LMFDB - Embedded newform 4026.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
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	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -4.00000 q^{21} -1.00000 q^{22} +1.00000 q^{24} -5.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +6.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} +8.00000 q^{37} -4.00000 q^{38} +2.00000 q^{39} +12.0000 q^{41} -4.00000 q^{42} +2.00000 q^{43} -1.00000 q^{44} +6.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -5.00000 q^{50} +6.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} -4.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} +12.0000 q^{59} +1.00000 q^{61} +2.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} -4.00000 q^{67} +6.00000 q^{68} -12.0000 q^{71} +1.00000 q^{72} +2.00000 q^{73} +8.00000 q^{74} -5.00000 q^{75} -4.00000 q^{76} +4.00000 q^{77} +2.00000 q^{78} -4.00000 q^{79} +1.00000 q^{81} +12.0000 q^{82} -6.00000 q^{83} -4.00000 q^{84} +2.00000 q^{86} +6.00000 q^{87} -1.00000 q^{88} -6.00000 q^{89} -8.00000 q^{91} +2.00000 q^{93} +6.00000 q^{94} +1.00000 q^{96} +2.00000 q^{97} +9.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	1.00000	0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	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
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.00000	0.204124
$25$	−5.00000	−1.00000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−4.00000	−0.648886
$39$	2.00000	0.320256
$40$	0	0
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	−4.00000	−0.617213
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	−5.00000	−0.707107
$51$	6.00000	0.840168
$52$	2.00000	0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.00000	−0.534522
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.00000	0.254000
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	8.00000	0.929981
$75$	−5.00000	−0.577350
$76$	−4.00000	−0.458831
$77$	4.00000	0.455842
$78$	2.00000	0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	2.00000	0.215666
$87$	6.00000	0.643268
$88$	−1.00000	−0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	0	0
$93$	2.00000	0.207390
$94$	6.00000	0.618853
$95$	0	0
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	9.00000	0.909137
$99$	−1.00000	−0.100504
$100$	−5.00000	−0.500000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	6.00000	0.594089
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	1.00000	0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−4.00000	−0.377964
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	6.00000	0.557086
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	−24.0000	−2.20008
$120$	0	0
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	12.0000	1.08200
$124$	2.00000	0.179605
$125$	0	0
$126$	−4.00000	−0.356348
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	−1.00000	−0.0870388
$133$	16.0000	1.38738
$134$	−4.00000	−0.345547
$135$	0	0
$136$	6.00000	0.514496
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	−12.0000	−1.00702
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	9.00000	0.742307
$148$	8.00000	0.657596
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−5.00000	−0.408248
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−4.00000	−0.324443
$153$	6.00000	0.485071
$154$	4.00000	0.322329
$155$	0	0
$156$	2.00000	0.160128
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−4.00000	−0.318223
$159$	6.00000	0.475831
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	−6.00000	−0.465690
$167$	−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
$171$	−4.00000	−0.305888
$172$	2.00000	0.152499
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	6.00000	0.454859
$175$	20.0000	1.51186
$176$	−1.00000	−0.0753778
$177$	12.0000	0.901975
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−8.00000	−0.592999
