LMFDB - Embedded newform 1400.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,4,Mod(1,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, 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("1400.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1400.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:	$82.6026740080$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-6.00000 q^{3} +7.00000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-6.00000 q^{3} +7.00000 q^{7} +9.00000 q^{9} +56.0000 q^{11} +28.0000 q^{13} +90.0000 q^{17} +74.0000 q^{19} -42.0000 q^{21} +96.0000 q^{23} +108.000 q^{27} -222.000 q^{29} -100.000 q^{31} -336.000 q^{33} -58.0000 q^{37} -168.000 q^{39} +422.000 q^{41} -512.000 q^{43} -148.000 q^{47} +49.0000 q^{49} -540.000 q^{51} +642.000 q^{53} -444.000 q^{57} -318.000 q^{59} +720.000 q^{61} +63.0000 q^{63} +412.000 q^{67} -576.000 q^{69} +448.000 q^{71} -994.000 q^{73} +392.000 q^{77} -296.000 q^{79} -891.000 q^{81} -386.000 q^{83} +1332.00 q^{87} -6.00000 q^{89} +196.000 q^{91} +600.000 q^{93} +138.000 q^{97} +504.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−6.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−6.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	56.0000	1.53497	0.767483	−	0.641069i	$-0.221509\pi$
$11$	56.0000	1.53497	0.767483	+	0.641069i	$0.221509\pi$
$12$	0	0
$13$	28.0000	0.597369	0.298685	−	0.954352i	$-0.403452\pi$
$13$	28.0000	0.597369	0.298685	+	0.954352i	$0.403452\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	90.0000	1.28401	0.642006	−	0.766700i	$-0.278102\pi$
$17$	90.0000	1.28401	0.642006	+	0.766700i	$0.278102\pi$
$18$	0	0
$19$	74.0000	0.893514	0.446757	−	0.894655i	$-0.352579\pi$
$19$	74.0000	0.893514	0.446757	+	0.894655i	$0.352579\pi$
$20$	0	0
$21$	−42.0000	−0.436436
$22$	0	0
$23$	96.0000	0.870321	0.435161	−	0.900353i	$-0.356692\pi$
$23$	96.0000	0.870321	0.435161	+	0.900353i	$0.356692\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	108.000	0.769800
$28$	0	0
$29$	−222.000	−1.42153	−0.710765	−	0.703430i	$-0.751651\pi$
$29$	−222.000	−1.42153	−0.710765	+	0.703430i	$0.751651\pi$
$30$	0	0
$31$	−100.000	−0.579372	−0.289686	−	0.957122i	$-0.593551\pi$
$31$	−100.000	−0.579372	−0.289686	+	0.957122i	$0.593551\pi$
$32$	0	0
$33$	−336.000	−1.77243
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−58.0000	−0.257707	−0.128853	−	0.991664i	$-0.541130\pi$
$37$	−58.0000	−0.257707	−0.128853	+	0.991664i	$0.541130\pi$
$38$	0	0
$39$	−168.000	−0.689783
$40$	0	0
$41$	422.000	1.60745	0.803724	−	0.595003i	$-0.202849\pi$
$41$	422.000	1.60745	0.803724	+	0.595003i	$0.202849\pi$
$42$	0	0
$43$	−512.000	−1.81580	−0.907898	−	0.419190i	$-0.862314\pi$
$43$	−512.000	−1.81580	−0.907898	+	0.419190i	$0.862314\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−148.000	−0.459320	−0.229660	−	0.973271i	$-0.573761\pi$
$47$	−148.000	−0.459320	−0.229660	+	0.973271i	$0.573761\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	−540.000	−1.48265
$52$	0	0
$53$	642.000	1.66388	0.831939	−	0.554868i	$-0.187231\pi$
$53$	642.000	1.66388	0.831939	+	0.554868i	$0.187231\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−444.000	−1.03174
$58$	0	0
$59$	−318.000	−0.701696	−0.350848	−	0.936432i	$-0.614107\pi$
$59$	−318.000	−0.701696	−0.350848	+	0.936432i	$0.614107\pi$
$60$	0	0
$61$	720.000	1.51125	0.755627	−	0.655002i	$-0.227332\pi$
$61$	720.000	1.51125	0.755627	+	0.655002i	$0.227332\pi$
$62$	0	0
$63$	63.0000	0.125988
$64$	0	0
$65$	0	0
$66$	0	0
$67$	412.000	0.751251	0.375625	−	0.926772i	$-0.377428\pi$
$67$	412.000	0.751251	0.375625	+	0.926772i	$0.377428\pi$
$68$	0	0
$69$	−576.000	−1.00496
$70$	0	0
$71$	448.000	0.748843	0.374421	−	0.927259i	$-0.377841\pi$
$71$	448.000	0.748843	0.374421	+	0.927259i	$0.377841\pi$
$72$	0	0
$73$	−994.000	−1.59368	−0.796842	−	0.604188i	$-0.793498\pi$
$73$	−994.000	−1.59368	−0.796842	+	0.604188i	$0.793498\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	392.000	0.580163
$78$	0	0
$79$	−296.000	−0.421552	−0.210776	−	0.977534i	$-0.567599\pi$
$79$	−296.000	−0.421552	−0.210776	+	0.977534i	$0.567599\pi$
$80$	0	0
$81$	−891.000	−1.22222
$82$	0	0
$83$	−386.000	−0.510470	−0.255235	−	0.966879i	$-0.582153\pi$
$83$	−386.000	−0.510470	−0.255235	+	0.966879i	$0.582153\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1332.00	1.64144
$88$	0	0
