LMFDB - Embedded newform 3549.2.a.bh.1.10

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
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			1.10
Root			$1.09372$ 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)

$f(q)$	$=$	$q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +3.68561 q^{10} +0.408118 q^{11} -0.803784 q^{12} -1.09372 q^{14} +3.36980 q^{15} -1.74636 q^{16} +0.412077 q^{17} +1.09372 q^{18} -1.06384 q^{19} -2.70859 q^{20} -1.00000 q^{21} +0.446365 q^{22} +8.83682 q^{23} -3.06655 q^{24} +6.35555 q^{25} +1.00000 q^{27} +0.803784 q^{28} -3.54528 q^{29} +3.68561 q^{30} +1.89809 q^{31} +4.22306 q^{32} +0.408118 q^{33} +0.450696 q^{34} -3.36980 q^{35} -0.803784 q^{36} +4.79988 q^{37} -1.16354 q^{38} -10.3336 q^{40} +10.0404 q^{41} -1.09372 q^{42} -2.32877 q^{43} -0.328038 q^{44} +3.36980 q^{45} +9.66498 q^{46} +8.84728 q^{47} -1.74636 q^{48} +1.00000 q^{49} +6.95117 q^{50} +0.412077 q^{51} -4.18910 q^{53} +1.09372 q^{54} +1.37527 q^{55} +3.06655 q^{56} -1.06384 q^{57} -3.87753 q^{58} -11.4506 q^{59} -2.70859 q^{60} +11.6354 q^{61} +2.07598 q^{62} -1.00000 q^{63} +8.11156 q^{64} +0.446365 q^{66} +2.39553 q^{67} -0.331221 q^{68} +8.83682 q^{69} -3.68561 q^{70} +14.6773 q^{71} -3.06655 q^{72} -14.5666 q^{73} +5.24970 q^{74} +6.35555 q^{75} +0.855097 q^{76} -0.408118 q^{77} +4.27789 q^{79} -5.88489 q^{80} +1.00000 q^{81} +10.9814 q^{82} -4.60644 q^{83} +0.803784 q^{84} +1.38862 q^{85} -2.54702 q^{86} -3.54528 q^{87} -1.25151 q^{88} +14.3179 q^{89} +3.68561 q^{90} -7.10290 q^{92} +1.89809 q^{93} +9.67642 q^{94} -3.58493 q^{95} +4.22306 q^{96} -12.3236 q^{97} +1.09372 q^{98} +0.408118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * 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 $

$2$	1.09372	0.773374	0.386687	−	0.922211i	$-0.373619\pi$
$2$	1.09372	0.773374	0.386687	+	0.922211i	$0.373619\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.803784	−0.401892
$5$	3.36980	1.50702	0.753510	−	0.657436i	$-0.228359\pi$
$5$	3.36980	1.50702	0.753510	+	0.657436i	$0.228359\pi$
$6$	1.09372	0.446508
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.06655	−1.08419
$9$	1.00000	0.333333
$10$	3.68561	1.16549
$11$	0.408118	0.123052	0.0615260	−	0.998105i	$-0.480403\pi$
$11$	0.408118	0.123052	0.0615260	+	0.998105i	$0.480403\pi$
$12$	−0.803784	−0.232032
$13$	0	0
$13$	0	0
$14$	−1.09372	−0.292308
$15$	3.36980	0.870079
$16$	−1.74636	−0.436591
$17$	0.412077	0.0999434	0.0499717	−	0.998751i	$-0.484087\pi$
$17$	0.412077	0.0999434	0.0499717	+	0.998751i	$0.484087\pi$
$18$	1.09372	0.257791
$19$	−1.06384	−0.244062	−0.122031	−	0.992526i	$-0.538941\pi$
$19$	−1.06384	−0.244062	−0.122031	+	0.992526i	$0.538941\pi$
$20$	−2.70859	−0.605659
$21$	−1.00000	−0.218218
$22$	0.446365	0.0951653
$23$	8.83682	1.84260	0.921302	−	0.388847i	$-0.127126\pi$
$23$	8.83682	1.84260	0.921302	+	0.388847i	$0.127126\pi$
$24$	−3.06655	−0.625956
$25$	6.35555	1.27111
$26$	0	0
$27$	1.00000	0.192450
$28$	0.803784	0.151901
$29$	−3.54528	−0.658341	−0.329171	−	0.944270i	$-0.606769\pi$
$29$	−3.54528	−0.658341	−0.329171	+	0.944270i	$0.606769\pi$
$30$	3.68561	0.672896
$31$	1.89809	0.340908	0.170454	−	0.985366i	$-0.445477\pi$
$31$	1.89809	0.340908	0.170454	+	0.985366i	$0.445477\pi$
$32$	4.22306	0.746539
$33$	0.408118	0.0710441
$34$	0.450696	0.0772937
$35$	−3.36980	−0.569600
$36$	−0.803784	−0.133964
$37$	4.79988	0.789095	0.394547	−	0.918876i	$-0.370901\pi$
$37$	4.79988	0.789095	0.394547	+	0.918876i	$0.370901\pi$
$38$	−1.16354	−0.188751
$39$	0	0
$40$	−10.3336	−1.63389
$41$	10.0404	1.56805	0.784025	−	0.620729i	$-0.213163\pi$
$41$	10.0404	1.56805	0.784025	+	0.620729i	$0.213163\pi$
$42$	−1.09372	−0.168764
$43$	−2.32877	−0.355135	−0.177567	−	0.984109i	$-0.556823\pi$
$43$	−2.32877	−0.355135	−0.177567	+	0.984109i	$0.556823\pi$
$44$	−0.328038	−0.0494536
$45$	3.36980	0.502340
$46$	9.66498	1.42502
$47$	8.84728	1.29051	0.645254	−	0.763968i	$-0.276751\pi$
$47$	8.84728	1.29051	0.645254	+	0.763968i	$0.276751\pi$
$48$	−1.74636	−0.252066
$49$	1.00000	0.142857
$50$	6.95117	0.983044
$51$	0.412077	0.0577024
$52$	0	0
$53$	−4.18910	−0.575418	−0.287709	−	0.957718i	$-0.592894\pi$
$53$	−4.18910	−0.575418	−0.287709	+	0.957718i	$0.592894\pi$
$54$	1.09372	0.148836
$55$	1.37527	0.185442
$56$	3.06655	0.409784
$57$	−1.06384	−0.140909
$58$	−3.87753	−0.509144
$59$	−11.4506	−1.49074	−0.745369	−	0.666652i	$-0.767727\pi$
$59$	−11.4506	−1.49074	−0.745369	+	0.666652i	$0.767727\pi$
$60$	−2.70859	−0.349678
$61$	11.6354	1.48976	0.744880	−	0.667199i	$-0.232507\pi$
$61$	11.6354	1.48976	0.744880	+	0.667199i	$0.232507\pi$
$62$	2.07598	0.263649
$63$	−1.00000	−0.125988
$64$	8.11156	1.01395
$65$	0	0
$66$	0.446365	0.0549437
$67$	2.39553	0.292661	0.146330	−	0.989236i	$-0.453254\pi$
$67$	2.39553	0.292661	0.146330	+	0.989236i	$0.453254\pi$
$68$	−0.331221	−0.0401665
$69$	8.83682	1.06383
$70$	−3.68561	−0.440514
$71$	14.6773	1.74188	0.870939	−	0.491391i	$-0.163511\pi$
$71$	14.6773	1.74188	0.870939	+	0.491391i	$0.163511\pi$
$72$	−3.06655	−0.361396
$73$	−14.5666	−1.70489	−0.852447	−	0.522814i	$-0.824882\pi$
$73$	−14.5666	−1.70489	−0.852447	+	0.522814i	$0.824882\pi$
$74$	5.24970	0.610266
$75$	6.35555	0.733876
$76$	0.855097	0.0980864
$77$	−0.408118	−0.0465093
$78$	0	0
$79$	4.27789	0.481300	0.240650	−	0.970612i	$-0.422639\pi$
$79$	4.27789	0.481300	0.240650	+	0.970612i	$0.422639\pi$
