	−0.0425580
$610$	36.9651	1.49667
$611$	0	0
$612$	0.213687	0.00863780
$613$	−40.4807	−1.63500	−0.817500	−	0.575929i	$-0.804641\pi$
$613$	−40.4807	−1.63500	−0.817500	+	0.575929i	$0.804641\pi$
$614$	27.9752	1.12899
$615$	−18.7648	−0.756670
$616$	2.55520	0.102952
$617$	25.1733	1.01344	0.506719	−	0.862111i	$-0.330858\pi$
$617$	25.1733	1.01344	0.506719	+	0.862111i	$0.330858\pi$
$618$	21.6473	0.870783
$619$	13.6306	0.547860	0.273930	−	0.961750i	$-0.411676\pi$
$619$	13.6306	0.547860	0.273930	+	0.961750i	$0.411676\pi$
$620$	0.647577	0.0260073
$621$	4.01590	0.161153
$622$	−40.5748	−1.62690
$623$	−6.52667	−0.261486
$624$	0	0
$625$	−30.7372	−1.22949
$626$	19.2817	0.770651
$627$	−7.34879	−0.293483
$628$	−1.07884	−0.0430506
$629$	4.82668	0.192453
$630$	−4.12559	−0.164367
$631$	−28.6584	−1.14087	−0.570436	−	0.821342i	$-0.693226\pi$
$631$	−28.6584	−1.14087	−0.570436	+	0.821342i	$0.693226\pi$
$632$	17.3281	0.689275
$633$	−3.82094	−0.151869
$634$	39.6963	1.57654
$635$	−20.9307	−0.830610
$636$	−0.478283	−0.0189652
$637$	0	0
$638$	−1.39161	−0.0550943
$639$	9.09996	0.359989
$640$	−34.0608	−1.34637
$641$	35.1830	1.38965	0.694823	−	0.719180i	$-0.255483\pi$
$641$	35.1830	1.38965	0.694823	+	0.719180i	$0.255483\pi$
$642$	17.4974	0.690567
$643$	−20.0777	−0.791789	−0.395894	−	0.918296i	$-0.629565\pi$
$643$	−20.0777	−0.791789	−0.395894	+	0.918296i	$0.629565\pi$
$644$	−0.287518	−0.0113298
$645$	−32.8031	−1.29162
$646$	−34.2919	−1.34920
$647$	−12.8586	−0.505523	−0.252762	−	0.967529i	$-0.581339\pi$
$647$	−12.8586	−0.505523	−0.252762	+	0.967529i	$0.581339\pi$
$648$	2.77556	0.109034
$649$	−9.19565	−0.360961
$650$	0	0
$651$	−3.15556	−0.123676
$652$	−0.649551	−0.0254384
$653$	−2.16027	−0.0845381	−0.0422690	−	0.999106i	$-0.513459\pi$
$653$	−2.16027	−0.0845381	−0.0422690	+	0.999106i	$0.513459\pi$
$654$	14.9640	0.585139
$655$	58.8469	2.29934
$656$	−27.0899	−1.05768
$657$	−7.52599	−0.293617
$658$	−6.67693	−0.260294
$659$	18.1795	0.708171	0.354086	−	0.935213i	$-0.384792\pi$
$659$	18.1795	0.708171	0.354086	+	0.935213i	$0.384792\pi$
$660$	−0.188925	−0.00735389
$661$	6.02892	0.234498	0.117249	−	0.993103i	$-0.462592\pi$
$661$	6.02892	0.234498	0.117249	+	0.993103i	$0.462592\pi$
$662$	28.5374	1.10914
$663$	0	0
$664$	−26.8267	−1.04108
$665$	22.8810	0.887287
$666$	−2.32758	−0.0901918
$667$	−4.21767	−0.163309
$668$	−0.424270	−0.0164155
$669$	−26.9148	−1.04059
$670$	46.4784	1.79562
$671$	−8.24861	−0.318434
$672$	−0.404809	−0.0156159
$673$	−25.7805	−0.993766	−0.496883	−	0.867818i	$-0.665522\pi$
$673$	−25.7805	−0.993766	−0.496883	+	0.867818i	$0.665522\pi$
$674$	7.54820	0.290746
$675$	−3.21612	−0.123788
$676$	0	0
