LMFDB - Embedded newform 8034.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$2$
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	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -5.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} -5.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -7.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} -2.00000 q^{20} +5.00000 q^{21} -5.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -5.00000 q^{28} +6.00000 q^{29} +2.00000 q^{30} -6.00000 q^{31} +1.00000 q^{32} +5.00000 q^{33} -7.00000 q^{34} +10.0000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -6.00000 q^{38} -1.00000 q^{39} -2.00000 q^{40} -6.00000 q^{41} +5.00000 q^{42} -6.00000 q^{43} -5.00000 q^{44} -2.00000 q^{45} +4.00000 q^{46} -12.0000 q^{47} -1.00000 q^{48} +18.0000 q^{49} -1.00000 q^{50} +7.00000 q^{51} +1.00000 q^{52} -9.00000 q^{53} -1.00000 q^{54} +10.0000 q^{55} -5.00000 q^{56} +6.00000 q^{57} +6.00000 q^{58} +2.00000 q^{60} -8.00000 q^{61} -6.00000 q^{62} -5.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} +5.00000 q^{66} -13.0000 q^{67} -7.00000 q^{68} -4.00000 q^{69} +10.0000 q^{70} -4.00000 q^{71} +1.00000 q^{72} -1.00000 q^{73} -2.00000 q^{74} +1.00000 q^{75} -6.00000 q^{76} +25.0000 q^{77} -1.00000 q^{78} -2.00000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -6.00000 q^{83} +5.00000 q^{84} +14.0000 q^{85} -6.00000 q^{86} -6.00000 q^{87} -5.00000 q^{88} +10.0000 q^{89} -2.00000 q^{90} -5.00000 q^{91} +4.00000 q^{92} +6.00000 q^{93} -12.0000 q^{94} +12.0000 q^{95} -1.00000 q^{96} -2.00000 q^{97} +18.0000 q^{98} -5.00000 q^{99} +O(q^{100})\)

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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−1.00000	−0.408248
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.00000	−1.33631
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−7.00000	−1.69775	−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−2.00000	−0.447214
$21$	5.00000	1.09109
$22$	−5.00000	−1.06600
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−5.00000	−0.944911
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	2.00000	0.365148
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	5.00000	0.870388
$34$	−7.00000	−1.20049
$35$	10.0000	1.69031
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−6.00000	−0.973329
$39$	−1.00000	−0.160128
$40$	−2.00000	−0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	5.00000	0.771517
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−5.00000	−0.753778
$45$	−2.00000	−0.298142
$46$	4.00000	0.589768
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	−1.00000	−0.144338
$49$	18.0000	2.57143
$50$	−1.00000	−0.141421
$51$	7.00000	0.980196
$52$	1.00000	0.138675
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	−1.00000	−0.136083
$55$	10.0000	1.34840
$56$	−5.00000	−0.668153
$57$	6.00000	0.794719
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	2.00000	0.258199
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	−6.00000	−0.762001
$63$	−5.00000	−0.629941
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	5.00000	0.615457
$67$	−13.0000	−1.58820	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000	−1.58820	−0.794101	+	0.607785i	$0.792058\pi$
$68$	−7.00000	−0.848875
$69$	−4.00000	−0.481543
$70$	10.0000	1.19523
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	1.00000	0.117851
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	−6.00000	−0.688247
$77$	25.0000	2.84901
$78$	−1.00000	−0.113228
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	5.00000	0.545545
$85$	14.0000	1.51851
$86$	−6.00000	−0.646997
$87$	−6.00000	−0.643268
$88$	−5.00000	−0.533002
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−2.00000	−0.210819
$91$	−5.00000	−0.524142
$92$	4.00000	0.417029
$93$	6.00000	0.622171
$94$	−12.0000	−1.23771
$95$	12.0000	1.23117
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	18.0000	1.81827
$99$	−5.00000	−0.502519
$100$	−1.00000	−0.100000
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	7.00000	0.693103
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−10.0000	−0.975900
$106$	−9.00000	−0.874157
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	−1.00000	−0.0962250
$109$	20.0000	1.91565	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000	1.91565	0.957826	+	0.287348i	$0.0927736\pi$
