LMFDB - Embedded newform 6025.2.a.j.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31571 q^{2} +0.792486 q^{3} -0.268903 q^{4} -1.04268 q^{6} +1.49796 q^{7} +2.98522 q^{8} -2.37197 q^{9} +O(q^{10})$	\(q-1.31571 q^{2} +0.792486 q^{3} -0.268903 q^{4} -1.04268 q^{6} +1.49796 q^{7} +2.98522 q^{8} -2.37197 q^{9} +4.87124 q^{11} -0.213102 q^{12} -5.90610 q^{13} -1.97088 q^{14} -3.38989 q^{16} -0.168015 q^{17} +3.12082 q^{18} -0.539327 q^{19} +1.18711 q^{21} -6.40915 q^{22} -1.93297 q^{23} +2.36575 q^{24} +7.77073 q^{26} -4.25721 q^{27} -0.402805 q^{28} +7.88450 q^{29} -1.14273 q^{31} -1.51033 q^{32} +3.86039 q^{33} +0.221059 q^{34} +0.637828 q^{36} +2.81554 q^{37} +0.709599 q^{38} -4.68050 q^{39} +10.8644 q^{41} -1.56189 q^{42} -12.0801 q^{43} -1.30989 q^{44} +2.54323 q^{46} -4.73286 q^{47} -2.68644 q^{48} -4.75613 q^{49} -0.133149 q^{51} +1.58817 q^{52} +12.8280 q^{53} +5.60126 q^{54} +4.47173 q^{56} -0.427410 q^{57} -10.3737 q^{58} -0.486188 q^{59} -7.44694 q^{61} +1.50350 q^{62} -3.55310 q^{63} +8.76693 q^{64} -5.07916 q^{66} -11.1679 q^{67} +0.0451796 q^{68} -1.53185 q^{69} +3.41410 q^{71} -7.08084 q^{72} -4.57808 q^{73} -3.70444 q^{74} +0.145027 q^{76} +7.29691 q^{77} +6.15819 q^{78} -4.21264 q^{79} +3.74212 q^{81} -14.2945 q^{82} -2.35078 q^{83} -0.319217 q^{84} +15.8939 q^{86} +6.24836 q^{87} +14.5417 q^{88} -16.1621 q^{89} -8.84708 q^{91} +0.519781 q^{92} -0.905594 q^{93} +6.22708 q^{94} -1.19692 q^{96} +8.47833 q^{97} +6.25769 q^{98} -11.5544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * 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 $

$2$	−1.31571	−0.930349	−0.465174	−	0.885219i	$-0.654008\pi$
$2$	−1.31571	−0.930349	−0.465174	+	0.885219i	$0.654008\pi$
$3$	0.792486	0.457542	0.228771	−	0.973480i	$-0.426529\pi$
$3$	0.792486	0.457542	0.228771	+	0.973480i	$0.426529\pi$
$4$	−0.268903	−0.134451
$5$	0	0
$5$	0	0
$6$	−1.04268	−0.425674
$7$	1.49796	0.566174	0.283087	−	0.959094i	$-0.408641\pi$
$7$	1.49796	0.566174	0.283087	+	0.959094i	$0.408641\pi$
$8$	2.98522	1.05544
$9$	−2.37197	−0.790655
$10$	0	0
$11$	4.87124	1.46874	0.734368	−	0.678752i	$-0.237479\pi$
$11$	4.87124	1.46874	0.734368	+	0.678752i	$0.237479\pi$
$12$	−0.213102	−0.0615171
$13$	−5.90610	−1.63806	−0.819029	−	0.573752i	$-0.805487\pi$
$13$	−5.90610	−1.63806	−0.819029	+	0.573752i	$0.805487\pi$
$14$	−1.97088	−0.526740
$15$	0	0
$16$	−3.38989	−0.847471
$17$	−0.168015	−0.0407495	−0.0203748	−	0.999792i	$-0.506486\pi$
$17$	−0.168015	−0.0407495	−0.0203748	+	0.999792i	$0.506486\pi$
$18$	3.12082	0.735585
$19$	−0.539327	−0.123730	−0.0618651	−	0.998085i	$-0.519705\pi$
$19$	−0.539327	−0.123730	−0.0618651	+	0.998085i	$0.519705\pi$
$20$	0	0
$21$	1.18711	0.259049
$22$	−6.40915	−1.36644
$23$	−1.93297	−0.403052	−0.201526	−	0.979483i	$-0.564590\pi$
$23$	−1.93297	−0.403052	−0.201526	+	0.979483i	$0.564590\pi$
$24$	2.36575	0.482906
$25$	0	0
$26$	7.77073	1.52396
$27$	−4.25721	−0.819300
$28$	−0.402805	−0.0761229
$29$	7.88450	1.46411	0.732057	−	0.681243i	$-0.238560\pi$
$29$	7.88450	1.46411	0.732057	+	0.681243i	$0.238560\pi$
$30$	0	0
$31$	−1.14273	−0.205239	−0.102620	−	0.994721i	$-0.532722\pi$
$31$	−1.14273	−0.205239	−0.102620	+	0.994721i	$0.532722\pi$
$32$	−1.51033	−0.266991
$33$	3.86039	0.672008
$34$	0.221059	0.0379113
$35$	0	0
$36$	0.637828	0.106305
$37$	2.81554	0.462872	0.231436	−	0.972850i	$-0.425658\pi$
$37$	2.81554	0.462872	0.231436	+	0.972850i	$0.425658\pi$
$38$	0.709599	0.115112
$39$	−4.68050	−0.749480
$40$	0	0
$41$	10.8644	1.69674	0.848370	−	0.529403i	$-0.177584\pi$
$41$	10.8644	1.69674	0.848370	+	0.529403i	$0.177584\pi$
$42$	−1.56189	−0.241006
$43$	−12.0801	−1.84220	−0.921100	−	0.389327i	$-0.872708\pi$
$43$	−12.0801	−1.84220	−0.921100	+	0.389327i	$0.872708\pi$
$44$	−1.30989	−0.197473
$45$	0	0
$46$	2.54323	0.374979
$47$	−4.73286	−0.690358	−0.345179	−	0.938537i	$-0.612182\pi$
$47$	−4.73286	−0.690358	−0.345179	+	0.938537i	$0.612182\pi$
$48$	−2.68644	−0.387754
$49$	−4.75613	−0.679447
$50$	0	0
$51$	−0.133149	−0.0186446
$52$	1.58817	0.220239
$53$	12.8280	1.76206	0.881028	−	0.473064i	$-0.156852\pi$
$53$	12.8280	1.76206	0.881028	+	0.473064i	$0.156852\pi$
$54$	5.60126	0.762235
$55$	0	0
$56$	4.47173	0.597560
$57$	−0.427410	−0.0566118
$58$	−10.3737	−1.36214
$59$	−0.486188	−0.0632963	−0.0316481	−	0.999499i	$-0.510076\pi$
$59$	−0.486188	−0.0632963	−0.0316481	+	0.999499i	$0.510076\pi$
$60$	0	0
$61$	−7.44694	−0.953483	−0.476741	−	0.879044i	$-0.658182\pi$
$61$	−7.44694	−0.953483	−0.476741	+	0.879044i	$0.658182\pi$
$62$	1.50350	0.190944
$63$	−3.55310	−0.447649
$64$	8.76693	1.09587
$65$	0	0
$66$	−5.07916	−0.625202
$67$	−11.1679	−1.36438	−0.682189	−	0.731176i	$-0.738972\pi$
$67$	−11.1679	−1.36438	−0.682189	+	0.731176i	$0.738972\pi$
$68$	0.0451796	0.00547883
$69$	−1.53185	−0.184413
$70$	0	0
$71$	3.41410	0.405179	0.202590	−	0.979264i	$-0.435064\pi$
$71$	3.41410	0.405179	0.202590	+	0.979264i	$0.435064\pi$
$72$	−7.08084	−0.834485
$73$	−4.57808	−0.535823	−0.267912	−	0.963443i	$-0.586334\pi$
$73$	−4.57808	−0.535823	−0.267912	+	0.963443i	$0.586334\pi$
$74$	−3.70444	−0.430633
$75$	0	0
$76$	0.145027	0.0166357
$77$	7.29691	0.831560
