LMFDB - Embedded newform 4598.2.a.bt.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.326909$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.05896 q^{3} +1.00000 q^{4} -1.32691 q^{5} -3.05896 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.35723 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.05896 q^{3} +1.00000 q^{4} -1.32691 q^{5} -3.05896 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.35723 q^{9} -1.32691 q^{10} -3.05896 q^{12} +0.653817 q^{13} -1.00000 q^{14} +4.05896 q^{15} +1.00000 q^{16} -2.23931 q^{17} +6.35723 q^{18} +1.00000 q^{19} -1.32691 q^{20} +3.05896 q^{21} -3.31755 q^{23} -3.05896 q^{24} -3.23931 q^{25} +0.653817 q^{26} -10.2696 q^{27} -1.00000 q^{28} -0.248675 q^{29} +4.05896 q^{30} +7.26447 q^{31} +1.00000 q^{32} -2.23931 q^{34} +1.32691 q^{35} +6.35723 q^{36} +1.22004 q^{37} +1.00000 q^{38} -2.00000 q^{39} -1.32691 q^{40} +4.04485 q^{41} +3.05896 q^{42} +4.49274 q^{43} -8.43547 q^{45} -3.31755 q^{46} -0.746577 q^{47} -3.05896 q^{48} -6.00000 q^{49} -3.23931 q^{50} +6.84997 q^{51} +0.653817 q^{52} +3.95209 q^{53} -10.2696 q^{54} -1.00000 q^{56} -3.05896 q^{57} -0.248675 q^{58} +9.86924 q^{59} +4.05896 q^{60} +8.07992 q^{61} +7.26447 q^{62} -6.35723 q^{63} +1.00000 q^{64} -0.867556 q^{65} -11.1034 q^{67} -2.23931 q^{68} +10.1482 q^{69} +1.32691 q^{70} +5.01621 q^{71} +6.35723 q^{72} +8.83586 q^{73} +1.22004 q^{74} +9.90893 q^{75} +1.00000 q^{76} -2.00000 q^{78} -15.4272 q^{79} -1.32691 q^{80} +12.3427 q^{81} +4.04485 q^{82} -8.49790 q^{83} +3.05896 q^{84} +2.97136 q^{85} +4.49274 q^{86} +0.760686 q^{87} +10.8166 q^{89} -8.43547 q^{90} -0.653817 q^{91} -3.31755 q^{92} -22.2217 q^{93} -0.746577 q^{94} -1.32691 q^{95} -3.05896 q^{96} -11.5866 q^{97} -6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{12} - 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 4 q^{32} - 4 q^{34} + 2 q^{35} - 10 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 2 q^{48} - 24 q^{49} - 8 q^{50} - 4 q^{52} - 6 q^{53} - 14 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 20 q^{65} - 20 q^{67} - 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} + 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} - 34 q^{83} + 2 q^{84} + 16 q^{86} + 8 q^{87} - 2 q^{89} - 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} - 2 q^{95} - 2 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^12 - 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 4 * q^32 - 4 * q^34 + 2 * q^35 - 10 * q^37 + 4 * q^38 - 8 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 8 * q^45 - 8 * q^46 - 2 * q^48 - 24 * q^49 - 8 * q^50 - 4 * q^52 - 6 * q^53 - 14 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 20 * q^65 - 20 * q^67 - 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 + 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 - 34 * q^83 + 2 * q^84 + 16 * q^86 + 8 * q^87 - 2 * q^89 - 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 - 2 * q^95 - 2 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.05896	−1.76609	−0.883046	−	0.469287i	$-0.844511\pi$
$3$	−3.05896	−1.76609	−0.883046	+	0.469287i	$0.844511\pi$
$4$	1.00000	0.500000
$5$	−1.32691	−0.593412	−0.296706	−	0.954969i	$-0.595888\pi$
$5$	−1.32691	−0.593412	−0.296706	+	0.954969i	$0.595888\pi$
$6$	−3.05896	−1.24881
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	6.35723	2.11908
$10$	−1.32691	−0.419605
$11$	0	0
$11$	0	0
$12$	−3.05896	−0.883046
$13$	0.653817	0.181336	0.0906681	−	0.995881i	$-0.471100\pi$
$13$	0.653817	0.181336	0.0906681	+	0.995881i	$0.471100\pi$
$14$	−1.00000	−0.267261
$15$	4.05896	1.04802
$16$	1.00000	0.250000
$17$	−2.23931	−0.543113	−0.271557	−	0.962422i	$-0.587538\pi$
$17$	−2.23931	−0.543113	−0.271557	+	0.962422i	$0.587538\pi$
$18$	6.35723	1.49841
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.32691	−0.296706
$21$	3.05896	0.667520
$22$	0	0
$23$	−3.31755	−0.691756	−0.345878	−	0.938279i	$-0.612419\pi$
$23$	−3.31755	−0.691756	−0.345878	+	0.938279i	$0.612419\pi$
$24$	−3.05896	−0.624407
$25$	−3.23931	−0.647863
$26$	0.653817	0.128224
$27$	−10.2696	−1.97639
$28$	−1.00000	−0.188982
$29$	−0.248675	−0.0461778	−0.0230889	−	0.999733i	$-0.507350\pi$
$29$	−0.248675	−0.0461778	−0.0230889	+	0.999733i	$0.507350\pi$
$30$	4.05896	0.741061
$31$	7.26447	1.30474	0.652369	−	0.757902i	$-0.273775\pi$
$31$	7.26447	1.30474	0.652369	+	0.757902i	$0.273775\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.23931	−0.384039
$35$	1.32691	0.224288
$36$	6.35723	1.05954
$37$	1.22004	0.200573	0.100287	−	0.994959i	$-0.468024\pi$
$37$	1.22004	0.200573	0.100287	+	0.994959i	$0.468024\pi$
$38$	1.00000	0.162221
$39$	−2.00000	−0.320256
$40$	−1.32691	−0.209803
$41$	4.04485	0.631699	0.315850	−	0.948809i	$-0.397710\pi$
$41$	4.04485	0.631699	0.315850	+	0.948809i	$0.397710\pi$
$42$	3.05896	0.472008
$43$	4.49274	0.685136	0.342568	−	0.939493i	$-0.388703\pi$
$43$	4.49274	0.685136	0.342568	+	0.939493i	$0.388703\pi$
$44$	0	0
$45$	−8.43547	−1.25749
$46$	−3.31755	−0.489146
$47$	−0.746577	−0.108899	−0.0544497	−	0.998517i	$-0.517340\pi$
$47$	−0.746577	−0.108899	−0.0544497	+	0.998517i	$0.517340\pi$
$48$	−3.05896	−0.441523
$49$	−6.00000	−0.857143
$50$	−3.23931	−0.458108
$51$	6.84997	0.959188
$52$	0.653817	0.0906681
$53$	3.95209	0.542861	0.271431	−	0.962458i	$-0.412503\pi$
$53$	3.95209	0.542861	0.271431	+	0.962458i	$0.412503\pi$
$54$	−10.2696	−1.39752
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−3.05896	−0.405169
$58$	−0.248675	−0.0326526
$59$	9.86924	1.28487	0.642433	−	0.766342i	$-0.277925\pi$
$59$	9.86924	1.28487	0.642433	+	0.766342i	$0.277925\pi$
$60$	4.05896	0.524009
