LMFDB - Embedded newform 1805.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} +O(q^{10})$	$q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} -2.23607 q^{10} -4.47214 q^{13} -4.47214 q^{14} -1.00000 q^{16} -2.00000 q^{17} -6.70820 q^{18} -3.00000 q^{20} +6.00000 q^{23} +1.00000 q^{25} -10.0000 q^{26} -6.00000 q^{28} -8.94427 q^{29} +8.94427 q^{31} -6.70820 q^{32} -4.47214 q^{34} +2.00000 q^{35} -9.00000 q^{36} -4.47214 q^{37} -2.23607 q^{40} -8.94427 q^{41} -6.00000 q^{43} +3.00000 q^{45} +13.4164 q^{46} -2.00000 q^{47} -3.00000 q^{49} +2.23607 q^{50} -13.4164 q^{52} +4.47214 q^{53} -4.47214 q^{56} -20.0000 q^{58} +8.94427 q^{59} -10.0000 q^{61} +20.0000 q^{62} +6.00000 q^{63} -13.0000 q^{64} +4.47214 q^{65} -6.00000 q^{68} +4.47214 q^{70} +8.94427 q^{71} -6.70820 q^{72} +14.0000 q^{73} -10.0000 q^{74} +8.94427 q^{79} +1.00000 q^{80} +9.00000 q^{81} -20.0000 q^{82} +14.0000 q^{83} +2.00000 q^{85} -13.4164 q^{86} -8.94427 q^{89} +6.70820 q^{90} +8.94427 q^{91} +18.0000 q^{92} -4.47214 q^{94} +13.4164 q^{97} -6.70820 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 6 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^9	$ 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9} - 2 q^{16} - 4 q^{17} - 6 q^{20} + 12 q^{23} + 2 q^{25} - 20 q^{26} - 12 q^{28} + 4 q^{35} - 18 q^{36} - 12 q^{43} + 6 q^{45} - 4 q^{47} - 6 q^{49} - 40 q^{58} - 20 q^{61} + 40 q^{62} + 12 q^{63} - 26 q^{64} - 12 q^{68} + 28 q^{73} - 20 q^{74} + 2 q^{80} + 18 q^{81} - 40 q^{82} + 28 q^{83} + 4 q^{85} + 36 q^{92}+O(q^{100}) $ 2 * q + 6 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^9 - 2 * q^16 - 4 * q^17 - 6 * q^20 + 12 * q^23 + 2 * q^25 - 20 * q^26 - 12 * q^28 + 4 * q^35 - 18 * q^36 - 12 * q^43 + 6 * q^45 - 4 * q^47 - 6 * q^49 - 40 * q^58 - 20 * q^61 + 40 * q^62 + 12 * q^63 - 26 * q^64 - 12 * q^68 + 28 * q^73 - 20 * q^74 + 2 * q^80 + 18 * q^81 - 40 * q^82 + 28 * q^83 + 4 * q^85 + 36 * q^92

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 $

$2$	2.23607	1.58114	0.790569	−	0.612372i	$-0.209785\pi$
$2$	2.23607	1.58114	0.790569	+	0.612372i	$0.209785\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	3.00000	1.50000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	2.23607	0.790569
$9$	−3.00000	−1.00000
$10$	−2.23607	−0.707107
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	−4.47214	−1.19523
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−6.70820	−1.58114
$19$	0	0
$19$	0	0
$20$	−3.00000	−0.670820
$21$	0	0
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−10.0000	−1.96116
$27$	0	0
$28$	−6.00000	−1.13389
$29$	−8.94427	−1.66091	−0.830455	−	0.557086i	$-0.811919\pi$
$29$	−8.94427	−1.66091	−0.830455	+	0.557086i	$0.811919\pi$
$30$	0	0
$31$	8.94427	1.60644	0.803219	−	0.595683i	$-0.203119\pi$
$31$	8.94427	1.60644	0.803219	+	0.595683i	$0.203119\pi$
$32$	−6.70820	−1.18585
$33$	0	0
$34$	−4.47214	−0.766965
$35$	2.00000	0.338062
$36$	−9.00000	−1.50000
$37$	−4.47214	−0.735215	−0.367607	−	0.929981i	$-0.619823\pi$
$37$	−4.47214	−0.735215	−0.367607	+	0.929981i	$0.619823\pi$
$38$	0	0
$39$	0	0
$40$	−2.23607	−0.353553
$41$	−8.94427	−1.39686	−0.698430	−	0.715678i	$-0.746118\pi$
$41$	−8.94427	−1.39686	−0.698430	+	0.715678i	$0.746118\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	3.00000	0.447214
$46$	13.4164	1.97814
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	2.23607	0.316228
$51$	0	0
$52$	−13.4164	−1.86052
$53$	4.47214	0.614295	0.307148	−	0.951662i	$-0.400625\pi$
$53$	4.47214	0.614295	0.307148	+	0.951662i	$0.400625\pi$
$54$	0	0
$55$	0	0
$56$	−4.47214	−0.597614
$57$	0	0
$58$	−20.0000	−2.62613
$59$	8.94427	1.16445	0.582223	−	0.813029i	$-0.302183\pi$
$59$	8.94427	1.16445	0.582223	+	0.813029i	$0.302183\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	20.0000	2.54000
$63$	6.00000	0.755929
$64$	−13.0000	−1.62500
$65$	4.47214	0.554700
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	4.47214	0.534522
$71$	8.94427	1.06149	0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427	1.06149	0.530745	+	0.847532i	$0.321912\pi$
