LMFDB - Embedded newform 5610.2.a.bi.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:	$0$
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)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +6.00000 q^{13} +4.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} -1.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +1.00000 q^{27} +4.00000 q^{28} -6.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.00000 q^{38} +6.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} +4.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +4.00000 q^{46} +1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +6.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} +1.00000 q^{55} +4.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +4.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} -1.00000 q^{66} -12.0000 q^{67} +1.00000 q^{68} +4.00000 q^{69} -4.00000 q^{70} +4.00000 q^{71} +1.00000 q^{72} +2.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} -4.00000 q^{77} +6.00000 q^{78} -4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} +4.00000 q^{84} -1.00000 q^{85} +4.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} +10.0000 q^{89} -1.00000 q^{90} +24.0000 q^{91} +4.00000 q^{92} +4.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} +9.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	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
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	4.00000	1.06904
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	4.00000	0.872872
$22$	−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
$26$	6.00000	1.17670
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−4.00000	−0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.00000	−0.648886
$39$	6.00000	0.960769
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	4.00000	0.617213
$43$	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
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	6.00000	0.832050
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	4.00000	0.534522
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	4.00000	0.508001
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−1.00000	−0.123091
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	1.00000	0.121268
$69$	4.00000	0.481543
$70$	−4.00000	−0.478091
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	2.00000	0.232495
$75$	1.00000	0.115470
$76$	−4.00000	−0.458831
$77$	−4.00000	−0.455842
$78$	6.00000	0.679366
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	4.00000	0.436436
$85$	−1.00000	−0.108465
$86$	4.00000	0.431331
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−1.00000	−0.105409
$91$	24.0000	2.51588
$92$	4.00000	0.417029
$93$	4.00000	0.414781
$94$	0	0
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	9.00000	0.909137
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	6.00000	0.588348
$105$	−4.00000	−0.390360
$106$	−10.0000	−0.971286
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	1.00000	0.0953463
$111$	2.00000	0.189832
$112$	4.00000	0.377964
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−4.00000	−0.374634
$115$	−4.00000	−0.373002
$116$	−6.00000	−0.557086
$117$	6.00000	0.554700
$118$	−4.00000	−0.368230
$119$	4.00000	0.366679
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	2.00000	0.180334
$124$	4.00000	0.359211
$125$	−1.00000	−0.0894427
$126$	4.00000	0.356348
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	4.00000	0.352180
$130$	−6.00000	−0.526235
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	−1.00000	−0.0870388
$133$	−16.0000	−1.38738
$134$	−12.0000	−1.03664
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	4.00000	0.340503
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	4.00000	0.335673
$143$	−6.00000	−0.501745
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	2.00000	0.165521
$147$	9.00000	0.742307
$148$	2.00000	0.164399
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	1.00000	0.0816497
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−4.00000	−0.324443
