LMFDB - Embedded newform 1805.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,4,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, 4, names="a")

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$106.498447560$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$

$=$

$q-5.00000 q^{2} +5.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -25.0000 q^{6} -19.0000 q^{7} -45.0000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-5.00000 q^{2} +5.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -25.0000 q^{6} -19.0000 q^{7} -45.0000 q^{8} -2.00000 q^{9} -25.0000 q^{10} +50.0000 q^{11} +85.0000 q^{12} +55.0000 q^{13} +95.0000 q^{14} +25.0000 q^{15} +89.0000 q^{16} +51.0000 q^{17} +10.0000 q^{18} +85.0000 q^{20} -95.0000 q^{21} -250.000 q^{22} -147.000 q^{23} -225.000 q^{24} +25.0000 q^{25} -275.000 q^{26} -145.000 q^{27} -323.000 q^{28} -165.000 q^{29} -125.000 q^{30} -70.0000 q^{31} -85.0000 q^{32} +250.000 q^{33} -255.000 q^{34} -95.0000 q^{35} -34.0000 q^{36} +210.000 q^{37} +275.000 q^{39} -225.000 q^{40} -80.0000 q^{41} +475.000 q^{42} -558.000 q^{43} +850.000 q^{44} -10.0000 q^{45} +735.000 q^{46} -464.000 q^{47} +445.000 q^{48} +18.0000 q^{49} -125.000 q^{50} +255.000 q^{51} +935.000 q^{52} +455.000 q^{53} +725.000 q^{54} +250.000 q^{55} +855.000 q^{56} +825.000 q^{58} +225.000 q^{59} +425.000 q^{60} +500.000 q^{61} +350.000 q^{62} +38.0000 q^{63} -287.000 q^{64} +275.000 q^{65} -1250.00 q^{66} +105.000 q^{67} +867.000 q^{68} -735.000 q^{69} +475.000 q^{70} -1140.00 q^{71} +90.0000 q^{72} -703.000 q^{73} -1050.00 q^{74} +125.000 q^{75} -950.000 q^{77} -1375.00 q^{78} +700.000 q^{79} +445.000 q^{80} -671.000 q^{81} +400.000 q^{82} -918.000 q^{83} -1615.00 q^{84} +255.000 q^{85} +2790.00 q^{86} -825.000 q^{87} -2250.00 q^{88} +870.000 q^{89} +50.0000 q^{90} -1045.00 q^{91} -2499.00 q^{92} -350.000 q^{93} +2320.00 q^{94} -425.000 q^{96} +1380.00 q^{97} -90.0000 q^{98} -100.000 q^{99} +O(q^{100})\)

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 $

$2$	−5.00000	−1.76777	−0.883883	−	0.467707i	$-0.845080\pi$
$2$	−5.00000	−1.76777	−0.883883	+	0.467707i	$0.845080\pi$
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	17.0000	2.12500
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−25.0000	−1.70103
$7$	−19.0000	−1.02590	−0.512952	−	0.858417i	$-0.671448\pi$
$7$	−19.0000	−1.02590	−0.512952	+	0.858417i	$0.671448\pi$
$8$	−45.0000	−1.98874
$9$	−2.00000	−0.0740741
$10$	−25.0000	−0.790569
$11$	50.0000	1.37051	0.685253	−	0.728305i	$-0.259692\pi$
$11$	50.0000	1.37051	0.685253	+	0.728305i	$0.259692\pi$
$12$	85.0000	2.04478
$13$	55.0000	1.17340	0.586702	−	0.809803i	$-0.300426\pi$
$13$	55.0000	1.17340	0.586702	+	0.809803i	$0.300426\pi$
$14$	95.0000	1.81356
$15$	25.0000	0.430331
$16$	89.0000	1.39062
$17$	51.0000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	51.0000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	10.0000	0.130946
$19$	0	0
$19$	0	0
$20$	85.0000	0.950329
$21$	−95.0000	−0.987176
$22$	−250.000	−2.42274
$23$	−147.000	−1.33268	−0.666340	−	0.745648i	$-0.732140\pi$
$23$	−147.000	−1.33268	−0.666340	+	0.745648i	$0.732140\pi$
$24$	−225.000	−1.91366
$25$	25.0000	0.200000
$26$	−275.000	−2.07431
$27$	−145.000	−1.03353
$28$	−323.000	−2.18005
$29$	−165.000	−1.05654	−0.528271	−	0.849076i	$-0.677160\pi$
$29$	−165.000	−1.05654	−0.528271	+	0.849076i	$0.677160\pi$
$30$	−125.000	−0.760726
$31$	−70.0000	−0.405560	−0.202780	−	0.979224i	$-0.564998\pi$
$31$	−70.0000	−0.405560	−0.202780	+	0.979224i	$0.564998\pi$
$32$	−85.0000	−0.469563
$33$	250.000	1.31877
$34$	−255.000	−1.28624
$35$	−95.0000	−0.458798
$36$	−34.0000	−0.157407
$37$	210.000	0.933075	0.466538	−	0.884501i	$-0.345501\pi$
$37$	210.000	0.933075	0.466538	+	0.884501i	$0.345501\pi$
$38$	0	0
$39$	275.000	1.12911
$40$	−225.000	−0.889391
$41$	−80.0000	−0.304729	−0.152365	−	0.988324i	$-0.548689\pi$
$41$	−80.0000	−0.304729	−0.152365	+	0.988324i	$0.548689\pi$
$42$	475.000	1.74510
$43$	−558.000	−1.97893	−0.989467	−	0.144755i	$-0.953760\pi$
$43$	−558.000	−1.97893	−0.989467	+	0.144755i	$0.953760\pi$
$44$	850.000	2.91233
$45$	−10.0000	−0.0331269
$46$	735.000	2.35587
$47$	−464.000	−1.44003	−0.720014	−	0.693959i	$-0.755865\pi$
$47$	−464.000	−1.44003	−0.720014	+	0.693959i	$0.755865\pi$
$48$	445.000	1.33813
$49$	18.0000	0.0524781
$50$	−125.000	−0.353553
$51$	255.000	0.700140
$52$	935.000	2.49348
$53$	455.000	1.17923	0.589614	−	0.807685i	$-0.299280\pi$
$53$	455.000	1.17923	0.589614	+	0.807685i	$0.299280\pi$
$54$	725.000	1.82704
$55$	250.000	0.612909
$56$	855.000	2.04025
$57$	0	0
$58$	825.000	1.86772
$59$	225.000	0.496483	0.248242	−	0.968698i	$-0.420147\pi$
$59$	225.000	0.496483	0.248242	+	0.968698i	$0.420147\pi$
$60$	425.000	0.914454
$61$	500.000	1.04948	0.524741	−	0.851262i	$-0.324162\pi$
$61$	500.000	1.04948	0.524741	+	0.851262i	$0.324162\pi$
$62$	350.000	0.716936
$63$	38.0000	0.0759929
$64$	−287.000	−0.560547
$65$	275.000	0.524762
$66$	−1250.00	−2.33128
$67$	105.000	0.191460	0.0957298	−	0.995407i	$-0.469482\pi$
$67$	105.000	0.191460	0.0957298	+	0.995407i	$0.469482\pi$
$68$	867.000	1.54616
$69$	−735.000	−1.28237
$70$	475.000	0.811048
