LMFDB - Embedded newform 327.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [327,2,Mod(1,327)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(327, 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("327.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 327 = 3 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	327.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:	$2.61110814610$
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	$\chi$	$=$	327.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} -1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{18} -7.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +1.00000 q^{22} +1.00000 q^{23} +3.00000 q^{24} -4.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +7.00000 q^{29} +1.00000 q^{30} -2.00000 q^{31} -5.00000 q^{32} -1.00000 q^{33} +4.00000 q^{34} +2.00000 q^{35} -1.00000 q^{36} -6.00000 q^{37} +7.00000 q^{38} -4.00000 q^{39} -3.00000 q^{40} -2.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} +7.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +4.00000 q^{50} -4.00000 q^{51} +4.00000 q^{52} -4.00000 q^{53} -1.00000 q^{54} +1.00000 q^{55} -6.00000 q^{56} -7.00000 q^{57} -7.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +11.0000 q^{61} +2.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -12.0000 q^{67} +4.00000 q^{68} +1.00000 q^{69} -2.00000 q^{70} -10.0000 q^{71} +3.00000 q^{72} +11.0000 q^{73} +6.00000 q^{74} -4.00000 q^{75} +7.00000 q^{76} +2.00000 q^{77} +4.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +14.0000 q^{83} +2.00000 q^{84} +4.00000 q^{85} -4.00000 q^{86} +7.00000 q^{87} -3.00000 q^{88} +5.00000 q^{89} +1.00000 q^{90} +8.00000 q^{91} -1.00000 q^{92} -2.00000 q^{93} -7.00000 q^{94} +7.00000 q^{95} -5.00000 q^{96} -7.00000 q^{97} +3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	−0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.00000	0.534522
$15$	−1.00000	−0.258199
$16$	−1.00000	−0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−1.00000	−0.235702
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	1.00000	0.213201
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	3.00000	0.612372
$25$	−4.00000	−0.800000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	7.00000	1.29987	0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000	1.29987	0.649934	+	0.759991i	$0.274797\pi$
$30$	1.00000	0.182574
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−5.00000	−0.883883
$33$	−1.00000	−0.174078
$34$	4.00000	0.685994
$35$	2.00000	0.338062
$36$	−1.00000	−0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	7.00000	1.13555
$39$	−4.00000	−0.640513
$40$	−3.00000	−0.474342
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	2.00000	0.308607
$43$	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
$46$	−1.00000	−0.147442
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	4.00000	0.565685
$51$	−4.00000	−0.560112
$52$	4.00000	0.554700
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−6.00000	−0.801784
$57$	−7.00000	−0.927173
$58$	−7.00000	−0.919145
$59$	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
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	2.00000	0.254000
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	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	$0.761888\pi$
$68$	4.00000	0.485071
$69$	1.00000	0.120386
$70$	−2.00000	−0.239046
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	3.00000	0.353553
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	6.00000	0.697486
$75$	−4.00000	−0.461880
$76$	7.00000	0.802955
$77$	2.00000	0.227921
$78$	4.00000	0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	2.00000	0.218218
$85$	4.00000	0.433861
$86$	−4.00000	−0.431331
$87$	7.00000	0.750479
$88$	−3.00000	−0.319801
$89$	5.00000	0.529999	0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000	0.529999	0.264999	+	0.964249i	$0.414628\pi$
$90$	1.00000	0.105409
$91$	8.00000	0.838628
$92$	−1.00000	−0.104257
$93$	−2.00000	−0.207390
$94$	−7.00000	−0.721995
$95$	7.00000	0.718185
$96$	−5.00000	−0.510310
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	3.00000	0.303046
$99$	−1.00000	−0.100504
$100$	4.00000	0.400000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	4.00000	0.396059
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	−12.0000	−1.17670
$105$	2.00000	0.195180
