LMFDB - Embedded newform 300.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,6,Mod(1,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("300.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	300.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:	$48.1151459439$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	300.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} -91.0000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} -91.0000 q^{7} +81.0000 q^{9} -174.000 q^{11} +785.000 q^{13} +1794.00 q^{17} -925.000 q^{19} +819.000 q^{21} -2346.00 q^{23} -729.000 q^{27} -726.000 q^{29} -811.000 q^{31} +1566.00 q^{33} +7922.00 q^{37} -7065.00 q^{39} -360.000 q^{41} -4951.00 q^{43} +9906.00 q^{47} -8526.00 q^{49} -16146.0 q^{51} -8292.00 q^{53} +8325.00 q^{57} +7014.00 q^{59} -51433.0 q^{61} -7371.00 q^{63} +581.000 q^{67} +21114.0 q^{69} -56520.0 q^{71} -42478.0 q^{73} +15834.0 q^{77} -28912.0 q^{79} +6561.00 q^{81} -104586. q^{83} +6534.00 q^{87} -118080. q^{89} -71435.0 q^{91} +7299.00 q^{93} +110273. q^{97} -14094.0 q^{99} +O(q^{100})$

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
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−91.0000	−0.701934	−0.350967	−	0.936388i	$-0.614147\pi$
$7$	−91.0000	−0.701934	−0.350967	+	0.936388i	$0.614147\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	−174.000	−0.433578	−0.216789	−	0.976218i	$-0.569558\pi$
$11$	−174.000	−0.433578	−0.216789	+	0.976218i	$0.569558\pi$
$12$	0	0
$13$	785.000	1.28828	0.644142	−	0.764906i	$-0.277215\pi$
$13$	785.000	1.28828	0.644142	+	0.764906i	$0.277215\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1794.00	1.50557	0.752784	−	0.658268i	$-0.228711\pi$
$17$	1794.00	1.50557	0.752784	+	0.658268i	$0.228711\pi$
$18$	0	0
$19$	−925.000	−0.587838	−0.293919	−	0.955830i	$-0.594960\pi$
$19$	−925.000	−0.587838	−0.293919	+	0.955830i	$0.594960\pi$
$20$	0	0
$21$	819.000	0.405262
$22$	0	0
$23$	−2346.00	−0.924716	−0.462358	−	0.886693i	$-0.652997\pi$
$23$	−2346.00	−0.924716	−0.462358	+	0.886693i	$0.652997\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	−726.000	−0.160303	−0.0801515	−	0.996783i	$-0.525540\pi$
$29$	−726.000	−0.160303	−0.0801515	+	0.996783i	$0.525540\pi$
$30$	0	0
$31$	−811.000	−0.151571	−0.0757856	−	0.997124i	$-0.524146\pi$
$31$	−811.000	−0.151571	−0.0757856	+	0.997124i	$0.524146\pi$
$32$	0	0
$33$	1566.00	0.250327
$34$	0	0
$35$	0	0
$36$	0	0
$37$	7922.00	0.951329	0.475664	−	0.879627i	$-0.342208\pi$
$37$	7922.00	0.951329	0.475664	+	0.879627i	$0.342208\pi$
$38$	0	0
$39$	−7065.00	−0.743791
$40$	0	0
$41$	−360.000	−0.0334459	−0.0167229	−	0.999860i	$-0.505323\pi$
$41$	−360.000	−0.0334459	−0.0167229	+	0.999860i	$0.505323\pi$
$42$	0	0
$43$	−4951.00	−0.408340	−0.204170	−	0.978935i	$-0.565450\pi$
$43$	−4951.00	−0.408340	−0.204170	+	0.978935i	$0.565450\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	9906.00	0.654114	0.327057	−	0.945005i	$-0.393943\pi$
$47$	9906.00	0.654114	0.327057	+	0.945005i	$0.393943\pi$
$48$	0	0
$49$	−8526.00	−0.507289
$50$	0	0
$51$	−16146.0	−0.869240
$52$	0	0
$53$	−8292.00	−0.405480	−0.202740	−	0.979233i	$-0.564985\pi$
$53$	−8292.00	−0.405480	−0.202740	+	0.979233i	$0.564985\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	8325.00	0.339388
$58$	0	0
$59$	7014.00	0.262323	0.131161	−	0.991361i	$-0.458129\pi$
$59$	7014.00	0.262323	0.131161	+	0.991361i	$0.458129\pi$
$60$	0	0
$61$	−51433.0	−1.76977	−0.884886	−	0.465808i	$-0.845764\pi$
$61$	−51433.0	−1.76977	−0.884886	+	0.465808i	$0.845764\pi$
$62$	0	0
$63$	−7371.00	−0.233978
$64$	0	0
$65$	0	0
$66$	0	0
$67$	581.000	0.0158121	0.00790604	−	0.999969i	$-0.497483\pi$
$67$	581.000	0.0158121	0.00790604	+	0.999969i	$0.497483\pi$
$68$	0	0
$69$	21114.0	0.533885
$70$	0	0
$71$	−56520.0	−1.33063	−0.665313	−	0.746564i	$-0.731702\pi$
$71$	−56520.0	−1.33063	−0.665313	+	0.746564i	$0.731702\pi$
$72$	0	0
$73$	−42478.0	−0.932947	−0.466473	−	0.884535i	$-0.654476\pi$
$73$	−42478.0	−0.932947	−0.466473	+	0.884535i	$0.654476\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	15834.0	0.304343
$78$	0	0
$79$	−28912.0	−0.521207	−0.260604	−	0.965446i	$-0.583922\pi$
$79$	−28912.0	−0.521207	−0.260604	+	0.965446i	$0.583922\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−104586.	−1.66640	−0.833198	−	0.552974i	$-0.813493\pi$
$83$	−104586.	−1.66640	−0.833198	+	0.552974i	$0.813493\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	6534.00	0.0925510
