LMFDB - Embedded newform 4598.2.a.bv.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:	$0$
Dimension:	$4$
Coefficient field:	4.4.258228.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 12x^{2} + 6x + 24 $ x^4 - 2x^3 - 12x^2 + 6*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.34628$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} +3.34628 q^{6} -4.77567 q^{7} +1.00000 q^{8} +8.19759 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} +3.34628 q^{6} -4.77567 q^{7} +1.00000 q^{8} +8.19759 q^{9} +2.34628 q^{10} +3.34628 q^{12} +1.57808 q^{13} -4.77567 q^{14} +7.85131 q^{15} +1.00000 q^{16} +3.77567 q^{17} +8.19759 q^{18} +1.00000 q^{19} +2.34628 q^{20} -15.9807 q^{21} -2.57808 q^{23} +3.34628 q^{24} +0.505030 q^{25} +1.57808 q^{26} +17.3926 q^{27} -4.77567 q^{28} -4.85131 q^{29} +7.85131 q^{30} +6.69256 q^{31} +1.00000 q^{32} +3.77567 q^{34} -11.2051 q^{35} +8.19759 q^{36} -10.8976 q^{37} +1.00000 q^{38} +5.28070 q^{39} +2.34628 q^{40} +7.00747 q^{41} -15.9807 q^{42} +11.8487 q^{43} +19.2338 q^{45} -2.57808 q^{46} -7.19759 q^{47} +3.34628 q^{48} +15.8070 q^{49} +0.505030 q^{50} +12.6345 q^{51} +1.57808 q^{52} -1.14869 q^{53} +17.3926 q^{54} -4.77567 q^{56} +3.34628 q^{57} -4.85131 q^{58} +4.92436 q^{59} +7.85131 q^{60} -4.04890 q^{61} +6.69256 q^{62} -39.1490 q^{63} +1.00000 q^{64} +3.70262 q^{65} +10.4369 q^{67} +3.77567 q^{68} -8.62698 q^{69} -11.2051 q^{70} -2.31491 q^{71} +8.19759 q^{72} -7.77567 q^{73} -10.8976 q^{74} +1.68997 q^{75} +1.00000 q^{76} +5.28070 q^{78} +0.992527 q^{79} +2.34628 q^{80} +33.6077 q^{81} +7.00747 q^{82} -8.34628 q^{83} -15.9807 q^{84} +8.85878 q^{85} +11.8487 q^{86} -16.2338 q^{87} -11.7000 q^{89} +19.2338 q^{90} -7.53640 q^{91} -2.57808 q^{92} +22.3952 q^{93} -7.19759 q^{94} +2.34628 q^{95} +3.34628 q^{96} -10.0000 q^{97} +15.8070 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9 - 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 + 26 * q^15 + 4 * q^16 - 7 * q^17 + 16 * q^18 + 4 * q^19 - 2 * q^20 - 9 * q^21 - 5 * q^23 + 2 * q^24 + 8 * q^25 + q^26 + 8 * q^27 + 3 * q^28 - 14 * q^29 + 26 * q^30 + 4 * q^31 + 4 * q^32 - 7 * q^34 - 12 * q^35 + 16 * q^36 + 12 * q^37 + 4 * q^38 + 5 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 14 * q^43 - 2 * q^45 - 5 * q^46 - 12 * q^47 + 2 * q^48 + 23 * q^49 + 8 * q^50 + 7 * q^51 + q^52 - 10 * q^53 + 8 * q^54 + 3 * q^56 + 2 * q^57 - 14 * q^58 + 3 * q^59 + 26 * q^60 + 6 * q^61 + 4 * q^62 - 18 * q^63 + 4 * q^64 + 4 * q^65 + 15 * q^67 - 7 * q^68 - 7 * q^69 - 12 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 - 44 * q^75 + 4 * q^76 + 5 * q^78 + 20 * q^79 - 2 * q^80 + 52 * q^81 + 12 * q^82 - 22 * q^83 - 9 * q^84 + 14 * q^85 + 14 * q^86 + 14 * q^87 - 8 * q^89 - 2 * q^90 - 18 * q^91 - 5 * q^92 + 56 * q^93 - 12 * q^94 - 2 * q^95 + 2 * q^96 - 40 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.34628	1.93198	0.965988	−	0.258587i	$-0.0832570\pi$
$3$	3.34628	1.93198	0.965988	+	0.258587i	$0.0832570\pi$
$4$	1.00000	0.500000
$5$	2.34628	1.04929	0.524644	−	0.851322i	$-0.324198\pi$
$5$	2.34628	1.04929	0.524644	+	0.851322i	$0.324198\pi$
$6$	3.34628	1.36611
$7$	−4.77567	−1.80503	−0.902517	−	0.430654i	$-0.858283\pi$
$7$	−4.77567	−1.80503	−0.902517	+	0.430654i	$0.858283\pi$
$8$	1.00000	0.353553
$9$	8.19759	2.73253
$10$	2.34628	0.741959
$11$	0	0
$11$	0	0
$12$	3.34628	0.965988
$13$	1.57808	0.437681	0.218840	−	0.975761i	$-0.429773\pi$
$13$	1.57808	0.437681	0.218840	+	0.975761i	$0.429773\pi$
$14$	−4.77567	−1.27635
$15$	7.85131	2.02720
$16$	1.00000	0.250000
$17$	3.77567	0.915735	0.457867	−	0.889020i	$-0.348613\pi$
$17$	3.77567	0.915735	0.457867	+	0.889020i	$0.348613\pi$
$18$	8.19759	1.93219
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.34628	0.524644
$21$	−15.9807	−3.48728
$22$	0	0
$23$	−2.57808	−0.537567	−0.268784	−	0.963201i	$-0.586622\pi$
$23$	−2.57808	−0.537567	−0.268784	+	0.963201i	$0.586622\pi$
$24$	3.34628	0.683057
$25$	0.505030	0.101006
$26$	1.57808	0.309487
$27$	17.3926	3.34721
$28$	−4.77567	−0.902517
$29$	−4.85131	−0.900866	−0.450433	−	0.892810i	$-0.648730\pi$
$29$	−4.85131	−0.900866	−0.450433	+	0.892810i	$0.648730\pi$
$30$	7.85131	1.43345
$31$	6.69256	1.20202	0.601010	−	0.799242i	$-0.294765\pi$
$31$	6.69256	1.20202	0.601010	+	0.799242i	$0.294765\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	3.77567	0.647522
$35$	−11.2051	−1.89400
$36$	8.19759	1.36627
$37$	−10.8976	−1.79156	−0.895779	−	0.444499i	$-0.853382\pi$
$37$	−10.8976	−1.79156	−0.895779	+	0.444499i	$0.853382\pi$
$38$	1.00000	0.162221
$39$	5.28070	0.845589
$40$	2.34628	0.370979
$41$	7.00747	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$41$	7.00747	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$42$	−15.9807	−2.46588
$43$	11.8487	1.80691	0.903457	−	0.428680i	$-0.141021\pi$
$43$	11.8487	1.80691	0.903457	+	0.428680i	$0.141021\pi$
$44$	0	0
$45$	19.2338	2.86721
$46$	−2.57808	−0.380117
$47$	−7.19759	−1.04988	−0.524938	−	0.851140i	$-0.675912\pi$
$47$	−7.19759	−1.04988	−0.524938	+	0.851140i	$0.675912\pi$
$48$	3.34628	0.482994
$49$	15.8070	2.25815
$50$	0.505030	0.0714221
$51$	12.6345	1.76918
$52$	1.57808	0.218840
$53$	−1.14869	−0.157785	−0.0788923	−	0.996883i	$-0.525138\pi$
$53$	−1.14869	−0.157785	−0.0788923	+	0.996883i	$0.525138\pi$
$54$	17.3926	2.36683
$55$	0	0
$56$	−4.77567	−0.638176
$57$	3.34628	0.443226
$58$	−4.85131	−0.637008
$59$	4.92436	0.641097	0.320549	−	0.947232i	$-0.396133\pi$
$59$	4.92436	0.641097	0.320549	+	0.947232i	$0.396133\pi$
$60$	7.85131	1.01360
