LMFDB - Embedded newform 4598.2.a.br.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$4$
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			1.1
Root			$-2.79836$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.79836 q^{3} +1.00000 q^{4} +0.116104 q^{5} +2.79836 q^{6} +2.35735 q^{7} -1.00000 q^{8} +4.83081 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.79836 q^{3} +1.00000 q^{4} +0.116104 q^{5} +2.79836 q^{6} +2.35735 q^{7} -1.00000 q^{8} +4.83081 q^{9} -0.116104 q^{10} -2.79836 q^{12} +2.88390 q^{13} -2.35735 q^{14} -0.324902 q^{15} +1.00000 q^{16} +2.91446 q^{17} -4.83081 q^{18} +1.00000 q^{19} +0.116104 q^{20} -6.59672 q^{21} -1.44101 q^{23} +2.79836 q^{24} -4.98652 q^{25} -2.88390 q^{26} -5.12326 q^{27} +2.35735 q^{28} +5.15383 q^{29} +0.324902 q^{30} +8.32490 q^{31} -1.00000 q^{32} -2.91446 q^{34} +0.273699 q^{35} +4.83081 q^{36} +10.5436 q^{37} -1.00000 q^{38} -8.07017 q^{39} -0.116104 q^{40} +9.98652 q^{41} +6.59672 q^{42} -2.76591 q^{43} +0.560878 q^{45} +1.44101 q^{46} +4.23221 q^{47} -2.79836 q^{48} -1.44289 q^{49} +4.98652 q^{50} -8.15571 q^{51} +2.88390 q^{52} +5.56427 q^{53} +5.12326 q^{54} -2.35735 q^{56} -2.79836 q^{57} -5.15383 q^{58} -8.51118 q^{59} -0.324902 q^{60} +2.71470 q^{61} -8.32490 q^{62} +11.3879 q^{63} +1.00000 q^{64} +0.334833 q^{65} +3.41044 q^{67} +2.91446 q^{68} +4.03245 q^{69} -0.273699 q^{70} -1.16919 q^{71} -4.83081 q^{72} -1.31775 q^{73} -10.5436 q^{74} +13.9541 q^{75} +1.00000 q^{76} +8.07017 q^{78} -1.93510 q^{79} +0.116104 q^{80} -0.155711 q^{81} -9.98652 q^{82} +4.05120 q^{83} -6.59672 q^{84} +0.338382 q^{85} +2.76591 q^{86} -14.4223 q^{87} -9.25833 q^{89} -0.560878 q^{90} +6.79836 q^{91} -1.44101 q^{92} -23.2961 q^{93} -4.23221 q^{94} +0.116104 q^{95} +2.79836 q^{96} +8.71094 q^{97} +1.44289 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.79836	−1.61563	−0.807816	−	0.589434i	$-0.799351\pi$
$3$	−2.79836	−1.61563	−0.807816	+	0.589434i	$0.799351\pi$
$4$	1.00000	0.500000
$5$	0.116104	0.0519234	0.0259617	−	0.999663i	$-0.491735\pi$
$5$	0.116104	0.0519234	0.0259617	+	0.999663i	$0.491735\pi$
$6$	2.79836	1.14242
$7$	2.35735	0.890995	0.445498	−	0.895283i	$-0.353027\pi$
$7$	2.35735	0.890995	0.445498	+	0.895283i	$0.353027\pi$
$8$	−1.00000	−0.353553
$9$	4.83081	1.61027
$10$	−0.116104	−0.0367154
$11$	0	0
$11$	0	0
$12$	−2.79836	−0.807816
$13$	2.88390	0.799849	0.399924	−	0.916548i	$-0.369036\pi$
$13$	2.88390	0.799849	0.399924	+	0.916548i	$0.369036\pi$
$14$	−2.35735	−0.630029
$15$	−0.324902	−0.0838892
$16$	1.00000	0.250000
$17$	2.91446	0.706861	0.353431	−	0.935461i	$-0.385015\pi$
$17$	2.91446	0.706861	0.353431	+	0.935461i	$0.385015\pi$
$18$	−4.83081	−1.13863
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.116104	0.0259617
$21$	−6.59672	−1.43952
$22$	0	0
$23$	−1.44101	−0.300471	−0.150235	−	0.988650i	$-0.548003\pi$
$23$	−1.44101	−0.300471	−0.150235	+	0.988650i	$0.548003\pi$
$24$	2.79836	0.571212
$25$	−4.98652	−0.997304
$26$	−2.88390	−0.565578
$27$	−5.12326	−0.985972
$28$	2.35735	0.445498
$29$	5.15383	0.957042	0.478521	−	0.878076i	$-0.341173\pi$
$29$	5.15383	0.957042	0.478521	+	0.878076i	$0.341173\pi$
$30$	0.324902	0.0593186
$31$	8.32490	1.49520	0.747598	−	0.664151i	$-0.231207\pi$
$31$	8.32490	1.49520	0.747598	+	0.664151i	$0.231207\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−2.91446	−0.499826
$35$	0.273699	0.0462636
$36$	4.83081	0.805135
$37$	10.5436	1.73336	0.866681	−	0.498863i	$-0.166249\pi$
$37$	10.5436	1.73336	0.866681	+	0.498863i	$0.166249\pi$
$38$	−1.00000	−0.162221
$39$	−8.07017	−1.29226
$40$	−0.116104	−0.0183577
$41$	9.98652	1.55963	0.779816	−	0.626009i	$-0.215313\pi$
$41$	9.98652	1.55963	0.779816	+	0.626009i	$0.215313\pi$
$42$	6.59672	1.01790
$43$	−2.76591	−0.421797	−0.210898	−	0.977508i	$-0.567639\pi$
$43$	−2.76591	−0.421797	−0.210898	+	0.977508i	$0.567639\pi$
$44$	0	0
$45$	0.560878	0.0836107
$46$	1.44101	0.212465
$47$	4.23221	0.617331	0.308666	−	0.951171i	$-0.400118\pi$
$47$	4.23221	0.617331	0.308666	+	0.951171i	$0.400118\pi$
$48$	−2.79836	−0.403908
$49$	−1.44289	−0.206127
$50$	4.98652	0.705200
$51$	−8.15571	−1.14203
$52$	2.88390	0.399924
$53$	5.56427	0.764311	0.382155	−	0.924098i	$-0.375182\pi$
$53$	5.56427	0.764311	0.382155	+	0.924098i	$0.375182\pi$
$54$	5.12326	0.697187
$55$	0	0
$56$	−2.35735	−0.315014
$57$	−2.79836	−0.370652
$58$	−5.15383	−0.676731
$59$	−8.51118	−1.10806	−0.554031	−	0.832496i	$-0.686911\pi$
$59$	−8.51118	−1.10806	−0.554031	+	0.832496i	$0.686911\pi$
$60$	−0.324902	−0.0419446
$61$	2.71470	0.347582	0.173791	−	0.984783i	$-0.444398\pi$
$61$	2.71470	0.347582	0.173791	+	0.984783i	$0.444398\pi$
$62$	−8.32490	−1.05726
$63$	11.3879	1.43474
$64$	1.00000	0.125000
$65$	0.334833	0.0415309
$66$	0	0
$67$	3.41044	0.416651	0.208326	−	0.978060i	$-0.433199\pi$
$67$	3.41044	0.416651	0.208326	+	0.978060i	$0.433199\pi$
$68$	2.91446	0.353431
$69$	4.03245	0.485450
$70$	−0.273699	−0.0327133
$71$	−1.16919	−0.138757	−0.0693787	−	0.997590i	$-0.522102\pi$
$71$	−1.16919	−0.138757	−0.0693787	+	0.997590i	$0.522102\pi$
$72$	−4.83081	−0.569316
$73$	−1.31775	−0.154231	−0.0771153	−	0.997022i	$-0.524571\pi$
$73$	−1.31775	−0.154231	−0.0771153	+	0.997022i	$0.524571\pi$
$74$	−10.5436	−1.22567
$75$	13.9541	1.61128
$76$	1.00000	0.114708
$77$	0	0
$78$	8.07017	0.913767
$79$	−1.93510	−0.217716	−0.108858	−	0.994057i	$-0.534719\pi$
