LMFDB - Embedded newform 4598.2.a.bz.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 22x^{5} + 34x^{4} - 68x^{3} - 28x^{2} + 60x - 4 $ x^8 - 2x^7 - 11x^6 + 22x^5 + 34x^4 - 68x^3 - 28x^2 + 60*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.18171$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.18171 q^{3} +1.00000 q^{4} -0.117838 q^{5} -1.18171 q^{6} +1.74369 q^{7} +1.00000 q^{8} -1.60355 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.18171 q^{3} +1.00000 q^{4} -0.117838 q^{5} -1.18171 q^{6} +1.74369 q^{7} +1.00000 q^{8} -1.60355 q^{9} -0.117838 q^{10} -1.18171 q^{12} -2.12340 q^{13} +1.74369 q^{14} +0.139251 q^{15} +1.00000 q^{16} -2.17581 q^{17} -1.60355 q^{18} -1.00000 q^{19} -0.117838 q^{20} -2.06054 q^{21} +6.90496 q^{23} -1.18171 q^{24} -4.98611 q^{25} -2.12340 q^{26} +5.44008 q^{27} +1.74369 q^{28} -2.90652 q^{29} +0.139251 q^{30} -2.04939 q^{31} +1.00000 q^{32} -2.17581 q^{34} -0.205473 q^{35} -1.60355 q^{36} -2.04407 q^{37} -1.00000 q^{38} +2.50925 q^{39} -0.117838 q^{40} -0.615233 q^{41} -2.06054 q^{42} +10.0414 q^{43} +0.188960 q^{45} +6.90496 q^{46} -6.09479 q^{47} -1.18171 q^{48} -3.95955 q^{49} -4.98611 q^{50} +2.57119 q^{51} -2.12340 q^{52} -9.17608 q^{53} +5.44008 q^{54} +1.74369 q^{56} +1.18171 q^{57} -2.90652 q^{58} +5.61487 q^{59} +0.139251 q^{60} -5.23243 q^{61} -2.04939 q^{62} -2.79609 q^{63} +1.00000 q^{64} +0.250217 q^{65} -13.9348 q^{67} -2.17581 q^{68} -8.15970 q^{69} -0.205473 q^{70} -9.17377 q^{71} -1.60355 q^{72} -13.4547 q^{73} -2.04407 q^{74} +5.89217 q^{75} -1.00000 q^{76} +2.50925 q^{78} +5.47532 q^{79} -0.117838 q^{80} -1.61798 q^{81} -0.615233 q^{82} -9.46753 q^{83} -2.06054 q^{84} +0.256394 q^{85} +10.0414 q^{86} +3.43468 q^{87} +4.79411 q^{89} +0.188960 q^{90} -3.70254 q^{91} +6.90496 q^{92} +2.42180 q^{93} -6.09479 q^{94} +0.117838 q^{95} -1.18171 q^{96} +11.1749 q^{97} -3.95955 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 2 q^{6} - 14 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 2 * q^6 - 14 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 2 q^{6} - 14 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} - 9 q^{13} - 14 q^{14} + 5 q^{15} + 8 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 2 q^{20} - 7 q^{21} - 13 q^{23} - 2 q^{24} + 4 q^{25} - 9 q^{26} + 4 q^{27} - 14 q^{28} - 10 q^{29} + 5 q^{30} - 2 q^{31} + 8 q^{32} - 3 q^{34} + 7 q^{35} + 2 q^{36} + 15 q^{37} - 8 q^{38} - 11 q^{39} - 2 q^{40} - 9 q^{41} - 7 q^{42} - 33 q^{43} - 21 q^{45} - 13 q^{46} - 19 q^{47} - 2 q^{48} + 12 q^{49} + 4 q^{50} - 22 q^{51} - 9 q^{52} + 10 q^{53} + 4 q^{54} - 14 q^{56} + 2 q^{57} - 10 q^{58} + q^{59} + 5 q^{60} - 26 q^{61} - 2 q^{62} - 19 q^{63} + 8 q^{64} - 26 q^{65} - 25 q^{67} - 3 q^{68} - 12 q^{69} + 7 q^{70} - 10 q^{71} + 2 q^{72} - 11 q^{73} + 15 q^{74} - 33 q^{75} - 8 q^{76} - 11 q^{78} - 10 q^{79} - 2 q^{80} - 40 q^{81} - 9 q^{82} - 16 q^{83} - 7 q^{84} - 33 q^{85} - 33 q^{86} - 2 q^{87} - 14 q^{89} - 21 q^{90} + 25 q^{91} - 13 q^{92} + 20 q^{93} - 19 q^{94} + 2 q^{95} - 2 q^{96} + 22 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 2 * q^6 - 14 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 - 9 * q^13 - 14 * q^14 + 5 * q^15 + 8 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 2 * q^20 - 7 * q^21 - 13 * q^23 - 2 * q^24 + 4 * q^25 - 9 * q^26 + 4 * q^27 - 14 * q^28 - 10 * q^29 + 5 * q^30 - 2 * q^31 + 8 * q^32 - 3 * q^34 + 7 * q^35 + 2 * q^36 + 15 * q^37 - 8 * q^38 - 11 * q^39 - 2 * q^40 - 9 * q^41 - 7 * q^42 - 33 * q^43 - 21 * q^45 - 13 * q^46 - 19 * q^47 - 2 * q^48 + 12 * q^49 + 4 * q^50 - 22 * q^51 - 9 * q^52 + 10 * q^53 + 4 * q^54 - 14 * q^56 + 2 * q^57 - 10 * q^58 + q^59 + 5 * q^60 - 26 * q^61 - 2 * q^62 - 19 * q^63 + 8 * q^64 - 26 * q^65 - 25 * q^67 - 3 * q^68 - 12 * q^69 + 7 * q^70 - 10 * q^71 + 2 * q^72 - 11 * q^73 + 15 * q^74 - 33 * q^75 - 8 * q^76 - 11 * q^78 - 10 * q^79 - 2 * q^80 - 40 * q^81 - 9 * q^82 - 16 * q^83 - 7 * q^84 - 33 * q^85 - 33 * q^86 - 2 * q^87 - 14 * q^89 - 21 * q^90 + 25 * q^91 - 13 * q^92 + 20 * q^93 - 19 * q^94 + 2 * q^95 - 2 * q^96 + 22 * 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
$3$	−1.18171	−0.682263	−0.341132	−	0.940016i	$-0.610810\pi$
$3$	−1.18171	−0.682263	−0.341132	+	0.940016i	$0.610810\pi$
$4$	1.00000	0.500000
$5$	−0.117838	−0.0526989	−0.0263495	−	0.999653i	$-0.508388\pi$
$5$	−0.117838	−0.0526989	−0.0263495	+	0.999653i	$0.508388\pi$
$6$	−1.18171	−0.482433
$7$	1.74369	0.659052	0.329526	−	0.944146i	$-0.393111\pi$
$7$	1.74369	0.659052	0.329526	+	0.944146i	$0.393111\pi$
$8$	1.00000	0.353553
$9$	−1.60355	−0.534517
$10$	−0.117838	−0.0372638
$11$	0	0
$11$	0	0
$12$	−1.18171	−0.341132
$13$	−2.12340	−0.588924	−0.294462	−	0.955663i	$-0.595140\pi$
$13$	−2.12340	−0.588924	−0.294462	+	0.955663i	$0.595140\pi$
$14$	1.74369	0.466020
$15$	0.139251	0.0359545
$16$	1.00000	0.250000
$17$	−2.17581	−0.527712	−0.263856	−	0.964562i	$-0.584994\pi$
$17$	−2.17581	−0.527712	−0.263856	+	0.964562i	$0.584994\pi$
$18$	−1.60355	−0.377960
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.117838	−0.0263495
$21$	−2.06054	−0.449647
$22$	0	0
$23$	6.90496	1.43978	0.719892	−	0.694086i	$-0.244191\pi$
$23$	6.90496	1.43978	0.719892	+	0.694086i	$0.244191\pi$
$24$	−1.18171	−0.241217
$25$	−4.98611	−0.997223
$26$	−2.12340	−0.416432
$27$	5.44008	1.04694
$28$	1.74369	0.329526
$29$	−2.90652	−0.539728	−0.269864	−	0.962898i	$-0.586979\pi$
$29$	−2.90652	−0.539728	−0.269864	+	0.962898i	$0.586979\pi$
$30$	0.139251	0.0254237
$31$	−2.04939	−0.368082	−0.184041	−	0.982919i	$-0.558918\pi$
$31$	−2.04939	−0.368082	−0.184041	+	0.982919i	$0.558918\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.17581	−0.373148
$35$	−0.205473	−0.0347313
$36$	−1.60355	−0.267258
$37$	−2.04407	−0.336043	−0.168021	−	0.985783i	$-0.553738\pi$
$37$	−2.04407	−0.336043	−0.168021	+	0.985783i	$0.553738\pi$
$38$	−1.00000	−0.162221
$39$	2.50925	0.401801
$40$	−0.117838	−0.0186319
