LMFDB - Embedded newform 4598.2.a.bq.1.2

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:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.43091$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +2.43091 q^{10} -0.698857 q^{12} -2.86182 q^{13} -1.00000 q^{14} +1.69886 q^{15} +1.00000 q^{16} -1.90931 q^{17} +2.51160 q^{18} -1.00000 q^{19} -2.43091 q^{20} -0.698857 q^{21} +6.50318 q^{23} +0.698857 q^{24} +0.909313 q^{25} +2.86182 q^{26} +3.85182 q^{27} +1.00000 q^{28} +7.02477 q^{29} -1.69886 q^{30} +5.43679 q^{31} -1.00000 q^{32} +1.90931 q^{34} -2.43091 q^{35} -2.51160 q^{36} +0.383411 q^{37} +1.00000 q^{38} +2.00000 q^{39} +2.43091 q^{40} +7.29703 q^{41} +0.698857 q^{42} -5.17726 q^{43} +6.10547 q^{45} -6.50318 q^{46} +4.08658 q^{47} -0.698857 q^{48} -6.00000 q^{49} -0.909313 q^{50} +1.33434 q^{51} -2.86182 q^{52} -0.348640 q^{53} -3.85182 q^{54} -1.00000 q^{56} +0.698857 q^{57} -7.02477 q^{58} -1.62706 q^{59} +1.69886 q^{60} +15.1777 q^{61} -5.43679 q^{62} -2.51160 q^{63} +1.00000 q^{64} +6.95681 q^{65} -7.75224 q^{67} -1.90931 q^{68} -4.54479 q^{69} +2.43091 q^{70} -13.9384 q^{71} +2.51160 q^{72} +8.33022 q^{73} -0.383411 q^{74} -0.635480 q^{75} -1.00000 q^{76} -2.00000 q^{78} -2.46253 q^{79} -2.43091 q^{80} +4.84293 q^{81} -7.29703 q^{82} -3.11135 q^{83} -0.698857 q^{84} +4.64136 q^{85} +5.17726 q^{86} -4.90931 q^{87} -3.03750 q^{89} -6.10547 q^{90} -2.86182 q^{91} +6.50318 q^{92} -3.79954 q^{93} -4.08658 q^{94} +2.43091 q^{95} +0.698857 q^{96} -12.8059 q^{97} +6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} - 2 q^{12} + 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 8 q^{23} + 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{30} - 4 q^{32} - 4 q^{34} - 2 q^{35} - 10 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 8 q^{45} + 8 q^{46} - 2 q^{48} - 24 q^{49} + 8 q^{50} + 4 q^{52} - 6 q^{53} + 14 q^{54} - 4 q^{56} + 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} + 2 q^{61} + 4 q^{64} + 20 q^{65} - 20 q^{67} + 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} + 10 q^{74} + 2 q^{75} - 4 q^{76} - 8 q^{78} - 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} + 34 q^{83} - 2 q^{84} + 16 q^{86} - 8 q^{87} - 2 q^{89} + 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} + 2 q^{95} + 2 q^{96} - 8 q^{97} + 24 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 - 2 * q^12 + 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 2 * q^21 - 8 * q^23 + 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 + 4 * q^28 - 2 * q^29 - 6 * q^30 - 4 * q^32 - 4 * q^34 - 2 * q^35 - 10 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^42 - 16 * q^43 - 8 * q^45 + 8 * q^46 - 2 * q^48 - 24 * q^49 + 8 * q^50 + 4 * q^52 - 6 * q^53 + 14 * q^54 - 4 * q^56 + 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 + 2 * q^61 + 4 * q^64 + 20 * q^65 - 20 * q^67 + 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 + 10 * q^74 + 2 * q^75 - 4 * q^76 - 8 * q^78 - 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 + 34 * q^83 - 2 * q^84 + 16 * q^86 - 8 * q^87 - 2 * q^89 + 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 + 2 * q^95 + 2 * q^96 - 8 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.698857	−0.403485	−0.201743	−	0.979439i	$-0.564660\pi$
$3$	−0.698857	−0.403485	−0.201743	+	0.979439i	$0.564660\pi$
$4$	1.00000	0.500000
$5$	−2.43091	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$5$	−2.43091	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$6$	0.698857	0.285307
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	−2.51160	−0.837200
$10$	2.43091	0.768721
$11$	0	0
$11$	0	0
$12$	−0.698857	−0.201743
$13$	−2.86182	−0.793725	−0.396862	−	0.917878i	$-0.629901\pi$
$13$	−2.86182	−0.793725	−0.396862	+	0.917878i	$0.629901\pi$
$14$	−1.00000	−0.267261
$15$	1.69886	0.438643
$16$	1.00000	0.250000
$17$	−1.90931	−0.463076	−0.231538	−	0.972826i	$-0.574376\pi$
$17$	−1.90931	−0.463076	−0.231538	+	0.972826i	$0.574376\pi$
$18$	2.51160	0.591990
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.43091	−0.543568
$21$	−0.698857	−0.152503
$22$	0	0
$23$	6.50318	1.35601	0.678003	−	0.735059i	$-0.262845\pi$
$23$	6.50318	1.35601	0.678003	+	0.735059i	$0.262845\pi$
$24$	0.698857	0.142654
$25$	0.909313	0.181863
$26$	2.86182	0.561248
$27$	3.85182	0.741283
$28$	1.00000	0.188982
$29$	7.02477	1.30447	0.652234	−	0.758018i	$-0.273832\pi$
$29$	7.02477	1.30447	0.652234	+	0.758018i	$0.273832\pi$
$30$	−1.69886	−0.310167
$31$	5.43679	0.976477	0.488238	−	0.872710i	$-0.337640\pi$
$31$	5.43679	0.976477	0.488238	+	0.872710i	$0.337640\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.90931	0.327444
$35$	−2.43091	−0.410898
$36$	−2.51160	−0.418600
$37$	0.383411	0.0630323	0.0315162	−	0.999503i	$-0.489966\pi$
$37$	0.383411	0.0630323	0.0315162	+	0.999503i	$0.489966\pi$
$38$	1.00000	0.162221
$39$	2.00000	0.320256
$40$	2.43091	0.384360
$41$	7.29703	1.13960	0.569802	−	0.821782i	$-0.307020\pi$
$41$	7.29703	1.13960	0.569802	+	0.821782i	$0.307020\pi$
$42$	0.698857	0.107836
$43$	−5.17726	−0.789525	−0.394763	−	0.918783i	$-0.629173\pi$
$43$	−5.17726	−0.789525	−0.394763	+	0.918783i	$0.629173\pi$
$44$	0	0
$45$	6.10547	0.910149
$46$	−6.50318	−0.958841
$47$	4.08658	0.596088	0.298044	−	0.954552i	$-0.403666\pi$
$47$	4.08658	0.596088	0.298044	+	0.954552i	$0.403666\pi$
$48$	−0.698857	−0.100871
$49$	−6.00000	−0.857143
$50$	−0.909313	−0.128596
$51$	1.33434	0.186845
$52$	−2.86182	−0.396862
$53$	−0.348640	−0.0478894	−0.0239447	−	0.999713i	$-0.507623\pi$
$53$	−0.348640	−0.0478894	−0.0239447	+	0.999713i	$0.507623\pi$
$54$	−3.85182	−0.524166
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0.698857	0.0925659
$58$	−7.02477	−0.922398
