LMFDB - Embedded newform 2550.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(1,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.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:	$20.3618525154$
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	$\chi$	$=$	2550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} +4.00000 q^{21} -2.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.00000 q^{26} +1.00000 q^{27} +4.00000 q^{28} -4.00000 q^{29} -2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +3.00000 q^{37} -8.00000 q^{38} +2.00000 q^{39} -1.00000 q^{41} -4.00000 q^{42} -6.00000 q^{43} +2.00000 q^{44} -1.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{51} +2.00000 q^{52} -13.0000 q^{53} -1.00000 q^{54} -4.00000 q^{56} +8.00000 q^{57} +4.00000 q^{58} +15.0000 q^{59} +5.00000 q^{61} +2.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -10.0000 q^{67} -1.00000 q^{68} +1.00000 q^{69} -1.00000 q^{71} -1.00000 q^{72} -16.0000 q^{73} -3.00000 q^{74} +8.00000 q^{76} +8.00000 q^{77} -2.00000 q^{78} +12.0000 q^{79} +1.00000 q^{81} +1.00000 q^{82} -11.0000 q^{83} +4.00000 q^{84} +6.00000 q^{86} -4.00000 q^{87} -2.00000 q^{88} -2.00000 q^{89} +8.00000 q^{91} +1.00000 q^{92} -2.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} -9.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	−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
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	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	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	−2.00000	−0.426401
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	4.00000	0.755929
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−8.00000	−1.29777
$39$	2.00000	0.320256
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	−4.00000	−0.617213
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	−13.0000	−1.78569	−0.892844	−	0.450367i	$-0.851293\pi$
$53$	−13.0000	−1.78569	−0.892844	+	0.450367i	$0.851293\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−4.00000	−0.534522
$57$	8.00000	1.05963
$58$	4.00000	0.525226
$59$	15.0000	1.95283	0.976417	−	0.215894i	$-0.0692665\pi$
$59$	15.0000	1.95283	0.976417	+	0.215894i	$0.0692665\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	2.00000	0.254000
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−1.00000	−0.121268
$69$	1.00000	0.120386
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−1.00000	−0.117851
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−3.00000	−0.348743
$75$	0	0
$76$	8.00000	0.917663
$77$	8.00000	0.911685
$78$	−2.00000	−0.226455
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	4.00000	0.436436
$85$	0	0
$86$	6.00000	0.646997
$87$	−4.00000	−0.428845
$88$	−2.00000	−0.213201
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	1.00000	0.104257
$93$	−2.00000	−0.207390
$94$	−4.00000	−0.412568
$95$	0	0
$96$	−1.00000	−0.102062
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	−9.00000	−0.909137
$99$	2.00000	0.201008
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	1.00000	0.0990148
$103$	3.00000	0.295599	0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000	0.295599	0.147799	+	0.989017i	$0.452781\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	13.0000	1.26267
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	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	$0.530535\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	4.00000	0.377964
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	−8.00000	−0.749269
$115$	0	0
$116$	−4.00000	−0.371391
$117$	2.00000	0.184900
$118$	−15.0000	−1.38086
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−5.00000	−0.452679
$123$	−1.00000	−0.0901670
$124$	−2.00000	−0.179605