$183$	1.00000	0.0739221
$184$	0	0
$185$	0	0
$186$	2.00000	0.146647
$187$	−6.00000	−0.438763
$188$	6.00000	0.437595
$189$	−4.00000	−0.290957
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	9.00000	0.642857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	−1.00000	−0.0710669
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−5.00000	−0.353553
$201$	−4.00000	−0.282138
$202$	−6.00000	−0.422159
$203$	−24.0000	−1.68447
$204$	6.00000	0.420084
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	2.00000	0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	6.00000	0.412082
$213$	−12.0000	−0.822226
$214$	18.0000	1.23045
$215$	0	0
$216$	1.00000	0.0680414
$217$	−8.00000	−0.543075
$218$	14.0000	0.948200
$219$	2.00000	0.135147
$220$	0	0
$221$	12.0000	0.807207
$222$	8.00000	0.536925
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	−4.00000	−0.267261
$225$	−5.00000	−0.333333
$226$	−18.0000	−1.19734
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	−4.00000	−0.264906
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	6.00000	0.393919
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	12.0000	0.781133
$237$	−4.00000	−0.259828
$238$	−24.0000	−1.55569
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	0	0
$246$	12.0000	0.765092
$247$	−8.00000	−0.509028
$248$	2.00000	0.127000
$249$	−6.00000	−0.380235
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	2.00000	0.124515
$259$	−32.0000	−1.98838
$260$	0	0
$261$	6.00000	0.371391
$262$	6.00000	0.370681
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	16.0000	0.981023
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	6.00000	0.363803
$273$	−8.00000	−0.484182
$274$	18.0000	1.08742
$275$	5.00000	0.301511
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−22.0000	−1.31947
$279$	2.00000	0.119737
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	6.00000	0.357295
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−2.00000	−0.118262
$287$	−48.0000	−2.83335
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	2.00000	0.117242
$292$	2.00000	0.117041
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	8.00000	0.464991
$297$	−1.00000	−0.0580259
$298$	18.0000	1.04271
$299$	0	0
$300$	−5.00000	−0.288675
$301$	−8.00000	−0.461112
$302$	8.00000	0.460348
$303$	−6.00000	−0.344691
$304$	−4.00000	−0.229416
$305$	0	0
$306$	6.00000	0.342997
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	4.00000	0.227921
$309$	−4.00000	−0.227552
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	2.00000	0.113228
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−4.00000	−0.225018
$317$	−24.0000	−1.34797	−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000	−1.34797	−0.673987	+	0.738743i	$0.735420\pi$
$318$	6.00000	0.336463
$319$	−6.00000	−0.335936
$320$	0	0
$321$	18.0000	1.00466
$322$	0	0
$323$	−24.0000	−1.33540
$324$	1.00000	0.0555556
$325$	−10.0000	−0.554700
$326$	−4.00000	−0.221540
$327$	14.0000	0.774202
$328$	12.0000	0.662589
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−6.00000	−0.329293
$333$	8.00000	0.438397
$334$	−24.0000	−1.31322
$335$	0	0
$336$	−4.00000	−0.218218
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−9.00000	−0.489535
$339$	−18.0000	−0.977626
$340$	0	0
$341$	−2.00000	−0.108306
$342$	−4.00000	−0.216295
$343$	−8.00000	−0.431959
$344$	2.00000	0.107833
$345$	0	0
$346$	−6.00000	−0.322562
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	6.00000	0.321634
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	20.0000	1.06904
$351$	2.00000	0.106752
$352$	−1.00000	−0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−6.00000	−0.317999
$357$	−24.0000	−1.27021
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	20.0000	1.05118
$363$	1.00000	0.0524864
$364$	−8.00000	−0.419314
$365$	0	0
$366$	1.00000	0.0522708
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	0	0
