LMFDB - Embedded newform 6025.2.a.q.1.7

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:	$0$
Dimension:	$66$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.48219 q^{2} -1.89252 q^{3} +4.16124 q^{4} +4.69758 q^{6} -3.72710 q^{7} -5.36461 q^{8} +0.581628 q^{9} +O(q^{10})$	\(q-2.48219 q^{2} -1.89252 q^{3} +4.16124 q^{4} +4.69758 q^{6} -3.72710 q^{7} -5.36461 q^{8} +0.581628 q^{9} +0.493450 q^{11} -7.87523 q^{12} -3.18589 q^{13} +9.25135 q^{14} +4.99346 q^{16} -1.84306 q^{17} -1.44371 q^{18} +1.78124 q^{19} +7.05361 q^{21} -1.22483 q^{22} -1.83960 q^{23} +10.1526 q^{24} +7.90797 q^{26} +4.57681 q^{27} -15.5094 q^{28} -0.633479 q^{29} -5.82197 q^{31} -1.66549 q^{32} -0.933864 q^{33} +4.57481 q^{34} +2.42030 q^{36} +7.74711 q^{37} -4.42137 q^{38} +6.02936 q^{39} -11.8128 q^{41} -17.5084 q^{42} -2.62964 q^{43} +2.05337 q^{44} +4.56623 q^{46} +8.11907 q^{47} -9.45023 q^{48} +6.89127 q^{49} +3.48802 q^{51} -13.2573 q^{52} -9.85819 q^{53} -11.3605 q^{54} +19.9944 q^{56} -3.37104 q^{57} +1.57241 q^{58} -13.7970 q^{59} -10.5220 q^{61} +14.4512 q^{62} -2.16779 q^{63} -5.85288 q^{64} +2.31802 q^{66} +2.88019 q^{67} -7.66941 q^{68} +3.48148 q^{69} -1.18849 q^{71} -3.12021 q^{72} -3.01047 q^{73} -19.2298 q^{74} +7.41218 q^{76} -1.83914 q^{77} -14.9660 q^{78} +0.737531 q^{79} -10.4066 q^{81} +29.3216 q^{82} -8.55088 q^{83} +29.3518 q^{84} +6.52726 q^{86} +1.19887 q^{87} -2.64717 q^{88} +10.3650 q^{89} +11.8741 q^{91} -7.65503 q^{92} +11.0182 q^{93} -20.1530 q^{94} +3.15196 q^{96} -4.79994 q^{97} -17.1054 q^{98} +0.287005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9}+O(q^{10}) $ 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9	$ 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9} + 48 q^{11} + 30 q^{14} + 98 q^{16} + 12 q^{19} + 18 q^{21} + 42 q^{24} + 48 q^{26} + 56 q^{29} + 48 q^{31} + 8 q^{34} + 158 q^{36} + 84 q^{39} + 56 q^{41} + 144 q^{44} + 36 q^{46} + 98 q^{49} + 44 q^{51} + 86 q^{54} + 104 q^{56} + 108 q^{59} + 22 q^{61} + 136 q^{64} + 74 q^{66} + 20 q^{69} + 212 q^{71} + 84 q^{74} + 6 q^{76} + 66 q^{79} + 162 q^{81} - 52 q^{84} + 100 q^{86} + 54 q^{89} + 72 q^{91} - 96 q^{94} + 122 q^{96} + 112 q^{99}+O(q^{100}) $ 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9 + 48 * q^11 + 30 * q^14 + 98 * q^16 + 12 * q^19 + 18 * q^21 + 42 * q^24 + 48 * q^26 + 56 * q^29 + 48 * q^31 + 8 * q^34 + 158 * q^36 + 84 * q^39 + 56 * q^41 + 144 * q^44 + 36 * q^46 + 98 * q^49 + 44 * q^51 + 86 * q^54 + 104 * q^56 + 108 * q^59 + 22 * q^61 + 136 * q^64 + 74 * q^66 + 20 * q^69 + 212 * q^71 + 84 * q^74 + 6 * q^76 + 66 * q^79 + 162 * q^81 - 52 * q^84 + 100 * q^86 + 54 * q^89 + 72 * q^91 - 96 * q^94 + 122 * q^96 + 112 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.48219	−1.75517	−0.877585	−	0.479421i	$-0.840847\pi$
$2$	−2.48219	−1.75517	−0.877585	+	0.479421i	$0.840847\pi$
$3$	−1.89252	−1.09265	−0.546323	−	0.837574i	$-0.683973\pi$
$3$	−1.89252	−1.09265	−0.546323	+	0.837574i	$0.683973\pi$
$4$	4.16124	2.08062
$5$	0	0
$5$	0	0
$6$	4.69758	1.91778
$7$	−3.72710	−1.40871	−0.704355	−	0.709847i	$-0.748764\pi$
$7$	−3.72710	−1.40871	−0.704355	+	0.709847i	$0.748764\pi$
$8$	−5.36461	−1.89668
$9$	0.581628	0.193876
$10$	0	0
$11$	0.493450	0.148781	0.0743904	−	0.997229i	$-0.476299\pi$
$11$	0.493450	0.148781	0.0743904	+	0.997229i	$0.476299\pi$
$12$	−7.87523	−2.27338
$13$	−3.18589	−0.883607	−0.441803	−	0.897112i	$-0.645661\pi$
$13$	−3.18589	−0.883607	−0.441803	+	0.897112i	$0.645661\pi$
$14$	9.25135	2.47253
$15$	0	0
$16$	4.99346	1.24837
$17$	−1.84306	−0.447007	−0.223503	−	0.974703i	$-0.571749\pi$
$17$	−1.84306	−0.447007	−0.223503	+	0.974703i	$0.571749\pi$
$18$	−1.44371	−0.340286
$19$	1.78124	0.408645	0.204323	−	0.978904i	$-0.434501\pi$
$19$	1.78124	0.408645	0.204323	+	0.978904i	$0.434501\pi$
$20$	0	0
$21$	7.05361	1.53922
$22$	−1.22483	−0.261136
$23$	−1.83960	−0.383583	−0.191792	−	0.981436i	$-0.561430\pi$
$23$	−1.83960	−0.383583	−0.191792	+	0.981436i	$0.561430\pi$
$24$	10.1526	2.07240
$25$	0	0
$26$	7.90797	1.55088
$27$	4.57681	0.880808
$28$	−15.5094	−2.93100
$29$	−0.633479	−0.117634	−0.0588170	−	0.998269i	$-0.518733\pi$
$29$	−0.633479	−0.117634	−0.0588170	+	0.998269i	$0.518733\pi$
$30$	0	0
$31$	−5.82197	−1.04566	−0.522829	−	0.852438i	$-0.675123\pi$
$31$	−5.82197	−1.04566	−0.522829	+	0.852438i	$0.675123\pi$
$32$	−1.66549	−0.294419
$33$	−0.933864	−0.162565
$34$	4.57481	0.784573
$35$	0	0
$36$	2.42030	0.403383
$37$	7.74711	1.27362	0.636808	−	0.771022i	$-0.280254\pi$
$37$	7.74711	1.27362	0.636808	+	0.771022i	$0.280254\pi$
$38$	−4.42137	−0.717242
$39$	6.02936	0.965470
$40$	0	0
$41$	−11.8128	−1.84485	−0.922425	−	0.386177i	$-0.873795\pi$
$41$	−11.8128	−1.84485	−0.922425	+	0.386177i	$0.873795\pi$
$42$	−17.5084	−2.70160
$43$	−2.62964	−0.401017	−0.200508	−	0.979692i	$-0.564259\pi$
$43$	−2.62964	−0.401017	−0.200508	+	0.979692i	$0.564259\pi$
$44$	2.05337	0.309557
$45$	0	0
$46$	4.56623	0.673254
$47$	8.11907	1.18429	0.592144	−	0.805832i	$-0.298282\pi$
$47$	8.11907	1.18429	0.592144	+	0.805832i	$0.298282\pi$
$48$	−9.45023	−1.36402
$49$	6.89127	0.984467
$50$	0	0
$51$	3.48802	0.488420
$52$	−13.2573	−1.83845
$53$	−9.85819	−1.35413	−0.677063	−	0.735925i	$-0.736748\pi$
$53$	−9.85819	−1.35413	−0.677063	+	0.735925i	$0.736748\pi$
$54$	−11.3605	−1.54597
$55$	0	0
$56$	19.9944	2.67187
$57$	−3.37104	−0.446505
$58$	1.57241	0.206468
