LMFDB - Embedded newform 6025.2.a.j.1.12

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			1.12
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)

$f(q)$	$=$	$q-0.707449 q^{2} -1.14949 q^{3} -1.49952 q^{4} +0.813204 q^{6} -1.94091 q^{7} +2.47573 q^{8} -1.67868 q^{9} +O(q^{10})$	\(q-0.707449 q^{2} -1.14949 q^{3} -1.49952 q^{4} +0.813204 q^{6} -1.94091 q^{7} +2.47573 q^{8} -1.67868 q^{9} +4.58088 q^{11} +1.72367 q^{12} +3.56621 q^{13} +1.37310 q^{14} +1.24758 q^{16} -6.32288 q^{17} +1.18758 q^{18} -2.19825 q^{19} +2.23105 q^{21} -3.24074 q^{22} -9.36924 q^{23} -2.84582 q^{24} -2.52292 q^{26} +5.37808 q^{27} +2.91043 q^{28} +5.33668 q^{29} +3.88834 q^{31} -5.83406 q^{32} -5.26566 q^{33} +4.47312 q^{34} +2.51721 q^{36} -0.0793096 q^{37} +1.55515 q^{38} -4.09932 q^{39} +0.604633 q^{41} -1.57836 q^{42} +12.1292 q^{43} -6.86910 q^{44} +6.62826 q^{46} -3.42847 q^{47} -1.43407 q^{48} -3.23286 q^{49} +7.26806 q^{51} -5.34759 q^{52} -9.94958 q^{53} -3.80472 q^{54} -4.80517 q^{56} +2.52686 q^{57} -3.77543 q^{58} -0.934533 q^{59} +5.44709 q^{61} -2.75080 q^{62} +3.25817 q^{63} +1.63215 q^{64} +3.72519 q^{66} +2.85245 q^{67} +9.48125 q^{68} +10.7698 q^{69} -6.57289 q^{71} -4.15596 q^{72} +12.8465 q^{73} +0.0561075 q^{74} +3.29631 q^{76} -8.89108 q^{77} +2.90006 q^{78} -2.00752 q^{79} -1.14599 q^{81} -0.427747 q^{82} -3.25482 q^{83} -3.34550 q^{84} -8.58076 q^{86} -6.13444 q^{87} +11.3410 q^{88} +7.86013 q^{89} -6.92171 q^{91} +14.0493 q^{92} -4.46960 q^{93} +2.42547 q^{94} +6.70617 q^{96} +5.44160 q^{97} +2.28708 q^{98} -7.68983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.707449	−0.500242	−0.250121	−	0.968215i	$-0.580470\pi$
$2$	−0.707449	−0.500242	−0.250121	+	0.968215i	$0.580470\pi$
$3$	−1.14949	−0.663656	−0.331828	−	0.943340i	$-0.607665\pi$
$3$	−1.14949	−0.663656	−0.331828	+	0.943340i	$0.607665\pi$
$4$	−1.49952	−0.749758
$5$	0	0
$5$	0	0
$6$	0.813204	0.331989
$7$	−1.94091	−0.733596	−0.366798	−	0.930301i	$-0.619546\pi$
$7$	−1.94091	−0.733596	−0.366798	+	0.930301i	$0.619546\pi$
$8$	2.47573	0.875303
$9$	−1.67868	−0.559560
$10$	0	0
$11$	4.58088	1.38119	0.690593	−	0.723243i	$-0.257349\pi$
$11$	4.58088	1.38119	0.690593	+	0.723243i	$0.257349\pi$
$12$	1.72367	0.497581
$13$	3.56621	0.989090	0.494545	−	0.869152i	$-0.335335\pi$
$13$	3.56621	0.989090	0.494545	+	0.869152i	$0.335335\pi$
$14$	1.37310	0.366976
$15$	0	0
$16$	1.24758	0.311894
$17$	−6.32288	−1.53352	−0.766761	−	0.641932i	$-0.778133\pi$
$17$	−6.32288	−1.53352	−0.766761	+	0.641932i	$0.778133\pi$
$18$	1.18758	0.279916
$19$	−2.19825	−0.504314	−0.252157	−	0.967686i	$-0.581140\pi$
$19$	−2.19825	−0.504314	−0.252157	+	0.967686i	$0.581140\pi$
$20$	0	0
$21$	2.23105	0.486856
$22$	−3.24074	−0.690928
$23$	−9.36924	−1.95362	−0.976811	−	0.214103i	$-0.931317\pi$
$23$	−9.36924	−1.95362	−0.976811	+	0.214103i	$0.931317\pi$
$24$	−2.84582	−0.580900
$25$	0	0
$26$	−2.52292	−0.494785
$27$	5.37808	1.03501
$28$	2.91043	0.550019
$29$	5.33668	0.990997	0.495498	−	0.868609i	$-0.334985\pi$
$29$	5.33668	0.990997	0.495498	+	0.868609i	$0.334985\pi$
$30$	0	0
$31$	3.88834	0.698367	0.349183	−	0.937054i	$-0.386459\pi$
$31$	3.88834	0.698367	0.349183	+	0.937054i	$0.386459\pi$
$32$	−5.83406	−1.03133
$33$	−5.26566	−0.916634
$34$	4.47312	0.767133
$35$	0	0
$36$	2.51721	0.419535
$37$	−0.0793096	−0.0130384	−0.00651921	−	0.999979i	$-0.502075\pi$
$37$	−0.0793096	−0.0130384	−0.00651921	+	0.999979i	$0.502075\pi$
$38$	1.55515	0.252279
$39$	−4.09932	−0.656416
$40$	0	0
$41$	0.604633	0.0944278	0.0472139	−	0.998885i	$-0.484966\pi$
$41$	0.604633	0.0944278	0.0472139	+	0.998885i	$0.484966\pi$
$42$	−1.57836	−0.243546
$43$	12.1292	1.84968	0.924839	−	0.380358i	$-0.124199\pi$
$43$	12.1292	1.84968	0.924839	+	0.380358i	$0.124199\pi$
$44$	−6.86910	−1.03556
$45$	0	0
$46$	6.62826	0.977284
$47$	−3.42847	−0.500093	−0.250047	−	0.968234i	$-0.580446\pi$
$47$	−3.42847	−0.500093	−0.250047	+	0.968234i	$0.580446\pi$
$48$	−1.43407	−0.206991
$49$	−3.23286	−0.461837
$50$	0	0
$51$	7.26806	1.01773
$52$	−5.34759	−0.741578
$53$	−9.94958	−1.36668	−0.683340	−	0.730100i	$-0.739473\pi$
$53$	−9.94958	−1.36668	−0.683340	+	0.730100i	$0.739473\pi$
$54$	−3.80472	−0.517757
$55$	0	0
$56$	−4.80517	−0.642118
$57$	2.52686	0.334691
$58$	−3.77543	−0.495738
$59$	−0.934533	−0.121666	−0.0608329	−	0.998148i	$-0.519376\pi$
$59$	−0.934533	−0.121666	−0.0608329	+	0.998148i	$0.519376\pi$
$60$	0	0
$61$	5.44709	0.697428	0.348714	−	0.937229i	$-0.386618\pi$
$61$	5.44709	0.697428	0.348714	+	0.937229i	$0.386618\pi$
$62$	−2.75080	−0.349353
$63$	3.25817	0.410491
$64$	1.63215	0.204018
$65$	0	0
$66$	3.72519	0.458539
$67$	2.85245	0.348482	0.174241	−	0.984703i	$-0.444253\pi$
$67$	2.85245	0.348482	0.174241	+	0.984703i	$0.444253\pi$
$68$	9.48125	1.14977
$69$	10.7698	1.29653
$70$	0	0
$71$	−6.57289	−0.780058	−0.390029	−	0.920802i	$-0.627535\pi$
$71$	−6.57289	−0.780058	−0.390029	+	0.920802i	$0.627535\pi$
$72$	−4.15596	−0.489785
$73$	12.8465	1.50357	0.751786	−	0.659407i	$-0.229193\pi$
$73$	12.8465	1.50357	0.751786	+	0.659407i	$0.229193\pi$
$74$	0.0561075	0.00652237
$75$	0	0
$76$	3.29631	0.378113
$77$	−8.89108	−1.01323