$369$	12.0000	0.624695
$370$	0	0
$371$	−24.0000	−1.24602
$372$	2.00000	0.103695
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	−6.00000	−0.310253
$375$	0	0
$376$	6.00000	0.309426
$377$	12.0000	0.618031
$378$	−4.00000	−0.205738
$379$	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
$381$	8.00000	0.409852
$382$	12.0000	0.613973
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.00000	−0.203595
$387$	2.00000	0.101666
$388$	2.00000	0.101535
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	0	0
$392$	9.00000	0.454569
$393$	6.00000	0.302660
$394$	−6.00000	−0.302276
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	20.0000	1.00251
$399$	16.0000	0.801002
$400$	−5.00000	−0.250000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	−4.00000	−0.199502
$403$	4.00000	0.199254
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−24.0000	−1.19110
$407$	−8.00000	−0.396545
$408$	6.00000	0.297044
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	18.0000	0.887875
$412$	−4.00000	−0.197066
$413$	−48.0000	−2.36193
$414$	0	0
$415$	0	0
$416$	2.00000	0.0980581
$417$	−22.0000	−1.07734
$418$	4.00000	0.195646
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	−4.00000	−0.194948	−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000	−0.194948	−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−10.0000	−0.486792
$423$	6.00000	0.291730
$424$	6.00000	0.291386
$425$	−30.0000	−1.45521
$426$	−12.0000	−0.581402
$427$	−4.00000	−0.193574
$428$	18.0000	0.870063
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	14.0000	0.670478
$437$	0	0
$438$	2.00000	0.0955637
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	12.0000	0.570782
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	2.00000	0.0947027
$447$	18.0000	0.851371
$448$	−4.00000	−0.188982
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	−5.00000	−0.235702
$451$	−12.0000	−0.565058
$452$	−18.0000	−0.846649
$453$	8.00000	0.375873
$454$	−24.0000	−1.12638
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	−22.0000	−1.02799
$459$	6.00000	0.280056
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	4.00000	0.186097
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	18.0000	0.833834
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	2.00000	0.0924500
$469$	16.0000	0.738811
$470$	0	0
$471$	−4.00000	−0.184310
$472$	12.0000	0.552345
$473$	−2.00000	−0.0919601
$474$	−4.00000	−0.183726
$475$	20.0000	0.917663
$476$	−24.0000	−1.10004
$477$	6.00000	0.274721
$478$	24.0000	1.09773
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	−22.0000	−1.00207
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	1.00000	0.0452679
$489$	−4.00000	−0.180886
$490$	0	0
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	12.0000	0.541002
$493$	36.0000	1.62136
$494$	−8.00000	−0.359937
$495$	0	0
$496$	2.00000	0.0898027
$497$	48.0000	2.15309
$498$	−6.00000	−0.268866
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	−12.0000	−0.535586
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	−4.00000	−0.178174
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	8.00000	0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	−6.00000	−0.264649
$515$	0	0
$516$	2.00000	0.0880451
$517$	−6.00000	−0.263880
$518$	−32.0000	−1.40600
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	6.00000	0.262613
$523$	38.0000	1.66162	0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000	1.66162	0.830812	+	0.556553i	$0.187876\pi$
$524$	6.00000	0.262111
$525$	20.0000	0.872872
$526$	−12.0000	−0.523225
$527$	12.0000	0.522728
$528$	−1.00000	−0.0435194
$529$	−23.0000	−1.00000
$530$	0	0
$531$	12.0000	0.520756
$532$	16.0000	0.693688
$533$	24.0000	1.03956
$534$	−6.00000	−0.259645
$535$	0	0
$536$	−4.00000	−0.172774
$537$	0	0
$538$	−24.0000	−1.03471
$539$	−9.00000	−0.387657
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−16.0000	−0.687259
