LMFDB - Embedded newform 3549.2.a.y.1.4

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.121819537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 25x^{4} + 55x^{3} + 224x^{2} - 252x - 728 $ x^6 - 3x^5 - 25x^4 + 55x^3 + 224x^2 - 252*x - 728
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			1.4
Root			$3.55940$ 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)

$f(q)$	$=$	$q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +3.55940 q^{5} +0.445042 q^{6} -1.00000 q^{7} +1.69202 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +3.55940 q^{5} +0.445042 q^{6} -1.00000 q^{7} +1.69202 q^{8} +1.00000 q^{9} -1.58408 q^{10} +1.60744 q^{11} +1.80194 q^{12} +0.445042 q^{14} -3.55940 q^{15} +2.85086 q^{16} -0.0554625 q^{17} -0.445042 q^{18} -4.41381 q^{19} -6.41381 q^{20} +1.00000 q^{21} -0.715376 q^{22} -7.96877 q^{23} -1.69202 q^{24} +7.66931 q^{25} -1.00000 q^{27} +1.80194 q^{28} +7.43938 q^{29} +1.58408 q^{30} -9.55729 q^{31} -4.65279 q^{32} -1.60744 q^{33} +0.0246831 q^{34} -3.55940 q^{35} -1.80194 q^{36} -8.02423 q^{37} +1.96433 q^{38} +6.02258 q^{40} +1.24342 q^{41} -0.445042 q^{42} -8.88995 q^{43} -2.89650 q^{44} +3.55940 q^{45} +3.54644 q^{46} +7.76918 q^{47} -2.85086 q^{48} +1.00000 q^{49} -3.41317 q^{50} +0.0554625 q^{51} +5.62811 q^{53} +0.445042 q^{54} +5.72150 q^{55} -1.69202 q^{56} +4.41381 q^{57} -3.31083 q^{58} +3.04840 q^{59} +6.41381 q^{60} -1.88406 q^{61} +4.25340 q^{62} -1.00000 q^{63} -3.63102 q^{64} +0.715376 q^{66} -9.63089 q^{67} +0.0999399 q^{68} +7.96877 q^{69} +1.58408 q^{70} +2.05381 q^{71} +1.69202 q^{72} -3.15229 q^{73} +3.57112 q^{74} -7.66931 q^{75} +7.95342 q^{76} -1.60744 q^{77} -16.3884 q^{79} +10.1473 q^{80} +1.00000 q^{81} -0.553374 q^{82} +12.3363 q^{83} -1.80194 q^{84} -0.197413 q^{85} +3.95640 q^{86} -7.43938 q^{87} +2.71982 q^{88} -7.13735 q^{89} -1.58408 q^{90} +14.3592 q^{92} +9.55729 q^{93} -3.45761 q^{94} -15.7105 q^{95} +4.65279 q^{96} +6.12252 q^{97} -0.445042 q^{98} +1.60744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9	$ 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9} - q^{10} + 2 q^{12} + 2 q^{14} - 3 q^{15} - 10 q^{16} - 9 q^{17} - 2 q^{18} + 11 q^{19} - q^{20} + 6 q^{21} + 7 q^{22} - 11 q^{23} + 29 q^{25} - 6 q^{27} + 2 q^{28} - 10 q^{29} + q^{30} + 7 q^{31} + 8 q^{32} + 10 q^{34} - 3 q^{35} - 2 q^{36} - 20 q^{37} - 6 q^{38} - 10 q^{41} - 2 q^{42} - 9 q^{43} + 3 q^{45} - 8 q^{46} + 36 q^{47} + 10 q^{48} + 6 q^{49} + 9 q^{50} + 9 q^{51} - 12 q^{53} + 2 q^{54} - 29 q^{55} - 11 q^{57} - 6 q^{58} - 41 q^{59} + q^{60} - 24 q^{61} - 6 q^{63} + 8 q^{64} - 7 q^{66} + 15 q^{67} + 10 q^{68} + 11 q^{69} + q^{70} + 13 q^{71} + 25 q^{73} + 2 q^{74} - 29 q^{75} + q^{76} - 16 q^{79} - 5 q^{80} + 6 q^{81} + q^{82} - 2 q^{83} - 2 q^{84} - 33 q^{85} - 4 q^{86} + 10 q^{87} - 14 q^{88} + 15 q^{89} - q^{90} + 13 q^{92} - 7 q^{93} - 33 q^{94} - 23 q^{95} - 8 q^{96} + 10 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9 - q^10 + 2 * q^12 + 2 * q^14 - 3 * q^15 - 10 * q^16 - 9 * q^17 - 2 * q^18 + 11 * q^19 - q^20 + 6 * q^21 + 7 * q^22 - 11 * q^23 + 29 * q^25 - 6 * q^27 + 2 * q^28 - 10 * q^29 + q^30 + 7 * q^31 + 8 * q^32 + 10 * q^34 - 3 * q^35 - 2 * q^36 - 20 * q^37 - 6 * q^38 - 10 * q^41 - 2 * q^42 - 9 * q^43 + 3 * q^45 - 8 * q^46 + 36 * q^47 + 10 * q^48 + 6 * q^49 + 9 * q^50 + 9 * q^51 - 12 * q^53 + 2 * q^54 - 29 * q^55 - 11 * q^57 - 6 * q^58 - 41 * q^59 + q^60 - 24 * q^61 - 6 * q^63 + 8 * q^64 - 7 * q^66 + 15 * q^67 + 10 * q^68 + 11 * q^69 + q^70 + 13 * q^71 + 25 * q^73 + 2 * q^74 - 29 * q^75 + q^76 - 16 * q^79 - 5 * q^80 + 6 * q^81 + q^82 - 2 * q^83 - 2 * q^84 - 33 * q^85 - 4 * q^86 + 10 * q^87 - 14 * q^88 + 15 * q^89 - q^90 + 13 * q^92 - 7 * q^93 - 33 * q^94 - 23 * q^95 - 8 * q^96 + 10 * q^97 - 2 * q^98

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 $

$2$	−0.445042	−0.314692	−0.157346	−	0.987544i	$-0.550294\pi$
$2$	−0.445042	−0.314692	−0.157346	+	0.987544i	$0.550294\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80194	−0.900969
$5$	3.55940	1.59181	0.795906	−	0.605421i	$-0.206995\pi$
$5$	3.55940	1.59181	0.795906	+	0.605421i	$0.206995\pi$
$6$	0.445042	0.181688
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.69202	0.598220
$9$	1.00000	0.333333
$10$	−1.58408	−0.500930
$11$	1.60744	0.484660	0.242330	−	0.970194i	$-0.422088\pi$
$11$	1.60744	0.484660	0.242330	+	0.970194i	$0.422088\pi$
$12$	1.80194	0.520175
$13$	0	0
$13$	0	0
$14$	0.445042	0.118942
$15$	−3.55940	−0.919033
$16$	2.85086	0.712714
$17$	−0.0554625	−0.0134516	−0.00672581	−	0.999977i	$-0.502141\pi$
$17$	−0.0554625	−0.0134516	−0.00672581	+	0.999977i	$0.502141\pi$
$18$	−0.445042	−0.104897
$19$	−4.41381	−1.01260	−0.506299	−	0.862358i	$-0.668987\pi$
$19$	−4.41381	−1.01260	−0.506299	+	0.862358i	$0.668987\pi$
$20$	−6.41381	−1.43417
$21$	1.00000	0.218218
$22$	−0.715376	−0.152519
$23$	−7.96877	−1.66160	−0.830802	−	0.556568i	$-0.812118\pi$
$23$	−7.96877	−1.66160	−0.830802	+	0.556568i	$0.812118\pi$
$24$	−1.69202	−0.345382
$25$	7.66931	1.53386
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.80194	0.340534
$29$	7.43938	1.38146	0.690729	−	0.723114i	$-0.257290\pi$
$29$	7.43938	1.38146	0.690729	+	0.723114i	$0.257290\pi$
$30$	1.58408	0.289212
$31$	−9.55729	−1.71654	−0.858270	−	0.513198i	$-0.828461\pi$
$31$	−9.55729	−1.71654	−0.858270	+	0.513198i	$0.828461\pi$
$32$	−4.65279	−0.822505
$33$	−1.60744	−0.279819
$34$	0.0246831	0.00423312
$35$	−3.55940	−0.601648
$36$	−1.80194	−0.300323
$37$	−8.02423	−1.31918	−0.659588	−	0.751627i	$-0.729269\pi$
$37$	−8.02423	−1.31918	−0.659588	+	0.751627i	$0.729269\pi$
$38$	1.96433	0.318657
$39$	0	0
$40$	6.02258	0.952253
$41$	1.24342	0.194189	0.0970947	−	0.995275i	$-0.469045\pi$
$41$	1.24342	0.194189	0.0970947	+	0.995275i	$0.469045\pi$
$42$	−0.445042	−0.0686715
$43$	−8.88995	−1.35571	−0.677853	−	0.735198i	$-0.737089\pi$