$78$	6.15819	0.697278
$79$	−4.21264	−0.473959	−0.236979	−	0.971515i	$-0.576157\pi$
$79$	−4.21264	−0.473959	−0.236979	+	0.971515i	$0.576157\pi$
$80$	0	0
$81$	3.74212	0.415791
$82$	−14.2945	−1.57856
$83$	−2.35078	−0.258032	−0.129016	−	0.991643i	$-0.541182\pi$
$83$	−2.35078	−0.258032	−0.129016	+	0.991643i	$0.541182\pi$
$84$	−0.319217	−0.0348294
$85$	0	0
$86$	15.8939	1.71389
$87$	6.24836	0.669894
$88$	14.5417	1.55015
$89$	−16.1621	−1.71318	−0.856589	−	0.516000i	$-0.827420\pi$
$89$	−16.1621	−1.71318	−0.856589	+	0.516000i	$0.827420\pi$
$90$	0	0
$91$	−8.84708	−0.927426
$92$	0.519781	0.0541909
$93$	−0.905594	−0.0939057
$94$	6.22708	0.642274
$95$	0	0
$96$	−1.19692	−0.122160
$97$	8.47833	0.860844	0.430422	−	0.902628i	$-0.358365\pi$
$97$	8.47833	0.860844	0.430422	+	0.902628i	$0.358365\pi$
$98$	6.25769	0.632122
$99$	−11.5544	−1.16126
$100$	0	0
$101$	−2.83240	−0.281835	−0.140917	−	0.990021i	$-0.545005\pi$
$101$	−2.83240	−0.281835	−0.140917	+	0.990021i	$0.545005\pi$
$102$	0.175186	0.0173460
$103$	−11.0597	−1.08975	−0.544873	−	0.838518i	$-0.683422\pi$
$103$	−11.0597	−1.08975	−0.544873	+	0.838518i	$0.683422\pi$
$104$	−17.6310	−1.72886
$105$	0	0
$106$	−16.8779	−1.63933
$107$	14.4128	1.39334	0.696668	−	0.717394i	$-0.254665\pi$
$107$	14.4128	1.39334	0.696668	+	0.717394i	$0.254665\pi$
$108$	1.14477	0.110156
$109$	−13.3056	−1.27445	−0.637223	−	0.770679i	$-0.719917\pi$
$109$	−13.3056	−1.27445	−0.637223	+	0.770679i	$0.719917\pi$
$110$	0	0
$111$	2.23128	0.211784
$112$	−5.07790	−0.479817
$113$	−16.1318	−1.51755	−0.758777	−	0.651350i	$-0.774203\pi$
$113$	−16.1318	−1.51755	−0.758777	+	0.651350i	$0.774203\pi$
$114$	0.562348	0.0526687
$115$	0	0
$116$	−2.12016	−0.196852
$117$	14.0091	1.29514
$118$	0.639683	0.0588876
$119$	−0.251679	−0.0230713
$120$	0	0
$121$	12.7290	1.15718
$122$	9.79802	0.887071
$123$	8.60992	0.776330
$124$	0.307282	0.0275947
$125$	0	0
$126$	4.67486	0.416469
$127$	2.56629	0.227722	0.113861	−	0.993497i	$-0.463678\pi$
$127$	2.56629	0.227722	0.113861	+	0.993497i	$0.463678\pi$
$128$	−8.51409	−0.752547
$129$	−9.57332	−0.842884
$130$	0	0
$131$	20.8670	1.82316	0.911578	−	0.411126i	$-0.134864\pi$
$131$	20.8670	1.82316	0.911578	+	0.411126i	$0.134864\pi$
$132$	−1.03807	−0.0903524
$133$	−0.807889	−0.0700529
$134$	14.6938	1.26935
$135$	0	0
$136$	−0.501561	−0.0430085
$137$	−9.63774	−0.823408	−0.411704	−	0.911318i	$-0.635066\pi$
$137$	−9.63774	−0.823408	−0.411704	+	0.911318i	$0.635066\pi$
$138$	2.01548	0.171569
$139$	−8.87649	−0.752894	−0.376447	−	0.926438i	$-0.622854\pi$
$139$	−8.87649	−0.752894	−0.376447	+	0.926438i	$0.622854\pi$
$140$	0	0
$141$	−3.75072	−0.315868
$142$	−4.49197	−0.376958
$143$	−28.7701	−2.40587
$144$	8.04069	0.670058
$145$	0	0
$146$	6.02343	0.498503
$147$	−3.76916	−0.310875
$148$	−0.757107	−0.0622338
$149$	11.6770	0.956619	0.478309	−	0.878191i	$-0.341250\pi$
$149$	11.6770	0.956619	0.478309	+	0.878191i	$0.341250\pi$
$150$	0	0
$151$	−3.61938	−0.294541	−0.147271	−	0.989096i	$-0.547049\pi$
$151$	−3.61938	−0.294541	−0.147271	+	0.989096i	$0.547049\pi$
$152$	−1.61001	−0.130589
$153$	0.398525	0.0322188
$154$	−9.60063	−0.773641
$155$	0	0
$156$	1.25860	0.100769
$157$	13.9971	1.11709	0.558546	−	0.829474i	$-0.311360\pi$
$157$	13.9971	1.11709	0.558546	+	0.829474i	$0.311360\pi$
$158$	5.54262	0.440947
$159$	10.1660	0.806215
$160$	0	0
$161$	−2.89551	−0.228198
$162$	−4.92355	−0.386831
$163$	12.0858	0.946629	0.473315	−	0.880894i	$-0.343057\pi$
$163$	12.0858	0.946629	0.473315	+	0.880894i	$0.343057\pi$
$164$	−2.92148	−0.228129
$165$	0	0
$166$	3.09295	0.240059
$167$	2.93988	0.227494	0.113747	−	0.993510i	$-0.463715\pi$
$167$	2.93988	0.227494	0.113747	+	0.993510i	$0.463715\pi$
$168$	3.54379	0.273409
$169$	21.8820	1.68323
$170$	0	0
$171$	1.27927	0.0978279
$172$	3.24837	0.247686
$173$	11.9172	0.906047	0.453024	−	0.891498i	$-0.350345\pi$
$173$	11.9172	0.906047	0.453024	+	0.891498i	$0.350345\pi$
$174$	−8.22104	−0.623235
$175$	0	0
$176$	−16.5130	−1.24471
$177$	−0.385297	−0.0289607
$178$	21.2646	1.59385
$179$	−17.7526	−1.32689	−0.663446	−	0.748224i	$-0.730907\pi$
$179$	−17.7526	−1.32689	−0.663446	+	0.748224i	$0.730907\pi$
$180$	0	0
$181$	8.92422	0.663332	0.331666	−	0.943397i	$-0.392389\pi$
$181$	8.92422	0.663332	0.331666	+	0.943397i	$0.392389\pi$
$182$	11.6402	0.862830
$183$	−5.90159	−0.436258
$184$	−5.77035	−0.425396
$185$	0	0
$186$	1.19150	0.0873650
$187$	−0.818440	−0.0598503
$188$	1.27268	0.0928196
$189$	−6.37711	−0.463867
$190$	0	0
$191$	5.66248	0.409723	0.204861	−	0.978791i	$-0.434326\pi$
$191$	5.66248	0.409723	0.204861	+	0.978791i	$0.434326\pi$
$192$	6.94767	0.501405
$193$	−8.50051	−0.611880	−0.305940	−	0.952051i	$-0.598971\pi$
$193$	−8.50051	−0.611880	−0.305940	+	0.952051i	$0.598971\pi$
$194$	−11.1550	−0.800885
$195$	0	0
$196$	1.27894	0.0913525
$197$	−25.5986	−1.82383	−0.911913	−	0.410382i	$-0.865395\pi$
$197$	−25.5986	−1.82383	−0.911913	+	0.410382i	$0.865395\pi$
$198$	15.2023	1.08038
$199$	11.7068	0.829870	0.414935	−	0.909851i	$-0.363804\pi$
$199$	11.7068	0.829870	0.414935	+	0.909851i	$0.363804\pi$
$200$	0	0
$201$	−8.85042	−0.624261
$202$	3.72662	0.262204
$203$	11.8106	0.828944