$89$	−6.00000	−0.00714605	−0.00357303	−	0.999994i	$-0.501137\pi$
$89$	−6.00000	−0.00714605	−0.00357303	+	0.999994i	$0.501137\pi$
$90$	0	0
$91$	196.000	0.225784
$92$	0	0
$93$	600.000	0.669001
$94$	0	0
$95$	0	0
$96$	0	0
$97$	138.000	0.144451	0.0722257	−	0.997388i	$-0.476990\pi$
$97$	138.000	0.144451	0.0722257	+	0.997388i	$0.476990\pi$
$98$	0	0
$99$	504.000	0.511656
$100$	0	0
$101$	−664.000	−0.654163	−0.327082	−	0.944996i	$-0.606065\pi$
$101$	−664.000	−0.654163	−0.327082	+	0.944996i	$0.606065\pi$
$102$	0	0
$103$	−2012.00	−1.92474	−0.962370	−	0.271742i	$-0.912400\pi$
$103$	−2012.00	−1.92474	−0.962370	+	0.271742i	$0.912400\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−900.000	−0.813143	−0.406571	−	0.913619i	$-0.633276\pi$
$107$	−900.000	−0.813143	−0.406571	+	0.913619i	$0.633276\pi$
$108$	0	0
$109$	1706.00	1.49913	0.749565	−	0.661931i	$-0.230263\pi$
$109$	1706.00	1.49913	0.749565	+	0.661931i	$0.230263\pi$
$110$	0	0
$111$	348.000	0.297574
$112$	0	0
$113$	442.000	0.367963	0.183982	−	0.982930i	$-0.441101\pi$
$113$	442.000	0.367963	0.183982	+	0.982930i	$0.441101\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	252.000	0.199123
$118$	0	0
$119$	630.000	0.485311
$120$	0	0
$121$	1805.00	1.35612
$122$	0	0
$123$	−2532.00	−1.85612
$124$	0	0
$125$	0	0
$126$	0	0
$127$	1952.00	1.36387	0.681937	−	0.731411i	$-0.261138\pi$
$127$	1952.00	1.36387	0.681937	+	0.731411i	$0.261138\pi$
$128$	0	0
$129$	3072.00	2.09670
$130$	0	0
$131$	−742.000	−0.494877	−0.247438	−	0.968904i	$-0.579589\pi$
$131$	−742.000	−0.494877	−0.247438	+	0.968904i	$0.579589\pi$
$132$	0	0
$133$	518.000	0.337717
$134$	0	0
$135$	0	0
$136$	0	0
$137$	1854.00	1.15619	0.578095	−	0.815970i	$-0.303796\pi$
$137$	1854.00	1.15619	0.578095	+	0.815970i	$0.303796\pi$
$138$	0	0
$139$	−74.0000	−0.0451554	−0.0225777	−	0.999745i	$-0.507187\pi$
$139$	−74.0000	−0.0451554	−0.0225777	+	0.999745i	$0.507187\pi$
$140$	0	0
$141$	888.000	0.530377
$142$	0	0
$143$	1568.00	0.916942
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−294.000	−0.164957
$148$	0	0
$149$	2502.00	1.37565	0.687825	−	0.725877i	$-0.258566\pi$
$149$	2502.00	1.37565	0.687825	+	0.725877i	$0.258566\pi$
$150$	0	0
$151$	−888.000	−0.478572	−0.239286	−	0.970949i	$-0.576913\pi$
$151$	−888.000	−0.478572	−0.239286	+	0.970949i	$0.576913\pi$
$152$	0	0
$153$	810.000	0.428004
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1092.00	−0.555102	−0.277551	−	0.960711i	$-0.589523\pi$
$157$	−1092.00	−0.555102	−0.277551	+	0.960711i	$0.589523\pi$
$158$	0	0
$159$	−3852.00	−1.92128
$160$	0	0
$161$	672.000	0.328950
$162$	0	0
$163$	1704.00	0.818820	0.409410	−	0.912351i	$-0.365735\pi$
$163$	1704.00	0.818820	0.409410	+	0.912351i	$0.365735\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−436.000	−0.202028	−0.101014	−	0.994885i	$-0.532209\pi$
$167$	−436.000	−0.202028	−0.101014	+	0.994885i	$0.532209\pi$
$168$	0	0
$169$	−1413.00	−0.643150
$170$	0	0
$171$	666.000	0.297838
$172$	0	0
$173$	996.000	0.437714	0.218857	−	0.975757i	$-0.429767\pi$
$173$	996.000	0.437714	0.218857	+	0.975757i	$0.429767\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1908.00	0.810249
$178$	0	0
$179$	1244.00	0.519447	0.259723	−	0.965683i	$-0.416369\pi$
$179$	1244.00	0.519447	0.259723	+	0.965683i	$0.416369\pi$
$180$	0	0
$181$	412.000	0.169192	0.0845959	−	0.996415i	$-0.473040\pi$
$181$	412.000	0.169192	0.0845959	+	0.996415i	$0.473040\pi$
$182$	0	0
$183$	−4320.00	−1.74505
$184$	0	0
$185$	0	0
$186$	0	0
$187$	5040.00	1.97092
$188$	0	0
$189$	756.000	0.290957
$190$	0	0
$191$	1160.00	0.439448	0.219724	−	0.975562i	$-0.429484\pi$
$191$	1160.00	0.439448	0.219724	+	0.975562i	$0.429484\pi$
$192$	0	0
$193$	3698.00	1.37921	0.689606	−	0.724185i	$-0.257784\pi$
$193$	3698.00	1.37921	0.689606	+	0.724185i	$0.257784\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	2874.00	1.03941	0.519706	−	0.854345i	$-0.326042\pi$
$197$	2874.00	1.03941	0.519706	+	0.854345i	$0.326042\pi$
$198$	0	0
$199$	3348.00	1.19263	0.596315	−	0.802750i	$-0.296631\pi$
$199$	3348.00	1.19263	0.596315	+	0.802750i	$0.296631\pi$
$200$	0	0
$201$	−2472.00	−0.867470
$202$	0	0
$203$	−1554.00	−0.537288
$204$	0	0
$205$	0	0
$206$	0	0
$207$	864.000	0.290107
$208$	0	0
$209$	4144.00	1.37151
$210$	0	0
$211$	−2556.00	−0.833945	−0.416972	−	0.908919i	$-0.636909\pi$
$211$	−2556.00	−0.833945	−0.416972	+	0.908919i	$0.636909\pi$
$212$	0	0
$213$	−2688.00	−0.864689
