LMFDB - Embedded newform 4598.2.a.cd.1.1

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.84834$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.84834 q^{3} +1.00000 q^{4} -3.07094 q^{5} -2.84834 q^{6} +4.67138 q^{7} +1.00000 q^{8} +5.11302 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.84834 q^{3} +1.00000 q^{4} -3.07094 q^{5} -2.84834 q^{6} +4.67138 q^{7} +1.00000 q^{8} +5.11302 q^{9} -3.07094 q^{10} -2.84834 q^{12} +4.99002 q^{13} +4.67138 q^{14} +8.74708 q^{15} +1.00000 q^{16} +3.75667 q^{17} +5.11302 q^{18} +1.00000 q^{19} -3.07094 q^{20} -13.3056 q^{21} -2.62984 q^{23} -2.84834 q^{24} +4.43069 q^{25} +4.99002 q^{26} -6.01858 q^{27} +4.67138 q^{28} +6.95137 q^{29} +8.74708 q^{30} +7.18499 q^{31} +1.00000 q^{32} +3.75667 q^{34} -14.3455 q^{35} +5.11302 q^{36} -7.95048 q^{37} +1.00000 q^{38} -14.2133 q^{39} -3.07094 q^{40} -9.26244 q^{41} -13.3056 q^{42} +5.70910 q^{43} -15.7018 q^{45} -2.62984 q^{46} +4.27977 q^{47} -2.84834 q^{48} +14.8218 q^{49} +4.43069 q^{50} -10.7002 q^{51} +4.99002 q^{52} +4.53901 q^{53} -6.01858 q^{54} +4.67138 q^{56} -2.84834 q^{57} +6.95137 q^{58} -11.8004 q^{59} +8.74708 q^{60} -2.82280 q^{61} +7.18499 q^{62} +23.8848 q^{63} +1.00000 q^{64} -15.3241 q^{65} +0.750979 q^{67} +3.75667 q^{68} +7.49066 q^{69} -14.3455 q^{70} +2.29387 q^{71} +5.11302 q^{72} -9.81695 q^{73} -7.95048 q^{74} -12.6201 q^{75} +1.00000 q^{76} -14.2133 q^{78} +4.49931 q^{79} -3.07094 q^{80} +1.80390 q^{81} -9.26244 q^{82} -14.8553 q^{83} -13.3056 q^{84} -11.5365 q^{85} +5.70910 q^{86} -19.7998 q^{87} +2.22383 q^{89} -15.7018 q^{90} +23.3103 q^{91} -2.62984 q^{92} -20.4653 q^{93} +4.27977 q^{94} -3.07094 q^{95} -2.84834 q^{96} +4.25517 q^{97} +14.8218 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * 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
$3$	−2.84834	−1.64449	−0.822244	−	0.569135i	$-0.807278\pi$
$3$	−2.84834	−1.64449	−0.822244	+	0.569135i	$0.807278\pi$
$4$	1.00000	0.500000
$5$	−3.07094	−1.37337	−0.686684	−	0.726956i	$-0.740934\pi$
$5$	−3.07094	−1.37337	−0.686684	+	0.726956i	$0.740934\pi$
$6$	−2.84834	−1.16283
$7$	4.67138	1.76561	0.882807	−	0.469736i	$-0.155651\pi$
$7$	4.67138	1.76561	0.882807	+	0.469736i	$0.155651\pi$
$8$	1.00000	0.353553
$9$	5.11302	1.70434
$10$	−3.07094	−0.971117
$11$	0	0
$11$	0	0
$12$	−2.84834	−0.822244
$13$	4.99002	1.38398	0.691992	−	0.721906i	$-0.256734\pi$
$13$	4.99002	1.38398	0.691992	+	0.721906i	$0.256734\pi$
$14$	4.67138	1.24848
$15$	8.74708	2.25849
$16$	1.00000	0.250000
$17$	3.75667	0.911125	0.455563	−	0.890204i	$-0.349438\pi$
$17$	3.75667	0.911125	0.455563	+	0.890204i	$0.349438\pi$
$18$	5.11302	1.20515
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.07094	−0.686684
$21$	−13.3056	−2.90353
$22$	0	0
$23$	−2.62984	−0.548359	−0.274179	−	0.961679i	$-0.588406\pi$
$23$	−2.62984	−0.548359	−0.274179	+	0.961679i	$0.588406\pi$
$24$	−2.84834	−0.581414
$25$	4.43069	0.886138
$26$	4.99002	0.978624
$27$	−6.01858	−1.15828
$28$	4.67138	0.882807
$29$	6.95137	1.29084	0.645418	−	0.763829i	$-0.276683\pi$
$29$	6.95137	1.29084	0.645418	+	0.763829i	$0.276683\pi$
$30$	8.74708	1.59699
$31$	7.18499	1.29046	0.645231	−	0.763988i	$-0.276761\pi$
$31$	7.18499	1.29046	0.645231	+	0.763988i	$0.276761\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	3.75667	0.644263
$35$	−14.3455	−2.42484
$36$	5.11302	0.852170
$37$	−7.95048	−1.30705	−0.653525	−	0.756905i	$-0.726711\pi$
$37$	−7.95048	−1.30705	−0.653525	+	0.756905i	$0.726711\pi$
$38$	1.00000	0.162221
$39$	−14.2133	−2.27594
$40$	−3.07094	−0.485559
$41$	−9.26244	−1.44655	−0.723275	−	0.690560i	$-0.757364\pi$
$41$	−9.26244	−1.44655	−0.723275	+	0.690560i	$0.757364\pi$
$42$	−13.3056	−2.05311
$43$	5.70910	0.870629	0.435315	−	0.900278i	$-0.356637\pi$
$43$	5.70910	0.870629	0.435315	+	0.900278i	$0.356637\pi$
$44$	0	0
$45$	−15.7018	−2.34068
$46$	−2.62984	−0.387748
$47$	4.27977	0.624268	0.312134	−	0.950038i	$-0.398956\pi$
$47$	4.27977	0.624268	0.312134	+	0.950038i	$0.398956\pi$
$48$	−2.84834	−0.411122
$49$	14.8218	2.11739
$50$	4.43069	0.626594
$51$	−10.7002	−1.49833
$52$	4.99002	0.691992
$53$	4.53901	0.623481	0.311740	−	0.950167i	$-0.399088\pi$
$53$	4.53901	0.623481	0.311740	+	0.950167i	$0.399088\pi$
$54$	−6.01858	−0.819026
$55$	0	0
$56$	4.67138	0.624239
$57$	−2.84834	−0.377271
$58$	6.95137	0.912759
$59$	−11.8004	−1.53628	−0.768142	−	0.640280i	$-0.778818\pi$
$59$	−11.8004	−1.53628	−0.768142	+	0.640280i	$0.778818\pi$
$60$	8.74708	1.12924
$61$	−2.82280	−0.361422	−0.180711	−	0.983536i	$-0.557840\pi$
$61$	−2.82280	−0.361422	−0.180711	+	0.983536i	$0.557840\pi$
$62$	7.18499	0.912494
$63$	23.8848	3.00921
$64$	1.00000	0.125000
$65$	−15.3241	−1.90072
$66$	0	0
$67$	0.750979	0.0917467	0.0458733	−	0.998947i	$-0.485393\pi$
$67$	0.750979	0.0917467	0.0458733	+	0.998947i	$0.485393\pi$
$68$	3.75667	0.455563
$69$	7.49066	0.901769
$70$	−14.3455	−1.71462
$71$	2.29387	0.272232	0.136116	−	0.990693i	$-0.456538\pi$
$71$	2.29387	0.272232	0.136116	+	0.990693i	$0.456538\pi$
$72$	5.11302	0.602575
$73$	−9.81695	−1.14899	−0.574493	−	0.818509i	$-0.694801\pi$
$73$	−9.81695	−1.14899	−0.574493	+	0.818509i	$0.694801\pi$
$74$	−7.95048	−0.924224
$75$	−12.6201	−1.45724
$76$	1.00000	0.114708
$77$	0	0
$78$	−14.2133	−1.60933
$79$	4.49931	0.506212	0.253106	−	0.967439i	$-0.418548\pi$
