LMFDB - Embedded newform 3549.2.a.u.1.2

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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ 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)

$f(q)$	$=$	$q+0.554958 q^{2} +1.00000 q^{3} -1.69202 q^{4} -1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} -2.04892 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.554958 q^{2} +1.00000 q^{3} -1.69202 q^{4} -1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} -2.04892 q^{8} +1.00000 q^{9} -0.753020 q^{10} -1.13706 q^{11} -1.69202 q^{12} -0.554958 q^{14} -1.35690 q^{15} +2.24698 q^{16} -0.554958 q^{17} +0.554958 q^{18} +4.10992 q^{19} +2.29590 q^{20} -1.00000 q^{21} -0.631023 q^{22} -6.78986 q^{23} -2.04892 q^{24} -3.15883 q^{25} +1.00000 q^{27} +1.69202 q^{28} -9.03684 q^{29} -0.753020 q^{30} +8.63102 q^{31} +5.34481 q^{32} -1.13706 q^{33} -0.307979 q^{34} +1.35690 q^{35} -1.69202 q^{36} +5.18060 q^{37} +2.28083 q^{38} +2.78017 q^{40} -0.219833 q^{41} -0.554958 q^{42} +3.89977 q^{43} +1.92394 q^{44} -1.35690 q^{45} -3.76809 q^{46} +8.13706 q^{47} +2.24698 q^{48} +1.00000 q^{49} -1.75302 q^{50} -0.554958 q^{51} +7.98792 q^{53} +0.554958 q^{54} +1.54288 q^{55} +2.04892 q^{56} +4.10992 q^{57} -5.01507 q^{58} -3.89977 q^{59} +2.29590 q^{60} +10.9215 q^{61} +4.78986 q^{62} -1.00000 q^{63} -1.52781 q^{64} -0.631023 q^{66} -0.762709 q^{67} +0.939001 q^{68} -6.78986 q^{69} +0.753020 q^{70} -4.50365 q^{71} -2.04892 q^{72} -8.50365 q^{73} +2.87502 q^{74} -3.15883 q^{75} -6.95407 q^{76} +1.13706 q^{77} -3.74094 q^{79} -3.04892 q^{80} +1.00000 q^{81} -0.121998 q^{82} +11.0586 q^{83} +1.69202 q^{84} +0.753020 q^{85} +2.16421 q^{86} -9.03684 q^{87} +2.32975 q^{88} +8.60388 q^{89} -0.753020 q^{90} +11.4886 q^{92} +8.63102 q^{93} +4.51573 q^{94} -5.57673 q^{95} +5.34481 q^{96} +14.9487 q^{97} +0.554958 q^{98} -1.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * q^98 + 2 * 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 $

$2$	0.554958	0.392415	0.196207	−	0.980562i	$-0.437137\pi$
$2$	0.554958	0.392415	0.196207	+	0.980562i	$0.437137\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.69202	−0.846011
$5$	−1.35690	−0.606822	−0.303411	−	0.952860i	$-0.598126\pi$
$5$	−1.35690	−0.606822	−0.303411	+	0.952860i	$0.598126\pi$
$6$	0.554958	0.226561
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.04892	−0.724402
$9$	1.00000	0.333333
$10$	−0.753020	−0.238126
$11$	−1.13706	−0.342837	−0.171419	−	0.985198i	$-0.554835\pi$
$11$	−1.13706	−0.342837	−0.171419	+	0.985198i	$0.554835\pi$
$12$	−1.69202	−0.488445
$13$	0	0
$13$	0	0
$14$	−0.554958	−0.148319
$15$	−1.35690	−0.350349
$16$	2.24698	0.561745
$17$	−0.554958	−0.134597	−0.0672986	−	0.997733i	$-0.521438\pi$
$17$	−0.554958	−0.134597	−0.0672986	+	0.997733i	$0.521438\pi$
$18$	0.554958	0.130805
$19$	4.10992	0.942879	0.471440	−	0.881898i	$-0.343734\pi$
$19$	4.10992	0.942879	0.471440	+	0.881898i	$0.343734\pi$
$20$	2.29590	0.513378
$21$	−1.00000	−0.218218
$22$	−0.631023	−0.134534
$23$	−6.78986	−1.41578	−0.707891	−	0.706321i	$-0.750353\pi$
$23$	−6.78986	−1.41578	−0.707891	+	0.706321i	$0.750353\pi$
$24$	−2.04892	−0.418234
$25$	−3.15883	−0.631767
$26$	0	0
$27$	1.00000	0.192450
$28$	1.69202	0.319762
$29$	−9.03684	−1.67810	−0.839049	−	0.544056i	$-0.816888\pi$
$29$	−9.03684	−1.67810	−0.839049	+	0.544056i	$0.816888\pi$
$30$	−0.753020	−0.137482
$31$	8.63102	1.55018	0.775089	−	0.631852i	$-0.217705\pi$
$31$	8.63102	1.55018	0.775089	+	0.631852i	$0.217705\pi$
$32$	5.34481	0.944839
$33$	−1.13706	−0.197937
$34$	−0.307979	−0.0528179
$35$	1.35690	0.229357
$36$	−1.69202	−0.282004
$37$	5.18060	0.851686	0.425843	−	0.904797i	$-0.359978\pi$
$37$	5.18060	0.851686	0.425843	+	0.904797i	$0.359978\pi$
$38$	2.28083	0.370000
$39$	0	0
$40$	2.78017	0.439583
$41$	−0.219833	−0.0343321	−0.0171660	−	0.999853i	$-0.505464\pi$
$41$	−0.219833	−0.0343321	−0.0171660	+	0.999853i	$0.505464\pi$
$42$	−0.554958	−0.0856319
$43$	3.89977	0.594710	0.297355	−	0.954767i	$-0.403896\pi$
$43$	3.89977	0.594710	0.297355	+	0.954767i	$0.403896\pi$
$44$	1.92394	0.290044
$45$	−1.35690	−0.202274
$46$	−3.76809	−0.555574
$47$	8.13706	1.18691	0.593456	−	0.804866i	$-0.297763\pi$
$47$	8.13706	1.18691	0.593456	+	0.804866i	$0.297763\pi$
$48$	2.24698	0.324324
$49$	1.00000	0.142857
$50$	−1.75302	−0.247915
$51$	−0.554958	−0.0777097
$52$	0	0
$53$	7.98792	1.09722	0.548612	−	0.836077i	$-0.315156\pi$
$53$	7.98792	1.09722	0.548612	+	0.836077i	$0.315156\pi$
$54$	0.554958	0.0755202
$55$	1.54288	0.208041
$56$	2.04892	0.273798
$57$	4.10992	0.544372
$58$	−5.01507	−0.658510
$59$	−3.89977	−0.507707	−0.253854	−	0.967243i	$-0.581698\pi$
$59$	−3.89977	−0.507707	−0.253854	+	0.967243i	$0.581698\pi$
$60$	2.29590	0.296399
$61$	10.9215	1.39836	0.699180	−	0.714946i	$-0.253549\pi$
$61$	10.9215	1.39836	0.699180	+	0.714946i	$0.253549\pi$
$62$	4.78986	0.608312
$63$	−1.00000	−0.125988
$64$	−1.52781	−0.190976
$65$	0	0
$66$	−0.631023	−0.0776735
$67$	−0.762709	−0.0931797	−0.0465899	−	0.998914i	$-0.514835\pi$
$67$	−0.762709	−0.0931797	−0.0465899	+	0.998914i	$0.514835\pi$
$68$	0.939001	0.113871
$69$	−6.78986	−0.817403
$70$	0.753020	0.0900032
$71$	−4.50365	−0.534485	−0.267242	−	0.963629i	$-0.586112\pi$
$71$	−4.50365	−0.534485	−0.267242	+	0.963629i	$0.586112\pi$
$72$	−2.04892	−0.241467
$73$	−8.50365	−0.995277	−0.497638	−	0.867385i	$-0.665799\pi$
$73$	−8.50365	−0.995277	−0.497638	+	0.867385i	$0.665799\pi$
$74$	2.87502	0.334214
$75$	−3.15883	−0.364751
