LMFDB - Embedded newform 637.2.h.l.471.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$637 = 7^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	637.h (of order $3$ , degree $2$ , not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1$ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.3
Root			$0.756174 + 1.30973i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.l.165.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.851125 q^{2} +(0.330612 - 0.572636i) q^{3} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 + 2.21944i) q^{9} +(-1.46456 + 2.53670i) q^{10} +(0.448993 - 0.777679i) q^{11} +(-0.421723 + 0.730446i) q^{12} +(3.07517 - 1.88237i) q^{13} +(-1.13779 - 1.97071i) q^{15} +0.178289 q^{16} -1.93681 q^{17} +(-1.09063 - 1.88902i) q^{18} +(0.519020 + 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +5.65013 q^{23} +(0.921723 - 1.59647i) q^{24} +(-3.42189 - 5.92688i) q^{25} +(-2.61736 + 1.60213i) q^{26} +3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} +(0.968404 + 1.67733i) q^{30} +(-4.56692 - 7.91014i) q^{31} -5.72761 q^{32} +(-0.296885 - 0.514219i) q^{33} +1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} -10.6000 q^{37} +(-0.441751 - 0.765135i) q^{38} +(-0.0612242 - 2.38329i) q^{39} +(4.79731 - 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +8.81977 q^{45} -4.80897 q^{46} +(3.59565 - 6.22784i) q^{47} +(0.0589445 - 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(-3.92265 + 2.40112i) q^{52} +(4.69324 + 8.12893i) q^{53} -3.13065 q^{54} +(-1.54520 - 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 - 1.35326i) q^{58} +0.510517 q^{59} +(1.45135 + 2.51382i) q^{60} +(0.718095 + 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(-0.318655 - 12.4043i) q^{65} +(0.252686 + 0.437665i) q^{66} +(4.22466 - 7.31732i) q^{67} +2.47057 q^{68} +(1.86800 - 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} +(3.57244 + 6.18764i) q^{72} +(5.45026 + 9.44013i) q^{73} +9.02195 q^{74} -4.52526 q^{75} +(-0.662054 - 1.14671i) q^{76} +(0.0521095 + 2.02848i) q^{78} +(6.04589 - 10.4718i) q^{79} +(0.306789 - 0.531375i) q^{80} +(-2.62811 + 4.55201i) q^{81} +(2.26886 + 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +1.21396 q^{87} +(1.25176 - 2.16812i) q^{88} -13.6078 q^{89} -7.50673 q^{90} -7.20722 q^{92} -6.03951 q^{93} +(-3.06035 + 5.30067i) q^{94} +3.57239 q^{95} +(-1.89362 + 3.27984i) q^{96} +(0.253120 - 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23}+ \cdots - 20 q^{99}+O(q^{100})$ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$ .

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.851125			−0.601837			−0.300918	−	0.953650i	$-0.597293\pi$
$2$	−0.851125			−0.601837			−0.300918	+	0.953650i	$0.597293\pi$
$3$	0.330612	−	0.572636i	0.190879	−	0.330612i	−0.754663	−	0.656113i	$-0.772200\pi$
$3$	0.330612	−	0.572636i	0.190879	−	0.330612i	0.945542	+	0.325501i	$0.105533\pi$
$4$	−1.27559			−0.637793
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	−0.168276	−	0.985740i	$-0.553820\pi$
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	0.937814	−	0.347139i	$-0.112847\pi$
$6$	−0.281392	+	0.487385i	−0.114878	+	0.198974i
$7$		0			0
$7$		0			0
$8$	2.78793			0.985684
$9$	1.28139	+	2.21944i	0.427131	+	0.739812i
$10$	−1.46456	+	2.53670i	−0.463136	+	0.802175i
$11$	0.448993	−	0.777679i	0.135377	−	0.234479i	−0.790365	−	0.612637i	$-0.790109\pi$
$11$	0.448993	−	0.777679i	0.135377	−	0.234479i	0.925741	+	0.378158i	$0.123442\pi$
$12$	−0.421723	+	0.730446i	−0.121741	+	0.210862i
$13$	3.07517	−	1.88237i	0.852900	−	0.522075i
$13$	3.07517	−	1.88237i	0.852900	−	0.522075i
$14$		0			0
$15$	−1.13779	−	1.97071i	−0.293777	−	0.508836i
$16$	0.178289			0.0445723
$17$	−1.93681			−0.469745			−0.234873	−	0.972026i	$-0.575467\pi$
$17$	−1.93681			−0.469745			−0.234873	+	0.972026i	$0.575467\pi$
$18$	−1.09063	−	1.88902i	−0.257063	−	0.445246i
$19$	0.519020	+	0.898968i	0.119071	+	0.206237i	0.919400	−	0.393324i	$-0.128675\pi$
$19$	0.519020	+	0.898968i	0.119071	+	0.206237i	−0.800329	+	0.599562i	$0.795342\pi$
$20$	−2.19495	+	3.80177i	−0.490806	+	0.850101i
$21$		0			0
$22$	−0.382150	+	0.661902i	−0.0814745	+	0.141118i
$23$	5.65013			1.17813			0.589067	−	0.808084i	$-0.299496\pi$
$23$	5.65013			1.17813			0.589067	+	0.808084i	$0.299496\pi$
$24$	0.921723	−	1.59647i	0.188146	−	0.325878i
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$	−2.61736	+	1.60213i	−0.513306	+	0.314204i
$27$	3.67824			0.707878
$28$		0			0
$29$	0.917969	+	1.58997i	0.170463	+	0.295250i	0.938582	−	0.345057i	$-0.112140\pi$
$29$	0.917969	+	1.58997i	0.170463	+	0.295250i	−0.768119	+	0.640307i	$0.778807\pi$
$30$	0.968404	+	1.67733i	0.176806	+	0.306236i
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	−0.905501	−	0.424345i	$-0.860505\pi$
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	0.0852573	−	0.996359i	$-0.472829\pi$
$32$	−5.72761			−1.01251
$33$	−0.296885	−	0.514219i	−0.0516810	−	0.0895141i
$34$	1.64847			0.282710
$35$		0			0
$36$	−1.63452	−	2.83108i	−0.272421	−	0.471847i
$37$	−10.6000			−1.74263			−0.871316	−	0.490722i	$-0.836733\pi$
$37$	−10.6000			−1.74263			−0.871316	+	0.490722i	$0.836733\pi$
$38$	−0.441751	−	0.765135i	−0.0716614	−	0.124121i
$39$	−0.0612242	−	2.38329i	−0.00980372	−	0.381631i
$40$	4.79731	−	8.30918i	0.758521	−	1.31380i
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	0.579251	−	0.815149i	$-0.303345\pi$
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	−0.995565	+	0.0940715i	$0.970012\pi$
$42$		0			0
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	−0.677302	−	0.735706i	$-0.736851\pi$
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	0.975790	+	0.218708i	$0.0701841\pi$
$44$	−0.572729	+	0.991996i	−0.0863422	+	0.149549i
$45$	8.81977			1.31477
$46$	−4.80897			−0.709044
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	−0.475115	−	0.879924i	$-0.657593\pi$
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	0.999594	−	0.0285004i	$-0.00907317\pi$
$48$	0.0589445	−	0.102095i	0.00850791	−	0.0147361i
$49$		0			0
$50$	2.91246	+	5.04452i	0.411883	+	0.713403i
$51$	−0.640331	+	1.10909i	−0.0896643	+	0.155303i
$52$	−3.92265	+	2.40112i	−0.543973	+	0.332976i
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	0.984378	+	0.176065i	$0.0563370\pi$
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	−0.339712	+	0.940529i	$0.610330\pi$
$54$	−3.13065			−0.426027
$55$	−1.54520	−	2.67637i	−0.208355	−	0.360881i
$56$		0			0
$57$	0.686375			0.0909127
$58$	−0.781307	−	1.35326i	−0.102591	−	0.177692i
$59$	0.510517			0.0664637			0.0332318	−	0.999448i	$-0.489420\pi$
$59$	0.510517			0.0664637			0.0332318	+	0.999448i	$0.489420\pi$
$60$	1.45135	+	2.51382i	0.187369	+	0.324532i
$61$	0.718095	+	1.24378i	0.0919426	+	0.159249i	0.908328	−	0.418258i	$-0.137359\pi$
$61$	0.718095	+	1.24378i	0.0919426	+	0.159249i	−0.816386	+	0.577507i	$0.804026\pi$
$62$	3.88702	+	6.73252i	0.493653	+	0.855031i
$63$		0			0
$64$	4.51834			0.564792
$65$	−0.318655	−	12.4043i	−0.0395242	−	1.53857i
$66$	0.252686	+	0.437665i	0.0311035	+	0.0538729i
$67$	4.22466	−	7.31732i	0.516124	−	0.893953i	−0.483701	−	0.875233i	$-0.660708\pi$
$67$	4.22466	−	7.31732i	0.516124	−	0.893953i	0.999825	−	0.0187197i	$-0.00595900\pi$
$68$	2.47057			0.299600
$69$	1.86800	−	3.23547i	0.224881	−	0.389504i
$70$		0			0
$71$	1.72419	−	2.98638i	0.204623	−	0.354418i	−0.745389	−	0.666629i	$-0.767736\pi$
$71$	1.72419	−	2.98638i	0.204623	−	0.354418i	0.950013	+	0.312211i	$0.101070\pi$
$72$	3.57244	+	6.18764i	0.421016	+	0.729221i
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	0.985892	+	0.167384i	$0.0535320\pi$
