LMFDB - Embedded newform 5610.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
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	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +1.00000 q^{30} -6.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} +8.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} -2.00000 q^{41} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} -4.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +8.00000 q^{53} -1.00000 q^{54} +1.00000 q^{55} -8.00000 q^{57} +4.00000 q^{59} -1.00000 q^{60} -10.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} -4.00000 q^{67} +1.00000 q^{68} +4.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} +8.00000 q^{74} +1.00000 q^{75} -8.00000 q^{76} -4.00000 q^{78} -8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} -12.0000 q^{83} -1.00000 q^{85} -4.00000 q^{86} +1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} +4.00000 q^{92} -6.00000 q^{93} +6.00000 q^{94} +8.00000 q^{95} -1.00000 q^{96} +10.0000 q^{97} +7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	1.00000	0.182574
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	8.00000	1.29777
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−4.00000	−0.589768
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	8.00000	1.09888	0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000	1.09888	0.549442	+	0.835532i	$0.314840\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	0	0
$57$	−8.00000	−1.05963
$58$	0	0
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	6.00000	0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	1.00000	0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	1.00000	0.121268
$69$	4.00000	0.481543
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	8.00000	0.929981
$75$	1.00000	0.115470
$76$	−8.00000	−0.917663
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	−4.00000	−0.431331
$87$	0	0
$88$	1.00000	0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	4.00000	0.417029
$93$	−6.00000	−0.622171
$94$	6.00000	0.618853
$95$	8.00000	0.820783
$96$	−1.00000	−0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	7.00000	0.707107
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−1.00000	−0.0990148
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−8.00000	−0.777029
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−1.00000	−0.0953463
$111$	−8.00000	−0.759326
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	8.00000	0.749269
$115$	−4.00000	−0.373002
$116$	0	0
$117$	4.00000	0.369800
$118$	−4.00000	−0.368230
$119$	0	0
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	−2.00000	−0.180334
$124$	−6.00000	−0.538816
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	4.00000	0.352180
$130$	4.00000	0.350823
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−4.00000	−0.340503
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	−8.00000	−0.671345
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.00000	−0.496564
$147$	−7.00000	−0.577350
$148$	−8.00000	−0.657596
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	−1.00000	−0.0816497
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	8.00000	0.648886
$153$	1.00000	0.0808452
$154$	0	0
$155$	6.00000	0.481932
$156$	4.00000	0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	8.00000	0.636446
$159$	8.00000	0.634441
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−2.00000	−0.156174
$165$	1.00000	0.0778499
$166$	12.0000	0.931381
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	−8.00000	−0.611775
$172$	4.00000	0.304997
$173$	−20.0000	−1.52057	−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000	−1.52057	−0.760286	+	0.649589i	$0.774941\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	−1.00000	−0.0745356
