LMFDB - Embedded newform 240.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,10,Mod(1,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("240.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	240.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:	$123.608600679$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	240.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-81.0000 q^{3} +625.000 q^{5} +7680.00 q^{7} +6561.00 q^{9} +O(q^{10})$

$q-81.0000 q^{3} +625.000 q^{5} +7680.00 q^{7} +6561.00 q^{9} +86404.0 q^{11} -149978. q^{13} -50625.0 q^{15} -207622. q^{17} -716284. q^{19} -622080. q^{21} -1.36992e6 q^{23} +390625. q^{25} -531441. q^{27} -3.19440e6 q^{29} +2.34900e6 q^{31} -6.99872e6 q^{33} +4.80000e6 q^{35} +1.87357e7 q^{37} +1.21482e7 q^{39} -2.92826e7 q^{41} +1.51672e6 q^{43} +4.10062e6 q^{45} -615752. q^{47} +1.86288e7 q^{49} +1.68174e7 q^{51} +4.74743e6 q^{53} +5.40025e7 q^{55} +5.80190e7 q^{57} -6.06161e7 q^{59} -1.26746e8 q^{61} +5.03885e7 q^{63} -9.37362e7 q^{65} +1.11183e8 q^{67} +1.10964e8 q^{69} +1.75552e8 q^{71} -6.12334e7 q^{73} -3.16406e7 q^{75} +6.63583e8 q^{77} -2.34431e8 q^{79} +4.30467e7 q^{81} -1.18910e8 q^{83} -1.29764e8 q^{85} +2.58747e8 q^{87} -3.16534e8 q^{89} -1.15183e9 q^{91} -1.90269e8 q^{93} -4.47678e8 q^{95} +2.42912e8 q^{97} +5.66897e8 q^{99} +O(q^{100})$

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
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	0	0
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	0	0
$7$	7680.00	1.20898	0.604491	−	0.796612i	$-0.293376\pi$
$7$	7680.00	1.20898	0.604491	+	0.796612i	$0.293376\pi$
$8$	0	0
$9$	6561.00	0.333333
$10$	0	0
$11$	86404.0	1.77937	0.889686	−	0.456573i	$-0.150923\pi$
$11$	86404.0	1.77937	0.889686	+	0.456573i	$0.150923\pi$
$12$	0	0
$13$	−149978.	−1.45641	−0.728203	−	0.685361i	$-0.759644\pi$
$13$	−149978.	−1.45641	−0.728203	+	0.685361i	$0.759644\pi$
$14$	0	0
$15$	−50625.0	−0.258199
$16$	0	0
$17$	−207622.	−0.602911	−0.301456	−	0.953480i	$-0.597472\pi$
$17$	−207622.	−0.602911	−0.301456	+	0.953480i	$0.597472\pi$
$18$	0	0
$19$	−716284.	−1.26094	−0.630469	−	0.776214i	$-0.717138\pi$
$19$	−716284.	−1.26094	−0.630469	+	0.776214i	$0.717138\pi$
$20$	0	0
$21$	−622080.	−0.698006
$22$	0	0
$23$	−1.36992e6	−1.02075	−0.510376	−	0.859952i	$-0.670494\pi$
$23$	−1.36992e6	−1.02075	−0.510376	+	0.859952i	$0.670494\pi$
$24$	0	0
$25$	390625.	0.200000
$26$	0	0
$27$	−531441.	−0.192450
$28$	0	0
$29$	−3.19440e6	−0.838684	−0.419342	−	0.907828i	$-0.637739\pi$
$29$	−3.19440e6	−0.838684	−0.419342	+	0.907828i	$0.637739\pi$
$30$	0	0
$31$	2.34900e6	0.456831	0.228415	−	0.973564i	$-0.426646\pi$
$31$	2.34900e6	0.456831	0.228415	+	0.973564i	$0.426646\pi$
$32$	0	0
$33$	−6.99872e6	−1.02732
$34$	0	0
$35$	4.80000e6	0.540673
$36$	0	0
$37$	1.87357e7	1.64347	0.821736	−	0.569868i	$-0.193006\pi$
$37$	1.87357e7	1.64347	0.821736	+	0.569868i	$0.193006\pi$
$38$	0	0
$39$	1.21482e7	0.840856
$40$	0	0
$41$	−2.92826e7	−1.61839	−0.809194	−	0.587541i	$-0.800096\pi$
$41$	−2.92826e7	−1.61839	−0.809194	+	0.587541i	$0.800096\pi$
$42$	0	0
$43$	1.51672e6	0.0676548	0.0338274	−	0.999428i	$-0.489230\pi$
$43$	1.51672e6	0.0676548	0.0338274	+	0.999428i	$0.489230\pi$
$44$	0	0
$45$	4.10062e6	0.149071
$46$	0	0
$47$	−615752.	−0.0184063	−0.00920313	−	0.999958i	$-0.502929\pi$
$47$	−615752.	−0.0184063	−0.00920313	+	0.999958i	$0.502929\pi$
$48$	0	0
$49$	1.86288e7	0.461639
$50$	0	0
$51$	1.68174e7	0.348091
$52$	0	0
$53$	4.74743e6	0.0826451	0.0413226	−	0.999146i	$-0.486843\pi$
$53$	4.74743e6	0.0826451	0.0413226	+	0.999146i	$0.486843\pi$
$54$	0	0
$55$	5.40025e7	0.795759
$56$	0	0
$57$	5.80190e7	0.728003
$58$	0	0
$59$	−6.06161e7	−0.651259	−0.325630	−	0.945497i	$-0.605576\pi$
$59$	−6.06161e7	−0.651259	−0.325630	+	0.945497i	$0.605576\pi$
$60$	0	0
$61$	−1.26746e8	−1.17206	−0.586029	−	0.810290i	$-0.699309\pi$
$61$	−1.26746e8	−1.17206	−0.586029	+	0.810290i	$0.699309\pi$
$62$	0	0
$63$	5.03885e7	0.402994
$64$	0	0
$65$	−9.37362e7	−0.651325
$66$	0	0
$67$	1.11183e8	0.674063	0.337031	−	0.941493i	$-0.390577\pi$
$67$	1.11183e8	0.674063	0.337031	+	0.941493i	$0.390577\pi$
$68$	0	0
$69$	1.10964e8	0.589331
$70$	0	0
$71$	1.75552e8	0.819865	0.409932	−	0.912116i	$-0.365552\pi$
$71$	1.75552e8	0.819865	0.409932	+	0.912116i	$0.365552\pi$
$72$	0	0
$73$	−6.12334e7	−0.252369	−0.126184	−	0.992007i	$-0.540273\pi$
$73$	−6.12334e7	−0.252369	−0.126184	+	0.992007i	$0.540273\pi$
$74$	0	0
$75$	−3.16406e7	−0.115470
$76$	0	0
$77$	6.63583e8	2.15123
$78$	0	0
$79$	−2.34431e8	−0.677163	−0.338582	−	0.940937i	$-0.609947\pi$
$79$	−2.34431e8	−0.677163	−0.338582	+	0.940937i	$0.609947\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	0	0
