LMFDB - Embedded newform 4025.2.a.bd.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22234 q^{2} -1.28664 q^{3} -0.505878 q^{4} -1.57271 q^{6} -1.00000 q^{7} -3.06304 q^{8} -1.34457 q^{9} +O(q^{10})$	\(q+1.22234 q^{2} -1.28664 q^{3} -0.505878 q^{4} -1.57271 q^{6} -1.00000 q^{7} -3.06304 q^{8} -1.34457 q^{9} -1.83173 q^{11} +0.650880 q^{12} -3.24693 q^{13} -1.22234 q^{14} -2.73233 q^{16} -5.53254 q^{17} -1.64352 q^{18} -2.06793 q^{19} +1.28664 q^{21} -2.23900 q^{22} -1.00000 q^{23} +3.94102 q^{24} -3.96886 q^{26} +5.58988 q^{27} +0.505878 q^{28} +2.29813 q^{29} -2.49162 q^{31} +2.78624 q^{32} +2.35677 q^{33} -6.76266 q^{34} +0.680188 q^{36} -7.37033 q^{37} -2.52772 q^{38} +4.17762 q^{39} +11.4498 q^{41} +1.57271 q^{42} +3.84395 q^{43} +0.926631 q^{44} -1.22234 q^{46} +5.75277 q^{47} +3.51552 q^{48} +1.00000 q^{49} +7.11836 q^{51} +1.64255 q^{52} +2.68696 q^{53} +6.83275 q^{54} +3.06304 q^{56} +2.66067 q^{57} +2.80910 q^{58} +5.19513 q^{59} -11.4038 q^{61} -3.04562 q^{62} +1.34457 q^{63} +8.87040 q^{64} +2.88078 q^{66} -13.4901 q^{67} +2.79879 q^{68} +1.28664 q^{69} -4.68945 q^{71} +4.11847 q^{72} +13.7534 q^{73} -9.00907 q^{74} +1.04612 q^{76} +1.83173 q^{77} +5.10648 q^{78} +5.30377 q^{79} -3.15843 q^{81} +13.9956 q^{82} -11.7821 q^{83} -0.650880 q^{84} +4.69863 q^{86} -2.95686 q^{87} +5.61066 q^{88} -12.4495 q^{89} +3.24693 q^{91} +0.505878 q^{92} +3.20581 q^{93} +7.03186 q^{94} -3.58487 q^{96} -9.36711 q^{97} +1.22234 q^{98} +2.46288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * 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 $

$2$	1.22234	0.864327	0.432163	−	0.901795i	$-0.357750\pi$
$2$	1.22234	0.864327	0.432163	+	0.901795i	$0.357750\pi$
$3$	−1.28664	−0.742839	−0.371420	−	0.928465i	$-0.621129\pi$
$3$	−1.28664	−0.742839	−0.371420	+	0.928465i	$0.621129\pi$
$4$	−0.505878	−0.252939
$5$	0	0
$5$	0	0
$6$	−1.57271	−0.642056
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.06304	−1.08295
$9$	−1.34457	−0.448190
$10$	0	0
$11$	−1.83173	−0.552287	−0.276143	−	0.961116i	$-0.589056\pi$
$11$	−1.83173	−0.552287	−0.276143	+	0.961116i	$0.589056\pi$
$12$	0.650880	0.187893
$13$	−3.24693	−0.900536	−0.450268	−	0.892893i	$-0.648672\pi$
$13$	−3.24693	−0.900536	−0.450268	+	0.892893i	$0.648672\pi$
$14$	−1.22234	−0.326685
$15$	0	0
$16$	−2.73233	−0.683083
$17$	−5.53254	−1.34184	−0.670919	−	0.741531i	$-0.734100\pi$
$17$	−5.53254	−1.34184	−0.670919	+	0.741531i	$0.734100\pi$
$18$	−1.64352	−0.387382
$19$	−2.06793	−0.474415	−0.237207	−	0.971459i	$-0.576232\pi$
$19$	−2.06793	−0.474415	−0.237207	+	0.971459i	$0.576232\pi$
$20$	0	0
$21$	1.28664	0.280767
$22$	−2.23900	−0.477356
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.94102	0.804457
$25$	0	0
$26$	−3.96886	−0.778358
$27$	5.58988	1.07577
$28$	0.505878	0.0956019
$29$	2.29813	0.426752	0.213376	−	0.976970i	$-0.431554\pi$
$29$	2.29813	0.426752	0.213376	+	0.976970i	$0.431554\pi$
$30$	0	0
$31$	−2.49162	−0.447509	−0.223754	−	0.974646i	$-0.571831\pi$
$31$	−2.49162	−0.447509	−0.223754	+	0.974646i	$0.571831\pi$
$32$	2.78624	0.492542
$33$	2.35677	0.410260
$34$	−6.76266	−1.15979
$35$	0	0
$36$	0.680188	0.113365
$37$	−7.37033	−1.21167	−0.605837	−	0.795589i	$-0.707162\pi$
$37$	−7.37033	−1.21167	−0.605837	+	0.795589i	$0.707162\pi$
$38$	−2.52772	−0.410050
$39$	4.17762	0.668954
$40$	0	0
$41$	11.4498	1.78816	0.894078	−	0.447912i	$-0.147832\pi$
$41$	11.4498	1.78816	0.894078	+	0.447912i	$0.147832\pi$
$42$	1.57271	0.242674
$43$	3.84395	0.586197	0.293099	−	0.956082i	$-0.405314\pi$
$43$	3.84395	0.586197	0.293099	+	0.956082i	$0.405314\pi$
$44$	0.926631	0.139695
$45$	0	0
$46$	−1.22234	−0.180225
$47$	5.75277	0.839128	0.419564	−	0.907726i	$-0.362183\pi$
$47$	5.75277	0.839128	0.419564	+	0.907726i	$0.362183\pi$
$48$	3.51552	0.507421
$49$	1.00000	0.142857
$50$	0	0
$51$	7.11836	0.996770
$52$	1.64255	0.227781
$53$	2.68696	0.369083	0.184541	−	0.982825i	$-0.440920\pi$
$53$	2.68696	0.369083	0.184541	+	0.982825i	$0.440920\pi$
$54$	6.83275	0.929819
$55$	0	0
$56$	3.06304	0.409316
$57$	2.66067	0.352414
$58$	2.80910	0.368853
$59$	5.19513	0.676348	0.338174	−	0.941084i	$-0.390191\pi$
$59$	5.19513	0.676348	0.338174	+	0.941084i	$0.390191\pi$
$60$	0	0
$61$	−11.4038	−1.46011	−0.730055	−	0.683388i	$-0.760506\pi$
$61$	−11.4038	−1.46011	−0.730055	+	0.683388i	$0.760506\pi$
$62$	−3.04562	−0.386794
$63$	1.34457	0.169400
$64$	8.87040	1.10880
$65$	0	0
$66$	2.88078	0.354599
$67$	−13.4901	−1.64808	−0.824039	−	0.566533i	$-0.808284\pi$
$67$	−13.4901	−1.64808	−0.824039	+	0.566533i	$0.808284\pi$
$68$	2.79879	0.339403
$69$	1.28664	0.154893
$70$	0	0
$71$	−4.68945	−0.556535	−0.278268	−	0.960504i	$-0.589760\pi$
$71$	−4.68945	−0.556535	−0.278268	+	0.960504i	$0.589760\pi$
$72$	4.11847	0.485366
$73$	13.7534	1.60972	0.804858	−	0.593467i	$-0.202241\pi$
$73$	13.7534	1.60972	0.804858	+	0.593467i	$0.202241\pi$
$74$	−9.00907	−1.04728
$75$	0	0
$76$	1.04612	0.119998
$77$	1.83173	0.208745
$78$	5.10648	0.578195
$79$	5.30377	0.596721	0.298360	−	0.954453i	$-0.403560\pi$
$79$	5.30377	0.596721	0.298360	+	0.954453i	$0.403560\pi$
$80$	0	0
$81$	−3.15843	−0.350936
$82$	13.9956	1.54555