$88$	0	0
$89$	−118080.	−1.58016	−0.790080	−	0.613003i	$-0.789961\pi$
$89$	−118080.	−1.58016	−0.790080	+	0.613003i	$0.789961\pi$
$90$	0	0
$91$	−71435.0	−0.904290
$92$	0	0
$93$	7299.00	0.0875097
$94$	0	0
$95$	0	0
$96$	0	0
$97$	110273.	1.18998	0.594990	−	0.803733i	$-0.297156\pi$
$97$	110273.	1.18998	0.594990	+	0.803733i	$0.297156\pi$
$98$	0	0
$99$	−14094.0	−0.144526
$100$	0	0
$101$	−193332.	−1.88582	−0.942910	−	0.333047i	$-0.891923\pi$
$101$	−193332.	−1.88582	−0.942910	+	0.333047i	$0.891923\pi$
$102$	0	0
$103$	−37684.0	−0.349997	−0.174998	−	0.984569i	$-0.555992\pi$
$103$	−37684.0	−0.349997	−0.174998	+	0.984569i	$0.555992\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	17292.0	0.146011	0.0730055	−	0.997332i	$-0.476741\pi$
$107$	17292.0	0.146011	0.0730055	+	0.997332i	$0.476741\pi$
$108$	0	0
$109$	142133.	1.14585	0.572926	−	0.819607i	$-0.305808\pi$
$109$	142133.	1.14585	0.572926	+	0.819607i	$0.305808\pi$
$110$	0	0
$111$	−71298.0	−0.549250
$112$	0	0
$113$	−68388.0	−0.503830	−0.251915	−	0.967749i	$-0.581060\pi$
$113$	−68388.0	−0.503830	−0.251915	+	0.967749i	$0.581060\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	63585.0	0.429428
$118$	0	0
$119$	−163254.	−1.05681
$120$	0	0
$121$	−130775.	−0.812010
$122$	0	0
$123$	3240.00	0.0193100
$124$	0	0
$125$	0	0
$126$	0	0
$127$	185384.	1.01991	0.509956	−	0.860200i	$-0.329662\pi$
$127$	185384.	1.01991	0.509956	+	0.860200i	$0.329662\pi$
$128$	0	0
$129$	44559.0	0.235755
$130$	0	0
$131$	329772.	1.67894	0.839471	−	0.543405i	$-0.182865\pi$
$131$	329772.	1.67894	0.839471	+	0.543405i	$0.182865\pi$
$132$	0	0
$133$	84175.0	0.412624
$134$	0	0
$135$	0	0
$136$	0	0
$137$	143982.	0.655401	0.327700	−	0.944782i	$-0.393726\pi$
$137$	143982.	0.655401	0.327700	+	0.944782i	$0.393726\pi$
$138$	0	0
$139$	−365644.	−1.60517	−0.802586	−	0.596537i	$-0.796543\pi$
$139$	−365644.	−1.60517	−0.802586	+	0.596537i	$0.796543\pi$
$140$	0	0
$141$	−89154.0	−0.377653
$142$	0	0
$143$	−136590.	−0.558572
$144$	0	0
$145$	0	0
$146$	0	0
$147$	76734.0	0.292883
$148$	0	0
$149$	155178.	0.572617	0.286309	−	0.958137i	$-0.407572\pi$
$149$	155178.	0.572617	0.286309	+	0.958137i	$0.407572\pi$
$150$	0	0
$151$	−227185.	−0.810844	−0.405422	−	0.914130i	$-0.632875\pi$
$151$	−227185.	−0.810844	−0.405422	+	0.914130i	$0.632875\pi$
$152$	0	0
$153$	145314.	0.501856
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−171277.	−0.554562	−0.277281	−	0.960789i	$-0.589433\pi$
$157$	−171277.	−0.554562	−0.277281	+	0.960789i	$0.589433\pi$
$158$	0	0
$159$	74628.0	0.234104
$160$	0	0
$161$	213486.	0.649090
$162$	0	0
$163$	110675.	0.326273	0.163136	−	0.986604i	$-0.447839\pi$
$163$	110675.	0.326273	0.163136	+	0.986604i	$0.447839\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−440628.	−1.22259	−0.611295	−	0.791403i	$-0.709351\pi$
$167$	−440628.	−1.22259	−0.611295	+	0.791403i	$0.709351\pi$
$168$	0	0
$169$	244932.	0.659673
$170$	0	0
$171$	−74925.0	−0.195946
$172$	0	0
$173$	−699834.	−1.77779	−0.888894	−	0.458114i	$-0.848525\pi$
$173$	−699834.	−1.77779	−0.888894	+	0.458114i	$0.848525\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−63126.0	−0.151452
$178$	0	0
$179$	−309786.	−0.722652	−0.361326	−	0.932440i	$-0.617676\pi$
$179$	−309786.	−0.722652	−0.361326	+	0.932440i	$0.617676\pi$
$180$	0	0
$181$	628625.	1.42625	0.713124	−	0.701038i	$-0.247280\pi$
$181$	628625.	1.42625	0.713124	+	0.701038i	$0.247280\pi$
$182$	0	0
$183$	462897.	1.02178
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−312156.	−0.652781
$188$	0	0
$189$	66339.0	0.135087
$190$	0	0
$191$	192774.	0.382353	0.191177	−	0.981556i	$-0.438770\pi$
$191$	192774.	0.382353	0.191177	+	0.981556i	$0.438770\pi$
$192$	0	0
$193$	708971.	1.37005	0.685023	−	0.728521i	$-0.259792\pi$
$193$	708971.	1.37005	0.685023	+	0.728521i	$0.259792\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−119154.	−0.218747	−0.109374	−	0.994001i	$-0.534885\pi$
$197$	−119154.	−0.218747	−0.109374	+	0.994001i	$0.534885\pi$
$198$	0	0
$199$	1.01864e6	1.82343	0.911715	−	0.410822i	$-0.134758\pi$
$199$	1.01864e6	1.82343	0.911715	+	0.410822i	$0.134758\pi$
$200$	0	0
$201$	−5229.00	−0.00912911
$202$	0	0
$203$	66066.0	0.112522
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−190026.	−0.308239
$208$	0	0
$209$	160950.	0.254874
$210$	0	0
$211$	−32245.0	−0.0498605	−0.0249302	−	0.999689i	$-0.507936\pi$
$211$	−32245.0	−0.0498605	−0.0249302	+	0.999689i	$0.507936\pi$
