LMFDB - Embedded newform 1183.2.a.r.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.149660$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.149660 q^{2} +2.76031 q^{3} -1.97760 q^{4} +4.13443 q^{5} -0.413107 q^{6} +1.00000 q^{7} +0.595288 q^{8} +4.61930 q^{9} +O(q^{10})$	\(q-0.149660 q^{2} +2.76031 q^{3} -1.97760 q^{4} +4.13443 q^{5} -0.413107 q^{6} +1.00000 q^{7} +0.595288 q^{8} +4.61930 q^{9} -0.618759 q^{10} -2.55320 q^{11} -5.45879 q^{12} -0.149660 q^{14} +11.4123 q^{15} +3.86611 q^{16} +1.50360 q^{17} -0.691324 q^{18} -5.93185 q^{19} -8.17626 q^{20} +2.76031 q^{21} +0.382113 q^{22} +6.55752 q^{23} +1.64318 q^{24} +12.0935 q^{25} +4.46975 q^{27} -1.97760 q^{28} +0.283949 q^{29} -1.70797 q^{30} -1.95156 q^{31} -1.76918 q^{32} -7.04763 q^{33} -0.225029 q^{34} +4.13443 q^{35} -9.13513 q^{36} +5.66775 q^{37} +0.887760 q^{38} +2.46118 q^{40} -6.70206 q^{41} -0.413107 q^{42} -8.14248 q^{43} +5.04922 q^{44} +19.0982 q^{45} -0.981398 q^{46} -3.94423 q^{47} +10.6717 q^{48} +1.00000 q^{49} -1.80992 q^{50} +4.15040 q^{51} -1.08139 q^{53} -0.668943 q^{54} -10.5561 q^{55} +0.595288 q^{56} -16.3737 q^{57} -0.0424957 q^{58} -3.71413 q^{59} -22.5690 q^{60} +1.93905 q^{61} +0.292070 q^{62} +4.61930 q^{63} -7.46745 q^{64} +1.05475 q^{66} -3.38134 q^{67} -2.97352 q^{68} +18.1008 q^{69} -0.618759 q^{70} +5.36923 q^{71} +2.74981 q^{72} +2.62686 q^{73} -0.848236 q^{74} +33.3819 q^{75} +11.7308 q^{76} -2.55320 q^{77} +7.89503 q^{79} +15.9842 q^{80} -1.51999 q^{81} +1.00303 q^{82} -10.5270 q^{83} -5.45879 q^{84} +6.21653 q^{85} +1.21860 q^{86} +0.783786 q^{87} -1.51989 q^{88} -6.64469 q^{89} -2.85823 q^{90} -12.9682 q^{92} -5.38690 q^{93} +0.590294 q^{94} -24.5248 q^{95} -4.88347 q^{96} +0.504498 q^{97} -0.149660 q^{98} -11.7940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * 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 $

$2$	−0.149660	−0.105826	−0.0529128	−	0.998599i	$-0.516851\pi$
$2$	−0.149660	−0.105826	−0.0529128	+	0.998599i	$0.516851\pi$
$3$	2.76031	1.59366	0.796832	−	0.604201i	$-0.206508\pi$
$3$	2.76031	1.59366	0.796832	+	0.604201i	$0.206508\pi$
$4$	−1.97760	−0.988801
$5$	4.13443	1.84897	0.924487	−	0.381213i	$-0.124494\pi$
$5$	4.13443	1.84897	0.924487	+	0.381213i	$0.124494\pi$
$6$	−0.413107	−0.168650
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.595288	0.210466
$9$	4.61930	1.53977
$10$	−0.618759	−0.195669
$11$	−2.55320	−0.769820	−0.384910	−	0.922954i	$-0.625768\pi$
$11$	−2.55320	−0.769820	−0.384910	+	0.922954i	$0.625768\pi$
$12$	−5.45879	−1.57582
$13$	0	0
$13$	0	0
$14$	−0.149660	−0.0399983
$15$	11.4123	2.94664
$16$	3.86611	0.966528
$17$	1.50360	0.364676	0.182338	−	0.983236i	$-0.441633\pi$
$17$	1.50360	0.364676	0.182338	+	0.983236i	$0.441633\pi$
$18$	−0.691324	−0.162947
$19$	−5.93185	−1.36086	−0.680430	−	0.732813i	$-0.738207\pi$
$19$	−5.93185	−1.36086	−0.680430	+	0.732813i	$0.738207\pi$
$20$	−8.17626	−1.82827
$21$	2.76031	0.602348
$22$	0.382113	0.0814667
$23$	6.55752	1.36734	0.683669	−	0.729792i	$-0.260383\pi$
$23$	6.55752	1.36734	0.683669	+	0.729792i	$0.260383\pi$
$24$	1.64318	0.335412
$25$	12.0935	2.41871
$26$	0	0
$27$	4.46975	0.860205
$28$	−1.97760	−0.373732
$29$	0.283949	0.0527279	0.0263640	−	0.999652i	$-0.491607\pi$
$29$	0.283949	0.0527279	0.0263640	+	0.999652i	$0.491607\pi$
$30$	−1.70797	−0.311830
$31$	−1.95156	−0.350510	−0.175255	−	0.984523i	$-0.556075\pi$
$31$	−1.95156	−0.350510	−0.175255	+	0.984523i	$0.556075\pi$
$32$	−1.76918	−0.312749
$33$	−7.04763	−1.22683
$34$	−0.225029	−0.0385921
$35$	4.13443	0.698847
$36$	−9.13513	−1.52252
$37$	5.66775	0.931773	0.465886	−	0.884845i	$-0.345736\pi$
$37$	5.66775	0.931773	0.465886	+	0.884845i	$0.345736\pi$
$38$	0.887760	0.144014
$39$	0	0
$40$	2.46118	0.389146
$41$	−6.70206	−1.04669	−0.523343	−	0.852122i	$-0.675315\pi$
$41$	−6.70206	−1.04669	−0.523343	+	0.852122i	$0.675315\pi$
$42$	−0.413107	−0.0637439
$43$	−8.14248	−1.24172	−0.620858	−	0.783923i	$-0.713216\pi$
$43$	−8.14248	−1.24172	−0.620858	+	0.783923i	$0.713216\pi$
$44$	5.04922	0.761199
$45$	19.0982	2.84699
$46$	−0.981398	−0.144699
$47$	−3.94423	−0.575326	−0.287663	−	0.957732i	$-0.592878\pi$
$47$	−3.94423	−0.575326	−0.287663	+	0.957732i	$0.592878\pi$
$48$	10.6717	1.54032
$49$	1.00000	0.142857
$50$	−1.80992	−0.255961
$51$	4.15040	0.581172
$52$	0	0
$53$	−1.08139	−0.148541	−0.0742705	−	0.997238i	$-0.523663\pi$
$53$	−1.08139	−0.148541	−0.0742705	+	0.997238i	$0.523663\pi$
$54$	−0.668943	−0.0910316
$55$	−10.5561	−1.42338
$56$	0.595288	0.0795487
$57$	−16.3737	−2.16875
$58$	−0.0424957	−0.00557997
$59$	−3.71413	−0.483538	−0.241769	−	0.970334i	$-0.577728\pi$
$59$	−3.71413	−0.483538	−0.241769	+	0.970334i	$0.577728\pi$
$60$	−22.5690	−2.91364
$61$	1.93905	0.248270	0.124135	−	0.992265i	$-0.460384\pi$
$61$	1.93905	0.248270	0.124135	+	0.992265i	$0.460384\pi$
$62$	0.292070	0.0370930
$63$	4.61930	0.581977
$64$	−7.46745	−0.933431
$65$	0	0
$66$	1.05475	0.129831
$67$	−3.38134	−0.413096	−0.206548	−	0.978436i	$-0.566223\pi$
$67$	−3.38134	−0.413096	−0.206548	+	0.978436i	$0.566223\pi$
$68$	−2.97352	−0.360592
$69$	18.1008	2.17908
$70$	−0.618759	−0.0739559
$71$	5.36923	0.637210	0.318605	−	0.947888i	$-0.396786\pi$
$71$	5.36923	0.637210	0.318605	+	0.947888i	$0.396786\pi$
$72$	2.74981	0.324068
$73$	2.62686	0.307451	0.153725	−	0.988114i	$-0.450873\pi$
$73$	2.62686	0.307451	0.153725	+	0.988114i	$0.450873\pi$
$74$	−0.848236	−0.0986054
$75$	33.3819	3.85461
$76$	11.7308	1.34562
