LMFDB - Embedded newform 5950.2.a.be.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5950,2,Mod(1,5950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5950 = 2 \cdot 5^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5950.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:	$47.5109892027$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.65109$ of defining polynomial
Character	$\chi$	$=$	5950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.65109 q^{3} +1.00000 q^{4} +1.65109 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.273891 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.65109 q^{3} +1.00000 q^{4} +1.65109 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.273891 q^{9} -5.92498 q^{11} -1.65109 q^{12} +0.622797 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +0.273891 q^{18} +0.444469 q^{19} +1.65109 q^{21} +5.92498 q^{22} +6.95328 q^{23} +1.65109 q^{24} -0.622797 q^{26} +5.40550 q^{27} -1.00000 q^{28} -5.57608 q^{29} -7.85772 q^{31} -1.00000 q^{32} +9.78270 q^{33} +1.00000 q^{34} -0.273891 q^{36} +5.20662 q^{37} -0.444469 q^{38} -1.02830 q^{39} +7.70769 q^{41} -1.65109 q^{42} +10.4338 q^{43} -5.92498 q^{44} -6.95328 q^{46} +7.95328 q^{47} -1.65109 q^{48} +1.00000 q^{49} +1.65109 q^{51} +0.622797 q^{52} -6.85772 q^{53} -5.40550 q^{54} +1.00000 q^{56} -0.733860 q^{57} +5.57608 q^{58} +1.93273 q^{59} +6.77495 q^{61} +7.85772 q^{62} +0.273891 q^{63} +1.00000 q^{64} -9.78270 q^{66} +9.19887 q^{67} -1.00000 q^{68} -11.4805 q^{69} +6.63267 q^{71} +0.273891 q^{72} -6.48052 q^{73} -5.20662 q^{74} +0.444469 q^{76} +5.92498 q^{77} +1.02830 q^{78} -3.37720 q^{79} -8.10331 q^{81} -7.70769 q^{82} -4.25547 q^{83} +1.65109 q^{84} -10.4338 q^{86} +9.20662 q^{87} +5.92498 q^{88} +5.76216 q^{89} -0.622797 q^{91} +6.95328 q^{92} +12.9738 q^{93} -7.95328 q^{94} +1.65109 q^{96} -15.0926 q^{97} -1.00000 q^{98} +1.62280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 3 * q^8 + q^9	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 3 q^{8} + q^{9} - 9 q^{11} + 2 q^{12} + 7 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - q^{18} + q^{19} - 2 q^{21} + 9 q^{22} - 2 q^{24} - 7 q^{26} - q^{27} - 3 q^{28} - q^{29} - 10 q^{31} - 3 q^{32} + 7 q^{33} + 3 q^{34} + q^{36} + 9 q^{37} - q^{38} + 9 q^{39} - 8 q^{41} + 2 q^{42} + 2 q^{43} - 9 q^{44} + 3 q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{51} + 7 q^{52} - 7 q^{53} + q^{54} + 3 q^{56} - 8 q^{57} + q^{58} + q^{59} - 6 q^{61} + 10 q^{62} - q^{63} + 3 q^{64} - 7 q^{66} + 17 q^{67} - 3 q^{68} - 26 q^{69} - 20 q^{71} - q^{72} - 11 q^{73} - 9 q^{74} + q^{76} + 9 q^{77} - 9 q^{78} - 5 q^{79} - 21 q^{81} + 8 q^{82} + 22 q^{83} - 2 q^{84} - 2 q^{86} + 21 q^{87} + 9 q^{88} + 11 q^{89} - 7 q^{91} + 2 q^{93} - 3 q^{94} - 2 q^{96} - 13 q^{97} - 3 q^{98} + 10 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 3 * q^8 + q^9 - 9 * q^11 + 2 * q^12 + 7 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - q^18 + q^19 - 2 * q^21 + 9 * q^22 - 2 * q^24 - 7 * q^26 - q^27 - 3 * q^28 - q^29 - 10 * q^31 - 3 * q^32 + 7 * q^33 + 3 * q^34 + q^36 + 9 * q^37 - q^38 + 9 * q^39 - 8 * q^41 + 2 * q^42 + 2 * q^43 - 9 * q^44 + 3 * q^47 + 2 * q^48 + 3 * q^49 - 2 * q^51 + 7 * q^52 - 7 * q^53 + q^54 + 3 * q^56 - 8 * q^57 + q^58 + q^59 - 6 * q^61 + 10 * q^62 - q^63 + 3 * q^64 - 7 * q^66 + 17 * q^67 - 3 * q^68 - 26 * q^69 - 20 * q^71 - q^72 - 11 * q^73 - 9 * q^74 + q^76 + 9 * q^77 - 9 * q^78 - 5 * q^79 - 21 * q^81 + 8 * q^82 + 22 * q^83 - 2 * q^84 - 2 * q^86 + 21 * q^87 + 9 * q^88 + 11 * q^89 - 7 * q^91 + 2 * q^93 - 3 * q^94 - 2 * q^96 - 13 * q^97 - 3 * q^98 + 10 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.65109	−0.953259	−0.476630	−	0.879104i	$-0.658142\pi$
$3$	−1.65109	−0.953259	−0.476630	+	0.879104i	$0.658142\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.65109	0.674056
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.273891	−0.0912969
$10$	0	0
$11$	−5.92498	−1.78645	−0.893225	−	0.449610i	$-0.851563\pi$
$11$	−5.92498	−1.78645	−0.893225	+	0.449610i	$0.851563\pi$
$12$	−1.65109	−0.476630
$13$	0.622797	0.172733	0.0863664	−	0.996263i	$-0.472474\pi$
$13$	0.622797	0.172733	0.0863664	+	0.996263i	$0.472474\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.273891	0.0645566
$19$	0.444469	0.101968	0.0509841	−	0.998699i	$-0.483764\pi$
$19$	0.444469	0.101968	0.0509841	+	0.998699i	$0.483764\pi$
$20$	0	0
$21$	1.65109	0.360298
$22$	5.92498	1.26321
$23$	6.95328	1.44986	0.724930	−	0.688823i	$-0.241872\pi$
$23$	6.95328	1.44986	0.724930	+	0.688823i	$0.241872\pi$
$24$	1.65109	0.337028
$25$	0	0
$26$	−0.622797	−0.122141
$27$	5.40550	1.04029
$28$	−1.00000	−0.188982
$29$	−5.57608	−1.03545	−0.517726	−	0.855547i	$-0.673221\pi$
$29$	−5.57608	−1.03545	−0.517726	+	0.855547i	$0.673221\pi$
$30$	0	0
$31$	−7.85772	−1.41129	−0.705644	−	0.708567i	$-0.749342\pi$
$31$	−7.85772	−1.41129	−0.705644	+	0.708567i	$0.749342\pi$
$32$	−1.00000	−0.176777
$33$	9.78270	1.70295
$34$	1.00000	0.171499
$35$	0	0
$36$	−0.273891	−0.0456484
$37$	5.20662	0.855964	0.427982	−	0.903787i	$-0.359225\pi$
$37$	5.20662	0.855964	0.427982	+	0.903787i	$0.359225\pi$
$38$	−0.444469	−0.0721024
$39$	−1.02830	−0.164659
$40$	0	0
$41$	7.70769	1.20374	0.601869	−	0.798595i	$-0.294423\pi$
$41$	7.70769	1.20374	0.601869	+	0.798595i	$0.294423\pi$
$42$	−1.65109	−0.254769
$43$	10.4338	1.59114	0.795569	−	0.605862i	$-0.207172\pi$
$43$	10.4338	1.59114	0.795569	+	0.605862i	$0.207172\pi$
$44$	−5.92498	−0.893225
$45$	0	0
$46$	−6.95328	−1.02521
$47$	7.95328	1.16011	0.580053	−	0.814579i	$-0.303032\pi$
