LMFDB - Embedded newform 1400.4.a.g.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
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)

$f(q)$

$=$

$q+4.00000 q^{3} -7.00000 q^{7} -11.0000 q^{9} +O(q^{10})$

$q+4.00000 q^{3} -7.00000 q^{7} -11.0000 q^{9} +20.0000 q^{11} +10.0000 q^{13} +14.0000 q^{17} +12.0000 q^{19} -28.0000 q^{21} -104.000 q^{23} -152.000 q^{27} -122.000 q^{29} +224.000 q^{31} +80.0000 q^{33} -158.000 q^{37} +40.0000 q^{39} +378.000 q^{41} -404.000 q^{43} -112.000 q^{47} +49.0000 q^{49} +56.0000 q^{51} -270.000 q^{53} +48.0000 q^{57} +324.000 q^{59} -186.000 q^{61} +77.0000 q^{63} -156.000 q^{67} -416.000 q^{69} -360.000 q^{71} +102.000 q^{73} -140.000 q^{77} -912.000 q^{79} -311.000 q^{81} -1068.00 q^{83} -488.000 q^{87} -1590.00 q^{89} -70.0000 q^{91} +896.000 q^{93} -866.000 q^{97} -220.000 q^{99} +O(q^{100})$

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
$3$	4.00000	0.769800	0.384900	−	0.922958i	$-0.374236\pi$
$3$	4.00000	0.769800	0.384900	+	0.922958i	$0.374236\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	0	0
$9$	−11.0000	−0.407407
$10$	0	0
$11$	20.0000	0.548202	0.274101	−	0.961701i	$-0.411620\pi$
$11$	20.0000	0.548202	0.274101	+	0.961701i	$0.411620\pi$
$12$	0	0
$13$	10.0000	0.213346	0.106673	−	0.994294i	$-0.465980\pi$
$13$	10.0000	0.213346	0.106673	+	0.994294i	$0.465980\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	14.0000	0.199735	0.0998676	−	0.995001i	$-0.468158\pi$
$17$	14.0000	0.199735	0.0998676	+	0.995001i	$0.468158\pi$
$18$	0	0
$19$	12.0000	0.144894	0.0724471	−	0.997372i	$-0.476919\pi$
$19$	12.0000	0.144894	0.0724471	+	0.997372i	$0.476919\pi$
$20$	0	0
$21$	−28.0000	−0.290957
$22$	0	0
$23$	−104.000	−0.942848	−0.471424	−	0.881907i	$-0.656260\pi$
$23$	−104.000	−0.942848	−0.471424	+	0.881907i	$0.656260\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−152.000	−1.08342
$28$	0	0
$29$	−122.000	−0.781201	−0.390601	−	0.920560i	$-0.627733\pi$
$29$	−122.000	−0.781201	−0.390601	+	0.920560i	$0.627733\pi$
$30$	0	0
$31$	224.000	1.29779	0.648897	−	0.760877i	$-0.275231\pi$
$31$	224.000	1.29779	0.648897	+	0.760877i	$0.275231\pi$
$32$	0	0
$33$	80.0000	0.422006
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−158.000	−0.702028	−0.351014	−	0.936370i	$-0.614163\pi$
$37$	−158.000	−0.702028	−0.351014	+	0.936370i	$0.614163\pi$
$38$	0	0
$39$	40.0000	0.164234
$40$	0	0
$41$	378.000	1.43985	0.719923	−	0.694054i	$-0.244177\pi$
$41$	378.000	1.43985	0.719923	+	0.694054i	$0.244177\pi$
$42$	0	0
$43$	−404.000	−1.43278	−0.716389	−	0.697701i	$-0.754206\pi$
$43$	−404.000	−1.43278	−0.716389	+	0.697701i	$0.754206\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−112.000	−0.347593	−0.173797	−	0.984782i	$-0.555604\pi$
$47$	−112.000	−0.347593	−0.173797	+	0.984782i	$0.555604\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	56.0000	0.153756
$52$	0	0
$53$	−270.000	−0.699761	−0.349881	−	0.936794i	$-0.613778\pi$
$53$	−270.000	−0.699761	−0.349881	+	0.936794i	$0.613778\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	48.0000	0.111540
$58$	0	0
$59$	324.000	0.714936	0.357468	−	0.933925i	$-0.383640\pi$
$59$	324.000	0.714936	0.357468	+	0.933925i	$0.383640\pi$
$60$	0	0
$61$	−186.000	−0.390408	−0.195204	−	0.980763i	$-0.562537\pi$
$61$	−186.000	−0.390408	−0.195204	+	0.980763i	$0.562537\pi$
$62$	0	0
$63$	77.0000	0.153986
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−156.000	−0.284454	−0.142227	−	0.989834i	$-0.545426\pi$
$67$	−156.000	−0.284454	−0.142227	+	0.989834i	$0.545426\pi$
$68$	0	0
$69$	−416.000	−0.725805
$70$	0	0
$71$	−360.000	−0.601748	−0.300874	−	0.953664i	$-0.597278\pi$
$71$	−360.000	−0.601748	−0.300874	+	0.953664i	$0.597278\pi$
$72$	0	0
$73$	102.000	0.163537	0.0817685	−	0.996651i	$-0.473943\pi$
$73$	102.000	0.163537	0.0817685	+	0.996651i	$0.473943\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−140.000	−0.207201
$78$	0	0
$79$	−912.000	−1.29884	−0.649418	−	0.760432i	$-0.724987\pi$
$79$	−912.000	−1.29884	−0.649418	+	0.760432i	$0.724987\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	0	0
$83$	−1068.00	−1.41239	−0.706194	−	0.708018i	$-0.749589\pi$
$83$	−1068.00	−1.41239	−0.706194	+	0.708018i	$0.749589\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−488.000	−0.601369
$88$	0	0