$106$	4.00000	0.388514
$107$	5.00000	0.483368	0.241684	−	0.970355i	$-0.422300\pi$
$107$	5.00000	0.483368	0.241684	+	0.970355i	$0.422300\pi$
$108$	−1.00000	−0.0962250
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−1.00000	−0.0953463
$111$	−6.00000	−0.569495
$112$	2.00000	0.188982
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	7.00000	0.655610
$115$	−1.00000	−0.0932505
$116$	−7.00000	−0.649934
$117$	−4.00000	−0.369800
$118$	−4.00000	−0.368230
$119$	8.00000	0.733359
$120$	−3.00000	−0.273861
$121$	−10.0000	−0.909091
$122$	−11.0000	−0.995893
$123$	−2.00000	−0.180334
$124$	2.00000	0.179605
$125$	9.00000	0.804984
$126$	2.00000	0.178174
$127$	3.00000	0.266207	0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000	0.266207	0.133103	+	0.991102i	$0.457506\pi$
$128$	3.00000	0.265165
$129$	4.00000	0.352180
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	1.00000	0.0870388
$133$	14.0000	1.21395
$134$	12.0000	1.03664
$135$	−1.00000	−0.0860663
$136$	−12.0000	−1.02899
$137$	−19.0000	−1.62328	−0.811640	−	0.584158i	$-0.801425\pi$
$137$	−19.0000	−1.62328	−0.811640	+	0.584158i	$0.801425\pi$
$138$	−1.00000	−0.0851257
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	−2.00000	−0.169031
$141$	7.00000	0.589506
$142$	10.0000	0.839181
$143$	4.00000	0.334497
$144$	−1.00000	−0.0833333
$145$	−7.00000	−0.581318
$146$	−11.0000	−0.910366
$147$	−3.00000	−0.247436
$148$	6.00000	0.493197
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	4.00000	0.326599
$151$	−13.0000	−1.05792	−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000	−1.05792	−0.528962	+	0.848645i	$0.677419\pi$
$152$	−21.0000	−1.70332
$153$	−4.00000	−0.323381
$154$	−2.00000	−0.161165
$155$	2.00000	0.160644
$156$	4.00000	0.320256
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	−8.00000	−0.636446
$159$	−4.00000	−0.317221
$160$	5.00000	0.395285
$161$	−2.00000	−0.157622
$162$	−1.00000	−0.0785674
$163$	−15.0000	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$163$	−15.0000	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$164$	2.00000	0.156174
$165$	1.00000	0.0778499
$166$	−14.0000	−1.08661
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	−6.00000	−0.462910
$169$	3.00000	0.230769
$170$	−4.00000	−0.306786
$171$	−7.00000	−0.535303
$172$	−4.00000	−0.304997
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−7.00000	−0.530669
$175$	8.00000	0.604743
$176$	1.00000	0.0753778
$177$	4.00000	0.300658
$178$	−5.00000	−0.374766
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	1.00000	0.0745356
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	−8.00000	−0.592999
$183$	11.0000	0.813143
$184$	3.00000	0.221163
$185$	6.00000	0.441129
$186$	2.00000	0.146647
$187$	4.00000	0.292509
$188$	−7.00000	−0.510527
$189$	−2.00000	−0.145479
$190$	−7.00000	−0.507833
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	7.00000	0.505181
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	7.00000	0.502571
$195$	4.00000	0.286446
$196$	3.00000	0.214286
$197$	−21.0000	−1.49619	−0.748094	−	0.663593i	$-0.769031\pi$
$197$	−21.0000	−1.49619	−0.748094	+	0.663593i	$0.769031\pi$
$198$	1.00000	0.0710669
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−12.0000	−0.848528
$201$	−12.0000	−0.846415
$202$	4.00000	0.281439
$203$	−14.0000	−0.982607
$204$	4.00000	0.280056
$205$	2.00000	0.139686
$206$	−7.00000	−0.487713
$207$	1.00000	0.0695048
$208$	4.00000	0.277350
$209$	7.00000	0.484200
$210$	−2.00000	−0.138013
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	4.00000	0.274721
$213$	−10.0000	−0.685189
$214$	−5.00000	−0.341793
$215$	−4.00000	−0.272798
$216$	3.00000	0.204124
$217$	4.00000	0.271538
$218$	−1.00000	−0.0677285
$219$	11.0000	0.743311
$220$	−1.00000	−0.0674200
$221$	16.0000	1.07628
$222$	6.00000	0.402694
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	10.0000	0.668153
$225$	−4.00000	−0.266667
$226$	18.0000	1.19734
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	7.00000	0.463586
$229$	−8.00000	−0.528655	−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000	−0.528655	−0.264327	+	0.964433i	$0.585150\pi$
$230$	1.00000	0.0659380
$231$	2.00000	0.131590
$232$	21.0000	1.37872
$233$	−27.0000	−1.76883	−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000	−1.76883	−0.884414	+	0.466702i	$0.845442\pi$
$234$	4.00000	0.261488
$235$	−7.00000	−0.456630
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	−8.00000	−0.518563