$47$	7.95328	1.16011	0.580053	+	0.814579i	$0.303032\pi$
$48$	−1.65109	−0.238315
$49$	1.00000	0.142857
$50$	0	0
$51$	1.65109	0.231199
$52$	0.622797	0.0863664
$53$	−6.85772	−0.941980	−0.470990	−	0.882139i	$-0.656103\pi$
$53$	−6.85772	−0.941980	−0.470990	+	0.882139i	$0.656103\pi$
$54$	−5.40550	−0.735595
$55$	0	0
$56$	1.00000	0.133631
$57$	−0.733860	−0.0972021
$58$	5.57608	0.732175
$59$	1.93273	0.251621	0.125810	−	0.992054i	$-0.459847\pi$
$59$	1.93273	0.251621	0.125810	+	0.992054i	$0.459847\pi$
$60$	0	0
$61$	6.77495	0.867444	0.433722	−	0.901047i	$-0.357200\pi$
$61$	6.77495	0.867444	0.433722	+	0.901047i	$0.357200\pi$
$62$	7.85772	0.997931
$63$	0.273891	0.0345070
$64$	1.00000	0.125000
$65$	0	0
$66$	−9.78270	−1.20417
$67$	9.19887	1.12382	0.561911	−	0.827198i	$-0.310066\pi$
$67$	9.19887	1.12382	0.561911	+	0.827198i	$0.310066\pi$
$68$	−1.00000	−0.121268
$69$	−11.4805	−1.38209
$70$	0	0
$71$	6.63267	0.787153	0.393577	−	0.919292i	$-0.371238\pi$
$71$	6.63267	0.787153	0.393577	+	0.919292i	$0.371238\pi$
$72$	0.273891	0.0322783
$73$	−6.48052	−0.758487	−0.379243	−	0.925297i	$-0.623816\pi$
$73$	−6.48052	−0.758487	−0.379243	+	0.925297i	$0.623816\pi$
$74$	−5.20662	−0.605258
$75$	0	0
$76$	0.444469	0.0509841
$77$	5.92498	0.675215
$78$	1.02830	0.116432
$79$	−3.37720	−0.379965	−0.189983	−	0.981787i	$-0.560843\pi$
$79$	−3.37720	−0.379965	−0.189983	+	0.981787i	$0.560843\pi$
$80$	0	0
$81$	−8.10331	−0.900368
$82$	−7.70769	−0.851172
$83$	−4.25547	−0.467098	−0.233549	−	0.972345i	$-0.575034\pi$
$83$	−4.25547	−0.467098	−0.233549	+	0.972345i	$0.575034\pi$
$84$	1.65109	0.180149
$85$	0	0
$86$	−10.4338	−1.12511
$87$	9.20662	0.987054
$88$	5.92498	0.631605
$89$	5.76216	0.610787	0.305394	−	0.952226i	$-0.401212\pi$
$89$	5.76216	0.610787	0.305394	+	0.952226i	$0.401212\pi$
$90$	0	0
$91$	−0.622797	−0.0652869
$92$	6.95328	0.724930
$93$	12.9738	1.34532
$94$	−7.95328	−0.820318
$95$	0	0
$96$	1.65109	0.168514
$97$	−15.0926	−1.53243	−0.766213	−	0.642587i	$-0.777861\pi$
$97$	−15.0926	−1.53243	−0.766213	+	0.642587i	$0.777861\pi$
$98$	−1.00000	−0.101015
$99$	1.62280	0.163097
$100$	0	0
$101$	−2.86839	−0.285416	−0.142708	−	0.989765i	$-0.545581\pi$
$101$	−2.86839	−0.285416	−0.142708	+	0.989765i	$0.545581\pi$
$102$	−1.65109	−0.163483
$103$	−12.4260	−1.22437	−0.612187	−	0.790713i	$-0.709710\pi$
$103$	−12.4260	−1.22437	−0.612187	+	0.790713i	$0.709710\pi$
$104$	−0.622797	−0.0610703
$105$	0	0
$106$	6.85772	0.666080
$107$	3.36945	0.325737	0.162869	−	0.986648i	$-0.447925\pi$
$107$	3.36945	0.325737	0.162869	+	0.986648i	$0.447925\pi$
$108$	5.40550	0.520144
$109$	2.92498	0.280163	0.140081	−	0.990140i	$-0.455264\pi$
$109$	2.92498	0.280163	0.140081	+	0.990140i	$0.455264\pi$
$110$	0	0
$111$	−8.59662	−0.815955
$112$	−1.00000	−0.0944911
$113$	−18.7827	−1.76693	−0.883464	−	0.468499i	$-0.844795\pi$
$113$	−18.7827	−1.76693	−0.883464	+	0.468499i	$0.844795\pi$
$114$	0.733860	0.0687322
$115$	0	0
$116$	−5.57608	−0.517726
$117$	−0.170578	−0.0157700
$118$	−1.93273	−0.177923
$119$	1.00000	0.0916698
$120$	0	0
$121$	24.1054	2.19140
$122$	−6.77495	−0.613375
$123$	−12.7261	−1.14747
$124$	−7.85772	−0.705644
$125$	0	0
$126$	−0.273891	−0.0244001
$127$	18.5838	1.64905	0.824524	−	0.565827i	$-0.191443\pi$
$127$	18.5838	1.64905	0.824524	+	0.565827i	$0.191443\pi$
$128$	−1.00000	−0.0883883
$129$	−17.2272	−1.51677
$130$	0	0
$131$	−8.92498	−0.779779	−0.389890	−	0.920862i	$-0.627487\pi$
$131$	−8.92498	−0.779779	−0.389890	+	0.920862i	$0.627487\pi$
$132$	9.78270	0.851475
$133$	−0.444469	−0.0385403
$134$	−9.19887	−0.794662
$135$	0	0
$136$	1.00000	0.0857493
$137$	−5.68714	−0.485885	−0.242943	−	0.970041i	$-0.578113\pi$
$137$	−5.68714	−0.485885	−0.242943	+	0.970041i	$0.578113\pi$
$138$	11.4805	0.977286
$139$	−5.56833	−0.472299	−0.236150	−	0.971717i	$-0.575886\pi$
$139$	−5.56833	−0.472299	−0.236150	+	0.971717i	$0.575886\pi$
$140$	0	0
$141$	−13.1316	−1.10588
$142$	−6.63267	−0.556601
$143$	−3.69006	−0.308579
$144$	−0.273891	−0.0228242
$145$	0	0
$146$	6.48052	0.536331
$147$	−1.65109	−0.136180
$148$	5.20662	0.427982
$149$	−18.4055	−1.50784	−0.753919	−	0.656968i	$-0.771839\pi$
$149$	−18.4055	−1.50784	−0.753919	+	0.656968i	$0.771839\pi$
$150$	0	0
$151$	4.59158	0.373657	0.186829	−	0.982393i	$-0.440179\pi$
$151$	4.59158	0.373657	0.186829	+	0.982393i	$0.440179\pi$
$152$	−0.444469	−0.0360512
$153$	0.273891	0.0221427
$154$	−5.92498	−0.477449
$155$	0	0
$156$	−1.02830	−0.0823296
$157$	13.7905	1.10060	0.550299	−	0.834968i	$-0.314514\pi$
$157$	13.7905	1.10060	0.550299	+	0.834968i	$0.314514\pi$
$158$	3.37720	0.268676
$159$	11.3227	0.897951
$160$	0	0
$161$	−6.95328	−0.547995
$162$	8.10331	0.636656
$163$	12.5371	0.981982	0.490991	−	0.871165i	$-0.336635\pi$
$163$	12.5371	0.981982	0.490991	+	0.871165i	$0.336635\pi$
$164$	7.70769	0.601869
$165$	0	0
$166$	4.25547	0.330288
$167$	−3.36945	−0.260736	−0.130368	−	0.991466i	$-0.541616\pi$
$167$	−3.36945	−0.260736	−0.130368	+	0.991466i	$0.541616\pi$
$168$	−1.65109	−0.127385
$169$	−12.6121	−0.970163
$170$	0	0
$171$	−0.121736	−0.00930937
$172$	10.4338	0.795569
$173$	−8.10331	−0.616083	−0.308042	−	0.951373i	$-0.599674\pi$
$173$	−8.10331	−0.616083	−0.308042	+	0.951373i	$0.599674\pi$
$174$	−9.20662	−0.697952
$175$	0	0
$176$	−5.92498	−0.446612
$177$	−3.19112	−0.239860
$178$	−5.76216	−0.431892
$179$	−1.93273	−0.144459	−0.0722297	−	0.997388i	$-0.523011\pi$
$179$	−1.93273	−0.144459	−0.0722297	+	0.997388i	$0.523011\pi$
$180$	0	0
$181$	−4.49894	−0.334403	−0.167202	−	0.985923i	$-0.553473\pi$
$181$	−4.49894	−0.334403	−0.167202	+	0.985923i	$0.553473\pi$
$182$	0.622797	0.0461648
$183$	−11.1861	−0.826899