$79$	4.49931	0.506212	0.253106	+	0.967439i	$0.418548\pi$
$80$	−3.07094	−0.343342
$81$	1.80390	0.200433
$82$	−9.26244	−1.02287
$83$	−14.8553	−1.63058	−0.815292	−	0.579050i	$-0.803424\pi$
$83$	−14.8553	−1.63058	−0.815292	+	0.579050i	$0.803424\pi$
$84$	−13.3056	−1.45177
$85$	−11.5365	−1.25131
$86$	5.70910	0.615628
$87$	−19.7998	−2.12276
$88$	0	0
$89$	2.22383	0.235725	0.117863	−	0.993030i	$-0.462396\pi$
$89$	2.22383	0.235725	0.117863	+	0.993030i	$0.462396\pi$
$90$	−15.7018	−1.65511
$91$	23.3103	2.44358
$92$	−2.62984	−0.274179
$93$	−20.4653	−2.12215
$94$	4.27977	0.441424
$95$	−3.07094	−0.315072
$96$	−2.84834	−0.290707
$97$	4.25517	0.432048	0.216024	−	0.976388i	$-0.430691\pi$
$97$	4.25517	0.432048	0.216024	+	0.976388i	$0.430691\pi$
$98$	14.8218	1.49722
$99$	0	0
$100$	4.43069	0.443069
$101$	2.98745	0.297262	0.148631	−	0.988893i	$-0.452513\pi$
$101$	2.98745	0.297262	0.148631	+	0.988893i	$0.452513\pi$
$102$	−10.7002	−1.05948
$103$	9.09704	0.896358	0.448179	−	0.893944i	$-0.352073\pi$
$103$	9.09704	0.896358	0.448179	+	0.893944i	$0.352073\pi$
$104$	4.99002	0.489312
$105$	40.8609	3.98761
$106$	4.53901	0.440868
$107$	−11.0024	−1.06364	−0.531821	−	0.846857i	$-0.678492\pi$
$107$	−11.0024	−1.06364	−0.531821	+	0.846857i	$0.678492\pi$
$108$	−6.01858	−0.579139
$109$	1.80676	0.173056	0.0865279	−	0.996249i	$-0.472423\pi$
$109$	1.80676	0.173056	0.0865279	+	0.996249i	$0.472423\pi$
$110$	0	0
$111$	22.6456	2.14943
$112$	4.67138	0.441404
$113$	9.85203	0.926801	0.463401	−	0.886149i	$-0.346629\pi$
$113$	9.85203	0.926801	0.463401	+	0.886149i	$0.346629\pi$
$114$	−2.84834	−0.266771
$115$	8.07608	0.753098
$116$	6.95137	0.645418
$117$	25.5141	2.35878
$118$	−11.8004	−1.08632
$119$	17.5488	1.60870
$120$	8.74708	0.798495
$121$	0	0
$122$	−2.82280	−0.255564
$123$	26.3826	2.37883
$124$	7.18499	0.645231
$125$	1.74832	0.156374
$126$	23.8848	2.12783
$127$	7.82848	0.694665	0.347333	−	0.937742i	$-0.387087\pi$
$127$	7.82848	0.694665	0.347333	+	0.937742i	$0.387087\pi$
$128$	1.00000	0.0883883
$129$	−16.2614	−1.43174
$130$	−15.3241	−1.34401
$131$	−11.1544	−0.974566	−0.487283	−	0.873244i	$-0.662012\pi$
$131$	−11.1544	−0.974566	−0.487283	+	0.873244i	$0.662012\pi$
$132$	0	0
$133$	4.67138	0.405060
$134$	0.750979	0.0648747
$135$	18.4827	1.59074
$136$	3.75667	0.322131
$137$	−3.77882	−0.322847	−0.161423	−	0.986885i	$-0.551608\pi$
$137$	−3.77882	−0.322847	−0.161423	+	0.986885i	$0.551608\pi$
$138$	7.49066	0.637647
$139$	4.40444	0.373579	0.186790	−	0.982400i	$-0.440192\pi$
$139$	4.40444	0.373579	0.186790	+	0.982400i	$0.440192\pi$
$140$	−14.3455	−1.21242
$141$	−12.1902	−1.02660
$142$	2.29387	0.192497
$143$	0	0
$144$	5.11302	0.426085
$145$	−21.3472	−1.77279
$146$	−9.81695	−0.812456
$147$	−42.2173	−3.48203
$148$	−7.95048	−0.653525
$149$	18.3826	1.50596	0.752980	−	0.658044i	$-0.228616\pi$
$149$	18.3826	1.50596	0.752980	+	0.658044i	$0.228616\pi$
$150$	−12.6201	−1.03043
$151$	7.57727	0.616630	0.308315	−	0.951284i	$-0.400235\pi$
$151$	7.57727	0.616630	0.308315	+	0.951284i	$0.400235\pi$
$152$	1.00000	0.0811107
$153$	19.2079	1.55287
$154$	0	0
$155$	−22.0647	−1.77228
$156$	−14.2133	−1.13797
$157$	−8.51114	−0.679263	−0.339631	−	0.940559i	$-0.610302\pi$
$157$	−8.51114	−0.679263	−0.339631	+	0.940559i	$0.610302\pi$
$158$	4.49931	0.357946
$159$	−12.9286	−1.02531
$160$	−3.07094	−0.242779
$161$	−12.2850	−0.968190
$162$	1.80390	0.141727
$163$	5.56483	0.435871	0.217936	−	0.975963i	$-0.430068\pi$
$163$	5.56483	0.435871	0.217936	+	0.975963i	$0.430068\pi$
$164$	−9.26244	−0.723275
$165$	0	0
$166$	−14.8553	−1.15300
$167$	10.0435	0.777192	0.388596	−	0.921408i	$-0.372960\pi$
$167$	10.0435	0.777192	0.388596	+	0.921408i	$0.372960\pi$
$168$	−13.3056	−1.02655
$169$	11.9003	0.915409
$170$	−11.5365	−0.884810
$171$	5.11302	0.391002
$172$	5.70910	0.435315
$173$	11.6411	0.885056	0.442528	−	0.896755i	$-0.354082\pi$
$173$	11.6411	0.885056	0.442528	+	0.896755i	$0.354082\pi$
$174$	−19.7998	−1.50102
$175$	20.6974	1.56458
$176$	0	0
$177$	33.6116	2.52640
$178$	2.22383	0.166683
$179$	7.79130	0.582349	0.291175	−	0.956670i	$-0.405954\pi$
$179$	7.79130	0.582349	0.291175	+	0.956670i	$0.405954\pi$
$180$	−15.7018	−1.17034
$181$	9.26925	0.688978	0.344489	−	0.938790i	$-0.388052\pi$
$181$	9.26925	0.688978	0.344489	+	0.938790i	$0.388052\pi$
$182$	23.3103	1.72787
$183$	8.04028	0.594354
$184$	−2.62984	−0.193874
$185$	24.4155	1.79506
$186$	−20.4653	−1.50059
$187$	0	0
$188$	4.27977	0.312134
$189$	−28.1151	−2.04507
$190$	−3.07094	−0.222790
$191$	11.6008	0.839404	0.419702	−	0.907662i	$-0.362135\pi$
$191$	11.6008	0.839404	0.419702	+	0.907662i	$0.362135\pi$
$192$	−2.84834	−0.205561
$193$	20.6890	1.48923	0.744613	−	0.667496i	$-0.232634\pi$
$193$	20.6890	1.48923	0.744613	+	0.667496i	$0.232634\pi$
$194$	4.25517	0.305504
$195$	43.6481	3.12571
$196$	14.8218	1.05870
$197$	−1.40065	−0.0997922	−0.0498961	−	0.998754i	$-0.515889\pi$
$197$	−1.40065	−0.0997922	−0.0498961	+	0.998754i	$0.515889\pi$
$198$	0	0
$199$	2.20887	0.156582	0.0782911	−	0.996931i	$-0.475054\pi$
$199$	2.20887	0.156582	0.0782911	+	0.996931i	$0.475054\pi$
$200$	4.43069	0.313297
$201$	−2.13904	−0.150876
$202$	2.98745	0.210196
$203$	32.4724	2.27912
$204$	−10.7002	−0.749167
$205$	28.4444	1.98665
$206$	9.09704	0.633821
$207$	−13.4464	−0.934589
$208$	4.99002	0.345996
$209$	0	0
$210$	40.8609	2.81967