$61$	−4.04890	−0.518409	−0.259204	−	0.965823i	$-0.583460\pi$
$61$	−4.04890	−0.518409	−0.259204	+	0.965823i	$0.583460\pi$
$62$	6.69256	0.849956
$63$	−39.1490	−4.93231
$64$	1.00000	0.125000
$65$	3.70262	0.459254
$66$	0	0
$67$	10.4369	1.27507	0.637533	−	0.770423i	$-0.279955\pi$
$67$	10.4369	1.27507	0.637533	+	0.770423i	$0.279955\pi$
$68$	3.77567	0.457867
$69$	−8.62698	−1.03857
$70$	−11.2051	−1.33926
$71$	−2.31491	−0.274730	−0.137365	−	0.990521i	$-0.543863\pi$
$71$	−2.31491	−0.274730	−0.137365	+	0.990521i	$0.543863\pi$
$72$	8.19759	0.966095
$73$	−7.77567	−0.910074	−0.455037	−	0.890473i	$-0.650374\pi$
$73$	−7.77567	−0.910074	−0.455037	+	0.890473i	$0.650374\pi$
$74$	−10.8976	−1.26682
$75$	1.68997	0.195141
$76$	1.00000	0.114708
$77$	0	0
$78$	5.28070	0.597922
$79$	0.992527	0.111668	0.0558340	−	0.998440i	$-0.482218\pi$
$79$	0.992527	0.111668	0.0558340	+	0.998440i	$0.482218\pi$
$80$	2.34628	0.262322
$81$	33.6077	3.73419
$82$	7.00747	0.773846
$83$	−8.34628	−0.916123	−0.458062	−	0.888920i	$-0.651456\pi$
$83$	−8.34628	−0.916123	−0.458062	+	0.888920i	$0.651456\pi$
$84$	−15.9807	−1.74364
$85$	8.85878	0.960870
$86$	11.8487	1.27768
$87$	−16.2338	−1.74045
$88$	0	0
$89$	−11.7000	−1.24020	−0.620101	−	0.784522i	$-0.712908\pi$
$89$	−11.7000	−1.24020	−0.620101	+	0.784522i	$0.712908\pi$
$90$	19.2338	2.02743
$91$	−7.53640	−0.790029
$92$	−2.57808	−0.268784
$93$	22.3952	2.32227
$94$	−7.19759	−0.742375
$95$	2.34628	0.240723
$96$	3.34628	0.341528
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	15.8070	1.59675
$99$	0	0
$100$	0.505030	0.0505030
$101$	1.35634	0.134961	0.0674805	−	0.997721i	$-0.478504\pi$
$101$	1.35634	0.134961	0.0674805	+	0.997721i	$0.478504\pi$
$102$	12.6345	1.25100
$103$	2.29997	0.226622	0.113311	−	0.993560i	$-0.463854\pi$
$103$	2.29997	0.226622	0.113311	+	0.993560i	$0.463854\pi$
$104$	1.57808	0.154744
$105$	−37.4953	−3.65916
$106$	−1.14869	−0.111571
$107$	−14.6583	−1.41708	−0.708538	−	0.705673i	$-0.750645\pi$
$107$	−14.6583	−1.41708	−0.708538	+	0.705673i	$0.750645\pi$
$108$	17.3926	1.67360
$109$	−2.92436	−0.280103	−0.140052	−	0.990144i	$-0.544727\pi$
$109$	−2.92436	−0.280103	−0.140052	+	0.990144i	$0.544727\pi$
$110$	0	0
$111$	−36.4665	−3.46125
$112$	−4.77567	−0.451259
$113$	−1.00747	−0.0947751	−0.0473875	−	0.998877i	$-0.515090\pi$
$113$	−1.00747	−0.0947751	−0.0473875	+	0.998877i	$0.515090\pi$
$114$	3.34628	0.313408
$115$	−6.04890	−0.564063
$116$	−4.85131	−0.450433
$117$	12.9365	1.19598
$118$	4.92436	0.453324
$119$	−18.0314	−1.65293
$120$	7.85131	0.716723
$121$	0	0
$122$	−4.04890	−0.366570
$123$	23.4490	2.11432
$124$	6.69256	0.601010
$125$	−10.5465	−0.943304
$126$	−39.1490	−3.48767
$127$	−1.14122	−0.101267	−0.0506333	−	0.998717i	$-0.516124\pi$
$127$	−1.14122	−0.101267	−0.0506333	+	0.998717i	$0.516124\pi$
$128$	1.00000	0.0883883
$129$	39.6491	3.49091
$130$	3.70262	0.324741
$131$	18.7075	1.63448	0.817241	−	0.576296i	$-0.195502\pi$
$131$	18.7075	1.63448	0.817241	+	0.576296i	$0.195502\pi$
$132$	0	0
$133$	−4.77567	−0.414103
$134$	10.4369	0.901608
$135$	40.8079	3.51218
$136$	3.77567	0.323761
$137$	12.0731	1.03147	0.515735	−	0.856748i	$-0.327519\pi$
$137$	12.0731	1.03147	0.515735	+	0.856748i	$0.327519\pi$
$138$	−8.62698	−0.734377
$139$	−21.7803	−1.84738	−0.923691	−	0.383139i	$-0.874843\pi$
$139$	−21.7803	−1.84738	−0.923691	+	0.383139i	$0.874843\pi$
$140$	−11.2051	−0.947001
$141$	−24.0852	−2.02834
$142$	−2.31491	−0.194263
$143$	0	0
$144$	8.19759	0.683133
$145$	−11.3825	−0.945268
$146$	−7.77567	−0.643519
$147$	52.8948	4.36269
$148$	−10.8976	−0.895779
$149$	−6.38024	−0.522689	−0.261345	−	0.965246i	$-0.584166\pi$
$149$	−6.38024	−0.522689	−0.261345	+	0.965246i	$0.584166\pi$
$150$	1.68997	0.137986
$151$	2.54387	0.207017	0.103509	−	0.994629i	$-0.466993\pi$
$151$	2.54387	0.207017	0.103509	+	0.994629i	$0.466993\pi$
$152$	1.00000	0.0811107
$153$	30.9514	2.50227
$154$	0	0
$155$	15.7026	1.26126
$156$	5.28070	0.422795
$157$	−5.60024	−0.446948	−0.223474	−	0.974710i	$-0.571740\pi$
$157$	−5.60024	−0.446948	−0.223474	+	0.974710i	$0.571740\pi$
$158$	0.992527	0.0789612
$159$	−3.84384	−0.304836
$160$	2.34628	0.185490
$161$	12.3121	0.970327
$162$	33.6077	2.64047
$163$	7.25396	0.568174	0.284087	−	0.958798i	$-0.408309\pi$
$163$	7.25396	0.568174	0.284087	+	0.958798i	$0.408309\pi$
$164$	7.00747	0.547192
$165$	0	0
$166$	−8.34628	−0.647797
$167$	2.85878	0.221219	0.110610	−	0.993864i	$-0.464720\pi$
$167$	2.85878	0.221219	0.110610	+	0.993864i	$0.464720\pi$
$168$	−15.9807	−1.23294
$169$	−10.5097	−0.808435
$170$	8.85878	0.679438
$171$	8.19759	0.626885
$172$	11.8487	0.903457
$173$	12.8663	0.978203	0.489102	−	0.872227i	$-0.337325\pi$
$173$	12.8663	0.978203	0.489102	+	0.872227i	$0.337325\pi$
$174$	−16.2338	−1.23068
$175$	−2.41186	−0.182319
$176$	0	0
$177$	16.4783	1.23858
$178$	−11.7000	−0.876955
$179$	−24.9290	−1.86328	−0.931640	−	0.363382i	$-0.881622\pi$
$179$	−24.9290	−1.86328	−0.931640	+	0.363382i	$0.881622\pi$
$180$	19.2338	1.43361
$181$	−17.7952	−1.32271	−0.661355	−	0.750073i	$-0.730018\pi$
$181$	−17.7952	−1.32271	−0.661355	+	0.750073i	$0.730018\pi$
$182$	−7.53640	−0.558635
$183$	−13.5488	−1.00155
$184$	−2.57808	−0.190059
$185$	−25.5689	−1.87986
$186$	22.3952	1.64209
$187$	0	0
$188$	−7.19759	−0.524938
$189$	−83.0613	−6.04182
$190$	2.34628	0.170217
$191$	−4.47829	−0.324038	−0.162019	−	0.986788i	$-0.551801\pi$
$191$	−4.47829	−0.324038	−0.162019	+	0.986788i	$0.551801\pi$
$192$	3.34628	0.241497
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	−10.0000	−0.717958
$195$	12.3900	0.887267
$196$	15.8070	1.12907
