LMFDB - Embedded newform 2601.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, 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("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 289)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30278 q^{2} +3.30278 q^{4} -2.30278 q^{5} -0.302776 q^{7} +3.00000 q^{8} +O(q^{10})$	$q+2.30278 q^{2} +3.30278 q^{4} -2.30278 q^{5} -0.302776 q^{7} +3.00000 q^{8} -5.30278 q^{10} -3.00000 q^{11} -3.30278 q^{13} -0.697224 q^{14} +0.302776 q^{16} +5.90833 q^{19} -7.60555 q^{20} -6.90833 q^{22} -2.30278 q^{23} +0.302776 q^{25} -7.60555 q^{26} -1.00000 q^{28} -9.90833 q^{29} +3.60555 q^{31} -5.30278 q^{32} +0.697224 q^{35} +0.605551 q^{37} +13.6056 q^{38} -6.90833 q^{40} -6.00000 q^{41} -2.39445 q^{43} -9.90833 q^{44} -5.30278 q^{46} -3.00000 q^{47} -6.90833 q^{49} +0.697224 q^{50} -10.9083 q^{52} -2.09167 q^{53} +6.90833 q^{55} -0.908327 q^{56} -22.8167 q^{58} -6.00000 q^{59} -8.81665 q^{61} +8.30278 q^{62} -12.8167 q^{64} +7.60555 q^{65} +12.6056 q^{67} +1.60555 q^{70} +3.21110 q^{71} +0.394449 q^{73} +1.39445 q^{74} +19.5139 q^{76} +0.908327 q^{77} +11.2111 q^{79} -0.697224 q^{80} -13.8167 q^{82} -2.51388 q^{83} -5.51388 q^{86} -9.00000 q^{88} -3.21110 q^{89} +1.00000 q^{91} -7.60555 q^{92} -6.90833 q^{94} -13.6056 q^{95} -10.9083 q^{97} -15.9083 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{4} - q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + 3 * q^4 - q^5 + 3 * q^7 + 6 * q^8	$ 2 q + q^{2} + 3 q^{4} - q^{5} + 3 q^{7} + 6 q^{8} - 7 q^{10} - 6 q^{11} - 3 q^{13} - 5 q^{14} - 3 q^{16} + q^{19} - 8 q^{20} - 3 q^{22} - q^{23} - 3 q^{25} - 8 q^{26} - 2 q^{28} - 9 q^{29} - 7 q^{32} + 5 q^{35} - 6 q^{37} + 20 q^{38} - 3 q^{40} - 12 q^{41} - 12 q^{43} - 9 q^{44} - 7 q^{46} - 6 q^{47} - 3 q^{49} + 5 q^{50} - 11 q^{52} - 15 q^{53} + 3 q^{55} + 9 q^{56} - 24 q^{58} - 12 q^{59} + 4 q^{61} + 13 q^{62} - 4 q^{64} + 8 q^{65} + 18 q^{67} - 4 q^{70} - 8 q^{71} + 8 q^{73} + 10 q^{74} + 21 q^{76} - 9 q^{77} + 8 q^{79} - 5 q^{80} - 6 q^{82} + 13 q^{83} + 7 q^{86} - 18 q^{88} + 8 q^{89} + 2 q^{91} - 8 q^{92} - 3 q^{94} - 20 q^{95} - 11 q^{97} - 21 q^{98}+O(q^{100}) $ 2 * q + q^2 + 3 * q^4 - q^5 + 3 * q^7 + 6 * q^8 - 7 * q^10 - 6 * q^11 - 3 * q^13 - 5 * q^14 - 3 * q^16 + q^19 - 8 * q^20 - 3 * q^22 - q^23 - 3 * q^25 - 8 * q^26 - 2 * q^28 - 9 * q^29 - 7 * q^32 + 5 * q^35 - 6 * q^37 + 20 * q^38 - 3 * q^40 - 12 * q^41 - 12 * q^43 - 9 * q^44 - 7 * q^46 - 6 * q^47 - 3 * q^49 + 5 * q^50 - 11 * q^52 - 15 * q^53 + 3 * q^55 + 9 * q^56 - 24 * q^58 - 12 * q^59 + 4 * q^61 + 13 * q^62 - 4 * q^64 + 8 * q^65 + 18 * q^67 - 4 * q^70 - 8 * q^71 + 8 * q^73 + 10 * q^74 + 21 * q^76 - 9 * q^77 + 8 * q^79 - 5 * q^80 - 6 * q^82 + 13 * q^83 + 7 * q^86 - 18 * q^88 + 8 * q^89 + 2 * q^91 - 8 * q^92 - 3 * q^94 - 20 * q^95 - 11 * q^97 - 21 * 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 $

$2$	2.30278	1.62831	0.814154	−	0.580649i	$-0.197201\pi$
$2$	2.30278	1.62831	0.814154	+	0.580649i	$0.197201\pi$
$3$	0	0
$3$	0	0
$4$	3.30278	1.65139
$5$	−2.30278	−1.02983	−0.514916	−	0.857240i	$-0.672177\pi$
$5$	−2.30278	−1.02983	−0.514916	+	0.857240i	$0.672177\pi$
$6$	0	0
$7$	−0.302776	−0.114438	−0.0572192	−	0.998362i	$-0.518223\pi$
$7$	−0.302776	−0.114438	−0.0572192	+	0.998362i	$0.518223\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	−5.30278	−1.67688
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−3.30278	−0.916025	−0.458013	−	0.888946i	$-0.651439\pi$
$13$	−3.30278	−0.916025	−0.458013	+	0.888946i	$0.651439\pi$
$14$	−0.697224	−0.186341
$15$	0	0
$16$	0.302776	0.0756939
$17$	0	0
$17$	0	0
$18$	0	0
$19$	5.90833	1.35546	0.677732	−	0.735309i	$-0.262963\pi$
$19$	5.90833	1.35546	0.677732	+	0.735309i	$0.262963\pi$
$20$	−7.60555	−1.70065
$21$	0	0
$22$	−6.90833	−1.47286
$23$	−2.30278	−0.480162	−0.240081	−	0.970753i	$-0.577174\pi$
$23$	−2.30278	−0.480162	−0.240081	+	0.970753i	$0.577174\pi$
$24$	0	0
$25$	0.302776	0.0605551
$26$	−7.60555	−1.49157
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−9.90833	−1.83993	−0.919965	−	0.392000i	$-0.871783\pi$
$29$	−9.90833	−1.83993	−0.919965	+	0.392000i	$0.871783\pi$
$30$	0	0
$31$	3.60555	0.647576	0.323788	−	0.946130i	$-0.395044\pi$
$31$	3.60555	0.647576	0.323788	+	0.946130i	$0.395044\pi$
$32$	−5.30278	−0.937407
$33$	0	0
$34$	0	0
$35$	0.697224	0.117852
$36$	0	0
$37$	0.605551	0.0995520	0.0497760	−	0.998760i	$-0.484149\pi$
$37$	0.605551	0.0995520	0.0497760	+	0.998760i	$0.484149\pi$
$38$	13.6056	2.20711
$39$	0	0
$40$	−6.90833	−1.09230
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−2.39445	−0.365150	−0.182575	−	0.983192i	$-0.558443\pi$
$43$	−2.39445	−0.365150	−0.182575	+	0.983192i	$0.558443\pi$
$44$	−9.90833	−1.49374
$45$	0	0
$46$	−5.30278	−0.781852
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	−6.90833	−0.986904
$50$	0.697224	0.0986024
$51$	0	0
$52$	−10.9083	−1.51271
$53$	−2.09167	−0.287313	−0.143657	−	0.989628i	$-0.545886\pi$
$53$	−2.09167	−0.287313	−0.143657	+	0.989628i	$0.545886\pi$
$54$	0	0
$55$	6.90833	0.931519
$56$	−0.908327	−0.121380
$57$	0	0
$58$	−22.8167	−2.99597
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−8.81665	−1.12886	−0.564428	−	0.825482i	$-0.690903\pi$