$59$	−13.7970	−1.79622	−0.898108	−	0.439775i	$-0.855058\pi$
$59$	−13.7970	−1.79622	−0.898108	+	0.439775i	$0.855058\pi$
$60$	0	0
$61$	−10.5220	−1.34720	−0.673601	−	0.739096i	$-0.735253\pi$
$61$	−10.5220	−1.34720	−0.673601	+	0.739096i	$0.735253\pi$
$62$	14.4512	1.83531
$63$	−2.16779	−0.273115
$64$	−5.85288	−0.731610
$65$	0	0
$66$	2.31802	0.285329
$67$	2.88019	0.351871	0.175936	−	0.984402i	$-0.443705\pi$
$67$	2.88019	0.351871	0.175936	+	0.984402i	$0.443705\pi$
$68$	−7.66941	−0.930052
$69$	3.48148	0.419121
$70$	0	0
$71$	−1.18849	−0.141047	−0.0705237	−	0.997510i	$-0.522467\pi$
$71$	−1.18849	−0.141047	−0.0705237	+	0.997510i	$0.522467\pi$
$72$	−3.12021	−0.367720
$73$	−3.01047	−0.352348	−0.176174	−	0.984359i	$-0.556372\pi$
$73$	−3.01047	−0.352348	−0.176174	+	0.984359i	$0.556372\pi$
$74$	−19.2298	−2.23541
$75$	0	0
$76$	7.41218	0.850236
$77$	−1.83914	−0.209589
$78$	−14.9660	−1.69456
$79$	0.737531	0.0829787	0.0414894	−	0.999139i	$-0.486790\pi$
$79$	0.737531	0.0829787	0.0414894	+	0.999139i	$0.486790\pi$
$80$	0	0
$81$	−10.4066	−1.15629
$82$	29.3216	3.23802
$83$	−8.55088	−0.938581	−0.469291	−	0.883044i	$-0.655490\pi$
$83$	−8.55088	−0.938581	−0.469291	+	0.883044i	$0.655490\pi$
$84$	29.3518	3.20254
$85$	0	0
$86$	6.52726	0.703852
$87$	1.19887	0.128532
$88$	−2.64717	−0.282189
$89$	10.3650	1.09868	0.549342	−	0.835598i	$-0.314878\pi$
$89$	10.3650	1.09868	0.549342	+	0.835598i	$0.314878\pi$
$90$	0	0
$91$	11.8741	1.24475
$92$	−7.65503	−0.798092
$93$	11.0182	1.14253
$94$	−20.1530	−2.07863
$95$	0	0
$96$	3.15196	0.321696
$97$	−4.79994	−0.487360	−0.243680	−	0.969856i	$-0.578355\pi$
$97$	−4.79994	−0.487360	−0.243680	+	0.969856i	$0.578355\pi$
$98$	−17.1054	−1.72791
$99$	0.287005	0.0288450
$100$	0	0
$101$	12.3530	1.22917	0.614586	−	0.788850i	$-0.289323\pi$
$101$	12.3530	1.22917	0.614586	+	0.788850i	$0.289323\pi$
$102$	−8.65791	−0.857261
$103$	−14.5130	−1.43000	−0.715002	−	0.699122i	$-0.753574\pi$
$103$	−14.5130	−1.43000	−0.715002	+	0.699122i	$0.753574\pi$
$104$	17.0910	1.67592
$105$	0	0
$106$	24.4698	2.37672
$107$	−10.7038	−1.03478	−0.517390	−	0.855750i	$-0.673096\pi$
$107$	−10.7038	−1.03478	−0.517390	+	0.855750i	$0.673096\pi$
$108$	19.0452	1.83263
$109$	−10.1486	−0.972057	−0.486028	−	0.873943i	$-0.661555\pi$
$109$	−10.1486	−0.972057	−0.486028	+	0.873943i	$0.661555\pi$
$110$	0	0
$111$	−14.6615	−1.39161
$112$	−18.6111	−1.75859
$113$	0.598757	0.0563263	0.0281631	−	0.999603i	$-0.491034\pi$
$113$	0.598757	0.0563263	0.0281631	+	0.999603i	$0.491034\pi$
$114$	8.36753	0.783691
$115$	0	0
$116$	−2.63606	−0.244752
$117$	−1.85300	−0.171310
$118$	34.2467	3.15267
$119$	6.86925	0.629703
$120$	0	0
$121$	−10.7565	−0.977864
$122$	26.1175	2.36457
$123$	22.3560	2.01577
$124$	−24.2267	−2.17562
$125$	0	0
$126$	5.38085	0.479364
$127$	−9.34165	−0.828937	−0.414469	−	0.910064i	$-0.636033\pi$
$127$	−9.34165	−0.828937	−0.414469	+	0.910064i	$0.636033\pi$
$128$	17.8589	1.57852
$129$	4.97665	0.438169
$130$	0	0
$131$	−10.4851	−0.916086	−0.458043	−	0.888930i	$-0.651449\pi$
$131$	−10.4851	−0.916086	−0.458043	+	0.888930i	$0.651449\pi$
$132$	−3.88603	−0.338236
$133$	−6.63887	−0.575663
$134$	−7.14917	−0.617594
$135$	0	0
$136$	9.88728	0.847827
$137$	−6.53019	−0.557911	−0.278956	−	0.960304i	$-0.589988\pi$
$137$	−6.53019	−0.557911	−0.278956	+	0.960304i	$0.589988\pi$
$138$	−8.64167	−0.735628
$139$	14.2893	1.21200	0.606002	−	0.795463i	$-0.292773\pi$
$139$	14.2893	1.21200	0.606002	+	0.795463i	$0.292773\pi$
$140$	0	0
$141$	−15.3655	−1.29401
$142$	2.95005	0.247562
$143$	−1.57208	−0.131464
$144$	2.90434	0.242028
$145$	0	0
$146$	7.47253	0.618431
$147$	−13.0419	−1.07567
$148$	32.2376	2.64991
$149$	19.4073	1.58991	0.794956	−	0.606668i	$-0.207494\pi$
$149$	19.4073	1.58991	0.794956	+	0.606668i	$0.207494\pi$
$150$	0	0
$151$	−6.66800	−0.542635	−0.271317	−	0.962490i	$-0.587459\pi$
$151$	−6.66800	−0.542635	−0.271317	+	0.962490i	$0.587459\pi$
$152$	−9.55567	−0.775067
$153$	−1.07197	−0.0866639
$154$	4.56508	0.367865
$155$	0	0
$156$	25.0896	2.00878
$157$	6.57321	0.524600	0.262300	−	0.964986i	$-0.415519\pi$
$157$	6.57321	0.524600	0.262300	+	0.964986i	$0.415519\pi$
$158$	−1.83069	−0.145642
$159$	18.6568	1.47958
$160$	0	0
$161$	6.85637	0.540358
$162$	25.8311	2.02948
$163$	−8.18457	−0.641065	−0.320533	−	0.947238i	$-0.603862\pi$
$163$	−8.18457	−0.641065	−0.320533	+	0.947238i	$0.603862\pi$
$164$	−49.1559	−3.83843
$165$	0	0
$166$	21.2249	1.64737
$167$	−14.3099	−1.10733	−0.553667	−	0.832738i	$-0.686772\pi$
$167$	−14.3099	−1.10733	−0.553667	+	0.832738i	$0.686772\pi$
$168$	−37.8398	−2.91941
$169$	−2.85011	−0.219239
$170$	0	0
$171$	1.03602	0.0792265
$172$	−10.9426	−0.834364
$173$	3.62076	0.275282	0.137641	−	0.990482i	$-0.456048\pi$
$173$	3.62076	0.275282	0.137641	+	0.990482i	$0.456048\pi$
$174$	−2.97582	−0.225596
$175$	0	0
$176$	2.46403	0.185733
$177$	26.1111	1.96263
$178$	−25.7278	−1.92838
$179$	4.11152	0.307310	0.153655	−	0.988125i	$-0.450896\pi$
$179$	4.11152	0.307310	0.153655	+	0.988125i	$0.450896\pi$
$180$	0	0
$181$	−12.5723	−0.934489	−0.467245	−	0.884128i	$-0.654753\pi$
$181$	−12.5723	−0.934489	−0.467245	+	0.884128i	$0.654753\pi$
$182$	−29.4738	−2.18474
$183$	19.9130	1.47201
$184$	9.86873	0.727533
$185$	0	0
$186$	−27.3492	−2.00534
$187$	−0.909456	−0.0665060
$188$	33.7854	2.46406
$189$	−17.0582	−1.24080
$190$	0	0
$191$	27.2164	1.96931	0.984655	−	0.174514i	$-0.0558354\pi$
$191$	27.2164	1.96931	0.984655	+	0.174514i	$0.0558354\pi$