$77$	−2.55320	−0.290965
$78$	0	0
$79$	7.89503	0.888260	0.444130	−	0.895962i	$-0.353513\pi$
$79$	7.89503	0.888260	0.444130	+	0.895962i	$0.353513\pi$
$80$	15.9842	1.78709
$81$	−1.51999	−0.168888
$82$	1.00303	0.110766
$83$	−10.5270	−1.15549	−0.577745	−	0.816218i	$-0.696067\pi$
$83$	−10.5270	−1.15549	−0.577745	+	0.816218i	$0.696067\pi$
$84$	−5.45879	−0.595603
$85$	6.21653	0.674277
$86$	1.21860	0.131405
$87$	0.783786	0.0840306
$88$	−1.51989	−0.162021
$89$	−6.64469	−0.704336	−0.352168	−	0.935937i	$-0.614555\pi$
$89$	−6.64469	−0.704336	−0.352168	+	0.935937i	$0.614555\pi$
$90$	−2.85823	−0.301284
$91$	0	0
$92$	−12.9682	−1.35202
$93$	−5.38690	−0.558596
$94$	0.590294	0.0608842
$95$	−24.5248	−2.51619
$96$	−4.88347	−0.498418
$97$	0.504498	0.0512240	0.0256120	−	0.999672i	$-0.491847\pi$
$97$	0.504498	0.0512240	0.0256120	+	0.999672i	$0.491847\pi$
$98$	−0.149660	−0.0151179
$99$	−11.7940	−1.18534
$100$	−23.9162	−2.39162
$101$	−7.18413	−0.714847	−0.357424	−	0.933942i	$-0.616345\pi$
$101$	−7.18413	−0.714847	−0.357424	+	0.933942i	$0.616345\pi$
$102$	−0.621148	−0.0615028
$103$	15.2582	1.50343	0.751716	−	0.659487i	$-0.229226\pi$
$103$	15.2582	1.50343	0.751716	+	0.659487i	$0.229226\pi$
$104$	0	0
$105$	11.4123	1.11373
$106$	0.161841	0.0157194
$107$	−3.47375	−0.335820	−0.167910	−	0.985802i	$-0.553702\pi$
$107$	−3.47375	−0.335820	−0.167910	+	0.985802i	$0.553702\pi$
$108$	−8.83939	−0.850571
$109$	16.6557	1.59533	0.797663	−	0.603103i	$-0.206069\pi$
$109$	16.6557	1.59533	0.797663	+	0.603103i	$0.206069\pi$
$110$	1.57982	0.150630
$111$	15.6447	1.48493
$112$	3.86611	0.365313
$113$	18.2871	1.72031	0.860153	−	0.510036i	$-0.170368\pi$
$113$	18.2871	1.72031	0.860153	+	0.510036i	$0.170368\pi$
$114$	2.45049	0.229510
$115$	27.1116	2.52817
$116$	−0.561537	−0.0521374
$117$	0	0
$118$	0.555856	0.0511707
$119$	1.50360	0.137835
$120$	6.79360	0.620168
$121$	−4.48114	−0.407377
$122$	−0.290199	−0.0262734
$123$	−18.4997	−1.66807
$124$	3.85941	0.346585
$125$	29.3277	2.62315
$126$	−0.691324	−0.0615880
$127$	−7.98164	−0.708256	−0.354128	−	0.935197i	$-0.615222\pi$
$127$	−7.98164	−0.708256	−0.354128	+	0.935197i	$0.615222\pi$
$128$	4.65593	0.411530
$129$	−22.4757	−1.97888
$130$	0	0
$131$	−18.7232	−1.63586	−0.817929	−	0.575319i	$-0.804878\pi$
$131$	−18.7232	−1.63586	−0.817929	+	0.575319i	$0.804878\pi$
$132$	13.9374	1.21310
$133$	−5.93185	−0.514357
$134$	0.506051	0.0437161
$135$	18.4799	1.59050
$136$	0.895074	0.0767520
$137$	2.32575	0.198703	0.0993513	−	0.995052i	$-0.468323\pi$
$137$	2.32575	0.198703	0.0993513	+	0.995052i	$0.468323\pi$
$138$	−2.70896	−0.230602
$139$	9.02263	0.765289	0.382645	−	0.923896i	$-0.375013\pi$
$139$	9.02263	0.765289	0.382645	+	0.923896i	$0.375013\pi$
$140$	−8.17626	−0.691020
$141$	−10.8873	−0.916876
$142$	−0.803558	−0.0674331
$143$	0	0
$144$	17.8587	1.48823
$145$	1.17397	0.0974926
$146$	−0.393136	−0.0325362
$147$	2.76031	0.227666
$148$	−11.2086	−0.921338
$149$	−13.5260	−1.10809	−0.554045	−	0.832486i	$-0.686917\pi$
$149$	−13.5260	−1.10809	−0.554045	+	0.832486i	$0.686917\pi$
$150$	−4.99593	−0.407916
$151$	−5.02665	−0.409063	−0.204531	−	0.978860i	$-0.565567\pi$
$151$	−5.02665	−0.409063	−0.204531	+	0.978860i	$0.565567\pi$
$152$	−3.53116	−0.286415
$153$	6.94557	0.561516
$154$	0.382113	0.0307915
$155$	−8.06859	−0.648085
$156$	0	0
$157$	−11.4938	−0.917308	−0.458654	−	0.888615i	$-0.651668\pi$
$157$	−11.4938	−0.917308	−0.458654	+	0.888615i	$0.651668\pi$
$158$	−1.18157	−0.0940006
$159$	−2.98498	−0.236724
$160$	−7.31455	−0.578266
$161$	6.55752	0.516805
$162$	0.227482	0.0178727
$163$	−12.8306	−1.00497	−0.502485	−	0.864586i	$-0.667581\pi$
$163$	−12.8306	−1.00497	−0.502485	+	0.864586i	$0.667581\pi$
$164$	13.2540	1.03496
$165$	−29.1379	−2.26839
$166$	1.57547	0.122280
$167$	−21.6586	−1.67600	−0.837998	−	0.545674i	$-0.816274\pi$
$167$	−21.6586	−1.67600	−0.837998	+	0.545674i	$0.816274\pi$
$168$	1.64318	0.126774
$169$	0	0
$170$	−0.930366	−0.0713558
$171$	−27.4010	−2.09540
$172$	16.1026	1.22781
$173$	16.3149	1.24040	0.620201	−	0.784443i	$-0.287051\pi$
$173$	16.3149	1.24040	0.620201	+	0.784443i	$0.287051\pi$
$174$	−0.117301	−0.00889259
$175$	12.0935	0.914185
$176$	−9.87098	−0.744053
$177$	−10.2521	−0.770598
$178$	0.994444	0.0745367
$179$	−1.42206	−0.106290	−0.0531450	−	0.998587i	$-0.516925\pi$
$179$	−1.42206	−0.106290	−0.0531450	+	0.998587i	$0.516925\pi$
$180$	−37.7686	−2.81510
$181$	−19.1896	−1.42635	−0.713174	−	0.700987i	$-0.752743\pi$
$181$	−19.1896	−1.42635	−0.713174	+	0.700987i	$0.752743\pi$
$182$	0	0
$183$	5.35238	0.395660
$184$	3.90361	0.287778
$185$	23.4329	1.72282
$186$	0.806204	0.0591137
$187$	−3.83900	−0.280735
$188$	7.80012	0.568883
$189$	4.46975	0.325127
$190$	3.67039	0.266278
$191$	14.0009	1.01307	0.506536	−	0.862219i	$-0.330926\pi$
$191$	14.0009	1.01307	0.506536	+	0.862219i	$0.330926\pi$
$192$	−20.6125	−1.48758
$193$	−1.26935	−0.0913695	−0.0456847	−	0.998956i	$-0.514547\pi$
$193$	−1.26935	−0.0913695	−0.0456847	+	0.998956i	$0.514547\pi$
$194$	−0.0755031	−0.00542081
$195$	0	0
$196$	−1.97760	−0.141257
$197$	−2.82033	−0.200940	−0.100470	−	0.994940i	$-0.532035\pi$
$197$	−2.82033	−0.200940	−0.100470	+	0.994940i	$0.532035\pi$
$198$	1.76509	0.125440
$199$	19.2600	1.36530	0.682652	−	0.730743i	$-0.260826\pi$
$199$	19.2600	1.36530	0.682652	+	0.730743i	$0.260826\pi$
$200$	7.19913	0.509055
$201$	−9.33353	−0.658337
$202$	1.07518	0.0756491
$203$	0.283949	0.0199293
$204$	−8.20783	−0.574663