$89$	−1590.00	−1.89370	−0.946852	−	0.321669i	$-0.895756\pi$
$89$	−1590.00	−1.89370	−0.946852	+	0.321669i	$0.895756\pi$
$90$	0	0
$91$	−70.0000	−0.0806373
$92$	0	0
$93$	896.000	0.999042
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−866.000	−0.906484	−0.453242	−	0.891387i	$-0.649733\pi$
$97$	−866.000	−0.906484	−0.453242	+	0.891387i	$0.649733\pi$
$98$	0	0
$99$	−220.000	−0.223342
$100$	0	0
$101$	702.000	0.691600	0.345800	−	0.938308i	$-0.387608\pi$
$101$	702.000	0.691600	0.345800	+	0.938308i	$0.387608\pi$
$102$	0	0
$103$	296.000	0.283163	0.141581	−	0.989927i	$-0.454781\pi$
$103$	296.000	0.283163	0.141581	+	0.989927i	$0.454781\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	44.0000	0.0397537	0.0198768	−	0.999802i	$-0.493673\pi$
$107$	44.0000	0.0397537	0.0198768	+	0.999802i	$0.493673\pi$
$108$	0	0
$109$	−650.000	−0.571181	−0.285590	−	0.958352i	$-0.592190\pi$
$109$	−650.000	−0.571181	−0.285590	+	0.958352i	$0.592190\pi$
$110$	0	0
$111$	−632.000	−0.540421
$112$	0	0
$113$	942.000	0.784212	0.392106	−	0.919920i	$-0.371747\pi$
$113$	942.000	0.784212	0.392106	+	0.919920i	$0.371747\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−110.000	−0.0869188
$118$	0	0
$119$	−98.0000	−0.0754928
$120$	0	0
$121$	−931.000	−0.699474
$122$	0	0
$123$	1512.00	1.10839
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−736.000	−0.514248	−0.257124	−	0.966378i	$-0.582775\pi$
$127$	−736.000	−0.514248	−0.257124	+	0.966378i	$0.582775\pi$
$128$	0	0
$129$	−1616.00	−1.10295
$130$	0	0
$131$	924.000	0.616261	0.308131	−	0.951344i	$-0.400297\pi$
$131$	924.000	0.616261	0.308131	+	0.951344i	$0.400297\pi$
$132$	0	0
$133$	−84.0000	−0.0547648
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−474.000	−0.295595	−0.147798	−	0.989018i	$-0.547218\pi$
$137$	−474.000	−0.295595	−0.147798	+	0.989018i	$0.547218\pi$
$138$	0	0
$139$	1012.00	0.617530	0.308765	−	0.951138i	$-0.400084\pi$
$139$	1012.00	0.617530	0.308765	+	0.951138i	$0.400084\pi$
$140$	0	0
$141$	−448.000	−0.267577
$142$	0	0
$143$	200.000	0.116957
$144$	0	0
$145$	0	0
$146$	0	0
$147$	196.000	0.109971
$148$	0	0
$149$	302.000	0.166046	0.0830228	−	0.996548i	$-0.473543\pi$
$149$	302.000	0.166046	0.0830228	+	0.996548i	$0.473543\pi$
$150$	0	0
$151$	−2104.00	−1.13391	−0.566957	−	0.823747i	$-0.691880\pi$
$151$	−2104.00	−1.13391	−0.566957	+	0.823747i	$0.691880\pi$
$152$	0	0
$153$	−154.000	−0.0813736
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1190.00	−0.604919	−0.302460	−	0.953162i	$-0.597808\pi$
$157$	−1190.00	−0.604919	−0.302460	+	0.953162i	$0.597808\pi$
$158$	0	0
$159$	−1080.00	−0.538677
$160$	0	0
$161$	728.000	0.356363
$162$	0	0
$163$	1732.00	0.832274	0.416137	−	0.909302i	$-0.363384\pi$
$163$	1732.00	0.832274	0.416137	+	0.909302i	$0.363384\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−2264.00	−1.04906	−0.524532	−	0.851391i	$-0.675760\pi$
$167$	−2264.00	−1.04906	−0.524532	+	0.851391i	$0.675760\pi$
$168$	0	0
$169$	−2097.00	−0.954483
$170$	0	0
$171$	−132.000	−0.0590309
$172$	0	0
$173$	1066.00	0.468477	0.234238	−	0.972179i	$-0.424740\pi$
$173$	1066.00	0.468477	0.234238	+	0.972179i	$0.424740\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1296.00	0.550358
$178$	0	0
$179$	−2356.00	−0.983775	−0.491887	−	0.870659i	$-0.663693\pi$
$179$	−2356.00	−0.983775	−0.491887	+	0.870659i	$0.663693\pi$
$180$	0	0
$181$	2158.00	0.886204	0.443102	−	0.896471i	$-0.353878\pi$
$181$	2158.00	0.886204	0.443102	+	0.896471i	$0.353878\pi$
$182$	0	0
$183$	−744.000	−0.300536
$184$	0	0
$185$	0	0
$186$	0	0
$187$	280.000	0.109495
$188$	0	0
$189$	1064.00	0.409495
$190$	0	0
$191$	−2688.00	−1.01831	−0.509154	−	0.860675i	$-0.670042\pi$
$191$	−2688.00	−1.01831	−0.509154	+	0.860675i	$0.670042\pi$
$192$	0	0
$193$	4414.00	1.64625	0.823126	−	0.567859i	$-0.192228\pi$
$193$	4414.00	1.64625	0.823126	+	0.567859i	$0.192228\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−3774.00	−1.36491	−0.682453	−	0.730930i	$-0.739087\pi$
$197$	−3774.00	−1.36491	−0.682453	+	0.730930i	$0.739087\pi$
$198$	0	0
$199$	664.000	0.236531	0.118266	−	0.992982i	$-0.462267\pi$
$199$	664.000	0.236531	0.118266	+	0.992982i	$0.462267\pi$
$200$	0	0
$201$	−624.000	−0.218973
$202$	0	0
$203$	854.000	0.295266
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1144.00	0.384123
$208$	0	0
$209$	240.000	0.0794313
