LMFDB - Embedded newform 4598.2.a.bc.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:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.2
Root			$-1.30278$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} -2.30278 q^{5} +0.302776 q^{6} -1.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} -2.30278 q^{5} +0.302776 q^{6} -1.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} -2.30278 q^{10} +0.302776 q^{12} +3.30278 q^{13} -1.30278 q^{14} -0.697224 q^{15} +1.00000 q^{16} +4.60555 q^{17} -2.90833 q^{18} -1.00000 q^{19} -2.30278 q^{20} -0.394449 q^{21} -1.39445 q^{23} +0.302776 q^{24} +0.302776 q^{25} +3.30278 q^{26} -1.78890 q^{27} -1.30278 q^{28} +8.30278 q^{29} -0.697224 q^{30} -3.30278 q^{31} +1.00000 q^{32} +4.60555 q^{34} +3.00000 q^{35} -2.90833 q^{36} +5.21110 q^{37} -1.00000 q^{38} +1.00000 q^{39} -2.30278 q^{40} -3.90833 q^{41} -0.394449 q^{42} -1.09167 q^{43} +6.69722 q^{45} -1.39445 q^{46} -6.00000 q^{47} +0.302776 q^{48} -5.30278 q^{49} +0.302776 q^{50} +1.39445 q^{51} +3.30278 q^{52} -10.6056 q^{53} -1.78890 q^{54} -1.30278 q^{56} -0.302776 q^{57} +8.30278 q^{58} -0.697224 q^{60} -11.2111 q^{61} -3.30278 q^{62} +3.78890 q^{63} +1.00000 q^{64} -7.60555 q^{65} -6.51388 q^{67} +4.60555 q^{68} -0.422205 q^{69} +3.00000 q^{70} -9.69722 q^{71} -2.90833 q^{72} +2.60555 q^{73} +5.21110 q^{74} +0.0916731 q^{75} -1.00000 q^{76} +1.00000 q^{78} -15.8167 q^{79} -2.30278 q^{80} +8.18335 q^{81} -3.90833 q^{82} -14.3028 q^{83} -0.394449 q^{84} -10.6056 q^{85} -1.09167 q^{86} +2.51388 q^{87} +4.60555 q^{89} +6.69722 q^{90} -4.30278 q^{91} -1.39445 q^{92} -1.00000 q^{93} -6.00000 q^{94} +2.30278 q^{95} +0.302776 q^{96} +8.00000 q^{97} -5.30278 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + q^{7} + 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + q^7 + 2 * q^8 + 5 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + q^{7} + 2 q^{8} + 5 q^{9} - q^{10} - 3 q^{12} + 3 q^{13} + q^{14} - 5 q^{15} + 2 q^{16} + 2 q^{17} + 5 q^{18} - 2 q^{19} - q^{20} - 8 q^{21} - 10 q^{23} - 3 q^{24} - 3 q^{25} + 3 q^{26} - 18 q^{27} + q^{28} + 13 q^{29} - 5 q^{30} - 3 q^{31} + 2 q^{32} + 2 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} - 2 q^{38} + 2 q^{39} - q^{40} + 3 q^{41} - 8 q^{42} - 13 q^{43} + 17 q^{45} - 10 q^{46} - 12 q^{47} - 3 q^{48} - 7 q^{49} - 3 q^{50} + 10 q^{51} + 3 q^{52} - 14 q^{53} - 18 q^{54} + q^{56} + 3 q^{57} + 13 q^{58} - 5 q^{60} - 8 q^{61} - 3 q^{62} + 22 q^{63} + 2 q^{64} - 8 q^{65} + 5 q^{67} + 2 q^{68} + 28 q^{69} + 6 q^{70} - 23 q^{71} + 5 q^{72} - 2 q^{73} - 4 q^{74} + 11 q^{75} - 2 q^{76} + 2 q^{78} - 10 q^{79} - q^{80} + 38 q^{81} + 3 q^{82} - 25 q^{83} - 8 q^{84} - 14 q^{85} - 13 q^{86} - 13 q^{87} + 2 q^{89} + 17 q^{90} - 5 q^{91} - 10 q^{92} - 2 q^{93} - 12 q^{94} + q^{95} - 3 q^{96} + 16 q^{97} - 7 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + q^7 + 2 * q^8 + 5 * q^9 - q^10 - 3 * q^12 + 3 * q^13 + q^14 - 5 * q^15 + 2 * q^16 + 2 * q^17 + 5 * q^18 - 2 * q^19 - q^20 - 8 * q^21 - 10 * q^23 - 3 * q^24 - 3 * q^25 + 3 * q^26 - 18 * q^27 + q^28 + 13 * q^29 - 5 * q^30 - 3 * q^31 + 2 * q^32 + 2 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 - 2 * q^38 + 2 * q^39 - q^40 + 3 * q^41 - 8 * q^42 - 13 * q^43 + 17 * q^45 - 10 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 - 3 * q^50 + 10 * q^51 + 3 * q^52 - 14 * q^53 - 18 * q^54 + q^56 + 3 * q^57 + 13 * q^58 - 5 * q^60 - 8 * q^61 - 3 * q^62 + 22 * q^63 + 2 * q^64 - 8 * q^65 + 5 * q^67 + 2 * q^68 + 28 * q^69 + 6 * q^70 - 23 * q^71 + 5 * q^72 - 2 * q^73 - 4 * q^74 + 11 * q^75 - 2 * q^76 + 2 * q^78 - 10 * q^79 - q^80 + 38 * q^81 + 3 * q^82 - 25 * q^83 - 8 * q^84 - 14 * q^85 - 13 * q^86 - 13 * q^87 + 2 * q^89 + 17 * q^90 - 5 * q^91 - 10 * q^92 - 2 * q^93 - 12 * q^94 + q^95 - 3 * q^96 + 16 * q^97 - 7 * 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
$3$	0.302776	0.174808	0.0874038	−	0.996173i	$-0.472143\pi$
$3$	0.302776	0.174808	0.0874038	+	0.996173i	$0.472143\pi$
$4$	1.00000	0.500000
$5$	−2.30278	−1.02983	−0.514916	−	0.857240i	$-0.672177\pi$
$5$	−2.30278	−1.02983	−0.514916	+	0.857240i	$0.672177\pi$
$6$	0.302776	0.123608
$7$	−1.30278	−0.492403	−0.246201	−	0.969219i	$-0.579182\pi$
$7$	−1.30278	−0.492403	−0.246201	+	0.969219i	$0.579182\pi$
$8$	1.00000	0.353553
$9$	−2.90833	−0.969442
$10$	−2.30278	−0.728202
$11$	0	0
$11$	0	0
$12$	0.302776	0.0874038
$13$	3.30278	0.916025	0.458013	−	0.888946i	$-0.348561\pi$
$13$	3.30278	0.916025	0.458013	+	0.888946i	$0.348561\pi$
$14$	−1.30278	−0.348181
$15$	−0.697224	−0.180023
$16$	1.00000	0.250000
$17$	4.60555	1.11701	0.558505	−	0.829501i	$-0.311375\pi$
$17$	4.60555	1.11701	0.558505	+	0.829501i	$0.311375\pi$
$18$	−2.90833	−0.685499
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.30278	−0.514916
$21$	−0.394449	−0.0860758
$22$	0	0
$23$	−1.39445	−0.290763	−0.145381	−	0.989376i	$-0.546441\pi$
$23$	−1.39445	−0.290763	−0.145381	+	0.989376i	$0.546441\pi$
$24$	0.302776	0.0618038
$25$	0.302776	0.0605551
$26$	3.30278	0.647728
$27$	−1.78890	−0.344273
$28$	−1.30278	−0.246201
$29$	8.30278	1.54179	0.770893	−	0.636964i	$-0.219810\pi$
$29$	8.30278	1.54179	0.770893	+	0.636964i	$0.219810\pi$
$30$	−0.697224	−0.127295
$31$	−3.30278	−0.593196	−0.296598	−	0.955002i	$-0.595852\pi$
$31$	−3.30278	−0.593196	−0.296598	+	0.955002i	$0.595852\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.60555	0.789846
$35$	3.00000	0.507093
$36$	−2.90833	−0.484721
$37$	5.21110	0.856700	0.428350	−	0.903613i	$-0.359095\pi$
$37$	5.21110	0.856700	0.428350	+	0.903613i	$0.359095\pi$
$38$	−1.00000	−0.162221
$39$	1.00000	0.160128
$40$	−2.30278	−0.364101
$41$	−3.90833	−0.610378	−0.305189	−	0.952292i	$-0.598720\pi$
$41$	−3.90833	−0.610378	−0.305189	+	0.952292i	$0.598720\pi$
