LMFDB - Embedded newform 297.2.f.b.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$297 = 3^{3} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	297.f (of order $5$ , degree $4$ , 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 9x^{14} + 51x^{12} - 249x^{10} + 1476x^{8} - 2875x^{6} + 2335x^{4} + 125x^{2} + 25$ x^16 - 9x^14 + 51x^12 - 249x^10 + 1476x^8 - 2875x^6 + 2335x^4 + 125*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.2
Root			$-1.35089 + 1.85934i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.b.136.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.255752 + 0.185814i) q^{2} +(-0.587152 + 1.80707i) q^{4} +(3.28092 + 2.38373i) q^{5} +(1.05386 - 3.24346i) q^{7} +(-0.380991 - 1.17257i) q^{8} -1.28203 q^{10} +(-1.15551 + 3.10883i) q^{11} +(-1.11803 + 0.812299i) q^{13} +(0.333154 + 1.02534i) q^{14} +(-2.75905 - 2.00457i) q^{16} +(5.20368 + 3.78070i) q^{17} +(-1.07684 - 3.31419i) q^{19} +(-6.23395 + 4.52923i) q^{20} +(-0.282141 - 1.00980i) q^{22} -3.73931 q^{23} +(3.53718 + 10.8863i) q^{25} +(0.135002 - 0.415494i) q^{26} +(5.24237 + 3.80880i) q^{28} +(0.0230611 - 0.0709748i) q^{29} +(3.02440 - 2.19736i) q^{31} +3.54393 q^{32} -2.03336 q^{34} +(11.1891 - 8.12939i) q^{35} +(-0.381966 + 1.17557i) q^{37} +(0.891228 + 0.647515i) q^{38} +(1.54508 - 4.75528i) q^{40} +(-2.87964 - 8.86262i) q^{41} -0.456334 q^{43} +(-4.93940 - 3.91344i) q^{44} +(0.956334 - 0.694818i) q^{46} +(0.678546 + 2.08835i) q^{47} +(-3.74627 - 2.72182i) q^{49} +(-2.92748 - 2.12694i) q^{50} +(-0.811424 - 2.49731i) q^{52} +(-0.729941 + 0.530333i) q^{53} +(-11.2017 + 7.44538i) q^{55} -4.20469 q^{56} +(0.00729022 + 0.0224370i) q^{58} +(2.47885 - 7.62911i) q^{59} +(-4.66942 - 3.39253i) q^{61} +(-0.365195 + 1.12395i) q^{62} +(4.61173 - 3.35062i) q^{64} -5.60448 q^{65} -5.85410 q^{67} +(-9.88733 + 7.18357i) q^{68} +(-1.35108 + 4.15821i) q^{70} +(-7.66424 - 5.56839i) q^{71} +(4.34379 - 13.3688i) q^{73} +(-0.120749 - 0.371629i) q^{74} +6.62123 q^{76} +(8.86559 + 7.02412i) q^{77} +(8.89129 - 6.45990i) q^{79} +(-4.27387 - 13.1536i) q^{80} +(2.38327 + 1.73155i) q^{82} +(-1.10689 - 0.804203i) q^{83} +(8.06071 + 24.8083i) q^{85} +(0.116708 - 0.0847935i) q^{86} +(4.08555 + 0.170482i) q^{88} +10.3758 q^{89} +(1.45640 + 4.48235i) q^{91} +(2.19554 - 6.75719i) q^{92} +(-0.561585 - 0.408015i) q^{94} +(4.36707 - 13.4405i) q^{95} +(6.67190 - 4.84742i) q^{97} +1.46387 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100})$ 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$ .

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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

)

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

$2$	−0.255752	+	0.185814i	−0.180844	+	0.131391i	−0.674524	−	0.738253i	$-0.735651\pi$
$2$	−0.255752	+	0.185814i	−0.180844	+	0.131391i	0.493681	+	0.869643i	$0.335651\pi$
$3$		0			0
$3$		0			0
$4$	−0.587152	+	1.80707i	−0.293576	+	0.903534i
$5$	3.28092	+	2.38373i	1.46727	+	1.06603i	0.981393	+	0.192008i	$0.0614999\pi$
$5$	3.28092	+	2.38373i	1.46727	+	1.06603i	0.485877	+	0.874027i	$0.338500\pi$
$6$		0			0
$7$	1.05386	−	3.24346i	0.398323	−	1.22591i	−0.528021	−	0.849231i	$-0.677066\pi$
$7$	1.05386	−	3.24346i	0.398323	−	1.22591i	0.926343	−	0.376680i	$-0.122934\pi$
$8$	−0.380991	−	1.17257i	−0.134701	−	0.414566i
$9$		0			0
$10$	−1.28203			−0.405414
$11$	−1.15551	+	3.10883i	−0.348400	+	0.937346i
$11$	−1.15551	+	3.10883i	−0.348400	+	0.937346i
$12$		0			0
$13$	−1.11803	+	0.812299i	−0.310087	+	0.225291i	−0.731934	−	0.681376i	$-0.761382\pi$
$13$	−1.11803	+	0.812299i	−0.310087	+	0.225291i	0.421847	+	0.906667i	$0.361382\pi$
$14$	0.333154	+	1.02534i	0.0890391	+	0.274034i
$15$		0			0
$16$	−2.75905	−	2.00457i	−0.689762	−	0.501142i
$17$	5.20368	+	3.78070i	1.26208	+	0.916954i	0.998858	−	0.0477820i	$-0.0152153\pi$
$17$	5.20368	+	3.78070i	1.26208	+	0.916954i	0.263221	+	0.964736i	$0.415215\pi$
$18$		0			0
$19$	−1.07684	−	3.31419i	−0.247045	−	0.760326i	−0.995293	−	0.0969076i	$-0.969105\pi$
$19$	−1.07684	−	3.31419i	−0.247045	−	0.760326i	0.748248	−	0.663419i	$-0.230895\pi$
$20$	−6.23395	+	4.52923i	−1.39395	+	1.01277i
$21$		0			0
$22$	−0.282141	−	1.00980i	−0.0601526	−	0.215290i
$23$	−3.73931			−0.779700			−0.389850	−	0.920878i	$-0.627473\pi$
$23$	−3.73931			−0.779700			−0.389850	+	0.920878i	$0.627473\pi$
$24$		0			0
$25$	3.53718	+	10.8863i	0.707437	+	2.17727i
$26$	0.135002	−	0.415494i	0.0264761	−	0.0814850i
$27$		0			0
$28$	5.24237	+	3.80880i	0.990715	+	0.719796i
$29$	0.0230611	−	0.0709748i	0.00428234	−	0.0131797i	−0.948893	−	0.315599i	$-0.897794\pi$
$29$	0.0230611	−	0.0709748i	0.00428234	−	0.0131797i	0.953175	+	0.302420i	$0.0977944\pi$
$30$		0			0
$31$	3.02440	−	2.19736i	0.543198	−	0.394657i	−0.282073	−	0.959393i	$-0.591022\pi$
$31$	3.02440	−	2.19736i	0.543198	−	0.394657i	0.825271	+	0.564736i	$0.191022\pi$
$32$	3.54393			0.626485
$33$		0			0
$34$	−2.03336			−0.348718
$35$	11.1891	−	8.12939i	1.89131	−	1.37412i
$36$		0			0
$37$	−0.381966	+	1.17557i	−0.0627948	+	0.193263i	−0.977532	−	0.210787i	$-0.932398\pi$
$37$	−0.381966	+	1.17557i	−0.0627948	+	0.193263i	0.914737	+	0.404049i	$0.132398\pi$
$38$	0.891228	+	0.647515i	0.144576	+	0.105041i
$39$		0			0
$40$	1.54508	−	4.75528i	0.244299	−	0.751876i
$41$	−2.87964	−	8.86262i	−0.449724	−	1.38411i	−0.877219	−	0.480091i	$-0.840604\pi$
$41$	−2.87964	−	8.86262i	−0.449724	−	1.38411i	0.427494	−	0.904018i	$-0.359396\pi$
$42$		0			0
$43$	−0.456334			−0.0695903			−0.0347952	−	0.999394i	$-0.511078\pi$
$43$	−0.456334			−0.0695903			−0.0347952	+	0.999394i	$0.511078\pi$
$44$	−4.93940	−	3.91344i	−0.744643	−	0.589973i
$45$		0			0
$46$	0.956334	−	0.694818i	0.141004	−	0.102445i
$47$	0.678546	+	2.08835i	0.0989761	+	0.304617i	0.988270	−	0.152720i	$-0.0488033\pi$
$47$	0.678546	+	2.08835i	0.0989761	+	0.304617i	−0.889293	+	0.457337i	$0.848803\pi$
$48$		0			0
$49$	−3.74627	−	2.72182i	−0.535181	−	0.388832i
$50$	−2.92748	−	2.12694i	−0.414008	−	0.300794i
$51$		0			0
$52$	−0.811424	−	2.49731i	−0.112524	−	0.346314i
$53$	−0.729941	+	0.530333i	−0.100265	+	0.0728469i	−0.636788	−	0.771039i	$-0.719737\pi$
$53$	−0.729941	+	0.530333i	−0.100265	+	0.0728469i	0.536523	+	0.843886i	$0.319737\pi$
$54$		0			0
$55$	−11.2017	+	7.44538i	−1.51044	+	1.00393i
$56$	−4.20469			−0.561876
$57$		0			0
$58$	0.00729022	+	0.0224370i	0.000957253	+	0.00294612i
$59$	2.47885	−	7.62911i	0.322718	−	0.993225i	−0.649742	−	0.760155i	$-0.725123\pi$
$59$	2.47885	−	7.62911i	0.322718	−	0.993225i	0.972460	−	0.233070i	$-0.0748771\pi$
$60$		0			0
$61$	−4.66942	−	3.39253i	−0.597858	−	0.434369i	0.247260	−	0.968949i	$-0.420470\pi$
$61$	−4.66942	−	3.39253i	−0.597858	−	0.434369i	−0.845118	+	0.534580i	$0.820470\pi$
$62$	−0.365195	+	1.12395i	−0.0463798	+	0.142742i
$63$		0			0
$64$	4.61173	−	3.35062i	0.576466	−	0.418827i
$65$	−5.60448			−0.695150
$66$		0			0
$67$	−5.85410			−0.715192			−0.357596	−	0.933876i	$-0.616404\pi$
$67$	−5.85410			−0.715192			−0.357596	+	0.933876i	$0.616404\pi$
$68$	−9.88733	+	7.18357i	−1.19901	+	0.871135i
$69$		0			0
$70$	−1.35108	+	4.15821i	−0.161485	+	0.497001i
$71$	−7.66424	−	5.56839i	−0.909577	−	0.660847i	0.0313305	−	0.999509i	$-0.490026\pi$
