LMFDB - Embedded newform 1450.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
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	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -3.00000 q^{9} -2.00000 q^{11} -4.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} -3.00000 q^{18} -8.00000 q^{19} -2.00000 q^{22} +2.00000 q^{23} -4.00000 q^{26} +1.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} -3.00000 q^{36} +7.00000 q^{37} -8.00000 q^{38} +2.00000 q^{41} -4.00000 q^{43} -2.00000 q^{44} +2.00000 q^{46} +9.00000 q^{47} -7.00000 q^{49} -4.00000 q^{52} +12.0000 q^{53} +1.00000 q^{58} -15.0000 q^{59} +11.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +3.00000 q^{67} -6.00000 q^{68} -6.00000 q^{71} -3.00000 q^{72} -12.0000 q^{73} +7.00000 q^{74} -8.00000 q^{76} +8.00000 q^{79} +9.00000 q^{81} +2.00000 q^{82} -8.00000 q^{83} -4.00000 q^{86} -2.00000 q^{88} -16.0000 q^{89} +2.00000 q^{92} +9.00000 q^{94} -2.00000 q^{97} -7.00000 q^{98} +6.00000 q^{99} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−3.00000	−0.707107
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0	0
$21$	0	0
$22$	−2.00000	−0.426401
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0	0
$25$	0	0
$26$	−4.00000	−0.784465
$27$	0	0
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−3.00000	−0.500000
$37$	7.00000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	−8.00000	−1.29777
$39$	0	0
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	2.00000	0.294884
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	−4.00000	−0.554700
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	1.00000	0.131306
$59$	−15.0000	−1.95283	−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−15.0000	−1.95283	−0.976417	+	0.215894i	$0.930733\pi$
$60$	0	0
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−3.00000	−0.353553
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	7.00000	0.813733
$75$	0	0
$76$	−8.00000	−0.917663
$77$	0	0
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	2.00000	0.220863
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	−2.00000	−0.213201
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	0	0
$91$	0	0
$92$	2.00000	0.208514
$93$	0	0
$94$	9.00000	0.928279
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−7.00000	−0.707107
$99$	6.00000	0.603023
$100$	0	0
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	12.0000	1.16554
$107$	17.0000	1.64345	0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000	1.64345	0.821726	+	0.569883i	$0.193011\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	0	0
$115$	0	0
$116$	1.00000	0.0928477
$117$	12.0000	1.10940
$118$	−15.0000	−1.38086
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	11.0000	0.995893
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	0	0
$127$	1.00000	0.0887357	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000	0.0887357	0.0443678	+	0.999015i	$0.485873\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	3.00000	0.259161
$135$	0	0
$136$	−6.00000	−0.514496
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	15.0000	1.27228	0.636142	−	0.771572i	$-0.280529\pi$
$139$	15.0000	1.27228	0.636142	+	0.771572i	$0.280529\pi$
$140$	0	0
$141$	0	0
$142$	−6.00000	−0.503509
$143$	8.00000	0.668994
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−12.0000	−0.993127
$147$	0	0
$148$	7.00000	0.575396
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	−8.00000	−0.648886
$153$	18.0000	1.45521
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1.00000	−0.0798087	−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000	−0.0798087	−0.0399043	+	0.999204i	$0.512705\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	0	0