$184$	−6.95328	−0.512603
$185$	0	0
$186$	−12.9738	−0.951287
$187$	5.92498	0.433278
$188$	7.95328	0.580053
$189$	−5.40550	−0.393192
$190$	0	0
$191$	−19.9066	−1.44039	−0.720194	−	0.693773i	$-0.755947\pi$
$191$	−19.9066	−1.44039	−0.720194	+	0.693773i	$0.755947\pi$
$192$	−1.65109	−0.119157
$193$	−9.88894	−0.711821	−0.355911	−	0.934520i	$-0.615829\pi$
$193$	−9.88894	−0.711821	−0.355911	+	0.934520i	$0.615829\pi$
$194$	15.0926	1.08359
$195$	0	0
$196$	1.00000	0.0714286
$197$	1.40550	0.100138	0.0500688	−	0.998746i	$-0.484056\pi$
$197$	1.40550	0.100138	0.0500688	+	0.998746i	$0.484056\pi$
$198$	−1.62280	−0.115327
$199$	21.6532	1.53496	0.767478	−	0.641075i	$-0.221511\pi$
$199$	21.6532	1.53496	0.767478	+	0.641075i	$0.221511\pi$
$200$	0	0
$201$	−15.1882	−1.07129
$202$	2.86839	0.201819
$203$	5.57608	0.391364
$204$	1.65109	0.115600
$205$	0	0
$206$	12.4260	0.865764
$207$	−1.90444	−0.132368
$208$	0.622797	0.0431832
$209$	−2.63347	−0.182161
$210$	0	0
$211$	11.6249	0.800292	0.400146	−	0.916451i	$-0.368959\pi$
$211$	11.6249	0.800292	0.400146	+	0.916451i	$0.368959\pi$
$212$	−6.85772	−0.470990
$213$	−10.9512	−0.750361
$214$	−3.36945	−0.230331
$215$	0	0
$216$	−5.40550	−0.367798
$217$	7.85772	0.533417
$218$	−2.92498	−0.198105
$219$	10.6999	0.723035
$220$	0	0
$221$	−0.622797	−0.0418939
$222$	8.59662	0.576968
$223$	12.2349	0.819311	0.409655	−	0.912240i	$-0.365649\pi$
$223$	12.2349	0.819311	0.409655	+	0.912240i	$0.365649\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	18.7827	1.24941
$227$	10.1989	0.676923	0.338462	−	0.940980i	$-0.390093\pi$
$227$	10.1989	0.676923	0.338462	+	0.940980i	$0.390093\pi$
$228$	−0.733860	−0.0486010
$229$	6.81100	0.450083	0.225042	−	0.974349i	$-0.427748\pi$
$229$	6.81100	0.450083	0.225042	+	0.974349i	$0.427748\pi$
$230$	0	0
$231$	−9.78270	−0.643655
$232$	5.57608	0.366087
$233$	10.1239	0.663236	0.331618	−	0.943414i	$-0.392405\pi$
$233$	10.1239	0.663236	0.331618	+	0.943414i	$0.392405\pi$
$234$	0.170578	0.0111510
$235$	0	0
$236$	1.93273	0.125810
$237$	5.57608	0.362205
$238$	−1.00000	−0.0648204
$239$	1.56833	0.101447	0.0507233	−	0.998713i	$-0.483847\pi$
$239$	1.56833	0.101447	0.0507233	+	0.998713i	$0.483847\pi$
$240$	0	0
$241$	13.5449	0.872501	0.436250	−	0.899825i	$-0.356306\pi$
$241$	13.5449	0.872501	0.436250	+	0.899825i	$0.356306\pi$
$242$	−24.1054	−1.54956
$243$	−2.83717	−0.182005
$244$	6.77495	0.433722
$245$	0	0
$246$	12.7261	0.811387
$247$	0.276814	0.0176132
$248$	7.85772	0.498966
$249$	7.02617	0.445266
$250$	0	0
$251$	−18.2739	−1.15344	−0.576719	−	0.816943i	$-0.695667\pi$
$251$	−18.2739	−1.15344	−0.576719	+	0.816943i	$0.695667\pi$
$252$	0.273891	0.0172535
$253$	−41.1981	−2.59010
$254$	−18.5838	−1.16605
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.8881	1.49010	0.745051	−	0.667008i	$-0.232425\pi$
$257$	23.8881	1.49010	0.745051	+	0.667008i	$0.232425\pi$
$258$	17.2272	1.07252
$259$	−5.20662	−0.323524
$260$	0	0
$261$	1.52723	0.0945335
$262$	8.92498	0.551387
$263$	20.1004	1.23944	0.619722	−	0.784822i	$-0.287246\pi$
$263$	20.1004	1.23944	0.619722	+	0.784822i	$0.287246\pi$
$264$	−9.78270	−0.602084
$265$	0	0
$266$	0.444469	0.0272521
$267$	−9.51386	−0.582239
$268$	9.19887	0.561911
$269$	15.9533	0.972689	0.486344	−	0.873767i	$-0.338330\pi$
$269$	15.9533	0.972689	0.486344	+	0.873767i	$0.338330\pi$
$270$	0	0
$271$	14.1132	0.857315	0.428657	−	0.903467i	$-0.358987\pi$
$271$	14.1132	0.857315	0.428657	+	0.903467i	$0.358987\pi$
$272$	−1.00000	−0.0606339
$273$	1.02830	0.0622353
$274$	5.68714	0.343573
$275$	0	0
$276$	−11.4805	−0.691046
$277$	−1.50881	−0.0906557	−0.0453278	−	0.998972i	$-0.514433\pi$
$277$	−1.50881	−0.0906557	−0.0453278	+	0.998972i	$0.514433\pi$
$278$	5.56833	0.333966
$279$	2.15215	0.128846
$280$	0	0
$281$	−20.8753	−1.24532	−0.622659	−	0.782493i	$-0.713948\pi$
$281$	−20.8753	−1.24532	−0.622659	+	0.782493i	$0.713948\pi$
$282$	13.1316	0.781976
$283$	−33.3793	−1.98419	−0.992097	−	0.125470i	$-0.959956\pi$
$283$	−33.3793	−1.98419	−0.992097	+	0.125470i	$0.959956\pi$
$284$	6.63267	0.393577
$285$	0	0
$286$	3.69006	0.218198
$287$	−7.70769	−0.454970
$288$	0.273891	0.0161392
$289$	1.00000	0.0588235
$290$	0	0
$291$	24.9194	1.46080
$292$	−6.48052	−0.379243
$293$	−6.73891	−0.393691	−0.196846	−	0.980435i	$-0.563070\pi$
$293$	−6.73891	−0.393691	−0.196846	+	0.980435i	$0.563070\pi$
$294$	1.65109	0.0962937
$295$	0	0
$296$	−5.20662	−0.302629
$297$	−32.0275	−1.85842
$298$	18.4055	1.06620
$299$	4.33048	0.250438
$300$	0	0
$301$	−10.4338	−0.601394
$302$	−4.59158	−0.264216
$303$	4.73598	0.272075
$304$	0.444469	0.0254920
$305$	0	0
$306$	−0.273891	−0.0156573
$307$	27.5838	1.57429	0.787146	−	0.616767i	$-0.211558\pi$
$307$	27.5838	1.57429	0.787146	+	0.616767i	$0.211558\pi$
$308$	5.92498	0.337607
$309$	20.5166	1.16715
$310$	0	0
$311$	−16.7282	−0.948571	−0.474286	−	0.880371i	$-0.657294\pi$
$311$	−16.7282	−0.948571	−0.474286	+	0.880371i	$0.657294\pi$
$312$	1.02830	0.0582158
$313$	−29.3793	−1.66062	−0.830309	−	0.557304i	$-0.811836\pi$
$313$	−29.3793	−1.66062	−0.830309	+	0.557304i	$0.811836\pi$
$314$	−13.7905	−0.778240
$315$	0	0
$316$	−3.37720	−0.189983
$317$	9.51868	0.534623	0.267311	−	0.963610i	$-0.413865\pi$
$317$	9.51868	0.534623	0.267311	+	0.963610i	$0.413865\pi$
$318$	−11.3227	−0.634947
$319$	33.0382	1.84978
$320$	0	0
$321$	−5.56328	−0.310512
$322$	6.95328	0.387491
$323$	−0.444469	−0.0247309
$324$	−8.10331	−0.450184
$325$	0	0
$326$	−12.5371	−0.694366
$327$	−4.82942	−0.267068
$328$	−7.70769	−0.425586
$329$	−7.95328	−0.438479
$330$	0	0
$331$	24.4466	1.34371	0.671853	−	0.740684i	$-0.265499\pi$