$192$	11.0767	0.799391
$193$	−10.0748	−0.725203	−0.362602	−	0.931944i	$-0.618111\pi$
$193$	−10.0748	−0.725203	−0.362602	+	0.931944i	$0.618111\pi$
$194$	11.9143	0.855399
$195$	0	0
$196$	28.6762	2.04830
$197$	−21.5219	−1.53337	−0.766686	−	0.642022i	$-0.778096\pi$
$197$	−21.5219	−1.53337	−0.766686	+	0.642022i	$0.778096\pi$
$198$	−0.712398	−0.0506280
$199$	−3.90331	−0.276699	−0.138349	−	0.990383i	$-0.544180\pi$
$199$	−3.90331	−0.276699	−0.138349	+	0.990383i	$0.544180\pi$
$200$	0	0
$201$	−5.45082	−0.384471
$202$	−30.6625	−2.15741
$203$	2.36104	0.165712
$204$	14.5145	1.01622
$205$	0	0
$206$	36.0239	2.50990
$207$	−1.06996	−0.0743676
$208$	−15.9086	−1.10306
$209$	0.878954	0.0607985
$210$	0	0
$211$	−4.16058	−0.286426	−0.143213	−	0.989692i	$-0.545743\pi$
$211$	−4.16058	−0.286426	−0.143213	+	0.989692i	$0.545743\pi$
$212$	−41.0223	−2.81742
$213$	2.24923	0.154115
$214$	26.5689	1.81622
$215$	0	0
$216$	−24.5528	−1.67061
$217$	21.6991	1.47303
$218$	25.1906	1.70612
$219$	5.69736	0.384992
$220$	0	0
$221$	5.87177	0.394978
$222$	36.3927	2.44252
$223$	−9.67179	−0.647671	−0.323835	−	0.946113i	$-0.604972\pi$
$223$	−9.67179	−0.647671	−0.323835	+	0.946113i	$0.604972\pi$
$224$	6.20743	0.414751
$225$	0	0
$226$	−1.48623	−0.0988622
$227$	9.83678	0.652890	0.326445	−	0.945216i	$-0.394149\pi$
$227$	9.83678	0.652890	0.326445	+	0.945216i	$0.394149\pi$
$228$	−14.0277	−0.929007
$229$	−8.65496	−0.571936	−0.285968	−	0.958239i	$-0.592315\pi$
$229$	−8.65496	−0.571936	−0.285968	+	0.958239i	$0.592315\pi$
$230$	0	0
$231$	3.48060	0.229007
$232$	3.39837	0.223114
$233$	1.52768	0.100082	0.0500408	−	0.998747i	$-0.484065\pi$
$233$	1.52768	0.100082	0.0500408	+	0.998747i	$0.484065\pi$
$234$	4.59950	0.300679
$235$	0	0
$236$	−57.4127	−3.73725
$237$	−1.39579	−0.0906664
$238$	−17.0508	−1.10524
$239$	−29.0049	−1.87617	−0.938087	−	0.346400i	$-0.887404\pi$
$239$	−29.0049	−1.87617	−0.938087	+	0.346400i	$0.887404\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	26.6996	1.71632
$243$	5.96423	0.382606
$244$	−43.7845	−2.80302
$245$	0	0
$246$	−55.4916	−3.53802
$247$	−5.67484	−0.361082
$248$	31.2326	1.98327
$249$	16.1827	1.02554
$250$	0	0
$251$	−2.33215	−0.147204	−0.0736020	−	0.997288i	$-0.523449\pi$
$251$	−2.33215	−0.147204	−0.0736020	+	0.997288i	$0.523449\pi$
$252$	−9.02069	−0.568250
$253$	−0.907751	−0.0570698
$254$	23.1877	1.45493
$255$	0	0
$256$	−32.6234	−2.03896
$257$	−23.1944	−1.44683	−0.723414	−	0.690415i	$-0.757428\pi$
$257$	−23.1944	−1.44683	−0.723414	+	0.690415i	$0.757428\pi$
$258$	−12.3530	−0.769062
$259$	−28.8742	−1.79416
$260$	0	0
$261$	−0.368449	−0.0228064
$262$	26.0259	1.60789
$263$	17.3304	1.06864	0.534319	−	0.845283i	$-0.320568\pi$
$263$	17.3304	1.06864	0.534319	+	0.845283i	$0.320568\pi$
$264$	5.00981	0.308333
$265$	0	0
$266$	16.4789	1.01039
$267$	−19.6159	−1.20047
$268$	11.9852	0.732111
$269$	−19.6205	−1.19628	−0.598142	−	0.801390i	$-0.704094\pi$
$269$	−19.6205	−1.19628	−0.598142	+	0.801390i	$0.704094\pi$
$270$	0	0
$271$	−10.7589	−0.653557	−0.326778	−	0.945101i	$-0.605963\pi$
$271$	−10.7589	−0.653557	−0.326778	+	0.945101i	$0.605963\pi$
$272$	−9.20324	−0.558028
$273$	−22.4720	−1.36007
$274$	16.2091	0.979230
$275$	0	0
$276$	14.4873	0.872032
$277$	−13.4873	−0.810375	−0.405188	−	0.914234i	$-0.632794\pi$
$277$	−13.4873	−0.810375	−0.405188	+	0.914234i	$0.632794\pi$
$278$	−35.4687	−2.12727
$279$	−3.38623	−0.202728
$280$	0	0
$281$	−7.17324	−0.427920	−0.213960	−	0.976842i	$-0.568636\pi$
$281$	−7.17324	−0.427920	−0.213960	+	0.976842i	$0.568636\pi$
$282$	38.1400	2.27121
$283$	−15.5597	−0.924927	−0.462463	−	0.886638i	$-0.653034\pi$
$283$	−15.5597	−0.924927	−0.462463	+	0.886638i	$0.653034\pi$
$284$	−4.94559	−0.293467
$285$	0	0
$286$	3.90219	0.230741
$287$	44.0275	2.59886
$288$	−0.968694	−0.0570808
$289$	−13.6031	−0.800185
$290$	0	0
$291$	9.08397	0.532512
$292$	−12.5273	−0.733104
$293$	4.92434	0.287683	0.143842	−	0.989601i	$-0.454054\pi$
$293$	4.92434	0.287683	0.143842	+	0.989601i	$0.454054\pi$
$294$	32.3723	1.88799
$295$	0	0
$296$	−41.5602	−2.41564
$297$	2.25843	0.131047
$298$	−48.1726	−2.79056
$299$	5.86076	0.338937
$300$	0	0
$301$	9.80093	0.564916
$302$	16.5512	0.952416
$303$	−23.3784	−1.34305
$304$	8.89457	0.510139
$305$	0	0
$306$	2.66084	0.152110
$307$	17.7367	1.01229	0.506144	−	0.862449i	$-0.331070\pi$
$307$	17.7367	1.01229	0.506144	+	0.862449i	$0.331070\pi$
$308$	−7.65310	−0.436076
$309$	27.4661	1.56249
$310$	0	0
$311$	10.7015	0.606828	0.303414	−	0.952859i	$-0.401874\pi$
$311$	10.7015	0.606828	0.303414	+	0.952859i	$0.401874\pi$
$312$	−32.3451	−1.83118
$313$	−9.51782	−0.537979	−0.268989	−	0.963143i	$-0.586690\pi$
$313$	−9.51782	−0.537979	−0.268989	+	0.963143i	$0.586690\pi$
$314$	−16.3159	−0.920762
$315$	0	0
$316$	3.06905	0.172647
$317$	11.8941	0.668041	0.334020	−	0.942566i	$-0.391595\pi$
$317$	11.8941	0.668041	0.334020	+	0.942566i	$0.391595\pi$
$318$	−46.3097	−2.59692
$319$	−0.312590	−0.0175017
$320$	0	0
$321$	20.2572	1.13065
$322$	−17.0188	−0.948420
$323$	−3.28293	−0.182667
$324$	−43.3044	−2.40580
$325$	0	0
$326$	20.3156	1.12518
$327$	19.2064	1.06211
$328$	63.3711	3.49908
$329$	−30.2606	−1.66832
$330$	0	0
$331$	−26.0858	−1.43380	−0.716902	−	0.697174i	$-0.754441\pi$
$331$	−26.0858	−1.43380	−0.716902	+	0.697174i	$0.754441\pi$
$332$	−35.5823	−1.95283
$333$	4.50594	0.246924
$334$	35.5198	1.94356
$335$	0	0
$336$	35.2219	1.92151