$161$	0	0
$162$	9.00000	0.707107
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−8.00000	−0.620920
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	24.0000	1.83533
$172$	−4.00000	−0.304997
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	−16.0000	−1.19925
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	0	0
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	0	0
$183$	0	0
$184$	2.00000	0.147442
$185$	0	0
$186$	0	0
$187$	12.0000	0.877527
$188$	9.00000	0.656392
$189$	0	0
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	0	0
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	−7.00000	−0.500000
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	6.00000	0.426401
$199$	26.0000	1.84309	0.921546	−	0.388270i	$-0.126927\pi$
$199$	26.0000	1.84309	0.921546	+	0.388270i	$0.126927\pi$
$200$	0	0
$201$	0	0
$202$	−9.00000	−0.633238
$203$	0	0
$204$	0	0
$205$	0	0
$206$	6.00000	0.418040
$207$	−6.00000	−0.417029
$208$	−4.00000	−0.277350
$209$	16.0000	1.10674
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	17.0000	1.16210
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−6.00000	−0.406371
$219$	0	0
$220$	0	0
$221$	24.0000	1.61441
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	0	0
$226$	4.00000	0.266076
$227$	11.0000	0.730096	0.365048	−	0.930989i	$-0.381053\pi$
$227$	11.0000	0.730096	0.365048	+	0.930989i	$0.381053\pi$
$228$	0	0
$229$	−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
$232$	1.00000	0.0656532
$233$	−23.0000	−1.50678	−0.753390	−	0.657574i	$-0.771583\pi$
$233$	−23.0000	−1.50678	−0.753390	+	0.657574i	$0.771583\pi$
$234$	12.0000	0.784465
$235$	0	0
$236$	−15.0000	−0.976417
$237$	0	0
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	7.00000	0.450910	0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000	0.450910	0.225455	+	0.974254i	$0.427613\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	11.0000	0.704203
$245$	0	0
$246$	0	0
$247$	32.0000	2.03611
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	1.00000	0.0627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	−26.0000	−1.62184	−0.810918	−	0.585160i	$-0.801032\pi$
$257$	−26.0000	−1.62184	−0.810918	+	0.585160i	$0.801032\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−3.00000	−0.185695
$262$	0	0
$263$	19.0000	1.17159	0.585795	−	0.810459i	$-0.300782\pi$
$263$	19.0000	1.17159	0.585795	+	0.810459i	$0.300782\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	3.00000	0.183254
$269$	23.0000	1.40233	0.701167	−	0.712997i	$-0.252663\pi$
$269$	23.0000	1.40233	0.701167	+	0.712997i	$0.252663\pi$
$270$	0	0
$271$	−5.00000	−0.303728	−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000	−0.303728	−0.151864	+	0.988401i	$0.548528\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	15.0000	0.899640
$279$	3.00000	0.179605
$280$	0	0
$281$	−13.0000	−0.775515	−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000	−0.775515	−0.387757	+	0.921761i	$0.626750\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	8.00000	0.473050
$287$	0	0
$288$	−3.00000	−0.176777
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−12.0000	−0.702247
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	0	0
$296$	7.00000	0.406867
$297$	0	0
$298$	−18.0000	−1.04271
$299$	−8.00000	−0.462652
$300$	0	0
$301$	0	0
$302$	−18.0000	−1.03578
$303$	0	0
$304$	−8.00000	−0.458831
$305$	0	0
$306$	18.0000	1.02899
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−27.0000	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$313$	−27.0000	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$314$	−1.00000	−0.0564333
$315$	0	0