$41$	−0.615233	−0.0960832	−0.0480416	−	0.998845i	$-0.515298\pi$
$41$	−0.615233	−0.0960832	−0.0480416	+	0.998845i	$0.515298\pi$
$42$	−2.06054	−0.317949
$43$	10.0414	1.53129	0.765647	−	0.643261i	$-0.222419\pi$
$43$	10.0414	1.53129	0.765647	+	0.643261i	$0.222419\pi$
$44$	0	0
$45$	0.188960	0.0281684
$46$	6.90496	1.01808
$47$	−6.09479	−0.889016	−0.444508	−	0.895775i	$-0.646621\pi$
$47$	−6.09479	−0.889016	−0.444508	+	0.895775i	$0.646621\pi$
$48$	−1.18171	−0.170566
$49$	−3.95955	−0.565650
$50$	−4.98611	−0.705143
$51$	2.57119	0.360038
$52$	−2.12340	−0.294462
$53$	−9.17608	−1.26043	−0.630216	−	0.776420i	$-0.717034\pi$
$53$	−9.17608	−1.26043	−0.630216	+	0.776420i	$0.717034\pi$
$54$	5.44008	0.740302
$55$	0	0
$56$	1.74369	0.233010
$57$	1.18171	0.156522
$58$	−2.90652	−0.381645
$59$	5.61487	0.730994	0.365497	−	0.930813i	$-0.380899\pi$
$59$	5.61487	0.730994	0.365497	+	0.930813i	$0.380899\pi$
$60$	0.139251	0.0179773
$61$	−5.23243	−0.669944	−0.334972	−	0.942228i	$-0.608727\pi$
$61$	−5.23243	−0.669944	−0.334972	+	0.942228i	$0.608727\pi$
$62$	−2.04939	−0.260273
$63$	−2.79609	−0.352275
$64$	1.00000	0.125000
$65$	0.250217	0.0310356
$66$	0	0
$67$	−13.9348	−1.70241	−0.851205	−	0.524833i	$-0.824128\pi$
$67$	−13.9348	−1.70241	−0.851205	+	0.524833i	$0.824128\pi$
$68$	−2.17581	−0.263856
$69$	−8.15970	−0.982312
$70$	−0.205473	−0.0245588
$71$	−9.17377	−1.08873	−0.544363	−	0.838850i	$-0.683229\pi$
$71$	−9.17377	−1.08873	−0.544363	+	0.838850i	$0.683229\pi$
$72$	−1.60355	−0.188980
$73$	−13.4547	−1.57475	−0.787374	−	0.616476i	$-0.788560\pi$
$73$	−13.4547	−1.57475	−0.787374	+	0.616476i	$0.788560\pi$
$74$	−2.04407	−0.237618
$75$	5.89217	0.680369
$76$	−1.00000	−0.114708
$77$	0	0
$78$	2.50925	0.284116
$79$	5.47532	0.616021	0.308011	−	0.951383i	$-0.400337\pi$
$79$	5.47532	0.616021	0.308011	+	0.951383i	$0.400337\pi$
$80$	−0.117838	−0.0131747
$81$	−1.61798	−0.179775
$82$	−0.615233	−0.0679411
$83$	−9.46753	−1.03920	−0.519598	−	0.854411i	$-0.673918\pi$
$83$	−9.46753	−1.03920	−0.519598	+	0.854411i	$0.673918\pi$
$84$	−2.06054	−0.224824
$85$	0.256394	0.0278098
$86$	10.0414	1.08279
$87$	3.43468	0.368236
$88$	0	0
$89$	4.79411	0.508174	0.254087	−	0.967181i	$-0.418225\pi$
$89$	4.79411	0.508174	0.254087	+	0.967181i	$0.418225\pi$
$90$	0.188960	0.0199181
$91$	−3.70254	−0.388132
$92$	6.90496	0.719892
$93$	2.42180	0.251129
$94$	−6.09479	−0.628629
$95$	0.117838	0.0120900
$96$	−1.18171	−0.120608
$97$	11.1749	1.13464	0.567320	−	0.823497i	$-0.307980\pi$
$97$	11.1749	1.13464	0.567320	+	0.823497i	$0.307980\pi$
$98$	−3.95955	−0.399975
$99$	0	0
$100$	−4.98611	−0.498611
$101$	−3.39318	−0.337634	−0.168817	−	0.985647i	$-0.553995\pi$
$101$	−3.39318	−0.337634	−0.168817	+	0.985647i	$0.553995\pi$
$102$	2.57119	0.254585
$103$	17.7010	1.74413	0.872066	−	0.489388i	$-0.162780\pi$
$103$	17.7010	1.74413	0.872066	+	0.489388i	$0.162780\pi$
$104$	−2.12340	−0.208216
$105$	0.242811	0.0236959
$106$	−9.17608	−0.891260
$107$	0.517003	0.0499806	0.0249903	−	0.999688i	$-0.492045\pi$
$107$	0.517003	0.0499806	0.0249903	+	0.999688i	$0.492045\pi$
$108$	5.44008	0.523472
$109$	7.94333	0.760833	0.380417	−	0.924815i	$-0.375781\pi$
$109$	7.94333	0.760833	0.380417	+	0.924815i	$0.375781\pi$
$110$	0	0
$111$	2.41550	0.229270
$112$	1.74369	0.164763
$113$	−16.1602	−1.52023	−0.760113	−	0.649791i	$-0.774856\pi$
$113$	−16.1602	−1.52023	−0.760113	+	0.649791i	$0.774856\pi$
$114$	1.18171	0.110678
$115$	−0.813669	−0.0758750
$116$	−2.90652	−0.269864
$117$	3.40497	0.314790
$118$	5.61487	0.516891
$119$	−3.79394	−0.347790
$120$	0.139251	0.0127118
$121$	0	0
$122$	−5.23243	−0.473722
$123$	0.727030	0.0655541
$124$	−2.04939	−0.184041
$125$	1.17675	0.105251
$126$	−2.79609	−0.249096
$127$	−2.77979	−0.246666	−0.123333	−	0.992365i	$-0.539358\pi$
$127$	−2.77979	−0.246666	−0.123333	+	0.992365i	$0.539358\pi$
$128$	1.00000	0.0883883
$129$	−11.8660	−1.04475
$130$	0.250217	0.0219455
$131$	10.0755	0.880298	0.440149	−	0.897925i	$-0.354926\pi$
$131$	10.0755	0.880298	0.440149	+	0.897925i	$0.354926\pi$
$132$	0	0
$133$	−1.74369	−0.151197
$134$	−13.9348	−1.20379
$135$	−0.641050	−0.0551728
$136$	−2.17581	−0.186574
$137$	−0.481832	−0.0411657	−0.0205828	−	0.999788i	$-0.506552\pi$
$137$	−0.481832	−0.0411657	−0.0205828	+	0.999788i	$0.506552\pi$
$138$	−8.15970	−0.694599
$139$	−19.7785	−1.67759	−0.838793	−	0.544450i	$-0.816738\pi$
$139$	−19.7785	−1.67759	−0.838793	+	0.544450i	$0.816738\pi$
$140$	−0.205473	−0.0173657
$141$	7.20230	0.606543
$142$	−9.17377	−0.769846
$143$	0	0
$144$	−1.60355	−0.133629
$145$	0.342500	0.0284431
$146$	−13.4547	−1.11351
$147$	4.67906	0.385922
$148$	−2.04407	−0.168021
$149$	−5.36868	−0.439819	−0.219910	−	0.975520i	$-0.570576\pi$
$149$	−5.36868	−0.439819	−0.219910	+	0.975520i	$0.570576\pi$
$150$	5.89217	0.481093
$151$	−20.7873	−1.69165	−0.845823	−	0.533464i	$-0.820890\pi$
$151$	−20.7873	−1.69165	−0.845823	+	0.533464i	$0.820890\pi$
$152$	−1.00000	−0.0811107
$153$	3.48902	0.282071
$154$	0	0
$155$	0.241497	0.0193975
$156$	2.50925	0.200901
$157$	6.73574	0.537571	0.268785	−	0.963200i	$-0.413378\pi$
$157$	6.73574	0.537571	0.268785	+	0.963200i	$0.413378\pi$
$158$	5.47532	0.435593
$159$	10.8435	0.859946
$160$	−0.117838	−0.00931594
$161$	12.0401	0.948893
$162$	−1.61798	−0.127120
$163$	4.52848	0.354698	0.177349	−	0.984148i	$-0.443248\pi$
$163$	4.52848	0.354698	0.177349	+	0.984148i	$0.443248\pi$
$164$	−0.615233	−0.0480416
$165$	0	0
$166$	−9.46753	−0.734823
$167$	4.96407	0.384131	0.192066	−	0.981382i	$-0.438481\pi$
$167$	4.96407	0.384131	0.192066	+	0.981382i	$0.438481\pi$
$168$	−2.06054	−0.158974
$169$	−8.49119	−0.653169
$170$	0.256394	0.0196645
$171$	1.60355	0.122627
$172$	10.0414	0.765647
$173$	−0.886634	−0.0674095	−0.0337048	−	0.999432i	$-0.510731\pi$
$173$	−0.886634	−0.0674095	−0.0337048	+	0.999432i	$0.510731\pi$
$174$	3.43468	0.260382
$175$	−8.69423	−0.657222
$176$	0	0
$177$	−6.63517	−0.498730
$178$	4.79411	0.359333
$179$	−2.70361	−0.202078	−0.101039	−	0.994882i	$-0.532217\pi$
$179$	−2.70361	−0.202078	−0.101039	+	0.994882i	$0.532217\pi$
