LMFDB - Embedded newform 4025.2.a.bd.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.35921 q^{2} -2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} -1.00000 q^{7} -3.69426 q^{8} +3.28760 q^{9} +O(q^{10})$	\(q-2.35921 q^{2} -2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} -1.00000 q^{7} -3.69426 q^{8} +3.28760 q^{9} +2.70134 q^{11} -8.94150 q^{12} -2.80434 q^{13} +2.35921 q^{14} +1.58378 q^{16} +1.99885 q^{17} -7.75616 q^{18} -1.11683 q^{19} +2.50751 q^{21} -6.37305 q^{22} -1.00000 q^{23} +9.26340 q^{24} +6.61603 q^{26} -0.721167 q^{27} -3.56589 q^{28} -8.42950 q^{29} +2.48252 q^{31} +3.65206 q^{32} -6.77365 q^{33} -4.71571 q^{34} +11.7232 q^{36} -0.807977 q^{37} +2.63485 q^{38} +7.03190 q^{39} +6.79798 q^{41} -5.91575 q^{42} -3.15924 q^{43} +9.63269 q^{44} +2.35921 q^{46} +10.0740 q^{47} -3.97133 q^{48} +1.00000 q^{49} -5.01213 q^{51} -9.99995 q^{52} +4.86545 q^{53} +1.70139 q^{54} +3.69426 q^{56} +2.80047 q^{57} +19.8870 q^{58} -12.1768 q^{59} +9.43038 q^{61} -5.85680 q^{62} -3.28760 q^{63} -11.7835 q^{64} +15.9805 q^{66} -7.25984 q^{67} +7.12767 q^{68} +2.50751 q^{69} -2.44213 q^{71} -12.1453 q^{72} -1.70335 q^{73} +1.90619 q^{74} -3.98250 q^{76} -2.70134 q^{77} -16.5898 q^{78} +15.4751 q^{79} -8.05448 q^{81} -16.0379 q^{82} -10.7887 q^{83} +8.94150 q^{84} +7.45333 q^{86} +21.1371 q^{87} -9.97947 q^{88} -8.27944 q^{89} +2.80434 q^{91} -3.56589 q^{92} -6.22495 q^{93} -23.7668 q^{94} -9.15757 q^{96} +13.2465 q^{97} -2.35921 q^{98} +8.88095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35921	−1.66822	−0.834108	−	0.551601i	$-0.814017\pi$
$2$	−2.35921	−1.66822	−0.834108	+	0.551601i	$0.814017\pi$
$3$	−2.50751	−1.44771	−0.723856	−	0.689952i	$-0.757632\pi$
$3$	−2.50751	−1.44771	−0.723856	+	0.689952i	$0.757632\pi$
$4$	3.56589	1.78294
$5$	0	0
$5$	0	0
$6$	5.91575	2.41509
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.69426	−1.30612
$9$	3.28760	1.09587
$10$	0	0
$11$	2.70134	0.814486	0.407243	−	0.913320i	$-0.366490\pi$
$11$	2.70134	0.814486	0.407243	+	0.913320i	$0.366490\pi$
$12$	−8.94150	−2.58119
$13$	−2.80434	−0.777783	−0.388892	−	0.921283i	$-0.627142\pi$
$13$	−2.80434	−0.777783	−0.388892	+	0.921283i	$0.627142\pi$
$14$	2.35921	0.630526
$15$	0	0
$16$	1.58378	0.395944
$17$	1.99885	0.484792	0.242396	−	0.970177i	$-0.422067\pi$
$17$	1.99885	0.484792	0.242396	+	0.970177i	$0.422067\pi$
$18$	−7.75616	−1.82814
$19$	−1.11683	−0.256219	−0.128110	−	0.991760i	$-0.540891\pi$
$19$	−1.11683	−0.256219	−0.128110	+	0.991760i	$0.540891\pi$
$20$	0	0
$21$	2.50751	0.547183
$22$	−6.37305	−1.35874
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	9.26340	1.89088
$25$	0	0
$26$	6.61603	1.29751
$27$	−0.721167	−0.138789
$28$	−3.56589	−0.673889
$29$	−8.42950	−1.56532	−0.782659	−	0.622450i	$-0.786137\pi$
$29$	−8.42950	−1.56532	−0.782659	+	0.622450i	$0.786137\pi$
$30$	0	0
$31$	2.48252	0.445875	0.222937	−	0.974833i	$-0.428435\pi$
$31$	2.48252	0.445875	0.222937	+	0.974833i	$0.428435\pi$
$32$	3.65206	0.645598
$33$	−6.77365	−1.17914
$34$	−4.71571	−0.808738
$35$	0	0
$36$	11.7232	1.95387
$37$	−0.807977	−0.132831	−0.0664153	−	0.997792i	$-0.521156\pi$
$37$	−0.807977	−0.132831	−0.0664153	+	0.997792i	$0.521156\pi$
$38$	2.63485	0.427429
$39$	7.03190	1.12601
$40$	0	0
$41$	6.79798	1.06167	0.530833	−	0.847477i	$-0.321879\pi$
$41$	6.79798	1.06167	0.530833	+	0.847477i	$0.321879\pi$
$42$	−5.91575	−0.912820
$43$	−3.15924	−0.481780	−0.240890	−	0.970552i	$-0.577439\pi$
$43$	−3.15924	−0.481780	−0.240890	+	0.970552i	$0.577439\pi$
$44$	9.63269	1.45218
$45$	0	0
$46$	2.35921	0.347847
$47$	10.0740	1.46945	0.734724	−	0.678366i	$-0.237312\pi$
$47$	10.0740	1.46945	0.734724	+	0.678366i	$0.237312\pi$
$48$	−3.97133	−0.573213
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.01213	−0.701839
$52$	−9.99995	−1.38674
$53$	4.86545	0.668322	0.334161	−	0.942516i	$-0.391547\pi$
$53$	4.86545	0.668322	0.334161	+	0.942516i	$0.391547\pi$
$54$	1.70139	0.231530
$55$	0	0
$56$	3.69426	0.493666
$57$	2.80047	0.370931
$58$	19.8870	2.61129
$59$	−12.1768	−1.58528	−0.792642	−	0.609688i	$-0.791295\pi$
$59$	−12.1768	−1.58528	−0.792642	+	0.609688i	$0.791295\pi$
$60$	0	0
$61$	9.43038	1.20744	0.603718	−	0.797198i	$-0.293685\pi$
$61$	9.43038	1.20744	0.603718	+	0.797198i	$0.293685\pi$
$62$	−5.85680	−0.743815
$63$	−3.28760	−0.414199
$64$	−11.7835	−1.47294
$65$	0	0
$66$	15.9805	1.96706
$67$	−7.25984	−0.886930	−0.443465	−	0.896292i	$-0.646251\pi$
$67$	−7.25984	−0.886930	−0.443465	+	0.896292i	$0.646251\pi$
$68$	7.12767	0.864357
$69$	2.50751	0.301869
$70$	0	0
$71$	−2.44213	−0.289828	−0.144914	−	0.989444i	$-0.546290\pi$
$71$	−2.44213	−0.289828	−0.144914	+	0.989444i	$0.546290\pi$
$72$	−12.1453	−1.43133
$73$	−1.70335	−0.199362	−0.0996808	−	0.995019i	$-0.531782\pi$
$73$	−1.70335	−0.199362	−0.0996808	+	0.995019i	$0.531782\pi$
$74$	1.90619	0.221590
$75$	0	0
$76$	−3.98250	−0.456824
$77$	−2.70134	−0.307847
$78$	−16.5898	−1.87842
$79$	15.4751	1.74108	0.870540	−	0.492098i	$-0.163770\pi$
$79$	15.4751	1.74108	0.870540	+	0.492098i	$0.163770\pi$
$80$	0	0
$81$	−8.05448	−0.894942
$82$	−16.0379	−1.77109