$153$	1.00000	0.0808452
$154$	−4.00000	−0.322329
$155$	−4.00000	−0.321288
$156$	6.00000	0.480384
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	−4.00000	−0.318223
$159$	−10.0000	−0.793052
$160$	−1.00000	−0.0790569
$161$	16.0000	1.26098
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	2.00000	0.156174
$165$	1.00000	0.0778499
$166$	12.0000	0.931381
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	4.00000	0.308607
$169$	23.0000	1.76923
$170$	−1.00000	−0.0766965
$171$	−4.00000	−0.305888
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−6.00000	−0.454859
$175$	4.00000	0.302372
$176$	−1.00000	−0.0753778
$177$	−4.00000	−0.300658
$178$	10.0000	0.749532
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.00000	−0.0745356
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	24.0000	1.77900
$183$	2.00000	0.147844
$184$	4.00000	0.294884
$185$	−2.00000	−0.147043
$186$	4.00000	0.293294
$187$	−1.00000	−0.0731272
$188$	0	0
$189$	4.00000	0.290957
$190$	4.00000	0.290191
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	1.00000	0.0721688
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	2.00000	0.143592
$195$	−6.00000	−0.429669
$196$	9.00000	0.642857
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	−1.00000	−0.0710669
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	1.00000	0.0707107
$201$	−12.0000	−0.846415
$202$	6.00000	0.422159
$203$	−24.0000	−1.68447
$204$	1.00000	0.0700140
$205$	−2.00000	−0.139686
$206$	−16.0000	−1.11477
$207$	4.00000	0.278019
$208$	6.00000	0.416025
$209$	4.00000	0.276686
$210$	−4.00000	−0.276026
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−10.0000	−0.686803
$213$	4.00000	0.274075
$214$	−12.0000	−0.820303
$215$	−4.00000	−0.272798
$216$	1.00000	0.0680414
$217$	16.0000	1.08615
$218$	10.0000	0.677285
$219$	2.00000	0.135147
$220$	1.00000	0.0674200
$221$	6.00000	0.403604
$222$	2.00000	0.134231
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	4.00000	0.267261
$225$	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	$0.630377\pi$
$228$	−4.00000	−0.264906
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	−4.00000	−0.263752
$231$	−4.00000	−0.263181
$232$	−6.00000	−0.393919
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−4.00000	−0.260378
$237$	−4.00000	−0.259828
$238$	4.00000	0.259281
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	−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
$244$	2.00000	0.128037
$245$	−9.00000	−0.574989
$246$	2.00000	0.127515
$247$	−24.0000	−1.52708
$248$	4.00000	0.254000
$249$	12.0000	0.760469
$250$	−1.00000	−0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	4.00000	0.251976
$253$	−4.00000	−0.251478
$254$	−8.00000	−0.501965
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	4.00000	0.249029
$259$	8.00000	0.497096
$260$	−6.00000	−0.372104
$261$	−6.00000	−0.371391
$262$	−20.0000	−1.23560
$263$	32.0000	1.97320	0.986602	−	0.163144i	$-0.0521635\pi$
$263$	32.0000	1.97320	0.986602	+	0.163144i	$0.0521635\pi$
$264$	−1.00000	−0.0615457
$265$	10.0000	0.614295
$266$	−16.0000	−0.981023
$267$	10.0000	0.611990
$268$	−12.0000	−0.733017
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	−1.00000	−0.0608581
$271$	−24.0000	−1.45790	−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000	−1.45790	−0.728948	+	0.684569i	$0.759990\pi$
$272$	1.00000	0.0606339
$273$	24.0000	1.45255
$274$	−6.00000	−0.362473
$275$	−1.00000	−0.0603023
$276$	4.00000	0.240772
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	20.0000	1.19952
$279$	4.00000	0.239474
$280$	−4.00000	−0.239046
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	4.00000	0.237356
$285$	4.00000	0.236940
$286$	−6.00000	−0.354787
$287$	8.00000	0.472225
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	2.00000	0.117242
$292$	2.00000	0.117041
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	9.00000	0.524891
$295$	4.00000	0.232889
$296$	2.00000	0.116248
$297$	−1.00000	−0.0580259
$298$	−18.0000	−1.04271
$299$	24.0000	1.38796
$300$	1.00000	0.0577350
$301$	16.0000	0.922225
$302$	0	0