$677$	1.37351	0.0527884	0.0263942	−	0.999652i	$-0.491597\pi$
$677$	1.37351	0.0527884	0.0263942	+	0.999652i	$0.491597\pi$
$678$	−22.0153	−0.845493
$679$	0.561935	0.0215651
$680$	23.7455	0.910598
$681$	−27.2647	−1.04479
$682$	−4.18122	−0.160107
$683$	11.5660	0.442560	0.221280	−	0.975210i	$-0.428976\pi$
$683$	11.5660	0.442560	0.221280	+	0.975210i	$0.428976\pi$
$684$	0.571509	0.0218522
$685$	−42.6985	−1.63143
$686$	−1.43930	−0.0549529
$687$	5.09112	0.194238
$688$	−47.3564	−1.80544
$689$	0	0
$690$	−16.5679	−0.630731
$691$	7.05165	0.268257	0.134129	−	0.990964i	$-0.457176\pi$
$691$	7.05165	0.268257	0.134129	+	0.990964i	$0.457176\pi$
$692$	−0.386333	−0.0146862
$693$	0.920607	0.0349710
$694$	−14.1685	−0.537830
$695$	−58.9040	−2.23436
$696$	−2.91501	−0.110493
$697$	19.5392	0.740102
$698$	−23.4302	−0.886848
$699$	−8.58247	−0.324619
$700$	0.230257	0.00870291
$701$	39.9328	1.50824	0.754121	−	0.656736i	$-0.228063\pi$
$701$	39.9328	1.50824	0.754121	+	0.656736i	$0.228063\pi$
$702$	0	0
$703$	12.9090	0.486873
$704$	7.08268	0.266938
$705$	−13.2971	−0.500798
$706$	−24.5505	−0.923969
$707$	−2.92723	−0.110090
$708$	0.715138	0.0268765
$709$	−47.5035	−1.78403	−0.892015	−	0.452006i	$-0.850709\pi$
$709$	−47.5035	−1.78403	−0.892015	+	0.452006i	$0.850709\pi$
$710$	−37.5427	−1.40895
$711$	6.24310	0.234135
$712$	−18.1152	−0.678895
$713$	−12.6724	−0.474586
$714$	4.29586	0.160768
$715$	0	0
$716$	0.914059	0.0341600
$717$	4.40895	0.164655
$718$	−52.8368	−1.97185
$719$	−4.97631	−0.185585	−0.0927925	−	0.995685i	$-0.529579\pi$
$719$	−4.97631	−0.185585	−0.0927925	+	0.995685i	$0.529579\pi$
$720$	−11.8613	−0.442043
$721$	15.0401	0.560124
$722$	−64.3672	−2.39550
$723$	−4.62930	−0.172166
$724$	−0.284099	−0.0105585
$725$	3.37771	0.125445
$726$	−14.6125	−0.542321
$727$	35.0729	1.30078	0.650391	−	0.759599i	$-0.274605\pi$
$727$	35.0729	1.30078	0.650391	+	0.759599i	$0.274605\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	31.0491	1.14918
$731$	34.1569	1.26334
$732$	0.641487	0.0237101
$733$	−39.1263	−1.44516	−0.722582	−	0.691285i	$-0.757045\pi$
$733$	−39.1263	−1.44516	−0.722582	+	0.691285i	$0.757045\pi$
$734$	14.0282	0.517791
$735$	−2.86638	−0.105728
$736$	−1.62567	−0.0599231
$737$	−10.3714	−0.382037
$738$	−9.42243	−0.346844
$739$	−14.0036	−0.515132	−0.257566	−	0.966261i	$-0.582921\pi$
$739$	−14.0036	−0.515132	−0.257566	+	0.966261i	$0.582921\pi$
$740$	0.331869	0.0121997
$741$	0	0
$742$	−9.61514	−0.352983
$743$	−28.7607	−1.05513	−0.527563	−	0.849516i	$-0.676894\pi$
$743$	−28.7607	−1.05513	−0.527563	+	0.849516i	$0.676894\pi$
$744$	−8.75845	−0.321100
$745$	37.2564	1.36497
$746$	−0.849081	−0.0310871
$747$	−9.66531	−0.353635
$748$	0.196722	0.00719287
