LMFDB - Embedded newform 1805.4.a.e.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:	no (minimal twist has level 95)
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)

$f(q)$

$=$

$q-1.00000 q^{2} -5.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} +5.00000 q^{6} +22.0000 q^{7} +15.0000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -5.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} +5.00000 q^{6} +22.0000 q^{7} +15.0000 q^{8} -2.00000 q^{9} -5.00000 q^{10} +9.00000 q^{11} +35.0000 q^{12} +54.0000 q^{13} -22.0000 q^{14} -25.0000 q^{15} +41.0000 q^{16} -54.0000 q^{17} +2.00000 q^{18} -35.0000 q^{20} -110.000 q^{21} -9.00000 q^{22} -92.0000 q^{23} -75.0000 q^{24} +25.0000 q^{25} -54.0000 q^{26} +145.000 q^{27} -154.000 q^{28} -134.000 q^{29} +25.0000 q^{30} -252.000 q^{31} -161.000 q^{32} -45.0000 q^{33} +54.0000 q^{34} +110.000 q^{35} +14.0000 q^{36} -236.000 q^{37} -270.000 q^{39} +75.0000 q^{40} -243.000 q^{41} +110.000 q^{42} +496.000 q^{43} -63.0000 q^{44} -10.0000 q^{45} +92.0000 q^{46} +502.000 q^{47} -205.000 q^{48} +141.000 q^{49} -25.0000 q^{50} +270.000 q^{51} -378.000 q^{52} +62.0000 q^{53} -145.000 q^{54} +45.0000 q^{55} +330.000 q^{56} +134.000 q^{58} +681.000 q^{59} +175.000 q^{60} -142.000 q^{61} +252.000 q^{62} -44.0000 q^{63} -167.000 q^{64} +270.000 q^{65} +45.0000 q^{66} +55.0000 q^{67} +378.000 q^{68} +460.000 q^{69} -110.000 q^{70} -974.000 q^{71} -30.0000 q^{72} +695.000 q^{73} +236.000 q^{74} -125.000 q^{75} +198.000 q^{77} +270.000 q^{78} -736.000 q^{79} +205.000 q^{80} -671.000 q^{81} +243.000 q^{82} -63.0000 q^{83} +770.000 q^{84} -270.000 q^{85} -496.000 q^{86} +670.000 q^{87} +135.000 q^{88} +726.000 q^{89} +10.0000 q^{90} +1188.00 q^{91} +644.000 q^{92} +1260.00 q^{93} -502.000 q^{94} +805.000 q^{96} -1167.00 q^{97} -141.000 q^{98} -18.0000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	5.00000	0.340207
$7$	22.0000	1.18789	0.593944	−	0.804506i	$-0.297570\pi$
$7$	22.0000	1.18789	0.593944	+	0.804506i	$0.297570\pi$
$8$	15.0000	0.662913
$9$	−2.00000	−0.0740741
$10$	−5.00000	−0.158114
$11$	9.00000	0.246691	0.123346	−	0.992364i	$-0.460638\pi$
$11$	9.00000	0.246691	0.123346	+	0.992364i	$0.460638\pi$
$12$	35.0000	0.841969
$13$	54.0000	1.15207	0.576035	−	0.817425i	$-0.304599\pi$
$13$	54.0000	1.15207	0.576035	+	0.817425i	$0.304599\pi$
$14$	−22.0000	−0.419982
$15$	−25.0000	−0.430331
$16$	41.0000	0.640625
$17$	−54.0000	−0.770407	−0.385204	−	0.922832i	$-0.625869\pi$
$17$	−54.0000	−0.770407	−0.385204	+	0.922832i	$0.625869\pi$
$18$	2.00000	0.0261891
$19$	0	0
$19$	0	0
$20$	−35.0000	−0.391312
$21$	−110.000	−1.14305
$22$	−9.00000	−0.0872185
$23$	−92.0000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−92.0000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−75.0000	−0.637888
$25$	25.0000	0.200000
$26$	−54.0000	−0.407318
$27$	145.000	1.03353
$28$	−154.000	−1.03940
$29$	−134.000	−0.858041	−0.429020	−	0.903295i	$-0.641141\pi$
$29$	−134.000	−0.858041	−0.429020	+	0.903295i	$0.641141\pi$
$30$	25.0000	0.152145
$31$	−252.000	−1.46002	−0.730009	−	0.683438i	$-0.760484\pi$
$31$	−252.000	−1.46002	−0.730009	+	0.683438i	$0.760484\pi$
$32$	−161.000	−0.889408
$33$	−45.0000	−0.237379
$34$	54.0000	0.272380
$35$	110.000	0.531240
$36$	14.0000	0.0648148
$37$	−236.000	−1.04860	−0.524299	−	0.851534i	$-0.675673\pi$
$37$	−236.000	−1.04860	−0.524299	+	0.851534i	$0.675673\pi$
$38$	0	0
$39$	−270.000	−1.10858
$40$	75.0000	0.296464
$41$	−243.000	−0.925615	−0.462808	−	0.886459i	$-0.653158\pi$
$41$	−243.000	−0.925615	−0.462808	+	0.886459i	$0.653158\pi$
$42$	110.000	0.404128
$43$	496.000	1.75905	0.879527	−	0.475850i	$-0.157859\pi$
$43$	496.000	1.75905	0.879527	+	0.475850i	$0.157859\pi$
$44$	−63.0000	−0.215855
$45$	−10.0000	−0.0331269
$46$	92.0000	0.294884
$47$	502.000	1.55796	0.778981	−	0.627047i	$-0.215737\pi$
$47$	502.000	1.55796	0.778981	+	0.627047i	$0.215737\pi$
$48$	−205.000	−0.616442
$49$	141.000	0.411079
$50$	−25.0000	−0.0707107
$51$	270.000	0.741325
$52$	−378.000	−1.00806
$53$	62.0000	0.160686	0.0803430	−	0.996767i	$-0.474398\pi$
$53$	62.0000	0.160686	0.0803430	+	0.996767i	$0.474398\pi$
$54$	−145.000	−0.365407
$55$	45.0000	0.110324
$56$	330.000	0.787466
$57$	0	0
$58$	134.000	0.303363
$59$	681.000	1.50269	0.751344	−	0.659910i	$-0.229406\pi$
$59$	681.000	1.50269	0.751344	+	0.659910i	$0.229406\pi$
$60$	175.000	0.376540
$61$	−142.000	−0.298053	−0.149027	−	0.988833i	$-0.547614\pi$
$61$	−142.000	−0.298053	−0.149027	+	0.988833i	$0.547614\pi$
$62$	252.000	0.516194
$63$	−44.0000	−0.0879917
$64$	−167.000	−0.326172
$65$	270.000	0.515221
$66$	45.0000	0.0839260
$67$	55.0000	0.100288	0.0501442	−	0.998742i	$-0.484032\pi$
$67$	55.0000	0.100288	0.0501442	+	0.998742i	$0.484032\pi$
$68$	378.000	0.674106
$69$	460.000	0.802572
$70$	−110.000	−0.187822
$71$	−974.000	−1.62806	−0.814032	−	0.580820i	$-0.802732\pi$
$71$	−974.000	−1.62806	−0.814032	+	0.580820i	$0.802732\pi$
$72$	−30.0000	−0.0491046
$73$	695.000	1.11430	0.557148	−	0.830413i	$-0.311896\pi$
$73$	695.000	1.11430	0.557148	+	0.830413i	$0.311896\pi$
$74$	236.000	0.370736
$75$	−125.000	−0.192450
$76$	0	0
$77$	198.000	0.293041
$78$	270.000	0.391942
$79$	−736.000	−1.04818	−0.524092	−	0.851662i	$-0.675595\pi$