$61$	−8.81665	−1.12886	−0.564428	+	0.825482i	$0.690903\pi$
$62$	8.30278	1.05445
$63$	0	0
$64$	−12.8167	−1.60208
$65$	7.60555	0.943353
$66$	0	0
$67$	12.6056	1.54001	0.770007	−	0.638036i	$-0.220253\pi$
$67$	12.6056	1.54001	0.770007	+	0.638036i	$0.220253\pi$
$68$	0	0
$69$	0	0
$70$	1.60555	0.191900
$71$	3.21110	0.381088	0.190544	−	0.981679i	$-0.438975\pi$
$71$	3.21110	0.381088	0.190544	+	0.981679i	$0.438975\pi$
$72$	0	0
$73$	0.394449	0.0461667	0.0230834	−	0.999734i	$-0.492652\pi$
$73$	0.394449	0.0461667	0.0230834	+	0.999734i	$0.492652\pi$
$74$	1.39445	0.162101
$75$	0	0
$76$	19.5139	2.23840
$77$	0.908327	0.103513
$78$	0	0
$79$	11.2111	1.26135	0.630674	−	0.776048i	$-0.282779\pi$
$79$	11.2111	1.26135	0.630674	+	0.776048i	$0.282779\pi$
$80$	−0.697224	−0.0779521
$81$	0	0
$82$	−13.8167	−1.52579
$83$	−2.51388	−0.275934	−0.137967	−	0.990437i	$-0.544057\pi$
$83$	−2.51388	−0.275934	−0.137967	+	0.990437i	$0.544057\pi$
$84$	0	0
$85$	0	0
$86$	−5.51388	−0.594577
$87$	0	0
$88$	−9.00000	−0.959403
$89$	−3.21110	−0.340376	−0.170188	−	0.985412i	$-0.554438\pi$
$89$	−3.21110	−0.340376	−0.170188	+	0.985412i	$0.554438\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−7.60555	−0.792934
$93$	0	0
$94$	−6.90833	−0.712540
$95$	−13.6056	−1.39590
$96$	0	0
$97$	−10.9083	−1.10757	−0.553786	−	0.832659i	$-0.686818\pi$
$97$	−10.9083	−1.10757	−0.553786	+	0.832659i	$0.686818\pi$
$98$	−15.9083	−1.60698
$99$	0	0
$100$	1.00000	0.100000
$101$	4.39445	0.437264	0.218632	−	0.975807i	$-0.429841\pi$
$101$	4.39445	0.437264	0.218632	+	0.975807i	$0.429841\pi$
$102$	0	0
$103$	2.00000	0.197066	0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000	0.197066	0.0985329	+	0.995134i	$0.468585\pi$
$104$	−9.90833	−0.971591
$105$	0	0
$106$	−4.81665	−0.467835
$107$	12.2111	1.18049	0.590246	−	0.807223i	$-0.299031\pi$
$107$	12.2111	1.18049	0.590246	+	0.807223i	$0.299031\pi$
$108$	0	0
$109$	14.2111	1.36118	0.680588	−	0.732666i	$-0.261724\pi$
$109$	14.2111	1.36118	0.680588	+	0.732666i	$0.261724\pi$
$110$	15.9083	1.51680
$111$	0	0
$112$	−0.0916731	−0.00866229
$113$	11.5139	1.08313	0.541567	−	0.840657i	$-0.317831\pi$
$113$	11.5139	1.08313	0.541567	+	0.840657i	$0.317831\pi$
$114$	0	0
$115$	5.30278	0.494486
$116$	−32.7250	−3.03844
$117$	0	0
$118$	−13.8167	−1.27193
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−20.3028	−1.83813
$123$	0	0
$124$	11.9083	1.06940
$125$	10.8167	0.967471
$126$	0	0
$127$	−14.8167	−1.31477	−0.657383	−	0.753557i	$-0.728336\pi$
$127$	−14.8167	−1.31477	−0.657383	+	0.753557i	$0.728336\pi$
$128$	−18.9083	−1.67128
$129$	0	0
$130$	17.5139	1.53607
$131$	4.60555	0.402389	0.201194	−	0.979551i	$-0.435518\pi$
$131$	4.60555	0.402389	0.201194	+	0.979551i	$0.435518\pi$
$132$	0	0
$133$	−1.78890	−0.155117
$134$	29.0278	2.50762
$135$	0	0
$136$	0	0
$137$	1.81665	0.155207	0.0776036	−	0.996984i	$-0.475273\pi$
$137$	1.81665	0.155207	0.0776036	+	0.996984i	$0.475273\pi$
$138$	0	0
$139$	19.5139	1.65515	0.827573	−	0.561358i	$-0.189721\pi$
$139$	19.5139	1.65515	0.827573	+	0.561358i	$0.189721\pi$
$140$	2.30278	0.194620
$141$	0	0
$142$	7.39445	0.620528
$143$	9.90833	0.828576
$144$	0	0
$145$	22.8167	1.89482
$146$	0.908327	0.0751737
$147$	0	0
$148$	2.00000	0.164399
$149$	1.39445	0.114238	0.0571188	−	0.998367i	$-0.481809\pi$
$149$	1.39445	0.114238	0.0571188	+	0.998367i	$0.481809\pi$
$150$	0	0
$151$	5.00000	0.406894	0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000	0.406894	0.203447	+	0.979086i	$0.434786\pi$
$152$	17.7250	1.43769
$153$	0	0
$154$	2.09167	0.168552
$155$	−8.30278	−0.666895
$156$	0	0
$157$	5.69722	0.454688	0.227344	−	0.973815i	$-0.426996\pi$
$157$	5.69722	0.454688	0.227344	+	0.973815i	$0.426996\pi$
$158$	25.8167	2.05386
$159$	0	0
$160$	12.2111	0.965372
$161$	0.697224	0.0549490
$162$	0	0
$163$	−17.6056	−1.37897	−0.689487	−	0.724298i	$-0.742164\pi$
$163$	−17.6056	−1.37897	−0.689487	+	0.724298i	$0.742164\pi$
$164$	−19.8167	−1.54742
$165$	0	0
$166$	−5.78890	−0.449306
$167$	−18.6972	−1.44683	−0.723417	−	0.690411i	$-0.757430\pi$
$167$	−18.6972	−1.44683	−0.723417	+	0.690411i	$0.757430\pi$
$168$	0	0
$169$	−2.09167	−0.160898
$170$	0	0
$171$	0	0
$172$	−7.90833	−0.603004
$173$	7.60555	0.578239	0.289120	−	0.957293i	$-0.406637\pi$
$173$	7.60555	0.578239	0.289120	+	0.957293i	$0.406637\pi$
$174$	0	0
$175$	−0.0916731	−0.00692983
$176$	−0.908327	−0.0684677
$177$	0	0
$178$	−7.39445	−0.554237
$179$	20.7250	1.54906	0.774529	−	0.632539i	$-0.217987\pi$
$179$	20.7250	1.54906	0.774529	+	0.632539i	$0.217987\pi$
$180$	0	0
$181$	−22.2111	−1.65094	−0.825469	−	0.564447i	$-0.809089\pi$
$181$	−22.2111	−1.65094	−0.825469	+	0.564447i	$0.809089\pi$
$182$	2.30278	0.170693
$183$	0	0
$184$	−6.90833	−0.509289
$185$	−1.39445	−0.102522
$186$	0	0
$187$	0	0
$188$	−9.90833	−0.722639
$189$	0	0
$190$	−31.3305	−2.27296
$191$	11.3028	0.817840	0.408920	−	0.912570i	$-0.365905\pi$
$191$	11.3028	0.817840	0.408920	+	0.912570i	$0.365905\pi$
$192$	0	0
$193$	20.6333	1.48522	0.742609	−	0.669725i	$-0.233588\pi$
$193$	20.6333	1.48522	0.742609	+	0.669725i	$0.233588\pi$
$194$	−25.1194	−1.80347
$195$	0	0
$196$	−22.8167	−1.62976
$197$	6.90833	0.492198	0.246099	−	0.969245i	$-0.420851\pi$
$197$	6.90833	0.492198	0.246099	+	0.969245i	$0.420851\pi$
$198$	0	0
