LMFDB - Embedded newform 585.2.a.n.1.3

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	585.1

$q$-expansion

$f(q)$	$=$	$q+2.48929 q^{2} +4.19656 q^{4} +1.00000 q^{5} -1.19656 q^{7} +5.46787 q^{8} +O(q^{10})$	\(q+2.48929 q^{2} +4.19656 q^{4} +1.00000 q^{5} -1.19656 q^{7} +5.46787 q^{8} +2.48929 q^{10} +1.19656 q^{11} +1.00000 q^{13} -2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} +6.97858 q^{19} +4.19656 q^{20} +2.97858 q^{22} -4.17513 q^{23} +1.00000 q^{25} +2.48929 q^{26} -5.02142 q^{28} -6.00000 q^{29} -2.97858 q^{31} +2.05333 q^{32} -15.3717 q^{34} -1.19656 q^{35} +7.78202 q^{37} +17.3717 q^{38} +5.46787 q^{40} +6.17513 q^{41} -9.95715 q^{43} +5.02142 q^{44} -10.3931 q^{46} +1.02142 q^{47} -5.56825 q^{49} +2.48929 q^{50} +4.19656 q^{52} -10.1751 q^{53} +1.19656 q^{55} -6.54262 q^{56} -14.9357 q^{58} -5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} -5.32464 q^{64} +1.00000 q^{65} +9.37169 q^{67} -25.9143 q^{68} -2.97858 q^{70} +5.19656 q^{71} -11.9572 q^{73} +19.3717 q^{74} +29.2860 q^{76} -1.43175 q^{77} -1.78202 q^{79} +5.21798 q^{80} +15.3717 q^{82} +5.37169 q^{83} -6.17513 q^{85} -24.7862 q^{86} +6.54262 q^{88} -10.1751 q^{89} -1.19656 q^{91} -17.5212 q^{92} +2.54262 q^{94} +6.97858 q^{95} -1.82487 q^{97} -13.8610 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 8 q^{4} + 3 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) $ 3 * q + 8 * q^4 + 3 * q^5 + q^7 - 6 * q^8	$ 3 q + 8 q^{4} + 3 q^{5} + q^{7} - 6 q^{8} - q^{11} + 3 q^{13} + 6 q^{14} + 26 q^{16} + q^{17} + 6 q^{19} + 8 q^{20} - 6 q^{22} + 7 q^{23} + 3 q^{25} - 30 q^{28} - 18 q^{29} + 6 q^{31} - 22 q^{32} - 22 q^{34} + q^{35} + 13 q^{37} + 28 q^{38} - 6 q^{40} - q^{41} + 30 q^{44} - 22 q^{46} + 18 q^{47} + 12 q^{49} + 8 q^{52} - 11 q^{53} - q^{55} + 16 q^{56} + 8 q^{59} + 9 q^{61} - 28 q^{62} + 30 q^{64} + 3 q^{65} + 4 q^{67} - 18 q^{68} + 6 q^{70} + 11 q^{71} - 6 q^{73} + 34 q^{74} + 4 q^{76} - 33 q^{77} + 5 q^{79} + 26 q^{80} + 22 q^{82} - 8 q^{83} + q^{85} - 56 q^{86} - 16 q^{88} - 11 q^{89} + q^{91} - 2 q^{92} - 28 q^{94} + 6 q^{95} - 25 q^{97} - 10 q^{98}+O(q^{100}) $ 3 * q + 8 * q^4 + 3 * q^5 + q^7 - 6 * q^8 - q^11 + 3 * q^13 + 6 * q^14 + 26 * q^16 + q^17 + 6 * q^19 + 8 * q^20 - 6 * q^22 + 7 * q^23 + 3 * q^25 - 30 * q^28 - 18 * q^29 + 6 * q^31 - 22 * q^32 - 22 * q^34 + q^35 + 13 * q^37 + 28 * q^38 - 6 * q^40 - q^41 + 30 * q^44 - 22 * q^46 + 18 * q^47 + 12 * q^49 + 8 * q^52 - 11 * q^53 - q^55 + 16 * q^56 + 8 * q^59 + 9 * q^61 - 28 * q^62 + 30 * q^64 + 3 * q^65 + 4 * q^67 - 18 * q^68 + 6 * q^70 + 11 * q^71 - 6 * q^73 + 34 * q^74 + 4 * q^76 - 33 * q^77 + 5 * q^79 + 26 * q^80 + 22 * q^82 - 8 * q^83 + q^85 - 56 * q^86 - 16 * q^88 - 11 * q^89 + q^91 - 2 * q^92 - 28 * q^94 + 6 * q^95 - 25 * q^97 - 10 * q^98

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 $

$2$	2.48929	1.76019	0.880096	−	0.474795i	$-0.157478\pi$
$2$	2.48929	1.76019	0.880096	+	0.474795i	$0.157478\pi$
$3$	0	0
$3$	0	0
$4$	4.19656	2.09828
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.19656	−0.452256	−0.226128	−	0.974098i	$-0.572607\pi$
$7$	−1.19656	−0.452256	−0.226128	+	0.974098i	$0.572607\pi$
$8$	5.46787	1.93318
$9$	0	0
$10$	2.48929	0.787182
$11$	1.19656	0.360776	0.180388	−	0.983596i	$-0.442265\pi$
$11$	1.19656	0.360776	0.180388	+	0.983596i	$0.442265\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.97858	−0.796058
$15$	0	0
$16$	5.21798	1.30450
$17$	−6.17513	−1.49769	−0.748845	−	0.662745i	$-0.769391\pi$
$17$	−6.17513	−1.49769	−0.748845	+	0.662745i	$0.769391\pi$
$18$	0	0
$19$	6.97858	1.60100	0.800498	−	0.599336i	$-0.204569\pi$
$19$	6.97858	1.60100	0.800498	+	0.599336i	$0.204569\pi$
$20$	4.19656	0.938379
$21$	0	0
$22$	2.97858	0.635035
$23$	−4.17513	−0.870576	−0.435288	−	0.900291i	$-0.643353\pi$
$23$	−4.17513	−0.870576	−0.435288	+	0.900291i	$0.643353\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.48929	0.488190
$27$	0	0
$28$	−5.02142	−0.948960
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−2.97858	−0.534968	−0.267484	−	0.963562i	$-0.586192\pi$
$31$	−2.97858	−0.534968	−0.267484	+	0.963562i	$0.586192\pi$
$32$	2.05333	0.362980
$33$	0	0
$34$	−15.3717	−2.63622
$35$	−1.19656	−0.202255
$36$	0	0
$37$	7.78202	1.27936	0.639678	−	0.768643i	$-0.279068\pi$
$37$	7.78202	1.27936	0.639678	+	0.768643i	$0.279068\pi$
$38$	17.3717	2.81806
$39$	0	0
$40$	5.46787	0.864545
$41$	6.17513	0.964394	0.482197	−	0.876063i	$-0.339839\pi$
$41$	6.17513	0.964394	0.482197	+	0.876063i	$0.339839\pi$
$42$	0	0
$43$	−9.95715	−1.51845	−0.759226	−	0.650827i	$-0.774422\pi$
$43$	−9.95715	−1.51845	−0.759226	+	0.650827i	$0.774422\pi$
$44$	5.02142	0.757008
$45$	0	0
$46$	−10.3931	−1.53238
$47$	1.02142	0.148990	0.0744949	−	0.997221i	$-0.476266\pi$
$47$	1.02142	0.148990	0.0744949	+	0.997221i	$0.476266\pi$
$48$	0	0
$49$	−5.56825	−0.795464
$50$	2.48929	0.352039
$51$	0	0
$52$	4.19656	0.581958
$53$	−10.1751	−1.39766	−0.698831	−	0.715287i	$-0.746296\pi$
$53$	−10.1751	−1.39766	−0.698831	+	0.715287i	$0.746296\pi$
$54$	0	0
$55$	1.19656	0.161344
$56$	−6.54262	−0.874294
$57$	0	0
$58$	−14.9357	−1.96116
$59$	−5.37169	−0.699335	−0.349667	−	0.936874i	$-0.613705\pi$
