LMFDB - Embedded newform 1617.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.3676752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 8x^{3} + 14x^{2} + 11x - 10 $ x^5 - 2x^4 - 8x^3 + 14x^2 + 11x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.614936$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.614936 q^{2} -1.00000 q^{3} -1.62185 q^{4} +1.49597 q^{5} -0.614936 q^{6} -2.22721 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.614936 q^{2} -1.00000 q^{3} -1.62185 q^{4} +1.49597 q^{5} -0.614936 q^{6} -2.22721 q^{8} +1.00000 q^{9} +0.919926 q^{10} +1.00000 q^{11} +1.62185 q^{12} -1.27568 q^{13} -1.49597 q^{15} +1.87412 q^{16} +0.614936 q^{17} +0.614936 q^{18} -2.66075 q^{19} -2.42625 q^{20} +0.614936 q^{22} +1.87412 q^{23} +2.22721 q^{24} -2.76207 q^{25} -0.784462 q^{26} -1.00000 q^{27} +8.44902 q^{29} -0.919926 q^{30} +4.62185 q^{31} +5.60688 q^{32} -1.00000 q^{33} +0.378146 q^{34} -1.62185 q^{36} +0.274157 q^{37} -1.63619 q^{38} +1.27568 q^{39} -3.33184 q^{40} -4.91993 q^{41} +9.42511 q^{43} -1.62185 q^{44} +1.49597 q^{45} +1.15246 q^{46} -3.16211 q^{47} -1.87412 q^{48} -1.69850 q^{50} -0.614936 q^{51} +2.06897 q^{52} +6.18832 q^{53} -0.614936 q^{54} +1.49597 q^{55} +2.66075 q^{57} +5.19561 q^{58} +1.87412 q^{59} +2.42625 q^{60} -8.52643 q^{61} +2.84214 q^{62} -0.300364 q^{64} -1.90838 q^{65} -0.614936 q^{66} +5.06243 q^{67} -0.997336 q^{68} -1.87412 q^{69} +16.0954 q^{71} -2.22721 q^{72} +8.75732 q^{73} +0.168589 q^{74} +2.76207 q^{75} +4.31534 q^{76} +0.784462 q^{78} +9.44966 q^{79} +2.80363 q^{80} +1.00000 q^{81} -3.02544 q^{82} +9.00578 q^{83} +0.919926 q^{85} +5.79584 q^{86} -8.44902 q^{87} -2.22721 q^{88} +10.6762 q^{89} +0.919926 q^{90} -3.03954 q^{92} -4.62185 q^{93} -1.94450 q^{94} -3.98040 q^{95} -5.60688 q^{96} -17.6881 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 2 q^{10} + 5 q^{11} - 10 q^{12} + 5 q^{13} + 4 q^{15} + 16 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 8 q^{20} + 2 q^{22} + 16 q^{23} - 6 q^{24} + 7 q^{25} - 10 q^{26} - 5 q^{27} - 2 q^{30} + 5 q^{31} + 4 q^{32} - 5 q^{33} + 20 q^{34} + 10 q^{36} + 15 q^{37} + 6 q^{38} - 5 q^{39} - 6 q^{40} - 22 q^{41} + 3 q^{43} + 10 q^{44} - 4 q^{45} + 16 q^{46} - 2 q^{47} - 16 q^{48} + 34 q^{50} - 2 q^{51} + 40 q^{52} + 6 q^{53} - 2 q^{54} - 4 q^{55} + 3 q^{57} + 12 q^{58} + 16 q^{59} + 8 q^{60} + 12 q^{61} - 4 q^{62} - 4 q^{64} - 28 q^{65} - 2 q^{66} + 7 q^{67} + 10 q^{68} - 16 q^{69} + 24 q^{71} + 6 q^{72} + 17 q^{73} - 36 q^{74} - 7 q^{75} + 30 q^{76} + 10 q^{78} + 7 q^{79} + 16 q^{80} + 5 q^{81} + 8 q^{82} - 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 68 q^{92} - 5 q^{93} + 82 q^{94} - 18 q^{95} - 4 q^{96} - 14 q^{97} + 5 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 2 * q^10 + 5 * q^11 - 10 * q^12 + 5 * q^13 + 4 * q^15 + 16 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 8 * q^20 + 2 * q^22 + 16 * q^23 - 6 * q^24 + 7 * q^25 - 10 * q^26 - 5 * q^27 - 2 * q^30 + 5 * q^31 + 4 * q^32 - 5 * q^33 + 20 * q^34 + 10 * q^36 + 15 * q^37 + 6 * q^38 - 5 * q^39 - 6 * q^40 - 22 * q^41 + 3 * q^43 + 10 * q^44 - 4 * q^45 + 16 * q^46 - 2 * q^47 - 16 * q^48 + 34 * q^50 - 2 * q^51 + 40 * q^52 + 6 * q^53 - 2 * q^54 - 4 * q^55 + 3 * q^57 + 12 * q^58 + 16 * q^59 + 8 * q^60 + 12 * q^61 - 4 * q^62 - 4 * q^64 - 28 * q^65 - 2 * q^66 + 7 * q^67 + 10 * q^68 - 16 * q^69 + 24 * q^71 + 6 * q^72 + 17 * q^73 - 36 * q^74 - 7 * q^75 + 30 * q^76 + 10 * q^78 + 7 * q^79 + 16 * q^80 + 5 * q^81 + 8 * q^82 - 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 68 * q^92 - 5 * q^93 + 82 * q^94 - 18 * q^95 - 4 * q^96 - 14 * q^97 + 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 $

$2$	0.614936	0.434825	0.217413	−	0.976080i	$-0.430238\pi$
$2$	0.614936	0.434825	0.217413	+	0.976080i	$0.430238\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.62185	−0.810927
$5$	1.49597	0.669019	0.334509	−	0.942392i	$-0.391429\pi$
$5$	1.49597	0.669019	0.334509	+	0.942392i	$0.391429\pi$
$6$	−0.614936	−0.251047
$7$	0	0
$7$	0	0
$8$	−2.22721	−0.787437
$9$	1.00000	0.333333
$10$	0.919926	0.290906
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.62185	0.468189
$13$	−1.27568	−0.353810	−0.176905	−	0.984228i	$-0.556609\pi$
$13$	−1.27568	−0.353810	−0.176905	+	0.984228i	$0.556609\pi$
$14$	0	0
$15$	−1.49597	−0.386258
$16$	1.87412	0.468529
$17$	0.614936	0.149144	0.0745719	−	0.997216i	$-0.476241\pi$
$17$	0.614936	0.149144	0.0745719	+	0.997216i	$0.476241\pi$
$18$	0.614936	0.144942
$19$	−2.66075	−0.610417	−0.305208	−	0.952286i	$-0.598726\pi$
$19$	−2.66075	−0.610417	−0.305208	+	0.952286i	$0.598726\pi$
$20$	−2.42625	−0.542525
$21$	0	0
$22$	0.614936	0.131105
$23$	1.87412	0.390780	0.195390	−	0.980726i	$-0.437403\pi$
$23$	1.87412	0.390780	0.195390	+	0.980726i	$0.437403\pi$
$24$	2.22721	0.454627
$25$	−2.76207	−0.552414
$26$	−0.784462	−0.153846
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.44902	1.56894	0.784472	−	0.620164i	$-0.212934\pi$
$29$	8.44902	1.56894	0.784472	+	0.620164i	$0.212934\pi$
$30$	−0.919926	−0.167955
$31$	4.62185	0.830109	0.415055	−	0.909796i	$-0.363762\pi$
$31$	4.62185	0.830109	0.415055	+	0.909796i	$0.363762\pi$
$32$	5.60688	0.991165
$33$	−1.00000	−0.174078
$34$	0.378146	0.0648515
$35$	0	0
$36$	−1.62185	−0.270309
$37$	0.274157	0.0450711	0.0225356	−	0.999746i	$-0.492826\pi$
$37$	0.274157	0.0450711	0.0225356	+	0.999746i	$0.492826\pi$
$38$	−1.63619	−0.265425
$39$	1.27568	0.204272
$40$	−3.33184	−0.526810
$41$	−4.91993	−0.768363	−0.384182	−	0.923258i	$-0.625516\pi$
$41$	−4.91993	−0.768363	−0.384182	+	0.923258i	$0.625516\pi$
$42$	0	0
$43$	9.42511	1.43732	0.718658	−	0.695364i	$-0.244757\pi$
$43$	9.42511	1.43732	0.718658	+	0.695364i	$0.244757\pi$
$44$	−1.62185	−0.244504
$45$	1.49597	0.223006
$46$	1.15246	0.169921
$47$	−3.16211	−0.461241	−0.230621	−	0.973044i	$-0.574076\pi$