$76$	−6.95407	−0.797686
$77$	1.13706	0.129580
$78$	0	0
$79$	−3.74094	−0.420888	−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094	−0.420888	−0.210444	+	0.977606i	$0.567491\pi$
$80$	−3.04892	−0.340879
$81$	1.00000	0.111111
$82$	−0.121998	−0.0134724
$83$	11.0586	1.21384	0.606920	−	0.794763i	$-0.292405\pi$
$83$	11.0586	1.21384	0.606920	+	0.794763i	$0.292405\pi$
$84$	1.69202	0.184615
$85$	0.753020	0.0816765
$86$	2.16421	0.233373
$87$	−9.03684	−0.968850
$88$	2.32975	0.248352
$89$	8.60388	0.912009	0.456004	−	0.889977i	$-0.349280\pi$
$89$	8.60388	0.912009	0.456004	+	0.889977i	$0.349280\pi$
$90$	−0.753020	−0.0793753
$91$	0	0
$92$	11.4886	1.19777
$93$	8.63102	0.894995
$94$	4.51573	0.465762
$95$	−5.57673	−0.572160
$96$	5.34481	0.545503
$97$	14.9487	1.51781	0.758905	−	0.651202i	$-0.225735\pi$
$97$	14.9487	1.51781	0.758905	+	0.651202i	$0.225735\pi$
$98$	0.554958	0.0560592
$99$	−1.13706	−0.114279
$100$	5.34481	0.534481
$101$	4.25236	0.423125	0.211563	−	0.977364i	$-0.432145\pi$
$101$	4.25236	0.423125	0.211563	+	0.977364i	$0.432145\pi$
$102$	−0.307979	−0.0304944
$103$	6.08575	0.599647	0.299824	−	0.953995i	$-0.403072\pi$
$103$	6.08575	0.599647	0.299824	+	0.953995i	$0.403072\pi$
$104$	0	0
$105$	1.35690	0.132419
$106$	4.43296	0.430567
$107$	−12.8562	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$107$	−12.8562	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$108$	−1.69202	−0.162815
$109$	6.84117	0.655265	0.327632	−	0.944805i	$-0.393749\pi$
$109$	6.84117	0.655265	0.327632	+	0.944805i	$0.393749\pi$
$110$	0.856232	0.0816385
$111$	5.18060	0.491721
$112$	−2.24698	−0.212320
$113$	18.6310	1.75266	0.876330	−	0.481712i	$-0.159985\pi$
$113$	18.6310	1.75266	0.876330	+	0.481712i	$0.159985\pi$
$114$	2.28083	0.213619
$115$	9.21313	0.859129
$116$	15.2905	1.41969
$117$	0	0
$118$	−2.16421	−0.199232
$119$	0.554958	0.0508729
$120$	2.78017	0.253793
$121$	−9.70709	−0.882462
$122$	6.06100	0.548737
$123$	−0.219833	−0.0198216
$124$	−14.6039	−1.31147
$125$	11.0707	0.990192
$126$	−0.554958	−0.0494396
$127$	4.61894	0.409865	0.204932	−	0.978776i	$-0.434303\pi$
$127$	4.61894	0.409865	0.204932	+	0.978776i	$0.434303\pi$
$128$	−11.5375	−1.01978
$129$	3.89977	0.343356
$130$	0	0
$131$	−3.35690	−0.293293	−0.146647	−	0.989189i	$-0.546848\pi$
$131$	−3.35690	−0.293293	−0.146647	+	0.989189i	$0.546848\pi$
$132$	1.92394	0.167457
$133$	−4.10992	−0.356375
$134$	−0.423272	−0.0365651
$135$	−1.35690	−0.116783
$136$	1.13706	0.0975024
$137$	21.5133	1.83801	0.919004	−	0.394248i	$-0.128995\pi$
$137$	21.5133	1.83801	0.919004	+	0.394248i	$0.128995\pi$
$138$	−3.76809	−0.320761
$139$	−8.09246	−0.686393	−0.343197	−	0.939264i	$-0.611510\pi$
$139$	−8.09246	−0.686393	−0.343197	+	0.939264i	$0.611510\pi$
$140$	−2.29590	−0.194039
$141$	8.13706	0.685264
$142$	−2.49934	−0.209740
$143$	0	0
$144$	2.24698	0.187248
$145$	12.2620	1.01831
$146$	−4.71917	−0.390561
$147$	1.00000	0.0824786
$148$	−8.76569	−0.720536
$149$	−3.25906	−0.266993	−0.133496	−	0.991049i	$-0.542620\pi$
$149$	−3.25906	−0.266993	−0.133496	+	0.991049i	$0.542620\pi$
$150$	−1.75302	−0.143134
$151$	6.81163	0.554322	0.277161	−	0.960823i	$-0.410606\pi$
$151$	6.81163	0.554322	0.277161	+	0.960823i	$0.410606\pi$
$152$	−8.42088	−0.683023
$153$	−0.554958	−0.0448657
$154$	0.631023	0.0508492
$155$	−11.7114	−0.940682
$156$	0	0
$157$	24.4306	1.94977	0.974886	−	0.222705i	$-0.0714888\pi$
$157$	24.4306	1.94977	0.974886	+	0.222705i	$0.0714888\pi$
$158$	−2.07606	−0.165163
$159$	7.98792	0.633483
$160$	−7.25236	−0.573349
$161$	6.78986	0.535116
$162$	0.554958	0.0436016
$163$	11.5483	0.904529	0.452265	−	0.891884i	$-0.350616\pi$
$163$	11.5483	0.904529	0.452265	+	0.891884i	$0.350616\pi$
$164$	0.371961	0.0290453
$165$	1.54288	0.120113
$166$	6.13706	0.476328
$167$	−4.82371	−0.373270	−0.186635	−	0.982429i	$-0.559758\pi$
$167$	−4.82371	−0.373270	−0.186635	+	0.982429i	$0.559758\pi$
$168$	2.04892	0.158077
$169$	0	0
$170$	0.417895	0.0320511
$171$	4.10992	0.314293
$172$	−6.59850	−0.503131
$173$	−21.6256	−1.64417	−0.822084	−	0.569367i	$-0.807188\pi$
$173$	−21.6256	−1.64417	−0.822084	+	0.569367i	$0.807188\pi$
$174$	−5.01507	−0.380191
$175$	3.15883	0.238785
$176$	−2.55496	−0.192587
$177$	−3.89977	−0.293125
$178$	4.77479	0.357886
$179$	25.4088	1.89914	0.949571	−	0.313551i	$-0.101519\pi$
$179$	25.4088	1.89914	0.949571	+	0.313551i	$0.101519\pi$
$180$	2.29590	0.171126
$181$	−7.67994	−0.570845	−0.285423	−	0.958402i	$-0.592134\pi$
$181$	−7.67994	−0.570845	−0.285423	+	0.958402i	$0.592134\pi$
$182$	0	0
$183$	10.9215	0.807344
$184$	13.9119	1.02560
$185$	−7.02954	−0.516822
$186$	4.78986	0.351209
$187$	0.631023	0.0461449
$188$	−13.7681	−1.00414
$189$	−1.00000	−0.0727393
$190$	−3.09485	−0.224524
$191$	9.50365	0.687660	0.343830	−	0.939032i	$-0.388276\pi$
$191$	9.50365	0.687660	0.343830	+	0.939032i	$0.388276\pi$
$192$	−1.52781	−0.110260
$193$	9.35152	0.673137	0.336569	−	0.941659i	$-0.390734\pi$
$193$	9.35152	0.673137	0.336569	+	0.941659i	$0.390734\pi$
$194$	8.29590	0.595611
$195$	0	0
$196$	−1.69202	−0.120859
$197$	−17.5157	−1.24794	−0.623972	−	0.781447i	$-0.714482\pi$
$197$	−17.5157	−1.24794	−0.623972	+	0.781447i	$0.714482\pi$
$198$	−0.631023	−0.0448448
$199$	−17.5894	−1.24688	−0.623440	−	0.781871i	$-0.714265\pi$
$199$	−17.5894	−1.24688	−0.623440	+	0.781871i	$0.714265\pi$
$200$	6.47219	0.457653
$201$	−0.762709	−0.0537974
$202$	2.35988	0.166041
$203$	9.03684	0.634262
$204$	0.939001	0.0657432
$205$	0.298290	0.0208335
