LMFDB - Embedded newform 6534.2.a.cv.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6534,2,Mod(1,6534)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6534, 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("6534.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6534 = 2 \cdot 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6534.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:	$52.1742526807$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.493090625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 20x^{4} + 15x^{3} + 115x^{2} + 73x - 11 $ x^6 - 2x^5 - 20x^4 + 15x^3 + 115x^2 + 73*x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 594)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.02098$ of defining polynomial
Character	$\chi$	$=$	6534.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} -1.02098 q^{5} -2.69661 q^{7} -1.00000 q^{8} +O(q^{10})$	$q-1.00000 q^{2} +1.00000 q^{4} -1.02098 q^{5} -2.69661 q^{7} -1.00000 q^{8} +1.02098 q^{10} -5.96663 q^{13} +2.69661 q^{14} +1.00000 q^{16} -2.88169 q^{17} -7.61225 q^{19} -1.02098 q^{20} -8.41814 q^{23} -3.95760 q^{25} +5.96663 q^{26} -2.69661 q^{28} -3.66000 q^{29} +4.53009 q^{31} -1.00000 q^{32} +2.88169 q^{34} +2.75319 q^{35} +3.59045 q^{37} +7.61225 q^{38} +1.02098 q^{40} -5.11418 q^{41} -3.46856 q^{43} +8.41814 q^{46} -10.4388 q^{47} +0.271723 q^{49} +3.95760 q^{50} -5.96663 q^{52} -6.61861 q^{53} +2.69661 q^{56} +3.66000 q^{58} +4.83705 q^{59} +12.8224 q^{61} -4.53009 q^{62} +1.00000 q^{64} +6.09182 q^{65} +11.7502 q^{67} -2.88169 q^{68} -2.75319 q^{70} -8.24898 q^{71} +2.59705 q^{73} -3.59045 q^{74} -7.61225 q^{76} +6.75815 q^{79} -1.02098 q^{80} +5.11418 q^{82} -8.16157 q^{83} +2.94215 q^{85} +3.46856 q^{86} +12.8442 q^{89} +16.0897 q^{91} -8.41814 q^{92} +10.4388 q^{94} +7.77196 q^{95} -3.30259 q^{97} -0.271723 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 + 2 * q^5 + q^7 - 6 * q^8	$ 6 q - 6 q^{2} + 6 q^{4} + 2 q^{5} + q^{7} - 6 q^{8} - 2 q^{10} - q^{13} - q^{14} + 6 q^{16} - 7 q^{19} + 2 q^{20} - 9 q^{23} + 14 q^{25} + q^{26} + q^{28} + q^{29} + 10 q^{31} - 6 q^{32} - 18 q^{35} + 12 q^{37} + 7 q^{38} - 2 q^{40} - 11 q^{41} - 5 q^{43} + 9 q^{46} - q^{47} + 29 q^{49} - 14 q^{50} - q^{52} + 6 q^{53} - q^{56} - q^{58} + 18 q^{59} + 17 q^{61} - 10 q^{62} + 6 q^{64} - 2 q^{65} + 14 q^{67} + 18 q^{70} + 10 q^{71} + 17 q^{73} - 12 q^{74} - 7 q^{76} + 22 q^{79} + 2 q^{80} + 11 q^{82} - 33 q^{83} - 35 q^{85} + 5 q^{86} - 12 q^{89} + 59 q^{91} - 9 q^{92} + q^{94} - 39 q^{95} + 29 q^{97} - 29 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 2 * q^5 + q^7 - 6 * q^8 - 2 * q^10 - q^13 - q^14 + 6 * q^16 - 7 * q^19 + 2 * q^20 - 9 * q^23 + 14 * q^25 + q^26 + q^28 + q^29 + 10 * q^31 - 6 * q^32 - 18 * q^35 + 12 * q^37 + 7 * q^38 - 2 * q^40 - 11 * q^41 - 5 * q^43 + 9 * q^46 - q^47 + 29 * q^49 - 14 * q^50 - q^52 + 6 * q^53 - q^56 - q^58 + 18 * q^59 + 17 * q^61 - 10 * q^62 + 6 * q^64 - 2 * q^65 + 14 * q^67 + 18 * q^70 + 10 * q^71 + 17 * q^73 - 12 * q^74 - 7 * q^76 + 22 * q^79 + 2 * q^80 + 11 * q^82 - 33 * q^83 - 35 * q^85 + 5 * q^86 - 12 * q^89 + 59 * q^91 - 9 * q^92 + q^94 - 39 * q^95 + 29 * q^97 - 29 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−1.02098	−0.456597	−0.228298	−	0.973591i	$-0.573316\pi$
$5$	−1.02098	−0.456597	−0.228298	+	0.973591i	$0.573316\pi$
$6$	0	0
$7$	−2.69661	−1.01922	−0.509612	−	0.860404i	$-0.670211\pi$
$7$	−2.69661	−1.01922	−0.509612	+	0.860404i	$0.670211\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	1.02098	0.322863
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−5.96663	−1.65485	−0.827423	−	0.561580i	$-0.810194\pi$
$13$	−5.96663	−1.65485	−0.827423	+	0.561580i	$0.810194\pi$
$14$	2.69661	0.720700
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.88169	−0.698911	−0.349456	−	0.936953i	$-0.613633\pi$
$17$	−2.88169	−0.698911	−0.349456	+	0.936953i	$0.613633\pi$
$18$	0	0
$19$	−7.61225	−1.74637	−0.873185	−	0.487390i	$-0.837949\pi$
$19$	−7.61225	−1.74637	−0.873185	+	0.487390i	$0.837949\pi$
$20$	−1.02098	−0.228298
$21$	0	0
$22$	0	0
$23$	−8.41814	−1.75530	−0.877652	−	0.479298i	$-0.840891\pi$
$23$	−8.41814	−1.75530	−0.877652	+	0.479298i	$0.840891\pi$
$24$	0	0
$25$	−3.95760	−0.791519
$26$	5.96663	1.17015
$27$	0	0
$28$	−2.69661	−0.509612
$29$	−3.66000	−0.679644	−0.339822	−	0.940490i	$-0.610367\pi$
$29$	−3.66000	−0.679644	−0.339822	+	0.940490i	$0.610367\pi$
$30$	0	0
$31$	4.53009	0.813628	0.406814	−	0.913511i	$-0.366640\pi$
$31$	4.53009	0.813628	0.406814	+	0.913511i	$0.366640\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.88169	0.494205
$35$	2.75319	0.465374
$36$	0	0
$37$	3.59045	0.590266	0.295133	−	0.955456i	$-0.404636\pi$
$37$	3.59045	0.590266	0.295133	+	0.955456i	$0.404636\pi$
$38$	7.61225	1.23487
$39$	0	0
$40$	1.02098	0.161431
$41$	−5.11418	−0.798700	−0.399350	−	0.916798i	$-0.630764\pi$
$41$	−5.11418	−0.798700	−0.399350	+	0.916798i	$0.630764\pi$
$42$	0	0
$43$	−3.46856	−0.528950	−0.264475	−	0.964392i	$-0.585199\pi$
$43$	−3.46856	−0.528950	−0.264475	+	0.964392i	$0.585199\pi$
$44$	0	0
$45$	0	0
$46$	8.41814	1.24119