$204$	0.0358042	0.00250679
$205$	0	0
$206$	14.5514	1.01384
$207$	4.58494	0.318675
$208$	20.0210	1.38821
$209$	−2.62720	−0.181727
$210$	0	0
$211$	−27.8399	−1.91658	−0.958289	−	0.285801i	$-0.907740\pi$
$211$	−27.8399	−1.91658	−0.958289	+	0.285801i	$0.907740\pi$
$212$	−3.44947	−0.236911
$213$	2.70563	0.185387
$214$	−18.9631	−1.29629
$215$	0	0
$216$	−12.7087	−0.864718
$217$	−1.71175	−0.116201
$218$	17.5064	1.18568
$219$	−3.62806	−0.245162
$220$	0	0
$221$	0.992311	0.0667501
$222$	−2.93572	−0.197033
$223$	16.7447	1.12131	0.560655	−	0.828049i	$-0.310549\pi$
$223$	16.7447	1.12131	0.560655	+	0.828049i	$0.310549\pi$
$224$	−2.26241	−0.151164
$225$	0	0
$226$	21.2248	1.41185
$227$	−19.7021	−1.30767	−0.653836	−	0.756636i	$-0.726841\pi$
$227$	−19.7021	−1.30767	−0.653836	+	0.756636i	$0.726841\pi$
$228$	0.114932	0.00761153
$229$	−23.4763	−1.55136	−0.775679	−	0.631128i	$-0.782592\pi$
$229$	−23.4763	−1.55136	−0.775679	+	0.631128i	$0.782592\pi$
$230$	0	0
$231$	5.78270	0.380474
$232$	23.5370	1.54528
$233$	18.0244	1.18082	0.590409	−	0.807104i	$-0.298966\pi$
$233$	18.0244	1.18082	0.590409	+	0.807104i	$0.298966\pi$
$234$	−18.4319	−1.20493
$235$	0	0
$236$	0.130737	0.00851027
$237$	−3.33846	−0.216856
$238$	0.331136	0.0214644
$239$	16.5734	1.07205	0.536023	−	0.844203i	$-0.319926\pi$
$239$	16.5734	1.07205	0.536023	+	0.844203i	$0.319926\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−16.7477	−1.07658
$243$	15.7372	1.00954
$244$	2.00250	0.128197
$245$	0	0
$246$	−11.3282	−0.722258
$247$	3.18532	0.202677
$248$	−3.41129	−0.216617
$249$	−1.86296	−0.118060
$250$	0	0
$251$	−21.4301	−1.35266	−0.676329	−	0.736600i	$-0.736430\pi$
$251$	−21.4301	−1.35266	−0.676329	+	0.736600i	$0.736430\pi$
$252$	0.955439	0.0601870
$253$	−9.41597	−0.591977
$254$	−3.37650	−0.211861
$255$	0	0
$256$	−6.33177	−0.395736
$257$	23.7979	1.48447	0.742237	−	0.670138i	$-0.233765\pi$
$257$	23.7979	1.48447	0.742237	+	0.670138i	$0.233765\pi$
$258$	12.5957	0.784176
$259$	4.21756	0.262066
$260$	0	0
$261$	−18.7018	−1.15761
$262$	−27.4549	−1.69617
$263$	−6.88093	−0.424296	−0.212148	−	0.977238i	$-0.568046\pi$
$263$	−6.88093	−0.424296	−0.212148	+	0.977238i	$0.568046\pi$
$264$	11.5241	0.709261
$265$	0	0
$266$	1.06295	0.0651736
$267$	−12.8082	−0.783851
$268$	3.00308	0.183443
$269$	1.33959	0.0816765	0.0408382	−	0.999166i	$-0.486997\pi$
$269$	1.33959	0.0816765	0.0408382	+	0.999166i	$0.486997\pi$
$270$	0	0
$271$	0.930855	0.0565454	0.0282727	−	0.999600i	$-0.490999\pi$
$271$	0.930855	0.0565454	0.0282727	+	0.999600i	$0.490999\pi$
$272$	0.569550	0.0345341
$273$	−7.01119	−0.424337
$274$	12.6805	0.766056
$275$	0	0
$276$	0.411919	0.0247946
$277$	−13.4651	−0.809039	−0.404519	−	0.914529i	$-0.632561\pi$
$277$	−13.4651	−0.809039	−0.404519	+	0.914529i	$0.632561\pi$
$278$	11.6789	0.700454
$279$	2.71050	0.162274
$280$	0	0
$281$	−6.10137	−0.363977	−0.181989	−	0.983301i	$-0.558253\pi$
$281$	−6.10137	−0.363977	−0.181989	+	0.983301i	$0.558253\pi$
$282$	4.93487	0.293867
$283$	−27.4176	−1.62981	−0.814904	−	0.579595i	$-0.803211\pi$
$283$	−27.4176	−1.62981	−0.814904	+	0.579595i	$0.803211\pi$
$284$	−0.918061	−0.0544769
$285$	0	0
$286$	37.8531	2.23830
$287$	16.2745	0.960651
$288$	3.58245	0.211098
$289$	−16.9718	−0.998339
$290$	0	0
$291$	6.71896	0.393872
$292$	1.23106	0.0720422
$293$	3.96534	0.231658	0.115829	−	0.993269i	$-0.463048\pi$
$293$	3.96534	0.231658	0.115829	+	0.993269i	$0.463048\pi$
$294$	4.95913	0.289223
$295$	0	0
$296$	8.40502	0.488532
$297$	−20.7379	−1.20333
$298$	−15.3636	−0.889989
$299$	11.4163	0.660223
$300$	0	0
$301$	−18.0955	−1.04301
$302$	4.76206	0.274026
$303$	−2.24464	−0.128951
$304$	1.82826	0.104858
$305$	0	0
$306$	−0.524344	−0.0299747
$307$	−7.72374	−0.440817	−0.220409	−	0.975408i	$-0.570739\pi$
$307$	−7.72374	−0.440817	−0.220409	+	0.975408i	$0.570739\pi$
$308$	−1.96216	−0.111804
$309$	−8.76467	−0.498605
$310$	0	0
$311$	−9.74455	−0.552563	−0.276281	−	0.961077i	$-0.589102\pi$
$311$	−9.74455	−0.552563	−0.276281	+	0.961077i	$0.589102\pi$
$312$	−13.9723	−0.791028
$313$	−14.2462	−0.805244	−0.402622	−	0.915366i	$-0.631901\pi$
$313$	−14.2462	−0.805244	−0.402622	+	0.915366i	$0.631901\pi$
$314$	−18.4162	−1.03928
$315$	0	0
$316$	1.13279	0.0637244
$317$	−5.51857	−0.309954	−0.154977	−	0.987918i	$-0.549530\pi$
$317$	−5.51857	−0.309954	−0.154977	+	0.987918i	$0.549530\pi$
$318$	−13.3755	−0.750061
$319$	38.4073	2.15040
$320$	0	0
$321$	11.4219	0.637509
$322$	3.80965	0.212304
$323$	0.0906149	0.00504195
$324$	−1.00627	−0.0559037
$325$	0	0
$326$	−15.9014	−0.880695
$327$	−10.5445	−0.583113
$328$	32.4328	1.79080
$329$	−7.08961	−0.390863
$330$	0	0
$331$	14.1357	0.776967	0.388484	−	0.921456i	$-0.372999\pi$
$331$	14.1357	0.776967	0.388484	+	0.921456i	$0.372999\pi$
$332$	0.632131	0.0346927
$333$	−6.67837	−0.365972
$334$	−3.86803	−0.211649
$335$	0	0
$336$	−4.02417	−0.219536
$337$	−6.27148	−0.341629	−0.170815	−	0.985303i	$-0.554640\pi$
$337$	−6.27148	−0.341629	−0.170815	+	0.985303i	$0.554640\pi$
$338$	−28.7904	−1.56599
$339$	−12.7842	−0.694345
$340$	0	0
$341$	−5.56649	−0.301442
$342$	−1.68315	−0.0910141
$343$	−17.6102	−0.950860
$344$	−36.0618	−1.94432
$345$	0	0