$239$	26.0000	1.68180	0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000	1.68180	0.840900	+	0.541190i	$0.182026\pi$
$240$	1.00000	0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	10.0000	0.642824
$243$	1.00000	0.0641500
$244$	−11.0000	−0.704203
$245$	3.00000	0.191663
$246$	2.00000	0.127515
$247$	28.0000	1.78160
$248$	−6.00000	−0.381000
$249$	14.0000	0.887214
$250$	−9.00000	−0.569210
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	2.00000	0.125988
$253$	−1.00000	−0.0628695
$254$	−3.00000	−0.188237
$255$	4.00000	0.250490
$256$	−17.0000	−1.06250
$257$	16.0000	0.998053	0.499026	−	0.866587i	$-0.333691\pi$
$257$	16.0000	0.998053	0.499026	+	0.866587i	$0.333691\pi$
$258$	−4.00000	−0.249029
$259$	12.0000	0.745644
$260$	−4.00000	−0.248069
$261$	7.00000	0.433289
$262$	0	0
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	−3.00000	−0.184637
$265$	4.00000	0.245718
$266$	−14.0000	−0.858395
$267$	5.00000	0.305995
$268$	12.0000	0.733017
$269$	−16.0000	−0.975537	−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	1.00000	0.0608581
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	4.00000	0.242536
$273$	8.00000	0.484182
$274$	19.0000	1.14783
$275$	4.00000	0.241209
$276$	−1.00000	−0.0601929
$277$	−20.0000	−1.20168	−0.600842	−	0.799368i	$-0.705168\pi$
$277$	−20.0000	−1.20168	−0.600842	+	0.799368i	$0.705168\pi$
$278$	8.00000	0.479808
$279$	−2.00000	−0.119737
$280$	6.00000	0.358569
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	−7.00000	−0.416844
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	10.0000	0.593391
$285$	7.00000	0.414644
$286$	−4.00000	−0.236525
$287$	4.00000	0.236113
$288$	−5.00000	−0.294628
$289$	−1.00000	−0.0588235
$290$	7.00000	0.411054
$291$	−7.00000	−0.410347
$292$	−11.0000	−0.643726
$293$	29.0000	1.69420	0.847099	−	0.531435i	$-0.178347\pi$
$293$	29.0000	1.69420	0.847099	+	0.531435i	$0.178347\pi$
$294$	3.00000	0.174964
$295$	−4.00000	−0.232889
$296$	−18.0000	−1.04623
$297$	−1.00000	−0.0580259
$298$	−6.00000	−0.347571
$299$	−4.00000	−0.231326
$300$	4.00000	0.230940
$301$	−8.00000	−0.461112
$302$	13.0000	0.748066
$303$	−4.00000	−0.229794
$304$	7.00000	0.401478
$305$	−11.0000	−0.629858
$306$	4.00000	0.228665
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−2.00000	−0.113961
$309$	7.00000	0.398216
$310$	−2.00000	−0.113592
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	−12.0000	−0.679366
$313$	−28.0000	−1.58265	−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000	−1.58265	−0.791327	+	0.611393i	$0.790609\pi$
$314$	−1.00000	−0.0564333
$315$	2.00000	0.112687
$316$	−8.00000	−0.450035
$317$	−28.0000	−1.57264	−0.786318	−	0.617822i	$-0.788015\pi$
$317$	−28.0000	−1.57264	−0.786318	+	0.617822i	$0.788015\pi$
$318$	4.00000	0.224309
$319$	−7.00000	−0.391925
$320$	−7.00000	−0.391312
$321$	5.00000	0.279073
$322$	2.00000	0.111456
$323$	28.0000	1.55796
$324$	−1.00000	−0.0555556
$325$	16.0000	0.887520
$326$	15.0000	0.830773
$327$	1.00000	0.0553001
$328$	−6.00000	−0.331295
$329$	−14.0000	−0.771845
$330$	−1.00000	−0.0550482
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−14.0000	−0.768350
$333$	−6.00000	−0.328798
$334$	16.0000	0.875481
$335$	12.0000	0.655630
$336$	2.00000	0.109109
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	−3.00000	−0.163178
$339$	−18.0000	−0.977626
$340$	−4.00000	−0.216930
$341$	2.00000	0.108306
$342$	7.00000	0.378517
$343$	20.0000	1.07990
$344$	12.0000	0.646997
$345$	−1.00000	−0.0538382
$346$	10.0000	0.537603
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	−7.00000	−0.375239
$349$	31.0000	1.65939	0.829696	−	0.558216i	$-0.188514\pi$
$349$	31.0000	1.65939	0.829696	+	0.558216i	$0.188514\pi$
$350$	−8.00000	−0.427618
$351$	−4.00000	−0.213504
$352$	5.00000	0.266501
$353$	−33.0000	−1.75641	−0.878206	−	0.478282i	$-0.841260\pi$
$353$	−33.0000	−1.75641	−0.878206	+	0.478282i	$0.841260\pi$
$354$	−4.00000	−0.212598
$355$	10.0000	0.530745
$356$	−5.00000	−0.264999
$357$	8.00000	0.423405
$358$	3.00000	0.158555
$359$	27.0000	1.42501	0.712503	−	0.701669i	$-0.247562\pi$
$359$	27.0000	1.42501	0.712503	+	0.701669i	$0.247562\pi$
$360$	−3.00000	−0.158114
$361$	30.0000	1.57895
$362$	−18.0000	−0.946059
$363$	−10.0000	−0.524864
$364$	−8.00000	−0.419314
$365$	−11.0000	−0.575766
$366$	−11.0000	−0.574979
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−1.00000	−0.0521286
$369$	−2.00000	−0.104116