$47$	−3.16211	−0.461241	−0.230621	+	0.973044i	$0.574076\pi$
$48$	−1.87412	−0.270506
$49$	0	0
$50$	−1.69850	−0.240204
$51$	−0.614936	−0.0861083
$52$	2.06897	0.286914
$53$	6.18832	0.850031	0.425015	−	0.905186i	$-0.360269\pi$
$53$	6.18832	0.850031	0.425015	+	0.905186i	$0.360269\pi$
$54$	−0.614936	−0.0836822
$55$	1.49597	0.201717
$56$	0	0
$57$	2.66075	0.352424
$58$	5.19561	0.682217
$59$	1.87412	0.243989	0.121995	−	0.992531i	$-0.461071\pi$
$59$	1.87412	0.243989	0.121995	+	0.992531i	$0.461071\pi$
$60$	2.42625	0.313227
$61$	−8.52643	−1.09170	−0.545849	−	0.837884i	$-0.683793\pi$
$61$	−8.52643	−1.09170	−0.545849	+	0.837884i	$0.683793\pi$
$62$	2.84214	0.360953
$63$	0	0
$64$	−0.300364	−0.0375455
$65$	−1.90838	−0.236706
$66$	−0.614936	−0.0756934
$67$	5.06243	0.618475	0.309237	−	0.950985i	$-0.399926\pi$
$67$	5.06243	0.618475	0.309237	+	0.950985i	$0.399926\pi$
$68$	−0.997336	−0.120945
$69$	−1.87412	−0.225617
$70$	0	0
$71$	16.0954	1.91018	0.955088	−	0.296322i	$-0.0957600\pi$
$71$	16.0954	1.91018	0.955088	+	0.296322i	$0.0957600\pi$
$72$	−2.22721	−0.262479
$73$	8.75732	1.02497	0.512483	−	0.858697i	$-0.328726\pi$
$73$	8.75732	1.02497	0.512483	+	0.858697i	$0.328726\pi$
$74$	0.168589	0.0195981
$75$	2.76207	0.318936
$76$	4.31534	0.495003
$77$	0	0
$78$	0.784462	0.0888228
$79$	9.44966	1.06317	0.531585	−	0.847005i	$-0.321597\pi$
$79$	9.44966	1.06317	0.531585	+	0.847005i	$0.321597\pi$
$80$	2.80363	0.313455
$81$	1.00000	0.111111
$82$	−3.02544	−0.334104
$83$	9.00578	0.988513	0.494256	−	0.869316i	$-0.335440\pi$
$83$	9.00578	0.988513	0.494256	+	0.869316i	$0.335440\pi$
$84$	0	0
$85$	0.919926	0.0997800
$86$	5.79584	0.624981
$87$	−8.44902	−0.905830
$88$	−2.22721	−0.237421
$89$	10.6762	1.13168	0.565839	−	0.824516i	$-0.308552\pi$
$89$	10.6762	1.13168	0.565839	+	0.824516i	$0.308552\pi$
$90$	0.919926	0.0969688
$91$	0	0
$92$	−3.03954	−0.316894
$93$	−4.62185	−0.479264
$94$	−1.94450	−0.200559
$95$	−3.98040	−0.408380
$96$	−5.60688	−0.572250
$97$	−17.6881	−1.79595	−0.897977	−	0.440042i	$-0.854964\pi$
$97$	−17.6881	−1.79595	−0.897977	+	0.440042i	$0.854964\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	4.47967	0.447967
$101$	4.70079	0.467746	0.233873	−	0.972267i	$-0.424860\pi$
$101$	4.70079	0.467746	0.233873	+	0.972267i	$0.424860\pi$
$102$	−0.378146	−0.0374421
$103$	17.5642	1.73065	0.865325	−	0.501211i	$-0.167112\pi$
$103$	17.5642	1.73065	0.865325	+	0.501211i	$0.167112\pi$
$104$	2.84121	0.278603
$105$	0	0
$106$	3.80542	0.369615
$107$	11.8341	1.14404	0.572022	−	0.820238i	$-0.306159\pi$
$107$	11.8341	1.14404	0.572022	+	0.820238i	$0.306159\pi$
$108$	1.62185	0.156063
$109$	−1.02392	−0.0980733	−0.0490367	−	0.998797i	$-0.515615\pi$
$109$	−1.02392	−0.0980733	−0.0490367	+	0.998797i	$0.515615\pi$
$110$	0.919926	0.0877115
$111$	−0.274157	−0.0260218
$112$	0	0
$113$	6.28526	0.591268	0.295634	−	0.955301i	$-0.404469\pi$
$113$	6.28526	0.591268	0.295634	+	0.955301i	$0.404469\pi$
$114$	1.63619	0.153243
$115$	2.80363	0.261439
$116$	−13.7031	−1.27230
$117$	−1.27568	−0.117937
$118$	1.15246	0.106093
$119$	0	0
$120$	3.33184	0.304154
$121$	1.00000	0.0909091
$122$	−5.24321	−0.474698
$123$	4.91993	0.443615
$124$	−7.49597	−0.673158
$125$	−11.6118	−1.03859
$126$	0	0
$127$	−19.7328	−1.75100	−0.875500	−	0.483218i	$-0.839468\pi$
$127$	−19.7328	−1.75100	−0.875500	+	0.483218i	$0.839468\pi$
$128$	−11.3985	−1.00749
$129$	−9.42511	−0.829834
$130$	−1.17353	−0.102926
$131$	−5.31572	−0.464437	−0.232218	−	0.972664i	$-0.574598\pi$
$131$	−5.31572	−0.464437	−0.232218	+	0.972664i	$0.574598\pi$
$132$	1.62185	0.141164
$133$	0	0
$134$	3.11307	0.268929
$135$	−1.49597	−0.128753
$136$	−1.36959	−0.117441
$137$	2.38817	0.204035	0.102017	−	0.994783i	$-0.467470\pi$
$137$	2.38817	0.204035	0.102017	+	0.994783i	$0.467470\pi$
$138$	−1.15246	−0.0981041
$139$	12.4948	1.05980	0.529899	−	0.848061i	$-0.322230\pi$
$139$	12.4948	1.05980	0.529899	+	0.848061i	$0.322230\pi$
$140$	0	0
$141$	3.16211	0.266298
$142$	9.89766	0.830593
$143$	−1.27568	−0.106678
$144$	1.87412	0.156176
$145$	12.6395	1.04965
$146$	5.38519	0.445681
$147$	0	0
$148$	−0.444643	−0.0365494
$149$	−6.70655	−0.549422	−0.274711	−	0.961527i	$-0.588582\pi$
$149$	−6.70655	−0.549422	−0.274711	+	0.961527i	$0.588582\pi$
$150$	1.69850	0.138682
$151$	−10.1690	−0.827544	−0.413772	−	0.910381i	$-0.635789\pi$
$151$	−10.1690	−0.827544	−0.413772	+	0.910381i	$0.635789\pi$
$152$	5.92603	0.480665
$153$	0.614936	0.0497146
$154$	0	0
$155$	6.91416	0.555359
$156$	−2.06897	−0.165650
$157$	21.8764	1.74593	0.872964	−	0.487784i	$-0.162195\pi$
$157$	21.8764	1.74593	0.872964	+	0.487784i	$0.162195\pi$
$158$	5.81094	0.462293
$159$	−6.18832	−0.490765
$160$	8.38773	0.663108
$161$	0	0
$162$	0.614936	0.0483139
$163$	17.2719	1.35284	0.676419	−	0.736517i	$-0.263531\pi$
$163$	17.2719	1.35284	0.676419	+	0.736517i	$0.263531\pi$
$164$	7.97940	0.623087
$165$	−1.49597	−0.116461
$166$	5.53798	0.429830
$167$	−13.4655	−1.04199	−0.520997	−	0.853559i	$-0.674440\pi$
$167$	−13.4655	−1.04199	−0.520997	+	0.853559i	$0.674440\pi$
$168$	0	0
$169$	−11.3726	−0.874818
$170$	0.565696	0.0433869
$171$	−2.66075	−0.203472
$172$	−15.2861	−1.16556
$173$	−18.0559	−1.37276	−0.686382	−	0.727241i	$-0.740802\pi$
$173$	−18.0559	−1.37276	−0.686382	+	0.727241i	$0.740802\pi$
$174$	−5.19561	−0.393878
$175$	0	0
$176$	1.87412	0.141267
$177$	−1.87412	−0.140867
$178$	6.56520	0.492082
$179$	−17.4693	−1.30572	−0.652860	−	0.757479i	$-0.726431\pi$
$179$	−17.4693	−1.30572	−0.652860	+	0.757479i	$0.726431\pi$
$180$	−2.42625	−0.180842
$181$	−2.68530	−0.199597	−0.0997985	−	0.995008i	$-0.531820\pi$
$181$	−2.68530	−0.199597	−0.0997985	+	0.995008i	$0.531820\pi$
$182$	0	0
$183$	8.52643	0.630292
$184$	−4.17405	−0.307715
$185$	0.410131	0.0301534
$186$	−2.84214	−0.208396
$187$	0.614936	0.0449686
$188$	5.12848	0.374033