$543$	20.0000	0.858282
$544$	6.00000	0.257248
$545$	0	0
$546$	−8.00000	−0.342368
$547$	26.0000	1.11168	0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000	1.11168	0.555840	+	0.831289i	$0.312397\pi$
$548$	18.0000	0.768922
$549$	1.00000	0.0426790
$550$	5.00000	0.213201
$551$	−24.0000	−1.02243
$552$	0	0
$553$	16.0000	0.680389
$554$	−22.0000	−0.934690
$555$	0	0
$556$	−22.0000	−0.933008
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	2.00000	0.0846668
$559$	4.00000	0.169182
$560$	0	0
$561$	−6.00000	−0.253320
$562$	6.00000	0.253095
$563$	30.0000	1.26435	0.632175	−	0.774826i	$-0.282163\pi$
$563$	30.0000	1.26435	0.632175	+	0.774826i	$0.282163\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	20.0000	0.840663
$567$	−4.00000	−0.167984
$568$	−12.0000	−0.503509
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	−2.00000	−0.0836242
$573$	12.0000	0.501307
$574$	−48.0000	−2.00348
$575$	0	0
$576$	1.00000	0.0416667
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	19.0000	0.790296
$579$	−4.00000	−0.166234
$580$	0	0
$581$	24.0000	0.995688
$582$	2.00000	0.0829027
$583$	−6.00000	−0.248495
$584$	2.00000	0.0827606
$585$	0	0
$586$	30.0000	1.23929
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	9.00000	0.371154
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−6.00000	−0.246807
$592$	8.00000	0.328798
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	18.0000	0.737309
$597$	20.0000	0.818546
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−5.00000	−0.204124
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−8.00000	−0.326056
$603$	−4.00000	−0.162893
$604$	8.00000	0.325515
$605$	0	0
$606$	−6.00000	−0.243733
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−4.00000	−0.162221
$609$	−24.0000	−0.972529
$610$	0	0
$611$	12.0000	0.485468
$612$	6.00000	0.242536
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	4.00000	0.161165
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	−4.00000	−0.160904
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	0	0
$621$	0	0
$622$	−12.0000	−0.481156
$623$	24.0000	0.961540
$624$	2.00000	0.0800641
$625$	25.0000	1.00000
$626$	14.0000	0.559553
$627$	4.00000	0.159745
$628$	−4.00000	−0.159617
$629$	48.0000	1.91389
$630$	0	0
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	−4.00000	−0.159111
$633$	−10.0000	−0.397464
$634$	−24.0000	−0.953162
$635$	0	0
$636$	6.00000	0.237915
$637$	18.0000	0.713186
$638$	−6.00000	−0.237542
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	18.0000	0.710403
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.00000	0.0392837
$649$	−12.0000	−0.471041
$650$	−10.0000	−0.392232
$651$	−8.00000	−0.313545
$652$	−4.00000	−0.156652
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	14.0000	0.547443
$655$	0	0
$656$	12.0000	0.468521
$657$	2.00000	0.0780274
$658$	−24.0000	−0.935617
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	−4.00000	−0.155464
$663$	12.0000	0.466041
$664$	−6.00000	−0.232845
$665$	0	0
$666$	8.00000	0.309994
$667$	0	0
$668$	−24.0000	−0.928588
$669$	2.00000	0.0773245
$670$	0	0
$671$	−1.00000	−0.0386046
$672$	−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	$0.681447\pi$
$674$	20.0000	0.770371
$675$	−5.00000	−0.192450
$676$	−9.00000	−0.346154
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	−18.0000	−0.691286
$679$	−8.00000	−0.307012
$680$	0	0
$681$	−24.0000	−0.919682
$682$	−2.00000	−0.0765840
$683$	−48.0000	−1.83667	−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000	−1.83667	−0.918334	+	0.395805i	$0.870466\pi$
$684$	−4.00000	−0.152944
$685$	0	0
$686$	−8.00000	−0.305441
$687$	−22.0000	−0.839352
$688$	2.00000	0.0762493
$689$	12.0000	0.457164
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−6.00000	−0.228086
$693$	4.00000	0.151947
$694$	30.0000	1.13878
$695$	0	0
$696$	6.00000	0.227429
$697$	72.0000	2.72719