$125$	0	0
$126$	−4.00000	−0.356348
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	−6.00000	−0.528271
$130$	0	0
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	2.00000	0.174078
$133$	32.0000	2.77475
$134$	10.0000	0.863868
$135$	0	0
$136$	1.00000	0.0857493
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	−1.00000	−0.0851257
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	1.00000	0.0839181
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	0	0
$146$	16.0000	1.32417
$147$	9.00000	0.742307
$148$	3.00000	0.246598
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	0	0
$151$	1.00000	0.0813788	0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000	0.0813788	0.0406894	+	0.999172i	$0.487045\pi$
$152$	−8.00000	−0.648886
$153$	−1.00000	−0.0808452
$154$	−8.00000	−0.644658
$155$	0	0
$156$	2.00000	0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−12.0000	−0.954669
$159$	−13.0000	−1.03097
$160$	0	0
$161$	4.00000	0.315244
$162$	−1.00000	−0.0785674
$163$	−7.00000	−0.548282	−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000	−0.548282	−0.274141	+	0.961689i	$0.588394\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	11.0000	0.853766
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	−4.00000	−0.308607
$169$	−9.00000	−0.692308
$170$	0	0
$171$	8.00000	0.611775
$172$	−6.00000	−0.457496
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	4.00000	0.303239
$175$	0	0
$176$	2.00000	0.150756
$177$	15.0000	1.12747
$178$	2.00000	0.149906
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	0	0
$181$	11.0000	0.817624	0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000	0.817624	0.408812	+	0.912619i	$0.365943\pi$
$182$	−8.00000	−0.592999
$183$	5.00000	0.369611
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	−2.00000	−0.146254
$188$	4.00000	0.291730
$189$	4.00000	0.290957
$190$	0	0
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	1.00000	0.0721688
$193$	24.0000	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$194$	0	0
$195$	0	0
$196$	9.00000	0.642857
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−2.00000	−0.142134
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	−10.0000	−0.705346
$202$	10.0000	0.703598
$203$	−16.0000	−1.12298
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	−3.00000	−0.209020
$207$	1.00000	0.0695048
$208$	2.00000	0.138675
$209$	16.0000	1.10674
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−13.0000	−0.892844
$213$	−1.00000	−0.0685189
$214$	−12.0000	−0.820303
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−8.00000	−0.543075
$218$	2.00000	0.135457
$219$	−16.0000	−1.08118
$220$	0	0
$221$	−2.00000	−0.134535
$222$	−3.00000	−0.201347
$223$	17.0000	1.13840	0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000	1.13840	0.569202	+	0.822198i	$0.307252\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	15.0000	0.997785
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	8.00000	0.529813
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	0	0
$231$	8.00000	0.526361
$232$	4.00000	0.262613
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	15.0000	0.976417
$237$	12.0000	0.779484
$238$	4.00000	0.259281
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	5.00000	0.320092
$245$	0	0
$246$	1.00000	0.0637577
$247$	16.0000	1.01806
$248$	2.00000	0.127000
$249$	−11.0000	−0.697097
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	4.00000	0.251976
$253$	2.00000	0.125739
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	6.00000	0.373544
$259$	12.0000	0.745644
$260$	0	0
$261$	−4.00000	−0.247594
$262$	−8.00000	−0.494242
$263$	4.00000	0.246651	0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000	0.246651	0.123325	+	0.992366i	$0.460644\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	−32.0000	−1.96205
