LMFDB - Embedded newform 783.2.u.a.397.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [783,2,Mod(181,783)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(783, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 18]))

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

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

chi := DirichletCharacter("783.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.u (of order $21$, degree $12$, 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:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			397.2
Character	$\chi$	$=$	783.397
Dual form			783.2.u.a.712.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.187058 + 2.49612i) q^{2} +(-4.21795 - 0.635753i) q^{4} +(0.730934 + 0.498342i) q^{5} +(-3.13454 + 0.472455i) q^{7} +(1.26192 - 5.52885i) q^{8} +(-1.38065 + 1.73128i) q^{10} +(-3.88874 - 1.19952i) q^{11} +(-0.789571 + 0.732615i) q^{13} +(-0.592963 - 7.91255i) q^{14} +(5.41243 + 1.66951i) q^{16} +5.99968 q^{17} +(-2.35611 + 2.95447i) q^{19} +(-2.76622 - 2.56667i) q^{20} +(3.72155 - 9.48236i) q^{22} +(-0.229754 - 3.06585i) q^{23} +(-1.54079 - 3.92586i) q^{25} +(-1.68100 - 2.10790i) q^{26} +13.5217 q^{28} +(4.05681 - 3.54152i) q^{29} +(-4.60383 - 3.13884i) q^{31} +(-1.03602 + 2.63973i) q^{32} +(-1.12229 + 14.9759i) q^{34} +(-2.52658 - 1.21674i) q^{35} +(2.53992 - 11.1281i) q^{37} +(-6.93398 - 6.43379i) q^{38} +(3.67764 - 3.41235i) q^{40} +(2.13847 + 3.70394i) q^{41} +(-4.83932 + 3.29939i) q^{43} +(15.6399 + 7.53177i) q^{44} +7.69570 q^{46} +(-4.69688 - 1.44880i) q^{47} +(2.91310 - 0.898572i) q^{49} +(10.0876 - 3.11162i) q^{50} +(3.79613 - 2.58816i) q^{52} +(-2.95463 + 1.42288i) q^{53} +(-2.24464 - 2.81469i) q^{55} +(-1.34341 + 17.9266i) q^{56} +(8.08118 + 10.7887i) q^{58} +(1.23521 + 2.13945i) q^{59} +(-4.04854 + 0.610220i) q^{61} +(8.69610 - 10.9046i) q^{62} +(3.81101 + 1.83529i) q^{64} +(-0.942217 + 0.142016i) q^{65} +(-6.60889 + 2.03857i) q^{67} +(-25.3063 - 3.81432i) q^{68} +(3.50974 - 6.07905i) q^{70} +(-2.34734 - 10.2844i) q^{71} +(-8.54599 - 4.11553i) q^{73} +(27.3020 + 8.42155i) q^{74} +(11.8163 - 10.9639i) q^{76} +(12.7561 + 1.92267i) q^{77} +(7.61429 + 7.06503i) q^{79} +(3.12414 + 3.91755i) q^{80} +(-9.64548 + 4.64502i) q^{82} +(3.73059 + 9.50538i) q^{83} +(4.38537 + 2.98990i) q^{85} +(-7.33043 - 12.6967i) q^{86} +(-11.5392 + 19.9865i) q^{88} +(-11.8062 + 5.68557i) q^{89} +(2.12881 - 2.66945i) q^{91} +(-0.980035 + 13.0777i) q^{92} +(4.49495 - 11.4530i) q^{94} +(-3.19450 + 0.985373i) q^{95} +(-2.49026 - 6.34507i) q^{97} +(1.69802 + 7.43952i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 5 q^{2} + 21 q^{4} + 9 q^{5} - 5 q^{7} - 2 q^{8} - 28 q^{10} + q^{11} - 5 q^{13} + 9 q^{14} + 21 q^{16} + 60 q^{17} - 20 q^{19} + 15 q^{20} - 13 q^{22} + 32 q^{23} + 15 q^{25} + 4 q^{26} - 72 q^{28}+ \cdots + 88 q^{98}+O(q^{100}) $ 336 * q + 5 * q^2 + 21 * q^4 + 9 * q^5 - 5 * q^7 - 2 * q^8 - 28 * q^10 + q^11 - 5 * q^13 + 9 * q^14 + 21 * q^16 + 60 * q^17 - 20 * q^19 + 15 * q^20 - 13 * q^22 + 32 * q^23 + 15 * q^25 + 4 * q^26 - 72 * q^28 + q^29 - 5 * q^31 - 7 * q^32 - 15 * q^34 - 16 * q^35 - 20 * q^37 - 63 * q^38 + 5 * q^40 + 20 * q^41 - 5 * q^43 + 8 * q^44 - 80 * q^46 - 5 * q^47 - 19 * q^49 + 3 * q^50 + q^52 + 4 * q^53 - 100 * q^55 + 5 * q^56 - 7 * q^58 - 154 * q^59 + 7 * q^61 + 4 * q^62 + 18 * q^64 + 65 * q^65 - 5 * q^67 + 9 * q^68 - 14 * q^70 - 18 * q^71 - 20 * q^73 + 77 * q^74 - 5 * q^76 - 39 * q^77 - 5 * q^79 + 104 * q^80 + 12 * q^82 + 23 * q^83 - 42 * q^85 - 128 * q^86 - 8 * q^88 - 34 * q^89 + 12 * q^91 + 115 * q^92 - 25 * q^94 - 89 * q^95 + 55 * q^97 + 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.187058	+	2.49612i	−0.132270	+	1.76502i	0.398182	+	0.917306i	$0.369641\pi$
$2$	−0.187058	+	2.49612i	−0.132270	+	1.76502i	−0.530452	+	0.847715i	$0.677978\pi$
$3$		0			0
$3$		0			0
$4$	−4.21795	−	0.635753i	−2.10897	−	0.317877i
$5$	0.730934	+	0.498342i	0.326883	+	0.222865i	0.715630	−	0.698479i	$-0.246140\pi$
$5$	0.730934	+	0.498342i	0.326883	+	0.222865i	−0.388747	+	0.921345i	$0.627092\pi$
$6$		0			0
$7$	−3.13454	+	0.472455i	−1.18474	+	0.178571i	−0.711710	−	0.702473i	$-0.752079\pi$
$7$	−3.13454	+	0.472455i	−1.18474	+	0.178571i	−0.473033	+	0.881044i	$0.656841\pi$
$8$	1.26192	−	5.52885i	0.446157	−	1.95474i
$9$		0			0
$10$	−1.38065	+	1.73128i	−0.436599	+	0.547478i
$11$	−3.88874	−	1.19952i	−1.17250	−	0.361668i	−0.353484	−	0.935441i	$-0.615003\pi$
$11$	−3.88874	−	1.19952i	−1.17250	−	0.361668i	−0.819014	+	0.573773i	$0.805479\pi$
$12$		0			0
$13$	−0.789571	+	0.732615i	−0.218988	+	0.203191i	−0.782036	−	0.623233i	$-0.785819\pi$
$13$	−0.789571	+	0.732615i	−0.218988	+	0.203191i	0.563049	+	0.826424i	$0.309628\pi$
$14$	−0.592963	−	7.91255i	−0.158476	−	2.11472i
$15$		0			0
$16$	5.41243	+	1.66951i	1.35311	+	0.417378i
$17$	5.99968			1.45514			0.727569	−	0.686035i	$-0.240650\pi$
$17$	5.99968			1.45514			0.727569	+	0.686035i	$0.240650\pi$
$18$		0			0
$19$	−2.35611	+	2.95447i	−0.540530	+	0.677803i	−0.974826	−	0.222967i	$-0.928426\pi$
$19$	−2.35611	+	2.95447i	−0.540530	+	0.677803i	0.434296	+	0.900770i	$0.356997\pi$
$20$	−2.76622	−	2.56667i	−0.618545	−	0.573926i
$21$		0			0
$22$	3.72155	−	9.48236i	0.793437	−	2.02165i
$23$	−0.229754	−	3.06585i	−0.0479070	−	0.639274i	−0.968542	−	0.248850i	$-0.919947\pi$
$23$	−0.229754	−	3.06585i	−0.0479070	−	0.639274i	0.920635	−	0.390424i	$-0.127672\pi$
$24$		0			0
$25$	−1.54079	−	3.92586i	−0.308157	−	0.785172i
$26$	−1.68100	−	2.10790i	−0.329671	−	0.413394i
$27$		0			0
$28$	13.5217			2.55536
$29$	4.05681	−	3.54152i	0.753330	−	0.657643i
$29$	4.05681	−	3.54152i	0.753330	−	0.657643i
$30$		0			0
$31$	−4.60383	−	3.13884i	−0.826873	−	0.563753i	0.0742880	−	0.997237i	$-0.476332\pi$
$31$	−4.60383	−	3.13884i	−0.826873	−	0.563753i	−0.901161	+	0.433484i	$0.857284\pi$
$32$	−1.03602	+	2.63973i	−0.183144	+	0.466644i
$33$		0			0
$34$	−1.12229	+	14.9759i	−0.192471	+	2.56835i
$35$	−2.52658	−	1.21674i	−0.427071	−	0.205666i
$36$		0			0
$37$	2.53992	−	11.1281i	0.417561	−	1.82945i	−0.128502	−	0.991709i	$-0.541017\pi$
$37$	2.53992	−	11.1281i	0.417561	−	1.82945i	0.546062	−	0.837744i	$-0.316126\pi$
$38$	−6.93398	−	6.43379i	−1.12484	−	1.04370i
$39$		0			0
$40$	3.67764	−	3.41235i	0.581486	−	0.539540i
$41$	2.13847	+	3.70394i	0.333973	+	0.578458i	0.983287	−	0.182062i	$-0.0582773\pi$
$41$	2.13847	+	3.70394i	0.333973	+	0.578458i	−0.649314	+	0.760520i	$0.724944\pi$
$42$		0			0
$43$	−4.83932	+	3.29939i	−0.737989	+	0.503152i	−0.873017	−	0.487689i	$-0.837840\pi$
$43$	−4.83932	+	3.29939i	−0.737989	+	0.503152i	0.135028	+	0.990842i	$0.456888\pi$
$44$	15.6399	+	7.53177i	2.35780	+	1.13546i
$45$		0			0
$46$	7.69570			1.13467
$47$	−4.69688	−	1.44880i	−0.685110	−	0.211329i	−0.0673904	−	0.997727i	$-0.521467\pi$
$47$	−4.69688	−	1.44880i	−0.685110	−	0.211329i	−0.617720	+	0.786398i	$0.711943\pi$
$48$		0			0
$49$	2.91310	−	0.898572i	0.416157	−	0.128367i
$50$	10.0876	−	3.11162i	1.42660	−	0.440049i
$51$		0			0
$52$	3.79613	−	2.58816i	0.526429	−	0.358913i
$53$	−2.95463	+	1.42288i	−0.405850	+	0.195447i	−0.625661	−	0.780095i	$-0.715170\pi$
$53$	−2.95463	+	1.42288i	−0.405850	+	0.195447i	0.219810	+	0.975543i	$0.429456\pi$
$54$		0			0
$55$	−2.24464	−	2.81469i	−0.302667	−	0.379532i
$56$	−1.34341	+	17.9266i	−0.179521	+	2.39554i
$57$		0			0
$58$	8.08118	+	10.7887i	1.06111	+	1.41663i
$59$	1.23521	+	2.13945i	0.160811	+	0.278532i	0.935160	−	0.354226i	$-0.115256\pi$
$59$	1.23521	+	2.13945i	0.160811	+	0.278532i	−0.774349	+	0.632759i	$0.781922\pi$
$60$		0			0
$61$	−4.04854	+	0.610220i	−0.518363	+	0.0781306i	−0.403013	−	0.915194i	$-0.632037\pi$
$61$	−4.04854	+	0.610220i	−0.518363	+	0.0781306i	−0.115350	+	0.993325i	$0.536799\pi$
$62$	8.69610	−	10.9046i	1.10441	−	1.38488i
$63$		0			0
$64$	3.81101	+	1.83529i	0.476376	+	0.229411i
$65$	−0.942217	+	0.142016i	−0.116868	+	0.0176150i
$66$		0			0