$749$	12.1569	0.444202
$750$	−7.35956	−0.268733
$751$	−49.2873	−1.79852	−0.899259	−	0.437417i	$-0.855893\pi$
$751$	−49.2873	−1.79852	−0.899259	+	0.437417i	$0.855893\pi$
$752$	−19.1965	−0.700023
$753$	16.4973	0.601195
$754$	0	0
$755$	−53.5897	−1.95033
$756$	−0.0715948	−0.00260388
$757$	−27.6292	−1.00420	−0.502101	−	0.864809i	$-0.667439\pi$
$757$	−27.6292	−1.00420	−0.502101	+	0.864809i	$0.667439\pi$
$758$	−5.22439	−0.189758
$759$	3.69707	0.134195
$760$	63.5076	2.30366
$761$	−0.554389	−0.0200966	−0.0100483	−	0.999950i	$-0.503199\pi$
$761$	−0.554389	−0.0200966	−0.0100483	+	0.999950i	$0.503199\pi$
$762$	−10.5100	−0.380738
$763$	10.3967	0.376386
$764$	1.56913	0.0567692
$765$	8.55521	0.309314
$766$	41.3047	1.49240
$767$	0	0
$768$	−1.71610	−0.0619244
$769$	42.2312	1.52290	0.761448	−	0.648226i	$-0.224489\pi$
$769$	42.2312	1.52290	0.761448	+	0.648226i	$0.224489\pi$
$770$	−3.79804	−0.136872
$771$	−15.8475	−0.570734
$772$	−0.736007	−0.0264895
$773$	−46.3178	−1.66594	−0.832968	−	0.553321i	$-0.813360\pi$
$773$	−46.3178	−1.66594	−0.832968	+	0.553321i	$0.813360\pi$
$774$	−16.4715	−0.592056
$775$	10.1487	0.364551
$776$	1.55968	0.0559894
$777$	−1.61715	−0.0580151
$778$	6.17140	0.221255
$779$	52.2579	1.87233
$780$	0	0
$781$	8.37749	0.299770
$782$	17.2517	0.616920
$783$	−1.05024	−0.0375326
$784$	−4.13806	−0.147788
$785$	−43.1927	−1.54161
$786$	29.5490	1.05398
$787$	−13.9450	−0.497087	−0.248543	−	0.968621i	$-0.579952\pi$
$787$	−13.9450	−0.497087	−0.248543	+	0.968621i	$0.579952\pi$
$788$	0.946054	0.0337018
$789$	−8.50599	−0.302821
$790$	−25.7565	−0.916374
$791$	−15.2958	−0.543856
$792$	2.55520	0.0907951
$793$	0	0
$794$	−44.9864	−1.59651
$795$	−19.1486	−0.679130
$796$	−1.45810	−0.0516811
$797$	−3.71124	−0.131459	−0.0657294	−	0.997837i	$-0.520937\pi$
$797$	−3.71124	−0.131459	−0.0657294	+	0.997837i	$0.520937\pi$
$798$	11.4893	0.406717
$799$	13.8459	0.489833
$800$	1.30191	0.0460296
$801$	−6.52667	−0.230609
$802$	35.1632	1.24166
$803$	−6.92848	−0.244501
$804$	0.806579	0.0284458
$805$	−11.5111	−0.405712
$806$	0	0
$807$	−2.14357	−0.0754573
$808$	−8.12471	−0.285826
$809$	7.85149	0.276044	0.138022	−	0.990429i	$-0.455926\pi$
$809$	7.85149	0.276044	0.138022	+	0.990429i	$0.455926\pi$
$810$	−4.12559	−0.144958
$811$	−49.1028	−1.72423	−0.862117	−	0.506710i	$-0.830861\pi$
$811$	−49.1028	−1.72423	−0.862117	+	0.506710i	$0.830861\pi$
$812$	0.0751920	0.00263872
$813$	−24.4875	−0.858813
$814$	−2.14278	−0.0751045
$815$	−26.0055	−0.910933
$816$	12.3508	0.432364
$817$	91.3530	3.19604
$818$	−25.0012	−0.874147
$819$	0	0
$820$	1.34346	0.0469157
$821$	−13.1916	−0.460391	−0.230196	−	0.973144i	$-0.573937\pi$