$43$	−8.88995	−1.35571	−0.677853	+	0.735198i	$0.737089\pi$
$44$	−2.89650	−0.436664
$45$	3.55940	0.530604
$46$	3.54644	0.522894
$47$	7.76918	1.13325	0.566626	−	0.823975i	$-0.308248\pi$
$47$	7.76918	1.13325	0.566626	+	0.823975i	$0.308248\pi$
$48$	−2.85086	−0.411485
$49$	1.00000	0.142857
$50$	−3.41317	−0.482695
$51$	0.0554625	0.00776630
$52$	0	0
$53$	5.62811	0.773080	0.386540	−	0.922273i	$-0.373670\pi$
$53$	5.62811	0.773080	0.386540	+	0.922273i	$0.373670\pi$
$54$	0.445042	0.0605625
$55$	5.72150	0.771488
$56$	−1.69202	−0.226106
$57$	4.41381	0.584624
$58$	−3.31083	−0.434734
$59$	3.04840	0.396867	0.198434	−	0.980114i	$-0.436415\pi$
$59$	3.04840	0.396867	0.198434	+	0.980114i	$0.436415\pi$
$60$	6.41381	0.828020
$61$	−1.88406	−0.241229	−0.120615	−	0.992699i	$-0.538487\pi$
$61$	−1.88406	−0.241229	−0.120615	+	0.992699i	$0.538487\pi$
$62$	4.25340	0.540182
$63$	−1.00000	−0.125988
$64$	−3.63102	−0.453878
$65$	0	0
$66$	0.715376	0.0880567
$67$	−9.63089	−1.17660	−0.588300	−	0.808642i	$-0.700203\pi$
$67$	−9.63089	−1.17660	−0.588300	+	0.808642i	$0.700203\pi$
$68$	0.0999399	0.0121195
$69$	7.96877	0.959327
$70$	1.58408	0.189334
$71$	2.05381	0.243742	0.121871	−	0.992546i	$-0.461111\pi$
$71$	2.05381	0.243742	0.121871	+	0.992546i	$0.461111\pi$
$72$	1.69202	0.199407
$73$	−3.15229	−0.368947	−0.184474	−	0.982837i	$-0.559058\pi$
$73$	−3.15229	−0.368947	−0.184474	+	0.982837i	$0.559058\pi$
$74$	3.57112	0.415134
$75$	−7.66931	−0.885576
$76$	7.95342	0.912320
$77$	−1.60744	−0.183184
$78$	0	0
$79$	−16.3884	−1.84383	−0.921917	−	0.387388i	$-0.873378\pi$
$79$	−16.3884	−1.84383	−0.921917	+	0.387388i	$0.873378\pi$
$80$	10.1473	1.13451
$81$	1.00000	0.111111
$82$	−0.553374	−0.0611099
$83$	12.3363	1.35408	0.677042	−	0.735944i	$-0.263262\pi$
$83$	12.3363	1.35408	0.677042	+	0.735944i	$0.263262\pi$
$84$	−1.80194	−0.196608
$85$	−0.197413	−0.0214124
$86$	3.95640	0.426630
$87$	−7.43938	−0.797585
$88$	2.71982	0.289933
$89$	−7.13735	−0.756558	−0.378279	−	0.925692i	$-0.623484\pi$
$89$	−7.13735	−0.756558	−0.378279	+	0.925692i	$0.623484\pi$
$90$	−1.58408	−0.166977
$91$	0	0
$92$	14.3592	1.49705
$93$	9.55729	0.991045
$94$	−3.45761	−0.356625
$95$	−15.7105	−1.61187
$96$	4.65279	0.474874
$97$	6.12252	0.621647	0.310824	−	0.950468i	$-0.399395\pi$
$97$	6.12252	0.621647	0.310824	+	0.950468i	$0.399395\pi$
$98$	−0.445042	−0.0449560
$99$	1.60744	0.161553
$100$	−13.8196	−1.38196
$101$	−11.7890	−1.17305	−0.586527	−	0.809930i	$-0.699505\pi$
$101$	−11.7890	−1.17305	−0.586527	+	0.809930i	$0.699505\pi$
$102$	−0.0246831	−0.00244399
$103$	9.68904	0.954689	0.477345	−	0.878716i	$-0.341599\pi$
$103$	9.68904	0.954689	0.477345	+	0.878716i	$0.341599\pi$
$104$	0	0
$105$	3.55940	0.347362
$106$	−2.50474	−0.243282
$107$	18.0772	1.74759	0.873796	−	0.486293i	$-0.161651\pi$
$107$	18.0772	1.74759	0.873796	+	0.486293i	$0.161651\pi$
$108$	1.80194	0.173392
$109$	1.62120	0.155283	0.0776416	−	0.996981i	$-0.475261\pi$
$109$	1.62120	0.155283	0.0776416	+	0.996981i	$0.475261\pi$
$110$	−2.54631	−0.242781
$111$	8.02423	0.761627
$112$	−2.85086	−0.269380
$113$	6.92138	0.651109	0.325554	−	0.945523i	$-0.394449\pi$
$113$	6.92138	0.651109	0.325554	+	0.945523i	$0.394449\pi$
$114$	−1.96433	−0.183977
$115$	−28.3640	−2.64496
$116$	−13.4053	−1.24465
$117$	0	0
$118$	−1.35666	−0.124891
$119$	0.0554625	0.00508424
$120$	−6.02258	−0.549784
$121$	−8.41615	−0.765105
$122$	0.838485	0.0759129
$123$	−1.24342	−0.112115
$124$	17.2216	1.54655
$125$	9.50115	0.849809
$126$	0.445042	0.0396475
$127$	4.36250	0.387110	0.193555	−	0.981089i	$-0.437998\pi$
$127$	4.36250	0.387110	0.193555	+	0.981089i	$0.437998\pi$
$128$	10.9215	0.965337
$129$	8.88995	0.782717
$130$	0	0
$131$	−17.1595	−1.49923	−0.749615	−	0.661874i	$-0.769762\pi$
$131$	−17.1595	−1.49923	−0.749615	+	0.661874i	$0.769762\pi$
$132$	2.89650	0.252108
$133$	4.41381	0.382726
$134$	4.28615	0.370267
$135$	−3.55940	−0.306344
$136$	−0.0938437	−0.00804703
$137$	−13.3321	−1.13904	−0.569521	−	0.821977i	$-0.692871\pi$
$137$	−13.3321	−1.13904	−0.569521	+	0.821977i	$0.692871\pi$
$138$	−3.54644	−0.301893
$139$	−12.7433	−1.08088	−0.540438	−	0.841384i	$-0.681741\pi$
$139$	−12.7433	−1.08088	−0.540438	+	0.841384i	$0.681741\pi$
$140$	6.41381	0.542066
$141$	−7.76918	−0.654283
$142$	−0.914030	−0.0767037
$143$	0	0
$144$	2.85086	0.237571
$145$	26.4797	2.19902
$146$	1.40290	0.116105
$147$	−1.00000	−0.0824786
$148$	14.4592	1.18854
$149$	18.2625	1.49612	0.748062	−	0.663628i	$-0.230984\pi$
$149$	18.2625	1.49612	0.748062	+	0.663628i	$0.230984\pi$
$150$	3.41317	0.278684
$151$	−19.6642	−1.60025	−0.800126	−	0.599832i	$-0.795234\pi$
$151$	−19.6642	−1.60025	−0.800126	+	0.599832i	$0.795234\pi$
$152$	−7.46827	−0.605756
$153$	−0.0554625	−0.00448388
$154$	0.715376	0.0576467
$155$	−34.0182	−2.73241
$156$	0	0
$157$	−14.0710	−1.12299	−0.561496	−	0.827480i	$-0.689774\pi$
$157$	−14.0710	−1.12299	−0.561496	+	0.827480i	$0.689774\pi$
$158$	7.29350	0.580240
$159$	−5.62811	−0.446338
$160$	−16.5611	−1.30927
$161$	7.96877	0.628027
$162$	−0.445042	−0.0349658
$163$	17.4301	1.36523	0.682615	−	0.730779i	$-0.260843\pi$
$163$	17.4301	1.36523	0.682615	+	0.730779i	$0.260843\pi$
$164$	−2.24056	−0.174959
$165$	−5.72150	−0.445419
$166$	−5.49017	−0.426120
$167$	−3.75827	−0.290824	−0.145412	−	0.989371i	$-0.546451\pi$
$167$	−3.75827	−0.290824	−0.145412	+	0.989371i	$0.546451\pi$
$168$	1.69202	0.130542
$169$	0	0
$170$	0.0878571	0.00673833
$171$	−4.41381	−0.337533
$172$	16.0191	1.22145
$173$	0.819684	0.0623194	0.0311597	−	0.999514i	$-0.490080\pi$
$173$	0.819684	0.0623194	0.0311597	+	0.999514i	$0.490080\pi$
$174$	3.31083	0.250994
$175$	−7.66931	−0.579746
$176$	4.58257	0.345424
$177$	−3.04840	−0.229132
$178$	3.17642	0.238083
$179$	5.48240	0.409774	0.204887	−	0.978786i	$-0.434317\pi$
$179$	5.48240	0.409774	0.204887	+	0.978786i	$0.434317\pi$
$180$	−6.41381	−0.478057
$181$	−9.47320	−0.704137	−0.352069	−	0.935974i	$-0.614522\pi$
