LMFDB - Embedded newform 5566.2.a.bt.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, 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("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.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:	$44.4447337650$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.0589037$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.941096 q^{3} +1.00000 q^{4} -1.56994 q^{5} -0.941096 q^{6} +3.96075 q^{7} -1.00000 q^{8} -2.11434 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.941096 q^{3} +1.00000 q^{4} -1.56994 q^{5} -0.941096 q^{6} +3.96075 q^{7} -1.00000 q^{8} -2.11434 q^{9} +1.56994 q^{10} +0.941096 q^{12} -2.44788 q^{13} -3.96075 q^{14} -1.47747 q^{15} +1.00000 q^{16} -1.45435 q^{17} +2.11434 q^{18} -2.84870 q^{19} -1.56994 q^{20} +3.72744 q^{21} -1.00000 q^{23} -0.941096 q^{24} -2.53528 q^{25} +2.44788 q^{26} -4.81308 q^{27} +3.96075 q^{28} +5.71692 q^{29} +1.47747 q^{30} +1.90865 q^{31} -1.00000 q^{32} +1.45435 q^{34} -6.21814 q^{35} -2.11434 q^{36} +3.57515 q^{37} +2.84870 q^{38} -2.30369 q^{39} +1.56994 q^{40} -1.83015 q^{41} -3.72744 q^{42} -5.06793 q^{43} +3.31939 q^{45} +1.00000 q^{46} +6.81998 q^{47} +0.941096 q^{48} +8.68752 q^{49} +2.53528 q^{50} -1.36868 q^{51} -2.44788 q^{52} +14.3581 q^{53} +4.81308 q^{54} -3.96075 q^{56} -2.68091 q^{57} -5.71692 q^{58} +0.992373 q^{59} -1.47747 q^{60} -12.2576 q^{61} -1.90865 q^{62} -8.37436 q^{63} +1.00000 q^{64} +3.84302 q^{65} +7.10203 q^{67} -1.45435 q^{68} -0.941096 q^{69} +6.21814 q^{70} +13.8215 q^{71} +2.11434 q^{72} -0.691036 q^{73} -3.57515 q^{74} -2.38594 q^{75} -2.84870 q^{76} +2.30369 q^{78} +9.17542 q^{79} -1.56994 q^{80} +1.81344 q^{81} +1.83015 q^{82} +9.92842 q^{83} +3.72744 q^{84} +2.28325 q^{85} +5.06793 q^{86} +5.38017 q^{87} +10.2925 q^{89} -3.31939 q^{90} -9.69542 q^{91} -1.00000 q^{92} +1.79622 q^{93} -6.81998 q^{94} +4.47230 q^{95} -0.941096 q^{96} -19.3138 q^{97} -8.68752 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.941096	0.543342	0.271671	−	0.962390i	$-0.412424\pi$
$3$	0.941096	0.543342	0.271671	+	0.962390i	$0.412424\pi$
$4$	1.00000	0.500000
$5$	−1.56994	−0.702100	−0.351050	−	0.936357i	$-0.614175\pi$
$5$	−1.56994	−0.702100	−0.351050	+	0.936357i	$0.614175\pi$
$6$	−0.941096	−0.384201
$7$	3.96075	1.49702	0.748511	−	0.663123i	$-0.230769\pi$
$7$	3.96075	1.49702	0.748511	+	0.663123i	$0.230769\pi$
$8$	−1.00000	−0.353553
$9$	−2.11434	−0.704779
$10$	1.56994	0.496459
$11$	0	0
$11$	0	0
$12$	0.941096	0.271671
$13$	−2.44788	−0.678919	−0.339459	−	0.940621i	$-0.610244\pi$
$13$	−2.44788	−0.678919	−0.339459	+	0.940621i	$0.610244\pi$
$14$	−3.96075	−1.05855
$15$	−1.47747	−0.381480
$16$	1.00000	0.250000
$17$	−1.45435	−0.352732	−0.176366	−	0.984325i	$-0.556434\pi$
$17$	−1.45435	−0.352732	−0.176366	+	0.984325i	$0.556434\pi$
$18$	2.11434	0.498354
$19$	−2.84870	−0.653538	−0.326769	−	0.945104i	$-0.605960\pi$
$19$	−2.84870	−0.653538	−0.326769	+	0.945104i	$0.605960\pi$
$20$	−1.56994	−0.351050
$21$	3.72744	0.813395
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.941096	−0.192100
$25$	−2.53528	−0.507056
$26$	2.44788	0.480068
$27$	−4.81308	−0.926279
$28$	3.96075	0.748511
$29$	5.71692	1.06161	0.530803	−	0.847495i	$-0.321891\pi$
$29$	5.71692	1.06161	0.530803	+	0.847495i	$0.321891\pi$
$30$	1.47747	0.269747
$31$	1.90865	0.342804	0.171402	−	0.985201i	$-0.445170\pi$
$31$	1.90865	0.342804	0.171402	+	0.985201i	$0.445170\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.45435	0.249419
$35$	−6.21814	−1.05106
$36$	−2.11434	−0.352390
$37$	3.57515	0.587752	0.293876	−	0.955844i	$-0.405055\pi$
$37$	3.57515	0.587752	0.293876	+	0.955844i	$0.405055\pi$
$38$	2.84870	0.462121
$39$	−2.30369	−0.368885
$40$	1.56994	0.248230
$41$	−1.83015	−0.285821	−0.142910	−	0.989736i	$-0.545646\pi$
$41$	−1.83015	−0.285821	−0.142910	+	0.989736i	$0.545646\pi$
$42$	−3.72744	−0.575157
$43$	−5.06793	−0.772852	−0.386426	−	0.922320i	$-0.626290\pi$
$43$	−5.06793	−0.772852	−0.386426	+	0.922320i	$0.626290\pi$
$44$	0	0
$45$	3.31939	0.494825
$46$	1.00000	0.147442
$47$	6.81998	0.994797	0.497398	−	0.867522i	$-0.334289\pi$
$47$	6.81998	0.994797	0.497398	+	0.867522i	$0.334289\pi$
$48$	0.941096	0.135836
$49$	8.68752	1.24107
$50$	2.53528	0.358543
$51$	−1.36868	−0.191654
$52$	−2.44788	−0.339459
$53$	14.3581	1.97224	0.986120	−	0.166032i	$-0.0530955\pi$
$53$	14.3581	1.97224	0.986120	+	0.166032i	$0.0530955\pi$
$54$	4.81308	0.654978
$55$	0	0
$56$	−3.96075	−0.529277
$57$	−2.68091	−0.355095
$58$	−5.71692	−0.750668
$59$	0.992373	0.129196	0.0645980	−	0.997911i	$-0.479424\pi$
$59$	0.992373	0.129196	0.0645980	+	0.997911i	$0.479424\pi$
$60$	−1.47747	−0.190740
$61$	−12.2576	−1.56942	−0.784712	−	0.619861i	$-0.787189\pi$
$61$	−12.2576	−1.56942	−0.784712	+	0.619861i	$0.787189\pi$
$62$	−1.90865	−0.242399
$63$	−8.37436	−1.05507
$64$	1.00000	0.125000
$65$	3.84302	0.476669
$66$	0	0
$67$	7.10203	0.867651	0.433826	−	0.900997i	$-0.357163\pi$
$67$	7.10203	0.867651	0.433826	+	0.900997i	$0.357163\pi$
$68$	−1.45435	−0.176366
$69$	−0.941096	−0.113295
$70$	6.21814	0.743210
$71$	13.8215	1.64031	0.820156	−	0.572140i	$-0.193887\pi$
$71$	13.8215	1.64031	0.820156	+	0.572140i	$0.193887\pi$
$72$	2.11434	0.249177
$73$	−0.691036	−0.0808796	−0.0404398	−	0.999182i	$-0.512876\pi$
$73$	−0.691036	−0.0808796	−0.0404398	+	0.999182i	$0.512876\pi$
$74$	−3.57515	−0.415603
$75$	−2.38594	−0.275505