$59$	−1.62706	−0.211825	−0.105913	−	0.994375i	$-0.533776\pi$
$59$	−1.62706	−0.211825	−0.105913	+	0.994375i	$0.533776\pi$
$60$	1.69886	0.219321
$61$	15.1777	1.94331	0.971655	−	0.236403i	$-0.0759686\pi$
$61$	15.1777	1.94331	0.971655	+	0.236403i	$0.0759686\pi$
$62$	−5.43679	−0.690473
$63$	−2.51160	−0.316432
$64$	1.00000	0.125000
$65$	6.95681	0.862886
$66$	0	0
$67$	−7.75224	−0.947087	−0.473543	−	0.880771i	$-0.657025\pi$
$67$	−7.75224	−0.947087	−0.473543	+	0.880771i	$0.657025\pi$
$68$	−1.90931	−0.231538
$69$	−4.54479	−0.547129
$70$	2.43091	0.290549
$71$	−13.9384	−1.65418	−0.827092	−	0.562067i	$-0.810006\pi$
$71$	−13.9384	−1.65418	−0.827092	+	0.562067i	$0.810006\pi$
$72$	2.51160	0.295995
$73$	8.33022	0.974979	0.487490	−	0.873129i	$-0.337913\pi$
$73$	8.33022	0.974979	0.487490	+	0.873129i	$0.337913\pi$
$74$	−0.383411	−0.0445706
$75$	−0.635480	−0.0733789
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−2.46253	−0.277056	−0.138528	−	0.990359i	$-0.544237\pi$
$79$	−2.46253	−0.277056	−0.138528	+	0.990359i	$0.544237\pi$
$80$	−2.43091	−0.271784
$81$	4.84293	0.538103
$82$	−7.29703	−0.805822
$83$	−3.11135	−0.341515	−0.170757	−	0.985313i	$-0.554621\pi$
$83$	−3.11135	−0.341515	−0.170757	+	0.985313i	$0.554621\pi$
$84$	−0.698857	−0.0762516
$85$	4.64136	0.503427
$86$	5.17726	0.558279
$87$	−4.90931	−0.526334
$88$	0	0
$89$	−3.03750	−0.321974	−0.160987	−	0.986956i	$-0.551468\pi$
$89$	−3.03750	−0.321974	−0.160987	+	0.986956i	$0.551468\pi$
$90$	−6.10547	−0.643573
$91$	−2.86182	−0.300000
$92$	6.50318	0.678003
$93$	−3.79954	−0.393994
$94$	−4.08658	−0.421498
$95$	2.43091	0.249406
$96$	0.698857	0.0713268
$97$	−12.8059	−1.30024	−0.650121	−	0.759831i	$-0.725282\pi$
$97$	−12.8059	−1.30024	−0.650121	+	0.759831i	$0.725282\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	0.909313	0.0909313
$101$	−6.27684	−0.624569	−0.312285	−	0.949989i	$-0.601094\pi$
$101$	−6.27684	−0.624569	−0.312285	+	0.949989i	$0.601094\pi$
$102$	−1.33434	−0.132119
$103$	−15.9384	−1.57046	−0.785228	−	0.619206i	$-0.787454\pi$
$103$	−15.9384	−1.57046	−0.785228	+	0.619206i	$0.787454\pi$
$104$	2.86182	0.280624
$105$	1.69886	0.165791
$106$	0.348640	0.0338629
$107$	−0.268424	−0.0259495	−0.0129748	−	0.999916i	$-0.504130\pi$
$107$	−0.268424	−0.0259495	−0.0129748	+	0.999916i	$0.504130\pi$
$108$	3.85182	0.370642
$109$	−1.61228	−0.154429	−0.0772143	−	0.997015i	$-0.524603\pi$
$109$	−1.61228	−0.154429	−0.0772143	+	0.997015i	$0.524603\pi$
$110$	0	0
$111$	−0.267949	−0.0254326
$112$	1.00000	0.0944911
$113$	9.13565	0.859410	0.429705	−	0.902969i	$-0.358618\pi$
$113$	9.13565	0.859410	0.429705	+	0.902969i	$0.358618\pi$
$114$	−0.698857	−0.0654540
$115$	−15.8086	−1.47416
$116$	7.02477	0.652234
$117$	7.18773	0.664506
$118$	1.62706	0.149783
$119$	−1.90931	−0.175026
$120$	−1.69886	−0.155084
$121$	0	0
$122$	−15.1777	−1.37413
$123$	−5.09958	−0.459814
$124$	5.43679	0.488238
$125$	9.94408	0.889426
$126$	2.51160	0.223751
$127$	16.0782	1.42671	0.713353	−	0.700805i	$-0.247176\pi$
$127$	16.0782	1.42671	0.713353	+	0.700805i	$0.247176\pi$
$128$	−1.00000	−0.0883883
$129$	3.61817	0.318562
$130$	−6.95681	−0.610153
$131$	2.20046	0.192255	0.0961275	−	0.995369i	$-0.469354\pi$
$131$	2.20046	0.192255	0.0961275	+	0.995369i	$0.469354\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	7.75224	0.669691
$135$	−9.36342	−0.805875
$136$	1.90931	0.163722
$137$	8.08246	0.690531	0.345266	−	0.938505i	$-0.387789\pi$
$137$	8.08246	0.690531	0.345266	+	0.938505i	$0.387789\pi$
$138$	4.54479	0.386878
$139$	−0.161382	−0.0136882	−0.00684412	−	0.999977i	$-0.502179\pi$
$139$	−0.161382	−0.0136882	−0.00684412	+	0.999977i	$0.502179\pi$
$140$	−2.43091	−0.205449
$141$	−2.85593	−0.240513
$142$	13.9384	1.16968
$143$	0	0
$144$	−2.51160	−0.209300
$145$	−17.0766	−1.41813
$146$	−8.33022	−0.689414
$147$	4.19314	0.345845
$148$	0.383411	0.0315162
$149$	12.8332	1.05134	0.525669	−	0.850689i	$-0.323815\pi$
$149$	12.8332	1.05134	0.525669	+	0.850689i	$0.323815\pi$
$150$	0.635480	0.0518867
$151$	8.17884	0.665584	0.332792	−	0.943000i	$-0.392009\pi$
$151$	8.17884	0.665584	0.332792	+	0.943000i	$0.392009\pi$
$152$	1.00000	0.0811107
$153$	4.79543	0.387687
$154$	0	0
$155$	−13.2163	−1.06156
$156$	2.00000	0.160128
$157$	−9.36041	−0.747042	−0.373521	−	0.927622i	$-0.621850\pi$
$157$	−9.36041	−0.747042	−0.373521	+	0.927622i	$0.621850\pi$
$158$	2.46253	0.195908
$159$	0.243650	0.0193227
$160$	2.43091	0.192180
$161$	6.50318	0.512522
$162$	−4.84293	−0.380496
$163$	−5.79954	−0.454255	−0.227128	−	0.973865i	$-0.572933\pi$
$163$	−5.79954	−0.454255	−0.227128	+	0.973865i	$0.572933\pi$
$164$	7.29703	0.569802
$165$	0	0
$166$	3.11135	0.241488
$167$	−10.6791	−0.826377	−0.413189	−	0.910646i	$-0.635585\pi$
$167$	−10.6791	−0.826377	−0.413189	+	0.910646i	$0.635585\pi$
$168$	0.698857	0.0539180
$169$	−4.81001	−0.370001
$170$	−4.64136	−0.355976
$171$	2.51160	0.192067
$172$	−5.17726	−0.394763
$173$	14.5839	1.10879	0.554396	−	0.832253i	$-0.312949\pi$
$173$	14.5839	1.10879	0.554396	+	0.832253i	$0.312949\pi$
$174$	4.90931	0.372174
$175$	0.909313	0.0687376
$176$	0	0
$177$	1.13708	0.0854684
$178$	3.03750	0.227670
$179$	−7.52906	−0.562748	−0.281374	−	0.959598i	$-0.590790\pi$
$179$	−7.52906	−0.562748	−0.281374	+	0.959598i	$0.590790\pi$
$180$	6.10547	0.455075
$181$	0.354524	0.0263516	0.0131758	−	0.999913i	$-0.495806\pi$
$181$	0.354524	0.0263516	0.0131758	+	0.999913i	$0.495806\pi$
$182$	2.86182	0.212132
$183$	−10.6071	−0.784097
$184$	−6.50318	−0.479421
$185$	−0.932036	−0.0685246
$186$	3.79954	0.278596
$187$	0	0
$188$	4.08658	0.298044
$189$	3.85182	0.280179
$190$	−2.43091	−0.176357
$191$	−5.89659	−0.426662	−0.213331	−	0.976980i	$-0.568431\pi$
$191$	−5.89659	−0.426662	−0.213331	+	0.976980i	$0.568431\pi$