$79$	−1.93510	−0.217716	−0.108858	+	0.994057i	$0.534719\pi$
$80$	0.116104	0.0129809
$81$	−0.155711	−0.0173012
$82$	−9.98652	−1.10283
$83$	4.05120	0.444677	0.222339	−	0.974970i	$-0.428631\pi$
$83$	4.05120	0.444677	0.222339	+	0.974970i	$0.428631\pi$
$84$	−6.59672	−0.719761
$85$	0.338382	0.0367027
$86$	2.76591	0.298255
$87$	−14.4223	−1.54623
$88$	0	0
$89$	−9.25833	−0.981382	−0.490691	−	0.871334i	$-0.663256\pi$
$89$	−9.25833	−0.981382	−0.490691	+	0.871334i	$0.663256\pi$
$90$	−0.560878	−0.0591217
$91$	6.79836	0.712662
$92$	−1.44101	−0.150235
$93$	−23.2961	−2.41569
$94$	−4.23221	−0.436519
$95$	0.116104	0.0119121
$96$	2.79836	0.285606
$97$	8.71094	0.884462	0.442231	−	0.896901i	$-0.354187\pi$
$97$	8.71094	0.884462	0.442231	+	0.896901i	$0.354187\pi$
$98$	1.44289	0.145754
$99$	0	0
$100$	−4.98652	−0.498652
$101$	−7.83269	−0.779382	−0.389691	−	0.920946i	$-0.627418\pi$
$101$	−7.83269	−0.779382	−0.389691	+	0.920946i	$0.627418\pi$
$102$	8.15571	0.807536
$103$	−1.94503	−0.191649	−0.0958247	−	0.995398i	$-0.530549\pi$
$103$	−1.94503	−0.191649	−0.0958247	+	0.995398i	$0.530549\pi$
$104$	−2.88390	−0.282789
$105$	−0.765907	−0.0747449
$106$	−5.56427	−0.540449
$107$	−6.57331	−0.635465	−0.317733	−	0.948180i	$-0.602921\pi$
$107$	−6.57331	−0.635465	−0.317733	+	0.948180i	$0.602921\pi$
$108$	−5.12326	−0.492986
$109$	3.02341	0.289590	0.144795	−	0.989462i	$-0.453748\pi$
$109$	3.02341	0.289590	0.144795	+	0.989462i	$0.453748\pi$
$110$	0	0
$111$	−29.5049	−2.80048
$112$	2.35735	0.222749
$113$	−0.478728	−0.0450350	−0.0225175	−	0.999746i	$-0.507168\pi$
$113$	−0.478728	−0.0450350	−0.0225175	+	0.999746i	$0.507168\pi$
$114$	2.79836	0.262090
$115$	−0.167307	−0.0156015
$116$	5.15383	0.478521
$117$	13.9315	1.28797
$118$	8.51118	0.783518
$119$	6.87042	0.629810
$120$	0.324902	0.0296593
$121$	0	0
$122$	−2.71470	−0.245778
$123$	−27.9459	−2.51979
$124$	8.32490	0.747598
$125$	−1.15948	−0.103707
$126$	−11.3879	−1.01452
$127$	−11.3645	−1.00844	−0.504219	−	0.863576i	$-0.668219\pi$
$127$	−11.3645	−1.00844	−0.504219	+	0.863576i	$0.668219\pi$
$128$	−1.00000	−0.0883883
$129$	7.74000	0.681469
$130$	−0.334833	−0.0293668
$131$	−19.6481	−1.71667	−0.858333	−	0.513093i	$-0.828500\pi$
$131$	−19.6481	−1.71667	−0.858333	+	0.513093i	$0.828500\pi$
$132$	0	0
$133$	2.35735	0.204408
$134$	−3.41044	−0.294617
$135$	−0.594833	−0.0511951
$136$	−2.91446	−0.249913
$137$	−5.18101	−0.442643	−0.221322	−	0.975201i	$-0.571037\pi$
$137$	−5.18101	−0.442643	−0.221322	+	0.975201i	$0.571037\pi$
$138$	−4.03245	−0.343265
$139$	21.5598	1.82868	0.914340	−	0.404947i	$-0.132710\pi$
$139$	21.5598	1.82868	0.914340	+	0.404947i	$0.132710\pi$
$140$	0.273699	0.0231318
$141$	−11.8432	−0.997380
$142$	1.16919	0.0981163
$143$	0	0
$144$	4.83081	0.402567
$145$	0.598382	0.0496929
$146$	1.31775	0.109057
$147$	4.03772	0.333026
$148$	10.5436	0.866681
$149$	−14.4518	−1.18393	−0.591967	−	0.805962i	$-0.701649\pi$
$149$	−14.4518	−1.18393	−0.591967	+	0.805962i	$0.701649\pi$
$150$	−13.9541	−1.13934
$151$	−23.3987	−1.90416	−0.952079	−	0.305853i	$-0.901058\pi$
$151$	−23.3987	−1.90416	−0.952079	+	0.305853i	$0.901058\pi$
$152$	−1.00000	−0.0811107
$153$	14.0792	1.13824
$154$	0	0
$155$	0.966557	0.0776357
$156$	−8.07017	−0.646131
$157$	19.0773	1.52254	0.761268	−	0.648437i	$-0.224577\pi$
$157$	19.0773	1.52254	0.761268	+	0.648437i	$0.224577\pi$
$158$	1.93510	0.153948
$159$	−15.5708	−1.23485
$160$	−0.116104	−0.00917885
$161$	−3.39696	−0.267718
$162$	0.155711	0.0122338
$163$	14.2465	1.11587	0.557937	−	0.829883i	$-0.311593\pi$
$163$	14.2465	1.11587	0.557937	+	0.829883i	$0.311593\pi$
$164$	9.98652	0.779816
$165$	0	0
$166$	−4.05120	−0.314434
$167$	−8.77584	−0.679095	−0.339547	−	0.940589i	$-0.610274\pi$
$167$	−8.77584	−0.679095	−0.339547	+	0.940589i	$0.610274\pi$
$168$	6.59672	0.508948
$169$	−4.68315	−0.360242
$170$	−0.338382	−0.0259527
$171$	4.83081	0.369421
$172$	−2.76591	−0.210898
$173$	2.93321	0.223008	0.111504	−	0.993764i	$-0.464433\pi$
$173$	2.93321	0.223008	0.111504	+	0.993764i	$0.464433\pi$
$174$	14.4223	1.09335
$175$	−11.7550	−0.888593
$176$	0	0
$177$	23.8173	1.79022
$178$	9.25833	0.693942
$179$	7.27182	0.543521	0.271760	−	0.962365i	$-0.412394\pi$
$179$	7.27182	0.543521	0.271760	+	0.962365i	$0.412394\pi$
$180$	0.560878	0.0418054
$181$	15.7408	1.17001	0.585003	−	0.811031i	$-0.301093\pi$
$181$	15.7408	1.17001	0.585003	+	0.811031i	$0.301093\pi$
$182$	−6.79836	−0.503928
$183$	−7.59672	−0.561565
$184$	1.44101	0.106232
$185$	1.22416	0.0900021
$186$	23.2961	1.70815
$187$	0	0
$188$	4.23221	0.308666
$189$	−12.0773	−0.878496
$190$	−0.116104	−0.00842309
$191$	24.2998	1.75827	0.879137	−	0.476569i	$-0.158120\pi$
$191$	24.2998	1.75827	0.879137	+	0.476569i	$0.158120\pi$
$192$	−2.79836	−0.201954
$193$	−10.9100	−0.785321	−0.392660	−	0.919684i	$-0.628445\pi$
$193$	−10.9100	−0.785321	−0.392660	+	0.919684i	$0.628445\pi$
$194$	−8.71094	−0.625409
$195$	−0.936982	−0.0670987
$196$	−1.44289	−0.103064
$197$	−3.53558	−0.251900	−0.125950	−	0.992037i	$-0.540198\pi$
$197$	−3.53558	−0.251900	−0.125950	+	0.992037i	$0.540198\pi$
$198$	0	0
$199$	6.09081	0.431766	0.215883	−	0.976419i	$-0.430737\pi$
$199$	6.09081	0.431766	0.215883	+	0.976419i	$0.430737\pi$
$200$	4.98652	0.352600
$201$	−9.54363	−0.673156
$202$	7.83269	0.551106
$203$	12.1494	0.852720
$204$	−8.15571	−0.571014
$205$	1.15948	0.0809815
$206$	1.94503	0.135517
$207$	−6.96122	−0.483839