$83$	−11.7821	−1.29326	−0.646629	−	0.762805i	$-0.723822\pi$
$83$	−11.7821	−1.29326	−0.646629	+	0.762805i	$0.723822\pi$
$84$	−0.650880	−0.0710169
$85$	0	0
$86$	4.69863	0.506666
$87$	−2.95686	−0.317008
$88$	5.61066	0.598098
$89$	−12.4495	−1.31965	−0.659823	−	0.751421i	$-0.729369\pi$
$89$	−12.4495	−1.31965	−0.659823	+	0.751421i	$0.729369\pi$
$90$	0	0
$91$	3.24693	0.340371
$92$	0.505878	0.0527414
$93$	3.20581	0.332427
$94$	7.03186	0.725281
$95$	0	0
$96$	−3.58487	−0.365879
$97$	−9.36711	−0.951086	−0.475543	−	0.879693i	$-0.657748\pi$
$97$	−9.36711	−0.951086	−0.475543	+	0.879693i	$0.657748\pi$
$98$	1.22234	0.123475
$99$	2.46288	0.247529
$100$	0	0
$101$	16.8806	1.67968	0.839839	−	0.542835i	$-0.182649\pi$
$101$	16.8806	1.67968	0.839839	+	0.542835i	$0.182649\pi$
$102$	8.70108	0.861535
$103$	−11.6971	−1.15255	−0.576273	−	0.817257i	$-0.695494\pi$
$103$	−11.6971	−1.15255	−0.576273	+	0.817257i	$0.695494\pi$
$104$	9.94548	0.975235
$105$	0	0
$106$	3.28439	0.319008
$107$	−0.260335	−0.0251675	−0.0125838	−	0.999921i	$-0.504006\pi$
$107$	−0.260335	−0.0251675	−0.0125838	+	0.999921i	$0.504006\pi$
$108$	−2.82779	−0.272105
$109$	12.3958	1.18730	0.593652	−	0.804722i	$-0.297686\pi$
$109$	12.3958	1.18730	0.593652	+	0.804722i	$0.297686\pi$
$110$	0	0
$111$	9.48293	0.900079
$112$	2.73233	0.258181
$113$	13.2257	1.24417	0.622084	−	0.782950i	$-0.286286\pi$
$113$	13.2257	1.24417	0.622084	+	0.782950i	$0.286286\pi$
$114$	3.25225	0.304601
$115$	0	0
$116$	−1.16257	−0.107942
$117$	4.36572	0.403611
$118$	6.35023	0.584586
$119$	5.53254	0.507167
$120$	0	0
$121$	−7.64477	−0.694979
$122$	−13.9394	−1.26201
$123$	−14.7317	−1.32831
$124$	1.26046	0.113192
$125$	0	0
$126$	1.64352	0.146417
$127$	−7.36812	−0.653815	−0.326908	−	0.945056i	$-0.606007\pi$
$127$	−7.36812	−0.653815	−0.326908	+	0.945056i	$0.606007\pi$
$128$	5.27020	0.465824
$129$	−4.94577	−0.435450
$130$	0	0
$131$	19.9771	1.74541	0.872704	−	0.488250i	$-0.162365\pi$
$131$	19.9771	1.74541	0.872704	+	0.488250i	$0.162365\pi$
$132$	−1.19224	−0.103771
$133$	2.06793	0.179312
$134$	−16.4895	−1.42448
$135$	0	0
$136$	16.9464	1.45314
$137$	14.3412	1.22525	0.612626	−	0.790373i	$-0.290113\pi$
$137$	14.3412	1.22525	0.612626	+	0.790373i	$0.290113\pi$
$138$	1.57271	0.133878
$139$	−5.88452	−0.499119	−0.249559	−	0.968359i	$-0.580286\pi$
$139$	−5.88452	−0.499119	−0.249559	+	0.968359i	$0.580286\pi$
$140$	0	0
$141$	−7.40172	−0.623337
$142$	−5.73212	−0.481029
$143$	5.94749	0.497354
$144$	3.67381	0.306151
$145$	0	0
$146$	16.8114	1.39132
$147$	−1.28664	−0.106120
$148$	3.72849	0.306480
$149$	−19.3463	−1.58491	−0.792455	−	0.609931i	$-0.791197\pi$
$149$	−19.3463	−1.58491	−0.792455	+	0.609931i	$0.791197\pi$
$150$	0	0
$151$	12.4932	1.01668	0.508339	−	0.861157i	$-0.330260\pi$
$151$	12.4932	1.01668	0.508339	+	0.861157i	$0.330260\pi$
$152$	6.33415	0.513767
$153$	7.43888	0.601398
$154$	2.23900	0.180424
$155$	0	0
$156$	−2.11336	−0.169204
$157$	5.89291	0.470305	0.235153	−	0.971958i	$-0.424441\pi$
$157$	5.89291	0.470305	0.235153	+	0.971958i	$0.424441\pi$
$158$	6.48302	0.515762
$159$	−3.45714	−0.274169
$160$	0	0
$161$	1.00000	0.0788110
$162$	−3.86068	−0.303324
$163$	−15.8132	−1.23858	−0.619292	−	0.785161i	$-0.712580\pi$
$163$	−15.8132	−1.23858	−0.619292	+	0.785161i	$0.712580\pi$
$164$	−5.79219	−0.452294
$165$	0	0
$166$	−14.4018	−1.11780
$167$	−11.3761	−0.880312	−0.440156	−	0.897921i	$-0.645077\pi$
$167$	−11.3761	−0.880312	−0.440156	+	0.897921i	$0.645077\pi$
$168$	−3.94102	−0.304056
$169$	−2.45745	−0.189035
$170$	0	0
$171$	2.78047	0.212628
$172$	−1.94457	−0.148272
$173$	2.91057	0.221287	0.110643	−	0.993860i	$-0.464709\pi$
$173$	2.91057	0.221287	0.110643	+	0.993860i	$0.464709\pi$
$174$	−3.61429	−0.273999
$175$	0	0
$176$	5.00489	0.377258
$177$	−6.68424	−0.502418
$178$	−15.2176	−1.14061
$179$	10.6611	0.796851	0.398426	−	0.917201i	$-0.369557\pi$
$179$	10.6611	0.796851	0.398426	+	0.917201i	$0.369557\pi$
$180$	0	0
$181$	21.1456	1.57174	0.785869	−	0.618393i	$-0.212216\pi$
$181$	21.1456	1.57174	0.785869	+	0.618393i	$0.212216\pi$
$182$	3.96886	0.294192
$183$	14.6726	1.08463
$184$	3.06304	0.225810
$185$	0	0
$186$	3.91860	0.287326
$187$	10.1341	0.741079
$188$	−2.91020	−0.212248
$189$	−5.58988	−0.406604
$190$	0	0
$191$	−11.0107	−0.796704	−0.398352	−	0.917233i	$-0.630418\pi$
$191$	−11.0107	−0.796704	−0.398352	+	0.917233i	$0.630418\pi$
$192$	−11.4130	−0.823660
$193$	7.87083	0.566555	0.283277	−	0.959038i	$-0.408578\pi$
$193$	7.87083	0.566555	0.283277	+	0.959038i	$0.408578\pi$
$194$	−11.4498	−0.822049
$195$	0	0
$196$	−0.505878	−0.0361341
$197$	−6.62074	−0.471708	−0.235854	−	0.971788i	$-0.575789\pi$
$197$	−6.62074	−0.471708	−0.235854	+	0.971788i	$0.575789\pi$
$198$	3.01049	0.213946
$199$	22.2199	1.57513	0.787564	−	0.616233i	$-0.211342\pi$
$199$	22.2199	1.57513	0.787564	+	0.616233i	$0.211342\pi$
$200$	0	0
$201$	17.3568	1.22426
$202$	20.6338	1.45179
$203$	−2.29813	−0.161297
$204$	−3.60102	−0.252122
$205$	0	0
$206$	−14.2978	−0.996177
$207$	1.34457	0.0934540
$208$	8.87169	0.615141
$209$	3.78788	0.262013
$210$	0	0
$211$	16.3521	1.12572	0.562862	−	0.826551i	$-0.309700\pi$
$211$	16.3521	1.12572	0.562862	+	0.826551i	$0.309700\pi$