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−700.000	−0.218982
$218$	0	0
$219$	5964.00	1.84023
$220$	0	0
$221$	2520.00	0.767030
$222$	0	0
$223$	312.000	0.0936909	0.0468454	−	0.998902i	$-0.485083\pi$
$223$	312.000	0.0936909	0.0468454	+	0.998902i	$0.485083\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−826.000	−0.241513	−0.120757	−	0.992682i	$-0.538532\pi$
$227$	−826.000	−0.241513	−0.120757	+	0.992682i	$0.538532\pi$
$228$	0	0
$229$	4036.00	1.16466	0.582328	−	0.812954i	$-0.302142\pi$
$229$	4036.00	1.16466	0.582328	+	0.812954i	$0.302142\pi$
$230$	0	0
$231$	−2352.00	−0.669914
$232$	0	0
$233$	2902.00	0.815950	0.407975	−	0.912993i	$-0.366235\pi$
$233$	2902.00	0.815950	0.407975	+	0.912993i	$0.366235\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	1776.00	0.486766
$238$	0	0
$239$	3176.00	0.859575	0.429787	−	0.902930i	$-0.358589\pi$
$239$	3176.00	0.859575	0.429787	+	0.902930i	$0.358589\pi$
$240$	0	0
$241$	−4682.00	−1.25143	−0.625714	−	0.780053i	$-0.715192\pi$
$241$	−4682.00	−1.25143	−0.625714	+	0.780053i	$0.715192\pi$
$242$	0	0
$243$	2430.00	0.641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	2072.00	0.533758
$248$	0	0
$249$	2316.00	0.589440
$250$	0	0
$251$	630.000	0.158427	0.0792136	−	0.996858i	$-0.474759\pi$
$251$	630.000	0.158427	0.0792136	+	0.996858i	$0.474759\pi$
$252$	0	0
$253$	5376.00	1.33591
$254$	0	0
$255$	0	0
$256$	0	0
$257$	1870.00	0.453881	0.226940	−	0.973909i	$-0.427128\pi$
$257$	1870.00	0.453881	0.226940	+	0.973909i	$0.427128\pi$
$258$	0	0
$259$	−406.000	−0.0974039
$260$	0	0
$261$	−1998.00	−0.473843
$262$	0	0
$263$	−3360.00	−0.787781	−0.393891	−	0.919157i	$-0.628871\pi$
$263$	−3360.00	−0.787781	−0.393891	+	0.919157i	$0.628871\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	36.0000	0.00825155
$268$	0	0
$269$	−5924.00	−1.34272	−0.671362	−	0.741130i	$-0.734290\pi$
$269$	−5924.00	−1.34272	−0.671362	+	0.741130i	$0.734290\pi$
$270$	0	0
$271$	2064.00	0.462653	0.231327	−	0.972876i	$-0.425693\pi$
$271$	2064.00	0.462653	0.231327	+	0.972876i	$0.425693\pi$
$272$	0	0
$273$	−1176.00	−0.260713
$274$	0	0
$275$	0	0
$276$	0	0
$277$	3314.00	0.718841	0.359421	−	0.933176i	$-0.382974\pi$
$277$	3314.00	0.718841	0.359421	+	0.933176i	$0.382974\pi$
$278$	0	0
$279$	−900.000	−0.193124
$280$	0	0
$281$	3018.00	0.640707	0.320354	−	0.947298i	$-0.396198\pi$
$281$	3018.00	0.640707	0.320354	+	0.947298i	$0.396198\pi$
$282$	0	0
$283$	−6802.00	−1.42875	−0.714376	−	0.699762i	$-0.753289\pi$
$283$	−6802.00	−1.42875	−0.714376	+	0.699762i	$0.753289\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	2954.00	0.607558
$288$	0	0
$289$	3187.00	0.648687
$290$	0	0
$291$	−828.000	−0.166798
$292$	0	0
$293$	−2784.00	−0.555096	−0.277548	−	0.960712i	$-0.589522\pi$
$293$	−2784.00	−0.555096	−0.277548	+	0.960712i	$0.589522\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	6048.00	1.18162
$298$	0	0
$299$	2688.00	0.519903
$300$	0	0
$301$	−3584.00	−0.686307
$302$	0	0
$303$	3984.00	0.755362
$304$	0	0
$305$	0	0
$306$	0	0
$307$	5654.00	1.05111	0.525555	−	0.850760i	$-0.323858\pi$
$307$	5654.00	1.05111	0.525555	+	0.850760i	$0.323858\pi$
$308$	0	0
$309$	12072.0	2.22250
$310$	0	0
$311$	2504.00	0.456556	0.228278	−	0.973596i	$-0.426691\pi$
$311$	2504.00	0.456556	0.228278	+	0.973596i	$0.426691\pi$
$312$	0	0
$313$	−6454.00	−1.16550	−0.582750	−	0.812651i	$-0.698023\pi$
$313$	−6454.00	−1.16550	−0.582750	+	0.812651i	$0.698023\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	4146.00	0.734582	0.367291	−	0.930106i	$-0.380285\pi$
$317$	4146.00	0.734582	0.367291	+	0.930106i	$0.380285\pi$
$318$	0	0
$319$	−12432.0	−2.18200
$320$	0	0
$321$	5400.00	0.938936
$322$	0	0
$323$	6660.00	1.14728
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−10236.0	−1.73105
$328$	0	0
$329$	−1036.00	−0.173606
$330$	0	0
$331$	10208.0	1.69511	0.847557	−	0.530705i	$-0.178073\pi$
$331$	10208.0	1.69511	0.847557	+	0.530705i	$0.178073\pi$
$332$	0	0
$333$	−522.000	−0.0859022
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−8078.00	−1.30575	−0.652873	−	0.757467i	$-0.726437\pi$
$337$	−8078.00	−1.30575	−0.652873	+	0.757467i	$0.726437\pi$
$338$	0	0
$339$	−2652.00	−0.424888
$340$	0	0
$341$	−5600.00	−0.889317
$342$	0	0
$343$	343.000	0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	3456.00	0.534662	0.267331	−	0.963605i	$-0.413858\pi$
$347$	3456.00	0.534662	0.267331	+	0.963605i	$0.413858\pi$