$210$	0	0
$211$	1260.00	0.411099	0.205550	−	0.978647i	$-0.434102\pi$
$211$	1260.00	0.411099	0.205550	+	0.978647i	$0.434102\pi$
$212$	0	0
$213$	−1440.00	−0.463226
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−1568.00	−0.490520
$218$	0	0
$219$	408.000	0.125891
$220$	0	0
$221$	140.000	0.0426128
$222$	0	0
$223$	1152.00	0.345936	0.172968	−	0.984927i	$-0.444664\pi$
$223$	1152.00	0.345936	0.172968	+	0.984927i	$0.444664\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−2588.00	−0.756703	−0.378352	−	0.925662i	$-0.623509\pi$
$227$	−2588.00	−0.756703	−0.378352	+	0.925662i	$0.623509\pi$
$228$	0	0
$229$	766.000	0.221042	0.110521	−	0.993874i	$-0.464748\pi$
$229$	766.000	0.221042	0.110521	+	0.993874i	$0.464748\pi$
$230$	0	0
$231$	−560.000	−0.159503
$232$	0	0
$233$	−6138.00	−1.72581	−0.862905	−	0.505366i	$-0.831357\pi$
$233$	−6138.00	−1.72581	−0.862905	+	0.505366i	$0.831357\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−3648.00	−0.999844
$238$	0	0
$239$	3856.00	1.04361	0.521807	−	0.853063i	$-0.325258\pi$
$239$	3856.00	1.04361	0.521807	+	0.853063i	$0.325258\pi$
$240$	0	0
$241$	2578.00	0.689060	0.344530	−	0.938775i	$-0.388038\pi$
$241$	2578.00	0.689060	0.344530	+	0.938775i	$0.388038\pi$
$242$	0	0
$243$	2860.00	0.755017
$244$	0	0
$245$	0	0
$246$	0	0
$247$	120.000	0.0309126
$248$	0	0
$249$	−4272.00	−1.08726
$250$	0	0
$251$	−1404.00	−0.353067	−0.176533	−	0.984295i	$-0.556488\pi$
$251$	−1404.00	−0.353067	−0.176533	+	0.984295i	$0.556488\pi$
$252$	0	0
$253$	−2080.00	−0.516871
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−2946.00	−0.715044	−0.357522	−	0.933905i	$-0.616378\pi$
$257$	−2946.00	−0.715044	−0.357522	+	0.933905i	$0.616378\pi$
$258$	0	0
$259$	1106.00	0.265342
$260$	0	0
$261$	1342.00	0.318267
$262$	0	0
$263$	3080.00	0.722133	0.361066	−	0.932540i	$-0.382413\pi$
$263$	3080.00	0.722133	0.361066	+	0.932540i	$0.382413\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6360.00	−1.45777
$268$	0	0
$269$	2294.00	0.519954	0.259977	−	0.965615i	$-0.416285\pi$
$269$	2294.00	0.519954	0.259977	+	0.965615i	$0.416285\pi$
$270$	0	0
$271$	−3728.00	−0.835645	−0.417823	−	0.908529i	$-0.637207\pi$
$271$	−3728.00	−0.835645	−0.417823	+	0.908529i	$0.637207\pi$
$272$	0	0
$273$	−280.000	−0.0620746
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−2734.00	−0.593033	−0.296516	−	0.955028i	$-0.595825\pi$
$277$	−2734.00	−0.593033	−0.296516	+	0.955028i	$0.595825\pi$
$278$	0	0
$279$	−2464.00	−0.528731
$280$	0	0
$281$	1034.00	0.219513	0.109757	−	0.993958i	$-0.464993\pi$
$281$	1034.00	0.219513	0.109757	+	0.993958i	$0.464993\pi$
$282$	0	0
$283$	5180.00	1.08805	0.544027	−	0.839068i	$-0.316899\pi$
$283$	5180.00	1.08805	0.544027	+	0.839068i	$0.316899\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−2646.00	−0.544211
$288$	0	0
$289$	−4717.00	−0.960106
$290$	0	0
$291$	−3464.00	−0.697812
$292$	0	0
$293$	−7934.00	−1.58194	−0.790971	−	0.611853i	$-0.790424\pi$
$293$	−7934.00	−1.58194	−0.790971	+	0.611853i	$0.790424\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−3040.00	−0.593935
$298$	0	0
$299$	−1040.00	−0.201153
$300$	0	0
$301$	2828.00	0.541539
$302$	0	0
$303$	2808.00	0.532394
$304$	0	0
$305$	0	0
$306$	0	0
$307$	3444.00	0.640259	0.320129	−	0.947374i	$-0.396274\pi$
$307$	3444.00	0.640259	0.320129	+	0.947374i	$0.396274\pi$
$308$	0	0
$309$	1184.00	0.217979
$310$	0	0
$311$	7656.00	1.39592	0.697961	−	0.716135i	$-0.254091\pi$
$311$	7656.00	1.39592	0.697961	+	0.716135i	$0.254091\pi$
$312$	0	0
$313$	3798.00	0.685865	0.342932	−	0.939360i	$-0.388580\pi$
$313$	3798.00	0.685865	0.342932	+	0.939360i	$0.388580\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−6822.00	−1.20871	−0.604356	−	0.796714i	$-0.706570\pi$
$317$	−6822.00	−1.20871	−0.604356	+	0.796714i	$0.706570\pi$
$318$	0	0
$319$	−2440.00	−0.428256
$320$	0	0
$321$	176.000	0.0306024
$322$	0	0
$323$	168.000	0.0289405
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−2600.00	−0.439695
$328$	0	0
$329$	784.000	0.131378
$330$	0	0
$331$	−6572.00	−1.09133	−0.545664	−	0.838004i	$-0.683723\pi$
$331$	−6572.00	−1.09133	−0.545664	+	0.838004i	$0.683723\pi$
$332$	0	0
$333$	1738.00	0.286011
$334$	0	0
$335$	0	0
$336$	0	0
$337$	11022.0	1.78162	0.890811	−	0.454374i	$-0.150137\pi$
$337$	11022.0	1.78162	0.890811	+	0.454374i	$0.150137\pi$
$338$	0	0
