LMFDB - Embedded newform 3525.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} -4.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} -4.00000 q^{7} +1.00000 q^{9} -2.00000 q^{12} -5.00000 q^{13} +8.00000 q^{14} -4.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} -2.00000 q^{19} +4.00000 q^{21} -1.00000 q^{23} +10.0000 q^{26} -1.00000 q^{27} -8.00000 q^{28} -6.00000 q^{29} -8.00000 q^{31} +8.00000 q^{32} +12.0000 q^{34} +2.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} +5.00000 q^{39} -2.00000 q^{41} -8.00000 q^{42} +5.00000 q^{43} +2.00000 q^{46} -1.00000 q^{47} +4.00000 q^{48} +9.00000 q^{49} +6.00000 q^{51} -10.0000 q^{52} -12.0000 q^{53} +2.00000 q^{54} +2.00000 q^{57} +12.0000 q^{58} -3.00000 q^{59} -1.00000 q^{61} +16.0000 q^{62} -4.00000 q^{63} -8.00000 q^{64} -8.00000 q^{67} -12.0000 q^{68} +1.00000 q^{69} +1.00000 q^{71} +13.0000 q^{73} +4.00000 q^{74} -4.00000 q^{76} -10.0000 q^{78} -1.00000 q^{79} +1.00000 q^{81} +4.00000 q^{82} -12.0000 q^{83} +8.00000 q^{84} -10.0000 q^{86} +6.00000 q^{87} -15.0000 q^{89} +20.0000 q^{91} -2.00000 q^{92} +8.00000 q^{93} +2.00000 q^{94} -8.00000 q^{96} +8.00000 q^{97} -18.0000 q^{98} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−2.00000	−0.577350
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	8.00000	2.13809
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−2.00000	−0.471405
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	0	0
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	0	0
$26$	10.0000	1.96116
$27$	−1.00000	−0.192450
$28$	−8.00000	−1.51186
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	8.00000	1.41421
$33$	0	0
$34$	12.0000	2.05798
$35$	0	0
$36$	2.00000	0.333333
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	4.00000	0.648886
$39$	5.00000	0.800641
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−8.00000	−1.23443
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	0	0
$45$	0	0
$46$	2.00000	0.294884
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	4.00000	0.577350
$49$	9.00000	1.28571
$50$	0	0
$51$	6.00000	0.840168
$52$	−10.0000	−1.38675
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	2.00000	0.272166
$55$	0	0
$56$	0	0
$57$	2.00000	0.264906
$58$	12.0000	1.57568
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	16.0000	2.03200
$63$	−4.00000	−0.503953
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−12.0000	−1.45521
$69$	1.00000	0.120386
$70$	0	0
$71$	1.00000	0.118678	0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000	0.118678	0.0593391	+	0.998238i	$0.481101\pi$
$72$	0	0
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	−4.00000	−0.458831
$77$	0	0
$78$	−10.0000	−1.13228
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	4.00000	0.441726
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	8.00000	0.872872
$85$	0	0
$86$	−10.0000	−1.07833
$87$	6.00000	0.643268
$88$	0	0
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	20.0000	2.09657
$92$	−2.00000	−0.208514
$93$	8.00000	0.829561
$94$	2.00000	0.206284
$95$	0	0
$96$	−8.00000	−0.816497
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−18.0000	−1.81827
$99$	0	0
$100$	0	0
$101$	13.0000	1.29355	0.646774	−	0.762682i	$-0.276118\pi$
$101$	13.0000	1.29355	0.646774	+	0.762682i	$0.276118\pi$
$102$	−12.0000	−1.18818
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	0	0
$105$	0	0
$106$	24.0000	2.33109
$107$	−9.00000	−0.870063	−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000	−0.870063	−0.435031	+	0.900415i	$0.643263\pi$
$108$	−2.00000	−0.192450
