LMFDB - Embedded newform 5203.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5203,2,Mod(1,5203)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5203, 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("5203.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5203 = 11^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5203.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:	$41.5461641717$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.173513.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1 $ x^5 - 2x^4 - 5x^3 + 3x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 473)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.859039$ of defining polynomial
Character	$\chi$	$=$	5203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81604 q^{2} -0.305052 q^{3} +1.29800 q^{4} -3.67508 q^{5} +0.553987 q^{6} +1.69495 q^{7} +1.27487 q^{8} -2.90694 q^{9} +O(q^{10})$	\(q-1.81604 q^{2} -0.305052 q^{3} +1.29800 q^{4} -3.67508 q^{5} +0.553987 q^{6} +1.69495 q^{7} +1.27487 q^{8} -2.90694 q^{9} +6.67408 q^{10} -0.395957 q^{12} +4.57612 q^{13} -3.07809 q^{14} +1.12109 q^{15} -4.91120 q^{16} -2.69721 q^{17} +5.27912 q^{18} -7.23133 q^{19} -4.77024 q^{20} -0.517048 q^{21} +6.32702 q^{23} -0.388901 q^{24} +8.50620 q^{25} -8.31042 q^{26} +1.80193 q^{27} +2.20004 q^{28} +4.58202 q^{29} -2.03594 q^{30} -4.29800 q^{31} +6.36919 q^{32} +4.89824 q^{34} -6.22906 q^{35} -3.77320 q^{36} -6.75629 q^{37} +13.1324 q^{38} -1.39596 q^{39} -4.68523 q^{40} +10.0705 q^{41} +0.938979 q^{42} -1.00000 q^{43} +10.6832 q^{45} -11.4901 q^{46} -11.7633 q^{47} +1.49817 q^{48} -4.12715 q^{49} -15.4476 q^{50} +0.822791 q^{51} +5.93979 q^{52} +7.23249 q^{53} -3.27237 q^{54} +2.16083 q^{56} +2.20593 q^{57} -8.32113 q^{58} +1.08810 q^{59} +1.45517 q^{60} +3.34689 q^{61} +7.80533 q^{62} -4.92712 q^{63} -1.74431 q^{64} -16.8176 q^{65} -6.45027 q^{67} -3.50097 q^{68} -1.93007 q^{69} +11.3122 q^{70} -1.84903 q^{71} -3.70596 q^{72} +5.87542 q^{73} +12.2697 q^{74} -2.59483 q^{75} -9.38624 q^{76} +2.53511 q^{78} -4.07809 q^{79} +18.0490 q^{80} +8.17115 q^{81} -18.2884 q^{82} -6.07429 q^{83} -0.671126 q^{84} +9.91247 q^{85} +1.81604 q^{86} -1.39776 q^{87} +10.8861 q^{89} -19.4012 q^{90} +7.75629 q^{91} +8.21245 q^{92} +1.31111 q^{93} +21.3627 q^{94} +26.5757 q^{95} -1.94294 q^{96} -17.9715 q^{97} +7.49507 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} - q^{3} + 7 q^{4} - 4 q^{5} + q^{6} + 9 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 - q^3 + 7 * q^4 - 4 * q^5 + q^6 + 9 * q^7 + 12 * q^8 + 4 * q^9	$ 5 q + 3 q^{2} - q^{3} + 7 q^{4} - 4 q^{5} + q^{6} + 9 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 5 q^{12} + 9 q^{13} + 7 q^{14} - 7 q^{15} + 7 q^{16} + 13 q^{17} + 19 q^{18} + 7 q^{19} + 10 q^{20} + 17 q^{21} + 8 q^{23} + 4 q^{24} + 5 q^{25} + 17 q^{26} - q^{27} + 19 q^{28} - 10 q^{29} - 21 q^{30} - 22 q^{31} + 22 q^{32} + 13 q^{34} - 15 q^{35} - 8 q^{36} - 13 q^{37} + 23 q^{38} + 23 q^{40} - 10 q^{41} + 30 q^{42} - 5 q^{43} - 7 q^{45} - 24 q^{46} - 37 q^{47} - 20 q^{48} - 2 q^{50} + 16 q^{51} + 53 q^{52} + 11 q^{53} + 15 q^{54} + 28 q^{56} - 37 q^{58} - 13 q^{59} - 30 q^{60} + 8 q^{61} - 27 q^{62} + 4 q^{63} + 32 q^{64} + 5 q^{65} - 21 q^{67} - 2 q^{68} + 14 q^{69} + 3 q^{70} - 3 q^{71} - 48 q^{72} - 2 q^{73} - 34 q^{74} + 4 q^{75} + 7 q^{76} + 3 q^{78} + 2 q^{79} + 76 q^{80} + 37 q^{81} - 40 q^{82} + 11 q^{83} + 23 q^{84} - 16 q^{85} - 3 q^{86} + 13 q^{87} + 14 q^{89} - 68 q^{90} + 18 q^{91} - 10 q^{92} - 2 q^{93} - 33 q^{94} + 28 q^{95} - 65 q^{96} - 30 q^{97} + 23 q^{98}+O(q^{100}) $ 5 * q + 3 * q^2 - q^3 + 7 * q^4 - 4 * q^5 + q^6 + 9 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 5 * q^12 + 9 * q^13 + 7 * q^14 - 7 * q^15 + 7 * q^16 + 13 * q^17 + 19 * q^18 + 7 * q^19 + 10 * q^20 + 17 * q^21 + 8 * q^23 + 4 * q^24 + 5 * q^25 + 17 * q^26 - q^27 + 19 * q^28 - 10 * q^29 - 21 * q^30 - 22 * q^31 + 22 * q^32 + 13 * q^34 - 15 * q^35 - 8 * q^36 - 13 * q^37 + 23 * q^38 + 23 * q^40 - 10 * q^41 + 30 * q^42 - 5 * q^43 - 7 * q^45 - 24 * q^46 - 37 * q^47 - 20 * q^48 - 2 * q^50 + 16 * q^51 + 53 * q^52 + 11 * q^53 + 15 * q^54 + 28 * q^56 - 37 * q^58 - 13 * q^59 - 30 * q^60 + 8 * q^61 - 27 * q^62 + 4 * q^63 + 32 * q^64 + 5 * q^65 - 21 * q^67 - 2 * q^68 + 14 * q^69 + 3 * q^70 - 3 * q^71 - 48 * q^72 - 2 * q^73 - 34 * q^74 + 4 * q^75 + 7 * q^76 + 3 * q^78 + 2 * q^79 + 76 * q^80 + 37 * q^81 - 40 * q^82 + 11 * q^83 + 23 * q^84 - 16 * q^85 - 3 * q^86 + 13 * q^87 + 14 * q^89 - 68 * q^90 + 18 * q^91 - 10 * q^92 - 2 * q^93 - 33 * q^94 + 28 * q^95 - 65 * q^96 - 30 * q^97 + 23 * 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 $

$2$	−1.81604	−1.28413	−0.642067	−	0.766649i	$-0.721923\pi$
$2$	−1.81604	−1.28413	−0.642067	+	0.766649i	$0.721923\pi$
$3$	−0.305052	−0.176122	−0.0880610	−	0.996115i	$-0.528067\pi$
$3$	−0.305052	−0.176122	−0.0880610	+	0.996115i	$0.528067\pi$
$4$	1.29800	0.648998
$5$	−3.67508	−1.64354	−0.821772	−	0.569816i	$-0.807014\pi$
$5$	−3.67508	−1.64354	−0.821772	+	0.569816i	$0.807014\pi$
$6$	0.553987	0.226164
$7$	1.69495	0.640630	0.320315	−	0.947311i	$-0.396211\pi$
$7$	1.69495	0.640630	0.320315	+	0.947311i	$0.396211\pi$
$8$	1.27487	0.450733
$9$	−2.90694	−0.968981
$10$	6.67408	2.11053
$11$	0	0
$11$	0	0
$12$	−0.395957	−0.114303
$13$	4.57612	1.26919	0.634594	−	0.772846i	$-0.281167\pi$
$13$	4.57612	1.26919	0.634594	+	0.772846i	$0.281167\pi$
$14$	−3.07809	−0.822654
$15$	1.12109	0.289464
$16$	−4.91120	−1.22780
$17$	−2.69721	−0.654170	−0.327085	−	0.944995i	$-0.606066\pi$
$17$	−2.69721	−0.654170	−0.327085	+	0.944995i	$0.606066\pi$
$18$	5.27912	1.24430
$19$	−7.23133	−1.65898	−0.829490	−	0.558521i	$-0.811369\pi$
$19$	−7.23133	−1.65898	−0.829490	+	0.558521i	$0.811369\pi$
$20$	−4.77024	−1.06666
$21$	−0.517048	−0.112829
$22$	0	0
$23$	6.32702	1.31928	0.659638	−	0.751584i	$-0.270710\pi$
$23$	6.32702	1.31928	0.659638	+	0.751584i	$0.270710\pi$
$24$	−0.388901	−0.0793840
$25$	8.50620	1.70124
$26$	−8.31042	−1.62981
$27$	1.80193	0.346781