$189$	0	0
$190$	−2.44769	−0.177574
$191$	−18.8394	−1.36317	−0.681586	−	0.731738i	$-0.738710\pi$
$191$	−18.8394	−1.36317	−0.681586	+	0.731738i	$0.738710\pi$
$192$	0.300364	0.0216769
$193$	14.2427	1.02521	0.512606	−	0.858624i	$-0.328680\pi$
$193$	14.2427	1.02521	0.512606	+	0.858624i	$0.328680\pi$
$194$	−10.8771	−0.780927
$195$	1.90838	0.136662
$196$	0	0
$197$	−13.5291	−0.963908	−0.481954	−	0.876196i	$-0.660073\pi$
$197$	−13.5291	−0.963908	−0.481954	+	0.876196i	$0.660073\pi$
$198$	0.614936	0.0437016
$199$	14.2356	1.00914	0.504569	−	0.863371i	$-0.331651\pi$
$199$	14.2356	1.00914	0.504569	+	0.863371i	$0.331651\pi$
$200$	6.15171	0.434991
$201$	−5.06243	−0.357077
$202$	2.89068	0.203388
$203$	0	0
$204$	0.997336	0.0698275
$205$	−7.36007	−0.514049
$206$	10.8008	0.752531
$207$	1.87412	0.130260
$208$	−2.39078	−0.165770
$209$	−2.66075	−0.184048
$210$	0	0
$211$	1.50124	0.103350	0.0516748	−	0.998664i	$-0.483544\pi$
$211$	1.50124	0.103350	0.0516748	+	0.998664i	$0.483544\pi$
$212$	−10.0365	−0.689313
$213$	−16.0954	−1.10284
$214$	7.27720	0.497459
$215$	14.0997	0.961591
$216$	2.22721	0.151542
$217$	0	0
$218$	−0.629642	−0.0426448
$219$	−8.75732	−0.591765
$220$	−2.42625	−0.163578
$221$	−0.784462	−0.0527686
$222$	−0.168589	−0.0113150
$223$	7.22937	0.484115	0.242057	−	0.970262i	$-0.422178\pi$
$223$	7.22937	0.484115	0.242057	+	0.970262i	$0.422178\pi$
$224$	0	0
$225$	−2.76207	−0.184138
$226$	3.86503	0.257098
$227$	−0.800079	−0.0531031	−0.0265516	−	0.999647i	$-0.508453\pi$
$227$	−0.800079	−0.0531031	−0.0265516	+	0.999647i	$0.508453\pi$
$228$	−4.31534	−0.285790
$229$	−8.54229	−0.564490	−0.282245	−	0.959342i	$-0.591079\pi$
$229$	−8.54229	−0.564490	−0.282245	+	0.959342i	$0.591079\pi$
$230$	1.72405	0.113680
$231$	0	0
$232$	−18.8177	−1.23544
$233$	1.83904	0.120480	0.0602398	−	0.998184i	$-0.480813\pi$
$233$	1.83904	0.120480	0.0602398	+	0.998184i	$0.480813\pi$
$234$	−0.784462	−0.0512819
$235$	−4.73043	−0.308579
$236$	−3.03954	−0.197857
$237$	−9.44966	−0.613822
$238$	0	0
$239$	−8.71500	−0.563726	−0.281863	−	0.959455i	$-0.590952\pi$
$239$	−8.71500	−0.563726	−0.281863	+	0.959455i	$0.590952\pi$
$240$	−2.80363	−0.180973
$241$	1.08051	0.0696019	0.0348010	−	0.999394i	$-0.488920\pi$
$241$	1.08051	0.0696019	0.0348010	+	0.999394i	$0.488920\pi$
$242$	0.614936	0.0395296
$243$	−1.00000	−0.0641500
$244$	13.8286	0.885287
$245$	0	0
$246$	3.02544	0.192895
$247$	3.39426	0.215972
$248$	−10.2938	−0.653659
$249$	−9.00578	−0.570718
$250$	−7.14053	−0.451607
$251$	−8.63296	−0.544908	−0.272454	−	0.962169i	$-0.587835\pi$
$251$	−8.63296	−0.544908	−0.272454	+	0.962169i	$0.587835\pi$
$252$	0	0
$253$	1.87412	0.117825
$254$	−12.1344	−0.761379
$255$	−0.919926	−0.0576080
$256$	−6.40860	−0.400537
$257$	14.7115	0.917679	0.458839	−	0.888519i	$-0.348265\pi$
$257$	14.7115	0.917679	0.458839	+	0.888519i	$0.348265\pi$
$258$	−5.79584	−0.360833
$259$	0	0
$260$	3.09512	0.191951
$261$	8.44902	0.522981
$262$	−3.26883	−0.201949
$263$	30.9280	1.90710	0.953551	−	0.301232i	$-0.0973978\pi$
$263$	30.9280	1.90710	0.953551	+	0.301232i	$0.0973978\pi$
$264$	2.22721	0.137075
$265$	9.25754	0.568686
$266$	0	0
$267$	−10.6762	−0.653375
$268$	−8.21053	−0.501538
$269$	−31.1163	−1.89720	−0.948598	−	0.316485i	$-0.897497\pi$
$269$	−31.1163	−1.89720	−0.948598	+	0.316485i	$0.897497\pi$
$270$	−0.919926	−0.0559849
$271$	2.76969	0.168247	0.0841233	−	0.996455i	$-0.473191\pi$
$271$	2.76969	0.168247	0.0841233	+	0.996455i	$0.473191\pi$
$272$	1.15246	0.0698783
$273$	0	0
$274$	1.46857	0.0887195
$275$	−2.76207	−0.166559
$276$	3.03954	0.182959
$277$	19.3029	1.15980	0.579900	−	0.814688i	$-0.303092\pi$
$277$	19.3029	1.15980	0.579900	+	0.814688i	$0.303092\pi$
$278$	7.68352	0.460827
$279$	4.62185	0.276703
$280$	0	0
$281$	−7.96061	−0.474890	−0.237445	−	0.971401i	$-0.576310\pi$
$281$	−7.96061	−0.474890	−0.237445	+	0.971401i	$0.576310\pi$
$282$	1.94450	0.115793
$283$	−8.55797	−0.508718	−0.254359	−	0.967110i	$-0.581865\pi$
$283$	−8.55797	−0.508718	−0.254359	+	0.967110i	$0.581865\pi$
$284$	−26.1044	−1.54901
$285$	3.98040	0.235778
$286$	−0.784462	−0.0463862
$287$	0	0
$288$	5.60688	0.330388
$289$	−16.6219	−0.977756
$290$	7.77248	0.456416
$291$	17.6881	1.03689
$292$	−14.2031	−0.831173
$293$	−28.2280	−1.64910	−0.824548	−	0.565792i	$-0.808571\pi$
$293$	−28.2280	−1.64910	−0.824548	+	0.565792i	$0.808571\pi$
$294$	0	0
$295$	2.80363	0.163233
$296$	−0.610605	−0.0354907
$297$	−1.00000	−0.0580259
$298$	−4.12410	−0.238903
$299$	−2.39078	−0.138262
$300$	−4.47967	−0.258634
$301$	0	0
$302$	−6.25330	−0.359837
$303$	−4.70079	−0.270053
$304$	−4.98655	−0.285998
$305$	−12.7553	−0.730366
$306$	0.378146	0.0216172
$307$	8.29757	0.473568	0.236784	−	0.971562i	$-0.423907\pi$
$307$	8.29757	0.473568	0.236784	+	0.971562i	$0.423907\pi$
$308$	0	0
$309$	−17.5642	−0.999191
$310$	4.25177	0.241484
$311$	−34.7221	−1.96891	−0.984453	−	0.175646i	$-0.943799\pi$
$311$	−34.7221	−1.96891	−0.984453	+	0.175646i	$0.943799\pi$
$312$	−2.84121	−0.160852
$313$	32.1941	1.81972	0.909859	−	0.414918i	$-0.136190\pi$
$313$	32.1941	1.81972	0.909859	+	0.414918i	$0.136190\pi$
$314$	13.4526	0.759174
$315$	0	0
$316$	−15.3260	−0.862153
$317$	−11.0109	−0.618431	−0.309216	−	0.950992i	$-0.600067\pi$
$317$	−11.0109	−0.618431	−0.309216	+	0.950992i	$0.600067\pi$
$318$	−3.80542	−0.213397
$319$	8.44902	0.473054
$320$	−0.449336	−0.0251186
$321$	−11.8341	−0.660514
$322$	0	0
$323$	−1.63619	−0.0910399
$324$	−1.62185	−0.0901030
$325$	3.52352	0.195450
$326$	10.6211	0.588248
$327$	1.02392	0.0566227
$328$	10.9577	0.605038
$329$	0	0
$330$	−0.919926	−0.0506403
$331$	14.4013	0.791567	0.395784	−	0.918344i	$-0.370473\pi$
$331$	14.4013	0.791567	0.395784	+	0.918344i	$0.370473\pi$
$332$	−14.6061	−0.801611
$333$	0.274157	0.0150237
$334$	−8.28043	−0.453085
$335$	7.57326	0.413771
$336$	0	0
$337$	−19.0458	−1.03749	−0.518746	−	0.854928i	$-0.673601\pi$
