LMFDB - Embedded newform 1035.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(1,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, 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("1035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1035 = 3^{2} \cdot 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1035.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:	$8.26451660920$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - 2$ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	1035.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.00000 q^{5} -2.41421 q^{7} +2.82843 q^{8} +1.41421 q^{10} +3.41421 q^{11} -2.58579 q^{13} +3.41421 q^{14} -4.00000 q^{16} +2.41421 q^{17} +2.24264 q^{19} -4.82843 q^{22} -1.00000 q^{23} +1.00000 q^{25} +3.65685 q^{26} +6.65685 q^{29} -6.65685 q^{31} -3.41421 q^{34} +2.41421 q^{35} -7.24264 q^{37} -3.17157 q^{38} -2.82843 q^{40} -2.65685 q^{41} +8.48528 q^{43} +1.41421 q^{46} -8.58579 q^{47} -1.17157 q^{49} -1.41421 q^{50} -7.24264 q^{53} -3.41421 q^{55} -6.82843 q^{56} -9.41421 q^{58} +3.34315 q^{59} -6.58579 q^{61} +9.41421 q^{62} +8.00000 q^{64} +2.58579 q^{65} -13.2426 q^{67} -3.41421 q^{70} -9.82843 q^{71} +4.24264 q^{73} +10.2426 q^{74} -8.24264 q^{77} +1.65685 q^{79} +4.00000 q^{80} +3.75736 q^{82} -0.414214 q^{83} -2.41421 q^{85} -12.0000 q^{86} +9.65685 q^{88} +5.17157 q^{89} +6.24264 q^{91} +12.1421 q^{94} -2.24264 q^{95} -12.1421 q^{97} +1.65685 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} + 4 q^{14} - 8 q^{16} + 2 q^{17} - 4 q^{19} - 4 q^{22} - 2 q^{23} + 2 q^{25} - 4 q^{26} + 2 q^{29} - 2 q^{31} - 4 q^{34} + 2 q^{35} - 6 q^{37} - 12 q^{38} + 6 q^{41}+ \cdots - 8 q^{98}+O(q^{100})$ 2 * q - 2 * q^5 - 2 * q^7 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 8 * q^16 + 2 * q^17 - 4 * q^19 - 4 * q^22 - 2 * q^23 + 2 * q^25 - 4 * q^26 + 2 * q^29 - 2 * q^31 - 4 * q^34 + 2 * q^35 - 6 * q^37 - 12 * q^38 + 6 * q^41 - 20 * q^47 - 8 * q^49 - 6 * q^53 - 4 * q^55 - 8 * q^56 - 16 * q^58 + 18 * q^59 - 16 * q^61 + 16 * q^62 + 16 * q^64 + 8 * q^65 - 18 * q^67 - 4 * q^70 - 14 * q^71 + 12 * q^74 - 8 * q^77 - 8 * q^79 + 8 * q^80 + 16 * q^82 + 2 * q^83 - 2 * q^85 - 24 * q^86 + 8 * q^88 + 16 * q^89 + 4 * q^91 - 4 * q^94 + 4 * q^95 + 4 * q^97 - 8 * q^98

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

)

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

$2$	−1.41421	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	0	0
$3$	0	0
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−2.41421	−0.912487	−0.456243	−	0.889855i	$-0.650805\pi$
$7$	−2.41421	−0.912487	−0.456243	+	0.889855i	$0.650805\pi$
$8$	2.82843	1.00000
$9$	0	0
$10$	1.41421	0.447214
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	0	0
$13$	−2.58579	−0.717168	−0.358584	−	0.933497i	$-0.616740\pi$
$13$	−2.58579	−0.717168	−0.358584	+	0.933497i	$0.616740\pi$
$14$	3.41421	0.912487
$15$	0	0
$16$	−4.00000	−1.00000
$17$	2.41421	0.585533	0.292766	−	0.956184i	$-0.405424\pi$
$17$	2.41421	0.585533	0.292766	+	0.956184i	$0.405424\pi$
$18$	0	0
$19$	2.24264	0.514497	0.257249	−	0.966345i	$-0.417184\pi$
$19$	2.24264	0.514497	0.257249	+	0.966345i	$0.417184\pi$
$20$	0	0
$21$	0	0
$22$	−4.82843	−1.02942
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	3.65685	0.717168
$27$	0	0
$28$	0	0
$29$	6.65685	1.23615	0.618073	−	0.786120i	$-0.287913\pi$
$29$	6.65685	1.23615	0.618073	+	0.786120i	$0.287913\pi$
$30$	0	0
$31$	−6.65685	−1.19561	−0.597803	−	0.801643i	$-0.703960\pi$
$31$	−6.65685	−1.19561	−0.597803	+	0.801643i	$0.703960\pi$
$32$	0	0
$33$	0	0
$34$	−3.41421	−0.585533
$35$	2.41421	0.408077
$36$	0	0
$37$	−7.24264	−1.19068	−0.595341	−	0.803473i	$-0.702983\pi$
$37$	−7.24264	−1.19068	−0.595341	+	0.803473i	$0.702983\pi$
$38$	−3.17157	−0.514497
$39$	0	0
$40$	−2.82843	−0.447214
$41$	−2.65685	−0.414931	−0.207465	−	0.978242i	$-0.566521\pi$
$41$	−2.65685	−0.414931	−0.207465	+	0.978242i	$0.566521\pi$
$42$	0	0
$43$	8.48528	1.29399	0.646997	−	0.762493i	$-0.276025\pi$
$43$	8.48528	1.29399	0.646997	+	0.762493i	$0.276025\pi$
$44$	0	0
$45$	0	0
$46$	1.41421	0.208514
$47$	−8.58579	−1.25237	−0.626183	−	0.779676i	$-0.715384\pi$
$47$	−8.58579	−1.25237	−0.626183	+	0.779676i	$0.715384\pi$
$48$	0	0
$49$	−1.17157	−0.167368
$50$	−1.41421	−0.200000
$51$	0	0
$52$	0	0
$53$	−7.24264	−0.994853	−0.497427	−	0.867506i	$-0.665722\pi$
$53$	−7.24264	−0.994853	−0.497427	+	0.867506i	$0.665722\pi$
$54$	0	0
$55$	−3.41421	−0.460372
$56$	−6.82843	−0.912487
$57$	0	0
$58$	−9.41421	−1.23615
$59$	3.34315	0.435241	0.217620	−	0.976034i	$-0.430171\pi$