$109$	−8.00000	−0.766261	−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000	−0.766261	−0.383131	+	0.923694i	$0.625154\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	16.0000	1.51186
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	−12.0000	−1.11417
$117$	−5.00000	−0.462250
$118$	6.00000	0.552345
$119$	24.0000	2.20008
$120$	0	0
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	2.00000	0.180334
$124$	−16.0000	−1.43684
$125$	0	0
$126$	8.00000	0.712697
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	0	0
$129$	−5.00000	−0.440225
$130$	0	0
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	0	0
$133$	8.00000	0.693688
$134$	16.0000	1.38219
$135$	0	0
$136$	0	0
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	−2.00000	−0.170251
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−2.00000	−0.167836
$143$	0	0
$144$	−4.00000	−0.333333
$145$	0	0
$146$	−26.0000	−2.15178
$147$	−9.00000	−0.742307
$148$	−4.00000	−0.328798
$149$	−23.0000	−1.88423	−0.942117	−	0.335285i	$-0.891167\pi$
$149$	−23.0000	−1.88423	−0.942117	+	0.335285i	$0.891167\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	10.0000	0.800641
$157$	20.0000	1.59617	0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000	1.59617	0.798087	+	0.602542i	$0.205846\pi$
$158$	2.00000	0.159111
$159$	12.0000	0.951662
$160$	0	0
$161$	4.00000	0.315244
$162$	−2.00000	−0.157135
$163$	19.0000	1.48819	0.744097	−	0.668071i	$-0.232880\pi$
$163$	19.0000	1.48819	0.744097	+	0.668071i	$0.232880\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	24.0000	1.86276
$167$	−19.0000	−1.47026	−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000	−1.47026	−0.735132	+	0.677924i	$0.762880\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	−2.00000	−0.152944
$172$	10.0000	0.762493
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−12.0000	−0.909718
$175$	0	0
$176$	0	0
$177$	3.00000	0.225494
$178$	30.0000	2.24860
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	−40.0000	−2.96500
$183$	1.00000	0.0739221
$184$	0	0
$185$	0	0
$186$	−16.0000	−1.17318
$187$	0	0
$188$	−2.00000	−0.145865
$189$	4.00000	0.290957
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	8.00000	0.577350
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−16.0000	−1.14873
$195$	0	0
$196$	18.0000	1.28571
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	−26.0000	−1.82935
$203$	24.0000	1.68447
$204$	12.0000	0.840168
$205$	0	0
$206$	32.0000	2.22955
$207$	−1.00000	−0.0695048
$208$	20.0000	1.38675
$209$	0	0
$210$	0	0
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	−24.0000	−1.64833
$213$	−1.00000	−0.0685189
$214$	18.0000	1.23045
$215$	0	0
$216$	0	0
$217$	32.0000	2.17230
$218$	16.0000	1.08366
$219$	−13.0000	−0.878459
$220$	0	0
$221$	30.0000	2.01802
$222$	−4.00000	−0.268462
$223$	−7.00000	−0.468755	−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000	−0.468755	−0.234377	+	0.972146i	$0.575305\pi$
$224$	−32.0000	−2.13809
$225$	0	0
$226$	30.0000	1.99557
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	4.00000	0.264906
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	10.0000	0.653720
$235$	0	0
$236$	−6.00000	−0.390567
$237$	1.00000	0.0649570
$238$	−48.0000	−3.11138
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	7.00000	0.450910	0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000	0.450910	0.225455	+	0.974254i	$0.427613\pi$
$242$	22.0000	1.41421
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−4.00000	−0.255031
$247$	10.0000	0.636285
$248$	0	0
$249$	12.0000	0.760469
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−8.00000	−0.503953
$253$	0	0
$254$	−16.0000	−1.00393