$79$	−736.000	−1.04818	−0.524092	+	0.851662i	$0.675595\pi$
$80$	205.000	0.286496
$81$	−671.000	−0.920439
$82$	243.000	0.327254
$83$	−63.0000	−0.0833150	−0.0416575	−	0.999132i	$-0.513264\pi$
$83$	−63.0000	−0.0833150	−0.0416575	+	0.999132i	$0.513264\pi$
$84$	770.000	1.00017
$85$	−270.000	−0.344537
$86$	−496.000	−0.621919
$87$	670.000	0.825650
$88$	135.000	0.163535
$89$	726.000	0.864672	0.432336	−	0.901712i	$-0.357689\pi$
$89$	726.000	0.864672	0.432336	+	0.901712i	$0.357689\pi$
$90$	10.0000	0.0117121
$91$	1188.00	1.36853
$92$	644.000	0.729800
$93$	1260.00	1.40490
$94$	−502.000	−0.550823
$95$	0	0
$96$	805.000	0.855833
$97$	−1167.00	−1.22156	−0.610778	−	0.791802i	$-0.709143\pi$
$97$	−1167.00	−1.22156	−0.610778	+	0.791802i	$0.709143\pi$
$98$	−141.000	−0.145338
$99$	−18.0000	−0.0182734
$100$	−175.000	−0.175000
$101$	−30.0000	−0.0295556	−0.0147778	−	0.999891i	$-0.504704\pi$
$101$	−30.0000	−0.0295556	−0.0147778	+	0.999891i	$0.504704\pi$
$102$	−270.000	−0.262098
$103$	−602.000	−0.575891	−0.287946	−	0.957647i	$-0.592972\pi$
$103$	−602.000	−0.575891	−0.287946	+	0.957647i	$0.592972\pi$
$104$	810.000	0.763721
$105$	−550.000	−0.511186
$106$	−62.0000	−0.0568111
$107$	660.000	0.596305	0.298152	−	0.954518i	$-0.403630\pi$
$107$	660.000	0.596305	0.298152	+	0.954518i	$0.403630\pi$
$108$	−1015.00	−0.904337
$109$	−120.000	−0.105449	−0.0527244	−	0.998609i	$-0.516790\pi$
$109$	−120.000	−0.105449	−0.0527244	+	0.998609i	$0.516790\pi$
$110$	−45.0000	−0.0390053
$111$	1180.00	1.00901
$112$	902.000	0.760991
$113$	1059.00	0.881614	0.440807	−	0.897602i	$-0.354692\pi$
$113$	1059.00	0.881614	0.440807	+	0.897602i	$0.354692\pi$
$114$	0	0
$115$	−460.000	−0.373002
$116$	938.000	0.750785
$117$	−108.000	−0.0853385
$118$	−681.000	−0.531281
$119$	−1188.00	−0.915158
$120$	−375.000	−0.285272
$121$	−1250.00	−0.939144
$122$	142.000	0.105378
$123$	1215.00	0.890674
$124$	1764.00	1.27752
$125$	125.000	0.0894427
$126$	44.0000	0.0311098
$127$	118.000	0.0824473	0.0412236	−	0.999150i	$-0.486874\pi$
$127$	118.000	0.0824473	0.0412236	+	0.999150i	$0.486874\pi$
$128$	1455.00	1.00473
$129$	−2480.00	−1.69265
$130$	−270.000	−0.182158
$131$	667.000	0.444855	0.222428	−	0.974949i	$-0.428602\pi$
$131$	667.000	0.444855	0.222428	+	0.974949i	$0.428602\pi$
$132$	315.000	0.207706
$133$	0	0
$134$	−55.0000	−0.0354573
$135$	725.000	0.462208
$136$	−810.000	−0.510713
$137$	−1051.00	−0.655423	−0.327712	−	0.944778i	$-0.606277\pi$
$137$	−1051.00	−0.655423	−0.327712	+	0.944778i	$0.606277\pi$
$138$	−460.000	−0.283752
$139$	−835.000	−0.509524	−0.254762	−	0.967004i	$-0.581997\pi$
$139$	−835.000	−0.509524	−0.254762	+	0.967004i	$0.581997\pi$
$140$	−770.000	−0.464835
$141$	−2510.00	−1.49915
$142$	974.000	0.575607
$143$	486.000	0.284205
$144$	−82.0000	−0.0474537
$145$	−670.000	−0.383727
$146$	−695.000	−0.393963
$147$	−705.000	−0.395561
$148$	1652.00	0.917524
$149$	2736.00	1.50431	0.752154	−	0.658988i	$-0.229015\pi$
$149$	2736.00	1.50431	0.752154	+	0.658988i	$0.229015\pi$
$150$	125.000	0.0680414
$151$	−376.000	−0.202639	−0.101319	−	0.994854i	$-0.532306\pi$
$151$	−376.000	−0.202639	−0.101319	+	0.994854i	$0.532306\pi$
$152$	0	0
$153$	108.000	0.0570672
$154$	−198.000	−0.103606
$155$	−1260.00	−0.652940
$156$	1890.00	0.970007
$157$	−992.000	−0.504269	−0.252134	−	0.967692i	$-0.581133\pi$
$157$	−992.000	−0.504269	−0.252134	+	0.967692i	$0.581133\pi$
$158$	736.000	0.370589
$159$	−310.000	−0.154620
$160$	−805.000	−0.397755
$161$	−2024.00	−0.990767
$162$	671.000	0.325424
$163$	3047.00	1.46417	0.732084	−	0.681214i	$-0.238548\pi$
$163$	3047.00	1.46417	0.732084	+	0.681214i	$0.238548\pi$
$164$	1701.00	0.809913
$165$	−225.000	−0.106159
$166$	63.0000	0.0294563
$167$	−1304.00	−0.604231	−0.302115	−	0.953271i	$-0.597693\pi$
$167$	−1304.00	−0.604231	−0.302115	+	0.953271i	$0.597693\pi$
$168$	−1650.00	−0.757740
$169$	719.000	0.327264
$170$	270.000	0.121812
$171$	0	0
$172$	−3472.00	−1.53917
$173$	198.000	0.0870154	0.0435077	−	0.999053i	$-0.486147\pi$
$173$	198.000	0.0870154	0.0435077	+	0.999053i	$0.486147\pi$
$174$	−670.000	−0.291911
$175$	550.000	0.237578
$176$	369.000	0.158036
$177$	−3405.00	−1.44596
$178$	−726.000	−0.305708
$179$	−1265.00	−0.528215	−0.264108	−	0.964493i	$-0.585077\pi$
$179$	−1265.00	−0.528215	−0.264108	+	0.964493i	$0.585077\pi$
$180$	70.0000	0.0289861
$181$	−4076.00	−1.67385	−0.836925	−	0.547318i	$-0.815649\pi$
$181$	−4076.00	−1.67385	−0.836925	+	0.547318i	$0.815649\pi$
$182$	−1188.00	−0.483848
$183$	710.000	0.286802
$184$	−1380.00	−0.552907
$185$	−1180.00	−0.468948
$186$	−1260.00	−0.496708
$187$	−486.000	−0.190053
$188$	−3514.00	−1.36322
$189$	3190.00	1.22772
$190$	0	0
$191$	3292.00	1.24712	0.623562	−	0.781774i	$-0.285685\pi$
$191$	3292.00	1.24712	0.623562	+	0.781774i	$0.285685\pi$
$192$	835.000	0.313859
$193$	1938.00	0.722799	0.361400	−	0.932411i	$-0.382299\pi$
$193$	1938.00	0.722799	0.361400	+	0.932411i	$0.382299\pi$
$194$	1167.00	0.431885
$195$	−1350.00	−0.495772
$196$	−987.000	−0.359694
$197$	4524.00	1.63615	0.818075	−	0.575111i	$-0.195041\pi$
$197$	4524.00	1.63615	0.818075	+	0.575111i	$0.195041\pi$
$198$	18.0000	0.00646063
$199$	4282.00	1.52534	0.762671	−	0.646787i	$-0.223888\pi$
$199$	4282.00	1.52534	0.762671	+	0.646787i	$0.223888\pi$