$80$	−5.88489	−0.657951
$81$	1.00000	0.111111
$82$	10.9814	1.21269
$83$	−4.60644	−0.505623	−0.252811	−	0.967516i	$-0.581355\pi$
$83$	−4.60644	−0.505623	−0.252811	+	0.967516i	$0.581355\pi$
$84$	0.803784	0.0877000
$85$	1.38862	0.150617
$86$	−2.54702	−0.274652
$87$	−3.54528	−0.380093
$88$	−1.25151	−0.133411
$89$	14.3179	1.51769	0.758846	−	0.651271i	$-0.225764\pi$
$89$	14.3179	1.51769	0.758846	+	0.651271i	$0.225764\pi$
$90$	3.68561	0.388497
$91$	0	0
$92$	−7.10290	−0.740528
$93$	1.89809	0.196823
$94$	9.67642	0.998046
$95$	−3.58493	−0.367806
$96$	4.22306	0.431015
$97$	−12.3236	−1.25127	−0.625633	−	0.780117i	$-0.715159\pi$
$97$	−12.3236	−1.25127	−0.625633	+	0.780117i	$0.715159\pi$
$98$	1.09372	0.110482
$99$	0.408118	0.0410174
$100$	−5.10849	−0.510849
$101$	−1.21016	−0.120416	−0.0602079	−	0.998186i	$-0.519176\pi$
$101$	−1.21016	−0.120416	−0.0602079	+	0.998186i	$0.519176\pi$
$102$	0.450696	0.0446255
$103$	13.5513	1.33525	0.667626	−	0.744497i	$-0.267311\pi$
$103$	13.5513	1.33525	0.667626	+	0.744497i	$0.267311\pi$
$104$	0	0
$105$	−3.36980	−0.328859
$106$	−4.58169	−0.445013
$107$	8.58829	0.830261	0.415131	−	0.909762i	$-0.363736\pi$
$107$	8.58829	0.830261	0.415131	+	0.909762i	$0.363736\pi$
$108$	−0.803784	−0.0773442
$109$	−19.6808	−1.88508	−0.942540	−	0.334093i	$-0.891570\pi$
$109$	−19.6808	−1.88508	−0.942540	+	0.334093i	$0.891570\pi$
$110$	1.50416	0.143416
$111$	4.79988	0.455584
$112$	1.74636	0.165016
$113$	1.36619	0.128520	0.0642602	−	0.997933i	$-0.479531\pi$
$113$	1.36619	0.128520	0.0642602	+	0.997933i	$0.479531\pi$
$114$	−1.16354	−0.108975
$115$	29.7783	2.77684
$116$	2.84964	0.264582
$117$	0	0
$118$	−12.5237	−1.15290
$119$	−0.412077	−0.0377751
$120$	−10.3336	−0.943328
$121$	−10.8334	−0.984858
$122$	12.7258	1.15214
$123$	10.0404	0.905314
$124$	−1.52566	−0.137008
$125$	4.56793	0.408568
$126$	−1.09372	−0.0974360
$127$	−16.5831	−1.47151	−0.735756	−	0.677247i	$-0.763173\pi$
$127$	−16.5831	−1.47151	−0.735756	+	0.677247i	$0.763173\pi$
$128$	0.425621	0.0376199
$129$	−2.32877	−0.205037
$130$	0	0
$131$	9.76818	0.853449	0.426725	−	0.904382i	$-0.359667\pi$
$131$	9.76818	0.853449	0.426725	+	0.904382i	$0.359667\pi$
$132$	−0.328038	−0.0285521
$133$	1.06384	0.0922466
$134$	2.62003	0.226336
$135$	3.36980	0.290026
$136$	−1.26365	−0.108357
$137$	−14.4867	−1.23768	−0.618839	−	0.785518i	$-0.712397\pi$
$137$	−14.4867	−1.23768	−0.618839	+	0.785518i	$0.712397\pi$
$138$	9.66498	0.822738
$139$	−7.75313	−0.657612	−0.328806	−	0.944398i	$-0.606646\pi$
$139$	−7.75313	−0.657612	−0.328806	+	0.944398i	$0.606646\pi$
$140$	2.70859	0.228918
$141$	8.84728	0.745075
$142$	16.0528	1.34712
$143$	0	0
$144$	−1.74636	−0.145530
$145$	−11.9469	−0.992133
$146$	−15.9318	−1.31852
$147$	1.00000	0.0824786
$148$	−3.85806	−0.317131
$149$	2.67814	0.219402	0.109701	−	0.993965i	$-0.465011\pi$
$149$	2.67814	0.219402	0.109701	+	0.993965i	$0.465011\pi$
$150$	6.95117	0.567561
$151$	−7.62102	−0.620190	−0.310095	−	0.950706i	$-0.600361\pi$
$151$	−7.62102	−0.620190	−0.310095	+	0.950706i	$0.600361\pi$
$152$	3.26231	0.264608
$153$	0.412077	0.0333145
$154$	−0.446365	−0.0359691
$155$	6.39620	0.513755
$156$	0	0
$157$	18.1947	1.45209	0.726047	−	0.687645i	$-0.241355\pi$
$157$	18.1947	1.45209	0.726047	+	0.687645i	$0.241355\pi$
$158$	4.67880	0.372225
$159$	−4.18910	−0.332218
$160$	14.2309	1.12505
$161$	−8.83682	−0.696439
$162$	1.09372	0.0859305
$163$	−19.5824	−1.53381	−0.766905	−	0.641760i	$-0.778204\pi$
$163$	−19.5824	−1.53381	−0.766905	+	0.641760i	$0.778204\pi$
$164$	−8.07033	−0.630187
$165$	1.37527	0.107065
$166$	−5.03814	−0.391036
$167$	6.00027	0.464315	0.232158	−	0.972678i	$-0.425422\pi$
$167$	6.00027	0.464315	0.232158	+	0.972678i	$0.425422\pi$
$168$	3.06655	0.236589
$169$	0	0
$170$	1.51875	0.116483
$171$	−1.06384	−0.0813539
$172$	1.87183	0.142726
$173$	−1.17561	−0.0893797	−0.0446899	−	0.999001i	$-0.514230\pi$
$173$	−1.17561	−0.0893797	−0.0446899	+	0.999001i	$0.514230\pi$
$174$	−3.87753	−0.293955
$175$	−6.35555	−0.480434
$176$	−0.712721	−0.0537234
$177$	−11.4506	−0.860678
$178$	15.6597	1.17374
$179$	0.249567	0.0186535	0.00932677	−	0.999957i	$-0.497031\pi$
$179$	0.249567	0.0186535	0.00932677	+	0.999957i	$0.497031\pi$
$180$	−2.70859	−0.201886
$181$	0.442464	0.0328881	0.0164440	−	0.999865i	$-0.494765\pi$
$181$	0.442464	0.0328881	0.0164440	+	0.999865i	$0.494765\pi$
$182$	0	0
$183$	11.6354	0.860113
$184$	−27.0985	−1.99773
$185$	16.1746	1.18918
$186$	2.07598	0.152218
$187$	0.168176	0.0122982
$188$	−7.11130	−0.518645
$189$	−1.00000	−0.0727393
$190$	−3.92089	−0.284452
$191$	15.8545	1.14719	0.573597	−	0.819138i	$-0.305548\pi$
$191$	15.8545	1.14719	0.573597	+	0.819138i	$0.305548\pi$
$192$	8.11156	0.585401
$193$	4.24322	0.305434	0.152717	−	0.988270i	$-0.451198\pi$
$193$	4.24322	0.305434	0.152717	+	0.988270i	$0.451198\pi$
$194$	−13.4785	−0.967698
$195$	0	0
$196$	−0.803784	−0.0574131
$197$	9.13404	0.650773	0.325387	−	0.945581i	$-0.394506\pi$
$197$	9.13404	0.650773	0.325387	+	0.945581i	$0.394506\pi$
$198$	0.446365	0.0317218
$199$	9.66460	0.685105	0.342553	−	0.939499i	$-0.388708\pi$
$199$	9.66460	0.685105	0.342553	+	0.939499i	$0.388708\pi$
$200$	−19.4896	−1.37812
$201$	2.39553	0.168968
$202$	−1.32358	−0.0931265
$203$	3.54528	0.248830
$204$	−0.331221	−0.0231901
$205$	33.8342	2.36308
$206$	14.8213	1.03265
$207$	8.83682	0.614202
$208$	0	0
$209$	−0.434172	−0.0300323