$339$	3768.00	0.603686
$340$	0	0
$341$	4480.00	0.711453
$342$	0	0
$343$	−343.000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	10908.0	1.68753	0.843764	−	0.536715i	$-0.180335\pi$
$347$	10908.0	1.68753	0.843764	+	0.536715i	$0.180335\pi$
$348$	0	0
$349$	−12058.0	−1.84943	−0.924713	−	0.380664i	$-0.875695\pi$
$349$	−12058.0	−1.84943	−0.924713	+	0.380664i	$0.875695\pi$
$350$	0	0
$351$	−1520.00	−0.231144
$352$	0	0
$353$	−1570.00	−0.236721	−0.118361	−	0.992971i	$-0.537764\pi$
$353$	−1570.00	−0.236721	−0.118361	+	0.992971i	$0.537764\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−392.000	−0.0581144
$358$	0	0
$359$	120.000	0.0176417	0.00882083	−	0.999961i	$-0.497192\pi$
$359$	120.000	0.0176417	0.00882083	+	0.999961i	$0.497192\pi$
$360$	0	0
$361$	−6715.00	−0.979006
$362$	0	0
$363$	−3724.00	−0.538455
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−4336.00	−0.616723	−0.308362	−	0.951269i	$-0.599781\pi$
$367$	−4336.00	−0.616723	−0.308362	+	0.951269i	$0.599781\pi$
$368$	0	0
$369$	−4158.00	−0.586604
$370$	0	0
$371$	1890.00	0.264485
$372$	0	0
$373$	−7758.00	−1.07693	−0.538464	−	0.842649i	$-0.680995\pi$
$373$	−7758.00	−1.07693	−0.538464	+	0.842649i	$0.680995\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−1220.00	−0.166666
$378$	0	0
$379$	10660.0	1.44477	0.722384	−	0.691492i	$-0.243046\pi$
$379$	10660.0	1.44477	0.722384	+	0.691492i	$0.243046\pi$
$380$	0	0
$381$	−2944.00	−0.395868
$382$	0	0
$383$	14304.0	1.90836	0.954178	−	0.299240i	$-0.0967331\pi$
$383$	14304.0	1.90836	0.954178	+	0.299240i	$0.0967331\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	4444.00	0.583724
$388$	0	0
$389$	−11970.0	−1.56016	−0.780081	−	0.625678i	$-0.784822\pi$
$389$	−11970.0	−1.56016	−0.780081	+	0.625678i	$0.784822\pi$
$390$	0	0
$391$	−1456.00	−0.188320
$392$	0	0
$393$	3696.00	0.474398
$394$	0	0
$395$	0	0
$396$	0	0
$397$	4106.00	0.519079	0.259539	−	0.965733i	$-0.416429\pi$
$397$	4106.00	0.519079	0.259539	+	0.965733i	$0.416429\pi$
$398$	0	0
$399$	−336.000	−0.0421580
$400$	0	0
$401$	−3790.00	−0.471979	−0.235989	−	0.971756i	$-0.575833\pi$
$401$	−3790.00	−0.471979	−0.235989	+	0.971756i	$0.575833\pi$
$402$	0	0
$403$	2240.00	0.276879
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−3160.00	−0.384854
$408$	0	0
$409$	−13366.0	−1.61591	−0.807954	−	0.589246i	$-0.799425\pi$
$409$	−13366.0	−1.61591	−0.807954	+	0.589246i	$0.799425\pi$
$410$	0	0
$411$	−1896.00	−0.227549
$412$	0	0
$413$	−2268.00	−0.270220
$414$	0	0
$415$	0	0
$416$	0	0
$417$	4048.00	0.475375
$418$	0	0
$419$	6524.00	0.760664	0.380332	−	0.924850i	$-0.375810\pi$
$419$	6524.00	0.760664	0.380332	+	0.924850i	$0.375810\pi$
$420$	0	0
$421$	−2978.00	−0.344748	−0.172374	−	0.985032i	$-0.555144\pi$
$421$	−2978.00	−0.344748	−0.172374	+	0.985032i	$0.555144\pi$
$422$	0	0
$423$	1232.00	0.141612
$424$	0	0
$425$	0	0
$426$	0	0
$427$	1302.00	0.147560
$428$	0	0
$429$	800.000	0.0900335
$430$	0	0
$431$	15760.0	1.76133	0.880664	−	0.473741i	$-0.157097\pi$
$431$	15760.0	1.76133	0.880664	+	0.473741i	$0.157097\pi$
$432$	0	0
$433$	−10322.0	−1.14560	−0.572799	−	0.819696i	$-0.694142\pi$
$433$	−10322.0	−1.14560	−0.572799	+	0.819696i	$0.694142\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−1248.00	−0.136613
$438$	0	0
$439$	−344.000	−0.0373991	−0.0186996	−	0.999825i	$-0.505953\pi$
$439$	−344.000	−0.0373991	−0.0186996	+	0.999825i	$0.505953\pi$
$440$	0	0
$441$	−539.000	−0.0582011
$442$	0	0
$443$	252.000	0.0270268	0.0135134	−	0.999909i	$-0.495698\pi$
$443$	252.000	0.0270268	0.0135134	+	0.999909i	$0.495698\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	1208.00	0.127822
$448$	0	0
$449$	−11966.0	−1.25771	−0.628854	−	0.777524i	$-0.716475\pi$
$449$	−11966.0	−1.25771	−0.628854	+	0.777524i	$0.716475\pi$
$450$	0	0
$451$	7560.00	0.789327
$452$	0	0
$453$	−8416.00	−0.872888
$454$	0	0
$455$	0	0
$456$	0	0
$457$	15846.0	1.62198	0.810990	−	0.585060i	$-0.198929\pi$
$457$	15846.0	1.62198	0.810990	+	0.585060i	$0.198929\pi$
$458$	0	0
$459$	−2128.00	−0.216398
$460$	0	0
$461$	5430.00	0.548591	0.274295	−	0.961645i	$-0.411555\pi$
$461$	5430.00	0.548591	0.274295	+	0.961645i	$0.411555\pi$
$462$	0	0
$463$	−8912.00	−0.894548	−0.447274	−	0.894397i	$-0.647605\pi$
$463$	−8912.00	−0.894548	−0.447274	+	0.894397i	$0.647605\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	11028.0	1.09275	0.546376	−	0.837540i	$-0.316007\pi$