$255$	0	0
$256$	16.0000	1.00000
$257$	23.0000	1.43470	0.717350	−	0.696713i	$-0.245355\pi$
$257$	23.0000	1.43470	0.717350	+	0.696713i	$0.245355\pi$
$258$	10.0000	0.622573
$259$	8.00000	0.497096
$260$	0	0
$261$	−6.00000	−0.371391
$262$	−30.0000	−1.85341
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	0	0
$266$	−16.0000	−0.981023
$267$	15.0000	0.917985
$268$	−16.0000	−0.977356
$269$	−17.0000	−1.03651	−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000	−1.03651	−0.518254	+	0.855227i	$0.673418\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	24.0000	1.45521
$273$	−20.0000	−1.21046
$274$	6.00000	0.362473
$275$	0	0
$276$	2.00000	0.120386
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−2.00000	−0.119098
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	0	0
$287$	8.00000	0.472225
$288$	8.00000	0.471405
$289$	19.0000	1.11765
$290$	0	0
$291$	−8.00000	−0.468968
$292$	26.0000	1.52153
$293$	17.0000	0.993151	0.496575	−	0.867994i	$-0.334591\pi$
$293$	17.0000	0.993151	0.496575	+	0.867994i	$0.334591\pi$
$294$	18.0000	1.04978
$295$	0	0
$296$	0	0
$297$	0	0
$298$	46.0000	2.66471
$299$	5.00000	0.289157
$300$	0	0
$301$	−20.0000	−1.15278
$302$	−8.00000	−0.460348
$303$	−13.0000	−0.746830
$304$	8.00000	0.458831
$305$	0	0
$306$	12.0000	0.685994
$307$	26.0000	1.48390	0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000	1.48390	0.741949	+	0.670456i	$0.233902\pi$
$308$	0	0
$309$	16.0000	0.910208
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−40.0000	−2.25733
$315$	0	0
$316$	−2.00000	−0.112509
$317$	−31.0000	−1.74113	−0.870567	−	0.492050i	$-0.836248\pi$
$317$	−31.0000	−1.74113	−0.870567	+	0.492050i	$0.836248\pi$
$318$	−24.0000	−1.34585
$319$	0	0
$320$	0	0
$321$	9.00000	0.502331
$322$	−8.00000	−0.445823
$323$	12.0000	0.667698
$324$	2.00000	0.111111
$325$	0	0
$326$	−38.0000	−2.10463
$327$	8.00000	0.442401
$328$	0	0
$329$	4.00000	0.220527
$330$	0	0
$331$	3.00000	0.164895	0.0824475	−	0.996595i	$-0.473726\pi$
$331$	3.00000	0.164895	0.0824475	+	0.996595i	$0.473726\pi$
$332$	−24.0000	−1.31717
$333$	−2.00000	−0.109599
$334$	38.0000	2.07927
$335$	0	0
$336$	−16.0000	−0.872872
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−24.0000	−1.30543
$339$	15.0000	0.814688
$340$	0	0
$341$	0	0
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	0	0
$345$	0	0
$346$	4.00000	0.215041
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	12.0000	0.643268
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	0	0
$353$	−16.0000	−0.851594	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−16.0000	−0.851594	−0.425797	+	0.904819i	$0.640006\pi$
$354$	−6.00000	−0.318896
$355$	0	0
$356$	−30.0000	−1.59000
$357$	−24.0000	−1.27021
$358$	0	0
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	16.0000	0.840941
$363$	11.0000	0.577350
$364$	40.0000	2.09657
$365$	0	0
$366$	−2.00000	−0.104542
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	4.00000	0.208514
$369$	−2.00000	−0.104116
$370$	0	0
$371$	48.0000	2.49204
$372$	16.0000	0.829561
$373$	−33.0000	−1.70868	−0.854338	−	0.519718i	$-0.826037\pi$
$373$	−33.0000	−1.70868	−0.854338	+	0.519718i	$0.826037\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	30.0000	1.54508
$378$	−8.00000	−0.411476
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	18.0000	0.920960
$383$	10.0000	0.510976	0.255488	−	0.966812i	$-0.417764\pi$
$383$	10.0000	0.510976	0.255488	+	0.966812i	$0.417764\pi$
$384$	0	0
$385$	0	0
$386$	20.0000	1.01797
$387$	5.00000	0.254164
$388$	16.0000	0.812277
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	0	0
$393$	−15.0000	−0.756650
