LMFDB - Embedded newform 2550.2.a.g.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:	$1$
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	$\chi$	$=$	2550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +5.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -5.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -7.00000 q^{19} -5.00000 q^{21} +1.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} +2.00000 q^{26} -1.00000 q^{27} +5.00000 q^{28} -10.0000 q^{29} -5.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} +3.00000 q^{37} +7.00000 q^{38} +2.00000 q^{39} -10.0000 q^{41} +5.00000 q^{42} -9.00000 q^{43} -1.00000 q^{44} -2.00000 q^{46} -7.00000 q^{47} -1.00000 q^{48} +18.0000 q^{49} -1.00000 q^{51} -2.00000 q^{52} -11.0000 q^{53} +1.00000 q^{54} -5.00000 q^{56} +7.00000 q^{57} +10.0000 q^{58} +2.00000 q^{61} +5.00000 q^{62} +5.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +13.0000 q^{67} +1.00000 q^{68} -2.00000 q^{69} -10.0000 q^{71} -1.00000 q^{72} +4.00000 q^{73} -3.00000 q^{74} -7.00000 q^{76} -5.00000 q^{77} -2.00000 q^{78} +3.00000 q^{79} +1.00000 q^{81} +10.0000 q^{82} +14.0000 q^{83} -5.00000 q^{84} +9.00000 q^{86} +10.0000 q^{87} +1.00000 q^{88} +4.00000 q^{89} -10.0000 q^{91} +2.00000 q^{92} +5.00000 q^{93} +7.00000 q^{94} +1.00000 q^{96} +6.00000 q^{97} -18.0000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−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
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−5.00000	−1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−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	$0.796740\pi$
$20$	0	0
$21$	−5.00000	−1.09109
$22$	1.00000	0.213201
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	5.00000	0.944911
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	7.00000	1.13555
$39$	2.00000	0.320256
$40$	0	0
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	5.00000	0.771517
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−2.00000	−0.294884
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	−1.00000	−0.144338
$49$	18.0000	2.57143
$50$	0	0
$51$	−1.00000	−0.140028
$52$	−2.00000	−0.277350
$53$	−11.0000	−1.51097	−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000	−1.51097	−0.755483	+	0.655168i	$0.772598\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−5.00000	−0.668153
$57$	7.00000	0.927173
$58$	10.0000	1.31306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	5.00000	0.635001
$63$	5.00000	0.629941
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	1.00000	0.121268
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−1.00000	−0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−3.00000	−0.348743
$75$	0	0
$76$	−7.00000	−0.802955
$77$	−5.00000	−0.569803
$78$	−2.00000	−0.226455
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	−5.00000	−0.545545
$85$	0	0
$86$	9.00000	0.970495
$87$	10.0000	1.07211
$88$	1.00000	0.106600
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	−10.0000	−1.04828
$92$	2.00000	0.208514
$93$	5.00000	0.518476
$94$	7.00000	0.721995
$95$	0	0
$96$	1.00000	0.102062
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−18.0000	−1.81827
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−7.00000	−0.696526	−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000	−0.696526	−0.348263	+	0.937397i	$0.613228\pi$
$102$	1.00000	0.0990148
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	11.0000	1.06841
$107$	−9.00000	−0.870063	−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000	−0.870063	−0.435031	+	0.900415i	$0.643263\pi$
$108$	−1.00000	−0.0962250
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	5.00000	0.472456
