LMFDB - Embedded newform 4029.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +6.75889 q^{10} -1.71911 q^{11} -4.29286 q^{12} -0.139018 q^{13} -9.39205 q^{14} +2.69434 q^{15} +5.84290 q^{16} -1.00000 q^{17} -2.50856 q^{18} +5.54406 q^{19} -11.5664 q^{20} -3.74400 q^{21} +4.31249 q^{22} +5.39210 q^{23} +5.75176 q^{24} +2.25944 q^{25} +0.348734 q^{26} -1.00000 q^{27} +16.0725 q^{28} +7.20257 q^{29} -6.75889 q^{30} -6.35822 q^{31} -3.15372 q^{32} +1.71911 q^{33} +2.50856 q^{34} -10.0876 q^{35} +4.29286 q^{36} -9.56660 q^{37} -13.9076 q^{38} +0.139018 q^{39} +15.4972 q^{40} +0.327658 q^{41} +9.39205 q^{42} +11.0164 q^{43} -7.37990 q^{44} -2.69434 q^{45} -13.5264 q^{46} -8.65194 q^{47} -5.84290 q^{48} +7.01757 q^{49} -5.66794 q^{50} +1.00000 q^{51} -0.596784 q^{52} +2.07677 q^{53} +2.50856 q^{54} +4.63187 q^{55} -21.5346 q^{56} -5.54406 q^{57} -18.0680 q^{58} +2.59407 q^{59} +11.5664 q^{60} +15.1344 q^{61} +15.9500 q^{62} +3.74400 q^{63} -3.77451 q^{64} +0.374561 q^{65} -4.31249 q^{66} +4.21389 q^{67} -4.29286 q^{68} -5.39210 q^{69} +25.3053 q^{70} +8.71318 q^{71} -5.75176 q^{72} +10.0129 q^{73} +23.9984 q^{74} -2.25944 q^{75} +23.7998 q^{76} -6.43637 q^{77} -0.348734 q^{78} +1.00000 q^{79} -15.7427 q^{80} +1.00000 q^{81} -0.821949 q^{82} -16.7409 q^{83} -16.0725 q^{84} +2.69434 q^{85} -27.6354 q^{86} -7.20257 q^{87} +9.88792 q^{88} -0.176143 q^{89} +6.75889 q^{90} -0.520484 q^{91} +23.1475 q^{92} +6.35822 q^{93} +21.7039 q^{94} -14.9376 q^{95} +3.15372 q^{96} -9.72863 q^{97} -17.6040 q^{98} -1.71911 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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 $

$2$	−2.50856	−1.77382	−0.886909	−	0.461945i	$-0.847152\pi$
$2$	−2.50856	−1.77382	−0.886909	+	0.461945i	$0.847152\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.29286	2.14643
$5$	−2.69434	−1.20494	−0.602472	−	0.798140i	$-0.705817\pi$
$5$	−2.69434	−1.20494	−0.602472	+	0.798140i	$0.705817\pi$
$6$	2.50856	1.02411
$7$	3.74400	1.41510	0.707550	−	0.706663i	$-0.249800\pi$
$7$	3.74400	1.41510	0.707550	+	0.706663i	$0.249800\pi$
$8$	−5.75176	−2.03355
$9$	1.00000	0.333333
$10$	6.75889	2.13735
$11$	−1.71911	−0.518332	−0.259166	−	0.965833i	$-0.583448\pi$
$11$	−1.71911	−0.518332	−0.259166	+	0.965833i	$0.583448\pi$
$12$	−4.29286	−1.23924
$13$	−0.139018	−0.0385566	−0.0192783	−	0.999814i	$-0.506137\pi$
$13$	−0.139018	−0.0385566	−0.0192783	+	0.999814i	$0.506137\pi$
$14$	−9.39205	−2.51013
$15$	2.69434	0.695674
$16$	5.84290	1.46072
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.50856	−0.591272
$19$	5.54406	1.27189	0.635947	−	0.771732i	$-0.280610\pi$
$19$	5.54406	1.27189	0.635947	+	0.771732i	$0.280610\pi$
$20$	−11.5664	−2.58632
$21$	−3.74400	−0.817009
$22$	4.31249	0.919427
$23$	5.39210	1.12433	0.562165	−	0.827025i	$-0.309968\pi$
$23$	5.39210	1.12433	0.562165	+	0.827025i	$0.309968\pi$
$24$	5.75176	1.17407
$25$	2.25944	0.451888
$26$	0.348734	0.0683924
$27$	−1.00000	−0.192450
$28$	16.0725	3.03741
$29$	7.20257	1.33748	0.668741	−	0.743495i	$-0.266833\pi$
$29$	7.20257	1.33748	0.668741	+	0.743495i	$0.266833\pi$
$30$	−6.75889	−1.23400
$31$	−6.35822	−1.14197	−0.570985	−	0.820961i	$-0.693439\pi$
$31$	−6.35822	−1.14197	−0.570985	+	0.820961i	$0.693439\pi$
$32$	−3.15372	−0.557504
$33$	1.71911	0.299259
$34$	2.50856	0.430214
$35$	−10.0876	−1.70512
$36$	4.29286	0.715476
$37$	−9.56660	−1.57274	−0.786370	−	0.617756i	$-0.788042\pi$
$37$	−9.56660	−1.57274	−0.786370	+	0.617756i	$0.788042\pi$
$38$	−13.9076	−2.25611
$39$	0.139018	0.0222607
$40$	15.4972	2.45032
$41$	0.327658	0.0511716	0.0255858	−	0.999673i	$-0.491855\pi$
$41$	0.327658	0.0511716	0.0255858	+	0.999673i	$0.491855\pi$
$42$	9.39205	1.44922
$43$	11.0164	1.67999	0.839996	−	0.542592i	$-0.182557\pi$
$43$	11.0164	1.67999	0.839996	+	0.542592i	$0.182557\pi$
$44$	−7.37990	−1.11256
$45$	−2.69434	−0.401648
$46$	−13.5264	−1.99436
$47$	−8.65194	−1.26202	−0.631008	−	0.775777i	$-0.717358\pi$
$47$	−8.65194	−1.26202	−0.631008	+	0.775777i	$0.717358\pi$
$48$	−5.84290	−0.843349
$49$	7.01757	1.00251
$50$	−5.66794	−0.801568
$51$	1.00000	0.140028
$52$	−0.596784	−0.0827590
$53$	2.07677	0.285267	0.142633	−	0.989776i	$-0.454443\pi$
$53$	2.07677	0.285267	0.142633	+	0.989776i	$0.454443\pi$
$54$	2.50856	0.341371
$55$	4.63187	0.624561
$56$	−21.5346	−2.87768
$57$	−5.54406	−0.734329
$58$	−18.0680	−2.37245
$59$	2.59407	0.337719	0.168860	−	0.985640i	$-0.445992\pi$
$59$	2.59407	0.337719	0.168860	+	0.985640i	$0.445992\pi$
$60$	11.5664	1.49321
$61$	15.1344	1.93776	0.968882	−	0.247522i	$-0.0796164\pi$
$61$	15.1344	1.93776	0.968882	+	0.247522i	$0.0796164\pi$
$62$	15.9500	2.02565
$63$	3.74400	0.471700
$64$	−3.77451	−0.471814
$65$	0.374561	0.0464585
$66$	−4.31249	−0.530831
$67$	4.21389	0.514809	0.257404	−	0.966304i	$-0.417133\pi$
$67$	4.21389	0.514809	0.257404	+	0.966304i	$0.417133\pi$
$68$	−4.29286	−0.520585
$69$	−5.39210	−0.649133
$70$	25.3053	3.02456
$71$	8.71318	1.03406	0.517032	−	0.855966i	$-0.327037\pi$
$71$	8.71318	1.03406	0.517032	+	0.855966i	$0.327037\pi$
$72$	−5.75176	−0.677851
$73$	10.0129	1.17192	0.585962	−	0.810339i	$-0.300717\pi$
$73$	10.0129	1.17192	0.585962	+	0.810339i	$0.300717\pi$
$74$	23.9984	2.78975
$75$	−2.25944	−0.260898
$76$	23.7998	2.73003
$77$	−6.43637	−0.733492
$78$	−0.348734	−0.0394864
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−15.7427	−1.76009
$81$	1.00000	0.111111
$82$	−0.821949	−0.0907691