$42$	−0.394449	−0.0608648
$43$	−1.09167	−0.166479	−0.0832393	−	0.996530i	$-0.526527\pi$
$43$	−1.09167	−0.166479	−0.0832393	+	0.996530i	$0.526527\pi$
$44$	0	0
$45$	6.69722	0.998363
$46$	−1.39445	−0.205600
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0.302776	0.0437019
$49$	−5.30278	−0.757539
$50$	0.302776	0.0428189
$51$	1.39445	0.195262
$52$	3.30278	0.458013
$53$	−10.6056	−1.45678	−0.728392	−	0.685160i	$-0.759732\pi$
$53$	−10.6056	−1.45678	−0.728392	+	0.685160i	$0.759732\pi$
$54$	−1.78890	−0.243438
$55$	0	0
$56$	−1.30278	−0.174091
$57$	−0.302776	−0.0401036
$58$	8.30278	1.09021
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−0.697224	−0.0900113
$61$	−11.2111	−1.43543	−0.717717	−	0.696335i	$-0.754813\pi$
$61$	−11.2111	−1.43543	−0.717717	+	0.696335i	$0.754813\pi$
$62$	−3.30278	−0.419453
$63$	3.78890	0.477356
$64$	1.00000	0.125000
$65$	−7.60555	−0.943353
$66$	0	0
$67$	−6.51388	−0.795797	−0.397898	−	0.917429i	$-0.630260\pi$
$67$	−6.51388	−0.795797	−0.397898	+	0.917429i	$0.630260\pi$
$68$	4.60555	0.558505
$69$	−0.422205	−0.0508275
$70$	3.00000	0.358569
$71$	−9.69722	−1.15085	−0.575424	−	0.817855i	$-0.695163\pi$
$71$	−9.69722	−1.15085	−0.575424	+	0.817855i	$0.695163\pi$
$72$	−2.90833	−0.342750
$73$	2.60555	0.304957	0.152478	−	0.988307i	$-0.451275\pi$
$73$	2.60555	0.304957	0.152478	+	0.988307i	$0.451275\pi$
$74$	5.21110	0.605778
$75$	0.0916731	0.0105855
$76$	−1.00000	−0.114708
$77$	0	0
$78$	1.00000	0.113228
$79$	−15.8167	−1.77951	−0.889756	−	0.456436i	$-0.849126\pi$
$79$	−15.8167	−1.77951	−0.889756	+	0.456436i	$0.849126\pi$
$80$	−2.30278	−0.257458
$81$	8.18335	0.909261
$82$	−3.90833	−0.431603
$83$	−14.3028	−1.56993	−0.784967	−	0.619538i	$-0.787320\pi$
$83$	−14.3028	−1.56993	−0.784967	+	0.619538i	$0.787320\pi$
$84$	−0.394449	−0.0430379
$85$	−10.6056	−1.15033
$86$	−1.09167	−0.117718
$87$	2.51388	0.269516
$88$	0	0
$89$	4.60555	0.488187	0.244094	−	0.969752i	$-0.421510\pi$
$89$	4.60555	0.488187	0.244094	+	0.969752i	$0.421510\pi$
$90$	6.69722	0.705949
$91$	−4.30278	−0.451053
$92$	−1.39445	−0.145381
$93$	−1.00000	−0.103695
$94$	−6.00000	−0.618853
$95$	2.30278	0.236260
$96$	0.302776	0.0309019
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−5.30278	−0.535661
$99$	0	0
$100$	0.302776	0.0302776
$101$	−7.81665	−0.777786	−0.388893	−	0.921283i	$-0.627142\pi$
$101$	−7.81665	−0.777786	−0.388893	+	0.921283i	$0.627142\pi$
$102$	1.39445	0.138071
$103$	−1.69722	−0.167232	−0.0836162	−	0.996498i	$-0.526647\pi$
$103$	−1.69722	−0.167232	−0.0836162	+	0.996498i	$0.526647\pi$
$104$	3.30278	0.323864
$105$	0.908327	0.0886436
$106$	−10.6056	−1.03010
$107$	−3.21110	−0.310429	−0.155215	−	0.987881i	$-0.549607\pi$
$107$	−3.21110	−0.310429	−0.155215	+	0.987881i	$0.549607\pi$
$108$	−1.78890	−0.172137
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	1.57779	0.149758
$112$	−1.30278	−0.123101
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−0.302776	−0.0283575
$115$	3.21110	0.299437
$116$	8.30278	0.770893
$117$	−9.60555	−0.888034
$118$	0	0
$119$	−6.00000	−0.550019
$120$	−0.697224	−0.0636476
$121$	0	0
$122$	−11.2111	−1.01501
$123$	−1.18335	−0.106699
$124$	−3.30278	−0.296598
$125$	10.8167	0.967471
$126$	3.78890	0.337542
$127$	5.39445	0.478680	0.239340	−	0.970936i	$-0.423069\pi$
$127$	5.39445	0.478680	0.239340	+	0.970936i	$0.423069\pi$
$128$	1.00000	0.0883883
$129$	−0.330532	−0.0291017
$130$	−7.60555	−0.667051
$131$	−19.1194	−1.67047	−0.835236	−	0.549891i	$-0.814669\pi$
$131$	−19.1194	−1.67047	−0.835236	+	0.549891i	$0.814669\pi$
$132$	0	0
$133$	1.30278	0.112965
$134$	−6.51388	−0.562713
$135$	4.11943	0.354544
$136$	4.60555	0.394923
$137$	−3.48612	−0.297839	−0.148920	−	0.988849i	$-0.547580\pi$
$137$	−3.48612	−0.297839	−0.148920	+	0.988849i	$0.547580\pi$
$138$	−0.422205	−0.0359405
$139$	6.30278	0.534594	0.267297	−	0.963614i	$-0.413869\pi$
$139$	6.30278	0.534594	0.267297	+	0.963614i	$0.413869\pi$
$140$	3.00000	0.253546
$141$	−1.81665	−0.152990
$142$	−9.69722	−0.813773
$143$	0	0
$144$	−2.90833	−0.242361
$145$	−19.1194	−1.58778
$146$	2.60555	0.215637
$147$	−1.60555	−0.132424
$148$	5.21110	0.428350
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0.0916731	0.00748508
$151$	16.4222	1.33642	0.668210	−	0.743973i	$-0.267061\pi$
$151$	16.4222	1.33642	0.668210	+	0.743973i	$0.267061\pi$
$152$	−1.00000	−0.0811107
$153$	−13.3944	−1.08288
$154$	0	0
$155$	7.60555	0.610893
$156$	1.00000	0.0800641
$157$	1.09167	0.0871250	0.0435625	−	0.999051i	$-0.486129\pi$
$157$	1.09167	0.0871250	0.0435625	+	0.999051i	$0.486129\pi$
$158$	−15.8167	−1.25831
$159$	−3.21110	−0.254657
$160$	−2.30278	−0.182050
$161$	1.81665	0.143172
$162$	8.18335	0.642944
$163$	−11.3944	−0.892482	−0.446241	−	0.894913i	$-0.647238\pi$
$163$	−11.3944	−0.892482	−0.446241	+	0.894913i	$0.647238\pi$
$164$	−3.90833	−0.305189
$165$	0	0
$166$	−14.3028	−1.11011
$167$	12.4222	0.961259	0.480630	−	0.876924i	$-0.340408\pi$
$167$	12.4222	0.961259	0.480630	+	0.876924i	$0.340408\pi$
$168$	−0.394449	−0.0304324
$169$	−2.09167	−0.160898
$170$	−10.6056	−0.813409
$171$	2.90833	0.222405
$172$	−1.09167	−0.0832393
$173$	19.3305	1.46967	0.734837	−	0.678244i	$-0.237259\pi$
$173$	19.3305	1.46967	0.734837	+	0.678244i	$0.237259\pi$
$174$	2.51388	0.190577
$175$	−0.394449	−0.0298175
$176$	0	0
$177$	0	0
$178$	4.60555	0.345201
$179$	−13.1194	−0.980592	−0.490296	−	0.871556i	$-0.663111\pi$
$179$	−13.1194	−0.980592	−0.490296	+	0.871556i	$0.663111\pi$
$180$	6.69722	0.499182
$181$	−15.0278	−1.11700	−0.558502	−	0.829503i	$-0.688624\pi$
$181$	−15.0278	−1.11700	−0.558502	+	0.829503i	$0.688624\pi$
$182$	−4.30278	−0.318943
$183$	−3.39445	−0.250925
$184$	−1.39445	−0.102800
$185$	−12.0000	−0.882258
$186$	−1.00000	−0.0733236
$187$	0	0