$206$	3.37734	0.235310
$207$	−6.78986	−0.471928
$208$	0	0
$209$	−4.67324	−0.323254
$210$	0.753020	0.0519633
$211$	1.36227	0.0937827	0.0468914	−	0.998900i	$-0.485069\pi$
$211$	1.36227	0.0937827	0.0468914	+	0.998900i	$0.485069\pi$
$212$	−13.5157	−0.928264
$213$	−4.50365	−0.308585
$214$	−7.13467	−0.487716
$215$	−5.29159	−0.360883
$216$	−2.04892	−0.139411
$217$	−8.63102	−0.585912
$218$	3.79656	0.257136
$219$	−8.50365	−0.574623
$220$	−2.61058	−0.176005
$221$	0	0
$222$	2.87502	0.192959
$223$	10.2862	0.688815	0.344408	−	0.938820i	$-0.388080\pi$
$223$	10.2862	0.688815	0.344408	+	0.938820i	$0.388080\pi$
$224$	−5.34481	−0.357115
$225$	−3.15883	−0.210589
$226$	10.3394	0.687769
$227$	−5.60819	−0.372228	−0.186114	−	0.982528i	$-0.559589\pi$
$227$	−5.60819	−0.372228	−0.186114	+	0.982528i	$0.559589\pi$
$228$	−6.95407	−0.460544
$229$	1.88040	0.124260	0.0621300	−	0.998068i	$-0.480211\pi$
$229$	1.88040	0.124260	0.0621300	+	0.998068i	$0.480211\pi$
$230$	5.11290	0.337135
$231$	1.13706	0.0748133
$232$	18.5157	1.21562
$233$	−6.38404	−0.418233	−0.209116	−	0.977891i	$-0.567059\pi$
$233$	−6.38404	−0.418233	−0.209116	+	0.977891i	$0.567059\pi$
$234$	0	0
$235$	−11.0411	−0.720245
$236$	6.59850	0.429526
$237$	−3.74094	−0.243000
$238$	0.307979	0.0199633
$239$	−1.90217	−0.123041	−0.0615204	−	0.998106i	$-0.519595\pi$
$239$	−1.90217	−0.123041	−0.0615204	+	0.998106i	$0.519595\pi$
$240$	−3.04892	−0.196807
$241$	−13.2121	−0.851064	−0.425532	−	0.904943i	$-0.639913\pi$
$241$	−13.2121	−0.851064	−0.425532	+	0.904943i	$0.639913\pi$
$242$	−5.38703	−0.346291
$243$	1.00000	0.0641500
$244$	−18.4795	−1.18303
$245$	−1.35690	−0.0866889
$246$	−0.121998	−0.00777830
$247$	0	0
$248$	−17.6843	−1.12295
$249$	11.0586	0.700811
$250$	6.14377	0.388566
$251$	7.54048	0.475951	0.237976	−	0.971271i	$-0.423516\pi$
$251$	7.54048	0.475951	0.237976	+	0.971271i	$0.423516\pi$
$252$	1.69202	0.106587
$253$	7.72050	0.485383
$254$	2.56332	0.160837
$255$	0.753020	0.0471560
$256$	−3.34721	−0.209200
$257$	13.4179	0.836985	0.418493	−	0.908220i	$-0.362559\pi$
$257$	13.4179	0.836985	0.418493	+	0.908220i	$0.362559\pi$
$258$	2.16421	0.134738
$259$	−5.18060	−0.321907
$260$	0	0
$261$	−9.03684	−0.559366
$262$	−1.86294	−0.115093
$263$	−11.1981	−0.690502	−0.345251	−	0.938510i	$-0.612206\pi$
$263$	−11.1981	−0.690502	−0.345251	+	0.938510i	$0.612206\pi$
$264$	2.32975	0.143386
$265$	−10.8388	−0.665821
$266$	−2.28083	−0.139847
$267$	8.60388	0.526549
$268$	1.29052	0.0788311
$269$	13.9172	0.848549	0.424274	−	0.905534i	$-0.360529\pi$
$269$	13.9172	0.848549	0.424274	+	0.905534i	$0.360529\pi$
$270$	−0.753020	−0.0458274
$271$	−1.98254	−0.120431	−0.0602154	−	0.998185i	$-0.519179\pi$
$271$	−1.98254	−0.120431	−0.0602154	+	0.998185i	$0.519179\pi$
$272$	−1.24698	−0.0756092
$273$	0	0
$274$	11.9390	0.721261
$275$	3.59179	0.216593
$276$	11.4886	0.691531
$277$	9.79954	0.588798	0.294399	−	0.955683i	$-0.404881\pi$
$277$	9.79954	0.588798	0.294399	+	0.955683i	$0.404881\pi$
$278$	−4.49098	−0.269351
$279$	8.63102	0.516726
$280$	−2.78017	−0.166147
$281$	25.7603	1.53673	0.768366	−	0.640011i	$-0.221070\pi$
$281$	25.7603	1.53673	0.768366	+	0.640011i	$0.221070\pi$
$282$	4.51573	0.268908
$283$	−0.0489173	−0.00290783	−0.00145392	−	0.999999i	$-0.500463\pi$
$283$	−0.0489173	−0.00290783	−0.00145392	+	0.999999i	$0.500463\pi$
$284$	7.62027	0.452180
$285$	−5.57673	−0.330337
$286$	0	0
$287$	0.219833	0.0129763
$288$	5.34481	0.314946
$289$	−16.6920	−0.981884
$290$	6.80492	0.399599
$291$	14.9487	0.876308
$292$	14.3884	0.842015
$293$	−21.3220	−1.24564	−0.622822	−	0.782364i	$-0.714014\pi$
$293$	−21.3220	−1.24564	−0.622822	+	0.782364i	$0.714014\pi$
$294$	0.554958	0.0323658
$295$	5.29159	0.308088
$296$	−10.6146	−0.616963
$297$	−1.13706	−0.0659791
$298$	−1.80864	−0.104772
$299$	0	0
$300$	5.34481	0.308583
$301$	−3.89977	−0.224779
$302$	3.78017	0.217524
$303$	4.25236	0.244291
$304$	9.23490	0.529658
$305$	−14.8194	−0.848556
$306$	−0.307979	−0.0176060
$307$	23.6528	1.34994	0.674968	−	0.737847i	$-0.264157\pi$
$307$	23.6528	1.34994	0.674968	+	0.737847i	$0.264157\pi$
$308$	−1.92394	−0.109626
$309$	6.08575	0.346206
$310$	−6.49934	−0.369137
$311$	16.5851	0.940454	0.470227	−	0.882545i	$-0.344172\pi$
$311$	16.5851	0.940454	0.470227	+	0.882545i	$0.344172\pi$
$312$	0	0
$313$	−6.90648	−0.390377	−0.195189	−	0.980766i	$-0.562532\pi$
$313$	−6.90648	−0.390377	−0.195189	+	0.980766i	$0.562532\pi$
$314$	13.5579	0.765119
$315$	1.35690	0.0764524
$316$	6.32975	0.356076
$317$	−26.0562	−1.46346	−0.731731	−	0.681593i	$-0.761287\pi$
$317$	−26.0562	−1.46346	−0.731731	+	0.681593i	$0.761287\pi$
$318$	4.43296	0.248588
$319$	10.2755	0.575315
$320$	2.07308	0.115889
$321$	−12.8562	−0.717565
$322$	3.76809	0.209987
$323$	−2.28083	−0.126909
$324$	−1.69202	−0.0940012
$325$	0	0
$326$	6.40880	0.354950
$327$	6.84117	0.378317
$328$	0.450419	0.0248702
$329$	−8.13706	−0.448611
$330$	0.856232	0.0471340
$331$	3.50066	0.192414	0.0962069	−	0.995361i	$-0.469329\pi$
$331$	3.50066	0.192414	0.0962069	+	0.995361i	$0.469329\pi$
$332$	−18.7114	−1.02692
$333$	5.18060	0.283895
$334$	−2.67696	−0.146477
$335$	1.03492	0.0565435
$336$	−2.24698	−0.122583
$337$	−4.14782	−0.225946	−0.112973	−	0.993598i	$-0.536037\pi$
$337$	−4.14782	−0.225946	−0.112973	+	0.993598i	$0.536037\pi$
$338$	0	0
$339$	18.6310	1.01190
$340$	−1.27413	−0.0690992
$341$	−9.81402	−0.531459
$342$	2.28083	0.123333
$343$	−1.00000	−0.0539949
$344$	−7.99031	−0.430809
$345$	9.21313	0.496018
$346$	−12.0013	−0.645195