$212$	−1.35927	−0.0933553
$213$	6.03361	0.413416
$214$	−0.318218	−0.0217530
$215$	0	0
$216$	−17.1220	−1.16501
$217$	2.49162	0.169142
$218$	15.1519	1.02622
$219$	−17.6956	−1.19576
$220$	0	0
$221$	17.9638	1.20837
$222$	11.5914	0.777963
$223$	20.0149	1.34030	0.670150	−	0.742226i	$-0.266230\pi$
$223$	20.0149	1.34030	0.670150	+	0.742226i	$0.266230\pi$
$224$	−2.78624	−0.186163
$225$	0	0
$226$	16.1663	1.07537
$227$	−11.6552	−0.773584	−0.386792	−	0.922167i	$-0.626417\pi$
$227$	−11.6552	−0.773584	−0.386792	+	0.922167i	$0.626417\pi$
$228$	−1.34597	−0.0891392
$229$	−5.91727	−0.391024	−0.195512	−	0.980701i	$-0.562637\pi$
$229$	−5.91727	−0.391024	−0.195512	+	0.980701i	$0.562637\pi$
$230$	0	0
$231$	−2.35677	−0.155064
$232$	−7.03927	−0.462151
$233$	−19.8087	−1.29771	−0.648854	−	0.760913i	$-0.724751\pi$
$233$	−19.8087	−1.29771	−0.648854	+	0.760913i	$0.724751\pi$
$234$	5.33641	0.348852
$235$	0	0
$236$	−2.62810	−0.171075
$237$	−6.82402	−0.443268
$238$	6.76266	0.438358
$239$	11.0911	0.717424	0.358712	−	0.933448i	$-0.383216\pi$
$239$	11.0911	0.717424	0.358712	+	0.933448i	$0.383216\pi$
$240$	0	0
$241$	17.1624	1.10553	0.552764	−	0.833338i	$-0.313573\pi$
$241$	17.1624	1.10553	0.552764	+	0.833338i	$0.313573\pi$
$242$	−9.34453	−0.600689
$243$	−12.7059	−0.815083
$244$	5.76894	0.369319
$245$	0	0
$246$	−18.0072	−1.14810
$247$	6.71441	0.427228
$248$	7.63195	0.484629
$249$	15.1593	0.960682
$250$	0	0
$251$	12.4425	0.785364	0.392682	−	0.919674i	$-0.371547\pi$
$251$	12.4425	0.785364	0.392682	+	0.919674i	$0.371547\pi$
$252$	−0.680188	−0.0428478
$253$	1.83173	0.115160
$254$	−9.00637	−0.565110
$255$	0	0
$256$	−11.2988	−0.706176
$257$	5.76924	0.359876	0.179938	−	0.983678i	$-0.442410\pi$
$257$	5.76924	0.359876	0.179938	+	0.983678i	$0.442410\pi$
$258$	−6.04542	−0.376371
$259$	7.37033	0.457970
$260$	0	0
$261$	−3.09000	−0.191266
$262$	24.4189	1.50860
$263$	9.57794	0.590601	0.295301	−	0.955404i	$-0.404580\pi$
$263$	9.57794	0.590601	0.295301	+	0.955404i	$0.404580\pi$
$264$	−7.21888	−0.444291
$265$	0	0
$266$	2.52772	0.154984
$267$	16.0180	0.980285
$268$	6.82434	0.416863
$269$	−6.93406	−0.422777	−0.211388	−	0.977402i	$-0.567799\pi$
$269$	−6.93406	−0.422777	−0.211388	+	0.977402i	$0.567799\pi$
$270$	0	0
$271$	13.6107	0.826789	0.413395	−	0.910552i	$-0.364343\pi$
$271$	13.6107	0.826789	0.413395	+	0.910552i	$0.364343\pi$
$272$	15.1167	0.916586
$273$	−4.17762	−0.252841
$274$	17.5299	1.05902
$275$	0	0
$276$	−0.650880	−0.0391784
$277$	−4.68173	−0.281298	−0.140649	−	0.990060i	$-0.544919\pi$
$277$	−4.68173	−0.281298	−0.140649	+	0.990060i	$0.544919\pi$
$278$	−7.19291	−0.431402
$279$	3.35016	0.200569
$280$	0	0
$281$	−18.3490	−1.09461	−0.547306	−	0.836933i	$-0.684347\pi$
$281$	−18.3490	−1.09461	−0.547306	+	0.836933i	$0.684347\pi$
$282$	−9.04744	−0.538767
$283$	0.485253	0.0288453	0.0144227	−	0.999896i	$-0.495409\pi$
$283$	0.485253	0.0288453	0.0144227	+	0.999896i	$0.495409\pi$
$284$	2.37229	0.140769
$285$	0	0
$286$	7.26988	0.429877
$287$	−11.4498	−0.675859
$288$	−3.74629	−0.220752
$289$	13.6090	0.800528
$290$	0	0
$291$	12.0521	0.706504
$292$	−6.95755	−0.407160
$293$	−27.8795	−1.62874	−0.814369	−	0.580347i	$-0.802917\pi$
$293$	−27.8795	−1.62874	−0.814369	+	0.580347i	$0.802917\pi$
$294$	−1.57271	−0.0917223
$295$	0	0
$296$	22.5756	1.31218
$297$	−10.2391	−0.594135
$298$	−23.6478	−1.36988
$299$	3.24693	0.187775
$300$	0	0
$301$	−3.84395	−0.221562
$302$	15.2709	0.878743
$303$	−21.7191	−1.24773
$304$	5.65026	0.324065
$305$	0	0
$306$	9.09286	0.519804
$307$	11.9358	0.681209	0.340605	−	0.940207i	$-0.389368\pi$
$307$	11.9358	0.681209	0.340605	+	0.940207i	$0.389368\pi$
$308$	−0.926631	−0.0527997
$309$	15.0499	0.856157
$310$	0	0
$311$	−13.2818	−0.753142	−0.376571	−	0.926388i	$-0.622897\pi$
$311$	−13.2818	−0.753142	−0.376571	+	0.926388i	$0.622897\pi$
$312$	−12.7962	−0.724443
$313$	−32.8495	−1.85676	−0.928382	−	0.371628i	$-0.878800\pi$
$313$	−32.8495	−1.85676	−0.928382	+	0.371628i	$0.878800\pi$
$314$	7.20316	0.406498
$315$	0	0
$316$	−2.68306	−0.150934
$317$	−3.92301	−0.220338	−0.110169	−	0.993913i	$-0.535139\pi$
$317$	−3.92301	−0.220338	−0.110169	+	0.993913i	$0.535139\pi$
$318$	−4.22581	−0.236972
$319$	−4.20955	−0.235690
$320$	0	0
$321$	0.334956	0.0186954
$322$	1.22234	0.0681185
$323$	11.4409	0.636588
$324$	1.59778	0.0887655
$325$	0	0
$326$	−19.3291	−1.07054
$327$	−15.9489	−0.881976
$328$	−35.0712	−1.93648
$329$	−5.75277	−0.317161
$330$	0	0
$331$	−29.3199	−1.61157	−0.805783	−	0.592211i	$-0.798255\pi$
$331$	−29.3199	−1.61157	−0.805783	+	0.592211i	$0.798255\pi$
$332$	5.96032	0.327115
$333$	9.90991	0.543060
$334$	−13.9055	−0.760877
$335$	0	0
$336$	−3.51552	−0.191787
$337$	−25.7628	−1.40339	−0.701695	−	0.712477i	$-0.747573\pi$
$337$	−25.7628	−1.40339	−0.701695	+	0.712477i	$0.747573\pi$
$338$	−3.00385	−0.163388
$339$	−17.0166	−0.924217
$340$	0	0
$341$	4.56398	0.247153
$342$	3.39869	0.183780
$343$	−1.00000	−0.0539949
$344$	−11.7742	−0.634822
$345$	0	0
$346$	3.55772	0.191264
$347$	−5.39327	−0.289526	−0.144763	−	0.989466i	$-0.546242\pi$
$347$	−5.39327	−0.289526	−0.144763	+	0.989466i	$0.546242\pi$