$211$	−0.559992	−0.0385514	−0.0192757	−	0.999814i	$-0.506136\pi$
$211$	−0.559992	−0.0385514	−0.0192757	+	0.999814i	$0.506136\pi$
$212$	4.53901	0.311740
$213$	−6.53370	−0.447682
$214$	−11.0024	−0.752108
$215$	−17.5323	−1.19569
$216$	−6.01858	−0.409513
$217$	33.5638	2.27846
$218$	1.80676	0.122369
$219$	27.9620	1.88949
$220$	0	0
$221$	18.7458	1.26098
$222$	22.6456	1.51987
$223$	3.57681	0.239521	0.119760	−	0.992803i	$-0.461787\pi$
$223$	3.57681	0.239521	0.119760	+	0.992803i	$0.461787\pi$
$224$	4.67138	0.312119
$225$	22.6542	1.51028
$226$	9.85203	0.655347
$227$	−28.6832	−1.90377	−0.951884	−	0.306458i	$-0.900856\pi$
$227$	−28.6832	−1.90377	−0.951884	+	0.306458i	$0.900856\pi$
$228$	−2.84834	−0.188636
$229$	−22.9248	−1.51491	−0.757457	−	0.652885i	$-0.773558\pi$
$229$	−22.9248	−1.51491	−0.757457	+	0.652885i	$0.773558\pi$
$230$	8.07608	0.532521
$231$	0	0
$232$	6.95137	0.456380
$233$	7.12205	0.466581	0.233291	−	0.972407i	$-0.425051\pi$
$233$	7.12205	0.466581	0.233291	+	0.972407i	$0.425051\pi$
$234$	25.5141	1.66791
$235$	−13.1429	−0.857349
$236$	−11.8004	−0.768142
$237$	−12.8156	−0.832460
$238$	17.5488	1.13752
$239$	−0.888204	−0.0574531	−0.0287266	−	0.999587i	$-0.509145\pi$
$239$	−0.888204	−0.0574531	−0.0287266	+	0.999587i	$0.509145\pi$
$240$	8.74708	0.564621
$241$	−10.9451	−0.705036	−0.352518	−	0.935805i	$-0.614675\pi$
$241$	−10.9451	−0.705036	−0.352518	+	0.935805i	$0.614675\pi$
$242$	0	0
$243$	12.9176	0.828668
$244$	−2.82280	−0.180711
$245$	−45.5167	−2.90796
$246$	26.3826	1.68209
$247$	4.99002	0.317507
$248$	7.18499	0.456247
$249$	42.3130	2.68148
$250$	1.74832	0.110573
$251$	10.3872	0.655632	0.327816	−	0.944742i	$-0.393687\pi$
$251$	10.3872	0.655632	0.327816	+	0.944742i	$0.393687\pi$
$252$	23.8848	1.50460
$253$	0	0
$254$	7.82848	0.491202
$255$	32.8599	2.05776
$256$	1.00000	0.0625000
$257$	−9.66733	−0.603032	−0.301516	−	0.953461i	$-0.597493\pi$
$257$	−9.66733	−0.603032	−0.301516	+	0.953461i	$0.597493\pi$
$258$	−16.2614	−1.01239
$259$	−37.1397	−2.30775
$260$	−15.3241	−0.950359
$261$	35.5425	2.20002
$262$	−11.1544	−0.689122
$263$	0.176363	0.0108750	0.00543749	−	0.999985i	$-0.498269\pi$
$263$	0.176363	0.0108750	0.00543749	+	0.999985i	$0.498269\pi$
$264$	0	0
$265$	−13.9390	−0.856268
$266$	4.67138	0.286420
$267$	−6.33421	−0.387647
$268$	0.750979	0.0458733
$269$	2.78225	0.169637	0.0848184	−	0.996396i	$-0.472969\pi$
$269$	2.78225	0.169637	0.0848184	+	0.996396i	$0.472969\pi$
$270$	18.4827	1.12482
$271$	18.3175	1.11271	0.556354	−	0.830945i	$-0.312200\pi$
$271$	18.3175	1.11271	0.556354	+	0.830945i	$0.312200\pi$
$272$	3.75667	0.227781
$273$	−66.3955	−4.01844
$274$	−3.77882	−0.228287
$275$	0	0
$276$	7.49066	0.450885
$277$	−12.0440	−0.723654	−0.361827	−	0.932245i	$-0.617847\pi$
$277$	−12.0440	−0.723654	−0.361827	+	0.932245i	$0.617847\pi$
$278$	4.40444	0.264161
$279$	36.7370	2.19938
$280$	−14.3455	−0.857309
$281$	26.5858	1.58598	0.792989	−	0.609237i	$-0.208524\pi$
$281$	26.5858	1.58598	0.792989	+	0.609237i	$0.208524\pi$
$282$	−12.1902	−0.725916
$283$	−14.1473	−0.840971	−0.420485	−	0.907299i	$-0.638140\pi$
$283$	−14.1473	−0.840971	−0.420485	+	0.907299i	$0.638140\pi$
$284$	2.29387	0.136116
$285$	8.74708	0.518132
$286$	0	0
$287$	−43.2684	−2.55405
$288$	5.11302	0.301287
$289$	−2.88746	−0.169850
$290$	−21.3472	−1.25355
$291$	−12.1202	−0.710497
$292$	−9.81695	−0.574493
$293$	−7.43523	−0.434371	−0.217185	−	0.976130i	$-0.569688\pi$
$293$	−7.43523	−0.434371	−0.217185	+	0.976130i	$0.569688\pi$
$294$	−42.2173	−2.46216
$295$	36.2384	2.10988
$296$	−7.95048	−0.462112
$297$	0	0
$298$	18.3826	1.06487
$299$	−13.1229	−0.758919
$300$	−12.6201	−0.728621
$301$	26.6693	1.53719
$302$	7.57727	0.436023
$303$	−8.50925	−0.488844
$304$	1.00000	0.0573539
$305$	8.66865	0.496365
$306$	19.2079	1.09804
$307$	5.07736	0.289780	0.144890	−	0.989448i	$-0.453717\pi$
$307$	5.07736	0.289780	0.144890	+	0.989448i	$0.453717\pi$
$308$	0	0
$309$	−25.9114	−1.47405
$310$	−22.0647	−1.25319
$311$	18.2969	1.03752	0.518762	−	0.854919i	$-0.326393\pi$
$311$	18.2969	1.03752	0.518762	+	0.854919i	$0.326393\pi$
$312$	−14.2133	−0.804667
$313$	−16.3593	−0.924685	−0.462342	−	0.886701i	$-0.652991\pi$
$313$	−16.3593	−0.924685	−0.462342	+	0.886701i	$0.652991\pi$
$314$	−8.51114	−0.480311
$315$	−73.3489	−4.13274
$316$	4.49931	0.253106
$317$	3.04038	0.170765	0.0853824	−	0.996348i	$-0.472789\pi$
$317$	3.04038	0.170765	0.0853824	+	0.996348i	$0.472789\pi$
$318$	−12.9286	−0.725001
$319$	0	0
$320$	−3.07094	−0.171671
$321$	31.3385	1.74914
$322$	−12.2850	−0.684614
$323$	3.75667	0.209027
$324$	1.80390	0.100216
$325$	22.1092	1.22640
$326$	5.56483	0.308208
$327$	−5.14625	−0.284588
$328$	−9.26244	−0.511433
$329$	19.9924	1.10222
$330$	0	0
$331$	21.0508	1.15706	0.578528	−	0.815662i	$-0.303627\pi$
$331$	21.0508	1.15706	0.578528	+	0.815662i	$0.303627\pi$
$332$	−14.8553	−0.815292
$333$	−40.6509	−2.22766
$334$	10.0435	0.549558
$335$	−2.30621	−0.126002
$336$	−13.3056	−0.725883
$337$	−23.8526	−1.29934	−0.649668	−	0.760218i	$-0.725092\pi$
$337$	−23.8526	−1.29934	−0.649668	+	0.760218i	$0.725092\pi$
$338$	11.9003	0.647292
$339$	−28.0619	−1.52411
$340$	−11.5365	−0.625655
$341$	0	0
$342$	5.11302	0.276480
$343$	36.5383	1.97288
$344$	5.70910	0.307814
$345$	−23.0034	−1.23846
$346$	11.6411	0.625829
$347$	−5.25123	−0.281901	−0.140950	−	0.990017i	$-0.545016\pi$