$205$	−27.7092	−1.93529
$206$	−2.28354	−0.159102
$207$	30.2911	2.10538
$208$	0	0
$209$	15.1452	1.04762
$210$	−1.70797	−0.117861
$211$	−12.8443	−0.884236	−0.442118	−	0.896957i	$-0.645773\pi$
$211$	−12.8443	−0.884236	−0.442118	+	0.896957i	$0.645773\pi$
$212$	2.13857	0.146877
$213$	14.8207	1.01550
$214$	0.519881	0.0355383
$215$	−33.6645	−2.29590
$216$	2.66079	0.181044
$217$	−1.95156	−0.132480
$218$	−2.49269	−0.168826
$219$	7.25094	0.489973
$220$	20.8757	1.40744
$221$	0	0
$222$	−2.34139	−0.157144
$223$	4.51539	0.302373	0.151187	−	0.988505i	$-0.451691\pi$
$223$	4.51539	0.302373	0.151187	+	0.988505i	$0.451691\pi$
$224$	−1.76918	−0.118208
$225$	55.8636	3.72424
$226$	−2.73685	−0.182052
$227$	−9.86924	−0.655044	−0.327522	−	0.944843i	$-0.606214\pi$
$227$	−9.86924	−0.655044	−0.327522	+	0.944843i	$0.606214\pi$
$228$	32.3807	2.14446
$229$	4.44617	0.293811	0.146906	−	0.989151i	$-0.453069\pi$
$229$	4.44617	0.293811	0.146906	+	0.989151i	$0.453069\pi$
$230$	−4.05752	−0.267545
$231$	−7.04763	−0.463700
$232$	0.169031	0.0110974
$233$	27.6514	1.81151	0.905753	−	0.423806i	$-0.139306\pi$
$233$	27.6514	1.81151	0.905753	+	0.423806i	$0.139306\pi$
$234$	0	0
$235$	−16.3072	−1.06376
$236$	7.34507	0.478123
$237$	21.7927	1.41559
$238$	−0.225029	−0.0145864
$239$	17.2370	1.11497	0.557483	−	0.830188i	$-0.311767\pi$
$239$	17.2370	1.11497	0.557483	+	0.830188i	$0.311767\pi$
$240$	44.1213	2.84801
$241$	26.4553	1.70414	0.852068	−	0.523431i	$-0.175348\pi$
$241$	26.4553	1.70414	0.852068	+	0.523431i	$0.175348\pi$
$242$	0.670648	0.0431109
$243$	−17.6049	−1.12936
$244$	−3.83468	−0.245490
$245$	4.13443	0.264139
$246$	2.76867	0.176524
$247$	0	0
$248$	−1.16174	−0.0737705
$249$	−29.0578	−1.84146
$250$	−4.38919	−0.277597
$251$	−7.91803	−0.499782	−0.249891	−	0.968274i	$-0.580395\pi$
$251$	−7.91803	−0.499782	−0.249891	+	0.968274i	$0.580395\pi$
$252$	−9.13513	−0.575459
$253$	−16.7427	−1.05260
$254$	1.19453	0.0749516
$255$	17.1595	1.07457
$256$	14.2381	0.889881
$257$	−19.9720	−1.24582	−0.622910	−	0.782293i	$-0.714050\pi$
$257$	−19.9720	−1.24582	−0.622910	+	0.782293i	$0.714050\pi$
$258$	3.36372	0.209416
$259$	5.66775	0.352177
$260$	0	0
$261$	1.31164	0.0811887
$262$	2.80212	0.173116
$263$	−2.88461	−0.177873	−0.0889364	−	0.996037i	$-0.528347\pi$
$263$	−2.88461	−0.177873	−0.0889364	+	0.996037i	$0.528347\pi$
$264$	−4.19537	−0.258207
$265$	−4.47095	−0.274648
$266$	0.887760	0.0544321
$267$	−18.3414	−1.12247
$268$	6.68694	0.408470
$269$	−12.5865	−0.767410	−0.383705	−	0.923456i	$-0.625352\pi$
$269$	−12.5865	−0.767410	−0.383705	+	0.923456i	$0.625352\pi$
$270$	−2.76570	−0.168315
$271$	−21.4007	−1.30000	−0.650001	−	0.759934i	$-0.725231\pi$
$271$	−21.4007	−1.30000	−0.650001	+	0.759934i	$0.725231\pi$
$272$	5.81308	0.352470
$273$	0	0
$274$	−0.348072	−0.0210278
$275$	−30.8773	−1.86197
$276$	−35.7961	−2.15467
$277$	−13.6063	−0.817524	−0.408762	−	0.912641i	$-0.634039\pi$
$277$	−13.6063	−0.817524	−0.408762	+	0.912641i	$0.634039\pi$
$278$	−1.35033	−0.0809872
$279$	−9.01483	−0.539704
$280$	2.46118	0.147083
$281$	30.7217	1.83270	0.916352	−	0.400374i	$-0.131120\pi$
$281$	30.7217	1.83270	0.916352	+	0.400374i	$0.131120\pi$
$282$	1.62939	0.0970289
$283$	27.7843	1.65160	0.825802	−	0.563961i	$-0.190723\pi$
$283$	27.7843	1.65160	0.825802	+	0.563961i	$0.190723\pi$
$284$	−10.6182	−0.630074
$285$	−67.6961	−4.00997
$286$	0	0
$287$	−6.70206	−0.395610
$288$	−8.17236	−0.481561
$289$	−14.7392	−0.867011
$290$	−0.175696	−0.0103172
$291$	1.39257	0.0816338
$292$	−5.19488	−0.304008
$293$	−0.146791	−0.00857560	−0.00428780	−	0.999991i	$-0.501365\pi$
$293$	−0.146791	−0.00857560	−0.00428780	+	0.999991i	$0.501365\pi$
$294$	−0.413107	−0.0240929
$295$	−15.3558	−0.894050
$296$	3.37394	0.196107
$297$	−11.4122	−0.662203
$298$	2.02430	0.117264
$299$	0	0
$300$	−66.0160	−3.81144
$301$	−8.14248	−0.469325
$302$	0.752288	0.0432893
$303$	−19.8304	−1.13923
$304$	−22.9332	−1.31531
$305$	8.01688	0.459045
$306$	−1.03947	−0.0594228
$307$	−31.6486	−1.80628	−0.903142	−	0.429342i	$-0.858745\pi$
$307$	−31.6486	−1.80628	−0.903142	+	0.429342i	$0.858745\pi$
$308$	5.04922	0.287706
$309$	42.1173	2.39597
$310$	1.20754	0.0685839
$311$	18.8608	1.06950	0.534748	−	0.845011i	$-0.320406\pi$
$311$	18.8608	1.06950	0.534748	+	0.845011i	$0.320406\pi$
$312$	0	0
$313$	−33.7796	−1.90934	−0.954668	−	0.297674i	$-0.903789\pi$
$313$	−33.7796	−1.90934	−0.954668	+	0.297674i	$0.903789\pi$
$314$	1.72017	0.0970746
$315$	19.0982	1.07606
$316$	−15.6132	−0.878312
$317$	−22.0847	−1.24040	−0.620201	−	0.784443i	$-0.712949\pi$
$317$	−22.0847	−1.24040	−0.620201	+	0.784443i	$0.712949\pi$
$318$	0.446732	0.0250515
$319$	−0.724979	−0.0405910
$320$	−30.8737	−1.72589
$321$	−9.58860	−0.535184
$322$	−0.981398	−0.0546912
$323$	−8.91912	−0.496273
$324$	3.00594	0.166997
$325$	0	0
$326$	1.92023	0.106352
$327$	45.9748	2.54241
$328$	−3.98965	−0.220292
$329$	−3.94423	−0.217453
$330$	4.36078	0.240053
$331$	−25.3399	−1.39281	−0.696404	−	0.717650i	$-0.745218\pi$
$331$	−25.3399	−1.39281	−0.696404	+	0.717650i	$0.745218\pi$
$332$	20.8182	1.14255
$333$	26.1810	1.43471
$334$	3.24143	0.177363
$335$	−13.9799	−0.763804
$336$	10.6717	0.582187
$337$	−26.2596	−1.43045	−0.715226	−	0.698893i	$-0.753676\pi$
$337$	−26.2596	−1.43045	−0.715226	+	0.698893i	$0.753676\pi$
$338$	0	0
$339$	50.4780	2.74159
$340$	−12.2938	−0.666726
$341$	4.98273	0.269830
$342$	4.10083	0.221747
$343$	1.00000	0.0539949
$344$	−4.84712	−0.261339
$345$	74.8364	4.02906