$208$	2.88390	0.199962
$209$	0	0
$210$	0.765907	0.0528526
$211$	23.5851	1.62367	0.811833	−	0.583889i	$-0.198470\pi$
$211$	23.5851	1.62367	0.811833	+	0.583889i	$0.198470\pi$
$212$	5.56427	0.382155
$213$	3.27182	0.224181
$214$	6.57331	0.449342
$215$	−0.321134	−0.0219011
$216$	5.12326	0.348594
$217$	19.6247	1.33221
$218$	−3.02341	−0.204771
$219$	3.68753	0.249180
$220$	0	0
$221$	8.40501	0.565382
$222$	29.5049	1.98024
$223$	1.82893	0.122474	0.0612369	−	0.998123i	$-0.480495\pi$
$223$	1.82893	0.122474	0.0612369	+	0.998123i	$0.480495\pi$
$224$	−2.35735	−0.157507
$225$	−24.0889	−1.60593
$226$	0.478728	0.0318445
$227$	8.91169	0.591489	0.295745	−	0.955267i	$-0.404432\pi$
$227$	8.91169	0.591489	0.295745	+	0.955267i	$0.404432\pi$
$228$	−2.79836	−0.185326
$229$	−9.45720	−0.624949	−0.312475	−	0.949926i	$-0.601158\pi$
$229$	−9.45720	−0.624949	−0.312475	+	0.949926i	$0.601158\pi$
$230$	0.167307	0.0110319
$231$	0	0
$232$	−5.15383	−0.338365
$233$	−17.4294	−1.14184	−0.570919	−	0.821006i	$-0.693413\pi$
$233$	−17.4294	−1.14184	−0.570919	+	0.821006i	$0.693413\pi$
$234$	−13.9315	−0.910734
$235$	0.491378	0.0320540
$236$	−8.51118	−0.554031
$237$	5.41510	0.351748
$238$	−6.87042	−0.445343
$239$	−25.0036	−1.61735	−0.808674	−	0.588256i	$-0.799815\pi$
$239$	−25.0036	−1.61735	−0.808674	+	0.588256i	$0.799815\pi$
$240$	−0.324902	−0.0209723
$241$	1.94503	0.125290	0.0626452	−	0.998036i	$-0.480046\pi$
$241$	1.94503	0.125290	0.0626452	+	0.998036i	$0.480046\pi$
$242$	0	0
$243$	15.8055	1.01392
$244$	2.71470	0.173791
$245$	−0.167526	−0.0107028
$246$	27.9459	1.78176
$247$	2.88390	0.183498
$248$	−8.32490	−0.528632
$249$	−11.3367	−0.718435
$250$	1.15948	0.0733318
$251$	−12.6048	−0.795606	−0.397803	−	0.917471i	$-0.630227\pi$
$251$	−12.6048	−0.795606	−0.397803	+	0.917471i	$0.630227\pi$
$252$	11.3879	0.717371
$253$	0	0
$254$	11.3645	0.713073
$255$	−0.946913	−0.0592980
$256$	1.00000	0.0625000
$257$	−2.53986	−0.158432	−0.0792161	−	0.996857i	$-0.525242\pi$
$257$	−2.53986	−0.158432	−0.0792161	+	0.996857i	$0.525242\pi$
$258$	−7.74000	−0.481871
$259$	24.8551	1.54442
$260$	0.334833	0.0207654
$261$	24.8972	1.54110
$262$	19.6481	1.21387
$263$	−31.0972	−1.91753	−0.958767	−	0.284192i	$-0.908275\pi$
$263$	−31.0972	−1.91753	−0.958767	+	0.284192i	$0.908275\pi$
$264$	0	0
$265$	0.646035	0.0396856
$266$	−2.35735	−0.144539
$267$	25.9081	1.58555
$268$	3.41044	0.208326
$269$	−21.4294	−1.30657	−0.653287	−	0.757110i	$-0.726611\pi$
$269$	−21.4294	−1.30657	−0.653287	+	0.757110i	$0.726611\pi$
$270$	0.594833	0.0362004
$271$	−18.0152	−1.09435	−0.547173	−	0.837020i	$-0.684296\pi$
$271$	−18.0152	−1.09435	−0.547173	+	0.837020i	$0.684296\pi$
$272$	2.91446	0.176715
$273$	−19.0242	−1.15140
$274$	5.18101	0.312996
$275$	0	0
$276$	4.03245	0.242725
$277$	27.1522	1.63142	0.815708	−	0.578464i	$-0.196348\pi$
$277$	27.1522	1.63142	0.815708	+	0.578464i	$0.196348\pi$
$278$	−21.5598	−1.29307
$279$	40.2160	2.40767
$280$	−0.273699	−0.0163566
$281$	16.1810	0.965278	0.482639	−	0.875819i	$-0.339678\pi$
$281$	16.1810	0.965278	0.482639	+	0.875819i	$0.339678\pi$
$282$	11.8432	0.705254
$283$	−23.8947	−1.42039	−0.710195	−	0.704005i	$-0.751393\pi$
$283$	−23.8947	−1.42039	−0.710195	+	0.704005i	$0.751393\pi$
$284$	−1.16919	−0.0693787
$285$	−0.324902	−0.0192455
$286$	0	0
$287$	23.5417	1.38963
$288$	−4.83081	−0.284658
$289$	−8.50591	−0.500348
$290$	−0.598382	−0.0351382
$291$	−24.3763	−1.42897
$292$	−1.31775	−0.0771153
$293$	5.58052	0.326018	0.163009	−	0.986625i	$-0.447880\pi$
$293$	5.58052	0.326018	0.163009	+	0.986625i	$0.447880\pi$
$294$	−4.03772	−0.235485
$295$	−0.988185	−0.0575343
$296$	−10.5436	−0.612836
$297$	0	0
$298$	14.4518	0.837168
$299$	−4.15571	−0.240331
$300$	13.9541	0.805639
$301$	−6.52022	−0.375819
$302$	23.3987	1.34644
$303$	21.9187	1.25920
$304$	1.00000	0.0573539
$305$	0.315189	0.0180477
$306$	−14.0792	−0.804855
$307$	−1.22416	−0.0698666	−0.0349333	−	0.999390i	$-0.511122\pi$
$307$	−1.22416	−0.0698666	−0.0349333	+	0.999390i	$0.511122\pi$
$308$	0	0
$309$	5.44289	0.309635
$310$	−0.966557	−0.0548968
$311$	28.1663	1.59716	0.798581	−	0.601888i	$-0.205584\pi$
$311$	28.1663	1.59716	0.798581	+	0.601888i	$0.205584\pi$
$312$	8.07017	0.456884
$313$	33.4796	1.89238	0.946188	−	0.323617i	$-0.104899\pi$
$313$	33.4796	1.89238	0.946188	+	0.323617i	$0.104899\pi$
$314$	−19.0773	−1.07660
$315$	1.32219	0.0744968
$316$	−1.93510	−0.108858
$317$	14.4644	0.812399	0.406200	−	0.913784i	$-0.366854\pi$
$317$	14.4644	0.812399	0.406200	+	0.913784i	$0.366854\pi$
$318$	15.5708	0.873168
$319$	0	0
$320$	0.116104	0.00649043
$321$	18.3945	1.02668
$322$	3.39696	0.189305
$323$	2.91446	0.162165
$324$	−0.155711	−0.00865059
$325$	−14.3806	−0.797692
$326$	−14.2465	−0.789042
$327$	−8.46059	−0.467872
$328$	−9.98652	−0.551413
$329$	9.97681	0.550039
$330$	0	0
$331$	−5.36895	−0.295104	−0.147552	−	0.989054i	$-0.547139\pi$
$331$	−5.36895	−0.295104	−0.147552	+	0.989054i	$0.547139\pi$
$332$	4.05120	0.222339
$333$	50.9343	2.79118
$334$	8.77584	0.480193
$335$	0.395967	0.0216340
$336$	−6.59672	−0.359880
$337$	29.2373	1.59266	0.796329	−	0.604864i	$-0.206772\pi$
$337$	29.2373	1.59266	0.796329	+	0.604864i	$0.206772\pi$
$338$	4.68315	0.254730
$339$	1.33965	0.0727600
$340$	0.338382	0.0183513
$341$	0	0
$342$	−4.83081	−0.261220
$343$	−19.9029	−1.07465
$344$	2.76591	0.149128
$345$	0.468185	0.0252062
$346$	−2.93321	−0.157691