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	−4.00000	−0.294884
$185$	8.00000	0.588172
$186$	6.00000	0.439941
$187$	−1.00000	−0.0731272
$188$	−6.00000	−0.437595
$189$	0	0
$190$	−8.00000	−0.580381
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	1.00000	0.0721688
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−10.0000	−0.717958
$195$	−4.00000	−0.286446
$196$	−7.00000	−0.500000
$197$	−16.0000	−1.13995	−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000	−1.13995	−0.569976	+	0.821661i	$0.693048\pi$
$198$	1.00000	0.0710669
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	−18.0000	−1.26648
$203$	0	0
$204$	1.00000	0.0700140
$205$	2.00000	0.139686
$206$	8.00000	0.557386
$207$	4.00000	0.278019
$208$	4.00000	0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	8.00000	0.549442
$213$	8.00000	0.548151
$214$	0	0
$215$	−4.00000	−0.272798
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	6.00000	0.405442
$220$	1.00000	0.0674200
$221$	4.00000	0.269069
$222$	8.00000	0.536925
$223$	−28.0000	−1.87502	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000	−1.87502	−0.937509	+	0.347960i	$0.886874\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−8.00000	−0.529813
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	0	0
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−4.00000	−0.261488
$235$	6.00000	0.391397
$236$	4.00000	0.260378
$237$	−8.00000	−0.519656
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	7.00000	0.447214
$246$	2.00000	0.127515
$247$	−32.0000	−2.03611
$248$	6.00000	0.381000
$249$	−12.0000	−0.760469
$250$	1.00000	0.0632456
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	14.0000	0.878438
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−16.0000	−0.988483
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	1.00000	0.0615457
$265$	−8.00000	−0.491436
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	1.00000	0.0608581
$271$	−14.0000	−0.850439	−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000	−0.850439	−0.425220	+	0.905090i	$0.639803\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−18.0000	−1.08742
$275$	−1.00000	−0.0603023
$276$	4.00000	0.240772
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	12.0000	0.719712
$279$	−6.00000	−0.359211
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	6.00000	0.357295
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	8.00000	0.474713
$285$	8.00000	0.473879
$286$	4.00000	0.236525
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	10.0000	0.586210
$292$	6.00000	0.351123
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	7.00000	0.408248
$295$	−4.00000	−0.232889
$296$	8.00000	0.464991
$297$	−1.00000	−0.0580259
$298$	−2.00000	−0.115857
$299$	16.0000	0.925304
$300$	1.00000	0.0577350
$301$	0	0
$302$	10.0000	0.575435
$303$	18.0000	1.03407
$304$	−8.00000	−0.458831
$305$	10.0000	0.572598
$306$	−1.00000	−0.0571662
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−6.00000	−0.340777
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−4.00000	−0.226455
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−8.00000	−0.448618
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	0	0
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−12.0000	−0.664619
$327$	−2.00000	−0.110600
$328$	2.00000	0.110432
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−12.0000	−0.658586
$333$	−8.00000	−0.438397
$334$	10.0000	0.547176
$335$	4.00000	0.218543
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−3.00000	−0.163178
$339$	−6.00000	−0.325875
$340$	−1.00000	−0.0542326
$341$	6.00000	0.324918
$342$	8.00000	0.432590
$343$	0	0
$344$	−4.00000	−0.215666
$345$	−4.00000	−0.215353