$346$	−2.44169	−0.131266
$347$	−4.13355	−0.221901	−0.110950	−	0.993826i	$-0.535389\pi$
$347$	−4.13355	−0.221901	−0.110950	+	0.993826i	$0.535389\pi$
$348$	−1.55002	−0.0830896
$349$	−4.02138	−0.215259	−0.107630	−	0.994191i	$-0.534326\pi$
$349$	−4.02138	−0.215259	−0.107630	+	0.994191i	$0.534326\pi$
$350$	−1.80992	−0.0967442
$351$	0	0
$352$	4.51707	0.240761
$353$	2.65565	0.141346	0.0706730	−	0.997500i	$-0.477485\pi$
$353$	2.65565	0.141346	0.0706730	+	0.997500i	$0.477485\pi$
$354$	1.53433	0.0815489
$355$	22.1987	1.17819
$356$	13.1406	0.696448
$357$	4.15040	0.219662
$358$	0.212826	0.0112482
$359$	5.18529	0.273669	0.136835	−	0.990594i	$-0.456307\pi$
$359$	5.18529	0.273669	0.136835	+	0.990594i	$0.456307\pi$
$360$	11.3689	0.599194
$361$	16.1868	0.851939
$362$	2.87191	0.150944
$363$	−12.3693	−0.649222
$364$	0	0
$365$	10.8606	0.568469
$366$	−0.801037	−0.0418709
$367$	−10.4931	−0.547737	−0.273869	−	0.961767i	$-0.588303\pi$
$367$	−10.4931	−0.547737	−0.273869	+	0.961767i	$0.588303\pi$
$368$	25.3521	1.32157
$369$	−30.9588	−1.61165
$370$	−3.50697	−0.182319
$371$	−1.08139	−0.0561432
$372$	10.6531	0.552340
$373$	−25.5655	−1.32373	−0.661866	−	0.749622i	$-0.730235\pi$
$373$	−25.5655	−1.32373	−0.661866	+	0.749622i	$0.730235\pi$
$374$	0.574544	0.0297090
$375$	80.9535	4.18042
$376$	−2.34795	−0.121087
$377$	0	0
$378$	−0.668943	−0.0344067
$379$	0.598162	0.0307255	0.0153627	−	0.999882i	$-0.495110\pi$
$379$	0.598162	0.0307255	0.0153627	+	0.999882i	$0.495110\pi$
$380$	48.5003	2.48802
$381$	−22.0318	−1.12872
$382$	−2.09538	−0.107209
$383$	−10.2676	−0.524649	−0.262325	−	0.964980i	$-0.584489\pi$
$383$	−10.2676	−0.524649	−0.262325	+	0.964980i	$0.584489\pi$
$384$	12.8518	0.655841
$385$	−10.5561	−0.537986
$386$	0.189970	0.00966923
$387$	−37.6125	−1.91195
$388$	−0.997695	−0.0506503
$389$	−3.10131	−0.157243	−0.0786213	−	0.996905i	$-0.525052\pi$
$389$	−3.10131	−0.157243	−0.0786213	+	0.996905i	$0.525052\pi$
$390$	0	0
$391$	9.85988	0.498636
$392$	0.595288	0.0300666
$393$	−51.6819	−2.60701
$394$	0.422090	0.0212646
$395$	32.6415	1.64237
$396$	23.3239	1.17207
$397$	8.88419	0.445885	0.222942	−	0.974832i	$-0.428434\pi$
$397$	8.88419	0.445885	0.222942	+	0.974832i	$0.428434\pi$
$398$	−2.88245	−0.144484
$399$	−16.3737	−0.819712
$400$	46.7550	2.33775
$401$	−5.31632	−0.265484	−0.132742	−	0.991151i	$-0.542378\pi$
$401$	−5.31632	−0.265484	−0.132742	+	0.991151i	$0.542378\pi$
$402$	1.39686	0.0696688
$403$	0	0
$404$	14.2073	0.706842
$405$	−6.28431	−0.312270
$406$	−0.0424957	−0.00210903
$407$	−14.4709	−0.717298
$408$	2.47068	0.122317
$409$	−1.71205	−0.0846556	−0.0423278	−	0.999104i	$-0.513477\pi$
$409$	−1.71205	−0.0846556	−0.0423278	+	0.999104i	$0.513477\pi$
$410$	4.14696	0.204804
$411$	6.41980	0.316665
$412$	−30.1746	−1.48660
$413$	−3.71413	−0.182760
$414$	−4.53337	−0.222803
$415$	−43.5232	−2.13647
$416$	0	0
$417$	24.9052	1.21961
$418$	−2.26663	−0.110865
$419$	−6.33942	−0.309701	−0.154850	−	0.987938i	$-0.549490\pi$
$419$	−6.33942	−0.309701	−0.154850	+	0.987938i	$0.549490\pi$
$420$	−22.5690	−1.10125
$421$	33.7640	1.64556	0.822779	−	0.568362i	$-0.192423\pi$
$421$	33.7640	1.64556	0.822779	+	0.568362i	$0.192423\pi$
$422$	1.92227	0.0935748
$423$	−18.2196	−0.885866
$424$	−0.643741	−0.0312628
$425$	18.1838	0.882045
$426$	−2.21807	−0.107466
$427$	1.93905	0.0938374
$428$	6.86969	0.332059
$429$	0	0
$430$	5.03823	0.242965
$431$	29.7020	1.43069	0.715346	−	0.698770i	$-0.246269\pi$
$431$	29.7020	1.43069	0.715346	+	0.698770i	$0.246269\pi$
$432$	17.2806	0.831412
$433$	−0.203068	−0.00975884	−0.00487942	−	0.999988i	$-0.501553\pi$
$433$	−0.203068	−0.00975884	−0.00487942	+	0.999988i	$0.501553\pi$
$434$	0.292070	0.0140198
$435$	3.24051	0.155370
$436$	−32.9383	−1.57746
$437$	−38.8982	−1.86075
$438$	−1.08518	−0.0518517
$439$	29.9951	1.43159	0.715794	−	0.698311i	$-0.246065\pi$
$439$	29.9951	1.43159	0.715794	+	0.698311i	$0.246065\pi$
$440$	−6.28389	−0.299573
$441$	4.61930	0.219966
$442$	0	0
$443$	1.17113	0.0556421	0.0278211	−	0.999613i	$-0.491143\pi$
$443$	1.17113	0.0556421	0.0278211	+	0.999613i	$0.491143\pi$
$444$	−30.9391	−1.46830
$445$	−27.4720	−1.30230
$446$	−0.675774	−0.0319988
$447$	−37.3358	−1.76592
$448$	−7.46745	−0.352804
$449$	9.29361	0.438593	0.219296	−	0.975658i	$-0.429624\pi$
$449$	9.29361	0.438593	0.219296	+	0.975658i	$0.429624\pi$
$450$	−8.36054	−0.394120
$451$	17.1117	0.805760
$452$	−36.1646	−1.70104
$453$	−13.8751	−0.651909
$454$	1.47703	0.0693205
$455$	0	0
$456$	−9.74708	−0.456449
$457$	30.3849	1.42134	0.710672	−	0.703523i	$-0.248391\pi$
$457$	30.3849	1.42134	0.710672	+	0.703523i	$0.248391\pi$
$458$	−0.665413	−0.0310927
$459$	6.72072	0.313696
$460$	−53.6160	−2.49986
$461$	27.9856	1.30342	0.651710	−	0.758468i	$-0.274052\pi$
$461$	27.9856	1.30342	0.651710	+	0.758468i	$0.274052\pi$
$462$	1.05475	0.0490713
$463$	4.38020	0.203565	0.101783	−	0.994807i	$-0.467545\pi$
$463$	4.38020	0.203565	0.101783	+	0.994807i	$0.467545\pi$
$464$	1.09778	0.0509630
$465$	−22.2718	−1.03283
$466$	−4.13831	−0.191704
$467$	9.59064	0.443802	0.221901	−	0.975069i	$-0.428774\pi$
$467$	9.59064	0.443802	0.221901	+	0.975069i	$0.428774\pi$
$468$	0	0
$469$	−3.38134	−0.156136
$470$	2.44053	0.112573
$471$	−31.7265	−1.46188
$472$	−2.21098	−0.101768
$473$	20.7894	0.955898
$474$	−3.26149	−0.149805
$475$	−71.7370	−3.29152
$476$	−2.97352	−0.136291
$477$	−4.99528	−0.228718
$478$	−2.57968	−0.117992
$479$	0.637948	0.0291486	0.0145743	−	0.999894i	$-0.495361\pi$