$192$	−0.698857	−0.0504357
$193$	−12.9095	−0.929247	−0.464623	−	0.885508i	$-0.653810\pi$
$193$	−12.9095	−0.929247	−0.464623	+	0.885508i	$0.653810\pi$
$194$	12.8059	0.919410
$195$	−4.86182	−0.348162
$196$	−6.00000	−0.428571
$197$	−22.0309	−1.56963	−0.784817	−	0.619728i	$-0.787243\pi$
$197$	−22.0309	−1.56963	−0.784817	+	0.619728i	$0.787243\pi$
$198$	0	0
$199$	−10.2235	−0.724722	−0.362361	−	0.932038i	$-0.618029\pi$
$199$	−10.2235	−0.724722	−0.362361	+	0.932038i	$0.618029\pi$
$200$	−0.909313	−0.0642981
$201$	5.41771	0.382136
$202$	6.27684	0.441637
$203$	7.02477	0.493043
$204$	1.33434	0.0934223
$205$	−17.7384	−1.23890
$206$	15.9384	1.11048
$207$	−16.3334	−1.13525
$208$	−2.86182	−0.198431
$209$	0	0
$210$	−1.69886	−0.117232
$211$	−10.4846	−0.721787	−0.360894	−	0.932607i	$-0.617528\pi$
$211$	−10.4846	−0.721787	−0.360894	+	0.932607i	$0.617528\pi$
$212$	−0.348640	−0.0239447
$213$	9.74095	0.667439
$214$	0.268424	0.0183491
$215$	12.5854	0.858320
$216$	−3.85182	−0.262083
$217$	5.43679	0.369073
$218$	1.61228	0.109198
$219$	−5.82164	−0.393390
$220$	0	0
$221$	5.46410	0.367555
$222$	0.267949	0.0179836
$223$	23.0671	1.54468	0.772342	−	0.635207i	$-0.219085\pi$
$223$	23.0671	1.54468	0.772342	+	0.635207i	$0.219085\pi$
$224$	−1.00000	−0.0668153
$225$	−2.28383	−0.152255
$226$	−9.13565	−0.607694
$227$	0.487299	0.0323432	0.0161716	−	0.999869i	$-0.494852\pi$
$227$	0.487299	0.0323432	0.0161716	+	0.999869i	$0.494852\pi$
$228$	0.698857	0.0462829
$229$	−29.2732	−1.93443	−0.967214	−	0.253963i	$-0.918266\pi$
$229$	−29.2732	−1.93443	−0.967214	+	0.253963i	$0.918266\pi$
$230$	15.8086	1.04239
$231$	0	0
$232$	−7.02477	−0.461199
$233$	−22.4082	−1.46801	−0.734005	−	0.679145i	$-0.762351\pi$
$233$	−22.4082	−1.46801	−0.734005	+	0.679145i	$0.762351\pi$
$234$	−7.18773	−0.469877
$235$	−9.93409	−0.648028
$236$	−1.62706	−0.105913
$237$	1.72095	0.111788
$238$	1.90931	0.123762
$239$	11.6847	0.755824	0.377912	−	0.925842i	$-0.376642\pi$
$239$	11.6847	0.755824	0.377912	+	0.925842i	$0.376642\pi$
$240$	1.69886	0.109661
$241$	−5.50571	−0.354654	−0.177327	−	0.984152i	$-0.556745\pi$
$241$	−5.50571	−0.354654	−0.177327	+	0.984152i	$0.556745\pi$
$242$	0	0
$243$	−14.9400	−0.958400
$244$	15.1777	0.971655
$245$	14.5854	0.931830
$246$	5.09958	0.325137
$247$	2.86182	0.182093
$248$	−5.43679	−0.345237
$249$	2.17439	0.137796
$250$	−9.94408	−0.628919
$251$	−6.89042	−0.434920	−0.217460	−	0.976069i	$-0.569777\pi$
$251$	−6.89042	−0.434920	−0.217460	+	0.976069i	$0.569777\pi$
$252$	−2.51160	−0.158216
$253$	0	0
$254$	−16.0782	−1.00883
$255$	−3.24365	−0.203125
$256$	1.00000	0.0625000
$257$	4.78366	0.298397	0.149198	−	0.988807i	$-0.452331\pi$
$257$	4.78366	0.298397	0.149198	+	0.988807i	$0.452331\pi$
$258$	−3.61817	−0.225257
$259$	0.383411	0.0238240
$260$	6.95681	0.431443
$261$	−17.6434	−1.09210
$262$	−2.20046	−0.135945
$263$	10.8979	0.671992	0.335996	−	0.941863i	$-0.390927\pi$
$263$	10.8979	0.671992	0.335996	+	0.941863i	$0.390927\pi$
$264$	0	0
$265$	0.847512	0.0520623
$266$	1.00000	0.0613139
$267$	2.12278	0.129912
$268$	−7.75224	−0.473543
$269$	−22.6577	−1.38147	−0.690733	−	0.723110i	$-0.742712\pi$
$269$	−22.6577	−1.38147	−0.690733	+	0.723110i	$0.742712\pi$
$270$	9.36342	0.569840
$271$	3.58655	0.217867	0.108934	−	0.994049i	$-0.465256\pi$
$271$	3.58655	0.217867	0.108934	+	0.994049i	$0.465256\pi$
$272$	−1.90931	−0.115769
$273$	2.00000	0.121046
$274$	−8.08246	−0.488279
$275$	0	0
$276$	−4.54479	−0.273564
$277$	0.0186108	0.00111822	0.000559109	−	1.00000i	$-0.499822\pi$
$277$	0.0186108	0.00111822	0.000559109		1.00000i	$0.499822\pi$
$278$	0.161382	0.00967905
$279$	−13.6550	−0.817506
$280$	2.43091	0.145275
$281$	21.2684	1.26877	0.634384	−	0.773018i	$-0.281254\pi$
$281$	21.2684	1.26877	0.634384	+	0.773018i	$0.281254\pi$
$282$	2.85593	0.170068
$283$	−23.1131	−1.37393	−0.686966	−	0.726689i	$-0.741058\pi$
$283$	−23.1131	−1.37393	−0.686966	+	0.726689i	$0.741058\pi$
$284$	−13.9384	−0.827092
$285$	−1.69886	−0.100632
$286$	0	0
$287$	7.29703	0.430730
$288$	2.51160	0.147997
$289$	−13.3545	−0.785560
$290$	17.0766	1.00277
$291$	8.94949	0.524629
$292$	8.33022	0.487490
$293$	3.69044	0.215598	0.107799	−	0.994173i	$-0.465620\pi$
$293$	3.69044	0.215598	0.107799	+	0.994173i	$0.465620\pi$
$294$	−4.19314	−0.244549
$295$	3.95523	0.230283
$296$	−0.383411	−0.0222853
$297$	0	0
$298$	−12.8332	−0.743408
$299$	−18.6109	−1.07630
$300$	−0.635480	−0.0366894
$301$	−5.17726	−0.298412
$302$	−8.17884	−0.470639
$303$	4.38662	0.252005
$304$	−1.00000	−0.0573539
$305$	−36.8957	−2.11264
$306$	−4.79543	−0.274136
$307$	−18.1852	−1.03788	−0.518942	−	0.854809i	$-0.673674\pi$
$307$	−18.1852	−1.03788	−0.518942	+	0.854809i	$0.673674\pi$
$308$	0	0
$309$	11.1387	0.633656
$310$	13.2163	0.750638
$311$	30.4630	1.72740	0.863699	−	0.504008i	$-0.168142\pi$
$311$	30.4630	1.72740	0.863699	+	0.504008i	$0.168142\pi$
$312$	−2.00000	−0.113228
$313$	−11.4830	−0.649057	−0.324529	−	0.945876i	$-0.605206\pi$
$313$	−11.4830	−0.649057	−0.324529	+	0.945876i	$0.605206\pi$
$314$	9.36041	0.528238
$315$	6.10547	0.344004
$316$	−2.46253	−0.138528
$317$	17.6836	0.993213	0.496606	−	0.867976i	$-0.334579\pi$
$317$	17.6836	0.993213	0.496606	+	0.867976i	$0.334579\pi$
$318$	−0.243650	−0.0136632
$319$	0	0
$320$	−2.43091	−0.135892
$321$	0.187590	0.0104703
$322$	−6.50318	−0.362408
$323$	1.90931	0.106237
$324$	4.84293	0.269051
$325$	−2.60229	−0.144349
$326$	5.79954	0.321207
$327$	1.12675	0.0623097
$328$	−7.29703	−0.402911
$329$	4.08658	0.225300
$330$	0	0
$331$	−22.1282	−1.21628	−0.608138	−	0.793832i	$-0.708083\pi$
$331$	−22.1282	−1.21628	−0.608138	+	0.793832i	$0.708083\pi$
$332$	−3.11135	−0.170757
$333$	−0.962974	−0.0527706
$334$	10.6791	0.584337
$335$	18.8450	1.02961
$336$	−0.698857	−0.0381258