$210$	−3.68561	−0.254331
$211$	−24.0587	−1.65627	−0.828135	−	0.560528i	$-0.810598\pi$
$211$	−24.0587	−1.65627	−0.828135	+	0.560528i	$0.810598\pi$
$212$	3.36714	0.231256
$213$	14.6773	1.00567
$214$	9.39315	0.642103
$215$	−7.84750	−0.535195
$216$	−3.06655	−0.208652
$217$	−1.89809	−0.128851
$218$	−21.5252	−1.45787
$219$	−14.5666	−0.984321
$220$	−1.10542	−0.0745276
$221$	0	0
$222$	5.24970	0.352337
$223$	−18.1487	−1.21532	−0.607662	−	0.794196i	$-0.707892\pi$
$223$	−18.1487	−1.21532	−0.607662	+	0.794196i	$0.707892\pi$
$224$	−4.22306	−0.282165
$225$	6.35555	0.423703
$226$	1.49423	0.0993944
$227$	−16.2228	−1.07674	−0.538372	−	0.842707i	$-0.680961\pi$
$227$	−16.2228	−1.07674	−0.538372	+	0.842707i	$0.680961\pi$
$228$	0.855097	0.0566302
$229$	0.980804	0.0648134	0.0324067	−	0.999475i	$-0.489683\pi$
$229$	0.980804	0.0648134	0.0324067	+	0.999475i	$0.489683\pi$
$230$	32.5690	2.14754
$231$	−0.408118	−0.0268522
$232$	10.8717	0.713765
$233$	−19.4629	−1.27506	−0.637528	−	0.770427i	$-0.720043\pi$
$233$	−19.4629	−1.27506	−0.637528	+	0.770427i	$0.720043\pi$
$234$	0	0
$235$	29.8136	1.94482
$236$	9.20379	0.599116
$237$	4.27789	0.277879
$238$	−0.450696	−0.0292143
$239$	18.7859	1.21516	0.607580	−	0.794259i	$-0.292141\pi$
$239$	18.7859	1.21516	0.607580	+	0.794259i	$0.292141\pi$
$240$	−5.88489	−0.379868
$241$	−9.08287	−0.585079	−0.292540	−	0.956253i	$-0.594500\pi$
$241$	−9.08287	−0.585079	−0.292540	+	0.956253i	$0.594500\pi$
$242$	−11.8487	−0.761664
$243$	1.00000	0.0641500
$244$	−9.35235	−0.598723
$245$	3.36980	0.215289
$246$	10.9814	0.700147
$247$	0	0
$248$	−5.82059	−0.369608
$249$	−4.60644	−0.291921
$250$	4.99602	0.315976
$251$	11.7323	0.740535	0.370267	−	0.928925i	$-0.379266\pi$
$251$	11.7323	0.740535	0.370267	+	0.928925i	$0.379266\pi$
$252$	0.803784	0.0506336
$253$	3.60646	0.226736
$254$	−18.1372	−1.13803
$255$	1.38862	0.0869586
$256$	−15.7576	−0.984851
$257$	20.0321	1.24957	0.624784	−	0.780797i	$-0.285187\pi$
$257$	20.0321	1.24957	0.624784	+	0.780797i	$0.285187\pi$
$258$	−2.54702	−0.158570
$259$	−4.79988	−0.298250
$260$	0	0
$261$	−3.54528	−0.219447
$262$	10.6836	0.660036
$263$	−5.06336	−0.312220	−0.156110	−	0.987740i	$-0.549895\pi$
$263$	−5.06336	−0.312220	−0.156110	+	0.987740i	$0.549895\pi$
$264$	−1.25151	−0.0770252
$265$	−14.1164	−0.867166
$266$	1.16354	0.0713412
$267$	14.3179	0.876239
$268$	−1.92549	−0.117618
$269$	4.89625	0.298530	0.149265	−	0.988797i	$-0.452309\pi$
$269$	4.89625	0.298530	0.149265	+	0.988797i	$0.452309\pi$
$270$	3.68561	0.224299
$271$	−27.2537	−1.65554	−0.827772	−	0.561064i	$-0.810392\pi$
$271$	−27.2537	−1.65554	−0.827772	+	0.561064i	$0.810392\pi$
$272$	−0.719637	−0.0436344
$273$	0	0
$274$	−15.8443	−0.957189
$275$	2.59381	0.156413
$276$	−7.10290	−0.427544
$277$	−2.91367	−0.175066	−0.0875328	−	0.996162i	$-0.527898\pi$
$277$	−2.91367	−0.175066	−0.0875328	+	0.996162i	$0.527898\pi$
$278$	−8.47972	−0.508580
$279$	1.89809	0.113636
$280$	10.3336	0.617553
$281$	−25.2705	−1.50751	−0.753757	−	0.657153i	$-0.771760\pi$
$281$	−25.2705	−1.50751	−0.753757	+	0.657153i	$0.771760\pi$
$282$	9.67642	0.576222
$283$	18.5059	1.10006	0.550031	−	0.835144i	$-0.314616\pi$
$283$	18.5059	1.10006	0.550031	+	0.835144i	$0.314616\pi$
$284$	−11.7974	−0.700047
$285$	−3.58493	−0.212353
$286$	0	0
$287$	−10.0404	−0.592667
$288$	4.22306	0.248846
$289$	−16.8302	−0.990011
$290$	−13.0665	−0.767291
$291$	−12.3236	−0.722419
$292$	11.7084	0.685183
$293$	5.10573	0.298280	0.149140	−	0.988816i	$-0.452350\pi$
$293$	5.10573	0.298280	0.149140	+	0.988816i	$0.452350\pi$
$294$	1.09372	0.0637868
$295$	−38.5861	−2.24657
$296$	−14.7190	−0.855527
$297$	0.408118	0.0236814
$298$	2.92912	0.169680
$299$	0	0
$300$	−5.10849	−0.294939
$301$	2.32877	0.134228
$302$	−8.33524	−0.479639
$303$	−1.21016	−0.0695221
$304$	1.85785	0.106555
$305$	39.2090	2.24510
$306$	0.450696	0.0257646
$307$	−0.145600	−0.00830986	−0.00415493	−	0.999991i	$-0.501323\pi$
$307$	−0.145600	−0.00830986	−0.00415493	+	0.999991i	$0.501323\pi$
$308$	0.328038	0.0186917
$309$	13.5513	0.770908
$310$	6.99563	0.397325
$311$	−27.0891	−1.53608	−0.768041	−	0.640400i	$-0.778769\pi$
$311$	−27.0891	−1.53608	−0.768041	+	0.640400i	$0.778769\pi$
$312$	0	0
$313$	29.6140	1.67388	0.836941	−	0.547293i	$-0.184342\pi$
$313$	29.6140	1.67388	0.836941	+	0.547293i	$0.184342\pi$
$314$	19.8998	1.12301
$315$	−3.36980	−0.189867
$316$	−3.43850	−0.193431
$317$	−23.9730	−1.34646	−0.673229	−	0.739434i	$-0.735093\pi$
$317$	−23.9730	−1.34646	−0.673229	+	0.739434i	$0.735093\pi$
$318$	−4.58169	−0.256929
$319$	−1.44689	−0.0810102
$320$	27.3343	1.52804
$321$	8.58829	0.479352
$322$	−9.66498	−0.538608
$323$	−0.438384	−0.0243924
$324$	−0.803784	−0.0446547
$325$	0	0
$326$	−21.4176	−1.18621
$327$	−19.6808	−1.08835
$328$	−30.7894	−1.70006
$329$	−8.84728	−0.487766
$330$	1.50416	0.0828013
$331$	5.54793	0.304942	0.152471	−	0.988308i	$-0.451277\pi$
$331$	5.54793	0.304942	0.152471	+	0.988308i	$0.451277\pi$
$332$	3.70258	0.203206
$333$	4.79988	0.263032
$334$	6.56260	0.359089
$335$	8.07247	0.441046
$336$	1.74636	0.0952719
$337$	5.52923	0.301196	0.150598	−	0.988595i	$-0.451880\pi$
$337$	5.52923	0.301196	0.150598	+	0.988595i	$0.451880\pi$
$338$	0	0
$339$	1.36619	0.0742013
$340$	−1.11615	−0.0605317
$341$	0.774646	0.0419494
$342$	−1.16354	−0.0629170
$343$	−1.00000	−0.0539949
$344$	7.14129	0.385032
$345$	29.7783	1.60321