$199$	3.60555	0.255591	0.127795	−	0.991801i	$-0.459210\pi$
$199$	3.60555	0.255591	0.127795	+	0.991801i	$0.459210\pi$
$200$	0.908327	0.0642284
$201$	0	0
$202$	10.1194	0.712001
$203$	3.00000	0.210559
$204$	0	0
$205$	13.8167	0.964997
$206$	4.60555	0.320884
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−17.7250	−1.22606
$210$	0	0
$211$	−9.09167	−0.625897	−0.312948	−	0.949770i	$-0.601317\pi$
$211$	−9.09167	−0.625897	−0.312948	+	0.949770i	$0.601317\pi$
$212$	−6.90833	−0.474466
$213$	0	0
$214$	28.1194	1.92220
$215$	5.51388	0.376043
$216$	0	0
$217$	−1.09167	−0.0741076
$218$	32.7250	2.21642
$219$	0	0
$220$	22.8167	1.53830
$221$	0	0
$222$	0	0
$223$	−27.5139	−1.84247	−0.921233	−	0.389012i	$-0.872817\pi$
$223$	−27.5139	−1.84247	−0.921233	+	0.389012i	$0.872817\pi$
$224$	1.60555	0.107275
$225$	0	0
$226$	26.5139	1.76368
$227$	−16.8167	−1.11616	−0.558080	−	0.829787i	$-0.688462\pi$
$227$	−16.8167	−1.11616	−0.558080	+	0.829787i	$0.688462\pi$
$228$	0	0
$229$	−10.4222	−0.688719	−0.344359	−	0.938838i	$-0.611904\pi$
$229$	−10.4222	−0.688719	−0.344359	+	0.938838i	$0.611904\pi$
$230$	12.2111	0.805176
$231$	0	0
$232$	−29.7250	−1.95154
$233$	−4.18335	−0.274060	−0.137030	−	0.990567i	$-0.543756\pi$
$233$	−4.18335	−0.274060	−0.137030	+	0.990567i	$0.543756\pi$
$234$	0	0
$235$	6.90833	0.450650
$236$	−19.8167	−1.28995
$237$	0	0
$238$	0	0
$239$	6.21110	0.401763	0.200881	−	0.979616i	$-0.435619\pi$
$239$	6.21110	0.401763	0.200881	+	0.979616i	$0.435619\pi$
$240$	0	0
$241$	−9.51388	−0.612843	−0.306421	−	0.951896i	$-0.599132\pi$
$241$	−9.51388	−0.612843	−0.306421	+	0.951896i	$0.599132\pi$
$242$	−4.60555	−0.296056
$243$	0	0
$244$	−29.1194	−1.86418
$245$	15.9083	1.01635
$246$	0	0
$247$	−19.5139	−1.24164
$248$	10.8167	0.686858
$249$	0	0
$250$	24.9083	1.57534
$251$	15.9083	1.00412	0.502062	−	0.864831i	$-0.332575\pi$
$251$	15.9083	1.00412	0.502062	+	0.864831i	$0.332575\pi$
$252$	0	0
$253$	6.90833	0.434323
$254$	−34.1194	−2.14084
$255$	0	0
$256$	−17.9083	−1.11927
$257$	−26.7250	−1.66706	−0.833529	−	0.552475i	$-0.813683\pi$
$257$	−26.7250	−1.66706	−0.833529	+	0.552475i	$0.813683\pi$
$258$	0	0
$259$	−0.183346	−0.0113926
$260$	25.1194	1.55784
$261$	0	0
$262$	10.6056	0.655213
$263$	−20.5139	−1.26494	−0.632470	−	0.774585i	$-0.717959\pi$
$263$	−20.5139	−1.26494	−0.632470	+	0.774585i	$0.717959\pi$
$264$	0	0
$265$	4.81665	0.295885
$266$	−4.11943	−0.252578
$267$	0	0
$268$	41.6333	2.54316
$269$	−1.11943	−0.0682528	−0.0341264	−	0.999418i	$-0.510865\pi$
$269$	−1.11943	−0.0682528	−0.0341264	+	0.999418i	$0.510865\pi$
$270$	0	0
$271$	−26.5416	−1.61229	−0.806145	−	0.591718i	$-0.798450\pi$
$271$	−26.5416	−1.61229	−0.806145	+	0.591718i	$0.798450\pi$
$272$	0	0
$273$	0	0
$274$	4.18335	0.252725
$275$	−0.908327	−0.0547742
$276$	0	0
$277$	−4.00000	−0.240337	−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000	−0.240337	−0.120168	+	0.992754i	$0.538343\pi$
$278$	44.9361	2.69509
$279$	0	0
$280$	2.09167	0.125001
$281$	−28.5416	−1.70265	−0.851326	−	0.524638i	$-0.824201\pi$
$281$	−28.5416	−1.70265	−0.851326	+	0.524638i	$0.824201\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	10.6056	0.629324
$285$	0	0
$286$	22.8167	1.34918
$287$	1.81665	0.107234
$288$	0	0
$289$	0	0
$290$	52.5416	3.08535
$291$	0	0
$292$	1.30278	0.0762392
$293$	25.8167	1.50823	0.754113	−	0.656745i	$-0.228067\pi$
$293$	25.8167	1.50823	0.754113	+	0.656745i	$0.228067\pi$
$294$	0	0
$295$	13.8167	0.804437
$296$	1.81665	0.105591
$297$	0	0
$298$	3.21110	0.186014
$299$	7.60555	0.439840
$300$	0	0
$301$	0.724981	0.0417872
$302$	11.5139	0.662549
$303$	0	0
$304$	1.78890	0.102600
$305$	20.3028	1.16253
$306$	0	0
$307$	12.1194	0.691692	0.345846	−	0.938291i	$-0.387592\pi$
$307$	12.1194	0.691692	0.345846	+	0.938291i	$0.387592\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	−19.1194	−1.08591
$311$	−15.4861	−0.878137	−0.439069	−	0.898453i	$-0.644692\pi$
$311$	−15.4861	−0.878137	−0.439069	+	0.898453i	$0.644692\pi$
$312$	0	0
$313$	9.81665	0.554870	0.277435	−	0.960744i	$-0.410516\pi$
$313$	9.81665	0.554870	0.277435	+	0.960744i	$0.410516\pi$
$314$	13.1194	0.740372
$315$	0	0
$316$	37.0278	2.08297
$317$	−23.2389	−1.30522	−0.652612	−	0.757692i	$-0.726327\pi$
$317$	−23.2389	−1.30522	−0.652612	+	0.757692i	$0.726327\pi$
$318$	0	0
$319$	29.7250	1.66428
$320$	29.5139	1.64988
$321$	0	0
$322$	1.60555	0.0894739
$323$	0	0
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	−40.5416	−2.24539
$327$	0	0
$328$	−18.0000	−0.993884
$329$	0.908327	0.0500777
$330$	0	0
$331$	−0.302776	−0.0166421	−0.00832103	−	0.999965i	$-0.502649\pi$
$331$	−0.302776	−0.0166421	−0.00832103	+	0.999965i	$0.502649\pi$
$332$	−8.30278	−0.455674
$333$	0	0
$334$	−43.0555	−2.35589
$335$	−29.0278	−1.58596
$336$	0	0
$337$	22.5139	1.22641	0.613205	−	0.789924i	$-0.289880\pi$
$337$	22.5139	1.22641	0.613205	+	0.789924i	$0.289880\pi$
$338$	−4.81665	−0.261991
$339$	0	0
$340$	0	0
$341$	−10.8167	−0.585755
$342$	0	0
$343$	4.21110	0.227378
$344$	−7.18335	−0.387300
$345$	0	0
$346$	17.5139	0.941552
$347$	17.3028	0.928862	0.464431	−	0.885609i	$-0.346259\pi$
$347$	17.3028	0.928862	0.464431	+	0.885609i	$0.346259\pi$
$348$	0	0
$349$	6.39445	0.342287	0.171143	−	0.985246i	$-0.445254\pi$
$349$	6.39445	0.342287	0.171143	+	0.985246i	$0.445254\pi$