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	−0.347987	+	0.937499i	$0.613135\pi$
$74$	9.02195			1.04878
$75$	−4.52526			−0.522532
$76$	−0.662054	−	1.14671i	−0.0759428	−	0.131537i
$77$		0			0
$78$	0.0521095	+	2.02848i	0.00590024	+	0.229680i
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	0.306789	−	0.531375i	0.0343001	−	0.0594095i
$81$	−2.62811	+	4.55201i	−0.292012	+	0.505779i
$82$	2.26886	+	3.92977i	0.250553	+	0.433971i
$83$	−1.51669			−0.166479			−0.0832393	−	0.996530i	$-0.526527\pi$
$83$	−1.51669			−0.166479			−0.0832393	+	0.996530i	$0.526527\pi$
$84$		0			0
$85$	−3.33274	+	5.77248i	−0.361487	+	0.626113i
$86$	−1.66593	+	2.88547i	−0.179642	+	0.311148i
$87$	1.21396			0.130151
$88$	1.25176	−	2.16812i	0.133438	−	0.231122i
$89$	−13.6078			−1.44243			−0.721213	−	0.692714i	$-0.756415\pi$
$89$	−13.6078			−1.44243			−0.721213	+	0.692714i	$0.756415\pi$
$90$	−7.50673			−0.791279
$91$		0			0
$92$	−7.20722			−0.751405
$93$	−6.03951			−0.626268
$94$	−3.06035	+	5.30067i	−0.315651	+	0.546723i
$95$	3.57239			0.366519
$96$	−1.89362	+	3.27984i	−0.193266	+	0.334747i
$97$	0.253120	−	0.438417i	0.0257005	−	0.0445145i	−0.852889	−	0.522092i	$-0.825152\pi$
$97$	0.253120	−	0.438417i	0.0257005	−	0.0445145i	0.878590	+	0.477578i	$0.158485\pi$
$98$		0			0
$99$	2.30134			0.231294
$100$	4.36491	+	7.56025i	0.436491	+	0.756025i
$101$	−2.99327	+	5.18450i	−0.297842	+	0.515877i	−0.975642	−	0.219369i	$-0.929600\pi$
$101$	−2.99327	+	5.18450i	−0.297842	+	0.515877i	0.677800	+	0.735246i	$0.262933\pi$
$102$	0.545002	−	0.943972i	0.0539633	−	0.0934671i
$103$	−2.06651	+	3.57930i	−0.203619	+	0.352679i	−0.949692	−	0.313186i	$-0.898604\pi$
$103$	−2.06651	+	3.57930i	−0.203619	+	0.352679i	0.746073	+	0.665865i	$0.231937\pi$
$104$	8.57338	−	5.24792i	0.840689	−	0.514601i
$105$		0			0
$106$	−3.99454	−	6.91874i	−0.387984	−	0.672008i
$107$	−14.1234			−1.36536			−0.682679	−	0.730718i	$-0.739185\pi$
$107$	−14.1234			−1.36536			−0.682679	+	0.730718i	$0.739185\pi$
$108$	−4.69191			−0.451479
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	0.948934	−	0.315475i	$-0.102164\pi$
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	−0.747677	+	0.664063i	$0.768831\pi$
$110$	1.31516	+	2.27792i	0.125396	+	0.217191i
$111$	−3.50449	+	6.06995i	−0.332631	+	0.576135i
$112$		0			0
$113$	−6.88472	+	11.9247i	−0.647660	+	1.12178i	0.336020	+	0.941855i	$0.390919\pi$
$113$	−6.88472	+	11.9247i	−0.647660	+	1.12178i	−0.983680	+	0.179926i	$0.942414\pi$
$114$	−0.584192			−0.0547146
$115$	9.72240	−	16.8397i	0.906618	−	1.57031i
$116$	−1.17095	−	2.02814i	−0.108720	−	0.188308i
$117$	8.11830	+	4.41310i	0.750537	+	0.407991i
$118$	−0.434514			−0.0400003
$119$		0			0
$120$	−3.17209	−	5.49422i	−0.289571	−	0.501552i
$121$	5.09681	+	8.82793i	0.463346	+	0.802539i
$122$	−0.611189	−	1.05861i	−0.0553344	−	0.0958420i
$123$	−3.52526			−0.317862
$124$	5.82550	+	10.0901i	0.523145	+	0.906114i
$125$	−6.34531			−0.567542
$126$		0			0
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	0.819648	−	0.572868i	$-0.194169\pi$
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	−0.905942	+	0.423402i	$0.860836\pi$
$128$	7.60956			0.672596
$129$	−1.29423	−	2.24167i	−0.113950	−	0.197368i
$130$	0.271215	+	10.5576i	0.0237871	+	0.925967i
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	0.473780	+	0.880643i	$0.342889\pi$
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	−0.999549	+	0.0300158i	$0.990444\pi$
$132$	0.378702	+	0.655931i	0.0329618	+	0.0570914i
$133$		0			0
$134$	−3.59571	+	6.22796i	−0.310622	+	0.538014i
$135$	6.32930	−	10.9627i	0.544739	−	0.943516i
$136$	−5.39970			−0.463020
$137$	8.71715			0.744756			0.372378	−	0.928081i	$-0.378543\pi$
$137$	8.71715			0.744756			0.372378	+	0.928081i	$0.378543\pi$
$138$	−1.58990	+	2.75379i	−0.135341	+	0.234418i
$139$	2.10625	−	3.64813i	0.178650	−	0.309430i	−0.762769	−	0.646672i	$-0.776160\pi$
$139$	2.10625	−	3.64813i	0.178650	−	0.309430i	0.941418	+	0.337241i	$0.109494\pi$
$140$		0			0
$141$	−2.37752	−	4.11799i	−0.200224	−	0.346798i
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$	−0.0831467	−	3.23667i	−0.00695307	−	0.270664i
$144$	0.228459	+	0.395702i	0.0190382	+	0.0329751i
$145$	6.31834			0.524710
$146$	−4.63885	−	8.03473i	−0.383914	−	0.664959i
$147$		0			0
$148$	13.5212			1.11144
$149$	−2.93242	−	5.07910i	−0.240233	−	0.416096i	0.720548	−	0.693406i	$-0.243891\pi$
$149$	−2.93242	−	5.07910i	−0.240233	−	0.416096i	−0.960781	+	0.277310i	$0.910557\pi$
$150$	3.85157			0.314479
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	0.973155	+	0.230150i	$0.0739216\pi$
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	−0.287262	+	0.957852i	$0.592745\pi$
$152$	1.44699	+	2.50626i	0.117367	+	0.203285i
$153$	−2.48181	−	4.29862i	−0.200643	−	0.347523i
$154$		0			0
$155$	−31.4339			−2.52483
$156$	0.0780967	+	3.04009i	0.00625274	+	0.243402i
$157$	−0.969500	−	1.67922i	−0.0773746	−	0.134017i	0.824742	−	0.565509i	$-0.191320\pi$
$157$	−0.969500	−	1.67922i	−0.0773746	−	0.134017i	−0.902116	+	0.431493i	$0.857987\pi$
$158$	−5.14581	+	8.91280i	−0.409379	+	0.709065i
$159$	6.20656			0.492212
$160$	−9.85573	+	17.0706i	−0.779164	+	1.34955i
$161$		0			0
$162$	2.23685	−	3.87433i	0.175743	−	0.304396i
$163$	5.94797	+	10.3022i	0.465881	+	0.806929i	0.999241	−	0.0389590i	$-0.0124042\pi$
$163$	5.94797	+	10.3022i	0.465881	+	0.806929i	−0.533360	+	0.845888i	$0.679071\pi$
$164$	3.40035	+	5.88957i	0.265522	+	0.459898i
$165$	−2.04344			−0.159082
$166$	1.29090			0.100193
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	0.985133	+	0.171796i	$0.0549569\pi$
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	−0.343787	+	0.939048i	$0.611710\pi$
$168$		0			0
$169$	5.91338	−	11.5772i	0.454875	−	0.890555i
$170$	2.83658	−	4.91310i	0.217556	−	0.376818i
$171$	−1.33013	+	2.30386i	−0.101718	+	0.176181i
$172$	−2.49673	+	4.32447i	−0.190374	+	0.329738i
$173$	−4.99328	−	8.64862i	−0.379632	−	0.657542i	0.611377	−	0.791340i	$-0.290616\pi$
$173$	−4.99328	−	8.64862i	−0.379632	−	0.657542i	−0.991009	+	0.133798i	$0.957283\pi$
$174$	−1.03324			−0.0783295
$175$		0			0
$176$	0.0800507	−	0.138652i	0.00603405	−	0.0104513i
$177$	0.168783	−	0.292341i	0.0126865	−	0.0219737i
$178$	11.5820			0.868105
$179$	−4.58829	+	7.94715i	−0.342945	+	0.593998i	−0.984978	−	0.172679i	$-0.944758\pi$
$179$	−4.58829	+	7.94715i	−0.342945	+	0.593998i	0.642033	+	0.766677i	$0.278091\pi$
$180$	−11.2504			−0.838553
$181$	−6.00489			−0.446340			−0.223170	−	0.974780i	$-0.571640\pi$
$181$	−6.00489			−0.446340			−0.223170	+	0.974780i	$0.571640\pi$
$182$		0			0
$183$	0.949642			0.0701995
$184$	15.7522			1.16127
$185$	−18.2399	+	31.5924i	−1.34102	+	2.32272i
$186$	5.14038			0.376911
$187$	−0.869614	+	1.50622i	−0.0635925	+	0.110145i
$188$	−4.58655	+	7.94415i	−0.334509	+	0.579386i
$189$		0			0
$190$	−3.04055			−0.220585
$191$	−0.658061	−	1.13980i	−0.0476156	−	0.0824727i	0.841235	−	0.540669i	$-0.181829\pi$
$191$	−0.658061	−	1.13980i	−0.0476156	−	0.0824727i	−0.888851	+	0.458197i	$0.848496\pi$
$192$	1.49382	−	2.58736i	0.107807	−	0.186727i
$193$	8.21270	−	14.2248i	0.591163	−	1.02392i	−0.402913	−	0.915238i	$-0.632002\pi$
$193$	8.21270	−	14.2248i	0.591163	−	1.02392i	0.994076	−	0.108686i	$-0.0346643\pi$
$194$	−0.215437	+	0.373148i	−0.0154675	+	0.0267905i
$195$	−7.20852	−	3.91854i	−0.516213	−	0.280613i
$196$		0			0
$197$	12.7938	+	22.1594i	0.911517	+	1.57879i	0.811922	+	0.583766i	$0.198421\pi$
$197$	12.7938	+	22.1594i	0.911517	+	1.57879i	0.0995951	+	0.995028i	$0.468245\pi$
$198$	−1.95873			−0.139201
$199$	25.3788			1.79906			0.899528	−	0.436864i	$-0.143911\pi$
$199$	25.3788			1.79906			0.899528	+	0.436864i	$0.143911\pi$