$71$	−1140.00	−1.90554	−0.952768	−	0.303698i	$-0.901779\pi$
$71$	−1140.00	−1.90554	−0.952768	+	0.303698i	$0.901779\pi$
$72$	90.0000	0.147314
$73$	−703.000	−1.12712	−0.563561	−	0.826074i	$-0.690569\pi$
$73$	−703.000	−1.12712	−0.563561	+	0.826074i	$0.690569\pi$
$74$	−1050.00	−1.64946
$75$	125.000	0.192450
$76$	0	0
$77$	−950.000	−1.40601
$78$	−1375.00	−1.99600
$79$	700.000	0.996913	0.498457	−	0.866915i	$-0.333900\pi$
$79$	700.000	0.996913	0.498457	+	0.866915i	$0.333900\pi$
$80$	445.000	0.621906
$81$	−671.000	−0.920439
$82$	400.000	0.538690
$83$	−918.000	−1.21402	−0.607010	−	0.794695i	$-0.707631\pi$
$83$	−918.000	−1.21402	−0.607010	+	0.794695i	$0.707631\pi$
$84$	−1615.00	−2.09775
$85$	255.000	0.325396
$86$	2790.00	3.49830
$87$	−825.000	−1.01666
$88$	−2250.00	−2.72558
$89$	870.000	1.03618	0.518089	−	0.855327i	$-0.326644\pi$
$89$	870.000	1.03618	0.518089	+	0.855327i	$0.326644\pi$
$90$	50.0000	0.0585607
$91$	−1045.00	−1.20380
$92$	−2499.00	−2.83194
$93$	−350.000	−0.390251
$94$	2320.00	2.54564
$95$	0	0
$96$	−425.000	−0.451837
$97$	1380.00	1.44451	0.722257	−	0.691625i	$-0.243105\pi$
$97$	1380.00	1.44451	0.722257	+	0.691625i	$0.243105\pi$
$98$	−90.0000	−0.0927691
$99$	−100.000	−0.101519
$100$	425.000	0.425000
$101$	150.000	0.147778	0.0738889	−	0.997266i	$-0.476459\pi$
$101$	150.000	0.147778	0.0738889	+	0.997266i	$0.476459\pi$
$102$	−1275.00	−1.23768
$103$	−1250.00	−1.19579	−0.597894	−	0.801575i	$-0.703996\pi$
$103$	−1250.00	−1.19579	−0.597894	+	0.801575i	$0.703996\pi$
$104$	−2475.00	−2.33359
$105$	−475.000	−0.441479
$106$	−2275.00	−2.08460
$107$	−1205.00	−1.08871	−0.544354	−	0.838856i	$-0.683225\pi$
$107$	−1205.00	−1.08871	−0.544354	+	0.838856i	$0.683225\pi$
$108$	−2465.00	−2.19625
$109$	1245.00	1.09403	0.547015	−	0.837122i	$-0.315764\pi$
$109$	1245.00	1.09403	0.547015	+	0.837122i	$0.315764\pi$
$110$	−1250.00	−1.08348
$111$	1050.00	0.897852
$112$	−1691.00	−1.42665
$113$	−480.000	−0.399598	−0.199799	−	0.979837i	$-0.564029\pi$
$113$	−480.000	−0.399598	−0.199799	+	0.979837i	$0.564029\pi$
$114$	0	0
$115$	−735.000	−0.595992
$116$	−2805.00	−2.24515
$117$	−110.000	−0.0869188
$118$	−1125.00	−0.877666
$119$	−969.000	−0.746454
$120$	−1125.00	−0.855816
$121$	1169.00	0.878287
$122$	−2500.00	−1.85524
$123$	−400.000	−0.293226
$124$	−1190.00	−0.861816
$125$	125.000	0.0894427
$126$	−190.000	−0.134338
$127$	100.000	0.0698706	0.0349353	−	0.999390i	$-0.488877\pi$
$127$	100.000	0.0698706	0.0349353	+	0.999390i	$0.488877\pi$
$128$	2115.00	1.46048
$129$	−2790.00	−1.90423
$130$	−1375.00	−0.927658
$131$	1158.00	0.772328	0.386164	−	0.922430i	$-0.373800\pi$
$131$	1158.00	0.772328	0.386164	+	0.922430i	$0.373800\pi$
$132$	4250.00	2.80239
$133$	0	0
$134$	−525.000	−0.338456
$135$	−725.000	−0.462208
$136$	−2295.00	−1.44702
$137$	1759.00	1.09695	0.548473	−	0.836168i	$-0.315209\pi$
$137$	1759.00	1.09695	0.548473	+	0.836168i	$0.315209\pi$
$138$	3675.00	2.26693
$139$	−2226.00	−1.35832	−0.679161	−	0.733989i	$-0.737656\pi$
$139$	−2226.00	−1.35832	−0.679161	+	0.733989i	$0.737656\pi$
$140$	−1615.00	−0.974946
$141$	−2320.00	−1.38567
$142$	5700.00	3.36854
$143$	2750.00	1.60816
$144$	−178.000	−0.103009
$145$	−825.000	−0.472500
$146$	3515.00	1.99249
$147$	90.0000	0.0504971
$148$	3570.00	1.98279
$149$	1736.00	0.954488	0.477244	−	0.878771i	$-0.341636\pi$
$149$	1736.00	0.954488	0.477244	+	0.878771i	$0.341636\pi$
$150$	−625.000	−0.340207
$151$	−790.000	−0.425757	−0.212878	−	0.977079i	$-0.568284\pi$
$151$	−790.000	−0.425757	−0.212878	+	0.977079i	$0.568284\pi$
$152$	0	0
$153$	−102.000	−0.0538968
$154$	4750.00	2.48549
$155$	−350.000	−0.181372
$156$	4675.00	2.39936
$157$	−1944.00	−0.988204	−0.494102	−	0.869404i	$-0.664503\pi$
$157$	−1944.00	−0.988204	−0.494102	+	0.869404i	$0.664503\pi$
$158$	−3500.00	−1.76231
$159$	2275.00	1.13471
$160$	−425.000	−0.209995
$161$	2793.00	1.36720
$162$	3355.00	1.62712
$163$	−3562.00	−1.71164	−0.855820	−	0.517273i	$-0.826947\pi$
$163$	−3562.00	−1.71164	−0.855820	+	0.517273i	$0.826947\pi$
$164$	−1360.00	−0.647550
$165$	1250.00	0.589772
$166$	4590.00	2.14610
$167$	3360.00	1.55691	0.778457	−	0.627698i	$-0.216003\pi$
$167$	3360.00	1.55691	0.778457	+	0.627698i	$0.216003\pi$
$168$	4275.00	1.96323
$169$	828.000	0.376878
$170$	−1275.00	−0.575224
$171$	0	0
$172$	−9486.00	−4.20524
$173$	−3870.00	−1.70076	−0.850378	−	0.526173i	$-0.823626\pi$
$173$	−3870.00	−1.70076	−0.850378	+	0.526173i	$0.823626\pi$
$174$	4125.00	1.79722
$175$	−475.000	−0.205181
$176$	4450.00	1.90586
$177$	1125.00	0.477741
$178$	−4350.00	−1.83172
$179$	3340.00	1.39466	0.697328	−	0.716752i	$-0.254372\pi$
$179$	3340.00	1.39466	0.697328	+	0.716752i	$0.254372\pi$
$180$	−170.000	−0.0703947
$181$	1790.00	0.735081	0.367540	−	0.930008i	$-0.380200\pi$
$181$	1790.00	0.735081	0.367540	+	0.930008i	$0.380200\pi$
$182$	5225.00	2.12804
$183$	2500.00	1.00987
$184$	6615.00	2.65035
$185$	1050.00	0.417284
$186$	1750.00	0.689872
$187$	2550.00	0.997190
$188$	−7888.00	−3.06006
$189$	2755.00	1.06030
$190$	0	0
$191$	−1647.00	−0.623941	−0.311971	−	0.950092i	$-0.600989\pi$
$191$	−1647.00	−0.623941	−0.311971	+	0.950092i	$0.600989\pi$
$192$	−1435.00	−0.539386
$193$	−1030.00	−0.384150	−0.192075	−	0.981380i	$-0.561522\pi$
$193$	−1030.00	−0.384150	−0.192075	+	0.981380i	$0.561522\pi$