$71$	−7.66424	−	5.56839i	−0.909577	−	0.660847i	−0.940908	+	0.338662i	$0.890026\pi$
$72$		0			0
$73$	4.34379	−	13.3688i	0.508403	−	1.56470i	−0.286571	−	0.958059i	$-0.592516\pi$
$73$	4.34379	−	13.3688i	0.508403	−	1.56470i	0.794974	−	0.606643i	$-0.207484\pi$
$74$	−0.120749	−	0.371629i	−0.0140368	−	0.0432010i
$75$		0			0
$76$	6.62123			0.759507
$77$	8.86559	+	7.02412i	1.01033	+	0.800473i
$78$		0			0
$79$	8.89129	−	6.45990i	1.00035	−	0.726795i	0.0381851	−	0.999271i	$-0.487842\pi$
$79$	8.89129	−	6.45990i	1.00035	−	0.726795i	0.962163	+	0.272475i	$0.0878423\pi$
$80$	−4.27387	−	13.1536i	−0.477834	−	1.47062i
$81$		0			0
$82$	2.38327	+	1.73155i	0.263189	+	0.191218i
$83$	−1.10689	−	0.804203i	−0.121497	−	0.0882728i	0.525377	−	0.850869i	$-0.323924\pi$
$83$	−1.10689	−	0.804203i	−0.121497	−	0.0882728i	−0.646874	+	0.762597i	$0.723924\pi$
$84$		0			0
$85$	8.06071	+	24.8083i	0.874306	+	2.69084i
$86$	0.116708	−	0.0847935i	0.0125850	−	0.00914352i
$87$		0			0
$88$	4.08555	+	0.170482i	0.435521	+	0.0181735i
$89$	10.3758			1.09983			0.549915	−	0.835221i	$-0.314660\pi$
$89$	10.3758			1.09983			0.549915	+	0.835221i	$0.314660\pi$
$90$		0			0
$91$	1.45640	+	4.48235i	0.152672	+	0.469878i
$92$	2.19554	−	6.75719i	0.228901	−	0.704486i
$93$		0			0
$94$	−0.561585	−	0.408015i	−0.0579230	−	0.0420836i
$95$	4.36707	−	13.4405i	0.448052	−	1.37896i
$96$		0			0
$97$	6.67190	−	4.84742i	0.677428	−	0.492181i	−0.195075	−	0.980788i	$-0.562495\pi$
$97$	6.67190	−	4.84742i	0.677428	−	0.492181i	0.872504	+	0.488608i	$0.162495\pi$
$98$	1.46387			0.147873
$99$		0			0
$100$	−21.7492			−2.17492
$101$	−9.02893	+	6.55990i	−0.898412	+	0.652734i	−0.938058	−	0.346479i	$-0.887377\pi$
$101$	−9.02893	+	6.55990i	−0.898412	+	0.652734i	0.0396458	+	0.999214i	$0.487377\pi$
$102$		0			0
$103$	2.43488	−	7.49380i	0.239916	−	0.738386i	−0.756515	−	0.653976i	$-0.773100\pi$
$103$	2.43488	−	7.49380i	0.239916	−	0.738386i	0.996431	−	0.0844097i	$-0.0269004\pi$
$104$	1.37844	+	1.00149i	0.135167	+	0.0982046i
$105$		0			0
$106$	0.0881400	−	0.271267i	0.00856091	−	0.0263478i
$107$	4.11132	+	12.6533i	0.397456	+	1.22325i	0.927032	+	0.374982i	$0.122351\pi$
$107$	4.11132	+	12.6533i	0.397456	+	1.22325i	−0.529575	+	0.848263i	$0.677649\pi$
$108$		0			0
$109$	9.70501			0.929571			0.464786	−	0.885423i	$-0.346131\pi$
$109$	9.70501			0.929571			0.464786	+	0.885423i	$0.346131\pi$
$110$	1.48140	−	3.98561i	0.141246	−	0.380013i
$111$		0			0
$112$	−9.40938	+	6.83632i	−0.889103	+	0.645971i
$113$	1.83406	+	5.64465i	0.172534	+	0.531004i	0.999512	−	0.0312296i	$-0.00994231\pi$
$113$	1.83406	+	5.64465i	0.172534	+	0.531004i	−0.826979	+	0.562233i	$0.809942\pi$
$114$		0			0
$115$	−12.2684	−	8.91349i	−1.14403	−	0.831187i
$116$	0.114716	+	0.0833460i	0.0106511	+	0.00773848i
$117$		0			0
$118$	0.783629	+	2.41176i	0.0721389	+	0.222021i
$119$	17.7465	−	12.8936i	1.62682	−	1.18195i
$120$		0			0
$121$	−8.32959	−	7.18456i	−0.757236	−	0.653142i
$122$	1.82459			0.165191
$123$		0			0
$124$	2.19499	+	6.75548i	0.197116	+	0.606660i
$125$	−8.07883	+	24.8641i	−0.722593	+	2.22391i
$126$		0			0
$127$	5.48073	+	3.98199i	0.486337	+	0.353344i	0.803774	−	0.594935i	$-0.202822\pi$
$127$	5.48073	+	3.98199i	0.486337	+	0.353344i	−0.317437	+	0.948279i	$0.602822\pi$
$128$	−2.74714	+	8.45481i	−0.242815	+	0.747307i
$129$		0			0
$130$	1.43335	−	1.04139i	0.125713	−	0.0913361i
$131$	−9.05370			−0.791026			−0.395513	−	0.918460i	$-0.629433\pi$
$131$	−9.05370			−0.791026			−0.395513	+	0.918460i	$0.629433\pi$
$132$		0			0
$133$	−11.8843			−1.03050
$134$	1.49720	−	1.08778i	0.129338	−	0.0939696i
$135$		0			0
$136$	2.45057	−	7.54209i	0.210135	−	0.646729i
$137$	−8.25718	−	5.99919i	−0.705459	−	0.512546i	0.176247	−	0.984346i	$-0.443604\pi$
$137$	−8.25718	−	5.99919i	−0.705459	−	0.512546i	−0.881705	+	0.471800i	$0.843604\pi$
$138$		0			0
$139$	2.18461	−	6.72355i	0.185296	−	0.570284i	−0.814657	−	0.579943i	$-0.803075\pi$
$139$	2.18461	−	6.72355i	0.185296	−	0.570284i	0.999953	+	0.00965948i	$0.00307476\pi$
$140$	8.12064	+	24.9927i	0.686319	+	2.11227i
$141$		0			0
$142$	2.99483			0.251320
$143$	−1.23340	−	4.41439i	−0.103142	−	0.369150i
$144$		0			0
$145$	0.244846	−	0.177891i	0.0203334	−	0.0147730i
$146$	1.37319	+	4.22624i	0.113646	+	0.349766i
$147$		0			0
$148$	−1.90006	−	1.38048i	−0.156184	−	0.113475i
$149$	−3.43045	−	2.49237i	−0.281033	−	0.204183i	0.438335	−	0.898812i	$-0.355568\pi$
$149$	−3.43045	−	2.49237i	−0.281033	−	0.204183i	−0.719368	+	0.694629i	$0.755568\pi$
$150$		0			0
$151$	3.41969	+	10.5247i	0.278291	+	0.856490i	0.988330	+	0.152328i	$0.0486771\pi$
$151$	3.41969	+	10.5247i	0.278291	+	0.856490i	−0.710039	+	0.704162i	$0.751323\pi$
$152$	−3.47585	+	2.52535i	−0.281928	+	0.204833i
$153$		0			0
$154$	−3.57257	−	0.149076i	−0.287886	−	0.0120129i
$155$	15.1607			1.21774
$156$		0			0
$157$	−3.48875	−	10.7373i	−0.278432	−	0.856926i	−0.988291	−	0.152582i	$-0.951241\pi$
$157$	−3.48875	−	10.7373i	−0.278432	−	0.856926i	0.709859	−	0.704344i	$-0.248759\pi$
$158$	−1.07362	+	3.30426i	−0.0854125	+	0.262873i
$159$		0			0
$160$	11.6274	+	8.44777i	0.919223	+	0.667855i
$161$	−3.94072	+	12.1283i	−0.310572	+	0.955843i
$162$		0			0
$163$	−10.0155	+	7.27670i	−0.784475	+	0.569955i	−0.906319	−	0.422595i	$-0.861119\pi$
$163$	−10.0155	+	7.27670i	−0.784475	+	0.569955i	0.121843	+	0.992549i	$0.461119\pi$
$164$	17.7061			1.38262
$165$		0			0
$166$	0.432521			0.0335702
$167$	−4.04817	+	2.94117i	−0.313257	+	0.227594i	−0.733293	−	0.679913i	$-0.762018\pi$
$167$	−4.04817	+	2.94117i	−0.313257	+	0.227594i	0.420036	+	0.907508i	$0.362018\pi$
$168$		0			0
$169$	−3.42705	+	10.5474i	−0.263619	+	0.811337i
$170$	−6.67128	−	4.84697i	−0.511664	−	0.371745i
$171$		0			0
$172$	0.267938	−	0.824628i	0.0204301	−	0.0628773i
$173$	2.00743	+	6.17824i	0.152622	+	0.469723i	0.997912	−	0.0645849i	$-0.0205723\pi$
$173$	2.00743	+	6.17824i	0.152622	+	0.469723i	−0.845290	+	0.534308i	$0.820572\pi$
$174$		0			0
$175$	39.0371			2.95092
$176$	9.41996	−	6.26110i	0.710056	−	0.471948i
$177$		0			0
$178$	−2.65362	+	1.92797i	−0.198897	+	0.144507i
$179$	3.79797	+	11.6890i	0.283874	+	0.873673i	0.986734	+	0.162345i	$0.0519059\pi$
$179$	3.79797	+	11.6890i	0.283874	+	0.873673i	−0.702860	+	0.711328i	$0.748094\pi$
$180$		0			0
$181$	4.86040	+	3.53129i	0.361271	+	0.262479i	0.753582	−	0.657354i	$-0.228324\pi$
$181$	4.86040	+	3.53129i	0.361271	+	0.262479i	−0.392311	+	0.919833i	$0.628324\pi$
$182$	−1.20536	−	0.875747i	−0.0893474	−	0.0649147i
$183$		0			0
$184$	1.42464	+	4.38460i	0.105026	+	0.323237i
$185$	−4.05544	+	2.94645i	−0.298162	+	0.216627i
$186$		0			0
$187$	−17.7664	+	11.8087i	−1.29921	+	0.863538i
$188$	−4.17220			−0.304289
$189$		0			0
$190$	1.38055	+	4.24889i	0.100155	+	0.308247i
$191$	−0.637974	+	1.96348i	−0.0461622	+	0.142073i	−0.971481	−	0.237118i	$-0.923797\pi$
$191$	−0.637974	+	1.96348i	−0.0461622	+	0.142073i	0.925319	+	0.379190i	$0.123797\pi$
$192$		0			0
$193$	−8.82865	−	6.41439i	−0.635500	−	0.461718i	0.222801	−	0.974864i	$-0.428480\pi$
$193$	−8.82865	−	6.41439i	−0.635500	−	0.461718i	−0.858301	+	0.513146i	$0.828480\pi$
$194$	−0.805628	+	2.47947i	−0.0578407	+	0.178015i
$195$		0			0
$196$	7.11814	−	5.17163i	0.508439	−	0.369402i
$197$	−20.4184			−1.45475			−0.727376	−	0.686239i	$-0.759261\pi$