$83$	−1.18910e8	−0.275023	−0.137511	−	0.990500i	$-0.543910\pi$
$83$	−1.18910e8	−0.275023	−0.137511	+	0.990500i	$0.543910\pi$
$84$	0	0
$85$	−1.29764e8	−0.269630
$86$	0	0
$87$	2.58747e8	0.484215
$88$	0	0
$89$	−3.16534e8	−0.534768	−0.267384	−	0.963590i	$-0.586159\pi$
$89$	−3.16534e8	−0.534768	−0.267384	+	0.963590i	$0.586159\pi$
$90$	0	0
$91$	−1.15183e9	−1.76077
$92$	0	0
$93$	−1.90269e8	−0.263751
$94$	0	0
$95$	−4.47678e8	−0.563909
$96$	0	0
$97$	2.42912e8	0.278597	0.139299	−	0.990250i	$-0.455515\pi$
$97$	2.42912e8	0.278597	0.139299	+	0.990250i	$0.455515\pi$
$98$	0	0
$99$	5.66897e8	0.593124
$100$	0	0
$101$	−6.53803e8	−0.625173	−0.312587	−	0.949889i	$-0.601195\pi$
$101$	−6.53803e8	−0.625173	−0.312587	+	0.949889i	$0.601195\pi$
$102$	0	0
$103$	−1.40420e9	−1.22931	−0.614656	−	0.788795i	$-0.710705\pi$
$103$	−1.40420e9	−1.22931	−0.614656	+	0.788795i	$0.710705\pi$
$104$	0	0
$105$	−3.88800e8	−0.312158
$106$	0	0
$107$	1.83854e9	1.35595	0.677977	−	0.735083i	$-0.262857\pi$
$107$	1.83854e9	1.35595	0.677977	+	0.735083i	$0.262857\pi$
$108$	0	0
$109$	−9.33452e8	−0.633392	−0.316696	−	0.948527i	$-0.602574\pi$
$109$	−9.33452e8	−0.633392	−0.316696	+	0.948527i	$0.602574\pi$
$110$	0	0
$111$	−1.51759e9	−0.948859
$112$	0	0
$113$	−9.28534e7	−0.0535728	−0.0267864	−	0.999641i	$-0.508527\pi$
$113$	−9.28534e7	−0.0535728	−0.0267864	+	0.999641i	$0.508527\pi$
$114$	0	0
$115$	−8.56200e8	−0.456494
$116$	0	0
$117$	−9.84006e8	−0.485469
$118$	0	0
$119$	−1.59454e9	−0.728909
$120$	0	0
$121$	5.10770e9	2.16616
$122$	0	0
$123$	2.37189e9	0.934377
$124$	0	0
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	−1.73819e9	−0.592900	−0.296450	−	0.955048i	$-0.595803\pi$
$127$	−1.73819e9	−0.592900	−0.296450	+	0.955048i	$0.595803\pi$
$128$	0	0
$129$	−1.22855e8	−0.0390605
$130$	0	0
$131$	2.49730e9	0.740882	0.370441	−	0.928856i	$-0.379207\pi$
$131$	2.49730e9	0.740882	0.370441	+	0.928856i	$0.379207\pi$
$132$	0	0
$133$	−5.50106e9	−1.52445
$134$	0	0
$135$	−3.32151e8	−0.0860663
$136$	0	0
$137$	−7.96226e9	−1.93105	−0.965526	−	0.260306i	$-0.916177\pi$
$137$	−7.96226e9	−1.93105	−0.965526	+	0.260306i	$0.916177\pi$
$138$	0	0
$139$	2.85565e9	0.648842	0.324421	−	0.945913i	$-0.394831\pi$
$139$	2.85565e9	0.648842	0.324421	+	0.945913i	$0.394831\pi$
$140$	0	0
$141$	4.98759e7	0.0106269
$142$	0	0
$143$	−1.29587e10	−2.59149
$144$	0	0
$145$	−1.99650e9	−0.375071
$146$	0	0
$147$	−1.50893e9	−0.266527
$148$	0	0
$149$	−9.63383e9	−1.60126	−0.800628	−	0.599161i	$-0.795501\pi$
$149$	−9.63383e9	−1.60126	−0.800628	+	0.599161i	$0.795501\pi$
$150$	0	0
$151$	5.38292e9	0.842601	0.421300	−	0.906921i	$-0.361574\pi$
$151$	5.38292e9	0.842601	0.421300	+	0.906921i	$0.361574\pi$
$152$	0	0
$153$	−1.36221e9	−0.200970
$154$	0	0
$155$	1.46812e9	0.204301
$156$	0	0
$157$	5.19434e8	0.0682310	0.0341155	−	0.999418i	$-0.489139\pi$
$157$	5.19434e8	0.0682310	0.0341155	+	0.999418i	$0.489139\pi$
$158$	0	0
$159$	−3.84542e8	−0.0477152
$160$	0	0
$161$	−1.05210e10	−1.23407
$162$	0	0
$163$	−9.41239e9	−1.04437	−0.522187	−	0.852831i	$-0.674884\pi$
$163$	−9.41239e9	−1.04437	−0.522187	+	0.852831i	$0.674884\pi$
$164$	0	0
$165$	−4.37420e9	−0.459432
$166$	0	0
$167$	−9.37241e9	−0.932453	−0.466227	−	0.884665i	$-0.654387\pi$
$167$	−9.37241e9	−0.932453	−0.466227	+	0.884665i	$0.654387\pi$
$168$	0	0
$169$	1.18889e10	1.12112
$170$	0	0
$171$	−4.69954e9	−0.420313
$172$	0	0
$173$	1.23573e10	1.04886	0.524428	−	0.851455i	$-0.324279\pi$
$173$	1.23573e10	1.04886	0.524428	+	0.851455i	$0.324279\pi$
$174$	0	0
$175$	3.00000e9	0.241797
$176$	0	0
$177$	4.90990e9	0.376005
$178$	0	0
$179$	6.66040e8	0.0484910	0.0242455	−	0.999706i	$-0.492282\pi$
$179$	6.66040e8	0.0484910	0.0242455	+	0.999706i	$0.492282\pi$
$180$	0	0
$181$	5.27207e9	0.365113	0.182557	−	0.983195i	$-0.441563\pi$
$181$	5.27207e9	0.365113	0.182557	+	0.983195i	$0.441563\pi$
$182$	0	0
$183$	1.02664e10	0.676688
$184$	0	0
$185$	1.17098e10	0.734983
$186$	0	0
$187$	−1.79394e10	−1.07280
$188$	0	0
$189$	−4.08147e9	−0.232669
$190$	0	0
$191$	2.93896e10	1.59788	0.798939	−	0.601412i	$-0.205395\pi$
$191$	2.93896e10	1.59788	0.798939	+	0.601412i	$0.205395\pi$
$192$	0	0
$193$	−1.48746e10	−0.771681	−0.385841	−	0.922565i	$-0.626089\pi$
$193$	−1.48746e10	−0.771681	−0.385841	+	0.922565i	$0.626089\pi$
$194$	0	0
$195$	7.59264e9	0.376042
$196$	0	0
$197$	4.98675e9	0.235895	0.117948	−	0.993020i	$-0.462368\pi$
$197$	4.98675e9	0.235895	0.117948	+	0.993020i	$0.462368\pi$
$198$	0	0
$199$	−1.45527e10	−0.657816	−0.328908	−	0.944362i	$-0.606681\pi$
$199$	−1.45527e10	−0.657816	−0.328908	+	0.944362i	$0.606681\pi$
$200$	0	0
$201$	−9.00579e9	−0.389170
$202$	0	0
$203$	−2.45330e10	−1.01395
$204$	0	0
$205$	−1.83016e10	−0.723765