$59$	3.34315	0.435241	0.217620	+	0.976034i	$0.430171\pi$
$60$	0	0
$61$	−6.58579	−0.843224	−0.421612	−	0.906776i	$-0.638535\pi$
$61$	−6.58579	−0.843224	−0.421612	+	0.906776i	$0.638535\pi$
$62$	9.41421	1.19561
$63$	0	0
$64$	8.00000	1.00000
$65$	2.58579	0.320727
$66$	0	0
$67$	−13.2426	−1.61785	−0.808923	−	0.587915i	$-0.799949\pi$
$67$	−13.2426	−1.61785	−0.808923	+	0.587915i	$0.799949\pi$
$68$	0	0
$69$	0	0
$70$	−3.41421	−0.408077
$71$	−9.82843	−1.16642	−0.583210	−	0.812322i	$-0.698203\pi$
$71$	−9.82843	−1.16642	−0.583210	+	0.812322i	$0.698203\pi$
$72$	0	0
$73$	4.24264	0.496564	0.248282	−	0.968688i	$-0.420134\pi$
$73$	4.24264	0.496564	0.248282	+	0.968688i	$0.420134\pi$
$74$	10.2426	1.19068
$75$	0	0
$76$	0	0
$77$	−8.24264	−0.939336
$78$	0	0
$79$	1.65685	0.186411	0.0932053	−	0.995647i	$-0.470289\pi$
$79$	1.65685	0.186411	0.0932053	+	0.995647i	$0.470289\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	3.75736	0.414931
$83$	−0.414214	−0.0454658	−0.0227329	−	0.999742i	$-0.507237\pi$
$83$	−0.414214	−0.0454658	−0.0227329	+	0.999742i	$0.507237\pi$
$84$	0	0
$85$	−2.41421	−0.261858
$86$	−12.0000	−1.29399
$87$	0	0
$88$	9.65685	1.02942
$89$	5.17157	0.548186	0.274093	−	0.961703i	$-0.411622\pi$
$89$	5.17157	0.548186	0.274093	+	0.961703i	$0.411622\pi$
$90$	0	0
$91$	6.24264	0.654407
$92$	0	0
$93$	0	0
$94$	12.1421	1.25237
$95$	−2.24264	−0.230090
$96$	0	0
$97$	−12.1421	−1.23285	−0.616424	−	0.787415i	$-0.711419\pi$
$97$	−12.1421	−1.23285	−0.616424	+	0.787415i	$0.711419\pi$
$98$	1.65685	0.167368
$99$	0	0
$100$	0	0
$101$	11.8284	1.17697	0.588486	−	0.808507i	$-0.299724\pi$
$101$	11.8284	1.17697	0.588486	+	0.808507i	$0.299724\pi$
$102$	0	0
$103$	−1.65685	−0.163255	−0.0816274	−	0.996663i	$-0.526012\pi$
$103$	−1.65685	−0.163255	−0.0816274	+	0.996663i	$0.526012\pi$
$104$	−7.31371	−0.717168
$105$	0	0
$106$	10.2426	0.994853
$107$	−12.8995	−1.24704	−0.623521	−	0.781807i	$-0.714298\pi$
$107$	−12.8995	−1.24704	−0.623521	+	0.781807i	$0.714298\pi$
$108$	0	0
$109$	−18.2426	−1.74733	−0.873664	−	0.486530i	$-0.838263\pi$
$109$	−18.2426	−1.74733	−0.873664	+	0.486530i	$0.838263\pi$
$110$	4.82843	0.460372
$111$	0	0
$112$	9.65685	0.912487
$113$	−12.8995	−1.21348	−0.606741	−	0.794899i	$-0.707524\pi$
$113$	−12.8995	−1.21348	−0.606741	+	0.794899i	$0.707524\pi$
$114$	0	0
$115$	1.00000	0.0932505
$116$	0	0
$117$	0	0
$118$	−4.72792	−0.435241
$119$	−5.82843	−0.534291
$120$	0	0
$121$	0.656854	0.0597140
$122$	9.31371	0.843224
$123$	0	0
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−6.24264	−0.553945	−0.276972	−	0.960878i	$-0.589331\pi$
$127$	−6.24264	−0.553945	−0.276972	+	0.960878i	$0.589331\pi$
$128$	−11.3137	−1.00000
$129$	0	0
$130$	−3.65685	−0.320727
$131$	0.828427	0.0723800	0.0361900	−	0.999345i	$-0.488478\pi$
$131$	0.828427	0.0723800	0.0361900	+	0.999345i	$0.488478\pi$
$132$	0	0
$133$	−5.41421	−0.469472
$134$	18.7279	1.61785
$135$	0	0
$136$	6.82843	0.585533
$137$	2.82843	0.241649	0.120824	−	0.992674i	$-0.461446\pi$
$137$	2.82843	0.241649	0.120824	+	0.992674i	$0.461446\pi$
$138$	0	0
$139$	15.4853	1.31344	0.656722	−	0.754133i	$-0.271942\pi$
$139$	15.4853	1.31344	0.656722	+	0.754133i	$0.271942\pi$
$140$	0	0
$141$	0	0
$142$	13.8995	1.16642
$143$	−8.82843	−0.738270
$144$	0	0
$145$	−6.65685	−0.552822
$146$	−6.00000	−0.496564
$147$	0	0
$148$	0	0
$149$	−1.89949	−0.155613	−0.0778063	−	0.996968i	$-0.524792\pi$
$149$	−1.89949	−0.155613	−0.0778063	+	0.996968i	$0.524792\pi$
$150$	0	0
$151$	−9.31371	−0.757939	−0.378969	−	0.925409i	$-0.623721\pi$
$151$	−9.31371	−0.757939	−0.378969	+	0.925409i	$0.623721\pi$
$152$	6.34315	0.514497
$153$	0	0
$154$	11.6569	0.939336
$155$	6.65685	0.534691
$156$	0	0
$157$	−17.7279	−1.41484	−0.707421	−	0.706792i	$-0.750142\pi$
$157$	−17.7279	−1.41484	−0.707421	+	0.706792i	$0.750142\pi$
$158$	−2.34315	−0.186411
$159$	0	0
$160$	0	0
$161$	2.41421	0.190267
$162$	0	0
$163$	6.48528	0.507966	0.253983	−	0.967209i	$-0.418259\pi$
$163$	6.48528	0.507966	0.253983	+	0.967209i	$0.418259\pi$
$164$	0	0
$165$	0	0
$166$	0.585786	0.0454658
$167$	−6.72792	−0.520622	−0.260311	−	0.965525i	$-0.583825\pi$
$167$	−6.72792	−0.520622	−0.260311	+	0.965525i	$0.583825\pi$
$168$	0	0
$169$	−6.31371	−0.485670
$170$	3.41421	0.261858
$171$	0	0
$172$	0	0
$173$	−10.3431	−0.786375	−0.393187	−	0.919458i	$-0.628628\pi$
$173$	−10.3431	−0.786375	−0.393187	+	0.919458i	$0.628628\pi$
$174$	0	0
$175$	−2.41421	−0.182497
$176$	−13.6569	−1.02942
$177$	0	0
$178$	−7.31371	−0.548186
$179$	−13.6569	−1.02076	−0.510381	−	0.859949i	$-0.670495\pi$
$179$	−13.6569	−1.02076	−0.510381	+	0.859949i	$0.670495\pi$
$180$	0	0
$181$	22.1421	1.64581	0.822906	−	0.568178i	$-0.192351\pi$