$346$	−15.6796	−0.842940
$347$	−14.8798	−0.798792	−0.399396	−	0.916778i	$-0.630780\pi$
$347$	−14.8798	−0.798792	−0.399396	+	0.916778i	$0.630780\pi$
$348$	−1.68020	−0.0900682
$349$	−19.5770	−1.04793	−0.523967	−	0.851739i	$-0.675548\pi$
$349$	−19.5770	−1.04793	−0.523967	+	0.851739i	$0.675548\pi$
$350$	0	0
$351$	25.1435	1.34206
$352$	−7.35719	−0.392140
$353$	19.6183	1.04417	0.522087	−	0.852892i	$-0.325154\pi$
$353$	19.6183	1.04417	0.522087	+	0.852892i	$0.325154\pi$
$354$	0.506940	0.0269436
$355$	0	0
$356$	4.34603	0.230339
$357$	−0.199452	−0.0105561
$358$	23.3573	1.23447
$359$	−17.3983	−0.918246	−0.459123	−	0.888373i	$-0.651836\pi$
$359$	−17.3983	−0.918246	−0.459123	+	0.888373i	$0.651836\pi$
$360$	0	0
$361$	−18.7091	−0.984691
$362$	−11.7417	−0.617130
$363$	10.0876	0.529460
$364$	2.37900	0.124694
$365$	0	0
$366$	7.76480	0.405872
$367$	−31.5476	−1.64677	−0.823386	−	0.567482i	$-0.807918\pi$
$367$	−31.5476	−1.64677	−0.823386	+	0.567482i	$0.807918\pi$
$368$	6.55255	0.341575
$369$	−25.7701	−1.34154
$370$	0	0
$371$	19.2157	0.997631
$372$	0.243517	0.0126257
$373$	−21.2313	−1.09932	−0.549658	−	0.835390i	$-0.685242\pi$
$373$	−21.2313	−1.09932	−0.549658	+	0.835390i	$0.685242\pi$
$374$	1.07683	0.0556816
$375$	0	0
$376$	−14.1286	−0.728628
$377$	−46.5667	−2.39830
$378$	8.39044	0.431558
$379$	−16.5649	−0.850882	−0.425441	−	0.904986i	$-0.639881\pi$
$379$	−16.5649	−0.850882	−0.425441	+	0.904986i	$0.639881\pi$
$380$	0	0
$381$	2.03375	0.104192
$382$	−7.45019	−0.381185
$383$	−11.1394	−0.569196	−0.284598	−	0.958647i	$-0.591860\pi$
$383$	−11.1394	−0.569196	−0.284598	+	0.958647i	$0.591860\pi$
$384$	−6.74730	−0.344322
$385$	0	0
$386$	11.1842	0.569262
$387$	28.6536	1.45654
$388$	−2.27985	−0.115742
$389$	−7.55510	−0.383059	−0.191529	−	0.981487i	$-0.561345\pi$
$389$	−7.55510	−0.383059	−0.191529	+	0.981487i	$0.561345\pi$
$390$	0	0
$391$	0.324767	0.0164242
$392$	−14.1981	−0.717112
$393$	16.5368	0.834171
$394$	33.6804	1.69680
$395$	0	0
$396$	3.10702	0.156133
$397$	5.06211	0.254060	0.127030	−	0.991899i	$-0.459456\pi$
$397$	5.06211	0.254060	0.127030	+	0.991899i	$0.459456\pi$
$398$	−15.4027	−0.772069
$399$	−0.640241	−0.0320521
$400$	0	0
$401$	14.6655	0.732361	0.366181	−	0.930544i	$-0.380665\pi$
$401$	14.6655	0.732361	0.366181	+	0.930544i	$0.380665\pi$
$402$	11.6446	0.580780
$403$	6.74905	0.336194
$404$	0.761641	0.0378930
$405$	0	0
$406$	−15.5394	−0.771207
$407$	13.7152	0.679837
$408$	−0.397480	−0.0196782
$409$	23.5902	1.16646	0.583231	−	0.812307i	$-0.301788\pi$
$409$	23.5902	1.16646	0.583231	+	0.812307i	$0.301788\pi$
$410$	0	0
$411$	−7.63778	−0.376744
$412$	2.97399	0.146518
$413$	−0.728288	−0.0358367
$414$	−6.03246	−0.296479
$415$	0	0
$416$	8.92017	0.437347
$417$	−7.03450	−0.344481
$418$	3.45663	0.169069
$419$	7.19346	0.351424	0.175712	−	0.984442i	$-0.443777\pi$
$419$	7.19346	0.351424	0.175712	+	0.984442i	$0.443777\pi$
$420$	0	0
$421$	−13.7206	−0.668703	−0.334351	−	0.942449i	$-0.608517\pi$
$421$	−13.7206	−0.668703	−0.334351	+	0.942449i	$0.608517\pi$
$422$	36.6293	1.78309
$423$	11.2262	0.545835
$424$	38.2943	1.85974
$425$	0	0
$426$	−3.55983	−0.172474
$427$	−11.1552	−0.539837
$428$	−3.87563	−0.187336
$429$	−22.7999	−1.10079
$430$	0	0
$431$	−25.0489	−1.20657	−0.603283	−	0.797527i	$-0.706141\pi$
$431$	−25.0489	−1.20657	−0.603283	+	0.797527i	$0.706141\pi$
$432$	14.4315	0.694334
$433$	6.25494	0.300593	0.150297	−	0.988641i	$-0.451977\pi$
$433$	6.25494	0.300593	0.150297	+	0.988641i	$0.451977\pi$
$434$	2.25217	0.108108
$435$	0	0
$436$	3.57791	0.171351
$437$	1.04250	0.0498697
$438$	4.77348	0.228086
$439$	20.3864	0.972991	0.486495	−	0.873683i	$-0.338275\pi$
$439$	20.3864	0.972991	0.486495	+	0.873683i	$0.338275\pi$
$440$	0	0
$441$	11.2814	0.537208
$442$	−1.30560	−0.0621008
$443$	36.2861	1.72401	0.862003	−	0.506903i	$-0.169210\pi$
$443$	36.2861	1.72401	0.862003	+	0.506903i	$0.169210\pi$
$444$	−0.599997	−0.0284746
$445$	0	0
$446$	−22.0313	−1.04321
$447$	9.25387	0.437693
$448$	13.1325	0.620451
$449$	−26.4559	−1.24853	−0.624265	−	0.781213i	$-0.714601\pi$
$449$	−26.4559	−1.24853	−0.624265	+	0.781213i	$0.714601\pi$
$450$	0	0
$451$	52.9233	2.49206
$452$	4.33789	0.204037
$453$	−2.86831	−0.134765
$454$	25.9222	1.21659
$455$	0	0
$456$	−1.27591	−0.0597501
$457$	6.83697	0.319820	0.159910	−	0.987132i	$-0.448880\pi$
$457$	6.83697	0.319820	0.159910	+	0.987132i	$0.448880\pi$
$458$	30.8880	1.44330
$459$	0.715273	0.0333861
$460$	0	0
$461$	12.7048	0.591721	0.295861	−	0.955231i	$-0.404394\pi$
$461$	12.7048	0.591721	0.295861	+	0.955231i	$0.404394\pi$
$462$	−7.60837	−0.353973
$463$	−14.8083	−0.688199	−0.344099	−	0.938933i	$-0.611816\pi$
$463$	−14.8083	−0.688199	−0.344099	+	0.938933i	$0.611816\pi$
$464$	−26.7276	−1.24080
$465$	0	0
$466$	−23.7149	−1.09857
$467$	−29.0325	−1.34347	−0.671733	−	0.740793i	$-0.734450\pi$
$467$	−29.0325	−1.34347	−0.671733	+	0.740793i	$0.734450\pi$
$468$	−3.76708	−0.174133
$469$	−16.7291	−0.772476
$470$	0	0
$471$	11.0925	0.511116
$472$	−1.45138	−0.0668051
$473$	−58.8451	−2.70570
$474$	4.39245	0.201752
$475$	0	0
$476$	0.0676770	0.00310197
$477$	−30.4275	−1.39318
$478$	−21.8059	−0.997377