$394$	−24.0000	−1.20910
$395$	0	0
$396$	0	0
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	32.0000	1.60402
$399$	−8.00000	−0.400501
$400$	0	0
$401$	−13.0000	−0.649189	−0.324595	−	0.945853i	$-0.605228\pi$
$401$	−13.0000	−0.649189	−0.324595	+	0.945853i	$0.605228\pi$
$402$	−16.0000	−0.798007
$403$	40.0000	1.99254
$404$	26.0000	1.29355
$405$	0	0
$406$	−48.0000	−2.38220
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	3.00000	0.147979
$412$	−32.0000	−1.57653
$413$	12.0000	0.590481
$414$	2.00000	0.0982946
$415$	0	0
$416$	−40.0000	−1.96116
$417$	0	0
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	4.00000	0.194948	0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000	0.194948	0.0974740	+	0.995238i	$0.468924\pi$
$422$	36.0000	1.75245
$423$	−1.00000	−0.0486217
$424$	0	0
$425$	0	0
$426$	2.00000	0.0969003
$427$	4.00000	0.193574
$428$	−18.0000	−0.870063
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	4.00000	0.192450
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−64.0000	−3.07210
$435$	0	0
$436$	−16.0000	−0.766261
$437$	2.00000	0.0956730
$438$	26.0000	1.24233
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	−60.0000	−2.85391
$443$	20.0000	0.950229	0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000	0.950229	0.475114	+	0.879924i	$0.342407\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	14.0000	0.662919
$447$	23.0000	1.08786
$448$	32.0000	1.51186
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	0	0
$452$	−30.0000	−1.41108
$453$	−4.00000	−0.187936
$454$	−40.0000	−1.87729
$455$	0	0
$456$	0	0
$457$	24.0000	1.12267	0.561336	−	0.827588i	$-0.310287\pi$
$457$	24.0000	1.12267	0.561336	+	0.827588i	$0.310287\pi$
$458$	20.0000	0.934539
$459$	6.00000	0.280056
$460$	0	0
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	19.0000	0.883005	0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000	0.883005	0.441502	+	0.897260i	$0.354446\pi$
$464$	24.0000	1.11417
$465$	0	0
$466$	52.0000	2.40885
$467$	35.0000	1.61961	0.809803	−	0.586701i	$-0.199574\pi$
$467$	35.0000	1.61961	0.809803	+	0.586701i	$0.199574\pi$
$468$	−10.0000	−0.462250
$469$	32.0000	1.47762
$470$	0	0
$471$	−20.0000	−0.921551
$472$	0	0
$473$	0	0
$474$	−2.00000	−0.0918630
$475$	0	0
$476$	48.0000	2.20008
$477$	−12.0000	−0.549442
$478$	0	0
$479$	27.0000	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	−14.0000	−0.637683
$483$	−4.00000	−0.182006
$484$	−22.0000	−1.00000
$485$	0	0
$486$	2.00000	0.0907218
$487$	−42.0000	−1.90320	−0.951601	−	0.307337i	$-0.900562\pi$
$487$	−42.0000	−1.90320	−0.951601	+	0.307337i	$0.900562\pi$
$488$	0	0
$489$	−19.0000	−0.859210
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	4.00000	0.180334
$493$	36.0000	1.62136
$494$	−20.0000	−0.899843
$495$	0	0
$496$	32.0000	1.43684
$497$	−4.00000	−0.179425
$498$	−24.0000	−1.07547
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	0	0
$501$	19.0000	0.848857
$502$	24.0000	1.07117
$503$	44.0000	1.96186	0.980932	−	0.194354i	$-0.0622609\pi$
$503$	44.0000	1.96186	0.980932	+	0.194354i	$0.0622609\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−12.0000	−0.532939
$508$	16.0000	0.709885
$509$	−44.0000	−1.95027	−0.975133	−	0.221621i	$-0.928865\pi$
$509$	−44.0000	−1.95027	−0.975133	+	0.221621i	$0.928865\pi$
$510$	0	0
$511$	−52.0000	−2.30034
$512$	−32.0000	−1.41421
$513$	2.00000	0.0883022
$514$	−46.0000	−2.02897
$515$	0	0
$516$	−10.0000	−0.440225
$517$	0	0
$518$	−16.0000	−0.703000
$519$	2.00000	0.0877903
$520$	0	0
$521$	11.0000	0.481919	0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000	0.481919	0.240959	+	0.970535i	$0.422538\pi$