$83$	−16.7409	−1.83755	−0.918776	−	0.394779i	$-0.870821\pi$
$83$	−16.7409	−1.83755	−0.918776	+	0.394779i	$0.870821\pi$
$84$	−16.0725	−1.75365
$85$	2.69434	0.292242
$86$	−27.6354	−2.98000
$87$	−7.20257	−0.772196
$88$	9.88792	1.05406
$89$	−0.176143	−0.0186711	−0.00933555	−	0.999956i	$-0.502972\pi$
$89$	−0.176143	−0.0186711	−0.00933555	+	0.999956i	$0.502972\pi$
$90$	6.75889	0.712450
$91$	−0.520484	−0.0545615
$92$	23.1475	2.41329
$93$	6.35822	0.659317
$94$	21.7039	2.23858
$95$	−14.9376	−1.53256
$96$	3.15372	0.321875
$97$	−9.72863	−0.987793	−0.493896	−	0.869521i	$-0.664428\pi$
$97$	−9.72863	−0.987793	−0.493896	+	0.869521i	$0.664428\pi$
$98$	−17.6040	−1.77827
$99$	−1.71911	−0.172777
$100$	9.69946	0.969946
$101$	−3.07310	−0.305785	−0.152892	−	0.988243i	$-0.548859\pi$
$101$	−3.07310	−0.305785	−0.152892	+	0.988243i	$0.548859\pi$
$102$	−2.50856	−0.248384
$103$	15.7707	1.55393	0.776966	−	0.629542i	$-0.216757\pi$
$103$	15.7707	1.55393	0.776966	+	0.629542i	$0.216757\pi$
$104$	0.799597	0.0784069
$105$	10.0876	0.984449
$106$	−5.20971	−0.506011
$107$	0.106214	0.0102681	0.00513403	−	0.999987i	$-0.498366\pi$
$107$	0.106214	0.0102681	0.00513403	+	0.999987i	$0.498366\pi$
$108$	−4.29286	−0.413080
$109$	−19.5268	−1.87033	−0.935163	−	0.354219i	$-0.884747\pi$
$109$	−19.5268	−1.87033	−0.935163	+	0.354219i	$0.884747\pi$
$110$	−11.6193	−1.10786
$111$	9.56660	0.908021
$112$	21.8758	2.06707
$113$	10.4099	0.979277	0.489639	−	0.871925i	$-0.337129\pi$
$113$	10.4099	0.979277	0.489639	+	0.871925i	$0.337129\pi$
$114$	13.9076	1.30256
$115$	−14.5281	−1.35475
$116$	30.9196	2.87081
$117$	−0.139018	−0.0128522
$118$	−6.50737	−0.599052
$119$	−3.74400	−0.343212
$120$	−15.4972	−1.41469
$121$	−8.04465	−0.731332
$122$	−37.9656	−3.43724
$123$	−0.327658	−0.0295440
$124$	−27.2949	−2.45116
$125$	7.38398	0.660443
$126$	−9.39205	−0.836710
$127$	−18.6065	−1.65106	−0.825532	−	0.564356i	$-0.809125\pi$
$127$	−18.6065	−1.65106	−0.825532	+	0.564356i	$0.809125\pi$
$128$	15.7760	1.39442
$129$	−11.0164	−0.969944
$130$	−0.939607	−0.0824090
$131$	−5.45234	−0.476373	−0.238187	−	0.971219i	$-0.576553\pi$
$131$	−5.45234	−0.476373	−0.238187	+	0.971219i	$0.576553\pi$
$132$	7.37990	0.642338
$133$	20.7570	1.79986
$134$	−10.5708	−0.913177
$135$	2.69434	0.231891
$136$	5.75176	0.493209
$137$	3.81445	0.325890	0.162945	−	0.986635i	$-0.447901\pi$
$137$	3.81445	0.325890	0.162945	+	0.986635i	$0.447901\pi$
$138$	13.5264	1.15144
$139$	−3.66939	−0.311233	−0.155617	−	0.987818i	$-0.549736\pi$
$139$	−3.66939	−0.311233	−0.155617	+	0.987818i	$0.549736\pi$
$140$	−43.3046	−3.65991
$141$	8.65194	0.728625
$142$	−21.8575	−1.83424
$143$	0.238987	0.0199851
$144$	5.84290	0.486908
$145$	−19.4061	−1.61159
$146$	−25.1180	−2.07878
$147$	−7.01757	−0.578799
$148$	−41.0680	−3.37577
$149$	10.2266	0.837799	0.418900	−	0.908032i	$-0.362416\pi$
$149$	10.2266	0.837799	0.418900	+	0.908032i	$0.362416\pi$
$150$	5.66794	0.462785
$151$	−15.0719	−1.22654	−0.613268	−	0.789875i	$-0.710146\pi$
$151$	−15.0719	−1.22654	−0.613268	+	0.789875i	$0.710146\pi$
$152$	−31.8881	−2.58647
$153$	−1.00000	−0.0808452
$154$	16.1460	1.30108
$155$	17.1312	1.37601
$156$	0.596784	0.0477809
$157$	2.91823	0.232900	0.116450	−	0.993197i	$-0.462848\pi$
$157$	2.91823	0.232900	0.116450	+	0.993197i	$0.462848\pi$
$158$	−2.50856	−0.199570
$159$	−2.07677	−0.164699
$160$	8.49718	0.671761
$161$	20.1880	1.59104
$162$	−2.50856	−0.197091
$163$	−19.6064	−1.53569	−0.767845	−	0.640635i	$-0.778671\pi$
$163$	−19.6064	−1.53569	−0.767845	+	0.640635i	$0.778671\pi$
$164$	1.40659	0.109836
$165$	−4.63187	−0.360590
$166$	41.9955	3.25948
$167$	−9.66602	−0.747979	−0.373990	−	0.927433i	$-0.622010\pi$
$167$	−9.66602	−0.747979	−0.373990	+	0.927433i	$0.622010\pi$
$168$	21.5346	1.66143
$169$	−12.9807	−0.998513
$170$	−6.75889	−0.518383
$171$	5.54406	0.423965
$172$	47.2920	3.60598
$173$	23.4494	1.78282	0.891411	−	0.453195i	$-0.149716\pi$
$173$	23.4494	1.78282	0.891411	+	0.453195i	$0.149716\pi$
$174$	18.0680	1.36973
$175$	8.45936	0.639468
$176$	−10.0446	−0.757140
$177$	−2.59407	−0.194982
$178$	0.441864	0.0331191
$179$	22.0195	1.64582	0.822909	−	0.568173i	$-0.192350\pi$
$179$	22.0195	1.64582	0.822909	+	0.568173i	$0.192350\pi$
$180$	−11.5664	−0.862108
$181$	8.02793	0.596712	0.298356	−	0.954455i	$-0.403562\pi$
$181$	8.02793	0.596712	0.298356	+	0.954455i	$0.403562\pi$
$182$	1.30566	0.0967821
$183$	−15.1344	−1.11877
$184$	−31.0140	−2.28639
$185$	25.7756	1.89506
$186$	−15.9500	−1.16951
$187$	1.71911	0.125714
$188$	−37.1415	−2.70882
$189$	−3.74400	−0.272336
$190$	37.4717	2.71848
$191$	−18.3556	−1.32816	−0.664082	−	0.747660i	$-0.731177\pi$
$191$	−18.3556	−1.32816	−0.664082	+	0.747660i	$0.731177\pi$
$192$	3.77451	0.272402
$193$	−10.0684	−0.724741	−0.362370	−	0.932034i	$-0.618032\pi$
$193$	−10.0684	−0.724741	−0.362370	+	0.932034i	$0.618032\pi$
$194$	24.4048	1.75216
$195$	−0.374561	−0.0268229
$196$	30.1254	2.15181
$197$	−15.7115	−1.11940	−0.559701	−	0.828695i	$-0.689084\pi$
$197$	−15.7115	−1.11940	−0.559701	+	0.828695i	$0.689084\pi$
$198$	4.31249	0.306476
$199$	10.4890	0.743543	0.371772	−	0.928324i	$-0.378750\pi$
$199$	10.4890	0.743543	0.371772	+	0.928324i	$0.378750\pi$
$200$	−12.9958	−0.918939
$201$	−4.21389	−0.297225
$202$	7.70904	0.542406
$203$	26.9664	1.89267
$204$	4.29286	0.300560
$205$	−0.882821	−0.0616589
$206$	−39.5617	−2.75639
$207$	5.39210	0.374777
$208$	−0.812267	−0.0563206
$209$	−9.53087	−0.659264
$210$	−25.3053	−1.74623