$76$	−2.84870	−0.326769
$77$	0	0
$78$	2.30369	0.260841
$79$	9.17542	1.03232	0.516158	−	0.856494i	$-0.327362\pi$
$79$	9.17542	1.03232	0.516158	+	0.856494i	$0.327362\pi$
$80$	−1.56994	−0.175525
$81$	1.81344	0.201493
$82$	1.83015	0.202106
$83$	9.92842	1.08979	0.544893	−	0.838506i	$-0.316570\pi$
$83$	9.92842	1.08979	0.544893	+	0.838506i	$0.316570\pi$
$84$	3.72744	0.406697
$85$	2.28325	0.247653
$86$	5.06793	0.546489
$87$	5.38017	0.576815
$88$	0	0
$89$	10.2925	1.09100	0.545499	−	0.838111i	$-0.316340\pi$
$89$	10.2925	1.09100	0.545499	+	0.838111i	$0.316340\pi$
$90$	−3.31939	−0.349894
$91$	−9.69542	−1.01636
$92$	−1.00000	−0.104257
$93$	1.79622	0.186260
$94$	−6.81998	−0.703428
$95$	4.47230	0.458849
$96$	−0.941096	−0.0960502
$97$	−19.3138	−1.96102	−0.980512	−	0.196461i	$-0.937055\pi$
$97$	−19.3138	−1.96102	−0.980512	+	0.196461i	$0.937055\pi$
$98$	−8.68752	−0.877572
$99$	0	0
$100$	−2.53528	−0.253528
$101$	17.0037	1.69193	0.845965	−	0.533238i	$-0.179025\pi$
$101$	17.0037	1.69193	0.845965	+	0.533238i	$0.179025\pi$
$102$	1.36868	0.135520
$103$	8.44460	0.832071	0.416036	−	0.909348i	$-0.363419\pi$
$103$	8.44460	0.832071	0.416036	+	0.909348i	$0.363419\pi$
$104$	2.44788	0.240034
$105$	−5.85187	−0.571084
$106$	−14.3581	−1.39458
$107$	1.81325	0.175294	0.0876469	−	0.996152i	$-0.472065\pi$
$107$	1.81325	0.175294	0.0876469	+	0.996152i	$0.472065\pi$
$108$	−4.81308	−0.463139
$109$	−2.57364	−0.246510	−0.123255	−	0.992375i	$-0.539333\pi$
$109$	−2.57364	−0.246510	−0.123255	+	0.992375i	$0.539333\pi$
$110$	0	0
$111$	3.36457	0.319350
$112$	3.96075	0.374255
$113$	8.81602	0.829342	0.414671	−	0.909971i	$-0.363897\pi$
$113$	8.81602	0.829342	0.414671	+	0.909971i	$0.363897\pi$
$114$	2.68091	0.251090
$115$	1.56994	0.146398
$116$	5.71692	0.530803
$117$	5.17564	0.478488
$118$	−0.992373	−0.0913553
$119$	−5.76031	−0.528047
$120$	1.47747	0.134874
$121$	0	0
$122$	12.2576	1.10975
$123$	−1.72234	−0.155299
$124$	1.90865	0.171402
$125$	11.8300	1.05810
$126$	8.37436	0.746047
$127$	0.758584	0.0673134	0.0336567	−	0.999433i	$-0.489285\pi$
$127$	0.758584	0.0673134	0.0336567	+	0.999433i	$0.489285\pi$
$128$	−1.00000	−0.0883883
$129$	−4.76941	−0.419923
$130$	−3.84302	−0.337056
$131$	−6.90871	−0.603617	−0.301808	−	0.953369i	$-0.597590\pi$
$131$	−6.90871	−0.603617	−0.301808	+	0.953369i	$0.597590\pi$
$132$	0	0
$133$	−11.2830	−0.978360
$134$	−7.10203	−0.613522
$135$	7.55627	0.650340
$136$	1.45435	0.124710
$137$	7.15747	0.611504	0.305752	−	0.952111i	$-0.401092\pi$
$137$	7.15747	0.611504	0.305752	+	0.952111i	$0.401092\pi$
$138$	0.941096	0.0801114
$139$	−5.71115	−0.484414	−0.242207	−	0.970225i	$-0.577871\pi$
$139$	−5.71115	−0.484414	−0.242207	+	0.970225i	$0.577871\pi$
$140$	−6.21814	−0.525529
$141$	6.41826	0.540515
$142$	−13.8215	−1.15988
$143$	0	0
$144$	−2.11434	−0.176195
$145$	−8.97523	−0.745353
$146$	0.691036	0.0571905
$147$	8.17579	0.674328
$148$	3.57515	0.293876
$149$	−6.04628	−0.495330	−0.247665	−	0.968846i	$-0.579663\pi$
$149$	−6.04628	−0.495330	−0.247665	+	0.968846i	$0.579663\pi$
$150$	2.38594	0.194811
$151$	12.5111	1.01814	0.509070	−	0.860725i	$-0.329990\pi$
$151$	12.5111	1.01814	0.509070	+	0.860725i	$0.329990\pi$
$152$	2.84870	0.231060
$153$	3.07499	0.248598
$154$	0	0
$155$	−2.99647	−0.240682
$156$	−2.30369	−0.184443
$157$	1.83735	0.146637	0.0733184	−	0.997309i	$-0.476641\pi$
$157$	1.83735	0.146637	0.0733184	+	0.997309i	$0.476641\pi$
$158$	−9.17542	−0.729957
$159$	13.5124	1.07160
$160$	1.56994	0.124115
$161$	−3.96075	−0.312151
$162$	−1.81344	−0.142477
$163$	−3.81662	−0.298940	−0.149470	−	0.988766i	$-0.547757\pi$
$163$	−3.81662	−0.298940	−0.149470	+	0.988766i	$0.547757\pi$
$164$	−1.83015	−0.142910
$165$	0	0
$166$	−9.92842	−0.770595
$167$	2.33223	0.180474	0.0902368	−	0.995920i	$-0.471238\pi$
$167$	2.33223	0.180474	0.0902368	+	0.995920i	$0.471238\pi$
$168$	−3.72744	−0.287579
$169$	−7.00790	−0.539069
$170$	−2.28325	−0.175117
$171$	6.02312	0.460600
$172$	−5.06793	−0.386426
$173$	6.19752	0.471188	0.235594	−	0.971852i	$-0.424296\pi$
$173$	6.19752	0.471188	0.235594	+	0.971852i	$0.424296\pi$
$174$	−5.38017	−0.407870
$175$	−10.0416	−0.759074
$176$	0	0
$177$	0.933918	0.0701976
$178$	−10.2925	−0.771452
$179$	10.0123	0.748358	0.374179	−	0.927357i	$-0.377925\pi$
$179$	10.0123	0.748358	0.374179	+	0.927357i	$0.377925\pi$
$180$	3.31939	0.247413
$181$	13.5756	1.00907	0.504534	−	0.863392i	$-0.331664\pi$
$181$	13.5756	1.00907	0.504534	+	0.863392i	$0.331664\pi$
$182$	9.69542	0.718672
$183$	−11.5356	−0.852734
$184$	1.00000	0.0737210
$185$	−5.61279	−0.412660
$186$	−1.79622	−0.131706
$187$	0	0
$188$	6.81998	0.497398
$189$	−19.0634	−1.38666
$190$	−4.47230	−0.324455
$191$	−9.75145	−0.705590	−0.352795	−	0.935701i	$-0.614769\pi$
$191$	−9.75145	−0.705590	−0.352795	+	0.935701i	$0.614769\pi$
$192$	0.941096	0.0679178
$193$	−11.0527	−0.795587	−0.397794	−	0.917475i	$-0.630224\pi$
$193$	−11.0527	−0.795587	−0.397794	+	0.917475i	$0.630224\pi$
$194$	19.3138	1.38665
$195$	3.61666	0.258994
$196$	8.68752	0.620537
$197$	−6.96722	−0.496394	−0.248197	−	0.968710i	$-0.579838\pi$
$197$	−6.96722	−0.496394	−0.248197	+	0.968710i	$0.579838\pi$
$198$	0	0
$199$	25.8586	1.83307	0.916533	−	0.399959i	$-0.130976\pi$
$199$	25.8586	1.83307	0.916533	+	0.399959i	$0.130976\pi$
$200$	2.53528	0.179271
$201$	6.68370	0.471432
$202$	−17.0037	−1.19638
$203$	22.6433	1.58925
$204$	−1.36868	−0.0958270
$205$	2.87323	0.200675