$346$	20.0000	1.07521
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	−4.00000	−0.212598
$355$	−8.00000	−0.424596
$356$	−6.00000	−0.317999
$357$	0	0
$358$	24.0000	1.26844
$359$	28.0000	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$360$	1.00000	0.0527046
$361$	45.0000	2.36842
$362$	−16.0000	−0.840941
$363$	1.00000	0.0524864
$364$	0	0
$365$	−6.00000	−0.314054
$366$	10.0000	0.522708
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	4.00000	0.208514
$369$	−2.00000	−0.104116
$370$	−8.00000	−0.415900
$371$	0	0
$372$	−6.00000	−0.311086
$373$	−12.0000	−0.621336	−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000	−0.621336	−0.310668	+	0.950518i	$0.600553\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	6.00000	0.309426
$377$	0	0
$378$	0	0
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	8.00000	0.410391
$381$	−14.0000	−0.717242
$382$	−6.00000	−0.306987
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.0000	0.712581
$387$	4.00000	0.203331
$388$	10.0000	0.507673
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	4.00000	0.202548
$391$	4.00000	0.202289
$392$	7.00000	0.353553
$393$	16.0000	0.807093
$394$	16.0000	0.806068
$395$	8.00000	0.402524
$396$	−1.00000	−0.0502519
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	−18.0000	−0.902258
$399$	0	0
$400$	1.00000	0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	4.00000	0.199502
$403$	−24.0000	−1.19553
$404$	18.0000	0.895533
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	8.00000	0.396545
$408$	−1.00000	−0.0495074
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−2.00000	−0.0987730
$411$	18.0000	0.887875
$412$	−8.00000	−0.394132
$413$	0	0
$414$	−4.00000	−0.196589
$415$	12.0000	0.589057
$416$	−4.00000	−0.196116
$417$	−12.0000	−0.587643
$418$	−8.00000	−0.391293
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	20.0000	0.973585
$423$	−6.00000	−0.291730
$424$	−8.00000	−0.388514
$425$	1.00000	0.0485071
$426$	−8.00000	−0.387601
$427$	0	0
$428$	0	0
$429$	−4.00000	−0.193122
$430$	4.00000	0.192897
$431$	−10.0000	−0.481683	−0.240842	−	0.970564i	$-0.577423\pi$
$431$	−10.0000	−0.481683	−0.240842	+	0.970564i	$0.577423\pi$
$432$	1.00000	0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−32.0000	−1.53077
$438$	−6.00000	−0.286691
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	−1.00000	−0.0476731
$441$	−7.00000	−0.333333
$442$	−4.00000	−0.190261
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	−8.00000	−0.379663
$445$	6.00000	0.284427
$446$	28.0000	1.32584
$447$	2.00000	0.0945968
$448$	0	0
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	−1.00000	−0.0471405
$451$	2.00000	0.0941763
$452$	−6.00000	−0.282216
$453$	−10.0000	−0.469841
$454$	12.0000	0.563188
$455$	0	0
$456$	8.00000	0.374634
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−18.0000	−0.841085
$459$	1.00000	0.0466760
$460$	−4.00000	−0.186501
$461$	22.0000	1.02464	0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000	1.02464	0.512321	+	0.858794i	$0.328786\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	0	0
$465$	6.00000	0.278243
$466$	−14.0000	−0.648537
$467$	40.0000	1.85098	0.925490	−	0.378773i	$-0.123654\pi$
$467$	40.0000	1.85098	0.925490	+	0.378773i	$0.123654\pi$
$468$	4.00000	0.184900
$469$	0	0
$470$	−6.00000	−0.276759
$471$	−14.0000	−0.645086
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	8.00000	0.367452
$475$	−8.00000	−0.367065
$476$	0	0
$477$	8.00000	0.366295
$478$	0	0
$479$	34.0000	1.55350	0.776750	−	0.629809i	$-0.216867\pi$
$479$	34.0000	1.55350	0.776750	+	0.629809i	$0.216867\pi$
$480$	1.00000	0.0456435
$481$	−32.0000	−1.45907
$482$	−10.0000	−0.455488
$483$	0	0
$484$	1.00000	0.0454545
$485$	−10.0000	−0.454077