$821$	−13.1916	−0.460391	−0.230196	+	0.973144i	$0.573937\pi$
$822$	−21.4404	−0.747818
$823$	−2.71369	−0.0945931	−0.0472966	−	0.998881i	$-0.515061\pi$
$823$	−2.71369	−0.0945931	−0.0472966	+	0.998881i	$0.515061\pi$
$824$	41.7448	1.45425
$825$	−2.96078	−0.103081
$826$	14.3767	0.500231
$827$	35.3979	1.23091	0.615453	−	0.788174i	$-0.288973\pi$
$827$	35.3979	1.23091	0.615453	+	0.788174i	$0.288973\pi$
$828$	−0.287518	−0.00999193
$829$	−11.0842	−0.384969	−0.192485	−	0.981300i	$-0.561655\pi$
$829$	−11.0842	−0.384969	−0.192485	+	0.981300i	$0.561655\pi$
$830$	39.8751	1.38408
$831$	−19.4563	−0.674932
$832$	0	0
$833$	2.98468	0.103413
$834$	−29.5777	−1.02419
$835$	−16.9861	−0.587829
$836$	0.526136	0.0181968
$837$	−3.15556	−0.109072
$838$	−47.8981	−1.65461
$839$	35.4634	1.22433	0.612166	−	0.790729i	$-0.290298\pi$
$839$	35.4634	1.22433	0.612166	+	0.790729i	$0.290298\pi$
$840$	−7.95580	−0.274501
$841$	−27.8970	−0.961965
$842$	41.4784	1.42944
$843$	−15.2398	−0.524886
$844$	0.273560	0.00941631
$845$	0	0
$846$	−6.67693	−0.229557
$847$	−10.1525	−0.348843
$848$	−27.6440	−0.949298
$849$	9.39124	0.322307
$850$	−13.8160	−0.473884
$851$	−6.49433	−0.222623
$852$	−0.651510	−0.0223204
$853$	10.0661	0.344656	0.172328	−	0.985040i	$-0.444871\pi$
$853$	10.0661	0.344656	0.172328	+	0.985040i	$0.444871\pi$
$854$	12.8961	0.441296
$855$	22.8810	0.782514
$856$	33.7421	1.15328
$857$	44.1981	1.50978	0.754890	−	0.655851i	$-0.227690\pi$
$857$	44.1981	1.50978	0.754890	+	0.655851i	$0.227690\pi$
$858$	0	0
$859$	33.6264	1.14732	0.573658	−	0.819095i	$-0.305524\pi$
$859$	33.6264	1.14732	0.573658	+	0.819095i	$0.305524\pi$
$860$	2.34853	0.0800842
$861$	−6.54652	−0.223105
$862$	−17.2436	−0.587319
$863$	23.7297	0.807767	0.403884	−	0.914810i	$-0.367660\pi$
$863$	23.7297	0.807767	0.403884	+	0.914810i	$0.367660\pi$
$864$	−0.404809	−0.0137719
$865$	−15.4672	−0.525902
$866$	18.7055	0.635638
$867$	8.09171	0.274809
$868$	0.225922	0.00766829
$869$	5.74744	0.194969
$870$	4.33287	0.146898
$871$	0	0
$872$	28.8566	0.977209
$873$	0.561935	0.0190186
$874$	46.1399	1.56071
$875$	−5.11328	−0.172860
$876$	0.538822	0.0182051
$877$	−9.30145	−0.314088	−0.157044	−	0.987592i	$-0.550196\pi$
$877$	−9.30145	−0.314088	−0.157044	+	0.987592i	$0.550196\pi$
$878$	−47.6996	−1.60978
$879$	−13.1364	−0.443080
$880$	−10.9196	−0.368098
$881$	19.5601	0.658997	0.329499	−	0.944156i	$-0.393120\pi$
$881$	19.5601	0.658997	0.329499	+	0.944156i	$0.393120\pi$
$882$	−1.43930	−0.0484639
$883$	−2.25927	−0.0760305	−0.0380152	−	0.999277i	$-0.512104\pi$
$883$	−2.25927	−0.0760305	−0.0380152	+	0.999277i	$0.512104\pi$
$884$	0	0
$885$	28.6313	0.962432
$886$	−35.5553	−1.19450
$887$	−21.8263	−0.732856	−0.366428	−	0.930446i	$-0.619419\pi$