$28$	2.20004	0.415768
$29$	4.58202	0.850860	0.425430	−	0.904991i	$-0.360123\pi$
$29$	4.58202	0.850860	0.425430	+	0.904991i	$0.360123\pi$
$30$	−2.03594	−0.371711
$31$	−4.29800	−0.771943	−0.385971	−	0.922511i	$-0.626134\pi$
$31$	−4.29800	−0.771943	−0.385971	+	0.922511i	$0.626134\pi$
$32$	6.36919	1.12593
$33$	0	0
$34$	4.89824	0.840042
$35$	−6.22906	−1.05290
$36$	−3.77320	−0.628867
$37$	−6.75629	−1.11073	−0.555363	−	0.831608i	$-0.687421\pi$
$37$	−6.75629	−1.11073	−0.555363	+	0.831608i	$0.687421\pi$
$38$	13.1324	2.13035
$39$	−1.39596	−0.223532
$40$	−4.68523	−0.740800
$41$	10.0705	1.57275	0.786374	−	0.617751i	$-0.211956\pi$
$41$	10.0705	1.57275	0.786374	+	0.617751i	$0.211956\pi$
$42$	0.938979	0.144888
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0	0
$45$	10.6832	1.59256
$46$	−11.4901	−1.69413
$47$	−11.7633	−1.71586	−0.857930	−	0.513766i	$-0.828250\pi$
$47$	−11.7633	−1.71586	−0.857930	+	0.513766i	$0.828250\pi$
$48$	1.49817	0.216243
$49$	−4.12715	−0.589593
$50$	−15.4476	−2.18462
$51$	0.822791	0.115214
$52$	5.93979	0.823701
$53$	7.23249	0.993459	0.496729	−	0.867906i	$-0.334534\pi$
$53$	7.23249	0.993459	0.496729	+	0.867906i	$0.334534\pi$
$54$	−3.27237	−0.445313
$55$	0	0
$56$	2.16083	0.288753
$57$	2.20593	0.292183
$58$	−8.32113	−1.09262
$59$	1.08810	0.141659	0.0708295	−	0.997488i	$-0.477435\pi$
$59$	1.08810	0.141659	0.0708295	+	0.997488i	$0.477435\pi$
$60$	1.45517	0.187862
$61$	3.34689	0.428526	0.214263	−	0.976776i	$-0.431265\pi$
$61$	3.34689	0.428526	0.214263	+	0.976776i	$0.431265\pi$
$62$	7.80533	0.991278
$63$	−4.92712	−0.620758
$64$	−1.74431	−0.218038
$65$	−16.8176	−2.08597
$66$	0	0
$67$	−6.45027	−0.788026	−0.394013	−	0.919105i	$-0.628913\pi$
$67$	−6.45027	−0.788026	−0.394013	+	0.919105i	$0.628913\pi$
$68$	−3.50097	−0.424555
$69$	−1.93007	−0.232354
$70$	11.3122	1.35207
$71$	−1.84903	−0.219439	−0.109720	−	0.993963i	$-0.534995\pi$
$71$	−1.84903	−0.219439	−0.109720	+	0.993963i	$0.534995\pi$
$72$	−3.70596	−0.436752
$73$	5.87542	0.687666	0.343833	−	0.939031i	$-0.388275\pi$
$73$	5.87542	0.687666	0.343833	+	0.939031i	$0.388275\pi$
$74$	12.2697	1.42632
$75$	−2.59483	−0.299626
$76$	−9.38624	−1.07668
$77$	0	0
$78$	2.53511	0.287045
$79$	−4.07809	−0.458821	−0.229411	−	0.973330i	$-0.573680\pi$
$79$	−4.07809	−0.458821	−0.229411	+	0.973330i	$0.573680\pi$
$80$	18.0490	2.01794
$81$	8.17115	0.907905
$82$	−18.2884	−2.01962
$83$	−6.07429	−0.666740	−0.333370	−	0.942796i	$-0.608186\pi$
$83$	−6.07429	−0.666740	−0.333370	+	0.942796i	$0.608186\pi$
$84$	−0.671126	−0.0732259
$85$	9.91247	1.07516
$86$	1.81604	0.195828
$87$	−1.39776	−0.149855
$88$	0	0
$89$	10.8861	1.15392	0.576961	−	0.816772i	$-0.304238\pi$
$89$	10.8861	1.15392	0.576961	+	0.816772i	$0.304238\pi$
$90$	−19.4012	−2.04506
$91$	7.75629	0.813080
$92$	8.21245	0.856208
$93$	1.31111	0.135956
$94$	21.3627	2.20339
$95$	26.5757	2.72661
$96$	−1.94294	−0.198300
$97$	−17.9715	−1.82473	−0.912367	−	0.409373i	$-0.865747\pi$
$97$	−17.9715	−1.82473	−0.912367	+	0.409373i	$0.865747\pi$
$98$	7.49507	0.757116
$99$	0	0
$100$	11.0410	1.10410
$101$	9.41087	0.936417	0.468208	−	0.883618i	$-0.344900\pi$
$101$	9.41087	0.936417	0.468208	+	0.883618i	$0.344900\pi$
$102$	−1.49422	−0.147950
$103$	−15.2573	−1.50334	−0.751671	−	0.659538i	$-0.770752\pi$
$103$	−15.2573	−1.50334	−0.751671	+	0.659538i	$0.770752\pi$
$104$	5.83394	0.572065
$105$	1.90019	0.185440
$106$	−13.1345	−1.27573
$107$	−15.4755	−1.49607	−0.748035	−	0.663659i	$-0.769003\pi$
$107$	−15.4755	−1.49607	−0.748035	+	0.663659i	$0.769003\pi$
$108$	2.33889	0.225060
$109$	−13.7505	−1.31706	−0.658529	−	0.752556i	$-0.728821\pi$
$109$	−13.7505	−1.31706	−0.658529	+	0.752556i	$0.728821\pi$
$110$	0	0
$111$	2.06102	0.195623
$112$	−8.32422	−0.786565
$113$	10.9962	1.03444	0.517218	−	0.855854i	$-0.326968\pi$
$113$	10.9962	1.03444	0.517218	+	0.855854i	$0.326968\pi$
$114$	−4.00606	−0.375202
$115$	−23.2523	−2.16829
$116$	5.94745	0.552207
$117$	−13.3025	−1.22982
$118$	−1.97604	−0.181909
$119$	−4.57164	−0.419081
$120$	1.42924	0.130471
$121$	0	0
$122$	−6.07809	−0.550284
$123$	−3.07203	−0.276996
$124$	−5.57878	−0.500990
$125$	−12.8855	−1.15252
$126$	8.94783	0.797136
$127$	−3.96548	−0.351880	−0.175940	−	0.984401i	$-0.556296\pi$
$127$	−3.96548	−0.351880	−0.175940	+	0.984401i	$0.556296\pi$
$128$	−9.57066	−0.845935
$129$	0.305052	0.0268584
$130$	30.5414	2.67866
$131$	−13.3991	−1.17068	−0.585340	−	0.810788i	$-0.699039\pi$
$131$	−13.3991	−1.17068	−0.585340	+	0.810788i	$0.699039\pi$
$132$	0	0
$133$	−12.2567	−1.06279
$134$	11.7139	1.01193
$135$	−6.62222	−0.569950
$136$	−3.43859	−0.294856
$137$	−17.0603	−1.45756	−0.728781	−	0.684747i	$-0.759913\pi$
$137$	−17.0603	−1.45756	−0.728781	+	0.684747i	$0.759913\pi$
$138$	3.50509	0.298373
$139$	0.0866761	0.00735177	0.00367589	−	0.999993i	$-0.498830\pi$
$139$	0.0866761	0.00735177	0.00367589	+	0.999993i	$0.498830\pi$
$140$	−8.08530	−0.683333
$141$	3.58844	0.302201
$142$	3.35790	0.281789
$143$	0	0
$144$	14.2766	1.18971
$145$	−16.8393	−1.39843
$146$	−10.6700	−0.883054
$147$	1.25900	0.103840
$148$	−8.76964	−0.720860
$149$	−9.20298	−0.753937	−0.376969	−	0.926226i	$-0.623034\pi$
$149$	−9.20298	−0.753937	−0.376969	+	0.926226i	$0.623034\pi$
$150$	4.71232	0.384759
$151$	7.92811	0.645181	0.322590	−	0.946539i	$-0.395446\pi$
$151$	7.92811	0.645181	0.322590	+	0.946539i	$0.395446\pi$
$152$	−9.21898	−0.747758
$153$	7.84065	0.633879
$154$	0	0
$155$	15.7955	1.26872
$156$	−1.81195	−0.145072
$157$	7.65028	0.610559	0.305279	−	0.952263i	$-0.401250\pi$
$157$	7.65028	0.610559	0.305279	+	0.952263i	$0.401250\pi$
$158$	7.40597	0.589187
$159$	−2.20629	−0.174970
$160$	−23.4073	−1.85051
$161$	10.7240	0.845168
$162$	−14.8391	−1.16587
$163$	−1.42025	−0.111242	−0.0556211	−	0.998452i	$-0.517714\pi$
$163$	−1.42025	−0.111242	−0.0556211	+	0.998452i	$0.517714\pi$
$164$	13.0715	1.02071
$165$	0	0
$166$	11.0312	0.856184
$167$	0.290777	0.0225010	0.0112505	−	0.999937i	$-0.496419\pi$
$167$	0.290777	0.0225010	0.0112505	+	0.999937i	$0.496419\pi$
$168$	−0.659166	−0.0508558