$200$	−9.54000	−	16.5238i	−0.674580	−	1.16841i
$201$	−2.79344	−	4.83838i	−0.197034	−	0.341273i
$202$	2.54765	−	4.41266i	0.179252	−	0.310473i
$203$		0			0
$204$	0.816797	−	1.41473i	0.0571873	−	0.0990512i
$205$	−18.3480			−1.28148
$206$	1.75886	−	3.04643i	0.122546	−	0.212255i
$207$	7.24003	+	12.5401i	0.503217	+	0.871597i
$208$	0.548271	−	0.335606i	0.0380157	−	0.0232701i
$209$	0.932145			0.0644778
$210$		0			0
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	0.947254	−	0.320483i	$-0.103845\pi$
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	−0.751173	+	0.660105i	$0.770512\pi$
$212$	−5.98663	−	10.3691i	−0.411164	−	0.712156i
$213$	−1.14007	−	1.97466i	−0.0781165	−	0.135302i
$214$	12.0208			0.821723
$215$	−6.73608	−	11.6672i	−0.459397	−	0.795699i
$216$	10.2547			0.697744
$217$		0			0
$218$	−1.78837	−	3.09755i	−0.121124	−	0.209793i
$219$	7.20768			0.487050
$220$	1.97104	+	3.41393i	0.132887	+	0.230167i
$221$	−5.95602	+	3.64579i	−0.400645	+	0.245242i
$222$	2.98276	−	5.16629i	0.200190	−	0.346739i
$223$	1.17906	+	2.04219i	0.0789558	+	0.136755i	0.902800	−	0.430061i	$-0.141508\pi$
$223$	1.17906	+	2.04219i	0.0789558	+	0.136755i	−0.823844	+	0.566817i	$0.808175\pi$
$224$		0			0
$225$	8.76956	−	15.1893i	0.584637	−	1.01262i
$226$	5.85976	−	10.1494i	0.389786	−	0.675129i
$227$	−26.2926			−1.74510			−0.872551	−	0.488523i	$-0.837536\pi$
$227$	−26.2926			−1.74510			−0.872551	+	0.488523i	$0.837536\pi$
$228$	−0.875531			−0.0579834
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	−0.864891	−	0.501960i	$-0.832612\pi$
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	0.867156	+	0.498037i	$0.165946\pi$
$230$	−8.27498	+	14.3327i	−0.545636	+	0.945069i
$231$		0			0
$232$	2.55924	+	4.43273i	0.168022	+	0.291023i
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	−0.999751	−	0.0223253i	$-0.992893\pi$
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	0.519210	+	0.854647i	$0.326226\pi$
$234$	−6.90969	−	3.75610i	−0.451701	−	0.245544i
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	−0.651208			−0.0423901
$237$	−3.99768	−	6.92419i	−0.259677	−	0.449774i
$238$		0			0
$239$	3.35434			0.216974			0.108487	−	0.994098i	$-0.465399\pi$
$239$	3.35434			0.216974			0.108487	+	0.994098i	$0.465399\pi$
$240$	−0.202856	−	0.351357i	−0.0130943	−	0.0226800i
$241$	8.57978			0.552672			0.276336	−	0.961061i	$-0.410880\pi$
$241$	8.57978			0.552672			0.276336	+	0.961061i	$0.410880\pi$
$242$	−4.33802	−	7.51368i	−0.278859	−	0.482998i
$243$	7.25513	+	12.5662i	0.465417	+	0.806125i
$244$	−0.915991	−	1.58654i	−0.0586403	−	0.101568i
$245$		0			0
$246$	3.00044			0.191301
$247$	3.28826	+	1.78750i	0.209227	+	0.113736i
$248$	−12.7323	−	22.0530i	−0.808501	−	1.40036i
$249$	−0.501436	+	0.868513i	−0.0317772	+	0.0550398i
$250$	5.40066			0.341568
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	−0.296270	−	0.955104i	$-0.595743\pi$
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	0.975280	−	0.220975i	$-0.0709238\pi$
$252$		0			0
$253$	2.53687	−	4.39399i	0.159492	−	0.276248i
$254$	0.827704	+	1.43363i	0.0519348	+	0.0899537i
$255$	2.20369	+	3.81690i	0.138000	+	0.239023i
$256$	−15.5134			−0.969585
$257$	−4.93792			−0.308019			−0.154010	−	0.988069i	$-0.549219\pi$
$257$	−4.93792			−0.308019			−0.154010	+	0.988069i	$0.549219\pi$
$258$	1.10155	+	1.90794i	0.0685795	+	0.118783i
$259$		0			0
$260$	0.406471	+	15.8228i	0.0252083	+	0.981288i
$261$	−2.35256	+	4.07475i	−0.145620	+	0.252221i
$262$	5.12182	−	8.87125i	0.316427	−	0.548068i
$263$	4.47719	−	7.75473i	0.276076	−	0.478177i	−0.694330	−	0.719656i	$-0.744299\pi$
$263$	4.47719	−	7.75473i	0.276076	−	0.478177i	0.970406	+	0.241480i	$0.0776327\pi$
$264$	−0.827695	−	1.43361i	−0.0509411	−	0.0882326i
$265$	32.3034			1.98438
$266$		0			0
$267$	−4.49890	+	7.79233i	−0.275328	+	0.476883i
$268$	−5.38891	+	9.33387i	−0.329180	+	0.570157i
$269$	4.82345			0.294091			0.147045	−	0.989130i	$-0.453024\pi$
$269$	4.82345			0.294091			0.147045	+	0.989130i	$0.453024\pi$
$270$	−5.38702	+	9.33060i	−0.327844	+	0.567842i
$271$	7.42144			0.450820			0.225410	−	0.974264i	$-0.427628\pi$
$271$	7.42144			0.450820			0.225410	+	0.974264i	$0.427628\pi$
$272$	−0.345312			−0.0209376
$273$		0			0
$274$	−7.41938			−0.448221
$275$	−6.14562			−0.370595
$276$	−2.38279	+	4.12712i	−0.143427	+	0.248423i
$277$	3.81631			0.229300			0.114650	−	0.993406i	$-0.463425\pi$
$277$	3.81631			0.229300			0.114650	+	0.993406i	$0.463425\pi$
$278$	−1.79268	+	3.10502i	−0.107518	+	0.186226i
$279$	11.7040	−	20.2720i	0.700702	−	1.21365i
$280$		0			0
$281$	8.54978			0.510037			0.255019	−	0.966936i	$-0.417918\pi$
$281$	8.54978			0.510037			0.255019	+	0.966936i	$0.417918\pi$
$282$	2.02357	+	3.50493i	0.120502	+	0.208715i
$283$	7.63217	−	13.2193i	0.453686	−	0.785807i	−0.544926	−	0.838484i	$-0.683442\pi$
$283$	7.63217	−	13.2193i	0.453686	−	0.785807i	0.998612	+	0.0526775i	$0.0167755\pi$
$284$	−2.19935	+	3.80938i	−0.130507	+	0.226045i
$285$	1.18107	−	2.04568i	0.0699607	−	0.121176i
$286$	0.0707683	+	2.75481i	0.00418461	+	0.162895i
$287$		0			0
$288$	−7.33932	−	12.7121i	−0.432474	−	0.749066i
$289$	−13.2488			−0.779340
$290$	−5.37770			−0.315790
$291$	−0.167369	−	0.289892i	−0.00981135	−	0.0169938i
$292$	−6.95227	−	12.0417i	−0.406851	−	0.704687i
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	−0.939641	−	0.342163i	$-0.888841\pi$
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	0.766142	+	0.642671i	$0.222174\pi$
$294$		0			0
$295$	0.878467	−	1.52155i	0.0511463	−	0.0885881i
$296$	−29.5522			−1.71768
$297$	1.65151	−	2.86049i	0.0958301	−	0.165983i
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$	17.3751	−	10.6356i	1.00483	−	0.615074i
$300$	5.77236			0.333267
$301$		0			0
$302$	−7.17362	−	12.4251i	−0.412796	−	0.714983i
$303$	1.97922	+	3.42811i	0.113703	+	0.196940i
$304$	0.0925356	+	0.160276i	0.00530728	+	0.00919248i
$305$	4.94262			0.283013
$306$	2.11233	+	3.65867i	0.120754	+	0.209152i
$307$	−22.2133			−1.26778			−0.633891	−	0.773422i	$-0.718543\pi$
$307$	−22.2133			−1.26778			−0.633891	+	0.773422i	$0.718543\pi$
$308$		0			0
$309$	1.36642	+	2.36672i	0.0777332	+	0.134638i
$310$	26.7542			1.51954
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	0.971152	−	0.238463i	$-0.0766435\pi$
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$312$	−0.170689	−	6.64445i	−0.00966337	−	0.376168i
$313$	−10.4563	+	18.1108i	−0.591023	+	1.02368i	0.403072	+	0.915168i	$0.367942\pi$
$313$	−10.4563	+	18.1108i	−0.591023	+	1.02368i	−0.994095	+	0.108513i	$0.965391\pi$
$314$	0.825166	+	1.42923i	0.0465668	+	0.0806561i
$315$		0			0
$316$	−7.71205	+	13.3577i	−0.433837	+	0.751427i
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	−0.251847	−	0.967767i	$-0.581038\pi$
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	0.964034	−	0.265778i	$-0.0856288\pi$
$318$	−5.28256			−0.296231
$319$	1.64865			0.0923065
$320$	7.77489	−	13.4665i	0.434629	−	0.752800i
$321$	−4.66935	+	8.08755i	−0.260618	+	0.451403i
$322$		0			0
$323$	−1.00524	−	1.74113i	−0.0559331	−	0.0968790i
$324$	3.35237	−	5.80648i	0.186243	−	0.322582i
$325$	−21.6795	−	11.7849i	−1.20256	−	0.653711i
$326$	−5.06247	−	8.76845i	−0.280384	−	0.485640i
$327$	2.77871			0.153663
$328$	−7.43183	−	12.8723i	−0.410354	−	0.710755i
$329$		0			0
$330$	1.73923			0.0957413
$331$	−0.891417	−	1.54398i	−0.0489967	−	0.0848648i	0.840487	−	0.541832i	$-0.182269\pi$
$331$	−0.891417	−	1.54398i	−0.0489967	−	0.0848648i	−0.889484	+	0.456967i	$0.848936\pi$
$332$	1.93467			0.106179
$333$	−13.5828	−	23.5261i	−0.744332	−	1.28922i
$334$	−7.05414	−	12.2181i	−0.385985	−	0.668546i
$335$	−14.5391	−	25.1824i	−0.794354	−	1.37586i
$336$		0			0