$337$	−19.0458	−1.03749	−0.518746	+	0.854928i	$0.673601\pi$
$338$	−6.99344	−0.380393
$339$	−6.28526	−0.341369
$340$	−1.49199	−0.0809143
$341$	4.62185	0.250287
$342$	−1.63619	−0.0884749
$343$	0	0
$344$	−20.9917	−1.13180
$345$	−2.80363	−0.150942
$346$	−11.1032	−0.596913
$347$	−17.4851	−0.938651	−0.469325	−	0.883025i	$-0.655503\pi$
$347$	−17.4851	−0.938651	−0.469325	+	0.883025i	$0.655503\pi$
$348$	13.7031	0.734562
$349$	31.9333	1.70935	0.854676	−	0.519162i	$-0.173756\pi$
$349$	31.9333	1.70935	0.854676	+	0.519162i	$0.173756\pi$
$350$	0	0
$351$	1.27568	0.0680908
$352$	5.60688	0.298848
$353$	−27.7531	−1.47715	−0.738574	−	0.674173i	$-0.764500\pi$
$353$	−27.7531	−1.47715	−0.738574	+	0.674173i	$0.764500\pi$
$354$	−1.15246	−0.0612527
$355$	24.0783	1.27794
$356$	−17.3153	−0.917708
$357$	0	0
$358$	−10.7425	−0.567760
$359$	6.60649	0.348677	0.174339	−	0.984686i	$-0.444221\pi$
$359$	6.60649	0.348677	0.174339	+	0.984686i	$0.444221\pi$
$360$	−3.33184	−0.175603
$361$	−11.9204	−0.627391
$362$	−1.65129	−0.0867898
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	13.1007	0.685722
$366$	5.24321	0.274067
$367$	−26.2452	−1.36999	−0.684995	−	0.728548i	$-0.740196\pi$
$367$	−26.2452	−1.36999	−0.684995	+	0.728548i	$0.740196\pi$
$368$	3.51232	0.183092
$369$	−4.91993	−0.256121
$370$	0.252204	0.0131115
$371$	0	0
$372$	7.49597	0.388648
$373$	−7.76233	−0.401918	−0.200959	−	0.979600i	$-0.564406\pi$
$373$	−7.76233	−0.401918	−0.200959	+	0.979600i	$0.564406\pi$
$374$	0.378146	0.0195535
$375$	11.6118	0.599632
$376$	7.04268	0.363198
$377$	−10.7783	−0.555108
$378$	0	0
$379$	15.4636	0.794310	0.397155	−	0.917752i	$-0.369998\pi$
$379$	15.4636	0.794310	0.397155	+	0.917752i	$0.369998\pi$
$380$	6.45562	0.331166
$381$	19.7328	1.01094
$382$	−11.5850	−0.592742
$383$	−26.7573	−1.36724	−0.683618	−	0.729840i	$-0.739594\pi$
$383$	−26.7573	−1.36724	−0.683618	+	0.729840i	$0.739594\pi$
$384$	11.3985	0.581675
$385$	0	0
$386$	8.75834	0.445788
$387$	9.42511	0.479105
$388$	28.6875	1.45639
$389$	19.7790	1.00283	0.501416	−	0.865206i	$-0.332812\pi$
$389$	19.7790	1.00283	0.501416	+	0.865206i	$0.332812\pi$
$390$	1.17353	0.0594241
$391$	1.15246	0.0582825
$392$	0	0
$393$	5.31572	0.268143
$394$	−8.31953	−0.419132
$395$	14.1364	0.711281
$396$	−1.62185	−0.0815012
$397$	−0.248788	−0.0124863	−0.00624316	−	0.999981i	$-0.501987\pi$
$397$	−0.248788	−0.0124863	−0.00624316	+	0.999981i	$0.501987\pi$
$398$	8.75401	0.438799
$399$	0	0
$400$	−5.17644	−0.258822
$401$	34.7875	1.73721	0.868603	−	0.495508i	$-0.165018\pi$
$401$	34.7875	1.73721	0.868603	+	0.495508i	$0.165018\pi$
$402$	−3.11307	−0.155266
$403$	−5.89601	−0.293701
$404$	−7.62399	−0.379308
$405$	1.49597	0.0743354
$406$	0	0
$407$	0.274157	0.0135895
$408$	1.36959	0.0678048
$409$	−1.80788	−0.0893939	−0.0446969	−	0.999001i	$-0.514232\pi$
$409$	−1.80788	−0.0893939	−0.0446969	+	0.999001i	$0.514232\pi$
$410$	−4.52597	−0.223522
$411$	−2.38817	−0.117800
$412$	−28.4865	−1.40343
$413$	0	0
$414$	1.15246	0.0566404
$415$	13.4724	0.661333
$416$	−7.15259	−0.350684
$417$	−12.4948	−0.611875
$418$	−1.63619	−0.0800286
$419$	25.7007	1.25556	0.627780	−	0.778391i	$-0.283964\pi$
$419$	25.7007	1.25556	0.627780	+	0.778391i	$0.283964\pi$
$420$	0	0
$421$	25.2666	1.23142	0.615710	−	0.787973i	$-0.288869\pi$
$421$	25.2666	1.23142	0.615710	+	0.787973i	$0.288869\pi$
$422$	0.923166	0.0449390
$423$	−3.16211	−0.153747
$424$	−13.7827	−0.669346
$425$	−1.69850	−0.0823892
$426$	−9.89766	−0.479543
$427$	0	0
$428$	−19.1932	−0.927736
$429$	1.27568	0.0615905
$430$	8.67040	0.418124
$431$	33.0300	1.59100	0.795499	−	0.605955i	$-0.207209\pi$
$431$	33.0300	1.59100	0.795499	+	0.605955i	$0.207209\pi$
$432$	−1.87412	−0.0901685
$433$	15.9029	0.764243	0.382122	−	0.924112i	$-0.375194\pi$
$433$	15.9029	0.764243	0.382122	+	0.924112i	$0.375194\pi$
$434$	0	0
$435$	−12.6395	−0.606017
$436$	1.66064	0.0795303
$437$	−4.98655	−0.238539
$438$	−5.38519	−0.257314
$439$	4.47623	0.213639	0.106819	−	0.994278i	$-0.465933\pi$
$439$	4.47623	0.213639	0.106819	+	0.994278i	$0.465933\pi$
$440$	−3.33184	−0.158839
$441$	0	0
$442$	−0.482394	−0.0229451
$443$	−1.63747	−0.0777986	−0.0388993	−	0.999243i	$-0.512385\pi$
$443$	−1.63747	−0.0777986	−0.0388993	+	0.999243i	$0.512385\pi$
$444$	0.444643	0.0211018
$445$	15.9713	0.757114
$446$	4.44560	0.210505
$447$	6.70655	0.317209
$448$	0	0
$449$	−2.45974	−0.116082	−0.0580412	−	0.998314i	$-0.518485\pi$
$449$	−2.45974	−0.116082	−0.0580412	+	0.998314i	$0.518485\pi$
$450$	−1.69850	−0.0800679
$451$	−4.91993	−0.231670
$452$	−10.1938	−0.479475
$453$	10.1690	0.477783
$454$	−0.491998	−0.0230906
$455$	0	0
$456$	−5.92603	−0.277512
$457$	−30.9963	−1.44994	−0.724972	−	0.688778i	$-0.758147\pi$
$457$	−30.9963	−1.44994	−0.724972	+	0.688778i	$0.758147\pi$
$458$	−5.25296	−0.245455
$459$	−0.614936	−0.0287028
$460$	−4.54707	−0.212008
$461$	−17.0555	−0.794355	−0.397177	−	0.917742i	$-0.630010\pi$
$461$	−17.0555	−0.794355	−0.397177	+	0.917742i	$0.630010\pi$
$462$	0	0
$463$	13.9963	0.650461	0.325231	−	0.945635i	$-0.394558\pi$
$463$	13.9963	0.650461	0.325231	+	0.945635i	$0.394558\pi$
$464$	15.8345	0.735096
$465$	−6.91416	−0.320636
$466$	1.13089	0.0523876
$467$	37.6382	1.74169	0.870845	−	0.491558i	$-0.163572\pi$
$467$	37.6382	1.74169	0.870845	+	0.491558i	$0.163572\pi$
$468$	2.06897	0.0956381
$469$	0	0
$470$	−2.90891	−0.134178
$471$	−21.8764	−1.00801
$472$	−4.17405	−0.192126
$473$	9.42511	0.433367
$474$	−5.81094	−0.266905
$475$	7.34916	0.337203
$476$	0	0
$477$	6.18832	0.283344
$478$	−5.35916	−0.245122
$479$	34.4990	1.57630	0.788149	−	0.615484i	$-0.211040\pi$
$479$	34.4990	1.57630	0.788149	+	0.615484i	$0.211040\pi$
$480$	−8.38773	−0.382846
$481$	−0.349737	−0.0159466
$482$	0.664446	0.0302647
$483$	0	0
$484$	−1.62185	−0.0737206
$485$	−26.4609	−1.20153
$486$	−0.614936	−0.0278941