$370$	−6.00000	−0.311925
$371$	8.00000	0.415339
$372$	2.00000	0.103695
$373$	−7.00000	−0.362446	−0.181223	−	0.983442i	$-0.558006\pi$
$373$	−7.00000	−0.362446	−0.181223	+	0.983442i	$0.558006\pi$
$374$	−4.00000	−0.206835
$375$	9.00000	0.464758
$376$	21.0000	1.08299
$377$	−28.0000	−1.44207
$378$	2.00000	0.102869
$379$	11.0000	0.565032	0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000	0.565032	0.282516	+	0.959263i	$0.408831\pi$
$380$	−7.00000	−0.359092
$381$	3.00000	0.153695
$382$	0	0
$383$	−19.0000	−0.970855	−0.485427	−	0.874277i	$-0.661336\pi$
$383$	−19.0000	−0.970855	−0.485427	+	0.874277i	$0.661336\pi$
$384$	3.00000	0.153093
$385$	−2.00000	−0.101929
$386$	13.0000	0.661683
$387$	4.00000	0.203331
$388$	7.00000	0.355371
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	−4.00000	−0.202548
$391$	−4.00000	−0.202289
$392$	−9.00000	−0.454569
$393$	0	0
$394$	21.0000	1.05796
$395$	−8.00000	−0.402524
$396$	1.00000	0.0502519
$397$	−16.0000	−0.803017	−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000	−0.803017	−0.401508	+	0.915855i	$0.631514\pi$
$398$	−16.0000	−0.802008
$399$	14.0000	0.700877
$400$	4.00000	0.200000
$401$	9.00000	0.449439	0.224719	−	0.974424i	$-0.427853\pi$
$401$	9.00000	0.449439	0.224719	+	0.974424i	$0.427853\pi$
$402$	12.0000	0.598506
$403$	8.00000	0.398508
$404$	4.00000	0.199007
$405$	−1.00000	−0.0496904
$406$	14.0000	0.694808
$407$	6.00000	0.297409
$408$	−12.0000	−0.594089
$409$	−39.0000	−1.92843	−0.964213	−	0.265129i	$-0.914585\pi$
$409$	−39.0000	−1.92843	−0.964213	+	0.265129i	$0.914585\pi$
$410$	−2.00000	−0.0987730
$411$	−19.0000	−0.937201
$412$	−7.00000	−0.344865
$413$	−8.00000	−0.393654
$414$	−1.00000	−0.0491473
$415$	−14.0000	−0.687233
$416$	20.0000	0.980581
$417$	−8.00000	−0.391762
$418$	−7.00000	−0.342381
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	−2.00000	−0.0975900
$421$	−23.0000	−1.12095	−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000	−1.12095	−0.560476	+	0.828171i	$0.689382\pi$
$422$	2.00000	0.0973585
$423$	7.00000	0.340352
$424$	−12.0000	−0.582772
$425$	16.0000	0.776114
$426$	10.0000	0.484502
$427$	−22.0000	−1.06465
$428$	−5.00000	−0.241684
$429$	4.00000	0.193122
$430$	4.00000	0.192897
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	22.0000	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$434$	−4.00000	−0.192006
$435$	−7.00000	−0.335624
$436$	−1.00000	−0.0478913
$437$	−7.00000	−0.334855
$438$	−11.0000	−0.525600
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	3.00000	0.143019
$441$	−3.00000	−0.142857
$442$	−16.0000	−0.761042
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	6.00000	0.284747
$445$	−5.00000	−0.237023
$446$	−6.00000	−0.284108
$447$	6.00000	0.283790
$448$	−14.0000	−0.661438
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	4.00000	0.188562
$451$	2.00000	0.0941763
$452$	18.0000	0.846649
$453$	−13.0000	−0.610793
$454$	−18.0000	−0.844782
$455$	−8.00000	−0.375046
$456$	−21.0000	−0.983415
$457$	37.0000	1.73079	0.865393	−	0.501093i	$-0.167069\pi$
$457$	37.0000	1.73079	0.865393	+	0.501093i	$0.167069\pi$
$458$	8.00000	0.373815
$459$	−4.00000	−0.186704
$460$	1.00000	0.0466252
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	−2.00000	−0.0930484
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	−7.00000	−0.324967
$465$	2.00000	0.0927478
$466$	27.0000	1.25075
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	4.00000	0.184900
$469$	24.0000	1.10822
$470$	7.00000	0.322886
$471$	1.00000	0.0460776
$472$	12.0000	0.552345
$473$	−4.00000	−0.183920
$474$	−8.00000	−0.367452
$475$	28.0000	1.28473
$476$	−8.00000	−0.366679
$477$	−4.00000	−0.183147
$478$	−26.0000	−1.18921
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	5.00000	0.228218
$481$	24.0000	1.09431
$482$	14.0000	0.637683
$483$	−2.00000	−0.0910032
$484$	10.0000	0.454545
$485$	7.00000	0.317854
$486$	−1.00000	−0.0453609
$487$	−31.0000	−1.40474	−0.702372	−	0.711810i	$-0.747876\pi$
$487$	−31.0000	−1.40474	−0.702372	+	0.711810i	$0.747876\pi$
$488$	33.0000	1.49384
$489$	−15.0000	−0.678323
$490$	−3.00000	−0.135526
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	2.00000	0.0901670
$493$	−28.0000	−1.26106
$494$	−28.0000	−1.25978
$495$	1.00000	0.0449467
$496$	2.00000	0.0898027
$497$	20.0000	0.897123
$498$	−14.0000	−0.627355
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	−9.00000	−0.402492
