LMFDB - Embedded newform 4598.2.a.bu.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.33452.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 7x - 1 $ x^4 - x^3 - 8x^2 + 7x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.669883$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.669883 q^{3} +1.00000 q^{4} -3.56566 q^{5} +0.669883 q^{6} -0.507202 q^{7} +1.00000 q^{8} -2.55126 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.669883 q^{3} +1.00000 q^{4} -3.56566 q^{5} +0.669883 q^{6} -0.507202 q^{7} +1.00000 q^{8} -2.55126 q^{9} -3.56566 q^{10} +0.669883 q^{12} -6.56566 q^{13} -0.507202 q^{14} -2.38858 q^{15} +1.00000 q^{16} +4.23554 q^{17} -2.55126 q^{18} -1.00000 q^{19} -3.56566 q^{20} -0.339766 q^{21} +0.177085 q^{23} +0.669883 q^{24} +7.71394 q^{25} -6.56566 q^{26} -3.71869 q^{27} -0.507202 q^{28} +7.08251 q^{29} -2.38858 q^{30} +10.3886 q^{31} +1.00000 q^{32} +4.23554 q^{34} +1.80851 q^{35} -2.55126 q^{36} -7.45668 q^{37} -1.00000 q^{38} -4.39822 q^{39} -3.56566 q^{40} +2.71394 q^{41} -0.339766 q^{42} +3.21149 q^{43} +9.09692 q^{45} +0.177085 q^{46} -3.13132 q^{47} +0.669883 q^{48} -6.74275 q^{49} +7.71394 q^{50} +2.83732 q^{51} -6.56566 q^{52} +2.54161 q^{53} -3.71869 q^{54} -0.507202 q^{56} -0.669883 q^{57} +7.08251 q^{58} +5.57531 q^{59} -2.38858 q^{60} +0.985596 q^{61} +10.3886 q^{62} +1.29400 q^{63} +1.00000 q^{64} +23.4109 q^{65} +12.6241 q^{67} +4.23554 q^{68} +0.118626 q^{69} +1.80851 q^{70} -8.55126 q^{71} -2.55126 q^{72} +1.10422 q^{73} -7.45668 q^{74} +5.16744 q^{75} -1.00000 q^{76} -4.39822 q^{78} +9.76275 q^{79} -3.56566 q^{80} +5.16268 q^{81} +2.71394 q^{82} -8.19709 q^{83} -0.339766 q^{84} -15.1025 q^{85} +3.21149 q^{86} +4.74445 q^{87} +12.4423 q^{89} +9.09692 q^{90} +3.33012 q^{91} +0.177085 q^{92} +6.95913 q^{93} -3.13132 q^{94} +3.56566 q^{95} +0.669883 q^{96} -8.82526 q^{97} -6.74275 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 + q^6 - q^7 + 4 * q^8 + 5 * q^9	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - q^{7} + 4 q^{8} + 5 q^{9} + 3 q^{10} + q^{12} - 9 q^{13} - q^{14} + 5 q^{15} + 4 q^{16} - 2 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 2 q^{23} + q^{24} + 15 q^{25} - 9 q^{26} - 2 q^{27} - q^{28} + 5 q^{29} + 5 q^{30} + 27 q^{31} + 4 q^{32} - 2 q^{34} + 12 q^{35} + 5 q^{36} + 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} + 2 q^{42} + q^{43} + 11 q^{45} - 2 q^{46} + 22 q^{47} + q^{48} - 7 q^{49} + 15 q^{50} + 12 q^{51} - 9 q^{52} - 2 q^{54} - q^{56} - q^{57} + 5 q^{58} + 5 q^{60} + 6 q^{61} + 27 q^{62} - 30 q^{63} + 4 q^{64} + 26 q^{65} + 17 q^{67} - 2 q^{68} + 14 q^{69} + 12 q^{70} - 19 q^{71} + 5 q^{72} + 20 q^{73} + 6 q^{74} + 23 q^{75} - 4 q^{76} + 2 q^{78} + 12 q^{79} + 3 q^{80} + 20 q^{81} - 5 q^{82} - 23 q^{83} + 2 q^{84} - 30 q^{85} + q^{86} + 45 q^{87} + 16 q^{89} + 11 q^{90} + 15 q^{91} - 2 q^{92} - 12 q^{93} + 22 q^{94} - 3 q^{95} + q^{96} + 8 q^{97} - 7 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 + q^6 - q^7 + 4 * q^8 + 5 * q^9 + 3 * q^10 + q^12 - 9 * q^13 - q^14 + 5 * q^15 + 4 * q^16 - 2 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 2 * q^23 + q^24 + 15 * q^25 - 9 * q^26 - 2 * q^27 - q^28 + 5 * q^29 + 5 * q^30 + 27 * q^31 + 4 * q^32 - 2 * q^34 + 12 * q^35 + 5 * q^36 + 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 + 2 * q^42 + q^43 + 11 * q^45 - 2 * q^46 + 22 * q^47 + q^48 - 7 * q^49 + 15 * q^50 + 12 * q^51 - 9 * q^52 - 2 * q^54 - q^56 - q^57 + 5 * q^58 + 5 * q^60 + 6 * q^61 + 27 * q^62 - 30 * q^63 + 4 * q^64 + 26 * q^65 + 17 * q^67 - 2 * q^68 + 14 * q^69 + 12 * q^70 - 19 * q^71 + 5 * q^72 + 20 * q^73 + 6 * q^74 + 23 * q^75 - 4 * q^76 + 2 * q^78 + 12 * q^79 + 3 * q^80 + 20 * q^81 - 5 * q^82 - 23 * q^83 + 2 * q^84 - 30 * q^85 + q^86 + 45 * q^87 + 16 * q^89 + 11 * q^90 + 15 * q^91 - 2 * q^92 - 12 * q^93 + 22 * q^94 - 3 * q^95 + q^96 + 8 * 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
$3$	0.669883	0.386757	0.193379	−	0.981124i	$-0.438055\pi$
$3$	0.669883	0.386757	0.193379	+	0.981124i	$0.438055\pi$
$4$	1.00000	0.500000
$5$	−3.56566	−1.59461	−0.797306	−	0.603575i	$-0.793742\pi$
$5$	−3.56566	−1.59461	−0.797306	+	0.603575i	$0.793742\pi$
$6$	0.669883	0.273479
$7$	−0.507202	−0.191704	−0.0958522	−	0.995396i	$-0.530558\pi$
$7$	−0.507202	−0.191704	−0.0958522	+	0.995396i	$0.530558\pi$
$8$	1.00000	0.353553
$9$	−2.55126	−0.850419
$10$	−3.56566	−1.12756
$11$	0	0
$11$	0	0
$12$	0.669883	0.193379
$13$	−6.56566	−1.82099	−0.910493	−	0.413524i	$-0.864298\pi$
$13$	−6.56566	−1.82099	−0.910493	+	0.413524i	$0.864298\pi$
$14$	−0.507202	−0.135555
$15$	−2.38858	−0.616728
$16$	1.00000	0.250000
$17$	4.23554	1.02727	0.513635	−	0.858009i	$-0.328299\pi$
$17$	4.23554	1.02727	0.513635	+	0.858009i	$0.328299\pi$
$18$	−2.55126	−0.601337
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.56566	−0.797306
$21$	−0.339766	−0.0741430
$22$	0	0
$23$	0.177085	0.0369248	0.0184624	−	0.999830i	$-0.494123\pi$
$23$	0.177085	0.0369248	0.0184624	+	0.999830i	$0.494123\pi$
$24$	0.669883	0.136739
$25$	7.71394	1.54279
$26$	−6.56566	−1.28763
$27$	−3.71869	−0.715663
$28$	−0.507202	−0.0958522
$29$	7.08251	1.31519	0.657595	−	0.753372i	$-0.271574\pi$
$29$	7.08251	1.31519	0.657595	+	0.753372i	$0.271574\pi$
$30$	−2.38858	−0.436092
$31$	10.3886	1.86584	0.932922	−	0.360079i	$-0.117250\pi$
$31$	10.3886	1.86584	0.932922	+	0.360079i	$0.117250\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.23554	0.726390
$35$	1.80851	0.305694
$36$	−2.55126	−0.425209
$37$	−7.45668	−1.22587	−0.612936	−	0.790133i	$-0.710012\pi$
$37$	−7.45668	−1.22587	−0.612936	+	0.790133i	$0.710012\pi$
$38$	−1.00000	−0.162221
$39$	−4.39822	−0.704280
$40$	−3.56566	−0.563780
$41$	2.71394	0.423846	0.211923	−	0.977286i	$-0.432027\pi$
$41$	2.71394	0.423846	0.211923	+	0.977286i	$0.432027\pi$
$42$	−0.339766	−0.0524270
$43$	3.21149	0.489748	0.244874	−	0.969555i	$-0.421253\pi$
