LMFDB - Embedded newform 702.2.j.b.593.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(161,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("702.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.j (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.4
Character	$\chi$	$=$	702.593
Dual form			702.2.j.b.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.730953 - 0.730953i) q^{5} +(-2.49696 + 2.49696i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.03372i q^{10} +(1.95374 + 1.95374i) q^{11} +(-3.21489 + 1.63232i) q^{13} -3.53123i q^{14} -1.00000 q^{16} +5.44078 q^{17} +(-5.99076 - 5.99076i) q^{19} +(-0.730953 - 0.730953i) q^{20} -2.76300 q^{22} -5.11422 q^{23} +3.93142i q^{25} +(1.11905 - 3.42750i) q^{26} +(2.49696 + 2.49696i) q^{28} +8.51991i q^{29} +(3.53068 + 3.53068i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.84721 + 3.84721i) q^{34} +3.65032i q^{35} +(-7.78749 + 7.78749i) q^{37} +8.47222 q^{38} +1.03372 q^{40} +(1.06181 - 1.06181i) q^{41} +3.79673i q^{43} +(1.95374 - 1.95374i) q^{44} +(3.61630 - 3.61630i) q^{46} +(-7.80931 - 7.80931i) q^{47} -5.46960i q^{49} +(-2.77993 - 2.77993i) q^{50} +(1.63232 + 3.21489i) q^{52} +11.7290i q^{53} +2.85618 q^{55} -3.53123 q^{56} +(-6.02449 - 6.02449i) q^{58} +(-1.86185 - 1.86185i) q^{59} +6.42979 q^{61} -4.99314 q^{62} +1.00000i q^{64} +(-1.15679 + 3.54308i) q^{65} +(0.887018 + 0.887018i) q^{67} -5.44078i q^{68} +(-2.58116 - 2.58116i) q^{70} +(-3.17883 + 3.17883i) q^{71} +(-2.31653 + 2.31653i) q^{73} -11.0132i q^{74} +(-5.99076 + 5.99076i) q^{76} -9.75681 q^{77} -5.29836 q^{79} +(-0.730953 + 0.730953i) q^{80} +1.50163i q^{82} +(4.77771 - 4.77771i) q^{83} +(3.97695 - 3.97695i) q^{85} +(-2.68469 - 2.68469i) q^{86} +2.76300i q^{88} +(0.144930 + 0.144930i) q^{89} +(3.95163 - 12.1033i) q^{91} +5.11422i q^{92} +11.0440 q^{94} -8.75793 q^{95} +(-4.66500 - 4.66500i) q^{97} +(3.86759 + 3.86759i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 24 q^{19} + 24 q^{34} + 24 q^{37} + 24 q^{46} + 48 q^{70} - 24 q^{73} - 24 q^{76} - 24 q^{79} - 24 q^{91} + 72 q^{94} + 96 q^{97}+O(q^{100}) $ 24 * q - 24 * q^16 - 24 * q^19 + 24 * q^34 + 24 * q^37 + 24 * q^46 + 48 * q^70 - 24 * q^73 - 24 * q^76 - 24 * q^79 - 24 * q^91 + 72 * q^94 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.730953	−	0.730953i	0.326892	−	0.326892i	−0.524511	−	0.851403i	$-0.675752\pi$
$5$	0.730953	−	0.730953i	0.326892	−	0.326892i	0.851403	+	0.524511i	$0.175752\pi$
$6$		0			0
$7$	−2.49696	+	2.49696i	−0.943761	+	0.943761i	−0.998501	−	0.0547394i	$-0.982567\pi$
$7$	−2.49696	+	2.49696i	−0.943761	+	0.943761i	0.0547394	+	0.998501i	$0.482567\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$			1.03372i			0.326892i
$11$	1.95374	+	1.95374i	0.589075	+	0.589075i	0.937381	−	0.348306i	$-0.113243\pi$
$11$	1.95374	+	1.95374i	0.589075	+	0.589075i	−0.348306	+	0.937381i	$0.613243\pi$
$12$		0			0
$13$	−3.21489	+	1.63232i	−0.891651	+	0.452723i
$13$	−3.21489	+	1.63232i	−0.891651	+	0.452723i
$14$		−	3.53123i		−	0.943761i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	5.44078			1.31958			0.659791	−	0.751449i	$-0.270645\pi$
$17$	5.44078			1.31958			0.659791	+	0.751449i	$0.270645\pi$
$18$		0			0
$19$	−5.99076	−	5.99076i	−1.37438	−	1.37438i	−0.853840	−	0.520536i	$-0.825732\pi$
$19$	−5.99076	−	5.99076i	−1.37438	−	1.37438i	−0.520536	−	0.853840i	$-0.674268\pi$
$20$	−0.730953	−	0.730953i	−0.163446	−	0.163446i
$21$		0			0
$22$	−2.76300			−0.589075
$23$	−5.11422			−1.06639			−0.533194	−	0.845993i	$-0.679009\pi$
$23$	−5.11422			−1.06639			−0.533194	+	0.845993i	$0.679009\pi$
$24$		0			0
$25$			3.93142i			0.786283i
$26$	1.11905	−	3.42750i	0.219464	−	0.672187i
$27$		0			0
$28$	2.49696	+	2.49696i	0.471881	+	0.471881i
$29$			8.51991i			1.58211i	0.611746	+	0.791054i	$0.290467\pi$
$29$			8.51991i			1.58211i	−0.611746	+	0.791054i	$0.709533\pi$
$30$		0			0
$31$	3.53068	+	3.53068i	0.634129	+	0.634129i	0.949101	−	0.314972i	$-0.101995\pi$
$31$	3.53068	+	3.53068i	0.634129	+	0.634129i	−0.314972	+	0.949101i	$0.601995\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−3.84721	+	3.84721i	−0.659791	+	0.659791i
$35$			3.65032i			0.617016i
$36$		0			0
$37$	−7.78749	+	7.78749i	−1.28026	+	1.28026i	−0.339734	+	0.940521i	$0.610337\pi$
$37$	−7.78749	+	7.78749i	−1.28026	+	1.28026i	−0.940521	+	0.339734i	$0.889663\pi$
$38$	8.47222			1.37438
$39$		0			0
$40$	1.03372			0.163446
$41$	1.06181	−	1.06181i	0.165827	−	0.165827i	−0.619315	−	0.785142i	$-0.712590\pi$
$41$	1.06181	−	1.06181i	0.165827	−	0.165827i	0.785142	+	0.619315i	$0.212590\pi$
$42$		0			0
$43$			3.79673i			0.578996i	0.957179	+	0.289498i	$0.0934883\pi$
$43$			3.79673i			0.578996i	−0.957179	+	0.289498i	$0.906512\pi$
$44$	1.95374	−	1.95374i	0.294537	−	0.294537i
$45$		0			0
$46$	3.61630	−	3.61630i	0.533194	−	0.533194i
$47$	−7.80931	−	7.80931i	−1.13910	−	1.13910i	−0.988611	−	0.150493i	$-0.951914\pi$
$47$	−7.80931	−	7.80931i	−1.13910	−	1.13910i	−0.150493	−	0.988611i	$-0.548086\pi$
$48$		0			0
$49$		−	5.46960i		−	0.781371i
$50$	−2.77993	−	2.77993i	−0.393142	−	0.393142i
$51$		0			0
$52$	1.63232	+	3.21489i	0.226362	+	0.445826i
$53$			11.7290i			1.61111i	0.592522	+	0.805554i	$0.298132\pi$
$53$			11.7290i			1.61111i	−0.592522	+	0.805554i	$0.701868\pi$
$54$		0			0
$55$	2.85618			0.385128
$56$	−3.53123			−0.471881
$57$		0			0
$58$	−6.02449	−	6.02449i	−0.791054	−	0.791054i
$59$	−1.86185	−	1.86185i	−0.242393	−	0.242393i	0.575447	−	0.817839i	$-0.304828\pi$
$59$	−1.86185	−	1.86185i	−0.242393	−	0.242393i	−0.817839	+	0.575447i	$0.804828\pi$
$60$		0			0
$61$	6.42979			0.823250			0.411625	−	0.911353i	$-0.364961\pi$
$61$	6.42979			0.823250			0.411625	+	0.911353i	$0.364961\pi$
$62$	−4.99314			−0.634129
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.15679	+	3.54308i	−0.143482	+	0.439465i
$66$		0			0
$67$	0.887018	+	0.887018i	0.108367	+	0.108367i	0.759211	−	0.650845i	$-0.225585\pi$
$67$	0.887018	+	0.887018i	0.108367	+	0.108367i	−0.650845	+	0.759211i	$0.725585\pi$
$68$		−	5.44078i		−	0.659791i
$69$		0			0
$70$	−2.58116	−	2.58116i	−0.308508	−	0.308508i
$71$	−3.17883	+	3.17883i	−0.377258	+	0.377258i	−0.870112	−	0.492854i	$-0.835954\pi$
$71$	−3.17883	+	3.17883i	−0.377258	+	0.377258i	0.492854	+	0.870112i	$0.335954\pi$
$72$		0			0
$73$	−2.31653	+	2.31653i	−0.271129	+	0.271129i	−0.829555	−	0.558425i	$-0.811406\pi$
$73$	−2.31653	+	2.31653i	−0.271129	+	0.271129i	0.558425	+	0.829555i	$0.311406\pi$
$74$		−	11.0132i		−	1.28026i
$75$		0			0
$76$	−5.99076	+	5.99076i	−0.687188	+	0.687188i
$77$	−9.75681			−1.11189
$78$		0			0
$79$	−5.29836			−0.596112			−0.298056	−	0.954548i	$-0.596338\pi$
$79$	−5.29836			−0.596112			−0.298056	+	0.954548i	$0.596338\pi$