$188$	−6.00000	−0.437595
$189$	2.33053	0.169521
$190$	2.30278	0.167061
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	0.302776	0.0218509
$193$	24.7250	1.77974	0.889872	−	0.456211i	$-0.150794\pi$
$193$	24.7250	1.77974	0.889872	+	0.456211i	$0.150794\pi$
$194$	8.00000	0.574367
$195$	−2.30278	−0.164905
$196$	−5.30278	−0.378770
$197$	−21.6333	−1.54131	−0.770655	−	0.637253i	$-0.780071\pi$
$197$	−21.6333	−1.54131	−0.770655	+	0.637253i	$0.780071\pi$
$198$	0	0
$199$	−2.18335	−0.154773	−0.0773867	−	0.997001i	$-0.524658\pi$
$199$	−2.18335	−0.154773	−0.0773867	+	0.997001i	$0.524658\pi$
$200$	0.302776	0.0214095
$201$	−1.97224	−0.139111
$202$	−7.81665	−0.549978
$203$	−10.8167	−0.759180
$204$	1.39445	0.0976309
$205$	9.00000	0.628587
$206$	−1.69722	−0.118251
$207$	4.05551	0.281878
$208$	3.30278	0.229006
$209$	0	0
$210$	0.908327	0.0626805
$211$	−24.6056	−1.69392	−0.846958	−	0.531660i	$-0.821569\pi$
$211$	−24.6056	−1.69392	−0.846958	+	0.531660i	$0.821569\pi$
$212$	−10.6056	−0.728392
$213$	−2.93608	−0.201177
$214$	−3.21110	−0.219506
$215$	2.51388	0.171445
$216$	−1.78890	−0.121719
$217$	4.30278	0.292091
$218$	−2.00000	−0.135457
$219$	0.788897	0.0533087
$220$	0	0
$221$	15.2111	1.02321
$222$	1.57779	0.105895
$223$	−25.2111	−1.68826	−0.844130	−	0.536138i	$-0.819883\pi$
$223$	−25.2111	−1.68826	−0.844130	+	0.536138i	$0.819883\pi$
$224$	−1.30278	−0.0870454
$225$	−0.880571	−0.0587047
$226$	0	0
$227$	−1.81665	−0.120576	−0.0602878	−	0.998181i	$-0.519202\pi$
$227$	−1.81665	−0.120576	−0.0602878	+	0.998181i	$0.519202\pi$
$228$	−0.302776	−0.0200518
$229$	11.9083	0.786924	0.393462	−	0.919341i	$-0.371277\pi$
$229$	11.9083	0.786924	0.393462	+	0.919341i	$0.371277\pi$
$230$	3.21110	0.211734
$231$	0	0
$232$	8.30278	0.545104
$233$	−9.21110	−0.603439	−0.301720	−	0.953397i	$-0.597561\pi$
$233$	−9.21110	−0.603439	−0.301720	+	0.953397i	$0.597561\pi$
$234$	−9.60555	−0.627935
$235$	13.8167	0.901299
$236$	0	0
$237$	−4.78890	−0.311072
$238$	−6.00000	−0.388922
$239$	23.9361	1.54830	0.774148	−	0.633004i	$-0.218178\pi$
$239$	23.9361	1.54830	0.774148	+	0.633004i	$0.218178\pi$
$240$	−0.697224	−0.0450056
$241$	−13.0917	−0.843309	−0.421654	−	0.906757i	$-0.638550\pi$
$241$	−13.0917	−0.843309	−0.421654	+	0.906757i	$0.638550\pi$
$242$	0	0
$243$	7.84441	0.503219
$244$	−11.2111	−0.717717
$245$	12.2111	0.780139
$246$	−1.18335	−0.0754474
$247$	−3.30278	−0.210151
$248$	−3.30278	−0.209726
$249$	−4.33053	−0.274436
$250$	10.8167	0.684105
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	3.78890	0.238678
$253$	0	0
$254$	5.39445	0.338478
$255$	−3.21110	−0.201087
$256$	1.00000	0.0625000
$257$	−4.60555	−0.287286	−0.143643	−	0.989630i	$-0.545882\pi$
$257$	−4.60555	−0.287286	−0.143643	+	0.989630i	$0.545882\pi$
$258$	−0.330532	−0.0205780
$259$	−6.78890	−0.421842
$260$	−7.60555	−0.471676
$261$	−24.1472	−1.49467
$262$	−19.1194	−1.18120
$263$	20.3028	1.25192	0.625961	−	0.779854i	$-0.284707\pi$
$263$	20.3028	1.25192	0.625961	+	0.779854i	$0.284707\pi$
$264$	0	0
$265$	24.4222	1.50024
$266$	1.30278	0.0798783
$267$	1.39445	0.0853389
$268$	−6.51388	−0.397898
$269$	−19.8167	−1.20824	−0.604121	−	0.796892i	$-0.706476\pi$
$269$	−19.8167	−1.20824	−0.604121	+	0.796892i	$0.706476\pi$
$270$	4.11943	0.250700
$271$	6.51388	0.395690	0.197845	−	0.980233i	$-0.436606\pi$
$271$	6.51388	0.395690	0.197845	+	0.980233i	$0.436606\pi$
$272$	4.60555	0.279253
$273$	−1.30278	−0.0788476
$274$	−3.48612	−0.210604
$275$	0	0
$276$	−0.422205	−0.0254138
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	6.30278	0.378015
$279$	9.60555	0.575069
$280$	3.00000	0.179284
$281$	0.486122	0.0289996	0.0144998	−	0.999895i	$-0.495384\pi$
$281$	0.486122	0.0289996	0.0144998	+	0.999895i	$0.495384\pi$
$282$	−1.81665	−0.108180
$283$	18.9361	1.12563	0.562817	−	0.826582i	$-0.309718\pi$
$283$	18.9361	1.12563	0.562817	+	0.826582i	$0.309718\pi$
$284$	−9.69722	−0.575424
$285$	0.697224	0.0413000
$286$	0	0
$287$	5.09167	0.300552
$288$	−2.90833	−0.171375
$289$	4.21110	0.247712
$290$	−19.1194	−1.12273
$291$	2.42221	0.141992
$292$	2.60555	0.152478
$293$	25.5416	1.49216	0.746079	−	0.665857i	$-0.231934\pi$
$293$	25.5416	1.49216	0.746079	+	0.665857i	$0.231934\pi$
$294$	−1.60555	−0.0936377
$295$	0	0
$296$	5.21110	0.302889
$297$	0	0
$298$	0	0
$299$	−4.60555	−0.266346
$300$	0.0916731	0.00529275
$301$	1.42221	0.0819745
$302$	16.4222	0.944992
$303$	−2.36669	−0.135963
$304$	−1.00000	−0.0573539
$305$	25.8167	1.47826
$306$	−13.3944	−0.765710
$307$	2.18335	0.124610	0.0623051	−	0.998057i	$-0.480155\pi$
$307$	2.18335	0.124610	0.0623051	+	0.998057i	$0.480155\pi$
$308$	0	0
$309$	−0.513878	−0.0292335
$310$	7.60555	0.431966
$311$	25.8167	1.46393	0.731964	−	0.681343i	$-0.238604\pi$
$311$	25.8167	1.46393	0.731964	+	0.681343i	$0.238604\pi$
$312$	1.00000	0.0566139
$313$	18.1194	1.02417	0.512085	−	0.858935i	$-0.328873\pi$
$313$	18.1194	1.02417	0.512085	+	0.858935i	$0.328873\pi$
$314$	1.09167	0.0616067
$315$	−8.72498	−0.491597
$316$	−15.8167	−0.889756
$317$	−13.8167	−0.776021	−0.388010	−	0.921655i	$-0.626838\pi$
$317$	−13.8167	−0.776021	−0.388010	+	0.921655i	$0.626838\pi$
$318$	−3.21110	−0.180070
$319$	0	0
$320$	−2.30278	−0.128729
$321$	−0.972244	−0.0542653
$322$	1.81665	0.101238
$323$	−4.60555	−0.256260
$324$	8.18335	0.454630
$325$	1.00000	0.0554700
$326$	−11.3944	−0.631080
$327$	−0.605551	−0.0334871
$328$	−3.90833	−0.215801
$329$	7.81665	0.430946
$330$	0	0
$331$	22.7250	1.24908	0.624539	−	0.780994i	$-0.285287\pi$
$331$	22.7250	1.24908	0.624539	+	0.780994i	$0.285287\pi$
$332$	−14.3028	−0.784967
$333$	−15.1556	−0.830521
$334$	12.4222	0.679713
$335$	15.0000	0.819538
$336$	−0.394449	−0.0215189
$337$	9.30278	0.506754	0.253377	−	0.967368i	$-0.418459\pi$
$337$	9.30278	0.506754	0.253377	+	0.967368i	$0.418459\pi$