$180$	0.188960	0.0140842
$181$	16.0464	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$181$	16.0464	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$182$	−3.70254	−0.274451
$183$	6.18324	0.457078
$184$	6.90496	0.509040
$185$	0.240869	0.0177091
$186$	2.42180	0.177575
$187$	0	0
$188$	−6.09479	−0.444508
$189$	9.48581	0.689991
$190$	0.117838	0.00854889
$191$	−23.4368	−1.69583	−0.847915	−	0.530133i	$-0.822142\pi$
$191$	−23.4368	−1.69583	−0.847915	+	0.530133i	$0.822142\pi$
$192$	−1.18171	−0.0852829
$193$	−8.29786	−0.597293	−0.298647	−	0.954364i	$-0.596535\pi$
$193$	−8.29786	−0.597293	−0.298647	+	0.954364i	$0.596535\pi$
$194$	11.1749	0.802312
$195$	−0.295686	−0.0211745
$196$	−3.95955	−0.282825
$197$	−25.7155	−1.83215	−0.916077	−	0.401003i	$-0.868662\pi$
$197$	−25.7155	−1.83215	−0.916077	+	0.401003i	$0.868662\pi$
$198$	0	0
$199$	7.28088	0.516128	0.258064	−	0.966128i	$-0.416915\pi$
$199$	7.28088	0.516128	0.258064	+	0.966128i	$0.416915\pi$
$200$	−4.98611	−0.352572
$201$	16.4670	1.16149
$202$	−3.39318	−0.238743
$203$	−5.06807	−0.355709
$204$	2.57119	0.180019
$205$	0.0724980	0.00506348
$206$	17.7010	1.23329
$207$	−11.0725	−0.769589
$208$	−2.12340	−0.147231
$209$	0	0
$210$	0.242811	0.0167555
$211$	−9.82812	−0.676596	−0.338298	−	0.941039i	$-0.609851\pi$
$211$	−9.82812	−0.676596	−0.338298	+	0.941039i	$0.609851\pi$
$212$	−9.17608	−0.630216
$213$	10.8408	0.742798
$214$	0.517003	0.0353416
$215$	−1.18326	−0.0806976
$216$	5.44008	0.370151
$217$	−3.57350	−0.242585
$218$	7.94333	0.537990
$219$	15.8996	1.07439
$220$	0	0
$221$	4.62011	0.310782
$222$	2.41550	0.162118
$223$	1.50507	0.100787	0.0503935	−	0.998729i	$-0.483952\pi$
$223$	1.50507	0.100787	0.0503935	+	0.998729i	$0.483952\pi$
$224$	1.74369	0.116505
$225$	7.99548	0.533032
$226$	−16.1602	−1.07496
$227$	−0.253304	−0.0168124	−0.00840619	−	0.999965i	$-0.502676\pi$
$227$	−0.253304	−0.0168124	−0.00840619	+	0.999965i	$0.502676\pi$
$228$	1.18171	0.0782610
$229$	−8.74819	−0.578097	−0.289048	−	0.957315i	$-0.593339\pi$
$229$	−8.74819	−0.578097	−0.289048	+	0.957315i	$0.593339\pi$
$230$	−0.813669	−0.0536518
$231$	0	0
$232$	−2.90652	−0.190823
$233$	−12.3584	−0.809624	−0.404812	−	0.914400i	$-0.632663\pi$
$233$	−12.3584	−0.809624	−0.404812	+	0.914400i	$0.632663\pi$
$234$	3.40497	0.222590
$235$	0.718200	0.0468502
$236$	5.61487	0.365497
$237$	−6.47027	−0.420289
$238$	−3.79394	−0.245924
$239$	−19.2245	−1.24353	−0.621766	−	0.783203i	$-0.713584\pi$
$239$	−19.2245	−1.24353	−0.621766	+	0.783203i	$0.713584\pi$
$240$	0.139251	0.00898863
$241$	−19.1933	−1.23635	−0.618176	−	0.786040i	$-0.712128\pi$
$241$	−19.1933	−1.23635	−0.618176	+	0.786040i	$0.712128\pi$
$242$	0	0
$243$	−14.4083	−0.924290
$244$	−5.23243	−0.334972
$245$	0.466587	0.0298091
$246$	0.727030	0.0463537
$247$	2.12340	0.135108
$248$	−2.04939	−0.130137
$249$	11.1879	0.709006
$250$	1.17675	0.0744240
$251$	−8.76635	−0.553327	−0.276664	−	0.960967i	$-0.589229\pi$
$251$	−8.76635	−0.553327	−0.276664	+	0.960967i	$0.589229\pi$
$252$	−2.79609	−0.176137
$253$	0	0
$254$	−2.77979	−0.174419
$255$	−0.302984	−0.0189736
$256$	1.00000	0.0625000
$257$	25.2635	1.57590	0.787948	−	0.615742i	$-0.211144\pi$
$257$	25.2635	1.57590	0.787948	+	0.615742i	$0.211144\pi$
$258$	−11.8660	−0.738747
$259$	−3.56422	−0.221470
$260$	0.250217	0.0155178
$261$	4.66075	0.288493
$262$	10.0755	0.622465
$263$	19.1737	1.18230	0.591149	−	0.806562i	$-0.298674\pi$
$263$	19.1737	1.18230	0.591149	+	0.806562i	$0.298674\pi$
$264$	0	0
$265$	1.08129	0.0664234
$266$	−1.74369	−0.106912
$267$	−5.66527	−0.346709
$268$	−13.9348	−0.851205
$269$	8.27109	0.504297	0.252149	−	0.967688i	$-0.418863\pi$
$269$	8.27109	0.504297	0.252149	+	0.967688i	$0.418863\pi$
$270$	−0.641050	−0.0390131
$271$	9.08710	0.552002	0.276001	−	0.961157i	$-0.410991\pi$
$271$	9.08710	0.552002	0.276001	+	0.961157i	$0.410991\pi$
$272$	−2.17581	−0.131928
$273$	4.37535	0.264808
$274$	−0.481832	−0.0291085
$275$	0	0
$276$	−8.15970	−0.491156
$277$	4.57116	0.274654	0.137327	−	0.990526i	$-0.456149\pi$
$277$	4.57116	0.274654	0.137327	+	0.990526i	$0.456149\pi$
$278$	−19.7785	−1.18623
$279$	3.28630	0.196746
$280$	−0.205473	−0.0122794
$281$	1.23096	0.0734327	0.0367163	−	0.999326i	$-0.488310\pi$
$281$	1.23096	0.0734327	0.0367163	+	0.999326i	$0.488310\pi$
$282$	7.20230	0.428891
$283$	−26.4279	−1.57098	−0.785489	−	0.618876i	$-0.787588\pi$
$283$	−26.4279	−1.57098	−0.785489	+	0.618876i	$0.787588\pi$
$284$	−9.17377	−0.544363
$285$	−0.139251	−0.00824854
$286$	0	0
$287$	−1.07277	−0.0633239
$288$	−1.60355	−0.0944901
$289$	−12.2658	−0.721521
$290$	0.342500	0.0201123
$291$	−13.2056	−0.774123
$292$	−13.4547	−0.787374
$293$	−6.30897	−0.368574	−0.184287	−	0.982872i	$-0.558998\pi$
$293$	−6.30897	−0.368574	−0.184287	+	0.982872i	$0.558998\pi$
$294$	4.67906	0.272888
$295$	−0.661647	−0.0385226
$296$	−2.04407	−0.118809
$297$	0	0
$298$	−5.36868	−0.310999
$299$	−14.6620	−0.847923
$300$	5.89217	0.340184
$301$	17.5090	1.00920
$302$	−20.7873	−1.19617
$303$	4.00977	0.230355
$304$	−1.00000	−0.0573539
$305$	0.616581	0.0353053
$306$	3.48902	0.199454
$307$	18.2913	1.04394	0.521971	−	0.852963i	$-0.325197\pi$
$307$	18.2913	1.04394	0.521971	+	0.852963i	$0.325197\pi$
$308$	0	0
$309$	−20.9175	−1.18996
$310$	0.241497	0.0137161
$311$	−28.9186	−1.63982	−0.819912	−	0.572490i	$-0.805978\pi$
$311$	−28.9186	−1.63982	−0.819912	+	0.572490i	$0.805978\pi$
$312$	2.50925	0.142058
$313$	18.3034	1.03457	0.517283	−	0.855814i	$-0.326943\pi$
$313$	18.3034	1.03457	0.517283	+	0.855814i	$0.326943\pi$
$314$	6.73574	0.380120
$315$	0.329487	0.0185645
$316$	5.47532	0.308011
$317$	22.5412	1.26604	0.633019	−	0.774136i	$-0.281816\pi$
$317$	22.5412	1.26604	0.633019	+	0.774136i	$0.281816\pi$
$318$	10.8435	0.608074
$319$	0	0
$320$	−0.117838	−0.00658736
$321$	−0.610951	−0.0340999
$322$	12.0401	0.670969
$323$	2.17581	0.121065
$324$	−1.61798	−0.0898876
$325$	10.5875	0.587288
$326$	4.52848	0.250809
$327$	−9.38675	−0.519089
$328$	−0.615233	−0.0339705