$83$	−10.7887	−1.18421	−0.592107	−	0.805860i	$-0.701704\pi$
$83$	−10.7887	−1.18421	−0.592107	+	0.805860i	$0.701704\pi$
$84$	8.94150	0.975597
$85$	0	0
$86$	7.45333	0.803713
$87$	21.1371	2.26613
$88$	−9.97947	−1.06382
$89$	−8.27944	−0.877619	−0.438809	−	0.898580i	$-0.644600\pi$
$89$	−8.27944	−0.877619	−0.438809	+	0.898580i	$0.644600\pi$
$90$	0	0
$91$	2.80434	0.293974
$92$	−3.56589	−0.371769
$93$	−6.22495	−0.645498
$94$	−23.7668	−2.45136
$95$	0	0
$96$	−9.15757	−0.934640
$97$	13.2465	1.34498	0.672491	−	0.740106i	$-0.265224\pi$
$97$	13.2465	1.34498	0.672491	+	0.740106i	$0.265224\pi$
$98$	−2.35921	−0.238317
$99$	8.88095	0.892569
$100$	0	0
$101$	−13.4521	−1.33854	−0.669268	−	0.743021i	$-0.733392\pi$
$101$	−13.4521	−1.33854	−0.669268	+	0.743021i	$0.733392\pi$
$102$	11.8247	1.17082
$103$	6.77042	0.667109	0.333554	−	0.942731i	$-0.391752\pi$
$103$	6.77042	0.667109	0.333554	+	0.942731i	$0.391752\pi$
$104$	10.3600	1.01588
$105$	0	0
$106$	−11.4786	−1.11490
$107$	10.0195	0.968619	0.484309	−	0.874897i	$-0.339071\pi$
$107$	10.0195	0.968619	0.484309	+	0.874897i	$0.339071\pi$
$108$	−2.57160	−0.247452
$109$	15.5089	1.48548	0.742740	−	0.669580i	$-0.233526\pi$
$109$	15.5089	1.48548	0.742740	+	0.669580i	$0.233526\pi$
$110$	0	0
$111$	2.02601	0.192300
$112$	−1.58378	−0.149653
$113$	0.178511	0.0167929	0.00839645	−	0.999965i	$-0.497327\pi$
$113$	0.178511	0.0167929	0.00839645	+	0.999965i	$0.497327\pi$
$114$	−6.60690	−0.618793
$115$	0	0
$116$	−30.0586	−2.79088
$117$	−9.21955	−0.852348
$118$	28.7277	2.64460
$119$	−1.99885	−0.183234
$120$	0	0
$121$	−3.70274	−0.336613
$122$	−22.2483	−2.01426
$123$	−17.0460	−1.53698
$124$	8.85240	0.794969
$125$	0	0
$126$	7.75616	0.690973
$127$	−4.36340	−0.387190	−0.193595	−	0.981082i	$-0.562015\pi$
$127$	−4.36340	−0.387190	−0.193595	+	0.981082i	$0.562015\pi$
$128$	20.4958	1.81159
$129$	7.92183	0.697479
$130$	0	0
$131$	−4.35393	−0.380405	−0.190202	−	0.981745i	$-0.560914\pi$
$131$	−4.35393	−0.380405	−0.190202	+	0.981745i	$0.560914\pi$
$132$	−24.1541	−2.10234
$133$	1.11683	0.0968417
$134$	17.1275	1.47959
$135$	0	0
$136$	−7.38427	−0.633196
$137$	−10.7306	−0.916780	−0.458390	−	0.888751i	$-0.651574\pi$
$137$	−10.7306	−0.916780	−0.458390	+	0.888751i	$0.651574\pi$
$138$	−5.91575	−0.503582
$139$	6.30819	0.535053	0.267527	−	0.963550i	$-0.413794\pi$
$139$	6.30819	0.535053	0.267527	+	0.963550i	$0.413794\pi$
$140$	0	0
$141$	−25.2607	−2.12734
$142$	5.76151	0.483495
$143$	−7.57548	−0.633494
$144$	5.20683	0.433902
$145$	0	0
$146$	4.01856	0.332578
$147$	−2.50751	−0.206816
$148$	−2.88116	−0.236830
$149$	−12.4249	−1.01789	−0.508943	−	0.860800i	$-0.669964\pi$
$149$	−12.4249	−1.01789	−0.508943	+	0.860800i	$0.669964\pi$
$150$	0	0
$151$	−11.9899	−0.975727	−0.487864	−	0.872920i	$-0.662224\pi$
$151$	−11.9899	−0.975727	−0.487864	+	0.872920i	$0.662224\pi$
$152$	4.12587	0.334653
$153$	6.57142	0.531268
$154$	6.37305	0.513555
$155$	0	0
$156$	25.0750	2.00760
$157$	−15.0216	−1.19885	−0.599427	−	0.800430i	$-0.704605\pi$
$157$	−15.0216	−1.19885	−0.599427	+	0.800430i	$0.704605\pi$
$158$	−36.5090	−2.90450
$159$	−12.2002	−0.967537
$160$	0	0
$161$	1.00000	0.0788110
$162$	19.0022	1.49296
$163$	−5.77178	−0.452080	−0.226040	−	0.974118i	$-0.572578\pi$
$163$	−5.77178	−0.452080	−0.226040	+	0.974118i	$0.572578\pi$
$164$	24.2408	1.89289
$165$	0	0
$166$	25.4528	1.97552
$167$	0.00532684	0.000412203 0	0.000206101	−	1.00000i	$-0.499934\pi$
$167$	0.00532684	0.000412203 0	0.000206101		1.00000i	$0.499934\pi$
$168$	−9.26340	−0.714686
$169$	−5.13569	−0.395053
$170$	0	0
$171$	−3.67170	−0.280782
$172$	−11.2655	−0.858987
$173$	−20.7072	−1.57434	−0.787168	−	0.616739i	$-0.788454\pi$
$173$	−20.7072	−1.57434	−0.787168	+	0.616739i	$0.788454\pi$
$174$	−49.8668	−3.78039
$175$	0	0
$176$	4.27833	0.322491
$177$	30.5334	2.29503
$178$	19.5330	1.46406
$179$	−12.1561	−0.908586	−0.454293	−	0.890852i	$-0.650108\pi$
$179$	−12.1561	−0.908586	−0.454293	+	0.890852i	$0.650108\pi$
$180$	0	0
$181$	−12.8574	−0.955683	−0.477842	−	0.878446i	$-0.658581\pi$
$181$	−12.8574	−0.955683	−0.477842	+	0.878446i	$0.658581\pi$
$182$	−6.61603	−0.490413
$183$	−23.6468	−1.74802
$184$	3.69426	0.272345
$185$	0	0
$186$	14.6860	1.07683
$187$	5.39958	0.394856
$188$	35.9228	2.61994
$189$	0.721167	0.0524572
$190$	0	0
$191$	12.9308	0.935639	0.467820	−	0.883824i	$-0.345040\pi$
$191$	12.9308	0.935639	0.467820	+	0.883824i	$0.345040\pi$
$192$	29.5473	2.13239
$193$	0.302842	0.0217991	0.0108995	−	0.999941i	$-0.496531\pi$
$193$	0.302842	0.0217991	0.0108995	+	0.999941i	$0.496531\pi$
$194$	−31.2514	−2.24372
$195$	0	0
$196$	3.56589	0.254706
$197$	−10.3678	−0.738672	−0.369336	−	0.929296i	$-0.620415\pi$
$197$	−10.3678	−0.738672	−0.369336	+	0.929296i	$0.620415\pi$
$198$	−20.9520	−1.48900
$199$	−11.9825	−0.849414	−0.424707	−	0.905331i	$-0.639623\pi$
$199$	−11.9825	−0.849414	−0.424707	+	0.905331i	$0.639623\pi$
$200$	0	0
$201$	18.2041	1.28402
$202$	31.7364	2.23297
$203$	8.42950	0.591635
$204$	−17.8727	−1.25134
$205$	0	0
$206$	−15.9729	−1.11288
$207$	−3.28760	−0.228504
$208$	−4.44144	−0.307959
$209$	−3.01695	−0.208687
$210$	0	0