$338$	−2.09167	−0.113772
$339$	0	0
$340$	−10.6056	−0.575167
$341$	0	0
$342$	2.90833	0.157264
$343$	16.0278	0.865417
$344$	−1.09167	−0.0588591
$345$	0.972244	0.0523438
$346$	19.3305	1.03922
$347$	−2.78890	−0.149716	−0.0748579	−	0.997194i	$-0.523850\pi$
$347$	−2.78890	−0.149716	−0.0748579	+	0.997194i	$0.523850\pi$
$348$	2.51388	0.134758
$349$	−32.4222	−1.73552	−0.867760	−	0.496983i	$-0.834441\pi$
$349$	−32.4222	−1.73552	−0.867760	+	0.496983i	$0.834441\pi$
$350$	−0.394449	−0.0210842
$351$	−5.90833	−0.315363
$352$	0	0
$353$	−15.2111	−0.809605	−0.404803	−	0.914404i	$-0.632660\pi$
$353$	−15.2111	−0.809605	−0.404803	+	0.914404i	$0.632660\pi$
$354$	0	0
$355$	22.3305	1.18518
$356$	4.60555	0.244094
$357$	−1.81665	−0.0961475
$358$	−13.1194	−0.693383
$359$	9.48612	0.500658	0.250329	−	0.968161i	$-0.419461\pi$
$359$	9.48612	0.500658	0.250329	+	0.968161i	$0.419461\pi$
$360$	6.69722	0.352975
$361$	1.00000	0.0526316
$362$	−15.0278	−0.789841
$363$	0	0
$364$	−4.30278	−0.225527
$365$	−6.00000	−0.314054
$366$	−3.39445	−0.177431
$367$	−7.21110	−0.376416	−0.188208	−	0.982129i	$-0.560268\pi$
$367$	−7.21110	−0.376416	−0.188208	+	0.982129i	$0.560268\pi$
$368$	−1.39445	−0.0726907
$369$	11.3667	0.591726
$370$	−12.0000	−0.623850
$371$	13.8167	0.717325
$372$	−1.00000	−0.0518476
$373$	−7.09167	−0.367193	−0.183596	−	0.983002i	$-0.558774\pi$
$373$	−7.09167	−0.367193	−0.183596	+	0.983002i	$0.558774\pi$
$374$	0	0
$375$	3.27502	0.169121
$376$	−6.00000	−0.309426
$377$	27.4222	1.41232
$378$	2.33053	0.119870
$379$	−13.4861	−0.692736	−0.346368	−	0.938099i	$-0.612585\pi$
$379$	−13.4861	−0.692736	−0.346368	+	0.938099i	$0.612585\pi$
$380$	2.30278	0.118130
$381$	1.63331	0.0836769
$382$	−6.00000	−0.306987
$383$	3.48612	0.178133	0.0890663	−	0.996026i	$-0.471612\pi$
$383$	3.48612	0.178133	0.0890663	+	0.996026i	$0.471612\pi$
$384$	0.302776	0.0154510
$385$	0	0
$386$	24.7250	1.25847
$387$	3.17494	0.161391
$388$	8.00000	0.406138
$389$	34.5416	1.75133	0.875665	−	0.482919i	$-0.160423\pi$
$389$	34.5416	1.75133	0.875665	+	0.482919i	$0.160423\pi$
$390$	−2.30278	−0.116606
$391$	−6.42221	−0.324785
$392$	−5.30278	−0.267831
$393$	−5.78890	−0.292011
$394$	−21.6333	−1.08987
$395$	36.4222	1.83260
$396$	0	0
$397$	−32.7527	−1.64381	−0.821906	−	0.569623i	$-0.807089\pi$
$397$	−32.7527	−1.64381	−0.821906	+	0.569623i	$0.807089\pi$
$398$	−2.18335	−0.109441
$399$	0.394449	0.0197471
$400$	0.302776	0.0151388
$401$	22.6056	1.12887	0.564434	−	0.825478i	$-0.309095\pi$
$401$	22.6056	1.12887	0.564434	+	0.825478i	$0.309095\pi$
$402$	−1.97224	−0.0983666
$403$	−10.9083	−0.543382
$404$	−7.81665	−0.388893
$405$	−18.8444	−0.936386
$406$	−10.8167	−0.536822
$407$	0	0
$408$	1.39445	0.0690355
$409$	−23.1472	−1.14455	−0.572277	−	0.820060i	$-0.693940\pi$
$409$	−23.1472	−1.14455	−0.572277	+	0.820060i	$0.693940\pi$
$410$	9.00000	0.444478
$411$	−1.05551	−0.0520646
$412$	−1.69722	−0.0836162
$413$	0	0
$414$	4.05551	0.199318
$415$	32.9361	1.61677
$416$	3.30278	0.161932
$417$	1.90833	0.0934512
$418$	0	0
$419$	8.78890	0.429366	0.214683	−	0.976684i	$-0.431128\pi$
$419$	8.78890	0.429366	0.214683	+	0.976684i	$0.431128\pi$
$420$	0.908327	0.0443218
$421$	−30.2389	−1.47375	−0.736876	−	0.676028i	$-0.763700\pi$
$421$	−30.2389	−1.47375	−0.736876	+	0.676028i	$0.763700\pi$
$422$	−24.6056	−1.19778
$423$	17.4500	0.848446
$424$	−10.6056	−0.515051
$425$	1.39445	0.0676407
$426$	−2.93608	−0.142254
$427$	14.6056	0.706812
$428$	−3.21110	−0.155215
$429$	0	0
$430$	2.51388	0.121230
$431$	−2.78890	−0.134336	−0.0671682	−	0.997742i	$-0.521396\pi$
$431$	−2.78890	−0.134336	−0.0671682	+	0.997742i	$0.521396\pi$
$432$	−1.78890	−0.0860684
$433$	−24.2389	−1.16485	−0.582423	−	0.812886i	$-0.697895\pi$
$433$	−24.2389	−1.16485	−0.582423	+	0.812886i	$0.697895\pi$
$434$	4.30278	0.206540
$435$	−5.78890	−0.277556
$436$	−2.00000	−0.0957826
$437$	1.39445	0.0667055
$438$	0.788897	0.0376950
$439$	25.2111	1.20326	0.601630	−	0.798775i	$-0.294518\pi$
$439$	25.2111	1.20326	0.601630	+	0.798775i	$0.294518\pi$
$440$	0	0
$441$	15.4222	0.734391
$442$	15.2111	0.723518
$443$	39.6333	1.88304	0.941518	−	0.336964i	$-0.109400\pi$
$443$	39.6333	1.88304	0.941518	+	0.336964i	$0.109400\pi$
$444$	1.57779	0.0748788
$445$	−10.6056	−0.502751
$446$	−25.2111	−1.19378
$447$	0	0
$448$	−1.30278	−0.0615504
$449$	−31.8167	−1.50152	−0.750760	−	0.660575i	$-0.770313\pi$
$449$	−31.8167	−1.50152	−0.750760	+	0.660575i	$0.770313\pi$
$450$	−0.880571	−0.0415105
$451$	0	0
$452$	0	0
$453$	4.97224	0.233616
$454$	−1.81665	−0.0852598
$455$	9.90833	0.464510
$456$	−0.302776	−0.0141788
$457$	−21.8167	−1.02054	−0.510270	−	0.860014i	$-0.670455\pi$
$457$	−21.8167	−1.02054	−0.510270	+	0.860014i	$0.670455\pi$
$458$	11.9083	0.556440
$459$	−8.23886	−0.384557
$460$	3.21110	0.149718
$461$	−6.42221	−0.299112	−0.149556	−	0.988753i	$-0.547784\pi$
$461$	−6.42221	−0.299112	−0.149556	+	0.988753i	$0.547784\pi$
$462$	0	0
$463$	−1.21110	−0.0562847	−0.0281424	−	0.999604i	$-0.508959\pi$
$463$	−1.21110	−0.0562847	−0.0281424	+	0.999604i	$0.508959\pi$
$464$	8.30278	0.385447
$465$	2.30278	0.106789
$466$	−9.21110	−0.426696
$467$	−22.6056	−1.04606	−0.523030	−	0.852314i	$-0.675198\pi$
$467$	−22.6056	−1.04606	−0.523030	+	0.852314i	$0.675198\pi$
$468$	−9.60555	−0.444017
$469$	8.48612	0.391853
$470$	13.8167	0.637315
$471$	0.330532	0.0152301
$472$	0	0
$473$	0	0
$474$	−4.78890	−0.219961
$475$	−0.302776	−0.0138923
$476$	−6.00000	−0.275010
$477$	30.8444	1.41227
$478$	23.9361	1.09481
$479$	−35.7250	−1.63232	−0.816158	−	0.577829i	$-0.803900\pi$
$479$	−35.7250	−1.63232	−0.816158	+	0.577829i	$0.803900\pi$
$480$	−0.697224	−0.0318238
$481$	17.2111	0.784759
$482$	−13.0917	−0.596309
$483$	0.550039	0.0250276
$484$	0	0
$485$	−18.4222	−0.836509
$486$	7.84441	0.355830