$181$	−9.47320	−0.704137	−0.352069	+	0.935974i	$0.614522\pi$
$182$	0	0
$183$	1.88406	0.139274
$184$	−13.4833	−0.994004
$185$	−28.5614	−2.09988
$186$	−4.25340	−0.311874
$187$	−0.0891524	−0.00651947
$188$	−13.9996	−1.02102
$189$	1.00000	0.0727393
$190$	6.99184	0.507241
$191$	−8.28702	−0.599628	−0.299814	−	0.953998i	$-0.596925\pi$
$191$	−8.28702	−0.599628	−0.299814	+	0.953998i	$0.596925\pi$
$192$	3.63102	0.262046
$193$	−17.5808	−1.26549	−0.632745	−	0.774360i	$-0.718072\pi$
$193$	−17.5808	−1.26549	−0.632745	+	0.774360i	$0.718072\pi$
$194$	−2.72478	−0.195628
$195$	0	0
$196$	−1.80194	−0.128710
$197$	−1.11477	−0.0794243	−0.0397122	−	0.999211i	$-0.512644\pi$
$197$	−1.11477	−0.0794243	−0.0397122	+	0.999211i	$0.512644\pi$
$198$	−0.715376	−0.0508396
$199$	−5.83074	−0.413330	−0.206665	−	0.978412i	$-0.566261\pi$
$199$	−5.83074	−0.413330	−0.206665	+	0.978412i	$0.566261\pi$
$200$	12.9766	0.917587
$201$	9.63089	0.679311
$202$	5.24662	0.369151
$203$	−7.43938	−0.522142
$204$	−0.0999399	−0.00699719
$205$	4.42582	0.309113
$206$	−4.31203	−0.300433
$207$	−7.96877	−0.553868
$208$	0	0
$209$	−7.09492	−0.490766
$210$	−1.58408	−0.109312
$211$	−7.33406	−0.504898	−0.252449	−	0.967610i	$-0.581236\pi$
$211$	−7.33406	−0.504898	−0.252449	+	0.967610i	$0.581236\pi$
$212$	−10.1415	−0.696521
$213$	−2.05381	−0.140724
$214$	−8.04513	−0.549953
$215$	−31.6429	−2.15803
$216$	−1.69202	−0.115127
$217$	9.55729	0.648791
$218$	−0.721504	−0.0488664
$219$	3.15229	0.213012
$220$	−10.3098	−0.695086
$221$	0	0
$222$	−3.57112	−0.239678
$223$	1.31086	0.0877817	0.0438908	−	0.999036i	$-0.486025\pi$
$223$	1.31086	0.0877817	0.0438908	+	0.999036i	$0.486025\pi$
$224$	4.65279	0.310878
$225$	7.66931	0.511288
$226$	−3.08030	−0.204899
$227$	−14.8275	−0.984136	−0.492068	−	0.870557i	$-0.663759\pi$
$227$	−14.8275	−0.984136	−0.492068	+	0.870557i	$0.663759\pi$
$228$	−7.95342	−0.526728
$229$	4.57818	0.302535	0.151267	−	0.988493i	$-0.451665\pi$
$229$	4.57818	0.302535	0.151267	+	0.988493i	$0.451665\pi$
$230$	12.6232	0.832348
$231$	1.60744	0.105762
$232$	12.5876	0.826415
$233$	−3.05947	−0.200433	−0.100216	−	0.994966i	$-0.531953\pi$
$233$	−3.05947	−0.200433	−0.100216	+	0.994966i	$0.531953\pi$
$234$	0	0
$235$	27.6536	1.80392
$236$	−5.49302	−0.357565
$237$	16.3884	1.06454
$238$	−0.0246831	−0.00159997
$239$	−2.01503	−0.130342	−0.0651709	−	0.997874i	$-0.520759\pi$
$239$	−2.01503	−0.130342	−0.0651709	+	0.997874i	$0.520759\pi$
$240$	−10.1473	−0.655007
$241$	25.8798	1.66707	0.833533	−	0.552470i	$-0.186315\pi$
$241$	25.8798	1.66707	0.833533	+	0.552470i	$0.186315\pi$
$242$	3.74554	0.240772
$243$	−1.00000	−0.0641500
$244$	3.39496	0.217340
$245$	3.55940	0.227402
$246$	0.553374	0.0352818
$247$	0	0
$248$	−16.1711	−1.02687
$249$	−12.3363	−0.781781
$250$	−4.22841	−0.267428
$251$	−18.7095	−1.18093	−0.590465	−	0.807063i	$-0.701056\pi$
$251$	−18.7095	−1.18093	−0.590465	+	0.807063i	$0.701056\pi$
$252$	1.80194	0.113511
$253$	−12.8093	−0.805313
$254$	−1.94150	−0.121820
$255$	0.197413	0.0123625
$256$	2.40150	0.150094
$257$	−18.7918	−1.17220	−0.586101	−	0.810238i	$-0.699338\pi$
$257$	−18.7918	−1.17220	−0.586101	+	0.810238i	$0.699338\pi$
$258$	−3.95640	−0.246315
$259$	8.02423	0.498602
$260$	0	0
$261$	7.43938	0.460486
$262$	7.63669	0.471796
$263$	10.3222	0.636496	0.318248	−	0.948007i	$-0.396905\pi$
$263$	10.3222	0.636496	0.318248	+	0.948007i	$0.396905\pi$
$264$	−2.71982	−0.167393
$265$	20.0327	1.23060
$266$	−1.96433	−0.120441
$267$	7.13735	0.436799
$268$	17.3543	1.06008
$269$	−18.2365	−1.11190	−0.555950	−	0.831216i	$-0.687645\pi$
$269$	−18.2365	−1.11190	−0.555950	+	0.831216i	$0.687645\pi$
$270$	1.58408	0.0964041
$271$	−11.1028	−0.674447	−0.337223	−	0.941425i	$-0.609488\pi$
$271$	−11.1028	−0.674447	−0.337223	+	0.941425i	$0.609488\pi$
$272$	−0.158115	−0.00958716
$273$	0	0
$274$	5.93336	0.358447
$275$	12.3279	0.743402
$276$	−14.3592	−0.864324
$277$	16.7114	1.00409	0.502044	−	0.864842i	$-0.332581\pi$
$277$	16.7114	1.00409	0.502044	+	0.864842i	$0.332581\pi$
$278$	5.67132	0.340143
$279$	−9.55729	−0.572180
$280$	−6.02258	−0.359918
$281$	9.09459	0.542538	0.271269	−	0.962504i	$-0.412557\pi$
$281$	9.09459	0.542538	0.271269	+	0.962504i	$0.412557\pi$
$282$	3.45761	0.205898
$283$	−28.1035	−1.67058	−0.835290	−	0.549810i	$-0.814700\pi$
$283$	−28.1035	−1.67058	−0.835290	+	0.549810i	$0.814700\pi$
$284$	−3.70083	−0.219604
$285$	15.7105	0.930611
$286$	0	0
$287$	−1.24342	−0.0733967
$288$	−4.65279	−0.274168
$289$	−16.9969	−0.999819
$290$	−11.7846	−0.692014
$291$	−6.12252	−0.358908
$292$	5.68023	0.332410
$293$	13.6457	0.797192	0.398596	−	0.917127i	$-0.369498\pi$
$293$	13.6457	0.797192	0.398596	+	0.917127i	$0.369498\pi$
$294$	0.445042	0.0259554
$295$	10.8505	0.631738
$296$	−13.5772	−0.789157
$297$	−1.60744	−0.0932729
$298$	−8.12759	−0.470819
$299$	0	0
$300$	13.8196	0.797877
$301$	8.88995	0.512408
$302$	8.75140	0.503587
$303$	11.7890	0.677263
$304$	−12.5831	−0.721693
$305$	−6.70612	−0.383991
$306$	0.0246831	0.00141104
$307$	3.80129	0.216951	0.108475	−	0.994099i	$-0.465403\pi$
$307$	3.80129	0.216951	0.108475	+	0.994099i	$0.465403\pi$
$308$	2.89650	0.165043
$309$	−9.68904	−0.551190
$310$	15.1395	0.859867
$311$	1.24668	0.0706925	0.0353463	−	0.999375i	$-0.488747\pi$
$311$	1.24668	0.0706925	0.0353463	+	0.999375i	$0.488747\pi$
$312$	0	0
$313$	28.6055	1.61688	0.808440	−	0.588578i	$-0.200312\pi$
$313$	28.6055	1.61688	0.808440	+	0.588578i	$0.200312\pi$
$314$	6.26220	0.353397
$315$	−3.55940	−0.200549
$316$	29.5308	1.66124
$317$	−32.9494	−1.85062	−0.925310	−	0.379210i	$-0.876196\pi$
$317$	−32.9494	−1.85062	−0.925310	+	0.379210i	$0.876196\pi$
$318$	2.50474	0.140459
$319$	11.9583	0.669537
$320$	−12.9243	−0.722488
$321$	−18.0772	−1.00897
$322$	−3.54644	−0.197635
$323$	0.244801	0.0136211
$324$	−1.80194	−0.100108
$325$	0	0
$326$	−7.75712	−0.429627
$327$	−1.62120	−0.0896528
$328$	2.10389	0.116168