$181$	22.1421	1.64581	0.822906	+	0.568178i	$0.192351\pi$
$182$	−8.82843	−0.654407
$183$	0	0
$184$	−2.82843	−0.208514
$185$	7.24264	0.532490
$186$	0	0
$187$	8.24264	0.602762
$188$	0	0
$189$	0	0
$190$	3.17157	0.230090
$191$	−4.24264	−0.306987	−0.153493	−	0.988150i	$-0.549052\pi$
$191$	−4.24264	−0.306987	−0.153493	+	0.988150i	$0.549052\pi$
$192$	0	0
$193$	16.9706	1.22157	0.610784	−	0.791797i	$-0.290854\pi$
$193$	16.9706	1.22157	0.610784	+	0.791797i	$0.290854\pi$
$194$	17.1716	1.23285
$195$	0	0
$196$	0	0
$197$	13.3137	0.948562	0.474281	−	0.880373i	$-0.342708\pi$
$197$	13.3137	0.948562	0.474281	+	0.880373i	$0.342708\pi$
$198$	0	0
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	2.82843	0.200000
$201$	0	0
$202$	−16.7279	−1.17697
$203$	−16.0711	−1.12797
$204$	0	0
$205$	2.65685	0.185563
$206$	2.34315	0.163255
$207$	0	0
$208$	10.3431	0.717168
$209$	7.65685	0.529636
$210$	0	0
$211$	15.1421	1.04243	0.521214	−	0.853426i	$-0.325479\pi$
$211$	15.1421	1.04243	0.521214	+	0.853426i	$0.325479\pi$
$212$	0	0
$213$	0	0
$214$	18.2426	1.24704
$215$	−8.48528	−0.578691
$216$	0	0
$217$	16.0711	1.09098
$218$	25.7990	1.74733
$219$	0	0
$220$	0	0
$221$	−6.24264	−0.419925
$222$	0	0
$223$	−5.51472	−0.369293	−0.184646	−	0.982805i	$-0.559114\pi$
$223$	−5.51472	−0.369293	−0.184646	+	0.982805i	$0.559114\pi$
$224$	0	0
$225$	0	0
$226$	18.2426	1.21348
$227$	22.6274	1.50183	0.750917	−	0.660396i	$-0.229612\pi$
$227$	22.6274	1.50183	0.750917	+	0.660396i	$0.229612\pi$
$228$	0	0
$229$	3.31371	0.218976	0.109488	−	0.993988i	$-0.465079\pi$
$229$	3.31371	0.218976	0.109488	+	0.993988i	$0.465079\pi$
$230$	−1.41421	−0.0932505
$231$	0	0
$232$	18.8284	1.23615
$233$	−22.8284	−1.49554	−0.747770	−	0.663958i	$-0.768875\pi$
$233$	−22.8284	−1.49554	−0.747770	+	0.663958i	$0.768875\pi$
$234$	0	0
$235$	8.58579	0.560075
$236$	0	0
$237$	0	0
$238$	8.24264	0.534291
$239$	14.6569	0.948073	0.474037	−	0.880505i	$-0.342796\pi$
$239$	14.6569	0.948073	0.474037	+	0.880505i	$0.342796\pi$
$240$	0	0
$241$	−26.0416	−1.67749	−0.838744	−	0.544525i	$-0.816710\pi$
$241$	−26.0416	−1.67749	−0.838744	+	0.544525i	$0.816710\pi$
$242$	−0.928932	−0.0597140
$243$	0	0
$244$	0	0
$245$	1.17157	0.0748490
$246$	0	0
$247$	−5.79899	−0.368981
$248$	−18.8284	−1.19561
$249$	0	0
$250$	1.41421	0.0894427
$251$	21.7990	1.37594	0.687970	−	0.725739i	$-0.258502\pi$
$251$	21.7990	1.37594	0.687970	+	0.725739i	$0.258502\pi$
$252$	0	0
$253$	−3.41421	−0.214650
$254$	8.82843	0.553945
$255$	0	0
$256$	0	0
$257$	1.07107	0.0668114	0.0334057	−	0.999442i	$-0.489365\pi$
$257$	1.07107	0.0668114	0.0334057	+	0.999442i	$0.489365\pi$
$258$	0	0
$259$	17.4853	1.08648
$260$	0	0
$261$	0	0
$262$	−1.17157	−0.0723800
$263$	30.2132	1.86303	0.931513	−	0.363708i	$-0.118489\pi$
$263$	30.2132	1.86303	0.931513	+	0.363708i	$0.118489\pi$
$264$	0	0
$265$	7.24264	0.444912
$266$	7.65685	0.469472
$267$	0	0
$268$	0	0
$269$	18.6569	1.13753	0.568764	−	0.822501i	$-0.307422\pi$
$269$	18.6569	1.13753	0.568764	+	0.822501i	$0.307422\pi$
$270$	0	0
$271$	0.514719	0.0312669	0.0156335	−	0.999878i	$-0.495024\pi$
$271$	0.514719	0.0312669	0.0156335	+	0.999878i	$0.495024\pi$
$272$	−9.65685	−0.585533
$273$	0	0
$274$	−4.00000	−0.241649
$275$	3.41421	0.205885
$276$	0	0
$277$	−19.1716	−1.15191	−0.575954	−	0.817482i	$-0.695369\pi$
$277$	−19.1716	−1.15191	−0.575954	+	0.817482i	$0.695369\pi$
$278$	−21.8995	−1.31344
$279$	0	0
$280$	6.82843	0.408077
$281$	11.4142	0.680915	0.340457	−	0.940260i	$-0.389418\pi$
$281$	11.4142	0.680915	0.340457	+	0.940260i	$0.389418\pi$
$282$	0	0
$283$	−11.3848	−0.676755	−0.338377	−	0.941011i	$-0.609878\pi$
$283$	−11.3848	−0.676755	−0.338377	+	0.941011i	$0.609878\pi$
$284$	0	0
$285$	0	0
$286$	12.4853	0.738270
$287$	6.41421	0.378619
$288$	0	0
$289$	−11.1716	−0.657151
$290$	9.41421	0.552822
$291$	0	0
$292$	0	0
$293$	−11.5858	−0.676849	−0.338424	−	0.940994i	$-0.609894\pi$
$293$	−11.5858	−0.676849	−0.338424	+	0.940994i	$0.609894\pi$
$294$	0	0
$295$	−3.34315	−0.194645
$296$	−20.4853	−1.19068
$297$	0	0
$298$	2.68629	0.155613
$299$	2.58579	0.149540
$300$	0	0
$301$	−20.4853	−1.18075
$302$	13.1716	0.757939
$303$	0	0
$304$	−8.97056	−0.514497
$305$	6.58579	0.377101
$306$	0	0
$307$	7.75736	0.442736	0.221368	−	0.975190i	$-0.428948\pi$
$307$	7.75736	0.442736	0.221368	+	0.975190i	$0.428948\pi$
$308$	0	0
$309$	0	0
$310$	−9.41421	−0.534691
$311$	−3.85786	−0.218759	−0.109380	−	0.994000i	$-0.534886\pi$
$311$	−3.85786	−0.218759	−0.109380	+	0.994000i	$0.534886\pi$
$312$	0	0
$313$	13.2426	0.748518	0.374259	−	0.927324i	$-0.377897\pi$
$313$	13.2426	0.748518	0.374259	+	0.927324i	$0.377897\pi$