$348$	1.49581	0.0801837
$349$	10.7377	0.574773	0.287387	−	0.957815i	$-0.407214\pi$
$349$	10.7377	0.574773	0.287387	+	0.957815i	$0.407214\pi$
$350$	0	0
$351$	−18.1499	−0.968772
$352$	−5.10363	−0.272024
$353$	12.4467	0.662470	0.331235	−	0.943548i	$-0.392535\pi$
$353$	12.4467	0.662470	0.331235	+	0.943548i	$0.392535\pi$
$354$	−8.17043	−0.434253
$355$	0	0
$356$	6.29794	0.333790
$357$	−7.11836	−0.376744
$358$	13.0316	0.688740
$359$	28.0071	1.47816	0.739080	−	0.673618i	$-0.235261\pi$
$359$	28.0071	1.47816	0.739080	+	0.673618i	$0.235261\pi$
$360$	0	0
$361$	−14.7237	−0.774931
$362$	25.8471	1.35850
$363$	9.83604	0.516258
$364$	−1.64255	−0.0860930
$365$	0	0
$366$	17.9349	0.937473
$367$	−14.2872	−0.745788	−0.372894	−	0.927874i	$-0.621634\pi$
$367$	−14.2872	−0.745788	−0.372894	+	0.927874i	$0.621634\pi$
$368$	2.73233	0.142433
$369$	−15.3950	−0.801433
$370$	0	0
$371$	−2.68696	−0.139500
$372$	−1.62175	−0.0840838
$373$	14.3470	0.742862	0.371431	−	0.928461i	$-0.378867\pi$
$373$	14.3470	0.742862	0.371431	+	0.928461i	$0.378867\pi$
$374$	12.3874	0.640535
$375$	0	0
$376$	−17.6210	−0.908733
$377$	−7.46187	−0.384306
$378$	−6.83275	−0.351439
$379$	16.1205	0.828057	0.414028	−	0.910264i	$-0.364121\pi$
$379$	16.1205	0.828057	0.414028	+	0.910264i	$0.364121\pi$
$380$	0	0
$381$	9.48009	0.485680
$382$	−13.4588	−0.688613
$383$	33.2713	1.70008	0.850041	−	0.526716i	$-0.176577\pi$
$383$	33.2713	1.70008	0.850041	+	0.526716i	$0.176577\pi$
$384$	−6.78082	−0.346032
$385$	0	0
$386$	9.62085	0.489689
$387$	−5.16846	−0.262727
$388$	4.73861	0.240567
$389$	−22.6075	−1.14625	−0.573123	−	0.819469i	$-0.694268\pi$
$389$	−22.6075	−1.14625	−0.573123	+	0.819469i	$0.694268\pi$
$390$	0	0
$391$	5.53254	0.279792
$392$	−3.06304	−0.154707
$393$	−25.7032	−1.29656
$394$	−8.09281	−0.407710
$395$	0	0
$396$	−1.24592	−0.0626098
$397$	21.9272	1.10050	0.550248	−	0.835001i	$-0.314533\pi$
$397$	21.9272	1.10050	0.550248	+	0.835001i	$0.314533\pi$
$398$	27.1603	1.36143
$399$	−2.66067	−0.133200
$400$	0	0
$401$	−3.61845	−0.180697	−0.0903483	−	0.995910i	$-0.528798\pi$
$401$	−3.61845	−0.180697	−0.0903483	+	0.995910i	$0.528798\pi$
$402$	21.2160	1.05816
$403$	8.09013	0.402998
$404$	−8.53950	−0.424856
$405$	0	0
$406$	−2.80910	−0.139414
$407$	13.5004	0.669192
$408$	−21.8038	−1.07945
$409$	27.0595	1.33801	0.669003	−	0.743259i	$-0.266721\pi$
$409$	27.0595	1.33801	0.669003	+	0.743259i	$0.266721\pi$
$410$	0	0
$411$	−18.4519	−0.910166
$412$	5.91729	0.291524
$413$	−5.19513	−0.255636
$414$	1.64352	0.0807748
$415$	0	0
$416$	−9.04672	−0.443552
$417$	7.57124	0.370765
$418$	4.63009	0.226465
$419$	16.2266	0.792724	0.396362	−	0.918094i	$-0.370273\pi$
$419$	16.2266	0.792724	0.396362	+	0.918094i	$0.370273\pi$
$420$	0	0
$421$	−28.0320	−1.36619	−0.683097	−	0.730328i	$-0.739367\pi$
$421$	−28.0320	−1.36619	−0.683097	+	0.730328i	$0.739367\pi$
$422$	19.9879	0.972994
$423$	−7.73500	−0.376088
$424$	−8.23028	−0.399698
$425$	0	0
$426$	7.37515	0.357327
$427$	11.4038	0.551870
$428$	0.131698	0.00636584
$429$	−7.65226	−0.369454
$430$	0	0
$431$	9.31498	0.448687	0.224343	−	0.974510i	$-0.427976\pi$
$431$	9.31498	0.448687	0.224343	+	0.974510i	$0.427976\pi$
$432$	−15.2734	−0.734842
$433$	−3.91036	−0.187920	−0.0939600	−	0.995576i	$-0.529953\pi$
$433$	−3.91036	−0.187920	−0.0939600	+	0.995576i	$0.529953\pi$
$434$	3.04562	0.146194
$435$	0	0
$436$	−6.27077	−0.300315
$437$	2.06793	0.0989223
$438$	−21.6302	−1.03353
$439$	24.9948	1.19294	0.596469	−	0.802636i	$-0.296570\pi$
$439$	24.9948	1.19294	0.596469	+	0.802636i	$0.296570\pi$
$440$	0	0
$441$	−1.34457	−0.0640271
$442$	21.9579	1.04443
$443$	−22.6965	−1.07834	−0.539171	−	0.842196i	$-0.681262\pi$
$443$	−22.6965	−1.07834	−0.539171	+	0.842196i	$0.681262\pi$
$444$	−4.79720	−0.227665
$445$	0	0
$446$	24.4651	1.15846
$447$	24.8916	1.17733
$448$	−8.87040	−0.419087
$449$	11.1526	0.526323	0.263161	−	0.964752i	$-0.415235\pi$
$449$	11.1526	0.526323	0.263161	+	0.964752i	$0.415235\pi$
$450$	0	0
$451$	−20.9729	−0.987575
$452$	−6.69058	−0.314699
$453$	−16.0741	−0.755229
$454$	−14.2467	−0.668629
$455$	0	0
$456$	−8.14974	−0.381646
$457$	−22.3240	−1.04427	−0.522136	−	0.852862i	$-0.674865\pi$
$457$	−22.3240	−1.04427	−0.522136	+	0.852862i	$0.674865\pi$
$458$	−7.23294	−0.337973
$459$	−30.9262	−1.44351
$460$	0	0
$461$	1.79562	0.0836303	0.0418151	−	0.999125i	$-0.486686\pi$
$461$	1.79562	0.0836303	0.0418151	+	0.999125i	$0.486686\pi$
$462$	−2.88078	−0.134026
$463$	−16.5492	−0.769106	−0.384553	−	0.923103i	$-0.625644\pi$
$463$	−16.5492	−0.769106	−0.384553	+	0.923103i	$0.625644\pi$
$464$	−6.27926	−0.291507
$465$	0	0
$466$	−24.2130	−1.12164
$467$	13.8185	0.639446	0.319723	−	0.947511i	$-0.396410\pi$
$467$	13.8185	0.639446	0.319723	+	0.947511i	$0.396410\pi$
$468$	−2.20852	−0.102089
$469$	13.4901	0.622915
$470$	0	0
$471$	−7.58203	−0.349361
$472$	−15.9129	−0.732450
$473$	−7.04107	−0.323749
$474$	−8.34129	−0.383128
$475$	0	0
$476$	−2.79879	−0.128282
$477$	−3.61281	−0.165419
$478$	13.5571	0.620089
$479$	37.2072	1.70004	0.850020	−	0.526750i	$-0.176590\pi$
$479$	37.2072	1.70004	0.850020	+	0.526750i	$0.176590\pi$
$480$	0	0
$481$	23.9309	1.09116
$482$	20.9784	0.955538