$348$	0	0
$349$	6348.00	0.973641	0.486820	−	0.873502i	$-0.338157\pi$
$349$	6348.00	0.973641	0.486820	+	0.873502i	$0.338157\pi$
$350$	0	0
$351$	3024.00	0.459855
$352$	0	0
$353$	−2290.00	−0.345282	−0.172641	−	0.984985i	$-0.555230\pi$
$353$	−2290.00	−0.345282	−0.172641	+	0.984985i	$0.555230\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−3780.00	−0.560389
$358$	0	0
$359$	−9912.00	−1.45720	−0.728601	−	0.684939i	$-0.759829\pi$
$359$	−9912.00	−1.45720	−0.728601	+	0.684939i	$0.759829\pi$
$360$	0	0
$361$	−1383.00	−0.201633
$362$	0	0
$363$	−10830.0	−1.56592
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−4840.00	−0.688409	−0.344204	−	0.938895i	$-0.611851\pi$
$367$	−4840.00	−0.688409	−0.344204	+	0.938895i	$0.611851\pi$
$368$	0	0
$369$	3798.00	0.535816
$370$	0	0
$371$	4494.00	0.628886
$372$	0	0
$373$	8090.00	1.12301	0.561507	−	0.827472i	$-0.310222\pi$
$373$	8090.00	1.12301	0.561507	+	0.827472i	$0.310222\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−6216.00	−0.849178
$378$	0	0
$379$	−7000.00	−0.948723	−0.474361	−	0.880330i	$-0.657321\pi$
$379$	−7000.00	−0.948723	−0.474361	+	0.880330i	$0.657321\pi$
$380$	0	0
$381$	−11712.0	−1.57487
$382$	0	0
$383$	−10308.0	−1.37523	−0.687616	−	0.726074i	$-0.741343\pi$
$383$	−10308.0	−1.37523	−0.687616	+	0.726074i	$0.741343\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−4608.00	−0.605266
$388$	0	0
$389$	−11510.0	−1.50021	−0.750103	−	0.661321i	$-0.769996\pi$
$389$	−11510.0	−1.50021	−0.750103	+	0.661321i	$0.769996\pi$
$390$	0	0
$391$	8640.00	1.11750
$392$	0	0
$393$	4452.00	0.571434
$394$	0	0
$395$	0	0
$396$	0	0
$397$	8132.00	1.02804	0.514022	−	0.857777i	$-0.328155\pi$
$397$	8132.00	1.02804	0.514022	+	0.857777i	$0.328155\pi$
$398$	0	0
$399$	−3108.00	−0.389961
$400$	0	0
$401$	−1074.00	−0.133748	−0.0668741	−	0.997761i	$-0.521303\pi$
$401$	−1074.00	−0.133748	−0.0668741	+	0.997761i	$0.521303\pi$
$402$	0	0
$403$	−2800.00	−0.346099
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−3248.00	−0.395571
$408$	0	0
$409$	3406.00	0.411775	0.205887	−	0.978576i	$-0.433992\pi$
$409$	3406.00	0.411775	0.205887	+	0.978576i	$0.433992\pi$
$410$	0	0
$411$	−11124.0	−1.33505
$412$	0	0
$413$	−2226.00	−0.265216
$414$	0	0
$415$	0	0
$416$	0	0
$417$	444.000	0.0521409
$418$	0	0
$419$	−13522.0	−1.57659	−0.788297	−	0.615295i	$-0.789037\pi$
$419$	−13522.0	−1.57659	−0.788297	+	0.615295i	$0.789037\pi$
$420$	0	0
$421$	1198.00	0.138686	0.0693432	−	0.997593i	$-0.477910\pi$
$421$	1198.00	0.138686	0.0693432	+	0.997593i	$0.477910\pi$
$422$	0	0
$423$	−1332.00	−0.153107
$424$	0	0
$425$	0	0
$426$	0	0
$427$	5040.00	0.571201
$428$	0	0
$429$	−9408.00	−1.05879
$430$	0	0
$431$	−12824.0	−1.43320	−0.716601	−	0.697483i	$-0.754303\pi$
$431$	−12824.0	−1.43320	−0.716601	+	0.697483i	$0.754303\pi$
$432$	0	0
$433$	12770.0	1.41729	0.708646	−	0.705565i	$-0.249307\pi$
$433$	12770.0	1.41729	0.708646	+	0.705565i	$0.249307\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	7104.00	0.777644
$438$	0	0
$439$	13224.0	1.43769	0.718846	−	0.695169i	$-0.244670\pi$
$439$	13224.0	1.43769	0.718846	+	0.695169i	$0.244670\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	0	0
$443$	−972.000	−0.104246	−0.0521232	−	0.998641i	$-0.516599\pi$
$443$	−972.000	−0.104246	−0.0521232	+	0.998641i	$0.516599\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−15012.0	−1.58846
$448$	0	0
$449$	6034.00	0.634214	0.317107	−	0.948390i	$-0.397289\pi$
$449$	6034.00	0.634214	0.317107	+	0.948390i	$0.397289\pi$
$450$	0	0
$451$	23632.0	2.46738
$452$	0	0
$453$	5328.00	0.552608
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−12742.0	−1.30426	−0.652129	−	0.758108i	$-0.726124\pi$
$457$	−12742.0	−1.30426	−0.652129	+	0.758108i	$0.726124\pi$
$458$	0	0
$459$	9720.00	0.988433
$460$	0	0
$461$	6132.00	0.619513	0.309757	−	0.950816i	$-0.399752\pi$
$461$	6132.00	0.619513	0.309757	+	0.950816i	$0.399752\pi$
$462$	0	0
$463$	−2672.00	−0.268204	−0.134102	−	0.990968i	$-0.542815\pi$
$463$	−2672.00	−0.268204	−0.134102	+	0.990968i	$0.542815\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	17246.0	1.70889	0.854443	−	0.519545i	$-0.173899\pi$
$467$	17246.0	1.70889	0.854443	+	0.519545i	$0.173899\pi$
$468$	0	0
$469$	2884.00	0.283946
$470$	0	0
$471$	6552.00	0.640977
$472$	0	0
$473$	−28672.0	−2.78719
$474$	0	0
$475$	0	0
$476$	0	0
$477$	5778.00	0.554626
$478$	0	0