$206$	0	0
$207$	−8.98805e9	−0.340250
$208$	0	0
$209$	−6.18898e10	−2.24368
$210$	0	0
$211$	−5.15407e10	−1.79011	−0.895054	−	0.445959i	$-0.852863\pi$
$211$	−5.15407e10	−1.79011	−0.895054	+	0.445959i	$0.852863\pi$
$212$	0	0
$213$	−1.42197e10	−0.473349
$214$	0	0
$215$	9.47952e8	0.0302561
$216$	0	0
$217$	1.80403e10	0.552300
$218$	0	0
$219$	4.95990e9	0.145705
$220$	0	0
$221$	3.11387e10	0.878083
$222$	0	0
$223$	−4.61272e10	−1.24907	−0.624533	−	0.780998i	$-0.714711\pi$
$223$	−4.61272e10	−1.24907	−0.624533	+	0.780998i	$0.714711\pi$
$224$	0	0
$225$	2.56289e9	0.0666667
$226$	0	0
$227$	3.75833e10	0.939460	0.469730	−	0.882810i	$-0.344351\pi$
$227$	3.75833e10	0.939460	0.469730	+	0.882810i	$0.344351\pi$
$228$	0	0
$229$	−6.41082e10	−1.54047	−0.770236	−	0.637759i	$-0.779862\pi$
$229$	−6.41082e10	−1.54047	−0.770236	+	0.637759i	$0.779862\pi$
$230$	0	0
$231$	−5.37502e10	−1.24201
$232$	0	0
$233$	6.96578e10	1.54835	0.774174	−	0.632973i	$-0.218166\pi$
$233$	6.96578e10	1.54835	0.774174	+	0.632973i	$0.218166\pi$
$234$	0	0
$235$	−3.84845e8	−0.00823153
$236$	0	0
$237$	1.89889e10	0.390960
$238$	0	0
$239$	−6.65825e10	−1.31999	−0.659993	−	0.751272i	$-0.729441\pi$
$239$	−6.65825e10	−1.31999	−0.659993	+	0.751272i	$0.729441\pi$
$240$	0	0
$241$	−4.41659e10	−0.843354	−0.421677	−	0.906746i	$-0.638558\pi$
$241$	−4.41659e10	−0.843354	−0.421677	+	0.906746i	$0.638558\pi$
$242$	0	0
$243$	−3.48678e9	−0.0641500
$244$	0	0
$245$	1.16430e10	0.206451
$246$	0	0
$247$	1.07427e11	1.83644
$248$	0	0
$249$	9.63174e9	0.158784
$250$	0	0
$251$	−8.36236e10	−1.32983	−0.664916	−	0.746918i	$-0.731533\pi$
$251$	−8.36236e10	−1.32983	−0.664916	+	0.746918i	$0.731533\pi$
$252$	0	0
$253$	−1.18367e11	−1.81630
$254$	0	0
$255$	1.05109e10	0.155671
$256$	0	0
$257$	−8.65274e10	−1.23724	−0.618621	−	0.785690i	$-0.712308\pi$
$257$	−8.65274e10	−1.23724	−0.618621	+	0.785690i	$0.712308\pi$
$258$	0	0
$259$	1.43890e11	1.98693
$260$	0	0
$261$	−2.09585e10	−0.279561
$262$	0	0
$263$	9.61535e10	1.23927	0.619633	−	0.784892i	$-0.287282\pi$
$263$	9.61535e10	1.23927	0.619633	+	0.784892i	$0.287282\pi$
$264$	0	0
$265$	2.96714e9	0.0369600
$266$	0	0
$267$	2.56393e10	0.308749
$268$	0	0
$269$	−1.09505e10	−0.127511	−0.0637557	−	0.997966i	$-0.520308\pi$
$269$	−1.09505e10	−0.127511	−0.0637557	+	0.997966i	$0.520308\pi$
$270$	0	0
$271$	−7.80287e10	−0.878805	−0.439403	−	0.898290i	$-0.644810\pi$
$271$	−7.80287e10	−0.878805	−0.439403	+	0.898290i	$0.644810\pi$
$272$	0	0
$273$	9.32983e10	1.01658
$274$	0	0
$275$	3.37516e10	0.355874
$276$	0	0
$277$	6.56840e10	0.670349	0.335174	−	0.942156i	$-0.391205\pi$
$277$	6.56840e10	0.670349	0.335174	+	0.942156i	$0.391205\pi$
$278$	0	0
$279$	1.54118e10	0.152277
$280$	0	0
$281$	−6.44906e10	−0.617046	−0.308523	−	0.951217i	$-0.599835\pi$
$281$	−6.44906e10	−0.617046	−0.308523	+	0.951217i	$0.599835\pi$
$282$	0	0
$283$	−9.63133e10	−0.892580	−0.446290	−	0.894888i	$-0.647255\pi$
$283$	−9.63133e10	−0.892580	−0.446290	+	0.894888i	$0.647255\pi$
$284$	0	0
$285$	3.62619e10	0.325573
$286$	0	0
$287$	−2.24891e11	−1.95660
$288$	0	0
$289$	−7.54810e10	−0.636498
$290$	0	0
$291$	−1.96759e10	−0.160848
$292$	0	0
$293$	8.16308e10	0.647068	0.323534	−	0.946217i	$-0.395129\pi$
$293$	8.16308e10	0.647068	0.323534	+	0.946217i	$0.395129\pi$
$294$	0	0
$295$	−3.78850e10	−0.291252
$296$	0	0
$297$	−4.59186e10	−0.342440
$298$	0	0
$299$	2.05458e11	1.48663
$300$	0	0
$301$	1.16484e10	0.0817935
$302$	0	0
$303$	5.29580e10	0.360944
$304$	0	0
$305$	−7.92161e10	−0.524160
$306$	0	0
$307$	2.95582e10	0.189914	0.0949568	−	0.995481i	$-0.469729\pi$
$307$	2.95582e10	0.189914	0.0949568	+	0.995481i	$0.469729\pi$
$308$	0	0
$309$	1.13740e11	0.709744
$310$	0	0
$311$	3.99071e10	0.241896	0.120948	−	0.992659i	$-0.461407\pi$
$311$	3.99071e10	0.241896	0.120948	+	0.992659i	$0.461407\pi$
$312$	0	0
$313$	1.85371e11	1.09167	0.545836	−	0.837892i	$-0.316212\pi$
$313$	1.85371e11	1.09167	0.545836	+	0.837892i	$0.316212\pi$
$314$	0	0
$315$	3.14928e10	0.180224
$316$	0	0
$317$	2.68895e11	1.49560	0.747800	−	0.663924i	$-0.231110\pi$
$317$	2.68895e11	1.49560	0.747800	+	0.663924i	$0.231110\pi$
$318$	0	0
$319$	−2.76009e11	−1.49233
$320$	0	0
$321$	−1.48921e11	−0.782860
$322$	0	0
$323$	1.48716e11	0.760234
$324$	0	0
$325$	−5.85852e10	−0.291281
$326$	0	0
$327$	7.56096e10	0.365689
$328$	0	0
$329$	−4.72898e9	−0.0222528
$330$	0	0
$331$	4.29099e11	1.96486	0.982430	−	0.186629i	$-0.0597562\pi$
$331$	4.29099e11	1.96486	0.982430	+	0.186629i	$0.0597562\pi$
$332$	0	0
$333$	1.22925e11	0.547824
$334$	0	0
$335$	6.94892e10	0.301450
$336$	0	0
$337$	−2.02598e10	−0.0855657	−0.0427828	−	0.999084i	$-0.513622\pi$
$337$	−2.02598e10	−0.0855657	−0.0427828	+	0.999084i	$0.513622\pi$