$113$	−3.00000	−0.282216	−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000	−0.282216	−0.141108	+	0.989994i	$0.545067\pi$
$114$	−7.00000	−0.655610
$115$	0	0
$116$	−10.0000	−0.928477
$117$	−2.00000	−0.184900
$118$	0	0
$119$	5.00000	0.458349
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−2.00000	−0.181071
$123$	10.0000	0.901670
$124$	−5.00000	−0.449013
$125$	0	0
$126$	−5.00000	−0.445435
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	9.00000	0.792406
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	1.00000	0.0870388
$133$	−35.0000	−3.03488
$134$	−13.0000	−1.12303
$135$	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	$0.328677\pi$
$138$	2.00000	0.170251
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	7.00000	0.589506
$142$	10.0000	0.839181
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	−4.00000	−0.331042
$147$	−18.0000	−1.48461
$148$	3.00000	0.246598
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	7.00000	0.567775
$153$	1.00000	0.0808452
$154$	5.00000	0.402911
$155$	0	0
$156$	2.00000	0.160128
$157$	−16.0000	−1.27694	−0.638470	−	0.769647i	$-0.720432\pi$
$157$	−16.0000	−1.27694	−0.638470	+	0.769647i	$0.720432\pi$
$158$	−3.00000	−0.238667
$159$	11.0000	0.872357
$160$	0	0
$161$	10.0000	0.788110
$162$	−1.00000	−0.0785674
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	−14.0000	−1.08661
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	5.00000	0.385758
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−7.00000	−0.535303
$172$	−9.00000	−0.686244
$173$	−20.0000	−1.52057	−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000	−1.52057	−0.760286	+	0.649589i	$0.774941\pi$
$174$	−10.0000	−0.758098
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−4.00000	−0.299813
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	17.0000	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$182$	10.0000	0.741249
$183$	−2.00000	−0.147844
$184$	−2.00000	−0.147442
$185$	0	0
$186$	−5.00000	−0.366618
$187$	−1.00000	−0.0731272
$188$	−7.00000	−0.510527
$189$	−5.00000	−0.363696
$190$	0	0
$191$	25.0000	1.80894	0.904468	−	0.426541i	$-0.140268\pi$
$191$	25.0000	1.80894	0.904468	+	0.426541i	$0.140268\pi$
$192$	−1.00000	−0.0721688
$193$	−24.0000	−1.72756	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−24.0000	−1.72756	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	18.0000	1.28571
$197$	−8.00000	−0.569976	−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000	−0.569976	−0.284988	+	0.958531i	$0.591990\pi$
$198$	1.00000	0.0710669
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	0	0
$201$	−13.0000	−0.916949
$202$	7.00000	0.492518
$203$	−50.0000	−3.50931
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	0	0
$207$	2.00000	0.139010
$208$	−2.00000	−0.138675
$209$	7.00000	0.484200
$210$	0	0
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	−11.0000	−0.755483
$213$	10.0000	0.685189
$214$	9.00000	0.615227
$215$	0	0
$216$	1.00000	0.0680414
$217$	−25.0000	−1.69711
$218$	−19.0000	−1.28684
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−2.00000	−0.134535
$222$	3.00000	0.201347
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	3.00000	0.199557
$227$	1.00000	0.0663723	0.0331862	−	0.999449i	$-0.489435\pi$
$227$	1.00000	0.0663723	0.0331862	+	0.999449i	$0.489435\pi$
$228$	7.00000	0.463586
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	0	0
$231$	5.00000	0.328976
$232$	10.0000	0.656532
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	0	0
$237$	−3.00000	−0.194871
$238$	−5.00000	−0.324102
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	10.0000	0.642824
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	0	0