$267$	−2.00000	−0.122398
$268$	−10.0000	−0.610847
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−21.0000	−1.27566	−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000	−1.27566	−0.637830	+	0.770178i	$0.720168\pi$
$272$	−1.00000	−0.0606339
$273$	8.00000	0.484182
$274$	−12.0000	−0.724947
$275$	0	0
$276$	1.00000	0.0601929
$277$	31.0000	1.86261	0.931305	−	0.364241i	$-0.118672\pi$
$277$	31.0000	1.86261	0.931305	+	0.364241i	$0.118672\pi$
$278$	−1.00000	−0.0599760
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	−4.00000	−0.238197
$283$	−7.00000	−0.416107	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	−7.00000	−0.416107	−0.208053	+	0.978117i	$0.566713\pi$
$284$	−1.00000	−0.0593391
$285$	0	0
$286$	−4.00000	−0.236525
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	−16.0000	−0.936329
$293$	−31.0000	−1.81104	−0.905520	−	0.424304i	$-0.860519\pi$
$293$	−31.0000	−1.81104	−0.905520	+	0.424304i	$0.860519\pi$
$294$	−9.00000	−0.524891
$295$	0	0
$296$	−3.00000	−0.174371
$297$	2.00000	0.116052
$298$	−1.00000	−0.0579284
$299$	2.00000	0.115663
$300$	0	0
$301$	−24.0000	−1.38334
$302$	−1.00000	−0.0575435
$303$	−10.0000	−0.574485
$304$	8.00000	0.458831
$305$	0	0
$306$	1.00000	0.0571662
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	8.00000	0.455842
$309$	3.00000	0.170664
$310$	0	0
$311$	5.00000	0.283524	0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000	0.283524	0.141762	+	0.989901i	$0.454723\pi$
$312$	−2.00000	−0.113228
$313$	20.0000	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	12.0000	0.675053
$317$	26.0000	1.46031	0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000	1.46031	0.730153	+	0.683284i	$0.239449\pi$
$318$	13.0000	0.729004
$319$	−8.00000	−0.447914
$320$	0	0
$321$	12.0000	0.669775
$322$	−4.00000	−0.222911
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	0	0
$326$	7.00000	0.387694
$327$	−2.00000	−0.110600
$328$	1.00000	0.0552158
$329$	16.0000	0.882109
$330$	0	0
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	−11.0000	−0.603703
$333$	3.00000	0.164399
$334$	24.0000	1.31322
$335$	0	0
$336$	4.00000	0.218218
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	9.00000	0.489535
$339$	−15.0000	−0.814688
$340$	0	0
$341$	−4.00000	−0.216612
$342$	−8.00000	−0.432590
$343$	8.00000	0.431959
$344$	6.00000	0.323498
$345$	0	0
$346$	−8.00000	−0.430083
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	−4.00000	−0.214423
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	−2.00000	−0.106600
$353$	16.0000	0.851594	0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000	0.851594	0.425797	+	0.904819i	$0.359994\pi$
$354$	−15.0000	−0.797241
$355$	0	0
$356$	−2.00000	−0.106000
$357$	−4.00000	−0.211702
$358$	−9.00000	−0.475665
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−11.0000	−0.578147
$363$	−7.00000	−0.367405
$364$	8.00000	0.419314
$365$	0	0
$366$	−5.00000	−0.261354
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	1.00000	0.0521286
$369$	−1.00000	−0.0520579
$370$	0	0
$371$	−52.0000	−2.69971
$372$	−2.00000	−0.103695
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	−4.00000	−0.206284
$377$	−8.00000	−0.412021
$378$	−4.00000	−0.205738
$379$	−1.00000	−0.0513665	−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000	−0.0513665	−0.0256833	+	0.999670i	$0.508176\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	−10.0000	−0.511645
$383$	−20.0000	−1.02195	−0.510976	−	0.859595i	$-0.670716\pi$
$383$	−20.0000	−1.02195	−0.510976	+	0.859595i	$0.670716\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−24.0000	−1.22157
$387$	−6.00000	−0.304997
$388$	0	0
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	0	0
$391$	−1.00000	−0.0505722