$72$	−6.70820	−0.790569
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	8.94427	1.00631	0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427	1.00631	0.503155	+	0.864196i	$0.332173\pi$
$80$	1.00000	0.111803
$81$	9.00000	1.00000
$82$	−20.0000	−2.20863
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	−13.4164	−1.44673
$87$	0	0
$88$	0	0
$89$	−8.94427	−0.948091	−0.474045	−	0.880500i	$-0.657207\pi$
$89$	−8.94427	−0.948091	−0.474045	+	0.880500i	$0.657207\pi$
$90$	6.70820	0.707107
$91$	8.94427	0.937614
$92$	18.0000	1.87663
$93$	0	0
$94$	−4.47214	−0.461266
$95$	0	0
$96$	0	0
$97$	13.4164	1.36223	0.681115	−	0.732177i	$-0.261495\pi$
$97$	13.4164	1.36223	0.681115	+	0.732177i	$0.261495\pi$
$98$	−6.70820	−0.677631
$99$	0	0
$100$	3.00000	0.300000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−8.94427	−0.881305	−0.440653	−	0.897678i	$-0.645253\pi$
$103$	−8.94427	−0.881305	−0.440653	+	0.897678i	$0.645253\pi$
$104$	−10.0000	−0.980581
$105$	0	0
$106$	10.0000	0.971286
$107$	−17.8885	−1.72935	−0.864675	−	0.502331i	$-0.832476\pi$
$107$	−17.8885	−1.72935	−0.864675	+	0.502331i	$0.832476\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	2.00000	0.188982
$113$	13.4164	1.26211	0.631055	−	0.775738i	$-0.282622\pi$
$113$	13.4164	1.26211	0.631055	+	0.775738i	$0.282622\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	−26.8328	−2.49136
$117$	13.4164	1.24035
$118$	20.0000	1.84115
$119$	4.00000	0.366679
$120$	0	0
$121$	−11.0000	−1.00000
$122$	−22.3607	−2.02444
$123$	0	0
$124$	26.8328	2.40966
$125$	−1.00000	−0.0894427
$126$	13.4164	1.19523
$127$	−8.94427	−0.793676	−0.396838	−	0.917889i	$-0.629892\pi$
$127$	−8.94427	−0.793676	−0.396838	+	0.917889i	$0.629892\pi$
$128$	−15.6525	−1.38350
$129$	0	0
$130$	10.0000	0.877058
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	−4.47214	−0.383482
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	6.00000	0.507093
$141$	0	0
$142$	20.0000	1.67836
$143$	0	0
$144$	3.00000	0.250000
$145$	8.94427	0.742781
$146$	31.3050	2.59082
$147$	0	0
$148$	−13.4164	−1.10282
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	17.8885	1.45575	0.727875	−	0.685710i	$-0.240508\pi$
$151$	17.8885	1.45575	0.727875	+	0.685710i	$0.240508\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	−8.94427	−0.718421
$156$	0	0
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	20.0000	1.59111
$159$	0	0
$160$	6.70820	0.530330
$161$	−12.0000	−0.945732
$162$	20.1246	1.58114
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	−26.8328	−2.09529
$165$	0	0
$166$	31.3050	2.42974
$167$	8.94427	0.692129	0.346064	−	0.938211i	$-0.387518\pi$
$167$	8.94427	0.692129	0.346064	+	0.938211i	$0.387518\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	4.47214	0.342997
$171$	0	0
$172$	−18.0000	−1.37249
$173$	4.47214	0.340010	0.170005	−	0.985443i	$-0.445622\pi$
$173$	4.47214	0.340010	0.170005	+	0.985443i	$0.445622\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	0	0
$177$	0	0
$178$	−20.0000	−1.49906
$179$	−8.94427	−0.668526	−0.334263	−	0.942480i	$-0.608487\pi$
$179$	−8.94427	−0.668526	−0.334263	+	0.942480i	$0.608487\pi$
$180$	9.00000	0.670820
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	20.0000	1.48250
$183$	0	0
$184$	13.4164	0.989071
$185$	4.47214	0.328798
$186$	0	0
$187$	0	0
$188$	−6.00000	−0.437595
$189$	0	0
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	13.4164	0.965734	0.482867	−	0.875694i	$-0.339595\pi$
$193$	13.4164	0.965734	0.482867	+	0.875694i	$0.339595\pi$
$194$	30.0000	2.15387
$195$	0	0
$196$	−9.00000	−0.642857
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	2.23607	0.158114
$201$	0	0
$202$	−22.3607	−1.57329
$203$	17.8885	1.25553
$204$	0	0
$205$	8.94427	0.624695
$206$	−20.0000	−1.39347
$207$	−18.0000	−1.25109
$208$	4.47214	0.310087
$209$	0	0
$210$	0	0
$211$	−17.8885	−1.23150	−0.615749	−	0.787942i	$-0.711146\pi$
$211$	−17.8885	−1.23150	−0.615749	+	0.787942i	$0.711146\pi$
$212$	13.4164	0.921443
$213$	0	0
$214$	−40.0000	−2.73434
$215$	6.00000	0.409197
$216$	0	0