$78$	2.90006	0.328367
$79$	−2.00752	−0.225864	−0.112932	−	0.993603i	$-0.536024\pi$
$79$	−2.00752	−0.225864	−0.112932	+	0.993603i	$0.536024\pi$
$80$	0	0
$81$	−1.14599	−0.127332
$82$	−0.427747	−0.0472368
$83$	−3.25482	−0.357263	−0.178632	−	0.983916i	$-0.557167\pi$
$83$	−3.25482	−0.357263	−0.178632	+	0.983916i	$0.557167\pi$
$84$	−3.34550	−0.365024
$85$	0	0
$86$	−8.58076	−0.925287
$87$	−6.13444	−0.657681
$88$	11.3410	1.20896
$89$	7.86013	0.833172	0.416586	−	0.909096i	$-0.363227\pi$
$89$	7.86013	0.833172	0.416586	+	0.909096i	$0.363227\pi$
$90$	0	0
$91$	−6.92171	−0.725592
$92$	14.0493	1.46474
$93$	−4.46960	−0.463475
$94$	2.42547	0.250168
$95$	0	0
$96$	6.70617	0.684446
$97$	5.44160	0.552511	0.276255	−	0.961084i	$-0.410906\pi$
$97$	5.44160	0.552511	0.276255	+	0.961084i	$0.410906\pi$
$98$	2.28708	0.231030
$99$	−7.68983	−0.772857
$100$	0	0
$101$	−1.88977	−0.188039	−0.0940196	−	0.995570i	$-0.529972\pi$
$101$	−1.88977	−0.188039	−0.0940196	+	0.995570i	$0.529972\pi$
$102$	−5.14179	−0.509113
$103$	−16.5674	−1.63243	−0.816216	−	0.577747i	$-0.803932\pi$
$103$	−16.5674	−1.63243	−0.816216	+	0.577747i	$0.803932\pi$
$104$	8.82898	0.865753
$105$	0	0
$106$	7.03883	0.683671
$107$	6.60638	0.638663	0.319331	−	0.947643i	$-0.396542\pi$
$107$	6.60638	0.638663	0.319331	+	0.947643i	$0.396542\pi$
$108$	−8.06451	−0.776008
$109$	15.8701	1.52008	0.760041	−	0.649875i	$-0.225179\pi$
$109$	15.8701	1.52008	0.760041	+	0.649875i	$0.225179\pi$
$110$	0	0
$111$	0.0911653	0.00865303
$112$	−2.42144	−0.228804
$113$	11.5119	1.08295	0.541476	−	0.840716i	$-0.317866\pi$
$113$	11.5119	1.08295	0.541476	+	0.840716i	$0.317866\pi$
$114$	−1.78763	−0.167427
$115$	0	0
$116$	−8.00243	−0.743007
$117$	−5.98653	−0.553455
$118$	0.661135	0.0608624
$119$	12.2721	1.12499
$120$	0	0
$121$	9.98445	0.907677
$122$	−3.85354	−0.348883
$123$	−0.695018	−0.0626676
$124$	−5.83063	−0.523606
$125$	0	0
$126$	−2.30499	−0.205345
$127$	21.9227	1.94533	0.972663	−	0.232221i	$-0.0745992\pi$
$127$	21.9227	1.94533	0.972663	+	0.232221i	$0.0745992\pi$
$128$	10.5135	0.929267
$129$	−13.9423	−1.22755
$130$	0	0
$131$	−0.514319	−0.0449363	−0.0224681	−	0.999748i	$-0.507152\pi$
$131$	−0.514319	−0.0449363	−0.0224681	+	0.999748i	$0.507152\pi$
$132$	7.89594	0.687253
$133$	4.26662	0.369963
$134$	−2.01796	−0.174326
$135$	0	0
$136$	−15.6537	−1.34230
$137$	−6.98510	−0.596777	−0.298389	−	0.954444i	$-0.596449\pi$
$137$	−6.98510	−0.596777	−0.298389	+	0.954444i	$0.596449\pi$
$138$	−7.61910	−0.648581
$139$	7.13321	0.605031	0.302516	−	0.953144i	$-0.402174\pi$
$139$	7.13321	0.605031	0.302516	+	0.953144i	$0.402174\pi$
$140$	0	0
$141$	3.94098	0.331890
$142$	4.64999	0.390218
$143$	16.3364	1.36612
$144$	−2.09428	−0.174524
$145$	0	0
$146$	−9.08827	−0.752150
$147$	3.71613	0.306501
$148$	0.118926	0.00977565
$149$	−8.19104	−0.671036	−0.335518	−	0.942034i	$-0.608911\pi$
$149$	−8.19104	−0.671036	−0.335518	+	0.942034i	$0.608911\pi$
$150$	0	0
$151$	−19.3455	−1.57431	−0.787156	−	0.616754i	$-0.788447\pi$
$151$	−19.3455	−1.57431	−0.787156	+	0.616754i	$0.788447\pi$
$152$	−5.44228	−0.441427
$153$	10.6141	0.858098
$154$	6.28999	0.506862
$155$	0	0
$156$	6.14699	0.492153
$157$	−10.2567	−0.818575	−0.409288	−	0.912405i	$-0.634223\pi$
$157$	−10.2567	−0.818575	−0.409288	+	0.912405i	$0.634223\pi$
$158$	1.42022	0.112987
$159$	11.4369	0.907006
$160$	0	0
$161$	18.1849	1.43317
$162$	0.810729	0.0636969
$163$	9.79569	0.767258	0.383629	−	0.923487i	$-0.374674\pi$
$163$	9.79569	0.767258	0.383629	+	0.923487i	$0.374674\pi$
$164$	−0.906657	−0.0707980
$165$	0	0
$166$	2.30262	0.178718
$167$	20.9915	1.62437	0.812187	−	0.583397i	$-0.198277\pi$
$167$	20.9915	1.62437	0.812187	+	0.583397i	$0.198277\pi$
$168$	5.52348	0.426146
$169$	−0.282117	−0.0217013
$170$	0	0
$171$	3.69017	0.282194
$172$	−18.1879	−1.38681
$173$	16.5032	1.25472	0.627359	−	0.778730i	$-0.284136\pi$
$173$	16.5032	1.25472	0.627359	+	0.778730i	$0.284136\pi$
$174$	4.33981	0.329000
$175$	0	0
$176$	5.71500	0.430784
$177$	1.07423	0.0807443
$178$	−5.56064	−0.416788
$179$	13.8338	1.03398	0.516992	−	0.855990i	$-0.327052\pi$
$179$	13.8338	1.03398	0.516992	+	0.855990i	$0.327052\pi$
$180$	0	0
$181$	−15.4138	−1.14570	−0.572850	−	0.819660i	$-0.694162\pi$
$181$	−15.4138	−1.14570	−0.572850	+	0.819660i	$0.694162\pi$
$182$	4.89676	0.362972
$183$	−6.26135	−0.462852
$184$	−23.1957	−1.71001
$185$	0	0
$186$	3.16201	0.231850
$187$	−28.9643	−2.11808
$188$	5.14104	0.374949
$189$	−10.4384	−0.759281
$190$	0	0
$191$	−2.53393	−0.183349	−0.0916743	−	0.995789i	$-0.529222\pi$
$191$	−2.53393	−0.183349	−0.0916743	+	0.995789i	$0.529222\pi$
$192$	−1.87613	−0.135398
$193$	−2.68705	−0.193418	−0.0967091	−	0.995313i	$-0.530832\pi$
$193$	−2.68705	−0.193418	−0.0967091	+	0.995313i	$0.530832\pi$
$194$	−3.84966	−0.276389
$195$	0	0
$196$	4.84772	0.346266
$197$	−2.22990	−0.158874	−0.0794368	−	0.996840i	$-0.525312\pi$
$197$	−2.22990	−0.158874	−0.0794368	+	0.996840i	$0.525312\pi$
$198$	5.44017	0.386616
$199$	−8.60343	−0.609881	−0.304941	−	0.952371i	$-0.598637\pi$
$199$	−8.60343	−0.609881	−0.304941	+	0.952371i	$0.598637\pi$
$200$	0	0
$201$	−3.27885	−0.231272
$202$	1.33692	0.0940652
$203$	−10.3580	−0.726991