$47$	−10.4388	−1.52265	−0.761325	−	0.648370i	$-0.775451\pi$
$47$	−10.4388	−1.52265	−0.761325	+	0.648370i	$0.775451\pi$
$48$	0	0
$49$	0.271723	0.0388176
$50$	3.95760	0.559689
$51$	0	0
$52$	−5.96663	−0.827423
$53$	−6.61861	−0.909136	−0.454568	−	0.890712i	$-0.650206\pi$
$53$	−6.61861	−0.909136	−0.454568	+	0.890712i	$0.650206\pi$
$54$	0	0
$55$	0	0
$56$	2.69661	0.360350
$57$	0	0
$58$	3.66000	0.480581
$59$	4.83705	0.629731	0.314865	−	0.949136i	$-0.398041\pi$
$59$	4.83705	0.629731	0.314865	+	0.949136i	$0.398041\pi$
$60$	0	0
$61$	12.8224	1.64174	0.820869	−	0.571117i	$-0.193490\pi$
$61$	12.8224	1.64174	0.820869	+	0.571117i	$0.193490\pi$
$62$	−4.53009	−0.575322
$63$	0	0
$64$	1.00000	0.125000
$65$	6.09182	0.755597
$66$	0	0
$67$	11.7502	1.43551	0.717756	−	0.696295i	$-0.245169\pi$
$67$	11.7502	1.43551	0.717756	+	0.696295i	$0.245169\pi$
$68$	−2.88169	−0.349456
$69$	0	0
$70$	−2.75319	−0.329069
$71$	−8.24898	−0.978973	−0.489487	−	0.872011i	$-0.662816\pi$
$71$	−8.24898	−0.978973	−0.489487	+	0.872011i	$0.662816\pi$
$72$	0	0
$73$	2.59705	0.303962	0.151981	−	0.988383i	$-0.451435\pi$
$73$	2.59705	0.303962	0.151981	+	0.988383i	$0.451435\pi$
$74$	−3.59045	−0.417381
$75$	0	0
$76$	−7.61225	−0.873185
$77$	0	0
$78$	0	0
$79$	6.75815	0.760351	0.380175	−	0.924914i	$-0.375864\pi$
$79$	6.75815	0.760351	0.380175	+	0.924914i	$0.375864\pi$
$80$	−1.02098	−0.114149
$81$	0	0
$82$	5.11418	0.564766
$83$	−8.16157	−0.895849	−0.447924	−	0.894071i	$-0.647837\pi$
$83$	−8.16157	−0.895849	−0.447924	+	0.894071i	$0.647837\pi$
$84$	0	0
$85$	2.94215	0.319121
$86$	3.46856	0.374024
$87$	0	0
$88$	0	0
$89$	12.8442	1.36148	0.680740	−	0.732525i	$-0.261658\pi$
$89$	12.8442	1.36148	0.680740	+	0.732525i	$0.261658\pi$
$90$	0	0
$91$	16.0897	1.68666
$92$	−8.41814	−0.877652
$93$	0	0
$94$	10.4388	1.07668
$95$	7.77196	0.797387
$96$	0	0
$97$	−3.30259	−0.335327	−0.167664	−	0.985844i	$-0.553622\pi$
$97$	−3.30259	−0.335327	−0.167664	+	0.985844i	$0.553622\pi$
$98$	−0.271723	−0.0274482
$99$	0	0
$100$	−3.95760	−0.395760
$101$	−6.48375	−0.645158	−0.322579	−	0.946543i	$-0.604550\pi$
$101$	−6.48375	−0.645158	−0.322579	+	0.946543i	$0.604550\pi$
$102$	0	0
$103$	2.62547	0.258695	0.129348	−	0.991599i	$-0.458712\pi$
$103$	2.62547	0.258695	0.129348	+	0.991599i	$0.458712\pi$
$104$	5.96663	0.585076
$105$	0	0
$106$	6.61861	0.642856
$107$	5.73279	0.554210	0.277105	−	0.960840i	$-0.410625\pi$
$107$	5.73279	0.554210	0.277105	+	0.960840i	$0.410625\pi$
$108$	0	0
$109$	−2.54747	−0.244003	−0.122002	−	0.992530i	$-0.538931\pi$
$109$	−2.54747	−0.244003	−0.122002	+	0.992530i	$0.538931\pi$
$110$	0	0
$111$	0	0
$112$	−2.69661	−0.254806
$113$	−7.48918	−0.704523	−0.352262	−	0.935902i	$-0.614587\pi$
$113$	−7.48918	−0.704523	−0.352262	+	0.935902i	$0.614587\pi$
$114$	0	0
$115$	8.59477	0.801466
$116$	−3.66000	−0.339822
$117$	0	0
$118$	−4.83705	−0.445287
$119$	7.77079	0.712347
$120$	0	0
$121$	0	0
$122$	−12.8224	−1.16088
$123$	0	0
$124$	4.53009	0.406814
$125$	9.14554	0.818002
$126$	0	0
$127$	15.2063	1.34934	0.674669	−	0.738120i	$-0.264286\pi$
$127$	15.2063	1.34934	0.674669	+	0.738120i	$0.264286\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−6.09182	−0.534288
$131$	−15.9631	−1.39470	−0.697350	−	0.716731i	$-0.745638\pi$
$131$	−15.9631	−1.39470	−0.697350	+	0.716731i	$0.745638\pi$
$132$	0	0
$133$	20.5273	1.77994
$134$	−11.7502	−1.01506
$135$	0	0
$136$	2.88169	0.247102
$137$	−10.5359	−0.900142	−0.450071	−	0.892993i	$-0.648601\pi$
$137$	−10.5359	−0.900142	−0.450071	+	0.892993i	$0.648601\pi$
$138$	0	0
$139$	−20.0037	−1.69669	−0.848346	−	0.529441i	$-0.822402\pi$
$139$	−20.0037	−1.69669	−0.848346	+	0.529441i	$0.822402\pi$
$140$	2.75319	0.232687
$141$	0	0
$142$	8.24898	0.692239
$143$	0	0
$144$	0	0
$145$	3.73679	0.310323
$146$	−2.59705	−0.214934
$147$	0	0
$148$	3.59045	0.295133
$149$	−0.714569	−0.0585398	−0.0292699	−	0.999572i	$-0.509318\pi$
$149$	−0.714569	−0.0585398	−0.0292699	+	0.999572i	$0.509318\pi$
$150$	0	0
$151$	−4.97993	−0.405261	−0.202630	−	0.979255i	$-0.564949\pi$
$151$	−4.97993	−0.405261	−0.202630	+	0.979255i	$0.564949\pi$
$152$	7.61225	0.617435
$153$	0	0
$154$	0	0
$155$	−4.62514	−0.371500
$156$	0	0
$157$	−15.2451	−1.21669	−0.608346	−	0.793672i	$-0.708167\pi$
$157$	−15.2451	−1.21669	−0.608346	+	0.793672i	$0.708167\pi$
$158$	−6.75815	−0.537649
$159$	0	0
$160$	1.02098	0.0807157
$161$	22.7005	1.78905
$162$	0	0
$163$	−16.2295	−1.27119	−0.635597	−	0.772021i	$-0.719246\pi$
$163$	−16.2295	−1.27119	−0.635597	+	0.772021i	$0.719246\pi$
$164$	−5.11418	−0.399350
$165$	0	0
$166$	8.16157	0.633461
$167$	−2.54077	−0.196611	−0.0983055	−	0.995156i	$-0.531342\pi$
$167$	−2.54077	−0.196611	−0.0983055	+	0.995156i	$0.531342\pi$
$168$	0	0
$169$	22.6007	1.73851
$170$	−2.94215	−0.225652
$171$	0	0
$172$	−3.46856	−0.264475
$173$	−9.76395	−0.742339	−0.371170	−	0.928565i	$-0.621043\pi$
$173$	−9.76395	−0.742339	−0.371170	+	0.928565i	$0.621043\pi$
$174$	0	0
$175$	10.6721	0.806736
$176$	0	0
$177$	0	0
$178$	−12.8442	−0.962712
$179$	−5.58446	−0.417402	−0.208701	−	0.977979i	$-0.566924\pi$
$179$	−5.58446	−0.417402	−0.208701	+	0.977979i	$0.566924\pi$
$180$	0	0
$181$	8.54491	0.635138	0.317569	−	0.948235i	$-0.397133\pi$