$479$	0.637948	0.0291486	0.0145743	+	0.999894i	$0.495361\pi$
$480$	−20.1904	−0.921561
$481$	0	0
$482$	−3.95930	−0.180341
$483$	18.1008	0.823614
$484$	8.86192	0.402815
$485$	2.08581	0.0947118
$486$	2.63475	0.119515
$487$	34.6352	1.56947	0.784736	−	0.619830i	$-0.212799\pi$
$487$	34.6352	1.56947	0.784736	+	0.619830i	$0.212799\pi$
$488$	1.15429	0.0522525
$489$	−35.4164	−1.60159
$490$	−0.618759	−0.0279527
$491$	28.5890	1.29020	0.645101	−	0.764097i	$-0.276815\pi$
$491$	28.5890	1.29020	0.645101	+	0.764097i	$0.276815\pi$
$492$	36.5851	1.64938
$493$	0.426945	0.0192286
$494$	0	0
$495$	−48.7615	−2.19167
$496$	−7.54495	−0.338778
$497$	5.36923	0.240843
$498$	4.34879	0.194874
$499$	35.1797	1.57486	0.787431	−	0.616403i	$-0.211411\pi$
$499$	35.1797	1.57486	0.787431	+	0.616403i	$0.211411\pi$
$500$	−57.9986	−2.59377
$501$	−59.7845	−2.67097
$502$	1.18501	0.0528897
$503$	9.42778	0.420364	0.210182	−	0.977662i	$-0.432594\pi$
$503$	9.42778	0.420364	0.210182	+	0.977662i	$0.432594\pi$
$504$	2.74981	0.122486
$505$	−29.7023	−1.32173
$506$	2.50571	0.111392
$507$	0	0
$508$	15.7845	0.700325
$509$	−2.62920	−0.116537	−0.0582686	−	0.998301i	$-0.518558\pi$
$509$	−2.62920	−0.116537	−0.0582686	+	0.998301i	$0.518558\pi$
$510$	−2.56809	−0.113717
$511$	2.62686	0.116205
$512$	−11.4427	−0.505703
$513$	−26.5139	−1.17062
$514$	2.98901	0.131840
$515$	63.0839	2.77981
$516$	44.4481	1.95672
$517$	10.0704	0.442897
$518$	−0.848236	−0.0372693
$519$	45.0343	1.97678
$520$	0	0
$521$	19.6001	0.858696	0.429348	−	0.903139i	$-0.358743\pi$
$521$	19.6001	0.858696	0.429348	+	0.903139i	$0.358743\pi$
$522$	−0.196300	−0.00859184
$523$	−14.8982	−0.651452	−0.325726	−	0.945464i	$-0.605609\pi$
$523$	−14.8982	−0.651452	−0.325726	+	0.945464i	$0.605609\pi$
$524$	37.0271	1.61754
$525$	33.3819	1.45690
$526$	0.431711	0.0188235
$527$	−2.93436	−0.127823
$528$	−27.2469	−1.18577
$529$	20.0011	0.869612
$530$	0.669122	0.0290648
$531$	−17.1567	−0.744535
$532$	11.7308	0.508596
$533$	0	0
$534$	2.74497	0.118787
$535$	−14.3620	−0.620922
$536$	−2.01287	−0.0869427
$537$	−3.92533	−0.169390
$538$	1.88369	0.0812116
$539$	−2.55320	−0.109974
$540$	−36.5459	−1.57268
$541$	−10.4746	−0.450339	−0.225170	−	0.974320i	$-0.572294\pi$
$541$	−10.4746	−0.450339	−0.225170	+	0.974320i	$0.572294\pi$
$542$	3.20283	0.137573
$543$	−52.9691	−2.27312
$544$	−2.66013	−0.114052
$545$	68.8618	2.94972
$546$	0	0
$547$	−24.9324	−1.06603	−0.533016	−	0.846105i	$-0.678942\pi$
$547$	−24.9324	−1.06603	−0.533016	+	0.846105i	$0.678942\pi$
$548$	−4.59942	−0.196477
$549$	8.95706	0.382278
$550$	4.62109	0.197044
$551$	−1.68434	−0.0717553
$552$	10.7752	0.458622
$553$	7.89503	0.335731
$554$	2.03632	0.0865150
$555$	64.6821	2.74560
$556$	−17.8432	−0.756719
$557$	33.0777	1.40155	0.700774	−	0.713384i	$-0.252838\pi$
$557$	33.0777	1.40155	0.700774	+	0.713384i	$0.252838\pi$
$558$	1.34916	0.0571144
$559$	0	0
$560$	15.9842	0.675455
$561$	−10.5968	−0.447398
$562$	−4.59781	−0.193947
$563$	−4.54152	−0.191402	−0.0957012	−	0.995410i	$-0.530509\pi$
$563$	−4.54152	−0.191402	−0.0957012	+	0.995410i	$0.530509\pi$
$564$	21.5307	0.906608
$565$	75.6068	3.18080
$566$	−4.15819	−0.174782
$567$	−1.51999	−0.0638337
$568$	3.19624	0.134111
$569$	−20.8507	−0.874105	−0.437053	−	0.899436i	$-0.643978\pi$
$569$	−20.8507	−0.874105	−0.437053	+	0.899436i	$0.643978\pi$
$570$	10.1314	0.424357
$571$	−31.9139	−1.33556	−0.667778	−	0.744360i	$-0.732755\pi$
$571$	−31.9139	−1.33556	−0.667778	+	0.744360i	$0.732755\pi$
$572$	0	0
$573$	38.6469	1.61450
$574$	1.00303	0.0418656
$575$	79.3036	3.30719
$576$	−34.4944	−1.43727
$577$	−13.7190	−0.571129	−0.285565	−	0.958359i	$-0.592181\pi$
$577$	−13.7190	−0.571129	−0.285565	+	0.958359i	$0.592181\pi$
$578$	2.20587	0.0917520
$579$	−3.50378	−0.145612
$580$	−2.32164	−0.0964008
$581$	−10.5270	−0.436734
$582$	−0.208412	−0.00863894
$583$	2.76102	0.114350
$584$	1.56374	0.0647079
$585$	0	0
$586$	0.0219687	0.000907518 0
$587$	25.0820	1.03525	0.517623	−	0.855609i	$-0.326817\pi$
$587$	25.0820	1.03525	0.517623	+	0.855609i	$0.326817\pi$
$588$	−5.45879	−0.225117
$589$	11.5764	0.476995
$590$	2.29815	0.0946134
$591$	−7.78497	−0.320231
$592$	21.9122	0.900585
$593$	26.7388	1.09803	0.549016	−	0.835812i	$-0.315003\pi$
$593$	26.7388	1.09803	0.549016	+	0.835812i	$0.315003\pi$
$594$	1.70795	0.0700780
$595$	6.21653	0.254853
$596$	26.7490	1.09568
$597$	53.1635	2.17584
$598$	0	0
$599$	21.1279	0.863264	0.431632	−	0.902050i	$-0.357938\pi$
$599$	21.1279	0.863264	0.431632	+	0.902050i	$0.357938\pi$
$600$	19.8718	0.811263
$601$	26.0691	1.06338	0.531691	−	0.846938i	$-0.321557\pi$
$601$	26.0691	1.06338	0.531691	+	0.846938i	$0.321557\pi$
$602$	1.21860	0.0496665
$603$	−15.6194	−0.636071
$604$	9.94071	0.404482
$605$	−18.5270	−0.753229
$606$	2.96782	0.120559
$607$	11.0294	0.447670	0.223835	−	0.974627i	$-0.428142\pi$
$607$	11.0294	0.447670	0.223835	+	0.974627i	$0.428142\pi$
$608$	10.4945	0.425608
$609$	0.783786	0.0317606
$610$	−1.19981	−0.0485788
$611$	0	0
$612$	−13.7356	−0.555228
$613$	−8.29847	−0.335172	−0.167586	−	0.985857i	$-0.553597\pi$
$613$	−8.29847	−0.335172	−0.167586	+	0.985857i	$0.553597\pi$
$614$	4.73654	0.191151
$615$	−76.4859	−3.08421
$616$	−1.51989	−0.0612382
$617$	−19.8547	−0.799320	−0.399660	−	0.916663i	$-0.630872\pi$
$617$	−19.8547	−0.799320	−0.399660	+	0.916663i	$0.630872\pi$
$618$	−6.30327	−0.253555
$619$	15.9751	0.642093	0.321047	−	0.947063i	$-0.395965\pi$
$619$	15.9751	0.642093	0.321047	+	0.947063i	$0.395965\pi$