$204$	−10.8986	−0.763053
$205$	0	0
$206$	11.7206	0.816612
$207$	15.7280	1.09317
$208$	4.44913	0.308491
$209$	−10.0699	−0.696552
$210$	0	0
$211$	−4.93085	−0.339454	−0.169727	−	0.985491i	$-0.554289\pi$
$211$	−4.93085	−0.339454	−0.169727	+	0.985491i	$0.554289\pi$
$212$	14.9196	1.02468
$213$	7.55545	0.517691
$214$	−4.67368	−0.319486
$215$	0	0
$216$	13.3147	0.905949
$217$	−7.54693	−0.512319
$218$	−11.2273	−0.760410
$219$	−14.7669	−0.997855
$220$	0	0
$221$	−22.5487	−1.51679
$222$	−0.0644948	−0.00432861
$223$	23.7811	1.59250	0.796249	−	0.604969i	$-0.206815\pi$
$223$	23.7811	1.59250	0.796249	+	0.604969i	$0.206815\pi$
$224$	11.3234	0.756576
$225$	0	0
$226$	−8.14411	−0.541738
$227$	−14.4491	−0.959023	−0.479511	−	0.877536i	$-0.659186\pi$
$227$	−14.4491	−0.959023	−0.479511	+	0.877536i	$0.659186\pi$
$228$	−3.78907	−0.250937
$229$	−21.5349	−1.42306	−0.711532	−	0.702654i	$-0.751998\pi$
$229$	−21.5349	−1.42306	−0.711532	+	0.702654i	$0.751998\pi$
$230$	0	0
$231$	10.2202	0.672439
$232$	13.2122	0.867422
$233$	−8.17375	−0.535480	−0.267740	−	0.963491i	$-0.586277\pi$
$233$	−8.17375	−0.535480	−0.267740	+	0.963491i	$0.586277\pi$
$234$	4.23517	0.276862
$235$	0	0
$236$	1.40135	0.0912199
$237$	2.30762	0.149896
$238$	−8.68192	−0.562766
$239$	−30.6916	−1.98527	−0.992637	−	0.121129i	$-0.961349\pi$
$239$	−30.6916	−1.98527	−0.992637	+	0.121129i	$0.961349\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−7.06349	−0.454059
$243$	−14.8169	−0.950507
$244$	−8.16799	−0.522902
$245$	0	0
$246$	0.491690	0.0313490
$247$	−7.83944	−0.498812
$248$	9.62648	0.611282
$249$	3.74138	0.237100
$250$	0	0
$251$	26.3929	1.66590	0.832951	−	0.553346i	$-0.186649\pi$
$251$	26.3929	1.66590	0.832951	+	0.553346i	$0.186649\pi$
$252$	−4.88568	−0.307769
$253$	−42.9194	−2.69832
$254$	−15.5092	−0.973134
$255$	0	0
$256$	−10.7020	−0.668877
$257$	−14.7789	−0.921883	−0.460942	−	0.887430i	$-0.652488\pi$
$257$	−14.7789	−0.921883	−0.460942	+	0.887430i	$0.652488\pi$
$258$	9.86347	0.614073
$259$	0.153933	0.00956493
$260$	0	0
$261$	−8.95858	−0.554522
$262$	0.363855	0.0224790
$263$	−25.1850	−1.55297	−0.776486	−	0.630134i	$-0.783000\pi$
$263$	−25.1850	−1.55297	−0.776486	+	0.630134i	$0.783000\pi$
$264$	−13.0363	−0.802332
$265$	0	0
$266$	−3.01842	−0.185071
$267$	−9.03511	−0.552940
$268$	−4.27729	−0.261277
$269$	−8.01272	−0.488544	−0.244272	−	0.969707i	$-0.578549\pi$
$269$	−8.01272	−0.488544	−0.244272	+	0.969707i	$0.578549\pi$
$270$	0	0
$271$	−2.04262	−0.124080	−0.0620402	−	0.998074i	$-0.519761\pi$
$271$	−2.04262	−0.124080	−0.0620402	+	0.998074i	$0.519761\pi$
$272$	−7.88828	−0.478297
$273$	7.95641	0.481544
$274$	4.94161	0.298533
$275$	0	0
$276$	−16.1495	−0.972086
$277$	−16.6612	−1.00107	−0.500536	−	0.865716i	$-0.666864\pi$
$277$	−16.6612	−1.00107	−0.500536	+	0.865716i	$0.666864\pi$
$278$	−5.04639	−0.302662
$279$	−6.52728	−0.390778
$280$	0	0
$281$	−21.5997	−1.28853	−0.644265	−	0.764802i	$-0.722837\pi$
$281$	−21.5997	−1.28853	−0.644265	+	0.764802i	$0.722837\pi$
$282$	−2.78804	−0.166026
$283$	−30.2189	−1.79633	−0.898163	−	0.439663i	$-0.855098\pi$
$283$	−30.2189	−1.79633	−0.898163	+	0.439663i	$0.855098\pi$
$284$	9.85615	0.584855
$285$	0	0
$286$	−11.5572	−0.683390
$287$	−1.17354	−0.0692719
$288$	9.79352	0.577089
$289$	22.9788	1.35169
$290$	0	0
$291$	−6.25505	−0.366677
$292$	−19.2636	−1.12731
$293$	−15.8042	−0.923289	−0.461645	−	0.887065i	$-0.652740\pi$
$293$	−15.8042	−0.923289	−0.461645	+	0.887065i	$0.652740\pi$
$294$	−2.62897	−0.153325
$295$	0	0
$296$	−0.196349	−0.0114126
$297$	24.6363	1.42955
$298$	5.79475	0.335681
$299$	−33.4127	−1.93231
$300$	0	0
$301$	−23.5416	−1.35692
$302$	13.6859	0.787537
$303$	2.17227	0.124793
$304$	−2.74249	−0.157293
$305$	0	0
$306$	−7.50893	−0.429257
$307$	−3.54199	−0.202152	−0.101076	−	0.994879i	$-0.532229\pi$
$307$	−3.54199	−0.202152	−0.101076	+	0.994879i	$0.532229\pi$
$308$	13.3323	0.759679
$309$	19.0440	1.08337
$310$	0	0
$311$	4.13175	0.234290	0.117145	−	0.993115i	$-0.462626\pi$
$311$	4.13175	0.234290	0.117145	+	0.993115i	$0.462626\pi$
$312$	−10.1488	−0.574562
$313$	26.0794	1.47410	0.737048	−	0.675840i	$-0.236219\pi$
$313$	26.0794	1.47410	0.737048	+	0.675840i	$0.236219\pi$
$314$	7.25611	0.409486
$315$	0	0
$316$	3.01031	0.169343
$317$	8.24305	0.462976	0.231488	−	0.972838i	$-0.425641\pi$
$317$	8.24305	0.462976	0.231488	+	0.972838i	$0.425641\pi$
$318$	−8.09104	−0.453723
$319$	24.4467	1.36875
$320$	0	0
$321$	−7.59394	−0.423853
$322$	−12.8649	−0.716932
$323$	13.8993	0.773377
$324$	1.71843	0.0954682
$325$	0	0
$326$	−6.92996	−0.383815
$327$	−18.2425	−1.00881
$328$	1.49691	0.0826529
$329$	6.65436	0.366866
$330$	0	0
$331$	15.3071	0.841356	0.420678	−	0.907210i	$-0.361792\pi$
$331$	15.3071	0.841356	0.420678	+	0.907210i	$0.361792\pi$
$332$	4.88066	0.267861
$333$	0.133135	0.00729578
$334$	−14.8505	−0.812581
$335$	0	0
$336$	2.78341	0.151847
$337$	9.54503	0.519951	0.259975	−	0.965615i	$-0.416286\pi$
$337$	9.54503	0.519951	0.259975	+	0.965615i	$0.416286\pi$
$338$	0.199584	0.0108559
$339$	−13.2328	−0.718708
$340$	0	0
$341$	17.8120	0.964575
$342$	−2.61061	−0.141165
$343$	19.8611	1.07240
$344$	30.0285	1.61903
$345$	0	0