$169$	7.94090	0.610838
$170$	−18.0014	−1.38065
$171$	21.0211	1.60752
$172$	−1.29800	−0.0989713
$173$	22.3128	1.69641	0.848207	−	0.529665i	$-0.177682\pi$
$173$	22.3128	1.69641	0.848207	+	0.529665i	$0.177682\pi$
$174$	2.53838	0.192434
$175$	14.4176	1.08986
$176$	0	0
$177$	−0.331929	−0.0249493
$178$	−19.7695	−1.48179
$179$	−1.28911	−0.0963524	−0.0481762	−	0.998839i	$-0.515341\pi$
$179$	−1.28911	−0.0963524	−0.0481762	+	0.998839i	$0.515341\pi$
$180$	13.8668	1.03357
$181$	12.1619	0.903988	0.451994	−	0.892021i	$-0.350713\pi$
$181$	12.1619	0.903988	0.451994	+	0.892021i	$0.350713\pi$
$182$	−14.0857	−1.04410
$183$	−1.02098	−0.0754729
$184$	8.06611	0.594641
$185$	24.8299	1.82553
$186$	−2.38103	−0.174586
$187$	0	0
$188$	−15.2688	−1.11359
$189$	3.05417	0.222158
$190$	−48.2625	−3.50133
$191$	6.62028	0.479027	0.239513	−	0.970893i	$-0.423012\pi$
$191$	6.62028	0.479027	0.239513	+	0.970893i	$0.423012\pi$
$192$	0.532105	0.0384013
$193$	−7.20973	−0.518968	−0.259484	−	0.965747i	$-0.583552\pi$
$193$	−7.20973	−0.518968	−0.259484	+	0.965747i	$0.583552\pi$
$194$	32.6370	2.34320
$195$	5.13025	0.367385
$196$	−5.35703	−0.382645
$197$	−3.22266	−0.229605	−0.114802	−	0.993388i	$-0.536623\pi$
$197$	−3.22266	−0.229605	−0.114802	+	0.993388i	$0.536623\pi$
$198$	0	0
$199$	−17.2469	−1.22260	−0.611299	−	0.791400i	$-0.709353\pi$
$199$	−17.2469	−1.22260	−0.611299	+	0.791400i	$0.709353\pi$
$200$	10.8443	0.766805
$201$	1.96767	0.138789
$202$	−17.0905	−1.20248
$203$	7.76629	0.545086
$204$	1.06798	0.0747736
$205$	−37.0099	−2.58488
$206$	27.7078	1.93049
$207$	−18.3923	−1.27835
$208$	−22.4742	−1.55831
$209$	0	0
$210$	−3.45082	−0.238129
$211$	17.0360	1.17281	0.586405	−	0.810018i	$-0.300543\pi$
$211$	17.0360	1.17281	0.586405	+	0.810018i	$0.300543\pi$
$212$	9.38774	0.644753
$213$	0.564050	0.0386480
$214$	28.1041	1.92115
$215$	3.67508	0.250638
$216$	2.29721	0.156306
$217$	−7.28488	−0.494530
$218$	24.9714	1.69128
$219$	−1.79231	−0.121113
$220$	0	0
$221$	−12.3428	−0.830265
$222$	−3.74289	−0.251207
$223$	−2.23175	−0.149449	−0.0747246	−	0.997204i	$-0.523808\pi$
$223$	−2.23175	−0.149449	−0.0747246	+	0.997204i	$0.523808\pi$
$224$	10.7955	0.721301
$225$	−24.7270	−1.64847
$226$	−19.9695	−1.32835
$227$	21.3784	1.41893	0.709466	−	0.704740i	$-0.248936\pi$
$227$	21.3784	1.41893	0.709466	+	0.704740i	$0.248936\pi$
$228$	2.86329	0.189626
$229$	−2.95358	−0.195178	−0.0975889	−	0.995227i	$-0.531113\pi$
$229$	−2.95358	−0.195178	−0.0975889	+	0.995227i	$0.531113\pi$
$230$	42.2271	2.78437
$231$	0	0
$232$	5.84146	0.383511
$233$	6.17674	0.404652	0.202326	−	0.979318i	$-0.435150\pi$
$233$	6.17674	0.404652	0.202326	+	0.979318i	$0.435150\pi$
$234$	24.1579	1.57925
$235$	43.2312	2.82009
$236$	1.41235	0.0919364
$237$	1.24403	0.0808085
$238$	8.30227	0.538156
$239$	−22.5608	−1.45934	−0.729668	−	0.683802i	$-0.760325\pi$
$239$	−22.5608	−1.45934	−0.729668	+	0.683802i	$0.760325\pi$
$240$	−5.50590	−0.355404
$241$	−7.82010	−0.503737	−0.251869	−	0.967761i	$-0.581045\pi$
$241$	−7.82010	−0.503737	−0.251869	+	0.967761i	$0.581045\pi$
$242$	0	0
$243$	−7.89841	−0.506683
$244$	4.34426	0.278113
$245$	15.1676	0.969023
$246$	5.57892	0.355699
$247$	−33.0915	−2.10556
$248$	−5.47937	−0.347940
$249$	1.85298	0.117428
$250$	23.4006	1.47999
$251$	11.9970	0.757243	0.378622	−	0.925551i	$-0.376398\pi$
$251$	11.9970	0.757243	0.378622	+	0.925551i	$0.376398\pi$
$252$	−6.39538	−0.402871
$253$	0	0
$254$	7.20147	0.451860
$255$	−3.02382	−0.189359
$256$	20.8693	1.30433
$257$	27.0990	1.69039	0.845195	−	0.534458i	$-0.179484\pi$
$257$	27.0990	1.69039	0.845195	+	0.534458i	$0.179484\pi$
$258$	−0.553987	−0.0344897
$259$	−11.4516	−0.711565
$260$	−21.8292	−1.35379
$261$	−13.3197	−0.824467
$262$	24.3332	1.50331
$263$	−21.6802	−1.33686	−0.668430	−	0.743775i	$-0.733033\pi$
$263$	−21.6802	−1.33686	−0.668430	+	0.743775i	$0.733033\pi$
$264$	0	0
$265$	−26.5800	−1.63279
$266$	22.2587	1.36477
$267$	−3.32082	−0.203231
$268$	−8.37242	−0.511427
$269$	7.39607	0.450946	0.225473	−	0.974249i	$-0.427607\pi$
$269$	7.39607	0.450946	0.225473	+	0.974249i	$0.427607\pi$
$270$	12.0262	0.731892
$271$	22.6224	1.37421	0.687105	−	0.726558i	$-0.258881\pi$
$271$	22.6224	1.37421	0.687105	+	0.726558i	$0.258881\pi$
$272$	13.2466	0.803190
$273$	−2.36607	−0.143201
$274$	30.9822	1.87170
$275$	0	0
$276$	−2.50523	−0.150797
$277$	6.90097	0.414639	0.207320	−	0.978273i	$-0.433526\pi$
$277$	6.90097	0.414639	0.207320	+	0.978273i	$0.433526\pi$
$278$	−0.157407	−0.00944066
$279$	12.4940	0.747998
$280$	−7.94122	−0.474579
$281$	24.0519	1.43481	0.717407	−	0.696654i	$-0.245329\pi$
$281$	24.0519	1.43481	0.717407	+	0.696654i	$0.245329\pi$
$282$	−6.51674	−0.388066
$283$	14.8785	0.884437	0.442218	−	0.896907i	$-0.354192\pi$
$283$	14.8785	0.884437	0.442218	+	0.896907i	$0.354192\pi$
$284$	−2.40003	−0.142416
$285$	−8.10698	−0.480216
$286$	0	0
$287$	17.0690	1.00755
$288$	−18.5149	−1.09100
$289$	−9.72504	−0.572061
$290$	30.5808	1.79577
$291$	5.48226	0.321376
$292$	7.62627	0.446294
$293$	6.36270	0.371713	0.185856	−	0.982577i	$-0.440494\pi$
$293$	6.36270	0.371713	0.185856	+	0.982577i	$0.440494\pi$
$294$	−2.28639	−0.133345
$295$	−3.99887	−0.232823
$296$	−8.61336	−0.500641
$297$	0	0
$298$	16.7130	0.968156
$299$	28.9532	1.67441
$300$	−3.36809	−0.194457
$301$	−1.69495	−0.0976952
$302$	−14.3978	−0.828498
$303$	−2.87081	−0.164924
$304$	35.5145	2.03690
$305$	−12.3001	−0.704302
$306$	−14.2389	−0.813985
$307$	24.3275	1.38844	0.694221	−	0.719761i	$-0.255749\pi$
$307$	24.3275	1.38844	0.694221	+	0.719761i	$0.255749\pi$
$308$	0	0
$309$	4.65426	0.264772
$310$	−28.6852	−1.62921
$311$	−9.15597	−0.519187	−0.259594	−	0.965718i	$-0.583589\pi$
$311$	−9.15597	−0.519187	−0.259594	+	0.965718i	$0.583589\pi$
$312$	−1.77966	−0.100753
$313$	8.87065	0.501399	0.250699	−	0.968065i	$-0.419339\pi$
$313$	8.87065	0.501399	0.250699	+	0.968065i	$0.419339\pi$
$314$	−13.8932	−0.784039
$315$	18.1075	1.02024
$316$	−5.29335	−0.297774
$317$	−24.9593	−1.40185	−0.700927	−	0.713233i	$-0.747230\pi$
$317$	−24.9593	−1.40185	−0.700927	+	0.713233i	$0.747230\pi$