$487$	−29.3305	−1.32909	−0.664547	−	0.747247i	$-0.731375\pi$
$487$	−29.3305	−1.32909	−0.664547	+	0.747247i	$0.731375\pi$
$488$	−11.2111	−0.507503
$489$	−3.44996	−0.156013
$490$	12.2111	0.551641
$491$	14.9361	0.674056	0.337028	−	0.941495i	$-0.390578\pi$
$491$	14.9361	0.674056	0.337028	+	0.941495i	$0.390578\pi$
$492$	−1.18335	−0.0533494
$493$	38.2389	1.72219
$494$	−3.30278	−0.148599
$495$	0	0
$496$	−3.30278	−0.148299
$497$	12.6333	0.566681
$498$	−4.33053	−0.194056
$499$	−34.0000	−1.52205	−0.761025	−	0.648723i	$-0.775303\pi$
$499$	−34.0000	−1.52205	−0.761025	+	0.648723i	$0.775303\pi$
$500$	10.8167	0.483735
$501$	3.76114	0.168035
$502$	24.0000	1.07117
$503$	−22.1194	−0.986257	−0.493128	−	0.869957i	$-0.664147\pi$
$503$	−22.1194	−0.986257	−0.493128	+	0.869957i	$0.664147\pi$
$504$	3.78890	0.168771
$505$	18.0000	0.800989
$506$	0	0
$507$	−0.633308	−0.0281262
$508$	5.39445	0.239340
$509$	−18.4222	−0.816550	−0.408275	−	0.912859i	$-0.633870\pi$
$509$	−18.4222	−0.816550	−0.408275	+	0.912859i	$0.633870\pi$
$510$	−3.21110	−0.142190
$511$	−3.39445	−0.150162
$512$	1.00000	0.0441942
$513$	1.78890	0.0789818
$514$	−4.60555	−0.203142
$515$	3.90833	0.172221
$516$	−0.330532	−0.0145509
$517$	0	0
$518$	−6.78890	−0.298287
$519$	5.85281	0.256910
$520$	−7.60555	−0.333525
$521$	36.4222	1.59569	0.797843	−	0.602865i	$-0.205974\pi$
$521$	36.4222	1.59569	0.797843	+	0.602865i	$0.205974\pi$
$522$	−24.1472	−1.05689
$523$	−19.0278	−0.832026	−0.416013	−	0.909359i	$-0.636573\pi$
$523$	−19.0278	−0.832026	−0.416013	+	0.909359i	$0.636573\pi$
$524$	−19.1194	−0.835236
$525$	−0.119429	−0.00521233
$526$	20.3028	0.885243
$527$	−15.2111	−0.662606
$528$	0	0
$529$	−21.0555	−0.915457
$530$	24.4222	1.06083
$531$	0	0
$532$	1.30278	0.0564825
$533$	−12.9083	−0.559122
$534$	1.39445	0.0603437
$535$	7.39445	0.319690
$536$	−6.51388	−0.281357
$537$	−3.97224	−0.171415
$538$	−19.8167	−0.854357
$539$	0	0
$540$	4.11943	0.177272
$541$	−3.81665	−0.164091	−0.0820454	−	0.996629i	$-0.526145\pi$
$541$	−3.81665	−0.164091	−0.0820454	+	0.996629i	$0.526145\pi$
$542$	6.51388	0.279795
$543$	−4.55004	−0.195261
$544$	4.60555	0.197461
$545$	4.60555	0.197280
$546$	−1.30278	−0.0557537
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	−3.48612	−0.148920
$549$	32.6056	1.39157
$550$	0	0
$551$	−8.30278	−0.353710
$552$	−0.422205	−0.0179702
$553$	20.6056	0.876237
$554$	10.0000	0.424859
$555$	−3.63331	−0.154225
$556$	6.30278	0.267297
$557$	27.6333	1.17086	0.585430	−	0.810723i	$-0.300926\pi$
$557$	27.6333	1.17086	0.585430	+	0.810723i	$0.300926\pi$
$558$	9.60555	0.406635
$559$	−3.60555	−0.152499
$560$	3.00000	0.126773
$561$	0	0
$562$	0.486122	0.0205058
$563$	−21.6333	−0.911735	−0.455868	−	0.890048i	$-0.650671\pi$
$563$	−21.6333	−0.911735	−0.455868	+	0.890048i	$0.650671\pi$
$564$	−1.81665	−0.0764949
$565$	0	0
$566$	18.9361	0.795943
$567$	−10.6611	−0.447723
$568$	−9.69722	−0.406886
$569$	−12.2750	−0.514596	−0.257298	−	0.966332i	$-0.582832\pi$
$569$	−12.2750	−0.514596	−0.257298	+	0.966332i	$0.582832\pi$
$570$	0.697224	0.0292035
$571$	6.93608	0.290266	0.145133	−	0.989412i	$-0.453639\pi$
$571$	6.93608	0.290266	0.145133	+	0.989412i	$0.453639\pi$
$572$	0	0
$573$	−1.81665	−0.0758918
$574$	5.09167	0.212522
$575$	−0.422205	−0.0176072
$576$	−2.90833	−0.121180
$577$	−18.0917	−0.753166	−0.376583	−	0.926383i	$-0.622901\pi$
$577$	−18.0917	−0.753166	−0.376583	+	0.926383i	$0.622901\pi$
$578$	4.21110	0.175159
$579$	7.48612	0.311113
$580$	−19.1194	−0.793891
$581$	18.6333	0.773040
$582$	2.42221	0.100404
$583$	0	0
$584$	2.60555	0.107818
$585$	22.1194	0.914526
$586$	25.5416	1.05512
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−1.60555	−0.0662118
$589$	3.30278	0.136088
$590$	0	0
$591$	−6.55004	−0.269433
$592$	5.21110	0.214175
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	13.8167	0.566428
$596$	0	0
$597$	−0.661064	−0.0270555
$598$	−4.60555	−0.188335
$599$	−19.8806	−0.812298	−0.406149	−	0.913807i	$-0.633129\pi$
$599$	−19.8806	−0.812298	−0.406149	+	0.913807i	$0.633129\pi$
$600$	0.0916731	0.00374254
$601$	−4.09167	−0.166903	−0.0834514	−	0.996512i	$-0.526594\pi$
$601$	−4.09167	−0.166903	−0.0834514	+	0.996512i	$0.526594\pi$
$602$	1.42221	0.0579648
$603$	18.9445	0.771479
$604$	16.4222	0.668210
$605$	0	0
$606$	−2.36669	−0.0961403
$607$	−3.81665	−0.154913	−0.0774566	−	0.996996i	$-0.524680\pi$
$607$	−3.81665	−0.154913	−0.0774566	+	0.996996i	$0.524680\pi$
$608$	−1.00000	−0.0405554
$609$	−3.27502	−0.132710
$610$	25.8167	1.04529
$611$	−19.8167	−0.801696
$612$	−13.3944	−0.541438
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	2.18335	0.0881127
$615$	2.72498	0.109882
$616$	0	0
$617$	2.09167	0.0842076	0.0421038	−	0.999113i	$-0.486594\pi$
$617$	2.09167	0.0842076	0.0421038	+	0.999113i	$0.486594\pi$
$618$	−0.513878	−0.0206712
$619$	−34.8444	−1.40052	−0.700258	−	0.713890i	$-0.746932\pi$
$619$	−34.8444	−1.40052	−0.700258	+	0.713890i	$0.746932\pi$
$620$	7.60555	0.305446
$621$	2.49453	0.100102
$622$	25.8167	1.03515
$623$	−6.00000	−0.240385
$624$	1.00000	0.0400320
$625$	−26.4222	−1.05689
$626$	18.1194	0.724198
$627$	0	0
$628$	1.09167	0.0435625
$629$	24.0000	0.956943
$630$	−8.72498	−0.347612
$631$	−45.0278	−1.79253	−0.896263	−	0.443522i	$-0.853729\pi$
$631$	−45.0278	−1.79253	−0.896263	+	0.443522i	$0.853729\pi$
$632$	−15.8167	−0.629153
$633$	−7.44996	−0.296109
$634$	−13.8167	−0.548729
$635$	−12.4222	−0.492960
$636$	−3.21110	−0.127328
$637$	−17.5139	−0.693925
$638$	0	0
$639$	28.2027	1.11568
$640$	−2.30278	−0.0910252
$641$	20.2389	0.799387	0.399693	−	0.916649i	$-0.369117\pi$
$641$	20.2389	0.799387	0.399693	+	0.916649i	$0.369117\pi$
$642$	−0.972244	−0.0383714
$643$	26.4222	1.04199	0.520995	−	0.853560i	$-0.325561\pi$
$643$	26.4222	1.04199	0.520995	+	0.853560i	$0.325561\pi$