$347$	26.6983	1.43324	0.716620	−	0.697464i	$-0.245688\pi$
$347$	26.6983	1.43324	0.716620	+	0.697464i	$0.245688\pi$
$348$	−14.4223	−0.773114
$349$	−9.89006	−0.529403	−0.264701	−	0.964330i	$-0.585273\pi$
$349$	−9.89006	−0.529403	−0.264701	+	0.964330i	$0.585273\pi$
$350$	11.7550	0.628330
$351$	−14.7749	−0.788628
$352$	0	0
$353$	34.4402	1.83307	0.916533	−	0.399960i	$-0.130976\pi$
$353$	34.4402	1.83307	0.916533	+	0.399960i	$0.130976\pi$
$354$	−23.8173	−1.26588
$355$	−0.135748	−0.00720476
$356$	−9.25833	−0.490691
$357$	−19.2259	−1.01754
$358$	−7.27182	−0.384327
$359$	−18.2006	−0.960590	−0.480295	−	0.877107i	$-0.659470\pi$
$359$	−18.2006	−0.960590	−0.480295	+	0.877107i	$0.659470\pi$
$360$	−0.560878	−0.0295609
$361$	1.00000	0.0526316
$362$	−15.7408	−0.827320
$363$	0	0
$364$	6.79836	0.356331
$365$	−0.152996	−0.00800818
$366$	7.59672	0.397087
$367$	−8.77961	−0.458292	−0.229146	−	0.973392i	$-0.573593\pi$
$367$	−8.77961	−0.458292	−0.229146	+	0.973392i	$0.573593\pi$
$368$	−1.44101	−0.0751176
$369$	48.2430	2.51143
$370$	−1.22416	−0.0636411
$371$	13.1169	0.680997
$372$	−23.2961	−1.20784
$373$	36.2449	1.87669	0.938344	−	0.345704i	$-0.112360\pi$
$373$	36.2449	1.87669	0.938344	+	0.345704i	$0.112360\pi$
$374$	0	0
$375$	3.24464	0.167552
$376$	−4.23221	−0.218259
$377$	14.8631	0.765489
$378$	12.0773	0.621191
$379$	21.2124	1.08961	0.544804	−	0.838563i	$-0.316604\pi$
$379$	21.2124	1.08961	0.544804	+	0.838563i	$0.316604\pi$
$380$	0.116104	0.00595603
$381$	31.8020	1.62926
$382$	−24.2998	−1.24329
$383$	−13.4808	−0.688838	−0.344419	−	0.938816i	$-0.611924\pi$
$383$	−13.4808	−0.688838	−0.344419	+	0.938816i	$0.611924\pi$
$384$	2.79836	0.142803
$385$	0	0
$386$	10.9100	0.555305
$387$	−13.3616	−0.679207
$388$	8.71094	0.442231
$389$	−5.06679	−0.256896	−0.128448	−	0.991716i	$-0.541000\pi$
$389$	−5.06679	−0.256896	−0.128448	+	0.991716i	$0.541000\pi$
$390$	0.936982	0.0474459
$391$	−4.19976	−0.212391
$392$	1.44289	0.0728769
$393$	54.9825	2.77350
$394$	3.53558	0.178120
$395$	−0.224673	−0.0113045
$396$	0	0
$397$	5.76862	0.289519	0.144759	−	0.989467i	$-0.453759\pi$
$397$	5.76862	0.289519	0.144759	+	0.989467i	$0.453759\pi$
$398$	−6.09081	−0.305305
$399$	−6.59672	−0.330249
$400$	−4.98652	−0.249326
$401$	18.9431	0.945976	0.472988	−	0.881069i	$-0.343175\pi$
$401$	18.9431	0.945976	0.472988	+	0.881069i	$0.343175\pi$
$402$	9.54363	0.475993
$403$	24.0081	1.19593
$404$	−7.83269	−0.389691
$405$	−0.0180787	−0.000898337 0
$406$	−12.1494	−0.602964
$407$	0	0
$408$	8.15571	0.403768
$409$	28.7314	1.42068	0.710338	−	0.703860i	$-0.248542\pi$
$409$	28.7314	1.42068	0.710338	+	0.703860i	$0.248542\pi$
$410$	−1.15948	−0.0572626
$411$	14.4983	0.715149
$412$	−1.94503	−0.0958247
$413$	−20.0638	−0.987277
$414$	6.96122	0.342126
$415$	0.470362	0.0230892
$416$	−2.88390	−0.141395
$417$	−60.3321	−2.95448
$418$	0	0
$419$	−32.9954	−1.61193	−0.805965	−	0.591963i	$-0.798353\pi$
$419$	−32.9954	−1.61193	−0.805965	+	0.591963i	$0.798353\pi$
$420$	−0.765907	−0.0373725
$421$	21.1197	1.02931	0.514656	−	0.857397i	$-0.327920\pi$
$421$	21.1197	1.02931	0.514656	+	0.857397i	$0.327920\pi$
$422$	−23.5851	−1.14811
$423$	20.4450	0.994070
$424$	−5.56427	−0.270225
$425$	−14.5330	−0.704955
$426$	−3.27182	−0.158520
$427$	6.39952	0.309694
$428$	−6.57331	−0.317733
$429$	0	0
$430$	0.321134	0.0154865
$431$	38.9916	1.87816	0.939080	−	0.343698i	$-0.111680\pi$
$431$	38.9916	1.87816	0.939080	+	0.343698i	$0.111680\pi$
$432$	−5.12326	−0.246493
$433$	15.8146	0.760002	0.380001	−	0.924986i	$-0.375924\pi$
$433$	15.8146	0.760002	0.380001	+	0.924986i	$0.375924\pi$
$434$	−19.6247	−0.942017
$435$	−1.67449	−0.0802855
$436$	3.02341	0.144795
$437$	−1.44101	−0.0689327
$438$	−3.68753	−0.176197
$439$	−14.6697	−0.700145	−0.350072	−	0.936723i	$-0.613843\pi$
$439$	−14.6697	−0.700145	−0.350072	+	0.936723i	$0.613843\pi$
$440$	0	0
$441$	−6.97032	−0.331920
$442$	−8.40501	−0.399785
$443$	18.4375	0.875990	0.437995	−	0.898977i	$-0.355689\pi$
$443$	18.4375	0.875990	0.437995	+	0.898977i	$0.355689\pi$
$444$	−29.5049	−1.40024
$445$	−1.07493	−0.0509567
$446$	−1.82893	−0.0866021
$447$	40.4412	1.91280
$448$	2.35735	0.111374
$449$	26.6266	1.25659	0.628294	−	0.777976i	$-0.283754\pi$
$449$	26.6266	1.25659	0.628294	+	0.777976i	$0.283754\pi$
$450$	24.0889	1.13556
$451$	0	0
$452$	−0.478728	−0.0225175
$453$	65.4779	3.07642
$454$	−8.91169	−0.418246
$455$	0.789319	0.0370038
$456$	2.79836	0.131045
$457$	5.75520	0.269217	0.134609	−	0.990899i	$-0.457022\pi$
$457$	5.75520	0.269217	0.134609	+	0.990899i	$0.457022\pi$
$458$	9.45720	0.441906
$459$	−14.9315	−0.696945
$460$	−0.167307	−0.00780073
$461$	18.3114	0.852848	0.426424	−	0.904523i	$-0.359773\pi$
$461$	18.3114	0.852848	0.426424	+	0.904523i	$0.359773\pi$
$462$	0	0
$463$	1.12176	0.0521324	0.0260662	−	0.999660i	$-0.491702\pi$
$463$	1.12176	0.0521324	0.0260662	+	0.999660i	$0.491702\pi$
$464$	5.15383	0.239260
$465$	−2.70477	−0.125431
$466$	17.4294	0.807402
$467$	−19.1053	−0.884090	−0.442045	−	0.896993i	$-0.645747\pi$
$467$	−19.1053	−0.884090	−0.442045	+	0.896993i	$0.645747\pi$
$468$	13.9315	0.643986
$469$	8.03961	0.371235
$470$	−0.491378	−0.0226656
$471$	−53.3852	−2.45986
$472$	8.51118	0.391759
$473$	0	0
$474$	−5.41510	−0.248724
$475$	−4.98652	−0.228797
$476$	6.87042	0.314905
$477$	26.8799	1.23075
$478$	25.0036	1.14364
$479$	16.7568	0.765638	0.382819	−	0.923823i	$-0.374953\pi$
