LMFDB - Embedded newform 2200.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2200,4,Mod(1,2200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2200, 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("2200.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2200 = 2^{3} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2200.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:	$129.804202013$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2200.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{3} +13.0000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+5.00000 q^{3} +13.0000 q^{7} -2.00000 q^{9} -11.0000 q^{11} -12.0000 q^{13} -67.0000 q^{17} +151.000 q^{19} +65.0000 q^{21} +12.0000 q^{23} -145.000 q^{27} -143.000 q^{29} -337.000 q^{31} -55.0000 q^{33} -125.000 q^{37} -60.0000 q^{39} -240.000 q^{41} +270.000 q^{43} +448.000 q^{47} -174.000 q^{49} -335.000 q^{51} -45.0000 q^{53} +755.000 q^{57} +704.000 q^{59} -217.000 q^{61} -26.0000 q^{63} +284.000 q^{67} +60.0000 q^{69} -515.000 q^{71} -1162.00 q^{73} -143.000 q^{77} -944.000 q^{79} -671.000 q^{81} -124.000 q^{83} -715.000 q^{87} +361.000 q^{89} -156.000 q^{91} -1685.00 q^{93} -916.000 q^{97} +22.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	13.0000	0.701934	0.350967	−	0.936388i	$-0.385853\pi$
$7$	13.0000	0.701934	0.350967	+	0.936388i	$0.385853\pi$
$8$	0	0
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	0	0
$13$	−12.0000	−0.256015	−0.128008	−	0.991773i	$-0.540858\pi$
$13$	−12.0000	−0.256015	−0.128008	+	0.991773i	$0.540858\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−67.0000	−0.955876	−0.477938	−	0.878394i	$-0.658616\pi$
$17$	−67.0000	−0.955876	−0.477938	+	0.878394i	$0.658616\pi$
$18$	0	0
$19$	151.000	1.82325	0.911626	−	0.411021i	$-0.134828\pi$
$19$	151.000	1.82325	0.911626	+	0.411021i	$0.134828\pi$
$20$	0	0
$21$	65.0000	0.675436
$22$	0	0
$23$	12.0000	0.108790	0.0543951	−	0.998519i	$-0.482677\pi$
$23$	12.0000	0.108790	0.0543951	+	0.998519i	$0.482677\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−145.000	−1.03353
$28$	0	0
$29$	−143.000	−0.915670	−0.457835	−	0.889037i	$-0.651375\pi$
$29$	−143.000	−0.915670	−0.457835	+	0.889037i	$0.651375\pi$
$30$	0	0
$31$	−337.000	−1.95248	−0.976242	−	0.216684i	$-0.930476\pi$
$31$	−337.000	−1.95248	−0.976242	+	0.216684i	$0.930476\pi$
$32$	0	0
$33$	−55.0000	−0.290129
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−125.000	−0.555402	−0.277701	−	0.960668i	$-0.589572\pi$
$37$	−125.000	−0.555402	−0.277701	+	0.960668i	$0.589572\pi$
$38$	0	0
$39$	−60.0000	−0.246351
$40$	0	0
$41$	−240.000	−0.914188	−0.457094	−	0.889418i	$-0.651110\pi$
$41$	−240.000	−0.914188	−0.457094	+	0.889418i	$0.651110\pi$
$42$	0	0
$43$	270.000	0.957549	0.478775	−	0.877938i	$-0.341081\pi$
$43$	270.000	0.957549	0.478775	+	0.877938i	$0.341081\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	448.000	1.39037	0.695186	−	0.718830i	$-0.255322\pi$
$47$	448.000	1.39037	0.695186	+	0.718830i	$0.255322\pi$
$48$	0	0
$49$	−174.000	−0.507289
$50$	0	0
$51$	−335.000	−0.919792
$52$	0	0
$53$	−45.0000	−0.116627	−0.0583134	−	0.998298i	$-0.518572\pi$
$53$	−45.0000	−0.116627	−0.0583134	+	0.998298i	$0.518572\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	755.000	1.75442
$58$	0	0
$59$	704.000	1.55344	0.776720	−	0.629846i	$-0.216882\pi$
$59$	704.000	1.55344	0.776720	+	0.629846i	$0.216882\pi$
$60$	0	0
$61$	−217.000	−0.455475	−0.227738	−	0.973723i	$-0.573133\pi$
$61$	−217.000	−0.455475	−0.227738	+	0.973723i	$0.573133\pi$
$62$	0	0
$63$	−26.0000	−0.0519951
$64$	0	0
$65$	0	0
$66$	0	0
$67$	284.000	0.517853	0.258926	−	0.965897i	$-0.416631\pi$
$67$	284.000	0.517853	0.258926	+	0.965897i	$0.416631\pi$
$68$	0	0
$69$	60.0000	0.104683
$70$	0	0
$71$	−515.000	−0.860835	−0.430417	−	0.902630i	$-0.641634\pi$
$71$	−515.000	−0.860835	−0.430417	+	0.902630i	$0.641634\pi$
$72$	0	0
$73$	−1162.00	−1.86304	−0.931519	−	0.363692i	$-0.881516\pi$
$73$	−1162.00	−1.86304	−0.931519	+	0.363692i	$0.881516\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−143.000	−0.211641
$78$	0	0
$79$	−944.000	−1.34441	−0.672204	−	0.740366i	$-0.734652\pi$
$79$	−944.000	−1.34441	−0.672204	+	0.740366i	$0.734652\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	0	0
$83$	−124.000	−0.163985	−0.0819926	−	0.996633i	$-0.526128\pi$