$197$	−20.4184			−1.45475			−0.727376	+	0.686239i	$0.759261\pi$
$198$		0			0
$199$	5.57032			0.394869			0.197435	−	0.980316i	$-0.436739\pi$
$199$	5.57032			0.394869			0.197435	+	0.980316i	$0.436739\pi$
$200$	11.4173	−	8.29519i	0.807329	−	0.586559i
$201$		0			0
$202$	1.09024	−	3.35541i	0.0767089	−	0.236086i
$203$	−0.205900	−	0.149595i	−0.0144514	−	0.0104995i
$204$		0			0
$205$	11.6782	−	35.9418i	0.815641	−	2.51028i
$206$	0.769731	+	2.36899i	0.0536297	+	0.165055i
$207$		0			0
$208$	4.71302			0.326789
$209$	11.5475	+	0.481856i	0.798759	+	0.0333307i
$210$		0			0
$211$	−17.6404	+	12.8165i	−1.21441	+	0.882324i	−0.995624	−	0.0934481i	$-0.970211\pi$
$211$	−17.6404	+	12.8165i	−1.21441	+	0.882324i	−0.218790	+	0.975772i	$0.570211\pi$
$212$	−0.529762	−	1.63044i	−0.0363842	−	0.111979i
$213$		0			0
$214$	−3.40265	−	2.47217i	−0.232600	−	0.168994i
$215$	−1.49720	−	1.08778i	−0.102108	−	0.0741857i
$216$		0			0
$217$	−3.93972	−	12.1252i	−0.267446	−	0.823114i
$218$	−2.48207	+	1.80333i	−0.168107	+	0.122137i
$219$		0			0
$220$	−6.87719	−	24.6138i	−0.463660	−	1.65947i
$221$	−8.88895			−0.597936
$222$		0			0
$223$	4.05386	+	12.4765i	0.271467	+	0.835489i	0.990133	+	0.140133i	$0.0447531\pi$
$223$	4.05386	+	12.4765i	0.271467	+	0.835489i	−0.718666	+	0.695356i	$0.755247\pi$
$224$	3.73482	−	11.4946i	0.249543	−	0.768015i
$225$		0			0
$226$	−1.51792	−	1.10283i	−0.100970	−	0.0733593i
$227$	7.09314	−	21.8304i	0.470788	−	1.44894i	−0.380766	−	0.924671i	$-0.624340\pi$
$227$	7.09314	−	21.8304i	0.470788	−	1.44894i	0.851555	−	0.524266i	$-0.175660\pi$
$228$		0			0
$229$	−20.2570	+	14.7176i	−1.33862	+	0.972565i	−0.339127	+	0.940741i	$0.610132\pi$
$229$	−20.2570	+	14.7176i	−1.33862	+	0.972565i	−0.999493	+	0.0318242i	$0.989868\pi$
$230$	4.79391			0.316101
$231$		0			0
$232$	−0.0920089			−0.00604068
$233$	−12.3212	+	8.95184i	−0.807185	+	0.586455i	−0.913013	−	0.407930i	$-0.866251\pi$
$233$	−12.3212	+	8.95184i	−0.807185	+	0.586455i	0.105828	+	0.994384i	$0.466251\pi$
$234$		0			0
$235$	−2.75180	+	8.46917i	−0.179508	+	0.552468i
$236$	12.3309	+	8.95889i	0.802670	+	0.583174i
$237$		0			0
$238$	−2.14288	+	6.59511i	−0.138902	+	0.427497i
$239$	−7.70731	−	23.7206i	−0.498544	−	1.53436i	−0.811360	−	0.584547i	$-0.801272\pi$
$239$	−7.70731	−	23.7206i	−0.498544	−	1.53436i	0.312816	−	0.949814i	$-0.398728\pi$
$240$		0			0
$241$	−11.2183			−0.722634			−0.361317	−	0.932443i	$-0.617673\pi$
$241$	−11.2183			−0.722634			−0.361317	+	0.932443i	$0.617673\pi$
$242$	3.46530	+	0.289705i	0.222758	+	0.0186229i
$243$		0			0
$244$	8.87220	−	6.44603i	0.567984	−	0.412665i
$245$	−5.80311	−	17.8601i	−0.370747	−	1.14104i
$246$		0			0
$247$	3.89606	+	2.83065i	0.247900	+	0.180110i
$248$	−3.72882	−	2.70915i	−0.236780	−	0.172031i
$249$		0			0
$250$	−2.55393	−	7.86019i	−0.161525	−	0.497122i
$251$	3.72882	−	2.70915i	0.235361	−	0.171000i	−0.463853	−	0.885912i	$-0.653533\pi$
$251$	3.72882	−	2.70915i	0.235361	−	0.171000i	0.699214	+	0.714912i	$0.253533\pi$
$252$		0			0
$253$	4.32081	−	11.6249i	0.271647	−	0.730849i
$254$	−2.14162			−0.134377
$255$		0			0
$256$	2.65461	+	8.17004i	0.165913	+	0.510628i
$257$	2.05355	−	6.32019i	0.128097	−	0.394243i	−0.866355	−	0.499428i	$-0.833544\pi$
$257$	2.05355	−	6.32019i	0.128097	−	0.394243i	0.994453	+	0.105185i	$0.0335436\pi$
$258$		0			0
$259$	3.41037	+	2.47778i	0.211910	+	0.153962i
$260$	3.29068	−	10.1277i	0.204079	−	0.628092i
$261$		0			0
$262$	2.31550	−	1.68231i	0.143052	−	0.103933i
$263$	−0.256029			−0.0157874			−0.00789371	−	0.999969i	$-0.502513\pi$
$263$	−0.256029			−0.0157874			−0.00789371	+	0.999969i	$0.502513\pi$
$264$		0			0
$265$	−3.65904			−0.224773
$266$	3.03942	−	2.20827i	0.186359	−	0.135398i
$267$		0			0
$268$	3.43725	−	10.5788i	0.209963	−	0.646201i
$269$	22.0359	+	16.0100i	1.34355	+	0.976148i	0.999305	+	0.0372682i	$0.0118656\pi$
$269$	22.0359	+	16.0100i	1.34355	+	0.976148i	0.344247	+	0.938879i	$0.388134\pi$
$270$		0			0
$271$	0.961217	−	2.95832i	0.0583898	−	0.179705i	−0.917608	−	0.397487i	$-0.869882\pi$
$271$	0.961217	−	2.95832i	0.0583898	−	0.179705i	0.975997	+	0.217782i	$0.0698822\pi$
$272$	−6.77856	−	20.8623i	−0.411010	−	1.26496i
$273$		0			0
$274$	3.22652			0.194921
$275$	−37.9310	−	1.58279i	−2.28732	−	0.0954455i
$276$		0			0
$277$	−5.75675	+	4.18253i	−0.345890	+	0.251304i	−0.747143	−	0.664664i	$-0.768575\pi$
$277$	−5.75675	+	4.18253i	−0.345890	+	0.251304i	0.401253	+	0.915967i	$0.368575\pi$
$278$	0.690613	+	2.12549i	0.0414202	+	0.127478i
$279$		0			0
$280$	−13.7952	−	10.0228i	−0.824424	−	0.598979i
$281$	−1.53900	−	1.11815i	−0.0918090	−	0.0667031i	0.540934	−	0.841065i	$-0.318071\pi$
$281$	−1.53900	−	1.11815i	−0.0918090	−	0.0667031i	−0.632743	+	0.774362i	$0.718071\pi$
$282$		0			0
$283$	4.19735	+	12.9181i	0.249507	+	0.767903i	0.994862	+	0.101236i	$0.0322797\pi$
$283$	4.19735	+	12.9181i	0.249507	+	0.767903i	−0.745356	+	0.666667i	$0.767720\pi$
$284$	14.5625	−	10.5803i	0.864128	−	0.627826i
$285$		0			0
$286$	1.13570	+	0.899805i	0.0671554	+	0.0532066i
$287$	−31.7803			−1.87593
$288$		0			0
$289$	7.53136	+	23.1791i	0.443021	+	1.36348i
$290$	−0.0295650	+	0.0909918i	−0.00173612	+	0.00534322i
$291$		0			0
$292$	21.6079	+	15.6991i	1.26451	+	0.918718i
$293$	−8.38365	+	25.8022i	−0.489778	+	1.50738i	0.335161	+	0.942161i	$0.391209\pi$
$293$	−8.38365	+	25.8022i	−0.489778	+	1.50738i	−0.824939	+	0.565222i	$0.808791\pi$
$294$		0			0
$295$	26.3186	−	19.1216i	1.53233	−	1.11330i
$296$	1.52396			0.0885786
$297$		0			0
$298$	1.34046			0.0776508
$299$	4.18068	−	3.03744i	0.241775	−	0.175660i
$300$		0			0
$301$	−0.480914	+	1.48010i	−0.0277194	+	0.0853116i
$302$	−2.83024	−	2.05629i	−0.162862	−	0.118326i
$303$		0			0
$304$	−3.67244	+	11.3026i	−0.210629	+	0.648249i
$305$	−7.23312	−	22.2612i	−0.414167	−	1.27468i
$306$		0			0
$307$	−2.18209			−0.124539			−0.0622694	−	0.998059i	$-0.519834\pi$
$307$	−2.18209			−0.124539			−0.0622694	+	0.998059i	$0.519834\pi$
$308$	−17.8985	+	11.8965i	−1.01986	+	0.677866i
$309$		0			0
$310$	−3.87737	+	2.81708i	−0.220220	+	0.159999i
$311$	−2.37887	−	7.32140i	−0.134893	−	0.415159i	0.860680	−	0.509146i	$-0.170039\pi$
$311$	−2.37887	−	7.32140i	−0.134893	−	0.415159i	−0.995573	+	0.0939874i	$0.970039\pi$
$312$		0			0
$313$	10.9182	+	7.93251i	0.617131	+	0.448372i	0.851918	−	0.523675i	$-0.175439\pi$
$313$	10.9182	+	7.93251i	0.617131	+	0.448372i	−0.234787	+	0.972047i	$0.575439\pi$
$314$	2.88739	+	2.09781i	0.162945	+	0.118386i
$315$		0			0
$316$	6.45294	+	19.8601i	0.363006	+	1.11722i
$317$	−18.7326	+	13.6101i	−1.05213	+	0.764417i	−0.972616	−	0.232417i	$-0.925337\pi$
$317$	−18.7326	+	13.6101i	−1.05213	+	0.764417i	−0.0795134	+	0.996834i	$0.525337\pi$
$318$		0			0
$319$	0.194001	+	0.153705i	0.0108620	+	0.00860583i
$320$	23.1177			1.29232
$321$		0			0
$322$	−1.24577	−	3.83407i	−0.0694238	−	0.213664i
$323$	6.92637	−	21.3172i	0.385394	−	1.18612i
$324$		0			0
$325$	−12.7977	−	9.29804i	−0.709886	−	0.515762i
$326$	1.20937	−	3.72205i	0.0669807	−	0.206145i
$327$		0			0
$328$	−9.29492	+	6.75316i	−0.513226	+	0.372881i
$329$	7.48857			0.412858
$330$		0			0
$331$	17.4367			0.958406			0.479203	−	0.877704i	$-0.340926\pi$
$331$	17.4367			0.958406			0.479203	+	0.877704i	$0.340926\pi$
$332$	2.10316	−	1.52804i	0.115426	−	0.0838620i