$200$	375.000	0.132583
$201$	−275.000	−0.0965025
$202$	30.0000	0.0104495
$203$	−2948.00	−1.01926
$204$	−1890.00	−0.648659
$205$	−1215.00	−0.413948
$206$	602.000	0.203608
$207$	184.000	0.0617820
$208$	2214.00	0.738045
$209$	0	0
$210$	550.000	0.180731
$211$	−1940.00	−0.632963	−0.316481	−	0.948599i	$-0.602501\pi$
$211$	−1940.00	−0.632963	−0.316481	+	0.948599i	$0.602501\pi$
$212$	−434.000	−0.140600
$213$	4870.00	1.56661
$214$	−660.000	−0.210826
$215$	2480.00	0.786673
$216$	2175.00	0.685139
$217$	−5544.00	−1.73434
$218$	120.000	0.0372818
$219$	−3475.00	−1.07223
$220$	−315.000	−0.0965332
$221$	−2916.00	−0.887563
$222$	−1180.00	−0.356741
$223$	−4156.00	−1.24801	−0.624005	−	0.781420i	$-0.714496\pi$
$223$	−4156.00	−1.24801	−0.624005	+	0.781420i	$0.714496\pi$
$224$	−3542.00	−1.05652
$225$	−50.0000	−0.0148148
$226$	−1059.00	−0.311697
$227$	2093.00	0.611970	0.305985	−	0.952036i	$-0.401014\pi$
$227$	2093.00	0.611970	0.305985	+	0.952036i	$0.401014\pi$
$228$	0	0
$229$	−4312.00	−1.24430	−0.622151	−	0.782898i	$-0.713741\pi$
$229$	−4312.00	−1.24430	−0.622151	+	0.782898i	$0.713741\pi$
$230$	460.000	0.131876
$231$	−990.000	−0.281979
$232$	−2010.00	−0.568806
$233$	−4229.00	−1.18906	−0.594530	−	0.804073i	$-0.702662\pi$
$233$	−4229.00	−1.18906	−0.594530	+	0.804073i	$0.702662\pi$
$234$	108.000	0.0301717
$235$	2510.00	0.696742
$236$	−4767.00	−1.31485
$237$	3680.00	1.00861
$238$	1188.00	0.323557
$239$	−5556.00	−1.50371	−0.751857	−	0.659326i	$-0.770842\pi$
$239$	−5556.00	−1.50371	−0.751857	+	0.659326i	$0.770842\pi$
$240$	−1025.00	−0.275681
$241$	−4419.00	−1.18113	−0.590566	−	0.806989i	$-0.701095\pi$
$241$	−4419.00	−1.18113	−0.590566	+	0.806989i	$0.701095\pi$
$242$	1250.00	0.332037
$243$	−560.000	−0.147835
$244$	994.000	0.260796
$245$	705.000	0.183840
$246$	−1215.00	−0.314901
$247$	0	0
$248$	−3780.00	−0.967864
$249$	315.000	0.0801699
$250$	−125.000	−0.0316228
$251$	−3957.00	−0.995074	−0.497537	−	0.867443i	$-0.665762\pi$
$251$	−3957.00	−0.995074	−0.497537	+	0.867443i	$0.665762\pi$
$252$	308.000	0.0769928
$253$	−828.000	−0.205755
$254$	−118.000	−0.0291495
$255$	1350.00	0.331531
$256$	−119.000	−0.0290527
$257$	−877.000	−0.212863	−0.106431	−	0.994320i	$-0.533942\pi$
$257$	−877.000	−0.212863	−0.106431	+	0.994320i	$0.533942\pi$
$258$	2480.00	0.598442
$259$	−5192.00	−1.24562
$260$	−1890.00	−0.450819
$261$	268.000	0.0635586
$262$	−667.000	−0.157280
$263$	−2430.00	−0.569735	−0.284867	−	0.958567i	$-0.591950\pi$
$263$	−2430.00	−0.569735	−0.284867	+	0.958567i	$0.591950\pi$
$264$	−675.000	−0.157361
$265$	310.000	0.0718609
$266$	0	0
$267$	−3630.00	−0.832031
$268$	−385.000	−0.0877523
$269$	4692.00	1.06348	0.531740	−	0.846907i	$-0.321538\pi$
$269$	4692.00	1.06348	0.531740	+	0.846907i	$0.321538\pi$
$270$	−725.000	−0.163415
$271$	−8762.00	−1.96404	−0.982018	−	0.188789i	$-0.939544\pi$
$271$	−8762.00	−1.96404	−0.982018	+	0.188789i	$0.939544\pi$
$272$	−2214.00	−0.493542
$273$	−5940.00	−1.31687
$274$	1051.00	0.231727
$275$	225.000	0.0493382
$276$	−3220.00	−0.702251
$277$	5014.00	1.08759	0.543794	−	0.839219i	$-0.316987\pi$
$277$	5014.00	1.08759	0.543794	+	0.839219i	$0.316987\pi$
$278$	835.000	0.180144
$279$	504.000	0.108149
$280$	1650.00	0.352166
$281$	−3865.00	−0.820522	−0.410261	−	0.911968i	$-0.634562\pi$
$281$	−3865.00	−0.820522	−0.410261	+	0.911968i	$0.634562\pi$
$282$	2510.00	0.530030
$283$	−593.000	−0.124559	−0.0622795	−	0.998059i	$-0.519837\pi$
$283$	−593.000	−0.124559	−0.0622795	+	0.998059i	$0.519837\pi$
$284$	6818.00	1.42456
$285$	0	0
$286$	−486.000	−0.100482
$287$	−5346.00	−1.09953
$288$	322.000	0.0658821
$289$	−1997.00	−0.406473
$290$	670.000	0.135668
$291$	5835.00	1.17544
$292$	−4865.00	−0.975009
$293$	−5838.00	−1.16403	−0.582013	−	0.813180i	$-0.697735\pi$
$293$	−5838.00	−1.16403	−0.582013	+	0.813180i	$0.697735\pi$
$294$	705.000	0.139852
$295$	3405.00	0.672023
$296$	−3540.00	−0.695129
$297$	1305.00	0.254962
$298$	−2736.00	−0.531853
$299$	−4968.00	−0.960893
$300$	875.000	0.168394
$301$	10912.0	2.08956
$302$	376.000	0.0716436
$303$	150.000	0.0284399
$304$	0	0
$305$	−710.000	−0.133293
$306$	−108.000	−0.0201763
$307$	247.000	0.0459187	0.0229593	−	0.999736i	$-0.492691\pi$
$307$	247.000	0.0459187	0.0229593	+	0.999736i	$0.492691\pi$
$308$	−1386.00	−0.256411
$309$	3010.00	0.554152
$310$	1260.00	0.230849
$311$	−10220.0	−1.86342	−0.931709	−	0.363206i	$-0.881682\pi$
$311$	−10220.0	−1.86342	−0.931709	+	0.363206i	$0.881682\pi$
$312$	−4050.00	−0.734891
$313$	−7835.00	−1.41489	−0.707445	−	0.706769i	$-0.750152\pi$
$313$	−7835.00	−1.41489	−0.707445	+	0.706769i	$0.750152\pi$
$314$	992.000	0.178286
$315$	−220.000	−0.0393511
$316$	5152.00	0.917160
$317$	−3774.00	−0.668672	−0.334336	−	0.942454i	$-0.608512\pi$
$317$	−3774.00	−0.668672	−0.334336	+	0.942454i	$0.608512\pi$
$318$	310.000	0.0546665
$319$	−1206.00	−0.211671
$320$	−835.000	−0.145868
$321$	−3300.00	−0.573795
$322$	2024.00	0.350289
$323$	0	0
$324$	4697.00	0.805384
$325$	1350.00	0.230414
$326$	−3047.00	−0.517662
$327$	600.000	0.101468
$328$	−3645.00	−0.613602
$329$	11044.0	1.85069
$330$	225.000	0.0375329
$331$	−5.00000	−0.000830287 0	−0.000415143	−	1.00000i	$-0.500132\pi$
$331$	−5.00000	−0.000830287 0	−0.000415143		1.00000i	$0.500132\pi$