$329$	−10.6274	−0.585908
$330$	0	0
$331$	8.07958	0.444094	0.222047	−	0.975036i	$-0.428726\pi$
$331$	8.07958	0.444094	0.222047	+	0.975036i	$0.428726\pi$
$332$	−9.46753	−0.519598
$333$	3.27776	0.179620
$334$	4.96407	0.271622
$335$	1.64206	0.0897151
$336$	−2.06054	−0.112412
$337$	−31.5951	−1.72109	−0.860547	−	0.509371i	$-0.829878\pi$
$337$	−31.5951	−1.72109	−0.860547	+	0.509371i	$0.829878\pi$
$338$	−8.49119	−0.461860
$339$	19.0968	1.03719
$340$	0.256394	0.0139049
$341$	0	0
$342$	1.60355	0.0867101
$343$	−19.1100	−1.03185
$344$	10.0414	0.541394
$345$	0.961525	0.0517668
$346$	−0.886634	−0.0476657
$347$	27.1440	1.45717	0.728584	−	0.684956i	$-0.240179\pi$
$347$	27.1440	1.45717	0.728584	+	0.684956i	$0.240179\pi$
$348$	3.43468	0.184118
$349$	9.47226	0.507039	0.253519	−	0.967330i	$-0.418412\pi$
$349$	9.47226	0.507039	0.253519	+	0.967330i	$0.418412\pi$
$350$	−8.69423	−0.464726
$351$	−11.5514	−0.616571
$352$	0	0
$353$	12.0966	0.643837	0.321918	−	0.946767i	$-0.395672\pi$
$353$	12.0966	0.643837	0.321918	+	0.946767i	$0.395672\pi$
$354$	−6.63517	−0.352656
$355$	1.08102	0.0573747
$356$	4.79411	0.254087
$357$	4.48335	0.237284
$358$	−2.70361	−0.142890
$359$	7.99672	0.422051	0.211025	−	0.977481i	$-0.432320\pi$
$359$	7.99672	0.422051	0.211025	+	0.977481i	$0.432320\pi$
$360$	0.188960	0.00995905
$361$	1.00000	0.0526316
$362$	16.0464	0.843380
$363$	0	0
$364$	−3.70254	−0.194066
$365$	1.58547	0.0829875
$366$	6.18324	0.323203
$367$	1.30614	0.0681802	0.0340901	−	0.999419i	$-0.489147\pi$
$367$	1.30614	0.0681802	0.0340901	+	0.999419i	$0.489147\pi$
$368$	6.90496	0.359946
$369$	0.986557	0.0513581
$370$	0.240869	0.0125222
$371$	−16.0002	−0.830691
$372$	2.42180	0.125564
$373$	−11.9113	−0.616744	−0.308372	−	0.951266i	$-0.599784\pi$
$373$	−11.9113	−0.616744	−0.308372	+	0.951266i	$0.599784\pi$
$374$	0	0
$375$	−1.39058	−0.0718092
$376$	−6.09479	−0.314315
$377$	6.17170	0.317858
$378$	9.48581	0.487898
$379$	−15.6318	−0.802954	−0.401477	−	0.915869i	$-0.631503\pi$
$379$	−15.6318	−0.802954	−0.401477	+	0.915869i	$0.631503\pi$
$380$	0.117838	0.00604498
$381$	3.28492	0.168291
$382$	−23.4368	−1.19913
$383$	−12.3471	−0.630910	−0.315455	−	0.948941i	$-0.602157\pi$
$383$	−12.3471	−0.630910	−0.315455	+	0.948941i	$0.602157\pi$
$384$	−1.18171	−0.0603041
$385$	0	0
$386$	−8.29786	−0.422350
$387$	−16.1018	−0.818503
$388$	11.1749	0.567320
$389$	−15.1540	−0.768338	−0.384169	−	0.923263i	$-0.625512\pi$
$389$	−15.1540	−0.768338	−0.384169	+	0.923263i	$0.625512\pi$
$390$	−0.295686	−0.0149726
$391$	−15.0239	−0.759791
$392$	−3.95955	−0.199987
$393$	−11.9063	−0.600595
$394$	−25.7155	−1.29553
$395$	−0.645202	−0.0324637
$396$	0	0
$397$	−1.08003	−0.0542050	−0.0271025	−	0.999633i	$-0.508628\pi$
$397$	−1.08003	−0.0542050	−0.0271025	+	0.999633i	$0.508628\pi$
$398$	7.28088	0.364957
$399$	2.06054	0.103156
$400$	−4.98611	−0.249306
$401$	22.8470	1.14093	0.570463	−	0.821323i	$-0.306764\pi$
$401$	22.8470	1.14093	0.570463	+	0.821323i	$0.306764\pi$
$402$	16.4670	0.821299
$403$	4.35167	0.216772
$404$	−3.39318	−0.168817
$405$	0.190660	0.00947396
$406$	−5.06807	−0.251524
$407$	0	0
$408$	2.57119	0.127293
$409$	−16.4866	−0.815210	−0.407605	−	0.913158i	$-0.633636\pi$
$409$	−16.4866	−0.815210	−0.407605	+	0.913158i	$0.633636\pi$
$410$	0.0724980	0.00358042
$411$	0.569388	0.0280858
$412$	17.7010	0.872066
$413$	9.79059	0.481763
$414$	−11.0725	−0.544181
$415$	1.11564	0.0547645
$416$	−2.12340	−0.104108
$417$	23.3725	1.14456
$418$	0	0
$419$	4.02294	0.196534	0.0982668	−	0.995160i	$-0.468670\pi$
$419$	4.02294	0.196534	0.0982668	+	0.995160i	$0.468670\pi$
$420$	0.242811	0.0118480
$421$	−9.30430	−0.453464	−0.226732	−	0.973957i	$-0.572804\pi$
$421$	−9.30430	−0.453464	−0.226732	+	0.973957i	$0.572804\pi$
$422$	−9.82812	−0.478425
$423$	9.77330	0.475194
$424$	−9.17608	−0.445630
$425$	10.8488	0.526246
$426$	10.8408	0.525238
$427$	−9.12373	−0.441528
$428$	0.517003	0.0249903
$429$	0	0
$430$	−1.18326	−0.0570618
$431$	2.55537	0.123088	0.0615439	−	0.998104i	$-0.480398\pi$
$431$	2.55537	0.123088	0.0615439	+	0.998104i	$0.480398\pi$
$432$	5.44008	0.261736
$433$	38.5263	1.85146	0.925728	−	0.378189i	$-0.123453\pi$
$433$	38.5263	1.85146	0.925728	+	0.378189i	$0.123453\pi$
$434$	−3.57350	−0.171534
$435$	−0.404737	−0.0194057
$436$	7.94333	0.380417
$437$	−6.90496	−0.330309
$438$	15.8996	0.759710
$439$	−34.2110	−1.63280	−0.816401	−	0.577485i	$-0.804034\pi$
$439$	−34.2110	−1.63280	−0.816401	+	0.577485i	$0.804034\pi$
$440$	0	0
$441$	6.34933	0.302349
$442$	4.62011	0.219756
$443$	28.3557	1.34722	0.673610	−	0.739087i	$-0.264743\pi$
$443$	28.3557	1.34722	0.673610	+	0.739087i	$0.264743\pi$
$444$	2.41550	0.114635
$445$	−0.564929	−0.0267802
$446$	1.50507	0.0712671
$447$	6.34425	0.300073
$448$	1.74369	0.0823816
$449$	19.7319	0.931206	0.465603	−	0.884994i	$-0.345838\pi$
$449$	19.7319	0.931206	0.465603	+	0.884994i	$0.345838\pi$
$450$	7.99548	0.376911
$451$	0	0
$452$	−16.1602	−0.760113
$453$	24.5647	1.15415
$454$	−0.253304	−0.0118881
$455$	0.436301	0.0204541
$456$	1.18171	0.0553389
$457$	−8.71834	−0.407827	−0.203913	−	0.978989i	$-0.565366\pi$
$457$	−8.71834	−0.407827	−0.203913	+	0.978989i	$0.565366\pi$
$458$	−8.74819	−0.408776
$459$	−11.8366	−0.552485
$460$	−0.813669	−0.0379375
$461$	−10.8220	−0.504033	−0.252016	−	0.967723i	$-0.581094\pi$
$461$	−10.8220	−0.504033	−0.252016	+	0.967723i	$0.581094\pi$
$462$	0	0
$463$	38.6978	1.79844	0.899220	−	0.437496i	$-0.144135\pi$
$463$	38.6978	1.79844	0.899220	+	0.437496i	$0.144135\pi$
$464$	−2.90652	−0.134932
$465$	−0.285381	−0.0132342
$466$	−12.3584	−0.572491
$467$	6.54021	0.302645	0.151322	−	0.988484i	$-0.451647\pi$
$467$	6.54021	0.302645	0.151322	+	0.988484i	$0.451647\pi$
$468$	3.40497	0.157395
$469$	−24.2980	−1.12198
$470$	0.718200	0.0331281
$471$	−7.95973	−0.366765
$472$	5.61487	0.258445
$473$	0	0
$474$	−6.47027	−0.297189
$475$	4.98611	0.228779
$476$	−3.79394	−0.173895
$477$	14.7143	0.673722
$478$	−19.2245	−0.879309
$479$	33.0437	1.50981	0.754903	−	0.655836i	$-0.227684\pi$