$347$	−11.5743	−0.621343	−0.310671	−	0.950517i	$-0.600554\pi$
$347$	−11.5743	−0.621343	−0.310671	+	0.950517i	$0.600554\pi$
$348$	15.2905	0.819658
$349$	13.0127	0.696552	0.348276	−	0.937392i	$-0.386767\pi$
$349$	13.0127	0.696552	0.348276	+	0.937392i	$0.386767\pi$
$350$	1.75302	0.0937029
$351$	0	0
$352$	−6.07739	−0.323926
$353$	−26.1914	−1.39403	−0.697013	−	0.717059i	$-0.745488\pi$
$353$	−26.1914	−1.39403	−0.697013	+	0.717059i	$0.745488\pi$
$354$	−2.16421	−0.115026
$355$	6.11098	0.324337
$356$	−14.5579	−0.771569
$357$	0.554958	0.0293715
$358$	14.1008	0.745251
$359$	−11.0750	−0.584516	−0.292258	−	0.956339i	$-0.594407\pi$
$359$	−11.0750	−0.584516	−0.292258	+	0.956339i	$0.594407\pi$
$360$	2.78017	0.146528
$361$	−2.10859	−0.110978
$362$	−4.26205	−0.224008
$363$	−9.70709	−0.509490
$364$	0	0
$365$	11.5386	0.603956
$366$	6.06100	0.316813
$367$	−13.3709	−0.697955	−0.348978	−	0.937131i	$-0.613471\pi$
$367$	−13.3709	−0.697955	−0.348978	+	0.937131i	$0.613471\pi$
$368$	−15.2567	−0.795309
$369$	−0.219833	−0.0114440
$370$	−3.90110	−0.202809
$371$	−7.98792	−0.414712
$372$	−14.6039	−0.757176
$373$	−36.7308	−1.90185	−0.950924	−	0.309425i	$-0.899863\pi$
$373$	−36.7308	−1.90185	−0.950924	+	0.309425i	$0.899863\pi$
$374$	0.350191	0.0181080
$375$	11.0707	0.571688
$376$	−16.6722	−0.859802
$377$	0	0
$378$	−0.554958	−0.0285440
$379$	−33.2814	−1.70955	−0.854776	−	0.518997i	$-0.826305\pi$
$379$	−33.2814	−1.70955	−0.854776	+	0.518997i	$0.826305\pi$
$380$	9.43594	0.484054
$381$	4.61894	0.236636
$382$	5.27413	0.269848
$383$	17.6233	0.900506	0.450253	−	0.892901i	$-0.351334\pi$
$383$	17.6233	0.900506	0.450253	+	0.892901i	$0.351334\pi$
$384$	−11.5375	−0.588771
$385$	−1.54288	−0.0786323
$386$	5.18970	0.264149
$387$	3.89977	0.198237
$388$	−25.2935	−1.28408
$389$	29.6340	1.50250	0.751252	−	0.660016i	$-0.229450\pi$
$389$	29.6340	1.50250	0.751252	+	0.660016i	$0.229450\pi$
$390$	0	0
$391$	3.76809	0.190560
$392$	−2.04892	−0.103486
$393$	−3.35690	−0.169333
$394$	−9.72050	−0.489712
$395$	5.07606	0.255405
$396$	1.92394	0.0966814
$397$	−19.2000	−0.963619	−0.481810	−	0.876276i	$-0.660020\pi$
$397$	−19.2000	−0.963619	−0.481810	+	0.876276i	$0.660020\pi$
$398$	−9.76138	−0.489294
$399$	−4.10992	−0.205753
$400$	−7.09783	−0.354892
$401$	−12.4993	−0.624187	−0.312094	−	0.950051i	$-0.601030\pi$
$401$	−12.4993	−0.624187	−0.312094	+	0.950051i	$0.601030\pi$
$402$	−0.423272	−0.0211109
$403$	0	0
$404$	−7.19508	−0.357969
$405$	−1.35690	−0.0674247
$406$	5.01507	0.248894
$407$	−5.89067	−0.291990
$408$	1.13706	0.0562930
$409$	16.7821	0.829821	0.414910	−	0.909862i	$-0.363813\pi$
$409$	16.7821	0.829821	0.414910	+	0.909862i	$0.363813\pi$
$410$	0.165538	0.00817536
$411$	21.5133	1.06117
$412$	−10.2972	−0.507308
$413$	3.89977	0.191895
$414$	−3.76809	−0.185191
$415$	−15.0054	−0.736585
$416$	0	0
$417$	−8.09246	−0.396289
$418$	−2.59345	−0.126850
$419$	−14.3642	−0.701737	−0.350868	−	0.936425i	$-0.614114\pi$
$419$	−14.3642	−0.701737	−0.350868	+	0.936425i	$0.614114\pi$
$420$	−2.29590	−0.112028
$421$	22.5526	1.09914	0.549572	−	0.835446i	$-0.314791\pi$
$421$	22.5526	1.09914	0.549572	+	0.835446i	$0.314791\pi$
$422$	0.756004	0.0368017
$423$	8.13706	0.395638
$424$	−16.3666	−0.794832
$425$	1.75302	0.0850340
$426$	−2.49934	−0.121093
$427$	−10.9215	−0.528530
$428$	21.7530	1.05147
$429$	0	0
$430$	−2.93661	−0.141616
$431$	−4.48965	−0.216259	−0.108129	−	0.994137i	$-0.534486\pi$
$431$	−4.48965	−0.216259	−0.108129	+	0.994137i	$0.534486\pi$
$432$	2.24698	0.108108
$433$	19.3612	0.930440	0.465220	−	0.885195i	$-0.345975\pi$
$433$	19.3612	0.930440	0.465220	+	0.885195i	$0.345975\pi$
$434$	−4.78986	−0.229920
$435$	12.2620	0.587920
$436$	−11.5754	−0.554361
$437$	−27.9057	−1.33491
$438$	−4.71917	−0.225491
$439$	27.2868	1.30233	0.651164	−	0.758937i	$-0.274281\pi$
$439$	27.2868	1.30233	0.651164	+	0.758937i	$0.274281\pi$
$440$	−3.16123	−0.150706
$441$	1.00000	0.0476190
$442$	0	0
$443$	−16.2319	−0.771202	−0.385601	−	0.922666i	$-0.626006\pi$
$443$	−16.2319	−0.771202	−0.385601	+	0.922666i	$0.626006\pi$
$444$	−8.76569	−0.416001
$445$	−11.6746	−0.553427
$446$	5.70841	0.270301
$447$	−3.25906	−0.154148
$448$	1.52781	0.0721823
$449$	24.2470	1.14429	0.572143	−	0.820154i	$-0.306112\pi$
$449$	24.2470	1.14429	0.572143	+	0.820154i	$0.306112\pi$
$450$	−1.75302	−0.0826382
$451$	0.249964	0.0117703
$452$	−31.5241	−1.48277
$453$	6.81163	0.320038
$454$	−3.11231	−0.146068
$455$	0	0
$456$	−8.42088	−0.394344
$457$	31.4902	1.47305	0.736526	−	0.676410i	$-0.236465\pi$
$457$	31.4902	1.47305	0.736526	+	0.676410i	$0.236465\pi$
$458$	1.04354	0.0487614
$459$	−0.554958	−0.0259032
$460$	−15.5888	−0.726832
$461$	−40.8568	−1.90289	−0.951446	−	0.307816i	$-0.900402\pi$
$461$	−40.8568	−1.90289	−0.951446	+	0.307816i	$0.900402\pi$
$462$	0.631023	0.0293578
$463$	−39.0941	−1.81686	−0.908429	−	0.418040i	$-0.862717\pi$
$463$	−39.0941	−1.81686	−0.908429	+	0.418040i	$0.862717\pi$
$464$	−20.3056	−0.942663
$465$	−11.7114	−0.543103
$466$	−3.54288	−0.164121
$467$	9.39804	0.434890	0.217445	−	0.976073i	$-0.430228\pi$
$467$	9.39804	0.434890	0.217445	+	0.976073i	$0.430228\pi$
$468$	0	0
$469$	0.762709	0.0352186
$470$	−6.12737	−0.282635
$471$	24.4306	1.12570
$472$	7.99031	0.367784
$473$	−4.43429	−0.203889
$474$	−2.07606	−0.0953568
$475$	−12.9825	−0.595680
$476$	−0.939001	−0.0430390
$477$	7.98792	0.365742
$478$	−1.05562	−0.0482830
$479$	2.03385	0.0929291	0.0464645	−	0.998920i	$-0.485205\pi$
$479$	2.03385	0.0929291	0.0464645	+	0.998920i	$0.485205\pi$