$194$	−6900.00	−2.55356
$195$	1375.00	0.504953
$196$	306.000	0.111516
$197$	−336.000	−0.121518	−0.0607589	−	0.998152i	$-0.519352\pi$
$197$	−336.000	−0.121518	−0.0607589	+	0.998152i	$0.519352\pi$
$198$	500.000	0.179462
$199$	−875.000	−0.311694	−0.155847	−	0.987781i	$-0.549811\pi$
$199$	−875.000	−0.311694	−0.155847	+	0.987781i	$0.549811\pi$
$200$	−1125.00	−0.397748
$201$	525.000	0.184232
$202$	−750.000	−0.261237
$203$	3135.00	1.08391
$204$	4335.00	1.48780
$205$	−400.000	−0.136279
$206$	6250.00	2.11387
$207$	294.000	0.0987170
$208$	4895.00	1.63177
$209$	0	0
$210$	2375.00	0.780431
$211$	−3935.00	−1.28387	−0.641935	−	0.766759i	$-0.721868\pi$
$211$	−3935.00	−1.28387	−0.641935	+	0.766759i	$0.721868\pi$
$212$	7735.00	2.50586
$213$	−5700.00	−1.83360
$214$	6025.00	1.92458
$215$	−2790.00	−0.885007
$216$	6525.00	2.05542
$217$	1330.00	0.416066
$218$	−6225.00	−1.93399
$219$	−3515.00	−1.08457
$220$	4250.00	1.30243
$221$	2805.00	0.853777
$222$	−5250.00	−1.58719
$223$	−5690.00	−1.70866	−0.854329	−	0.519733i	$-0.826031\pi$
$223$	−5690.00	−1.70866	−0.854329	+	0.519733i	$0.826031\pi$
$224$	1615.00	0.481726
$225$	−50.0000	−0.0148148
$226$	2400.00	0.706397
$227$	−2715.00	−0.793836	−0.396918	−	0.917854i	$-0.629920\pi$
$227$	−2715.00	−0.793836	−0.396918	+	0.917854i	$0.629920\pi$
$228$	0	0
$229$	−716.000	−0.206614	−0.103307	−	0.994650i	$-0.532942\pi$
$229$	−716.000	−0.206614	−0.103307	+	0.994650i	$0.532942\pi$
$230$	3675.00	1.05358
$231$	−4750.00	−1.35293
$232$	7425.00	2.10119
$233$	3182.00	0.894677	0.447339	−	0.894365i	$-0.352372\pi$
$233$	3182.00	0.894677	0.447339	+	0.894365i	$0.352372\pi$
$234$	550.000	0.153652
$235$	−2320.00	−0.644000
$236$	3825.00	1.05503
$237$	3500.00	0.959280
$238$	4845.00	1.31956
$239$	−4275.00	−1.15702	−0.578508	−	0.815677i	$-0.696365\pi$
$239$	−4275.00	−1.15702	−0.578508	+	0.815677i	$0.696365\pi$
$240$	2225.00	0.598430
$241$	−280.000	−0.0748398	−0.0374199	−	0.999300i	$-0.511914\pi$
$241$	−280.000	−0.0748398	−0.0374199	+	0.999300i	$0.511914\pi$
$242$	−5845.00	−1.55261
$243$	560.000	0.147835
$244$	8500.00	2.23015
$245$	90.0000	0.0234689
$246$	2000.00	0.518355
$247$	0	0
$248$	3150.00	0.806553
$249$	−4590.00	−1.16819
$250$	−625.000	−0.158114
$251$	1152.00	0.289696	0.144848	−	0.989454i	$-0.453731\pi$
$251$	1152.00	0.289696	0.144848	+	0.989454i	$0.453731\pi$
$252$	646.000	0.161485
$253$	−7350.00	−1.82644
$254$	−500.000	−0.123515
$255$	1275.00	0.313112
$256$	−8279.00	−2.02124
$257$	870.000	0.211164	0.105582	−	0.994411i	$-0.466329\pi$
$257$	870.000	0.211164	0.105582	+	0.994411i	$0.466329\pi$
$258$	13950.0	3.36624
$259$	−3990.00	−0.957245
$260$	4675.00	1.11512
$261$	330.000	0.0782624
$262$	−5790.00	−1.36530
$263$	−5688.00	−1.33360	−0.666801	−	0.745236i	$-0.732337\pi$
$263$	−5688.00	−1.33360	−0.666801	+	0.745236i	$0.732337\pi$
$264$	−11250.0	−2.62269
$265$	2275.00	0.527367
$266$	0	0
$267$	4350.00	0.997062
$268$	1785.00	0.406852
$269$	−1010.00	−0.228925	−0.114462	−	0.993428i	$-0.536515\pi$
$269$	−1010.00	−0.228925	−0.114462	+	0.993428i	$0.536515\pi$
$270$	3625.00	0.817076
$271$	25.0000	0.00560384	0.00280192	−	0.999996i	$-0.499108\pi$
$271$	25.0000	0.00560384	0.00280192	+	0.999996i	$0.499108\pi$
$272$	4539.00	1.01183
$273$	−5225.00	−1.15836
$274$	−8795.00	−1.93914
$275$	1250.00	0.274101
$276$	−12495.0	−2.72504
$277$	3646.00	0.790855	0.395428	−	0.918497i	$-0.370596\pi$
$277$	3646.00	0.790855	0.395428	+	0.918497i	$0.370596\pi$
$278$	11130.0	2.40120
$279$	140.000	0.0300415
$280$	4275.00	0.912429
$281$	6000.00	1.27377	0.636886	−	0.770958i	$-0.280222\pi$
$281$	6000.00	1.27377	0.636886	+	0.770958i	$0.280222\pi$
$282$	11600.0	2.44954
$283$	5018.00	1.05403	0.527013	−	0.849857i	$-0.323312\pi$
$283$	5018.00	1.05403	0.527013	+	0.849857i	$0.323312\pi$
$284$	−19380.0	−4.04927
$285$	0	0
$286$	−13750.0	−2.84285
$287$	1520.00	0.312623
$288$	170.000	0.0347825
$289$	−2312.00	−0.470588
$290$	4125.00	0.835270
$291$	6900.00	1.38998
$292$	−11951.0	−2.39513
$293$	−7035.00	−1.40269	−0.701347	−	0.712820i	$-0.747417\pi$
$293$	−7035.00	−1.40269	−0.701347	+	0.712820i	$0.747417\pi$
$294$	−450.000	−0.0892671
$295$	1125.00	0.222034
$296$	−9450.00	−1.85564
$297$	−7250.00	−1.41646
$298$	−8680.00	−1.68731
$299$	−8085.00	−1.56377
$300$	2125.00	0.408956
$301$	10602.0	2.03020
$302$	3950.00	0.752639
$303$	750.000	0.142199
$304$	0	0
$305$	2500.00	0.469343
$306$	510.000	0.0952770
$307$	−4460.00	−0.829139	−0.414569	−	0.910018i	$-0.636068\pi$
$307$	−4460.00	−0.829139	−0.414569	+	0.910018i	$0.636068\pi$
$308$	−16150.0	−2.98777
$309$	−6250.00	−1.15065
$310$	1750.00	0.320624
$311$	6825.00	1.24441	0.622203	−	0.782856i	$-0.286238\pi$
$311$	6825.00	1.24441	0.622203	+	0.782856i	$0.286238\pi$
$312$	−12375.0	−2.24550
$313$	4537.00	0.819318	0.409659	−	0.912239i	$-0.365648\pi$
$313$	4537.00	0.819318	0.409659	+	0.912239i	$0.365648\pi$
$314$	9720.00	1.74692
$315$	190.000	0.0339850
$316$	11900.0	2.11844
$317$	7845.00	1.38997	0.694983	−	0.719026i	$-0.255412\pi$
$317$	7845.00	1.38997	0.694983	+	0.719026i	$0.255412\pi$
$318$	−11375.0	−2.00591
$319$	−8250.00	−1.44800
$320$	−1435.00	−0.250684
$321$	−6025.00	−1.04761
$322$	−13965.0	−2.41689
$323$	0	0
$324$	−11407.0	−1.95593