$329$	−7.76918	−0.428329
$330$	2.54631	0.140170
$331$	22.6342	1.24409	0.622044	−	0.782982i	$-0.286302\pi$
$331$	22.6342	1.24409	0.622044	+	0.782982i	$0.286302\pi$
$332$	−22.2292	−1.21999
$333$	−8.02423	−0.439725
$334$	1.67259	0.0915199
$335$	−34.2802	−1.87293
$336$	2.85086	0.155527
$337$	−24.7954	−1.35069	−0.675346	−	0.737501i	$-0.736005\pi$
$337$	−24.7954	−1.35069	−0.675346	+	0.737501i	$0.736005\pi$
$338$	0	0
$339$	−6.92138	−0.375918
$340$	0.355726	0.0192919
$341$	−15.3627	−0.831939
$342$	1.96433	0.106219
$343$	−1.00000	−0.0539949
$344$	−15.0420	−0.811010
$345$	28.3640	1.52707
$346$	−0.364794	−0.0196114
$347$	6.80055	0.365073	0.182536	−	0.983199i	$-0.441569\pi$
$347$	6.80055	0.365073	0.182536	+	0.983199i	$0.441569\pi$
$348$	13.4053	0.718599
$349$	14.1930	0.759732	0.379866	−	0.925042i	$-0.375970\pi$
$349$	14.1930	0.759732	0.379866	+	0.925042i	$0.375970\pi$
$350$	3.41317	0.182441
$351$	0	0
$352$	−7.47907	−0.398636
$353$	−28.5761	−1.52095	−0.760476	−	0.649367i	$-0.775034\pi$
$353$	−28.5761	−1.52095	−0.760476	+	0.649367i	$0.775034\pi$
$354$	1.35666	0.0721059
$355$	7.31031	0.387991
$356$	12.8611	0.681635
$357$	−0.0554625	−0.00293539
$358$	−2.43990	−0.128952
$359$	−16.9017	−0.892038	−0.446019	−	0.895023i	$-0.647159\pi$
$359$	−16.9017	−0.892038	−0.446019	+	0.895023i	$0.647159\pi$
$360$	6.02258	0.317418
$361$	0.481751	0.0253553
$362$	4.21597	0.221586
$363$	8.41615	0.441733
$364$	0	0
$365$	−11.2202	−0.587295
$366$	−0.838485	−0.0438283
$367$	−20.0253	−1.04531	−0.522657	−	0.852543i	$-0.675059\pi$
$367$	−20.0253	−1.04531	−0.522657	+	0.852543i	$0.675059\pi$
$368$	−22.7178	−1.18425
$369$	1.24342	0.0647298
$370$	12.7110	0.660815
$371$	−5.62811	−0.292197
$372$	−17.2216	−0.892901
$373$	−28.1607	−1.45811	−0.729053	−	0.684457i	$-0.760039\pi$
$373$	−28.1607	−1.45811	−0.729053	+	0.684457i	$0.760039\pi$
$374$	0.0396765	0.00205162
$375$	−9.50115	−0.490637
$376$	13.1456	0.677934
$377$	0	0
$378$	−0.445042	−0.0228905
$379$	−34.4242	−1.76825	−0.884126	−	0.467249i	$-0.845245\pi$
$379$	−34.4242	−1.76825	−0.884126	+	0.467249i	$0.845245\pi$
$380$	28.3094	1.45224
$381$	−4.36250	−0.223498
$382$	3.68807	0.188698
$383$	31.4155	1.60526	0.802628	−	0.596480i	$-0.203435\pi$
$383$	31.4155	1.60526	0.802628	+	0.596480i	$0.203435\pi$
$384$	−10.9215	−0.557338
$385$	−5.72150	−0.291595
$386$	7.82417	0.398240
$387$	−8.88995	−0.451902
$388$	−11.0324	−0.560085
$389$	16.1140	0.817010	0.408505	−	0.912756i	$-0.366050\pi$
$389$	16.1140	0.817010	0.408505	+	0.912756i	$0.366050\pi$
$390$	0	0
$391$	0.441968	0.0223513
$392$	1.69202	0.0854600
$393$	17.1595	0.865581
$394$	0.496121	0.0249942
$395$	−58.3327	−2.93504
$396$	−2.89650	−0.145555
$397$	−29.1667	−1.46383	−0.731917	−	0.681393i	$-0.761374\pi$
$397$	−29.1667	−1.46383	−0.731917	+	0.681393i	$0.761374\pi$
$398$	2.59492	0.130072
$399$	−4.41381	−0.220967
$400$	21.8641	1.09321
$401$	−9.41919	−0.470372	−0.235186	−	0.971950i	$-0.575570\pi$
$401$	−9.41919	−0.470372	−0.235186	+	0.971950i	$0.575570\pi$
$402$	−4.28615	−0.213774
$403$	0	0
$404$	21.2431	1.05689
$405$	3.55940	0.176868
$406$	3.31083	0.164314
$407$	−12.8984	−0.639352
$408$	0.0938437	0.00464596
$409$	−20.0707	−0.992434	−0.496217	−	0.868198i	$-0.665278\pi$
$409$	−20.0707	−0.992434	−0.496217	+	0.868198i	$0.665278\pi$
$410$	−1.96968	−0.0972754
$411$	13.3321	0.657626
$412$	−17.4590	−0.860145
$413$	−3.04840	−0.150002
$414$	3.54644	0.174298
$415$	43.9098	2.15545
$416$	0	0
$417$	12.7433	0.624044
$418$	3.15754	0.154440
$419$	31.0724	1.51799	0.758994	−	0.651098i	$-0.225691\pi$
$419$	31.0724	1.51799	0.758994	+	0.651098i	$0.225691\pi$
$420$	−6.41381	−0.312962
$421$	−15.8124	−0.770649	−0.385325	−	0.922781i	$-0.625911\pi$
$421$	−15.8124	−0.770649	−0.385325	+	0.922781i	$0.625911\pi$
$422$	3.26396	0.158887
$423$	7.76918	0.377751
$424$	9.52288	0.462472
$425$	−0.425359	−0.0206329
$426$	0.914030	0.0442849
$427$	1.88406	0.0911760
$428$	−32.5740	−1.57453
$429$	0	0
$430$	14.0824	0.679114
$431$	−16.9939	−0.818568	−0.409284	−	0.912407i	$-0.634221\pi$
$431$	−16.9939	−0.818568	−0.409284	+	0.912407i	$0.634221\pi$
$432$	−2.85086	−0.137162
$433$	20.7188	0.995681	0.497841	−	0.867269i	$-0.334126\pi$
$433$	20.7188	0.995681	0.497841	+	0.867269i	$0.334126\pi$
$434$	−4.25340	−0.204170
$435$	−26.4797	−1.26960
$436$	−2.92131	−0.139905
$437$	35.1727	1.68254
$438$	−1.40290	−0.0670332
$439$	−3.68470	−0.175861	−0.0879306	−	0.996127i	$-0.528025\pi$
$439$	−3.68470	−0.175861	−0.0879306	+	0.996127i	$0.528025\pi$
$440$	9.68091	0.461519
$441$	1.00000	0.0476190
$442$	0	0
$443$	−9.08099	−0.431451	−0.215726	−	0.976454i	$-0.569212\pi$
$443$	−9.08099	−0.431451	−0.215726	+	0.976454i	$0.569212\pi$
$444$	−14.4592	−0.686202
$445$	−25.4047	−1.20430
$446$	−0.583388	−0.0276242
$447$	−18.2625	−0.863788
$448$	3.63102	0.171550
$449$	−16.4672	−0.777135	−0.388568	−	0.921420i	$-0.627030\pi$
$449$	−16.4672	−0.777135	−0.388568	+	0.921420i	$0.627030\pi$
$450$	−3.41317	−0.160898
$451$	1.99872	0.0941159
$452$	−12.4719	−0.586629
$453$	19.6642	0.923906
$454$	6.59886	0.309700
$455$	0	0
$456$	7.46827	0.349734
$457$	−34.9901	−1.63677	−0.818384	−	0.574672i	$-0.805130\pi$
$457$	−34.9901	−1.63677	−0.818384	+	0.574672i	$0.805130\pi$
$458$	−2.03748	−0.0952053
$459$	0.0554625	0.00258877
$460$	51.1102	2.38303
$461$	23.2112	1.08105	0.540527	−	0.841327i	$-0.318225\pi$
$461$	23.2112	1.08105	0.540527	+	0.841327i	$0.318225\pi$
$462$	−0.715376	−0.0332823
$463$	13.3932	0.622435	0.311218	−	0.950339i	$-0.399263\pi$
$463$	13.3932	0.622435	0.311218	+	0.950339i	$0.399263\pi$
$464$	21.2086	0.984584
$465$	34.0182	1.57756
$466$	1.36159	0.0630746
$467$	−10.0508	−0.465095	−0.232548	−	0.972585i	$-0.574706\pi$
$467$	−10.0508	−0.465095	−0.232548	+	0.972585i	$0.574706\pi$
$468$	0	0
$469$	9.63089	0.444713
$470$	−12.3070	−0.567680
$471$	14.0710	0.648360
$472$	5.15795	0.237414
$473$	−14.2900	−0.657056
$474$	−7.29350	−0.335002