$479$	16.7568	0.765638	0.382819	+	0.923823i	$0.374953\pi$
$480$	0.324902	0.0148297
$481$	30.4067	1.38643
$482$	−1.94503	−0.0885937
$483$	9.50591	0.432534
$484$	0	0
$485$	1.01138	0.0459243
$486$	−15.8055	−0.716953
$487$	−1.61042	−0.0729749	−0.0364874	−	0.999334i	$-0.511617\pi$
$487$	−1.61042	−0.0729749	−0.0364874	+	0.999334i	$0.511617\pi$
$488$	−2.71470	−0.122889
$489$	−39.8669	−1.80284
$490$	0.167526	0.00756804
$491$	−0.200650	−0.00905520	−0.00452760	−	0.999990i	$-0.501441\pi$
$491$	−0.200650	−0.00905520	−0.00452760	+	0.999990i	$0.501441\pi$
$492$	−27.9459	−1.25990
$493$	15.0206	0.676495
$494$	−2.88390	−0.129753
$495$	0	0
$496$	8.32490	0.373799
$497$	−2.75619	−0.123632
$498$	11.3367	0.508010
$499$	−22.9954	−1.02942	−0.514708	−	0.857366i	$-0.672100\pi$
$499$	−22.9954	−1.02942	−0.514708	+	0.857366i	$0.672100\pi$
$500$	−1.15948	−0.0518534
$501$	24.5579	1.09717
$502$	12.6048	0.562578
$503$	−19.3795	−0.864089	−0.432044	−	0.901852i	$-0.642208\pi$
$503$	−19.3795	−0.864089	−0.432044	+	0.901852i	$0.642208\pi$
$504$	−11.3879	−0.507258
$505$	−0.909410	−0.0404682
$506$	0	0
$507$	13.1051	0.582019
$508$	−11.3645	−0.504219
$509$	−20.0485	−0.888633	−0.444317	−	0.895870i	$-0.646554\pi$
$509$	−20.0485	−0.888633	−0.444317	+	0.895870i	$0.646554\pi$
$510$	0.946913	0.0419300
$511$	−3.10639	−0.137419
$512$	−1.00000	−0.0441942
$513$	−5.12326	−0.226197
$514$	2.53986	0.112029
$515$	−0.225826	−0.00995110
$516$	7.74000	0.340735
$517$	0	0
$518$	−24.8551	−1.09207
$519$	−8.20819	−0.360299
$520$	−0.334833	−0.0146834
$521$	−37.7371	−1.65329	−0.826645	−	0.562723i	$-0.809754\pi$
$521$	−37.7371	−1.65329	−0.826645	+	0.562723i	$0.809754\pi$
$522$	−24.8972	−1.08972
$523$	−19.3222	−0.844900	−0.422450	−	0.906386i	$-0.638830\pi$
$523$	−19.3222	−0.844900	−0.422450	+	0.906386i	$0.638830\pi$
$524$	−19.6481	−0.858333
$525$	32.8947	1.43564
$526$	31.0972	1.35590
$527$	24.2626	1.05690
$528$	0	0
$529$	−20.9235	−0.909717
$530$	−0.646035	−0.0280620
$531$	−41.1159	−1.78428
$532$	2.35735	0.102204
$533$	28.8001	1.24747
$534$	−25.9081	−1.12115
$535$	−0.763189	−0.0329956
$536$	−3.41044	−0.147309
$537$	−20.3491	−0.878130
$538$	21.4294	0.923887
$539$	0	0
$540$	−0.594833	−0.0255975
$541$	36.4375	1.56657	0.783284	−	0.621664i	$-0.213543\pi$
$541$	36.4375	1.56657	0.783284	+	0.621664i	$0.213543\pi$
$542$	18.0152	0.773819
$543$	−44.0485	−1.89030
$544$	−2.91446	−0.124957
$545$	0.351031	0.0150365
$546$	19.0242	0.814162
$547$	0.362012	0.0154785	0.00773926	−	0.999970i	$-0.497536\pi$
$547$	0.362012	0.0154785	0.00773926	+	0.999970i	$0.497536\pi$
$548$	−5.18101	−0.221322
$549$	13.1142	0.559701
$550$	0	0
$551$	5.15383	0.219560
$552$	−4.03245	−0.171633
$553$	−4.56171	−0.193984
$554$	−27.1522	−1.15358
$555$	−3.42564	−0.145410
$556$	21.5598	0.914340
$557$	16.2646	0.689153	0.344577	−	0.938758i	$-0.388022\pi$
$557$	16.2646	0.689153	0.344577	+	0.938758i	$0.388022\pi$
$558$	−40.2160	−1.70248
$559$	−7.97659	−0.337374
$560$	0.273699	0.0115659
$561$	0	0
$562$	−16.1810	−0.682555
$563$	−27.4256	−1.15585	−0.577926	−	0.816089i	$-0.696138\pi$
$563$	−27.4256	−1.15585	−0.577926	+	0.816089i	$0.696138\pi$
$564$	−11.8432	−0.498690
$565$	−0.0555824	−0.00233837
$566$	23.8947	1.00437
$567$	−0.367065	−0.0154153
$568$	1.16919	0.0490582
$569$	−29.5183	−1.23747	−0.618736	−	0.785599i	$-0.712355\pi$
$569$	−29.5183	−1.23747	−0.618736	+	0.785599i	$0.712355\pi$
$570$	0.324902	0.0136086
$571$	11.2449	0.470583	0.235291	−	0.971925i	$-0.424396\pi$
$571$	11.2449	0.470583	0.235291	+	0.971925i	$0.424396\pi$
$572$	0	0
$573$	−67.9996	−2.84072
$574$	−23.5417	−0.982614
$575$	7.18560	0.299660
$576$	4.83081	0.201284
$577$	3.62933	0.151091	0.0755455	−	0.997142i	$-0.475930\pi$
$577$	3.62933	0.151091	0.0755455	+	0.997142i	$0.475930\pi$
$578$	8.50591	0.353799
$579$	30.5301	1.26879
$580$	0.598382	0.0248464
$581$	9.55011	0.396205
$582$	24.3763	1.01043
$583$	0	0
$584$	1.31775	0.0545287
$585$	1.61751	0.0668759
$586$	−5.58052	−0.230529
$587$	3.55545	0.146749	0.0733745	−	0.997304i	$-0.476623\pi$
$587$	3.55545	0.146749	0.0733745	+	0.997304i	$0.476623\pi$
$588$	4.03772	0.166513
$589$	8.32490	0.343022
$590$	0.988185	0.0406829
$591$	9.89383	0.406978
$592$	10.5436	0.433341
$593$	40.0017	1.64267	0.821336	−	0.570445i	$-0.193229\pi$
$593$	40.0017	1.64267	0.821336	+	0.570445i	$0.193229\pi$
$594$	0	0
$595$	0.797685	0.0327019
$596$	−14.4518	−0.591967
$597$	−17.0443	−0.697575
$598$	4.15571	0.169940
$599$	5.82276	0.237912	0.118956	−	0.992900i	$-0.462045\pi$
$599$	5.82276	0.237912	0.118956	+	0.992900i	$0.462045\pi$
$600$	−13.9541	−0.569672
$601$	−38.8791	−1.58591	−0.792955	−	0.609280i	$-0.791459\pi$
$601$	−38.8791	−1.58591	−0.792955	+	0.609280i	$0.791459\pi$
$602$	6.52022	0.265744
$603$	16.4752	0.670921
$604$	−23.3987	−0.952079
$605$	0	0
$606$	−21.9187	−0.890386
$607$	5.26210	0.213582	0.106791	−	0.994281i	$-0.465942\pi$
$607$	5.26210	0.213582	0.106791	+	0.994281i	$0.465942\pi$
$608$	−1.00000	−0.0405554
$609$	−33.9983	−1.37768
$610$	−0.315189	−0.0127616
$611$	12.2052	0.493771
$612$	14.0792	0.569118
$613$	−41.7855	−1.68770	−0.843851	−	0.536577i	$-0.819717\pi$
$613$	−41.7855	−1.68770	−0.843851	+	0.536577i	$0.819717\pi$
$614$	1.22416	0.0494031
$615$	−3.24464	−0.130836
$616$	0	0
$617$	18.7661	0.755496	0.377748	−	0.925908i	$-0.376699\pi$
$617$	18.7661	0.755496	0.377748	+	0.925908i	$0.376699\pi$
$618$	−5.44289	−0.218945
