LMFDB - Embedded newform 775.2.ck.c.49.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	775.49
Dual form			775.2.ck.c.174.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26139 + 1.73615i) q^{2} +(-0.138074 - 0.310120i) q^{3} +(-0.805084 + 2.47779i) q^{4} +(0.364249 - 0.630898i) q^{6} +(1.83635 - 1.65346i) q^{7} +(-1.23541 + 0.401408i) q^{8} +(1.93028 - 2.14380i) q^{9} +(0.0336808 - 0.00715908i) q^{11} +(0.879574 - 0.0924470i) q^{12} +(0.857233 + 0.0900989i) q^{13} +(5.18700 + 1.10253i) q^{14} +(1.96024 + 1.42420i) q^{16} +(0.358278 - 1.68556i) q^{17} +(6.15678 + 0.647103i) q^{18} +(0.158669 + 1.50963i) q^{19} +(-0.766324 - 0.341189i) q^{21} +(0.0549137 + 0.0494445i) q^{22} +(-3.41410 + 1.10931i) q^{23} +(0.295063 + 0.327700i) q^{24} +(0.924877 + 1.60193i) q^{26} +(-1.89992 - 0.617320i) q^{27} +(2.61851 + 5.88128i) q^{28} +(4.30334 - 3.12656i) q^{29} +(4.25923 + 3.58594i) q^{31} +7.79771i q^{32} +(-0.00687063 - 0.00945661i) q^{33} +(3.37832 - 1.50412i) q^{34} +(3.75784 + 6.50877i) q^{36} +(1.14087 + 0.658683i) q^{37} +(-2.42081 + 2.17970i) q^{38} +(-0.0904204 - 0.278285i) q^{39} +(1.12138 + 0.499269i) q^{41} +(-0.374274 - 1.76082i) q^{42} +(-12.1413 + 1.27610i) q^{43} +(-0.00937716 + 0.0892178i) q^{44} +(-6.23243 - 4.52812i) q^{46} +(-5.47765 + 7.53934i) q^{47} +(0.171014 - 0.804556i) q^{48} +(-0.0934359 + 0.888983i) q^{49} +(-0.572196 + 0.121624i) q^{51} +(-0.913391 + 2.05151i) q^{52} +(-7.98460 - 7.18936i) q^{53} +(-1.32477 - 4.07722i) q^{54} +(-1.60493 + 2.77982i) q^{56} +(0.446259 - 0.257648i) q^{57} +(10.8564 + 3.52744i) q^{58} +(6.55294 - 2.91755i) q^{59} -12.3227 q^{61} +(-0.853205 + 11.9179i) q^{62} -7.12841i q^{63} +(-9.61749 + 6.98752i) q^{64} +(0.00775156 - 0.0238569i) q^{66} +(2.17857 - 1.25780i) q^{67} +(3.88804 + 2.24476i) q^{68} +(0.815419 + 0.905614i) q^{69} +(4.44824 - 4.94027i) q^{71} +(-1.52415 + 3.42329i) q^{72} +(2.63702 + 12.4062i) q^{73} +(0.295509 + 2.81158i) q^{74} +(-3.86830 - 0.822233i) q^{76} +(0.0500126 - 0.0688365i) q^{77} +(0.369090 - 0.508008i) q^{78} +(9.79690 + 2.08239i) q^{79} +(-0.833733 - 7.93244i) q^{81} +(0.547683 + 2.57665i) q^{82} +(3.45672 - 7.76391i) q^{83} +(1.46235 - 1.62411i) q^{84} +(-17.5304 - 19.4694i) q^{86} +(-1.56379 - 0.902855i) q^{87} +(-0.0387358 + 0.0223641i) q^{88} +(0.401874 - 1.23684i) q^{89} +(1.72316 - 1.25195i) q^{91} -9.35253i q^{92} +(0.523983 - 1.81600i) q^{93} -19.9988 q^{94} +(2.41822 - 1.07666i) q^{96} +(2.13701 + 0.694355i) q^{97} +(-1.66127 + 0.959132i) q^{98} +(0.0496659 - 0.0860238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{13}{15}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.26139	+	1.73615i	0.891934	+	1.22764i	0.972970	+	0.230931i	$0.0741772\pi$
$2$	1.26139	+	1.73615i	0.891934	+	1.22764i	−0.0810357	+	0.996711i	$0.525823\pi$
$3$	−0.138074	−	0.310120i	−0.0797172	−	0.179048i	0.869290	−	0.494303i	$-0.164577\pi$
$3$	−0.138074	−	0.310120i	−0.0797172	−	0.179048i	−0.949007	+	0.315255i	$0.897910\pi$
$4$	−0.805084	+	2.47779i	−0.402542	+	1.23890i
$5$		0			0
$5$		0			0
$6$	0.364249	−	0.630898i	0.148704	−	0.257563i
$7$	1.83635	−	1.65346i	0.694076	−	0.624949i	−0.244651	−	0.969611i	$-0.578673\pi$
$7$	1.83635	−	1.65346i	0.694076	−	0.624949i	0.938727	+	0.344662i	$0.112007\pi$
$8$	−1.23541	+	0.401408i	−0.436783	+	0.141919i
$9$	1.93028	−	2.14380i	0.643427	−	0.714598i
$10$		0			0
$11$	0.0336808	−	0.00715908i	0.0101551	−	0.00215854i	−0.202831	−	0.979214i	$-0.565014\pi$
$11$	0.0336808	−	0.00715908i	0.0101551	−	0.00215854i	0.212986	+	0.977055i	$0.431681\pi$
$12$	0.879574	−	0.0924470i	0.253911	−	0.0266871i
$13$	0.857233	+	0.0900989i	0.237754	+	0.0249889i	0.222656	−	0.974897i	$-0.428527\pi$
$13$	0.857233	+	0.0900989i	0.237754	+	0.0249889i	0.0150979	+	0.999886i	$0.495194\pi$
$14$	5.18700	+	1.10253i	1.38628	+	0.294664i
$15$		0			0
$16$	1.96024	+	1.42420i	0.490061	+	0.356050i
$17$	0.358278	−	1.68556i	0.0868951	−	0.408809i	−0.913104	−	0.407726i	$-0.866322\pi$
$17$	0.358278	−	1.68556i	0.0868951	−	0.408809i	0.999999	−	0.00108331i	$-0.000344830\pi$
$18$	6.15678	+	0.647103i	1.45117	+	0.152524i
$19$	0.158669	+	1.50963i	0.0364012	+	0.346334i	0.997530	+	0.0702352i	$0.0223750\pi$
$19$	0.158669	+	1.50963i	0.0364012	+	0.346334i	−0.961129	+	0.276099i	$0.910958\pi$
$20$		0			0
$21$	−0.766324	−	0.341189i	−0.167226	−	0.0744536i
$22$	0.0549137	+	0.0494445i	0.0117076	+	0.0105416i
$23$	−3.41410	+	1.10931i	−0.711890	+	0.231307i	−0.642503	−	0.766283i	$-0.722104\pi$
$23$	−3.41410	+	1.10931i	−0.711890	+	0.231307i	−0.0693865	+	0.997590i	$0.522104\pi$
$24$	0.295063	+	0.327700i	0.0602294	+	0.0668915i
$25$		0			0
$26$	0.924877	+	1.60193i	0.181383	+	0.314165i
$27$	−1.89992	−	0.617320i	−0.365639	−	0.118803i
$28$	2.61851	+	5.88128i	0.494852	+	1.11146i
$29$	4.30334	−	3.12656i	0.799111	−	0.580588i	−0.111542	−	0.993760i	$-0.535579\pi$
$29$	4.30334	−	3.12656i	0.799111	−	0.580588i	0.910653	+	0.413172i	$0.135579\pi$
$30$		0			0
$31$	4.25923	+	3.58594i	0.764980	+	0.644055i
$31$	4.25923	+	3.58594i	0.764980	+	0.644055i
$32$			7.79771i			1.37845i
$33$	−0.00687063	−	0.00945661i	−0.00119602	−	0.00164618i
$34$	3.37832	−	1.50412i	0.579376	−	0.257955i
$35$		0			0
$36$	3.75784	+	6.50877i	0.626307	+	1.08480i
$37$	1.14087	+	0.658683i	0.187558	+	0.108287i	0.590839	−	0.806790i	$-0.298797\pi$
$37$	1.14087	+	0.658683i	0.187558	+	0.108287i	−0.403281	+	0.915076i	$0.632130\pi$
$38$	−2.42081	+	2.17970i	−0.392707	+	0.353595i
$39$	−0.0904204	−	0.278285i	−0.0144789	−	0.0445613i
$40$		0			0
$41$	1.12138	+	0.499269i	0.175129	+	0.0779727i	0.492429	−	0.870353i	$-0.336109\pi$
$41$	1.12138	+	0.499269i	0.175129	+	0.0779727i	−0.317299	+	0.948326i	$0.602776\pi$
$42$	−0.374274	−	1.76082i	−0.0577518	−	0.271701i
$43$	−12.1413	+	1.27610i	−1.85153	+	0.194604i	−0.963956	−	0.266062i	$-0.914277\pi$
$43$	−12.1413	+	1.27610i	−1.85153	+	0.194604i	−0.887574	+	0.460666i	$0.847611\pi$
$44$	−0.00937716	+	0.0892178i	−0.00141366	+	0.0134501i
$45$		0			0
$46$	−6.23243	−	4.52812i	−0.918922	−	0.667636i
$47$	−5.47765	+	7.53934i	−0.798997	+	1.09973i	0.193932	+	0.981015i	$0.437876\pi$
$47$	−5.47765	+	7.53934i	−0.798997	+	1.09973i	−0.992929	+	0.118710i	$0.962124\pi$
$48$	0.171014	−	0.804556i	0.0246837	−	0.116128i
$49$	−0.0934359	+	0.888983i	−0.0133480	+	0.126998i
$50$		0			0
$51$	−0.572196	+	0.121624i	−0.0801234	+	0.0170308i
$52$	−0.913391	+	2.05151i	−0.126665	+	0.284493i
$53$	−7.98460	−	7.18936i	−1.09677	−	0.987535i	−0.0967990	−	0.995304i	$-0.530860\pi$
$53$	−7.98460	−	7.18936i	−1.09677	−	0.987535i	−0.999970	+	0.00776892i	$0.997527\pi$
$54$	−1.32477	−	4.07722i	−0.180278	−	0.554839i
$55$		0			0
$56$	−1.60493	+	2.77982i	−0.214468	+	0.371470i
$57$	0.446259	−	0.257648i	0.0591085	−	0.0341263i
$58$	10.8564	+	3.52744i	1.42551	+	0.463176i
$59$	6.55294	−	2.91755i	0.853120	−	0.379833i	0.0668844	−	0.997761i	$-0.478694\pi$
$59$	6.55294	−	2.91755i	0.853120	−	0.379833i	0.786235	+	0.617927i	$0.212027\pi$
$60$		0			0
$61$	−12.3227			−1.57776			−0.788879	−	0.614548i	$-0.789338\pi$
$61$	−12.3227			−1.57776			−0.788879	+	0.614548i	$0.789338\pi$
$62$	−0.853205	+	11.9179i	−0.108357	+	1.51358i
$63$		−	7.12841i		−	0.898095i
$64$	−9.61749	+	6.98752i	−1.20219	+	0.873440i
$65$		0			0
$66$	0.00775156	−	0.0238569i	0.000954151	−	0.00293658i
$67$	2.17857	−	1.25780i	0.266154	−	0.153664i	−0.360984	−	0.932572i	$-0.617559\pi$
$67$	2.17857	−	1.25780i	0.266154	−	0.153664i	0.627139	+	0.778908i	$0.284226\pi$
$68$	3.88804	+	2.24476i	0.471494	+	0.272217i
$69$	0.815419	+	0.905614i	0.0981649	+	0.109023i
$70$		0			0
$71$	4.44824	−	4.94027i	0.527909	−	0.586302i	−0.418927	−	0.908020i	$-0.637594\pi$
$71$	4.44824	−	4.94027i	0.527909	−	0.586302i	0.946836	+	0.321718i	$0.104260\pi$
$72$	−1.52415	+	3.42329i	−0.179623	+	0.403439i
$73$	2.63702	+	12.4062i	0.308640	+	1.45204i	0.809811	+	0.586690i	$0.199569\pi$
$73$	2.63702	+	12.4062i	0.308640	+	1.45204i	−0.501171	+	0.865348i	$0.667097\pi$
$74$	0.295509	+	2.81158i	0.0343522	+	0.326839i
$75$		0			0
$76$	−3.86830	−	0.822233i	−0.443725	−	0.0943166i
$77$	0.0500126	−	0.0688365i	0.00569947	−	0.00784464i
$78$	0.369090	−	0.508008i	0.0417912	−	0.0575206i
$79$	9.79690	+	2.08239i	1.10224	+	0.234288i	0.722887	−	0.690966i	$-0.242815\pi$
$79$	9.79690	+	2.08239i	1.10224	+	0.234288i	0.379349	+	0.925253i	$0.376148\pi$
$80$		0			0
$81$	−0.833733	−	7.93244i	−0.0926370	−	0.881382i