$331$	24.4466	1.34371	0.671853	+	0.740684i	$0.265499\pi$
$332$	−4.25547	−0.233549
$333$	−1.42605	−0.0781468
$334$	3.36945	0.184368
$335$	0	0
$336$	1.65109	0.0900745
$337$	−25.7467	−1.40251	−0.701255	−	0.712911i	$-0.747376\pi$
$337$	−25.7467	−1.40251	−0.701255	+	0.712911i	$0.747376\pi$
$338$	12.6121	0.686009
$339$	31.0120	1.68434
$340$	0	0
$341$	46.5569	2.52119
$342$	0.121736	0.00658272
$343$	−1.00000	−0.0539949
$344$	−10.4338	−0.562553
$345$	0	0
$346$	8.10331	0.435637
$347$	−11.8315	−0.635151	−0.317575	−	0.948233i	$-0.602869\pi$
$347$	−11.8315	−0.635151	−0.317575	+	0.948233i	$0.602869\pi$
$348$	9.20662	0.493527
$349$	−11.0107	−0.589388	−0.294694	−	0.955592i	$-0.595218\pi$
$349$	−11.0107	−0.589388	−0.294694	+	0.955592i	$0.595218\pi$
$350$	0	0
$351$	3.36653	0.179692
$352$	5.92498	0.315803
$353$	19.1960	1.02170	0.510849	−	0.859671i	$-0.329331\pi$
$353$	19.1960	1.02170	0.510849	+	0.859671i	$0.329331\pi$
$354$	3.19112	0.169606
$355$	0	0
$356$	5.76216	0.305394
$357$	−1.65109	−0.0873851
$358$	1.93273	0.102148
$359$	−29.9554	−1.58099	−0.790493	−	0.612471i	$-0.790176\pi$
$359$	−29.9554	−1.58099	−0.790493	+	0.612471i	$0.790176\pi$
$360$	0	0
$361$	−18.8024	−0.989602
$362$	4.49894	0.236459
$363$	−39.8003	−2.08898
$364$	−0.622797	−0.0326434
$365$	0	0
$366$	11.1861	0.584706
$367$	−9.52936	−0.497428	−0.248714	−	0.968577i	$-0.580008\pi$
$367$	−9.52936	−0.497428	−0.248714	+	0.968577i	$0.580008\pi$
$368$	6.95328	0.362465
$369$	−2.11106	−0.109898
$370$	0	0
$371$	6.85772	0.356035
$372$	12.9738	0.672662
$373$	−26.1415	−1.35355	−0.676777	−	0.736188i	$-0.736624\pi$
$373$	−26.1415	−1.35355	−0.676777	+	0.736188i	$0.736624\pi$
$374$	−5.92498	−0.306374
$375$	0	0
$376$	−7.95328	−0.410159
$377$	−3.47277	−0.178857
$378$	5.40550	0.278029
$379$	−32.2010	−1.65405	−0.827027	−	0.562162i	$-0.809970\pi$
$379$	−32.2010	−1.65405	−0.827027	+	0.562162i	$0.809970\pi$
$380$	0	0
$381$	−30.6836	−1.57197
$382$	19.9066	1.01851
$383$	−19.6503	−1.00408	−0.502042	−	0.864844i	$-0.667418\pi$
$383$	−19.6503	−1.00408	−0.502042	+	0.864844i	$0.667418\pi$
$384$	1.65109	0.0842570
$385$	0	0
$386$	9.88894	0.503334
$387$	−2.85772	−0.145266
$388$	−15.0926	−0.766213
$389$	−6.89376	−0.349528	−0.174764	−	0.984610i	$-0.555916\pi$
$389$	−6.89376	−0.349528	−0.174764	+	0.984610i	$0.555916\pi$
$390$	0	0
$391$	−6.95328	−0.351642
$392$	−1.00000	−0.0505076
$393$	14.7360	0.743332
$394$	−1.40550	−0.0708080
$395$	0	0
$396$	1.62280	0.0815486
$397$	24.3326	1.22122	0.610609	−	0.791932i	$-0.290925\pi$
$397$	24.3326	1.22122	0.610609	+	0.791932i	$0.290925\pi$
$398$	−21.6532	−1.08538
$399$	0.733860	0.0367389
$400$	0	0
$401$	−27.1415	−1.35538	−0.677690	−	0.735347i	$-0.737019\pi$
$401$	−27.1415	−1.35538	−0.677690	+	0.735347i	$0.737019\pi$
$402$	15.1882	0.757519
$403$	−4.89376	−0.243776
$404$	−2.86839	−0.142708
$405$	0	0
$406$	−5.57608	−0.276736
$407$	−30.8492	−1.52914
$408$	−1.65109	−0.0817413
$409$	−38.6425	−1.91075	−0.955375	−	0.295394i	$-0.904549\pi$
$409$	−38.6425	−1.91075	−0.955375	+	0.295394i	$0.904549\pi$
$410$	0	0
$411$	9.39000	0.463174
$412$	−12.4260	−0.612187
$413$	−1.93273	−0.0951036
$414$	1.90444	0.0935980
$415$	0	0
$416$	−0.622797	−0.0305351
$417$	9.19383	0.450224
$418$	2.63347	0.128807
$419$	−4.74453	−0.231786	−0.115893	−	0.993262i	$-0.536973\pi$
$419$	−4.74453	−0.231786	−0.115893	+	0.993262i	$0.536973\pi$
$420$	0	0
$421$	23.3969	1.14030	0.570149	−	0.821541i	$-0.306886\pi$
$421$	23.3969	1.14030	0.570149	+	0.821541i	$0.306886\pi$
$422$	−11.6249	−0.565892
$423$	−2.17833	−0.105914
$424$	6.85772	0.333040
$425$	0	0
$426$	10.9512	0.530585
$427$	−6.77495	−0.327863
$428$	3.36945	0.162869
$429$	6.09264	0.294155
$430$	0	0
$431$	4.65109	0.224035	0.112018	−	0.993706i	$-0.464269\pi$
$431$	4.65109	0.224035	0.112018	+	0.993706i	$0.464269\pi$
$432$	5.40550	0.260072
$433$	−5.26322	−0.252934	−0.126467	−	0.991971i	$-0.540364\pi$
$433$	−5.26322	−0.252934	−0.126467	+	0.991971i	$0.540364\pi$
$434$	−7.85772	−0.377183
$435$	0	0
$436$	2.92498	0.140081
$437$	3.09052	0.147839
$438$	−10.6999	−0.511263
$439$	12.5294	0.597994	0.298997	−	0.954254i	$-0.403348\pi$
$439$	12.5294	0.597994	0.298997	+	0.954254i	$0.403348\pi$
$440$	0	0
$441$	−0.273891	−0.0130424
$442$	0.622797	0.0296234
$443$	−21.1853	−1.00654	−0.503271	−	0.864128i	$-0.667870\pi$
$443$	−21.1853	−1.00654	−0.503271	+	0.864128i	$0.667870\pi$
$444$	−8.59662	−0.407978
$445$	0	0
$446$	−12.2349	−0.579340
$447$	30.3892	1.43736
$448$	−1.00000	−0.0472456
$449$	3.97383	0.187536	0.0937682	−	0.995594i	$-0.470109\pi$
$449$	3.97383	0.187536	0.0937682	+	0.995594i	$0.470109\pi$
$450$	0	0
$451$	−45.6679	−2.15042
$452$	−18.7827	−0.883464
$453$	−7.58112	−0.356192
$454$	−10.1989	−0.478657
$455$	0	0
$456$	0.733860	0.0343661
$457$	10.5860	0.495190	0.247595	−	0.968864i	$-0.420360\pi$
$457$	10.5860	0.495190	0.247595	+	0.968864i	$0.420360\pi$
$458$	−6.81100	−0.318257
$459$	−5.40550	−0.252307
$460$	0	0
$461$	−4.51868	−0.210456	−0.105228	−	0.994448i	$-0.533557\pi$
$461$	−4.51868	−0.210456	−0.105228	+	0.994448i	$0.533557\pi$
$462$	9.78270	0.455132
$463$	−31.3900	−1.45882	−0.729408	−	0.684078i	$-0.760205\pi$
$463$	−31.3900	−1.45882	−0.729408	+	0.684078i	$0.760205\pi$
$464$	−5.57608	−0.258863
$465$	0	0
$466$	−10.1239	−0.468979
$467$	30.9837	1.43375	0.716877	−	0.697199i	$-0.245571\pi$
$467$	30.9837	1.43375	0.716877	+	0.697199i	$0.245571\pi$
$468$	−0.170578	−0.00788498
$469$	−9.19887	−0.424765
$470$	0	0
$471$	−22.7693	−1.04916
$472$	−1.93273	−0.0889613
$473$	−61.8201	−2.84249
$474$	−5.57608	−0.256118
$475$	0	0
$476$	1.00000	0.0458349
$477$	1.87826	0.0859998
$478$	−1.56833	−0.0717336