$246$	−10.0000	−0.637577
$247$	14.0000	0.890799
$248$	5.00000	0.317500
$249$	−14.0000	−0.887214
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	5.00000	0.314970
$253$	−2.00000	−0.125739
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	−9.00000	−0.560316
$259$	15.0000	0.932055
$260$	0	0
$261$	−10.0000	−0.618984
$262$	4.00000	0.247121
$263$	17.0000	1.04826	0.524132	−	0.851637i	$-0.324390\pi$
$263$	17.0000	1.04826	0.524132	+	0.851637i	$0.324390\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	35.0000	2.14599
$267$	−4.00000	−0.244796
$268$	13.0000	0.794101
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−6.00000	−0.364474	−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000	−0.364474	−0.182237	+	0.983255i	$0.558334\pi$
$272$	1.00000	0.0606339
$273$	10.0000	0.605228
$274$	−12.0000	−0.724947
$275$	0	0
$276$	−2.00000	−0.120386
$277$	23.0000	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	20.0000	1.19952
$279$	−5.00000	−0.299342
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−7.00000	−0.416844
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	−2.00000	−0.118262
$287$	−50.0000	−2.95141
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	−6.00000	−0.351726
$292$	4.00000	0.234082
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	18.0000	1.04978
$295$	0	0
$296$	−3.00000	−0.174371
$297$	1.00000	0.0580259
$298$	2.00000	0.115857
$299$	−4.00000	−0.231326
$300$	0	0
$301$	−45.0000	−2.59376
$302$	8.00000	0.460348
$303$	7.00000	0.402139
$304$	−7.00000	−0.401478
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	−5.00000	−0.284901
$309$	0	0
$310$	0	0
$311$	26.0000	1.47432	0.737162	−	0.675716i	$-0.236165\pi$
$311$	26.0000	1.47432	0.737162	+	0.675716i	$0.236165\pi$
$312$	−2.00000	−0.113228
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	16.0000	0.902932
$315$	0	0
$316$	3.00000	0.168763
$317$	−20.0000	−1.12331	−0.561656	−	0.827371i	$-0.689836\pi$
$317$	−20.0000	−1.12331	−0.561656	+	0.827371i	$0.689836\pi$
$318$	−11.0000	−0.616849
$319$	10.0000	0.559893
$320$	0	0
$321$	9.00000	0.502331
$322$	−10.0000	−0.557278
$323$	−7.00000	−0.389490
$324$	1.00000	0.0555556
$325$	0	0
$326$	−16.0000	−0.886158
$327$	−19.0000	−1.05070
$328$	10.0000	0.552158
$329$	−35.0000	−1.92961
$330$	0	0
$331$	7.00000	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$332$	14.0000	0.768350
$333$	3.00000	0.164399
$334$	6.00000	0.328305
$335$	0	0
$336$	−5.00000	−0.272772
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	9.00000	0.489535
$339$	3.00000	0.162938
$340$	0	0
$341$	5.00000	0.270765
$342$	7.00000	0.378517
$343$	55.0000	2.96972
$344$	9.00000	0.485247
$345$	0	0
$346$	20.0000	1.07521
$347$	5.00000	0.268414	0.134207	−	0.990953i	$-0.457151\pi$
$347$	5.00000	0.268414	0.134207	+	0.990953i	$0.457151\pi$
$348$	10.0000	0.536056
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	1.00000	0.0533002
$353$	2.00000	0.106449	0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000	0.106449	0.0532246	+	0.998583i	$0.483050\pi$
$354$	0	0
$355$	0	0
$356$	4.00000	0.212000
$357$	−5.00000	−0.264628
$358$	12.0000	0.634220
$359$	−3.00000	−0.158334	−0.0791670	−	0.996861i	$-0.525226\pi$
$359$	−3.00000	−0.158334	−0.0791670	+	0.996861i	$0.525226\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−17.0000	−0.893500
$363$	10.0000	0.524864
$364$	−10.0000	−0.524142
$365$	0	0
$366$	2.00000	0.104542
$367$	−5.00000	−0.260998	−0.130499	−	0.991448i	$-0.541658\pi$
$367$	−5.00000	−0.260998	−0.130499	+	0.991448i	$0.541658\pi$
$368$	2.00000	0.104257
$369$	−10.0000	−0.520579
$370$	0	0
$371$	−55.0000	−2.85546
$372$	5.00000	0.259238
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	1.00000	0.0517088