$67$	−6.60889	+	2.03857i	−0.807404	+	0.249051i	−0.670861	−	0.741583i	$-0.734075\pi$
$67$	−6.60889	+	2.03857i	−0.807404	+	0.249051i	−0.136543	+	0.990634i	$0.543599\pi$
$68$	−25.3063	−	3.81432i	−3.06884	−	0.462554i
$69$		0			0
$70$	3.50974	−	6.07905i	0.419494	−	0.726585i
$71$	−2.34734	−	10.2844i	−0.278578	−	1.22053i	−0.899592	−	0.436731i	$-0.856136\pi$
$71$	−2.34734	−	10.2844i	−0.278578	−	1.22053i	0.621014	−	0.783800i	$-0.286721\pi$
$72$		0			0
$73$	−8.54599	−	4.11553i	−1.00023	−	0.481686i	−0.139215	−	0.990262i	$-0.544458\pi$
$73$	−8.54599	−	4.11553i	−1.00023	−	0.481686i	−0.861017	+	0.508576i	$0.830172\pi$
$74$	27.3020	+	8.42155i	3.17379	+	0.978986i
$75$		0			0
$76$	11.8163	−	10.9639i	1.35542	−	1.25765i
$77$	12.7561	+	1.92267i	1.45369	+	0.219109i
$78$		0			0
$79$	7.61429	+	7.06503i	0.856674	+	0.794878i	0.980313	−	0.197450i	$-0.0632659\pi$
$79$	7.61429	+	7.06503i	0.856674	+	0.794878i	−0.123639	+	0.992327i	$0.539456\pi$
$80$	3.12414	+	3.91755i	0.349289	+	0.437995i
$81$		0			0
$82$	−9.64548	+	4.64502i	−1.06517	+	0.512956i
$83$	3.73059	+	9.50538i	0.409485	+	1.04335i	0.975703	+	0.219096i	$0.0703107\pi$
$83$	3.73059	+	9.50538i	0.409485	+	1.04335i	−0.566218	+	0.824255i	$0.691594\pi$
$84$		0			0
$85$	4.38537	+	2.98990i	0.475660	+	0.324300i
$86$	−7.33043	−	12.6967i	−0.790461	−	1.36912i
$87$		0			0
$88$	−11.5392	+	19.9865i	−1.23009	+	2.13057i
$89$	−11.8062	+	5.68557i	−1.25146	+	0.602669i	−0.937902	−	0.346901i	$-0.887234\pi$
$89$	−11.8062	+	5.68557i	−1.25146	+	0.602669i	−0.313554	+	0.949570i	$0.601520\pi$
$90$		0			0
$91$	2.12881	−	2.66945i	0.223160	−	0.279834i
$92$	−0.980035	+	13.0777i	−0.102176	+	1.36344i
$93$		0			0
$94$	4.49495	−	11.4530i	0.463619	−	1.18128i
$95$	−3.19450	+	0.985373i	−0.327749	+	0.101097i
$96$		0			0
$97$	−2.49026	−	6.34507i	−0.252847	−	0.644244i	0.746940	−	0.664892i	$-0.231522\pi$
$97$	−2.49026	−	6.34507i	−0.252847	−	0.644244i	−0.999787	+	0.0206477i	$0.993427\pi$
$98$	1.69802	+	7.43952i	0.171526	+	0.751505i
$99$		0			0
$100$	4.00308	+	17.5386i	0.400308	+	1.75386i
$101$	−9.98856	+	6.81009i	−0.993899	+	0.677629i	−0.946988	−	0.321270i	$-0.895890\pi$
$101$	−9.98856	+	6.81009i	−0.993899	+	0.677629i	−0.0469115	+	0.998899i	$0.514938\pi$
$102$		0			0
$103$	−13.6037	+	12.6224i	−1.34041	+	1.24372i	−0.394658	+	0.918828i	$0.629137\pi$
$103$	−13.6037	+	12.6224i	−1.34041	+	1.24372i	−0.945752	+	0.324890i	$0.894673\pi$
$104$	3.05414	+	5.28992i	0.299483	+	0.518720i
$105$		0			0
$106$	−2.99898	−	7.64127i	−0.291287	−	0.742186i
$107$	−2.91384	+	12.7663i	−0.281691	+	1.23417i	0.613933	+	0.789358i	$0.289586\pi$
$107$	−2.91384	+	12.7663i	−0.281691	+	1.23417i	−0.895624	+	0.444811i	$0.853271\pi$
$108$		0			0
$109$	−3.52478	−	4.41994i	−0.337613	−	0.423353i	0.583824	−	0.811880i	$-0.301556\pi$
$109$	−3.52478	−	4.41994i	−0.337613	−	0.423353i	−0.921438	+	0.388527i	$0.872984\pi$
$110$	7.44567	−	5.07637i	0.709916	−	0.484013i
$111$		0			0
$112$	−17.7542	−	2.67602i	−1.67762	−	0.252860i
$113$	0.877706	−	2.23636i	0.0825677	−	0.210379i	−0.883628	−	0.468190i	$-0.844906\pi$
$113$	0.877706	−	2.23636i	0.0825677	−	0.210379i	0.966195	+	0.257811i	$0.0830013\pi$
$114$		0			0
$115$	1.35991	−	2.35543i	0.126812	−	0.219645i
$116$	−19.3629	+	12.3588i	−1.79780	+	1.14749i
$117$		0			0
$118$	−5.57137	+	2.68303i	−0.512886	+	0.246993i
$119$	−18.8062	+	2.83458i	−1.72396	+	0.259846i
$120$		0			0
$121$	4.59480	+	3.13268i	0.417709	+	0.284789i
$122$	−0.765867	−	10.2198i	−0.0693383	−	0.925255i
$123$		0			0
$124$	17.4232	+	16.1664i	1.56465	+	1.45178i
$125$	1.81448	−	7.94974i	0.162292	−	0.711046i
$126$		0			0
$127$	−0.808610	−	3.54275i	−0.0717525	−	0.314368i	0.926297	−	0.376794i	$-0.122974\pi$
$127$	−0.808610	−	3.54275i	−0.0717525	−	0.314368i	−0.998050	+	0.0624257i	$0.980116\pi$
$128$	−8.12973	+	14.0811i	−0.718573	+	1.24461i
$129$		0			0
$130$	−0.178240	−	2.37845i	−0.0156327	−	0.208604i
$131$	0.651429	+	8.69272i	0.0569156	+	0.759486i	0.950526	+	0.310644i	$0.100545\pi$
$131$	0.651429	+	8.69272i	0.0569156	+	0.759486i	−0.893611	+	0.448843i	$0.851836\pi$
$132$		0			0
$133$	5.98947	−	10.3741i	0.519353	−	0.899546i
$134$	−3.85227	−	16.8779i	−0.332785	−	1.45803i
$135$		0			0
$136$	7.57114	−	33.1713i	0.649220	−	2.84442i
$137$	−9.12378	−	8.46563i	−0.779498	−	0.723268i	0.186321	−	0.982489i	$-0.440344\pi$
$137$	−9.12378	−	8.46563i	−0.779498	−	0.723268i	−0.965818	+	0.259221i	$0.916534\pi$
$138$		0			0
$139$	−1.45591	−	19.4278i	−0.123489	−	1.64784i	−0.623499	−	0.781824i	$-0.714289\pi$
$139$	−1.45591	−	19.4278i	−0.123489	−	1.64784i	0.500010	−	0.866020i	$-0.333330\pi$
$140$	9.88345	+	6.73842i	0.835304	+	0.569500i
$141$		0			0
$142$	26.1101	−	3.93546i	2.19111	−	0.330257i
$143$	3.94922	−	1.90184i	0.330250	−	0.159040i
$144$		0			0
$145$	4.73014	−	0.566936i	0.392817	−	0.0470814i
$146$	11.8714	−	20.5619i	0.982488	−	1.70172i
$147$		0			0
$148$	−17.7880	+	45.3231i	−1.46216	+	3.72554i
$149$	6.34835	+	0.956859i	0.520077	+	0.0783890i	0.403835	−	0.914832i	$-0.367677\pi$
$149$	6.34835	+	0.956859i	0.520077	+	0.0783890i	0.116242	+	0.993221i	$0.462915\pi$
$150$		0			0
$151$	1.35513	−	0.923912i	0.110279	−	0.0751869i	−0.506925	−	0.861990i	$-0.669218\pi$
$151$	1.35513	−	0.923912i	0.110279	−	0.0751869i	0.617204	+	0.786803i	$0.288265\pi$
$152$	13.3616	+	16.7549i	1.08377	+	1.35900i
$153$		0			0
$154$	−7.18535	+	31.4811i	−0.579012	+	2.53682i
$155$	−1.80088	−	4.58857i	−0.144650	−	0.368563i
$156$		0			0
$157$	6.60828	+	11.4459i	0.527398	+	0.913481i	0.999490	+	0.0319312i	$0.0101657\pi$
$157$	6.60828	+	11.4459i	0.527398	+	0.913481i	−0.472092	+	0.881549i	$0.656501\pi$
$158$	−19.0594	+	17.6846i	−1.51629	+	1.40691i
$159$		0			0
$160$	−2.07275	+	1.41318i	−0.163865	+	0.111722i
$161$	2.16865	+	9.50148i	0.170914	+	0.748821i
$162$		0			0
$163$	−4.13036	−	18.0963i	−0.323515	−	1.41741i	−0.831250	−	0.555899i	$-0.812374\pi$
$163$	−4.13036	−	18.0963i	−0.323515	−	1.41741i	0.507735	−	0.861513i	$-0.330483\pi$
$164$	−6.66516	−	16.9825i	−0.520461	−	1.32611i
$165$		0			0
$166$	−24.4244	+	7.53392i	−1.89570	+	0.584746i
$167$	1.34700	−	3.43211i	0.104234	−	0.265585i	−0.869236	−	0.494397i	$-0.835389\pi$
$167$	1.34700	−	3.43211i	0.104234	−	0.265585i	0.973471	+	0.228812i	$0.0734842\pi$
$168$		0			0
$169$	−0.884793	+	11.8067i	−0.0680610	+	0.908211i
$170$	−8.28345	+	10.3871i	−0.635311	+	0.796655i
$171$		0			0
$172$	22.5096	−	10.8400i	1.71634	−	0.826545i
$173$	9.19208	−	15.9212i	0.698861	−	1.21046i	−0.270000	−	0.962860i	$-0.587024\pi$
$173$	9.19208	−	15.9212i	0.698861	−	1.21046i	0.968862	−	0.247603i	$-0.0796428\pi$
$174$		0			0
$175$	6.68444	+	11.5778i	0.505297	+	0.875199i
$176$	−19.0449	−	12.9846i	−1.43556	−	0.978751i
$177$		0			0
$178$	−11.9834	−	30.5332i	−0.898194	−	2.28856i
$179$	5.72547	−	2.75724i	0.427942	−	0.206086i	−0.207499	−	0.978235i	$-0.566532\pi$
$179$	5.72547	−	2.75724i	0.427942	−	0.206086i	0.635441	+	0.772149i	$0.280818\pi$
$180$		0			0
$181$	0.610028	+	0.764951i	0.0453430	+	0.0568583i	0.803986	−	0.594648i	$-0.202709\pi$
$181$	0.610028	+	0.764951i	0.0453430	+	0.0568583i	−0.758643	+	0.651507i	$0.774137\pi$
$182$	6.26504	+	5.81311i	0.464396	+	0.430896i
$183$		0			0
$184$	−17.2406	−	2.59860i	−1.27099	−	0.191571i
$185$	7.40213	−	6.86818i	0.544216	−	0.504958i
$186$		0			0
$187$	−23.3312	−	7.19672i	−1.70615	−	0.526276i
$188$	18.8901	+	9.09700i	1.37770	+	0.663467i
$189$		0			0
$190$	−1.86205	−	8.15817i	−0.135087	−	0.591856i
$191$	7.67720	−	13.2973i	0.555503	−	0.962159i	−0.442361	−	0.896837i	$-0.645859\pi$
$191$	7.67720	−	13.2973i	0.555503	−	0.962159i	0.997864	−	0.0653223i	$-0.0208076\pi$
$192$		0			0
$193$	−21.1364	−	3.18580i	−1.52143	−	0.229319i	−0.665496	−	0.746401i	$-0.731780\pi$
$193$	−21.1364	−	3.18580i	−1.52143	−	0.229319i	−0.855936	+	0.517082i	$0.827018\pi$
$194$	16.3039	−	5.02907i	1.17055	−	0.361066i
$195$		0			0
$196$	−12.8586	+	1.93812i	−0.918469	+	0.138437i
$197$	2.63806	+	1.27042i	0.187954	+	0.0905140i	0.525494	−	0.850797i	$-0.323880\pi$