$211$	17.5312	1.20690	0.603449	−	0.797401i	$-0.293793\pi$
$211$	17.5312	1.20690	0.603449	+	0.797401i	$0.293793\pi$
$212$	8.91529	0.612305
$213$	−8.71318	−0.597017
$214$	−0.266443	−0.0182137
$215$	−29.6820	−2.02430
$216$	5.75176	0.391357
$217$	−23.8052	−1.61600
$218$	48.9840	3.31762
$219$	−10.0129	−0.676610
$220$	19.8839	1.34057
$221$	0.139018	0.00935136
$222$	−23.9984	−1.61066
$223$	1.07333	0.0718756	0.0359378	−	0.999354i	$-0.488558\pi$
$223$	1.07333	0.0718756	0.0359378	+	0.999354i	$0.488558\pi$
$224$	−11.8075	−0.788924
$225$	2.25944	0.150629
$226$	−26.1137	−1.73706
$227$	−6.66723	−0.442520	−0.221260	−	0.975215i	$-0.571017\pi$
$227$	−6.66723	−0.442520	−0.221260	+	0.975215i	$0.571017\pi$
$228$	−23.7998	−1.57618
$229$	20.5325	1.35683	0.678414	−	0.734680i	$-0.262668\pi$
$229$	20.5325	1.35683	0.678414	+	0.734680i	$0.262668\pi$
$230$	36.4446	2.40309
$231$	6.43637	0.423482
$232$	−41.4274	−2.71984
$233$	−26.4189	−1.73076	−0.865378	−	0.501119i	$-0.832922\pi$
$233$	−26.4189	−1.73076	−0.865378	+	0.501119i	$0.832922\pi$
$234$	0.348734	0.0227975
$235$	23.3112	1.52066
$236$	11.1360	0.724890
$237$	−1.00000	−0.0649570
$238$	9.39205	0.608796
$239$	−12.3541	−0.799120	−0.399560	−	0.916707i	$-0.630837\pi$
$239$	−12.3541	−0.799120	−0.399560	+	0.916707i	$0.630837\pi$
$240$	15.7427	1.01619
$241$	4.32551	0.278630	0.139315	−	0.990248i	$-0.455510\pi$
$241$	4.32551	0.278630	0.139315	+	0.990248i	$0.455510\pi$
$242$	20.1805	1.29725
$243$	−1.00000	−0.0641500
$244$	64.9699	4.15927
$245$	−18.9077	−1.20797
$246$	0.821949	0.0524056
$247$	−0.770724	−0.0490400
$248$	36.5709	2.32226
$249$	16.7409	1.06091
$250$	−18.5231	−1.17151
$251$	19.3106	1.21887	0.609436	−	0.792835i	$-0.291396\pi$
$251$	19.3106	1.21887	0.609436	+	0.792835i	$0.291396\pi$
$252$	16.0725	1.01247
$253$	−9.26963	−0.582777
$254$	46.6756	2.92868
$255$	−2.69434	−0.168726
$256$	−32.0260	−2.00162
$257$	23.6722	1.47663	0.738315	−	0.674456i	$-0.235622\pi$
$257$	23.6722	1.47663	0.738315	+	0.674456i	$0.235622\pi$
$258$	27.6354	1.72050
$259$	−35.8174	−2.22558
$260$	1.60794	0.0997199
$261$	7.20257	0.445828
$262$	13.6775	0.844999
$263$	−9.98045	−0.615421	−0.307710	−	0.951480i	$-0.599563\pi$
$263$	−9.98045	−0.615421	−0.307710	+	0.951480i	$0.599563\pi$
$264$	−9.88792	−0.608559
$265$	−5.59553	−0.343730
$266$	−52.0701	−3.19262
$267$	0.176143	0.0107798
$268$	18.0896	1.10500
$269$	1.01465	0.0618644	0.0309322	−	0.999521i	$-0.490152\pi$
$269$	1.01465	0.0618644	0.0309322	+	0.999521i	$0.490152\pi$
$270$	−6.75889	−0.411333
$271$	−0.893528	−0.0542780	−0.0271390	−	0.999632i	$-0.508640\pi$
$271$	−0.893528	−0.0542780	−0.0271390	+	0.999632i	$0.508640\pi$
$272$	−5.84290	−0.354278
$273$	0.520484	0.0315011
$274$	−9.56875	−0.578069
$275$	−3.88424	−0.234228
$276$	−23.1475	−1.39332
$277$	−2.86557	−0.172176	−0.0860878	−	0.996288i	$-0.527437\pi$
$277$	−2.86557	−0.172176	−0.0860878	+	0.996288i	$0.527437\pi$
$278$	9.20486	0.552071
$279$	−6.35822	−0.380657
$280$	58.0214	3.46744
$281$	−6.62580	−0.395262	−0.197631	−	0.980276i	$-0.563325\pi$
$281$	−6.62580	−0.395262	−0.197631	+	0.980276i	$0.563325\pi$
$282$	−21.7039	−1.29245
$283$	−12.7835	−0.759900	−0.379950	−	0.925007i	$-0.624059\pi$
$283$	−12.7835	−0.759900	−0.379950	+	0.925007i	$0.624059\pi$
$284$	37.4044	2.21954
$285$	14.9376	0.884825
$286$	−0.599514	−0.0354500
$287$	1.22675	0.0724130
$288$	−3.15372	−0.185835
$289$	1.00000	0.0588235
$290$	48.6814	2.85867
$291$	9.72863	0.570302
$292$	42.9840	2.51545
$293$	11.8071	0.689780	0.344890	−	0.938643i	$-0.387916\pi$
$293$	11.8071	0.689780	0.344890	+	0.938643i	$0.387916\pi$
$294$	17.6040	1.02668
$295$	−6.98930	−0.406933
$296$	55.0247	3.19825
$297$	1.71911	0.0997531
$298$	−25.6541	−1.48610
$299$	−0.749598	−0.0433504
$300$	−9.69946	−0.559999
$301$	41.2456	2.37736
$302$	37.8088	2.17565
$303$	3.07310	0.176545
$304$	32.3934	1.85789
$305$	−40.7772	−2.33490
$306$	2.50856	0.143405
$307$	18.2181	1.03976	0.519880	−	0.854239i	$-0.325977\pi$
$307$	18.2181	1.03976	0.519880	+	0.854239i	$0.325977\pi$
$308$	−27.6304	−1.57439
$309$	−15.7707	−0.897164
$310$	−42.9745	−2.44079
$311$	10.1159	0.573620	0.286810	−	0.957987i	$-0.407405\pi$
$311$	10.1159	0.573620	0.286810	+	0.957987i	$0.407405\pi$
$312$	−0.799597	−0.0452683
$313$	−16.4058	−0.927310	−0.463655	−	0.886016i	$-0.653462\pi$
$313$	−16.4058	−0.927310	−0.463655	+	0.886016i	$0.653462\pi$
$314$	−7.32055	−0.413122
$315$	−10.0876	−0.568372
$316$	4.29286	0.241492
$317$	12.8397	0.721148	0.360574	−	0.932731i	$-0.382581\pi$
$317$	12.8397	0.721148	0.360574	+	0.932731i	$0.382581\pi$
$318$	5.20971	0.292146
$319$	−12.3820	−0.693260
$320$	10.1698	0.568509
$321$	−0.106214	−0.00592827
$322$	−50.6428	−2.82222
$323$	−5.54406	−0.308480
$324$	4.29286	0.238492
$325$	−0.314103	−0.0174233
$326$	49.1837	2.72403
$327$	19.5268	1.07983
$328$	−1.88461	−0.104060
$329$	−32.3929	−1.78588
$330$	11.6193	0.639621
$331$	32.1823	1.76890	0.884451	−	0.466634i	$-0.154533\pi$
$331$	32.1823	1.76890	0.884451	+	0.466634i	$0.154533\pi$
$332$	−71.8663	−3.94417
$333$	−9.56660	−0.524246
$334$	24.2478	1.32678
$335$	−11.3536	−0.620316
$336$	−21.8758	−1.19342
$337$	31.9269	1.73917	0.869584	−	0.493786i	$-0.164387\pi$
$337$	31.9269	1.73917	0.869584	+	0.493786i	$0.164387\pi$
$338$	32.5628	1.77118
$339$	−10.4099	−0.565386
$340$	11.5664	0.627276
$341$	10.9305	0.591920
$342$	−13.9076	−0.752036
$343$	0.0657671	0.00355109
$344$	−63.3639	−3.41635
$345$	14.5281	0.782168
$346$	−58.8241	−3.16240