$346$	−1.28578	−0.0691240
$347$	29.0528	1.55964	0.779818	−	0.626007i	$-0.215312\pi$
$347$	29.0528	1.55964	0.779818	+	0.626007i	$0.215312\pi$
$348$	2.84964	0.152757
$349$	−15.4431	−0.826652	−0.413326	−	0.910583i	$-0.635633\pi$
$349$	−15.4431	−0.826652	−0.413326	+	0.910583i	$0.635633\pi$
$350$	−6.95117	−0.371556
$351$	0	0
$352$	1.72351	0.0918632
$353$	−18.6976	−0.995175	−0.497587	−	0.867414i	$-0.665781\pi$
$353$	−18.6976	−0.995175	−0.497587	+	0.867414i	$0.665781\pi$
$354$	−12.5237	−0.665626
$355$	49.4596	2.62505
$356$	−11.5085	−0.609948
$357$	−0.412077	−0.0218094
$358$	0.272956	0.0144262
$359$	10.9693	0.578939	0.289470	−	0.957187i	$-0.406521\pi$
$359$	10.9693	0.578939	0.289470	+	0.957187i	$0.406521\pi$
$360$	−10.3336	−0.544631
$361$	−17.8682	−0.940434
$362$	0.483930	0.0254348
$363$	−10.8334	−0.568608
$364$	0	0
$365$	−49.0866	−2.56931
$366$	12.7258	0.665190
$367$	11.8585	0.619011	0.309505	−	0.950898i	$-0.399837\pi$
$367$	11.8585	0.619011	0.309505	+	0.950898i	$0.399837\pi$
$368$	−15.4323	−0.804464
$369$	10.0404	0.522683
$370$	17.6905	0.919683
$371$	4.18910	0.217487
$372$	−1.52566	−0.0791017
$373$	8.62231	0.446446	0.223223	−	0.974767i	$-0.428342\pi$
$373$	8.62231	0.446446	0.223223	+	0.974767i	$0.428342\pi$
$374$	0.183937	0.00951115
$375$	4.56793	0.235887
$376$	−27.1306	−1.39915
$377$	0	0
$378$	−1.09372	−0.0562547
$379$	30.5029	1.56683	0.783413	−	0.621501i	$-0.213477\pi$
$379$	30.5029	1.56683	0.783413	+	0.621501i	$0.213477\pi$
$380$	2.88151	0.147818
$381$	−16.5831	−0.849578
$382$	17.3404	0.887211
$383$	25.7592	1.31623	0.658117	−	0.752915i	$-0.271353\pi$
$383$	25.7592	1.31623	0.658117	+	0.752915i	$0.271353\pi$
$384$	0.425621	0.0217199
$385$	−1.37527	−0.0700905
$386$	4.64088	0.236215
$387$	−2.32877	−0.118378
$388$	9.90547	0.502874
$389$	16.5425	0.838737	0.419368	−	0.907816i	$-0.362252\pi$
$389$	16.5425	0.838737	0.419368	+	0.907816i	$0.362252\pi$
$390$	0	0
$391$	3.64145	0.184156
$392$	−3.06655	−0.154884
$393$	9.76818	0.492739
$394$	9.99005	0.503291
$395$	14.4156	0.725329
$396$	−0.328038	−0.0164845
$397$	8.82355	0.442841	0.221421	−	0.975178i	$-0.428931\pi$
$397$	8.82355	0.442841	0.221421	+	0.975178i	$0.428931\pi$
$398$	10.5703	0.529843
$399$	1.06384	0.0532586
$400$	−11.0991	−0.554955
$401$	−10.8101	−0.539832	−0.269916	−	0.962884i	$-0.586996\pi$
$401$	−10.8101	−0.539832	−0.269916	+	0.962884i	$0.586996\pi$
$402$	2.62003	0.130675
$403$	0	0
$404$	0.972710	0.0483941
$405$	3.36980	0.167447
$406$	3.87753	0.192438
$407$	1.95891	0.0970998
$408$	−1.26365	−0.0625602
$409$	−19.5162	−0.965015	−0.482507	−	0.875892i	$-0.660274\pi$
$409$	−19.5162	−0.965015	−0.482507	+	0.875892i	$0.660274\pi$
$410$	37.0050	1.82755
$411$	−14.4867	−0.714574
$412$	−10.8923	−0.536627
$413$	11.4506	0.563446
$414$	9.66498	0.475008
$415$	−15.5228	−0.761983
$416$	0	0
$417$	−7.75313	−0.379672
$418$	−0.474861	−0.0232262
$419$	2.14931	0.105001	0.0525004	−	0.998621i	$-0.483281\pi$
$419$	2.14931	0.105001	0.0525004	+	0.998621i	$0.483281\pi$
$420$	2.70859	0.132166
$421$	17.1850	0.837547	0.418774	−	0.908091i	$-0.362460\pi$
$421$	17.1850	0.837547	0.418774	+	0.908091i	$0.362460\pi$
$422$	−26.3134	−1.28092
$423$	8.84728	0.430169
$424$	12.8461	0.623861
$425$	2.61898	0.127039
$426$	16.0528	0.777762
$427$	−11.6354	−0.563076
$428$	−6.90313	−0.333675
$429$	0	0
$430$	−8.58294	−0.413906
$431$	−12.4147	−0.597997	−0.298998	−	0.954254i	$-0.596653\pi$
$431$	−12.4147	−0.597997	−0.298998	+	0.954254i	$0.596653\pi$
$432$	−1.74636	−0.0840219
$433$	−1.89315	−0.0909791	−0.0454896	−	0.998965i	$-0.514485\pi$
$433$	−1.89315	−0.0909791	−0.0454896	+	0.998965i	$0.514485\pi$
$434$	−2.07598	−0.0996501
$435$	−11.9469	−0.572808
$436$	15.8191	0.757599
$437$	−9.40096	−0.449709
$438$	−15.9318	−0.761249
$439$	−4.57342	−0.218277	−0.109139	−	0.994027i	$-0.534809\pi$
$439$	−4.57342	−0.218277	−0.109139	+	0.994027i	$0.534809\pi$
$440$	−4.21734	−0.201054
$441$	1.00000	0.0476190
$442$	0	0
$443$	28.3955	1.34911	0.674556	−	0.738224i	$-0.264335\pi$
$443$	28.3955	1.34911	0.674556	+	0.738224i	$0.264335\pi$
$444$	−3.85806	−0.183096
$445$	48.2484	2.28719
$446$	−19.8495	−0.939901
$447$	2.67814	0.126672
$448$	−8.11156	−0.383235
$449$	−35.6530	−1.68257	−0.841284	−	0.540594i	$-0.818200\pi$
$449$	−35.6530	−1.68257	−0.841284	+	0.540594i	$0.818200\pi$
$450$	6.95117	0.327681
$451$	4.09767	0.192952
$452$	−1.09812	−0.0516513
$453$	−7.62102	−0.358067
$454$	−17.7431	−0.832727
$455$	0	0
$456$	3.26231	0.152772
$457$	−31.4697	−1.47209	−0.736045	−	0.676933i	$-0.763309\pi$
$457$	−31.4697	−1.47209	−0.736045	+	0.676933i	$0.763309\pi$
$458$	1.07272	0.0501250
$459$	0.412077	0.0192341
$460$	−23.9353	−1.11599
$461$	−21.2279	−0.988680	−0.494340	−	0.869269i	$-0.664590\pi$
$461$	−21.2279	−0.988680	−0.494340	+	0.869269i	$0.664590\pi$
$462$	−0.446365	−0.0207668
$463$	8.12061	0.377397	0.188698	−	0.982035i	$-0.439573\pi$
$463$	8.12061	0.377397	0.188698	+	0.982035i	$0.439573\pi$
$464$	6.19134	0.287426
$465$	6.39620	0.296617
$466$	−21.2869	−0.986095
$467$	−26.8288	−1.24149	−0.620743	−	0.784014i	$-0.713169\pi$
$467$	−26.8288	−1.24149	−0.620743	+	0.784014i	$0.713169\pi$
$468$	0	0
$469$	−2.39553	−0.110615
$470$	32.6076	1.50408
$471$	18.1947	0.838367
$472$	35.1137	1.61624
$473$	−0.950413	−0.0437000
$474$	4.67880	0.214904
$475$	−6.76129	−0.310229
$476$	0.331221	0.0151815
$477$	−4.18910	−0.191806
$478$	20.5465	0.939773