$212$	0	0
$213$	508680.	0.768238
$214$	0	0
$215$	0	0
$216$	0	0
$217$	73801.0	0.106393
$218$	0	0
$219$	382302.	0.538637
$220$	0	0
$221$	1.40829e6	1.93960
$222$	0	0
$223$	815765.	1.09851	0.549254	−	0.835656i	$-0.314912\pi$
$223$	815765.	1.09851	0.549254	+	0.835656i	$0.314912\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−1.45908e6	−1.87938	−0.939690	−	0.342028i	$-0.888886\pi$
$227$	−1.45908e6	−1.87938	−0.939690	+	0.342028i	$0.888886\pi$
$228$	0	0
$229$	406241.	0.511912	0.255956	−	0.966688i	$-0.417610\pi$
$229$	406241.	0.511912	0.255956	+	0.966688i	$0.417610\pi$
$230$	0	0
$231$	−142506.	−0.175713
$232$	0	0
$233$	−901080.	−1.08736	−0.543680	−	0.839292i	$-0.682970\pi$
$233$	−901080.	−1.08736	−0.543680	+	0.839292i	$0.682970\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	260208.	0.300919
$238$	0	0
$239$	−1.36513e6	−1.54589	−0.772947	−	0.634470i	$-0.781218\pi$
$239$	−1.36513e6	−1.54589	−0.772947	+	0.634470i	$0.781218\pi$
$240$	0	0
$241$	−180247.	−0.199906	−0.0999529	−	0.994992i	$-0.531869\pi$
$241$	−180247.	−0.199906	−0.0999529	+	0.994992i	$0.531869\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−726125.	−0.757302
$248$	0	0
$249$	941274.	0.962094
$250$	0	0
$251$	1.87739e6	1.88092	0.940459	−	0.339908i	$-0.110396\pi$
$251$	1.87739e6	1.88092	0.940459	+	0.339908i	$0.110396\pi$
$252$	0	0
$253$	408204.	0.400937
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−825108.	−0.779252	−0.389626	−	0.920973i	$-0.627396\pi$
$257$	−825108.	−0.779252	−0.389626	+	0.920973i	$0.627396\pi$
$258$	0	0
$259$	−720902.	−0.667770
$260$	0	0
$261$	−58806.0	−0.0534343
$262$	0	0
$263$	196944.	0.175571	0.0877856	−	0.996139i	$-0.472021\pi$
$263$	196944.	0.175571	0.0877856	+	0.996139i	$0.472021\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	1.06272e6	0.912306
$268$	0	0
$269$	−20874.0	−0.0175883	−0.00879417	−	0.999961i	$-0.502799\pi$
$269$	−20874.0	−0.0175883	−0.00879417	+	0.999961i	$0.502799\pi$
$270$	0	0
$271$	770024.	0.636914	0.318457	−	0.947937i	$-0.396835\pi$
$271$	770024.	0.636914	0.318457	+	0.947937i	$0.396835\pi$
$272$	0	0
$273$	642915.	0.522092
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1.75169e6	1.37170	0.685849	−	0.727744i	$-0.259431\pi$
$277$	1.75169e6	1.37170	0.685849	+	0.727744i	$0.259431\pi$
$278$	0	0
$279$	−65691.0	−0.0505237
$280$	0	0
$281$	1.72693e6	1.30469	0.652346	−	0.757921i	$-0.273785\pi$
$281$	1.72693e6	1.30469	0.652346	+	0.757921i	$0.273785\pi$
$282$	0	0
$283$	2.20061e6	1.63334	0.816670	−	0.577105i	$-0.195818\pi$
$283$	2.20061e6	1.63334	0.816670	+	0.577105i	$0.195818\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	32760.0	0.0234768
$288$	0	0
$289$	1.79858e6	1.26673
$290$	0	0
$291$	−992457.	−0.687036
$292$	0	0
$293$	−2.04086e6	−1.38881	−0.694406	−	0.719583i	$-0.744333\pi$
$293$	−2.04086e6	−1.38881	−0.694406	+	0.719583i	$0.744333\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	126846.	0.0834422
$298$	0	0
$299$	−1.84161e6	−1.19130
$300$	0	0
$301$	450541.	0.286628
$302$	0	0
$303$	1.73999e6	1.08878
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−433153.	−0.262298	−0.131149	−	0.991363i	$-0.541867\pi$
$307$	−433153.	−0.262298	−0.131149	+	0.991363i	$0.541867\pi$
$308$	0	0
$309$	339156.	0.202071
$310$	0	0
$311$	−2.20663e6	−1.29368	−0.646841	−	0.762625i	$-0.723910\pi$
$311$	−2.20663e6	−1.29368	−0.646841	+	0.762625i	$0.723910\pi$
$312$	0	0
$313$	−2.17607e6	−1.25549	−0.627743	−	0.778421i	$-0.716021\pi$
$313$	−2.17607e6	−1.25549	−0.627743	+	0.778421i	$0.716021\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−380136.	−0.212467	−0.106233	−	0.994341i	$-0.533879\pi$
$317$	−380136.	−0.212467	−0.106233	+	0.994341i	$0.533879\pi$
$318$	0	0
$319$	126324.	0.0695039
$320$	0	0
$321$	−155628.	−0.0842995
$322$	0	0
$323$	−1.65945e6	−0.885030
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−1.27920e6	−0.661558
$328$	0	0
$329$	−901446.	−0.459145
$330$	0	0
$331$	−3.43599e6	−1.72378	−0.861890	−	0.507096i	$-0.830719\pi$
$331$	−3.43599e6	−1.72378	−0.861890	+	0.507096i	$0.830719\pi$
$332$	0	0
$333$	641682.	0.317110
$334$	0	0
$335$	0	0
$336$	0	0
$337$	1.57718e6	0.756494	0.378247	−	0.925705i	$-0.376527\pi$
$337$	1.57718e6	0.756494	0.378247	+	0.925705i	$0.376527\pi$
$338$	0	0
$339$	615492.	0.290886
$340$	0	0
$341$	141114.	0.0657180
$342$	0	0
$343$	2.30530e6	1.05802
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2.08744e6	0.930659	0.465330	−	0.885137i	$-0.345936\pi$