$619$	−26.7901	−1.07679	−0.538394	−	0.842694i	$-0.680969\pi$
$619$	−26.7901	−1.07679	−0.538394	+	0.842694i	$0.680969\pi$
$620$	0.966557	0.0388179
$621$	7.38265	0.296255
$622$	−28.1663	−1.12936
$623$	−21.8252	−0.874406
$624$	−8.07017	−0.323065
$625$	24.7980	0.991919
$626$	−33.4796	−1.33811
$627$	0	0
$628$	19.0773	0.761268
$629$	30.7290	1.22525
$630$	−1.32219	−0.0526772
$631$	10.0038	0.398244	0.199122	−	0.979975i	$-0.436191\pi$
$631$	10.0038	0.398244	0.199122	+	0.979975i	$0.436191\pi$
$632$	1.93510	0.0769741
$633$	−65.9996	−2.62325
$634$	−14.4644	−0.574453
$635$	−1.31947	−0.0523615
$636$	−15.5708	−0.617423
$637$	−4.16114	−0.164871
$638$	0	0
$639$	−5.64814	−0.223437
$640$	−0.116104	−0.00458943
$641$	−17.8470	−0.704914	−0.352457	−	0.935828i	$-0.614654\pi$
$641$	−17.8470	−0.704914	−0.352457	+	0.935828i	$0.614654\pi$
$642$	−18.3945	−0.725972
$643$	37.1053	1.46329	0.731646	−	0.681685i	$-0.238752\pi$
$643$	37.1053	1.46329	0.731646	+	0.681685i	$0.238752\pi$
$644$	−3.39696	−0.133859
$645$	0.898648	0.0353842
$646$	−2.91446	−0.114668
$647$	28.7099	1.12870	0.564351	−	0.825535i	$-0.309126\pi$
$647$	28.7099	1.12870	0.564351	+	0.825535i	$0.309126\pi$
$648$	0.155711	0.00611689
$649$	0	0
$650$	14.3806	0.564054
$651$	−54.9170	−2.15237
$652$	14.2465	0.557937
$653$	−23.2212	−0.908717	−0.454358	−	0.890819i	$-0.650131\pi$
$653$	−23.2212	−0.908717	−0.454358	+	0.890819i	$0.650131\pi$
$654$	8.46059	0.330835
$655$	−2.28123	−0.0891352
$656$	9.98652	0.389908
$657$	−6.36578	−0.248353
$658$	−9.97681	−0.388936
$659$	9.79370	0.381508	0.190754	−	0.981638i	$-0.438907\pi$
$659$	9.79370	0.381508	0.190754	+	0.981638i	$0.438907\pi$
$660$	0	0
$661$	25.9368	1.00883	0.504413	−	0.863463i	$-0.331709\pi$
$661$	25.9368	1.00883	0.504413	+	0.863463i	$0.331709\pi$
$662$	5.36895	0.208670
$663$	−23.5202	−0.913450
$664$	−4.05120	−0.157217
$665$	0.273699	0.0106136
$666$	−50.9343	−1.97366
$667$	−7.42669	−0.287563
$668$	−8.77584	−0.339547
$669$	−5.11799	−0.197873
$670$	−0.395967	−0.0152975
$671$	0	0
$672$	6.59672	0.254474
$673$	−16.0695	−0.619434	−0.309717	−	0.950829i	$-0.600234\pi$
$673$	−16.0695	−0.619434	−0.309717	+	0.950829i	$0.600234\pi$
$674$	−29.2373	−1.12618
$675$	25.5472	0.983314
$676$	−4.68315	−0.180121
$677$	18.9254	0.727362	0.363681	−	0.931524i	$-0.381520\pi$
$677$	18.9254	0.727362	0.363681	+	0.931524i	$0.381520\pi$
$678$	−1.33965	−0.0514491
$679$	20.5347	0.788051
$680$	−0.338382	−0.0129763
$681$	−24.9381	−0.955630
$682$	0	0
$683$	24.8175	0.949617	0.474809	−	0.880089i	$-0.342517\pi$
$683$	24.8175	0.949617	0.474809	+	0.880089i	$0.342517\pi$
$684$	4.83081	0.184711
$685$	−0.601537	−0.0229836
$686$	19.9029	0.759895
$687$	26.4646	1.00969
$688$	−2.76591	−0.105449
$689$	16.0468	0.611333
$690$	−0.468185	−0.0178235
$691$	−0.761528	−0.0289699	−0.0144849	−	0.999895i	$-0.504611\pi$
$691$	−0.761528	−0.0289699	−0.0144849	+	0.999895i	$0.504611\pi$
$692$	2.93321	0.111504
$693$	0	0
$694$	−26.6983	−1.01345
$695$	2.50319	0.0949514
$696$	14.4223	0.546674
$697$	29.1053	1.10244
$698$	9.89006	0.374344
$699$	48.7737	1.84479
$700$	−11.7550	−0.444297
$701$	−37.8593	−1.42993	−0.714964	−	0.699162i	$-0.753557\pi$
$701$	−37.8593	−1.42993	−0.714964	+	0.699162i	$0.753557\pi$
$702$	14.7749	0.557644
$703$	10.5436	0.397661
$704$	0	0
$705$	−1.37505	−0.0517874
$706$	−34.4402	−1.29617
$707$	−18.4644	−0.694426
$708$	23.8173	0.895110
$709$	10.3898	0.390197	0.195099	−	0.980784i	$-0.437497\pi$
$709$	10.3898	0.390197	0.195099	+	0.980784i	$0.437497\pi$
$710$	0.135748	0.00509454
$711$	−9.34809	−0.350581
$712$	9.25833	0.346971
$713$	−11.9962	−0.449262
$714$	19.2259	0.719511
$715$	0	0
$716$	7.27182	0.271760
$717$	69.9690	2.61304
$718$	18.2006	0.679240
$719$	−49.0175	−1.82805	−0.914023	−	0.405663i	$-0.867041\pi$
$719$	−49.0175	−1.82805	−0.914023	+	0.405663i	$0.867041\pi$
$720$	0.560878	0.0209027
$721$	−4.58512	−0.170759
$722$	−1.00000	−0.0372161
$723$	−5.44289	−0.202423
$724$	15.7408	0.585003
$725$	−25.6997	−0.954461
$726$	0	0
$727$	−5.39418	−0.200059	−0.100030	−	0.994984i	$-0.531894\pi$
$727$	−5.39418	−0.200059	−0.100030	+	0.994984i	$0.531894\pi$
$728$	−6.79836	−0.251964
$729$	−43.7624	−1.62083
$730$	0.152996	0.00566264
$731$	−8.06113	−0.298152
$732$	−7.59672	−0.280783
$733$	19.9693	0.737582	0.368791	−	0.929512i	$-0.379772\pi$
$733$	19.9693	0.737582	0.368791	+	0.929512i	$0.379772\pi$
$734$	8.77961	0.324061
$735$	0.468797	0.0172918
$736$	1.44101	0.0531162
$737$	0	0
$738$	−48.2430	−1.77585
$739$	−48.7027	−1.79156	−0.895778	−	0.444501i	$-0.853381\pi$
$739$	−48.7027	−1.79156	−0.895778	+	0.444501i	$0.853381\pi$
$740$	1.22416	0.0450011
$741$	−8.07017	−0.296465
$742$	−13.1169	−0.481538
$743$	37.5929	1.37915	0.689576	−	0.724214i	$-0.257797\pi$
$743$	37.5929	1.37915	0.689576	+	0.724214i	$0.257797\pi$
$744$	23.2961	0.854075
$745$	−1.67791	−0.0614740
$746$	−36.2449	−1.32702
$747$	19.5706	0.716050
$748$	0	0
$749$	−15.4956	−0.566197
$750$	−3.24464	−0.118477
$751$	−26.4442	−0.964964	−0.482482	−	0.875906i	$-0.660265\pi$
$751$	−26.4442	−0.964964	−0.482482	+	0.875906i	$0.660265\pi$
$752$	4.23221	0.154333
$753$	35.2726	1.28541
$754$	−14.8631	−0.541282
$755$	−2.71669	−0.0988704
$756$	−12.0773	−0.439248
$757$	49.7039	1.80652	0.903260	−	0.429093i	$-0.141167\pi$
$757$	49.7039	1.80652	0.903260	+	0.429093i	$0.141167\pi$
$758$	−21.2124	−0.770469
$759$	0	0
$760$	−0.116104	−0.00421155