$644$	1.81665	0.0715862
$645$	0.761141	0.0299699
$646$	−4.60555	−0.181203
$647$	25.8167	1.01496	0.507479	−	0.861664i	$-0.330578\pi$
$647$	25.8167	1.01496	0.507479	+	0.861664i	$0.330578\pi$
$648$	8.18335	0.321472
$649$	0	0
$650$	1.00000	0.0392232
$651$	1.30278	0.0510598
$652$	−11.3944	−0.446241
$653$	22.3305	0.873861	0.436931	−	0.899495i	$-0.356066\pi$
$653$	22.3305	0.873861	0.436931	+	0.899495i	$0.356066\pi$
$654$	−0.605551	−0.0236789
$655$	44.0278	1.72031
$656$	−3.90833	−0.152595
$657$	−7.57779	−0.295638
$658$	7.81665	0.304725
$659$	−29.0278	−1.13076	−0.565380	−	0.824830i	$-0.691271\pi$
$659$	−29.0278	−1.13076	−0.565380	+	0.824830i	$0.691271\pi$
$660$	0	0
$661$	23.6333	0.919229	0.459615	−	0.888118i	$-0.347988\pi$
$661$	23.6333	0.919229	0.459615	+	0.888118i	$0.347988\pi$
$662$	22.7250	0.883231
$663$	4.60555	0.178865
$664$	−14.3028	−0.555055
$665$	−3.00000	−0.116335
$666$	−15.1556	−0.587267
$667$	−11.5778	−0.448294
$668$	12.4222	0.480630
$669$	−7.63331	−0.295121
$670$	15.0000	0.579501
$671$	0	0
$672$	−0.394449	−0.0152162
$673$	−1.30278	−0.0502183	−0.0251092	−	0.999685i	$-0.507993\pi$
$673$	−1.30278	−0.0502183	−0.0251092	+	0.999685i	$0.507993\pi$
$674$	9.30278	0.358330
$675$	−0.541635	−0.0208475
$676$	−2.09167	−0.0804490
$677$	8.30278	0.319102	0.159551	−	0.987190i	$-0.448995\pi$
$677$	8.30278	0.319102	0.159551	+	0.987190i	$0.448995\pi$
$678$	0	0
$679$	−10.4222	−0.399968
$680$	−10.6056	−0.406704
$681$	−0.550039	−0.0210775
$682$	0	0
$683$	−17.5778	−0.672596	−0.336298	−	0.941756i	$-0.609175\pi$
$683$	−17.5778	−0.672596	−0.336298	+	0.941756i	$0.609175\pi$
$684$	2.90833	0.111203
$685$	8.02776	0.306725
$686$	16.0278	0.611943
$687$	3.60555	0.137560
$688$	−1.09167	−0.0416196
$689$	−35.0278	−1.33445
$690$	0.972244	0.0370127
$691$	32.4222	1.23340	0.616699	−	0.787199i	$-0.288469\pi$
$691$	32.4222	1.23340	0.616699	+	0.787199i	$0.288469\pi$
$692$	19.3305	0.734837
$693$	0	0
$694$	−2.78890	−0.105865
$695$	−14.5139	−0.550543
$696$	2.51388	0.0952883
$697$	−18.0000	−0.681799
$698$	−32.4222	−1.22720
$699$	−2.78890	−0.105486
$700$	−0.394449	−0.0149088
$701$	27.6333	1.04370	0.521848	−	0.853039i	$-0.325243\pi$
$701$	27.6333	1.04370	0.521848	+	0.853039i	$0.325243\pi$
$702$	−5.90833	−0.222995
$703$	−5.21110	−0.196540
$704$	0	0
$705$	4.18335	0.157554
$706$	−15.2111	−0.572477
$707$	10.1833	0.382984
$708$	0	0
$709$	14.6972	0.551966	0.275983	−	0.961163i	$-0.410997\pi$
$709$	14.6972	0.551966	0.275983	+	0.961163i	$0.410997\pi$
$710$	22.3305	0.838050
$711$	46.0000	1.72513
$712$	4.60555	0.172600
$713$	4.60555	0.172479
$714$	−1.81665	−0.0679866
$715$	0	0
$716$	−13.1194	−0.490296
$717$	7.24726	0.270654
$718$	9.48612	0.354019
$719$	−25.8167	−0.962799	−0.481399	−	0.876501i	$-0.659871\pi$
$719$	−25.8167	−0.962799	−0.481399	+	0.876501i	$0.659871\pi$
$720$	6.69722	0.249591
$721$	2.21110	0.0823458
$722$	1.00000	0.0372161
$723$	−3.96384	−0.147417
$724$	−15.0278	−0.558502
$725$	2.51388	0.0933631
$726$	0	0
$727$	−0.366692	−0.0135999	−0.00679993	−	0.999977i	$-0.502165\pi$
$727$	−0.366692	−0.0135999	−0.00679993	+	0.999977i	$0.502165\pi$
$728$	−4.30278	−0.159471
$729$	−22.1749	−0.821294
$730$	−6.00000	−0.222070
$731$	−5.02776	−0.185958
$732$	−3.39445	−0.125462
$733$	7.21110	0.266348	0.133174	−	0.991093i	$-0.457483\pi$
$733$	7.21110	0.266348	0.133174	+	0.991093i	$0.457483\pi$
$734$	−7.21110	−0.266167
$735$	3.69722	0.136374
$736$	−1.39445	−0.0514001
$737$	0	0
$738$	11.3667	0.418414
$739$	40.3583	1.48460	0.742302	−	0.670066i	$-0.233734\pi$
$739$	40.3583	1.48460	0.742302	+	0.670066i	$0.233734\pi$
$740$	−12.0000	−0.441129
$741$	−1.00000	−0.0367359
$742$	13.8167	0.507225
$743$	−2.36669	−0.0868255	−0.0434128	−	0.999057i	$-0.513823\pi$
$743$	−2.36669	−0.0868255	−0.0434128	+	0.999057i	$0.513823\pi$
$744$	−1.00000	−0.0366618
$745$	0	0
$746$	−7.09167	−0.259645
$747$	41.5971	1.52196
$748$	0	0
$749$	4.18335	0.152856
$750$	3.27502	0.119587
$751$	−40.8444	−1.49043	−0.745217	−	0.666822i	$-0.767654\pi$
$751$	−40.8444	−1.49043	−0.745217	+	0.666822i	$0.767654\pi$
$752$	−6.00000	−0.218797
$753$	7.26662	0.264810
$754$	27.4222	0.998658
$755$	−37.8167	−1.37629
$756$	2.33053	0.0847606
$757$	30.5416	1.11005	0.555027	−	0.831832i	$-0.312708\pi$
$757$	30.5416	1.11005	0.555027	+	0.831832i	$0.312708\pi$
$758$	−13.4861	−0.489838
$759$	0	0
$760$	2.30278	0.0835305
$761$	−20.2389	−0.733658	−0.366829	−	0.930288i	$-0.619557\pi$
$761$	−20.2389	−0.733658	−0.366829	+	0.930288i	$0.619557\pi$
$762$	1.63331	0.0591685
$763$	2.60555	0.0943273
$764$	−6.00000	−0.217072
$765$	30.8444	1.11518
$766$	3.48612	0.125959
$767$	0	0
$768$	0.302776	0.0109255
$769$	37.6333	1.35709	0.678546	−	0.734558i	$-0.262610\pi$
$769$	37.6333	1.35709	0.678546	+	0.734558i	$0.262610\pi$
$770$	0	0
$771$	−1.39445	−0.0502198
$772$	24.7250	0.889872
$773$	48.4222	1.74163	0.870813	−	0.491615i	$-0.163593\pi$
$773$	48.4222	1.74163	0.870813	+	0.491615i	$0.163593\pi$
$774$	3.17494	0.114121
$775$	−1.00000	−0.0359211
$776$	8.00000	0.287183
$777$	−2.05551	−0.0737411
$778$	34.5416	1.23838
$779$	3.90833	0.140030
$780$	−2.30278	−0.0824526
$781$	0	0
$782$	−6.42221	−0.229658
$783$	−14.8528	−0.530796
$784$	−5.30278	−0.189385
$785$	−2.51388	−0.0897242
$786$	−5.78890	−0.206483
$787$	15.0278	0.535682	0.267841	−	0.963463i	$-0.413690\pi$
$787$	15.0278	0.535682	0.267841	+	0.963463i	$0.413690\pi$
$788$	−21.6333	−0.770655
$789$	6.14719	0.218846
$790$	36.4222	1.29584
$791$	0	0
$792$	0	0
$793$	−37.0278	−1.31489
$794$	−32.7527	−1.16235
$795$	7.39445	0.262254
$796$	−2.18335	−0.0773867
$797$	16.6056	0.588199	0.294099	−	0.955775i	$-0.404980\pi$
$797$	16.6056	0.588199	0.294099	+	0.955775i	$0.404980\pi$
$798$	0.394449	0.0139633
$799$	−27.6333	−0.977596
$800$	0.302776	0.0107047