$217$	−17.8885	−1.21435
$218$	0	0
$219$	0	0
$220$	0	0
$221$	8.94427	0.601657
$222$	0	0
$223$	26.8328	1.79686	0.898429	−	0.439119i	$-0.144709\pi$
$223$	26.8328	1.79686	0.898429	+	0.439119i	$0.144709\pi$
$224$	13.4164	0.896421
$225$	−3.00000	−0.200000
$226$	30.0000	1.99557
$227$	17.8885	1.18730	0.593652	−	0.804722i	$-0.297686\pi$
$227$	17.8885	1.18730	0.593652	+	0.804722i	$0.297686\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−13.4164	−0.884652
$231$	0	0
$232$	−20.0000	−1.31306
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	30.0000	1.96116
$235$	2.00000	0.130466
$236$	26.8328	1.74667
$237$	0	0
$238$	8.94427	0.579771
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	0	0
$241$	8.94427	0.576151	0.288076	−	0.957608i	$-0.406985\pi$
$241$	8.94427	0.576151	0.288076	+	0.957608i	$0.406985\pi$
$242$	−24.5967	−1.58114
$243$	0	0
$244$	−30.0000	−1.92055
$245$	3.00000	0.191663
$246$	0	0
$247$	0	0
$248$	20.0000	1.27000
$249$	0	0
$250$	−2.23607	−0.141421
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	18.0000	1.13389
$253$	0	0
$254$	−20.0000	−1.25491
$255$	0	0
$256$	−9.00000	−0.562500
$257$	4.47214	0.278964	0.139482	−	0.990225i	$-0.455456\pi$
$257$	4.47214	0.278964	0.139482	+	0.990225i	$0.455456\pi$
$258$	0	0
$259$	8.94427	0.555770
$260$	13.4164	0.832050
$261$	26.8328	1.66091
$262$	−26.8328	−1.65774
$263$	−26.0000	−1.60323	−0.801614	−	0.597841i	$-0.796025\pi$
$263$	−26.0000	−1.60323	−0.801614	+	0.597841i	$0.796025\pi$
$264$	0	0
$265$	−4.47214	−0.274721
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−17.8885	−1.09068	−0.545342	−	0.838214i	$-0.683600\pi$
$269$	−17.8885	−1.09068	−0.545342	+	0.838214i	$0.683600\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−40.2492	−2.43154
$275$	0	0
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−8.94427	−0.536442
$279$	−26.8328	−1.60644
$280$	4.47214	0.267261
$281$	8.94427	0.533571	0.266785	−	0.963756i	$-0.414039\pi$
$281$	8.94427	0.533571	0.266785	+	0.963756i	$0.414039\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	26.8328	1.59223
$285$	0	0
$286$	0	0
$287$	17.8885	1.05593
$288$	20.1246	1.18585
$289$	−13.0000	−0.764706
$290$	20.0000	1.17444
$291$	0	0
$292$	42.0000	2.45786
$293$	−13.4164	−0.783795	−0.391897	−	0.920009i	$-0.628181\pi$
$293$	−13.4164	−0.783795	−0.391897	+	0.920009i	$0.628181\pi$
$294$	0	0
$295$	−8.94427	−0.520756
$296$	−10.0000	−0.581238
$297$	0	0
$298$	−13.4164	−0.777192
$299$	−26.8328	−1.55178
$300$	0	0
$301$	12.0000	0.691669
$302$	40.0000	2.30174
$303$	0	0
$304$	0	0
$305$	10.0000	0.572598
$306$	13.4164	0.766965
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	−20.0000	−1.13592
$311$	20.0000	1.13410	0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000	1.13410	0.567048	+	0.823685i	$0.308085\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−4.47214	−0.252377
$315$	−6.00000	−0.338062
$316$	26.8328	1.50946
$317$	−4.47214	−0.251180	−0.125590	−	0.992082i	$-0.540082\pi$
$317$	−4.47214	−0.251180	−0.125590	+	0.992082i	$0.540082\pi$
$318$	0	0
$319$	0	0
$320$	13.0000	0.726722
$321$	0	0
$322$	−26.8328	−1.49533
$323$	0	0
$324$	27.0000	1.50000
$325$	−4.47214	−0.248069
$326$	−31.3050	−1.73382
$327$	0	0
$328$	−20.0000	−1.10432
$329$	4.00000	0.220527
$330$	0	0
$331$	17.8885	0.983243	0.491622	−	0.870809i	$-0.336404\pi$
$331$	17.8885	0.983243	0.491622	+	0.870809i	$0.336404\pi$
$332$	42.0000	2.30505
$333$	13.4164	0.735215
$334$	20.0000	1.09435
$335$	0	0
$336$	0	0
$337$	−4.47214	−0.243613	−0.121806	−	0.992554i	$-0.538869\pi$
$337$	−4.47214	−0.243613	−0.121806	+	0.992554i	$0.538869\pi$
$338$	15.6525	0.851382
$339$	0	0
$340$	6.00000	0.325396
$341$	0	0
$342$	0	0
$343$	20.0000	1.07990
$344$	−13.4164	−0.723364
$345$	0	0
$346$	10.0000	0.537603
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−4.47214	−0.239046
$351$	0	0
$352$	0	0
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	−8.94427	−0.474713
$356$	−26.8328	−1.42214
$357$	0	0
$358$	−20.0000	−1.05703
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	6.70820	0.353553
$361$	0	0