$475$	−33.8509	−1.55319
$476$	−0.0999399	−0.00458074
$477$	5.62811	0.257693
$478$	0.896775	0.0410175
$479$	23.1013	1.05552	0.527762	−	0.849392i	$-0.323031\pi$
$479$	23.1013	1.05552	0.527762	+	0.849392i	$0.323031\pi$
$480$	16.5611	0.755909
$481$	0	0
$482$	−11.5176	−0.524612
$483$	−7.96877	−0.362592
$484$	15.1654	0.689335
$485$	21.7925	0.989545
$486$	0.445042	0.0201875
$487$	11.4301	0.517948	0.258974	−	0.965884i	$-0.416616\pi$
$487$	11.4301	0.517948	0.258974	+	0.965884i	$0.416616\pi$
$488$	−3.18787	−0.144308
$489$	−17.4301	−0.788215
$490$	−1.58408	−0.0715615
$491$	35.8889	1.61964	0.809821	−	0.586677i	$-0.199564\pi$
$491$	35.8889	1.61964	0.809821	+	0.586677i	$0.199564\pi$
$492$	2.24056	0.101012
$493$	−0.412606	−0.0185828
$494$	0	0
$495$	5.72150	0.257163
$496$	−27.2465	−1.22340
$497$	−2.05381	−0.0921258
$498$	5.49017	0.246020
$499$	35.0866	1.57069	0.785347	−	0.619056i	$-0.212485\pi$
$499$	35.0866	1.57069	0.785347	+	0.619056i	$0.212485\pi$
$500$	−17.1205	−0.765651
$501$	3.75827	0.167907
$502$	8.32649	0.371629
$503$	27.7065	1.23537	0.617687	−	0.786424i	$-0.288070\pi$
$503$	27.7065	1.23537	0.617687	+	0.786424i	$0.288070\pi$
$504$	−1.69202	−0.0753686
$505$	−41.9619	−1.86728
$506$	5.70067	0.253426
$507$	0	0
$508$	−7.86096	−0.348774
$509$	38.0005	1.68434	0.842172	−	0.539209i	$-0.181277\pi$
$509$	38.0005	1.68434	0.842172	+	0.539209i	$0.181277\pi$
$510$	−0.0878571	−0.00389038
$511$	3.15229	0.139449
$512$	−22.9119	−1.01257
$513$	4.41381	0.194875
$514$	8.36315	0.368883
$515$	34.4871	1.51968
$516$	−16.0191	−0.705204
$517$	12.4885	0.549242
$518$	−3.57112	−0.156906
$519$	−0.819684	−0.0359802
$520$	0	0
$521$	−3.31164	−0.145086	−0.0725429	−	0.997365i	$-0.523111\pi$
$521$	−3.31164	−0.145086	−0.0725429	+	0.997365i	$0.523111\pi$
$522$	−3.31083	−0.144911
$523$	31.1804	1.36342	0.681712	−	0.731621i	$-0.261236\pi$
$523$	31.1804	1.36342	0.681712	+	0.731621i	$0.261236\pi$
$524$	30.9203	1.35076
$525$	7.66931	0.334716
$526$	−4.59383	−0.200300
$527$	0.530071	0.0230903
$528$	−4.58257	−0.199431
$529$	40.5013	1.76093
$530$	−8.91538	−0.387259
$531$	3.04840	0.132289
$532$	−7.95342	−0.344824
$533$	0	0
$534$	−3.17642	−0.137457
$535$	64.3441	2.78184
$536$	−16.2957	−0.703866
$537$	−5.48240	−0.236583
$538$	8.11601	0.349906
$539$	1.60744	0.0692372
$540$	6.41381	0.276007
$541$	24.0458	1.03381	0.516904	−	0.856043i	$-0.327084\pi$
$541$	24.0458	1.03381	0.516904	+	0.856043i	$0.327084\pi$
$542$	4.94121	0.212243
$543$	9.47320	0.406534
$544$	0.258055	0.0110640
$545$	5.77051	0.247182
$546$	0	0
$547$	−1.96084	−0.0838395	−0.0419198	−	0.999121i	$-0.513347\pi$
$547$	−1.96084	−0.0838395	−0.0419198	+	0.999121i	$0.513347\pi$
$548$	24.0237	1.02624
$549$	−1.88406	−0.0804097
$550$	−5.48645	−0.233943
$551$	−32.8360	−1.39886
$552$	13.4833	0.573889
$553$	16.3884	0.696904
$554$	−7.43726	−0.315979
$555$	28.5614	1.21237
$556$	22.9627	0.973835
$557$	12.5095	0.530045	0.265022	−	0.964242i	$-0.414621\pi$
$557$	12.5095	0.530045	0.265022	+	0.964242i	$0.414621\pi$
$558$	4.25340	0.180061
$559$	0	0
$560$	−10.1473	−0.428803
$561$	0.0891524	0.00376402
$562$	−4.04747	−0.170732
$563$	3.67811	0.155014	0.0775069	−	0.996992i	$-0.475304\pi$
$563$	3.67811	0.155014	0.0775069	+	0.996992i	$0.475304\pi$
$564$	13.9996	0.589489
$565$	24.6360	1.03644
$566$	12.5072	0.525718
$567$	−1.00000	−0.0419961
$568$	3.47508	0.145811
$569$	−12.4448	−0.521714	−0.260857	−	0.965378i	$-0.584005\pi$
$569$	−12.4448	−0.521714	−0.260857	+	0.965378i	$0.584005\pi$
$570$	−6.99184	−0.292856
$571$	−7.50203	−0.313950	−0.156975	−	0.987603i	$-0.550174\pi$
$571$	−7.50203	−0.313950	−0.156975	+	0.987603i	$0.550174\pi$
$572$	0	0
$573$	8.28702	0.346195
$574$	0.553374	0.0230974
$575$	−61.1150	−2.54867
$576$	−3.63102	−0.151293
$577$	7.48016	0.311403	0.155702	−	0.987804i	$-0.450236\pi$
$577$	7.48016	0.311403	0.155702	+	0.987804i	$0.450236\pi$
$578$	7.56434	0.314635
$579$	17.5808	0.730631
$580$	−47.7148	−1.98125
$581$	−12.3363	−0.511796
$582$	2.72478	0.112946
$583$	9.04683	0.374681
$584$	−5.33374	−0.220712
$585$	0	0
$586$	−6.07292	−0.250870
$587$	24.2860	1.00239	0.501196	−	0.865334i	$-0.332894\pi$
$587$	24.2860	1.00239	0.501196	+	0.865334i	$0.332894\pi$
$588$	1.80194	0.0743107
$589$	42.1841	1.73817
$590$	−4.82891	−0.198803
$591$	1.11477	0.0458557
$592$	−22.8759	−0.940195
$593$	−3.17629	−0.130435	−0.0652174	−	0.997871i	$-0.520774\pi$
$593$	−3.17629	−0.130435	−0.0652174	+	0.997871i	$0.520774\pi$
$594$	0.715376	0.0293522
$595$	0.197413	0.00809314
$596$	−32.9079	−1.34796
$597$	5.83074	0.238636
$598$	0	0
$599$	−35.8889	−1.46638	−0.733191	−	0.680023i	$-0.761970\pi$
$599$	−35.8889	−1.46638	−0.733191	+	0.680023i	$0.761970\pi$
$600$	−12.9766	−0.529769
$601$	−38.8412	−1.58436	−0.792182	−	0.610285i	$-0.791055\pi$
$601$	−38.8412	−1.58436	−0.792182	+	0.610285i	$0.791055\pi$
$602$	−3.95640	−0.161251
$603$	−9.63089	−0.392200
$604$	35.4337	1.44178
$605$	−29.9564	−1.21790
$606$	−5.24662	−0.213129
$607$	20.3182	0.824691	0.412345	−	0.911028i	$-0.364710\pi$
$607$	20.3182	0.824691	0.412345	+	0.911028i	$0.364710\pi$
$608$	20.5366	0.832867
$609$	7.43938	0.301459
$610$	2.98450	0.120839
$611$	0	0
$612$	0.0999399	0.00403983
$613$	15.1451	0.611704	0.305852	−	0.952079i	$-0.401059\pi$
$613$	15.1451	0.611704	0.305852	+	0.952079i	$0.401059\pi$
$614$	−1.69173	−0.0682728
$615$	−4.42582	−0.178466
$616$	−2.71982	−0.109585
$617$	24.2592	0.976640	0.488320	−	0.872665i	$-0.337610\pi$
$617$	24.2592	0.976640	0.488320	+	0.872665i	$0.337610\pi$
$618$	4.31203	0.173455
$619$	−22.1250	−0.889279	−0.444640	−	0.895710i	$-0.646668\pi$
$619$	−22.1250	−0.889279	−0.444640	+	0.895710i	$0.646668\pi$
$620$	61.2987	2.46181
$621$	7.96877	0.319776
$622$	−0.554823	−0.0222464
$623$	7.13735	0.285952
$624$	0	0
$625$	−4.52819	−0.181128
$626$	−12.7307	−0.508819
$627$	7.09492	0.283344
$628$	25.3551	1.01178
$629$	0.445044	0.0177451
$630$	1.58408	0.0631113
