LMFDB - Embedded newform 1840.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1840,4,Mod(1,1840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1840, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1840.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1840 = 2^{4} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1840.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:	$108.563514411$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} -5.00000 q^{5} +18.0000 q^{7} -26.0000 q^{9} +32.0000 q^{11} -47.0000 q^{13} +5.00000 q^{15} +20.0000 q^{17} -36.0000 q^{19} -18.0000 q^{21} +23.0000 q^{23} +25.0000 q^{25} +53.0000 q^{27} -27.0000 q^{29} +33.0000 q^{31} -32.0000 q^{33} -90.0000 q^{35} +56.0000 q^{37} +47.0000 q^{39} -157.000 q^{41} -18.0000 q^{43} +130.000 q^{45} -65.0000 q^{47} -19.0000 q^{49} -20.0000 q^{51} -14.0000 q^{53} -160.000 q^{55} +36.0000 q^{57} +744.000 q^{59} +552.000 q^{61} -468.000 q^{63} +235.000 q^{65} +156.000 q^{67} -23.0000 q^{69} -699.000 q^{71} -609.000 q^{73} -25.0000 q^{75} +576.000 q^{77} +644.000 q^{79} +649.000 q^{81} -512.000 q^{83} -100.000 q^{85} +27.0000 q^{87} -102.000 q^{89} -846.000 q^{91} -33.0000 q^{93} +180.000 q^{95} +578.000 q^{97} -832.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−1.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	0	0
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	18.0000	0.971909	0.485954	−	0.873984i	$-0.338472\pi$
$7$	18.0000	0.971909	0.485954	+	0.873984i	$0.338472\pi$
$8$	0	0
$9$	−26.0000	−0.962963
$10$	0	0
$11$	32.0000	0.877124	0.438562	−	0.898701i	$-0.355488\pi$
$11$	32.0000	0.877124	0.438562	+	0.898701i	$0.355488\pi$
$12$	0	0
$13$	−47.0000	−1.00273	−0.501364	−	0.865237i	$-0.667168\pi$
$13$	−47.0000	−1.00273	−0.501364	+	0.865237i	$0.667168\pi$
$14$	0	0
$15$	5.00000	0.0860663
$16$	0	0
$17$	20.0000	0.285336	0.142668	−	0.989771i	$-0.454432\pi$
$17$	20.0000	0.285336	0.142668	+	0.989771i	$0.454432\pi$
$18$	0	0
$19$	−36.0000	−0.434682	−0.217341	−	0.976096i	$-0.569738\pi$
$19$	−36.0000	−0.434682	−0.217341	+	0.976096i	$0.569738\pi$
$20$	0	0
$21$	−18.0000	−0.187044
$22$	0	0
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	53.0000	0.377772
$28$	0	0
$29$	−27.0000	−0.172889	−0.0864444	−	0.996257i	$-0.527550\pi$
$29$	−27.0000	−0.172889	−0.0864444	+	0.996257i	$0.527550\pi$
$30$	0	0
$31$	33.0000	0.191193	0.0955964	−	0.995420i	$-0.469524\pi$
$31$	33.0000	0.191193	0.0955964	+	0.995420i	$0.469524\pi$
$32$	0	0
$33$	−32.0000	−0.168803
$34$	0	0
$35$	−90.0000	−0.434651
$36$	0	0
$37$	56.0000	0.248820	0.124410	−	0.992231i	$-0.460296\pi$
$37$	56.0000	0.248820	0.124410	+	0.992231i	$0.460296\pi$
$38$	0	0
$39$	47.0000	0.192975
$40$	0	0
$41$	−157.000	−0.598031	−0.299016	−	0.954248i	$-0.596658\pi$
$41$	−157.000	−0.598031	−0.299016	+	0.954248i	$0.596658\pi$
$42$	0	0
$43$	−18.0000	−0.0638366	−0.0319183	−	0.999490i	$-0.510162\pi$
$43$	−18.0000	−0.0638366	−0.0319183	+	0.999490i	$0.510162\pi$
$44$	0	0
$45$	130.000	0.430650
$46$	0	0
$47$	−65.0000	−0.201728	−0.100864	−	0.994900i	$-0.532161\pi$
$47$	−65.0000	−0.201728	−0.100864	+	0.994900i	$0.532161\pi$
$48$	0	0
$49$	−19.0000	−0.0553936
$50$	0	0
$51$	−20.0000	−0.0549129
$52$	0	0
$53$	−14.0000	−0.0362839	−0.0181420	−	0.999835i	$-0.505775\pi$
$53$	−14.0000	−0.0362839	−0.0181420	+	0.999835i	$0.505775\pi$
$54$	0	0
$55$	−160.000	−0.392262
$56$	0	0
$57$	36.0000	0.0836547
$58$	0	0
$59$	744.000	1.64170	0.820852	−	0.571141i	$-0.193499\pi$
$59$	744.000	1.64170	0.820852	+	0.571141i	$0.193499\pi$
$60$	0	0
$61$	552.000	1.15863	0.579314	−	0.815104i	$-0.303320\pi$
$61$	552.000	1.15863	0.579314	+	0.815104i	$0.303320\pi$
$62$	0	0
$63$	−468.000	−0.935912
$64$	0	0
$65$	235.000	0.448433
$66$	0	0
$67$	156.000	0.284454	0.142227	−	0.989834i	$-0.454574\pi$
$67$	156.000	0.284454	0.142227	+	0.989834i	$0.454574\pi$
$68$	0	0
$69$	−23.0000	−0.0401286
$70$	0	0
$71$	−699.000	−1.16839	−0.584197	−	0.811612i	$-0.698591\pi$
$71$	−699.000	−1.16839	−0.584197	+	0.811612i	$0.698591\pi$
$72$	0	0
$73$	−609.000	−0.976412	−0.488206	−	0.872728i	$-0.662348\pi$
$73$	−609.000	−0.976412	−0.488206	+	0.872728i	$0.662348\pi$
$74$	0	0
$75$	−25.0000	−0.0384900
$76$	0	0
$77$	576.000	0.852484
$78$	0	0
$79$	644.000	0.917160	0.458580	−	0.888653i	$-0.348358\pi$
$79$	644.000	0.917160	0.458580	+	0.888653i	$0.348358\pi$
$80$	0	0
$81$	649.000	0.890261
$82$	0	0