$362$	0	0
$363$	0	0
$364$	26.8328	1.40642
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	−6.00000	−0.312772
$369$	26.8328	1.39686
$370$	10.0000	0.519875
$371$	−8.94427	−0.464363
$372$	0	0
$373$	−31.3050	−1.62091	−0.810454	−	0.585802i	$-0.800780\pi$
$373$	−31.3050	−1.62091	−0.810454	+	0.585802i	$0.800780\pi$
$374$	0	0
$375$	0	0
$376$	−4.47214	−0.230633
$377$	40.0000	2.06010
$378$	0	0
$379$	−35.7771	−1.83775	−0.918873	−	0.394554i	$-0.870899\pi$
$379$	−35.7771	−1.83775	−0.918873	+	0.394554i	$0.870899\pi$
$380$	0	0
$381$	0	0
$382$	17.8885	0.915258
$383$	−8.94427	−0.457031	−0.228515	−	0.973540i	$-0.573387\pi$
$383$	−8.94427	−0.457031	−0.228515	+	0.973540i	$0.573387\pi$
$384$	0	0
$385$	0	0
$386$	30.0000	1.52696
$387$	18.0000	0.914991
$388$	40.2492	2.04334
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	−12.0000	−0.606866
$392$	−6.70820	−0.338815
$393$	0	0
$394$	4.47214	0.225303
$395$	−8.94427	−0.450035
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−44.7214	−2.24168
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	−40.0000	−1.99254
$404$	−30.0000	−1.49256
$405$	−9.00000	−0.447214
$406$	40.0000	1.98517
$407$	0	0
$408$	0	0
$409$	−17.8885	−0.884532	−0.442266	−	0.896884i	$-0.645825\pi$
$409$	−17.8885	−0.884532	−0.442266	+	0.896884i	$0.645825\pi$
$410$	20.0000	0.987730
$411$	0	0
$412$	−26.8328	−1.32196
$413$	−17.8885	−0.880238
$414$	−40.2492	−1.97814
$415$	−14.0000	−0.687233
$416$	30.0000	1.47087
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	8.94427	0.435917	0.217959	−	0.975958i	$-0.430060\pi$
$421$	8.94427	0.435917	0.217959	+	0.975958i	$0.430060\pi$
$422$	−40.0000	−1.94717
$423$	6.00000	0.291730
$424$	10.0000	0.485643
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	20.0000	0.967868
$428$	−53.6656	−2.59403
$429$	0	0
$430$	13.4164	0.646997
$431$	17.8885	0.861661	0.430830	−	0.902433i	$-0.358221\pi$
$431$	17.8885	0.861661	0.430830	+	0.902433i	$0.358221\pi$
$432$	0	0
$433$	−4.47214	−0.214917	−0.107459	−	0.994210i	$-0.534271\pi$
$433$	−4.47214	−0.214917	−0.107459	+	0.994210i	$0.534271\pi$
$434$	−40.0000	−1.92006
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	26.8328	1.28066	0.640330	−	0.768100i	$-0.278798\pi$
$439$	26.8328	1.28066	0.640330	+	0.768100i	$0.278798\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	20.0000	0.951303
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	0	0
$445$	8.94427	0.423999
$446$	60.0000	2.84108
$447$	0	0
$448$	26.0000	1.22838
$449$	17.8885	0.844213	0.422106	−	0.906546i	$-0.361291\pi$
$449$	17.8885	0.844213	0.422106	+	0.906546i	$0.361291\pi$
$450$	−6.70820	−0.316228
$451$	0	0
$452$	40.2492	1.89316
$453$	0	0
$454$	40.0000	1.87729
$455$	−8.94427	−0.419314
$456$	0	0
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	13.4164	0.626908
$459$	0	0
$460$	−18.0000	−0.839254
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	0	0
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	8.94427	0.415227
$465$	0	0
$466$	−13.4164	−0.621503
$467$	2.00000	0.0925490	0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000	0.0925490	0.0462745	+	0.998929i	$0.485265\pi$
$468$	40.2492	1.86052
$469$	0	0
$470$	4.47214	0.206284
$471$	0	0
$472$	20.0000	0.920575
$473$	0	0
$474$	0	0
$475$	0	0
$476$	12.0000	0.550019
$477$	−13.4164	−0.614295
$478$	−44.7214	−2.04551
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	20.0000	0.910975
$483$	0	0
$484$	−33.0000	−1.50000
$485$	−13.4164	−0.609208
$486$	0	0
$487$	26.8328	1.21591	0.607955	−	0.793971i	$-0.291990\pi$
$487$	26.8328	1.21591	0.607955	+	0.793971i	$0.291990\pi$
$488$	−22.3607	−1.01222
$489$	0	0
$490$	6.70820	0.303046
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	0	0
$493$	17.8885	0.805659
$494$	0	0
$495$	0	0
$496$	−8.94427	−0.401610
$497$	−17.8885	−0.802411
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	26.8328	1.19761
$503$	6.00000	0.267527	0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000	0.267527	0.133763	+	0.991013i	$0.457294\pi$
$504$	13.4164	0.597614
$505$	10.0000	0.444994
$506$	0	0
$507$	0	0