$467$	11028.0	1.09275	0.546376	+	0.837540i	$0.316007\pi$
$468$	0	0
$469$	1092.00	0.107514
$470$	0	0
$471$	−4760.00	−0.465667
$472$	0	0
$473$	−8080.00	−0.785452
$474$	0	0
$475$	0	0
$476$	0	0
$477$	2970.00	0.285088
$478$	0	0
$479$	5856.00	0.558596	0.279298	−	0.960204i	$-0.409898\pi$
$479$	5856.00	0.558596	0.279298	+	0.960204i	$0.409898\pi$
$480$	0	0
$481$	−1580.00	−0.149775
$482$	0	0
$483$	2912.00	0.274328
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−10264.0	−0.955044	−0.477522	−	0.878620i	$-0.658465\pi$
$487$	−10264.0	−0.955044	−0.477522	+	0.878620i	$0.658465\pi$
$488$	0	0
$489$	6928.00	0.640685
$490$	0	0
$491$	2804.00	0.257725	0.128862	−	0.991663i	$-0.458867\pi$
$491$	2804.00	0.257725	0.128862	+	0.991663i	$0.458867\pi$
$492$	0	0
$493$	−1708.00	−0.156033
$494$	0	0
$495$	0	0
$496$	0	0
$497$	2520.00	0.227440
$498$	0	0
$499$	8716.00	0.781927	0.390964	−	0.920406i	$-0.372142\pi$
$499$	8716.00	0.781927	0.390964	+	0.920406i	$0.372142\pi$
$500$	0	0
$501$	−9056.00	−0.807569
$502$	0	0
$503$	−2504.00	−0.221964	−0.110982	−	0.993822i	$-0.535400\pi$
$503$	−2504.00	−0.221964	−0.110982	+	0.993822i	$0.535400\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−8388.00	−0.734762
$508$	0	0
$509$	17094.0	1.48856	0.744281	−	0.667866i	$-0.232792\pi$
$509$	17094.0	1.48856	0.744281	+	0.667866i	$0.232792\pi$
$510$	0	0
$511$	−714.000	−0.0618112
$512$	0	0
$513$	−1824.00	−0.156982
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−2240.00	−0.190551
$518$	0	0
$519$	4264.00	0.360634
$520$	0	0
$521$	9882.00	0.830976	0.415488	−	0.909599i	$-0.363611\pi$
$521$	9882.00	0.830976	0.415488	+	0.909599i	$0.363611\pi$
$522$	0	0
$523$	7532.00	0.629735	0.314867	−	0.949136i	$-0.398040\pi$
$523$	7532.00	0.629735	0.314867	+	0.949136i	$0.398040\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3136.00	0.259215
$528$	0	0
$529$	−1351.00	−0.111038
$530$	0	0
$531$	−3564.00	−0.291270
$532$	0	0
$533$	3780.00	0.307186
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−9424.00	−0.757310
$538$	0	0
$539$	980.000	0.0783146
$540$	0	0
$541$	−17338.0	−1.37785	−0.688927	−	0.724831i	$-0.741918\pi$
$541$	−17338.0	−1.37785	−0.688927	+	0.724831i	$0.741918\pi$
$542$	0	0
$543$	8632.00	0.682200
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−764.000	−0.0597190	−0.0298595	−	0.999554i	$-0.509506\pi$
$547$	−764.000	−0.0597190	−0.0298595	+	0.999554i	$0.509506\pi$
$548$	0	0
$549$	2046.00	0.159055
$550$	0	0
$551$	−1464.00	−0.113191
$552$	0	0
$553$	6384.00	0.490914
$554$	0	0
$555$	0	0
$556$	0	0
$557$	2442.00	0.185765	0.0928823	−	0.995677i	$-0.470392\pi$
$557$	2442.00	0.185765	0.0928823	+	0.995677i	$0.470392\pi$
$558$	0	0
$559$	−4040.00	−0.305678
$560$	0	0
$561$	1120.00	0.0842895
$562$	0	0
$563$	−8972.00	−0.671625	−0.335812	−	0.941929i	$-0.609011\pi$
$563$	−8972.00	−0.671625	−0.335812	+	0.941929i	$0.609011\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	2177.00	0.161244
$568$	0	0
$569$	8682.00	0.639663	0.319832	−	0.947474i	$-0.396374\pi$
$569$	8682.00	0.639663	0.319832	+	0.947474i	$0.396374\pi$
$570$	0	0
$571$	15524.0	1.13776	0.568878	−	0.822422i	$-0.307377\pi$
$571$	15524.0	1.13776	0.568878	+	0.822422i	$0.307377\pi$
$572$	0	0
$573$	−10752.0	−0.783894
$574$	0	0
$575$	0	0
$576$	0	0
$577$	19774.0	1.42669	0.713347	−	0.700811i	$-0.247178\pi$
$577$	19774.0	1.42669	0.713347	+	0.700811i	$0.247178\pi$
$578$	0	0
$579$	17656.0	1.26729
$580$	0	0
$581$	7476.00	0.533833
$582$	0	0
$583$	−5400.00	−0.383611
$584$	0	0
$585$	0	0
$586$	0	0
$587$	6700.00	0.471105	0.235552	−	0.971862i	$-0.424310\pi$
$587$	6700.00	0.471105	0.235552	+	0.971862i	$0.424310\pi$
$588$	0	0
$589$	2688.00	0.188043
$590$	0	0
$591$	−15096.0	−1.05070
$592$	0	0
$593$	1294.00	0.0896091	0.0448046	−	0.998996i	$-0.485733\pi$
$593$	1294.00	0.0896091	0.0448046	+	0.998996i	$0.485733\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	2656.00	0.182082
$598$	0	0
$599$	19720.0	1.34514	0.672569	−	0.740035i	$-0.265191\pi$
$599$	19720.0	1.34514	0.672569	+	0.740035i	$0.265191\pi$
$600$	0	0
$601$	21450.0	1.45585	0.727923	−	0.685659i	$-0.240486\pi$
$601$	21450.0	1.45585	0.727923	+	0.685659i	$0.240486\pi$
$602$	0	0
$603$	1716.00	0.115889
$604$	0	0
$605$	0	0
$606$	0	0
$607$	19264.0	1.28814	0.644071	−	0.764966i	$-0.277244\pi$