$43$	3.21149	0.489748	0.244874	+	0.969555i	$0.421253\pi$
$44$	0	0
$45$	9.09692	1.35609
$46$	0.177085	0.0261098
$47$	−3.13132	−0.456750	−0.228375	−	0.973573i	$-0.573341\pi$
$47$	−3.13132	−0.456750	−0.228375	+	0.973573i	$0.573341\pi$
$48$	0.669883	0.0966893
$49$	−6.74275	−0.963249
$50$	7.71394	1.09092
$51$	2.83732	0.397304
$52$	−6.56566	−0.910493
$53$	2.54161	0.349117	0.174558	−	0.984647i	$-0.444150\pi$
$53$	2.54161	0.349117	0.174558	+	0.984647i	$0.444150\pi$
$54$	−3.71869	−0.506050
$55$	0	0
$56$	−0.507202	−0.0677777
$57$	−0.669883	−0.0887282
$58$	7.08251	0.929979
$59$	5.57531	0.725844	0.362922	−	0.931820i	$-0.381779\pi$
$59$	5.57531	0.725844	0.362922	+	0.931820i	$0.381779\pi$
$60$	−2.38858	−0.308364
$61$	0.985596	0.126193	0.0630963	−	0.998007i	$-0.479902\pi$
$61$	0.985596	0.126193	0.0630963	+	0.998007i	$0.479902\pi$
$62$	10.3886	1.31935
$63$	1.29400	0.163029
$64$	1.00000	0.125000
$65$	23.4109	2.90377
$66$	0	0
$67$	12.6241	1.54228	0.771141	−	0.636665i	$-0.219686\pi$
$67$	12.6241	1.54228	0.771141	+	0.636665i	$0.219686\pi$
$68$	4.23554	0.513635
$69$	0.118626	0.0142809
$70$	1.80851	0.216158
$71$	−8.55126	−1.01485	−0.507424	−	0.861697i	$-0.669402\pi$
$71$	−8.55126	−1.01485	−0.507424	+	0.861697i	$0.669402\pi$
$72$	−2.55126	−0.300668
$73$	1.10422	0.129239	0.0646197	−	0.997910i	$-0.479417\pi$
$73$	1.10422	0.129239	0.0646197	+	0.997910i	$0.479417\pi$
$74$	−7.45668	−0.866822
$75$	5.16744	0.596684
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−4.39822	−0.498001
$79$	9.76275	1.09839	0.549197	−	0.835693i	$-0.314933\pi$
$79$	9.76275	1.09839	0.549197	+	0.835693i	$0.314933\pi$
$80$	−3.56566	−0.398653
$81$	5.16268	0.573631
$82$	2.71394	0.299704
$83$	−8.19709	−0.899747	−0.449874	−	0.893092i	$-0.648531\pi$
$83$	−8.19709	−0.899747	−0.449874	+	0.893092i	$0.648531\pi$
$84$	−0.339766	−0.0370715
$85$	−15.1025	−1.63810
$86$	3.21149	0.346304
$87$	4.74445	0.508659
$88$	0	0
$89$	12.4423	1.31888	0.659439	−	0.751758i	$-0.270794\pi$
$89$	12.4423	1.31888	0.659439	+	0.751758i	$0.270794\pi$
$90$	9.09692	0.958899
$91$	3.33012	0.349091
$92$	0.177085	0.0184624
$93$	6.95913	0.721628
$94$	−3.13132	−0.322971
$95$	3.56566	0.365829
$96$	0.669883	0.0683697
$97$	−8.82526	−0.896069	−0.448035	−	0.894016i	$-0.647876\pi$
$97$	−8.82526	−0.896069	−0.448035	+	0.894016i	$0.647876\pi$
$98$	−6.74275	−0.681120
$99$	0	0
$100$	7.71394	0.771394
$101$	7.36857	0.733201	0.366600	−	0.930379i	$-0.380522\pi$
$101$	7.36857	0.733201	0.366600	+	0.930379i	$0.380522\pi$
$102$	2.83732	0.280936
$103$	16.0367	1.58015	0.790074	−	0.613012i	$-0.210042\pi$
$103$	16.0367	1.58015	0.790074	+	0.613012i	$0.210042\pi$
$104$	−6.56566	−0.643816
$105$	1.21149	0.118229
$106$	2.54161	0.246863
$107$	12.7458	1.23218	0.616091	−	0.787675i	$-0.288715\pi$
$107$	12.7458	1.23218	0.616091	+	0.787675i	$0.288715\pi$
$108$	−3.71869	−0.357831
$109$	10.0856	0.966021	0.483011	−	0.875614i	$-0.339543\pi$
$109$	10.0856	0.966021	0.483011	+	0.875614i	$0.339543\pi$
$110$	0	0
$111$	−4.99511	−0.474114
$112$	−0.507202	−0.0479261
$113$	9.69394	0.911929	0.455964	−	0.889998i	$-0.349294\pi$
$113$	9.69394	0.911929	0.455964	+	0.889998i	$0.349294\pi$
$114$	−0.669883	−0.0627403
$115$	−0.631426	−0.0588807
$116$	7.08251	0.657595
$117$	16.7507	1.54860
$118$	5.57531	0.513249
$119$	−2.14828	−0.196932
$120$	−2.38858	−0.218046
$121$	0	0
$122$	0.985596	0.0892317
$123$	1.81802	0.163925
$124$	10.3886	0.932922
$125$	−9.67698	−0.865536
$126$	1.29400	0.115279
$127$	11.7916	1.04633	0.523166	−	0.852231i	$-0.324751\pi$
$127$	11.7916	1.04633	0.523166	+	0.852231i	$0.324751\pi$
$128$	1.00000	0.0883883
$129$	2.15132	0.189413
$130$	23.4109	2.05327
$131$	−7.81645	−0.682927	−0.341463	−	0.939895i	$-0.610922\pi$
$131$	−7.81645	−0.682927	−0.341463	+	0.939895i	$0.610922\pi$
$132$	0	0
$133$	0.507202	0.0439800
$134$	12.6241	1.09056
$135$	13.2596	1.14120
$136$	4.23554	0.363195
$137$	6.32841	0.540672	0.270336	−	0.962766i	$-0.412865\pi$
$137$	6.32841	0.540672	0.270336	+	0.962766i	$0.412865\pi$
$138$	0.118626	0.0100981
$139$	−15.0319	−1.27499	−0.637493	−	0.770456i	$-0.720028\pi$
$139$	−15.0319	−1.27499	−0.637493	+	0.770456i	$0.720028\pi$
$140$	1.80851	0.152847
$141$	−2.09762	−0.176651
$142$	−8.55126	−0.717606
$143$	0	0
$144$	−2.55126	−0.212605
$145$	−25.2538	−2.09722
$146$	1.10422	0.0913861
$147$	−4.51685	−0.372544
$148$	−7.45668	−0.612936
$149$	−21.1218	−1.73037	−0.865183	−	0.501456i	$-0.832798\pi$
$149$	−21.1218	−1.73037	−0.865183	+	0.501456i	$0.832798\pi$
$150$	5.16744	0.421919
$151$	−23.2387	−1.89114	−0.945570	−	0.325417i	$-0.894495\pi$
$151$	−23.2387	−1.89114	−0.945570	+	0.325417i	$0.894495\pi$
$152$	−1.00000	−0.0811107
$153$	−10.8060	−0.873610
$154$	0	0
$155$	−37.0421	−2.97530
$156$	−4.39822	−0.352140
$157$	8.88613	0.709190	0.354595	−	0.935020i	$-0.384619\pi$
$157$	8.88613	0.709190	0.354595	+	0.935020i	$0.384619\pi$
$158$	9.76275	0.776682
$159$	1.70258	0.135023
$160$	−3.56566	−0.281890
$161$	−0.0898180	−0.00707865
$162$	5.16268	0.405619
$163$	11.4374	0.895845	0.447923	−	0.894072i	$-0.352164\pi$
$163$	11.4374	0.895845	0.447923	+	0.894072i	$0.352164\pi$
$164$	2.71394	0.211923
$165$	0	0
$166$	−8.19709	−0.636217
$167$	−16.5880	−1.28362	−0.641809	−	0.766864i	$-0.721816\pi$
$167$	−16.5880	−1.28362	−0.641809	+	0.766864i	$0.721816\pi$
$168$	−0.339766	−0.0262135
$169$	30.1079	2.31599
$170$	−15.1025	−1.15831
$171$	2.55126	0.195099
$172$	3.21149	0.244874
$173$	−3.84292	−0.292172	−0.146086	−	0.989272i	$-0.546668\pi$
$173$	−3.84292	−0.292172	−0.146086	+	0.989272i	$0.546668\pi$
$174$	4.74445	0.359676
$175$	−3.91253	−0.295759
$176$	0	0
$177$	3.73481	0.280725
$178$	12.4423	0.932588
$179$	−1.72834	−0.129182	−0.0645912	−	0.997912i	$-0.520574\pi$
$179$	−1.72834	−0.129182	−0.0645912	+	0.997912i	$0.520574\pi$
$180$	9.09692	0.678044
$181$	−2.29655	−0.170701	−0.0853507	−	0.996351i	$-0.527201\pi$