$347$	2.08744e6	0.930659	0.465330	+	0.885137i	$0.345936\pi$
$348$	0	0
$349$	542426.	0.238384	0.119192	−	0.992871i	$-0.461970\pi$
$349$	542426.	0.238384	0.119192	+	0.992871i	$0.461970\pi$
$350$	0	0
$351$	−572265.	−0.247930
$352$	0	0
$353$	−4.16054e6	−1.77710	−0.888552	−	0.458776i	$-0.848288\pi$
$353$	−4.16054e6	−1.77710	−0.888552	+	0.458776i	$0.848288\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	1.46929e6	0.610149
$358$	0	0
$359$	−1.69018e6	−0.692143	−0.346071	−	0.938208i	$-0.612485\pi$
$359$	−1.69018e6	−0.692143	−0.346071	+	0.938208i	$0.612485\pi$
$360$	0	0
$361$	−1.62047e6	−0.654446
$362$	0	0
$363$	1.17698e6	0.468814
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−846061.	−0.327896	−0.163948	−	0.986469i	$-0.552423\pi$
$367$	−846061.	−0.327896	−0.163948	+	0.986469i	$0.552423\pi$
$368$	0	0
$369$	−29160.0	−0.0111486
$370$	0	0
$371$	754572.	0.284620
$372$	0	0
$373$	−1.25910e6	−0.468585	−0.234293	−	0.972166i	$-0.575277\pi$
$373$	−1.25910e6	−0.468585	−0.234293	+	0.972166i	$0.575277\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−569910.	−0.206516
$378$	0	0
$379$	−4.37437e6	−1.56429	−0.782145	−	0.623097i	$-0.785874\pi$
$379$	−4.37437e6	−1.56429	−0.782145	+	0.623097i	$0.785874\pi$
$380$	0	0
$381$	−1.66846e6	−0.588847
$382$	0	0
$383$	−4.77827e6	−1.66446	−0.832230	−	0.554430i	$-0.812936\pi$
$383$	−4.77827e6	−1.66446	−0.832230	+	0.554430i	$0.812936\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−401031.	−0.136113
$388$	0	0
$389$	2.98618e6	1.00056	0.500278	−	0.865865i	$-0.333231\pi$
$389$	2.98618e6	1.00056	0.500278	+	0.865865i	$0.333231\pi$
$390$	0	0
$391$	−4.20872e6	−1.39222
$392$	0	0
$393$	−2.96795e6	−0.969337
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−238633.	−0.0759896	−0.0379948	−	0.999278i	$-0.512097\pi$
$397$	−238633.	−0.0759896	−0.0379948	+	0.999278i	$0.512097\pi$
$398$	0	0
$399$	−757575.	−0.238228
$400$	0	0
$401$	−1.66856e6	−0.518182	−0.259091	−	0.965853i	$-0.583423\pi$
$401$	−1.66856e6	−0.518182	−0.259091	+	0.965853i	$0.583423\pi$
$402$	0	0
$403$	−636635.	−0.195267
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−1.37843e6	−0.412475
$408$	0	0
$409$	3.05242e6	0.902269	0.451135	−	0.892456i	$-0.351019\pi$
$409$	3.05242e6	0.902269	0.451135	+	0.892456i	$0.351019\pi$
$410$	0	0
$411$	−1.29584e6	−0.378396
$412$	0	0
$413$	−638274.	−0.184133
$414$	0	0
$415$	0	0
$416$	0	0
$417$	3.29080e6	0.926746
$418$	0	0
$419$	−3.16223e6	−0.879950	−0.439975	−	0.898010i	$-0.645013\pi$
$419$	−3.16223e6	−0.879950	−0.439975	+	0.898010i	$0.645013\pi$
$420$	0	0
$421$	−2.76169e6	−0.759398	−0.379699	−	0.925110i	$-0.623973\pi$
$421$	−2.76169e6	−0.759398	−0.379699	+	0.925110i	$0.623973\pi$
$422$	0	0
$423$	802386.	0.218038
$424$	0	0
$425$	0	0
$426$	0	0
$427$	4.68040e6	1.24226
$428$	0	0
$429$	1.22931e6	0.322491
$430$	0	0
$431$	−2.46832e6	−0.640042	−0.320021	−	0.947410i	$-0.603690\pi$
$431$	−2.46832e6	−0.640042	−0.320021	+	0.947410i	$0.603690\pi$
$432$	0	0
$433$	838931.	0.215034	0.107517	−	0.994203i	$-0.465710\pi$
$433$	838931.	0.215034	0.107517	+	0.994203i	$0.465710\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	2.17005e6	0.543583
$438$	0	0
$439$	−481867.	−0.119334	−0.0596672	−	0.998218i	$-0.519004\pi$
$439$	−481867.	−0.119334	−0.0596672	+	0.998218i	$0.519004\pi$
$440$	0	0
$441$	−690606.	−0.169096
$442$	0	0
$443$	4.83550e6	1.17066	0.585331	−	0.810794i	$-0.300964\pi$
$443$	4.83550e6	1.17066	0.585331	+	0.810794i	$0.300964\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−1.39660e6	−0.330601
$448$	0	0
$449$	−1.64449e6	−0.384960	−0.192480	−	0.981301i	$-0.561653\pi$
$449$	−1.64449e6	−0.384960	−0.192480	+	0.981301i	$0.561653\pi$
$450$	0	0
$451$	62640.0	0.0145014
$452$	0	0
$453$	2.04466e6	0.468141
$454$	0	0
$455$	0	0
$456$	0	0
$457$	6.59903e6	1.47805	0.739026	−	0.673677i	$-0.235286\pi$
$457$	6.59903e6	1.47805	0.739026	+	0.673677i	$0.235286\pi$
$458$	0	0
$459$	−1.30783e6	−0.289747
$460$	0	0
$461$	253836.	0.0556290	0.0278145	−	0.999613i	$-0.491145\pi$
$461$	253836.	0.0556290	0.0278145	+	0.999613i	$0.491145\pi$
$462$	0	0
$463$	−5.03985e6	−1.09261	−0.546305	−	0.837586i	$-0.683966\pi$
$463$	−5.03985e6	−1.09261	−0.546305	+	0.837586i	$0.683966\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−419958.	−0.0891074	−0.0445537	−	0.999007i	$-0.514187\pi$
$467$	−419958.	−0.0891074	−0.0445537	+	0.999007i	$0.514187\pi$
$468$	0	0