$332$	441.000	0.0729007
$333$	472.000	0.0776740
$334$	1304.00	0.213628
$335$	275.000	0.0448503
$336$	−4510.00	−0.732264
$337$	−6357.00	−1.02756	−0.513780	−	0.857922i	$-0.671755\pi$
$337$	−6357.00	−1.02756	−0.513780	+	0.857922i	$0.671755\pi$
$338$	−719.000	−0.115705
$339$	−5295.00	−0.848333
$340$	1890.00	0.301470
$341$	−2268.00	−0.360173
$342$	0	0
$343$	−4444.00	−0.699573
$344$	7440.00	1.16610
$345$	2300.00	0.358921
$346$	−198.000	−0.0307646
$347$	−12559.0	−1.94295	−0.971473	−	0.237149i	$-0.923787\pi$
$347$	−12559.0	−1.94295	−0.971473	+	0.237149i	$0.923787\pi$
$348$	−4690.00	−0.722444
$349$	7336.00	1.12518	0.562589	−	0.826737i	$-0.309805\pi$
$349$	7336.00	1.12518	0.562589	+	0.826737i	$0.309805\pi$
$350$	−550.000	−0.0839964
$351$	7830.00	1.19070
$352$	−1449.00	−0.219409
$353$	10451.0	1.57578	0.787890	−	0.615816i	$-0.211173\pi$
$353$	10451.0	1.57578	0.787890	+	0.615816i	$0.211173\pi$
$354$	3405.00	0.511225
$355$	−4870.00	−0.728092
$356$	−5082.00	−0.756588
$357$	5940.00	0.880611
$358$	1265.00	0.186752
$359$	7300.00	1.07320	0.536601	−	0.843836i	$-0.319708\pi$
$359$	7300.00	1.07320	0.536601	+	0.843836i	$0.319708\pi$
$360$	−150.000	−0.0219603
$361$	0	0
$362$	4076.00	0.591795
$363$	6250.00	0.903691
$364$	−8316.00	−1.19746
$365$	3475.00	0.498328
$366$	−710.000	−0.101400
$367$	−632.000	−0.0898914	−0.0449457	−	0.998989i	$-0.514311\pi$
$367$	−632.000	−0.0898914	−0.0449457	+	0.998989i	$0.514311\pi$
$368$	−3772.00	−0.534318
$369$	486.000	0.0685641
$370$	1180.00	0.165798
$371$	1364.00	0.190877
$372$	−8820.00	−1.22929
$373$	−96.0000	−0.0133263	−0.00666313	−	0.999978i	$-0.502121\pi$
$373$	−96.0000	−0.0133263	−0.00666313	+	0.999978i	$0.502121\pi$
$374$	486.000	0.0671937
$375$	−625.000	−0.0860663
$376$	7530.00	1.03279
$377$	−7236.00	−0.988522
$378$	−3190.00	−0.434063
$379$	10964.0	1.48597	0.742985	−	0.669308i	$-0.233409\pi$
$379$	10964.0	1.48597	0.742985	+	0.669308i	$0.233409\pi$
$380$	0	0
$381$	−590.000	−0.0793349
$382$	−3292.00	−0.440925
$383$	2018.00	0.269230	0.134615	−	0.990898i	$-0.457020\pi$
$383$	2018.00	0.269230	0.134615	+	0.990898i	$0.457020\pi$
$384$	−7275.00	−0.966799
$385$	990.000	0.131052
$386$	−1938.00	−0.255548
$387$	−992.000	−0.130300
$388$	8169.00	1.06886
$389$	8728.00	1.13760	0.568801	−	0.822475i	$-0.307407\pi$
$389$	8728.00	1.13760	0.568801	+	0.822475i	$0.307407\pi$
$390$	1350.00	0.175282
$391$	4968.00	0.642564
$392$	2115.00	0.272509
$393$	−3335.00	−0.428062
$394$	−4524.00	−0.578467
$395$	−3680.00	−0.468762
$396$	126.000	0.0159892
$397$	9564.00	1.20908	0.604538	−	0.796576i	$-0.293358\pi$
$397$	9564.00	1.20908	0.604538	+	0.796576i	$0.293358\pi$
$398$	−4282.00	−0.539290
$399$	0	0
$400$	1025.00	0.128125
$401$	−5867.00	−0.730633	−0.365317	−	0.930883i	$-0.619039\pi$
$401$	−5867.00	−0.730633	−0.365317	+	0.930883i	$0.619039\pi$
$402$	275.000	0.0341188
$403$	−13608.0	−1.68204
$404$	210.000	0.0258611
$405$	−3355.00	−0.411633
$406$	2948.00	0.360362
$407$	−2124.00	−0.258680
$408$	4050.00	0.491434
$409$	−835.000	−0.100949	−0.0504744	−	0.998725i	$-0.516073\pi$
$409$	−835.000	−0.100949	−0.0504744	+	0.998725i	$0.516073\pi$
$410$	1215.00	0.146353
$411$	5255.00	0.630681
$412$	4214.00	0.503905
$413$	14982.0	1.78503
$414$	−184.000	−0.0218433
$415$	−315.000	−0.0372596
$416$	−8694.00	−1.02466
$417$	4175.00	0.490289
$418$	0	0
$419$	756.000	0.0881456	0.0440728	−	0.999028i	$-0.485967\pi$
$419$	756.000	0.0881456	0.0440728	+	0.999028i	$0.485967\pi$
$420$	3850.00	0.447288
$421$	−3900.00	−0.451483	−0.225742	−	0.974187i	$-0.572480\pi$
$421$	−3900.00	−0.451483	−0.225742	+	0.974187i	$0.572480\pi$
$422$	1940.00	0.223786
$423$	−1004.00	−0.115405
$424$	930.000	0.106521
$425$	−1350.00	−0.154081
$426$	−4870.00	−0.553879
$427$	−3124.00	−0.354054
$428$	−4620.00	−0.521767
$429$	−2430.00	−0.273477
$430$	−2480.00	−0.278131
$431$	14706.0	1.64353	0.821767	−	0.569824i	$-0.192989\pi$
$431$	14706.0	1.64353	0.821767	+	0.569824i	$0.192989\pi$
$432$	5945.00	0.662104
$433$	7838.00	0.869908	0.434954	−	0.900453i	$-0.356765\pi$
$433$	7838.00	0.869908	0.434954	+	0.900453i	$0.356765\pi$
$434$	5544.00	0.613181
$435$	3350.00	0.369242
$436$	840.000	0.0922677
$437$	0	0
$438$	3475.00	0.379091
$439$	17628.0	1.91649	0.958244	−	0.285951i	$-0.0923093\pi$
$439$	17628.0	1.91649	0.958244	+	0.285951i	$0.0923093\pi$
$440$	675.000	0.0731349
$441$	−282.000	−0.0304503
$442$	2916.00	0.313801
$443$	9267.00	0.993879	0.496940	−	0.867785i	$-0.334457\pi$
$443$	9267.00	0.993879	0.496940	+	0.867785i	$0.334457\pi$
$444$	−8260.00	−0.882888
$445$	3630.00	0.386693
$446$	4156.00	0.441238
$447$	−13680.0	−1.44752
$448$	−3674.00	−0.387456
$449$	−9371.00	−0.984955	−0.492478	−	0.870325i	$-0.663909\pi$
$449$	−9371.00	−0.984955	−0.492478	+	0.870325i	$0.663909\pi$
$450$	50.0000	0.00523783
$451$	−2187.00	−0.228341
$452$	−7413.00	−0.771412
$453$	1880.00	0.194989
$454$	−2093.00	−0.216364
$455$	5940.00	0.612025
$456$	0	0
$457$	−4107.00	−0.420388	−0.210194	−	0.977660i	$-0.567410\pi$
$457$	−4107.00	−0.420388	−0.210194	+	0.977660i	$0.567410\pi$
$458$	4312.00	0.439927
$459$	−7830.00	−0.796238
$460$	3220.00	0.326377
$461$	−5430.00	−0.548591	−0.274295	−	0.961645i	$-0.588445\pi$
$461$	−5430.00	−0.548591	−0.274295	+	0.961645i	$0.588445\pi$