$316$	8.00000	0.450035
$317$	11.0000	0.617822	0.308911	−	0.951091i	$-0.400036\pi$
$317$	11.0000	0.617822	0.308911	+	0.951091i	$0.400036\pi$
$318$	0	0
$319$	−2.00000	−0.111979
$320$	0	0
$321$	0	0
$322$	0	0
$323$	48.0000	2.67079
$324$	9.00000	0.500000
$325$	0	0
$326$	6.00000	0.332309
$327$	0	0
$328$	2.00000	0.110432
$329$	0	0
$330$	0	0
$331$	−6.00000	−0.329790	−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000	−0.329790	−0.164895	+	0.986311i	$0.552728\pi$
$332$	−8.00000	−0.439057
$333$	−21.0000	−1.15079
$334$	−16.0000	−0.875481
$335$	0	0
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	0	0
$341$	2.00000	0.108306
$342$	24.0000	1.29777
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	12.0000	0.645124
$347$	−27.0000	−1.44944	−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000	−1.44944	−0.724718	+	0.689046i	$0.758030\pi$
$348$	0	0
$349$	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
$351$	0	0
$352$	−2.00000	−0.106600
$353$	25.0000	1.33062	0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000	1.33062	0.665308	+	0.746569i	$0.268300\pi$
$354$	0	0
$355$	0	0
$356$	−16.0000	−0.847998
$357$	0	0
$358$	−9.00000	−0.475665
$359$	11.0000	0.580558	0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000	0.580558	0.290279	+	0.956942i	$0.406252\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−8.00000	−0.420471
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	2.00000	0.104257
$369$	−6.00000	−0.312348
$370$	0	0
$371$	0	0
$372$	0	0
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	12.0000	0.620505
$375$	0	0
$376$	9.00000	0.464140
$377$	−4.00000	−0.206010
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	0	0
$381$	0	0
$382$	−3.00000	−0.153493
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	0	0
$385$	0	0
$386$	4.00000	0.203595
$387$	12.0000	0.609994
$388$	−2.00000	−0.101535
$389$	3.00000	0.152106	0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000	0.152106	0.0760530	+	0.997104i	$0.475768\pi$
$390$	0	0
$391$	−12.0000	−0.606866
$392$	−7.00000	−0.353553
$393$	0	0
$394$	−18.0000	−0.906827
$395$	0	0
$396$	6.00000	0.301511
$397$	−32.0000	−1.60603	−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000	−1.60603	−0.803017	+	0.595956i	$0.796773\pi$
$398$	26.0000	1.30326
$399$	0	0
$400$	0	0
$401$	5.00000	0.249688	0.124844	−	0.992176i	$-0.460157\pi$
$401$	5.00000	0.249688	0.124844	+	0.992176i	$0.460157\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	−9.00000	−0.447767
$405$	0	0
$406$	0	0
$407$	−14.0000	−0.693954
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	6.00000	0.295599
$413$	0	0
$414$	−6.00000	−0.294884
$415$	0	0
$416$	−4.00000	−0.196116
$417$	0	0
$418$	16.0000	0.782586
$419$	13.0000	0.635092	0.317546	−	0.948243i	$-0.397141\pi$
$419$	13.0000	0.635092	0.317546	+	0.948243i	$0.397141\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	14.0000	0.681509
$423$	−27.0000	−1.31278
$424$	12.0000	0.582772
$425$	0	0
$426$	0	0
$427$	0	0
$428$	17.0000	0.821726
$429$	0	0
$430$	0	0
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	0	0
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−16.0000	−0.765384
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	21.0000	1.00000
$442$	24.0000	1.14156
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	0	0
$445$	0	0
$446$	8.00000	0.378811
$447$	0	0
$448$	0	0
$449$	−8.00000	−0.377543	−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000	−0.377543	−0.188772	+	0.982021i	$0.560451\pi$
$450$	0	0
$451$	−4.00000	−0.188353
$452$	4.00000	0.188144
$453$	0	0
$454$	11.0000	0.516256
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−23.0000	−1.06545