$325$	1375.00	0.234681
$326$	17810.0	3.02578
$327$	6225.00	1.05273
$328$	3600.00	0.606027
$329$	8816.00	1.47733
$330$	−6250.00	−1.04258
$331$	7075.00	1.17486	0.587428	−	0.809277i	$-0.300141\pi$
$331$	7075.00	1.17486	0.587428	+	0.809277i	$0.300141\pi$
$332$	−15606.0	−2.57979
$333$	−420.000	−0.0691167
$334$	−16800.0	−2.75226
$335$	525.000	0.0856233
$336$	−8455.00	−1.37279
$337$	−11710.0	−1.89283	−0.946416	−	0.322950i	$-0.895325\pi$
$337$	−11710.0	−1.89283	−0.946416	+	0.322950i	$0.895325\pi$
$338$	−4140.00	−0.666232
$339$	−2400.00	−0.384514
$340$	4335.00	0.691466
$341$	−3500.00	−0.555823
$342$	0	0
$343$	6175.00	0.972066
$344$	25110.0	3.93558
$345$	−3675.00	−0.573494
$346$	19350.0	3.00654
$347$	−336.000	−0.0519811	−0.0259905	−	0.999662i	$-0.508274\pi$
$347$	−336.000	−0.0519811	−0.0259905	+	0.999662i	$0.508274\pi$
$348$	−14025.0	−2.16040
$349$	−700.000	−0.107364	−0.0536822	−	0.998558i	$-0.517096\pi$
$349$	−700.000	−0.107364	−0.0536822	+	0.998558i	$0.517096\pi$
$350$	2375.00	0.362712
$351$	−7975.00	−1.21275
$352$	−4250.00	−0.643539
$353$	−8923.00	−1.34539	−0.672696	−	0.739919i	$-0.734864\pi$
$353$	−8923.00	−1.34539	−0.672696	+	0.739919i	$0.734864\pi$
$354$	−5625.00	−0.844535
$355$	−5700.00	−0.852182
$356$	14790.0	2.20188
$357$	−4845.00	−0.718276
$358$	−16700.0	−2.46543
$359$	−7521.00	−1.10569	−0.552846	−	0.833284i	$-0.686458\pi$
$359$	−7521.00	−1.10569	−0.552846	+	0.833284i	$0.686458\pi$
$360$	450.000	0.0658808
$361$	0	0
$362$	−8950.00	−1.29945
$363$	5845.00	0.845132
$364$	−17765.0	−2.55807
$365$	−3515.00	−0.504064
$366$	−12500.0	−1.78521
$367$	4624.00	0.657686	0.328843	−	0.944385i	$-0.393341\pi$
$367$	4624.00	0.657686	0.328843	+	0.944385i	$0.393341\pi$
$368$	−13083.0	−1.85326
$369$	160.000	0.0225725
$370$	−5250.00	−0.737661
$371$	−8645.00	−1.20977
$372$	−5950.00	−0.829283
$373$	−9015.00	−1.25142	−0.625709	−	0.780056i	$-0.715190\pi$
$373$	−9015.00	−1.25142	−0.625709	+	0.780056i	$0.715190\pi$
$374$	−12750.0	−1.76280
$375$	625.000	0.0860663
$376$	20880.0	2.86384
$377$	−9075.00	−1.23975
$378$	−13775.0	−1.87436
$379$	−3895.00	−0.527896	−0.263948	−	0.964537i	$-0.585025\pi$
$379$	−3895.00	−0.527896	−0.263948	+	0.964537i	$0.585025\pi$
$380$	0	0
$381$	500.000	0.0672330
$382$	8235.00	1.10298
$383$	9690.00	1.29278	0.646391	−	0.763006i	$-0.276277\pi$
$383$	9690.00	1.29278	0.646391	+	0.763006i	$0.276277\pi$
$384$	10575.0	1.40535
$385$	−4750.00	−0.628785
$386$	5150.00	0.679088
$387$	1116.00	0.146588
$388$	23460.0	3.06959
$389$	−5650.00	−0.736417	−0.368209	−	0.929743i	$-0.620029\pi$
$389$	−5650.00	−0.736417	−0.368209	+	0.929743i	$0.620029\pi$
$390$	−6875.00	−0.892639
$391$	−7497.00	−0.969666
$392$	−810.000	−0.104365
$393$	5790.00	0.743173
$394$	1680.00	0.214815
$395$	3500.00	0.445833
$396$	−1700.00	−0.215728
$397$	3386.00	0.428057	0.214028	−	0.976827i	$-0.431342\pi$
$397$	3386.00	0.428057	0.214028	+	0.976827i	$0.431342\pi$
$398$	4375.00	0.551002
$399$	0	0
$400$	2225.00	0.278125
$401$	−11840.0	−1.47447	−0.737234	−	0.675638i	$-0.763868\pi$
$401$	−11840.0	−1.47447	−0.737234	+	0.675638i	$0.763868\pi$
$402$	−2625.00	−0.325679
$403$	−3850.00	−0.475886
$404$	2550.00	0.314028
$405$	−3355.00	−0.411633
$406$	−15675.0	−1.91610
$407$	10500.0	1.27879
$408$	−11475.0	−1.39239
$409$	−6770.00	−0.818472	−0.409236	−	0.912429i	$-0.634205\pi$
$409$	−6770.00	−0.818472	−0.409236	+	0.912429i	$0.634205\pi$
$410$	2000.00	0.240910
$411$	8795.00	1.05554
$412$	−21250.0	−2.54105
$413$	−4275.00	−0.509344
$414$	−1470.00	−0.174509
$415$	−4590.00	−0.542926
$416$	−4675.00	−0.550987
$417$	−11130.0	−1.30705
$418$	0	0
$419$	4550.00	0.530506	0.265253	−	0.964179i	$-0.414545\pi$
$419$	4550.00	0.530506	0.265253	+	0.964179i	$0.414545\pi$
$420$	−8075.00	−0.938142
$421$	−3085.00	−0.357135	−0.178567	−	0.983928i	$-0.557146\pi$
$421$	−3085.00	−0.357135	−0.178567	+	0.983928i	$0.557146\pi$
$422$	19675.0	2.26958
$423$	928.000	0.106669
$424$	−20475.0	−2.34517
$425$	1275.00	0.145521
$426$	28500.0	3.24138
$427$	−9500.00	−1.07667
$428$	−20485.0	−2.31350
$429$	13750.0	1.54745
$430$	13950.0	1.56449
$431$	4780.00	0.534210	0.267105	−	0.963667i	$-0.413933\pi$
$431$	4780.00	0.534210	0.267105	+	0.963667i	$0.413933\pi$
$432$	−12905.0	−1.43725
$433$	−8570.00	−0.951150	−0.475575	−	0.879675i	$-0.657760\pi$
$433$	−8570.00	−0.951150	−0.475575	+	0.879675i	$0.657760\pi$
$434$	−6650.00	−0.735507
$435$	−4125.00	−0.454663
$436$	21165.0	2.32482
$437$	0	0
$438$	17575.0	1.91727
$439$	−7220.00	−0.784947	−0.392474	−	0.919763i	$-0.628381\pi$
$439$	−7220.00	−0.784947	−0.392474	+	0.919763i	$0.628381\pi$
$440$	−11250.0	−1.21892
$441$	−36.0000	−0.00388727
$442$	−14025.0	−1.50928
$443$	−10258.0	−1.10016	−0.550082	−	0.835111i	$-0.685403\pi$
$443$	−10258.0	−1.10016	−0.550082	+	0.835111i	$0.685403\pi$
$444$	17850.0	1.90794
$445$	4350.00	0.463393
$446$	28450.0	3.02051
$447$	8680.00	0.918456
$448$	5453.00	0.575067
$449$	7530.00	0.791454	0.395727	−	0.918368i	$-0.370493\pi$
$449$	7530.00	0.791454	0.395727	+	0.918368i	$0.370493\pi$
$450$	250.000	0.0261891
$451$	−4000.00	−0.417633
$452$	−8160.00	−0.849146
$453$	−3950.00	−0.409685
$454$	13575.0	1.40332
$455$	−5225.00	−0.538356
$456$	0	0
$457$	−8819.00	−0.902703	−0.451352	−	0.892346i	$-0.649058\pi$