$80$	−0.730953	+	0.730953i	−0.0817230	+	0.0817230i
$81$		0			0
$82$			1.50163i			0.165827i
$83$	4.77771	−	4.77771i	0.524422	−	0.524422i	−0.394482	−	0.918904i	$-0.629076\pi$
$83$	4.77771	−	4.77771i	0.524422	−	0.524422i	0.918904	+	0.394482i	$0.129076\pi$
$84$		0			0
$85$	3.97695	−	3.97695i	0.431361	−	0.431361i
$86$	−2.68469	−	2.68469i	−0.289498	−	0.289498i
$87$		0			0
$88$			2.76300i			0.294537i
$89$	0.144930	+	0.144930i	0.0153625	+	0.0153625i	0.714746	−	0.699384i	$-0.246542\pi$
$89$	0.144930	+	0.144930i	0.0153625	+	0.0153625i	−0.699384	+	0.714746i	$0.746542\pi$
$90$		0			0
$91$	3.95163	−	12.1033i	0.414243	−	1.26877i
$92$			5.11422i			0.533194i
$93$		0			0
$94$	11.0440			1.13910
$95$	−8.75793			−0.898545
$96$		0			0
$97$	−4.66500	−	4.66500i	−0.473659	−	0.473659i	0.429438	−	0.903097i	$-0.358712\pi$
$97$	−4.66500	−	4.66500i	−0.473659	−	0.473659i	−0.903097	+	0.429438i	$0.858712\pi$
$98$	3.86759	+	3.86759i	0.390685	+	0.390685i
$99$		0			0
$100$	3.93142			0.393142
$101$	16.6680			1.65853			0.829266	−	0.558855i	$-0.188759\pi$
$101$	16.6680			1.65853			0.829266	+	0.558855i	$0.188759\pi$
$102$		0			0
$103$		−	1.83045i		−	0.180360i	−0.995925	−	0.0901799i	$-0.971256\pi$
$103$		−	1.83045i		−	0.180360i	0.995925	−	0.0901799i	$-0.0287442\pi$
$104$	−3.42750	−	1.11905i	−0.336094	−	0.109732i
$105$		0			0
$106$	−8.29369	−	8.29369i	−0.805554	−	0.805554i
$107$			9.43019i			0.911651i	0.890069	+	0.455825i	$0.150656\pi$
$107$			9.43019i			0.911651i	−0.890069	+	0.455825i	$0.849344\pi$
$108$		0			0
$109$	−6.65317	−	6.65317i	−0.637259	−	0.637259i	0.312620	−	0.949878i	$-0.398793\pi$
$109$	−6.65317	−	6.65317i	−0.637259	−	0.637259i	−0.949878	+	0.312620i	$0.898793\pi$
$110$	−2.01963	+	2.01963i	−0.192564	+	0.192564i
$111$		0			0
$112$	2.49696	−	2.49696i	0.235940	−	0.235940i
$113$		−	13.5909i		−	1.27852i	−0.768989	−	0.639262i	$-0.779240\pi$
$113$		−	13.5909i		−	1.27852i	0.768989	−	0.639262i	$-0.220760\pi$
$114$		0			0
$115$	−3.73825	+	3.73825i	−0.348594	+	0.348594i
$116$	8.51991			0.791054
$117$		0			0
$118$	2.63306			0.242393
$119$	−13.5854	+	13.5854i	−1.24537	+	1.24537i
$120$		0			0
$121$		−	3.36580i		−	0.305982i
$122$	−4.54655	+	4.54655i	−0.411625	+	0.411625i
$123$		0			0
$124$	3.53068	−	3.53068i	0.317065	−	0.317065i
$125$	6.52844	+	6.52844i	0.583922	+	0.583922i
$126$		0			0
$127$			11.0838i			0.983531i	0.870728	+	0.491766i	$0.163648\pi$
$127$			11.0838i			0.983531i	−0.870728	+	0.491766i	$0.836352\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−1.68736	−	3.32331i	−0.147992	−	0.291474i
$131$		−	12.1356i		−	1.06029i	−0.847906	−	0.530146i	$-0.822137\pi$
$131$		−	12.1356i		−	1.06029i	0.847906	−	0.530146i	$-0.177863\pi$
$132$		0			0
$133$	29.9174			2.59416
$134$	−1.25443			−0.108367
$135$		0			0
$136$	3.84721	+	3.84721i	0.329896	+	0.329896i
$137$	9.00744	+	9.00744i	0.769558	+	0.769558i	0.978029	−	0.208471i	$-0.0668486\pi$
$137$	9.00744	+	9.00744i	0.769558	+	0.769558i	−0.208471	+	0.978029i	$0.566849\pi$
$138$		0			0
$139$	3.26746			0.277142			0.138571	−	0.990352i	$-0.455749\pi$
$139$	3.26746			0.277142			0.138571	+	0.990352i	$0.455749\pi$
$140$	3.65032			0.308508
$141$		0			0
$142$		−	4.49554i		−	0.377258i
$143$	−9.47019	−	3.09194i	−0.791937	−	0.258561i
$144$		0			0
$145$	6.22765	+	6.22765i	0.517178	+	0.517178i
$146$		−	3.27607i		−	0.271129i
$147$		0			0
$148$	7.78749	+	7.78749i	0.640128	+	0.640128i
$149$	10.6695	−	10.6695i	0.874082	−	0.874082i	−0.118832	−	0.992914i	$-0.537915\pi$
$149$	10.6695	−	10.6695i	0.874082	−	0.874082i	0.992914	+	0.118832i	$0.0379150\pi$
$150$		0			0
$151$	10.4284	−	10.4284i	0.848649	−	0.848649i	−0.141316	−	0.989965i	$-0.545133\pi$
$151$	10.4284	−	10.4284i	0.848649	−	0.848649i	0.989965	+	0.141316i	$0.0451332\pi$
$152$		−	8.47222i		−	0.687188i
$153$		0			0
$154$	6.89911	−	6.89911i	0.555946	−	0.555946i
$155$	5.16152			0.414583
$156$		0			0
$157$	9.82931			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$157$	9.82931			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$158$	3.74650	−	3.74650i	0.298056	−	0.298056i
$159$		0			0
$160$		−	1.03372i		−	0.0817230i
$161$	12.7700	−	12.7700i	1.00642	−	1.00642i
$162$		0			0
$163$	−0.658684	+	0.658684i	−0.0515921	+	0.0515921i	−0.732432	−	0.680840i	$-0.761615\pi$
$163$	−0.658684	+	0.658684i	−0.0515921	+	0.0515921i	0.680840	+	0.732432i	$0.261615\pi$
$164$	−1.06181	−	1.06181i	−0.0829136	−	0.0829136i
$165$		0			0
$166$			6.75670i			0.524422i
$167$	12.5357	+	12.5357i	0.970041	+	0.970041i	0.999564	−	0.0295232i	$-0.00939889\pi$
$167$	12.5357	+	12.5357i	0.970041	+	0.970041i	−0.0295232	+	0.999564i	$0.509399\pi$
$168$		0			0
$169$	7.67108	−	10.4955i	0.590083	−	0.807342i
$170$			5.62426i			0.431361i
$171$		0			0
$172$	3.79673			0.289498
$173$	−3.87945			−0.294949			−0.147475	−	0.989066i	$-0.547115\pi$
$173$	−3.87945			−0.294949			−0.147475	+	0.989066i	$0.547115\pi$
$174$		0			0
$175$	−9.81658	−	9.81658i	−0.742064	−	0.742064i
$176$	−1.95374	−	1.95374i	−0.147269	−	0.147269i
$177$		0			0
$178$	−0.204962			−0.0153625
$179$	−5.10968			−0.381916			−0.190958	−	0.981598i	$-0.561159\pi$
$179$	−5.10968			−0.381916			−0.190958	+	0.981598i	$0.561159\pi$
$180$		0			0
$181$		−	4.01356i		−	0.298326i	−0.988813	−	0.149163i	$-0.952342\pi$
$181$		−	4.01356i		−	0.298326i	0.988813	−	0.149163i	$-0.0476579\pi$
$182$	5.76409	+	11.3525i	0.427263	+	0.841506i
$183$		0			0
$184$	−3.61630	−	3.61630i	−0.266597	−	0.266597i
$185$			11.3846i			0.837011i
$186$		0			0
$187$	10.6299	+	10.6299i	0.777332	+	0.777332i
$188$	−7.80931	+	7.80931i	−0.569552	+	0.569552i
$189$		0			0
$190$	6.19279	−	6.19279i	0.449272	−	0.449272i
$191$			22.1476i			1.60254i	0.598302	+	0.801271i	$0.295842\pi$
$191$			22.1476i			1.60254i	−0.598302	+	0.801271i	$0.704158\pi$
$192$		0			0
$193$	−2.20149	+	2.20149i	−0.158467	+	0.158467i	−0.781887	−	0.623420i	$-0.785743\pi$
$193$	−2.20149	+	2.20149i	−0.158467	+	0.158467i	0.623420	+	0.781887i	$0.285743\pi$
$194$	6.59730			0.473659
$195$		0			0
$196$	−5.46960			−0.390685
$197$	2.43748	−	2.43748i	0.173663	−	0.173663i	−0.614923	−	0.788587i	$-0.710813\pi$
$197$	2.43748	−	2.43748i	0.173663	−	0.173663i	0.788587	+	0.614923i	$0.210813\pi$
$198$		0			0
$199$		−	8.47213i		−	0.600573i	−0.953849	−	0.300287i	$-0.902918\pi$
$199$		−	8.47213i		−	0.600573i	0.953849	−	0.300287i	$-0.0970823\pi$
$200$	−2.77993	+	2.77993i	−0.196571	+	0.196571i
$201$		0			0
$202$	−11.7861	+	11.7861i	−0.829266	+	0.829266i
$203$	−21.2739	−	21.2739i	−1.49313	−	1.49313i
$204$		0			0
$205$		−	1.55227i		−	0.108415i
$206$	1.29432	+	1.29432i	0.0901799	+	0.0901799i
$207$		0			0
$208$	3.21489	−	1.63232i	0.222913	−	0.113181i
$209$		−	23.4088i		−	1.61922i
$210$		0			0