$318$	4.00670	0.224685
$319$	0	0
$320$	6.41046	0.358356
$321$	4.72083	0.263491
$322$	−19.4752	−1.08531
$323$	19.5044	1.08526
$324$	10.6061	0.589229
$325$	38.9254	2.15919
$326$	2.57922	0.142850
$327$	4.19462	0.231963
$328$	12.8385	0.708890
$329$	−19.9383	−1.09923
$330$	0	0
$331$	0.439417	0.0241525	0.0120763	−	0.999927i	$-0.496156\pi$
$331$	0.439417	0.0241525	0.0120763	+	0.999927i	$0.496156\pi$
$332$	−7.88441	−0.432713
$333$	19.6401	1.07627
$334$	−0.528062	−0.0288943
$335$	23.7052	1.29516
$336$	2.53932	0.138531
$337$	20.4070	1.11164	0.555820	−	0.831302i	$-0.312404\pi$
$337$	20.4070	1.11164	0.555820	+	0.831302i	$0.312404\pi$
$338$	−14.4210	−0.784398
$339$	−3.35442	−0.182187
$340$	12.8663	0.697776
$341$	0	0
$342$	−38.1751	−2.06427
$343$	−18.8599	−1.01834
$344$	−1.27487	−0.0687362
$345$	7.09317	0.381883
$346$	−40.5210	−2.17842
$347$	24.8001	1.33134	0.665668	−	0.746248i	$-0.268147\pi$
$347$	24.8001	1.33134	0.665668	+	0.746248i	$0.268147\pi$
$348$	−1.81428	−0.0972557
$349$	−14.8053	−0.792511	−0.396256	−	0.918140i	$-0.629691\pi$
$349$	−14.8053	−0.792511	−0.396256	+	0.918140i	$0.629691\pi$
$350$	−26.1828	−1.39953
$351$	8.24584	0.440130
$352$	0	0
$353$	−37.3022	−1.98540	−0.992698	−	0.120624i	$-0.961510\pi$
$353$	−37.3022	−1.98540	−0.992698	+	0.120624i	$0.961510\pi$
$354$	0.602795	0.0320382
$355$	6.79531	0.360658
$356$	14.1301	0.748893
$357$	1.39459	0.0738094
$358$	2.34107	0.123729
$359$	22.6447	1.19514	0.597570	−	0.801817i	$-0.296133\pi$
$359$	22.6447	1.19514	0.597570	+	0.801817i	$0.296133\pi$
$360$	13.6197	0.717821
$361$	33.2921	1.75222
$362$	−22.0865	−1.16084
$363$	0	0
$364$	10.0676	0.527687
$365$	−21.5926	−1.13021
$366$	1.85414	0.0969172
$367$	−34.7990	−1.81649	−0.908247	−	0.418434i	$-0.862579\pi$
$367$	−34.7990	−1.81649	−0.908247	+	0.418434i	$0.862579\pi$
$368$	−31.0733	−1.61981
$369$	−29.2744	−1.52396
$370$	−45.0920	−2.34422
$371$	12.2587	0.636439
$372$	1.70182	0.0882353
$373$	25.1275	1.30105	0.650527	−	0.759483i	$-0.274548\pi$
$373$	25.1275	1.30105	0.650527	+	0.759483i	$0.274548\pi$
$374$	0	0
$375$	3.93076	0.202984
$376$	−14.9967	−0.773395
$377$	20.9679	1.07990
$378$	−5.54649	−0.285281
$379$	−6.83473	−0.351076	−0.175538	−	0.984473i	$-0.556167\pi$
$379$	−6.83473	−0.351076	−0.175538	+	0.984473i	$0.556167\pi$
$380$	34.4952	1.76956
$381$	1.20968	0.0619738
$382$	−12.0227	−0.615134
$383$	32.3776	1.65442	0.827208	−	0.561895i	$-0.189928\pi$
$383$	32.3776	1.65442	0.827208	+	0.561895i	$0.189928\pi$
$384$	2.91955	0.148988
$385$	0	0
$386$	13.0931	0.666424
$387$	2.90694	0.147768
$388$	−23.3270	−1.18425
$389$	27.7264	1.40578	0.702892	−	0.711297i	$-0.251892\pi$
$389$	27.7264	1.40578	0.702892	+	0.711297i	$0.251892\pi$
$390$	−9.31673	−0.471771
$391$	−17.0653	−0.863031
$392$	−5.26157	−0.265749
$393$	4.08741	0.206183
$394$	5.85247	0.294843
$395$	14.9873	0.754093
$396$	0	0
$397$	28.2170	1.41617	0.708084	−	0.706128i	$-0.249560\pi$
$397$	28.2170	1.41617	0.708084	+	0.706128i	$0.249560\pi$
$398$	31.3210	1.56998
$399$	3.73894	0.187181
$400$	−41.7756	−2.08878
$401$	−1.11940	−0.0559001	−0.0279500	−	0.999609i	$-0.508898\pi$
$401$	−1.11940	−0.0559001	−0.0279500	+	0.999609i	$0.508898\pi$
$402$	−3.57336	−0.178223
$403$	−19.6682	−0.979741
$404$	12.2153	0.607733
$405$	−30.0296	−1.49218
$406$	−14.1039	−0.699964
$407$	0	0
$408$	1.04895	0.0519307
$409$	3.16278	0.156389	0.0781946	−	0.996938i	$-0.475084\pi$
$409$	3.16278	0.156389	0.0781946	+	0.996938i	$0.475084\pi$
$410$	67.2114	3.31933
$411$	5.20429	0.256709
$412$	−19.8039	−0.975667
$413$	1.84428	0.0907510
$414$	33.4011	1.64158
$415$	22.3235	1.09582
$416$	29.1462	1.42901
$417$	−0.0264408	−0.00129481
$418$	0	0
$419$	−5.35721	−0.261717	−0.130858	−	0.991401i	$-0.541773\pi$
$419$	−5.35721	−0.261717	−0.130858	+	0.991401i	$0.541773\pi$
$420$	2.46644	0.120350
$421$	−7.01352	−0.341818	−0.170909	−	0.985287i	$-0.554670\pi$
$421$	−7.01352	−0.341818	−0.170909	+	0.985287i	$0.554670\pi$
$422$	−30.9381	−1.50604
$423$	34.1954	1.66264
$424$	9.22045	0.447785
$425$	−22.9430	−1.11290
$426$	−1.02434	−0.0496292
$427$	5.67281	0.274527
$428$	−20.0871	−0.970947
$429$	0	0
$430$	−6.67408	−0.321853
$431$	−15.0866	−0.726697	−0.363349	−	0.931653i	$-0.618367\pi$
$431$	−15.0866	−0.726697	−0.363349	+	0.931653i	$0.618367\pi$
$432$	−8.84962	−0.425777
$433$	18.9520	0.910775	0.455388	−	0.890293i	$-0.349501\pi$
$433$	18.9520	0.910775	0.455388	+	0.890293i	$0.349501\pi$
$434$	13.2296	0.635042
$435$	5.13686	0.246294
$436$	−17.8481	−0.854768
$437$	−45.7528	−2.18865
$438$	3.25490	0.155525
$439$	5.03104	0.240118	0.120059	−	0.992767i	$-0.461692\pi$
$439$	5.03104	0.240118	0.120059	+	0.992767i	$0.461692\pi$
$440$	0	0
$441$	11.9974	0.571305
$442$	22.4150	1.06617
$443$	14.3049	0.679647	0.339824	−	0.940489i	$-0.389633\pi$
$443$	14.3049	0.679647	0.339824	+	0.940489i	$0.389633\pi$
$444$	2.67520	0.126959
$445$	−40.0072	−1.89652
$446$	4.05295	0.191913
$447$	2.80739	0.132785
$448$	−2.95651	−0.139682
$449$	35.5399	1.67723	0.838616	−	0.544723i	$-0.183365\pi$
$449$	35.5399	1.67723	0.838616	+	0.544723i	$0.183365\pi$
$450$	44.9052	2.11685
$451$	0	0
$452$	14.2730	0.671347
$453$	−2.41849	−0.113631
$454$	−38.8239	−1.82210
$455$	−28.5050	−1.33633
$456$	2.81227	0.131697
$457$	3.56176	0.166612	0.0833060	−	0.996524i	$-0.473452\pi$
$457$	3.56176	0.166612	0.0833060	+	0.996524i	$0.473452\pi$
$458$	5.36381	0.250634
$459$	−4.86018	−0.226854
$460$	−30.1814	−1.40722
$461$	−39.7024	−1.84912	−0.924562	−	0.381032i	$-0.875569\pi$
$461$	−39.7024	−1.84912	−0.924562	+	0.381032i	$0.875569\pi$
$462$	0	0
$463$	−0.441888	−0.0205363	−0.0102681	−	0.999947i	$-0.503269\pi$
$463$	−0.441888	−0.0205363	−0.0102681	+	0.999947i	$0.503269\pi$
$464$	−22.5032	−1.04469
$465$	−4.81844	−0.223450
$466$	−11.2172	−0.519627
$467$	29.1111	1.34710	0.673550	−	0.739142i	$-0.264769\pi$
$467$	29.1111	1.34710	0.673550	+	0.739142i	$0.264769\pi$
$468$	−17.2666	−0.798150
$469$	−10.9329	−0.504833
$470$	−78.5095	−3.62137
$471$	−2.33373	−0.107533
$472$	1.38719	0.0638504
$473$	0	0
$474$	−2.25921	−0.103769