$375$	0	0
$376$	7.00000	0.360997
$377$	20.0000	1.03005
$378$	5.00000	0.257172
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	4.00000	0.204926
$382$	−25.0000	−1.27911
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	24.0000	1.22157
$387$	−9.00000	−0.457496
$388$	6.00000	0.304604
$389$	−15.0000	−0.760530	−0.380265	−	0.924878i	$-0.624167\pi$
$389$	−15.0000	−0.760530	−0.380265	+	0.924878i	$0.624167\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	−18.0000	−0.909137
$393$	4.00000	0.201773
$394$	8.00000	0.403034
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	3.00000	0.150566	0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000	0.150566	0.0752828	+	0.997162i	$0.476014\pi$
$398$	−7.00000	−0.350878
$399$	35.0000	1.75219
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	13.0000	0.648381
$403$	10.0000	0.498135
$404$	−7.00000	−0.348263
$405$	0	0
$406$	50.0000	2.48146
$407$	−3.00000	−0.148704
$408$	1.00000	0.0495074
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	0	0
$413$	0	0
$414$	−2.00000	−0.0982946
$415$	0	0
$416$	2.00000	0.0980581
$417$	20.0000	0.979404
$418$	−7.00000	−0.342381
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−30.0000	−1.46211	−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000	−1.46211	−0.731055	+	0.682318i	$0.760972\pi$
$422$	14.0000	0.681509
$423$	−7.00000	−0.340352
$424$	11.0000	0.534207
$425$	0	0
$426$	−10.0000	−0.484502
$427$	10.0000	0.483934
$428$	−9.00000	−0.435031
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−1.00000	−0.0481125
$433$	−35.0000	−1.68199	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−35.0000	−1.68199	−0.840996	+	0.541041i	$0.818030\pi$
$434$	25.0000	1.20004
$435$	0	0
$436$	19.0000	0.909935
$437$	−14.0000	−0.669711
$438$	4.00000	0.191127
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	2.00000	0.0951303
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	−3.00000	−0.142374
$445$	0	0
$446$	−10.0000	−0.473514
$447$	2.00000	0.0945968
$448$	5.00000	0.236228
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	10.0000	0.470882
$452$	−3.00000	−0.141108
$453$	8.00000	0.375873
$454$	−1.00000	−0.0469323
$455$	0	0
$456$	−7.00000	−0.327805
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	12.0000	0.560723
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	35.0000	1.63011	0.815056	−	0.579382i	$-0.196706\pi$
$461$	35.0000	1.63011	0.815056	+	0.579382i	$0.196706\pi$
$462$	−5.00000	−0.232621
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	18.0000	0.833834
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	−2.00000	−0.0924500
$469$	65.0000	3.00142
$470$	0	0
$471$	16.0000	0.737241
$472$	0	0
$473$	9.00000	0.413820
$474$	3.00000	0.137795
$475$	0	0
$476$	5.00000	0.229175
$477$	−11.0000	−0.503655
$478$	−15.0000	−0.686084
$479$	−22.0000	−1.00521	−0.502603	−	0.864517i	$-0.667624\pi$
$479$	−22.0000	−1.00521	−0.502603	+	0.864517i	$0.667624\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	20.0000	0.910975
$483$	−10.0000	−0.455016
$484$	−10.0000	−0.454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	−2.00000	−0.0905357
$489$	−16.0000	−0.723545
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	10.0000	0.450835
$493$	−10.0000	−0.450377
$494$	−14.0000	−0.629890
$495$	0	0
$496$	−5.00000	−0.224507
$497$	−50.0000	−2.24281
$498$	14.0000	0.627355
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	−2.00000	−0.0892644
$503$	−22.0000	−0.980932	−0.490466	−	0.871460i	$-0.663173\pi$
$503$	−22.0000	−0.980932	−0.490466	+	0.871460i	$0.663173\pi$
$504$	−5.00000	−0.222718
$505$	0	0
$506$	2.00000	0.0889108
$507$	9.00000	0.399704
$508$	−4.00000	−0.177471