$887$	−21.8263	−0.732856	−0.366428	+	0.930446i	$0.619419\pi$
$888$	−4.48851	−0.150625
$889$	−7.30215	−0.244906
$890$	26.9264	0.902574
$891$	0.920607	0.0308415
$892$	1.92696	0.0645195
$893$	37.0310	1.23920
$894$	18.7077	0.625679
$895$	36.5953	1.22325
$896$	−11.8829	−0.396979
$897$	0	0
$898$	31.6638	1.05663
$899$	3.31411	0.110532
$900$	0.230257	0.00767525
$901$	19.9389	0.664260
$902$	−8.67436	−0.288824
$903$	−11.4441	−0.380835
$904$	−42.4545	−1.41201
$905$	−11.3742	−0.378092
$906$	−26.9092	−0.893997
$907$	−46.7145	−1.55113	−0.775565	−	0.631268i	$-0.782535\pi$
$907$	−46.7145	−1.55113	−0.775565	+	0.631268i	$0.782535\pi$
$908$	1.95201	0.0647798
$909$	−2.92723	−0.0970902
$910$	0	0
$911$	29.4791	0.976686	0.488343	−	0.872652i	$-0.337602\pi$
$911$	29.4791	0.976686	0.488343	+	0.872652i	$0.337602\pi$
$912$	33.0323	1.09381
$913$	−8.89796	−0.294479
$914$	−51.2964	−1.69673
$915$	25.6826	0.849042
$916$	−0.364498	−0.0120433
$917$	20.5301	0.677963
$918$	4.29586	0.141784
$919$	−1.08672	−0.0358477	−0.0179239	−	0.999839i	$-0.505706\pi$
$919$	−1.08672	−0.0358477	−0.0179239	+	0.999839i	$0.505706\pi$
$920$	−31.9497	−1.05335
$921$	19.4366	0.640457
$922$	33.8238	1.11393
$923$	0	0
$924$	−0.0659107	−0.00216830
$925$	5.20096	0.171007
$926$	48.9807	1.60961
$927$	15.0401	0.493983
$928$	0.425148	0.0139562
$929$	52.2100	1.71295	0.856477	−	0.516185i	$-0.172648\pi$
$929$	52.2100	1.71295	0.856477	+	0.516185i	$0.172648\pi$
$930$	13.0185	0.426895
$931$	7.98255	0.261618
$932$	0.614461	0.0201273
$933$	−28.1906	−0.922918
$934$	30.9668	1.01326
$935$	7.87599	0.257572
$936$	0	0
$937$	−7.44303	−0.243153	−0.121577	−	0.992582i	$-0.538795\pi$
$937$	−7.44303	−0.243153	−0.121577	+	0.992582i	$0.538795\pi$
$938$	16.2150	0.529439
$939$	13.3965	0.437179
$940$	0.952005	0.0310510
$941$	−41.0689	−1.33881	−0.669403	−	0.742899i	$-0.733450\pi$
$941$	−41.0689	−1.33881	−0.669403	+	0.742899i	$0.733450\pi$
$942$	−21.6885	−0.706649
$943$	−26.2902	−0.856126
$944$	41.3338	1.34530
$945$	−2.86638	−0.0932433
$946$	−15.1638	−0.493018
$947$	3.81057	0.123827	0.0619135	−	0.998082i	$-0.480280\pi$
$947$	3.81057	0.123827	0.0619135	+	0.998082i	$0.480280\pi$
$948$	−0.446974	−0.0145170
$949$	0	0
$950$	−36.9510	−1.19885
$951$	27.5802	0.894349
$952$	8.28415	0.268491
$953$	−33.9461	−1.09962	−0.549811	−	0.835289i	$-0.685300\pi$
$953$	−33.9461	−1.09962	−0.549811	+	0.835289i	$0.685300\pi$
$954$	−9.61514	−0.311302
$955$	62.8219	2.03287
$956$	−0.315658	−0.0102091
$957$	−0.966861	−0.0312542
$958$	14.2685	0.460994
$959$	−14.8963	−0.481028
$960$	−22.0524	−0.711739
$961$	−21.0424	−0.678788
$962$	0	0
$963$	12.1569	0.391749
$964$	0.331434	0.0106748