$197$	−12.5614	−0.894963	−0.447481	−	0.894293i	$-0.647679\pi$
$197$	−12.5614	−0.894963	−0.447481	+	0.894293i	$0.647679\pi$
$198$	0	0
$199$	−0.750666	−0.0532133	−0.0266066	−	0.999646i	$-0.508470\pi$
$199$	−0.750666	−0.0532133	−0.0266066	+	0.999646i	$0.508470\pi$
$200$	0.505030	0.0357110
$201$	34.9247	2.46340
$202$	1.35634	0.0954318
$203$	23.1683	1.62609
$204$	12.6345	0.884589
$205$	16.4415	1.14832
$206$	2.29997	0.160246
$207$	−21.1341	−1.46892
$208$	1.57808	0.109420
$209$	0	0
$210$	−37.4953	−2.58742
$211$	4.66867	0.321404	0.160702	−	0.987003i	$-0.448624\pi$
$211$	4.66867	0.321404	0.160702	+	0.987003i	$0.448624\pi$
$212$	−1.14869	−0.0788923
$213$	−7.74635	−0.530771
$214$	−14.6583	−1.00202
$215$	27.8004	1.89597
$216$	17.3926	1.18342
$217$	−31.9615	−2.16969
$218$	−2.92436	−0.198063
$219$	−26.0196	−1.75824
$220$	0	0
$221$	5.95832	0.400800
$222$	−36.4665	−2.44747
$223$	23.8663	1.59820	0.799101	−	0.601196i	$-0.205309\pi$
$223$	23.8663	1.59820	0.799101	+	0.601196i	$0.205309\pi$
$224$	−4.77567	−0.319088
$225$	4.14003	0.276002
$226$	−1.00747	−0.0670161
$227$	13.5097	0.896668	0.448334	−	0.893866i	$-0.352018\pi$
$227$	13.5097	0.896668	0.448334	+	0.893866i	$0.352018\pi$
$228$	3.34628	0.221613
$229$	−8.22896	−0.543785	−0.271892	−	0.962328i	$-0.587649\pi$
$229$	−8.22896	−0.543785	−0.271892	+	0.962328i	$0.587649\pi$
$230$	−6.04890	−0.398853
$231$	0	0
$232$	−4.85131	−0.318504
$233$	−0.490085	−0.0321065	−0.0160533	−	0.999871i	$-0.505110\pi$
$233$	−0.490085	−0.0321065	−0.0160533	+	0.999871i	$0.505110\pi$
$234$	12.9365	0.845683
$235$	−16.8876	−1.10162
$236$	4.92436	0.320549
$237$	3.32127	0.215740
$238$	−18.0314	−1.16880
$239$	20.5364	1.32839	0.664195	−	0.747560i	$-0.268775\pi$
$239$	20.5364	1.32839	0.664195	+	0.747560i	$0.268775\pi$
$240$	7.85131	0.506800
$241$	−19.4654	−1.25388	−0.626938	−	0.779069i	$-0.715692\pi$
$241$	−19.4654	−1.25388	−0.626938	+	0.779069i	$0.715692\pi$
$242$	0	0
$243$	60.2831	3.86716
$244$	−4.04890	−0.259204
$245$	37.0877	2.36945
$246$	23.4490	1.49505
$247$	1.57808	0.100411
$248$	6.69256	0.424978
$249$	−27.9290	−1.76993
$250$	−10.5465	−0.667017
$251$	−9.84872	−0.621646	−0.310823	−	0.950468i	$-0.600605\pi$
$251$	−9.84872	−0.621646	−0.310823	+	0.950468i	$0.600605\pi$
$252$	−39.1490	−2.46616
$253$	0	0
$254$	−1.14122	−0.0716063
$255$	29.6440	1.85638
$256$	1.00000	0.0625000
$257$	11.2540	0.702003	0.351001	−	0.936375i	$-0.385841\pi$
$257$	11.2540	0.702003	0.351001	+	0.936375i	$0.385841\pi$
$258$	39.6491	2.46845
$259$	52.0435	3.23382
$260$	3.70262	0.229627
$261$	−39.7691	−2.46164
$262$	18.7075	1.15575
$263$	3.49008	0.215208	0.107604	−	0.994194i	$-0.465682\pi$
$263$	3.49008	0.215208	0.107604	+	0.994194i	$0.465682\pi$
$264$	0	0
$265$	−2.69515	−0.165562
$266$	−4.77567	−0.292815
$267$	−39.1516	−2.39604
$268$	10.4369	0.637533
$269$	−20.1737	−1.23001	−0.615006	−	0.788522i	$-0.710846\pi$
$269$	−20.1737	−1.23001	−0.615006	+	0.788522i	$0.710846\pi$
$270$	40.8079	2.48349
$271$	0.239274	0.0145349	0.00726743	−	0.999974i	$-0.497687\pi$
$271$	0.239274	0.0145349	0.00726743	+	0.999974i	$0.497687\pi$
$272$	3.77567	0.228934
$273$	−25.2189	−1.52632
$274$	12.0731	0.729360
$275$	0	0
$276$	−8.62698	−0.519283
$277$	−13.1901	−0.792517	−0.396259	−	0.918139i	$-0.629692\pi$
$277$	−13.1901	−0.792517	−0.396259	+	0.918139i	$0.629692\pi$
$278$	−21.7803	−1.30630
$279$	54.8629	3.28455
$280$	−11.2051	−0.669631
$281$	6.54387	0.390375	0.195187	−	0.980766i	$-0.437469\pi$
$281$	6.54387	0.390375	0.195187	+	0.980766i	$0.437469\pi$
$282$	−24.0852	−1.43425
$283$	9.08774	0.540210	0.270105	−	0.962831i	$-0.412942\pi$
$283$	9.08774	0.540210	0.270105	+	0.962831i	$0.412942\pi$
$284$	−2.31491	−0.137365
$285$	7.85131	0.465071
$286$	0	0
$287$	−33.4654	−1.97540
$288$	8.19759	0.483048
$289$	−2.74430	−0.161430
$290$	−11.3825	−0.668405
$291$	−33.4628	−1.96162
$292$	−7.77567	−0.455037
$293$	20.2051	1.18039	0.590196	−	0.807260i	$-0.299050\pi$
$293$	20.2051	1.18039	0.590196	+	0.807260i	$0.299050\pi$
$294$	52.8948	3.08489
$295$	11.5539	0.672696
$296$	−10.8976	−0.633411
$297$	0	0
$298$	−6.38024	−0.369597
$299$	−4.06842	−0.235283
$300$	1.68997	0.0975706
$301$	−56.5856	−3.26154
$302$	2.54387	0.146383
$303$	4.53870	0.260741
$304$	1.00000	0.0573539
$305$	−9.49985	−0.543960
$306$	30.9514	1.76937
$307$	−20.2514	−1.15581	−0.577904	−	0.816105i	$-0.696129\pi$
$307$	−20.2514	−1.15581	−0.577904	+	0.816105i	$0.696129\pi$
$308$	0	0
$309$	7.69633	0.437829
$310$	15.7026	0.891849
$311$	29.3897	1.66654	0.833270	−	0.552866i	$-0.186466\pi$
$311$	29.3897	1.66654	0.833270	+	0.552866i	$0.186466\pi$
$312$	5.28070	0.298961
$313$	−0.229213	−0.0129559	−0.00647796	−	0.999979i	$-0.502062\pi$
$313$	−0.229213	−0.0129559	−0.00647796	+	0.999979i	$0.502062\pi$
$314$	−5.60024	−0.316040
$315$	−91.8545	−5.17542
$316$	0.992527	0.0558340
$317$	−19.6908	−1.10595	−0.552974	−	0.833199i	$-0.686507\pi$
$317$	−19.6908	−1.10595	−0.552974	+	0.833199i	$0.686507\pi$
$318$	−3.84384	−0.215552
$319$	0	0
$320$	2.34628	0.131161
$321$	−49.0509	−2.73776
$322$	12.3121	0.686125
$323$	3.77567	0.210084
$324$	33.6077	1.86710
$325$	0.796979	0.0442084
$326$	7.25396	0.401760
$327$	−9.78573	−0.541152
$328$	7.00747	0.386923
$329$	34.3733	1.89506
$330$	0	0
$331$	−16.9707	−0.932793	−0.466396	−	0.884576i	$-0.654448\pi$
$331$	−16.9707	−0.932793	−0.466396	+	0.884576i	$0.654448\pi$
$332$	−8.34628	−0.458062
$333$	−89.3343	−4.89549
$334$	2.85878	0.156426
$335$	24.4878	1.33791
$336$	−15.9807	−0.871821
$337$	−8.01236	−0.436461	−0.218230	−	0.975897i	$-0.570028\pi$
$337$	−8.01236	−0.436461	−0.218230	+	0.975897i	$0.570028\pi$