$508$	−26.8328	−1.19051
$509$	−8.94427	−0.396448	−0.198224	−	0.980157i	$-0.563517\pi$
$509$	−8.94427	−0.396448	−0.198224	+	0.980157i	$0.563517\pi$
$510$	0	0
$511$	−28.0000	−1.23865
$512$	11.1803	0.494106
$513$	0	0
$514$	10.0000	0.441081
$515$	8.94427	0.394132
$516$	0	0
$517$	0	0
$518$	20.0000	0.878750
$519$	0	0
$520$	10.0000	0.438529
$521$	−17.8885	−0.783711	−0.391856	−	0.920027i	$-0.628167\pi$
$521$	−17.8885	−0.783711	−0.391856	+	0.920027i	$0.628167\pi$
$522$	60.0000	2.62613
$523$	17.8885	0.782211	0.391106	−	0.920346i	$-0.372093\pi$
$523$	17.8885	0.782211	0.391106	+	0.920346i	$0.372093\pi$
$524$	−36.0000	−1.57267
$525$	0	0
$526$	−58.1378	−2.53493
$527$	−17.8885	−0.779237
$528$	0	0
$529$	13.0000	0.565217
$530$	−10.0000	−0.434372
$531$	−26.8328	−1.16445
$532$	0	0
$533$	40.0000	1.73259
$534$	0	0
$535$	17.8885	0.773389
$536$	0	0
$537$	0	0
$538$	−40.0000	−1.72452
$539$	0	0
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−44.7214	−1.92095
$543$	0	0
$544$	13.4164	0.575224
$545$	0	0
$546$	0	0
$547$	−35.7771	−1.52972	−0.764859	−	0.644198i	$-0.777191\pi$
$547$	−35.7771	−1.52972	−0.764859	+	0.644198i	$0.777191\pi$
$548$	−54.0000	−2.30677
$549$	30.0000	1.28037
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−17.8885	−0.760698
$554$	−4.47214	−0.190003
$555$	0	0
$556$	−12.0000	−0.508913
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	−60.0000	−2.54000
$559$	26.8328	1.13491
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	20.0000	0.843649
$563$	17.8885	0.753912	0.376956	−	0.926231i	$-0.376971\pi$
$563$	17.8885	0.753912	0.376956	+	0.926231i	$0.376971\pi$
$564$	0	0
$565$	−13.4164	−0.564433
$566$	13.4164	0.563934
$567$	−18.0000	−0.755929
$568$	20.0000	0.839181
$569$	−17.8885	−0.749927	−0.374963	−	0.927040i	$-0.622345\pi$
$569$	−17.8885	−0.749927	−0.374963	+	0.927040i	$0.622345\pi$
$570$	0	0
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	0	0
$573$	0	0
$574$	40.0000	1.66957
$575$	6.00000	0.250217
$576$	39.0000	1.62500
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−29.0689	−1.20911
$579$	0	0
$580$	26.8328	1.11417
$581$	−28.0000	−1.16164
$582$	0	0
$583$	0	0
$584$	31.3050	1.29541
$585$	−13.4164	−0.554700
$586$	−30.0000	−1.23929
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	0	0
$590$	−20.0000	−0.823387
$591$	0	0
$592$	4.47214	0.183804
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	−4.00000	−0.163984
$596$	−18.0000	−0.737309
$597$	0	0
$598$	−60.0000	−2.45358
$599$	−26.8328	−1.09636	−0.548180	−	0.836361i	$-0.684679\pi$
$599$	−26.8328	−1.09636	−0.548180	+	0.836361i	$0.684679\pi$
$600$	0	0
$601$	−44.7214	−1.82422	−0.912111	−	0.409943i	$-0.865549\pi$
$601$	−44.7214	−1.82422	−0.912111	+	0.409943i	$0.865549\pi$
$602$	26.8328	1.09362
$603$	0	0
$604$	53.6656	2.18362
$605$	11.0000	0.447214
$606$	0	0
$607$	−26.8328	−1.08911	−0.544555	−	0.838725i	$-0.683302\pi$
$607$	−26.8328	−1.08911	−0.544555	+	0.838725i	$0.683302\pi$
$608$	0	0
$609$	0	0
$610$	22.3607	0.905357
$611$	8.94427	0.361847
$612$	18.0000	0.727607
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−26.8328	−1.07763
$621$	0	0
$622$	44.7214	1.79316
$623$	17.8885	0.716689
$624$	0	0
$625$	1.00000	0.0400000
$626$	−13.4164	−0.536228
$627$	0	0
$628$	−6.00000	−0.239426
$629$	8.94427	0.356631
$630$	−13.4164	−0.534522
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	20.0000	0.795557
$633$	0	0
$634$	−10.0000	−0.397151
$635$	8.94427	0.354943
$636$	0	0
$637$	13.4164	0.531577
$638$	0	0
$639$	−26.8328	−1.06149
$640$	15.6525	0.618718
$641$	−26.8328	−1.05983	−0.529916	−	0.848050i	$-0.677777\pi$
$641$	−26.8328	−1.05983	−0.529916	+	0.848050i	$0.677777\pi$
$642$	0	0
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	−36.0000	−1.41860
$645$	0	0
$646$	0	0
$647$	18.0000	0.707653	0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000	0.707653	0.353827	+	0.935311i	$0.384880\pi$
$648$	20.1246	0.790569
$649$	0	0
$650$	−10.0000	−0.392232
$651$	0	0
$652$	−42.0000	−1.64485
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	12.0000	0.468879