$620$	15.9565	0.640827
$621$	29.3105	1.17619
$622$	−2.82270	−0.113180
$623$	−6.64469	−0.266214
$624$	0	0
$625$	60.7858	2.43143
$626$	5.05545	0.202057
$627$	41.8055	1.66955
$628$	22.7302	0.907035
$629$	8.52203	0.339796
$630$	−2.85823	−0.113875
$631$	29.5325	1.17567	0.587835	−	0.808981i	$-0.299981\pi$
$631$	29.5325	1.17567	0.587835	+	0.808981i	$0.299981\pi$
$632$	4.69981	0.186949
$633$	−35.4541	−1.40918
$634$	3.30520	0.131266
$635$	−32.9996	−1.30955
$636$	5.90310	0.234073
$637$	0	0
$638$	0.108500	0.00429557
$639$	24.8021	0.981154
$640$	19.2496	0.760909
$641$	25.6564	1.01337	0.506683	−	0.862132i	$-0.330871\pi$
$641$	25.6564	1.01337	0.506683	+	0.862132i	$0.330871\pi$
$642$	1.43503	0.0566361
$643$	−27.8289	−1.09746	−0.548732	−	0.835998i	$-0.684889\pi$
$643$	−27.8289	−1.09746	−0.548732	+	0.835998i	$0.684889\pi$
$644$	−12.9682	−0.511017
$645$	−92.9244	−3.65890
$646$	1.33484	0.0525184
$647$	14.0636	0.552899	0.276449	−	0.961028i	$-0.410842\pi$
$647$	14.0636	0.552899	0.276449	+	0.961028i	$0.410842\pi$
$648$	−0.904834	−0.0355452
$649$	9.48293	0.372238
$650$	0	0
$651$	−5.38690	−0.211129
$652$	25.3738	0.993716
$653$	32.1381	1.25766	0.628831	−	0.777542i	$-0.283534\pi$
$653$	32.1381	1.25766	0.628831	+	0.777542i	$0.283534\pi$
$654$	−6.88059	−0.269052
$655$	−77.4100	−3.02466
$656$	−25.9109	−1.01165
$657$	12.1342	0.473402
$658$	0.590294	0.0230121
$659$	38.7643	1.51004	0.755021	−	0.655700i	$-0.227627\pi$
$659$	38.7643	1.51004	0.755021	+	0.655700i	$0.227627\pi$
$660$	57.6233	2.24298
$661$	−31.1898	−1.21314	−0.606571	−	0.795029i	$-0.707455\pi$
$661$	−31.1898	−1.21314	−0.606571	+	0.795029i	$0.707455\pi$
$662$	3.79237	0.147395
$663$	0	0
$664$	−6.26660	−0.243191
$665$	−24.5248	−0.951032
$666$	−3.91825	−0.151829
$667$	1.86200	0.0720969
$668$	42.8321	1.65723
$669$	12.4639	0.481881
$670$	2.09223	0.0808300
$671$	−4.95080	−0.191124
$672$	−4.88347	−0.188384
$673$	−6.51491	−0.251131	−0.125566	−	0.992085i	$-0.540075\pi$
$673$	−6.51491	−0.251131	−0.125566	+	0.992085i	$0.540075\pi$
$674$	3.93001	0.151379
$675$	54.0551	2.08058
$676$	0	0
$677$	26.3121	1.01126	0.505629	−	0.862751i	$-0.331260\pi$
$677$	26.3121	1.01126	0.505629	+	0.862751i	$0.331260\pi$
$678$	−7.55454	−0.290130
$679$	0.504498	0.0193608
$680$	3.70062	0.141912
$681$	−27.2421	−1.04392
$682$	−0.745715	−0.0285549
$683$	20.2861	0.776226	0.388113	−	0.921612i	$-0.373127\pi$
$683$	20.2861	0.776226	0.388113	+	0.921612i	$0.373127\pi$
$684$	54.1882	2.07194
$685$	9.61567	0.367396
$686$	−0.149660	−0.00571404
$687$	12.2728	0.468236
$688$	−31.4797	−1.20015
$689$	0	0
$690$	−11.2000	−0.426377
$691$	8.37956	0.318773	0.159387	−	0.987216i	$-0.449048\pi$
$691$	8.37956	0.318773	0.159387	+	0.987216i	$0.449048\pi$
$692$	−32.2645	−1.22651
$693$	−11.7940	−0.448017
$694$	0.618627	0.0234828
$695$	37.3034	1.41500
$696$	0.466578	0.0176856
$697$	−10.0772	−0.381701
$698$	0.601839	0.0227800
$699$	76.3265	2.88693
$700$	−23.9162	−0.903947
$701$	−49.5870	−1.87288	−0.936438	−	0.350832i	$-0.885899\pi$
$701$	−49.5870	−1.87288	−0.936438	+	0.350832i	$0.885899\pi$
$702$	0	0
$703$	−33.6203	−1.26801
$704$	19.0659	0.718574
$705$	−45.0128	−1.69528
$706$	−0.397445	−0.0149580
$707$	−7.18413	−0.270187
$708$	20.2746	0.761968
$709$	14.4361	0.542160	0.271080	−	0.962557i	$-0.412619\pi$
$709$	14.4361	0.542160	0.271080	+	0.962557i	$0.412619\pi$
$710$	−3.32226	−0.124682
$711$	36.4695	1.36771
$712$	−3.95550	−0.148239
$713$	−12.7974	−0.479266
$714$	−0.621148	−0.0232459
$715$	0	0
$716$	2.81227	0.105100
$717$	47.5793	1.77688
$718$	−0.776031	−0.0289612
$719$	19.6313	0.732122	0.366061	−	0.930591i	$-0.380706\pi$
$719$	19.6313	0.732122	0.366061	+	0.930591i	$0.380706\pi$
$720$	73.8357	2.75169
$721$	15.2582	0.568244
$722$	−2.42252	−0.0901569
$723$	73.0248	2.71582
$724$	37.9493	1.41037
$725$	3.43394	0.127533
$726$	1.85119	0.0687043
$727$	−36.3713	−1.34894	−0.674468	−	0.738304i	$-0.735627\pi$
$727$	−36.3713	−1.34894	−0.674468	+	0.738304i	$0.735627\pi$
$728$	0	0
$729$	−44.0350	−1.63093
$730$	−1.62539	−0.0601585
$731$	−12.2430	−0.452825
$732$	−10.5849	−0.391228
$733$	24.4766	0.904064	0.452032	−	0.892002i	$-0.350699\pi$
$733$	24.4766	0.904064	0.452032	+	0.892002i	$0.350699\pi$
$734$	1.57040	0.0579646
$735$	11.4123	0.420949
$736$	−11.6014	−0.427634
$737$	8.63325	0.318010
$738$	4.63329	0.170554
$739$	36.3349	1.33660	0.668300	−	0.743892i	$-0.267022\pi$
$739$	36.3349	1.33660	0.668300	+	0.743892i	$0.267022\pi$
$740$	−46.3410	−1.70353
$741$	0	0
$742$	0.161841	0.00594139
$743$	1.66844	0.0612092	0.0306046	−	0.999532i	$-0.490257\pi$
$743$	1.66844	0.0612092	0.0306046	+	0.999532i	$0.490257\pi$
$744$	−3.20676	−0.117565
$745$	−55.9222	−2.04883
$746$	3.82614	0.140085
$747$	−48.6274	−1.77918
$748$	7.59201	0.277591
$749$	−3.47375	−0.126928
$750$	−12.1155	−0.442396
$751$	−25.6435	−0.935743	−0.467871	−	0.883797i	$-0.654979\pi$
$751$	−25.6435	−0.935743	−0.467871	+	0.883797i	$0.654979\pi$
$752$	−15.2489	−0.556069
$753$	−21.8562	−0.796484
$754$	0	0
$755$	−20.7823	−0.756347
$756$	−8.83939	−0.321486
$757$	29.6442	1.07744	0.538719	−	0.842485i	$-0.318908\pi$
$757$	29.6442	1.07744	0.538719	+	0.842485i	$0.318908\pi$
$758$	−0.0895209	−0.00325154
$759$	−46.2150	−1.67750
$760$	−14.5993	−0.529573
$761$	−28.5689	−1.03562	−0.517811	−	0.855495i	$-0.673253\pi$
$761$	−28.5689	−1.03562	−0.517811	+	0.855495i	$0.673253\pi$
$762$	3.29728	0.119448
$763$	16.6557	0.602977
$764$	−27.6883	−1.00173
$765$	28.7160	1.03823
$766$	1.53665	0.0555213