$211$	4.56205			0.314064			0.157032	−	0.987594i	$-0.449807\pi$
$211$	4.56205			0.314064			0.157032	+	0.987594i	$0.449807\pi$
$212$	11.7290			0.805554
$213$		0			0
$214$	−6.66815	−	6.66815i	−0.455825	−	0.455825i
$215$	2.77523	+	2.77523i	0.189269	+	0.189269i
$216$		0			0
$217$	−17.6319			−1.19693
$218$	9.40901			0.637259
$219$		0			0
$220$		−	2.85618i		−	0.192564i
$221$	−17.4915	+	8.88107i	−1.17661	+	0.597406i
$222$		0			0
$223$	2.22483	+	2.22483i	0.148985	+	0.148985i	0.777665	−	0.628679i	$-0.216404\pi$
$223$	2.22483	+	2.22483i	0.148985	+	0.148985i	−0.628679	+	0.777665i	$0.716404\pi$
$224$			3.53123i			0.235940i
$225$		0			0
$226$	9.61022	+	9.61022i	0.639262	+	0.639262i
$227$	1.28867	−	1.28867i	0.0855323	−	0.0855323i	−0.663046	−	0.748578i	$-0.730737\pi$
$227$	1.28867	−	1.28867i	0.0855323	−	0.0855323i	0.748578	+	0.663046i	$0.230737\pi$
$228$		0			0
$229$	−9.06136	+	9.06136i	−0.598792	+	0.598792i	−0.939991	−	0.341199i	$-0.889167\pi$
$229$	−9.06136	+	9.06136i	−0.598792	+	0.598792i	0.341199	+	0.939991i	$0.389167\pi$
$230$		−	5.28669i		−	0.348594i
$231$		0			0
$232$	−6.02449	+	6.02449i	−0.395527	+	0.395527i
$233$	5.22631			0.342387			0.171193	−	0.985237i	$-0.445238\pi$
$233$	5.22631			0.342387			0.171193	+	0.985237i	$0.445238\pi$
$234$		0			0
$235$	−11.4165			−0.744728
$236$	−1.86185	+	1.86185i	−0.121196	+	0.121196i
$237$		0			0
$238$		−	19.2126i		−	1.24537i
$239$	7.28487	−	7.28487i	0.471219	−	0.471219i	−0.431090	−	0.902309i	$-0.641871\pi$
$239$	7.28487	−	7.28487i	0.471219	−	0.471219i	0.902309	+	0.431090i	$0.141871\pi$
$240$		0			0
$241$	−18.8070	+	18.8070i	−1.21147	+	1.21147i	−0.240923	+	0.970544i	$0.577450\pi$
$241$	−18.8070	+	18.8070i	−1.21147	+	1.21147i	−0.970544	+	0.240923i	$0.922550\pi$
$242$	2.37998	+	2.37998i	0.152991	+	0.152991i
$243$		0			0
$244$		−	6.42979i		−	0.411625i
$245$	−3.99802	−	3.99802i	−0.255424	−	0.255424i
$246$		0			0
$247$	29.0385	+	9.48085i	1.84768	+	0.603252i
$248$			4.99314i			0.317065i
$249$		0			0
$250$	−9.23261			−0.583922
$251$	14.2652			0.900408			0.450204	−	0.892926i	$-0.351351\pi$
$251$	14.2652			0.900408			0.450204	+	0.892926i	$0.351351\pi$
$252$		0			0
$253$	−9.99186	−	9.99186i	−0.628183	−	0.628183i
$254$	−7.83746	−	7.83746i	−0.491766	−	0.491766i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.06194			0.440512			0.220256	−	0.975442i	$-0.429311\pi$
$257$	7.06194			0.440512			0.220256	+	0.975442i	$0.429311\pi$
$258$		0			0
$259$		−	38.8901i		−	2.41651i
$260$	3.54308	+	1.15679i	0.219733	+	0.0717410i
$261$		0			0
$262$	8.58116	+	8.58116i	0.530146	+	0.530146i
$263$		−	24.5931i		−	1.51648i	−0.651977	−	0.758239i	$-0.726060\pi$
$263$		−	24.5931i		−	1.51648i	0.651977	−	0.758239i	$-0.273940\pi$
$264$		0			0
$265$	8.57338	+	8.57338i	0.526658	+	0.526658i
$266$	−21.1548	+	21.1548i	−1.29708	+	1.29708i
$267$		0			0
$268$	0.887018	−	0.887018i	0.0541833	−	0.0541833i
$269$		−	13.0138i		−	0.793464i	−0.917934	−	0.396732i	$-0.870144\pi$
$269$		−	13.0138i		−	0.793464i	0.917934	−	0.396732i	$-0.129856\pi$
$270$		0			0
$271$	2.41921	−	2.41921i	0.146956	−	0.146956i	−0.629801	−	0.776757i	$-0.716863\pi$
$271$	2.41921	−	2.41921i	0.146956	−	0.146956i	0.776757	+	0.629801i	$0.216863\pi$
$272$	−5.44078			−0.329896
$273$		0			0
$274$	−12.7384			−0.769558
$275$	−7.68096	+	7.68096i	−0.463180	+	0.463180i
$276$		0			0
$277$		−	25.0593i		−	1.50567i	−0.658211	−	0.752833i	$-0.728687\pi$
$277$		−	25.0593i		−	1.50567i	0.658211	−	0.752833i	$-0.271313\pi$
$278$	−2.31044	+	2.31044i	−0.138571	+	0.138571i
$279$		0			0
$280$	−2.58116	+	2.58116i	−0.154254	+	0.154254i
$281$	−9.20333	−	9.20333i	−0.549024	−	0.549024i	0.377134	−	0.926159i	$-0.376910\pi$
$281$	−9.20333	−	9.20333i	−0.549024	−	0.549024i	−0.926159	+	0.377134i	$0.876910\pi$
$282$		0			0
$283$			31.0477i			1.84559i	0.385289	+	0.922796i	$0.374102\pi$
$283$			31.0477i			1.84559i	−0.385289	+	0.922796i	$0.625898\pi$
$284$	3.17883	+	3.17883i	0.188629	+	0.188629i
$285$		0			0
$286$	8.88277	−	4.51010i	0.525249	−	0.266688i
$287$			5.30260i			0.313002i
$288$		0			0
$289$	12.6021			0.741298
$290$	−8.80723			−0.517178
$291$		0			0
$292$	2.31653	+	2.31653i	0.135565	+	0.135565i
$293$	19.8206	+	19.8206i	1.15793	+	1.15793i	0.984920	+	0.173009i	$0.0553490\pi$
$293$	19.8206	+	19.8206i	1.15793	+	1.15793i	0.173009	+	0.984920i	$0.444651\pi$
$294$		0			0
$295$	−2.72185			−0.158473
$296$	−11.0132			−0.640128
$297$		0			0
$298$			15.0890i			0.874082i
$299$	16.4417	−	8.34803i	0.950847	−	0.482779i
$300$		0			0
$301$	−9.48027	−	9.48027i	−0.546434	−	0.546434i
$302$			14.7479i			0.848649i
$303$		0			0
$304$	5.99076	+	5.99076i	0.343594	+	0.343594i
$305$	4.69987	−	4.69987i	0.269114	−	0.269114i
$306$		0			0
$307$	−12.6972	+	12.6972i	−0.724668	+	0.724668i	−0.969552	−	0.244885i	$-0.921250\pi$
$307$	−12.6972	+	12.6972i	−0.724668	+	0.724668i	0.244885	+	0.969552i	$0.421250\pi$
$308$			9.75681i			0.555946i
$309$		0			0
$310$	−3.64975	+	3.64975i	−0.207292	+	0.207292i
$311$	−12.3667			−0.701250			−0.350625	−	0.936516i	$-0.614031\pi$
$311$	−12.3667			−0.701250			−0.350625	+	0.936516i	$0.614031\pi$
$312$		0			0
$313$	−10.4672			−0.591639			−0.295820	−	0.955244i	$-0.595593\pi$
$313$	−10.4672			−0.591639			−0.295820	+	0.955244i	$0.595593\pi$
$314$	−6.95037	+	6.95037i	−0.392232	+	0.392232i
$315$		0			0
$316$			5.29836i			0.298056i
$317$	−10.8423	+	10.8423i	−0.608967	+	0.608967i	−0.942676	−	0.333709i	$-0.891700\pi$
$317$	−10.8423	+	10.8423i	−0.608967	+	0.608967i	0.333709	+	0.942676i	$0.391700\pi$
$318$		0			0
$319$	−16.6457	+	16.6457i	−0.931980	+	0.931980i
$320$	0.730953	+	0.730953i	0.0408615	+	0.0408615i
$321$		0			0
$322$			18.0595i			1.00642i
$323$	−32.5944	−	32.5944i	−1.81360	−	1.81360i
$324$		0			0
$325$	−6.41732	−	12.6391i	−0.355969	−	0.701090i
$326$		−	0.931520i		−	0.0515921i
$327$		0			0
$328$	1.50163			0.0829136
$329$	38.9990			2.15009
$330$		0			0
$331$	19.4823	+	19.4823i	1.07084	+	1.07084i	0.997291	+	0.0735518i	$0.0234334\pi$
$331$	19.4823	+	19.4823i	1.07084	+	1.07084i	0.0735518	+	0.997291i	$0.476567\pi$
$332$	−4.77771	−	4.77771i	−0.262211	−	0.262211i
$333$		0			0
$334$	−17.7281			−0.970041
$335$	1.29674			0.0708483
$336$		0			0
$337$		−	22.0991i		−	1.20381i	−0.798566	−	0.601907i	$-0.794408\pi$
$337$		−	22.0991i		−	1.20381i	0.798566	−	0.601907i	$-0.205592\pi$
$338$	1.99713	+	12.8457i	0.108629	+	0.698713i
$339$		0			0
$340$	−3.97695	−	3.97695i	−0.215680	−	0.215680i
$341$			13.7961i			0.747099i
$342$		0			0
$343$	−3.82136	−	3.82136i	−0.206334	−	0.206334i
$344$	−2.68469	+	2.68469i	−0.144749	+	0.144749i
$345$		0			0
$346$	2.74319	−	2.74319i	0.147475	−	0.147475i
$347$		−	2.56427i		−	0.137657i	−0.997629	−	0.0688285i	$-0.978074\pi$