$82$	0.547683	+	2.57665i	0.0604815	+	0.284543i
$83$	3.45672	−	7.76391i	0.379424	−	0.852200i	−0.618375	−	0.785883i	$-0.712209\pi$
$83$	3.45672	−	7.76391i	0.379424	−	0.852200i	0.997799	−	0.0663168i	$-0.0211248\pi$
$84$	1.46235	−	1.62411i	0.159556	−	0.177204i
$85$		0			0
$86$	−17.5304	−	19.4694i	−1.89035	−	2.09944i
$87$	−1.56379	−	0.902855i	−0.167656	−	0.0967962i
$88$	−0.0387358	+	0.0223641i	−0.00412925	+	0.00238403i
$89$	0.401874	−	1.23684i	0.0425986	−	0.131105i	−0.927495	−	0.373835i	$-0.878043\pi$
$89$	0.401874	−	1.23684i	0.0425986	−	0.131105i	0.970094	+	0.242730i	$0.0780428\pi$
$90$		0			0
$91$	1.72316	−	1.25195i	0.180636	−	0.131240i
$92$		−	9.35253i		−	0.975069i
$93$	0.523983	−	1.81600i	0.0543345	−	0.188310i
$94$	−19.9988			−2.06272
$95$		0			0
$96$	2.41822	−	1.07666i	0.246809	−	0.109886i
$97$	2.13701	+	0.694355i	0.216980	+	0.0705011i	0.415490	−	0.909598i	$-0.363610\pi$
$97$	2.13701	+	0.694355i	0.216980	+	0.0705011i	−0.198510	+	0.980099i	$0.563610\pi$
$98$	−1.66127	+	0.959132i	−0.167813	+	0.0968870i
$99$	0.0496659	−	0.0860238i	0.00499161	−	0.00864572i
$100$		0			0
$101$	2.82475	+	8.69369i	0.281073	+	0.865054i	0.987548	+	0.157316i	$0.0502842\pi$
$101$	2.82475	+	8.69369i	0.281073	+	0.865054i	−0.706475	+	0.707738i	$0.749716\pi$
$102$	−0.932917	−	0.840002i	−0.0923725	−	0.0831726i
$103$	2.22567	−	4.99893i	0.219301	−	0.492559i	−0.770072	−	0.637957i	$-0.779780\pi$
$103$	2.22567	−	4.99893i	0.219301	−	0.492559i	0.989373	+	0.145398i	$0.0464463\pi$
$104$	−1.09520	+	0.232792i	−0.107393	+	0.0228271i
$105$		0			0
$106$	2.41015	−	22.9310i	0.234094	−	2.22726i
$107$	−2.50059	+	11.7644i	−0.241741	+	1.13730i	0.674999	+	0.737819i	$0.264144\pi$
$107$	−2.50059	+	11.7644i	−0.241741	+	1.13730i	−0.916740	+	0.399484i	$0.869189\pi$
$108$	3.05918	−	4.21061i	0.294370	−	0.405166i
$109$	−9.42799	−	6.84984i	−0.903038	−	0.656095i	0.0362066	−	0.999344i	$-0.488473\pi$
$109$	−9.42799	−	6.84984i	−0.903038	−	0.656095i	−0.939244	+	0.343249i	$0.888473\pi$
$110$		0			0
$111$	0.0467455	−	0.444754i	0.00443689	−	0.0422142i
$112$	5.95456	−	0.625849i	0.562653	−	0.0591372i
$113$	−3.53272	−	16.6201i	−0.332330	−	1.56349i	−0.754082	−	0.656780i	$-0.771918\pi$
$113$	−3.53272	−	16.6201i	−0.332330	−	1.56349i	0.421752	−	0.906711i	$-0.361415\pi$
$114$	1.01022	+	0.449779i	0.0946158	+	0.0421257i
$115$		0			0
$116$	4.28242	+	13.1799i	0.397613	+	1.22373i
$117$	1.84786	−	1.66382i	0.170834	−	0.153820i
$118$	13.3311	+	7.69671i	1.22723	+	0.708539i
$119$	−2.12909	−	3.68769i	−0.195173	−	0.338050i
$120$		0			0
$121$	−10.0479	+	4.47362i	−0.913447	+	0.406693i
$122$	−15.5437	−	21.3940i	−1.40726	−	1.93692i
$123$		−	0.416697i		−	0.0375723i
$124$	−12.3143	+	7.66649i	−1.10585	+	0.688471i
$125$		0			0
$126$	12.3760	−	8.99167i	1.10254	−	0.801042i
$127$	−0.589284	−	1.32355i	−0.0522905	−	0.117446i	0.885511	−	0.464619i	$-0.153809\pi$
$127$	−0.589284	−	1.32355i	−0.0522905	−	0.117446i	−0.937801	+	0.347172i	$0.887142\pi$
$128$	−9.43061	−	3.06419i	−0.833556	−	0.270839i
$129$	2.07214	+	3.58906i	0.182442	+	0.315999i
$130$		0			0
$131$	3.07515	+	3.41530i	0.268677	+	0.298396i	0.862353	−	0.506308i	$-0.168990\pi$
$131$	3.07515	+	3.41530i	0.268677	+	0.298396i	−0.593675	+	0.804705i	$0.702324\pi$
$132$	0.0289629	−	0.00941063i	0.00252090	−	0.000819090i
$133$	2.78749	+	2.50987i	0.241706	+	0.217633i
$134$	4.93173	+	2.19575i	0.426037	+	0.189684i
$135$		0			0
$136$	0.233980	+	2.22617i	0.0200637	+	0.190893i
$137$	−3.04376	−	0.319912i	−0.260046	−	0.0273320i	−0.0263918	−	0.999652i	$-0.508402\pi$
$137$	−3.04376	−	0.319912i	−0.260046	−	0.0273320i	−0.233654	+	0.972320i	$0.575068\pi$
$138$	−0.543723	+	2.55802i	−0.0462848	+	0.217753i
$139$	−9.44000	−	6.85856i	−0.800691	−	0.581736i	0.110426	−	0.993884i	$-0.464778\pi$
$139$	−9.44000	−	6.85856i	−0.800691	−	0.581736i	−0.911117	+	0.412149i	$0.864778\pi$
$140$		0			0
$141$	3.09442	+	0.657739i	0.260597	+	0.0553916i
$142$	14.1880	+	1.49122i	1.19063	+	0.125140i
$143$	0.0295174	−	0.00310240i	0.00246836	−	0.000259436i
$144$	6.83702	−	1.45325i	0.569751	−	0.121104i
$145$		0			0
$146$	−18.2127	+	20.2273i	−1.50730	+	1.67402i
$147$	0.288592	−	0.0937694i	0.0238027	−	0.00773397i
$148$	−2.55058	+	2.29655i	−0.209656	+	0.188775i
$149$	9.58706	−	16.6053i	0.785403	−	1.36036i	−0.143355	−	0.989671i	$-0.545789\pi$
$149$	9.58706	−	16.6053i	0.785403	−	1.36036i	0.928758	−	0.370686i	$-0.120878\pi$
$150$		0			0
$151$	−1.24220	+	3.82309i	−0.101089	+	0.311119i	−0.988793	−	0.149296i	$-0.952299\pi$
$151$	−1.24220	+	3.82309i	−0.101089	+	0.311119i	0.887704	+	0.460415i	$0.152299\pi$
$152$	−0.802000	−	1.80132i	−0.0650508	−	0.146107i
$153$	−2.92193	−	4.02169i	−0.236224	−	0.325134i
$154$	0.182596			0.0147140
$155$		0			0
$156$	0.762330			0.0610352
$157$	−10.3678	−	14.2701i	−0.827444	−	1.13888i	−0.988393	−	0.151917i	$-0.951456\pi$
$157$	−10.3678	−	14.2701i	−0.827444	−	1.13888i	0.160949	−	0.986963i	$-0.448544\pi$
$158$	8.74232	+	19.6356i	0.695501	+	1.56212i
$159$	−1.12710	+	3.46885i	−0.0893846	+	0.275098i
$160$		0			0
$161$	−4.43530	+	7.68217i	−0.349551	+	0.605440i
$162$	12.7202	−	11.4533i	0.999396	−	0.899860i
$163$	−23.0030	+	7.47414i	−1.80174	+	0.585420i	−0.999926	−	0.0121588i	$-0.996130\pi$
$163$	−23.0030	+	7.47414i	−1.80174	+	0.585420i	−0.801810	+	0.597578i	$0.796130\pi$
$164$	−2.13989	+	2.37658i	−0.167097	+	0.185580i
$165$		0			0
$166$	17.8396	−	3.79192i	1.38462	−	0.294310i
$167$	−10.5743	+	1.11140i	−0.818262	+	0.0860028i	−0.504405	−	0.863467i	$-0.668288\pi$
$167$	−10.5743	+	1.11140i	−0.818262	+	0.0860028i	−0.313857	+	0.949470i	$0.601621\pi$
$168$	1.08368	+	0.113899i	0.0836076	+	0.00878751i
$169$	−11.9892	−	2.54838i	−0.922245	−	0.196029i
$170$		0			0
$171$	3.54262	+	2.57387i	0.270911	+	0.196828i
$172$	6.61284	−	31.1110i	0.504224	−	2.37219i
$173$	7.90211	+	0.830545i	0.600786	+	0.0631452i	0.400039	−	0.916498i	$-0.368996\pi$
$173$	7.90211	+	0.830545i	0.600786	+	0.0631452i	0.200747	+	0.979643i	$0.435663\pi$
$174$	−0.405053	−	3.85382i	−0.0307070	−	0.292157i
$175$		0			0
$176$	0.0762186	+	0.0339347i	0.00574519	+	0.00255792i
$177$	−1.80958	−	1.62936i	−0.136017	−	0.122470i
$178$	2.65426	−	0.862421i	0.198945	−	0.0646412i
$179$	3.74794	+	4.16251i	0.280134	+	0.311120i	0.866748	−	0.498746i	$-0.166206\pi$
$179$	3.74794	+	4.16251i	0.280134	+	0.311120i	−0.586614	+	0.809867i	$0.699539\pi$
$180$		0			0
$181$	12.7202	+	22.0320i	0.945482	+	1.63762i	0.754784	+	0.655974i	$0.227742\pi$
$181$	12.7202	+	22.0320i	0.945482	+	1.63762i	0.190698	+	0.981649i	$0.438925\pi$
$182$	4.34713	+	1.41247i	0.322231	+	0.104699i
$183$	1.70145	+	3.82151i	0.125774	+	0.282494i
$184$	3.77252	−	2.74090i	0.278114	−	0.202062i
$185$		0			0
$186$	3.81378	−	1.38096i	0.279640	−	0.101257i
$187$		−	0.0593361i		−	0.00433909i
$188$	−14.2709	−	19.6423i	−1.04082	−	1.43256i
$189$	−4.50963	+	2.00782i	−0.328027	+	0.146047i
$190$		0			0
$191$	6.28076	+	10.8786i	0.454460	+	0.787147i	0.998657	−	0.0518101i	$-0.0164990\pi$
$191$	6.28076	+	10.8786i	0.454460	+	0.787147i	−0.544197	+	0.838957i	$0.683166\pi$
$192$	3.49490	+	2.01778i	0.252222	+	0.145621i
$193$	−2.93299	+	2.64087i	−0.211121	+	0.190094i	−0.767906	−	0.640562i	$-0.778701\pi$
$193$	−2.93299	+	2.64087i	−0.211121	+	0.190094i	0.556785	+	0.830657i	$0.312035\pi$
$194$	1.49008	+	4.58601i	0.106982	+	0.329256i
$195$		0			0
$196$	−2.12749	−	0.947221i	−0.151964	−	0.0676586i
$197$	−4.04791	−	19.0439i	−0.288402	−	1.35682i	−0.848849	−	0.528635i	$-0.822704\pi$
$197$	−4.04791	−	19.0439i	−0.288402	−	1.35682i	0.560448	−	0.828190i	$-0.310629\pi$
$198$	0.211998	−	0.0222819i	0.0150660	−	0.00158350i
$199$	−2.50605	+	23.8435i	−0.177649	+	1.69022i	0.435450	+	0.900213i	$0.356589\pi$
$199$	−2.50605	+	23.8435i	−0.177649	+	1.69022i	−0.613099	+	0.790006i	$0.710078\pi$
$200$		0			0
$201$	−0.690871	−	0.501947i	−0.0487303	−	0.0354046i
$202$	−11.5304	+	15.8703i	−0.811278	+	1.11663i
$203$	2.73281	−	12.8569i	0.191806	−	0.902376i
$204$	0.159307	−	1.51570i	0.0111537	−	0.106120i
$205$		0			0
$206$	11.4863	−	2.44149i	0.800289	−	0.170107i
$207$	−4.21205	+	9.46042i	−0.292758	+	0.657545i
$208$	1.55207	+	1.39749i	0.107616	+	0.0968983i
$209$	0.0161517	+	0.0497098i	0.00111724	+	0.00343850i
$210$		0			0
$211$	−5.74590	+	9.95219i	−0.395564	+	0.685137i	−0.993173	−	0.116650i	$-0.962784\pi$
$211$	−5.74590	+	9.95219i	−0.395564	+	0.685137i	0.597609	+	0.801788i	$0.296118\pi$