$479$	−19812.0	−1.88984	−0.944920	−	0.327301i	$-0.893861\pi$
$479$	−19812.0	−1.88984	−0.944920	+	0.327301i	$0.893861\pi$
$480$	0	0
$481$	−1624.00	−0.153946
$482$	0	0
$483$	−4032.00	−0.379839
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−14864.0	−1.38306	−0.691532	−	0.722346i	$-0.743064\pi$
$487$	−14864.0	−1.38306	−0.691532	+	0.722346i	$0.743064\pi$
$488$	0	0
$489$	−10224.0	−0.945491
$490$	0	0
$491$	15756.0	1.44818	0.724092	−	0.689703i	$-0.242259\pi$
$491$	15756.0	1.44818	0.724092	+	0.689703i	$0.242259\pi$
$492$	0	0
$493$	−19980.0	−1.82526
$494$	0	0
$495$	0	0
$496$	0	0
$497$	3136.00	0.283036
$498$	0	0
$499$	1604.00	0.143898	0.0719488	−	0.997408i	$-0.477078\pi$
$499$	1604.00	0.143898	0.0719488	+	0.997408i	$0.477078\pi$
$500$	0	0
$501$	2616.00	0.233282
$502$	0	0
$503$	19232.0	1.70480	0.852398	−	0.522893i	$-0.175147\pi$
$503$	19232.0	1.70480	0.852398	+	0.522893i	$0.175147\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	8478.00	0.742645
$508$	0	0
$509$	76.0000	0.00661815	0.00330908	−	0.999995i	$-0.498947\pi$
$509$	76.0000	0.00661815	0.00330908	+	0.999995i	$0.498947\pi$
$510$	0	0
$511$	−6958.00	−0.602356
$512$	0	0
$513$	7992.00	0.687827
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−8288.00	−0.705040
$518$	0	0
$519$	−5976.00	−0.505428
$520$	0	0
$521$	−12570.0	−1.05701	−0.528505	−	0.848930i	$-0.677247\pi$
$521$	−12570.0	−1.05701	−0.528505	+	0.848930i	$0.677247\pi$
$522$	0	0
$523$	11510.0	0.962327	0.481164	−	0.876631i	$-0.340214\pi$
$523$	11510.0	0.962327	0.481164	+	0.876631i	$0.340214\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−9000.00	−0.743921
$528$	0	0
$529$	−2951.00	−0.242541
$530$	0	0
$531$	−2862.00	−0.233899
$532$	0	0
$533$	11816.0	0.960240
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−7464.00	−0.599805
$538$	0	0
$539$	2744.00	0.219281
$540$	0	0
$541$	23438.0	1.86262	0.931311	−	0.364225i	$-0.118666\pi$
$541$	23438.0	1.86262	0.931311	+	0.364225i	$0.118666\pi$
$542$	0	0
$543$	−2472.00	−0.195366
$544$	0	0
$545$	0	0
$546$	0	0
$547$	5328.00	0.416470	0.208235	−	0.978079i	$-0.433228\pi$
$547$	5328.00	0.416470	0.208235	+	0.978079i	$0.433228\pi$
$548$	0	0
$549$	6480.00	0.503752
$550$	0	0
$551$	−16428.0	−1.27016
$552$	0	0
$553$	−2072.00	−0.159332
$554$	0	0
$555$	0	0
$556$	0	0
$557$	2386.00	0.181505	0.0907523	−	0.995873i	$-0.471073\pi$
$557$	2386.00	0.181505	0.0907523	+	0.995873i	$0.471073\pi$
$558$	0	0
$559$	−14336.0	−1.08470
$560$	0	0
$561$	−30240.0	−2.27582
$562$	0	0
$563$	−13094.0	−0.980189	−0.490094	−	0.871669i	$-0.663038\pi$
$563$	−13094.0	−0.980189	−0.490094	+	0.871669i	$0.663038\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−6237.00	−0.461957
$568$	0	0
$569$	15638.0	1.15216	0.576080	−	0.817393i	$-0.304582\pi$
$569$	15638.0	1.15216	0.576080	+	0.817393i	$0.304582\pi$
$570$	0	0
$571$	−4040.00	−0.296092	−0.148046	−	0.988980i	$-0.547298\pi$
$571$	−4040.00	−0.296092	−0.148046	+	0.988980i	$0.547298\pi$
$572$	0	0
$573$	−6960.00	−0.507431
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−9154.00	−0.660461	−0.330231	−	0.943900i	$-0.607126\pi$
$577$	−9154.00	−0.660461	−0.330231	+	0.943900i	$0.607126\pi$
$578$	0	0
$579$	−22188.0	−1.59258
$580$	0	0
$581$	−2702.00	−0.192939
$582$	0	0
$583$	35952.0	2.55400
$584$	0	0
$585$	0	0
$586$	0	0
$587$	2754.00	0.193645	0.0968226	−	0.995302i	$-0.469132\pi$
$587$	2754.00	0.193645	0.0968226	+	0.995302i	$0.469132\pi$
$588$	0	0
$589$	−7400.00	−0.517677
$590$	0	0
$591$	−17244.0	−1.20021
$592$	0	0
$593$	20678.0	1.43195	0.715973	−	0.698128i	$-0.245983\pi$
$593$	20678.0	1.43195	0.715973	+	0.698128i	$0.245983\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−20088.0	−1.37713
$598$	0	0
$599$	−10200.0	−0.695761	−0.347880	−	0.937539i	$-0.613098\pi$
$599$	−10200.0	−0.695761	−0.347880	+	0.937539i	$0.613098\pi$
$600$	0	0
$601$	−23782.0	−1.61412	−0.807062	−	0.590467i	$-0.798943\pi$
$601$	−23782.0	−1.61412	−0.807062	+	0.590467i	$0.798943\pi$
$602$	0	0
$603$	3708.00	0.250417
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−9920.00	−0.663328	−0.331664	−	0.943397i	$-0.607610\pi$
$607$	−9920.00	−0.663328	−0.331664	+	0.943397i	$0.607610\pi$
$608$	0	0
$609$	9324.00	0.620406
$610$	0	0
$611$	−4144.00	−0.274383
$612$	0	0
$613$	21030.0	1.38563	0.692817	−	0.721113i	$-0.256369\pi$
$613$	21030.0	1.38563	0.692817	+	0.721113i	$0.256369\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−8854.00	−0.577713	−0.288856	−	0.957372i	$-0.593275\pi$