$83$	−124.000	−0.163985	−0.0819926	+	0.996633i	$0.526128\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−715.000	−0.881104
$88$	0	0
$89$	361.000	0.429954	0.214977	−	0.976619i	$-0.431032\pi$
$89$	361.000	0.429954	0.214977	+	0.976619i	$0.431032\pi$
$90$	0	0
$91$	−156.000	−0.179706
$92$	0	0
$93$	−1685.00	−1.87878
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−916.000	−0.958822	−0.479411	−	0.877591i	$-0.659150\pi$
$97$	−916.000	−0.958822	−0.479411	+	0.877591i	$0.659150\pi$
$98$	0	0
$99$	22.0000	0.0223342
$100$	0	0
$101$	−1190.00	−1.17237	−0.586185	−	0.810177i	$-0.699371\pi$
$101$	−1190.00	−1.17237	−0.586185	+	0.810177i	$0.699371\pi$
$102$	0	0
$103$	1460.00	1.39668	0.698340	−	0.715766i	$-0.253922\pi$
$103$	1460.00	1.39668	0.698340	+	0.715766i	$0.253922\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1124.00	−1.01553	−0.507763	−	0.861497i	$-0.669527\pi$
$107$	−1124.00	−1.01553	−0.507763	+	0.861497i	$0.669527\pi$
$108$	0	0
$109$	1582.00	1.39017	0.695083	−	0.718929i	$-0.255368\pi$
$109$	1582.00	1.39017	0.695083	+	0.718929i	$0.255368\pi$
$110$	0	0
$111$	−625.000	−0.534436
$112$	0	0
$113$	−914.000	−0.760902	−0.380451	−	0.924801i	$-0.624231\pi$
$113$	−914.000	−0.760902	−0.380451	+	0.924801i	$0.624231\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	24.0000	0.0189641
$118$	0	0
$119$	−871.000	−0.670962
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	−1200.00	−0.879678
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−40.0000	−0.0279482	−0.0139741	−	0.999902i	$-0.504448\pi$
$127$	−40.0000	−0.0279482	−0.0139741	+	0.999902i	$0.504448\pi$
$128$	0	0
$129$	1350.00	0.921402
$130$	0	0
$131$	−1005.00	−0.670284	−0.335142	−	0.942168i	$-0.608784\pi$
$131$	−1005.00	−0.670284	−0.335142	+	0.942168i	$0.608784\pi$
$132$	0	0
$133$	1963.00	1.27980
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−1692.00	−1.05516	−0.527581	−	0.849504i	$-0.676901\pi$
$137$	−1692.00	−1.05516	−0.527581	+	0.849504i	$0.676901\pi$
$138$	0	0
$139$	564.000	0.344157	0.172079	−	0.985083i	$-0.444952\pi$
$139$	564.000	0.344157	0.172079	+	0.985083i	$0.444952\pi$
$140$	0	0
$141$	2240.00	1.33789
$142$	0	0
$143$	132.000	0.0771916
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−870.000	−0.488139
$148$	0	0
$149$	−2681.00	−1.47407	−0.737034	−	0.675856i	$-0.763774\pi$
$149$	−2681.00	−1.47407	−0.737034	+	0.675856i	$0.763774\pi$
$150$	0	0
$151$	970.000	0.522765	0.261382	−	0.965235i	$-0.415822\pi$
$151$	970.000	0.522765	0.261382	+	0.965235i	$0.415822\pi$
$152$	0	0
$153$	134.000	0.0708056
$154$	0	0
$155$	0	0
$156$	0	0
$157$	2551.00	1.29676	0.648382	−	0.761315i	$-0.275446\pi$
$157$	2551.00	1.29676	0.648382	+	0.761315i	$0.275446\pi$
$158$	0	0
$159$	−225.000	−0.112224
$160$	0	0
$161$	156.000	0.0763635
$162$	0	0
$163$	2377.00	1.14221	0.571107	−	0.820875i	$-0.306514\pi$
$163$	2377.00	1.14221	0.571107	+	0.820875i	$0.306514\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	1113.00	0.515728	0.257864	−	0.966181i	$-0.416981\pi$
$167$	1113.00	0.515728	0.257864	+	0.966181i	$0.416981\pi$
$168$	0	0
$169$	−2053.00	−0.934456
$170$	0	0
$171$	−302.000	−0.135056
$172$	0	0
$173$	−2222.00	−0.976506	−0.488253	−	0.872702i	$-0.662366\pi$
$173$	−2222.00	−0.976506	−0.488253	+	0.872702i	$0.662366\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	3520.00	1.49480
$178$	0	0
$179$	2986.00	1.24684	0.623419	−	0.781888i	$-0.285743\pi$
$179$	2986.00	1.24684	0.623419	+	0.781888i	$0.285743\pi$
$180$	0	0
$181$	302.000	0.124019	0.0620096	−	0.998076i	$-0.480249\pi$
$181$	302.000	0.124019	0.0620096	+	0.998076i	$0.480249\pi$
$182$	0	0
$183$	−1085.00	−0.438281
$184$	0	0
$185$	0	0
$186$	0	0
$187$	737.000	0.288207
$188$	0	0
$189$	−1885.00	−0.725469
$190$	0	0
$191$	−1416.00	−0.536430	−0.268215	−	0.963359i	$-0.586434\pi$
$191$	−1416.00	−0.536430	−0.268215	+	0.963359i	$0.586434\pi$
$192$	0	0
$193$	−4655.00	−1.73614	−0.868068	−	0.496445i	$-0.834638\pi$
$193$	−4655.00	−1.73614	−0.868068	+	0.496445i	$0.834638\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−4146.00	−1.49944	−0.749721	−	0.661753i	$-0.769813\pi$
$197$	−4146.00	−1.49944	−0.749721	+	0.661753i	$0.769813\pi$
$198$	0	0
$199$	−3703.00	−1.31909	−0.659544	−	0.751666i	$-0.729251\pi$
$199$	−3703.00	−1.31909	−0.659544	+	0.751666i	$0.729251\pi$
$200$	0	0
$201$	1420.00	0.498304
$202$	0	0
$203$	−1859.00	−0.642740