$212$	24.2420	−	13.9961i	1.66495	−	0.961259i
$213$	−2.14626	−	0.697363i	−0.147059	−	0.0477825i
$214$	−23.5789	+	10.4980i	−1.61182	+	0.717628i
$215$		0			0
$216$	2.59497			0.176565
$217$	13.7507	−	0.457398i	0.933455	−	0.0310502i
$218$		−	25.0087i		−	1.69380i
$219$	3.48331	−	2.53077i	0.235380	−	0.171014i
$220$		0			0
$221$	0.458995	−	1.41264i	0.0308754	−	0.0950246i
$222$	0.831123	−	0.479849i	0.0557813	−	0.0322054i
$223$	3.87842	+	2.23921i	0.259718	+	0.149949i	0.624206	−	0.781260i	$-0.285423\pi$
$223$	3.87842	+	2.23921i	0.259718	+	0.149949i	−0.364488	+	0.931208i	$0.618756\pi$
$224$	12.8932	+	14.3193i	0.861463	+	0.956751i
$225$		0			0
$226$	24.3989	−	27.0977i	1.62299	−	1.80251i
$227$	6.40556	−	14.3871i	0.425152	−	0.954906i	−0.566272	−	0.824218i	$-0.691615\pi$
$227$	6.40556	−	14.3871i	0.425152	−	0.954906i	0.991424	−	0.130688i	$-0.0417185\pi$
$228$	0.279122	+	1.31317i	0.0184853	+	0.0869666i
$229$	0.240431	+	2.28755i	0.0158881	+	0.151166i	0.999590	−	0.0286434i	$-0.00911873\pi$
$229$	0.240431	+	2.28755i	0.0158881	+	0.151166i	−0.983702	+	0.179809i	$0.942452\pi$
$230$		0			0
$231$	−0.0282530	−	0.00600536i	−0.00185891	−	0.000395124i
$232$	−4.06136	+	5.58998i	−0.266641	+	0.367000i
$233$	−11.9800	+	16.4891i	−0.784837	+	1.08023i	0.209895	+	0.977724i	$0.432688\pi$
$233$	−11.9800	+	16.4891i	−0.784837	+	1.08023i	−0.994732	+	0.102511i	$0.967312\pi$
$234$	5.21949	+	1.10944i	0.341209	+	0.0725262i
$235$		0			0
$236$	1.95344	+	18.5857i	0.127158	+	1.20983i
$237$	−0.706907	−	3.32574i	−0.0459185	−	0.216030i
$238$	3.71677	−	8.34801i	0.240923	−	0.541121i
$239$	−9.71312	+	10.7875i	−0.628290	+	0.697786i	−0.970299	−	0.241910i	$-0.922226\pi$
$239$	−9.71312	+	10.7875i	−0.628290	+	0.697786i	0.342009	+	0.939697i	$0.388893\pi$
$240$		0			0
$241$	−9.51662	−	10.5693i	−0.613019	−	0.680827i	0.354083	−	0.935214i	$-0.384793\pi$
$241$	−9.51662	−	10.5693i	−0.613019	−	0.680827i	−0.967103	+	0.254387i	$0.918126\pi$
$242$	−20.4412	−	11.8017i	−1.31401	−	0.758643i
$243$	−7.53504	+	4.35036i	−0.483373	+	0.279076i
$244$	9.92079	−	30.5331i	0.635114	−	1.95468i
$245$		0			0
$246$	0.723448	−	0.525616i	0.0461254	−	0.0335120i
$247$			1.30840i			0.0832518i
$248$	−6.70131	−	2.72041i	−0.425533	−	0.172746i
$249$	−2.88503			−0.182831
$250$		0			0
$251$	22.2381	−	9.90103i	1.40365	−	0.624947i	0.441453	−	0.897285i	$-0.354463\pi$
$251$	22.2381	−	9.90103i	1.40365	−	0.624947i	0.962202	+	0.272337i	$0.0877966\pi$
$252$	17.6627	+	5.73896i	1.11265	+	0.361521i
$253$	−0.107048	+	0.0618043i	−0.00673006	+	0.00388560i
$254$	1.55457	−	2.69259i	0.0975424	−	0.168948i
$255$		0			0
$256$	0.771361	+	2.37401i	0.0482101	+	0.148375i
$257$	15.7467	+	14.1784i	0.982252	+	0.884424i	0.993306	−	0.115515i	$-0.0368519\pi$
$257$	15.7467	+	14.1784i	0.982252	+	0.884424i	−0.0110538	+	0.999939i	$0.503519\pi$
$258$	−3.61737	+	8.12474i	−0.225207	+	0.505824i
$259$	3.18415	−	0.676812i	0.197853	−	0.0420550i
$260$		0			0
$261$	1.60396	−	15.2606i	0.0992825	−	0.944610i
$262$	−2.05052	+	9.64694i	−0.126682	+	0.595990i
$263$	−3.74515	+	5.15476i	−0.230936	+	0.317856i	−0.908721	−	0.417404i	$-0.862940\pi$
$263$	−3.74515	+	5.15476i	−0.230936	+	0.317856i	0.677785	+	0.735260i	$0.262940\pi$
$264$	0.0122840	+	0.00892484i	0.000756027	+	0.000549286i
$265$		0			0
$266$	−0.841403	+	8.00541i	−0.0515897	+	0.490843i
$267$	−0.439057	+	0.0461468i	−0.0268699	+	0.00282414i
$268$	1.36263	+	6.41067i	0.0832358	+	0.391594i
$269$	−24.1414	−	10.7485i	−1.47193	−	0.655345i	−0.494996	−	0.868895i	$-0.664831\pi$
$269$	−24.1414	−	10.7485i	−1.47193	−	0.655345i	−0.976932	+	0.213550i	$0.931497\pi$
$270$		0			0
$271$	−4.94971	−	15.2336i	−0.300673	−	0.925377i	−0.981256	−	0.192706i	$-0.938274\pi$
$271$	−4.94971	−	15.2336i	−0.300673	−	0.925377i	0.680583	−	0.732671i	$-0.261726\pi$
$272$	3.10289	−	2.79386i	0.188140	−	0.169402i
$273$	−0.626177	−	0.361524i	−0.0378980	−	0.0218804i
$274$	−3.28394	−	5.68796i	−0.198390	−	0.343622i
$275$		0			0
$276$	−2.90041	+	1.29134i	−0.174584	+	0.0777297i
$277$	−4.90164	−	6.74652i	−0.294511	−	0.405359i	0.635962	−	0.771720i	$-0.280603\pi$
$277$	−4.90164	−	6.74652i	−0.294511	−	0.405359i	−0.930473	+	0.366361i	$0.880603\pi$
$278$		−	25.0405i		−	1.50183i
$279$	15.9090	−	2.20902i	0.952449	−	0.132251i
$280$		0			0
$281$	7.87455	−	5.72119i	0.469756	−	0.341298i	−0.327590	−	0.944820i	$-0.606237\pi$
$281$	7.87455	−	5.72119i	0.469756	−	0.341298i	0.797346	+	0.603522i	$0.206237\pi$
$282$	2.76132	+	6.20203i	0.164434	+	0.369326i
$283$	12.7603	+	4.14607i	0.758521	+	0.246459i	0.662644	−	0.748935i	$-0.269434\pi$
$283$	12.7603	+	4.14607i	0.758521	+	0.246459i	0.0958775	+	0.995393i	$0.469434\pi$
$284$	8.65976	+	14.9991i	0.513862	+	0.890035i
$285$		0			0
$286$	0.0426190	+	0.0473332i	0.00252011	+	0.00279887i
$287$	2.88476	−	0.937316i	0.170282	−	0.0553280i
$288$	16.7167	+	15.0518i	0.985040	+	0.886934i
$289$	12.8175	+	5.70672i	0.753971	+	0.335690i
$290$		0			0
$291$	−0.0797321	−	0.758600i	−0.00467398	−	0.0444699i
$292$	−32.8631	−	3.45405i	−1.92317	−	0.202133i
$293$	0.999813	−	4.70375i	0.0584097	−	0.274796i	−0.939245	−	0.343248i	$-0.888473\pi$
$293$	0.999813	−	4.70375i	0.0584097	−	0.274796i	0.997654	+	0.0684523i	$0.0218061\pi$
$294$	0.526824	+	0.382760i	0.0307250	+	0.0223230i
$295$		0			0
$296$	−1.67384	−	0.355786i	−0.0972901	−	0.0206797i
$297$	−0.0684102	−	0.00719020i	−0.00396956	−	0.000417218i
$298$	40.9222	−	4.30110i	2.37056	−	0.249156i
$299$	−3.02663	+	0.643330i	−0.175035	+	0.0372048i
$300$		0			0
$301$	−20.1857	+	22.4185i	−1.16348	+	1.29218i
$302$	−8.20435	+	2.66575i	−0.472107	+	0.153397i
$303$	2.30606	−	2.07638i	0.132480	−	0.119285i
$304$	−1.83899	+	3.18523i	−0.105473	+	0.182685i
$305$		0			0
$306$	3.29657	−	10.1458i	0.188452	−	0.579997i
$307$	11.1600	+	25.0657i	0.636934	+	1.43058i	0.886734	+	0.462280i	$0.152968\pi$
$307$	11.1600	+	25.0657i	0.636934	+	1.43058i	−0.249800	+	0.968297i	$0.580365\pi$
$308$	0.130298	+	0.179340i	0.00742443	+	0.0102188i
$309$	−1.85757			−0.105674
$310$		0			0
$311$	−34.7671			−1.97146			−0.985730	−	0.168335i	$-0.946161\pi$
$311$	−34.7671			−1.97146			−0.985730	+	0.168335i	$0.946161\pi$
$312$	0.223412	+	0.307500i	0.0126482	+	0.0174088i
$313$	8.38497	+	18.8330i	0.473947	+	1.06450i	0.979452	+	0.201678i	$0.0646395\pi$
$313$	8.38497	+	18.8330i	0.473947	+	1.06450i	−0.505505	+	0.862824i	$0.668694\pi$
$314$	11.6972	−	36.0002i	0.660110	−	2.03161i
$315$		0			0
$316$	−13.0471	+	22.5982i	−0.733955	+	1.27125i
$317$	15.1579	−	13.6482i	0.851353	−	0.766562i	−0.122804	−	0.992431i	$-0.539189\pi$
$317$	15.1579	−	13.6482i	0.851353	−	0.766562i	0.974158	+	0.225869i	$0.0725221\pi$
$318$	−7.44414	+	2.41875i	−0.417447	+	0.135637i
$319$	0.122557	−	0.136113i	0.00686187	−	0.00762088i
$320$		0			0
$321$	3.99363	−	0.848871i	0.222902	−	0.0473794i
$322$	−18.9320	+	1.98983i	−1.05504	+	0.110889i
$323$	2.60143	+	0.273422i	0.144748	+	0.0152136i
$324$	20.3262	+	4.32046i	1.12923	+	0.240025i
$325$		0			0
$326$	−41.9919	−	30.5089i	−2.32572	−	1.68973i
$327$	−0.822507	+	3.86959i	−0.0454848	+	0.213989i
$328$	−1.58577	−	0.166671i	−0.0875593	−	0.00920286i
$329$	2.40709	+	22.9019i	0.132707	+	1.26263i
$330$		0			0
$331$	−28.6028	−	12.7348i	−1.57215	−	0.699968i	−0.578843	−	0.815439i	$-0.696496\pi$
$331$	−28.6028	−	12.7348i	−1.57215	−	0.699968i	−0.993311	+	0.115471i	$0.963162\pi$
$332$	16.4544	+	14.8156i	0.903054	+	0.813113i
$333$	3.61429	−	1.17435i	0.198062	−	0.0643541i
$334$	−15.2678	−	16.9566i	−0.835417	−	0.927825i
$335$		0			0
$336$	−1.01626	−	1.76021i	−0.0554415	−	0.0960274i
$337$	−10.7432	−	3.49068i	−0.585219	−	0.190149i	0.00141805	−	0.999999i	$-0.499549\pi$
$337$	−10.7432	−	3.49068i	−0.585219	−	0.190149i	−0.586637	+	0.809850i	$0.699549\pi$
$338$	−10.6986	−	24.0295i	−0.581928	−	1.30703i
$339$	−4.66646	+	3.39038i	−0.253447	+	0.184140i
$340$		0			0
$341$	0.169126	+	0.0902854i	0.00915870	+	0.00488923i
$342$			9.39716i			0.508140i
$343$	11.4655	+	15.7809i	0.619077	+	0.852087i
$344$	14.4872	−	6.45012i	0.781098	−	0.347767i
$345$		0			0
$346$	8.52566	+	14.7669i	0.458342	+	0.793872i
$347$	2.17038	+	1.25307i	0.116512	+	0.0672684i	0.557124	−	0.830430i	$-0.311905\pi$
$347$	2.17038	+	1.25307i	0.116512	+	0.0672684i	−0.440611	+	0.897698i	$0.645238\pi$
$348$	3.49607	−	3.14787i	0.187409	−	0.168744i
$349$	0.527266	+	1.62276i	0.0282239	+	0.0868642i	0.964176	−	0.265262i	$-0.0854586\pi$