$181$	−2.29655	−0.170701	−0.0853507	+	0.996351i	$0.527201\pi$
$182$	3.33012	0.246845
$183$	0.660234	0.0488059
$184$	0.177085	0.0130549
$185$	26.5880	1.95479
$186$	6.95913	0.510268
$187$	0	0
$188$	−3.13132	−0.228375
$189$	1.88613	0.137196
$190$	3.56566	0.258680
$191$	7.88053	0.570215	0.285108	−	0.958496i	$-0.407971\pi$
$191$	7.88053	0.570215	0.285108	+	0.958496i	$0.407971\pi$
$192$	0.669883	0.0483446
$193$	0.254703	0.0183339	0.00916697	−	0.999958i	$-0.497082\pi$
$193$	0.254703	0.0183339	0.00916697	+	0.999958i	$0.497082\pi$
$194$	−8.82526	−0.633617
$195$	15.6826	1.12305
$196$	−6.74275	−0.481625
$197$	18.2626	1.30116	0.650580	−	0.759438i	$-0.274526\pi$
$197$	18.2626	1.30116	0.650580	+	0.759438i	$0.274526\pi$
$198$	0	0
$199$	8.60007	0.609643	0.304821	−	0.952410i	$-0.401403\pi$
$199$	8.60007	0.609643	0.304821	+	0.952410i	$0.401403\pi$
$200$	7.71394	0.545458
$201$	8.45668	0.596488
$202$	7.36857	0.518451
$203$	−3.59226	−0.252128
$204$	2.83732	0.198652
$205$	−9.67698	−0.675870
$206$	16.0367	1.11733
$207$	−0.451790	−0.0314016
$208$	−6.56566	−0.455247
$209$	0	0
$210$	1.21149	0.0836008
$211$	−10.8661	−0.748055	−0.374028	−	0.927418i	$-0.622023\pi$
$211$	−10.8661	−0.748055	−0.374028	+	0.927418i	$0.622023\pi$
$212$	2.54161	0.174558
$213$	−5.72834	−0.392500
$214$	12.7458	0.871284
$215$	−11.4511	−0.780958
$216$	−3.71869	−0.253025
$217$	−5.26911	−0.357690
$218$	10.0856	0.683080
$219$	0.739700	0.0499843
$220$	0	0
$221$	−27.8091	−1.87065
$222$	−4.99511	−0.335250
$223$	−12.4711	−0.835126	−0.417563	−	0.908648i	$-0.637116\pi$
$223$	−12.4711	−0.835126	−0.417563	+	0.908648i	$0.637116\pi$
$224$	−0.507202	−0.0338889
$225$	−19.6802	−1.31202
$226$	9.69394	0.644831
$227$	−29.8483	−1.98110	−0.990551	−	0.137146i	$-0.956207\pi$
$227$	−29.8483	−1.98110	−0.990551	+	0.137146i	$0.956207\pi$
$228$	−0.669883	−0.0443641
$229$	−19.3115	−1.27614	−0.638068	−	0.769980i	$-0.720266\pi$
$229$	−19.3115	−1.27614	−0.638068	+	0.769980i	$0.720266\pi$
$230$	−0.631426	−0.0416350
$231$	0	0
$232$	7.08251	0.464990
$233$	10.0288	0.657009	0.328505	−	0.944502i	$-0.393455\pi$
$233$	10.0288	0.657009	0.328505	+	0.944502i	$0.393455\pi$
$234$	16.7507	1.09503
$235$	11.1652	0.728339
$236$	5.57531	0.362922
$237$	6.53990	0.424812
$238$	−2.14828	−0.139252
$239$	−11.2291	−0.726349	−0.363174	−	0.931721i	$-0.618307\pi$
$239$	−11.2291	−0.726349	−0.363174	+	0.931721i	$0.618307\pi$
$240$	−2.38858	−0.154182
$241$	16.0367	1.03302	0.516509	−	0.856282i	$-0.327231\pi$
$241$	16.0367	1.03302	0.516509	+	0.856282i	$0.327231\pi$
$242$	0	0
$243$	14.6145	0.937519
$244$	0.985596	0.0630963
$245$	24.0423	1.53601
$246$	1.81802	0.115913
$247$	6.56566	0.417763
$248$	10.3886	0.659675
$249$	−5.49109	−0.347984
$250$	−9.67698	−0.612026
$251$	27.0591	1.70795	0.853977	−	0.520310i	$-0.174184\pi$
$251$	27.0591	1.70795	0.853977	+	0.520310i	$0.174184\pi$
$252$	1.29400	0.0815145
$253$	0	0
$254$	11.7916	0.739868
$255$	−10.1169	−0.633546
$256$	1.00000	0.0625000
$257$	29.2963	1.82746	0.913728	−	0.406327i	$-0.133190\pi$
$257$	29.2963	1.82746	0.913728	+	0.406327i	$0.133190\pi$
$258$	2.15132	0.133936
$259$	3.78205	0.235005
$260$	23.4109	1.45188
$261$	−18.0693	−1.11846
$262$	−7.81645	−0.482902
$263$	−30.7129	−1.89384	−0.946918	−	0.321475i	$-0.895821\pi$
$263$	−30.7129	−1.89384	−0.946918	+	0.321475i	$0.895821\pi$
$264$	0	0
$265$	−9.06251	−0.556706
$266$	0.507202	0.0310986
$267$	8.33487	0.510086
$268$	12.6241	0.771141
$269$	−14.0288	−0.855352	−0.427676	−	0.903932i	$-0.640667\pi$
$269$	−14.0288	−0.855352	−0.427676	+	0.903932i	$0.640667\pi$
$270$	13.2596	0.806953
$271$	−12.4350	−0.755371	−0.377685	−	0.925934i	$-0.623280\pi$
$271$	−12.4350	−0.755371	−0.377685	+	0.925934i	$0.623280\pi$
$272$	4.23554	0.256818
$273$	2.23079	0.135013
$274$	6.32841	0.382313
$275$	0	0
$276$	0.118626	0.00714047
$277$	16.6761	1.00197	0.500985	−	0.865456i	$-0.332971\pi$
$277$	16.6761	1.00197	0.500985	+	0.865456i	$0.332971\pi$
$278$	−15.0319	−0.901551
$279$	−26.5039	−1.58675
$280$	1.80851	0.108079
$281$	−4.67159	−0.278684	−0.139342	−	0.990244i	$-0.544499\pi$
$281$	−4.67159	−0.278684	−0.139342	+	0.990244i	$0.544499\pi$
$282$	−2.09762	−0.124911
$283$	−6.37907	−0.379196	−0.189598	−	0.981862i	$-0.560718\pi$
$283$	−6.37907	−0.379196	−0.189598	+	0.981862i	$0.560718\pi$
$284$	−8.55126	−0.507424
$285$	2.38858	0.141487
$286$	0	0
$287$	−1.37651	−0.0812531
$288$	−2.55126	−0.150334
$289$	0.939832	0.0552843
$290$	−25.2538	−1.48296
$291$	−5.91189	−0.346561
$292$	1.10422	0.0646197
$293$	12.8283	0.749438	0.374719	−	0.927139i	$-0.377739\pi$
$293$	12.8283	0.749438	0.374719	+	0.927139i	$0.377739\pi$
$294$	−4.51685	−0.263428
$295$	−19.8797	−1.15744
$296$	−7.45668	−0.433411
$297$	0	0
$298$	−21.1218	−1.22355
$299$	−1.16268	−0.0672396
$300$	5.16744	0.298342
$301$	−1.62887	−0.0938868
$302$	−23.2387	−1.33724
$303$	4.93608	0.283571
$304$	−1.00000	−0.0573539
$305$	−3.51430	−0.201228
$306$	−10.8060	−0.617736
$307$	26.5880	1.51746	0.758729	−	0.651407i	$-0.225821\pi$
$307$	26.5880	1.51746	0.758729	+	0.651407i	$0.225821\pi$
$308$	0	0
$309$	10.7427	0.611133
$310$	−37.0421	−2.10385
$311$	13.5664	0.769278	0.384639	−	0.923067i	$-0.374326\pi$
$311$	13.5664	0.769278	0.384639	+	0.923067i	$0.374326\pi$
$312$	−4.39822	−0.249000
$313$	15.1608	0.856941	0.428470	−	0.903556i	$-0.359053\pi$
$313$	15.1608	0.856941	0.428470	+	0.903556i	$0.359053\pi$
$314$	8.88613	0.501473
$315$	−4.61398	−0.259968
$316$	9.76275	0.549197
$317$	26.5958	1.49377	0.746885	−	0.664954i	$-0.231549\pi$
$317$	26.5958	1.49377	0.746885	+	0.664954i	$0.231549\pi$
$318$	1.70258	0.0954759
$319$	0	0
$320$	−3.56566	−0.199327
$321$	8.53819	0.476555
$322$	−0.0898180	−0.00500536
$323$	−4.23554	−0.235672
$324$	5.16268	0.286816
$325$	−50.6471	−2.80940
$326$	11.4374	0.633458
$327$	6.75614	0.373616
$328$	2.71394	0.149852
$329$	1.58821	0.0875610
$330$	0	0
$331$	−9.30131	−0.511246	−0.255623	−	0.966777i	$-0.582281\pi$