$475$	−61.5111	−2.82232
$476$	−5.93397	−0.271983
$477$	−21.0244	−0.962643
$478$	40.9712	1.87398
$479$	26.9157	1.22981	0.614906	−	0.788600i	$-0.289194\pi$
$479$	26.9157	1.22981	0.614906	+	0.788600i	$0.289194\pi$
$480$	7.14045	0.325915
$481$	−30.9176	−1.40972
$482$	14.2016	0.646866
$483$	−3.27137	−0.148853
$484$	0	0
$485$	66.0468	2.99903
$486$	14.3438	0.650649
$487$	−1.35534	−0.0614163	−0.0307082	−	0.999528i	$-0.509776\pi$
$487$	−1.35534	−0.0614163	−0.0307082	+	0.999528i	$0.509776\pi$
$488$	4.26684	0.193151
$489$	0.433249	0.0195922
$490$	−27.5450	−1.24435
$491$	−25.2144	−1.13791	−0.568954	−	0.822369i	$-0.692652\pi$
$491$	−25.2144	−1.13791	−0.568954	+	0.822369i	$0.692652\pi$
$492$	−3.98748	−0.179770
$493$	−12.3587	−0.556607
$494$	60.0954	2.70382
$495$	0	0
$496$	21.1083	0.947791
$497$	−3.13400	−0.140579
$498$	−3.36508	−0.150793
$499$	−18.3180	−0.820027	−0.410013	−	0.912080i	$-0.634476\pi$
$499$	−18.3180	−0.820027	−0.410013	+	0.912080i	$0.634476\pi$
$500$	−16.7254	−0.747982
$501$	−0.0887022	−0.00396292
$502$	−21.7870	−0.972402
$503$	14.5676	0.649539	0.324769	−	0.945793i	$-0.394713\pi$
$503$	14.5676	0.649539	0.324769	+	0.945793i	$0.394713\pi$
$504$	−6.28141	−0.279796
$505$	−34.5857	−1.53904
$506$	0	0
$507$	−2.42239	−0.107582
$508$	−5.14718	−0.228369
$509$	8.37151	0.371060	0.185530	−	0.982639i	$-0.440600\pi$
$509$	8.37151	0.371060	0.185530	+	0.982639i	$0.440600\pi$
$510$	5.49138	0.243162
$511$	9.95852	0.440539
$512$	−18.7581	−0.829000
$513$	−13.0303	−0.575303
$514$	−49.2129	−2.17069
$515$	56.0716	2.47081
$516$	0.395957	0.0174310
$517$	0	0
$518$	20.7965	0.913744
$519$	−6.80658	−0.298776
$520$	−21.4402	−0.940215
$521$	−27.6086	−1.20955	−0.604776	−	0.796395i	$-0.706737\pi$
$521$	−27.6086	−1.20955	−0.604776	+	0.796395i	$0.706737\pi$
$522$	24.1890	1.05873
$523$	6.85374	0.299693	0.149847	−	0.988709i	$-0.452122\pi$
$523$	6.85374	0.299693	0.149847	+	0.988709i	$0.452122\pi$
$524$	−17.3919	−0.759770
$525$	−4.39811	−0.191949
$526$	39.3721	1.71671
$527$	11.5926	0.504982
$528$	0	0
$529$	17.0312	0.740489
$530$	48.2702	2.09672
$531$	−3.16306	−0.137265
$532$	−15.9092	−0.689751
$533$	46.0838	1.99611
$534$	6.03074	0.260976
$535$	56.8736	2.45886
$536$	−8.22323	−0.355189
$537$	0.393245	0.0169698
$538$	−13.4315	−0.579075
$539$	0	0
$540$	−8.59562	−0.369896
$541$	19.4086	0.834441	0.417221	−	0.908805i	$-0.363004\pi$
$541$	19.4086	0.834441	0.417221	+	0.908805i	$0.363004\pi$
$542$	−41.0831	−1.76467
$543$	−3.71002	−0.159212
$544$	−17.1791	−0.736547
$545$	50.5341	2.16464
$546$	4.29688	0.183890
$547$	24.6752	1.05504	0.527519	−	0.849543i	$-0.323122\pi$
$547$	24.6752	1.05504	0.527519	+	0.849543i	$0.323122\pi$
$548$	−22.1442	−0.945955
$549$	−9.72923	−0.415234
$550$	0	0
$551$	−33.1341	−1.41156
$552$	−2.46058	−0.104729
$553$	−6.91215	−0.293935
$554$	−12.5324	−0.532452
$555$	−7.57441	−0.321516
$556$	0.112505	0.00477129
$557$	−13.0290	−0.552057	−0.276028	−	0.961150i	$-0.589018\pi$
$557$	−13.0290	−0.552057	−0.276028	+	0.961150i	$0.589018\pi$
$558$	−22.6896	−0.960529
$559$	−4.57612	−0.193549
$560$	30.5922	1.29276
$561$	0	0
$562$	−43.6791	−1.84249
$563$	−10.4985	−0.442461	−0.221230	−	0.975222i	$-0.571007\pi$
$563$	−10.4985	−0.442461	−0.221230	+	0.975222i	$0.571007\pi$
$564$	4.65778	0.196128
$565$	−40.4119	−1.70014
$566$	−27.0200	−1.13573
$567$	13.8497	0.581631
$568$	−2.35726	−0.0989084
$569$	31.0513	1.30174	0.650868	−	0.759191i	$-0.274405\pi$
$569$	31.0513	1.30174	0.650868	+	0.759191i	$0.274405\pi$
$570$	14.7226	0.616661
$571$	13.3803	0.559950	0.279975	−	0.960007i	$-0.409674\pi$
$571$	13.3803	0.559950	0.279975	+	0.960007i	$0.409674\pi$
$572$	0	0
$573$	−2.01953	−0.0843672
$574$	−30.9979	−1.29383
$575$	53.8189	2.24440
$576$	5.07060	0.211275
$577$	32.6977	1.36122	0.680612	−	0.732644i	$-0.261714\pi$
$577$	32.6977	1.36122	0.680612	+	0.732644i	$0.261714\pi$
$578$	17.6610	0.734603
$579$	2.19934	0.0914016
$580$	−21.8573	−0.907576
$581$	−10.2956	−0.427134
$582$	−9.95600	−0.412689
$583$	0	0
$584$	7.49037	0.309954
$585$	48.8878	2.02126
$586$	−11.5549	−0.477329
$587$	18.5172	0.764288	0.382144	−	0.924103i	$-0.375186\pi$
$587$	18.5172	0.764288	0.382144	+	0.924103i	$0.375186\pi$
$588$	1.63417	0.0673922
$589$	31.0802	1.28064
$590$	7.26209	0.298976
$591$	0.983079	0.0404385
$592$	33.1815	1.36375
$593$	7.01816	0.288201	0.144101	−	0.989563i	$-0.453971\pi$
$593$	7.01816	0.288201	0.144101	+	0.989563i	$0.453971\pi$
$594$	0	0
$595$	16.8011	0.688779
$596$	−11.9454	−0.489304
$597$	5.26120	0.215326
$598$	−52.5802	−2.15016
$599$	−15.1817	−0.620307	−0.310154	−	0.950686i	$-0.600380\pi$
$599$	−15.1817	−0.620307	−0.310154	+	0.950686i	$0.600380\pi$
$600$	−3.30807	−0.135051
$601$	23.2310	0.947611	0.473805	−	0.880630i	$-0.342880\pi$
$601$	23.2310	0.947611	0.473805	+	0.880630i	$0.342880\pi$
$602$	3.07809	0.125454
$603$	18.7506	0.763582
$604$	10.2907	0.418721
$605$	0	0
$606$	5.21350	0.211784
$607$	21.3389	0.866119	0.433059	−	0.901365i	$-0.357434\pi$
$607$	21.3389	0.866119	0.433059	+	0.901365i	$0.357434\pi$
$608$	−46.0577	−1.86789
$609$	−2.36912	−0.0960017
$610$	22.3375	0.904417
$611$	−53.8305	−2.17775
$612$	10.1771	0.411386
$613$	16.7720	0.677414	0.338707	−	0.940892i	$-0.390011\pi$
$613$	16.7720	0.677414	0.338707	+	0.940892i	$0.390011\pi$
$614$	−44.1797	−1.78295
$615$	11.2899	0.455255
$616$	0	0
$617$	−31.2703	−1.25890	−0.629448	−	0.777043i	$-0.716719\pi$
$617$	−31.2703	−1.25890	−0.629448	+	0.777043i	$0.716719\pi$
$618$	−8.45232	−0.340002
$619$	41.2111	1.65642	0.828208	−	0.560421i	$-0.189361\pi$
$619$	41.2111	1.65642	0.828208	+	0.560421i	$0.189361\pi$
$620$	20.5025	0.823399
$621$	11.4008	0.457500
$622$	16.6276	0.666705
$623$	18.4513	0.739237
$624$	6.85582	0.274452
$625$	4.82439	0.192976
$626$	−16.1094	−0.643863
$627$	0	0
$628$	9.93003	0.396251
$629$	18.2232	0.726605
$630$	−32.8840	−1.31013
$631$	5.95746	0.237163	0.118581	−	0.992944i	$-0.462165\pi$
$631$	5.95746	0.237163	0.118581	+	0.992944i	$0.462165\pi$
$632$	−5.19902	−0.206806
$633$	−5.19688	−0.206558
$634$	45.3271	1.80017
