LMFDB - Embedded newform 400.4.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,4,Mod(1,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("400.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	400.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:	$23.6007640023$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+7.00000 q^{3} +6.00000 q^{7} +22.0000 q^{9} +O(q^{10})$

$q+7.00000 q^{3} +6.00000 q^{7} +22.0000 q^{9} +43.0000 q^{11} +28.0000 q^{13} -91.0000 q^{17} +35.0000 q^{19} +42.0000 q^{21} +162.000 q^{23} -35.0000 q^{27} +160.000 q^{29} -42.0000 q^{31} +301.000 q^{33} +314.000 q^{37} +196.000 q^{39} -203.000 q^{41} +92.0000 q^{43} +196.000 q^{47} -307.000 q^{49} -637.000 q^{51} -82.0000 q^{53} +245.000 q^{57} +280.000 q^{59} -518.000 q^{61} +132.000 q^{63} +141.000 q^{67} +1134.00 q^{69} -412.000 q^{71} +763.000 q^{73} +258.000 q^{77} -510.000 q^{79} -839.000 q^{81} +777.000 q^{83} +1120.00 q^{87} -945.000 q^{89} +168.000 q^{91} -294.000 q^{93} -1246.00 q^{97} +946.000 q^{99} +O(q^{100})$

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
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	6.00000	0.323970	0.161985	−	0.986793i	$-0.448210\pi$
$7$	6.00000	0.323970	0.161985	+	0.986793i	$0.448210\pi$
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	43.0000	1.17864	0.589318	−	0.807901i	$-0.299397\pi$
$11$	43.0000	1.17864	0.589318	+	0.807901i	$0.299397\pi$
$12$	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
$17$	−91.0000	−1.29828	−0.649139	−	0.760669i	$-0.724871\pi$
$17$	−91.0000	−1.29828	−0.649139	+	0.760669i	$0.724871\pi$
$18$	0	0
$19$	35.0000	0.422608	0.211304	−	0.977420i	$-0.432229\pi$
$19$	35.0000	0.422608	0.211304	+	0.977420i	$0.432229\pi$
$20$	0	0
$21$	42.0000	0.436436
$22$	0	0
$23$	162.000	1.46867	0.734333	−	0.678789i	$-0.237495\pi$
$23$	162.000	1.46867	0.734333	+	0.678789i	$0.237495\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−35.0000	−0.249472
$28$	0	0
$29$	160.000	1.02453	0.512263	−	0.858829i	$-0.328807\pi$
$29$	160.000	1.02453	0.512263	+	0.858829i	$0.328807\pi$
$30$	0	0
$31$	−42.0000	−0.243336	−0.121668	−	0.992571i	$-0.538824\pi$
$31$	−42.0000	−0.243336	−0.121668	+	0.992571i	$0.538824\pi$
$32$	0	0
$33$	301.000	1.58780
$34$	0	0
$35$	0	0
$36$	0	0
$37$	314.000	1.39517	0.697585	−	0.716502i	$-0.254258\pi$
$37$	314.000	1.39517	0.697585	+	0.716502i	$0.254258\pi$
$38$	0	0
$39$	196.000	0.804747
$40$	0	0
$41$	−203.000	−0.773251	−0.386625	−	0.922237i	$-0.626359\pi$
$41$	−203.000	−0.773251	−0.386625	+	0.922237i	$0.626359\pi$
$42$	0	0
$43$	92.0000	0.326276	0.163138	−	0.986603i	$-0.447838\pi$
$43$	92.0000	0.326276	0.163138	+	0.986603i	$0.447838\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	196.000	0.608288	0.304144	−	0.952626i	$-0.401630\pi$
$47$	196.000	0.608288	0.304144	+	0.952626i	$0.401630\pi$
$48$	0	0
$49$	−307.000	−0.895044
$50$	0	0
$51$	−637.000	−1.74898
$52$	0	0
$53$	−82.0000	−0.212520	−0.106260	−	0.994338i	$-0.533888\pi$
$53$	−82.0000	−0.212520	−0.106260	+	0.994338i	$0.533888\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	245.000	0.569317
$58$	0	0
$59$	280.000	0.617846	0.308923	−	0.951087i	$-0.400032\pi$
$59$	280.000	0.617846	0.308923	+	0.951087i	$0.400032\pi$
$60$	0	0
$61$	−518.000	−1.08726	−0.543632	−	0.839324i	$-0.682951\pi$
$61$	−518.000	−1.08726	−0.543632	+	0.839324i	$0.682951\pi$
$62$	0	0
$63$	132.000	0.263975
$64$	0	0
$65$	0	0
$66$	0	0
$67$	141.000	0.257103	0.128551	−	0.991703i	$-0.458967\pi$
$67$	141.000	0.257103	0.128551	+	0.991703i	$0.458967\pi$
$68$	0	0
$69$	1134.00	1.97852
$70$	0	0
$71$	−412.000	−0.688668	−0.344334	−	0.938847i	$-0.611895\pi$
$71$	−412.000	−0.688668	−0.344334	+	0.938847i	$0.611895\pi$
$72$	0	0
$73$	763.000	1.22332	0.611660	−	0.791121i	$-0.290502\pi$
$73$	763.000	1.22332	0.611660	+	0.791121i	$0.290502\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	258.000	0.381842
$78$	0	0
$79$	−510.000	−0.726323	−0.363161	−	0.931726i	$-0.618303\pi$
$79$	−510.000	−0.726323	−0.363161	+	0.931726i	$0.618303\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	777.000	1.02755	0.513776	−	0.857924i	$-0.328246\pi$
$83$	777.000	1.02755	0.513776	+	0.857924i	$0.328246\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	1120.00	1.38019
$88$	0	0
$89$	−945.000	−1.12550	−0.562752	−	0.826626i	$-0.690257\pi$
$89$	−945.000	−1.12550	−0.562752	+	0.826626i	$0.690257\pi$