$501$	−16.0000	−0.714827
$502$	−9.00000	−0.401690
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−6.00000	−0.267261
$505$	4.00000	0.177998
$506$	1.00000	0.0444554
$507$	3.00000	0.133235
$508$	−3.00000	−0.133103
$509$	10.0000	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$510$	−4.00000	−0.177123
$511$	−22.0000	−0.973223
$512$	11.0000	0.486136
$513$	−7.00000	−0.309058
$514$	−16.0000	−0.705730
$515$	−7.00000	−0.308457
$516$	−4.00000	−0.176090
$517$	−7.00000	−0.307860
$518$	−12.0000	−0.527250
$519$	−10.0000	−0.438951
$520$	12.0000	0.526235
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	−7.00000	−0.306382
$523$	6.00000	0.262362	0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000	0.262362	0.131181	+	0.991358i	$0.458123\pi$
$524$	0	0
$525$	8.00000	0.349149
$526$	−6.00000	−0.261612
$527$	8.00000	0.348485
$528$	1.00000	0.0435194
$529$	−22.0000	−0.956522
$530$	−4.00000	−0.173749
$531$	4.00000	0.173585
$532$	−14.0000	−0.606977
$533$	8.00000	0.346518
$534$	−5.00000	−0.216371
$535$	−5.00000	−0.216169
$536$	−36.0000	−1.55496
$537$	−3.00000	−0.129460
$538$	16.0000	0.689809
$539$	3.00000	0.129219
$540$	1.00000	0.0430331
$541$	3.00000	0.128980	0.0644900	−	0.997918i	$-0.479458\pi$
$541$	3.00000	0.128980	0.0644900	+	0.997918i	$0.479458\pi$
$542$	−5.00000	−0.214768
$543$	18.0000	0.772454
$544$	20.0000	0.857493
$545$	−1.00000	−0.0428353
$546$	−8.00000	−0.342368
$547$	43.0000	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$547$	43.0000	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$548$	19.0000	0.811640
$549$	11.0000	0.469469
$550$	−4.00000	−0.170561
$551$	−49.0000	−2.08747
$552$	3.00000	0.127688
$553$	−16.0000	−0.680389
$554$	20.0000	0.849719
$555$	6.00000	0.254686
$556$	8.00000	0.339276
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	2.00000	0.0846668
$559$	−16.0000	−0.676728
$560$	−2.00000	−0.0845154
$561$	4.00000	0.168880
$562$	−15.0000	−0.632737
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	−7.00000	−0.294753
$565$	18.0000	0.757266
$566$	13.0000	0.546431
$567$	−2.00000	−0.0839921
$568$	−30.0000	−1.25877
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	−7.00000	−0.293198
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	−4.00000	−0.166957
$575$	−4.00000	−0.166812
$576$	7.00000	0.291667
$577$	−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
$579$	−13.0000	−0.540262
$580$	7.00000	0.290659
$581$	−28.0000	−1.16164
$582$	7.00000	0.290159
$583$	4.00000	0.165663
$584$	33.0000	1.36555
$585$	4.00000	0.165380
$586$	−29.0000	−1.19798
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	3.00000	0.123718
$589$	14.0000	0.576860
$590$	4.00000	0.164677
$591$	−21.0000	−0.863825
$592$	6.00000	0.246598
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	1.00000	0.0410305
$595$	−8.00000	−0.327968
$596$	−6.00000	−0.245770
$597$	16.0000	0.654836
$598$	4.00000	0.163572
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−12.0000	−0.489898
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	8.00000	0.326056
$603$	−12.0000	−0.488678
$604$	13.0000	0.528962
$605$	10.0000	0.406558
$606$	4.00000	0.162489
$607$	−11.0000	−0.446476	−0.223238	−	0.974764i	$-0.571663\pi$
$607$	−11.0000	−0.446476	−0.223238	+	0.974764i	$0.571663\pi$
$608$	35.0000	1.41944
$609$	−14.0000	−0.567309
$610$	11.0000	0.445377
$611$	−28.0000	−1.13276
$612$	4.00000	0.161690
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	20.0000	0.807134
$615$	2.00000	0.0806478
$616$	6.00000	0.241747
$617$	2.00000	0.0805170	0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000	0.0805170	0.0402585	+	0.999189i	$0.487182\pi$
$618$	−7.00000	−0.281581
$619$	−14.0000	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$620$	−2.00000	−0.0803219
$621$	1.00000	0.0401286
$622$	−18.0000	−0.721734
$623$	−10.0000	−0.400642
$624$	4.00000	0.160128
$625$	11.0000	0.440000
$626$	28.0000	1.11911
$627$	7.00000	0.279553
$628$	−1.00000	−0.0399043
$629$	24.0000	0.956943
$630$	−2.00000	−0.0796819
$631$	−29.0000	−1.15447	−0.577236	−	0.816577i	$-0.695869\pi$
$631$	−29.0000	−1.15447	−0.577236	+	0.816577i	$0.695869\pi$
$632$	24.0000	0.954669
$633$	−2.00000	−0.0794929
$634$	28.0000	1.11202
$635$	−3.00000	−0.119051
$636$	4.00000	0.158610
$637$	12.0000	0.475457
$638$	7.00000	0.277133
$639$	−10.0000	−0.395594
$640$	−3.00000	−0.118585
$641$	20.0000	0.789953	0.394976	−	0.918691i	$-0.370753\pi$