$331$	−9.30131	−0.511246	−0.255623	+	0.966777i	$0.582281\pi$
$332$	−8.19709	−0.449874
$333$	19.0239	1.04250
$334$	−16.5880	−0.907655
$335$	−45.0133	−2.45934
$336$	−0.339766	−0.0185358
$337$	32.8355	1.78867	0.894333	−	0.447402i	$-0.147651\pi$
$337$	32.8355	1.78867	0.894333	+	0.447402i	$0.147651\pi$
$338$	30.1079	1.63765
$339$	6.49380	0.352695
$340$	−15.1025	−0.819049
$341$	0	0
$342$	2.55126	0.137956
$343$	6.97035	0.376364
$344$	3.21149	0.173152
$345$	−0.422981	−0.0227725
$346$	−3.84292	−0.206596
$347$	11.6844	0.627253	0.313626	−	0.949546i	$-0.398456\pi$
$347$	11.6844	0.627253	0.313626	+	0.949546i	$0.398456\pi$
$348$	4.74445	0.254329
$349$	−26.0735	−1.39568	−0.697841	−	0.716253i	$-0.745856\pi$
$349$	−26.0735	−1.39568	−0.697841	+	0.716253i	$0.745856\pi$
$350$	−3.91253	−0.209133
$351$	24.4157	1.30321
$352$	0	0
$353$	−6.91592	−0.368097	−0.184049	−	0.982917i	$-0.558920\pi$
$353$	−6.91592	−0.368097	−0.184049	+	0.982917i	$0.558920\pi$
$354$	3.73481	0.198503
$355$	30.4909	1.61829
$356$	12.4423	0.659439
$357$	−1.43909	−0.0761649
$358$	−1.72834	−0.0913457
$359$	6.60482	0.348589	0.174295	−	0.984694i	$-0.444236\pi$
$359$	6.60482	0.348589	0.174295	+	0.984694i	$0.444236\pi$
$360$	9.09692	0.479450
$361$	1.00000	0.0526316
$362$	−2.29655	−0.120704
$363$	0	0
$364$	3.33012	0.174546
$365$	−3.93728	−0.206087
$366$	0.660234	0.0345110
$367$	2.74834	0.143462	0.0717312	−	0.997424i	$-0.477148\pi$
$367$	2.74834	0.143462	0.0717312	+	0.997424i	$0.477148\pi$
$368$	0.177085	0.00923120
$369$	−6.92395	−0.360447
$370$	26.5880	1.38224
$371$	−1.28911	−0.0669272
$372$	6.95913	0.360814
$373$	−1.84378	−0.0954675	−0.0477337	−	0.998860i	$-0.515200\pi$
$373$	−1.84378	−0.0954675	−0.0477337	+	0.998860i	$0.515200\pi$
$374$	0	0
$375$	−6.48245	−0.334752
$376$	−3.13132	−0.161486
$377$	−46.5014	−2.39494
$378$	1.88613	0.0970120
$379$	−9.27484	−0.476417	−0.238208	−	0.971214i	$-0.576560\pi$
$379$	−9.27484	−0.476417	−0.238208	+	0.971214i	$0.576560\pi$
$380$	3.56566	0.182915
$381$	7.89896	0.404676
$382$	7.88053	0.403203
$383$	14.4479	0.738252	0.369126	−	0.929379i	$-0.379657\pi$
$383$	14.4479	0.738252	0.369126	+	0.929379i	$0.379657\pi$
$384$	0.669883	0.0341848
$385$	0	0
$386$	0.254703	0.0129641
$387$	−8.19334	−0.416491
$388$	−8.82526	−0.448035
$389$	−4.15708	−0.210773	−0.105386	−	0.994431i	$-0.533608\pi$
$389$	−4.15708	−0.210773	−0.105386	+	0.994431i	$0.533608\pi$
$390$	15.6826	0.794118
$391$	0.750052	0.0379318
$392$	−6.74275	−0.340560
$393$	−5.23611	−0.264127
$394$	18.2626	0.920059
$395$	−34.8106	−1.75151
$396$	0	0
$397$	4.98609	0.250245	0.125122	−	0.992141i	$-0.460068\pi$
$397$	4.98609	0.250245	0.125122	+	0.992141i	$0.460068\pi$
$398$	8.60007	0.431082
$399$	0.339766	0.0170096
$400$	7.71394	0.385697
$401$	−5.95658	−0.297457	−0.148729	−	0.988878i	$-0.547518\pi$
$401$	−5.95658	−0.297457	−0.148729	+	0.988878i	$0.547518\pi$
$402$	8.45668	0.421781
$403$	−68.2079	−3.39768
$404$	7.36857	0.366600
$405$	−18.4084	−0.914719
$406$	−3.59226	−0.178281
$407$	0	0
$408$	2.83732	0.140468
$409$	23.8957	1.18157	0.590783	−	0.806830i	$-0.298819\pi$
$409$	23.8957	1.18157	0.590783	+	0.806830i	$0.298819\pi$
$410$	−9.67698	−0.477912
$411$	4.23929	0.209109
$412$	16.0367	0.790074
$413$	−2.82781	−0.139147
$414$	−0.451790	−0.0222042
$415$	29.2280	1.43475
$416$	−6.56566	−0.321908
$417$	−10.0696	−0.493110
$418$	0	0
$419$	20.5785	1.00533	0.502663	−	0.864483i	$-0.332354\pi$
$419$	20.5785	1.00533	0.502663	+	0.864483i	$0.332354\pi$
$420$	1.21149	0.0591147
$421$	−18.7947	−0.916000	−0.458000	−	0.888952i	$-0.651434\pi$
$421$	−18.7947	−0.916000	−0.458000	+	0.888952i	$0.651434\pi$
$422$	−10.8661	−0.528955
$423$	7.98881	0.388429
$424$	2.54161	0.123431
$425$	32.6727	1.58486
$426$	−5.72834	−0.277539
$427$	−0.499896	−0.0241917
$428$	12.7458	0.616091
$429$	0	0
$430$	−11.4511	−0.552220
$431$	28.4182	1.36885	0.684427	−	0.729081i	$-0.260052\pi$
$431$	28.4182	1.36885	0.684427	+	0.729081i	$0.260052\pi$
$432$	−3.71869	−0.178916
$433$	−3.03980	−0.146083	−0.0730416	−	0.997329i	$-0.523271\pi$
$433$	−3.03980	−0.146083	−0.0730416	+	0.997329i	$0.523271\pi$
$434$	−5.26911	−0.252925
$435$	−16.9171	−0.811114
$436$	10.0856	0.483011
$437$	−0.177085	−0.00847113
$438$	0.739700	0.0353442
$439$	−32.8218	−1.56650	−0.783250	−	0.621706i	$-0.786440\pi$
$439$	−32.8218	−1.56650	−0.783250	+	0.621706i	$0.786440\pi$
$440$	0	0
$441$	17.2025	0.819166
$442$	−27.8091	−1.32275
$443$	−21.6905	−1.03055	−0.515274	−	0.857026i	$-0.672310\pi$
$443$	−21.6905	−1.03055	−0.515274	+	0.857026i	$0.672310\pi$
$444$	−4.99511	−0.237057
$445$	−44.3649	−2.10310
$446$	−12.4711	−0.590523
$447$	−14.1491	−0.669232
$448$	−0.507202	−0.0239630
$449$	19.1889	0.905582	0.452791	−	0.891617i	$-0.350428\pi$
$449$	19.1889	0.905582	0.452791	+	0.891617i	$0.350428\pi$
$450$	−19.6802	−0.927735
$451$	0	0
$452$	9.69394	0.455964
$453$	−15.5672	−0.731412
$454$	−29.8483	−1.40085
$455$	−11.8741	−0.556665
$456$	−0.669883	−0.0313701
$457$	34.5863	1.61788	0.808939	−	0.587892i	$-0.200042\pi$
$457$	34.5863	1.61788	0.808939	+	0.587892i	$0.200042\pi$
$458$	−19.3115	−0.902365
$459$	−15.7507	−0.735179
$460$	−0.631426	−0.0294404
$461$	−7.67464	−0.357444	−0.178722	−	0.983900i	$-0.557196\pi$
$461$	−7.67464	−0.357444	−0.178722	+	0.983900i	$0.557196\pi$
$462$	0	0
$463$	18.1938	0.845539	0.422770	−	0.906237i	$-0.361058\pi$
$463$	18.1938	0.845539	0.422770	+	0.906237i	$0.361058\pi$
$464$	7.08251	0.328797
$465$	−24.8139	−1.15072
$466$	10.0288	0.464576
$467$	−1.49500	−0.0691805	−0.0345902	−	0.999402i	$-0.511013\pi$
$467$	−1.49500	−0.0691805	−0.0345902	+	0.999402i	$0.511013\pi$
$468$	16.7507	0.774301
$469$	−6.40298	−0.295662
$470$	11.1652	0.515014
$471$	5.95267	0.274284
$472$	5.57531	0.256624
$473$	0	0
$474$	6.53990	0.300388
$475$	−7.71394	−0.353940
$476$	−2.14828	−0.0984661
$477$	−6.48429	−0.296895
$478$	−11.2291	−0.513606