$347$	2.87151	0.154151	0.0770755	−	0.997025i	$-0.475442\pi$
$347$	2.87151	0.154151	0.0770755	+	0.997025i	$0.475442\pi$
$348$	−30.9196	−1.65746
$349$	21.8859	1.17152	0.585762	−	0.810483i	$-0.300795\pi$
$349$	21.8859	1.17152	0.585762	+	0.810483i	$0.300795\pi$
$350$	−21.2208	−1.13430
$351$	0.139018	0.00742023
$352$	5.42160	0.288972
$353$	30.1911	1.60691	0.803455	−	0.595365i	$-0.202993\pi$
$353$	30.1911	1.60691	0.803455	+	0.595365i	$0.202993\pi$
$354$	6.50737	0.345863
$355$	−23.4762	−1.24599
$356$	−0.756155	−0.0400761
$357$	3.74400	0.198154
$358$	−55.2373	−2.91938
$359$	28.3388	1.49567	0.747833	−	0.663887i	$-0.231095\pi$
$359$	28.3388	1.49567	0.747833	+	0.663887i	$0.231095\pi$
$360$	15.4972	0.816772
$361$	11.7366	0.617716
$362$	−20.1385	−1.05846
$363$	8.04465	0.422235
$364$	−2.23436	−0.117112
$365$	−26.9781	−1.41210
$366$	37.9656	1.98449
$367$	−24.0440	−1.25509	−0.627543	−	0.778582i	$-0.715940\pi$
$367$	−24.0440	−1.25509	−0.627543	+	0.778582i	$0.715940\pi$
$368$	31.5055	1.64234
$369$	0.327658	0.0170572
$370$	−64.6596	−3.36149
$371$	7.77545	0.403681
$372$	27.2949	1.41518
$373$	−5.63709	−0.291878	−0.145939	−	0.989294i	$-0.546620\pi$
$373$	−5.63709	−0.291878	−0.145939	+	0.989294i	$0.546620\pi$
$374$	−4.31249	−0.222994
$375$	−7.38398	−0.381307
$376$	49.7639	2.56638
$377$	−1.00129	−0.0515688
$378$	9.39205	0.483075
$379$	33.3778	1.71450	0.857250	−	0.514901i	$-0.172171\pi$
$379$	33.3778	1.71450	0.857250	+	0.514901i	$0.172171\pi$
$380$	−64.1248	−3.28953
$381$	18.6065	0.953242
$382$	46.0460	2.35592
$383$	−11.5476	−0.590054	−0.295027	−	0.955489i	$-0.595329\pi$
$383$	−11.5476	−0.590054	−0.295027	+	0.955489i	$0.595329\pi$
$384$	−15.7760	−0.805066
$385$	17.3417	0.883816
$386$	25.2572	1.28556
$387$	11.0164	0.559997
$388$	−41.7636	−2.12023
$389$	−7.53981	−0.382283	−0.191142	−	0.981562i	$-0.561219\pi$
$389$	−7.53981	−0.382283	−0.191142	+	0.981562i	$0.561219\pi$
$390$	0.939607	0.0475788
$391$	−5.39210	−0.272690
$392$	−40.3633	−2.03866
$393$	5.45234	0.275034
$394$	39.4133	1.98561
$395$	−2.69434	−0.135567
$396$	−7.37990	−0.370854
$397$	−18.5849	−0.932747	−0.466373	−	0.884588i	$-0.654440\pi$
$397$	−18.5849	−0.932747	−0.466373	+	0.884588i	$0.654440\pi$
$398$	−26.3122	−1.31891
$399$	−20.7570	−1.03915
$400$	13.2017	0.660084
$401$	2.06309	0.103026	0.0515128	−	0.998672i	$-0.483596\pi$
$401$	2.06309	0.103026	0.0515128	+	0.998672i	$0.483596\pi$
$402$	10.5708	0.527223
$403$	0.883906	0.0440305
$404$	−13.1924	−0.656344
$405$	−2.69434	−0.133883
$406$	−67.6468	−3.35726
$407$	16.4461	0.815201
$408$	−5.75176	−0.284754
$409$	11.2813	0.557824	0.278912	−	0.960317i	$-0.410026\pi$
$409$	11.2813	0.557824	0.278912	+	0.960317i	$0.410026\pi$
$410$	2.21461	0.109372
$411$	−3.81445	−0.188153
$412$	67.7013	3.33540
$413$	9.71221	0.477907
$414$	−13.5264	−0.664786
$415$	45.1056	2.21415
$416$	0.438423	0.0214955
$417$	3.66939	0.179691
$418$	23.9087	1.16941
$419$	−13.1347	−0.641671	−0.320835	−	0.947135i	$-0.603964\pi$
$419$	−13.1347	−0.641671	−0.320835	+	0.947135i	$0.603964\pi$
$420$	43.3046	2.11305
$421$	37.6913	1.83696	0.918480	−	0.395467i	$-0.129417\pi$
$421$	37.6913	1.83696	0.918480	+	0.395467i	$0.129417\pi$
$422$	−43.9780	−2.14082
$423$	−8.65194	−0.420672
$424$	−11.9451	−0.580105
$425$	−2.25944	−0.109599
$426$	21.8575	1.05900
$427$	56.6633	2.74213
$428$	0.455960	0.0220397
$429$	−0.238987	−0.0115384
$430$	74.4590	3.59073
$431$	38.0414	1.83239	0.916194	−	0.400735i	$-0.131245\pi$
$431$	38.0414	1.83239	0.916194	+	0.400735i	$0.131245\pi$
$432$	−5.84290	−0.281116
$433$	35.0692	1.68532	0.842659	−	0.538448i	$-0.180989\pi$
$433$	35.0692	1.68532	0.842659	+	0.538448i	$0.180989\pi$
$434$	59.7167	2.86649
$435$	19.4061	0.930452
$436$	−83.8256	−4.01452
$437$	29.8941	1.43003
$438$	25.1180	1.20018
$439$	7.87788	0.375991	0.187995	−	0.982170i	$-0.439801\pi$
$439$	7.87788	0.375991	0.187995	+	0.982170i	$0.439801\pi$
$440$	−26.6414	−1.27008
$441$	7.01757	0.334170
$442$	−0.348734	−0.0165876
$443$	3.69444	0.175528	0.0877641	−	0.996141i	$-0.472028\pi$
$443$	3.69444	0.175528	0.0877641	+	0.996141i	$0.472028\pi$
$444$	41.0680	1.94900
$445$	0.474588	0.0224976
$446$	−2.69251	−0.127494
$447$	−10.2266	−0.483704
$448$	−14.1318	−0.667664
$449$	−3.62828	−0.171229	−0.0856146	−	0.996328i	$-0.527285\pi$
$449$	−3.62828	−0.171229	−0.0856146	+	0.996328i	$0.527285\pi$
$450$	−5.66794	−0.267189
$451$	−0.563282	−0.0265239
$452$	44.6880	2.10195
$453$	15.0719	0.708141
$454$	16.7251	0.784949
$455$	1.40236	0.0657435
$456$	31.8881	1.49330
$457$	−7.63909	−0.357342	−0.178671	−	0.983909i	$-0.557180\pi$
$457$	−7.63909	−0.357342	−0.178671	+	0.983909i	$0.557180\pi$
$458$	−51.5070	−2.40677
$459$	1.00000	0.0466760
$460$	−62.3671	−2.90788
$461$	38.1537	1.77700	0.888498	−	0.458880i	$-0.151749\pi$
$461$	38.1537	1.77700	0.888498	+	0.458880i	$0.151749\pi$
$462$	−16.1460	−0.751179
$463$	4.62234	0.214818	0.107409	−	0.994215i	$-0.465745\pi$
$463$	4.62234	0.214818	0.107409	+	0.994215i	$0.465745\pi$
$464$	42.0838	1.95369
$465$	−17.1312	−0.794439
$466$	66.2732	3.07005
$467$	14.6418	0.677540	0.338770	−	0.940869i	$-0.389989\pi$
$467$	14.6418	0.677540	0.338770	+	0.940869i	$0.389989\pi$
$468$	−0.596784	−0.0275863
$469$	15.7768	0.728506
$470$	−58.4775	−2.69737
$471$	−2.91823	−0.134465
$472$	−14.9205	−0.686770
$473$	−18.9385	−0.870794
$474$	2.50856	0.115222
$475$	12.5265	0.574755
$476$	−16.0725	−0.736680
$477$	2.07677	0.0950890
$478$	30.9910	1.41749