$698$	26.0000	0.984115
$699$	18.0000	0.680823
$700$	20.0000	0.755929
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	2.00000	0.0754851
$703$	−32.0000	−1.20690
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−6.00000	−0.225813
$707$	24.0000	0.902613
$708$	12.0000	0.450988
$709$	44.0000	1.65245	0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000	1.65245	0.826227	+	0.563337i	$0.190483\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−24.0000	−0.898177
$715$	0	0
$716$	0	0
$717$	24.0000	0.896296
$718$	0	0
$719$	42.0000	1.56634	0.783168	−	0.621810i	$-0.213603\pi$
$719$	42.0000	1.56634	0.783168	+	0.621810i	$0.213603\pi$
$720$	0	0
$721$	16.0000	0.595871
$722$	−3.00000	−0.111648
$723$	−22.0000	−0.818189
$724$	20.0000	0.743294
$725$	−30.0000	−1.11417
$726$	1.00000	0.0371135
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	0	0
$731$	12.0000	0.443836
$732$	1.00000	0.0369611
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	0	0
$737$	4.00000	0.147342
$738$	12.0000	0.441726
$739$	14.0000	0.514998	0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000	0.514998	0.257499	+	0.966279i	$0.417102\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	−24.0000	−0.881068
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	2.00000	0.0733236
$745$	0	0
$746$	26.0000	0.951928
$747$	−6.00000	−0.219529
$748$	−6.00000	−0.219382
$749$	−72.0000	−2.63082
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	6.00000	0.218797
$753$	−12.0000	−0.437304
$754$	12.0000	0.437014
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	8.00000	0.289809
$763$	−56.0000	−2.02734
$764$	12.0000	0.434145
$765$	0	0
$766$	36.0000	1.30073
$767$	24.0000	0.866590
$768$	1.00000	0.0360844
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	−4.00000	−0.143963
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	2.00000	0.0718885
$775$	−10.0000	−0.359211
$776$	2.00000	0.0717958
$777$	−32.0000	−1.14799
$778$	−30.0000	−1.07555
$779$	−48.0000	−1.71978
$780$	0	0
$781$	12.0000	0.429394
$782$	0	0
$783$	6.00000	0.214423
$784$	9.00000	0.321429
$785$	0	0
$786$	6.00000	0.214013
$787$	14.0000	0.499046	0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000	0.499046	0.249523	+	0.968369i	$0.419726\pi$
$788$	−6.00000	−0.213741
$789$	−12.0000	−0.427211
$790$	0	0
$791$	72.0000	2.56003
$792$	−1.00000	−0.0355335
$793$	2.00000	0.0710221
$794$	8.00000	0.283909
$795$	0	0
$796$	20.0000	0.708881
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	16.0000	0.566394
$799$	36.0000	1.27359
$800$	−5.00000	−0.176777
$801$	−6.00000	−0.212000
$802$	−18.0000	−0.635602
$803$	−2.00000	−0.0705785
$804$	−4.00000	−0.141069
$805$	0	0
$806$	4.00000	0.140894
$807$	−24.0000	−0.844840
$808$	−6.00000	−0.211079
$809$	−48.0000	−1.68759	−0.843795	−	0.536666i	$-0.819684\pi$
$809$	−48.0000	−1.68759	−0.843795	+	0.536666i	$0.819684\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	−24.0000	−0.842235
$813$	−16.0000	−0.561144
$814$	−8.00000	−0.280400
$815$	0	0
$816$	6.00000	0.210042
$817$	−8.00000	−0.279885
$818$	−4.00000	−0.139857
$819$	−8.00000	−0.279543
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	18.0000	0.627822
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	−4.00000	−0.139347
$825$	5.00000	0.174078
$826$	−48.0000	−1.67013
$827$	−42.0000	−1.46048	−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000	−1.46048	−0.730242	+	0.683189i	$0.760592\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	0	0
$831$	−22.0000	−0.763172
$832$	2.00000	0.0693375
$833$	54.0000	1.87099
$834$	−22.0000	−0.761798
$835$	0	0
$836$	4.00000	0.138343
$837$	2.00000	0.0691301
$838$	36.0000	1.24360
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−4.00000	−0.137849
$843$	6.00000	0.206651
$844$	−10.0000	−0.344214
$845$	0	0
$846$	6.00000	0.206284
$847$	−4.00000	−0.137442
$848$	6.00000	0.206041
$849$	20.0000	0.686398