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−24.0000	−0.00805853
$208$	0	0
$209$	−1661.00	−0.549731
$210$	0	0
$211$	5231.00	1.70672	0.853358	−	0.521326i	$-0.174562\pi$
$211$	5231.00	1.70672	0.853358	+	0.521326i	$0.174562\pi$
$212$	0	0
$213$	−2575.00	−0.828338
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−4381.00	−1.37051
$218$	0	0
$219$	−5810.00	−1.79271
$220$	0	0
$221$	804.000	0.244719
$222$	0	0
$223$	−3742.00	−1.12369	−0.561845	−	0.827243i	$-0.689908\pi$
$223$	−3742.00	−1.12369	−0.561845	+	0.827243i	$0.689908\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	1260.00	0.368410	0.184205	−	0.982888i	$-0.441029\pi$
$227$	1260.00	0.368410	0.184205	+	0.982888i	$0.441029\pi$
$228$	0	0
$229$	1704.00	0.491718	0.245859	−	0.969306i	$-0.420930\pi$
$229$	1704.00	0.491718	0.245859	+	0.969306i	$0.420930\pi$
$230$	0	0
$231$	−715.000	−0.203652
$232$	0	0
$233$	−4939.00	−1.38869	−0.694345	−	0.719643i	$-0.744306\pi$
$233$	−4939.00	−1.38869	−0.694345	+	0.719643i	$0.744306\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−4720.00	−1.29366
$238$	0	0
$239$	5224.00	1.41386	0.706930	−	0.707284i	$-0.250080\pi$
$239$	5224.00	1.41386	0.706930	+	0.707284i	$0.250080\pi$
$240$	0	0
$241$	1128.00	0.301497	0.150749	−	0.988572i	$-0.451832\pi$
$241$	1128.00	0.301497	0.150749	+	0.988572i	$0.451832\pi$
$242$	0	0
$243$	560.000	0.147835
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1812.00	−0.466781
$248$	0	0
$249$	−620.000	−0.157795
$250$	0	0
$251$	−4110.00	−1.03355	−0.516775	−	0.856121i	$-0.672868\pi$
$251$	−4110.00	−1.03355	−0.516775	+	0.856121i	$0.672868\pi$
$252$	0	0
$253$	−132.000	−0.0328015
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−1356.00	−0.329124	−0.164562	−	0.986367i	$-0.552621\pi$
$257$	−1356.00	−0.329124	−0.164562	+	0.986367i	$0.552621\pi$
$258$	0	0
$259$	−1625.00	−0.389856
$260$	0	0
$261$	286.000	0.0678274
$262$	0	0
$263$	3063.00	0.718147	0.359074	−	0.933309i	$-0.383093\pi$
$263$	3063.00	0.718147	0.359074	+	0.933309i	$0.383093\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	1805.00	0.413724
$268$	0	0
$269$	−344.000	−0.0779704	−0.0389852	−	0.999240i	$-0.512413\pi$
$269$	−344.000	−0.0779704	−0.0389852	+	0.999240i	$0.512413\pi$
$270$	0	0
$271$	7086.00	1.58835	0.794177	−	0.607687i	$-0.207902\pi$
$271$	7086.00	1.58835	0.794177	+	0.607687i	$0.207902\pi$
$272$	0	0
$273$	−780.000	−0.172922
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1156.00	0.250748	0.125374	−	0.992110i	$-0.459987\pi$
$277$	1156.00	0.250748	0.125374	+	0.992110i	$0.459987\pi$
$278$	0	0
$279$	674.000	0.144628
$280$	0	0
$281$	7174.00	1.52301	0.761503	−	0.648161i	$-0.224462\pi$
$281$	7174.00	1.52301	0.761503	+	0.648161i	$0.224462\pi$
$282$	0	0
$283$	−2072.00	−0.435221	−0.217611	−	0.976036i	$-0.569826\pi$
$283$	−2072.00	−0.435221	−0.217611	+	0.976036i	$0.569826\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−3120.00	−0.641700
$288$	0	0
$289$	−424.000	−0.0863016
$290$	0	0
$291$	−4580.00	−0.922627
$292$	0	0
$293$	4736.00	0.944301	0.472150	−	0.881518i	$-0.343478\pi$
$293$	4736.00	0.944301	0.472150	+	0.881518i	$0.343478\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	1595.00	0.311620
$298$	0	0
$299$	−144.000	−0.0278520
$300$	0	0
$301$	3510.00	0.672136
$302$	0	0
$303$	−5950.00	−1.12811
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−4216.00	−0.783778	−0.391889	−	0.920013i	$-0.628178\pi$
$307$	−4216.00	−0.783778	−0.391889	+	0.920013i	$0.628178\pi$
$308$	0	0
$309$	7300.00	1.34396
$310$	0	0
$311$	−6605.00	−1.20429	−0.602147	−	0.798386i	$-0.705688\pi$
$311$	−6605.00	−1.20429	−0.602147	+	0.798386i	$0.705688\pi$
$312$	0	0
$313$	4842.00	0.874396	0.437198	−	0.899365i	$-0.355971\pi$
$313$	4842.00	0.874396	0.437198	+	0.899365i	$0.355971\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−7211.00	−1.27763	−0.638817	−	0.769359i	$-0.720576\pi$
$317$	−7211.00	−1.27763	−0.638817	+	0.769359i	$0.720576\pi$
$318$	0	0
$319$	1573.00	0.276085
$320$	0	0
$321$	−5620.00	−0.977189
$322$	0	0
$323$	−10117.0	−1.74280
$324$	0	0
$325$	0	0
$326$	0	0
$327$	7910.00	1.33769
$328$	0	0
$329$	5824.00	0.975950
$330$	0	0
$331$	−4426.00	−0.734970	−0.367485	−	0.930030i	$-0.619781\pi$
$331$	−4426.00	−0.734970	−0.367485	+	0.930030i	$0.619781\pi$
$332$	0	0
$333$	250.000	0.0411409
$334$	0	0
$335$	0	0
$336$	0	0