$347$		−	2.56427i		−	0.137657i	0.997629	−	0.0688285i	$-0.0219261\pi$
$348$		0			0
$349$	−25.9102	+	25.9102i	−1.38694	+	1.38694i	−0.555276	+	0.831666i	$0.687387\pi$
$349$	−25.9102	+	25.9102i	−1.38694	+	1.38694i	−0.831666	+	0.555276i	$0.812613\pi$
$350$	13.8827			0.742064
$351$		0			0
$352$	2.76300			0.147269
$353$	4.90973	−	4.90973i	0.261319	−	0.261319i	−0.564271	−	0.825590i	$-0.690843\pi$
$353$	4.90973	−	4.90973i	0.261319	−	0.261319i	0.825590	+	0.564271i	$0.190843\pi$
$354$		0			0
$355$			4.64715i			0.246645i
$356$	0.144930	−	0.144930i	0.00768126	−	0.00768126i
$357$		0			0
$358$	3.61309	−	3.61309i	0.190958	−	0.190958i
$359$	−17.3664	−	17.3664i	−0.916563	−	0.916563i	0.0802151	−	0.996778i	$-0.474439\pi$
$359$	−17.3664	−	17.3664i	−0.916563	−	0.916563i	−0.996778	+	0.0802151i	$0.974439\pi$
$360$		0			0
$361$			52.7785i			2.77782i
$362$	2.83802	+	2.83802i	0.149163	+	0.149163i
$363$		0			0
$364$	−12.1033	−	3.95163i	−0.634384	−	0.207122i
$365$			3.38655i			0.177260i
$366$		0			0
$367$	3.21535			0.167840			0.0839199	−	0.996473i	$-0.473256\pi$
$367$	3.21535			0.167840			0.0839199	+	0.996473i	$0.473256\pi$
$368$	5.11422			0.266597
$369$		0			0
$370$	−8.05011	−	8.05011i	−0.418505	−	0.418505i
$371$	−29.2869	−	29.2869i	−1.52050	−	1.52050i
$372$		0			0
$373$	23.0464			1.19330			0.596648	−	0.802503i	$-0.296499\pi$
$373$	23.0464			1.19330			0.596648	+	0.802503i	$0.296499\pi$
$374$	−15.0329			−0.777332
$375$		0			0
$376$		−	11.0440i		−	0.569552i
$377$	−13.9072	−	27.3906i	−0.716257	−	1.41069i
$378$		0			0
$379$	−12.6790	−	12.6790i	−0.651276	−	0.651276i	0.302024	−	0.953300i	$-0.402338\pi$
$379$	−12.6790	−	12.6790i	−0.651276	−	0.651276i	−0.953300	+	0.302024i	$0.902338\pi$
$380$			8.75793i			0.449272i
$381$		0			0
$382$	−15.6607	−	15.6607i	−0.801271	−	0.801271i
$383$	2.64413	−	2.64413i	0.135109	−	0.135109i	−0.636318	−	0.771427i	$-0.719543\pi$
$383$	2.64413	−	2.64413i	0.135109	−	0.135109i	0.771427	+	0.636318i	$0.219543\pi$
$384$		0			0
$385$	−7.13177	+	7.13177i	−0.363469	+	0.363469i
$386$		−	3.11337i		−	0.158467i
$387$		0			0
$388$	−4.66500	+	4.66500i	−0.236829	+	0.236829i
$389$	22.7276			1.15234			0.576169	−	0.817331i	$-0.304547\pi$
$389$	22.7276			1.15234			0.576169	+	0.817331i	$0.304547\pi$
$390$		0			0
$391$	−27.8253			−1.40719
$392$	3.86759	−	3.86759i	0.195343	−	0.195343i
$393$		0			0
$394$			3.44712i			0.173663i
$395$	−3.87285	+	3.87285i	−0.194864	+	0.194864i
$396$		0			0
$397$	−5.15592	+	5.15592i	−0.258768	+	0.258768i	−0.824553	−	0.565785i	$-0.808573\pi$
$397$	−5.15592	+	5.15592i	−0.258768	+	0.258768i	0.565785	+	0.824553i	$0.308573\pi$
$398$	5.99070	+	5.99070i	0.300287	+	0.300287i
$399$		0			0
$400$		−	3.93142i		−	0.196571i
$401$	−13.8525	−	13.8525i	−0.691763	−	0.691763i	0.270857	−	0.962620i	$-0.412693\pi$
$401$	−13.8525	−	13.8525i	−0.691763	−	0.691763i	−0.962620	+	0.270857i	$0.912693\pi$
$402$		0			0
$403$	−17.1140	−	5.58757i	−0.852507	−	0.278337i
$404$		−	16.6680i		−	0.829266i
$405$		0			0
$406$	30.0858			1.49313
$407$	−30.4295			−1.50833
$408$		0			0
$409$	−11.1285	−	11.1285i	−0.550269	−	0.550269i	0.376249	−	0.926519i	$-0.377214\pi$
$409$	−11.1285	−	11.1285i	−0.550269	−	0.550269i	−0.926519	+	0.376249i	$0.877214\pi$
$410$	1.09762	+	1.09762i	0.0542076	+	0.0542076i
$411$		0			0
$412$	−1.83045			−0.0901799
$413$	9.29794			0.457522
$414$		0			0
$415$		−	6.98456i		−	0.342859i
$416$	−1.11905	+	3.42750i	−0.0548660	+	0.168047i
$417$		0			0
$418$	16.5525	+	16.5525i	0.809610	+	0.809610i
$419$			28.7408i			1.40408i	0.712137	+	0.702041i	$0.247728\pi$
$419$			28.7408i			1.40408i	−0.712137	+	0.702041i	$0.752272\pi$
$420$		0			0
$421$	15.4602	+	15.4602i	0.753484	+	0.753484i	0.975128	−	0.221643i	$-0.0711421\pi$
$421$	15.4602	+	15.4602i	0.753484	+	0.753484i	−0.221643	+	0.975128i	$0.571142\pi$
$422$	−3.22585	+	3.22585i	−0.157032	+	0.157032i
$423$		0			0
$424$	−8.29369	+	8.29369i	−0.402777	+	0.402777i
$425$			21.3900i			1.03757i
$426$		0			0
$427$	−16.0549	+	16.0549i	−0.776951	+	0.776951i
$428$	9.43019			0.455825
$429$		0			0
$430$	−3.92477			−0.189269
$431$	−3.04773	+	3.04773i	−0.146804	+	0.146804i	−0.776689	−	0.629885i	$-0.783102\pi$
$431$	−3.04773	+	3.04773i	−0.146804	+	0.146804i	0.629885	+	0.776689i	$0.283102\pi$
$432$		0			0
$433$			10.5849i			0.508676i	0.967115	+	0.254338i	$0.0818575\pi$
$433$			10.5849i			0.508676i	−0.967115	+	0.254338i	$0.918142\pi$
$434$	12.4677	−	12.4677i	0.598466	−	0.598466i
$435$		0			0
$436$	−6.65317	+	6.65317i	−0.318629	+	0.318629i
$437$	30.6381	+	30.6381i	1.46562	+	1.46562i
$438$		0			0
$439$			0.756908i			0.0361252i	0.999837	+	0.0180626i	$0.00574982\pi$
$439$			0.756908i			0.0361252i	−0.999837	+	0.0180626i	$0.994250\pi$
$440$	2.01963	+	2.01963i	0.0962819	+	0.0962819i
$441$		0			0
$442$	6.08851	−	18.6482i	0.289601	−	0.887006i
$443$			36.7332i			1.74525i	0.488393	+	0.872624i	$0.337583\pi$
$443$			36.7332i			1.74525i	−0.488393	+	0.872624i	$0.662417\pi$
$444$		0			0
$445$	0.211874			0.0100438
$446$	−3.14638			−0.148985
$447$		0			0
$448$	−2.49696	−	2.49696i	−0.117970	−	0.117970i
$449$	16.5702	+	16.5702i	0.781996	+	0.781996i	0.980167	−	0.198172i	$-0.0635003\pi$
$449$	16.5702	+	16.5702i	0.781996	+	0.781996i	−0.198172	+	0.980167i	$0.563500\pi$
$450$		0			0
$451$	4.14901			0.195369
$452$	−13.5909			−0.639262
$453$		0			0
$454$			1.82246i			0.0855323i
$455$	−5.95847	−	11.7354i	−0.279337	−	0.550163i
$456$		0			0
$457$	−0.692812	−	0.692812i	−0.0324084	−	0.0324084i	0.690717	−	0.723125i	$-0.257295\pi$
$457$	−0.692812	−	0.692812i	−0.0324084	−	0.0324084i	−0.723125	+	0.690717i	$0.757295\pi$
$458$		−	12.8147i		−	0.598792i
$459$		0			0
$460$	3.73825	+	3.73825i	0.174297	+	0.174297i
$461$	8.54391	−	8.54391i	0.397930	−	0.397930i	−0.479573	−	0.877502i	$-0.659208\pi$
$461$	8.54391	−	8.54391i	0.397930	−	0.397930i	0.877502	+	0.479573i	$0.159208\pi$
$462$		0			0
$463$	−10.8803	+	10.8803i	−0.505650	+	0.505650i	−0.913188	−	0.407538i	$-0.866387\pi$
$463$	−10.8803	+	10.8803i	−0.505650	+	0.505650i	0.407538	+	0.913188i	$0.366387\pi$
$464$		−	8.51991i		−	0.395527i
$465$		0			0
$466$	−3.69556	+	3.69556i	−0.171193	+	0.171193i
$467$	−18.8587			−0.872678			−0.436339	−	0.899782i	$-0.643725\pi$
$467$	−18.8587			−0.872678			−0.436339	+	0.899782i	$0.643725\pi$
$468$		0			0
$469$	−4.42970			−0.204544
$470$	8.07266	−	8.07266i	0.372364	−	0.372364i
$471$		0			0
$472$		−	2.63306i		−	0.121196i
$473$	−7.41782	+	7.41782i	−0.341072	+	0.341072i
$474$		0			0
$475$	23.5522	−	23.5522i	1.08065	−	1.08065i
$476$	13.5854	+	13.5854i	0.622685	+	0.622685i
$477$		0			0
$478$			10.3024i			0.471219i
$479$	−10.5691	−	10.5691i	−0.482915	−	0.482915i	0.423146	−	0.906061i	$-0.360926\pi$
$479$	−10.5691	−	10.5691i	−0.482915	−	0.482915i	−0.906061	+	0.423146i	$0.860926\pi$