$338$	0	0
$339$	7.52112e9	0.0309303
$340$	0	0
$341$	2.02963e11	0.812872
$342$	0	0
$343$	−1.66847e11	−0.650869
$344$	0	0
$345$	6.93522e10	0.263557
$346$	0	0
$347$	−2.92783e10	−0.108409	−0.0542043	−	0.998530i	$-0.517262\pi$
$347$	−2.92783e10	−0.108409	−0.0542043	+	0.998530i	$0.517262\pi$
$348$	0	0
$349$	7.05132e10	0.254423	0.127211	−	0.991876i	$-0.459397\pi$
$349$	7.05132e10	0.254423	0.127211	+	0.991876i	$0.459397\pi$
$350$	0	0
$351$	7.97045e10	0.280285
$352$	0	0
$353$	−6.57350e10	−0.225325	−0.112663	−	0.993633i	$-0.535938\pi$
$353$	−6.57350e10	−0.225325	−0.112663	+	0.993633i	$0.535938\pi$
$354$	0	0
$355$	1.09720e11	0.366655
$356$	0	0
$357$	1.29157e11	0.420836
$358$	0	0
$359$	−5.81702e11	−1.84831	−0.924157	−	0.382013i	$-0.875231\pi$
$359$	−5.81702e11	−1.84831	−0.924157	+	0.382013i	$0.875231\pi$
$360$	0	0
$361$	1.90375e11	0.589967
$362$	0	0
$363$	−4.13724e11	−1.25064
$364$	0	0
$365$	−3.82708e10	−0.112863
$366$	0	0
$367$	4.17070e11	1.20008	0.600042	−	0.799969i	$-0.295151\pi$
$367$	4.17070e11	1.20008	0.600042	+	0.799969i	$0.295151\pi$
$368$	0	0
$369$	−1.92123e11	−0.539463
$370$	0	0
$371$	3.64603e10	0.0999165
$372$	0	0
$373$	−7.60417e10	−0.203405	−0.101703	−	0.994815i	$-0.532429\pi$
$373$	−7.60417e10	−0.203405	−0.101703	+	0.994815i	$0.532429\pi$
$374$	0	0
$375$	−1.97754e10	−0.0516398
$376$	0	0
$377$	4.79090e11	1.22147
$378$	0	0
$379$	1.79180e11	0.446080	0.223040	−	0.974809i	$-0.428402\pi$
$379$	1.79180e11	0.446080	0.223040	+	0.974809i	$0.428402\pi$
$380$	0	0
$381$	1.40794e11	0.342311
$382$	0	0
$383$	7.95018e11	1.88792	0.943958	−	0.330066i	$-0.107071\pi$
$383$	7.95018e11	1.88792	0.943958	+	0.330066i	$0.107071\pi$
$384$	0	0
$385$	4.14739e11	0.962059
$386$	0	0
$387$	9.95123e9	0.0225516
$388$	0	0
$389$	−1.79533e11	−0.397532	−0.198766	−	0.980047i	$-0.563693\pi$
$389$	−1.79533e11	−0.397532	−0.198766	+	0.980047i	$0.563693\pi$
$390$	0	0
$391$	2.84426e11	0.615422
$392$	0	0
$393$	−2.02281e11	−0.427749
$394$	0	0
$395$	−1.46519e11	−0.302837
$396$	0	0
$397$	−3.43730e11	−0.694480	−0.347240	−	0.937776i	$-0.612881\pi$
$397$	−3.43730e11	−0.694480	−0.347240	+	0.937776i	$0.612881\pi$
$398$	0	0
$399$	4.45586e11	0.880143
$400$	0	0
$401$	7.72080e11	1.49112	0.745560	−	0.666438i	$-0.232182\pi$
$401$	7.72080e11	1.49112	0.745560	+	0.666438i	$0.232182\pi$
$402$	0	0
$403$	−3.52298e11	−0.665331
$404$	0	0
$405$	2.69042e10	0.0496904
$406$	0	0
$407$	1.61884e12	2.92435
$408$	0	0
$409$	2.60632e11	0.460546	0.230273	−	0.973126i	$-0.426038\pi$
$409$	2.60632e11	0.460546	0.230273	+	0.973126i	$0.426038\pi$
$410$	0	0
$411$	6.44943e11	1.11489
$412$	0	0
$413$	−4.65531e11	−0.787361
$414$	0	0
$415$	−7.43190e10	−0.122994
$416$	0	0
$417$	−2.31308e11	−0.374609
$418$	0	0
$419$	5.60166e11	0.887879	0.443939	−	0.896057i	$-0.353581\pi$
$419$	5.60166e11	0.887879	0.443939	+	0.896057i	$0.353581\pi$
$420$	0	0
$421$	1.68321e11	0.261137	0.130569	−	0.991439i	$-0.458320\pi$
$421$	1.68321e11	0.261137	0.130569	+	0.991439i	$0.458320\pi$
$422$	0	0
$423$	−4.03995e9	−0.00613542
$424$	0	0
$425$	−8.11023e10	−0.120582
$426$	0	0
$427$	−9.73407e11	−1.41700
$428$	0	0
$429$	1.04965e12	1.49620
$430$	0	0
$431$	−4.48383e11	−0.625895	−0.312948	−	0.949770i	$-0.601316\pi$
$431$	−4.48383e11	−0.625895	−0.312948	+	0.949770i	$0.601316\pi$
$432$	0	0
$433$	−1.08485e12	−1.48311	−0.741556	−	0.670891i	$-0.765912\pi$
$433$	−1.08485e12	−1.48311	−0.741556	+	0.670891i	$0.765912\pi$
$434$	0	0
$435$	1.61717e11	0.216547
$436$	0	0
$437$	9.81252e11	1.28711
$438$	0	0
$439$	−4.60548e11	−0.591814	−0.295907	−	0.955217i	$-0.595622\pi$
$439$	−4.60548e11	−0.591814	−0.295907	+	0.955217i	$0.595622\pi$
$440$	0	0
$441$	1.22224e11	0.153880
$442$	0	0
$443$	1.32095e10	0.0162956	0.00814779	−	0.999967i	$-0.497406\pi$
$443$	1.32095e10	0.0162956	0.00814779	+	0.999967i	$0.497406\pi$
$444$	0	0
$445$	−1.97834e11	−0.239156
$446$	0	0
$447$	7.80341e11	0.924486
$448$	0	0
$449$	−6.91889e11	−0.803393	−0.401696	−	0.915773i	$-0.631579\pi$
$449$	−6.91889e11	−0.803393	−0.401696	+	0.915773i	$0.631579\pi$
$450$	0	0
$451$	−2.53014e12	−2.87971
$452$	0	0
$453$	−4.36017e11	−0.486476
$454$	0	0
$455$	−7.19894e11	−0.787440
$456$	0	0
$457$	−3.73135e11	−0.400168	−0.200084	−	0.979779i	$-0.564122\pi$
$457$	−3.73135e11	−0.400168	−0.200084	+	0.979779i	$0.564122\pi$
$458$	0	0
$459$	1.10339e11	0.116030
$460$	0	0
$461$	−1.45940e12	−1.50494	−0.752470	−	0.658627i	$-0.771138\pi$
$461$	−1.45940e12	−1.50494	−0.752470	+	0.658627i	$0.771138\pi$
$462$	0	0
$463$	−1.34213e11	−0.135732	−0.0678658	−	0.997694i	$-0.521619\pi$
$463$	−1.34213e11	−0.135732	−0.0678658	+	0.997694i	$0.521619\pi$
$464$	0	0
$465$	−1.18918e11	−0.117953
$466$	0	0
$467$	3.64531e10	0.0354657	0.0177329	−	0.999843i	$-0.494355\pi$