$457$	−8819.00	−0.902703	−0.451352	+	0.892346i	$0.649058\pi$
$458$	3580.00	0.365245
$459$	−7395.00	−0.752002
$460$	−12495.0	−1.26648
$461$	10232.0	1.03373	0.516867	−	0.856065i	$-0.327098\pi$
$461$	10232.0	1.03373	0.516867	+	0.856065i	$0.327098\pi$
$462$	23750.0	2.39167
$463$	−12112.0	−1.21575	−0.607875	−	0.794033i	$-0.707978\pi$
$463$	−12112.0	−1.21575	−0.607875	+	0.794033i	$0.707978\pi$
$464$	−14685.0	−1.46925
$465$	−1750.00	−0.174525
$466$	−15910.0	−1.58158
$467$	−5076.00	−0.502975	−0.251487	−	0.967861i	$-0.580920\pi$
$467$	−5076.00	−0.502975	−0.251487	+	0.967861i	$0.580920\pi$
$468$	−1870.00	−0.184703
$469$	−1995.00	−0.196419
$470$	11600.0	1.13844
$471$	−9720.00	−0.950900
$472$	−10125.0	−0.987375
$473$	−27900.0	−2.71214
$474$	−17500.0	−1.69578
$475$	0	0
$476$	−16473.0	−1.58622
$477$	−910.000	−0.0873502
$478$	21375.0	2.04533
$479$	15384.0	1.46746	0.733730	−	0.679442i	$-0.237778\pi$
$479$	15384.0	1.46746	0.733730	+	0.679442i	$0.237778\pi$
$480$	−2125.00	−0.202068
$481$	11550.0	1.09487
$482$	1400.00	0.132299
$483$	13965.0	1.31559
$484$	19873.0	1.86636
$485$	6900.00	0.646006
$486$	−2800.00	−0.261339
$487$	−8350.00	−0.776950	−0.388475	−	0.921459i	$-0.626998\pi$
$487$	−8350.00	−0.776950	−0.388475	+	0.921459i	$0.626998\pi$
$488$	−22500.0	−2.08715
$489$	−17810.0	−1.64703
$490$	−450.000	−0.0414876
$491$	−8772.00	−0.806262	−0.403131	−	0.915142i	$-0.632078\pi$
$491$	−8772.00	−0.806262	−0.403131	+	0.915142i	$0.632078\pi$
$492$	−6800.00	−0.623105
$493$	−8415.00	−0.768748
$494$	0	0
$495$	−500.000	−0.0454007
$496$	−6230.00	−0.563982
$497$	21660.0	1.95490
$498$	22950.0	2.06509
$499$	−2786.00	−0.249937	−0.124968	−	0.992161i	$-0.539883\pi$
$499$	−2786.00	−0.249937	−0.124968	+	0.992161i	$0.539883\pi$
$500$	2125.00	0.190066
$501$	16800.0	1.49814
$502$	−5760.00	−0.512114
$503$	−727.000	−0.0644440	−0.0322220	−	0.999481i	$-0.510258\pi$
$503$	−727.000	−0.0644440	−0.0322220	+	0.999481i	$0.510258\pi$
$504$	−1710.00	−0.151130
$505$	750.000	0.0660882
$506$	36750.0	3.22873
$507$	4140.00	0.362651
$508$	1700.00	0.148475
$509$	−2370.00	−0.206382	−0.103191	−	0.994662i	$-0.532905\pi$
$509$	−2370.00	−0.206382	−0.103191	+	0.994662i	$0.532905\pi$
$510$	−6375.00	−0.553509
$511$	13357.0	1.15632
$512$	24475.0	2.11260
$513$	0	0
$514$	−4350.00	−0.373288
$515$	−6250.00	−0.534773
$516$	−47430.0	−4.04649
$517$	−23200.0	−1.97357
$518$	19950.0	1.69219
$519$	−19350.0	−1.63655
$520$	−12375.0	−1.04361
$521$	12460.0	1.04776	0.523880	−	0.851792i	$-0.324484\pi$
$521$	12460.0	1.04776	0.523880	+	0.851792i	$0.324484\pi$
$522$	−1650.00	−0.138350
$523$	−14705.0	−1.22945	−0.614727	−	0.788740i	$-0.710734\pi$
$523$	−14705.0	−1.22945	−0.614727	+	0.788740i	$0.710734\pi$
$524$	19686.0	1.64120
$525$	−2375.00	−0.197435
$526$	28440.0	2.35750
$527$	−3570.00	−0.295089
$528$	22250.0	1.83391
$529$	9442.00	0.776034
$530$	−11375.0	−0.932261
$531$	−450.000	−0.0367765
$532$	0	0
$533$	−4400.00	−0.357571
$534$	−21750.0	−1.76257
$535$	−6025.00	−0.486885
$536$	−4725.00	−0.380763
$537$	16700.0	1.34201
$538$	5050.00	0.404686
$539$	900.000	0.0719216
$540$	−12325.0	−0.982192
$541$	−11450.0	−0.909933	−0.454967	−	0.890508i	$-0.650349\pi$
$541$	−11450.0	−0.909933	−0.454967	+	0.890508i	$0.650349\pi$
$542$	−125.000	−0.00990629
$543$	8950.00	0.707332
$544$	−4335.00	−0.341657
$545$	6225.00	0.489266
$546$	26125.0	2.04770
$547$	−12500.0	−0.977078	−0.488539	−	0.872542i	$-0.662470\pi$
$547$	−12500.0	−0.977078	−0.488539	+	0.872542i	$0.662470\pi$
$548$	29903.0	2.33101
$549$	−1000.00	−0.0777395
$550$	−6250.00	−0.484547
$551$	0	0
$552$	33075.0	2.55030
$553$	−13300.0	−1.02274
$554$	−18230.0	−1.39805
$555$	5250.00	0.401532
$556$	−37842.0	−2.88644
$557$	8006.00	0.609022	0.304511	−	0.952509i	$-0.401507\pi$
$557$	8006.00	0.609022	0.304511	+	0.952509i	$0.401507\pi$
$558$	−700.000	−0.0531064
$559$	−30690.0	−2.32209
$560$	−8455.00	−0.638016
$561$	12750.0	0.959546
$562$	−30000.0	−2.25173
$563$	−7280.00	−0.544965	−0.272483	−	0.962161i	$-0.587845\pi$
$563$	−7280.00	−0.544965	−0.272483	+	0.962161i	$0.587845\pi$
$564$	−39440.0	−2.94455
$565$	−2400.00	−0.178706
$566$	−25090.0	−1.86327
$567$	12749.0	0.944282
$568$	51300.0	3.78961
$569$	−2080.00	−0.153248	−0.0766240	−	0.997060i	$-0.524414\pi$
$569$	−2080.00	−0.153248	−0.0766240	+	0.997060i	$0.524414\pi$
$570$	0	0
$571$	7700.00	0.564334	0.282167	−	0.959365i	$-0.408947\pi$
$571$	7700.00	0.564334	0.282167	+	0.959365i	$0.408947\pi$
$572$	46750.0	3.41734
$573$	−8235.00	−0.600388
$574$	−7600.00	−0.552644
$575$	−3675.00	−0.266536
$576$	574.000	0.0415220
$577$	23171.0	1.67179	0.835894	−	0.548891i	$-0.184950\pi$
$577$	23171.0	1.67179	0.835894	+	0.548891i	$0.184950\pi$
$578$	11560.0	0.831890
$579$	−5150.00	−0.369649
$580$	−14025.0	−1.00406
$581$	17442.0	1.24547
$582$	−34500.0	−2.45717
$583$	22750.0	1.61614
$584$	31635.0	2.24155
$585$	−550.000	−0.0388713
$586$	35175.0	2.47963
$587$	−3984.00	−0.280132	−0.140066	−	0.990142i	$-0.544731\pi$
$587$	−3984.00	−0.280132	−0.140066	+	0.990142i	$0.544731\pi$
$588$	1530.00	0.107306
$589$	0	0
$590$	−5625.00	−0.392504
$591$	−1680.00	−0.116931
$592$	18690.0	1.29756
$593$	−7458.00	−0.516464	−0.258232	−	0.966083i	$-0.583140\pi$