$509$	−37.0000	−1.64000	−0.819998	−	0.572366i	$-0.806026\pi$
$509$	−37.0000	−1.64000	−0.819998	+	0.572366i	$0.806026\pi$
$510$	0	0
$511$	20.0000	0.884748
$512$	−1.00000	−0.0441942
$513$	7.00000	0.309058
$514$	−18.0000	−0.793946
$515$	0	0
$516$	9.00000	0.396203
$517$	7.00000	0.307860
$518$	−15.0000	−0.659062
$519$	20.0000	0.877903
$520$	0	0
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	10.0000	0.437688
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−17.0000	−0.741235
$527$	−5.00000	−0.217803
$528$	1.00000	0.0435194
$529$	−19.0000	−0.826087
$530$	0	0
$531$	0	0
$532$	−35.0000	−1.51744
$533$	20.0000	0.866296
$534$	4.00000	0.173097
$535$	0	0
$536$	−13.0000	−0.561514
$537$	12.0000	0.517838
$538$	−6.00000	−0.258678
$539$	−18.0000	−0.775315
$540$	0	0
$541$	−39.0000	−1.67674	−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000	−1.67674	−0.838370	+	0.545101i	$0.816491\pi$
$542$	6.00000	0.257722
$543$	−17.0000	−0.729540
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−10.0000	−0.427960
$547$	38.0000	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$548$	12.0000	0.512615
$549$	2.00000	0.0853579
$550$	0	0
$551$	70.0000	2.98210
$552$	2.00000	0.0851257
$553$	15.0000	0.637865
$554$	−23.0000	−0.977176
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−29.0000	−1.22877	−0.614385	−	0.789007i	$-0.710596\pi$
$557$	−29.0000	−1.22877	−0.614385	+	0.789007i	$0.710596\pi$
$558$	5.00000	0.211667
$559$	18.0000	0.761319
$560$	0	0
$561$	1.00000	0.0422200
$562$	−22.0000	−0.928014
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	7.00000	0.294753
$565$	0	0
$566$	14.0000	0.588464
$567$	5.00000	0.209980
$568$	10.0000	0.419591
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	2.00000	0.0836242
$573$	−25.0000	−1.04439
$574$	50.0000	2.08696
$575$	0	0
$576$	1.00000	0.0416667
$577$	−39.0000	−1.62359	−0.811796	−	0.583942i	$-0.801510\pi$
$577$	−39.0000	−1.62359	−0.811796	+	0.583942i	$0.801510\pi$
$578$	−1.00000	−0.0415945
$579$	24.0000	0.997406
$580$	0	0
$581$	70.0000	2.90409
$582$	6.00000	0.248708
$583$	11.0000	0.455573
$584$	−4.00000	−0.165521
$585$	0	0
$586$	14.0000	0.578335
$587$	26.0000	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$587$	26.0000	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$588$	−18.0000	−0.742307
$589$	35.0000	1.44215
$590$	0	0
$591$	8.00000	0.329076
$592$	3.00000	0.123299
$593$	12.0000	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	−7.00000	−0.286491
$598$	4.00000	0.163572
$599$	33.0000	1.34834	0.674172	−	0.738575i	$-0.264501\pi$
$599$	33.0000	1.34834	0.674172	+	0.738575i	$0.264501\pi$
$600$	0	0
$601$	18.0000	0.734235	0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000	0.734235	0.367118	+	0.930175i	$0.380345\pi$
$602$	45.0000	1.83406
$603$	13.0000	0.529401
$604$	−8.00000	−0.325515
$605$	0	0
$606$	−7.00000	−0.284356
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	7.00000	0.283887
$609$	50.0000	2.02610
$610$	0	0
$611$	14.0000	0.566379
$612$	1.00000	0.0404226
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	5.00000	0.201456
$617$	−9.00000	−0.362326	−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000	−0.362326	−0.181163	+	0.983453i	$0.557986\pi$
$618$	0	0
$619$	−16.0000	−0.643094	−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000	−0.643094	−0.321547	+	0.946894i	$0.604203\pi$
$620$	0	0
$621$	−2.00000	−0.0802572
$622$	−26.0000	−1.04251
$623$	20.0000	0.801283
$624$	2.00000	0.0800641
$625$	0	0
$626$	2.00000	0.0799361
$627$	−7.00000	−0.279553
$628$	−16.0000	−0.638470
$629$	3.00000	0.119618
$630$	0	0
$631$	38.0000	1.51276	0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000	1.51276	0.756378	+	0.654135i	$0.226967\pi$
$632$	−3.00000	−0.119334