$90$	0	0
$91$	168.000	0.193530
$92$	0	0
$93$	−294.000	−0.327811
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1246.00	−1.30425	−0.652124	−	0.758112i	$-0.726122\pi$
$97$	−1246.00	−1.30425	−0.652124	+	0.758112i	$0.726122\pi$
$98$	0	0
$99$	946.000	0.960369
$100$	0	0
$101$	1302.00	1.28271	0.641356	−	0.767244i	$-0.278372\pi$
$101$	1302.00	1.28271	0.641356	+	0.767244i	$0.278372\pi$
$102$	0	0
$103$	532.000	0.508927	0.254464	−	0.967082i	$-0.418101\pi$
$103$	532.000	0.508927	0.254464	+	0.967082i	$0.418101\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1269.00	−1.14653	−0.573266	−	0.819370i	$-0.694324\pi$
$107$	−1269.00	−1.14653	−0.573266	+	0.819370i	$0.694324\pi$
$108$	0	0
$109$	1070.00	0.940251	0.470126	−	0.882599i	$-0.344209\pi$
$109$	1070.00	0.940251	0.470126	+	0.882599i	$0.344209\pi$
$110$	0	0
$111$	2198.00	1.87950
$112$	0	0
$113$	503.000	0.418746	0.209373	−	0.977836i	$-0.432858\pi$
$113$	503.000	0.418746	0.209373	+	0.977836i	$0.432858\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	616.000	0.486745
$118$	0	0
$119$	−546.000	−0.420603
$120$	0	0
$121$	518.000	0.389181
$122$	0	0
$123$	−1421.00	−1.04169
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−874.000	−0.610669	−0.305334	−	0.952245i	$-0.598768\pi$
$127$	−874.000	−0.610669	−0.305334	+	0.952245i	$0.598768\pi$
$128$	0	0
$129$	644.000	0.439543
$130$	0	0
$131$	−1092.00	−0.728309	−0.364155	−	0.931339i	$-0.618642\pi$
$131$	−1092.00	−0.728309	−0.364155	+	0.931339i	$0.618642\pi$
$132$	0	0
$133$	210.000	0.136912
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−411.000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−411.000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	0	0
$139$	595.000	0.363074	0.181537	−	0.983384i	$-0.441893\pi$
$139$	595.000	0.363074	0.181537	+	0.983384i	$0.441893\pi$
$140$	0	0
$141$	1372.00	0.819456
$142$	0	0
$143$	1204.00	0.704081
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−2149.00	−1.20576
$148$	0	0
$149$	−3200.00	−1.75942	−0.879712	−	0.475507i	$-0.842265\pi$
$149$	−3200.00	−1.75942	−0.879712	+	0.475507i	$0.842265\pi$
$150$	0	0
$151$	−202.000	−0.108864	−0.0544322	−	0.998517i	$-0.517335\pi$
$151$	−202.000	−0.108864	−0.0544322	+	0.998517i	$0.517335\pi$
$152$	0	0
$153$	−2002.00	−1.05786
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−406.000	−0.206384	−0.103192	−	0.994661i	$-0.532906\pi$
$157$	−406.000	−0.206384	−0.103192	+	0.994661i	$0.532906\pi$
$158$	0	0
$159$	−574.000	−0.286297
$160$	0	0
$161$	972.000	0.475803
$162$	0	0
$163$	−3803.00	−1.82745	−0.913724	−	0.406336i	$-0.866806\pi$
$163$	−3803.00	−1.82745	−0.913724	+	0.406336i	$0.866806\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	4116.00	1.90722	0.953610	−	0.301046i	$-0.0973357\pi$
$167$	4116.00	1.90722	0.953610	+	0.301046i	$0.0973357\pi$
$168$	0	0
$169$	−1413.00	−0.643150
$170$	0	0
$171$	770.000	0.344347
$172$	0	0
$173$	−1512.00	−0.664481	−0.332241	−	0.943195i	$-0.607805\pi$
$173$	−1512.00	−0.664481	−0.332241	+	0.943195i	$0.607805\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1960.00	0.832331
$178$	0	0
$179$	−2585.00	−1.07940	−0.539698	−	0.841859i	$-0.681462\pi$
$179$	−2585.00	−1.07940	−0.539698	+	0.841859i	$0.681462\pi$
$180$	0	0
$181$	−2758.00	−1.13260	−0.566300	−	0.824199i	$-0.691626\pi$
$181$	−2758.00	−1.13260	−0.566300	+	0.824199i	$0.691626\pi$
$182$	0	0
$183$	−3626.00	−1.46471
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−3913.00	−1.53020
$188$	0	0
$189$	−210.000	−0.0808214
$190$	0	0
$191$	2378.00	0.900869	0.450435	−	0.892809i	$-0.351269\pi$
$191$	2378.00	0.900869	0.450435	+	0.892809i	$0.351269\pi$
$192$	0	0
$193$	−3067.00	−1.14387	−0.571937	−	0.820298i	$-0.693808\pi$
$193$	−3067.00	−1.14387	−0.571937	+	0.820298i	$0.693808\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−2346.00	−0.848455	−0.424227	−	0.905556i	$-0.639454\pi$
$197$	−2346.00	−0.848455	−0.424227	+	0.905556i	$0.639454\pi$
$198$	0	0
$199$	−4900.00	−1.74549	−0.872743	−	0.488180i	$-0.837661\pi$
$199$	−4900.00	−1.74549	−0.872743	+	0.488180i	$0.837661\pi$
$200$	0	0
$201$	987.000	0.346356
$202$	0	0
$203$	960.000	0.331915
$204$	0	0
$205$	0	0
$206$	0	0
$207$	3564.00	1.19669
$208$	0	0
$209$	1505.00	0.498101
$210$	0	0
$211$	−4307.00	−1.40524	−0.702621	−	0.711564i	$-0.747987\pi$
$211$	−4307.00	−1.40524	−0.702621	+	0.711564i	$0.747987\pi$
$212$	0	0
$213$	−2884.00	−0.927739