$110$	10.0000	0.953463
$111$	2.00000	0.189832
$112$	−5.00000	−0.472456
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	6.00000	0.561951
$115$	−8.00000	−0.746004
$116$	6.00000	0.557086
$117$	1.00000	0.0924500
$118$	0	0
$119$	35.0000	3.20844
$120$	2.00000	0.182574
$121$	14.0000	1.27273
$122$	−8.00000	−0.724286
$123$	6.00000	0.541002
$124$	−6.00000	−0.538816
$125$	12.0000	1.07331
$126$	−5.00000	−0.445435
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	−2.00000	−0.175412
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	5.00000	0.435194
$133$	30.0000	2.60133
$134$	−13.0000	−1.12303
$135$	2.00000	0.172133
$136$	−7.00000	−0.600245
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−4.00000	−0.340503
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	10.0000	0.845154
$141$	12.0000	1.01058
$142$	−4.00000	−0.335673
$143$	−5.00000	−0.418121
$144$	1.00000	0.0833333
$145$	−12.0000	−0.996546
$146$	−1.00000	−0.0827606
$147$	−18.0000	−1.48461
$148$	−2.00000	−0.164399
$149$	−19.0000	−1.55654	−0.778270	−	0.627929i	$-0.783903\pi$
$149$	−19.0000	−1.55654	−0.778270	+	0.627929i	$0.783903\pi$
$150$	1.00000	0.0816497
$151$	18.0000	1.46482	0.732410	−	0.680864i	$-0.238396\pi$
$151$	18.0000	1.46482	0.732410	+	0.680864i	$0.238396\pi$
$152$	−6.00000	−0.486664
$153$	−7.00000	−0.565916
$154$	25.0000	2.01456
$155$	12.0000	0.963863
$156$	−1.00000	−0.0800641
$157$	11.0000	0.877896	0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000	0.877896	0.438948	+	0.898513i	$0.355351\pi$
$158$	−2.00000	−0.159111
$159$	9.00000	0.713746
$160$	−2.00000	−0.158114
$161$	−20.0000	−1.57622
$162$	1.00000	0.0785674
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	−6.00000	−0.468521
$165$	−10.0000	−0.778499
$166$	−6.00000	−0.465690
$167$	−9.00000	−0.696441	−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000	−0.696441	−0.348220	+	0.937413i	$0.613214\pi$
$168$	5.00000	0.385758
$169$	1.00000	0.0769231
$170$	14.0000	1.07375
$171$	−6.00000	−0.458831
$172$	−6.00000	−0.457496
$173$	7.00000	0.532200	0.266100	−	0.963945i	$-0.414265\pi$
$173$	7.00000	0.532200	0.266100	+	0.963945i	$0.414265\pi$
$174$	−6.00000	−0.454859
$175$	5.00000	0.377964
$176$	−5.00000	−0.376889
$177$	0	0
$178$	10.0000	0.749532
$179$	5.00000	0.373718	0.186859	−	0.982387i	$-0.440169\pi$
$179$	5.00000	0.373718	0.186859	+	0.982387i	$0.440169\pi$
$180$	−2.00000	−0.149071
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	−5.00000	−0.370625
$183$	8.00000	0.591377
$184$	4.00000	0.294884
$185$	4.00000	0.294086
$186$	6.00000	0.439941
$187$	35.0000	2.55945
$188$	−12.0000	−0.875190
$189$	5.00000	0.363696
$190$	12.0000	0.870572
$191$	7.00000	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−2.00000	−0.143592
$195$	2.00000	0.143223
$196$	18.0000	1.28571
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	−5.00000	−0.355335
$199$	15.0000	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$199$	15.0000	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$200$	−1.00000	−0.0707107
$201$	13.0000	0.916949
$202$	−5.00000	−0.351799
$203$	−30.0000	−2.10559
$204$	7.00000	0.490098
$205$	12.0000	0.838116
$206$	1.00000	0.0696733
$207$	4.00000	0.278019
$208$	1.00000	0.0693375
$209$	30.0000	2.07514
$210$	−10.0000	−0.690066
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−9.00000	−0.618123
$213$	4.00000	0.274075
$214$	15.0000	1.02538
$215$	12.0000	0.818393
$216$	−1.00000	−0.0680414
$217$	30.0000	2.03653
$218$	20.0000	1.35457
$219$	1.00000	0.0675737
$220$	10.0000	0.674200
$221$	−7.00000	−0.470871
$222$	2.00000	0.134231
$223$	−11.0000	−0.736614	−0.368307	−	0.929704i	$-0.620063\pi$
$223$	−11.0000	−0.736614	−0.368307	+	0.929704i	$0.620063\pi$
$224$	−5.00000	−0.334077
$225$	−1.00000	−0.0666667
$226$	4.00000	0.266076
$227$	−9.00000	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$228$	6.00000	0.397360
$229$	−26.0000	−1.71813	−0.859064	−	0.511868i	$-0.828954\pi$
$229$	−26.0000	−1.71813	−0.859064	+	0.511868i	$0.828954\pi$
$230$	−8.00000	−0.527504
$231$	−25.0000	−1.64488
$232$	6.00000	0.393919
$233$	−12.0000	−0.786146	−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000	−0.786146	−0.393073	+	0.919507i	$0.628588\pi$
$234$	1.00000	0.0653720
$235$	24.0000	1.56559
$236$	0	0
$237$	2.00000	0.129914
$238$	35.0000	2.26871