$965$	−29.4668	−0.948571
$966$	−5.78010	−0.185972
$967$	30.5375	0.982021	0.491010	−	0.871154i	$-0.336628\pi$
$967$	30.5375	0.982021	0.491010	+	0.871154i	$0.336628\pi$
$968$	−28.1788	−0.905702
$969$	−23.8253	−0.765380
$970$	−2.31831	−0.0744365
$971$	−8.15552	−0.261723	−0.130862	−	0.991401i	$-0.541774\pi$
$971$	−8.15552	−0.261723	−0.130862	+	0.991401i	$0.541774\pi$
$972$	−0.0715948	−0.00229641
$973$	−20.5500	−0.658803
$974$	−16.9950	−0.544554
$975$	0	0
$976$	37.0769	1.18680
$977$	−43.2570	−1.38391	−0.691957	−	0.721939i	$-0.743251\pi$
$977$	−43.2570	−1.38391	−0.691957	+	0.721939i	$0.743251\pi$
$978$	−13.0582	−0.417556
$979$	−6.00850	−0.192033
$980$	0.205218	0.00655544
$981$	10.3967	0.331941
$982$	42.9707	1.37125
$983$	−40.4255	−1.28937	−0.644687	−	0.764447i	$-0.723012\pi$
$983$	−40.4255	−1.28937	−0.644687	+	0.764447i	$0.723012\pi$
$984$	−18.1703	−0.579247
$985$	37.8763	1.20684
$986$	−4.51169	−0.143682
$987$	−4.63900	−0.147661
$988$	0	0
$989$	−45.9583	−1.46139
$990$	−3.79804	−0.120710
$991$	2.08489	0.0662287	0.0331144	−	0.999452i	$-0.489457\pi$
$991$	2.08489	0.0662287	0.0331144	+	0.999452i	$0.489457\pi$
$992$	1.27740	0.0405575
$993$	19.8272	0.629198
$994$	−13.0976	−0.415431
$995$	−58.3767	−1.85067
$996$	0.691986	0.0219264
$997$	17.6142	0.557846	0.278923	−	0.960313i	$-0.410023\pi$
$997$	17.6142	0.557846	0.278923	+	0.960313i	$0.410023\pi$
$998$	−29.6967	−0.940032
$999$	−1.61715	−0.0511645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.be.1.3	✓	9
13.12	even	2		3549.2.a.bf.1.7	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.3	✓	9	1.1	even	1	trivial
3549.2.a.bf.1.7	yes	9	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} +2.86638 q^{5} +1.43930 q^{6} +1.00000 q^{7} +2.77556 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} +2.86638 q^{5} +1.43930 q^{6} +1.00000 q^{7} +2.77556 q^{8} +1.00000 q^{9} -4.12559 q^{10} +0.920607 q^{11} -0.0715948 q^{12} -1.43930 q^{14} -2.86638 q^{15} -4.13806 q^{16} +2.98468 q^{17} -1.43930 q^{18} +7.98255 q^{19} +0.205218 q^{20} -1.00000 q^{21} -1.32503 q^{22} -4.01590 q^{23} -2.77556 q^{24} +3.21612 q^{25} -1.00000 q^{27} +0.0715948 q^{28} +1.05024 q^{29} +4.12559 q^{30} +3.15556 q^{31} +0.404809 q^{32} -0.920607 q^{33} -4.29586 q^{34} +2.86638 q^{35} +0.0715948 q^{36} +1.61715 q^{37} -11.4893 q^{38} +7.95580 q^{40} +6.54652 q^{41} +1.43930 q^{42} +11.4441 q^{43} +0.0659107 q^{44} +2.86638 q^{45} +5.78010 q^{46} +4.63900 q^{47} +4.13806 q^{48} +1.00000 q^{49} -4.62897 q^{50} -2.98468 q^{51} +6.68041 q^{53} +1.43930 q^{54} +2.63881 q^{55} +2.77556 q^{56} -7.98255 q^{57} -1.51162 q^{58} -9.98868 q^{59} -0.205218 q^{60} -8.95997 q^{61} -4.54181 