$617$	−8854.00	−0.577713	−0.288856	+	0.957372i	$0.593275\pi$
$618$	0	0
$619$	−1214.00	−0.0788284	−0.0394142	−	0.999223i	$-0.512549\pi$
$619$	−1214.00	−0.0788284	−0.0394142	+	0.999223i	$0.512549\pi$
$620$	0	0
$621$	10368.0	0.669973
$622$	0	0
$623$	−42.0000	−0.00270095
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−24864.0	−1.58369
$628$	0	0
$629$	−5220.00	−0.330898
$630$	0	0
$631$	−1200.00	−0.0757072	−0.0378536	−	0.999283i	$-0.512052\pi$
$631$	−1200.00	−0.0757072	−0.0378536	+	0.999283i	$0.512052\pi$
$632$	0	0
$633$	15336.0	0.962956
$634$	0	0
$635$	0	0
$636$	0	0
$637$	1372.00	0.0853385
$638$	0	0
$639$	4032.00	0.249614
$640$	0	0
$641$	6894.00	0.424800	0.212400	−	0.977183i	$-0.431872\pi$
$641$	6894.00	0.424800	0.212400	+	0.977183i	$0.431872\pi$
$642$	0	0
$643$	−13174.0	−0.807981	−0.403991	−	0.914763i	$-0.632377\pi$
$643$	−13174.0	−0.807981	−0.403991	+	0.914763i	$0.632377\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−1684.00	−0.102326	−0.0511630	−	0.998690i	$-0.516293\pi$
$647$	−1684.00	−0.102326	−0.0511630	+	0.998690i	$0.516293\pi$
$648$	0	0
$649$	−17808.0	−1.07708
$650$	0	0
$651$	4200.00	0.252859
$652$	0	0
$653$	20582.0	1.23344	0.616720	−	0.787183i	$-0.288461\pi$
$653$	20582.0	1.23344	0.616720	+	0.787183i	$0.288461\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−8946.00	−0.531228
$658$	0	0
$659$	22416.0	1.32504	0.662522	−	0.749043i	$-0.269486\pi$
$659$	22416.0	1.32504	0.662522	+	0.749043i	$0.269486\pi$
$660$	0	0
$661$	20864.0	1.22771	0.613854	−	0.789419i	$-0.289618\pi$
$661$	20864.0	1.22771	0.613854	+	0.789419i	$0.289618\pi$
$662$	0	0
$663$	−15120.0	−0.885690
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−21312.0	−1.23719
$668$	0	0
$669$	−1872.00	−0.108185
$670$	0	0
$671$	40320.0	2.31973
$672$	0	0
$673$	14438.0	0.826960	0.413480	−	0.910513i	$-0.364313\pi$
$673$	14438.0	0.826960	0.413480	+	0.910513i	$0.364313\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	2724.00	0.154641	0.0773204	−	0.997006i	$-0.475364\pi$
$677$	2724.00	0.154641	0.0773204	+	0.997006i	$0.475364\pi$
$678$	0	0
$679$	966.000	0.0545975
$680$	0	0
$681$	4956.00	0.278876
$682$	0	0
$683$	−5676.00	−0.317988	−0.158994	−	0.987280i	$-0.550825\pi$
$683$	−5676.00	−0.317988	−0.158994	+	0.987280i	$0.550825\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−24216.0	−1.34483
$688$	0	0
$689$	17976.0	0.993949
$690$	0	0
$691$	−2534.00	−0.139505	−0.0697525	−	0.997564i	$-0.522221\pi$
$691$	−2534.00	−0.139505	−0.0697525	+	0.997564i	$0.522221\pi$
$692$	0	0
$693$	3528.00	0.193388
$694$	0	0
$695$	0	0
$696$	0	0
$697$	37980.0	2.06398
$698$	0	0
$699$	−17412.0	−0.942178
$700$	0	0
$701$	−15558.0	−0.838256	−0.419128	−	0.907927i	$-0.637664\pi$
$701$	−15558.0	−0.838256	−0.419128	+	0.907927i	$0.637664\pi$
$702$	0	0
$703$	−4292.00	−0.230264
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−4648.00	−0.247250
$708$	0	0
$709$	14538.0	0.770079	0.385040	−	0.922900i	$-0.374188\pi$
$709$	14538.0	0.770079	0.385040	+	0.922900i	$0.374188\pi$
$710$	0	0
$711$	−2664.00	−0.140517
$712$	0	0
$713$	−9600.00	−0.504240
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−19056.0	−0.992551
$718$	0	0
$719$	16364.0	0.848782	0.424391	−	0.905479i	$-0.360488\pi$
$719$	16364.0	0.848782	0.424391	+	0.905479i	$0.360488\pi$
$720$	0	0
$721$	−14084.0	−0.727483
$722$	0	0
$723$	28092.0	1.44502
$724$	0	0
$725$	0	0
$726$	0	0
$727$	24884.0	1.26946	0.634729	−	0.772735i	$-0.281112\pi$
$727$	24884.0	1.26946	0.634729	+	0.772735i	$0.281112\pi$
$728$	0	0
$729$	9477.00	0.481481
$730$	0	0
$731$	−46080.0	−2.33151
$732$	0	0
$733$	−9248.00	−0.466006	−0.233003	−	0.972476i	$-0.574855\pi$
$733$	−9248.00	−0.466006	−0.233003	+	0.972476i	$0.574855\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	23072.0	1.15315
$738$	0	0
$739$	3928.00	0.195526	0.0977631	−	0.995210i	$-0.468831\pi$
$739$	3928.00	0.195526	0.0977631	+	0.995210i	$0.468831\pi$
$740$	0	0
$741$	−12432.0	−0.616331
$742$	0	0
$743$	−2840.00	−0.140228	−0.0701141	−	0.997539i	$-0.522336\pi$
$743$	−2840.00	−0.140228	−0.0701141	+	0.997539i	$0.522336\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−3474.00	−0.170157
$748$	0	0
$749$	−6300.00	−0.307339
$750$	0	0
$751$	904.000	0.0439247	0.0219623	−	0.999759i	$-0.493009\pi$
$751$	904.000	0.0439247	0.0219623	+	0.999759i	$0.493009\pi$