$641$	20.0000	0.789953	0.394976	+	0.918691i	$0.370753\pi$
$642$	−5.00000	−0.197334
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	2.00000	0.0788110
$645$	−4.00000	−0.157500
$646$	−28.0000	−1.10165
$647$	−40.0000	−1.57256	−0.786281	−	0.617869i	$-0.787996\pi$
$647$	−40.0000	−1.57256	−0.786281	+	0.617869i	$0.787996\pi$
$648$	3.00000	0.117851
$649$	−4.00000	−0.157014
$650$	−16.0000	−0.627572
$651$	4.00000	0.156772
$652$	15.0000	0.587445
$653$	9.00000	0.352197	0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000	0.352197	0.176099	+	0.984373i	$0.443652\pi$
$654$	−1.00000	−0.0391031
$655$	0	0
$656$	2.00000	0.0780869
$657$	11.0000	0.429151
$658$	14.0000	0.545777
$659$	42.0000	1.63609	0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000	1.63609	0.818044	+	0.575156i	$0.195059\pi$
$660$	−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	$0.412226\pi$
$662$	−8.00000	−0.310929
$663$	16.0000	0.621389
$664$	42.0000	1.62992
$665$	−14.0000	−0.542897
$666$	6.00000	0.232495
$667$	7.00000	0.271041
$668$	16.0000	0.619059
$669$	6.00000	0.231973
$670$	−12.0000	−0.463600
$671$	−11.0000	−0.424650
$672$	10.0000	0.385758
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	8.00000	0.308148
$675$	−4.00000	−0.153960
$676$	−3.00000	−0.115385
$677$	−8.00000	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$678$	18.0000	0.691286
$679$	14.0000	0.537271
$680$	12.0000	0.460179
$681$	18.0000	0.689761
$682$	−2.00000	−0.0765840
$683$	−18.0000	−0.688751	−0.344375	−	0.938832i	$-0.611909\pi$
$683$	−18.0000	−0.688751	−0.344375	+	0.938832i	$0.611909\pi$
$684$	7.00000	0.267652
$685$	19.0000	0.725953
$686$	−20.0000	−0.763604
$687$	−8.00000	−0.305219
$688$	−4.00000	−0.152499
$689$	16.0000	0.609551
$690$	1.00000	0.0380693
$691$	29.0000	1.10321	0.551606	−	0.834105i	$-0.314015\pi$
$691$	29.0000	1.10321	0.551606	+	0.834105i	$0.314015\pi$
$692$	10.0000	0.380143
$693$	2.00000	0.0759737
$694$	−2.00000	−0.0759190
$695$	8.00000	0.303457
$696$	21.0000	0.796003
$697$	8.00000	0.303022
$698$	−31.0000	−1.17337
$699$	−27.0000	−1.02123
$700$	−8.00000	−0.302372
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	4.00000	0.150970
$703$	42.0000	1.58406
$704$	−7.00000	−0.263822
$705$	−7.00000	−0.263635
$706$	33.0000	1.24197
$707$	8.00000	0.300871
$708$	−4.00000	−0.150329
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	−10.0000	−0.375293
$711$	8.00000	0.300023
$712$	15.0000	0.562149
$713$	−2.00000	−0.0749006
$714$	−8.00000	−0.299392
$715$	−4.00000	−0.149592
$716$	3.00000	0.112115
$717$	26.0000	0.970988
$718$	−27.0000	−1.00763
$719$	−5.00000	−0.186469	−0.0932343	−	0.995644i	$-0.529721\pi$
$719$	−5.00000	−0.186469	−0.0932343	+	0.995644i	$0.529721\pi$
$720$	1.00000	0.0372678
$721$	−14.0000	−0.521387
$722$	−30.0000	−1.11648
$723$	−14.0000	−0.520666
$724$	−18.0000	−0.668965
$725$	−28.0000	−1.03989
$726$	10.0000	0.371135
$727$	−52.0000	−1.92857	−0.964287	−	0.264861i	$-0.914674\pi$
$727$	−52.0000	−1.92857	−0.964287	+	0.264861i	$0.914674\pi$
$728$	24.0000	0.889499
$729$	1.00000	0.0370370
$730$	11.0000	0.407128
$731$	−16.0000	−0.591781
$732$	−11.0000	−0.406572
$733$	−20.0000	−0.738717	−0.369358	−	0.929287i	$-0.620423\pi$
$733$	−20.0000	−0.738717	−0.369358	+	0.929287i	$0.620423\pi$
$734$	0	0
$735$	3.00000	0.110657
$736$	−5.00000	−0.184302
$737$	12.0000	0.442026
$738$	2.00000	0.0736210
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	−6.00000	−0.220564
$741$	28.0000	1.02861
$742$	−8.00000	−0.293689
$743$	−22.0000	−0.807102	−0.403551	−	0.914957i	$-0.632224\pi$
$743$	−22.0000	−0.807102	−0.403551	+	0.914957i	$0.632224\pi$
$744$	−6.00000	−0.219971
$745$	−6.00000	−0.219823
$746$	7.00000	0.256288
$747$	14.0000	0.512233
$748$	−4.00000	−0.146254
$749$	−10.0000	−0.365392
$750$	−9.00000	−0.328634
$751$	36.0000	1.31366	0.656829	−	0.754039i	$-0.271897\pi$
$751$	36.0000	1.31366	0.656829	+	0.754039i	$0.271897\pi$
$752$	−7.00000	−0.255264
$753$	9.00000	0.327978
$754$	28.0000	1.01970
$755$	13.0000	0.473118
$756$	2.00000	0.0727393
$757$	30.0000	1.09037	0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000	1.09037	0.545184	+	0.838316i	$0.316460\pi$
$758$	−11.0000	−0.399538
$759$	−1.00000	−0.0362977
$760$	21.0000	0.761750
$761$	−24.0000	−0.869999	−0.435000	−	0.900431i	$-0.643252\pi$
$761$	−24.0000	−0.869999	−0.435000	+	0.900431i	$0.643252\pi$
$762$	−3.00000	−0.108679
$763$	−2.00000	−0.0724049
$764$	0	0
$765$	4.00000	0.144620