$59$	−5.37169	−0.699335	−0.349667	+	0.936874i	$0.613705\pi$
$60$	0	0
$61$	12.5682	1.60920	0.804600	−	0.593818i	$-0.202380\pi$
$61$	12.5682	1.60920	0.804600	+	0.593818i	$0.202380\pi$
$62$	−7.41454	−0.941647
$63$	0	0
$64$	−5.32464	−0.665579
$65$	1.00000	0.124035
$66$	0	0
$67$	9.37169	1.14493	0.572467	−	0.819928i	$-0.305986\pi$
$67$	9.37169	1.14493	0.572467	+	0.819928i	$0.305986\pi$
$68$	−25.9143	−3.14257
$69$	0	0
$70$	−2.97858	−0.356008
$71$	5.19656	0.616718	0.308359	−	0.951270i	$-0.400220\pi$
$71$	5.19656	0.616718	0.308359	+	0.951270i	$0.400220\pi$
$72$	0	0
$73$	−11.9572	−1.39948	−0.699740	−	0.714398i	$-0.746701\pi$
$73$	−11.9572	−1.39948	−0.699740	+	0.714398i	$0.746701\pi$
$74$	19.3717	2.25191
$75$	0	0
$76$	29.2860	3.35933
$77$	−1.43175	−0.163163
$78$	0	0
$79$	−1.78202	−0.200493	−0.100246	−	0.994963i	$-0.531963\pi$
$79$	−1.78202	−0.200493	−0.100246	+	0.994963i	$0.531963\pi$
$80$	5.21798	0.583388
$81$	0	0
$82$	15.3717	1.69752
$83$	5.37169	0.589620	0.294810	−	0.955556i	$-0.404744\pi$
$83$	5.37169	0.589620	0.294810	+	0.955556i	$0.404744\pi$
$84$	0	0
$85$	−6.17513	−0.669787
$86$	−24.7862	−2.67277
$87$	0	0
$88$	6.54262	0.697445
$89$	−10.1751	−1.07856	−0.539281	−	0.842126i	$-0.681304\pi$
$89$	−10.1751	−1.07856	−0.539281	+	0.842126i	$0.681304\pi$
$90$	0	0
$91$	−1.19656	−0.125433
$92$	−17.5212	−1.82671
$93$	0	0
$94$	2.54262	0.262251
$95$	6.97858	0.715987
$96$	0	0
$97$	−1.82487	−0.185287	−0.0926435	−	0.995699i	$-0.529532\pi$
$97$	−1.82487	−0.185287	−0.0926435	+	0.995699i	$0.529532\pi$
$98$	−13.8610	−1.40017
$99$	0	0
$100$	4.19656	0.419656
$101$	10.3503	1.02989	0.514945	−	0.857223i	$-0.327812\pi$
$101$	10.3503	1.02989	0.514945	+	0.857223i	$0.327812\pi$
$102$	0	0
$103$	18.7434	1.84684	0.923420	−	0.383790i	$-0.125381\pi$
$103$	18.7434	1.84684	0.923420	+	0.383790i	$0.125381\pi$
$104$	5.46787	0.536168
$105$	0	0
$106$	−25.3288	−2.46016
$107$	18.5682	1.79506	0.897530	−	0.440953i	$-0.145359\pi$
$107$	18.5682	1.79506	0.897530	+	0.440953i	$0.145359\pi$
$108$	0	0
$109$	8.39312	0.803915	0.401957	−	0.915658i	$-0.368330\pi$
$109$	8.39312	0.803915	0.401957	+	0.915658i	$0.368330\pi$
$110$	2.97858	0.283996
$111$	0	0
$112$	−6.24361	−0.589966
$113$	−7.95715	−0.748546	−0.374273	−	0.927319i	$-0.622108\pi$
$113$	−7.95715	−0.748546	−0.374273	+	0.927319i	$0.622108\pi$
$114$	0	0
$115$	−4.17513	−0.389333
$116$	−25.1793	−2.33784
$117$	0	0
$118$	−13.3717	−1.23096
$119$	7.38890	0.677340
$120$	0	0
$121$	−9.56825	−0.869841
$122$	31.2860	2.83250
$123$	0	0
$124$	−12.4998	−1.12251
$125$	1.00000	0.0894427
$126$	0	0
$127$	−10.3931	−0.922240	−0.461120	−	0.887338i	$-0.652552\pi$
$127$	−10.3931	−0.922240	−0.461120	+	0.887338i	$0.652552\pi$
$128$	−17.3612	−1.53453
$129$	0	0
$130$	2.48929	0.218325
$131$	6.39312	0.558569	0.279285	−	0.960208i	$-0.409903\pi$
$131$	6.39312	0.558569	0.279285	+	0.960208i	$0.409903\pi$
$132$	0	0
$133$	−8.35027	−0.724060
$134$	23.3288	2.01531
$135$	0	0
$136$	−33.7648	−2.89531
$137$	−16.7434	−1.43048	−0.715242	−	0.698877i	$-0.753684\pi$
$137$	−16.7434	−1.43048	−0.715242	+	0.698877i	$0.753684\pi$
$138$	0	0
$139$	5.78202	0.490424	0.245212	−	0.969469i	$-0.421142\pi$
$139$	5.78202	0.490424	0.245212	+	0.969469i	$0.421142\pi$
$140$	−5.02142	−0.424388
$141$	0	0
$142$	12.9357	1.08554
$143$	1.19656	0.100061
$144$	0	0
$145$	−6.00000	−0.498273
$146$	−29.7648	−2.46335
$147$	0	0
$148$	32.6577	2.68445
$149$	−15.3461	−1.25720	−0.628599	−	0.777730i	$-0.716371\pi$
$149$	−15.3461	−1.25720	−0.628599	+	0.777730i	$0.716371\pi$
$150$	0	0
$151$	−8.58546	−0.698675	−0.349337	−	0.936997i	$-0.613593\pi$
$151$	−8.58546	−0.698675	−0.349337	+	0.936997i	$0.613593\pi$
$152$	38.1579	3.09502
$153$	0	0
$154$	−3.56404	−0.287198
$155$	−2.97858	−0.239245
$156$	0	0
$157$	2.78623	0.222365	0.111183	−	0.993800i	$-0.464536\pi$
$157$	2.78623	0.222365	0.111183	+	0.993800i	$0.464536\pi$
$158$	−4.43596	−0.352906
$159$	0	0
$160$	2.05333	0.162330
$161$	4.99579	0.393723
$162$	0	0
$163$	8.76060	0.686183	0.343091	−	0.939302i	$-0.388526\pi$
$163$	8.76060	0.686183	0.343091	+	0.939302i	$0.388526\pi$
$164$	25.9143	2.02357
$165$	0	0
$166$	13.3717	1.03784
$167$	17.3717	1.34426	0.672131	−	0.740432i	$-0.265379\pi$
$167$	17.3717	1.34426	0.672131	+	0.740432i	$0.265379\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−15.3717	−1.17895
$171$	0	0
$172$	−41.7858	−3.18614
$173$	7.95715	0.604971	0.302486	−	0.953154i	$-0.402184\pi$
$173$	7.95715	0.604971	0.302486	+	0.953154i	$0.402184\pi$
$174$	0	0
$175$	−1.19656	−0.0904513
$176$	6.24361	0.470630
$177$	0	0
$178$	−25.3288	−1.89848
$179$	15.5640	1.16331	0.581655	−	0.813435i	$-0.302405\pi$
$179$	15.5640	1.16331	0.581655	+	0.813435i	$0.302405\pi$
$180$	0	0
$181$	15.7820	1.17307	0.586534	−	0.809925i	$-0.300492\pi$
$181$	15.7820	1.17307	0.586534	+	0.809925i	$0.300492\pi$
$182$	−2.97858	−0.220787
$183$	0	0
$184$	−22.8291	−1.68298
$185$	7.78202	0.572145
$186$	0	0
$187$	−7.38890	−0.540330
$188$	4.28646	0.312622
$189$	0	0
$190$	17.3717	1.26028
$191$	−10.7434	−0.777364	−0.388682	−	0.921372i	$-0.627070\pi$
$191$	−10.7434	−0.777364	−0.388682	+	0.921372i	$0.627070\pi$
$192$	0	0
$193$	9.73917	0.701041	0.350521	−	0.936555i	$-0.386005\pi$
$193$	9.73917	0.701041	0.350521	+	0.936555i	$0.386005\pi$