$337$	−14.3793	−0.783290	−0.391645	−	0.920116i	$-0.628094\pi$
$337$	−14.3793	−0.783290	−0.391645	+	0.920116i	$0.628094\pi$
$338$	4.81001	0.261630
$339$	−6.38451	−0.346759
$340$	4.64136	0.251713
$341$	0	0
$342$	−2.51160	−0.135812
$343$	−13.0000	−0.701934
$344$	5.17726	0.279139
$345$	11.0480	0.594803
$346$	−14.5839	−0.784034
$347$	0.879129	0.0471941	0.0235971	−	0.999722i	$-0.492488\pi$
$347$	0.879129	0.0471941	0.0235971	+	0.999722i	$0.492488\pi$
$348$	−4.90931	−0.263167
$349$	−6.50859	−0.348397	−0.174198	−	0.984711i	$-0.555733\pi$
$349$	−6.50859	−0.348397	−0.174198	+	0.984711i	$0.555733\pi$
$350$	−0.909313	−0.0486048
$351$	−11.0232	−0.588375
$352$	0	0
$353$	2.71932	0.144735	0.0723675	−	0.997378i	$-0.476945\pi$
$353$	2.71932	0.144735	0.0723675	+	0.997378i	$0.476945\pi$
$354$	−1.13708	−0.0604353
$355$	33.8830	1.79832
$356$	−3.03750	−0.160987
$357$	1.33434	0.0706206
$358$	7.52906	0.397923
$359$	23.1057	1.21947	0.609735	−	0.792605i	$-0.291276\pi$
$359$	23.1057	1.21947	0.609735	+	0.792605i	$0.291276\pi$
$360$	−6.10547	−0.321786
$361$	1.00000	0.0526316
$362$	−0.354524	−0.0186334
$363$	0	0
$364$	−2.86182	−0.150000
$365$	−20.2500	−1.05993
$366$	10.6071	0.554440
$367$	−26.2311	−1.36925	−0.684627	−	0.728894i	$-0.740035\pi$
$367$	−26.2311	−1.36925	−0.684627	+	0.728894i	$0.740035\pi$
$368$	6.50318	0.339002
$369$	−18.3272	−0.954077
$370$	0.932036	0.0484542
$371$	−0.348640	−0.0181005
$372$	−3.79954	−0.196997
$373$	−11.4943	−0.595152	−0.297576	−	0.954698i	$-0.596178\pi$
$373$	−11.4943	−0.595152	−0.297576	+	0.954698i	$0.596178\pi$
$374$	0	0
$375$	−6.94949	−0.358870
$376$	−4.08658	−0.210749
$377$	−20.1036	−1.03539
$378$	−3.85182	−0.198116
$379$	0.416325	0.0213852	0.0106926	−	0.999943i	$-0.496596\pi$
$379$	0.416325	0.0213852	0.0106926	+	0.999943i	$0.496596\pi$
$380$	2.43091	0.124703
$381$	−11.2363	−0.575655
$382$	5.89659	0.301696
$383$	31.8396	1.62693	0.813463	−	0.581617i	$-0.197580\pi$
$383$	31.8396	1.62693	0.813463	+	0.581617i	$0.197580\pi$
$384$	0.698857	0.0356634
$385$	0	0
$386$	12.9095	0.657077
$387$	13.0032	0.660990
$388$	−12.8059	−0.650121
$389$	−3.34864	−0.169783	−0.0848914	−	0.996390i	$-0.527054\pi$
$389$	−3.34864	−0.169783	−0.0848914	+	0.996390i	$0.527054\pi$
$390$	4.86182	0.246188
$391$	−12.4166	−0.627935
$392$	6.00000	0.303046
$393$	−1.53781	−0.0775721
$394$	22.0309	1.10990
$395$	5.98617	0.301197
$396$	0	0
$397$	2.41230	0.121070	0.0605349	−	0.998166i	$-0.480719\pi$
$397$	2.41230	0.121070	0.0605349	+	0.998166i	$0.480719\pi$
$398$	10.2235	0.512456
$399$	0.698857	0.0349866
$400$	0.909313	0.0454656
$401$	−32.1979	−1.60789	−0.803944	−	0.594705i	$-0.797269\pi$
$401$	−32.1979	−1.60789	−0.803944	+	0.594705i	$0.797269\pi$
$402$	−5.41771	−0.270211
$403$	−15.5591	−0.775054
$404$	−6.27684	−0.312285
$405$	−11.7727	−0.584990
$406$	−7.02477	−0.348634
$407$	0	0
$408$	−1.33434	−0.0660595
$409$	34.0985	1.68606	0.843032	−	0.537863i	$-0.180768\pi$
$409$	34.0985	1.68606	0.843032	+	0.537863i	$0.180768\pi$
$410$	17.7384	0.876038
$411$	−5.64849	−0.278619
$412$	−15.9384	−0.785228
$413$	−1.62706	−0.0800624
$414$	16.3334	0.802742
$415$	7.56340	0.371273
$416$	2.86182	0.140312
$417$	0.112783	0.00552301
$418$	0	0
$419$	17.3423	0.847225	0.423613	−	0.905843i	$-0.360762\pi$
$419$	17.3423	0.847225	0.423613	+	0.905843i	$0.360762\pi$
$420$	1.69886	0.0828957
$421$	−6.36356	−0.310141	−0.155071	−	0.987903i	$-0.549560\pi$
$421$	−6.36356	−0.310141	−0.155071	+	0.987903i	$0.549560\pi$
$422$	10.4846	0.510381
$423$	−10.2638	−0.499045
$424$	0.348640	0.0169315
$425$	−1.73616	−0.0842163
$426$	−9.74095	−0.471950
$427$	15.1777	0.734502
$428$	−0.268424	−0.0129748
$429$	0	0
$430$	−12.5854	−0.606924
$431$	25.2529	1.21639	0.608194	−	0.793788i	$-0.291894\pi$
$431$	25.2529	1.21639	0.608194	+	0.793788i	$0.291894\pi$
$432$	3.85182	0.185321
$433$	7.31865	0.351712	0.175856	−	0.984416i	$-0.443731\pi$
$433$	7.31865	0.351712	0.175856	+	0.984416i	$0.443731\pi$
$434$	−5.43679	−0.260974
$435$	11.9341	0.572196
$436$	−1.61228	−0.0772143
$437$	−6.50318	−0.311089
$438$	5.82164	0.278169
$439$	−8.02861	−0.383185	−0.191592	−	0.981475i	$-0.561365\pi$
$439$	−8.02861	−0.383185	−0.191592	+	0.981475i	$0.561365\pi$
$440$	0	0
$441$	15.0696	0.717600
$442$	−5.46410	−0.259901
$443$	−33.0740	−1.57140	−0.785698	−	0.618611i	$-0.787696\pi$
$443$	−33.0740	−1.57140	−0.785698	+	0.618611i	$0.787696\pi$
$444$	−0.267949	−0.0127163
$445$	7.38389	0.350030
$446$	−23.0671	−1.09226
$447$	−8.96858	−0.424199
$448$	1.00000	0.0472456
$449$	8.93958	0.421885	0.210942	−	0.977498i	$-0.432347\pi$
$449$	8.93958	0.421885	0.210942	+	0.977498i	$0.432347\pi$
$450$	2.28383	0.107661
$451$	0	0
$452$	9.13565	0.429705
$453$	−5.71584	−0.268554
$454$	−0.487299	−0.0228701
$455$	6.95681	0.326140
$456$	−0.698857	−0.0327270
$457$	1.90520	0.0891215	0.0445608	−	0.999007i	$-0.485811\pi$
$457$	1.90520	0.0891215	0.0445608	+	0.999007i	$0.485811\pi$
$458$	29.2732	1.36785
$459$	−7.35433	−0.343271
$460$	−15.8086	−0.737081
$461$	−21.7813	−1.01446	−0.507229	−	0.861812i	$-0.669330\pi$
$461$	−21.7813	−1.01446	−0.507229	+	0.861812i	$0.669330\pi$
$462$	0	0
$463$	−36.0716	−1.67639	−0.838196	−	0.545370i	$-0.816389\pi$
$463$	−36.0716	−1.67639	−0.838196	+	0.545370i	$0.816389\pi$
$464$	7.02477	0.326117
$465$	9.23633	0.428325
$466$	22.4082	1.03804
$467$	−15.8955	−0.735555	−0.367778	−	0.929914i	$-0.619881\pi$
$467$	−15.8955	−0.735555	−0.367778	+	0.929914i	$0.619881\pi$
$468$	7.18773	0.332253
$469$	−7.75224	−0.357965
$470$	9.93409	0.458225
$471$	6.54159	0.301420
$472$	1.62706	0.0748915
$473$	0	0
$474$	−1.72095	−0.0790460
$475$	−0.909313	−0.0417221
$476$	−1.90931	−0.0875132
$477$	0.875644	0.0400930
$478$	−11.6847	−0.534448
$479$	5.40799	0.247097	0.123549	−	0.992339i	$-0.460572\pi$