$635$	14.5735	0.578330
$636$	−2.86375	−0.113555
$637$	−18.8864	−0.748305
$638$	0	0
$639$	5.37501	0.212632
$640$	35.1729	1.39033
$641$	−2.93806	−0.116046	−0.0580231	−	0.998315i	$-0.518480\pi$
$641$	−2.93806	−0.116046	−0.0580231	+	0.998315i	$0.518480\pi$
$642$	−8.57321	−0.338358
$643$	26.9283	1.06195	0.530975	−	0.847388i	$-0.321826\pi$
$643$	26.9283	1.06195	0.530975	+	0.847388i	$0.321826\pi$
$644$	13.9197	0.548512
$645$	−1.12109	−0.0441429
$646$	−35.4208	−1.39361
$647$	2.52674	0.0993364	0.0496682	−	0.998766i	$-0.484184\pi$
$647$	2.52674	0.0993364	0.0496682	+	0.998766i	$0.484184\pi$
$648$	10.4171	0.409223
$649$	0	0
$650$	−70.6900	−2.77269
$651$	2.22227	0.0870976
$652$	−1.84347	−0.0721960
$653$	9.45716	0.370087	0.185044	−	0.982730i	$-0.440757\pi$
$653$	9.45716	0.370087	0.185044	+	0.982730i	$0.440757\pi$
$654$	−7.61758	−0.297871
$655$	49.2426	1.92407
$656$	−49.4582	−1.93102
$657$	−17.0795	−0.666335
$658$	36.2086	1.41156
$659$	−19.2772	−0.750932	−0.375466	−	0.926836i	$-0.622517\pi$
$659$	−19.2772	−0.750932	−0.375466	+	0.926836i	$0.622517\pi$
$660$	0	0
$661$	5.57506	0.216845	0.108422	−	0.994105i	$-0.465420\pi$
$661$	5.57506	0.216845	0.108422	+	0.994105i	$0.465420\pi$
$662$	−0.797998	−0.0310151
$663$	3.76519	0.146228
$664$	−7.74391	−0.300522
$665$	45.0444	1.74675
$666$	−35.6673	−1.38208
$667$	28.9906	1.12252
$668$	0.377428	0.0146031
$669$	0.680801	0.0263213
$670$	−43.0496	−1.66315
$671$	0	0
$672$	−3.29318	−0.127037
$673$	−18.4553	−0.711398	−0.355699	−	0.934601i	$-0.615757\pi$
$673$	−18.4553	−0.711398	−0.355699	+	0.934601i	$0.615757\pi$
$674$	−37.0599	−1.42749
$675$	15.3275	0.589957
$676$	10.3073	0.396433
$677$	7.50666	0.288504	0.144252	−	0.989541i	$-0.453922\pi$
$677$	7.50666	0.288504	0.144252	+	0.989541i	$0.453922\pi$
$678$	6.09175	0.233952
$679$	−30.4608	−1.16898
$680$	12.6371	0.484609
$681$	−6.52152	−0.249905
$682$	0	0
$683$	−33.6593	−1.28794	−0.643968	−	0.765052i	$-0.722713\pi$
$683$	−33.6593	−1.28794	−0.643968	+	0.765052i	$0.722713\pi$
$684$	27.2853	1.04328
$685$	62.6980	2.39557
$686$	34.2504	1.30769
$687$	0.900995	0.0343751
$688$	4.91120	0.187238
$689$	33.0968	1.26089
$690$	−12.8815	−0.490389
$691$	34.7772	1.32299	0.661494	−	0.749950i	$-0.269923\pi$
$691$	34.7772	1.32299	0.661494	+	0.749950i	$0.269923\pi$
$692$	28.9620	1.10097
$693$	0	0
$694$	−45.0379	−1.70961
$695$	−0.318542	−0.0120830
$696$	−1.78195	−0.0675447
$697$	−27.1623	−1.02885
$698$	26.8870	1.01769
$699$	−1.88423	−0.0712681
$700$	18.7139	0.707320
$701$	−22.6611	−0.855897	−0.427949	−	0.903803i	$-0.640764\pi$
$701$	−22.6611	−0.855897	−0.427949	+	0.903803i	$0.640764\pi$
$702$	−14.9748	−0.565186
$703$	48.8570	1.84267
$704$	0	0
$705$	−13.1878	−0.496680
$706$	67.7423	2.54951
$707$	15.9509	0.599897
$708$	−0.430842	−0.0161920
$709$	20.9544	0.786958	0.393479	−	0.919334i	$-0.371271\pi$
$709$	20.9544	0.786958	0.393479	+	0.919334i	$0.371271\pi$
$710$	−12.3406	−0.463133
$711$	11.8548	0.444589
$712$	13.8783	0.520111
$713$	−27.1935	−1.01841
$714$	−2.53263	−0.0947811
$715$	0	0
$716$	−1.67326	−0.0625325
$717$	6.88222	0.257021
$718$	−41.1236	−1.53472
$719$	−0.506869	−0.0189030	−0.00945151	−	0.999955i	$-0.503009\pi$
$719$	−0.506869	−0.0189030	−0.00945151	+	0.999955i	$0.503009\pi$
$720$	−52.4675	−1.95535
$721$	−25.8603	−0.963086
$722$	−60.4598	−2.25008
$723$	2.38554	0.0887192
$724$	15.7861	0.586686
$725$	38.9756	1.44752
$726$	0	0
$727$	−33.9326	−1.25849	−0.629245	−	0.777207i	$-0.716636\pi$
$727$	−33.9326	−1.25849	−0.629245	+	0.777207i	$0.716636\pi$
$728$	9.88823	0.366482
$729$	−22.1040	−0.818667
$730$	39.2130	1.45134
$731$	2.69721	0.0997600
$732$	−1.32523	−0.0489818
$733$	−10.1908	−0.376406	−0.188203	−	0.982130i	$-0.560266\pi$
$733$	−10.1908	−0.376406	−0.188203	+	0.982130i	$0.560266\pi$
$734$	63.1964	2.33262
$735$	−4.62691	−0.170666
$736$	40.2980	1.48541
$737$	0	0
$738$	53.1634	1.95697
$739$	−19.0554	−0.700965	−0.350483	−	0.936569i	$-0.613982\pi$
$739$	−19.0554	−0.700965	−0.350483	+	0.936569i	$0.613982\pi$
$740$	32.2291	1.18477
$741$	10.0946	0.370835
$742$	−22.2623	−0.817273
$743$	−0.530328	−0.0194559	−0.00972793	−	0.999953i	$-0.503097\pi$
$743$	−0.530328	−0.0194559	−0.00972793	+	0.999953i	$0.503097\pi$
$744$	1.67149	0.0612799
$745$	33.8217	1.23913
$746$	−45.6326	−1.67073
$747$	17.6576	0.646059
$748$	0	0
$749$	−26.2301	−0.958428
$750$	−7.13842	−0.260658
$751$	28.0401	1.02320	0.511599	−	0.859224i	$-0.329053\pi$
$751$	28.0401	1.02320	0.511599	+	0.859224i	$0.329053\pi$
$752$	57.7721	2.10673
$753$	−3.65971	−0.133367
$754$	−38.0785	−1.38674
$755$	−29.1364	−1.06038
$756$	3.96430	0.144180
$757$	8.43826	0.306694	0.153347	−	0.988172i	$-0.450995\pi$
$757$	8.43826	0.306694	0.153347	+	0.988172i	$0.450995\pi$
$758$	12.4121	0.450829
$759$	0	0
$760$	33.8805	1.22897
$761$	47.3032	1.71474	0.857369	−	0.514702i	$-0.172098\pi$
$761$	47.3032	1.71474	0.857369	+	0.514702i	$0.172098\pi$
$762$	−2.19683	−0.0795826
$763$	−23.3063	−0.843746
$764$	8.59310	0.310887
$765$	−28.8150	−1.04181
$766$	−58.7989	−2.12449
$767$	4.97930	0.179792
$768$	−6.36623	−0.229721
$769$	13.1289	0.473439	0.236719	−	0.971578i	$-0.423928\pi$
$769$	13.1289	0.473439	0.236719	+	0.971578i	$0.423928\pi$
$770$	0	0
$771$	−8.26662	−0.297715
$772$	−9.35820	−0.336809
$773$	−54.1985	−1.94938	−0.974692	−	0.223551i	$-0.928235\pi$
$773$	−54.1985	−1.94938	−0.974692	+	0.223551i	$0.928235\pi$
$774$	−5.27912	−0.189754
$775$	−36.5596	−1.31326
$776$	−22.9113	−0.822468
$777$	3.49332	0.125322
$778$	−50.3522	−1.80521
$779$	−72.8231	−2.60916
$780$	6.65905	0.238432
$781$	0	0
$782$	30.9913	1.10825
$783$	8.25647	0.295062
$784$	20.2693	0.723902
$785$	−28.1154	−1.00348
$786$	−7.42290	−0.264766
$787$	−17.2359	−0.614392	−0.307196	−	0.951646i	$-0.599391\pi$
$787$	−17.2359	−0.614392	−0.307196	+	0.951646i	$0.599391\pi$
$788$	−4.18300	−0.149013
$789$	6.61360	0.235451
$790$	−27.2175	−0.968356
$791$	18.6380	0.662691
$792$	0	0
$793$	15.3158	0.543880
$794$	−51.2431	−1.81855
$795$	8.10828	0.287571
$796$	−22.3864	−0.793464
$797$	37.2292	1.31873	0.659363	−	0.751825i	$-0.270826\pi$