$181$	8.54491	0.635138	0.317569	+	0.948235i	$0.397133\pi$
$182$	−16.0897	−1.19265
$183$	0	0
$184$	8.41814	0.620594
$185$	−3.66578	−0.269514
$186$	0	0
$187$	0	0
$188$	−10.4388	−0.761325
$189$	0	0
$190$	−7.77196	−0.563837
$191$	8.29625	0.600296	0.300148	−	0.953893i	$-0.402964\pi$
$191$	8.29625	0.600296	0.300148	+	0.953893i	$0.402964\pi$
$192$	0	0
$193$	−11.4039	−0.820870	−0.410435	−	0.911890i	$-0.634623\pi$
$193$	−11.4039	−0.820870	−0.410435	+	0.911890i	$0.634623\pi$
$194$	3.30259	0.237112
$195$	0	0
$196$	0.271723	0.0194088
$197$	20.6678	1.47252	0.736258	−	0.676701i	$-0.236591\pi$
$197$	20.6678	1.47252	0.736258	+	0.676701i	$0.236591\pi$
$198$	0	0
$199$	9.35776	0.663354	0.331677	−	0.943393i	$-0.392386\pi$
$199$	9.35776	0.663354	0.331677	+	0.943393i	$0.392386\pi$
$200$	3.95760	0.279844
$201$	0	0
$202$	6.48375	0.456195
$203$	9.86960	0.692710
$204$	0	0
$205$	5.22148	0.364684
$206$	−2.62547	−0.182925
$207$	0	0
$208$	−5.96663	−0.413711
$209$	0	0
$210$	0	0
$211$	9.24210	0.636253	0.318126	−	0.948048i	$-0.396946\pi$
$211$	9.24210	0.636253	0.318126	+	0.948048i	$0.396946\pi$
$212$	−6.61861	−0.454568
$213$	0	0
$214$	−5.73279	−0.391885
$215$	3.54134	0.241517
$216$	0	0
$217$	−12.2159	−0.829270
$218$	2.54747	0.172536
$219$	0	0
$220$	0	0
$221$	17.1939	1.15659
$222$	0	0
$223$	−5.88718	−0.394235	−0.197117	−	0.980380i	$-0.563158\pi$
$223$	−5.88718	−0.394235	−0.197117	+	0.980380i	$0.563158\pi$
$224$	2.69661	0.180175
$225$	0	0
$226$	7.48918	0.498173
$227$	−24.0659	−1.59731	−0.798653	−	0.601791i	$-0.794454\pi$
$227$	−24.0659	−1.59731	−0.798653	+	0.601791i	$0.794454\pi$
$228$	0	0
$229$	−11.9412	−0.789094	−0.394547	−	0.918876i	$-0.629098\pi$
$229$	−11.9412	−0.789094	−0.394547	+	0.918876i	$0.629098\pi$
$230$	−8.59477	−0.566722
$231$	0	0
$232$	3.66000	0.240291
$233$	8.22092	0.538570	0.269285	−	0.963060i	$-0.413213\pi$
$233$	8.22092	0.538570	0.269285	+	0.963060i	$0.413213\pi$
$234$	0	0
$235$	10.6578	0.695237
$236$	4.83705	0.314865
$237$	0	0
$238$	−7.77079	−0.503706
$239$	−8.77252	−0.567447	−0.283724	−	0.958906i	$-0.591570\pi$
$239$	−8.77252	−0.567447	−0.283724	+	0.958906i	$0.591570\pi$
$240$	0	0
$241$	−8.22569	−0.529863	−0.264932	−	0.964267i	$-0.585349\pi$
$241$	−8.22569	−0.529863	−0.264932	+	0.964267i	$0.585349\pi$
$242$	0	0
$243$	0	0
$244$	12.8224	0.820869
$245$	−0.277425	−0.0177240
$246$	0	0
$247$	45.4195	2.88997
$248$	−4.53009	−0.287661
$249$	0	0
$250$	−9.14554	−0.578415
$251$	15.7958	0.997022	0.498511	−	0.866884i	$-0.333880\pi$
$251$	15.7958	0.997022	0.498511	+	0.866884i	$0.333880\pi$
$252$	0	0
$253$	0	0
$254$	−15.2063	−0.954127
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0367	0.750826	0.375413	−	0.926858i	$-0.377501\pi$
$257$	12.0367	0.750826	0.375413	+	0.926858i	$0.377501\pi$
$258$	0	0
$259$	−9.68206	−0.601614
$260$	6.09182	0.377799
$261$	0	0
$262$	15.9631	0.986202
$263$	13.4131	0.827088	0.413544	−	0.910484i	$-0.364291\pi$
$263$	13.4131	0.827088	0.413544	+	0.910484i	$0.364291\pi$
$264$	0	0
$265$	6.75748	0.415109
$266$	−20.5273	−1.25861
$267$	0	0
$268$	11.7502	0.717756
$269$	13.5977	0.829064	0.414532	−	0.910035i	$-0.363945\pi$
$269$	13.5977	0.829064	0.414532	+	0.910035i	$0.363945\pi$
$270$	0	0
$271$	28.1272	1.70861	0.854304	−	0.519774i	$-0.173984\pi$
$271$	28.1272	1.70861	0.854304	+	0.519774i	$0.173984\pi$
$272$	−2.88169	−0.174728
$273$	0	0
$274$	10.5359	0.636497
$275$	0	0
$276$	0	0
$277$	6.94099	0.417044	0.208522	−	0.978018i	$-0.433135\pi$
$277$	6.94099	0.417044	0.208522	+	0.978018i	$0.433135\pi$
$278$	20.0037	1.19974
$279$	0	0
$280$	−2.75319	−0.164535
$281$	−11.6662	−0.695950	−0.347975	−	0.937504i	$-0.613131\pi$
$281$	−11.6662	−0.695950	−0.347975	+	0.937504i	$0.613131\pi$
$282$	0	0
$283$	−32.4272	−1.92760	−0.963798	−	0.266633i	$-0.914089\pi$
$283$	−32.4272	−1.92760	−0.963798	+	0.266633i	$0.914089\pi$
$284$	−8.24898	−0.489487
$285$	0	0
$286$	0	0
$287$	13.7910	0.814054
$288$	0	0
$289$	−8.69589	−0.511523
$290$	−3.73679	−0.219432
$291$	0	0
$292$	2.59705	0.151981
$293$	−20.4665	−1.19566	−0.597832	−	0.801621i	$-0.703971\pi$
$293$	−20.4665	−1.19566	−0.597832	+	0.801621i	$0.703971\pi$
$294$	0	0
$295$	−4.93854	−0.287533
$296$	−3.59045	−0.208691
$297$	0	0
$298$	0.714569	0.0413939
$299$	50.2279	2.90476
$300$	0	0
$301$	9.35336	0.539119
$302$	4.97993	0.286563
$303$	0	0
$304$	−7.61225	−0.436592
$305$	−13.0914	−0.749612
$306$	0	0
$307$	4.90302	0.279830	0.139915	−	0.990163i	$-0.455317\pi$
$307$	4.90302	0.279830	0.139915	+	0.990163i	$0.455317\pi$
$308$	0	0
$309$	0	0
$310$	4.62514	0.262690
$311$	6.30898	0.357750	0.178875	−	0.983872i	$-0.442754\pi$
$311$	6.30898	0.357750	0.178875	+	0.983872i	$0.442754\pi$
$312$	0	0
$313$	20.0549	1.13357	0.566786	−	0.823865i	$-0.308187\pi$
$313$	20.0549	1.13357	0.566786	+	0.823865i	$0.308187\pi$
$314$	15.2451	0.860332
$315$	0	0
$316$	6.75815	0.380175
$317$	14.5147	0.815226	0.407613	−	0.913155i	$-0.366361\pi$
$317$	14.5147	0.815226	0.407613	+	0.913155i	$0.366361\pi$
$318$	0	0
$319$	0	0
$320$	−1.02098	−0.0570746
$321$	0	0
$322$	−22.7005	−1.26505
$323$	21.9361	1.22056
$324$	0	0
$325$	23.6135	1.30984
$326$	16.2295	0.898869
$327$	0	0
$328$	5.11418	0.282383
$329$	28.1493	1.55192