$633$	14.0000	0.556450
$634$	20.0000	0.794301
$635$	0	0
$636$	11.0000	0.436178
$637$	−36.0000	−1.42637
$638$	−10.0000	−0.395904
$639$	−10.0000	−0.395594
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−9.00000	−0.355202
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	10.0000	0.394055
$645$	0	0
$646$	7.00000	0.275411
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	0	0
$651$	25.0000	0.979827
$652$	16.0000	0.626608
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	19.0000	0.742959
$655$	0	0
$656$	−10.0000	−0.390434
$657$	4.00000	0.156055
$658$	35.0000	1.36444
$659$	44.0000	1.71400	0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000	1.71400	0.856998	+	0.515319i	$0.172327\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	−7.00000	−0.272063
$663$	2.00000	0.0776736
$664$	−14.0000	−0.543305
$665$	0	0
$666$	−3.00000	−0.116248
$667$	−20.0000	−0.774403
$668$	−6.00000	−0.232147
$669$	−10.0000	−0.386622
$670$	0	0
$671$	−2.00000	−0.0772091
$672$	5.00000	0.192879
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	36.0000	1.38359	0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000	1.38359	0.691796	+	0.722093i	$0.256820\pi$
$678$	−3.00000	−0.115214
$679$	30.0000	1.15129
$680$	0	0
$681$	−1.00000	−0.0383201
$682$	−5.00000	−0.191460
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	−7.00000	−0.267652
$685$	0	0
$686$	−55.0000	−2.09991
$687$	12.0000	0.457829
$688$	−9.00000	−0.343122
$689$	22.0000	0.838133
$690$	0	0
$691$	4.00000	0.152167	0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000	0.152167	0.0760836	+	0.997101i	$0.475758\pi$
$692$	−20.0000	−0.760286
$693$	−5.00000	−0.189934
$694$	−5.00000	−0.189797
$695$	0	0
$696$	−10.0000	−0.379049
$697$	−10.0000	−0.378777
$698$	2.00000	0.0757011
$699$	18.0000	0.680823
$700$	0	0
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	−2.00000	−0.0754851
$703$	−21.0000	−0.792030
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−2.00000	−0.0752710
$707$	−35.0000	−1.31631
$708$	0	0
$709$	−17.0000	−0.638448	−0.319224	−	0.947679i	$-0.603422\pi$
$709$	−17.0000	−0.638448	−0.319224	+	0.947679i	$0.603422\pi$
$710$	0	0
$711$	3.00000	0.112509
$712$	−4.00000	−0.149906
$713$	−10.0000	−0.374503
$714$	5.00000	0.187120
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−15.0000	−0.560185
$718$	3.00000	0.111959
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	0	0
$721$	0	0
$722$	−30.0000	−1.11648
$723$	20.0000	0.743808
$724$	17.0000	0.631800
$725$	0	0
$726$	−10.0000	−0.371135
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	10.0000	0.370625
$729$	1.00000	0.0370370
$730$	0	0
$731$	−9.00000	−0.332877
$732$	−2.00000	−0.0739221
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	5.00000	0.184553
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	−13.0000	−0.478861
$738$	10.0000	0.368105
$739$	−51.0000	−1.87607	−0.938033	−	0.346547i	$-0.887354\pi$
$739$	−51.0000	−1.87607	−0.938033	+	0.346547i	$0.887354\pi$
$740$	0	0
$741$	−14.0000	−0.514303
$742$	55.0000	2.01911
$743$	34.0000	1.24734	0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000	1.24734	0.623670	+	0.781688i	$0.285641\pi$
$744$	−5.00000	−0.183309
$745$	0	0
$746$	−26.0000	−0.951928
$747$	14.0000	0.512233
$748$	−1.00000	−0.0365636
$749$	−45.0000	−1.64426
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	−7.00000	−0.255264
$753$	−2.00000	−0.0728841
$754$	−20.0000	−0.728357
$755$	0	0
$756$	−5.00000	−0.181848
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−20.0000	−0.726433
$759$	2.00000	0.0725954
$760$	0	0
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	−4.00000	−0.144905
$763$	95.0000	3.43923
$764$	25.0000	0.904468
$765$	0	0