$303$	6.00000	0.344691
$304$	−4.00000	−0.229416
$305$	−2.00000	−0.114520
$306$	1.00000	0.0571662
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−4.00000	−0.227921
$309$	−16.0000	−0.910208
$310$	−4.00000	−0.227185
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	6.00000	0.339683
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	22.0000	1.24153
$315$	−4.00000	−0.225374
$316$	−4.00000	−0.225018
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	−10.0000	−0.560772
$319$	6.00000	0.335936
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	16.0000	0.891645
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	6.00000	0.332820
$326$	4.00000	0.221540
$327$	10.0000	0.553001
$328$	2.00000	0.110432
$329$	0	0
$330$	1.00000	0.0550482
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	12.0000	0.658586
$333$	2.00000	0.109599
$334$	12.0000	0.656611
$335$	12.0000	0.655630
$336$	4.00000	0.218218
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	23.0000	1.25104
$339$	−6.00000	−0.325875
$340$	−1.00000	−0.0542326
$341$	−4.00000	−0.216612
$342$	−4.00000	−0.216295
$343$	8.00000	0.431959
$344$	4.00000	0.215666
$345$	−4.00000	−0.215353
$346$	−6.00000	−0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−6.00000	−0.321634
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	4.00000	0.213809
$351$	6.00000	0.320256
$352$	−1.00000	−0.0533002
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	−4.00000	−0.212598
$355$	−4.00000	−0.212298
$356$	10.0000	0.529999
$357$	4.00000	0.211702
$358$	12.0000	0.634220
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−14.0000	−0.735824
$363$	1.00000	0.0524864
$364$	24.0000	1.25794
$365$	−2.00000	−0.104685
$366$	2.00000	0.104542
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	4.00000	0.208514
$369$	2.00000	0.104116
$370$	−2.00000	−0.103975
$371$	−40.0000	−2.07670
$372$	4.00000	0.207390
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	−36.0000	−1.85409
$378$	4.00000	0.205738
$379$	−36.0000	−1.84920	−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000	−1.84920	−0.924598	+	0.380945i	$0.875599\pi$
$380$	4.00000	0.205196
$381$	−8.00000	−0.409852
$382$	16.0000	0.818631
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	2.00000	0.101797
$387$	4.00000	0.203331
$388$	2.00000	0.101535
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	−6.00000	−0.303822
$391$	4.00000	0.202289
$392$	9.00000	0.454569
$393$	−20.0000	−1.00887
$394$	−22.0000	−1.10834
$395$	4.00000	0.201262
$396$	−1.00000	−0.0502519
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	4.00000	0.200502
$399$	−16.0000	−0.801002
$400$	1.00000	0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	−12.0000	−0.598506
$403$	24.0000	1.19553
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	−24.0000	−1.19110
$407$	−2.00000	−0.0991363
$408$	1.00000	0.0495074
$409$	−38.0000	−1.87898	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000	−1.87898	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−2.00000	−0.0987730
$411$	−6.00000	−0.295958
$412$	−16.0000	−0.788263
$413$	−16.0000	−0.787309
$414$	4.00000	0.196589
$415$	−12.0000	−0.589057
$416$	6.00000	0.294174
$417$	20.0000	0.979404
$418$	4.00000	0.195646
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	−4.00000	−0.195180
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	12.0000	0.584151
$423$	0	0
$424$	−10.0000	−0.485643
$425$	1.00000	0.0485071
$426$	4.00000	0.193801
$427$	8.00000	0.387147
$428$	−12.0000	−0.580042
$429$	−6.00000	−0.289683
$430$	−4.00000	−0.192897
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	18.0000	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$434$	16.0000	0.768025
$435$	6.00000	0.287678
$436$	10.0000	0.478913
$437$	−16.0000	−0.765384
$438$	2.00000	0.0955637
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	1.00000	0.0476731
$441$	9.00000	0.428571
$442$	6.00000	0.285391
$443$	28.0000	1.33032	0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000	1.33032	0.665160	+	0.746701i	$0.268363\pi$
$444$	2.00000	0.0949158