$850$	−30.0000	−1.02899
$851$	0	0
$852$	−12.0000	−0.411113
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	−4.00000	−0.136877
$855$	0	0
$856$	18.0000	0.615227
$857$	24.0000	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$858$	−2.00000	−0.0682789
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	−48.0000	−1.63584
$862$	12.0000	0.408722
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	26.0000	0.883516
$867$	19.0000	0.645274
$868$	−8.00000	−0.271538
$869$	4.00000	0.135691
$870$	0	0
$871$	−8.00000	−0.271070
$872$	14.0000	0.474100
$873$	2.00000	0.0676897
$874$	0	0
$875$	0	0
$876$	2.00000	0.0675737
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	8.00000	0.269987
$879$	30.0000	1.01187
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	9.00000	0.303046
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	−36.0000	−1.20944
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	8.00000	0.268462
$889$	−32.0000	−1.07325
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	2.00000	0.0669650
$893$	−24.0000	−0.803129
$894$	18.0000	0.602010
$895$	0	0
$896$	−4.00000	−0.133631
$897$	0	0
$898$	−18.0000	−0.600668
$899$	12.0000	0.400222
$900$	−5.00000	−0.166667
$901$	36.0000	1.19933
$902$	−12.0000	−0.399556
$903$	−8.00000	−0.266223
$904$	−18.0000	−0.598671
$905$	0	0
$906$	8.00000	0.265782
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−24.0000	−0.796468
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−18.0000	−0.596367	−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000	−0.596367	−0.298183	+	0.954509i	$0.596381\pi$
$912$	−4.00000	−0.132453
$913$	6.00000	0.198571
$914$	−16.0000	−0.529233
$915$	0	0
$916$	−22.0000	−0.726900
$917$	−24.0000	−0.792550
$918$	6.00000	0.198030
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	2.00000	0.0659022
$922$	−30.0000	−0.987997
$923$	−24.0000	−0.789970
$924$	4.00000	0.131590
$925$	−40.0000	−1.31519
$926$	−4.00000	−0.131448
$927$	−4.00000	−0.131377
$928$	6.00000	0.196960
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−36.0000	−1.17985
$932$	18.0000	0.589610
$933$	−12.0000	−0.392862
$934$	−12.0000	−0.392652
$935$	0	0
$936$	2.00000	0.0653720
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	16.0000	0.522419
$939$	14.0000	0.456873
$940$	0	0
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	−4.00000	−0.130327
$943$	0	0
$944$	12.0000	0.390567
$945$	0	0
$946$	−2.00000	−0.0650256
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−4.00000	−0.129914
$949$	4.00000	0.129845
$950$	20.0000	0.648886
$951$	−24.0000	−0.778253
$952$	−24.0000	−0.777844
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	24.0000	0.776215
$957$	−6.00000	−0.193952
$958$	−12.0000	−0.387702
$959$	−72.0000	−2.32500
$960$	0	0
$961$	−27.0000	−0.870968
$962$	16.0000	0.515861
$963$	18.0000	0.580042
$964$	−22.0000	−0.708572
$965$	0	0
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	0.0321412
$969$	−24.0000	−0.770991
$970$	0	0
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	1.00000	0.0320750
$973$	88.0000	2.82115
$974$	−4.00000	−0.128168
$975$	−10.0000	−0.320256
$976$	1.00000	0.0320092
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	−4.00000	−0.127906
$979$	6.00000	0.191761
$980$	0	0
$981$	14.0000	0.446986
$982$	−42.0000	−1.34027
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	36.0000	1.14647
$987$	−24.0000	−0.763928
$988$	−8.00000	−0.254514
$989$	0	0
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	2.00000	0.0635001
$993$	−4.00000	−0.126936
$994$	48.0000	1.52247
$995$	0	0
$996$	−6.00000	−0.190117
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−40.0000	−1.26618
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.i.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.i.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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