$607$	19264.0	1.28814	0.644071	+	0.764966i	$0.277244\pi$
$608$	0	0
$609$	3416.00	0.227296
$610$	0	0
$611$	−1120.00	−0.0741577
$612$	0	0
$613$	−13150.0	−0.866433	−0.433217	−	0.901290i	$-0.642621\pi$
$613$	−13150.0	−0.866433	−0.433217	+	0.901290i	$0.642621\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	15238.0	0.994261	0.497130	−	0.867676i	$-0.334387\pi$
$617$	15238.0	0.994261	0.497130	+	0.867676i	$0.334387\pi$
$618$	0	0
$619$	23764.0	1.54306	0.771531	−	0.636191i	$-0.219491\pi$
$619$	23764.0	1.54306	0.771531	+	0.636191i	$0.219491\pi$
$620$	0	0
$621$	15808.0	1.02150
$622$	0	0
$623$	11130.0	0.715753
$624$	0	0
$625$	0	0
$626$	0	0
$627$	960.000	0.0611463
$628$	0	0
$629$	−2212.00	−0.140220
$630$	0	0
$631$	−2008.00	−0.126683	−0.0633417	−	0.997992i	$-0.520176\pi$
$631$	−2008.00	−0.126683	−0.0633417	+	0.997992i	$0.520176\pi$
$632$	0	0
$633$	5040.00	0.316464
$634$	0	0
$635$	0	0
$636$	0	0
$637$	490.000	0.0304780
$638$	0	0
$639$	3960.00	0.245157
$640$	0	0
$641$	13058.0	0.804618	0.402309	−	0.915504i	$-0.368208\pi$
$641$	13058.0	0.804618	0.402309	+	0.915504i	$0.368208\pi$
$642$	0	0
$643$	−24188.0	−1.48349	−0.741743	−	0.670684i	$-0.766001\pi$
$643$	−24188.0	−1.48349	−0.741743	+	0.670684i	$0.766001\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−6648.00	−0.403956	−0.201978	−	0.979390i	$-0.564737\pi$
$647$	−6648.00	−0.403956	−0.201978	+	0.979390i	$0.564737\pi$
$648$	0	0
$649$	6480.00	0.391930
$650$	0	0
$651$	−6272.00	−0.377602
$652$	0	0
$653$	−9814.00	−0.588134	−0.294067	−	0.955785i	$-0.595009\pi$
$653$	−9814.00	−0.588134	−0.294067	+	0.955785i	$0.595009\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−1122.00	−0.0666262
$658$	0	0
$659$	26540.0	1.56882	0.784409	−	0.620243i	$-0.212966\pi$
$659$	26540.0	1.56882	0.784409	+	0.620243i	$0.212966\pi$
$660$	0	0
$661$	−1330.00	−0.0782617	−0.0391309	−	0.999234i	$-0.512459\pi$
$661$	−1330.00	−0.0782617	−0.0391309	+	0.999234i	$0.512459\pi$
$662$	0	0
$663$	560.000	0.0328033
$664$	0	0
$665$	0	0
$666$	0	0
$667$	12688.0	0.736554
$668$	0	0
$669$	4608.00	0.266301
$670$	0	0
$671$	−3720.00	−0.214022
$672$	0	0
$673$	17950.0	1.02812	0.514058	−	0.857756i	$-0.328142\pi$
$673$	17950.0	1.02812	0.514058	+	0.857756i	$0.328142\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−23742.0	−1.34783	−0.673914	−	0.738810i	$-0.735388\pi$
$677$	−23742.0	−1.34783	−0.673914	+	0.738810i	$0.735388\pi$
$678$	0	0
$679$	6062.00	0.342619
$680$	0	0
$681$	−10352.0	−0.582510
$682$	0	0
$683$	−6356.00	−0.356084	−0.178042	−	0.984023i	$-0.556976\pi$
$683$	−6356.00	−0.356084	−0.178042	+	0.984023i	$0.556976\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	3064.00	0.170159
$688$	0	0
$689$	−2700.00	−0.149291
$690$	0	0
$691$	−3156.00	−0.173748	−0.0868740	−	0.996219i	$-0.527688\pi$
$691$	−3156.00	−0.173748	−0.0868740	+	0.996219i	$0.527688\pi$
$692$	0	0
$693$	1540.00	0.0844152
$694$	0	0
$695$	0	0
$696$	0	0
$697$	5292.00	0.287588
$698$	0	0
$699$	−24552.0	−1.32853
$700$	0	0
$701$	−18330.0	−0.987610	−0.493805	−	0.869573i	$-0.664394\pi$
$701$	−18330.0	−0.987610	−0.493805	+	0.869573i	$0.664394\pi$
$702$	0	0
$703$	−1896.00	−0.101720
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−4914.00	−0.261400
$708$	0	0
$709$	19070.0	1.01014	0.505070	−	0.863079i	$-0.331467\pi$
$709$	19070.0	1.01014	0.505070	+	0.863079i	$0.331467\pi$
$710$	0	0
$711$	10032.0	0.529155
$712$	0	0
$713$	−23296.0	−1.22362
$714$	0	0
$715$	0	0
$716$	0	0
$717$	15424.0	0.803375
$718$	0	0
$719$	−4176.00	−0.216604	−0.108302	−	0.994118i	$-0.534541\pi$
$719$	−4176.00	−0.216604	−0.108302	+	0.994118i	$0.534541\pi$
$720$	0	0
$721$	−2072.00	−0.107025
$722$	0	0
$723$	10312.0	0.530439
$724$	0	0
$725$	0	0
$726$	0	0
$727$	10520.0	0.536678	0.268339	−	0.963324i	$-0.413525\pi$
$727$	10520.0	0.536678	0.268339	+	0.963324i	$0.413525\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	−5656.00	−0.286176
$732$	0	0
$733$	6874.00	0.346381	0.173190	−	0.984888i	$-0.444592\pi$
$733$	6874.00	0.346381	0.173190	+	0.984888i	$0.444592\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3120.00	−0.155939
$738$	0	0
$739$	11804.0	0.587574	0.293787	−	0.955871i	$-0.405084\pi$
$739$	11804.0	0.587574	0.293787	+	0.955871i	$0.405084\pi$
$740$	0	0
$741$	480.000	0.0237965
$742$	0	0
$743$	20648.0	1.01952	0.509759	−	0.860317i	$-0.329735\pi$