$445$	−10.0000	−0.474045
$446$	8.00000	0.378811
$447$	−18.0000	−0.851371
$448$	4.00000	0.188982
$449$	42.0000	1.98210	0.991051	−	0.133482i	$-0.0426157\pi$
$449$	42.0000	1.98210	0.991051	+	0.133482i	$0.0426157\pi$
$450$	1.00000	0.0471405
$451$	−2.00000	−0.0941763
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−12.0000	−0.563188
$455$	−24.0000	−1.12514
$456$	−4.00000	−0.187317
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	22.0000	1.02799
$459$	1.00000	0.0466760
$460$	−4.00000	−0.186501
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	−4.00000	−0.186097
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−6.00000	−0.278543
$465$	−4.00000	−0.185496
$466$	2.00000	0.0926482
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	6.00000	0.277350
$469$	−48.0000	−2.21643
$470$	0	0
$471$	22.0000	1.01371
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	−4.00000	−0.183726
$475$	−4.00000	−0.183533
$476$	4.00000	0.183340
$477$	−10.0000	−0.457869
$478$	−24.0000	−1.09773
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	−1.00000	−0.0456435
$481$	12.0000	0.547153
$482$	10.0000	0.455488
$483$	16.0000	0.728025
$484$	1.00000	0.0454545
$485$	−2.00000	−0.0908153
$486$	1.00000	0.0453609
$487$	36.0000	1.63132	0.815658	−	0.578535i	$-0.196375\pi$
$487$	36.0000	1.63132	0.815658	+	0.578535i	$0.196375\pi$
$488$	2.00000	0.0905357
$489$	4.00000	0.180886
$490$	−9.00000	−0.406579
$491$	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
$493$	−6.00000	−0.270226
$494$	−24.0000	−1.07981
$495$	1.00000	0.0449467
$496$	4.00000	0.179605
$497$	16.0000	0.717698
$498$	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
$501$	12.0000	0.536120
$502$	−12.0000	−0.535586
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	4.00000	0.178174
$505$	−6.00000	−0.266996
$506$	−4.00000	−0.177822
$507$	23.0000	1.02147
$508$	−8.00000	−0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−1.00000	−0.0442807
$511$	8.00000	0.353899
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	2.00000	0.0882162
$515$	16.0000	0.705044
$516$	4.00000	0.176090
$517$	0	0
$518$	8.00000	0.351500
$519$	−6.00000	−0.263371
$520$	−6.00000	−0.263117
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	−6.00000	−0.262613
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−20.0000	−0.873704
$525$	4.00000	0.174574
$526$	32.0000	1.39527
$527$	4.00000	0.174243
$528$	−1.00000	−0.0435194
$529$	−7.00000	−0.304348
$530$	10.0000	0.434372
$531$	−4.00000	−0.173585
$532$	−16.0000	−0.693688
$533$	12.0000	0.519778
$534$	10.0000	0.432742
$535$	12.0000	0.518805
$536$	−12.0000	−0.518321
$537$	12.0000	0.517838
$538$	2.00000	0.0862261
$539$	−9.00000	−0.387657
$540$	−1.00000	−0.0430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−24.0000	−1.03089
$543$	−14.0000	−0.600798
$544$	1.00000	0.0428746
$545$	−10.0000	−0.428353
$546$	24.0000	1.02711
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−6.00000	−0.256307
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	24.0000	1.02243
$552$	4.00000	0.170251
$553$	−16.0000	−0.680389
$554$	−14.0000	−0.594803
$555$	−2.00000	−0.0848953
$556$	20.0000	0.848189
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	4.00000	0.169334
$559$	24.0000	1.01509
$560$	−4.00000	−0.169031
$561$	−1.00000	−0.0422200
$562$	10.0000	0.421825
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	4.00000	0.168133
$567$	4.00000	0.167984
$568$	4.00000	0.167836
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	4.00000	0.167542
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−6.00000	−0.250873
$573$	16.0000	0.668410
$574$	8.00000	0.333914
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	1.00000	0.0415945
$579$	2.00000	0.0831172
$580$	6.00000	0.249136
$581$	48.0000	1.99138
$582$	2.00000	0.0829027
$583$	10.0000	0.414158
$584$	2.00000	0.0827606
$585$	−6.00000	−0.248069
$586$	6.00000	0.247858
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	9.00000	0.371154
$589$	−16.0000	−0.659269
$590$	4.00000	0.164677
$591$	−22.0000	−0.904959
$592$	2.00000	0.0821995