$766$	19.0000	0.686498
$767$	−16.0000	−0.577727
$768$	−17.0000	−0.613435
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	2.00000	0.0720750
$771$	16.0000	0.576226
$772$	13.0000	0.467880
$773$	8.00000	0.287740	0.143870	−	0.989597i	$-0.454045\pi$
$773$	8.00000	0.287740	0.143870	+	0.989597i	$0.454045\pi$
$774$	−4.00000	−0.143777
$775$	8.00000	0.287368
$776$	−21.0000	−0.753856
$777$	12.0000	0.430498
$778$	0	0
$779$	14.0000	0.501602
$780$	−4.00000	−0.143223
$781$	10.0000	0.357828
$782$	4.00000	0.143040
$783$	7.00000	0.250160
$784$	3.00000	0.107143
$785$	−1.00000	−0.0356915
$786$	0	0
$787$	55.0000	1.96054	0.980269	−	0.197667i	$-0.0633366\pi$
$787$	55.0000	1.96054	0.980269	+	0.197667i	$0.0633366\pi$
$788$	21.0000	0.748094
$789$	6.00000	0.213606
$790$	8.00000	0.284627
$791$	36.0000	1.28001
$792$	−3.00000	−0.106600
$793$	−44.0000	−1.56249
$794$	16.0000	0.567819
$795$	4.00000	0.141865
$796$	−16.0000	−0.567105
$797$	50.0000	1.77109	0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000	1.77109	0.885545	+	0.464553i	$0.153785\pi$
$798$	−14.0000	−0.495595
$799$	−28.0000	−0.990569
$800$	20.0000	0.707107
$801$	5.00000	0.176666
$802$	−9.00000	−0.317801
$803$	−11.0000	−0.388182
$804$	12.0000	0.423207
$805$	2.00000	0.0704907
$806$	−8.00000	−0.281788
$807$	−16.0000	−0.563227
$808$	−12.0000	−0.422159
$809$	−45.0000	−1.58212	−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000	−1.58212	−0.791058	+	0.611741i	$0.790469\pi$
$810$	1.00000	0.0351364
$811$	−22.0000	−0.772524	−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000	−0.772524	−0.386262	+	0.922389i	$0.626234\pi$
$812$	14.0000	0.491304
$813$	5.00000	0.175358
$814$	−6.00000	−0.210300
$815$	15.0000	0.525427
$816$	4.00000	0.140028
$817$	−28.0000	−0.979596
$818$	39.0000	1.36360
$819$	8.00000	0.279543
$820$	−2.00000	−0.0698430
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	19.0000	0.662701
$823$	42.0000	1.46403	0.732014	−	0.681290i	$-0.238581\pi$
$823$	42.0000	1.46403	0.732014	+	0.681290i	$0.238581\pi$
$824$	21.0000	0.731570
$825$	4.00000	0.139262
$826$	8.00000	0.278356
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−1.00000	−0.0347524
$829$	27.0000	0.937749	0.468874	−	0.883265i	$-0.344660\pi$
$829$	27.0000	0.937749	0.468874	+	0.883265i	$0.344660\pi$
$830$	14.0000	0.485947
$831$	−20.0000	−0.693792
$832$	−28.0000	−0.970725
$833$	12.0000	0.415775
$834$	8.00000	0.277017
$835$	16.0000	0.553703
$836$	−7.00000	−0.242100
$837$	−2.00000	−0.0691301
$838$	−24.0000	−0.829066
$839$	−15.0000	−0.517858	−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000	−0.517858	−0.258929	+	0.965896i	$0.583369\pi$
$840$	6.00000	0.207020
$841$	20.0000	0.689655
$842$	23.0000	0.792632
$843$	15.0000	0.516627
$844$	2.00000	0.0688428
$845$	−3.00000	−0.103203
$846$	−7.00000	−0.240665
$847$	20.0000	0.687208
$848$	4.00000	0.137361
$849$	−13.0000	−0.446159
$850$	−16.0000	−0.548795
$851$	−6.00000	−0.205677
$852$	10.0000	0.342594
$853$	8.00000	0.273915	0.136957	−	0.990577i	$-0.456268\pi$
$853$	8.00000	0.273915	0.136957	+	0.990577i	$0.456268\pi$
$854$	22.0000	0.752825
$855$	7.00000	0.239395
$856$	15.0000	0.512689
$857$	−9.00000	−0.307434	−0.153717	−	0.988115i	$-0.549124\pi$
$857$	−9.00000	−0.307434	−0.153717	+	0.988115i	$0.549124\pi$
$858$	−4.00000	−0.136558
$859$	−41.0000	−1.39890	−0.699451	−	0.714681i	$-0.746572\pi$
$859$	−41.0000	−1.39890	−0.699451	+	0.714681i	$0.746572\pi$
$860$	4.00000	0.136399
$861$	4.00000	0.136320
$862$	0	0
$863$	−54.0000	−1.83818	−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000	−1.83818	−0.919091	+	0.394046i	$0.871075\pi$
$864$	−5.00000	−0.170103
$865$	10.0000	0.340010
$866$	−22.0000	−0.747590
$867$	−1.00000	−0.0339618
$868$	−4.00000	−0.135769
$869$	−8.00000	−0.271381
$870$	7.00000	0.237322
$871$	48.0000	1.62642
$872$	3.00000	0.101593
$873$	−7.00000	−0.236914
$874$	7.00000	0.236779
$875$	−18.0000	−0.608511
$876$	−11.0000	−0.371656
$877$	54.0000	1.82345	0.911725	−	0.410801i	$-0.134751\pi$
$877$	54.0000	1.82345	0.911725	+	0.410801i	$0.134751\pi$
$878$	−10.0000	−0.337484
$879$	29.0000	0.978146
$880$	−1.00000	−0.0337100
$881$	21.0000	0.707508	0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000	0.707508	0.353754	+	0.935339i	$0.384905\pi$
$882$	3.00000	0.101015
$883$	33.0000	1.11054	0.555269	−	0.831671i	$-0.312615\pi$
$883$	33.0000	1.11054	0.555269	+	0.831671i	$0.312615\pi$
$884$	−16.0000	−0.538138