$347$	−5.25123	−0.281901	−0.140950	+	0.990017i	$0.545016\pi$
$348$	−19.7998	−1.06138
$349$	24.3437	1.30309	0.651546	−	0.758610i	$-0.274121\pi$
$349$	24.3437	1.30309	0.651546	+	0.758610i	$0.274121\pi$
$350$	20.6974	1.10632
$351$	−30.0329	−1.60304
$352$	0	0
$353$	−32.3329	−1.72091	−0.860454	−	0.509529i	$-0.829820\pi$
$353$	−32.3329	−1.72091	−0.860454	+	0.509529i	$0.829820\pi$
$354$	33.6116	1.78643
$355$	−7.04433	−0.373874
$356$	2.22383	0.117863
$357$	−49.9849	−2.64548
$358$	7.79130	0.411783
$359$	−2.92296	−0.154268	−0.0771339	−	0.997021i	$-0.524577\pi$
$359$	−2.92296	−0.154268	−0.0771339	+	0.997021i	$0.524577\pi$
$360$	−15.7018	−0.827557
$361$	1.00000	0.0526316
$362$	9.26925	0.487181
$363$	0	0
$364$	23.3103	1.22179
$365$	30.1473	1.57798
$366$	8.04028	0.420272
$367$	−8.51869	−0.444672	−0.222336	−	0.974970i	$-0.571368\pi$
$367$	−8.51869	−0.444672	−0.222336	+	0.974970i	$0.571368\pi$
$368$	−2.62984	−0.137090
$369$	−47.3590	−2.46541
$370$	24.4155	1.26930
$371$	21.2034	1.10083
$372$	−20.4653	−1.06107
$373$	17.7978	0.921533	0.460767	−	0.887521i	$-0.347574\pi$
$373$	17.7978	0.921533	0.460767	+	0.887521i	$0.347574\pi$
$374$	0	0
$375$	−4.97980	−0.257156
$376$	4.27977	0.220712
$377$	34.6875	1.78650
$378$	−28.1151	−1.44608
$379$	−24.6959	−1.26854	−0.634272	−	0.773110i	$-0.718700\pi$
$379$	−24.6959	−1.26854	−0.634272	+	0.773110i	$0.718700\pi$
$380$	−3.07094	−0.157536
$381$	−22.2981	−1.14237
$382$	11.6008	0.593548
$383$	25.8795	1.32238	0.661191	−	0.750217i	$-0.270051\pi$
$383$	25.8795	1.32238	0.661191	+	0.750217i	$0.270051\pi$
$384$	−2.84834	−0.145354
$385$	0	0
$386$	20.6890	1.05304
$387$	29.1907	1.48385
$388$	4.25517	0.216024
$389$	−21.3500	−1.08249	−0.541245	−	0.840865i	$-0.682047\pi$
$389$	−21.3500	−1.08249	−0.541245	+	0.840865i	$0.682047\pi$
$390$	43.6481	2.21021
$391$	−9.87942	−0.499624
$392$	14.8218	0.748611
$393$	31.7715	1.60266
$394$	−1.40065	−0.0705637
$395$	−13.8171	−0.695215
$396$	0	0
$397$	−19.1973	−0.963486	−0.481743	−	0.876312i	$-0.659996\pi$
$397$	−19.1973	−0.963486	−0.481743	+	0.876312i	$0.659996\pi$
$398$	2.20887	0.110720
$399$	−13.3056	−0.666116
$400$	4.43069	0.221535
$401$	−26.4631	−1.32151	−0.660753	−	0.750604i	$-0.729763\pi$
$401$	−26.4631	−1.32151	−0.660753	+	0.750604i	$0.729763\pi$
$402$	−2.13904	−0.106686
$403$	35.8532	1.78598
$404$	2.98745	0.148631
$405$	−5.53966	−0.275268
$406$	32.4724	1.61158
$407$	0	0
$408$	−10.7002	−0.529741
$409$	−1.01714	−0.0502944	−0.0251472	−	0.999684i	$-0.508005\pi$
$409$	−1.01714	−0.0502944	−0.0251472	+	0.999684i	$0.508005\pi$
$410$	28.4444	1.40477
$411$	10.7634	0.530917
$412$	9.09704	0.448179
$413$	−55.1242	−2.71248
$414$	−13.4464	−0.660854
$415$	45.6199	2.23939
$416$	4.99002	0.244656
$417$	−12.5453	−0.614347
$418$	0	0
$419$	−21.4898	−1.04985	−0.524924	−	0.851149i	$-0.675906\pi$
$419$	−21.4898	−1.04985	−0.524924	+	0.851149i	$0.675906\pi$
$420$	40.8609	1.99381
$421$	−20.1741	−0.983228	−0.491614	−	0.870813i	$-0.663593\pi$
$421$	−20.1741	−0.983228	−0.491614	+	0.870813i	$0.663593\pi$
$422$	−0.559992	−0.0272600
$423$	21.8825	1.06396
$424$	4.53901	0.220434
$425$	16.6446	0.807383
$426$	−6.53370	−0.316559
$427$	−13.1863	−0.638132
$428$	−11.0024	−0.531821
$429$	0	0
$430$	−17.5323	−0.845483
$431$	−19.2766	−0.928520	−0.464260	−	0.885699i	$-0.653680\pi$
$431$	−19.2766	−0.928520	−0.464260	+	0.885699i	$0.653680\pi$
$432$	−6.01858	−0.289569
$433$	13.9062	0.668291	0.334145	−	0.942522i	$-0.391552\pi$
$433$	13.9062	0.668291	0.334145	+	0.942522i	$0.391552\pi$
$434$	33.5638	1.61111
$435$	60.8041	2.91534
$436$	1.80676	0.0865279
$437$	−2.62984	−0.125802
$438$	27.9620	1.33607
$439$	−22.7552	−1.08604	−0.543022	−	0.839718i	$-0.682720\pi$
$439$	−22.7552	−1.08604	−0.543022	+	0.839718i	$0.682720\pi$
$440$	0	0
$441$	75.7839	3.60876
$442$	18.7458	0.891649
$443$	17.9777	0.854147	0.427074	−	0.904217i	$-0.359544\pi$
$443$	17.9777	0.854147	0.427074	+	0.904217i	$0.359544\pi$
$444$	22.6456	1.07471
$445$	−6.82924	−0.323737
$446$	3.57681	0.169367
$447$	−52.3597	−2.47653
$448$	4.67138	0.220702
$449$	22.1893	1.04718	0.523588	−	0.851971i	$-0.324593\pi$
$449$	22.1893	1.04718	0.523588	+	0.851971i	$0.324593\pi$
$450$	22.6542	1.06793
$451$	0	0
$452$	9.85203	0.463401
$453$	−21.5826	−1.01404
$454$	−28.6832	−1.34617
$455$	−71.5845	−3.35593
$456$	−2.84834	−0.133386
$457$	32.4663	1.51871	0.759356	−	0.650676i	$-0.225514\pi$
$457$	32.4663	1.51871	0.759356	+	0.650676i	$0.225514\pi$
$458$	−22.9248	−1.07121
$459$	−22.6098	−1.05534
$460$	8.07608	0.376549
$461$	−17.0908	−0.795998	−0.397999	−	0.917386i	$-0.630295\pi$
$461$	−17.0908	−0.795998	−0.397999	+	0.917386i	$0.630295\pi$
$462$	0	0
$463$	11.6930	0.543421	0.271711	−	0.962379i	$-0.412411\pi$
$463$	11.6930	0.543421	0.271711	+	0.962379i	$0.412411\pi$
$464$	6.95137	0.322709
$465$	62.8476	2.91449
$466$	7.12205	0.329923
$467$	13.2058	0.611092	0.305546	−	0.952177i	$-0.401161\pi$
$467$	13.2058	0.611092	0.305546	+	0.952177i	$0.401161\pi$
$468$	25.5141	1.17939
$469$	3.50811	0.161989
$470$	−13.1429	−0.606237
$471$	24.2426	1.11704
$472$	−11.8004	−0.543158
$473$	0	0
$474$	−12.8156	−0.588638
$475$	4.43069	0.203294
$476$	17.5488	0.804348
$477$	23.2080	1.06262
$478$	−0.888204	−0.0406255
$479$	−2.85672	−0.130527	−0.0652634	−	0.997868i	$-0.520789\pi$
$479$	−2.85672	−0.130527	−0.0652634	+	0.997868i	$0.520789\pi$
$480$	8.74708	0.399248