$346$	−11.6752	−0.627663
$347$	−23.6188	−1.26792	−0.633962	−	0.773364i	$-0.718572\pi$
$347$	−23.6188	−1.26792	−0.633962	+	0.773364i	$0.718572\pi$
$348$	9.19869	0.493101
$349$	−26.3884	−1.41254	−0.706270	−	0.707943i	$-0.749624\pi$
$349$	−26.3884	−1.41254	−0.706270	+	0.707943i	$0.749624\pi$
$350$	0	0
$351$	19.1794	1.02372
$352$	−26.7251	−1.42445
$353$	4.00765	0.213306	0.106653	−	0.994296i	$-0.465987\pi$
$353$	4.00765	0.213306	0.106653	+	0.994296i	$0.465987\pi$
$354$	−0.759966	−0.0403917
$355$	0	0
$356$	−11.7864	−0.624677
$357$	−14.1067	−0.746604
$358$	−9.78668	−0.517242
$359$	−8.26413	−0.436164	−0.218082	−	0.975930i	$-0.569980\pi$
$359$	−8.26413	−0.436164	−0.218082	+	0.975930i	$0.569980\pi$
$360$	0	0
$361$	−14.1677	−0.745667
$362$	10.9045	0.573128
$363$	−11.4770	−0.602386
$364$	10.3792	0.544018
$365$	0	0
$366$	4.42959	0.231538
$367$	14.8282	0.774023	0.387012	−	0.922075i	$-0.373507\pi$
$367$	14.8282	0.774023	0.387012	+	0.922075i	$0.373507\pi$
$368$	−11.6889	−0.609324
$369$	−1.01499	−0.0528381
$370$	0	0
$371$	19.3113	1.00259
$372$	6.70223	0.347494
$373$	5.82782	0.301753	0.150877	−	0.988553i	$-0.451790\pi$
$373$	5.82782	0.301753	0.150877	+	0.988553i	$0.451790\pi$
$374$	20.4908	1.05955
$375$	0	0
$376$	−8.48796	−0.437733
$377$	19.0317	0.980185
$378$	7.38463	0.379824
$379$	−20.4274	−1.04929	−0.524643	−	0.851323i	$-0.675801\pi$
$379$	−20.4274	−1.04929	−0.524643	+	0.851323i	$0.675801\pi$
$380$	0	0
$381$	−25.1999	−1.29103
$382$	1.79262	0.0917187
$383$	−27.6159	−1.41111	−0.705554	−	0.708656i	$-0.749302\pi$
$383$	−27.6159	−1.41111	−0.705554	+	0.708656i	$0.749302\pi$
$384$	−12.0851	−0.616714
$385$	0	0
$386$	1.90095	0.0967559
$387$	−20.3610	−1.03501
$388$	−8.15976	−0.414249
$389$	−9.63360	−0.488443	−0.244222	−	0.969719i	$-0.578532\pi$
$389$	−9.63360	−0.488443	−0.244222	+	0.969719i	$0.578532\pi$
$390$	0	0
$391$	59.2406	2.99592
$392$	−8.00369	−0.404247
$393$	0.591203	0.0298222
$394$	1.57754	0.0794753
$395$	0	0
$396$	11.5310	0.579456
$397$	−14.7614	−0.740854	−0.370427	−	0.928862i	$-0.620789\pi$
$397$	−14.7614	−0.740854	−0.370427	+	0.928862i	$0.620789\pi$
$398$	6.08649	0.305088
$399$	−4.90442	−0.245528
$400$	0	0
$401$	12.0743	0.602960	0.301480	−	0.953472i	$-0.402519\pi$
$401$	12.0743	0.602960	0.301480	+	0.953472i	$0.402519\pi$
$402$	2.31962	0.115692
$403$	13.8667	0.690747
$404$	2.83374	0.140984
$405$	0	0
$406$	7.32778	0.363672
$407$	−0.363308	−0.0180085
$408$	17.9938	0.890824
$409$	−30.2215	−1.49436	−0.747179	−	0.664623i	$-0.768592\pi$
$409$	−30.2215	−1.49436	−0.747179	+	0.664623i	$0.768592\pi$
$410$	0	0
$411$	8.02928	0.396055
$412$	24.8430	1.22393
$413$	1.81385	0.0892536
$414$	−11.1267	−0.546849
$415$	0	0
$416$	−20.8055	−1.02007
$417$	−8.19953	−0.401533
$418$	7.12397	0.348445
$419$	−11.3013	−0.552104	−0.276052	−	0.961143i	$-0.589026\pi$
$419$	−11.3013	−0.552104	−0.276052	+	0.961143i	$0.589026\pi$
$420$	0	0
$421$	−1.31460	−0.0640699	−0.0320350	−	0.999487i	$-0.510199\pi$
$421$	−1.31460	−0.0640699	−0.0320350	+	0.999487i	$0.510199\pi$
$422$	3.48833	0.169809
$423$	5.75530	0.279832
$424$	−24.6325	−1.19626
$425$	0	0
$426$	−5.34510	−0.258971
$427$	−10.5723	−0.511630
$428$	−9.90637	−0.478842
$429$	−18.7785	−0.906633
$430$	0	0
$431$	1.01385	0.0488355	0.0244178	−	0.999702i	$-0.492227\pi$
$431$	1.01385	0.0488355	0.0244178	+	0.999702i	$0.492227\pi$
$432$	6.70957	0.322814
$433$	−0.242734	−0.0116650	−0.00583252	−	0.999983i	$-0.501857\pi$
$433$	−0.242734	−0.0116650	−0.00583252	+	0.999983i	$0.501857\pi$
$434$	5.33907	0.256284
$435$	0	0
$436$	−23.7975	−1.13969
$437$	20.5960	0.985239
$438$	10.4468	0.499169
$439$	5.32828	0.254305	0.127152	−	0.991883i	$-0.459416\pi$
$439$	5.32828	0.254305	0.127152	+	0.991883i	$0.459416\pi$
$440$	0	0
$441$	5.42694	0.258426
$442$	15.9521	0.758763
$443$	−9.23482	−0.438760	−0.219380	−	0.975640i	$-0.570403\pi$
$443$	−9.23482	−0.438760	−0.219380	+	0.975640i	$0.570403\pi$
$444$	−0.136704	−0.00648767
$445$	0	0
$446$	−16.8239	−0.796634
$447$	9.41549	0.445337
$448$	−3.16785	−0.149667
$449$	31.1657	1.47080	0.735400	−	0.677633i	$-0.236994\pi$
$449$	31.1657	1.47080	0.735400	+	0.677633i	$0.236994\pi$
$450$	0	0
$451$	2.76975	0.130422
$452$	−17.2623	−0.811951
$453$	22.2373	1.04480
$454$	10.2220	0.479744
$455$	0	0
$456$	6.25583	0.292956
$457$	14.9445	0.699075	0.349538	−	0.936922i	$-0.386339\pi$
$457$	14.9445	0.699075	0.349538	+	0.936922i	$0.386339\pi$
$458$	15.2348	0.711877
$459$	−34.0049	−1.58721
$460$	0	0
$461$	3.88674	0.181023	0.0905117	−	0.995895i	$-0.471150\pi$
$461$	3.88674	0.181023	0.0905117	+	0.995895i	$0.471150\pi$
$462$	−7.23026	−0.336382
$463$	−26.2343	−1.21921	−0.609605	−	0.792706i	$-0.708672\pi$
$463$	−26.2343	−1.21921	−0.609605	+	0.792706i	$0.708672\pi$
$464$	6.65792	0.309086
$465$	0	0
$466$	5.78252	0.267870
$467$	41.6248	1.92617	0.963083	−	0.269203i	$-0.0867603\pi$
$467$	41.6248	1.92617	0.963083	+	0.269203i	$0.0867603\pi$
$468$	8.97690	0.414957
$469$	−5.53635	−0.255645
$470$	0	0
$471$	11.7900	0.543253
$472$	−2.31365	−0.106494
$473$	55.5622	2.55475
$474$	−1.63253	−0.0749844
$475$	0	0
$476$	−18.4023	−0.843467
$477$	16.7022	0.764740
$478$	21.7127	0.993118