$522$	12.0000	0.525226
$523$	−22.0000	−0.961993	−0.480996	−	0.876723i	$-0.659725\pi$
$523$	−22.0000	−0.961993	−0.480996	+	0.876723i	$0.659725\pi$
$524$	30.0000	1.31056
$525$	0	0
$526$	−48.0000	−2.09290
$527$	48.0000	2.09091
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	−3.00000	−0.130189
$532$	16.0000	0.693688
$533$	10.0000	0.433148
$534$	−30.0000	−1.29823
$535$	0	0
$536$	0	0
$537$	0	0
$538$	34.0000	1.46584
$539$	0	0
$540$	0	0
$541$	−25.0000	−1.07483	−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000	−1.07483	−0.537417	+	0.843317i	$0.680600\pi$
$542$	−32.0000	−1.37452
$543$	8.00000	0.343313
$544$	−48.0000	−2.05798
$545$	0	0
$546$	40.0000	1.71184
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−6.00000	−0.256307
$549$	−1.00000	−0.0426790
$550$	0	0
$551$	12.0000	0.511217
$552$	0	0
$553$	4.00000	0.170097
$554$	−12.0000	−0.509831
$555$	0	0
$556$	0	0
$557$	−33.0000	−1.39825	−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000	−1.39825	−0.699127	+	0.714997i	$0.746428\pi$
$558$	16.0000	0.677334
$559$	−25.0000	−1.05739
$560$	0	0
$561$	0	0
$562$	12.0000	0.506189
$563$	−15.0000	−0.632175	−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000	−0.632175	−0.316087	+	0.948730i	$0.602369\pi$
$564$	2.00000	0.0842152
$565$	0	0
$566$	−16.0000	−0.672530
$567$	−4.00000	−0.167984
$568$	0	0
$569$	−16.0000	−0.670755	−0.335377	−	0.942084i	$-0.608864\pi$
$569$	−16.0000	−0.670755	−0.335377	+	0.942084i	$0.608864\pi$
$570$	0	0
$571$	−33.0000	−1.38101	−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000	−1.38101	−0.690504	+	0.723329i	$0.742611\pi$
$572$	0	0
$573$	9.00000	0.375980
$574$	−16.0000	−0.667827
$575$	0	0
$576$	−8.00000	−0.333333
$577$	−11.0000	−0.457936	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000	−0.457936	−0.228968	+	0.973434i	$0.573535\pi$
$578$	−38.0000	−1.58059
$579$	10.0000	0.415586
$580$	0	0
$581$	48.0000	1.99138
$582$	16.0000	0.663221
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−34.0000	−1.40453
$587$	−27.0000	−1.11441	−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000	−1.11441	−0.557205	+	0.830375i	$0.688126\pi$
$588$	−18.0000	−0.742307
$589$	16.0000	0.659269
$590$	0	0
$591$	−12.0000	−0.493614
$592$	8.00000	0.328798
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	0	0
$596$	−46.0000	−1.88423
$597$	16.0000	0.654836
$598$	−10.0000	−0.408930
$599$	−10.0000	−0.408589	−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000	−0.408589	−0.204294	+	0.978909i	$0.565490\pi$
$600$	0	0
$601$	−35.0000	−1.42768	−0.713840	−	0.700309i	$-0.753046\pi$
$601$	−35.0000	−1.42768	−0.713840	+	0.700309i	$0.753046\pi$
$602$	40.0000	1.63028
$603$	−8.00000	−0.325785
$604$	8.00000	0.325515
$605$	0	0
$606$	26.0000	1.05618
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	−16.0000	−0.648886
$609$	−24.0000	−0.972529
$610$	0	0
$611$	5.00000	0.202278
$612$	−12.0000	−0.485071
$613$	−42.0000	−1.69636	−0.848182	−	0.529705i	$-0.822303\pi$
$613$	−42.0000	−1.69636	−0.848182	+	0.529705i	$0.822303\pi$
$614$	−52.0000	−2.09855
$615$	0	0
$616$	0	0
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	−32.0000	−1.28723
$619$	−1.00000	−0.0401934	−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000	−0.0401934	−0.0200967	+	0.999798i	$0.506397\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	12.0000	0.481156
$623$	60.0000	2.40385
$624$	−20.0000	−0.800641
$625$	0	0
$626$	−52.0000	−2.07834
$627$	0	0
$628$	40.0000	1.59617
$629$	12.0000	0.478471
$630$	0	0
$631$	10.0000	0.398094	0.199047	−	0.979990i	$-0.436215\pi$
$631$	10.0000	0.398094	0.199047	+	0.979990i	$0.436215\pi$
$632$	0	0