$206$	−8.44460	−0.588363
$207$	2.11434	0.146957
$208$	−2.44788	−0.169730
$209$	0	0
$210$	5.85187	0.403818
$211$	−13.8943	−0.956524	−0.478262	−	0.878217i	$-0.658733\pi$
$211$	−13.8943	−0.956524	−0.478262	+	0.878217i	$0.658733\pi$
$212$	14.3581	0.986120
$213$	13.0074	0.891251
$214$	−1.81325	−0.123951
$215$	7.95635	0.542619
$216$	4.81308	0.327489
$217$	7.55968	0.513185
$218$	2.57364	0.174309
$219$	−0.650331	−0.0439453
$220$	0	0
$221$	3.56007	0.239476
$222$	−3.36457	−0.225815
$223$	11.2567	0.753804	0.376902	−	0.926253i	$-0.376989\pi$
$223$	11.2567	0.753804	0.376902	+	0.926253i	$0.376989\pi$
$224$	−3.96075	−0.264639
$225$	5.36044	0.357363
$226$	−8.81602	−0.586433
$227$	−9.64070	−0.639876	−0.319938	−	0.947438i	$-0.603662\pi$
$227$	−9.64070	−0.639876	−0.319938	+	0.947438i	$0.603662\pi$
$228$	−2.68091	−0.177547
$229$	−29.7112	−1.96337	−0.981686	−	0.190504i	$-0.938988\pi$
$229$	−29.7112	−1.96337	−0.981686	+	0.190504i	$0.938988\pi$
$230$	−1.56994	−0.103519
$231$	0	0
$232$	−5.71692	−0.375334
$233$	−17.3712	−1.13803	−0.569013	−	0.822329i	$-0.692675\pi$
$233$	−17.3712	−1.13803	−0.569013	+	0.822329i	$0.692675\pi$
$234$	−5.17564	−0.338342
$235$	−10.7070	−0.698446
$236$	0.992373	0.0645980
$237$	8.63495	0.560900
$238$	5.76031	0.373386
$239$	15.3344	0.991897	0.495949	−	0.868352i	$-0.334820\pi$
$239$	15.3344	0.991897	0.495949	+	0.868352i	$0.334820\pi$
$240$	−1.47747	−0.0953701
$241$	2.77209	0.178566	0.0892828	−	0.996006i	$-0.471542\pi$
$241$	2.77209	0.178566	0.0892828	+	0.996006i	$0.471542\pi$
$242$	0	0
$243$	16.1459	1.03576
$244$	−12.2576	−0.784712
$245$	−13.6389	−0.871357
$246$	1.72234	0.109813
$247$	6.97328	0.443699
$248$	−1.90865	−0.121199
$249$	9.34360	0.592126
$250$	−11.8300	−0.748192
$251$	1.77135	0.111807	0.0559033	−	0.998436i	$-0.482196\pi$
$251$	1.77135	0.111807	0.0559033	+	0.998436i	$0.482196\pi$
$252$	−8.37436	−0.527535
$253$	0	0
$254$	−0.758584	−0.0475978
$255$	2.14876	0.134560
$256$	1.00000	0.0625000
$257$	−11.9480	−0.745299	−0.372649	−	0.927972i	$-0.621551\pi$
$257$	−11.9480	−0.745299	−0.372649	+	0.927972i	$0.621551\pi$
$258$	4.76941	0.296930
$259$	14.1603	0.879877
$260$	3.84302	0.238334
$261$	−12.0875	−0.748197
$262$	6.90871	0.426821
$263$	1.64957	0.101717	0.0508584	−	0.998706i	$-0.483804\pi$
$263$	1.64957	0.101717	0.0508584	+	0.998706i	$0.483804\pi$
$264$	0	0
$265$	−22.5414	−1.38471
$266$	11.2830	0.691805
$267$	9.68620	0.592786
$268$	7.10203	0.433826
$269$	1.11381	0.0679104	0.0339552	−	0.999423i	$-0.489190\pi$
$269$	1.11381	0.0679104	0.0339552	+	0.999423i	$0.489190\pi$
$270$	−7.55627	−0.459860
$271$	28.3391	1.72148	0.860738	−	0.509048i	$-0.170002\pi$
$271$	28.3391	1.72148	0.860738	+	0.509048i	$0.170002\pi$
$272$	−1.45435	−0.0881830
$273$	−9.12432	−0.552229
$274$	−7.15747	−0.432399
$275$	0	0
$276$	−0.941096	−0.0566473
$277$	−20.2508	−1.21675	−0.608376	−	0.793649i	$-0.708179\pi$
$277$	−20.2508	−1.21675	−0.608376	+	0.793649i	$0.708179\pi$
$278$	5.71115	0.342532
$279$	−4.03553	−0.241601
$280$	6.21814	0.371605
$281$	−24.4363	−1.45775	−0.728875	−	0.684647i	$-0.759957\pi$
$281$	−24.4363	−1.45775	−0.728875	+	0.684647i	$0.759957\pi$
$282$	−6.41826	−0.382202
$283$	6.65456	0.395573	0.197786	−	0.980245i	$-0.436625\pi$
$283$	6.65456	0.395573	0.197786	+	0.980245i	$0.436625\pi$
$284$	13.8215	0.820156
$285$	4.20887	0.249312
$286$	0	0
$287$	−7.24875	−0.427880
$288$	2.11434	0.124589
$289$	−14.8849	−0.875580
$290$	8.97523	0.527044
$291$	−18.1762	−1.06551
$292$	−0.691036	−0.0404398
$293$	27.5327	1.60848	0.804238	−	0.594307i	$-0.202574\pi$
$293$	27.5327	1.60848	0.804238	+	0.594307i	$0.202574\pi$
$294$	−8.17579	−0.476822
$295$	−1.55797	−0.0907084
$296$	−3.57515	−0.207802
$297$	0	0
$298$	6.04628	0.350251
$299$	2.44788	0.141564
$300$	−2.38594	−0.137753
$301$	−20.0728	−1.15698
$302$	−12.5111	−0.719933
$303$	16.0021	0.919297
$304$	−2.84870	−0.163384
$305$	19.2437	1.10189
$306$	−3.07499	−0.175785
$307$	4.28667	0.244653	0.122327	−	0.992490i	$-0.460964\pi$
$307$	4.28667	0.244653	0.122327	+	0.992490i	$0.460964\pi$
$308$	0	0
$309$	7.94718	0.452099
$310$	2.99647	0.170188
$311$	29.1109	1.65073	0.825364	−	0.564602i	$-0.190970\pi$
$311$	29.1109	1.65073	0.825364	+	0.564602i	$0.190970\pi$
$312$	2.30369	0.130421
$313$	33.9093	1.91667	0.958334	−	0.285648i	$-0.0922090\pi$
$313$	33.9093	1.91667	0.958334	+	0.285648i	$0.0922090\pi$
$314$	−1.83735	−0.103688
$315$	13.1473	0.740764
$316$	9.17542	0.516158
$317$	−22.4544	−1.26117	−0.630583	−	0.776122i	$-0.717184\pi$
$317$	−22.4544	−1.26117	−0.630583	+	0.776122i	$0.717184\pi$
$318$	−13.5124	−0.757737
$319$	0	0
$320$	−1.56994	−0.0877624
$321$	1.70644	0.0952445
$322$	3.96075	0.220724
$323$	4.14302	0.230524
$324$	1.81344	0.100747
$325$	6.20605	0.344250
$326$	3.81662	0.211383
$327$	−2.42205	−0.133939
$328$	1.83015	0.101053
$329$	27.0122	1.48923
$330$	0	0
$331$	11.3655	0.624707	0.312353	−	0.949966i	$-0.398883\pi$
$331$	11.3655	0.624707	0.312353	+	0.949966i	$0.398883\pi$
$332$	9.92842	0.544893
$333$	−7.55909	−0.414235
$334$	−2.33223	−0.127614
$335$	−11.1498	−0.609178
$336$	3.72744	0.203349
$337$	9.09474	0.495422	0.247711	−	0.968834i	$-0.420322\pi$
$337$	9.09474	0.495422	0.247711	+	0.968834i	$0.420322\pi$
$338$	7.00790	0.381180
$339$	8.29673	0.450616
$340$	2.28325	0.123826
$341$	0	0
$342$	−6.02312	−0.325693
$343$	6.68382	0.360892
$344$	5.06793	0.273244
$345$	1.47747	0.0795441
$346$	−6.19752	−0.333181