$480$	−7.25236	−0.331023
$481$	0	0
$482$	−7.33214	−0.333970
$483$	6.78986	0.308949
$484$	16.4246	0.746573
$485$	−20.2838	−0.921041
$486$	0.554958	0.0251734
$487$	30.2881	1.37249	0.686243	−	0.727372i	$-0.259259\pi$
$487$	30.2881	1.37249	0.686243	+	0.727372i	$0.259259\pi$
$488$	−22.3773	−1.01297
$489$	11.5483	0.522230
$490$	−0.753020	−0.0340180
$491$	−29.1890	−1.31728	−0.658640	−	0.752458i	$-0.728868\pi$
$491$	−29.1890	−1.31728	−0.658640	+	0.752458i	$0.728868\pi$
$492$	0.371961	0.0167693
$493$	5.01507	0.225867
$494$	0	0
$495$	1.54288	0.0693471
$496$	19.3937	0.870804
$497$	4.50365	0.202016
$498$	6.13706	0.275008
$499$	−1.24937	−0.0559296	−0.0279648	−	0.999609i	$-0.508903\pi$
$499$	−1.24937	−0.0559296	−0.0279648	+	0.999609i	$0.508903\pi$
$500$	−18.7318	−0.837713
$501$	−4.82371	−0.215507
$502$	4.18465	0.186770
$503$	21.0194	0.937208	0.468604	−	0.883408i	$-0.344757\pi$
$503$	21.0194	0.937208	0.468604	+	0.883408i	$0.344757\pi$
$504$	2.04892	0.0912660
$505$	−5.77000	−0.256762
$506$	4.28455	0.190472
$507$	0	0
$508$	−7.81535	−0.346750
$509$	−23.6775	−1.04949	−0.524744	−	0.851260i	$-0.675839\pi$
$509$	−23.6775	−1.04949	−0.524744	+	0.851260i	$0.675839\pi$
$510$	0.417895	0.0185047
$511$	8.50365	0.376179
$512$	21.2174	0.937687
$513$	4.10992	0.181457
$514$	7.44637	0.328445
$515$	−8.25773	−0.363879
$516$	−6.59850	−0.290483
$517$	−9.25236	−0.406918
$518$	−2.87502	−0.126321
$519$	−21.6256	−0.949260
$520$	0	0
$521$	2.47783	0.108556	0.0542778	−	0.998526i	$-0.482714\pi$
$521$	2.47783	0.108556	0.0542778	+	0.998526i	$0.482714\pi$
$522$	−5.01507	−0.219503
$523$	7.10560	0.310706	0.155353	−	0.987859i	$-0.450348\pi$
$523$	7.10560	0.310706	0.155353	+	0.987859i	$0.450348\pi$
$524$	5.67994	0.248129
$525$	3.15883	0.137863
$526$	−6.21446	−0.270963
$527$	−4.78986	−0.208649
$528$	−2.55496	−0.111190
$529$	23.1021	1.00444
$530$	−6.01507	−0.261278
$531$	−3.89977	−0.169236
$532$	6.95407	0.301497
$533$	0	0
$534$	4.77479	0.206625
$535$	17.4446	0.754194
$536$	1.56273	0.0674996
$537$	25.4088	1.09647
$538$	7.72348	0.332983
$539$	−1.13706	−0.0489768
$540$	2.29590	0.0987997
$541$	35.7157	1.53554	0.767769	−	0.640727i	$-0.221367\pi$
$541$	35.7157	1.53554	0.767769	+	0.640727i	$0.221367\pi$
$542$	−1.10023	−0.0472588
$543$	−7.67994	−0.329578
$544$	−2.96615	−0.127173
$545$	−9.28275	−0.397629
$546$	0	0
$547$	10.1395	0.433532	0.216766	−	0.976224i	$-0.430449\pi$
$547$	10.1395	0.433532	0.216766	+	0.976224i	$0.430449\pi$
$548$	−36.4010	−1.55497
$549$	10.9215	0.466120
$550$	1.99330	0.0849944
$551$	−37.1406	−1.58224
$552$	13.9119	0.592128
$553$	3.74094	0.159081
$554$	5.43834	0.231053
$555$	−7.02954	−0.298387
$556$	13.6926	0.580696
$557$	−3.63342	−0.153953	−0.0769764	−	0.997033i	$-0.524527\pi$
$557$	−3.63342	−0.153953	−0.0769764	+	0.997033i	$0.524527\pi$
$558$	4.78986	0.202771
$559$	0	0
$560$	3.04892	0.128840
$561$	0.631023	0.0266418
$562$	14.2959	0.603036
$563$	39.8364	1.67890	0.839452	−	0.543434i	$-0.182876\pi$
$563$	39.8364	1.67890	0.839452	+	0.543434i	$0.182876\pi$
$564$	−13.7681	−0.579741
$565$	−25.2804	−1.06355
$566$	−0.0271471	−0.00114108
$567$	−1.00000	−0.0419961
$568$	9.22760	0.387182
$569$	2.68127	0.112405	0.0562023	−	0.998419i	$-0.482101\pi$
$569$	2.68127	0.112405	0.0562023	+	0.998419i	$0.482101\pi$
$570$	−3.09485	−0.129629
$571$	−6.76138	−0.282955	−0.141477	−	0.989941i	$-0.545185\pi$
$571$	−6.76138	−0.282955	−0.141477	+	0.989941i	$0.545185\pi$
$572$	0	0
$573$	9.50365	0.397021
$574$	0.121998	0.00509209
$575$	21.4480	0.894445
$576$	−1.52781	−0.0636588
$577$	6.73556	0.280405	0.140203	−	0.990123i	$-0.455225\pi$
$577$	6.73556	0.280405	0.140203	+	0.990123i	$0.455225\pi$
$578$	−9.26337	−0.385306
$579$	9.35152	0.388636
$580$	−20.7476	−0.861499
$581$	−11.0586	−0.458788
$582$	8.29590	0.343876
$583$	−9.08277	−0.376170
$584$	17.4233	0.720980
$585$	0	0
$586$	−11.8328	−0.488809
$587$	23.2529	0.959752	0.479876	−	0.877336i	$-0.340682\pi$
$587$	23.2529	0.959752	0.479876	+	0.877336i	$0.340682\pi$
$588$	−1.69202	−0.0697778
$589$	35.4728	1.46163
$590$	2.93661	0.120898
$591$	−17.5157	−0.720501
$592$	11.6407	0.478430
$593$	25.4717	1.04600	0.522999	−	0.852333i	$-0.324813\pi$
$593$	25.4717	1.04600	0.522999	+	0.852333i	$0.324813\pi$
$594$	−0.631023	−0.0258912
$595$	−0.753020	−0.0308708
$596$	5.51440	0.225879
$597$	−17.5894	−0.719886
$598$	0	0
$599$	−16.7453	−0.684192	−0.342096	−	0.939665i	$-0.611137\pi$
$599$	−16.7453	−0.684192	−0.342096	+	0.939665i	$0.611137\pi$
$600$	6.47219	0.264226
$601$	0.412518	0.0168270	0.00841348	−	0.999965i	$-0.497322\pi$
$601$	0.412518	0.0168270	0.00841348	+	0.999965i	$0.497322\pi$
$602$	−2.16421	−0.0882066
$603$	−0.762709	−0.0310599
$604$	−11.5254	−0.468963
$605$	13.1715	0.535498
$606$	2.35988	0.0958636
$607$	−41.0113	−1.66460	−0.832300	−	0.554326i	$-0.812976\pi$
$607$	−41.0113	−1.66460	−0.832300	+	0.554326i	$0.812976\pi$
$608$	21.9667	0.890869
$609$	9.03684	0.366191
$610$	−8.22414	−0.332986
$611$	0	0
$612$	0.939001	0.0379569
$613$	−28.8495	−1.16522	−0.582611	−	0.812751i	$-0.697969\pi$
$613$	−28.8495	−1.16522	−0.582611	+	0.812751i	$0.697969\pi$
$614$	13.1263	0.529735
$615$	0.298290	0.0120282
$616$	−2.32975	−0.0938683
$617$	3.30857	0.133198	0.0665990	−	0.997780i	$-0.478785\pi$
$617$	3.30857	0.133198	0.0665990	+	0.997780i	$0.478785\pi$
$618$	3.37734	0.135856
$619$	36.0737	1.44992	0.724962	−	0.688789i	$-0.241857\pi$
$619$	36.0737	1.44992	0.724962	+	0.688789i	$0.241857\pi$
$620$	19.8159	0.795827
$621$	−6.78986	−0.272468