$479$	−28.8815	−1.31963	−0.659815	−	0.751428i	$-0.729366\pi$
$479$	−28.8815	−1.31963	−0.659815	+	0.751428i	$0.729366\pi$
$480$	0	0
$481$	−0.282835	−0.0128962
$482$	0.707449	0.0322234
$483$	−20.9033	−0.951132
$484$	−14.9718	−0.680538
$485$	0	0
$486$	10.4822	0.475484
$487$	−23.8443	−1.08049	−0.540244	−	0.841508i	$-0.681668\pi$
$487$	−23.8443	−1.08049	−0.540244	+	0.841508i	$0.681668\pi$
$488$	13.4855	0.610460
$489$	−11.2600	−0.509196
$490$	0	0
$491$	−26.1815	−1.18155	−0.590776	−	0.806835i	$-0.701178\pi$
$491$	−26.1815	−1.18155	−0.590776	+	0.806835i	$0.701178\pi$
$492$	1.04219	0.0469855
$493$	−33.7432	−1.51972
$494$	5.54601	0.249527
$495$	0	0
$496$	4.85101	0.217817
$497$	12.7574	0.572248
$498$	−2.64684	−0.118608
$499$	8.93178	0.399841	0.199921	−	0.979812i	$-0.435932\pi$
$499$	8.93178	0.399841	0.199921	+	0.979812i	$0.435932\pi$
$500$	0	0
$501$	−24.1295	−1.07803
$502$	−18.6716	−0.833355
$503$	−18.0639	−0.805431	−0.402715	−	0.915325i	$-0.631934\pi$
$503$	−18.0639	−0.805431	−0.402715	+	0.915325i	$0.631934\pi$
$504$	8.06635	0.359304
$505$	0	0
$506$	30.3633	1.34981
$507$	0.324290	0.0144022
$508$	−32.8734	−1.45852
$509$	−1.06427	−0.0471730	−0.0235865	−	0.999722i	$-0.507509\pi$
$509$	−1.06427	−0.0471730	−0.0235865	+	0.999722i	$0.507509\pi$
$510$	0	0
$511$	−24.9340	−1.10301
$512$	−13.4558	−0.594666
$513$	−11.8224	−0.521971
$514$	10.4553	0.461165
$515$	0	0
$516$	20.9067	0.920366
$517$	−15.7054	−0.690723
$518$	−0.108900	−0.00478478
$519$	−18.9702	−0.832701
$520$	0	0
$521$	32.9610	1.44405	0.722023	−	0.691869i	$-0.243212\pi$
$521$	32.9610	1.44405	0.722023	+	0.691869i	$0.243212\pi$
$522$	6.33774	0.277395
$523$	−27.1584	−1.18755	−0.593777	−	0.804630i	$-0.702364\pi$
$523$	−27.1584	−1.18755	−0.593777	+	0.804630i	$0.702364\pi$
$524$	0.771229	0.0336913
$525$	0	0
$526$	17.8171	0.776863
$527$	−24.5855	−1.07096
$528$	−6.56932	−0.285893
$529$	64.7827	2.81664
$530$	0	0
$531$	1.56878	0.0680794
$532$	−6.39786	−0.277382
$533$	2.15625	0.0933976
$534$	6.39188	0.276604
$535$	0	0
$536$	7.06190	0.305027
$537$	−15.9017	−0.686210
$538$	5.66859	0.244390
$539$	−14.8093	−0.637883
$540$	0	0
$541$	25.5905	1.10022	0.550111	−	0.835092i	$-0.314585\pi$
$541$	25.5905	1.10022	0.550111	+	0.835092i	$0.314585\pi$
$542$	1.44505	0.0620702
$543$	17.7180	0.760352
$544$	36.8880	1.58156
$545$	0	0
$546$	−5.62876	−0.240889
$547$	2.42201	0.103558	0.0517788	−	0.998659i	$-0.483511\pi$
$547$	2.42201	0.103558	0.0517788	+	0.998659i	$0.483511\pi$
$548$	10.4743	0.447438
$549$	−9.14392	−0.390253
$550$	0	0
$551$	−11.7314	−0.499773
$552$	26.6632	1.13486
$553$	3.89643	0.165693
$554$	11.7869	0.500778
$555$	0	0
$556$	−10.6964	−0.453627
$557$	17.5717	0.744539	0.372269	−	0.928125i	$-0.378580\pi$
$557$	17.5717	0.744539	0.372269	+	0.928125i	$0.378580\pi$
$558$	4.61772	0.195484
$559$	43.2552	1.82950
$560$	0	0
$561$	33.2941	1.40568
$562$	15.2807	0.644577
$563$	−37.5020	−1.58052	−0.790261	−	0.612770i	$-0.790055\pi$
$563$	−37.5020	−1.58052	−0.790261	+	0.612770i	$0.790055\pi$
$564$	−5.90956	−0.248837
$565$	0	0
$566$	21.3783	0.898598
$567$	2.22426	0.0934103
$568$	−16.2727	−0.682787
$569$	−25.3900	−1.06440	−0.532201	−	0.846618i	$-0.678635\pi$
$569$	−25.3900	−1.06440	−0.532201	+	0.846618i	$0.678635\pi$
$570$	0	0
$571$	16.4450	0.688203	0.344102	−	0.938932i	$-0.388183\pi$
$571$	16.4450	0.688203	0.344102	+	0.938932i	$0.388183\pi$
$572$	−24.4967	−1.02426
$573$	2.91271	0.121680
$574$	0.830220	0.0346527
$575$	0	0
$576$	−2.73985	−0.114160
$577$	−10.3731	−0.431839	−0.215920	−	0.976411i	$-0.569275\pi$
$577$	−10.3731	−0.431839	−0.215920	+	0.976411i	$0.569275\pi$
$578$	−16.2563	−0.676174
$579$	3.08873	0.128363
$580$	0	0
$581$	6.31733	0.262087
$582$	4.42513	0.183427
$583$	−45.5778	−1.88764
$584$	31.8045	1.31608
$585$	0	0
$586$	11.1806	0.461868
$587$	−8.50516	−0.351045	−0.175523	−	0.984475i	$-0.556162\pi$
$587$	−8.50516	−0.351045	−0.175523	+	0.984475i	$0.556162\pi$
$588$	−5.57239	−0.229802
$589$	−8.54756	−0.352196
$590$	0	0
$591$	2.56324	0.105437
$592$	−0.0989449	−0.00406661
$593$	−15.1141	−0.620660	−0.310330	−	0.950629i	$-0.600439\pi$
$593$	−15.1141	−0.620660	−0.310330	+	0.950629i	$0.600439\pi$
$594$	−17.4290	−0.715119
$595$	0	0
$596$	12.2826	0.503114
$597$	9.88953	0.404752
$598$	23.6378	0.966622
$599$	−38.0498	−1.55467	−0.777337	−	0.629085i	$-0.783430\pi$
$599$	−38.0498	−1.55467	−0.777337	+	0.629085i	$0.783430\pi$
$600$	0	0
$601$	8.58953	0.350374	0.175187	−	0.984535i	$-0.443947\pi$
$601$	8.58953	0.350374	0.175187	+	0.984535i	$0.443947\pi$
$602$	16.6545	0.678787
$603$	−4.78835	−0.194997
$604$	29.0088	1.18035
$605$	0	0
$606$	−1.53677	−0.0624270
$607$	−23.2057	−0.941891	−0.470945	−	0.882162i	$-0.656087\pi$
$607$	−23.2057	−0.941891	−0.470945	+	0.882162i	$0.656087\pi$
$608$	12.8247	0.520112
$609$	11.9064	0.482472
$610$	0	0
$611$	−12.2267	−0.494637
$612$	−15.9160	−0.643366
$613$	8.16722	0.329871	0.164935	−	0.986304i	$-0.447258\pi$
$613$	8.16722	0.329871	0.164935	+	0.986304i	$0.447258\pi$
$614$	2.50578	0.101125
$615$	0	0
$616$	−22.0119	−0.886886
$617$	12.1606	0.489567	0.244784	−	0.969578i	$-0.421283\pi$
$617$	12.1606	0.489567	0.244784	+	0.969578i	$0.421283\pi$
$618$	−13.4727	−0.541950