$656$	8.94427	0.349215
$657$	−42.0000	−1.63858
$658$	8.94427	0.348684
$659$	−8.94427	−0.348419	−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427	−0.348419	−0.174210	+	0.984709i	$0.555737\pi$
$660$	0	0
$661$	−26.8328	−1.04368	−0.521838	−	0.853045i	$-0.674753\pi$
$661$	−26.8328	−1.04368	−0.521838	+	0.853045i	$0.674753\pi$
$662$	40.0000	1.55464
$663$	0	0
$664$	31.3050	1.21487
$665$	0	0
$666$	30.0000	1.16248
$667$	−53.6656	−2.07794
$668$	26.8328	1.03819
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−13.4164	−0.517165	−0.258582	−	0.965989i	$-0.583255\pi$
$673$	−13.4164	−0.517165	−0.258582	+	0.965989i	$0.583255\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	21.0000	0.807692
$677$	4.47214	0.171878	0.0859391	−	0.996300i	$-0.472611\pi$
$677$	4.47214	0.171878	0.0859391	+	0.996300i	$0.472611\pi$
$678$	0	0
$679$	−26.8328	−1.02975
$680$	4.47214	0.171499
$681$	0	0
$682$	0	0
$683$	35.7771	1.36897	0.684486	−	0.729026i	$-0.260027\pi$
$683$	35.7771	1.36897	0.684486	+	0.729026i	$0.260027\pi$
$684$	0	0
$685$	18.0000	0.687745
$686$	44.7214	1.70747
$687$	0	0
$688$	6.00000	0.228748
$689$	−20.0000	−0.761939
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	13.4164	0.510015
$693$	0	0
$694$	4.47214	0.169760
$695$	4.00000	0.151729
$696$	0	0
$697$	17.8885	0.677577
$698$	22.3607	0.846364
$699$	0	0
$700$	−6.00000	−0.226779
$701$	10.0000	0.377695	0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000	0.377695	0.188847	+	0.982006i	$0.439525\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	31.3050	1.17818
$707$	20.0000	0.752177
$708$	0	0
$709$	50.0000	1.87779	0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000	1.87779	0.938895	+	0.344204i	$0.111851\pi$
$710$	−20.0000	−0.750587
$711$	−26.8328	−1.00631
$712$	−20.0000	−0.749532
$713$	53.6656	2.00979
$714$	0	0
$715$	0	0
$716$	−26.8328	−1.00279
$717$	0	0
$718$	−53.6656	−2.00278
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−3.00000	−0.111803
$721$	17.8885	0.666204
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−8.94427	−0.332182
$726$	0	0
$727$	22.0000	0.815935	0.407967	−	0.912996i	$-0.366238\pi$
$727$	22.0000	0.815935	0.407967	+	0.912996i	$0.366238\pi$
$728$	20.0000	0.741249
$729$	−27.0000	−1.00000
$730$	−31.3050	−1.15865
$731$	12.0000	0.443836
$732$	0	0
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	−40.2492	−1.48563
$735$	0	0
$736$	−40.2492	−1.48361
$737$	0	0
$738$	60.0000	2.20863
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	13.4164	0.493197
$741$	0	0
$742$	−20.0000	−0.734223
$743$	−44.7214	−1.64067	−0.820334	−	0.571885i	$-0.806212\pi$
$743$	−44.7214	−1.64067	−0.820334	+	0.571885i	$0.806212\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−70.0000	−2.56288
$747$	−42.0000	−1.53670
$748$	0	0
$749$	35.7771	1.30727
$750$	0	0
$751$	35.7771	1.30552	0.652762	−	0.757563i	$-0.273610\pi$
$751$	35.7771	1.30552	0.652762	+	0.757563i	$0.273610\pi$
$752$	2.00000	0.0729325
$753$	0	0
$754$	89.4427	3.25731
$755$	−17.8885	−0.651031
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−80.0000	−2.90573
$759$	0	0
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	0	0
$764$	24.0000	0.868290
$765$	−6.00000	−0.216930
$766$	−20.0000	−0.722629
$767$	−40.0000	−1.44432
$768$	0	0
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	0	0
$772$	40.2492	1.44860
$773$	49.1935	1.76937	0.884684	−	0.466192i	$-0.154374\pi$
$773$	49.1935	1.76937	0.884684	+	0.466192i	$0.154374\pi$
$774$	40.2492	1.44673
$775$	8.94427	0.321288
$776$	30.0000	1.07694
$777$	0	0
$778$	22.3607	0.801669
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−26.8328	−0.959540
$783$	0	0
$784$	3.00000	0.107143
$785$	2.00000	0.0713831
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	−20.0000	−0.711568
$791$	−26.8328	−0.954065
$792$	0	0
$793$	44.7214	1.58810
$794$	−4.47214	−0.158710
$795$	0	0
$796$	−60.0000	−2.12664
$797$	22.3607	0.792056	0.396028	−	0.918238i	$-0.370388\pi$
$797$	22.3607	0.792056	0.396028	+	0.918238i	$0.370388\pi$
$798$	0	0
$799$	4.00000	0.141510
$800$	−6.70820	−0.237171