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	−5.03303	+	9.85366i	−0.273761	+	0.535969i
$339$	4.55234	+	7.88488i	0.247249	+	0.428248i
$340$	4.25120	−	7.36329i	0.230554	−	0.399331i
$341$	−8.20207			−0.444167
$342$	1.13211	−	1.96087i	0.0612176	−	0.106032i
$343$		0			0
$344$	5.45689	−	9.45160i	0.294216	−	0.509596i
$345$	−6.42867	−	11.1348i	−0.346108	−	0.599477i
$346$	4.24991	+	7.36106i	0.228477	+	0.395733i
$347$	0.633389			0.0340021			0.0170010	−	0.999855i	$-0.494588\pi$
$347$	0.633389			0.0340021			0.0170010	+	0.999855i	$0.494588\pi$
$348$	−1.54852			−0.0830092
$349$	15.2994	+	26.4994i	0.818960	+	1.41848i	0.906449	+	0.422315i	$0.138783\pi$
$349$	15.2994	+	26.4994i	0.818960	+	1.41848i	−0.0874885	+	0.996166i	$0.527884\pi$
$350$		0			0
$351$	11.3112	−	6.92381i	0.603749	−	0.369565i
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	−0.550173	+	0.952928i	−0.0292828	+	0.0507192i	−0.880295	−	0.474426i	$-0.842656\pi$
$353$	−0.550173	+	0.952928i	−0.0292828	+	0.0507192i	0.851013	+	0.525145i	$0.175989\pi$
$354$	−0.143655	+	0.248819i	−0.00763520	+	0.0132246i
$355$	−5.93375	−	10.2776i	−0.314931	−	0.545476i
$356$	17.3579			0.919969
$357$		0			0
$358$	3.90521	−	6.76402i	0.206397	−	0.357489i
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	−0.707763	−	0.706450i	$-0.750295\pi$
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	0.965685	+	0.259716i	$0.0836288\pi$
$360$	24.5889			1.29595
$361$	8.96124	−	15.5213i	0.471644	−	0.816912i
$362$	5.11091			0.268624
$363$	6.74026			0.353772
$364$		0			0
$365$	37.5139			1.96357
$366$	−0.808264			−0.0422487
$367$	−5.57363	+	9.65381i	−0.290941	+	0.503925i	−0.974033	−	0.226408i	$-0.927302\pi$
$367$	−5.57363	+	9.65381i	−0.290941	+	0.503925i	0.683092	+	0.730333i	$0.260635\pi$
$368$	1.00736			0.0525121
$369$	6.83165	−	11.8328i	0.355641	−	0.615989i
$370$	15.5244	−	26.8891i	0.807076	−	1.39790i
$371$		0			0
$372$	7.70391			0.399429
$373$	15.3651	+	26.6131i	0.795573	+	1.37797i	0.922475	+	0.386057i	$0.126163\pi$
$373$	15.3651	+	26.6131i	0.795573	+	1.37797i	−0.126902	+	0.991915i	$0.540504\pi$
$374$	0.740150	−	1.28198i	0.0382723	−	0.0662895i
$375$	−2.09783	+	3.63355i	−0.108332	+	0.187636i
$376$	10.0244	−	17.3628i	0.516970	−	0.895419i
$377$	5.81582	+	3.16147i	0.299530	+	0.162824i
$378$		0			0
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	−0.995253	−	0.0973246i	$-0.968972\pi$
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	0.413341	−	0.910576i	$-0.364362\pi$
$380$	−4.55689			−0.233763
$381$	−1.28606			−0.0658866
$382$	0.560093	+	0.970109i	0.0286568	+	0.0496351i
$383$	−0.294631	−	0.510317i	−0.0150550	−	0.0260760i	0.858400	−	0.512981i	$-0.171459\pi$
$383$	−0.294631	−	0.510317i	−0.0150550	−	0.0260760i	−0.873455	+	0.486905i	$0.838126\pi$
$384$	2.51581	−	4.35751i	0.128384	−	0.222368i
$385$		0			0
$386$	−6.99004	+	12.1071i	−0.355783	+	0.616235i
$387$	10.0324			0.509975
$388$	−0.322877	+	0.559239i	−0.0163916	+	0.0283910i
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	0.784695	−	0.619883i	$-0.212820\pi$
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	−0.929181	+	0.369624i	$0.879486\pi$
$390$	6.13536	+	3.33517i	0.310676	+	0.168883i
$391$	−10.9432			−0.553422
$392$		0			0
$393$	3.97904	+	6.89191i	0.200716	+	0.347651i
$394$	−10.8891	−	18.8605i	−0.548584	−	0.950176i
$395$	−20.8068	−	36.0384i	−1.04690	−	1.81329i
$396$	−2.93556			−0.147518
$397$	−12.7641	−	22.1082i	−0.640614	−	1.10958i	−0.985296	−	0.170857i	$-0.945346\pi$
$397$	−12.7641	−	22.1082i	−0.640614	−	1.10958i	0.344682	−	0.938720i	$-0.387987\pi$
$398$	−21.6005			−1.08274
$399$		0			0
$400$	−0.610086	−	1.05670i	−0.0305043	−	0.0528350i
$401$	25.5011			1.27347			0.636733	−	0.771085i	$-0.280286\pi$
$401$	25.5011			1.27347			0.636733	+	0.771085i	$0.280286\pi$
$402$	2.37757	+	4.11807i	0.118582	+	0.205391i
$403$	−28.9339	−	15.7284i	−1.44130	−	0.783489i
$404$	3.81817	−	6.61327i	0.189961	−	0.329022i
$405$	9.04457	+	15.6657i	0.449428	+	0.778433i
$406$		0			0
$407$	−4.75934	+	8.24341i	−0.235912	+	0.408611i
$408$	−1.78520	+	3.09206i	−0.0883807	+	0.153080i
$409$	−0.146988			−0.00726807			−0.00363403	−	0.999993i	$-0.501157\pi$
$409$	−0.146988			−0.00726807			−0.00363403	+	0.999993i	$0.501157\pi$
$410$	15.6164			0.771241
$411$	2.88199	−	4.99175i	0.142158	−	0.246225i
$412$	2.63601	−	4.56570i	0.129867	−	0.224936i
$413$		0			0
$414$	−6.16217	−	10.6732i	−0.302854	−	0.524559i
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$	−17.6134	+	10.7815i	−0.863568	+	0.528606i
$417$	−1.39270	−	2.41223i	−0.0682008	−	0.118127i
$418$	−0.793372			−0.0388051
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	0.983397	−	0.181466i	$-0.0580844\pi$
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	−0.648853	+	0.760914i	$0.724751\pi$
$420$		0			0
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	−2.42421	−	4.19885i	−0.118009	−	0.204397i
$423$	18.4297			0.896084
$424$	13.0844	+	22.6629i	0.635437	+	1.10061i
$425$	6.62754	+	11.4792i	0.321483	+	0.556825i
$426$	0.970345	+	1.68069i	0.0470134	+	0.0814295i
$427$		0			0
$428$	18.0156			0.870816
$429$	−1.88092	−	1.02247i	−0.0908118	−	0.0493652i
$430$	5.73325	+	9.93028i	0.276482	+	0.478881i
$431$	−11.1455	+	19.3046i	−0.536861	+	0.929870i	0.462210	+	0.886771i	$0.347057\pi$
$431$	−11.1455	+	19.3046i	−0.536861	+	0.929870i	−0.999071	+	0.0430997i	$0.986277\pi$
$432$	0.655791			0.0315518
$433$	−12.9481	+	22.4268i	−0.622247	+	1.07776i	0.366819	+	0.930292i	$0.380447\pi$
$433$	−12.9481	+	22.4268i	−0.622247	+	1.07776i	−0.989066	+	0.147472i	$0.952886\pi$
$434$		0			0
$435$	2.08892	−	3.61811i	0.100156	−	0.173475i
$436$	−2.68024	−	4.64232i	−0.128360	−	0.222327i
$437$	2.93253	+	5.07929i	0.140282	+	0.242975i
$438$	−6.13464			−0.293124
$439$	27.9838			1.33560			0.667798	−	0.744343i	$-0.267237\pi$
$439$	27.9838			1.33560			0.667798	+	0.744343i	$0.267237\pi$
$440$	−4.30792	−	7.46153i	−0.205372	−	0.355715i
$441$		0			0
$442$	5.06932	−	3.10302i	0.241123	−	0.147596i
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	0.137741	+	0.990468i	$0.456016\pi$
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	−0.926641	+	0.375947i	$0.877317\pi$
$444$	4.47028	−	7.74275i	0.212150	−	0.367454i
$445$	−23.4155	+	40.5568i	−1.11000	+	1.92258i
$446$	−1.00353	−	1.73816i	−0.0475185	−	0.0823044i
$447$	−3.87796			−0.183421
$448$		0			0
$449$	−9.84320	+	17.0489i	−0.464529	+	0.804589i	−0.999180	−	0.0404845i	$-0.987110\pi$
$449$	−9.84320	+	17.0489i	−0.464529	+	0.804589i	0.534651	+	0.845073i	$0.320443\pi$
$450$	−7.46399	+	12.9280i	−0.351856	+	0.609433i
$451$	−4.78755			−0.225437
$452$	8.78205	−	15.2110i	0.413073	−	0.715464i
$453$	11.1461			0.523690
$454$	22.3783			1.05027
$455$		0			0
$456$	1.91357			0.0896111
$457$	−0.746942			−0.0349405			−0.0174702	−	0.999847i	$-0.505561\pi$
$457$	−0.746942			−0.0349405			−0.0174702	+	0.999847i	$0.505561\pi$
$458$	−0.0291746	+	0.0505320i	−0.00136324	+	0.00236120i
$459$	−7.12405			−0.332522
$460$	−12.4017	+	21.4805i	−0.578235	+	1.00153i
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	0.163744	+	0.986503i	$0.447643\pi$
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	−0.936209	+	0.351445i	$0.885691\pi$
$462$		0			0
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	0.163664	+	0.283475i	0.00759792	+	0.0131600i
$465$	−10.3924	+	18.0002i	−0.481937	+	0.834740i
$466$	6.24313	−	10.8134i	0.289207	−	0.500922i
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	0.288420	+	0.957504i	$0.406870\pi$
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	−0.973433	+	0.228973i	$0.926463\pi$
$468$	−10.3556	−	5.62928i	−0.478687	−	0.260214i
$469$		0			0
$470$	10.5321	+	18.2422i	0.485810	+	0.841448i