$194$	−4.54262	−0.326141
$195$	0	0
$196$	−23.3675	−1.66911
$197$	9.56404	0.681410	0.340705	−	0.940170i	$-0.389334\pi$
$197$	9.56404	0.681410	0.340705	+	0.940170i	$0.389334\pi$
$198$	0	0
$199$	5.95715	0.422291	0.211146	−	0.977455i	$-0.432281\pi$
$199$	5.95715	0.422291	0.211146	+	0.977455i	$0.432281\pi$
$200$	5.46787	0.386636
$201$	0	0
$202$	25.7648	1.81281
$203$	7.17935	0.503891
$204$	0	0
$205$	6.17513	0.431290
$206$	46.6577	3.25080
$207$	0	0
$208$	5.21798	0.361802
$209$	8.35027	0.577600
$210$	0	0
$211$	23.9143	1.64633	0.823164	−	0.567803i	$-0.192206\pi$
$211$	23.9143	1.64633	0.823164	+	0.567803i	$0.192206\pi$
$212$	−42.7005	−2.93269
$213$	0	0
$214$	46.2217	3.15965
$215$	−9.95715	−0.679072
$216$	0	0
$217$	3.56404	0.241943
$218$	20.8929	1.41504
$219$	0	0
$220$	5.02142	0.338544
$221$	−6.17513	−0.415385
$222$	0	0
$223$	2.62831	0.176004	0.0880022	−	0.996120i	$-0.471952\pi$
$223$	2.62831	0.176004	0.0880022	+	0.996120i	$0.471952\pi$
$224$	−2.45692	−0.164160
$225$	0	0
$226$	−19.8077	−1.31759
$227$	−15.7648	−1.04635	−0.523174	−	0.852226i	$-0.675252\pi$
$227$	−15.7648	−1.04635	−0.523174	+	0.852226i	$0.675252\pi$
$228$	0	0
$229$	8.74338	0.577779	0.288890	−	0.957362i	$-0.406714\pi$
$229$	8.74338	0.577779	0.288890	+	0.957362i	$0.406714\pi$
$230$	−10.3931	−0.685302
$231$	0	0
$232$	−32.8072	−2.15390
$233$	2.17513	0.142498	0.0712489	−	0.997459i	$-0.477302\pi$
$233$	2.17513	0.142498	0.0712489	+	0.997459i	$0.477302\pi$
$234$	0	0
$235$	1.02142	0.0666303
$236$	−22.5426	−1.46740
$237$	0	0
$238$	18.3931	1.19225
$239$	−2.80344	−0.181340	−0.0906698	−	0.995881i	$-0.528901\pi$
$239$	−2.80344	−0.181340	−0.0906698	+	0.995881i	$0.528901\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−23.8181	−1.53109
$243$	0	0
$244$	52.7434	3.37655
$245$	−5.56825	−0.355742
$246$	0	0
$247$	6.97858	0.444036
$248$	−16.2865	−1.03419
$249$	0	0
$250$	2.48929	0.157436
$251$	23.9143	1.50946	0.754729	−	0.656037i	$-0.227768\pi$
$251$	23.9143	1.50946	0.754729	+	0.656037i	$0.227768\pi$
$252$	0	0
$253$	−4.99579	−0.314083
$254$	−25.8715	−1.62332
$255$	0	0
$256$	−32.5678	−2.03549
$257$	19.9572	1.24489	0.622447	−	0.782662i	$-0.286139\pi$
$257$	19.9572	1.24489	0.622447	+	0.782662i	$0.286139\pi$
$258$	0	0
$259$	−9.31163	−0.578597
$260$	4.19656	0.260259
$261$	0	0
$262$	15.9143	0.983189
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	0	0
$265$	−10.1751	−0.625054
$266$	−20.7862	−1.27449
$267$	0	0
$268$	39.3288	2.40239
$269$	2.35027	0.143298	0.0716492	−	0.997430i	$-0.477174\pi$
$269$	2.35027	0.143298	0.0716492	+	0.997430i	$0.477174\pi$
$270$	0	0
$271$	10.9786	0.666901	0.333451	−	0.942768i	$-0.391787\pi$
$271$	10.9786	0.666901	0.333451	+	0.942768i	$0.391787\pi$
$272$	−32.2217	−1.95373
$273$	0	0
$274$	−41.6791	−2.51793
$275$	1.19656	0.0721551
$276$	0	0
$277$	1.21377	0.0729283	0.0364642	−	0.999335i	$-0.488391\pi$
$277$	1.21377	0.0729283	0.0364642	+	0.999335i	$0.488391\pi$
$278$	14.3931	0.863242
$279$	0	0
$280$	−6.54262	−0.390996
$281$	−11.9572	−0.713304	−0.356652	−	0.934237i	$-0.616082\pi$
$281$	−11.9572	−0.713304	−0.356652	+	0.934237i	$0.616082\pi$
$282$	0	0
$283$	−29.8715	−1.77567	−0.887837	−	0.460158i	$-0.847793\pi$
$283$	−29.8715	−1.77567	−0.887837	+	0.460158i	$0.847793\pi$
$284$	21.8077	1.29405
$285$	0	0
$286$	2.97858	0.176127
$287$	−7.38890	−0.436153
$288$	0	0
$289$	21.1323	1.24308
$290$	−14.9357	−0.877056
$291$	0	0
$292$	−50.1789	−2.93650
$293$	−0.777809	−0.0454401	−0.0227200	−	0.999742i	$-0.507233\pi$
$293$	−0.777809	−0.0454401	−0.0227200	+	0.999742i	$0.507233\pi$
$294$	0	0
$295$	−5.37169	−0.312752
$296$	42.5510	2.47323
$297$	0	0
$298$	−38.2008	−2.21291
$299$	−4.17513	−0.241454
$300$	0	0
$301$	11.9143	0.686729
$302$	−21.3717	−1.22980
$303$	0	0
$304$	36.4141	2.08849
$305$	12.5682	0.719656
$306$	0	0
$307$	0.760597	0.0434095	0.0217048	−	0.999764i	$-0.493091\pi$
$307$	0.760597	0.0434095	0.0217048	+	0.999764i	$0.493091\pi$
$308$	−6.00842	−0.342362
$309$	0	0
$310$	−7.41454	−0.421117
$311$	23.1281	1.31147	0.655736	−	0.754990i	$-0.272358\pi$
$311$	23.1281	1.31147	0.655736	+	0.754990i	$0.272358\pi$
$312$	0	0
$313$	−33.9143	−1.91695	−0.958475	−	0.285176i	$-0.907948\pi$
$313$	−33.9143	−1.91695	−0.958475	+	0.285176i	$0.907948\pi$
$314$	6.93573	0.391406
$315$	0	0
$316$	−7.47835	−0.420690
$317$	−9.64973	−0.541983	−0.270991	−	0.962582i	$-0.587352\pi$
$317$	−9.64973	−0.541983	−0.270991	+	0.962582i	$0.587352\pi$
$318$	0	0
$319$	−7.17935	−0.401966
$320$	−5.32464	−0.297656
$321$	0	0
$322$	12.4360	0.693029
$323$	−43.0937	−2.39780
$324$	0	0
$325$	1.00000	0.0554700
$326$	21.8077	1.20781
$327$	0	0
$328$	33.7648	1.86435
$329$	−1.22219	−0.0673816
$330$	0	0
$331$	15.3288	0.842550	0.421275	−	0.906933i	$-0.361583\pi$
$331$	15.3288	0.842550	0.421275	+	0.906933i	$0.361583\pi$
$332$	22.5426	1.23719
$333$	0	0
$334$	43.2432	2.36616
$335$	9.37169	0.512030
$336$	0	0
$337$	−22.3503	−1.21750	−0.608748	−	0.793363i	$-0.708328\pi$
$337$	−22.3503	−1.21750	−0.608748	+	0.793363i	$0.708328\pi$
$338$	2.48929	0.135399
$339$	0	0
$340$	−25.9143	−1.40540
$341$	−3.56404	−0.193004
$342$	0	0
$343$	15.0386	0.812010
$344$	−54.4444	−2.93544
$345$	0	0
$346$	19.8077	1.06487