$487$	−2.07482	−0.0940192	−0.0470096	−	0.998894i	$-0.514969\pi$
$487$	−2.07482	−0.0940192	−0.0470096	+	0.998894i	$0.514969\pi$
$488$	18.9901	0.859643
$489$	−17.2719	−0.781061
$490$	0	0
$491$	−29.9003	−1.34938	−0.674692	−	0.738100i	$-0.735723\pi$
$491$	−29.9003	−1.34938	−0.674692	+	0.738100i	$0.735723\pi$
$492$	−7.97940	−0.359739
$493$	5.19561	0.233998
$494$	2.08725	0.0939100
$495$	1.49597	0.0672389
$496$	8.66190	0.388931
$497$	0	0
$498$	−5.53798	−0.248163
$499$	1.37815	0.0616943	0.0308471	−	0.999524i	$-0.490179\pi$
$499$	1.37815	0.0616943	0.0308471	+	0.999524i	$0.490179\pi$
$500$	18.8327	0.842224
$501$	13.4655	0.601595
$502$	−5.30872	−0.236940
$503$	34.3693	1.53245	0.766226	−	0.642571i	$-0.222132\pi$
$503$	34.3693	1.53245	0.766226	+	0.642571i	$0.222132\pi$
$504$	0	0
$505$	7.03224	0.312931
$506$	1.15246	0.0512332
$507$	11.3726	0.505077
$508$	32.0037	1.41993
$509$	−32.1962	−1.42707	−0.713536	−	0.700619i	$-0.752907\pi$
$509$	−32.1962	−1.42707	−0.713536	+	0.700619i	$0.752907\pi$
$510$	−0.565696	−0.0250494
$511$	0	0
$512$	18.8560	0.833327
$513$	2.66075	0.117475
$514$	9.04664	0.399030
$515$	26.2755	1.15784
$516$	15.2861	0.672935
$517$	−3.16211	−0.139069
$518$	0	0
$519$	18.0559	0.792566
$520$	4.25036	0.186391
$521$	27.1775	1.19067	0.595334	−	0.803479i	$-0.297020\pi$
$521$	27.1775	1.19067	0.595334	+	0.803479i	$0.297020\pi$
$522$	5.19561	0.227406
$523$	−0.989920	−0.0432862	−0.0216431	−	0.999766i	$-0.506890\pi$
$523$	−0.989920	−0.0432862	−0.0216431	+	0.999766i	$0.506890\pi$
$524$	8.62133	0.376624
$525$	0	0
$526$	19.0187	0.829256
$527$	2.84214	0.123806
$528$	−1.87412	−0.0815605
$529$	−19.4877	−0.847291
$530$	5.69280	0.247279
$531$	1.87412	0.0813298
$532$	0	0
$533$	6.27626	0.271855
$534$	−6.56520	−0.284104
$535$	17.7035	0.765387
$536$	−11.2751	−0.487010
$537$	17.4693	0.753858
$538$	−19.1345	−0.824949
$539$	0	0
$540$	2.42625	0.104409
$541$	−25.5459	−1.09830	−0.549151	−	0.835723i	$-0.685049\pi$
$541$	−25.5459	−1.09830	−0.549151	+	0.835723i	$0.685049\pi$
$542$	1.70318	0.0731579
$543$	2.68530	0.115237
$544$	3.44787	0.147826
$545$	−1.53175	−0.0656129
$546$	0	0
$547$	−5.97544	−0.255491	−0.127746	−	0.991807i	$-0.540774\pi$
$547$	−5.97544	−0.255491	−0.127746	+	0.991807i	$0.540774\pi$
$548$	−3.87326	−0.165457
$549$	−8.52643	−0.363899
$550$	−1.69850	−0.0724241
$551$	−22.4807	−0.957710
$552$	4.17405	0.177659
$553$	0	0
$554$	11.8701	0.504310
$555$	−0.410131	−0.0174091
$556$	−20.2648	−0.859419
$557$	−14.9614	−0.633933	−0.316967	−	0.948437i	$-0.602664\pi$
$557$	−14.9614	−0.633933	−0.316967	+	0.948437i	$0.602664\pi$
$558$	2.84214	0.120318
$559$	−12.0234	−0.508537
$560$	0	0
$561$	−0.614936	−0.0259626
$562$	−4.89527	−0.206494
$563$	−38.2276	−1.61110	−0.805551	−	0.592527i	$-0.798130\pi$
$563$	−38.2276	−1.61110	−0.805551	+	0.592527i	$0.798130\pi$
$564$	−5.12848	−0.215948
$565$	9.40257	0.395569
$566$	−5.26260	−0.221204
$567$	0	0
$568$	−35.8479	−1.50414
$569$	9.95889	0.417498	0.208749	−	0.977969i	$-0.433061\pi$
$569$	9.95889	0.417498	0.208749	+	0.977969i	$0.433061\pi$
$570$	2.44769	0.102522
$571$	−26.2511	−1.09858	−0.549288	−	0.835633i	$-0.685101\pi$
$571$	−26.2511	−1.09858	−0.549288	+	0.835633i	$0.685101\pi$
$572$	2.06897	0.0865079
$573$	18.8394	0.787028
$574$	0	0
$575$	−5.17644	−0.215873
$576$	−0.300364	−0.0125152
$577$	11.5066	0.479024	0.239512	−	0.970893i	$-0.423012\pi$
$577$	11.5066	0.479024	0.239512	+	0.970893i	$0.423012\pi$
$578$	−10.2214	−0.425153
$579$	−14.2427	−0.591906
$580$	−20.4994	−0.851192
$581$	0	0
$582$	10.8771	0.450868
$583$	6.18832	0.256294
$584$	−19.5044	−0.807097
$585$	−1.90838	−0.0789019
$586$	−17.3584	−0.717069
$587$	21.1030	0.871013	0.435506	−	0.900186i	$-0.356569\pi$
$587$	21.1030	0.871013	0.435506	+	0.900186i	$0.356569\pi$
$588$	0	0
$589$	−12.2976	−0.506713
$590$	1.72405	0.0709780
$591$	13.5291	0.556513
$592$	0.513802	0.0211171
$593$	19.4100	0.797074	0.398537	−	0.917152i	$-0.369518\pi$
$593$	19.4100	0.797074	0.398537	+	0.917152i	$0.369518\pi$
$594$	−0.614936	−0.0252311
$595$	0	0
$596$	10.8771	0.445541
$597$	−14.2356	−0.582626
$598$	−1.47017	−0.0601199
$599$	7.40460	0.302544	0.151272	−	0.988492i	$-0.451663\pi$
$599$	7.40460	0.302544	0.151272	+	0.988492i	$0.451663\pi$
$600$	−6.15171	−0.251142
$601$	−11.5056	−0.469322	−0.234661	−	0.972077i	$-0.575398\pi$
$601$	−11.5056	−0.469322	−0.234661	+	0.972077i	$0.575398\pi$
$602$	0	0
$603$	5.06243	0.206158
$604$	16.4927	0.671077
$605$	1.49597	0.0608199
$606$	−2.89068	−0.117426
$607$	45.0283	1.82764	0.913821	−	0.406118i	$-0.133118\pi$
$607$	45.0283	1.82764	0.913821	+	0.406118i	$0.133118\pi$
$608$	−14.9185	−0.605024
$609$	0	0
$610$	−7.84369	−0.317582
$611$	4.03384	0.163192
$612$	−0.997336	−0.0403149
$613$	−17.8422	−0.720638	−0.360319	−	0.932829i	$-0.617332\pi$
$613$	−17.8422	−0.720638	−0.360319	+	0.932829i	$0.617332\pi$
$614$	5.10248	0.205919
$615$	7.36007	0.296787
$616$	0	0
$617$	11.7052	0.471235	0.235617	−	0.971846i	$-0.424289\pi$
$617$	11.7052	0.471235	0.235617	+	0.971846i	$0.424289\pi$
$618$	−10.8008	−0.434474
$619$	−7.51913	−0.302219	−0.151110	−	0.988517i	$-0.548285\pi$
$619$	−7.51913	−0.302219	−0.151110	+	0.988517i	$0.548285\pi$
$620$	−11.2138	−0.450355
$621$	−1.87412	−0.0752057
$622$	−21.3518	−0.856131
$623$	0	0
$624$	2.39078	0.0957076
$625$	−3.56062	−0.142425
$626$	19.7973	0.791259
$627$	2.66075	0.106260
$628$	−35.4804	−1.41582
$629$	0.168589	0.00672208
$630$	0	0
$631$	27.1694	1.08159	0.540797	−	0.841153i	$-0.318123\pi$
$631$	27.1694	1.08159	0.540797	+	0.841153i	$0.318123\pi$
$632$	−21.0464	−0.837180
$633$	−1.50124	−0.0596689
$634$	−6.77097	−0.268910
$635$	−29.5197	−1.17145
$636$	10.0365	0.397975
$637$	0	0
$638$	5.19561	0.205696
$639$	16.0954	0.636725
$640$	−17.0518	−0.674030
$641$	−12.3538	−0.487945	−0.243973	−	0.969782i	$-0.578451\pi$
$641$	−12.3538	−0.487945	−0.243973	+	0.969782i	$0.578451\pi$