$333$		0			0
$334$	0.488815	−	1.50442i	0.0267468	−	0.0823180i
$335$	−19.2068	−	13.9546i	−1.04938	−	0.762420i
$336$		0			0
$337$	2.93939	−	9.04651i	0.160119	−	0.492795i	−0.838525	−	0.544863i	$-0.816581\pi$
$337$	2.93939	−	9.04651i	0.160119	−	0.492795i	0.998644	+	0.0520687i	$0.0165815\pi$
$338$	−1.08338	−	3.33430i	−0.0589282	−	0.181362i
$339$		0			0
$340$	−49.5632			−2.68794
$341$	3.33647	+	11.9414i	0.180680	+	0.646663i
$342$		0			0
$343$	6.53718	−	4.74954i	0.352975	−	0.256451i
$344$	0.173859	+	0.535084i	0.00937387	+	0.0288498i
$345$		0			0
$346$	−1.66141	−	1.20708i	−0.0893179	−	0.0648933i
$347$	18.0841	+	13.1389i	0.970807	+	0.705333i	0.955635	−	0.294552i	$-0.0951704\pi$
$347$	18.0841	+	13.1389i	0.970807	+	0.705333i	0.0151720	+	0.999885i	$0.495170\pi$
$348$		0			0
$349$	−7.59976	−	23.3896i	−0.406806	−	1.25202i	−0.919378	−	0.393375i	$-0.871307\pi$
$349$	−7.59976	−	23.3896i	−0.406806	−	1.25202i	0.512572	−	0.858644i	$-0.328693\pi$
$350$	−9.98379	+	7.25365i	−0.533656	+	0.387724i
$351$		0			0
$352$	−4.09505	+	11.0175i	−0.218267	+	0.587233i
$353$	−7.66599			−0.408019			−0.204010	−	0.978969i	$-0.565397\pi$
$353$	−7.66599			−0.408019			−0.204010	+	0.978969i	$0.565397\pi$
$354$		0			0
$355$	−11.8722	−	36.5389i	−0.630111	−	1.93928i
$356$	−6.09216	+	18.7497i	−0.322884	+	0.993734i
$357$		0			0
$358$	−3.14331	−	2.28375i	−0.166129	−	0.120700i
$359$	5.86366	−	18.0465i	0.309472	−	0.952457i	−0.668498	−	0.743714i	$-0.733063\pi$
$359$	5.86366	−	18.0465i	0.309472	−	0.952457i	0.977970	−	0.208743i	$-0.0669373\pi$
$360$		0			0
$361$	5.54709	−	4.03020i	0.291952	−	0.212116i
$362$	−1.89922			−0.0998208
$363$		0			0
$364$	−8.95504			−0.469372
$365$	46.1192	−	33.5076i	2.41399	−	1.75387i
$366$		0			0
$367$	−9.41521	+	28.9770i	−0.491470	+	1.51259i	0.330916	+	0.943660i	$0.392642\pi$
$367$	−9.41521	+	28.9770i	−0.491470	+	1.51259i	−0.822386	+	0.568929i	$0.807358\pi$
$368$	10.3169	+	7.49570i	0.537808	+	0.390740i
$369$		0			0
$370$	0.489692	−	1.50712i	0.0254579	−	0.0783513i
$371$	0.950855	+	2.92643i	0.0493659	+	0.151933i
$372$		0			0
$373$	29.3360			1.51896			0.759480	−	0.650530i	$-0.225453\pi$
$373$	29.3360			1.51896			0.759480	+	0.650530i	$0.225453\pi$
$374$	2.34957	−	6.32135i	0.121493	−	0.326869i
$375$		0			0
$376$	2.19022	−	1.59129i	0.112952	−	0.0820643i
$377$	0.0318697	+	0.0980847i	0.00164137	+	0.00505162i
$378$		0			0
$379$	−29.1894	−	21.2073i	−1.49936	−	1.08935i	−0.970637	−	0.240551i	$-0.922672\pi$
$379$	−29.1894	−	21.2073i	−1.49936	−	1.08935i	−0.528721	−	0.848796i	$-0.677328\pi$
$380$	21.7237	+	15.7832i	1.11440	+	0.809661i
$381$		0			0
$382$	−0.201680	−	0.620708i	−0.0103189	−	0.0317582i
$383$	−17.3575	+	12.6109i	−0.886925	+	0.644388i	−0.935074	−	0.354452i	$-0.884668\pi$
$383$	−17.3575	+	12.6109i	−0.886925	+	0.644388i	0.0481498	+	0.998840i	$0.484668\pi$
$384$		0			0
$385$	12.3437	+	44.1787i	0.629092	+	2.25156i
$386$	3.44982			0.175591
$387$		0			0
$388$	4.84220	+	14.9027i	0.245825	+	0.756572i
$389$	0.0153125	−	0.0471270i	0.000776374	−	0.00238943i	−0.950668	−	0.310211i	$-0.899600\pi$
$389$	0.0153125	−	0.0471270i	0.000776374	−	0.00238943i	0.951444	+	0.307822i	$0.0996001\pi$
$390$		0			0
$391$	−19.4582	−	14.1372i	−0.984043	−	0.714949i
$392$	−1.76423	+	5.42975i	−0.0891072	+	0.274244i
$393$		0			0
$394$	5.22204	−	3.79404i	0.263083	−	0.191141i
$395$	44.5702			2.24257
$396$		0			0
$397$	0.432880			0.0217256			0.0108628	−	0.999941i	$-0.496542\pi$
$397$	0.432880			0.0217256			0.0108628	+	0.999941i	$0.496542\pi$
$398$	−1.42462	+	1.03504i	−0.0714096	+	0.0518821i
$399$		0			0
$400$	12.0631	−	37.1264i	0.603156	−	1.85632i
$401$	15.5206	+	11.2764i	0.775063	+	0.563116i	0.903493	−	0.428602i	$-0.140994\pi$
$401$	15.5206	+	11.2764i	0.775063	+	0.563116i	−0.128430	+	0.991719i	$0.540994\pi$
$402$		0			0
$403$	−1.59647	+	4.91344i	−0.0795259	+	0.244756i
$404$	−6.55283	−	20.1675i	−0.326016	−	1.00337i
$405$		0			0
$406$	0.0804563			0.00399298
$407$	−3.21328	−	2.54585i	−0.159276	−	0.126193i
$408$		0			0
$409$	25.6325	−	18.6231i	1.26745	−	0.920853i	0.268347	−	0.963322i	$-0.413523\pi$
$409$	25.6325	−	18.6231i	1.26745	−	0.920853i	0.999098	+	0.0424695i	$0.0135225\pi$
$410$	3.69179	+	11.3621i	0.182324	+	0.561136i
$411$		0			0
$412$	12.1122	+	8.80000i	0.596723	+	0.433545i
$413$	−22.1323	−	16.0801i	−1.08906	−	0.791248i
$414$		0			0
$415$	−1.71462	−	5.27705i	−0.0841672	−	0.259040i
$416$	−3.96224	+	2.87873i	−0.194265	+	0.141142i
$417$		0			0
$418$	−3.04283	+	2.02246i	−0.148830	+	0.0989218i
$419$	−10.6473			−0.520155			−0.260077	−	0.965588i	$-0.583748\pi$
$419$	−10.6473			−0.520155			−0.260077	+	0.965588i	$0.583748\pi$
$420$		0			0
$421$	0.669464	+	2.06040i	0.0326277	+	0.100418i	0.966044	−	0.258377i	$-0.0831878\pi$
$421$	0.669464	+	2.06040i	0.0326277	+	0.100418i	−0.933416	+	0.358795i	$0.883188\pi$
$422$	2.13007	−	6.55568i	0.103690	−	0.319125i
$423$		0			0
$424$	0.899954	+	0.653855i	0.0437056	+	0.0317540i
$425$	−22.7515	+	70.0220i	−1.10361	+	3.39657i
$426$		0			0
$427$	−15.9245	+	11.5698i	−0.770639	+	0.559902i
$428$	−25.2794			−1.22193
$429$		0			0
$430$	0.585035			0.0282129
$431$	−26.3798	+	19.1661i	−1.27067	+	0.923197i	−0.999229	−	0.0392570i	$-0.987501\pi$
$431$	−26.3798	+	19.1661i	−1.27067	+	0.923197i	−0.271443	+	0.962454i	$0.587501\pi$
$432$		0			0
$433$	−7.68894	+	23.6641i	−0.369507	+	1.13723i	0.577604	+	0.816317i	$0.303988\pi$
$433$	−7.68894	+	23.6641i	−0.369507	+	1.13723i	−0.947110	+	0.320908i	$0.896012\pi$
$434$	3.26063	+	2.36899i	0.156515	+	0.113715i
$435$		0			0
$436$	−5.69832	+	17.5376i	−0.272900	+	0.839899i
$437$	4.02665	+	12.3928i	0.192621	+	0.592827i
$438$		0			0
$439$	−17.6523			−0.842500			−0.421250	−	0.906945i	$-0.638409\pi$
$439$	−17.6523			−0.842500			−0.421250	+	0.906945i	$0.638409\pi$
$440$	12.9980	+	10.2982i	0.619654	+	0.490946i
$441$		0			0
$442$	2.27336	−	1.65169i	0.108133	−	0.0785631i
$443$	9.04672	+	27.8429i	0.429822	+	1.32286i	0.898300	+	0.439382i	$0.144803\pi$
$443$	9.04672	+	27.8429i	0.429822	+	1.32286i	−0.468478	+	0.883475i	$0.655197\pi$
$444$		0			0
$445$	34.0421	+	24.7330i	1.61375	+	1.17246i
$446$	−3.35510	−	2.43762i	−0.158868	−	0.115425i
$447$		0			0
$448$	−6.00746	−	18.4890i	−0.283826	−	0.873525i
$449$	11.9284	−	8.66649i	0.562936	−	0.408997i	−0.269596	−	0.962973i	$-0.586890\pi$
$449$	11.9284	−	8.66649i	0.562936	−	0.408997i	0.832532	+	0.553976i	$0.186890\pi$
$450$		0			0
$451$	30.8798	+	1.28855i	1.45407	+	0.0606756i
$452$	−11.2771			−0.530432
$453$		0			0
$454$	2.24233	+	6.90118i	0.105238	+	0.323888i
$455$	−5.90635	+	18.1779i	−0.276894	+	0.852192i
$456$		0			0
$457$	8.21662	+	5.96973i	0.384357	+	0.279252i	0.763139	−	0.646234i	$-0.223657\pi$
$457$	8.21662	+	5.96973i	0.384357	+	0.279252i	−0.378782	+	0.925486i	$0.623657\pi$
$458$	2.44602	−	7.52809i	0.114295	−	0.351764i
$459$		0			0
$460$	23.3107	−	16.9362i	1.08687	−	0.789655i
$461$	4.17865			0.194619			0.0973095	−	0.995254i	$-0.468976\pi$
$461$	4.17865			0.194619			0.0973095	+	0.995254i	$0.468976\pi$
$462$		0			0
$463$	−9.50797			−0.441873			−0.220937	−	0.975288i	$-0.570911\pi$
$463$	−9.50797			−0.441873			−0.220937	+	0.975288i	$0.570911\pi$
$464$	−0.205900	+	0.149595i	−0.00955868	+	0.00694479i
$465$		0			0