$801$	−13.3944	−0.473270
$802$	22.6056	0.798230
$803$	0	0
$804$	−1.97224	−0.0695557
$805$	−4.18335	−0.147444
$806$	−10.9083	−0.384229
$807$	−6.00000	−0.211210
$808$	−7.81665	−0.274989
$809$	−33.2111	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$809$	−33.2111	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$810$	−18.8444	−0.662125
$811$	−29.6333	−1.04057	−0.520283	−	0.853994i	$-0.674174\pi$
$811$	−29.6333	−1.04057	−0.520283	+	0.853994i	$0.674174\pi$
$812$	−10.8167	−0.379590
$813$	1.97224	0.0691696
$814$	0	0
$815$	26.2389	0.919107
$816$	1.39445	0.0488155
$817$	1.09167	0.0381928
$818$	−23.1472	−0.809322
$819$	12.5139	0.437270
$820$	9.00000	0.314294
$821$	34.6056	1.20774	0.603871	−	0.797082i	$-0.293624\pi$
$821$	34.6056	1.20774	0.603871	+	0.797082i	$0.293624\pi$
$822$	−1.05551	−0.0368152
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	−1.69722	−0.0591256
$825$	0	0
$826$	0	0
$827$	−22.0555	−0.766945	−0.383473	−	0.923552i	$-0.625272\pi$
$827$	−22.0555	−0.766945	−0.383473	+	0.923552i	$0.625272\pi$
$828$	4.05551	0.140939
$829$	−27.5778	−0.957816	−0.478908	−	0.877865i	$-0.658967\pi$
$829$	−27.5778	−0.957816	−0.478908	+	0.877865i	$0.658967\pi$
$830$	32.9361	1.14323
$831$	3.02776	0.105032
$832$	3.30278	0.114503
$833$	−24.4222	−0.846179
$834$	1.90833	0.0660800
$835$	−28.6056	−0.989936
$836$	0	0
$837$	5.90833	0.204222
$838$	8.78890	0.303607
$839$	19.8806	0.686354	0.343177	−	0.939271i	$-0.388497\pi$
$839$	19.8806	0.686354	0.343177	+	0.939271i	$0.388497\pi$
$840$	0.908327	0.0313403
$841$	39.9361	1.37711
$842$	−30.2389	−1.04210
$843$	0.147186	0.00506935
$844$	−24.6056	−0.846958
$845$	4.81665	0.165698
$846$	17.4500	0.599942
$847$	0	0
$848$	−10.6056	−0.364196
$849$	5.73338	0.196769
$850$	1.39445	0.0478292
$851$	−7.26662	−0.249096
$852$	−2.93608	−0.100589
$853$	46.4222	1.58947	0.794733	−	0.606959i	$-0.207611\pi$
$853$	46.4222	1.58947	0.794733	+	0.606959i	$0.207611\pi$
$854$	14.6056	0.499792
$855$	−6.69722	−0.229040
$856$	−3.21110	−0.109753
$857$	43.5416	1.48735	0.743677	−	0.668539i	$-0.233080\pi$
$857$	43.5416	1.48735	0.743677	+	0.668539i	$0.233080\pi$
$858$	0	0
$859$	8.84441	0.301767	0.150884	−	0.988552i	$-0.451788\pi$
$859$	8.84441	0.301767	0.150884	+	0.988552i	$0.451788\pi$
$860$	2.51388	0.0857225
$861$	1.54163	0.0525388
$862$	−2.78890	−0.0949902
$863$	−17.7250	−0.603365	−0.301683	−	0.953408i	$-0.597548\pi$
$863$	−17.7250	−0.603365	−0.301683	+	0.953408i	$0.597548\pi$
$864$	−1.78890	−0.0608595
$865$	−44.5139	−1.51352
$866$	−24.2389	−0.823670
$867$	1.27502	0.0433019
$868$	4.30278	0.146046
$869$	0	0
$870$	−5.78890	−0.196262
$871$	−21.5139	−0.728970
$872$	−2.00000	−0.0677285
$873$	−23.2666	−0.787456
$874$	1.39445	0.0471679
$875$	−14.0917	−0.476385
$876$	0.788897	0.0266544
$877$	−47.5694	−1.60630	−0.803152	−	0.595774i	$-0.796845\pi$
$877$	−47.5694	−1.60630	−0.803152	+	0.595774i	$0.796845\pi$
$878$	25.2111	0.850833
$879$	7.73338	0.260841
$880$	0	0
$881$	−33.9083	−1.14240	−0.571200	−	0.820811i	$-0.693522\pi$
$881$	−33.9083	−1.14240	−0.571200	+	0.820811i	$0.693522\pi$
$882$	15.4222	0.519293
$883$	−39.0278	−1.31339	−0.656694	−	0.754157i	$-0.728046\pi$
$883$	−39.0278	−1.31339	−0.656694	+	0.754157i	$0.728046\pi$
$884$	15.2111	0.511605
$885$	0	0
$886$	39.6333	1.33151
$887$	−24.8444	−0.834194	−0.417097	−	0.908862i	$-0.636952\pi$
$887$	−24.8444	−0.834194	−0.417097	+	0.908862i	$0.636952\pi$
$888$	1.57779	0.0529473
$889$	−7.02776	−0.235703
$890$	−10.6056	−0.355499
$891$	0	0
$892$	−25.2111	−0.844130
$893$	6.00000	0.200782
$894$	0	0
$895$	30.2111	1.00985
$896$	−1.30278	−0.0435227
$897$	−1.39445	−0.0465593
$898$	−31.8167	−1.06174
$899$	−27.4222	−0.914582
$900$	−0.880571	−0.0293524
$901$	−48.8444	−1.62724
$902$	0	0
$903$	0.430609	0.0143298
$904$	0	0
$905$	34.6056	1.15033
$906$	4.97224	0.165192
$907$	−4.84441	−0.160856	−0.0804280	−	0.996760i	$-0.525629\pi$
$907$	−4.84441	−0.160856	−0.0804280	+	0.996760i	$0.525629\pi$
$908$	−1.81665	−0.0602878
$909$	22.7334	0.754019
$910$	9.90833	0.328458
$911$	27.6333	0.915532	0.457766	−	0.889073i	$-0.348650\pi$
$911$	27.6333	0.915532	0.457766	+	0.889073i	$0.348650\pi$
$912$	−0.302776	−0.0100259
$913$	0	0
$914$	−21.8167	−0.721631
$915$	7.81665	0.258411
$916$	11.9083	0.393462
$917$	24.9083	0.822545
$918$	−8.23886	−0.271923
$919$	−6.11943	−0.201861	−0.100931	−	0.994893i	$-0.532182\pi$
$919$	−6.11943	−0.201861	−0.100931	+	0.994893i	$0.532182\pi$
$920$	3.21110	0.105867
$921$	0.661064	0.0217828
$922$	−6.42221	−0.211504
$923$	−32.0278	−1.05421
$924$	0	0
$925$	1.57779	0.0518776
$926$	−1.21110	−0.0397993
$927$	4.93608	0.162122
$928$	8.30278	0.272552
$929$	−8.51388	−0.279331	−0.139666	−	0.990199i	$-0.544603\pi$
$929$	−8.51388	−0.279331	−0.139666	+	0.990199i	$0.544603\pi$
$930$	2.30278	0.0755110
$931$	5.30278	0.173791
$932$	−9.21110	−0.301720
$933$	7.81665	0.255906
$934$	−22.6056	−0.739676
$935$	0	0
$936$	−9.60555	−0.313967
$937$	−1.15559	−0.0377515	−0.0188757	−	0.999822i	$-0.506009\pi$
$937$	−1.15559	−0.0377515	−0.0188757	+	0.999822i	$0.506009\pi$
$938$	8.48612	0.277082
$939$	5.48612	0.179033
$940$	13.8167	0.450650
$941$	57.6333	1.87879	0.939396	−	0.342834i	$-0.111387\pi$
$941$	57.6333	1.87879	0.939396	+	0.342834i	$0.111387\pi$
$942$	0.330532	0.0107693
$943$	5.44996	0.177475
$944$	0	0
$945$	−5.36669	−0.174579
$946$	0	0
$947$	25.8167	0.838929	0.419464	−	0.907772i	$-0.362218\pi$
$947$	25.8167	0.838929	0.419464	+	0.907772i	$0.362218\pi$
$948$	−4.78890	−0.155536
$949$	8.60555	0.279348
$950$	−0.302776	−0.00982334
$951$	−4.18335	−0.135654
$952$	−6.00000	−0.194461
$953$	21.6333	0.700772	0.350386	−	0.936605i	$-0.386050\pi$
$953$	21.6333	0.700772	0.350386	+	0.936605i	$0.386050\pi$
$954$	30.8444	0.998625
$955$	13.8167	0.447096
$956$	23.9361	0.774148