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−252.000	−0.0788335
$218$	0	0
$219$	5341.00	1.64800
$220$	0	0
$221$	−2548.00	−0.775552
$222$	0	0
$223$	2212.00	0.664244	0.332122	−	0.943236i	$-0.392235\pi$
$223$	2212.00	0.664244	0.332122	+	0.943236i	$0.392235\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	476.000	0.139177	0.0695886	−	0.997576i	$-0.477831\pi$
$227$	476.000	0.139177	0.0695886	+	0.997576i	$0.477831\pi$
$228$	0	0
$229$	−2940.00	−0.848387	−0.424194	−	0.905572i	$-0.639442\pi$
$229$	−2940.00	−0.848387	−0.424194	+	0.905572i	$0.639442\pi$
$230$	0	0
$231$	1806.00	0.514399
$232$	0	0
$233$	−1002.00	−0.281730	−0.140865	−	0.990029i	$-0.544988\pi$
$233$	−1002.00	−0.281730	−0.140865	+	0.990029i	$0.544988\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−3570.00	−0.978466
$238$	0	0
$239$	−2480.00	−0.671204	−0.335602	−	0.942004i	$-0.608940\pi$
$239$	−2480.00	−0.671204	−0.335602	+	0.942004i	$0.608940\pi$
$240$	0	0
$241$	1897.00	0.507039	0.253520	−	0.967330i	$-0.418412\pi$
$241$	1897.00	0.507039	0.253520	+	0.967330i	$0.418412\pi$
$242$	0	0
$243$	−4928.00	−1.30095
$244$	0	0
$245$	0	0
$246$	0	0
$247$	980.000	0.252453
$248$	0	0
$249$	5439.00	1.38427
$250$	0	0
$251$	2373.00	0.596743	0.298371	−	0.954450i	$-0.403557\pi$
$251$	2373.00	0.596743	0.298371	+	0.954450i	$0.403557\pi$
$252$	0	0
$253$	6966.00	1.73102
$254$	0	0
$255$	0	0
$256$	0	0
$257$	4494.00	1.09077	0.545385	−	0.838185i	$-0.316383\pi$
$257$	4494.00	1.09077	0.545385	+	0.838185i	$0.316383\pi$
$258$	0	0
$259$	1884.00	0.451993
$260$	0	0
$261$	3520.00	0.834799
$262$	0	0
$263$	722.000	0.169279	0.0846396	−	0.996412i	$-0.473026\pi$
$263$	722.000	0.169279	0.0846396	+	0.996412i	$0.473026\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6615.00	−1.51622
$268$	0	0
$269$	−6160.00	−1.39621	−0.698107	−	0.715993i	$-0.745974\pi$
$269$	−6160.00	−1.39621	−0.698107	+	0.715993i	$0.745974\pi$
$270$	0	0
$271$	7238.00	1.62243	0.811213	−	0.584751i	$-0.198808\pi$
$271$	7238.00	1.62243	0.811213	+	0.584751i	$0.198808\pi$
$272$	0	0
$273$	1176.00	0.260713
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−1776.00	−0.385233	−0.192616	−	0.981274i	$-0.561697\pi$
$277$	−1776.00	−0.385233	−0.192616	+	0.981274i	$0.561697\pi$
$278$	0	0
$279$	−924.000	−0.198274
$280$	0	0
$281$	4542.00	0.964246	0.482123	−	0.876104i	$-0.339866\pi$
$281$	4542.00	0.964246	0.482123	+	0.876104i	$0.339866\pi$
$282$	0	0
$283$	7077.00	1.48652	0.743258	−	0.669005i	$-0.233280\pi$
$283$	7077.00	1.48652	0.743258	+	0.669005i	$0.233280\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−1218.00	−0.250510
$288$	0	0
$289$	3368.00	0.685528
$290$	0	0
$291$	−8722.00	−1.75702
$292$	0	0
$293$	4158.00	0.829054	0.414527	−	0.910037i	$-0.363947\pi$
$293$	4158.00	0.829054	0.414527	+	0.910037i	$0.363947\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1505.00	−0.294037
$298$	0	0
$299$	4536.00	0.877337
$300$	0	0
$301$	552.000	0.105703
$302$	0	0
$303$	9114.00	1.72801
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2569.00	−0.477591	−0.238796	−	0.971070i	$-0.576753\pi$
$307$	−2569.00	−0.477591	−0.238796	+	0.971070i	$0.576753\pi$
$308$	0	0
$309$	3724.00	0.685602
$310$	0	0
$311$	−2982.00	−0.543710	−0.271855	−	0.962338i	$-0.587637\pi$
$311$	−2982.00	−0.543710	−0.271855	+	0.962338i	$0.587637\pi$
$312$	0	0
$313$	−2422.00	−0.437379	−0.218689	−	0.975795i	$-0.570178\pi$
$313$	−2422.00	−0.437379	−0.218689	+	0.975795i	$0.570178\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	9484.00	1.68036	0.840181	−	0.542307i	$-0.182449\pi$
$317$	9484.00	1.68036	0.840181	+	0.542307i	$0.182449\pi$
$318$	0	0
$319$	6880.00	1.20754
$320$	0	0
$321$	−8883.00	−1.54455
$322$	0	0
$323$	−3185.00	−0.548663
$324$	0	0
$325$	0	0
$326$	0	0
$327$	7490.00	1.26666
$328$	0	0
$329$	1176.00	0.197067
$330$	0	0
$331$	183.000	0.0303885	0.0151942	−	0.999885i	$-0.495163\pi$
$331$	183.000	0.0303885	0.0151942	+	0.999885i	$0.495163\pi$
$332$	0	0
$333$	6908.00	1.13681
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−2861.00	−0.462459	−0.231229	−	0.972899i	$-0.574275\pi$
$337$	−2861.00	−0.462459	−0.231229	+	0.972899i	$0.574275\pi$
$338$	0	0
$339$	3521.00	0.564113
$340$	0	0
$341$	−1806.00	−0.286805
$342$	0	0
$343$	−3900.00	−0.613936
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−629.000	−0.0973098	−0.0486549	−	0.998816i	$-0.515493\pi$
$347$	−629.000	−0.0973098	−0.0486549	+	0.998816i	$0.515493\pi$