$486$	−1.00000	−0.0453609
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	10.0000	0.452679
$489$	12.0000	0.542659
$490$	−7.00000	−0.316228
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	−2.00000	−0.0901670
$493$	0	0
$494$	32.0000	1.43975
$495$	1.00000	0.0449467
$496$	−6.00000	−0.269408
$497$	0	0
$498$	12.0000	0.537733
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−1.00000	−0.0447214
$501$	−10.0000	−0.446767
$502$	16.0000	0.714115
$503$	−2.00000	−0.0891756	−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000	−0.0891756	−0.0445878	+	0.999005i	$0.514197\pi$
$504$	0	0
$505$	−18.0000	−0.800989
$506$	4.00000	0.177822
$507$	3.00000	0.133235
$508$	−14.0000	−0.621150
$509$	40.0000	1.77297	0.886484	−	0.462758i	$-0.153140\pi$
$509$	40.0000	1.77297	0.886484	+	0.462758i	$0.153140\pi$
$510$	1.00000	0.0442807
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	18.0000	0.793946
$515$	8.00000	0.352522
$516$	4.00000	0.176090
$517$	6.00000	0.263880
$518$	0	0
$519$	−20.0000	−0.877903
$520$	4.00000	0.175412
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	0	0
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	16.0000	0.698963
$525$	0	0
$526$	12.0000	0.523225
$527$	−6.00000	−0.261364
$528$	−1.00000	−0.0435194
$529$	−7.00000	−0.304348
$530$	8.00000	0.347498
$531$	4.00000	0.173585
$532$	0	0
$533$	−8.00000	−0.346518
$534$	6.00000	0.259645
$535$	0	0
$536$	4.00000	0.172774
$537$	−24.0000	−1.03568
$538$	6.00000	0.258678
$539$	7.00000	0.301511
$540$	−1.00000	−0.0430331
$541$	−6.00000	−0.257960	−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000	−0.257960	−0.128980	+	0.991647i	$0.541170\pi$
$542$	14.0000	0.601351
$543$	16.0000	0.686626
$544$	−1.00000	−0.0428746
$545$	2.00000	0.0856706
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	18.0000	0.768922
$549$	−10.0000	−0.426790
$550$	1.00000	0.0426401
$551$	0	0
$552$	−4.00000	−0.170251
$553$	0	0
$554$	22.0000	0.934690
$555$	8.00000	0.339581
$556$	−12.0000	−0.508913
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	6.00000	0.254000
$559$	16.0000	0.676728
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	22.0000	0.928014
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−6.00000	−0.252646
$565$	6.00000	0.252422
$566$	−28.0000	−1.17693
$567$	0	0
$568$	−8.00000	−0.335673
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	−8.00000	−0.335083
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−4.00000	−0.167248
$573$	6.00000	0.250654
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	46.0000	1.91501	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000	1.91501	0.957503	+	0.288425i	$0.0931316\pi$
$578$	−1.00000	−0.0415945
$579$	−14.0000	−0.581820
$580$	0	0
$581$	0	0
$582$	−10.0000	−0.414513
$583$	−8.00000	−0.331326
$584$	−6.00000	−0.248282
$585$	−4.00000	−0.165380
$586$	−18.0000	−0.743573
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	−7.00000	−0.288675
$589$	48.0000	1.97781
$590$	4.00000	0.164677
$591$	−16.0000	−0.658152
$592$	−8.00000	−0.328798
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	2.00000	0.0819232
$597$	18.0000	0.736691
$598$	−16.0000	−0.654289
$599$	−10.0000	−0.408589	−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000	−0.408589	−0.204294	+	0.978909i	$0.565490\pi$
$600$	−1.00000	−0.0408248
$601$	38.0000	1.55005	0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000	1.55005	0.775026	+	0.631929i	$0.217737\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	−10.0000	−0.406894
$605$	−1.00000	−0.0406558
$606$	−18.0000	−0.731200
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	8.00000	0.324443
$609$	0	0
$610$	−10.0000	−0.404888
$611$	−24.0000	−0.970936
$612$	1.00000	0.0404226