$466$	1.48777	−	4.57889i	0.0689197	−	0.212113i
$467$	28.2253	+	20.5069i	1.30611	+	0.948944i	0.999995	−	0.00305082i	$-0.000971107\pi$
$467$	28.2253	+	20.5069i	1.30611	+	0.948944i	0.306114	+	0.951995i	$0.400971\pi$
$468$		0			0
$469$	−6.16942	+	18.9875i	−0.284877	+	0.876763i
$470$	−0.869917	−	2.67733i	−0.0401263	−	0.123496i
$471$		0			0
$472$	−9.89008			−0.455228
$473$	0.527299	−	1.41866i	0.0242452	−	0.0652302i
$474$		0			0
$475$	32.2703	−	23.4458i	1.48066	−	1.07577i
$476$	12.8797	+	39.6396i	0.590340	+	1.81688i
$477$		0			0
$478$	6.37879	+	4.63446i	0.291759	+	0.211975i
$479$	−8.58551	−	6.23774i	−0.392282	−	0.285010i	0.374108	−	0.927385i	$-0.377949\pi$
$479$	−8.58551	−	6.23774i	−0.392282	−	0.285010i	−0.766390	+	0.642376i	$0.777949\pi$
$480$		0			0
$481$	−0.527864	−	1.62460i	−0.0240685	−	0.0740753i
$482$	2.86910	−	2.08452i	0.130684	−	0.0949473i
$483$		0			0
$484$	17.8737	−	10.8337i	0.812442	−	0.492441i
$485$	33.4449			1.51865
$486$		0			0
$487$	−10.4706	−	32.2252i	−0.474468	−	1.46026i	−0.846673	−	0.532113i	$-0.821398\pi$
$487$	−10.4706	−	32.2252i	−0.474468	−	1.46026i	0.372205	−	0.928151i	$-0.378602\pi$
$488$	−2.19897	+	6.76775i	−0.0995429	+	0.306361i
$489$		0			0
$490$	4.80283	+	3.48946i	0.216970	+	0.157638i
$491$	5.40461	−	16.6337i	0.243907	−	0.750667i	−0.751908	−	0.659268i	$-0.770866\pi$
$491$	5.40461	−	16.6337i	0.243907	−	0.750667i	0.995814	−	0.0913990i	$-0.0291339\pi$
$492$		0			0
$493$	0.388337	−	0.282143i	0.0174898	−	0.0127071i
$494$	−1.52240			−0.0684960
$495$		0			0
$496$	−12.7492			−0.572457
$497$	−26.1379	+	18.9903i	−1.17244	+	0.851831i
$498$		0			0
$499$	−1.82716	+	5.62341i	−0.0817948	+	0.251739i	−0.983588	−	0.180429i	$-0.942251\pi$
$499$	−1.82716	+	5.62341i	−0.0817948	+	0.251739i	0.901793	+	0.432168i	$0.142251\pi$
$500$	−40.1876	−	29.1980i	−1.79724	−	1.30577i
$501$		0			0
$502$	−0.450253	+	1.38574i	−0.0200958	+	0.0618485i
$503$	9.46873	+	29.1417i	0.422190	+	1.29937i	0.905660	+	0.424005i	$0.139376\pi$
$503$	9.46873	+	29.1417i	0.422190	+	1.29937i	−0.483470	+	0.875361i	$0.660624\pi$
$504$		0			0
$505$	−45.2602			−2.01405
$506$	1.05501	+	3.77595i	0.0469010	+	0.167861i
$507$		0			0
$508$	−10.4137	+	7.56603i	−0.462035	+	0.335688i
$509$	−12.4985	−	38.4665i	−0.553987	−	1.70500i	−0.698604	−	0.715508i	$-0.746195\pi$
$509$	−12.4985	−	38.4665i	−0.553987	−	1.70500i	0.144618	−	0.989488i	$-0.453805\pi$
$510$		0			0
$511$	−38.7834	−	28.1778i	−1.71568	−	1.24651i
$512$	−16.5812	−	12.0470i	−0.732793	−	0.532406i
$513$		0			0
$514$	0.649183	+	1.99798i	0.0286342	+	0.0881271i
$515$	25.8518	−	18.7824i	1.13917	−	0.827653i
$516$		0			0
$517$	−7.27638	−	0.303629i	−0.320015	−	0.0133536i
$518$	−1.33262			−0.0585517
$519$		0			0
$520$	2.13525	+	6.57164i	0.0936371	+	0.288185i
$521$	8.37094	−	25.7631i	0.366738	−	1.12870i	−0.582148	−	0.813083i	$-0.697788\pi$
$521$	8.37094	−	25.7631i	0.366738	−	1.12870i	0.948886	−	0.315620i	$-0.102212\pi$
$522$		0			0
$523$	−12.4413	−	9.03910i	−0.544018	−	0.395252i	0.281557	−	0.959544i	$-0.409149\pi$
$523$	−12.4413	−	9.03910i	−0.544018	−	0.395252i	−0.825575	+	0.564292i	$0.809149\pi$
$524$	5.31590	−	16.3607i	0.232226	−	0.714719i
$525$		0			0
$526$	0.0654798	−	0.0475738i	0.00285505	−	0.00207432i
$527$	24.0456			1.04744
$528$		0			0
$529$	−9.01756			−0.392068
$530$	0.935806	−	0.679903i	0.0406488	−	0.0295331i
$531$		0			0
$532$	6.97787	−	21.4757i	0.302529	−	0.931089i
$533$	10.4186	+	7.56958i	0.451281	+	0.327875i
$534$		0			0
$535$	−16.6732	+	51.3149i	−0.720846	+	2.21853i
$536$	2.23036	+	6.86434i	0.0963369	+	0.296494i
$537$		0			0
$538$	−8.61060			−0.371229
$539$	12.7905	−	8.50139i	0.550927	−	0.366181i
$540$		0			0
$541$	−19.3592	+	14.0653i	−0.832319	+	0.604715i	−0.920214	−	0.391415i	$-0.871986\pi$
$541$	−19.3592	+	14.0653i	−0.832319	+	0.604715i	0.0878957	+	0.996130i	$0.471986\pi$
$542$	0.303866	+	0.935204i	0.0130522	+	0.0401704i
$543$		0			0
$544$	18.4415	+	13.3985i	0.790673	+	0.574458i
$545$	31.8413	+	23.1341i	1.36393	+	0.990955i
$546$		0			0
$547$	−6.79463	−	20.9117i	−0.290518	−	0.894121i	−0.984690	−	0.174313i	$-0.944230\pi$
$547$	−6.79463	−	20.9117i	−0.290518	−	0.894121i	0.694173	−	0.719808i	$-0.255770\pi$
$548$	15.6892	−	11.3989i	0.670208	−	0.486935i
$549$		0			0
$550$	9.99501	−	6.64332i	0.426189	−	0.283272i
$551$	−0.260057			−0.0110788
$552$		0			0
$553$	−11.5822	−	35.6463i	−0.492525	−	1.51584i
$554$	0.695125	−	2.13937i	0.0295330	−	0.0908933i
$555$		0			0
$556$	10.8672	+	7.89549i	0.460872	+	0.334843i
$557$	11.4341	−	35.1905i	0.484477	−	1.49107i	−0.348259	−	0.937398i	$-0.613227\pi$
$557$	11.4341	−	35.1905i	0.484477	−	1.49107i	0.832736	−	0.553670i	$-0.186773\pi$
$558$		0			0
$559$	0.510197	−	0.370680i	0.0215791	−	0.0156781i
$560$	−47.1673			−1.99318
$561$		0			0
$562$	0.601369			0.0253672
$563$	−13.5355	+	9.83411i	−0.570453	+	0.414458i	−0.835270	−	0.549840i	$-0.814689\pi$
$563$	−13.5355	+	9.83411i	−0.570453	+	0.414458i	0.264817	+	0.964299i	$0.414689\pi$
$564$		0			0
$565$	−7.43790	+	22.8915i	−0.312915	+	0.963053i
$566$	−3.47385	−	2.52390i	−0.146017	−	0.106088i
$567$		0			0
$568$	−3.60932	+	11.1084i	−0.151444	+	0.466096i
$569$	11.8830	+	36.5721i	0.498162	+	1.53318i	0.811971	+	0.583698i	$0.198395\pi$
$569$	11.8830	+	36.5721i	0.498162	+	1.53318i	−0.313809	+	0.949486i	$0.601605\pi$
$570$		0			0
$571$	22.4984			0.941530			0.470765	−	0.882259i	$-0.343978\pi$
$571$	22.4984			0.941530			0.470765	+	0.882259i	$0.343978\pi$
$572$	8.70130	+	0.363088i	0.363820	+	0.0151815i
$573$		0			0
$574$	8.12785	−	5.90523i	0.339250	−	0.246480i
$575$	−13.2266	−	40.7074i	−0.551589	−	1.69762i
$576$		0			0
$577$	32.9059	+	23.9076i	1.36989	+	0.995284i	0.997746	+	0.0671101i	$0.0213779\pi$
$577$	32.9059	+	23.9076i	1.36989	+	0.995284i	0.372146	+	0.928174i	$0.378622\pi$
$578$	−6.23317	−	4.52866i	−0.259266	−	0.188368i
$579$		0			0
$580$	0.177699	+	0.546903i	0.00737857	+	0.0227089i
$581$	−3.77491	+	2.74263i	−0.156610	+	0.113784i
$582$		0			0
$583$	−0.805259	−	2.88206i	−0.0333504	−	0.119363i
$584$	−17.3308			−0.717155
$585$		0			0
$586$	−2.65029	−	8.15676i	−0.109483	−	0.336953i
$587$	−7.38326	+	22.7233i	−0.304740	+	0.937892i	0.675034	+	0.737786i	$0.264129\pi$
$587$	−7.38326	+	22.7233i	−0.304740	+	0.937892i	−0.979774	+	0.200106i	$0.935871\pi$
$588$		0			0
$589$	−10.5393	−	7.65721i	−0.434262	−	0.315510i
$590$	−3.17796	+	9.78074i	−0.130834	+	0.402667i
$591$		0			0
$592$	3.41037	−	2.47778i	0.140165	−	0.101836i
$593$	−36.6237			−1.50395			−0.751977	−	0.659190i	$-0.770900\pi$
$593$	−36.6237			−1.50395			−0.751977	+	0.659190i	$0.770900\pi$
$594$		0			0
$595$	88.9596			3.64699
$596$	6.51807	−	4.73566i	0.266991	−	0.193980i
$597$		0			0
$598$	−0.504815	+	1.55366i	−0.0206434	+	0.0635339i
$599$	−25.1879	−	18.3001i	−1.02915	−	0.747720i	−0.0610100	−	0.998137i	$-0.519432\pi$
$599$	−25.1879	−	18.3001i	−1.02915	−	0.747720i	−0.968138	+	0.250417i	$0.919432\pi$
$600$		0			0
$601$	6.46577	−	19.8996i	0.263744	−	0.811721i	−0.728236	−	0.685326i	$-0.759660\pi$
$601$	6.46577	−	19.8996i	0.263744	−	0.811721i	0.991980	−	0.126394i	$-0.0403405\pi$
$602$	−0.152030	−	0.467899i	−0.00619626	−	0.0190701i
$603$		0			0
$604$	−21.0268			−0.855568
$605$	−10.2027	−	43.4274i	−0.414798	−	1.76558i
$606$		0			0