$766$	−8.00000	−0.289052
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−13.0000	−0.468792	−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000	−0.468792	−0.234396	+	0.972141i	$0.575311\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−24.0000	−0.863779
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	9.00000	0.323498
$775$	0	0
$776$	−6.00000	−0.215387
$777$	−15.0000	−0.538122
$778$	15.0000	0.537776
$779$	70.0000	2.50801
$780$	0	0
$781$	10.0000	0.357828
$782$	−2.00000	−0.0715199
$783$	10.0000	0.357371
$784$	18.0000	0.642857
$785$	0	0
$786$	−4.00000	−0.142675
$787$	18.0000	0.641631	0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000	0.641631	0.320815	+	0.947142i	$0.396043\pi$
$788$	−8.00000	−0.284988
$789$	−17.0000	−0.605216
$790$	0	0
$791$	−15.0000	−0.533339
$792$	1.00000	0.0355335
$793$	−4.00000	−0.142044
$794$	−3.00000	−0.106466
$795$	0	0
$796$	7.00000	0.248108
$797$	−41.0000	−1.45229	−0.726147	−	0.687539i	$-0.758691\pi$
$797$	−41.0000	−1.45229	−0.726147	+	0.687539i	$0.758691\pi$
$798$	−35.0000	−1.23899
$799$	−7.00000	−0.247642
$800$	0	0
$801$	4.00000	0.141333
$802$	−30.0000	−1.05934
$803$	−4.00000	−0.141157
$804$	−13.0000	−0.458475
$805$	0	0
$806$	−10.0000	−0.352235
$807$	−6.00000	−0.211210
$808$	7.00000	0.246259
$809$	45.0000	1.58212	0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000	1.58212	0.791058	+	0.611741i	$0.209531\pi$
$810$	0	0
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−50.0000	−1.75466
$813$	6.00000	0.210429
$814$	3.00000	0.105150
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	63.0000	2.20409
$818$	26.0000	0.909069
$819$	−10.0000	−0.349428
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	12.0000	0.418548
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	23.0000	0.799788	0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000	0.799788	0.399894	+	0.916561i	$0.369047\pi$
$828$	2.00000	0.0695048
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	0	0
$831$	−23.0000	−0.797861
$832$	−2.00000	−0.0693375
$833$	18.0000	0.623663
$834$	−20.0000	−0.692543
$835$	0	0
$836$	7.00000	0.242100
$837$	5.00000	0.172825
$838$	0	0
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	30.0000	1.03387
$843$	−22.0000	−0.757720
$844$	−14.0000	−0.481900
$845$	0	0
$846$	7.00000	0.240665
$847$	−50.0000	−1.71802
$848$	−11.0000	−0.377742
$849$	14.0000	0.480479
$850$	0	0
$851$	6.00000	0.205677
$852$	10.0000	0.342594
$853$	5.00000	0.171197	0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000	0.171197	0.0855984	+	0.996330i	$0.472720\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	9.00000	0.307614
$857$	23.0000	0.785665	0.392833	−	0.919610i	$-0.371495\pi$
$857$	23.0000	0.785665	0.392833	+	0.919610i	$0.371495\pi$
$858$	2.00000	0.0682789
$859$	−47.0000	−1.60362	−0.801810	−	0.597580i	$-0.796129\pi$
$859$	−47.0000	−1.60362	−0.801810	+	0.597580i	$0.796129\pi$
$860$	0	0
$861$	50.0000	1.70400
$862$	16.0000	0.544962
$863$	−43.0000	−1.46374	−0.731869	−	0.681446i	$-0.761351\pi$
$863$	−43.0000	−1.46374	−0.731869	+	0.681446i	$0.761351\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	35.0000	1.18935
$867$	−1.00000	−0.0339618
$868$	−25.0000	−0.848555
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−26.0000	−0.880976
$872$	−19.0000	−0.643421
$873$	6.00000	0.203069
$874$	14.0000	0.473557
$875$	0	0
$876$	−4.00000	−0.135147
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	24.0000	0.809961
$879$	14.0000	0.472208
$880$	0	0
$881$	3.00000	0.101073	0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000	0.101073	0.0505363	+	0.998722i	$0.483907\pi$
$882$	−18.0000	−0.606092
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	0	0