$197$	2.63806	+	1.27042i	0.187954	+	0.0905140i	−0.337540	+	0.941311i	$0.609595\pi$
$198$		0			0
$199$	−10.4646	+	13.1221i	−0.741813	+	0.930204i	−0.999349	−	0.0360642i	$-0.988518\pi$
$199$	−10.4646	+	13.1221i	−0.741813	+	0.930204i	0.257536	+	0.966269i	$0.417089\pi$
$200$	−23.6498	+	3.56464i	−1.67230	+	0.252058i
$201$		0			0
$202$	−15.1303	−	26.2065i	−1.06457	−	1.84388i
$203$	−11.0430	+	13.0177i	−0.775067	+	0.913661i
$204$		0			0
$205$	−0.282749	+	3.77302i	−0.0197480	+	0.263519i
$206$	−28.9622	−	36.3175i	−2.01789	−	2.53036i
$207$		0			0
$208$	−5.49661	+	2.64703i	−0.381121	+	0.183538i
$209$	12.7062	−	8.66297i	0.878909	−	0.599230i
$210$		0			0
$211$	20.7853	−	6.41142i	1.43092	−	0.441380i	0.520072	−	0.854122i	$-0.325905\pi$
$211$	20.7853	−	6.41142i	1.43092	−	0.441380i	0.910848	+	0.412742i	$0.135429\pi$
$212$	13.3671	−	4.12320i	0.918055	−	0.283183i
$213$		0			0
$214$	−31.3212	−	9.66132i	−2.14108	−	0.660434i
$215$	−5.18145			−0.353372
$216$		0			0
$217$	15.9139	+	7.66371i	1.08030	+	0.520246i
$218$	11.6920	−	7.97149i	0.791884	−	0.539897i
$219$		0			0
$220$	7.67832	+	13.2992i	0.517672	+	0.896634i
$221$	−4.73718	+	4.39546i	−0.318657	+	0.295671i
$222$		0			0
$223$	15.1181	+	14.0275i	1.01238	+	0.939352i	0.998165	−	0.0605468i	$-0.0192844\pi$
$223$	15.1181	+	14.0275i	1.01238	+	0.939352i	0.0142155	+	0.999899i	$0.495475\pi$
$224$	2.00028	−	8.76382i	0.133650	−	0.585557i
$225$		0			0
$226$	5.41803	+	2.60919i	0.360402	+	0.173561i
$227$	2.04778	−	27.3257i	0.135916	−	1.81367i	−0.346850	−	0.937921i	$-0.612749\pi$
$227$	2.04778	−	27.3257i	0.135916	−	1.81367i	0.482766	−	0.875750i	$-0.339632\pi$
$228$		0			0
$229$	−2.89065	+	7.36526i	−0.191020	+	0.486710i	−0.994011	−	0.109281i	$-0.965145\pi$
$229$	−2.89065	+	7.36526i	−0.191020	+	0.486710i	0.802991	+	0.595991i	$0.203240\pi$
$230$	5.62505	+	3.83509i	0.370905	+	0.252878i
$231$		0			0
$232$	−14.4611	−	26.8986i	−0.949419	−	1.76598i
$233$	0.137282			0.00899364			0.00449682	−	0.999990i	$-0.498569\pi$
$233$	0.137282			0.00899364			0.00449682	+	0.999990i	$0.498569\pi$
$234$		0			0
$235$	−2.71111	−	3.39963i	−0.176853	−	0.221767i
$236$	−3.84989	−	9.80936i	−0.250607	−	0.638535i
$237$		0			0
$238$	−3.55759	−	47.4728i	−0.230605	−	3.07720i
$239$	6.83054	−	17.4039i	0.441831	−	1.12577i	−0.520495	−	0.853865i	$-0.674252\pi$
$239$	6.83054	−	17.4039i	0.441831	−	1.12577i	0.962325	−	0.271901i	$-0.0876524\pi$
$240$		0			0
$241$	−14.3976	−	13.3590i	−0.927429	−	0.860529i	0.0630751	−	0.998009i	$-0.479909\pi$
$241$	−14.3976	−	13.3590i	−0.927429	−	0.860529i	−0.990505	+	0.137480i	$0.956100\pi$
$242$	−8.67903	+	10.8832i	−0.557909	+	0.699596i
$243$		0			0
$244$	17.4645			1.11805
$245$	2.57708	+	0.794924i	0.164644	+	0.0507858i
$246$		0			0
$247$	−0.304172	−	4.05889i	−0.0193540	−	0.258261i
$248$	−23.1639	+	21.4929i	−1.47091	+	1.36480i
$249$		0			0
$250$	19.5041	+	6.01621i	1.23355	+	0.380498i
$251$	−6.72717	+	8.43561i	−0.424615	+	0.532451i	−0.947416	−	0.320004i	$-0.896316\pi$
$251$	−6.72717	+	8.43561i	−0.424615	+	0.532451i	0.522801	+	0.852455i	$0.324887\pi$
$252$		0			0
$253$	−2.78409	+	12.1979i	−0.175034	+	0.766874i
$254$	8.99437	−	1.35568i	0.564357	−	0.0850632i
$255$		0			0
$256$	−26.6375	−	18.1612i	−1.66485	−	1.13507i
$257$	−27.3546	−	4.12305i	−1.70633	−	0.257189i	−0.777820	−	0.628487i	$-0.783675\pi$
$257$	−27.3546	−	4.12305i	−1.70633	−	0.257189i	−0.928514	+	0.371298i	$0.878913\pi$
$258$		0			0
$259$	−2.70394	+	36.0815i	−0.168015	+	2.24200i
$260$	4.06451			0.252070
$261$		0			0
$262$	−21.8199			−1.34804
$263$	−1.81231	+	24.1836i	−0.111752	+	1.49122i	0.606301	+	0.795236i	$0.292653\pi$
$263$	−1.81231	+	24.1836i	−0.111752	+	1.49122i	−0.718052	+	0.695989i	$0.754966\pi$
$264$		0			0
$265$	−2.86872	−	0.432390i	−0.176224	−	0.0265615i
$266$	24.7745	+	16.8910i	1.51902	+	1.03565i
$267$		0			0
$268$	29.1720	−	4.39697i	1.78196	−	0.268587i
$269$	−3.73894	+	16.3814i	−0.227967	+	0.998791i	0.723327	+	0.690506i	$0.242612\pi$
$269$	−3.73894	+	16.3814i	−0.227967	+	0.998791i	−0.951294	+	0.308285i	$0.900245\pi$
$270$		0			0
$271$	−0.616154	+	0.772632i	−0.0374287	+	0.0469341i	−0.800194	−	0.599742i	$-0.795270\pi$
$271$	−0.616154	+	0.772632i	−0.0374287	+	0.0469341i	0.762765	+	0.646676i	$0.223841\pi$
$272$	32.4729	+	10.0166i	1.96896	+	0.607343i
$273$		0			0
$274$	22.8379	−	21.1905i	1.37969	−	1.28016i
$275$	1.28258	+	17.1148i	0.0773424	+	1.03206i
$276$		0			0
$277$	5.76285	+	1.77760i	0.346256	+	0.106806i	0.463005	−	0.886356i	$-0.346771\pi$
$277$	5.76285	+	1.77760i	0.346256	+	0.106806i	−0.116749	+	0.993161i	$0.537247\pi$
$278$	48.7664			2.92481
$279$		0			0
$280$	−9.91551	+	12.4337i	−0.592565	+	0.743053i
$281$	2.69477	+	2.50038i	0.160757	+	0.149160i	0.756450	−	0.654052i	$-0.226932\pi$
$281$	2.69477	+	2.50038i	0.160757	+	0.149160i	−0.595693	+	0.803212i	$0.703123\pi$
$282$		0			0
$283$	−2.00570	+	5.11045i	−0.119227	+	0.303785i	−0.978011	−	0.208552i	$-0.933125\pi$
$283$	−2.00570	+	5.11045i	−0.119227	+	0.303785i	0.858785	+	0.512337i	$0.171220\pi$
$284$	3.36264	+	44.8713i	0.199536	+	2.66262i
$285$		0			0
$286$	4.00849	+	10.2135i	0.237027	+	0.603935i
$287$	−8.45306	−	10.5998i	−0.498968	−	0.625686i
$288$		0			0
$289$	18.9962			1.11742
$290$	0.530326	+	11.9130i	0.0311418	+	0.699558i
$291$		0			0
$292$	33.4301	+	22.7922i	1.95635	+	1.33381i
$293$	−10.0571	+	25.6250i	−0.587541	+	1.49703i	0.259629	+	0.965708i	$0.416400\pi$
$293$	−10.0571	+	25.6250i	−0.587541	+	1.49703i	−0.847170	+	0.531322i	$0.821696\pi$
$294$		0			0
$295$	−0.163320	+	2.17935i	−0.00950885	+	0.126887i
$296$	−58.3205	−	28.0857i	−3.38981	−	1.63245i
$297$		0			0
$298$	−3.57594	+	15.6672i	−0.207149	+	0.907578i
$299$	2.42750	+	2.25239i	0.140386	+	0.130259i
$300$		0			0
$301$	13.6102	−	12.6284i	0.784479	−	0.727890i
$302$	2.05270	+	3.55539i	0.118120	+	0.204590i
$303$		0			0
$304$	−17.6848	+	12.0573i	−1.01430	+	0.691535i
$305$	−3.26331	−	1.57153i	−0.186857	−	0.0899855i
$306$		0			0
$307$	−8.42970			−0.481108			−0.240554	−	0.970636i	$-0.577329\pi$
$307$	−8.42970			−0.481108			−0.240554	+	0.970636i	$0.577329\pi$
$308$	−52.5822	−	16.2195i	−2.99615	−	0.924190i
$309$		0			0
$310$	11.7905	−	3.63688i	0.669654	−	0.206561i
$311$	24.9091	−	7.68345i	1.41247	−	0.435689i	0.507678	−	0.861547i	$-0.330504\pi$
$311$	24.9091	−	7.68345i	1.41247	−	0.435689i	0.904790	+	0.425859i	$0.140028\pi$
$312$		0			0
$313$	2.73544	−	1.86499i	0.154616	−	0.105416i	−0.483541	−	0.875322i	$-0.660649\pi$
$313$	2.73544	−	1.86499i	0.154616	−	0.105416i	0.638157	+	0.769906i	$0.279697\pi$
$314$	−29.8064	+	14.3540i	−1.68207	+	0.810043i
$315$		0			0
$316$	−27.6250	−	34.6407i	−1.55403	−	1.94869i
$317$	−1.77512	+	23.6873i	−0.0997005	+	1.33041i	0.693061	+	0.720879i	$0.256262\pi$
$317$	−1.77512	+	23.6873i	−0.0997005	+	1.33041i	−0.792761	+	0.609532i	$0.791357\pi$
$318$		0			0
$319$	−20.0239	+	8.90581i	−1.12113	+	0.498630i
$320$	1.87100	+	3.24066i	0.104592	+	0.181158i
$321$		0			0
$322$	−24.1225	+	3.63588i	−1.34429	+	0.202619i
$323$	−14.1359	+	17.7259i	−0.786545	+	0.986296i
$324$		0			0
$325$	4.09270	+	1.97094i	0.227022	+	0.109328i
$326$	45.9431	−	6.92481i	2.54455	−	0.383530i
$327$		0			0
$328$	23.1771	−	7.14919i	1.27974	−	0.394748i
$329$	15.4070	+	2.32224i	0.849418	+	0.128029i
$330$		0			0
$331$	10.4506	−	18.1009i	0.574415	−	0.994916i	−0.421690	−	0.906740i	$-0.638563\pi$
$331$	10.4506	−	18.1009i	0.574415	−	0.994916i	0.996105	−	0.0881761i	$-0.0281038\pi$
$332$	−9.69234	−	42.4649i	−0.531936	−	2.33057i
$333$		0			0
$334$	8.31498	+	4.00428i	0.454975	+	0.219105i
$335$	−5.84657	−	1.80343i	−0.319432	−	0.0985317i
$336$		0			0
$337$	−6.18563	+	5.73942i	−0.336953	+	0.312646i	−0.830442	−	0.557106i	$-0.811912\pi$
$337$	−6.18563	+	5.73942i	−0.336953	+	0.312646i	0.493489	+	0.869752i	$0.335721\pi$
$338$	−29.3055	−	4.41709i	−1.59401	−	0.240258i
$339$		0			0
$340$	−16.5964	−	15.3992i	−0.900067	−	0.835140i
$341$	14.1380	+	17.7285i	0.765616	+	0.960052i