$479$	−30.2186	−1.38072	−0.690362	−	0.723464i	$-0.742549\pi$
$479$	−30.2186	−1.38072	−0.690362	+	0.723464i	$0.742549\pi$
$480$	0	0
$481$	3.24267	0.147853
$482$	−13.5449	−0.616951
$483$	11.4805	0.522382
$484$	24.1054	1.09570
$485$	0	0
$486$	2.83717	0.128697
$487$	−28.9058	−1.30985	−0.654923	−	0.755696i	$-0.727299\pi$
$487$	−28.9058	−1.30985	−0.654923	+	0.755696i	$0.727299\pi$
$488$	−6.77495	−0.306688
$489$	−20.6999	−0.936083
$490$	0	0
$491$	−9.41405	−0.424850	−0.212425	−	0.977177i	$-0.568136\pi$
$491$	−9.41405	−0.424850	−0.212425	+	0.977177i	$0.568136\pi$
$492$	−12.7261	−0.573737
$493$	5.57608	0.251134
$494$	−0.276814	−0.0124544
$495$	0	0
$496$	−7.85772	−0.352822
$497$	−6.63267	−0.297516
$498$	−7.02617	−0.314850
$499$	−6.27389	−0.280858	−0.140429	−	0.990091i	$-0.544848\pi$
$499$	−6.27389	−0.280858	−0.140429	+	0.990091i	$0.544848\pi$
$500$	0	0
$501$	5.56328	0.248549
$502$	18.2739	0.815604
$503$	−11.7154	−0.522365	−0.261183	−	0.965289i	$-0.584113\pi$
$503$	−11.7154	−0.522365	−0.261183	+	0.965289i	$0.584113\pi$
$504$	−0.273891	−0.0122001
$505$	0	0
$506$	41.1981	1.83148
$507$	20.8238	0.924817
$508$	18.5838	0.824524
$509$	−29.9533	−1.32766	−0.663828	−	0.747885i	$-0.731069\pi$
$509$	−29.9533	−1.32766	−0.663828	+	0.747885i	$0.731069\pi$
$510$	0	0
$511$	6.48052	0.286681
$512$	−1.00000	−0.0441942
$513$	2.40258	0.106076
$514$	−23.8881	−1.05366
$515$	0	0
$516$	−17.2272	−0.758384
$517$	−47.1231	−2.07247
$518$	5.20662	0.228766
$519$	13.3793	0.587287
$520$	0	0
$521$	−29.4522	−1.29033	−0.645163	−	0.764045i	$-0.723210\pi$
$521$	−29.4522	−1.29033	−0.645163	+	0.764045i	$0.723210\pi$
$522$	−1.52723	−0.0668453
$523$	20.1140	0.879523	0.439762	−	0.898115i	$-0.355063\pi$
$523$	20.1140	0.879523	0.439762	+	0.898115i	$0.355063\pi$
$524$	−8.92498	−0.389890
$525$	0	0
$526$	−20.1004	−0.876419
$527$	7.85772	0.342288
$528$	9.78270	0.425737
$529$	25.3481	1.10209
$530$	0	0
$531$	−0.529358	−0.0229722
$532$	−0.444469	−0.0192702
$533$	4.80032	0.207925
$534$	9.51386	0.411705
$535$	0	0
$536$	−9.19887	−0.397331
$537$	3.19112	0.137707
$538$	−15.9533	−0.687795
$539$	−5.92498	−0.255207
$540$	0	0
$541$	−19.8988	−0.855517	−0.427758	−	0.903893i	$-0.640697\pi$
$541$	−19.8988	−0.855517	−0.427758	+	0.903893i	$0.640697\pi$
$542$	−14.1132	−0.606213
$543$	7.42817	0.318773
$544$	1.00000	0.0428746
$545$	0	0
$546$	−1.02830	−0.0440070
$547$	43.6679	1.86711	0.933553	−	0.358440i	$-0.116691\pi$
$547$	43.6679	1.86711	0.933553	+	0.358440i	$0.116691\pi$
$548$	−5.68714	−0.242943
$549$	−1.85560	−0.0791949
$550$	0	0
$551$	−2.47839	−0.105583
$552$	11.4805	0.488643
$553$	3.37720	0.143613
$554$	1.50881	0.0641033
$555$	0	0
$556$	−5.56833	−0.236150
$557$	6.13161	0.259805	0.129902	−	0.991527i	$-0.458534\pi$
$557$	6.13161	0.259805	0.129902	+	0.991527i	$0.458534\pi$
$558$	−2.15215	−0.0911080
$559$	6.49814	0.274842
$560$	0	0
$561$	−9.78270	−0.413026
$562$	20.8753	0.880573
$563$	8.27601	0.348792	0.174396	−	0.984676i	$-0.444203\pi$
$563$	8.27601	0.348792	0.174396	+	0.984676i	$0.444203\pi$
$564$	−13.1316	−0.552940
$565$	0	0
$566$	33.3793	1.40304
$567$	8.10331	0.340307
$568$	−6.63267	−0.278301
$569$	−28.8307	−1.20865	−0.604324	−	0.796739i	$-0.706557\pi$
$569$	−28.8307	−1.20865	−0.604324	+	0.796739i	$0.706557\pi$
$570$	0	0
$571$	25.9143	1.08448	0.542240	−	0.840224i	$-0.317576\pi$
$571$	25.9143	1.08448	0.542240	+	0.840224i	$0.317576\pi$
$572$	−3.69006	−0.154289
$573$	32.8676	1.37306
$574$	7.70769	0.321713
$575$	0	0
$576$	−0.273891	−0.0114121
$577$	21.2683	0.885409	0.442705	−	0.896667i	$-0.354019\pi$
$577$	21.2683	0.885409	0.442705	+	0.896667i	$0.354019\pi$
$578$	−1.00000	−0.0415945
$579$	16.3276	0.678550
$580$	0	0
$581$	4.25547	0.176547
$582$	−24.9194	−1.03294
$583$	40.6319	1.68280
$584$	6.48052	0.268166
$585$	0	0
$586$	6.73891	0.278382
$587$	−7.05872	−0.291344	−0.145672	−	0.989333i	$-0.546534\pi$
$587$	−7.05872	−0.291344	−0.145672	+	0.989333i	$0.546534\pi$
$588$	−1.65109	−0.0680899
$589$	−3.49251	−0.143906
$590$	0	0
$591$	−2.32061	−0.0954572
$592$	5.20662	0.213991
$593$	4.08277	0.167659	0.0838296	−	0.996480i	$-0.473285\pi$
$593$	4.08277	0.167659	0.0838296	+	0.996480i	$0.473285\pi$
$594$	32.0275	1.31410
$595$	0	0
$596$	−18.4055	−0.753919
$597$	−35.7515	−1.46321
$598$	−4.33048	−0.177087
$599$	30.1423	1.23158	0.615790	−	0.787910i	$-0.288837\pi$
$599$	30.1423	1.23158	0.615790	+	0.787910i	$0.288837\pi$
$600$	0	0
$601$	29.6658	1.21009	0.605046	−	0.796190i	$-0.293155\pi$
$601$	29.6658	1.21009	0.605046	+	0.796190i	$0.293155\pi$
$602$	10.4338	0.425250
$603$	−2.51948	−0.102601
$604$	4.59158	0.186829
$605$	0	0
$606$	−4.73598	−0.192386
$607$	−3.57608	−0.145149	−0.0725743	−	0.997363i	$-0.523121\pi$
$607$	−3.57608	−0.145149	−0.0725743	+	0.997363i	$0.523121\pi$
$608$	−0.444469	−0.0180256
$609$	−9.20662	−0.373071
$610$	0	0
$611$	4.95328	0.200388
$612$	0.273891	0.0110714
$613$	−26.9447	−1.08829	−0.544144	−	0.838992i	$-0.683145\pi$
$613$	−26.9447	−1.08829	−0.544144	+	0.838992i	$0.683145\pi$
$614$	−27.5838	−1.11319
$615$	0	0
$616$	−5.92498	−0.238724
$617$	−24.3772	−0.981389	−0.490695	−	0.871332i	$-0.663257\pi$
$617$	−24.3772	−0.981389	−0.490695	+	0.871332i	$0.663257\pi$
$618$	−20.5166	−0.825297
$619$	0.987204	0.0396791	0.0198395	−	0.999803i	$-0.493684\pi$
$619$	0.987204	0.0396791	0.0198395	+	0.999803i	$0.493684\pi$
$620$	0	0
$621$	37.5860	1.50827
$622$	16.7282	0.670741
$623$	−5.76216	−0.230856
$624$	−1.02830	−0.0411648
$625$	0	0
$626$	29.3793	1.17423
$627$	4.34811	0.173647
$628$	13.7905	0.550299
$629$	−5.20662	−0.207602
$630$	0	0
$631$	14.4883	0.576769	0.288384	−	0.957515i	$-0.406882\pi$