$479$	−34.8658	−1.59306	−0.796529	−	0.604601i	$-0.793333\pi$
$479$	−34.8658	−1.59306	−0.796529	+	0.604601i	$0.793333\pi$
$480$	−2.38858	−0.109023
$481$	48.9581	2.23230
$482$	16.0367	0.730454
$483$	−0.0601675	−0.00273772
$484$	0	0
$485$	31.4679	1.42888
$486$	14.6145	0.662926
$487$	17.2996	0.783920	0.391960	−	0.919982i	$-0.371797\pi$
$487$	17.2996	0.783920	0.391960	+	0.919982i	$0.371797\pi$
$488$	0.985596	0.0446158
$489$	7.66171	0.346475
$490$	24.0423	1.08612
$491$	−38.2536	−1.72636	−0.863181	−	0.504895i	$-0.831531\pi$
$491$	−38.2536	−1.72636	−0.863181	+	0.504895i	$0.831531\pi$
$492$	1.81802	0.0819627
$493$	29.9983	1.35106
$494$	6.56566	0.295403
$495$	0	0
$496$	10.3886	0.466461
$497$	4.33722	0.194551
$498$	−5.49109	−0.246062
$499$	30.5785	1.36888	0.684441	−	0.729069i	$-0.260046\pi$
$499$	30.5785	1.36888	0.684441	+	0.729069i	$0.260046\pi$
$500$	−9.67698	−0.432768
$501$	−11.1120	−0.496449
$502$	27.0591	1.20771
$503$	14.0304	0.625583	0.312791	−	0.949822i	$-0.398736\pi$
$503$	14.0304	0.625583	0.312791	+	0.949822i	$0.398736\pi$
$504$	1.29400	0.0576395
$505$	−26.2738	−1.16917
$506$	0	0
$507$	20.1688	0.895727
$508$	11.7916	0.523166
$509$	22.4616	0.995592	0.497796	−	0.867294i	$-0.334143\pi$
$509$	22.4616	0.995592	0.497796	+	0.867294i	$0.334143\pi$
$510$	−10.1169	−0.447985
$511$	−0.560064	−0.0247758
$512$	1.00000	0.0441942
$513$	3.71869	0.164184
$514$	29.2963	1.29221
$515$	−57.1816	−2.51972
$516$	2.15132	0.0947067
$517$	0	0
$518$	3.78205	0.166174
$519$	−2.57430	−0.112999
$520$	23.4109	1.02664
$521$	−5.86378	−0.256897	−0.128449	−	0.991716i	$-0.541000\pi$
$521$	−5.86378	−0.256897	−0.128449	+	0.991716i	$0.541000\pi$
$522$	−18.0693	−0.790872
$523$	−25.2701	−1.10498	−0.552492	−	0.833518i	$-0.686323\pi$
$523$	−25.2701	−1.10498	−0.552492	+	0.833518i	$0.686323\pi$
$524$	−7.81645	−0.341463
$525$	−2.62093	−0.114387
$526$	−30.7129	−1.33914
$527$	44.0013	1.91673
$528$	0	0
$529$	−22.9686	−0.998637
$530$	−9.06251	−0.393650
$531$	−14.2240	−0.617271
$532$	0.507202	0.0219900
$533$	−17.8188	−0.771818
$534$	8.33487	0.360685
$535$	−45.4472	−1.96485
$536$	12.6241	0.545279
$537$	−1.15779	−0.0499622
$538$	−14.0288	−0.604825
$539$	0	0
$540$	13.2596	0.570602
$541$	3.69052	0.158668	0.0793339	−	0.996848i	$-0.474721\pi$
$541$	3.69052	0.158668	0.0793339	+	0.996848i	$0.474721\pi$
$542$	−12.4350	−0.534128
$543$	−1.53842	−0.0660200
$544$	4.23554	0.181597
$545$	−35.9617	−1.54043
$546$	2.23079	0.0954690
$547$	22.6568	0.968736	0.484368	−	0.874864i	$-0.339050\pi$
$547$	22.6568	0.968736	0.484368	+	0.874864i	$0.339050\pi$
$548$	6.32841	0.270336
$549$	−2.51451	−0.107317
$550$	0	0
$551$	−7.08251	−0.301725
$552$	0.118626	0.00504907
$553$	−4.95169	−0.210567
$554$	16.6761	0.708500
$555$	17.8109	0.756029
$556$	−15.0319	−0.637493
$557$	−31.8458	−1.34935	−0.674674	−	0.738116i	$-0.735716\pi$
$557$	−31.8458	−1.34935	−0.674674	+	0.738116i	$0.735716\pi$
$558$	−26.5039	−1.12200
$559$	−21.0856	−0.891824
$560$	1.80851	0.0764235
$561$	0	0
$562$	−4.67159	−0.197059
$563$	6.18915	0.260841	0.130421	−	0.991459i	$-0.458367\pi$
$563$	6.18915	0.260841	0.130421	+	0.991459i	$0.458367\pi$
$564$	−2.09762	−0.0883257
$565$	−34.5653	−1.45417
$566$	−6.37907	−0.268132
$567$	−2.61852	−0.109968
$568$	−8.55126	−0.358803
$569$	17.7090	0.742402	0.371201	−	0.928553i	$-0.378946\pi$
$569$	17.7090	0.742402	0.371201	+	0.928553i	$0.378946\pi$
$570$	2.38858	0.100046
$571$	23.1562	0.969058	0.484529	−	0.874775i	$-0.338991\pi$
$571$	23.1562	0.969058	0.484529	+	0.874775i	$0.338991\pi$
$572$	0	0
$573$	5.27903	0.220535
$574$	−1.37651	−0.0574546
$575$	1.36602	0.0569671
$576$	−2.55126	−0.106302
$577$	42.8476	1.78377	0.891885	−	0.452263i	$-0.149383\pi$
$577$	42.8476	1.78377	0.891885	+	0.452263i	$0.149383\pi$
$578$	0.939832	0.0390919
$579$	0.170621	0.00709078
$580$	−25.2538	−1.04861
$581$	4.15758	0.172485
$582$	−5.91189	−0.245056
$583$	0	0
$584$	1.10422	0.0456930
$585$	−59.7273	−2.46942
$586$	12.8283	0.529932
$587$	−33.3363	−1.37594	−0.687969	−	0.725740i	$-0.741498\pi$
$587$	−33.3363	−1.37594	−0.687969	+	0.725740i	$0.741498\pi$
$588$	−4.51685	−0.186272
$589$	−10.3886	−0.428054
$590$	−19.8797	−0.818433
$591$	12.2338	0.503233
$592$	−7.45668	−0.306468
$593$	−23.7095	−0.973634	−0.486817	−	0.873504i	$-0.661842\pi$
$593$	−23.7095	−0.973634	−0.486817	+	0.873504i	$0.661842\pi$
$594$	0	0
$595$	7.66003	0.314030
$596$	−21.1218	−0.865183
$597$	5.76104	0.235784
$598$	−1.16268	−0.0475456
$599$	31.1681	1.27349	0.636746	−	0.771073i	$-0.280280\pi$
$599$	31.1681	1.27349	0.636746	+	0.771073i	$0.280280\pi$
$600$	5.16744	0.210960
$601$	13.6609	0.557241	0.278621	−	0.960401i	$-0.410123\pi$
$601$	13.6609	0.557241	0.278621	+	0.960401i	$0.410123\pi$
$602$	−1.62887	−0.0663880
$603$	−32.2074	−1.31159
$604$	−23.2387	−0.945570
$605$	0	0
$606$	4.93608	0.200515
$607$	2.60262	0.105637	0.0528185	−	0.998604i	$-0.483180\pi$
$607$	2.60262	0.105637	0.0528185	+	0.998604i	$0.483180\pi$
$608$	−1.00000	−0.0405554
$609$	−2.40640	−0.0975121
$610$	−3.51430	−0.142290
$611$	20.5592	0.831736
$612$	−10.8060	−0.436805
$613$	−32.5978	−1.31661	−0.658306	−	0.752750i	$-0.728727\pi$
$613$	−32.5978	−1.31661	−0.658306	+	0.752750i	$0.728727\pi$
$614$	26.5880	1.07300
$615$	−6.48245	−0.261397
$616$	0	0
$617$	−5.46228	−0.219903	−0.109952	−	0.993937i	$-0.535070\pi$
$617$	−5.46228	−0.219903	−0.109952	+	0.993937i	$0.535070\pi$
$618$	10.7427	0.432137
$619$	−5.98070	−0.240385	−0.120192	−	0.992751i	$-0.538351\pi$
$619$	−5.98070	−0.240385	−0.120192	+	0.992751i	$0.538351\pi$
$620$	−37.0421	−1.48765
$621$	−0.658525	−0.0264257
$622$	13.5664	0.543962
$623$	−6.31075	−0.252835
$624$	−4.39822	−0.176070
$625$	−4.06485	−0.162594
$626$	15.1608	0.605949
$627$	0	0
$628$	8.88613	0.354595
$629$	−31.5831	−1.25930
$630$	−4.61398	−0.183825
$631$	23.8397	0.949042	0.474521	−	0.880244i	$-0.342621\pi$
$631$	23.8397	0.949042	0.474521	+	0.880244i	$0.342621\pi$
$632$	9.76275	0.388341