$61$	8.07992	1.03453	0.517264	−	0.855826i	$-0.326951\pi$
$61$	8.07992	1.03453	0.517264	+	0.855826i	$0.326951\pi$
$62$	7.26447	0.922589
$63$	−6.35723	−0.800936
$64$	1.00000	0.125000
$65$	−0.867556	−0.107607
$66$	0	0
$67$	−11.1034	−1.35650	−0.678248	−	0.734833i	$-0.737260\pi$
$67$	−11.1034	−1.35650	−0.678248	+	0.734833i	$0.737260\pi$
$68$	−2.23931	−0.271557
$69$	10.1482	1.22170
$70$	1.32691	0.158596
$71$	5.01621	0.595315	0.297658	−	0.954673i	$-0.403795\pi$
$71$	5.01621	0.595315	0.297658	+	0.954673i	$0.403795\pi$
$72$	6.35723	0.749207
$73$	8.83586	1.03416	0.517080	−	0.855937i	$-0.327019\pi$
$73$	8.83586	1.03416	0.517080	+	0.855937i	$0.327019\pi$
$74$	1.22004	0.141827
$75$	9.90893	1.14418
$76$	1.00000	0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−15.4272	−1.73570	−0.867850	−	0.496826i	$-0.834499\pi$
$79$	−15.4272	−1.73570	−0.867850	+	0.496826i	$0.834499\pi$
$80$	−1.32691	−0.148353
$81$	12.3427	1.37141
$82$	4.04485	0.446679
$83$	−8.49790	−0.932766	−0.466383	−	0.884583i	$-0.654443\pi$
$83$	−8.49790	−0.932766	−0.466383	+	0.884583i	$0.654443\pi$
$84$	3.05896	0.333760
$85$	2.97136	0.322290
$86$	4.49274	0.484464
$87$	0.760686	0.0815541
$88$	0	0
$89$	10.8166	1.14656	0.573278	−	0.819361i	$-0.305672\pi$
$89$	10.8166	1.14656	0.573278	+	0.819361i	$0.305672\pi$
$90$	−8.43547	−0.889176
$91$	−0.653817	−0.0685387
$92$	−3.31755	−0.345878
$93$	−22.2217	−2.30429
$94$	−0.746577	−0.0770035
$95$	−1.32691	−0.136138
$96$	−3.05896	−0.312204
$97$	−11.5866	−1.17644	−0.588222	−	0.808699i	$-0.700172\pi$
$97$	−11.5866	−1.17644	−0.588222	+	0.808699i	$0.700172\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−3.23931	−0.323931
$101$	−11.8803	−1.18213	−0.591067	−	0.806623i	$-0.701293\pi$
$101$	−11.8803	−1.18213	−0.591067	+	0.806623i	$0.701293\pi$
$102$	6.84997	0.678248
$103$	3.01621	0.297196	0.148598	−	0.988898i	$-0.452524\pi$
$103$	3.01621	0.297196	0.148598	+	0.988898i	$0.452524\pi$
$104$	0.653817	0.0641120
$105$	−4.05896	−0.396114
$106$	3.95209	0.383861
$107$	−18.8406	−1.82139	−0.910695	−	0.413079i	$-0.864453\pi$
$107$	−18.8406	−1.82139	−0.910695	+	0.413079i	$0.864453\pi$
$108$	−10.2696	−0.988196
$109$	8.80554	0.843417	0.421709	−	0.906731i	$-0.361430\pi$
$109$	8.80554	0.843417	0.421709	+	0.906731i	$0.361430\pi$
$110$	0	0
$111$	−3.73205	−0.354231
$112$	−1.00000	−0.0944911
$113$	13.3234	1.25336	0.626682	−	0.779275i	$-0.284413\pi$
$113$	13.3234	1.25336	0.626682	+	0.779275i	$0.284413\pi$
$114$	−3.05896	−0.286498
$115$	4.40208	0.410496
$116$	−0.248675	−0.0230889
$117$	4.15647	0.384266
$118$	9.86924	0.908538
$119$	2.23931	0.205278
$120$	4.05896	0.370531
$121$	0	0
$122$	8.07992	0.731522
$123$	−12.3730	−1.11564
$124$	7.26447	0.652369
$125$	10.9328	0.977861
$126$	−6.35723	−0.566347
$127$	−10.2931	−0.913366	−0.456683	−	0.889630i	$-0.650963\pi$
$127$	−10.2931	−0.913366	−0.456683	+	0.889630i	$0.650963\pi$
$128$	1.00000	0.0883883
$129$	−13.7431	−1.21001
$130$	−0.867556	−0.0760897
$131$	16.2217	1.41730	0.708649	−	0.705561i	$-0.249305\pi$
$131$	16.2217	1.41730	0.708649	+	0.705561i	$0.249305\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	−11.1034	−0.959187
$135$	13.6269	1.17281
$136$	−2.23931	−0.192020
$137$	−5.73247	−0.489758	−0.244879	−	0.969554i	$-0.578748\pi$
$137$	−5.73247	−0.489758	−0.244879	+	0.969554i	$0.578748\pi$
$138$	10.1482	0.863876
$139$	−15.3683	−1.30352	−0.651760	−	0.758425i	$-0.725969\pi$
$139$	−15.3683	−1.30352	−0.651760	+	0.758425i	$0.725969\pi$
$140$	1.32691	0.112144
$141$	2.28375	0.192326
$142$	5.01621	0.420951
$143$	0	0
$144$	6.35723	0.529769
$145$	0.329969	0.0274024
$146$	8.83586	0.731261
$147$	18.3538	1.51379
$148$	1.22004	0.100287
$149$	−2.85806	−0.234141	−0.117071	−	0.993124i	$-0.537350\pi$
$149$	−2.85806	−0.234141	−0.117071	+	0.993124i	$0.537350\pi$
$150$	9.90893	0.809061
$151$	−18.4559	−1.50192	−0.750959	−	0.660349i	$-0.770408\pi$
$151$	−18.4559	−1.50192	−0.750959	+	0.660349i	$0.770408\pi$
$152$	1.00000	0.0811107
$153$	−14.2358	−1.15090
$154$	0	0
$155$	−9.63929	−0.774247
$156$	−2.00000	−0.160128
$157$	−10.9230	−0.871753	−0.435877	−	0.900006i	$-0.643562\pi$
$157$	−10.9230	−0.871753	−0.435877	+	0.900006i	$0.643562\pi$
$158$	−15.4272	−1.22733
$159$	−12.0893	−0.958743
$160$	−1.32691	−0.104901
$161$	3.31755	0.261459
$162$	12.3427	0.969735
$163$	−24.2217	−1.89719	−0.948596	−	0.316489i	$-0.897496\pi$
$163$	−24.2217	−1.89719	−0.948596	+	0.316489i	$0.897496\pi$
$164$	4.04485	0.315850
$165$	0	0
$166$	−8.49790	−0.659565
$167$	−16.3491	−1.26513	−0.632567	−	0.774505i	$-0.717999\pi$
$167$	−16.3491	−1.26513	−0.632567	+	0.774505i	$0.717999\pi$
$168$	3.05896	0.236004
$169$	−12.5725	−0.967117
$170$	2.97136	0.227893
$171$	6.35723	0.486150
$172$	4.49274	0.342568
$173$	3.00169	0.228214	0.114107	−	0.993468i	$-0.463599\pi$
$173$	3.00169	0.228214	0.114107	+	0.993468i	$0.463599\pi$
$174$	0.760686	0.0576675
$175$	3.23931	0.244869
$176$	0	0
$177$	−30.1896	−2.26919
$178$	10.8166	0.810737
$179$	−24.4669	−1.82874	−0.914372	−	0.404875i	$-0.867315\pi$
$179$	−24.4669	−1.82874	−0.914372	+	0.404875i	$0.867315\pi$
$180$	−8.43547	−0.628743
$181$	−1.01453	−0.0754091	−0.0377046	−	0.999289i	$-0.512005\pi$
$181$	−1.01453	−0.0754091	−0.0377046	+	0.999289i	$0.512005\pi$
$182$	−0.653817	−0.0484641
$183$	−24.7162	−1.82707
$184$	−3.31755	−0.244573
$185$	−1.61888	−0.119022
$186$	−22.2217	−1.62938
$187$	0	0
$188$	−0.746577	−0.0544497
$189$	10.2696	0.747006
$190$	−1.32691	−0.0962641
$191$	−8.82595	−0.638623	−0.319312	−	0.947650i	$-0.603452\pi$
$191$	−8.82595	−0.638623	−0.319312	+	0.947650i	$0.603452\pi$
$192$	−3.05896	−0.220761
$193$	−8.25078	−0.593904	−0.296952	−	0.954892i	$-0.595970\pi$