$479$	33.0437	1.50981	0.754903	+	0.655836i	$0.227684\pi$
$480$	0.139251	0.00635592
$481$	4.34036	0.197903
$482$	−19.1933	−0.874232
$483$	−14.2280	−0.647395
$484$	0	0
$485$	−1.31683	−0.0597943
$486$	−14.4083	−0.653572
$487$	6.39992	0.290008	0.145004	−	0.989431i	$-0.453680\pi$
$487$	6.39992	0.290008	0.145004	+	0.989431i	$0.453680\pi$
$488$	−5.23243	−0.236861
$489$	−5.35137	−0.241997
$490$	0.466587	0.0210782
$491$	29.6576	1.33843	0.669213	−	0.743070i	$-0.266631\pi$
$491$	29.6576	1.33843	0.669213	+	0.743070i	$0.266631\pi$
$492$	0.727030	0.0327770
$493$	6.32404	0.284820
$494$	2.12340	0.0955361
$495$	0	0
$496$	−2.04939	−0.0920204
$497$	−15.9962	−0.717528
$498$	11.1879	0.501343
$499$	−10.3794	−0.464644	−0.232322	−	0.972639i	$-0.574632\pi$
$499$	−10.3794	−0.464644	−0.232322	+	0.972639i	$0.574632\pi$
$500$	1.17675	0.0526257
$501$	−5.86612	−0.262079
$502$	−8.76635	−0.391261
$503$	−5.31870	−0.237149	−0.118575	−	0.992945i	$-0.537832\pi$
$503$	−5.31870	−0.237149	−0.118575	+	0.992945i	$0.537832\pi$
$504$	−2.79609	−0.124548
$505$	0.399847	0.0177930
$506$	0	0
$507$	10.0342	0.445633
$508$	−2.77979	−0.123333
$509$	21.7015	0.961900	0.480950	−	0.876748i	$-0.340292\pi$
$509$	21.7015	0.961900	0.480950	+	0.876748i	$0.340292\pi$
$510$	−0.302984	−0.0134164
$511$	−23.4607	−1.03784
$512$	1.00000	0.0441942
$513$	−5.44008	−0.240186
$514$	25.2635	1.11433
$515$	−2.08586	−0.0919138
$516$	−11.8660	−0.522373
$517$	0	0
$518$	−3.56422	−0.156603
$519$	1.04775	0.0459911
$520$	0.250217	0.0109728
$521$	15.5863	0.682850	0.341425	−	0.939909i	$-0.389090\pi$
$521$	15.5863	0.682850	0.341425	+	0.939909i	$0.389090\pi$
$522$	4.66075	0.203996
$523$	3.48124	0.152224	0.0761121	−	0.997099i	$-0.475749\pi$
$523$	3.48124	0.152224	0.0761121	+	0.997099i	$0.475749\pi$
$524$	10.0755	0.440149
$525$	10.2741	0.448399
$526$	19.1737	0.836011
$527$	4.45909	0.194241
$528$	0	0
$529$	24.6785	1.07298
$530$	1.08129	0.0469684
$531$	−9.00372	−0.390728
$532$	−1.74369	−0.0755985
$533$	1.30638	0.0565857
$534$	−5.66527	−0.245160
$535$	−0.0609228	−0.00263392
$536$	−13.9348	−0.601893
$537$	3.19490	0.137870
$538$	8.27109	0.356592
$539$	0	0
$540$	−0.641050	−0.0275864
$541$	2.10312	0.0904200	0.0452100	−	0.998978i	$-0.485604\pi$
$541$	2.10312	0.0904200	0.0452100	+	0.998978i	$0.485604\pi$
$542$	9.08710	0.390324
$543$	−18.9623	−0.813749
$544$	−2.17581	−0.0932871
$545$	−0.936029	−0.0400951
$546$	4.37535	0.187248
$547$	−10.1274	−0.433015	−0.216508	−	0.976281i	$-0.569467\pi$
$547$	−10.1274	−0.433015	−0.216508	+	0.976281i	$0.569467\pi$
$548$	−0.481832	−0.0205828
$549$	8.39046	0.358096
$550$	0	0
$551$	2.90652	0.123822
$552$	−8.15970	−0.347300
$553$	9.54725	0.405990
$554$	4.57116	0.194210
$555$	−0.284639	−0.0120823
$556$	−19.7785	−0.838793
$557$	−0.610984	−0.0258882	−0.0129441	−	0.999916i	$-0.504120\pi$
$557$	−0.610984	−0.0258882	−0.0129441	+	0.999916i	$0.504120\pi$
$558$	3.28630	0.139120
$559$	−21.3218	−0.901816
$560$	−0.205473	−0.00868284
$561$	0	0
$562$	1.23096	0.0519248
$563$	27.5671	1.16181	0.580907	−	0.813970i	$-0.302698\pi$
$563$	27.5671	1.16181	0.580907	+	0.813970i	$0.302698\pi$
$564$	7.20230	0.303272
$565$	1.90429	0.0801142
$566$	−26.4279	−1.11085
$567$	−2.82125	−0.118481
$568$	−9.17377	−0.384923
$569$	−21.4875	−0.900802	−0.450401	−	0.892826i	$-0.648719\pi$
$569$	−21.4875	−0.900802	−0.450401	+	0.892826i	$0.648719\pi$
$570$	−0.139251	−0.00583260
$571$	−29.1419	−1.21955	−0.609775	−	0.792575i	$-0.708740\pi$
$571$	−29.1419	−1.21955	−0.609775	+	0.792575i	$0.708740\pi$
$572$	0	0
$573$	27.6956	1.15700
$574$	−1.07277	−0.0447767
$575$	−34.4289	−1.43579
$576$	−1.60355	−0.0668146
$577$	−35.9617	−1.49711	−0.748553	−	0.663075i	$-0.769251\pi$
$577$	−35.9617	−1.49711	−0.748553	+	0.663075i	$0.769251\pi$
$578$	−12.2658	−0.510192
$579$	9.80571	0.407511
$580$	0.342500	0.0142215
$581$	−16.5084	−0.684885
$582$	−13.2056	−0.547388
$583$	0	0
$584$	−13.4547	−0.556757
$585$	−0.401236	−0.0165891
$586$	−6.30897	−0.260621
$587$	39.7008	1.63863	0.819315	−	0.573344i	$-0.194354\pi$
$587$	39.7008	1.63863	0.819315	+	0.573344i	$0.194354\pi$
$588$	4.67906	0.192961
$589$	2.04939	0.0844437
$590$	−0.661647	−0.0272396
$591$	30.3884	1.25001
$592$	−2.04407	−0.0840106
$593$	16.7269	0.686892	0.343446	−	0.939172i	$-0.388406\pi$
$593$	16.7269	0.686892	0.343446	+	0.939172i	$0.388406\pi$
$594$	0	0
$595$	0.447071	0.0183281
$596$	−5.36868	−0.219910
$597$	−8.60392	−0.352135
$598$	−14.6620	−0.599572
$599$	43.4562	1.77557	0.887787	−	0.460255i	$-0.152242\pi$
$599$	43.4562	1.77557	0.887787	+	0.460255i	$0.152242\pi$
$600$	5.89217	0.240547
$601$	6.03054	0.245991	0.122996	−	0.992407i	$-0.460750\pi$
$601$	6.03054	0.245991	0.122996	+	0.992407i	$0.460750\pi$
$602$	17.5090	0.713615
$603$	22.3452	0.909966
$604$	−20.7873	−0.845823
$605$	0	0
$606$	4.00977	0.162886
$607$	−43.6680	−1.77243	−0.886215	−	0.463275i	$-0.846674\pi$
$607$	−43.6680	−1.77243	−0.886215	+	0.463275i	$0.846674\pi$
$608$	−1.00000	−0.0405554
$609$	5.98901	0.242687
$610$	0.616581	0.0249646
$611$	12.9416	0.523563
$612$	3.48902	0.141035
$613$	22.0091	0.888938	0.444469	−	0.895794i	$-0.353392\pi$
$613$	22.0091	0.888938	0.444469	+	0.895794i	$0.353392\pi$
$614$	18.2913	0.738178
$615$	−0.0856720	−0.00345463
$616$	0	0
$617$	2.73799	0.110227	0.0551137	−	0.998480i	$-0.482448\pi$
$617$	2.73799	0.110227	0.0551137	+	0.998480i	$0.482448\pi$
$618$	−20.9175	−0.841427
$619$	21.3716	0.858996	0.429498	−	0.903068i	$-0.358691\pi$
$619$	21.3716	0.858996	0.429498	+	0.903068i	$0.358691\pi$
$620$	0.241497	0.00969875
$621$	37.5636	1.50737
$622$	−28.9186	−1.15953
$623$	8.35943	0.334913
$624$	2.50925	0.100450
$625$	24.7919	0.991676
$626$	18.3034	0.731549
$627$	0	0
$628$	6.73574	0.268785
$629$	4.44750	0.177334
$630$	0.329487	0.0131271
$631$	−32.2346	−1.28324	−0.641620	−	0.767022i	$-0.721737\pi$
$631$	−32.2346	−1.28324	−0.641620	+	0.767022i	$0.721737\pi$
$632$	5.47532	0.217796
$633$	11.6140	0.461616
$634$	22.5412	0.895224
$635$	0.327566	0.0129990
$636$	10.8435	0.429973