$801$	26.8328	0.948091
$802$	0	0
$803$	0	0
$804$	0	0
$805$	12.0000	0.422944
$806$	−89.4427	−3.15049
$807$	0	0
$808$	−22.3607	−0.786646
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	−20.1246	−0.707107
$811$	8.94427	0.314076	0.157038	−	0.987593i	$-0.449806\pi$
$811$	8.94427	0.314076	0.157038	+	0.987593i	$0.449806\pi$
$812$	53.6656	1.88329
$813$	0	0
$814$	0	0
$815$	14.0000	0.490399
$816$	0	0
$817$	0	0
$818$	−40.0000	−1.39857
$819$	−26.8328	−0.937614
$820$	26.8328	0.937043
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	0	0
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	−20.0000	−0.696733
$825$	0	0
$826$	−40.0000	−1.39178
$827$	17.8885	0.622046	0.311023	−	0.950402i	$-0.399328\pi$
$827$	17.8885	0.622046	0.311023	+	0.950402i	$0.399328\pi$
$828$	−54.0000	−1.87663
$829$	53.6656	1.86388	0.931942	−	0.362607i	$-0.118113\pi$
$829$	53.6656	1.86388	0.931942	+	0.362607i	$0.118113\pi$
$830$	−31.3050	−1.08661
$831$	0	0
$832$	58.1378	2.01556
$833$	6.00000	0.207888
$834$	0	0
$835$	−8.94427	−0.309529
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−44.7214	−1.54395	−0.771976	−	0.635651i	$-0.780732\pi$
$839$	−44.7214	−1.54395	−0.771976	+	0.635651i	$0.780732\pi$
$840$	0	0
$841$	51.0000	1.75862
$842$	20.0000	0.689246
$843$	0	0
$844$	−53.6656	−1.84725
$845$	−7.00000	−0.240807
$846$	13.4164	0.461266
$847$	22.0000	0.755929
$848$	−4.47214	−0.153574
$849$	0	0
$850$	−4.47214	−0.153393
$851$	−26.8328	−0.919817
$852$	0	0
$853$	34.0000	1.16414	0.582069	−	0.813139i	$-0.302243\pi$
$853$	34.0000	1.16414	0.582069	+	0.813139i	$0.302243\pi$
$854$	44.7214	1.53033
$855$	0	0
$856$	−40.0000	−1.36717
$857$	−31.3050	−1.06936	−0.534678	−	0.845056i	$-0.679567\pi$
$857$	−31.3050	−1.06936	−0.534678	+	0.845056i	$0.679567\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	18.0000	0.613795
$861$	0	0
$862$	40.0000	1.36241
$863$	8.94427	0.304467	0.152233	−	0.988345i	$-0.451353\pi$
$863$	8.94427	0.304467	0.152233	+	0.988345i	$0.451353\pi$
$864$	0	0
$865$	−4.47214	−0.152057
$866$	−10.0000	−0.339814
$867$	0	0
$868$	−53.6656	−1.82153
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−40.2492	−1.36223
$874$	0	0
$875$	2.00000	0.0676123
$876$	0	0
$877$	−13.4164	−0.453040	−0.226520	−	0.974007i	$-0.572735\pi$
$877$	−13.4164	−0.453040	−0.226520	+	0.974007i	$0.572735\pi$
$878$	60.0000	2.02490
$879$	0	0
$880$	0	0
$881$	−50.0000	−1.68454	−0.842271	−	0.539054i	$-0.818782\pi$
$881$	−50.0000	−1.68454	−0.842271	+	0.539054i	$0.818782\pi$
$882$	20.1246	0.677631
$883$	26.0000	0.874970	0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000	0.874970	0.437485	+	0.899226i	$0.355869\pi$
$884$	26.8328	0.902485
$885$	0	0
$886$	−58.1378	−1.95318
$887$	44.7214	1.50160	0.750798	−	0.660532i	$-0.229669\pi$
$887$	44.7214	1.50160	0.750798	+	0.660532i	$0.229669\pi$
$888$	0	0
$889$	17.8885	0.599963
$890$	20.0000	0.670402
$891$	0	0
$892$	80.4984	2.69529
$893$	0	0
$894$	0	0
$895$	8.94427	0.298974
$896$	31.3050	1.04583
$897$	0	0
$898$	40.0000	1.33482
$899$	−80.0000	−2.66815
$900$	−9.00000	−0.300000
$901$	−8.94427	−0.297977
$902$	0	0
$903$	0	0
$904$	30.0000	0.997785
$905$	0	0
$906$	0	0
$907$	53.6656	1.78194	0.890969	−	0.454064i	$-0.150026\pi$
$907$	53.6656	1.78194	0.890969	+	0.454064i	$0.150026\pi$
$908$	53.6656	1.78096
$909$	30.0000	0.995037
$910$	−20.0000	−0.662994
$911$	35.7771	1.18535	0.592674	−	0.805443i	$-0.298072\pi$
$911$	35.7771	1.18535	0.592674	+	0.805443i	$0.298072\pi$
$912$	0	0
$913$	0	0
$914$	−49.1935	−1.62718
$915$	0	0
$916$	18.0000	0.594737
$917$	24.0000	0.792550
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	−13.4164	−0.442326
$921$	0	0
$922$	4.47214	0.147282
$923$	−40.0000	−1.31662
$924$	0	0
$925$	−4.47214	−0.147043
$926$	13.4164	0.440891
$927$	26.8328	0.881305
$928$	60.0000	1.96960
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	0	0
$931$	0	0
$932$	−18.0000	−0.589610
$933$	0	0
$934$	4.47214	0.146333
$935$	0	0
$936$	30.0000	0.980581
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	0	0
$940$	6.00000	0.195698
$941$	53.6656	1.74945	0.874725	−	0.484620i	$-0.161042\pi$