$314$	25.0711	1.41484
$315$	0	0
$316$	0	0
$317$	7.89949	0.443680	0.221840	−	0.975083i	$-0.428794\pi$
$317$	7.89949	0.443680	0.221840	+	0.975083i	$0.428794\pi$
$318$	0	0
$319$	22.7279	1.27252
$320$	−8.00000	−0.447214
$321$	0	0
$322$	−3.41421	−0.190267
$323$	5.41421	0.301255
$324$	0	0
$325$	−2.58579	−0.143434
$326$	−9.17157	−0.507966
$327$	0	0
$328$	−7.51472	−0.414931
$329$	20.7279	1.14277
$330$	0	0
$331$	−27.9706	−1.53740	−0.768701	−	0.639609i	$-0.779096\pi$
$331$	−27.9706	−1.53740	−0.768701	+	0.639609i	$0.779096\pi$
$332$	0	0
$333$	0	0
$334$	9.51472	0.520622
$335$	13.2426	0.723523
$336$	0	0
$337$	−7.51472	−0.409353	−0.204676	−	0.978830i	$-0.565614\pi$
$337$	−7.51472	−0.409353	−0.204676	+	0.978830i	$0.565614\pi$
$338$	8.92893	0.485670
$339$	0	0
$340$	0	0
$341$	−22.7279	−1.23079
$342$	0	0
$343$	19.7279	1.06521
$344$	24.0000	1.29399
$345$	0	0
$346$	14.6274	0.786375
$347$	−31.3137	−1.68101	−0.840504	−	0.541805i	$-0.817741\pi$
$347$	−31.3137	−1.68101	−0.840504	+	0.541805i	$0.817741\pi$
$348$	0	0
$349$	−10.1716	−0.544472	−0.272236	−	0.962231i	$-0.587763\pi$
$349$	−10.1716	−0.544472	−0.272236	+	0.962231i	$0.587763\pi$
$350$	3.41421	0.182497
$351$	0	0
$352$	0	0
$353$	4.38478	0.233378	0.116689	−	0.993168i	$-0.462772\pi$
$353$	4.38478	0.233378	0.116689	+	0.993168i	$0.462772\pi$
$354$	0	0
$355$	9.82843	0.521639
$356$	0	0
$357$	0	0
$358$	19.3137	1.02076
$359$	7.07107	0.373197	0.186598	−	0.982436i	$-0.440254\pi$
$359$	7.07107	0.373197	0.186598	+	0.982436i	$0.440254\pi$
$360$	0	0
$361$	−13.9706	−0.735293
$362$	−31.3137	−1.64581
$363$	0	0
$364$	0	0
$365$	−4.24264	−0.222070
$366$	0	0
$367$	21.7279	1.13419	0.567094	−	0.823653i	$-0.308068\pi$
$367$	21.7279	1.13419	0.567094	+	0.823653i	$0.308068\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	−10.2426	−0.532490
$371$	17.4853	0.907791
$372$	0	0
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	−11.6569	−0.602762
$375$	0	0
$376$	−24.2843	−1.25237
$377$	−17.2132	−0.886525
$378$	0	0
$379$	−4.97056	−0.255321	−0.127660	−	0.991818i	$-0.540747\pi$
$379$	−4.97056	−0.255321	−0.127660	+	0.991818i	$0.540747\pi$
$380$	0	0
$381$	0	0
$382$	6.00000	0.306987
$383$	5.92893	0.302954	0.151477	−	0.988461i	$-0.451597\pi$
$383$	5.92893	0.302954	0.151477	+	0.988461i	$0.451597\pi$
$384$	0	0
$385$	8.24264	0.420084
$386$	−24.0000	−1.22157
$387$	0	0
$388$	0	0
$389$	9.51472	0.482415	0.241208	−	0.970474i	$-0.422456\pi$
$389$	9.51472	0.482415	0.241208	+	0.970474i	$0.422456\pi$
$390$	0	0
$391$	−2.41421	−0.122092
$392$	−3.31371	−0.167368
$393$	0	0
$394$	−18.8284	−0.948562
$395$	−1.65685	−0.0833654
$396$	0	0
$397$	30.6274	1.53715	0.768573	−	0.639762i	$-0.220967\pi$
$397$	30.6274	1.53715	0.768573	+	0.639762i	$0.220967\pi$
$398$	−19.7990	−0.992434
$399$	0	0
$400$	−4.00000	−0.200000
$401$	3.85786	0.192653	0.0963263	−	0.995350i	$-0.469291\pi$
$401$	3.85786	0.192653	0.0963263	+	0.995350i	$0.469291\pi$
$402$	0	0
$403$	17.2132	0.857451
$404$	0	0
$405$	0	0
$406$	22.7279	1.12797
$407$	−24.7279	−1.22572
$408$	0	0
$409$	−34.9411	−1.72773	−0.863864	−	0.503726i	$-0.831962\pi$
$409$	−34.9411	−1.72773	−0.863864	+	0.503726i	$0.831962\pi$
$410$	−3.75736	−0.185563
$411$	0	0
$412$	0	0
$413$	−8.07107	−0.397151
$414$	0	0
$415$	0.414214	0.0203329
$416$	0	0
$417$	0	0
$418$	−10.8284	−0.529636
$419$	32.8701	1.60581	0.802904	−	0.596109i	$-0.203287\pi$
$419$	32.8701	1.60581	0.802904	+	0.596109i	$0.203287\pi$
$420$	0	0
$421$	−30.7279	−1.49759	−0.748794	−	0.662803i	$-0.769367\pi$
$421$	−30.7279	−1.49759	−0.748794	+	0.662803i	$0.769367\pi$
$422$	−21.4142	−1.04243
$423$	0	0
$424$	−20.4853	−0.994853
$425$	2.41421	0.117107
$426$	0	0
$427$	15.8995	0.769430
$428$	0	0
$429$	0	0
$430$	12.0000	0.578691
$431$	21.6569	1.04317	0.521587	−	0.853198i	$-0.325340\pi$
$431$	21.6569	1.04317	0.521587	+	0.853198i	$0.325340\pi$
$432$	0	0
$433$	8.41421	0.404361	0.202181	−	0.979348i	$-0.435197\pi$
$433$	8.41421	0.404361	0.202181	+	0.979348i	$0.435197\pi$
$434$	−22.7279	−1.09098
$435$	0	0
$436$	0	0
$437$	−2.24264	−0.107280
$438$	0	0
$439$	−30.4853	−1.45498	−0.727492	−	0.686117i	$-0.759314\pi$
$439$	−30.4853	−1.45498	−0.727492	+	0.686117i	$0.759314\pi$
$440$	−9.65685	−0.460372
$441$	0	0
$442$	8.82843	0.419925
$443$	0.100505	0.00477514	0.00238757	−	0.999997i	$-0.499240\pi$
$443$	0.100505	0.00477514	0.00238757	+	0.999997i	$0.499240\pi$
$444$	0	0
$445$	−5.17157	−0.245156
$446$	7.79899	0.369293
$447$	0	0
$448$	−19.3137	−0.912487
$449$	−41.4853	−1.95781	−0.978906	−	0.204312i	$-0.934504\pi$
$449$	−41.4853	−1.95781	−0.978906	+	0.204312i	$0.934504\pi$
$450$	0	0
$451$	−9.07107	−0.427140