$211$	28.1068	1.93495	0.967477	−	0.252960i	$-0.0814039\pi$
$211$	28.1068	1.93495	0.967477	+	0.252960i	$0.0814039\pi$
$212$	17.3497	1.19158
$213$	6.12366	0.419587
$214$	−23.6381	−1.61586
$215$	0	0
$216$	2.66418	0.181275
$217$	−2.48252	−0.168525
$218$	−36.5887	−2.47810
$219$	4.27116	0.288618
$220$	0	0
$221$	−5.60545	−0.377063
$222$	−4.77979	−0.320799
$223$	12.7655	0.854844	0.427422	−	0.904052i	$-0.359422\pi$
$223$	12.7655	0.854844	0.427422	+	0.904052i	$0.359422\pi$
$224$	−3.65206	−0.244013
$225$	0	0
$226$	−0.421145	−0.0280142
$227$	1.81853	0.120700	0.0603499	−	0.998177i	$-0.480778\pi$
$227$	1.81853	0.120700	0.0603499	+	0.998177i	$0.480778\pi$
$228$	9.98616	0.661349
$229$	5.42321	0.358376	0.179188	−	0.983815i	$-0.442653\pi$
$229$	5.42321	0.358376	0.179188	+	0.983815i	$0.442653\pi$
$230$	0	0
$231$	6.77365	0.445673
$232$	31.1408	2.04449
$233$	−9.74067	−0.638133	−0.319066	−	0.947732i	$-0.603369\pi$
$233$	−9.74067	−0.638133	−0.319066	+	0.947732i	$0.603369\pi$
$234$	21.7509	1.42190
$235$	0	0
$236$	−43.4211	−2.82647
$237$	−38.8039	−2.52058
$238$	4.71571	0.305674
$239$	−21.1865	−1.37044	−0.685220	−	0.728336i	$-0.740294\pi$
$239$	−21.1865	−1.37044	−0.685220	+	0.728336i	$0.740294\pi$
$240$	0	0
$241$	13.8166	0.890008	0.445004	−	0.895529i	$-0.353202\pi$
$241$	13.8166	0.890008	0.445004	+	0.895529i	$0.353202\pi$
$242$	8.73555	0.561543
$243$	22.3602	1.43441
$244$	33.6277	2.15279
$245$	0	0
$246$	40.2151	2.56402
$247$	3.13198	0.199283
$248$	−9.17110	−0.582365
$249$	27.0528	1.71440
$250$	0	0
$251$	−11.9432	−0.753850	−0.376925	−	0.926244i	$-0.623019\pi$
$251$	−11.9432	−0.753850	−0.376925	+	0.926244i	$0.623019\pi$
$252$	−11.7232	−0.738494
$253$	−2.70134	−0.169832
$254$	10.2942	0.645916
$255$	0	0
$256$	−24.7868	−1.54917
$257$	16.5580	1.03286	0.516431	−	0.856329i	$-0.327260\pi$
$257$	16.5580	1.03286	0.516431	+	0.856329i	$0.327260\pi$
$258$	−18.6893	−1.16354
$259$	0.807977	0.0502053
$260$	0	0
$261$	−27.7129	−1.71538
$262$	10.2719	0.634597
$263$	−17.5430	−1.08175	−0.540873	−	0.841104i	$-0.681906\pi$
$263$	−17.5430	−1.08175	−0.540873	+	0.841104i	$0.681906\pi$
$264$	25.0236	1.54010
$265$	0	0
$266$	−2.63485	−0.161553
$267$	20.7608	1.27054
$268$	−25.8878	−1.58135
$269$	30.8143	1.87878	0.939389	−	0.342853i	$-0.111393\pi$
$269$	30.8143	1.87878	0.939389	+	0.342853i	$0.111393\pi$
$270$	0	0
$271$	20.4786	1.24398	0.621992	−	0.783023i	$-0.286324\pi$
$271$	20.4786	1.24398	0.621992	+	0.783023i	$0.286324\pi$
$272$	3.16573	0.191951
$273$	−7.03190	−0.425590
$274$	25.3159	1.52939
$275$	0	0
$276$	8.94150	0.538215
$277$	−31.9578	−1.92016	−0.960080	−	0.279727i	$-0.909756\pi$
$277$	−31.9578	−1.92016	−0.960080	+	0.279727i	$0.909756\pi$
$278$	−14.8824	−0.892584
$279$	8.16156	0.488620
$280$	0	0
$281$	12.8548	0.766852	0.383426	−	0.923572i	$-0.374744\pi$
$281$	12.8548	0.766852	0.383426	+	0.923572i	$0.374744\pi$
$282$	59.5954	3.54885
$283$	25.7504	1.53070	0.765351	−	0.643613i	$-0.222566\pi$
$283$	25.7504	1.53070	0.765351	+	0.643613i	$0.222566\pi$
$284$	−8.70836	−0.516746
$285$	0	0
$286$	17.8722	1.05680
$287$	−6.79798	−0.401272
$288$	12.0065	0.707491
$289$	−13.0046	−0.764977
$290$	0	0
$291$	−33.2158	−1.94714
$292$	−6.07394	−0.355451
$293$	14.9716	0.874651	0.437325	−	0.899303i	$-0.355926\pi$
$293$	14.9716	0.874651	0.437325	+	0.899303i	$0.355926\pi$
$294$	5.91575	0.345014
$295$	0	0
$296$	2.98488	0.173493
$297$	−1.94812	−0.113041
$298$	29.3130	1.69805
$299$	2.80434	0.162179
$300$	0	0
$301$	3.15924	0.182096
$302$	28.2868	1.62772
$303$	33.7313	1.93781
$304$	−1.76881	−0.101448
$305$	0	0
$306$	−15.5034	−0.886270
$307$	29.1203	1.66198	0.830990	−	0.556287i	$-0.187774\pi$
$307$	29.1203	1.66198	0.830990	+	0.556287i	$0.187774\pi$
$308$	−9.63269	−0.548873
$309$	−16.9769	−0.965781
$310$	0	0
$311$	27.9131	1.58281	0.791405	−	0.611293i	$-0.209350\pi$
$311$	27.9131	1.58281	0.791405	+	0.611293i	$0.209350\pi$
$312$	−25.9777	−1.47070
$313$	34.6962	1.96115	0.980573	−	0.196152i	$-0.0628447\pi$
$313$	34.6962	1.96115	0.980573	+	0.196152i	$0.0628447\pi$
$314$	35.4391	1.99995
$315$	0	0
$316$	55.1823	3.10425
$317$	22.9724	1.29026	0.645130	−	0.764073i	$-0.276803\pi$
$317$	22.9724	1.29026	0.645130	+	0.764073i	$0.276803\pi$
$318$	28.7828	1.61406
$319$	−22.7710	−1.27493
$320$	0	0
$321$	−25.1239	−1.40228
$322$	−2.35921	−0.131474
$323$	−2.23238	−0.124213
$324$	−28.7213	−1.59563
$325$	0	0
$326$	13.6168	0.754167
$327$	−38.8886	−2.15055
$328$	−25.1135	−1.38666
$329$	−10.0740	−0.555399
$330$	0	0
$331$	−14.4248	−0.792858	−0.396429	−	0.918065i	$-0.629751\pi$
$331$	−14.4248	−0.792858	−0.396429	+	0.918065i	$0.629751\pi$
$332$	−38.4713	−2.11139
$333$	−2.65631	−0.145565
$334$	−0.0125671	−0.000687643 0
$335$	0	0
$336$	3.97133	0.216654
$337$	3.73562	0.203492	0.101746	−	0.994810i	$-0.467557\pi$
$337$	3.73562	0.203492	0.101746	+	0.994810i	$0.467557\pi$
$338$	12.1162	0.659034
$339$	−0.447618	−0.0243113
$340$	0	0
$341$	6.70615	0.363159
$342$	8.66233	0.468405
$343$	−1.00000	−0.0539949
$344$	11.6711	0.629262
$345$	0	0
$346$	48.8526	2.62633
$347$	−15.9464	−0.856045	−0.428023	−	0.903768i	$-0.640790\pi$
$347$	−15.9464	−0.856045	−0.428023	+	0.903768i	$0.640790\pi$