$337$	1751.00	0.283036	0.141518	−	0.989936i	$-0.454802\pi$
$337$	1751.00	0.283036	0.141518	+	0.989936i	$0.454802\pi$
$338$	0	0
$339$	−4570.00	−0.732178
$340$	0	0
$341$	3707.00	0.588696
$342$	0	0
$343$	−6721.00	−1.05802
$344$	0	0
$345$	0	0
$346$	0	0
$347$	1494.00	0.231130	0.115565	−	0.993300i	$-0.463132\pi$
$347$	1494.00	0.231130	0.115565	+	0.993300i	$0.463132\pi$
$348$	0	0
$349$	1822.00	0.279454	0.139727	−	0.990190i	$-0.455378\pi$
$349$	1822.00	0.279454	0.139727	+	0.990190i	$0.455378\pi$
$350$	0	0
$351$	1740.00	0.264599
$352$	0	0
$353$	−1390.00	−0.209581	−0.104791	−	0.994494i	$-0.533417\pi$
$353$	−1390.00	−0.209581	−0.104791	+	0.994494i	$0.533417\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−4355.00	−0.645633
$358$	0	0
$359$	−224.000	−0.0329311	−0.0164656	−	0.999864i	$-0.505241\pi$
$359$	−224.000	−0.0329311	−0.0164656	+	0.999864i	$0.505241\pi$
$360$	0	0
$361$	15942.0	2.32425
$362$	0	0
$363$	605.000	0.0874773
$364$	0	0
$365$	0	0
$366$	0	0
$367$	8256.00	1.17428	0.587139	−	0.809486i	$-0.300254\pi$
$367$	8256.00	1.17428	0.587139	+	0.809486i	$0.300254\pi$
$368$	0	0
$369$	480.000	0.0677176
$370$	0	0
$371$	−585.000	−0.0818644
$372$	0	0
$373$	−11348.0	−1.57527	−0.787637	−	0.616140i	$-0.788696\pi$
$373$	−11348.0	−1.57527	−0.787637	+	0.616140i	$0.788696\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	1716.00	0.234426
$378$	0	0
$379$	3710.00	0.502823	0.251411	−	0.967880i	$-0.419105\pi$
$379$	3710.00	0.502823	0.251411	+	0.967880i	$0.419105\pi$
$380$	0	0
$381$	−200.000	−0.0268932
$382$	0	0
$383$	−14370.0	−1.91716	−0.958581	−	0.284822i	$-0.908066\pi$
$383$	−14370.0	−1.91716	−0.958581	+	0.284822i	$0.908066\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−540.000	−0.0709296
$388$	0	0
$389$	6186.00	0.806279	0.403140	−	0.915138i	$-0.367919\pi$
$389$	6186.00	0.806279	0.403140	+	0.915138i	$0.367919\pi$
$390$	0	0
$391$	−804.000	−0.103990
$392$	0	0
$393$	−5025.00	−0.644981
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−13634.0	−1.72360	−0.861802	−	0.507245i	$-0.830664\pi$
$397$	−13634.0	−1.72360	−0.861802	+	0.507245i	$0.830664\pi$
$398$	0	0
$399$	9815.00	1.23149
$400$	0	0
$401$	−7237.00	−0.901243	−0.450622	−	0.892715i	$-0.648798\pi$
$401$	−7237.00	−0.901243	−0.450622	+	0.892715i	$0.648798\pi$
$402$	0	0
$403$	4044.00	0.499866
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1375.00	0.167460
$408$	0	0
$409$	−2420.00	−0.292570	−0.146285	−	0.989242i	$-0.546732\pi$
$409$	−2420.00	−0.292570	−0.146285	+	0.989242i	$0.546732\pi$
$410$	0	0
$411$	−8460.00	−1.01533
$412$	0	0
$413$	9152.00	1.09041
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2820.00	0.331165
$418$	0	0
$419$	−9140.00	−1.06568	−0.532838	−	0.846217i	$-0.678874\pi$
$419$	−9140.00	−1.06568	−0.532838	+	0.846217i	$0.678874\pi$
$420$	0	0
$421$	−10884.0	−1.25999	−0.629993	−	0.776601i	$-0.716942\pi$
$421$	−10884.0	−1.25999	−0.629993	+	0.776601i	$0.716942\pi$
$422$	0	0
$423$	−896.000	−0.102991
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−2821.00	−0.319714
$428$	0	0
$429$	660.000	0.0742776
$430$	0	0
$431$	1752.00	0.195802	0.0979012	−	0.995196i	$-0.468787\pi$
$431$	1752.00	0.195802	0.0979012	+	0.995196i	$0.468787\pi$
$432$	0	0
$433$	−5302.00	−0.588448	−0.294224	−	0.955737i	$-0.595061\pi$
$433$	−5302.00	−0.588448	−0.294224	+	0.955737i	$0.595061\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1812.00	0.198352
$438$	0	0
$439$	−3502.00	−0.380732	−0.190366	−	0.981713i	$-0.560967\pi$
$439$	−3502.00	−0.380732	−0.190366	+	0.981713i	$0.560967\pi$
$440$	0	0
$441$	348.000	0.0375769
$442$	0	0
$443$	−7508.00	−0.805228	−0.402614	−	0.915370i	$-0.631898\pi$
$443$	−7508.00	−0.805228	−0.402614	+	0.915370i	$0.631898\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−13405.0	−1.41842
$448$	0	0
$449$	12062.0	1.26780	0.633899	−	0.773416i	$-0.281454\pi$
$449$	12062.0	1.26780	0.633899	+	0.773416i	$0.281454\pi$
$450$	0	0
$451$	2640.00	0.275638
$452$	0	0
$453$	4850.00	0.503031
$454$	0	0
$455$	0	0
$456$	0	0
$457$	4691.00	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$457$	4691.00	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$458$	0	0
$459$	9715.00	0.987925
$460$	0	0
$461$	951.000	0.0960791	0.0480396	−	0.998845i	$-0.484703\pi$
$461$	951.000	0.0960791	0.0480396	+	0.998845i	$0.484703\pi$
$462$	0	0
$463$	−5784.00	−0.580573	−0.290286	−	0.956940i	$-0.593751\pi$