$479$	5.40799	0.247097	0.123549	+	0.992339i	$0.460572\pi$
$480$	−1.69886	−0.0775419
$481$	−1.09725	−0.0500303
$482$	5.50571	0.250778
$483$	−4.54479	−0.206795
$484$	0	0
$485$	31.1300	1.41354
$486$	14.9400	0.677691
$487$	−17.5518	−0.795347	−0.397674	−	0.917527i	$-0.630182\pi$
$487$	−17.5518	−0.795347	−0.397674	+	0.917527i	$0.630182\pi$
$488$	−15.1777	−0.687064
$489$	4.05305	0.183285
$490$	−14.5854	−0.658903
$491$	−1.28718	−0.0580895	−0.0290448	−	0.999578i	$-0.509247\pi$
$491$	−1.28718	−0.0580895	−0.0290448	+	0.999578i	$0.509247\pi$
$492$	−5.09958	−0.229907
$493$	−13.4125	−0.604068
$494$	−2.86182	−0.128759
$495$	0	0
$496$	5.43679	0.244119
$497$	−13.9384	−0.625222
$498$	−2.17439	−0.0974367
$499$	−34.0586	−1.52467	−0.762337	−	0.647180i	$-0.775948\pi$
$499$	−34.0586	−1.52467	−0.762337	+	0.647180i	$0.775948\pi$
$500$	9.94408	0.444713
$501$	7.46320	0.333431
$502$	6.89042	0.307535
$503$	−19.2313	−0.857482	−0.428741	−	0.903427i	$-0.641043\pi$
$503$	−19.2313	−0.857482	−0.428741	+	0.903427i	$0.641043\pi$
$504$	2.51160	0.111876
$505$	15.2584	0.678991
$506$	0	0
$507$	3.36151	0.149290
$508$	16.0782	0.713353
$509$	−18.7783	−0.832334	−0.416167	−	0.909288i	$-0.636627\pi$
$509$	−18.7783	−0.832334	−0.416167	+	0.909288i	$0.636627\pi$
$510$	3.24365	0.143631
$511$	8.33022	0.368507
$512$	−1.00000	−0.0441942
$513$	−3.85182	−0.170062
$514$	−4.78366	−0.210998
$515$	38.7448	1.70730
$516$	3.61817	0.159281
$517$	0	0
$518$	−0.383411	−0.0168461
$519$	−10.1920	−0.447381
$520$	−6.95681	−0.305076
$521$	−18.2036	−0.797515	−0.398757	−	0.917056i	$-0.630558\pi$
$521$	−18.2036	−0.797515	−0.398757	+	0.917056i	$0.630558\pi$
$522$	17.6434	0.772231
$523$	−34.9866	−1.52986	−0.764930	−	0.644114i	$-0.777226\pi$
$523$	−34.9866	−1.52986	−0.764930	+	0.644114i	$0.777226\pi$
$524$	2.20046	0.0961275
$525$	−0.635480	−0.0277346
$526$	−10.8979	−0.475170
$527$	−10.3805	−0.452183
$528$	0	0
$529$	19.2913	0.838754
$530$	−0.847512	−0.0368136
$531$	4.08652	0.177340
$532$	−1.00000	−0.0433555
$533$	−20.8828	−0.904533
$534$	−2.12278	−0.0918616
$535$	0.652514	0.0282106
$536$	7.75224	0.334846
$537$	5.26173	0.227061
$538$	22.6577	0.976844
$539$	0	0
$540$	−9.36342	−0.402937
$541$	−26.3177	−1.13149	−0.565743	−	0.824582i	$-0.691411\pi$
$541$	−26.3177	−1.13149	−0.565743	+	0.824582i	$0.691411\pi$
$542$	−3.58655	−0.154055
$543$	−0.247762	−0.0106325
$544$	1.90931	0.0818611
$545$	3.91931	0.167885
$546$	−2.00000	−0.0855921
$547$	45.9751	1.96575	0.982876	−	0.184268i	$-0.0589913\pi$
$547$	45.9751	1.96575	0.982876	+	0.184268i	$0.0589913\pi$
$548$	8.08246	0.345266
$549$	−38.1204	−1.62694
$550$	0	0
$551$	−7.02477	−0.299265
$552$	4.54479	0.193439
$553$	−2.46253	−0.104717
$554$	−0.0186108	−0.000790699 0
$555$	0.651360	0.0276487
$556$	−0.161382	−0.00684412
$557$	−11.7236	−0.496746	−0.248373	−	0.968664i	$-0.579896\pi$
$557$	−11.7236	−0.496746	−0.248373	+	0.968664i	$0.579896\pi$
$558$	13.6550	0.578064
$559$	14.8164	0.626666
$560$	−2.43091	−0.102725
$561$	0	0
$562$	−21.2684	−0.897154
$563$	−3.37184	−0.142106	−0.0710530	−	0.997473i	$-0.522636\pi$
$563$	−3.37184	−0.142106	−0.0710530	+	0.997473i	$0.522636\pi$
$564$	−2.85593	−0.120256
$565$	−22.2079	−0.934294
$566$	23.1131	0.971517
$567$	4.84293	0.203384
$568$	13.9384	0.584842
$569$	−37.3809	−1.56709	−0.783544	−	0.621336i	$-0.786590\pi$
$569$	−37.3809	−1.56709	−0.783544	+	0.621336i	$0.786590\pi$
$570$	1.69886	0.0711573
$571$	−19.2610	−0.806046	−0.403023	−	0.915190i	$-0.632041\pi$
$571$	−19.2610	−0.806046	−0.403023	+	0.915190i	$0.632041\pi$
$572$	0	0
$573$	4.12087	0.172152
$574$	−7.29703	−0.304572
$575$	5.91342	0.246607
$576$	−2.51160	−0.104650
$577$	−0.476971	−0.0198566	−0.00992829	−	0.999951i	$-0.503160\pi$
$577$	−0.476971	−0.0198566	−0.00992829	+	0.999951i	$0.503160\pi$
$578$	13.3545	0.555475
$579$	9.02190	0.374937
$580$	−17.0766	−0.709066
$581$	−3.11135	−0.129081
$582$	−8.94949	−0.370968
$583$	0	0
$584$	−8.33022	−0.344707
$585$	−17.4727	−0.722408
$586$	−3.69044	−0.152451
$587$	−26.4582	−1.09205	−0.546024	−	0.837770i	$-0.683859\pi$
$587$	−26.4582	−1.09205	−0.546024	+	0.837770i	$0.683859\pi$
$588$	4.19314	0.172922
$589$	−5.43679	−0.224019
$590$	−3.95523	−0.162834
$591$	15.3964	0.633324
$592$	0.383411	0.0157581
$593$	7.81097	0.320758	0.160379	−	0.987056i	$-0.448728\pi$
$593$	7.81097	0.320758	0.160379	+	0.987056i	$0.448728\pi$
$594$	0	0
$595$	4.64136	0.190277
$596$	12.8332	0.525669
$597$	7.14474	0.292415
$598$	18.6109	0.761056
$599$	−29.5804	−1.20862	−0.604312	−	0.796748i	$-0.706552\pi$
$599$	−29.5804	−1.20862	−0.604312	+	0.796748i	$0.706552\pi$
$600$	0.635480	0.0259434
$601$	13.6808	0.558051	0.279025	−	0.960284i	$-0.409989\pi$
$601$	13.6808	0.558051	0.279025	+	0.960284i	$0.409989\pi$
$602$	5.17726	0.211009
$603$	19.4705	0.792901
$604$	8.17884	0.332792
$605$	0	0
$606$	−4.38662	−0.178194
$607$	−8.70651	−0.353386	−0.176693	−	0.984266i	$-0.556540\pi$
$607$	−8.70651	−0.353386	−0.176693	+	0.984266i	$0.556540\pi$
$608$	1.00000	0.0405554
$609$	−4.90931	−0.198935
$610$	36.8957	1.49386
$611$	−11.6950	−0.473130
$612$	4.79543	0.193844
$613$	43.4395	1.75451	0.877253	−	0.480029i	$-0.159374\pi$
$613$	43.4395	1.75451	0.877253	+	0.480029i	$0.159374\pi$
$614$	18.1852	0.733895
$615$	12.3966	0.499880
$616$	0	0
$617$	−37.5815	−1.51298	−0.756488	−	0.654008i	$-0.773086\pi$
$617$	−37.5815	−1.51298	−0.756488	+	0.654008i	$0.773086\pi$
$618$	−11.1387	−0.448063
$619$	46.0731	1.85183	0.925917	−	0.377727i	$-0.123294\pi$
$619$	46.0731	1.85183	0.925917	+	0.377727i	$0.123294\pi$
$620$	−13.2163	−0.530781
$621$	25.0491	1.00518
$622$	−30.4630	−1.22146
$623$	−3.03750	−0.121695
$624$	2.00000	0.0800641
$625$	−28.7197	−1.14879
$626$	11.4830	0.458953
$627$	0	0
$628$	−9.36041	−0.373521
$629$	−0.732051	−0.0291888