$479$	−16.7934	−0.767311	−0.383655	−	0.923476i	$-0.625335\pi$
$479$	−16.7934	−0.767311	−0.383655	+	0.923476i	$0.625335\pi$
$480$	−8.49718	−0.387841
$481$	1.32993	0.0606395
$482$	−10.8508	−0.494239
$483$	−20.1880	−0.918588
$484$	−34.5345	−1.56975
$485$	26.2122	1.19023
$486$	2.50856	0.113790
$487$	−33.0770	−1.49886	−0.749432	−	0.662082i	$-0.769673\pi$
$487$	−33.0770	−1.49886	−0.749432	+	0.662082i	$0.769673\pi$
$488$	−87.0495	−3.94055
$489$	19.6064	0.886631
$490$	47.4310	2.14271
$491$	−10.9250	−0.493038	−0.246519	−	0.969138i	$-0.579287\pi$
$491$	−10.9250	−0.493038	−0.246519	+	0.969138i	$0.579287\pi$
$492$	−1.40659	−0.0634140
$493$	−7.20257	−0.324387
$494$	1.93340	0.0869879
$495$	4.63187	0.208187
$496$	−37.1504	−1.66810
$497$	32.6222	1.46331
$498$	−41.9955	−1.88186
$499$	35.2632	1.57860	0.789299	−	0.614009i	$-0.210444\pi$
$499$	35.2632	1.57860	0.789299	+	0.614009i	$0.210444\pi$
$500$	31.6984	1.41759
$501$	9.66602	0.431846
$502$	−48.4417	−2.16206
$503$	−0.658137	−0.0293449	−0.0146724	−	0.999892i	$-0.504671\pi$
$503$	−0.658137	−0.0293449	−0.0146724	+	0.999892i	$0.504671\pi$
$504$	−21.5346	−0.959227
$505$	8.27995	0.368453
$506$	23.2534	1.03374
$507$	12.9807	0.576492
$508$	−79.8752	−3.54389
$509$	9.43187	0.418060	0.209030	−	0.977909i	$-0.432969\pi$
$509$	9.43187	0.418060	0.209030	+	0.977909i	$0.432969\pi$
$510$	6.75889	0.299289
$511$	37.4884	1.65839
$512$	48.7870	2.15610
$513$	−5.54406	−0.244776
$514$	−59.3830	−2.61927
$515$	−42.4915	−1.87240
$516$	−47.2920	−2.08191
$517$	14.8737	0.654143
$518$	89.8499	3.94778
$519$	−23.4494	−1.02931
$520$	−2.15438	−0.0944759
$521$	35.4738	1.55413	0.777067	−	0.629418i	$-0.216707\pi$
$521$	35.4738	1.55413	0.777067	+	0.629418i	$0.216707\pi$
$522$	−18.0680	−0.790817
$523$	17.7537	0.776317	0.388158	−	0.921593i	$-0.373111\pi$
$523$	17.7537	0.776317	0.388158	+	0.921593i	$0.373111\pi$
$524$	−23.4061	−1.02250
$525$	−8.45936	−0.369197
$526$	25.0365	1.09164
$527$	6.35822	0.276968
$528$	10.0446	0.437135
$529$	6.07474	0.264119
$530$	14.0367	0.609715
$531$	2.59407	0.112573
$532$	89.1067	3.86327
$533$	−0.0455504	−0.00197301
$534$	−0.441864	−0.0191213
$535$	−0.286175	−0.0123724
$536$	−24.2373	−1.04689
$537$	−22.0195	−0.950213
$538$	−2.54531	−0.109736
$539$	−12.0640	−0.519633
$540$	11.5664	0.497738
$541$	1.45853	0.0627070	0.0313535	−	0.999508i	$-0.490018\pi$
$541$	1.45853	0.0627070	0.0313535	+	0.999508i	$0.490018\pi$
$542$	2.24147	0.0962792
$543$	−8.02793	−0.344512
$544$	3.15372	0.135215
$545$	52.6117	2.25364
$546$	−1.30566	−0.0558772
$547$	−27.0237	−1.15545	−0.577725	−	0.816232i	$-0.696059\pi$
$547$	−27.0237	−1.15545	−0.577725	+	0.816232i	$0.696059\pi$
$548$	16.3749	0.699499
$549$	15.1344	0.645921
$550$	9.74383	0.415478
$551$	39.9315	1.70114
$552$	31.0140	1.32005
$553$	3.74400	0.159211
$554$	7.18846	0.305408
$555$	−25.7756	−1.09411
$556$	−15.7521	−0.668040
$557$	−34.8372	−1.47610	−0.738050	−	0.674746i	$-0.764253\pi$
$557$	−34.8372	−1.47610	−0.738050	+	0.674746i	$0.764253\pi$
$558$	15.9500	0.675215
$559$	−1.53148	−0.0647748
$560$	−58.9408	−2.49070
$561$	−1.71911	−0.0725810
$562$	16.6212	0.701123
$563$	28.5743	1.20426	0.602131	−	0.798397i	$-0.294318\pi$
$563$	28.5743	1.20426	0.602131	+	0.798397i	$0.294318\pi$
$564$	37.1415	1.56394
$565$	−28.0477	−1.17997
$566$	32.0681	1.34792
$567$	3.74400	0.157233
$568$	−50.1161	−2.10282
$569$	28.5706	1.19774	0.598871	−	0.800846i	$-0.295616\pi$
$569$	28.5706	1.19774	0.598871	+	0.800846i	$0.295616\pi$
$570$	−37.4717	−1.56952
$571$	−4.76657	−0.199475	−0.0997373	−	0.995014i	$-0.531800\pi$
$571$	−4.76657	−0.199475	−0.0997373	+	0.995014i	$0.531800\pi$
$572$	1.02594	0.0428967
$573$	18.3556	0.766816
$574$	−3.07738	−0.128447
$575$	12.1831	0.508072
$576$	−3.77451	−0.157271
$577$	8.93976	0.372167	0.186084	−	0.982534i	$-0.440420\pi$
$577$	8.93976	0.372167	0.186084	+	0.982534i	$0.440420\pi$
$578$	−2.50856	−0.104342
$579$	10.0684	0.418429
$580$	−83.3077	−3.45916
$581$	−62.6780	−2.60032
$582$	−24.4048	−1.01161
$583$	−3.57021	−0.147863
$584$	−57.5918	−2.38317
$585$	0.374561	0.0154862
$586$	−29.6188	−1.22354
$587$	−27.6439	−1.14099	−0.570493	−	0.821303i	$-0.693248\pi$
$587$	−27.6439	−1.14099	−0.570493	+	0.821303i	$0.693248\pi$
$588$	−30.1254	−1.24235
$589$	−35.2503	−1.45247
$590$	17.5330	0.721824
$591$	15.7115	0.646287
$592$	−55.8966	−2.29734
$593$	24.3651	1.00055	0.500277	−	0.865866i	$-0.333232\pi$
$593$	24.3651	1.00055	0.500277	+	0.865866i	$0.333232\pi$
$594$	−4.31249	−0.176944
$595$	10.0876	0.413551
$596$	43.9015	1.79828
$597$	−10.4890	−0.429285
$598$	1.88041	0.0768957
$599$	−38.3834	−1.56830	−0.784151	−	0.620570i	$-0.786901\pi$
$599$	−38.3834	−1.56830	−0.784151	+	0.620570i	$0.786901\pi$
$600$	12.9958	0.530550
$601$	10.1591	0.414399	0.207200	−	0.978299i	$-0.433565\pi$
$601$	10.1591	0.414399	0.207200	+	0.978299i	$0.433565\pi$
$602$	−103.467	−4.21700
$603$	4.21389	0.171603
$604$	−64.7016	−2.63267
$605$	21.6750	0.881213
$606$	−7.70904	−0.313158
$607$	36.5524	1.48362	0.741809	−	0.670611i	$-0.233968\pi$
$607$	36.5524	1.48362	0.741809	+	0.670611i	$0.233968\pi$
$608$	−17.4844	−0.709086
$609$	−26.9664	−1.09273
$610$	102.292	4.14168
$611$	1.20277	0.0486591
$612$	−4.29286	−0.173528
$613$	−25.7134	−1.03855	−0.519276	−	0.854606i	$-0.673798\pi$
$613$	−25.7134	−1.03855	−0.519276	+	0.854606i	$0.673798\pi$
$614$	−45.7011	−1.84434
$615$	0.882821	0.0355988
$616$	37.0204	1.49160
$617$	−23.4453	−0.943871	−0.471935	−	0.881633i	$-0.656444\pi$