$193$	−8.25078	−0.593904	−0.296952	+	0.954892i	$0.595970\pi$
$194$	−11.5866	−0.831872
$195$	2.65382	0.190044
$196$	−6.00000	−0.428571
$197$	1.17477	0.0836992	0.0418496	−	0.999124i	$-0.486675\pi$
$197$	1.17477	0.0836992	0.0418496	+	0.999124i	$0.486675\pi$
$198$	0	0
$199$	8.92473	0.632657	0.316329	−	0.948650i	$-0.397550\pi$
$199$	8.92473	0.632657	0.316329	+	0.948650i	$0.397550\pi$
$200$	−3.23931	−0.229054
$201$	33.9648	2.39569
$202$	−11.8803	−0.835895
$203$	0.248675	0.0174536
$204$	6.84997	0.479594
$205$	−5.36715	−0.374858
$206$	3.01621	0.210150
$207$	−21.0904	−1.46589
$208$	0.653817	0.0453341
$209$	0	0
$210$	−4.05896	−0.280095
$211$	4.81015	0.331144	0.165572	−	0.986198i	$-0.447053\pi$
$211$	4.81015	0.331144	0.165572	+	0.986198i	$0.447053\pi$
$212$	3.95209	0.271431
$213$	−15.3444	−1.05138
$214$	−18.8406	−1.28792
$215$	−5.96145	−0.406568
$216$	−10.2696	−0.698760
$217$	−7.26447	−0.493145
$218$	8.80554	0.596386
$219$	−27.0285	−1.82642
$220$	0	0
$221$	−1.46410	−0.0984861
$222$	−3.73205	−0.250479
$223$	−28.1661	−1.88614	−0.943072	−	0.332588i	$-0.892078\pi$
$223$	−28.1661	−1.88614	−0.943072	+	0.332588i	$0.892078\pi$
$224$	−1.00000	−0.0668153
$225$	−20.5931	−1.37287
$226$	13.3234	0.886262
$227$	24.1786	1.60479	0.802394	−	0.596795i	$-0.203559\pi$
$227$	24.1786	1.60479	0.802394	+	0.596795i	$0.203559\pi$
$228$	−3.05896	−0.202585
$229$	20.4388	1.35064	0.675318	−	0.737526i	$-0.264006\pi$
$229$	20.4388	1.35064	0.675318	+	0.737526i	$0.264006\pi$
$230$	4.40208	0.290265
$231$	0	0
$232$	−0.248675	−0.0163263
$233$	16.4687	1.07890	0.539451	−	0.842017i	$-0.318632\pi$
$233$	16.4687	1.07890	0.539451	+	0.842017i	$0.318632\pi$
$234$	4.15647	0.271717
$235$	0.990639	0.0646222
$236$	9.86924	0.642433
$237$	47.1913	3.06540
$238$	2.23931	0.145153
$239$	6.85039	0.443115	0.221557	−	0.975147i	$-0.428886\pi$
$239$	6.85039	0.443115	0.221557	+	0.975147i	$0.428886\pi$
$240$	4.05896	0.262005
$241$	−6.29480	−0.405484	−0.202742	−	0.979232i	$-0.564985\pi$
$241$	−6.29480	−0.405484	−0.202742	+	0.979232i	$0.564985\pi$
$242$	0	0
$243$	−6.94693	−0.445645
$244$	8.07992	0.517264
$245$	7.96145	0.508638
$246$	−12.3730	−0.788876
$247$	0.653817	0.0416014
$248$	7.26447	0.461294
$249$	25.9947	1.64735
$250$	10.9328	0.691452
$251$	−12.4496	−0.785810	−0.392905	−	0.919579i	$-0.628530\pi$
$251$	−12.4496	−0.785810	−0.392905	+	0.919579i	$0.628530\pi$
$252$	−6.35723	−0.400468
$253$	0	0
$254$	−10.2931	−0.645847
$255$	−9.08928	−0.569193
$256$	1.00000	0.0625000
$257$	8.36071	0.521527	0.260763	−	0.965403i	$-0.416026\pi$
$257$	8.36071	0.521527	0.260763	+	0.965403i	$0.416026\pi$
$258$	−13.7431	−0.855608
$259$	−1.22004	−0.0758096
$260$	−0.867556	−0.0538035
$261$	−1.58088	−0.0978543
$262$	16.2217	1.00218
$263$	−30.3503	−1.87148	−0.935739	−	0.352693i	$-0.885266\pi$
$263$	−30.3503	−1.87148	−0.935739	+	0.352693i	$0.885266\pi$
$264$	0	0
$265$	−5.24406	−0.322140
$266$	−1.00000	−0.0613139
$267$	−33.0875	−2.02492
$268$	−11.1034	−0.678248
$269$	−7.31700	−0.446125	−0.223063	−	0.974804i	$-0.571605\pi$
$269$	−7.31700	−0.446125	−0.223063	+	0.974804i	$0.571605\pi$
$270$	13.6269	0.829305
$271$	−30.4973	−1.85258	−0.926288	−	0.376816i	$-0.877019\pi$
$271$	−30.4973	−1.85258	−0.926288	+	0.376816i	$0.877019\pi$
$272$	−2.23931	−0.135778
$273$	2.00000	0.121046
$274$	−5.73247	−0.346311
$275$	0	0
$276$	10.1482	0.610852
$277$	4.12770	0.248009	0.124005	−	0.992282i	$-0.460426\pi$
$277$	4.12770	0.248009	0.124005	+	0.992282i	$0.460426\pi$
$278$	−15.3683	−0.921728
$279$	46.1819	2.76484
$280$	1.32691	0.0792980
$281$	−2.15939	−0.128819	−0.0644093	−	0.997924i	$-0.520516\pi$
$281$	−2.15939	−0.128819	−0.0644093	+	0.997924i	$0.520516\pi$
$282$	2.28375	0.135995
$283$	5.45377	0.324193	0.162097	−	0.986775i	$-0.448174\pi$
$283$	5.45377	0.324193	0.162097	+	0.986775i	$0.448174\pi$
$284$	5.01621	0.297658
$285$	4.05896	0.240432
$286$	0	0
$287$	−4.04485	−0.238760
$288$	6.35723	0.374604
$289$	−11.9855	−0.705028
$290$	0.329969	0.0193764
$291$	35.4430	2.07771
$292$	8.83586	0.517080
$293$	−5.09864	−0.297866	−0.148933	−	0.988847i	$-0.547584\pi$
$293$	−5.09864	−0.297866	−0.148933	+	0.988847i	$0.547584\pi$
$294$	18.3538	1.07041
$295$	−13.0956	−0.762454
$296$	1.22004	0.0709133
$297$	0	0
$298$	−2.85806	−0.165563
$299$	−2.16907	−0.125441
$300$	9.90893	0.572092
$301$	−4.49274	−0.258957
$302$	−18.4559	−1.06202
$303$	36.3413	2.08776
$304$	1.00000	0.0573539
$305$	−10.7213	−0.613901
$306$	−14.2358	−0.813809
$307$	8.82078	0.503429	0.251714	−	0.967802i	$-0.419006\pi$
$307$	8.82078	0.503429	0.251714	+	0.967802i	$0.419006\pi$
$308$	0	0
$309$	−9.22648	−0.524876
$310$	−9.63929	−0.547475
$311$	−9.99990	−0.567042	−0.283521	−	0.958966i	$-0.591503\pi$
$311$	−9.99990	−0.567042	−0.283521	+	0.958966i	$0.591503\pi$
$312$	−2.00000	−0.113228
$313$	5.15299	0.291264	0.145632	−	0.989339i	$-0.453478\pi$
$313$	5.15299	0.291264	0.145632	+	0.989339i	$0.453478\pi$
$314$	−10.9230	−0.616423
$315$	8.43547	0.475285
$316$	−15.4272	−0.867850
$317$	−34.3862	−1.93132	−0.965660	−	0.259808i	$-0.916341\pi$
$317$	−34.3862	−1.93132	−0.965660	+	0.259808i	$0.916341\pi$
$318$	−12.0893	−0.677933
$319$	0	0
$320$	−1.32691	−0.0741764
$321$	57.6327	3.21674
$322$	3.31755	0.184880
$323$	−2.23931	−0.124599
$324$	12.3427	0.685706
$325$	−2.11792	−0.117481
$326$	−24.2217	−1.34152
$327$	−26.9358	−1.48955
$328$	4.04485	0.223339
$329$	0.746577	0.0411601
$330$	0	0
$331$	−12.4227	−0.682815	−0.341407	−	0.939915i	$-0.610904\pi$
$331$	−12.4227	−0.682815	−0.341407	+	0.939915i	$0.610904\pi$
$332$	−8.49790	−0.466383
$333$	7.75607	0.425030
$334$	−16.3491	−0.894585
$335$	14.7332	0.804960
$336$	3.05896	0.166880
$337$	6.23415	0.339596	0.169798	−	0.985479i	$-0.445689\pi$