$349$	0.527266	+	1.62276i	0.0282239	+	0.0868642i	−0.935952	+	0.352127i	$0.885459\pi$
$350$		0			0
$351$	−1.57305	−	0.700368i	−0.0839633	−	0.0373829i
$352$	0.0558244	+	0.262633i	0.00297545	+	0.0139984i
$353$	−7.98033	+	0.838766i	−0.424750	+	0.0446430i	−0.314492	−	0.949260i	$-0.601834\pi$
$353$	−7.98033	+	0.838766i	−0.424750	+	0.0446430i	−0.110258	+	0.993903i	$0.535168\pi$
$354$	0.546222	−	5.19695i	0.0290314	−	0.276215i
$355$		0			0
$356$	2.74109	+	1.99152i	0.145278	+	0.105550i
$357$	−0.849653	+	1.16945i	−0.0449684	+	0.0618937i
$358$	−2.49914	+	11.7575i	−0.132083	+	0.621404i
$359$	0.214085	−	2.03688i	0.0112989	−	0.107502i	−0.987419	−	0.158127i	$-0.949455\pi$
$359$	0.214085	−	2.03688i	0.0112989	−	0.107502i	0.998718	+	0.0506245i	$0.0161212\pi$
$360$		0			0
$361$	16.3310	−	3.47126i	0.859526	−	0.182698i
$362$	−22.2057	+	49.8749i	−1.16711	+	2.62137i
$363$	2.77472	+	2.49837i	0.145635	+	0.131130i
$364$	1.71478	+	5.27755i	0.0898789	+	0.276619i
$365$		0			0
$366$	−4.48853	+	7.77436i	−0.234619	+	0.406372i
$367$	−5.88693	+	3.39882i	−0.307295	+	0.177417i	−0.645716	−	0.763578i	$-0.723441\pi$
$367$	−5.88693	+	3.39882i	−0.307295	+	0.177417i	0.338420	+	0.940995i	$0.390107\pi$
$368$	−8.27235	−	2.68785i	−0.431226	−	0.140114i
$369$	3.23490	−	1.44027i	0.168402	−	0.0749775i
$370$		0			0
$371$	−26.5499			−1.37840
$372$	4.07781	+	2.76035i	0.211425	+	0.143118i
$373$		−	19.0749i		−	0.987662i	−0.869558	−	0.493831i	$-0.835596\pi$
$373$		−	19.0749i		−	0.987662i	0.869558	−	0.493831i	$-0.164404\pi$
$374$	0.103016	−	0.0748457i	0.00532685	−	0.00387018i
$375$		0			0
$376$	3.74078	−	11.5129i	0.192916	−	0.593734i
$377$	3.97067	−	2.29247i	0.204500	−	0.118068i
$378$	−9.17425	−	5.29676i	−0.471873	−	0.272436i
$379$	4.57029	+	5.07582i	0.234760	+	0.260727i	0.849001	−	0.528391i	$-0.177204\pi$
$379$	4.57029	+	5.07582i	0.234760	+	0.260727i	−0.614241	+	0.789118i	$0.710538\pi$
$380$		0			0
$381$	−0.329095	+	0.365497i	−0.0168600	+	0.0187250i
$382$	−10.9644	+	24.6264i	−0.560987	+	1.26000i
$383$	3.18109	+	14.9658i	0.162546	+	0.764719i	0.981592	+	0.190991i	$0.0611701\pi$
$383$	3.18109	+	14.9658i	0.162546	+	0.764719i	−0.819046	+	0.573728i	$0.805497\pi$
$384$	0.351858	+	3.34771i	0.0179557	+	0.170837i
$385$		0			0
$386$	−8.28458	−	1.76094i	−0.421674	−	0.0896295i
$387$	−20.7004	+	28.4917i	−1.05226	+	1.44831i
$388$	−3.44094	+	4.73604i	−0.174687	+	0.240436i
$389$	−35.2480	−	7.49219i	−1.78714	−	0.379869i	−0.809002	−	0.587806i	$-0.799992\pi$
$389$	−35.2480	−	7.49219i	−1.78714	−	0.379869i	−0.978142	+	0.207937i	$0.933325\pi$
$390$		0			0
$391$	0.646615	+	6.15213i	0.0327007	+	0.311127i
$392$	−0.241414	−	1.13576i	−0.0121932	−	0.0573647i
$393$	0.634554	−	1.42523i	0.0320090	−	0.0718934i
$394$	27.9571	−	31.0495i	1.40846	−	1.56425i
$395$		0			0
$396$	0.173164	+	0.192318i	0.00870182	+	0.00966435i
$397$	10.2745	+	5.93197i	0.515661	+	0.297717i	0.735158	−	0.677896i	$-0.237108\pi$
$397$	10.2745	+	5.93197i	0.515661	+	0.297717i	−0.219496	+	0.975613i	$0.570441\pi$
$398$	−44.5569	+	25.7249i	−2.23344	+	1.28947i
$399$	0.393479	−	1.21100i	0.0196986	−	0.0606260i
$400$		0			0
$401$	31.2668	−	22.7167i	1.56139	−	1.13442i	0.626533	−	0.779395i	$-0.284473\pi$
$401$	31.2668	−	22.7167i	1.56139	−	1.13442i	0.934858	−	0.355022i	$-0.115527\pi$
$402$		−	1.83260i		−	0.0914020i
$403$	3.32806	+	3.45774i	0.165783	+	0.172242i
$404$	−23.8153			−1.18486
$405$		0			0
$406$	25.7686	−	11.4729i	1.27887	−	0.569391i
$407$	0.0431411	+	0.0140174i	0.00213842	+	0.000694816i
$408$	0.658074	−	0.379939i	0.0325795	−	0.0188098i
$409$	−1.77446	+	3.07346i	−0.0877416	+	0.151973i	−0.906556	−	0.422085i	$-0.861298\pi$
$409$	−1.77446	+	3.07346i	−0.0877416	+	0.151973i	0.818815	+	0.574058i	$0.194632\pi$
$410$		0			0
$411$	0.321054	+	0.988103i	0.0158364	+	0.0487395i
$412$	10.5945	+	9.53929i	0.521951	+	0.469967i
$413$	7.20944	−	16.1927i	0.354753	−	0.796789i
$414$	−21.7377	+	4.62049i	−1.06835	+	0.227085i
$415$		0			0
$416$	−0.702565	+	6.68446i	−0.0344461	+	0.327732i
$417$	−0.823555	+	3.87452i	−0.0403297	+	0.189736i
$418$	−0.0659301	+	0.0907450i	−0.00322475	+	0.00443848i
$419$	9.72888	+	7.06844i	0.475287	+	0.345316i	0.799498	−	0.600669i	$-0.205099\pi$
$419$	9.72888	+	7.06844i	0.475287	+	0.345316i	−0.324211	+	0.945985i	$0.605099\pi$
$420$		0			0
$421$	−1.71081	+	16.2773i	−0.0833798	+	0.793306i	0.870308	+	0.492508i	$0.163920\pi$
$421$	−1.71081	+	16.2773i	−0.0833798	+	0.793306i	−0.953688	+	0.300798i	$0.902747\pi$
$422$	−24.5263	+	2.57782i	−1.19392	+	0.125486i
$423$	5.58939	+	26.2960i	0.271765	+	1.27856i
$424$	12.7501	+	5.67671i	0.619200	+	0.275685i
$425$		0			0
$426$	−1.49654	−	4.60587i	−0.0725076	−	0.223155i
$427$	−22.6288	+	20.3751i	−1.09508	+	0.986018i
$428$	−27.1364	−	15.6672i	−1.31169	−	0.757304i
$429$	−0.00503770	−	0.00872555i	−0.000243222	−	0.000421274i
$430$		0			0
$431$	−7.89927	+	3.51698i	−0.380494	+	0.169407i	−0.588066	−	0.808813i	$-0.700111\pi$
$431$	−7.89927	+	3.51698i	−0.380494	+	0.169407i	0.207572	+	0.978220i	$0.433444\pi$
$432$	−2.84511	−	3.91596i	−0.136885	−	0.188407i
$433$			11.7623i			0.565262i	0.959229	+	0.282631i	$0.0912072\pi$
$433$			11.7623i			0.565262i	−0.959229	+	0.282631i	$0.908793\pi$
$434$	18.1390	+	23.2962i	0.870699	+	1.11825i
$435$		0			0
$436$	24.5628	−	17.8459i	1.17634	−	0.854665i
$437$	−2.21636	−	4.97804i	−0.106023	−	0.238132i
$438$	8.78760	+	2.85526i	0.419888	+	0.136430i
$439$	14.0078	+	24.2623i	0.668557	+	1.15797i	0.978308	+	0.207156i	$0.0664209\pi$
$439$	14.0078	+	24.2623i	0.668557	+	1.15797i	−0.309751	+	0.950818i	$0.600246\pi$
$440$		0			0
$441$	1.72544	+	1.91630i	0.0821638	+	0.0912522i
$442$	3.03153	−	0.985002i	0.144195	−	0.0468518i
$443$	10.7138	+	9.64677i	0.509029	+	0.458332i	0.883179	−	0.469037i	$-0.155399\pi$
$443$	10.7138	+	9.64677i	0.509029	+	0.458332i	−0.374150	+	0.927368i	$0.622065\pi$
$444$	1.06437	+	0.473890i	0.0505130	+	0.0224898i
$445$		0			0
$446$	1.00459	+	9.55803i	0.0475687	+	0.452586i
$447$	−6.47335	−	0.680377i	−0.306179	−	0.0321807i
$448$	−6.10753	+	28.7337i	−0.288554	+	1.35754i
$449$	−19.5658	−	14.2154i	−0.923369	−	0.670867i	0.0209913	−	0.999780i	$-0.493318\pi$
$449$	−19.5658	−	14.2154i	−0.923369	−	0.670867i	−0.944360	+	0.328913i	$0.893318\pi$
$450$		0			0
$451$	0.0413432	+	0.00878776i	0.00194677	+	0.000413800i
$452$	44.0254	+	4.62726i	2.07078	+	0.217648i
$453$	1.35713	−	0.142640i	0.0637637	−	0.00670183i
$454$	33.0580	−	7.02670i	1.55149	−	0.329780i
$455$		0			0
$456$	−0.447890	+	0.497432i	−0.0209744	+	0.0232944i
$457$	29.2518	−	9.50449i	1.36834	−	0.444601i	0.469523	−	0.882920i	$-0.344426\pi$
$457$	29.2518	−	9.50449i	1.36834	−	0.444601i	0.898819	+	0.438319i	$0.144426\pi$
$458$	−3.66825	+	3.30291i	−0.171406	+	0.154335i
$459$	−1.72123	+	2.98126i	−0.0803402	+	0.139153i
$460$		0			0
$461$	−2.77077	+	8.52756i	−0.129048	+	0.397168i	−0.994617	−	0.103621i	$-0.966957\pi$
$461$	−2.77077	+	8.52756i	−0.129048	+	0.397168i	0.865569	+	0.500790i	$0.166957\pi$
$462$	−0.0252117	−	0.0566265i	−0.00117296	−	0.00263450i
$463$	−18.1482	−	24.9789i	−0.843420	−	1.16087i	−0.985274	−	0.170980i	$-0.945307\pi$
$463$	−18.1482	−	24.9789i	−0.843420	−	1.16087i	0.141855	−	0.989887i	$-0.454693\pi$
$464$	12.8885			0.598331
$465$		0			0
$466$	−43.7389			−2.02616
$467$	−16.5536	−	22.7841i	−0.766010	−	1.05432i	−0.996690	−	0.0812924i	$-0.974095\pi$
$467$	−16.5536	−	22.7841i	−0.766010	−	1.05432i	0.230681	−	0.973030i	$-0.425905\pi$
$468$	2.63491	+	5.91812i	0.121799	+	0.273565i
$469$	1.92090	−	5.91193i	0.0886990	−	0.272987i
$470$		0			0
$471$	−2.99391	+	5.18561i	−0.137952	+	0.238940i
$472$	−6.92442	+	6.23477i	−0.318722	+	0.286979i
$473$	−0.399793	+	0.129901i	−0.0183825	+	0.00597284i
$474$	4.88229	−	5.42233i	0.224251	−	0.249056i
$475$		0			0
$476$	10.8514	−	2.30654i	0.497374	−	0.105720i
$477$	−30.8250	+	3.23984i	−1.41138	+	0.148342i
$478$	−30.9807	−	3.25620i	−1.41703	−	0.148935i
$479$	1.20986	+	0.257165i	0.0552801	+	0.0117501i	0.235469	−	0.971882i	$-0.424337\pi$
$479$	1.20986	+	0.257165i	0.0552801	+	0.0117501i	−0.180189	+	0.983632i	$0.557671\pi$
$480$		0			0
$481$	0.918647	+	0.667436i	0.0418867	+	0.0304325i
$482$	6.34571	−	29.8542i	0.289039	−	1.35982i
$483$	2.99479	+	0.314765i	0.136268	+	0.0143223i
$484$	−2.99529	−	28.4983i	−0.136150	−	1.29538i
$485$		0			0
$486$	−17.0575	−	7.59447i	−0.773742	−	0.344492i
$487$	10.2185	+	9.20079i	0.463045	+	0.416928i	0.867352	−	0.497696i	$-0.165820\pi$