$631$	14.4883	0.576769	0.288384	+	0.957515i	$0.406882\pi$
$632$	3.37720	0.134338
$633$	−19.1938	−0.762886
$634$	−9.51868	−0.378035
$635$	0	0
$636$	11.3227	0.448976
$637$	0.622797	0.0246761
$638$	−33.0382	−1.30799
$639$	−1.81663	−0.0718646
$640$	0	0
$641$	−12.9914	−0.513131	−0.256566	−	0.966527i	$-0.582591\pi$
$641$	−12.9914	−0.513131	−0.256566	+	0.966527i	$0.582591\pi$
$642$	5.56328	0.219565
$643$	19.4181	0.765774	0.382887	−	0.923795i	$-0.374930\pi$
$643$	19.4181	0.765774	0.382887	+	0.923795i	$0.374930\pi$
$644$	−6.95328	−0.273998
$645$	0	0
$646$	0.444469	0.0174874
$647$	−8.93756	−0.351372	−0.175686	−	0.984446i	$-0.556214\pi$
$647$	−8.93756	−0.351372	−0.175686	+	0.984446i	$0.556214\pi$
$648$	8.10331	0.318328
$649$	−11.4514	−0.449507
$650$	0	0
$651$	−12.9738	−0.508484
$652$	12.5371	0.490991
$653$	−12.4437	−0.486958	−0.243479	−	0.969906i	$-0.578289\pi$
$653$	−12.4437	−0.486958	−0.243479	+	0.969906i	$0.578289\pi$
$654$	4.82942	0.188845
$655$	0	0
$656$	7.70769	0.300935
$657$	1.77495	0.0692475
$658$	7.95328	0.310051
$659$	15.9164	0.620016	0.310008	−	0.950734i	$-0.399668\pi$
$659$	15.9164	0.620016	0.310008	+	0.950734i	$0.399668\pi$
$660$	0	0
$661$	−8.05872	−0.313448	−0.156724	−	0.987642i	$-0.550093\pi$
$661$	−8.05872	−0.313448	−0.156724	+	0.987642i	$0.550093\pi$
$662$	−24.4466	−0.950144
$663$	1.02830	0.0399357
$664$	4.25547	0.165144
$665$	0	0
$666$	1.42605	0.0552581
$667$	−38.7720	−1.50126
$668$	−3.36945	−0.130368
$669$	−20.2010	−0.781016
$670$	0	0
$671$	−40.1415	−1.54964
$672$	−1.65109	−0.0636923
$673$	−20.3177	−0.783189	−0.391595	−	0.920138i	$-0.628076\pi$
$673$	−20.3177	−0.783189	−0.391595	+	0.920138i	$0.628076\pi$
$674$	25.7467	0.991724
$675$	0	0
$676$	−12.6121	−0.485082
$677$	8.05872	0.309722	0.154861	−	0.987936i	$-0.450507\pi$
$677$	8.05872	0.309722	0.154861	+	0.987936i	$0.450507\pi$
$678$	−31.0120	−1.19101
$679$	15.0926	0.579202
$680$	0	0
$681$	−16.8393	−0.645283
$682$	−46.5569	−1.78275
$683$	51.1457	1.95704	0.978518	−	0.206159i	$-0.0660965\pi$
$683$	51.1457	1.95704	0.978518	+	0.206159i	$0.0660965\pi$
$684$	−0.121736	−0.00465469
$685$	0	0
$686$	1.00000	0.0381802
$687$	−11.2456	−0.429046
$688$	10.4338	0.397785
$689$	−4.27097	−0.162711
$690$	0	0
$691$	34.9504	1.32957	0.664787	−	0.747033i	$-0.268522\pi$
$691$	34.9504	1.32957	0.664787	+	0.747033i	$0.268522\pi$
$692$	−8.10331	−0.308042
$693$	−1.62280	−0.0616450
$694$	11.8315	0.449119
$695$	0	0
$696$	−9.20662	−0.348976
$697$	−7.70769	−0.291949
$698$	11.0107	0.416760
$699$	−16.7154	−0.632236
$700$	0	0
$701$	−6.81180	−0.257278	−0.128639	−	0.991691i	$-0.541061\pi$
$701$	−6.81180	−0.257278	−0.128639	+	0.991691i	$0.541061\pi$
$702$	−3.36653	−0.127061
$703$	2.31418	0.0872810
$704$	−5.92498	−0.223306
$705$	0	0
$706$	−19.1960	−0.722449
$707$	2.86839	0.107877
$708$	−3.19112	−0.119930
$709$	−20.6920	−0.777103	−0.388552	−	0.921427i	$-0.627024\pi$
$709$	−20.6920	−0.777103	−0.388552	+	0.921427i	$0.627024\pi$
$710$	0	0
$711$	0.924984	0.0346896
$712$	−5.76216	−0.215946
$713$	−54.6369	−2.04617
$714$	1.65109	0.0617906
$715$	0	0
$716$	−1.93273	−0.0722297
$717$	−2.58945	−0.0967050
$718$	29.9554	1.11793
$719$	−19.8470	−0.740170	−0.370085	−	0.928998i	$-0.620671\pi$
$719$	−19.8470	−0.740170	−0.370085	+	0.928998i	$0.620671\pi$
$720$	0	0
$721$	12.4260	0.462770
$722$	18.8024	0.699755
$723$	−22.3638	−0.831720
$724$	−4.49894	−0.167202
$725$	0	0
$726$	39.8003	1.47713
$727$	−45.3171	−1.68072	−0.840359	−	0.542030i	$-0.817656\pi$
$727$	−45.3171	−1.68072	−0.840359	+	0.542030i	$0.817656\pi$
$728$	0.622797	0.0230824
$729$	28.9944	1.07387
$730$	0	0
$731$	−10.4338	−0.385908
$732$	−11.1861	−0.413449
$733$	41.2400	1.52323	0.761616	−	0.648028i	$-0.224406\pi$
$733$	41.2400	1.52323	0.761616	+	0.648028i	$0.224406\pi$
$734$	9.52936	0.351735
$735$	0	0
$736$	−6.95328	−0.256301
$737$	−54.5032	−2.00765
$738$	2.11106	0.0777093
$739$	9.01067	0.331463	0.165731	−	0.986171i	$-0.447001\pi$
$739$	9.01067	0.331463	0.165731	+	0.986171i	$0.447001\pi$
$740$	0	0
$741$	−0.457046	−0.0167900
$742$	−6.85772	−0.251755
$743$	−14.4960	−0.531807	−0.265904	−	0.964000i	$-0.585670\pi$
$743$	−14.4960	−0.531807	−0.265904	+	0.964000i	$0.585670\pi$
$744$	−12.9738	−0.475644
$745$	0	0
$746$	26.1415	0.957108
$747$	1.16553	0.0426446
$748$	5.92498	0.216639
$749$	−3.36945	−0.123117
$750$	0	0
$751$	−47.3396	−1.72744	−0.863722	−	0.503968i	$-0.831873\pi$
$751$	−47.3396	−1.72744	−0.863722	+	0.503968i	$0.831873\pi$
$752$	7.95328	0.290026
$753$	30.1719	1.09953
$754$	3.47277	0.126471
$755$	0	0
$756$	−5.40550	−0.196596
$757$	9.52161	0.346069	0.173034	−	0.984916i	$-0.444643\pi$
$757$	9.52161	0.346069	0.173034	+	0.984916i	$0.444643\pi$
$758$	32.2010	1.16959
$759$	68.0219	2.46904
$760$	0	0
$761$	28.7693	1.04289	0.521444	−	0.853286i	$-0.325394\pi$
$761$	28.7693	1.04289	0.521444	+	0.853286i	$0.325394\pi$
$762$	30.6836	1.11155
$763$	−2.92498	−0.105892
$764$	−19.9066	−0.720194
$765$	0	0
$766$	19.6503	0.709994
$767$	1.20370	0.0434631
$768$	−1.65109	−0.0595787
$769$	19.1423	0.690288	0.345144	−	0.938550i	$-0.387830\pi$
$769$	19.1423	0.690288	0.345144	+	0.938550i	$0.387830\pi$
$770$	0	0
$771$	−39.4415	−1.42045
$772$	−9.88894	−0.355911
$773$	−10.8081	−0.388739	−0.194370	−	0.980928i	$-0.562266\pi$
$773$	−10.8081	−0.388739	−0.194370	+	0.980928i	$0.562266\pi$
$774$	2.85772	0.102719
$775$	0	0
$776$	15.0926	0.541794
$777$	8.59662	0.308402
$778$	6.89376	0.247153
$779$	3.42583	0.122743
$780$	0	0
$781$	−39.2985	−1.40621
$782$	6.95328	0.248649
$783$	−30.1415	−1.07717
$784$	1.00000	0.0357143
$785$	0	0
$786$	−14.7360	−0.525615
$787$	−37.0616	−1.32110	−0.660552	−	0.750780i	$-0.729678\pi$