$471$	−1.28211			−0.0590766
$472$	1.42329			0.0655122
$473$	−1.75765	−	3.04434i	−0.0808168	−	0.139979i
$474$	3.40253	+	5.89335i	0.156283	+	0.270691i
$475$	3.55205	−	6.15234i	0.162979	−	0.282289i
$476$		0			0
$477$	−12.0278	+	20.8327i	−0.550714	+	0.953864i
$478$	−2.85496			−0.130583
$479$	7.04527	−	12.2028i	0.321907	−	0.557559i	−0.658975	−	0.752165i	$-0.729010\pi$
$479$	7.04527	−	12.2028i	0.321907	−	0.557559i	0.980881	+	0.194606i	$0.0623429\pi$
$480$	6.51684	+	11.2875i	0.297452	+	0.515201i
$481$	−32.5969	+	19.9531i	−1.48629	+	0.909785i
$482$	−7.30247			−0.332618
$483$		0			0
$484$	−6.50142	−	11.2608i	−0.295519	−	0.511854i
$485$	−0.871108	−	1.50880i	−0.0395550	−	0.0685112i
$486$	−6.17502	−	10.6955i	−0.280105	−	0.485156i
$487$	−16.7955			−0.761075			−0.380537	−	0.924766i	$-0.624261\pi$
$487$	−16.7955			−0.761075			−0.380537	+	0.924766i	$0.624261\pi$
$488$	2.00200	+	3.46757i	0.0906263	+	0.156969i
$489$	7.86587			0.355707
$490$		0			0
$491$	−10.8345	−	18.7659i	−0.488954	−	0.846893i	0.510965	−	0.859601i	$-0.329288\pi$
$491$	−10.8345	−	18.7659i	−0.488954	−	0.846893i	−0.999919	+	0.0127081i	$0.995955\pi$
$492$	4.49677			0.202730
$493$	−1.77793	−	3.07947i	−0.0800740	−	0.138692i
$494$	−2.79873	−	1.52138i	−0.125921	−	0.0684503i
$495$	3.96001	−	6.85895i	0.177989	−	0.308287i
$496$	−0.814234	−	1.41029i	−0.0365602	−	0.0633241i
$497$		0			0
$498$	0.426785	−	0.739213i	0.0191247	−	0.0331249i
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	−0.478051	−	0.878332i	$-0.658656\pi$
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	0.999683	−	0.0251622i	$-0.00801023\pi$
$500$	8.09399			0.361974
$501$	10.9605			0.489677
$502$	−9.15601	+	15.8587i	−0.408653	+	0.707807i
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.309816	+	0.950796i	$0.600268\pi$
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.668506	+	0.743707i	$0.733066\pi$
$504$		0			0
$505$	10.3013	+	17.8423i	0.458401	+	0.793974i
$506$	−2.15919	+	3.73983i	−0.0959879	+	0.166256i
$507$	−4.67450	−	7.21378i	−0.207602	−	0.320375i
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	−19.9242			−0.883125			−0.441563	−	0.897230i	$-0.645576\pi$
$509$	−19.9242			−0.883125			−0.441563	+	0.897230i	$0.645576\pi$
$510$	−1.87561	−	3.24866i	−0.0830536	−	0.143853i
$511$		0			0
$512$	−2.01529			−0.0890641
$513$	1.90908	+	3.30662i	0.0842879	+	0.145991i
$514$	4.20279			0.185377
$515$	7.11185	+	12.3181i	0.313386	+	0.542800i
$516$	1.65090	+	2.85944i	0.0726767	+	0.125880i
$517$	−3.22884	−	5.59252i	−0.142004	−	0.245959i
$518$		0			0
$519$	−6.60335			−0.289855
$520$	−0.888388	−	34.5825i	−0.0389584	−	1.51654i
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	0.626318	−	0.779568i	$-0.284561\pi$
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	−0.988284	+	0.152623i	$0.951228\pi$
$522$	2.00232	−	3.46812i	0.0876392	−	0.151796i
$523$	11.9962			0.524556			0.262278	−	0.964992i	$-0.415526\pi$
$523$	11.9962			0.524556			0.262278	+	0.964992i	$0.415526\pi$
$524$	7.67609	−	13.2954i	0.335332	−	0.580812i
$525$		0			0
$526$	−3.81065	+	6.60024i	−0.166152	+	0.287784i
$527$	8.84526	+	15.3204i	0.385305	+	0.667369i
$528$	−0.0529314	−	0.0916798i	−0.00230354	−	0.00398985i
$529$	8.92395			0.387998
$530$	−27.4942			−1.19427
$531$	0.654173	+	1.13306i	0.0283887	+	0.0491706i
$532$		0			0
$533$	−16.8887	−	9.18068i	−0.731531	−	0.397660i
$534$	3.82913	−	6.63225i	0.165703	−	0.287005i
$535$	−24.3026	+	42.0934i	−1.05070	+	1.81986i
$536$	11.7781	−	20.4002i	0.508735	−	0.881155i
$537$	3.03388	+	5.25484i	0.130922	+	0.226763i
$538$	−4.10536			−0.176995
$539$		0			0
$540$	−8.07356	+	13.9838i	−0.347431	+	0.601767i
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	0.153739	+	0.988112i	$0.450869\pi$
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	−6.31658			−0.271320
$543$	−1.98529	+	3.43862i	−0.0851968	+	0.147565i
$544$	11.0933			0.475621
$545$	14.4624			0.619500
$546$		0			0
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	−11.1195			−0.475000
$549$	−1.84032	+	3.18753i	−0.0785430	+	0.136040i
$550$	5.23069			0.223037
$551$	−0.952888	+	1.65045i	−0.0405944	+	0.0703115i
$552$	5.20786	−	9.02027i	0.221661	−	0.383928i
$553$		0			0
$554$	−3.24816			−0.138001
$555$	12.0606	+	20.8896i	0.511945	+	0.886715i
$556$	−2.68670	+	4.65350i	−0.113941	+	0.197352i
$557$	−5.41399	+	9.37731i	−0.229398	+	0.397329i	−0.957630	−	0.288002i	$-0.907009\pi$
$557$	−5.41399	+	9.37731i	−0.229398	+	0.397329i	0.728232	+	0.685331i	$0.240342\pi$
$558$	−9.96160	+	17.2540i	−0.421708	+	0.730420i
$559$	−0.362466	−	14.1098i	−0.0153307	−	0.596781i
$560$		0			0
$561$	0.575009	+	0.995945i	0.0242769	+	0.0420488i
$562$	−7.27694			−0.306959
$563$	13.8599			0.584127			0.292064	−	0.956399i	$-0.405658\pi$
$563$	13.8599			0.584127			0.292064	+	0.956399i	$0.405658\pi$
$564$	3.03274	+	5.25285i	0.127701	+	0.221185i
$565$	23.6936	+	41.0386i	0.996798	+	1.72651i
$566$	−6.49594	+	11.2513i	−0.273045	+	0.472927i
$567$		0			0
$568$	4.80692	−	8.32583i	0.201694	−	0.349344i
$569$	27.4120			1.14917			0.574586	−	0.818444i	$-0.305163\pi$
$569$	27.4120			1.14917			0.574586	+	0.818444i	$0.305163\pi$
$570$	−1.00524	+	1.74113i	−0.0421049	+	0.0729279i
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$	0.106061	+	4.12865i	0.00443462	+	0.172627i
$573$	−0.870251			−0.0363552
$574$		0			0
$575$	−19.3341	−	33.4876i	−0.806288	−	1.39653i
$576$	5.78976	+	10.0282i	0.241240	+	0.417840i
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$578$	11.2764			0.469035
$579$	−5.43043	−	9.40577i	−0.225681	−	0.390891i
$580$	−8.05959			−0.334656
$581$		0			0
$582$	0.142452	+	0.246734i	0.00590483	+	0.0102275i
$583$	8.42893			0.349091
$584$	15.1950	+	26.3185i	0.628772	+	1.08907i
$585$	27.1223	−	16.6020i	1.12137	−	0.686410i
$586$	2.52769	−	4.37809i	0.104418	−	0.180857i
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	0.667399	−	0.744701i	$-0.267408\pi$
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	−0.978629	+	0.205634i	$0.934074\pi$
$588$		0			0
$589$	4.74064	−	8.21104i	0.195335	−	0.338330i
$590$	−0.747686	+	1.29503i	−0.0307817	+	0.0533155i
$591$	16.9191			0.695957
$592$	−1.88987			−0.0776732
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	−0.468609	−	0.883405i	$-0.655245\pi$
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	0.999356	−	0.0358751i	$-0.0114218\pi$
$594$	−1.40564	+	2.43464i	−0.0576740	+	0.0998944i
$595$		0			0
$596$	3.74055	+	6.47882i	0.153219	+	0.265383i
$597$	8.39052	−	14.5328i	0.343401	−	0.594788i
$598$	−14.7884	+	9.05225i	−0.604743	+	0.370174i
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	0.958477	+	0.285170i	$0.0920501\pi$
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	−0.232274	+	0.972650i	$0.574617\pi$
$600$	−12.6161			−0.515052
$601$	−13.6474	−	23.6379i	−0.556688	−	0.964212i	−0.997770	−	0.0667449i	$-0.978739\pi$
$601$	−13.6474	−	23.6379i	−0.556688	−	0.964212i	0.441082	−	0.897467i	$-0.354595\pi$
$602$		0			0
$603$	21.6538			0.881810
$604$	−10.7511	−	18.6215i	−0.437458	−	0.757699i
$605$	35.0811			1.42625
$606$	−1.68456	−	2.91775i	−0.0684308	−	0.118526i
$607$	−19.4629	−	33.7108i	−0.789976	−	1.36828i	−0.925981	−	0.377570i	$-0.876760\pi$
$607$	−19.4629	−	33.7108i	−0.789976	−	1.36828i	0.136006	−	0.990708i	$-0.456574\pi$
$608$	−2.97274	−	5.14894i	−0.120561	−	0.208817i
$609$		0			0
$610$	−4.20679			−0.170328
$611$	−0.665859	−	25.9200i	−0.0269378	−	1.04861i
$612$	3.16576	+	5.48326i	0.127968	+	0.221648i
$613$	−0.443322	+	0.767857i	−0.0179056	+	0.0310135i	−0.874839	−	0.484413i	$-0.839033\pi$
$613$	−0.443322	+	0.767857i	−0.0179056	+	0.0310135i	0.856934	+	0.515427i	$0.172367\pi$
$614$	18.9063			0.762997