$348$	0	0
$349$	5950.00	0.912597	0.456298	−	0.889827i	$-0.349175\pi$
$349$	5950.00	0.912597	0.456298	+	0.889827i	$0.349175\pi$
$350$	0	0
$351$	−980.000	−0.149027
$352$	0	0
$353$	11718.0	1.76682	0.883408	−	0.468604i	$-0.155243\pi$
$353$	11718.0	1.76682	0.883408	+	0.468604i	$0.155243\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−3822.00	−0.566615
$358$	0	0
$359$	−8070.00	−1.18640	−0.593201	−	0.805054i	$-0.702136\pi$
$359$	−8070.00	−1.18640	−0.593201	+	0.805054i	$0.702136\pi$
$360$	0	0
$361$	−5634.00	−0.821403
$362$	0	0
$363$	3626.00	0.524286
$364$	0	0
$365$	0	0
$366$	0	0
$367$	8316.00	1.18281	0.591406	−	0.806374i	$-0.298573\pi$
$367$	8316.00	1.18281	0.591406	+	0.806374i	$0.298573\pi$
$368$	0	0
$369$	−4466.00	−0.630056
$370$	0	0
$371$	−492.000	−0.0688500
$372$	0	0
$373$	−12062.0	−1.67439	−0.837194	−	0.546906i	$-0.815805\pi$
$373$	−12062.0	−1.67439	−0.837194	+	0.546906i	$0.815805\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	4480.00	0.612021
$378$	0	0
$379$	−1735.00	−0.235148	−0.117574	−	0.993064i	$-0.537512\pi$
$379$	−1735.00	−0.235148	−0.117574	+	0.993064i	$0.537512\pi$
$380$	0	0
$381$	−6118.00	−0.822663
$382$	0	0
$383$	7602.00	1.01421	0.507107	−	0.861883i	$-0.330715\pi$
$383$	7602.00	1.01421	0.507107	+	0.861883i	$0.330715\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	2024.00	0.265855
$388$	0	0
$389$	3030.00	0.394928	0.197464	−	0.980310i	$-0.436729\pi$
$389$	3030.00	0.394928	0.197464	+	0.980310i	$0.436729\pi$
$390$	0	0
$391$	−14742.0	−1.90674
$392$	0	0
$393$	−7644.00	−0.981142
$394$	0	0
$395$	0	0
$396$	0	0
$397$	1204.00	0.152209	0.0761046	−	0.997100i	$-0.475752\pi$
$397$	1204.00	0.152209	0.0761046	+	0.997100i	$0.475752\pi$
$398$	0	0
$399$	1470.00	0.184441
$400$	0	0
$401$	1077.00	0.134122	0.0670609	−	0.997749i	$-0.478638\pi$
$401$	1077.00	0.134122	0.0670609	+	0.997749i	$0.478638\pi$
$402$	0	0
$403$	−1176.00	−0.145362
$404$	0	0
$405$	0	0
$406$	0	0
$407$	13502.0	1.64440
$408$	0	0
$409$	−3955.00	−0.478147	−0.239074	−	0.971001i	$-0.576844\pi$
$409$	−3955.00	−0.478147	−0.239074	+	0.971001i	$0.576844\pi$
$410$	0	0
$411$	−2877.00	−0.345285
$412$	0	0
$413$	1680.00	0.200163
$414$	0	0
$415$	0	0
$416$	0	0
$417$	4165.00	0.489115
$418$	0	0
$419$	−6265.00	−0.730466	−0.365233	−	0.930916i	$-0.619011\pi$
$419$	−6265.00	−0.730466	−0.365233	+	0.930916i	$0.619011\pi$
$420$	0	0
$421$	−3788.00	−0.438517	−0.219259	−	0.975667i	$-0.570364\pi$
$421$	−3788.00	−0.438517	−0.219259	+	0.975667i	$0.570364\pi$
$422$	0	0
$423$	4312.00	0.495642
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−3108.00	−0.352240
$428$	0	0
$429$	8428.00	0.948503
$430$	0	0
$431$	15258.0	1.70523	0.852613	−	0.522544i	$-0.175017\pi$
$431$	15258.0	1.70523	0.852613	+	0.522544i	$0.175017\pi$
$432$	0	0
$433$	13573.0	1.50641	0.753206	−	0.657784i	$-0.228506\pi$
$433$	13573.0	1.50641	0.753206	+	0.657784i	$0.228506\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	5670.00	0.620670
$438$	0	0
$439$	8120.00	0.882794	0.441397	−	0.897312i	$-0.354483\pi$
$439$	8120.00	0.882794	0.441397	+	0.897312i	$0.354483\pi$
$440$	0	0
$441$	−6754.00	−0.729295
$442$	0	0
$443$	−6183.00	−0.663122	−0.331561	−	0.943434i	$-0.607575\pi$
$443$	−6183.00	−0.663122	−0.331561	+	0.943434i	$0.607575\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−22400.0	−2.37021
$448$	0	0
$449$	−1975.00	−0.207586	−0.103793	−	0.994599i	$-0.533098\pi$
$449$	−1975.00	−0.207586	−0.103793	+	0.994599i	$0.533098\pi$
$450$	0	0
$451$	−8729.00	−0.911380
$452$	0	0
$453$	−1414.00	−0.146657
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−11831.0	−1.21101	−0.605504	−	0.795842i	$-0.707029\pi$
$457$	−11831.0	−1.21101	−0.605504	+	0.795842i	$0.707029\pi$
$458$	0	0
$459$	3185.00	0.323885
$460$	0	0
$461$	1932.00	0.195189	0.0975946	−	0.995226i	$-0.468885\pi$
$461$	1932.00	0.195189	0.0975946	+	0.995226i	$0.468885\pi$
$462$	0	0
$463$	−9228.00	−0.926267	−0.463133	−	0.886289i	$-0.653275\pi$
$463$	−9228.00	−0.926267	−0.463133	+	0.886289i	$0.653275\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	13916.0	1.37892	0.689460	−	0.724324i	$-0.257848\pi$
$467$	13916.0	1.37892	0.689460	+	0.724324i	$0.257848\pi$
$468$	0	0
$469$	846.000	0.0832935
$470$	0	0
$471$	−2842.00	−0.278031
$472$	0	0
$473$	3956.00	0.384560
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1804.00	−0.173165
$478$	0	0