$787$	−37.0616	−1.32110	−0.660552	+	0.750780i	$0.729678\pi$
$788$	1.40550	0.0500688
$789$	−33.1876	−1.18151
$790$	0	0
$791$	18.7827	0.667836
$792$	−1.62280	−0.0576636
$793$	4.21942	0.149836
$794$	−24.3326	−0.863532
$795$	0	0
$796$	21.6532	0.767478
$797$	−0.669517	−0.0237155	−0.0118578	−	0.999930i	$-0.503775\pi$
$797$	−0.669517	−0.0237155	−0.0118578	+	0.999930i	$0.503775\pi$
$798$	−0.733860	−0.0259783
$799$	−7.95328	−0.281367
$800$	0	0
$801$	−1.57820	−0.0557630
$802$	27.1415	0.958399
$803$	38.3969	1.35500
$804$	−15.1882	−0.535647
$805$	0	0
$806$	4.89376	0.172375
$807$	−26.3404	−0.927224
$808$	2.86839	0.100910
$809$	31.0000	1.08990	0.544951	−	0.838468i	$-0.316548\pi$
$809$	31.0000	1.08990	0.544951	+	0.838468i	$0.316548\pi$
$810$	0	0
$811$	31.4883	1.10570	0.552851	−	0.833280i	$-0.313540\pi$
$811$	31.4883	1.10570	0.552851	+	0.833280i	$0.313540\pi$
$812$	5.57608	0.195682
$813$	−23.3022	−0.817243
$814$	30.8492	1.08126
$815$	0	0
$816$	1.65109	0.0577998
$817$	4.63750	0.162245
$818$	38.6425	1.35110
$819$	0.170578	0.00596049
$820$	0	0
$821$	−46.7976	−1.63325	−0.816624	−	0.577170i	$-0.804157\pi$
$821$	−46.7976	−1.63325	−0.816624	+	0.577170i	$0.804157\pi$
$822$	−9.39000	−0.327514
$823$	16.4026	0.571758	0.285879	−	0.958266i	$-0.407714\pi$
$823$	16.4026	0.571758	0.285879	+	0.958266i	$0.407714\pi$
$824$	12.4260	0.432882
$825$	0	0
$826$	1.93273	0.0672484
$827$	8.91723	0.310083	0.155041	−	0.987908i	$-0.450449\pi$
$827$	8.91723	0.310083	0.155041	+	0.987908i	$0.450449\pi$
$828$	−1.90444	−0.0661838
$829$	−55.0870	−1.91325	−0.956625	−	0.291321i	$-0.905905\pi$
$829$	−55.0870	−1.91325	−0.956625	+	0.291321i	$0.905905\pi$
$830$	0	0
$831$	2.49119	0.0864184
$832$	0.622797	0.0215916
$833$	−1.00000	−0.0346479
$834$	−9.19383	−0.318356
$835$	0	0
$836$	−2.63347	−0.0910805
$837$	−42.4749	−1.46815
$838$	4.74453	0.163897
$839$	−31.4124	−1.08448	−0.542239	−	0.840224i	$-0.682423\pi$
$839$	−31.4124	−1.08448	−0.542239	+	0.840224i	$0.682423\pi$
$840$	0	0
$841$	2.09264	0.0721600
$842$	−23.3969	−0.806312
$843$	34.4671	1.18711
$844$	11.6249	0.400146
$845$	0	0
$846$	2.17833	0.0748925
$847$	−24.1054	−0.828273
$848$	−6.85772	−0.235495
$849$	55.1124	1.89145
$850$	0	0
$851$	36.2031	1.24103
$852$	−10.9512	−0.375180
$853$	25.6377	0.877819	0.438909	−	0.898531i	$-0.355365\pi$
$853$	25.6377	0.877819	0.438909	+	0.898531i	$0.355365\pi$
$854$	6.77495	0.231834
$855$	0	0
$856$	−3.36945	−0.115166
$857$	53.7840	1.83723	0.918614	−	0.395157i	$-0.129310\pi$
$857$	53.7840	1.83723	0.918614	+	0.395157i	$0.129310\pi$
$858$	−6.09264	−0.207999
$859$	39.0558	1.33257	0.666283	−	0.745699i	$-0.267884\pi$
$859$	39.0558	1.33257	0.666283	+	0.745699i	$0.267884\pi$
$860$	0	0
$861$	12.7261	0.433705
$862$	−4.65109	−0.158417
$863$	7.58383	0.258156	0.129078	−	0.991634i	$-0.458798\pi$
$863$	7.58383	0.258156	0.129078	+	0.991634i	$0.458798\pi$
$864$	−5.40550	−0.183899
$865$	0	0
$866$	5.26322	0.178851
$867$	−1.65109	−0.0560741
$868$	7.85772	0.266708
$869$	20.0099	0.678788
$870$	0	0
$871$	5.72903	0.194121
$872$	−2.92498	−0.0990525
$873$	4.13373	0.139906
$874$	−3.09052	−0.104538
$875$	0	0
$876$	10.6999	0.361517
$877$	−32.7672	−1.10647	−0.553235	−	0.833025i	$-0.686607\pi$
$877$	−32.7672	−1.10647	−0.553235	+	0.833025i	$0.686607\pi$
$878$	−12.5294	−0.422845
$879$	11.1266	0.375290
$880$	0	0
$881$	17.2320	0.580561	0.290280	−	0.956942i	$-0.406251\pi$
$881$	17.2320	0.580561	0.290280	+	0.956942i	$0.406251\pi$
$882$	0.273891	0.00922237
$883$	−57.2207	−1.92563	−0.962816	−	0.270159i	$-0.912924\pi$
$883$	−57.2207	−1.92563	−0.962816	+	0.270159i	$0.912924\pi$
$884$	−0.622797	−0.0209469
$885$	0	0
$886$	21.1853	0.711733
$887$	−49.5200	−1.66272	−0.831360	−	0.555735i	$-0.812437\pi$
$887$	−49.5200	−1.66272	−0.831360	+	0.555735i	$0.812437\pi$
$888$	8.59662	0.288484
$889$	−18.5838	−0.623282
$890$	0	0
$891$	48.0120	1.60846
$892$	12.2349	0.409655
$893$	3.53499	0.118294
$894$	−30.3892	−1.01637
$895$	0	0
$896$	1.00000	0.0334077
$897$	−7.15003	−0.238733
$898$	−3.97383	−0.132608
$899$	43.8152	1.46132
$900$	0	0
$901$	6.85772	0.228464
$902$	45.6679	1.52058
$903$	17.2272	0.573284
$904$	18.7827	0.624703
$905$	0	0
$906$	7.58112	0.251866
$907$	−20.6503	−0.685682	−0.342841	−	0.939393i	$-0.611389\pi$
$907$	−20.6503	−0.685682	−0.342841	+	0.939393i	$0.611389\pi$
$908$	10.1989	0.338462
$909$	0.785625	0.0260575
$910$	0	0
$911$	−7.07019	−0.234246	−0.117123	−	0.993117i	$-0.537367\pi$
$911$	−7.07019	−0.234246	−0.117123	+	0.993117i	$0.537367\pi$
$912$	−0.733860	−0.0243005
$913$	25.2136	0.834448
$914$	−10.5860	−0.350152
$915$	0	0
$916$	6.81100	0.225042
$917$	8.92498	0.294729
$918$	5.40550	0.178408
$919$	18.0459	0.595280	0.297640	−	0.954678i	$-0.403801\pi$
$919$	18.0459	0.595280	0.297640	+	0.954678i	$0.403801\pi$
$920$	0	0
$921$	−45.5435	−1.50071
$922$	4.51868	0.148815
$923$	4.13081	0.135967
$924$	−9.78270	−0.321827
$925$	0	0
$926$	31.3900	1.03154
$927$	3.40338	0.111782
$928$	5.57608	0.183044
$929$	50.7771	1.66594	0.832971	−	0.553317i	$-0.186638\pi$
$929$	50.7771	1.66594	0.832971	+	0.553317i	$0.186638\pi$
$930$	0	0
$931$	0.444469	0.0145669
$932$	10.1239	0.331618
$933$	27.6199	0.904234
$934$	−30.9837	−1.01382
$935$	0	0
$936$	0.170578	0.00557552
$937$	38.4749	1.25692	0.628460	−	0.777842i	$-0.283686\pi$
$937$	38.4749	1.25692	0.628460	+	0.777842i	$0.283686\pi$
$938$	9.19887	0.300354
$939$	48.5080	1.58300
$940$	0	0
$941$	−56.5724	−1.84421	−0.922103	−	0.386944i	$-0.873530\pi$
$941$	−56.5724	−1.84421	−0.922103	+	0.386944i	$0.873530\pi$
$942$	22.7693	0.741865
$943$	53.5937	1.74525
$944$	1.93273	0.0629051
$945$	0	0