$752$	0	0
$753$	−3780.00	−0.182936
$754$	0	0
$755$	0	0
$756$	0	0
$757$	326.000	0.0156521	0.00782607	−	0.999969i	$-0.497509\pi$
$757$	326.000	0.0156521	0.00782607	+	0.999969i	$0.497509\pi$
$758$	0	0
$759$	−32256.0	−1.54258
$760$	0	0
$761$	13902.0	0.662217	0.331108	−	0.943593i	$-0.392577\pi$
$761$	13902.0	0.662217	0.331108	+	0.943593i	$0.392577\pi$
$762$	0	0
$763$	11942.0	0.566618
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−8904.00	−0.419172
$768$	0	0
$769$	−19378.0	−0.908698	−0.454349	−	0.890824i	$-0.650128\pi$
$769$	−19378.0	−0.908698	−0.454349	+	0.890824i	$0.650128\pi$
$770$	0	0
$771$	−11220.0	−0.524097
$772$	0	0
$773$	33280.0	1.54851	0.774255	−	0.632874i	$-0.218125\pi$
$773$	33280.0	1.54851	0.774255	+	0.632874i	$0.218125\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	2436.00	0.112472
$778$	0	0
$779$	31228.0	1.43628
$780$	0	0
$781$	25088.0	1.14945
$782$	0	0
$783$	−23976.0	−1.09429
$784$	0	0
$785$	0	0
$786$	0	0
$787$	32974.0	1.49351	0.746757	−	0.665097i	$-0.231610\pi$
$787$	32974.0	1.49351	0.746757	+	0.665097i	$0.231610\pi$
$788$	0	0
$789$	20160.0	0.909651
$790$	0	0
$791$	3094.00	0.139077
$792$	0	0
$793$	20160.0	0.902778
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−17244.0	−0.766391	−0.383196	−	0.923667i	$-0.625176\pi$
$797$	−17244.0	−0.766391	−0.383196	+	0.923667i	$0.625176\pi$
$798$	0	0
$799$	−13320.0	−0.589772
$800$	0	0
$801$	−54.0000	−0.00238202
$802$	0	0
$803$	−55664.0	−2.44625
$804$	0	0
$805$	0	0
$806$	0	0
$807$	35544.0	1.55044
$808$	0	0
$809$	−27178.0	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$809$	−27178.0	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$810$	0	0
$811$	33514.0	1.45109	0.725546	−	0.688174i	$-0.241587\pi$
$811$	33514.0	1.45109	0.725546	+	0.688174i	$0.241587\pi$
$812$	0	0
$813$	−12384.0	−0.534226
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−37888.0	−1.62244
$818$	0	0
$819$	1764.00	0.0752615
$820$	0	0
$821$	−10978.0	−0.466669	−0.233334	−	0.972397i	$-0.574964\pi$
$821$	−10978.0	−0.466669	−0.233334	+	0.972397i	$0.574964\pi$
$822$	0	0
$823$	2376.00	0.100634	0.0503172	−	0.998733i	$-0.483977\pi$
$823$	2376.00	0.100634	0.0503172	+	0.998733i	$0.483977\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	12844.0	0.540060	0.270030	−	0.962852i	$-0.412966\pi$
$827$	12844.0	0.540060	0.270030	+	0.962852i	$0.412966\pi$
$828$	0	0
$829$	−30880.0	−1.29374	−0.646868	−	0.762602i	$-0.723921\pi$
$829$	−30880.0	−1.29374	−0.646868	+	0.762602i	$0.723921\pi$
$830$	0	0
$831$	−19884.0	−0.830046
$832$	0	0
$833$	4410.00	0.183430
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−10800.0	−0.446001
$838$	0	0
$839$	−27924.0	−1.14904	−0.574519	−	0.818491i	$-0.694811\pi$
$839$	−27924.0	−1.14904	−0.574519	+	0.818491i	$0.694811\pi$
$840$	0	0
$841$	24895.0	1.02075
$842$	0	0
$843$	−18108.0	−0.739825
$844$	0	0
$845$	0	0
$846$	0	0
$847$	12635.0	0.512566
$848$	0	0
$849$	40812.0	1.64978
$850$	0	0
$851$	−5568.00	−0.224287
$852$	0	0
$853$	10636.0	0.426928	0.213464	−	0.976951i	$-0.431525\pi$
$853$	10636.0	0.426928	0.213464	+	0.976951i	$0.431525\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−41934.0	−1.67146	−0.835728	−	0.549143i	$-0.814954\pi$
$857$	−41934.0	−1.67146	−0.835728	+	0.549143i	$0.814954\pi$
$858$	0	0
$859$	−15946.0	−0.633377	−0.316688	−	0.948530i	$-0.602571\pi$
$859$	−15946.0	−0.633377	−0.316688	+	0.948530i	$0.602571\pi$
$860$	0	0
$861$	−17724.0	−0.701547
$862$	0	0
$863$	−16984.0	−0.669921	−0.334961	−	0.942232i	$-0.608723\pi$
$863$	−16984.0	−0.669921	−0.334961	+	0.942232i	$0.608723\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−19122.0	−0.749039
$868$	0	0
$869$	−16576.0	−0.647068
$870$	0	0
$871$	11536.0	0.448774
$872$	0	0
$873$	1242.00	0.0481504
$874$	0	0
$875$	0	0
$876$	0	0
$877$	6702.00	0.258051	0.129025	−	0.991641i	$-0.458815\pi$
$877$	6702.00	0.258051	0.129025	+	0.991641i	$0.458815\pi$
$878$	0	0
$879$	16704.0	0.640969
$880$	0	0
$881$	36810.0	1.40767	0.703837	−	0.710362i	$-0.251469\pi$
$881$	36810.0	1.40767	0.703837	+	0.710362i	$0.251469\pi$
$882$	0	0
$883$	5060.00	0.192845	0.0964227	−	0.995340i	$-0.469260\pi$
$883$	5060.00	0.192845	0.0964227	+	0.995340i	$0.469260\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−32156.0	−1.21724	−0.608621	−	0.793461i	$-0.708277\pi$
$887$	−32156.0	−1.21724	−0.608621	+	0.793461i	$0.708277\pi$
$888$	0	0
$889$	13664.0	0.515496