$957$	0	0
$958$	−35.7250	−1.15422
$959$	4.54163	0.146657
$960$	−0.697224	−0.0225028
$961$	−20.0917	−0.648118
$962$	17.2111	0.554908
$963$	9.33894	0.300943
$964$	−13.0917	−0.421654
$965$	−56.9361	−1.83284
$966$	0.550039	0.0176972
$967$	−23.6333	−0.759996	−0.379998	−	0.924987i	$-0.624075\pi$
$967$	−23.6333	−0.759996	−0.379998	+	0.924987i	$0.624075\pi$
$968$	0	0
$969$	−1.39445	−0.0447961
$970$	−18.4222	−0.591501
$971$	−23.9361	−0.768145	−0.384073	−	0.923303i	$-0.625479\pi$
$971$	−23.9361	−0.768145	−0.384073	+	0.923303i	$0.625479\pi$
$972$	7.84441	0.251610
$973$	−8.21110	−0.263236
$974$	−29.3305	−0.939811
$975$	0.302776	0.00969658
$976$	−11.2111	−0.358859
$977$	27.6333	0.884068	0.442034	−	0.896998i	$-0.354257\pi$
$977$	27.6333	0.884068	0.442034	+	0.896998i	$0.354257\pi$
$978$	−3.44996	−0.110318
$979$	0	0
$980$	12.2111	0.390069
$981$	5.81665	0.185711
$982$	14.9361	0.476630
$983$	23.3028	0.743243	0.371622	−	0.928384i	$-0.378802\pi$
$983$	23.3028	0.743243	0.371622	+	0.928384i	$0.378802\pi$
$984$	−1.18335	−0.0377237
$985$	49.8167	1.58729
$986$	38.2389	1.21777
$987$	2.36669	0.0753326
$988$	−3.30278	−0.105075
$989$	1.52228	0.0484058
$990$	0	0
$991$	−25.9083	−0.823005	−0.411503	−	0.911409i	$-0.634996\pi$
$991$	−25.9083	−0.823005	−0.411503	+	0.911409i	$0.634996\pi$
$992$	−3.30278	−0.104863
$993$	6.88057	0.218348
$994$	12.6333	0.400704
$995$	5.02776	0.159391
$996$	−4.33053	−0.137218
$997$	−0.183346	−0.00580663	−0.00290332	−	0.999996i	$-0.500924\pi$
$997$	−0.183346	−0.00580663	−0.00290332	+	0.999996i	$0.500924\pi$
$998$	−34.0000	−1.07625
$999$	−9.32213	−0.294939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bc.1.2		2
11.10	odd	2		418.2.a.d.1.2	✓	2
33.32	even	2		3762.2.a.bb.1.2		2
44.43	even	2		3344.2.a.o.1.1		2
209.208	even	2		7942.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.d.1.2	✓	2	11.10	odd	2
3344.2.a.o.1.1		2	44.43	even	2
3762.2.a.bb.1.2		2	33.32	even	2
4598.2.a.bc.1.2		2	1.1	even	1	trivial
7942.2.a.bb.1.1		2	209.208	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} -2.30278 q^{5} +0.302776 q^{6} -1.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} -2.30278 q^{5} +0.302776 q^{6} -1.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} -2.30278 q^{10} +0.302776 q^{12} +3.30278 q^{13} -1.30278 q^{14} -0.697224 q^{15} +1.00000 q^{16} +4.60555 q^{17} -2.90833 q^{18} -1.00000 q^{19} -2.30278 q^{20} -0.394449 q^{21} -1.39445 q^{23} +0.302776 q^{24} +0.302776 q^{25} +3.30278 q^{26} -1.78890 q^{27} -1.30278 q^{28} +8.30278 q^{29} -0.697224 q^{30} -3.30278 q^{31} +1.00000 q^{32} +4.60555 q^{34} +3.00000 q^{35} -2.90833 q^{36} +5.21110 q^{37} -1.00000 q^{38} +1.00000 q^{39} -2.30278 q^{40} -3.90833 q^{41} -0.394449 q^{42} -1.09167 q^{43} +6.69722 q^{45} -1.39445 q^{46} -6.00000 q^{47} +0.302776 q^{48} -5.30278 q^{49} +0.302776 q^{50} +1.39445 q^{51} +3.30278 q^{52} -10.6056 q^{53} -1.78890 q^{54} -1.30278 q^{56} -0.302776 q^{57} +8.30278 q^{58} -0.697224 q^{60} -11.2111 q^{61} -3.30278 q^{62} +3.78890 q^{63} +1.00000 q^{64} -7.60555 q^{65} -6.51388 q^{67} +4.60555 q^{68} -0.422205 q^{69} +3.00000 q^{70} -9.69722 q^{71} -2.90833 q^{72} +2.60555 q^{73} +5.21110 q^{74} +0.0916731 q^{75} -1.00000 q^{76} +1.00000 q^{78} -15.8167 q^{79} -2.30278 q^{80} +8.18335 q^{81} -3.90833 q^{82} -14.3028 q^{83} -0.394449 q^{84} -10.6056 q^{85} -1.09167 q^{86} +2.51388 q^{87} +4.60555 q^{89} +6.69722 q^{90} -4.30278 q^{91} -1.39445 q^{92} -1.00000 q^{93} -6.00000 q^{94} +2.30278 q^{95} +0.302776 q^{96} +8.00000 q^{97} -5.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + q^{7} + 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + q^7 + 2 * q^8 + 5 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + q^{7} + 2 q^{8} + 5 q^{9} - q^{10} - 3 q^{12} + 3 q^{13} + q^{14} - 5 q^{15} + 2 q^{16} + 2 q^{17} + 5 q^{18} - 2 q^{19} - q^{20} - 8 q^{21} - 10 q^{23} - 3 q^{24} - 3 q^{25} + 3 q^{26} - 18 q^{27} + q^{28} + 13 q^{29} - 5 q^{30} - 3 q^{31} + 2 q^{32} + 2 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} - 2 q^{38} + 2 q^{39} - q^{40} + 3 q^{41} - 8 q^{42} - 13 q^{43} + 17 q^{45} - 10 q^{46} - 12 q^{47} - 3 q^{48} - 7 q^{49} - 3 q^{50} + 10 q^{51} + 3 q^{52} - 14 q^{53} - 18 q^{54} + q^{56} + 3 q^{57} + 13 q^{58} - 5 q^{60} - 8 q^{61} - 3 q^{62} + 22 q^{63} + 2 q^{64} - 8 q^{65} + 5 q^{67} + 2 q^{68} + 28 q^{69} + 6 q^{70} - 23 q^{71} + 5 q^{72} - 2 q^{73} - 4 q^{74} + 11 q^{75} - 2 q^{76} + 2 q^{78} - 10 q^{79} - q^{80} + 38 q^{81} + 3 q^{82} - 25 q^{83} - 8 q^{84} - 14 q^{85} - 13 q^{86} - 13 q^{87} + 2 q^{89} + 17 q^{90} - 5 q^{91} - 10 q^{92} - 2 q^{93} - 12 q^{94} + q^{95} - 3 q^{96} + 16 q^{97} - 7 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + q^7 + 2 * q^8 + 5 * q^9 - q^10 - 3 * q^12 + 3 * q^13 + q^14 - 5 * q^15 + 2 * q^16 + 2 * q^17 + 5 * q^18 - 2 * q^19 - q^20 - 8 * q^21 - 10 * q^23 - 3 * q^24 - 3 * q^25 + 3 * q^26 - 18 * q^27 + q^28 + 13 * q^29 - 5 * q^30 - 3 * q^31 + 2 * q^32 + 2 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 - 2 * q^38 + 2 * q^39 - q^40 + 3 * q^41 - 8 * q^42 - 13 * q^43 + 17 * q^45 - 10 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 - 3 * q^50 + 10 * q^51 + 3 * q^52 - 14 * q^53 - 18 * q^54 + q^56 + 3 * q^57 + 13 * q^58 - 5 * q^60 - 8 * q^61 - 3 * q^62 + 22 * q^63 + 2 * q^64 - 8 * q^65 + 5 * q^67 + 2 * q^68 + 28 * q^69 + 6 * q^70 - 23 * q^71 + 5 * q^72 - 2 * q^73 - 4 * q^74 + 11 * q^75 - 2 * q^76 + 2 * q^78 - 10 * q^79 - q^80 + 38 * q^81 + 3 * q^82 - 25 * q^83 - 8 * q^84 - 14 * q^85 - 13 * q^86 - 13 * q^87 + 2 * q^89 + 17 * q^90 - 5 * q^91 - 10 * q^92 - 2 * q^93 - 12 * q^94 + q^95 - 3 * q^96 + 16 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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