$348$	75.3723	4.04038
$349$	3.27234	0.175164	0.0875821	−	0.996157i	$-0.472086\pi$
$349$	3.27234	0.175164	0.0875821	+	0.996157i	$0.472086\pi$
$350$	0	0
$351$	2.02240	0.107948
$352$	9.86546	0.525831
$353$	−10.3265	−0.549623	−0.274812	−	0.961498i	$-0.588615\pi$
$353$	−10.3265	−0.549623	−0.274812	+	0.961498i	$0.588615\pi$
$354$	−72.0349	−3.82861
$355$	0	0
$356$	−29.5235	−1.56474
$357$	5.01213	0.265270
$358$	28.6787	1.51572
$359$	15.5797	0.822263	0.411131	−	0.911576i	$-0.365134\pi$
$359$	15.5797	0.822263	0.411131	+	0.911576i	$0.365134\pi$
$360$	0	0
$361$	−17.7527	−0.934352
$362$	30.3334	1.59429
$363$	9.28466	0.487318
$364$	9.99995	0.524140
$365$	0	0
$366$	55.7878	2.91607
$367$	21.5509	1.12495	0.562475	−	0.826814i	$-0.309849\pi$
$367$	21.5509	1.12495	0.562475	+	0.826814i	$0.309849\pi$
$368$	−1.58378	−0.0825601
$369$	22.3490	1.16344
$370$	0	0
$371$	−4.86545	−0.252602
$372$	−22.1975	−1.15089
$373$	20.5515	1.06412	0.532059	−	0.846707i	$-0.321418\pi$
$373$	20.5515	1.06412	0.532059	+	0.846707i	$0.321418\pi$
$374$	−12.7388	−0.658706
$375$	0	0
$376$	−37.2161	−1.91927
$377$	23.6392	1.21748
$378$	−1.70139	−0.0875099
$379$	13.3073	0.683552	0.341776	−	0.939781i	$-0.388972\pi$
$379$	13.3073	0.683552	0.341776	+	0.939781i	$0.388972\pi$
$380$	0	0
$381$	10.9413	0.560539
$382$	−30.5065	−1.56085
$383$	−10.7300	−0.548277	−0.274139	−	0.961690i	$-0.588393\pi$
$383$	−10.7300	−0.548277	−0.274139	+	0.961690i	$0.588393\pi$
$384$	−51.3933	−2.62265
$385$	0	0
$386$	−0.714469	−0.0363655
$387$	−10.3863	−0.527967
$388$	47.2356	2.39803
$389$	−29.3543	−1.48832	−0.744161	−	0.668001i	$-0.767150\pi$
$389$	−29.3543	−1.48832	−0.744161	+	0.668001i	$0.767150\pi$
$390$	0	0
$391$	−1.99885	−0.101086
$392$	−3.69426	−0.186588
$393$	10.9175	0.550716
$394$	24.4598	1.23226
$395$	0	0
$396$	31.6685	1.59140
$397$	7.32590	0.367676	0.183838	−	0.982957i	$-0.441148\pi$
$397$	7.32590	0.367676	0.183838	+	0.982957i	$0.441148\pi$
$398$	28.2692	1.41701
$399$	−2.80047	−0.140199
$400$	0	0
$401$	11.7248	0.585510	0.292755	−	0.956187i	$-0.405428\pi$
$401$	11.7248	0.585510	0.292755	+	0.956187i	$0.405428\pi$
$402$	−42.9474	−2.14202
$403$	−6.96184	−0.346794
$404$	−47.9688	−2.38653
$405$	0	0
$406$	−19.8870	−0.986975
$407$	−2.18262	−0.108189
$408$	18.5161	0.916685
$409$	9.34310	0.461987	0.230993	−	0.972955i	$-0.425802\pi$
$409$	9.34310	0.461987	0.230993	+	0.972955i	$0.425802\pi$
$410$	0	0
$411$	26.9072	1.32723
$412$	24.1425	1.18942
$413$	12.1768	0.599181
$414$	7.75616	0.381194
$415$	0	0
$416$	−10.2416	−0.502136
$417$	−15.8178	−0.774603
$418$	7.11763	0.348135
$419$	22.0474	1.07709	0.538543	−	0.842598i	$-0.318975\pi$
$419$	22.0474	1.07709	0.538543	+	0.842598i	$0.318975\pi$
$420$	0	0
$421$	5.11313	0.249199	0.124599	−	0.992207i	$-0.460235\pi$
$421$	5.11313	0.249199	0.124599	+	0.992207i	$0.460235\pi$
$422$	−66.3100	−3.22792
$423$	33.1194	1.61032
$424$	−17.9743	−0.872907
$425$	0	0
$426$	−14.4470	−0.699961
$427$	−9.43038	−0.456368
$428$	35.7283	1.72699
$429$	18.9956	0.917116
$430$	0	0
$431$	8.08201	0.389296	0.194648	−	0.980873i	$-0.437643\pi$
$431$	8.08201	0.389296	0.194648	+	0.980873i	$0.437643\pi$
$432$	−1.14217	−0.0549526
$433$	−38.6561	−1.85769	−0.928847	−	0.370464i	$-0.879199\pi$
$433$	−38.6561	−1.85769	−0.928847	+	0.370464i	$0.879199\pi$
$434$	5.85680	0.281136
$435$	0	0
$436$	55.3028	2.64853
$437$	1.11683	0.0534254
$438$	−10.0766	−0.481477
$439$	2.29718	0.109638	0.0548192	−	0.998496i	$-0.482542\pi$
$439$	2.29718	0.109638	0.0548192	+	0.998496i	$0.482542\pi$
$440$	0	0
$441$	3.28760	0.156553
$442$	13.2245	0.629023
$443$	29.1842	1.38658	0.693292	−	0.720657i	$-0.256160\pi$
$443$	29.1842	1.38658	0.693292	+	0.720657i	$0.256160\pi$
$444$	7.22452	0.342861
$445$	0	0
$446$	−30.1166	−1.42606
$447$	31.1555	1.47361
$448$	11.7835	0.556720
$449$	20.8373	0.983374	0.491687	−	0.870772i	$-0.336380\pi$
$449$	20.8373	0.983374	0.491687	+	0.870772i	$0.336380\pi$
$450$	0	0
$451$	18.3637	0.864712
$452$	0.636550	0.0299408
$453$	30.0649	1.41257
$454$	−4.29029	−0.201353
$455$	0	0
$456$	−10.3457	−0.484480
$457$	−13.4806	−0.630596	−0.315298	−	0.948993i	$-0.602105\pi$
$457$	−13.4806	−0.630596	−0.315298	+	0.948993i	$0.602105\pi$
$458$	−12.7945	−0.597849
$459$	−1.44151	−0.0672837
$460$	0	0
$461$	−34.2227	−1.59391	−0.796954	−	0.604040i	$-0.793557\pi$
$461$	−34.2227	−1.59391	−0.796954	+	0.604040i	$0.793557\pi$
$462$	−15.9805	−0.743479
$463$	−28.0881	−1.30536	−0.652681	−	0.757632i	$-0.726356\pi$
$463$	−28.0881	−1.30536	−0.652681	+	0.757632i	$0.726356\pi$
$464$	−13.3504	−0.619779
$465$	0	0
$466$	22.9803	1.06454
$467$	27.6544	1.27969	0.639846	−	0.768503i	$-0.278998\pi$
$467$	27.6544	1.27969	0.639846	+	0.768503i	$0.278998\pi$
$468$	−32.8759	−1.51969
$469$	7.25984	0.335228
$470$	0	0
$471$	37.6668	1.73559
$472$	44.9843	2.07057
$473$	−8.53421	−0.392403
$474$	91.5466	4.20487
$475$	0	0
$476$	−7.12767	−0.326696
$477$	15.9957	0.732392
$478$	49.9834	2.28619
$479$	−7.07484	−0.323258	−0.161629	−	0.986852i	$-0.551675\pi$
$479$	−7.07484	−0.323258	−0.161629	+	0.986852i	$0.551675\pi$
$480$	0	0
$481$	2.26584	0.103313
$482$	−32.5964	−1.48473