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	−1.00000	−0.0410305
$595$	−4.00000	−0.163984
$596$	−18.0000	−0.737309
$597$	4.00000	0.163709
$598$	24.0000	0.981433
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	1.00000	0.0408248
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	16.0000	0.652111
$603$	−12.0000	−0.488678
$604$	0	0
$605$	−1.00000	−0.0406558
$606$	6.00000	0.243733
$607$	20.0000	0.811775	0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000	0.811775	0.405887	+	0.913923i	$0.366962\pi$
$608$	−4.00000	−0.162221
$609$	−24.0000	−0.972529
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	1.00000	0.0404226
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	−20.0000	−0.807134
$615$	−2.00000	−0.0806478
$616$	−4.00000	−0.161165
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	−16.0000	−0.643614
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−4.00000	−0.160644
$621$	4.00000	0.160514
$622$	−20.0000	−0.801927
$623$	40.0000	1.60257
$624$	6.00000	0.240192
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	4.00000	0.159745
$628$	22.0000	0.877896
$629$	2.00000	0.0797452
$630$	−4.00000	−0.159364
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	−4.00000	−0.159111
$633$	12.0000	0.476957
$634$	−22.0000	−0.873732
$635$	8.00000	0.317470
$636$	−10.0000	−0.396526
$637$	54.0000	2.13956
$638$	6.00000	0.237542
$639$	4.00000	0.158238
$640$	−1.00000	−0.0395285
$641$	−22.0000	−0.868948	−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000	−0.868948	−0.434474	+	0.900684i	$0.643066\pi$
$642$	−12.0000	−0.473602
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	16.0000	0.630488
$645$	−4.00000	−0.157500
$646$	−4.00000	−0.157378
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	1.00000	0.0392837
$649$	4.00000	0.157014
$650$	6.00000	0.235339
$651$	16.0000	0.627089
$652$	4.00000	0.156652
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	10.0000	0.391031
$655$	20.0000	0.781465
$656$	2.00000	0.0780869
$657$	2.00000	0.0780274
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	1.00000	0.0389249
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	28.0000	1.08825
$663$	6.00000	0.233021
$664$	12.0000	0.465690
$665$	16.0000	0.620453
$666$	2.00000	0.0774984
$667$	−24.0000	−0.929284
$668$	12.0000	0.464294
$669$	8.00000	0.309298
$670$	12.0000	0.463600
$671$	−2.00000	−0.0772091
$672$	4.00000	0.154303
$673$	−46.0000	−1.77317	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000	−1.77317	−0.886585	+	0.462566i	$0.846929\pi$
$674$	−6.00000	−0.231111
$675$	1.00000	0.0384900
$676$	23.0000	0.884615
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	−6.00000	−0.230429
$679$	8.00000	0.307012
$680$	−1.00000	−0.0383482
$681$	−12.0000	−0.459841
$682$	−4.00000	−0.153168
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−4.00000	−0.152944
$685$	6.00000	0.229248
$686$	8.00000	0.305441
$687$	22.0000	0.839352
$688$	4.00000	0.152499
$689$	−60.0000	−2.28582
$690$	−4.00000	−0.152277
$691$	−52.0000	−1.97817	−0.989087	−	0.147335i	$-0.952930\pi$
$691$	−52.0000	−1.97817	−0.989087	+	0.147335i	$0.952930\pi$
$692$	−6.00000	−0.228086
$693$	−4.00000	−0.151947
$694$	12.0000	0.455514
$695$	−20.0000	−0.758643
$696$	−6.00000	−0.227429
$697$	2.00000	0.0757554
$698$	−2.00000	−0.0757011
$699$	2.00000	0.0756469
$700$	4.00000	0.151186
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	6.00000	0.226455
$703$	−8.00000	−0.301726
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	18.0000	0.677439
$707$	24.0000	0.902613
$708$	−4.00000	−0.150329
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	−4.00000	−0.150117
$711$	−4.00000	−0.150012
$712$	10.0000	0.374766
$713$	16.0000	0.599205
$714$	4.00000	0.149696
$715$	6.00000	0.224387
$716$	12.0000	0.448461
$717$	−24.0000	−0.896296
$718$	8.00000	0.298557
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	−1.00000	−0.0372678
$721$	−64.0000	−2.38348
$722$	−3.00000	−0.111648
$723$	10.0000	0.371904
$724$	−14.0000	−0.520306
$725$	−6.00000	−0.222834
$726$	1.00000	0.0371135