$622$	9.20403	0.369048
$623$	−8.60388	−0.344707
$624$	0	0
$625$	0.772398	0.0308959
$626$	−3.83281	−0.153190
$627$	−4.67324	−0.186631
$628$	−41.3370	−1.64953
$629$	−2.87502	−0.114634
$630$	0.753020	0.0300011
$631$	38.4631	1.53119	0.765596	−	0.643322i	$-0.222444\pi$
$631$	38.4631	1.53119	0.765596	+	0.643322i	$0.222444\pi$
$632$	7.66487	0.304892
$633$	1.36227	0.0541455
$634$	−14.4601	−0.574284
$635$	−6.26742	−0.248715
$636$	−13.5157	−0.535934
$637$	0	0
$638$	5.70245	0.225762
$639$	−4.50365	−0.178162
$640$	15.6552	0.618826
$641$	−4.26098	−0.168299	−0.0841493	−	0.996453i	$-0.526817\pi$
$641$	−4.26098	−0.168299	−0.0841493	+	0.996453i	$0.526817\pi$
$642$	−7.13467	−0.281583
$643$	3.59658	0.141835	0.0709176	−	0.997482i	$-0.477407\pi$
$643$	3.59658	0.141835	0.0709176	+	0.997482i	$0.477407\pi$
$644$	−11.4886	−0.452714
$645$	−5.29159	−0.208356
$646$	−1.26577	−0.0498009
$647$	−44.7144	−1.75790	−0.878952	−	0.476910i	$-0.841757\pi$
$647$	−44.7144	−1.75790	−0.878952	+	0.476910i	$0.841757\pi$
$648$	−2.04892	−0.0804891
$649$	4.43429	0.174061
$650$	0	0
$651$	−8.63102	−0.338276
$652$	−19.5399	−0.765241
$653$	−33.1957	−1.29905	−0.649523	−	0.760342i	$-0.725032\pi$
$653$	−33.1957	−1.29905	−0.649523	+	0.760342i	$0.725032\pi$
$654$	3.79656	0.148457
$655$	4.55496	0.177977
$656$	−0.493959	−0.0192859
$657$	−8.50365	−0.331759
$658$	−4.51573	−0.176041
$659$	47.7469	1.85996	0.929978	−	0.367616i	$-0.119826\pi$
$659$	47.7469	1.85996	0.929978	+	0.367616i	$0.119826\pi$
$660$	−2.61058	−0.101617
$661$	−7.29052	−0.283568	−0.141784	−	0.989898i	$-0.545284\pi$
$661$	−7.29052	−0.283568	−0.141784	+	0.989898i	$0.545284\pi$
$662$	1.94272	0.0755060
$663$	0	0
$664$	−22.6582	−0.879308
$665$	5.57673	0.216256
$666$	2.87502	0.111405
$667$	61.3588	2.37582
$668$	8.16182	0.315790
$669$	10.2862	0.397688
$670$	0.574335	0.0221885
$671$	−12.4185	−0.479410
$672$	−5.34481	−0.206181
$673$	−33.8842	−1.30614	−0.653071	−	0.757297i	$-0.726520\pi$
$673$	−33.8842	−1.30614	−0.653071	+	0.757297i	$0.726520\pi$
$674$	−2.30186	−0.0886645
$675$	−3.15883	−0.121584
$676$	0	0
$677$	−36.2989	−1.39508	−0.697540	−	0.716546i	$-0.745722\pi$
$677$	−36.2989	−1.39508	−0.697540	+	0.716546i	$0.745722\pi$
$678$	10.3394	0.397084
$679$	−14.9487	−0.573678
$680$	−1.54288	−0.0591666
$681$	−5.60819	−0.214906
$682$	−5.44637	−0.208552
$683$	1.13647	0.0434859	0.0217430	−	0.999764i	$-0.493078\pi$
$683$	1.13647	0.0434859	0.0217430	+	0.999764i	$0.493078\pi$
$684$	−6.95407	−0.265895
$685$	−29.1914	−1.11534
$686$	−0.554958	−0.0211884
$687$	1.88040	0.0717415
$688$	8.76271	0.334075
$689$	0	0
$690$	5.11290	0.194645
$691$	35.4601	1.34897	0.674483	−	0.738290i	$-0.264367\pi$
$691$	35.4601	1.34897	0.674483	+	0.738290i	$0.264367\pi$
$692$	36.5911	1.39098
$693$	1.13706	0.0431935
$694$	−6.42327	−0.243824
$695$	10.9806	0.416519
$696$	18.5157	0.701837
$697$	0.121998	0.00462100
$698$	7.22149	0.273337
$699$	−6.38404	−0.241467
$700$	−5.34481	−0.202015
$701$	31.7265	1.19829	0.599146	−	0.800640i	$-0.295507\pi$
$701$	31.7265	1.19829	0.599146	+	0.800640i	$0.295507\pi$
$702$	0	0
$703$	21.2918	0.803037
$704$	1.73722	0.0654739
$705$	−11.0411	−0.415834
$706$	−14.5351	−0.547036
$707$	−4.25236	−0.159926
$708$	6.59850	0.247987
$709$	35.1825	1.32131	0.660654	−	0.750691i	$-0.270279\pi$
$709$	35.1825	1.32131	0.660654	+	0.750691i	$0.270279\pi$
$710$	3.39134	0.127275
$711$	−3.74094	−0.140296
$712$	−17.6286	−0.660661
$713$	−58.6034	−2.19471
$714$	0.307979	0.0115258
$715$	0	0
$716$	−42.9922	−1.60670
$717$	−1.90217	−0.0710377
$718$	−6.14616	−0.229373
$719$	−1.94198	−0.0724238	−0.0362119	−	0.999344i	$-0.511529\pi$
$719$	−1.94198	−0.0724238	−0.0362119	+	0.999344i	$0.511529\pi$
$720$	−3.04892	−0.113626
$721$	−6.08575	−0.226645
$722$	−1.17018	−0.0435495
$723$	−13.2121	−0.491362
$724$	12.9946	0.482941
$725$	28.5459	1.06017
$726$	−5.38703	−0.199931
$727$	8.95838	0.332248	0.166124	−	0.986105i	$-0.446875\pi$
$727$	8.95838	0.332248	0.166124	+	0.986105i	$0.446875\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.40342	0.237001
$731$	−2.16421	−0.0800462
$732$	−18.4795	−0.683021
$733$	−9.11662	−0.336730	−0.168365	−	0.985725i	$-0.553849\pi$
$733$	−9.11662	−0.336730	−0.168365	+	0.985725i	$0.553849\pi$
$734$	−7.42029	−0.273888
$735$	−1.35690	−0.0500499
$736$	−36.2905	−1.33769
$737$	0.867249	0.0319455
$738$	−0.121998	−0.00449080
$739$	28.8334	1.06065	0.530327	−	0.847793i	$-0.322069\pi$
$739$	28.8334	1.06065	0.530327	+	0.847793i	$0.322069\pi$
$740$	11.8941	0.437237
$741$	0	0
$742$	−4.43296	−0.162739
$743$	−50.2010	−1.84170	−0.920849	−	0.389920i	$-0.872503\pi$
$743$	−50.2010	−1.84170	−0.920849	+	0.389920i	$0.872503\pi$
$744$	−17.6843	−0.648336
$745$	4.42221	0.162017
$746$	−20.3840	−0.746313
$747$	11.0586	0.404613
$748$	−1.06770	−0.0390391
$749$	12.8562	0.469756
$750$	6.14377	0.224339
$751$	−8.02954	−0.293002	−0.146501	−	0.989211i	$-0.546801\pi$
$751$	−8.02954	−0.293002	−0.146501	+	0.989211i	$0.546801\pi$
$752$	18.2838	0.666742
$753$	7.54048	0.274790
$754$	0	0
$755$	−9.24267	−0.336375
$756$	1.69202	0.0615382
$757$	46.7502	1.69916	0.849582	−	0.527457i	$-0.176854\pi$
$757$	46.7502	1.69916	0.849582	+	0.527457i	$0.176854\pi$
$758$	−18.4698	−0.670853
$759$	7.72050	0.280236
$760$	11.4263	0.414474
$761$	−6.31336	−0.228859	−0.114429	−	0.993431i	$-0.536504\pi$
$761$	−6.31336	−0.228859	−0.114429	+	0.993431i	$0.536504\pi$
$762$	2.56332	0.0928592
$763$	−6.84117	−0.247667
$764$	−16.0804	−0.581768
$765$	0.753020	0.0272255
$766$	9.78017	0.353372
$767$	0	0