q^{62} +1.00000 q^{63} +7.69348 q^{64} +1.32503 q^{66} -11.2659 q^{67} +0.213687 q^{68} +4.01590 q^{69} -4.12559 q^{70} +9.09996 q^{71} +2.77556 q^{72} -7.52599 q^{73} -2.32758 q^{74} -3.21612 q^{75} +0.571509 q^{76} +0.920607 q^{77} +6.24310 q^{79} -11.8613 q^{80} +1.00000 q^{81} -9.42243 q^{82} -9.66531 q^{83} -0.0715948 q^{84} +8.55521 q^{85} -16.4715 q^{86} -1.05024 q^{87} +2.55520 q^{88} -6.52667 q^{89} -4.12559 q^{90} -0.287518 q^{92} -3.15556 q^{93} -6.67693 q^{94} +22.8810 q^{95} -0.404809 q^{96} +0.561935 q^{97} -1.43930 q^{98} +0.920607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9} + q^{10} - q^{11} - 5 q^{12} - q^{14} - 9 q^{15} + 5 q^{16} + 11 q^{17} - q^{18} + 7 q^{19} + 23 q^{20} - 9 q^{21} - 3 q^{22} + 22 q^{23} + 6 q^{24} - 8 q^{25} - 9 q^{27} + 5 q^{28} + 11 q^{29} - q^{30} + 7 q^{31} - 18 q^{32} + q^{33} - 6 q^{34} + 9 q^{35} + 5 q^{36} - q^{37} - 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 32 q^{43} + 18 q^{44} + 9 q^{45} - 9 q^{46} - 12 q^{47} - 5 q^{48} + 9 q^{49} + 10 q^{50} - 11 q^{51} + 13 q^{53} + q^{54} + 9 q^{55} - 6 q^{56} - 7 q^{57} + 4 q^{58} + 29 q^{59} - 23 q^{60} - 12 q^{61} + 30 q^{62} + 9 q^{63} + 6 q^{64} + 3 q^{66} - 20 q^{67} + 34 q^{68} - 22 q^{69} + q^{70} - 2 q^{71} - 6 q^{72} + q^{73} + 43 q^{74} + 8 q^{75} + 13 q^{76} - q^{77} + 3 q^{79} - 39 q^{80} + 9 q^{81} - 19 q^{82} + 24 q^{83} - 5 q^{84} + 15 q^{85} - 28 q^{86} - 11 q^{87} - 19 q^{88} + 11 q^{89} + q^{90} + 73 q^{92} - 7 q^{93} + 15 q^{94} + 39 q^{95} + 18 q^{96} + 20 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 9 * q - q^2 - 9 * q^3 + 5 * q^4 + 9 * q^5 + q^6 + 9 * q^7 - 6 * q^8 + 9 * q^9 + q^10 - q^11 - 5 * q^12 - q^14 - 9 * q^15 + 5 * q^16 + 11 * q^17 - q^18 + 7 * q^19 + 23 * q^20 - 9 * q^21 - 3 * q^22 + 22 * q^23 + 6 * q^24 - 8 * q^25 - 9 * q^27 + 5 * q^28 + 11 * q^29 - q^30 + 7 * q^31 - 18 * q^32 + q^33 - 6 * q^34 + 9 * q^35 + 5 * q^36 - q^37 - 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 32 * q^43 + 18 * q^44 + 9 * q^45 - 9 * q^46 - 12 * q^47 - 5 * q^48 + 9 * q^49 + 10 * q^50 - 11 * q^51 + 13 * q^53 + q^54 + 9 * q^55 - 6 * q^56 - 7 * q^57 + 4 * q^58 + 29 * q^59 - 23 * q^60 - 12 * q^61 + 30 * q^62 + 9 * q^63 + 6 * q^64 + 3 * q^66 - 20 * q^67 + 34 * q^68 - 22 * q^69 + q^70 - 2 * q^71 - 6 * q^72 + q^73 + 43 * q^74 + 8 * q^75 + 13 * q^76 - q^77 + 3 * q^79 - 39 * q^80 + 9 * q^81 - 19 * q^82 + 24 * q^83 - 5 * q^84 + 15 * q^85 - 28 * q^86 - 11 * q^87 - 19 * q^88 + 11 * q^89 + q^90 + 73 * q^92 - 7 * q^93 + 15 * q^94 + 39 * q^95 + 18 * q^96 + 20 * q^97 - q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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