$593$	−7458.00	−0.516464	−0.258232	+	0.966083i	$0.583140\pi$
$594$	36250.0	2.50397
$595$	−4845.00	−0.333825
$596$	29512.0	2.02829
$597$	−4375.00	−0.299928
$598$	40425.0	2.76438
$599$	22000.0	1.50066	0.750330	−	0.661063i	$-0.229894\pi$
$599$	22000.0	1.50066	0.750330	+	0.661063i	$0.229894\pi$
$600$	−5625.00	−0.382733
$601$	−25270.0	−1.71512	−0.857558	−	0.514387i	$-0.828019\pi$
$601$	−25270.0	−1.71512	−0.857558	+	0.514387i	$0.828019\pi$
$602$	−53010.0	−3.58891
$603$	−210.000	−0.0141822
$604$	−13430.0	−0.904733
$605$	5845.00	0.392782
$606$	−3750.00	−0.251375
$607$	780.000	0.0521569	0.0260784	−	0.999660i	$-0.491698\pi$
$607$	780.000	0.0521569	0.0260784	+	0.999660i	$0.491698\pi$
$608$	0	0
$609$	15675.0	1.04299
$610$	−12500.0	−0.829689
$611$	−25520.0	−1.68974
$612$	−1734.00	−0.114531
$613$	−7162.00	−0.471893	−0.235947	−	0.971766i	$-0.575819\pi$
$613$	−7162.00	−0.471893	−0.235947	+	0.971766i	$0.575819\pi$
$614$	22300.0	1.46572
$615$	−2000.00	−0.131135
$616$	42750.0	2.79618
$617$	−14174.0	−0.924836	−0.462418	−	0.886662i	$-0.653018\pi$
$617$	−14174.0	−0.924836	−0.462418	+	0.886662i	$0.653018\pi$
$618$	31250.0	2.03408
$619$	10844.0	0.704131	0.352066	−	0.935975i	$-0.385479\pi$
$619$	10844.0	0.704131	0.352066	+	0.935975i	$0.385479\pi$
$620$	−5950.00	−0.385416
$621$	21315.0	1.37736
$622$	−34125.0	−2.19982
$623$	−16530.0	−1.06302
$624$	24475.0	1.57017
$625$	625.000	0.0400000
$626$	−22685.0	−1.44836
$627$	0	0
$628$	−33048.0	−2.09993
$629$	10710.0	0.678912
$630$	−950.000	−0.0600776
$631$	−26200.0	−1.65294	−0.826470	−	0.562980i	$-0.809655\pi$
$631$	−26200.0	−1.65294	−0.826470	+	0.562980i	$0.809655\pi$
$632$	−31500.0	−1.98260
$633$	−19675.0	−1.23540
$634$	−39225.0	−2.45714
$635$	500.000	0.0312471
$636$	38675.0	2.41126
$637$	990.000	0.0615781
$638$	41250.0	2.55972
$639$	2280.00	0.141151
$640$	10575.0	0.653146
$641$	11970.0	0.737577	0.368788	−	0.929513i	$-0.379773\pi$
$641$	11970.0	0.737577	0.368788	+	0.929513i	$0.379773\pi$
$642$	30125.0	1.85193
$643$	−6792.00	−0.416564	−0.208282	−	0.978069i	$-0.566787\pi$
$643$	−6792.00	−0.416564	−0.208282	+	0.978069i	$0.566787\pi$
$644$	47481.0	2.90530
$645$	−13950.0	−0.851598
$646$	0	0
$647$	11561.0	0.702488	0.351244	−	0.936284i	$-0.385759\pi$
$647$	11561.0	0.702488	0.351244	+	0.936284i	$0.385759\pi$
$648$	30195.0	1.83051
$649$	11250.0	0.680433
$650$	−6875.00	−0.414861
$651$	6650.00	0.400360
$652$	−60554.0	−3.63724
$653$	20198.0	1.21043	0.605213	−	0.796063i	$-0.293088\pi$
$653$	20198.0	1.21043	0.605213	+	0.796063i	$0.293088\pi$
$654$	−31125.0	−1.86098
$655$	5790.00	0.345395
$656$	−7120.00	−0.423764
$657$	1406.00	0.0834905
$658$	−44080.0	−2.61158
$659$	−8445.00	−0.499197	−0.249598	−	0.968349i	$-0.580299\pi$
$659$	−8445.00	−0.499197	−0.249598	+	0.968349i	$0.580299\pi$
$660$	21250.0	1.25327
$661$	−3095.00	−0.182120	−0.0910602	−	0.995845i	$-0.529026\pi$
$661$	−3095.00	−0.182120	−0.0910602	+	0.995845i	$0.529026\pi$
$662$	−35375.0	−2.07687
$663$	14025.0	0.821547
$664$	41310.0	2.41437
$665$	0	0
$666$	2100.00	0.122182
$667$	24255.0	1.40803
$668$	57120.0	3.30844
$669$	−28450.0	−1.64416
$670$	−2625.00	−0.151362
$671$	25000.0	1.43832
$672$	8075.00	0.463541
$673$	−7880.00	−0.451340	−0.225670	−	0.974204i	$-0.572457\pi$
$673$	−7880.00	−0.451340	−0.225670	+	0.974204i	$0.572457\pi$
$674$	58550.0	3.34609
$675$	−3625.00	−0.206706
$676$	14076.0	0.800865
$677$	−3975.00	−0.225660	−0.112830	−	0.993614i	$-0.535992\pi$
$677$	−3975.00	−0.225660	−0.112830	+	0.993614i	$0.535992\pi$
$678$	12000.0	0.679730
$679$	−26220.0	−1.48193
$680$	−11475.0	−0.647127
$681$	−13575.0	−0.763870
$682$	17500.0	0.982565
$683$	19140.0	1.07229	0.536143	−	0.844127i	$-0.319881\pi$
$683$	19140.0	1.07229	0.536143	+	0.844127i	$0.319881\pi$
$684$	0	0
$685$	8795.00	0.490569
$686$	−30875.0	−1.71839
$687$	−3580.00	−0.198814
$688$	−49662.0	−2.75196
$689$	25025.0	1.38371
$690$	18375.0	1.01380
$691$	−17200.0	−0.946916	−0.473458	−	0.880816i	$-0.656994\pi$
$691$	−17200.0	−0.946916	−0.473458	+	0.880816i	$0.656994\pi$
$692$	−65790.0	−3.61410
$693$	1900.00	0.104149
$694$	1680.00	0.0918904
$695$	−11130.0	−0.607460
$696$	37125.0	2.02187
$697$	−4080.00	−0.221723
$698$	3500.00	0.189795
$699$	15910.0	0.860903
$700$	−8075.00	−0.436009
$701$	10400.0	0.560346	0.280173	−	0.959950i	$-0.409608\pi$
$701$	10400.0	0.560346	0.280173	+	0.959950i	$0.409608\pi$
$702$	39875.0	2.14385
$703$	0	0
$704$	−14350.0	−0.768233
$705$	−11600.0	−0.619690
$706$	44615.0	2.37834
$707$	−2850.00	−0.151606
$708$	19125.0	1.01520
$709$	10800.0	0.572077	0.286038	−	0.958218i	$-0.407661\pi$
$709$	10800.0	0.572077	0.286038	+	0.958218i	$0.407661\pi$
$710$	28500.0	1.50646
$711$	−1400.00	−0.0738454
$712$	−39150.0	−2.06069
$713$	10290.0	0.540482
$714$	24225.0	1.26974
$715$	13750.0	0.719190
$716$	56780.0	2.96364
$717$	−21375.0	−1.11334
$718$	37605.0	1.95460
$719$	16569.0	0.859415	0.429708	−	0.902968i	$-0.358617\pi$
$719$	16569.0	0.859415	0.429708	+	0.902968i	$0.358617\pi$
$720$	−890.000	−0.0460671
$721$	23750.0	1.22676
$722$	0	0
$723$	−1400.00	−0.0720146
$724$	30430.0	1.56205
$725$	−4125.00	−0.211308
$726$	−29225.0	−1.49400
$727$	−371.000	−0.0189266	−0.00946329	−	0.999955i	$-0.503012\pi$
$727$	−371.000	−0.0189266	−0.00946329	+	0.999955i	$0.503012\pi$