$637$	8.40769	0.333125
$638$	0	0
$639$	14.7106	0.581943
$640$	−0.117838	−0.00465797
$641$	25.7010	1.01513	0.507564	−	0.861614i	$-0.330546\pi$
$641$	25.7010	1.01513	0.507564	+	0.861614i	$0.330546\pi$
$642$	−0.610951	−0.0241123
$643$	−6.65036	−0.262264	−0.131132	−	0.991365i	$-0.541861\pi$
$643$	−6.65036	−0.262264	−0.131132	+	0.991365i	$0.541861\pi$
$644$	12.0401	0.474447
$645$	1.39827	0.0550570
$646$	2.17581	0.0856061
$647$	−30.2529	−1.18936	−0.594681	−	0.803962i	$-0.702722\pi$
$647$	−30.2529	−1.18936	−0.594681	+	0.803962i	$0.702722\pi$
$648$	−1.61798	−0.0635602
$649$	0	0
$650$	10.5875	0.415276
$651$	4.22286	0.165507
$652$	4.52848	0.177349
$653$	16.0667	0.628737	0.314369	−	0.949301i	$-0.398207\pi$
$653$	16.0667	0.628737	0.314369	+	0.949301i	$0.398207\pi$
$654$	−9.38675	−0.367051
$655$	−1.18728	−0.0463908
$656$	−0.615233	−0.0240208
$657$	21.5752	0.841729
$658$	−10.6274	−0.414300
$659$	8.59809	0.334934	0.167467	−	0.985878i	$-0.446441\pi$
$659$	8.59809	0.334934	0.167467	+	0.985878i	$0.446441\pi$
$660$	0	0
$661$	−24.7734	−0.963573	−0.481787	−	0.876289i	$-0.660012\pi$
$661$	−24.7734	−0.963573	−0.481787	+	0.876289i	$0.660012\pi$
$662$	8.07958	0.314022
$663$	−5.45965	−0.212035
$664$	−9.46753	−0.367411
$665$	0.205473	0.00796792
$666$	3.27776	0.127011
$667$	−20.0694	−0.777091
$668$	4.96407	0.192066
$669$	−1.77856	−0.0687632
$670$	1.64206	0.0634382
$671$	0	0
$672$	−2.06054	−0.0794872
$673$	39.1789	1.51024	0.755118	−	0.655588i	$-0.227579\pi$
$673$	39.1789	1.51024	0.755118	+	0.655588i	$0.227579\pi$
$674$	−31.5951	−1.21700
$675$	−27.1249	−1.04404
$676$	−8.49119	−0.326584
$677$	−17.1360	−0.658590	−0.329295	−	0.944227i	$-0.606811\pi$
$677$	−17.1360	−0.658590	−0.329295	+	0.944227i	$0.606811\pi$
$678$	19.0968	0.733407
$679$	19.4856	0.747787
$680$	0.256394	0.00983226
$681$	0.299333	0.0114705
$682$	0	0
$683$	45.1219	1.72654	0.863271	−	0.504740i	$-0.168412\pi$
$683$	45.1219	1.72654	0.863271	+	0.504740i	$0.168412\pi$
$684$	1.60355	0.0613133
$685$	0.0567783	0.00216939
$686$	−19.1100	−0.729625
$687$	10.3379	0.394414
$688$	10.0414	0.382824
$689$	19.4844	0.742298
$690$	0.961525	0.0366046
$691$	−7.30049	−0.277724	−0.138862	−	0.990312i	$-0.544344\pi$
$691$	−7.30049	−0.277724	−0.138862	+	0.990312i	$0.544344\pi$
$692$	−0.886634	−0.0337048
$693$	0	0
$694$	27.1440	1.03037
$695$	2.33066	0.0884070
$696$	3.43468	0.130191
$697$	1.33863	0.0507042
$698$	9.47226	0.358530
$699$	14.6041	0.552377
$700$	−8.69423	−0.328611
$701$	28.9718	1.09425	0.547125	−	0.837051i	$-0.315722\pi$
$701$	28.9718	1.09425	0.547125	+	0.837051i	$0.315722\pi$
$702$	−11.5514	−0.435981
$703$	2.04407	0.0770934
$704$	0	0
$705$	−0.848707	−0.0319642
$706$	12.0966	0.455261
$707$	−5.91665	−0.222519
$708$	−6.63517	−0.249365
$709$	33.5745	1.26092	0.630459	−	0.776223i	$-0.282867\pi$
$709$	33.5745	1.26092	0.630459	+	0.776223i	$0.282867\pi$
$710$	1.08102	0.0405700
$711$	−8.77995	−0.329274
$712$	4.79411	0.179667
$713$	−14.1510	−0.529958
$714$	4.48335	0.167785
$715$	0	0
$716$	−2.70361	−0.101039
$717$	22.7179	0.848416
$718$	7.99672	0.298435
$719$	10.7658	0.401496	0.200748	−	0.979643i	$-0.435663\pi$
$719$	10.7658	0.401496	0.200748	+	0.979643i	$0.435663\pi$
$720$	0.188960	0.00704211
$721$	30.8650	1.14947
$722$	1.00000	0.0372161
$723$	22.6810	0.843517
$724$	16.0464	0.596360
$725$	14.4923	0.538229
$726$	0	0
$727$	−6.94503	−0.257577	−0.128788	−	0.991672i	$-0.541109\pi$
$727$	−6.94503	−0.257577	−0.128788	+	0.991672i	$0.541109\pi$
$728$	−3.70254	−0.137225
$729$	21.8804	0.810385
$730$	1.58547	0.0586810
$731$	−21.8481	−0.808082
$732$	6.18324	0.228539
$733$	−29.4453	−1.08759	−0.543794	−	0.839219i	$-0.683013\pi$
$733$	−29.4453	−1.08759	−0.543794	+	0.839219i	$0.683013\pi$
$734$	1.30614	0.0482106
$735$	−0.551372	−0.0203377
$736$	6.90496	0.254520
$737$	0	0
$738$	0.986557	0.0363157
$739$	42.1940	1.55213	0.776066	−	0.630651i	$-0.217212\pi$
$739$	42.1940	1.55213	0.776066	+	0.630651i	$0.217212\pi$
$740$	0.240869	0.00885454
$741$	−2.50925	−0.0921795
$742$	−16.0002	−0.587387
$743$	−31.7864	−1.16613	−0.583065	−	0.812426i	$-0.698147\pi$
$743$	−31.7864	−1.16613	−0.583065	+	0.812426i	$0.698147\pi$
$744$	2.42180	0.0887874
$745$	0.632636	0.0231780
$746$	−11.9113	−0.436104
$747$	15.1817	0.555468
$748$	0	0
$749$	0.901493	0.0329398
$750$	−1.39058	−0.0507768
$751$	12.6241	0.460659	0.230329	−	0.973113i	$-0.426020\pi$
$751$	12.6241	0.460659	0.230329	+	0.973113i	$0.426020\pi$
$752$	−6.09479	−0.222254
$753$	10.3593	0.377515
$754$	6.17170	0.224760
$755$	2.44954	0.0891479
$756$	9.48581	0.344996
$757$	−14.9575	−0.543639	−0.271819	−	0.962348i	$-0.587625\pi$
$757$	−14.9575	−0.543639	−0.271819	+	0.962348i	$0.587625\pi$
$758$	−15.6318	−0.567774
$759$	0	0
$760$	0.117838	0.00427445
$761$	50.6321	1.83541	0.917705	−	0.397262i	$-0.130039\pi$
$761$	50.6321	1.83541	0.917705	+	0.397262i	$0.130039\pi$
$762$	3.28492	0.119000
$763$	13.8507	0.501429
$764$	−23.4368	−0.847915
$765$	−0.411140	−0.0148648
$766$	−12.3471	−0.446121
$767$	−11.9226	−0.430500
$768$	−1.18171	−0.0426415
$769$	−29.6272	−1.06839	−0.534193	−	0.845363i	$-0.679384\pi$
$769$	−29.6272	−1.06839	−0.534193	+	0.845363i	$0.679384\pi$
$770$	0	0
$771$	−29.8543	−1.07518
$772$	−8.29786	−0.298647
$773$	3.17632	0.114244	0.0571221	−	0.998367i	$-0.481808\pi$
$773$	3.17632	0.114244	0.0571221	+	0.998367i	$0.481808\pi$
$774$	−16.1018	−0.578769
$775$	10.2185	0.367060
$776$	11.1749	0.401156
$777$	4.21189	0.151101
$778$	−15.1540	−0.543297
$779$	0.615233	0.0220430
$780$	−0.295686	−0.0105872
$781$	0	0
$782$	−15.0239	−0.537253
$783$	−15.8117	−0.565065
$784$	−3.95955	−0.141412
$785$	−0.793729	−0.0283294
$786$	−11.9063	−0.424685
$787$	25.6936	0.915878	0.457939	−	0.888984i	$-0.348588\pi$
$787$	25.6936	0.915878	0.457939	+	0.888984i	$0.348588\pi$
$788$	−25.7155	−0.916077
$789$	−22.6578	−0.806639
$790$	−0.645202	−0.0229553
$791$	−28.1784	−1.00191
$792$	0	0
$793$	11.1105	0.394546
$794$	−1.08003	−0.0383287
$795$	−1.27778	−0.0453182
$796$	7.28088	0.258064