$619$	−4.18509	−0.168213	−0.0841065	−	0.996457i	$-0.526804\pi$
$619$	−4.18509	−0.168213	−0.0841065	+	0.996457i	$0.526804\pi$
$620$	0	0
$621$	−50.3885	−2.02202
$622$	−2.92300	−0.117202
$623$	−15.2558	−0.611211
$624$	−5.11421	−0.204732
$625$	0	0
$626$	−18.4499	−0.737405
$627$	11.5753	0.462271
$628$	15.3801	0.613733
$629$	0.501465	0.0199947
$630$	0	0
$631$	6.43840	0.256309	0.128154	−	0.991754i	$-0.459095\pi$
$631$	6.43840	0.256309	0.128154	+	0.991754i	$0.459095\pi$
$632$	−4.97009	−0.197700
$633$	5.66795	0.225281
$634$	−5.83154	−0.231600
$635$	0	0
$636$	−17.1498	−0.680035
$637$	−11.5291	−0.456798
$638$	−17.2948	−0.684707
$639$	11.0338	0.436490
$640$	0	0
$641$	−32.2029	−1.27194	−0.635969	−	0.771715i	$-0.719399\pi$
$641$	−32.2029	−1.27194	−0.635969	+	0.771715i	$0.719399\pi$
$642$	5.37233	0.212029
$643$	−6.04696	−0.238469	−0.119234	−	0.992866i	$-0.538044\pi$
$643$	−6.04696	−0.238469	−0.119234	+	0.992866i	$0.538044\pi$
$644$	−27.2685	−1.07453
$645$	0	0
$646$	−9.83304	−0.386876
$647$	−24.2616	−0.953824	−0.476912	−	0.878951i	$-0.658244\pi$
$647$	−24.2616	−0.953824	−0.476912	+	0.878951i	$0.658244\pi$
$648$	−2.83716	−0.111454
$649$	−4.28098	−0.168043
$650$	0	0
$651$	8.67509	0.340004
$652$	−14.6888	−0.575258
$653$	−8.06295	−0.315527	−0.157764	−	0.987477i	$-0.550428\pi$
$653$	−8.06295	−0.315527	−0.157764	+	0.987477i	$0.550428\pi$
$654$	12.9056	0.504651
$655$	0	0
$656$	0.754326	0.0294515
$657$	−21.5652	−0.841339
$658$	−4.70762	−0.183522
$659$	2.48600	0.0968407	0.0484204	−	0.998827i	$-0.484581\pi$
$659$	2.48600	0.0968407	0.0484204	+	0.998827i	$0.484581\pi$
$660$	0	0
$661$	−14.8505	−0.577617	−0.288809	−	0.957387i	$-0.593259\pi$
$661$	−14.8505	−0.577617	−0.288809	+	0.957387i	$0.593259\pi$
$662$	−10.8290	−0.420882
$663$	25.9195	1.00663
$664$	−8.05807	−0.312714
$665$	0	0
$666$	−0.0941866	−0.00364966
$667$	−50.0006	−1.93603
$668$	−31.4771	−1.21789
$669$	−27.3360	−1.05687
$670$	0	0
$671$	24.9524	0.963278
$672$	−13.0161	−0.502106
$673$	−0.424614	−0.0163677	−0.00818383	−	0.999967i	$-0.502605\pi$
$673$	−0.424614	−0.0163677	−0.00818383	+	0.999967i	$0.502605\pi$
$674$	−6.75263	−0.260101
$675$	0	0
$676$	0.423039	0.0162707
$677$	18.0898	0.695249	0.347624	−	0.937634i	$-0.386988\pi$
$677$	18.0898	0.695249	0.347624	+	0.937634i	$0.386988\pi$
$678$	9.36154	0.359528
$679$	−10.5617	−0.405320
$680$	0	0
$681$	16.6091	0.636461
$682$	−12.6011	−0.482521
$683$	−14.8112	−0.566735	−0.283368	−	0.959011i	$-0.591452\pi$
$683$	−14.8112	−0.566735	−0.283368	+	0.959011i	$0.591452\pi$
$684$	−5.53346	−0.211577
$685$	0	0
$686$	−14.0507	−0.536459
$687$	24.7540	0.944425
$688$	15.1321	0.576904
$689$	−35.4823	−1.35177
$690$	0	0
$691$	−25.2871	−0.961968	−0.480984	−	0.876729i	$-0.659721\pi$
$691$	−25.2871	−0.961968	−0.480984	+	0.876729i	$0.659721\pi$
$692$	−24.7468	−0.940734
$693$	14.9253	0.566965
$694$	16.7091	0.634269
$695$	0	0
$696$	−15.1872	−0.575670
$697$	−3.82302	−0.144807
$698$	18.6685	0.706612
$699$	9.39562	0.355375
$700$	0	0
$701$	2.61490	0.0987635	0.0493817	−	0.998780i	$-0.484275\pi$
$701$	2.61490	0.0987635	0.0493817	+	0.998780i	$0.484275\pi$
$702$	−13.5684	−0.512108
$703$	0.174343	0.00657546
$704$	7.47666	0.281787
$705$	0	0
$706$	−2.83521	−0.106705
$707$	3.66788	0.137945
$708$	−1.61083	−0.0605387
$709$	23.1617	0.869857	0.434929	−	0.900465i	$-0.356774\pi$
$709$	23.1617	0.869857	0.434929	+	0.900465i	$0.356774\pi$
$710$	0	0
$711$	3.36999	0.126385
$712$	19.4595	0.729277
$713$	−36.4308	−1.36434
$714$	9.97975	0.373483
$715$	0	0
$716$	−20.7439	−0.775237
$717$	35.2796	1.31754
$718$	5.84645	0.218188
$719$	34.7688	1.29666	0.648330	−	0.761360i	$-0.275468\pi$
$719$	34.7688	1.29666	0.648330	+	0.761360i	$0.275468\pi$
$720$	0	0
$721$	32.1558	1.19755
$722$	10.0229	0.373014
$723$	1.14949	0.0427499
$724$	23.1133	0.858998
$725$	0	0
$726$	8.11939	0.301339
$727$	−0.877372	−0.0325399	−0.0162700	−	0.999868i	$-0.505179\pi$
$727$	−0.877372	−0.0325399	−0.0162700	+	0.999868i	$0.505179\pi$
$728$	−17.1363	−0.635113
$729$	20.4698	0.758142
$730$	0	0
$731$	−76.6911	−2.83652
$732$	9.38899	0.347027
$733$	−27.7368	−1.02448	−0.512241	−	0.858841i	$-0.671185\pi$
$733$	−27.7368	−1.02448	−0.512241	+	0.858841i	$0.671185\pi$
$734$	−10.4902	−0.387199
$735$	0	0
$736$	54.6607	2.01482
$737$	13.0667	0.481319
$738$	0.718051	0.0264318
$739$	49.1204	1.80692	0.903461	−	0.428670i	$-0.141018\pi$
$739$	49.1204	1.80692	0.903461	+	0.428670i	$0.141018\pi$
$740$	0	0
$741$	9.01133	0.331040
$742$	−13.6617	−0.501538
$743$	8.29457	0.304298	0.152149	−	0.988358i	$-0.451381\pi$
$743$	8.29457	0.304298	0.152149	+	0.988358i	$0.451381\pi$
$744$	−11.0655	−0.405681
$745$	0	0
$746$	−4.12289	−0.150950
$747$	5.46381	0.199910
$748$	43.4325	1.58805
$749$	−12.8224	−0.468520
$750$	0	0
$751$	−4.89869	−0.178756	−0.0893779	−	0.995998i	$-0.528488\pi$
$751$	−4.89869	−0.178756	−0.0893779	+	0.995998i	$0.528488\pi$
$752$	−4.27728	−0.155976
$753$	−30.3382	−1.10559
$754$	−13.4640	−0.490330
$755$	0	0
$756$	15.6525	0.569276
$757$	−47.9537	−1.74291	−0.871454	−	0.490477i	$-0.836823\pi$
$757$	−47.9537	−1.74291	−0.871454	+	0.490477i	$0.836823\pi$
$758$	14.4514	0.524897
$759$	49.3352	1.79076