$462$	990.000	0.0996947
$463$	−14222.0	−1.42754	−0.713771	−	0.700379i	$-0.753014\pi$
$463$	−14222.0	−1.42754	−0.713771	+	0.700379i	$0.753014\pi$
$464$	−5494.00	−0.549682
$465$	6300.00	0.628291
$466$	4229.00	0.420396
$467$	−3885.00	−0.384960	−0.192480	−	0.981301i	$-0.561653\pi$
$467$	−3885.00	−0.384960	−0.192480	+	0.981301i	$0.561653\pi$
$468$	756.000	0.0746712
$469$	1210.00	0.119131
$470$	−2510.00	−0.246335
$471$	4960.00	0.485233
$472$	10215.0	0.996151
$473$	4464.00	0.433943
$474$	−3680.00	−0.356599
$475$	0	0
$476$	8316.00	0.800763
$477$	−124.000	−0.0119027
$478$	5556.00	0.531643
$479$	4380.00	0.417802	0.208901	−	0.977937i	$-0.433011\pi$
$479$	4380.00	0.417802	0.208901	+	0.977937i	$0.433011\pi$
$480$	4025.00	0.382740
$481$	−12744.0	−1.20806
$482$	4419.00	0.417593
$483$	10120.0	0.953366
$484$	8750.00	0.821751
$485$	−5835.00	−0.546296
$486$	560.000	0.0522677
$487$	−18856.0	−1.75451	−0.877256	−	0.480024i	$-0.840628\pi$
$487$	−18856.0	−1.75451	−0.877256	+	0.480024i	$0.840628\pi$
$488$	−2130.00	−0.197583
$489$	−15235.0	−1.40890
$490$	−705.000	−0.0649973
$491$	1588.00	0.145958	0.0729791	−	0.997333i	$-0.476749\pi$
$491$	1588.00	0.145958	0.0729791	+	0.997333i	$0.476749\pi$
$492$	−8505.00	−0.779339
$493$	7236.00	0.661041
$494$	0	0
$495$	−90.0000	−0.00817212
$496$	−10332.0	−0.935324
$497$	−21428.0	−1.93396
$498$	−315.000	−0.0283444
$499$	11157.0	1.00091	0.500457	−	0.865761i	$-0.333165\pi$
$499$	11157.0	1.00091	0.500457	+	0.865761i	$0.333165\pi$
$500$	−875.000	−0.0782624
$501$	6520.00	0.581421
$502$	3957.00	0.351812
$503$	−18048.0	−1.59984	−0.799921	−	0.600105i	$-0.795125\pi$
$503$	−18048.0	−1.59984	−0.799921	+	0.600105i	$0.795125\pi$
$504$	−660.000	−0.0583308
$505$	−150.000	−0.0132176
$506$	828.000	0.0727452
$507$	−3595.00	−0.314910
$508$	−826.000	−0.0721414
$509$	−4188.00	−0.364695	−0.182348	−	0.983234i	$-0.558370\pi$
$509$	−4188.00	−0.364695	−0.182348	+	0.983234i	$0.558370\pi$
$510$	−1350.00	−0.117214
$511$	15290.0	1.32366
$512$	−11521.0	−0.994455
$513$	0	0
$514$	877.000	0.0752584
$515$	−3010.00	−0.257546
$516$	17360.0	1.48107
$517$	4518.00	0.384335
$518$	5192.00	0.440393
$519$	−990.000	−0.0837306
$520$	4050.00	0.341547
$521$	20405.0	1.71585	0.857926	−	0.513773i	$-0.171753\pi$
$521$	20405.0	1.71585	0.857926	+	0.513773i	$0.171753\pi$
$522$	−268.000	−0.0224713
$523$	7208.00	0.602646	0.301323	−	0.953522i	$-0.402572\pi$
$523$	7208.00	0.602646	0.301323	+	0.953522i	$0.402572\pi$
$524$	−4669.00	−0.389248
$525$	−2750.00	−0.228609
$526$	2430.00	0.201432
$527$	13608.0	1.12481
$528$	−1845.00	−0.152071
$529$	−3703.00	−0.304348
$530$	−310.000	−0.0254067
$531$	−1362.00	−0.111310
$532$	0	0
$533$	−13122.0	−1.06637
$534$	3630.00	0.294168
$535$	3300.00	0.266676
$536$	825.000	0.0664824
$537$	6325.00	0.508275
$538$	−4692.00	−0.375997
$539$	1269.00	0.101409
$540$	−5075.00	−0.404432
$541$	3408.00	0.270834	0.135417	−	0.990789i	$-0.456763\pi$
$541$	3408.00	0.270834	0.135417	+	0.990789i	$0.456763\pi$
$542$	8762.00	0.694391
$543$	20380.0	1.61066
$544$	8694.00	0.685206
$545$	−600.000	−0.0471581
$546$	5940.00	0.465583
$547$	−9416.00	−0.736013	−0.368006	−	0.929823i	$-0.619960\pi$
$547$	−9416.00	−0.736013	−0.368006	+	0.929823i	$0.619960\pi$
$548$	7357.00	0.573495
$549$	284.000	0.0220780
$550$	−225.000	−0.0174437
$551$	0	0
$552$	6900.00	0.532035
$553$	−16192.0	−1.24512
$554$	−5014.00	−0.384521
$555$	5900.00	0.451245
$556$	5845.00	0.445833
$557$	−15912.0	−1.21044	−0.605218	−	0.796060i	$-0.706914\pi$
$557$	−15912.0	−1.21044	−0.605218	+	0.796060i	$0.706914\pi$
$558$	−504.000	−0.0382366
$559$	26784.0	2.02655
$560$	4510.00	0.340326
$561$	2430.00	0.182878
$562$	3865.00	0.290098
$563$	1533.00	0.114757	0.0573785	−	0.998352i	$-0.481726\pi$
$563$	1533.00	0.114757	0.0573785	+	0.998352i	$0.481726\pi$
$564$	17570.0	1.31176
$565$	5295.00	0.394270
$566$	593.000	0.0440382
$567$	−14762.0	−1.09338
$568$	−14610.0	−1.07926
$569$	−16070.0	−1.18399	−0.591994	−	0.805942i	$-0.701659\pi$
$569$	−16070.0	−1.18399	−0.591994	+	0.805942i	$0.701659\pi$
$570$	0	0
$571$	−8097.00	−0.593431	−0.296715	−	0.954966i	$-0.595891\pi$
$571$	−8097.00	−0.593431	−0.296715	+	0.954966i	$0.595891\pi$
$572$	−3402.00	−0.248680
$573$	−16460.0	−1.20005
$574$	5346.00	0.388742
$575$	−2300.00	−0.166812
$576$	334.000	0.0241609
$577$	17927.0	1.29343	0.646716	−	0.762731i	$-0.276142\pi$
$577$	17927.0	1.29343	0.646716	+	0.762731i	$0.276142\pi$
$578$	1997.00	0.143710
$579$	−9690.00	−0.695514
$580$	4690.00	0.335761
$581$	−1386.00	−0.0989690
$582$	−5835.00	−0.415582
$583$	558.000	0.0396398
$584$	10425.0	0.738681
$585$	−540.000	−0.0381645
$586$	5838.00	0.411545
$587$	−19808.0	−1.39278	−0.696392	−	0.717662i	$-0.745212\pi$
$587$	−19808.0	−1.39278	−0.696392	+	0.717662i	$0.745212\pi$
$588$	4935.00	0.346116
$589$	0	0
$590$	−3405.00	−0.237596
$591$	−22620.0	−1.57439
$592$	−9676.00	−0.671759
$593$	−5581.00	−0.386483	−0.193241	−	0.981151i	$-0.561900\pi$
$593$	−5581.00	−0.386483	−0.193241	+	0.981151i	$0.561900\pi$
$594$	−1305.00	−0.0901428
$595$	−5940.00	−0.409271
$596$	−19152.0	−1.31627
$597$	−21410.0	−1.46776
$598$	4968.00	0.339727
$599$	−24788.0	−1.69084	−0.845418	−	0.534106i	$-0.820648\pi$
$599$	−24788.0	−1.69084	−0.845418	+	0.534106i	$0.820648\pi$