$338$	−10.5097	−0.571650
$339$	−3.37129	−0.183103
$340$	8.85878	0.480435
$341$	0	0
$342$	8.19759	0.443275
$343$	−42.0595	−2.27100
$344$	11.8487	0.638840
$345$	−20.2413	−1.08976
$346$	12.8663	0.691694
$347$	−27.7613	−1.49030	−0.745152	−	0.666895i	$-0.767623\pi$
$347$	−27.7613	−1.49030	−0.745152	+	0.666895i	$0.767623\pi$
$348$	−16.2338	−0.870225
$349$	−11.4886	−0.614971	−0.307486	−	0.951553i	$-0.599488\pi$
$349$	−11.4886	−0.614971	−0.307486	+	0.951553i	$0.599488\pi$
$350$	−2.41186	−0.128919
$351$	27.4469	1.46501
$352$	0	0
$353$	−26.2853	−1.39903	−0.699514	−	0.714619i	$-0.746600\pi$
$353$	−26.2853	−1.39903	−0.699514	+	0.714619i	$0.746600\pi$
$354$	16.4783	0.875811
$355$	−5.43143	−0.288271
$356$	−11.7000	−0.620101
$357$	−60.3380	−3.19343
$358$	−24.9290	−1.31754
$359$	18.0731	0.953859	0.476930	−	0.878942i	$-0.341750\pi$
$359$	18.0731	0.953859	0.476930	+	0.878942i	$0.341750\pi$
$360$	19.2338	1.01371
$361$	1.00000	0.0526316
$362$	−17.7952	−0.935297
$363$	0	0
$364$	−7.53640	−0.395015
$365$	−18.2439	−0.954930
$366$	−13.5488	−0.708205
$367$	33.9051	1.76983	0.884916	−	0.465751i	$-0.154216\pi$
$367$	33.9051	1.76983	0.884916	+	0.465751i	$0.154216\pi$
$368$	−2.57808	−0.134392
$369$	57.4444	2.99044
$370$	−25.5689	−1.32926
$371$	5.48576	0.284807
$372$	22.3952	1.16114
$373$	10.9342	0.566150	0.283075	−	0.959098i	$-0.408646\pi$
$373$	10.9342	0.566150	0.283075	+	0.959098i	$0.408646\pi$
$374$	0	0
$375$	−35.2914	−1.82244
$376$	−7.19759	−0.371187
$377$	−7.65576	−0.394292
$378$	−83.0613	−4.27221
$379$	−24.8395	−1.27592	−0.637960	−	0.770069i	$-0.720222\pi$
$379$	−24.8395	−1.27592	−0.637960	+	0.770069i	$0.720222\pi$
$380$	2.34628	0.120362
$381$	−3.81883	−0.195645
$382$	−4.47829	−0.229129
$383$	−2.82372	−0.144285	−0.0721426	−	0.997394i	$-0.522984\pi$
$383$	−2.82372	−0.144285	−0.0721426	+	0.997394i	$0.522984\pi$
$384$	3.34628	0.170764
$385$	0	0
$386$	8.00000	0.407189
$387$	97.1310	4.93744
$388$	−10.0000	−0.507673
$389$	−7.03884	−0.356883	−0.178442	−	0.983950i	$-0.557106\pi$
$389$	−7.03884	−0.356883	−0.178442	+	0.983950i	$0.557106\pi$
$390$	12.3900	0.627392
$391$	−9.73399	−0.492269
$392$	15.8070	0.798376
$393$	62.6006	3.15778
$394$	−12.5614	−0.632834
$395$	2.32875	0.117172
$396$	0	0
$397$	4.67761	0.234763	0.117381	−	0.993087i	$-0.462550\pi$
$397$	4.67761	0.234763	0.117381	+	0.993087i	$0.462550\pi$
$398$	−0.750666	−0.0376275
$399$	−15.9807	−0.800037
$400$	0.505030	0.0252515
$401$	14.5588	0.727033	0.363516	−	0.931588i	$-0.381576\pi$
$401$	14.5588	0.727033	0.363516	+	0.931588i	$0.381576\pi$
$402$	34.9247	1.74188
$403$	10.5614	0.526101
$404$	1.35634	0.0674805
$405$	78.8531	3.91824
$406$	23.1683	1.14982
$407$	0	0
$408$	12.6345	0.625499
$409$	−9.71757	−0.480503	−0.240251	−	0.970711i	$-0.577230\pi$
$409$	−9.71757	−0.480503	−0.240251	+	0.970711i	$0.577230\pi$
$410$	16.4415	0.811987
$411$	40.3998	1.99278
$412$	2.29997	0.113311
$413$	−23.5171	−1.15720
$414$	−21.1341	−1.03868
$415$	−19.5827	−0.961277
$416$	1.57808	0.0773718
$417$	−72.8830	−3.56910
$418$	0	0
$419$	6.13227	0.299581	0.149790	−	0.988718i	$-0.452140\pi$
$419$	6.13227	0.299581	0.149790	+	0.988718i	$0.452140\pi$
$420$	−37.4953	−1.82958
$421$	−3.79957	−0.185180	−0.0925898	−	0.995704i	$-0.529515\pi$
$421$	−3.79957	−0.185180	−0.0925898	+	0.995704i	$0.529515\pi$
$422$	4.66867	0.227267
$423$	−59.0029	−2.86882
$424$	−1.14869	−0.0557853
$425$	1.90683	0.0924948
$426$	−7.74635	−0.375312
$427$	19.3362	0.935745
$428$	−14.6583	−0.708538
$429$	0	0
$430$	27.8004	1.34066
$431$	8.69515	0.418831	0.209415	−	0.977827i	$-0.432844\pi$
$431$	8.69515	0.418831	0.209415	+	0.977827i	$0.432844\pi$
$432$	17.3926	0.836802
$433$	3.30744	0.158945	0.0794727	−	0.996837i	$-0.474676\pi$
$433$	3.30744	0.158945	0.0794727	+	0.996837i	$0.474676\pi$
$434$	−31.9615	−1.53420
$435$	−38.0891	−1.82623
$436$	−2.92436	−0.140052
$437$	−2.57808	−0.123326
$438$	−26.0196	−1.24326
$439$	4.54128	0.216744	0.108372	−	0.994110i	$-0.465436\pi$
$439$	4.54128	0.216744	0.108372	+	0.994110i	$0.465436\pi$
$440$	0	0
$441$	129.580	6.17046
$442$	5.95832	0.283408
$443$	17.8637	0.848728	0.424364	−	0.905492i	$-0.360498\pi$
$443$	17.8637	0.848728	0.424364	+	0.905492i	$0.360498\pi$
$444$	−36.4665	−1.73062
$445$	−27.4516	−1.30133
$446$	23.8663	1.13010
$447$	−21.3501	−1.00982
$448$	−4.77567	−0.225629
$449$	−21.8487	−1.03110	−0.515552	−	0.856858i	$-0.672413\pi$
$449$	−21.8487	−1.03110	−0.515552	+	0.856858i	$0.672413\pi$
$450$	4.14003	0.195163
$451$	0	0
$452$	−1.00747	−0.0473875
$453$	8.51250	0.399952
$454$	13.5097	0.634040
$455$	−17.6825	−0.828968
$456$	3.34628	0.156704
$457$	−5.73424	−0.268237	−0.134118	−	0.990965i	$-0.542820\pi$
$457$	−5.73424	−0.268237	−0.134118	+	0.990965i	$0.542820\pi$
$458$	−8.22896	−0.384514
$459$	65.6687	3.06515
$460$	−6.04890	−0.282031
$461$	12.5752	0.585687	0.292844	−	0.956160i	$-0.405398\pi$
$461$	12.5752	0.585687	0.292844	+	0.956160i	$0.405398\pi$
$462$	0	0
$463$	19.2853	0.896265	0.448133	−	0.893967i	$-0.352089\pi$
$463$	19.2853	0.896265	0.448133	+	0.893967i	$0.352089\pi$
$464$	−4.85131	−0.225216
$465$	52.5454	2.43673
$466$	−0.490085	−0.0227027
$467$	15.8004	0.731156	0.365578	−	0.930781i	$-0.380871\pi$
$467$	15.8004	0.731156	0.365578	+	0.930781i	$0.380871\pi$
$468$	12.9365	0.597988
$469$	−49.8430	−2.30154
$470$	−16.8876	−0.778965
$471$	−18.7400	−0.863493
$472$	4.92436	0.226662
$473$	0	0
$474$	3.32127	0.152551
$475$	0.505030	0.0231724
$476$	−18.0314	−0.826466
$477$	−9.41649	−0.431151
$478$	20.5364	0.939313
$479$	−17.0149	−0.777433	−0.388716	−	0.921357i	$-0.627081\pi$