$760$	0	0
$761$	−20.6853	−0.749840	−0.374920	−	0.927057i	$-0.622330\pi$
$761$	−20.6853	−0.749840	−0.374920	+	0.927057i	$0.622330\pi$
$762$	17.8276	0.645827
$763$	−30.8025	−1.11513
$764$	3.79966	0.137467
$765$	0	0
$766$	19.5369	0.705896
$767$	−3.33274	−0.120338
$768$	12.3018	0.443904
$769$	−4.25022	−0.153267	−0.0766334	−	0.997059i	$-0.524417\pi$
$769$	−4.25022	−0.153267	−0.0766334	+	0.997059i	$0.524417\pi$
$770$	0	0
$771$	16.9882	0.611814
$772$	4.02927	0.145017
$773$	29.7472	1.06993	0.534967	−	0.844873i	$-0.320324\pi$
$773$	29.7472	1.06993	0.534967	+	0.844873i	$0.320324\pi$
$774$	14.4044	0.517754
$775$	0	0
$776$	13.4719	0.483614
$777$	−0.176944	−0.00634783
$778$	6.81529	0.244340
$779$	−1.32914	−0.0476213
$780$	0	0
$781$	−30.1096	−1.07741
$782$	−41.9097	−1.49869
$783$	28.7011	1.02569
$784$	−4.03324	−0.144044
$785$	0	0
$786$	−0.418246	−0.0149183
$787$	−45.8095	−1.63293	−0.816466	−	0.577394i	$-0.804070\pi$
$787$	−45.8095	−1.63293	−0.816466	+	0.577394i	$0.804070\pi$
$788$	3.34377	0.119117
$789$	28.9498	1.03064
$790$	0	0
$791$	−22.3436	−0.794449
$792$	−19.0379	−0.676484
$793$	19.4255	0.689819
$794$	10.4430	0.370607
$795$	0	0
$796$	12.9010	0.457263
$797$	37.2028	1.31779	0.658896	−	0.752234i	$-0.271024\pi$
$797$	37.2028	1.31779	0.658896	+	0.752234i	$0.271024\pi$
$798$	3.46963	0.122823
$799$	21.6778	0.766905
$800$	0	0
$801$	−13.1946	−0.466210
$802$	−8.54194	−0.301626
$803$	58.8484	2.07671
$804$	4.91669	0.173398
$805$	0	0
$806$	−9.80996	−0.345541
$807$	9.21051	0.324225
$808$	−4.67856	−0.164591
$809$	51.3283	1.80461	0.902303	−	0.431102i	$-0.141875\pi$
$809$	51.3283	1.80461	0.902303	+	0.431102i	$0.141875\pi$
$810$	0	0
$811$	−41.6992	−1.46426	−0.732128	−	0.681167i	$-0.761473\pi$
$811$	−41.6992	−1.46426	−0.732128	+	0.681167i	$0.761473\pi$
$812$	15.5320	0.545067
$813$	2.34796	0.0823467
$814$	0.257022	0.00900861
$815$	0	0
$816$	9.06747	0.317425
$817$	−26.6630	−0.932819
$818$	21.3802	0.747541
$819$	11.6193	0.406013
$820$	0	0
$821$	−28.4923	−0.994389	−0.497194	−	0.867639i	$-0.665636\pi$
$821$	−28.4923	−0.994389	−0.497194	+	0.867639i	$0.665636\pi$
$822$	−5.68031	−0.198124
$823$	50.2513	1.75165	0.875826	−	0.482628i	$-0.160318\pi$
$823$	50.2513	1.75165	0.875826	+	0.482628i	$0.160318\pi$
$824$	−41.0164	−1.42887
$825$	0	0
$826$	−1.28320	−0.0446484
$827$	−11.9762	−0.416455	−0.208227	−	0.978080i	$-0.566769\pi$
$827$	−11.9762	−0.416455	−0.208227	+	0.978080i	$0.566769\pi$
$828$	−23.5843	−0.819612
$829$	2.09303	0.0726939	0.0363469	−	0.999339i	$-0.488428\pi$
$829$	2.09303	0.0726939	0.0363469	+	0.999339i	$0.488428\pi$
$830$	0	0
$831$	19.1518	0.664368
$832$	5.82058	0.201792
$833$	20.4410	0.708238
$834$	5.80075	0.200864
$835$	0	0
$836$	15.1000	0.522245
$837$	20.9118	0.722818
$838$	7.99509	0.276186
$839$	52.0397	1.79661	0.898305	−	0.439372i	$-0.144799\pi$
$839$	52.0397	1.79661	0.898305	+	0.439372i	$0.144799\pi$
$840$	0	0
$841$	−0.519852	−0.0179259
$842$	0.930016	0.0320505
$843$	24.8286	0.855141
$844$	7.39389	0.254508
$845$	0	0
$846$	−4.07159	−0.139984
$847$	−19.3789	−0.665868
$848$	−12.4129	−0.426260
$849$	34.7362	1.19214
$850$	0	0
$851$	0.743071	0.0254721
$852$	−11.3295	−0.388143
$853$	−12.1401	−0.415669	−0.207834	−	0.978164i	$-0.566641\pi$
$853$	−12.1401	−0.415669	−0.207834	+	0.978164i	$0.566641\pi$
$854$	7.47938	0.255939
$855$	0	0
$856$	16.3556	0.559023
$857$	5.75219	0.196491	0.0982455	−	0.995162i	$-0.468677\pi$
$857$	5.75219	0.196491	0.0982455	+	0.995162i	$0.468677\pi$
$858$	13.2848	0.453536
$859$	−41.2259	−1.40661	−0.703304	−	0.710889i	$-0.748293\pi$
$859$	−41.2259	−1.40661	−0.703304	+	0.710889i	$0.748293\pi$
$860$	0	0
$861$	1.34897	0.0459727
$862$	−0.717249	−0.0244296
$863$	−13.9529	−0.474961	−0.237481	−	0.971392i	$-0.576322\pi$
$863$	−13.9529	−0.474961	−0.237481	+	0.971392i	$0.576322\pi$
$864$	−31.3760	−1.06743
$865$	0	0
$866$	0.171722	0.00583535
$867$	−26.4138	−0.897059
$868$	11.3167	0.384115
$869$	−9.19623	−0.311961
$870$	0	0
$871$	10.1724	0.344680
$872$	39.2902	1.33053
$873$	−9.13471	−0.309163
$874$	−14.5706	−0.492858
$875$	0	0
$876$	22.1432	0.748150
$877$	37.7428	1.27448	0.637242	−	0.770664i	$-0.280075\pi$
$877$	37.7428	1.27448	0.637242	+	0.770664i	$0.280075\pi$
$878$	−3.76949	−0.127214
$879$	18.1667	0.612747
$880$	0	0
$881$	−9.98103	−0.336270	−0.168135	−	0.985764i	$-0.553774\pi$
$881$	−9.98103	−0.336270	−0.168135	+	0.985764i	$0.553774\pi$
$882$	−3.83929	−0.129275
$883$	20.3361	0.684364	0.342182	−	0.939634i	$-0.388834\pi$
$883$	20.3361	0.684364	0.342182	+	0.939634i	$0.388834\pi$
$884$	33.8122	1.13723
$885$	0	0
$886$	6.53317	0.219486
$887$	26.0756	0.875535	0.437767	−	0.899088i	$-0.355769\pi$
$887$	26.0756	0.875535	0.437767	+	0.899088i	$0.355769\pi$
$888$	0.225701	0.00757402
$889$	−42.5501	−1.42708
$890$	0	0
$891$	−5.24964	−0.175869
$892$	−35.6601	−1.19399
$893$	7.53664	0.252204
$894$	−6.66098	−0.222777
$895$	0	0
$896$	−20.4057	−0.681706
$897$	38.4075	1.28239
$898$	−22.0482	−0.735757
$899$	20.7508	0.692079
$900$	0	0
$901$	62.9100	2.09584
$902$	−1.95946	−0.0652428
$903$	27.0608	0.900526
$904$	28.5004	0.947910
$905$	0	0
$906$	−15.7318	−0.522654
$907$	−9.68519	−0.321592	−0.160796	−	0.986988i	$-0.551406\pi$