$337$	−0.441008	−0.0240233	−0.0120116	−	0.999928i	$-0.503824\pi$
$337$	−0.441008	−0.0240233	−0.0120116	+	0.999928i	$0.503824\pi$
$338$	7.07450	0.384802
$339$	−1.13316	−0.0615447
$340$	0	0
$341$	−2.87285	−0.155574
$342$	−2.57160	−0.139056
$343$	0.405260	0.0218820
$344$	14.1070	0.760598
$345$	0	0
$346$	−8.98741	−0.483166
$347$	20.1319	1.08073	0.540367	−	0.841429i	$-0.318285\pi$
$347$	20.1319	1.08073	0.540367	+	0.841429i	$0.318285\pi$
$348$	4.98879	0.267427
$349$	−16.0102	−0.857005	−0.428502	−	0.903541i	$-0.640959\pi$
$349$	−16.0102	−0.857005	−0.428502	+	0.903541i	$0.640959\pi$
$350$	0	0
$351$	−14.5812	−0.778288
$352$	−0.821834	−0.0438039
$353$	−18.0749	−0.962030	−0.481015	−	0.876712i	$-0.659732\pi$
$353$	−18.0749	−0.962030	−0.481015	+	0.876712i	$0.659732\pi$
$354$	−64.8126	−3.44475
$355$	0	0
$356$	43.1311	2.28595
$357$	−13.0002	−0.688043
$358$	−10.2056	−0.539381
$359$	−34.0226	−1.79564	−0.897822	−	0.440358i	$-0.854851\pi$
$359$	−34.0226	−1.79564	−0.897822	+	0.440358i	$0.854851\pi$
$360$	0	0
$361$	−15.8272	−0.833009
$362$	31.2067	1.64019
$363$	20.3569	1.06846
$364$	49.4111	2.58985
$365$	0	0
$366$	−49.4279	−2.58364
$367$	2.37959	0.124213	0.0621067	−	0.998070i	$-0.480218\pi$
$367$	2.37959	0.124213	0.0621067	+	0.998070i	$0.480218\pi$
$368$	−9.18598	−0.478852
$369$	−6.87066	−0.357672
$370$	0	0
$371$	36.7424	1.90757
$372$	45.8494	2.37718
$373$	−5.57822	−0.288829	−0.144415	−	0.989517i	$-0.546130\pi$
$373$	−5.57822	−0.288829	−0.144415	+	0.989517i	$0.546130\pi$
$374$	2.25744	0.116729
$375$	0	0
$376$	−43.5556	−2.24621
$377$	2.01819	0.103942
$378$	42.3417	2.17782
$379$	24.0331	1.23450	0.617249	−	0.786768i	$-0.288247\pi$
$379$	24.0331	1.23450	0.617249	+	0.786768i	$0.288247\pi$
$380$	0	0
$381$	17.6792	0.905735
$382$	−67.5561	−3.45647
$383$	18.1047	0.925109	0.462554	−	0.886591i	$-0.346933\pi$
$383$	18.1047	0.925109	0.462554	+	0.886591i	$0.346933\pi$
$384$	−33.7983	−1.72476
$385$	0	0
$386$	25.0076	1.27286
$387$	−1.52947	−0.0777475
$388$	−19.9737	−1.01401
$389$	11.9667	0.606734	0.303367	−	0.952874i	$-0.401889\pi$
$389$	11.9667	0.606734	0.303367	+	0.952874i	$0.401889\pi$
$390$	0	0
$391$	3.39049	0.171464
$392$	−36.9689	−1.86721
$393$	19.8432	1.00096
$394$	53.4213	2.69133
$395$	0	0
$396$	1.19430	0.0600156
$397$	−2.14962	−0.107886	−0.0539432	−	0.998544i	$-0.517179\pi$
$397$	−2.14962	−0.107886	−0.0539432	+	0.998544i	$0.517179\pi$
$398$	9.68875	0.485653
$399$	12.5642	0.628996
$400$	0	0
$401$	3.12564	0.156087	0.0780435	−	0.996950i	$-0.475133\pi$
$401$	3.12564	0.156087	0.0780435	+	0.996950i	$0.475133\pi$
$402$	13.5299	0.674812
$403$	18.5482	0.923950
$404$	51.4040	2.55744
$405$	0	0
$406$	−5.86053	−0.290853
$407$	3.82281	0.189490
$408$	−18.7119	−0.926375
$409$	−19.8881	−0.983405	−0.491702	−	0.870763i	$-0.663625\pi$
$409$	−19.8881	−0.983405	−0.491702	+	0.870763i	$0.663625\pi$
$410$	0	0
$411$	12.3585	0.609600
$412$	−60.3920	−2.97530
$413$	51.4228	2.53035
$414$	2.65585	0.130528
$415$	0	0
$416$	5.30606	0.260151
$417$	−27.0428	−1.32429
$418$	−2.18173	−0.106712
$419$	3.38332	0.165286	0.0826431	−	0.996579i	$-0.473664\pi$
$419$	3.38332	0.165286	0.0826431	+	0.996579i	$0.473664\pi$
$420$	0	0
$421$	−19.5274	−0.951705	−0.475853	−	0.879525i	$-0.657860\pi$
$421$	−19.5274	−0.951705	−0.475853	+	0.879525i	$0.657860\pi$
$422$	10.3273	0.502727
$423$	4.72228	0.229605
$424$	52.8853	2.56834
$425$	0	0
$426$	−5.58302	−0.270498
$427$	39.2165	1.89782
$428$	−44.5413	−2.15299
$429$	2.97519	0.143643
$430$	0	0
$431$	36.1145	1.73957	0.869787	−	0.493427i	$-0.164256\pi$
$431$	36.1145	1.73957	0.869787	+	0.493427i	$0.164256\pi$
$432$	22.8542	1.09957
$433$	31.7970	1.52806	0.764032	−	0.645178i	$-0.223217\pi$
$433$	31.7970	1.52806	0.764032	+	0.645178i	$0.223217\pi$
$434$	−53.8611	−2.58542
$435$	0	0
$436$	−42.2307	−2.02248
$437$	−3.27677	−0.156749
$438$	−14.1419	−0.675727
$439$	−13.6211	−0.650102	−0.325051	−	0.945697i	$-0.605381\pi$
$439$	−13.6211	−0.650102	−0.325051	+	0.945697i	$0.605381\pi$
$440$	0	0
$441$	4.00816	0.190865
$442$	−14.5748	−0.693254
$443$	15.3451	0.729069	0.364534	−	0.931190i	$-0.381228\pi$
$443$	15.3451	0.729069	0.364534	+	0.931190i	$0.381228\pi$
$444$	−61.0103	−2.89542
$445$	0	0
$446$	24.0072	1.13677
$447$	−36.7288	−1.73721
$448$	21.8143	1.03063
$449$	24.6256	1.16215	0.581077	−	0.813849i	$-0.302632\pi$
$449$	24.6256	1.16215	0.581077	+	0.813849i	$0.302632\pi$
$450$	0	0
$451$	−5.82903	−0.274478
$452$	2.49157	0.117194
$453$	12.6193	0.592908
$454$	−24.4167	−1.14593
$455$	0	0
$456$	18.0843	0.846874
$457$	−34.7238	−1.62431	−0.812156	−	0.583440i	$-0.801706\pi$
$457$	−34.7238	−1.62431	−0.812156	+	0.583440i	$0.801706\pi$
$458$	21.4832	1.00384
$459$	−8.43533	−0.393727
$460$	0	0
$461$	2.99313	0.139404	0.0697019	−	0.997568i	$-0.477795\pi$
$461$	2.99313	0.139404	0.0697019	+	0.997568i	$0.477795\pi$
$462$	−8.63950	−0.401946
$463$	3.45680	0.160651	0.0803255	−	0.996769i	$-0.474404\pi$
$463$	3.45680	0.160651	0.0803255	+	0.996769i	$0.474404\pi$
$464$	−3.16325	−0.146850
$465$	0	0
$466$	−3.79198	−0.175660
$467$	21.3933	0.989965	0.494982	−	0.868903i	$-0.335174\pi$
$467$	21.3933	0.989965	0.494982	+	0.868903i	$0.335174\pi$
$468$	−7.71080	−0.356432
$469$	−10.7348	−0.495685
$470$	0	0
$471$	−12.4399	−0.573202
$472$	74.0155	3.40684
$473$	−1.29760	−0.0596636
$474$	3.46461	0.159135
$475$	0	0
$476$	28.5846	1.31017
$477$	−5.73380	−0.262533
$478$	71.9957	3.29300
$479$	3.75139	0.171405	0.0857027	−	0.996321i	$-0.472686\pi$