$479$	9.75257	0.445606	0.222803	−	0.974863i	$-0.428479\pi$
$479$	9.75257	0.445606	0.222803	+	0.974863i	$0.428479\pi$
$480$	14.2309	0.649548
$481$	0	0
$482$	−9.93409	−0.452485
$483$	−8.83682	−0.402089
$484$	8.70775	0.395807
$485$	−41.5279	−1.88568
$486$	1.09372	0.0496120
$487$	−21.8869	−0.991791	−0.495895	−	0.868382i	$-0.665160\pi$
$487$	−21.8869	−0.991791	−0.495895	+	0.868382i	$0.665160\pi$
$488$	−35.6805	−1.61518
$489$	−19.5824	−0.885546
$490$	3.68561	0.166499
$491$	33.1640	1.49667	0.748336	−	0.663320i	$-0.230853\pi$
$491$	33.1640	1.49667	0.748336	+	0.663320i	$0.230853\pi$
$492$	−8.07033	−0.363838
$493$	−1.46093	−0.0657969
$494$	0	0
$495$	1.37527	0.0618140
$496$	−3.31476	−0.148837
$497$	−14.6773	−0.658368
$498$	−5.03814	−0.225764
$499$	40.6778	1.82099	0.910494	−	0.413522i	$-0.135702\pi$
$499$	40.6778	1.82099	0.910494	+	0.413522i	$0.135702\pi$
$500$	−3.67163	−0.164200
$501$	6.00027	0.268072
$502$	12.8318	0.572710
$503$	−35.7797	−1.59534	−0.797669	−	0.603096i	$-0.793934\pi$
$503$	−35.7797	−1.59534	−0.797669	+	0.603096i	$0.793934\pi$
$504$	3.06655	0.136595
$505$	−4.07801	−0.181469
$506$	3.94445	0.175352
$507$	0	0
$508$	13.3292	0.591389
$509$	−39.4278	−1.74761	−0.873803	−	0.486279i	$-0.838354\pi$
$509$	−39.4278	−1.74761	−0.873803	+	0.486279i	$0.838354\pi$
$510$	1.51875	0.0672516
$511$	14.5666	0.644389
$512$	−18.0856	−0.799278
$513$	−1.06384	−0.0469697
$514$	21.9095	0.966385
$515$	45.6652	2.01225
$516$	1.87183	0.0824027
$517$	3.61073	0.158800
$518$	−5.24970	−0.230659
$519$	−1.17561	−0.0516034
$520$	0	0
$521$	−37.1536	−1.62773	−0.813865	−	0.581055i	$-0.802640\pi$
$521$	−37.1536	−1.62773	−0.813865	+	0.581055i	$0.802640\pi$
$522$	−3.87753	−0.169715
$523$	−18.8684	−0.825057	−0.412529	−	0.910945i	$-0.635354\pi$
$523$	−18.8684	−0.825057	−0.412529	+	0.910945i	$0.635354\pi$
$524$	−7.85150	−0.342995
$525$	−6.35555	−0.277379
$526$	−5.53788	−0.241463
$527$	0.782162	0.0340715
$528$	−0.712721	−0.0310172
$529$	55.0894	2.39519
$530$	−15.4394	−0.670644
$531$	−11.4506	−0.496913
$532$	−0.855097	−0.0370732
$533$	0	0
$534$	15.6597	0.677661
$535$	28.9408	1.25122
$536$	−7.34601	−0.317299
$537$	0.249567	0.0107696
$538$	5.35511	0.230875
$539$	0.408118	0.0175789
$540$	−2.70859	−0.116559
$541$	34.2960	1.47450	0.737250	−	0.675620i	$-0.236124\pi$
$541$	34.2960	1.47450	0.737250	+	0.675620i	$0.236124\pi$
$542$	−29.8078	−1.28036
$543$	0.442464	0.0189879
$544$	1.74023	0.0746117
$545$	−66.3204	−2.84085
$546$	0	0
$547$	30.2529	1.29352	0.646761	−	0.762693i	$-0.276123\pi$
$547$	30.2529	1.29352	0.646761	+	0.762693i	$0.276123\pi$
$548$	11.6441	0.497413
$549$	11.6354	0.496587
$550$	2.83689	0.120966
$551$	3.77160	0.160676
$552$	−27.0985	−1.15339
$553$	−4.27789	−0.181914
$554$	−3.18673	−0.135391
$555$	16.1746	0.686575
$556$	6.23184	0.264289
$557$	23.7963	1.00828	0.504141	−	0.863622i	$-0.331809\pi$
$557$	23.7963	1.00828	0.504141	+	0.863622i	$0.331809\pi$
$558$	2.07598	0.0878831
$559$	0	0
$560$	5.88489	0.248682
$561$	0.168176	0.00710040
$562$	−27.6388	−1.16587
$563$	−20.0697	−0.845839	−0.422919	−	0.906167i	$-0.638995\pi$
$563$	−20.0697	−0.845839	−0.422919	+	0.906167i	$0.638995\pi$
$564$	−7.11130	−0.299440
$565$	4.60379	0.193683
$566$	20.2402	0.850760
$567$	−1.00000	−0.0419961
$568$	−45.0087	−1.88852
$569$	−35.6422	−1.49420	−0.747100	−	0.664712i	$-0.768554\pi$
$569$	−35.6422	−1.49420	−0.747100	+	0.664712i	$0.768554\pi$
$570$	−3.92089	−0.164228
$571$	27.9511	1.16972	0.584859	−	0.811135i	$-0.301150\pi$
$571$	27.9511	1.16972	0.584859	+	0.811135i	$0.301150\pi$
$572$	0	0
$573$	15.8545	0.662333
$574$	−10.9814	−0.458354
$575$	56.1629	2.34215
$576$	8.11156	0.337982
$577$	16.1295	0.671481	0.335741	−	0.941954i	$-0.391013\pi$
$577$	16.1295	0.671481	0.335741	+	0.941954i	$0.391013\pi$
$578$	−18.4075	−0.765649
$579$	4.24322	0.176342
$580$	9.60270	0.398730
$581$	4.60644	0.191107
$582$	−13.4785	−0.558701
$583$	−1.70965	−0.0708063
$584$	44.6692	1.84842
$585$	0	0
$586$	5.58422	0.230682
$587$	−25.2546	−1.04237	−0.521184	−	0.853445i	$-0.674509\pi$
$587$	−25.2546	−1.04237	−0.521184	+	0.853445i	$0.674509\pi$
$588$	−0.803784	−0.0331475
$589$	−2.01927	−0.0832025
$590$	−42.2023	−1.73744
$591$	9.13404	0.375724
$592$	−8.38233	−0.344512
$593$	−3.67915	−0.151085	−0.0755424	−	0.997143i	$-0.524069\pi$
$593$	−3.67915	−0.151085	−0.0755424	+	0.997143i	$0.524069\pi$
$594$	0.446365	0.0183146
$595$	−1.38862	−0.0569278
$596$	−2.15264	−0.0881758
$597$	9.66460	0.395546
$598$	0	0
$599$	−24.1745	−0.987744	−0.493872	−	0.869535i	$-0.664419\pi$
$599$	−24.1745	−0.987744	−0.493872	+	0.869535i	$0.664419\pi$
$600$	−19.4896	−0.795659
$601$	−9.85564	−0.402020	−0.201010	−	0.979589i	$-0.564422\pi$
$601$	−9.85564	−0.402020	−0.201010	+	0.979589i	$0.564422\pi$
$602$	2.54702	0.103809
$603$	2.39553	0.0975537
$604$	6.12566	0.249249
$605$	−36.5065	−1.48420
$606$	−1.32358	−0.0537666
$607$	4.87139	0.197724	0.0988619	−	0.995101i	$-0.468480\pi$
$607$	4.87139	0.197724	0.0988619	+	0.995101i	$0.468480\pi$
$608$	−4.49266	−0.182202
$609$	3.54528	0.143662
$610$	42.8835	1.73630
$611$	0	0
$612$	−0.331221	−0.0133888
$613$	−19.7564	−0.797954	−0.398977	−	0.916961i	$-0.630635\pi$
$613$	−19.7564	−0.797954	−0.398977	+	0.916961i	$0.630635\pi$
$614$	−0.159246	−0.00642663
$615$	33.8342	1.36433
$616$	1.25151	0.0504248
$617$	−4.52746	−0.182269	−0.0911343	−	0.995839i	$-0.529049\pi$