$483$	−2.50751	−0.114096
$484$	−13.2036	−0.600162
$485$	0	0
$486$	−52.7524	−2.39290
$487$	41.7092	1.89002	0.945012	−	0.327037i	$-0.106050\pi$
$487$	41.7092	1.89002	0.945012	+	0.327037i	$0.106050\pi$
$488$	−34.8383	−1.57706
$489$	14.4728	0.654482
$490$	0	0
$491$	2.60678	0.117642	0.0588212	−	0.998269i	$-0.481266\pi$
$491$	2.60678	0.117642	0.0588212	+	0.998269i	$0.481266\pi$
$492$	−60.7841	−2.74036
$493$	−16.8493	−0.758854
$494$	−7.38900	−0.332447
$495$	0	0
$496$	3.93176	0.176541
$497$	2.44213	0.109545
$498$	−63.8232	−2.85999
$499$	35.7391	1.59990	0.799951	−	0.600066i	$-0.204859\pi$
$499$	35.7391	1.59990	0.799951	+	0.600066i	$0.204859\pi$
$500$	0	0
$501$	−0.0133571	−0.000596751 0
$502$	28.1766	1.25758
$503$	26.8250	1.19607	0.598033	−	0.801472i	$-0.295949\pi$
$503$	26.8250	1.19607	0.598033	+	0.801472i	$0.295949\pi$
$504$	12.1453	0.540993
$505$	0	0
$506$	6.37305	0.283316
$507$	12.8778	0.571923
$508$	−15.5594	−0.690337
$509$	−10.6497	−0.472038	−0.236019	−	0.971748i	$-0.575843\pi$
$509$	−10.6497	−0.472038	−0.236019	+	0.971748i	$0.575843\pi$
$510$	0	0
$511$	1.70335	0.0753516
$512$	17.4858	0.772771
$513$	0.805424	0.0355603
$514$	−39.0639	−1.72304
$515$	0	0
$516$	28.2484	1.24357
$517$	27.2134	1.19684
$518$	−1.90619	−0.0837532
$519$	51.9234	2.27918
$520$	0	0
$521$	−10.9869	−0.481346	−0.240673	−	0.970606i	$-0.577368\pi$
$521$	−10.9869	−0.481346	−0.240673	+	0.970606i	$0.577368\pi$
$522$	65.3805	2.86163
$523$	28.5035	1.24637	0.623185	−	0.782074i	$-0.285838\pi$
$523$	28.5035	1.24637	0.623185	+	0.782074i	$0.285838\pi$
$524$	−15.5256	−0.678240
$525$	0	0
$526$	41.3876	1.80459
$527$	4.96219	0.216157
$528$	−10.7279	−0.466874
$529$	1.00000	0.0434783
$530$	0	0
$531$	−40.0325	−1.73726
$532$	3.98250	0.172663
$533$	−19.0638	−0.825746
$534$	−48.9791	−2.11953
$535$	0	0
$536$	26.8197	1.15844
$537$	30.4814	1.31537
$538$	−72.6974	−3.13421
$539$	2.70134	0.116355
$540$	0	0
$541$	−16.2056	−0.696735	−0.348367	−	0.937358i	$-0.613264\pi$
$541$	−16.2056	−0.696735	−0.348367	+	0.937358i	$0.613264\pi$
$542$	−48.3133	−2.07523
$543$	32.2401	1.38355
$544$	7.29991	0.312981
$545$	0	0
$546$	16.5898	0.709976
$547$	−1.49191	−0.0637895	−0.0318948	−	0.999491i	$-0.510154\pi$
$547$	−1.49191	−0.0637895	−0.0318948	+	0.999491i	$0.510154\pi$
$548$	−38.2643	−1.63457
$549$	31.0033	1.32319
$550$	0	0
$551$	9.41434	0.401065
$552$	−9.26340	−0.394276
$553$	−15.4751	−0.658066
$554$	75.3953	3.20324
$555$	0	0
$556$	22.4943	0.953970
$557$	−21.1267	−0.895167	−0.447584	−	0.894242i	$-0.647715\pi$
$557$	−21.1267	−0.895167	−0.447584	+	0.894242i	$0.647715\pi$
$558$	−19.2548	−0.815123
$559$	8.85959	0.374721
$560$	0	0
$561$	−13.5395	−0.571638
$562$	−30.3272	−1.27927
$563$	11.4806	0.483851	0.241926	−	0.970295i	$-0.422221\pi$
$563$	11.4806	0.483851	0.241926	+	0.970295i	$0.422221\pi$
$564$	−90.0768	−3.79292
$565$	0	0
$566$	−60.7506	−2.55354
$567$	8.05448	0.338256
$568$	9.02187	0.378549
$569$	19.7215	0.826768	0.413384	−	0.910557i	$-0.364347\pi$
$569$	19.7215	0.826768	0.413384	+	0.910557i	$0.364347\pi$
$570$	0	0
$571$	22.6321	0.947126	0.473563	−	0.880760i	$-0.342968\pi$
$571$	22.6321	0.947126	0.473563	+	0.880760i	$0.342968\pi$
$572$	−27.0133	−1.12948
$573$	−32.4241	−1.35454
$574$	16.0379	0.669408
$575$	0	0
$576$	−38.7396	−1.61415
$577$	1.42011	0.0591199	0.0295599	−	0.999563i	$-0.490589\pi$
$577$	1.42011	0.0591199	0.0295599	+	0.999563i	$0.490589\pi$
$578$	30.6806	1.27615
$579$	−0.759379	−0.0315587
$580$	0	0
$581$	10.7887	0.447590
$582$	78.3632	3.24826
$583$	13.1433	0.544338
$584$	6.29261	0.260390
$585$	0	0
$586$	−35.3212	−1.45911
$587$	12.0482	0.497281	0.248640	−	0.968596i	$-0.420016\pi$
$587$	12.0482	0.497281	0.248640	+	0.968596i	$0.420016\pi$
$588$	−8.94150	−0.368741
$589$	−2.77257	−0.114242
$590$	0	0
$591$	25.9973	1.06938
$592$	−1.27966	−0.0525935
$593$	13.4535	0.552471	0.276235	−	0.961090i	$-0.410913\pi$
$593$	13.4535	0.552471	0.276235	+	0.961090i	$0.410913\pi$
$594$	4.59603	0.188578
$595$	0	0
$596$	−44.3057	−1.81483
$597$	30.0461	1.22971
$598$	−6.61603	−0.270550
$599$	43.1777	1.76419	0.882096	−	0.471069i	$-0.156132\pi$
$599$	43.1777	1.76419	0.882096	+	0.471069i	$0.156132\pi$
$600$	0	0
$601$	−20.3297	−0.829266	−0.414633	−	0.909989i	$-0.636090\pi$
$601$	−20.3297	−0.829266	−0.414633	+	0.909989i	$0.636090\pi$
$602$	−7.45333	−0.303775
$603$	−23.8675	−0.971958
$604$	−42.7548	−1.73967
$605$	0	0
$606$	−79.5794	−3.23269
$607$	0.793889	0.0322230	0.0161115	−	0.999870i	$-0.494871\pi$
$607$	0.793889	0.0322230	0.0161115	+	0.999870i	$0.494871\pi$
$608$	−4.07874	−0.165415
$609$	−21.1371	−0.856516
$610$	0	0
$611$	−28.2510	−1.14291
$612$	23.4330	0.947221
$613$	−1.43440	−0.0579349	−0.0289674	−	0.999580i	$-0.509222\pi$
$613$	−1.43440	−0.0579349	−0.0289674	+	0.999580i	$0.509222\pi$
$614$	−68.7009	−2.77254
$615$	0	0
$616$	9.97947	0.402084
$617$	−46.1995	−1.85992	−0.929960	−	0.367660i	$-0.880159\pi$
$617$	−46.1995	−1.85992	−0.929960	+	0.367660i	$0.880159\pi$
$618$	40.0521	1.61113
$619$	2.94224	0.118259	0.0591294	−	0.998250i	$-0.481168\pi$
$619$	2.94224	0.118259	0.0591294	+	0.998250i	$0.481168\pi$
$620$	0	0
$621$	0.721167	0.0289395