$479$	3.75139	0.171405	0.0857027	+	0.996321i	$0.472686\pi$
$480$	0	0
$481$	−24.6814	−1.12538
$482$	2.48219	0.113060
$483$	−12.9758	−0.590420
$484$	−44.7605	−2.03457
$485$	0	0
$486$	−14.8043	−0.671538
$487$	−9.56113	−0.433256	−0.216628	−	0.976254i	$-0.569506\pi$
$487$	−9.56113	−0.433256	−0.216628	+	0.976254i	$0.569506\pi$
$488$	56.4463	2.55520
$489$	15.4895	0.700457
$490$	0	0
$491$	38.9884	1.75952	0.879760	−	0.475418i	$-0.157703\pi$
$491$	38.9884	1.75952	0.879760	+	0.475418i	$0.157703\pi$
$492$	93.0286	4.19405
$493$	1.16754	0.0525832
$494$	14.0860	0.633759
$495$	0	0
$496$	−29.0718	−1.30536
$497$	4.42961	0.198695
$498$	−40.1685	−1.79999
$499$	33.2982	1.49063	0.745316	−	0.666712i	$-0.232299\pi$
$499$	33.2982	1.49063	0.745316	+	0.666712i	$0.232299\pi$
$500$	0	0
$501$	27.0818	1.20992
$502$	5.78883	0.258368
$503$	−43.4333	−1.93660	−0.968298	−	0.249797i	$-0.919636\pi$
$503$	−43.4333	−1.93660	−0.968298	+	0.249797i	$0.919636\pi$
$504$	11.6293	0.518011
$505$	0	0
$506$	2.25321	0.100167
$507$	5.39388	0.239551
$508$	−38.8729	−1.72471
$509$	3.61845	0.160385	0.0801926	−	0.996779i	$-0.474446\pi$
$509$	3.61845	0.160385	0.0801926	+	0.996779i	$0.474446\pi$
$510$	0	0
$511$	11.2203	0.496357
$512$	45.2594	2.00020
$513$	8.15242	0.359938
$514$	57.5728	2.53943
$515$	0	0
$516$	20.7090	0.911665
$517$	4.00636	0.176199
$518$	71.6712	3.14905
$519$	−6.85237	−0.300785
$520$	0	0
$521$	17.2798	0.757042	0.378521	−	0.925593i	$-0.376433\pi$
$521$	17.2798	0.757042	0.378521	+	0.925593i	$0.376433\pi$
$522$	0.914559	0.0400292
$523$	−32.4914	−1.42075	−0.710374	−	0.703824i	$-0.751474\pi$
$523$	−32.4914	−1.42075	−0.710374	+	0.703824i	$0.751474\pi$
$524$	−43.6310	−1.90603
$525$	0	0
$526$	−43.0172	−1.87564
$527$	10.7302	0.467416
$528$	−4.66321	−0.202940
$529$	−19.6159	−0.852864
$530$	0	0
$531$	−8.02473	−0.348243
$532$	−27.6259	−1.19774
$533$	37.6343	1.63012
$534$	48.6903	2.10703
$535$	0	0
$536$	−15.4511	−0.667386
$537$	−7.78114	−0.335781
$538$	48.7017	2.09968
$539$	3.40050	0.146470
$540$	0	0
$541$	−25.4146	−1.09266	−0.546329	−	0.837571i	$-0.683975\pi$
$541$	−25.4146	−1.09266	−0.546329	+	0.837571i	$0.683975\pi$
$542$	26.7056	1.14710
$543$	23.7933	1.02107
$544$	3.06958	0.131607
$545$	0	0
$546$	55.7797	2.38715
$547$	36.9341	1.57919	0.789594	−	0.613630i	$-0.210291\pi$
$547$	36.9341	1.57919	0.789594	+	0.613630i	$0.210291\pi$
$548$	−27.1737	−1.16080
$549$	−6.11988	−0.261190
$550$	0	0
$551$	−1.12838	−0.0480706
$552$	−18.6768	−0.794936
$553$	−2.74885	−0.116893
$554$	33.4781	1.42235
$555$	0	0
$556$	59.4613	2.52172
$557$	−23.7480	−1.00623	−0.503117	−	0.864218i	$-0.667814\pi$
$557$	−23.7480	−1.00623	−0.503117	+	0.864218i	$0.667814\pi$
$558$	8.40524	0.355822
$559$	8.37775	0.354341
$560$	0	0
$561$	1.72116	0.0726676
$562$	17.8053	0.751072
$563$	33.4693	1.41056	0.705280	−	0.708928i	$-0.250821\pi$
$563$	33.4693	1.41056	0.705280	+	0.708928i	$0.250821\pi$
$564$	−63.9396	−2.69234
$565$	0	0
$566$	38.6220	1.62340
$567$	38.7864	1.62888
$568$	6.37577	0.267521
$569$	15.2590	0.639690	0.319845	−	0.947470i	$-0.396369\pi$
$569$	15.2590	0.639690	0.319845	+	0.947470i	$0.396369\pi$
$570$	0	0
$571$	31.1606	1.30403	0.652015	−	0.758206i	$-0.273924\pi$
$571$	31.1606	1.30403	0.652015	+	0.758206i	$0.273924\pi$
$572$	−6.54180	−0.273526
$573$	−51.5075	−2.15176
$574$	−109.284	−4.56144
$575$	0	0
$576$	−3.40420	−0.141842
$577$	14.8636	0.618779	0.309389	−	0.950935i	$-0.399875\pi$
$577$	14.8636	0.618779	0.309389	+	0.950935i	$0.399875\pi$
$578$	33.7655	1.40446
$579$	19.0668	0.792391
$580$	0	0
$581$	31.8700	1.32219
$582$	−22.5481	−0.934649
$583$	−4.86452	−0.201468
$584$	16.1500	0.668291
$585$	0	0
$586$	−12.2231	−0.504933
$587$	12.6453	0.521928	0.260964	−	0.965349i	$-0.415960\pi$
$587$	12.6453	0.521928	0.260964	+	0.965349i	$0.415960\pi$
$588$	−54.2703	−2.23807
$589$	−10.3703	−0.427303
$590$	0	0
$591$	40.7306	1.67543
$592$	38.6849	1.58994
$593$	−33.6521	−1.38192	−0.690962	−	0.722891i	$-0.742813\pi$
$593$	−33.6521	−1.38192	−0.690962	+	0.722891i	$0.742813\pi$
$594$	−5.60584	−0.230010
$595$	0	0
$596$	80.7587	3.30800
$597$	7.38710	0.302334
$598$	−14.5475	−0.594892
$599$	4.10338	0.167659	0.0838297	−	0.996480i	$-0.473285\pi$
$599$	4.10338	0.167659	0.0838297	+	0.996480i	$0.473285\pi$
$600$	0	0
$601$	−9.60351	−0.391735	−0.195868	−	0.980630i	$-0.562752\pi$
$601$	−9.60351	−0.391735	−0.195868	+	0.980630i	$0.562752\pi$
$602$	−24.3277	−0.991524
$603$	1.67520	0.0682195
$604$	−27.7472	−1.12902
$605$	0	0
$606$	58.0294	2.35728
$607$	11.7106	0.475321	0.237660	−	0.971348i	$-0.423619\pi$
$607$	11.7106	0.475321	0.237660	+	0.971348i	$0.423619\pi$
$608$	−2.96663	−0.120313
$609$	−4.46831	−0.181065
$610$	0	0
$611$	−25.8665	−1.04645
$612$	−4.46074	−0.180315
$613$	−3.77858	−0.152615	−0.0763077	−	0.997084i	$-0.524313\pi$
$613$	−3.77858	−0.152615	−0.0763077	+	0.997084i	$0.524313\pi$
$614$	−44.0259	−1.77674
$615$	0	0
$616$	9.86625	0.397523
$617$	−15.4815	−0.623261	−0.311630	−	0.950203i	$-0.600875\pi$
$617$	−15.4815	−0.623261	−0.311630	+	0.950203i	$0.600875\pi$
$618$	−68.1758	−2.74243
$619$	25.8434	1.03873	0.519367	−	0.854551i	$-0.326168\pi$
$619$	25.8434	1.03873	0.519367	+	0.854551i	$0.326168\pi$
$620$	0	0
$621$	−8.41951	−0.337863
$622$	−26.5632	−1.06509
$623$	−38.6312	−1.54773
$624$	30.1074	1.20526
$625$	0	0
$626$	23.6250	0.944244
$627$	−1.66344	−0.0664313
$628$	27.3528	1.09149
$629$	−14.2784	−0.569315