$600$	−1875.00	−0.127578
$601$	−413.000	−0.0280310	−0.0140155	−	0.999902i	$-0.504461\pi$
$601$	−413.000	−0.0280310	−0.0140155	+	0.999902i	$0.504461\pi$
$602$	−10912.0	−0.738771
$603$	−110.000	−0.00742877
$604$	2632.00	0.177309
$605$	−6250.00	−0.419998
$606$	−150.000	−0.0100550
$607$	−22778.0	−1.52311	−0.761557	−	0.648098i	$-0.775565\pi$
$607$	−22778.0	−1.52311	−0.761557	+	0.648098i	$0.775565\pi$
$608$	0	0
$609$	14740.0	0.980780
$610$	710.000	0.0471263
$611$	27108.0	1.79488
$612$	−756.000	−0.0499338
$613$	−9458.00	−0.623173	−0.311586	−	0.950218i	$-0.600860\pi$
$613$	−9458.00	−0.623173	−0.311586	+	0.950218i	$0.600860\pi$
$614$	−247.000	−0.0162347
$615$	6075.00	0.398321
$616$	2970.00	0.194261
$617$	−12629.0	−0.824027	−0.412013	−	0.911178i	$-0.635174\pi$
$617$	−12629.0	−0.824027	−0.412013	+	0.911178i	$0.635174\pi$
$618$	−3010.00	−0.195922
$619$	−4984.00	−0.323625	−0.161812	−	0.986822i	$-0.551734\pi$
$619$	−4984.00	−0.323625	−0.161812	+	0.986822i	$0.551734\pi$
$620$	8820.00	0.571322
$621$	−13340.0	−0.862022
$622$	10220.0	0.658818
$623$	15972.0	1.02713
$624$	−11070.0	−0.710184
$625$	625.000	0.0400000
$626$	7835.00	0.500239
$627$	0	0
$628$	6944.00	0.441235
$629$	12744.0	0.807848
$630$	220.000	0.0139127
$631$	−6154.00	−0.388252	−0.194126	−	0.980977i	$-0.562187\pi$
$631$	−6154.00	−0.388252	−0.194126	+	0.980977i	$0.562187\pi$
$632$	−11040.0	−0.694854
$633$	9700.00	0.609069
$634$	3774.00	0.236411
$635$	590.000	0.0368716
$636$	2170.00	0.135293
$637$	7614.00	0.473591
$638$	1206.00	0.0748370
$639$	1948.00	0.120597
$640$	7275.00	0.449328
$641$	2701.00	0.166432	0.0832161	−	0.996532i	$-0.473481\pi$
$641$	2701.00	0.166432	0.0832161	+	0.996532i	$0.473481\pi$
$642$	3300.00	0.202867
$643$	−1993.00	−0.122234	−0.0611168	−	0.998131i	$-0.519466\pi$
$643$	−1993.00	−0.122234	−0.0611168	+	0.998131i	$0.519466\pi$
$644$	14168.0	0.866921
$645$	−12400.0	−0.756976
$646$	0	0
$647$	15638.0	0.950221	0.475111	−	0.879926i	$-0.342408\pi$
$647$	15638.0	0.950221	0.475111	+	0.879926i	$0.342408\pi$
$648$	−10065.0	−0.610171
$649$	6129.00	0.370700
$650$	−1350.00	−0.0814636
$651$	27720.0	1.66887
$652$	−21329.0	−1.28115
$653$	3180.00	0.190571	0.0952856	−	0.995450i	$-0.469624\pi$
$653$	3180.00	0.190571	0.0952856	+	0.995450i	$0.469624\pi$
$654$	−600.000	−0.0358744
$655$	3335.00	0.198945
$656$	−9963.00	−0.592972
$657$	−1390.00	−0.0825404
$658$	−11044.0	−0.654316
$659$	300.000	0.0177334	0.00886672	−	0.999961i	$-0.497178\pi$
$659$	300.000	0.0177334	0.00886672	+	0.999961i	$0.497178\pi$
$660$	1575.00	0.0928891
$661$	1790.00	0.105330	0.0526648	−	0.998612i	$-0.483228\pi$
$661$	1790.00	0.105330	0.0526648	+	0.998612i	$0.483228\pi$
$662$	5.00000	0.000293551 0
$663$	14580.0	0.854058
$664$	−945.000	−0.0552306
$665$	0	0
$666$	−472.000	−0.0274619
$667$	12328.0	0.715655
$668$	9128.00	0.528702
$669$	20780.0	1.20090
$670$	−275.000	−0.0158570
$671$	−1278.00	−0.0735270
$672$	17710.0	1.01663
$673$	−13830.0	−0.792136	−0.396068	−	0.918221i	$-0.629625\pi$
$673$	−13830.0	−0.792136	−0.396068	+	0.918221i	$0.629625\pi$
$674$	6357.00	0.363297
$675$	3625.00	0.206706
$676$	−5033.00	−0.286356
$677$	−6090.00	−0.345728	−0.172864	−	0.984946i	$-0.555302\pi$
$677$	−6090.00	−0.345728	−0.172864	+	0.984946i	$0.555302\pi$
$678$	5295.00	0.299931
$679$	−25674.0	−1.45107
$680$	−4050.00	−0.228398
$681$	−10465.0	−0.588869
$682$	2268.00	0.127340
$683$	−21180.0	−1.18657	−0.593287	−	0.804991i	$-0.702170\pi$
$683$	−21180.0	−1.18657	−0.593287	+	0.804991i	$0.702170\pi$
$684$	0	0
$685$	−5255.00	−0.293114
$686$	4444.00	0.247336
$687$	21560.0	1.19733
$688$	20336.0	1.12689
$689$	3348.00	0.185121
$690$	−2300.00	−0.126898
$691$	−14812.0	−0.815449	−0.407724	−	0.913105i	$-0.633678\pi$
$691$	−14812.0	−0.815449	−0.407724	+	0.913105i	$0.633678\pi$
$692$	−1386.00	−0.0761385
$693$	−396.000	−0.0217068
$694$	12559.0	0.686935
$695$	−4175.00	−0.227866
$696$	10050.0	0.547334
$697$	13122.0	0.713101
$698$	−7336.00	−0.397810
$699$	21145.0	1.14417
$700$	−3850.00	−0.207880
$701$	33186.0	1.78804	0.894021	−	0.448024i	$-0.147872\pi$
$701$	33186.0	1.78804	0.894021	+	0.448024i	$0.147872\pi$
$702$	−7830.00	−0.420975
$703$	0	0
$704$	−1503.00	−0.0804637
$705$	−12550.0	−0.670440
$706$	−10451.0	−0.557123
$707$	−660.000	−0.0351087
$708$	23835.0	1.26522
$709$	31240.0	1.65479	0.827393	−	0.561624i	$-0.189823\pi$
$709$	31240.0	1.65479	0.827393	+	0.561624i	$0.189823\pi$
$710$	4870.00	0.257419
$711$	1472.00	0.0776432
$712$	10890.0	0.573202
$713$	23184.0	1.21774
$714$	−5940.00	−0.311343
$715$	2430.00	0.127100
$716$	8855.00	0.462188
$717$	27780.0	1.44695
$718$	−7300.00	−0.379434
$719$	14226.0	0.737886	0.368943	−	0.929452i	$-0.379720\pi$
$719$	14226.0	0.737886	0.368943	+	0.929452i	$0.379720\pi$
$720$	−410.000	−0.0212219
$721$	−13244.0	−0.684095
$722$	0	0
$723$	22095.0	1.13654
$724$	28532.0	1.46462
$725$	−3350.00	−0.171608
$726$	−6250.00	−0.319503
$727$	10376.0	0.529332	0.264666	−	0.964340i	$-0.414738\pi$
$727$	10376.0	0.529332	0.264666	+	0.964340i	$0.414738\pi$
$728$	17820.0	0.907216
$729$	20917.0	1.06269
$730$	−3475.00	−0.176186
$731$	−26784.0	−1.35519
$732$	−4970.00	−0.250951
$733$	−21868.0	−1.10193	−0.550964	−	0.834529i	$-0.685740\pi$
$733$	−21868.0	−1.10193	−0.550964	+	0.834529i	$0.685740\pi$