$479$	−2310.00	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$479$	−2310.00	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$480$	0	0
$481$	8792.00	0.833432
$482$	0	0
$483$	6804.00	0.640979
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−17114.0	−1.59242	−0.796211	−	0.605019i	$-0.793165\pi$
$487$	−17114.0	−1.59242	−0.796211	+	0.605019i	$0.793165\pi$
$488$	0	0
$489$	−26621.0	−2.46185
$490$	0	0
$491$	17228.0	1.58348	0.791740	−	0.610858i	$-0.209175\pi$
$491$	17228.0	1.58348	0.791740	+	0.610858i	$0.209175\pi$
$492$	0	0
$493$	−14560.0	−1.33012
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−2472.00	−0.223107
$498$	0	0
$499$	12500.0	1.12140	0.560698	−	0.828020i	$-0.310533\pi$
$499$	12500.0	1.12140	0.560698	+	0.828020i	$0.310533\pi$
$500$	0	0
$501$	28812.0	2.56931
$502$	0	0
$503$	−868.000	−0.0769428	−0.0384714	−	0.999260i	$-0.512249\pi$
$503$	−868.000	−0.0769428	−0.0384714	+	0.999260i	$0.512249\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−9891.00	−0.866420
$508$	0	0
$509$	13370.0	1.16427	0.582136	−	0.813091i	$-0.302217\pi$
$509$	13370.0	1.16427	0.582136	+	0.813091i	$0.302217\pi$
$510$	0	0
$511$	4578.00	0.396319
$512$	0	0
$513$	−1225.00	−0.105429
$514$	0	0
$515$	0	0
$516$	0	0
$517$	8428.00	0.716950
$518$	0	0
$519$	−10584.0	−0.895156
$520$	0	0
$521$	21637.0	1.81945	0.909726	−	0.415210i	$-0.136292\pi$
$521$	21637.0	1.81945	0.909726	+	0.415210i	$0.136292\pi$
$522$	0	0
$523$	287.000	0.0239955	0.0119977	−	0.999928i	$-0.496181\pi$
$523$	287.000	0.0239955	0.0119977	+	0.999928i	$0.496181\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3822.00	0.315918
$528$	0	0
$529$	14077.0	1.15698
$530$	0	0
$531$	6160.00	0.503430
$532$	0	0
$533$	−5684.00	−0.461916
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−18095.0	−1.45411
$538$	0	0
$539$	−13201.0	−1.05493
$540$	0	0
$541$	−5328.00	−0.423417	−0.211709	−	0.977333i	$-0.567903\pi$
$541$	−5328.00	−0.423417	−0.211709	+	0.977333i	$0.567903\pi$
$542$	0	0
$543$	−19306.0	−1.52578
$544$	0	0
$545$	0	0
$546$	0	0
$547$	71.0000	0.00554980	0.00277490	−	0.999996i	$-0.499117\pi$
$547$	71.0000	0.00554980	0.00277490	+	0.999996i	$0.499117\pi$
$548$	0	0
$549$	−11396.0	−0.885919
$550$	0	0
$551$	5600.00	0.432973
$552$	0	0
$553$	−3060.00	−0.235306
$554$	0	0
$555$	0	0
$556$	0	0
$557$	18444.0	1.40305	0.701524	−	0.712646i	$-0.252503\pi$
$557$	18444.0	1.40305	0.701524	+	0.712646i	$0.252503\pi$
$558$	0	0
$559$	2576.00	0.194907
$560$	0	0
$561$	−27391.0	−2.06141
$562$	0	0
$563$	672.000	0.0503045	0.0251522	−	0.999684i	$-0.491993\pi$
$563$	672.000	0.0503045	0.0251522	+	0.999684i	$0.491993\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−5034.00	−0.372854
$568$	0	0
$569$	−10935.0	−0.805657	−0.402829	−	0.915275i	$-0.631973\pi$
$569$	−10935.0	−0.805657	−0.402829	+	0.915275i	$0.631973\pi$
$570$	0	0
$571$	13588.0	0.995867	0.497934	−	0.867215i	$-0.334092\pi$
$571$	13588.0	0.995867	0.497934	+	0.867215i	$0.334092\pi$
$572$	0	0
$573$	16646.0	1.21361
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−8701.00	−0.627777	−0.313889	−	0.949460i	$-0.601632\pi$
$577$	−8701.00	−0.627777	−0.313889	+	0.949460i	$0.601632\pi$
$578$	0	0
$579$	−21469.0	−1.54097
$580$	0	0
$581$	4662.00	0.332896
$582$	0	0
$583$	−3526.00	−0.250484
$584$	0	0
$585$	0	0
$586$	0	0
$587$	11361.0	0.798839	0.399420	−	0.916768i	$-0.369212\pi$
$587$	11361.0	0.798839	0.399420	+	0.916768i	$0.369212\pi$
$588$	0	0
$589$	−1470.00	−0.102836
$590$	0	0
$591$	−16422.0	−1.14300
$592$	0	0
$593$	−11417.0	−0.790624	−0.395312	−	0.918547i	$-0.629364\pi$
$593$	−11417.0	−0.790624	−0.395312	+	0.918547i	$0.629364\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−34300.0	−2.35143
$598$	0	0
$599$	21050.0	1.43586	0.717930	−	0.696116i	$-0.245090\pi$
$599$	21050.0	1.43586	0.717930	+	0.696116i	$0.245090\pi$
$600$	0	0
$601$	7427.00	0.504083	0.252041	−	0.967716i	$-0.418898\pi$
$601$	7427.00	0.504083	0.252041	+	0.967716i	$0.418898\pi$
$602$	0	0
$603$	3102.00	0.209491
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−4144.00	−0.277100	−0.138550	−	0.990355i	$-0.544244\pi$
$607$	−4144.00	−0.277100	−0.138550	+	0.990355i	$0.544244\pi$
$608$	0	0
$609$	6720.00	0.447140
$610$	0	0
$611$	5488.00	0.363373
$612$	0	0
$613$	−30122.0	−1.98469	−0.992346	−	0.123489i	$-0.960592\pi$
$613$	−30122.0	−1.98469	−0.992346	+	0.123489i	$0.960592\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	11934.0	0.778679	0.389339	−	0.921094i	$-0.372703\pi$