$342$		0			0
$343$	11.2855	−	5.43479i	0.609357	−	0.293451i
$344$	12.1350	+	30.9194i	0.654274	+	1.66706i
$345$		0			0
$346$	38.0216	+	25.9227i	2.04405	+	1.39361i
$347$	−1.60263	−	2.77583i	−0.0860334	−	0.149014i	0.819798	−	0.572653i	$-0.194086\pi$
$347$	−1.60263	−	2.77583i	−0.0860334	−	0.149014i	−0.905831	+	0.423639i	$0.860753\pi$
$348$		0			0
$349$	−2.78553	+	4.82468i	−0.149106	+	0.258259i	−0.930897	−	0.365281i	$-0.880973\pi$
$349$	−2.78553	+	4.82468i	−0.149106	+	0.258259i	0.781791	+	0.623540i	$0.214306\pi$
$350$	−30.1499	+	14.5194i	−1.61158	+	0.776096i
$351$		0			0
$352$	7.19521	−	9.02251i	0.383506	−	0.480901i
$353$	0.789451	−	10.5345i	0.0420183	−	0.560695i	−0.935976	−	0.352063i	$-0.885480\pi$
$353$	0.789451	−	10.5345i	0.0420183	−	0.560695i	0.977994	−	0.208631i	$-0.0669008\pi$
$354$		0			0
$355$	3.40939	−	8.68698i	0.180951	−	0.461057i
$356$	53.4126	−	16.4756i	2.83086	−	0.873205i
$357$		0			0
$358$	5.81140	+	14.8072i	0.307142	+	0.782586i
$359$	3.72680	+	16.3282i	0.196693	+	0.861769i	0.972888	+	0.231276i	$0.0742900\pi$
$359$	3.72680	+	16.3282i	0.196693	+	0.861769i	−0.776195	+	0.630493i	$0.782853\pi$
$360$		0			0
$361$	1.05026	+	4.60147i	0.0552767	+	0.242183i
$362$	−2.02352	+	1.37961i	−0.106354	+	0.0725107i
$363$		0			0
$364$	−10.6763	+	9.90618i	−0.559592	+	0.519225i
$365$	−4.19561	−	7.26701i	−0.219608	−	0.380372i
$366$		0			0
$367$	12.7261	+	32.4256i	0.664297	+	1.69260i	0.719835	+	0.694145i	$0.244218\pi$
$367$	12.7261	+	32.4256i	0.664297	+	1.69260i	−0.0555376	+	0.998457i	$0.517687\pi$
$368$	3.87495	−	16.9773i	0.201996	−	0.885002i
$369$		0			0
$370$	15.7591	+	19.7613i	0.819279	+	1.02734i
$371$	8.58917	−	5.85599i	0.445927	−	0.304028i
$372$		0			0
$373$	0.450470	+	0.0678974i	0.0233244	+	0.00351559i	0.160694	−	0.987004i	$-0.448627\pi$
$373$	0.450470	+	0.0678974i	0.0233244	+	0.00351559i	−0.137370	+	0.990520i	$0.543865\pi$
$374$	22.3281	−	56.8912i	1.15456	−	2.94177i
$375$		0			0
$376$	−13.9373	+	24.1401i	−0.718760	+	1.24493i
$377$	−0.608570	+	5.76836i	−0.0313429	+	0.297085i
$378$		0			0
$379$	2.09017	−	1.00658i	0.107365	−	0.0517043i	−0.379430	−	0.925220i	$-0.623880\pi$
$379$	2.09017	−	1.00658i	0.107365	−	0.0517043i	0.486795	+	0.873516i	$0.338166\pi$
$380$	14.1007	−	2.12534i	0.723350	−	0.109027i
$381$		0			0
$382$	31.7555	+	21.6506i	1.62475	+	1.10774i
$383$	1.00028	+	13.3479i	0.0511121	+	0.682044i	0.962636	+	0.270797i	$0.0872873\pi$
$383$	1.00028	+	13.3479i	0.0511121	+	0.682044i	−0.911524	+	0.411246i	$0.865094\pi$
$384$		0			0
$385$	8.36572	+	7.76225i	0.426356	+	0.395601i
$386$	11.9059	−	52.1630i	0.605993	−	2.65503i
$387$		0			0
$388$	6.46987	+	28.3463i	0.328458	+	1.43907i
$389$	16.0062	−	27.7235i	0.811544	−	1.40564i	−0.100239	−	0.994963i	$-0.531961\pi$
$389$	16.0062	−	27.7235i	0.811544	−	1.40564i	0.911783	−	0.410672i	$-0.134706\pi$
$390$		0			0
$391$	−1.37845	−	18.3941i	−0.0697112	−	0.930232i
$392$	−1.29196	−	17.2400i	−0.0652538	−	0.870752i
$393$		0			0
$394$	−3.66460	+	6.34727i	−0.184620	+	0.319771i
$395$	2.04474	+	8.95859i	0.102882	+	0.450755i
$396$		0			0
$397$	−3.06938	+	13.4479i	−0.154048	+	0.674928i	0.837636	+	0.546229i	$0.183937\pi$
$397$	−3.06938	+	13.4479i	−0.154048	+	0.674928i	−0.991684	+	0.128699i	$0.958920\pi$
$398$	−30.7969	−	28.5754i	−1.54371	−	1.43235i
$399$		0			0
$400$	−1.78512	−	23.8208i	−0.0892561	−	1.19104i
$401$	−10.6382	−	7.25301i	−0.531247	−	0.362198i	0.267792	−	0.963477i	$-0.413706\pi$
$401$	−10.6382	−	7.25301i	−0.531247	−	0.362198i	−0.799040	+	0.601278i	$0.794658\pi$
$402$		0			0
$403$	5.93462	−	0.894500i	0.295624	−	0.0445582i
$404$	46.4607	−	22.3743i	2.31151	−	1.11316i
$405$		0			0
$406$	−30.4279	−	29.9997i	−1.51011	−	1.48886i
$407$	−23.2255	+	40.2277i	−1.15124	+	1.99401i
$408$		0			0
$409$	−2.48140	+	6.32251i	−0.122697	+	0.312628i	−0.979004	−	0.203839i	$-0.934658\pi$
$409$	−2.48140	+	6.32251i	−0.122697	+	0.312628i	0.856307	+	0.516467i	$0.172753\pi$
$410$	−9.36501	−	1.41155i	−0.462505	−	0.0697114i
$411$		0			0
$412$	65.4043	−	44.5919i	3.22224	−	2.19688i
$413$	−4.88261	−	6.12260i	−0.240257	−	0.301273i
$414$		0			0
$415$	−2.01012	+	8.80691i	−0.0986729	+	0.432314i
$416$	−1.11590	−	2.84326i	−0.0547114	−	0.139402i
$417$		0			0
$418$	19.2470	+	33.3367i	0.941401	+	1.63055i
$419$	0.221291	−	0.205328i	0.0108108	−	0.0100309i	−0.674749	−	0.738047i	$-0.735748\pi$
$419$	0.221291	−	0.205328i	0.0108108	−	0.0100309i	0.685560	+	0.728016i	$0.259558\pi$
$420$		0			0
$421$	8.62075	−	5.87753i	0.420150	−	0.286453i	−0.334733	−	0.942313i	$-0.608646\pi$
$421$	8.62075	−	5.87753i	0.420150	−	0.286453i	0.754883	+	0.655860i	$0.227694\pi$
$422$	12.1156	+	53.0819i	0.589778	+	2.58398i
$423$		0			0
$424$	4.13835	+	18.1313i	0.200976	+	0.880533i
$425$	−9.24423	−	23.5539i	−0.448411	−	1.14253i
$426$		0			0
$427$	12.4020	−	3.82551i	0.600175	−	0.185129i
$428$	20.4066	−	51.9953i	0.986392	−	2.51329i
$429$		0			0
$430$	0.969231	−	12.9335i	0.0467405	−	0.623708i
$431$	10.1298	−	12.7023i	0.487934	−	0.611850i	−0.475526	−	0.879702i	$-0.657742\pi$
$431$	10.1298	−	12.7023i	0.487934	−	0.611850i	0.963460	+	0.267852i	$0.0863137\pi$
$432$		0			0
$433$	18.6301	−	8.97180i	0.895307	−	0.431157i	0.0711152	−	0.997468i	$-0.477344\pi$
$433$	18.6301	−	8.97180i	0.895307	−	0.431157i	0.824192	+	0.566311i	$0.191630\pi$
$434$	−22.1063	+	38.2893i	−1.06114	+	1.83794i
$435$		0			0
$436$	12.0574	+	20.8840i	0.577443	+	1.00016i
$437$	9.59930	+	6.54469i	0.459197	+	0.313075i
$438$		0			0
$439$	−3.95578	−	10.0792i	−0.188799	−	0.481052i	0.804863	−	0.593461i	$-0.202239\pi$
$439$	−3.95578	−	10.0792i	−0.188799	−	0.481052i	−0.993662	+	0.112408i	$0.964144\pi$
$440$	−18.3945	+	8.85834i	−0.876925	+	0.422305i
$441$		0			0
$442$	−10.0855	−	12.6468i	−0.479716	−	0.601545i
$443$	−9.89605	−	9.18219i	−0.470175	−	0.436259i	0.409159	−	0.912463i	$-0.365822\pi$
$443$	−9.89605	−	9.18219i	−0.470175	−	0.436259i	−0.879335	+	0.476204i	$0.842012\pi$
$444$		0			0
$445$	−11.4629	−	1.72776i	−0.543394	−	0.0819035i
$446$	−37.8423	+	35.1125i	−1.79188	+	1.66263i
$447$		0			0
$448$	−12.8128	−	3.95224i	−0.605350	−	0.186726i
$449$	17.8781	+	8.60963i	0.843718	+	0.406313i	0.805242	−	0.592946i	$-0.202035\pi$
$449$	17.8781	+	8.60963i	0.843718	+	0.406313i	0.0384763	+	0.999260i	$0.487750\pi$
$450$		0			0
$451$	−3.87301	−	16.9688i	−0.182373	−	0.799028i
$452$	−5.12389	+	8.87484i	−0.241008	+	0.417437i
$453$		0			0
$454$	67.8251	+	10.2230i	3.18319	+	0.479788i
$455$	2.88632	−	0.890311i	0.135313	−	0.0417384i
$456$		0			0
$457$	−3.45918	+	0.521388i	−0.161814	+	0.0243895i	−0.229449	−	0.973321i	$-0.573693\pi$
$457$	−3.45918	+	0.521388i	−0.161814	+	0.0243895i	0.0676357	+	0.997710i	$0.478454\pi$
$458$	−17.8438	−	8.59313i	−0.833787	−	0.401531i
$459$		0			0
$460$	−7.23349	+	9.07051i	−0.337263	+	0.422915i
$461$	2.98783	−	0.450343i	0.139157	−	0.0209746i	−0.0790943	−	0.996867i	$-0.525203\pi$
$461$	2.98783	−	0.450343i	0.139157	−	0.0209746i	0.218251	+	0.975893i	$0.429965\pi$
$462$		0			0
$463$	−17.5448	−	30.3885i	−0.815377	−	1.41227i	−0.909057	−	0.416672i	$-0.863196\pi$
$463$	−17.5448	−	30.3885i	−0.815377	−	1.41227i	0.0936794	−	0.995602i	$-0.470137\pi$
$464$	27.8698	−	12.3953i	1.29382	−	0.575438i
$465$		0			0
$466$	−0.0256797	+	0.342672i	−0.00118959	+	0.0158740i
$467$	−0.619173	−	0.776418i	−0.0286519	−	0.0359284i	0.767299	−	0.641289i	$-0.221600\pi$
$467$	−0.619173	−	0.776418i	−0.0286519	−	0.0359284i	−0.795951	+	0.605361i	$0.793029\pi$
$468$		0			0
$469$	19.7527	−	9.51239i	0.912094	−	0.439241i
$470$	8.99300	−	6.13132i	0.414816	−	0.282817i
$471$		0			0
$472$	13.3874	−	4.12947i	0.616206	−	0.190074i
$473$	22.7765	−	7.02562i	1.04726	−	0.323038i
$474$		0			0
$475$	15.2291	+	4.69756i	0.698760	+	0.215539i
$476$	81.1258			3.71839
$477$		0			0
$478$	42.1645	+	20.3054i	1.92856	+	0.928745i
$479$	−0.343405	+	0.234130i	−0.0156906	+	0.0106977i	−0.571140	−	0.820853i	$-0.693499\pi$
$479$	−0.343405	+	0.234130i	−0.0156906	+	0.0106977i	0.555449	+	0.831550i	$0.312546\pi$