$347$	5.78202	0.310395	0.155198	−	0.987883i	$-0.450399\pi$
$347$	5.78202	0.310395	0.155198	+	0.987883i	$0.450399\pi$
$348$	0	0
$349$	−27.5212	−1.47318	−0.736588	−	0.676342i	$-0.763564\pi$
$349$	−27.5212	−1.47318	−0.736588	+	0.676342i	$0.763564\pi$
$350$	−2.97858	−0.159212
$351$	0	0
$352$	2.45692	0.130955
$353$	28.7434	1.52986	0.764928	−	0.644116i	$-0.222775\pi$
$353$	28.7434	1.52986	0.764928	+	0.644116i	$0.222775\pi$
$354$	0	0
$355$	5.19656	0.275805
$356$	−42.7005	−2.26312
$357$	0	0
$358$	38.7434	2.04765
$359$	12.5855	0.664235	0.332118	−	0.943238i	$-0.392237\pi$
$359$	12.5855	0.664235	0.332118	+	0.943238i	$0.392237\pi$
$360$	0	0
$361$	29.7005	1.56319
$362$	39.2860	2.06483
$363$	0	0
$364$	−5.02142	−0.263194
$365$	−11.9572	−0.625866
$366$	0	0
$367$	−27.9143	−1.45712	−0.728558	−	0.684985i	$-0.759809\pi$
$367$	−27.9143	−1.45712	−0.728558	+	0.684985i	$0.759809\pi$
$368$	−21.7858	−1.13566
$369$	0	0
$370$	19.3717	1.00709
$371$	12.1751	0.632102
$372$	0	0
$373$	−2.35027	−0.121692	−0.0608462	−	0.998147i	$-0.519380\pi$
$373$	−2.35027	−0.121692	−0.0608462	+	0.998147i	$0.519380\pi$
$374$	−18.3931	−0.951085
$375$	0	0
$376$	5.58500	0.288025
$377$	−6.00000	−0.309016
$378$	0	0
$379$	24.5510	1.26110	0.630551	−	0.776148i	$-0.282829\pi$
$379$	24.5510	1.26110	0.630551	+	0.776148i	$0.282829\pi$
$380$	29.2860	1.50234
$381$	0	0
$382$	−26.7434	−1.36831
$383$	−5.80765	−0.296757	−0.148379	−	0.988931i	$-0.547405\pi$
$383$	−5.80765	−0.296757	−0.148379	+	0.988931i	$0.547405\pi$
$384$	0	0
$385$	−1.43175	−0.0729687
$386$	24.2436	1.23397
$387$	0	0
$388$	−7.65815	−0.388784
$389$	−13.6497	−0.692069	−0.346034	−	0.938222i	$-0.612472\pi$
$389$	−13.6497	−0.692069	−0.346034	+	0.938222i	$0.612472\pi$
$390$	0	0
$391$	25.7820	1.30385
$392$	−30.4464	−1.53778
$393$	0	0
$394$	23.8077	1.19941
$395$	−1.78202	−0.0896631
$396$	0	0
$397$	−12.1323	−0.608902	−0.304451	−	0.952528i	$-0.598473\pi$
$397$	−12.1323	−0.608902	−0.304451	+	0.952528i	$0.598473\pi$
$398$	14.8291	0.743314
$399$	0	0
$400$	5.21798	0.260899
$401$	37.4439	1.86986	0.934930	−	0.354832i	$-0.115462\pi$
$401$	37.4439	1.86986	0.934930	+	0.354832i	$0.115462\pi$
$402$	0	0
$403$	−2.97858	−0.148373
$404$	43.4355	2.16100
$405$	0	0
$406$	17.8715	0.886946
$407$	9.31163	0.461561
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	15.3717	0.759154
$411$	0	0
$412$	78.6577	3.87519
$413$	6.42754	0.316279
$414$	0	0
$415$	5.37169	0.263686
$416$	2.05333	0.100673
$417$	0	0
$418$	20.7862	1.01669
$419$	−3.17935	−0.155321	−0.0776606	−	0.996980i	$-0.524745\pi$
$419$	−3.17935	−0.155321	−0.0776606	+	0.996980i	$0.524745\pi$
$420$	0	0
$421$	−16.3074	−0.794775	−0.397388	−	0.917651i	$-0.630083\pi$
$421$	−16.3074	−0.794775	−0.397388	+	0.917651i	$0.630083\pi$
$422$	59.5296	2.89786
$423$	0	0
$424$	−55.6363	−2.70194
$425$	−6.17513	−0.299538
$426$	0	0
$427$	−15.0386	−0.727771
$428$	77.9227	3.76654
$429$	0	0
$430$	−24.7862	−1.19530
$431$	−4.58546	−0.220874	−0.110437	−	0.993883i	$-0.535225\pi$
$431$	−4.58546	−0.220874	−0.110437	+	0.993883i	$0.535225\pi$
$432$	0	0
$433$	−38.3503	−1.84300	−0.921498	−	0.388383i	$-0.873034\pi$
$433$	−38.3503	−1.84300	−0.921498	+	0.388383i	$0.873034\pi$
$434$	8.87192	0.425866
$435$	0	0
$436$	35.2222	1.68684
$437$	−29.1365	−1.39379
$438$	0	0
$439$	7.73917	0.369371	0.184685	−	0.982798i	$-0.440873\pi$
$439$	7.73917	0.369371	0.184685	+	0.982798i	$0.440873\pi$
$440$	6.54262	0.311907
$441$	0	0
$442$	−15.3717	−0.731157
$443$	−34.9185	−1.65903	−0.829514	−	0.558485i	$-0.811383\pi$
$443$	−34.9185	−1.65903	−0.829514	+	0.558485i	$0.811383\pi$
$444$	0	0
$445$	−10.1751	−0.482348
$446$	6.54262	0.309802
$447$	0	0
$448$	6.37123	0.301012
$449$	6.17513	0.291423	0.145711	−	0.989327i	$-0.453453\pi$
$449$	6.17513	0.291423	0.145711	+	0.989327i	$0.453453\pi$
$450$	0	0
$451$	7.38890	0.347930
$452$	−33.3927	−1.57066
$453$	0	0
$454$	−39.2432	−1.84177
$455$	−1.19656	−0.0560955
$456$	0	0
$457$	1.38890	0.0649702	0.0324851	−	0.999472i	$-0.489658\pi$
$457$	1.38890	0.0649702	0.0324851	+	0.999472i	$0.489658\pi$
$458$	21.7648	1.01700
$459$	0	0
$460$	−17.5212	−0.816930
$461$	−28.4826	−1.32657	−0.663283	−	0.748369i	$-0.730837\pi$
$461$	−28.4826	−1.32657	−0.663283	+	0.748369i	$0.730837\pi$
$462$	0	0
$463$	16.3759	0.761053	0.380526	−	0.924770i	$-0.375743\pi$
$463$	16.3759	0.761053	0.380526	+	0.924770i	$0.375743\pi$
$464$	−31.3079	−1.45343
$465$	0	0
$466$	5.41454	0.250824
$467$	−25.7476	−1.19146	−0.595728	−	0.803186i	$-0.703136\pi$
$467$	−25.7476	−1.19146	−0.595728	+	0.803186i	$0.703136\pi$
$468$	0	0
$469$	−11.2138	−0.517804
$470$	2.54262	0.117282
$471$	0	0
$472$	−29.3717	−1.35194
$473$	−11.9143	−0.547820
$474$	0	0
$475$	6.97858	0.320199
$476$	31.0080	1.42125
$477$	0	0
$478$	−6.97858	−0.319193
$479$	7.58967	0.346781	0.173391	−	0.984853i	$-0.444528\pi$
$479$	7.58967	0.346781	0.173391	+	0.984853i	$0.444528\pi$
$480$	0	0
$481$	7.78202	0.354830
$482$	−14.9357	−0.680304
$483$	0	0
$484$	−40.1537	−1.82517
$485$	−1.82487	−0.0828629
$486$	0	0
$487$	4.41033	0.199851	0.0999255	−	0.994995i	$-0.468140\pi$
$487$	4.41033	0.199851	0.0999255	+	0.994995i	$0.468140\pi$
$488$	68.7215	3.11088
$489$	0	0
$490$	−13.8610	−0.626175
$491$	0.0856914	0.00386720	0.00193360	−	0.999998i	$-0.499385\pi$