$633$	−7.27903	−0.289316
$634$	26.5958	1.05625
$635$	−42.0447	−1.66849
$636$	1.70258	0.0675117
$637$	44.2706	1.75406
$638$	0	0
$639$	21.8165	0.863045
$640$	−3.56566	−0.140945
$641$	−21.9373	−0.866471	−0.433235	−	0.901281i	$-0.642628\pi$
$641$	−21.9373	−0.866471	−0.433235	+	0.901281i	$0.642628\pi$
$642$	8.53819	0.336975
$643$	19.4950	0.768808	0.384404	−	0.923165i	$-0.374407\pi$
$643$	19.4950	0.768808	0.384404	+	0.923165i	$0.374407\pi$
$644$	−0.0898180	−0.00353932
$645$	−7.67089	−0.302041
$646$	−4.23554	−0.166645
$647$	−3.89032	−0.152944	−0.0764721	−	0.997072i	$-0.524366\pi$
$647$	−3.89032	−0.152944	−0.0764721	+	0.997072i	$0.524366\pi$
$648$	5.16268	0.202809
$649$	0	0
$650$	−50.6471	−1.98654
$651$	−3.52969	−0.138339
$652$	11.4374	0.447923
$653$	−26.6031	−1.04106	−0.520530	−	0.853843i	$-0.674266\pi$
$653$	−26.6031	−1.04106	−0.520530	+	0.853843i	$0.674266\pi$
$654$	6.75614	0.264186
$655$	27.8708	1.08900
$656$	2.71394	0.105961
$657$	−2.81715	−0.109908
$658$	1.58821	0.0619150
$659$	−27.4941	−1.07102	−0.535510	−	0.844529i	$-0.679880\pi$
$659$	−27.4941	−1.07102	−0.535510	+	0.844529i	$0.679880\pi$
$660$	0	0
$661$	−9.38616	−0.365079	−0.182540	−	0.983198i	$-0.558432\pi$
$661$	−9.38616	−0.365079	−0.182540	+	0.983198i	$0.558432\pi$
$662$	−9.30131	−0.361506
$663$	−18.6289	−0.723486
$664$	−8.19709	−0.318109
$665$	−1.80851	−0.0701310
$666$	19.0239	0.737162
$667$	1.25421	0.0485631
$668$	−16.5880	−0.641809
$669$	−8.35417	−0.322991
$670$	−45.0133	−1.73902
$671$	0	0
$672$	−0.339766	−0.0131068
$673$	13.9317	0.537027	0.268513	−	0.963276i	$-0.413468\pi$
$673$	13.9317	0.537027	0.268513	+	0.963276i	$0.413468\pi$
$674$	32.8355	1.26478
$675$	−28.6858	−1.10412
$676$	30.1079	1.15800
$677$	−27.8885	−1.07184	−0.535921	−	0.844268i	$-0.680035\pi$
$677$	−27.8885	−1.07184	−0.535921	+	0.844268i	$0.680035\pi$
$678$	6.49380	0.249393
$679$	4.47619	0.171780
$680$	−15.1025	−0.579155
$681$	−19.9949	−0.766205
$682$	0	0
$683$	−19.9390	−0.762943	−0.381472	−	0.924381i	$-0.624583\pi$
$683$	−19.9390	−0.762943	−0.381472	+	0.924381i	$0.624583\pi$
$684$	2.55126	0.0975497
$685$	−22.5650	−0.862163
$686$	6.97035	0.266129
$687$	−12.9364	−0.493555
$688$	3.21149	0.122437
$689$	−16.6873	−0.635737
$690$	−0.422981	−0.0161026
$691$	29.1567	1.10917	0.554587	−	0.832126i	$-0.312876\pi$
$691$	29.1567	1.10917	0.554587	+	0.832126i	$0.312876\pi$
$692$	−3.84292	−0.146086
$693$	0	0
$694$	11.6844	0.443535
$695$	53.5985	2.03311
$696$	4.74445	0.179838
$697$	11.4950	0.435404
$698$	−26.0735	−0.986896
$699$	6.71813	0.254103
$700$	−3.91253	−0.147880
$701$	−37.3410	−1.41035	−0.705176	−	0.709033i	$-0.749132\pi$
$701$	−37.3410	−1.41035	−0.705176	+	0.709033i	$0.749132\pi$
$702$	24.4157	0.921510
$703$	7.45668	0.281234
$704$	0	0
$705$	7.47940	0.281690
$706$	−6.91592	−0.260284
$707$	−3.73736	−0.140558
$708$	3.73481	0.140363
$709$	4.62583	0.173727	0.0868633	−	0.996220i	$-0.472316\pi$
$709$	4.62583	0.173727	0.0868633	+	0.996220i	$0.472316\pi$
$710$	30.4909	1.14430
$711$	−24.9073	−0.934096
$712$	12.4423	0.466294
$713$	1.83966	0.0688959
$714$	−1.43909	−0.0538567
$715$	0	0
$716$	−1.72834	−0.0645912
$717$	−7.52217	−0.280921
$718$	6.60482	0.246490
$719$	8.05534	0.300414	0.150207	−	0.988655i	$-0.452006\pi$
$719$	8.05534	0.300414	0.150207	+	0.988655i	$0.452006\pi$
$720$	9.09692	0.339022
$721$	−8.13387	−0.302921
$722$	1.00000	0.0372161
$723$	10.7427	0.399527
$724$	−2.29655	−0.0853507
$725$	54.6341	2.02906
$726$	0	0
$727$	−29.9940	−1.11242	−0.556209	−	0.831043i	$-0.687744\pi$
$727$	−29.9940	−1.11242	−0.556209	+	0.831043i	$0.687744\pi$
$728$	3.33012	0.123422
$729$	−5.69806	−0.211039
$730$	−3.93728	−0.145725
$731$	13.6024	0.503103
$732$	0.660234	0.0244029
$733$	19.2675	0.711663	0.355831	−	0.934550i	$-0.384198\pi$
$733$	19.2675	0.711663	0.355831	+	0.934550i	$0.384198\pi$
$734$	2.74834	0.101443
$735$	16.1056	0.594063
$736$	0.177085	0.00652744
$737$	0	0
$738$	−6.92395	−0.254874
$739$	40.6838	1.49658	0.748288	−	0.663373i	$-0.230876\pi$
$739$	40.6838	1.49658	0.748288	+	0.663373i	$0.230876\pi$
$740$	26.5880	0.977395
$741$	4.39822	0.161573
$742$	−1.28911	−0.0473247
$743$	−16.8206	−0.617087	−0.308543	−	0.951210i	$-0.599842\pi$
$743$	−16.8206	−0.617087	−0.308543	+	0.951210i	$0.599842\pi$
$744$	6.95913	0.255134
$745$	75.3132	2.75926
$746$	−1.84378	−0.0675057
$747$	20.9129	0.765162
$748$	0	0
$749$	−6.46469	−0.236215
$750$	−6.48245	−0.236705
$751$	36.8011	1.34289	0.671446	−	0.741053i	$-0.265673\pi$
$751$	36.8011	1.34289	0.671446	+	0.741053i	$0.265673\pi$
$752$	−3.13132	−0.114188
$753$	18.1264	0.660564
$754$	−46.5014	−1.69348
$755$	82.8614	3.01564
$756$	1.88613	0.0685978
$757$	32.0751	1.16579	0.582894	−	0.812548i	$-0.301920\pi$
$757$	32.0751	1.16579	0.582894	+	0.812548i	$0.301920\pi$
$758$	−9.27484	−0.336877
$759$	0	0
$760$	3.56566	0.129340
$761$	5.99220	0.217217	0.108609	−	0.994085i	$-0.465361\pi$
$761$	5.99220	0.217217	0.108609	+	0.994085i	$0.465361\pi$
$762$	7.89896	0.286149
$763$	−5.11542	−0.185191
$764$	7.88053	0.285108
$765$	38.5304	1.39307
$766$	14.4479	0.522023
$767$	−36.6056	−1.32175
$768$	0.669883	0.0241723
$769$	3.11373	0.112284	0.0561420	−	0.998423i	$-0.482120\pi$
$769$	3.11373	0.112284	0.0561420	+	0.998423i	$0.482120\pi$
$770$	0	0
$771$	19.6251	0.706782
$772$	0.254703	0.00916697
$773$	−22.8477	−0.821774	−0.410887	−	0.911686i	$-0.634781\pi$
$773$	−22.8477	−0.821774	−0.410887	+	0.911686i	$0.634781\pi$
$774$	−8.19334	−0.294503
$775$	80.1368	2.87860
$776$	−8.82526	−0.316808
$777$	2.53353	0.0908898
$778$	−4.15708	−0.149039
$779$	−2.71394	−0.0972369
$780$	15.6826	0.561526
$781$	0	0
$782$	0.750052	0.0268218
$783$	−26.3377	−0.941232
$784$	−6.74275	−0.240812
$785$	−31.6849	−1.13088
$786$	−5.23611	−0.186766
$787$	34.6929	1.23667	0.618333	−	0.785916i	$-0.287808\pi$
$787$	34.6929	1.23667	0.618333	+	0.785916i	$0.287808\pi$
$788$	18.2626	0.650580
$789$	−20.5740	−0.732455