$463$	−5784.00	−0.580573	−0.290286	+	0.956940i	$0.593751\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	9233.00	0.914887	0.457444	−	0.889239i	$-0.348765\pi$
$467$	9233.00	0.914887	0.457444	+	0.889239i	$0.348765\pi$
$468$	0	0
$469$	3692.00	0.363498
$470$	0	0
$471$	12755.0	1.24781
$472$	0	0
$473$	−2970.00	−0.288712
$474$	0	0
$475$	0	0
$476$	0	0
$477$	90.0000	0.00863903
$478$	0	0
$479$	−7562.00	−0.721329	−0.360665	−	0.932696i	$-0.617450\pi$
$479$	−7562.00	−0.721329	−0.360665	+	0.932696i	$0.617450\pi$
$480$	0	0
$481$	1500.00	0.142192
$482$	0	0
$483$	780.000	0.0734808
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−8346.00	−0.776578	−0.388289	−	0.921538i	$-0.626934\pi$
$487$	−8346.00	−0.776578	−0.388289	+	0.921538i	$0.626934\pi$
$488$	0	0
$489$	11885.0	1.09910
$490$	0	0
$491$	−6045.00	−0.555615	−0.277808	−	0.960637i	$-0.589608\pi$
$491$	−6045.00	−0.555615	−0.277808	+	0.960637i	$0.589608\pi$
$492$	0	0
$493$	9581.00	0.875267
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−6695.00	−0.604249
$498$	0	0
$499$	11056.0	0.991853	0.495926	−	0.868365i	$-0.334829\pi$
$499$	11056.0	0.991853	0.495926	+	0.868365i	$0.334829\pi$
$500$	0	0
$501$	5565.00	0.496259
$502$	0	0
$503$	936.000	0.0829705	0.0414853	−	0.999139i	$-0.486791\pi$
$503$	936.000	0.0829705	0.0414853	+	0.999139i	$0.486791\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−10265.0	−0.899181
$508$	0	0
$509$	1684.00	0.146644	0.0733222	−	0.997308i	$-0.476640\pi$
$509$	1684.00	0.146644	0.0733222	+	0.997308i	$0.476640\pi$
$510$	0	0
$511$	−15106.0	−1.30773
$512$	0	0
$513$	−21895.0	−1.88438
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−4928.00	−0.419213
$518$	0	0
$519$	−11110.0	−0.939643
$520$	0	0
$521$	13190.0	1.10914	0.554572	−	0.832136i	$-0.312882\pi$
$521$	13190.0	1.10914	0.554572	+	0.832136i	$0.312882\pi$
$522$	0	0
$523$	5432.00	0.454158	0.227079	−	0.973876i	$-0.427082\pi$
$523$	5432.00	0.454158	0.227079	+	0.973876i	$0.427082\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	22579.0	1.86633
$528$	0	0
$529$	−12023.0	−0.988165
$530$	0	0
$531$	−1408.00	−0.115070
$532$	0	0
$533$	2880.00	0.234046
$534$	0	0
$535$	0	0
$536$	0	0
$537$	14930.0	1.19977
$538$	0	0
$539$	1914.00	0.152953
$540$	0	0
$541$	6237.00	0.495655	0.247828	−	0.968804i	$-0.420283\pi$
$541$	6237.00	0.495655	0.247828	+	0.968804i	$0.420283\pi$
$542$	0	0
$543$	1510.00	0.119338
$544$	0	0
$545$	0	0
$546$	0	0
$547$	11400.0	0.891095	0.445547	−	0.895258i	$-0.353009\pi$
$547$	11400.0	0.891095	0.445547	+	0.895258i	$0.353009\pi$
$548$	0	0
$549$	434.000	0.0337389
$550$	0	0
$551$	−21593.0	−1.66950
$552$	0	0
$553$	−12272.0	−0.943686
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−2588.00	−0.196871	−0.0984354	−	0.995143i	$-0.531384\pi$
$557$	−2588.00	−0.196871	−0.0984354	+	0.995143i	$0.531384\pi$
$558$	0	0
$559$	−3240.00	−0.245147
$560$	0	0
$561$	3685.00	0.277328
$562$	0	0
$563$	12708.0	0.951294	0.475647	−	0.879636i	$-0.342214\pi$
$563$	12708.0	0.951294	0.475647	+	0.879636i	$0.342214\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−8723.00	−0.646087
$568$	0	0
$569$	9828.00	0.724097	0.362049	−	0.932159i	$-0.382077\pi$
$569$	9828.00	0.724097	0.362049	+	0.932159i	$0.382077\pi$
$570$	0	0
$571$	16585.0	1.21552	0.607759	−	0.794122i	$-0.292069\pi$
$571$	16585.0	1.21552	0.607759	+	0.794122i	$0.292069\pi$
$572$	0	0
$573$	−7080.00	−0.516180
$574$	0	0
$575$	0	0
$576$	0	0
$577$	2992.00	0.215873	0.107936	−	0.994158i	$-0.465576\pi$
$577$	2992.00	0.215873	0.107936	+	0.994158i	$0.465576\pi$
$578$	0	0
$579$	−23275.0	−1.67060
$580$	0	0
$581$	−1612.00	−0.115107
$582$	0	0
$583$	495.000	0.0351643
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−20325.0	−1.42914	−0.714568	−	0.699566i	$-0.753377\pi$
$587$	−20325.0	−1.42914	−0.714568	+	0.699566i	$0.753377\pi$
$588$	0	0
$589$	−50887.0	−3.55987
$590$	0	0
$591$	−20730.0	−1.44284
$592$	0	0
$593$	−5226.00	−0.361899	−0.180949	−	0.983492i	$-0.557917\pi$
$593$	−5226.00	−0.361899	−0.180949	+	0.983492i	$0.557917\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−18515.0	−1.26929
$598$	0	0
$599$	2171.00	0.148088	0.0740440	−	0.997255i	$-0.476409\pi$
$599$	2171.00	0.148088	0.0740440	+	0.997255i	$0.476409\pi$
$600$	0	0
$601$	20786.0	1.41078	0.705390	−	0.708820i	$-0.250772\pi$
$601$	20786.0	1.41078	0.705390	+	0.708820i	$0.250772\pi$