$83$	−512.000	−0.677100	−0.338550	−	0.940948i	$-0.609936\pi$
$83$	−512.000	−0.677100	−0.338550	+	0.940948i	$0.609936\pi$
$84$	0	0
$85$	−100.000	−0.127606
$86$	0	0
$87$	27.0000	0.0332725
$88$	0	0
$89$	−102.000	−0.121483	−0.0607415	−	0.998154i	$-0.519347\pi$
$89$	−102.000	−0.121483	−0.0607415	+	0.998154i	$0.519347\pi$
$90$	0	0
$91$	−846.000	−0.974559
$92$	0	0
$93$	−33.0000	−0.0367951
$94$	0	0
$95$	180.000	0.194396
$96$	0	0
$97$	578.000	0.605021	0.302510	−	0.953146i	$-0.402175\pi$
$97$	578.000	0.605021	0.302510	+	0.953146i	$0.402175\pi$
$98$	0	0
$99$	−832.000	−0.844638
$100$	0	0
$101$	−6.00000	−0.00591111	−0.00295556	−	0.999996i	$-0.500941\pi$
$101$	−6.00000	−0.00591111	−0.00295556	+	0.999996i	$0.500941\pi$
$102$	0	0
$103$	160.000	0.153061	0.0765304	−	0.997067i	$-0.475616\pi$
$103$	160.000	0.153061	0.0765304	+	0.997067i	$0.475616\pi$
$104$	0	0
$105$	90.0000	0.0836486
$106$	0	0
$107$	−380.000	−0.343327	−0.171663	−	0.985156i	$-0.554914\pi$
$107$	−380.000	−0.343327	−0.171663	+	0.985156i	$0.554914\pi$
$108$	0	0
$109$	250.000	0.219685	0.109842	−	0.993949i	$-0.464965\pi$
$109$	250.000	0.219685	0.109842	+	0.993949i	$0.464965\pi$
$110$	0	0
$111$	−56.0000	−0.0478854
$112$	0	0
$113$	−390.000	−0.324674	−0.162337	−	0.986735i	$-0.551903\pi$
$113$	−390.000	−0.324674	−0.162337	+	0.986735i	$0.551903\pi$
$114$	0	0
$115$	−115.000	−0.0932505
$116$	0	0
$117$	1222.00	0.965589
$118$	0	0
$119$	360.000	0.277321
$120$	0	0
$121$	−307.000	−0.230654
$122$	0	0
$123$	157.000	0.115091
$124$	0	0
$125$	−125.000	−0.0894427
$126$	0	0
$127$	769.000	0.537305	0.268652	−	0.963237i	$-0.413422\pi$
$127$	769.000	0.537305	0.268652	+	0.963237i	$0.413422\pi$
$128$	0	0
$129$	18.0000	0.0122854
$130$	0	0
$131$	213.000	0.142060	0.0710301	−	0.997474i	$-0.477371\pi$
$131$	213.000	0.142060	0.0710301	+	0.997474i	$0.477371\pi$
$132$	0	0
$133$	−648.000	−0.422472
$134$	0	0
$135$	−265.000	−0.168945
$136$	0	0
$137$	2836.00	1.76858	0.884291	−	0.466936i	$-0.154642\pi$
$137$	2836.00	1.76858	0.884291	+	0.466936i	$0.154642\pi$
$138$	0	0
$139$	1631.00	0.995249	0.497625	−	0.867393i	$-0.334206\pi$
$139$	1631.00	0.995249	0.497625	+	0.867393i	$0.334206\pi$
$140$	0	0
$141$	65.0000	0.0388226
$142$	0	0
$143$	−1504.00	−0.879516
$144$	0	0
$145$	135.000	0.0773182
$146$	0	0
$147$	19.0000	0.0106605
$148$	0	0
$149$	−1966.00	−1.08095	−0.540473	−	0.841361i	$-0.681755\pi$
$149$	−1966.00	−1.08095	−0.540473	+	0.841361i	$0.681755\pi$
$150$	0	0
$151$	−35.0000	−0.0188626	−0.00943132	−	0.999956i	$-0.503002\pi$
$151$	−35.0000	−0.0188626	−0.00943132	+	0.999956i	$0.503002\pi$
$152$	0	0
$153$	−520.000	−0.274768
$154$	0	0
$155$	−165.000	−0.0855040
$156$	0	0
$157$	1702.00	0.865187	0.432594	−	0.901589i	$-0.357599\pi$
$157$	1702.00	0.865187	0.432594	+	0.901589i	$0.357599\pi$
$158$	0	0
$159$	14.0000	0.00698284
$160$	0	0
$161$	414.000	0.202657
$162$	0	0
$163$	2045.00	0.982680	0.491340	−	0.870968i	$-0.336507\pi$
$163$	2045.00	0.982680	0.491340	+	0.870968i	$0.336507\pi$
$164$	0	0
$165$	160.000	0.0754908
$166$	0	0
$167$	−1016.00	−0.470781	−0.235391	−	0.971901i	$-0.575637\pi$
$167$	−1016.00	−0.470781	−0.235391	+	0.971901i	$0.575637\pi$
$168$	0	0
$169$	12.0000	0.00546199
$170$	0	0
$171$	936.000	0.418583
$172$	0	0
$173$	598.000	0.262804	0.131402	−	0.991329i	$-0.458052\pi$
$173$	598.000	0.262804	0.131402	+	0.991329i	$0.458052\pi$
$174$	0	0
$175$	450.000	0.194382
$176$	0	0
$177$	−744.000	−0.315946
$178$	0	0
$179$	4607.00	1.92371	0.961853	−	0.273567i	$-0.0882036\pi$
$179$	4607.00	1.92371	0.961853	+	0.273567i	$0.0882036\pi$
$180$	0	0
$181$	−1212.00	−0.497720	−0.248860	−	0.968540i	$-0.580056\pi$
$181$	−1212.00	−0.497720	−0.248860	+	0.968540i	$0.580056\pi$
$182$	0	0
$183$	−552.000	−0.222978
$184$	0	0
$185$	−280.000	−0.111276
$186$	0	0
$187$	640.000	0.250275
$188$	0	0
$189$	954.000	0.367160
$190$	0	0
$191$	1058.00	0.400807	0.200404	−	0.979713i	$-0.435775\pi$
$191$	1058.00	0.400807	0.200404	+	0.979713i	$0.435775\pi$
$192$	0	0
$193$	1047.00	0.390491	0.195245	−	0.980754i	$-0.437450\pi$
$193$	1047.00	0.390491	0.195245	+	0.980754i	$0.437450\pi$
$194$	0	0
$195$	−235.000	−0.0863010
$196$	0	0
$197$	251.000	0.0907767	0.0453883	−	0.998969i	$-0.485547\pi$
$197$	251.000	0.0907767	0.0453883	+	0.998969i	$0.485547\pi$
$198$	0	0
$199$	3508.00	1.24963	0.624813	−	0.780775i	$-0.285175\pi$
$199$	3508.00	1.24963	0.624813	+	0.780775i	$0.285175\pi$
$200$	0	0
$201$	−156.000	−0.0547432