$607$	−12.7376	+	9.25441i	−0.517003	+	0.375625i	−0.815474	−	0.578794i	$-0.803524\pi$
$607$	−12.7376	+	9.25441i	−0.517003	+	0.375625i	0.298471	+	0.954419i	$0.403524\pi$
$608$	−3.81626	−	11.7453i	−0.154770	−	0.476333i
$609$		0			0
$610$	5.98634	+	4.34933i	0.242380	+	0.176099i
$611$	−2.45500	−	1.78366i	−0.0993188	−	0.0721593i
$612$		0			0
$613$	−0.750717	−	2.31047i	−0.0303212	−	0.0933190i	0.934751	−	0.355304i	$-0.115623\pi$
$613$	−0.750717	−	2.31047i	−0.0303212	−	0.0933190i	−0.965072	+	0.261985i	$0.915623\pi$
$614$	0.558074	−	0.405464i	0.0225220	−	0.0163632i
$615$		0			0
$616$	4.85857	−	13.0717i	0.195757	−	0.526672i
$617$	42.9992			1.73108			0.865542	−	0.500837i	$-0.166974\pi$
$617$	42.9992			1.73108			0.865542	+	0.500837i	$0.166974\pi$
$618$		0			0
$619$	10.6058	+	32.6411i	0.426281	+	1.31196i	0.901762	+	0.432232i	$0.142274\pi$
$619$	10.6058	+	32.6411i	0.426281	+	1.31196i	−0.475481	+	0.879726i	$0.657726\pi$
$620$	−8.90164	+	27.3964i	−0.357498	+	1.10027i
$621$		0			0
$622$	1.96882	+	1.43043i	0.0789425	+	0.0573551i
$623$	10.9346	−	33.6534i	0.438087	−	1.34829i
$624$		0			0
$625$	−39.4728	+	28.6787i	−1.57891	+	1.14715i
$626$	−4.26631			−0.170516
$627$		0			0
$628$	21.4514			0.856003
$629$	−6.43211	+	4.67320i	−0.256465	+	0.186333i
$630$		0			0
$631$	−4.45465	+	13.7100i	−0.177337	+	0.545786i	−0.999732	−	0.0231295i	$-0.992637\pi$
$631$	−4.45465	+	13.7100i	−0.177337	+	0.545786i	0.822396	+	0.568916i	$0.192637\pi$
$632$	−10.9622	−	7.96449i	−0.436052	−	0.316810i
$633$		0			0
$634$	2.26196	−	6.96159i	0.0898338	−	0.276480i
$635$	8.48987	+	26.1291i	0.336910	+	1.03690i
$636$		0			0
$637$	6.39939			0.253553
$638$	−0.0781766	−	0.00326216i	−0.00309504	−	0.000129150i
$639$		0			0
$640$	−29.1671	+	21.1911i	−1.15293	+	0.837653i
$641$	−9.59782	−	29.5391i	−0.379091	−	1.16672i	−0.940677	−	0.339304i	$-0.889808\pi$
$641$	−9.59782	−	29.5391i	−0.379091	−	1.16672i	0.561586	−	0.827419i	$-0.310192\pi$
$642$		0			0
$643$	4.29223	+	3.11849i	0.169269	+	0.122981i	0.669194	−	0.743087i	$-0.266639\pi$
$643$	4.29223	+	3.11849i	0.169269	+	0.122981i	−0.499926	+	0.866068i	$0.666639\pi$
$644$	−19.6029	−	14.2423i	−0.772461	−	0.561225i
$645$		0			0
$646$	2.18961	+	6.73892i	0.0861490	+	0.265139i
$647$	10.3325	−	7.50697i	0.406211	−	0.295130i	−0.365855	−	0.930672i	$-0.619223\pi$
$647$	10.3325	−	7.50697i	0.406211	−	0.295130i	0.772066	+	0.635542i	$0.219223\pi$
$648$		0			0
$649$	20.8532	+	16.5218i	0.818561	+	0.648538i
$650$	5.00073			0.196145
$651$		0			0
$652$	−7.26886	−	22.3712i	−0.284670	−	0.876125i
$653$	0.580580	−	1.78684i	0.0227199	−	0.0699246i	−0.939054	−	0.343770i	$-0.888296\pi$
$653$	0.580580	−	1.78684i	0.0227199	−	0.0699246i	0.961774	+	0.273846i	$0.0882958\pi$
$654$		0			0
$655$	−29.7045	−	21.5815i	−1.16065	−	0.843261i
$656$	−9.82065	+	30.2248i	−0.383432	+	1.18008i
$657$		0			0
$658$	−1.91521	+	1.39148i	−0.0746628	+	0.0542457i
$659$	24.3868			0.949976			0.474988	−	0.879992i	$-0.342452\pi$
$659$	24.3868			0.949976			0.474988	+	0.879992i	$0.342452\pi$
$660$		0			0
$661$	46.3444			1.80259			0.901295	−	0.433206i	$-0.142618\pi$
$661$	46.3444			1.80259			0.901295	+	0.433206i	$0.142618\pi$
$662$	−4.45945	+	3.23998i	−0.173322	+	0.125926i
$663$		0			0
$664$	−0.521269	+	1.60430i	−0.0202292	+	0.0622589i
$665$	−38.9913	−	28.3288i	−1.51202	−	1.09854i
$666$		0			0
$667$	−0.0862326	+	0.265397i	−0.00333894	+	0.0102762i
$668$	−2.93800	−	9.04224i	−0.113675	−	0.349855i
$669$		0			0
$670$	7.50514			0.289949
$671$	15.9424	−	10.5963i	0.615448	−	0.409066i
$672$		0			0
$673$	−1.67073	+	1.21386i	−0.0644019	+	0.0467907i	−0.619520	−	0.784981i	$-0.712673\pi$
$673$	−1.67073	+	1.21386i	−0.0644019	+	0.0467907i	0.555119	+	0.831771i	$0.312673\pi$
$674$	0.929218	+	2.85984i	0.0357921	+	0.110157i
$675$		0			0
$676$	−17.0476	−	12.3858i	−0.655678	−	0.476378i
$677$	−35.7836	−	25.9983i	−1.37527	−	0.999195i	−0.997304	−	0.0733768i	$-0.976622\pi$
$677$	−35.7836	−	25.9983i	−1.37527	−	0.999195i	−0.377969	−	0.925818i	$-0.623378\pi$
$678$		0			0
$679$	−8.69112	−	26.7485i	−0.333535	−	1.02651i
$680$	26.0184	−	18.9035i	0.997761	−	0.724915i
$681$		0			0
$682$	−3.07219	−	2.43407i	−0.117640	−	0.0932053i
$683$	−9.13079			−0.349380			−0.174690	−	0.984623i	$-0.555892\pi$
$683$	−9.13079			−0.349380			−0.174690	+	0.984623i	$0.555892\pi$
$684$		0			0
$685$	−12.7907	−	39.3657i	−0.488707	−	1.50409i
$686$	−0.789362	+	2.42941i	−0.0301380	+	0.0927551i
$687$		0			0
$688$	1.25905	+	0.914753i	0.0480008	+	0.0348746i
$689$	0.385310	−	1.18586i	0.0146791	−	0.0451777i
$690$		0			0
$691$	−35.0395	+	25.4577i	−1.33296	+	0.968455i	−0.333293	+	0.942823i	$0.608160\pi$
$691$	−35.0395	+	25.4577i	−1.33296	+	0.968455i	−0.999671	+	0.0256317i	$0.991840\pi$
$692$	−12.3432			−0.469217
$693$		0			0
$694$	−7.06644			−0.268238
$695$	23.1946	−	16.8519i	0.879822	−	0.639228i
$696$		0			0
$697$	18.5221	−	57.0053i	0.701576	−	2.15923i
$698$	6.28978	+	4.56979i	0.238072	+	0.172969i
$699$		0			0
$700$	−22.9207	+	70.5426i	−0.866321	+	2.66626i
$701$	−5.97820	−	18.3990i	−0.225794	−	0.694921i	−0.998210	−	0.0598049i	$-0.980952\pi$
$701$	−5.97820	−	18.3990i	−0.225794	−	0.694921i	0.772417	−	0.635116i	$-0.219048\pi$
$702$		0			0
$703$	4.30738			0.162456
$704$	5.08759	+	18.2087i	0.191746	+	0.686268i
$705$		0			0
$706$	1.96059	−	1.42445i	0.0737877	−	0.0536099i
$707$	11.7615	+	36.1982i	0.442337	+	1.36137i
$708$		0			0
$709$	3.24539	+	2.35791i	0.121883	+	0.0885533i	0.647057	−	0.762442i	$-0.276000\pi$
$709$	3.24539	+	2.35791i	0.121883	+	0.0885533i	−0.525174	+	0.850995i	$0.676000\pi$
$710$	9.82578	+	7.13885i	0.368755	+	0.267916i
$711$		0			0
$712$	−3.95308	−	12.1663i	−0.148148	−	0.455952i
$713$	−11.3092	+	8.21660i	−0.423532	+	0.307714i
$714$		0			0
$715$	6.47603	−	17.4233i	0.242190	−	0.651596i
$716$	−23.3527			−0.872732
$717$		0			0
$718$	1.85366	+	5.70497i	0.0691778	+	0.212907i
$719$	1.76766	−	5.44030i	0.0659227	−	0.202889i	−0.912669	−	0.408699i	$-0.865983\pi$
$719$	1.76766	−	5.44030i	0.0659227	−	0.202889i	0.978592	+	0.205810i	$0.0659827\pi$
$720$		0			0
$721$	−21.7398	−	15.7949i	−0.809632	−	0.588232i
$722$	−0.669809	+	2.06146i	−0.0249277	+	0.0767196i
$723$		0			0
$724$	−9.23508	+	6.70968i	−0.343219	+	0.249363i
$725$	0.854226			0.0317252
$726$		0			0
$727$	26.1198			0.968730			0.484365	−	0.874866i	$-0.339051\pi$
$727$	26.1198			0.968730			0.484365	+	0.874866i	$0.339051\pi$
$728$	4.70099	−	3.41547i	0.174230	−	0.126586i
$729$		0			0
$730$	−5.56887	+	17.1392i	−0.206113	+	0.634352i
$731$	−2.37462	−	1.72526i	−0.0878285	−	0.0638111i
$732$		0			0
$733$	−3.61891	+	11.1379i	−0.133668	+	0.411386i	−0.995380	−	0.0960099i	$-0.969392\pi$
$733$	−3.61891	+	11.1379i	−0.133668	+	0.411386i	0.861713	+	0.507396i	$0.169392\pi$
$734$	−2.97640	−	9.16041i	−0.109861	−	0.338117i
$735$		0			0
$736$	−13.2519			−0.488470
$737$	6.76448	−	18.1994i	0.249173	−	0.670383i
$738$		0			0
$739$	10.0031	−	7.26770i	0.367971	−	0.267347i	−0.388398	−	0.921492i	$-0.626971\pi$
$739$	10.0031	−	7.26770i	0.367971	−	0.267347i	0.756369	+	0.654145i	$0.226971\pi$
$740$	−2.94327	−	9.05846i	−0.108197	−	0.332996i
$741$		0			0
$742$	−0.786955	−	0.571757i	−0.0288900	−	0.0209898i
$743$	−15.3240	−	11.1335i	−0.562182	−	0.408449i	0.270075	−	0.962839i	$-0.412952\pi$