$622$	−65.8531	−2.64047
$623$	8.27944	0.331709
$624$	11.1370	0.445835
$625$	0	0
$626$	−81.8558	−3.27162
$627$	7.56503	0.302118
$628$	−53.5653	−2.13749
$629$	−1.61502	−0.0643953
$630$	0	0
$631$	28.4317	1.13185	0.565924	−	0.824458i	$-0.308520\pi$
$631$	28.4317	1.13185	0.565924	+	0.824458i	$0.308520\pi$
$632$	−57.1689	−2.27406
$633$	−70.4781	−2.80125
$634$	−54.1968	−2.15243
$635$	0	0
$636$	−43.5044	−1.72506
$637$	−2.80434	−0.111112
$638$	53.7216	2.12686
$639$	−8.02875	−0.317613
$640$	0	0
$641$	44.8580	1.77178	0.885892	−	0.463892i	$-0.153547\pi$
$641$	44.8580	1.77178	0.885892	+	0.463892i	$0.153547\pi$
$642$	59.2727	2.33931
$643$	0.903492	0.0356302	0.0178151	−	0.999841i	$-0.494329\pi$
$643$	0.903492	0.0356302	0.0178151	+	0.999841i	$0.494329\pi$
$644$	3.56589	0.140516
$645$	0	0
$646$	5.26666	0.207214
$647$	−17.0363	−0.669765	−0.334882	−	0.942260i	$-0.608697\pi$
$647$	−17.0363	−0.669765	−0.334882	+	0.942260i	$0.608697\pi$
$648$	29.7553	1.16890
$649$	−32.8937	−1.29119
$650$	0	0
$651$	6.22495	0.243975
$652$	−20.5815	−0.806034
$653$	23.1721	0.906793	0.453397	−	0.891309i	$-0.350212\pi$
$653$	23.1721	0.906793	0.453397	+	0.891309i	$0.350212\pi$
$654$	91.7465	3.58757
$655$	0	0
$656$	10.7665	0.420360
$657$	−5.59993	−0.218474
$658$	23.7668	0.926525
$659$	−25.0481	−0.975737	−0.487868	−	0.872917i	$-0.662225\pi$
$659$	−25.0481	−0.975737	−0.487868	+	0.872917i	$0.662225\pi$
$660$	0	0
$661$	−8.53827	−0.332100	−0.166050	−	0.986117i	$-0.553101\pi$
$661$	−8.53827	−0.332100	−0.166050	+	0.986117i	$0.553101\pi$
$662$	34.0311	1.32266
$663$	14.0557	0.545879
$664$	39.8563	1.54672
$665$	0	0
$666$	6.26680	0.242833
$667$	8.42950	0.326392
$668$	0.0189949	0.000734934 0
$669$	−32.0097	−1.23757
$670$	0	0
$671$	25.4747	0.983440
$672$	9.15757	0.353261
$673$	−23.9052	−0.921477	−0.460738	−	0.887536i	$-0.652415\pi$
$673$	−23.9052	−0.921477	−0.460738	+	0.887536i	$0.652415\pi$
$674$	−8.81313	−0.339469
$675$	0	0
$676$	−18.3133	−0.704357
$677$	−29.3023	−1.12618	−0.563090	−	0.826395i	$-0.690388\pi$
$677$	−29.3023	−1.12618	−0.563090	+	0.826395i	$0.690388\pi$
$678$	1.05603	0.0405564
$679$	−13.2465	−0.508355
$680$	0	0
$681$	−4.55997	−0.174739
$682$	−15.8212	−0.605827
$683$	−28.8697	−1.10467	−0.552334	−	0.833623i	$-0.686263\pi$
$683$	−28.8697	−1.10467	−0.552334	+	0.833623i	$0.686263\pi$
$684$	−13.0929	−0.500619
$685$	0	0
$686$	2.35921	0.0900752
$687$	−13.5988	−0.518825
$688$	−5.00354	−0.190758
$689$	−13.6444	−0.519809
$690$	0	0
$691$	13.1773	0.501290	0.250645	−	0.968079i	$-0.419357\pi$
$691$	13.1773	0.501290	0.250645	+	0.968079i	$0.419357\pi$
$692$	−73.8394	−2.80695
$693$	−8.88095	−0.337359
$694$	37.6208	1.42807
$695$	0	0
$696$	−78.0858	−2.95983
$697$	13.5881	0.514687
$698$	−7.72014	−0.292212
$699$	24.4248	0.923832
$700$	0	0
$701$	32.1209	1.21319	0.606595	−	0.795011i	$-0.292535\pi$
$701$	32.1209	1.21319	0.606595	+	0.795011i	$0.292535\pi$
$702$	−4.77127	−0.180080
$703$	0.902376	0.0340337
$704$	−31.8314	−1.19969
$705$	0	0
$706$	24.3624	0.916890
$707$	13.4521	0.505919
$708$	108.879	4.09191
$709$	39.6975	1.49087	0.745435	−	0.666578i	$-0.232242\pi$
$709$	39.6975	1.49087	0.745435	+	0.666578i	$0.232242\pi$
$710$	0	0
$711$	50.8758	1.90799
$712$	30.5864	1.14627
$713$	−2.48252	−0.0929713
$714$	−11.8247	−0.442528
$715$	0	0
$716$	−43.3471	−1.61996
$717$	53.1253	1.98400
$718$	−36.7557	−1.37171
$719$	28.5811	1.06590	0.532948	−	0.846148i	$-0.321084\pi$
$719$	28.5811	1.06590	0.532948	+	0.846148i	$0.321084\pi$
$720$	0	0
$721$	−6.77042	−0.252143
$722$	41.8824	1.55870
$723$	−34.6454	−1.28847
$724$	−45.8481	−1.70393
$725$	0	0
$726$	−21.9045	−0.812952
$727$	9.67378	0.358781	0.179390	−	0.983778i	$-0.442588\pi$
$727$	9.67378	0.358781	0.179390	+	0.983778i	$0.442588\pi$
$728$	−10.3600	−0.383966
$729$	−31.9049	−1.18166
$730$	0	0
$731$	−6.31485	−0.233563
$732$	−84.3217	−3.11662
$733$	23.1744	0.855966	0.427983	−	0.903787i	$-0.359224\pi$
$733$	23.1744	0.855966	0.427983	+	0.903787i	$0.359224\pi$
$734$	−50.8433	−1.87666
$735$	0	0
$736$	−3.65206	−0.134617
$737$	−19.6113	−0.722392
$738$	−52.7262	−1.94088
$739$	−29.2997	−1.07781	−0.538904	−	0.842367i	$-0.681161\pi$
$739$	−29.2997	−1.07781	−0.538904	+	0.842367i	$0.681161\pi$
$740$	0	0
$741$	−7.85346	−0.288504
$742$	11.4786	0.421394
$743$	−36.8301	−1.35116	−0.675582	−	0.737285i	$-0.736108\pi$
$743$	−36.8301	−1.35116	−0.675582	+	0.737285i	$0.736108\pi$
$744$	22.9966	0.843097
$745$	0	0
$746$	−48.4855	−1.77518
$747$	−35.4689	−1.29774
$748$	19.2543	0.704007
$749$	−10.0195	−0.366103
$750$	0	0
$751$	37.5423	1.36994	0.684969	−	0.728572i	$-0.259816\pi$
$751$	37.5423	1.36994	0.684969	+	0.728572i	$0.259816\pi$
$752$	15.9550	0.581819
$753$	29.9478	1.09136
$754$	−55.7698	−2.03102
$755$	0	0
$756$	2.57160	0.0935282
$757$	−17.3405	−0.630250	−0.315125	−	0.949050i	$-0.602046\pi$
$757$	−17.3405	−0.630250	−0.315125	+	0.949050i	$0.602046\pi$
$758$	−31.3948	−1.14031
$759$	6.77365	0.245868
$760$	0	0
$761$	−44.6219	−1.61754	−0.808771	−	0.588123i	$-0.799867\pi$
$761$	−44.6219	−1.61754	−0.808771	+	0.588123i	$0.799867\pi$
$762$	−25.8128	−0.935099
$763$	−15.5089	−0.561458