$487$	10.2185	+	9.20079i	0.463045	+	0.416928i	−0.404307	+	0.914624i	$0.632487\pi$
$488$	15.2235	−	4.94643i	0.689137	−	0.223914i
$489$	5.49400	+	6.10171i	0.248447	+	0.275929i
$490$		0			0
$491$	3.73427	+	6.46795i	0.168525	+	0.291894i	0.937902	−	0.346902i	$-0.112766\pi$
$491$	3.73427	+	6.46795i	0.168525	+	0.291894i	−0.769376	+	0.638796i	$0.779433\pi$
$492$	1.03249	+	0.335476i	0.0465482	+	0.0151244i
$493$	−3.72823	−	8.37374i	−0.167911	−	0.377134i
$494$	−2.27158	+	1.65040i	−0.102203	+	0.0742551i
$495$		0			0
$496$	3.24202	+	13.0953i	0.145571	+	0.587997i
$497$		−	16.4271i		−	0.736854i
$498$	−3.63913	−	5.00884i	−0.163073	−	0.224451i
$499$	18.1126	−	8.06423i	0.810829	−	0.361004i	0.0409236	−	0.999162i	$-0.486970\pi$
$499$	18.1126	−	8.06423i	0.810829	−	0.361004i	0.769906	+	0.638158i	$0.220303\pi$
$500$		0			0
$501$	1.80470	+	3.12584i	0.0806282	+	0.139652i
$502$	45.2404	+	26.1196i	2.01918	+	1.16577i
$503$	5.73527	−	5.16406i	0.255723	−	0.230254i	−0.531290	−	0.847190i	$-0.678293\pi$
$503$	5.73527	−	5.16406i	0.255723	−	0.230254i	0.787014	+	0.616935i	$0.211626\pi$
$504$	2.86140	+	8.80649i	0.127457	+	0.392272i
$505$		0			0
$506$	−0.242331	−	0.107893i	−0.0107729	−	0.00479641i
$507$	0.865095	+	4.06995i	0.0384202	+	0.180753i
$508$	3.75391	−	0.394552i	0.166553	−	0.0175054i
$509$	3.56093	−	33.8800i	0.157835	−	1.50170i	−0.573229	−	0.819395i	$-0.694309\pi$
$509$	3.56093	−	33.8800i	0.157835	−	1.50170i	0.731064	−	0.682309i	$-0.239024\pi$
$510$		0			0
$511$	25.3557	+	18.4220i	1.12167	+	0.814941i
$512$	−14.8055	+	20.3781i	−0.654318	+	0.900591i
$513$	0.630470	−	2.96613i	0.0278359	−	0.130958i
$514$	−4.75313	+	45.2230i	−0.209652	+	1.99470i
$515$		0			0
$516$	−10.5612	+	2.24485i	−0.464931	+	0.0988240i
$517$	−0.130517	+	0.293146i	−0.00574013	+	0.0128925i
$518$	5.19148	+	4.67443i	0.228101	+	0.205383i
$519$	−0.833509	−	2.56528i	−0.0365870	−	0.112603i
$520$		0			0
$521$	11.6725	−	20.2174i	0.511384	−	0.885742i	−0.488529	−	0.872547i	$-0.662466\pi$
$521$	11.6725	−	20.2174i	0.511384	−	0.885742i	0.999913	−	0.0131949i	$-0.00420018\pi$
$522$	28.5179	−	16.4648i	1.24820	−	0.720647i
$523$	30.0253	+	9.75582i	1.31292	+	0.426592i	0.880056	−	0.474869i	$-0.157505\pi$
$523$	30.0253	+	9.75582i	1.31292	+	0.426592i	0.432859	+	0.901461i	$0.357505\pi$
$524$	−10.9382	+	4.86999i	−0.477836	+	0.212746i
$525$		0			0
$526$	−13.6735			−0.596194
$527$	7.57033	−	5.89443i	0.329769	−	0.256766i
$528$		−	0.0283224i		−	0.00123257i
$529$	−8.18185	+	5.94446i	−0.355733	+	0.258455i
$530$		0			0
$531$	6.39437	−	19.6799i	0.277492	−	0.854033i
$532$	−8.46310	+	4.88617i	−0.366922	+	0.211842i
$533$	0.916297	+	0.529025i	0.0396892	+	0.0229146i
$534$	−0.633938	−	0.704060i	−0.0274332	−	0.0304677i
$535$		0			0
$536$	−2.18653	+	2.42838i	−0.0944436	+	0.104890i
$537$	0.773382	−	1.73705i	0.0333739	−	0.0749590i
$538$	−11.7907	−	55.4710i	−0.508335	−	2.39153i
$539$	0.00321730	+	0.0306106i	0.000138579	+	0.00131849i
$540$		0			0
$541$	24.7849	+	5.26819i	1.06558	+	0.226497i	0.707154	−	0.707059i	$-0.249979\pi$
$541$	24.7849	+	5.26819i	1.06558	+	0.226497i	0.358431	+	0.933556i	$0.383312\pi$
$542$	20.2044	−	27.8089i	0.867851	−	1.19449i
$543$	5.07622	−	6.98682i	0.217841	−	0.299833i
$544$	13.1435	+	2.79375i	0.563525	+	0.119781i
$545$		0			0
$546$	−0.162192	−	1.54316i	−0.00694119	−	0.0660411i
$547$	−5.50600	−	25.9037i	−0.235419	−	1.10756i	−0.923997	−	0.382399i	$-0.875098\pi$
$547$	−5.50600	−	25.9037i	−0.235419	−	1.10756i	0.688578	−	0.725162i	$-0.258235\pi$
$548$	3.24316	−	7.28426i	0.138541	−	0.311168i
$549$	−23.7863	+	26.4173i	−1.01517	+	1.12746i
$550$		0			0
$551$	5.40277	+	6.00039i	0.230166	+	0.255625i
$552$	−1.37090	−	0.791487i	−0.0583492	−	0.0336879i
$553$	21.4337	−	12.3748i	0.911454	−	0.526228i
$554$	5.53011	−	17.0199i	0.234952	−	0.723108i
$555$		0			0
$556$	24.5941	−	17.8687i	1.04302	−	0.757800i
$557$		−	6.77607i		−	0.287111i	−0.989642	−	0.143556i	$-0.954146\pi$
$557$		−	6.77607i		−	0.287111i	0.989642	−	0.143556i	$-0.0458536\pi$
$558$	23.9026	+	24.8340i	1.01188	+	1.05131i
$559$	−10.5229			−0.445071
$560$		0			0
$561$	−0.0184013	+	0.00819279i	−0.000776904	+	0.000345900i
$562$	19.8657	+	6.45475i	0.837983	+	0.272277i
$563$	−10.6621	+	6.15575i	−0.449353	+	0.259434i	−0.707557	−	0.706656i	$-0.750203\pi$
$563$	−10.6621	+	6.15575i	−0.449353	+	0.259434i	0.258204	+	0.966090i	$0.416869\pi$
$564$	−4.12101	+	7.13779i	−0.173526	+	0.300555i
$565$		0			0
$566$	8.89747	+	27.3836i	0.373988	+	1.15102i
$567$	−14.6470	−	13.1882i	−0.615116	−	0.553853i
$568$	−3.51232	+	7.88881i	−0.147374	+	0.331007i
$569$	8.71280	−	1.85196i	0.365259	−	0.0776383i	−0.0216258	−	0.999766i	$-0.506884\pi$
$569$	8.71280	−	1.85196i	0.365259	−	0.0776383i	0.386885	+	0.922128i	$0.373551\pi$
$570$		0			0
$571$	2.36325	−	22.4848i	0.0988989	−	0.940960i	−0.826748	−	0.562572i	$-0.809812\pi$
$571$	2.36325	−	22.4848i	0.0988989	−	0.940960i	0.925647	−	0.378388i	$-0.123521\pi$
$572$	−0.0160768	+	0.0756356i	−0.000672206	+	0.00316248i
$573$	2.50646	−	3.44984i	0.104709	−	0.144119i
$574$	5.26612	+	3.82606i	0.219804	+	0.159697i
$575$		0			0
$576$	−3.58467	+	34.1058i	−0.149361	+	1.42108i
$577$	30.5685	−	3.21288i	1.27259	−	0.133754i	0.555958	−	0.831210i	$-0.312352\pi$
$577$	30.5685	−	3.21288i	1.27259	−	0.133754i	0.716627	+	0.697456i	$0.245685\pi$
$578$	6.26010	+	29.4515i	0.260386	+	1.22502i
$579$	1.22396	+	0.544941i	0.0508659	+	0.0226470i
$580$		0			0
$581$	−6.48956	−	19.9728i	−0.269232	−	0.828612i
$582$	1.21647	−	1.09531i	0.0504243	−	0.0454022i
$583$	−0.320397	−	0.184981i	−0.0132695	−	0.00766114i
$584$	−8.23776	−	14.2682i	−0.340881	−	0.590423i
$585$		0			0
$586$	9.42756	−	4.19742i	0.389449	−	0.173394i
$587$	13.1855	+	18.1483i	0.544224	+	0.749060i	0.989214	−	0.146476i	$-0.0467930\pi$
$587$	13.1855	+	18.1483i	0.544224	+	0.749060i	−0.444991	+	0.895535i	$0.646793\pi$
$588$			0.790564i			0.0326023i
$589$	−4.73766	+	6.99885i	−0.195212	+	0.288383i
$590$		0			0
$591$	−5.34699	+	3.88482i	−0.219946	+	0.159800i
$592$	1.29829	+	2.91601i	0.0533594	+	0.119847i
$593$	25.0867	+	8.15116i	1.03019	+	0.334728i	0.774864	−	0.632128i	$-0.217818\pi$
$593$	25.0867	+	8.15116i	1.03019	+	0.334728i	0.255323	+	0.966856i	$0.417818\pi$
$594$	−0.0738084	−	0.127840i	−0.00302839	−	0.00524533i
$595$		0			0
$596$	33.4261	+	37.1234i	1.36918	+	1.52063i
$597$	7.74035	−	2.51499i	0.316792	−	0.102932i
$598$	−4.93467	−	4.44319i	−0.201794	−	0.181696i
$599$	21.7931	+	9.70292i	0.890443	+	0.396451i	0.800385	−	0.599486i	$-0.204628\pi$
$599$	21.7931	+	9.70292i	0.890443	+	0.396451i	0.0900576	+	0.995937i	$0.471295\pi$
$600$		0			0
$601$	−0.708227	−	6.73833i	−0.0288892	−	0.274862i	−0.999425	−	0.0339054i	$-0.989205\pi$
$601$	−0.708227	−	6.73833i	−0.0288892	−	0.274862i	0.970536	−	0.240957i	$-0.0774612\pi$
$602$	−64.3838	−	6.76701i	−2.62409	−	0.275803i
$603$	1.50879	−	7.09830i	0.0614427	−	0.289065i
$604$	−8.47276	−	6.15582i	−0.344752	−	0.250477i
$605$		0			0
$606$	6.51374	+	1.38454i	0.264603	+	0.0562430i
$607$	36.2222	+	3.80710i	1.47021	+	0.154526i	0.805510	−	0.592582i	$-0.201891\pi$
$607$	36.2222	+	3.80710i	1.47021	+	0.154526i	0.664703	+	0.747108i	$0.268558\pi$
$608$	−11.7717	+	1.23725i	−0.477405	+	0.0501773i
$609$	−4.36450	+	0.927704i	−0.176859	+	0.0375925i
$610$		0			0
$611$	−5.37491	+	5.96944i	−0.217446	+	0.241498i
$612$	12.3173	−	4.00214i	0.497898	−	0.161777i
$613$	21.1145	−	19.0116i	0.852807	−	0.767871i	−0.121619	−	0.992577i	$-0.538809\pi$
$613$	21.1145	−	19.0116i	0.852807	−	0.767871i	0.974427	+	0.224706i	$0.0721421\pi$
$614$	−29.4408	+	50.9930i	−1.18813	+	2.05791i
$615$		0			0
$616$	−0.0341544	+	0.105117i	−0.00137612	+	0.00423527i
$617$	−0.779979	−	1.75186i	−0.0314008	−	0.0705272i	0.897164	−	0.441697i	$-0.145623\pi$
$617$	−0.779979	−	1.75186i	−0.0314008	−	0.0705272i	−0.928565	+	0.371170i	$0.878957\pi$
$618$	−2.34312	−	3.22502i	−0.0942540	−	0.129729i
$619$	19.2014			0.771768			0.385884	−	0.922547i	$-0.373896\pi$
$619$	19.2014			0.771768			0.385884	+	0.922547i	$0.373896\pi$
$620$		0			0
$621$	7.17131			0.287775
$622$	−43.8547	−	60.3608i	−1.75841	−	2.42025i
$623$	−1.30708	−	2.93576i	−0.0523672	−	0.117619i
$624$	0.219088	−	0.674284i	0.00877054	−	0.0269930i
$625$		0			0
$626$	−22.1201	+	38.3132i	−0.884098	+	1.53130i
$627$	0.0131859	−	0.0118726i	0.000526593	−	0.000474146i
$628$	43.7054	−	14.2007i	1.74403	−	0.566671i