$350$	−0.211103	−0.0112839
$351$	0	0
$352$	15.9083	0.847917
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	−7.39445	−0.392457
$356$	−10.6056	−0.562093
$357$	0	0
$358$	47.7250	2.52234
$359$	11.0917	0.585396	0.292698	−	0.956205i	$-0.405447\pi$
$359$	11.0917	0.585396	0.292698	+	0.956205i	$0.405447\pi$
$360$	0	0
$361$	15.9083	0.837280
$362$	−51.1472	−2.68824
$363$	0	0
$364$	3.30278	0.173112
$365$	−0.908327	−0.0475440
$366$	0	0
$367$	24.6056	1.28440	0.642200	−	0.766537i	$-0.278022\pi$
$367$	24.6056	1.28440	0.642200	+	0.766537i	$0.278022\pi$
$368$	−0.697224	−0.0363453
$369$	0	0
$370$	−3.21110	−0.166937
$371$	0.633308	0.0328797
$372$	0	0
$373$	8.21110	0.425155	0.212577	−	0.977144i	$-0.431814\pi$
$373$	8.21110	0.425155	0.212577	+	0.977144i	$0.431814\pi$
$374$	0	0
$375$	0	0
$376$	−9.00000	−0.464140
$377$	32.7250	1.68542
$378$	0	0
$379$	−8.39445	−0.431194	−0.215597	−	0.976482i	$-0.569170\pi$
$379$	−8.39445	−0.431194	−0.215597	+	0.976482i	$0.569170\pi$
$380$	−44.9361	−2.30517
$381$	0	0
$382$	26.0278	1.33170
$383$	−3.90833	−0.199706	−0.0998531	−	0.995002i	$-0.531837\pi$
$383$	−3.90833	−0.199706	−0.0998531	+	0.995002i	$0.531837\pi$
$384$	0	0
$385$	−2.09167	−0.106602
$386$	47.5139	2.41839
$387$	0	0
$388$	−36.0278	−1.82903
$389$	−12.6333	−0.640534	−0.320267	−	0.947327i	$-0.603773\pi$
$389$	−12.6333	−0.640534	−0.320267	+	0.947327i	$0.603773\pi$
$390$	0	0
$391$	0	0
$392$	−20.7250	−1.04677
$393$	0	0
$394$	15.9083	0.801450
$395$	−25.8167	−1.29898
$396$	0	0
$397$	0.394449	0.0197968	0.00989841	−	0.999951i	$-0.496849\pi$
$397$	0.394449	0.0197968	0.00989841	+	0.999951i	$0.496849\pi$
$398$	8.30278	0.416181
$399$	0	0
$400$	0.0916731	0.00458365
$401$	15.6972	0.783882	0.391941	−	0.919990i	$-0.371804\pi$
$401$	15.6972	0.783882	0.391941	+	0.919990i	$0.371804\pi$
$402$	0	0
$403$	−11.9083	−0.593196
$404$	14.5139	0.722092
$405$	0	0
$406$	6.90833	0.342855
$407$	−1.81665	−0.0900482
$408$	0	0
$409$	−11.1833	−0.552981	−0.276490	−	0.961017i	$-0.589171\pi$
$409$	−11.1833	−0.552981	−0.276490	+	0.961017i	$0.589171\pi$
$410$	31.8167	1.57131
$411$	0	0
$412$	6.60555	0.325432
$413$	1.81665	0.0893917
$414$	0	0
$415$	5.78890	0.284166
$416$	17.5139	0.858689
$417$	0	0
$418$	−40.8167	−1.99641
$419$	−11.7889	−0.575925	−0.287963	−	0.957642i	$-0.592978\pi$
$419$	−11.7889	−0.575925	−0.287963	+	0.957642i	$0.592978\pi$
$420$	0	0
$421$	−27.9361	−1.36152	−0.680761	−	0.732506i	$-0.738351\pi$
$421$	−27.9361	−1.36152	−0.680761	+	0.732506i	$0.738351\pi$
$422$	−20.9361	−1.01915
$423$	0	0
$424$	−6.27502	−0.304742
$425$	0	0
$426$	0	0
$427$	2.66947	0.129185
$428$	40.3305	1.94945
$429$	0	0
$430$	12.6972	0.612315
$431$	−11.0917	−0.534267	−0.267134	−	0.963660i	$-0.586076\pi$
$431$	−11.0917	−0.534267	−0.267134	+	0.963660i	$0.586076\pi$
$432$	0	0
$433$	−28.0000	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$434$	−2.51388	−0.120670
$435$	0	0
$436$	46.9361	2.24783
$437$	−13.6056	−0.650842
$438$	0	0
$439$	−21.0278	−1.00360	−0.501800	−	0.864984i	$-0.667329\pi$
$439$	−21.0278	−1.00360	−0.501800	+	0.864984i	$0.667329\pi$
$440$	20.7250	0.988025
$441$	0	0
$442$	0	0
$443$	35.2389	1.67425	0.837124	−	0.547013i	$-0.184235\pi$
$443$	35.2389	1.67425	0.837124	+	0.547013i	$0.184235\pi$
$444$	0	0
$445$	7.39445	0.350530
$446$	−63.3583	−3.00010
$447$	0	0
$448$	3.88057	0.183340
$449$	8.51388	0.401795	0.200897	−	0.979612i	$-0.435614\pi$
$449$	8.51388	0.401795	0.200897	+	0.979612i	$0.435614\pi$
$450$	0	0
$451$	18.0000	0.847587
$452$	38.0278	1.78868
$453$	0	0
$454$	−38.7250	−1.81745
$455$	−2.30278	−0.107956
$456$	0	0
$457$	−9.51388	−0.445040	−0.222520	−	0.974928i	$-0.571428\pi$
$457$	−9.51388	−0.445040	−0.222520	+	0.974928i	$0.571428\pi$
$458$	−24.0000	−1.12145
$459$	0	0
$460$	17.5139	0.816589
$461$	12.4222	0.578560	0.289280	−	0.957245i	$-0.406584\pi$
$461$	12.4222	0.578560	0.289280	+	0.957245i	$0.406584\pi$
$462$	0	0
$463$	15.8167	0.735062	0.367531	−	0.930011i	$-0.380203\pi$
$463$	15.8167	0.735062	0.367531	+	0.930011i	$0.380203\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−9.63331	−0.446254
$467$	−24.9083	−1.15262	−0.576310	−	0.817231i	$-0.695508\pi$
$467$	−24.9083	−1.15262	−0.576310	+	0.817231i	$0.695508\pi$
$468$	0	0
$469$	−3.81665	−0.176237
$470$	15.9083	0.733796
$471$	0	0
$472$	−18.0000	−0.828517
$473$	7.18335	0.330291
$474$	0	0
$475$	1.78890	0.0820802
$476$	0	0
$477$	0	0
$478$	14.3028	0.654194
$479$	−12.6333	−0.577231	−0.288615	−	0.957445i	$-0.593195\pi$
$479$	−12.6333	−0.577231	−0.288615	+	0.957445i	$0.593195\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	−21.9083	−0.997897
$483$	0	0
$484$	−6.60555	−0.300252
$485$	25.1194	1.14061
$486$	0	0
$487$	−12.0917	−0.547926	−0.273963	−	0.961740i	$-0.588335\pi$
$487$	−12.0917	−0.547926	−0.273963	+	0.961740i	$0.588335\pi$
$488$	−26.4500	−1.19733
$489$	0	0
$490$	36.6333	1.65492
$491$	22.1194	0.998236	0.499118	−	0.866534i	$-0.333657\pi$
$491$	22.1194	0.998236	0.499118	+	0.866534i	$0.333657\pi$
$492$	0	0
$493$	0	0
$494$	−44.9361	−2.02177
$495$	0	0
$496$	1.09167	0.0490176
$497$	−0.972244	−0.0436111
$498$	0	0
$499$	−22.9083	−1.02552	−0.512759	−	0.858533i	$-0.671376\pi$
$499$	−22.9083	−1.02552	−0.512759	+	0.858533i	$0.671376\pi$