$337$	6.23415	0.339596	0.169798	+	0.985479i	$0.445689\pi$
$338$	−12.5725	−0.683855
$339$	−40.7558	−2.21355
$340$	2.97136	0.161145
$341$	0	0
$342$	6.35723	0.343760
$343$	13.0000	0.701934
$344$	4.49274	0.242232
$345$	−13.4658	−0.724974
$346$	3.00169	0.161372
$347$	21.9982	1.18093	0.590463	−	0.807065i	$-0.298945\pi$
$347$	21.9982	1.18093	0.590463	+	0.807065i	$0.298945\pi$
$348$	0.760686	0.0407771
$349$	22.1927	1.18795	0.593973	−	0.804485i	$-0.297558\pi$
$349$	22.1927	1.18795	0.593973	+	0.804485i	$0.297558\pi$
$350$	3.23931	0.173149
$351$	−6.71446	−0.358392
$352$	0	0
$353$	6.33321	0.337083	0.168541	−	0.985695i	$-0.446094\pi$
$353$	6.33321	0.337083	0.168541	+	0.985695i	$0.446094\pi$
$354$	−30.1896	−1.60456
$355$	−6.65606	−0.353267
$356$	10.8166	0.573278
$357$	−6.84997	−0.362539
$358$	−24.4669	−1.29312
$359$	8.44693	0.445812	0.222906	−	0.974840i	$-0.428446\pi$
$359$	8.44693	0.445812	0.222906	+	0.974840i	$0.428446\pi$
$360$	−8.43547	−0.444588
$361$	1.00000	0.0526316
$362$	−1.01453	−0.0533223
$363$	0	0
$364$	−0.653817	−0.0342693
$365$	−11.7244	−0.613682
$366$	−24.7162	−1.29193
$367$	−3.96451	−0.206946	−0.103473	−	0.994632i	$-0.532996\pi$
$367$	−3.96451	−0.206946	−0.103473	+	0.994632i	$0.532996\pi$
$368$	−3.31755	−0.172939
$369$	25.7140	1.33862
$370$	−1.61888	−0.0841616
$371$	−3.95209	−0.205182
$372$	−22.2217	−1.15214
$373$	23.2948	1.20616	0.603079	−	0.797681i	$-0.293940\pi$
$373$	23.2948	1.20616	0.603079	+	0.797681i	$0.293940\pi$
$374$	0	0
$375$	−33.4430	−1.72699
$376$	−0.746577	−0.0385017
$377$	−0.162588	−0.00837370
$378$	10.2696	0.528213
$379$	0.990223	0.0508643	0.0254322	−	0.999677i	$-0.491904\pi$
$379$	0.990223	0.0508643	0.0254322	+	0.999677i	$0.491904\pi$
$380$	−1.32691	−0.0680690
$381$	31.4862	1.61309
$382$	−8.82595	−0.451575
$383$	2.22296	0.113588	0.0567941	−	0.998386i	$-0.481912\pi$
$383$	2.22296	0.113588	0.0567941	+	0.998386i	$0.481912\pi$
$384$	−3.05896	−0.156102
$385$	0	0
$386$	−8.25078	−0.419954
$387$	28.5614	1.45186
$388$	−11.5866	−0.588222
$389$	0.952090	0.0482729	0.0241364	−	0.999709i	$-0.492316\pi$
$389$	0.952090	0.0482729	0.0241364	+	0.999709i	$0.492316\pi$
$390$	2.65382	0.134381
$391$	7.42903	0.375702
$392$	−6.00000	−0.303046
$393$	−49.6216	−2.50308
$394$	1.17477	0.0591842
$395$	20.4705	1.02998
$396$	0	0
$397$	5.45460	0.273759	0.136879	−	0.990588i	$-0.456293\pi$
$397$	5.45460	0.273759	0.136879	+	0.990588i	$0.456293\pi$
$398$	8.92473	0.447356
$399$	3.05896	0.153140
$400$	−3.23931	−0.161966
$401$	−15.7555	−0.786793	−0.393397	−	0.919369i	$-0.628700\pi$
$401$	−15.7555	−0.786793	−0.393397	+	0.919369i	$0.628700\pi$
$402$	33.9648	1.69401
$403$	4.74964	0.236596
$404$	−11.8803	−0.591067
$405$	−16.3776	−0.813812
$406$	0.248675	0.0123415
$407$	0	0
$408$	6.84997	0.339124
$409$	−18.1171	−0.895832	−0.447916	−	0.894076i	$-0.647834\pi$
$409$	−18.1171	−0.895832	−0.447916	+	0.894076i	$0.647834\pi$
$410$	−5.36715	−0.265064
$411$	17.5354	0.864957
$412$	3.01621	0.148598
$413$	−9.86924	−0.485634
$414$	−21.0904	−1.03654
$415$	11.2759	0.553514
$416$	0.653817	0.0320560
$417$	47.0109	2.30214
$418$	0	0
$419$	0.478075	0.0233555	0.0116778	−	0.999932i	$-0.496283\pi$
$419$	0.478075	0.0233555	0.0116778	+	0.999932i	$0.496283\pi$
$420$	−4.05896	−0.198057
$421$	−29.8493	−1.45477	−0.727383	−	0.686231i	$-0.759264\pi$
$421$	−29.8493	−1.45477	−0.727383	+	0.686231i	$0.759264\pi$
$422$	4.81015	0.234154
$423$	−4.74616	−0.230766
$424$	3.95209	0.191930
$425$	7.25384	0.351863
$426$	−15.3444	−0.743438
$427$	−8.07992	−0.391015
$428$	−18.8406	−0.910695
$429$	0	0
$430$	−5.96145	−0.287487
$431$	−20.7631	−1.00012	−0.500062	−	0.865990i	$-0.666689\pi$
$431$	−20.7631	−1.00012	−0.500062	+	0.865990i	$0.666689\pi$
$432$	−10.2696	−0.494098
$433$	−32.7225	−1.57254	−0.786270	−	0.617883i	$-0.787991\pi$
$433$	−32.7225	−1.57254	−0.786270	+	0.617883i	$0.787991\pi$
$434$	−7.26447	−0.348706
$435$	−1.00936	−0.0483952
$436$	8.80554	0.421709
$437$	−3.31755	−0.158700
$438$	−27.0285	−1.29147
$439$	15.7958	0.753890	0.376945	−	0.926236i	$-0.376974\pi$
$439$	15.7958	0.753890	0.376945	+	0.926236i	$0.376974\pi$
$440$	0	0
$441$	−38.1434	−1.81635
$442$	−1.46410	−0.0696402
$443$	−18.3072	−0.869802	−0.434901	−	0.900478i	$-0.643217\pi$
$443$	−18.3072	−0.869802	−0.434901	+	0.900478i	$0.643217\pi$
$444$	−3.73205	−0.177115
$445$	−14.3526	−0.680379
$446$	−28.1661	−1.33371
$447$	8.74268	0.413515
$448$	−1.00000	−0.0472456
$449$	34.9699	1.65033	0.825165	−	0.564892i	$-0.191082\pi$
$449$	34.9699	1.65033	0.825165	+	0.564892i	$0.191082\pi$
$450$	−20.5931	−0.970767
$451$	0	0
$452$	13.3234	0.626682
$453$	56.4558	2.65252
$454$	24.1786	1.13476
$455$	0.867556	0.0406716
$456$	−3.05896	−0.143249
$457$	11.2252	0.525093	0.262546	−	0.964919i	$-0.415438\pi$
$457$	11.2252	0.525093	0.262546	+	0.964919i	$0.415438\pi$
$458$	20.4388	0.955044
$459$	22.9969	1.07341
$460$	4.40208	0.205248
$461$	10.3265	0.480953	0.240476	−	0.970655i	$-0.422696\pi$
$461$	10.3265	0.480953	0.240476	+	0.970655i	$0.422696\pi$
$462$	0	0
$463$	28.7529	1.33626	0.668131	−	0.744044i	$-0.267095\pi$
$463$	28.7529	1.33626	0.668131	+	0.744044i	$0.267095\pi$
$464$	−0.248675	−0.0115444
$465$	29.4862	1.36739
$466$	16.4687	0.762898
$467$	14.7099	0.680691	0.340345	−	0.940300i	$-0.389456\pi$
$467$	14.7099	0.680691	0.340345	+	0.940300i	$0.389456\pi$
$468$	4.15647	0.192133
$469$	11.1034	0.512707
$470$	0.990639	0.0456948
$471$	33.4131	1.53960
$472$	9.86924	0.454269
$473$	0	0
$474$	47.1913	2.16757
$475$	−3.23931	−0.148630
$476$	2.23931	0.102639
$477$	25.1244	1.15037
$478$	6.85039	0.313329
$479$	−16.4802	−0.752999	−0.376499	−	0.926417i	$-0.622872\pi$