$347$	33.0617	1.77485	0.887423	−	0.460956i	$-0.152493\pi$
$347$	33.0617	1.77485	0.887423	+	0.460956i	$0.152493\pi$
$348$	5.38017	0.288407
$349$	3.14489	0.168342	0.0841710	−	0.996451i	$-0.473176\pi$
$349$	3.14489	0.168342	0.0841710	+	0.996451i	$0.473176\pi$
$350$	10.0416	0.536746
$351$	11.7818	0.628868
$352$	0	0
$353$	0.389745	0.0207440	0.0103720	−	0.999946i	$-0.496698\pi$
$353$	0.389745	0.0207440	0.0103720	+	0.999946i	$0.496698\pi$
$354$	−0.933918	−0.0496372
$355$	−21.6990	−1.15166
$356$	10.2925	0.545499
$357$	−5.42101	−0.286910
$358$	−10.0123	−0.529169
$359$	−35.4856	−1.87286	−0.936429	−	0.350857i	$-0.885890\pi$
$359$	−35.4856	−1.87286	−0.936429	+	0.350857i	$0.885890\pi$
$360$	−3.31939	−0.174947
$361$	−10.8849	−0.572889
$362$	−13.5756	−0.713519
$363$	0	0
$364$	−9.69542	−0.508178
$365$	1.08489	0.0567855
$366$	11.5356	0.602974
$367$	23.0095	1.20109	0.600544	−	0.799592i	$-0.294951\pi$
$367$	23.0095	1.20109	0.600544	+	0.799592i	$0.294951\pi$
$368$	−1.00000	−0.0521286
$369$	3.86955	0.201441
$370$	5.61279	0.291795
$371$	56.8689	2.95249
$372$	1.79622	0.0931299
$373$	7.85299	0.406613	0.203306	−	0.979115i	$-0.434831\pi$
$373$	7.85299	0.406613	0.203306	+	0.979115i	$0.434831\pi$
$374$	0	0
$375$	11.1331	0.574912
$376$	−6.81998	−0.351714
$377$	−13.9943	−0.720744
$378$	19.0634	0.980516
$379$	11.3217	0.581558	0.290779	−	0.956790i	$-0.406086\pi$
$379$	11.3217	0.581558	0.290779	+	0.956790i	$0.406086\pi$
$380$	4.47230	0.229424
$381$	0.713901	0.0365742
$382$	9.75145	0.498928
$383$	21.6574	1.10664	0.553320	−	0.832969i	$-0.313361\pi$
$383$	21.6574	1.10664	0.553320	+	0.832969i	$0.313361\pi$
$384$	−0.941096	−0.0480251
$385$	0	0
$386$	11.0527	0.562565
$387$	10.7153	0.544690
$388$	−19.3138	−0.980512
$389$	18.1828	0.921907	0.460953	−	0.887424i	$-0.347508\pi$
$389$	18.1828	0.921907	0.460953	+	0.887424i	$0.347508\pi$
$390$	−3.61666	−0.183137
$391$	1.45435	0.0735497
$392$	−8.68752	−0.438786
$393$	−6.50176	−0.327970
$394$	6.96722	0.351003
$395$	−14.4049	−0.724788
$396$	0	0
$397$	28.6860	1.43971	0.719854	−	0.694125i	$-0.244209\pi$
$397$	28.6860	1.43971	0.719854	+	0.694125i	$0.244209\pi$
$398$	−25.8586	−1.29617
$399$	−10.6184	−0.531584
$400$	−2.53528	−0.126764
$401$	−28.1033	−1.40341	−0.701707	−	0.712466i	$-0.747578\pi$
$401$	−28.1033	−1.40341	−0.701707	+	0.712466i	$0.747578\pi$
$402$	−6.68370	−0.333352
$403$	−4.67214	−0.232736
$404$	17.0037	0.845965
$405$	−2.84699	−0.141468
$406$	−22.6433	−1.12377
$407$	0	0
$408$	1.36868	0.0677600
$409$	12.3327	0.609811	0.304906	−	0.952383i	$-0.401375\pi$
$409$	12.3327	0.609811	0.304906	+	0.952383i	$0.401375\pi$
$410$	−2.87323	−0.141899
$411$	6.73587	0.332256
$412$	8.44460	0.416036
$413$	3.93054	0.193409
$414$	−2.11434	−0.103914
$415$	−15.5870	−0.765138
$416$	2.44788	0.120017
$417$	−5.37474	−0.263202
$418$	0	0
$419$	−12.2389	−0.597909	−0.298955	−	0.954267i	$-0.596638\pi$
$419$	−12.2389	−0.597909	−0.298955	+	0.954267i	$0.596638\pi$
$420$	−5.85187	−0.285542
$421$	−40.0879	−1.95377	−0.976883	−	0.213776i	$-0.931424\pi$
$421$	−40.0879	−1.95377	−0.976883	+	0.213776i	$0.931424\pi$
$422$	13.8943	0.676365
$423$	−14.4197	−0.701112
$424$	−14.3581	−0.697292
$425$	3.68719	0.178855
$426$	−13.0074	−0.630209
$427$	−48.5492	−2.34946
$428$	1.81325	0.0876469
$429$	0	0
$430$	−7.95635	−0.383689
$431$	−38.8529	−1.87148	−0.935739	−	0.352693i	$-0.885266\pi$
$431$	−38.8529	−1.87148	−0.935739	+	0.352693i	$0.885266\pi$
$432$	−4.81308	−0.231570
$433$	−13.1858	−0.633667	−0.316834	−	0.948481i	$-0.602620\pi$
$433$	−13.1858	−0.633667	−0.316834	+	0.948481i	$0.602620\pi$
$434$	−7.55968	−0.362876
$435$	−8.44656	−0.404982
$436$	−2.57364	−0.123255
$437$	2.84870	0.136272
$438$	0.650331	0.0310740
$439$	17.8311	0.851033	0.425516	−	0.904951i	$-0.360093\pi$
$439$	17.8311	0.851033	0.425516	+	0.904951i	$0.360093\pi$
$440$	0	0
$441$	−18.3683	−0.874683
$442$	−3.56007	−0.169335
$443$	−8.46317	−0.402097	−0.201049	−	0.979581i	$-0.564435\pi$
$443$	−8.46317	−0.402097	−0.201049	+	0.979581i	$0.564435\pi$
$444$	3.36457	0.159675
$445$	−16.1586	−0.765990
$446$	−11.2567	−0.533020
$447$	−5.69013	−0.269134
$448$	3.96075	0.187128
$449$	34.2198	1.61493	0.807466	−	0.589914i	$-0.200838\pi$
$449$	34.2198	1.61493	0.807466	+	0.589914i	$0.200838\pi$
$450$	−5.36044	−0.252694
$451$	0	0
$452$	8.81602	0.414671
$453$	11.7742	0.553198
$454$	9.64070	0.452461
$455$	15.2212	0.713583
$456$	2.68091	0.125545
$457$	−16.6042	−0.776711	−0.388356	−	0.921510i	$-0.626957\pi$
$457$	−16.6042	−0.776711	−0.388356	+	0.921510i	$0.626957\pi$
$458$	29.7112	1.38831
$459$	6.99991	0.326728
$460$	1.56994	0.0731989
$461$	−18.7650	−0.873972	−0.436986	−	0.899468i	$-0.643954\pi$
$461$	−18.7650	−0.873972	−0.436986	+	0.899468i	$0.643954\pi$
$462$	0	0
$463$	−4.49563	−0.208929	−0.104465	−	0.994529i	$-0.533313\pi$
$463$	−4.49563	−0.208929	−0.104465	+	0.994529i	$0.533313\pi$
$464$	5.71692	0.265401
$465$	−2.81997	−0.130773
$466$	17.3712	0.804706
$467$	0.244058	0.0112937	0.00564683	−	0.999984i	$-0.498203\pi$
$467$	0.244058	0.0112937	0.00564683	+	0.999984i	$0.498203\pi$
$468$	5.17564	0.239244
$469$	28.1293	1.29889
$470$	10.7070	0.493876
$471$	1.72913	0.0796740
$472$	−0.992373	−0.0456777
$473$	0	0
$474$	−8.63495	−0.396617
$475$	7.22227	0.331380
$476$	−5.76031	−0.264024
$477$	−30.3579	−1.38999
$478$	−15.3344	−0.701377
$479$	7.36618	0.336570	0.168285	−	0.985738i	$-0.446177\pi$
$479$	7.36618	0.336570	0.168285	+	0.985738i	$0.446177\pi$