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	3.00000	0.100673
$889$	−20.0000	−0.670778
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	10.0000	0.334825
$893$	49.0000	1.63972
$894$	−2.00000	−0.0668900
$895$	0	0
$896$	−5.00000	−0.167038
$897$	4.00000	0.133556
$898$	−9.00000	−0.300334
$899$	50.0000	1.66759
$900$	0	0
$901$	−11.0000	−0.366463
$902$	−10.0000	−0.332964
$903$	45.0000	1.49751
$904$	3.00000	0.0997785
$905$	0	0
$906$	−8.00000	−0.265782
$907$	−38.0000	−1.26177	−0.630885	−	0.775877i	$-0.717308\pi$
$907$	−38.0000	−1.26177	−0.630885	+	0.775877i	$0.717308\pi$
$908$	1.00000	0.0331862
$909$	−7.00000	−0.232175
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	7.00000	0.231793
$913$	−14.0000	−0.463332
$914$	17.0000	0.562310
$915$	0	0
$916$	−12.0000	−0.396491
$917$	−20.0000	−0.660458
$918$	1.00000	0.0330049
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	−35.0000	−1.15266
$923$	20.0000	0.658308
$924$	5.00000	0.164488
$925$	0	0
$926$	−16.0000	−0.525793
$927$	0	0
$928$	10.0000	0.328266
$929$	−9.00000	−0.295280	−0.147640	−	0.989041i	$-0.547168\pi$
$929$	−9.00000	−0.295280	−0.147640	+	0.989041i	$0.547168\pi$
$930$	0	0
$931$	−126.000	−4.12948
$932$	−18.0000	−0.589610
$933$	−26.0000	−0.851202
$934$	−6.00000	−0.196326
$935$	0	0
$936$	2.00000	0.0653720
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	−65.0000	−2.12233
$939$	2.00000	0.0652675
$940$	0	0
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	−16.0000	−0.521308
$943$	−20.0000	−0.651290
$944$	0	0
$945$	0	0
$946$	−9.00000	−0.292615
$947$	41.0000	1.33232	0.666160	−	0.745808i	$-0.267937\pi$
$947$	41.0000	1.33232	0.666160	+	0.745808i	$0.267937\pi$
$948$	−3.00000	−0.0974355
$949$	−8.00000	−0.259691
$950$	0	0
$951$	20.0000	0.648544
$952$	−5.00000	−0.162051
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	11.0000	0.356138
$955$	0	0
$956$	15.0000	0.485135
$957$	−10.0000	−0.323254
$958$	22.0000	0.710788
$959$	60.0000	1.93750
$960$	0	0
$961$	−6.00000	−0.193548
$962$	6.00000	0.193448
$963$	−9.00000	−0.290021
$964$	−20.0000	−0.644157
$965$	0	0
$966$	10.0000	0.321745
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	10.0000	0.321412
$969$	7.00000	0.224872
$970$	0	0
$971$	22.0000	0.706014	0.353007	−	0.935621i	$-0.385159\pi$
$971$	22.0000	0.706014	0.353007	+	0.935621i	$0.385159\pi$
$972$	−1.00000	−0.0320750
$973$	−100.000	−3.20585
$974$	−8.00000	−0.256337
$975$	0	0
$976$	2.00000	0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	16.0000	0.511624
$979$	−4.00000	−0.127841
$980$	0	0
$981$	19.0000	0.606623
$982$	−12.0000	−0.382935
$983$	−10.0000	−0.318950	−0.159475	−	0.987202i	$-0.550980\pi$
$983$	−10.0000	−0.318950	−0.159475	+	0.987202i	$0.550980\pi$
$984$	−10.0000	−0.318788
$985$	0	0
$986$	10.0000	0.318465
$987$	35.0000	1.11406
$988$	14.0000	0.445399
$989$	−18.0000	−0.572367
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	5.00000	0.158750
$993$	−7.00000	−0.222138
$994$	50.0000	1.58590
$995$	0	0
$996$	−14.0000	−0.443607
$997$	43.0000	1.36182	0.680912	−	0.732365i	$-0.261584\pi$
$997$	43.0000	1.36182	0.680912	+	0.732365i	$0.261584\pi$
$998$	−22.0000	−0.696398
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.a.g.1.1	✓	1
3.2	odd	2		7650.2.a.cp.1.1		1
5.2	odd	4		2550.2.d.p.2449.1		2
5.3	odd	4		2550.2.d.p.2449.2		2
5.4	even	2		2550.2.a.ba.1.1	yes	1
15.14	odd	2		7650.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.g.1.1	✓	1	1.1	even	1	trivial
2550.2.a.ba.1.1	yes	1	5.4	even	2
2550.2.d.p.2449.1		2	5.2	odd	4
2550.2.d.p.2449.2		2	5.3	odd	4
7650.2.a.b.1.1		1	15.14	odd	2
7650.2.a.cp.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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