$479$	−16.4802	−0.752999	−0.376499	+	0.926417i	$0.622872\pi$
$480$	4.05896	0.185265
$481$	0.797683	0.0363712
$482$	−6.29480	−0.286720
$483$	−10.1482	−0.461761
$484$	0	0
$485$	15.3744	0.698116
$486$	−6.94693	−0.315119
$487$	−39.3251	−1.78199	−0.890996	−	0.454012i	$-0.849992\pi$
$487$	−39.3251	−1.78199	−0.890996	+	0.454012i	$0.849992\pi$
$488$	8.07992	0.365761
$489$	74.0933	3.35061
$490$	7.96145	0.359662
$491$	24.5079	1.10603	0.553013	−	0.833173i	$-0.313478\pi$
$491$	24.5079	1.10603	0.553013	+	0.833173i	$0.313478\pi$
$492$	−12.3730	−0.557819
$493$	0.556861	0.0250798
$494$	0.653817	0.0294166
$495$	0	0
$496$	7.26447	0.326184
$497$	−5.01621	−0.225008
$498$	25.9947	1.16485
$499$	18.1265	0.811452	0.405726	−	0.913995i	$-0.367019\pi$
$499$	18.1265	0.811452	0.405726	+	0.913995i	$0.367019\pi$
$500$	10.9328	0.488930
$501$	50.0114	2.23434
$502$	−12.4496	−0.555652
$503$	−20.0470	−0.893849	−0.446925	−	0.894572i	$-0.647481\pi$
$503$	−20.0470	−0.893849	−0.446925	+	0.894572i	$0.647481\pi$
$504$	−6.35723	−0.283174
$505$	15.7641	0.701492
$506$	0	0
$507$	38.4588	1.70802
$508$	−10.2931	−0.456683
$509$	−31.8764	−1.41290	−0.706448	−	0.707765i	$-0.749704\pi$
$509$	−31.8764	−1.41290	−0.706448	+	0.707765i	$0.749704\pi$
$510$	−9.08928	−0.402480
$511$	−8.83586	−0.390875
$512$	1.00000	0.0441942
$513$	−10.2696	−0.453416
$514$	8.36071	0.368775
$515$	−4.00224	−0.176360
$516$	−13.7431	−0.605006
$517$	0	0
$518$	−1.22004	−0.0536055
$519$	−9.18204	−0.403047
$520$	−0.867556	−0.0380448
$521$	−21.7046	−0.950894	−0.475447	−	0.879744i	$-0.657714\pi$
$521$	−21.7046	−0.950894	−0.475447	+	0.879744i	$0.657714\pi$
$522$	−1.58088	−0.0691934
$523$	−14.0432	−0.614066	−0.307033	−	0.951699i	$-0.599336\pi$
$523$	−14.0432	−0.614066	−0.307033	+	0.951699i	$0.599336\pi$
$524$	16.2217	0.708649
$525$	−9.90893	−0.432461
$526$	−30.3503	−1.32334
$527$	−16.2674	−0.708621
$528$	0	0
$529$	−11.9939	−0.521473
$530$	−5.24406	−0.227788
$531$	62.7411	2.72273
$532$	−1.00000	−0.0433555
$533$	2.64459	0.114550
$534$	−33.0875	−1.43184
$535$	24.9998	1.08083
$536$	−11.1034	−0.479594
$537$	74.8433	3.22973
$538$	−7.31700	−0.315458
$539$	0	0
$540$	13.6269	0.586407
$541$	−0.782065	−0.0336236	−0.0168118	−	0.999859i	$-0.505352\pi$
$541$	−0.782065	−0.0336236	−0.0168118	+	0.999859i	$0.505352\pi$
$542$	−30.4973	−1.30997
$543$	3.10339	0.133179
$544$	−2.23931	−0.0960098
$545$	−11.6841	−0.500494
$546$	2.00000	0.0855921
$547$	25.9298	1.10868	0.554339	−	0.832291i	$-0.312971\pi$
$547$	25.9298	1.10868	0.554339	+	0.832291i	$0.312971\pi$
$548$	−5.73247	−0.244879
$549$	51.3659	2.19224
$550$	0	0
$551$	−0.248675	−0.0105939
$552$	10.1482	0.431938
$553$	15.4272	0.656033
$554$	4.12770	0.175369
$555$	4.95209	0.210205
$556$	−15.3683	−0.651760
$557$	7.30763	0.309634	0.154817	−	0.987943i	$-0.450521\pi$
$557$	7.30763	0.309634	0.154817	+	0.987943i	$0.450521\pi$
$558$	46.1819	1.95504
$559$	2.93743	0.124240
$560$	1.32691	0.0560721
$561$	0	0
$562$	−2.15939	−0.0910884
$563$	−18.6666	−0.786701	−0.393351	−	0.919388i	$-0.628684\pi$
$563$	−18.6666	−0.786701	−0.393351	+	0.919388i	$0.628684\pi$
$564$	2.28375	0.0961631
$565$	−17.6790	−0.743760
$566$	5.45377	0.229239
$567$	−12.3427	−0.518345
$568$	5.01621	0.210476
$569$	40.1973	1.68516	0.842579	−	0.538573i	$-0.181036\pi$
$569$	40.1973	1.68516	0.842579	+	0.538573i	$0.181036\pi$
$570$	4.05896	0.170011
$571$	−13.7413	−0.575056	−0.287528	−	0.957772i	$-0.592833\pi$
$571$	−13.7413	−0.575056	−0.287528	+	0.957772i	$0.592833\pi$
$572$	0	0
$573$	26.9982	1.12787
$574$	−4.04485	−0.168829
$575$	10.7466	0.448163
$576$	6.35723	0.264885
$577$	−32.9468	−1.37159	−0.685797	−	0.727793i	$-0.740546\pi$
$577$	−32.9468	−1.37159	−0.685797	+	0.727793i	$0.740546\pi$
$578$	−11.9855	−0.498530
$579$	25.2388	1.04889
$580$	0.329969	0.0137012
$581$	8.49790	0.352552
$582$	35.4430	1.46916
$583$	0	0
$584$	8.83586	0.365630
$585$	−5.51525	−0.228028
$586$	−5.09864	−0.210623
$587$	−16.5983	−0.685087	−0.342543	−	0.939502i	$-0.611288\pi$
$587$	−16.5983	−0.685087	−0.342543	+	0.939502i	$0.611288\pi$
$588$	18.3538	0.756896
$589$	7.26447	0.299327
$590$	−13.0956	−0.539137
$591$	−3.59359	−0.147820
$592$	1.22004	0.0501433
$593$	−2.63213	−0.108089	−0.0540444	−	0.998539i	$-0.517211\pi$
$593$	−2.63213	−0.108089	−0.0540444	+	0.998539i	$0.517211\pi$
$594$	0	0
$595$	−2.97136	−0.121814
$596$	−2.85806	−0.117071
$597$	−27.3004	−1.11733
$598$	−2.16907	−0.0886998
$599$	36.5717	1.49428	0.747140	−	0.664667i	$-0.231427\pi$
$599$	36.5717	1.49428	0.747140	+	0.664667i	$0.231427\pi$
$600$	9.90893	0.404530
$601$	−32.6399	−1.33141	−0.665705	−	0.746215i	$-0.731869\pi$
$601$	−32.6399	−1.33141	−0.665705	+	0.746215i	$0.731869\pi$
$602$	−4.49274	−0.183110
$603$	−70.5868	−2.87452
$604$	−18.4559	−0.750959
$605$	0	0
$606$	36.3413	1.47627
$607$	7.94820	0.322607	0.161304	−	0.986905i	$-0.448430\pi$
$607$	7.94820	0.322607	0.161304	+	0.986905i	$0.448430\pi$
$608$	1.00000	0.0405554
$609$	−0.760686	−0.0308246
$610$	−10.7213	−0.434093
$611$	−0.488125	−0.0197474
$612$	−14.2358	−0.575450
$613$	5.92917	0.239477	0.119738	−	0.992805i	$-0.461794\pi$
$613$	5.92917	0.239477	0.119738	+	0.992805i	$0.461794\pi$
$614$	8.82078	0.355978
$615$	16.4179	0.662033
$616$	0	0
$617$	−4.96410	−0.199847	−0.0999235	−	0.994995i	$-0.531860\pi$
$617$	−4.96410	−0.199847	−0.0999235	+	0.994995i	$0.531860\pi$
$618$	−9.22648	−0.371143
$619$	44.2476	1.77846	0.889231	−	0.457459i	$-0.151240\pi$
$619$	44.2476	1.77846	0.889231	+	0.457459i	$0.151240\pi$
$620$	−9.63929	−0.387123
$621$	34.0700	1.36718
$622$	−9.99990	−0.400959
$623$	−10.8166	−0.433357
$624$	−2.00000	−0.0800641
$625$	1.68972	0.0675889
$626$	5.15299	0.205955
$627$	0	0
$628$	−10.9230	−0.435877