$629$	1.51900	−	1.68702i	0.0605665	−	0.0672659i
$630$		0			0
$631$	30.5762	−	6.49917i	1.21722	−	0.258728i	0.445845	−	0.895110i	$-0.352903\pi$
$631$	30.5762	−	6.49917i	1.21722	−	0.258728i	0.771374	+	0.636382i	$0.219570\pi$
$632$	−12.9390	+	1.35995i	−0.514688	+	0.0540959i
$633$	3.87973	+	0.407776i	0.154206	+	0.0162077i
$634$	42.8154	+	9.10069i	1.70042	+	0.361434i
$635$		0			0
$636$	−7.68768	−	5.58543i	−0.304836	−	0.221477i
$637$	−0.160193	+	0.753648i	−0.00634707	+	0.0298606i
$638$	0.390904	+	0.0410857i	0.0154760	+	0.00162660i
$639$	−2.00457	−	19.0722i	−0.0792996	−	0.754486i
$640$		0			0
$641$	−23.6057	−	10.5099i	−0.932369	−	0.415118i	−0.116393	−	0.993203i	$-0.537133\pi$
$641$	−23.6057	−	10.5099i	−0.932369	−	0.415118i	−0.815976	+	0.578086i	$0.803800\pi$
$642$	6.51127	+	5.86277i	0.256979	+	0.231385i
$643$	−42.3232	+	13.7516i	−1.66906	+	0.542311i	−0.982741	−	0.184986i	$-0.940776\pi$
$643$	−42.3232	+	13.7516i	−1.66906	+	0.542311i	−0.686322	+	0.727298i	$0.740776\pi$
$644$	−15.4640	−	17.1745i	−0.609368	−	0.676772i
$645$		0			0
$646$	2.80671	+	4.86136i	0.110429	+	0.191268i
$647$	−29.1894	−	9.48422i	−1.14756	−	0.372863i	−0.327333	−	0.944909i	$-0.606150\pi$
$647$	−29.1894	−	9.48422i	−1.14756	−	0.372863i	−0.820222	+	0.572046i	$0.806150\pi$
$648$	4.21415	+	9.46513i	0.165547	+	0.371825i
$649$	0.199821	−	0.145179i	0.00784367	−	0.00569876i
$650$		0			0
$651$	−2.04046	−	4.20120i	−0.0799719	−	0.164658i
$652$		−	63.0141i		−	2.46782i
$653$	2.80185	+	3.85641i	0.109645	+	0.150913i	0.860313	−	0.509767i	$-0.170268\pi$
$653$	2.80185	+	3.85641i	0.109645	+	0.150913i	−0.750668	+	0.660680i	$0.770268\pi$
$654$	−7.75569	+	3.45305i	−0.303271	+	0.135025i
$655$		0			0
$656$	1.48711	+	2.57575i	0.0580619	+	0.100566i
$657$	31.6866	+	18.2943i	1.23621	+	0.713727i
$658$	−36.7249	+	33.0673i	−1.43169	+	1.28910i
$659$	−11.2644	−	34.6682i	−0.438797	−	1.35048i	−0.889145	−	0.457626i	$-0.848700\pi$
$659$	−11.2644	−	34.6682i	−0.438797	−	1.35048i	0.450347	−	0.892853i	$-0.351300\pi$
$660$		0			0
$661$	6.40261	+	2.85063i	0.249033	+	0.110877i	0.527457	−	0.849582i	$-0.323145\pi$
$661$	6.40261	+	2.85063i	0.249033	+	0.110877i	−0.278424	+	0.960458i	$0.589812\pi$
$662$	−13.9697	−	65.7223i	−0.542948	−	2.55437i
$663$	−0.501464	+	0.0527059i	−0.0194752	+	0.00204693i
$664$	−1.15396	+	10.9792i	−0.0447822	+	0.426074i
$665$		0			0
$666$	6.59786	+	4.79362i	0.255662	+	0.185749i
$667$	−11.2237	+	15.4482i	−0.434585	+	0.598155i
$668$	5.75936	−	27.0956i	0.222836	−	1.04836i
$669$	0.158913	−	1.51195i	0.00614392	−	0.0584555i
$670$		0			0
$671$	−0.415038	+	0.0882191i	−0.0160224	+	0.00340566i
$672$	2.66049	−	5.97557i	0.102631	−	0.230513i
$673$	4.90504	+	4.41652i	0.189076	+	0.170244i	0.758232	−	0.651985i	$-0.226063\pi$
$673$	4.90504	+	4.41652i	0.189076	+	0.170244i	−0.569156	+	0.822229i	$0.692730\pi$
$674$	−7.49098	−	23.0549i	−0.288542	−	0.888041i
$675$		0			0
$676$	15.9667	−	27.6551i	0.614102	−	1.06366i
$677$	6.81514	−	3.93472i	0.261927	−	0.151224i	−0.363286	−	0.931678i	$-0.618345\pi$
$677$	6.81514	−	3.93472i	0.261927	−	0.151224i	0.625213	+	0.780454i	$0.285012\pi$
$678$	−11.7724	−	3.82509i	−0.452116	−	0.146902i
$679$	5.07238	−	2.25837i	0.194660	−	0.0866683i
$680$		0			0
$681$	−5.34617			−0.204866
$682$	0.0565846	+	0.407513i	0.00216674	+	0.0156045i
$683$			0.381978i			0.0146160i	0.999973	+	0.00730798i	$0.00232622\pi$
$683$			0.381978i			0.0146160i	−0.999973	+	0.00730798i	$0.997674\pi$
$684$	−9.22961	+	6.70571i	−0.352903	+	0.256399i
$685$		0			0
$686$	−12.9355	+	39.8115i	−0.493881	+	1.52001i
$687$	0.676217	−	0.390414i	0.0257993	−	0.0148952i
$688$	−25.6173	−	14.7902i	−0.976651	−	0.563869i
$689$	−6.19691	−	6.88237i	−0.236083	−	0.262197i
$690$		0			0
$691$	−9.85330	+	10.9432i	−0.374837	+	0.416299i	−0.900818	−	0.434198i	$-0.857032\pi$
$691$	−9.85330	+	10.9432i	−0.374837	+	0.416299i	0.525980	+	0.850497i	$0.323699\pi$
$692$	−8.41978	+	18.9111i	−0.320072	+	0.718893i
$693$	−0.0510328	−	0.240091i	−0.00193858	−	0.00912029i
$694$	0.562173	+	5.34872i	0.0213398	+	0.203035i
$695$		0			0
$696$	2.29433	+	0.487675i	0.0869664	+	0.0184853i
$697$	1.24331	−	1.71127i	0.0470939	−	0.0648191i
$698$	−2.15226	+	2.96234i	−0.0814644	+	0.112126i
$699$	6.76772	+	1.43852i	0.255979	+	0.0544099i
$700$		0			0
$701$	−2.11136	−	20.0883i	−0.0797451	−	0.758724i	−0.959197	−	0.282737i	$-0.908758\pi$
$701$	−2.11136	−	20.0883i	−0.0797451	−	0.758724i	0.879452	−	0.475987i	$-0.157909\pi$
$702$	−0.768283	−	3.61449i	−0.0289970	−	0.136420i
$703$	−0.813349	+	1.82681i	−0.0306760	+	0.0688995i
$704$	−0.273901	+	0.304198i	−0.0103230	+	0.0114649i
$705$		0			0
$706$	−11.5225	−	12.7970i	−0.433655	−	0.481622i
$707$	19.5619	+	11.2941i	0.735701	+	0.424757i
$708$	5.49407	−	3.17200i	0.206480	−	0.119211i
$709$	9.27986	−	28.5605i	0.348513	−	1.07261i	−0.611164	−	0.791504i	$-0.709298\pi$
$709$	9.27986	−	28.5605i	0.348513	−	1.07261i	0.959676	−	0.281107i	$-0.0907017\pi$
$710$		0			0
$711$	23.3750	−	16.9829i	0.876631	−	0.636910i
$712$			1.68932i			0.0633099i
$713$	−18.5194	−	7.51799i	−0.693556	−	0.281551i
$714$	−3.10207			−0.116092
$715$		0			0
$716$	−13.3312	+	5.93545i	−0.498212	+	0.221818i
$717$	4.68655	+	1.52275i	0.175023	+	0.0568683i
$718$	3.80637	−	2.19761i	0.142052	−	0.0820139i
$719$	6.61620	−	11.4596i	0.246743	−	0.427371i	−0.715877	−	0.698226i	$-0.753973\pi$
$719$	6.61620	−	11.4596i	0.246743	−	0.427371i	0.962620	+	0.270855i	$0.0873064\pi$
$720$		0			0
$721$	−4.17842	−	12.8598i	−0.155612	−	0.478926i
$722$	26.6263	+	23.9744i	0.990928	+	0.892236i
$723$	−1.96374	+	4.41064i	−0.0730324	+	0.164033i
$724$	−64.8314	+	13.7803i	−2.40944	+	0.512142i
$725$		0			0
$726$	−0.837547	+	7.96872i	−0.0310843	+	0.295747i
$727$	−2.37478	+	11.1725i	−0.0880758	+	0.414364i	0.911916	+	0.410376i	$0.134603\pi$
$727$	−2.37478	+	11.1725i	−0.0880758	+	0.414364i	−0.999992	+	0.00398775i	$0.998731\pi$
$728$	−1.62626	+	2.23836i	−0.0602732	+	0.0829590i
$729$	−16.9689	−	12.3287i	−0.628480	−	0.456617i
$730$		0			0
$731$	−2.19900	+	20.9221i	−0.0813331	+	0.773833i
$732$	−10.8387	+	1.13919i	−0.400610	+	0.0421059i
$733$	−6.50083	−	30.5840i	−0.240114	−	1.12965i	−0.918648	−	0.395077i	$-0.870718\pi$
$733$	−6.50083	−	30.5840i	−0.240114	−	1.12965i	0.678534	−	0.734569i	$-0.262616\pi$
$734$	−13.3265	−	5.93336i	−0.491892	−	0.219004i
$735$		0			0
$736$	−8.65007	−	26.6222i	−0.318846	−	0.981307i
$737$	0.0643712	−	0.0579601i	0.00237114	−	0.00213499i
$738$	6.58098	+	3.79953i	0.242249	+	0.139863i
$739$	9.76743	+	16.9177i	0.359301	+	0.622327i	0.987844	−	0.155447i	$-0.0496819\pi$
$739$	9.76743	+	16.9177i	0.359301	+	0.622327i	−0.628543	+	0.777774i	$0.716349\pi$
$740$		0			0
$741$	0.405762	−	0.180657i	0.0149060	−	0.00663660i
$742$	−33.4896	−	46.0945i	−1.22944	−	1.69218i
$743$			23.5592i			0.864305i	0.901801	+	0.432152i	$0.142246\pi$
$743$			23.5592i			0.864305i	−0.901801	+	0.432152i	$0.857754\pi$
$744$	0.0816235	+	2.45383i	0.00299246	+	0.0899617i
$745$		0			0
$746$	33.1169	−	24.0608i	1.21250	−	0.880930i
$747$	−9.97180	−	22.3970i	−0.364849	−	0.819465i
$748$	0.147023	+	0.0477705i	0.00537568	+	0.00174666i
$749$	14.8599	+	25.7381i	0.542969	+	0.940451i
$750$		0			0
$751$	5.94733	+	6.60518i	0.217021	+	0.241026i	0.841819	−	0.539760i	$-0.181485\pi$
$751$	5.94733	+	6.60518i	0.217021	+	0.241026i	−0.624798	+	0.780787i	$0.714818\pi$
$752$	−21.4750	+	6.97766i	−0.783114	+	0.254449i
$753$	−6.14101	−	5.52939i	−0.223791	−	0.201502i
$754$	8.98861	+	4.00199i	0.327346	+	0.145744i
$755$		0			0
$756$	−1.34432	−	12.7904i	−0.0488926	−	0.465182i
$757$	−13.4594	−	1.41464i	−0.489191	−	0.0514161i	−0.143278	−	0.989683i	$-0.545764\pi$
$757$	−13.4594	−	1.41464i	−0.489191	−	0.0514161i	−0.345913	+	0.938266i	$0.612431\pi$
$758$	−3.04748	+	14.3373i	−0.110689	+	0.520753i
$759$	0.0339473	+	0.0246642i	0.00123221	+	0.000895253i
$760$		0			0
$761$	39.5104	+	8.39820i	1.43225	+	0.304435i	0.857750	−	0.514068i	$-0.171862\pi$
$761$	39.5104	+	8.39820i	1.43225	+	0.304435i	0.574503	+	0.818502i	$0.305195\pi$
$762$	−1.04967	−	0.110325i	−0.0380256	−	0.00399666i
$763$	−28.6391	+	3.01009i	−1.03680	+	0.108972i
$764$	−32.0114	+	6.80424i	−1.15813	+	0.246169i
$765$		0			0
$766$	−21.9704	+	24.4005i	−0.793821	+	0.881628i
$767$	5.88026	−	1.91061i	0.212324	−	0.0689883i
$768$	0.629721	−	0.567004i	0.0227231	−	0.0204600i
$769$	−2.49942	+	4.32912i	−0.0901313	+	0.156112i	−0.907566	−	0.419909i	$-0.862062\pi$