$481$	−39.6730	−1.80894
$482$	−10.9451	−0.498536
$483$	34.9917	1.59218
$484$	0	0
$485$	−13.0674	−0.593360
$486$	12.9176	0.585956
$487$	39.3249	1.78198	0.890991	−	0.454021i	$-0.150011\pi$
$487$	39.3249	1.78198	0.890991	+	0.454021i	$0.150011\pi$
$488$	−2.82280	−0.127782
$489$	−15.8505	−0.716785
$490$	−45.5167	−2.05624
$491$	30.8491	1.39220	0.696099	−	0.717946i	$-0.254917\pi$
$491$	30.8491	1.39220	0.696099	+	0.717946i	$0.254917\pi$
$492$	26.3826	1.18942
$493$	26.1140	1.17611
$494$	4.99002	0.224512
$495$	0	0
$496$	7.18499	0.322615
$497$	10.7155	0.480656
$498$	42.3130	1.89609
$499$	27.7786	1.24354	0.621771	−	0.783199i	$-0.286413\pi$
$499$	27.7786	1.24354	0.621771	+	0.783199i	$0.286413\pi$
$500$	1.74832	0.0781872
$501$	−28.6074	−1.27808
$502$	10.3872	0.463602
$503$	6.08995	0.271538	0.135769	−	0.990741i	$-0.456650\pi$
$503$	6.08995	0.271538	0.135769	+	0.990741i	$0.456650\pi$
$504$	23.8848	1.06391
$505$	−9.17427	−0.408250
$506$	0	0
$507$	−33.8961	−1.50538
$508$	7.82848	0.347333
$509$	−16.4395	−0.728668	−0.364334	−	0.931268i	$-0.618703\pi$
$509$	−16.4395	−0.728668	−0.364334	+	0.931268i	$0.618703\pi$
$510$	32.8599	1.45506
$511$	−45.8587	−2.02867
$512$	1.00000	0.0441942
$513$	−6.01858	−0.265727
$514$	−9.66733	−0.426408
$515$	−27.9365	−1.23103
$516$	−16.2614	−0.715869
$517$	0	0
$518$	−37.1397	−1.63182
$519$	−33.1577	−1.45546
$520$	−15.3241	−0.672005
$521$	11.9116	0.521857	0.260929	−	0.965358i	$-0.415971\pi$
$521$	11.9116	0.521857	0.260929	+	0.965358i	$0.415971\pi$
$522$	35.5425	1.55565
$523$	−16.4150	−0.717776	−0.358888	−	0.933381i	$-0.616844\pi$
$523$	−16.4150	−0.717776	−0.358888	+	0.933381i	$0.616844\pi$
$524$	−11.1544	−0.487283
$525$	−58.9532	−2.57293
$526$	0.176363	0.00768977
$527$	26.9916	1.17577
$528$	0	0
$529$	−16.0840	−0.699303
$530$	−13.9390	−0.605473
$531$	−60.3357	−2.61835
$532$	4.67138	0.202530
$533$	−46.2198	−2.00200
$534$	−6.33421	−0.274108
$535$	33.7877	1.46077
$536$	0.750979	0.0324374
$537$	−22.1922	−0.957666
$538$	2.78225	0.119951
$539$	0	0
$540$	18.4827	0.795370
$541$	11.0149	0.473568	0.236784	−	0.971562i	$-0.423907\pi$
$541$	11.0149	0.473568	0.236784	+	0.971562i	$0.423907\pi$
$542$	18.3175	0.786803
$543$	−26.4019	−1.13302
$544$	3.75667	0.161066
$545$	−5.54844	−0.237669
$546$	−66.3955	−2.84146
$547$	23.6489	1.01115	0.505577	−	0.862781i	$-0.331280\pi$
$547$	23.6489	1.01115	0.505577	+	0.862781i	$0.331280\pi$
$548$	−3.77882	−0.161423
$549$	−14.4330	−0.615986
$550$	0	0
$551$	6.95137	0.296138
$552$	7.49066	0.318824
$553$	21.0180	0.893775
$554$	−12.0440	−0.511700
$555$	−69.5434	−2.95195
$556$	4.40444	0.186790
$557$	−17.3985	−0.737199	−0.368600	−	0.929588i	$-0.620163\pi$
$557$	−17.3985	−0.737199	−0.368600	+	0.929588i	$0.620163\pi$
$558$	36.7370	1.55520
$559$	28.4885	1.20494
$560$	−14.3455	−0.606209
$561$	0	0
$562$	26.5858	1.12146
$563$	6.81924	0.287397	0.143698	−	0.989622i	$-0.454101\pi$
$563$	6.81924	0.287397	0.143698	+	0.989622i	$0.454101\pi$
$564$	−12.1902	−0.513300
$565$	−30.2550	−1.27284
$566$	−14.1473	−0.594656
$567$	8.42668	0.353887
$568$	2.29387	0.0962485
$569$	−39.2455	−1.64526	−0.822628	−	0.568580i	$-0.807493\pi$
$569$	−39.2455	−1.64526	−0.822628	+	0.568580i	$0.807493\pi$
$570$	8.74708	0.366375
$571$	41.1842	1.72351	0.861753	−	0.507327i	$-0.169367\pi$
$571$	41.1842	1.72351	0.861753	+	0.507327i	$0.169367\pi$
$572$	0	0
$573$	−33.0430	−1.38039
$574$	−43.2684	−1.80599
$575$	−11.6520	−0.485922
$576$	5.11302	0.213042
$577$	−31.1157	−1.29536	−0.647681	−	0.761912i	$-0.724261\pi$
$577$	−31.1157	−1.29536	−0.647681	+	0.761912i	$0.724261\pi$
$578$	−2.88746	−0.120102
$579$	−58.9292	−2.44901
$580$	−21.3472	−0.886396
$581$	−69.3948	−2.87898
$582$	−12.1202	−0.502397
$583$	0	0
$584$	−9.81695	−0.406228
$585$	−78.3522	−3.23947
$586$	−7.43523	−0.307147
$587$	23.0239	0.950300	0.475150	−	0.879905i	$-0.342394\pi$
$587$	23.0239	0.950300	0.475150	+	0.879905i	$0.342394\pi$
$588$	−42.2173	−1.74101
$589$	7.18499	0.296052
$590$	36.2384	1.49191
$591$	3.98952	0.164107
$592$	−7.95048	−0.326763
$593$	−37.0616	−1.52194	−0.760969	−	0.648788i	$-0.775276\pi$
$593$	−37.0616	−1.52194	−0.760969	+	0.648788i	$0.775276\pi$
$594$	0	0
$595$	−53.8914	−2.20933
$596$	18.3826	0.752980
$597$	−6.29159	−0.257498
$598$	−13.1229	−0.536637
$599$	48.0895	1.96489	0.982443	−	0.186566i	$-0.0597357\pi$
$599$	48.0895	1.96489	0.982443	+	0.186566i	$0.0597357\pi$
$600$	−12.6201	−0.515213
$601$	10.6038	0.432539	0.216269	−	0.976334i	$-0.430611\pi$
$601$	10.6038	0.432539	0.216269	+	0.976334i	$0.430611\pi$
$602$	26.6693	1.08696
$603$	3.83977	0.156367
$604$	7.57727	0.308315
$605$	0	0
$606$	−8.50925	−0.345665
$607$	41.3219	1.67720	0.838601	−	0.544746i	$-0.183374\pi$
$607$	41.3219	1.67720	0.838601	+	0.544746i	$0.183374\pi$
$608$	1.00000	0.0405554
$609$	−92.4924	−3.74798
$610$	8.66865	0.350983
$611$	21.3561	0.863976
$612$	19.2079	0.776433
$613$	−45.4527	−1.83582	−0.917909	−	0.396790i	$-0.870124\pi$
$613$	−45.4527	−1.83582	−0.917909	+	0.396790i	$0.870124\pi$
$614$	5.07736	0.204906
$615$	−81.0193	−3.26701
$616$	0	0
$617$	25.1547	1.01269	0.506345	−	0.862331i	$-0.330996\pi$
$617$	25.1547	1.01269	0.506345	+	0.862331i	$0.330996\pi$
$618$	−25.9114	−1.04231
$619$	2.01720	0.0810782	0.0405391	−	0.999178i	$-0.487092\pi$
$619$	2.01720	0.0810782	0.0405391	+	0.999178i	$0.487092\pi$
$620$	−22.0647	−0.886139