$613$	−44.0000	−1.77714	−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000	−1.77714	−0.888572	+	0.458738i	$0.848302\pi$
$614$	8.00000	0.322854
$615$	2.00000	0.0806478
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	8.00000	0.321807
$619$	−44.0000	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$620$	6.00000	0.240966
$621$	4.00000	0.160514
$622$	−4.00000	−0.160385
$623$	0	0
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	8.00000	0.319489
$628$	−14.0000	−0.558661
$629$	−8.00000	−0.318981
$630$	0	0
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	8.00000	0.318223
$633$	−20.0000	−0.794929
$634$	6.00000	0.238290
$635$	14.0000	0.555573
$636$	8.00000	0.317221
$637$	−28.0000	−1.10940
$638$	0	0
$639$	8.00000	0.316475
$640$	1.00000	0.0395285
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	8.00000	0.314756
$647$	46.0000	1.80845	0.904223	−	0.427060i	$-0.140451\pi$
$647$	46.0000	1.80845	0.904223	+	0.427060i	$0.140451\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	−4.00000	−0.156893
$651$	0	0
$652$	12.0000	0.469956
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	2.00000	0.0782062
$655$	−16.0000	−0.625172
$656$	−2.00000	−0.0780869
$657$	6.00000	0.234082
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	1.00000	0.0389249
$661$	−50.0000	−1.94477	−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000	−1.94477	−0.972387	+	0.233373i	$0.925024\pi$
$662$	20.0000	0.777322
$663$	4.00000	0.155347
$664$	12.0000	0.465690
$665$	0	0
$666$	8.00000	0.309994
$667$	0	0
$668$	−10.0000	−0.386912
$669$	−28.0000	−1.08254
$670$	−4.00000	−0.154533
$671$	10.0000	0.386046
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	22.0000	0.847408
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	24.0000	0.922395	0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000	0.922395	0.461197	+	0.887298i	$0.347420\pi$
$678$	6.00000	0.230429
$679$	0	0
$680$	1.00000	0.0383482
$681$	−12.0000	−0.459841
$682$	−6.00000	−0.229752
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−8.00000	−0.305888
$685$	−18.0000	−0.687745
$686$	0	0
$687$	18.0000	0.686743
$688$	4.00000	0.152499
$689$	32.0000	1.21910
$690$	4.00000	0.152277
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	−20.0000	−0.760286
$693$	0	0
$694$	8.00000	0.303676
$695$	12.0000	0.455186
$696$	0	0
$697$	−2.00000	−0.0757554
$698$	0	0
$699$	14.0000	0.529529
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	−4.00000	−0.150970
$703$	64.0000	2.41381
$704$	−1.00000	−0.0376889
$705$	6.00000	0.225973
$706$	26.0000	0.978523
$707$	0	0
$708$	4.00000	0.150329
$709$	28.0000	1.05156	0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000	1.05156	0.525781	+	0.850620i	$0.323773\pi$
$710$	8.00000	0.300235
$711$	−8.00000	−0.300023
$712$	6.00000	0.224860
$713$	−24.0000	−0.898807
$714$	0	0
$715$	4.00000	0.149592
$716$	−24.0000	−0.896922
$717$	0	0
$718$	−28.0000	−1.04495
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−45.0000	−1.67473
$723$	10.0000	0.371904
$724$	16.0000	0.594635
$725$	0	0
$726$	−1.00000	−0.0371135
$727$	−20.0000	−0.741759	−0.370879	−	0.928681i	$-0.620944\pi$
$727$	−20.0000	−0.741759	−0.370879	+	0.928681i	$0.620944\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	4.00000	0.147945
$732$	−10.0000	−0.369611
$733$	−44.0000	−1.62518	−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000	−1.62518	−0.812589	+	0.582838i	$0.801942\pi$
$734$	−14.0000	−0.516749
$735$	7.00000	0.258199
$736$	−4.00000	−0.147442
$737$	4.00000	0.147342
$738$	2.00000	0.0736210
$739$	−36.0000	−1.32428	−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000	−1.32428	−0.662141	+	0.749380i	$0.730352\pi$
$740$	8.00000	0.294086
$741$	−32.0000	−1.17555
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	6.00000	0.219971