$617$	11934.0	0.778679	0.389339	+	0.921094i	$0.372703\pi$
$618$	0	0
$619$	−8540.00	−0.554526	−0.277263	−	0.960794i	$-0.589427\pi$
$619$	−8540.00	−0.554526	−0.277263	+	0.960794i	$0.589427\pi$
$620$	0	0
$621$	−5670.00	−0.366392
$622$	0	0
$623$	−5670.00	−0.364629
$624$	0	0
$625$	0	0
$626$	0	0
$627$	10535.0	0.671017
$628$	0	0
$629$	−28574.0	−1.81132
$630$	0	0
$631$	3158.00	0.199236	0.0996181	−	0.995026i	$-0.468238\pi$
$631$	3158.00	0.199236	0.0996181	+	0.995026i	$0.468238\pi$
$632$	0	0
$633$	−30149.0	−1.89307
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−8596.00	−0.534672
$638$	0	0
$639$	−9064.00	−0.561137
$640$	0	0
$641$	−4278.00	−0.263605	−0.131803	−	0.991276i	$-0.542076\pi$
$641$	−4278.00	−0.263605	−0.131803	+	0.991276i	$0.542076\pi$
$642$	0	0
$643$	−11508.0	−0.705803	−0.352901	−	0.935661i	$-0.614805\pi$
$643$	−11508.0	−0.705803	−0.352901	+	0.935661i	$0.614805\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−8204.00	−0.498505	−0.249252	−	0.968439i	$-0.580185\pi$
$647$	−8204.00	−0.498505	−0.249252	+	0.968439i	$0.580185\pi$
$648$	0	0
$649$	12040.0	0.728215
$650$	0	0
$651$	−1764.00	−0.106201
$652$	0	0
$653$	5518.00	0.330683	0.165342	−	0.986236i	$-0.447127\pi$
$653$	5518.00	0.330683	0.165342	+	0.986236i	$0.447127\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	16786.0	0.996780
$658$	0	0
$659$	−13295.0	−0.785887	−0.392944	−	0.919563i	$-0.628543\pi$
$659$	−13295.0	−0.785887	−0.392944	+	0.919563i	$0.628543\pi$
$660$	0	0
$661$	−9968.00	−0.586551	−0.293276	−	0.956028i	$-0.594745\pi$
$661$	−9968.00	−0.586551	−0.293276	+	0.956028i	$0.594745\pi$
$662$	0	0
$663$	−17836.0	−1.04479
$664$	0	0
$665$	0	0
$666$	0	0
$667$	25920.0	1.50469
$668$	0	0
$669$	15484.0	0.894837
$670$	0	0
$671$	−22274.0	−1.28149
$672$	0	0
$673$	15738.0	0.901419	0.450710	−	0.892671i	$-0.351171\pi$
$673$	15738.0	0.901419	0.450710	+	0.892671i	$0.351171\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	19824.0	1.12540	0.562702	−	0.826660i	$-0.309762\pi$
$677$	19824.0	1.12540	0.562702	+	0.826660i	$0.309762\pi$
$678$	0	0
$679$	−7476.00	−0.422537
$680$	0	0
$681$	3332.00	0.187493
$682$	0	0
$683$	−11073.0	−0.620346	−0.310173	−	0.950680i	$-0.600387\pi$
$683$	−11073.0	−0.620346	−0.310173	+	0.950680i	$0.600387\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−20580.0	−1.14291
$688$	0	0
$689$	−2296.00	−0.126953
$690$	0	0
$691$	6503.00	0.358011	0.179006	−	0.983848i	$-0.442712\pi$
$691$	6503.00	0.358011	0.179006	+	0.983848i	$0.442712\pi$
$692$	0	0
$693$	5676.00	0.311130
$694$	0	0
$695$	0	0
$696$	0	0
$697$	18473.0	1.00389
$698$	0	0
$699$	−7014.00	−0.379533
$700$	0	0
$701$	−10148.0	−0.546768	−0.273384	−	0.961905i	$-0.588143\pi$
$701$	−10148.0	−0.546768	−0.273384	+	0.961905i	$0.588143\pi$
$702$	0	0
$703$	10990.0	0.589610
$704$	0	0
$705$	0	0
$706$	0	0
$707$	7812.00	0.415559
$708$	0	0
$709$	−9980.00	−0.528641	−0.264321	−	0.964435i	$-0.585148\pi$
$709$	−9980.00	−0.528641	−0.264321	+	0.964435i	$0.585148\pi$
$710$	0	0
$711$	−11220.0	−0.591818
$712$	0	0
$713$	−6804.00	−0.357380
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−17360.0	−0.904214
$718$	0	0
$719$	27510.0	1.42691	0.713456	−	0.700700i	$-0.247129\pi$
$719$	27510.0	1.42691	0.713456	+	0.700700i	$0.247129\pi$
$720$	0	0
$721$	3192.00	0.164877
$722$	0	0
$723$	13279.0	0.683059
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−17024.0	−0.868480	−0.434240	−	0.900797i	$-0.642983\pi$
$727$	−17024.0	−0.868480	−0.434240	+	0.900797i	$0.642983\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	−8372.00	−0.423597
$732$	0	0
$733$	34748.0	1.75095	0.875475	−	0.483263i	$-0.160549\pi$
$733$	34748.0	1.75095	0.875475	+	0.483263i	$0.160549\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	6063.00	0.303030
$738$	0	0
$739$	12020.0	0.598326	0.299163	−	0.954202i	$-0.403293\pi$
$739$	12020.0	0.598326	0.299163	+	0.954202i	$0.403293\pi$
$740$	0	0
$741$	6860.00	0.340092
$742$	0	0
$743$	28642.0	1.41423	0.707115	−	0.707098i	$-0.249996\pi$
$743$	28642.0	1.41423	0.707115	+	0.707098i	$0.249996\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	17094.0	0.837265
$748$	0	0
$749$	−7614.00	−0.371441
$750$	0	0
$751$	−8752.00	−0.425253	−0.212627	−	0.977134i	$-0.568202\pi$
$751$	−8752.00	−0.425253	−0.212627	+	0.977134i	$0.568202\pi$
$752$	0	0
$753$	16611.0	0.803902
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−10256.0	−0.492418	−0.246209	−	0.969217i	$-0.579185\pi$