$483$	−1.28664	−0.0585439
$484$	3.86732	0.175787
$485$	0	0
$486$	−15.5309	−0.704498
$487$	−8.57640	−0.388634	−0.194317	−	0.980939i	$-0.562249\pi$
$487$	−8.57640	−0.388634	−0.194317	+	0.980939i	$0.562249\pi$
$488$	34.9304	1.58123
$489$	20.3458	0.920069
$490$	0	0
$491$	−3.32697	−0.150144	−0.0750720	−	0.997178i	$-0.523919\pi$
$491$	−3.32697	−0.150144	−0.0750720	+	0.997178i	$0.523919\pi$
$492$	7.45244	0.335982
$493$	−12.7145	−0.572632
$494$	8.20731	0.369264
$495$	0	0
$496$	6.80794	0.305686
$497$	4.68945	0.210351
$498$	18.5299	0.830344
$499$	26.9826	1.20791	0.603954	−	0.797019i	$-0.293591\pi$
$499$	26.9826	1.20791	0.603954	+	0.797019i	$0.293591\pi$
$500$	0	0
$501$	14.6369	0.653930
$502$	15.2090	0.678811
$503$	1.73343	0.0772897	0.0386449	−	0.999253i	$-0.487696\pi$
$503$	1.73343	0.0772897	0.0386449	+	0.999253i	$0.487696\pi$
$504$	−4.11847	−0.183451
$505$	0	0
$506$	2.23900	0.0995357
$507$	3.16184	0.140422
$508$	3.72737	0.165375
$509$	−14.2686	−0.632444	−0.316222	−	0.948685i	$-0.602414\pi$
$509$	−14.2686	−0.632444	−0.316222	+	0.948685i	$0.602414\pi$
$510$	0	0
$511$	−13.7534	−0.608416
$512$	−24.3514	−1.07619
$513$	−11.5595	−0.510362
$514$	7.05200	0.311050
$515$	0	0
$516$	2.50195	0.110142
$517$	−10.5375	−0.463439
$518$	9.00907	0.395836
$519$	−3.74484	−0.164380
$520$	0	0
$521$	−10.9174	−0.478300	−0.239150	−	0.970983i	$-0.576869\pi$
$521$	−10.9174	−0.478300	−0.239150	+	0.970983i	$0.576869\pi$
$522$	−3.77703	−0.165316
$523$	29.9714	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$523$	29.9714	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$524$	−10.1060	−0.441481
$525$	0	0
$526$	11.7075	0.510473
$527$	13.7850	0.600484
$528$	−6.43947	−0.280242
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.98521	−0.303132
$532$	−1.04612	−0.0453550
$533$	−37.1766	−1.61030
$534$	19.5795	0.847287
$535$	0	0
$536$	41.3208	1.78478
$537$	−13.7170	−0.591933
$538$	−8.47580	−0.365418
$539$	−1.83173	−0.0788981
$540$	0	0
$541$	−16.6528	−0.715962	−0.357981	−	0.933729i	$-0.616535\pi$
$541$	−16.6528	−0.715962	−0.357981	+	0.933729i	$0.616535\pi$
$542$	16.6369	0.714616
$543$	−27.2066	−1.16755
$544$	−15.4150	−0.660911
$545$	0	0
$546$	−5.10648	−0.218537
$547$	−32.1095	−1.37290	−0.686451	−	0.727176i	$-0.740832\pi$
$547$	−32.1095	−1.37290	−0.686451	+	0.727176i	$0.740832\pi$
$548$	−7.25490	−0.309914
$549$	15.3332	0.654407
$550$	0	0
$551$	−4.75237	−0.202458
$552$	−3.94102	−0.167741
$553$	−5.30377	−0.225539
$554$	−5.72268	−0.243134
$555$	0	0
$556$	2.97685	0.126247
$557$	12.5917	0.533529	0.266765	−	0.963762i	$-0.414045\pi$
$557$	12.5917	0.533529	0.266765	+	0.963762i	$0.414045\pi$
$558$	4.09504	0.173357
$559$	−12.4810	−0.527892
$560$	0	0
$561$	−13.0389	−0.550503
$562$	−22.4288	−0.946102
$563$	−26.3644	−1.11113	−0.555563	−	0.831474i	$-0.687497\pi$
$563$	−26.3644	−1.11113	−0.555563	+	0.831474i	$0.687497\pi$
$564$	3.74437	0.157666
$565$	0	0
$566$	0.593146	0.0249318
$567$	3.15843	0.132642
$568$	14.3640	0.602699
$569$	−25.7791	−1.08071	−0.540357	−	0.841436i	$-0.681711\pi$
$569$	−25.7791	−1.08071	−0.540357	+	0.841436i	$0.681711\pi$
$570$	0	0
$571$	41.2960	1.72818	0.864092	−	0.503334i	$-0.167893\pi$
$571$	41.2960	1.72818	0.864092	+	0.503334i	$0.167893\pi$
$572$	−3.00870	−0.125800
$573$	14.1667	0.591823
$574$	−13.9956	−0.584163
$575$	0	0
$576$	−11.9269	−0.496953
$577$	−10.2107	−0.425076	−0.212538	−	0.977153i	$-0.568173\pi$
$577$	−10.2107	−0.425076	−0.212538	+	0.977153i	$0.568173\pi$
$578$	16.6348	0.691918
$579$	−10.1269	−0.420859
$580$	0	0
$581$	11.7821	0.488805
$582$	14.7317	0.610650
$583$	−4.92178	−0.203839
$584$	−42.1273	−1.74324
$585$	0	0
$586$	−34.0783	−1.40776
$587$	10.4814	0.432612	0.216306	−	0.976326i	$-0.430599\pi$
$587$	10.4814	0.432612	0.216306	+	0.976326i	$0.430599\pi$
$588$	0.650880	0.0268419
$589$	5.15249	0.212305
$590$	0	0
$591$	8.51848	0.350403
$592$	20.1382	0.827674
$593$	8.27127	0.339660	0.169830	−	0.985473i	$-0.445678\pi$
$593$	8.27127	0.339660	0.169830	+	0.985473i	$0.445678\pi$
$594$	−12.5157	−0.513527
$595$	0	0
$596$	9.78686	0.400885
$597$	−28.5889	−1.17007
$598$	3.96886	0.162299
$599$	−21.5408	−0.880132	−0.440066	−	0.897965i	$-0.645045\pi$
$599$	−21.5408	−0.880132	−0.440066	+	0.897965i	$0.645045\pi$
$600$	0	0
$601$	27.9173	1.13877	0.569385	−	0.822071i	$-0.307181\pi$
$601$	27.9173	1.13877	0.569385	+	0.822071i	$0.307181\pi$
$602$	−4.69863	−0.191502
$603$	18.1384	0.738652
$604$	−6.32001	−0.257157
$605$	0	0
$606$	−26.5482	−1.07845
$607$	12.0650	0.489705	0.244852	−	0.969560i	$-0.421261\pi$
$607$	12.0650	0.489705	0.244852	+	0.969560i	$0.421261\pi$
$608$	−5.76173	−0.233669
$609$	2.95686	0.119818
$610$	0	0
$611$	−18.6788	−0.755665
$612$	−3.76316	−0.152117
$613$	−18.2200	−0.735900	−0.367950	−	0.929846i	$-0.619940\pi$
$613$	−18.2200	−0.735900	−0.367950	+	0.929846i	$0.619940\pi$
$614$	14.5896	0.588788
$615$	0	0
$616$	−5.61066	−0.226060
$617$	2.56162	0.103127	0.0515634	−	0.998670i	$-0.483580\pi$
$617$	2.56162	0.103127	0.0515634	+	0.998670i	$0.483580\pi$
$618$	18.3961	0.740000
$619$	−4.51140	−0.181328	−0.0906642	−	0.995882i	$-0.528899\pi$
$619$	−4.51140	−0.181328	−0.0906642	+	0.995882i	$0.528899\pi$