$617$	−4.52746	−0.182269	−0.0911343	+	0.995839i	$0.529049\pi$
$618$	14.8213	0.596200
$619$	−40.5342	−1.62921	−0.814604	−	0.580017i	$-0.803046\pi$
$619$	−40.5342	−1.62921	−0.814604	+	0.580017i	$0.803046\pi$
$620$	−5.14116	−0.206474
$621$	8.83682	0.354609
$622$	−29.6278	−1.18797
$623$	−14.3179	−0.573633
$624$	0	0
$625$	−16.3847	−0.655389
$626$	32.3893	1.29454
$627$	−0.434172	−0.0173391
$628$	−14.6246	−0.583585
$629$	1.97792	0.0788648
$630$	−3.68561	−0.146838
$631$	9.09532	0.362079	0.181039	−	0.983476i	$-0.442054\pi$
$631$	9.09532	0.362079	0.181039	+	0.983476i	$0.442054\pi$
$632$	−13.1183	−0.521819
$633$	−24.0587	−0.956248
$634$	−26.2197	−1.04132
$635$	−55.8817	−2.21760
$636$	3.36714	0.133516
$637$	0	0
$638$	−1.58249	−0.0626512
$639$	14.6773	0.580626
$640$	1.43426	0.0566940
$641$	−27.6571	−1.09239	−0.546194	−	0.837658i	$-0.683924\pi$
$641$	−27.6571	−1.09239	−0.546194	+	0.837658i	$0.683924\pi$
$642$	9.39315	0.370718
$643$	−27.7846	−1.09572	−0.547859	−	0.836571i	$-0.684557\pi$
$643$	−27.7846	−1.09572	−0.547859	+	0.836571i	$0.684557\pi$
$644$	7.10290	0.279893
$645$	−7.84750	−0.308995
$646$	−0.479468	−0.0188644
$647$	−42.0045	−1.65137	−0.825685	−	0.564132i	$-0.809211\pi$
$647$	−42.0045	−1.65137	−0.825685	+	0.564132i	$0.809211\pi$
$648$	−3.06655	−0.120465
$649$	−4.67318	−0.183438
$650$	0	0
$651$	−1.89809	−0.0743922
$652$	15.7400	0.616426
$653$	−6.17528	−0.241657	−0.120829	−	0.992673i	$-0.538555\pi$
$653$	−6.17528	−0.241657	−0.120829	+	0.992673i	$0.538555\pi$
$654$	−21.5252	−0.841703
$655$	32.9168	1.28617
$656$	−17.5342	−0.684596
$657$	−14.5666	−0.568298
$658$	−9.67642	−0.377226
$659$	−16.3984	−0.638790	−0.319395	−	0.947622i	$-0.603480\pi$
$659$	−16.3984	−0.638790	−0.319395	+	0.947622i	$0.603480\pi$
$660$	−1.10542	−0.0430286
$661$	−5.90374	−0.229629	−0.114814	−	0.993387i	$-0.536627\pi$
$661$	−5.90374	−0.229629	−0.114814	+	0.993387i	$0.536627\pi$
$662$	6.06786	0.235834
$663$	0	0
$664$	14.1259	0.548190
$665$	3.58493	0.139018
$666$	5.24970	0.203422
$667$	−31.3290	−1.21306
$668$	−4.82292	−0.186605
$669$	−18.1487	−0.701668
$670$	8.82899	0.341094
$671$	4.74861	0.183318
$672$	−4.22306	−0.162908
$673$	−1.67667	−0.0646308	−0.0323154	−	0.999478i	$-0.510288\pi$
$673$	−1.67667	−0.0646308	−0.0323154	+	0.999478i	$0.510288\pi$
$674$	6.04741	0.232937
$675$	6.35555	0.244625
$676$	0	0
$677$	33.3324	1.28107	0.640535	−	0.767929i	$-0.278713\pi$
$677$	33.3324	1.28107	0.640535	+	0.767929i	$0.278713\pi$
$678$	1.49423	0.0573854
$679$	12.3236	0.472934
$680$	−4.25826	−0.163297
$681$	−16.2228	−0.621659
$682$	0.847243	0.0324426
$683$	−24.7425	−0.946746	−0.473373	−	0.880862i	$-0.656964\pi$
$683$	−24.7425	−0.946746	−0.473373	+	0.880862i	$0.656964\pi$
$684$	0.855097	0.0326955
$685$	−48.8171	−1.86521
$686$	−1.09372	−0.0417583
$687$	0.980804	0.0374200
$688$	4.06688	0.155048
$689$	0	0
$690$	32.5690	1.23988
$691$	48.1772	1.83275	0.916374	−	0.400323i	$-0.131102\pi$
$691$	48.1772	1.83275	0.916374	+	0.400323i	$0.131102\pi$
$692$	0.944934	0.0359210
$693$	−0.408118	−0.0155031
$694$	31.7755	1.20618
$695$	−26.1265	−0.991034
$696$	10.8717	0.412092
$697$	4.13743	0.156716
$698$	−16.8904	−0.639311
$699$	−19.4629	−0.736154
$700$	5.10849	0.193083
$701$	41.5798	1.57045	0.785224	−	0.619212i	$-0.212548\pi$
$701$	41.5798	1.57045	0.785224	+	0.619212i	$0.212548\pi$
$702$	0	0
$703$	−5.10630	−0.192588
$704$	3.31047	0.124768
$705$	29.8136	1.12284
$706$	−20.4499	−0.769642
$707$	1.21016	0.0455129
$708$	9.20379	0.345900
$709$	−35.6206	−1.33776	−0.668879	−	0.743371i	$-0.733226\pi$
$709$	−35.6206	−1.33776	−0.668879	+	0.743371i	$0.733226\pi$
$710$	54.0948	2.03014
$711$	4.27789	0.160433
$712$	−43.9064	−1.64546
$713$	16.7731	0.628158
$714$	−0.450696	−0.0168669
$715$	0	0
$716$	−0.200598	−0.00749671
$717$	18.7859	0.701573
$718$	11.9973	0.447737
$719$	8.40093	0.313302	0.156651	−	0.987654i	$-0.449930\pi$
$719$	8.40093	0.313302	0.156651	+	0.987654i	$0.449930\pi$
$720$	−5.88489	−0.219317
$721$	−13.5513	−0.504678
$722$	−19.5428	−0.727308
$723$	−9.08287	−0.337796
$724$	−0.355645	−0.0132175
$725$	−22.5322	−0.836824
$726$	−11.8487	−0.439747
$727$	−16.4191	−0.608950	−0.304475	−	0.952520i	$-0.598481\pi$
$727$	−16.4191	−0.608950	−0.304475	+	0.952520i	$0.598481\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−53.6868	−1.98704
$731$	−0.959635	−0.0354934
$732$	−9.35235	−0.345673
$733$	−50.9943	−1.88352	−0.941759	−	0.336288i	$-0.890829\pi$
$733$	−50.9943	−1.88352	−0.941759	+	0.336288i	$0.890829\pi$
$734$	12.9699	0.478727
$735$	3.36980	0.124297
$736$	37.3185	1.37558
$737$	0.977659	0.0360125
$738$	10.9814	0.404230
$739$	−13.3896	−0.492545	−0.246272	−	0.969201i	$-0.579206\pi$
$739$	−13.3896	−0.492545	−0.246272	+	0.969201i	$0.579206\pi$
$740$	−13.0009	−0.477923
$741$	0	0
$742$	4.58169	0.168199
$743$	35.2833	1.29442	0.647209	−	0.762313i	$-0.275936\pi$
$743$	35.2833	1.29442	0.647209	+	0.762313i	$0.275936\pi$
$744$	−5.82059	−0.213393
$745$	9.02479	0.330643
$746$	9.43037	0.345270
$747$	−4.60644	−0.168541
$748$	−0.135177	−0.00494257
$749$	−8.58829	−0.313809
$750$	4.99602	0.182429
$751$	−17.2150	−0.628183	−0.314091	−	0.949393i	$-0.601700\pi$
$751$	−17.2150	−0.628183	−0.314091	+	0.949393i	$0.601700\pi$
$752$	−15.4506	−0.563424
$753$	11.7323	0.427548
$754$	0	0
$755$	−25.6813	−0.934639
$756$	0.803784	0.0292333
$757$	25.2096	0.916260	0.458130	−	0.888885i	$-0.348519\pi$
$757$	25.2096	0.916260	0.458130	+	0.888885i	$0.348519\pi$