$615$	−6.06606	+	10.5067i	−0.244607	+	0.423672i
$616$		0			0
$617$	−17.3944	+	30.1280i	−0.700272	+	1.21291i	0.268099	+	0.963391i	$0.413605\pi$
$617$	−17.3944	+	30.1280i	−0.700272	+	1.21291i	−0.968371	+	0.249515i	$0.919729\pi$
$618$	−1.16300	−	2.01437i	−0.0467827	−	0.0810300i
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	0.885942	−	0.463797i	$-0.153513\pi$
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	−0.844631	+	0.535350i	$0.820180\pi$
$620$	40.0967			1.61032
$621$	20.7825			0.833975
$622$	−4.18864	−	7.25494i	−0.167949	−	0.290897i
$623$		0			0
$624$	−0.0109156	−	0.424915i	−0.000436975	−	0.0170102i
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	8.89959	−	15.4145i	0.355699	−	0.616089i
$627$	0.308178	−	0.533780i	0.0123074	−	0.0213171i
$628$	1.23668	+	2.14199i	0.0493489	+	0.0854749i
$629$	20.5302			0.818593
$630$		0			0
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.0733401	−	0.997307i	$-0.476634\pi$
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.827023	−	0.562168i	$-0.190033\pi$
$632$	16.8555	−	29.1946i	0.670477	−	1.16130i
$633$	3.76665			0.149711
$634$	−10.7924	+	18.6930i	−0.428621	+	0.742393i
$635$	−6.69355			−0.265625
$636$	−7.91700			−0.313929
$637$		0			0
$638$	−1.40321			−0.0555534
$639$	8.83744			0.349604
$640$	13.0941	−	22.6796i	0.517588	−	0.896489i
$641$	−19.0619			−0.752902			−0.376451	−	0.926437i	$-0.622856\pi$
$641$	−19.0619			−0.752902			−0.376451	+	0.926437i	$0.622856\pi$
$642$	3.97420	−	6.88352i	0.156849	−	0.271671i
$643$	−5.26755	+	9.12367i	−0.207732	+	0.359802i	−0.951000	−	0.309192i	$-0.899942\pi$
$643$	−5.26755	+	9.12367i	−0.207732	+	0.359802i	0.743268	+	0.668994i	$0.233275\pi$
$644$		0			0
$645$	−8.90811			−0.350756
$646$	0.855587	+	1.48192i	0.0336626	+	0.0583053i
$647$	−12.0804	+	20.9239i	−0.474930	+	0.822603i	−0.999588	−	0.0287105i	$-0.990860\pi$
$647$	−12.0804	+	20.9239i	−0.474930	+	0.822603i	0.524658	+	0.851313i	$0.324193\pi$
$648$	−7.32699	+	12.6907i	−0.287831	+	0.498538i
$649$	0.229219	−	0.397019i	0.00899762	−	0.0155843i
$650$	18.4520	+	10.0305i	0.723745	+	0.393427i
$651$		0			0
$652$	−7.58714	−	13.1413i	−0.297135	−	0.514654i
$653$	−33.6890			−1.31835			−0.659176	−	0.751988i	$-0.729095\pi$
$653$	−33.6890			−1.31835			−0.659176	+	0.751988i	$0.729095\pi$
$654$	−2.36503			−0.0924799
$655$	20.7098	+	35.8704i	0.809199	+	1.40157i
$656$	−0.475268	−	0.823189i	−0.0185561	−	0.0321401i
$657$	−13.9678	+	24.1930i	−0.544937	+	0.943859i
$658$		0			0
$659$	2.10030	−	3.63782i	0.0818159	−	0.141709i	−0.822214	−	0.569178i	$-0.807261\pi$
$659$	2.10030	−	3.63782i	0.0818159	−	0.141709i	0.904030	+	0.427469i	$0.140595\pi$
$660$	2.60659			0.101461
$661$	8.83631	−	15.3049i	0.343693	−	0.595293i	−0.641423	−	0.767188i	$-0.721655\pi$
$661$	8.83631	−	15.3049i	0.343693	−	0.595293i	0.985115	+	0.171894i	$0.0549888\pi$
$662$	0.758708	+	1.31412i	0.0294880	+	0.0510748i
$663$	0.118580	+	4.61597i	0.00460525	+	0.179270i
$664$	−4.22844			−0.164095
$665$		0			0
$666$	11.5607	+	20.0236i	0.447966	+	0.775900i
$667$	5.18664	+	8.98353i	0.200828	+	0.347844i
$668$	−10.5721	−	18.3114i	−0.409046	−	0.708488i
$669$	1.55925			0.0602839
$670$	12.3746	+	21.4334i	0.478071	+	0.828044i
$671$	1.28968			0.0497875
$672$		0			0
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	0.993384	−	0.114843i	$-0.0366366\pi$
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	−0.596149	+	0.802874i	$0.703303\pi$
$674$	−8.13803			−0.313465
$675$	−12.5865	−	21.8005i	−0.484456	−	0.839102i
$676$	−7.54302	+	14.7677i	−0.290116	+	0.567990i
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	−0.994829	−	0.101567i	$-0.967614\pi$
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	0.585374	+	0.810763i	$0.300948\pi$
$678$	−3.87461	−	6.71102i	−0.148804	−	0.257735i
$679$		0			0
$680$	−9.29147	+	16.0933i	−0.356312	+	0.617150i
$681$	−8.69264	+	15.0561i	−0.333103	+	0.576951i
$682$	6.98099			0.267316
$683$	−6.69757			−0.256275			−0.128138	−	0.991756i	$-0.540900\pi$
$683$	−6.69757			−0.256275			−0.128138	+	0.991756i	$0.540900\pi$
$684$	1.69670	−	2.93877i	0.0648750	−	0.112367i
$685$	14.9999	−	25.9806i	0.573118	−	0.992670i
$686$		0			0
$687$	−0.0226652	−	0.0392573i	−0.000864732	−	0.00149776i
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$	29.7342	+	16.1635i	1.13278	+	0.615779i
$690$	5.47161	+	9.47710i	0.208301	+	0.360787i
$691$	24.9263			0.948242			0.474121	−	0.880460i	$-0.342766\pi$
$691$	24.9263			0.948242			0.474121	+	0.880460i	$0.342766\pi$
$692$	6.36936	+	11.0321i	0.242127	+	0.419376i
$693$		0			0
$694$	−0.539093			−0.0204637
$695$	−7.24861	−	12.5550i	−0.274955	−	0.476237i
$696$	3.38445			0.128287
$697$	5.16298	+	8.94254i	0.195562	+	0.338723i
$698$	−13.0217	−	22.5543i	−0.492880	−	0.853694i
$699$	4.85017	+	8.40073i	0.183450	+	0.317745i
$700$		0			0
$701$	−4.94583			−0.186801			−0.0934007	−	0.995629i	$-0.529774\pi$
$701$	−4.94583			−0.186801			−0.0934007	+	0.995629i	$0.529774\pi$
$702$	−9.62728	+	5.89303i	−0.363358	+	0.222418i
$703$	−5.50162	−	9.52908i	−0.207497	−	0.359396i
$704$	2.02870	−	3.51382i	0.0764597	−	0.132432i
$705$	−16.3644			−0.616319
$706$	0.468266	−	0.811061i	0.0176234	−	0.0305247i
$707$		0			0
$708$	−0.215297	+	0.372905i	−0.00809136	+	0.0140146i
$709$	2.32249	+	4.02267i	0.0872228	+	0.151074i	0.906336	−	0.422557i	$-0.138867\pi$
$709$	2.32249	+	4.02267i	0.0872228	+	0.151074i	−0.819113	+	0.573632i	$0.805534\pi$
$710$	5.05037	+	8.74749i	0.189537	+	0.328288i
$711$	30.9886			1.16216
$712$	−37.9377			−1.42178
$713$	−25.8037	−	44.6933i	−0.966356	−	1.67378i
$714$		0			0
$715$	−9.78966	−	5.32165i	−0.366113	−	0.199018i
$716$	5.85275	−	10.1373i	0.218728	−	0.378847i
$717$	1.10898	−	1.92082i	0.0414157	−	0.0717342i
$718$	−4.15939	+	7.20427i	−0.155227	+	0.268861i
$719$	15.8706	+	27.4887i	0.591875	+	1.02516i	0.993980	+	0.109564i	$0.0349453\pi$
$719$	15.8706	+	27.4887i	0.591875	+	1.02516i	−0.402105	+	0.915594i	$0.631721\pi$
$720$	1.57247			0.0586025
$721$		0			0
$722$	−7.62714	+	13.2106i	−0.283853	+	0.491647i
$723$	2.83658	−	4.91309i	0.105493	−	0.182720i
$724$	7.65975			0.284672
$725$	6.28237	−	10.8814i	0.233322	−	0.404125i
$726$	−5.73681			−0.212913
$727$	−47.8755			−1.77560			−0.887801	−	0.460227i	$-0.847768\pi$
$727$	−47.8755			−1.77560			−0.887801	+	0.460227i	$0.847768\pi$
$728$		0			0
$729$	−6.17412			−0.228671
$730$	−31.9290			−1.18175
$731$	−3.79096	+	6.56613i	−0.140214	+	0.242857i
$732$	−1.21135			−0.0447728
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	−0.927645	−	0.373463i	$-0.878170\pi$
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	0.787251	+	0.616633i	$0.211504\pi$
$734$	4.74386	−	8.21660i	0.175099	−	0.303280i
$735$		0			0
$736$	−32.3618			−1.19287
$737$	−3.79368	−	6.57086i	−0.139742	−	0.242041i
$738$	−5.81459	+	10.0712i	−0.214038	+	0.370725i
$739$	16.7118	−	28.9457i	0.614754	−	1.06479i	−0.375673	−	0.926752i	$-0.622589\pi$
$739$	16.7118	−	28.9457i	0.614754	−	1.06479i	0.990428	−	0.138033i	$-0.0440781\pi$
$740$	23.2665	−	40.2988i	0.855294	−	1.48141i
$741$	2.11072	−	1.29201i	0.0775394	−	0.0474632i
$742$		0			0
$743$	1.46912	+	2.54458i	0.0538966	+	0.0933517i	0.891715	−	0.452597i	$-0.149503\pi$
$743$	1.46912	+	2.54458i	0.0538966	+	0.0933517i	−0.837818	+	0.545949i	$0.816169\pi$
$744$	−16.8378			−0.617302
$745$	−20.1837			−0.739474
$746$	−13.0776	−	22.6511i	−0.478805	−	0.829314i
$747$	−1.94348	−	3.36620i	−0.0711081	−	0.123163i
$748$	1.10927	−	1.92131i	0.0405588	−	0.0702499i
$749$		0			0
$750$	1.78552	−	3.09261i	0.0651980	−	0.112926i
$751$	1.19678			0.0436711			0.0218355	−	0.999762i	$-0.493049\pi$
$751$	1.19678			0.0436711			0.0218355	+	0.999762i	$0.493049\pi$
$752$	0.641065	−	1.11036i	0.0233773	−	0.0404906i