$500$	35.7250	1.59767
$501$	0	0
$502$	36.6333	1.63502
$503$	−36.6333	−1.63340	−0.816699	−	0.577064i	$-0.804198\pi$
$503$	−36.6333	−1.63340	−0.816699	+	0.577064i	$0.804198\pi$
$504$	0	0
$505$	−10.1194	−0.450309
$506$	15.9083	0.707211
$507$	0	0
$508$	−48.9361	−2.17119
$509$	−4.39445	−0.194781	−0.0973903	−	0.995246i	$-0.531049\pi$
$509$	−4.39445	−0.194781	−0.0973903	+	0.995246i	$0.531049\pi$
$510$	0	0
$511$	−0.119429	−0.00528325
$512$	−3.42221	−0.151242
$513$	0	0
$514$	−61.5416	−2.71449
$515$	−4.60555	−0.202945
$516$	0	0
$517$	9.00000	0.395820
$518$	−0.422205	−0.0185506
$519$	0	0
$520$	22.8167	1.00058
$521$	12.8444	0.562724	0.281362	−	0.959602i	$-0.409214\pi$
$521$	12.8444	0.562724	0.281362	+	0.959602i	$0.409214\pi$
$522$	0	0
$523$	−13.4222	−0.586912	−0.293456	−	0.955973i	$-0.594805\pi$
$523$	−13.4222	−0.586912	−0.293456	+	0.955973i	$0.594805\pi$
$524$	15.2111	0.664500
$525$	0	0
$526$	−47.2389	−2.05971
$527$	0	0
$528$	0	0
$529$	−17.6972	−0.769445
$530$	11.0917	0.481791
$531$	0	0
$532$	−5.90833	−0.256158
$533$	19.8167	0.858355
$534$	0	0
$535$	−28.1194	−1.21571
$536$	37.8167	1.63343
$537$	0	0
$538$	−2.57779	−0.111137
$539$	20.7250	0.892688
$540$	0	0
$541$	−6.51388	−0.280053	−0.140027	−	0.990148i	$-0.544719\pi$
$541$	−6.51388	−0.280053	−0.140027	+	0.990148i	$0.544719\pi$
$542$	−61.1194	−2.62530
$543$	0	0
$544$	0	0
$545$	−32.7250	−1.40178
$546$	0	0
$547$	25.2389	1.07914	0.539568	−	0.841942i	$-0.318588\pi$
$547$	25.2389	1.07914	0.539568	+	0.841942i	$0.318588\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	−2.09167	−0.0891892
$551$	−58.5416	−2.49396
$552$	0	0
$553$	−3.39445	−0.144347
$554$	−9.21110	−0.391342
$555$	0	0
$556$	64.4500	2.73329
$557$	−27.6333	−1.17086	−0.585430	−	0.810723i	$-0.699074\pi$
$557$	−27.6333	−1.17086	−0.585430	+	0.810723i	$0.699074\pi$
$558$	0	0
$559$	7.90833	0.334487
$560$	0.211103	0.00892071
$561$	0	0
$562$	−65.7250	−2.77244
$563$	−16.6056	−0.699841	−0.349920	−	0.936779i	$-0.613791\pi$
$563$	−16.6056	−0.699841	−0.349920	+	0.936779i	$0.613791\pi$
$564$	0	0
$565$	−26.5139	−1.11545
$566$	46.0555	1.93586
$567$	0	0
$568$	9.63331	0.404205
$569$	−10.3944	−0.435758	−0.217879	−	0.975976i	$-0.569914\pi$
$569$	−10.3944	−0.435758	−0.217879	+	0.975976i	$0.569914\pi$
$570$	0	0
$571$	−7.48612	−0.313284	−0.156642	−	0.987655i	$-0.550067\pi$
$571$	−7.48612	−0.313284	−0.156642	+	0.987655i	$0.550067\pi$
$572$	32.7250	1.36830
$573$	0	0
$574$	4.18335	0.174609
$575$	−0.697224	−0.0290763
$576$	0	0
$577$	37.2389	1.55027	0.775137	−	0.631793i	$-0.217681\pi$
$577$	37.2389	1.55027	0.775137	+	0.631793i	$0.217681\pi$
$578$	0	0
$579$	0	0
$580$	75.3583	3.12908
$581$	0.761141	0.0315775
$582$	0	0
$583$	6.27502	0.259885
$584$	1.18335	0.0489672
$585$	0	0
$586$	59.4500	2.45586
$587$	4.88057	0.201443	0.100721	−	0.994915i	$-0.467885\pi$
$587$	4.88057	0.201443	0.100721	+	0.994915i	$0.467885\pi$
$588$	0	0
$589$	21.3028	0.877766
$590$	31.8167	1.30987
$591$	0	0
$592$	0.183346	0.00753548
$593$	36.6333	1.50435	0.752175	−	0.658964i	$-0.229005\pi$
$593$	36.6333	1.50435	0.752175	+	0.658964i	$0.229005\pi$
$594$	0	0
$595$	0	0
$596$	4.60555	0.188651
$597$	0	0
$598$	17.5139	0.716196
$599$	12.6333	0.516183	0.258091	−	0.966120i	$-0.416906\pi$
$599$	12.6333	0.516183	0.258091	+	0.966120i	$0.416906\pi$
$600$	0	0
$601$	−27.3028	−1.11370	−0.556852	−	0.830612i	$-0.687991\pi$
$601$	−27.3028	−1.11370	−0.556852	+	0.830612i	$0.687991\pi$
$602$	1.66947	0.0680424
$603$	0	0
$604$	16.5139	0.671940
$605$	4.60555	0.187242
$606$	0	0
$607$	−16.6333	−0.675125	−0.337563	−	0.941303i	$-0.609602\pi$
$607$	−16.6333	−0.675125	−0.337563	+	0.941303i	$0.609602\pi$
$608$	−31.3305	−1.27062
$609$	0	0
$610$	46.7527	1.89296
$611$	9.90833	0.400848
$612$	0	0
$613$	−27.0278	−1.09164	−0.545820	−	0.837902i	$-0.683782\pi$
$613$	−27.0278	−1.09164	−0.545820	+	0.837902i	$0.683782\pi$
$614$	27.9083	1.12629
$615$	0	0
$616$	2.72498	0.109793
$617$	21.0000	0.845428	0.422714	−	0.906263i	$-0.361077\pi$
$617$	21.0000	0.845428	0.422714	+	0.906263i	$0.361077\pi$
$618$	0	0
$619$	−35.0555	−1.40900	−0.704500	−	0.709704i	$-0.748829\pi$
$619$	−35.0555	−1.40900	−0.704500	+	0.709704i	$0.748829\pi$
$620$	−27.4222	−1.10130
$621$	0	0
$622$	−35.6611	−1.42988
$623$	0.972244	0.0389521
$624$	0	0
$625$	−26.4222	−1.05689
$626$	22.6056	0.903500
$627$	0	0
$628$	18.8167	0.750866
$629$	0	0
$630$	0	0
$631$	26.1472	1.04090	0.520452	−	0.853891i	$-0.325764\pi$
$631$	26.1472	1.04090	0.520452	+	0.853891i	$0.325764\pi$
$632$	33.6333	1.33786
$633$	0	0
$634$	−53.5139	−2.12531
$635$	34.1194	1.35399
$636$	0	0
$637$	22.8167	0.904029
$638$	68.4500	2.70996
$639$	0	0
$640$	43.5416	1.72113
$641$	−9.90833	−0.391355	−0.195678	−	0.980668i	$-0.562691\pi$
$641$	−9.90833	−0.391355	−0.195678	+	0.980668i	$0.562691\pi$
$642$	0	0
$643$	−29.8167	−1.17585	−0.587927	−	0.808914i	$-0.700056\pi$
$643$	−29.8167	−1.17585	−0.587927	+	0.808914i	$0.700056\pi$
$644$	2.30278	0.0907421
$645$	0	0
$646$	0	0
$647$	−43.0555	−1.69269	−0.846343	−	0.532638i	$-0.821201\pi$
$647$	−43.0555	−1.69269	−0.846343	+	0.532638i	$0.821201\pi$
$648$	0	0
$649$	18.0000	0.706562
$650$	−2.30278	−0.0903223
$651$	0	0
$652$	−58.1472	−2.27722
$653$	7.18335	0.281106	0.140553	−	0.990073i	$-0.455112\pi$