$480$		0			0
$481$	6.14719	+	10.6472i	0.280288	+	0.485472i
$482$	36.0388	−	33.4391i	1.64152	−	1.52311i
$483$		0			0
$484$	−17.3890	−	16.1346i	−0.790409	−	0.733393i
$485$	1.34180	−	5.87882i	0.0609282	−	0.266944i
$486$		0			0
$487$	−6.26437	−	3.01676i	−0.283866	−	0.136702i	0.286533	−	0.958070i	$-0.407497\pi$
$487$	−6.26437	−	3.01676i	−0.283866	−	0.136702i	−0.570399	+	0.821368i	$0.693211\pi$
$488$	−1.73514	+	23.1538i	−0.0785460	+	1.04812i
$489$		0			0
$490$	−2.46629	+	6.28399i	−0.111415	+	0.283882i
$491$	0.610617	+	0.416312i	0.0275568	+	0.0187879i	0.577020	−	0.816730i	$-0.304215\pi$
$491$	0.610617	+	0.416312i	0.0275568	+	0.0187879i	−0.549463	+	0.835518i	$0.685168\pi$
$492$		0			0
$493$	24.3395	−	21.2480i	1.09620	−	0.956961i
$494$	10.1884			0.458396
$495$		0			0
$496$	−19.6776	−	24.6749i	−0.883550	−	1.10794i
$497$	12.2167	+	31.1277i	0.547996	+	1.39627i
$498$		0			0
$499$	0.421807	+	5.62863i	0.0188827	+	0.251972i	0.998655	+	0.0518546i	$0.0165133\pi$
$499$	0.421807	+	5.62863i	0.0188827	+	0.251972i	−0.979772	+	0.200117i	$0.935868\pi$
$500$	−12.7074	+	32.3780i	−0.568294	+	1.44799i
$501$		0			0
$502$	−19.7979	−	18.3698i	−0.883623	−	0.819882i
$503$	8.14676	−	10.2157i	0.363246	−	0.455496i	−0.566302	−	0.824198i	$-0.691626\pi$
$503$	8.14676	−	10.2157i	0.363246	−	0.455496i	0.929548	+	0.368702i	$0.120198\pi$
$504$		0			0
$505$	−10.6947			−0.475909
$506$	−29.9265	−	9.23112i	−1.33040	−	0.410373i
$507$		0			0
$508$	1.15836	+	15.4572i	0.0513938	+	0.685802i
$509$	−1.78841	+	1.65940i	−0.0792699	+	0.0735517i	−0.718813	−	0.695204i	$-0.755314\pi$
$509$	−1.78841	+	1.65940i	−0.0792699	+	0.0735517i	0.639543	+	0.768755i	$0.279124\pi$
$510$		0			0
$511$	28.7321	+	8.86269i	1.27103	+	0.392062i
$512$	30.0399	−	37.6689i	1.32759	−	1.66474i
$513$		0			0
$514$	15.4085	−	67.5091i	0.679640	−	2.97770i
$515$	−16.2336	+	2.44683i	−0.715340	+	0.107820i
$516$		0			0
$517$	16.5271	+	11.2680i	0.726860	+	0.495565i
$518$	−89.5580	−	13.4987i	−3.93495	−	0.593098i
$519$		0			0
$520$	−0.403819	+	5.38859i	−0.0177086	+	0.236305i
$521$	−26.6176			−1.16614			−0.583070	−	0.812422i	$-0.698149\pi$
$521$	−26.6176			−1.16614			−0.583070	+	0.812422i	$0.698149\pi$
$522$		0			0
$523$	−26.3711			−1.15313			−0.576564	−	0.817052i	$-0.695607\pi$
$523$	−26.3711			−1.15313			−0.576564	+	0.817052i	$0.695607\pi$
$524$	2.77873	−	37.0796i	0.121389	−	1.61983i
$525$		0			0
$526$	−60.0261	−	9.04747i	−2.61726	−	0.394489i
$527$	−27.6216	−	18.8321i	−1.20321	−	0.820337i
$528$		0			0
$529$	13.3965	−	2.01919i	0.582454	−	0.0877909i
$530$	1.61591	−	7.07978i	0.0701908	−	0.307526i
$531$		0			0
$532$	−31.8586	+	39.9494i	−1.38125	+	1.73203i
$533$	−4.40204	−	1.35785i	−0.190673	−	0.0588149i
$534$		0			0
$535$	−8.49183	+	7.87927i	−0.367134	+	0.340650i
$536$	2.93104	+	39.1121i	0.126602	+	1.68938i
$537$		0			0
$538$	−40.1904	−	12.3971i	−1.73273	−	0.534477i
$539$	−12.4061			−0.534370
$540$		0			0
$541$	1.36338	−	1.70962i	0.0586163	−	0.0735025i	−0.751659	−	0.659552i	$-0.770746\pi$
$541$	1.36338	−	1.70962i	0.0586163	−	0.0735025i	0.810275	+	0.586049i	$0.199318\pi$
$542$	−1.81332	−	1.68252i	−0.0778889	−	0.0722704i
$543$		0			0
$544$	−6.21579	+	15.8376i	−0.266500	+	0.679030i
$545$	−0.373741	−	4.98723i	−0.0160093	−	0.213629i
$546$		0			0
$547$	−3.46885	−	8.83848i	−0.148317	−	0.377906i	0.837336	−	0.546688i	$-0.184112\pi$
$547$	−3.46885	−	8.83848i	−0.148317	−	0.377906i	−0.985653	+	0.168782i	$0.946017\pi$
$548$	33.1016	+	41.5081i	1.41403	+	1.77314i
$549$		0			0
$550$	−42.9605			−1.83184
$551$	0.905017	+	20.3299i	0.0385550	+	0.866085i
$552$		0			0
$553$	−27.2052	−	18.5482i	−1.15688	−	0.788749i
$554$	−5.51509	+	14.0522i	−0.234314	+	0.597022i
$555$		0			0
$556$	−6.21032	+	82.8710i	−0.263376	+	3.51451i
$557$	−11.3897	−	5.48500i	−0.482598	−	0.232407i	0.176734	−	0.984259i	$-0.443447\pi$
$557$	−11.3897	−	5.48500i	−0.482598	−	0.232407i	−0.659332	+	0.751852i	$0.729161\pi$
$558$		0			0
$559$	1.40380	−	6.15046i	0.0593745	−	0.260137i
$560$	−11.6436	−	10.8037i	−0.492032	−	0.456539i
$561$		0			0
$562$	−6.74532	+	6.25875i	−0.284534	+	0.264009i
$563$	10.7605	+	18.6377i	0.453499	+	0.785484i	0.998601	−	0.0528862i	$-0.0168421\pi$
$563$	10.7605	+	18.6377i	0.453499	+	0.785484i	−0.545101	+	0.838370i	$0.683509\pi$
$564$		0			0
$565$	1.75602	−	1.19723i	0.0738762	−	0.0503679i
$566$	−12.3811	−	5.96242i	−0.520416	−	0.250619i
$567$		0			0
$568$	−59.8229			−2.51011
$569$	−1.91961	−	0.592121i	−0.0804743	−	0.0248230i	0.254257	−	0.967137i	$-0.418169\pi$
$569$	−1.91961	−	0.592121i	−0.0804743	−	0.0248230i	−0.334731	+	0.942314i	$0.608645\pi$
$570$		0			0
$571$	−42.6242	+	13.1478i	−1.78377	+	0.550220i	−0.997691	−	0.0679096i	$-0.978367\pi$
$571$	−42.6242	+	13.1478i	−1.78377	+	0.550220i	−0.786077	+	0.618129i	$0.787891\pi$
$572$	−17.8667	+	5.51114i	−0.747044	+	0.230432i
$573$		0			0
$574$	28.0396	−	19.1170i	1.17035	−	0.797930i
$575$	−11.6821	+	5.62580i	−0.487177	+	0.234612i
$576$		0			0
$577$	15.5915	+	19.5511i	0.649081	+	0.813922i	0.992106	−	0.125405i	$-0.0400229\pi$
$577$	15.5915	+	19.5511i	0.649081	+	0.813922i	−0.343025	+	0.939326i	$0.611451\pi$
$578$	−3.55339	+	47.4167i	−0.147802	+	1.97228i
$579$		0			0
$580$	−20.3119	−	0.615898i	−0.843406	−	0.0255738i
$581$	−16.1845	−	28.0324i	−0.671448	−	1.16298i
$582$		0			0
$583$	13.1966	−	1.98906i	0.546546	−	0.0823785i
$584$	−33.5385	+	42.0560i	−1.38783	+	1.74029i
$585$		0			0
$586$	−62.0818	−	29.8970i	−2.56458	−	1.23503i
$587$	−8.01721	+	1.20840i	−0.330906	+	0.0498760i	−0.312394	−	0.949953i	$-0.601131\pi$
$587$	−8.01721	+	1.20840i	−0.330906	+	0.0498760i	−0.0185117	+	0.999829i	$0.505893\pi$
$588$		0			0
$589$	20.1208	−	6.20644i	0.829063	−	0.255732i
$590$	−5.40937	−	0.815331i	−0.222700	−	0.0335666i
$591$		0			0
$592$	32.3257	−	55.9898i	1.32858	−	2.30117i
$593$	−3.54355	−	15.5253i	−0.145516	−	0.637547i	−0.994098	−	0.108484i	$-0.965400\pi$
$593$	−3.54355	−	15.5253i	−0.145516	−	0.637547i	0.848582	−	0.529064i	$-0.177457\pi$
$594$		0			0
$595$	−15.1587	−	7.30005i	−0.621446	−	0.299273i
$596$	−26.1687	−	8.07196i	−1.07191	−	0.330640i
$597$		0			0
$598$	−6.07630	+	5.63799i	−0.248479	+	0.230554i
$599$	1.56835	+	0.236390i	0.0640808	+	0.00965863i	0.181004	−	0.983482i	$-0.442065\pi$
$599$	1.56835	+	0.236390i	0.0640808	+	0.00965863i	−0.116924	+	0.993141i	$0.537303\pi$
$600$		0			0
$601$	−5.61986	−	5.21447i	−0.229239	−	0.212703i	0.557187	−	0.830387i	$-0.311881\pi$
$601$	−5.61986	−	5.21447i	−0.229239	−	0.212703i	−0.786426	+	0.617684i	$0.788071\pi$
$602$	28.9761	+	36.3349i	1.18098	+	1.48090i
$603$		0			0
$604$	−6.30324	+	3.03548i	−0.256475	+	0.123512i
$605$	1.79735	+	4.57956i	0.0730725	+	0.186186i
$606$		0			0
$607$	4.27104	+	2.91194i	0.173356	+	0.118192i	0.646890	−	0.762584i	$-0.276069\pi$
$607$	4.27104	+	2.91194i	0.173356	+	0.118192i	−0.473534	+	0.880776i	$0.657022\pi$
$608$	−5.35805	−	9.28041i	−0.217298	−	0.376370i
$609$		0			0
$610$	4.53315	−	7.85164i	0.183542	−	0.317904i
$611$	4.76993	−	2.29708i	0.192971	−	0.0929298i
$612$		0			0
$613$	−6.69400	+	8.39402i	−0.270368	+	0.339031i	−0.898417	−	0.439143i	$-0.855282\pi$
$613$	−6.69400	+	8.39402i	−0.270368	+	0.339031i	0.628049	+	0.778174i	$0.283854\pi$
$614$	1.57684	−	21.0415i	0.0636362	−	0.849167i
$615$		0			0
$616$	26.7274	−	68.1003i	1.07688	−	2.74384i
$617$	−25.2213	+	7.77973i	−1.01537	+	0.313200i	−0.757399	−	0.652952i	$-0.773530\pi$
$617$	−25.2213	+	7.77973i	−1.01537	+	0.313200i	−0.257971	+	0.966153i	$0.583054\pi$
$618$		0			0
$619$	−2.60230	−	6.63056i	−0.104595	−	0.266505i	0.868989	−	0.494831i	$-0.164770\pi$
$619$	−2.60230	−	6.63056i	−0.104595	−	0.266505i	−0.973585	+	0.228326i	$0.926675\pi$
$620$	4.67882	+	20.4993i	0.187906	+	0.823270i
$621$		0			0
$622$	14.5193	+	63.6134i	0.582172	+	2.55066i
$623$	34.3208	−	23.3995i	1.37503	−	0.937483i
$624$		0			0
$625$	−10.1699	+	9.43627i	−0.406795	+	0.377451i
$626$	4.14356	+	7.17685i	0.165610	+	0.286845i