$330$	0	0
$331$	−13.3722	−0.735001	−0.367501	−	0.930023i	$-0.619786\pi$
$331$	−13.3722	−0.735001	−0.367501	+	0.930023i	$0.619786\pi$
$332$	−8.16157	−0.447924
$333$	0	0
$334$	2.54077	0.139025
$335$	−11.9967	−0.655450
$336$	0	0
$337$	−14.8006	−0.806239	−0.403120	−	0.915147i	$-0.632074\pi$
$337$	−14.8006	−0.806239	−0.403120	+	0.915147i	$0.632074\pi$
$338$	−22.6007	−1.22931
$339$	0	0
$340$	2.94215	0.159560
$341$	0	0
$342$	0	0
$343$	18.1436	0.979660
$344$	3.46856	0.187012
$345$	0	0
$346$	9.76395	0.524913
$347$	−4.80647	−0.258025	−0.129013	−	0.991643i	$-0.541181\pi$
$347$	−4.80647	−0.258025	−0.129013	+	0.991643i	$0.541181\pi$
$348$	0	0
$349$	−16.8854	−0.903855	−0.451927	−	0.892055i	$-0.649263\pi$
$349$	−16.8854	−0.903855	−0.451927	+	0.892055i	$0.649263\pi$
$350$	−10.6721	−0.570448
$351$	0	0
$352$	0	0
$353$	−13.3209	−0.708999	−0.354500	−	0.935056i	$-0.615349\pi$
$353$	−13.3209	−0.708999	−0.354500	+	0.935056i	$0.615349\pi$
$354$	0	0
$355$	8.42205	0.446996
$356$	12.8442	0.680740
$357$	0	0
$358$	5.58446	0.295148
$359$	−10.1373	−0.535024	−0.267512	−	0.963555i	$-0.586202\pi$
$359$	−10.1373	−0.535024	−0.267512	+	0.963555i	$0.586202\pi$
$360$	0	0
$361$	38.9463	2.04981
$362$	−8.54491	−0.449111
$363$	0	0
$364$	16.0897	0.843329
$365$	−2.65154	−0.138788
$366$	0	0
$367$	−26.3236	−1.37408	−0.687041	−	0.726619i	$-0.741091\pi$
$367$	−26.3236	−1.37408	−0.687041	+	0.726619i	$0.741091\pi$
$368$	−8.41814	−0.438826
$369$	0	0
$370$	3.66578	0.190575
$371$	17.8478	0.926614
$372$	0	0
$373$	−6.47563	−0.335295	−0.167648	−	0.985847i	$-0.553617\pi$
$373$	−6.47563	−0.335295	−0.167648	+	0.985847i	$0.553617\pi$
$374$	0	0
$375$	0	0
$376$	10.4388	0.538338
$377$	21.8378	1.12471
$378$	0	0
$379$	−15.1194	−0.776629	−0.388315	−	0.921527i	$-0.626943\pi$
$379$	−15.1194	−0.776629	−0.388315	+	0.921527i	$0.626943\pi$
$380$	7.77196	0.398693
$381$	0	0
$382$	−8.29625	−0.424473
$383$	−30.5362	−1.56033	−0.780164	−	0.625575i	$-0.784864\pi$
$383$	−30.5362	−1.56033	−0.780164	+	0.625575i	$0.784864\pi$
$384$	0	0
$385$	0	0
$386$	11.4039	0.580442
$387$	0	0
$388$	−3.30259	−0.167664
$389$	−34.3377	−1.74099	−0.870494	−	0.492179i	$-0.836201\pi$
$389$	−34.3377	−1.74099	−0.870494	+	0.492179i	$0.836201\pi$
$390$	0	0
$391$	24.2584	1.22680
$392$	−0.271723	−0.0137241
$393$	0	0
$394$	−20.6678	−1.04123
$395$	−6.89994	−0.347174
$396$	0	0
$397$	8.00116	0.401567	0.200783	−	0.979636i	$-0.435651\pi$
$397$	8.00116	0.401567	0.200783	+	0.979636i	$0.435651\pi$
$398$	−9.35776	−0.469062
$399$	0	0
$400$	−3.95760	−0.197880
$401$	−33.7690	−1.68634	−0.843171	−	0.537645i	$-0.819314\pi$
$401$	−33.7690	−1.68634	−0.843171	+	0.537645i	$0.819314\pi$
$402$	0	0
$403$	−27.0294	−1.34643
$404$	−6.48375	−0.322579
$405$	0	0
$406$	−9.86960	−0.489820
$407$	0	0
$408$	0	0
$409$	−8.15827	−0.403401	−0.201700	−	0.979447i	$-0.564647\pi$
$409$	−8.15827	−0.403401	−0.201700	+	0.979447i	$0.564647\pi$
$410$	−5.22148	−0.257871
$411$	0	0
$412$	2.62547	0.129348
$413$	−13.0437	−0.641837
$414$	0	0
$415$	8.33281	0.409042
$416$	5.96663	0.292538
$417$	0	0
$418$	0	0
$419$	4.49368	0.219531	0.109765	−	0.993958i	$-0.464990\pi$
$419$	4.49368	0.219531	0.109765	+	0.993958i	$0.464990\pi$
$420$	0	0
$421$	11.2236	0.547005	0.273503	−	0.961871i	$-0.411818\pi$
$421$	11.2236	0.547005	0.273503	+	0.961871i	$0.411818\pi$
$422$	−9.24210	−0.449899
$423$	0	0
$424$	6.61861	0.321428
$425$	11.4045	0.553202
$426$	0	0
$427$	−34.5770	−1.67330
$428$	5.73279	0.277105
$429$	0	0
$430$	−3.54134	−0.170778
$431$	−40.4797	−1.94984	−0.974918	−	0.222563i	$-0.928558\pi$
$431$	−40.4797	−1.94984	−0.974918	+	0.222563i	$0.928558\pi$
$432$	0	0
$433$	−34.7337	−1.66919	−0.834597	−	0.550861i	$-0.814299\pi$
$433$	−34.7337	−1.66919	−0.834597	+	0.550861i	$0.814299\pi$
$434$	12.2159	0.586382
$435$	0	0
$436$	−2.54747	−0.122002
$437$	64.0810	3.06541
$438$	0	0
$439$	−0.559897	−0.0267224	−0.0133612	−	0.999911i	$-0.504253\pi$
$439$	−0.559897	−0.0267224	−0.0133612	+	0.999911i	$0.504253\pi$
$440$	0	0
$441$	0	0
$442$	−17.1939	−0.817833
$443$	−32.3722	−1.53805	−0.769025	−	0.639218i	$-0.779258\pi$
$443$	−32.3722	−1.53805	−0.769025	+	0.639218i	$0.779258\pi$
$444$	0	0
$445$	−13.1137	−0.621647
$446$	5.88718	0.278766
$447$	0	0
$448$	−2.69661	−0.127403
$449$	−3.20540	−0.151272	−0.0756360	−	0.997135i	$-0.524099\pi$
$449$	−3.20540	−0.151272	−0.0756360	+	0.997135i	$0.524099\pi$
$450$	0	0
$451$	0	0
$452$	−7.48918	−0.352262
$453$	0	0
$454$	24.0659	1.12947
$455$	−16.4273	−0.770123
$456$	0	0
$457$	25.5717	1.19619	0.598097	−	0.801424i	$-0.295924\pi$
$457$	25.5717	1.19619	0.598097	+	0.801424i	$0.295924\pi$
$458$	11.9412	0.557973
$459$	0	0
$460$	8.59477	0.400733
$461$	37.9409	1.76708	0.883541	−	0.468354i	$-0.155153\pi$
$461$	37.9409	1.76708	0.883541	+	0.468354i	$0.155153\pi$
$462$	0	0
$463$	30.2788	1.40717	0.703587	−	0.710609i	$-0.251581\pi$
$463$	30.2788	1.40717	0.703587	+	0.710609i	$0.251581\pi$
$464$	−3.66000	−0.169911
$465$	0	0
$466$	−8.22092	−0.380827
$467$	−15.1810	−0.702495	−0.351248	−	0.936283i	$-0.614242\pi$
$467$	−15.1810	−0.702495	−0.351248	+	0.936283i	$0.614242\pi$
$468$	0	0
$469$	−31.6857	−1.46311
$470$	−10.6578	−0.491607
$471$	0	0
$472$	−4.83705	−0.222643