$745$	−2.00000	−0.0732743
$746$	12.0000	0.439351
$747$	−12.0000	−0.439057
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	1.00000	0.0365148
$751$	−42.0000	−1.53260	−0.766301	−	0.642482i	$-0.777905\pi$
$751$	−42.0000	−1.53260	−0.766301	+	0.642482i	$0.777905\pi$
$752$	−6.00000	−0.218797
$753$	−16.0000	−0.583072
$754$	0	0
$755$	10.0000	0.363937
$756$	0	0
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−24.0000	−0.871719
$759$	−4.00000	−0.145191
$760$	−8.00000	−0.290191
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	14.0000	0.507166
$763$	0	0
$764$	6.00000	0.217072
$765$	−1.00000	−0.0361551
$766$	10.0000	0.361315
$767$	16.0000	0.577727
$768$	1.00000	0.0360844
$769$	22.0000	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−14.0000	−0.503871
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	−4.00000	−0.143777
$775$	−6.00000	−0.215526
$776$	−10.0000	−0.358979
$777$	0	0
$778$	8.00000	0.286814
$779$	16.0000	0.573259
$780$	−4.00000	−0.143223
$781$	−8.00000	−0.286263
$782$	−4.00000	−0.143040
$783$	0	0
$784$	−7.00000	−0.250000
$785$	14.0000	0.499681
$786$	−16.0000	−0.570701
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−16.0000	−0.569976
$789$	−12.0000	−0.427211
$790$	−8.00000	−0.284627
$791$	0	0
$792$	1.00000	0.0355335
$793$	−40.0000	−1.42044
$794$	20.0000	0.709773
$795$	−8.00000	−0.283731
$796$	18.0000	0.637993
$797$	16.0000	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$797$	16.0000	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$798$	0	0
$799$	−6.00000	−0.212265
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	−6.00000	−0.211735
$804$	−4.00000	−0.141069
$805$	0	0
$806$	24.0000	0.845364
$807$	−6.00000	−0.211210
$808$	−18.0000	−0.633238
$809$	14.0000	0.492214	0.246107	−	0.969243i	$-0.420849\pi$
$809$	14.0000	0.492214	0.246107	+	0.969243i	$0.420849\pi$
$810$	1.00000	0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	−14.0000	−0.491001
$814$	−8.00000	−0.280400
$815$	−12.0000	−0.420342
$816$	1.00000	0.0350070
$817$	−32.0000	−1.11954
$818$	−14.0000	−0.489499
$819$	0	0
$820$	2.00000	0.0698430
$821$	−44.0000	−1.53561	−0.767805	−	0.640683i	$-0.778651\pi$
$821$	−44.0000	−1.53561	−0.767805	+	0.640683i	$0.778651\pi$
$822$	−18.0000	−0.627822
$823$	38.0000	1.32460	0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000	1.32460	0.662298	+	0.749240i	$0.269581\pi$
$824$	8.00000	0.278693
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	4.00000	0.139010
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	−12.0000	−0.416526
$831$	−22.0000	−0.763172
$832$	4.00000	0.138675
$833$	−7.00000	−0.242536
$834$	12.0000	0.415526
$835$	10.0000	0.346064
$836$	8.00000	0.276686
$837$	−6.00000	−0.207390
$838$	20.0000	0.690889
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	14.0000	0.482472
$843$	−22.0000	−0.757720
$844$	−20.0000	−0.688428
$845$	−3.00000	−0.103203
$846$	6.00000	0.206284
$847$	0	0
$848$	8.00000	0.274721
$849$	28.0000	0.960958
$850$	−1.00000	−0.0342997
$851$	−32.0000	−1.09695
$852$	8.00000	0.274075
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	0	0
$855$	8.00000	0.273594
$856$	0	0
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	4.00000	0.136558
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	−4.00000	−0.136399
$861$	0	0
$862$	10.0000	0.340601
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	−1.00000	−0.0340207
$865$	20.0000	0.680020
$866$	2.00000	0.0679628
$867$	1.00000	0.0339618
$868$	0	0
$869$	8.00000	0.271381
$870$	0	0
$871$	−16.0000	−0.542139
$872$	2.00000	0.0677285
$873$	10.0000	0.338449
$874$	32.0000	1.08242
$875$	0	0
$876$	6.00000	0.202721
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	20.0000	0.674967
$879$	18.0000	0.607125