$627$		0			0
$628$	−20.5966	−	52.4793i	−0.821895	−	2.09415i
$629$	15.2387	−	66.7653i	0.607608	−	2.66211i
$630$		0			0
$631$	0.371221	+	0.465496i	0.0147781	+	0.0185311i	0.789166	−	0.614180i	$-0.210513\pi$
$631$	0.371221	+	0.465496i	0.0147781	+	0.0185311i	−0.774388	+	0.632712i	$0.781942\pi$
$632$	48.6701	−	33.1827i	1.93599	−	1.31994i
$633$		0			0
$634$	−58.7942	−	8.86180i	−2.33502	−	0.351947i
$635$	1.17446	−	2.99248i	0.0466071	−	0.118753i
$636$		0			0
$637$	−1.64179	+	2.84367i	−0.0650502	+	0.112670i
$638$	−18.4843	−	51.6480i	−0.731801	−	2.04476i
$639$		0			0
$640$	−12.9595	+	6.24097i	−0.512269	+	0.246696i
$641$	41.0761	−	6.19123i	1.62241	−	0.244539i	0.725977	−	0.687719i	$-0.241388\pi$
$641$	41.0761	−	6.19123i	1.62241	−	0.244539i	0.896432	+	0.443181i	$0.146150\pi$
$642$		0			0
$643$	−13.8311	−	9.42990i	−0.545446	−	0.371879i	0.259025	−	0.965871i	$-0.416599\pi$
$643$	−13.8311	−	9.42990i	−0.545446	−	0.371879i	−0.804471	+	0.593992i	$0.797551\pi$
$644$	−3.10666	−	41.4554i	−0.122419	−	1.63357i
$645$		0			0
$646$	−41.6017	−	38.6007i	−1.63680	−	1.51873i
$647$	0.331767	−	1.45357i	0.0130431	−	0.0571456i	−0.967988	−	0.250998i	$-0.919241\pi$
$647$	0.331767	−	1.45357i	0.0130431	−	0.0571456i	0.981031	+	0.193853i	$0.0620983\pi$
$648$		0			0
$649$	−2.23711	−	9.80140i	−0.0878141	−	0.384739i
$650$	−5.68528	+	9.84719i	−0.222995	+	0.386238i
$651$		0			0
$652$	5.91687	+	78.9551i	0.231722	+	3.09212i
$653$	2.00722	+	26.7844i	0.0785484	+	1.04816i	0.887660	+	0.460500i	$0.152330\pi$
$653$	2.00722	+	26.7844i	0.0785484	+	1.04816i	−0.809111	+	0.587655i	$0.800051\pi$
$654$		0			0
$655$	−3.85580	+	6.67843i	−0.150658	+	0.260948i
$656$	5.39054	+	23.6175i	0.210465	+	0.922109i
$657$		0			0
$658$	−8.67859	+	38.0234i	−0.338327	+	1.48231i
$659$	11.9109	+	11.0517i	0.463982	+	0.430512i	0.877204	−	0.480118i	$-0.159406\pi$
$659$	11.9109	+	11.0517i	0.463982	+	0.430512i	−0.413222	+	0.910630i	$0.635597\pi$
$660$		0			0
$661$	−0.0879444	−	1.17354i	−0.00342064	−	0.0456453i	0.995232	−	0.0975332i	$-0.0310952\pi$
$661$	−0.0879444	−	1.17354i	−0.00342064	−	0.0456453i	−0.998653	+	0.0518879i	$0.983476\pi$
$662$	43.2271	+	29.4718i	1.68007	+	1.14545i
$663$		0			0
$664$	57.2615	−	8.63078i	2.22218	−	0.334939i
$665$	9.54774	−	4.59795i	0.370245	−	0.178301i
$666$		0			0
$667$	−11.7898	−	11.6239i	−0.456504	−	0.450079i
$668$	−7.86356	+	13.6201i	−0.304250	+	0.526977i
$669$		0			0
$670$	5.59521	−	14.2564i	0.216162	−	0.550771i
$671$	16.4757	+	2.48331i	0.636036	+	0.0958671i
$672$		0			0
$673$	−39.1126	+	26.6665i	−1.50768	+	1.02792i	−0.523242	+	0.852184i	$0.675278\pi$
$673$	−39.1126	+	26.6665i	−1.50768	+	1.02792i	−0.984438	+	0.175735i	$0.943770\pi$
$674$	−13.1692	−	16.5136i	−0.507258	−	0.636082i
$675$		0			0
$676$	11.2382	−	49.2377i	0.432238	−	1.89376i
$677$	8.56297	+	21.8181i	0.329102	+	0.838538i	0.995658	+	0.0930833i	$0.0296723\pi$
$677$	8.56297	+	21.8181i	0.329102	+	0.838538i	−0.666556	+	0.745455i	$0.732232\pi$
$678$		0			0
$679$	10.8036	+	18.7123i	0.414603	+	0.718113i
$680$	22.0647	−	20.4730i	0.846142	−	0.785105i
$681$		0			0
$682$	−46.8970	+	31.9739i	−1.79578	+	1.22434i
$683$	0.00571427	+	0.0250358i	0.000218650	+	0.000957970i	0.975037	−	0.222042i	$-0.0712722\pi$
$683$	0.00571427	+	0.0250358i	0.000218650	+	0.000957970i	−0.974818	+	0.223000i	$0.928415\pi$
$684$		0			0
$685$	−2.45010	−	10.7346i	−0.0936135	−	0.410147i
$686$	11.4548	+	29.1864i	0.437347	+	1.11434i
$687$		0			0
$688$	−31.7009	+	9.77842i	−1.20858	+	0.372799i
$689$	1.29047	−	3.28807i	0.0491631	−	0.125266i
$690$		0			0
$691$	2.74912	−	36.6844i	0.104581	−	1.39554i	−0.660122	−	0.751158i	$-0.729495\pi$
$691$	2.74912	−	36.6844i	0.104581	−	1.39554i	0.764703	−	0.644382i	$-0.222885\pi$
$692$	−48.8936	+	61.3107i	−1.85866	+	2.33068i
$693$		0			0
$694$	7.22858	−	3.48110i	0.274393	−	0.132141i
$695$	8.61751	−	14.9260i	0.326881	−	0.566174i
$696$		0			0
$697$	12.8301	+	22.2225i	0.485976	+	0.841736i
$698$	−11.5219	−	7.85551i	−0.436111	−	0.297335i
$699$		0			0
$700$	−20.8340	−	53.0842i	−0.787451	−	2.00639i
$701$	31.5385	−	15.1881i	1.19119	−	0.573648i	0.270039	−	0.962849i	$-0.412963\pi$
$701$	31.5385	−	15.1881i	1.19119	−	0.573648i	0.921152	+	0.389202i	$0.127249\pi$
$702$		0			0
$703$	26.8934	+	33.7233i	1.01430	+	1.27190i
$704$	−12.6186	−	11.7083i	−0.475580	−	0.441274i
$705$		0			0
$706$	26.1477	+	3.94113i	0.984080	+	0.148326i
$707$	28.0921	−	26.0656i	1.05651	−	0.980298i
$708$		0			0
$709$	16.2558	+	5.01425i	0.610499	+	0.188314i	0.584561	−	0.811350i	$-0.301267\pi$
$709$	16.2558	+	5.01425i	0.610499	+	0.188314i	0.0259376	+	0.999664i	$0.491743\pi$
$710$	21.0460	+	10.1352i	0.789840	+	0.380367i
$711$		0			0
$712$	16.5361	+	72.4495i	0.619717	+	2.71516i
$713$	−8.56547	+	14.8358i	−0.320780	+	0.555606i
$714$		0			0
$715$	3.83438	+	0.577941i	0.143398	+	0.0216138i
$716$	−25.9027	+	7.98991i	−0.968028	+	0.298597i
$717$		0			0
$718$	−41.4542	+	6.24821i	−1.54706	+	0.233181i
$719$	17.7357	+	8.54109i	0.661432	+	0.318529i	0.734312	−	0.678812i	$-0.237505\pi$
$719$	17.7357	+	8.54109i	0.661432	+	0.318529i	−0.0728804	+	0.997341i	$0.523219\pi$
$720$		0			0
$721$	36.6777	−	45.9924i	1.36595	−	1.71285i
$722$	−11.6823	+	1.76082i	−0.434769	+	0.0655309i
$723$		0			0
$724$	−2.08674	−	3.61435i	−0.0775532	−	0.134326i
$725$	−20.1542	−	10.4697i	−0.748507	−	0.388836i
$726$		0			0
$727$	1.95557	−	26.0952i	0.0725279	−	0.967818i	−0.835658	−	0.549250i	$-0.814913\pi$
$727$	1.95557	−	26.0952i	0.0725279	−	0.967818i	0.908186	−	0.418567i	$-0.137468\pi$
$728$	−12.0726	−	15.1385i	−0.447439	−	0.561071i
$729$		0			0
$730$	18.9241	−	9.11337i	0.700413	−	0.337301i
$731$	−29.0344	+	19.7953i	−1.07388	+	0.732156i
$732$		0			0
$733$	31.9449	−	9.85370i	1.17991	−	0.363955i	0.358083	−	0.933690i	$-0.383430\pi$
$733$	31.9449	−	9.85370i	1.17991	−	0.363955i	0.821828	+	0.569735i	$0.192954\pi$
$734$	−83.3186	+	25.7004i	−3.07534	+	0.948618i
$735$		0			0
$736$	8.33106	+	2.56979i	0.307087	+	0.0947238i
$737$	28.1455			1.03675
$738$		0			0
$739$	4.50561	+	2.16979i	0.165741	+	0.0798168i	0.514915	−	0.857241i	$-0.327823\pi$
$739$	4.50561	+	2.16979i	0.165741	+	0.0798168i	−0.349174	+	0.937058i	$0.613538\pi$
$740$	−35.5883	+	24.2637i	−1.30825	+	0.891950i
$741$		0			0
$742$	13.0106	+	22.5350i	0.477633	+	0.827285i
$743$	22.8051	−	21.1600i	0.836638	−	0.776286i	−0.140233	−	0.990119i	$-0.544785\pi$
$743$	22.8051	−	21.1600i	0.836638	−	0.776286i	0.976870	+	0.213832i	$0.0685946\pi$
$744$		0			0
$745$	4.16338	+	3.86305i	0.152534	+	0.141531i
$746$	−0.253744	+	1.11172i	−0.00929022	+	0.0407031i
$747$		0			0
$748$	93.8343	+	45.1882i	3.43092	+	1.65225i
$749$	3.10200	−	41.3932i	0.113344	−	1.51248i
$750$		0			0
$751$	5.28243	−	13.4594i	0.192759	−	0.491141i	−0.801519	−	0.597969i	$-0.795974\pi$
$751$	5.28243	−	13.4594i	0.192759	−	0.491141i	0.994277	+	0.106829i	$0.0340696\pi$
$752$	−23.0028	−	15.6830i	−0.838824	−	0.571901i
$753$		0			0
$754$	−14.2847	−	2.59808i	−0.520216	−	0.0946164i
$755$	1.45093			0.0528049
$756$		0			0
$757$	−6.49403	−	8.14326i	−0.236030	−	0.295972i	0.649684	−	0.760205i	$-0.274901\pi$
$757$	−6.49403	−	8.14326i	−0.236030	−	0.295972i	−0.885713	+	0.464233i	$0.846330\pi$
$758$	2.12154	+	5.40561i	0.0770580	+	0.196341i
$759$		0			0
$760$	1.41676	+	18.9054i	0.0513914	+	0.685770i
$761$	4.08835	−	10.4169i	0.148202	−	0.377614i	−0.837424	−	0.546554i	$-0.815939\pi$
$761$	4.08835	−	10.4169i	0.148202	−	0.377614i	0.985626	+	0.168940i	$0.0540346\pi$
$762$		0			0
$763$	13.1368	+	12.1892i	0.475584	+	0.441277i
$764$	−40.8358	+	51.2065i	−1.47739	+	1.85259i
$765$		0			0
$766$	−33.5049			−1.21058
$767$	−2.54268	−	0.784313i	−0.0918108	−	0.0283199i
$768$		0			0
$769$	0.237992	+	3.17578i	0.00858222	+	0.114522i	0.999850	−	0.0173459i	$-0.00552166\pi$
$769$	0.237992	+	3.17578i	0.00858222	+	0.114522i	−0.991267	+	0.131868i	$0.957903\pi$
$770$	−20.9404	+	19.4298i	−0.754638	+	0.700202i
$771$		0			0