$473$	0	0
$474$	0	0
$475$	30.1262	1.38229
$476$	7.77079	0.356174
$477$	0	0
$478$	8.77252	0.401246
$479$	2.03785	0.0931117	0.0465559	−	0.998916i	$-0.485175\pi$
$479$	2.03785	0.0931117	0.0465559	+	0.998916i	$0.485175\pi$
$480$	0	0
$481$	−21.4229	−0.976800
$482$	8.22569	0.374670
$483$	0	0
$484$	0	0
$485$	3.37188	0.153109
$486$	0	0
$487$	−18.0162	−0.816391	−0.408195	−	0.912895i	$-0.633842\pi$
$487$	−18.0162	−0.816391	−0.408195	+	0.912895i	$0.633842\pi$
$488$	−12.8224	−0.580442
$489$	0	0
$490$	0.277425	0.0125328
$491$	−17.1354	−0.773310	−0.386655	−	0.922224i	$-0.626370\pi$
$491$	−17.1354	−0.773310	−0.386655	+	0.922224i	$0.626370\pi$
$492$	0	0
$493$	10.5470	0.475011
$494$	−45.4195	−2.04352
$495$	0	0
$496$	4.53009	0.203407
$497$	22.2443	0.997793
$498$	0	0
$499$	32.7864	1.46772	0.733861	−	0.679299i	$-0.237716\pi$
$499$	32.7864	1.46772	0.733861	+	0.679299i	$0.237716\pi$
$500$	9.14554	0.409001
$501$	0	0
$502$	−15.7958	−0.705001
$503$	0.766757	0.0341880	0.0170940	−	0.999854i	$-0.494559\pi$
$503$	0.766757	0.0341880	0.0170940	+	0.999854i	$0.494559\pi$
$504$	0	0
$505$	6.61979	0.294577
$506$	0	0
$507$	0	0
$508$	15.2063	0.674669
$509$	9.36077	0.414909	0.207454	−	0.978245i	$-0.433482\pi$
$509$	9.36077	0.414909	0.207454	+	0.978245i	$0.433482\pi$
$510$	0	0
$511$	−7.00325	−0.309805
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−12.0367	−0.530914
$515$	−2.68056	−0.118119
$516$	0	0
$517$	0	0
$518$	9.68206	0.425405
$519$	0	0
$520$	−6.09182	−0.267144
$521$	8.91060	0.390380	0.195190	−	0.980765i	$-0.437468\pi$
$521$	8.91060	0.390380	0.195190	+	0.980765i	$0.437468\pi$
$522$	0	0
$523$	19.1513	0.837426	0.418713	−	0.908119i	$-0.362481\pi$
$523$	19.1513	0.837426	0.418713	+	0.908119i	$0.362481\pi$
$524$	−15.9631	−0.697350
$525$	0	0
$526$	−13.4131	−0.584839
$527$	−13.0543	−0.568654
$528$	0	0
$529$	47.8651	2.08109
$530$	−6.75748	−0.293526
$531$	0	0
$532$	20.5273	0.889971
$533$	30.5144	1.32173
$534$	0	0
$535$	−5.85307	−0.253050
$536$	−11.7502	−0.507530
$537$	0	0
$538$	−13.5977	−0.586237
$539$	0	0
$540$	0	0
$541$	12.1984	0.524449	0.262225	−	0.965007i	$-0.415544\pi$
$541$	12.1984	0.524449	0.262225	+	0.965007i	$0.415544\pi$
$542$	−28.1272	−1.20817
$543$	0	0
$544$	2.88169	0.123551
$545$	2.60092	0.111411
$546$	0	0
$547$	27.2769	1.16627	0.583137	−	0.812374i	$-0.301825\pi$
$547$	27.2769	1.16627	0.583137	+	0.812374i	$0.301825\pi$
$548$	−10.5359	−0.450071
$549$	0	0
$550$	0	0
$551$	27.8608	1.18691
$552$	0	0
$553$	−18.2241	−0.774968
$554$	−6.94099	−0.294894
$555$	0	0
$556$	−20.0037	−0.848346
$557$	35.1053	1.48746	0.743730	−	0.668480i	$-0.233055\pi$
$557$	35.1053	1.48746	0.743730	+	0.668480i	$0.233055\pi$
$558$	0	0
$559$	20.6956	0.875331
$560$	2.75319	0.116344
$561$	0	0
$562$	11.6662	0.492111
$563$	36.6137	1.54308	0.771542	−	0.636178i	$-0.219486\pi$
$563$	36.6137	1.54308	0.771542	+	0.636178i	$0.219486\pi$
$564$	0	0
$565$	7.64632	0.321683
$566$	32.4272	1.36302
$567$	0	0
$568$	8.24898	0.346119
$569$	44.9454	1.88421	0.942105	−	0.335317i	$-0.108844\pi$
$569$	44.9454	1.88421	0.942105	+	0.335317i	$0.108844\pi$
$570$	0	0
$571$	−7.32530	−0.306554	−0.153277	−	0.988183i	$-0.548983\pi$
$571$	−7.32530	−0.306554	−0.153277	+	0.988183i	$0.548983\pi$
$572$	0	0
$573$	0	0
$574$	−13.7910	−0.575623
$575$	33.3156	1.38936
$576$	0	0
$577$	16.4612	0.685288	0.342644	−	0.939465i	$-0.388677\pi$
$577$	16.4612	0.685288	0.342644	+	0.939465i	$0.388677\pi$
$578$	8.69589	0.361701
$579$	0	0
$580$	3.73679	0.155162
$581$	22.0086	0.913070
$582$	0	0
$583$	0	0
$584$	−2.59705	−0.107467
$585$	0	0
$586$	20.4665	0.845463
$587$	−37.2322	−1.53674	−0.768368	−	0.640008i	$-0.778931\pi$
$587$	−37.2322	−1.53674	−0.768368	+	0.640008i	$0.778931\pi$
$588$	0	0
$589$	−34.4842	−1.42090
$590$	4.93854	0.203317
$591$	0	0
$592$	3.59045	0.147567
$593$	−35.7875	−1.46962	−0.734808	−	0.678275i	$-0.762728\pi$
$593$	−35.7875	−1.46962	−0.734808	+	0.678275i	$0.762728\pi$
$594$	0	0
$595$	−7.93383	−0.325255
$596$	−0.714569	−0.0292699
$597$	0	0
$598$	−50.2279	−2.05397
$599$	−19.3698	−0.791431	−0.395715	−	0.918373i	$-0.629503\pi$
$599$	−19.3698	−0.791431	−0.395715	+	0.918373i	$0.629503\pi$
$600$	0	0
$601$	−0.934597	−0.0381230	−0.0190615	−	0.999818i	$-0.506068\pi$
$601$	−0.934597	−0.0381230	−0.0190615	+	0.999818i	$0.506068\pi$
$602$	−9.35336	−0.381215
$603$	0	0
$604$	−4.97993	−0.202630
$605$	0	0
$606$	0	0
$607$	−35.1138	−1.42522	−0.712612	−	0.701558i	$-0.752488\pi$
$607$	−35.1138	−1.42522	−0.712612	+	0.701558i	$0.752488\pi$
$608$	7.61225	0.308717
$609$	0	0
$610$	13.0914	0.530056
$611$	62.2843	2.51975
$612$	0	0
$613$	−13.4723	−0.544140	−0.272070	−	0.962277i	$-0.587708\pi$
$613$	−13.4723	−0.544140	−0.272070	+	0.962277i	$0.587708\pi$
$614$	−4.90302	−0.197870
$615$	0	0
$616$	0	0
$617$	14.9755	0.602892	0.301446	−	0.953483i	$-0.402531\pi$
$617$	14.9755	0.602892	0.301446	+	0.953483i	$0.402531\pi$
$618$	0	0
$619$	29.6443	1.19150	0.595752	−	0.803168i	$-0.296854\pi$
$619$	29.6443	1.19150	0.595752	+	0.803168i	$0.296854\pi$
$620$	−4.62514	−0.185750
$621$	0	0
$622$	−6.30898	−0.252967
$623$	−34.6358	−1.38765
$624$	0	0
$625$	10.4506	0.418022
$626$	−20.0549	−0.801557
$627$	0	0