$202$	0	0
$203$	−486.000	−0.168032
$204$	0	0
$205$	785.000	0.267448
$206$	0	0
$207$	−598.000	−0.200792
$208$	0	0
$209$	−1152.00	−0.381270
$210$	0	0
$211$	3296.00	1.07538	0.537692	−	0.843141i	$-0.319296\pi$
$211$	3296.00	1.07538	0.537692	+	0.843141i	$0.319296\pi$
$212$	0	0
$213$	699.000	0.224858
$214$	0	0
$215$	90.0000	0.0285486
$216$	0	0
$217$	594.000	0.185822
$218$	0	0
$219$	609.000	0.187911
$220$	0	0
$221$	−940.000	−0.286114
$222$	0	0
$223$	2720.00	0.816792	0.408396	−	0.912805i	$-0.366088\pi$
$223$	2720.00	0.816792	0.408396	+	0.912805i	$0.366088\pi$
$224$	0	0
$225$	−650.000	−0.192593
$226$	0	0
$227$	4134.00	1.20874	0.604368	−	0.796705i	$-0.293426\pi$
$227$	4134.00	1.20874	0.604368	+	0.796705i	$0.293426\pi$
$228$	0	0
$229$	−4510.00	−1.30144	−0.650719	−	0.759319i	$-0.725532\pi$
$229$	−4510.00	−1.30144	−0.650719	+	0.759319i	$0.725532\pi$
$230$	0	0
$231$	−576.000	−0.164061
$232$	0	0
$233$	−5003.00	−1.40668	−0.703342	−	0.710852i	$-0.748310\pi$
$233$	−5003.00	−1.40668	−0.703342	+	0.710852i	$0.748310\pi$
$234$	0	0
$235$	325.000	0.0902156
$236$	0	0
$237$	−644.000	−0.176508
$238$	0	0
$239$	6309.00	1.70751	0.853756	−	0.520674i	$-0.174319\pi$
$239$	6309.00	1.70751	0.853756	+	0.520674i	$0.174319\pi$
$240$	0	0
$241$	3038.00	0.812012	0.406006	−	0.913871i	$-0.366921\pi$
$241$	3038.00	0.812012	0.406006	+	0.913871i	$0.366921\pi$
$242$	0	0
$243$	−2080.00	−0.549103
$244$	0	0
$245$	95.0000	0.0247728
$246$	0	0
$247$	1692.00	0.435868
$248$	0	0
$249$	512.000	0.130308
$250$	0	0
$251$	1332.00	0.334961	0.167480	−	0.985875i	$-0.446437\pi$
$251$	1332.00	0.334961	0.167480	+	0.985875i	$0.446437\pi$
$252$	0	0
$253$	736.000	0.182893
$254$	0	0
$255$	100.000	0.0245578
$256$	0	0
$257$	3301.00	0.801209	0.400605	−	0.916251i	$-0.368800\pi$
$257$	3301.00	0.801209	0.400605	+	0.916251i	$0.368800\pi$
$258$	0	0
$259$	1008.00	0.241830
$260$	0	0
$261$	702.000	0.166485
$262$	0	0
$263$	−2072.00	−0.485798	−0.242899	−	0.970052i	$-0.578098\pi$
$263$	−2072.00	−0.485798	−0.242899	+	0.970052i	$0.578098\pi$
$264$	0	0
$265$	70.0000	0.0162267
$266$	0	0
$267$	102.000	0.0233794
$268$	0	0
$269$	5721.00	1.29671	0.648356	−	0.761337i	$-0.275457\pi$
$269$	5721.00	1.29671	0.648356	+	0.761337i	$0.275457\pi$
$270$	0	0
$271$	5900.00	1.32251	0.661254	−	0.750162i	$-0.270025\pi$
$271$	5900.00	1.32251	0.661254	+	0.750162i	$0.270025\pi$
$272$	0	0
$273$	846.000	0.187554
$274$	0	0
$275$	800.000	0.175425
$276$	0	0
$277$	6371.00	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	6371.00	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	0	0
$279$	−858.000	−0.184112
$280$	0	0
$281$	3190.00	0.677222	0.338611	−	0.940926i	$-0.390043\pi$
$281$	3190.00	0.677222	0.338611	+	0.940926i	$0.390043\pi$
$282$	0	0
$283$	4226.00	0.887667	0.443833	−	0.896109i	$-0.353618\pi$
$283$	4226.00	0.887667	0.443833	+	0.896109i	$0.353618\pi$
$284$	0	0
$285$	−180.000	−0.0374115
$286$	0	0
$287$	−2826.00	−0.581232
$288$	0	0
$289$	−4513.00	−0.918583
$290$	0	0
$291$	−578.000	−0.116436
$292$	0	0
$293$	6048.00	1.20590	0.602949	−	0.797780i	$-0.293992\pi$
$293$	6048.00	1.20590	0.602949	+	0.797780i	$0.293992\pi$
$294$	0	0
$295$	−3720.00	−0.734192
$296$	0	0
$297$	1696.00	0.331353
$298$	0	0
$299$	−1081.00	−0.209083
$300$	0	0
$301$	−324.000	−0.0620434
$302$	0	0
$303$	6.00000	0.00113759
$304$	0	0
$305$	−2760.00	−0.518155
$306$	0	0
$307$	−8628.00	−1.60399	−0.801997	−	0.597328i	$-0.796229\pi$
$307$	−8628.00	−1.60399	−0.801997	+	0.597328i	$0.796229\pi$
$308$	0	0
$309$	−160.000	−0.0294566
$310$	0	0
$311$	−8247.00	−1.50368	−0.751840	−	0.659346i	$-0.770833\pi$
$311$	−8247.00	−1.50368	−0.751840	+	0.659346i	$0.770833\pi$
$312$	0	0
$313$	2620.00	0.473135	0.236567	−	0.971615i	$-0.423978\pi$
$313$	2620.00	0.473135	0.236567	+	0.971615i	$0.423978\pi$
$314$	0	0
$315$	2340.00	0.418553
$316$	0	0
$317$	9906.00	1.75513	0.877565	−	0.479457i	$-0.159166\pi$
$317$	9906.00	1.75513	0.877565	+	0.479457i	$0.159166\pi$
$318$	0	0
$319$	−864.000	−0.151645
$320$	0	0
$321$	380.000	0.0660733
$322$	0	0
$323$	−720.000	−0.124031
$324$	0	0
$325$	−1175.00	−0.200545
$326$	0	0
$327$	−250.000	−0.0422784
$328$	0	0
$329$	−1170.00	−0.196061
$330$	0	0
$331$	8115.00	1.34756	0.673778	−	0.738934i	$-0.264671\pi$
$331$	8115.00	1.34756	0.673778	+	0.738934i	$0.264671\pi$
$332$	0	0
$333$	−1456.00	−0.239605
$334$	0	0
$335$	−780.000	−0.127212
$336$	0	0
$337$	−7586.00	−1.22622	−0.613109	−	0.789998i	$-0.710082\pi$