$633$	18.0000	0.715436
$634$	62.0000	2.46233
$635$	0	0
$636$	24.0000	0.951662
$637$	−45.0000	−1.78296
$638$	0	0
$639$	1.00000	0.0395594
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	−18.0000	−0.710403
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−30.0000	−1.17942	−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000	−1.17942	−0.589711	+	0.807614i	$0.700758\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−32.0000	−1.25418
$652$	38.0000	1.48819
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	−16.0000	−0.625650
$655$	0	0
$656$	8.00000	0.312348
$657$	13.0000	0.507178
$658$	−8.00000	−0.311872
$659$	−43.0000	−1.67504	−0.837521	−	0.546405i	$-0.815996\pi$
$659$	−43.0000	−1.67504	−0.837521	+	0.546405i	$0.815996\pi$
$660$	0	0
$661$	−31.0000	−1.20576	−0.602880	−	0.797832i	$-0.705980\pi$
$661$	−31.0000	−1.20576	−0.602880	+	0.797832i	$0.705980\pi$
$662$	−6.00000	−0.233197
$663$	−30.0000	−1.16510
$664$	0	0
$665$	0	0
$666$	4.00000	0.154997
$667$	6.00000	0.232321
$668$	−38.0000	−1.47026
$669$	7.00000	0.270636
$670$	0	0
$671$	0	0
$672$	32.0000	1.23443
$673$	−41.0000	−1.58043	−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000	−1.58043	−0.790217	+	0.612827i	$0.790032\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	24.0000	0.923077
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	−30.0000	−1.15214
$679$	−32.0000	−1.22805
$680$	0	0
$681$	−20.0000	−0.766402
$682$	0	0
$683$	−22.0000	−0.841807	−0.420903	−	0.907106i	$-0.638287\pi$
$683$	−22.0000	−0.841807	−0.420903	+	0.907106i	$0.638287\pi$
$684$	−4.00000	−0.152944
$685$	0	0
$686$	16.0000	0.610883
$687$	10.0000	0.381524
$688$	−20.0000	−0.762493
$689$	60.0000	2.28582
$690$	0	0
$691$	18.0000	0.684752	0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000	0.684752	0.342376	+	0.939563i	$0.388768\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	36.0000	1.36654
$695$	0	0
$696$	0	0
$697$	12.0000	0.454532
$698$	−16.0000	−0.605609
$699$	26.0000	0.983410
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−10.0000	−0.377426
$703$	4.00000	0.150863
$704$	0	0
$705$	0	0
$706$	32.0000	1.20434
$707$	−52.0000	−1.95566
$708$	6.00000	0.225494
$709$	−47.0000	−1.76512	−0.882561	−	0.470198i	$-0.844183\pi$
$709$	−47.0000	−1.76512	−0.882561	+	0.470198i	$0.844183\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	0	0
$713$	8.00000	0.299602
$714$	48.0000	1.79635
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−20.0000	−0.746393
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	0	0
$721$	64.0000	2.38348
$722$	30.0000	1.11648
$723$	−7.00000	−0.260333
$724$	−16.0000	−0.594635
$725$	0	0
$726$	−22.0000	−0.816497
$727$	5.00000	0.185440	0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000	0.185440	0.0927199	+	0.995692i	$0.470444\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−30.0000	−1.10959
$732$	2.00000	0.0739221
$733$	52.0000	1.92066	0.960332	−	0.278859i	$-0.0899564\pi$
$733$	52.0000	1.92066	0.960332	+	0.278859i	$0.0899564\pi$
$734$	0	0
$735$	0	0
$736$	−8.00000	−0.294884
$737$	0	0
$738$	4.00000	0.147242
$739$	41.0000	1.50821	0.754105	−	0.656754i	$-0.228071\pi$
$739$	41.0000	1.50821	0.754105	+	0.656754i	$0.228071\pi$
$740$	0	0
$741$	−10.0000	−0.367359
$742$	−96.0000	−3.52427
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	0	0
$746$	66.0000	2.41643
$747$	−12.0000	−0.439057
$748$	0	0
$749$	36.0000	1.31541
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	4.00000	0.145865
$753$	12.0000	0.437304
$754$	−60.0000	−2.18507
$755$	0	0
$756$	8.00000	0.290957