$758$	33.3615	1.21174
$759$	3.60646	0.130906
$760$	10.9933	0.398770
$761$	−5.13105	−0.186000	−0.0930001	−	0.995666i	$-0.529646\pi$
$761$	−5.13105	−0.186000	−0.0930001	+	0.995666i	$0.529646\pi$
$762$	−18.1372	−0.657042
$763$	19.6808	0.712493
$764$	−12.7436	−0.461048
$765$	1.38862	0.0502056
$766$	28.1733	1.01794
$767$	0	0
$768$	−15.7576	−0.568604
$769$	−20.5305	−0.740349	−0.370174	−	0.928962i	$-0.620702\pi$
$769$	−20.5305	−0.740349	−0.370174	+	0.928962i	$0.620702\pi$
$770$	−1.50416	−0.0542062
$771$	20.0321	0.721439
$772$	−3.41063	−0.122751
$773$	−10.8128	−0.388911	−0.194455	−	0.980911i	$-0.562294\pi$
$773$	−10.8128	−0.388911	−0.194455	+	0.980911i	$0.562294\pi$
$774$	−2.54702	−0.0915507
$775$	12.0634	0.433331
$776$	37.7907	1.35661
$777$	−4.79988	−0.172195
$778$	18.0928	0.648658
$779$	−10.6814	−0.382701
$780$	0	0
$781$	5.99007	0.214342
$782$	3.98272	0.142422
$783$	−3.54528	−0.126698
$784$	−1.74636	−0.0623701
$785$	61.3125	2.18834
$786$	10.6836	0.381072
$787$	30.3280	1.08108	0.540538	−	0.841320i	$-0.318221\pi$
$787$	30.3280	1.08108	0.540538	+	0.841320i	$0.318221\pi$
$788$	−7.34180	−0.261541
$789$	−5.06336	−0.180260
$790$	15.7666	0.560951
$791$	−1.36619	−0.0485762
$792$	−1.25151	−0.0444705
$793$	0	0
$794$	9.65047	0.342482
$795$	−14.1164	−0.500659
$796$	−7.76825	−0.275338
$797$	−18.9162	−0.670046	−0.335023	−	0.942210i	$-0.608744\pi$
$797$	−18.9162	−0.670046	−0.335023	+	0.942210i	$0.608744\pi$
$798$	1.16354	0.0411888
$799$	3.64576	0.128978
$800$	26.8399	0.948934
$801$	14.3179	0.505897
$802$	−11.8232	−0.417492
$803$	−5.94489	−0.209791
$804$	−1.92549	−0.0679068
$805$	−29.7783	−1.04955
$806$	0	0
$807$	4.89625	0.172356
$808$	3.71102	0.130553
$809$	33.8433	1.18987	0.594934	−	0.803774i	$-0.297178\pi$
$809$	33.8433	1.18987	0.594934	+	0.803774i	$0.297178\pi$
$810$	3.68561	0.129499
$811$	29.5769	1.03859	0.519293	−	0.854596i	$-0.326195\pi$
$811$	29.5769	1.03859	0.519293	+	0.854596i	$0.326195\pi$
$812$	−2.84964	−0.100003
$813$	−27.2537	−0.955829
$814$	2.14250	0.0750945
$815$	−65.9887	−2.31148
$816$	−0.719637	−0.0251923
$817$	2.47744	0.0866747
$818$	−21.3452	−0.746318
$819$	0	0
$820$	−27.1954	−0.949704
$821$	12.1069	0.422533	0.211266	−	0.977429i	$-0.432241\pi$
$821$	12.1069	0.422533	0.211266	+	0.977429i	$0.432241\pi$
$822$	−15.8443	−0.552633
$823$	−55.2074	−1.92441	−0.962204	−	0.272330i	$-0.912206\pi$
$823$	−55.2074	−1.92441	−0.962204	+	0.272330i	$0.912206\pi$
$824$	−41.5557	−1.44766
$825$	2.59381	0.0903049
$826$	12.5237	0.435755
$827$	−30.5277	−1.06155	−0.530777	−	0.847512i	$-0.678100\pi$
$827$	−30.5277	−1.06155	−0.530777	+	0.847512i	$0.678100\pi$
$828$	−7.10290	−0.246843
$829$	−2.22089	−0.0771346	−0.0385673	−	0.999256i	$-0.512279\pi$
$829$	−2.22089	−0.0771346	−0.0385673	+	0.999256i	$0.512279\pi$
$830$	−16.9775	−0.589299
$831$	−2.91367	−0.101074
$832$	0	0
$833$	0.412077	0.0142776
$834$	−8.47972	−0.293629
$835$	20.2197	0.699732
$836$	0.348980	0.0120697
$837$	1.89809	0.0656077
$838$	2.35074	0.0812050
$839$	−10.0791	−0.347970	−0.173985	−	0.984748i	$-0.555664\pi$
$839$	−10.0791	−0.347970	−0.173985	+	0.984748i	$0.555664\pi$
$840$	10.3336	0.356545
$841$	−16.4310	−0.566587
$842$	18.7955	0.647737
$843$	−25.2705	−0.870363
$844$	19.3380	0.665642
$845$	0	0
$846$	9.67642	0.332682
$847$	10.8334	0.372241
$848$	7.31570	0.251222
$849$	18.5059	0.635121
$850$	2.86442	0.0982488
$851$	42.4157	1.45399
$852$	−11.7974	−0.404172
$853$	13.2747	0.454516	0.227258	−	0.973835i	$-0.427024\pi$
$853$	13.2747	0.454516	0.227258	+	0.973835i	$0.427024\pi$
$854$	−12.7258	−0.435469
$855$	−3.58493	−0.122602
$856$	−26.3364	−0.900159
$857$	24.4586	0.835490	0.417745	−	0.908564i	$-0.362821\pi$
$857$	24.4586	0.835490	0.417745	+	0.908564i	$0.362821\pi$
$858$	0	0
$859$	2.20774	0.0753272	0.0376636	−	0.999290i	$-0.488008\pi$
$859$	2.20774	0.0753272	0.0376636	+	0.999290i	$0.488008\pi$
$860$	6.30769	0.215091
$861$	−10.0404	−0.342177
$862$	−13.5782	−0.462476
$863$	9.06990	0.308743	0.154371	−	0.988013i	$-0.450665\pi$
$863$	9.06990	0.308743	0.154371	+	0.988013i	$0.450665\pi$
$864$	4.22306	0.143672
$865$	−3.96156	−0.134697
$866$	−2.07057	−0.0703609
$867$	−16.8302	−0.571583
$868$	1.52566	0.0517842
$869$	1.74588	0.0592250
$870$	−13.0665	−0.442995
$871$	0	0
$872$	60.3521	2.04378
$873$	−12.3236	−0.417089
$874$	−10.2820	−0.347793
$875$	−4.56793	−0.154424
$876$	11.7084	0.395591
$877$	−5.06468	−0.171022	−0.0855110	−	0.996337i	$-0.527252\pi$
$877$	−5.06468	−0.171022	−0.0855110	+	0.996337i	$0.527252\pi$
$878$	−5.00202	−0.168810
$879$	5.10573	0.172212
$880$	−2.40173	−0.0809622
$881$	−10.4132	−0.350828	−0.175414	−	0.984495i	$-0.556126\pi$
$881$	−10.4132	−0.350828	−0.175414	+	0.984495i	$0.556126\pi$
$882$	1.09372	0.0368274
$883$	39.6733	1.33511	0.667556	−	0.744560i	$-0.267340\pi$
$883$	39.6733	1.33511	0.667556	+	0.744560i	$0.267340\pi$
$884$	0	0
$885$	−38.5861	−1.29706
$886$	31.0567	1.04337
$887$	−19.9363	−0.669394	−0.334697	−	0.942326i	$-0.608634\pi$
$887$	−19.9363	−0.669394	−0.334697	+	0.942326i	$0.608634\pi$
$888$	−14.7190	−0.493939
$889$	16.5831	0.556179
$890$	52.7700	1.76886
$891$	0.408118	0.0136725
$892$	14.5876	0.488429
$893$	−9.41209	−0.314964
$894$	2.92912	0.0979646
$895$	0.840992	0.0281113
$896$	−0.425621	−0.0142190
$897$	0	0
$898$	−38.9942	−1.30125
$899$	−6.72927	−0.224434
$900$	−5.10849	−0.170283
$901$	−1.72623	−0.0575092