$479$	38.7414	1.77014	0.885071	−	0.465456i	$-0.154110\pi$
$479$	38.7414	1.77014	0.885071	+	0.465456i	$0.154110\pi$
$480$	0	0
$481$	−16.6289	−0.758211
$482$	1.31571	0.0599290
$483$	−2.29465	−0.104410
$484$	−3.42287	−0.155585
$485$	0	0
$486$	−20.7056	−0.939226
$487$	−23.8577	−1.08110	−0.540549	−	0.841313i	$-0.681783\pi$
$487$	−23.8577	−1.08110	−0.540549	+	0.841313i	$0.681783\pi$
$488$	−22.2308	−1.00634
$489$	9.57779	0.433123
$490$	0	0
$491$	−16.8136	−0.758788	−0.379394	−	0.925235i	$-0.623868\pi$
$491$	−16.8136	−0.758788	−0.379394	+	0.925235i	$0.623868\pi$
$492$	−2.31523	−0.104379
$493$	−1.32471	−0.0596620
$494$	−4.19097	−0.188560
$495$	0	0
$496$	3.87371	0.173935
$497$	5.11418	0.229402
$498$	2.45112	0.109837
$499$	30.4314	1.36230	0.681149	−	0.732145i	$-0.261480\pi$
$499$	30.4314	1.36230	0.681149	+	0.732145i	$0.261480\pi$
$500$	0	0
$501$	2.32981	0.104088
$502$	28.1959	1.25844
$503$	−19.2034	−0.856235	−0.428118	−	0.903723i	$-0.640823\pi$
$503$	−19.2034	−0.856235	−0.428118	+	0.903723i	$0.640823\pi$
$504$	−10.6068	−0.472464
$505$	0	0
$506$	12.3887	0.550745
$507$	17.3412	0.770150
$508$	−0.690083	−0.0306175
$509$	−23.9106	−1.05982	−0.529909	−	0.848054i	$-0.677774\pi$
$509$	−23.9106	−1.05982	−0.529909	+	0.848054i	$0.677774\pi$
$510$	0	0
$511$	−6.85776	−0.303369
$512$	25.3590	1.12072
$513$	2.29603	0.101372
$514$	−31.3112	−1.38108
$515$	0	0
$516$	2.57429	0.113327
$517$	−23.0549	−1.01395
$518$	−5.54909	−0.243813
$519$	9.44421	0.414555
$520$	0	0
$521$	−36.4671	−1.59765	−0.798827	−	0.601561i	$-0.794546\pi$
$521$	−36.4671	−1.59765	−0.798827	+	0.601561i	$0.794546\pi$
$522$	24.6061	1.07698
$523$	16.3959	0.716944	0.358472	−	0.933541i	$-0.383298\pi$
$523$	16.3959	0.716944	0.358472	+	0.933541i	$0.383298\pi$
$524$	−5.61119	−0.245126
$525$	0	0
$526$	9.05331	0.394743
$527$	0.191994	0.00836341
$528$	−13.0863	−0.569508
$529$	−19.2636	−0.837549
$530$	0	0
$531$	1.15322	0.0500455
$532$	0.217244	0.00941870
$533$	−64.1665	−2.77936
$534$	16.8519	0.729254
$535$	0	0
$536$	−33.3387	−1.44001
$537$	−14.0687	−0.607109
$538$	−1.76252	−0.0759876
$539$	−23.1682	−0.997927
$540$	0	0
$541$	−24.5039	−1.05350	−0.526752	−	0.850019i	$-0.676590\pi$
$541$	−24.5039	−1.05350	−0.526752	+	0.850019i	$0.676590\pi$
$542$	−1.22474	−0.0526070
$543$	7.07232	0.303502
$544$	0.253758	0.0108798
$545$	0	0
$546$	9.22471	0.394781
$547$	−18.0471	−0.771637	−0.385818	−	0.922575i	$-0.626081\pi$
$547$	−18.0471	−0.771637	−0.385818	+	0.922575i	$0.626081\pi$
$548$	2.59161	0.110708
$549$	17.6639	0.753876
$550$	0	0
$551$	−4.25233	−0.181155
$552$	−4.57292	−0.194636
$553$	−6.31035	−0.268343
$554$	17.7162	0.752688
$555$	0	0
$556$	2.38691	0.101228
$557$	21.0335	0.891216	0.445608	−	0.895228i	$-0.352988\pi$
$557$	21.0335	0.891216	0.445608	+	0.895228i	$0.352988\pi$
$558$	−3.56624	−0.150971
$559$	71.3463	3.01763
$560$	0	0
$561$	−0.648602	−0.0273840
$562$	8.02765	0.338626
$563$	−25.8990	−1.09151	−0.545757	−	0.837943i	$-0.683758\pi$
$563$	−25.8990	−1.09151	−0.545757	+	0.837943i	$0.683758\pi$
$564$	1.00858	0.0424689
$565$	0	0
$566$	36.0737	1.51629
$567$	5.60553	0.235410
$568$	10.1919	0.427641
$569$	44.9539	1.88457	0.942283	−	0.334819i	$-0.108675\pi$
$569$	44.9539	1.88457	0.942283	+	0.334819i	$0.108675\pi$
$570$	0	0
$571$	10.5319	0.440747	0.220373	−	0.975416i	$-0.429272\pi$
$571$	10.5319	0.440747	0.220373	+	0.975416i	$0.429272\pi$
$572$	7.73635	0.323473
$573$	4.48744	0.187465
$574$	−21.4125	−0.893740
$575$	0	0
$576$	−20.7949	−0.866453
$577$	−31.2124	−1.29939	−0.649695	−	0.760195i	$-0.725104\pi$
$577$	−31.2124	−1.29939	−0.649695	+	0.760195i	$0.725104\pi$
$578$	22.3300	0.928804
$579$	−6.73654	−0.279961
$580$	0	0
$581$	−3.52137	−0.146091
$582$	−8.84022	−0.366439
$583$	62.4881	2.58799
$584$	−13.6666	−0.565527
$585$	0	0
$586$	−5.21724	−0.215522
$587$	10.4924	0.433067	0.216533	−	0.976275i	$-0.430525\pi$
$587$	10.4924	0.433067	0.216533	+	0.976275i	$0.430525\pi$
$588$	1.01354	0.0417976
$589$	0.616303	0.0253943
$590$	0	0
$591$	−20.2866	−0.834478
$592$	−9.54437	−0.392271
$593$	−16.7486	−0.687784	−0.343892	−	0.939009i	$-0.611745\pi$
$593$	−16.7486	−0.687784	−0.343892	+	0.939009i	$0.611745\pi$
$594$	27.2851	1.11952
$595$	0	0
$596$	−3.13998	−0.128619
$597$	9.27745	0.379701
$598$	−15.0206	−0.614238
$599$	−28.4288	−1.16157	−0.580785	−	0.814057i	$-0.697254\pi$
$599$	−28.4288	−1.16157	−0.580785	+	0.814057i	$0.697254\pi$
$600$	0	0
$601$	−19.9614	−0.814242	−0.407121	−	0.913374i	$-0.633467\pi$
$601$	−19.9614	−0.814242	−0.407121	+	0.913374i	$0.633467\pi$
$602$	23.8084	0.970359
$603$	26.4899	1.07875
$604$	0.973262	0.0396015
$605$	0	0
$606$	2.95330	0.119970
$607$	−44.4599	−1.80457	−0.902286	−	0.431138i	$-0.858112\pi$
$607$	−44.4599	−1.80457	−0.902286	+	0.431138i	$0.858112\pi$
$608$	0.814563	0.0330349
$609$	9.35977	0.379277
$610$	0	0
$611$	27.9527	1.13085
$612$	−0.107164	−0.00433186
$613$	−3.89159	−0.157180	−0.0785898	−	0.996907i	$-0.525042\pi$
$613$	−3.89159	−0.157180	−0.0785898	+	0.996907i	$0.525042\pi$
$614$	10.1622	0.410114
$615$	0	0
$616$	21.7829	0.877658
$617$	46.3863	1.86744	0.933720	−	0.358004i	$-0.116543\pi$
$617$	46.3863	1.86744	0.933720	+	0.358004i	$0.116543\pi$