$480$		0			0
$481$	12.3243	−	37.7476i	0.561940	−	1.72114i
$482$		−	26.5972i		−	1.21147i
$483$		0			0
$484$	−3.36580			−0.152991
$485$	−6.81979			−0.309671
$486$		0			0
$487$	−20.2191	−	20.2191i	−0.916214	−	0.916214i	0.0805378	−	0.996752i	$-0.474336\pi$
$487$	−20.2191	−	20.2191i	−0.916214	−	0.916214i	−0.996752	+	0.0805378i	$0.974336\pi$
$488$	4.54655	+	4.54655i	0.205812	+	0.205812i
$489$		0			0
$490$	5.65405			0.255424
$491$	28.8492			1.30195			0.650973	−	0.759101i	$-0.274361\pi$
$491$	28.8492			1.30195			0.650973	+	0.759101i	$0.274361\pi$
$492$		0			0
$493$			46.3549i			2.08772i
$494$	−27.2373	+	13.8293i	−1.22546	+	0.622212i
$495$		0			0
$496$	−3.53068	−	3.53068i	−0.158532	−	0.158532i
$497$		−	15.8748i		−	0.712082i
$498$		0			0
$499$	10.5258	+	10.5258i	0.471199	+	0.471199i	0.902303	−	0.431103i	$-0.141876\pi$
$499$	10.5258	+	10.5258i	0.471199	+	0.471199i	−0.431103	+	0.902303i	$0.641876\pi$
$500$	6.52844	−	6.52844i	0.291961	−	0.291961i
$501$		0			0
$502$	−10.0870	+	10.0870i	−0.450204	+	0.450204i
$503$		−	8.87705i		−	0.395808i	−0.980221	−	0.197904i	$-0.936587\pi$
$503$		−	8.87705i		−	0.395808i	0.980221	−	0.197904i	$-0.0634134\pi$
$504$		0			0
$505$	12.1835	−	12.1835i	0.542161	−	0.542161i
$506$	14.1306			0.628183
$507$		0			0
$508$	11.0838			0.491766
$509$	17.5845	−	17.5845i	0.779418	−	0.779418i	−0.200314	−	0.979732i	$-0.564196\pi$
$509$	17.5845	−	17.5845i	0.779418	−	0.779418i	0.979732	+	0.200314i	$0.0641962\pi$
$510$		0			0
$511$		−	11.5686i		−	0.511763i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−4.99355	+	4.99355i	−0.220256	+	0.220256i
$515$	−1.33797	−	1.33797i	−0.0589582	−	0.0589582i
$516$		0			0
$517$		−	30.5147i		−	1.34204i
$518$	27.4994	+	27.4994i	1.20826	+	1.20826i
$519$		0			0
$520$	−3.32331	+	1.68736i	−0.145737	+	0.0739958i
$521$			7.10124i			0.311111i	0.987827	+	0.155556i	$0.0497168\pi$
$521$			7.10124i			0.311111i	−0.987827	+	0.155556i	$0.950283\pi$
$522$		0			0
$523$	28.9433			1.26560			0.632801	−	0.774314i	$-0.281905\pi$
$523$	28.9433			1.26560			0.632801	+	0.774314i	$0.281905\pi$
$524$	−12.1356			−0.530146
$525$		0			0
$526$	17.3900	+	17.3900i	0.758239	+	0.758239i
$527$	19.2096	+	19.2096i	0.836785	+	0.836785i
$528$		0			0
$529$	3.15525			0.137185
$530$	−12.1246			−0.526658
$531$		0			0
$532$		−	29.9174i		−	1.29708i
$533$	−1.68040	+	5.14683i	−0.0727862	+	0.222934i
$534$		0			0
$535$	6.89302	+	6.89302i	0.298011	+	0.298011i
$536$			1.25443i			0.0541833i
$537$		0			0
$538$	9.20213	+	9.20213i	0.396732	+	0.396732i
$539$	10.6862	−	10.6862i	0.460286	−	0.460286i
$540$		0			0
$541$	9.21585	−	9.21585i	0.396221	−	0.396221i	−0.480677	−	0.876898i	$-0.659609\pi$
$541$	9.21585	−	9.21585i	0.396221	−	0.396221i	0.876898	+	0.480677i	$0.159609\pi$
$542$			3.42128i			0.146956i
$543$		0			0
$544$	3.84721	−	3.84721i	0.164948	−	0.164948i
$545$	−9.72631			−0.416629
$546$		0			0
$547$	−8.53557			−0.364955			−0.182477	−	0.983210i	$-0.558412\pi$
$547$	−8.53557			−0.364955			−0.182477	+	0.983210i	$0.558412\pi$
$548$	9.00744	−	9.00744i	0.384779	−	0.384779i
$549$		0			0
$550$		−	10.8625i		−	0.463180i
$551$	51.0408	−	51.0408i	2.17441	−	2.17441i
$552$		0			0
$553$	13.2298	−	13.2298i	0.562587	−	0.562587i
$554$	17.7196	+	17.7196i	0.752833	+	0.752833i
$555$		0			0
$556$		−	3.26746i		−	0.138571i
$557$	10.9056	+	10.9056i	0.462083	+	0.462083i	0.899338	−	0.437255i	$-0.144049\pi$
$557$	10.9056	+	10.9056i	0.462083	+	0.462083i	−0.437255	+	0.899338i	$0.644049\pi$
$558$		0			0
$559$	−6.19746	−	12.2061i	−0.262125	−	0.516262i
$560$		−	3.65032i		−	0.154254i
$561$		0			0
$562$	13.0155			0.549024
$563$	−6.06531			−0.255622			−0.127811	−	0.991799i	$-0.540795\pi$
$563$	−6.06531			−0.255622			−0.127811	+	0.991799i	$0.540795\pi$
$564$		0			0
$565$	−9.93430	−	9.93430i	−0.417939	−	0.417939i
$566$	−21.9540	−	21.9540i	−0.922796	−	0.922796i
$567$		0			0
$568$	−4.49554			−0.188629
$569$	14.3081			0.599827			0.299913	−	0.953966i	$-0.403042\pi$
$569$	14.3081			0.599827			0.299913	+	0.953966i	$0.403042\pi$
$570$		0			0
$571$			5.93459i			0.248355i	0.992260	+	0.124177i	$0.0396292\pi$
$571$			5.93459i			0.248355i	−0.992260	+	0.124177i	$0.960371\pi$
$572$	−3.09194	+	9.47019i	−0.129281	+	0.395968i
$573$		0			0
$574$	−3.74950	−	3.74950i	−0.156501	−	0.156501i
$575$		−	20.1061i		−	0.838484i
$576$		0			0
$577$	20.4971	+	20.4971i	0.853304	+	0.853304i	0.990539	−	0.137235i	$-0.0438215\pi$
$577$	20.4971	+	20.4971i	0.853304	+	0.853304i	−0.137235	+	0.990539i	$0.543821\pi$
$578$	−8.91100	+	8.91100i	−0.370649	+	0.370649i
$579$		0			0
$580$	6.22765	−	6.22765i	0.258589	−	0.258589i
$581$			23.8595i			0.989858i
$582$		0			0
$583$	−22.9155	+	22.9155i	−0.949063	+	0.949063i
$584$	−3.27607			−0.135565
$585$		0			0
$586$	−28.0305			−1.15793
$587$	−27.9522	+	27.9522i	−1.15371	+	1.15371i	−0.167907	+	0.985803i	$0.553701\pi$
$587$	−27.9522	+	27.9522i	−1.15371	+	1.15371i	−0.985803	+	0.167907i	$0.946299\pi$
$588$		0			0
$589$		−	42.3030i		−	1.74306i
$590$	1.92464	−	1.92464i	0.0792363	−	0.0792363i
$591$		0			0
$592$	7.78749	−	7.78749i	0.320064	−	0.320064i
$593$	−21.8876	−	21.8876i	−0.898816	−	0.898816i	0.0965155	−	0.995331i	$-0.469230\pi$
$593$	−21.8876	−	21.8876i	−0.898816	−	0.898816i	−0.995331	+	0.0965155i	$0.969230\pi$
$594$		0			0
$595$			19.8606i			0.814203i
$596$	−10.6695	−	10.6695i	−0.437041	−	0.437041i
$597$		0			0
$598$	−5.72307	+	17.5290i	−0.234034	+	0.716813i
$599$			30.4677i			1.24488i	0.782668	+	0.622439i	$0.213858\pi$
$599$			30.4677i			1.24488i	−0.782668	+	0.622439i	$0.786142\pi$
$600$		0			0
$601$	10.5012			0.428354			0.214177	−	0.976795i	$-0.431293\pi$
$601$	10.5012			0.428354			0.214177	+	0.976795i	$0.431293\pi$
$602$	13.4071			0.546434
$603$		0			0
$604$	−10.4284	−	10.4284i	−0.424325	−	0.424325i
$605$	−2.46024	−	2.46024i	−0.100023	−	0.100023i
$606$		0			0
$607$	16.5851			0.673168			0.336584	−	0.941653i	$-0.390728\pi$
$607$	16.5851			0.673168			0.336584	+	0.941653i	$0.390728\pi$
$608$	−8.47222			−0.343594
$609$		0			0
$610$			6.64662i			0.269114i
$611$	37.8534	+	12.3588i	1.53138	+	0.499985i
$612$		0			0
$613$	13.3912	+	13.3912i	0.540866	+	0.540866i	0.923783	−	0.382917i	$-0.125080\pi$
$613$	13.3912	+	13.3912i	0.540866	+	0.540866i	−0.382917	+	0.923783i	$0.625080\pi$
$614$		−	17.9566i		−	0.724668i
$615$		0			0
$616$	−6.89911	−	6.89911i	−0.277973	−	0.277973i
$617$	−5.96507	+	5.96507i	−0.240145	+	0.240145i	−0.816910	−	0.576765i	$-0.804315\pi$
$617$	−5.96507	+	5.96507i	−0.240145	+	0.240145i	0.576765	+	0.816910i	$0.304315\pi$
$618$		0			0
$619$	8.99098	−	8.99098i	0.361378	−	0.361378i	−0.502942	−	0.864320i	$-0.667749\pi$
$619$	8.99098	−	8.99098i	0.361378	−	0.361378i	0.864320	+	0.502942i	$0.167749\pi$