$491$	0.0856914	0.00386720	0.00193360	+	0.999998i	$0.499385\pi$
$492$	0	0
$493$	37.0508	1.66868
$494$	17.3717	0.781589
$495$	0	0
$496$	−15.5422	−0.697863
$497$	−6.21798	−0.278915
$498$	0	0
$499$	−17.7220	−0.793344	−0.396672	−	0.917960i	$-0.629835\pi$
$499$	−17.7220	−0.793344	−0.396672	+	0.917960i	$0.629835\pi$
$500$	4.19656	0.187676
$501$	0	0
$502$	59.5296	2.65694
$503$	8.70054	0.387938	0.193969	−	0.981008i	$-0.437864\pi$
$503$	8.70054	0.387938	0.193969	+	0.981008i	$0.437864\pi$
$504$	0	0
$505$	10.3503	0.460581
$506$	−12.4360	−0.552846
$507$	0	0
$508$	−43.6153	−1.93512
$509$	33.3545	1.47841	0.739206	−	0.673480i	$-0.235201\pi$
$509$	33.3545	1.47841	0.739206	+	0.673480i	$0.235201\pi$
$510$	0	0
$511$	14.3074	0.632923
$512$	−46.3482	−2.04832
$513$	0	0
$514$	49.6791	2.19125
$515$	18.7434	0.825932
$516$	0	0
$517$	1.22219	0.0537519
$518$	−23.1793	−1.01844
$519$	0	0
$520$	5.46787	0.239782
$521$	−18.7005	−0.819285	−0.409643	−	0.912246i	$-0.634347\pi$
$521$	−18.7005	−0.819285	−0.409643	+	0.912246i	$0.634347\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	26.8291	1.17203
$525$	0	0
$526$	−19.9143	−0.868305
$527$	18.3931	0.801217
$528$	0	0
$529$	−5.56825	−0.242098
$530$	−25.3288	−1.10021
$531$	0	0
$532$	−35.0424	−1.51928
$533$	6.17513	0.267475
$534$	0	0
$535$	18.5682	0.802775
$536$	51.2432	2.21337
$537$	0	0
$538$	5.85050	0.252233
$539$	−6.66273	−0.286984
$540$	0	0
$541$	−41.5296	−1.78550	−0.892749	−	0.450555i	$-0.851226\pi$
$541$	−41.5296	−1.78550	−0.892749	+	0.450555i	$0.851226\pi$
$542$	27.3288	1.17387
$543$	0	0
$544$	−12.6796	−0.543632
$545$	8.39312	0.359522
$546$	0	0
$547$	−7.91431	−0.338391	−0.169196	−	0.985582i	$-0.554117\pi$
$547$	−7.91431	−0.338391	−0.169196	+	0.985582i	$0.554117\pi$
$548$	−70.2646	−3.00155
$549$	0	0
$550$	2.97858	0.127007
$551$	−41.8715	−1.78378
$552$	0	0
$553$	2.13229	0.0906742
$554$	3.02142	0.128368
$555$	0	0
$556$	24.2646	1.02905
$557$	−42.7005	−1.80928	−0.904640	−	0.426177i	$-0.859860\pi$
$557$	−42.7005	−1.80928	−0.904640	+	0.426177i	$0.859860\pi$
$558$	0	0
$559$	−9.95715	−0.421143
$560$	−6.24361	−0.263841
$561$	0	0
$562$	−29.7648	−1.25555
$563$	−1.04706	−0.0441282	−0.0220641	−	0.999757i	$-0.507024\pi$
$563$	−1.04706	−0.0441282	−0.0220641	+	0.999757i	$0.507024\pi$
$564$	0	0
$565$	−7.95715	−0.334760
$566$	−74.3587	−3.12553
$567$	0	0
$568$	28.4141	1.19223
$569$	−16.7778	−0.703362	−0.351681	−	0.936120i	$-0.614390\pi$
$569$	−16.7778	−0.703362	−0.351681	+	0.936120i	$0.614390\pi$
$570$	0	0
$571$	−20.6111	−0.862548	−0.431274	−	0.902221i	$-0.641936\pi$
$571$	−20.6111	−0.862548	−0.431274	+	0.902221i	$0.641936\pi$
$572$	5.02142	0.209956
$573$	0	0
$574$	−18.3931	−0.767714
$575$	−4.17513	−0.174115
$576$	0	0
$577$	1.38890	0.0578208	0.0289104	−	0.999582i	$-0.490796\pi$
$577$	1.38890	0.0578208	0.0289104	+	0.999582i	$0.490796\pi$
$578$	52.6044	2.18805
$579$	0	0
$580$	−25.1793	−1.04552
$581$	−6.42754	−0.266659
$582$	0	0
$583$	−12.1751	−0.504243
$584$	−65.3801	−2.70545
$585$	0	0
$586$	−1.93619	−0.0799833
$587$	0.935731	0.0386218	0.0193109	−	0.999814i	$-0.493853\pi$
$587$	0.935731	0.0386218	0.0193109	+	0.999814i	$0.493853\pi$
$588$	0	0
$589$	−20.7862	−0.856482
$590$	−13.3717	−0.550504
$591$	0	0
$592$	40.6064	1.66891
$593$	0.478807	0.0196622	0.00983112	−	0.999952i	$-0.496871\pi$
$593$	0.478807	0.0196622	0.00983112	+	0.999952i	$0.496871\pi$
$594$	0	0
$595$	7.38890	0.302916
$596$	−64.4006	−2.63795
$597$	0	0
$598$	−10.3931	−0.425006
$599$	−29.0852	−1.18839	−0.594195	−	0.804321i	$-0.702529\pi$
$599$	−29.0852	−1.18839	−0.594195	+	0.804321i	$0.702529\pi$
$600$	0	0
$601$	11.4318	0.466311	0.233155	−	0.972439i	$-0.425095\pi$
$601$	11.4318	0.466311	0.233155	+	0.972439i	$0.425095\pi$
$602$	29.6582	1.20878
$603$	0	0
$604$	−36.0294	−1.46601
$605$	−9.56825	−0.389005
$606$	0	0
$607$	27.9143	1.13301	0.566503	−	0.824059i	$-0.308296\pi$
$607$	27.9143	1.13301	0.566503	+	0.824059i	$0.308296\pi$
$608$	14.3293	0.581130
$609$	0	0
$610$	31.2860	1.26673
$611$	1.02142	0.0413223
$612$	0	0
$613$	−4.65394	−0.187971	−0.0939855	−	0.995574i	$-0.529961\pi$
$613$	−4.65394	−0.187971	−0.0939855	+	0.995574i	$0.529961\pi$
$614$	1.89334	0.0764092
$615$	0	0
$616$	−7.82862	−0.315424
$617$	15.9572	0.642411	0.321205	−	0.947010i	$-0.395912\pi$
$617$	15.9572	0.642411	0.321205	+	0.947010i	$0.395912\pi$
$618$	0	0
$619$	1.02142	0.0410545	0.0205272	−	0.999789i	$-0.493466\pi$
$619$	1.02142	0.0410545	0.0205272	+	0.999789i	$0.493466\pi$
$620$	−12.4998	−0.502003
$621$	0	0
$622$	57.5725	2.30845
$623$	12.1751	0.487786
$624$	0	0
$625$	1.00000	0.0400000
$626$	−84.4225	−3.37420
$627$	0	0
$628$	11.6926	0.466585
$629$	−48.0550	−1.91608
$630$	0	0
$631$	−20.4998	−0.816083	−0.408041	−	0.912963i	$-0.633788\pi$
$631$	−20.4998	−0.816083	−0.408041	+	0.912963i	$0.633788\pi$
$632$	−9.74384	−0.387589
$633$	0	0
$634$	−24.0210	−0.953994
$635$	−10.3931	−0.412438
$636$	0	0
$637$	−5.56825	−0.220622
$638$	−17.8715	−0.707538
$639$	0	0
$640$	−17.3612	−0.686262
$641$	−38.2646	−1.51136	−0.755680	−	0.654941i	$-0.772693\pi$
$641$	−38.2646	−1.51136	−0.755680	+	0.654941i	$0.772693\pi$
$642$	0	0
$643$	−33.1109	−1.30577	−0.652883	−	0.757459i	$-0.726440\pi$