$452$	0	0
$453$	0	0
$454$	−32.0000	−1.50183
$455$	−6.24264	−0.292660
$456$	0	0
$457$	8.21320	0.384197	0.192099	−	0.981376i	$-0.438471\pi$
$457$	8.21320	0.384197	0.192099	+	0.981376i	$0.438471\pi$
$458$	−4.68629	−0.218976
$459$	0	0
$460$	0	0
$461$	−20.4853	−0.954095	−0.477047	−	0.878878i	$-0.658293\pi$
$461$	−20.4853	−0.954095	−0.477047	+	0.878878i	$0.658293\pi$
$462$	0	0
$463$	2.58579	0.120172	0.0600858	−	0.998193i	$-0.480863\pi$
$463$	2.58579	0.120172	0.0600858	+	0.998193i	$0.480863\pi$
$464$	−26.6274	−1.23615
$465$	0	0
$466$	32.2843	1.49554
$467$	18.0711	0.836229	0.418115	−	0.908394i	$-0.362691\pi$
$467$	18.0711	0.836229	0.418115	+	0.908394i	$0.362691\pi$
$468$	0	0
$469$	31.9706	1.47626
$470$	−12.1421	−0.560075
$471$	0	0
$472$	9.45584	0.435241
$473$	28.9706	1.33207
$474$	0	0
$475$	2.24264	0.102899
$476$	0	0
$477$	0	0
$478$	−20.7279	−0.948073
$479$	0.727922	0.0332596	0.0166298	−	0.999862i	$-0.494706\pi$
$479$	0.727922	0.0332596	0.0166298	+	0.999862i	$0.494706\pi$
$480$	0	0
$481$	18.7279	0.853920
$482$	36.8284	1.67749
$483$	0	0
$484$	0	0
$485$	12.1421	0.551346
$486$	0	0
$487$	11.4142	0.517227	0.258614	−	0.965981i	$-0.416734\pi$
$487$	11.4142	0.517227	0.258614	+	0.965981i	$0.416734\pi$
$488$	−18.6274	−0.843224
$489$	0	0
$490$	−1.65685	−0.0748490
$491$	−31.1421	−1.40542	−0.702712	−	0.711474i	$-0.748028\pi$
$491$	−31.1421	−1.40542	−0.702712	+	0.711474i	$0.748028\pi$
$492$	0	0
$493$	16.0711	0.723804
$494$	8.20101	0.368981
$495$	0	0
$496$	26.6274	1.19561
$497$	23.7279	1.06434
$498$	0	0
$499$	−34.9411	−1.56418	−0.782090	−	0.623166i	$-0.785846\pi$
$499$	−34.9411	−1.56418	−0.782090	+	0.623166i	$0.785846\pi$
$500$	0	0
$501$	0	0
$502$	−30.8284	−1.37594
$503$	−21.7279	−0.968800	−0.484400	−	0.874847i	$-0.660962\pi$
$503$	−21.7279	−0.968800	−0.484400	+	0.874847i	$0.660962\pi$
$504$	0	0
$505$	−11.8284	−0.526358
$506$	4.82843	0.214650
$507$	0	0
$508$	0	0
$509$	−34.2843	−1.51962	−0.759812	−	0.650143i	$-0.774709\pi$
$509$	−34.2843	−1.51962	−0.759812	+	0.650143i	$0.774709\pi$
$510$	0	0
$511$	−10.2426	−0.453108
$512$	22.6274	1.00000
$513$	0	0
$514$	−1.51472	−0.0668114
$515$	1.65685	0.0730097
$516$	0	0
$517$	−29.3137	−1.28922
$518$	−24.7279	−1.08648
$519$	0	0
$520$	7.31371	0.320727
$521$	29.5563	1.29489	0.647444	−	0.762113i	$-0.275838\pi$
$521$	29.5563	1.29489	0.647444	+	0.762113i	$0.275838\pi$
$522$	0	0
$523$	−27.9411	−1.22178	−0.610890	−	0.791715i	$-0.709188\pi$
$523$	−27.9411	−1.22178	−0.610890	+	0.791715i	$0.709188\pi$
$524$	0	0
$525$	0	0
$526$	−42.7279	−1.86303
$527$	−16.0711	−0.700067
$528$	0	0
$529$	1.00000	0.0434783
$530$	−10.2426	−0.444912
$531$	0	0
$532$	0	0
$533$	6.87006	0.297575
$534$	0	0
$535$	12.8995	0.557694
$536$	−37.4558	−1.61785
$537$	0	0
$538$	−26.3848	−1.13753
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−1.85786	−0.0798758	−0.0399379	−	0.999202i	$-0.512716\pi$
$541$	−1.85786	−0.0798758	−0.0399379	+	0.999202i	$0.512716\pi$
$542$	−0.727922	−0.0312669
$543$	0	0
$544$	0	0
$545$	18.2426	0.781429
$546$	0	0
$547$	−44.9706	−1.92280	−0.961401	−	0.275150i	$-0.911272\pi$
$547$	−44.9706	−1.92280	−0.961401	+	0.275150i	$0.911272\pi$
$548$	0	0
$549$	0	0
$550$	−4.82843	−0.205885
$551$	14.9289	0.635994
$552$	0	0
$553$	−4.00000	−0.170097
$554$	27.1127	1.15191
$555$	0	0
$556$	0	0
$557$	−31.5858	−1.33833	−0.669166	−	0.743113i	$-0.733349\pi$
$557$	−31.5858	−1.33833	−0.669166	+	0.743113i	$0.733349\pi$
$558$	0	0
$559$	−21.9411	−0.928011
$560$	−9.65685	−0.408077
$561$	0	0
$562$	−16.1421	−0.680915
$563$	33.5858	1.41547	0.707736	−	0.706477i	$-0.249717\pi$
$563$	33.5858	1.41547	0.707736	+	0.706477i	$0.249717\pi$
$564$	0	0
$565$	12.8995	0.542686
$566$	16.1005	0.676755
$567$	0	0
$568$	−27.7990	−1.16642
$569$	−31.6569	−1.32712	−0.663562	−	0.748121i	$-0.730956\pi$
$569$	−31.6569	−1.32712	−0.663562	+	0.748121i	$0.730956\pi$
$570$	0	0
$571$	11.7574	0.492030	0.246015	−	0.969266i	$-0.420879\pi$
$571$	11.7574	0.492030	0.246015	+	0.969266i	$0.420879\pi$
$572$	0	0
$573$	0	0
$574$	−9.07107	−0.378619
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	29.4558	1.22626	0.613131	−	0.789981i	$-0.289910\pi$
$577$	29.4558	1.22626	0.613131	+	0.789981i	$0.289910\pi$
$578$	15.7990	0.657151
$579$	0	0
$580$	0	0
$581$	1.00000	0.0414870
$582$	0	0
$583$	−24.7279	−1.02413
$584$	12.0000	0.496564
$585$	0	0
$586$	16.3848	0.676849
$587$	−34.2843	−1.41506	−0.707532	−	0.706682i	$-0.750191\pi$
$587$	−34.2843	−1.41506	−0.707532	+	0.706682i	$0.750191\pi$
$588$	0	0
$589$	−14.9289	−0.615136
$590$	4.72792	0.194645
$591$	0	0
$592$	28.9706	1.19068
$593$	13.0711	0.536764	0.268382	−	0.963313i	$-0.413511\pi$