$902$	4.48169	0.149224
$903$	2.32877	0.0774967
$904$	−4.18949	−0.139340
$905$	1.49101	0.0495630
$906$	−8.33524	−0.276920
$907$	25.9765	0.862535	0.431268	−	0.902224i	$-0.358066\pi$
$907$	25.9765	0.862535	0.431268	+	0.902224i	$0.358066\pi$
$908$	13.0396	0.432735
$909$	−1.21016	−0.0401386
$910$	0	0
$911$	26.4073	0.874911	0.437456	−	0.899240i	$-0.355880\pi$
$911$	26.4073	0.874911	0.437456	+	0.899240i	$0.355880\pi$
$912$	1.85785	0.0615196
$913$	−1.87997	−0.0622179
$914$	−34.4189	−1.13848
$915$	39.2090	1.29621
$916$	−0.788355	−0.0260480
$917$	−9.76818	−0.322574
$918$	0.450696	0.0148752
$919$	−24.8301	−0.819068	−0.409534	−	0.912295i	$-0.634309\pi$
$919$	−24.8301	−0.819068	−0.409534	+	0.912295i	$0.634309\pi$
$920$	−91.3166	−3.01062
$921$	−0.145600	−0.00479770
$922$	−23.2173	−0.764620
$923$	0	0
$924$	0.328038	0.0107917
$925$	30.5059	1.00303
$926$	8.88164	0.291869
$927$	13.5513	0.445084
$928$	−14.9719	−0.491477
$929$	−18.6678	−0.612472	−0.306236	−	0.951956i	$-0.599070\pi$
$929$	−18.6678	−0.612472	−0.306236	+	0.951956i	$0.599070\pi$
$930$	6.99563	0.229396
$931$	−1.06384	−0.0348659
$932$	15.6439	0.512435
$933$	−27.0891	−0.886858
$934$	−29.3431	−0.960134
$935$	0.566719	0.0185337
$936$	0	0
$937$	2.93693	0.0959453	0.0479727	−	0.998849i	$-0.484724\pi$
$937$	2.93693	0.0959453	0.0479727	+	0.998849i	$0.484724\pi$
$938$	−2.62003	−0.0855472
$939$	29.6140	0.966416
$940$	−23.9637	−0.781609
$941$	−50.7259	−1.65362	−0.826808	−	0.562484i	$-0.809846\pi$
$941$	−50.7259	−1.65362	−0.826808	+	0.562484i	$0.809846\pi$
$942$	19.8998	0.648372
$943$	88.7254	2.88930
$944$	19.9969	0.650842
$945$	−3.36980	−0.109620
$946$	−1.03948	−0.0337965
$947$	−25.8256	−0.839220	−0.419610	−	0.907704i	$-0.637833\pi$
$947$	−25.8256	−0.839220	−0.419610	+	0.907704i	$0.637833\pi$
$948$	−3.43850	−0.111677
$949$	0	0
$950$	−7.39493	−0.239923
$951$	−23.9730	−0.777378
$952$	1.26365	0.0409553
$953$	−42.6541	−1.38170	−0.690851	−	0.722998i	$-0.742764\pi$
$953$	−42.6541	−1.38170	−0.690851	+	0.722998i	$0.742764\pi$
$954$	−4.58169	−0.148338
$955$	53.4266	1.72884
$956$	−15.0998	−0.488363
$957$	−1.44689	−0.0467713
$958$	10.6666	0.344621
$959$	14.4867	0.467798
$960$	27.3343	0.882212
$961$	−27.3972	−0.883782
$962$	0	0
$963$	8.58829	0.276754
$964$	7.30067	0.235139
$965$	14.2988	0.460295
$966$	−9.66498	−0.310966
$967$	37.4458	1.20418	0.602088	−	0.798430i	$-0.294336\pi$
$967$	37.4458	1.20418	0.602088	+	0.798430i	$0.294336\pi$
$968$	33.2212	1.06777
$969$	−0.438384	−0.0140829
$970$	−45.4197	−1.45834
$971$	22.1197	0.709855	0.354928	−	0.934894i	$-0.384505\pi$
$971$	22.1197	0.709855	0.354928	+	0.934894i	$0.384505\pi$
$972$	−0.803784	−0.0257814
$973$	7.75313	0.248554
$974$	−23.9381	−0.767026
$975$	0	0
$976$	−20.3196	−0.650415
$977$	39.8028	1.27340	0.636702	−	0.771110i	$-0.280298\pi$
$977$	39.8028	1.27340	0.636702	+	0.771110i	$0.280298\pi$
$978$	−21.4176	−0.684859
$979$	5.84337	0.186755
$980$	−2.70859	−0.0865228
$981$	−19.6808	−0.628360
$982$	36.2720	1.15749
$983$	21.8790	0.697832	0.348916	−	0.937154i	$-0.386550\pi$
$983$	21.8790	0.697832	0.348916	+	0.937154i	$0.386550\pi$
$984$	−30.7894	−0.981530
$985$	30.7799	0.980729
$986$	−1.59784	−0.0508856
$987$	−8.84728	−0.281612
$988$	0	0
$989$	−20.5790	−0.654373
$990$	1.50416	0.0478054
$991$	35.6459	1.13233	0.566164	−	0.824293i	$-0.308427\pi$
$991$	35.6459	1.13233	0.566164	+	0.824293i	$0.308427\pi$
$992$	8.01577	0.254501
$993$	5.54793	0.176058
$994$	−16.0528	−0.509165
$995$	32.5678	1.03247
$996$	3.70258	0.117321
$997$	46.5398	1.47393	0.736965	−	0.675931i	$-0.236258\pi$
$997$	46.5398	1.47393	0.736965	+	0.675931i	$0.236258\pi$
$998$	44.4900	1.40831
$999$	4.79988	0.151861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.10	yes	15
13.12	even	2		3549.2.a.bg.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.6	✓	15	13.12	even	2
3549.2.a.bh.1.10	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +3.68561 q^{10} +0.408118 q^{11} -0.803784 q^{12} -1.09372 q^{14} +3.36980 q^{15} -1.74636 q^{16} +0.412077 q^{17} +1.09372 q^{18} -1.06384 q^{19} -2.70859 q^{20} -1.00000 q^{21} +0.446365 q^{22} +8.83682 q^{23} -3.06655 q^{24} +6.35555 q^{25} +1.00000 q^{27} +0.803784 q^{28} -3.54528 q^{29} +3.68561 q^{30} +1.89809 q^{31} +4.22306 q^{32} +0.408118 q^{33} +0.450696 q^{34} -3.36980 q^{35} -0.803784 q^{36} +4.79988 q^{37} -1.16354 q^{38} -10.3336 q^{40} +10.0404 q^{41} -1.09372 q^{42} -2.32877 q^{43} -0.328038 q^{44} +3.36980 q^{45} +9.66498 q^{46} +8.84728 q^{47} -1.74636 q^{48} +1.00000 q^{49} +6.95117 q^{50} +0.412077 q^{51} -4.18910 q^{53} +1.09372 q^{54} +1.37527 q^{55} +3.06655 q^{56} -1.06384 q^{57} -3.87753 q^{58} -11.4506 q^{59} -2.70859 q^{60} +11.6354 q^{61} +2.07598 q^{62} -1.00000 q^{63} +8.11156 q^{64} +0.446365 q^{66} +2.39553 q^{67} -0.331221 q^{68} +8.83682 q^{69} -3.68561 q^{70} +14.6773 q^{71} -3.06655 q^{72} -14.5666 q^{73} +5.24970 q^{74} +6.35555 q^{75} +0.855097 q^{76} -0.408118 q^{77} +4.27789 q^{79} -5.88489 q^{80} +1.00000 q^{81} +10.9814 q^{82} -4.60644 q^{83} +0.803784 q^{84} +1.38862 q^{85} -2.54702 q^{86} -3.54528 q^{87} -1.25151 q^{88} +14.3179 q^{89} +3.68561 q^{90} -7.10290 q^{92} +1.89809 q^{93} +9.67642 q^{94} -3.58493 q^{95} +4.22306 q^{96} -12.3236 q^{97} +1.09372 q^{98} +0.408118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

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