$768$	−3.34721	−0.120782
$769$	−41.8732	−1.50999	−0.754993	−	0.655732i	$-0.772360\pi$
$769$	−41.8732	−1.50999	−0.754993	+	0.655732i	$0.772360\pi$
$770$	−0.856232	−0.0308565
$771$	13.4179	0.483234
$772$	−15.8230	−0.569481
$773$	39.2640	1.41223	0.706113	−	0.708099i	$-0.250447\pi$
$773$	39.2640	1.41223	0.706113	+	0.708099i	$0.250447\pi$
$774$	2.16421	0.0777909
$775$	−27.2640	−0.979350
$776$	−30.6286	−1.09950
$777$	−5.18060	−0.185853
$778$	16.4456	0.589605
$779$	−0.903493	−0.0323710
$780$	0	0
$781$	5.12093	0.183241
$782$	2.09113	0.0747787
$783$	−9.03684	−0.322950
$784$	2.24698	0.0802493
$785$	−33.1497	−1.18316
$786$	−1.86294	−0.0664488
$787$	36.0054	1.28345	0.641727	−	0.766934i	$-0.278218\pi$
$787$	36.0054	1.28345	0.641727	+	0.766934i	$0.278218\pi$
$788$	29.6370	1.05577
$789$	−11.1981	−0.398662
$790$	2.81700	0.100224
$791$	−18.6310	−0.662443
$792$	2.32975	0.0827840
$793$	0	0
$794$	−10.6552	−0.378138
$795$	−10.8388	−0.384412
$796$	29.7616	1.05487
$797$	−18.1511	−0.642944	−0.321472	−	0.946919i	$-0.604178\pi$
$797$	−18.1511	−0.642944	−0.321472	+	0.946919i	$0.604178\pi$
$798$	−2.28083	−0.0807406
$799$	−4.51573	−0.159755
$800$	−16.8834	−0.596918
$801$	8.60388	0.304003
$802$	−6.93661	−0.244940
$803$	9.66919	0.341218
$804$	1.29052	0.0455131
$805$	−9.21313	−0.324720
$806$	0	0
$807$	13.9172	0.489910
$808$	−8.71273	−0.306513
$809$	37.2833	1.31081	0.655406	−	0.755277i	$-0.272497\pi$
$809$	37.2833	1.31081	0.655406	+	0.755277i	$0.272497\pi$
$810$	−0.753020	−0.0264584
$811$	−37.7657	−1.32613	−0.663066	−	0.748561i	$-0.730745\pi$
$811$	−37.7657	−1.32613	−0.663066	+	0.748561i	$0.730745\pi$
$812$	−15.2905	−0.536592
$813$	−1.98254	−0.0695308
$814$	−3.26908	−0.114581
$815$	−15.6698	−0.548888
$816$	−1.24698	−0.0436530
$817$	16.0277	0.560740
$818$	9.31336	0.325634
$819$	0	0
$820$	−0.504713	−0.0176253
$821$	−1.61463	−0.0563509	−0.0281755	−	0.999603i	$-0.508970\pi$
$821$	−1.61463	−0.0563509	−0.0281755	+	0.999603i	$0.508970\pi$
$822$	11.9390	0.416420
$823$	34.1099	1.18900	0.594498	−	0.804097i	$-0.297351\pi$
$823$	34.1099	1.18900	0.594498	+	0.804097i	$0.297351\pi$
$824$	−12.4692	−0.434385
$825$	3.59179	0.125050
$826$	2.16421	0.0753025
$827$	−23.1360	−0.804517	−0.402259	−	0.915526i	$-0.631775\pi$
$827$	−23.1360	−0.804517	−0.402259	+	0.915526i	$0.631775\pi$
$828$	11.4886	0.399256
$829$	0.391339	0.0135918	0.00679588	−	0.999977i	$-0.497837\pi$
$829$	0.391339	0.0135918	0.00679588	+	0.999977i	$0.497837\pi$
$830$	−8.32736	−0.289047
$831$	9.79954	0.339942
$832$	0	0
$833$	−0.554958	−0.0192282
$834$	−4.49098	−0.155510
$835$	6.54527	0.226508
$836$	7.90721	0.273477
$837$	8.63102	0.298332
$838$	−7.97152	−0.275372
$839$	24.5381	0.847149	0.423574	−	0.905861i	$-0.360775\pi$
$839$	24.5381	0.847149	0.423574	+	0.905861i	$0.360775\pi$
$840$	−2.78017	−0.0959249
$841$	52.6644	1.81601
$842$	12.5157	0.431321
$843$	25.7603	0.887232
$844$	−2.30499	−0.0793412
$845$	0	0
$846$	4.51573	0.155254
$847$	9.70709	0.333539
$848$	17.9487	0.616361
$849$	−0.0489173	−0.00167884
$850$	0.972853	0.0333686
$851$	−35.1756	−1.20580
$852$	7.62027	0.261066
$853$	19.6786	0.673783	0.336891	−	0.941544i	$-0.390624\pi$
$853$	19.6786	0.673783	0.336891	+	0.941544i	$0.390624\pi$
$854$	−6.06100	−0.207403
$855$	−5.57673	−0.190720
$856$	26.3414	0.900329
$857$	−22.5429	−0.770050	−0.385025	−	0.922906i	$-0.625807\pi$
$857$	−22.5429	−0.770050	−0.385025	+	0.922906i	$0.625807\pi$
$858$	0	0
$859$	−23.8931	−0.815221	−0.407610	−	0.913156i	$-0.633638\pi$
$859$	−23.8931	−0.815221	−0.407610	+	0.913156i	$0.633638\pi$
$860$	8.95348	0.305311
$861$	0.219833	0.00749187
$862$	−2.49157	−0.0848631
$863$	−15.5821	−0.530421	−0.265211	−	0.964191i	$-0.585441\pi$
$863$	−15.5821	−0.530421	−0.265211	+	0.964191i	$0.585441\pi$
$864$	5.34481	0.181834
$865$	29.3437	0.997717
$866$	10.7447	0.365118
$867$	−16.6920	−0.566891
$868$	14.6039	0.495688
$869$	4.25368	0.144296
$870$	6.80492	0.230708
$871$	0	0
$872$	−14.0170	−0.474675
$873$	14.9487	0.505936
$874$	−15.4865	−0.523839
$875$	−11.0707	−0.374258
$876$	14.3884	0.486137
$877$	−17.6770	−0.596908	−0.298454	−	0.954424i	$-0.596471\pi$
$877$	−17.6770	−0.596908	−0.298454	+	0.954424i	$0.596471\pi$
$878$	15.1430	0.511053
$879$	−21.3220	−0.719173
$880$	3.46681	0.116866
$881$	45.5368	1.53417	0.767086	−	0.641544i	$-0.221706\pi$
$881$	45.5368	1.53417	0.767086	+	0.641544i	$0.221706\pi$
$882$	0.554958	0.0186864
$883$	7.13361	0.240065	0.120032	−	0.992770i	$-0.461700\pi$
$883$	7.13361	0.240065	0.120032	+	0.992770i	$0.461700\pi$
$884$	0	0
$885$	5.29159	0.177875
$886$	−9.00803	−0.302631
$887$	−42.9181	−1.44105	−0.720524	−	0.693430i	$-0.756099\pi$
$887$	−42.9181	−1.44105	−0.720524	+	0.693430i	$0.756099\pi$
$888$	−10.6146	−0.356204
$889$	−4.61894	−0.154914
$890$	−6.47889	−0.217173
$891$	−1.13706	−0.0380931
$892$	−17.4045	−0.582745
$893$	33.4426	1.11912
$894$	−1.80864	−0.0604901
$895$	−34.4771	−1.15244
$896$	11.5375	0.385441
$897$	0	0
$898$	13.4561	0.449034
$899$	−77.9971	−2.60135
$900$	5.34481	0.178160
$901$	−4.43296	−0.147683
$902$	0.138719	0.00461885
$903$	−3.89977	−0.129776
$904$	−38.1734	−1.26963
$905$	10.4209	0.346402
$906$	3.78017	0.125588
$907$	34.9259	1.15969	0.579847	−	0.814725i	$-0.303112\pi$
$907$	34.9259	1.15969	0.579847	+	0.814725i	$0.303112\pi$
$908$	9.48917	0.314909
$909$	4.25236	0.141042
$910$	0	0
$911$	56.0810	1.85805	0.929023	−	0.370023i	$-0.120650\pi$
$911$	56.0810	1.85805	0.929023	+	0.370023i	$0.120650\pi$
$912$	9.23490	0.305798
$913$	−12.5743	−0.416150