$753$	−7.11313	−	12.3203i	−0.259217	−	0.448977i
$754$	−4.94999	−	2.69081i	−0.180268	−	0.0979936i
$755$	58.0123			2.11128
$756$		0			0
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	0.741830	−	0.670588i	$-0.233958\pi$
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	−0.951661	+	0.307150i	$0.900625\pi$
$758$	9.64207	+	16.7006i	0.350216	+	0.606592i
$759$	−1.67744	−	2.90541i	−0.0608871	−	0.105460i
$760$	9.95959			0.361272
$761$	17.3249	+	30.0075i	0.628026	+	1.08777i	0.987947	+	0.154790i	$0.0494702\pi$
$761$	17.3249	+	30.0075i	0.628026	+	1.08777i	−0.359921	+	0.932983i	$0.617197\pi$
$762$	1.09459			0.0396530
$763$		0			0
$764$	0.839413	+	1.45391i	0.0303689	+	0.0526005i
$765$	−17.0822			−0.617608
$766$	0.250768	+	0.434344i	0.00906063	+	0.0156935i
$767$	1.56993	−	0.960982i	0.0566869	−	0.0346990i
$768$	−5.12890	+	8.88351i	−0.185073	+	0.320556i
$769$	−3.27437	−	5.67138i	−0.118077	−	0.204515i	0.800929	−	0.598760i	$-0.204340\pi$
$769$	−3.27437	−	5.67138i	−0.118077	−	0.204515i	−0.919006	+	0.394245i	$0.871006\pi$
$770$		0			0
$771$	−1.63253	+	2.82763i	−0.0587943	+	0.101835i
$772$	−10.4760	+	18.1450i	−0.377039	+	0.653051i
$773$	−33.9275			−1.22029			−0.610143	−	0.792291i	$-0.708888\pi$
$773$	−33.9275			−1.22029			−0.610143	+	0.792291i	$0.708888\pi$
$774$	−8.53882			−0.306922
$775$	−31.2550	+	54.1352i	−1.12271	+	1.94459i
$776$	0.705683	−	1.22228i	0.0253325	−	0.0438772i
$777$		0			0
$778$	2.42547	+	4.20104i	0.0869575	+	0.150615i
$779$	2.76711	−	4.79278i	0.0991422	−	0.171719i
$780$	9.19508	+	4.99844i	0.329237	+	0.178973i
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	9.31405			0.333070
$783$	3.37651	+	5.84829i	0.120667	+	0.209001i
$784$		0			0
$785$	−6.67303			−0.238171
$786$	−3.38667	−	5.86588i	−0.120798	−	0.209229i
$787$	−12.9743			−0.462485			−0.231243	−	0.972896i	$-0.574279\pi$
$787$	−12.9743			−0.462485			−0.231243	+	0.972896i	$0.574279\pi$
$788$	−16.3195	−	28.2662i	−0.581359	−	1.00694i
$789$	−2.96042	−	5.12760i	−0.105394	−	0.182548i
$790$	17.7092	+	30.6732i	0.630065	+	1.09130i
$791$		0			0
$792$	6.41600			0.227983
$793$	4.54951	+	2.47311i	0.161558	+	0.0878227i
$794$	10.8639	+	18.8168i	0.385545	+	0.667784i
$795$	10.6799	−	18.4981i	0.378776	−	0.656059i
$796$	−32.3728			−1.14742
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	−0.824235	−	0.566247i	$-0.808395\pi$
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	0.902502	+	0.430685i	$0.141728\pi$
$798$		0			0
$799$	−6.96408	+	12.0621i	−0.246371	+	0.426728i
$800$	19.5993	+	33.9469i	0.692938	+	1.20020i
$801$	−17.4369	−	30.2017i	−0.616104	−	1.06712i
$802$	−21.7047			−0.766418
$803$	9.78852			0.345429
$804$	3.56327	+	6.17177i	0.125667	+	0.217662i
$805$		0			0
$806$	24.6264	+	13.3869i	0.867427	+	0.471532i
$807$	1.59469	−	2.76208i	0.0561356	−	0.0972298i
$808$	−8.34504	+	14.4540i	−0.293578	+	0.508491i
$809$	−5.73580	+	9.93470i	−0.201660	+	0.349285i	−0.949063	−	0.315085i	$-0.897967\pi$
$809$	−5.73580	+	9.93470i	−0.201660	+	0.349285i	0.747403	+	0.664371i	$0.231300\pi$
$810$	−7.69807	−	13.3334i	−0.270482	−	0.468489i
$811$	−23.8664			−0.838063			−0.419032	−	0.907972i	$-0.637630\pi$
$811$	−23.8664			−0.838063			−0.419032	+	0.907972i	$0.637630\pi$
$812$		0			0
$813$	2.45361	−	4.24978i	0.0860520	−	0.149046i
$814$	4.05079	−	7.01618i	0.141980	−	0.245917i
$815$	40.9396			1.43405
$816$	−0.114164	+	0.197738i	−0.00399655	+	0.00692223i
$817$	4.06355			0.142166
$818$	0.125105			0.00437419
$819$		0			0
$820$	23.4044			0.817318
$821$	30.9694			1.08084			0.540420	−	0.841395i	$-0.318265\pi$
$821$	30.9694			1.08084			0.540420	+	0.841395i	$0.318265\pi$
$822$	−2.45293	+	4.24861i	−0.0855559	+	0.148187i
$823$	−8.61357			−0.300250			−0.150125	−	0.988667i	$-0.547968\pi$
$823$	−8.61357			−0.300250			−0.150125	+	0.988667i	$0.547968\pi$
$824$	−5.76129	+	9.97885i	−0.200704	+	0.347630i
$825$	−2.03181	+	3.51920i	−0.0707386	+	0.122523i
$826$		0			0
$827$	22.9128			0.796756			0.398378	−	0.917221i	$-0.369573\pi$
$827$	22.9128			0.796756			0.398378	+	0.917221i	$0.369573\pi$
$828$	−9.23528	−	15.9960i	−0.320948	−	0.555898i
$829$	−21.2806	+	36.8590i	−0.739104	+	1.28017i	0.213795	+	0.976879i	$0.431418\pi$
$829$	−21.2806	+	36.8590i	−0.739104	+	1.28017i	−0.952899	+	0.303287i	$0.901916\pi$
$830$	2.22129	−	3.84739i	0.0771022	−	0.133545i
$831$	1.26172	−	2.18536i	0.0437685	−	0.0758093i
$832$	13.8947	−	8.50518i	0.481711	−	0.294864i
$833$		0			0
$834$	1.18536	+	2.05311i	0.0410458	+	0.0710933i
$835$	57.0460			1.97416
$836$	−1.18903			−0.0411235
$837$	−16.7982	−	29.0954i	−0.580632	−	1.00568i
$838$	−5.82846	−	10.0952i	−0.201341	−	0.348733i
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	−0.849698	−	0.527270i	$-0.823216\pi$
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	0.881478	+	0.472225i	$0.156549\pi$
$840$		0			0
$841$	12.8147	−	22.1957i	0.441885	−	0.765367i
$842$	−2.92931			−0.100951
$843$	2.82666	−	4.89591i	0.0973553	−	0.168624i
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$	−24.3294	−	37.5457i	−0.836958	−	1.29161i
$846$	−15.6860			−0.539296
$847$		0			0
$848$	0.836755	+	1.44930i	0.0287343	+	0.0497692i
$849$	−5.04657	−	8.74092i	−0.173198	−	0.299988i
$850$	−5.64087	−	9.77027i	−0.193480	−	0.335118i
$851$	−59.8915			−2.05305
$852$	1.45426	+	2.51885i	0.0498221	+	0.0862944i
$853$	27.0293			0.925466			0.462733	−	0.886498i	$-0.346869\pi$
$853$	27.0293			0.925466			0.462733	+	0.886498i	$0.346869\pi$
$854$		0			0
$855$	4.57763	+	7.92869i	0.156552	+	0.271155i
$856$	−39.3750			−1.34581
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	0.973017	−	0.230732i	$-0.0741122\pi$
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	−0.686329	+	0.727291i	$0.740779\pi$
$858$	1.60090	+	0.870248i	0.0546538	+	0.0297098i
$859$	25.8058	−	44.6969i	0.880482	−	1.52504i	0.0296769	−	0.999560i	$-0.490552\pi$
$859$	25.8058	−	44.6969i	0.880482	−	1.52504i	0.850806	−	0.525481i	$-0.176114\pi$
$860$	8.59245	+	14.8826i	0.293000	+	0.507491i
$861$		0			0
$862$	9.48624	−	16.4306i	0.323102	−	0.559630i
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	−0.990145	−	0.140049i	$-0.955274\pi$
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	0.616358	+	0.787466i	$0.288607\pi$
$864$	−21.0676			−0.716733
$865$	−34.3685			−1.16857
$866$	11.0205	−	19.0880i	0.374491	−	0.648638i
$867$	−4.38020	+	7.58673i	−0.148759	+	0.257659i
$868$		0			0
$869$	−5.42913	−	9.40352i	−0.184170	−	0.318993i
$870$	−1.77793	+	3.07947i	−0.0602775	+	0.104404i
$871$	−0.782342	−	30.4544i	−0.0265086	−	1.03191i
$872$	5.85797	+	10.1463i	0.198376	+	0.343597i
$873$	1.29739			0.0439098
$874$	−2.49595	−	4.32311i	−0.0844267	−	0.146231i
$875$		0			0
$876$	−9.19401			−0.310637
$877$	4.80873	+	8.32896i	0.162379	+	0.281249i	0.935721	−	0.352740i	$-0.114750\pi$
$877$	4.80873	+	8.32896i	0.162379	+	0.281249i	−0.773342	+	0.633989i	$0.781417\pi$
$878$	−23.8178			−0.803811
$879$	1.96371	+	3.40125i	0.0662344	+	0.114721i
$880$	−0.275493	−	0.477167i	−0.00928686	−	0.0160853i
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	0.999906	−	0.0137383i	$-0.00437318\pi$
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	−0.511851	+	0.859075i	$0.671040\pi$
$882$		0			0
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	7.59742	−	4.65051i	0.255529	−	0.156414i
$885$	−0.580863	−	1.00608i	−0.0195255	−	0.0338191i
$886$	14.1325	−	24.4781i	0.474789	−	0.822359i
$887$	31.4144			1.05479			0.527397	−	0.849619i	$-0.323168\pi$
$887$	31.4144			1.05479			0.527397	+	0.849619i	$0.323168\pi$
$888$	−9.77029	+	16.9226i	−0.327869	+	0.567886i
$889$		0			0
$890$	19.9295	−	34.5190i	0.668039	−	1.15708i
$891$	2.36000	+	4.08765i	0.0790631	+	0.136941i