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	12.0000	0.554700
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−15.0000	−0.690431
$473$	8.00000	0.367840
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−36.0000	−1.64833
$478$	−6.00000	−0.274434
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−28.0000	−1.27669
$482$	7.00000	0.318841
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	38.0000	1.72194	0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000	1.72194	0.860972	+	0.508652i	$0.169856\pi$
$488$	11.0000	0.497947
$489$	0	0
$490$	0	0
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	32.0000	1.43975
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	0	0
$498$	0	0
$499$	−31.0000	−1.38775	−0.693875	−	0.720095i	$-0.744098\pi$
$499$	−31.0000	−1.38775	−0.693875	+	0.720095i	$0.744098\pi$
$500$	0	0
$501$	0	0
$502$	2.00000	0.0892644
$503$	−33.0000	−1.47140	−0.735699	−	0.677309i	$-0.763146\pi$
$503$	−33.0000	−1.47140	−0.735699	+	0.677309i	$0.763146\pi$
$504$	0	0
$505$	0	0
$506$	−4.00000	−0.177822
$507$	0	0
$508$	1.00000	0.0443678
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−26.0000	−1.14681
$515$	0	0
$516$	0	0
$517$	−18.0000	−0.791639
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−23.0000	−1.00765	−0.503824	−	0.863806i	$-0.668074\pi$
$521$	−23.0000	−1.00765	−0.503824	+	0.863806i	$0.668074\pi$
$522$	−3.00000	−0.131306
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	0	0
$525$	0	0
$526$	19.0000	0.828439
$527$	6.00000	0.261364
$528$	0	0
$529$	−19.0000	−0.826087
$530$	0	0
$531$	45.0000	1.95283
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	0	0
$536$	3.00000	0.129580
$537$	0	0
$538$	23.0000	0.991600
$539$	14.0000	0.603023
$540$	0	0
$541$	43.0000	1.84871	0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000	1.84871	0.924357	+	0.381528i	$0.124602\pi$
$542$	−5.00000	−0.214768
$543$	0	0
$544$	−6.00000	−0.257248
$545$	0	0
$546$	0	0
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	0	0
$549$	−33.0000	−1.40841
$550$	0	0
$551$	−8.00000	−0.340811
$552$	0	0
$553$	0	0
$554$	−8.00000	−0.339887
$555$	0	0
$556$	15.0000	0.636142
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	3.00000	0.127000
$559$	16.0000	0.676728
$560$	0	0
$561$	0	0
$562$	−13.0000	−0.548372
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	0	0
$565$	0	0
$566$	20.0000	0.840663
$567$	0	0
$568$	−6.00000	−0.251754
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−29.0000	−1.21361	−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000	−1.21361	−0.606806	+	0.794850i	$0.707550\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−3.00000	−0.125000
$577$	24.0000	0.999133	0.499567	−	0.866276i	$-0.333493\pi$
$577$	24.0000	0.999133	0.499567	+	0.866276i	$0.333493\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−24.0000	−0.993978
$584$	−12.0000	−0.496564
$585$	0	0
$586$	−9.00000	−0.371787
$587$	7.00000	0.288921	0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000	0.288921	0.144460	+	0.989511i	$0.453855\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	0	0
$591$	0	0
$592$	7.00000	0.287698
$593$	21.0000	0.862367	0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000	0.862367	0.431183	+	0.902264i	$0.358096\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	−8.00000	−0.327144
$599$	27.0000	1.10319	0.551595	−	0.834112i	$-0.314019\pi$
$599$	27.0000	1.10319	0.551595	+	0.834112i	$0.314019\pi$
$600$	0	0
$601$	−12.0000	−0.489490	−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000	−0.489490	−0.244745	+	0.969587i	$0.578704\pi$
$602$	0	0
$603$	−9.00000	−0.366508
$604$	−18.0000	−0.732410
$605$	0	0
$606$	0	0
$607$	1.00000	0.0405887	0.0202944	−	0.999794i	$-0.493540\pi$