$469$	−52871.0	−0.0110990
$470$	0	0
$471$	1.54149e6	0.320176
$472$	0	0
$473$	861474.	0.177047
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−671652.	−0.135160
$478$	0	0
$479$	−7.28623e6	−1.45099	−0.725494	−	0.688228i	$-0.758389\pi$
$479$	−7.28623e6	−1.45099	−0.725494	+	0.688228i	$0.758389\pi$
$480$	0	0
$481$	6.21877e6	1.22558
$482$	0	0
$483$	−1.92137e6	−0.374752
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−7.48420e6	−1.42996	−0.714978	−	0.699147i	$-0.753563\pi$
$487$	−7.48420e6	−1.42996	−0.714978	+	0.699147i	$0.753563\pi$
$488$	0	0
$489$	−996075.	−0.188374
$490$	0	0
$491$	−339816.	−0.0636122	−0.0318061	−	0.999494i	$-0.510126\pi$
$491$	−339816.	−0.0636122	−0.0318061	+	0.999494i	$0.510126\pi$
$492$	0	0
$493$	−1.30244e6	−0.241347
$494$	0	0
$495$	0	0
$496$	0	0
$497$	5.14332e6	0.934012
$498$	0	0
$499$	280499.	0.0504290	0.0252145	−	0.999682i	$-0.491973\pi$
$499$	280499.	0.0504290	0.0252145	+	0.999682i	$0.491973\pi$
$500$	0	0
$501$	3.96565e6	0.705863
$502$	0	0
$503$	2.41522e6	0.425634	0.212817	−	0.977092i	$-0.431736\pi$
$503$	2.41522e6	0.425634	0.212817	+	0.977092i	$0.431736\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−2.20439e6	−0.380862
$508$	0	0
$509$	8.09746e6	1.38533	0.692667	−	0.721258i	$-0.256436\pi$
$509$	8.09746e6	1.38533	0.692667	+	0.721258i	$0.256436\pi$
$510$	0	0
$511$	3.86550e6	0.654867
$512$	0	0
$513$	674325.	0.113129
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−1.72364e6	−0.283610
$518$	0	0
$519$	6.29851e6	1.02641
$520$	0	0
$521$	−3.52334e6	−0.568670	−0.284335	−	0.958725i	$-0.591773\pi$
$521$	−3.52334e6	−0.568670	−0.284335	+	0.958725i	$0.591773\pi$
$522$	0	0
$523$	4.27241e6	0.682996	0.341498	−	0.939882i	$-0.389066\pi$
$523$	4.27241e6	0.682996	0.341498	+	0.939882i	$0.389066\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−1.45493e6	−0.228201
$528$	0	0
$529$	−932627.	−0.144900
$530$	0	0
$531$	568134.	0.0874409
$532$	0	0
$533$	−282600.	−0.0430878
$534$	0	0
$535$	0	0
$536$	0	0
$537$	2.78807e6	0.417223
$538$	0	0
$539$	1.48352e6	0.219949
$540$	0	0
$541$	3.80585e6	0.559061	0.279530	−	0.960137i	$-0.409821\pi$
$541$	3.80585e6	0.559061	0.279530	+	0.960137i	$0.409821\pi$
$542$	0	0
$543$	−5.65762e6	−0.823445
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−7.46327e6	−1.06650	−0.533250	−	0.845958i	$-0.679030\pi$
$547$	−7.46327e6	−1.06650	−0.533250	+	0.845958i	$0.679030\pi$
$548$	0	0
$549$	−4.16607e6	−0.589924
$550$	0	0
$551$	671550.	0.0942322
$552$	0	0
$553$	2.63099e6	0.365853
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−6.26290e6	−0.855338	−0.427669	−	0.903935i	$-0.640665\pi$
$557$	−6.26290e6	−0.855338	−0.427669	+	0.903935i	$0.640665\pi$
$558$	0	0
$559$	−3.88654e6	−0.526057
$560$	0	0
$561$	2.80940e6	0.376883
$562$	0	0
$563$	1.34426e7	1.78735	0.893677	−	0.448710i	$-0.148117\pi$
$563$	1.34426e7	1.78735	0.893677	+	0.448710i	$0.148117\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−597051.	−0.0779927
$568$	0	0
$569$	1.25046e7	1.61916	0.809579	−	0.587011i	$-0.199695\pi$
$569$	1.25046e7	1.61916	0.809579	+	0.587011i	$0.199695\pi$
$570$	0	0
$571$	6.80272e6	0.873156	0.436578	−	0.899666i	$-0.356190\pi$
$571$	6.80272e6	0.873156	0.436578	+	0.899666i	$0.356190\pi$
$572$	0	0
$573$	−1.73497e6	−0.220752
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−375517.	−0.0469559	−0.0234779	−	0.999724i	$-0.507474\pi$
$577$	−375517.	−0.0469559	−0.0234779	+	0.999724i	$0.507474\pi$
$578$	0	0
$579$	−6.38074e6	−0.790997
$580$	0	0
$581$	9.51733e6	1.16970
$582$	0	0
$583$	1.44281e6	0.175807
$584$	0	0
$585$	0	0
$586$	0	0
$587$	3.36164e6	0.402677	0.201338	−	0.979522i	$-0.435471\pi$
$587$	3.36164e6	0.402677	0.201338	+	0.979522i	$0.435471\pi$
$588$	0	0
$589$	750175.	0.0890993
$590$	0	0
$591$	1.07239e6	0.126294
$592$	0	0
$593$	9.31214e6	1.08746	0.543730	−	0.839260i	$-0.317012\pi$
$593$	9.31214e6	1.08746	0.543730	+	0.839260i	$0.317012\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−9.16779e6	−1.05276
$598$	0	0
$599$	1.03007e7	1.17301	0.586503	−	0.809947i	$-0.300504\pi$
$599$	1.03007e7	1.17301	0.586503	+	0.809947i	$0.300504\pi$
$600$	0	0
$601$	−4.14328e6	−0.467905	−0.233953	−	0.972248i	$-0.575166\pi$
$601$	−4.14328e6	−0.467905	−0.233953	+	0.972248i	$0.575166\pi$
$602$	0	0
$603$	47061.0	0.00527069
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−6.42729e6	−0.708037	−0.354019	−	0.935238i	$-0.615185\pi$
$607$	−6.42729e6	−0.708037	−0.354019	+	0.935238i	$0.615185\pi$