$892$	−1.50399	−	2.60499i	−0.0503574	−	0.0872216i
$893$	7.46484			0.249801
$894$	3.30063			0.110390
$895$	15.7905	+	27.3499i	0.527818	+	0.914208i
$896$		0			0
$897$	−0.345925	−	13.4659i	−0.0115501	−	0.449613i
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	8.38459	−	14.5225i	0.279642	−	0.484354i
$900$	−11.1863	+	19.3753i	−0.372877	+	0.645843i
$901$	−9.08991	−	15.7442i	−0.302829	−	0.524515i
$902$	4.07480			0.135676
$903$		0			0
$904$	−19.1942	+	33.2453i	−0.638388	+	1.10572i
$905$	−10.3328	+	17.8970i	−0.343475	+	0.594917i
$906$	−9.48673			−0.315176
$907$	−4.86821	+	8.43198i	−0.161646	+	0.279979i	−0.935459	−	0.353435i	$-0.885014\pi$
$907$	−4.86821	+	8.43198i	−0.161646	+	0.279979i	0.773813	+	0.633414i	$0.218347\pi$
$908$	33.5385			1.11301
$909$	−15.3422			−0.508869
$910$		0			0
$911$	−38.4372			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$911$	−38.4372			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$912$	0.122373			0.00405219
$913$	−0.680984	+	1.17950i	−0.0225373	+	0.0390357i
$914$	0.635741			0.0210285
$915$	1.63409	−	2.83032i	0.0540212	−	0.0935675i
$916$	−0.0437242	+	0.0757325i	−0.00144469	+	0.00250227i
$917$		0			0
$918$	6.06346			0.200124
$919$	−27.1402	−	47.0082i	−0.895273	−	1.55066i	−0.833467	−	0.552569i	$-0.813647\pi$
$919$	−27.1402	−	47.0082i	−0.895273	−	1.55066i	−0.0618056	−	0.998088i	$-0.519686\pi$
$920$	27.1054	−	46.9479i	0.893639	−	1.54783i
$921$	−7.34398	+	12.7202i	−0.241993	+	0.419143i
$922$	14.1164	−	24.4502i	0.464897	−	0.805226i
$923$	−0.319293	−	12.4292i	−0.0105097	−	0.409112i
$924$		0			0
$925$	36.2721	+	62.8251i	1.19262	+	2.06568i
$926$	26.1739			0.860128
$927$	−10.5920			−0.347888
$928$	−5.25777	−	9.10673i	−0.172595	−	0.298943i
$929$	−19.0960	−	33.0752i	−0.626519	−	1.08516i	−0.988245	−	0.152878i	$-0.951146\pi$
$929$	−19.0960	−	33.0752i	−0.626519	−	1.08516i	0.361726	−	0.932284i	$-0.382188\pi$
$930$	8.84526	−	15.3204i	0.290047	−	0.502377i
$931$		0			0
$932$	9.35660	−	16.2061i	0.306486	−	0.530849i
$933$	6.50815			0.213067
$934$	12.5994	−	21.8228i	0.412266	−	0.714065i
$935$	2.99276	+	5.18361i	0.0978736	+	0.169522i
$936$	22.6333	+	12.3034i	0.739792	+	0.402150i
$937$	19.0376			0.621931			0.310966	−	0.950421i	$-0.399348\pi$
$937$	19.0376			0.621931			0.310966	+	0.950421i	$0.399348\pi$
$938$		0			0
$939$	6.91392	+	11.9753i	0.225627	+	0.390798i
$940$	15.7845	+	27.3396i	0.514835	+	0.891720i
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	0.946646	+	0.322275i	$0.104448\pi$
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	−0.194224	+	0.980957i	$0.562219\pi$
$942$	1.09124			0.0355545
$943$	−15.0616	−	26.0875i	−0.490474	−	0.849526i
$944$	0.0910198			0.00296244
$945$		0			0
$946$	1.49598	+	2.59111i	0.0486385	+	0.0842443i
$947$	−9.19374			−0.298756			−0.149378	−	0.988780i	$-0.547727\pi$
$947$	−9.19374			−0.298756			−0.149378	+	0.988780i	$0.547727\pi$
$948$	5.09938	+	8.83239i	0.165620	+	0.286863i
$949$	34.5303	+	18.7706i	1.12090	+	0.609320i
$950$	−3.02324	+	5.23641i	−0.0980869	+	0.169892i
$951$	−8.38440	−	14.5222i	−0.271883	−	0.470915i
$952$		0			0
$953$	22.3232	−	38.6648i	0.723118	−	1.25248i	−0.236626	−	0.971601i	$-0.576042\pi$
$953$	22.3232	−	38.6648i	0.723118	−	1.25248i	0.959744	−	0.280876i	$-0.0906250\pi$
$954$	10.2371	−	17.7312i	0.331440	−	0.574070i
$955$	−4.52941			−0.146568
$956$	−4.27874			−0.138385
$957$	0.545062	−	0.944075i	0.0176194	−	0.0305176i
$958$	−5.99641	+	10.3861i	−0.193735	+	0.335559i
$959$		0			0
$960$	−5.14093	−	8.90436i	−0.165923	−	0.287387i
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$	27.7441	−	16.9826i	0.894504	−	0.547542i
$963$	−18.0976	−	31.3459i	−0.583186	−	1.01011i
$964$	−10.9442			−0.352490
$965$	−28.2638	−	48.9544i	−0.909845	−	1.57590i
$966$		0			0
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	14.2096	+	24.6117i	0.456713	+	0.791050i
$969$	−1.32938			−0.0427058
$970$	0.741422	+	1.28418i	0.0238056	+	0.0412326i
$971$	3.63437	+	6.29491i	0.116632	+	0.202013i	0.918431	−	0.395581i	$-0.129457\pi$
$971$	3.63437	+	6.29491i	0.116632	+	0.202013i	−0.801799	+	0.597594i	$0.796123\pi$
$972$	−9.25454	−	16.0293i	−0.296839	−	0.514141i
$973$		0			0
$974$	14.2950			0.458043
$975$	−13.9160	+	8.51821i	−0.445668	+	0.272801i
$976$	0.128029	+	0.221752i	0.00409810	+	0.00709811i
$977$	−21.4050	+	37.0746i	−0.684808	+	1.18612i	0.288689	+	0.957423i	$0.406781\pi$
$977$	−21.4050	+	37.0746i	−0.684808	+	1.18612i	−0.973497	+	0.228699i	$0.926553\pi$
$978$	−6.69484			−0.214077
$979$	−6.10982	+	10.5825i	−0.195271	+	0.338219i
$980$		0			0
$981$	−5.38489	+	9.32690i	−0.171926	+	0.297785i
$982$	9.22152	+	15.9721i	0.294270	+	0.509691i
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	−0.953166	−	0.302448i	$-0.902196\pi$
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	0.214655	−	0.976690i	$-0.431137\pi$
$984$	−9.82820			−0.313312
$985$	88.0588			2.80579
$986$	1.51324	+	2.62101i	0.0481914	+	0.0834700i
$987$		0			0
$988$	−4.19446	−	2.28010i	−0.133444	−	0.0725398i
$989$	11.0591	−	19.1550i	0.351660	−	0.609092i
$990$	−3.37047	+	5.83782i	−0.107121	+	0.185538i
$991$	29.1162	−	50.4307i	0.924907	−	1.60199i	0.133195	−	0.991090i	$-0.457476\pi$
$991$	29.1162	−	50.4307i	0.924907	−	1.60199i	0.791711	−	0.610896i	$-0.209190\pi$
$992$	26.1576	+	45.3062i	0.830504	+	1.43847i
$993$	−1.17885			−0.0374097
$994$		0			0
$995$	43.6703	−	75.6392i	1.38444	−	2.39792i
$996$	0.639625	−	1.10786i	0.0202673	−	0.0351040i
$997$	4.49479			0.142351			0.0711757	−	0.997464i	$-0.477325\pi$
$997$	4.49479			0.142351			0.0711757	+	0.997464i	$0.477325\pi$
$998$	−9.91765	+	17.1779i	−0.313938	+	0.543756i
$999$	−38.9894			−1.23357

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	637.2.h.l.471.3		12
7.2	even	3		637.2.f.j.393.4		12
7.3	odd	6		91.2.g.b.81.4	yes	12
7.4	even	3		637.2.g.l.263.4		12
7.5	odd	6		637.2.f.k.393.4		12
7.6	odd	2		91.2.h.b.16.3	yes	12
13.9	even	3		637.2.g.l.373.4		12
21.17	even	6		819.2.n.d.172.3		12
21.20	even	2		819.2.s.d.289.4		12
91.3	odd	6		1183.2.e.h.508.4		12
91.9	even	3		637.2.f.j.295.4		12
91.10	odd	6		1183.2.e.g.508.3		12
91.16	even	3		8281.2.a.ca.1.3		6
91.23	even	6		8281.2.a.cf.1.4		6
91.48	odd	6		91.2.g.b.9.4	✓	12
91.55	odd	6		1183.2.e.h.170.4		12
91.61	odd	6		637.2.f.k.295.4		12
91.62	odd	6		1183.2.e.g.170.3		12
91.68	odd	6		8281.2.a.bz.1.3		6
91.74	even	3	inner	637.2.h.l.165.3		12
91.75	odd	6		8281.2.a.ce.1.4		6
91.87	odd	6		91.2.h.b.74.3	yes	12
273.230	even	6		819.2.n.d.100.3		12
273.269	even	6		819.2.s.d.802.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	91.48	odd	6
91.2.g.b.81.4	yes	12	7.3	odd	6
91.2.h.b.16.3	yes	12	7.6	odd	2
91.2.h.b.74.3	yes	12	91.87	odd	6
637.2.f.j.295.4		12	91.9	even	3
637.2.f.j.393.4		12	7.2	even	3
637.2.f.k.295.4		12	91.61	odd	6
637.2.f.k.393.4		12	7.5	odd	6
637.2.g.l.263.4		12	7.4	even	3
637.2.g.l.373.4		12	13.9	even	3
637.2.h.l.165.3		12	91.74	even	3	inner
637.2.h.l.471.3		12	1.1	even	1	trivial
819.2.n.d.100.3		12	273.230	even	6
819.2.n.d.172.3		12	21.17	even	6
819.2.s.d.289.4		12	21.20	even	2
819.2.s.d.802.4		12	273.269	even	6
1183.2.e.g.170.3		12	91.62	odd	6
1183.2.e.g.508.3		12	91.10	odd	6
1183.2.e.h.170.4		12	91.55	odd	6
1183.2.e.h.508.4		12	91.3	odd	6
8281.2.a.bz.1.3		6	91.68	odd	6
8281.2.a.ca.1.3		6	91.16	even	3
8281.2.a.ce.1.4		6	91.75	odd	6
8281.2.a.cf.1.4		6	91.23	even	6

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

Related objects

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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	637.2.h.l.471.3

Level	$637$
Weight	$2$
Character	637.471
Analytic conductor	$5.086$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$