$602$	0	0
$603$	−568.000	−0.0383594
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−11841.0	−0.791781	−0.395891	−	0.918298i	$-0.629564\pi$
$607$	−11841.0	−0.791781	−0.395891	+	0.918298i	$0.629564\pi$
$608$	0	0
$609$	−9295.00	−0.618477
$610$	0	0
$611$	−5376.00	−0.355957
$612$	0	0
$613$	21782.0	1.43518	0.717591	−	0.696465i	$-0.245245\pi$
$613$	21782.0	1.43518	0.717591	+	0.696465i	$0.245245\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	25604.0	1.67063	0.835315	−	0.549772i	$-0.185285\pi$
$617$	25604.0	1.67063	0.835315	+	0.549772i	$0.185285\pi$
$618$	0	0
$619$	−3492.00	−0.226745	−0.113373	−	0.993553i	$-0.536165\pi$
$619$	−3492.00	−0.226745	−0.113373	+	0.993553i	$0.536165\pi$
$620$	0	0
$621$	−1740.00	−0.112438
$622$	0	0
$623$	4693.00	0.301799
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−8305.00	−0.528979
$628$	0	0
$629$	8375.00	0.530895
$630$	0	0
$631$	−6027.00	−0.380239	−0.190120	−	0.981761i	$-0.560888\pi$
$631$	−6027.00	−0.380239	−0.190120	+	0.981761i	$0.560888\pi$
$632$	0	0
$633$	26155.0	1.64229
$634$	0	0
$635$	0	0
$636$	0	0
$637$	2088.00	0.129874
$638$	0	0
$639$	1030.00	0.0637655
$640$	0	0
$641$	−25937.0	−1.59821	−0.799103	−	0.601194i	$-0.794692\pi$
$641$	−25937.0	−1.59821	−0.799103	+	0.601194i	$0.794692\pi$
$642$	0	0
$643$	−2827.00	−0.173384	−0.0866921	−	0.996235i	$-0.527630\pi$
$643$	−2827.00	−0.173384	−0.0866921	+	0.996235i	$0.527630\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	228.000	0.0138541	0.00692705	−	0.999976i	$-0.497795\pi$
$647$	228.000	0.0138541	0.00692705	+	0.999976i	$0.497795\pi$
$648$	0	0
$649$	−7744.00	−0.468380
$650$	0	0
$651$	−21905.0	−1.31878
$652$	0	0
$653$	7377.00	0.442089	0.221045	−	0.975264i	$-0.429053\pi$
$653$	7377.00	0.442089	0.221045	+	0.975264i	$0.429053\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	2324.00	0.138003
$658$	0	0
$659$	−6879.00	−0.406628	−0.203314	−	0.979114i	$-0.565171\pi$
$659$	−6879.00	−0.406628	−0.203314	+	0.979114i	$0.565171\pi$
$660$	0	0
$661$	20260.0	1.19217	0.596084	−	0.802922i	$-0.296723\pi$
$661$	20260.0	1.19217	0.596084	+	0.802922i	$0.296723\pi$
$662$	0	0
$663$	4020.00	0.235481
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−1716.00	−0.0996159
$668$	0	0
$669$	−18710.0	−1.08127
$670$	0	0
$671$	2387.00	0.137331
$672$	0	0
$673$	1489.00	0.0852849	0.0426424	−	0.999090i	$-0.486422\pi$
$673$	1489.00	0.0852849	0.0426424	+	0.999090i	$0.486422\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−5640.00	−0.320181	−0.160091	−	0.987102i	$-0.551179\pi$
$677$	−5640.00	−0.320181	−0.160091	+	0.987102i	$0.551179\pi$
$678$	0	0
$679$	−11908.0	−0.673030
$680$	0	0
$681$	6300.00	0.354503
$682$	0	0
$683$	8019.00	0.449251	0.224626	−	0.974445i	$-0.427884\pi$
$683$	8019.00	0.449251	0.224626	+	0.974445i	$0.427884\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	8520.00	0.473156
$688$	0	0
$689$	540.000	0.0298583
$690$	0	0
$691$	20440.0	1.12529	0.562644	−	0.826699i	$-0.309784\pi$
$691$	20440.0	1.12529	0.562644	+	0.826699i	$0.309784\pi$
$692$	0	0
$693$	286.000	0.0156771
$694$	0	0
$695$	0	0
$696$	0	0
$697$	16080.0	0.873850
$698$	0	0
$699$	−24695.0	−1.33627
$700$	0	0
$701$	10911.0	0.587878	0.293939	−	0.955824i	$-0.405034\pi$
$701$	10911.0	0.587878	0.293939	+	0.955824i	$0.405034\pi$
$702$	0	0
$703$	−18875.0	−1.01264
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−15470.0	−0.822927
$708$	0	0
$709$	24666.0	1.30656	0.653280	−	0.757116i	$-0.273392\pi$
$709$	24666.0	1.30656	0.653280	+	0.757116i	$0.273392\pi$
$710$	0	0
$711$	1888.00	0.0995858
$712$	0	0
$713$	−4044.00	−0.212411
$714$	0	0
$715$	0	0
$716$	0	0
$717$	26120.0	1.36049
$718$	0	0
$719$	17399.0	0.902466	0.451233	−	0.892406i	$-0.350984\pi$
$719$	17399.0	0.902466	0.451233	+	0.892406i	$0.350984\pi$
$720$	0	0
$721$	18980.0	0.980377
$722$	0	0
$723$	5640.00	0.290116
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−19794.0	−1.00979	−0.504896	−	0.863180i	$-0.668469\pi$
$727$	−19794.0	−1.00979	−0.504896	+	0.863180i	$0.668469\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	0	0
$731$	−18090.0	−0.915298
$732$	0	0
$733$	−32454.0	−1.63536	−0.817678	−	0.575676i	$-0.804739\pi$
$733$	−32454.0	−1.63536	−0.817678	+	0.575676i	$0.804739\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3124.00	−0.156138
$738$	0	0