$890$	0	0
$891$	−49896.0	−1.87607
$892$	0	0
$893$	−10952.0	−0.410408
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−16128.0	−0.600332
$898$	0	0
$899$	22200.0	0.823594
$900$	0	0
$901$	57780.0	2.13644
$902$	0	0
$903$	21504.0	0.792479
$904$	0	0
$905$	0	0
$906$	0	0
$907$	2716.00	0.0994303	0.0497152	−	0.998763i	$-0.484169\pi$
$907$	2716.00	0.0994303	0.0497152	+	0.998763i	$0.484169\pi$
$908$	0	0
$909$	−5976.00	−0.218054
$910$	0	0
$911$	42048.0	1.52921	0.764606	−	0.644498i	$-0.222934\pi$
$911$	42048.0	1.52921	0.764606	+	0.644498i	$0.222934\pi$
$912$	0	0
$913$	−21616.0	−0.783554
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−5194.00	−0.187046
$918$	0	0
$919$	−7816.00	−0.280551	−0.140275	−	0.990113i	$-0.544799\pi$
$919$	−7816.00	−0.280551	−0.140275	+	0.990113i	$0.544799\pi$
$920$	0	0
$921$	−33924.0	−1.21372
$922$	0	0
$923$	12544.0	0.447336
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−18108.0	−0.641580
$928$	0	0
$929$	−15578.0	−0.550159	−0.275079	−	0.961422i	$-0.588704\pi$
$929$	−15578.0	−0.550159	−0.275079	+	0.961422i	$0.588704\pi$
$930$	0	0
$931$	3626.00	0.127645
$932$	0	0
$933$	−15024.0	−0.527185
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−46210.0	−1.61112	−0.805558	−	0.592518i	$-0.798134\pi$
$937$	−46210.0	−1.61112	−0.805558	+	0.592518i	$0.798134\pi$
$938$	0	0
$939$	38724.0	1.34580
$940$	0	0
$941$	−24816.0	−0.859701	−0.429850	−	0.902900i	$-0.641434\pi$
$941$	−24816.0	−0.859701	−0.429850	+	0.902900i	$0.641434\pi$
$942$	0	0
$943$	40512.0	1.39899
$944$	0	0
$945$	0	0
$946$	0	0
$947$	12800.0	0.439223	0.219611	−	0.975587i	$-0.429521\pi$
$947$	12800.0	0.439223	0.219611	+	0.975587i	$0.429521\pi$
$948$	0	0
$949$	−27832.0	−0.952018
$950$	0	0
$951$	−24876.0	−0.848222
$952$	0	0
$953$	16902.0	0.574512	0.287256	−	0.957854i	$-0.407257\pi$
$953$	16902.0	0.574512	0.287256	+	0.957854i	$0.407257\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	74592.0	2.51956
$958$	0	0
$959$	12978.0	0.436998
$960$	0	0
$961$	−19791.0	−0.664328
$962$	0	0
$963$	−8100.00	−0.271048
$964$	0	0
$965$	0	0
$966$	0	0
$967$	4000.00	0.133021	0.0665105	−	0.997786i	$-0.478813\pi$
$967$	4000.00	0.133021	0.0665105	+	0.997786i	$0.478813\pi$
$968$	0	0
$969$	−39960.0	−1.32477
$970$	0	0
$971$	−27486.0	−0.908412	−0.454206	−	0.890897i	$-0.650077\pi$
$971$	−27486.0	−0.908412	−0.454206	+	0.890897i	$0.650077\pi$
$972$	0	0
$973$	−518.000	−0.0170671
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1126.00	0.0368720	0.0184360	−	0.999830i	$-0.494131\pi$
$977$	1126.00	0.0368720	0.0184360	+	0.999830i	$0.494131\pi$
$978$	0	0
$979$	−336.000	−0.0109690
$980$	0	0
$981$	15354.0	0.499710
$982$	0	0
$983$	−4668.00	−0.151461	−0.0757305	−	0.997128i	$-0.524129\pi$
$983$	−4668.00	−0.151461	−0.0757305	+	0.997128i	$0.524129\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	6216.00	0.200463
$988$	0	0
$989$	−49152.0	−1.58033
$990$	0	0
$991$	2048.00	0.0656477	0.0328238	−	0.999461i	$-0.489550\pi$
$991$	2048.00	0.0656477	0.0328238	+	0.999461i	$0.489550\pi$
$992$	0	0
$993$	−61248.0	−1.95735
$994$	0	0
$995$	0	0
$996$	0	0
$997$	26864.0	0.853351	0.426676	−	0.904405i	$-0.359685\pi$
$997$	26864.0	0.853351	0.426676	+	0.904405i	$0.359685\pi$
$998$	0	0
$999$	−6264.00	−0.198383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.4.a.b.1.1		1
5.2	odd	4		1400.4.g.b.449.2		2
5.3	odd	4		1400.4.g.b.449.1		2
5.4	even	2		56.4.a.b.1.1	✓	1
15.14	odd	2		504.4.a.a.1.1		1
20.19	odd	2		112.4.a.b.1.1		1
35.4	even	6		392.4.i.a.177.1		2
35.9	even	6		392.4.i.a.361.1		2
35.19	odd	6		392.4.i.h.361.1		2
35.24	odd	6		392.4.i.h.177.1		2
35.34	odd	2		392.4.a.a.1.1		1
40.19	odd	2		448.4.a.n.1.1		1
40.29	even	2		448.4.a.c.1.1		1
60.59	even	2		1008.4.a.e.1.1		1
140.139	even	2		784.4.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.a.b.1.1	✓	1	5.4	even	2
112.4.a.b.1.1		1	20.19	odd	2
392.4.a.a.1.1		1	35.34	odd	2
392.4.i.a.177.1		2	35.4	even	6
392.4.i.a.361.1		2	35.9	even	6
392.4.i.h.177.1		2	35.24	odd	6
392.4.i.h.361.1		2	35.19	odd	6
448.4.a.c.1.1		1	40.29	even	2
448.4.a.n.1.1		1	40.19	odd	2
504.4.a.a.1.1		1	15.14	odd	2
784.4.a.q.1.1		1	140.139	even	2
1008.4.a.e.1.1		1	60.59	even	2
1400.4.a.b.1.1		1	1.1	even	1	trivial
1400.4.g.b.449.1		2	5.3	odd	4
1400.4.g.b.449.2		2	5.2	odd	4

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1400.a (trivial)

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