$797$	−33.3921	−1.18281	−0.591404	−	0.806376i	$-0.701426\pi$
$797$	−33.3921	−1.18281	−0.591404	+	0.806376i	$0.701426\pi$
$798$	2.06054	0.0729424
$799$	13.2611	0.469144
$800$	−4.98611	−0.176286
$801$	−7.68759	−0.271628
$802$	22.8470	0.806757
$803$	0	0
$804$	16.4670	0.580746
$805$	−1.41879	−0.0500056
$806$	4.35167	0.153281
$807$	−9.77407	−0.344064
$808$	−3.39318	−0.119372
$809$	−19.3830	−0.681470	−0.340735	−	0.940159i	$-0.610676\pi$
$809$	−19.3830	−0.681470	−0.340735	+	0.940159i	$0.610676\pi$
$810$	0.190660	0.00669910
$811$	48.1203	1.68973	0.844866	−	0.534978i	$-0.179680\pi$
$811$	48.1203	1.68973	0.844866	+	0.534978i	$0.179680\pi$
$812$	−5.06807	−0.177854
$813$	−10.7384	−0.376611
$814$	0	0
$815$	−0.533629	−0.0186922
$816$	2.57119	0.0900096
$817$	−10.0414	−0.351303
$818$	−16.4866	−0.576440
$819$	5.93721	0.207463
$820$	0.0724980	0.00253174
$821$	−25.7151	−0.897464	−0.448732	−	0.893666i	$-0.648124\pi$
$821$	−25.7151	−0.897464	−0.448732	+	0.893666i	$0.648124\pi$
$822$	0.569388	0.0198597
$823$	−37.2402	−1.29811	−0.649057	−	0.760740i	$-0.724836\pi$
$823$	−37.2402	−1.29811	−0.649057	+	0.760740i	$0.724836\pi$
$824$	17.7010	0.616644
$825$	0	0
$826$	9.79059	0.340658
$827$	−22.5824	−0.785266	−0.392633	−	0.919695i	$-0.628436\pi$
$827$	−22.5824	−0.785266	−0.392633	+	0.919695i	$0.628436\pi$
$828$	−11.0725	−0.384794
$829$	34.3518	1.19309	0.596544	−	0.802580i	$-0.296540\pi$
$829$	34.3518	1.19309	0.596544	+	0.802580i	$0.296540\pi$
$830$	1.11564	0.0387244
$831$	−5.40181	−0.187387
$832$	−2.12340	−0.0736155
$833$	8.61523	0.298500
$834$	23.3725	0.809323
$835$	−0.584958	−0.0202433
$836$	0	0
$837$	−11.1489	−0.385361
$838$	4.02294	0.138970
$839$	3.05628	0.105514	0.0527572	−	0.998607i	$-0.483199\pi$
$839$	3.05628	0.105514	0.0527572	+	0.998607i	$0.483199\pi$
$840$	0.242811	0.00837777
$841$	−20.5521	−0.708694
$842$	−9.30430	−0.320647
$843$	−1.45464	−0.0501004
$844$	−9.82812	−0.338298
$845$	1.00059	0.0344213
$846$	9.77330	0.336013
$847$	0	0
$848$	−9.17608	−0.315108
$849$	31.2303	1.07182
$850$	10.8488	0.372112
$851$	−14.1142	−0.483829
$852$	10.8408	0.371399
$853$	3.27449	0.112116	0.0560582	−	0.998428i	$-0.482147\pi$
$853$	3.27449	0.112116	0.0560582	+	0.998428i	$0.482147\pi$
$854$	−9.12373	−0.312208
$855$	−0.188960	−0.00646228
$856$	0.517003	0.0176708
$857$	6.04478	0.206486	0.103243	−	0.994656i	$-0.467078\pi$
$857$	6.04478	0.206486	0.103243	+	0.994656i	$0.467078\pi$
$858$	0	0
$859$	1.52525	0.0520409	0.0260204	−	0.999661i	$-0.491717\pi$
$859$	1.52525	0.0520409	0.0260204	+	0.999661i	$0.491717\pi$
$860$	−1.18326	−0.0403488
$861$	1.26771	0.0432036
$862$	2.55537	0.0870363
$863$	−36.5453	−1.24402	−0.622009	−	0.783010i	$-0.713683\pi$
$863$	−36.5453	−1.24402	−0.622009	+	0.783010i	$0.713683\pi$
$864$	5.44008	0.185075
$865$	0.104479	0.00355241
$866$	38.5263	1.30918
$867$	14.4947	0.492267
$868$	−3.57350	−0.121293
$869$	0	0
$870$	−0.404737	−0.0137219
$871$	29.5891	1.00259
$872$	7.94333	0.268995
$873$	−17.9195	−0.606484
$874$	−6.90496	−0.233564
$875$	2.05188	0.0693662
$876$	15.8996	0.537196
$877$	8.18220	0.276293	0.138147	−	0.990412i	$-0.455885\pi$
$877$	8.18220	0.276293	0.138147	+	0.990412i	$0.455885\pi$
$878$	−34.2110	−1.15457
$879$	7.45540	0.251465
$880$	0	0
$881$	−23.0229	−0.775662	−0.387831	−	0.921731i	$-0.626776\pi$
$881$	−23.0229	−0.775662	−0.387831	+	0.921731i	$0.626776\pi$
$882$	6.34933	0.213793
$883$	54.0069	1.81748	0.908739	−	0.417364i	$-0.137046\pi$
$883$	54.0069	1.81748	0.908739	+	0.417364i	$0.137046\pi$
$884$	4.62011	0.155391
$885$	0.781878	0.0262825
$886$	28.3557	0.952629
$887$	−31.5228	−1.05843	−0.529216	−	0.848487i	$-0.677514\pi$
$887$	−31.5228	−1.05843	−0.529216	+	0.848487i	$0.677514\pi$
$888$	2.41550	0.0810590
$889$	−4.84709	−0.162566
$890$	−0.564929	−0.0189365
$891$	0	0
$892$	1.50507	0.0503935
$893$	6.09479	0.203954
$894$	6.34425	0.212183
$895$	0.318589	0.0106493
$896$	1.74369	0.0582526
$897$	17.3263	0.578507
$898$	19.7319	0.658462
$899$	5.95661	0.198664
$900$	7.99548	0.266516
$901$	19.9654	0.665144
$902$	0	0
$903$	−20.6907	−0.688543
$904$	−16.1602	−0.537481
$905$	−1.89088	−0.0628550
$906$	24.5647	0.816106
$907$	1.92997	0.0640837	0.0320418	−	0.999487i	$-0.489799\pi$
$907$	1.92997	0.0640837	0.0320418	+	0.999487i	$0.489799\pi$
$908$	−0.253304	−0.00840619
$909$	5.44114	0.180471
$910$	0.436301	0.0144632
$911$	0.402087	0.0133217	0.00666087	−	0.999978i	$-0.497880\pi$
$911$	0.402087	0.0133217	0.00666087	+	0.999978i	$0.497880\pi$
$912$	1.18171	0.0391305
$913$	0	0
$914$	−8.71834	−0.288377
$915$	−0.728623	−0.0240875
$916$	−8.74819	−0.289048
$917$	17.5685	0.580163
$918$	−11.8366	−0.390666
$919$	38.8202	1.28056	0.640279	−	0.768142i	$-0.278819\pi$
$919$	38.8202	1.28056	0.640279	+	0.768142i	$0.278819\pi$
$920$	−0.813669	−0.0268259
$921$	−21.6151	−0.712243
$922$	−10.8220	−0.356405
$923$	19.4795	0.641177
$924$	0	0
$925$	10.1920	0.335109
$926$	38.6978	1.27169
$927$	−28.3844	−0.932268
$928$	−2.90652	−0.0954113
$929$	−5.83093	−0.191307	−0.0956533	−	0.995415i	$-0.530494\pi$
$929$	−5.83093	−0.191307	−0.0956533	+	0.995415i	$0.530494\pi$
$930$	−0.285381	−0.00935800
$931$	3.95955	0.129769
$932$	−12.3584	−0.404812
$933$	34.1735	1.11879
$934$	6.54021	0.214002
$935$	0	0
$936$	3.40497	0.111295
$937$	−13.7532	−0.449296	−0.224648	−	0.974440i	$-0.572123\pi$
$937$	−13.7532	−0.449296	−0.224648	+	0.974440i	$0.572123\pi$
$938$	−24.2980	−0.793358
$939$	−21.6293	−0.705847
$940$	0.718200	0.0234251
$941$	41.5800	1.35547	0.677734	−	0.735307i	$-0.262962\pi$
$941$	41.5800	1.35547	0.677734	+	0.735307i	$0.262962\pi$
$942$	−7.95973	−0.259342
$943$	−4.24816	−0.138339
$944$	5.61487	0.182748
$945$	−1.11779	−0.0363618
$946$	0	0
$947$	14.7404	0.478999	0.239500	−	0.970896i	$-0.423017\pi$
$947$	14.7404	0.478999	0.239500	+	0.970896i	$0.423017\pi$
$948$	−6.47027	−0.210144
$949$	28.5695	0.927406
$950$	4.98611	0.161771
$951$	−26.6372	−0.863771
$952$	−3.79394	−0.122962
$953$	30.4382	0.985990	0.492995	−	0.870032i	$-0.335902\pi$
$953$	30.4382	0.985990	0.492995	+	0.870032i	$0.335902\pi$