$761$	7.24019	0.262457	0.131228	−	0.991352i	$-0.458108\pi$
$761$	7.24019	0.262457	0.131228	+	0.991352i	$0.458108\pi$
$762$	−31.8020	−1.15206
$763$	7.12725	0.258024
$764$	24.2998	0.879137
$765$	1.63466	0.0591012
$766$	13.4808	0.487082
$767$	−24.5454	−0.886281
$768$	−2.79836	−0.100977
$769$	−31.5373	−1.13726	−0.568632	−	0.822592i	$-0.692527\pi$
$769$	−31.5373	−1.13726	−0.568632	+	0.822592i	$0.692527\pi$
$770$	0	0
$771$	7.10744	0.255968
$772$	−10.9100	−0.392660
$773$	−36.0430	−1.29638	−0.648188	−	0.761480i	$-0.724473\pi$
$773$	−36.0430	−1.29638	−0.648188	+	0.761480i	$0.724473\pi$
$774$	13.3616	0.480272
$775$	−41.5123	−1.49117
$776$	−8.71094	−0.312704
$777$	−69.5533	−2.49521
$778$	5.06679	0.181653
$779$	9.98652	0.357804
$780$	−0.936982	−0.0335493
$781$	0	0
$782$	4.19976	0.150183
$783$	−26.4044	−0.943616
$784$	−1.44289	−0.0515318
$785$	2.21496	0.0790553
$786$	−54.9825	−1.96116
$787$	24.5894	0.876517	0.438259	−	0.898849i	$-0.355595\pi$
$787$	24.5894	0.876517	0.438259	+	0.898849i	$0.355595\pi$
$788$	−3.53558	−0.125950
$789$	87.0211	3.09803
$790$	0.224673	0.00799352
$791$	−1.12853	−0.0401260
$792$	0	0
$793$	7.82893	0.278013
$794$	−5.76862	−0.204721
$795$	−1.80784	−0.0641174
$796$	6.09081	0.215883
$797$	−39.0060	−1.38166	−0.690832	−	0.723016i	$-0.742755\pi$
$797$	−39.0060	−1.38166	−0.690832	+	0.723016i	$0.742755\pi$
$798$	6.59672	0.233521
$799$	12.3346	0.436367
$800$	4.98652	0.176300
$801$	−44.7252	−1.58029
$802$	−18.9431	−0.668906
$803$	0	0
$804$	−9.54363	−0.336578
$805$	−0.394402	−0.0139008
$806$	−24.0081	−0.845651
$807$	59.9672	2.11094
$808$	7.83269	0.275553
$809$	−37.8563	−1.33096	−0.665478	−	0.746418i	$-0.731772\pi$
$809$	−37.8563	−1.33096	−0.665478	+	0.746418i	$0.731772\pi$
$810$	0.0180787	0.000635220 0
$811$	37.2754	1.30891	0.654457	−	0.756099i	$-0.272897\pi$
$811$	37.2754	1.30891	0.654457	+	0.756099i	$0.272897\pi$
$812$	12.1494	0.426360
$813$	50.4130	1.76806
$814$	0	0
$815$	1.65408	0.0579400
$816$	−8.15571	−0.285507
$817$	−2.76591	−0.0967669
$818$	−28.7314	−1.00457
$819$	32.8416	1.14758
$820$	1.15948	0.0404907
$821$	1.94263	0.0677984	0.0338992	−	0.999425i	$-0.489207\pi$
$821$	1.94263	0.0677984	0.0338992	+	0.999425i	$0.489207\pi$
$822$	−14.4983	−0.505687
$823$	29.1781	1.01708	0.508542	−	0.861037i	$-0.330185\pi$
$823$	29.1781	1.01708	0.508542	+	0.861037i	$0.330185\pi$
$824$	1.94503	0.0677583
$825$	0	0
$826$	20.0638	0.698111
$827$	−4.87930	−0.169670	−0.0848349	−	0.996395i	$-0.527036\pi$
$827$	−4.87930	−0.169670	−0.0848349	+	0.996395i	$0.527036\pi$
$828$	−6.96122	−0.241919
$829$	15.4007	0.534889	0.267445	−	0.963573i	$-0.413821\pi$
$829$	15.4007	0.534889	0.267445	+	0.963573i	$0.413821\pi$
$830$	−0.470362	−0.0163265
$831$	−75.9815	−2.63577
$832$	2.88390	0.0999811
$833$	−4.20525	−0.145703
$834$	60.3321	2.08913
$835$	−1.01891	−0.0352609
$836$	0	0
$837$	−42.6506	−1.47422
$838$	32.9954	1.13981
$839$	−0.435061	−0.0150200	−0.00750999	−	0.999972i	$-0.502391\pi$
$839$	−0.435061	−0.0150200	−0.00750999	+	0.999972i	$0.502391\pi$
$840$	0.765907	0.0264263
$841$	−2.43807	−0.0840713
$842$	−21.1197	−0.727833
$843$	−45.2803	−1.55953
$844$	23.5851	0.811833
$845$	−0.543734	−0.0187050
$846$	−20.4450	−0.702913
$847$	0	0
$848$	5.56427	0.191078
$849$	66.8658	2.29483
$850$	14.5330	0.498479
$851$	−15.1934	−0.520824
$852$	3.27182	0.112091
$853$	30.7594	1.05318	0.526591	−	0.850119i	$-0.323470\pi$
$853$	30.7594	1.05318	0.526591	+	0.850119i	$0.323470\pi$
$854$	−6.39952	−0.218987
$855$	0.560878	0.0191816
$856$	6.57331	0.224671
$857$	19.0071	0.649270	0.324635	−	0.945839i	$-0.394759\pi$
$857$	19.0071	0.649270	0.324635	+	0.945839i	$0.394759\pi$
$858$	0	0
$859$	−40.7564	−1.39059	−0.695295	−	0.718724i	$-0.744726\pi$
$859$	−40.7564	−1.39059	−0.695295	+	0.718724i	$0.744726\pi$
$860$	−0.321134	−0.0109506
$861$	−65.8782	−2.24512
$862$	−38.9916	−1.32806
$863$	−40.9208	−1.39296	−0.696480	−	0.717576i	$-0.745251\pi$
$863$	−40.9208	−1.39296	−0.696480	+	0.717576i	$0.745251\pi$
$864$	5.12326	0.174297
$865$	0.340559	0.0115794
$866$	−15.8146	−0.537402
$867$	23.8026	0.808378
$868$	19.6247	0.666107
$869$	0	0
$870$	1.67449	0.0567704
$871$	9.83535	0.333258
$872$	−3.02341	−0.102386
$873$	42.0809	1.42422
$874$	1.44101	0.0487428
$875$	−2.73330	−0.0924024
$876$	3.68753	0.124590
$877$	−41.0999	−1.38785	−0.693923	−	0.720050i	$-0.744119\pi$
$877$	−41.0999	−1.38785	−0.693923	+	0.720050i	$0.744119\pi$
$878$	14.6697	0.495077
$879$	−15.6163	−0.526725
$880$	0	0
$881$	−28.0388	−0.944650	−0.472325	−	0.881424i	$-0.656585\pi$
$881$	−28.0388	−0.944650	−0.472325	+	0.881424i	$0.656585\pi$
$882$	6.97032	0.234703
$883$	−9.46358	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$883$	−9.46358	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$884$	8.40501	0.282691
$885$	2.76530	0.0929544
$886$	−18.4375	−0.619418
$887$	11.8774	0.398804	0.199402	−	0.979918i	$-0.436100\pi$
$887$	11.8774	0.398804	0.199402	+	0.979918i	$0.436100\pi$
$888$	29.5049	0.990118
$889$	−26.7901	−0.898513
$890$	1.07493	0.0360318
$891$	0	0
$892$	1.82893	0.0612369
$893$	4.23221	0.141625
$894$	−40.4412	−1.35256
$895$	0.844289	0.0282215
$896$	−2.35735	−0.0787536
$897$	11.6292	0.388287
$898$	−26.6266	−0.888541
$899$	42.9051	1.43097
$900$	−24.0889	−0.802964
$901$	16.2168	0.540261
$902$	0	0
$903$	18.2459	0.607186
$904$	0.478728	0.0159223
$905$	1.82758	0.0607508
$906$	−65.4779	−2.17536