$767$	0	0
$768$	39.3015	1.41817
$769$	−26.6293	−0.960276	−0.480138	−	0.877193i	$-0.659413\pi$
$769$	−26.6293	−0.960276	−0.480138	+	0.877193i	$0.659413\pi$
$770$	1.57982	0.0569327
$771$	−55.1289	−1.98542
$772$	2.51026	0.0903462
$773$	45.5999	1.64011	0.820056	−	0.572283i	$-0.193942\pi$
$773$	45.5999	1.64011	0.820056	+	0.572283i	$0.193942\pi$
$774$	5.62909	0.202333
$775$	−23.6012	−0.847781
$776$	0.300321	0.0107809
$777$	15.6447	0.561252
$778$	0.464142	0.0166403
$779$	39.7556	1.42439
$780$	0	0
$781$	−13.7087	−0.490537
$782$	−1.47563	−0.0527684
$783$	1.26918	0.0453568
$784$	3.86611	0.138075
$785$	−47.5205	−1.69608
$786$	7.73471	0.275888
$787$	27.5508	0.982079	0.491040	−	0.871137i	$-0.336617\pi$
$787$	27.5508	0.982079	0.491040	+	0.871137i	$0.336617\pi$
$788$	5.57749	0.198690
$789$	−7.96242	−0.283470
$790$	−4.88512	−0.173805
$791$	18.2871	0.650215
$792$	−7.02083	−0.249474
$793$	0	0
$794$	−1.32961	−0.0471860
$795$	−12.3412	−0.437697
$796$	−38.0886	−1.35001
$797$	14.4713	0.512599	0.256299	−	0.966597i	$-0.417497\pi$
$797$	14.4713	0.512599	0.256299	+	0.966597i	$0.417497\pi$
$798$	2.45049	0.0867465
$799$	−5.93055	−0.209808
$800$	−21.3956	−0.756449
$801$	−30.6938	−1.08451
$802$	0.795640	0.0280950
$803$	−6.70691	−0.236682
$804$	18.4580	0.650964
$805$	27.1116	0.955559
$806$	0	0
$807$	−34.7425	−1.22299
$808$	−4.27662	−0.150451
$809$	45.2178	1.58977	0.794886	−	0.606758i	$-0.207530\pi$
$809$	45.2178	1.58977	0.794886	+	0.606758i	$0.207530\pi$
$810$	0.940510	0.0330462
$811$	21.8610	0.767644	0.383822	−	0.923407i	$-0.374608\pi$
$811$	21.8610	0.767644	0.383822	+	0.923407i	$0.374608\pi$
$812$	−0.561537	−0.0197061
$813$	−59.0726	−2.07176
$814$	2.16572	0.0759084
$815$	−53.0473	−1.85816
$816$	16.0459	0.561719
$817$	48.2999	1.68980
$818$	0.256226	0.00895872
$819$	0	0
$820$	54.7978	1.91362
$821$	−38.5812	−1.34649	−0.673247	−	0.739417i	$-0.735101\pi$
$821$	−38.5812	−1.34649	−0.673247	+	0.739417i	$0.735101\pi$
$822$	−0.960786	−0.0335113
$823$	−12.9067	−0.449899	−0.224949	−	0.974370i	$-0.572222\pi$
$823$	−12.9067	−0.449899	−0.224949	+	0.974370i	$0.572222\pi$
$824$	9.08301	0.316421
$825$	−85.2307	−2.96735
$826$	0.555856	0.0193407
$827$	−18.4205	−0.640544	−0.320272	−	0.947326i	$-0.603774\pi$
$827$	−18.4205	−0.640544	−0.320272	+	0.947326i	$0.603774\pi$
$828$	−59.9038	−2.08180
$829$	24.6596	0.856464	0.428232	−	0.903669i	$-0.359137\pi$
$829$	24.6596	0.856464	0.428232	+	0.903669i	$0.359137\pi$
$830$	6.51368	0.226093
$831$	−37.5576	−1.30286
$832$	0	0
$833$	1.50360	0.0520966
$834$	−3.72731	−0.129066
$835$	−89.5461	−3.09887
$836$	−29.9512	−1.03588
$837$	−8.72299	−0.301511
$838$	0.948757	0.0327743
$839$	37.4397	1.29256	0.646281	−	0.763100i	$-0.276323\pi$
$839$	37.4397	1.29256	0.646281	+	0.763100i	$0.276323\pi$
$840$	6.79360	0.234402
$841$	−28.9194	−0.997220
$842$	−5.05312	−0.174142
$843$	84.8014	2.92071
$844$	25.4009	0.874333
$845$	0	0
$846$	2.72674	0.0937473
$847$	−4.48114	−0.153974
$848$	−4.18079	−0.143569
$849$	76.6931	2.63210
$850$	−2.72139	−0.0933429
$851$	37.1664	1.27405
$852$	−29.3095	−1.00413
$853$	−17.6278	−0.603563	−0.301782	−	0.953377i	$-0.597581\pi$
$853$	−17.6278	−0.603563	−0.301782	+	0.953377i	$0.597581\pi$
$854$	−0.290199	−0.00993039
$855$	−113.287	−3.87435
$856$	−2.06788	−0.0706786
$857$	−2.90411	−0.0992026	−0.0496013	−	0.998769i	$-0.515795\pi$
$857$	−2.90411	−0.0992026	−0.0496013	+	0.998769i	$0.515795\pi$
$858$	0	0
$859$	18.7011	0.638074	0.319037	−	0.947742i	$-0.396640\pi$
$859$	18.7011	0.638074	0.319037	+	0.947742i	$0.396640\pi$
$860$	66.5750	2.27019
$861$	−18.4997	−0.630469
$862$	−4.44519	−0.151404
$863$	−36.1575	−1.23082	−0.615409	−	0.788208i	$-0.711009\pi$
$863$	−36.1575	−1.23082	−0.615409	+	0.788208i	$0.711009\pi$
$864$	−7.90779	−0.269028
$865$	67.4530	2.29347
$866$	0.0303912	0.00103274
$867$	−40.6847	−1.38172
$868$	3.85941	0.130997
$869$	−20.1576	−0.683800
$870$	−0.484974	−0.0164422
$871$	0	0
$872$	9.91493	0.335762
$873$	2.33042	0.0788729
$874$	5.82151	0.196915
$875$	29.3277	0.991458
$876$	−14.3395	−0.484486
$877$	−16.1122	−0.544069	−0.272035	−	0.962287i	$-0.587697\pi$
$877$	−16.1122	−0.544069	−0.272035	+	0.962287i	$0.587697\pi$
$878$	−4.48907	−0.151499
$879$	−0.405187	−0.0136666
$880$	−40.8109	−1.37573
$881$	−8.87299	−0.298939	−0.149469	−	0.988766i	$-0.547757\pi$
$881$	−8.87299	−0.298939	−0.149469	+	0.988766i	$0.547757\pi$
$882$	−0.691324	−0.0232781
$883$	14.8164	0.498613	0.249306	−	0.968425i	$-0.419797\pi$
$883$	14.8164	0.498613	0.249306	+	0.968425i	$0.419797\pi$
$884$	0	0
$885$	−42.3868	−1.42482
$886$	−0.175271	−0.00588836
$887$	22.0508	0.740392	0.370196	−	0.928954i	$-0.379290\pi$
$887$	22.0508	0.740392	0.370196	+	0.928954i	$0.379290\pi$
$888$	9.31312	0.312528
$889$	−7.98164	−0.267696
$890$	4.11146	0.137817
$891$	3.88086	0.130014
$892$	−8.92965	−0.298987
$893$	23.3966	0.782937
$894$	5.58768	0.186880
$895$	−5.87942	−0.196527
$896$	4.65593	0.155544
$897$	0	0
$898$	−1.39088	−0.0464143
$899$	−0.554142	−0.0184817
$900$	−110.476	−3.68253
$901$	−1.62598	−0.0541694
$902$	−2.56094	−0.0852700
$903$	−22.4757	−0.747946
$904$	10.8861	0.362066
$905$	−79.3379	−2.63728
$906$	2.07655	0.0689886
$907$	−10.0602	−0.334044	−0.167022	−	0.985953i	$-0.553415\pi$
$907$	−10.0602	−0.334044	−0.167022	+	0.985953i	$0.553415\pi$
$908$	19.5174	0.647709
$909$	−33.1856	−1.10070
$910$	0	0
$911$	−33.0112	−1.09371	−0.546856	−	0.837227i	$-0.684175\pi$
$911$	−33.0112	−1.09371	−0.546856	+	0.837227i	$0.684175\pi$