$728$	47025.0	2.39404
$729$	20917.0	1.06269
$730$	17575.0	0.891068
$731$	−28458.0	−1.43989
$732$	42500.0	2.14596
$733$	−35318.0	−1.77967	−0.889836	−	0.456280i	$-0.849182\pi$
$733$	−35318.0	−1.77967	−0.889836	+	0.456280i	$0.849182\pi$
$734$	−23120.0	−1.16264
$735$	450.000	0.0225830
$736$	12495.0	0.625777
$737$	5250.00	0.262397
$738$	−800.000	−0.0399030
$739$	−8600.00	−0.428087	−0.214043	−	0.976824i	$-0.568663\pi$
$739$	−8600.00	−0.428087	−0.214043	+	0.976824i	$0.568663\pi$
$740$	17850.0	0.886728
$741$	0	0
$742$	43225.0	2.13860
$743$	−29730.0	−1.46795	−0.733976	−	0.679176i	$-0.762337\pi$
$743$	−29730.0	−1.46795	−0.733976	+	0.679176i	$0.762337\pi$
$744$	15750.0	0.776106
$745$	8680.00	0.426860
$746$	45075.0	2.21222
$747$	1836.00	0.0899273
$748$	43350.0	2.11903
$749$	22895.0	1.11691
$750$	−3125.00	−0.152145
$751$	10680.0	0.518933	0.259467	−	0.965752i	$-0.416453\pi$
$751$	10680.0	0.518933	0.259467	+	0.965752i	$0.416453\pi$
$752$	−41296.0	−2.00254
$753$	5760.00	0.278760
$754$	45375.0	2.19159
$755$	−3950.00	−0.190404
$756$	46835.0	2.25314
$757$	35444.0	1.70176	0.850881	−	0.525358i	$-0.176069\pi$
$757$	35444.0	1.70176	0.850881	+	0.525358i	$0.176069\pi$
$758$	19475.0	0.933198
$759$	−36750.0	−1.75750
$760$	0	0
$761$	−14525.0	−0.691893	−0.345947	−	0.938254i	$-0.612442\pi$
$761$	−14525.0	−0.691893	−0.345947	+	0.938254i	$0.612442\pi$
$762$	−2500.00	−0.118852
$763$	−23655.0	−1.12237
$764$	−27999.0	−1.32587
$765$	−510.000	−0.0241034
$766$	−48450.0	−2.28534
$767$	12375.0	0.582575
$768$	−41395.0	−1.94494
$769$	22169.0	1.03958	0.519788	−	0.854295i	$-0.326011\pi$
$769$	22169.0	1.03958	0.519788	+	0.854295i	$0.326011\pi$
$770$	23750.0	1.11155
$771$	4350.00	0.203193
$772$	−17510.0	−0.816320
$773$	−26435.0	−1.23001	−0.615007	−	0.788522i	$-0.710847\pi$
$773$	−26435.0	−1.23001	−0.615007	+	0.788522i	$0.710847\pi$
$774$	−5580.00	−0.259133
$775$	−1750.00	−0.0811121
$776$	−62100.0	−2.87276
$777$	−19950.0	−0.921110
$778$	28250.0	1.30181
$779$	0	0
$780$	23375.0	1.07302
$781$	−57000.0	−2.61155
$782$	37485.0	1.71414
$783$	23925.0	1.09197
$784$	1602.00	0.0729774
$785$	−9720.00	−0.441938
$786$	−28950.0	−1.31376
$787$	−37175.0	−1.68379	−0.841897	−	0.539638i	$-0.818561\pi$
$787$	−37175.0	−1.68379	−0.841897	+	0.539638i	$0.818561\pi$
$788$	−5712.00	−0.258225
$789$	−28440.0	−1.28326
$790$	−17500.0	−0.788129
$791$	9120.00	0.409949
$792$	4500.00	0.201895
$793$	27500.0	1.23147
$794$	−16930.0	−0.756704
$795$	11375.0	0.507459
$796$	−14875.0	−0.662350
$797$	−16205.0	−0.720214	−0.360107	−	0.932911i	$-0.617260\pi$
$797$	−16205.0	−0.720214	−0.360107	+	0.932911i	$0.617260\pi$
$798$	0	0
$799$	−23664.0	−1.04777
$800$	−2125.00	−0.0939126
$801$	−1740.00	−0.0767539
$802$	59200.0	2.60651
$803$	−35150.0	−1.54473
$804$	8925.00	0.391493
$805$	13965.0	0.611431
$806$	19250.0	0.841256
$807$	−5050.00	−0.220283
$808$	−6750.00	−0.293891
$809$	−13675.0	−0.594298	−0.297149	−	0.954831i	$-0.596036\pi$
$809$	−13675.0	−0.594298	−0.297149	+	0.954831i	$0.596036\pi$
$810$	16775.0	0.727671
$811$	9275.00	0.401590	0.200795	−	0.979633i	$-0.435648\pi$
$811$	9275.00	0.401590	0.200795	+	0.979633i	$0.435648\pi$
$812$	53295.0	2.30331
$813$	125.000	0.00539230
$814$	−52500.0	−2.26059
$815$	−17810.0	−0.765469
$816$	22695.0	0.973632
$817$	0	0
$818$	33850.0	1.44687
$819$	2090.00	0.0891703
$820$	−6800.00	−0.289593
$821$	9938.00	0.422459	0.211229	−	0.977437i	$-0.432253\pi$
$821$	9938.00	0.422459	0.211229	+	0.977437i	$0.432253\pi$
$822$	−43975.0	−1.86594
$823$	8203.00	0.347435	0.173717	−	0.984796i	$-0.444422\pi$
$823$	8203.00	0.347435	0.173717	+	0.984796i	$0.444422\pi$
$824$	56250.0	2.37811
$825$	6250.00	0.263754
$826$	21375.0	0.900401
$827$	31905.0	1.34153	0.670765	−	0.741670i	$-0.265966\pi$
$827$	31905.0	1.34153	0.670765	+	0.741670i	$0.265966\pi$
$828$	4998.00	0.209774
$829$	7325.00	0.306885	0.153443	−	0.988158i	$-0.450964\pi$
$829$	7325.00	0.306885	0.153443	+	0.988158i	$0.450964\pi$
$830$	22950.0	0.959766
$831$	18230.0	0.761001
$832$	−15785.0	−0.657748
$833$	918.000	0.0381835
$834$	55650.0	2.31055
$835$	16800.0	0.696273
$836$	0	0
$837$	10150.0	0.419158
$838$	−22750.0	−0.937811
$839$	26370.0	1.08509	0.542547	−	0.840026i	$-0.317460\pi$
$839$	26370.0	1.08509	0.542547	+	0.840026i	$0.317460\pi$
$840$	21375.0	0.877985
$841$	2836.00	0.116282
$842$	15425.0	0.631331
$843$	30000.0	1.22569
$844$	−66895.0	−2.72822
$845$	4140.00	0.168545
$846$	−4640.00	−0.188566
$847$	−22211.0	−0.901038
$848$	40495.0	1.63986
$849$	25090.0	1.01424
$850$	−6375.00	−0.257248
$851$	−30870.0	−1.24349
$852$	−96900.0	−3.89641
$853$	−8898.00	−0.357165	−0.178582	−	0.983925i	$-0.557151\pi$
$853$	−8898.00	−0.357165	−0.178582	+	0.983925i	$0.557151\pi$
$854$	47500.0	1.90330
$855$	0	0
$856$	54225.0	2.16515
$857$	−33200.0	−1.32333	−0.661663	−	0.749801i	$-0.730149\pi$
$857$	−33200.0	−1.32333	−0.661663	+	0.749801i	$0.730149\pi$
$858$	−68750.0	−2.73553
$859$	15450.0	0.613675	0.306838	−	0.951762i	$-0.400729\pi$
$859$	15450.0	0.613675	0.306838	+	0.951762i	$0.400729\pi$
$860$	−47430.0	−1.88064
$861$	7600.00	0.300821
$862$	−23900.0	−0.944359
$863$	18140.0	0.715519	0.357759	−	0.933814i	$-0.383541\pi$
$863$	18140.0	0.715519	0.357759	+	0.933814i	$0.383541\pi$