$239$	−11.0000	−0.711531	−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000	−0.711531	−0.355765	+	0.934575i	$0.615780\pi$
$240$	2.00000	0.129099
$241$	−5.00000	−0.322078	−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000	−0.322078	−0.161039	+	0.986948i	$0.551485\pi$
$242$	14.0000	0.899954
$243$	−1.00000	−0.0641500
$244$	−8.00000	−0.512148
$245$	−36.0000	−2.29996
$246$	6.00000	0.382546
$247$	−6.00000	−0.381771
$248$	−6.00000	−0.381000
$249$	6.00000	0.380235
$250$	12.0000	0.758947
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	−5.00000	−0.314970
$253$	−20.0000	−1.25739
$254$	7.00000	0.439219
$255$	−14.0000	−0.876714
$256$	1.00000	0.0625000
$257$	−26.0000	−1.62184	−0.810918	−	0.585160i	$-0.801032\pi$
$257$	−26.0000	−1.62184	−0.810918	+	0.585160i	$0.801032\pi$
$258$	6.00000	0.373544
$259$	10.0000	0.621370
$260$	−2.00000	−0.124035
$261$	6.00000	0.371391
$262$	4.00000	0.247121
$263$	−5.00000	−0.308313	−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000	−0.308313	−0.154157	+	0.988046i	$0.549266\pi$
$264$	5.00000	0.307729
$265$	18.0000	1.10573
$266$	30.0000	1.83942
$267$	−10.0000	−0.611990
$268$	−13.0000	−0.794101
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	2.00000	0.121716
$271$	18.0000	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$271$	18.0000	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$272$	−7.00000	−0.424437
$273$	5.00000	0.302614
$274$	−18.0000	−1.08742
$275$	5.00000	0.301511
$276$	−4.00000	−0.240772
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−13.0000	−0.779688
$279$	−6.00000	−0.359211
$280$	10.0000	0.597614
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	12.0000	0.714590
$283$	−10.0000	−0.594438	−0.297219	−	0.954809i	$-0.596059\pi$
$283$	−10.0000	−0.594438	−0.297219	+	0.954809i	$0.596059\pi$
$284$	−4.00000	−0.237356
$285$	−12.0000	−0.710819
$286$	−5.00000	−0.295656
$287$	30.0000	1.77084
$288$	1.00000	0.0589256
$289$	32.0000	1.88235
$290$	−12.0000	−0.704664
$291$	2.00000	0.117242
$292$	−1.00000	−0.0585206
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	−18.0000	−1.04978
$295$	0	0
$296$	−2.00000	−0.116248
$297$	5.00000	0.290129
$298$	−19.0000	−1.10064
$299$	4.00000	0.231326
$300$	1.00000	0.0577350
$301$	30.0000	1.72917
$302$	18.0000	1.03578
$303$	5.00000	0.287242
$304$	−6.00000	−0.344124
$305$	16.0000	0.916157
$306$	−7.00000	−0.400163
$307$	11.0000	0.627803	0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000	0.627803	0.313902	+	0.949456i	$0.398364\pi$
$308$	25.0000	1.42451
$309$	−1.00000	−0.0568880
$310$	12.0000	0.681554
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	−1.00000	−0.0566139
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	11.0000	0.620766
$315$	10.0000	0.563436
$316$	−2.00000	−0.112509
$317$	23.0000	1.29181	0.645904	−	0.763418i	$-0.276480\pi$
$317$	23.0000	1.29181	0.645904	+	0.763418i	$0.276480\pi$
$318$	9.00000	0.504695
$319$	−30.0000	−1.67968
$320$	−2.00000	−0.111803
$321$	−15.0000	−0.837218
$322$	−20.0000	−1.11456
$323$	42.0000	2.33694
$324$	1.00000	0.0555556
$325$	−1.00000	−0.0554700
$326$	2.00000	0.110770
$327$	−20.0000	−1.10600
$328$	−6.00000	−0.331295
$329$	60.0000	3.30791
$330$	−10.0000	−0.550482
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	−6.00000	−0.329293
$333$	−2.00000	−0.109599
$334$	−9.00000	−0.492458
$335$	26.0000	1.42053
$336$	5.00000	0.272772
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	1.00000	0.0543928
$339$	−4.00000	−0.217250
$340$	14.0000	0.759257
$341$	30.0000	1.62459
$342$	−6.00000	−0.324443
$343$	−55.0000	−2.96972
$344$	−6.00000	−0.323498
$345$	8.00000	0.430706
$346$	7.00000	0.376322
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	−6.00000	−0.321634
$349$	4.00000	0.214115	0.107058	−	0.994253i	$-0.465857\pi$
$349$	4.00000	0.214115	0.107058	+	0.994253i	$0.465857\pi$
$350$	5.00000	0.267261
$351$	−1.00000	−0.0533761
$352$	−5.00000	−0.266501
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	10.0000	0.529999
$357$	−35.0000	−1.85240
$358$	5.00000	0.264258
$359$	23.0000	1.21389	0.606947	−	0.794742i	$-0.292394\pi$
$359$	23.0000	1.21389	0.606947	+	0.794742i	$0.292394\pi$
$360$	−2.00000	−0.105409
$361$	17.0000	0.894737
$362$	7.00000	0.367912
$363$	−14.0000	−0.734809
$364$	−5.00000	−0.262071
$365$	2.00000	0.104685
$366$	8.00000	0.418167