$630$	−6.10547	−0.243248
$631$	38.3314	1.52595	0.762974	−	0.646429i	$-0.223738\pi$
$631$	38.3314	1.52595	0.762974	+	0.646429i	$0.223738\pi$
$632$	2.46253	0.0979540
$633$	7.32721	0.291231
$634$	−17.6836	−0.702307
$635$	−39.0845	−1.55102
$636$	0.243650	0.00966134
$637$	17.1709	0.680336
$638$	0	0
$639$	35.0077	1.38488
$640$	2.43091	0.0960901
$641$	20.5407	0.811308	0.405654	−	0.914027i	$-0.367044\pi$
$641$	20.5407	0.811308	0.405654	+	0.914027i	$0.367044\pi$
$642$	−0.187590	−0.00740359
$643$	15.0492	0.593483	0.296741	−	0.954958i	$-0.404100\pi$
$643$	15.0492	0.593483	0.296741	+	0.954958i	$0.404100\pi$
$644$	6.50318	0.256261
$645$	−8.79543	−0.346320
$646$	−1.90931	−0.0751209
$647$	35.5585	1.39795	0.698975	−	0.715146i	$-0.253640\pi$
$647$	35.5585	1.39795	0.698975	+	0.715146i	$0.253640\pi$
$648$	−4.84293	−0.190248
$649$	0	0
$650$	2.60229	0.102070
$651$	−3.79954	−0.148916
$652$	−5.79954	−0.227128
$653$	24.7113	0.967028	0.483514	−	0.875337i	$-0.339360\pi$
$653$	24.7113	0.967028	0.483514	+	0.875337i	$0.339360\pi$
$654$	−1.12675	−0.0440596
$655$	−5.34911	−0.209007
$656$	7.29703	0.284901
$657$	−20.9222	−0.816252
$658$	−4.08658	−0.159311
$659$	−1.39211	−0.0542289	−0.0271144	−	0.999632i	$-0.508632\pi$
$659$	−1.39211	−0.0542289	−0.0271144	+	0.999632i	$0.508632\pi$
$660$	0	0
$661$	27.7243	1.07835	0.539175	−	0.842194i	$-0.318736\pi$
$661$	27.7243	1.07835	0.539175	+	0.842194i	$0.318736\pi$
$662$	22.1282	0.860036
$663$	−3.81863	−0.148303
$664$	3.11135	0.120744
$665$	2.43091	0.0942666
$666$	0.962974	0.0373145
$667$	45.6834	1.76887
$668$	−10.6791	−0.413189
$669$	−16.1206	−0.623257
$670$	−18.8450	−0.728045
$671$	0	0
$672$	0.698857	0.0269590
$673$	49.5016	1.90815	0.954073	−	0.299574i	$-0.0968445\pi$
$673$	49.5016	1.90815	0.954073	+	0.299574i	$0.0968445\pi$
$674$	14.3793	0.553870
$675$	3.50251	0.134812
$676$	−4.81001	−0.185000
$677$	−28.2443	−1.08552	−0.542758	−	0.839889i	$-0.682620\pi$
$677$	−28.2443	−1.08552	−0.542758	+	0.839889i	$0.682620\pi$
$678$	6.38451	0.245196
$679$	−12.8059	−0.491445
$680$	−4.64136	−0.177988
$681$	−0.340553	−0.0130500
$682$	0	0
$683$	28.7090	1.09852	0.549261	−	0.835651i	$-0.314909\pi$
$683$	28.7090	1.09852	0.549261	+	0.835651i	$0.314909\pi$
$684$	2.51160	0.0960334
$685$	−19.6477	−0.750701
$686$	13.0000	0.496342
$687$	20.4578	0.780513
$688$	−5.17726	−0.197381
$689$	0.997744	0.0380110
$690$	−11.0480	−0.420589
$691$	−33.4941	−1.27418	−0.637088	−	0.770791i	$-0.719861\pi$
$691$	−33.4941	−1.27418	−0.637088	+	0.770791i	$0.719861\pi$
$692$	14.5839	0.554396
$693$	0	0
$694$	−0.879129	−0.0333713
$695$	0.392305	0.0148810
$696$	4.90931	0.186087
$697$	−13.9323	−0.527724
$698$	6.50859	0.246354
$699$	15.6601	0.592320
$700$	0.909313	0.0343688
$701$	44.3759	1.67605	0.838026	−	0.545630i	$-0.183709\pi$
$701$	44.3759	1.67605	0.838026	+	0.545630i	$0.183709\pi$
$702$	11.0232	0.416044
$703$	−0.383411	−0.0144606
$704$	0	0
$705$	6.94251	0.261470
$706$	−2.71932	−0.102343
$707$	−6.27684	−0.236065
$708$	1.13708	0.0427342
$709$	1.80084	0.0676319	0.0338159	−	0.999428i	$-0.489234\pi$
$709$	1.80084	0.0676319	0.0338159	+	0.999428i	$0.489234\pi$
$710$	−33.8830	−1.27160
$711$	6.18487	0.231951
$712$	3.03750	0.113835
$713$	35.3564	1.32411
$714$	−1.33434	−0.0499363
$715$	0	0
$716$	−7.52906	−0.281374
$717$	−8.16597	−0.304964
$718$	−23.1057	−0.862296
$719$	−21.3837	−0.797479	−0.398740	−	0.917064i	$-0.630552\pi$
$719$	−21.3837	−0.797479	−0.398740	+	0.917064i	$0.630552\pi$
$720$	6.10547	0.227537
$721$	−15.9384	−0.593577
$722$	−1.00000	−0.0372161
$723$	3.84771	0.143098
$724$	0.354524	0.0131758
$725$	6.38772	0.237234
$726$	0	0
$727$	−25.0005	−0.927218	−0.463609	−	0.886040i	$-0.653446\pi$
$727$	−25.0005	−0.927218	−0.463609	+	0.886040i	$0.653446\pi$
$728$	2.86182	0.106066
$729$	−4.08787	−0.151403
$730$	20.2500	0.749486
$731$	9.88501	0.365610
$732$	−10.6071	−0.392049
$733$	−35.4714	−1.31017	−0.655083	−	0.755557i	$-0.727367\pi$
$733$	−35.4714	−1.31017	−0.655083	+	0.755557i	$0.727367\pi$
$734$	26.2311	0.968208
$735$	−10.1931	−0.375980
$736$	−6.50318	−0.239710
$737$	0	0
$738$	18.3272	0.674634
$739$	21.1764	0.778988	0.389494	−	0.921029i	$-0.372650\pi$
$739$	21.1764	0.778988	0.389494	+	0.921029i	$0.372650\pi$
$740$	−0.932036	−0.0342623
$741$	−2.00000	−0.0734718
$742$	0.348640	0.0127990
$743$	0.450425	0.0165245	0.00826225	−	0.999966i	$-0.497370\pi$
$743$	0.450425	0.0165245	0.00826225	+	0.999966i	$0.497370\pi$
$744$	3.79954	0.139298
$745$	−31.1963	−1.14295
$746$	11.4943	0.420836
$747$	7.81446	0.285916
$748$	0	0
$749$	−0.268424	−0.00980800
$750$	6.94949	0.253760
$751$	24.8901	0.908252	0.454126	−	0.890938i	$-0.349952\pi$
$751$	24.8901	0.908252	0.454126	+	0.890938i	$0.349952\pi$
$752$	4.08658	0.149022
$753$	4.81542	0.175484
$754$	20.1036	0.732130
$755$	−19.8820	−0.723580
$756$	3.85182	0.140089
$757$	−42.0173	−1.52715	−0.763573	−	0.645722i	$-0.776557\pi$
$757$	−42.0173	−1.52715	−0.763573	+	0.645722i	$0.776557\pi$
$758$	−0.416325	−0.0151216
$759$	0	0
$760$	−2.43091	−0.0881783
$761$	22.7584	0.824991	0.412496	−	0.910960i	$-0.364657\pi$
$761$	22.7584	0.824991	0.412496	+	0.910960i	$0.364657\pi$
$762$	11.2363	0.407049
$763$	−1.61228	−0.0583685
$764$	−5.89659	−0.213331
$765$	−11.6572	−0.421469
$766$	−31.8396	−1.15041
$767$	4.65635	0.168131
$768$	−0.698857	−0.0252178
$769$	15.3289	0.552775	0.276388	−	0.961046i	$-0.410863\pi$
$769$	15.3289	0.552775	0.276388	+	0.961046i	$0.410863\pi$
$770$	0	0
$771$	−3.34309	−0.120399
$772$	−12.9095	−0.464623
$773$	32.8077	1.18001	0.590006	−	0.807399i	$-0.299125\pi$
$773$	32.8077	1.18001	0.590006	+	0.807399i	$0.299125\pi$
$774$	−13.0032	−0.467391
$775$	4.94375	0.177585
$776$	12.8059	0.459705
$777$	−0.267949	−0.00961262
$778$	3.34864	0.120055
$779$	−7.29703	−0.261443