$631$	−6.12725	−0.243922	−0.121961	−	0.992535i	$-0.538918\pi$
$631$	−6.12725	−0.243922	−0.121961	+	0.992535i	$0.538918\pi$
$632$	−27.7294	−1.10302
$633$	7.33406	0.291503
$634$	14.6638	0.582376
$635$	15.5279	0.616205
$636$	10.1415	0.402137
$637$	0	0
$638$	−5.32195	−0.210698
$639$	2.05381	0.0812473
$640$	38.8741	1.53663
$641$	−5.45467	−0.215447	−0.107723	−	0.994181i	$-0.534356\pi$
$641$	−5.45467	−0.215447	−0.107723	+	0.994181i	$0.534356\pi$
$642$	8.04513	0.317516
$643$	4.73517	0.186737	0.0933684	−	0.995632i	$-0.470237\pi$
$643$	4.73517	0.186737	0.0933684	+	0.995632i	$0.470237\pi$
$644$	−14.3592	−0.565833
$645$	31.6429	1.24594
$646$	−0.108947	−0.00428645
$647$	10.7086	0.421000	0.210500	−	0.977594i	$-0.432491\pi$
$647$	10.7086	0.421000	0.210500	+	0.977594i	$0.432491\pi$
$648$	1.69202	0.0664689
$649$	4.90010	0.192346
$650$	0	0
$651$	−9.55729	−0.374580
$652$	−31.4079	−1.23003
$653$	−4.35974	−0.170610	−0.0853049	−	0.996355i	$-0.527186\pi$
$653$	−4.35974	−0.170610	−0.0853049	+	0.996355i	$0.527186\pi$
$654$	0.721504	0.0282130
$655$	−61.0774	−2.38649
$656$	3.54481	0.138401
$657$	−3.15229	−0.122982
$658$	3.45761	0.134792
$659$	−24.5836	−0.957639	−0.478820	−	0.877913i	$-0.658935\pi$
$659$	−24.5836	−0.957639	−0.478820	+	0.877913i	$0.658935\pi$
$660$	10.3098	0.401308
$661$	−0.455051	−0.0176994	−0.00884972	−	0.999961i	$-0.502817\pi$
$661$	−0.455051	−0.0176994	−0.00884972	+	0.999961i	$0.502817\pi$
$662$	−10.0732	−0.391505
$663$	0	0
$664$	20.8733	0.810040
$665$	15.7105	0.609228
$666$	3.57112	0.138378
$667$	−59.2827	−2.29543
$668$	6.77216	0.262023
$669$	−1.31086	−0.0506808
$670$	15.2561	0.589395
$671$	−3.02850	−0.116914
$672$	−4.65279	−0.179485
$673$	6.02585	0.232280	0.116140	−	0.993233i	$-0.462948\pi$
$673$	6.02585	0.232280	0.116140	+	0.993233i	$0.462948\pi$
$674$	11.0350	0.425052
$675$	−7.66931	−0.295192
$676$	0	0
$677$	−13.6948	−0.526333	−0.263166	−	0.964750i	$-0.584767\pi$
$677$	−13.6948	−0.526333	−0.263166	+	0.964750i	$0.584767\pi$
$678$	3.08030	0.118298
$679$	−6.12252	−0.234961
$680$	−0.334027	−0.0128094
$681$	14.8275	0.568191
$682$	6.83706	0.261805
$683$	32.6850	1.25066	0.625328	−	0.780362i	$-0.284965\pi$
$683$	32.6850	1.25066	0.625328	+	0.780362i	$0.284965\pi$
$684$	7.95342	0.304107
$685$	−47.4544	−1.81314
$686$	0.445042	0.0169918
$687$	−4.57818	−0.174669
$688$	−25.3440	−0.966230
$689$	0	0
$690$	−12.6232	−0.480556
$691$	49.7650	1.89315	0.946575	−	0.322483i	$-0.104517\pi$
$691$	49.7650	1.89315	0.946575	+	0.322483i	$0.104517\pi$
$692$	−1.47702	−0.0561479
$693$	−1.60744	−0.0610614
$694$	−3.02653	−0.114886
$695$	−45.3586	−1.72055
$696$	−12.5876	−0.477131
$697$	−0.0689631	−0.00261216
$698$	−6.31646	−0.239082
$699$	3.05947	0.115720
$700$	13.8196	0.522333
$701$	−9.03713	−0.341328	−0.170664	−	0.985329i	$-0.554591\pi$
$701$	−9.03713	−0.341328	−0.170664	+	0.985329i	$0.554591\pi$
$702$	0	0
$703$	35.4175	1.33580
$704$	−5.83664	−0.219977
$705$	−27.6536	−1.04150
$706$	12.7176	0.478631
$707$	11.7890	0.443373
$708$	5.49302	0.206440
$709$	7.58071	0.284700	0.142350	−	0.989816i	$-0.454534\pi$
$709$	7.58071	0.284700	0.142350	+	0.989816i	$0.454534\pi$
$710$	−3.25340	−0.122098
$711$	−16.3884	−0.614611
$712$	−12.0766	−0.452588
$713$	76.1599	2.85221
$714$	0.0246831	0.000923743 0
$715$	0	0
$716$	−9.87894	−0.369193
$717$	2.01503	0.0752529
$718$	7.52197	0.280717
$719$	−47.5391	−1.77291	−0.886455	−	0.462815i	$-0.846840\pi$
$719$	−47.5391	−1.77291	−0.886455	+	0.462815i	$0.846840\pi$
$720$	10.1473	0.378169
$721$	−9.68904	−0.360839
$722$	−0.214399	−0.00797911
$723$	−25.8798	−0.962481
$724$	17.0701	0.634406
$725$	57.0549	2.11897
$726$	−3.74554	−0.139010
$727$	40.5707	1.50468	0.752341	−	0.658773i	$-0.228924\pi$
$727$	40.5707	1.50468	0.752341	+	0.658773i	$0.228924\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.99348	0.184817
$731$	0.493059	0.0182364
$732$	−3.39496	−0.125481
$733$	−2.59934	−0.0960090	−0.0480045	−	0.998847i	$-0.515286\pi$
$733$	−2.59934	−0.0960090	−0.0480045	+	0.998847i	$0.515286\pi$
$734$	8.91211	0.328952
$735$	−3.55940	−0.131290
$736$	37.0770	1.36668
$737$	−15.4810	−0.570252
$738$	−0.553374	−0.0203700
$739$	20.1536	0.741363	0.370681	−	0.928760i	$-0.379124\pi$
$739$	20.1536	0.741363	0.370681	+	0.928760i	$0.379124\pi$
$740$	51.4659	1.89193
$741$	0	0
$742$	2.50474	0.0919521
$743$	32.6703	1.19856	0.599278	−	0.800541i	$-0.295454\pi$
$743$	32.6703	1.19856	0.599278	+	0.800541i	$0.295454\pi$
$744$	16.1711	0.592863
$745$	65.0036	2.38155
$746$	12.5327	0.458855
$747$	12.3363	0.451361
$748$	0.160647	0.00587384
$749$	−18.0772	−0.660528
$750$	4.22841	0.154400
$751$	40.6328	1.48271	0.741356	−	0.671112i	$-0.234183\pi$
$751$	40.6328	1.48271	0.741356	+	0.671112i	$0.234183\pi$
$752$	22.1488	0.807684
$753$	18.7095	0.681810
$754$	0	0
$755$	−69.9928	−2.54730
$756$	−1.80194	−0.0655358
$757$	−48.3376	−1.75686	−0.878430	−	0.477872i	$-0.841408\pi$
$757$	−48.3376	−1.75686	−0.878430	+	0.477872i	$0.841408\pi$
$758$	15.3202	0.556455
$759$	12.8093	0.464948
$760$	−26.5825	−0.964250
$761$	−21.3321	−0.773289	−0.386644	−	0.922229i	$-0.626366\pi$
$761$	−21.3321	−0.773289	−0.386644	+	0.922229i	$0.626366\pi$
$762$	1.94150	0.0703330
$763$	−1.62120	−0.0586915
$764$	14.9327	0.540246
$765$	−0.197413	−0.00713748
$766$	−13.9812	−0.505161
$767$	0	0
$768$	−2.40150	−0.0866567
$769$	−0.465907	−0.0168010	−0.00840052	−	0.999965i	$-0.502674\pi$
$769$	−0.465907	−0.0168010	−0.00840052	+	0.999965i	$0.502674\pi$
$770$	2.54631	0.0917626
$771$	18.7918	0.676771
$772$	31.6794	1.14017
$773$	−8.94973	−0.321899	−0.160950	−	0.986963i	$-0.551456\pi$
$773$	−8.94973	−0.321899	−0.160950	+	0.986963i	$0.551456\pi$
$774$	3.95640	0.142210
$775$	−73.2979	−2.63294
$776$	10.3594	0.371882
$777$	−8.02423	−0.287868
$778$	−7.17139	−0.257107
$779$	−5.48822	−0.196636
$780$	0	0
$781$	3.30136	0.118132
$782$	−0.196694	−0.00703377
$783$	−7.43938	−0.265862
$784$	2.85086	0.101816