$480$	1.47747	0.0674368
$481$	−8.75154	−0.399036
$482$	−2.77209	−0.126265
$483$	−3.72744	−0.169605
$484$	0	0
$485$	30.3216	1.37683
$486$	−16.1459	−0.732392
$487$	39.6464	1.79655	0.898274	−	0.439435i	$-0.144821\pi$
$487$	39.6464	1.79655	0.898274	+	0.439435i	$0.144821\pi$
$488$	12.2576	0.554875
$489$	−3.59180	−0.162427
$490$	13.6389	0.616143
$491$	28.6608	1.29345	0.646723	−	0.762725i	$-0.276139\pi$
$491$	28.6608	1.29345	0.646723	+	0.762725i	$0.276139\pi$
$492$	−1.72234	−0.0776493
$493$	−8.31441	−0.374462
$494$	−6.97328	−0.313743
$495$	0	0
$496$	1.90865	0.0857009
$497$	54.7435	2.45558
$498$	−9.34360	−0.418697
$499$	−6.79775	−0.304309	−0.152155	−	0.988357i	$-0.548621\pi$
$499$	−6.79775	−0.304309	−0.152155	+	0.988357i	$0.548621\pi$
$500$	11.8300	0.529052
$501$	2.19486	0.0980589
$502$	−1.77135	−0.0790591
$503$	25.3511	1.13035	0.565174	−	0.824971i	$-0.308809\pi$
$503$	25.3511	1.13035	0.565174	+	0.824971i	$0.308809\pi$
$504$	8.37436	0.373023
$505$	−26.6948	−1.18790
$506$	0	0
$507$	−6.59511	−0.292899
$508$	0.758584	0.0336567
$509$	20.4965	0.908490	0.454245	−	0.890877i	$-0.349909\pi$
$509$	20.4965	0.908490	0.454245	+	0.890877i	$0.349909\pi$
$510$	−2.14876	−0.0951485
$511$	−2.73702	−0.121079
$512$	−1.00000	−0.0441942
$513$	13.7111	0.605358
$514$	11.9480	0.527006
$515$	−13.2575	−0.584197
$516$	−4.76941	−0.209961
$517$	0	0
$518$	−14.1603	−0.622167
$519$	5.83246	0.256017
$520$	−3.84302	−0.168528
$521$	−10.6304	−0.465726	−0.232863	−	0.972510i	$-0.574809\pi$
$521$	−10.6304	−0.465726	−0.232863	+	0.972510i	$0.574809\pi$
$522$	12.0875	0.529055
$523$	−32.9671	−1.44155	−0.720776	−	0.693168i	$-0.756214\pi$
$523$	−32.9671	−1.44155	−0.720776	+	0.693168i	$0.756214\pi$
$524$	−6.90871	−0.301808
$525$	−9.45012	−0.412437
$526$	−1.64957	−0.0719246
$527$	−2.77585	−0.120918
$528$	0	0
$529$	1.00000	0.0434783
$530$	22.5414	0.979137
$531$	−2.09821	−0.0910546
$532$	−11.2830	−0.489180
$533$	4.47997	0.194049
$534$	−9.68620	−0.419163
$535$	−2.84670	−0.123074
$536$	−7.10203	−0.306761
$537$	9.42258	0.406614
$538$	−1.11381	−0.0480199
$539$	0	0
$540$	7.55627	0.325170
$541$	28.4454	1.22296	0.611481	−	0.791259i	$-0.290574\pi$
$541$	28.4454	1.22296	0.611481	+	0.791259i	$0.290574\pi$
$542$	−28.3391	−1.21727
$543$	12.7760	0.548269
$544$	1.45435	0.0623548
$545$	4.04047	0.173075
$546$	9.12432	0.390485
$547$	4.30986	0.184276	0.0921382	−	0.995746i	$-0.470630\pi$
$547$	4.30986	0.184276	0.0921382	+	0.995746i	$0.470630\pi$
$548$	7.15747	0.305752
$549$	25.9167	1.10610
$550$	0	0
$551$	−16.2858	−0.693799
$552$	0.941096	0.0400557
$553$	36.3415	1.54540
$554$	20.2508	0.860374
$555$	−5.28217	−0.224216
$556$	−5.71115	−0.242207
$557$	−45.7969	−1.94048	−0.970238	−	0.242152i	$-0.922147\pi$
$557$	−45.7969	−1.94048	−0.970238	+	0.242152i	$0.922147\pi$
$558$	4.03553	0.170838
$559$	12.4057	0.524703
$560$	−6.21814	−0.262765
$561$	0	0
$562$	24.4363	1.03079
$563$	20.4732	0.862843	0.431422	−	0.902150i	$-0.358012\pi$
$563$	20.4732	0.862843	0.431422	+	0.902150i	$0.358012\pi$
$564$	6.41826	0.270258
$565$	−13.8406	−0.582281
$566$	−6.65456	−0.279712
$567$	7.18257	0.301639
$568$	−13.8215	−0.579938
$569$	1.08745	0.0455883	0.0227942	−	0.999740i	$-0.492744\pi$
$569$	1.08745	0.0455883	0.0227942	+	0.999740i	$0.492744\pi$
$570$	−4.20887	−0.176290
$571$	−32.2846	−1.35107	−0.675534	−	0.737328i	$-0.736087\pi$
$571$	−32.2846	−1.35107	−0.675534	+	0.737328i	$0.736087\pi$
$572$	0	0
$573$	−9.17705	−0.383377
$574$	7.24875	0.302557
$575$	2.53528	0.105729
$576$	−2.11434	−0.0880974
$577$	−14.6504	−0.609905	−0.304952	−	0.952368i	$-0.598641\pi$
$577$	−14.6504	−0.609905	−0.304952	+	0.952368i	$0.598641\pi$
$578$	14.8849	0.619129
$579$	−10.4016	−0.432276
$580$	−8.97523	−0.372676
$581$	39.3239	1.63143
$582$	18.1762	0.753427
$583$	0	0
$584$	0.691036	0.0285953
$585$	−8.12545	−0.335946
$586$	−27.5327	−1.13736
$587$	−39.3210	−1.62295	−0.811476	−	0.584385i	$-0.801336\pi$
$587$	−39.3210	−1.62295	−0.811476	+	0.584385i	$0.801336\pi$
$588$	8.17579	0.337164
$589$	−5.43718	−0.224035
$590$	1.55797	0.0641405
$591$	−6.55682	−0.269712
$592$	3.57515	0.146938
$593$	31.0824	1.27640	0.638201	−	0.769870i	$-0.279679\pi$
$593$	31.0824	1.27640	0.638201	+	0.769870i	$0.279679\pi$
$594$	0	0
$595$	9.04336	0.370742
$596$	−6.04628	−0.247665
$597$	24.3354	0.995982
$598$	−2.44788	−0.100101
$599$	20.3944	0.833293	0.416646	−	0.909069i	$-0.363205\pi$
$599$	20.3944	0.833293	0.416646	+	0.909069i	$0.363205\pi$
$600$	2.38594	0.0974057
$601$	8.04831	0.328297	0.164149	−	0.986436i	$-0.447512\pi$
$601$	8.04831	0.328297	0.164149	+	0.986436i	$0.447512\pi$
$602$	20.0728	0.818105
$603$	−15.0161	−0.611503
$604$	12.5111	0.509070
$605$	0	0
$606$	−16.0021	−0.650041
$607$	−13.5687	−0.550737	−0.275368	−	0.961339i	$-0.588800\pi$
$607$	−13.5687	−0.550737	−0.275368	+	0.961339i	$0.588800\pi$
$608$	2.84870	0.115530
$609$	21.3095	0.863504
$610$	−19.2437	−0.779155
$611$	−16.6945	−0.675386
$612$	3.07499	0.124299
$613$	13.2535	0.535302	0.267651	−	0.963516i	$-0.413753\pi$
$613$	13.2535	0.535302	0.267651	+	0.963516i	$0.413753\pi$
$614$	−4.28667	−0.172996
$615$	2.70398	0.109035
$616$	0	0
$617$	−24.3186	−0.979029	−0.489515	−	0.871995i	$-0.662826\pi$
$617$	−24.3186	−0.979029	−0.489515	+	0.871995i	$0.662826\pi$
$618$	−7.94718	−0.319683
$619$	−17.1238	−0.688263	−0.344132	−	0.938921i	$-0.611827\pi$
$619$	−17.1238	−0.688263	−0.344132	+	0.938921i	$0.611827\pi$
$620$	−2.99647	−0.120341