$467$	3.64531e10	0.0354657	0.0177329	+	0.999843i	$0.494355\pi$
$468$	0	0
$469$	8.53883e11	0.814930
$470$	0	0
$471$	−4.20741e10	−0.0393932
$472$	0	0
$473$	1.31051e11	0.120383
$474$	0	0
$475$	−2.79798e11	−0.252188
$476$	0	0
$477$	3.11479e10	0.0275484
$478$	0	0
$479$	−8.82280e11	−0.765767	−0.382883	−	0.923797i	$-0.625069\pi$
$479$	−8.82280e11	−0.765767	−0.382883	+	0.923797i	$0.625069\pi$
$480$	0	0
$481$	−2.80994e12	−2.39356
$482$	0	0
$483$	8.52200e11	0.712491
$484$	0	0
$485$	1.51820e11	0.124592
$486$	0	0
$487$	−5.09840e11	−0.410727	−0.205364	−	0.978686i	$-0.565838\pi$
$487$	−5.09840e11	−0.410727	−0.205364	+	0.978686i	$0.565838\pi$
$488$	0	0
$489$	7.62404e11	0.602969
$490$	0	0
$491$	1.52131e12	1.18128	0.590638	−	0.806937i	$-0.298876\pi$
$491$	1.52131e12	1.18128	0.590638	+	0.806937i	$0.298876\pi$
$492$	0	0
$493$	6.63228e11	0.505652
$494$	0	0
$495$	3.54310e11	0.265253
$496$	0	0
$497$	1.34824e12	0.991202
$498$	0	0
$499$	−7.03413e11	−0.507876	−0.253938	−	0.967220i	$-0.581726\pi$
$499$	−7.03413e11	−0.507876	−0.253938	+	0.967220i	$0.581726\pi$
$500$	0	0
$501$	7.59165e11	0.538352
$502$	0	0
$503$	−3.78018e8	−0.000263304 0	−0.000131652	−	1.00000i	$-0.500042\pi$
$503$	−3.78018e8	−0.000263304 0	−0.000131652		1.00000i	$0.500042\pi$
$504$	0	0
$505$	−4.08627e11	−0.279586
$506$	0	0
$507$	−9.63001e11	−0.647278
$508$	0	0
$509$	1.32057e12	0.872027	0.436013	−	0.899940i	$-0.356390\pi$
$509$	1.32057e12	0.872027	0.436013	+	0.899940i	$0.356390\pi$
$510$	0	0
$511$	−4.70272e11	−0.305109
$512$	0	0
$513$	3.80663e11	0.242668
$514$	0	0
$515$	−8.77627e11	−0.549765
$516$	0	0
$517$	−5.32034e10	−0.0327516
$518$	0	0
$519$	−1.00094e12	−0.605558
$520$	0	0
$521$	−1.31853e12	−0.784009	−0.392005	−	0.919963i	$-0.628218\pi$
$521$	−1.31853e12	−0.784009	−0.392005	+	0.919963i	$0.628218\pi$
$522$	0	0
$523$	1.69211e12	0.988945	0.494472	−	0.869193i	$-0.335361\pi$
$523$	1.69211e12	0.988945	0.494472	+	0.869193i	$0.335361\pi$
$524$	0	0
$525$	−2.43000e11	−0.139601
$526$	0	0
$527$	−4.87704e11	−0.275428
$528$	0	0
$529$	7.55281e10	0.0419332
$530$	0	0
$531$	−3.97702e11	−0.217086
$532$	0	0
$533$	4.39175e12	2.35703
$534$	0	0
$535$	1.14908e12	0.606401
$536$	0	0
$537$	−5.39492e10	−0.0279963
$538$	0	0
$539$	1.60960e12	0.821427
$540$	0	0
$541$	−1.86369e12	−0.935373	−0.467687	−	0.883894i	$-0.654912\pi$
$541$	−1.86369e12	−0.935373	−0.467687	+	0.883894i	$0.654912\pi$
$542$	0	0
$543$	−4.27037e11	−0.210798
$544$	0	0
$545$	−5.83408e11	−0.283262
$546$	0	0
$547$	−4.37242e11	−0.208823	−0.104412	−	0.994534i	$-0.533296\pi$
$547$	−4.37242e11	−0.208823	−0.104412	+	0.994534i	$0.533296\pi$
$548$	0	0
$549$	−8.31578e11	−0.390686
$550$	0	0
$551$	2.28810e12	1.05753
$552$	0	0
$553$	−1.80043e12	−0.818679
$554$	0	0
$555$	−9.48495e11	−0.424343
$556$	0	0
$557$	−7.09146e11	−0.312167	−0.156084	−	0.987744i	$-0.549887\pi$
$557$	−7.09146e11	−0.312167	−0.156084	+	0.987744i	$0.549887\pi$
$558$	0	0
$559$	−2.27475e11	−0.0985328
$560$	0	0
$561$	1.45309e12	0.619383
$562$	0	0
$563$	−3.77472e10	−0.0158342	−0.00791711	−	0.999969i	$-0.502520\pi$
$563$	−3.77472e10	−0.0158342	−0.00791711	+	0.999969i	$0.502520\pi$
$564$	0	0
$565$	−5.80334e10	−0.0239585
$566$	0	0
$567$	3.30599e11	0.134331
$568$	0	0
$569$	−3.56270e11	−0.142487	−0.0712433	−	0.997459i	$-0.522697\pi$
$569$	−3.56270e11	−0.142487	−0.0712433	+	0.997459i	$0.522697\pi$
$570$	0	0
$571$	−3.87932e12	−1.52719	−0.763596	−	0.645694i	$-0.776568\pi$
$571$	−3.87932e12	−1.52719	−0.763596	+	0.645694i	$0.776568\pi$
$572$	0	0
$573$	−2.38056e12	−0.922535
$574$	0	0
$575$	−5.35125e11	−0.204150
$576$	0	0
$577$	−4.28876e12	−1.61080	−0.805399	−	0.592734i	$-0.798049\pi$
$577$	−4.28876e12	−1.61080	−0.805399	+	0.592734i	$0.798049\pi$
$578$	0	0
$579$	1.20484e12	0.445530
$580$	0	0
$581$	−9.13232e11	−0.332498
$582$	0	0
$583$	4.10197e11	0.147056
$584$	0	0
$585$	−6.15004e11	−0.217108
$586$	0	0
$587$	−4.43245e12	−1.54089	−0.770447	−	0.637504i	$-0.779967\pi$
$587$	−4.43245e12	−1.54089	−0.770447	+	0.637504i	$0.779967\pi$
$588$	0	0
$589$	−1.68255e12	−0.576036
$590$	0	0
$591$	−4.03927e11	−0.136194
$592$	0	0
$593$	−5.10104e12	−1.69400	−0.846998	−	0.531596i	$-0.821593\pi$
$593$	−5.10104e12	−1.69400	−0.846998	+	0.531596i	$0.821593\pi$
$594$	0	0
$595$	−9.96586e11	−0.325978
$596$	0	0
$597$	1.17877e12	0.379790
$598$	0	0
$599$	7.04599e11	0.223626	0.111813	−	0.993729i	$-0.464334\pi$
$599$	7.04599e11	0.223626	0.111813	+	0.993729i	$0.464334\pi$
$600$	0	0
$601$	−1.73879e12	−0.543641	−0.271821	−	0.962348i	$-0.587626\pi$
$601$	−1.73879e12	−0.543641	−0.271821	+	0.962348i	$0.587626\pi$
$602$	0	0
$603$	7.29469e11	0.224688
$604$	0	0
$605$	3.19231e12	0.968738
$606$	0	0