$593$	13.0711	0.536764	0.268382	+	0.963313i	$0.413511\pi$
$594$	0	0
$595$	5.82843	0.238942
$596$	0	0
$597$	0	0
$598$	−3.65685	−0.149540
$599$	11.6569	0.476286	0.238143	−	0.971230i	$-0.423461\pi$
$599$	11.6569	0.476286	0.238143	+	0.971230i	$0.423461\pi$
$600$	0	0
$601$	−6.31371	−0.257542	−0.128771	−	0.991674i	$-0.541103\pi$
$601$	−6.31371	−0.257542	−0.128771	+	0.991674i	$0.541103\pi$
$602$	28.9706	1.18075
$603$	0	0
$604$	0	0
$605$	−0.656854	−0.0267049
$606$	0	0
$607$	30.5269	1.23905	0.619525	−	0.784977i	$-0.287325\pi$
$607$	30.5269	1.23905	0.619525	+	0.784977i	$0.287325\pi$
$608$	0	0
$609$	0	0
$610$	−9.31371	−0.377101
$611$	22.2010	0.898157
$612$	0	0
$613$	−18.1421	−0.732754	−0.366377	−	0.930467i	$-0.619402\pi$
$613$	−18.1421	−0.732754	−0.366377	+	0.930467i	$0.619402\pi$
$614$	−10.9706	−0.442736
$615$	0	0
$616$	−23.3137	−0.939336
$617$	31.3848	1.26350	0.631752	−	0.775171i	$-0.282336\pi$
$617$	31.3848	1.26350	0.631752	+	0.775171i	$0.282336\pi$
$618$	0	0
$619$	−2.34315	−0.0941790	−0.0470895	−	0.998891i	$-0.514995\pi$
$619$	−2.34315	−0.0941790	−0.0470895	+	0.998891i	$0.514995\pi$
$620$	0	0
$621$	0	0
$622$	5.45584	0.218759
$623$	−12.4853	−0.500212
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.7279	−0.748518
$627$	0	0
$628$	0	0
$629$	−17.4853	−0.697184
$630$	0	0
$631$	12.7279	0.506691	0.253345	−	0.967376i	$-0.418469\pi$
$631$	12.7279	0.506691	0.253345	+	0.967376i	$0.418469\pi$
$632$	4.68629	0.186411
$633$	0	0
$634$	−11.1716	−0.443680
$635$	6.24264	0.247732
$636$	0	0
$637$	3.02944	0.120031
$638$	−32.1421	−1.27252
$639$	0	0
$640$	11.3137	0.447214
$641$	2.44365	0.0965184	0.0482592	−	0.998835i	$-0.484633\pi$
$641$	2.44365	0.0965184	0.0482592	+	0.998835i	$0.484633\pi$
$642$	0	0
$643$	30.2132	1.19149	0.595746	−	0.803173i	$-0.296856\pi$
$643$	30.2132	1.19149	0.595746	+	0.803173i	$0.296856\pi$
$644$	0	0
$645$	0	0
$646$	−7.65685	−0.301255
$647$	−2.78680	−0.109560	−0.0547801	−	0.998498i	$-0.517446\pi$
$647$	−2.78680	−0.109560	−0.0547801	+	0.998498i	$0.517446\pi$
$648$	0	0
$649$	11.4142	0.448047
$650$	3.65685	0.143434
$651$	0	0
$652$	0	0
$653$	−40.0416	−1.56695	−0.783475	−	0.621423i	$-0.786555\pi$
$653$	−40.0416	−1.56695	−0.783475	+	0.621423i	$0.786555\pi$
$654$	0	0
$655$	−0.828427	−0.0323693
$656$	10.6274	0.414931
$657$	0	0
$658$	−29.3137	−1.14277
$659$	−12.1005	−0.471369	−0.235684	−	0.971830i	$-0.575733\pi$
$659$	−12.1005	−0.471369	−0.235684	+	0.971830i	$0.575733\pi$
$660$	0	0
$661$	−6.97056	−0.271123	−0.135562	−	0.990769i	$-0.543284\pi$
$661$	−6.97056	−0.271123	−0.135562	+	0.990769i	$0.543284\pi$
$662$	39.5563	1.53740
$663$	0	0
$664$	−1.17157	−0.0454658
$665$	5.41421	0.209954
$666$	0	0
$667$	−6.65685	−0.257754
$668$	0	0
$669$	0	0
$670$	−18.7279	−0.723523
$671$	−22.4853	−0.868035
$672$	0	0
$673$	11.6985	0.450943	0.225472	−	0.974250i	$-0.427608\pi$
$673$	11.6985	0.450943	0.225472	+	0.974250i	$0.427608\pi$
$674$	10.6274	0.409353
$675$	0	0
$676$	0	0
$677$	7.24264	0.278357	0.139179	−	0.990267i	$-0.455554\pi$
$677$	7.24264	0.278357	0.139179	+	0.990267i	$0.455554\pi$
$678$	0	0
$679$	29.3137	1.12496
$680$	−6.82843	−0.261858
$681$	0	0
$682$	32.1421	1.23079
$683$	10.2426	0.391924	0.195962	−	0.980612i	$-0.437217\pi$
$683$	10.2426	0.391924	0.195962	+	0.980612i	$0.437217\pi$
$684$	0	0
$685$	−2.82843	−0.108069
$686$	−27.8995	−1.06521
$687$	0	0
$688$	−33.9411	−1.29399
$689$	18.7279	0.713477
$690$	0	0
$691$	37.3137	1.41948	0.709740	−	0.704464i	$-0.248812\pi$
$691$	37.3137	1.41948	0.709740	+	0.704464i	$0.248812\pi$
$692$	0	0
$693$	0	0
$694$	44.2843	1.68101
$695$	−15.4853	−0.587390
$696$	0	0
$697$	−6.41421	−0.242956
$698$	14.3848	0.544472
$699$	0	0
$700$	0	0
$701$	44.5269	1.68176	0.840879	−	0.541223i	$-0.182039\pi$
$701$	44.5269	1.68176	0.840879	+	0.541223i	$0.182039\pi$
$702$	0	0
$703$	−16.2426	−0.612603
$704$	27.3137	1.02942
$705$	0	0
$706$	−6.20101	−0.233378
$707$	−28.5563	−1.07397
$708$	0	0
$709$	−25.6985	−0.965127	−0.482563	−	0.875861i	$-0.660294\pi$
$709$	−25.6985	−0.965127	−0.482563	+	0.875861i	$0.660294\pi$
$710$	−13.8995	−0.521639
$711$	0	0
$712$	14.6274	0.548186
$713$	6.65685	0.249301
$714$	0	0
$715$	8.82843	0.330164
$716$	0	0
$717$	0	0
$718$	−10.0000	−0.373197
$719$	−1.97056	−0.0734896	−0.0367448	−	0.999325i	$-0.511699\pi$
$719$	−1.97056	−0.0734896	−0.0367448	+	0.999325i	$0.511699\pi$
$720$	0	0
$721$	4.00000	0.148968
$722$	19.7574	0.735293
$723$	0	0
$724$	0	0
$725$	6.65685	0.247229
$726$	0	0
$727$	11.2426	0.416966	0.208483	−	0.978026i	$-0.433147\pi$
$727$	11.2426	0.416966	0.208483	+	0.978026i	$0.433147\pi$
$728$	17.6569	0.654407
$729$	0	0
$730$	6.00000	0.222070