$392$	−9.00000	−0.454569
$393$	8.00000	0.403547
$394$	−2.00000	−0.100759
$395$	0	0
$396$	2.00000	0.100504
$397$	−21.0000	−1.05396	−0.526980	−	0.849878i	$-0.676676\pi$
$397$	−21.0000	−1.05396	−0.526980	+	0.849878i	$0.676676\pi$
$398$	−10.0000	−0.501255
$399$	32.0000	1.60200
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	10.0000	0.498755
$403$	−4.00000	−0.199254
$404$	−10.0000	−0.497519
$405$	0	0
$406$	16.0000	0.794067
$407$	6.00000	0.297409
$408$	1.00000	0.0495074
$409$	19.0000	0.939490	0.469745	−	0.882802i	$-0.344346\pi$
$409$	19.0000	0.939490	0.469745	+	0.882802i	$0.344346\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	3.00000	0.147799
$413$	60.0000	2.95241
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	1.00000	0.0489702
$418$	−16.0000	−0.782586
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	−24.0000	−1.16969	−0.584844	−	0.811146i	$-0.698844\pi$
$421$	−24.0000	−1.16969	−0.584844	+	0.811146i	$0.698844\pi$
$422$	−4.00000	−0.194717
$423$	4.00000	0.194487
$424$	13.0000	0.631336
$425$	0	0
$426$	1.00000	0.0484502
$427$	20.0000	0.967868
$428$	12.0000	0.580042
$429$	4.00000	0.193122
$430$	0	0
$431$	−28.0000	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$431$	−28.0000	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$432$	1.00000	0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	8.00000	0.382692
$438$	16.0000	0.764510
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	2.00000	0.0951303
$443$	−39.0000	−1.85295	−0.926473	−	0.376361i	$-0.877175\pi$
$443$	−39.0000	−1.85295	−0.926473	+	0.376361i	$0.877175\pi$
$444$	3.00000	0.142374
$445$	0	0
$446$	−17.0000	−0.804973
$447$	1.00000	0.0472984
$448$	4.00000	0.188982
$449$	−42.0000	−1.98210	−0.991051	−	0.133482i	$-0.957384\pi$
$449$	−42.0000	−1.98210	−0.991051	+	0.133482i	$0.957384\pi$
$450$	0	0
$451$	−2.00000	−0.0941763
$452$	−15.0000	−0.705541
$453$	1.00000	0.0469841
$454$	22.0000	1.03251
$455$	0	0
$456$	−8.00000	−0.374634
$457$	−31.0000	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−31.0000	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$458$	18.0000	0.841085
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−1.00000	−0.0465746	−0.0232873	−	0.999729i	$-0.507413\pi$
$461$	−1.00000	−0.0465746	−0.0232873	+	0.999729i	$0.507413\pi$
$462$	−8.00000	−0.372194
$463$	35.0000	1.62659	0.813294	−	0.581853i	$-0.197672\pi$
$463$	35.0000	1.62659	0.813294	+	0.581853i	$0.197672\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	−3.00000	−0.138972
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	2.00000	0.0924500
$469$	−40.0000	−1.84703
$470$	0	0
$471$	−14.0000	−0.645086
$472$	−15.0000	−0.690431
$473$	−12.0000	−0.551761
$474$	−12.0000	−0.551178
$475$	0	0
$476$	−4.00000	−0.183340
$477$	−13.0000	−0.595229
$478$	−6.00000	−0.274434
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	14.0000	0.637683
$483$	4.00000	0.182006
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−5.00000	−0.226339
$489$	−7.00000	−0.316551
$490$	0	0
$491$	39.0000	1.76005	0.880023	−	0.474932i	$-0.157527\pi$
$491$	39.0000	1.76005	0.880023	+	0.474932i	$0.157527\pi$
$492$	−1.00000	−0.0450835
$493$	4.00000	0.180151
$494$	−16.0000	−0.719874
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	−4.00000	−0.179425
$498$	11.0000	0.492922
$499$	−41.0000	−1.83541	−0.917706	−	0.397260i	$-0.869961\pi$
$499$	−41.0000	−1.83541	−0.917706	+	0.397260i	$0.869961\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	4.00000	0.178529
$503$	−41.0000	−1.82810	−0.914050	−	0.405602i	$-0.867062\pi$
$503$	−41.0000	−1.82810	−0.914050	+	0.405602i	$0.867062\pi$
$504$	−4.00000	−0.178174
$505$	0	0
$506$	−2.00000	−0.0889108
$507$	−9.00000	−0.399704
$508$	16.0000	0.709885