$618$	11.5318	0.463876
$619$	23.7504	0.954609	0.477305	−	0.878738i	$-0.341614\pi$
$619$	23.7504	0.954609	0.477305	+	0.878738i	$0.341614\pi$
$620$	0	0
$621$	8.22906	0.330221
$622$	12.8210	0.514076
$623$	−24.2101	−0.969957
$624$	15.8664	0.635163
$625$	0	0
$626$	18.7439	0.749158
$627$	−2.08202	−0.0831477
$628$	−3.76386	−0.150194
$629$	−0.473052	−0.0188618
$630$	0	0
$631$	−20.4988	−0.816043	−0.408022	−	0.912972i	$-0.633781\pi$
$631$	−20.4988	−0.816043	−0.408022	+	0.912972i	$0.633781\pi$
$632$	−12.5757	−0.500233
$633$	−22.0627	−0.876915
$634$	7.26084	0.288365
$635$	0	0
$636$	−2.73366	−0.108397
$637$	28.0902	1.11297
$638$	−50.5330	−2.00062
$639$	−8.09813	−0.320357
$640$	0	0
$641$	−26.9447	−1.06425	−0.532126	−	0.846665i	$-0.678607\pi$
$641$	−26.9447	−1.06425	−0.532126	+	0.846665i	$0.678607\pi$
$642$	−15.0280	−0.593106
$643$	11.5572	0.455770	0.227885	−	0.973688i	$-0.426819\pi$
$643$	11.5572	0.455770	0.227885	+	0.973688i	$0.426819\pi$
$644$	0.778609	0.0306815
$645$	0	0
$646$	−0.119223	−0.00469077
$647$	45.4127	1.78536	0.892680	−	0.450692i	$-0.148823\pi$
$647$	45.4127	1.78536	0.892680	+	0.450692i	$0.148823\pi$
$648$	11.1711	0.438840
$649$	−2.36834	−0.0929654
$650$	0	0
$651$	−1.35654	−0.0531670
$652$	−3.24989	−0.127276
$653$	26.4135	1.03364	0.516820	−	0.856094i	$-0.327116\pi$
$653$	26.4135	1.03364	0.516820	+	0.856094i	$0.327116\pi$
$654$	13.8735	0.542498
$655$	0	0
$656$	−36.8292	−1.43794
$657$	10.8590	0.423652
$658$	9.32789	0.363639
$659$	28.0994	1.09460	0.547298	−	0.836938i	$-0.315656\pi$
$659$	28.0994	1.09460	0.547298	+	0.836938i	$0.315656\pi$
$660$	0	0
$661$	8.12932	0.316194	0.158097	−	0.987424i	$-0.449464\pi$
$661$	8.12932	0.316194	0.158097	+	0.987424i	$0.449464\pi$
$662$	−18.5985	−0.722851
$663$	0.786393	0.0305410
$664$	−7.01760	−0.272336
$665$	0	0
$666$	8.78681	0.340482
$667$	−15.2405	−0.590115
$668$	−0.790540	−0.0305869
$669$	13.2700	0.513047
$670$	0	0
$671$	−36.2758	−1.40041
$672$	−1.79293	−0.0691637
$673$	−16.2898	−0.627924	−0.313962	−	0.949436i	$-0.601656\pi$
$673$	−16.2898	−0.627924	−0.313962	+	0.949436i	$0.601656\pi$
$674$	8.25145	0.317834
$675$	0	0
$676$	−5.88414	−0.226313
$677$	−24.0521	−0.924396	−0.462198	−	0.886777i	$-0.652939\pi$
$677$	−24.0521	−0.924396	−0.462198	+	0.886777i	$0.652939\pi$
$678$	16.8204	0.645983
$679$	12.7002	0.487388
$680$	0	0
$681$	−15.6136	−0.598315
$682$	7.32390	0.280447
$683$	29.8123	1.14073	0.570367	−	0.821390i	$-0.306801\pi$
$683$	29.8123	1.14073	0.570367	+	0.821390i	$0.306801\pi$
$684$	−0.343998	−0.0131531
$685$	0	0
$686$	23.1699	0.884631
$687$	−18.6046	−0.709811
$688$	40.9502	1.56121
$689$	−75.7633	−2.88635
$690$	0	0
$691$	13.9489	0.530640	0.265320	−	0.964160i	$-0.414522\pi$
$691$	13.9489	0.530640	0.265320	+	0.964160i	$0.414522\pi$
$692$	−3.20456	−0.121819
$693$	−17.3080	−0.657477
$694$	19.5776	0.743155
$695$	0	0
$696$	18.6527	0.707030
$697$	−1.82538	−0.0691414
$698$	25.7577	0.974943
$699$	14.2841	0.540274
$700$	0	0
$701$	−45.9425	−1.73523	−0.867613	−	0.497240i	$-0.834347\pi$
$701$	−45.9425	−1.73523	−0.867613	+	0.497240i	$0.834347\pi$
$702$	−33.0816	−1.24858
$703$	−1.51850	−0.0572713
$704$	42.7059	1.60954
$705$	0	0
$706$	−25.8120	−0.971446
$707$	−4.24281	−0.159567
$708$	0.103607	0.00389381
$709$	−8.98226	−0.337336	−0.168668	−	0.985673i	$-0.553947\pi$
$709$	−8.98226	−0.337336	−0.168668	+	0.985673i	$0.553947\pi$
$710$	0	0
$711$	9.99223	0.374738
$712$	−48.2474	−1.80815
$713$	2.20885	0.0827223
$714$	0.262421	0.00982086
$715$	0	0
$716$	4.77372	0.178402
$717$	13.1342	0.490506
$718$	22.8911	0.854289
$719$	−27.5144	−1.02611	−0.513057	−	0.858355i	$-0.671487\pi$
$719$	−27.5144	−1.02611	−0.513057	+	0.858355i	$0.671487\pi$
$720$	0	0
$721$	−16.5670	−0.616986
$722$	24.6158	0.916106
$723$	−0.792486	−0.0294729
$724$	−2.39975	−0.0891859
$725$	0	0
$726$	−13.2723	−0.492582
$727$	19.1553	0.710432	0.355216	−	0.934784i	$-0.384407\pi$
$727$	19.1553	0.710432	0.355216	+	0.934784i	$0.384407\pi$
$728$	−26.4105	−0.978838
$729$	1.24516	0.0461170
$730$	0	0
$731$	2.02963	0.0750687
$732$	1.58695	0.0586555
$733$	37.0581	1.36877	0.684386	−	0.729119i	$-0.260070\pi$
$733$	37.0581	1.36877	0.684386	+	0.729119i	$0.260070\pi$
$734$	41.5076	1.53207
$735$	0	0
$736$	2.91943	0.107611
$737$	−54.4017	−2.00391
$738$	33.9060	1.24810
$739$	4.40292	0.161964	0.0809820	−	0.996716i	$-0.474194\pi$
$739$	4.40292	0.161964	0.0809820	+	0.996716i	$0.474194\pi$
$740$	0	0
$741$	2.52432	0.0927334
$742$	−25.2824	−0.928145
$743$	−2.26132	−0.0829599	−0.0414800	−	0.999139i	$-0.513207\pi$
$743$	−2.26132	−0.0829599	−0.0414800	+	0.999139i	$0.513207\pi$
$744$	−2.70340	−0.0991114
$745$	0	0
$746$	27.9343	1.02275
$747$	5.57597	0.204014
$748$	0.220081	0.00804695
$749$	21.5897	0.788871
$750$	0	0
$751$	4.38740	0.160099	0.0800493	−	0.996791i	$-0.474492\pi$
$751$	4.38740	0.160099	0.0800493	+	0.996791i	$0.474492\pi$
$752$	16.0438	0.585059
$753$	−16.9831	−0.618898
$754$	61.2683	2.23126
$755$	0	0
$756$	1.71482	0.0623675
$757$	39.0564	1.41953	0.709765	−	0.704439i	$-0.248801\pi$
$757$	39.0564	1.41953	0.709765	+	0.704439i	$0.248801\pi$
$758$	21.7946	0.791617
$759$	−7.46203	−0.270854
$760$	0	0