$912$	−63.3027	−2.09616
$913$	26.8776	0.889519
$914$	−4.54740	−0.150415
$915$	22.1291	0.731564
$916$	−8.79275	−0.290521
$917$	−18.7232	−0.618296
$918$	−1.00582	−0.0331971
$919$	13.5362	0.446518	0.223259	−	0.974759i	$-0.428330\pi$
$919$	13.5362	0.446518	0.223259	+	0.974759i	$0.428330\pi$
$920$	16.1392	0.532094
$921$	−87.3600	−2.87861
$922$	−4.18832	−0.137935
$923$	0	0
$924$	13.9374	0.458507
$925$	68.5431	2.25368
$926$	−0.655541	−0.0215424
$927$	70.4820	2.31493
$928$	−0.502356	−0.0164906
$929$	16.5687	0.543601	0.271801	−	0.962354i	$-0.412381\pi$
$929$	16.5687	0.543601	0.271801	+	0.962354i	$0.412381\pi$
$930$	3.33319	0.109300
$931$	−5.93185	−0.194408
$932$	−54.6835	−1.79122
$933$	52.0615	1.70442
$934$	−1.43533	−0.0469656
$935$	−15.8721	−0.519072
$936$	0	0
$937$	35.2063	1.15014	0.575070	−	0.818104i	$-0.304975\pi$
$937$	35.2063	1.15014	0.575070	+	0.818104i	$0.304975\pi$
$938$	0.506051	0.0165231
$939$	−93.2420	−3.04284
$940$	32.2491	1.05185
$941$	29.0236	0.946142	0.473071	−	0.881024i	$-0.343145\pi$
$941$	29.0236	0.946142	0.473071	+	0.881024i	$0.343145\pi$
$942$	4.74819	0.154704
$943$	−43.9489	−1.43117
$944$	−14.3592	−0.467353
$945$	18.4799	0.601151
$946$	−3.11134	−0.101158
$947$	−43.1704	−1.40285	−0.701425	−	0.712744i	$-0.747452\pi$
$947$	−43.1704	−1.40285	−0.701425	+	0.712744i	$0.747452\pi$
$948$	−43.0973	−1.39973
$949$	0	0
$950$	10.7362	0.348327
$951$	−60.9606	−1.97678
$952$	0.895074	0.0290095
$953$	12.7569	0.413236	0.206618	−	0.978422i	$-0.433754\pi$
$953$	12.7569	0.413236	0.206618	+	0.978422i	$0.433754\pi$
$954$	0.747593	0.0242042
$955$	57.8859	1.87314
$956$	−34.0878	−1.10248
$957$	−2.00117	−0.0646885
$958$	−0.0954753	−0.00308467
$959$	2.32575	0.0751025
$960$	−85.2208	−2.75049
$961$	−27.1914	−0.877143
$962$	0	0
$963$	−16.0463	−0.517083
$964$	−52.3181	−1.68505
$965$	−5.24802	−0.168940
$966$	−2.70896	−0.0871594
$967$	24.7647	0.796380	0.398190	−	0.917303i	$-0.369639\pi$
$967$	24.7647	0.796380	0.398190	+	0.917303i	$0.369639\pi$
$968$	−2.66757	−0.0857390
$969$	−24.6195	−0.790893
$970$	−0.312162	−0.0100229
$971$	6.83748	0.219425	0.109713	−	0.993963i	$-0.465007\pi$
$971$	6.83748	0.219425	0.109713	+	0.993963i	$0.465007\pi$
$972$	34.8155	1.11671
$973$	9.02263	0.289252
$974$	−5.18351	−0.166090
$975$	0	0
$976$	7.49660	0.239960
$977$	15.5220	0.496594	0.248297	−	0.968684i	$-0.420129\pi$
$977$	15.5220	0.496594	0.248297	+	0.968684i	$0.420129\pi$
$978$	5.30042	0.169489
$979$	16.9653	0.542212
$980$	−8.17626	−0.261181
$981$	76.9376	2.45643
$982$	−4.27862	−0.136536
$983$	−2.75887	−0.0879941	−0.0439971	−	0.999032i	$-0.514009\pi$
$983$	−2.75887	−0.0879941	−0.0439971	+	0.999032i	$0.514009\pi$
$984$	−11.0127	−0.351071
$985$	−11.6605	−0.371533
$986$	−0.0638966	−0.00203488
$987$	−10.8873	−0.346547
$988$	0	0
$989$	−53.3945	−1.69784
$990$	7.29765	0.231935
$991$	24.2991	0.771886	0.385943	−	0.922523i	$-0.373876\pi$
$991$	24.2991	0.771886	0.385943	+	0.922523i	$0.373876\pi$
$992$	3.45265	0.109622
$993$	−69.9460	−2.21967
$994$	−0.803558	−0.0254873
$995$	79.6291	2.52441
$996$	57.4647	1.82084
$997$	13.5557	0.429313	0.214657	−	0.976690i	$-0.431137\pi$
$997$	13.5557	0.429313	0.214657	+	0.976690i	$0.431137\pi$
$998$	−5.26500	−0.166661
$999$	25.3335	0.801515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.6	yes	12
7.6	odd	2		8281.2.a.cq.1.6		12
13.5	odd	4		1183.2.c.j.337.13		24
13.8	odd	4		1183.2.c.j.337.12		24
13.12	even	2		1183.2.a.q.1.7	✓	12
91.90	odd	2		8281.2.a.cn.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.7	✓	12	13.12	even	2
1183.2.a.r.1.6	yes	12	1.1	even	1	trivial
1183.2.c.j.337.12		24	13.8	odd	4
1183.2.c.j.337.13		24	13.5	odd	4
8281.2.a.cn.1.7		12	91.90	odd	2
8281.2.a.cq.1.6		12	7.6	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-0.149660 q^{2} +2.76031 q^{3} -1.97760 q^{4} +4.13443 q^{5} -0.413107 q^{6} +1.00000 q^{7} +0.595288 q^{8} +4.61930 q^{9} +O(q^{10})\)	\(q-0.149660 q^{2} +2.76031 q^{3} -1.97760 q^{4} +4.13443 q^{5} -0.413107 q^{6} +1.00000 q^{7} +0.595288 q^{8} +4.61930 q^{9} -0.618759 q^{10} -2.55320 q^{11} -5.45879 q^{12} -0.149660 q^{14} +11.4123 q^{15} +3.86611 q^{16} +1.50360 q^{17} -0.691324 q^{18} -5.93185 q^{19} -8.17626 q^{20} +2.76031 q^{21} +0.382113 q^{22} +6.55752 q^{23} +1.64318 q^{24} +12.0935 q^{25} +4.46975 q^{27} -1.97760 q^{28} +0.283949 q^{29} -1.70797 q^{30} -1.95156 q^{31} -1.76918 q^{32} -7.04763 q^{33} -0.225029 q^{34} +4.13443 q^{35} -9.13513 q^{36} +5.66775 q^{37} +0.887760 q^{38} +2.46118 q^{40} -6.70206 q^{41} -0.413107 q^{42} -8.14248 q^{43} +5.04922 q^{44} +19.0982 q^{45} -0.981398 q^{46} -3.94423 q^{47} +10.6717 q^{48} +1.00000 q^{49} -1.80992 q^{50} +4.15040 q^{51} -1.08139 q^{53} -0.668943 q^{54} -10.5561 q^{55} +0.595288 q^{56} -16.3737 q^{57} -0.0424957 q^{58} -3.71413 q^{59} -22.5690 q^{60} +1.93905 q^{61} +0.292070 q^{62} +4.61930 q^{63} -7.46745 q^{64} +1.05475 q^{66} -3.38134 q^{67} -2.97352 q^{68} +18.1008 q^{69} -0.618759 q^{70} +5.36923 q^{71} +2.74981 q^{72} +2.62686 q^{73} -0.848236 q^{74} +33.3819 q^{75} +11.7308 q^{76} -2.55320 q^{77} +7.89503 q^{79} +15.9842 q^{80} -1.51999 q^{81} +1.00303 q^{82} -10.5270 q^{83} -5.45879 q^{84} +6.21653 q^{85} +1.21860 q^{86} +0.783786 q^{87} -1.51989 q^{88} -6.64469 q^{89} -2.85823 q^{90} -12.9682 q^{92} -5.38690 q^{93} +0.590294 q^{94} -24.5248 q^{95} -4.88347 q^{96} +0.504498 q^{97} -0.149660 q^{98} -11.7940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more