$337$	−7586.00	−1.22622	−0.613109	+	0.789998i	$0.710082\pi$
$338$	0	0
$339$	390.000	0.0624835
$340$	0	0
$341$	1056.00	0.167700
$342$	0	0
$343$	−6516.00	−1.02575
$344$	0	0
$345$	115.000	0.0179461
$346$	0	0
$347$	−1356.00	−0.209781	−0.104890	−	0.994484i	$-0.533449\pi$
$347$	−1356.00	−0.209781	−0.104890	+	0.994484i	$0.533449\pi$
$348$	0	0
$349$	6649.00	1.01981	0.509904	−	0.860231i	$-0.329681\pi$
$349$	6649.00	1.01981	0.509904	+	0.860231i	$0.329681\pi$
$350$	0	0
$351$	−2491.00	−0.378803
$352$	0	0
$353$	10691.0	1.61197	0.805984	−	0.591938i	$-0.201637\pi$
$353$	10691.0	1.61197	0.805984	+	0.591938i	$0.201637\pi$
$354$	0	0
$355$	3495.00	0.522522
$356$	0	0
$357$	−360.000	−0.0533704
$358$	0	0
$359$	6420.00	0.943829	0.471915	−	0.881644i	$-0.343563\pi$
$359$	6420.00	0.943829	0.471915	+	0.881644i	$0.343563\pi$
$360$	0	0
$361$	−5563.00	−0.811051
$362$	0	0
$363$	307.000	0.0443893
$364$	0	0
$365$	3045.00	0.436665
$366$	0	0
$367$	524.000	0.0745302	0.0372651	−	0.999305i	$-0.488135\pi$
$367$	524.000	0.0745302	0.0372651	+	0.999305i	$0.488135\pi$
$368$	0	0
$369$	4082.00	0.575882
$370$	0	0
$371$	−252.000	−0.0352647
$372$	0	0
$373$	5566.00	0.772645	0.386322	−	0.922364i	$-0.373745\pi$
$373$	5566.00	0.772645	0.386322	+	0.922364i	$0.373745\pi$
$374$	0	0
$375$	125.000	0.0172133
$376$	0	0
$377$	1269.00	0.173360
$378$	0	0
$379$	−2240.00	−0.303591	−0.151796	−	0.988412i	$-0.548506\pi$
$379$	−2240.00	−0.303591	−0.151796	+	0.988412i	$0.548506\pi$
$380$	0	0
$381$	−769.000	−0.103404
$382$	0	0
$383$	−8778.00	−1.17111	−0.585555	−	0.810633i	$-0.699123\pi$
$383$	−8778.00	−1.17111	−0.585555	+	0.810633i	$0.699123\pi$
$384$	0	0
$385$	−2880.00	−0.381243
$386$	0	0
$387$	468.000	0.0614723
$388$	0	0
$389$	4056.00	0.528656	0.264328	−	0.964433i	$-0.414850\pi$
$389$	4056.00	0.528656	0.264328	+	0.964433i	$0.414850\pi$
$390$	0	0
$391$	460.000	0.0594967
$392$	0	0
$393$	−213.000	−0.0273395
$394$	0	0
$395$	−3220.00	−0.410167
$396$	0	0
$397$	−9151.00	−1.15687	−0.578433	−	0.815730i	$-0.696335\pi$
$397$	−9151.00	−1.15687	−0.578433	+	0.815730i	$0.696335\pi$
$398$	0	0
$399$	648.000	0.0813047
$400$	0	0
$401$	15930.0	1.98381	0.991903	−	0.126997i	$-0.0405340\pi$
$401$	15930.0	1.98381	0.991903	+	0.126997i	$0.0405340\pi$
$402$	0	0
$403$	−1551.00	−0.191714
$404$	0	0
$405$	−3245.00	−0.398137
$406$	0	0
$407$	1792.00	0.218246
$408$	0	0
$409$	−5891.00	−0.712203	−0.356102	−	0.934447i	$-0.615894\pi$
$409$	−5891.00	−0.712203	−0.356102	+	0.934447i	$0.615894\pi$
$410$	0	0
$411$	−2836.00	−0.340364
$412$	0	0
$413$	13392.0	1.59559
$414$	0	0
$415$	2560.00	0.302808
$416$	0	0
$417$	−1631.00	−0.191536
$418$	0	0
$419$	−15282.0	−1.78180	−0.890900	−	0.454199i	$-0.849926\pi$
$419$	−15282.0	−1.78180	−0.890900	+	0.454199i	$0.849926\pi$
$420$	0	0
$421$	−10934.0	−1.26577	−0.632887	−	0.774244i	$-0.718130\pi$
$421$	−10934.0	−1.26577	−0.632887	+	0.774244i	$0.718130\pi$
$422$	0	0
$423$	1690.00	0.194257
$424$	0	0
$425$	500.000	0.0570672
$426$	0	0
$427$	9936.00	1.12608
$428$	0	0
$429$	1504.00	0.169263
$430$	0	0
$431$	2794.00	0.312256	0.156128	−	0.987737i	$-0.450099\pi$
$431$	2794.00	0.312256	0.156128	+	0.987737i	$0.450099\pi$
$432$	0	0
$433$	−15062.0	−1.67167	−0.835835	−	0.548980i	$-0.815016\pi$
$433$	−15062.0	−1.67167	−0.835835	+	0.548980i	$0.815016\pi$
$434$	0	0
$435$	−135.000	−0.0148799
$436$	0	0
$437$	−828.000	−0.0906376
$438$	0	0
$439$	−261.000	−0.0283755	−0.0141878	−	0.999899i	$-0.504516\pi$
$439$	−261.000	−0.0283755	−0.0141878	+	0.999899i	$0.504516\pi$
$440$	0	0
$441$	494.000	0.0533420
$442$	0	0
$443$	7083.00	0.759647	0.379823	−	0.925059i	$-0.375985\pi$
$443$	7083.00	0.759647	0.379823	+	0.925059i	$0.375985\pi$
$444$	0	0
$445$	510.000	0.0543288
$446$	0	0
$447$	1966.00	0.208028
$448$	0	0
$449$	−10370.0	−1.08996	−0.544978	−	0.838450i	$-0.683462\pi$
$449$	−10370.0	−1.08996	−0.544978	+	0.838450i	$0.683462\pi$
$450$	0	0
$451$	−5024.00	−0.524547
$452$	0	0
$453$	35.0000	0.00363012
$454$	0	0
$455$	4230.00	0.435836
$456$	0	0
$457$	−10496.0	−1.07436	−0.537180	−	0.843468i	$-0.680510\pi$
$457$	−10496.0	−1.07436	−0.537180	+	0.843468i	$0.680510\pi$
$458$	0	0
$459$	1060.00	0.107792
$460$	0	0
$461$	18021.0	1.82065	0.910327	−	0.413889i	$-0.135830\pi$
$461$	18021.0	1.82065	0.910327	+	0.413889i	$0.135830\pi$
$462$	0	0
$463$	17188.0	1.72526	0.862629	−	0.505838i	$-0.168817\pi$
$463$	17188.0	1.72526	0.862629	+	0.505838i	$0.168817\pi$