$864$	12325.0	0.485307
$865$	−19350.0	−0.760601
$866$	42850.0	1.68141
$867$	−11560.0	−0.452824
$868$	22610.0	0.884140
$869$	35000.0	1.36628
$870$	20625.0	0.803739
$871$	5775.00	0.224659
$872$	−56025.0	−2.17574
$873$	−2760.00	−0.107001
$874$	0	0
$875$	−2375.00	−0.0917596
$876$	−59755.0	−2.30472
$877$	−22655.0	−0.872298	−0.436149	−	0.899875i	$-0.643658\pi$
$877$	−22655.0	−0.872298	−0.436149	+	0.899875i	$0.643658\pi$
$878$	36100.0	1.38760
$879$	−35175.0	−1.34974
$880$	22250.0	0.852327
$881$	−43350.0	−1.65777	−0.828887	−	0.559416i	$-0.811025\pi$
$881$	−43350.0	−1.65777	−0.828887	+	0.559416i	$0.811025\pi$
$882$	180.000	0.00687179
$883$	24568.0	0.936330	0.468165	−	0.883641i	$-0.344915\pi$
$883$	24568.0	0.936330	0.468165	+	0.883641i	$0.344915\pi$
$884$	47685.0	1.81428
$885$	5625.00	0.213652
$886$	51290.0	1.94483
$887$	32060.0	1.21361	0.606804	−	0.794852i	$-0.292451\pi$
$887$	32060.0	1.21361	0.606804	+	0.794852i	$0.292451\pi$
$888$	−47250.0	−1.78559
$889$	−1900.00	−0.0716805
$890$	−21750.0	−0.819170
$891$	−33550.0	−1.26147
$892$	−96730.0	−3.63090
$893$	0	0
$894$	−43400.0	−1.62362
$895$	16700.0	0.623709
$896$	−40185.0	−1.49831
$897$	−40425.0	−1.50474
$898$	−37650.0	−1.39911
$899$	11550.0	0.428492
$900$	−850.000	−0.0314815
$901$	23205.0	0.858014
$902$	20000.0	0.738278
$903$	53010.0	1.95356
$904$	21600.0	0.794696
$905$	8950.00	0.328738
$906$	19750.0	0.724227
$907$	13295.0	0.486718	0.243359	−	0.969936i	$-0.421751\pi$
$907$	13295.0	0.486718	0.243359	+	0.969936i	$0.421751\pi$
$908$	−46155.0	−1.68690
$909$	−300.000	−0.0109465
$910$	26125.0	0.951687
$911$	190.000	0.00690997	0.00345498	−	0.999994i	$-0.498900\pi$
$911$	190.000	0.00690997	0.00345498	+	0.999994i	$0.498900\pi$
$912$	0	0
$913$	−45900.0	−1.66382
$914$	44095.0	1.59577
$915$	12500.0	0.451625
$916$	−12172.0	−0.439055
$917$	−22002.0	−0.792334
$918$	36975.0	1.32936
$919$	−2725.00	−0.0978122	−0.0489061	−	0.998803i	$-0.515574\pi$
$919$	−2725.00	−0.0978122	−0.0489061	+	0.998803i	$0.515574\pi$
$920$	33075.0	1.18527
$921$	−22300.0	−0.797839
$922$	−51160.0	−1.82740
$923$	−62700.0	−2.23596
$924$	−80750.0	−2.87498
$925$	5250.00	0.186615
$926$	60560.0	2.14916
$927$	2500.00	0.0885769
$928$	14025.0	0.496113
$929$	16825.0	0.594198	0.297099	−	0.954847i	$-0.403981\pi$
$929$	16825.0	0.594198	0.297099	+	0.954847i	$0.403981\pi$
$930$	8750.00	0.308520
$931$	0	0
$932$	54094.0	1.90119
$933$	34125.0	1.19743
$934$	25380.0	0.889142
$935$	12750.0	0.445957
$936$	4950.00	0.172859
$937$	−19259.0	−0.671466	−0.335733	−	0.941957i	$-0.608984\pi$
$937$	−19259.0	−0.671466	−0.335733	+	0.941957i	$0.608984\pi$
$938$	9975.00	0.347223
$939$	22685.0	0.788389
$940$	−39440.0	−1.36850
$941$	11435.0	0.396143	0.198071	−	0.980188i	$-0.436532\pi$
$941$	11435.0	0.396143	0.198071	+	0.980188i	$0.436532\pi$
$942$	48600.0	1.68097
$943$	11760.0	0.406106
$944$	20025.0	0.690422
$945$	13775.0	0.474181
$946$	139500.	4.79444
$947$	−20014.0	−0.686766	−0.343383	−	0.939195i	$-0.611573\pi$
$947$	−20014.0	−0.686766	−0.343383	+	0.939195i	$0.611573\pi$
$948$	59500.0	2.03847
$949$	−38665.0	−1.32257
$950$	0	0
$951$	39225.0	1.33750
$952$	43605.0	1.48450
$953$	26970.0	0.916730	0.458365	−	0.888764i	$-0.348435\pi$
$953$	26970.0	0.916730	0.458365	+	0.888764i	$0.348435\pi$
$954$	4550.00	0.154415
$955$	−8235.00	−0.279035
$956$	−72675.0	−2.45866
$957$	−41250.0	−1.39334
$958$	−76920.0	−2.59413
$959$	−33421.0	−1.12536
$960$	−7175.00	−0.241221
$961$	−24891.0	−0.835521
$962$	−57750.0	−1.93548
$963$	2410.00	0.0806450
$964$	−4760.00	−0.159035
$965$	−5150.00	−0.171797
$966$	−69825.0	−2.32565
$967$	7024.00	0.233585	0.116792	−	0.993156i	$-0.462739\pi$
$967$	7024.00	0.233585	0.116792	+	0.993156i	$0.462739\pi$
$968$	−52605.0	−1.74668
$969$	0	0
$970$	−34500.0	−1.14199
$971$	−12960.0	−0.428328	−0.214164	−	0.976798i	$-0.568703\pi$
$971$	−12960.0	−0.428328	−0.214164	+	0.976798i	$0.568703\pi$
$972$	9520.00	0.314150
$973$	42294.0	1.39351
$974$	41750.0	1.37347
$975$	6875.00	0.225822
$976$	44500.0	1.45944
$977$	−5550.00	−0.181740	−0.0908701	−	0.995863i	$-0.528965\pi$
$977$	−5550.00	−0.181740	−0.0908701	+	0.995863i	$0.528965\pi$
$978$	89050.0	2.91156
$979$	43500.0	1.42009
$980$	1530.00	0.0498715
$981$	−2490.00	−0.0810393
$982$	43860.0	1.42528
$983$	−14480.0	−0.469827	−0.234914	−	0.972016i	$-0.575481\pi$
$983$	−14480.0	−0.469827	−0.234914	+	0.972016i	$0.575481\pi$
$984$	18000.0	0.583149
$985$	−1680.00	−0.0543444
$986$	42075.0	1.35897
$987$	44080.0	1.42156
$988$	0	0
$989$	82026.0	2.63729
$990$	2500.00	0.0802578
$991$	21670.0	0.694622	0.347311	−	0.937750i	$-0.387095\pi$
$991$	21670.0	0.694622	0.347311	+	0.937750i	$0.387095\pi$
$992$	5950.00	0.190436
$993$	35375.0	1.13051
$994$	−108300.	−3.45580
$995$	−4375.00	−0.139394
$996$	−78030.0	−2.48240
$997$	−40686.0	−1.29242	−0.646208	−	0.763161i	$-0.723646\pi$
$997$	−40686.0	−1.29242	−0.646208	+	0.763161i	$0.723646\pi$
$998$	13930.0	0.441830
$999$	−30450.0	−0.964360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.4.a.b.1.1	✓	1
19.18	odd	2		1805.4.a.i.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.4.a.b.1.1	✓	1	1.1	even	1	trivial
1805.4.a.i.1.1	yes	1	19.18	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more