$907$	36.1192	1.19932	0.599659	−	0.800256i	$-0.295303\pi$
$907$	36.1192	1.19932	0.599659	+	0.800256i	$0.295303\pi$
$908$	8.91169	0.295745
$909$	−37.8382	−1.25502
$910$	−0.789319	−0.0261657
$911$	27.7855	0.920576	0.460288	−	0.887770i	$-0.347746\pi$
$911$	27.7855	0.920576	0.460288	+	0.887770i	$0.347746\pi$
$912$	−2.79836	−0.0926629
$913$	0	0
$914$	−5.75520	−0.190365
$915$	−0.882012	−0.0291584
$916$	−9.45720	−0.312475
$917$	−46.3176	−1.52954
$918$	14.9315	0.492815
$919$	46.5464	1.53542	0.767712	−	0.640795i	$-0.221395\pi$
$919$	46.5464	1.53542	0.767712	+	0.640795i	$0.221395\pi$
$920$	0.167307	0.00551595
$921$	3.42564	0.112879
$922$	−18.3114	−0.603055
$923$	−3.37182	−0.110985
$924$	0	0
$925$	−52.5760	−1.72869
$926$	−1.12176	−0.0368632
$927$	−9.39607	−0.308607
$928$	−5.15383	−0.169183
$929$	28.6551	0.940144	0.470072	−	0.882628i	$-0.344228\pi$
$929$	28.6551	0.940144	0.470072	+	0.882628i	$0.344228\pi$
$930$	2.70477	0.0886930
$931$	−1.44289	−0.0472888
$932$	−17.4294	−0.570919
$933$	−78.8193	−2.58043
$934$	19.1053	0.625146
$935$	0	0
$936$	−13.9315	−0.455367
$937$	37.8593	1.23681	0.618404	−	0.785860i	$-0.287779\pi$
$937$	37.8593	1.23681	0.618404	+	0.785860i	$0.287779\pi$
$938$	−8.03961	−0.262502
$939$	−93.6878	−3.05739
$940$	0.491378	0.0160270
$941$	4.46036	0.145403	0.0727017	−	0.997354i	$-0.476838\pi$
$941$	4.46036	0.145403	0.0727017	+	0.997354i	$0.476838\pi$
$942$	53.3852	1.73938
$943$	−14.3906	−0.468624
$944$	−8.51118	−0.277015
$945$	−1.40223	−0.0456146
$946$	0	0
$947$	29.2314	0.949892	0.474946	−	0.880015i	$-0.342468\pi$
$947$	29.2314	0.949892	0.474946	+	0.880015i	$0.342468\pi$
$948$	5.41510	0.175874
$949$	−3.80024	−0.123361
$950$	4.98652	0.161784
$951$	−40.4765	−1.31254
$952$	−6.87042	−0.222671
$953$	5.00428	0.162105	0.0810523	−	0.996710i	$-0.474172\pi$
$953$	5.00428	0.162105	0.0810523	+	0.996710i	$0.474172\pi$
$954$	−26.8799	−0.870269
$955$	2.82132	0.0912956
$956$	−25.0036	−0.808674
$957$	0	0
$958$	−16.7568	−0.541388
$959$	−12.2135	−0.394393
$960$	−0.324902	−0.0104862
$961$	38.3040	1.23561
$962$	−30.4067	−0.980352
$963$	−31.7544	−1.02327
$964$	1.94503	0.0626452
$965$	−1.26670	−0.0407765
$966$	−9.50591	−0.305848
$967$	−33.5154	−1.07778	−0.538891	−	0.842375i	$-0.681157\pi$
$967$	−33.5154	−1.07778	−0.538891	+	0.842375i	$0.681157\pi$
$968$	0	0
$969$	−8.15571	−0.261999
$970$	−1.01138	−0.0324734
$971$	55.5902	1.78398	0.891988	−	0.452060i	$-0.149311\pi$
$971$	55.5902	1.78398	0.891988	+	0.452060i	$0.149311\pi$
$972$	15.8055	0.506962
$973$	50.8241	1.62935
$974$	1.61042	0.0516010
$975$	40.2421	1.28878
$976$	2.71470	0.0868956
$977$	55.0510	1.76124	0.880618	−	0.473826i	$-0.157127\pi$
$977$	55.0510	1.76124	0.880618	+	0.473826i	$0.157127\pi$
$978$	39.8669	1.27480
$979$	0	0
$980$	−0.167526	−0.00535141
$981$	14.6055	0.466318
$982$	0.200650	0.00640299
$983$	−42.1648	−1.34485	−0.672424	−	0.740166i	$-0.734747\pi$
$983$	−42.1648	−1.34485	−0.672424	+	0.740166i	$0.734747\pi$
$984$	27.9459	0.890881
$985$	−0.410497	−0.0130795
$986$	−15.0206	−0.478354
$987$	−27.9187	−0.888661
$988$	2.88390	0.0917489
$989$	3.98569	0.126738
$990$	0	0
$991$	−50.2222	−1.59536	−0.797680	−	0.603081i	$-0.793940\pi$
$991$	−50.2222	−1.59536	−0.797680	+	0.603081i	$0.793940\pi$
$992$	−8.32490	−0.264316
$993$	15.0242	0.476780
$994$	2.75619	0.0874212
$995$	0.707169	0.0224188
$996$	−11.3367	−0.359218
$997$	−41.3157	−1.30848	−0.654241	−	0.756286i	$-0.727012\pi$
$997$	−41.3157	−1.30848	−0.654241	+	0.756286i	$0.727012\pi$
$998$	22.9954	0.727907
$999$	−54.0178	−1.70905

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.79836 q^{3} +1.00000 q^{4} +0.116104 q^{5} +2.79836 q^{6} +2.35735 q^{7} -1.00000 q^{8} +4.83081 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.79836 q^{3} +1.00000 q^{4} +0.116104 q^{5} +2.79836 q^{6} +2.35735 q^{7} -1.00000 q^{8} +4.83081 q^{9} -0.116104 q^{10} -2.79836 q^{12} +2.88390 q^{13} -2.35735 q^{14} -0.324902 q^{15} +1.00000 q^{16} +2.91446 q^{17} -4.83081 q^{18} +1.00000 q^{19} +0.116104 q^{20} -6.59672 q^{21} -1.44101 q^{23} +2.79836 q^{24} -4.98652 q^{25} -2.88390 q^{26} -5.12326 q^{27} +2.35735 q^{28} +5.15383 q^{29} +0.324902 q^{30} +8.32490 q^{31} -1.00000 q^{32} -2.91446 q^{34} +0.273699 q^{35} +4.83081 q^{36} +10.5436 q^{37} -1.00000 q^{38} -8.07017 q^{39} -0.116104 q^{40} +9.98652 q^{41} +6.59672 q^{42} -2.76591 q^{43} +0.560878 q^{45} +1.44101 q^{46} +4.23221 q^{47} -2.79836 q^{48} -1.44289 q^{49} +4.98652 q^{50} -8.15571 q^{51} +2.88390 q^{52} +5.56427 q^{53} +5.12326 q^{54} -2.35735 q^{56} -2.79836 q^{57} -5.15383 q^{58} -8.51118 q^{59} -0.324902 q^{60} +2.71470 q^{61} -8.32490 q^{62} +11.3879 q^{63} +1.00000 q^{64} +0.334833 q^{65} +3.41044 q^{67} +2.91446 q^{68} +4.03245 q^{69} -0.273699 q^{70} -1.16919 q^{71} -4.83081 q^{72} -1.31775 q^{73} -10.5436 q^{74} +13.9541 q^{75} +1.00000 q^{76} +8.07017 q^{78} -1.93510 q^{79} +0.116104 q^{80} -0.155711 q^{81} -9.98652 q^{82} +4.05120 q^{83} -6.59672 q^{84} +0.338382 q^{85} +2.76591 q^{86} -14.4223 q^{87} -9.25833 q^{89} -0.560878 q^{90} +6.79836 q^{91} -1.44101 q^{92} -23.2961 q^{93} -4.23221 q^{94} +0.116104 q^{95} +2.79836 q^{96} +8.71094 q^{97} +1.44289 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 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

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Database

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