$464$	0	0
$465$	165.000	0.0164553
$466$	0	0
$467$	15246.0	1.51071	0.755354	−	0.655317i	$-0.227465\pi$
$467$	15246.0	1.51071	0.755354	+	0.655317i	$0.227465\pi$
$468$	0	0
$469$	2808.00	0.276464
$470$	0	0
$471$	−1702.00	−0.166505
$472$	0	0
$473$	−576.000	−0.0559926
$474$	0	0
$475$	−900.000	−0.0869365
$476$	0	0
$477$	364.000	0.0349401
$478$	0	0
$479$	8556.00	0.816145	0.408073	−	0.912949i	$-0.366201\pi$
$479$	8556.00	0.816145	0.408073	+	0.912949i	$0.366201\pi$
$480$	0	0
$481$	−2632.00	−0.249499
$482$	0	0
$483$	−414.000	−0.0390014
$484$	0	0
$485$	−2890.00	−0.270573
$486$	0	0
$487$	1805.00	0.167951	0.0839757	−	0.996468i	$-0.473238\pi$
$487$	1805.00	0.167951	0.0839757	+	0.996468i	$0.473238\pi$
$488$	0	0
$489$	−2045.00	−0.189117
$490$	0	0
$491$	−5245.00	−0.482085	−0.241042	−	0.970515i	$-0.577489\pi$
$491$	−5245.00	−0.482085	−0.241042	+	0.970515i	$0.577489\pi$
$492$	0	0
$493$	−540.000	−0.0493314
$494$	0	0
$495$	4160.00	0.377734
$496$	0	0
$497$	−12582.0	−1.13557
$498$	0	0
$499$	−9027.00	−0.809828	−0.404914	−	0.914355i	$-0.632698\pi$
$499$	−9027.00	−0.809828	−0.404914	+	0.914355i	$0.632698\pi$
$500$	0	0
$501$	1016.00	0.0906019
$502$	0	0
$503$	−3522.00	−0.312203	−0.156102	−	0.987741i	$-0.549893\pi$
$503$	−3522.00	−0.312203	−0.156102	+	0.987741i	$0.549893\pi$
$504$	0	0
$505$	30.0000	0.00264353
$506$	0	0
$507$	−12.0000	−0.00105116
$508$	0	0
$509$	3949.00	0.343883	0.171941	−	0.985107i	$-0.444996\pi$
$509$	3949.00	0.343883	0.171941	+	0.985107i	$0.444996\pi$
$510$	0	0
$511$	−10962.0	−0.948983
$512$	0	0
$513$	−1908.00	−0.164211
$514$	0	0
$515$	−800.000	−0.0684509
$516$	0	0
$517$	−2080.00	−0.176941
$518$	0	0
$519$	−598.000	−0.0505767
$520$	0	0
$521$	3236.00	0.272115	0.136057	−	0.990701i	$-0.456557\pi$
$521$	3236.00	0.272115	0.136057	+	0.990701i	$0.456557\pi$
$522$	0	0
$523$	−12394.0	−1.03624	−0.518118	−	0.855309i	$-0.673367\pi$
$523$	−12394.0	−1.03624	−0.518118	+	0.855309i	$0.673367\pi$
$524$	0	0
$525$	−450.000	−0.0374088
$526$	0	0
$527$	660.000	0.0545542
$528$	0	0
$529$	529.000	0.0434783
$530$	0	0
$531$	−19344.0	−1.58090
$532$	0	0
$533$	7379.00	0.599662
$534$	0	0
$535$	1900.00	0.153540
$536$	0	0
$537$	−4607.00	−0.370217
$538$	0	0
$539$	−608.000	−0.0485870
$540$	0	0
$541$	−7159.00	−0.568927	−0.284463	−	0.958687i	$-0.591815\pi$
$541$	−7159.00	−0.568927	−0.284463	+	0.958687i	$0.591815\pi$
$542$	0	0
$543$	1212.00	0.0957862
$544$	0	0
$545$	−1250.00	−0.0982461
$546$	0	0
$547$	19761.0	1.54464	0.772321	−	0.635232i	$-0.219096\pi$
$547$	19761.0	1.54464	0.772321	+	0.635232i	$0.219096\pi$
$548$	0	0
$549$	−14352.0	−1.11572
$550$	0	0
$551$	972.000	0.0751517
$552$	0	0
$553$	11592.0	0.891396
$554$	0	0
$555$	280.000	0.0214150
$556$	0	0
$557$	18010.0	1.37003	0.685016	−	0.728528i	$-0.259795\pi$
$557$	18010.0	1.37003	0.685016	+	0.728528i	$0.259795\pi$
$558$	0	0
$559$	846.000	0.0640107
$560$	0	0
$561$	−640.000	−0.0481655
$562$	0	0
$563$	2648.00	0.198224	0.0991118	−	0.995076i	$-0.468400\pi$
$563$	2648.00	0.198224	0.0991118	+	0.995076i	$0.468400\pi$
$564$	0	0
$565$	1950.00	0.145198
$566$	0	0
$567$	11682.0	0.865252
$568$	0	0
$569$	−1566.00	−0.115378	−0.0576890	−	0.998335i	$-0.518373\pi$
$569$	−1566.00	−0.115378	−0.0576890	+	0.998335i	$0.518373\pi$
$570$	0	0
$571$	−2864.00	−0.209903	−0.104952	−	0.994477i	$-0.533469\pi$
$571$	−2864.00	−0.209903	−0.104952	+	0.994477i	$0.533469\pi$
$572$	0	0
$573$	−1058.00	−0.0771354
$574$	0	0
$575$	575.000	0.0417029
$576$	0	0
$577$	−929.000	−0.0670273	−0.0335137	−	0.999438i	$-0.510670\pi$
$577$	−929.000	−0.0670273	−0.0335137	+	0.999438i	$0.510670\pi$
$578$	0	0
$579$	−1047.00	−0.0751500
$580$	0	0
$581$	−9216.00	−0.658079
$582$	0	0
$583$	−448.000	−0.0318255
$584$	0	0
$585$	−6110.00	−0.431825
$586$	0	0
$587$	19499.0	1.37106	0.685528	−	0.728046i	$-0.259571\pi$
$587$	19499.0	1.37106	0.685528	+	0.728046i	$0.259571\pi$
$588$	0	0
$589$	−1188.00	−0.0831081
$590$	0	0
$591$	−251.000	−0.0174700
$592$	0	0
$593$	6570.00	0.454971	0.227485	−	0.973782i	$-0.426950\pi$
$593$	6570.00	0.454971	0.227485	+	0.973782i	$0.426950\pi$
$594$	0	0
$595$	−1800.00	−0.124022
$596$	0	0
$597$	−3508.00	−0.240491
$598$	0	0
$599$	−1880.00	−0.128238	−0.0641191	−	0.997942i	$-0.520424\pi$
$599$	−1880.00	−0.128238	−0.0641191	+	0.997942i	$0.520424\pi$
$600$	0	0
$601$	3701.00	0.251193	0.125596	−	0.992081i	$-0.459916\pi$
$601$	3701.00	0.251193	0.125596	+	0.992081i	$0.459916\pi$
$602$	0	0