$620$		−	5.16152i		−	0.207292i
$621$		0			0
$622$	8.74456	−	8.74456i	0.350625	−	0.350625i
$623$	−0.723767			−0.0289971
$624$		0			0
$625$	−10.1131			−0.404525
$626$	7.40140	−	7.40140i	0.295820	−	0.295820i
$627$		0			0
$628$		−	9.82931i		−	0.392232i
$629$	−42.3700	+	42.3700i	−1.68940	+	1.68940i
$630$		0			0
$631$	13.1946	−	13.1946i	0.525267	−	0.525267i	−0.393890	−	0.919157i	$-0.628871\pi$
$631$	13.1946	−	13.1946i	0.525267	−	0.525267i	0.919157	+	0.393890i	$0.128871\pi$
$632$	−3.74650	−	3.74650i	−0.149028	−	0.149028i
$633$		0			0
$634$		−	15.3334i		−	0.608967i
$635$	8.10176	+	8.10176i	0.321509	+	0.321509i
$636$		0			0
$637$	8.92811	+	17.5842i	0.353745	+	0.696710i
$638$		−	23.5406i		−	0.931980i
$639$		0			0
$640$	−1.03372			−0.0408615
$641$	−2.95203			−0.116598			−0.0582992	−	0.998299i	$-0.518568\pi$
$641$	−2.95203			−0.116598			−0.0582992	+	0.998299i	$0.518568\pi$
$642$		0			0
$643$	−23.5471	−	23.5471i	−0.928607	−	0.928607i	0.0690092	−	0.997616i	$-0.478016\pi$
$643$	−23.5471	−	23.5471i	−0.928607	−	0.928607i	−0.997616	+	0.0690092i	$0.978016\pi$
$644$	−12.7700	−	12.7700i	−0.503208	−	0.503208i
$645$		0			0
$646$	46.0955			1.81360
$647$	21.5988			0.849138			0.424569	−	0.905396i	$-0.360426\pi$
$647$	21.5988			0.849138			0.424569	+	0.905396i	$0.360426\pi$
$648$		0			0
$649$		−	7.27516i		−	0.285575i
$650$	13.4749	+	4.39945i	0.528529	+	0.172561i
$651$		0			0
$652$	0.658684	+	0.658684i	0.0257961	+	0.0257961i
$653$			5.01350i			0.196194i	0.995177	+	0.0980968i	$0.0312755\pi$
$653$			5.01350i			0.196194i	−0.995177	+	0.0980968i	$0.968725\pi$
$654$		0			0
$655$	−8.87055	−	8.87055i	−0.346601	−	0.346601i
$656$	−1.06181	+	1.06181i	−0.0414568	+	0.0414568i
$657$		0			0
$658$	−27.5765	+	27.5765i	−1.07504	+	1.07504i
$659$			21.4750i			0.836546i	0.908321	+	0.418273i	$0.137364\pi$
$659$			21.4750i			0.836546i	−0.908321	+	0.418273i	$0.862636\pi$
$660$		0			0
$661$	−7.22887	+	7.22887i	−0.281171	+	0.281171i	−0.833576	−	0.552405i	$-0.813710\pi$
$661$	−7.22887	+	7.22887i	−0.281171	+	0.281171i	0.552405	+	0.833576i	$0.313710\pi$
$662$	−27.5521			−1.07084
$663$		0			0
$664$	6.75670			0.262211
$665$	21.8682	−	21.8682i	0.848012	−	0.848012i
$666$		0			0
$667$		−	43.5727i		−	1.68714i
$668$	12.5357	−	12.5357i	0.485020	−	0.485020i
$669$		0			0
$670$	−0.916932	+	0.916932i	−0.0354242	+	0.0354242i
$671$	12.5621	+	12.5621i	0.484956	+	0.484956i
$672$		0			0
$673$		−	18.2056i		−	0.701774i	−0.936418	−	0.350887i	$-0.885880\pi$
$673$		−	18.2056i		−	0.701774i	0.936418	−	0.350887i	$-0.114120\pi$
$674$	15.6264	+	15.6264i	0.601907	+	0.601907i
$675$		0			0
$676$	−10.4955	−	7.67108i	−0.403671	−	0.295042i
$677$			14.3760i			0.552515i	0.961084	+	0.276257i	$0.0890942\pi$
$677$			14.3760i			0.552515i	−0.961084	+	0.276257i	$0.910906\pi$
$678$		0			0
$679$	23.2966			0.894042
$680$	5.62426			0.215680
$681$		0			0
$682$	−9.75529	−	9.75529i	−0.373549	−	0.373549i
$683$	11.7572	+	11.7572i	0.449877	+	0.449877i	0.895313	−	0.445437i	$-0.146952\pi$
$683$	11.7572	+	11.7572i	0.449877	+	0.449877i	−0.445437	+	0.895313i	$0.646952\pi$
$684$		0			0
$685$	13.1680			0.503125
$686$	5.40421			0.206334
$687$		0			0
$688$		−	3.79673i		−	0.144749i
$689$	−19.1455	−	37.7076i	−0.729386	−	1.43655i
$690$		0			0
$691$	14.9559	+	14.9559i	0.568948	+	0.568948i	0.931834	−	0.362886i	$-0.118209\pi$
$691$	14.9559	+	14.9559i	0.568948	+	0.568948i	−0.362886	+	0.931834i	$0.618209\pi$
$692$			3.87945i			0.147475i
$693$		0			0
$694$	1.81321	+	1.81321i	0.0688285	+	0.0688285i
$695$	2.38836	−	2.38836i	0.0905956	−	0.0905956i
$696$		0			0
$697$	5.77708	−	5.77708i	0.218823	−	0.218823i
$698$		−	36.6426i		−	1.38694i
$699$		0			0
$700$	−9.81658	+	9.81658i	−0.371032	+	0.371032i
$701$	−45.3798			−1.71397			−0.856985	−	0.515342i	$-0.827665\pi$
$701$	−45.3798			−1.71397			−0.856985	+	0.515342i	$0.827665\pi$
$702$		0			0
$703$	93.3061			3.51910
$704$	−1.95374	+	1.95374i	−0.0736343	+	0.0736343i
$705$		0			0
$706$			6.94341i			0.261319i
$707$	−41.6194	+	41.6194i	−1.56526	+	1.56526i
$708$		0			0
$709$	−24.8489	+	24.8489i	−0.933218	+	0.933218i	−0.997906	−	0.0646873i	$-0.979395\pi$
$709$	−24.8489	+	24.8489i	−0.933218	+	0.933218i	0.0646873	+	0.997906i	$0.479395\pi$
$710$	−3.28603	−	3.28603i	−0.123323	−	0.123323i
$711$		0			0
$712$			0.204962i			0.00768126i
$713$	−18.0567	−	18.0567i	−0.676228	−	0.676228i
$714$		0			0
$715$	−9.18232	+	4.66219i	−0.343399	+	0.174356i
$716$			5.10968i			0.190958i
$717$		0			0
$718$	24.5598			0.916563
$719$	−34.3801			−1.28216			−0.641081	−	0.767473i	$-0.721514\pi$
$719$	−34.3801			−1.28216			−0.641081	+	0.767473i	$0.721514\pi$
$720$		0			0
$721$	4.57056	+	4.57056i	0.170217	+	0.170217i
$722$	−37.3200	−	37.3200i	−1.38891	−	1.38891i
$723$		0			0
$724$	−4.01356			−0.149163
$725$	−33.4953			−1.24398
$726$		0			0
$727$		−	7.44017i		−	0.275941i	−0.990436	−	0.137970i	$-0.955942\pi$
$727$		−	7.44017i		−	0.275941i	0.990436	−	0.137970i	$-0.0440579\pi$
$728$	11.3525	−	5.76409i	0.420753	−	0.213631i
$729$		0			0
$730$	−2.39465	−	2.39465i	−0.0886300	−	0.0886300i
$731$			20.6572i			0.764032i
$732$		0			0
$733$	36.0059	+	36.0059i	1.32991	+	1.32991i	0.905446	+	0.424460i	$0.139536\pi$
$733$	36.0059	+	36.0059i	1.32991	+	1.32991i	0.424460	+	0.905446i	$0.360464\pi$
$734$	−2.27359	+	2.27359i	−0.0839199	+	0.0839199i
$735$		0			0
$736$	−3.61630	+	3.61630i	−0.133299	+	0.133299i
$737$			3.46601i			0.127672i
$738$		0			0
$739$	17.8745	−	17.8745i	0.657525	−	0.657525i	−0.297269	−	0.954794i	$-0.596076\pi$
$739$	17.8745	−	17.8745i	0.657525	−	0.657525i	0.954794	+	0.297269i	$0.0960757\pi$
$740$	11.3846			0.418505
$741$		0			0
$742$	41.4180			1.52050
$743$	6.18249	−	6.18249i	0.226814	−	0.226814i	−0.584547	−	0.811360i	$-0.698728\pi$
$743$	6.18249	−	6.18249i	0.226814	−	0.226814i	0.811360	+	0.584547i	$0.198728\pi$
$744$		0			0
$745$		−	15.5979i		−	0.571461i
$746$	−16.2962	+	16.2962i	−0.596648	+	0.596648i
$747$		0			0
$748$	10.6299	−	10.6299i	0.388666	−	0.388666i
$749$	−23.5468	−	23.5468i	−0.860381	−	0.860381i
$750$		0			0
$751$			18.2839i			0.667189i	0.942717	+	0.333594i	$0.108262\pi$
$751$			18.2839i			0.667189i	−0.942717	+	0.333594i	$0.891738\pi$
$752$	7.80931	+	7.80931i	0.284776	+	0.284776i
$753$		0			0
$754$	29.2020	+	9.53421i	1.06347	+	0.347216i
$755$		−	15.2453i		−	0.554833i
$756$		0			0
$757$	−7.47864			−0.271816			−0.135908	−	0.990721i	$-0.543395\pi$
$757$	−7.47864			−0.271816			−0.135908	+	0.990721i	$0.543395\pi$
$758$	17.9308			0.651276
$759$		0			0
$760$	−6.19279	−	6.19279i	−0.224636	−	0.224636i
$761$	2.80360	+	2.80360i	0.101630	+	0.101630i	0.756094	−	0.654463i	$-0.227105\pi$
$761$	2.80360	+	2.80360i	0.101630	+	0.101630i	−0.654463	+	0.756094i	$0.727105\pi$