$731$	20.4853	0.757676
$732$	0	0
$733$	−4.75736	−0.175717	−0.0878585	−	0.996133i	$-0.528002\pi$
$733$	−4.75736	−0.175717	−0.0878585	+	0.996133i	$0.528002\pi$
$734$	−30.7279	−1.13419
$735$	0	0
$736$	0	0
$737$	−45.2132	−1.66545
$738$	0	0
$739$	1.82843	0.0672598	0.0336299	−	0.999434i	$-0.489293\pi$
$739$	1.82843	0.0672598	0.0336299	+	0.999434i	$0.489293\pi$
$740$	0	0
$741$	0	0
$742$	−24.7279	−0.907791
$743$	20.2843	0.744158	0.372079	−	0.928201i	$-0.378645\pi$
$743$	20.2843	0.744158	0.372079	+	0.928201i	$0.378645\pi$
$744$	0	0
$745$	1.89949	0.0695921
$746$	36.7696	1.34623
$747$	0	0
$748$	0	0
$749$	31.1421	1.13791
$750$	0	0
$751$	−43.2132	−1.57687	−0.788436	−	0.615117i	$-0.789109\pi$
$751$	−43.2132	−1.57687	−0.788436	+	0.615117i	$0.789109\pi$
$752$	34.3431	1.25237
$753$	0	0
$754$	24.3431	0.886525
$755$	9.31371	0.338961
$756$	0	0
$757$	9.72792	0.353567	0.176784	−	0.984250i	$-0.443431\pi$
$757$	9.72792	0.353567	0.176784	+	0.984250i	$0.443431\pi$
$758$	7.02944	0.255321
$759$	0	0
$760$	−6.34315	−0.230090
$761$	−15.6863	−0.568628	−0.284314	−	0.958731i	$-0.591766\pi$
$761$	−15.6863	−0.568628	−0.284314	+	0.958731i	$0.591766\pi$
$762$	0	0
$763$	44.0416	1.59441
$764$	0	0
$765$	0	0
$766$	−8.38478	−0.302954
$767$	−8.64466	−0.312141
$768$	0	0
$769$	−34.3848	−1.23995	−0.619973	−	0.784623i	$-0.712857\pi$
$769$	−34.3848	−1.23995	−0.619973	+	0.784623i	$0.712857\pi$
$770$	−11.6569	−0.420084
$771$	0	0
$772$	0	0
$773$	3.85786	0.138758	0.0693789	−	0.997590i	$-0.477898\pi$
$773$	3.85786	0.138758	0.0693789	+	0.997590i	$0.477898\pi$
$774$	0	0
$775$	−6.65685	−0.239121
$776$	−34.3431	−1.23285
$777$	0	0
$778$	−13.4558	−0.482415
$779$	−5.95837	−0.213481
$780$	0	0
$781$	−33.5563	−1.20074
$782$	3.41421	0.122092
$783$	0	0
$784$	4.68629	0.167368
$785$	17.7279	0.632737
$786$	0	0
$787$	43.8701	1.56380	0.781899	−	0.623405i	$-0.214251\pi$
$787$	43.8701	1.56380	0.781899	+	0.623405i	$0.214251\pi$
$788$	0	0
$789$	0	0
$790$	2.34315	0.0833654
$791$	31.1421	1.10729
$792$	0	0
$793$	17.0294	0.604733
$794$	−43.3137	−1.53715
$795$	0	0
$796$	0	0
$797$	6.21320	0.220083	0.110041	−	0.993927i	$-0.464902\pi$
$797$	6.21320	0.220083	0.110041	+	0.993927i	$0.464902\pi$
$798$	0	0
$799$	−20.7279	−0.733301
$800$	0	0
$801$	0	0
$802$	−5.45584	−0.192653
$803$	14.4853	0.511174
$804$	0	0
$805$	−2.41421	−0.0850898
$806$	−24.3431	−0.857451
$807$	0	0
$808$	33.4558	1.17697
$809$	−11.1421	−0.391737	−0.195868	−	0.980630i	$-0.562753\pi$
$809$	−11.1421	−0.391737	−0.195868	+	0.980630i	$0.562753\pi$
$810$	0	0
$811$	39.2843	1.37946	0.689729	−	0.724068i	$-0.257730\pi$
$811$	39.2843	1.37946	0.689729	+	0.724068i	$0.257730\pi$
$812$	0	0
$813$	0	0
$814$	34.9706	1.22572
$815$	−6.48528	−0.227169
$816$	0	0
$817$	19.0294	0.665756
$818$	49.4142	1.72773
$819$	0	0
$820$	0	0
$821$	52.6274	1.83671	0.918355	−	0.395758i	$-0.129518\pi$
$821$	52.6274	1.83671	0.918355	+	0.395758i	$0.129518\pi$
$822$	0	0
$823$	25.1716	0.877426	0.438713	−	0.898627i	$-0.355434\pi$
$823$	25.1716	0.877426	0.438713	+	0.898627i	$0.355434\pi$
$824$	−4.68629	−0.163255
$825$	0	0
$826$	11.4142	0.397151
$827$	27.3848	0.952262	0.476131	−	0.879374i	$-0.342039\pi$
$827$	27.3848	0.952262	0.476131	+	0.879374i	$0.342039\pi$
$828$	0	0
$829$	9.00000	0.312583	0.156291	−	0.987711i	$-0.450046\pi$
$829$	9.00000	0.312583	0.156291	+	0.987711i	$0.450046\pi$
$830$	−0.585786	−0.0203329
$831$	0	0
$832$	−20.6863	−0.717168
$833$	−2.82843	−0.0979992
$834$	0	0
$835$	6.72792	0.232829
$836$	0	0
$837$	0	0
$838$	−46.4853	−1.60581
$839$	−40.6274	−1.40261	−0.701307	−	0.712859i	$-0.747400\pi$
$839$	−40.6274	−1.40261	−0.701307	+	0.712859i	$0.747400\pi$
$840$	0	0
$841$	15.3137	0.528059
$842$	43.4558	1.49759
$843$	0	0
$844$	0	0
$845$	6.31371	0.217198
$846$	0	0
$847$	−1.58579	−0.0544883
$848$	28.9706	0.994853
$849$	0	0
$850$	−3.41421	−0.117107
$851$	7.24264	0.248275
$852$	0	0
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	−22.4853	−0.769430
$855$	0	0
$856$	−36.4853	−1.24704
$857$	8.14214	0.278130	0.139065	−	0.990283i	$-0.455590\pi$
$857$	8.14214	0.278130	0.139065	+	0.990283i	$0.455590\pi$
$858$	0	0
$859$	3.00000	0.102359	0.0511793	−	0.998689i	$-0.483702\pi$
$859$	3.00000	0.102359	0.0511793	+	0.998689i	$0.483702\pi$
$860$	0	0
$861$	0	0
$862$	−30.6274	−1.04317
$863$	24.6274	0.838327	0.419164	−	0.907911i	$-0.362323\pi$
$863$	24.6274	0.838327	0.419164	+	0.907911i	$0.362323\pi$
$864$	0	0
$865$	10.3431	0.351678
$866$	−11.8995	−0.404361
$867$	0	0
$868$	0	0
$869$	5.65685	0.191896
$870$	0	0
$871$	34.2426	1.16027
$872$	−51.5980	−1.74733
$873$	0	0
$874$	3.17157	0.107280
$875$	2.41421	0.0816153