$642$	−7.27720	−0.287208
$643$	−21.3948	−0.843728	−0.421864	−	0.906659i	$-0.638624\pi$
$643$	−21.3948	−0.843728	−0.421864	+	0.906659i	$0.638624\pi$
$644$	0	0
$645$	−14.0997	−0.555175
$646$	−1.00615	−0.0395865
$647$	2.75530	0.108322	0.0541609	−	0.998532i	$-0.482752\pi$
$647$	2.75530	0.108322	0.0541609	+	0.998532i	$0.482752\pi$
$648$	−2.22721	−0.0874930
$649$	1.87412	0.0735655
$650$	2.16674	0.0849865
$651$	0	0
$652$	−28.0125	−1.09705
$653$	−8.66698	−0.339165	−0.169583	−	0.985516i	$-0.554242\pi$
$653$	−8.66698	−0.339165	−0.169583	+	0.985516i	$0.554242\pi$
$654$	0.629642	0.0246210
$655$	−7.95217	−0.310717
$656$	−9.22052	−0.360001
$657$	8.75732	0.341656
$658$	0	0
$659$	−32.2924	−1.25793	−0.628967	−	0.777432i	$-0.716522\pi$
$659$	−32.2924	−1.25793	−0.628967	+	0.777432i	$0.716522\pi$
$660$	2.42625	0.0944415
$661$	−12.7559	−0.496146	−0.248073	−	0.968741i	$-0.579797\pi$
$661$	−12.7559	−0.496146	−0.248073	+	0.968741i	$0.579797\pi$
$662$	8.85588	0.344194
$663$	0.784462	0.0304660
$664$	−20.0577	−0.778391
$665$	0	0
$666$	0.168589	0.00653269
$667$	15.8345	0.613113
$668$	21.8391	0.844980
$669$	−7.22937	−0.279504
$670$	4.65707	0.179918
$671$	−8.52643	−0.329159
$672$	0	0
$673$	43.6075	1.68095	0.840473	−	0.541853i	$-0.182277\pi$
$673$	43.6075	1.68095	0.840473	+	0.541853i	$0.182277\pi$
$674$	−11.7120	−0.451128
$675$	2.76207	0.106312
$676$	18.4448	0.709414
$677$	2.16774	0.0833132	0.0416566	−	0.999132i	$-0.486736\pi$
$677$	2.16774	0.0833132	0.0416566	+	0.999132i	$0.486736\pi$
$678$	−3.86503	−0.148436
$679$	0	0
$680$	−2.04887	−0.0785705
$681$	0.800079	0.0306591
$682$	2.84214	0.108831
$683$	23.9590	0.916767	0.458383	−	0.888755i	$-0.348429\pi$
$683$	23.9590	0.916767	0.458383	+	0.888755i	$0.348429\pi$
$684$	4.31534	0.165001
$685$	3.57263	0.136503
$686$	0	0
$687$	8.54229	0.325909
$688$	17.6638	0.673424
$689$	−7.89432	−0.300750
$690$	−1.72405	−0.0656335
$691$	5.05889	0.192449	0.0962246	−	0.995360i	$-0.469323\pi$
$691$	5.05889	0.192449	0.0962246	+	0.995360i	$0.469323\pi$
$692$	29.2840	1.11321
$693$	0	0
$694$	−10.7522	−0.408149
$695$	18.6919	0.709024
$696$	18.8177	0.713284
$697$	−3.02544	−0.114597
$698$	19.6370	0.743270
$699$	−1.83904	−0.0695589
$700$	0	0
$701$	−21.7177	−0.820265	−0.410132	−	0.912026i	$-0.634517\pi$
$701$	−21.7177	−0.820265	−0.410132	+	0.912026i	$0.634517\pi$
$702$	0.784462	0.0296076
$703$	−0.729462	−0.0275122
$704$	−0.300364	−0.0113204
$705$	4.73043	0.178158
$706$	−17.0664	−0.642301
$707$	0	0
$708$	3.03954	0.114233
$709$	5.59190	0.210008	0.105004	−	0.994472i	$-0.466514\pi$
$709$	5.59190	0.210008	0.105004	+	0.994472i	$0.466514\pi$
$710$	14.8066	0.555682
$711$	9.44966	0.354390
$712$	−23.7782	−0.891125
$713$	8.66190	0.324391
$714$	0	0
$715$	−1.90838	−0.0713694
$716$	28.3327	1.05884
$717$	8.71500	0.325467
$718$	4.06257	0.151614
$719$	7.72426	0.288066	0.144033	−	0.989573i	$-0.453993\pi$
$719$	7.72426	0.288066	0.144033	+	0.989573i	$0.453993\pi$
$720$	2.80363	0.104485
$721$	0	0
$722$	−7.33030	−0.272806
$723$	−1.08051	−0.0401847
$724$	4.35517	0.161859
$725$	−23.3368	−0.866707
$726$	−0.614936	−0.0228224
$727$	−35.7990	−1.32771	−0.663855	−	0.747861i	$-0.731081\pi$
$727$	−35.7990	−1.32771	−0.663855	+	0.747861i	$0.731081\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.05609	0.298169
$731$	5.79584	0.214367
$732$	−13.8286	−0.511121
$733$	16.2538	0.600347	0.300174	−	0.953885i	$-0.402955\pi$
$733$	16.2538	0.600347	0.300174	+	0.953885i	$0.402955\pi$
$734$	−16.1391	−0.595707
$735$	0	0
$736$	10.5079	0.387328
$737$	5.06243	0.186477
$738$	−3.02544	−0.111368
$739$	0.574082	0.0211179	0.0105590	−	0.999944i	$-0.496639\pi$
$739$	0.574082	0.0211179	0.0105590	+	0.999944i	$0.496639\pi$
$740$	−0.665172	−0.0244522
$741$	−3.39426	−0.124691
$742$	0	0
$743$	25.6448	0.940818	0.470409	−	0.882449i	$-0.344106\pi$
$743$	25.6448	0.940818	0.470409	+	0.882449i	$0.344106\pi$
$744$	10.2938	0.377390
$745$	−10.0328	−0.367574
$746$	−4.77333	−0.174764
$747$	9.00578	0.329504
$748$	−0.997336	−0.0364662
$749$	0	0
$750$	7.14053	0.260735
$751$	29.9121	1.09151	0.545755	−	0.837945i	$-0.316243\pi$
$751$	29.9121	1.09151	0.545755	+	0.837945i	$0.316243\pi$
$752$	−5.92617	−0.216105
$753$	8.63296	0.314603
$754$	−6.62794	−0.241375
$755$	−15.2126	−0.553642
$756$	0	0
$757$	13.9358	0.506505	0.253252	−	0.967400i	$-0.418500\pi$
$757$	13.9358	0.506505	0.253252	+	0.967400i	$0.418500\pi$
$758$	9.50910	0.345386
$759$	−1.87412	−0.0680261
$760$	8.86517	0.321574
$761$	−36.4563	−1.32154	−0.660770	−	0.750589i	$-0.729770\pi$
$761$	−36.4563	−1.32154	−0.660770	+	0.750589i	$0.729770\pi$
$762$	12.1344	0.439583
$763$	0	0
$764$	30.5548	1.10543
$765$	0.919926	0.0332600
$766$	−16.4540	−0.594509
$767$	−2.39078	−0.0863259
$768$	6.40860	0.231250
$769$	−10.7416	−0.387354	−0.193677	−	0.981065i	$-0.562041\pi$
$769$	−10.7416	−0.387354	−0.193677	+	0.981065i	$0.562041\pi$
$770$	0	0
$771$	−14.7115	−0.529822
$772$	−23.0996	−0.831372
$773$	−1.82374	−0.0655953	−0.0327976	−	0.999462i	$-0.510442\pi$
$773$	−1.82374	−0.0655953	−0.0327976	+	0.999462i	$0.510442\pi$
$774$	5.79584	0.208327
$775$	−12.7659	−0.458564
$776$	39.3951	1.41420
$777$	0	0
$778$	12.1628	0.436057
$779$	13.0907	0.469022
$780$	−3.09512	−0.110823
$781$	16.0954	0.575940
$782$	0.708690	0.0253427
$783$	−8.44902	−0.301943
$784$	0	0
$785$	32.7265	1.16806
$786$	3.26883	0.116595
$787$	24.9933	0.890916	0.445458	−	0.895303i	$-0.353041\pi$
$787$	24.9933	0.890916	0.445458	+	0.895303i	$0.353041\pi$
$788$	21.9422	0.781659
$789$	−30.9280	−1.10107
$790$	8.69300	0.309283
$791$	0	0
$792$	−2.22721	−0.0791404
$793$	10.8770	0.386254
$794$	−0.152989	−0.00542937
$795$	−9.25754	−0.328331
$796$	−23.0881	−0.818338
$797$	−14.0330	−0.497074	−0.248537	−	0.968622i	$-0.579950\pi$
$797$	−14.0330	−0.497074	−0.248537	+	0.968622i	$0.579950\pi$
$798$	0	0
$799$	−1.94450	−0.0687913
$800$	−15.4866	−0.547534