$620$	0	0
$621$	−5.58988	−0.224314
$622$	−16.2349	−0.650961
$623$	12.4495	0.498779
$624$	−11.4146	−0.456951
$625$	0	0
$626$	−40.1534	−1.60485
$627$	−4.87362	−0.194634
$628$	−2.98109	−0.118959
$629$	40.7766	1.62587
$630$	0	0
$631$	−1.72514	−0.0686766	−0.0343383	−	0.999410i	$-0.510932\pi$
$631$	−1.72514	−0.0686766	−0.0343383	+	0.999410i	$0.510932\pi$
$632$	−16.2457	−0.646218
$633$	−21.0392	−0.836232
$634$	−4.79526	−0.190444
$635$	0	0
$636$	1.74889	0.0693480
$637$	−3.24693	−0.128648
$638$	−5.14552	−0.203713
$639$	6.30529	0.249433
$640$	0	0
$641$	−6.13847	−0.242455	−0.121227	−	0.992625i	$-0.538683\pi$
$641$	−6.13847	−0.242455	−0.121227	+	0.992625i	$0.538683\pi$
$642$	0.409431	0.0161590
$643$	−1.81209	−0.0714620	−0.0357310	−	0.999361i	$-0.511376\pi$
$643$	−1.81209	−0.0714620	−0.0357310	+	0.999361i	$0.511376\pi$
$644$	−0.505878	−0.0199344
$645$	0	0
$646$	13.9847	0.550220
$647$	3.41295	0.134177	0.0670885	−	0.997747i	$-0.478629\pi$
$647$	3.41295	0.134177	0.0670885	+	0.997747i	$0.478629\pi$
$648$	9.67440	0.380046
$649$	−9.51606	−0.373538
$650$	0	0
$651$	−3.20581	−0.125646
$652$	7.99954	0.313286
$653$	2.90584	0.113714	0.0568572	−	0.998382i	$-0.481892\pi$
$653$	2.90584	0.113714	0.0568572	+	0.998382i	$0.481892\pi$
$654$	−19.4950	−0.762315
$655$	0	0
$656$	−31.2846	−1.22146
$657$	−18.4924	−0.721458
$658$	−7.03186	−0.274130
$659$	−31.6685	−1.23363	−0.616814	−	0.787109i	$-0.711577\pi$
$659$	−31.6685	−1.23363	−0.616814	+	0.787109i	$0.711577\pi$
$660$	0	0
$661$	−2.28949	−0.0890508	−0.0445254	−	0.999008i	$-0.514178\pi$
$661$	−2.28949	−0.0890508	−0.0445254	+	0.999008i	$0.514178\pi$
$662$	−35.8389	−1.39292
$663$	−23.1128	−0.897627
$664$	36.0892	1.40053
$665$	0	0
$666$	12.1133	0.469381
$667$	−2.29813	−0.0889840
$668$	5.75493	0.222665
$669$	−25.7519	−0.995628
$670$	0	0
$671$	20.8887	0.806400
$672$	3.58487	0.138289
$673$	37.1348	1.43144	0.715721	−	0.698386i	$-0.246098\pi$
$673$	37.1348	1.43144	0.715721	+	0.698386i	$0.246098\pi$
$674$	−31.4910	−1.21299
$675$	0	0
$676$	1.24317	0.0478142
$677$	20.5072	0.788154	0.394077	−	0.919077i	$-0.371064\pi$
$677$	20.5072	0.788154	0.394077	+	0.919077i	$0.371064\pi$
$678$	−20.8002	−0.798826
$679$	9.36711	0.359477
$680$	0	0
$681$	14.9960	0.574648
$682$	5.57875	0.213621
$683$	36.7749	1.40715	0.703577	−	0.710619i	$-0.251585\pi$
$683$	36.7749	1.40715	0.703577	+	0.710619i	$0.251585\pi$
$684$	−1.40658	−0.0537818
$685$	0	0
$686$	−1.22234	−0.0466693
$687$	7.61338	0.290468
$688$	−10.5030	−0.400421
$689$	−8.72438	−0.332372
$690$	0	0
$691$	−4.44402	−0.169059	−0.0845293	−	0.996421i	$-0.526939\pi$
$691$	−4.44402	−0.169059	−0.0845293	+	0.996421i	$0.526939\pi$
$692$	−1.47239	−0.0559720
$693$	−2.46288	−0.0935573
$694$	−6.59242	−0.250245
$695$	0	0
$696$	9.05698	0.343304
$697$	−63.3463	−2.39941
$698$	13.1251	0.496792
$699$	25.4865	0.963989
$700$	0	0
$701$	5.33291	0.201421	0.100711	−	0.994916i	$-0.467888\pi$
$701$	5.33291	0.201421	0.100711	+	0.994916i	$0.467888\pi$
$702$	−22.1854	−0.837336
$703$	15.2413	0.574836
$704$	−16.2482	−0.612376
$705$	0	0
$706$	15.2141	0.572591
$707$	−16.8806	−0.634859
$708$	3.38141	0.127081
$709$	−17.4747	−0.656276	−0.328138	−	0.944630i	$-0.606421\pi$
$709$	−17.4747	−0.656276	−0.328138	+	0.944630i	$0.606421\pi$
$710$	0	0
$711$	−7.13128	−0.267444
$712$	38.1334	1.42911
$713$	2.49162	0.0933120
$714$	−8.70108	−0.325630
$715$	0	0
$716$	−5.39324	−0.201555
$717$	−14.2702	−0.532930
$718$	34.2343	1.27761
$719$	20.0248	0.746797	0.373399	−	0.927671i	$-0.378192\pi$
$719$	20.0248	0.746797	0.373399	+	0.927671i	$0.378192\pi$
$720$	0	0
$721$	11.6971	0.435622
$722$	−17.9974	−0.669793
$723$	−22.0818	−0.821230
$724$	−10.6971	−0.397554
$725$	0	0
$726$	12.0230	0.446216
$727$	21.4754	0.796479	0.398240	−	0.917281i	$-0.369621\pi$
$727$	21.4754	0.796479	0.398240	+	0.917281i	$0.369621\pi$
$728$	−9.94548	−0.368604
$729$	25.8231	0.956412
$730$	0	0
$731$	−21.2668	−0.786581
$732$	−7.42253	−0.274345
$733$	−15.8543	−0.585594	−0.292797	−	0.956175i	$-0.594586\pi$
$733$	−15.8543	−0.585594	−0.292797	+	0.956175i	$0.594586\pi$
$734$	−17.4639	−0.644605
$735$	0	0
$736$	−2.78624	−0.102702
$737$	24.7102	0.910212
$738$	−18.8180	−0.692700
$739$	−8.79859	−0.323661	−0.161831	−	0.986819i	$-0.551740\pi$
$739$	−8.79859	−0.323661	−0.161831	+	0.986819i	$0.551740\pi$
$740$	0	0
$741$	−8.63900	−0.317362
$742$	−3.28439	−0.120574
$743$	−33.6377	−1.23405	−0.617024	−	0.786945i	$-0.711662\pi$
$743$	−33.6377	−1.23405	−0.617024	+	0.786945i	$0.711662\pi$
$744$	−9.81954	−0.360002
$745$	0	0
$746$	17.5370	0.642076
$747$	15.8419	0.579624
$748$	−5.12662	−0.187448
$749$	0.260335	0.00951243
$750$	0	0
$751$	−15.6386	−0.570662	−0.285331	−	0.958429i	$-0.592104\pi$
$751$	−15.6386	−0.570662	−0.285331	+	0.958429i	$0.592104\pi$
$752$	−15.7185	−0.573194
$753$	−16.0090	−0.583399
$754$	−9.12096	−0.332166
$755$	0	0
$756$	2.82779	0.102846
$757$	8.01891	0.291452	0.145726	−	0.989325i	$-0.453448\pi$
$757$	8.01891	0.291452	0.145726	+	0.989325i	$0.453448\pi$
$758$	19.7048	0.715712
$759$	−2.35677	−0.0855452
$760$	0	0
$761$	−24.9368	−0.903960	−0.451980	−	0.892028i	$-0.649282\pi$
$761$	−24.9368	−0.903960	−0.451980	+	0.892028i	$0.649282\pi$