$761$	0.290222	0.0105205	0.00526027	−	0.999986i	$-0.498326\pi$
$761$	0.290222	0.0105205	0.00526027	+	0.999986i	$0.498326\pi$
$762$	−2.67583	−0.0969351
$763$	−19.9312	−0.721559
$764$	−1.52266	−0.0550878
$765$	0	0
$766$	14.6562	0.529551
$767$	2.87147	0.103683
$768$	−5.01784	−0.181066
$769$	39.2104	1.41396	0.706982	−	0.707232i	$-0.250056\pi$
$769$	39.2104	1.41396	0.706982	+	0.707232i	$0.250056\pi$
$770$	0	0
$771$	18.8595	0.679209
$772$	2.28581	0.0822681
$773$	11.7851	0.423882	0.211941	−	0.977282i	$-0.432022\pi$
$773$	11.7851	0.423882	0.211941	+	0.977282i	$0.432022\pi$
$774$	−37.6999	−1.35509
$775$	0	0
$776$	25.3097	0.908565
$777$	3.34236	0.119906
$778$	9.94033	0.356378
$779$	−5.85949	−0.209938
$780$	0	0
$781$	16.6309	0.595101
$782$	−0.427300	−0.0152802
$783$	−33.5660	−1.19955
$784$	16.1227	0.575812
$785$	0	0
$786$	−21.7577	−0.776070
$787$	−15.4269	−0.549910	−0.274955	−	0.961457i	$-0.588663\pi$
$787$	−15.4269	−0.549910	−0.274955	+	0.961457i	$0.588663\pi$
$788$	6.88354	0.245216
$789$	−5.45304	−0.194133
$790$	0	0
$791$	−24.1648	−0.859200
$792$	−34.4925	−1.22564
$793$	43.9824	1.56186
$794$	−6.66028	−0.236364
$795$	0	0
$796$	−3.14798	−0.111577
$797$	−36.5648	−1.29519	−0.647596	−	0.761984i	$-0.724225\pi$
$797$	−36.5648	−1.29519	−0.647596	+	0.761984i	$0.724225\pi$
$798$	0.842372	0.0298197
$799$	0.795189	0.0281318
$800$	0	0
$801$	38.3359	1.35453
$802$	−19.2956	−0.681351
$803$	−22.3009	−0.786983
$804$	2.37990	0.0839327
$805$	0	0
$806$	−8.87980	−0.312778
$807$	1.06161	0.0373704
$808$	−8.45535	−0.297458
$809$	−2.74767	−0.0966029	−0.0483015	−	0.998833i	$-0.515381\pi$
$809$	−2.74767	−0.0966029	−0.0483015	+	0.998833i	$0.515381\pi$
$810$	0	0
$811$	5.24291	0.184104	0.0920518	−	0.995754i	$-0.470657\pi$
$811$	5.24291	0.184104	0.0920518	+	0.995754i	$0.470657\pi$
$812$	−3.17591	−0.111453
$813$	0.737690	0.0258719
$814$	−18.0452	−0.632485
$815$	0	0
$816$	0.451361	0.0158008
$817$	6.51513	0.227936
$818$	−31.0379	−1.08522
$819$	20.9850	0.733274
$820$	0	0
$821$	−37.0020	−1.29138	−0.645689	−	0.763601i	$-0.723430\pi$
$821$	−37.0020	−1.29138	−0.645689	+	0.763601i	$0.723430\pi$
$822$	10.0491	0.350503
$823$	−0.840700	−0.0293049	−0.0146525	−	0.999893i	$-0.504664\pi$
$823$	−0.840700	−0.0293049	−0.0146525	+	0.999893i	$0.504664\pi$
$824$	−33.0157	−1.15016
$825$	0	0
$826$	0.958217	0.0333406
$827$	−32.4199	−1.12735	−0.563676	−	0.825996i	$-0.690613\pi$
$827$	−32.4199	−1.12735	−0.563676	+	0.825996i	$0.690613\pi$
$828$	−1.23290	−0.0428463
$829$	−22.6168	−0.785513	−0.392757	−	0.919642i	$-0.628479\pi$
$829$	−22.6168	−0.785513	−0.392757	+	0.919642i	$0.628479\pi$
$830$	0	0
$831$	−10.6709	−0.370169
$832$	−51.7784	−1.79509
$833$	0.799099	0.0276871
$834$	9.25537	0.320487
$835$	0	0
$836$	0.706460	0.0244334
$837$	4.86482	0.168153
$838$	−9.46452	−0.326947
$839$	−48.6992	−1.68128	−0.840642	−	0.541591i	$-0.817822\pi$
$839$	−48.6992	−1.68128	−0.840642	+	0.541591i	$0.817822\pi$
$840$	0	0
$841$	33.1653	1.14363
$842$	18.0524	0.622127
$843$	−4.83525	−0.166535
$844$	7.48622	0.257686
$845$	0	0
$846$	−14.7704	−0.507817
$847$	19.0675	0.655167
$848$	−43.4853	−1.49329
$849$	−21.7281	−0.745706
$850$	0	0
$851$	−5.44236	−0.186562
$852$	−0.727551	−0.0249255
$853$	9.58094	0.328045	0.164022	−	0.986457i	$-0.447553\pi$
$853$	9.58094	0.328045	0.164022	+	0.986457i	$0.447553\pi$
$854$	14.6770	0.502237
$855$	0	0
$856$	43.0253	1.47058
$857$	34.5920	1.18164	0.590821	−	0.806803i	$-0.298804\pi$
$857$	34.5920	1.18164	0.590821	+	0.806803i	$0.298804\pi$
$858$	29.9981	1.02412
$859$	−0.294800	−0.0100585	−0.00502923	−	0.999987i	$-0.501601\pi$
$859$	−0.294800	−0.0100585	−0.00502923	+	0.999987i	$0.501601\pi$
$860$	0	0
$861$	12.8973	0.439538
$862$	32.9572	1.12253
$863$	20.0104	0.681163	0.340582	−	0.940215i	$-0.389376\pi$
$863$	20.0104	0.681163	0.340582	+	0.940215i	$0.389376\pi$
$864$	6.42979	0.218746
$865$	0	0
$866$	−8.22970	−0.279657
$867$	−13.4499	−0.456782
$868$	0.460295	0.0156234
$869$	−20.5208	−0.696120
$870$	0	0
$871$	65.9589	2.23493
$872$	−39.7202	−1.34510
$873$	−20.1103	−0.680631
$874$	−1.37164	−0.0463963
$875$	0	0
$876$	0.975596	0.0329623
$877$	6.24297	0.210810	0.105405	−	0.994429i	$-0.466386\pi$
$877$	6.24297	0.210810	0.105405	+	0.994429i	$0.466386\pi$
$878$	−26.8226	−0.905220
$879$	3.14248	0.105993
$880$	0	0
$881$	9.93111	0.334588	0.167294	−	0.985907i	$-0.446497\pi$
$881$	9.93111	0.334588	0.167294	+	0.985907i	$0.446497\pi$
$882$	−14.8430	−0.499791
$883$	−40.6434	−1.36776	−0.683880	−	0.729594i	$-0.739709\pi$
$883$	−40.6434	−1.36776	−0.683880	+	0.729594i	$0.739709\pi$
$884$	−0.266835	−0.00897464
$885$	0	0
$886$	−47.7421	−1.60393
$887$	20.3114	0.681992	0.340996	−	0.940065i	$-0.389236\pi$
$887$	20.3114	0.681992	0.340996	+	0.940065i	$0.389236\pi$
$888$	6.66086	0.223524
$889$	3.84419	0.128930
$890$	0	0
$891$	18.2288	0.610687
$892$	−4.50271	−0.150762
$893$	2.55256	0.0854182
$894$	−12.1754	−0.407207
$895$	0	0
$896$	−12.7537	−0.426073
$897$	9.04728	0.302080
$898$	34.8083	1.16157
$899$	−9.00982	−0.300494
$900$	0	0
$901$	−2.15529	−0.0718030
$902$	−69.6318	−2.31849
$903$	−14.3404	−0.477219
$904$	−48.1571	−1.60168
$905$	0	0
$906$	3.77387	0.125378