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	−64.0000	−2.83119
$512$	−1.00000	−0.0441942
$513$	8.00000	0.353209
$514$	−12.0000	−0.529297
$515$	0	0
$516$	−6.00000	−0.264135
$517$	8.00000	0.351840
$518$	−12.0000	−0.527250
$519$	8.00000	0.351161
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	4.00000	0.175075
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	−4.00000	−0.174408
$527$	2.00000	0.0871214
$528$	2.00000	0.0870388
$529$	−22.0000	−0.956522
$530$	0	0
$531$	15.0000	0.650945
$532$	32.0000	1.38738
$533$	−2.00000	−0.0866296
$534$	2.00000	0.0865485
$535$	0	0
$536$	10.0000	0.431934
$537$	9.00000	0.388379
$538$	6.00000	0.258678
$539$	18.0000	0.775315
$540$	0	0
$541$	15.0000	0.644900	0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000	0.644900	0.322450	+	0.946586i	$0.395494\pi$
$542$	21.0000	0.902027
$543$	11.0000	0.472055
$544$	1.00000	0.0428746
$545$	0	0
$546$	−8.00000	−0.342368
$547$	13.0000	0.555840	0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000	0.555840	0.277920	+	0.960604i	$0.410355\pi$
$548$	12.0000	0.512615
$549$	5.00000	0.213395
$550$	0	0
$551$	−32.0000	−1.36325
$552$	−1.00000	−0.0425628
$553$	48.0000	2.04117
$554$	−31.0000	−1.31706
$555$	0	0
$556$	1.00000	0.0424094
$557$	−31.0000	−1.31351	−0.656756	−	0.754103i	$-0.728072\pi$
$557$	−31.0000	−1.31351	−0.656756	+	0.754103i	$0.728072\pi$
$558$	2.00000	0.0846668
$559$	−12.0000	−0.507546
$560$	0	0
$561$	−2.00000	−0.0844401
$562$	2.00000	0.0843649
$563$	15.0000	0.632175	0.316087	−	0.948730i	$-0.397631\pi$
$563$	15.0000	0.632175	0.316087	+	0.948730i	$0.397631\pi$
$564$	4.00000	0.168430
$565$	0	0
$566$	7.00000	0.294232
$567$	4.00000	0.167984
$568$	1.00000	0.0419591
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−41.0000	−1.71580	−0.857898	−	0.513820i	$-0.828230\pi$
$571$	−41.0000	−1.71580	−0.857898	+	0.513820i	$0.828230\pi$
$572$	4.00000	0.167248
$573$	10.0000	0.417756
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−33.0000	−1.37381	−0.686904	−	0.726748i	$-0.741031\pi$
$577$	−33.0000	−1.37381	−0.686904	+	0.726748i	$0.741031\pi$
$578$	−1.00000	−0.0415945
$579$	24.0000	0.997406
$580$	0	0
$581$	−44.0000	−1.82543
$582$	0	0
$583$	−26.0000	−1.07681
$584$	16.0000	0.662085
$585$	0	0
$586$	31.0000	1.28060
$587$	25.0000	1.03186	0.515930	−	0.856631i	$-0.327446\pi$
$587$	25.0000	1.03186	0.515930	+	0.856631i	$0.327446\pi$
$588$	9.00000	0.371154
$589$	−16.0000	−0.659269
$590$	0	0
$591$	2.00000	0.0822690
$592$	3.00000	0.123299
$593$	−12.0000	−0.492781	−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000	−0.492781	−0.246390	+	0.969171i	$0.579245\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	1.00000	0.0409616
$597$	10.0000	0.409273
$598$	−2.00000	−0.0817861
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	24.0000	0.978167
$603$	−10.0000	−0.407231
$604$	1.00000	0.0406894
$605$	0	0
$606$	10.0000	0.406222
$607$	−34.0000	−1.38002	−0.690009	−	0.723801i	$-0.742393\pi$
$607$	−34.0000	−1.38002	−0.690009	+	0.723801i	$0.742393\pi$
$608$	−8.00000	−0.324443
$609$	−16.0000	−0.648353
$610$	0	0
$611$	8.00000	0.323645
$612$	−1.00000	−0.0404226
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−22.0000	−0.887848
$615$	0	0
$616$	−8.00000	−0.322329
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	−3.00000	−0.120678
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	−5.00000	−0.200482
$623$	−8.00000	−0.320513
$624$	2.00000	0.0800641
$625$	0	0
$626$	−20.0000	−0.799361
$627$	16.0000	0.638978
$628$	−14.0000	−0.558661
$629$	−3.00000	−0.119618
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	−12.0000	−0.477334
$633$	4.00000	0.158986
$634$	−26.0000	−1.03259
$635$	0	0
$636$	−13.0000	−0.515484
$637$	18.0000	0.713186
$638$	8.00000	0.316723
$639$	−1.00000	−0.0395594