$479$	−17.0149	−0.777433	−0.388716	+	0.921357i	$0.627081\pi$
$480$	7.85131	0.358362
$481$	−17.1973	−0.784131
$482$	−19.4654	−0.886624
$483$	41.1996	1.87465
$484$	0	0
$485$	−23.4628	−1.06539
$486$	60.2831	2.73449
$487$	12.8387	0.581775	0.290888	−	0.956757i	$-0.406049\pi$
$487$	12.8387	0.581775	0.290888	+	0.956757i	$0.406049\pi$
$488$	−4.04890	−0.183285
$489$	24.2738	1.09770
$490$	37.0877	1.67545
$491$	−21.1654	−0.955182	−0.477591	−	0.878582i	$-0.658490\pi$
$491$	−21.1654	−0.955182	−0.477591	+	0.878582i	$0.658490\pi$
$492$	23.4490	1.05716
$493$	−18.3170	−0.824954
$494$	1.57808	0.0710012
$495$	0	0
$496$	6.69256	0.300505
$497$	11.0553	0.495896
$498$	−27.9290	−1.25153
$499$	−5.35634	−0.239783	−0.119891	−	0.992787i	$-0.538255\pi$
$499$	−5.35634	−0.239783	−0.119891	+	0.992787i	$0.538255\pi$
$500$	−10.5465	−0.471652
$501$	9.56629	0.427390
$502$	−9.84872	−0.439570
$503$	−13.8634	−0.618139	−0.309070	−	0.951039i	$-0.600018\pi$
$503$	−13.8634	−0.618139	−0.309070	+	0.951039i	$0.600018\pi$
$504$	−39.1490	−1.74384
$505$	3.18235	0.141613
$506$	0	0
$507$	−35.1683	−1.56188
$508$	−1.14122	−0.0506333
$509$	28.9902	1.28497	0.642485	−	0.766298i	$-0.277903\pi$
$509$	28.9902	1.28497	0.642485	+	0.766298i	$0.277903\pi$
$510$	29.6440	1.31266
$511$	37.1341	1.64271
$512$	1.00000	0.0441942
$513$	17.3926	0.767902
$514$	11.2540	0.496391
$515$	5.39637	0.237792
$516$	39.6491	1.74546
$517$	0	0
$518$	52.0435	2.28666
$519$	43.0541	1.88987
$520$	3.70262	0.162371
$521$	24.3417	1.06643	0.533215	−	0.845980i	$-0.320984\pi$
$521$	24.3417	1.06643	0.533215	+	0.845980i	$0.320984\pi$
$522$	−39.7691	−1.74064
$523$	37.2347	1.62816	0.814080	−	0.580753i	$-0.197242\pi$
$523$	37.2347	1.62816	0.814080	+	0.580753i	$0.197242\pi$
$524$	18.7075	0.817241
$525$	−8.07075	−0.352237
$526$	3.49008	0.152175
$527$	25.2689	1.10073
$528$	0	0
$529$	−16.3535	−0.711022
$530$	−2.69515	−0.117070
$531$	40.3679	1.75182
$532$	−4.77567	−0.207052
$533$	11.0584	0.478991
$534$	−39.1516	−1.69425
$535$	−34.3926	−1.48692
$536$	10.4369	0.450804
$537$	−83.4194	−3.59981
$538$	−20.1737	−0.869750
$539$	0	0
$540$	40.8079	1.75609
$541$	−4.31750	−0.185624	−0.0928119	−	0.995684i	$-0.529586\pi$
$541$	−4.31750	−0.185624	−0.0928119	+	0.995684i	$0.529586\pi$
$542$	0.239274	0.0102777
$543$	−59.5479	−2.55544
$544$	3.77567	0.161881
$545$	−6.86137	−0.293909
$546$	−25.2189	−1.07927
$547$	−25.0104	−1.06937	−0.534683	−	0.845053i	$-0.679569\pi$
$547$	−25.0104	−1.06937	−0.534683	+	0.845053i	$0.679569\pi$
$548$	12.0731	0.515735
$549$	−33.1912	−1.41657
$550$	0	0
$551$	−4.85131	−0.206673
$552$	−8.62698	−0.367189
$553$	−4.73998	−0.201565
$554$	−13.1901	−0.560394
$555$	−85.5606	−3.63185
$556$	−21.7803	−0.923691
$557$	−31.3667	−1.32905	−0.664525	−	0.747266i	$-0.731366\pi$
$557$	−31.3667	−1.32905	−0.664525	+	0.747266i	$0.731366\pi$
$558$	54.8629	2.32253
$559$	18.6982	0.790852
$560$	−11.2051	−0.473500
$561$	0	0
$562$	6.54387	0.276037
$563$	11.4924	0.484346	0.242173	−	0.970233i	$-0.422140\pi$
$563$	11.4924	0.484346	0.242173	+	0.970233i	$0.422140\pi$
$564$	−24.0852	−1.01417
$565$	−2.36381	−0.0994464
$566$	9.08774	0.381986
$567$	−160.499	−6.74034
$568$	−2.31491	−0.0971316
$569$	−18.5614	−0.778135	−0.389067	−	0.921209i	$-0.627203\pi$
$569$	−18.5614	−0.778135	−0.389067	+	0.921209i	$0.627203\pi$
$570$	7.85131	0.328855
$571$	−36.2099	−1.51534	−0.757670	−	0.652638i	$-0.773662\pi$
$571$	−36.2099	−1.51534	−0.757670	+	0.652638i	$0.773662\pi$
$572$	0	0
$573$	−14.9856	−0.626033
$574$	−33.4654	−1.39682
$575$	−1.30201	−0.0542975
$576$	8.19759	0.341566
$577$	29.5560	1.23043	0.615216	−	0.788359i	$-0.289069\pi$
$577$	29.5560	1.23043	0.615216	+	0.788359i	$0.289069\pi$
$578$	−2.74430	−0.114148
$579$	26.7702	1.11253
$580$	−11.3825	−0.472634
$581$	39.8591	1.65363
$582$	−33.4628	−1.38708
$583$	0	0
$584$	−7.77567	−0.321760
$585$	30.3526	1.25492
$586$	20.2051	0.834663
$587$	−33.4340	−1.37997	−0.689985	−	0.723824i	$-0.742383\pi$
$587$	−33.4340	−1.37997	−0.689985	+	0.723824i	$0.742383\pi$
$588$	52.8948	2.18134
$589$	6.69256	0.275762
$590$	11.5539	0.475668
$591$	−42.0340	−1.72905
$592$	−10.8976	−0.447890
$593$	15.2753	0.627280	0.313640	−	0.949542i	$-0.398451\pi$
$593$	15.2753	0.627280	0.313640	+	0.949542i	$0.398451\pi$
$594$	0	0
$595$	−42.3066	−1.73440
$596$	−6.38024	−0.261345
$597$	−2.51194	−0.102807
$598$	−4.06842	−0.166370
$599$	13.3316	0.544716	0.272358	−	0.962196i	$-0.412196\pi$
$599$	13.3316	0.544716	0.272358	+	0.962196i	$0.412196\pi$
$600$	1.68997	0.0689928
$601$	48.4729	1.97725	0.988625	−	0.150404i	$-0.0480574\pi$
$601$	48.4729	1.97725	0.988625	+	0.150404i	$0.0480574\pi$
$602$	−56.5856	−2.30626
$603$	85.5571	3.48416
$604$	2.54387	0.103509
$605$	0	0
$606$	4.53870	0.184372
$607$	43.4176	1.76227	0.881133	−	0.472869i	$-0.156781\pi$
$607$	43.4176	1.76227	0.881133	+	0.472869i	$0.156781\pi$
$608$	1.00000	0.0405554
$609$	77.5275	3.14157
$610$	−9.49985	−0.384638
$611$	−11.3584	−0.459511
$612$	30.9514	1.25114
$613$	−44.8876	−1.81299	−0.906496	−	0.422215i	$-0.861253\pi$
$613$	−44.8876	−1.81299	−0.906496	+	0.422215i	$0.861253\pi$
$614$	−20.2514	−0.817279
$615$	55.0178	2.21853
$616$	0	0
$617$	−17.2275	−0.693552	−0.346776	−	0.937948i	$-0.612724\pi$
$617$	−17.2275	−0.693552	−0.346776	+	0.937948i	$0.612724\pi$
$618$	7.69633	0.309592
$619$	17.8004	0.715459	0.357730	−	0.933825i	$-0.383551\pi$
$619$	17.8004	0.715459	0.357730	+	0.933825i	$0.383551\pi$
$620$	15.7026	0.630632
$621$	−44.8395	−1.79935
$622$	29.3897	1.17842
$623$	55.8755	2.23861
$624$	5.28070	0.211397
$625$	−27.2701	−1.09080
$626$	−0.229213	−0.00916121
$627$	0	0