$607$	5.78292e11	0.172901	0.0864507	−	0.996256i	$-0.472447\pi$
$607$	5.78292e11	0.172901	0.0864507	+	0.996256i	$0.472447\pi$
$608$	0	0
$609$	1.98717e12	0.585407
$610$	0	0
$611$	9.23493e10	0.0268070
$612$	0	0
$613$	3.74595e12	1.07150	0.535748	−	0.844378i	$-0.320030\pi$
$613$	3.74595e12	1.07150	0.535748	+	0.844378i	$0.320030\pi$
$614$	0	0
$615$	1.48243e12	0.417866
$616$	0	0
$617$	−3.94875e12	−1.09692	−0.548461	−	0.836176i	$-0.684786\pi$
$617$	−3.94875e12	−1.09692	−0.548461	+	0.836176i	$0.684786\pi$
$618$	0	0
$619$	−3.42253e12	−0.937000	−0.468500	−	0.883463i	$-0.655205\pi$
$619$	−3.42253e12	−0.937000	−0.468500	+	0.883463i	$0.655205\pi$
$620$	0	0
$621$	7.28032e11	0.196444
$622$	0	0
$623$	−2.43098e12	−0.646526
$624$	0	0
$625$	1.52588e11	0.0400000
$626$	0	0
$627$	5.01307e12	1.29539
$628$	0	0
$629$	−3.88995e12	−0.990868
$630$	0	0
$631$	−5.84755e12	−1.46839	−0.734196	−	0.678938i	$-0.762440\pi$
$631$	−5.84755e12	−1.46839	−0.734196	+	0.678938i	$0.762440\pi$
$632$	0	0
$633$	4.17479e12	1.03352
$634$	0	0
$635$	−1.08637e12	−0.265153
$636$	0	0
$637$	−2.79391e12	−0.672334
$638$	0	0
$639$	1.15179e12	0.273288
$640$	0	0
$641$	2.66671e12	0.623899	0.311950	−	0.950099i	$-0.399018\pi$
$641$	2.66671e12	0.623899	0.311950	+	0.950099i	$0.399018\pi$
$642$	0	0
$643$	−9.68716e10	−0.0223484	−0.0111742	−	0.999938i	$-0.503557\pi$
$643$	−9.68716e10	−0.0223484	−0.0111742	+	0.999938i	$0.503557\pi$
$644$	0	0
$645$	−7.67842e10	−0.0174684
$646$	0	0
$647$	−4.47368e10	−0.0100368	−0.00501840	−	0.999987i	$-0.501597\pi$
$647$	−4.47368e10	−0.0100368	−0.00501840	+	0.999987i	$0.501597\pi$
$648$	0	0
$649$	−5.23747e12	−1.15883
$650$	0	0
$651$	−1.46127e12	−0.318871
$652$	0	0
$653$	4.95385e12	1.06619	0.533094	−	0.846056i	$-0.321029\pi$
$653$	4.95385e12	1.06619	0.533094	+	0.846056i	$0.321029\pi$
$654$	0	0
$655$	1.56081e12	0.331333
$656$	0	0
$657$	−4.01752e11	−0.0841228
$658$	0	0
$659$	5.85077e12	1.20845	0.604225	−	0.796814i	$-0.293483\pi$
$659$	5.85077e12	1.20845	0.604225	+	0.796814i	$0.293483\pi$
$660$	0	0
$661$	−8.81007e11	−0.179503	−0.0897517	−	0.995964i	$-0.528607\pi$
$661$	−8.81007e11	−0.179503	−0.0897517	+	0.995964i	$0.528607\pi$
$662$	0	0
$663$	−2.52224e12	−0.506962
$664$	0	0
$665$	−3.43816e12	−0.681756
$666$	0	0
$667$	4.37608e12	0.856088
$668$	0	0
$669$	3.73630e12	0.721149
$670$	0	0
$671$	−1.09513e13	−2.08553
$672$	0	0
$673$	−8.66521e12	−1.62821	−0.814107	−	0.580715i	$-0.802773\pi$
$673$	−8.66521e12	−1.62821	−0.814107	+	0.580715i	$0.802773\pi$
$674$	0	0
$675$	−2.07594e11	−0.0384900
$676$	0	0
$677$	8.98549e12	1.64397	0.821983	−	0.569512i	$-0.192868\pi$
$677$	8.98549e12	1.64397	0.821983	+	0.569512i	$0.192868\pi$
$678$	0	0
$679$	1.86557e12	0.336819
$680$	0	0
$681$	−3.04425e12	−0.542397
$682$	0	0
$683$	3.86477e12	0.679564	0.339782	−	0.940504i	$-0.389647\pi$
$683$	3.86477e12	0.679564	0.339782	+	0.940504i	$0.389647\pi$
$684$	0	0
$685$	−4.97642e12	−0.863593
$686$	0	0
$687$	5.19276e12	0.889392
$688$	0	0
$689$	−7.12010e11	−0.120365
$690$	0	0
$691$	7.08564e12	1.18230	0.591150	−	0.806561i	$-0.298674\pi$
$691$	7.08564e12	1.18230	0.591150	+	0.806561i	$0.298674\pi$
$692$	0	0
$693$	4.35377e12	0.717077
$694$	0	0
$695$	1.78478e12	0.290171
$696$	0	0
$697$	6.07972e12	0.975744
$698$	0	0
$699$	−5.64229e12	−0.893939
$700$	0	0
$701$	4.69380e12	0.734165	0.367083	−	0.930188i	$-0.380357\pi$
$701$	4.69380e12	0.734165	0.367083	+	0.930188i	$0.380357\pi$
$702$	0	0
$703$	−1.34201e13	−2.07232
$704$	0	0
$705$	3.11724e10	0.00475247
$706$	0	0
$707$	−5.02120e12	−0.755824
$708$	0	0
$709$	1.06645e13	1.58501	0.792503	−	0.609868i	$-0.208777\pi$
$709$	1.06645e13	1.58501	0.792503	+	0.609868i	$0.208777\pi$
$710$	0	0
$711$	−1.53810e12	−0.225721
$712$	0	0
$713$	−3.21794e12	−0.466311
$714$	0	0
$715$	−8.09919e12	−1.15895
$716$	0	0
$717$	5.39318e12	0.762095
$718$	0	0
$719$	8.15663e12	1.13823	0.569116	−	0.822257i	$-0.307285\pi$
$719$	8.15663e12	1.13823	0.569116	+	0.822257i	$0.307285\pi$
$720$	0	0
$721$	−1.07843e13	−1.48622
$722$	0	0
$723$	3.57743e12	0.486911
$724$	0	0
$725$	−1.24781e12	−0.167737
$726$	0	0
$727$	−6.64771e12	−0.882606	−0.441303	−	0.897358i	$-0.645484\pi$
$727$	−6.64771e12	−0.882606	−0.441303	+	0.897358i	$0.645484\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−3.14905e11	−0.0407898
$732$	0	0
$733$	7.07821e12	0.905640	0.452820	−	0.891602i	$-0.350418\pi$
$733$	7.07821e12	0.905640	0.452820	+	0.891602i	$0.350418\pi$
$734$	0	0
$735$	−9.43083e11	−0.119195
$736$	0	0
$737$	9.60663e12	1.19941
$738$	0	0
$739$	2.61052e12	0.321979	0.160989	−	0.986956i	$-0.448532\pi$
$739$	2.61052e12	0.321979	0.160989	+	0.986956i	$0.448532\pi$
$740$	0	0
$741$	−8.70157e12	−1.06027
$742$	0	0
$743$	1.41841e13	1.70747	0.853734	−	0.520709i	$-0.174333\pi$