$907$	−9.68519	−0.321592	−0.160796	+	0.986988i	$0.551406\pi$
$908$	21.6667	0.719035
$909$	3.17232	0.105219
$910$	0	0
$911$	−57.4528	−1.90350	−0.951748	−	0.306881i	$-0.900715\pi$
$911$	−57.4528	−1.90350	−0.951748	+	0.306881i	$0.900715\pi$
$912$	3.15246	0.104388
$913$	−14.9100	−0.493448
$914$	−10.5725	−0.349707
$915$	0	0
$916$	32.2919	1.06695
$917$	0.998248	0.0329651
$918$	24.0568	0.793992
$919$	−31.4867	−1.03865	−0.519326	−	0.854576i	$-0.673817\pi$
$919$	−31.4867	−1.03865	−0.519326	+	0.854576i	$0.673817\pi$
$920$	0	0
$921$	4.07147	0.134160
$922$	−2.74967	−0.0905556
$923$	−23.4403	−0.771548
$924$	−15.3253	−0.504166
$925$	0	0
$926$	18.5594	0.609900
$927$	27.8113	0.913444
$928$	−31.1345	−1.02204
$929$	22.1447	0.726544	0.363272	−	0.931683i	$-0.381660\pi$
$929$	22.1447	0.726544	0.363272	+	0.931683i	$0.381660\pi$
$930$	0	0
$931$	7.10665	0.232911
$932$	12.2567	0.401481
$933$	−4.74939	−0.155488
$934$	−29.4475	−0.963550
$935$	0	0
$936$	−14.8210	−0.484441
$937$	47.0466	1.53695	0.768473	−	0.639882i	$-0.221017\pi$
$937$	47.0466	1.53695	0.768473	+	0.639882i	$0.221017\pi$
$938$	3.91669	0.127884
$939$	−29.9779	−0.978293
$940$	0	0
$941$	−27.1974	−0.886609	−0.443304	−	0.896371i	$-0.646194\pi$
$941$	−27.1974	−0.886609	−0.443304	+	0.896371i	$0.646194\pi$
$942$	−8.34080	−0.271758
$943$	−5.66495	−0.184476
$944$	−1.16590	−0.0379469
$945$	0	0
$946$	−39.3074	−1.27799
$947$	−7.34195	−0.238581	−0.119291	−	0.992859i	$-0.538062\pi$
$947$	−7.34195	−0.238581	−0.119291	+	0.992859i	$0.538062\pi$
$948$	−3.46032	−0.112386
$949$	45.8135	1.48717
$950$	0	0
$951$	−9.47528	−0.307257
$952$	30.3825	0.984703
$953$	−52.7142	−1.70758	−0.853791	−	0.520616i	$-0.825702\pi$
$953$	−52.7142	−1.70758	−0.853791	+	0.520616i	$0.825702\pi$
$954$	−11.8159	−0.382555
$955$	0	0
$956$	46.0225	1.48847
$957$	−28.1011	−0.908381
$958$	20.4322	0.660135
$959$	13.5575	0.437793
$960$	0	0
$961$	−15.8808	−0.512284
$962$	0.200091	0.00645121
$963$	−11.0900	−0.357370
$964$	1.49952	0.0482961
$965$	0	0
$966$	14.7880	0.475796
$967$	−56.3214	−1.81117	−0.905587	−	0.424162i	$-0.860569\pi$
$967$	−56.3214	−1.81117	−0.905587	+	0.424162i	$0.860569\pi$
$968$	24.7188	0.794492
$969$	−15.9770	−0.513257
$970$	0	0
$971$	5.63059	0.180694	0.0903471	−	0.995910i	$-0.471202\pi$
$971$	5.63059	0.180694	0.0903471	+	0.995910i	$0.471202\pi$
$972$	22.2182	0.712650
$973$	−13.8449	−0.443848
$974$	16.8686	0.540506
$975$	0	0
$976$	6.79566	0.217524
$977$	15.4040	0.492818	0.246409	−	0.969166i	$-0.420749\pi$
$977$	15.4040	0.492818	0.246409	+	0.969166i	$0.420749\pi$
$978$	7.96589	0.254721
$979$	36.0063	1.15077
$980$	0	0
$981$	−26.6409	−0.850578
$982$	18.5221	0.591062
$983$	31.7043	1.01121	0.505605	−	0.862765i	$-0.331269\pi$
$983$	31.7043	1.01121	0.505605	+	0.862765i	$0.331269\pi$
$984$	−1.72068	−0.0548531
$985$	0	0
$986$	23.8716	0.760226
$987$	−7.64909	−0.243473
$988$	11.7554	0.373988
$989$	−113.641	−3.61357
$990$	0	0
$991$	−23.4472	−0.744825	−0.372413	−	0.928067i	$-0.621469\pi$
$991$	−23.4472	−0.744825	−0.372413	+	0.928067i	$0.621469\pi$
$992$	−22.6848	−0.720243
$993$	−17.5953	−0.558371
$994$	−9.02521	−0.286262
$995$	0	0
$996$	−5.61025	−0.177768
$997$	46.4547	1.47124	0.735618	−	0.677397i	$-0.236892\pi$
$997$	46.4547	1.47124	0.735618	+	0.677397i	$0.236892\pi$
$998$	−6.31878	−0.200018
$999$	−0.426533	−0.0134949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.12		25
5.4	even	2		1205.2.a.e.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.14	✓	25	5.4	even	2
6025.2.a.j.1.12		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.707449 q^{2} -1.14949 q^{3} -1.49952 q^{4} +0.813204 q^{6} -1.94091 q^{7} +2.47573 q^{8} -1.67868 q^{9} +O(q^{10})\)	\(q-0.707449 q^{2} -1.14949 q^{3} -1.49952 q^{4} +0.813204 q^{6} -1.94091 q^{7} +2.47573 q^{8} -1.67868 q^{9} +4.58088 q^{11} +1.72367 q^{12} +3.56621 q^{13} +1.37310 q^{14} +1.24758 q^{16} -6.32288 q^{17} +1.18758 q^{18} -2.19825 q^{19} +2.23105 q^{21} -3.24074 q^{22} -9.36924 q^{23} -2.84582 q^{24} -2.52292 q^{26} +5.37808 q^{27} +2.91043 q^{28} +5.33668 q^{29} +3.88834 q^{31} -5.83406 q^{32} -5.26566 q^{33} +4.47312 q^{34} +2.51721 q^{36} -0.0793096 q^{37} +1.55515 q^{38} -4.09932 q^{39} +0.604633 q^{41} -1.57836 q^{42} +12.1292 q^{43} -6.86910 q^{44} +6.62826 q^{46} -3.42847 q^{47} -1.43407 q^{48} -3.23286 q^{49} +7.26806 q^{51} -5.34759 q^{52} -9.94958 q^{53} -3.80472 q^{54} -4.80517 q^{56} +2.52686 q^{57} -3.77543 q^{58} -0.934533 q^{59} +5.44709 q^{61} -2.75080 q^{62} +3.25817 q^{63} +1.63215 q^{64} +3.72519 q^{66} +2.85245 q^{67} +9.48125 q^{68} +10.7698 q^{69} -6.57289 q^{71} -4.15596 q^{72} +12.8465 q^{73} +0.0561075 q^{74} +3.29631 q^{76} -8.89108 q^{77} +2.90006 q^{78} -2.00752 q^{79} -1.14599 q^{81} -0.427747 q^{82} -3.25482 q^{83} -3.34550 q^{84} -8.58076 q^{86} -6.13444 q^{87} +11.3410 q^{88} +7.86013 q^{89} -6.92171 q^{91} +14.0493 q^{92} -4.46960 q^{93} +2.42547 q^{94} +6.70617 q^{96} +5.44160 q^{97} +2.28708 q^{98} -7.68983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 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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