$617$	−23.4453	−0.943871	−0.471935	+	0.881633i	$0.656444\pi$
$618$	39.5617	1.59140
$619$	35.7309	1.43615	0.718074	−	0.695967i	$-0.245024\pi$
$619$	35.7309	1.43615	0.718074	+	0.695967i	$0.245024\pi$
$620$	73.5416	2.95350
$621$	−5.39210	−0.216378
$622$	−25.3763	−1.01750
$623$	−0.659479	−0.0264215
$624$	0.812267	0.0325167
$625$	−31.1921	−1.24769
$626$	41.1548	1.64488
$627$	9.53087	0.380626
$628$	12.5275	0.499904
$629$	9.56660	0.381445
$630$	25.3053	1.00819
$631$	16.7832	0.668129	0.334065	−	0.942550i	$-0.391580\pi$
$631$	16.7832	0.668129	0.334065	+	0.942550i	$0.391580\pi$
$632$	−5.75176	−0.228793
$633$	−17.5312	−0.696803
$634$	−32.2091	−1.27919
$635$	50.1323	1.98944
$636$	−8.91529	−0.353514
$637$	−0.975567	−0.0386534
$638$	31.0610	1.22972
$639$	8.71318	0.344688
$640$	−42.5058	−1.68019
$641$	−29.9402	−1.18257	−0.591283	−	0.806464i	$-0.701378\pi$
$641$	−29.9402	−1.18257	−0.591283	+	0.806464i	$0.701378\pi$
$642$	0.266443	0.0105157
$643$	7.06091	0.278455	0.139228	−	0.990260i	$-0.455538\pi$
$643$	7.06091	0.278455	0.139228	+	0.990260i	$0.455538\pi$
$644$	86.6643	3.41505
$645$	29.6820	1.16873
$646$	13.9076	0.547187
$647$	17.0182	0.669054	0.334527	−	0.942386i	$-0.391423\pi$
$647$	17.0182	0.669054	0.334527	+	0.942386i	$0.391423\pi$
$648$	−5.75176	−0.225950
$649$	−4.45950	−0.175051
$650$	0.787945	0.0309057
$651$	23.8052	0.932999
$652$	−84.1674	−3.29625
$653$	29.1632	1.14124	0.570622	−	0.821213i	$-0.306702\pi$
$653$	29.1632	1.14124	0.570622	+	0.821213i	$0.306702\pi$
$654$	−48.9840	−1.91543
$655$	14.6904	0.574003
$656$	1.91447	0.0747476
$657$	10.0129	0.390641
$658$	81.2594	3.16782
$659$	21.4490	0.835535	0.417768	−	0.908554i	$-0.362813\pi$
$659$	21.4490	0.835535	0.417768	+	0.908554i	$0.362813\pi$
$660$	−19.8839	−0.773981
$661$	−26.4673	−1.02946	−0.514730	−	0.857352i	$-0.672108\pi$
$661$	−26.4673	−1.02946	−0.514730	+	0.857352i	$0.672108\pi$
$662$	−80.7312	−3.13771
$663$	−0.139018	−0.00539901
$664$	96.2896	3.73676
$665$	−55.9263	−2.16873
$666$	23.9984	0.929917
$667$	38.8370	1.50377
$668$	−41.4948	−1.60548
$669$	−1.07333	−0.0414974
$670$	28.4812	1.10033
$671$	−26.0178	−1.00441
$672$	11.8075	0.455486
$673$	5.99232	0.230987	0.115493	−	0.993308i	$-0.463155\pi$
$673$	5.99232	0.230987	0.115493	+	0.993308i	$0.463155\pi$
$674$	−80.0903	−3.08496
$675$	−2.25944	−0.0869660
$676$	−55.7242	−2.14324
$677$	−32.1490	−1.23559	−0.617794	−	0.786340i	$-0.711973\pi$
$677$	−32.1490	−1.23559	−0.617794	+	0.786340i	$0.711973\pi$
$678$	26.1137	1.00289
$679$	−36.4240	−1.39783
$680$	−15.4972	−0.594289
$681$	6.66723	0.255489
$682$	−27.4198	−1.04996
$683$	−30.6438	−1.17255	−0.586276	−	0.810111i	$-0.699407\pi$
$683$	−30.6438	−1.17255	−0.586276	+	0.810111i	$0.699407\pi$
$684$	23.7998	0.910010
$685$	−10.2774	−0.392679
$686$	−0.164981	−0.00629899
$687$	−20.5325	−0.783365
$688$	64.3679	2.45400
$689$	−0.288709	−0.0109989
$690$	−36.4446	−1.38742
$691$	−6.24184	−0.237451	−0.118725	−	0.992927i	$-0.537881\pi$
$691$	−6.24184	−0.237451	−0.118725	+	0.992927i	$0.537881\pi$
$692$	100.665	3.82670
$693$	−6.43637	−0.244497
$694$	−7.20336	−0.273436
$695$	9.88655	0.375018
$696$	41.4274	1.57030
$697$	−0.327658	−0.0124109
$698$	−54.9019	−2.07807
$699$	26.4189	0.999253
$700$	36.3148	1.37257
$701$	25.8694	0.977072	0.488536	−	0.872544i	$-0.337531\pi$
$701$	25.8694	0.977072	0.488536	+	0.872544i	$0.337531\pi$
$702$	−0.348734	−0.0131621
$703$	−53.0378	−2.00036
$704$	6.48881	0.244556
$705$	−23.3112	−0.877952
$706$	−75.7361	−2.85037
$707$	−11.5057	−0.432716
$708$	−11.1360	−0.418515
$709$	−30.6086	−1.14953	−0.574766	−	0.818318i	$-0.694907\pi$
$709$	−30.6086	−1.14953	−0.574766	+	0.818318i	$0.694907\pi$
$710$	58.8915	2.21016
$711$	1.00000	0.0375029
$712$	1.01313	0.0379687
$713$	−34.2842	−1.28395
$714$	−9.39205	−0.351488
$715$	−0.643912	−0.0240810
$716$	94.5267	3.53263
$717$	12.3541	0.461372
$718$	−71.0895	−2.65304
$719$	11.5708	0.431518	0.215759	−	0.976447i	$-0.430777\pi$
$719$	11.5708	0.431518	0.215759	+	0.976447i	$0.430777\pi$
$720$	−15.7427	−0.586696
$721$	59.0455	2.19897
$722$	−29.4419	−1.09572
$723$	−4.32551	−0.160867
$724$	34.4628	1.28080
$725$	16.2738	0.604393
$726$	−20.1805	−0.748967
$727$	−24.7108	−0.916473	−0.458237	−	0.888830i	$-0.651519\pi$
$727$	−24.7108	−0.916473	−0.458237	+	0.888830i	$0.651519\pi$
$728$	2.99369	0.110954
$729$	1.00000	0.0370370
$730$	67.6762	2.50481
$731$	−11.0164	−0.407458
$732$	−64.9699	−2.40136
$733$	51.8781	1.91616	0.958080	−	0.286500i	$-0.0924918\pi$
$733$	51.8781	1.91616	0.958080	+	0.286500i	$0.0924918\pi$
$734$	60.3157	2.22629
$735$	18.9077	0.697420
$736$	−17.0052	−0.626819
$737$	−7.24416	−0.266842
$738$	−0.821949	−0.0302564
$739$	44.8867	1.65118	0.825592	−	0.564267i	$-0.190841\pi$
$739$	44.8867	1.65118	0.825592	+	0.564267i	$0.190841\pi$
$740$	110.651	4.06761
$741$	0.770724	0.0283132
$742$	−19.5052	−0.716057
$743$	30.8520	1.13185	0.565926	−	0.824456i	$-0.308519\pi$
$743$	30.8520	1.13185	0.565926	+	0.824456i	$0.308519\pi$
$744$	−36.5709	−1.34076
$745$	−27.5540	−1.00950
$746$	14.1410	0.517737
$747$	−16.7409	−0.612517
$748$	7.37990	0.269836
$749$	0.397665	0.0145303
$750$	18.5231	0.676369
$751$	19.7178	0.719513	0.359757	−	0.933046i	$-0.382860\pi$
$751$	19.7178	0.719513	0.359757	+	0.933046i	$0.382860\pi$
$752$	−50.5524	−1.84346
$753$	−19.3106	−0.703716
$754$	2.51178	0.0914737
$755$	40.6089	1.47791
$756$	−16.0725	−0.584550
$757$	15.8870	0.577424	0.288712	−	0.957416i	$-0.406773\pi$