$790$	−34.8106	−1.23851
$791$	−4.91678	−0.174821
$792$	0	0
$793$	−6.47109	−0.229795
$794$	4.98609	0.176950
$795$	−6.07082	−0.215310
$796$	8.60007	0.304821
$797$	50.7079	1.79617	0.898083	−	0.439826i	$-0.144960\pi$
$797$	50.7079	1.79617	0.898083	+	0.439826i	$0.144960\pi$
$798$	0.339766	0.0120276
$799$	−13.2629	−0.469206
$800$	7.71394	0.272729
$801$	−31.7434	−1.12160
$802$	−5.95658	−0.210334
$803$	0	0
$804$	8.45668	0.298244
$805$	0.320260	0.0112877
$806$	−68.2079	−2.40252
$807$	−9.39766	−0.330813
$808$	7.36857	0.259226
$809$	26.4677	0.930555	0.465277	−	0.885165i	$-0.345955\pi$
$809$	26.4677	0.930555	0.465277	+	0.885165i	$0.345955\pi$
$810$	−18.4084	−0.646804
$811$	−18.9010	−0.663705	−0.331852	−	0.943331i	$-0.607674\pi$
$811$	−18.9010	−0.663705	−0.331852	+	0.943331i	$0.607674\pi$
$812$	−3.59226	−0.126064
$813$	−8.32998	−0.292145
$814$	0	0
$815$	−40.7818	−1.42853
$816$	2.83732	0.0993260
$817$	−3.21149	−0.112356
$818$	23.8957	0.835494
$819$	−8.49598	−0.296874
$820$	−9.67698	−0.337935
$821$	−37.4421	−1.30674	−0.653369	−	0.757040i	$-0.726645\pi$
$821$	−37.4421	−1.30674	−0.653369	+	0.757040i	$0.726645\pi$
$822$	4.23929	0.147862
$823$	−4.31330	−0.150352	−0.0751761	−	0.997170i	$-0.523952\pi$
$823$	−4.31330	−0.150352	−0.0751761	+	0.997170i	$0.523952\pi$
$824$	16.0367	0.558667
$825$	0	0
$826$	−2.82781	−0.0983921
$827$	2.87123	0.0998424	0.0499212	−	0.998753i	$-0.484103\pi$
$827$	2.87123	0.0998424	0.0499212	+	0.998753i	$0.484103\pi$
$828$	−0.451790	−0.0157008
$829$	25.7498	0.894329	0.447165	−	0.894452i	$-0.352434\pi$
$829$	25.7498	0.894329	0.447165	+	0.894452i	$0.352434\pi$
$830$	29.2280	1.01452
$831$	11.1710	0.387519
$832$	−6.56566	−0.227623
$833$	−28.5592	−0.989518
$834$	−10.0696	−0.348681
$835$	59.1472	2.04687
$836$	0	0
$837$	−38.6319	−1.33531
$838$	20.5785	0.710872
$839$	−13.7883	−0.476025	−0.238013	−	0.971262i	$-0.576496\pi$
$839$	−13.7883	−0.476025	−0.238013	+	0.971262i	$0.576496\pi$
$840$	1.21149	0.0418004
$841$	21.1620	0.729723
$842$	−18.7947	−0.647710
$843$	−3.12942	−0.107783
$844$	−10.8661	−0.374028
$845$	−107.355	−3.69311
$846$	7.98881	0.274661
$847$	0	0
$848$	2.54161	0.0872792
$849$	−4.27323	−0.146657
$850$	32.6727	1.12067
$851$	−1.32047	−0.0452651
$852$	−5.72834	−0.196250
$853$	29.2868	1.00276	0.501381	−	0.865227i	$-0.332825\pi$
$853$	29.2868	1.00276	0.501381	+	0.865227i	$0.332825\pi$
$854$	−0.499896	−0.0171061
$855$	−9.09692	−0.311108
$856$	12.7458	0.435642
$857$	−48.1428	−1.64453	−0.822263	−	0.569107i	$-0.807289\pi$
$857$	−48.1428	−1.64453	−0.822263	+	0.569107i	$0.807289\pi$
$858$	0	0
$859$	−17.6634	−0.602669	−0.301334	−	0.953519i	$-0.597432\pi$
$859$	−17.6634	−0.602669	−0.301334	+	0.953519i	$0.597432\pi$
$860$	−11.4511	−0.390479
$861$	−0.922104	−0.0314252
$862$	28.4182	0.967926
$863$	3.69002	0.125610	0.0628049	−	0.998026i	$-0.479995\pi$
$863$	3.69002	0.125610	0.0628049	+	0.998026i	$0.479995\pi$
$864$	−3.71869	−0.126512
$865$	13.7025	0.465900
$866$	−3.03980	−0.103296
$867$	0.629578	0.0213816
$868$	−5.26911	−0.178845
$869$	0	0
$870$	−16.9171	−0.573544
$871$	−82.8857	−2.80847
$872$	10.0856	0.341540
$873$	22.5155	0.762034
$874$	−0.177085	−0.00598999
$875$	4.90819	0.165927
$876$	0.739700	0.0249921
$877$	−21.9383	−0.740802	−0.370401	−	0.928872i	$-0.620780\pi$
$877$	−21.9383	−0.740802	−0.370401	+	0.928872i	$0.620780\pi$
$878$	−32.8218	−1.10768
$879$	8.59346	0.289850
$880$	0	0
$881$	13.3359	0.449296	0.224648	−	0.974440i	$-0.427877\pi$
$881$	13.3359	0.449296	0.224648	+	0.974440i	$0.427877\pi$
$882$	17.2025	0.579237
$883$	45.0015	1.51442	0.757210	−	0.653171i	$-0.226562\pi$
$883$	45.0015	1.51442	0.757210	+	0.653171i	$0.226562\pi$
$884$	−27.8091	−0.935323
$885$	−13.3171	−0.447648
$886$	−21.6905	−0.728707
$887$	44.9327	1.50869	0.754346	−	0.656477i	$-0.227954\pi$
$887$	44.9327	1.50869	0.754346	+	0.656477i	$0.227954\pi$
$888$	−4.99511	−0.167625
$889$	−5.98070	−0.200586
$890$	−44.3649	−1.48712
$891$	0	0
$892$	−12.4711	−0.417563
$893$	3.13132	0.104786
$894$	−14.1491	−0.473218
$895$	6.16268	0.205996
$896$	−0.507202	−0.0169444
$897$	−0.778860	−0.0260054
$898$	19.1889	0.640343
$899$	73.5772	2.45394
$900$	−19.6802	−0.656008
$901$	10.7651	0.358637
$902$	0	0
$903$	−1.09116	−0.0363114
$904$	9.69394	0.322416
$905$	8.18873	0.272203
$906$	−15.5672	−0.517187
$907$	56.6039	1.87950	0.939751	−	0.341860i	$-0.111057\pi$
$907$	56.6039	1.87950	0.939751	+	0.341860i	$0.111057\pi$
$908$	−29.8483	−0.990551
$909$	−18.7991	−0.623528
$910$	−11.8741	−0.393622
$911$	−46.5978	−1.54385	−0.771927	−	0.635711i	$-0.780707\pi$
$911$	−46.5978	−1.54385	−0.771927	+	0.635711i	$0.780707\pi$
$912$	−0.669883	−0.0221820
$913$	0	0
$914$	34.5863	1.14401
$915$	−2.35417	−0.0778265
$916$	−19.3115	−0.638068
$917$	3.96452	0.130920
$918$	−15.7507	−0.519850
$919$	47.4246	1.56439	0.782197	−	0.623032i	$-0.214099\pi$
$919$	47.4246	1.56439	0.782197	+	0.623032i	$0.214099\pi$
$920$	−0.631426	−0.0208175
$921$	17.8109	0.586888
$922$	−7.67464	−0.252751
$923$	56.1447	1.84802
$924$	0	0
$925$	−57.5204	−1.89126
$926$	18.1938	0.597886
$927$	−40.9139	−1.34379
$928$	7.08251	0.232495
$929$	−46.6008	−1.52892	−0.764462	−	0.644669i	$-0.776995\pi$
$929$	−46.6008	−1.52892	−0.764462	+	0.644669i	$0.776995\pi$
$930$	−24.8139	−0.813680
$931$	6.74275	0.220985
$932$	10.0288	0.328505
$933$	9.08788	0.297524
$934$	−1.49500	−0.0489180
$935$	0	0
$936$	16.7507	0.547513
$937$	10.4826	0.342451	0.171226	−	0.985232i	$-0.445227\pi$
$937$	10.4826	0.342451	0.171226	+	0.985232i	$0.445227\pi$
$938$	−6.40298	−0.209065
$939$	10.1560	0.331428
$940$	11.1652	0.364170
$941$	−11.6226	−0.378885	−0.189443	−	0.981892i	$-0.560668\pi$
$941$	−11.6226	−0.378885	−0.189443	+	0.981892i	$0.560668\pi$
$942$	5.95267	0.193948
$943$	0.480598	0.0156504
$944$	5.57531	0.181461
$945$	−6.72530	−0.218774
$946$	0	0
$947$	−17.8702	−0.580702	−0.290351	−	0.956920i	$-0.593772\pi$
$947$	−17.8702	−0.580702	−0.290351	+	0.956920i	$0.593772\pi$