$608$	0	0
$609$	−594594.	−0.0649647
$610$	0	0
$611$	7.77621e6	0.842684
$612$	0	0
$613$	−2.11824e6	−0.227679	−0.113840	−	0.993499i	$-0.536315\pi$
$613$	−2.11824e6	−0.227679	−0.113840	+	0.993499i	$0.536315\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−1.53399e7	−1.62222	−0.811111	−	0.584892i	$-0.801137\pi$
$617$	−1.53399e7	−1.62222	−0.811111	+	0.584892i	$0.801137\pi$
$618$	0	0
$619$	1.04124e7	1.09226	0.546128	−	0.837702i	$-0.316101\pi$
$619$	1.04124e7	1.09226	0.546128	+	0.837702i	$0.316101\pi$
$620$	0	0
$621$	1.71023e6	0.177962
$622$	0	0
$623$	1.07453e7	1.10917
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−1.44855e6	−0.147151
$628$	0	0
$629$	1.42121e7	1.43229
$630$	0	0
$631$	2.88626e6	0.288577	0.144288	−	0.989536i	$-0.453911\pi$
$631$	2.88626e6	0.288577	0.144288	+	0.989536i	$0.453911\pi$
$632$	0	0
$633$	290205.	0.0287869
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−6.69291e6	−0.653531
$638$	0	0
$639$	−4.57812e6	−0.443542
$640$	0	0
$641$	−1.48587e7	−1.42835	−0.714176	−	0.699967i	$-0.753198\pi$
$641$	−1.48587e7	−1.42835	−0.714176	+	0.699967i	$0.753198\pi$
$642$	0	0
$643$	−9.59676e6	−0.915371	−0.457686	−	0.889114i	$-0.651322\pi$
$643$	−9.59676e6	−0.915371	−0.457686	+	0.889114i	$0.651322\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	1.08529e7	1.01926	0.509632	−	0.860393i	$-0.329782\pi$
$647$	1.08529e7	1.01926	0.509632	+	0.860393i	$0.329782\pi$
$648$	0	0
$649$	−1.22044e6	−0.113737
$650$	0	0
$651$	−664209.	−0.0614260
$652$	0	0
$653$	1.20352e7	1.10451	0.552254	−	0.833676i	$-0.313768\pi$
$653$	1.20352e7	1.10451	0.552254	+	0.833676i	$0.313768\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−3.44072e6	−0.310982
$658$	0	0
$659$	−5.80711e6	−0.520891	−0.260445	−	0.965489i	$-0.583869\pi$
$659$	−5.80711e6	−0.520891	−0.260445	+	0.965489i	$0.583869\pi$
$660$	0	0
$661$	1.91093e7	1.70114	0.850570	−	0.525861i	$-0.176257\pi$
$661$	1.91093e7	1.70114	0.850570	+	0.525861i	$0.176257\pi$
$662$	0	0
$663$	−1.26746e7	−1.11983
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.70320e6	0.148235
$668$	0	0
$669$	−7.34189e6	−0.634223
$670$	0	0
$671$	8.94934e6	0.767335
$672$	0	0
$673$	−2.15545e6	−0.183443	−0.0917213	−	0.995785i	$-0.529237\pi$
$673$	−2.15545e6	−0.183443	−0.0917213	+	0.995785i	$0.529237\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	8.69543e6	0.729155	0.364577	−	0.931173i	$-0.381214\pi$
$677$	8.69543e6	0.729155	0.364577	+	0.931173i	$0.381214\pi$
$678$	0	0
$679$	−1.00348e7	−0.835288
$680$	0	0
$681$	1.31317e7	1.08506
$682$	0	0
$683$	781896.	0.0641353	0.0320677	−	0.999486i	$-0.489791\pi$
$683$	781896.	0.0641353	0.0320677	+	0.999486i	$0.489791\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−3.65617e6	−0.295552
$688$	0	0
$689$	−6.50922e6	−0.522373
$690$	0	0
$691$	1.13518e7	0.904416	0.452208	−	0.891912i	$-0.350636\pi$
$691$	1.13518e7	0.904416	0.452208	+	0.891912i	$0.350636\pi$
$692$	0	0
$693$	1.28255e6	0.101448
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−645840.	−0.0503550
$698$	0	0
$699$	8.10972e6	0.627788
$700$	0	0
$701$	−1.99404e7	−1.53263	−0.766317	−	0.642462i	$-0.777913\pi$
$701$	−1.99404e7	−1.53263	−0.766317	+	0.642462i	$0.777913\pi$
$702$	0	0
$703$	−7.32785e6	−0.559227
$704$	0	0
$705$	0	0
$706$	0	0
$707$	1.75932e7	1.32372
$708$	0	0
$709$	−1.75367e7	−1.31018	−0.655092	−	0.755549i	$-0.727370\pi$
$709$	−1.75367e7	−1.31018	−0.655092	+	0.755549i	$0.727370\pi$
$710$	0	0
$711$	−2.34187e6	−0.173736
$712$	0	0
$713$	1.90261e6	0.140160
$714$	0	0
$715$	0	0
$716$	0	0
$717$	1.22862e7	0.892523
$718$	0	0
$719$	1.78220e7	1.28568	0.642842	−	0.765999i	$-0.277755\pi$
$719$	1.78220e7	1.28568	0.642842	+	0.765999i	$0.277755\pi$
$720$	0	0
$721$	3.42924e6	0.245675
$722$	0	0
$723$	1.62222e6	0.115416
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−8.29063e6	−0.581770	−0.290885	−	0.956758i	$-0.593950\pi$
$727$	−8.29063e6	−0.581770	−0.290885	+	0.956758i	$0.593950\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−8.88209e6	−0.614783
$732$	0	0
$733$	1.69219e7	1.16330	0.581648	−	0.813441i	$-0.302408\pi$
$733$	1.69219e7	1.16330	0.581648	+	0.813441i	$0.302408\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−101094.	−0.00685578
$738$	0	0
$739$	9.40718e6	0.633648	0.316824	−	0.948484i	$-0.397383\pi$
$739$	9.40718e6	0.633648	0.316824	+	0.948484i	$0.397383\pi$
$740$	0	0
$741$	6.53512e6	0.437228
$742$	0	0