$367$	−12.0000	−0.626395	−0.313197	−	0.949688i	$-0.601400\pi$
$367$	−12.0000	−0.626395	−0.313197	+	0.949688i	$0.601400\pi$
$368$	4.00000	0.208514
$369$	−6.00000	−0.312348
$370$	4.00000	0.207950
$371$	45.0000	2.33628
$372$	6.00000	0.311086
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	35.0000	1.80981
$375$	−12.0000	−0.619677
$376$	−12.0000	−0.618853
$377$	6.00000	0.309016
$378$	5.00000	0.257172
$379$	−17.0000	−0.873231	−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000	−0.873231	−0.436616	+	0.899648i	$0.643823\pi$
$380$	12.0000	0.615587
$381$	−7.00000	−0.358621
$382$	7.00000	0.358151
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	−1.00000	−0.0510310
$385$	−50.0000	−2.54824
$386$	−10.0000	−0.508987
$387$	−6.00000	−0.304997
$388$	−2.00000	−0.101535
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	2.00000	0.101274
$391$	−28.0000	−1.41602
$392$	18.0000	0.909137
$393$	−4.00000	−0.201773
$394$	22.0000	1.10834
$395$	4.00000	0.201262
$396$	−5.00000	−0.251259
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	15.0000	0.751882
$399$	−30.0000	−1.50188
$400$	−1.00000	−0.0500000
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	13.0000	0.648381
$403$	−6.00000	−0.298881
$404$	−5.00000	−0.248759
$405$	−2.00000	−0.0993808
$406$	−30.0000	−1.48888
$407$	10.0000	0.495682
$408$	7.00000	0.346552
$409$	4.00000	0.197787	0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000	0.197787	0.0988936	+	0.995098i	$0.468470\pi$
$410$	12.0000	0.592638
$411$	18.0000	0.887875
$412$	1.00000	0.0492665
$413$	0	0
$414$	4.00000	0.196589
$415$	12.0000	0.589057
$416$	1.00000	0.0490290
$417$	13.0000	0.636613
$418$	30.0000	1.46735
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	−10.0000	−0.487950
$421$	−27.0000	−1.31590	−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000	−1.31590	−0.657950	+	0.753062i	$0.728576\pi$
$422$	−8.00000	−0.389434
$423$	−12.0000	−0.583460
$424$	−9.00000	−0.437079
$425$	7.00000	0.339550
$426$	4.00000	0.193801
$427$	40.0000	1.93574
$428$	15.0000	0.725052
$429$	5.00000	0.241402
$430$	12.0000	0.578691
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	−1.00000	−0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	30.0000	1.44005
$435$	12.0000	0.575356
$436$	20.0000	0.957826
$437$	−24.0000	−1.14808
$438$	1.00000	0.0477818
$439$	−35.0000	−1.67046	−0.835229	−	0.549902i	$-0.814665\pi$
$439$	−35.0000	−1.67046	−0.835229	+	0.549902i	$0.814665\pi$
$440$	10.0000	0.476731
$441$	18.0000	0.857143
$442$	−7.00000	−0.332956
$443$	−32.0000	−1.52037	−0.760183	−	0.649709i	$-0.774891\pi$
$443$	−32.0000	−1.52037	−0.760183	+	0.649709i	$0.774891\pi$
$444$	2.00000	0.0949158
$445$	−20.0000	−0.948091
$446$	−11.0000	−0.520865
$447$	19.0000	0.898669
$448$	−5.00000	−0.236228
$449$	17.0000	0.802280	0.401140	−	0.916017i	$-0.368614\pi$
$449$	17.0000	0.802280	0.401140	+	0.916017i	$0.368614\pi$
$450$	−1.00000	−0.0471405
$451$	30.0000	1.41264
$452$	4.00000	0.188144
$453$	−18.0000	−0.845714
$454$	−9.00000	−0.422391
$455$	10.0000	0.468807
$456$	6.00000	0.280976
$457$	42.0000	1.96468	0.982339	−	0.187112i	$-0.0599128\pi$
$457$	42.0000	1.96468	0.982339	+	0.187112i	$0.0599128\pi$
$458$	−26.0000	−1.21490
$459$	7.00000	0.326732
$460$	−8.00000	−0.373002
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	−25.0000	−1.16311
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	6.00000	0.278543
$465$	−12.0000	−0.556487
$466$	−12.0000	−0.555889
$467$	−21.0000	−0.971764	−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000	−0.971764	−0.485882	+	0.874024i	$0.661502\pi$
$468$	1.00000	0.0462250
$469$	65.0000	3.00142
$470$	24.0000	1.10704
$471$	−11.0000	−0.506853
$472$	0	0
$473$	30.0000	1.37940
$474$	2.00000	0.0918630
$475$	6.00000	0.275299
$476$	35.0000	1.60422
$477$	−9.00000	−0.412082
$478$	−11.0000	−0.503128
$479$	22.0000	1.00521	0.502603	−	0.864517i	$-0.332376\pi$
$479$	22.0000	1.00521	0.502603	+	0.864517i	$0.332376\pi$
$480$	2.00000	0.0912871
$481$	−2.00000	−0.0911922
$482$	−5.00000	−0.227744
$483$	20.0000	0.910032
$484$	14.0000	0.636364
$485$	4.00000	0.181631
$486$	−1.00000	−0.0453609
$487$	−14.0000	−0.634401	−0.317200	−	0.948359i	$-0.602743\pi$
$487$	−14.0000	−0.634401	−0.317200	+	0.948359i	$0.602743\pi$
$488$	−8.00000	−0.362143
$489$	−2.00000	−0.0904431
$490$	−36.0000	−1.62631