$743$	1.41841e13	1.70747	0.853734	+	0.520709i	$0.174333\pi$
$744$	0	0
$745$	−6.02115e12	−0.716104
$746$	0	0
$747$	−7.80171e11	−0.0916742
$748$	0	0
$749$	1.41199e13	1.63932
$750$	0	0
$751$	−8.44355e11	−0.0968603	−0.0484301	−	0.998827i	$-0.515422\pi$
$751$	−8.44355e11	−0.0968603	−0.0484301	+	0.998827i	$0.515422\pi$
$752$	0	0
$753$	6.77351e12	0.767779
$754$	0	0
$755$	3.36433e12	0.376822
$756$	0	0
$757$	9.05305e12	1.00199	0.500995	−	0.865450i	$-0.332968\pi$
$757$	9.05305e12	1.00199	0.500995	+	0.865450i	$0.332968\pi$
$758$	0	0
$759$	9.58769e12	1.04864
$760$	0	0
$761$	−6.97701e12	−0.754116	−0.377058	−	0.926190i	$-0.623064\pi$
$761$	−6.97701e12	−0.754116	−0.377058	+	0.926190i	$0.623064\pi$
$762$	0	0
$763$	−7.16891e12	−0.765760
$764$	0	0
$765$	−8.51380e11	−0.0898767
$766$	0	0
$767$	9.09108e12	0.948498
$768$	0	0
$769$	−1.07233e13	−1.10576	−0.552879	−	0.833261i	$-0.686471\pi$
$769$	−1.07233e13	−1.10576	−0.552879	+	0.833261i	$0.686471\pi$
$770$	0	0
$771$	7.00872e12	0.714322
$772$	0	0
$773$	−1.37568e13	−1.38583	−0.692916	−	0.721019i	$-0.743674\pi$
$773$	−1.37568e13	−1.38583	−0.692916	+	0.721019i	$0.743674\pi$
$774$	0	0
$775$	9.17578e11	0.0913662
$776$	0	0
$777$	−1.16551e13	−1.14715
$778$	0	0
$779$	2.09747e13	2.04069
$780$	0	0
$781$	1.51684e13	1.45884
$782$	0	0
$783$	1.69764e12	0.161405
$784$	0	0
$785$	3.24646e11	0.0305138
$786$	0	0
$787$	1.27539e13	1.18510	0.592551	−	0.805533i	$-0.298121\pi$
$787$	1.27539e13	1.18510	0.592551	+	0.805533i	$0.298121\pi$
$788$	0	0
$789$	−7.78843e12	−0.715490
$790$	0	0
$791$	−7.13114e11	−0.0647686
$792$	0	0
$793$	1.90091e13	1.70699
$794$	0	0
$795$	−2.40339e11	−0.0213389
$796$	0	0
$797$	1.27845e13	1.12233	0.561164	−	0.827704i	$-0.310354\pi$
$797$	1.27845e13	1.12233	0.561164	+	0.827704i	$0.310354\pi$
$798$	0	0
$799$	1.27844e11	0.0110973
$800$	0	0
$801$	−2.07678e12	−0.178256
$802$	0	0
$803$	−5.29081e12	−0.449057
$804$	0	0
$805$	−6.57562e12	−0.551893
$806$	0	0
$807$	8.86992e11	0.0736188
$808$	0	0
$809$	6.03746e12	0.495548	0.247774	−	0.968818i	$-0.420301\pi$
$809$	6.03746e12	0.495548	0.247774	+	0.968818i	$0.420301\pi$
$810$	0	0
$811$	2.50043e12	0.202965	0.101482	−	0.994837i	$-0.467641\pi$
$811$	2.50043e12	0.202965	0.101482	+	0.994837i	$0.467641\pi$
$812$	0	0
$813$	6.32033e12	0.507379
$814$	0	0
$815$	−5.88275e12	−0.467058
$816$	0	0
$817$	−1.08641e12	−0.0853085
$818$	0	0
$819$	−7.55716e12	−0.586923
$820$	0	0
$821$	−4.21082e12	−0.323461	−0.161731	−	0.986835i	$-0.551708\pi$
$821$	−4.21082e12	−0.323461	−0.161731	+	0.986835i	$0.551708\pi$
$822$	0	0
$823$	−2.08206e11	−0.0158196	−0.00790978	−	0.999969i	$-0.502518\pi$
$823$	−2.08206e11	−0.0158196	−0.00790978	+	0.999969i	$0.502518\pi$
$824$	0	0
$825$	−2.73388e12	−0.205464
$826$	0	0
$827$	9.26106e12	0.688472	0.344236	−	0.938883i	$-0.388138\pi$
$827$	9.26106e12	0.688472	0.344236	+	0.938883i	$0.388138\pi$
$828$	0	0
$829$	2.42762e13	1.78519	0.892597	−	0.450856i	$-0.148881\pi$
$829$	2.42762e13	1.78519	0.892597	+	0.450856i	$0.148881\pi$
$830$	0	0
$831$	−5.32041e12	−0.387026
$832$	0	0
$833$	−3.86775e12	−0.278327
$834$	0	0
$835$	−5.85776e12	−0.417006
$836$	0	0
$837$	−1.24835e12	−0.0879171
$838$	0	0
$839$	1.25546e13	0.874728	0.437364	−	0.899285i	$-0.355912\pi$
$839$	1.25546e13	0.874728	0.437364	+	0.899285i	$0.355912\pi$
$840$	0	0
$841$	−4.30294e12	−0.296608
$842$	0	0
$843$	5.22374e12	0.356252
$844$	0	0
$845$	7.43056e12	0.501379
$846$	0	0
$847$	3.92272e13	2.61886
$848$	0	0
$849$	7.80137e12	0.515331
$850$	0	0
$851$	−2.56664e13	−1.67758
$852$	0	0
$853$	−1.36320e13	−0.881632	−0.440816	−	0.897597i	$-0.645311\pi$
$853$	−1.36320e13	−0.881632	−0.440816	+	0.897597i	$0.645311\pi$
$854$	0	0
$855$	−2.93721e12	−0.187970
$856$	0	0
$857$	1.73987e13	1.10180	0.550901	−	0.834570i	$-0.314284\pi$
$857$	1.73987e13	1.10180	0.550901	+	0.834570i	$0.314284\pi$
$858$	0	0
$859$	6.43355e10	0.00403163	0.00201582	−	0.999998i	$-0.499358\pi$
$859$	6.43355e10	0.00403163	0.00201582	+	0.999998i	$0.499358\pi$
$860$	0	0
$861$	1.82161e13	1.12965
$862$	0	0
$863$	−3.32120e12	−0.203820	−0.101910	−	0.994794i	$-0.532495\pi$
$863$	−3.32120e12	−0.203820	−0.101910	+	0.994794i	$0.532495\pi$
$864$	0	0
$865$	7.72331e12	0.469063
$866$	0	0
$867$	6.11396e12	0.367482
$868$	0	0
$869$	−2.02558e13	−1.20493
$870$	0	0
$871$	−1.66750e13	−0.981709
$872$	0	0
$873$	1.59375e12	0.0928657
$874$	0	0
$875$	1.87500e12	0.108135
$876$	0	0
$877$	1.95832e12	0.111786	0.0558928	−	0.998437i	$-0.482200\pi$
$877$	1.95832e12	0.111786	0.0558928	+	0.998437i	$0.482200\pi$
$878$	0	0
$879$	−6.61210e12	−0.373585
$880$	0	0
$881$	−3.02253e13	−1.69036	−0.845179	−	0.534483i	$-0.820506\pi$
$881$	−3.02253e13	−1.69036	−0.845179	+	0.534483i	$0.820506\pi$