$629$	−2.73205	−0.108934
$630$	8.43547	0.336077
$631$	−40.9926	−1.63189	−0.815946	−	0.578129i	$-0.803783\pi$
$631$	−40.9926	−1.63189	−0.815946	+	0.578129i	$0.803783\pi$
$632$	−15.4272	−0.613663
$633$	−14.7140	−0.584831
$634$	−34.3862	−1.36565
$635$	13.6580	0.542002
$636$	−12.0893	−0.479371
$637$	−3.92290	−0.155431
$638$	0	0
$639$	31.8892	1.26152
$640$	−1.32691	−0.0524507
$641$	−3.13413	−0.123791	−0.0618954	−	0.998083i	$-0.519715\pi$
$641$	−3.13413	−0.123791	−0.0618954	+	0.998083i	$0.519715\pi$
$642$	57.6327	2.27458
$643$	−27.9674	−1.10293	−0.551463	−	0.834200i	$-0.685930\pi$
$643$	−27.9674	−1.10293	−0.551463	+	0.834200i	$0.685930\pi$
$644$	3.31755	0.130730
$645$	18.2358	0.718035
$646$	−2.23931	−0.0881046
$647$	3.66709	0.144168	0.0720842	−	0.997399i	$-0.477035\pi$
$647$	3.66709	0.144168	0.0720842	+	0.997399i	$0.477035\pi$
$648$	12.3427	0.484867
$649$	0	0
$650$	−2.11792	−0.0830716
$651$	22.2217	0.870938
$652$	−24.2217	−0.948596
$653$	−6.65004	−0.260236	−0.130118	−	0.991499i	$-0.541536\pi$
$653$	−6.65004	−0.260236	−0.130118	+	0.991499i	$0.541536\pi$
$654$	−26.9358	−1.05327
$655$	−21.5247	−0.841042
$656$	4.04485	0.157925
$657$	56.1716	2.19146
$658$	0.746577	0.0291046
$659$	−2.38084	−0.0927443	−0.0463722	−	0.998924i	$-0.514766\pi$
$659$	−2.38084	−0.0927443	−0.0463722	+	0.998924i	$0.514766\pi$
$660$	0	0
$661$	−16.2765	−0.633082	−0.316541	−	0.948579i	$-0.602522\pi$
$661$	−16.2765	−0.633082	−0.316541	+	0.948579i	$0.602522\pi$
$662$	−12.4227	−0.482823
$663$	4.47863	0.173935
$664$	−8.49790	−0.329783
$665$	1.32691	0.0514553
$666$	7.75607	0.300542
$667$	0.824991	0.0319438
$668$	−16.3491	−0.632567
$669$	86.1591	3.33110
$670$	14.7332	0.569193
$671$	0	0
$672$	3.05896	0.118002
$673$	3.48562	0.134361	0.0671803	−	0.997741i	$-0.478600\pi$
$673$	3.48562	0.134361	0.0671803	+	0.997741i	$0.478600\pi$
$674$	6.23415	0.240130
$675$	33.2666	1.28043
$676$	−12.5725	−0.483559
$677$	39.8142	1.53019	0.765093	−	0.643920i	$-0.222693\pi$
$677$	39.8142	1.53019	0.765093	+	0.643920i	$0.222693\pi$
$678$	−40.7558	−1.56522
$679$	11.5866	0.444654
$680$	2.97136	0.113947
$681$	−73.9613	−2.83420
$682$	0	0
$683$	25.9709	0.993751	0.496875	−	0.867822i	$-0.334481\pi$
$683$	25.9709	0.993751	0.496875	+	0.867822i	$0.334481\pi$
$684$	6.35723	0.243075
$685$	7.60646	0.290628
$686$	13.0000	0.496342
$687$	−62.5216	−2.38535
$688$	4.49274	0.171284
$689$	2.58394	0.0984404
$690$	−13.4658	−0.512634
$691$	33.3863	1.27008	0.635038	−	0.772481i	$-0.280985\pi$
$691$	33.3863	1.27008	0.635038	+	0.772481i	$0.280985\pi$
$692$	3.00169	0.114107
$693$	0	0
$694$	21.9982	0.835041
$695$	20.3923	0.773524
$696$	0.760686	0.0288337
$697$	−9.05769	−0.343084
$698$	22.1927	0.840005
$699$	−50.3771	−1.90544
$700$	3.23931	0.122435
$701$	12.3359	0.465919	0.232960	−	0.972486i	$-0.425159\pi$
$701$	12.3359	0.465919	0.232960	+	0.972486i	$0.425159\pi$
$702$	−6.71446	−0.253421
$703$	1.22004	0.0460147
$704$	0	0
$705$	−3.03032	−0.114129
$706$	6.33321	0.238353
$707$	11.8803	0.446804
$708$	−30.1896	−1.13460
$709$	36.7461	1.38003	0.690014	−	0.723796i	$-0.257605\pi$
$709$	36.7461	1.38003	0.690014	+	0.723796i	$0.257605\pi$
$710$	−6.65606	−0.249797
$711$	−98.0746	−3.67808
$712$	10.8166	0.405369
$713$	−24.1002	−0.902561
$714$	−6.84997	−0.256354
$715$	0	0
$716$	−24.4669	−0.914372
$717$	−20.9551	−0.782581
$718$	8.44693	0.315237
$719$	46.8288	1.74642	0.873210	−	0.487344i	$-0.162034\pi$
$719$	46.8288	1.74642	0.873210	+	0.487344i	$0.162034\pi$
$720$	−8.43547	−0.314371
$721$	−3.01621	−0.112330
$722$	1.00000	0.0372161
$723$	19.2555	0.716121
$724$	−1.01453	−0.0377046
$725$	0.805536	0.0299169
$726$	0	0
$727$	−37.4533	−1.38906	−0.694532	−	0.719462i	$-0.744389\pi$
$727$	−37.4533	−1.38906	−0.694532	+	0.719462i	$0.744389\pi$
$728$	−0.653817	−0.0242321
$729$	−15.7778	−0.584361
$730$	−11.7244	−0.433939
$731$	−10.0606	−0.372106
$732$	−24.7162	−0.913535
$733$	−4.03959	−0.149205	−0.0746027	−	0.997213i	$-0.523769\pi$
$733$	−4.03959	−0.149205	−0.0746027	+	0.997213i	$0.523769\pi$
$734$	−3.96451	−0.146333
$735$	−24.3538	−0.898302
$736$	−3.31755	−0.122286
$737$	0	0
$738$	25.7140	0.946547
$739$	18.6043	0.684369	0.342184	−	0.939633i	$-0.388833\pi$
$739$	18.6043	0.684369	0.342184	+	0.939633i	$0.388833\pi$
$740$	−1.61888	−0.0595112
$741$	−2.00000	−0.0734718
$742$	−3.95209	−0.145086
$743$	−45.7465	−1.67828	−0.839138	−	0.543919i	$-0.816940\pi$
$743$	−45.7465	−1.67828	−0.839138	+	0.543919i	$0.816940\pi$
$744$	−22.2217	−0.814688
$745$	3.79238	0.138942
$746$	23.2948	0.852883
$747$	−54.0231	−1.97660
$748$	0	0
$749$	18.8406	0.688421
$750$	−33.4430	−1.22117
$751$	−31.2201	−1.13924	−0.569618	−	0.821909i	$-0.692909\pi$
$751$	−31.2201	−1.13924	−0.569618	+	0.821909i	$0.692909\pi$
$752$	−0.746577	−0.0272248
$753$	38.0827	1.38781
$754$	−0.162588	−0.00592110
$755$	24.4893	0.891255
$756$	10.2696	0.373503
$757$	−21.3480	−0.775905	−0.387953	−	0.921679i	$-0.626818\pi$
$757$	−21.3480	−0.775905	−0.387953	+	0.921679i	$0.626818\pi$
$758$	0.990223	0.0359665
$759$	0	0
$760$	−1.32691	−0.0481320
$761$	−23.4798	−0.851141	−0.425570	−	0.904925i	$-0.639927\pi$
$761$	−23.4798	−0.851141	−0.425570	+	0.904925i	$0.639927\pi$
$762$	31.4862	1.14062
$763$	−8.80554	−0.318782
$764$	−8.82595	−0.319312
$765$	18.8897	0.682957
$766$	2.22296	0.0803189
$767$	6.45268	0.232993
$768$	−3.05896	−0.110381
$769$	18.3602	0.662085	0.331043	−	0.943616i	$-0.392600\pi$
$769$	18.3602	0.662085	0.331043	+	0.943616i	$0.392600\pi$
$770$	0	0
$771$	−25.5751	−0.921064
$772$	−8.25078	−0.296952
$773$	−37.9493	−1.36494	−0.682472	−	0.730912i	$-0.739095\pi$
$773$	−37.9493	−1.36494	−0.682472	+	0.730912i	$0.739095\pi$
$774$	28.5614	1.02662