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	6.00000	0.270501
$493$	−42.0000	−1.89158
$494$	−6.00000	−0.269953
$495$	10.0000	0.449467
$496$	−6.00000	−0.269408
$497$	20.0000	0.897123
$498$	6.00000	0.268866
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	12.0000	0.536656
$501$	9.00000	0.402090
$502$	−8.00000	−0.357057
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	−5.00000	−0.222718
$505$	10.0000	0.444994
$506$	−20.0000	−0.889108
$507$	−1.00000	−0.0444116
$508$	7.00000	0.310575
$509$	35.0000	1.55135	0.775674	−	0.631134i	$-0.217410\pi$
$509$	35.0000	1.55135	0.775674	+	0.631134i	$0.217410\pi$
$510$	−14.0000	−0.619930
$511$	5.00000	0.221187
$512$	1.00000	0.0441942
$513$	6.00000	0.264906
$514$	−26.0000	−1.14681
$515$	−2.00000	−0.0881305
$516$	6.00000	0.264135
$517$	60.0000	2.63880
$518$	10.0000	0.439375
$519$	−7.00000	−0.307266
$520$	−2.00000	−0.0877058
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	6.00000	0.262613
$523$	31.0000	1.35554	0.677768	−	0.735276i	$-0.262948\pi$
$523$	31.0000	1.35554	0.677768	+	0.735276i	$0.262948\pi$
$524$	4.00000	0.174741
$525$	−5.00000	−0.218218
$526$	−5.00000	−0.218010
$527$	42.0000	1.82955
$528$	5.00000	0.217597
$529$	−7.00000	−0.304348
$530$	18.0000	0.781870
$531$	0	0
$532$	30.0000	1.30066
$533$	−6.00000	−0.259889
$534$	−10.0000	−0.432742
$535$	−30.0000	−1.29701
$536$	−13.0000	−0.561514
$537$	−5.00000	−0.215766
$538$	−6.00000	−0.258678
$539$	−90.0000	−3.87657
$540$	2.00000	0.0860663
$541$	−1.00000	−0.0429934	−0.0214967	−	0.999769i	$-0.506843\pi$
$541$	−1.00000	−0.0429934	−0.0214967	+	0.999769i	$0.506843\pi$
$542$	18.0000	0.773166
$543$	−7.00000	−0.300399
$544$	−7.00000	−0.300123
$545$	−40.0000	−1.71341
$546$	5.00000	0.213980
$547$	16.0000	0.684111	0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000	0.684111	0.342055	+	0.939680i	$0.388877\pi$
$548$	−18.0000	−0.768922
$549$	−8.00000	−0.341432
$550$	5.00000	0.213201
$551$	−36.0000	−1.53365
$552$	−4.00000	−0.170251
$553$	10.0000	0.425243
$554$	26.0000	1.10463
$555$	−4.00000	−0.169791
$556$	−13.0000	−0.551323
$557$	−36.0000	−1.52537	−0.762684	−	0.646771i	$-0.776119\pi$
$557$	−36.0000	−1.52537	−0.762684	+	0.646771i	$0.776119\pi$
$558$	−6.00000	−0.254000
$559$	−6.00000	−0.253773
$560$	10.0000	0.422577
$561$	−35.0000	−1.47770
$562$	−18.0000	−0.759284
$563$	−18.0000	−0.758610	−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000	−0.758610	−0.379305	+	0.925272i	$0.623837\pi$
$564$	12.0000	0.505291
$565$	−8.00000	−0.336563
$566$	−10.0000	−0.420331
$567$	−5.00000	−0.209980
$568$	−4.00000	−0.167836
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	−12.0000	−0.502625
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−5.00000	−0.209061
$573$	−7.00000	−0.292429
$574$	30.0000	1.25218
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−37.0000	−1.54033	−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000	−1.54033	−0.770165	+	0.637845i	$0.779826\pi$
$578$	32.0000	1.33102
$579$	10.0000	0.415586
$580$	−12.0000	−0.498273
$581$	30.0000	1.24461
$582$	2.00000	0.0829027
$583$	45.0000	1.86371
$584$	−1.00000	−0.0413803
$585$	−2.00000	−0.0826898
$586$	−24.0000	−0.991431
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	−18.0000	−0.742307
$589$	36.0000	1.48335
$590$	0	0
$591$	−22.0000	−0.904959
$592$	−2.00000	−0.0821995
$593$	−7.00000	−0.287456	−0.143728	−	0.989617i	$-0.545909\pi$
$593$	−7.00000	−0.287456	−0.143728	+	0.989617i	$0.545909\pi$
$594$	5.00000	0.205152
$595$	−70.0000	−2.86972
$596$	−19.0000	−0.778270
$597$	−15.0000	−0.613909
$598$	4.00000	0.163572
$599$	−7.00000	−0.286012	−0.143006	−	0.989722i	$-0.545677\pi$
$599$	−7.00000	−0.286012	−0.143006	+	0.989722i	$0.545677\pi$
$600$	1.00000	0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	30.0000	1.22271
$603$	−13.0000	−0.529401
$604$	18.0000	0.732410
$605$	−28.0000	−1.13836
$606$	5.00000	0.203111
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	−6.00000	−0.243332
$609$	30.0000	1.21566
$610$	16.0000	0.647821
$611$	−12.0000	−0.485468
$612$	−7.00000	−0.282958
$613$	−29.0000	−1.17130	−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000	−1.17130	−0.585649	+	0.810564i	$0.699160\pi$
$614$	11.0000	0.443924
$615$	−12.0000	−0.483887
$616$	25.0000	1.00728
$617$	−38.0000	−1.52982	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000	−1.52982	−0.764911	+	0.644136i	$0.777217\pi$