$880$	1.00000	0.0337100
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	7.00000	0.235702
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	4.00000	0.134535
$885$	−4.00000	−0.134459
$886$	−36.0000	−1.20944
$887$	26.0000	0.872995	0.436497	−	0.899706i	$-0.356219\pi$
$887$	26.0000	0.872995	0.436497	+	0.899706i	$0.356219\pi$
$888$	8.00000	0.268462
$889$	0	0
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	−28.0000	−0.937509
$893$	48.0000	1.60626
$894$	−2.00000	−0.0668900
$895$	24.0000	0.802232
$896$	0	0
$897$	16.0000	0.534224
$898$	18.0000	0.600668
$899$	0	0
$900$	1.00000	0.0333333
$901$	8.00000	0.266519
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	6.00000	0.199557
$905$	−16.0000	−0.531858
$906$	10.0000	0.332228
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	−12.0000	−0.398234
$909$	18.0000	0.597022
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	−8.00000	−0.264906
$913$	12.0000	0.397142
$914$	−10.0000	−0.330771
$915$	10.0000	0.330590
$916$	18.0000	0.594737
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	−6.00000	−0.197922	−0.0989609	−	0.995091i	$-0.531552\pi$
$919$	−6.00000	−0.197922	−0.0989609	+	0.995091i	$0.531552\pi$
$920$	4.00000	0.131876
$921$	−8.00000	−0.263609
$922$	−22.0000	−0.724531
$923$	32.0000	1.05329
$924$	0	0
$925$	−8.00000	−0.263038
$926$	−40.0000	−1.31448
$927$	−8.00000	−0.262754
$928$	0	0
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	−6.00000	−0.196748
$931$	56.0000	1.83533
$932$	14.0000	0.458585
$933$	4.00000	0.130954
$934$	−40.0000	−1.30884
$935$	1.00000	0.0327035
$936$	−4.00000	−0.130744
$937$	−10.0000	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$938$	0	0
$939$	18.0000	0.587408
$940$	6.00000	0.195698
$941$	−4.00000	−0.130396	−0.0651981	−	0.997872i	$-0.520768\pi$
$941$	−4.00000	−0.130396	−0.0651981	+	0.997872i	$0.520768\pi$
$942$	14.0000	0.456145
$943$	−8.00000	−0.260516
$944$	4.00000	0.130189
$945$	0	0
$946$	4.00000	0.130051
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	−8.00000	−0.259828
$949$	24.0000	0.779073
$950$	8.00000	0.259554
$951$	−6.00000	−0.194563
$952$	0	0
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	−8.00000	−0.259010
$955$	−6.00000	−0.194155
$956$	0	0
$957$	0	0
$958$	−34.0000	−1.09849
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	5.00000	0.161290
$962$	32.0000	1.03172
$963$	0	0
$964$	10.0000	0.322078
$965$	14.0000	0.450676
$966$	0	0
$967$	−10.0000	−0.321578	−0.160789	−	0.986989i	$-0.551404\pi$
$967$	−10.0000	−0.321578	−0.160789	+	0.986989i	$0.551404\pi$
$968$	−1.00000	−0.0321412
$969$	−8.00000	−0.256997
$970$	10.0000	0.321081
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−18.0000	−0.576757
$975$	4.00000	0.128103
$976$	−10.0000	−0.320092
$977$	34.0000	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$978$	−12.0000	−0.383718
$979$	6.00000	0.191761
$980$	7.00000	0.223607
$981$	−2.00000	−0.0638551
$982$	−4.00000	−0.127645
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	2.00000	0.0637577
$985$	16.0000	0.509802
$986$	0	0
$987$	0	0
$988$	−32.0000	−1.01806
$989$	16.0000	0.508770
$990$	−1.00000	−0.0317821
$991$	−58.0000	−1.84243	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000	−1.84243	−0.921215	+	0.389053i	$0.872802\pi$
$992$	6.00000	0.190500
$993$	−20.0000	−0.634681
$994$	0	0
$995$	−18.0000	−0.570638
$996$	−12.0000	−0.380235
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	20.0000	0.633089
$999$	−8.00000	−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.m.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.m.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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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