$948$	6.53990	0.212406
$949$	−7.24995	−0.235343
$950$	−7.71394	−0.250273
$951$	17.8161	0.577726
$952$	−2.14828	−0.0696260
$953$	41.5590	1.34623	0.673114	−	0.739539i	$-0.264956\pi$
$953$	41.5590	1.34623	0.673114	+	0.739539i	$0.264956\pi$
$954$	−6.48429	−0.209937
$955$	−28.0993	−0.909272
$956$	−11.2291	−0.363174
$957$	0	0
$958$	−34.8658	−1.12646
$959$	−3.20978	−0.103649
$960$	−2.38858	−0.0770910
$961$	76.9225	2.48137
$962$	48.9581	1.57847
$963$	−32.5178	−1.04787
$964$	16.0367	0.516509
$965$	−0.908185	−0.0292355
$966$	−0.0601675	−0.00193586
$967$	−0.275849	−0.00887071	−0.00443536	−	0.999990i	$-0.501412\pi$
$967$	−0.275849	−0.00887071	−0.00443536	+	0.999990i	$0.501412\pi$
$968$	0	0
$969$	−2.83732	−0.0911478
$970$	31.4679	1.01037
$971$	−11.8381	−0.379902	−0.189951	−	0.981794i	$-0.560833\pi$
$971$	−11.8381	−0.379902	−0.189951	+	0.981794i	$0.560833\pi$
$972$	14.6145	0.468759
$973$	7.62419	0.244420
$974$	17.2996	0.554315
$975$	−33.9276	−1.08655
$976$	0.985596	0.0315482
$977$	35.9868	1.15132	0.575660	−	0.817689i	$-0.304745\pi$
$977$	35.9868	1.15132	0.575660	+	0.817689i	$0.304745\pi$
$978$	7.66171	0.244994
$979$	0	0
$980$	24.0423	0.768005
$981$	−25.7308	−0.821523
$982$	−38.2536	−1.22072
$983$	28.7010	0.915420	0.457710	−	0.889102i	$-0.348670\pi$
$983$	28.7010	0.915420	0.457710	+	0.889102i	$0.348670\pi$
$984$	1.81802	0.0579564
$985$	−65.1184	−2.07484
$986$	29.9983	0.955340
$987$	1.06392	0.0338648
$988$	6.56566	0.208881
$989$	0.568707	0.0180838
$990$	0	0
$991$	56.1431	1.78344	0.891722	−	0.452584i	$-0.149498\pi$
$991$	56.1431	1.78344	0.891722	+	0.452584i	$0.149498\pi$
$992$	10.3886	0.329838
$993$	−6.23079	−0.197728
$994$	4.33722	0.137568
$995$	−30.6649	−0.972143
$996$	−5.49109	−0.173992
$997$	−15.8844	−0.503062	−0.251531	−	0.967849i	$-0.580934\pi$
$997$	−15.8844	−0.503062	−0.251531	+	0.967849i	$0.580934\pi$
$998$	30.5785	0.967945
$999$	27.7291	0.877310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bu.1.3	yes	4
11.10	odd	2		4598.2.a.br.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.br.1.3	✓	4	11.10	odd	2
4598.2.a.bu.1.3	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.669883 q^{3} +1.00000 q^{4} -3.56566 q^{5} +0.669883 q^{6} -0.507202 q^{7} +1.00000 q^{8} -2.55126 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.669883 q^{3} +1.00000 q^{4} -3.56566 q^{5} +0.669883 q^{6} -0.507202 q^{7} +1.00000 q^{8} -2.55126 q^{9} -3.56566 q^{10} +0.669883 q^{12} -6.56566 q^{13} -0.507202 q^{14} -2.38858 q^{15} +1.00000 q^{16} +4.23554 q^{17} -2.55126 q^{18} -1.00000 q^{19} -3.56566 q^{20} -0.339766 q^{21} +0.177085 q^{23} +0.669883 q^{24} +7.71394 q^{25} -6.56566 q^{26} -3.71869 q^{27} -0.507202 q^{28} +7.08251 q^{29} -2.38858 q^{30} +10.3886 q^{31} +1.00000 q^{32} +4.23554 q^{34} +1.80851 q^{35} -2.55126 q^{36} -7.45668 q^{37} -1.00000 q^{38} -4.39822 q^{39} -3.56566 q^{40} +2.71394 q^{41} -0.339766 q^{42} +3.21149 q^{43} +9.09692 q^{45} +0.177085 q^{46} -3.13132 q^{47} +0.669883 q^{48} -6.74275 q^{49} +7.71394 q^{50} +2.83732 q^{51} -6.56566 q^{52} +2.54161 q^{53} -3.71869 q^{54} -0.507202 q^{56} -0.669883 q^{57} +7.08251 q^{58} +5.57531 q^{59} -2.38858 q^{60} +0.985596 q^{61} +10.3886 q^{62} +1.29400 q^{63} +1.00000 q^{64} +23.4109 q^{65} +12.6241 q^{67} +4.23554 q^{68} +0.118626 q^{69} +1.80851 q^{70} -8.55126 q^{71} -2.55126 q^{72} +1.10422 q^{73} -7.45668 q^{74} +5.16744 q^{75} -1.00000 q^{76} -4.39822 q^{78} +9.76275 q^{79} -3.56566 q^{80} +5.16268 q^{81} +2.71394 q^{82} -8.19709 q^{83} -0.339766 q^{84} -15.1025 q^{85} +3.21149 q^{86} +4.74445 q^{87} +12.4423 q^{89} +9.09692 q^{90} +3.33012 q^{91} +0.177085 q^{92} +6.95913 q^{93} -3.13132 q^{94} +3.56566 q^{95} +0.669883 q^{96} -8.82526 q^{97} -6.74275 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 + q^6 - q^7 + 4 * q^8 + 5 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - q^{7} + 4 q^{8} + 5 q^{9} + 3 q^{10} + q^{12} - 9 q^{13} - q^{14} + 5 q^{15} + 4 q^{16} - 2 q^{17} + 5 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 2 q^{23} + q^{24} + 15 q^{25} - 9 q^{26} - 2 q^{27} - q^{28} + 5 q^{29} + 5 q^{30} + 27 q^{31} + 4 q^{32} - 2 q^{34} + 12 q^{35} + 5 q^{36} + 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} + 2 q^{42} + q^{43} + 11 q^{45} - 2 q^{46} + 22 q^{47} + q^{48} - 7 q^{49} + 15 q^{50} + 12 q^{51} - 9 q^{52} - 2 q^{54} - q^{56} - q^{57} + 5 q^{58} + 5 q^{60} + 6 q^{61} + 27 q^{62} - 30 q^{63} + 4 q^{64} + 26 q^{65} + 17 q^{67} - 2 q^{68} + 14 q^{69} + 12 q^{70} - 19 q^{71} + 5 q^{72} + 20 q^{73} + 6 q^{74} + 23 q^{75} - 4 q^{76} + 2 q^{78} + 12 q^{79} + 3 q^{80} + 20 q^{81} - 5 q^{82} - 23 q^{83} + 2 q^{84} - 30 q^{85} + q^{86} + 45 q^{87} + 16 q^{89} + 11 q^{90} + 15 q^{91} - 2 q^{92} - 12 q^{93} + 22 q^{94} - 3 q^{95} + q^{96} + 8 q^{97} - 7 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 + q^6 - q^7 + 4 * q^8 + 5 * q^9 + 3 * q^10 + q^12 - 9 * q^13 - q^14 + 5 * q^15 + 4 * q^16 - 2 * q^17 + 5 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 2 * q^23 + q^24 + 15 * q^25 - 9 * q^26 - 2 * q^27 - q^28 + 5 * q^29 + 5 * q^30 + 27 * q^31 + 4 * q^32 - 2 * q^34 + 12 * q^35 + 5 * q^36 + 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 + 2 * q^42 + q^43 + 11 * q^45 - 2 * q^46 + 22 * q^47 + q^48 - 7 * q^49 + 15 * q^50 + 12 * q^51 - 9 * q^52 - 2 * q^54 - q^56 - q^57 + 5 * q^58 + 5 * q^60 + 6 * q^61 + 27 * q^62 - 30 * q^63 + 4 * q^64 + 26 * q^65 + 17 * q^67 - 2 * q^68 + 14 * q^69 + 12 * q^70 - 19 * q^71 + 5 * q^72 + 20 * q^73 + 6 * q^74 + 23 * q^75 - 4 * q^76 + 2 * q^78 + 12 * q^79 + 3 * q^80 + 20 * q^81 - 5 * q^82 - 23 * q^83 + 2 * q^84 - 30 * q^85 + q^86 + 45 * q^87 + 16 * q^89 + 11 * q^90 + 15 * q^91 - 2 * q^92 - 12 * q^93 + 22 * q^94 - 3 * q^95 + q^96 + 8 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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