$772$	87.1269	+	26.8751i	3.13576	+	0.967255i
$773$	21.5343	−	27.0032i	0.774536	−	0.971237i	−0.225460	−	0.974253i	$-0.572388\pi$
$773$	21.5343	−	27.0032i	0.774536	−	0.971237i	0.999995	+	0.00301519i	$0.000959767\pi$
$774$		0			0
$775$	−5.22912	+	22.9103i	−0.187836	+	0.822962i
$776$	−38.2234	+	5.76125i	−1.37214	+	0.206817i
$777$		0			0
$778$	66.2069	+	45.1391i	2.37363	+	1.61832i
$779$	−15.9817	−	2.40885i	−0.572603	−	0.0863060i
$780$		0			0
$781$	−3.20808	+	42.8089i	−0.114794	+	1.53182i
$782$	46.1718			1.65110
$783$		0			0
$784$	17.2671			0.616683
$785$	−0.873748	+	11.6594i	−0.0311854	+	0.416141i
$786$		0			0
$787$	12.8611	+	1.93849i	0.458447	+	0.0690998i	0.374206	−	0.927346i	$-0.377915\pi$
$787$	12.8611	+	1.93849i	0.458447	+	0.0690998i	0.0842411	+	0.996445i	$0.473153\pi$
$788$	−10.3195	−	7.03574i	−0.367618	−	0.250638i
$789$		0			0
$790$	−22.7442	+	3.42813i	−0.809201	+	0.121967i
$791$	−1.69462	+	7.42463i	−0.0602539	+	0.263989i
$792$		0			0
$793$	2.74956	−	3.44784i	0.0976396	−	0.122436i
$794$	−32.9932	−	10.1771i	−1.17089	−	0.361171i
$795$		0			0
$796$	52.4814	−	48.6956i	1.86015	−	1.72597i
$797$	−1.66546	−	22.2240i	−0.0589936	−	0.787215i	−0.945733	−	0.324945i	$-0.894654\pi$
$797$	−1.66546	−	22.2240i	−0.0589936	−	0.787215i	0.886739	−	0.462270i	$-0.152965\pi$
$798$		0			0
$799$	−28.1798	−	8.69232i	−0.996930	−	0.307512i
$800$	11.9595			0.422833
$801$		0			0
$802$	20.0943	−	25.1975i	0.709556	−	0.889755i
$803$	28.2964	+	26.2553i	0.998560	+	0.926528i
$804$		0			0
$805$	−3.14985	+	8.02568i	−0.111018	+	0.282868i
$806$	1.12266	+	14.9808i	0.0395439	+	0.527677i
$807$		0			0
$808$	25.0471	+	63.8190i	0.881155	+	2.24515i
$809$	19.2405	+	24.1268i	0.676460	+	0.848254i	0.995023	−	0.0996477i	$-0.0317716\pi$
$809$	19.2405	+	24.1268i	0.676460	+	0.848254i	−0.318563	+	0.947902i	$0.603200\pi$
$810$		0			0
$811$	−7.84939			−0.275629			−0.137815	−	0.990458i	$-0.544008\pi$
$811$	−7.84939			−0.275629			−0.137815	+	0.990458i	$0.544008\pi$
$812$	54.8548	−	47.8872i	1.92503	−	1.68051i
$813$		0			0
$814$	−96.0685	−	65.4984i	−3.36720	−	2.29572i
$815$	5.99913	−	15.2855i	0.210140	−	0.535429i
$816$		0			0
$817$	1.65402	−	22.0714i	0.0578669	−	0.772180i
$818$	−15.3176	−	7.37655i	−0.535566	−	0.257915i
$819$		0			0
$820$	3.59133	−	15.7346i	0.125415	−	0.549478i
$821$	7.88702	+	7.31808i	0.275259	+	0.255403i	0.805707	−	0.592315i	$-0.201786\pi$
$821$	7.88702	+	7.31808i	0.275259	+	0.255403i	−0.530448	+	0.847718i	$0.677976\pi$
$822$		0			0
$823$	−38.0620	+	35.3163i	−1.32676	+	1.23105i	−0.373959	+	0.927445i	$0.622000\pi$
$823$	−38.0620	+	35.3163i	−1.32676	+	1.23105i	−0.952798	+	0.303605i	$0.901810\pi$
$824$	52.6203	+	91.1411i	1.83312	+	3.17505i
$825$		0			0
$826$	16.1960	−	11.0423i	0.563533	−	0.384210i
$827$	−35.8253	−	17.2526i	−1.24577	−	0.599930i	−0.309394	−	0.950934i	$-0.600126\pi$
$827$	−35.8253	−	17.2526i	−1.24577	−	0.599930i	−0.936374	+	0.351004i	$0.885840\pi$
$828$		0			0
$829$	−1.49247			−0.0518358			−0.0259179	−	0.999664i	$-0.508251\pi$
$829$	−1.49247			−0.0518358			−0.0259179	+	0.999664i	$0.508251\pi$
$830$	−21.6071	−	6.66490i	−0.749992	−	0.231342i
$831$		0			0
$832$	−4.35362	+	1.34291i	−0.150935	+	0.0465572i
$833$	17.4777	−	5.39115i	0.605566	−	0.186792i
$834$		0			0
$835$	2.69494	−	1.83738i	0.0932621	−	0.0635850i
$836$	−59.1018	+	28.4619i	−2.04408	+	0.984376i
$837$		0			0
$838$	0.471128	+	0.590775i	0.0162748	+	0.0204080i
$839$	1.69799	−	22.6581i	0.0586212	−	0.782245i	−0.887989	−	0.459865i	$-0.847898\pi$
$839$	1.69799	−	22.6581i	0.0586212	−	0.782245i	0.946610	−	0.322380i	$-0.104483\pi$
$840$		0			0
$841$	3.91534	−	28.7345i	0.135012	−	0.990844i
$842$	13.0584	+	22.6178i	0.450023	+	0.779463i
$843$		0			0
$844$	−91.7474	+	13.8287i	−3.15808	+	0.476003i
$845$	−6.53052	+	8.18902i	−0.224657	+	0.281711i
$846$		0			0
$847$	−15.8826	−	7.64867i	−0.545733	−	0.262811i
$848$	−18.3673	+	2.76842i	−0.630735	+	0.0950679i
$849$		0			0
$850$	60.5225	−	18.6687i	2.07591	−	0.640332i
$851$	−34.7008	−	5.23030i	−1.18953	−	0.179292i
$852$		0			0
$853$	−15.8038	+	27.3729i	−0.541111	+	0.937231i	0.457730	+	0.889091i	$0.348663\pi$
$853$	−15.8038	+	27.3729i	−0.541111	+	0.937231i	−0.998841	+	0.0481400i	$0.984671\pi$
$854$	7.22903	+	31.6724i	0.247372	+	1.08381i
$855$		0			0
$856$	66.9061	+	32.2203i	2.28680	+	1.10127i
$857$	−16.3464	−	5.04220i	−0.558383	−	0.172238i	0.00270233	−	0.999996i	$-0.499140\pi$
$857$	−16.3464	−	5.04220i	−0.558383	−	0.172238i	−0.561085	+	0.827758i	$0.689616\pi$
$858$		0			0
$859$	−1.35426	+	1.25657i	−0.0462068	+	0.0428736i	−0.702938	−	0.711251i	$-0.748129\pi$
$859$	−1.35426	+	1.25657i	−0.0462068	+	0.0428736i	0.656731	+	0.754125i	$0.271939\pi$
$860$	21.8551	+	3.29412i	0.745251	+	0.112329i
$861$		0			0
$862$	29.8117	+	27.6612i	1.01539	+	0.942143i
$863$	−19.7728	−	24.7944i	−0.673075	−	0.844010i	0.321621	−	0.946869i	$-0.395772\pi$
$863$	−19.7728	−	24.7944i	−0.673075	−	0.844010i	−0.994696	+	0.102859i	$0.967201\pi$
$864$		0			0
$865$	14.6530	−	7.05651i	0.498216	−	0.239928i
$866$	18.9097	+	48.1812i	0.642579	+	1.63726i
$867$		0			0
$868$	−62.2515	−	42.4424i	−2.11296	−	1.44059i
$869$	−21.1353	−	36.6075i	−0.716967	−	1.24182i
$870$		0			0
$871$	3.72470	−	6.45137i	0.126207	−	0.218596i
$872$	−28.8852	+	13.9104i	−0.978175	+	0.471064i
$873$		0			0
$874$	−18.1319	+	22.7367i	−0.613322	+	0.769082i
$875$	−1.93165	+	25.7760i	−0.0653015	+	0.871388i
$876$		0			0
$877$	−1.82867	+	4.65937i	−0.0617497	+	0.157336i	−0.958419	−	0.285366i	$-0.907885\pi$
$877$	−1.82867	+	4.65937i	−0.0617497	+	0.157336i	0.896669	+	0.442702i	$0.145980\pi$
$878$	25.8987	−	7.98870i	0.874040	−	0.269606i
$879$		0			0
$880$	−7.44979	−	18.9818i	−0.251132	−	0.639875i
$881$	8.99154	+	39.3945i	0.302933	+	1.32724i	0.865677	+	0.500604i	$0.166889\pi$
$881$	8.99154	+	39.3945i	0.302933	+	1.32724i	−0.562744	+	0.826631i	$0.690254\pi$
$882$		0			0
$883$	−11.7833	−	51.6258i	−0.396538	−	1.73735i	−0.640864	−	0.767655i	$-0.721424\pi$
$883$	−11.7833	−	51.6258i	−0.396538	−	1.73735i	0.244325	−	0.969693i	$-0.421434\pi$
$884$	22.7756	−	15.5281i	0.766026	−	0.522268i
$885$		0			0
$886$	24.7710	−	22.9841i	0.832197	−	0.772166i
$887$	−15.6494	−	27.1055i	−0.525454	−	0.910113i	−0.999560	−	0.0296453i	$-0.990562\pi$
$887$	−15.6494	−	27.1055i	−0.525454	−	0.910113i	0.474107	−	0.880467i	$-0.342771\pi$
$888$		0			0
$889$	4.20841	+	10.7228i	0.141145	+	0.359633i
$890$	6.45691	−	28.2896i	0.216436	−	0.948269i
$891$		0			0
$892$	−54.8492	−	68.7787i	−1.83649	−	2.30288i
$893$	15.3468	−	10.4633i	0.513562	−	0.350140i
$894$		0			0
$895$	5.55899	+	0.837883i	0.185817	+	0.0280074i
$896$	18.8302	−	47.9787i	0.629074	−	1.60286i
$897$		0			0
$898$	−24.8349	+	43.0153i	−0.828750	+	1.43544i
$899$	−29.7931	+	3.57088i	−0.993656	+	0.119096i
$900$		0			0
$901$	−17.7269	+	8.53681i	−0.590568	+	0.284402i
$902$	43.0805	−	6.49334i	1.43442	−	0.216205i
$903$		0			0
$904$	−11.2569	−	7.67482i	−0.374399	−	0.255261i
$905$	0.0646827	+	0.863131i	0.00215013	+	0.0286914i
$906$		0			0
$907$	−24.2045	−	22.4585i	−0.803696	−	0.745721i	0.167020	−	0.985954i	$-0.446586\pi$
$907$	−24.2045	−	22.4585i	−0.803696	−	0.745721i	−0.970715	+	0.240233i	$0.922776\pi$
$908$	−26.0098	+	113.956i	−0.863166	+	3.78178i
$909$		0			0
$910$	1.68241	+	7.37113i	0.0557714	+	0.244351i
$911$	−19.6029	+	33.9531i	−0.649472	+	1.12492i	0.333778	+	0.942652i	$0.391677\pi$
$911$	−19.6029	+	33.9531i	−0.649472	+	1.12492i	−0.983249	+	0.182266i	$0.941657\pi$
$912$		0			0
$913$	−3.10541	−	41.4388i	−0.102774	−	1.37142i
$914$	−0.654377	−	8.73205i	−0.0216449	−	0.288831i
$915$		0			0
$916$	16.8751	−	29.2285i	0.557569	−	0.965737i
$917$	−6.14885	−	26.9399i	−0.203053	−	0.889633i
$918$		0			0
$919$	13.1695	−	57.6995i	0.434423	−	1.90333i	0.00550808	−	0.999985i	$-0.498247\pi$
$919$	13.1695	−	57.6995i	0.434423	−	1.90333i	0.428915	−	0.903345i	$-0.358896\pi$
$920$	−11.3067	−	10.4911i	−0.372771	−	0.345881i
$921$		0			0
$922$	0.565211	+	7.54221i	0.0186142	+	0.248390i