$618$	−1.00000	−0.0402259
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	12.0000	0.481932
$621$	−4.00000	−0.160514
$622$	−30.0000	−1.20289
$623$	−50.0000	−2.00321
$624$	−1.00000	−0.0400320
$625$	−19.0000	−0.760000
$626$	−10.0000	−0.399680
$627$	−30.0000	−1.19808
$628$	11.0000	0.438948
$629$	14.0000	0.558217
$630$	10.0000	0.398410
$631$	11.0000	0.437903	0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000	0.437903	0.218952	+	0.975736i	$0.429736\pi$
$632$	−2.00000	−0.0795557
$633$	8.00000	0.317971
$634$	23.0000	0.913447
$635$	−14.0000	−0.555573
$636$	9.00000	0.356873
$637$	18.0000	0.713186
$638$	−30.0000	−1.18771
$639$	−4.00000	−0.158238
$640$	−2.00000	−0.0790569
$641$	−27.0000	−1.06644	−0.533218	−	0.845978i	$-0.679017\pi$
$641$	−27.0000	−1.06644	−0.533218	+	0.845978i	$0.679017\pi$
$642$	−15.0000	−0.592003
$643$	6.00000	0.236617	0.118308	−	0.992977i	$-0.462253\pi$
$643$	6.00000	0.236617	0.118308	+	0.992977i	$0.462253\pi$
$644$	−20.0000	−0.788110
$645$	−12.0000	−0.472500
$646$	42.0000	1.65247
$647$	−26.0000	−1.02217	−0.511083	−	0.859532i	$-0.670755\pi$
$647$	−26.0000	−1.02217	−0.511083	+	0.859532i	$0.670755\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	−30.0000	−1.17579
$652$	2.00000	0.0783260
$653$	34.0000	1.33052	0.665261	−	0.746611i	$-0.268320\pi$
$653$	34.0000	1.33052	0.665261	+	0.746611i	$0.268320\pi$
$654$	−20.0000	−0.782062
$655$	−8.00000	−0.312586
$656$	−6.00000	−0.234261
$657$	−1.00000	−0.0390137
$658$	60.0000	2.33904
$659$	27.0000	1.05177	0.525885	−	0.850555i	$-0.323734\pi$
$659$	27.0000	1.05177	0.525885	+	0.850555i	$0.323734\pi$
$660$	−10.0000	−0.389249
$661$	12.0000	0.466746	0.233373	−	0.972387i	$-0.425024\pi$
$661$	12.0000	0.466746	0.233373	+	0.972387i	$0.425024\pi$
$662$	−17.0000	−0.660724
$663$	7.00000	0.271857
$664$	−6.00000	−0.232845
$665$	−60.0000	−2.32670
$666$	−2.00000	−0.0774984
$667$	24.0000	0.929284
$668$	−9.00000	−0.348220
$669$	11.0000	0.425285
$670$	26.0000	1.00447
$671$	40.0000	1.54418
$672$	5.00000	0.192879
$673$	−49.0000	−1.88881	−0.944406	−	0.328783i	$-0.893362\pi$
$673$	−49.0000	−1.88881	−0.944406	+	0.328783i	$0.893362\pi$
$674$	−5.00000	−0.192593
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	−26.0000	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$678$	−4.00000	−0.153619
$679$	10.0000	0.383765
$680$	14.0000	0.536875
$681$	9.00000	0.344881
$682$	30.0000	1.14876
$683$	3.00000	0.114792	0.0573959	−	0.998351i	$-0.481720\pi$
$683$	3.00000	0.114792	0.0573959	+	0.998351i	$0.481720\pi$
$684$	−6.00000	−0.229416
$685$	36.0000	1.37549
$686$	−55.0000	−2.09991
$687$	26.0000	0.991962
$688$	−6.00000	−0.228748
$689$	−9.00000	−0.342873
$690$	8.00000	0.304555
$691$	−44.0000	−1.67384	−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000	−1.67384	−0.836919	+	0.547326i	$0.815646\pi$
$692$	7.00000	0.266100
$693$	25.0000	0.949671
$694$	−36.0000	−1.36654
$695$	26.0000	0.986236
$696$	−6.00000	−0.227429
$697$	42.0000	1.59086
$698$	4.00000	0.151402
$699$	12.0000	0.453882
$700$	5.00000	0.188982
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	−1.00000	−0.0377426
$703$	12.0000	0.452589
$704$	−5.00000	−0.188445
$705$	−24.0000	−0.903892
$706$	21.0000	0.790345
$707$	25.0000	0.940222
$708$	0	0
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	8.00000	0.300235
$711$	−2.00000	−0.0750059
$712$	10.0000	0.374766
$713$	−24.0000	−0.898807
$714$	−35.0000	−1.30984
$715$	10.0000	0.373979
$716$	5.00000	0.186859
$717$	11.0000	0.410803
$718$	23.0000	0.858352
$719$	29.0000	1.08152	0.540759	−	0.841178i	$-0.318137\pi$
$719$	29.0000	1.08152	0.540759	+	0.841178i	$0.318137\pi$
$720$	−2.00000	−0.0745356
$721$	−5.00000	−0.186210
$722$	17.0000	0.632674
$723$	5.00000	0.185952
$724$	7.00000	0.260153
$725$	−6.00000	−0.222834
$726$	−14.0000	−0.519589
$727$	−5.00000	−0.185440	−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	−5.00000	−0.185440	−0.0927199	+	0.995692i	$0.529556\pi$
$728$	−5.00000	−0.185312
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	42.0000	1.55343
$732$	8.00000	0.295689
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−12.0000	−0.442928
$735$	36.0000	1.32788
$736$	4.00000	0.147442
$737$	65.0000	2.39431
$738$	−6.00000	−0.220863
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	4.00000	0.147043
$741$	6.00000	0.220416