$757$	−6.00000	−0.218074	−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000	−0.218074	−0.109037	+	0.994038i	$0.534777\pi$
$758$	−72.0000	−2.61516
$759$	0	0
$760$	0	0
$761$	−13.0000	−0.471250	−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000	−0.471250	−0.235625	+	0.971844i	$0.575714\pi$
$762$	16.0000	0.579619
$763$	32.0000	1.15848
$764$	−18.0000	−0.651217
$765$	0	0
$766$	−20.0000	−0.722629
$767$	15.0000	0.541619
$768$	−16.0000	−0.577350
$769$	31.0000	1.11789	0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000	1.11789	0.558944	+	0.829205i	$0.311207\pi$
$770$	0	0
$771$	−23.0000	−0.828325
$772$	−20.0000	−0.719816
$773$	−20.0000	−0.719350	−0.359675	−	0.933078i	$-0.617112\pi$
$773$	−20.0000	−0.719350	−0.359675	+	0.933078i	$0.617112\pi$
$774$	−10.0000	−0.359443
$775$	0	0
$776$	0	0
$777$	−8.00000	−0.286998
$778$	−24.0000	−0.860442
$779$	4.00000	0.143315
$780$	0	0
$781$	0	0
$782$	−12.0000	−0.429119
$783$	6.00000	0.214423
$784$	−36.0000	−1.28571
$785$	0	0
$786$	30.0000	1.07006
$787$	19.0000	0.677277	0.338638	−	0.940917i	$-0.390034\pi$
$787$	19.0000	0.677277	0.338638	+	0.940917i	$0.390034\pi$
$788$	24.0000	0.854965
$789$	−24.0000	−0.854423
$790$	0	0
$791$	60.0000	2.13335
$792$	0	0
$793$	5.00000	0.177555
$794$	16.0000	0.567819
$795$	0	0
$796$	−32.0000	−1.13421
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	16.0000	0.566394
$799$	6.00000	0.212265
$800$	0	0
$801$	−15.0000	−0.529999
$802$	26.0000	0.918092
$803$	0	0
$804$	16.0000	0.564276
$805$	0	0
$806$	−80.0000	−2.81788
$807$	17.0000	0.598428
$808$	0	0
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	0	0
$811$	40.0000	1.40459	0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000	1.40459	0.702295	+	0.711886i	$0.252159\pi$
$812$	48.0000	1.68447
$813$	−16.0000	−0.561144
$814$	0	0
$815$	0	0
$816$	−24.0000	−0.840168
$817$	−10.0000	−0.349856
$818$	0	0
$819$	20.0000	0.698857
$820$	0	0
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	−6.00000	−0.209274
$823$	28.0000	0.976019	0.488009	−	0.872838i	$-0.337723\pi$
$823$	28.0000	0.976019	0.488009	+	0.872838i	$0.337723\pi$
$824$	0	0
$825$	0	0
$826$	−24.0000	−0.835067
$827$	54.0000	1.87776	0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000	1.87776	0.938882	+	0.344239i	$0.111863\pi$
$828$	−2.00000	−0.0695048
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	−6.00000	−0.208138
$832$	40.0000	1.38675
$833$	−54.0000	−1.87099
$834$	0	0
$835$	0	0
$836$	0	0
$837$	8.00000	0.276520
$838$	−48.0000	−1.65813
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−8.00000	−0.275698
$843$	6.00000	0.206651
$844$	−36.0000	−1.23917
$845$	0	0
$846$	2.00000	0.0687614
$847$	44.0000	1.51186
$848$	48.0000	1.64833
$849$	−8.00000	−0.274559
$850$	0	0
$851$	2.00000	0.0685591
$852$	−2.00000	−0.0685189
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	0	0
$857$	11.0000	0.375753	0.187876	−	0.982193i	$-0.439840\pi$
$857$	11.0000	0.375753	0.187876	+	0.982193i	$0.439840\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	−8.00000	−0.272639
$862$	0	0
$863$	−26.0000	−0.885050	−0.442525	−	0.896756i	$-0.645917\pi$
$863$	−26.0000	−0.885050	−0.442525	+	0.896756i	$0.645917\pi$
$864$	−8.00000	−0.272166
$865$	0	0
$866$	−28.0000	−0.951479
$867$	−19.0000	−0.645274
$868$	64.0000	2.17230
$869$	0	0
$870$	0	0
$871$	40.0000	1.35535
$872$	0	0
$873$	8.00000	0.270759
$874$	−4.00000	−0.135302
$875$	0	0
$876$	−26.0000	−0.878459
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	−70.0000	−2.36239
$879$	−17.0000	−0.573396
$880$	0	0
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	−18.0000	−0.606092
$883$	−26.0000	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$884$	60.0000	2.01802