$743$	−15.3240	−	11.1335i	−0.562182	−	0.408449i	−0.832257	+	0.554390i	$0.812952\pi$
$744$		0			0
$745$	−5.31390	−	16.3545i	−0.194686	−	0.599183i
$746$	−7.50273	+	5.45105i	−0.274694	+	0.199577i
$747$		0			0
$748$	−10.9075	−	39.0387i	−0.398819	−	1.42740i
$749$	45.3734			1.65791
$750$		0			0
$751$	−7.64734	−	23.5361i	−0.279056	−	0.858845i	−0.988118	−	0.153699i	$-0.950881\pi$
$751$	−7.64734	−	23.5361i	−0.279056	−	0.858845i	0.709062	−	0.705146i	$-0.249119\pi$
$752$	2.31409	−	7.12205i	0.0843864	−	0.259715i
$753$		0			0
$754$	−0.0263763	−	0.0191635i	−0.000960567	−	0.000697893i
$755$	−13.8683	+	42.6824i	−0.504721	+	1.55337i
$756$		0			0
$757$	−12.1358	+	8.81721i	−0.441085	+	0.320467i	−0.786066	−	0.618143i	$-0.787885\pi$
$757$	−12.1358	+	8.81721i	−0.441085	+	0.320467i	0.344981	+	0.938610i	$0.387885\pi$
$758$	11.4059			0.414279
$759$		0			0
$760$	−17.4237			−0.632024
$761$	−20.8422	+	15.1428i	−0.755531	+	0.548925i	−0.897536	−	0.440941i	$-0.854645\pi$
$761$	−20.8422	+	15.1428i	−0.755531	+	0.548925i	0.142005	+	0.989866i	$0.454645\pi$
$762$		0			0
$763$	10.2277	−	31.4778i	0.370269	−	1.13957i
$764$	−3.17356	−	2.30572i	−0.114815	−	0.0834182i
$765$		0			0
$766$	2.09590	−	6.45053i	0.0757281	−	0.233067i
$767$	3.42568	+	10.5432i	0.123694	+	0.380692i
$768$		0			0
$769$	−0.639008			−0.0230432			−0.0115216	−	0.999934i	$-0.503668\pi$
$769$	−0.639008			−0.0230432			−0.0115216	+	0.999934i	$0.503668\pi$
$770$	−11.3660	−	9.00514i	−0.409601	−	0.324523i
$771$		0			0
$772$	16.7750	−	12.1877i	0.603745	−	0.438647i
$773$	7.97807	+	24.5540i	0.286951	+	0.883145i	0.985807	+	0.167883i	$0.0536929\pi$
$773$	7.97807	+	24.5540i	0.286951	+	0.883145i	−0.698856	+	0.715263i	$0.746307\pi$
$774$		0			0
$775$	34.6190	+	25.1522i	1.24355	+	0.903493i
$776$	−8.22587	−	5.97644i	−0.295291	−	0.214542i
$777$		0			0
$778$	0.00484068	+	0.0148981i	0.000173547	+	0.000534122i
$779$	−26.2714	+	19.0873i	−0.941272	+	0.683874i
$780$		0			0
$781$	26.1673	−	17.3924i	0.936338	−	0.622350i
$782$	7.60336			0.271895
$783$		0			0
$784$	4.88006	+	15.0193i	0.174288	+	0.536403i
$785$	14.1484	−	43.5443i	0.504978	−	1.55416i
$786$		0			0
$787$	39.4754	+	28.6806i	1.40715	+	1.02235i	0.993730	+	0.111810i	$0.0356647\pi$
$787$	39.4754	+	28.6806i	1.40715	+	1.02235i	0.413417	+	0.910542i	$0.364335\pi$
$788$	11.9887	−	36.8975i	0.427081	−	1.31442i
$789$		0			0
$790$	−11.3989	+	8.28178i	−0.405555	+	0.294653i
$791$	20.2410			0.719687
$792$		0			0
$793$	7.97632			0.283248
$794$	−0.110710	+	0.0804352i	−0.00392894	+	0.00285454i
$795$		0			0
$796$	−3.27062	+	10.0659i	−0.115924	+	0.356778i
$797$	42.2081	+	30.6660i	1.49509	+	1.08625i	0.972287	+	0.233791i	$0.0751130\pi$
$797$	42.2081	+	30.6660i	1.49509	+	1.08625i	0.522801	+	0.852455i	$0.324887\pi$
$798$		0			0
$799$	−4.36448	+	13.4325i	−0.154404	+	0.475207i
$800$	12.5355	+	38.5804i	0.443199	+	1.36402i
$801$		0			0
$802$	−6.06474			−0.214153
$803$	36.5420	+	28.9519i	1.28954	+	1.02169i
$804$		0			0
$805$	−41.8397	+	30.3983i	−1.47466	+	1.07140i
$806$	−0.504687	−	1.55327i	−0.0177768	−	0.0547115i
$807$		0			0
$808$	11.1319	+	8.08778i	0.391618	+	0.284527i
$809$	25.5517	+	18.5644i	0.898351	+	0.652690i	0.938042	−	0.346522i	$-0.112637\pi$
$809$	25.5517	+	18.5644i	0.898351	+	0.652690i	−0.0396909	+	0.999212i	$0.512637\pi$
$810$		0			0
$811$	8.82436	+	27.1586i	0.309865	+	0.953667i	0.977817	+	0.209462i	$0.0671714\pi$
$811$	8.82436	+	27.1586i	0.309865	+	0.953667i	−0.667951	+	0.744205i	$0.732829\pi$
$812$	0.391224	−	0.284241i	0.0137293	−	0.00997490i
$813$		0			0
$814$	1.29486	+	0.0540318i	0.0453847	+	0.00189381i
$815$	−50.2057			−1.75863
$816$		0			0
$817$	0.491401	+	1.51238i	0.0171919	+	0.0529114i
$818$	−3.09511	+	9.52577i	−0.108218	+	0.333061i
$819$		0			0
$820$	58.0924	+	42.2066i	2.02868	+	1.47392i
$821$	14.8884	−	45.8218i	0.519609	−	1.59919i	−0.255129	−	0.966907i	$-0.582118\pi$
$821$	14.8884	−	45.8218i	0.519609	−	1.59919i	0.774737	−	0.632283i	$-0.217882\pi$
$822$		0			0
$823$	−21.9250	+	15.9294i	−0.764258	+	0.555266i	−0.900213	−	0.435449i	$-0.856590\pi$
$823$	−21.9250	+	15.9294i	−0.764258	+	0.555266i	0.135956	+	0.990715i	$0.456590\pi$
$824$	−9.71467			−0.338427
$825$		0			0
$826$	8.64828			0.300912
$827$	2.48207	−	1.80333i	0.0863100	−	0.0627079i	−0.543793	−	0.839219i	$-0.683012\pi$
$827$	2.48207	−	1.80333i	0.0863100	−	0.0627079i	0.630103	+	0.776511i	$0.283012\pi$
$828$		0			0
$829$	8.89545	−	27.3774i	0.308952	−	0.950855i	−0.669221	−	0.743063i	$-0.733372\pi$
$829$	8.89545	−	27.3774i	0.308952	−	0.950855i	0.978173	−	0.207792i	$-0.0666278\pi$
$830$	1.41907	+	1.03101i	0.0492565	+	0.0357870i
$831$		0			0
$832$	−2.43437	+	7.49221i	−0.0843965	+	0.259746i
$833$	−9.20400	−	28.3270i	−0.318900	−	0.981472i
$834$		0			0
$835$	−20.2927			−0.702256
$836$	−7.65090	+	20.5843i	−0.264612	+	0.711921i
$837$		0			0
$838$	2.72306	−	1.97842i	0.0940666	−	0.0683434i
$839$	10.6458	+	32.7643i	0.367533	+	1.13115i	0.948380	+	0.317137i	$0.102722\pi$
$839$	10.6458	+	32.7643i	0.367533	+	1.13115i	−0.580847	+	0.814013i	$0.697278\pi$
$840$		0			0
$841$	23.4570	+	17.0425i	0.808862	+	0.587672i
$842$	−0.554068	−	0.402554i	−0.0190944	−	0.0138729i
$843$		0			0
$844$	−12.8027	−	39.4026i	−0.440687	−	1.35629i
$845$	−36.3859	+	26.4359i	−1.25171	+	0.909424i
$846$		0			0
$847$	−32.0811	+	19.4451i	−1.10232	+	0.668142i
$848$	3.07703			0.105666
$849$		0			0
$850$	−7.19236	−	22.1358i	−0.246696	−	0.759252i
$851$	1.42829	−	4.39582i	0.0489611	−	0.150687i
$852$		0			0
$853$	−32.3254	−	23.4858i	−1.10680	−	0.804139i	−0.124645	−	0.992201i	$-0.539779\pi$
$853$	−32.3254	−	23.4858i	−1.10680	−	0.804139i	−0.982157	+	0.188063i	$0.939779\pi$
$854$	1.92287	−	5.91799i	0.0657993	−	0.202509i
$855$		0			0
$856$	13.2706	−	9.64162i	0.453578	−	0.329544i
$857$	5.82947			0.199131			0.0995654	−	0.995031i	$-0.468255\pi$
$857$	5.82947			0.199131			0.0995654	+	0.995031i	$0.468255\pi$
$858$		0			0
$859$	13.1832			0.449804			0.224902	−	0.974381i	$-0.427794\pi$
$859$	13.1832			0.449804			0.224902	+	0.974381i	$0.427794\pi$
$860$	2.84477	−	2.06684i	0.0970058	−	0.0704788i
$861$		0			0
$862$	3.18535	−	9.80351i	0.108494	−	0.333909i
$863$	−15.5600	−	11.3050i	−0.529668	−	0.384826i	0.290565	−	0.956855i	$-0.406157\pi$
$863$	−15.5600	−	11.3050i	−0.529668	−	0.384826i	−0.820234	+	0.572029i	$0.806157\pi$
$864$		0			0
$865$	−8.14102	+	25.0555i	−0.276803	+	0.851911i
$866$	−2.43068	−	7.48085i	−0.0825977	−	0.254210i
$867$		0			0
$868$	24.2243			0.822227
$869$	9.80872	+	35.1059i	0.332738	+	1.19089i
$870$		0			0
$871$	6.54508	−	4.75528i	0.221772	−	0.161127i
$872$	−3.69752	−	11.3798i	−0.125214	−	0.385369i
$873$		0			0
$874$	−3.33258	−	2.42126i	−0.112726	−	0.0819003i
$875$	72.1316	+	52.4067i	2.43849	+	1.77167i
$876$		0			0
$877$	5.49723	+	16.9187i	0.185628	+	0.571305i	0.999959	−	0.00909649i	$-0.00289554\pi$
$877$	5.49723	+	16.9187i	0.185628	+	0.571305i	−0.814330	+	0.580402i	$0.802896\pi$
$878$	4.51461	−	3.28006i	0.152361	−	0.110697i
$879$		0			0
$880$	45.8309	+	1.91243i	1.54496	+	0.0644681i
$881$	−9.68529			−0.326306			−0.163153	−	0.986601i	$-0.552166\pi$
$881$	−9.68529			−0.326306			−0.163153	+	0.986601i	$0.552166\pi$
$882$		0			0
$883$	−13.4731	−	41.4658i	−0.453404	−	1.39544i	−0.872998	−	0.487723i	$-0.837827\pi$