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	−12.0000	−0.473602
$643$	29.0000	1.14365	0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000	1.14365	0.571824	+	0.820376i	$0.306236\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	8.00000	0.314756
$647$	−38.0000	−1.49393	−0.746967	−	0.664861i	$-0.768491\pi$
$647$	−38.0000	−1.49393	−0.746967	+	0.664861i	$0.768491\pi$
$648$	−1.00000	−0.0392837
$649$	30.0000	1.17760
$650$	0	0
$651$	−8.00000	−0.313545
$652$	−7.00000	−0.274141
$653$	−12.0000	−0.469596	−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000	−0.469596	−0.234798	+	0.972044i	$0.575443\pi$
$654$	2.00000	0.0782062
$655$	0	0
$656$	−1.00000	−0.0390434
$657$	−16.0000	−0.624219
$658$	−16.0000	−0.623745
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	−10.0000	−0.388661
$663$	−2.00000	−0.0776736
$664$	11.0000	0.426883
$665$	0	0
$666$	−3.00000	−0.116248
$667$	−4.00000	−0.154881
$668$	−24.0000	−0.928588
$669$	17.0000	0.657258
$670$	0	0
$671$	10.0000	0.386046
$672$	−4.00000	−0.154303
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	15.0000	0.576072
$679$	0	0
$680$	0	0
$681$	−22.0000	−0.843042
$682$	4.00000	0.153168
$683$	−6.00000	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	−8.00000	−0.305441
$687$	−18.0000	−0.686743
$688$	−6.00000	−0.228748
$689$	−26.0000	−0.990521
$690$	0	0
$691$	−41.0000	−1.55971	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000	−1.55971	−0.779857	+	0.625958i	$0.784708\pi$
$692$	8.00000	0.304114
$693$	8.00000	0.303895
$694$	−16.0000	−0.607352
$695$	0	0
$696$	4.00000	0.151620
$697$	1.00000	0.0378777
$698$	14.0000	0.529908
$699$	3.00000	0.113470
$700$	0	0
$701$	−3.00000	−0.113308	−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000	−0.113308	−0.0566542	+	0.998394i	$0.518043\pi$
$702$	−2.00000	−0.0754851
$703$	24.0000	0.905177
$704$	2.00000	0.0753778
$705$	0	0
$706$	−16.0000	−0.602168
$707$	−40.0000	−1.50435
$708$	15.0000	0.563735
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	2.00000	0.0749532
$713$	−2.00000	−0.0749006
$714$	4.00000	0.149696
$715$	0	0
$716$	9.00000	0.336346
$717$	6.00000	0.224074
$718$	−36.0000	−1.34351
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	12.0000	0.446903
$722$	−45.0000	−1.67473
$723$	−14.0000	−0.520666
$724$	11.0000	0.408812
$725$	0	0
$726$	7.00000	0.259794
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	0	0
$731$	6.00000	0.221918
$732$	5.00000	0.184805
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	−2.00000	−0.0738213
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−20.0000	−0.736709
$738$	1.00000	0.0368105
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	52.0000	1.90898
$743$	17.0000	0.623670	0.311835	−	0.950136i	$-0.399056\pi$
$743$	17.0000	0.623670	0.311835	+	0.950136i	$0.399056\pi$
$744$	2.00000	0.0733236
$745$	0	0
$746$	−4.00000	−0.146450
$747$	−11.0000	−0.402469
$748$	−2.00000	−0.0731272
$749$	48.0000	1.75388
$750$	0	0
$751$	−48.0000	−1.75154	−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000	−1.75154	−0.875772	+	0.482724i	$0.839647\pi$
$752$	4.00000	0.145865
$753$	−4.00000	−0.145768
$754$	8.00000	0.291343
$755$	0	0
$756$	4.00000	0.145479
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	1.00000	0.0363216
$759$	2.00000	0.0725954
$760$	0	0
$761$	36.0000	1.30500	0.652499	−	0.757789i	$-0.273720\pi$
$761$	36.0000	1.30500	0.652499	+	0.757789i	$0.273720\pi$
$762$	−16.0000	−0.579619
$763$	−8.00000	−0.289619
$764$	10.0000	0.361787
$765$	0	0
$766$	20.0000	0.722629
$767$	30.0000	1.08324
$768$	1.00000	0.0360844
$769$	−37.0000	−1.33425	−0.667127	−	0.744944i	$-0.732476\pi$
$769$	−37.0000	−1.33425	−0.667127	+	0.744944i	$0.732476\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	24.0000	0.863779