$941$	53.6656	1.74945	0.874725	+	0.484620i	$0.161042\pi$
$942$	0	0
$943$	−53.6656	−1.74759
$944$	−8.94427	−0.291111
$945$	0	0
$946$	0	0
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	−62.6099	−2.03240
$950$	0	0
$951$	0	0
$952$	8.94427	0.289886
$953$	22.3607	0.724333	0.362167	−	0.932113i	$-0.382037\pi$
$953$	22.3607	0.724333	0.362167	+	0.932113i	$0.382037\pi$
$954$	−30.0000	−0.971286
$955$	−8.00000	−0.258874
$956$	−60.0000	−1.94054
$957$	0	0
$958$	35.7771	1.15591
$959$	36.0000	1.16250
$960$	0	0
$961$	49.0000	1.58065
$962$	44.7214	1.44187
$963$	53.6656	1.72935
$964$	26.8328	0.864227
$965$	−13.4164	−0.431889
$966$	0	0
$967$	−38.0000	−1.22200	−0.610999	−	0.791632i	$-0.709232\pi$
$967$	−38.0000	−1.22200	−0.610999	+	0.791632i	$0.709232\pi$
$968$	−24.5967	−0.790569
$969$	0	0
$970$	−30.0000	−0.963242
$971$	44.7214	1.43518	0.717588	−	0.696467i	$-0.245246\pi$
$971$	44.7214	1.43518	0.717588	+	0.696467i	$0.245246\pi$
$972$	0	0
$973$	8.00000	0.256468
$974$	60.0000	1.92252
$975$	0	0
$976$	10.0000	0.320092
$977$	40.2492	1.28769	0.643843	−	0.765157i	$-0.277339\pi$
$977$	40.2492	1.28769	0.643843	+	0.765157i	$0.277339\pi$
$978$	0	0
$979$	0	0
$980$	9.00000	0.287494
$981$	0	0
$982$	62.6099	1.99796
$983$	−8.94427	−0.285278	−0.142639	−	0.989775i	$-0.545559\pi$
$983$	−8.94427	−0.285278	−0.142639	+	0.989775i	$0.545559\pi$
$984$	0	0
$985$	−2.00000	−0.0637253
$986$	40.0000	1.27386
$987$	0	0
$988$	0	0
$989$	−36.0000	−1.14473
$990$	0	0
$991$	−17.8885	−0.568248	−0.284124	−	0.958787i	$-0.591703\pi$
$991$	−17.8885	−0.568248	−0.284124	+	0.958787i	$0.591703\pi$
$992$	−60.0000	−1.90500
$993$	0	0
$994$	−40.0000	−1.26872
$995$	20.0000	0.634043
$996$	0	0
$997$	−18.0000	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$998$	−8.94427	−0.283126
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.d.1.2	yes	2
5.4	even	2		9025.2.a.q.1.1		2
19.18	odd	2	inner	1805.2.a.d.1.1	✓	2
95.94	odd	2		9025.2.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.d.1.1	✓	2	19.18	odd	2	inner
1805.2.a.d.1.2	yes	2	1.1	even	1	trivial
9025.2.a.q.1.1		2	5.4	even	2
9025.2.a.q.1.2		2	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} -2.23607 q^{10} -4.47214 q^{13} -4.47214 q^{14} -1.00000 q^{16} -2.00000 q^{17} -6.70820 q^{18} -3.00000 q^{20} +6.00000 q^{23} +1.00000 q^{25} -10.0000 q^{26} -6.00000 q^{28} -8.94427 q^{29} +8.94427 q^{31} -6.70820 q^{32} -4.47214 q^{34} +2.00000 q^{35} -9.00000 q^{36} -4.47214 q^{37} -2.23607 q^{40} -8.94427 q^{41} -6.00000 q^{43} +3.00000 q^{45} +13.4164 q^{46} -2.00000 q^{47} -3.00000 q^{49} +2.23607 q^{50} -13.4164 q^{52} +4.47214 q^{53} -4.47214 q^{56} -20.0000 q^{58} +8.94427 q^{59} -10.0000 q^{61} +20.0000 q^{62} +6.00000 q^{63} -13.0000 q^{64} +4.47214 q^{65} -6.00000 q^{68} +4.47214 q^{70} +8.94427 q^{71} -6.70820 q^{72} +14.0000 q^{73} -10.0000 q^{74} +8.94427 q^{79} +1.00000 q^{80} +9.00000 q^{81} -20.0000 q^{82} +14.0000 q^{83} +2.00000 q^{85} -13.4164 q^{86} -8.94427 q^{89} +6.70820 q^{90} +8.94427 q^{91} +18.0000 q^{92} -4.47214 q^{94} +13.4164 q^{97} -6.70820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 6 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^9	\( 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9} - 2 q^{16} - 4 q^{17} - 6 q^{20} + 12 q^{23} + 2 q^{25} - 20 q^{26} - 12 q^{28} + 4 q^{35} - 18 q^{36} - 12 q^{43} + 6 q^{45} - 4 q^{47} - 6 q^{49} - 40 q^{58} - 20 q^{61} + 40 q^{62} + 12 q^{63} - 26 q^{64} - 12 q^{68} + 28 q^{73} - 20 q^{74} + 2 q^{80} + 18 q^{81} - 40 q^{82} + 28 q^{83} + 4 q^{85} + 36 q^{92}+O(q^{100}) \) 2 * q + 6 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^9 - 2 * q^16 - 4 * q^17 - 6 * q^20 + 12 * q^23 + 2 * q^25 - 20 * q^26 - 12 * q^28 + 4 * q^35 - 18 * q^36 - 12 * q^43 + 6 * q^45 - 4 * q^47 - 6 * q^49 - 40 * q^58 - 20 * q^61 + 40 * q^62 + 12 * q^63 - 26 * q^64 - 12 * q^68 + 28 * q^73 - 20 * q^74 + 2 * q^80 + 18 * q^81 - 40 * q^82 + 28 * q^83 + 4 * q^85 + 36 * q^92

Introduction

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