$914$	17.4758	0.578047
$915$	−14.8194	−0.489914
$916$	−3.18167	−0.105125
$917$	3.35690	0.110854
$918$	−0.307979	−0.0101648
$919$	−31.6082	−1.04266	−0.521329	−	0.853356i	$-0.674564\pi$
$919$	−31.6082	−1.04266	−0.521329	+	0.853356i	$0.674564\pi$
$920$	−18.8769	−0.622354
$921$	23.6528	0.779386
$922$	−22.6738	−0.746723
$923$	0	0
$924$	−1.92394	−0.0632928
$925$	−16.3647	−0.538067
$926$	−21.6956	−0.712962
$927$	6.08575	0.199882
$928$	−48.3002	−1.58553
$929$	−24.5230	−0.804574	−0.402287	−	0.915514i	$-0.631785\pi$
$929$	−24.5230	−0.804574	−0.402287	+	0.915514i	$0.631785\pi$
$930$	−6.49934	−0.213122
$931$	4.10992	0.134697
$932$	10.8019	0.353829
$933$	16.5851	0.542971
$934$	5.21552	0.170657
$935$	−0.856232	−0.0280018
$936$	0	0
$937$	−11.1943	−0.365703	−0.182852	−	0.983141i	$-0.558533\pi$
$937$	−11.1943	−0.365703	−0.182852	+	0.983141i	$0.558533\pi$
$938$	0.423272	0.0138203
$939$	−6.90648	−0.225384
$940$	18.6819	0.609335
$941$	−9.92931	−0.323686	−0.161843	−	0.986816i	$-0.551744\pi$
$941$	−9.92931	−0.323686	−0.161843	+	0.986816i	$0.551744\pi$
$942$	13.5579	0.441742
$943$	1.49263	0.0486068
$944$	−8.76271	−0.285202
$945$	1.35690	0.0441398
$946$	−2.46084	−0.0800090
$947$	44.2602	1.43826	0.719132	−	0.694873i	$-0.244540\pi$
$947$	44.2602	1.43826	0.719132	+	0.694873i	$0.244540\pi$
$948$	6.32975	0.205581
$949$	0	0
$950$	−7.20477	−0.233754
$951$	−26.0562	−0.844931
$952$	−1.13706	−0.0368524
$953$	31.1312	1.00844	0.504219	−	0.863576i	$-0.331780\pi$
$953$	31.1312	1.00844	0.504219	+	0.863576i	$0.331780\pi$
$954$	4.43296	0.143522
$955$	−12.8955	−0.417287
$956$	3.21850	0.104094
$957$	10.2755	0.332158
$958$	1.12870	0.0364667
$959$	−21.5133	−0.694702
$960$	2.07308	0.0669084
$961$	43.4946	1.40305
$962$	0	0
$963$	−12.8562	−0.414286
$964$	22.3551	0.720009
$965$	−12.6890	−0.408475
$966$	3.76809	0.121236
$967$	15.9745	0.513706	0.256853	−	0.966451i	$-0.417314\pi$
$967$	15.9745	0.513706	0.256853	+	0.966451i	$0.417314\pi$
$968$	19.8890	0.639257
$969$	−2.28083	−0.0732709
$970$	−11.2567	−0.361430
$971$	−37.8525	−1.21474	−0.607372	−	0.794417i	$-0.707776\pi$
$971$	−37.8525	−1.21474	−0.607372	+	0.794417i	$0.707776\pi$
$972$	−1.69202	−0.0542716
$973$	8.09246	0.259432
$974$	16.8086	0.538584
$975$	0	0
$976$	24.5405	0.785522
$977$	1.92394	0.0615522	0.0307761	−	0.999526i	$-0.490202\pi$
$977$	1.92394	0.0615522	0.0307761	+	0.999526i	$0.490202\pi$
$978$	6.40880	0.204931
$979$	−9.78315	−0.312671
$980$	2.29590	0.0733397
$981$	6.84117	0.218422
$982$	−16.1987	−0.516920
$983$	−47.7922	−1.52434	−0.762168	−	0.647379i	$-0.775865\pi$
$983$	−47.7922	−1.52434	−0.762168	+	0.647379i	$0.775865\pi$
$984$	0.450419	0.0143588
$985$	23.7670	0.757280
$986$	2.78315	0.0886336
$987$	−8.13706	−0.259006
$988$	0	0
$989$	−26.4789	−0.841980
$990$	0.856232	0.0272128
$991$	44.0683	1.39988	0.699938	−	0.714204i	$-0.253211\pi$
$991$	44.0683	1.39988	0.699938	+	0.714204i	$0.253211\pi$
$992$	46.1312	1.46467
$993$	3.50066	0.111090
$994$	2.49934	0.0792741
$995$	23.8670	0.756634
$996$	−18.7114	−0.592893
$997$	48.2344	1.52760	0.763800	−	0.645453i	$-0.223331\pi$
$997$	48.2344	1.52760	0.763800	+	0.645453i	$0.223331\pi$
$998$	−0.693349	−0.0219476
$999$	5.18060	0.163907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.u.1.2		3
13.4	even	6		273.2.k.c.211.2	yes	6
13.10	even	6		273.2.k.c.22.2	✓	6
13.12	even	2		3549.2.a.i.1.2		3
39.17	odd	6		819.2.o.e.757.2		6
39.23	odd	6		819.2.o.e.568.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.2	✓	6	13.10	even	6
273.2.k.c.211.2	yes	6	13.4	even	6
819.2.o.e.568.2		6	39.23	odd	6
819.2.o.e.757.2		6	39.17	odd	6
3549.2.a.i.1.2		3	13.12	even	2
3549.2.a.u.1.2		3	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)

\(f(q)\)	\(=\)	\(q+0.554958 q^{2} +1.00000 q^{3} -1.69202 q^{4} -1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} -2.04892 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.554958 q^{2} +1.00000 q^{3} -1.69202 q^{4} -1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} -2.04892 q^{8} +1.00000 q^{9} -0.753020 q^{10} -1.13706 q^{11} -1.69202 q^{12} -0.554958 q^{14} -1.35690 q^{15} +2.24698 q^{16} -0.554958 q^{17} +0.554958 q^{18} +4.10992 q^{19} +2.29590 q^{20} -1.00000 q^{21} -0.631023 q^{22} -6.78986 q^{23} -2.04892 q^{24} -3.15883 q^{25} +1.00000 q^{27} +1.69202 q^{28} -9.03684 q^{29} -0.753020 q^{30} +8.63102 q^{31} +5.34481 q^{32} -1.13706 q^{33} -0.307979 q^{34} +1.35690 q^{35} -1.69202 q^{36} +5.18060 q^{37} +2.28083 q^{38} +2.78017 q^{40} -0.219833 q^{41} -0.554958 q^{42} +3.89977 q^{43} +1.92394 q^{44} -1.35690 q^{45} -3.76809 q^{46} +8.13706 q^{47} +2.24698 q^{48} +1.00000 q^{49} -1.75302 q^{50} -0.554958 q^{51} +7.98792 q^{53} +0.554958 q^{54} +1.54288 q^{55} +2.04892 q^{56} +4.10992 q^{57} -5.01507 q^{58} -3.89977 q^{59} +2.29590 q^{60} +10.9215 q^{61} +4.78986 q^{62} -1.00000 q^{63} -1.52781 q^{64} -0.631023 q^{66} -0.762709 q^{67} +0.939001 q^{68} -6.78986 q^{69} +0.753020 q^{70} -4.50365 q^{71} -2.04892 q^{72} -8.50365 q^{73} +2.87502 q^{74} -3.15883 q^{75} -6.95407 q^{76} +1.13706 q^{77} -3.74094 q^{79} -3.04892 q^{80} +1.00000 q^{81} -0.121998 q^{82} +11.0586 q^{83} +1.69202 q^{84} +0.753020 q^{85} +2.16421 q^{86} -9.03684 q^{87} +2.32975 q^{88} +8.60388 q^{89} -0.753020 q^{90} +11.4886 q^{92} +8.63102 q^{93} +4.51573 q^{94} -5.57673 q^{95} +5.34481 q^{96} +14.9487 q^{97} +0.554958 q^{98} -1.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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