$773$	−15.0000	−0.539513	−0.269756	−	0.962929i	$-0.586943\pi$
$773$	−15.0000	−0.539513	−0.269756	+	0.962929i	$0.586943\pi$
$774$	6.00000	0.215666
$775$	0	0
$776$	0	0
$777$	12.0000	0.430498
$778$	−9.00000	−0.322666
$779$	−8.00000	−0.286630
$780$	0	0
$781$	−2.00000	−0.0715656
$782$	1.00000	0.0357599
$783$	−4.00000	−0.142948
$784$	9.00000	0.321429
$785$	0	0
$786$	−8.00000	−0.285351
$787$	3.00000	0.106938	0.0534692	−	0.998569i	$-0.482972\pi$
$787$	3.00000	0.106938	0.0534692	+	0.998569i	$0.482972\pi$
$788$	2.00000	0.0712470
$789$	4.00000	0.142404
$790$	0	0
$791$	−60.0000	−2.13335
$792$	−2.00000	−0.0710669
$793$	10.0000	0.355110
$794$	21.0000	0.745262
$795$	0	0
$796$	10.0000	0.354441
$797$	−31.0000	−1.09808	−0.549038	−	0.835797i	$-0.685006\pi$
$797$	−31.0000	−1.09808	−0.549038	+	0.835797i	$0.685006\pi$
$798$	−32.0000	−1.13279
$799$	−4.00000	−0.141510
$800$	0	0
$801$	−2.00000	−0.0706665
$802$	−3.00000	−0.105934
$803$	−32.0000	−1.12926
$804$	−10.0000	−0.352673
$805$	0	0
$806$	4.00000	0.140894
$807$	−6.00000	−0.211210
$808$	10.0000	0.351799
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	−16.0000	−0.561490
$813$	−21.0000	−0.736502
$814$	−6.00000	−0.210300
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	−48.0000	−1.67931
$818$	−19.0000	−0.664319
$819$	8.00000	0.279543
$820$	0	0
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	−12.0000	−0.418548
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−3.00000	−0.104510
$825$	0	0
$826$	−60.0000	−2.08767
$827$	−38.0000	−1.32139	−0.660695	−	0.750655i	$-0.729738\pi$
$827$	−38.0000	−1.32139	−0.660695	+	0.750655i	$0.729738\pi$
$828$	1.00000	0.0347524
$829$	−16.0000	−0.555703	−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000	−0.555703	−0.277851	+	0.960624i	$0.589622\pi$
$830$	0	0
$831$	31.0000	1.07538
$832$	2.00000	0.0693375
$833$	−9.00000	−0.311832
$834$	−1.00000	−0.0346272
$835$	0	0
$836$	16.0000	0.553372
$837$	−2.00000	−0.0691301
$838$	−24.0000	−0.829066
$839$	27.0000	0.932144	0.466072	−	0.884747i	$-0.345669\pi$
$839$	27.0000	0.932144	0.466072	+	0.884747i	$0.345669\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	24.0000	0.827095
$843$	−2.00000	−0.0688837
$844$	4.00000	0.137686
$845$	0	0
$846$	−4.00000	−0.137523
$847$	−28.0000	−0.962091
$848$	−13.0000	−0.446422
$849$	−7.00000	−0.240239
$850$	0	0
$851$	3.00000	0.102839
$852$	−1.00000	−0.0342594
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−20.0000	−0.684386
$855$	0	0
$856$	−12.0000	−0.410152
$857$	7.00000	0.239115	0.119558	−	0.992827i	$-0.461852\pi$
$857$	7.00000	0.239115	0.119558	+	0.992827i	$0.461852\pi$
$858$	−4.00000	−0.136558
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	28.0000	0.953684
$863$	40.0000	1.36162	0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000	1.36162	0.680808	+	0.732462i	$0.261629\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−14.0000	−0.475739
$867$	1.00000	0.0339618
$868$	−8.00000	−0.271538
$869$	24.0000	0.814144
$870$	0	0
$871$	−20.0000	−0.677674
$872$	2.00000	0.0677285
$873$	0	0
$874$	−8.00000	−0.270604
$875$	0	0
$876$	−16.0000	−0.540590
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	12.0000	0.404980
$879$	−31.0000	−1.04560
$880$	0	0
$881$	33.0000	1.11180	0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000	1.11180	0.555899	+	0.831250i	$0.312374\pi$
$882$	−9.00000	−0.303046
$883$	−50.0000	−1.68263	−0.841317	−	0.540542i	$-0.818219\pi$
$883$	−50.0000	−1.68263	−0.841317	+	0.540542i	$0.818219\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	39.0000	1.31023
$887$	15.0000	0.503651	0.251825	−	0.967773i	$-0.418969\pi$
$887$	15.0000	0.503651	0.251825	+	0.967773i	$0.418969\pi$
$888$	−3.00000	−0.100673
$889$	64.0000	2.14649
$890$	0	0
$891$	2.00000	0.0670025
$892$	17.0000	0.569202