$923$	9.38788	+	6.40055i	0.309006	+	0.210677i
$924$		0			0
$925$	−47.6010	+	7.17469i	−1.56511	+	0.235902i
$926$	79.1352	−	38.1095i	2.60054	−	1.25236i
$927$		0			0
$928$	5.14573	+	14.3780i	0.168917	+	0.471980i
$929$	11.2940	−	19.5618i	0.370544	−	0.641801i	−0.619105	−	0.785308i	$-0.712505\pi$
$929$	11.2940	−	19.5618i	0.370544	−	0.641801i	0.989649	+	0.143507i	$0.0458380\pi$
$930$		0			0
$931$	−4.20879	+	10.7238i	−0.137937	+	0.351459i
$932$	−0.579048	−	0.0872774i	−0.0189673	−	0.00285887i
$933$		0			0
$934$	2.05385	−	1.40029i	0.0672041	−	0.0458190i
$935$	−13.4671	−	16.8872i	−0.440422	−	0.552272i
$936$		0			0
$937$	−4.65368	+	20.3891i	−0.152029	+	0.666083i	0.840265	+	0.542176i	$0.182399\pi$
$937$	−4.65368	+	20.3891i	−0.152029	+	0.666083i	−0.992294	+	0.123906i	$0.960458\pi$
$938$	20.0491	+	51.0843i	0.654627	+	1.66796i
$939$		0			0
$940$	9.27400	+	16.0630i	0.302485	+	0.523919i
$941$	9.36425	−	8.68875i	0.305266	−	0.283245i	−0.512632	−	0.858608i	$-0.671330\pi$
$941$	9.36425	−	8.68875i	0.305266	−	0.283245i	0.817898	+	0.575363i	$0.195139\pi$
$942$		0			0
$943$	10.8644	−	7.40722i	0.353794	−	0.241212i
$944$	3.11366	+	13.6418i	0.101341	+	0.444003i
$945$		0			0
$946$	13.2762	+	58.1670i	0.431648	+	1.89117i
$947$	11.5612	+	29.4575i	0.375689	+	0.957240i	0.986248	+	0.165270i	$0.0528495\pi$
$947$	11.5612	+	29.4575i	0.375689	+	0.957240i	−0.610559	+	0.791971i	$0.709055\pi$
$948$		0			0
$949$	9.76277	−	3.01142i	0.316913	−	0.0977547i
$950$	−14.5744	+	37.1349i	−0.472856	+	1.20482i
$951$		0			0
$952$	−8.06004	+	107.554i	−0.261227	+	3.48584i
$953$	7.65483	−	9.59885i	0.247964	−	0.310937i	−0.642236	−	0.766507i	$-0.721993\pi$
$953$	7.65483	−	9.59885i	0.247964	−	0.310937i	0.890200	+	0.455570i	$0.150564\pi$
$954$		0			0
$955$	12.2381	−	5.89357i	0.396017	−	0.190712i
$956$	−39.8754	+	69.0663i	−1.28966	+	2.23376i
$957$		0			0
$958$	−0.520178	−	0.900975i	−0.0168062	−	0.0291092i
$959$	32.5985	+	22.2253i	1.05266	+	0.717691i
$960$		0			0
$961$	0.0173985	+	0.0443307i	0.000561242	+	0.00143002i
$962$	−27.7266	+	13.3524i	−0.893943	+	0.430500i
$963$		0			0
$964$	52.2352	+	65.5008i	1.68238	+	2.10964i
$965$	−13.8617	−	12.8618i	−0.446224	−	0.414035i
$966$		0			0
$967$	−34.4923	−	5.19888i	−1.10920	−	0.167185i	−0.431205	−	0.902254i	$-0.641912\pi$
$967$	−34.4923	−	5.19888i	−1.10920	−	0.167185i	−0.677992	+	0.735069i	$0.737150\pi$
$968$	23.1184	−	21.4507i	0.743053	−	0.689453i
$969$		0			0
$970$	14.4232	+	4.44898i	0.463102	+	0.142848i
$971$	4.81331	+	2.31797i	0.154466	+	0.0743871i	0.509520	−	0.860459i	$-0.329823\pi$
$971$	4.81331	+	2.31797i	0.154466	+	0.0743871i	−0.355053	+	0.934846i	$0.615537\pi$
$972$		0			0
$973$	13.7424	+	60.2093i	0.440560	+	1.93022i
$974$	8.70199	−	15.0723i	0.278830	−	0.482947i
$975$		0			0
$976$	−22.9312	−	3.45633i	−0.734011	−	0.110634i
$977$	3.00569	−	0.927134i	0.0961607	−	0.0296616i	−0.246301	−	0.969193i	$-0.579215\pi$
$977$	3.00569	−	0.927134i	0.0961607	−	0.0296616i	0.342462	+	0.939532i	$0.388739\pi$
$978$		0			0
$979$	52.7311	−	7.94794i	1.68529	−	0.254017i
$980$	−10.3646	−	4.99133i	−0.331085	−	0.159442i
$981$		0			0
$982$	−1.15338	+	1.44630i	−0.0368059	+	0.0461532i
$983$	−29.7635	+	4.48613i	−0.949308	+	0.143085i	−0.605403	−	0.795919i	$-0.706988\pi$
$983$	−29.7635	+	4.48613i	−0.949308	+	0.143085i	−0.343905	+	0.939004i	$0.611750\pi$
$984$		0			0
$985$	1.29514	+	2.24325i	0.0412667	+	0.0714760i
$986$	48.4845	+	64.7290i	1.54406	+	2.06139i
$987$		0			0
$988$	−1.29747	+	17.3136i	−0.0412781	+	0.550818i
$989$	11.2273	+	14.0786i	0.357007	+	0.447673i
$990$		0			0
$991$	−44.1488	+	21.2609i	−1.40243	+	0.675375i	−0.973653	−	0.228034i	$-0.926770\pi$
$991$	−44.1488	+	21.2609i	−1.40243	+	0.675375i	−0.428778	+	0.903410i	$0.641056\pi$
$992$	13.0554	−	8.90100i	0.414508	−	0.282607i
$993$		0			0
$994$	−79.9837	+	24.6717i	−2.53693	+	0.782539i
$995$	−14.1882	+	4.37649i	−0.449797	+	0.138744i
$996$		0			0
$997$	−47.0161	−	14.5025i	−1.48901	−	0.459300i	−0.559733	−	0.828673i	$-0.689096\pi$
$997$	−47.0161	−	14.5025i	−1.48901	−	0.459300i	−0.929281	+	0.369373i	$0.879572\pi$
$998$	−14.1286			−0.447233
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.u.a.397.2		336
3.2	odd	2		261.2.q.a.223.27	yes	336
9.4	even	3	inner	783.2.u.a.658.2		336
9.5	odd	6		261.2.q.a.49.27	yes	336
29.16	even	7	inner	783.2.u.a.451.2		336
87.74	odd	14		261.2.q.a.16.27	✓	336
261.103	even	21	inner	783.2.u.a.712.2		336
261.248	odd	42		261.2.q.a.103.27	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.27	✓	336	87.74	odd	14
261.2.q.a.49.27	yes	336	9.5	odd	6
261.2.q.a.103.27	yes	336	261.248	odd	42
261.2.q.a.223.27	yes	336	3.2	odd	2
783.2.u.a.397.2		336	1.1	even	1	trivial
783.2.u.a.451.2		336	29.16	even	7	inner
783.2.u.a.658.2		336	9.4	even	3	inner
783.2.u.a.712.2		336	261.103	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.u (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.187058 + 2.49612i) q^{2} +(-4.21795 - 0.635753i) q^{4} +(0.730934 + 0.498342i) q^{5} +(-3.13454 + 0.472455i) q^{7} +(1.26192 - 5.52885i) q^{8} +(-1.38065 + 1.73128i) q^{10} +(-3.88874 - 1.19952i) q^{11} +(-0.789571 + 0.732615i) q^{13} +(-0.592963 - 7.91255i) q^{14} +(5.41243 + 1.66951i) q^{16} +5.99968 q^{17} +(-2.35611 + 2.95447i) q^{19} +(-2.76622 - 2.56667i) q^{20} +(3.72155 - 9.48236i) q^{22} +(-0.229754 - 3.06585i) q^{23} +(-1.54079 - 3.92586i) q^{25} +(-1.68100 - 2.10790i) q^{26} +13.5217 q^{28} +(4.05681 - 3.54152i) q^{29} +(-4.60383 - 3.13884i) q^{31} +(-1.03602 + 2.63973i) q^{32} +(-1.12229 + 14.9759i) q^{34} +(-2.52658 - 1.21674i) q^{35} +(2.53992 - 11.1281i) q^{37} +(-6.93398 - 6.43379i) q^{38} +(3.67764 - 3.41235i) q^{40} +(2.13847 + 3.70394i) q^{41} +(-4.83932 + 3.29939i) q^{43} +(15.6399 + 7.53177i) q^{44} +7.69570 q^{46} +(-4.69688 - 1.44880i) q^{47} +(2.91310 - 0.898572i) q^{49} +(10.0876 - 3.11162i) q^{50} +(3.79613 - 2.58816i) q^{52} +(-2.95463 + 1.42288i) q^{53} +(-2.24464 - 2.81469i) q^{55} +(-1.34341 + 17.9266i) q^{56} +(8.08118 + 10.7887i) q^{58} +(1.23521 + 2.13945i) q^{59} +(-4.04854 + 0.610220i) q^{61} +(8.69610 - 10.9046i) q^{62} +(3.81101 + 1.83529i) q^{64} +(-0.942217 + 0.142016i) q^{65} +(-6.60889 + 2.03857i) q^{67} +(-25.3063 - 3.81432i) q^{68} +(3.50974 - 6.07905i) q^{70} +(-2.34734 - 10.2844i) q^{71} +(-8.54599 - 4.11553i) q^{73} +(27.3020 + 8.42155i) q^{74} +(11.8163 - 10.9639i) q^{76} +(12.7561 + 1.92267i) q^{77} +(7.61429 + 7.06503i) q^{79} +(3.12414 + 3.91755i) q^{80} +(-9.64548 + 4.64502i) q^{82} +(3.73059 + 9.50538i) q^{83} +(4.38537 + 2.98990i) q^{85} +(-7.33043 - 12.6967i) q^{86} +(-11.5392 + 19.9865i) q^{88} +(-11.8062 + 5.68557i) q^{89} +(2.12881 - 2.66945i) q^{91} +(-0.980035 + 13.0777i) q^{92} +(4.49495 - 11.4530i) q^{94} +(-3.19450 + 0.985373i) q^{95} +(-2.49026 - 6.34507i) q^{97} +(1.69802 + 7.43952i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 5 q^{2} + 21 q^{4} + 9 q^{5} - 5 q^{7} - 2 q^{8} - 28 q^{10} + q^{11} - 5 q^{13} + 9 q^{14} + 21 q^{16} + 60 q^{17} - 20 q^{19} + 15 q^{20} - 13 q^{22} + 32 q^{23} + 15 q^{25} + 4 q^{26} - 72 q^{28}+ \cdots + 88 q^{98}+O(q^{100}) \) 336 * q + 5 * q^2 + 21 * q^4 + 9 * q^5 - 5 * q^7 - 2 * q^8 - 28 * q^10 + q^11 - 5 * q^13 + 9 * q^14 + 21 * q^16 + 60 * q^17 - 20 * q^19 + 15 * q^20 - 13 * q^22 + 32 * q^23 + 15 * q^25 + 4 * q^26 - 72 * q^28 + q^29 - 5 * q^31 - 7 * q^32 - 15 * q^34 - 16 * q^35 - 20 * q^37 - 63 * q^38 + 5 * q^40 + 20 * q^41 - 5 * q^43 + 8 * q^44 - 80 * q^46 - 5 * q^47 - 19 * q^49 + 3 * q^50 + q^52 + 4 * q^53 - 100 * q^55 + 5 * q^56 - 7 * q^58 - 154 * q^59 + 7 * q^61 + 4 * q^62 + 18 * q^64 + 65 * q^65 - 5 * q^67 + 9 * q^68 - 14 * q^70 - 18 * q^71 - 20 * q^73 + 77 * q^74 - 5 * q^76 - 39 * q^77 - 5 * q^79 + 104 * q^80 + 12 * q^82 + 23 * q^83 - 42 * q^85 - 128 * q^86 - 8 * q^88 - 34 * q^89 + 12 * q^91 + 115 * q^92 - 25 * q^94 - 89 * q^95 + 55 * q^97 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more