$734$	632.000	0.0317814
$735$	−3525.00	−0.176900
$736$	14812.0	0.741817
$737$	495.000	0.0247402
$738$	−486.000	−0.0242411
$739$	−21071.0	−1.04886	−0.524431	−	0.851453i	$-0.675722\pi$
$739$	−21071.0	−1.04886	−0.524431	+	0.851453i	$0.675722\pi$
$740$	8260.00	0.410329
$741$	0	0
$742$	−1364.00	−0.0674852
$743$	−14400.0	−0.711016	−0.355508	−	0.934673i	$-0.615692\pi$
$743$	−14400.0	−0.711016	−0.355508	+	0.934673i	$0.615692\pi$
$744$	18900.0	0.931327
$745$	13680.0	0.672747
$746$	96.0000	0.00471154
$747$	126.000	0.00617148
$748$	3402.00	0.166296
$749$	14520.0	0.708343
$750$	625.000	0.0304290
$751$	34586.0	1.68051	0.840254	−	0.542193i	$-0.182406\pi$
$751$	34586.0	1.68051	0.840254	+	0.542193i	$0.182406\pi$
$752$	20582.0	0.998070
$753$	19785.0	0.957511
$754$	7236.00	0.349495
$755$	−1880.00	−0.0906228
$756$	−22330.0	−1.07425
$757$	−5678.00	−0.272616	−0.136308	−	0.990666i	$-0.543524\pi$
$757$	−5678.00	−0.272616	−0.136308	+	0.990666i	$0.543524\pi$
$758$	−10964.0	−0.525370
$759$	4140.00	0.197987
$760$	0	0
$761$	−12243.0	−0.583191	−0.291596	−	0.956542i	$-0.594186\pi$
$761$	−12243.0	−0.583191	−0.291596	+	0.956542i	$0.594186\pi$
$762$	590.000	0.0280491
$763$	−2640.00	−0.125261
$764$	−23044.0	−1.09123
$765$	540.000	0.0255212
$766$	−2018.00	−0.0951871
$767$	36774.0	1.73120
$768$	595.000	0.0279560
$769$	−31250.0	−1.46541	−0.732707	−	0.680544i	$-0.761744\pi$
$769$	−31250.0	−1.46541	−0.732707	+	0.680544i	$0.761744\pi$
$770$	−990.000	−0.0463339
$771$	4385.00	0.204827
$772$	−13566.0	−0.632450
$773$	30042.0	1.39785	0.698923	−	0.715196i	$-0.253663\pi$
$773$	30042.0	1.39785	0.698923	+	0.715196i	$0.253663\pi$
$774$	992.000	0.0460681
$775$	−6300.00	−0.292003
$776$	−17505.0	−0.809785
$777$	25960.0	1.19860
$778$	−8728.00	−0.402203
$779$	0	0
$780$	9450.00	0.433800
$781$	−8766.00	−0.401629
$782$	−4968.00	−0.227181
$783$	−19430.0	−0.886809
$784$	5781.00	0.263347
$785$	−4960.00	−0.225516
$786$	3335.00	0.151343
$787$	−43141.0	−1.95402	−0.977008	−	0.213203i	$-0.931611\pi$
$787$	−43141.0	−1.95402	−0.977008	+	0.213203i	$0.931611\pi$
$788$	−31668.0	−1.43163
$789$	12150.0	0.548227
$790$	3680.00	0.165732
$791$	23298.0	1.04726
$792$	−270.000	−0.0121137
$793$	−7668.00	−0.343378
$794$	−9564.00	−0.427473
$795$	−1550.00	−0.0691482
$796$	−29974.0	−1.33467
$797$	8008.00	0.355907	0.177954	−	0.984039i	$-0.443052\pi$
$797$	8008.00	0.355907	0.177954	+	0.984039i	$0.443052\pi$
$798$	0	0
$799$	−27108.0	−1.20027
$800$	−4025.00	−0.177882
$801$	−1452.00	−0.0640498
$802$	5867.00	0.258318
$803$	6255.00	0.274887
$804$	1925.00	0.0844397
$805$	−10120.0	−0.443085
$806$	13608.0	0.594692
$807$	−23460.0	−1.02333
$808$	−450.000	−0.0195928
$809$	9053.00	0.393432	0.196716	−	0.980461i	$-0.436972\pi$
$809$	9053.00	0.393432	0.196716	+	0.980461i	$0.436972\pi$
$810$	3355.00	0.145534
$811$	−2956.00	−0.127989	−0.0639946	−	0.997950i	$-0.520384\pi$
$811$	−2956.00	−0.127989	−0.0639946	+	0.997950i	$0.520384\pi$
$812$	20636.0	0.891849
$813$	43810.0	1.88989
$814$	2124.00	0.0914572
$815$	15235.0	0.654796
$816$	11070.0	0.474911
$817$	0	0
$818$	835.000	0.0356908
$819$	−2376.00	−0.101373
$820$	8505.00	0.362204
$821$	18906.0	0.803683	0.401842	−	0.915709i	$-0.368370\pi$
$821$	18906.0	0.803683	0.401842	+	0.915709i	$0.368370\pi$
$822$	−5255.00	−0.222980
$823$	−14750.0	−0.624730	−0.312365	−	0.949962i	$-0.601121\pi$
$823$	−14750.0	−0.624730	−0.312365	+	0.949962i	$0.601121\pi$
$824$	−9030.00	−0.381766
$825$	−1125.00	−0.0474757
$826$	−14982.0	−0.631102
$827$	39087.0	1.64352	0.821758	−	0.569836i	$-0.192993\pi$
$827$	39087.0	1.64352	0.821758	+	0.569836i	$0.192993\pi$
$828$	−1288.00	−0.0540593
$829$	168.000	0.00703846	0.00351923	−	0.999994i	$-0.498880\pi$
$829$	168.000	0.00703846	0.00351923	+	0.999994i	$0.498880\pi$
$830$	315.000	0.0131733
$831$	−25070.0	−1.04653
$832$	−9018.00	−0.375773
$833$	−7614.00	−0.316698
$834$	−4175.00	−0.173343
$835$	−6520.00	−0.270220
$836$	0	0
$837$	−36540.0	−1.50897
$838$	−756.000	−0.0311642
$839$	−30658.0	−1.26154	−0.630770	−	0.775970i	$-0.717261\pi$
$839$	−30658.0	−1.26154	−0.630770	+	0.775970i	$0.717261\pi$
$840$	−8250.00	−0.338871
$841$	−6433.00	−0.263766
$842$	3900.00	0.159623
$843$	19325.0	0.789547
$844$	13580.0	0.553842
$845$	3595.00	0.146357
$846$	1004.00	0.0408017
$847$	−27500.0	−1.11560
$848$	2542.00	0.102939
$849$	2965.00	0.119857
$850$	1350.00	0.0544760
$851$	21712.0	0.874592
$852$	−34090.0	−1.37078
$853$	−29818.0	−1.19689	−0.598446	−	0.801163i	$-0.704215\pi$
$853$	−29818.0	−1.19689	−0.598446	+	0.801163i	$0.704215\pi$
$854$	3124.00	0.125177
$855$	0	0
$856$	9900.00	0.395298
$857$	−32471.0	−1.29427	−0.647134	−	0.762376i	$-0.724033\pi$
$857$	−32471.0	−1.29427	−0.647134	+	0.762376i	$0.724033\pi$
$858$	2430.00	0.0966886
$859$	−35821.0	−1.42281	−0.711407	−	0.702781i	$-0.751942\pi$
$859$	−35821.0	−1.42281	−0.711407	+	0.702781i	$0.751942\pi$
$860$	−17360.0	−0.688338
$861$	26730.0	1.05802
$862$	−14706.0	−0.581077
$863$	39300.0	1.55016	0.775080	−	0.631863i	$-0.217710\pi$
$863$	39300.0	1.55016	0.775080	+	0.631863i	$0.217710\pi$
$864$	−23345.0	−0.919228
$865$	990.000	0.0389145
$866$	−7838.00	−0.307559
$867$	9985.00	0.391128
$868$	38808.0	1.51755
$869$	−6624.00	−0.258577
$870$	−3350.00	−0.130547