$630$	0	0
$631$	−5.99020	−0.238466	−0.119233	−	0.992866i	$-0.538044\pi$
$631$	−5.99020	−0.238466	−0.119233	+	0.992866i	$0.538044\pi$
$632$	−3.95656	−0.157384
$633$	7.87398	0.312963
$634$	−29.5234	−1.17252
$635$	0	0
$636$	77.6355	3.07845
$637$	−21.9548	−0.869881
$638$	0.775907	0.0307184
$639$	−0.691258	−0.0273457
$640$	0	0
$641$	−14.0917	−0.556588	−0.278294	−	0.960496i	$-0.589769\pi$
$641$	−14.0917	−0.556588	−0.278294	+	0.960496i	$0.589769\pi$
$642$	−50.2822	−1.98448
$643$	−21.2106	−0.836466	−0.418233	−	0.908340i	$-0.637350\pi$
$643$	−21.2106	−0.836466	−0.418233	+	0.908340i	$0.637350\pi$
$644$	28.5310	1.12428
$645$	0	0
$646$	8.14884	0.320612
$647$	40.7265	1.60112	0.800561	−	0.599251i	$-0.204535\pi$
$647$	40.7265	1.60112	0.800561	+	0.599251i	$0.204535\pi$
$648$	55.8273	2.19310
$649$	−6.80813	−0.267243
$650$	0	0
$651$	−41.0659	−1.60950
$652$	−34.0580	−1.33381
$653$	37.6383	1.47290	0.736450	−	0.676493i	$-0.236501\pi$
$653$	37.6383	1.47290	0.736450	+	0.676493i	$0.236501\pi$
$654$	−47.6737	−1.86419
$655$	0	0
$656$	−58.9868	−2.30305
$657$	−1.75097	−0.0683119
$658$	75.1124	2.92819
$659$	44.8779	1.74819	0.874097	−	0.485751i	$-0.161454\pi$
$659$	44.8779	1.74819	0.874097	+	0.485751i	$0.161454\pi$
$660$	0	0
$661$	45.0274	1.75136	0.875682	−	0.482888i	$-0.160412\pi$
$661$	45.0274	1.75136	0.875682	+	0.482888i	$0.160412\pi$
$662$	64.7497	2.51657
$663$	−11.1124	−0.431572
$664$	45.8721	1.78018
$665$	0	0
$666$	−11.1846	−0.433393
$667$	1.16535	0.0451224
$668$	−59.5470	−2.30394
$669$	18.3040	0.707675
$670$	0	0
$671$	−5.19207	−0.200438
$672$	−11.7477	−0.453177
$673$	13.1538	0.507040	0.253520	−	0.967330i	$-0.418412\pi$
$673$	13.1538	0.507040	0.253520	+	0.967330i	$0.418412\pi$
$674$	1.09466	0.0421649
$675$	0	0
$676$	−11.8600	−0.456154
$677$	−40.7502	−1.56616	−0.783079	−	0.621922i	$-0.786352\pi$
$677$	−40.7502	−1.56616	−0.783079	+	0.621922i	$0.786352\pi$
$678$	2.81271	0.108021
$679$	17.8898	0.686549
$680$	0	0
$681$	−18.6163	−0.713378
$682$	7.13096	0.273058
$683$	48.7434	1.86512	0.932558	−	0.361020i	$-0.117572\pi$
$683$	48.7434	1.86512	0.932558	+	0.361020i	$0.117572\pi$
$684$	4.31114	0.164840
$685$	0	0
$686$	−1.00593	−0.0384066
$687$	16.3797	0.624924
$688$	−13.1310	−0.500615
$689$	31.4071	1.19651
$690$	0	0
$691$	−2.74256	−0.104332	−0.0521659	−	0.998638i	$-0.516612\pi$
$691$	−2.74256	−0.104332	−0.0521659	+	0.998638i	$0.516612\pi$
$692$	15.0669	0.572757
$693$	−1.06969	−0.0406343
$694$	−49.9710	−1.89687
$695$	0	0
$696$	−6.43147	−0.243784
$697$	21.7717	0.824660
$698$	39.7402	1.50419
$699$	−2.89116	−0.109354
$700$	0	0
$701$	−12.6033	−0.476020	−0.238010	−	0.971263i	$-0.576495\pi$
$701$	−12.6033	−0.476020	−0.238010	+	0.971263i	$0.576495\pi$
$702$	36.1933	1.36603
$703$	13.7995	0.520457
$704$	−2.88811	−0.108850
$705$	0	0
$706$	44.8653	1.68853
$707$	−46.0410	−1.73155
$708$	108.655	4.08349
$709$	49.6415	1.86432	0.932162	−	0.362040i	$-0.117920\pi$
$709$	49.6415	1.86432	0.932162	+	0.362040i	$0.117920\pi$
$710$	0	0
$711$	0.428969	0.0160876
$712$	−55.6040	−2.08385
$713$	10.7101	0.401097
$714$	32.2689	1.20763
$715$	0	0
$716$	17.1091	0.639395
$717$	54.8924	2.04999
$718$	84.4504	3.15166
$719$	−10.0569	−0.375060	−0.187530	−	0.982259i	$-0.560048\pi$
$719$	−10.0569	−0.375060	−0.187530	+	0.982259i	$0.560048\pi$
$720$	0	0
$721$	54.0912	2.01446
$722$	39.2860	1.46207
$723$	1.89252	0.0703835
$724$	−52.3163	−1.94432
$725$	0	0
$726$	−50.5296	−1.87533
$727$	43.8294	1.62554	0.812771	−	0.582583i	$-0.197958\pi$
$727$	43.8294	1.62554	0.812771	+	0.582583i	$0.197958\pi$
$728$	−63.7000	−2.36088
$729$	19.9324	0.738235
$730$	0	0
$731$	4.84658	0.179257
$732$	82.8630	3.06271
$733$	−44.9694	−1.66098	−0.830492	−	0.557031i	$-0.811941\pi$
$733$	−44.9694	−1.66098	−0.830492	+	0.557031i	$0.811941\pi$
$734$	−5.90658	−0.218016
$735$	0	0
$736$	3.06383	0.112934
$737$	1.42123	0.0523517
$738$	17.0543	0.627776
$739$	33.2002	1.22129	0.610645	−	0.791905i	$-0.290910\pi$
$739$	33.2002	1.22129	0.610645	+	0.791905i	$0.290910\pi$
$740$	0	0
$741$	10.7397	0.394534
$742$	−91.2015	−3.34811
$743$	10.0082	0.367166	0.183583	−	0.983004i	$-0.441230\pi$
$743$	10.0082	0.367166	0.183583	+	0.983004i	$0.441230\pi$
$744$	−59.1083	−2.16702
$745$	0	0
$746$	13.8462	0.506944
$747$	−4.97344	−0.181969
$748$	−3.78447	−0.138374
$749$	39.8943	1.45771
$750$	0	0
$751$	16.8964	0.616558	0.308279	−	0.951296i	$-0.400247\pi$
$751$	16.8964	0.616558	0.308279	+	0.951296i	$0.400247\pi$
$752$	40.5423	1.47843
$753$	4.41364	0.160842
$754$	−5.00953	−0.182436
$755$	0	0
$756$	−70.9835	−2.58164
$757$	29.5066	1.07244	0.536219	−	0.844079i	$-0.319852\pi$
$757$	29.5066	1.07244	0.536219	+	0.844079i	$0.319852\pi$
$758$	−59.6546	−2.16675
$759$	1.71794	0.0623571
$760$	0	0
$761$	−23.0947	−0.837183	−0.418591	−	0.908175i	$-0.637476\pi$
$761$	−23.0947	−0.837183	−0.418591	+	0.908175i	$0.637476\pi$
$762$	−43.8832	−1.58972
$763$	37.8247	1.36935
$764$	113.254	4.09739
$765$	0	0
$766$	−44.9393	−1.62372
$767$	43.9557	1.58715
$768$	61.7403	2.22786
$769$	50.9881	1.83868	0.919338	−	0.393468i	$-0.128725\pi$
$769$	50.9881	1.83868	0.919338	+	0.393468i	$0.128725\pi$
$770$	0	0
$771$	43.8959	1.58087
$772$	−41.9239	−1.50887
$773$	−25.6742	−0.923437	−0.461718	−	0.887027i	$-0.652767\pi$
$773$	−25.6742	−0.923437	−0.461718	+	0.887027i	$0.652767\pi$
$774$	3.79644	0.136460
$775$	0	0
$776$	25.7498	0.924363
$777$	54.6450	1.96038
$778$	−29.7035	−1.06492