$797$	37.2292	1.31873	0.659363	+	0.751825i	$0.270826\pi$
$798$	−6.79006	−0.240366
$799$	31.7283	1.12246
$800$	54.1776	1.91547
$801$	−31.6452	−1.11813
$802$	2.03287	0.0717831
$803$	0	0
$804$	2.55403	0.0900736
$805$	−39.4114	−1.38907
$806$	35.7181	1.25812
$807$	−2.25619	−0.0794216
$808$	11.9976	0.422074
$809$	−22.5494	−0.792795	−0.396398	−	0.918079i	$-0.629740\pi$
$809$	−22.5494	−0.792795	−0.396398	+	0.918079i	$0.629740\pi$
$810$	54.5349	1.91616
$811$	21.5863	0.757996	0.378998	−	0.925398i	$-0.376269\pi$
$811$	21.5863	0.757996	0.378998	+	0.925398i	$0.376269\pi$
$812$	10.0806	0.353760
$813$	−6.90100	−0.242029
$814$	0	0
$815$	5.21951	0.182831
$816$	−4.04089	−0.141459
$817$	7.23133	0.252992
$818$	−5.74373	−0.200825
$819$	−22.5471	−0.787859
$820$	−48.0387	−1.67758
$821$	0.0514641	0.00179611	0.000898055	−	1.00000i	$-0.499714\pi$
$821$	0.0514641	0.00179611	0.000898055		1.00000i	$0.499714\pi$
$822$	−9.45119	−0.329648
$823$	−21.0281	−0.732993	−0.366496	−	0.930419i	$-0.619443\pi$
$823$	−21.0281	−0.732993	−0.366496	+	0.930419i	$0.619443\pi$
$824$	−19.4510	−0.677606
$825$	0	0
$826$	−3.34928	−0.116536
$827$	43.8171	1.52367	0.761836	−	0.647770i	$-0.224298\pi$
$827$	43.8171	1.52367	0.761836	+	0.647770i	$0.224298\pi$
$828$	−23.8731	−0.829649
$829$	−35.7788	−1.24265	−0.621324	−	0.783553i	$-0.713405\pi$
$829$	−35.7788	−1.24265	−0.621324	+	0.783553i	$0.713405\pi$
$830$	−40.5403	−1.40718
$831$	−2.10516	−0.0730271
$832$	−7.98216	−0.276732
$833$	11.1318	0.385694
$834$	0.0480174	0.00166271
$835$	−1.06863	−0.0369814
$836$	0	0
$837$	−7.74467	−0.267695
$838$	9.72890	0.336079
$839$	24.4614	0.844502	0.422251	−	0.906479i	$-0.361240\pi$
$839$	24.4614	0.844502	0.422251	+	0.906479i	$0.361240\pi$
$840$	2.42249	0.0835838
$841$	−8.00509	−0.276037
$842$	12.7368	0.438940
$843$	−7.33708	−0.252702
$844$	22.1127	0.761151
$845$	−29.1834	−1.00394
$846$	−62.1001	−2.13505
$847$	0	0
$848$	−35.5202	−1.21977
$849$	−4.53873	−0.155769
$850$	41.6654	1.42911
$851$	−42.7472	−1.46536
$852$	0.732134	0.0250825
$853$	17.1103	0.585847	0.292923	−	0.956136i	$-0.405372\pi$
$853$	17.1103	0.585847	0.292923	+	0.956136i	$0.405372\pi$
$854$	−10.3020	−0.352529
$855$	−77.2541	−2.64203
$856$	−19.7292	−0.674329
$857$	49.7591	1.69974	0.849869	−	0.526994i	$-0.176681\pi$
$857$	49.7591	1.69974	0.849869	+	0.526994i	$0.176681\pi$
$858$	0	0
$859$	45.0213	1.53611	0.768053	−	0.640386i	$-0.221226\pi$
$859$	45.0213	1.53611	0.768053	+	0.640386i	$0.221226\pi$
$860$	4.77024	0.162664
$861$	−5.20693	−0.177452
$862$	27.3979	0.933176
$863$	−28.5688	−0.972493	−0.486246	−	0.873822i	$-0.661634\pi$
$863$	−28.5688	−0.972493	−0.486246	+	0.873822i	$0.661634\pi$
$864$	11.4768	0.390449
$865$	−82.0014	−2.78813
$866$	−34.4176	−1.16956
$867$	2.96665	0.100753
$868$	−9.45575	−0.320949
$869$	0	0
$870$	−9.32874	−0.316274
$871$	−29.5172	−1.00015
$872$	−17.5300	−0.593641
$873$	52.2423	1.76813
$874$	83.0889	2.81052
$875$	−21.8403	−0.738338
$876$	−2.32641	−0.0786021
$877$	13.3572	0.451040	0.225520	−	0.974238i	$-0.427592\pi$
$877$	13.3572	0.451040	0.225520	+	0.974238i	$0.427592\pi$
$878$	−9.13656	−0.308344
$879$	−1.94096	−0.0654668
$880$	0	0
$881$	22.8410	0.769531	0.384766	−	0.923014i	$-0.374282\pi$
$881$	22.8410	0.769531	0.384766	+	0.923014i	$0.374282\pi$
$882$	−21.7877	−0.733631
$883$	17.5197	0.589585	0.294792	−	0.955561i	$-0.404750\pi$
$883$	17.5197	0.589585	0.294792	+	0.955561i	$0.404750\pi$
$884$	−16.0209	−0.538841
$885$	1.21986	0.0410052
$886$	−25.9783	−0.872757
$887$	1.01107	0.0339483	0.0169742	−	0.999856i	$-0.494597\pi$
$887$	1.01107	0.0339483	0.0169742	+	0.999856i	$0.494597\pi$
$888$	2.62753	0.0881740
$889$	−6.72129	−0.225425
$890$	72.6546	2.43539
$891$	0	0
$892$	−2.89681	−0.0969922
$893$	85.0646	2.84658
$894$	−5.09833	−0.170514
$895$	4.73757	0.158359
$896$	−16.2218	−0.541931
$897$	−8.83225	−0.294900
$898$	−64.5419	−2.15379
$899$	−19.6935	−0.656815
$900$	−32.0956	−1.06985
$901$	−19.5076	−0.649891
$902$	0	0
$903$	0.517048	0.0172063
$904$	14.0187	0.466255
$905$	−44.6960	−1.48574
$906$	4.39207	0.145917
$907$	−42.6108	−1.41487	−0.707434	−	0.706779i	$-0.750148\pi$
$907$	−42.6108	−1.41487	−0.707434	+	0.706779i	$0.750148\pi$
$908$	27.7490	0.920884
$909$	−27.3569	−0.907370
$910$	51.7661	1.71603
$911$	34.9403	1.15762	0.578811	−	0.815462i	$-0.303517\pi$
$911$	34.9403	1.15762	0.578811	+	0.815462i	$0.303517\pi$
$912$	−10.8338	−0.358742
$913$	0	0
$914$	−6.46829	−0.213952
$915$	3.75217	0.124043
$916$	−3.83373	−0.126670
$917$	−22.7107	−0.749973
$918$	8.82628	0.291311
$919$	26.1613	0.862981	0.431491	−	0.902117i	$-0.357988\pi$
$919$	26.1613	0.862981	0.431491	+	0.902117i	$0.357988\pi$
$920$	−29.6436	−0.977320
$921$	−7.42116	−0.244535
$922$	72.1010	2.37452
$923$	−8.46137	−0.278509
$924$	0	0
$925$	−57.4703	−1.88961
$926$	0.802485	0.0263713
$927$	44.3520	1.45671
$928$	29.1838	0.958004
$929$	6.38212	0.209391	0.104695	−	0.994504i	$-0.466613\pi$
$929$	6.38212	0.209391	0.104695	+	0.994504i	$0.466613\pi$
$930$	8.75048	0.286940
$931$	29.8448	0.978124
$932$	8.01739	0.262618
$933$	2.79305	0.0914403
$934$	−52.8668	−1.72986
$935$	0	0
$936$	−16.9589	−0.554320
$937$	10.0030	0.326783	0.163392	−	0.986561i	$-0.447757\pi$
$937$	10.0030	0.326783	0.163392	+	0.986561i	$0.447757\pi$
$938$	19.8545	0.648273
$939$	−2.70601	−0.0883074
$940$	56.1139	1.83024
$941$	10.2061	0.332709	0.166355	−	0.986066i	$-0.446800\pi$
$941$	10.2061	0.332709	0.166355	+	0.986066i	$0.446800\pi$
$942$	4.23815	0.138086
$943$	63.7163	2.07489
$944$	−5.34389	−0.173929
$945$	−11.2243	−0.365127
$946$	0	0
$947$	25.3721	0.824481	0.412241	−	0.911075i	$-0.364746\pi$
$947$	25.3721	0.824481	0.412241	+	0.911075i	$0.364746\pi$
$948$	1.61475	0.0524446
$949$	26.8866	0.872777
$950$	111.707	3.62424
$951$	7.61389	0.246897
$952$	−5.82822	−0.188894
$953$	−3.25015	−0.105283	−0.0526413	−	0.998613i	$-0.516764\pi$
$953$	−3.25015	−0.105283	−0.0526413	+	0.998613i	$0.516764\pi$
$954$	38.1812	1.23616
$955$	−24.3300	−0.787302
$956$	−29.2838	−0.947106
$957$	0	0
$958$	−48.8800	−1.57924
$959$	−28.9164	−0.933758