$954$	14.7143	0.476393
$955$	2.76176	0.0893683
$956$	−19.2245	−0.621766
$957$	0	0
$958$	33.0437	1.06759
$959$	−0.840165	−0.0271303
$960$	0.139251	0.00449432
$961$	−26.8000	−0.864516
$962$	4.34036	0.139939
$963$	−0.829041	−0.0267155
$964$	−19.1933	−0.618176
$965$	0.977806	0.0314767
$966$	−14.2280	−0.457777
$967$	−9.20321	−0.295955	−0.147978	−	0.988991i	$-0.547276\pi$
$967$	−9.20321	−0.295955	−0.147978	+	0.988991i	$0.547276\pi$
$968$	0	0
$969$	−2.57119	−0.0825984
$970$	−1.31683	−0.0422809
$971$	12.2766	0.393976	0.196988	−	0.980406i	$-0.436884\pi$
$971$	12.2766	0.393976	0.196988	+	0.980406i	$0.436884\pi$
$972$	−14.4083	−0.462145
$973$	−34.4875	−1.10562
$974$	6.39992	0.205067
$975$	−12.5114	−0.400685
$976$	−5.23243	−0.167486
$977$	−24.4956	−0.783684	−0.391842	−	0.920032i	$-0.628162\pi$
$977$	−24.4956	−0.783684	−0.391842	+	0.920032i	$0.628162\pi$
$978$	−5.35137	−0.171118
$979$	0	0
$980$	0.466587	0.0149046
$981$	−12.7375	−0.406678
$982$	29.6576	0.946411
$983$	−33.4093	−1.06559	−0.532796	−	0.846244i	$-0.678859\pi$
$983$	−33.4093	−1.06559	−0.532796	+	0.846244i	$0.678859\pi$
$984$	0.727030	0.0231769
$985$	3.03027	0.0965525
$986$	6.32404	0.201399
$987$	12.5586	0.399744
$988$	2.12340	0.0675542
$989$	69.3353	2.20473
$990$	0	0
$991$	−18.4683	−0.586664	−0.293332	−	0.956011i	$-0.594764\pi$
$991$	−18.4683	−0.586664	−0.293332	+	0.956011i	$0.594764\pi$
$992$	−2.04939	−0.0650683
$993$	−9.54776	−0.302989
$994$	−15.9962	−0.507369
$995$	−0.857967	−0.0271994
$996$	11.1879	0.354503
$997$	−37.2820	−1.18073	−0.590367	−	0.807135i	$-0.701017\pi$
$997$	−37.2820	−1.18073	−0.590367	+	0.807135i	$0.701017\pi$
$998$	−10.3794	−0.328553
$999$	−11.1199	−0.351818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bz.1.4		8
11.7	odd	10		418.2.f.g.115.3	✓	16
11.8	odd	10		418.2.f.g.229.3	yes	16
11.10	odd	2		4598.2.a.bw.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.115.3	✓	16	11.7	odd	10
418.2.f.g.229.3	yes	16	11.8	odd	10
4598.2.a.bw.1.4		8	11.10	odd	2
4598.2.a.bz.1.4		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.18171 q^{3} +1.00000 q^{4} -0.117838 q^{5} -1.18171 q^{6} +1.74369 q^{7} +1.00000 q^{8} -1.60355 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.18171 q^{3} +1.00000 q^{4} -0.117838 q^{5} -1.18171 q^{6} +1.74369 q^{7} +1.00000 q^{8} -1.60355 q^{9} -0.117838 q^{10} -1.18171 q^{12} -2.12340 q^{13} +1.74369 q^{14} +0.139251 q^{15} +1.00000 q^{16} -2.17581 q^{17} -1.60355 q^{18} -1.00000 q^{19} -0.117838 q^{20} -2.06054 q^{21} +6.90496 q^{23} -1.18171 q^{24} -4.98611 q^{25} -2.12340 q^{26} +5.44008 q^{27} +1.74369 q^{28} -2.90652 q^{29} +0.139251 q^{30} -2.04939 q^{31} +1.00000 q^{32} -2.17581 q^{34} -0.205473 q^{35} -1.60355 q^{36} -2.04407 q^{37} -1.00000 q^{38} +2.50925 q^{39} -0.117838 q^{40} -0.615233 q^{41} -2.06054 q^{42} +10.0414 q^{43} +0.188960 q^{45} +6.90496 q^{46} -6.09479 q^{47} -1.18171 q^{48} -3.95955 q^{49} -4.98611 q^{50} +2.57119 q^{51} -2.12340 q^{52} -9.17608 q^{53} +5.44008 q^{54} +1.74369 q^{56} +1.18171 q^{57} -2.90652 q^{58} +5.61487 q^{59} +0.139251 q^{60} -5.23243 q^{61} -2.04939 q^{62} -2.79609 q^{63} +1.00000 q^{64} +0.250217 q^{65} -13.9348 q^{67} -2.17581 q^{68} -8.15970 q^{69} -0.205473 q^{70} -9.17377 q^{71} -1.60355 q^{72} -13.4547 q^{73} -2.04407 q^{74} +5.89217 q^{75} -1.00000 q^{76} +2.50925 q^{78} +5.47532 q^{79} -0.117838 q^{80} -1.61798 q^{81} -0.615233 q^{82} -9.46753 q^{83} -2.06054 q^{84} +0.256394 q^{85} +10.0414 q^{86} +3.43468 q^{87} +4.79411 q^{89} +0.188960 q^{90} -3.70254 q^{91} +6.90496 q^{92} +2.42180 q^{93} -6.09479 q^{94} +0.117838 q^{95} -1.18171 q^{96} +11.1749 q^{97} -3.95955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 2 q^{6} - 14 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 2 * q^6 - 14 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 2 q^{6} - 14 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} - 9 q^{13} - 14 q^{14} + 5 q^{15} + 8 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 2 q^{20} - 7 q^{21} - 13 q^{23} - 2 q^{24} + 4 q^{25} - 9 q^{26} + 4 q^{27} - 14 q^{28} - 10 q^{29} + 5 q^{30} - 2 q^{31} + 8 q^{32} - 3 q^{34} + 7 q^{35} + 2 q^{36} + 15 q^{37} - 8 q^{38} - 11 q^{39} - 2 q^{40} - 9 q^{41} - 7 q^{42} - 33 q^{43} - 21 q^{45} - 13 q^{46} - 19 q^{47} - 2 q^{48} + 12 q^{49} + 4 q^{50} - 22 q^{51} - 9 q^{52} + 10 q^{53} + 4 q^{54} - 14 q^{56} + 2 q^{57} - 10 q^{58} + q^{59} + 5 q^{60} - 26 q^{61} - 2 q^{62} - 19 q^{63} + 8 q^{64} - 26 q^{65} - 25 q^{67} - 3 q^{68} - 12 q^{69} + 7 q^{70} - 10 q^{71} + 2 q^{72} - 11 q^{73} + 15 q^{74} - 33 q^{75} - 8 q^{76} - 11 q^{78} - 10 q^{79} - 2 q^{80} - 40 q^{81} - 9 q^{82} - 16 q^{83} - 7 q^{84} - 33 q^{85} - 33 q^{86} - 2 q^{87} - 14 q^{89} - 21 q^{90} + 25 q^{91} - 13 q^{92} + 20 q^{93} - 19 q^{94} + 2 q^{95} - 2 q^{96} + 22 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 2 * q^6 - 14 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 - 9 * q^13 - 14 * q^14 + 5 * q^15 + 8 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 2 * q^20 - 7 * q^21 - 13 * q^23 - 2 * q^24 + 4 * q^25 - 9 * q^26 + 4 * q^27 - 14 * q^28 - 10 * q^29 + 5 * q^30 - 2 * q^31 + 8 * q^32 - 3 * q^34 + 7 * q^35 + 2 * q^36 + 15 * q^37 - 8 * q^38 - 11 * q^39 - 2 * q^40 - 9 * q^41 - 7 * q^42 - 33 * q^43 - 21 * q^45 - 13 * q^46 - 19 * q^47 - 2 * q^48 + 12 * q^49 + 4 * q^50 - 22 * q^51 - 9 * q^52 + 10 * q^53 + 4 * q^54 - 14 * q^56 + 2 * q^57 - 10 * q^58 + q^59 + 5 * q^60 - 26 * q^61 - 2 * q^62 - 19 * q^63 + 8 * q^64 - 26 * q^65 - 25 * q^67 - 3 * q^68 - 12 * q^69 + 7 * q^70 - 10 * q^71 + 2 * q^72 - 11 * q^73 + 15 * q^74 - 33 * q^75 - 8 * q^76 - 11 * q^78 - 10 * q^79 - 2 * q^80 - 40 * q^81 - 9 * q^82 - 16 * q^83 - 7 * q^84 - 33 * q^85 - 33 * q^86 - 2 * q^87 - 14 * q^89 - 21 * q^90 + 25 * q^91 - 13 * q^92 + 20 * q^93 - 19 * q^94 + 2 * q^95 - 2 * q^96 + 22 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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