$607$	1.00000	0.0405887	0.0202944	+	0.999794i	$0.493540\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	0	0
$611$	−36.0000	−1.45640
$612$	18.0000	0.727607
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	42.0000	1.68812	0.844061	−	0.536247i	$-0.180158\pi$
$619$	42.0000	1.68812	0.844061	+	0.536247i	$0.180158\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	−27.0000	−1.07914
$627$	0	0
$628$	−1.00000	−0.0399043
$629$	−42.0000	−1.67465
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	11.0000	0.436866
$635$	0	0
$636$	0	0
$637$	28.0000	1.10940
$638$	−2.00000	−0.0791808
$639$	18.0000	0.712069
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	11.0000	0.433798	0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000	0.433798	0.216899	+	0.976194i	$0.430406\pi$
$644$	0	0
$645$	0	0
$646$	48.0000	1.88853
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	9.00000	0.353553
$649$	30.0000	1.17760
$650$	0	0
$651$	0	0
$652$	6.00000	0.234978
$653$	9.00000	0.352197	0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000	0.352197	0.176099	+	0.984373i	$0.443652\pi$
$654$	0	0
$655$	0	0
$656$	2.00000	0.0780869
$657$	36.0000	1.40449
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−6.00000	−0.233197
$663$	0	0
$664$	−8.00000	−0.310460
$665$	0	0
$666$	−21.0000	−0.813733
$667$	2.00000	0.0774403
$668$	−16.0000	−0.619059
$669$	0	0
$670$	0	0
$671$	−22.0000	−0.849301
$672$	0	0
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	3.00000	0.115385
$677$	−25.0000	−0.960828	−0.480414	−	0.877042i	$-0.659514\pi$
$677$	−25.0000	−0.960828	−0.480414	+	0.877042i	$0.659514\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	2.00000	0.0765840
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	24.0000	0.917663
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−48.0000	−1.82865
$690$	0	0
$691$	5.00000	0.190209	0.0951045	−	0.995467i	$-0.469681\pi$
$691$	5.00000	0.190209	0.0951045	+	0.995467i	$0.469681\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	−27.0000	−1.02491
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	8.00000	0.302804
$699$	0	0
$700$	0	0
$701$	−32.0000	−1.20862	−0.604312	−	0.796748i	$-0.706552\pi$
$701$	−32.0000	−1.20862	−0.604312	+	0.796748i	$0.706552\pi$
$702$	0	0
$703$	−56.0000	−2.11208
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	25.0000	0.940887
$707$	0	0
$708$	0	0
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	0	0
$711$	−24.0000	−0.900070
$712$	−16.0000	−0.599625
$713$	−2.00000	−0.0749006
$714$	0	0
$715$	0	0
$716$	−9.00000	−0.336346
$717$	0	0
$718$	11.0000	0.410516
$719$	34.0000	1.26799	0.633993	−	0.773339i	$-0.281415\pi$
$719$	34.0000	1.26799	0.633993	+	0.773339i	$0.281415\pi$
$720$	0	0
$721$	0	0
$722$	45.0000	1.67473
$723$	0	0
$724$	−8.00000	−0.297318
$725$	0	0
$726$	0	0
$727$	−48.0000	−1.78022	−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000	−1.78022	−0.890111	+	0.455744i	$0.849373\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	24.0000	0.887672
$732$	0	0
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	2.00000	0.0737210
$737$	−6.00000	−0.221013
$738$	−6.00000	−0.220863
$739$	22.0000	0.809283	0.404642	−	0.914475i	$-0.367396\pi$
$739$	22.0000	0.809283	0.404642	+	0.914475i	$0.367396\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−32.0000	−1.17397	−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000	−1.17397	−0.586983	+	0.809599i	$0.699684\pi$
$744$	0	0
$745$	0	0
$746$	16.0000	0.585802
$747$	24.0000	0.878114
$748$	12.0000	0.438763
$749$	0	0
$750$	0	0
$751$	13.0000	0.474377	0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000	0.474377	0.237188	+	0.971464i	$0.423774\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	−4.00000	−0.145671