$785$	−50.0845	−1.78759
$786$	−7.63669	−0.272392
$787$	20.7674	0.740278	0.370139	−	0.928976i	$-0.379310\pi$
$787$	20.7674	0.740278	0.370139	+	0.928976i	$0.379310\pi$
$788$	2.00875	0.0715589
$789$	−10.3222	−0.367481
$790$	25.9605	0.923632
$791$	−6.92138	−0.246096
$792$	2.71982	0.0966445
$793$	0	0
$794$	12.9804	0.460657
$795$	−20.0327	−0.710486
$796$	10.5066	0.372398
$797$	−17.2874	−0.612350	−0.306175	−	0.951975i	$-0.599049\pi$
$797$	−17.2874	−0.612350	−0.306175	+	0.951975i	$0.599049\pi$
$798$	1.96433	0.0695366
$799$	−0.430898	−0.0152441
$800$	−35.6837	−1.26161
$801$	−7.13735	−0.252186
$802$	4.19193	0.148022
$803$	−5.06710	−0.178814
$804$	−17.3543	−0.612038
$805$	28.3640	0.999701
$806$	0	0
$807$	18.2365	0.641956
$808$	−19.9473	−0.701744
$809$	−3.13943	−0.110377	−0.0551883	−	0.998476i	$-0.517576\pi$
$809$	−3.13943	−0.110377	−0.0551883	+	0.998476i	$0.517576\pi$
$810$	−1.58408	−0.0556589
$811$	−10.4018	−0.365256	−0.182628	−	0.983182i	$-0.558460\pi$
$811$	−10.4018	−0.365256	−0.182628	+	0.983182i	$0.558460\pi$
$812$	13.4053	0.470434
$813$	11.1028	0.389392
$814$	5.74035	0.201199
$815$	62.0406	2.17319
$816$	0.158115	0.00553515
$817$	39.2386	1.37278
$818$	8.93232	0.312311
$819$	0	0
$820$	−7.97506	−0.278501
$821$	7.27815	0.254009	0.127005	−	0.991902i	$-0.459464\pi$
$821$	7.27815	0.254009	0.127005	+	0.991902i	$0.459464\pi$
$822$	−5.93336	−0.206950
$823$	25.8576	0.901340	0.450670	−	0.892691i	$-0.351185\pi$
$823$	25.8576	0.901340	0.450670	+	0.892691i	$0.351185\pi$
$824$	16.3941	0.571114
$825$	−12.3279	−0.429203
$826$	1.35666	0.0472044
$827$	50.7845	1.76595	0.882975	−	0.469420i	$-0.155537\pi$
$827$	50.7845	1.76595	0.882975	+	0.469420i	$0.155537\pi$
$828$	14.3592	0.499018
$829$	47.3766	1.64546	0.822729	−	0.568434i	$-0.192451\pi$
$829$	47.3766	1.64546	0.822729	+	0.568434i	$0.192451\pi$
$830$	−19.5417	−0.678302
$831$	−16.7114	−0.579711
$832$	0	0
$833$	−0.0554625	−0.00192166
$834$	−5.67132	−0.196382
$835$	−13.3772	−0.462936
$836$	12.7846	0.442165
$837$	9.55729	0.330348
$838$	−13.8285	−0.477699
$839$	17.7359	0.612310	0.306155	−	0.951982i	$-0.400957\pi$
$839$	17.7359	0.612310	0.306155	+	0.951982i	$0.400957\pi$
$840$	6.02258	0.207799
$841$	26.3443	0.908425
$842$	7.03718	0.242517
$843$	−9.09459	−0.313234
$844$	13.2155	0.454897
$845$	0	0
$846$	−3.45761	−0.118875
$847$	8.41615	0.289182
$848$	16.0449	0.550985
$849$	28.1035	0.964510
$850$	0.189303	0.00649303
$851$	63.9433	2.19195
$852$	3.70083	0.126788
$853$	3.27245	0.112047	0.0560234	−	0.998429i	$-0.482158\pi$
$853$	3.27245	0.112047	0.0560234	+	0.998429i	$0.482158\pi$
$854$	−0.838485	−0.0286924
$855$	−15.7105	−0.537288
$856$	30.5871	1.04544
$857$	−27.7973	−0.949536	−0.474768	−	0.880111i	$-0.657468\pi$
$857$	−27.7973	−0.949536	−0.474768	+	0.880111i	$0.657468\pi$
$858$	0	0
$859$	−56.6207	−1.93187	−0.965937	−	0.258777i	$-0.916680\pi$
$859$	−56.6207	−1.93187	−0.965937	+	0.258777i	$0.916680\pi$
$860$	57.0185	1.94432
$861$	1.24342	0.0423756
$862$	7.56300	0.257597
$863$	11.9383	0.406384	0.203192	−	0.979139i	$-0.434868\pi$
$863$	11.9383	0.406384	0.203192	+	0.979139i	$0.434868\pi$
$864$	4.65279	0.158291
$865$	2.91758	0.0992008
$866$	−9.22073	−0.313333
$867$	16.9969	0.577246
$868$	−17.2216	−0.584541
$869$	−26.3432	−0.893633
$870$	11.7846	0.399535
$871$	0	0
$872$	2.74311	0.0928935
$873$	6.12252	0.207216
$874$	−15.6533	−0.529481
$875$	−9.50115	−0.321198
$876$	−5.68023	−0.191917
$877$	−23.2312	−0.784463	−0.392231	−	0.919867i	$-0.628297\pi$
$877$	−23.2312	−0.784463	−0.392231	+	0.919867i	$0.628297\pi$
$878$	1.63985	0.0553421
$879$	−13.6457	−0.460259
$880$	16.3112	0.549850
$881$	−58.9370	−1.98564	−0.992819	−	0.119630i	$-0.961829\pi$
$881$	−58.9370	−1.98564	−0.992819	+	0.119630i	$0.961829\pi$
$882$	−0.445042	−0.0149853
$883$	−24.0822	−0.810430	−0.405215	−	0.914221i	$-0.632803\pi$
$883$	−24.0822	−0.810430	−0.405215	+	0.914221i	$0.632803\pi$
$884$	0	0
$885$	−10.8505	−0.364734
$886$	4.04142	0.135774
$887$	4.39366	0.147525	0.0737624	−	0.997276i	$-0.476499\pi$
$887$	4.39366	0.147525	0.0737624	+	0.997276i	$0.476499\pi$
$888$	13.5772	0.455620
$889$	−4.36250	−0.146314
$890$	11.3061	0.378983
$891$	1.60744	0.0538511
$892$	−2.36209	−0.0790886
$893$	−34.2917	−1.14753
$894$	8.12759	0.271827
$895$	19.5140	0.652282
$896$	−10.9215	−0.364863
$897$	0	0
$898$	7.32859	0.244558
$899$	−71.1003	−2.37133
$900$	−13.8196	−0.460654
$901$	−0.312149	−0.0103992
$902$	−0.889513	−0.0296175
$903$	−8.88995	−0.295839
$904$	11.7111	0.389506
$905$	−33.7189	−1.12085
$906$	−8.75140	−0.290746
$907$	−40.1629	−1.33359	−0.666793	−	0.745243i	$-0.732333\pi$
$907$	−40.1629	−1.33359	−0.666793	+	0.745243i	$0.732333\pi$
$908$	26.7182	0.886676
$909$	−11.7890	−0.391018
$910$	0	0
$911$	−21.5423	−0.713728	−0.356864	−	0.934156i	$-0.616154\pi$
$911$	−21.5423	−0.713728	−0.356864	+	0.934156i	$0.616154\pi$
$912$	12.5831	0.416669
$913$	19.8298	0.656271
$914$	15.5721	0.515078
$915$	6.70612	0.221697
$916$	−8.24960	−0.272575
$917$	17.1595	0.566656
$918$	−0.0246831	−0.000814664 0
$919$	−41.6125	−1.37267	−0.686335	−	0.727286i	$-0.740781\pi$
$919$	−41.6125	−1.37267	−0.686335	+	0.727286i	$0.740781\pi$
$920$	−47.9925	−1.58227
$921$	−3.80129	−0.125257
$922$	−10.3300	−0.340199
$923$	0	0
$924$	−2.89650	−0.0952878
$925$	−61.5404	−2.02344
$926$	−5.96054	−0.195876
$927$	9.68904	0.318230
$928$	−34.6139	−1.13626
$929$	18.3028	0.600496	0.300248	−	0.953861i	$-0.402931\pi$
$929$	18.3028	0.600496	0.300248	+	0.953861i	$0.402931\pi$
$930$	−15.1395	−0.496445
$931$	−4.41381	−0.144657
$932$	5.51298	0.180584
$933$	−1.24668	−0.0408143
$934$	4.47302	0.146362
$935$	−0.317329	−0.0103778
$936$	0	0
$937$	−26.8372	−0.876734	−0.438367	−	0.898796i	$-0.644443\pi$
$937$	−26.8372	−0.876734	−0.438367	+	0.898796i	$0.644443\pi$
$938$	−4.28615	−0.139948
$939$	−28.6055	−0.933506
$940$	−49.8301	−1.62528
$941$	48.2336	1.57237	0.786185	−	0.617991i	$-0.212053\pi$