$653$	7.18335	0.281106	0.140553	+	0.990073i	$0.455112\pi$
$654$	0	0
$655$	−10.6056	−0.414393
$656$	−1.81665	−0.0709284
$657$	0	0
$658$	2.09167	0.0815419
$659$	43.6056	1.69863	0.849316	−	0.527885i	$-0.177015\pi$
$659$	43.6056	1.69863	0.849316	+	0.527885i	$0.177015\pi$
$660$	0	0
$661$	−0.724981	−0.0281985	−0.0140992	−	0.999901i	$-0.504488\pi$
$661$	−0.724981	−0.0281985	−0.0140992	+	0.999901i	$0.504488\pi$
$662$	−0.697224	−0.0270984
$663$	0	0
$664$	−7.54163	−0.292672
$665$	4.11943	0.159745
$666$	0	0
$667$	22.8167	0.883464
$668$	−61.7527	−2.38929
$669$	0	0
$670$	−66.8444	−2.58242
$671$	26.4500	1.02109
$672$	0	0
$673$	4.36669	0.168324	0.0841618	−	0.996452i	$-0.473179\pi$
$673$	4.36669	0.168324	0.0841618	+	0.996452i	$0.473179\pi$
$674$	51.8444	1.99697
$675$	0	0
$676$	−6.90833	−0.265705
$677$	−9.90833	−0.380808	−0.190404	−	0.981706i	$-0.560980\pi$
$677$	−9.90833	−0.380808	−0.190404	+	0.981706i	$0.560980\pi$
$678$	0	0
$679$	3.30278	0.126749
$680$	0	0
$681$	0	0
$682$	−24.9083	−0.953789
$683$	46.7527	1.78894	0.894472	−	0.447124i	$-0.147552\pi$
$683$	46.7527	1.78894	0.894472	+	0.447124i	$0.147552\pi$
$684$	0	0
$685$	−4.18335	−0.159837
$686$	9.69722	0.370242
$687$	0	0
$688$	−0.724981	−0.0276396
$689$	6.90833	0.263186
$690$	0	0
$691$	2.42221	0.0921450	0.0460725	−	0.998938i	$-0.485329\pi$
$691$	2.42221	0.0921450	0.0460725	+	0.998938i	$0.485329\pi$
$692$	25.1194	0.954897
$693$	0	0
$694$	39.8444	1.51247
$695$	−44.9361	−1.70452
$696$	0	0
$697$	0	0
$698$	14.7250	0.557349
$699$	0	0
$700$	−0.302776	−0.0114438
$701$	−36.6333	−1.38362	−0.691810	−	0.722079i	$-0.743187\pi$
$701$	−36.6333	−1.38362	−0.691810	+	0.722079i	$0.743187\pi$
$702$	0	0
$703$	3.57779	0.134939
$704$	38.4500	1.44914
$705$	0	0
$706$	−6.90833	−0.259998
$707$	−1.33053	−0.0500398
$708$	0	0
$709$	2.27502	0.0854401	0.0427201	−	0.999087i	$-0.486398\pi$
$709$	2.27502	0.0854401	0.0427201	+	0.999087i	$0.486398\pi$
$710$	−17.0278	−0.639040
$711$	0	0
$712$	−9.63331	−0.361023
$713$	−8.30278	−0.310941
$714$	0	0
$715$	−22.8167	−0.853294
$716$	68.4500	2.55810
$717$	0	0
$718$	25.5416	0.953205
$719$	−34.3944	−1.28270	−0.641348	−	0.767250i	$-0.721625\pi$
$719$	−34.3944	−1.28270	−0.641348	+	0.767250i	$0.721625\pi$
$720$	0	0
$721$	−0.605551	−0.0225519
$722$	36.6333	1.36335
$723$	0	0
$724$	−73.3583	−2.72634
$725$	−3.00000	−0.111417
$726$	0	0
$727$	28.7889	1.06772	0.533861	−	0.845573i	$-0.320741\pi$
$727$	28.7889	1.06772	0.533861	+	0.845573i	$0.320741\pi$
$728$	3.00000	0.111187
$729$	0	0
$730$	−2.09167	−0.0774163
$731$	0	0
$732$	0	0
$733$	14.6972	0.542854	0.271427	−	0.962459i	$-0.412504\pi$
$733$	14.6972	0.542854	0.271427	+	0.962459i	$0.412504\pi$
$734$	56.6611	2.09140
$735$	0	0
$736$	12.2111	0.450107
$737$	−37.8167	−1.39299
$738$	0	0
$739$	5.42221	0.199459	0.0997295	−	0.995015i	$-0.468202\pi$
$739$	5.42221	0.199459	0.0997295	+	0.995015i	$0.468202\pi$
$740$	−4.60555	−0.169303
$741$	0	0
$742$	1.45837	0.0535383
$743$	−28.8167	−1.05718	−0.528590	−	0.848877i	$-0.677279\pi$
$743$	−28.8167	−1.05718	−0.528590	+	0.848877i	$0.677279\pi$
$744$	0	0
$745$	−3.21110	−0.117646
$746$	18.9083	0.692283
$747$	0	0
$748$	0	0
$749$	−3.69722	−0.135094
$750$	0	0
$751$	−44.2666	−1.61531	−0.807656	−	0.589654i	$-0.799264\pi$
$751$	−44.2666	−1.61531	−0.807656	+	0.589654i	$0.799264\pi$
$752$	−0.908327	−0.0331233
$753$	0	0
$754$	75.3583	2.74439
$755$	−11.5139	−0.419033
$756$	0	0
$757$	−40.2111	−1.46150	−0.730749	−	0.682647i	$-0.760829\pi$
$757$	−40.2111	−1.46150	−0.730749	+	0.682647i	$0.760829\pi$
$758$	−19.3305	−0.702117
$759$	0	0
$760$	−40.8167	−1.48058
$761$	−11.7889	−0.427347	−0.213674	−	0.976905i	$-0.568543\pi$
$761$	−11.7889	−0.427347	−0.213674	+	0.976905i	$0.568543\pi$
$762$	0	0
$763$	−4.30278	−0.155771
$764$	37.3305	1.35057
$765$	0	0
$766$	−9.00000	−0.325183
$767$	19.8167	0.715538
$768$	0	0
$769$	−18.9361	−0.682853	−0.341426	−	0.939909i	$-0.610910\pi$
$769$	−18.9361	−0.682853	−0.341426	+	0.939909i	$0.610910\pi$
$770$	−4.81665	−0.173580
$771$	0	0
$772$	68.1472	2.45267
$773$	−21.8444	−0.785689	−0.392844	−	0.919605i	$-0.628509\pi$
$773$	−21.8444	−0.785689	−0.392844	+	0.919605i	$0.628509\pi$
$774$	0	0
$775$	1.09167	0.0392141
$776$	−32.7250	−1.17476
$777$	0	0
$778$	−29.0917	−1.04299
$779$	−35.4500	−1.27013
$780$	0	0
$781$	−9.63331	−0.344707
$782$	0	0
$783$	0	0
$784$	−2.09167	−0.0747026
$785$	−13.1194	−0.468253
$786$	0	0
$787$	−33.0278	−1.17731	−0.588656	−	0.808384i	$-0.700343\pi$
$787$	−33.0278	−1.17731	−0.588656	+	0.808384i	$0.700343\pi$
$788$	22.8167	0.812810
$789$	0	0
$790$	−59.4500	−2.11513
$791$	−3.48612	−0.123952
$792$	0	0
$793$	29.1194	1.03406
$794$	0.908327	0.0322353
$795$	0	0
$796$	11.9083	0.422079
$797$	45.4222	1.60894	0.804469	−	0.593995i	$-0.202450\pi$
$797$	45.4222	1.60894	0.804469	+	0.593995i	$0.202450\pi$
$798$	0	0
$799$	0	0
$800$	−1.60555	−0.0567648
$801$	0	0
$802$	36.1472	1.27640
$803$	−1.18335	−0.0417594
$804$	0	0
$805$	−1.60555	−0.0565882
$806$	−27.4222	−0.965906
$807$	0	0
$808$	13.1833	0.463788
$809$	17.0278	0.598664	0.299332	−	0.954149i	$-0.403236\pi$
$809$	17.0278	0.598664	0.299332	+	0.954149i	$0.403236\pi$
$810$	0	0
$811$	28.2389	0.991600	0.495800	−	0.868437i	$-0.334875\pi$
$811$	28.2389	0.991600	0.495800	+	0.868437i	$0.334875\pi$
$812$	9.90833	0.347714