$764$	46.1097	1.66819
$765$	0	0
$766$	25.3143	0.914644
$767$	34.1478	1.23301
$768$	62.1531	2.24276
$769$	38.4931	1.38810	0.694048	−	0.719929i	$-0.255826\pi$
$769$	38.4931	1.38810	0.694048	+	0.719929i	$0.255826\pi$
$770$	0	0
$771$	−41.5194	−1.49528
$772$	1.07990	0.0388665
$773$	54.2437	1.95101	0.975505	−	0.219976i	$-0.0705978\pi$
$773$	54.2437	1.95101	0.975505	+	0.219976i	$0.0705978\pi$
$774$	24.5036	0.880763
$775$	0	0
$776$	−48.9362	−1.75671
$777$	−2.02601	−0.0726827
$778$	69.2530	2.48284
$779$	−7.59220	−0.272019
$780$	0	0
$781$	−6.59703	−0.236060
$782$	4.71571	0.168634
$783$	6.07908	0.217249
$784$	1.58378	0.0565635
$785$	0	0
$786$	−25.7568	−0.918714
$787$	−4.83401	−0.172314	−0.0861570	−	0.996282i	$-0.527459\pi$
$787$	−4.83401	−0.172314	−0.0861570	+	0.996282i	$0.527459\pi$
$788$	−36.9703	−1.31701
$789$	43.9892	1.56606
$790$	0	0
$791$	−0.178511	−0.00634712
$792$	−32.8085	−1.16580
$793$	−26.4460	−0.939124
$794$	−17.2834	−0.613363
$795$	0	0
$796$	−42.7281	−1.51446
$797$	−44.4895	−1.57590	−0.787950	−	0.615739i	$-0.788857\pi$
$797$	−44.4895	−1.57590	−0.787950	+	0.615739i	$0.788857\pi$
$798$	6.60690	0.233882
$799$	20.1365	0.712377
$800$	0	0
$801$	−27.2195	−0.961754
$802$	−27.6614	−0.976757
$803$	−4.60133	−0.162377
$804$	64.9138	2.28933
$805$	0	0
$806$	16.4245	0.578527
$807$	−77.2670	−2.71993
$808$	49.6957	1.74829
$809$	−19.7547	−0.694540	−0.347270	−	0.937765i	$-0.612891\pi$
$809$	−19.7547	−0.694540	−0.347270	+	0.937765i	$0.612891\pi$
$810$	0	0
$811$	11.3167	0.397382	0.198691	−	0.980062i	$-0.436331\pi$
$811$	11.3167	0.397382	0.198691	+	0.980062i	$0.436331\pi$
$812$	30.0586	1.05485
$813$	−51.3502	−1.80093
$814$	5.14928	0.180482
$815$	0	0
$816$	−7.93810	−0.277889
$817$	3.52835	0.123441
$818$	−22.0424	−0.770694
$819$	9.21955	0.322157
$820$	0	0
$821$	−17.5446	−0.612310	−0.306155	−	0.951982i	$-0.599043\pi$
$821$	−17.5446	−0.612310	−0.306155	+	0.951982i	$0.599043\pi$
$822$	−63.4798	−2.21411
$823$	47.0147	1.63883	0.819415	−	0.573201i	$-0.194299\pi$
$823$	47.0147	1.63883	0.819415	+	0.573201i	$0.194299\pi$
$824$	−25.0117	−0.871323
$825$	0	0
$826$	−28.7277	−0.999563
$827$	−1.29703	−0.0451022	−0.0225511	−	0.999746i	$-0.507179\pi$
$827$	−1.29703	−0.0451022	−0.0225511	+	0.999746i	$0.507179\pi$
$828$	−11.7232	−0.407410
$829$	57.4555	1.99551	0.997757	−	0.0669420i	$-0.0213243\pi$
$829$	57.4555	1.99551	0.997757	+	0.0669420i	$0.0213243\pi$
$830$	0	0
$831$	80.1345	2.77984
$832$	33.0450	1.14563
$833$	1.99885	0.0692560
$834$	37.3176	1.29220
$835$	0	0
$836$	−10.7581	−0.372077
$837$	−1.79032	−0.0618824
$838$	−52.0145	−1.79681
$839$	−53.3764	−1.84276	−0.921379	−	0.388664i	$-0.872937\pi$
$839$	−53.3764	−1.84276	−0.921379	+	0.388664i	$0.872937\pi$
$840$	0	0
$841$	42.0565	1.45022
$842$	−12.0630	−0.415717
$843$	−32.2335	−1.11018
$844$	100.226	3.44991
$845$	0	0
$846$	−78.1357	−2.68636
$847$	3.70274	0.127228
$848$	7.70579	0.264618
$849$	−64.5693	−2.21601
$850$	0	0
$851$	0.807977	0.0276971
$852$	21.8363	0.748099
$853$	20.9398	0.716966	0.358483	−	0.933536i	$-0.383294\pi$
$853$	20.9398	0.716966	0.358483	+	0.933536i	$0.383294\pi$
$854$	22.2483	0.761320
$855$	0	0
$856$	−37.0145	−1.26513
$857$	−12.5261	−0.427883	−0.213941	−	0.976846i	$-0.568630\pi$
$857$	−12.5261	−0.427883	−0.213941	+	0.976846i	$0.568630\pi$
$858$	−44.8147	−1.52995
$859$	39.2473	1.33910	0.669550	−	0.742767i	$-0.266487\pi$
$859$	39.2473	1.33910	0.669550	+	0.742767i	$0.266487\pi$
$860$	0	0
$861$	17.0460	0.580926
$862$	−19.0672	−0.649431
$863$	50.8955	1.73250	0.866251	−	0.499608i	$-0.166523\pi$
$863$	50.8955	1.73250	0.866251	+	0.499608i	$0.166523\pi$
$864$	−2.63374	−0.0896018
$865$	0	0
$866$	91.1980	3.09903
$867$	32.6092	1.10747
$868$	−8.85240	−0.300470
$869$	41.8035	1.41809
$870$	0	0
$871$	20.3590	0.689840
$872$	−57.2938	−1.94021
$873$	43.5493	1.47392
$874$	−2.63485	−0.0891250
$875$	0	0
$876$	15.2305	0.514590
$877$	−48.7836	−1.64730	−0.823652	−	0.567095i	$-0.808067\pi$
$877$	−48.7836	−1.64730	−0.823652	+	0.567095i	$0.808067\pi$
$878$	−5.41953	−0.182900
$879$	−37.5414	−1.26624
$880$	0	0
$881$	18.7616	0.632093	0.316047	−	0.948744i	$-0.397644\pi$
$881$	18.7616	0.632093	0.316047	+	0.948744i	$0.397644\pi$
$882$	−7.75616	−0.261163
$883$	−24.0146	−0.808157	−0.404078	−	0.914724i	$-0.632408\pi$
$883$	−24.0146	−0.808157	−0.404078	+	0.914724i	$0.632408\pi$
$884$	−19.9884	−0.672283
$885$	0	0
$886$	−68.8518	−2.31312
$887$	1.47725	0.0496012	0.0248006	−	0.999692i	$-0.492105\pi$
$887$	1.47725	0.0496012	0.0248006	+	0.999692i	$0.492105\pi$
$888$	−7.48461	−0.251167
$889$	4.36340	0.146344
$890$	0	0
$891$	−21.7579	−0.728917
$892$	45.5205	1.52414
$893$	−11.2510	−0.376500
$894$	−73.5025	−2.45829
$895$	0	0
$896$	−20.4958	−0.684715
$897$	−7.03190	−0.234788
$898$	−49.1597	−1.64048
$899$	−20.9264	−0.697936
$900$	0	0
$901$	9.72531	0.323997
$902$	−43.3238	−1.44253
$903$	−7.92183	−0.263622
$904$	−0.659466	−0.0219335
$905$	0	0
$906$	−70.9295	−2.35647
$907$	−17.3795	−0.577077	−0.288539	−	0.957468i	$-0.593169\pi$
$907$	−17.3795	−0.577077	−0.288539	+	0.957468i	$0.593169\pi$
$908$	6.48466	0.215201
$909$	−44.2252	−1.46686
$910$	0	0