$628$	−15.2451	−0.608346
$629$	−10.3465	−0.412544
$630$	0	0
$631$	11.0769	0.440964	0.220482	−	0.975391i	$-0.429237\pi$
$631$	11.0769	0.440964	0.220482	+	0.975391i	$0.429237\pi$
$632$	−6.75815	−0.268825
$633$	0	0
$634$	−14.5147	−0.576452
$635$	−15.5253	−0.616104
$636$	0	0
$637$	−1.62127	−0.0642372
$638$	0	0
$639$	0	0
$640$	1.02098	0.0403578
$641$	−49.0356	−1.93679	−0.968394	−	0.249424i	$-0.919759\pi$
$641$	−49.0356	−1.93679	−0.968394	+	0.249424i	$0.919759\pi$
$642$	0	0
$643$	−10.5136	−0.414617	−0.207308	−	0.978276i	$-0.566470\pi$
$643$	−10.5136	−0.414617	−0.207308	+	0.978276i	$0.566470\pi$
$644$	22.7005	0.894524
$645$	0	0
$646$	−21.9361	−0.863064
$647$	−7.77452	−0.305648	−0.152824	−	0.988253i	$-0.548837\pi$
$647$	−7.77452	−0.305648	−0.152824	+	0.988253i	$0.548837\pi$
$648$	0	0
$649$	0	0
$650$	−23.6135	−0.926198
$651$	0	0
$652$	−16.2295	−0.635597
$653$	41.6290	1.62907	0.814535	−	0.580114i	$-0.196992\pi$
$653$	41.6290	1.62907	0.814535	+	0.580114i	$0.196992\pi$
$654$	0	0
$655$	16.2980	0.636816
$656$	−5.11418	−0.199675
$657$	0	0
$658$	−28.1493	−1.09737
$659$	−12.0454	−0.469223	−0.234612	−	0.972089i	$-0.575382\pi$
$659$	−12.0454	−0.469223	−0.234612	+	0.972089i	$0.575382\pi$
$660$	0	0
$661$	−35.7313	−1.38979	−0.694894	−	0.719112i	$-0.744549\pi$
$661$	−35.7313	−1.38979	−0.694894	+	0.719112i	$0.744549\pi$
$662$	13.3722	0.519725
$663$	0	0
$664$	8.16157	0.316730
$665$	−20.9580	−0.812716
$666$	0	0
$667$	30.8104	1.19298
$668$	−2.54077	−0.0983055
$669$	0	0
$670$	11.9967	0.463473
$671$	0	0
$672$	0	0
$673$	−3.21312	−0.123857	−0.0619283	−	0.998081i	$-0.519725\pi$
$673$	−3.21312	−0.123857	−0.0619283	+	0.998081i	$0.519725\pi$
$674$	14.8006	0.570097
$675$	0	0
$676$	22.6007	0.869257
$677$	−9.88451	−0.379892	−0.189946	−	0.981794i	$-0.560831\pi$
$677$	−9.88451	−0.379892	−0.189946	+	0.981794i	$0.560831\pi$
$678$	0	0
$679$	8.90580	0.341773
$680$	−2.94215	−0.112826
$681$	0	0
$682$	0	0
$683$	20.1234	0.770000	0.385000	−	0.922917i	$-0.374201\pi$
$683$	20.1234	0.770000	0.385000	+	0.922917i	$0.374201\pi$
$684$	0	0
$685$	10.7570	0.411002
$686$	−18.1436	−0.692724
$687$	0	0
$688$	−3.46856	−0.132238
$689$	39.4908	1.50448
$690$	0	0
$691$	11.9933	0.456246	0.228123	−	0.973632i	$-0.426741\pi$
$691$	11.9933	0.456246	0.228123	+	0.973632i	$0.426741\pi$
$692$	−9.76395	−0.371170
$693$	0	0
$694$	4.80647	0.182451
$695$	20.4234	0.774705
$696$	0	0
$697$	14.7374	0.558221
$698$	16.8854	0.639122
$699$	0	0
$700$	10.6721	0.403368
$701$	38.5188	1.45484	0.727418	−	0.686194i	$-0.240720\pi$
$701$	38.5188	1.45484	0.727418	+	0.686194i	$0.240720\pi$
$702$	0	0
$703$	−27.3314	−1.03082
$704$	0	0
$705$	0	0
$706$	13.3209	0.501338
$707$	17.4842	0.657560
$708$	0	0
$709$	−11.9729	−0.449652	−0.224826	−	0.974399i	$-0.572181\pi$
$709$	−11.9729	−0.449652	−0.224826	+	0.974399i	$0.572181\pi$
$710$	−8.42205	−0.316074
$711$	0	0
$712$	−12.8442	−0.481356
$713$	−38.1350	−1.42817
$714$	0	0
$715$	0	0
$716$	−5.58446	−0.208701
$717$	0	0
$718$	10.1373	0.378319
$719$	1.10676	0.0412751	0.0206375	−	0.999787i	$-0.493430\pi$
$719$	1.10676	0.0412751	0.0206375	+	0.999787i	$0.493430\pi$
$720$	0	0
$721$	−7.07988	−0.263668
$722$	−38.9463	−1.44943
$723$	0	0
$724$	8.54491	0.317569
$725$	14.4848	0.537952
$726$	0	0
$727$	7.10527	0.263520	0.131760	−	0.991282i	$-0.457937\pi$
$727$	7.10527	0.263520	0.131760	+	0.991282i	$0.457937\pi$
$728$	−16.0897	−0.596324
$729$	0	0
$730$	2.65154	0.0981380
$731$	9.99530	0.369689
$732$	0	0
$733$	33.3433	1.23156	0.615781	−	0.787918i	$-0.288841\pi$
$733$	33.3433	1.23156	0.615781	+	0.787918i	$0.288841\pi$
$734$	26.3236	0.971622
$735$	0	0
$736$	8.41814	0.310297
$737$	0	0
$738$	0	0
$739$	19.3771	0.712797	0.356399	−	0.934334i	$-0.384004\pi$
$739$	19.3771	0.712797	0.356399	+	0.934334i	$0.384004\pi$
$740$	−3.66578	−0.134757
$741$	0	0
$742$	−17.8478	−0.655215
$743$	26.1576	0.959628	0.479814	−	0.877370i	$-0.340704\pi$
$743$	26.1576	0.959628	0.479814	+	0.877370i	$0.340704\pi$
$744$	0	0
$745$	0.729562	0.0267291
$746$	6.47563	0.237090
$747$	0	0
$748$	0	0
$749$	−15.4591	−0.564864
$750$	0	0
$751$	−33.2620	−1.21375	−0.606874	−	0.794798i	$-0.707577\pi$
$751$	−33.2620	−1.21375	−0.606874	+	0.794798i	$0.707577\pi$
$752$	−10.4388	−0.380663
$753$	0	0
$754$	−21.8378	−0.795287
$755$	5.08441	0.185041
$756$	0	0
$757$	−15.4816	−0.562689	−0.281344	−	0.959607i	$-0.590780\pi$
$757$	−15.4816	−0.562689	−0.281344	+	0.959607i	$0.590780\pi$
$758$	15.1194	0.549160
$759$	0	0
$760$	−7.77196	−0.281919
$761$	21.1175	0.765507	0.382754	−	0.923850i	$-0.374976\pi$
$761$	21.1175	0.765507	0.382754	+	0.923850i	$0.374976\pi$
$762$	0	0
$763$	6.86954	0.248694
$764$	8.29625	0.300148
$765$	0	0
$766$	30.5362	1.10332
$767$	−28.8609	−1.04211
$768$	0	0
$769$	12.7234	0.458818	0.229409	−	0.973330i	$-0.426321\pi$
$769$	12.7234	0.458818	0.229409	+	0.973330i	$0.426321\pi$
$770$	0	0
$771$	0	0
$772$	−11.4039	−0.410435
$773$	46.7874	1.68283	0.841413	−	0.540393i	$-0.181725\pi$
$773$	46.7874	1.68283	0.841413	+	0.540393i	$0.181725\pi$
$774$	0	0
$775$	−17.9283	−0.644003
$776$	3.30259	0.118556
$777$	0	0
$778$	34.3377	1.23106
$779$	38.9304	1.39483
$780$	0	0
$781$	0	0
$782$	−24.2584	−0.867480
$783$	0	0