$739$	8024.00	0.399415	0.199707	−	0.979856i	$-0.436001\pi$
$739$	8024.00	0.399415	0.199707	+	0.979856i	$0.436001\pi$
$740$	0	0
$741$	−9060.00	−0.449160
$742$	0	0
$743$	−24159.0	−1.19288	−0.596439	−	0.802659i	$-0.703418\pi$
$743$	−24159.0	−1.19288	−0.596439	+	0.802659i	$0.703418\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	248.000	0.0121470
$748$	0	0
$749$	−14612.0	−0.712832
$750$	0	0
$751$	−38477.0	−1.86957	−0.934784	−	0.355216i	$-0.884407\pi$
$751$	−38477.0	−1.86957	−0.934784	+	0.355216i	$0.884407\pi$
$752$	0	0
$753$	−20550.0	−0.994533
$754$	0	0
$755$	0	0
$756$	0	0
$757$	5014.00	0.240736	0.120368	−	0.992729i	$-0.461593\pi$
$757$	5014.00	0.240736	0.120368	+	0.992729i	$0.461593\pi$
$758$	0	0
$759$	−660.000	−0.0315632
$760$	0	0
$761$	15764.0	0.750913	0.375456	−	0.926840i	$-0.377486\pi$
$761$	15764.0	0.750913	0.375456	+	0.926840i	$0.377486\pi$
$762$	0	0
$763$	20566.0	0.975805
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−8448.00	−0.397705
$768$	0	0
$769$	614.000	0.0287925	0.0143962	−	0.999896i	$-0.495417\pi$
$769$	614.000	0.0287925	0.0143962	+	0.999896i	$0.495417\pi$
$770$	0	0
$771$	−6780.00	−0.316700
$772$	0	0
$773$	5943.00	0.276526	0.138263	−	0.990396i	$-0.455848\pi$
$773$	5943.00	0.276526	0.138263	+	0.990396i	$0.455848\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−8125.00	−0.375139
$778$	0	0
$779$	−36240.0	−1.66679
$780$	0	0
$781$	5665.00	0.259551
$782$	0	0
$783$	20735.0	0.946371
$784$	0	0
$785$	0	0
$786$	0	0
$787$	26154.0	1.18461	0.592306	−	0.805713i	$-0.298218\pi$
$787$	26154.0	1.18461	0.592306	+	0.805713i	$0.298218\pi$
$788$	0	0
$789$	15315.0	0.691037
$790$	0	0
$791$	−11882.0	−0.534103
$792$	0	0
$793$	2604.00	0.116609
$794$	0	0
$795$	0	0
$796$	0	0
$797$	3270.00	0.145332	0.0726658	−	0.997356i	$-0.476849\pi$
$797$	3270.00	0.145332	0.0726658	+	0.997356i	$0.476849\pi$
$798$	0	0
$799$	−30016.0	−1.32902
$800$	0	0
$801$	−722.000	−0.0318485
$802$	0	0
$803$	12782.0	0.561727
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−1720.00	−0.0750271
$808$	0	0
$809$	14306.0	0.621721	0.310860	−	0.950456i	$-0.399383\pi$
$809$	14306.0	0.621721	0.310860	+	0.950456i	$0.399383\pi$
$810$	0	0
$811$	−959.000	−0.0415229	−0.0207614	−	0.999784i	$-0.506609\pi$
$811$	−959.000	−0.0415229	−0.0207614	+	0.999784i	$0.506609\pi$
$812$	0	0
$813$	35430.0	1.52839
$814$	0	0
$815$	0	0
$816$	0	0
$817$	40770.0	1.74585
$818$	0	0
$819$	312.000	0.0133116
$820$	0	0
$821$	14190.0	0.603209	0.301604	−	0.953433i	$-0.402478\pi$
$821$	14190.0	0.603209	0.301604	+	0.953433i	$0.402478\pi$
$822$	0	0
$823$	34010.0	1.44048	0.720239	−	0.693726i	$-0.244032\pi$
$823$	34010.0	1.44048	0.720239	+	0.693726i	$0.244032\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−14218.0	−0.597833	−0.298917	−	0.954279i	$-0.596625\pi$
$827$	−14218.0	−0.597833	−0.298917	+	0.954279i	$0.596625\pi$
$828$	0	0
$829$	33172.0	1.38976	0.694880	−	0.719126i	$-0.255457\pi$
$829$	33172.0	1.38976	0.694880	+	0.719126i	$0.255457\pi$
$830$	0	0
$831$	5780.00	0.241283
$832$	0	0
$833$	11658.0	0.484905
$834$	0	0
$835$	0	0
$836$	0	0
$837$	48865.0	2.01795
$838$	0	0
$839$	28656.0	1.17916	0.589580	−	0.807710i	$-0.299293\pi$
$839$	28656.0	1.17916	0.589580	+	0.807710i	$0.299293\pi$
$840$	0	0
$841$	−3940.00	−0.161548
$842$	0	0
$843$	35870.0	1.46551
$844$	0	0
$845$	0	0
$846$	0	0
$847$	1573.00	0.0638122
$848$	0	0
$849$	−10360.0	−0.418792
$850$	0	0
$851$	−1500.00	−0.0604223
$852$	0	0
$853$	10244.0	0.411193	0.205597	−	0.978637i	$-0.434087\pi$
$853$	10244.0	0.411193	0.205597	+	0.978637i	$0.434087\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	11401.0	0.454435	0.227217	−	0.973844i	$-0.427037\pi$
$857$	11401.0	0.454435	0.227217	+	0.973844i	$0.427037\pi$
$858$	0	0
$859$	26846.0	1.06633	0.533163	−	0.846013i	$-0.321003\pi$
$859$	26846.0	1.06633	0.533163	+	0.846013i	$0.321003\pi$
$860$	0	0
$861$	−15600.0	−0.617476
$862$	0	0
$863$	−40972.0	−1.61611	−0.808055	−	0.589107i	$-0.799480\pi$
$863$	−40972.0	−1.61611	−0.808055	+	0.589107i	$0.799480\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−2120.00	−0.0830438
$868$	0	0
$869$	10384.0	0.405355
$870$	0	0
$871$	−3408.00	−0.132578
$872$	0	0
$873$	1832.00	0.0710238
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−15614.0	−0.601194	−0.300597	−	0.953751i	$-0.597186\pi$
$877$	−15614.0	−0.601194	−0.300597	+	0.953751i	$0.597186\pi$
$878$	0	0