$755$	0	0
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	0	0
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	0	0
$763$	0	0
$764$	−3.00000	−0.108536
$765$	0	0
$766$	−10.0000	−0.361315
$767$	60.0000	2.16647
$768$	0	0
$769$	40.0000	1.44244	0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000	1.44244	0.721218	+	0.692708i	$0.243582\pi$
$770$	0	0
$771$	0	0
$772$	4.00000	0.143963
$773$	−17.0000	−0.611448	−0.305724	−	0.952120i	$-0.598898\pi$
$773$	−17.0000	−0.611448	−0.305724	+	0.952120i	$0.598898\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	3.00000	0.107555
$779$	−16.0000	−0.573259
$780$	0	0
$781$	12.0000	0.429394
$782$	−12.0000	−0.429119
$783$	0	0
$784$	−7.00000	−0.250000
$785$	0	0
$786$	0	0
$787$	29.0000	1.03374	0.516869	−	0.856064i	$-0.327097\pi$
$787$	29.0000	1.03374	0.516869	+	0.856064i	$0.327097\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	0	0
$791$	0	0
$792$	6.00000	0.213201
$793$	−44.0000	−1.56249
$794$	−32.0000	−1.13564
$795$	0	0
$796$	26.0000	0.921546
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	−54.0000	−1.91038
$800$	0	0
$801$	48.0000	1.69600
$802$	5.00000	0.176556
$803$	24.0000	0.846942
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	−9.00000	−0.316619
$809$	−16.0000	−0.562530	−0.281265	−	0.959630i	$-0.590754\pi$
$809$	−16.0000	−0.562530	−0.281265	+	0.959630i	$0.590754\pi$
$810$	0	0
$811$	−17.0000	−0.596951	−0.298475	−	0.954417i	$-0.596478\pi$
$811$	−17.0000	−0.596951	−0.298475	+	0.954417i	$0.596478\pi$
$812$	0	0
$813$	0	0
$814$	−14.0000	−0.490700
$815$	0	0
$816$	0	0
$817$	32.0000	1.11954
$818$	0	0
$819$	0	0
$820$	0	0
$821$	44.0000	1.53561	0.767805	−	0.640683i	$-0.221349\pi$
$821$	44.0000	1.53561	0.767805	+	0.640683i	$0.221349\pi$
$822$	0	0
$823$	−56.0000	−1.95204	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−56.0000	−1.95204	−0.976019	+	0.217687i	$0.930149\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	0	0
$827$	−14.0000	−0.486828	−0.243414	−	0.969923i	$-0.578267\pi$
$827$	−14.0000	−0.486828	−0.243414	+	0.969923i	$0.578267\pi$
$828$	−6.00000	−0.208514
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	0	0
$831$	0	0
$832$	−4.00000	−0.138675
$833$	42.0000	1.45521
$834$	0	0
$835$	0	0
$836$	16.0000	0.553372
$837$	0	0
$838$	13.0000	0.449078
$839$	43.0000	1.48452	0.742262	−	0.670109i	$-0.233753\pi$
$839$	43.0000	1.48452	0.742262	+	0.670109i	$0.233753\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	17.0000	0.585859
$843$	0	0
$844$	14.0000	0.481900
$845$	0	0
$846$	−27.0000	−0.928279
$847$	0	0
$848$	12.0000	0.412082
$849$	0	0
$850$	0	0
$851$	14.0000	0.479914
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	0	0
$855$	0	0
$856$	17.0000	0.581048
$857$	−14.0000	−0.478231	−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000	−0.478231	−0.239115	+	0.970991i	$0.576857\pi$
$858$	0	0
$859$	−54.0000	−1.84246	−0.921228	−	0.389023i	$-0.872813\pi$
$859$	−54.0000	−1.84246	−0.921228	+	0.389023i	$0.872813\pi$
$860$	0	0
$861$	0	0
$862$	−2.00000	−0.0681203
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	0	0
$865$	0	0
$866$	−30.0000	−1.01944
$867$	0	0
$868$	0	0
$869$	−16.0000	−0.542763
$870$	0	0
$871$	−12.0000	−0.406604
$872$	−6.00000	−0.203186
$873$	6.00000	0.203069
$874$	−16.0000	−0.541208
$875$	0	0
$876$	0	0
$877$	−36.0000	−1.21563	−0.607817	−	0.794077i	$-0.707955\pi$
$877$	−36.0000	−1.21563	−0.607817	+	0.794077i	$0.707955\pi$
$878$	20.0000	0.674967
$879$	0	0
$880$	0	0
$881$	−32.0000	−1.07811	−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000	−1.07811	−0.539054	+	0.842271i	$0.681218\pi$