$727$	−24.0000	−0.890111	−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000	−0.890111	−0.445055	+	0.895503i	$0.646816\pi$
$728$	24.0000	0.889499
$729$	1.00000	0.0370370
$730$	−2.00000	−0.0740233
$731$	4.00000	0.147945
$732$	2.00000	0.0739221
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	28.0000	1.03350
$735$	−9.00000	−0.331970
$736$	4.00000	0.147442
$737$	12.0000	0.442026
$738$	2.00000	0.0736210
$739$	28.0000	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$740$	−2.00000	−0.0735215
$741$	−24.0000	−0.881662
$742$	−40.0000	−1.46845
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	4.00000	0.146647
$745$	18.0000	0.659469
$746$	14.0000	0.512576
$747$	12.0000	0.439057
$748$	−1.00000	−0.0365636
$749$	−48.0000	−1.75388
$750$	−1.00000	−0.0365148
$751$	−36.0000	−1.31366	−0.656829	−	0.754039i	$-0.728103\pi$
$751$	−36.0000	−1.31366	−0.656829	+	0.754039i	$0.728103\pi$
$752$	0	0
$753$	−12.0000	−0.437304
$754$	−36.0000	−1.31104
$755$	0	0
$756$	4.00000	0.145479
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	−36.0000	−1.30758
$759$	−4.00000	−0.145191
$760$	4.00000	0.145095
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	−8.00000	−0.289809
$763$	40.0000	1.44810
$764$	16.0000	0.578860
$765$	−1.00000	−0.0361551
$766$	0	0
$767$	−24.0000	−0.866590
$768$	1.00000	0.0360844
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	4.00000	0.144150
$771$	2.00000	0.0720282
$772$	2.00000	0.0719816
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	2.00000	0.0717958
$777$	8.00000	0.286998
$778$	−10.0000	−0.358517
$779$	−8.00000	−0.286630
$780$	−6.00000	−0.214834
$781$	−4.00000	−0.143131
$782$	4.00000	0.143040
$783$	−6.00000	−0.214423
$784$	9.00000	0.321429
$785$	−22.0000	−0.785214
$786$	−20.0000	−0.713376
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	−22.0000	−0.783718
$789$	32.0000	1.13923
$790$	4.00000	0.142314
$791$	−24.0000	−0.853342
$792$	−1.00000	−0.0355335
$793$	12.0000	0.426132
$794$	−38.0000	−1.34857
$795$	10.0000	0.354663
$796$	4.00000	0.141776
$797$	−34.0000	−1.20434	−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000	−1.20434	−0.602171	+	0.798367i	$0.705697\pi$
$798$	−16.0000	−0.566394
$799$	0	0
$800$	1.00000	0.0353553
$801$	10.0000	0.353333
$802$	10.0000	0.353112
$803$	−2.00000	−0.0705785
$804$	−12.0000	−0.423207
$805$	−16.0000	−0.563926
$806$	24.0000	0.845364
$807$	2.00000	0.0704033
$808$	6.00000	0.211079
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	−1.00000	−0.0351364
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	−24.0000	−0.842235
$813$	−24.0000	−0.841717
$814$	−2.00000	−0.0701000
$815$	−4.00000	−0.140114
$816$	1.00000	0.0350070
$817$	−16.0000	−0.559769
$818$	−38.0000	−1.32864
$819$	24.0000	0.838628
$820$	−2.00000	−0.0698430
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	−6.00000	−0.209274
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−16.0000	−0.557386
$825$	−1.00000	−0.0348155
$826$	−16.0000	−0.556711
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	4.00000	0.139010
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−12.0000	−0.416526
$831$	−14.0000	−0.485655
$832$	6.00000	0.208013
$833$	9.00000	0.311832
$834$	20.0000	0.692543
$835$	−12.0000	−0.415277
$836$	4.00000	0.138343
$837$	4.00000	0.138260
$838$	36.0000	1.24360
$839$	−28.0000	−0.966667	−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000	−0.966667	−0.483334	+	0.875436i	$0.660574\pi$
$840$	−4.00000	−0.138013
$841$	7.00000	0.241379
$842$	−2.00000	−0.0689246
$843$	10.0000	0.344418
$844$	12.0000	0.413057
$845$	−23.0000	−0.791224
$846$	0	0
$847$	4.00000	0.137442
$848$	−10.0000	−0.343401
$849$	4.00000	0.137280
$850$	1.00000	0.0342997
$851$	8.00000	0.274236
$852$	4.00000	0.137038
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	8.00000	0.273754
$855$	4.00000	0.136797
$856$	−12.0000	−0.410152
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	−6.00000	−0.204837
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	−4.00000	−0.136399
$861$	8.00000	0.272639
$862$	12.0000	0.408722
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	1.00000	0.0340207