$769$	−2.49942	+	4.32912i	−0.0901313	+	0.156112i	0.817435	+	0.576021i	$0.195395\pi$
$770$		0			0
$771$	2.22279	−	6.84103i	0.0800517	−	0.246374i
$772$	−4.18224	−	9.39346i	−0.150522	−	0.338078i
$773$	10.0896	+	13.8871i	0.362897	+	0.499485i	0.950953	−	0.309335i	$-0.100106\pi$
$773$	10.0896	+	13.8871i	0.362897	+	0.499485i	−0.588056	+	0.808820i	$0.700106\pi$
$774$	−75.5770			−2.71656
$775$		0			0
$776$	−2.91879			−0.104779
$777$	−0.649542	−	0.894017i	−0.0233022	−	0.0320727i
$778$	−31.4538	−	70.6463i	−1.12767	−	2.53279i
$779$	−0.575786	+	1.77209i	−0.0206297	+	0.0634916i
$780$		0			0
$781$	0.114453	−	0.198238i	0.00409543	−	0.00709350i
$782$	−9.86539	+	8.88283i	−0.352785	+	0.317649i
$783$	−10.1061	+	3.28367i	−0.361162	+	0.117349i
$784$	−1.44925	+	1.60955i	−0.0517588	+	0.0574840i
$785$		0			0
$786$	3.27483	−	0.696087i	0.116809	−	0.0248286i
$787$	−17.3086	+	1.81921i	−0.616986	+	0.0648478i	−0.407865	−	0.913042i	$-0.633727\pi$
$787$	−17.3086	+	1.81921i	−0.616986	+	0.0648478i	−0.209120	+	0.977890i	$0.567060\pi$
$788$	50.4458	+	5.30207i	1.79706	+	0.188879i
$789$	2.11570	+	0.449707i	0.0753210	+	0.0160100i
$790$		0			0
$791$	−33.9680	−	24.6792i	−1.20776	−	0.877492i
$792$	−0.0268269	+	0.126211i	−0.000953253	+	0.00448471i
$793$	−10.5634	−	1.11026i	−0.375118	−	0.0394265i
$794$	2.66129	+	25.3205i	0.0944458	+	0.898592i
$795$		0			0
$796$	−57.0616	−	25.4055i	−2.02249	−	0.900473i
$797$	30.5421	+	27.5002i	1.08186	+	0.974107i	0.999746	−	0.0225160i	$-0.00716766\pi$
$797$	30.5421	+	27.5002i	1.08186	+	0.974107i	0.0821094	+	0.996623i	$0.473834\pi$
$798$	2.59881	−	0.844405i	0.0919970	−	0.0298916i
$799$	10.7455	+	11.9341i	0.380149	+	0.422198i
$800$		0			0
$801$	−1.87580	−	3.24899i	−0.0662783	−	0.114797i
$802$	78.8791	+	25.6294i	2.78532	+	0.905004i
$803$	0.177634	+	0.398973i	0.00626858	+	0.0140795i
$804$	1.79993	−	1.30773i	0.0634787	−	0.0461199i
$805$		0			0
$806$	−1.80519	+	10.1396i	−0.0635850	+	0.357151i
$807$			8.97082i			0.315788i
$808$	−6.97943	−	9.60637i	−0.245536	−	0.337951i
$809$	4.58996	−	2.04358i	0.161374	−	0.0718484i	−0.324460	−	0.945899i	$-0.605183\pi$
$809$	4.58996	−	2.04358i	0.161374	−	0.0718484i	0.485834	+	0.874051i	$0.338516\pi$
$810$		0			0
$811$	−7.40329	−	12.8229i	−0.259965	−	0.450272i	0.706267	−	0.707945i	$-0.250378\pi$
$811$	−7.40329	−	12.8229i	−0.259965	−	0.450272i	−0.966232	+	0.257673i	$0.917044\pi$
$812$	29.6565	+	17.1222i	1.04074	+	0.600872i
$813$	−4.04082	+	3.63837i	−0.141718	+	0.127603i
$814$	0.0300813	+	0.0925806i	0.00105435	+	0.00324495i
$815$		0			0
$816$	−1.29486	−	0.576509i	−0.0453292	−	0.0201818i
$817$	−3.85289	−	18.1264i	−0.134796	−	0.634163i
$818$	−7.57427	+	0.796088i	−0.264828	+	0.0278346i
$819$	0.642261	−	6.11071i	0.0224424	−	0.213525i
$820$		0			0
$821$	−9.98059	−	7.25132i	−0.348325	−	0.253073i	0.399841	−	0.916584i	$-0.369065\pi$
$821$	−9.98059	−	7.25132i	−0.348325	−	0.253073i	−0.748166	+	0.663512i	$0.769065\pi$
$822$	−1.31052	+	1.80378i	−0.0457096	+	0.0629139i
$823$	−0.499605	+	2.35046i	−0.0174152	+	0.0819318i	−0.985997	−	0.166763i	$-0.946668\pi$
$823$	−0.499605	+	2.35046i	−0.0174152	+	0.0819318i	0.968582	+	0.248695i	$0.0800017\pi$
$824$	−0.742994	+	7.06911i	−0.0258834	+	0.246264i
$825$		0			0
$826$	37.2068	−	7.90854i	1.29459	−	0.275173i
$827$	−12.0844	+	27.1421i	−0.420217	+	0.943823i	0.572110	+	0.820177i	$0.306125\pi$
$827$	−12.0844	+	27.1421i	−0.420217	+	0.943823i	−0.992326	+	0.123645i	$0.960541\pi$
$828$	−20.0499	−	18.0530i	−0.696783	−	0.627386i
$829$	−12.0353	−	37.0408i	−0.418003	−	1.28648i	−0.909537	−	0.415622i	$-0.863564\pi$
$829$	−12.0353	−	37.0408i	−0.418003	−	1.28648i	0.491535	−	0.870858i	$-0.336436\pi$
$830$		0			0
$831$	−1.41544	+	2.45162i	−0.0491011	+	0.0850456i
$832$	−8.87400	+	5.12341i	−0.307651	+	0.177622i
$833$	1.46496	+	0.475995i	0.0507579	+	0.0164923i
$834$	−7.76557	+	3.45745i	−0.268900	+	0.119722i
$835$		0			0
$836$	−0.136174			−0.00470968
$837$	−5.87850	−	9.44230i	−0.203191	−	0.326374i
$838$			25.8068i			0.891481i
$839$	−10.0592	+	7.30841i	−0.347281	+	0.252314i	−0.747727	−	0.664006i	$-0.768855\pi$
$839$	−10.0592	+	7.30841i	−0.347281	+	0.252314i	0.400447	+	0.916320i	$0.368855\pi$
$840$		0			0
$841$	−0.218112	+	0.671281i	−0.00752111	+	0.0231476i
$842$	−30.4178	+	17.5617i	−1.04827	+	0.605216i
$843$	−2.86153	−	1.65210i	−0.0985562	−	0.0569015i
$844$	−20.0335	−	22.2495i	−0.689583	−	0.765860i
$845$		0			0
$846$	−38.6034	+	42.8734i	−1.32721	+	1.47402i
$847$	−11.0546	+	24.8290i	−0.379840	+	0.853133i
$848$	−5.41266	−	25.4646i	−0.185872	−	0.874457i
$849$	−0.476090	−	4.52969i	−0.0163394	−	0.155459i
$850$		0			0
$851$	−4.62574	−	0.983231i	−0.158568	−	0.0337047i
$852$	3.45584	−	4.75656i	0.118395	−	0.162957i
$853$	24.4039	−	33.5891i	0.835573	−	1.15007i	−0.151287	−	0.988490i	$-0.548342\pi$
$853$	24.4039	−	33.5891i	0.835573	−	1.15007i	0.986860	−	0.161578i	$-0.0516584\pi$
$854$	−63.9178	−	13.5861i	−2.18722	−	0.464908i
$855$		0			0
$856$	−1.63306	−	15.5375i	−0.0558168	−	0.531062i
$857$	1.72963	+	8.13729i	0.0590832	+	0.277965i	0.997765	−	0.0668199i	$-0.0212853\pi$
$857$	1.72963	+	8.13729i	0.0590832	+	0.277965i	−0.938682	+	0.344785i	$0.887952\pi$
$858$	0.00879437	−	0.0197525i	0.000300235	−	0.000674339i
$859$	−16.2822	+	18.0832i	−0.555540	+	0.616990i	−0.953858	−	0.300258i	$-0.902927\pi$
$859$	−16.2822	+	18.0832i	−0.555540	+	0.616990i	0.398318	+	0.917247i	$0.369594\pi$
$860$		0			0
$861$	−0.688992	−	0.765203i	−0.0234808	−	0.0260780i
$862$	−16.0700	−	9.27803i	−0.547347	−	0.316011i
$863$	34.7442	−	20.0596i	1.18271	−	0.682835i	0.226066	−	0.974112i	$-0.427413\pi$
$863$	34.7442	−	20.0596i	1.18271	−	0.682835i	0.956639	+	0.291277i	$0.0940800\pi$
$864$	4.81368	−	14.8150i	0.163765	−	0.504016i
$865$		0			0
$866$	−20.4212	+	14.8369i	−0.693940	+	0.504177i
$867$		−	4.76291i		−	0.161757i
$868$	−9.93709	+	34.4395i	−0.337287	+	1.16895i
$869$	0.344876			0.0116991
$870$		0			0
$871$	1.98087	−	0.881938i	0.0671191	−	0.0298833i
$872$	14.3970	+	4.67787i	0.487544	+	0.158413i
$873$	5.61358	−	3.24100i	0.189991	−	0.109691i
$874$	5.84692	−	10.1272i	0.197775	−	0.342556i
$875$		0			0
$876$	3.46638	+	10.6684i	0.117118	+	0.360452i
$877$	−17.4978	−	15.7551i	−0.590858	−	0.532011i	0.318556	−	0.947904i	$-0.396802\pi$
$877$	−17.4978	−	15.7551i	−0.590858	−	0.532011i	−0.909413	+	0.415894i	$0.863469\pi$
$878$	−24.4536	+	54.9237i	−0.825269	+	1.85359i
$879$	−1.59677	+	0.339405i	−0.0538578	+	0.0114478i
$880$		0			0
$881$	4.75745	−	45.2641i	0.160282	−	1.52499i	−0.558356	−	0.829602i	$-0.688568\pi$
$881$	4.75745	−	45.2641i	0.160282	−	1.52499i	0.718638	−	0.695384i	$-0.244766\pi$
$882$	−1.15053	+	5.41281i	−0.0387403	+	0.182259i
$883$	7.30265	−	10.0512i	0.245754	−	0.338251i	−0.668265	−	0.743924i	$-0.732963\pi$
$883$	7.30265	−	10.0512i	0.245754	−	0.338251i	0.914018	+	0.405673i	$0.132963\pi$
$884$	3.13070	+	2.27459i	0.105297	+	0.0765027i
$885$		0			0
$886$	−3.23396	+	30.7691i	−0.108647	+	1.03371i
$887$	−35.7742	+	3.76002i	−1.20118	+	0.126249i	−0.683906	−	0.729570i	$-0.739720\pi$
$887$	−35.7742	+	3.76002i	−1.20118	+	0.126249i	−0.517275	+	0.855819i	$0.673053\pi$
$888$	0.120778	+	0.568217i	0.00405305	+	0.0190681i
$889$	−3.27057	−	1.45615i	−0.109691	−	0.0488378i
$890$		0			0
$891$	−0.0848697	−	0.261202i	−0.00284324	−	0.00875060i
$892$	−8.67075	+	7.80718i	−0.290318	+	0.261404i
$893$	−12.2508	−	7.07299i	−0.409956	−	0.236688i
$894$	−6.98416	−	12.0969i	−0.233585	−	0.404582i
$895$		0			0
$896$	−22.3845	+	9.96620i	−0.747812	+	0.332947i
$897$	0.617409	+	0.849791i	0.0206147	+	0.0283737i
$898$		−	51.9003i		−	1.73194i
$899$	29.5406	+	2.11482i	0.985234	+	0.0705331i
$900$		0			0
$901$	−14.9788	+	10.8828i	−0.499017	+	0.362557i
$902$	0.0368928	+	0.0828626i	0.00122840	+	0.00275902i
$903$	9.73955	+	3.16457i	0.324112	+	0.105310i
$904$	11.0358	+	19.1146i	0.367046	+	0.635742i
$905$		0			0
$906$	1.95951	+	2.17626i	0.0651004	+	0.0723014i
$907$	15.4692	−	5.02626i	0.513648	−	0.166894i	−0.0407129	−	0.999171i	$-0.512963\pi$
$907$	15.4692	−	5.02626i	0.513648	−	0.166894i	0.554360	+	0.832277i	$0.312963\pi$
$908$	30.4913	+	27.4545i	1.01189	+	0.911109i
$909$	24.0900	+	10.7256i	0.799016	+	0.355745i
$910$		0			0
$911$	−1.45830	−	13.8748i	−0.0483157	−	0.459694i	−0.991755	−	0.128148i	$-0.959097\pi$
$911$	−1.45830	−	13.8748i	−0.0483157	−	0.459694i	0.943439	−	0.331545i	$-0.107570\pi$