$603$	−4056.00	−0.273919
$604$	0	0
$605$	1535.00	0.103151
$606$	0	0
$607$	3080.00	0.205953	0.102976	−	0.994684i	$-0.467163\pi$
$607$	3080.00	0.205953	0.102976	+	0.994684i	$0.467163\pi$
$608$	0	0
$609$	486.000	0.0323378
$610$	0	0
$611$	3055.00	0.202278
$612$	0	0
$613$	24004.0	1.58159	0.790793	−	0.612083i	$-0.209668\pi$
$613$	24004.0	1.58159	0.790793	+	0.612083i	$0.209668\pi$
$614$	0	0
$615$	−785.000	−0.0514703
$616$	0	0
$617$	780.000	0.0508940	0.0254470	−	0.999676i	$-0.491899\pi$
$617$	780.000	0.0508940	0.0254470	+	0.999676i	$0.491899\pi$
$618$	0	0
$619$	−21892.0	−1.42151	−0.710754	−	0.703440i	$-0.751646\pi$
$619$	−21892.0	−1.42151	−0.710754	+	0.703440i	$0.751646\pi$
$620$	0	0
$621$	1219.00	0.0787710
$622$	0	0
$623$	−1836.00	−0.118070
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	1152.00	0.0733755
$628$	0	0
$629$	1120.00	0.0709973
$630$	0	0
$631$	−8050.00	−0.507869	−0.253935	−	0.967221i	$-0.581725\pi$
$631$	−8050.00	−0.507869	−0.253935	+	0.967221i	$0.581725\pi$
$632$	0	0
$633$	−3296.00	−0.206958
$634$	0	0
$635$	−3845.00	−0.240290
$636$	0	0
$637$	893.000	0.0555447
$638$	0	0
$639$	18174.0	1.12512
$640$	0	0
$641$	−25890.0	−1.59531	−0.797655	−	0.603114i	$-0.793926\pi$
$641$	−25890.0	−1.59531	−0.797655	+	0.603114i	$0.793926\pi$
$642$	0	0
$643$	−4774.00	−0.292797	−0.146398	−	0.989226i	$-0.546768\pi$
$643$	−4774.00	−0.292797	−0.146398	+	0.989226i	$0.546768\pi$
$644$	0	0
$645$	−90.0000	−0.00549418
$646$	0	0
$647$	−3349.00	−0.203497	−0.101749	−	0.994810i	$-0.532444\pi$
$647$	−3349.00	−0.203497	−0.101749	+	0.994810i	$0.532444\pi$
$648$	0	0
$649$	23808.0	1.43998
$650$	0	0
$651$	−594.000	−0.0357614
$652$	0	0
$653$	24813.0	1.48699	0.743497	−	0.668739i	$-0.233166\pi$
$653$	24813.0	1.48699	0.743497	+	0.668739i	$0.233166\pi$
$654$	0	0
$655$	−1065.00	−0.0635313
$656$	0	0
$657$	15834.0	0.940248
$658$	0	0
$659$	−18180.0	−1.07465	−0.537323	−	0.843376i	$-0.680565\pi$
$659$	−18180.0	−1.07465	−0.537323	+	0.843376i	$0.680565\pi$
$660$	0	0
$661$	−29250.0	−1.72117	−0.860585	−	0.509307i	$-0.829902\pi$
$661$	−29250.0	−1.72117	−0.860585	+	0.509307i	$0.829902\pi$
$662$	0	0
$663$	940.000	0.0550627
$664$	0	0
$665$	3240.00	0.188935
$666$	0	0
$667$	−621.000	−0.0360498
$668$	0	0
$669$	−2720.00	−0.157192
$670$	0	0
$671$	17664.0	1.01626
$672$	0	0
$673$	−23027.0	−1.31891	−0.659454	−	0.751745i	$-0.729213\pi$
$673$	−23027.0	−1.31891	−0.659454	+	0.751745i	$0.729213\pi$
$674$	0	0
$675$	1325.00	0.0755545
$676$	0	0
$677$	20106.0	1.14141	0.570706	−	0.821154i	$-0.306669\pi$
$677$	20106.0	1.14141	0.570706	+	0.821154i	$0.306669\pi$
$678$	0	0
$679$	10404.0	0.588025
$680$	0	0
$681$	−4134.00	−0.232621
$682$	0	0
$683$	18745.0	1.05016	0.525079	−	0.851054i	$-0.324036\pi$
$683$	18745.0	1.05016	0.525079	+	0.851054i	$0.324036\pi$
$684$	0	0
$685$	−14180.0	−0.790934
$686$	0	0
$687$	4510.00	0.250462
$688$	0	0
$689$	658.000	0.0363829
$690$	0	0
$691$	−24424.0	−1.34462	−0.672310	−	0.740270i	$-0.734698\pi$
$691$	−24424.0	−1.34462	−0.672310	+	0.740270i	$0.734698\pi$
$692$	0	0
$693$	−14976.0	−0.820911
$694$	0	0
$695$	−8155.00	−0.445089
$696$	0	0
$697$	−3140.00	−0.170640
$698$	0	0
$699$	5003.00	0.270717
$700$	0	0
$701$	−27278.0	−1.46972	−0.734862	−	0.678217i	$-0.762753\pi$
$701$	−27278.0	−1.46972	−0.734862	+	0.678217i	$0.762753\pi$
$702$	0	0
$703$	−2016.00	−0.108158
$704$	0	0
$705$	−325.000	−0.0173620
$706$	0	0
$707$	−108.000	−0.00574506
$708$	0	0
$709$	12214.0	0.646977	0.323488	−	0.946232i	$-0.395144\pi$
$709$	12214.0	0.646977	0.323488	+	0.946232i	$0.395144\pi$
$710$	0	0
$711$	−16744.0	−0.883191
$712$	0	0
$713$	759.000	0.0398664
$714$	0	0
$715$	7520.00	0.393332
$716$	0	0
$717$	−6309.00	−0.328611
$718$	0	0
$719$	−12932.0	−0.670768	−0.335384	−	0.942082i	$-0.608866\pi$
$719$	−12932.0	−0.670768	−0.335384	+	0.942082i	$0.608866\pi$
$720$	0	0
$721$	2880.00	0.148761
$722$	0	0
$723$	−3038.00	−0.156272
$724$	0	0
$725$	−675.000	−0.0345778
$726$	0	0
$727$	−10046.0	−0.512497	−0.256249	−	0.966611i	$-0.582487\pi$
$727$	−10046.0	−0.512497	−0.256249	+	0.966611i	$0.582487\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	0	0
$731$	−360.000	−0.0182149
$732$	0	0
$733$	−5924.00	−0.298510	−0.149255	−	0.988799i	$-0.547688\pi$
$733$	−5924.00	−0.298510	−0.149255	+	0.988799i	$0.547688\pi$
$734$	0	0
$735$	−95.0000	−0.00476752
$736$	0	0
$737$	4992.00	0.249502
$738$	0	0
$739$	−829.000	−0.0412656	−0.0206328	−	0.999787i	$-0.506568\pi$