$762$		0			0
$763$	33.2254			1.20284
$764$	22.1476			0.801271
$765$		0			0
$766$			3.73937i			0.135109i
$767$	9.02480	+	2.94653i	0.325867	+	0.106393i
$768$		0			0
$769$	−0.486296	−	0.486296i	−0.0175363	−	0.0175363i	0.698284	−	0.715821i	$-0.253947\pi$
$769$	−0.486296	−	0.486296i	−0.0175363	−	0.0175363i	−0.715821	+	0.698284i	$0.753947\pi$
$770$		−	10.0858i		−	0.363469i
$771$		0			0
$772$	2.20149	+	2.20149i	0.0792333	+	0.0792333i
$773$	−15.2154	+	15.2154i	−0.547261	+	0.547261i	−0.925648	−	0.378387i	$-0.876479\pi$
$773$	−15.2154	+	15.2154i	−0.547261	+	0.547261i	0.378387	+	0.925648i	$0.376479\pi$
$774$		0			0
$775$	−13.8806	+	13.8806i	−0.498605	+	0.498605i
$776$		−	6.59730i		−	0.236829i
$777$		0			0
$778$	−16.0709	+	16.0709i	−0.576169	+	0.576169i
$779$	−12.7221			−0.455818
$780$		0			0
$781$	−12.4212			−0.444466
$782$	19.6755	−	19.6755i	0.703594	−	0.703594i
$783$		0			0
$784$			5.46960i			0.195343i
$785$	7.18476	−	7.18476i	0.256435	−	0.256435i
$786$		0			0
$787$	0.495643	−	0.495643i	0.0176678	−	0.0176678i	−0.698218	−	0.715885i	$-0.746023\pi$
$787$	0.495643	−	0.495643i	0.0176678	−	0.0176678i	0.715885	+	0.698218i	$0.246023\pi$
$788$	−2.43748	−	2.43748i	−0.0868317	−	0.0868317i
$789$		0			0
$790$		−	5.47703i		−	0.194864i
$791$	33.9359	+	33.9359i	1.20662	+	1.20662i
$792$		0			0
$793$	−20.6711	+	10.4955i	−0.734052	+	0.372704i
$794$		−	7.29157i		−	0.258768i
$795$		0			0
$796$	−8.47213			−0.300287
$797$	17.9090			0.634369			0.317185	−	0.948364i	$-0.397263\pi$
$797$	17.9090			0.634369			0.317185	+	0.948364i	$0.397263\pi$
$798$		0			0
$799$	−42.4887	−	42.4887i	−1.50314	−	1.50314i
$800$	2.77993	+	2.77993i	0.0982854	+	0.0982854i
$801$		0			0
$802$	19.5904			0.691763
$803$	−9.05179			−0.319431
$804$		0			0
$805$		−	18.6685i		−	0.657979i
$806$	16.0524	−	8.15038i	0.565422	−	0.287085i
$807$		0			0
$808$	11.7861	+	11.7861i	0.414633	+	0.414633i
$809$		−	27.2029i		−	0.956402i	−0.878250	−	0.478201i	$-0.841289\pi$
$809$		−	27.2029i		−	0.956402i	0.878250	−	0.478201i	$-0.158711\pi$
$810$		0			0
$811$	−31.6498	−	31.6498i	−1.11138	−	1.11138i	−0.992965	−	0.118412i	$-0.962220\pi$
$811$	−31.6498	−	31.6498i	−1.11138	−	1.11138i	−0.118412	−	0.992965i	$-0.537780\pi$
$812$	−21.2739	+	21.2739i	−0.746566	+	0.746566i
$813$		0			0
$814$	21.5169	−	21.5169i	0.754166	−	0.754166i
$815$			0.962934i			0.0337301i
$816$		0			0
$817$	22.7453	−	22.7453i	0.795757	−	0.795757i
$818$	15.7381			0.550269
$819$		0			0
$820$	−1.55227			−0.0542076
$821$	−32.8949	+	32.8949i	−1.14804	+	1.14804i	−0.161104	+	0.986937i	$0.551505\pi$
$821$	−32.8949	+	32.8949i	−1.14804	+	1.14804i	−0.986937	+	0.161104i	$0.948495\pi$
$822$		0			0
$823$			6.29469i			0.219419i	0.993964	+	0.109710i	$0.0349921\pi$
$823$			6.29469i			0.219419i	−0.993964	+	0.109710i	$0.965008\pi$
$824$	1.29432	−	1.29432i	0.0450899	−	0.0450899i
$825$		0			0
$826$	−6.57464	+	6.57464i	−0.228761	+	0.228761i
$827$	23.3955	+	23.3955i	0.813543	+	0.813543i	0.985163	−	0.171620i	$-0.0549002\pi$
$827$	23.3955	+	23.3955i	0.813543	+	0.813543i	−0.171620	+	0.985163i	$0.554900\pi$
$828$		0			0
$829$		−	3.14079i		−	0.109084i	−0.998511	−	0.0545421i	$-0.982630\pi$
$829$		−	3.14079i		−	0.109084i	0.998511	−	0.0545421i	$-0.0173699\pi$
$830$	4.93883	+	4.93883i	0.171429	+	0.171429i
$831$		0			0
$832$	−1.63232	−	3.21489i	−0.0565904	−	0.111456i
$833$		−	29.7589i		−	1.03108i
$834$		0			0
$835$	18.3260			0.634197
$836$	−23.4088			−0.809610
$837$		0			0
$838$	−20.3228	−	20.3228i	−0.702041	−	0.702041i
$839$	28.0370	+	28.0370i	0.967944	+	0.967944i	0.999502	−	0.0315577i	$-0.0100468\pi$
$839$	28.0370	+	28.0370i	0.967944	+	0.967944i	−0.0315577	+	0.999502i	$0.510047\pi$
$840$		0			0
$841$	−43.5889			−1.50307
$842$	−21.8640			−0.753484
$843$		0			0
$844$		−	4.56205i		−	0.157032i
$845$	−2.06448	−	13.2789i	−0.0710202	−	0.456807i
$846$		0			0
$847$	8.40427	+	8.40427i	0.288774	+	0.288774i
$848$		−	11.7290i		−	0.402777i
$849$		0			0
$850$	−15.1250	−	15.1250i	−0.518783	−	0.518783i
$851$	39.8270	−	39.8270i	1.36525	−	1.36525i
$852$		0			0
$853$	−5.31816	+	5.31816i	−0.182090	+	0.182090i	−0.792266	−	0.610176i	$-0.791099\pi$
$853$	−5.31816	+	5.31816i	−0.182090	+	0.182090i	0.610176	+	0.792266i	$0.291099\pi$
$854$		−	22.7051i		−	0.776951i
$855$		0			0
$856$	−6.66815	+	6.66815i	−0.227913	+	0.227913i
$857$	13.1601			0.449540			0.224770	−	0.974412i	$-0.427837\pi$
$857$	13.1601			0.449540			0.224770	+	0.974412i	$0.427837\pi$
$858$		0			0
$859$	−39.9763			−1.36397			−0.681987	−	0.731365i	$-0.738884\pi$
$859$	−39.9763			−1.36397			−0.681987	+	0.731365i	$0.738884\pi$
$860$	2.77523	−	2.77523i	0.0946345	−	0.0946345i
$861$		0			0
$862$		−	4.31015i		−	0.146804i
$863$	−19.5420	+	19.5420i	−0.665217	+	0.665217i	−0.956605	−	0.291388i	$-0.905883\pi$
$863$	−19.5420	+	19.5420i	−0.665217	+	0.665217i	0.291388	+	0.956605i	$0.405883\pi$
$864$		0			0
$865$	−2.83570	+	2.83570i	−0.0964166	+	0.0964166i
$866$	−7.48462	−	7.48462i	−0.254338	−	0.254338i
$867$		0			0
$868$			17.6319i			0.598466i
$869$	−10.3516	−	10.3516i	−0.351154	−	0.351154i
$870$		0			0
$871$	−4.29957	−	1.40377i	−0.145685	−	0.0475651i
$872$		−	9.40901i		−	0.318629i
$873$		0			0
$874$	−43.3288			−1.46562
$875$	−32.6025			−1.10217
$876$		0			0
$877$	10.6502	+	10.6502i	0.359633	+	0.359633i	0.863678	−	0.504045i	$-0.168155\pi$
$877$	10.6502	+	10.6502i	0.359633	+	0.359633i	−0.504045	+	0.863678i	$0.668155\pi$
$878$	−0.535215	−	0.535215i	−0.0180626	−	0.0180626i
$879$		0			0
$880$	−2.85618			−0.0962819
$881$	−5.09673			−0.171713			−0.0858567	−	0.996307i	$-0.527363\pi$
$881$	−5.09673			−0.171713			−0.0858567	+	0.996307i	$0.527363\pi$
$882$		0			0
$883$			43.6345i			1.46842i	0.678924	+	0.734209i	$0.262447\pi$
$883$			43.6345i			1.46842i	−0.678924	+	0.734209i	$0.737553\pi$
$884$	8.88107	+	17.4915i	0.298703	+	0.588304i
$885$		0			0
$886$	−25.9743	−	25.9743i	−0.872624	−	0.872624i
$887$		−	53.9013i		−	1.80983i	−0.425593	−	0.904915i	$-0.639934\pi$
$887$		−	53.9013i		−	1.80983i	0.425593	−	0.904915i	$-0.360066\pi$
$888$		0			0
$889$	−27.6759	−	27.6759i	−0.928219	−	0.928219i
$890$	−0.149817	+	0.149817i	−0.00502189	+	0.00502189i
$891$		0			0
$892$	2.22483	−	2.22483i	0.0744927	−	0.0744927i
$893$			93.5674i			3.13111i
$894$		0			0
$895$	−3.73494	+	3.73494i	−0.124845	+	0.124845i
$896$	3.53123			0.117970
$897$		0			0
$898$	−23.4338			−0.781996
$899$	−30.0811	+	30.0811i	−1.00326	+	1.00326i
$900$		0			0
$901$			63.8151i			2.12599i
$902$	−2.93379	+	2.93379i	−0.0976846	+	0.0976846i
$903$		0			0
$904$	9.61022	−	9.61022i	0.319631	−	0.319631i
$905$	−2.93372	−	2.93372i	−0.0975203	−	0.0975203i
$906$		0			0
$907$			7.07627i			0.234964i	0.993075	+	0.117482i	$0.0374822\pi$