$784$	0.271723	0.00970441
$785$	15.5650	0.555538
$786$	0	0
$787$	−15.7005	−0.559662	−0.279831	−	0.960049i	$-0.590279\pi$
$787$	−15.7005	−0.559662	−0.279831	+	0.960049i	$0.590279\pi$
$788$	20.6678	0.736258
$789$	0	0
$790$	6.89994	0.245489
$791$	20.1954	0.718067
$792$	0	0
$793$	−76.5064	−2.71682
$794$	−8.00116	−0.283950
$795$	0	0
$796$	9.35776	0.331677
$797$	−15.5782	−0.551808	−0.275904	−	0.961185i	$-0.588977\pi$
$797$	−15.5782	−0.551808	−0.275904	+	0.961185i	$0.588977\pi$
$798$	0	0
$799$	30.0812	1.06420
$800$	3.95760	0.139922
$801$	0	0
$802$	33.7690	1.19242
$803$	0	0
$804$	0	0
$805$	−23.1768	−0.816874
$806$	27.0294	0.952069
$807$	0	0
$808$	6.48375	0.228098
$809$	11.7803	0.414172	0.207086	−	0.978323i	$-0.433602\pi$
$809$	11.7803	0.414172	0.207086	+	0.978323i	$0.433602\pi$
$810$	0	0
$811$	−21.9430	−0.770524	−0.385262	−	0.922807i	$-0.625889\pi$
$811$	−21.9430	−0.770524	−0.385262	+	0.922807i	$0.625889\pi$
$812$	9.86960	0.346355
$813$	0	0
$814$	0	0
$815$	16.5700	0.580423
$816$	0	0
$817$	26.4035	0.923743
$818$	8.15827	0.285247
$819$	0	0
$820$	5.22148	0.182342
$821$	−44.5166	−1.55364	−0.776821	−	0.629722i	$-0.783169\pi$
$821$	−44.5166	−1.55364	−0.776821	+	0.629722i	$0.783169\pi$
$822$	0	0
$823$	34.5198	1.20328	0.601642	−	0.798766i	$-0.294513\pi$
$823$	34.5198	1.20328	0.601642	+	0.798766i	$0.294513\pi$
$824$	−2.62547	−0.0914626
$825$	0	0
$826$	13.0437	0.453847
$827$	−10.1790	−0.353957	−0.176979	−	0.984215i	$-0.556632\pi$
$827$	−10.1790	−0.353957	−0.176979	+	0.984215i	$0.556632\pi$
$828$	0	0
$829$	20.6760	0.718106	0.359053	−	0.933317i	$-0.383100\pi$
$829$	20.6760	0.718106	0.359053	+	0.933317i	$0.383100\pi$
$830$	−8.33281	−0.289236
$831$	0	0
$832$	−5.96663	−0.206856
$833$	−0.783021	−0.0271301
$834$	0	0
$835$	2.59408	0.0897719
$836$	0	0
$837$	0	0
$838$	−4.49368	−0.155232
$839$	5.57778	0.192566	0.0962831	−	0.995354i	$-0.469305\pi$
$839$	5.57778	0.192566	0.0962831	+	0.995354i	$0.469305\pi$
$840$	0	0
$841$	−15.6044	−0.538084
$842$	−11.2236	−0.386791
$843$	0	0
$844$	9.24210	0.318126
$845$	−23.0749	−0.793800
$846$	0	0
$847$	0	0
$848$	−6.61861	−0.227284
$849$	0	0
$850$	−11.4045	−0.391173
$851$	−30.2249	−1.03610
$852$	0	0
$853$	−0.295536	−0.0101189	−0.00505947	−	0.999987i	$-0.501610\pi$
$853$	−0.295536	−0.0101189	−0.00505947	+	0.999987i	$0.501610\pi$
$854$	34.5770	1.18320
$855$	0	0
$856$	−5.73279	−0.195943
$857$	−11.2380	−0.383881	−0.191941	−	0.981407i	$-0.561478\pi$
$857$	−11.2380	−0.383881	−0.191941	+	0.981407i	$0.561478\pi$
$858$	0	0
$859$	1.02820	0.0350817	0.0175408	−	0.999846i	$-0.494416\pi$
$859$	1.02820	0.0350817	0.0175408	+	0.999846i	$0.494416\pi$
$860$	3.54134	0.120759
$861$	0	0
$862$	40.4797	1.37874
$863$	−31.4180	−1.06948	−0.534741	−	0.845016i	$-0.679591\pi$
$863$	−31.4180	−1.06948	−0.534741	+	0.845016i	$0.679591\pi$
$864$	0	0
$865$	9.96881	0.338950
$866$	34.7337	1.18030
$867$	0	0
$868$	−12.2159	−0.414635
$869$	0	0
$870$	0	0
$871$	−70.1089	−2.37555
$872$	2.54747	0.0862682
$873$	0	0
$874$	−64.0810	−2.16757
$875$	−24.6620	−0.833727
$876$	0	0
$877$	14.3283	0.483833	0.241917	−	0.970297i	$-0.422224\pi$
$877$	14.3283	0.483833	0.241917	+	0.970297i	$0.422224\pi$
$878$	0.559897	0.0188956
$879$	0	0
$880$	0	0
$881$	−1.40503	−0.0473367	−0.0236683	−	0.999720i	$-0.507535\pi$
$881$	−1.40503	−0.0473367	−0.0236683	+	0.999720i	$0.507535\pi$
$882$	0	0
$883$	3.15870	0.106299	0.0531493	−	0.998587i	$-0.483074\pi$
$883$	3.15870	0.106299	0.0531493	+	0.998587i	$0.483074\pi$
$884$	17.1939	0.578295
$885$	0	0
$886$	32.3722	1.08757
$887$	23.3374	0.783594	0.391797	−	0.920052i	$-0.371854\pi$
$887$	23.3374	0.783594	0.391797	+	0.920052i	$0.371854\pi$
$888$	0	0
$889$	−41.0054	−1.37528
$890$	13.1137	0.439571
$891$	0	0
$892$	−5.88718	−0.197117
$893$	79.4625	2.65911
$894$	0	0
$895$	5.70163	0.190584
$896$	2.69661	0.0900875
$897$	0	0
$898$	3.20540	0.106965
$899$	−16.5801	−0.552978
$900$	0	0
$901$	19.0728	0.635406
$902$	0	0
$903$	0	0
$904$	7.48918	0.249087
$905$	−8.72420	−0.290002
$906$	0	0
$907$	9.47730	0.314689	0.157344	−	0.987544i	$-0.449707\pi$
$907$	9.47730	0.314689	0.157344	+	0.987544i	$0.449707\pi$
$908$	−24.0659	−0.798653
$909$	0	0
$910$	16.4273	0.544559
$911$	−29.6018	−0.980753	−0.490376	−	0.871511i	$-0.663141\pi$
$911$	−29.6018	−0.980753	−0.490376	+	0.871511i	$0.663141\pi$
$912$	0	0
$913$	0	0
$914$	−25.5717	−0.845837
$915$	0	0
$916$	−11.9412	−0.394547
$917$	43.0462	1.42151
$918$	0	0
$919$	−23.9658	−0.790557	−0.395279	−	0.918561i	$-0.629352\pi$
$919$	−23.9658	−0.790557	−0.395279	+	0.918561i	$0.629352\pi$
$920$	−8.59477	−0.283361
$921$	0	0
$922$	−37.9409	−1.24952
$923$	49.2186	1.62005
$924$	0	0
$925$	−14.2096	−0.467207
$926$	−30.2788	−0.995022
$927$	0	0
$928$	3.66000	0.120145
$929$	−37.1861	−1.22004	−0.610018	−	0.792388i	$-0.708838\pi$
$929$	−37.1861	−1.22004	−0.610018	+	0.792388i	$0.708838\pi$
$930$	0	0
$931$	−2.06843	−0.0677899
$932$	8.22092	0.269285
$933$	0	0
$934$	15.1810	0.496739
$935$	0	0
$936$	0	0
$937$	−0.344189	−0.0112441	−0.00562207	−	0.999984i	$-0.501790\pi$
$937$	−0.344189	−0.0112441	−0.00562207	+	0.999984i	$0.501790\pi$
$938$	31.6857	1.03457
$939$	0	0
$940$	10.6578	0.347619
$941$	6.44410	0.210072	0.105036	−	0.994468i	$-0.466504\pi$