$643$	−33.1109	−1.30577	−0.652883	+	0.757459i	$0.726440\pi$
$644$	20.9651	0.826141
$645$	0	0
$646$	−107.273	−4.22058
$647$	16.9614	0.666820	0.333410	−	0.942782i	$-0.391801\pi$
$647$	16.9614	0.666820	0.333410	+	0.942782i	$0.391801\pi$
$648$	0	0
$649$	−6.42754	−0.252303
$650$	2.48929	0.0976379
$651$	0	0
$652$	36.7643	1.43980
$653$	19.1709	0.750216	0.375108	−	0.926981i	$-0.377606\pi$
$653$	19.1709	0.750216	0.375108	+	0.926981i	$0.377606\pi$
$654$	0	0
$655$	6.39312	0.249800
$656$	32.2217	1.25805
$657$	0	0
$658$	−3.04239	−0.118605
$659$	−37.8715	−1.47526	−0.737631	−	0.675204i	$-0.764056\pi$
$659$	−37.8715	−1.47526	−0.737631	+	0.675204i	$0.764056\pi$
$660$	0	0
$661$	24.3931	0.948782	0.474391	−	0.880314i	$-0.342668\pi$
$661$	24.3931	0.948782	0.474391	+	0.880314i	$0.342668\pi$
$662$	38.1579	1.48305
$663$	0	0
$664$	29.3717	1.13984
$665$	−8.35027	−0.323810
$666$	0	0
$667$	25.0508	0.969971
$668$	72.9013	2.82064
$669$	0	0
$670$	23.3288	0.901272
$671$	15.0386	0.580560
$672$	0	0
$673$	−21.1281	−0.814428	−0.407214	−	0.913333i	$-0.633500\pi$
$673$	−21.1281	−0.814428	−0.407214	+	0.913333i	$0.633500\pi$
$674$	−55.6363	−2.14303
$675$	0	0
$676$	4.19656	0.161406
$677$	15.3973	0.591767	0.295884	−	0.955224i	$-0.404386\pi$
$677$	15.3973	0.591767	0.295884	+	0.955224i	$0.404386\pi$
$678$	0	0
$679$	2.18356	0.0837972
$680$	−33.7648	−1.29482
$681$	0	0
$682$	−8.87192	−0.339723
$683$	−30.0722	−1.15068	−0.575341	−	0.817914i	$-0.695131\pi$
$683$	−30.0722	−1.15068	−0.575341	+	0.817914i	$0.695131\pi$
$684$	0	0
$685$	−16.7434	−0.639732
$686$	37.4355	1.42929
$687$	0	0
$688$	−51.9562	−1.98081
$689$	−10.1751	−0.387642
$690$	0	0
$691$	−8.14950	−0.310022	−0.155011	−	0.987913i	$-0.549541\pi$
$691$	−8.14950	−0.310022	−0.155011	+	0.987913i	$0.549541\pi$
$692$	33.3927	1.26940
$693$	0	0
$694$	14.3931	0.546355
$695$	5.78202	0.219325
$696$	0	0
$697$	−38.1323	−1.44436
$698$	−68.5082	−2.59307
$699$	0	0
$700$	−5.02142	−0.189792
$701$	28.6921	1.08369	0.541843	−	0.840480i	$-0.317727\pi$
$701$	28.6921	1.08369	0.541843	+	0.840480i	$0.317727\pi$
$702$	0	0
$703$	54.3074	2.04824
$704$	−6.37123	−0.240125
$705$	0	0
$706$	71.5506	2.69284
$707$	−12.3847	−0.465774
$708$	0	0
$709$	12.3074	0.462215	0.231108	−	0.972928i	$-0.425765\pi$
$709$	12.3074	0.462215	0.231108	+	0.972928i	$0.425765\pi$
$710$	12.9357	0.485469
$711$	0	0
$712$	−55.6363	−2.08506
$713$	12.4360	0.465730
$714$	0	0
$715$	1.19656	0.0447487
$716$	65.3154	2.44095
$717$	0	0
$718$	31.3288	1.16918
$719$	28.7862	1.07355	0.536773	−	0.843727i	$-0.319643\pi$
$719$	28.7862	1.07355	0.536773	+	0.843727i	$0.319643\pi$
$720$	0	0
$721$	−22.4275	−0.835245
$722$	73.9332	2.75151
$723$	0	0
$724$	66.2302	2.46142
$725$	−6.00000	−0.222834
$726$	0	0
$727$	34.3931	1.27557	0.637785	−	0.770214i	$-0.279851\pi$
$727$	34.3931	1.27557	0.637785	+	0.770214i	$0.279851\pi$
$728$	−6.54262	−0.242485
$729$	0	0
$730$	−29.7648	−1.10164
$731$	61.4868	2.27417
$732$	0	0
$733$	−29.0042	−1.07129	−0.535647	−	0.844442i	$-0.679932\pi$
$733$	−29.0042	−1.07129	−0.535647	+	0.844442i	$0.679932\pi$
$734$	−69.4868	−2.56480
$735$	0	0
$736$	−8.57292	−0.316002
$737$	11.2138	0.413065
$738$	0	0
$739$	−6.27804	−0.230941	−0.115471	−	0.993311i	$-0.536838\pi$
$739$	−6.27804	−0.230941	−0.115471	+	0.993311i	$0.536838\pi$
$740$	32.6577	1.20052
$741$	0	0
$742$	30.3074	1.11262
$743$	−12.2352	−0.448866	−0.224433	−	0.974490i	$-0.572053\pi$
$743$	−12.2352	−0.448866	−0.224433	+	0.974490i	$0.572053\pi$
$744$	0	0
$745$	−15.3461	−0.562236
$746$	−5.85050	−0.214202
$747$	0	0
$748$	−31.0080	−1.13376
$749$	−22.2180	−0.811827
$750$	0	0
$751$	−28.8757	−1.05369	−0.526844	−	0.849962i	$-0.676625\pi$
$751$	−28.8757	−1.05369	−0.526844	+	0.849962i	$0.676625\pi$
$752$	5.32976	0.194357
$753$	0	0
$754$	−14.9357	−0.543927
$755$	−8.58546	−0.312457
$756$	0	0
$757$	30.3503	1.10310	0.551550	−	0.834142i	$-0.314037\pi$
$757$	30.3503	1.10310	0.551550	+	0.834142i	$0.314037\pi$
$758$	61.1146	2.21978
$759$	0	0
$760$	38.1579	1.38413
$761$	27.1709	0.984945	0.492473	−	0.870328i	$-0.336093\pi$
$761$	27.1709	0.984945	0.492473	+	0.870328i	$0.336093\pi$
$762$	0	0
$763$	−10.0428	−0.363575
$764$	−45.0852	−1.63113
$765$	0	0
$766$	−14.4569	−0.522350
$767$	−5.37169	−0.193961
$768$	0	0
$769$	−38.3503	−1.38295	−0.691473	−	0.722402i	$-0.743038\pi$
$769$	−38.3503	−1.38295	−0.691473	+	0.722402i	$0.743038\pi$
$770$	−3.56404	−0.128439
$771$	0	0
$772$	40.8710	1.47098
$773$	50.2646	1.80789	0.903946	−	0.427647i	$-0.140658\pi$
$773$	50.2646	1.80789	0.903946	+	0.427647i	$0.140658\pi$
$774$	0	0
$775$	−2.97858	−0.106994
$776$	−9.97812	−0.358194
$777$	0	0
$778$	−33.9781	−1.21817
$779$	43.0937	1.54399
$780$	0	0
$781$	6.21798	0.222497
$782$	64.1789	2.29503
$783$	0	0
$784$	−29.0550	−1.03768
$785$	2.78623	0.0994448
$786$	0	0
$787$	−13.2860	−0.473595	−0.236797	−	0.971559i	$-0.576098\pi$
$787$	−13.2860	−0.473595	−0.236797	+	0.971559i	$0.576098\pi$
$788$	40.1360	1.42979
$789$	0	0
$790$	−4.43596	−0.157824
$791$	9.52119	0.338535
$792$	0	0
$793$	12.5682	0.446312
$794$	−30.2008	−1.07179
$795$	0	0
$796$	24.9995	0.886085
$797$	−9.82487	−0.348015	−0.174007	−	0.984744i	$-0.555672\pi$
$797$	−9.82487	−0.348015	−0.174007	+	0.984744i	$0.555672\pi$