$946$	61.8201	2.00994
$947$	−24.9661	−0.811288	−0.405644	−	0.914031i	$-0.632953\pi$
$947$	−24.9661	−0.811288	−0.405644	+	0.914031i	$0.632953\pi$
$948$	5.57608	0.181103
$949$	−4.03605	−0.131016
$950$	0	0
$951$	−15.7162	−0.509634
$952$	−1.00000	−0.0324102
$953$	39.3580	1.27493	0.637465	−	0.770479i	$-0.279983\pi$
$953$	39.3580	1.27493	0.637465	+	0.770479i	$0.279983\pi$
$954$	−1.87826	−0.0608110
$955$	0	0
$956$	1.56833	0.0507233
$957$	−54.5491	−1.76332
$958$	30.2186	0.976319
$959$	5.68714	0.183647
$960$	0	0
$961$	30.7437	0.991733
$962$	−3.24267	−0.104548
$963$	−0.922861	−0.0297388
$964$	13.5449	0.436250
$965$	0	0
$966$	−11.4805	−0.369380
$967$	−48.0040	−1.54371	−0.771853	−	0.635801i	$-0.780670\pi$
$967$	−48.0040	−1.54371	−0.771853	+	0.635801i	$0.780670\pi$
$968$	−24.1054	−0.774778
$969$	0.733860	0.0235750
$970$	0	0
$971$	54.7792	1.75795	0.878974	−	0.476870i	$-0.158229\pi$
$971$	54.7792	1.75795	0.878974	+	0.476870i	$0.158229\pi$
$972$	−2.83717	−0.0910023
$973$	5.56833	0.178512
$974$	28.9058	0.926200
$975$	0	0
$976$	6.77495	0.216861
$977$	−52.1231	−1.66756	−0.833782	−	0.552094i	$-0.813829\pi$
$977$	−52.1231	−1.66756	−0.833782	+	0.552094i	$0.813829\pi$
$978$	20.6999	0.661911
$979$	−34.1407	−1.09114
$980$	0	0
$981$	−0.801125	−0.0255780
$982$	9.41405	0.300414
$983$	8.56540	0.273194	0.136597	−	0.990627i	$-0.456383\pi$
$983$	8.56540	0.273194	0.136597	+	0.990627i	$0.456383\pi$
$984$	12.7261	0.405694
$985$	0	0
$986$	−5.57608	−0.177578
$987$	13.1316	0.417984
$988$	0.276814	0.00880662
$989$	72.5491	2.30693
$990$	0	0
$991$	−51.7819	−1.64491	−0.822453	−	0.568833i	$-0.807395\pi$
$991$	−51.7819	−1.64491	−0.822453	+	0.568833i	$0.807395\pi$
$992$	7.85772	0.249483
$993$	−40.3636	−1.28090
$994$	6.63267	0.210376
$995$	0	0
$996$	7.02617	0.222633
$997$	−10.1324	−0.320897	−0.160448	−	0.987044i	$-0.551294\pi$
$997$	−10.1324	−0.320897	−0.160448	+	0.987044i	$0.551294\pi$
$998$	6.27389	0.198597
$999$	28.1444	0.890450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5950.2.a.be.1.1	✓	3
5.4	even	2		5950.2.a.bg.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5950.2.a.be.1.1	✓	3	1.1	even	1	trivial
5950.2.a.bg.1.3	yes	3	5.4	even	2

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:	\( N \)	\(=\)	\( 5950 = 2 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5950.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.65109 q^{3} +1.00000 q^{4} +1.65109 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.273891 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.65109 q^{3} +1.00000 q^{4} +1.65109 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.273891 q^{9} -5.92498 q^{11} -1.65109 q^{12} +0.622797 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +0.273891 q^{18} +0.444469 q^{19} +1.65109 q^{21} +5.92498 q^{22} +6.95328 q^{23} +1.65109 q^{24} -0.622797 q^{26} +5.40550 q^{27} -1.00000 q^{28} -5.57608 q^{29} -7.85772 q^{31} -1.00000 q^{32} +9.78270 q^{33} +1.00000 q^{34} -0.273891 q^{36} +5.20662 q^{37} -0.444469 q^{38} -1.02830 q^{39} +7.70769 q^{41} -1.65109 q^{42} +10.4338 q^{43} -5.92498 q^{44} -6.95328 q^{46} +7.95328 q^{47} -1.65109 q^{48} +1.00000 q^{49} +1.65109 q^{51} +0.622797 q^{52} -6.85772 q^{53} -5.40550 q^{54} +1.00000 q^{56} -0.733860 q^{57} +5.57608 q^{58} +1.93273 q^{59} +6.77495 q^{61} +7.85772 q^{62} +0.273891 q^{63} +1.00000 q^{64} -9.78270 q^{66} +9.19887 q^{67} -1.00000 q^{68} -11.4805 q^{69} +6.63267 q^{71} +0.273891 q^{72} -6.48052 q^{73} -5.20662 q^{74} +0.444469 q^{76} +5.92498 q^{77} +1.02830 q^{78} -3.37720 q^{79} -8.10331 q^{81} -7.70769 q^{82} -4.25547 q^{83} +1.65109 q^{84} -10.4338 q^{86} +9.20662 q^{87} +5.92498 q^{88} +5.76216 q^{89} -0.622797 q^{91} +6.95328 q^{92} +12.9738 q^{93} -7.95328 q^{94} +1.65109 q^{96} -15.0926 q^{97} -1.00000 q^{98} +1.62280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 3 * q^8 + q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 3 q^{8} + q^{9} - 9 q^{11} + 2 q^{12} + 7 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - q^{18} + q^{19} - 2 q^{21} + 9 q^{22} - 2 q^{24} - 7 q^{26} - q^{27} - 3 q^{28} - q^{29} - 10 q^{31} - 3 q^{32} + 7 q^{33} + 3 q^{34} + q^{36} + 9 q^{37} - q^{38} + 9 q^{39} - 8 q^{41} + 2 q^{42} + 2 q^{43} - 9 q^{44} + 3 q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{51} + 7 q^{52} - 7 q^{53} + q^{54} + 3 q^{56} - 8 q^{57} + q^{58} + q^{59} - 6 q^{61} + 10 q^{62} - q^{63} + 3 q^{64} - 7 q^{66} + 17 q^{67} - 3 q^{68} - 26 q^{69} - 20 q^{71} - q^{72} - 11 q^{73} - 9 q^{74} + q^{76} + 9 q^{77} - 9 q^{78} - 5 q^{79} - 21 q^{81} + 8 q^{82} + 22 q^{83} - 2 q^{84} - 2 q^{86} + 21 q^{87} + 9 q^{88} + 11 q^{89} - 7 q^{91} + 2 q^{93} - 3 q^{94} - 2 q^{96} - 13 q^{97} - 3 q^{98} + 10 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 3 * q^8 + q^9 - 9 * q^11 + 2 * q^12 + 7 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - q^18 + q^19 - 2 * q^21 + 9 * q^22 - 2 * q^24 - 7 * q^26 - q^27 - 3 * q^28 - q^29 - 10 * q^31 - 3 * q^32 + 7 * q^33 + 3 * q^34 + q^36 + 9 * q^37 - q^38 + 9 * q^39 - 8 * q^41 + 2 * q^42 + 2 * q^43 - 9 * q^44 + 3 * q^47 + 2 * q^48 + 3 * q^49 - 2 * q^51 + 7 * q^52 - 7 * q^53 + q^54 + 3 * q^56 - 8 * q^57 + q^58 + q^59 - 6 * q^61 + 10 * q^62 - q^63 + 3 * q^64 - 7 * q^66 + 17 * q^67 - 3 * q^68 - 26 * q^69 - 20 * q^71 - q^72 - 11 * q^73 - 9 * q^74 + q^76 + 9 * q^77 - 9 * q^78 - 5 * q^79 - 21 * q^81 + 8 * q^82 + 22 * q^83 - 2 * q^84 - 2 * q^86 + 21 * q^87 + 9 * q^88 + 11 * q^89 - 7 * q^91 + 2 * q^93 - 3 * q^94 - 2 * q^96 - 13 * q^97 - 3 * q^98 + 10 * q^99

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