$960$	−1.95553	−0.0631143
$961$	−12.5272	−0.404104
$962$	56.1476	1.81027
$963$	44.9863	1.44966
$964$	−10.1505	−0.326924
$965$	26.4963	0.852947
$966$	5.94094	0.191147
$967$	−41.1889	−1.32455	−0.662273	−	0.749262i	$-0.730408\pi$
$967$	−41.1889	−1.32455	−0.662273	+	0.749262i	$0.730408\pi$
$968$	0	0
$969$	−5.94988	−0.191138
$970$	−119.944	−3.85116
$971$	−14.7243	−0.472525	−0.236262	−	0.971689i	$-0.575922\pi$
$971$	−14.7243	−0.472525	−0.236262	+	0.971689i	$0.575922\pi$
$972$	−10.2521	−0.328836
$973$	0.146912	0.00470977
$974$	2.46135	0.0788668
$975$	−11.8743	−0.380281
$976$	−16.4373	−0.526144
$977$	−11.9106	−0.381052	−0.190526	−	0.981682i	$-0.561019\pi$
$977$	−11.9106	−0.381052	−0.190526	+	0.981682i	$0.561019\pi$
$978$	−0.786797	−0.0251590
$979$	0	0
$980$	19.6875	0.628894
$981$	39.9719	1.27620
$982$	45.7902	1.46123
$983$	34.3504	1.09561	0.547804	−	0.836607i	$-0.315464\pi$
$983$	34.3504	1.09561	0.547804	+	0.836607i	$0.315464\pi$
$984$	−3.91642	−0.124851
$985$	11.8435	0.377366
$986$	22.4439	0.714758
$987$	6.08221	0.193599
$988$	−42.9526	−1.36650
$989$	−6.32702	−0.201188
$990$	0	0
$991$	−19.6167	−0.623146	−0.311573	−	0.950222i	$-0.600856\pi$
$991$	−19.6167	−0.623146	−0.311573	+	0.950222i	$0.600856\pi$
$992$	−27.3748	−0.869150
$993$	−0.134045	−0.00425379
$994$	5.69147	0.180522
$995$	63.3836	2.00939
$996$	2.40516	0.0762104
$997$	24.2401	0.767693	0.383847	−	0.923397i	$-0.374599\pi$
$997$	24.2401	0.767693	0.383847	+	0.923397i	$0.374599\pi$
$998$	33.2662	1.05302
$999$	−12.1743	−0.385179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5203.2.a.i.1.1		5
11.10	odd	2		473.2.a.d.1.5	✓	5
33.32	even	2		4257.2.a.o.1.1		5
44.43	even	2		7568.2.a.bc.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
473.2.a.d.1.5	✓	5	11.10	odd	2
4257.2.a.o.1.1		5	33.32	even	2
5203.2.a.i.1.1		5	1.1	even	1	trivial
7568.2.a.bc.1.3		5	44.43	even	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:	\( N \)	\(=\)	\( 5203 = 11^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5203.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81604 q^{2} -0.305052 q^{3} +1.29800 q^{4} -3.67508 q^{5} +0.553987 q^{6} +1.69495 q^{7} +1.27487 q^{8} -2.90694 q^{9} +O(q^{10})\)	\(q-1.81604 q^{2} -0.305052 q^{3} +1.29800 q^{4} -3.67508 q^{5} +0.553987 q^{6} +1.69495 q^{7} +1.27487 q^{8} -2.90694 q^{9} +6.67408 q^{10} -0.395957 q^{12} +4.57612 q^{13} -3.07809 q^{14} +1.12109 q^{15} -4.91120 q^{16} -2.69721 q^{17} +5.27912 q^{18} -7.23133 q^{19} -4.77024 q^{20} -0.517048 q^{21} +6.32702 q^{23} -0.388901 q^{24} +8.50620 q^{25} -8.31042 q^{26} +1.80193 q^{27} +2.20004 q^{28} +4.58202 q^{29} -2.03594 q^{30} -4.29800 q^{31} +6.36919 q^{32} +4.89824 q^{34} -6.22906 q^{35} -3.77320 q^{36} -6.75629 q^{37} +13.1324 q^{38} -1.39596 q^{39} -4.68523 q^{40} +10.0705 q^{41} +0.938979 q^{42} -1.00000 q^{43} +10.6832 q^{45} -11.4901 q^{46} -11.7633 q^{47} +1.49817 q^{48} -4.12715 q^{49} -15.4476 q^{50} +0.822791 q^{51} +5.93979 q^{52} +7.23249 q^{53} -3.27237 q^{54} +2.16083 q^{56} +2.20593 q^{57} -8.32113 q^{58} +1.08810 q^{59} +1.45517 q^{60} +3.34689 q^{61} +7.80533 q^{62} -4.92712 q^{63} -1.74431 q^{64} -16.8176 q^{65} -6.45027 q^{67} -3.50097 q^{68} -1.93007 q^{69} +11.3122 q^{70} -1.84903 q^{71} -3.70596 q^{72} +5.87542 q^{73} +12.2697 q^{74} -2.59483 q^{75} -9.38624 q^{76} +2.53511 q^{78} -4.07809 q^{79} +18.0490 q^{80} +8.17115 q^{81} -18.2884 q^{82} -6.07429 q^{83} -0.671126 q^{84} +9.91247 q^{85} +1.81604 q^{86} -1.39776 q^{87} +10.8861 q^{89} -19.4012 q^{90} +7.75629 q^{91} +8.21245 q^{92} +1.31111 q^{93} +21.3627 q^{94} +26.5757 q^{95} -1.94294 q^{96} -17.9715 q^{97} +7.49507 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} - q^{3} + 7 q^{4} - 4 q^{5} + q^{6} + 9 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 - q^3 + 7 * q^4 - 4 * q^5 + q^6 + 9 * q^7 + 12 * q^8 + 4 * q^9	\( 5 q + 3 q^{2} - q^{3} + 7 q^{4} - 4 q^{5} + q^{6} + 9 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 5 q^{12} + 9 q^{13} + 7 q^{14} - 7 q^{15} + 7 q^{16} + 13 q^{17} + 19 q^{18} + 7 q^{19} + 10 q^{20} + 17 q^{21} + 8 q^{23} + 4 q^{24} + 5 q^{25} + 17 q^{26} - q^{27} + 19 q^{28} - 10 q^{29} - 21 q^{30} - 22 q^{31} + 22 q^{32} + 13 q^{34} - 15 q^{35} - 8 q^{36} - 13 q^{37} + 23 q^{38} + 23 q^{40} - 10 q^{41} + 30 q^{42} - 5 q^{43} - 7 q^{45} - 24 q^{46} - 37 q^{47} - 20 q^{48} - 2 q^{50} + 16 q^{51} + 53 q^{52} + 11 q^{53} + 15 q^{54} + 28 q^{56} - 37 q^{58} - 13 q^{59} - 30 q^{60} + 8 q^{61} - 27 q^{62} + 4 q^{63} + 32 q^{64} + 5 q^{65} - 21 q^{67} - 2 q^{68} + 14 q^{69} + 3 q^{70} - 3 q^{71} - 48 q^{72} - 2 q^{73} - 34 q^{74} + 4 q^{75} + 7 q^{76} + 3 q^{78} + 2 q^{79} + 76 q^{80} + 37 q^{81} - 40 q^{82} + 11 q^{83} + 23 q^{84} - 16 q^{85} - 3 q^{86} + 13 q^{87} + 14 q^{89} - 68 q^{90} + 18 q^{91} - 10 q^{92} - 2 q^{93} - 33 q^{94} + 28 q^{95} - 65 q^{96} - 30 q^{97} + 23 q^{98}+O(q^{100}) \) 5 * q + 3 * q^2 - q^3 + 7 * q^4 - 4 * q^5 + q^6 + 9 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 5 * q^12 + 9 * q^13 + 7 * q^14 - 7 * q^15 + 7 * q^16 + 13 * q^17 + 19 * q^18 + 7 * q^19 + 10 * q^20 + 17 * q^21 + 8 * q^23 + 4 * q^24 + 5 * q^25 + 17 * q^26 - q^27 + 19 * q^28 - 10 * q^29 - 21 * q^30 - 22 * q^31 + 22 * q^32 + 13 * q^34 - 15 * q^35 - 8 * q^36 - 13 * q^37 + 23 * q^38 + 23 * q^40 - 10 * q^41 + 30 * q^42 - 5 * q^43 - 7 * q^45 - 24 * q^46 - 37 * q^47 - 20 * q^48 - 2 * q^50 + 16 * q^51 + 53 * q^52 + 11 * q^53 + 15 * q^54 + 28 * q^56 - 37 * q^58 - 13 * q^59 - 30 * q^60 + 8 * q^61 - 27 * q^62 + 4 * q^63 + 32 * q^64 + 5 * q^65 - 21 * q^67 - 2 * q^68 + 14 * q^69 + 3 * q^70 - 3 * q^71 - 48 * q^72 - 2 * q^73 - 34 * q^74 + 4 * q^75 + 7 * q^76 + 3 * q^78 + 2 * q^79 + 76 * q^80 + 37 * q^81 - 40 * q^82 + 11 * q^83 + 23 * q^84 - 16 * q^85 - 3 * q^86 + 13 * q^87 + 14 * q^89 - 68 * q^90 + 18 * q^91 - 10 * q^92 - 2 * q^93 - 33 * q^94 + 28 * q^95 - 65 * q^96 - 30 * q^97 + 23 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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