$879$	23680.0	0.908654
$880$	0	0
$881$	−39938.0	−1.52729	−0.763647	−	0.645634i	$-0.776593\pi$
$881$	−39938.0	−1.52729	−0.763647	+	0.645634i	$0.776593\pi$
$882$	0	0
$883$	48467.0	1.84716	0.923581	−	0.383403i	$-0.125248\pi$
$883$	48467.0	1.84716	0.923581	+	0.383403i	$0.125248\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−25776.0	−0.975731	−0.487865	−	0.872919i	$-0.662224\pi$
$887$	−25776.0	−0.975731	−0.487865	+	0.872919i	$0.662224\pi$
$888$	0	0
$889$	−520.000	−0.0196178
$890$	0	0
$891$	7381.00	0.277523
$892$	0	0
$893$	67648.0	2.53500
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−720.000	−0.0268006
$898$	0	0
$899$	48191.0	1.78783
$900$	0	0
$901$	3015.00	0.111481
$902$	0	0
$903$	17550.0	0.646763
$904$	0	0
$905$	0	0
$906$	0	0
$907$	23701.0	0.867672	0.433836	−	0.900992i	$-0.357160\pi$
$907$	23701.0	0.867672	0.433836	+	0.900992i	$0.357160\pi$
$908$	0	0
$909$	2380.00	0.0868423
$910$	0	0
$911$	24189.0	0.879712	0.439856	−	0.898068i	$-0.355030\pi$
$911$	24189.0	0.879712	0.439856	+	0.898068i	$0.355030\pi$
$912$	0	0
$913$	1364.00	0.0494434
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−13065.0	−0.470495
$918$	0	0
$919$	−24590.0	−0.882643	−0.441322	−	0.897349i	$-0.645490\pi$
$919$	−24590.0	−0.882643	−0.441322	+	0.897349i	$0.645490\pi$
$920$	0	0
$921$	−21080.0	−0.754191
$922$	0	0
$923$	6180.00	0.220387
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−2920.00	−0.103458
$928$	0	0
$929$	16575.0	0.585369	0.292685	−	0.956209i	$-0.405451\pi$
$929$	16575.0	0.585369	0.292685	+	0.956209i	$0.405451\pi$
$930$	0	0
$931$	−26274.0	−0.924915
$932$	0	0
$933$	−33025.0	−1.15883
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−15542.0	−0.541873	−0.270937	−	0.962597i	$-0.587333\pi$
$937$	−15542.0	−0.541873	−0.270937	+	0.962597i	$0.587333\pi$
$938$	0	0
$939$	24210.0	0.841388
$940$	0	0
$941$	10893.0	0.377366	0.188683	−	0.982038i	$-0.439578\pi$
$941$	10893.0	0.377366	0.188683	+	0.982038i	$0.439578\pi$
$942$	0	0
$943$	−2880.00	−0.0994546
$944$	0	0
$945$	0	0
$946$	0	0
$947$	23831.0	0.817744	0.408872	−	0.912592i	$-0.365922\pi$
$947$	23831.0	0.817744	0.408872	+	0.912592i	$0.365922\pi$
$948$	0	0
$949$	13944.0	0.476967
$950$	0	0
$951$	−36055.0	−1.22940
$952$	0	0
$953$	3771.00	0.128179	0.0640895	−	0.997944i	$-0.479586\pi$
$953$	3771.00	0.128179	0.0640895	+	0.997944i	$0.479586\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	7865.00	0.265663
$958$	0	0
$959$	−21996.0	−0.740655
$960$	0	0
$961$	83778.0	2.81219
$962$	0	0
$963$	2248.00	0.0752241
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−50413.0	−1.67650	−0.838249	−	0.545288i	$-0.816420\pi$
$967$	−50413.0	−1.67650	−0.838249	+	0.545288i	$0.816420\pi$
$968$	0	0
$969$	−50585.0	−1.67701
$970$	0	0
$971$	492.000	0.0162606	0.00813029	−	0.999967i	$-0.497412\pi$
$971$	492.000	0.0162606	0.00813029	+	0.999967i	$0.497412\pi$
$972$	0	0
$973$	7332.00	0.241576
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−56748.0	−1.85827	−0.929135	−	0.369741i	$-0.879446\pi$
$977$	−56748.0	−1.85827	−0.929135	+	0.369741i	$0.879446\pi$
$978$	0	0
$979$	−3971.00	−0.129636
$980$	0	0
$981$	−3164.00	−0.102975
$982$	0	0
$983$	−49302.0	−1.59968	−0.799842	−	0.600210i	$-0.795083\pi$
$983$	−49302.0	−1.59968	−0.799842	+	0.600210i	$0.795083\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	29120.0	0.939108
$988$	0	0
$989$	3240.00	0.104172
$990$	0	0
$991$	5064.00	0.162324	0.0811621	−	0.996701i	$-0.474137\pi$
$991$	5064.00	0.162324	0.0811621	+	0.996701i	$0.474137\pi$
$992$	0	0
$993$	−22130.0	−0.707225
$994$	0	0
$995$	0	0
$996$	0	0
$997$	61018.0	1.93827	0.969137	−	0.246522i	$-0.0792878\pi$
$997$	61018.0	1.93827	0.969137	+	0.246522i	$0.0792878\pi$
$998$	0	0
$999$	18125.0	0.574024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2200.4.a.j.1.1		1
5.2	odd	4		440.4.b.a.89.1	✓	2
5.3	odd	4		440.4.b.a.89.2	yes	2
5.4	even	2		2200.4.a.c.1.1		1
20.3	even	4		880.4.b.c.529.1		2
20.7	even	4		880.4.b.c.529.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.4.b.a.89.1	✓	2	5.2	odd	4
440.4.b.a.89.2	yes	2	5.3	odd	4
880.4.b.c.529.1		2	20.3	even	4
880.4.b.c.529.2		2	20.7	even	4
2200.4.a.c.1.1		1	5.4	even	2
2200.4.a.j.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2200.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

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