$780$	−4.86182	−0.174081
$781$	0	0
$782$	12.4166	0.444017
$783$	27.0582	0.966980
$784$	−6.00000	−0.214286
$785$	22.7543	0.812135
$786$	1.53781	0.0548518
$787$	−35.5721	−1.26801	−0.634004	−	0.773330i	$-0.718590\pi$
$787$	−35.5721	−1.26801	−0.634004	+	0.773330i	$0.718590\pi$
$788$	−22.0309	−0.784817
$789$	−7.61606	−0.271139
$790$	−5.98617	−0.212978
$791$	9.13565	0.324826
$792$	0	0
$793$	−43.4359	−1.54245
$794$	−2.41230	−0.0856092
$795$	−0.592290	−0.0210064
$796$	−10.2235	−0.362361
$797$	−8.21915	−0.291137	−0.145569	−	0.989348i	$-0.546501\pi$
$797$	−8.21915	−0.291137	−0.145569	+	0.989348i	$0.546501\pi$
$798$	−0.698857	−0.0247393
$799$	−7.80255	−0.276034
$800$	−0.909313	−0.0321491
$801$	7.62898	0.269557
$802$	32.1979	1.13695
$803$	0	0
$804$	5.41771	0.191068
$805$	−15.8086	−0.557181
$806$	15.5591	0.548046
$807$	15.8345	0.557401
$808$	6.27684	0.220819
$809$	−46.9337	−1.65010	−0.825050	−	0.565060i	$-0.808853\pi$
$809$	−46.9337	−1.65010	−0.825050	+	0.565060i	$0.808853\pi$
$810$	11.7727	0.413651
$811$	43.6344	1.53221	0.766105	−	0.642715i	$-0.222192\pi$
$811$	43.6344	1.53221	0.766105	+	0.642715i	$0.222192\pi$
$812$	7.02477	0.246521
$813$	−2.50648	−0.0879063
$814$	0	0
$815$	14.0981	0.493837
$816$	1.33434	0.0467111
$817$	5.17726	0.181129
$818$	−34.0985	−1.19223
$819$	7.18773	0.251160
$820$	−17.7384	−0.619452
$821$	−45.3423	−1.58246	−0.791228	−	0.611521i	$-0.790558\pi$
$821$	−45.3423	−1.58246	−0.791228	+	0.611521i	$0.790558\pi$
$822$	5.64849	0.197014
$823$	−19.3037	−0.672884	−0.336442	−	0.941704i	$-0.609224\pi$
$823$	−19.3037	−0.672884	−0.336442	+	0.941704i	$0.609224\pi$
$824$	15.9384	0.555240
$825$	0	0
$826$	1.62706	0.0566127
$827$	−28.3611	−0.986211	−0.493106	−	0.869969i	$-0.664138\pi$
$827$	−28.3611	−0.986211	−0.493106	+	0.869969i	$0.664138\pi$
$828$	−16.3334	−0.567624
$829$	−19.0610	−0.662015	−0.331008	−	0.943628i	$-0.607389\pi$
$829$	−19.0610	−0.662015	−0.331008	+	0.943628i	$0.607389\pi$
$830$	−7.56340	−0.262530
$831$	−0.0130063	−0.000451184 0
$832$	−2.86182	−0.0992156
$833$	11.4559	0.396923
$834$	−0.112783	−0.00390535
$835$	25.9600	0.898383
$836$	0	0
$837$	20.9415	0.723846
$838$	−17.3423	−0.599079
$839$	17.8711	0.616979	0.308489	−	0.951228i	$-0.400177\pi$
$839$	17.8711	0.616979	0.308489	+	0.951228i	$0.400177\pi$
$840$	−1.69886	−0.0586161
$841$	20.3475	0.701636
$842$	6.36356	0.219303
$843$	−14.8636	−0.511929
$844$	−10.4846	−0.360894
$845$	11.6927	0.402241
$846$	10.2638	0.352878
$847$	0	0
$848$	−0.348640	−0.0119724
$849$	16.1528	0.554362
$850$	1.73616	0.0595499
$851$	2.49339	0.0854722
$852$	9.74095	0.333719
$853$	−57.3285	−1.96289	−0.981445	−	0.191743i	$-0.938586\pi$
$853$	−57.3285	−1.96289	−0.981445	+	0.191743i	$0.938586\pi$
$854$	−15.1777	−0.519371
$855$	−6.10547	−0.208803
$856$	0.268424	0.00917454
$857$	32.8463	1.12201	0.561004	−	0.827813i	$-0.310415\pi$
$857$	32.8463	1.12201	0.561004	+	0.827813i	$0.310415\pi$
$858$	0	0
$859$	24.3172	0.829693	0.414846	−	0.909891i	$-0.363835\pi$
$859$	24.3172	0.829693	0.414846	+	0.909891i	$0.363835\pi$
$860$	12.5854	0.429160
$861$	−5.09958	−0.173793
$862$	−25.2529	−0.860117
$863$	−2.59536	−0.0883470	−0.0441735	−	0.999024i	$-0.514065\pi$
$863$	−2.59536	−0.0883470	−0.0441735	+	0.999024i	$0.514065\pi$
$864$	−3.85182	−0.131042
$865$	−35.4520	−1.20541
$866$	−7.31865	−0.248698
$867$	9.33290	0.316962
$868$	5.43679	0.184537
$869$	0	0
$870$	−11.9341	−0.404603
$871$	22.1855	0.751726
$872$	1.61228	0.0545988
$873$	32.1633	1.08856
$874$	6.50318	0.219973
$875$	9.94408	0.336171
$876$	−5.82164	−0.196695
$877$	−20.3719	−0.687910	−0.343955	−	0.938986i	$-0.611767\pi$
$877$	−20.3719	−0.687910	−0.343955	+	0.938986i	$0.611767\pi$
$878$	8.02861	0.270952
$879$	−2.57909	−0.0869905
$880$	0	0
$881$	3.78366	0.127475	0.0637374	−	0.997967i	$-0.479698\pi$
$881$	3.78366	0.127475	0.0637374	+	0.997967i	$0.479698\pi$
$882$	−15.0696	−0.507420
$883$	−31.6886	−1.06641	−0.533203	−	0.845988i	$-0.679012\pi$
$883$	−31.6886	−1.06641	−0.533203	+	0.845988i	$0.679012\pi$
$884$	5.46410	0.183778
$885$	−2.76414	−0.0929156
$886$	33.0740	1.11114
$887$	42.0343	1.41137	0.705687	−	0.708523i	$-0.250638\pi$
$887$	42.0343	1.41137	0.705687	+	0.708523i	$0.250638\pi$
$888$	0.267949	0.00899179
$889$	16.0782	0.539244
$890$	−7.38389	−0.247508
$891$	0	0
$892$	23.0671	0.772342
$893$	−4.08658	−0.136752
$894$	8.96858	0.299954
$895$	18.3024	0.611783
$896$	−1.00000	−0.0334077
$897$	13.0064	0.434270
$898$	−8.93958	−0.298318
$899$	38.1922	1.27378
$900$	−2.28383	−0.0761276
$901$	0.665663	0.0221765
$902$	0	0
$903$	3.61817	0.120405
$904$	−9.13565	−0.303847
$905$	−0.861816	−0.0286477
$906$	5.71584	0.189896
$907$	−20.8469	−0.692211	−0.346106	−	0.938196i	$-0.612496\pi$
$907$	−20.8469	−0.692211	−0.346106	+	0.938196i	$0.612496\pi$
$908$	0.487299	0.0161716
$909$	15.7649	0.522889
$910$	−6.95681	−0.230616
$911$	−26.1538	−0.866513	−0.433257	−	0.901271i	$-0.642636\pi$
$911$	−26.1538	−0.866513	−0.433257	+	0.901271i	$0.642636\pi$
$912$	0.698857	0.0231415
$913$	0	0
$914$	−1.90520	−0.0630184
$915$	25.7848	0.852419
$916$	−29.2732	−0.967214
$917$	2.20046	0.0726656
$918$	7.35433	0.242729
$919$	−41.4222	−1.36639	−0.683196	−	0.730235i	$-0.739411\pi$
$919$	−41.4222	−1.36639	−0.683196	+	0.730235i	$0.739411\pi$
$920$	15.8086	0.521195
$921$	12.7089	0.418771
$922$	21.7813	0.717330
$923$	39.8891	1.31297
$924$	0	0
$925$	0.348640	0.0114632
$926$	36.0716	1.18539
$927$	40.0309	1.31479
$928$	−7.02477	−0.230600
$929$	35.8540	1.17633	0.588165	−	0.808741i	$-0.299850\pi$
$929$	35.8540	1.17633	0.588165	+	0.808741i	$0.299850\pi$
$930$	−9.23633	−0.302871
$931$	6.00000	0.196642
$932$	−22.4082	−0.734005
$933$	−21.2893	−0.696980
$934$	15.8955	0.520116
$935$	0	0
$936$	−7.18773	−0.234938