$742$	45.0000	1.65200
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	6.00000	0.219971
$745$	38.0000	1.39221
$746$	16.0000	0.585802
$747$	−6.00000	−0.219529
$748$	35.0000	1.27973
$749$	−75.0000	−2.74044
$750$	−12.0000	−0.438178
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	−12.0000	−0.437595
$753$	8.00000	0.291536
$754$	6.00000	0.218507
$755$	−36.0000	−1.31017
$756$	5.00000	0.181848
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	−17.0000	−0.617468
$759$	20.0000	0.725954
$760$	12.0000	0.435286
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−7.00000	−0.253583
$763$	−100.000	−3.62024
$764$	7.00000	0.253251
$765$	14.0000	0.506171
$766$	−12.0000	−0.433578
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	35.0000	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$770$	−50.0000	−1.80187
$771$	26.0000	0.936367
$772$	−10.0000	−0.359908
$773$	−9.00000	−0.323708	−0.161854	−	0.986815i	$-0.551747\pi$
$773$	−9.00000	−0.323708	−0.161854	+	0.986815i	$0.551747\pi$
$774$	−6.00000	−0.215666
$775$	6.00000	0.215526
$776$	−2.00000	−0.0717958
$777$	−10.0000	−0.358748
$778$	−21.0000	−0.752886
$779$	36.0000	1.28983
$780$	2.00000	0.0716115
$781$	20.0000	0.715656
$782$	−28.0000	−1.00128
$783$	−6.00000	−0.214423
$784$	18.0000	0.642857
$785$	−22.0000	−0.785214
$786$	−4.00000	−0.142675
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	22.0000	0.783718
$789$	5.00000	0.178005
$790$	4.00000	0.142314
$791$	−20.0000	−0.711118
$792$	−5.00000	−0.177667
$793$	−8.00000	−0.284088
$794$	22.0000	0.780751
$795$	−18.0000	−0.638394
$796$	15.0000	0.531661
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	−30.0000	−1.06199
$799$	84.0000	2.97171
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	12.0000	0.423735
$803$	5.00000	0.176446
$804$	13.0000	0.458475
$805$	40.0000	1.40981
$806$	−6.00000	−0.211341
$807$	6.00000	0.211210
$808$	−5.00000	−0.175899
$809$	−26.0000	−0.914111	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000	−0.914111	−0.457056	+	0.889438i	$0.651096\pi$
$810$	−2.00000	−0.0702728
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−30.0000	−1.05279
$813$	−18.0000	−0.631288
$814$	10.0000	0.350500
$815$	−4.00000	−0.140114
$816$	7.00000	0.245049
$817$	36.0000	1.25948
$818$	4.00000	0.139857
$819$	−5.00000	−0.174714
$820$	12.0000	0.419058
$821$	−25.0000	−0.872506	−0.436253	−	0.899824i	$-0.643695\pi$
$821$	−25.0000	−0.872506	−0.436253	+	0.899824i	$0.643695\pi$
$822$	18.0000	0.627822
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	1.00000	0.0348367
$825$	−5.00000	−0.174078
$826$	0	0
$827$	24.0000	0.834562	0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000	0.834562	0.417281	+	0.908778i	$0.362983\pi$
$828$	4.00000	0.139010
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	12.0000	0.416526
$831$	−26.0000	−0.901930
$832$	1.00000	0.0346688
$833$	−126.000	−4.36564
$834$	13.0000	0.450153
$835$	18.0000	0.622916
$836$	30.0000	1.03757
$837$	6.00000	0.207390
$838$	−9.00000	−0.310900
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	−10.0000	−0.345033
$841$	7.00000	0.241379
$842$	−27.0000	−0.930481
$843$	18.0000	0.619953
$844$	−8.00000	−0.275371
$845$	−2.00000	−0.0688021
$846$	−12.0000	−0.412568
$847$	−70.0000	−2.40523
$848$	−9.00000	−0.309061
$849$	10.0000	0.343199
$850$	7.00000	0.240098
$851$	−8.00000	−0.274236
$852$	4.00000	0.137038
$853$	−51.0000	−1.74621	−0.873103	−	0.487535i	$-0.837896\pi$
$853$	−51.0000	−1.74621	−0.873103	+	0.487535i	$0.837896\pi$
$854$	40.0000	1.36877
$855$	12.0000	0.410391
$856$	15.0000	0.512689
$857$	29.0000	0.990621	0.495311	−	0.868716i	$-0.335054\pi$
$857$	29.0000	0.990621	0.495311	+	0.868716i	$0.335054\pi$
$858$	5.00000	0.170697
$859$	22.0000	0.750630	0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000	0.750630	0.375315	+	0.926897i	$0.377534\pi$
$860$	12.0000	0.409197
$861$	−30.0000	−1.02240
$862$	16.0000	0.544962
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	−1.00000	−0.0340207
$865$	−14.0000	−0.476014
$866$	2.00000	0.0679628
$867$	−32.0000	−1.08678
$868$	30.0000	1.01827
$869$	10.0000	0.339227
$870$	12.0000	0.406838
$871$	−13.0000	−0.440488
$872$	20.0000	0.677285
$873$	−2.00000	−0.0676897
$874$	−24.0000	−0.811812
$875$	−60.0000	−2.02837
$876$	1.00000	0.0337869
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	−35.0000	−1.18119