$757$	−10256.0	−0.492418	−0.246209	+	0.969217i	$0.579185\pi$
$758$	0	0
$759$	48762.0	2.33195
$760$	0	0
$761$	33957.0	1.61753	0.808765	−	0.588132i	$-0.200136\pi$
$761$	33957.0	1.61753	0.808765	+	0.588132i	$0.200136\pi$
$762$	0	0
$763$	6420.00	0.304613
$764$	0	0
$765$	0	0
$766$	0	0
$767$	7840.00	0.369082
$768$	0	0
$769$	27965.0	1.31137	0.655685	−	0.755034i	$-0.272380\pi$
$769$	27965.0	1.31137	0.655685	+	0.755034i	$0.272380\pi$
$770$	0	0
$771$	31458.0	1.46943
$772$	0	0
$773$	−9912.00	−0.461203	−0.230601	−	0.973048i	$-0.574069\pi$
$773$	−9912.00	−0.461203	−0.230601	+	0.973048i	$0.574069\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	13188.0	0.608902
$778$	0	0
$779$	−7105.00	−0.326782
$780$	0	0
$781$	−17716.0	−0.811688
$782$	0	0
$783$	−5600.00	−0.255591
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−25564.0	−1.15789	−0.578944	−	0.815367i	$-0.696535\pi$
$787$	−25564.0	−1.15789	−0.578944	+	0.815367i	$0.696535\pi$
$788$	0	0
$789$	5054.00	0.228045
$790$	0	0
$791$	3018.00	0.135661
$792$	0	0
$793$	−14504.0	−0.649498
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−12446.0	−0.553149	−0.276575	−	0.960992i	$-0.589199\pi$
$797$	−12446.0	−0.553149	−0.276575	+	0.960992i	$0.589199\pi$
$798$	0	0
$799$	−17836.0	−0.789728
$800$	0	0
$801$	−20790.0	−0.917077
$802$	0	0
$803$	32809.0	1.44185
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−43120.0	−1.88091
$808$	0	0
$809$	33970.0	1.47629	0.738147	−	0.674640i	$-0.235701\pi$
$809$	33970.0	1.47629	0.738147	+	0.674640i	$0.235701\pi$
$810$	0	0
$811$	−18732.0	−0.811060	−0.405530	−	0.914082i	$-0.632913\pi$
$811$	−18732.0	−0.811060	−0.405530	+	0.914082i	$0.632913\pi$
$812$	0	0
$813$	50666.0	2.18565
$814$	0	0
$815$	0	0
$816$	0	0
$817$	3220.00	0.137887
$818$	0	0
$819$	3696.00	0.157691
$820$	0	0
$821$	6162.00	0.261943	0.130972	−	0.991386i	$-0.458190\pi$
$821$	6162.00	0.261943	0.130972	+	0.991386i	$0.458190\pi$
$822$	0	0
$823$	−25388.0	−1.07530	−0.537649	−	0.843169i	$-0.680687\pi$
$823$	−25388.0	−1.07530	−0.537649	+	0.843169i	$0.680687\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	25201.0	1.05964	0.529821	−	0.848109i	$-0.322259\pi$
$827$	25201.0	1.05964	0.529821	+	0.848109i	$0.322259\pi$
$828$	0	0
$829$	−19740.0	−0.827019	−0.413509	−	0.910500i	$-0.635697\pi$
$829$	−19740.0	−0.827019	−0.413509	+	0.910500i	$0.635697\pi$
$830$	0	0
$831$	−12432.0	−0.518967
$832$	0	0
$833$	27937.0	1.16202
$834$	0	0
$835$	0	0
$836$	0	0
$837$	1470.00	0.0607057
$838$	0	0
$839$	−29680.0	−1.22130	−0.610648	−	0.791902i	$-0.709091\pi$
$839$	−29680.0	−1.22130	−0.610648	+	0.791902i	$0.709091\pi$
$840$	0	0
$841$	1211.00	0.0496535
$842$	0	0
$843$	31794.0	1.29898
$844$	0	0
$845$	0	0
$846$	0	0
$847$	3108.00	0.126083
$848$	0	0
$849$	49539.0	2.00256
$850$	0	0
$851$	50868.0	2.04904
$852$	0	0
$853$	1218.00	0.0488904	0.0244452	−	0.999701i	$-0.492218\pi$
$853$	1218.00	0.0488904	0.0244452	+	0.999701i	$0.492218\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−38731.0	−1.54379	−0.771894	−	0.635752i	$-0.780690\pi$
$857$	−38731.0	−1.54379	−0.771894	+	0.635752i	$0.780690\pi$
$858$	0	0
$859$	23555.0	0.935607	0.467803	−	0.883833i	$-0.345046\pi$
$859$	23555.0	0.935607	0.467803	+	0.883833i	$0.345046\pi$
$860$	0	0
$861$	−8526.00	−0.337474
$862$	0	0
$863$	24872.0	0.981058	0.490529	−	0.871425i	$-0.336804\pi$
$863$	24872.0	0.981058	0.490529	+	0.871425i	$0.336804\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	23576.0	0.923510
$868$	0	0
$869$	−21930.0	−0.856069
$870$	0	0
$871$	3948.00	0.153585
$872$	0	0
$873$	−27412.0	−1.06272
$874$	0	0
$875$	0	0
$876$	0	0
$877$	17124.0	0.659335	0.329667	−	0.944097i	$-0.393063\pi$
$877$	17124.0	0.659335	0.329667	+	0.944097i	$0.393063\pi$
$878$	0	0
$879$	29106.0	1.11686
$880$	0	0
$881$	−658.000	−0.0251630	−0.0125815	−	0.999921i	$-0.504005\pi$
$881$	−658.000	−0.0251630	−0.0125815	+	0.999921i	$0.504005\pi$
$882$	0	0
$883$	33727.0	1.28540	0.642698	−	0.766120i	$-0.277815\pi$
$883$	33727.0	1.28540	0.642698	+	0.766120i	$0.277815\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	36036.0	1.36412	0.682058	−	0.731298i	$-0.261085\pi$
$887$	36036.0	1.36412	0.682058	+	0.731298i	$0.261085\pi$
$888$	0	0
$889$	−5244.00	−0.197838
$890$	0	0
$891$	−36077.0	−1.35648
$892$	0	0
$893$	6860.00	0.257067
$894$	0	0
$895$	0	0
$896$	0	0
$897$	31752.0	1.18190
$898$	0	0
$899$	−6720.00	−0.249304