$779$	−21.0415	−0.753889
$780$	0	0
$781$	−0.586459	−0.0209852
$782$	−8.41582	−0.300949
$783$	−2.89931	−0.103613
$784$	34.4113	1.22897
$785$	0	0
$786$	−49.2545	−1.75685
$787$	−44.9770	−1.60326	−0.801628	−	0.597824i	$-0.796032\pi$
$787$	−44.9770	−1.60326	−0.801628	+	0.597824i	$0.796032\pi$
$788$	−89.5579	−3.19037
$789$	−32.7981	−1.16764
$790$	0	0
$791$	−2.23163	−0.0793475
$792$	−1.53967	−0.0547097
$793$	33.5219	1.19040
$794$	5.33576	0.189359
$795$	0	0
$796$	−16.2426	−0.575705
$797$	−39.0116	−1.38186	−0.690930	−	0.722921i	$-0.742799\pi$
$797$	−39.0116	−1.38186	−0.690930	+	0.722921i	$0.742799\pi$
$798$	−31.1866	−1.10399
$799$	−14.9639	−0.529385
$800$	0	0
$801$	6.02856	0.213009
$802$	−7.75842	−0.273959
$803$	−1.48551	−0.0524227
$804$	−22.6822	−0.799939
$805$	0	0
$806$	−46.0400	−1.62169
$807$	37.1322	1.30711
$808$	−66.2692	−2.33134
$809$	2.74283	0.0964328	0.0482164	−	0.998837i	$-0.484646\pi$
$809$	2.74283	0.0964328	0.0482164	+	0.998837i	$0.484646\pi$
$810$	0	0
$811$	−6.03293	−0.211845	−0.105922	−	0.994374i	$-0.533780\pi$
$811$	−6.03293	−0.211845	−0.105922	+	0.994374i	$0.533780\pi$
$812$	9.82485	0.344785
$813$	20.3614	0.714106
$814$	−9.48893	−0.332587
$815$	0	0
$816$	17.4173	0.609727
$817$	−4.68403	−0.163873
$818$	49.3660	1.72604
$819$	6.90633	0.241327
$820$	0	0
$821$	55.5398	1.93835	0.969177	−	0.246367i	$-0.0792368\pi$
$821$	55.5398	1.93835	0.969177	+	0.246367i	$0.0792368\pi$
$822$	−30.6761	−1.06995
$823$	−26.8844	−0.937131	−0.468565	−	0.883429i	$-0.655229\pi$
$823$	−26.8844	−0.937131	−0.468565	+	0.883429i	$0.655229\pi$
$824$	77.8564	2.71225
$825$	0	0
$826$	−127.641	−4.44119
$827$	6.23337	0.216755	0.108378	−	0.994110i	$-0.465434\pi$
$827$	6.23337	0.216755	0.108378	+	0.994110i	$0.465434\pi$
$828$	−4.45238	−0.154731
$829$	−40.1586	−1.39476	−0.697382	−	0.716699i	$-0.745652\pi$
$829$	−40.1586	−1.39476	−0.697382	+	0.716699i	$0.745652\pi$
$830$	0	0
$831$	25.5250	0.885454
$832$	18.6466	0.646456
$833$	−12.7010	−0.440063
$834$	67.1252	2.32436
$835$	0	0
$836$	3.65754	0.126499
$837$	−26.6461	−0.921024
$838$	−8.39804	−0.290105
$839$	54.2725	1.87370	0.936848	−	0.349738i	$-0.113729\pi$
$839$	54.2725	1.87370	0.936848	+	0.349738i	$0.113729\pi$
$840$	0	0
$841$	−28.5987	−0.986162
$842$	48.4705	1.67040
$843$	13.5755	0.467565
$844$	−17.3132	−0.595945
$845$	0	0
$846$	−11.7216	−0.402996
$847$	40.0906	1.37753
$848$	−49.2265	−1.69044
$849$	29.4470	1.01062
$850$	0	0
$851$	−14.2516	−0.488538
$852$	9.35962	0.320655
$853$	29.2923	1.00295	0.501475	−	0.865172i	$-0.332791\pi$
$853$	29.2923	1.00295	0.501475	+	0.865172i	$0.332791\pi$
$854$	−97.3425	−3.33099
$855$	0	0
$856$	57.4220	1.96264
$857$	29.0560	0.992535	0.496267	−	0.868170i	$-0.334704\pi$
$857$	29.0560	0.992535	0.496267	+	0.868170i	$0.334704\pi$
$858$	−7.38496	−0.252119
$859$	−44.6159	−1.52227	−0.761137	−	0.648591i	$-0.775359\pi$
$859$	−44.6159	−1.52227	−0.761137	+	0.648591i	$0.775359\pi$
$860$	0	0
$861$	−83.3228	−2.83963
$862$	−89.6429	−3.05325
$863$	8.41963	0.286607	0.143304	−	0.989679i	$-0.454227\pi$
$863$	8.41963	0.286607	0.143304	+	0.989679i	$0.454227\pi$
$864$	−7.62262	−0.259327
$865$	0	0
$866$	−78.9260	−2.68201
$867$	25.7442	0.874319
$868$	90.2951	3.06482
$869$	0.363935	0.0123456
$870$	0	0
$871$	−9.17597	−0.310916
$872$	54.4431	1.84368
$873$	−2.79178	−0.0944874
$874$	8.13356	0.275122
$875$	0	0
$876$	23.7081	0.801023
$877$	22.7943	0.769709	0.384855	−	0.922977i	$-0.374252\pi$
$877$	22.7943	0.769709	0.384855	+	0.922977i	$0.374252\pi$
$878$	33.8102	1.14104
$879$	−9.31941	−0.314336
$880$	0	0
$881$	29.9141	1.00783	0.503916	−	0.863753i	$-0.331892\pi$
$881$	29.9141	1.00783	0.503916	+	0.863753i	$0.331892\pi$
$882$	−9.94899	−0.335000
$883$	−20.6405	−0.694608	−0.347304	−	0.937753i	$-0.612903\pi$
$883$	−20.6405	−0.694608	−0.347304	+	0.937753i	$0.612903\pi$
$884$	24.4339	0.821800
$885$	0	0
$886$	−38.0894	−1.27964
$887$	−37.5515	−1.26085	−0.630427	−	0.776248i	$-0.717120\pi$
$887$	−37.5515	−1.26085	−0.630427	+	0.776248i	$0.717120\pi$
$888$	78.6535	2.63944
$889$	34.8173	1.16773
$890$	0	0
$891$	−5.13513	−0.172033
$892$	−40.2467	−1.34756
$893$	14.4620	0.483954
$894$	91.1676	3.04910
$895$	0	0
$896$	−66.5619	−2.22368
$897$	−11.0916	−0.370338
$898$	−61.1253	−2.03978
$899$	3.68810	0.123005
$900$	0	0
$901$	18.1692	0.605304
$902$	14.4687	0.481756
$903$	−18.5485	−0.617254
$904$	−3.21210	−0.106833
$905$	0	0
$906$	−31.3235	−1.04065
$907$	27.8753	0.925584	0.462792	−	0.886467i	$-0.346848\pi$
$907$	27.8753	0.925584	0.462792	+	0.886467i	$0.346848\pi$
$908$	40.9332	1.35842
$909$	7.18487	0.238307
$910$	0	0
$911$	−38.5461	−1.27709	−0.638545	−	0.769584i	$-0.720464\pi$
$911$	−38.5461	−1.27709	−0.638545	+	0.769584i	$0.720464\pi$
$912$	−16.8331	−0.557401
$913$	−4.21943	−0.139643
$914$	86.1910	2.85094
$915$	0	0
$916$	−36.0154	−1.18998
$917$	39.0789	1.29050
$918$	20.9380	0.691058
$919$	−54.3044	−1.79134	−0.895669	−	0.444721i	$-0.853303\pi$
$919$	−54.3044	−1.79134	−0.895669	+	0.444721i	$0.853303\pi$
$920$	0	0
$921$	−33.5671	−1.10607
$922$	−7.42950	−0.244677
$923$	3.78639	0.124631
$924$	14.4836	0.476477
$925$	0	0
$926$	−8.58041	−0.281970
$927$	−8.44115	−0.277244
$928$	1.05505	0.0346337
$929$	−19.2789	−0.632520	−0.316260	−	0.948673i	$-0.602427\pi$
$929$	−19.2789	−0.632520	−0.316260	+	0.948673i	$0.602427\pi$
$930$	0	0
$931$	12.2750	0.402297
$932$	6.35705	0.208232
$933$	−20.2528	−0.663048
$934$	−53.1022	−1.73756
$935$	0	0