$775$	−23.5319	−0.845291
$776$	−11.5866	−0.415936
$777$	3.73205	0.133887
$778$	0.952090	0.0341341
$779$	4.04485	0.144922
$780$	2.65382	0.0950219
$781$	0	0
$782$	7.42903	0.265662
$783$	2.55380	0.0912654
$784$	−6.00000	−0.214286
$785$	14.4939	0.517309
$786$	−49.6216	−1.76994
$787$	−20.0817	−0.715837	−0.357918	−	0.933753i	$-0.616513\pi$
$787$	−20.0817	−0.715837	−0.357918	+	0.933753i	$0.616513\pi$
$788$	1.17477	0.0418496
$789$	92.8403	3.30520
$790$	20.4705	0.728309
$791$	−13.3234	−0.473727
$792$	0	0
$793$	5.28279	0.187597
$794$	5.45460	0.193577
$795$	16.0414	0.568929
$796$	8.92473	0.316329
$797$	2.89915	0.102693	0.0513466	−	0.998681i	$-0.483649\pi$
$797$	2.89915	0.102693	0.0513466	+	0.998681i	$0.483649\pi$
$798$	3.05896	0.108286
$799$	1.67182	0.0591447
$800$	−3.23931	−0.114527
$801$	68.7635	2.42964
$802$	−15.7555	−0.556347
$803$	0	0
$804$	33.9648	1.19785
$805$	−4.40208	−0.155153
$806$	4.74964	0.167299
$807$	22.3824	0.787898
$808$	−11.8803	−0.417947
$809$	−37.1106	−1.30474	−0.652369	−	0.757902i	$-0.726225\pi$
$809$	−37.1106	−1.30474	−0.652369	+	0.757902i	$0.726225\pi$
$810$	−16.3776	−0.575452
$811$	0.444728	0.0156165	0.00780825	−	0.999970i	$-0.497515\pi$
$811$	0.444728	0.0156165	0.00780825	+	0.999970i	$0.497515\pi$
$812$	0.248675	0.00872678
$813$	93.2898	3.27182
$814$	0	0
$815$	32.1400	1.12582
$816$	6.84997	0.239797
$817$	4.49274	0.157181
$818$	−18.1171	−0.633449
$819$	−4.15647	−0.145239
$820$	−5.36715	−0.187429
$821$	28.4781	0.993892	0.496946	−	0.867782i	$-0.334455\pi$
$821$	28.4781	0.993892	0.496946	+	0.867782i	$0.334455\pi$
$822$	17.5354	0.611617
$823$	−14.9638	−0.521605	−0.260802	−	0.965392i	$-0.583987\pi$
$823$	−14.9638	−0.521605	−0.260802	+	0.965392i	$0.583987\pi$
$824$	3.01621	0.105075
$825$	0	0
$826$	−9.86924	−0.343395
$827$	−9.66109	−0.335949	−0.167974	−	0.985791i	$-0.553723\pi$
$827$	−9.66109	−0.335949	−0.167974	+	0.985791i	$0.553723\pi$
$828$	−21.0904	−0.732943
$829$	18.0922	0.628370	0.314185	−	0.949362i	$-0.398269\pi$
$829$	18.0922	0.628370	0.314185	+	0.949362i	$0.398269\pi$
$830$	11.2759	0.391394
$831$	−12.6265	−0.438007
$832$	0.653817	0.0226670
$833$	13.4359	0.465526
$834$	47.0109	1.62786
$835$	21.6938	0.750746
$836$	0	0
$837$	−74.6035	−2.57867
$838$	0.478075	0.0165148
$839$	−39.9815	−1.38031	−0.690157	−	0.723660i	$-0.742458\pi$
$839$	−39.9815	−1.38031	−0.690157	+	0.723660i	$0.742458\pi$
$840$	−4.05896	−0.140047
$841$	−28.9382	−0.997868
$842$	−29.8493	−1.02868
$843$	6.60549	0.227505
$844$	4.81015	0.165572
$845$	16.6826	0.573898
$846$	−4.74616	−0.163176
$847$	0	0
$848$	3.95209	0.135715
$849$	−16.6829	−0.572555
$850$	7.25384	0.248805
$851$	−4.04754	−0.138748
$852$	−15.3444	−0.525690
$853$	49.0335	1.67887	0.839437	−	0.543457i	$-0.182885\pi$
$853$	49.0335	1.67887	0.839437	+	0.543457i	$0.182885\pi$
$854$	−8.07992	−0.276489
$855$	−8.43547	−0.288487
$856$	−18.8406	−0.643959
$857$	−45.2575	−1.54597	−0.772984	−	0.634426i	$-0.781237\pi$
$857$	−45.2575	−1.54597	−0.772984	+	0.634426i	$0.781237\pi$
$858$	0	0
$859$	19.7906	0.675246	0.337623	−	0.941281i	$-0.390377\pi$
$859$	19.7906	0.675246	0.337623	+	0.941281i	$0.390377\pi$
$860$	−5.96145	−0.203284
$861$	12.3730	0.421672
$862$	−20.7631	−0.707194
$863$	3.56537	0.121366	0.0606832	−	0.998157i	$-0.480672\pi$
$863$	3.56537	0.121366	0.0606832	+	0.998157i	$0.480672\pi$
$864$	−10.2696	−0.349380
$865$	−3.98297	−0.135425
$866$	−32.7225	−1.11195
$867$	36.6631	1.24514
$868$	−7.26447	−0.246572
$869$	0	0
$870$	−1.00936	−0.0342205
$871$	−7.25959	−0.245982
$872$	8.80554	0.298193
$873$	−73.6589	−2.49298
$874$	−3.31755	−0.112218
$875$	−10.9328	−0.369597
$876$	−27.0285	−0.913210
$877$	33.3594	1.12647	0.563233	−	0.826298i	$-0.309557\pi$
$877$	33.3594	1.12647	0.563233	+	0.826298i	$0.309557\pi$
$878$	15.7958	0.533081
$879$	15.5965	0.526058
$880$	0	0
$881$	7.36071	0.247989	0.123994	−	0.992283i	$-0.460430\pi$
$881$	7.36071	0.247989	0.123994	+	0.992283i	$0.460430\pi$
$882$	−38.1434	−1.28435
$883$	4.50823	0.151714	0.0758570	−	0.997119i	$-0.475831\pi$
$883$	4.50823	0.151714	0.0758570	+	0.997119i	$0.475831\pi$
$884$	−1.46410	−0.0492431
$885$	40.0589	1.34656
$886$	−18.3072	−0.615043
$887$	25.9478	0.871242	0.435621	−	0.900130i	$-0.356529\pi$
$887$	25.9478	0.871242	0.435621	+	0.900130i	$0.356529\pi$
$888$	−3.73205	−0.125239
$889$	10.2931	0.345220
$890$	−14.3526	−0.481101
$891$	0	0
$892$	−28.1661	−0.943072
$893$	−0.746577	−0.0249832
$894$	8.74268	0.292399
$895$	32.4654	1.08520
$896$	−1.00000	−0.0334077
$897$	6.63509	0.221539
$898$	34.9699	1.16696
$899$	−1.80649	−0.0602499
$900$	−20.5931	−0.686436
$901$	−8.84997	−0.294835
$902$	0	0
$903$	13.7431	0.457342
$904$	13.3234	0.443131
$905$	1.34618	0.0447486
$906$	56.4558	1.87562
$907$	6.32660	0.210071	0.105036	−	0.994468i	$-0.466504\pi$
$907$	6.32660	0.210071	0.105036	+	0.994468i	$0.466504\pi$
$908$	24.1786	0.802394
$909$	−75.5258	−2.50503
$910$	0.867556	0.0287592
$911$	−16.5635	−0.548772	−0.274386	−	0.961620i	$-0.588475\pi$
$911$	−16.5635	−0.548772	−0.274386	+	0.961620i	$0.588475\pi$
$912$	−3.05896	−0.101292
$913$	0	0
$914$	11.2252	0.371297
$915$	32.7961	1.08420
$916$	20.4388	0.675318
$917$	−16.2217	−0.535689
$918$	22.9969	0.759012
$919$	12.7229	0.419688	0.209844	−	0.977735i	$-0.432704\pi$
$919$	12.7229	0.419688	0.209844	+	0.977735i	$0.432704\pi$
$920$	4.40208	0.145132
$921$	−26.9824	−0.889101
$922$	10.3265	0.340085
$923$	3.27969	0.107952
$924$	0	0
$925$	−3.95209	−0.129944
$926$	28.7529	0.944879
$927$	19.1748	0.629782
$928$	−0.248675	−0.00816315
$929$	−18.3409	−0.601745	−0.300873	−	0.953664i	$-0.597278\pi$
$929$	−18.3409	−0.601745	−0.300873	+	0.953664i	$0.597278\pi$
$930$	29.4862	0.966891