$907$	52.0351	1.72780	0.863899	−	0.503665i	$-0.168015\pi$
$907$	52.0351	1.72780	0.863899	+	0.503665i	$0.168015\pi$
$908$	5.29794	0.175818
$909$	6.71836	0.222834
$910$	0	0
$911$	−54.5255	−1.80651	−0.903255	−	0.429104i	$-0.858829\pi$
$911$	−54.5255	−1.80651	−0.903255	+	0.429104i	$0.858829\pi$
$912$	1.44887	0.0479769
$913$	−11.4512	−0.378980
$914$	−8.99548	−0.297544
$915$	0	0
$916$	6.31284	0.208582
$917$	31.2578	1.03222
$918$	−0.941093	−0.0310607
$919$	−13.6116	−0.449004	−0.224502	−	0.974474i	$-0.572076\pi$
$919$	−13.6116	−0.449004	−0.224502	+	0.974474i	$0.572076\pi$
$920$	0	0
$921$	−6.12096	−0.201693
$922$	−16.7159	−0.550507
$923$	−20.1640	−0.663707
$924$	−1.55498	−0.0511552
$925$	0	0
$926$	19.4834	0.640265
$927$	26.2333	0.861614
$928$	−11.9082	−0.390906
$929$	14.2799	0.468507	0.234254	−	0.972176i	$-0.424735\pi$
$929$	14.2799	0.468507	0.234254	+	0.972176i	$0.424735\pi$
$930$	0	0
$931$	2.56511	0.0840681
$932$	−4.84681	−0.158763
$933$	−7.72242	−0.252821
$934$	38.1985	1.24989
$935$	0	0
$936$	41.8202	1.36694
$937$	33.6599	1.09962	0.549811	−	0.835289i	$-0.314700\pi$
$937$	33.6599	1.09962	0.549811	+	0.835289i	$0.314700\pi$
$938$	22.0106	0.718672
$939$	−11.2899	−0.368433
$940$	0	0
$941$	−34.7406	−1.13251	−0.566256	−	0.824229i	$-0.691609\pi$
$941$	−34.7406	−1.13251	−0.566256	+	0.824229i	$0.691609\pi$
$942$	−14.5946	−0.475516
$943$	−21.0006	−0.683875
$944$	1.64812	0.0536418
$945$	0	0
$946$	77.4232	2.51725
$947$	50.7342	1.64864	0.824321	−	0.566123i	$-0.191557\pi$
$947$	50.7342	1.64864	0.824321	+	0.566123i	$0.191557\pi$
$948$	0.897720	0.0291566
$949$	27.0386	0.877710
$950$	0	0
$951$	−4.37339	−0.141817
$952$	−0.751316	−0.0243503
$953$	−49.4805	−1.60283	−0.801416	−	0.598108i	$-0.795919\pi$
$953$	−49.4805	−1.60283	−0.801416	+	0.598108i	$0.795919\pi$
$954$	40.0338	1.29614
$955$	0	0
$956$	−4.45664	−0.144138
$957$	30.4373	0.983897
$958$	−50.9726	−1.64685
$959$	−14.4369	−0.466192
$960$	0	0
$961$	−29.6942	−0.957877
$962$	21.8788	0.705401
$963$	−34.1866	−1.10165
$964$	0.268903	0.00866077
$965$	0	0
$966$	3.01910	0.0971378
$967$	−10.9937	−0.353534	−0.176767	−	0.984253i	$-0.556564\pi$
$967$	−10.9937	−0.353534	−0.176767	+	0.984253i	$0.556564\pi$
$968$	37.9989	1.22133
$969$	0.0718110	0.00230690
$970$	0	0
$971$	30.2653	0.971260	0.485630	−	0.874164i	$-0.338590\pi$
$971$	30.2653	0.971260	0.485630	+	0.874164i	$0.338590\pi$
$972$	−4.23178	−0.135734
$973$	−13.2966	−0.426269
$974$	31.3899	1.00580
$975$	0	0
$976$	25.2443	0.808049
$977$	−29.1189	−0.931595	−0.465798	−	0.884891i	$-0.654233\pi$
$977$	−29.1189	−0.931595	−0.465798	+	0.884891i	$0.654233\pi$
$978$	−12.6016	−0.402955
$979$	−78.7294	−2.51620
$980$	0	0
$981$	31.5605	1.00765
$982$	22.1219	0.705938
$983$	36.6989	1.17051	0.585256	−	0.810849i	$-0.300994\pi$
$983$	36.6989	1.17051	0.585256	+	0.810849i	$0.300994\pi$
$984$	25.7025	0.819366
$985$	0	0
$986$	1.74294	0.0555065
$987$	−5.61842	−0.178836
$988$	−0.856542	−0.0272502
$989$	23.3505	0.742503
$990$	0	0
$991$	11.9747	0.380389	0.190195	−	0.981746i	$-0.439088\pi$
$991$	11.9747	0.380389	0.190195	+	0.981746i	$0.439088\pi$
$992$	1.72589	0.0547972
$993$	11.2023	0.355495
$994$	−6.72878	−0.213424
$995$	0	0
$996$	0.500955	0.0158734
$997$	−7.64884	−0.242241	−0.121121	−	0.992638i	$-0.538649\pi$
$997$	−7.64884	−0.242241	−0.121121	+	0.992638i	$0.538649\pi$
$998$	−40.0390	−1.26741
$999$	−11.9863	−0.379231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.9		25
5.4	even	2		1205.2.a.e.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.17	✓	25	5.4	even	2
6025.2.a.j.1.9		25	1.1	even	1	trivial

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31571 q^{2} +0.792486 q^{3} -0.268903 q^{4} -1.04268 q^{6} +1.49796 q^{7} +2.98522 q^{8} -2.37197 q^{9} +O(q^{10})\)	\(q-1.31571 q^{2} +0.792486 q^{3} -0.268903 q^{4} -1.04268 q^{6} +1.49796 q^{7} +2.98522 q^{8} -2.37197 q^{9} +4.87124 q^{11} -0.213102 q^{12} -5.90610 q^{13} -1.97088 q^{14} -3.38989 q^{16} -0.168015 q^{17} +3.12082 q^{18} -0.539327 q^{19} +1.18711 q^{21} -6.40915 q^{22} -1.93297 q^{23} +2.36575 q^{24} +7.77073 q^{26} -4.25721 q^{27} -0.402805 q^{28} +7.88450 q^{29} -1.14273 q^{31} -1.51033 q^{32} +3.86039 q^{33} +0.221059 q^{34} +0.637828 q^{36} +2.81554 q^{37} +0.709599 q^{38} -4.68050 q^{39} +10.8644 q^{41} -1.56189 q^{42} -12.0801 q^{43} -1.30989 q^{44} +2.54323 q^{46} -4.73286 q^{47} -2.68644 q^{48} -4.75613 q^{49} -0.133149 q^{51} +1.58817 q^{52} +12.8280 q^{53} +5.60126 q^{54} +4.47173 q^{56} -0.427410 q^{57} -10.3737 q^{58} -0.486188 q^{59} -7.44694 q^{61} +1.50350 q^{62} -3.55310 q^{63} +8.76693 q^{64} -5.07916 q^{66} -11.1679 q^{67} +0.0451796 q^{68} -1.53185 q^{69} +3.41410 q^{71} -7.08084 q^{72} -4.57808 q^{73} -3.70444 q^{74} +0.145027 q^{76} +7.29691 q^{77} +6.15819 q^{78} -4.21264 q^{79} +3.74212 q^{81} -14.2945 q^{82} -2.35078 q^{83} -0.319217 q^{84} +15.8939 q^{86} +6.24836 q^{87} +14.5417 q^{88} -16.1621 q^{89} -8.84708 q^{91} +0.519781 q^{92} -0.905594 q^{93} +6.22708 q^{94} -1.19692 q^{96} +8.47833 q^{97} +6.25769 q^{98} -11.5544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Introduction

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