$739$	−829.000	−0.0412656	−0.0206328	+	0.999787i	$0.506568\pi$
$740$	0	0
$741$	−1692.00	−0.0838828
$742$	0	0
$743$	−7072.00	−0.349188	−0.174594	−	0.984641i	$-0.555861\pi$
$743$	−7072.00	−0.349188	−0.174594	+	0.984641i	$0.555861\pi$
$744$	0	0
$745$	9830.00	0.483414
$746$	0	0
$747$	13312.0	0.652022
$748$	0	0
$749$	−6840.00	−0.333682
$750$	0	0
$751$	−16234.0	−0.788798	−0.394399	−	0.918939i	$-0.629047\pi$
$751$	−16234.0	−0.788798	−0.394399	+	0.918939i	$0.629047\pi$
$752$	0	0
$753$	−1332.00	−0.0644632
$754$	0	0
$755$	175.000	0.00843563
$756$	0	0
$757$	9128.00	0.438260	0.219130	−	0.975696i	$-0.429678\pi$
$757$	9128.00	0.438260	0.219130	+	0.975696i	$0.429678\pi$
$758$	0	0
$759$	−736.000	−0.0351978
$760$	0	0
$761$	165.000	0.00785972	0.00392986	−	0.999992i	$-0.498749\pi$
$761$	165.000	0.00785972	0.00392986	+	0.999992i	$0.498749\pi$
$762$	0	0
$763$	4500.00	0.213514
$764$	0	0
$765$	2600.00	0.122880
$766$	0	0
$767$	−34968.0	−1.64618
$768$	0	0
$769$	−20834.0	−0.976974	−0.488487	−	0.872571i	$-0.662451\pi$
$769$	−20834.0	−0.976974	−0.488487	+	0.872571i	$0.662451\pi$
$770$	0	0
$771$	−3301.00	−0.154193
$772$	0	0
$773$	−31782.0	−1.47881	−0.739404	−	0.673262i	$-0.764893\pi$
$773$	−31782.0	−1.47881	−0.739404	+	0.673262i	$0.764893\pi$
$774$	0	0
$775$	825.000	0.0382385
$776$	0	0
$777$	−1008.00	−0.0465403
$778$	0	0
$779$	5652.00	0.259954
$780$	0	0
$781$	−22368.0	−1.02483
$782$	0	0
$783$	−1431.00	−0.0653126
$784$	0	0
$785$	−8510.00	−0.386923
$786$	0	0
$787$	−33104.0	−1.49940	−0.749701	−	0.661776i	$-0.769803\pi$
$787$	−33104.0	−1.49940	−0.749701	+	0.661776i	$0.769803\pi$
$788$	0	0
$789$	2072.00	0.0934920
$790$	0	0
$791$	−7020.00	−0.315553
$792$	0	0
$793$	−25944.0	−1.16179
$794$	0	0
$795$	−70.0000	−0.00312282
$796$	0	0
$797$	4736.00	0.210486	0.105243	−	0.994447i	$-0.466438\pi$
$797$	4736.00	0.210486	0.105243	+	0.994447i	$0.466438\pi$
$798$	0	0
$799$	−1300.00	−0.0575603
$800$	0	0
$801$	2652.00	0.116984
$802$	0	0
$803$	−19488.0	−0.856434
$804$	0	0
$805$	−2070.00	−0.0906309
$806$	0	0
$807$	−5721.00	−0.249552
$808$	0	0
$809$	−7470.00	−0.324637	−0.162318	−	0.986738i	$-0.551897\pi$
$809$	−7470.00	−0.324637	−0.162318	+	0.986738i	$0.551897\pi$
$810$	0	0
$811$	−19919.0	−0.862455	−0.431227	−	0.902243i	$-0.641919\pi$
$811$	−19919.0	−0.862455	−0.431227	+	0.902243i	$0.641919\pi$
$812$	0	0
$813$	−5900.00	−0.254517
$814$	0	0
$815$	−10225.0	−0.439468
$816$	0	0
$817$	648.000	0.0277487
$818$	0	0
$819$	21996.0	0.938465
$820$	0	0
$821$	−22694.0	−0.964709	−0.482354	−	0.875976i	$-0.660218\pi$
$821$	−22694.0	−0.964709	−0.482354	+	0.875976i	$0.660218\pi$
$822$	0	0
$823$	31907.0	1.35141	0.675704	−	0.737173i	$-0.263840\pi$
$823$	31907.0	1.35141	0.675704	+	0.737173i	$0.263840\pi$
$824$	0	0
$825$	−800.000	−0.0337605
$826$	0	0
$827$	15236.0	0.640638	0.320319	−	0.947310i	$-0.396210\pi$
$827$	15236.0	0.640638	0.320319	+	0.947310i	$0.396210\pi$
$828$	0	0
$829$	27286.0	1.14316	0.571581	−	0.820545i	$-0.306330\pi$
$829$	27286.0	1.14316	0.571581	+	0.820545i	$0.306330\pi$
$830$	0	0
$831$	−6371.00	−0.265954
$832$	0	0
$833$	−380.000	−0.0158058
$834$	0	0
$835$	5080.00	0.210540
$836$	0	0
$837$	1749.00	0.0722273
$838$	0	0
$839$	−23054.0	−0.948644	−0.474322	−	0.880351i	$-0.657307\pi$
$839$	−23054.0	−0.948644	−0.474322	+	0.880351i	$0.657307\pi$
$840$	0	0
$841$	−23660.0	−0.970109
$842$	0	0
$843$	−3190.00	−0.130331
$844$	0	0
$845$	−60.0000	−0.00244268
$846$	0	0
$847$	−5526.00	−0.224174
$848$	0	0
$849$	−4226.00	−0.170832
$850$	0	0
$851$	1288.00	0.0518826
$852$	0	0
$853$	−34506.0	−1.38507	−0.692534	−	0.721385i	$-0.743506\pi$
$853$	−34506.0	−1.38507	−0.692534	+	0.721385i	$0.743506\pi$
$854$	0	0
$855$	−4680.00	−0.187196
$856$	0	0
$857$	−22263.0	−0.887386	−0.443693	−	0.896179i	$-0.646332\pi$
$857$	−22263.0	−0.887386	−0.443693	+	0.896179i	$0.646332\pi$
$858$	0	0
$859$	−12851.0	−0.510443	−0.255221	−	0.966883i	$-0.582148\pi$
$859$	−12851.0	−0.510443	−0.255221	+	0.966883i	$0.582148\pi$
$860$	0	0
$861$	2826.00	0.111858
$862$	0	0
$863$	−15723.0	−0.620182	−0.310091	−	0.950707i	$-0.600360\pi$
$863$	−15723.0	−0.620182	−0.310091	+	0.950707i	$0.600360\pi$
$864$	0	0
$865$	−2990.00	−0.117530
$866$	0	0
$867$	4513.00	0.176781
$868$	0	0
$869$	20608.0	0.804463
$870$	0	0
$871$	−7332.00	−0.285230
$872$	0	0
$873$	−15028.0	−0.582613
$874$	0	0
$875$	−2250.00	−0.0869302
$876$	0	0
$877$	−886.000	−0.0341141	−0.0170571	−	0.999855i	$-0.505430\pi$