$937$	15.3764	0.502324	0.251162	−	0.967945i	$-0.419187\pi$
$937$	15.3764	0.502324	0.251162	+	0.967945i	$0.419187\pi$
$938$	7.75224	0.253120
$939$	8.02497	0.261885
$940$	−9.93409	−0.324014
$941$	−9.70010	−0.316214	−0.158107	−	0.987422i	$-0.550539\pi$
$941$	−9.70010	−0.316214	−0.158107	+	0.987422i	$0.550539\pi$
$942$	−6.54159	−0.213136
$943$	47.4539	1.54531
$944$	−1.62706	−0.0529563
$945$	−9.36342	−0.304592
$946$	0	0
$947$	−0.368148	−0.0119632	−0.00598161	−	0.999982i	$-0.501904\pi$
$947$	−0.368148	−0.0119632	−0.00598161	+	0.999982i	$0.501904\pi$
$948$	1.72095	0.0558940
$949$	−23.8396	−0.773865
$950$	0.909313	0.0295020
$951$	−12.3583	−0.400747
$952$	1.90931	0.0618812
$953$	−36.0925	−1.16915	−0.584575	−	0.811340i	$-0.698739\pi$
$953$	−36.0925	−1.16915	−0.584575	+	0.811340i	$0.698739\pi$
$954$	−0.875644	−0.0283500
$955$	14.3341	0.463839
$956$	11.6847	0.377912
$957$	0	0
$958$	−5.40799	−0.174724
$959$	8.08246	0.260996
$960$	1.69886	0.0548304
$961$	−1.44129	−0.0464934
$962$	1.09725	0.0353768
$963$	0.674173	0.0217249
$964$	−5.50571	−0.177327
$965$	31.3818	1.01022
$966$	4.54479	0.146226
$967$	−34.0953	−1.09643	−0.548216	−	0.836337i	$-0.684693\pi$
$967$	−34.0953	−1.09643	−0.548216	+	0.836337i	$0.684693\pi$
$968$	0	0
$969$	−1.33434	−0.0428651
$970$	−31.1300	−0.999523
$971$	−3.83183	−0.122969	−0.0614846	−	0.998108i	$-0.519584\pi$
$971$	−3.83183	−0.122969	−0.0614846	+	0.998108i	$0.519584\pi$
$972$	−14.9400	−0.479200
$973$	−0.161382	−0.00517367
$974$	17.5518	0.562395
$975$	1.81863	0.0582426
$976$	15.1777	0.485828
$977$	−3.59086	−0.114882	−0.0574408	−	0.998349i	$-0.518294\pi$
$977$	−3.59086	−0.114882	−0.0574408	+	0.998349i	$0.518294\pi$
$978$	−4.05305	−0.129602
$979$	0	0
$980$	14.5854	0.465915
$981$	4.04941	0.129288
$982$	1.28718	0.0410755
$983$	−46.3130	−1.47715	−0.738577	−	0.674169i	$-0.764502\pi$
$983$	−46.3130	−1.47715	−0.738577	+	0.674169i	$0.764502\pi$
$984$	5.09958	0.162569
$985$	53.5550	1.70640
$986$	13.4125	0.427141
$987$	−2.85593	−0.0909053
$988$	2.86182	0.0910465
$989$	−33.6687	−1.07060
$990$	0	0
$991$	−3.58292	−0.113815	−0.0569076	−	0.998379i	$-0.518124\pi$
$991$	−3.58292	−0.113815	−0.0569076	+	0.998379i	$0.518124\pi$
$992$	−5.43679	−0.172618
$993$	15.4644	0.490749
$994$	13.9384	0.442099
$995$	24.8523	0.787871
$996$	2.17439	0.0688981
$997$	24.0222	0.760789	0.380395	−	0.924824i	$-0.375788\pi$
$997$	24.0222	0.760789	0.380395	+	0.924824i	$0.375788\pi$
$998$	34.0586	1.07811
$999$	1.47683	0.0467248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bq.1.2	✓	4
11.10	odd	2		4598.2.a.bt.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bq.1.2	✓	4	1.1	even	1	trivial
4598.2.a.bt.1.2	yes	4	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +2.43091 q^{10} -0.698857 q^{12} -2.86182 q^{13} -1.00000 q^{14} +1.69886 q^{15} +1.00000 q^{16} -1.90931 q^{17} +2.51160 q^{18} -1.00000 q^{19} -2.43091 q^{20} -0.698857 q^{21} +6.50318 q^{23} +0.698857 q^{24} +0.909313 q^{25} +2.86182 q^{26} +3.85182 q^{27} +1.00000 q^{28} +7.02477 q^{29} -1.69886 q^{30} +5.43679 q^{31} -1.00000 q^{32} +1.90931 q^{34} -2.43091 q^{35} -2.51160 q^{36} +0.383411 q^{37} +1.00000 q^{38} +2.00000 q^{39} +2.43091 q^{40} +7.29703 q^{41} +0.698857 q^{42} -5.17726 q^{43} +6.10547 q^{45} -6.50318 q^{46} +4.08658 q^{47} -0.698857 q^{48} -6.00000 q^{49} -0.909313 q^{50} +1.33434 q^{51} -2.86182 q^{52} -0.348640 q^{53} -3.85182 q^{54} -1.00000 q^{56} +0.698857 q^{57} -7.02477 q^{58} -1.62706 q^{59} +1.69886 q^{60} +15.1777 q^{61} -5.43679 q^{62} -2.51160 q^{63} +1.00000 q^{64} +6.95681 q^{65} -7.75224 q^{67} -1.90931 q^{68} -4.54479 q^{69} +2.43091 q^{70} -13.9384 q^{71} +2.51160 q^{72} +8.33022 q^{73} -0.383411 q^{74} -0.635480 q^{75} -1.00000 q^{76} -2.00000 q^{78} -2.46253 q^{79} -2.43091 q^{80} +4.84293 q^{81} -7.29703 q^{82} -3.11135 q^{83} -0.698857 q^{84} +4.64136 q^{85} +5.17726 q^{86} -4.90931 q^{87} -3.03750 q^{89} -6.10547 q^{90} -2.86182 q^{91} +6.50318 q^{92} -3.79954 q^{93} -4.08658 q^{94} +2.43091 q^{95} +0.698857 q^{96} -12.8059 q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} - 2 q^{12} + 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 8 q^{23} + 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{30} - 4 q^{32} - 4 q^{34} - 2 q^{35} - 10 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 8 q^{45} + 8 q^{46} - 2 q^{48} - 24 q^{49} + 8 q^{50} + 4 q^{52} - 6 q^{53} + 14 q^{54} - 4 q^{56} + 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} + 2 q^{61} + 4 q^{64} + 20 q^{65} - 20 q^{67} + 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} + 10 q^{74} + 2 q^{75} - 4 q^{76} - 8 q^{78} - 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} + 34 q^{83} - 2 q^{84} + 16 q^{86} - 8 q^{87} - 2 q^{89} + 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} + 2 q^{95} + 2 q^{96} - 8 q^{97} + 24 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 - 2 * q^12 + 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 2 * q^21 - 8 * q^23 + 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 + 4 * q^28 - 2 * q^29 - 6 * q^30 - 4 * q^32 - 4 * q^34 - 2 * q^35 - 10 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^42 - 16 * q^43 - 8 * q^45 + 8 * q^46 - 2 * q^48 - 24 * q^49 + 8 * q^50 + 4 * q^52 - 6 * q^53 + 14 * q^54 - 4 * q^56 + 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 + 2 * q^61 + 4 * q^64 + 20 * q^65 - 20 * q^67 + 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 + 10 * q^74 + 2 * q^75 - 4 * q^76 - 8 * q^78 - 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 + 34 * q^83 - 2 * q^84 + 16 * q^86 - 8 * q^87 - 2 * q^89 + 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 + 2 * q^95 + 2 * q^96 - 8 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more