$621$	4.81308	0.193142
$622$	−29.1109	−1.16724
$623$	40.7658	1.63325
$624$	−2.30369	−0.0922213
$625$	−5.89595	−0.235838
$626$	−33.9093	−1.35529
$627$	0	0
$628$	1.83735	0.0733184
$629$	−5.19953	−0.207319
$630$	−13.1473	−0.523799
$631$	−7.63473	−0.303934	−0.151967	−	0.988386i	$-0.548561\pi$
$631$	−7.63473	−0.303934	−0.151967	+	0.988386i	$0.548561\pi$
$632$	−9.17542	−0.364979
$633$	−13.0759	−0.519720
$634$	22.4544	0.891778
$635$	−1.19093	−0.0472607
$636$	13.5124	0.535801
$637$	−21.2660	−0.842588
$638$	0	0
$639$	−29.2234	−1.15606
$640$	1.56994	0.0620574
$641$	−10.4395	−0.412336	−0.206168	−	0.978517i	$-0.566099\pi$
$641$	−10.4395	−0.412336	−0.206168	+	0.978517i	$0.566099\pi$
$642$	−1.70644	−0.0673480
$643$	47.8677	1.88772	0.943859	−	0.330350i	$-0.107167\pi$
$643$	47.8677	1.88772	0.943859	+	0.330350i	$0.107167\pi$
$644$	−3.96075	−0.156075
$645$	7.48769	0.294828
$646$	−4.14302	−0.163005
$647$	−27.8521	−1.09498	−0.547490	−	0.836812i	$-0.684417\pi$
$647$	−27.8521	−1.09498	−0.547490	+	0.836812i	$0.684417\pi$
$648$	−1.81344	−0.0712386
$649$	0	0
$650$	−6.20605	−0.243421
$651$	7.11439	0.278835
$652$	−3.81662	−0.149470
$653$	30.1408	1.17950	0.589750	−	0.807586i	$-0.299226\pi$
$653$	30.1408	1.17950	0.589750	+	0.807586i	$0.299226\pi$
$654$	2.42205	0.0947095
$655$	10.8463	0.423799
$656$	−1.83015	−0.0714552
$657$	1.46108	0.0570023
$658$	−27.0122	−1.05305
$659$	35.6033	1.38691	0.693453	−	0.720501i	$-0.256088\pi$
$659$	35.6033	1.38691	0.693453	+	0.720501i	$0.256088\pi$
$660$	0	0
$661$	26.2600	1.02140	0.510699	−	0.859760i	$-0.329387\pi$
$661$	26.2600	1.02140	0.510699	+	0.859760i	$0.329387\pi$
$662$	−11.3655	−0.441734
$663$	3.35037	0.130118
$664$	−9.92842	−0.385297
$665$	17.7137	0.686906
$666$	7.55909	0.292909
$667$	−5.71692	−0.221360
$668$	2.33223	0.0902368
$669$	10.5936	0.409574
$670$	11.1498	0.430754
$671$	0	0
$672$	−3.72744	−0.143789
$673$	24.0404	0.926688	0.463344	−	0.886178i	$-0.346649\pi$
$673$	24.0404	0.926688	0.463344	+	0.886178i	$0.346649\pi$
$674$	−9.09474	−0.350316
$675$	12.2025	0.469675
$676$	−7.00790	−0.269535
$677$	6.73988	0.259035	0.129517	−	0.991577i	$-0.458657\pi$
$677$	6.73988	0.259035	0.129517	+	0.991577i	$0.458657\pi$
$678$	−8.29673	−0.318634
$679$	−76.4972	−2.93569
$680$	−2.28325	−0.0875585
$681$	−9.07283	−0.347672
$682$	0	0
$683$	−27.4987	−1.05221	−0.526105	−	0.850420i	$-0.676348\pi$
$683$	−27.4987	−1.05221	−0.526105	+	0.850420i	$0.676348\pi$
$684$	6.02312	0.230300
$685$	−11.2368	−0.429337
$686$	−6.68382	−0.255189
$687$	−27.9611	−1.06678
$688$	−5.06793	−0.193213
$689$	−35.1469	−1.33899
$690$	−1.47747	−0.0562462
$691$	4.08404	0.155364	0.0776821	−	0.996978i	$-0.475248\pi$
$691$	4.08404	0.155364	0.0776821	+	0.996978i	$0.475248\pi$
$692$	6.19752	0.235594
$693$	0	0
$694$	−33.0617	−1.25501
$695$	8.96618	0.340107
$696$	−5.38017	−0.203935
$697$	2.66168	0.100818
$698$	−3.14489	−0.119036
$699$	−16.3480	−0.618337
$700$	−10.0416	−0.379537
$701$	−8.69121	−0.328263	−0.164131	−	0.986438i	$-0.552482\pi$
$701$	−8.69121	−0.328263	−0.164131	+	0.986438i	$0.552482\pi$
$702$	−11.7818	−0.444677
$703$	−10.1846	−0.384118
$704$	0	0
$705$	−10.0763	−0.379495
$706$	−0.389745	−0.0146683
$707$	67.3473	2.53286
$708$	0.933918	0.0350988
$709$	−18.9982	−0.713491	−0.356745	−	0.934202i	$-0.616114\pi$
$709$	−18.9982	−0.713491	−0.356745	+	0.934202i	$0.616114\pi$
$710$	21.6990	0.814348
$711$	−19.3999	−0.727554
$712$	−10.2925	−0.385726
$713$	−1.90865	−0.0714795
$714$	5.42101	0.202876
$715$	0	0
$716$	10.0123	0.374179
$717$	14.4311	0.538940
$718$	35.4856	1.32431
$719$	−23.6576	−0.882279	−0.441139	−	0.897439i	$-0.645426\pi$
$719$	−23.6576	−0.882279	−0.441139	+	0.897439i	$0.645426\pi$
$720$	3.31939	0.123706
$721$	33.4469	1.24563
$722$	10.8849	0.405093
$723$	2.60880	0.0970223
$724$	13.5756	0.504534
$725$	−14.4940	−0.538293
$726$	0	0
$727$	−22.9416	−0.850858	−0.425429	−	0.904992i	$-0.639877\pi$
$727$	−22.9416	−0.850858	−0.425429	+	0.904992i	$0.639877\pi$
$728$	9.69542	0.359336
$729$	9.75451	0.361278
$730$	−1.08489	−0.0401534
$731$	7.37054	0.272609
$732$	−11.5356	−0.426367
$733$	−3.46254	−0.127892	−0.0639460	−	0.997953i	$-0.520369\pi$
$733$	−3.46254	−0.127892	−0.0639460	+	0.997953i	$0.520369\pi$
$734$	−23.0095	−0.849298
$735$	−12.8355	−0.473445
$736$	1.00000	0.0368605
$737$	0	0
$738$	−3.86955	−0.142440
$739$	47.6291	1.75207	0.876033	−	0.482251i	$-0.160181\pi$
$739$	47.6291	1.75207	0.876033	+	0.482251i	$0.160181\pi$
$740$	−5.61279	−0.206330
$741$	6.56252	0.241080
$742$	−56.8689	−2.08772
$743$	2.96698	0.108848	0.0544240	−	0.998518i	$-0.482668\pi$
$743$	2.96698	0.108848	0.0544240	+	0.998518i	$0.482668\pi$
$744$	−1.79622	−0.0658528
$745$	9.49231	0.347771
$746$	−7.85299	−0.287519
$747$	−20.9920	−0.768058
$748$	0	0
$749$	7.18183	0.262418
$750$	−11.1331	−0.406524
$751$	38.7241	1.41306	0.706532	−	0.707681i	$-0.250259\pi$
$751$	38.7241	1.41306	0.706532	+	0.707681i	$0.250259\pi$
$752$	6.81998	0.248699
$753$	1.66701	0.0607492
$754$	13.9943	0.509643
$755$	−19.6417	−0.714835
$756$	−19.0634	−0.693329
$757$	19.2858	0.700954	0.350477	−	0.936571i	$-0.386019\pi$
$757$	19.2858	0.700954	0.350477	+	0.936571i	$0.386019\pi$
$758$	−11.3217	−0.411224
$759$	0	0
$760$	−4.47230	−0.162227
$761$	−14.6914	−0.532563	−0.266282	−	0.963895i	$-0.585795\pi$
$761$	−14.6914	−0.532563	−0.266282	+	0.963895i	$0.585795\pi$
$762$	−0.713901	−0.0258619
$763$	−10.1935	−0.369031