$893$	32.0000	1.07084
$894$	−1.00000	−0.0334450
$895$	0	0
$896$	−4.00000	−0.133631
$897$	2.00000	0.0667781
$898$	42.0000	1.40156
$899$	8.00000	0.266815
$900$	0	0
$901$	13.0000	0.433093
$902$	2.00000	0.0665927
$903$	−24.0000	−0.798670
$904$	15.0000	0.498893
$905$	0	0
$906$	−1.00000	−0.0332228
$907$	23.0000	0.763702	0.381851	−	0.924224i	$-0.375287\pi$
$907$	23.0000	0.763702	0.381851	+	0.924224i	$0.375287\pi$
$908$	−22.0000	−0.730096
$909$	−10.0000	−0.331679
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	8.00000	0.264906
$913$	−22.0000	−0.728094
$914$	31.0000	1.02539
$915$	0	0
$916$	−18.0000	−0.594737
$917$	32.0000	1.05673
$918$	1.00000	0.0330049
$919$	−47.0000	−1.55039	−0.775193	−	0.631724i	$-0.782348\pi$
$919$	−47.0000	−1.55039	−0.775193	+	0.631724i	$0.782348\pi$
$920$	0	0
$921$	22.0000	0.724925
$922$	1.00000	0.0329332
$923$	−2.00000	−0.0658308
$924$	8.00000	0.263181
$925$	0	0
$926$	−35.0000	−1.15017
$927$	3.00000	0.0985329
$928$	4.00000	0.131306
$929$	−15.0000	−0.492134	−0.246067	−	0.969253i	$-0.579138\pi$
$929$	−15.0000	−0.492134	−0.246067	+	0.969253i	$0.579138\pi$
$930$	0	0
$931$	72.0000	2.35970
$932$	3.00000	0.0982683
$933$	5.00000	0.163693
$934$	−3.00000	−0.0981630
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	−17.0000	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$937$	−17.0000	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$938$	40.0000	1.30605
$939$	20.0000	0.652675
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	14.0000	0.456145
$943$	−1.00000	−0.0325645
$944$	15.0000	0.488208
$945$	0	0
$946$	12.0000	0.390154
$947$	16.0000	0.519930	0.259965	−	0.965618i	$-0.416289\pi$
$947$	16.0000	0.519930	0.259965	+	0.965618i	$0.416289\pi$
$948$	12.0000	0.389742
$949$	−32.0000	−1.03876
$950$	0	0
$951$	26.0000	0.843108
$952$	4.00000	0.129641
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	13.0000	0.420891
$955$	0	0
$956$	6.00000	0.194054
$957$	−8.00000	−0.258603
$958$	16.0000	0.516937
$959$	48.0000	1.55000
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−6.00000	−0.193448
$963$	12.0000	0.386695
$964$	−14.0000	−0.450910
$965$	0	0
$966$	−4.00000	−0.128698
$967$	1.00000	0.0321578	0.0160789	−	0.999871i	$-0.494882\pi$
$967$	1.00000	0.0321578	0.0160789	+	0.999871i	$0.494882\pi$
$968$	7.00000	0.224989
$969$	−8.00000	−0.256997
$970$	0	0
$971$	25.0000	0.802288	0.401144	−	0.916015i	$-0.368613\pi$
$971$	25.0000	0.802288	0.401144	+	0.916015i	$0.368613\pi$
$972$	1.00000	0.0320750
$973$	4.00000	0.128234
$974$	2.00000	0.0640841
$975$	0	0
$976$	5.00000	0.160046
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	7.00000	0.223835
$979$	−4.00000	−0.127841
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	−39.0000	−1.24454
$983$	−8.00000	−0.255160	−0.127580	−	0.991828i	$-0.540721\pi$
$983$	−8.00000	−0.255160	−0.127580	+	0.991828i	$0.540721\pi$
$984$	1.00000	0.0318788
$985$	0	0
$986$	−4.00000	−0.127386
$987$	16.0000	0.509286
$988$	16.0000	0.509028
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	2.00000	0.0635001
$993$	10.0000	0.317340
$994$	4.00000	0.126872
$995$	0	0
$996$	−11.0000	−0.348548
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	41.0000	1.29783
$999$	3.00000	0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.a.q.1.1	✓	1
3.2	odd	2		7650.2.a.cj.1.1		1
5.2	odd	4		2550.2.d.h.2449.1		2
5.3	odd	4		2550.2.d.h.2449.2		2
5.4	even	2		2550.2.a.t.1.1	yes	1
15.14	odd	2		7650.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.q.1.1	✓	1	1.1	even	1	trivial
2550.2.a.t.1.1	yes	1	5.4	even	2
2550.2.d.h.2449.1		2	5.2	odd	4
2550.2.d.h.2449.2		2	5.3	odd	4
7650.2.a.c.1.1		1	15.14	odd	2
7650.2.a.cj.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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