$885$	0	0
$886$	−40.0000	−1.34383
$887$	−13.0000	−0.436497	−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000	−0.436497	−0.218249	+	0.975893i	$0.570034\pi$
$888$	0	0
$889$	−32.0000	−1.07325
$890$	0	0
$891$	0	0
$892$	−14.0000	−0.468755
$893$	2.00000	0.0669274
$894$	−46.0000	−1.53847
$895$	0	0
$896$	0	0
$897$	−5.00000	−0.166945
$898$	−44.0000	−1.46830
$899$	48.0000	1.60089
$900$	0	0
$901$	72.0000	2.39867
$902$	0	0
$903$	20.0000	0.665558
$904$	0	0
$905$	0	0
$906$	8.00000	0.265782
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	40.0000	1.32745
$909$	13.0000	0.431183
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	−8.00000	−0.264906
$913$	0	0
$914$	−48.0000	−1.58770
$915$	0	0
$916$	−20.0000	−0.660819
$917$	−60.0000	−1.98137
$918$	−12.0000	−0.396059
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	0	0
$921$	−26.0000	−0.856729
$922$	−20.0000	−0.658665
$923$	−5.00000	−0.164577
$924$	0	0
$925$	0	0
$926$	−38.0000	−1.24876
$927$	−16.0000	−0.525509
$928$	−48.0000	−1.57568
$929$	−25.0000	−0.820223	−0.410112	−	0.912035i	$-0.634510\pi$
$929$	−25.0000	−0.820223	−0.410112	+	0.912035i	$0.634510\pi$
$930$	0	0
$931$	−18.0000	−0.589926
$932$	−52.0000	−1.70332
$933$	6.00000	0.196431
$934$	−70.0000	−2.29047
$935$	0	0
$936$	0	0
$937$	−39.0000	−1.27407	−0.637037	−	0.770833i	$-0.719840\pi$
$937$	−39.0000	−1.27407	−0.637037	+	0.770833i	$0.719840\pi$
$938$	−64.0000	−2.08967
$939$	−26.0000	−0.848478
$940$	0	0
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	40.0000	1.30327
$943$	2.00000	0.0651290
$944$	12.0000	0.390567
$945$	0	0
$946$	0	0
$947$	−40.0000	−1.29983	−0.649913	−	0.760009i	$-0.725195\pi$
$947$	−40.0000	−1.29983	−0.649913	+	0.760009i	$0.725195\pi$
$948$	2.00000	0.0649570
$949$	−65.0000	−2.10999
$950$	0	0
$951$	31.0000	1.00524
$952$	0	0
$953$	29.0000	0.939402	0.469701	−	0.882826i	$-0.344362\pi$
$953$	29.0000	0.939402	0.469701	+	0.882826i	$0.344362\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	0	0
$957$	0	0
$958$	−54.0000	−1.74466
$959$	12.0000	0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	−20.0000	−0.644826
$963$	−9.00000	−0.290021
$964$	14.0000	0.450910
$965$	0	0
$966$	8.00000	0.257396
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	0	0
$969$	−12.0000	−0.385496
$970$	0	0
$971$	32.0000	1.02693	0.513464	−	0.858111i	$-0.328362\pi$
$971$	32.0000	1.02693	0.513464	+	0.858111i	$0.328362\pi$
$972$	−2.00000	−0.0641500
$973$	0	0
$974$	84.0000	2.69153
$975$	0	0
$976$	4.00000	0.128037
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	38.0000	1.21511
$979$	0	0
$980$	0	0
$981$	−8.00000	−0.255420
$982$	0	0
$983$	15.0000	0.478426	0.239213	−	0.970967i	$-0.423111\pi$
$983$	15.0000	0.478426	0.239213	+	0.970967i	$0.423111\pi$
$984$	0	0
$985$	0	0
$986$	−72.0000	−2.29295
$987$	−4.00000	−0.127321
$988$	20.0000	0.636285
$989$	−5.00000	−0.158991
$990$	0	0
$991$	−3.00000	−0.0952981	−0.0476491	−	0.998864i	$-0.515173\pi$
$991$	−3.00000	−0.0952981	−0.0476491	+	0.998864i	$0.515173\pi$
$992$	−64.0000	−2.03200
$993$	−3.00000	−0.0952021
$994$	8.00000	0.253745
$995$	0	0
$996$	24.0000	0.760469
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−64.0000	−2.02588
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.a.1.1		1
5.2	odd	4		705.2.c.a.424.1	✓	2
5.3	odd	4		705.2.c.a.424.2	yes	2
5.4	even	2		3525.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.a.424.1	✓	2	5.2	odd	4
705.2.c.a.424.2	yes	2	5.3	odd	4
3525.2.a.a.1.1		1	1.1	even	1	trivial
3525.2.a.o.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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