$801$	10.6762	0.377226
$802$	21.3921	0.755381
$803$	8.75732	0.309039
$804$	8.21053	0.289563
$805$	0	0
$806$	−3.62567	−0.127709
$807$	31.1163	1.09535
$808$	−10.4696	−0.368320
$809$	−39.5483	−1.39045	−0.695223	−	0.718795i	$-0.744694\pi$
$809$	−39.5483	−1.39045	−0.695223	+	0.718795i	$0.744694\pi$
$810$	0.919926	0.0323229
$811$	19.9504	0.700555	0.350277	−	0.936646i	$-0.386087\pi$
$811$	19.9504	0.700555	0.350277	+	0.936646i	$0.386087\pi$
$812$	0	0
$813$	−2.76969	−0.0971372
$814$	0.168589	0.00590904
$815$	25.8382	0.905074
$816$	−1.15246	−0.0403442
$817$	−25.0778	−0.877361
$818$	−1.11173	−0.0388707
$819$	0	0
$820$	11.9370	0.416857
$821$	1.03529	0.0361319	0.0180659	−	0.999837i	$-0.494249\pi$
$821$	1.03529	0.0361319	0.0180659	+	0.999837i	$0.494249\pi$
$822$	−1.46857	−0.0512222
$823$	7.90025	0.275386	0.137693	−	0.990475i	$-0.456031\pi$
$823$	7.90025	0.275386	0.137693	+	0.990475i	$0.456031\pi$
$824$	−39.1191	−1.36278
$825$	2.76207	0.0961629
$826$	0	0
$827$	−19.4794	−0.677364	−0.338682	−	0.940901i	$-0.609981\pi$
$827$	−19.4794	−0.677364	−0.338682	+	0.940901i	$0.609981\pi$
$828$	−3.03954	−0.105631
$829$	25.5634	0.887854	0.443927	−	0.896063i	$-0.353585\pi$
$829$	25.5634	0.887854	0.443927	+	0.896063i	$0.353585\pi$
$830$	8.28465	0.287565
$831$	−19.3029	−0.669611
$832$	0.383168	0.0132840
$833$	0	0
$834$	−7.68352	−0.266059
$835$	−20.1440	−0.697113
$836$	4.31534	0.149249
$837$	−4.62185	−0.159755
$838$	15.8043	0.545949
$839$	29.1936	1.00787	0.503937	−	0.863740i	$-0.331884\pi$
$839$	29.1936	1.00787	0.503937	+	0.863740i	$0.331884\pi$
$840$	0	0
$841$	42.3860	1.46159
$842$	15.5374	0.535453
$843$	7.96061	0.274178
$844$	−2.43479	−0.0838090
$845$	−17.0131	−0.585270
$846$	−1.94450	−0.0668531
$847$	0	0
$848$	11.5976	0.398264
$849$	8.55797	0.293709
$850$	−1.04447	−0.0358249
$851$	0.513802	0.0176129
$852$	26.1044	0.894323
$853$	3.81162	0.130507	0.0652536	−	0.997869i	$-0.479214\pi$
$853$	3.81162	0.130507	0.0652536	+	0.997869i	$0.479214\pi$
$854$	0	0
$855$	−3.98040	−0.136127
$856$	−26.3570	−0.900863
$857$	−34.6870	−1.18488	−0.592442	−	0.805613i	$-0.701836\pi$
$857$	−34.6870	−1.18488	−0.592442	+	0.805613i	$0.701836\pi$
$858$	0.784462	0.0267811
$859$	−48.6058	−1.65841	−0.829205	−	0.558945i	$-0.811206\pi$
$859$	−48.6058	−1.65841	−0.829205	+	0.558945i	$0.811206\pi$
$860$	−22.8676	−0.779780
$861$	0	0
$862$	20.3113	0.691806
$863$	21.6564	0.737191	0.368596	−	0.929590i	$-0.379839\pi$
$863$	21.6564	0.737191	0.368596	+	0.929590i	$0.379839\pi$
$864$	−5.60688	−0.190750
$865$	−27.0111	−0.918405
$866$	9.77925	0.332312
$867$	16.6219	0.564508
$868$	0	0
$869$	9.44966	0.320558
$870$	−7.77248	−0.263512
$871$	−6.45805	−0.218823
$872$	2.28047	0.0772266
$873$	−17.6881	−0.598652
$874$	−3.06641	−0.103723
$875$	0	0
$876$	14.2031	0.479878
$877$	−16.0026	−0.540370	−0.270185	−	0.962808i	$-0.587085\pi$
$877$	−16.0026	−0.540370	−0.270185	+	0.962808i	$0.587085\pi$
$878$	2.75260	0.0928956
$879$	28.2280	0.952106
$880$	2.80363	0.0945102
$881$	−36.2250	−1.22045	−0.610226	−	0.792228i	$-0.708921\pi$
$881$	−36.2250	−1.22045	−0.610226	+	0.792228i	$0.708921\pi$
$882$	0	0
$883$	−4.78873	−0.161154	−0.0805768	−	0.996748i	$-0.525676\pi$
$883$	−4.78873	−0.161154	−0.0805768	+	0.996748i	$0.525676\pi$
$884$	1.27228	0.0427915
$885$	−2.80363	−0.0942428
$886$	−1.00694	−0.0338288
$887$	−54.4131	−1.82701	−0.913507	−	0.406823i	$-0.866636\pi$
$887$	−54.4131	−1.82701	−0.913507	+	0.406823i	$0.866636\pi$
$888$	0.610605	0.0204906
$889$	0	0
$890$	9.82135	0.329212
$891$	1.00000	0.0335013
$892$	−11.7250	−0.392582
$893$	8.41357	0.281549
$894$	4.12410	0.137931
$895$	−26.1336	−0.873551
$896$	0	0
$897$	2.39078	0.0798257
$898$	−1.51258	−0.0504756
$899$	39.0501	1.30240
$900$	4.47967	0.149322
$901$	3.80542	0.126777
$902$	−3.02544	−0.100736
$903$	0	0
$904$	−13.9986	−0.465586
$905$	−4.01713	−0.133534
$906$	6.25330	0.207752
$907$	53.8600	1.78839	0.894196	−	0.447676i	$-0.147748\pi$
$907$	53.8600	1.78839	0.894196	+	0.447676i	$0.147748\pi$
$908$	1.29761	0.0430628
$909$	4.70079	0.155915
$910$	0	0
$911$	−22.0506	−0.730571	−0.365285	−	0.930896i	$-0.619029\pi$
$911$	−22.0506	−0.730571	−0.365285	+	0.930896i	$0.619029\pi$
$912$	4.98655	0.165121
$913$	9.00578	0.298048
$914$	−19.0607	−0.630473
$915$	12.7553	0.421677
$916$	13.8543	0.457760
$917$	0	0
$918$	−0.378146	−0.0124807
$919$	6.34908	0.209437	0.104718	−	0.994502i	$-0.466606\pi$
$919$	6.34908	0.209437	0.104718	+	0.994502i	$0.466606\pi$
$920$	−6.24426	−0.205867
$921$	−8.29757	−0.273414
$922$	−10.4880	−0.345406
$923$	−20.5326	−0.675840
$924$	0	0
$925$	−0.757241	−0.0248979
$926$	8.60680	0.282837
$927$	17.5642	0.576883
$928$	47.3726	1.55508
$929$	57.8664	1.89854	0.949268	−	0.314469i	$-0.101826\pi$
$929$	57.8664	1.89854	0.949268	+	0.314469i	$0.101826\pi$
$930$	−4.25177	−0.139421
$931$	0	0
$932$	−2.98266	−0.0977001
$933$	34.7221	1.13675
$934$	23.1451	0.757331
$935$	0.919926	0.0300848
$936$	2.84121	0.0928678
$937$	16.1657	0.528110	0.264055	−	0.964508i	$-0.414940\pi$
$937$	16.1657	0.528110	0.264055	+	0.964508i	$0.414940\pi$
$938$	0	0
$939$	−32.1941	−1.05061
$940$	7.67206	0.250235
$941$	53.1550	1.73280	0.866401	−	0.499348i	$-0.166427\pi$
$941$	53.1550	1.73280	0.866401	+	0.499348i	$0.166427\pi$
$942$	−13.4526	−0.438309
$943$	−9.22052	−0.300261
$944$	3.51232	0.114316
$945$	0	0
$946$	5.79584	0.188439
$947$	−15.0920	−0.490423	−0.245211	−	0.969470i	$-0.578857\pi$
$947$	−15.0920	−0.490423	−0.245211	+	0.969470i	$0.578857\pi$
$948$	15.3260	0.497764
$949$	−11.1715	−0.362644
$950$	4.51927	0.146624
$951$	11.0109	0.357052
$952$	0	0
$953$	−27.2774	−0.883602	−0.441801	−	0.897113i	$-0.645660\pi$
$953$	−27.2774	−0.883602	−0.441801	+	0.897113i	$0.645660\pi$
$954$	3.80542	0.123205
$955$	−28.1832	−0.911988
$956$	14.1344	0.457141
$957$	−8.44902	−0.273118
$958$	21.2147	0.685414
$959$	0	0