$757$	15.8870	0.577424	0.288712	+	0.957416i	$0.406773\pi$
$758$	−83.7300	−3.04121
$759$	9.26963	0.336466
$760$	85.9172	3.11654
$761$	25.0751	0.908972	0.454486	−	0.890754i	$-0.349823\pi$
$761$	25.0751	0.908972	0.454486	+	0.890754i	$0.349823\pi$
$762$	−46.6756	−1.69088
$763$	−73.1083	−2.64670
$764$	−78.7979	−2.85081
$765$	2.69434	0.0974139
$766$	28.9677	1.04665
$767$	−0.360622	−0.0130213
$768$	32.0260	1.15564
$769$	17.2244	0.621127	0.310564	−	0.950553i	$-0.399482\pi$
$769$	17.2244	0.621127	0.310564	+	0.950553i	$0.399482\pi$
$770$	−43.5027	−1.56773
$771$	−23.6722	−0.852533
$772$	−43.2223	−1.55560
$773$	24.4961	0.881063	0.440531	−	0.897737i	$-0.354790\pi$
$773$	24.4961	0.881063	0.440531	+	0.897737i	$0.354790\pi$
$774$	−27.6354	−0.993333
$775$	−14.3660	−0.516043
$776$	55.9567	2.00873
$777$	35.8174	1.28494
$778$	18.9140	0.678101
$779$	1.81656	0.0650849
$780$	−1.60794	−0.0575733
$781$	−14.9789	−0.535989
$782$	13.5264	0.483703
$783$	−7.20257	−0.257399
$784$	41.0029	1.46439
$785$	−7.86269	−0.280632
$786$	−13.6775	−0.487860
$787$	−31.2735	−1.11478	−0.557389	−	0.830251i	$-0.688197\pi$
$787$	−31.2735	−1.11478	−0.557389	+	0.830251i	$0.688197\pi$
$788$	−67.4474	−2.40271
$789$	9.98045	0.355313
$790$	6.75889	0.240471
$791$	38.9746	1.38578
$792$	9.88792	0.351352
$793$	−2.10396	−0.0747137
$794$	46.6211	1.65452
$795$	5.59553	0.198453
$796$	45.0276	1.59596
$797$	−50.7016	−1.79594	−0.897972	−	0.440053i	$-0.854959\pi$
$797$	−50.7016	−1.79594	−0.897972	+	0.440053i	$0.854959\pi$
$798$	52.0701	1.84326
$799$	8.65194	0.306084
$800$	−7.12565	−0.251930
$801$	−0.176143	−0.00622370
$802$	−5.17537	−0.182749
$803$	−17.2133	−0.607445
$804$	−18.0896	−0.637972
$805$	−54.3934	−1.91711
$806$	−2.21733	−0.0781021
$807$	−1.01465	−0.0357174
$808$	17.6757	0.621829
$809$	4.30764	0.151449	0.0757243	−	0.997129i	$-0.475873\pi$
$809$	4.30764	0.151449	0.0757243	+	0.997129i	$0.475873\pi$
$810$	6.75889	0.237483
$811$	−9.54767	−0.335264	−0.167632	−	0.985850i	$-0.553612\pi$
$811$	−9.54767	−0.335264	−0.167632	+	0.985850i	$0.553612\pi$
$812$	115.763	4.06248
$813$	0.893528	0.0313374
$814$	−41.2559	−1.44602
$815$	52.8262	1.85042
$816$	5.84290	0.204542
$817$	61.0758	2.13677
$818$	−28.2998	−0.989478
$819$	−0.520484	−0.0181872
$820$	−3.78982	−0.132346
$821$	39.9747	1.39513	0.697564	−	0.716523i	$-0.254267\pi$
$821$	39.9747	1.39513	0.697564	+	0.716523i	$0.254267\pi$
$822$	9.56875	0.333748
$823$	−19.6790	−0.685968	−0.342984	−	0.939341i	$-0.611438\pi$
$823$	−19.6790	−0.685968	−0.342984	+	0.939341i	$0.611438\pi$
$824$	−90.7092	−3.16000
$825$	3.88424	0.135232
$826$	−24.3636	−0.847719
$827$	31.9137	1.10975	0.554873	−	0.831935i	$-0.312767\pi$
$827$	31.9137	1.10975	0.554873	+	0.831935i	$0.312767\pi$
$828$	23.1475	0.804431
$829$	−10.6270	−0.369092	−0.184546	−	0.982824i	$-0.559081\pi$
$829$	−10.6270	−0.369092	−0.184546	+	0.982824i	$0.559081\pi$
$830$	−113.150	−3.92749
$831$	2.86557	0.0994057
$832$	0.524724	0.0181915
$833$	−7.01757	−0.243144
$834$	−9.20486	−0.318738
$835$	26.0435	0.901273
$836$	−40.9146	−1.41506
$837$	6.35822	0.219772
$838$	32.9491	1.13821
$839$	10.1406	0.350091	0.175046	−	0.984560i	$-0.443993\pi$
$839$	10.1406	0.350091	0.175046	+	0.984560i	$0.443993\pi$
$840$	−58.0214	−2.00193
$841$	22.8769	0.788860
$842$	−94.5507	−3.25843
$843$	6.62580	0.228205
$844$	75.2590	2.59052
$845$	34.9743	1.20315
$846$	21.7039	0.746195
$847$	−30.1192	−1.03491
$848$	12.1344	0.416696
$849$	12.7835	0.438729
$850$	5.66794	0.194409
$851$	−51.5841	−1.76828
$852$	−37.4044	−1.28145
$853$	−19.6341	−0.672260	−0.336130	−	0.941816i	$-0.609118\pi$
$853$	−19.6341	−0.672260	−0.336130	+	0.941816i	$0.609118\pi$
$854$	−142.143	−4.86404
$855$	−14.9376	−0.510854
$856$	−0.610915	−0.0208807
$857$	−21.5317	−0.735508	−0.367754	−	0.929923i	$-0.619873\pi$
$857$	−21.5317	−0.735508	−0.367754	+	0.929923i	$0.619873\pi$
$858$	0.599514	0.0204671
$859$	30.3366	1.03507	0.517535	−	0.855662i	$-0.326850\pi$
$859$	30.3366	1.03507	0.517535	+	0.855662i	$0.326850\pi$
$860$	−127.421	−4.34500
$861$	−1.22675	−0.0418077
$862$	−95.4289	−3.25032
$863$	35.4483	1.20667	0.603337	−	0.797486i	$-0.293837\pi$
$863$	35.4483	1.20667	0.603337	+	0.797486i	$0.293837\pi$
$864$	3.15372	0.107292
$865$	−63.1805	−2.14820
$866$	−87.9730	−2.98945
$867$	−1.00000	−0.0339618
$868$	−102.192	−3.46863
$869$	−1.71911	−0.0583169
$870$	−48.6814	−1.65045
$871$	−0.585807	−0.0198493
$872$	112.313	3.80341
$873$	−9.72863	−0.329264
$874$	−74.9911	−2.53661
$875$	27.6457	0.934594
$876$	−42.9840	−1.45229
$877$	−17.4436	−0.589029	−0.294514	−	0.955647i	$-0.595158\pi$
$877$	−17.4436	−0.589029	−0.294514	+	0.955647i	$0.595158\pi$
$878$	−19.7621	−0.666939
$879$	−11.8071	−0.398245
$880$	27.0635	0.912311
$881$	−12.5196	−0.421794	−0.210897	−	0.977508i	$-0.567639\pi$
$881$	−12.5196	−0.421794	−0.210897	+	0.977508i	$0.567639\pi$
$882$	−17.6040	−0.592756
$883$	−22.4719	−0.756241	−0.378120	−	0.925756i	$-0.623429\pi$
$883$	−22.4719	−0.756241	−0.378120	+	0.925756i	$0.623429\pi$
$884$	0.596784	0.0200720
$885$	6.98930	0.234943
$886$	−9.26771	−0.311355
$887$	26.2816	0.882448	0.441224	−	0.897397i	$-0.354544\pi$
$887$	26.2816	0.882448	0.441224	+	0.897397i	$0.354544\pi$
$888$	−55.0247	−1.84651
$889$	−69.6630	−2.33642
$890$	−1.19053	−0.0399066
$891$	−1.71911	−0.0575925
$892$	4.60766	0.154276
$893$	−47.9669	−1.60515
$894$	25.6541	0.858002
$895$	−59.3280	−1.98312
$896$	59.0654	1.97324
$897$	0.749598	0.0250284
$898$	9.10175	0.303729
$899$	−45.7955	−1.52736