$743$	1.81581e7	1.20670	0.603348	−	0.797478i	$-0.293833\pi$
$743$	1.81581e7	1.20670	0.603348	+	0.797478i	$0.293833\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−8.47147e6	−0.555465
$748$	0	0
$749$	−1.57357e6	−0.102490
$750$	0	0
$751$	−2.81468e7	−1.82108	−0.910541	−	0.413420i	$-0.864334\pi$
$751$	−2.81468e7	−1.82108	−0.910541	+	0.413420i	$0.864334\pi$
$752$	0	0
$753$	−1.68965e7	−1.08595
$754$	0	0
$755$	0	0
$756$	0	0
$757$	7.50436e6	0.475964	0.237982	−	0.971270i	$-0.423514\pi$
$757$	7.50436e6	0.475964	0.237982	+	0.971270i	$0.423514\pi$
$758$	0	0
$759$	−3.67384e6	−0.231481
$760$	0	0
$761$	−3.18499e7	−1.99364	−0.996820	−	0.0796919i	$-0.974606\pi$
$761$	−3.18499e7	−1.99364	−0.996820	+	0.0796919i	$0.974606\pi$
$762$	0	0
$763$	−1.29341e7	−0.804313
$764$	0	0
$765$	0	0
$766$	0	0
$767$	5.50599e6	0.337946
$768$	0	0
$769$	−2.38750e7	−1.45588	−0.727942	−	0.685638i	$-0.759523\pi$
$769$	−2.38750e7	−1.45588	−0.727942	+	0.685638i	$0.759523\pi$
$770$	0	0
$771$	7.42597e6	0.449901
$772$	0	0
$773$	8.43665e6	0.507833	0.253917	−	0.967226i	$-0.418281\pi$
$773$	8.43665e6	0.507833	0.253917	+	0.967226i	$0.418281\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	6.48812e6	0.385537
$778$	0	0
$779$	333000.	0.0196608
$780$	0	0
$781$	9.83448e6	0.576931
$782$	0	0
$783$	529254.	0.0308503
$784$	0	0
$785$	0	0
$786$	0	0
$787$	2.55971e7	1.47317	0.736587	−	0.676343i	$-0.236436\pi$
$787$	2.55971e7	1.47317	0.736587	+	0.676343i	$0.236436\pi$
$788$	0	0
$789$	−1.77250e6	−0.101366
$790$	0	0
$791$	6.22331e6	0.353655
$792$	0	0
$793$	−4.03749e7	−2.27997
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−1.22343e7	−0.682231	−0.341116	−	0.940021i	$-0.610805\pi$
$797$	−1.22343e7	−0.682231	−0.341116	+	0.940021i	$0.610805\pi$
$798$	0	0
$799$	1.77714e7	0.984813
$800$	0	0
$801$	−9.56448e6	−0.526720
$802$	0	0
$803$	7.39117e6	0.404506
$804$	0	0
$805$	0	0
$806$	0	0
$807$	187866.	0.0101546
$808$	0	0
$809$	−2.82538e7	−1.51777	−0.758885	−	0.651224i	$-0.774256\pi$
$809$	−2.82538e7	−1.51777	−0.758885	+	0.651224i	$0.774256\pi$
$810$	0	0
$811$	−2.02221e7	−1.07963	−0.539815	−	0.841784i	$-0.681506\pi$
$811$	−2.02221e7	−1.07963	−0.539815	+	0.841784i	$0.681506\pi$
$812$	0	0
$813$	−6.93022e6	−0.367723
$814$	0	0
$815$	0	0
$816$	0	0
$817$	4.57968e6	0.240038
$818$	0	0
$819$	−5.78624e6	−0.301430
$820$	0	0
$821$	2.92645e6	0.151524	0.0757622	−	0.997126i	$-0.475861\pi$
$821$	2.92645e6	0.151524	0.0757622	+	0.997126i	$0.475861\pi$
$822$	0	0
$823$	−1.19976e7	−0.617439	−0.308720	−	0.951153i	$-0.599900\pi$
$823$	−1.19976e7	−0.617439	−0.308720	+	0.951153i	$0.599900\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	2.87877e7	1.46367	0.731836	−	0.681481i	$-0.238664\pi$
$827$	2.87877e7	1.46367	0.731836	+	0.681481i	$0.238664\pi$
$828$	0	0
$829$	6.76584e6	0.341929	0.170964	−	0.985277i	$-0.445312\pi$
$829$	6.76584e6	0.341929	0.170964	+	0.985277i	$0.445312\pi$
$830$	0	0
$831$	−1.57652e7	−0.791950
$832$	0	0
$833$	−1.52956e7	−0.763757
$834$	0	0
$835$	0	0
$836$	0	0
$837$	591219.	0.0291699
$838$	0	0
$839$	1.64443e7	0.806512	0.403256	−	0.915087i	$-0.367878\pi$
$839$	1.64443e7	0.806512	0.403256	+	0.915087i	$0.367878\pi$
$840$	0	0
$841$	−1.99841e7	−0.974303
$842$	0	0
$843$	−1.55423e7	−0.753264
$844$	0	0
$845$	0	0
$846$	0	0
$847$	1.19005e7	0.569977
$848$	0	0
$849$	−1.98055e7	−0.943009
$850$	0	0
$851$	−1.85850e7	−0.879709
$852$	0	0
$853$	1.17440e7	0.552642	0.276321	−	0.961065i	$-0.410885\pi$
$853$	1.17440e7	0.552642	0.276321	+	0.961065i	$0.410885\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−2.59380e7	−1.20638	−0.603191	−	0.797597i	$-0.706104\pi$
$857$	−2.59380e7	−1.20638	−0.603191	+	0.797597i	$0.706104\pi$
$858$	0	0
$859$	−4.81132e6	−0.222475	−0.111238	−	0.993794i	$-0.535481\pi$
$859$	−4.81132e6	−0.222475	−0.111238	+	0.993794i	$0.535481\pi$
$860$	0	0
$861$	−294840.	−0.0135543
$862$	0	0
$863$	−8.80123e6	−0.402269	−0.201134	−	0.979564i	$-0.564463\pi$
$863$	−8.80123e6	−0.402269	−0.201134	+	0.979564i	$0.564463\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.61872e7	−0.731348
$868$	0	0
$869$	5.03069e6	0.225984
$870$	0	0
$871$	456085.	0.0203704
$872$	0	0
$873$	8.93211e6	0.396660
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−1.47823e7	−0.648998	−0.324499	−	0.945886i	$-0.605196\pi$
$877$	−1.47823e7	−0.648998	−0.324499	+	0.945886i	$0.605196\pi$
$878$	0	0
$879$	1.83677e7	0.801831
$880$	0	0
$881$	−2.47219e7	−1.07311	−0.536553	−	0.843867i	$-0.680274\pi$