$764$	−9.75145	−0.352795
$765$	−4.82756	−0.174541
$766$	−21.6574	−0.782512
$767$	−2.42921	−0.0877135
$768$	0.941096	0.0339589
$769$	13.4993	0.486798	0.243399	−	0.969926i	$-0.421738\pi$
$769$	13.4993	0.486798	0.243399	+	0.969926i	$0.421738\pi$
$770$	0	0
$771$	−11.2443	−0.404952
$772$	−11.0527	−0.397794
$773$	4.46878	0.160731	0.0803655	−	0.996765i	$-0.474391\pi$
$773$	4.46878	0.160731	0.0803655	+	0.996765i	$0.474391\pi$
$774$	−10.7153	−0.385154
$775$	−4.83896	−0.173821
$776$	19.3138	0.693326
$777$	13.3262	0.478074
$778$	−18.1828	−0.651887
$779$	5.21355	0.186795
$780$	3.61666	0.129497
$781$	0	0
$782$	−1.45435	−0.0520075
$783$	−27.5160	−0.983342
$784$	8.68752	0.310268
$785$	−2.88454	−0.102954
$786$	6.50176	0.231910
$787$	53.1493	1.89457	0.947285	−	0.320393i	$-0.103815\pi$
$787$	53.1493	1.89457	0.947285	+	0.320393i	$0.103815\pi$
$788$	−6.96722	−0.248197
$789$	1.55240	0.0552670
$790$	14.4049	0.512503
$791$	34.9180	1.24154
$792$	0	0
$793$	30.0051	1.06551
$794$	−28.6860	−1.01803
$795$	−21.2137	−0.752371
$796$	25.8586	0.916533
$797$	5.46839	0.193700	0.0968502	−	0.995299i	$-0.469123\pi$
$797$	5.46839	0.193700	0.0968502	+	0.995299i	$0.469123\pi$
$798$	10.6184	0.375887
$799$	−9.91865	−0.350897
$800$	2.53528	0.0896357
$801$	−21.7617	−0.768913
$802$	28.1033	0.992363
$803$	0	0
$804$	6.68370	0.235716
$805$	6.21814	0.219161
$806$	4.67214	0.164569
$807$	1.04821	0.0368986
$808$	−17.0037	−0.598188
$809$	12.9497	0.455289	0.227644	−	0.973744i	$-0.426898\pi$
$809$	12.9497	0.455289	0.227644	+	0.973744i	$0.426898\pi$
$810$	2.84699	0.100033
$811$	19.7067	0.691997	0.345999	−	0.938235i	$-0.387540\pi$
$811$	19.7067	0.691997	0.345999	+	0.938235i	$0.387540\pi$
$812$	22.6433	0.794623
$813$	26.6698	0.935351
$814$	0	0
$815$	5.99187	0.209886
$816$	−1.36868	−0.0479135
$817$	14.4370	0.505088
$818$	−12.3327	−0.431202
$819$	20.4994	0.716307
$820$	2.87323	0.100337
$821$	−36.3741	−1.26947	−0.634733	−	0.772731i	$-0.718890\pi$
$821$	−36.3741	−1.26947	−0.634733	+	0.772731i	$0.718890\pi$
$822$	−6.73587	−0.234941
$823$	41.9903	1.46369	0.731844	−	0.681472i	$-0.238660\pi$
$823$	41.9903	1.46369	0.731844	+	0.681472i	$0.238660\pi$
$824$	−8.44460	−0.294182
$825$	0	0
$826$	−3.93054	−0.136761
$827$	−17.0484	−0.592831	−0.296415	−	0.955059i	$-0.595791\pi$
$827$	−17.0484	−0.592831	−0.296415	+	0.955059i	$0.595791\pi$
$828$	2.11434	0.0734783
$829$	−18.5614	−0.644665	−0.322332	−	0.946627i	$-0.604467\pi$
$829$	−18.5614	−0.644665	−0.322332	+	0.946627i	$0.604467\pi$
$830$	15.5870	0.541034
$831$	−19.0580	−0.661113
$832$	−2.44788	−0.0848648
$833$	−12.6347	−0.437766
$834$	5.37474	0.186112
$835$	−3.66147	−0.126710
$836$	0	0
$837$	−9.18650	−0.317532
$838$	12.2389	0.422786
$839$	48.4573	1.67293	0.836466	−	0.548018i	$-0.184618\pi$
$839$	48.4573	1.67293	0.836466	+	0.548018i	$0.184618\pi$
$840$	5.85187	0.201909
$841$	3.68317	0.127006
$842$	40.0879	1.38152
$843$	−22.9970	−0.792057
$844$	−13.8943	−0.478262
$845$	11.0020	0.378480
$846$	14.4197	0.495761
$847$	0	0
$848$	14.3581	0.493060
$849$	6.26258	0.214931
$850$	−3.68719	−0.126469
$851$	−3.57515	−0.122555
$852$	13.0074	0.445625
$853$	−47.3434	−1.62101	−0.810503	−	0.585734i	$-0.800806\pi$
$853$	−47.3434	−1.62101	−0.810503	+	0.585734i	$0.800806\pi$
$854$	48.5492	1.66132
$855$	−9.45596	−0.323387
$856$	−1.81325	−0.0619757
$857$	11.2174	0.383181	0.191590	−	0.981475i	$-0.438636\pi$
$857$	11.2174	0.383181	0.191590	+	0.981475i	$0.438636\pi$
$858$	0	0
$859$	−41.5633	−1.41812	−0.709060	−	0.705148i	$-0.750881\pi$
$859$	−41.5633	−1.41812	−0.709060	+	0.705148i	$0.750881\pi$
$860$	7.95635	0.271309
$861$	−6.82177	−0.232485
$862$	38.8529	1.32334
$863$	28.7840	0.979817	0.489909	−	0.871774i	$-0.337030\pi$
$863$	28.7840	0.979817	0.489909	+	0.871774i	$0.337030\pi$
$864$	4.81308	0.163744
$865$	−9.72974	−0.330821
$866$	13.1858	0.448070
$867$	−14.0081	−0.475740
$868$	7.55968	0.256592
$869$	0	0
$870$	8.44656	0.286365
$871$	−17.3849	−0.589065
$872$	2.57364	0.0871545
$873$	40.8360	1.38209
$874$	−2.84870	−0.0963589
$875$	46.8555	1.58400
$876$	−0.650331	−0.0219727
$877$	43.6426	1.47371	0.736853	−	0.676053i	$-0.236311\pi$
$877$	43.6426	1.47371	0.736853	+	0.676053i	$0.236311\pi$
$878$	−17.8311	−0.601771
$879$	25.9109	0.873953
$880$	0	0
$881$	26.9560	0.908172	0.454086	−	0.890958i	$-0.349966\pi$
$881$	26.9560	0.908172	0.454086	+	0.890958i	$0.349966\pi$
$882$	18.3683	0.618494
$883$	−16.7115	−0.562386	−0.281193	−	0.959651i	$-0.590730\pi$
$883$	−16.7115	−0.562386	−0.281193	+	0.959651i	$0.590730\pi$
$884$	3.56007	0.119738
$885$	−1.46620	−0.0492857
$886$	8.46317	0.284326
$887$	−4.24300	−0.142466	−0.0712330	−	0.997460i	$-0.522693\pi$
$887$	−4.24300	−0.142466	−0.0712330	+	0.997460i	$0.522693\pi$
$888$	−3.36457	−0.112907
$889$	3.00456	0.100770
$890$	16.1586	0.541636
$891$	0	0
$892$	11.2567	0.376902
$893$	−19.4281	−0.650137
$894$	5.69013	0.190306
$895$	−15.7188	−0.525422
$896$	−3.96075	−0.132319
$897$	2.30369	0.0769179
$898$	−34.2198	−1.14193
$899$	10.9116	0.363922
$900$	5.36044	0.178681
$901$	−20.8818	−0.695672
$902$	0	0
$903$	−18.8904	−0.628634
$904$	−8.81602	−0.293217
$905$	−21.3129	−0.708466
$906$	−11.7742	−0.391170
$907$	−12.1158	−0.402297	−0.201148	−	0.979561i	$-0.564467\pi$
$907$	−12.1158	−0.402297	−0.201148	+	0.979561i	$0.564467\pi$
$908$	−9.64070	−0.319938
$909$	−35.9516	−1.19244
$910$	−15.2212	−0.504579
$911$	41.2385	1.36629	0.683146	−	0.730282i	$-0.260611\pi$