$871$	2970.00	0.115539
$872$	−1800.00	−0.0699033
$873$	2334.00	0.0904856
$874$	0	0
$875$	2750.00	0.106248
$876$	24325.0	0.938203
$877$	22854.0	0.879960	0.439980	−	0.898008i	$-0.354986\pi$
$877$	22854.0	0.879960	0.439980	+	0.898008i	$0.354986\pi$
$878$	−17628.0	−0.677581
$879$	29190.0	1.12008
$880$	1845.00	0.0706761
$881$	25347.0	0.969310	0.484655	−	0.874705i	$-0.338945\pi$
$881$	25347.0	0.969310	0.484655	+	0.874705i	$0.338945\pi$
$882$	282.000	0.0107658
$883$	−14869.0	−0.566684	−0.283342	−	0.959019i	$-0.591443\pi$
$883$	−14869.0	−0.566684	−0.283342	+	0.959019i	$0.591443\pi$
$884$	20412.0	0.776617
$885$	−17025.0	−0.646654
$886$	−9267.00	−0.351389
$887$	−8052.00	−0.304802	−0.152401	−	0.988319i	$-0.548701\pi$
$887$	−8052.00	−0.304802	−0.152401	+	0.988319i	$0.548701\pi$
$888$	17700.0	0.668889
$889$	2596.00	0.0979382
$890$	−3630.00	−0.136717
$891$	−6039.00	−0.227064
$892$	29092.0	1.09201
$893$	0	0
$894$	13680.0	0.511776
$895$	−6325.00	−0.236225
$896$	32010.0	1.19350
$897$	24840.0	0.924619
$898$	9371.00	0.348234
$899$	33768.0	1.25275
$900$	350.000	0.0129630
$901$	−3348.00	−0.123794
$902$	2187.00	0.0807307
$903$	−54560.0	−2.01068
$904$	15885.0	0.584433
$905$	−20380.0	−0.748568
$906$	−1880.00	−0.0689391
$907$	−4621.00	−0.169171	−0.0845853	−	0.996416i	$-0.526957\pi$
$907$	−4621.00	−0.169171	−0.0845853	+	0.996416i	$0.526957\pi$
$908$	−14651.0	−0.535474
$909$	60.0000	0.00218930
$910$	−5940.00	−0.216384
$911$	−41004.0	−1.49124	−0.745622	−	0.666369i	$-0.767847\pi$
$911$	−41004.0	−1.49124	−0.745622	+	0.666369i	$0.767847\pi$
$912$	0	0
$913$	−567.000	−0.0205531
$914$	4107.00	0.148630
$915$	3550.00	0.128262
$916$	30184.0	1.08876
$917$	14674.0	0.528439
$918$	7830.00	0.281513
$919$	−45946.0	−1.64920	−0.824602	−	0.565713i	$-0.808601\pi$
$919$	−45946.0	−1.64920	−0.824602	+	0.565713i	$0.808601\pi$
$920$	−6900.00	−0.247268
$921$	−1235.00	−0.0441853
$922$	5430.00	0.193956
$923$	−52596.0	−1.87564
$924$	6930.00	0.246732
$925$	−5900.00	−0.209720
$926$	14222.0	0.504713
$927$	1204.00	0.0426586
$928$	21574.0	0.763148
$929$	−46611.0	−1.64613	−0.823066	−	0.567945i	$-0.807739\pi$
$929$	−46611.0	−1.64613	−0.823066	+	0.567945i	$0.807739\pi$
$930$	−6300.00	−0.222135
$931$	0	0
$932$	29603.0	1.04043
$933$	51100.0	1.79307
$934$	3885.00	0.136104
$935$	−2430.00	−0.0849941
$936$	−1620.00	−0.0565720
$937$	−33357.0	−1.16299	−0.581497	−	0.813548i	$-0.697533\pi$
$937$	−33357.0	−1.16299	−0.581497	+	0.813548i	$0.697533\pi$
$938$	−1210.00	−0.0421193
$939$	39175.0	1.36148
$940$	−17570.0	−0.609649
$941$	−41890.0	−1.45120	−0.725598	−	0.688119i	$-0.758437\pi$
$941$	−41890.0	−1.45120	−0.725598	+	0.688119i	$0.758437\pi$
$942$	−4960.00	−0.171556
$943$	22356.0	0.772016
$944$	27921.0	0.962660
$945$	15950.0	0.549051
$946$	−4464.00	−0.153422
$947$	−11964.0	−0.410536	−0.205268	−	0.978706i	$-0.565807\pi$
$947$	−11964.0	−0.410536	−0.205268	+	0.978706i	$0.565807\pi$
$948$	−25760.0	−0.882538
$949$	37530.0	1.28375
$950$	0	0
$951$	18870.0	0.643430
$952$	−17820.0	−0.606670
$953$	11073.0	0.376379	0.188190	−	0.982133i	$-0.439738\pi$
$953$	11073.0	0.376379	0.188190	+	0.982133i	$0.439738\pi$
$954$	124.000	0.00420823
$955$	16460.0	0.557731
$956$	38892.0	1.31575
$957$	6030.00	0.203680
$958$	−4380.00	−0.147715
$959$	−23122.0	−0.778570
$960$	4175.00	0.140362
$961$	33713.0	1.13165
$962$	12744.0	0.427113
$963$	−1320.00	−0.0441707
$964$	30933.0	1.03349
$965$	9690.00	0.323246
$966$	−10120.0	−0.337066
$967$	−14246.0	−0.473754	−0.236877	−	0.971540i	$-0.576124\pi$
$967$	−14246.0	−0.473754	−0.236877	+	0.971540i	$0.576124\pi$
$968$	−18750.0	−0.622570
$969$	0	0
$970$	5835.00	0.193145
$971$	31411.0	1.03813	0.519066	−	0.854734i	$-0.326280\pi$
$971$	31411.0	1.03813	0.519066	+	0.854734i	$0.326280\pi$
$972$	3920.00	0.129356
$973$	−18370.0	−0.605257
$974$	18856.0	0.620313
$975$	−6750.00	−0.221716
$976$	−5822.00	−0.190940
$977$	18657.0	0.610942	0.305471	−	0.952201i	$-0.401186\pi$
$977$	18657.0	0.610942	0.305471	+	0.952201i	$0.401186\pi$
$978$	15235.0	0.498120
$979$	6534.00	0.213307
$980$	−4935.00	−0.160860
$981$	240.000	0.00781102
$982$	−1588.00	−0.0516040
$983$	−57412.0	−1.86283	−0.931413	−	0.363963i	$-0.881423\pi$
$983$	−57412.0	−1.86283	−0.931413	+	0.363963i	$0.881423\pi$
$984$	18225.0	0.590439
$985$	22620.0	0.731709
$986$	−7236.00	−0.233713
$987$	−55220.0	−1.78082
$988$	0	0
$989$	−45632.0	−1.46715
$990$	90.0000	0.00288928
$991$	2624.00	0.0841111	0.0420556	−	0.999115i	$-0.486609\pi$
$991$	2624.00	0.0841111	0.0420556	+	0.999115i	$0.486609\pi$
$992$	40572.0	1.29855
$993$	25.0000	0.000798944 0
$994$	21428.0	0.683757
$995$	21410.0	0.682153
$996$	−2205.00	−0.0701487
$997$	−12658.0	−0.402089	−0.201045	−	0.979582i	$-0.564434\pi$
$997$	−12658.0	−0.402089	−0.201045	+	0.979582i	$0.564434\pi$
$998$	−11157.0	−0.353876
$999$	−34220.0	−1.08376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.4.a.e.1.1		1
19.7	even	3		95.4.e.a.11.1	✓	2
19.11	even	3		95.4.e.a.26.1	yes	2
19.18	odd	2		1805.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.e.a.11.1	✓	2	19.7	even	3
95.4.e.a.26.1	yes	2	19.11	even	3
1805.4.a.e.1.1		1	1.1	even	1	trivial
1805.4.a.g.1.1		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

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