$877$	−886.000	−0.0341141	−0.0170571	+	0.999855i	$0.505430\pi$
$878$	0	0
$879$	−6048.00	−0.232075
$880$	0	0
$881$	−37120.0	−1.41953	−0.709764	−	0.704439i	$-0.751199\pi$
$881$	−37120.0	−1.41953	−0.709764	+	0.704439i	$0.751199\pi$
$882$	0	0
$883$	7524.00	0.286753	0.143376	−	0.989668i	$-0.454204\pi$
$883$	7524.00	0.286753	0.143376	+	0.989668i	$0.454204\pi$
$884$	0	0
$885$	3720.00	0.141295
$886$	0	0
$887$	−9221.00	−0.349054	−0.174527	−	0.984652i	$-0.555840\pi$
$887$	−9221.00	−0.349054	−0.174527	+	0.984652i	$0.555840\pi$
$888$	0	0
$889$	13842.0	0.522211
$890$	0	0
$891$	20768.0	0.780869
$892$	0	0
$893$	2340.00	0.0876877
$894$	0	0
$895$	−23035.0	−0.860307
$896$	0	0
$897$	1081.00	0.0402381
$898$	0	0
$899$	−891.000	−0.0330551
$900$	0	0
$901$	−280.000	−0.0103531
$902$	0	0
$903$	324.000	0.0119402
$904$	0	0
$905$	6060.00	0.222587
$906$	0	0
$907$	−29116.0	−1.06591	−0.532955	−	0.846143i	$-0.678919\pi$
$907$	−29116.0	−1.06591	−0.532955	+	0.846143i	$0.678919\pi$
$908$	0	0
$909$	156.000	0.00569218
$910$	0	0
$911$	−11440.0	−0.416053	−0.208026	−	0.978123i	$-0.566704\pi$
$911$	−11440.0	−0.416053	−0.208026	+	0.978123i	$0.566704\pi$
$912$	0	0
$913$	−16384.0	−0.593901
$914$	0	0
$915$	2760.00	0.0997189
$916$	0	0
$917$	3834.00	0.138070
$918$	0	0
$919$	−2958.00	−0.106176	−0.0530878	−	0.998590i	$-0.516906\pi$
$919$	−2958.00	−0.106176	−0.0530878	+	0.998590i	$0.516906\pi$
$920$	0	0
$921$	8628.00	0.308689
$922$	0	0
$923$	32853.0	1.17158
$924$	0	0
$925$	1400.00	0.0497640
$926$	0	0
$927$	−4160.00	−0.147392
$928$	0	0
$929$	20907.0	0.738360	0.369180	−	0.929358i	$-0.379639\pi$
$929$	20907.0	0.738360	0.369180	+	0.929358i	$0.379639\pi$
$930$	0	0
$931$	684.000	0.0240786
$932$	0	0
$933$	8247.00	0.289383
$934$	0	0
$935$	−3200.00	−0.111926
$936$	0	0
$937$	9748.00	0.339865	0.169932	−	0.985456i	$-0.445645\pi$
$937$	9748.00	0.339865	0.169932	+	0.985456i	$0.445645\pi$
$938$	0	0
$939$	−2620.00	−0.0910548
$940$	0	0
$941$	19624.0	0.679834	0.339917	−	0.940455i	$-0.389601\pi$
$941$	19624.0	0.679834	0.339917	+	0.940455i	$0.389601\pi$
$942$	0	0
$943$	−3611.00	−0.124698
$944$	0	0
$945$	−4770.00	−0.164199
$946$	0	0
$947$	41859.0	1.43636	0.718181	−	0.695856i	$-0.244975\pi$
$947$	41859.0	1.43636	0.718181	+	0.695856i	$0.244975\pi$
$948$	0	0
$949$	28623.0	0.979075
$950$	0	0
$951$	−9906.00	−0.337775
$952$	0	0
$953$	29226.0	0.993413	0.496707	−	0.867918i	$-0.334542\pi$
$953$	29226.0	0.993413	0.496707	+	0.867918i	$0.334542\pi$
$954$	0	0
$955$	−5290.00	−0.179246
$956$	0	0
$957$	864.000	0.0291841
$958$	0	0
$959$	51048.0	1.71890
$960$	0	0
$961$	−28702.0	−0.963445
$962$	0	0
$963$	9880.00	0.330611
$964$	0	0
$965$	−5235.00	−0.174633
$966$	0	0
$967$	29849.0	0.992636	0.496318	−	0.868141i	$-0.334685\pi$
$967$	29849.0	0.992636	0.496318	+	0.868141i	$0.334685\pi$
$968$	0	0
$969$	720.000	0.0238697
$970$	0	0
$971$	9390.00	0.310339	0.155170	−	0.987888i	$-0.450408\pi$
$971$	9390.00	0.310339	0.155170	+	0.987888i	$0.450408\pi$
$972$	0	0
$973$	29358.0	0.967291
$974$	0	0
$975$	1175.00	0.0385950
$976$	0	0
$977$	33536.0	1.09817	0.549085	−	0.835767i	$-0.314976\pi$
$977$	33536.0	1.09817	0.549085	+	0.835767i	$0.314976\pi$
$978$	0	0
$979$	−3264.00	−0.106556
$980$	0	0
$981$	−6500.00	−0.211548
$982$	0	0
$983$	−28994.0	−0.940758	−0.470379	−	0.882465i	$-0.655883\pi$
$983$	−28994.0	−0.940758	−0.470379	+	0.882465i	$0.655883\pi$
$984$	0	0
$985$	−1255.00	−0.0405966
$986$	0	0
$987$	1170.00	0.0377320
$988$	0	0
$989$	−414.000	−0.0133109
$990$	0	0
$991$	−11272.0	−0.361319	−0.180659	−	0.983546i	$-0.557823\pi$
$991$	−11272.0	−0.361319	−0.180659	+	0.983546i	$0.557823\pi$
$992$	0	0
$993$	−8115.00	−0.259337
$994$	0	0
$995$	−17540.0	−0.558850
$996$	0	0
$997$	61186.0	1.94361	0.971805	−	0.235784i	$-0.0757658\pi$
$997$	61186.0	1.94361	0.971805	+	0.235784i	$0.0757658\pi$
$998$	0	0
$999$	2968.00	0.0939974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1840.4.a.d.1.1		1
4.3	odd	2		230.4.a.e.1.1	✓	1
12.11	even	2		2070.4.a.e.1.1		1
20.3	even	4		1150.4.b.f.599.1		2
20.7	even	4		1150.4.b.f.599.2		2
20.19	odd	2		1150.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.e.1.1	✓	1	4.3	odd	2
1150.4.a.b.1.1		1	20.19	odd	2
1150.4.b.f.599.1		2	20.3	even	4
1150.4.b.f.599.2		2	20.7	even	4
1840.4.a.d.1.1		1	1.1	even	1	trivial
2070.4.a.e.1.1		1	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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