$907$			7.07627i			0.234964i	−0.993075	+	0.117482i	$0.962518\pi$
$908$	−1.28867	−	1.28867i	−0.0427661	−	0.0427661i
$909$		0			0
$910$	12.5114	+	4.08489i	0.414750	+	0.135413i
$911$			20.6283i			0.683447i	0.939801	+	0.341723i	$0.111011\pi$
$911$			20.6283i			0.683447i	−0.939801	+	0.341723i	$0.888989\pi$
$912$		0			0
$913$	18.6688			0.617847
$914$	0.979785			0.0324084
$915$		0			0
$916$	9.06136	+	9.06136i	0.299396	+	0.299396i
$917$	30.3021	+	30.3021i	1.00066	+	1.00066i
$918$		0			0
$919$	−27.6811			−0.913115			−0.456558	−	0.889694i	$-0.650918\pi$
$919$	−27.6811			−0.913115			−0.456558	+	0.889694i	$0.650918\pi$
$920$	−5.28669			−0.174297
$921$		0			0
$922$			12.0829i			0.397930i
$923$	5.03074	−	15.4085i	0.165589	−	0.507176i
$924$		0			0
$925$	−30.6159	−	30.6159i	−1.00664	−	1.00664i
$926$		−	15.3871i		−	0.505650i
$927$		0			0
$928$	6.02449	+	6.02449i	0.197763	+	0.197763i
$929$	19.1542	−	19.1542i	0.628430	−	0.628430i	−0.319243	−	0.947673i	$-0.603429\pi$
$929$	19.1542	−	19.1542i	0.628430	−	0.628430i	0.947673	+	0.319243i	$0.103429\pi$
$930$		0			0
$931$	−32.7671	+	32.7671i	−1.07390	+	1.07390i
$932$		−	5.22631i		−	0.171193i
$933$		0			0
$934$	13.3351	−	13.3351i	0.436339	−	0.436339i
$935$	15.5399			0.508208
$936$		0			0
$937$	−14.2237			−0.464668			−0.232334	−	0.972636i	$-0.574636\pi$
$937$	−14.2237			−0.464668			−0.232334	+	0.972636i	$0.574636\pi$
$938$	3.13227	−	3.13227i	0.102272	−	0.102272i
$939$		0			0
$940$			11.4165i			0.372364i
$941$	−25.7864	+	25.7864i	−0.840613	+	0.840613i	−0.988939	−	0.148325i	$-0.952612\pi$
$941$	−25.7864	+	25.7864i	−0.840613	+	0.840613i	0.148325	+	0.988939i	$0.452612\pi$
$942$		0			0
$943$	−5.43034	+	5.43034i	−0.176836	+	0.176836i
$944$	1.86185	+	1.86185i	0.0605982	+	0.0605982i
$945$		0			0
$946$		−	10.4904i		−	0.341072i
$947$	−5.61473	−	5.61473i	−0.182454	−	0.182454i	0.609970	−	0.792424i	$-0.291181\pi$
$947$	−5.61473	−	5.61473i	−0.182454	−	0.182454i	−0.792424	+	0.609970i	$0.791181\pi$
$948$		0			0
$949$	3.66609	−	11.2287i	0.119006	−	0.364499i
$950$			33.3078i			1.08065i
$951$		0			0
$952$	−19.2126			−0.622685
$953$	35.0177			1.13434			0.567168	−	0.823602i	$-0.308039\pi$
$953$	35.0177			1.13434			0.567168	+	0.823602i	$0.308039\pi$
$954$		0			0
$955$	16.1888	+	16.1888i	0.523858	+	0.523858i
$956$	−7.28487	−	7.28487i	−0.235609	−	0.235609i
$957$		0			0
$958$	14.9470			0.482915
$959$	−44.9824			−1.45256
$960$		0			0
$961$		−	6.06858i		−	0.195761i
$962$	17.9770	+	35.4062i	0.579602	+	1.14154i
$963$		0			0
$964$	18.8070	+	18.8070i	0.605734	+	0.605734i
$965$			3.21837i			0.103603i
$966$		0			0
$967$	28.4024	+	28.4024i	0.913361	+	0.913361i	0.996535	−	0.0831742i	$-0.0265058\pi$
$967$	28.4024	+	28.4024i	0.913361	+	0.913361i	−0.0831742	+	0.996535i	$0.526506\pi$
$968$	2.37998	−	2.37998i	0.0764955	−	0.0764955i
$969$		0			0
$970$	4.82232	−	4.82232i	0.154835	−	0.154835i
$971$		−	18.0510i		−	0.579283i	−0.957135	−	0.289642i	$-0.906464\pi$
$971$		−	18.0510i		−	0.579283i	0.957135	−	0.289642i	$-0.0935361\pi$
$972$		0			0
$973$	−8.15871	+	8.15871i	−0.261556	+	0.261556i
$974$	28.5941			0.916214
$975$		0			0
$976$	−6.42979			−0.205812
$977$	8.94926	−	8.94926i	0.286312	−	0.286312i	−0.549308	−	0.835620i	$-0.685109\pi$
$977$	8.94926	−	8.94926i	0.286312	−	0.286312i	0.835620	+	0.549308i	$0.185109\pi$
$978$		0			0
$979$			0.566310i			0.0180994i
$980$	−3.99802	+	3.99802i	−0.127712	+	0.127712i
$981$		0			0
$982$	−20.3995	+	20.3995i	−0.650973	+	0.650973i
$983$	27.8757	+	27.8757i	0.889098	+	0.889098i	0.994436	−	0.105338i	$-0.0335925\pi$
$983$	27.8757	+	27.8757i	0.889098	+	0.889098i	−0.105338	+	0.994436i	$0.533593\pi$
$984$		0			0
$985$		−	3.56337i		−	0.113538i
$986$	−32.7779	−	32.7779i	−1.04386	−	1.04386i
$987$		0			0
$988$	9.48085	−	29.0385i	0.301626	−	0.923838i
$989$		−	19.4173i		−	0.617434i
$990$		0			0
$991$	10.8811			0.345649			0.172825	−	0.984953i	$-0.444711\pi$
$991$	10.8811			0.345649			0.172825	+	0.984953i	$0.444711\pi$
$992$	4.99314			0.158532
$993$		0			0
$994$	11.2252	+	11.2252i	0.356041	+	0.356041i
$995$	−6.19272	−	6.19272i	−0.196323	−	0.196323i
$996$		0			0
$997$	−10.4383			−0.330585			−0.165292	−	0.986245i	$-0.552857\pi$
$997$	−10.4383			−0.330585			−0.165292	+	0.986245i	$0.552857\pi$
$998$	−14.8857			−0.471199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.j.b.593.4	yes	24
3.2	odd	2	inner	702.2.j.b.593.9	yes	24
13.5	odd	4	inner	702.2.j.b.161.9	yes	24
39.5	even	4	inner	702.2.j.b.161.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.j.b.161.4	✓	24	39.5	even	4	inner
702.2.j.b.161.9	yes	24	13.5	odd	4	inner
702.2.j.b.593.4	yes	24	1.1	even	1	trivial
702.2.j.b.593.9	yes	24	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.730953 - 0.730953i) q^{5} +(-2.49696 + 2.49696i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.03372i q^{10} +(1.95374 + 1.95374i) q^{11} +(-3.21489 + 1.63232i) q^{13} -3.53123i q^{14} -1.00000 q^{16} +5.44078 q^{17} +(-5.99076 - 5.99076i) q^{19} +(-0.730953 - 0.730953i) q^{20} -2.76300 q^{22} -5.11422 q^{23} +3.93142i q^{25} +(1.11905 - 3.42750i) q^{26} +(2.49696 + 2.49696i) q^{28} +8.51991i q^{29} +(3.53068 + 3.53068i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.84721 + 3.84721i) q^{34} +3.65032i q^{35} +(-7.78749 + 7.78749i) q^{37} +8.47222 q^{38} +1.03372 q^{40} +(1.06181 - 1.06181i) q^{41} +3.79673i q^{43} +(1.95374 - 1.95374i) q^{44} +(3.61630 - 3.61630i) q^{46} +(-7.80931 - 7.80931i) q^{47} -5.46960i q^{49} +(-2.77993 - 2.77993i) q^{50} +(1.63232 + 3.21489i) q^{52} +11.7290i q^{53} +2.85618 q^{55} -3.53123 q^{56} +(-6.02449 - 6.02449i) q^{58} +(-1.86185 - 1.86185i) q^{59} +6.42979 q^{61} -4.99314 q^{62} +1.00000i q^{64} +(-1.15679 + 3.54308i) q^{65} +(0.887018 + 0.887018i) q^{67} -5.44078i q^{68} +(-2.58116 - 2.58116i) q^{70} +(-3.17883 + 3.17883i) q^{71} +(-2.31653 + 2.31653i) q^{73} -11.0132i q^{74} +(-5.99076 + 5.99076i) q^{76} -9.75681 q^{77} -5.29836 q^{79} +(-0.730953 + 0.730953i) q^{80} +1.50163i q^{82} +(4.77771 - 4.77771i) q^{83} +(3.97695 - 3.97695i) q^{85} +(-2.68469 - 2.68469i) q^{86} +2.76300i q^{88} +(0.144930 + 0.144930i) q^{89} +(3.95163 - 12.1033i) q^{91} +5.11422i q^{92} +11.0440 q^{94} -8.75793 q^{95} +(-4.66500 - 4.66500i) q^{97} +(3.86759 + 3.86759i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 24 q^{19} + 24 q^{34} + 24 q^{37} + 24 q^{46} + 48 q^{70} - 24 q^{73} - 24 q^{76} - 24 q^{79} - 24 q^{91} + 72 q^{94} + 96 q^{97}+O(q^{100}) \) 24 * q - 24 * q^16 - 24 * q^19 + 24 * q^34 + 24 * q^37 + 24 * q^46 + 48 * q^70 - 24 * q^73 - 24 * q^76 - 24 * q^79 - 24 * q^91 + 72 * q^94 + 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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