$882$	21.0000	0.707107
$883$	41.0000	1.37976	0.689880	−	0.723924i	$-0.257663\pi$
$883$	41.0000	1.37976	0.689880	+	0.723924i	$0.257663\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−26.0000	−0.873487
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−18.0000	−0.603023
$892$	8.00000	0.267860
$893$	−72.0000	−2.40939
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−8.00000	−0.266963
$899$	−1.00000	−0.0333519
$900$	0	0
$901$	−72.0000	−2.39867
$902$	−4.00000	−0.133185
$903$	0	0
$904$	4.00000	0.133038
$905$	0	0
$906$	0	0
$907$	42.0000	1.39459	0.697294	−	0.716786i	$-0.254387\pi$
$907$	42.0000	1.39459	0.697294	+	0.716786i	$0.254387\pi$
$908$	11.0000	0.365048
$909$	27.0000	0.895533
$910$	0	0
$911$	−7.00000	−0.231920	−0.115960	−	0.993254i	$-0.536994\pi$
$911$	−7.00000	−0.231920	−0.115960	+	0.993254i	$0.536994\pi$
$912$	0	0
$913$	16.0000	0.529523
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	−28.0000	−0.923635	−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000	−0.923635	−0.461817	+	0.886975i	$0.652802\pi$
$920$	0	0
$921$	0	0
$922$	−6.00000	−0.197599
$923$	24.0000	0.789970
$924$	0	0
$925$	0	0
$926$	8.00000	0.262896
$927$	−18.0000	−0.591198
$928$	1.00000	0.0328266
$929$	−13.0000	−0.426516	−0.213258	−	0.976996i	$-0.568408\pi$
$929$	−13.0000	−0.426516	−0.213258	+	0.976996i	$0.568408\pi$
$930$	0	0
$931$	56.0000	1.83533
$932$	−23.0000	−0.753390
$933$	0	0
$934$	0	0
$935$	0	0
$936$	12.0000	0.392232
$937$	13.0000	0.424691	0.212346	−	0.977195i	$-0.431890\pi$
$937$	13.0000	0.424691	0.212346	+	0.977195i	$0.431890\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	0	0
$943$	4.00000	0.130258
$944$	−15.0000	−0.488208
$945$	0	0
$946$	8.00000	0.260102
$947$	2.00000	0.0649913	0.0324956	−	0.999472i	$-0.489654\pi$
$947$	2.00000	0.0649913	0.0324956	+	0.999472i	$0.489654\pi$
$948$	0	0
$949$	48.0000	1.55815
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−50.0000	−1.61966	−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000	−1.61966	−0.809829	+	0.586665i	$0.800440\pi$
$954$	−36.0000	−1.16554
$955$	0	0
$956$	−6.00000	−0.194054
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−28.0000	−0.902756
$963$	−51.0000	−1.64345
$964$	7.00000	0.225455
$965$	0	0
$966$	0	0
$967$	44.0000	1.41494	0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000	1.41494	0.707472	+	0.706741i	$0.249835\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	0	0
$974$	38.0000	1.21760
$975$	0	0
$976$	11.0000	0.352101
$977$	−51.0000	−1.63163	−0.815817	−	0.578310i	$-0.803713\pi$
$977$	−51.0000	−1.63163	−0.815817	+	0.578310i	$0.803713\pi$
$978$	0	0
$979$	32.0000	1.02272
$980$	0	0
$981$	18.0000	0.574696
$982$	−42.0000	−1.34027
$983$	1.00000	0.0318950	0.0159475	−	0.999873i	$-0.494924\pi$
$983$	1.00000	0.0318950	0.0159475	+	0.999873i	$0.494924\pi$
$984$	0	0
$985$	0	0
$986$	−6.00000	−0.191079
$987$	0	0
$988$	32.0000	1.01806
$989$	−8.00000	−0.254385
$990$	0	0
$991$	48.0000	1.52477	0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000	1.52477	0.762385	+	0.647124i	$0.224028\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	29.0000	0.918439	0.459220	−	0.888323i	$-0.348129\pi$
$997$	29.0000	0.918439	0.459220	+	0.888323i	$0.348129\pi$
$998$	−31.0000	−0.981288
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.f.1.1	yes	1
5.2	odd	4		1450.2.b.c.349.2		2
5.3	odd	4		1450.2.b.c.349.1		2
5.4	even	2		1450.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.b.1.1	✓	1	5.4	even	2
1450.2.a.f.1.1	yes	1	1.1	even	1	trivial
1450.2.b.c.349.1		2	5.3	odd	4
1450.2.b.c.349.2		2	5.2	odd	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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