$941$	48.2336	1.57237	0.786185	+	0.617991i	$0.212053\pi$
$942$	−6.26220	−0.204034
$943$	−9.90852	−0.322666
$944$	8.69054	0.282853
$945$	3.55940	0.115787
$946$	6.35966	0.206770
$947$	41.6128	1.35223	0.676117	−	0.736794i	$-0.263661\pi$
$947$	41.6128	1.35223	0.676117	+	0.736794i	$0.263661\pi$
$948$	−29.5308	−0.959116
$949$	0	0
$950$	15.0651	0.488776
$951$	32.9494	1.06846
$952$	0.0938437	0.00304149
$953$	51.6383	1.67273	0.836365	−	0.548174i	$-0.184677\pi$
$953$	51.6383	1.67273	0.836365	+	0.548174i	$0.184677\pi$
$954$	−2.50474	−0.0810941
$955$	−29.4968	−0.954494
$956$	3.63097	0.117434
$957$	−11.9583	−0.386558
$958$	−10.2810	−0.332165
$959$	13.3321	0.430517
$960$	12.9243	0.417129
$961$	60.3418	1.94651
$962$	0	0
$963$	18.0772	0.582531
$964$	−46.6338	−1.50197
$965$	−62.5769	−2.01442
$966$	3.54644	0.114105
$967$	−33.4653	−1.07617	−0.538086	−	0.842890i	$-0.680853\pi$
$967$	−33.4653	−1.07617	−0.538086	+	0.842890i	$0.680853\pi$
$968$	−14.2403	−0.457701
$969$	−0.244801	−0.00786414
$970$	−9.69857	−0.311402
$971$	−58.3170	−1.87148	−0.935741	−	0.352689i	$-0.885267\pi$
$971$	−58.3170	−1.87148	−0.935741	+	0.352689i	$0.885267\pi$
$972$	1.80194	0.0577972
$973$	12.7433	0.408532
$974$	−5.08688	−0.162994
$975$	0	0
$976$	−5.37118	−0.171927
$977$	−5.07297	−0.162299	−0.0811493	−	0.996702i	$-0.525859\pi$
$977$	−5.07297	−0.162299	−0.0811493	+	0.996702i	$0.525859\pi$
$978$	7.75712	0.248045
$979$	−11.4728	−0.366673
$980$	−6.41381	−0.204882
$981$	1.62120	0.0517611
$982$	−15.9720	−0.509688
$983$	45.2951	1.44469	0.722344	−	0.691533i	$-0.243065\pi$
$983$	45.2951	1.44469	0.722344	+	0.691533i	$0.243065\pi$
$984$	−2.10389	−0.0670696
$985$	−3.96792	−0.126429
$986$	0.183627	0.00584788
$987$	7.76918	0.247296
$988$	0	0
$989$	70.8420	2.25265
$990$	−2.54631	−0.0809270
$991$	26.7267	0.849003	0.424501	−	0.905427i	$-0.360449\pi$
$991$	26.7267	0.849003	0.424501	+	0.905427i	$0.360449\pi$
$992$	44.4681	1.41186
$993$	−22.6342	−0.718275
$994$	0.914030	0.0289913
$995$	−20.7539	−0.657944
$996$	22.2292	0.704360
$997$	31.1408	0.986238	0.493119	−	0.869962i	$-0.335857\pi$
$997$	31.1408	0.986238	0.493119	+	0.869962i	$0.335857\pi$
$998$	−15.6150	−0.494285
$999$	8.02423	0.253876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.y.1.4	✓	6
13.12	even	2		3549.2.a.z.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.y.1.4	✓	6	1.1	even	1	trivial
3549.2.a.z.1.3	yes	6	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)

\(f(q)\)	\(=\)	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +3.55940 q^{5} +0.445042 q^{6} -1.00000 q^{7} +1.69202 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +3.55940 q^{5} +0.445042 q^{6} -1.00000 q^{7} +1.69202 q^{8} +1.00000 q^{9} -1.58408 q^{10} +1.60744 q^{11} +1.80194 q^{12} +0.445042 q^{14} -3.55940 q^{15} +2.85086 q^{16} -0.0554625 q^{17} -0.445042 q^{18} -4.41381 q^{19} -6.41381 q^{20} +1.00000 q^{21} -0.715376 q^{22} -7.96877 q^{23} -1.69202 q^{24} +7.66931 q^{25} -1.00000 q^{27} +1.80194 q^{28} +7.43938 q^{29} +1.58408 q^{30} -9.55729 q^{31} -4.65279 q^{32} -1.60744 q^{33} +0.0246831 q^{34} -3.55940 q^{35} -1.80194 q^{36} -8.02423 q^{37} +1.96433 q^{38} +6.02258 q^{40} +1.24342 q^{41} -0.445042 q^{42} -8.88995 q^{43} -2.89650 q^{44} +3.55940 q^{45} +3.54644 q^{46} +7.76918 q^{47} -2.85086 q^{48} +1.00000 q^{49} -3.41317 q^{50} +0.0554625 q^{51} +5.62811 q^{53} +0.445042 q^{54} +5.72150 q^{55} -1.69202 q^{56} +4.41381 q^{57} -3.31083 q^{58} +3.04840 q^{59} +6.41381 q^{60} -1.88406 q^{61} +4.25340 q^{62} -1.00000 q^{63} -3.63102 q^{64} +0.715376 q^{66} -9.63089 q^{67} +0.0999399 q^{68} +7.96877 q^{69} +1.58408 q^{70} +2.05381 q^{71} +1.69202 q^{72} -3.15229 q^{73} +3.57112 q^{74} -7.66931 q^{75} +7.95342 q^{76} -1.60744 q^{77} -16.3884 q^{79} +10.1473 q^{80} +1.00000 q^{81} -0.553374 q^{82} +12.3363 q^{83} -1.80194 q^{84} -0.197413 q^{85} +3.95640 q^{86} -7.43938 q^{87} +2.71982 q^{88} -7.13735 q^{89} -1.58408 q^{90} +14.3592 q^{92} +9.55729 q^{93} -3.45761 q^{94} -15.7105 q^{95} +4.65279 q^{96} +6.12252 q^{97} -0.445042 q^{98} +1.60744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9} - q^{10} + 2 q^{12} + 2 q^{14} - 3 q^{15} - 10 q^{16} - 9 q^{17} - 2 q^{18} + 11 q^{19} - q^{20} + 6 q^{21} + 7 q^{22} - 11 q^{23} + 29 q^{25} - 6 q^{27} + 2 q^{28} - 10 q^{29} + q^{30} + 7 q^{31} + 8 q^{32} + 10 q^{34} - 3 q^{35} - 2 q^{36} - 20 q^{37} - 6 q^{38} - 10 q^{41} - 2 q^{42} - 9 q^{43} + 3 q^{45} - 8 q^{46} + 36 q^{47} + 10 q^{48} + 6 q^{49} + 9 q^{50} + 9 q^{51} - 12 q^{53} + 2 q^{54} - 29 q^{55} - 11 q^{57} - 6 q^{58} - 41 q^{59} + q^{60} - 24 q^{61} - 6 q^{63} + 8 q^{64} - 7 q^{66} + 15 q^{67} + 10 q^{68} + 11 q^{69} + q^{70} + 13 q^{71} + 25 q^{73} + 2 q^{74} - 29 q^{75} + q^{76} - 16 q^{79} - 5 q^{80} + 6 q^{81} + q^{82} - 2 q^{83} - 2 q^{84} - 33 q^{85} - 4 q^{86} + 10 q^{87} - 14 q^{88} + 15 q^{89} - q^{90} + 13 q^{92} - 7 q^{93} - 33 q^{94} - 23 q^{95} - 8 q^{96} + 10 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9 - q^10 + 2 * q^12 + 2 * q^14 - 3 * q^15 - 10 * q^16 - 9 * q^17 - 2 * q^18 + 11 * q^19 - q^20 + 6 * q^21 + 7 * q^22 - 11 * q^23 + 29 * q^25 - 6 * q^27 + 2 * q^28 - 10 * q^29 + q^30 + 7 * q^31 + 8 * q^32 + 10 * q^34 - 3 * q^35 - 2 * q^36 - 20 * q^37 - 6 * q^38 - 10 * q^41 - 2 * q^42 - 9 * q^43 + 3 * q^45 - 8 * q^46 + 36 * q^47 + 10 * q^48 + 6 * q^49 + 9 * q^50 + 9 * q^51 - 12 * q^53 + 2 * q^54 - 29 * q^55 - 11 * q^57 - 6 * q^58 - 41 * q^59 + q^60 - 24 * q^61 - 6 * q^63 + 8 * q^64 - 7 * q^66 + 15 * q^67 + 10 * q^68 + 11 * q^69 + q^70 + 13 * q^71 + 25 * q^73 + 2 * q^74 - 29 * q^75 + q^76 - 16 * q^79 - 5 * q^80 + 6 * q^81 + q^82 - 2 * q^83 - 2 * q^84 - 33 * q^85 - 4 * q^86 + 10 * q^87 - 14 * q^88 + 15 * q^89 - q^90 + 13 * q^92 - 7 * q^93 - 33 * q^94 - 23 * q^95 - 8 * q^96 + 10 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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