$798$	0	0
$799$	−6.30742	−0.223141
$800$	2.05333	0.0725961
$801$	0	0
$802$	93.2087	3.29131
$803$	−14.3074	−0.504898
$804$	0	0
$805$	4.99579	0.176078
$806$	−7.41454	−0.261166
$807$	0	0
$808$	56.5939	1.99097
$809$	9.91431	0.348569	0.174284	−	0.984695i	$-0.444239\pi$
$809$	9.91431	0.348569	0.174284	+	0.984695i	$0.444239\pi$
$810$	0	0
$811$	−36.5855	−1.28469	−0.642345	−	0.766416i	$-0.722038\pi$
$811$	−36.5855	−1.28469	−0.642345	+	0.766416i	$0.722038\pi$
$812$	30.1285	1.05730
$813$	0	0
$814$	23.1793	0.812436
$815$	8.76060	0.306870
$816$	0	0
$817$	−69.4868	−2.43103
$818$	−34.8500	−1.21850
$819$	0	0
$820$	25.9143	0.904967
$821$	34.4741	1.20316	0.601578	−	0.798814i	$-0.294539\pi$
$821$	34.4741	1.20316	0.601578	+	0.798814i	$0.294539\pi$
$822$	0	0
$823$	13.2566	0.462097	0.231048	−	0.972942i	$-0.425784\pi$
$823$	13.2566	0.462097	0.231048	+	0.972942i	$0.425784\pi$
$824$	102.486	3.57028
$825$	0	0
$826$	16.0000	0.556711
$827$	−28.1495	−0.978854	−0.489427	−	0.872044i	$-0.662794\pi$
$827$	−28.1495	−0.978854	−0.489427	+	0.872044i	$0.662794\pi$
$828$	0	0
$829$	16.3418	0.567576	0.283788	−	0.958887i	$-0.408409\pi$
$829$	16.3418	0.567576	0.283788	+	0.958887i	$0.408409\pi$
$830$	13.3717	0.464138
$831$	0	0
$832$	−5.32464	−0.184599
$833$	34.3847	1.19136
$834$	0	0
$835$	17.3717	0.601172
$836$	35.0424	1.21197
$837$	0	0
$838$	−7.91431	−0.273395
$839$	30.3675	1.04840	0.524201	−	0.851595i	$-0.324364\pi$
$839$	30.3675	1.04840	0.524201	+	0.851595i	$0.324364\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−40.5939	−1.39896
$843$	0	0
$844$	100.358	3.45446
$845$	1.00000	0.0344010
$846$	0	0
$847$	11.4490	0.393391
$848$	−53.0937	−1.82324
$849$	0	0
$850$	−15.3717	−0.527245
$851$	−32.4910	−1.11378
$852$	0	0
$853$	−42.1407	−1.44287	−0.721435	−	0.692482i	$-0.756517\pi$
$853$	−42.1407	−1.44287	−0.721435	+	0.692482i	$0.756517\pi$
$854$	−37.4355	−1.28102
$855$	0	0
$856$	101.529	3.47018
$857$	2.17513	0.0743012	0.0371506	−	0.999310i	$-0.488172\pi$
$857$	2.17513	0.0743012	0.0371506	+	0.999310i	$0.488172\pi$
$858$	0	0
$859$	18.5682	0.633541	0.316770	−	0.948502i	$-0.397402\pi$
$859$	18.5682	0.633541	0.316770	+	0.948502i	$0.397402\pi$
$860$	−41.7858	−1.42488
$861$	0	0
$862$	−11.4145	−0.388781
$863$	−33.7220	−1.14791	−0.573954	−	0.818887i	$-0.694591\pi$
$863$	−33.7220	−1.14791	−0.573954	+	0.818887i	$0.694591\pi$
$864$	0	0
$865$	7.95715	0.270551
$866$	−95.4649	−3.24403
$867$	0	0
$868$	14.9567	0.507663
$869$	−2.13229	−0.0723330
$870$	0	0
$871$	9.37169	0.317548
$872$	45.8924	1.55411
$873$	0	0
$874$	−72.5292	−2.45334
$875$	−1.19656	−0.0404510
$876$	0	0
$877$	43.4868	1.46844	0.734222	−	0.678910i	$-0.237547\pi$
$877$	43.4868	1.46844	0.734222	+	0.678910i	$0.237547\pi$
$878$	19.2650	0.650164
$879$	0	0
$880$	6.24361	0.210472
$881$	−26.7005	−0.899564	−0.449782	−	0.893138i	$-0.648498\pi$
$881$	−26.7005	−0.899564	−0.449782	+	0.893138i	$0.648498\pi$
$882$	0	0
$883$	20.2990	0.683116	0.341558	−	0.939861i	$-0.389045\pi$
$883$	20.2990	0.683116	0.341558	+	0.939861i	$0.389045\pi$
$884$	−25.9143	−0.871593
$885$	0	0
$886$	−86.9223	−2.92021
$887$	−36.0550	−1.21061	−0.605305	−	0.795994i	$-0.706949\pi$
$887$	−36.0550	−1.21061	−0.605305	+	0.795994i	$0.706949\pi$
$888$	0	0
$889$	12.4360	0.417089
$890$	−25.3288	−0.849025
$891$	0	0
$892$	11.0298	0.369307
$893$	7.12808	0.238532
$894$	0	0
$895$	15.5640	0.520248
$896$	20.7737	0.694000
$897$	0	0
$898$	15.3717	0.512960
$899$	17.8715	0.596047
$900$	0	0
$901$	62.8328	2.09326
$902$	18.3931	0.612424
$903$	0	0
$904$	−43.5087	−1.44708
$905$	15.7820	0.524612
$906$	0	0
$907$	−7.26504	−0.241232	−0.120616	−	0.992699i	$-0.538487\pi$
$907$	−7.26504	−0.241232	−0.120616	+	0.992699i	$0.538487\pi$
$908$	−66.1579	−2.19553
$909$	0	0
$910$	−2.97858	−0.0987389
$911$	6.65769	0.220579	0.110290	−	0.993899i	$-0.464822\pi$
$911$	6.65769	0.220579	0.110290	+	0.993899i	$0.464822\pi$
$912$	0	0
$913$	6.42754	0.212721
$914$	3.45738	0.114360
$915$	0	0
$916$	36.6921	1.21234
$917$	−7.64973	−0.252616
$918$	0	0
$919$	−27.1831	−0.896688	−0.448344	−	0.893861i	$-0.647986\pi$
$919$	−27.1831	−0.896688	−0.448344	+	0.893861i	$0.647986\pi$
$920$	−22.8291	−0.752652
$921$	0	0
$922$	−70.9013	−2.33501
$923$	5.19656	0.171047
$924$	0	0
$925$	7.78202	0.255871
$926$	40.7643	1.33960
$927$	0	0
$928$	−12.3200	−0.404423
$929$	15.3973	0.505170	0.252585	−	0.967575i	$-0.418719\pi$
$929$	15.3973	0.505170	0.252585	+	0.967575i	$0.418719\pi$
$930$	0	0
$931$	−38.8585	−1.27353
$932$	9.12808	0.299000
$933$	0	0
$934$	−64.0932	−2.09719
$935$	−7.38890	−0.241643
$936$	0	0
$937$	1.12808	0.0368527	0.0184264	−	0.999830i	$-0.494134\pi$
$937$	1.12808	0.0368527	0.0184264	+	0.999830i	$0.494134\pi$
$938$	−27.9143	−0.911434
$939$	0	0
$940$	4.28646	0.139809
$941$	30.1407	0.982559	0.491280	−	0.871002i	$-0.336529\pi$
$941$	30.1407	0.982559	0.491280	+	0.871002i	$0.336529\pi$
$942$	0	0
$943$	−25.7820	−0.839578
$944$	−28.0294	−0.912279
$945$	0	0
$946$	−29.6582	−0.964270
$947$	20.0294	0.650868	0.325434	−	0.945565i	$-0.394490\pi$
$947$	20.0294	0.650868	0.325434	+	0.945565i	$0.394490\pi$
$948$	0	0
$949$	−11.9572	−0.388146
$950$	17.3717	0.563612
$951$	0	0
$952$	40.4015	1.30942
$953$	43.2259	1.40023	0.700113	−	0.714032i	$-0.253133\pi$