$628$	−5.60024	−0.223474
$629$	−41.1458	−1.64059
$630$	−91.8545	−3.65957
$631$	14.4202	0.574059	0.287029	−	0.957922i	$-0.407332\pi$
$631$	14.4202	0.574059	0.287029	+	0.957922i	$0.407332\pi$
$632$	0.992527	0.0394806
$633$	15.6227	0.620945
$634$	−19.6908	−0.782023
$635$	−2.67761	−0.106258
$636$	−3.84384	−0.152418
$637$	24.9448	0.988349
$638$	0	0
$639$	−18.9767	−0.750707
$640$	2.34628	0.0927449
$641$	−29.1386	−1.15091	−0.575453	−	0.817835i	$-0.695174\pi$
$641$	−29.1386	−1.15091	−0.575453	+	0.817835i	$0.695174\pi$
$642$	−49.0509	−1.93589
$643$	37.4979	1.47877	0.739386	−	0.673282i	$-0.235116\pi$
$643$	37.4979	1.47877	0.739386	+	0.673282i	$0.235116\pi$
$644$	12.3121	0.485163
$645$	93.0280	3.66297
$646$	3.77567	0.148552
$647$	40.4294	1.58945	0.794723	−	0.606973i	$-0.207616\pi$
$647$	40.4294	1.58945	0.794723	+	0.606973i	$0.207616\pi$
$648$	33.6077	1.32024
$649$	0	0
$650$	0.796979	0.0312601
$651$	−106.952	−4.19178
$652$	7.25396	0.284087
$653$	33.8102	1.32310	0.661548	−	0.749903i	$-0.269900\pi$
$653$	33.8102	1.32310	0.661548	+	0.749903i	$0.269900\pi$
$654$	−9.78573	−0.382652
$655$	43.8930	1.71504
$656$	7.00747	0.273596
$657$	−63.7418	−2.48680
$658$	34.3733	1.34001
$659$	−25.2586	−0.983935	−0.491968	−	0.870614i	$-0.663722\pi$
$659$	−25.2586	−0.983935	−0.491968	+	0.870614i	$0.663722\pi$
$660$	0	0
$661$	−3.42965	−0.133398	−0.0666989	−	0.997773i	$-0.521247\pi$
$661$	−3.42965	−0.133398	−0.0666989	+	0.997773i	$0.521247\pi$
$662$	−16.9707	−0.659584
$663$	19.9382	0.774335
$664$	−8.34628	−0.323898
$665$	−11.2051	−0.434514
$666$	−89.3343	−3.46163
$667$	12.5071	0.484276
$668$	2.85878	0.110610
$669$	79.8632	3.08769
$670$	24.4878	0.946047
$671$	0	0
$672$	−15.9807	−0.616470
$673$	21.4855	0.828206	0.414103	−	0.910230i	$-0.364095\pi$
$673$	21.4855	0.828206	0.414103	+	0.910230i	$0.364095\pi$
$674$	−8.01236	−0.308624
$675$	8.78378	0.338088
$676$	−10.5097	−0.404218
$677$	33.2825	1.27915	0.639575	−	0.768729i	$-0.279110\pi$
$677$	33.2825	1.27915	0.639575	+	0.768729i	$0.279110\pi$
$678$	−3.37129	−0.129473
$679$	47.7567	1.83273
$680$	8.85878	0.339719
$681$	45.2071	1.73234
$682$	0	0
$683$	−29.1176	−1.11416	−0.557078	−	0.830460i	$-0.688077\pi$
$683$	−29.1176	−1.11416	−0.557078	+	0.830460i	$0.688077\pi$
$684$	8.19759	0.313443
$685$	28.3268	1.08231
$686$	−42.0595	−1.60584
$687$	−27.5364	−1.05058
$688$	11.8487	0.451728
$689$	−1.81273	−0.0690593
$690$	−20.2413	−0.770574
$691$	−43.2143	−1.64395	−0.821975	−	0.569523i	$-0.807128\pi$
$691$	−43.2143	−1.64395	−0.821975	+	0.569523i	$0.807128\pi$
$692$	12.8663	0.489102
$693$	0	0
$694$	−27.7613	−1.05380
$695$	−51.1027	−1.93844
$696$	−16.2338	−0.615342
$697$	26.4579	1.00217
$698$	−11.4886	−0.434850
$699$	−1.63996	−0.0620290
$700$	−2.41186	−0.0911597
$701$	30.8680	1.16587	0.582935	−	0.812519i	$-0.301904\pi$
$701$	30.8680	1.16587	0.582935	+	0.812519i	$0.301904\pi$
$702$	27.4469	1.03592
$703$	−10.8976	−0.411012
$704$	0	0
$705$	−56.5105	−2.12831
$706$	−26.2853	−0.989261
$707$	−6.47744	−0.243609
$708$	16.4783	0.619292
$709$	8.14610	0.305933	0.152967	−	0.988231i	$-0.451117\pi$
$709$	8.14610	0.305933	0.152967	+	0.988231i	$0.451117\pi$
$710$	−5.43143	−0.203838
$711$	8.13633	0.305136
$712$	−11.7000	−0.438477
$713$	−17.2540	−0.646166
$714$	−60.3380	−2.25809
$715$	0	0
$716$	−24.9290	−0.931640
$717$	68.7205	2.56642
$718$	18.0731	0.674480
$719$	43.5545	1.62431	0.812154	−	0.583443i	$-0.198295\pi$
$719$	43.5545	1.62431	0.812154	+	0.583443i	$0.198295\pi$
$720$	19.2338	0.716803
$721$	−10.9839	−0.409061
$722$	1.00000	0.0372161
$723$	−65.1366	−2.42246
$724$	−17.7952	−0.661355
$725$	−2.45006	−0.0909929
$726$	0	0
$727$	−35.4415	−1.31445	−0.657226	−	0.753693i	$-0.728270\pi$
$727$	−35.4415	−1.31445	−0.657226	+	0.753693i	$0.728270\pi$
$728$	−7.53640	−0.279317
$729$	100.901	3.73707
$730$	−18.2439	−0.675237
$731$	44.7369	1.65465
$732$	−13.5488	−0.500776
$733$	−4.60970	−0.170263	−0.0851317	−	0.996370i	$-0.527131\pi$
$733$	−4.60970	−0.170263	−0.0851317	+	0.996370i	$0.527131\pi$
$734$	33.9051	1.25146
$735$	124.106	4.57772
$736$	−2.57808	−0.0950293
$737$	0	0
$738$	57.4444	2.11456
$739$	19.1423	0.704162	0.352081	−	0.935970i	$-0.385474\pi$
$739$	19.1423	0.704162	0.352081	+	0.935970i	$0.385474\pi$
$740$	−25.5689	−0.939931
$741$	5.28070	0.193991
$742$	5.48576	0.201389
$743$	−41.0970	−1.50770	−0.753851	−	0.657045i	$-0.771806\pi$
$743$	−41.0970	−1.50770	−0.753851	+	0.657045i	$0.771806\pi$
$744$	22.3952	0.821047
$745$	−14.9698	−0.548452
$746$	10.9342	0.400328
$747$	−68.4194	−2.50333
$748$	0	0
$749$	70.0035	2.55787
$750$	−35.2914	−1.28866
$751$	−38.8882	−1.41905	−0.709525	−	0.704681i	$-0.751090\pi$
$751$	−38.8882	−1.41905	−0.709525	+	0.704681i	$0.751090\pi$
$752$	−7.19759	−0.262469
$753$	−32.9566	−1.20100
$754$	−7.65576	−0.278806
$755$	5.96863	0.217221
$756$	−83.0613	−3.02091
$757$	25.2051	0.916094	0.458047	−	0.888928i	$-0.348549\pi$
$757$	25.2051	0.916094	0.458047	+	0.888928i	$0.348549\pi$
$758$	−24.8395	−0.902212
$759$	0	0
$760$	2.34628	0.0851085
$761$	17.9247	0.649769	0.324884	−	0.945754i	$-0.394675\pi$
$761$	17.9247	0.649769	0.324884	+	0.945754i	$0.394675\pi$
$762$	−3.81883	−0.138342
$763$	13.9658	0.505596
$764$	−4.47829	−0.162019
$765$	72.6207	2.62561
$766$	−2.82372	−0.102025
$767$	7.77104	0.280596
$768$	3.34628	0.120748
$769$	−17.4101	−0.627825	−0.313913	−	0.949452i	$-0.601640\pi$
$769$	−17.4101	−0.627825	−0.313913	+	0.949452i	$0.601640\pi$
$770$	0	0
$771$	37.6589	1.35625
$772$	8.00000	0.287926
$773$	42.5071	1.52887	0.764437	−	0.644699i	$-0.223017\pi$
$773$	42.5071	1.52887	0.764437	+	0.644699i	$0.223017\pi$