$813$	0	0
$814$	−4.18335	−0.146626
$815$	40.5416	1.42011
$816$	0	0
$817$	−14.1472	−0.494947
$818$	−25.7527	−0.900423
$819$	0	0
$820$	45.6333	1.59358
$821$	−16.8167	−0.586905	−0.293453	−	0.955974i	$-0.594804\pi$
$821$	−16.8167	−0.586905	−0.293453	+	0.955974i	$0.594804\pi$
$822$	0	0
$823$	34.4500	1.20085	0.600425	−	0.799681i	$-0.294998\pi$
$823$	34.4500	1.20085	0.600425	+	0.799681i	$0.294998\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	4.18335	0.145557
$827$	−14.4500	−0.502474	−0.251237	−	0.967926i	$-0.580837\pi$
$827$	−14.4500	−0.502474	−0.251237	+	0.967926i	$0.580837\pi$
$828$	0	0
$829$	31.4500	1.09230	0.546151	−	0.837687i	$-0.316092\pi$
$829$	31.4500	1.09230	0.546151	+	0.837687i	$0.316092\pi$
$830$	13.3305	0.462710
$831$	0	0
$832$	42.3305	1.46755
$833$	0	0
$834$	0	0
$835$	43.0555	1.49000
$836$	−58.5416	−2.02470
$837$	0	0
$838$	−27.1472	−0.937784
$839$	−50.2389	−1.73444	−0.867219	−	0.497927i	$-0.834095\pi$
$839$	−50.2389	−1.73444	−0.867219	+	0.497927i	$0.834095\pi$
$840$	0	0
$841$	69.1749	2.38534
$842$	−64.3305	−2.21698
$843$	0	0
$844$	−30.0278	−1.03360
$845$	4.81665	0.165698
$846$	0	0
$847$	0.605551	0.0208070
$848$	−0.633308	−0.0217479
$849$	0	0
$850$	0	0
$851$	−1.39445	−0.0478011
$852$	0	0
$853$	5.00000	0.171197	0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000	0.171197	0.0855984	+	0.996330i	$0.472720\pi$
$854$	6.14719	0.210352
$855$	0	0
$856$	36.6333	1.25210
$857$	15.9722	0.545601	0.272801	−	0.962071i	$-0.412050\pi$
$857$	15.9722	0.545601	0.272801	+	0.962071i	$0.412050\pi$
$858$	0	0
$859$	48.6056	1.65840	0.829200	−	0.558952i	$-0.188796\pi$
$859$	48.6056	1.65840	0.829200	+	0.558952i	$0.188796\pi$
$860$	18.2111	0.620993
$861$	0	0
$862$	−25.5416	−0.869952
$863$	49.3305	1.67923	0.839615	−	0.543181i	$-0.182780\pi$
$863$	49.3305	1.67923	0.839615	+	0.543181i	$0.182780\pi$
$864$	0	0
$865$	−17.5139	−0.595490
$866$	−64.4777	−2.19104
$867$	0	0
$868$	−3.60555	−0.122380
$869$	−33.6333	−1.14093
$870$	0	0
$871$	−41.6333	−1.41069
$872$	42.6333	1.44375
$873$	0	0
$874$	−31.3305	−1.05977
$875$	−3.27502	−0.110716
$876$	0	0
$877$	−11.8806	−0.401178	−0.200589	−	0.979675i	$-0.564286\pi$
$877$	−11.8806	−0.401178	−0.200589	+	0.979675i	$0.564286\pi$
$878$	−48.4222	−1.63417
$879$	0	0
$880$	2.09167	0.0705103
$881$	19.1194	0.644150	0.322075	−	0.946714i	$-0.395620\pi$
$881$	19.1194	0.644150	0.322075	+	0.946714i	$0.395620\pi$
$882$	0	0
$883$	−10.6972	−0.359990	−0.179995	−	0.983668i	$-0.557608\pi$
$883$	−10.6972	−0.359990	−0.179995	+	0.983668i	$0.557608\pi$
$884$	0	0
$885$	0	0
$886$	81.1472	2.72619
$887$	−44.7250	−1.50172	−0.750859	−	0.660463i	$-0.770360\pi$
$887$	−44.7250	−1.50172	−0.750859	+	0.660463i	$0.770360\pi$
$888$	0	0
$889$	4.48612	0.150460
$890$	17.0278	0.570772
$891$	0	0
$892$	−90.8722	−3.04263
$893$	−17.7250	−0.593144
$894$	0	0
$895$	−47.7250	−1.59527
$896$	5.72498	0.191258
$897$	0	0
$898$	19.6056	0.654246
$899$	−35.7250	−1.19149
$900$	0	0
$901$	0	0
$902$	41.4500	1.38013
$903$	0	0
$904$	34.5416	1.14884
$905$	51.1472	1.70019
$906$	0	0
$907$	−47.5416	−1.57859	−0.789297	−	0.614012i	$-0.789555\pi$
$907$	−47.5416	−1.57859	−0.789297	+	0.614012i	$0.789555\pi$
$908$	−55.5416	−1.84321
$909$	0	0
$910$	−5.30278	−0.175785
$911$	−1.88057	−0.0623061	−0.0311530	−	0.999515i	$-0.509918\pi$
$911$	−1.88057	−0.0623061	−0.0311530	+	0.999515i	$0.509918\pi$
$912$	0	0
$913$	7.54163	0.249592
$914$	−21.9083	−0.724663
$915$	0	0
$916$	−34.4222	−1.13734
$917$	−1.39445	−0.0460488
$918$	0	0
$919$	25.3028	0.834662	0.417331	−	0.908755i	$-0.362966\pi$
$919$	25.3028	0.834662	0.417331	+	0.908755i	$0.362966\pi$
$920$	15.9083	0.524482
$921$	0	0
$922$	28.6056	0.942074
$923$	−10.6056	−0.349086
$924$	0	0
$925$	0.183346	0.00602839
$926$	36.4222	1.19691
$927$	0	0
$928$	52.5416	1.72476
$929$	−59.7250	−1.95951	−0.979757	−	0.200193i	$-0.935843\pi$
$929$	−59.7250	−1.95951	−0.979757	+	0.200193i	$0.935843\pi$
$930$	0	0
$931$	−40.8167	−1.33771
$932$	−13.8167	−0.452580
$933$	0	0
$934$	−57.3583	−1.87682
$935$	0	0
$936$	0	0
$937$	−47.7527	−1.56001	−0.780007	−	0.625771i	$-0.784785\pi$
$937$	−47.7527	−1.56001	−0.780007	+	0.625771i	$0.784785\pi$
$938$	−8.78890	−0.286968
$939$	0	0
$940$	22.8167	0.744197
$941$	−48.9083	−1.59437	−0.797183	−	0.603738i	$-0.793677\pi$
$941$	−48.9083	−1.59437	−0.797183	+	0.603738i	$0.793677\pi$
$942$	0	0
$943$	13.8167	0.449932
$944$	−1.81665	−0.0591270
$945$	0	0
$946$	16.5416	0.537815
$947$	26.5778	0.863662	0.431831	−	0.901954i	$-0.357868\pi$
$947$	26.5778	0.863662	0.431831	+	0.901954i	$0.357868\pi$
$948$	0	0
$949$	−1.30278	−0.0422899
$950$	4.11943	0.133652
$951$	0	0
$952$	0	0
$953$	0.486122	0.0157470	0.00787352	−	0.999969i	$-0.497494\pi$
$953$	0.486122	0.0157470	0.00787352	+	0.999969i	$0.497494\pi$
$954$	0	0
$955$	−26.0278	−0.842238
$956$	20.5139	0.663466
$957$	0	0
$958$	−29.0917	−0.939909
$959$	−0.550039	−0.0177617
$960$	0	0
$961$	−18.0000	−0.580645
$962$	−4.60555	−0.148489
$963$	0	0
$964$	−31.4222	−1.01204
$965$	−47.5139	−1.52953
$966$	0	0
$967$	1.93608	0.0622602	0.0311301	−	0.999515i	$-0.490089\pi$
$967$	1.93608	0.0622602	0.0311301	+	0.999515i	$0.490089\pi$
$968$	−6.00000	−0.192847
$969$	0	0
$970$	57.8444	1.85727
$971$	−15.2750	−0.490199	−0.245099	−	0.969498i	$-0.578821\pi$