$881$	−2.47219e7	−1.07311	−0.536553	+	0.843867i	$0.680274\pi$
$882$	0	0
$883$	−1.63912e7	−0.707470	−0.353735	−	0.935346i	$-0.615089\pi$
$883$	−1.63912e7	−0.707470	−0.353735	+	0.935346i	$0.615089\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	3.47481e7	1.48293	0.741467	−	0.670989i	$-0.234130\pi$
$887$	3.47481e7	1.48293	0.741467	+	0.670989i	$0.234130\pi$
$888$	0	0
$889$	−1.68699e7	−0.715911
$890$	0	0
$891$	−1.14161e6	−0.0481754
$892$	0	0
$893$	−9.16305e6	−0.384513
$894$	0	0
$895$	0	0
$896$	0	0
$897$	1.65745e7	0.687795
$898$	0	0
$899$	588786.	0.0242973
$900$	0	0
$901$	−1.48758e7	−0.610478
$902$	0	0
$903$	−4.05487e6	−0.165485
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−4.42672e7	−1.78675	−0.893375	−	0.449312i	$-0.851669\pi$
$907$	−4.42672e7	−1.78675	−0.893375	+	0.449312i	$0.851669\pi$
$908$	0	0
$909$	−1.56599e7	−0.628607
$910$	0	0
$911$	5.78972e6	0.231133	0.115566	−	0.993300i	$-0.463132\pi$
$911$	5.78972e6	0.231133	0.115566	+	0.993300i	$0.463132\pi$
$912$	0	0
$913$	1.81980e7	0.722513
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−3.00093e7	−1.17851
$918$	0	0
$919$	6.95894e6	0.271803	0.135902	−	0.990722i	$-0.456607\pi$
$919$	6.95894e6	0.271803	0.135902	+	0.990722i	$0.456607\pi$
$920$	0	0
$921$	3.89838e6	0.151438
$922$	0	0
$923$	−4.43682e7	−1.71422
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−3.05240e6	−0.116666
$928$	0	0
$929$	1.13281e7	0.430643	0.215321	−	0.976543i	$-0.430920\pi$
$929$	1.13281e7	0.430643	0.215321	+	0.976543i	$0.430920\pi$
$930$	0	0
$931$	7.88655e6	0.298204
$932$	0	0
$933$	1.98596e7	0.746908
$934$	0	0
$935$	0	0
$936$	0	0
$937$	3.38002e7	1.25768	0.628840	−	0.777534i	$-0.283530\pi$
$937$	3.38002e7	1.25768	0.628840	+	0.777534i	$0.283530\pi$
$938$	0	0
$939$	1.95846e7	0.724855
$940$	0	0
$941$	−1.01912e7	−0.375190	−0.187595	−	0.982246i	$-0.560069\pi$
$941$	−1.01912e7	−0.375190	−0.187595	+	0.982246i	$0.560069\pi$
$942$	0	0
$943$	844560.	0.0309280
$944$	0	0
$945$	0	0
$946$	0	0
$947$	2.78585e7	1.00944	0.504722	−	0.863282i	$-0.331595\pi$
$947$	2.78585e7	1.00944	0.504722	+	0.863282i	$0.331595\pi$
$948$	0	0
$949$	−3.33452e7	−1.20190
$950$	0	0
$951$	3.42122e6	0.122668
$952$	0	0
$953$	1.26828e7	0.452358	0.226179	−	0.974086i	$-0.427377\pi$
$953$	1.26828e7	0.452358	0.226179	+	0.974086i	$0.427377\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−1.13692e6	−0.0401281
$958$	0	0
$959$	−1.31024e7	−0.460048
$960$	0	0
$961$	−2.79714e7	−0.977026
$962$	0	0
$963$	1.40065e6	0.0486704
$964$	0	0
$965$	0	0
$966$	0	0
$967$	3.17434e7	1.09166	0.545831	−	0.837896i	$-0.316214\pi$
$967$	3.17434e7	1.09166	0.545831	+	0.837896i	$0.316214\pi$
$968$	0	0
$969$	1.49350e7	0.510972
$970$	0	0
$971$	1.81895e7	0.619117	0.309558	−	0.950880i	$-0.399819\pi$
$971$	1.81895e7	0.619117	0.309558	+	0.950880i	$0.399819\pi$
$972$	0	0
$973$	3.32736e7	1.12672
$974$	0	0
$975$	0	0
$976$	0	0
$977$	2.61267e7	0.875684	0.437842	−	0.899052i	$-0.355743\pi$
$977$	2.61267e7	0.875684	0.437842	+	0.899052i	$0.355743\pi$
$978$	0	0
$979$	2.05459e7	0.685123
$980$	0	0
$981$	1.15128e7	0.381951
$982$	0	0
$983$	6.44653e6	0.212786	0.106393	−	0.994324i	$-0.466070\pi$
$983$	6.44653e6	0.212786	0.106393	+	0.994324i	$0.466070\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	8.11301e6	0.265088
$988$	0	0
$989$	1.16150e7	0.377598
$990$	0	0
$991$	2.16146e7	0.699139	0.349570	−	0.936910i	$-0.386328\pi$
$991$	2.16146e7	0.699139	0.349570	+	0.936910i	$0.386328\pi$
$992$	0	0
$993$	3.09239e7	0.995224
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−2.16105e7	−0.688538	−0.344269	−	0.938871i	$-0.611873\pi$
$997$	−2.16105e7	−0.688538	−0.344269	+	0.938871i	$0.611873\pi$
$998$	0	0
$999$	−5.77514e6	−0.183083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.6.a.a.1.1	✓	1
3.2	odd	2		900.6.a.d.1.1		1
5.2	odd	4		300.6.d.b.49.2		2
5.3	odd	4		300.6.d.b.49.1		2
5.4	even	2		300.6.a.f.1.1	yes	1
15.2	even	4		900.6.d.g.649.1		2
15.8	even	4		900.6.d.g.649.2		2
15.14	odd	2		900.6.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.6.a.a.1.1	✓	1	1.1	even	1	trivial
300.6.a.f.1.1	yes	1	5.4	even	2
300.6.d.b.49.1		2	5.3	odd	4
300.6.d.b.49.2		2	5.2	odd	4
900.6.a.d.1.1		1	3.2	odd	2
900.6.a.i.1.1		1	15.14	odd	2
900.6.d.g.649.1		2	15.2	even	4
900.6.d.g.649.2		2	15.8	even	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	300.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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