$876$	0	0
$877$	30.9706	1.04580	0.522901	−	0.852394i	$-0.324850\pi$
$877$	30.9706	1.04580	0.522901	+	0.852394i	$0.324850\pi$
$878$	43.1127	1.45498
$879$	0	0
$880$	13.6569	0.460372
$881$	−49.4975	−1.66761	−0.833806	−	0.552057i	$-0.813843\pi$
$881$	−49.4975	−1.66761	−0.833806	+	0.552057i	$0.813843\pi$
$882$	0	0
$883$	53.5563	1.80231	0.901157	−	0.433492i	$-0.142719\pi$
$883$	53.5563	1.80231	0.901157	+	0.433492i	$0.142719\pi$
$884$	0	0
$885$	0	0
$886$	−0.142136	−0.00477514
$887$	44.3431	1.48890	0.744449	−	0.667680i	$-0.232712\pi$
$887$	44.3431	1.48890	0.744449	+	0.667680i	$0.232712\pi$
$888$	0	0
$889$	15.0711	0.505467
$890$	7.31371	0.245156
$891$	0	0
$892$	0	0
$893$	−19.2548	−0.644338
$894$	0	0
$895$	13.6569	0.456498
$896$	27.3137	0.912487
$897$	0	0
$898$	58.6690	1.95781
$899$	−44.3137	−1.47794
$900$	0	0
$901$	−17.4853	−0.582519
$902$	12.8284	0.427140
$903$	0	0
$904$	−36.4853	−1.21348
$905$	−22.1421	−0.736029
$906$	0	0
$907$	1.44365	0.0479356	0.0239678	−	0.999713i	$-0.492370\pi$
$907$	1.44365	0.0479356	0.0239678	+	0.999713i	$0.492370\pi$
$908$	0	0
$909$	0	0
$910$	8.82843	0.292660
$911$	38.8284	1.28644	0.643222	−	0.765680i	$-0.277597\pi$
$911$	38.8284	1.28644	0.643222	+	0.765680i	$0.277597\pi$
$912$	0	0
$913$	−1.41421	−0.0468036
$914$	−11.6152	−0.384197
$915$	0	0
$916$	0	0
$917$	−2.00000	−0.0660458
$918$	0	0
$919$	45.4558	1.49945	0.749725	−	0.661750i	$-0.230186\pi$
$919$	45.4558	1.49945	0.749725	+	0.661750i	$0.230186\pi$
$920$	2.82843	0.0932505
$921$	0	0
$922$	28.9706	0.954095
$923$	25.4142	0.836519
$924$	0	0
$925$	−7.24264	−0.238137
$926$	−3.65685	−0.120172
$927$	0	0
$928$	0	0
$929$	−34.7990	−1.14172	−0.570859	−	0.821048i	$-0.693390\pi$
$929$	−34.7990	−1.14172	−0.570859	+	0.821048i	$0.693390\pi$
$930$	0	0
$931$	−2.62742	−0.0861101
$932$	0	0
$933$	0	0
$934$	−25.5563	−0.836229
$935$	−8.24264	−0.269563
$936$	0	0
$937$	−34.7696	−1.13587	−0.567936	−	0.823073i	$-0.692258\pi$
$937$	−34.7696	−1.13587	−0.567936	+	0.823073i	$0.692258\pi$
$938$	−45.2132	−1.47626
$939$	0	0
$940$	0	0
$941$	57.9828	1.89018	0.945092	−	0.326805i	$-0.105972\pi$
$941$	57.9828	1.89018	0.945092	+	0.326805i	$0.105972\pi$
$942$	0	0
$943$	2.65685	0.0865191
$944$	−13.3726	−0.435241
$945$	0	0
$946$	−40.9706	−1.33207
$947$	−51.7990	−1.68324	−0.841621	−	0.540069i	$-0.818398\pi$
$947$	−51.7990	−1.68324	−0.841621	+	0.540069i	$0.818398\pi$
$948$	0	0
$949$	−10.9706	−0.356120
$950$	−3.17157	−0.102899
$951$	0	0
$952$	−16.4853	−0.534291
$953$	24.3431	0.788552	0.394276	−	0.918992i	$-0.370995\pi$
$953$	24.3431	0.788552	0.394276	+	0.918992i	$0.370995\pi$
$954$	0	0
$955$	4.24264	0.137289
$956$	0	0
$957$	0	0
$958$	−1.02944	−0.0332596
$959$	−6.82843	−0.220501
$960$	0	0
$961$	13.3137	0.429474
$962$	−26.4853	−0.853920
$963$	0	0
$964$	0	0
$965$	−16.9706	−0.546302
$966$	0	0
$967$	−5.55635	−0.178680	−0.0893401	−	0.996001i	$-0.528476\pi$
$967$	−5.55635	−0.178680	−0.0893401	+	0.996001i	$0.528476\pi$
$968$	1.85786	0.0597140
$969$	0	0
$970$	−17.1716	−0.551346
$971$	−59.3970	−1.90614	−0.953070	−	0.302751i	$-0.902095\pi$
$971$	−59.3970	−1.90614	−0.953070	+	0.302751i	$0.902095\pi$
$972$	0	0
$973$	−37.3848	−1.19850
$974$	−16.1421	−0.517227
$975$	0	0
$976$	26.3431	0.843224
$977$	11.9289	0.381640	0.190820	−	0.981625i	$-0.438885\pi$
$977$	11.9289	0.381640	0.190820	+	0.981625i	$0.438885\pi$
$978$	0	0
$979$	17.6569	0.564316
$980$	0	0
$981$	0	0
$982$	44.0416	1.40542
$983$	−23.3848	−0.745859	−0.372929	−	0.927860i	$-0.621647\pi$
$983$	−23.3848	−0.745859	−0.372929	+	0.927860i	$0.621647\pi$
$984$	0	0
$985$	−13.3137	−0.424210
$986$	−22.7279	−0.723804
$987$	0	0
$988$	0	0
$989$	−8.48528	−0.269816
$990$	0	0
$991$	27.8284	0.883999	0.442000	−	0.897015i	$-0.354269\pi$
$991$	27.8284	0.883999	0.442000	+	0.897015i	$0.354269\pi$
$992$	0	0
$993$	0	0
$994$	−33.5563	−1.06434
$995$	−14.0000	−0.443830
$996$	0	0
$997$	−30.6274	−0.969980	−0.484990	−	0.874520i	$-0.661177\pi$
$997$	−30.6274	−0.969980	−0.484990	+	0.874520i	$0.661177\pi$
$998$	49.4142	1.56418
$999$	0	0

Display

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.a.h.1.1	✓	2
3.2	odd	2		1035.2.a.i.1.2	yes	2
5.4	even	2		5175.2.a.bi.1.2		2
15.14	odd	2		5175.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.a.h.1.1	✓	2	1.1	even	1	trivial
1035.2.a.i.1.2	yes	2	3.2	odd	2
5175.2.a.bh.1.1		2	15.14	odd	2
5175.2.a.bi.1.2		2	5.4	even	2

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

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1035.2.a.h.1.1

Level	$1035$
Weight	$2$
Character	1035.1
Self dual	yes
Analytic conductor	$8.265$
Analytic rank	$1$
Dimension	$2$
CM	no
Inner twists	$1$