$900$	0	0
$901$	7462.00	0.275910
$902$	0	0
$903$	3864.00	0.142399
$904$	0	0
$905$	0	0
$906$	0	0
$907$	39156.0	1.43347	0.716733	−	0.697348i	$-0.245637\pi$
$907$	39156.0	1.43347	0.716733	+	0.697348i	$0.245637\pi$
$908$	0	0
$909$	28644.0	1.04517
$910$	0	0
$911$	−43532.0	−1.58318	−0.791591	−	0.611051i	$-0.790747\pi$
$911$	−43532.0	−1.58318	−0.791591	+	0.611051i	$0.790747\pi$
$912$	0	0
$913$	33411.0	1.21111
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−6552.00	−0.235950
$918$	0	0
$919$	28610.0	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$919$	28610.0	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$920$	0	0
$921$	−17983.0	−0.643388
$922$	0	0
$923$	−11536.0	−0.411389
$924$	0	0
$925$	0	0
$926$	0	0
$927$	11704.0	0.414682
$928$	0	0
$929$	−24290.0	−0.857835	−0.428918	−	0.903344i	$-0.641105\pi$
$929$	−24290.0	−0.857835	−0.428918	+	0.903344i	$0.641105\pi$
$930$	0	0
$931$	−10745.0	−0.378253
$932$	0	0
$933$	−20874.0	−0.732459
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−34461.0	−1.20149	−0.600743	−	0.799442i	$-0.705128\pi$
$937$	−34461.0	−1.20149	−0.600743	+	0.799442i	$0.705128\pi$
$938$	0	0
$939$	−16954.0	−0.589215
$940$	0	0
$941$	−40628.0	−1.40748	−0.703738	−	0.710460i	$-0.748487\pi$
$941$	−40628.0	−1.40748	−0.703738	+	0.710460i	$0.748487\pi$
$942$	0	0
$943$	−32886.0	−1.13565
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−20904.0	−0.717306	−0.358653	−	0.933471i	$-0.616764\pi$
$947$	−20904.0	−0.717306	−0.358653	+	0.933471i	$0.616764\pi$
$948$	0	0
$949$	21364.0	0.730774
$950$	0	0
$951$	66388.0	2.26370
$952$	0	0
$953$	−1807.00	−0.0614213	−0.0307106	−	0.999528i	$-0.509777\pi$
$953$	−1807.00	−0.0614213	−0.0307106	+	0.999528i	$0.509777\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	48160.0	1.62674
$958$	0	0
$959$	−2466.00	−0.0830358
$960$	0	0
$961$	−28027.0	−0.940787
$962$	0	0
$963$	−27918.0	−0.934211
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−57584.0	−1.91497	−0.957485	−	0.288482i	$-0.906849\pi$
$967$	−57584.0	−1.91497	−0.957485	+	0.288482i	$0.906849\pi$
$968$	0	0
$969$	−22295.0	−0.739132
$970$	0	0
$971$	−27237.0	−0.900182	−0.450091	−	0.892983i	$-0.648608\pi$
$971$	−27237.0	−0.900182	−0.450091	+	0.892983i	$0.648608\pi$
$972$	0	0
$973$	3570.00	0.117625
$974$	0	0
$975$	0	0
$976$	0	0
$977$	13649.0	0.446950	0.223475	−	0.974710i	$-0.428260\pi$
$977$	13649.0	0.446950	0.223475	+	0.974710i	$0.428260\pi$
$978$	0	0
$979$	−40635.0	−1.32656
$980$	0	0
$981$	23540.0	0.766131
$982$	0	0
$983$	16002.0	0.519211	0.259606	−	0.965715i	$-0.416407\pi$
$983$	16002.0	0.519211	0.259606	+	0.965715i	$0.416407\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	8232.00	0.265479
$988$	0	0
$989$	14904.0	0.479191
$990$	0	0
$991$	−37022.0	−1.18672	−0.593362	−	0.804936i	$-0.702200\pi$
$991$	−37022.0	−1.18672	−0.593362	+	0.804936i	$0.702200\pi$
$992$	0	0
$993$	1281.00	0.0409379
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−18396.0	−0.584360	−0.292180	−	0.956363i	$-0.594381\pi$
$997$	−18396.0	−0.584360	−0.292180	+	0.956363i	$0.594381\pi$
$998$	0	0
$999$	−10990.0	−0.348056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.4.a.s.1.1		1
4.3	odd	2		25.4.a.a.1.1	✓	1
5.2	odd	4		400.4.c.e.49.1		2
5.3	odd	4		400.4.c.e.49.2		2
5.4	even	2		400.4.a.c.1.1		1
8.3	odd	2		1600.4.a.bt.1.1		1
8.5	even	2		1600.4.a.h.1.1		1
12.11	even	2		225.4.a.e.1.1		1
20.3	even	4		25.4.b.b.24.2		2
20.7	even	4		25.4.b.b.24.1		2
20.19	odd	2		25.4.a.b.1.1	yes	1
28.27	even	2		1225.4.a.h.1.1		1
40.19	odd	2		1600.4.a.i.1.1		1
40.29	even	2		1600.4.a.bs.1.1		1
60.23	odd	4		225.4.b.f.199.1		2
60.47	odd	4		225.4.b.f.199.2		2
60.59	even	2		225.4.a.c.1.1		1
140.139	even	2		1225.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.a.a.1.1	✓	1	4.3	odd	2
25.4.a.b.1.1	yes	1	20.19	odd	2
25.4.b.b.24.1		2	20.7	even	4
25.4.b.b.24.2		2	20.3	even	4
225.4.a.c.1.1		1	60.59	even	2
225.4.a.e.1.1		1	12.11	even	2
225.4.b.f.199.1		2	60.23	odd	4
225.4.b.f.199.2		2	60.47	odd	4
400.4.a.c.1.1		1	5.4	even	2
400.4.a.s.1.1		1	1.1	even	1	trivial
400.4.c.e.49.1		2	5.2	odd	4
400.4.c.e.49.2		2	5.3	odd	4
1225.4.a.h.1.1		1	28.27	even	2
1225.4.a.i.1.1		1	140.139	even	2
1600.4.a.h.1.1		1	8.5	even	2
1600.4.a.i.1.1		1	40.19	odd	2
1600.4.a.bs.1.1		1	40.29	even	2
1600.4.a.bt.1.1		1	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	400.a (trivial)

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