$911$	41.2385	1.36629	0.683146	+	0.730282i	$0.260611\pi$
$912$	−2.68091	−0.0887736
$913$	0	0
$914$	16.6042	0.549218
$915$	18.1102	0.598704
$916$	−29.7112	−0.981686
$917$	−27.3636	−0.903627
$918$	−6.99991	−0.231032
$919$	−11.1386	−0.367428	−0.183714	−	0.982980i	$-0.558812\pi$
$919$	−11.1386	−0.367428	−0.183714	+	0.982980i	$0.558812\pi$
$920$	−1.56994	−0.0517595
$921$	4.03417	0.132930
$922$	18.7650	0.617991
$923$	−33.8334	−1.11364
$924$	0	0
$925$	−9.06402	−0.298023
$926$	4.49563	0.147735
$927$	−17.8547	−0.586427
$928$	−5.71692	−0.187667
$929$	−32.7054	−1.07303	−0.536515	−	0.843891i	$-0.680260\pi$
$929$	−32.7054	−1.07303	−0.536515	+	0.843891i	$0.680260\pi$
$930$	2.81997	0.0924704
$931$	−24.7482	−0.811088
$932$	−17.3712	−0.569013
$933$	27.3962	0.896910
$934$	−0.244058	−0.00798583
$935$	0	0
$936$	−5.17564	−0.169171
$937$	6.22366	0.203318	0.101659	−	0.994819i	$-0.467585\pi$
$937$	6.22366	0.203318	0.101659	+	0.994819i	$0.467585\pi$
$938$	−28.1293	−0.918456
$939$	31.9119	1.04141
$940$	−10.7070	−0.349223
$941$	36.0659	1.17571	0.587857	−	0.808965i	$-0.299972\pi$
$941$	36.0659	1.17571	0.587857	+	0.808965i	$0.299972\pi$
$942$	−1.72913	−0.0563380
$943$	1.83015	0.0595978
$944$	0.992373	0.0322990
$945$	29.9285	0.973573
$946$	0	0
$947$	−51.2502	−1.66541	−0.832705	−	0.553718i	$-0.813209\pi$
$947$	−51.2502	−1.66541	−0.832705	+	0.553718i	$0.813209\pi$
$948$	8.63495	0.280450
$949$	1.69157	0.0549107
$950$	−7.22227	−0.234321
$951$	−21.1318	−0.685244
$952$	5.76031	0.186693
$953$	−16.1418	−0.522884	−0.261442	−	0.965219i	$-0.584198\pi$
$953$	−16.1418	−0.522884	−0.261442	+	0.965219i	$0.584198\pi$
$954$	30.3579	0.982874
$955$	15.3092	0.495395
$956$	15.3344	0.495949
$957$	0	0
$958$	−7.36618	−0.237991
$959$	28.3489	0.915435
$960$	−1.47747	−0.0476850
$961$	−27.3571	−0.882486
$962$	8.75154	0.282161
$963$	−3.83383	−0.123543
$964$	2.77209	0.0892828
$965$	17.3520	0.558582
$966$	3.72744	0.119929
$967$	56.7063	1.82355	0.911776	−	0.410688i	$-0.134711\pi$
$967$	56.7063	1.82355	0.911776	+	0.410688i	$0.134711\pi$
$968$	0	0
$969$	3.89898	0.125253
$970$	−30.3216	−0.973568
$971$	−14.8723	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$971$	−14.8723	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$972$	16.1459	0.517879
$973$	−22.6204	−0.725178
$974$	−39.6464	−1.27035
$975$	5.84049	0.187045
$976$	−12.2576	−0.392356
$977$	−21.1684	−0.677238	−0.338619	−	0.940924i	$-0.609960\pi$
$977$	−21.1684	−0.677238	−0.338619	+	0.940924i	$0.609960\pi$
$978$	3.59180	0.114853
$979$	0	0
$980$	−13.6389	−0.435679
$981$	5.44155	0.173735
$982$	−28.6608	−0.914604
$983$	40.9306	1.30548	0.652742	−	0.757580i	$-0.273619\pi$
$983$	40.9306	1.30548	0.652742	+	0.757580i	$0.273619\pi$
$984$	1.72234	0.0549063
$985$	10.9381	0.348518
$986$	8.31441	0.264785
$987$	25.4211	0.809163
$988$	6.97328	0.221849
$989$	5.06793	0.161151
$990$	0	0
$991$	−12.6269	−0.401106	−0.200553	−	0.979683i	$-0.564274\pi$
$991$	−12.6269	−0.401106	−0.200553	+	0.979683i	$0.564274\pi$
$992$	−1.90865	−0.0605997
$993$	10.6961	0.339429
$994$	−54.7435	−1.73636
$995$	−40.5965	−1.28699
$996$	9.34360	0.296063
$997$	8.95935	0.283745	0.141873	−	0.989885i	$-0.454688\pi$
$997$	8.95935	0.283745	0.141873	+	0.989885i	$0.454688\pi$
$998$	6.79775	0.215179
$999$	−17.2075	−0.544422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.5		10
11.2	odd	10		506.2.e.h.323.3	yes	20
11.6	odd	10		506.2.e.h.47.3	✓	20
11.10	odd	2		5566.2.a.bu.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.47.3	✓	20	11.6	odd	10
506.2.e.h.323.3	yes	20	11.2	odd	10
5566.2.a.bt.1.5		10	1.1	even	1	trivial
5566.2.a.bu.1.5		10	11.10	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:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.941096 q^{3} +1.00000 q^{4} -1.56994 q^{5} -0.941096 q^{6} +3.96075 q^{7} -1.00000 q^{8} -2.11434 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.941096 q^{3} +1.00000 q^{4} -1.56994 q^{5} -0.941096 q^{6} +3.96075 q^{7} -1.00000 q^{8} -2.11434 q^{9} +1.56994 q^{10} +0.941096 q^{12} -2.44788 q^{13} -3.96075 q^{14} -1.47747 q^{15} +1.00000 q^{16} -1.45435 q^{17} +2.11434 q^{18} -2.84870 q^{19} -1.56994 q^{20} +3.72744 q^{21} -1.00000 q^{23} -0.941096 q^{24} -2.53528 q^{25} +2.44788 q^{26} -4.81308 q^{27} +3.96075 q^{28} +5.71692 q^{29} +1.47747 q^{30} +1.90865 q^{31} -1.00000 q^{32} +1.45435 q^{34} -6.21814 q^{35} -2.11434 q^{36} +3.57515 q^{37} +2.84870 q^{38} -2.30369 q^{39} +1.56994 q^{40} -1.83015 q^{41} -3.72744 q^{42} -5.06793 q^{43} +3.31939 q^{45} +1.00000 q^{46} +6.81998 q^{47} +0.941096 q^{48} +8.68752 q^{49} +2.53528 q^{50} -1.36868 q^{51} -2.44788 q^{52} +14.3581 q^{53} +4.81308 q^{54} -3.96075 q^{56} -2.68091 q^{57} -5.71692 q^{58} +0.992373 q^{59} -1.47747 q^{60} -12.2576 q^{61} -1.90865 q^{62} -8.37436 q^{63} +1.00000 q^{64} +3.84302 q^{65} +7.10203 q^{67} -1.45435 q^{68} -0.941096 q^{69} +6.21814 q^{70} +13.8215 q^{71} +2.11434 q^{72} -0.691036 q^{73} -3.57515 q^{74} -2.38594 q^{75} -2.84870 q^{76} +2.30369 q^{78} +9.17542 q^{79} -1.56994 q^{80} +1.81344 q^{81} +1.83015 q^{82} +9.92842 q^{83} +3.72744 q^{84} +2.28325 q^{85} +5.06793 q^{86} +5.38017 q^{87} +10.2925 q^{89} -3.31939 q^{90} -9.69542 q^{91} -1.00000 q^{92} +1.79622 q^{93} -6.81998 q^{94} +4.47230 q^{95} -0.941096 q^{96} -19.3138 q^{97} -8.68752 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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