$879$	24.0000	0.809500
$880$	10.0000	0.337100
$881$	−4.00000	−0.134763	−0.0673817	−	0.997727i	$-0.521465\pi$
$881$	−4.00000	−0.134763	−0.0673817	+	0.997727i	$0.521465\pi$
$882$	18.0000	0.606092
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	−7.00000	−0.235435
$885$	0	0
$886$	−32.0000	−1.07506
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	2.00000	0.0671156
$889$	−35.0000	−1.17386
$890$	−20.0000	−0.670402
$891$	−5.00000	−0.167506
$892$	−11.0000	−0.368307
$893$	72.0000	2.40939
$894$	19.0000	0.635455
$895$	−10.0000	−0.334263
$896$	−5.00000	−0.167038
$897$	−4.00000	−0.133556
$898$	17.0000	0.567297
$899$	−36.0000	−1.20067
$900$	−1.00000	−0.0333333
$901$	63.0000	2.09883
$902$	30.0000	0.998891
$903$	−30.0000	−0.998337
$904$	4.00000	0.133038
$905$	−14.0000	−0.465376
$906$	−18.0000	−0.598010
$907$	−13.0000	−0.431658	−0.215829	−	0.976431i	$-0.569245\pi$
$907$	−13.0000	−0.431658	−0.215829	+	0.976431i	$0.569245\pi$
$908$	−9.00000	−0.298675
$909$	−5.00000	−0.165840
$910$	10.0000	0.331497
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	6.00000	0.198680
$913$	30.0000	0.992855
$914$	42.0000	1.38924
$915$	−16.0000	−0.528944
$916$	−26.0000	−0.859064
$917$	−20.0000	−0.660458
$918$	7.00000	0.231034
$919$	−39.0000	−1.28649	−0.643246	−	0.765660i	$-0.722413\pi$
$919$	−39.0000	−1.28649	−0.643246	+	0.765660i	$0.722413\pi$
$920$	−8.00000	−0.263752
$921$	−11.0000	−0.362462
$922$	−18.0000	−0.592798
$923$	−4.00000	−0.131662
$924$	−25.0000	−0.822440
$925$	2.00000	0.0657596
$926$	−26.0000	−0.854413
$927$	1.00000	0.0328443
$928$	6.00000	0.196960
$929$	4.00000	0.131236	0.0656179	−	0.997845i	$-0.479098\pi$
$929$	4.00000	0.131236	0.0656179	+	0.997845i	$0.479098\pi$
$930$	−12.0000	−0.393496
$931$	−108.000	−3.53956
$932$	−12.0000	−0.393073
$933$	30.0000	0.982156
$934$	−21.0000	−0.687141
$935$	−70.0000	−2.28924
$936$	1.00000	0.0326860
$937$	46.0000	1.50275	0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000	1.50275	0.751377	+	0.659873i	$0.229390\pi$
$938$	65.0000	2.12233
$939$	10.0000	0.326338
$940$	24.0000	0.782794
$941$	−35.0000	−1.14097	−0.570484	−	0.821309i	$-0.693244\pi$
$941$	−35.0000	−1.14097	−0.570484	+	0.821309i	$0.693244\pi$
$942$	−11.0000	−0.358399
$943$	−24.0000	−0.781548
$944$	0	0
$945$	−10.0000	−0.325300
$946$	30.0000	0.975384
$947$	20.0000	0.649913	0.324956	−	0.945729i	$-0.394650\pi$
$947$	20.0000	0.649913	0.324956	+	0.945729i	$0.394650\pi$
$948$	2.00000	0.0649570
$949$	−1.00000	−0.0324614
$950$	6.00000	0.194666
$951$	−23.0000	−0.745826
$952$	35.0000	1.13436
$953$	33.0000	1.06897	0.534487	−	0.845176i	$-0.320505\pi$
$953$	33.0000	1.06897	0.534487	+	0.845176i	$0.320505\pi$
$954$	−9.00000	−0.291386
$955$	−14.0000	−0.453029
$956$	−11.0000	−0.355765
$957$	30.0000	0.969762
$958$	22.0000	0.710788
$959$	90.0000	2.90625
$960$	2.00000	0.0645497
$961$	5.00000	0.161290
$962$	−2.00000	−0.0644826
$963$	15.0000	0.483368
$964$	−5.00000	−0.161039
$965$	20.0000	0.643823
$966$	20.0000	0.643489
$967$	58.0000	1.86515	0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000	1.86515	0.932577	+	0.360971i	$0.117555\pi$
$968$	14.0000	0.449977
$969$	−42.0000	−1.34923
$970$	4.00000	0.128432
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	−1.00000	−0.0320750
$973$	65.0000	2.08380
$974$	−14.0000	−0.448589
$975$	1.00000	0.0320256
$976$	−8.00000	−0.256074
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	−2.00000	−0.0639529
$979$	−50.0000	−1.59801
$980$	−36.0000	−1.14998
$981$	20.0000	0.638551
$982$	−15.0000	−0.478669
$983$	−41.0000	−1.30770	−0.653848	−	0.756626i	$-0.726847\pi$
$983$	−41.0000	−1.30770	−0.653848	+	0.756626i	$0.726847\pi$
$984$	6.00000	0.191273
$985$	−44.0000	−1.40196
$986$	−42.0000	−1.33755
$987$	−60.0000	−1.90982
$988$	−6.00000	−0.190885
$989$	−24.0000	−0.763156
$990$	10.0000	0.317821
$991$	−34.0000	−1.08005	−0.540023	−	0.841650i	$-0.681584\pi$
$991$	−34.0000	−1.08005	−0.540023	+	0.841650i	$0.681584\pi$
$992$	−6.00000	−0.190500
$993$	17.0000	0.539479
$994$	20.0000	0.634361
$995$	−30.0000	−0.951064
$996$	6.00000	0.190117
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	4.00000	0.126618
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.d.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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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