$621$	15.8279	0.635151
$622$	18.2969	0.733641
$623$	10.3883	0.416200
$624$	−14.2133	−0.568986
$625$	−27.5224	−1.10090
$626$	−16.3593	−0.653851
$627$	0	0
$628$	−8.51114	−0.339631
$629$	−29.8673	−1.19089
$630$	−73.3489	−2.92229
$631$	−6.98652	−0.278129	−0.139064	−	0.990283i	$-0.544410\pi$
$631$	−6.98652	−0.278129	−0.139064	+	0.990283i	$0.544410\pi$
$632$	4.49931	0.178973
$633$	1.59505	0.0633974
$634$	3.04038	0.120749
$635$	−24.0408	−0.954030
$636$	−12.9286	−0.512653
$637$	73.9609	2.93044
$638$	0	0
$639$	11.7286	0.463975
$640$	−3.07094	−0.121390
$641$	−33.8595	−1.33737	−0.668685	−	0.743546i	$-0.733143\pi$
$641$	−33.8595	−1.33737	−0.668685	+	0.743546i	$0.733143\pi$
$642$	31.3385	1.23683
$643$	13.6200	0.537122	0.268561	−	0.963263i	$-0.413452\pi$
$643$	13.6200	0.537122	0.268561	+	0.963263i	$0.413452\pi$
$644$	−12.2850	−0.484095
$645$	49.9379	1.96630
$646$	3.75667	0.147804
$647$	−29.8807	−1.17473	−0.587366	−	0.809322i	$-0.699835\pi$
$647$	−29.8807	−1.17473	−0.587366	+	0.809322i	$0.699835\pi$
$648$	1.80390	0.0708637
$649$	0	0
$650$	22.1092	0.867196
$651$	−95.6009	−3.74689
$652$	5.56483	0.217936
$653$	4.17720	0.163466	0.0817332	−	0.996654i	$-0.473954\pi$
$653$	4.17720	0.163466	0.0817332	+	0.996654i	$0.473954\pi$
$654$	−5.14625	−0.201234
$655$	34.2546	1.33844
$656$	−9.26244	−0.361638
$657$	−50.1942	−1.95826
$658$	19.9924	0.779385
$659$	−20.8496	−0.812183	−0.406092	−	0.913832i	$-0.633109\pi$
$659$	−20.8496	−0.812183	−0.406092	+	0.913832i	$0.633109\pi$
$660$	0	0
$661$	14.8506	0.577620	0.288810	−	0.957386i	$-0.406740\pi$
$661$	14.8506	0.577620	0.288810	+	0.957386i	$0.406740\pi$
$662$	21.0508	0.818163
$663$	−53.3945	−2.07367
$664$	−14.8553	−0.576499
$665$	−14.3455	−0.556296
$666$	−40.6509	−1.57519
$667$	−18.2810	−0.707841
$668$	10.0435	0.388596
$669$	−10.1880	−0.393889
$670$	−2.30621	−0.0890968
$671$	0	0
$672$	−13.3056	−0.513276
$673$	−3.75594	−0.144781	−0.0723905	−	0.997376i	$-0.523063\pi$
$673$	−3.75594	−0.144781	−0.0723905	+	0.997376i	$0.523063\pi$
$674$	−23.8526	−0.918770
$675$	−26.6665	−1.02639
$676$	11.9003	0.457704
$677$	−18.3727	−0.706119	−0.353060	−	0.935601i	$-0.614859\pi$
$677$	−18.3727	−0.706119	−0.353060	+	0.935601i	$0.614859\pi$
$678$	−28.0619	−1.07771
$679$	19.8775	0.762829
$680$	−11.5365	−0.442405
$681$	81.6993	3.13072
$682$	0	0
$683$	22.9763	0.879164	0.439582	−	0.898202i	$-0.355127\pi$
$683$	22.9763	0.879164	0.439582	+	0.898202i	$0.355127\pi$
$684$	5.11302	0.195501
$685$	11.6046	0.443387
$686$	36.5383	1.39504
$687$	65.2976	2.49126
$688$	5.70910	0.217657
$689$	22.6498	0.862887
$690$	−23.0034	−0.875724
$691$	−42.5832	−1.61994	−0.809970	−	0.586472i	$-0.800517\pi$
$691$	−42.5832	−1.61994	−0.809970	+	0.586472i	$0.800517\pi$
$692$	11.6411	0.442528
$693$	0	0
$694$	−5.25123	−0.199334
$695$	−13.5258	−0.513062
$696$	−19.7998	−0.750510
$697$	−34.7959	−1.31799
$698$	24.3437	0.921425
$699$	−20.2860	−0.767287
$700$	20.6974	0.782289
$701$	32.8825	1.24195	0.620977	−	0.783829i	$-0.286736\pi$
$701$	32.8825	1.24195	0.620977	+	0.783829i	$0.286736\pi$
$702$	−30.0329	−1.13352
$703$	−7.95048	−0.299858
$704$	0	0
$705$	37.4354	1.40990
$706$	−32.3329	−1.21687
$707$	13.9555	0.524850
$708$	33.6116	1.26320
$709$	28.5840	1.07349	0.536747	−	0.843743i	$-0.319653\pi$
$709$	28.5840	1.07349	0.536747	+	0.843743i	$0.319653\pi$
$710$	−7.04433	−0.264369
$711$	23.0051	0.862757
$712$	2.22383	0.0833414
$713$	−18.8953	−0.707636
$714$	−49.9849	−1.87064
$715$	0	0
$716$	7.79130	0.291175
$717$	2.52990	0.0944810
$718$	−2.92296	−0.109084
$719$	36.6527	1.36692	0.683458	−	0.729990i	$-0.260475\pi$
$719$	36.6527	1.36692	0.683458	+	0.729990i	$0.260475\pi$
$720$	−15.7018	−0.585171
$721$	42.4957	1.58262
$722$	1.00000	0.0372161
$723$	31.1753	1.15942
$724$	9.26925	0.344489
$725$	30.7994	1.14386
$726$	0	0
$727$	26.2284	0.972758	0.486379	−	0.873748i	$-0.338317\pi$
$727$	26.2284	0.972758	0.486379	+	0.873748i	$0.338317\pi$
$728$	23.3103	0.863936
$729$	−42.2055	−1.56317
$730$	30.1473	1.11580
$731$	21.4472	0.793252
$732$	8.04028	0.297177
$733$	7.21028	0.266318	0.133159	−	0.991095i	$-0.457488\pi$
$733$	7.21028	0.266318	0.133159	+	0.991095i	$0.457488\pi$
$734$	−8.51869	−0.314431
$735$	129.647	4.78210
$736$	−2.62984	−0.0969370
$737$	0	0
$738$	−47.3590	−1.74331
$739$	31.1485	1.14582	0.572909	−	0.819619i	$-0.305815\pi$
$739$	31.1485	1.14582	0.572909	+	0.819619i	$0.305815\pi$
$740$	24.4155	0.897530
$741$	−14.2133	−0.522137
$742$	21.2034	0.778402
$743$	5.26583	0.193184	0.0965922	−	0.995324i	$-0.469206\pi$
$743$	5.26583	0.193184	0.0965922	+	0.995324i	$0.469206\pi$
$744$	−20.4653	−0.750293
$745$	−56.4518	−2.06824
$746$	17.7978	0.651622
$747$	−75.9556	−2.77907
$748$	0	0
$749$	−51.3963	−1.87798
$750$	−4.97980	−0.181836
$751$	−43.9606	−1.60414	−0.802072	−	0.597227i	$-0.796269\pi$
$751$	−43.9606	−1.60414	−0.802072	+	0.597227i	$0.796269\pi$
$752$	4.27977	0.156067
$753$	−29.5861	−1.07818
$754$	34.6875	1.26324
$755$	−23.2694	−0.846859
$756$	−28.1151	−1.02254
$757$	25.2216	0.916693	0.458347	−	0.888774i	$-0.348442\pi$
$757$	25.2216	0.916693	0.458347	+	0.888774i	$0.348442\pi$
$758$	−24.6959	−0.896996
$759$	0	0
$760$	−3.07094	−0.111395
$761$	−32.1203	−1.16436	−0.582181	−	0.813060i	$-0.697800\pi$
$761$	−32.1203	−1.16436	−0.582181	+	0.813060i	$0.697800\pi$
$762$	−22.2981	−0.807776
$763$	8.44003	0.305550
$764$	11.6008	0.419702