$936$	9.94064	0.324920
$937$	−34.7536	−1.13535	−0.567675	−	0.823252i	$-0.692157\pi$
$937$	−34.7536	−1.13535	−0.567675	+	0.823252i	$0.692157\pi$
$938$	26.6457	0.870012
$939$	18.0126	0.587821
$940$	0	0
$941$	17.9788	0.586092	0.293046	−	0.956098i	$-0.405331\pi$
$941$	17.9788	0.586092	0.293046	+	0.956098i	$0.405331\pi$
$942$	30.8782	1.00607
$943$	21.7308	0.707653
$944$	−68.8948	−2.24234
$945$	0	0
$946$	3.22088	0.104720
$947$	−23.9851	−0.779412	−0.389706	−	0.920939i	$-0.627423\pi$
$947$	−23.9851	−0.779412	−0.389706	+	0.920939i	$0.627423\pi$
$948$	−5.80823	−0.188643
$949$	9.59101	0.311337
$950$	0	0
$951$	−22.5099	−0.729932
$952$	−36.8509	−1.19434
$953$	−31.4803	−1.01975	−0.509874	−	0.860249i	$-0.670308\pi$
$953$	−31.4803	−1.01975	−0.509874	+	0.860249i	$0.670308\pi$
$954$	14.2324	0.460790
$955$	0	0
$956$	−120.697	−3.90361
$957$	0.591583	0.0191232
$958$	−9.31164	−0.300846
$959$	24.3387	0.785936
$960$	0	0
$961$	2.89538	0.0933995
$962$	61.2639	1.97523
$963$	−6.22566	−0.200619
$964$	−4.16124	−0.134025
$965$	0	0
$966$	32.2084	1.03629
$967$	−8.22632	−0.264541	−0.132270	−	0.991214i	$-0.542227\pi$
$967$	−8.22632	−0.264541	−0.132270	+	0.991214i	$0.542227\pi$
$968$	57.7044	1.85469
$969$	6.21301	0.199591
$970$	0	0
$971$	−59.8528	−1.92077	−0.960384	−	0.278680i	$-0.910103\pi$
$971$	−59.8528	−1.92077	−0.960384	+	0.278680i	$0.910103\pi$
$972$	24.8186	0.796058
$973$	−53.2577	−1.70736
$974$	23.7325	0.760438
$975$	0	0
$976$	−52.5411	−1.68180
$977$	−26.3955	−0.844468	−0.422234	−	0.906487i	$-0.638754\pi$
$977$	−26.3955	−0.844468	−0.422234	+	0.906487i	$0.638754\pi$
$978$	−38.4477	−1.22942
$979$	5.11459	0.163463
$980$	0	0
$981$	−5.90269	−0.188459
$982$	−96.7763	−3.08826
$983$	47.8741	1.52695	0.763474	−	0.645839i	$-0.223492\pi$
$983$	47.8741	1.52695	0.763474	+	0.645839i	$0.223492\pi$
$984$	−119.931	−3.82326
$985$	0	0
$986$	−2.89804	−0.0922925
$987$	57.2687	1.82288
$988$	−23.6144	−0.751274
$989$	4.83749	0.153823
$990$	0	0
$991$	−32.1509	−1.02131	−0.510654	−	0.859786i	$-0.670597\pi$
$991$	−32.1509	−1.02131	−0.510654	+	0.859786i	$0.670597\pi$
$992$	9.69642	0.307862
$993$	49.3678	1.56664
$994$	−10.9951	−0.348744
$995$	0	0
$996$	67.3402	2.13376
$997$	−17.9662	−0.568994	−0.284497	−	0.958677i	$-0.591827\pi$
$997$	−17.9662	−0.568994	−0.284497	+	0.958677i	$0.591827\pi$
$998$	−82.6523	−2.61631
$999$	35.4571	1.12181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.q.1.7		66
5.2	odd	4		1205.2.b.d.724.7	✓	66
5.3	odd	4		1205.2.b.d.724.60	yes	66
5.4	even	2	inner	6025.2.a.q.1.60		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.d.724.7	✓	66	5.2	odd	4
1205.2.b.d.724.60	yes	66	5.3	odd	4
6025.2.a.q.1.7		66	1.1	even	1	trivial
6025.2.a.q.1.60		66	5.4	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-2.48219 q^{2} -1.89252 q^{3} +4.16124 q^{4} +4.69758 q^{6} -3.72710 q^{7} -5.36461 q^{8} +0.581628 q^{9} +O(q^{10})\)	\(q-2.48219 q^{2} -1.89252 q^{3} +4.16124 q^{4} +4.69758 q^{6} -3.72710 q^{7} -5.36461 q^{8} +0.581628 q^{9} +0.493450 q^{11} -7.87523 q^{12} -3.18589 q^{13} +9.25135 q^{14} +4.99346 q^{16} -1.84306 q^{17} -1.44371 q^{18} +1.78124 q^{19} +7.05361 q^{21} -1.22483 q^{22} -1.83960 q^{23} +10.1526 q^{24} +7.90797 q^{26} +4.57681 q^{27} -15.5094 q^{28} -0.633479 q^{29} -5.82197 q^{31} -1.66549 q^{32} -0.933864 q^{33} +4.57481 q^{34} +2.42030 q^{36} +7.74711 q^{37} -4.42137 q^{38} +6.02936 q^{39} -11.8128 q^{41} -17.5084 q^{42} -2.62964 q^{43} +2.05337 q^{44} +4.56623 q^{46} +8.11907 q^{47} -9.45023 q^{48} +6.89127 q^{49} +3.48802 q^{51} -13.2573 q^{52} -9.85819 q^{53} -11.3605 q^{54} +19.9944 q^{56} -3.37104 q^{57} +1.57241 q^{58} -13.7970 q^{59} -10.5220 q^{61} +14.4512 q^{62} -2.16779 q^{63} -5.85288 q^{64} +2.31802 q^{66} +2.88019 q^{67} -7.66941 q^{68} +3.48148 q^{69} -1.18849 q^{71} -3.12021 q^{72} -3.01047 q^{73} -19.2298 q^{74} +7.41218 q^{76} -1.83914 q^{77} -14.9660 q^{78} +0.737531 q^{79} -10.4066 q^{81} +29.3216 q^{82} -8.55088 q^{83} +29.3518 q^{84} +6.52726 q^{86} +1.19887 q^{87} -2.64717 q^{88} +10.3650 q^{89} +11.8741 q^{91} -7.65503 q^{92} +11.0182 q^{93} -20.1530 q^{94} +3.15196 q^{96} -4.79994 q^{97} -17.1054 q^{98} +0.287005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9}+O(q^{10}) \) 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9	\( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9} + 48 q^{11} + 30 q^{14} + 98 q^{16} + 12 q^{19} + 18 q^{21} + 42 q^{24} + 48 q^{26} + 56 q^{29} + 48 q^{31} + 8 q^{34} + 158 q^{36} + 84 q^{39} + 56 q^{41} + 144 q^{44} + 36 q^{46} + 98 q^{49} + 44 q^{51} + 86 q^{54} + 104 q^{56} + 108 q^{59} + 22 q^{61} + 136 q^{64} + 74 q^{66} + 20 q^{69} + 212 q^{71} + 84 q^{74} + 6 q^{76} + 66 q^{79} + 162 q^{81} - 52 q^{84} + 100 q^{86} + 54 q^{89} + 72 q^{91} - 96 q^{94} + 122 q^{96} + 112 q^{99}+O(q^{100}) \) 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9 + 48 * q^11 + 30 * q^14 + 98 * q^16 + 12 * q^19 + 18 * q^21 + 42 * q^24 + 48 * q^26 + 56 * q^29 + 48 * q^31 + 8 * q^34 + 158 * q^36 + 84 * q^39 + 56 * q^41 + 144 * q^44 + 36 * q^46 + 98 * q^49 + 44 * q^51 + 86 * q^54 + 104 * q^56 + 108 * q^59 + 22 * q^61 + 136 * q^64 + 74 * q^66 + 20 * q^69 + 212 * q^71 + 84 * q^74 + 6 * q^76 + 66 * q^79 + 162 * q^81 - 52 * q^84 + 100 * q^86 + 54 * q^89 + 72 * q^91 - 96 * q^94 + 122 * q^96 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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