$941$	6.44410	0.210072	0.105036	+	0.994468i	$0.466504\pi$
$942$	0	0
$943$	43.0519	1.40196
$944$	4.83705	0.157433
$945$	0	0
$946$	0	0
$947$	−24.9101	−0.809470	−0.404735	−	0.914434i	$-0.632636\pi$
$947$	−24.9101	−0.809470	−0.404735	+	0.914434i	$0.632636\pi$
$948$	0	0
$949$	−15.4957	−0.503010
$950$	−30.1262	−0.977423
$951$	0	0
$952$	−7.77079	−0.251853
$953$	−15.8459	−0.513299	−0.256649	−	0.966505i	$-0.582619\pi$
$953$	−15.8459	−0.513299	−0.256649	+	0.966505i	$0.582619\pi$
$954$	0	0
$955$	−8.47032	−0.274093
$956$	−8.77252	−0.283724
$957$	0	0
$958$	−2.03785	−0.0658399
$959$	28.4112	0.917447
$960$	0	0
$961$	−10.4783	−0.338009
$962$	21.4229	0.690702
$963$	0	0
$964$	−8.22569	−0.264932
$965$	11.6432	0.374806
$966$	0	0
$967$	−13.1803	−0.423849	−0.211925	−	0.977286i	$-0.567973\pi$
$967$	−13.1803	−0.423849	−0.211925	+	0.977286i	$0.567973\pi$
$968$	0	0
$969$	0	0
$970$	−3.37188	−0.108265
$971$	−27.8472	−0.893660	−0.446830	−	0.894619i	$-0.647447\pi$
$971$	−27.8472	−0.893660	−0.446830	+	0.894619i	$0.647447\pi$
$972$	0	0
$973$	53.9423	1.72931
$974$	18.0162	0.577275
$975$	0	0
$976$	12.8224	0.410434
$977$	−43.7030	−1.39818	−0.699091	−	0.715033i	$-0.746412\pi$
$977$	−43.7030	−1.39818	−0.699091	+	0.715033i	$0.746412\pi$
$978$	0	0
$979$	0	0
$980$	−0.277425	−0.00886200
$981$	0	0
$982$	17.1354	0.546813
$983$	−59.9033	−1.91062	−0.955310	−	0.295606i	$-0.904478\pi$
$983$	−59.9033	−1.91062	−0.955310	+	0.295606i	$0.904478\pi$
$984$	0	0
$985$	−21.1014	−0.672346
$986$	−10.5470	−0.335884
$987$	0	0
$988$	45.4195	1.44499
$989$	29.1988	0.928469
$990$	0	0
$991$	24.5233	0.779009	0.389504	−	0.921025i	$-0.372646\pi$
$991$	24.5233	0.779009	0.389504	+	0.921025i	$0.372646\pi$
$992$	−4.53009	−0.143831
$993$	0	0
$994$	−22.2443	−0.705546
$995$	−9.55409	−0.302885
$996$	0	0
$997$	−20.3191	−0.643513	−0.321757	−	0.946822i	$-0.604273\pi$
$997$	−20.3191	−0.643513	−0.321757	+	0.946822i	$0.604273\pi$
$998$	−32.7864	−1.03784
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.cv.1.3		6
3.2	odd	2		6534.2.a.cw.1.4		6
11.7	odd	10		594.2.f.k.379.2	yes	12
11.8	odd	10		594.2.f.k.163.2	✓	12
11.10	odd	2		6534.2.a.cx.1.3		6
33.8	even	10		594.2.f.l.163.2	yes	12
33.29	even	10		594.2.f.l.379.2	yes	12
33.32	even	2		6534.2.a.cu.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.k.163.2	✓	12	11.8	odd	10
594.2.f.k.379.2	yes	12	11.7	odd	10
594.2.f.l.163.2	yes	12	33.8	even	10
594.2.f.l.379.2	yes	12	33.29	even	10
6534.2.a.cu.1.4		6	33.32	even	2
6534.2.a.cv.1.3		6	1.1	even	1	trivial
6534.2.a.cw.1.4		6	3.2	odd	2
6534.2.a.cx.1.3		6	11.10	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6534.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} -1.02098 q^{5} -2.69661 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} -1.02098 q^{5} -2.69661 q^{7} -1.00000 q^{8} +1.02098 q^{10} -5.96663 q^{13} +2.69661 q^{14} +1.00000 q^{16} -2.88169 q^{17} -7.61225 q^{19} -1.02098 q^{20} -8.41814 q^{23} -3.95760 q^{25} +5.96663 q^{26} -2.69661 q^{28} -3.66000 q^{29} +4.53009 q^{31} -1.00000 q^{32} +2.88169 q^{34} +2.75319 q^{35} +3.59045 q^{37} +7.61225 q^{38} +1.02098 q^{40} -5.11418 q^{41} -3.46856 q^{43} +8.41814 q^{46} -10.4388 q^{47} +0.271723 q^{49} +3.95760 q^{50} -5.96663 q^{52} -6.61861 q^{53} +2.69661 q^{56} +3.66000 q^{58} +4.83705 q^{59} +12.8224 q^{61} -4.53009 q^{62} +1.00000 q^{64} +6.09182 q^{65} +11.7502 q^{67} -2.88169 q^{68} -2.75319 q^{70} -8.24898 q^{71} +2.59705 q^{73} -3.59045 q^{74} -7.61225 q^{76} +6.75815 q^{79} -1.02098 q^{80} +5.11418 q^{82} -8.16157 q^{83} +2.94215 q^{85} +3.46856 q^{86} +12.8442 q^{89} +16.0897 q^{91} -8.41814 q^{92} +10.4388 q^{94} +7.77196 q^{95} -3.30259 q^{97} -0.271723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 2 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 + 2 * q^5 + q^7 - 6 * q^8	\( 6 q - 6 q^{2} + 6 q^{4} + 2 q^{5} + q^{7} - 6 q^{8} - 2 q^{10} - q^{13} - q^{14} + 6 q^{16} - 7 q^{19} + 2 q^{20} - 9 q^{23} + 14 q^{25} + q^{26} + q^{28} + q^{29} + 10 q^{31} - 6 q^{32} - 18 q^{35} + 12 q^{37} + 7 q^{38} - 2 q^{40} - 11 q^{41} - 5 q^{43} + 9 q^{46} - q^{47} + 29 q^{49} - 14 q^{50} - q^{52} + 6 q^{53} - q^{56} - q^{58} + 18 q^{59} + 17 q^{61} - 10 q^{62} + 6 q^{64} - 2 q^{65} + 14 q^{67} + 18 q^{70} + 10 q^{71} + 17 q^{73} - 12 q^{74} - 7 q^{76} + 22 q^{79} + 2 q^{80} + 11 q^{82} - 33 q^{83} - 35 q^{85} + 5 q^{86} - 12 q^{89} + 59 q^{91} - 9 q^{92} + q^{94} - 39 q^{95} + 29 q^{97} - 29 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 2 * q^5 + q^7 - 6 * q^8 - 2 * q^10 - q^13 - q^14 + 6 * q^16 - 7 * q^19 + 2 * q^20 - 9 * q^23 + 14 * q^25 + q^26 + q^28 + q^29 + 10 * q^31 - 6 * q^32 - 18 * q^35 + 12 * q^37 + 7 * q^38 - 2 * q^40 - 11 * q^41 - 5 * q^43 + 9 * q^46 - q^47 + 29 * q^49 - 14 * q^50 - q^52 + 6 * q^53 - q^56 - q^58 + 18 * q^59 + 17 * q^61 - 10 * q^62 + 6 * q^64 - 2 * q^65 + 14 * q^67 + 18 * q^70 + 10 * q^71 + 17 * q^73 - 12 * q^74 - 7 * q^76 + 22 * q^79 + 2 * q^80 + 11 * q^82 - 33 * q^83 - 35 * q^85 + 5 * q^86 - 12 * q^89 + 59 * q^91 - 9 * q^92 + q^94 - 39 * q^95 + 29 * q^97 - 29 * q^98

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