$765$	−58.9864	−2.13266
$766$	25.8795	0.935066
$767$	−58.8843	−2.12619
$768$	−2.84834	−0.102780
$769$	18.3016	0.659972	0.329986	−	0.943986i	$-0.392956\pi$
$769$	18.3016	0.659972	0.329986	+	0.943986i	$0.392956\pi$
$770$	0	0
$771$	27.5358	0.991678
$772$	20.6890	0.744613
$773$	36.6563	1.31843	0.659217	−	0.751953i	$-0.270888\pi$
$773$	36.6563	1.31843	0.659217	+	0.751953i	$0.270888\pi$
$774$	29.1907	1.04924
$775$	31.8345	1.14353
$776$	4.25517	0.152752
$777$	105.786	3.79506
$778$	−21.3500	−0.765436
$779$	−9.26244	−0.331862
$780$	43.6481	1.56285
$781$	0	0
$782$	−9.87942	−0.353287
$783$	−41.8374	−1.49515
$784$	14.8218	0.529348
$785$	26.1372	0.932877
$786$	31.7715	1.13325
$787$	−0.0673841	−0.00240199	−0.00120099	−	0.999999i	$-0.500382\pi$
$787$	−0.0673841	−0.00240199	−0.00120099	+	0.999999i	$0.500382\pi$
$788$	−1.40065	−0.0498961
$789$	−0.502340	−0.0178838
$790$	−13.8171	−0.491592
$791$	46.0225	1.63637
$792$	0	0
$793$	−14.0858	−0.500202
$794$	−19.1973	−0.681288
$795$	39.7031	1.40812
$796$	2.20887	0.0782911
$797$	31.9422	1.13145	0.565725	−	0.824594i	$-0.308596\pi$
$797$	31.9422	1.13145	0.565725	+	0.824594i	$0.308596\pi$
$798$	−13.3056	−0.471015
$799$	16.0777	0.568786
$800$	4.43069	0.156649
$801$	11.3705	0.401756
$802$	−26.4631	−0.934445
$803$	0	0
$804$	−2.13904	−0.0754381
$805$	37.7264	1.32968
$806$	35.8532	1.26288
$807$	−7.92479	−0.278966
$808$	2.98745	0.105098
$809$	−33.3982	−1.17422	−0.587109	−	0.809508i	$-0.699734\pi$
$809$	−33.3982	−1.17422	−0.587109	+	0.809508i	$0.699734\pi$
$810$	−5.53966	−0.194644
$811$	−25.1960	−0.884751	−0.442375	−	0.896830i	$-0.645864\pi$
$811$	−25.1960	−0.884751	−0.442375	+	0.896830i	$0.645864\pi$
$812$	32.4724	1.13956
$813$	−52.1743	−1.82983
$814$	0	0
$815$	−17.0893	−0.598611
$816$	−10.7002	−0.374584
$817$	5.70910	0.199736
$818$	−1.01714	−0.0355635
$819$	119.186	4.16469
$820$	28.4444	0.993323
$821$	−16.6144	−0.579847	−0.289924	−	0.957050i	$-0.593630\pi$
$821$	−16.6144	−0.579847	−0.289924	+	0.957050i	$0.593630\pi$
$822$	10.7634	0.375415
$823$	56.3263	1.96341	0.981705	−	0.190408i	$-0.0609812\pi$
$823$	56.3263	1.96341	0.981705	+	0.190408i	$0.0609812\pi$
$824$	9.09704	0.316910
$825$	0	0
$826$	−55.1242	−1.91802
$827$	−28.9988	−1.00839	−0.504194	−	0.863590i	$-0.668210\pi$
$827$	−28.9988	−1.00839	−0.504194	+	0.863590i	$0.668210\pi$
$828$	−13.4464	−0.467295
$829$	−19.3896	−0.673427	−0.336714	−	0.941607i	$-0.609315\pi$
$829$	−19.3896	−0.673427	−0.336714	+	0.941607i	$0.609315\pi$
$830$	45.6199	1.58349
$831$	34.3053	1.19004
$832$	4.99002	0.172998
$833$	55.6804	1.92921
$834$	−12.5453	−0.434409
$835$	−30.8431	−1.06737
$836$	0	0
$837$	−43.2434	−1.49471
$838$	−21.4898	−0.742354
$839$	7.11876	0.245767	0.122883	−	0.992421i	$-0.460786\pi$
$839$	7.11876	0.245767	0.122883	+	0.992421i	$0.460786\pi$
$840$	40.8609	1.40983
$841$	19.3215	0.666258
$842$	−20.1741	−0.695247
$843$	−75.7253	−2.60812
$844$	−0.559992	−0.0192757
$845$	−36.5452	−1.25719
$846$	21.8825	0.752336
$847$	0	0
$848$	4.53901	0.155870
$849$	40.2963	1.38297
$850$	16.6446	0.570906
$851$	20.9084	0.716732
$852$	−6.53370	−0.223841
$853$	−22.8765	−0.783276	−0.391638	−	0.920119i	$-0.628091\pi$
$853$	−22.8765	−0.783276	−0.391638	+	0.920119i	$0.628091\pi$
$854$	−13.1863	−0.451228
$855$	−15.7018	−0.536990
$856$	−11.0024	−0.376054
$857$	−37.1958	−1.27059	−0.635293	−	0.772271i	$-0.719121\pi$
$857$	−37.1958	−1.27059	−0.635293	+	0.772271i	$0.719121\pi$
$858$	0	0
$859$	−37.3580	−1.27464	−0.637319	−	0.770600i	$-0.719956\pi$
$859$	−37.3580	−1.27464	−0.637319	+	0.770600i	$0.719956\pi$
$860$	−17.5323	−0.597847
$861$	123.243	4.20010
$862$	−19.2766	−0.656563
$863$	26.3380	0.896557	0.448278	−	0.893894i	$-0.352037\pi$
$863$	26.3380	0.896557	0.448278	+	0.893894i	$0.352037\pi$
$864$	−6.01858	−0.204756
$865$	−35.7491	−1.21551
$866$	13.9062	0.472553
$867$	8.22445	0.279317
$868$	33.5638	1.13923
$869$	0	0
$870$	60.8041	2.06145
$871$	3.74740	0.126976
$872$	1.80676	0.0611845
$873$	21.7568	0.736356
$874$	−2.62984	−0.0889555
$875$	8.16705	0.276097
$876$	27.9620	0.944747
$877$	10.4497	0.352861	0.176431	−	0.984313i	$-0.443545\pi$
$877$	10.4497	0.352861	0.176431	+	0.984313i	$0.443545\pi$
$878$	−22.7552	−0.767950
$879$	21.1780	0.714317
$880$	0	0
$881$	10.9831	0.370029	0.185015	−	0.982736i	$-0.440767\pi$
$881$	10.9831	0.370029	0.185015	+	0.982736i	$0.440767\pi$
$882$	75.7839	2.55178
$883$	−43.0840	−1.44989	−0.724946	−	0.688806i	$-0.758135\pi$
$883$	−43.0840	−1.44989	−0.724946	+	0.688806i	$0.758135\pi$
$884$	18.7458	0.630491
$885$	−103.219	−3.46967
$886$	17.9777	0.603973
$887$	−27.0696	−0.908907	−0.454453	−	0.890770i	$-0.650165\pi$
$887$	−27.0696	−0.908907	−0.454453	+	0.890770i	$0.650165\pi$
$888$	22.6456	0.759937
$889$	36.5698	1.22651
$890$	−6.82924	−0.228917
$891$	0	0
$892$	3.57681	0.119760
$893$	4.27977	0.143217
$894$	−52.3597	−1.75117
$895$	−23.9266	−0.799780
$896$	4.67138	0.156060
$897$	37.3785	1.24803
$898$	22.1893	0.740466
$899$	49.9455	1.66577
$900$	22.6542	0.755140
$901$	17.0515	0.568069
$902$	0	0
$903$	−75.9632	−2.52790
$904$	9.85203	0.327674
$905$	−28.4653	−0.946220
$906$	−21.5826	−0.717035
$907$	41.3843	1.37414	0.687072	−	0.726590i	$-0.258896\pi$
$907$	41.3843	1.37414	0.687072	+	0.726590i	$0.258896\pi$
$908$	−28.6832	−0.951884
$909$	15.2749	0.506635
$910$	−71.5845	−2.37300