$953$	43.2259	1.40023	0.700113	+	0.714032i	$0.253133\pi$
$954$	0	0
$955$	−10.7434	−0.347648
$956$	−11.7648	−0.380501
$957$	0	0
$958$	18.8929	0.610401
$959$	20.0344	0.646945
$960$	0	0
$961$	−22.1281	−0.713809
$962$	19.3717	0.624568
$963$	0	0
$964$	−25.1793	−0.810972
$965$	9.73917	0.313515
$966$	0	0
$967$	57.6875	1.85511	0.927553	−	0.373691i	$-0.121908\pi$
$967$	57.6875	1.85511	0.927553	+	0.373691i	$0.121908\pi$
$968$	−52.3179	−1.68156
$969$	0	0
$970$	−4.54262	−0.145855
$971$	19.5296	0.626735	0.313368	−	0.949632i	$-0.398543\pi$
$971$	19.5296	0.626735	0.313368	+	0.949632i	$0.398543\pi$
$972$	0	0
$973$	−6.91852	−0.221798
$974$	10.9786	0.351776
$975$	0	0
$976$	65.5809	2.09919
$977$	40.3074	1.28955	0.644774	−	0.764373i	$-0.276951\pi$
$977$	40.3074	1.28955	0.644774	+	0.764373i	$0.276951\pi$
$978$	0	0
$979$	−12.1751	−0.389119
$980$	−23.3675	−0.746447
$981$	0	0
$982$	0.213311	0.00680702
$983$	−32.2008	−1.02705	−0.513523	−	0.858076i	$-0.671660\pi$
$983$	−32.2008	−1.02705	−0.513523	+	0.858076i	$0.671660\pi$
$984$	0	0
$985$	9.56404	0.304736
$986$	92.2302	2.93721
$987$	0	0
$988$	29.2860	0.931712
$989$	41.5725	1.32193
$990$	0	0
$991$	26.4826	0.841246	0.420623	−	0.907235i	$-0.361811\pi$
$991$	26.4826	0.841246	0.420623	+	0.907235i	$0.361811\pi$
$992$	−6.11599	−0.194183
$993$	0	0
$994$	−15.4783	−0.490943
$995$	5.95715	0.188854
$996$	0	0
$997$	35.1365	1.11278	0.556392	−	0.830920i	$-0.312185\pi$
$997$	35.1365	1.11278	0.556392	+	0.830920i	$0.312185\pi$
$998$	−44.1151	−1.39644
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.a.n.1.3		3
3.2	odd	2		195.2.a.e.1.1	✓	3
4.3	odd	2		9360.2.a.dd.1.2		3
5.2	odd	4		2925.2.c.w.2224.5		6
5.3	odd	4		2925.2.c.w.2224.2		6
5.4	even	2		2925.2.a.bh.1.1		3
12.11	even	2		3120.2.a.bj.1.2		3
13.12	even	2		7605.2.a.bx.1.1		3
15.2	even	4		975.2.c.i.274.2		6
15.8	even	4		975.2.c.i.274.5		6
15.14	odd	2		975.2.a.o.1.3		3
21.20	even	2		9555.2.a.bq.1.1		3
39.38	odd	2		2535.2.a.bc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.1	✓	3	3.2	odd	2
585.2.a.n.1.3		3	1.1	even	1	trivial
975.2.a.o.1.3		3	15.14	odd	2
975.2.c.i.274.2		6	15.2	even	4
975.2.c.i.274.5		6	15.8	even	4
2535.2.a.bc.1.3		3	39.38	odd	2
2925.2.a.bh.1.1		3	5.4	even	2
2925.2.c.w.2224.2		6	5.3	odd	4
2925.2.c.w.2224.5		6	5.2	odd	4
3120.2.a.bj.1.2		3	12.11	even	2
7605.2.a.bx.1.1		3	13.12	even	2
9360.2.a.dd.1.2		3	4.3	odd	2
9555.2.a.bq.1.1		3	21.20	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

\(f(q)\)	\(=\)	\(q+2.48929 q^{2} +4.19656 q^{4} +1.00000 q^{5} -1.19656 q^{7} +5.46787 q^{8} +O(q^{10})\)	\(q+2.48929 q^{2} +4.19656 q^{4} +1.00000 q^{5} -1.19656 q^{7} +5.46787 q^{8} +2.48929 q^{10} +1.19656 q^{11} +1.00000 q^{13} -2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} +6.97858 q^{19} +4.19656 q^{20} +2.97858 q^{22} -4.17513 q^{23} +1.00000 q^{25} +2.48929 q^{26} -5.02142 q^{28} -6.00000 q^{29} -2.97858 q^{31} +2.05333 q^{32} -15.3717 q^{34} -1.19656 q^{35} +7.78202 q^{37} +17.3717 q^{38} +5.46787 q^{40} +6.17513 q^{41} -9.95715 q^{43} +5.02142 q^{44} -10.3931 q^{46} +1.02142 q^{47} -5.56825 q^{49} +2.48929 q^{50} +4.19656 q^{52} -10.1751 q^{53} +1.19656 q^{55} -6.54262 q^{56} -14.9357 q^{58} -5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} -5.32464 q^{64} +1.00000 q^{65} +9.37169 q^{67} -25.9143 q^{68} -2.97858 q^{70} +5.19656 q^{71} -11.9572 q^{73} +19.3717 q^{74} +29.2860 q^{76} -1.43175 q^{77} -1.78202 q^{79} +5.21798 q^{80} +15.3717 q^{82} +5.37169 q^{83} -6.17513 q^{85} -24.7862 q^{86} +6.54262 q^{88} -10.1751 q^{89} -1.19656 q^{91} -17.5212 q^{92} +2.54262 q^{94} +6.97858 q^{95} -1.82487 q^{97} -13.8610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 8 q^{4} + 3 q^{5} + q^{7} - 6 q^{8}+O(q^{10}) \) 3 * q + 8 * q^4 + 3 * q^5 + q^7 - 6 * q^8	\( 3 q + 8 q^{4} + 3 q^{5} + q^{7} - 6 q^{8} - q^{11} + 3 q^{13} + 6 q^{14} + 26 q^{16} + q^{17} + 6 q^{19} + 8 q^{20} - 6 q^{22} + 7 q^{23} + 3 q^{25} - 30 q^{28} - 18 q^{29} + 6 q^{31} - 22 q^{32} - 22 q^{34} + q^{35} + 13 q^{37} + 28 q^{38} - 6 q^{40} - q^{41} + 30 q^{44} - 22 q^{46} + 18 q^{47} + 12 q^{49} + 8 q^{52} - 11 q^{53} - q^{55} + 16 q^{56} + 8 q^{59} + 9 q^{61} - 28 q^{62} + 30 q^{64} + 3 q^{65} + 4 q^{67} - 18 q^{68} + 6 q^{70} + 11 q^{71} - 6 q^{73} + 34 q^{74} + 4 q^{76} - 33 q^{77} + 5 q^{79} + 26 q^{80} + 22 q^{82} - 8 q^{83} + q^{85} - 56 q^{86} - 16 q^{88} - 11 q^{89} + q^{91} - 2 q^{92} - 28 q^{94} + 6 q^{95} - 25 q^{97} - 10 q^{98}+O(q^{100}) \) 3 * q + 8 * q^4 + 3 * q^5 + q^7 - 6 * q^8 - q^11 + 3 * q^13 + 6 * q^14 + 26 * q^16 + q^17 + 6 * q^19 + 8 * q^20 - 6 * q^22 + 7 * q^23 + 3 * q^25 - 30 * q^28 - 18 * q^29 + 6 * q^31 - 22 * q^32 - 22 * q^34 + q^35 + 13 * q^37 + 28 * q^38 - 6 * q^40 - q^41 + 30 * q^44 - 22 * q^46 + 18 * q^47 + 12 * q^49 + 8 * q^52 - 11 * q^53 - q^55 + 16 * q^56 + 8 * q^59 + 9 * q^61 - 28 * q^62 + 30 * q^64 + 3 * q^65 + 4 * q^67 - 18 * q^68 + 6 * q^70 + 11 * q^71 - 6 * q^73 + 34 * q^74 + 4 * q^76 - 33 * q^77 + 5 * q^79 + 26 * q^80 + 22 * q^82 - 8 * q^83 + q^85 - 56 * q^86 - 16 * q^88 - 11 * q^89 + q^91 - 2 * q^92 - 28 * q^94 + 6 * q^95 - 25 * q^97 - 10 * q^98

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