$882$	0	0
$883$	9.30097e12	0.514879	0.257439	−	0.966294i	$-0.417121\pi$
$883$	9.30097e12	0.514879	0.257439	+	0.966294i	$0.417121\pi$
$884$	0	0
$885$	3.06869e12	0.168154
$886$	0	0
$887$	−9.27171e12	−0.502925	−0.251463	−	0.967867i	$-0.580912\pi$
$887$	−9.27171e12	−0.502925	−0.251463	+	0.967867i	$0.580912\pi$
$888$	0	0
$889$	−1.33493e13	−0.716805
$890$	0	0
$891$	3.71941e12	0.197708
$892$	0	0
$893$	4.41053e11	0.0232092
$894$	0	0
$895$	4.16275e11	0.0216859
$896$	0	0
$897$	−1.66421e13	−0.858305
$898$	0	0
$899$	−7.50365e12	−0.383137
$900$	0	0
$901$	−9.85671e11	−0.0498276
$902$	0	0
$903$	−9.43524e11	−0.0472235
$904$	0	0
$905$	3.29504e12	0.163284
$906$	0	0
$907$	−1.32868e12	−0.0651908	−0.0325954	−	0.999469i	$-0.510377\pi$
$907$	−1.32868e12	−0.0651908	−0.0325954	+	0.999469i	$0.510377\pi$
$908$	0	0
$909$	−4.28960e12	−0.208391
$910$	0	0
$911$	−2.71297e12	−0.130501	−0.0652503	−	0.997869i	$-0.520785\pi$
$911$	−2.71297e12	−0.130501	−0.0652503	+	0.997869i	$0.520785\pi$
$912$	0	0
$913$	−1.02743e13	−0.489368
$914$	0	0
$915$	6.41650e12	0.302624
$916$	0	0
$917$	1.91792e13	0.895714
$918$	0	0
$919$	−1.32139e12	−0.0611100	−0.0305550	−	0.999533i	$-0.509727\pi$
$919$	−1.32139e12	−0.0611100	−0.0305550	+	0.999533i	$0.509727\pi$
$920$	0	0
$921$	−2.39422e12	−0.109647
$922$	0	0
$923$	−2.63289e13	−1.19406
$924$	0	0
$925$	7.31864e12	0.328694
$926$	0	0
$927$	−9.21297e12	−0.409771
$928$	0	0
$929$	1.16124e12	0.0511507	0.0255754	−	0.999673i	$-0.491858\pi$
$929$	1.16124e12	0.0511507	0.0255754	+	0.999673i	$0.491858\pi$
$930$	0	0
$931$	−1.33435e13	−0.582098
$932$	0	0
$933$	−3.23247e12	−0.139659
$934$	0	0
$935$	−1.12121e13	−0.479772
$936$	0	0
$937$	3.40914e13	1.44483	0.722415	−	0.691460i	$-0.243032\pi$
$937$	3.40914e13	1.44483	0.722415	+	0.691460i	$0.243032\pi$
$938$	0	0
$939$	−1.50151e13	−0.630277
$940$	0	0
$941$	−1.60215e12	−0.0666114	−0.0333057	−	0.999445i	$-0.510603\pi$
$941$	−1.60215e12	−0.0666114	−0.0333057	+	0.999445i	$0.510603\pi$
$942$	0	0
$943$	4.01149e13	1.65197
$944$	0	0
$945$	−2.55092e12	−0.104053
$946$	0	0
$947$	3.38850e13	1.36909	0.684546	−	0.728969i	$-0.260000\pi$
$947$	3.38850e13	1.36909	0.684546	+	0.728969i	$0.260000\pi$
$948$	0	0
$949$	9.18366e12	0.367551
$950$	0	0
$951$	−2.17805e13	−0.863485
$952$	0	0
$953$	2.15757e13	0.847320	0.423660	−	0.905821i	$-0.360745\pi$
$953$	2.15757e13	0.847320	0.423660	+	0.905821i	$0.360745\pi$
$954$	0	0
$955$	1.83685e13	0.714592
$956$	0	0
$957$	2.23567e13	0.861598
$958$	0	0
$959$	−6.11502e13	−2.33461
$960$	0	0
$961$	−2.09218e13	−0.791306
$962$	0	0
$963$	1.20626e13	0.451985
$964$	0	0
$965$	−9.29664e12	−0.345106
$966$	0	0
$967$	−3.06249e13	−1.12630	−0.563152	−	0.826353i	$-0.690411\pi$
$967$	−3.06249e13	−1.12630	−0.563152	+	0.826353i	$0.690411\pi$
$968$	0	0
$969$	−1.20460e13	−0.438921
$970$	0	0
$971$	−1.92365e12	−0.0694447	−0.0347224	−	0.999397i	$-0.511055\pi$
$971$	−1.92365e12	−0.0694447	−0.0347224	+	0.999397i	$0.511055\pi$
$972$	0	0
$973$	2.19314e13	0.784438
$974$	0	0
$975$	4.74540e12	0.168171
$976$	0	0
$977$	−1.83893e13	−0.645714	−0.322857	−	0.946448i	$-0.604643\pi$
$977$	−1.83893e13	−0.645714	−0.322857	+	0.946448i	$0.604643\pi$
$978$	0	0
$979$	−2.73498e13	−0.951552
$980$	0	0
$981$	−6.12438e12	−0.211131
$982$	0	0
$983$	4.63273e13	1.58251	0.791254	−	0.611488i	$-0.209429\pi$
$983$	4.63273e13	1.58251	0.791254	+	0.611488i	$0.209429\pi$
$984$	0	0
$985$	3.11672e12	0.105496
$986$	0	0
$987$	3.83047e11	0.0128477
$988$	0	0
$989$	−2.07779e12	−0.0690587
$990$	0	0
$991$	−2.76252e12	−0.0909857	−0.0454929	−	0.998965i	$-0.514486\pi$
$991$	−2.76252e12	−0.0909857	−0.0454929	+	0.998965i	$0.514486\pi$
$992$	0	0
$993$	−3.47570e13	−1.13441
$994$	0	0
$995$	−9.09544e12	−0.294184
$996$	0	0
$997$	−1.74502e13	−0.559337	−0.279668	−	0.960097i	$-0.590224\pi$
$997$	−1.74502e13	−0.559337	−0.279668	+	0.960097i	$0.590224\pi$
$998$	0	0
$999$	−9.95692e12	−0.316286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.10.a.c.1.1		1
4.3	odd	2		15.10.a.a.1.1	✓	1
12.11	even	2		45.10.a.b.1.1		1
20.3	even	4		75.10.b.d.49.2		2
20.7	even	4		75.10.b.d.49.1		2
20.19	odd	2		75.10.a.c.1.1		1
60.23	odd	4		225.10.b.e.199.1		2
60.47	odd	4		225.10.b.e.199.2		2
60.59	even	2		225.10.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.a.1.1	✓	1	4.3	odd	2
45.10.a.b.1.1		1	12.11	even	2
75.10.a.c.1.1		1	20.19	odd	2
75.10.b.d.49.1		2	20.7	even	4
75.10.b.d.49.2		2	20.3	even	4
225.10.a.c.1.1		1	60.59	even	2
225.10.b.e.199.1		2	60.23	odd	4
225.10.b.e.199.2		2	60.47	odd	4
240.10.a.c.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	240.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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