$912$	1.24172	+	0.130510i	0.0411174	+	0.00432162i
$913$	0.0608426	−	0.286242i	0.00201360	−	0.00947322i
$914$	53.3990	+	38.7967i	1.76628	+	1.28328i
$915$		0			0
$916$	−5.86164	−	1.24593i	−0.193674	−	0.0411667i
$917$	11.2941	+	1.18706i	0.372965	+	0.0392002i
$918$	−7.34704	+	0.772206i	−0.242489	+	0.0254866i
$919$	54.0648	−	11.4918i	1.78343	−	0.379081i	0.806267	−	0.591552i	$-0.201485\pi$
$919$	54.0648	−	11.4918i	1.78343	−	0.379081i	0.977167	+	0.212472i	$0.0681513\pi$
$920$		0			0
$921$	6.23248	−	6.92186i	0.205367	−	0.228083i
$922$	−18.3001	+	5.94607i	−0.602683	+	0.195823i
$923$	4.25829	−	3.83418i	0.140163	−	0.126204i
$924$	0.0376261	−	0.0651703i	0.00123781	−	0.00214394i
$925$		0			0
$926$	20.4752	−	63.0160i	0.672855	−	2.07084i
$927$	−6.42051	−	14.4207i	−0.210877	−	0.473638i
$928$	24.3800	+	33.5562i	0.800314	+	1.10154i
$929$	−28.9662			−0.950350			−0.475175	−	0.879891i	$-0.657615\pi$
$929$	−28.9662			−0.950350			−0.475175	+	0.879891i	$0.657615\pi$
$930$		0			0
$931$	−1.35686			−0.0444695
$932$	−31.2116	−	42.9591i	−1.02237	−	1.40717i
$933$	4.80044	+	10.7820i	0.157159	+	0.352985i
$934$	18.6761	−	57.4791i	0.611100	−	1.88077i
$935$		0			0
$936$	−1.61499	+	2.79724i	−0.0527874	+	0.0914305i
$937$	0.886112	−	0.797859i	0.0289480	−	0.0260649i	−0.654530	−	0.756036i	$-0.727133\pi$
$937$	0.886112	−	0.797859i	0.0289480	−	0.0260649i	0.683478	+	0.729971i	$0.260467\pi$
$938$	12.6870	−	4.12225i	0.414245	−	0.134596i
$939$	4.68272	−	5.20069i	0.152815	−	0.169718i
$940$		0			0
$941$	−46.5525	+	9.89504i	−1.51757	+	0.322569i	−0.889988	−	0.455983i	$-0.849288\pi$
$941$	−46.5525	+	9.89504i	−1.51757	+	0.322569i	−0.627580	+	0.778552i	$0.715954\pi$
$942$	−12.7795	+	1.34318i	−0.416378	+	0.0437630i
$943$	−4.38234	−	0.460602i	−0.142709	−	0.0149993i
$944$	17.0005	+	3.61357i	0.553320	+	0.117612i
$945$		0			0
$946$	−0.729820	−	0.530245i	−0.0237285	−	0.0172398i
$947$	5.02930	−	23.6610i	0.163430	−	0.768879i	−0.817717	−	0.575620i	$-0.804761\pi$
$947$	5.02930	−	23.6610i	0.163430	−	0.768879i	0.981148	−	0.193259i	$-0.0619059\pi$
$948$	8.80961	+	0.925927i	0.286123	+	0.0300727i
$949$	1.14276	+	10.8726i	0.0370955	+	0.352940i
$950$		0			0
$951$	−6.32551	−	2.81630i	−0.205119	−	0.0913247i
$952$	4.11056	+	3.70116i	0.133224	+	0.119955i
$953$	39.2490	−	12.7528i	1.27140	−	0.413103i	0.405857	−	0.913937i	$-0.366973\pi$
$953$	39.2490	−	12.7528i	1.27140	−	0.413103i	0.865544	+	0.500834i	$0.166973\pi$
$954$	−44.5071	−	49.4302i	−1.44097	−	1.60036i
$955$		0			0
$956$	−18.9093	−	32.7520i	−0.611572	−	1.05927i
$957$	−0.0591333	−	0.0192136i	−0.00191151	−	0.000621087i
$958$	1.07963	+	2.42489i	0.0348812	+	0.0783446i
$959$	−6.11839	+	4.44527i	−0.197573	+	0.143545i
$960$		0			0
$961$	5.28201	+	30.5467i	0.170387	+	0.985377i
$962$			2.43680i			0.0785656i
$963$	20.3935	+	28.0693i	0.657172	+	0.904520i
$964$	33.8502	−	15.0711i	1.09024	−	0.485406i
$965$		0			0
$966$	3.23111	+	5.59645i	0.103959	+	0.180063i
$967$	34.7954	+	20.0891i	1.11894	+	0.646023i	0.941131	−	0.338041i	$-0.109764\pi$
$967$	34.7954	+	20.0891i	1.11894	+	0.646023i	0.177813	+	0.984064i	$0.443098\pi$
$968$	10.6175	−	9.56006i	0.341260	−	0.307272i
$969$	−0.274397	−	0.844508i	−0.00881491	−	0.0271295i
$970$		0			0
$971$	34.2354	+	15.2426i	1.09867	+	0.489158i	0.874319	−	0.485351i	$-0.161308\pi$
$971$	34.2354	+	15.2426i	1.09867	+	0.489158i	0.224348	+	0.974509i	$0.427975\pi$
$972$	−4.71295	−	22.1727i	−0.151168	−	0.711189i
$973$	−28.6755	+	3.01392i	−0.919295	+	0.0966218i
$974$	−3.08445	+	29.3466i	−0.0988322	+	0.940326i
$975$		0			0
$976$	−24.1555	−	17.5500i	−0.773198	−	0.561761i
$977$	9.16432	−	12.6136i	0.293193	−	0.403545i	−0.636855	−	0.770983i	$-0.719765\pi$
$977$	9.16432	−	12.6136i	0.293193	−	0.403545i	0.930048	+	0.367438i	$0.119765\pi$
$978$	−3.66342	+	17.2350i	−0.117143	+	0.551115i
$979$	0.00468080	−	0.0445349i	0.000149599	−	0.00142334i
$980$		0			0
$981$	−32.8833	+	6.98957i	−1.04988	+	0.223160i
$982$	−6.51896	+	14.6418i	−0.208028	+	0.467239i
$983$	16.4362	+	14.7992i	0.524233	+	0.472022i	0.888243	−	0.459373i	$-0.151926\pi$
$983$	16.4362	+	14.7992i	0.524233	+	0.472022i	−0.364010	+	0.931395i	$0.618593\pi$
$984$	0.167266	+	0.514791i	0.00533223	+	0.0164109i
$985$		0			0
$986$	9.83532	−	17.0353i	0.313221	−	0.542514i
$987$	6.76999	−	3.90866i	0.215491	−	0.124414i
$988$	−3.24196	−	1.05338i	−0.103140	−	0.0335123i
$989$	40.0360	−	17.8252i	1.27307	−	0.566808i
$990$		0			0
$991$	57.8161			1.83659			0.918295	−	0.395896i	$-0.129566\pi$
$991$	57.8161			1.83659			0.918295	+	0.395896i	$0.129566\pi$
$992$	−27.9621	+	33.2122i	−0.887799	+	1.05449i
$993$			10.6287i			0.337290i
$994$	28.5198	−	20.7209i	0.904594	−	0.657226i
$995$		0			0
$996$	2.32269	−	7.14850i	0.0735972	−	0.226509i
$997$	−1.10658	+	0.638886i	−0.0350458	+	0.0202337i	−0.517421	−	0.855731i	$-0.673108\pi$
$997$	−1.10658	+	0.638886i	−0.0350458	+	0.0202337i	0.482375	+	0.875965i	$0.339774\pi$
$998$	36.8476	+	21.2740i	1.16639	+	0.673416i
$999$	−1.76094	−	1.95573i	−0.0557138	−	0.0618764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.c.49.10		80
5.2	odd	4		775.2.bl.c.576.1		40
5.3	odd	4		155.2.q.a.111.5	yes	40
5.4	even	2	inner	775.2.ck.c.49.1		80
31.19	even	15	inner	775.2.ck.c.174.1		80
155.19	even	30	inner	775.2.ck.c.174.10		80
155.53	even	60		4805.2.a.y.1.3		20
155.112	odd	60		775.2.bl.c.701.1		40
155.133	odd	60		4805.2.a.x.1.3		20
155.143	odd	60		155.2.q.a.81.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.5	✓	40	155.143	odd	60
155.2.q.a.111.5	yes	40	5.3	odd	4
775.2.bl.c.576.1		40	5.2	odd	4
775.2.bl.c.701.1		40	155.112	odd	60
775.2.ck.c.49.1		80	5.4	even	2	inner
775.2.ck.c.49.10		80	1.1	even	1	trivial
775.2.ck.c.174.1		80	31.19	even	15	inner
775.2.ck.c.174.10		80	155.19	even	30	inner
4805.2.a.x.1.3		20	155.133	odd	60
4805.2.a.y.1.3		20	155.53	even	60

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26139 + 1.73615i) q^{2} +(-0.138074 - 0.310120i) q^{3} +(-0.805084 + 2.47779i) q^{4} +(0.364249 - 0.630898i) q^{6} +(1.83635 - 1.65346i) q^{7} +(-1.23541 + 0.401408i) q^{8} +(1.93028 - 2.14380i) q^{9} +(0.0336808 - 0.00715908i) q^{11} +(0.879574 - 0.0924470i) q^{12} +(0.857233 + 0.0900989i) q^{13} +(5.18700 + 1.10253i) q^{14} +(1.96024 + 1.42420i) q^{16} +(0.358278 - 1.68556i) q^{17} +(6.15678 + 0.647103i) q^{18} +(0.158669 + 1.50963i) q^{19} +(-0.766324 - 0.341189i) q^{21} +(0.0549137 + 0.0494445i) q^{22} +(-3.41410 + 1.10931i) q^{23} +(0.295063 + 0.327700i) q^{24} +(0.924877 + 1.60193i) q^{26} +(-1.89992 - 0.617320i) q^{27} +(2.61851 + 5.88128i) q^{28} +(4.30334 - 3.12656i) q^{29} +(4.25923 + 3.58594i) q^{31} +7.79771i q^{32} +(-0.00687063 - 0.00945661i) q^{33} +(3.37832 - 1.50412i) q^{34} +(3.75784 + 6.50877i) q^{36} +(1.14087 + 0.658683i) q^{37} +(-2.42081 + 2.17970i) q^{38} +(-0.0904204 - 0.278285i) q^{39} +(1.12138 + 0.499269i) q^{41} +(-0.374274 - 1.76082i) q^{42} +(-12.1413 + 1.27610i) q^{43} +(-0.00937716 + 0.0892178i) q^{44} +(-6.23243 - 4.52812i) q^{46} +(-5.47765 + 7.53934i) q^{47} +(0.171014 - 0.804556i) q^{48} +(-0.0934359 + 0.888983i) q^{49} +(-0.572196 + 0.121624i) q^{51} +(-0.913391 + 2.05151i) q^{52} +(-7.98460 - 7.18936i) q^{53} +(-1.32477 - 4.07722i) q^{54} +(-1.60493 + 2.77982i) q^{56} +(0.446259 - 0.257648i) q^{57} +(10.8564 + 3.52744i) q^{58} +(6.55294 - 2.91755i) q^{59} -12.3227 q^{61} +(-0.853205 + 11.9179i) q^{62} -7.12841i q^{63} +(-9.61749 + 6.98752i) q^{64} +(0.00775156 - 0.0238569i) q^{66} +(2.17857 - 1.25780i) q^{67} +(3.88804 + 2.24476i) q^{68} +(0.815419 + 0.905614i) q^{69} +(4.44824 - 4.94027i) q^{71} +(-1.52415 + 3.42329i) q^{72} +(2.63702 + 12.4062i) q^{73} +(0.295509 + 2.81158i) q^{74} +(-3.86830 - 0.822233i) q^{76} +(0.0500126 - 0.0688365i) q^{77} +(0.369090 - 0.508008i) q^{78} +(9.79690 + 2.08239i) q^{79} +(-0.833733 - 7.93244i) q^{81} +(0.547683 + 2.57665i) q^{82} +(3.45672 - 7.76391i) q^{83} +(1.46235 - 1.62411i) q^{84} +(-17.5304 - 19.4694i) q^{86} +(-1.56379 - 0.902855i) q^{87} +(-0.0387358 + 0.0223641i) q^{88} +(0.401874 - 1.23684i) q^{89} +(1.72316 - 1.25195i) q^{91} -9.35253i q^{92} +(0.523983 - 1.81600i) q^{93} -19.9988 q^{94} +(2.41822 - 1.07666i) q^{96} +(2.13701 + 0.694355i) q^{97} +(-1.66127 + 0.959132i) q^{98} +(0.0496659 - 0.0860238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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