$774$	97.1310	3.49130
$775$	3.37994	0.121411
$776$	−10.0000	−0.358979
$777$	174.152	6.24767
$778$	−7.03884	−0.252355
$779$	7.00747	0.251069
$780$	12.3900	0.443633
$781$	0	0
$782$	−9.73399	−0.348087
$783$	−84.3769	−3.01538
$784$	15.8070	0.564537
$785$	−13.1397	−0.468977
$786$	62.6006	2.23289
$787$	0.289907	0.0103341	0.00516703	−	0.999987i	$-0.498355\pi$
$787$	0.289907	0.0103341	0.00516703	+	0.999987i	$0.498355\pi$
$788$	−12.5614	−0.447481
$789$	11.6788	0.415776
$790$	2.32875	0.0828531
$791$	4.81136	0.171072
$792$	0	0
$793$	−6.38949	−0.226898
$794$	4.67761	0.166002
$795$	−9.01872	−0.319861
$796$	−0.750666	−0.0266066
$797$	20.2557	0.717494	0.358747	−	0.933435i	$-0.383204\pi$
$797$	20.2557	0.717494	0.358747	+	0.933435i	$0.383204\pi$
$798$	−15.9807	−0.565712
$799$	−27.1757	−0.961408
$800$	0.505030	0.0178555
$801$	−95.9121	−3.38889
$802$	14.5588	0.514090
$803$	0	0
$804$	34.9247	1.23170
$805$	28.8876	1.01815
$806$	10.5614	0.372010
$807$	−67.5068	−2.37635
$808$	1.35634	0.0477159
$809$	11.8902	0.418035	0.209018	−	0.977912i	$-0.432973\pi$
$809$	11.8902	0.418035	0.209018	+	0.977912i	$0.432973\pi$
$810$	78.8531	2.77062
$811$	−37.3725	−1.31232	−0.656162	−	0.754620i	$-0.727821\pi$
$811$	−37.3725	−1.31232	−0.656162	+	0.754620i	$0.727821\pi$
$812$	23.1683	0.813047
$813$	0.800677	0.0280810
$814$	0	0
$815$	17.0198	0.596179
$816$	12.6345	0.442294
$817$	11.8487	0.414534
$818$	−9.71757	−0.339767
$819$	−61.7803	−2.15878
$820$	16.4415	0.574162
$821$	15.7165	0.548508	0.274254	−	0.961657i	$-0.411569\pi$
$821$	15.7165	0.548508	0.274254	+	0.961657i	$0.411569\pi$
$822$	40.3998	1.40911
$823$	41.3066	1.43986	0.719929	−	0.694047i	$-0.244174\pi$
$823$	41.3066	1.43986	0.719929	+	0.694047i	$0.244174\pi$
$824$	2.29997	0.0801232
$825$	0	0
$826$	−23.5171	−0.818266
$827$	15.7406	0.547354	0.273677	−	0.961822i	$-0.411760\pi$
$827$	15.7406	0.547354	0.273677	+	0.961822i	$0.411760\pi$
$828$	−21.1341	−0.734459
$829$	−0.255696	−0.00888069	−0.00444034	−	0.999990i	$-0.501413\pi$
$829$	−0.255696	−0.00888069	−0.00444034	+	0.999990i	$0.501413\pi$
$830$	−19.5827	−0.679726
$831$	−44.1378	−1.53112
$832$	1.57808	0.0547101
$833$	59.6822	2.06787
$834$	−72.8830	−2.52373
$835$	6.70751	0.232123
$836$	0	0
$837$	116.401	4.02341
$838$	6.13227	0.211836
$839$	−14.2764	−0.492875	−0.246438	−	0.969159i	$-0.579260\pi$
$839$	−14.2764	−0.492875	−0.246438	+	0.969159i	$0.579260\pi$
$840$	−37.4953	−1.29371
$841$	−5.46479	−0.188441
$842$	−3.79957	−0.130942
$843$	21.8976	0.754194
$844$	4.66867	0.160702
$845$	−24.6586	−0.848282
$846$	−59.0029	−2.02856
$847$	0	0
$848$	−1.14869	−0.0394462
$849$	30.4101	1.04367
$850$	1.90683	0.0654037
$851$	28.0950	0.963083
$852$	−7.74635	−0.265385
$853$	−31.1027	−1.06494	−0.532468	−	0.846450i	$-0.678735\pi$
$853$	−31.1027	−1.06494	−0.532468	+	0.846450i	$0.678735\pi$
$854$	19.3362	0.661672
$855$	19.2338	0.657784
$856$	−14.6583	−0.501012
$857$	16.9715	0.579736	0.289868	−	0.957067i	$-0.406389\pi$
$857$	16.9715	0.579736	0.289868	+	0.957067i	$0.406389\pi$
$858$	0	0
$859$	39.5169	1.34830	0.674149	−	0.738595i	$-0.264510\pi$
$859$	39.5169	1.34830	0.674149	+	0.738595i	$0.264510\pi$
$860$	27.8004	0.947987
$861$	−111.985	−3.81642
$862$	8.69515	0.296158
$863$	55.4294	1.88684	0.943420	−	0.331600i	$-0.107588\pi$
$863$	55.4294	1.88684	0.943420	+	0.331600i	$0.107588\pi$
$864$	17.3926	0.591708
$865$	30.1878	1.02642
$866$	3.30744	0.112391
$867$	−9.18321	−0.311878
$868$	−31.9615	−1.08484
$869$	0	0
$870$	−38.0891	−1.29134
$871$	16.4702	0.558072
$872$	−2.92436	−0.0990314
$873$	−81.9759	−2.77446
$874$	−2.57808	−0.0872049
$875$	50.3664	1.70270
$876$	−26.0196	−0.879120
$877$	−23.3069	−0.787018	−0.393509	−	0.919321i	$-0.628739\pi$
$877$	−23.3069	−0.787018	−0.393509	+	0.919321i	$0.628739\pi$
$878$	4.54128	0.153261
$879$	67.6118	2.28049
$880$	0	0
$881$	53.8830	1.81536	0.907682	−	0.419659i	$-0.137850\pi$
$881$	53.8830	1.81536	0.907682	+	0.419659i	$0.137850\pi$
$882$	129.580	4.36317
$883$	46.0638	1.55017	0.775086	−	0.631856i	$-0.217707\pi$
$883$	46.0638	1.55017	0.775086	+	0.631856i	$0.217707\pi$
$884$	5.95832	0.200400
$885$	38.6627	1.29963
$886$	17.8637	0.600142
$887$	14.9246	0.501120	0.250560	−	0.968101i	$-0.419385\pi$
$887$	14.9246	0.501120	0.250560	+	0.968101i	$0.419385\pi$
$888$	−36.4665	−1.22374
$889$	5.45008	0.182790
$890$	−27.4516	−0.920178
$891$	0	0
$892$	23.8663	0.799101
$893$	−7.19759	−0.240858
$894$	−21.3501	−0.714053
$895$	−58.4904	−1.95512
$896$	−4.77567	−0.159544
$897$	−13.6141	−0.454561
$898$	−21.8487	−0.729101
$899$	−32.4677	−1.08286
$900$	4.14003	0.138001
$901$	−4.33708	−0.144489
$902$	0	0
$903$	−189.351	−6.30122
$904$	−1.00747	−0.0335080
$905$	−41.7526	−1.38790
$906$	8.51250	0.282809
$907$	−14.6419	−0.486177	−0.243089	−	0.970004i	$-0.578161\pi$
$907$	−14.6419	−0.486177	−0.243089	+	0.970004i	$0.578161\pi$
$908$	13.5097	0.448334
$909$	11.1187	0.368785
$910$	−17.6825	−0.586169
$911$	−5.41760	−0.179493	−0.0897465	−	0.995965i	$-0.528606\pi$
$911$	−5.41760	−0.179493	−0.0897465	+	0.995965i	$0.528606\pi$
$912$	3.34628	0.110806
$913$	0	0
$914$	−5.73424	−0.189672
$915$	−31.7892	−1.05092
$916$	−8.22896	−0.271892
$917$	−89.3409	−2.95030
$918$	65.6687	2.16739
$919$	33.1536	1.09364	0.546819	−	0.837251i	$-0.315839\pi$
$919$	33.1536	1.09364	0.546819	+	0.837251i	$0.315839\pi$
$920$	−6.04890	−0.199426
$921$	−67.7668	−2.23299
$922$	12.5752	0.414143
$923$	−3.65312	−0.120244
$924$	0	0
$925$	−5.50363	−0.180958
$926$	19.2853	0.633755
$927$	18.8542	0.619253
$928$	−4.85131	−0.159252
$929$	−0.322385	−0.0105771	−0.00528856	−	0.999986i	$-0.501683\pi$