$911$	−16.7320	−0.554356	−0.277178	−	0.960819i	$-0.589399\pi$
$911$	−16.7320	−0.554356	−0.277178	+	0.960819i	$0.589399\pi$
$912$	−2.84834	−0.0943178
$913$	0	0
$914$	32.4663	1.07389
$915$	−24.6912	−0.816267
$916$	−22.9248	−0.757457
$917$	−52.1065	−1.72071
$918$	−22.6098	−0.746235
$919$	−45.0748	−1.48688	−0.743440	−	0.668802i	$-0.766807\pi$
$919$	−45.0748	−1.48688	−0.743440	+	0.668802i	$0.766807\pi$
$920$	8.07608	0.266260
$921$	−14.4620	−0.476540
$922$	−17.0908	−0.562856
$923$	11.4464	0.376764
$924$	0	0
$925$	−35.2261	−1.15823
$926$	11.6930	0.384257
$927$	46.5133	1.52770
$928$	6.95137	0.228190
$929$	−30.9057	−1.01398	−0.506991	−	0.861951i	$-0.669242\pi$
$929$	−30.9057	−1.01398	−0.506991	+	0.861951i	$0.669242\pi$
$930$	62.8476	2.06086
$931$	14.8218	0.485763
$932$	7.12205	0.233291
$933$	−52.1158	−1.70620
$934$	13.2058	0.432107
$935$	0	0
$936$	25.5141	0.833953
$937$	46.0884	1.50564	0.752822	−	0.658225i	$-0.228692\pi$
$937$	46.0884	1.50564	0.752822	+	0.658225i	$0.228692\pi$
$938$	3.50811	0.114544
$939$	46.5969	1.52063
$940$	−13.1429	−0.428675
$941$	−6.62700	−0.216034	−0.108017	−	0.994149i	$-0.534450\pi$
$941$	−6.62700	−0.216034	−0.108017	+	0.994149i	$0.534450\pi$
$942$	24.2426	0.789866
$943$	24.3587	0.793229
$944$	−11.8004	−0.384071
$945$	86.3398	2.80863
$946$	0	0
$947$	−31.8512	−1.03502	−0.517512	−	0.855676i	$-0.673142\pi$
$947$	−31.8512	−1.03502	−0.517512	+	0.855676i	$0.673142\pi$
$948$	−12.8156	−0.416230
$949$	−48.9868	−1.59018
$950$	4.43069	0.143751
$951$	−8.66003	−0.280821
$952$	17.5488	0.568760
$953$	54.7163	1.77243	0.886217	−	0.463270i	$-0.153324\pi$
$953$	54.7163	1.77243	0.886217	+	0.463270i	$0.153324\pi$
$954$	23.2080	0.751388
$955$	−35.6254	−1.15281
$956$	−0.888204	−0.0287266
$957$	0	0
$958$	−2.85672	−0.0922964
$959$	−17.6523	−0.570023
$960$	8.74708	0.282311
$961$	20.6240	0.665291
$962$	−39.6730	−1.27911
$963$	−56.2554	−1.81281
$964$	−10.9451	−0.352518
$965$	−63.5347	−2.04525
$966$	34.9917	1.12584
$967$	19.0229	0.611734	0.305867	−	0.952074i	$-0.401054\pi$
$967$	19.0229	0.611734	0.305867	+	0.952074i	$0.401054\pi$
$968$	0	0
$969$	−10.7002	−0.343742
$970$	−13.0674	−0.419569
$971$	15.9817	0.512876	0.256438	−	0.966561i	$-0.417451\pi$
$971$	15.9817	0.512876	0.256438	+	0.966561i	$0.417451\pi$
$972$	12.9176	0.414334
$973$	20.5748	0.659597
$974$	39.3249	1.26005
$975$	−62.9745	−2.01680
$976$	−2.82280	−0.0903556
$977$	54.7668	1.75215	0.876073	−	0.482179i	$-0.160154\pi$
$977$	54.7668	1.75215	0.876073	+	0.482179i	$0.160154\pi$
$978$	−15.8505	−0.506843
$979$	0	0
$980$	−45.5167	−1.45398
$981$	9.23797	0.294946
$982$	30.8491	0.984433
$983$	−9.28744	−0.296223	−0.148112	−	0.988971i	$-0.547320\pi$
$983$	−9.28744	−0.296223	−0.148112	+	0.988971i	$0.547320\pi$
$984$	26.3826	0.841045
$985$	4.30132	0.137051
$986$	26.1140	0.831638
$987$	−56.9450	−1.81258
$988$	4.99002	0.158754
$989$	−15.0140	−0.477417
$990$	0	0
$991$	32.9413	1.04641	0.523207	−	0.852206i	$-0.324735\pi$
$991$	32.9413	1.04641	0.523207	+	0.852206i	$0.324735\pi$
$992$	7.18499	0.228124
$993$	−59.9597	−1.90277
$994$	10.7155	0.339875
$995$	−6.78330	−0.215045
$996$	42.3130	1.34074
$997$	24.7269	0.783109	0.391554	−	0.920155i	$-0.371937\pi$
$997$	24.7269	0.783109	0.391554	+	0.920155i	$0.371937\pi$
$998$	27.7786	0.879318
$999$	47.8506	1.51393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.1		10
11.7	odd	10		418.2.f.h.115.5	✓	20
11.8	odd	10		418.2.f.h.229.5	yes	20
11.10	odd	2		4598.2.a.cc.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.5	✓	20	11.7	odd	10
418.2.f.h.229.5	yes	20	11.8	odd	10
4598.2.a.cc.1.1		10	11.10	odd	2
4598.2.a.cd.1.1		10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.84834 q^{3} +1.00000 q^{4} -3.07094 q^{5} -2.84834 q^{6} +4.67138 q^{7} +1.00000 q^{8} +5.11302 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.84834 q^{3} +1.00000 q^{4} -3.07094 q^{5} -2.84834 q^{6} +4.67138 q^{7} +1.00000 q^{8} +5.11302 q^{9} -3.07094 q^{10} -2.84834 q^{12} +4.99002 q^{13} +4.67138 q^{14} +8.74708 q^{15} +1.00000 q^{16} +3.75667 q^{17} +5.11302 q^{18} +1.00000 q^{19} -3.07094 q^{20} -13.3056 q^{21} -2.62984 q^{23} -2.84834 q^{24} +4.43069 q^{25} +4.99002 q^{26} -6.01858 q^{27} +4.67138 q^{28} +6.95137 q^{29} +8.74708 q^{30} +7.18499 q^{31} +1.00000 q^{32} +3.75667 q^{34} -14.3455 q^{35} +5.11302 q^{36} -7.95048 q^{37} +1.00000 q^{38} -14.2133 q^{39} -3.07094 q^{40} -9.26244 q^{41} -13.3056 q^{42} +5.70910 q^{43} -15.7018 q^{45} -2.62984 q^{46} +4.27977 q^{47} -2.84834 q^{48} +14.8218 q^{49} +4.43069 q^{50} -10.7002 q^{51} +4.99002 q^{52} +4.53901 q^{53} -6.01858 q^{54} +4.67138 q^{56} -2.84834 q^{57} +6.95137 q^{58} -11.8004 q^{59} +8.74708 q^{60} -2.82280 q^{61} +7.18499 q^{62} +23.8848 q^{63} +1.00000 q^{64} -15.3241 q^{65} +0.750979 q^{67} +3.75667 q^{68} +7.49066 q^{69} -14.3455 q^{70} +2.29387 q^{71} +5.11302 q^{72} -9.81695 q^{73} -7.95048 q^{74} -12.6201 q^{75} +1.00000 q^{76} -14.2133 q^{78} +4.49931 q^{79} -3.07094 q^{80} +1.80390 q^{81} -9.26244 q^{82} -14.8553 q^{83} -13.3056 q^{84} -11.5365 q^{85} +5.70910 q^{86} -19.7998 q^{87} +2.22383 q^{89} -15.7018 q^{90} +23.3103 q^{91} -2.62984 q^{92} -20.4653 q^{93} +4.27977 q^{94} -3.07094 q^{95} -2.84834 q^{96} +4.25517 q^{97} +14.8218 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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