$900$	9.69946	0.323315
$901$	−2.07677	−0.0691874
$902$	1.41302	0.0470485
$903$	−41.2456	−1.37257
$904$	−59.8750	−1.99141
$905$	−21.6299	−0.719004
$906$	−37.8088	−1.25611
$907$	−1.93038	−0.0640972	−0.0320486	−	0.999486i	$-0.510203\pi$
$907$	−1.93038	−0.0640972	−0.0320486	+	0.999486i	$0.510203\pi$
$908$	−28.6215	−0.949837
$909$	−3.07310	−0.101928
$910$	−3.51789	−0.116617
$911$	23.1841	0.768123	0.384061	−	0.923308i	$-0.374525\pi$
$911$	23.1841	0.768123	0.384061	+	0.923308i	$0.374525\pi$
$912$	−32.3934	−1.07265
$913$	28.7795	0.952463
$914$	19.1631	0.633859
$915$	40.7772	1.34805
$916$	88.1432	2.91233
$917$	−20.4136	−0.674116
$918$	−2.50856	−0.0827947
$919$	−30.5628	−1.00817	−0.504087	−	0.863653i	$-0.668171\pi$
$919$	−30.5628	−1.00817	−0.504087	+	0.863653i	$0.668171\pi$
$920$	83.5622	2.75497
$921$	−18.2181	−0.600306
$922$	−95.7108	−3.15207
$923$	−1.21129	−0.0398700
$924$	27.6304	0.908973
$925$	−21.6152	−0.710703
$926$	−11.5954	−0.381049
$927$	15.7707	0.517978
$928$	−22.7149	−0.745652
$929$	7.06537	0.231807	0.115904	−	0.993260i	$-0.463024\pi$
$929$	7.06537	0.231807	0.115904	+	0.993260i	$0.463024\pi$
$930$	42.9745	1.40919
$931$	38.9058	1.27509
$932$	−113.412	−3.71494
$933$	−10.1159	−0.331180
$934$	−36.7297	−1.20183
$935$	−4.63187	−0.151478
$936$	0.799597	0.0261356
$937$	−16.4990	−0.538999	−0.269500	−	0.963000i	$-0.586858\pi$
$937$	−16.4990	−0.538999	−0.269500	+	0.963000i	$0.586858\pi$
$938$	−39.5771	−1.29224
$939$	16.4058	0.535382
$940$	100.072	3.26398
$941$	4.21742	0.137484	0.0687420	−	0.997634i	$-0.478101\pi$
$941$	4.21742	0.137484	0.0687420	+	0.997634i	$0.478101\pi$
$942$	7.32055	0.238516
$943$	1.76677	0.0575338
$944$	15.1569	0.493315
$945$	10.0876	0.328150
$946$	47.5083	1.54463
$947$	8.56505	0.278327	0.139163	−	0.990269i	$-0.455559\pi$
$947$	8.56505	0.278327	0.139163	+	0.990269i	$0.455559\pi$
$948$	−4.29286	−0.139425
$949$	−1.39197	−0.0451854
$950$	−31.4234	−1.01951
$951$	−12.8397	−0.416355
$952$	21.5346	0.697940
$953$	−59.0273	−1.91208	−0.956041	−	0.293231i	$-0.905269\pi$
$953$	−59.0273	−1.91208	−0.956041	+	0.293231i	$0.905269\pi$
$954$	−5.20971	−0.168670
$955$	49.4561	1.60036
$956$	−53.0344	−1.71525
$957$	12.3820	0.400254
$958$	42.1272	1.36107
$959$	14.2813	0.461167
$960$	−10.1698	−0.328229
$961$	9.42695	0.304095
$962$	−3.33620	−0.107563
$963$	0.106214	0.00342269
$964$	18.5688	0.598060
$965$	27.1277	0.873271
$966$	50.6428	1.62941
$967$	−15.1871	−0.488385	−0.244193	−	0.969727i	$-0.578523\pi$
$967$	−15.1871	−0.488385	−0.244193	+	0.969727i	$0.578523\pi$
$968$	46.2709	1.48720
$969$	5.54406	0.178101
$970$	−65.7547	−2.11126
$971$	−47.5157	−1.52485	−0.762426	−	0.647076i	$-0.775992\pi$
$971$	−47.5157	−1.52485	−0.762426	+	0.647076i	$0.775992\pi$
$972$	−4.29286	−0.137693
$973$	−13.7382	−0.440426
$974$	82.9756	2.65871
$975$	0.314103	0.0100593
$976$	88.4288	2.83054
$977$	−32.4199	−1.03720	−0.518602	−	0.855016i	$-0.673547\pi$
$977$	−32.4199	−1.03720	−0.518602	+	0.855016i	$0.673547\pi$
$978$	−49.1837	−1.57272
$979$	0.302809	0.00967783
$980$	−81.1679	−2.59281
$981$	−19.5268	−0.623442
$982$	27.4059	0.874559
$983$	3.04172	0.0970157	0.0485078	−	0.998823i	$-0.484553\pi$
$983$	3.04172	0.0970157	0.0485078	+	0.998823i	$0.484553\pi$
$984$	1.88461	0.0600792
$985$	42.3322	1.34881
$986$	18.0680	0.575404
$987$	32.3929	1.03108
$988$	−3.30860	−0.105261
$989$	59.4018	1.88887
$990$	−11.6193	−0.369286
$991$	32.8602	1.04384	0.521920	−	0.852995i	$-0.325216\pi$
$991$	32.8602	1.04384	0.521920	+	0.852995i	$0.325216\pi$
$992$	20.0520	0.636653
$993$	−32.1823	−1.02128
$994$	−81.8346	−2.59564
$995$	−28.2608	−0.895927
$996$	71.8663	2.27717
$997$	22.0507	0.698352	0.349176	−	0.937057i	$-0.386462\pi$
$997$	22.0507	0.698352	0.349176	+	0.937057i	$0.386462\pi$
$998$	−88.4598	−2.80014
$999$	9.56660	0.302674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.4	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +6.75889 q^{10} -1.71911 q^{11} -4.29286 q^{12} -0.139018 q^{13} -9.39205 q^{14} +2.69434 q^{15} +5.84290 q^{16} -1.00000 q^{17} -2.50856 q^{18} +5.54406 q^{19} -11.5664 q^{20} -3.74400 q^{21} +4.31249 q^{22} +5.39210 q^{23} +5.75176 q^{24} +2.25944 q^{25} +0.348734 q^{26} -1.00000 q^{27} +16.0725 q^{28} +7.20257 q^{29} -6.75889 q^{30} -6.35822 q^{31} -3.15372 q^{32} +1.71911 q^{33} +2.50856 q^{34} -10.0876 q^{35} +4.29286 q^{36} -9.56660 q^{37} -13.9076 q^{38} +0.139018 q^{39} +15.4972 q^{40} +0.327658 q^{41} +9.39205 q^{42} +11.0164 q^{43} -7.37990 q^{44} -2.69434 q^{45} -13.5264 q^{46} -8.65194 q^{47} -5.84290 q^{48} +7.01757 q^{49} -5.66794 q^{50} +1.00000 q^{51} -0.596784 q^{52} +2.07677 q^{53} +2.50856 q^{54} +4.63187 q^{55} -21.5346 q^{56} -5.54406 q^{57} -18.0680 q^{58} +2.59407 q^{59} +11.5664 q^{60} +15.1344 q^{61} +15.9500 q^{62} +3.74400 q^{63} -3.77451 q^{64} +0.374561 q^{65} -4.31249 q^{66} +4.21389 q^{67} -4.29286 q^{68} -5.39210 q^{69} +25.3053 q^{70} +8.71318 q^{71} -5.75176 q^{72} +10.0129 q^{73} +23.9984 q^{74} -2.25944 q^{75} +23.7998 q^{76} -6.43637 q^{77} -0.348734 q^{78} +1.00000 q^{79} -15.7427 q^{80} +1.00000 q^{81} -0.821949 q^{82} -16.7409 q^{83} -16.0725 q^{84} +2.69434 q^{85} -27.6354 q^{86} -7.20257 q^{87} +9.88792 q^{88} -0.176143 q^{89} +6.75889 q^{90} -0.520484 q^{91} +23.1475 q^{92} +6.35822 q^{93} +21.7039 q^{94} -14.9376 q^{95} +3.15372 q^{96} -9.72863 q^{97} -17.6040 q^{98} -1.71911 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more