$929$	−0.322385	−0.0105771	−0.00528856	+	0.999986i	$0.501683\pi$
$930$	52.5454	1.72303
$931$	15.8070	0.518055
$932$	−0.490085	−0.0160533
$933$	98.3463	3.21971
$934$	15.8004	0.517006
$935$	0	0
$936$	12.9365	0.422842
$937$	−2.64545	−0.0864229	−0.0432115	−	0.999066i	$-0.513759\pi$
$937$	−2.64545	−0.0864229	−0.0432115	+	0.999066i	$0.513759\pi$
$938$	−49.8430	−1.62743
$939$	−0.767013	−0.0250305
$940$	−16.8876	−0.550812
$941$	−11.1772	−0.364367	−0.182183	−	0.983265i	$-0.558316\pi$
$941$	−11.1772	−0.364367	−0.182183	+	0.983265i	$0.558316\pi$
$942$	−18.7400	−0.610582
$943$	−18.0658	−0.588304
$944$	4.92436	0.160274
$945$	−194.885	−6.33961
$946$	0	0
$947$	11.6693	0.379200	0.189600	−	0.981861i	$-0.439281\pi$
$947$	11.6693	0.379200	0.189600	+	0.981861i	$0.439281\pi$
$948$	3.32127	0.107870
$949$	−12.2706	−0.398322
$950$	0.505030	0.0163853
$951$	−65.8910	−2.13666
$952$	−18.0314	−0.584400
$953$	42.6900	1.38286	0.691432	−	0.722442i	$-0.256980\pi$
$953$	42.6900	1.38286	0.691432	+	0.722442i	$0.256980\pi$
$954$	−9.41649	−0.304870
$955$	−10.5073	−0.340009
$956$	20.5364	0.664195
$957$	0	0
$958$	−17.0149	−0.549728
$959$	−57.6569	−1.86184
$960$	7.85131	0.253400
$961$	13.7904	0.444850
$962$	−17.1973	−0.554464
$963$	−120.163	−3.87220
$964$	−19.4654	−0.626938
$965$	18.7702	0.604235
$966$	41.1996	1.32558
$967$	−15.6705	−0.503928	−0.251964	−	0.967737i	$-0.581076\pi$
$967$	−15.6705	−0.503928	−0.251964	+	0.967737i	$0.581076\pi$
$968$	0	0
$969$	12.6345	0.405877
$970$	−23.4628	−0.753345
$971$	−36.0369	−1.15648	−0.578239	−	0.815868i	$-0.696260\pi$
$971$	−36.0369	−1.15648	−0.578239	+	0.815868i	$0.696260\pi$
$972$	60.2831	1.93358
$973$	104.016	3.33459
$974$	12.8387	0.411377
$975$	2.66691	0.0854096
$976$	−4.04890	−0.129602
$977$	−6.06273	−0.193964	−0.0969820	−	0.995286i	$-0.530919\pi$
$977$	−6.06273	−0.193964	−0.0969820	+	0.995286i	$0.530919\pi$
$978$	24.2738	0.776190
$979$	0	0
$980$	37.0877	1.18472
$981$	−23.9727	−0.765390
$982$	−21.1654	−0.675416
$983$	−8.49608	−0.270983	−0.135491	−	0.990779i	$-0.543261\pi$
$983$	−8.49608	−0.270983	−0.135491	+	0.990779i	$0.543261\pi$
$984$	23.4490	0.747526
$985$	−29.4726	−0.939074
$986$	−18.3170	−0.583331
$987$	115.023	3.66122
$988$	1.57808	0.0502055
$989$	−30.5470	−0.971337
$990$	0	0
$991$	−25.2663	−0.802611	−0.401306	−	0.915944i	$-0.631443\pi$
$991$	−25.2663	−0.802611	−0.401306	+	0.915944i	$0.631443\pi$
$992$	6.69256	0.212489
$993$	−56.7886	−1.80213
$994$	11.0553	0.350652
$995$	−1.76127	−0.0558361
$996$	−27.9290	−0.884964
$997$	−45.5853	−1.44370	−0.721850	−	0.692049i	$-0.756708\pi$
$997$	−45.5853	−1.44370	−0.721850	+	0.692049i	$0.756708\pi$
$998$	−5.35634	−0.169552
$999$	−189.538	−5.99671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bv.1.4	yes	4
11.10	odd	2		4598.2.a.bs.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bs.1.4	✓	4	11.10	odd	2
4598.2.a.bv.1.4	yes	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} +3.34628 q^{6} -4.77567 q^{7} +1.00000 q^{8} +8.19759 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} +3.34628 q^{6} -4.77567 q^{7} +1.00000 q^{8} +8.19759 q^{9} +2.34628 q^{10} +3.34628 q^{12} +1.57808 q^{13} -4.77567 q^{14} +7.85131 q^{15} +1.00000 q^{16} +3.77567 q^{17} +8.19759 q^{18} +1.00000 q^{19} +2.34628 q^{20} -15.9807 q^{21} -2.57808 q^{23} +3.34628 q^{24} +0.505030 q^{25} +1.57808 q^{26} +17.3926 q^{27} -4.77567 q^{28} -4.85131 q^{29} +7.85131 q^{30} +6.69256 q^{31} +1.00000 q^{32} +3.77567 q^{34} -11.2051 q^{35} +8.19759 q^{36} -10.8976 q^{37} +1.00000 q^{38} +5.28070 q^{39} +2.34628 q^{40} +7.00747 q^{41} -15.9807 q^{42} +11.8487 q^{43} +19.2338 q^{45} -2.57808 q^{46} -7.19759 q^{47} +3.34628 q^{48} +15.8070 q^{49} +0.505030 q^{50} +12.6345 q^{51} +1.57808 q^{52} -1.14869 q^{53} +17.3926 q^{54} -4.77567 q^{56} +3.34628 q^{57} -4.85131 q^{58} +4.92436 q^{59} +7.85131 q^{60} -4.04890 q^{61} +6.69256 q^{62} -39.1490 q^{63} +1.00000 q^{64} +3.70262 q^{65} +10.4369 q^{67} +3.77567 q^{68} -8.62698 q^{69} -11.2051 q^{70} -2.31491 q^{71} +8.19759 q^{72} -7.77567 q^{73} -10.8976 q^{74} +1.68997 q^{75} +1.00000 q^{76} +5.28070 q^{78} +0.992527 q^{79} +2.34628 q^{80} +33.6077 q^{81} +7.00747 q^{82} -8.34628 q^{83} -15.9807 q^{84} +8.85878 q^{85} +11.8487 q^{86} -16.2338 q^{87} -11.7000 q^{89} +19.2338 q^{90} -7.53640 q^{91} -2.57808 q^{92} +22.3952 q^{93} -7.19759 q^{94} +2.34628 q^{95} +3.34628 q^{96} -10.0000 q^{97} +15.8070 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9 - 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 + 26 * q^15 + 4 * q^16 - 7 * q^17 + 16 * q^18 + 4 * q^19 - 2 * q^20 - 9 * q^21 - 5 * q^23 + 2 * q^24 + 8 * q^25 + q^26 + 8 * q^27 + 3 * q^28 - 14 * q^29 + 26 * q^30 + 4 * q^31 + 4 * q^32 - 7 * q^34 - 12 * q^35 + 16 * q^36 + 12 * q^37 + 4 * q^38 + 5 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 14 * q^43 - 2 * q^45 - 5 * q^46 - 12 * q^47 + 2 * q^48 + 23 * q^49 + 8 * q^50 + 7 * q^51 + q^52 - 10 * q^53 + 8 * q^54 + 3 * q^56 + 2 * q^57 - 14 * q^58 + 3 * q^59 + 26 * q^60 + 6 * q^61 + 4 * q^62 - 18 * q^63 + 4 * q^64 + 4 * q^65 + 15 * q^67 - 7 * q^68 - 7 * q^69 - 12 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 - 44 * q^75 + 4 * q^76 + 5 * q^78 + 20 * q^79 - 2 * q^80 + 52 * q^81 + 12 * q^82 - 22 * q^83 - 9 * q^84 + 14 * q^85 + 14 * q^86 + 14 * q^87 - 8 * q^89 - 2 * q^90 - 18 * q^91 - 5 * q^92 + 56 * q^93 - 12 * q^94 - 2 * q^95 + 2 * q^96 - 40 * q^97 + 23 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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