$865$	6.00000	0.204006
$866$	18.0000	0.611665
$867$	1.00000	0.0339618
$868$	16.0000	0.543075
$869$	4.00000	0.135691
$870$	6.00000	0.203419
$871$	−72.0000	−2.43963
$872$	10.0000	0.338643
$873$	2.00000	0.0676897
$874$	−16.0000	−0.541208
$875$	−4.00000	−0.135225
$876$	2.00000	0.0675737
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	−4.00000	−0.134993
$879$	6.00000	0.202375
$880$	1.00000	0.0337100
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	9.00000	0.303046
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	6.00000	0.201802
$885$	4.00000	0.134459
$886$	28.0000	0.940678
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	2.00000	0.0671156
$889$	−32.0000	−1.07325
$890$	−10.0000	−0.335201
$891$	−1.00000	−0.0335013
$892$	8.00000	0.267860
$893$	0	0
$894$	−18.0000	−0.602010
$895$	−12.0000	−0.401116
$896$	4.00000	0.133631
$897$	24.0000	0.801337
$898$	42.0000	1.40156
$899$	−24.0000	−0.800445
$900$	1.00000	0.0333333
$901$	−10.0000	−0.333148
$902$	−2.00000	−0.0665927
$903$	16.0000	0.532447
$904$	−6.00000	−0.199557
$905$	14.0000	0.465376
$906$	0	0
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	−12.0000	−0.398234
$909$	6.00000	0.199007
$910$	−24.0000	−0.795592
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	−4.00000	−0.132453
$913$	−12.0000	−0.397142
$914$	10.0000	0.330771
$915$	−2.00000	−0.0661180
$916$	22.0000	0.726900
$917$	−80.0000	−2.64183
$918$	1.00000	0.0330049
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	−4.00000	−0.131876
$921$	−20.0000	−0.659022
$922$	−18.0000	−0.592798
$923$	24.0000	0.789970
$924$	−4.00000	−0.131590
$925$	2.00000	0.0657596
$926$	−8.00000	−0.262896
$927$	−16.0000	−0.525509
$928$	−6.00000	−0.196960
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	−4.00000	−0.131165
$931$	−36.0000	−1.17985
$932$	2.00000	0.0655122
$933$	−20.0000	−0.654771
$934$	−28.0000	−0.916188
$935$	1.00000	0.0327035
$936$	6.00000	0.196116
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	−48.0000	−1.56726
$939$	−6.00000	−0.195803
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	22.0000	0.716799
$943$	8.00000	0.260516
$944$	−4.00000	−0.130189
$945$	−4.00000	−0.130120
$946$	−4.00000	−0.130051
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	−4.00000	−0.129914
$949$	12.0000	0.389536
$950$	−4.00000	−0.129777
$951$	−22.0000	−0.713399
$952$	4.00000	0.129641
$953$	58.0000	1.87880	0.939402	−	0.342817i	$-0.111381\pi$
$953$	58.0000	1.87880	0.939402	+	0.342817i	$0.111381\pi$
$954$	−10.0000	−0.323762
$955$	−16.0000	−0.517748
$956$	−24.0000	−0.776215
$957$	6.00000	0.193952
$958$	−28.0000	−0.904639
$959$	−24.0000	−0.775000
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	12.0000	0.386896
$963$	−12.0000	−0.386695
$964$	10.0000	0.322078
$965$	−2.00000	−0.0643823
$966$	16.0000	0.514792
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	1.00000	0.0321412
$969$	−4.00000	−0.128499
$970$	−2.00000	−0.0642161
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	1.00000	0.0320750
$973$	80.0000	2.56468
$974$	36.0000	1.15351
$975$	6.00000	0.192154
$976$	2.00000	0.0640184
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	4.00000	0.127906
$979$	−10.0000	−0.319601
$980$	−9.00000	−0.287494
$981$	10.0000	0.319275
$982$	4.00000	0.127645
$983$	−52.0000	−1.65854	−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000	−1.65854	−0.829271	+	0.558846i	$0.811244\pi$
$984$	2.00000	0.0637577
$985$	22.0000	0.700978
$986$	−6.00000	−0.191079
$987$	0	0
$988$	−24.0000	−0.763542
$989$	16.0000	0.508770
$990$	1.00000	0.0317821
$991$	44.0000	1.39771	0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000	1.39771	0.698853	+	0.715265i	$0.253694\pi$
$992$	4.00000	0.127000
$993$	28.0000	0.888553
$994$	16.0000	0.507489
$995$	−4.00000	−0.126809
$996$	12.0000	0.380235
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	−20.0000	−0.633089
$999$	2.00000	0.0632772

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bi.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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