$743$	20648.0	1.01952	0.509759	+	0.860317i	$0.329735\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	11748.0	0.575417
$748$	0	0
$749$	−308.000	−0.0150255
$750$	0	0
$751$	1232.00	0.0598619	0.0299310	−	0.999552i	$-0.490471\pi$
$751$	1232.00	0.0598619	0.0299310	+	0.999552i	$0.490471\pi$
$752$	0	0
$753$	−5616.00	−0.271791
$754$	0	0
$755$	0	0
$756$	0	0
$757$	11250.0	0.540143	0.270071	−	0.962840i	$-0.412953\pi$
$757$	11250.0	0.540143	0.270071	+	0.962840i	$0.412953\pi$
$758$	0	0
$759$	−8320.00	−0.397888
$760$	0	0
$761$	14698.0	0.700134	0.350067	−	0.936725i	$-0.386159\pi$
$761$	14698.0	0.700134	0.350067	+	0.936725i	$0.386159\pi$
$762$	0	0
$763$	4550.00	0.215886
$764$	0	0
$765$	0	0
$766$	0	0
$767$	3240.00	0.152529
$768$	0	0
$769$	−30014.0	−1.40745	−0.703727	−	0.710470i	$-0.748482\pi$
$769$	−30014.0	−1.40745	−0.703727	+	0.710470i	$0.748482\pi$
$770$	0	0
$771$	−11784.0	−0.550441
$772$	0	0
$773$	34018.0	1.58285	0.791425	−	0.611267i	$-0.209340\pi$
$773$	34018.0	1.58285	0.791425	+	0.611267i	$0.209340\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	4424.00	0.204260
$778$	0	0
$779$	4536.00	0.208625
$780$	0	0
$781$	−7200.00	−0.329880
$782$	0	0
$783$	18544.0	0.846371
$784$	0	0
$785$	0	0
$786$	0	0
$787$	18516.0	0.838658	0.419329	−	0.907834i	$-0.362265\pi$
$787$	18516.0	0.838658	0.419329	+	0.907834i	$0.362265\pi$
$788$	0	0
$789$	12320.0	0.555898
$790$	0	0
$791$	−6594.00	−0.296404
$792$	0	0
$793$	−1860.00	−0.0832920
$794$	0	0
$795$	0	0
$796$	0	0
$797$	38618.0	1.71634	0.858168	−	0.513369i	$-0.171603\pi$
$797$	38618.0	1.71634	0.858168	+	0.513369i	$0.171603\pi$
$798$	0	0
$799$	−1568.00	−0.0694266
$800$	0	0
$801$	17490.0	0.771509
$802$	0	0
$803$	2040.00	0.0896514
$804$	0	0
$805$	0	0
$806$	0	0
$807$	9176.00	0.400261
$808$	0	0
$809$	19514.0	0.848054	0.424027	−	0.905650i	$-0.360616\pi$
$809$	19514.0	0.848054	0.424027	+	0.905650i	$0.360616\pi$
$810$	0	0
$811$	−31020.0	−1.34311	−0.671553	−	0.740956i	$-0.734373\pi$
$811$	−31020.0	−1.34311	−0.671553	+	0.740956i	$0.734373\pi$
$812$	0	0
$813$	−14912.0	−0.643280
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4848.00	−0.207601
$818$	0	0
$819$	770.000	0.0328522
$820$	0	0
$821$	3726.00	0.158390	0.0791951	−	0.996859i	$-0.474765\pi$
$821$	3726.00	0.158390	0.0791951	+	0.996859i	$0.474765\pi$
$822$	0	0
$823$	−32904.0	−1.39363	−0.696817	−	0.717249i	$-0.745401\pi$
$823$	−32904.0	−1.39363	−0.696817	+	0.717249i	$0.745401\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	39868.0	1.67636	0.838178	−	0.545397i	$-0.183621\pi$
$827$	39868.0	1.67636	0.838178	+	0.545397i	$0.183621\pi$
$828$	0	0
$829$	−26810.0	−1.12322	−0.561610	−	0.827402i	$-0.689818\pi$
$829$	−26810.0	−1.12322	−0.561610	+	0.827402i	$0.689818\pi$
$830$	0	0
$831$	−10936.0	−0.456517
$832$	0	0
$833$	686.000	0.0285336
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−34048.0	−1.40606
$838$	0	0
$839$	−37096.0	−1.52646	−0.763228	−	0.646130i	$-0.776387\pi$
$839$	−37096.0	−1.52646	−0.763228	+	0.646130i	$0.776387\pi$
$840$	0	0
$841$	−9505.00	−0.389725
$842$	0	0
$843$	4136.00	0.168982
$844$	0	0
$845$	0	0
$846$	0	0
$847$	6517.00	0.264376
$848$	0	0
$849$	20720.0	0.837584
$850$	0	0
$851$	16432.0	0.661906
$852$	0	0
$853$	14386.0	0.577453	0.288726	−	0.957412i	$-0.406768\pi$
$853$	14386.0	0.577453	0.288726	+	0.957412i	$0.406768\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	118.000	0.00470339	0.00235169	−	0.999997i	$-0.499251\pi$
$857$	118.000	0.00470339	0.00235169	+	0.999997i	$0.499251\pi$
$858$	0	0
$859$	−25116.0	−0.997610	−0.498805	−	0.866714i	$-0.666228\pi$
$859$	−25116.0	−0.997610	−0.498805	+	0.866714i	$0.666228\pi$
$860$	0	0
$861$	−10584.0	−0.418934
$862$	0	0
$863$	11776.0	0.464496	0.232248	−	0.972657i	$-0.425392\pi$
$863$	11776.0	0.464496	0.232248	+	0.972657i	$0.425392\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−18868.0	−0.739090
$868$	0	0
$869$	−18240.0	−0.712025
$870$	0	0
$871$	−1560.00	−0.0606872
$872$	0	0
$873$	9526.00	0.369308
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−24694.0	−0.950806	−0.475403	−	0.879768i	$-0.657698\pi$
$877$	−24694.0	−0.950806	−0.475403	+	0.879768i	$0.657698\pi$
$878$	0	0
$879$	−31736.0	−1.21778
$880$	0	0
$881$	32850.0	1.25624	0.628118	−	0.778118i	$-0.283825\pi$
$881$	32850.0	1.25624	0.628118	+	0.778118i	$0.283825\pi$