$911$	−52.6898	−1.74569	−0.872846	−	0.487996i	$-0.837728\pi$
$911$	−52.6898	−1.74569	−0.872846	+	0.487996i	$0.837728\pi$
$912$	4.43532	0.146868
$913$	−29.1440	−0.964525
$914$	31.8036	1.05197
$915$	0	0
$916$	19.3386	0.638964
$917$	4.35393	0.143780
$918$	3.40082	0.112244
$919$	−3.45752	−0.114053	−0.0570266	−	0.998373i	$-0.518162\pi$
$919$	−3.45752	−0.114053	−0.0570266	+	0.998373i	$0.518162\pi$
$920$	0	0
$921$	−73.0193	−2.40607
$922$	80.7386	2.65898
$923$	6.84856	0.225423
$924$	24.1541	0.794610
$925$	0	0
$926$	66.2657	2.17763
$927$	22.2584	0.731063
$928$	−30.7850	−1.01057
$929$	−12.8336	−0.421057	−0.210529	−	0.977588i	$-0.567519\pi$
$929$	−12.8336	−0.421057	−0.210529	+	0.977588i	$0.567519\pi$
$930$	0	0
$931$	−1.11683	−0.0366027
$932$	−34.7341	−1.13775
$933$	−69.9925	−2.29145
$934$	−65.2426	−2.13480
$935$	0	0
$936$	34.0594	1.11327
$937$	32.5335	1.06282	0.531411	−	0.847114i	$-0.321662\pi$
$937$	32.5335	1.06282	0.531411	+	0.847114i	$0.321662\pi$
$938$	−17.1275	−0.559233
$939$	−87.0011	−2.83917
$940$	0	0
$941$	44.7486	1.45876	0.729381	−	0.684108i	$-0.239808\pi$
$941$	44.7486	1.45876	0.729381	+	0.684108i	$0.239808\pi$
$942$	−88.8640	−2.89534
$943$	−6.79798	−0.221373
$944$	−19.2853	−0.627684
$945$	0	0
$946$	20.1340	0.654613
$947$	13.4275	0.436336	0.218168	−	0.975911i	$-0.429992\pi$
$947$	13.4275	0.436336	0.218168	+	0.975911i	$0.429992\pi$
$948$	−138.370	−4.49405
$949$	4.77676	0.155060
$950$	0	0
$951$	−57.6035	−1.86792
$952$	7.38427	0.239326
$953$	7.99902	0.259114	0.129557	−	0.991572i	$-0.458645\pi$
$953$	7.99902	0.259114	0.129557	+	0.991572i	$0.458645\pi$
$954$	−37.7372	−1.22179
$955$	0	0
$956$	−75.5486	−2.44342
$957$	57.0984	1.84573
$958$	16.6910	0.539263
$959$	10.7306	0.346510
$960$	0	0
$961$	−24.8371	−0.801196
$962$	−5.34560	−0.172349
$963$	32.9400	1.06148
$964$	49.2686	1.58683
$965$	0	0
$966$	5.91575	0.190336
$967$	−43.6769	−1.40455	−0.702277	−	0.711904i	$-0.747833\pi$
$967$	−43.6769	−1.40455	−0.702277	+	0.711904i	$0.747833\pi$
$968$	13.6789	0.439656
$969$	5.59772	0.179825
$970$	0	0
$971$	7.16184	0.229834	0.114917	−	0.993375i	$-0.463340\pi$
$971$	7.16184	0.229834	0.114917	+	0.993375i	$0.463340\pi$
$972$	79.7339	2.55746
$973$	−6.30819	−0.202231
$974$	−98.4009	−3.15297
$975$	0	0
$976$	14.9356	0.478077
$977$	−15.6590	−0.500977	−0.250488	−	0.968120i	$-0.580591\pi$
$977$	−15.6590	−0.500977	−0.250488	+	0.968120i	$0.580591\pi$
$978$	−34.1444	−1.09182
$979$	−22.3656	−0.714808
$980$	0	0
$981$	50.9870	1.62789
$982$	−6.14996	−0.196253
$983$	41.2674	1.31623	0.658113	−	0.752919i	$-0.271355\pi$
$983$	41.2674	1.31623	0.658113	+	0.752919i	$0.271355\pi$
$984$	62.9723	2.00748
$985$	0	0
$986$	39.7511	1.26593
$987$	25.2607	0.804057
$988$	11.1683	0.355310
$989$	3.15924	0.100458
$990$	0	0
$991$	55.1091	1.75060	0.875300	−	0.483581i	$-0.160664\pi$
$991$	55.1091	1.75060	0.875300	+	0.483581i	$0.160664\pi$
$992$	9.06632	0.287856
$993$	36.1703	1.14783
$994$	−5.76151	−0.182744
$995$	0	0
$996$	96.4671	3.05668
$997$	−4.56403	−0.144544	−0.0722721	−	0.997385i	$-0.523025\pi$
$997$	−4.56403	−0.144544	−0.0722721	+	0.997385i	$0.523025\pi$
$998$	−84.3161	−2.66898
$999$	0.582687	0.0184354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.4		21
5.2	odd	4		805.2.c.c.484.7	✓	42
5.3	odd	4		805.2.c.c.484.36	yes	42
5.4	even	2		4025.2.a.be.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.7	✓	42	5.2	odd	4
805.2.c.c.484.36	yes	42	5.3	odd	4
4025.2.a.bd.1.4		21	1.1	even	1	trivial
4025.2.a.be.1.18		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)

\(f(q)\)	\(=\)	\(q-2.35921 q^{2} -2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} -1.00000 q^{7} -3.69426 q^{8} +3.28760 q^{9} +O(q^{10})\)	\(q-2.35921 q^{2} -2.50751 q^{3} +3.56589 q^{4} +5.91575 q^{6} -1.00000 q^{7} -3.69426 q^{8} +3.28760 q^{9} +2.70134 q^{11} -8.94150 q^{12} -2.80434 q^{13} +2.35921 q^{14} +1.58378 q^{16} +1.99885 q^{17} -7.75616 q^{18} -1.11683 q^{19} +2.50751 q^{21} -6.37305 q^{22} -1.00000 q^{23} +9.26340 q^{24} +6.61603 q^{26} -0.721167 q^{27} -3.56589 q^{28} -8.42950 q^{29} +2.48252 q^{31} +3.65206 q^{32} -6.77365 q^{33} -4.71571 q^{34} +11.7232 q^{36} -0.807977 q^{37} +2.63485 q^{38} +7.03190 q^{39} +6.79798 q^{41} -5.91575 q^{42} -3.15924 q^{43} +9.63269 q^{44} +2.35921 q^{46} +10.0740 q^{47} -3.97133 q^{48} +1.00000 q^{49} -5.01213 q^{51} -9.99995 q^{52} +4.86545 q^{53} +1.70139 q^{54} +3.69426 q^{56} +2.80047 q^{57} +19.8870 q^{58} -12.1768 q^{59} +9.43038 q^{61} -5.85680 q^{62} -3.28760 q^{63} -11.7835 q^{64} +15.9805 q^{66} -7.25984 q^{67} +7.12767 q^{68} +2.50751 q^{69} -2.44213 q^{71} -12.1453 q^{72} -1.70335 q^{73} +1.90619 q^{74} -3.98250 q^{76} -2.70134 q^{77} -16.5898 q^{78} +15.4751 q^{79} -8.05448 q^{81} -16.0379 q^{82} -10.7887 q^{83} +8.94150 q^{84} +7.45333 q^{86} +21.1371 q^{87} -9.97947 q^{88} -8.27944 q^{89} +2.80434 q^{91} -3.56589 q^{92} -6.22495 q^{93} -23.7668 q^{94} -9.15757 q^{96} +13.2465 q^{97} -2.35921 q^{98} +8.88095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 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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