$931$	−6.00000	−0.196642
$932$	16.4687	0.539451
$933$	30.5893	1.00145
$934$	14.7099	0.481321
$935$	0	0
$936$	4.15647	0.135858
$937$	−43.2343	−1.41240	−0.706202	−	0.708010i	$-0.749593\pi$
$937$	−43.2343	−1.41240	−0.706202	+	0.708010i	$0.749593\pi$
$938$	11.1034	0.362539
$939$	−15.7628	−0.514399
$940$	0.990639	0.0323111
$941$	−6.44262	−0.210024	−0.105012	−	0.994471i	$-0.533488\pi$
$941$	−6.44262	−0.210024	−0.105012	+	0.994471i	$0.533488\pi$
$942$	33.4131	1.08866
$943$	−13.4190	−0.436982
$944$	9.86924	0.321217
$945$	−13.6269	−0.443282
$946$	0	0
$947$	−10.2625	−0.333488	−0.166744	−	0.986000i	$-0.553325\pi$
$947$	−10.2625	−0.333488	−0.166744	+	0.986000i	$0.553325\pi$
$948$	47.1913	1.53270
$949$	5.77704	0.187531
$950$	−3.23931	−0.105097
$951$	105.186	3.41089
$952$	2.23931	0.0725766
$953$	34.1910	1.10755	0.553777	−	0.832665i	$-0.313186\pi$
$953$	34.1910	1.10755	0.553777	+	0.832665i	$0.313186\pi$
$954$	25.1244	0.813431
$955$	11.7112	0.378966
$956$	6.85039	0.221557
$957$	0	0
$958$	−16.4802	−0.532450
$959$	5.73247	0.185111
$960$	4.05896	0.131002
$961$	21.7726	0.702341
$962$	0.797683	0.0257183
$963$	−119.774	−3.85967
$964$	−6.29480	−0.202742
$965$	10.9480	0.352430
$966$	−10.1482	−0.326514
$967$	59.6785	1.91913	0.959565	−	0.281487i	$-0.0908277\pi$
$967$	59.6785	1.91913	0.959565	+	0.281487i	$0.0908277\pi$
$968$	0	0
$969$	6.84997	0.220053
$970$	15.3744	0.493642
$971$	34.1165	1.09485	0.547426	−	0.836854i	$-0.315608\pi$
$971$	34.1165	1.09485	0.547426	+	0.836854i	$0.315608\pi$
$972$	−6.94693	−0.222823
$973$	15.3683	0.492684
$974$	−39.3251	−1.26006
$975$	6.47863	0.207482
$976$	8.07992	0.258632
$977$	−22.4717	−0.718933	−0.359466	−	0.933158i	$-0.617041\pi$
$977$	−22.4717	−0.718933	−0.359466	+	0.933158i	$0.617041\pi$
$978$	74.0933	2.36924
$979$	0	0
$980$	7.96145	0.254319
$981$	55.9788	1.78727
$982$	24.5079	0.782078
$983$	45.8764	1.46323	0.731615	−	0.681718i	$-0.238767\pi$
$983$	45.8764	1.46323	0.731615	+	0.681718i	$0.238767\pi$
$984$	−12.3730	−0.394438
$985$	−1.55882	−0.0496681
$986$	0.556861	0.0177341
$987$	−2.28375	−0.0726925
$988$	0.653817	0.0208007
$989$	−14.9049	−0.473947
$990$	0	0
$991$	−31.1436	−0.989310	−0.494655	−	0.869089i	$-0.664706\pi$
$991$	−31.1436	−0.989310	−0.494655	+	0.869089i	$0.664706\pi$
$992$	7.26447	0.230647
$993$	38.0006	1.20591
$994$	−5.01621	−0.159105
$995$	−11.8423	−0.375426
$996$	25.9947	0.823675
$997$	−7.77565	−0.246257	−0.123129	−	0.992391i	$-0.539293\pi$
$997$	−7.77565	−0.246257	−0.123129	+	0.992391i	$0.539293\pi$
$998$	18.1265	0.573783
$999$	−12.5294	−0.396411

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bq.1.1	✓	4	11.10	odd	2
4598.2.a.bt.1.1	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.05896 q^{3} +1.00000 q^{4} -1.32691 q^{5} -3.05896 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.35723 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.05896 q^{3} +1.00000 q^{4} -1.32691 q^{5} -3.05896 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.35723 q^{9} -1.32691 q^{10} -3.05896 q^{12} +0.653817 q^{13} -1.00000 q^{14} +4.05896 q^{15} +1.00000 q^{16} -2.23931 q^{17} +6.35723 q^{18} +1.00000 q^{19} -1.32691 q^{20} +3.05896 q^{21} -3.31755 q^{23} -3.05896 q^{24} -3.23931 q^{25} +0.653817 q^{26} -10.2696 q^{27} -1.00000 q^{28} -0.248675 q^{29} +4.05896 q^{30} +7.26447 q^{31} +1.00000 q^{32} -2.23931 q^{34} +1.32691 q^{35} +6.35723 q^{36} +1.22004 q^{37} +1.00000 q^{38} -2.00000 q^{39} -1.32691 q^{40} +4.04485 q^{41} +3.05896 q^{42} +4.49274 q^{43} -8.43547 q^{45} -3.31755 q^{46} -0.746577 q^{47} -3.05896 q^{48} -6.00000 q^{49} -3.23931 q^{50} +6.84997 q^{51} +0.653817 q^{52} +3.95209 q^{53} -10.2696 q^{54} -1.00000 q^{56} -3.05896 q^{57} -0.248675 q^{58} +9.86924 q^{59} +4.05896 q^{60} +8.07992 q^{61} +7.26447 q^{62} -6.35723 q^{63} +1.00000 q^{64} -0.867556 q^{65} -11.1034 q^{67} -2.23931 q^{68} +10.1482 q^{69} +1.32691 q^{70} +5.01621 q^{71} +6.35723 q^{72} +8.83586 q^{73} +1.22004 q^{74} +9.90893 q^{75} +1.00000 q^{76} -2.00000 q^{78} -15.4272 q^{79} -1.32691 q^{80} +12.3427 q^{81} +4.04485 q^{82} -8.49790 q^{83} +3.05896 q^{84} +2.97136 q^{85} +4.49274 q^{86} +0.760686 q^{87} +10.8166 q^{89} -8.43547 q^{90} -0.653817 q^{91} -3.31755 q^{92} -22.2217 q^{93} -0.746577 q^{94} -1.32691 q^{95} -3.05896 q^{96} -11.5866 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{12} - 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 4 q^{32} - 4 q^{34} + 2 q^{35} - 10 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 2 q^{48} - 24 q^{49} - 8 q^{50} - 4 q^{52} - 6 q^{53} - 14 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 20 q^{65} - 20 q^{67} - 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} + 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} - 34 q^{83} + 2 q^{84} + 16 q^{86} + 8 q^{87} - 2 q^{89} - 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} - 2 q^{95} - 2 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^12 - 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 4 * q^32 - 4 * q^34 + 2 * q^35 - 10 * q^37 + 4 * q^38 - 8 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 8 * q^45 - 8 * q^46 - 2 * q^48 - 24 * q^49 - 8 * q^50 - 4 * q^52 - 6 * q^53 - 14 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 20 * q^65 - 20 * q^67 - 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 + 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 - 34 * q^83 + 2 * q^84 + 16 * q^86 + 8 * q^87 - 2 * q^89 - 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 - 2 * q^95 - 2 * q^96 - 8 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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