$882$	0	0
$883$	−47340.0	−1.80421	−0.902105	−	0.431516i	$-0.857979\pi$
$883$	−47340.0	−1.80421	−0.902105	+	0.431516i	$0.857979\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−1992.00	−0.0754057	−0.0377028	−	0.999289i	$-0.512004\pi$
$887$	−1992.00	−0.0754057	−0.0377028	+	0.999289i	$0.512004\pi$
$888$	0	0
$889$	5152.00	0.194367
$890$	0	0
$891$	−6220.00	−0.233870
$892$	0	0
$893$	−1344.00	−0.0503642
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−4160.00	−0.154848
$898$	0	0
$899$	−27328.0	−1.01384
$900$	0	0
$901$	−3780.00	−0.139767
$902$	0	0
$903$	11312.0	0.416877
$904$	0	0
$905$	0	0
$906$	0	0
$907$	13516.0	0.494809	0.247404	−	0.968912i	$-0.420422\pi$
$907$	13516.0	0.494809	0.247404	+	0.968912i	$0.420422\pi$
$908$	0	0
$909$	−7722.00	−0.281763
$910$	0	0
$911$	−3408.00	−0.123943	−0.0619715	−	0.998078i	$-0.519739\pi$
$911$	−3408.00	−0.123943	−0.0619715	+	0.998078i	$0.519739\pi$
$912$	0	0
$913$	−21360.0	−0.774275
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−6468.00	−0.232925
$918$	0	0
$919$	39240.0	1.40850	0.704248	−	0.709954i	$-0.251284\pi$
$919$	39240.0	1.40850	0.704248	+	0.709954i	$0.251284\pi$
$920$	0	0
$921$	13776.0	0.492871
$922$	0	0
$923$	−3600.00	−0.128381
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−3256.00	−0.115363
$928$	0	0
$929$	21922.0	0.774206	0.387103	−	0.922036i	$-0.373476\pi$
$929$	21922.0	0.774206	0.387103	+	0.922036i	$0.373476\pi$
$930$	0	0
$931$	588.000	0.0206992
$932$	0	0
$933$	30624.0	1.07458
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−186.000	−0.00648490	−0.00324245	−	0.999995i	$-0.501032\pi$
$937$	−186.000	−0.00648490	−0.00324245	+	0.999995i	$0.501032\pi$
$938$	0	0
$939$	15192.0	0.527979
$940$	0	0
$941$	−18282.0	−0.633343	−0.316672	−	0.948535i	$-0.602565\pi$
$941$	−18282.0	−0.633343	−0.316672	+	0.948535i	$0.602565\pi$
$942$	0	0
$943$	−39312.0	−1.35756
$944$	0	0
$945$	0	0
$946$	0	0
$947$	16980.0	0.582657	0.291328	−	0.956623i	$-0.405903\pi$
$947$	16980.0	0.582657	0.291328	+	0.956623i	$0.405903\pi$
$948$	0	0
$949$	1020.00	0.0348900
$950$	0	0
$951$	−27288.0	−0.930467
$952$	0	0
$953$	44310.0	1.50613	0.753065	−	0.657946i	$-0.228575\pi$
$953$	44310.0	1.50613	0.753065	+	0.657946i	$0.228575\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−9760.00	−0.329672
$958$	0	0
$959$	3318.00	0.111725
$960$	0	0
$961$	20385.0	0.684267
$962$	0	0
$963$	−484.000	−0.0161959
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−51512.0	−1.71304	−0.856522	−	0.516110i	$-0.827380\pi$
$967$	−51512.0	−1.71304	−0.856522	+	0.516110i	$0.827380\pi$
$968$	0	0
$969$	672.000	0.0222784
$970$	0	0
$971$	1844.00	0.0609442	0.0304721	−	0.999536i	$-0.490299\pi$
$971$	1844.00	0.0609442	0.0304721	+	0.999536i	$0.490299\pi$
$972$	0	0
$973$	−7084.00	−0.233405
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−34162.0	−1.11867	−0.559334	−	0.828942i	$-0.688943\pi$
$977$	−34162.0	−1.11867	−0.559334	+	0.828942i	$0.688943\pi$
$978$	0	0
$979$	−31800.0	−1.03813
$980$	0	0
$981$	7150.00	0.232703
$982$	0	0
$983$	216.000	0.00700847	0.00350424	−	0.999994i	$-0.498885\pi$
$983$	216.000	0.00700847	0.00350424	+	0.999994i	$0.498885\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	3136.00	0.101135
$988$	0	0
$989$	42016.0	1.35089
$990$	0	0
$991$	52832.0	1.69351	0.846753	−	0.531987i	$-0.178554\pi$
$991$	52832.0	1.69351	0.846753	+	0.531987i	$0.178554\pi$
$992$	0	0
$993$	−26288.0	−0.840105
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−5054.00	−0.160543	−0.0802717	−	0.996773i	$-0.525579\pi$
$997$	−5054.00	−0.160543	−0.0802717	+	0.996773i	$0.525579\pi$
$998$	0	0
$999$	24016.0	0.760593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.4.a.g.1.1		1
5.2	odd	4		1400.4.g.e.449.1		2
5.3	odd	4		1400.4.g.e.449.2		2
5.4	even	2		280.4.a.a.1.1	✓	1
20.19	odd	2		560.4.a.l.1.1		1
35.34	odd	2		1960.4.a.g.1.1		1
40.19	odd	2		2240.4.a.l.1.1		1
40.29	even	2		2240.4.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.4.a.a.1.1	✓	1	5.4	even	2
560.4.a.l.1.1		1	20.19	odd	2
1400.4.a.g.1.1		1	1.1	even	1	trivial
1400.4.g.e.449.1		2	5.2	odd	4
1400.4.g.e.449.2		2	5.3	odd	4
1960.4.a.g.1.1		1	35.34	odd	2
2240.4.a.l.1.1		1	40.19	odd	2
2240.4.a.z.1.1		1	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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