$960$	0.449336	0.0145022
$961$	−9.63847	−0.310918
$962$	−0.215066	−0.00693400
$963$	11.8341	0.381348
$964$	−1.75243	−0.0564421
$965$	21.3067	0.685886
$966$	0	0
$967$	47.7400	1.53521	0.767607	−	0.640920i	$-0.221447\pi$
$967$	47.7400	1.53521	0.767607	+	0.640920i	$0.221447\pi$
$968$	−2.22721	−0.0715852
$969$	1.63619	0.0525619
$970$	−16.2718	−0.522455
$971$	−27.6966	−0.888826	−0.444413	−	0.895822i	$-0.646588\pi$
$971$	−27.6966	−0.888826	−0.444413	+	0.895822i	$0.646588\pi$
$972$	1.62185	0.0520210
$973$	0	0
$974$	−1.27588	−0.0408819
$975$	−3.52352	−0.112843
$976$	−15.9795	−0.511492
$977$	17.9202	0.573318	0.286659	−	0.958033i	$-0.407455\pi$
$977$	17.9202	0.573318	0.286659	+	0.958033i	$0.407455\pi$
$978$	−10.6211	−0.339625
$979$	10.6762	0.341214
$980$	0	0
$981$	−1.02392	−0.0326911
$982$	−18.3868	−0.586746
$983$	30.4192	0.970220	0.485110	−	0.874453i	$-0.338779\pi$
$983$	30.4192	0.970220	0.485110	+	0.874453i	$0.338779\pi$
$984$	−10.9577	−0.349319
$985$	−20.2391	−0.644873
$986$	3.19497	0.101748
$987$	0	0
$988$	−5.50500	−0.175137
$989$	17.6638	0.561675
$990$	0.919926	0.0292372
$991$	14.2095	0.451379	0.225689	−	0.974199i	$-0.427537\pi$
$991$	14.2095	0.451379	0.225689	+	0.974199i	$0.427537\pi$
$992$	25.9142	0.822776
$993$	−14.4013	−0.457012
$994$	0	0
$995$	21.2961	0.675132
$996$	14.6061	0.462811
$997$	−0.997451	−0.0315896	−0.0157948	−	0.999875i	$-0.505028\pi$
$997$	−0.997451	−0.0315896	−0.0157948	+	0.999875i	$0.505028\pi$
$998$	0.847472	0.0268262
$999$	−0.274157	−0.00867394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.ba.1.3		5
3.2	odd	2		4851.2.a.ca.1.3		5
7.2	even	3		231.2.i.f.67.3	✓	10
7.4	even	3		231.2.i.f.100.3	yes	10
7.6	odd	2		1617.2.a.bb.1.3		5
21.2	odd	6		693.2.i.j.298.3		10
21.11	odd	6		693.2.i.j.100.3		10
21.20	even	2		4851.2.a.bz.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.3	✓	10	7.2	even	3
231.2.i.f.100.3	yes	10	7.4	even	3
693.2.i.j.100.3		10	21.11	odd	6
693.2.i.j.298.3		10	21.2	odd	6
1617.2.a.ba.1.3		5	1.1	even	1	trivial
1617.2.a.bb.1.3		5	7.6	odd	2
4851.2.a.bz.1.3		5	21.20	even	2
4851.2.a.ca.1.3		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+0.614936 q^{2} -1.00000 q^{3} -1.62185 q^{4} +1.49597 q^{5} -0.614936 q^{6} -2.22721 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.614936 q^{2} -1.00000 q^{3} -1.62185 q^{4} +1.49597 q^{5} -0.614936 q^{6} -2.22721 q^{8} +1.00000 q^{9} +0.919926 q^{10} +1.00000 q^{11} +1.62185 q^{12} -1.27568 q^{13} -1.49597 q^{15} +1.87412 q^{16} +0.614936 q^{17} +0.614936 q^{18} -2.66075 q^{19} -2.42625 q^{20} +0.614936 q^{22} +1.87412 q^{23} +2.22721 q^{24} -2.76207 q^{25} -0.784462 q^{26} -1.00000 q^{27} +8.44902 q^{29} -0.919926 q^{30} +4.62185 q^{31} +5.60688 q^{32} -1.00000 q^{33} +0.378146 q^{34} -1.62185 q^{36} +0.274157 q^{37} -1.63619 q^{38} +1.27568 q^{39} -3.33184 q^{40} -4.91993 q^{41} +9.42511 q^{43} -1.62185 q^{44} +1.49597 q^{45} +1.15246 q^{46} -3.16211 q^{47} -1.87412 q^{48} -1.69850 q^{50} -0.614936 q^{51} +2.06897 q^{52} +6.18832 q^{53} -0.614936 q^{54} +1.49597 q^{55} +2.66075 q^{57} +5.19561 q^{58} +1.87412 q^{59} +2.42625 q^{60} -8.52643 q^{61} +2.84214 q^{62} -0.300364 q^{64} -1.90838 q^{65} -0.614936 q^{66} +5.06243 q^{67} -0.997336 q^{68} -1.87412 q^{69} +16.0954 q^{71} -2.22721 q^{72} +8.75732 q^{73} +0.168589 q^{74} +2.76207 q^{75} +4.31534 q^{76} +0.784462 q^{78} +9.44966 q^{79} +2.80363 q^{80} +1.00000 q^{81} -3.02544 q^{82} +9.00578 q^{83} +0.919926 q^{85} +5.79584 q^{86} -8.44902 q^{87} -2.22721 q^{88} +10.6762 q^{89} +0.919926 q^{90} -3.03954 q^{92} -4.62185 q^{93} -1.94450 q^{94} -3.98040 q^{95} -5.60688 q^{96} -17.6881 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} - 5 q^{3} + 10 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 2 q^{10} + 5 q^{11} - 10 q^{12} + 5 q^{13} + 4 q^{15} + 16 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 8 q^{20} + 2 q^{22} + 16 q^{23} - 6 q^{24} + 7 q^{25} - 10 q^{26} - 5 q^{27} - 2 q^{30} + 5 q^{31} + 4 q^{32} - 5 q^{33} + 20 q^{34} + 10 q^{36} + 15 q^{37} + 6 q^{38} - 5 q^{39} - 6 q^{40} - 22 q^{41} + 3 q^{43} + 10 q^{44} - 4 q^{45} + 16 q^{46} - 2 q^{47} - 16 q^{48} + 34 q^{50} - 2 q^{51} + 40 q^{52} + 6 q^{53} - 2 q^{54} - 4 q^{55} + 3 q^{57} + 12 q^{58} + 16 q^{59} + 8 q^{60} + 12 q^{61} - 4 q^{62} - 4 q^{64} - 28 q^{65} - 2 q^{66} + 7 q^{67} + 10 q^{68} - 16 q^{69} + 24 q^{71} + 6 q^{72} + 17 q^{73} - 36 q^{74} - 7 q^{75} + 30 q^{76} + 10 q^{78} + 7 q^{79} + 16 q^{80} + 5 q^{81} + 8 q^{82} - 12 q^{83} + 2 q^{85} - 18 q^{86} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 68 q^{92} - 5 q^{93} + 82 q^{94} - 18 q^{95} - 4 q^{96} - 14 q^{97} + 5 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 5 * q^3 + 10 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 2 * q^10 + 5 * q^11 - 10 * q^12 + 5 * q^13 + 4 * q^15 + 16 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 8 * q^20 + 2 * q^22 + 16 * q^23 - 6 * q^24 + 7 * q^25 - 10 * q^26 - 5 * q^27 - 2 * q^30 + 5 * q^31 + 4 * q^32 - 5 * q^33 + 20 * q^34 + 10 * q^36 + 15 * q^37 + 6 * q^38 - 5 * q^39 - 6 * q^40 - 22 * q^41 + 3 * q^43 + 10 * q^44 - 4 * q^45 + 16 * q^46 - 2 * q^47 - 16 * q^48 + 34 * q^50 - 2 * q^51 + 40 * q^52 + 6 * q^53 - 2 * q^54 - 4 * q^55 + 3 * q^57 + 12 * q^58 + 16 * q^59 + 8 * q^60 + 12 * q^61 - 4 * q^62 - 4 * q^64 - 28 * q^65 - 2 * q^66 + 7 * q^67 + 10 * q^68 - 16 * q^69 + 24 * q^71 + 6 * q^72 + 17 * q^73 - 36 * q^74 - 7 * q^75 + 30 * q^76 + 10 * q^78 + 7 * q^79 + 16 * q^80 + 5 * q^81 + 8 * q^82 - 12 * q^83 + 2 * q^85 - 18 * q^86 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 68 * q^92 - 5 * q^93 + 82 * q^94 - 18 * q^95 - 4 * q^96 - 14 * q^97 + 5 * q^99

Introduction

L-functions

Modular forms

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Database

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