$971$	−15.2750	−0.490199	−0.245099	+	0.969498i	$0.578821\pi$
$972$	0	0
$973$	−5.90833	−0.189412
$974$	−27.8444	−0.892192
$975$	0	0
$976$	−2.66947	−0.0854476
$977$	37.5416	1.20106	0.600532	−	0.799601i	$-0.294956\pi$
$977$	37.5416	1.20106	0.600532	+	0.799601i	$0.294956\pi$
$978$	0	0
$979$	9.63331	0.307882
$980$	52.5416	1.67838
$981$	0	0
$982$	50.9361	1.62544
$983$	33.6333	1.07274	0.536368	−	0.843984i	$-0.319796\pi$
$983$	33.6333	1.07274	0.536368	+	0.843984i	$0.319796\pi$
$984$	0	0
$985$	−15.9083	−0.506881
$986$	0	0
$987$	0	0
$988$	−64.4500	−2.05043
$989$	5.51388	0.175331
$990$	0	0
$991$	30.7527	0.976893	0.488446	−	0.872594i	$-0.337564\pi$
$991$	30.7527	0.976893	0.488446	+	0.872594i	$0.337564\pi$
$992$	−19.1194	−0.607042
$993$	0	0
$994$	−2.23886	−0.0710123
$995$	−8.30278	−0.263216
$996$	0	0
$997$	−41.1194	−1.30227	−0.651133	−	0.758964i	$-0.725706\pi$
$997$	−41.1194	−1.30227	−0.651133	+	0.758964i	$0.725706\pi$
$998$	−52.7527	−1.66986
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.r.1.2		2
3.2	odd	2		289.2.a.c.1.1	yes	2
12.11	even	2		4624.2.a.j.1.2		2
15.14	odd	2		7225.2.a.m.1.2		2
17.16	even	2		2601.2.a.s.1.2		2
51.2	odd	8		289.2.c.b.38.1		8
51.5	even	16		289.2.d.e.110.4		16
51.8	odd	8		289.2.c.b.251.4		8
51.11	even	16		289.2.d.e.155.2		16
51.14	even	16		289.2.d.e.179.2		16
51.20	even	16		289.2.d.e.179.1		16
51.23	even	16		289.2.d.e.155.1		16
51.26	odd	8		289.2.c.b.251.3		8
51.29	even	16		289.2.d.e.110.3		16
51.32	odd	8		289.2.c.b.38.2		8
51.38	odd	4		289.2.b.c.288.4		4
51.41	even	16		289.2.d.e.134.4		16
51.44	even	16		289.2.d.e.134.3		16
51.47	odd	4		289.2.b.c.288.3		4
51.50	odd	2		289.2.a.b.1.1	✓	2
204.203	even	2		4624.2.a.v.1.1		2
255.254	odd	2		7225.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.b.1.1	✓	2	51.50	odd	2
289.2.a.c.1.1	yes	2	3.2	odd	2
289.2.b.c.288.3		4	51.47	odd	4
289.2.b.c.288.4		4	51.38	odd	4
289.2.c.b.38.1		8	51.2	odd	8
289.2.c.b.38.2		8	51.32	odd	8
289.2.c.b.251.3		8	51.26	odd	8
289.2.c.b.251.4		8	51.8	odd	8
289.2.d.e.110.3		16	51.29	even	16
289.2.d.e.110.4		16	51.5	even	16
289.2.d.e.134.3		16	51.44	even	16
289.2.d.e.134.4		16	51.41	even	16
289.2.d.e.155.1		16	51.23	even	16
289.2.d.e.155.2		16	51.11	even	16
289.2.d.e.179.1		16	51.20	even	16
289.2.d.e.179.2		16	51.14	even	16
2601.2.a.r.1.2		2	1.1	even	1	trivial
2601.2.a.s.1.2		2	17.16	even	2
4624.2.a.j.1.2		2	12.11	even	2
4624.2.a.v.1.1		2	204.203	even	2
7225.2.a.m.1.2		2	15.14	odd	2
7225.2.a.n.1.2		2	255.254	odd	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q+2.30278 q^{2} +3.30278 q^{4} -2.30278 q^{5} -0.302776 q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+2.30278 q^{2} +3.30278 q^{4} -2.30278 q^{5} -0.302776 q^{7} +3.00000 q^{8} -5.30278 q^{10} -3.00000 q^{11} -3.30278 q^{13} -0.697224 q^{14} +0.302776 q^{16} +5.90833 q^{19} -7.60555 q^{20} -6.90833 q^{22} -2.30278 q^{23} +0.302776 q^{25} -7.60555 q^{26} -1.00000 q^{28} -9.90833 q^{29} +3.60555 q^{31} -5.30278 q^{32} +0.697224 q^{35} +0.605551 q^{37} +13.6056 q^{38} -6.90833 q^{40} -6.00000 q^{41} -2.39445 q^{43} -9.90833 q^{44} -5.30278 q^{46} -3.00000 q^{47} -6.90833 q^{49} +0.697224 q^{50} -10.9083 q^{52} -2.09167 q^{53} +6.90833 q^{55} -0.908327 q^{56} -22.8167 q^{58} -6.00000 q^{59} -8.81665 q^{61} +8.30278 q^{62} -12.8167 q^{64} +7.60555 q^{65} +12.6056 q^{67} +1.60555 q^{70} +3.21110 q^{71} +0.394449 q^{73} +1.39445 q^{74} +19.5139 q^{76} +0.908327 q^{77} +11.2111 q^{79} -0.697224 q^{80} -13.8167 q^{82} -2.51388 q^{83} -5.51388 q^{86} -9.00000 q^{88} -3.21110 q^{89} +1.00000 q^{91} -7.60555 q^{92} -6.90833 q^{94} -13.6056 q^{95} -10.9083 q^{97} -15.9083 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{4} - q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + 3 * q^4 - q^5 + 3 * q^7 + 6 * q^8	\( 2 q + q^{2} + 3 q^{4} - q^{5} + 3 q^{7} + 6 q^{8} - 7 q^{10} - 6 q^{11} - 3 q^{13} - 5 q^{14} - 3 q^{16} + q^{19} - 8 q^{20} - 3 q^{22} - q^{23} - 3 q^{25} - 8 q^{26} - 2 q^{28} - 9 q^{29} - 7 q^{32} + 5 q^{35} - 6 q^{37} + 20 q^{38} - 3 q^{40} - 12 q^{41} - 12 q^{43} - 9 q^{44} - 7 q^{46} - 6 q^{47} - 3 q^{49} + 5 q^{50} - 11 q^{52} - 15 q^{53} + 3 q^{55} + 9 q^{56} - 24 q^{58} - 12 q^{59} + 4 q^{61} + 13 q^{62} - 4 q^{64} + 8 q^{65} + 18 q^{67} - 4 q^{70} - 8 q^{71} + 8 q^{73} + 10 q^{74} + 21 q^{76} - 9 q^{77} + 8 q^{79} - 5 q^{80} - 6 q^{82} + 13 q^{83} + 7 q^{86} - 18 q^{88} + 8 q^{89} + 2 q^{91} - 8 q^{92} - 3 q^{94} - 20 q^{95} - 11 q^{97} - 21 q^{98}+O(q^{100}) \) 2 * q + q^2 + 3 * q^4 - q^5 + 3 * q^7 + 6 * q^8 - 7 * q^10 - 6 * q^11 - 3 * q^13 - 5 * q^14 - 3 * q^16 + q^19 - 8 * q^20 - 3 * q^22 - q^23 - 3 * q^25 - 8 * q^26 - 2 * q^28 - 9 * q^29 - 7 * q^32 + 5 * q^35 - 6 * q^37 + 20 * q^38 - 3 * q^40 - 12 * q^41 - 12 * q^43 - 9 * q^44 - 7 * q^46 - 6 * q^47 - 3 * q^49 + 5 * q^50 - 11 * q^52 - 15 * q^53 + 3 * q^55 + 9 * q^56 - 24 * q^58 - 12 * q^59 + 4 * q^61 + 13 * q^62 - 4 * q^64 + 8 * q^65 + 18 * q^67 - 4 * q^70 - 8 * q^71 + 8 * q^73 + 10 * q^74 + 21 * q^76 - 9 * q^77 + 8 * q^79 - 5 * q^80 - 6 * q^82 + 13 * q^83 + 7 * q^86 - 18 * q^88 + 8 * q^89 + 2 * q^91 - 8 * q^92 - 3 * q^94 - 20 * q^95 - 11 * q^97 - 21 * q^98

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