$885$	−4.00000	−0.134459
$886$	−26.0000	−0.873487
$887$	−58.0000	−1.94745	−0.973725	−	0.227728i	$-0.926870\pi$
$887$	−58.0000	−1.94745	−0.973725	+	0.227728i	$0.926870\pi$
$888$	−18.0000	−0.604040
$889$	−6.00000	−0.201234
$890$	5.00000	0.167600
$891$	−1.00000	−0.0335013
$892$	−6.00000	−0.200895
$893$	−49.0000	−1.63972
$894$	−6.00000	−0.200670
$895$	3.00000	0.100279
$896$	−6.00000	−0.200446
$897$	−4.00000	−0.133556
$898$	0	0
$899$	−14.0000	−0.466926
$900$	4.00000	0.133333
$901$	16.0000	0.533037
$902$	−2.00000	−0.0665927
$903$	−8.00000	−0.266223
$904$	−54.0000	−1.79601
$905$	−18.0000	−0.598340
$906$	13.0000	0.431896
$907$	−16.0000	−0.531271	−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000	−0.531271	−0.265636	+	0.964073i	$0.585582\pi$
$908$	−18.0000	−0.597351
$909$	−4.00000	−0.132672
$910$	8.00000	0.265197
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	7.00000	0.231793
$913$	−14.0000	−0.463332
$914$	−37.0000	−1.22385
$915$	−11.0000	−0.363649
$916$	8.00000	0.264327
$917$	0	0
$918$	4.00000	0.132020
$919$	−31.0000	−1.02260	−0.511298	−	0.859404i	$-0.670835\pi$
$919$	−31.0000	−1.02260	−0.511298	+	0.859404i	$0.670835\pi$
$920$	−3.00000	−0.0989071
$921$	−20.0000	−0.659022
$922$	−2.00000	−0.0658665
$923$	40.0000	1.31662
$924$	−2.00000	−0.0657952
$925$	24.0000	0.789115
$926$	40.0000	1.31448
$927$	7.00000	0.229910
$928$	−35.0000	−1.14893
$929$	20.0000	0.656179	0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000	0.656179	0.328089	+	0.944647i	$0.393595\pi$
$930$	−2.00000	−0.0655826
$931$	21.0000	0.688247
$932$	27.0000	0.884414
$933$	18.0000	0.589294
$934$	6.00000	0.196326
$935$	−4.00000	−0.130814
$936$	−12.0000	−0.392232
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	−24.0000	−0.783628
$939$	−28.0000	−0.913745
$940$	7.00000	0.228315
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−1.00000	−0.0325818
$943$	−2.00000	−0.0651290
$944$	−4.00000	−0.130189
$945$	2.00000	0.0650600
$946$	4.00000	0.130051
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	−8.00000	−0.259828
$949$	−44.0000	−1.42830
$950$	−28.0000	−0.908440
$951$	−28.0000	−0.907962
$952$	24.0000	0.777844
$953$	−55.0000	−1.78162	−0.890812	−	0.454371i	$-0.849864\pi$
$953$	−55.0000	−1.78162	−0.890812	+	0.454371i	$0.849864\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	−26.0000	−0.840900
$957$	−7.00000	−0.226278
$958$	−12.0000	−0.387702
$959$	38.0000	1.22708
$960$	−7.00000	−0.225924
$961$	−27.0000	−0.870968
$962$	−24.0000	−0.773791
$963$	5.00000	0.161123
$964$	14.0000	0.450910
$965$	13.0000	0.418485
$966$	2.00000	0.0643489
$967$	−39.0000	−1.25416	−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000	−1.25416	−0.627078	+	0.778957i	$0.715749\pi$
$968$	−30.0000	−0.964237
$969$	28.0000	0.899490
$970$	−7.00000	−0.224756
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	−1.00000	−0.0320750
$973$	16.0000	0.512936
$974$	31.0000	0.993304
$975$	16.0000	0.512410
$976$	−11.0000	−0.352101
$977$	21.0000	0.671850	0.335925	−	0.941889i	$-0.390951\pi$
$977$	21.0000	0.671850	0.335925	+	0.941889i	$0.390951\pi$
$978$	15.0000	0.479647
$979$	−5.00000	−0.159801
$980$	−3.00000	−0.0958315
$981$	1.00000	0.0319275
$982$	0	0
$983$	−45.0000	−1.43528	−0.717639	−	0.696416i	$-0.754777\pi$
$983$	−45.0000	−1.43528	−0.717639	+	0.696416i	$0.754777\pi$
$984$	−6.00000	−0.191273
$985$	21.0000	0.669116
$986$	28.0000	0.891702
$987$	−14.0000	−0.445625
$988$	−28.0000	−0.890799
$989$	4.00000	0.127193
$990$	−1.00000	−0.0317821
$991$	35.0000	1.11181	0.555906	−	0.831245i	$-0.312372\pi$
$991$	35.0000	1.11181	0.555906	+	0.831245i	$0.312372\pi$
$992$	10.0000	0.317500
$993$	8.00000	0.253872
$994$	−20.0000	−0.634361
$995$	−16.0000	−0.507234
$996$	−14.0000	−0.443607
$997$	54.0000	1.71020	0.855099	−	0.518465i	$-0.173497\pi$
$997$	54.0000	1.71020	0.855099	+	0.518465i	$0.173497\pi$
$998$	16.0000	0.506471
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	327.2.a.a.1.1	✓	1
3.2	odd	2		981.2.a.b.1.1		1
4.3	odd	2		5232.2.a.c.1.1		1
5.4	even	2		8175.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
327.2.a.a.1.1	✓	1	1.1	even	1	trivial
981.2.a.b.1.1		1	3.2	odd	2
5232.2.a.c.1.1		1	4.3	odd	2
8175.2.a.e.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 327 = 3 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	327.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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