$883$	−13.4731	−	41.4658i	−0.453404	−	1.39544i	0.419594	−	0.907712i	$-0.362173\pi$
$884$	5.21917	−	16.0629i	0.175540	−	0.540255i
$885$		0			0
$886$	−7.48733	−	5.43986i	−0.251542	−	0.182756i
$887$	−13.8884	+	42.7442i	−0.466328	+	1.43521i	0.390977	+	0.920400i	$0.372137\pi$
$887$	−13.8884	+	42.7442i	−0.466328	+	1.43521i	−0.857305	+	0.514809i	$0.827863\pi$
$888$		0			0
$889$	18.6913	−	13.5801i	0.626888	−	0.455461i
$890$	−13.3021			−0.445886
$891$		0			0
$892$	−24.9261			−0.834589
$893$	6.19049	−	4.49766i	0.207157	−	0.150508i
$894$		0			0
$895$	−15.4024	+	47.4038i	−0.514846	+	1.58453i
$896$	24.5277	+	17.8204i	0.819414	+	0.595339i
$897$		0			0
$898$	−1.44035	+	4.43294i	−0.0480651	+	0.147929i
$899$	−0.0862108	−	0.265330i	−0.00287529	−	0.00884924i
$900$		0			0
$901$	−5.80341			−0.193340
$902$	−8.13699	+	5.40836i	−0.270932	+	0.180079i
$903$		0			0
$904$	5.91998	−	4.30112i	0.196896	−	0.143053i
$905$	7.52896	+	23.1717i	0.250271	+	0.770255i
$906$		0			0
$907$	24.4120	+	17.7364i	0.810589	+	0.588927i	0.914001	−	0.405711i	$-0.132976\pi$
$907$	24.4120	+	17.7364i	0.810589	+	0.588927i	−0.103413	+	0.994639i	$0.532976\pi$
$908$	35.2843	+	25.6356i	1.17095	+	0.850747i
$909$		0			0
$910$	−1.86715	−	5.74650i	−0.0618955	−	0.190495i
$911$	−10.7648	+	7.82112i	−0.356655	+	0.259125i	−0.751656	−	0.659556i	$-0.770744\pi$
$911$	−10.7648	+	7.82112i	−0.356655	+	0.259125i	0.395000	+	0.918681i	$0.370744\pi$
$912$		0			0
$913$	3.77915	−	2.51186i	0.125072	−	0.0831306i
$914$	−3.21068			−0.106200
$915$		0			0
$916$	−14.7017	−	45.2472i	−0.485759	−	1.49501i
$917$	−9.54136	+	29.3653i	−0.315084	+	0.969727i
$918$		0			0
$919$	−31.6854	−	23.0208i	−1.04520	−	0.759385i	−0.0739092	−	0.997265i	$-0.523547\pi$
$919$	−31.6854	−	23.0208i	−1.04520	−	0.759385i	−0.971295	+	0.237880i	$0.923547\pi$
$920$	−5.77755	+	17.7815i	−0.190480	+	0.586238i
$921$		0			0
$922$	−1.06870	+	0.776453i	−0.0351956	+	0.0255711i
$923$	13.0921			0.430931
$924$		0			0
$925$	−14.1487			−0.465208
$926$	2.43168	−	1.76672i	0.0799099	−	0.0580580i
$927$		0			0
$928$	0.0817270	−	0.251530i	0.00268282	−	0.00825687i
$929$	25.9588	+	18.8601i	0.851679	+	0.618781i	0.925609	−	0.378482i	$-0.123554\pi$
$929$	25.9588	+	18.8601i	0.851679	+	0.618781i	−0.0739292	+	0.997263i	$0.523554\pi$
$930$		0			0
$931$	−4.98648	+	15.3468i	−0.163425	+	0.502971i
$932$	−8.94220	−	27.5213i	−0.292911	−	0.901489i
$933$		0			0
$934$	−11.0291			−0.360884
$935$	−86.4389	−	3.60693i	−2.82686	−	0.117959i
$936$		0			0
$937$	4.15646	−	3.01984i	0.135786	−	0.0986540i	−0.517819	−	0.855490i	$-0.673256\pi$
$937$	4.15646	−	3.01984i	0.135786	−	0.0986540i	0.653605	+	0.756836i	$0.273256\pi$
$938$	−1.95032	−	6.00246i	−0.0636801	−	0.195987i
$939$		0			0
$940$	−13.6886	−	9.94539i	−0.446475	−	0.324383i
$941$	−18.2632	−	13.2690i	−0.595364	−	0.432557i	0.248866	−	0.968538i	$-0.419942\pi$
$941$	−18.2632	−	13.2690i	−0.595364	−	0.432557i	−0.844230	+	0.535981i	$0.819942\pi$
$942$		0			0
$943$	10.7679	+	33.1401i	0.350650	+	1.07919i
$944$	−22.1323	+	16.0801i	−0.720345	+	0.523362i
$945$		0			0
$946$	0.128751	+	0.460805i	0.00418604	+	0.0149821i
$947$	−37.5922			−1.22158			−0.610792	−	0.791791i	$-0.709149\pi$
$947$	−37.5922			−1.22158			−0.610792	+	0.791791i	$0.709149\pi$
$948$		0			0
$949$	6.00298	+	18.4753i	0.194865	+	0.599732i
$950$	−3.89663	+	11.9926i	−0.126423	+	0.389091i
$951$		0			0
$952$	−21.8799	−	15.8967i	−0.709131	−	0.515214i
$953$	−13.3423	+	41.0634i	−0.432199	+	1.33017i	0.463730	+	0.885976i	$0.346511\pi$
$953$	−13.3423	+	41.0634i	−0.432199	+	1.33017i	−0.895930	+	0.444196i	$0.853489\pi$
$954$		0			0
$955$	−6.77354	+	4.92127i	−0.219187	+	0.159248i
$956$	47.3902			1.53271
$957$		0			0
$958$	3.35482			0.108389
$959$	−28.1601	+	20.4595i	−0.909336	+	0.660671i
$960$		0			0
$961$	−5.26090	+	16.1914i	−0.169706	+	0.522303i
$962$	0.436876	+	0.317409i	0.0140854	+	0.0102337i
$963$		0			0
$964$	6.58684	−	20.2722i	0.212148	−	0.652924i
$965$	−13.6759	−	42.0901i	−0.440243	−	1.35493i
$966$		0			0
$967$	−19.4808			−0.626460			−0.313230	−	0.949677i	$-0.601411\pi$
$967$	−19.4808			−0.626460			−0.313230	+	0.949677i	$0.601411\pi$
$968$	−5.25090	+	12.5043i	−0.168770	+	0.401903i
$969$		0			0
$970$	−8.55357	+	6.21453i	−0.274639	+	0.199537i
$971$	−13.1483	−	40.4662i	−0.421948	−	1.29862i	−0.905887	−	0.423520i	$-0.860794\pi$
$971$	−13.1483	−	40.4662i	−0.421948	−	1.29862i	0.483939	−	0.875102i	$-0.339206\pi$
$972$		0			0
$973$	−19.5052	−	14.1714i	−0.625309	−	0.454314i
$974$	8.66578	+	6.29606i	0.277670	+	0.201739i
$975$		0			0
$976$	6.08260	+	18.7203i	0.194699	+	0.599223i
$977$	32.4439	−	23.5719i	1.03797	−	0.754132i	0.0680848	−	0.997680i	$-0.478311\pi$
$977$	32.4439	−	23.5719i	1.03797	−	0.754132i	0.969889	+	0.243547i	$0.0783112\pi$
$978$		0			0
$979$	−11.9893	+	32.2565i	−0.383180	+	1.03092i
$980$	35.6818			1.13981
$981$		0			0
$982$	1.70854	+	5.25834i	0.0545217	+	0.167800i
$983$	−0.673401	+	2.07252i	−0.0214782	+	0.0661030i	−0.961221	−	0.275779i	$-0.911064\pi$
$983$	−0.673401	+	2.07252i	−0.0214782	+	0.0661030i	0.939743	+	0.341882i	$0.111064\pi$
$984$		0			0
$985$	−66.9912	−	48.6719i	−2.13452	−	1.55082i
$986$	−0.0468915	+	0.144317i	−0.00149333	+	0.00459599i
$987$		0			0
$988$	−7.40276	+	5.37842i	−0.235513	+	0.171110i
$989$	1.70638			0.0542596
$990$		0			0
$991$	−7.93293			−0.251998			−0.125999	−	0.992030i	$-0.540214\pi$
$991$	−7.93293			−0.251998			−0.125999	+	0.992030i	$0.540214\pi$
$992$	10.7183	−	7.78728i	0.340306	−	0.247246i
$993$		0			0
$994$	3.15614	−	9.71359i	0.100107	−	0.308096i
$995$	18.2758	+	13.2781i	0.579380	+	0.420944i
$996$		0			0
$997$	0.623596	−	1.91923i	0.0197495	−	0.0607826i	−0.940696	−	0.339251i	$-0.889827\pi$
$997$	0.623596	−	1.91923i	0.0197495	−	0.0607826i	0.960446	+	0.278468i	$0.0898266\pi$
$998$	−0.577612	−	1.77771i	−0.0182840	−	0.0562724i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.b.190.2	yes	16
3.2	odd	2	inner	297.2.f.b.190.3	yes	16
9.2	odd	6		891.2.n.h.190.2		32
9.4	even	3		891.2.n.h.784.2		32
9.5	odd	6		891.2.n.h.784.3		32
9.7	even	3		891.2.n.h.190.3		32
11.2	odd	10		3267.2.a.bi.1.4		8
11.4	even	5	inner	297.2.f.b.136.2	✓	16
11.9	even	5		3267.2.a.bj.1.5		8
33.2	even	10		3267.2.a.bi.1.5		8
33.20	odd	10		3267.2.a.bj.1.4		8
33.26	odd	10	inner	297.2.f.b.136.3	yes	16
99.4	even	15		891.2.n.h.136.3		32
99.59	odd	30		891.2.n.h.136.2		32
99.70	even	15		891.2.n.h.433.2		32
99.92	odd	30		891.2.n.h.433.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.136.2	✓	16	11.4	even	5	inner
297.2.f.b.136.3	yes	16	33.26	odd	10	inner
297.2.f.b.190.2	yes	16	1.1	even	1	trivial
297.2.f.b.190.3	yes	16	3.2	odd	2	inner
891.2.n.h.136.2		32	99.59	odd	30
891.2.n.h.136.3		32	99.4	even	15
891.2.n.h.190.2		32	9.2	odd	6
891.2.n.h.190.3		32	9.7	even	3
891.2.n.h.433.2		32	99.70	even	15
891.2.n.h.433.3		32	99.92	odd	30
891.2.n.h.784.2		32	9.4	even	3
891.2.n.h.784.3		32	9.5	odd	6
3267.2.a.bi.1.4		8	11.2	odd	10
3267.2.a.bi.1.5		8	33.2	even	10
3267.2.a.bj.1.4		8	33.20	odd	10
3267.2.a.bj.1.5		8	11.9	even	5

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	297.2.f.b.190.2

Level	$297$
Weight	$2$
Character	297.190
Analytic conductor	$2.372$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$