$762$	11.5879	0.419786
$763$	−12.3958	−0.448758
$764$	5.57005	0.201517
$765$	0	0
$766$	40.6689	1.46943
$767$	−16.8682	−0.609076
$768$	14.5375	0.524575
$769$	49.2378	1.77556	0.887781	−	0.460266i	$-0.152246\pi$
$769$	49.2378	1.77556	0.887781	+	0.460266i	$0.152246\pi$
$770$	0	0
$771$	−7.42292	−0.267330
$772$	−3.98168	−0.143304
$773$	11.9397	0.429439	0.214720	−	0.976676i	$-0.431116\pi$
$773$	11.9397	0.429439	0.214720	+	0.976676i	$0.431116\pi$
$774$	−6.31763	−0.227082
$775$	0	0
$776$	28.6918	1.02998
$777$	−9.48293	−0.340198
$778$	−27.6341	−0.990732
$779$	−23.6773	−0.848327
$780$	0	0
$781$	8.58980	0.307367
$782$	6.76266	0.241832
$783$	12.8463	0.459088
$784$	−2.73233	−0.0975833
$785$	0	0
$786$	−31.4182	−1.12065
$787$	−29.9433	−1.06736	−0.533681	−	0.845686i	$-0.679192\pi$
$787$	−29.9433	−1.06736	−0.533681	+	0.845686i	$0.679192\pi$
$788$	3.34928	0.119313
$789$	−12.3233	−0.438722
$790$	0	0
$791$	−13.2257	−0.470251
$792$	−7.54392	−0.268061
$793$	37.0274	1.31488
$794$	26.8026	0.951188
$795$	0	0
$796$	−11.2406	−0.398411
$797$	26.6201	0.942933	0.471467	−	0.881884i	$-0.343725\pi$
$797$	26.6201	0.942933	0.471467	+	0.881884i	$0.343725\pi$
$798$	−3.25225	−0.115128
$799$	−31.8274	−1.12597
$800$	0	0
$801$	16.7392	0.591452
$802$	−4.42298	−0.156181
$803$	−25.1925	−0.889025
$804$	−8.78044	−0.309662
$805$	0	0
$806$	9.88891	0.348322
$807$	8.92161	0.314055
$808$	−51.7059	−1.81901
$809$	−51.3101	−1.80397	−0.901984	−	0.431770i	$-0.857889\pi$
$809$	−51.3101	−1.80397	−0.901984	+	0.431770i	$0.857889\pi$
$810$	0	0
$811$	7.55071	0.265141	0.132571	−	0.991174i	$-0.457677\pi$
$811$	7.55071	0.265141	0.132571	+	0.991174i	$0.457677\pi$
$812$	1.16257	0.0407983
$813$	−17.5120	−0.614172
$814$	16.5022	0.578401
$815$	0	0
$816$	−19.4497	−0.680876
$817$	−7.94901	−0.278101
$818$	33.0760	1.15648
$819$	−4.36572	−0.152551
$820$	0	0
$821$	−30.3218	−1.05824	−0.529119	−	0.848548i	$-0.677478\pi$
$821$	−30.3218	−1.05824	−0.529119	+	0.848548i	$0.677478\pi$
$822$	−22.5546	−0.786681
$823$	−10.7919	−0.376182	−0.188091	−	0.982152i	$-0.560230\pi$
$823$	−10.7919	−0.376182	−0.188091	+	0.982152i	$0.560230\pi$
$824$	35.8286	1.24815
$825$	0	0
$826$	−6.35023	−0.220953
$827$	49.8826	1.73459	0.867293	−	0.497797i	$-0.165858\pi$
$827$	49.8826	1.73459	0.867293	+	0.497797i	$0.165858\pi$
$828$	−0.680188	−0.0236382
$829$	−31.6939	−1.10078	−0.550388	−	0.834909i	$-0.685520\pi$
$829$	−31.6939	−1.10078	−0.550388	+	0.834909i	$0.685520\pi$
$830$	0	0
$831$	6.02368	0.208959
$832$	−28.8016	−0.998515
$833$	−5.53254	−0.191691
$834$	9.25465	0.320462
$835$	0	0
$836$	−1.91620	−0.0662733
$837$	−13.9279	−0.481418
$838$	19.8345	0.685172
$839$	1.58217	0.0546224	0.0273112	−	0.999627i	$-0.491305\pi$
$839$	1.58217	0.0546224	0.0273112	+	0.999627i	$0.491305\pi$
$840$	0	0
$841$	−23.7186	−0.817883
$842$	−34.2647	−1.18084
$843$	23.6085	0.813121
$844$	−8.27216	−0.284739
$845$	0	0
$846$	−9.45482	−0.325063
$847$	7.64477	0.262677
$848$	−7.34167	−0.252114
$849$	−0.624344	−0.0214274
$850$	0	0
$851$	7.37033	0.252652
$852$	−3.05227	−0.104569
$853$	15.6024	0.534215	0.267107	−	0.963667i	$-0.413932\pi$
$853$	15.6024	0.534215	0.267107	+	0.963667i	$0.413932\pi$
$854$	13.9394	0.476996
$855$	0	0
$856$	0.797416	0.0272551
$857$	−39.0023	−1.33229	−0.666147	−	0.745821i	$-0.732058\pi$
$857$	−39.0023	−1.33229	−0.666147	+	0.745821i	$0.732058\pi$
$858$	−9.35368	−0.319329
$859$	29.7529	1.01516	0.507578	−	0.861606i	$-0.330541\pi$
$859$	29.7529	1.01516	0.507578	+	0.861606i	$0.330541\pi$
$860$	0	0
$861$	14.7317	0.502055
$862$	11.3861	0.387812
$863$	27.6730	0.941999	0.471000	−	0.882133i	$-0.343893\pi$
$863$	27.6730	0.941999	0.471000	+	0.882133i	$0.343893\pi$
$864$	15.5747	0.529863
$865$	0	0
$866$	−4.77980	−0.162424
$867$	−17.5098	−0.594663
$868$	−1.26046	−0.0427827
$869$	−9.71506	−0.329561
$870$	0	0
$871$	43.8014	1.48415
$872$	−37.9689	−1.28579
$873$	12.5947	0.426267
$874$	2.52772	0.0855012
$875$	0	0
$876$	8.95184	0.302454
$877$	3.88233	0.131097	0.0655486	−	0.997849i	$-0.479120\pi$
$877$	3.88233	0.131097	0.0655486	+	0.997849i	$0.479120\pi$
$878$	30.5523	1.03109
$879$	35.8708	1.20989
$880$	0	0
$881$	−50.3839	−1.69748	−0.848739	−	0.528812i	$-0.822638\pi$
$881$	−50.3839	−1.69748	−0.848739	+	0.528812i	$0.822638\pi$
$882$	−1.64352	−0.0553403
$883$	0.536806	0.0180650	0.00903248	−	0.999959i	$-0.497125\pi$
$883$	0.536806	0.0180650	0.00903248	+	0.999959i	$0.497125\pi$
$884$	−9.08747	−0.305645
$885$	0	0
$886$	−27.7429	−0.932041
$887$	13.9844	0.469551	0.234776	−	0.972050i	$-0.424564\pi$
$887$	13.9844	0.469551	0.234776	+	0.972050i	$0.424564\pi$
$888$	−29.0466	−0.974740
$889$	7.36812	0.247119
$890$	0	0
$891$	5.78538	0.193818
$892$	−10.1251	−0.339014
$893$	−11.8963	−0.398095
$894$	30.4261	1.01760
$895$	0	0
$896$	−5.27020	−0.176065
$897$	−4.17762	−0.139487
$898$	13.6323	0.454915
$899$	−5.72608	−0.190975
$900$	0	0
$901$	−14.8657	−0.495249
$902$	−25.6361	−0.853587
$903$	4.94577	0.164585
$904$	−40.5108	−1.34737
$905$	0	0
$906$	−19.6481	−0.652765
$907$	30.0013	0.996176	0.498088	−	0.867126i	$-0.334036\pi$
$907$	30.0013	0.996176	0.498088	+	0.867126i	$0.334036\pi$
$908$	5.89611	0.195669
$909$	−22.6971	−0.752814
$910$	0	0
$911$	−23.0932	−0.765111	−0.382555	−	0.923933i	$-0.624956\pi$
$911$	−23.0932	−0.765111	−0.382555	+	0.923933i	$0.624956\pi$
$912$	−7.26983	−0.240728
$913$	21.5817	0.714249
$914$	−27.2876	−0.902593
$915$	0	0
$916$	2.99342	0.0989053
$917$	−19.9771	−0.659702
$918$	−37.8024	−1.24767
$919$	−22.8223	−0.752837	−0.376419	−	0.926450i	$-0.622845\pi$
$919$	−22.8223	−0.752837	−0.376419	+	0.926450i	$0.622845\pi$
$920$	0	0
$921$	−15.3570	−0.506029
$922$	2.19486	0.0722839
$923$	15.2263	0.501180
$924$	1.19224	0.0392217
$925$	0	0
$926$	−20.2288	−0.664759
$927$	15.7275	0.516559
$928$	6.40314	0.210193
$929$	24.1707	0.793015	0.396508	−	0.918031i	$-0.370222\pi$
$929$	24.1707	0.793015	0.396508	+	0.918031i	$0.370222\pi$
$930$	0	0
$931$	−2.06793	−0.0677736
$932$	10.0208	0.328241
$933$	17.0888	0.559463
$934$	16.8910	0.552690
$935$	0	0
$936$	−13.3724	−0.437090
$937$	26.9840	0.881530	0.440765	−	0.897622i	$-0.354707\pi$
$937$	26.9840	0.881530	0.440765	+	0.897622i	$0.354707\pi$
$938$	16.4895	0.538402
$939$	42.2653	1.37928
$940$	0	0
$941$	−19.4776	−0.634950	−0.317475	−	0.948267i	$-0.602835\pi$
$941$	−19.4776	−0.634950	−0.317475	+	0.948267i	$0.602835\pi$
$942$	−9.26784	−0.301962
$943$	−11.4498	−0.372856
$944$	−14.1948	−0.462002
$945$	0	0
$946$	−8.60661	−0.279825
$947$	37.7344	1.22620	0.613102	−	0.790004i	$-0.289921\pi$
$947$	37.7344	1.22620	0.613102	+	0.790004i	$0.289921\pi$
$948$	3.45212	0.112120
$949$	−44.6564	−1.44961
$950$	0	0
$951$	5.04748	0.163676
$952$	−16.9464	−0.549236
$953$	58.4372	1.89297	0.946483	−	0.322754i	$-0.104609\pi$
$953$	58.4372	1.89297	0.946483	+	0.322754i	$0.104609\pi$
$954$	−4.41609	−0.142976
$955$	0	0
$956$	−5.61074	−0.181464
$957$	5.41616	0.175080
$958$	45.4800	1.46939
$959$	−14.3412	−0.463102
$960$	0	0
$961$	−24.7918	−0.799736
$962$	29.2518	0.943116
$963$	0.350038	0.0112798
$964$	−8.68208	−0.279631
$965$	0	0
$966$	−1.57271	−0.0506011
$967$	37.3817	1.20211	0.601057	−	0.799206i	$-0.294747\pi$
$967$	37.3817	1.20211	0.601057	+	0.799206i	$0.294747\pi$
$968$	23.4163	0.752627
$969$	−14.7202	−0.472882
$970$	0	0
$971$	−1.35376	−0.0434442	−0.0217221	−	0.999764i	$-0.506915\pi$
$971$	−1.35376	−0.0434442	−0.0217221	+	0.999764i	$0.506915\pi$
$972$	6.42762	0.206166
$973$	5.88452	0.188649
$974$	−10.4833	−0.335907
$975$	0	0
$976$	31.1591	0.997377
$977$	7.23001	0.231308	0.115654	−	0.993290i	$-0.463104\pi$
$977$	7.23001	0.231308	0.115654	+	0.993290i	$0.463104\pi$
$978$	24.8696	0.795241
$979$	22.8041	0.728823
$980$	0	0
$981$	−16.6670	−0.532137
$982$	−4.06670	−0.129774
$983$	−17.0572	−0.544040	−0.272020	−	0.962292i	$-0.587692\pi$
$983$	−17.0572	−0.544040	−0.272020	+	0.962292i	$0.587692\pi$
$984$	45.1238	1.43849
$985$	0	0
$986$	−15.5415	−0.494941
$987$	7.40172	0.235599
$988$	−3.39667	−0.108063
$989$	−3.84395	−0.122231
$990$	0	0
$991$	19.7805	0.628348	0.314174	−	0.949365i	$-0.398272\pi$
$991$	19.7805	0.628348	0.314174	+	0.949365i	$0.398272\pi$
$992$	−6.94225	−0.220417
$993$	37.7240	1.19713
$994$	5.73212	0.181812
$995$	0	0
$996$	−7.66876	−0.242994
$997$	17.1094	0.541861	0.270931	−	0.962599i	$-0.412669\pi$
$997$	17.1094	0.541861	0.270931	+	0.962599i	$0.412669\pi$
$998$	32.9820	1.04403
$999$	−41.1992	−1.30349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.15		21
5.2	odd	4		805.2.c.c.484.28	yes	42
5.3	odd	4		805.2.c.c.484.15	✓	42
5.4	even	2		4025.2.a.be.1.7		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.15	✓	42	5.3	odd	4
805.2.c.c.484.28	yes	42	5.2	odd	4
4025.2.a.bd.1.15		21	1.1	even	1	trivial
4025.2.a.be.1.7		21	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.22234 q^{2} -1.28664 q^{3} -0.505878 q^{4} -1.57271 q^{6} -1.00000 q^{7} -3.06304 q^{8} -1.34457 q^{9} +O(q^{10})\)	\(q+1.22234 q^{2} -1.28664 q^{3} -0.505878 q^{4} -1.57271 q^{6} -1.00000 q^{7} -3.06304 q^{8} -1.34457 q^{9} -1.83173 q^{11} +0.650880 q^{12} -3.24693 q^{13} -1.22234 q^{14} -2.73233 q^{16} -5.53254 q^{17} -1.64352 q^{18} -2.06793 q^{19} +1.28664 q^{21} -2.23900 q^{22} -1.00000 q^{23} +3.94102 q^{24} -3.96886 q^{26} +5.58988 q^{27} +0.505878 q^{28} +2.29813 q^{29} -2.49162 q^{31} +2.78624 q^{32} +2.35677 q^{33} -6.76266 q^{34} +0.680188 q^{36} -7.37033 q^{37} -2.52772 q^{38} +4.17762 q^{39} +11.4498 q^{41} +1.57271 q^{42} +3.84395 q^{43} +0.926631 q^{44} -1.22234 q^{46} +5.75277 q^{47} +3.51552 q^{48} +1.00000 q^{49} +7.11836 q^{51} +1.64255 q^{52} +2.68696 q^{53} +6.83275 q^{54} +3.06304 q^{56} +2.66067 q^{57} +2.80910 q^{58} +5.19513 q^{59} -11.4038 q^{61} -3.04562 q^{62} +1.34457 q^{63} +8.87040 q^{64} +2.88078 q^{66} -13.4901 q^{67} +2.79879 q^{68} +1.28664 q^{69} -4.68945 q^{71} +4.11847 q^{72} +13.7534 q^{73} -9.00907 q^{74} +1.04612 q^{76} +1.83173 q^{77} +5.10648 q^{78} +5.30377 q^{79} -3.15843 q^{81} +13.9956 q^{82} -11.7821 q^{83} -0.650880 q^{84} +4.69863 q^{86} -2.95686 q^{87} +5.61066 q^{88} -12.4495 q^{89} +3.24693 q^{91} +0.505878 q^{92} +3.20581 q^{93} +7.03186 q^{94} -3.58487 q^{96} -9.36711 q^{97} +1.22234 q^{98} +2.46288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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