LMFDB - Embedded newform 845.2.m.f.316.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(316,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.316"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4] 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	845.316
Dual form			845.2.m.f.361.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.358719 + 0.207107i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000i q^{5} +(-0.507306 + 0.292893i) q^{6} +(-0.717439 + 0.414214i) q^{7} -1.58579i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.207107 - 0.358719i) q^{10} +(-0.507306 - 0.292893i) q^{11} +2.58579 q^{12} -0.343146 q^{14} +(1.22474 + 0.707107i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-2.41421 - 4.18154i) q^{17} +0.414214i q^{18} +(-2.95680 + 1.70711i) q^{19} +(-1.58346 + 0.914214i) q^{20} -1.17157i q^{21} +(-0.121320 - 0.210133i) q^{22} +(-0.707107 + 1.22474i) q^{23} +(1.94218 + 1.12132i) q^{24} -1.00000 q^{25} -5.65685 q^{27} +(1.31178 + 0.757359i) q^{28} +(-2.82843 + 4.89898i) q^{29} +(0.292893 + 0.507306i) q^{30} -10.2426i q^{31} +(-3.82282 + 2.20711i) q^{32} +(0.717439 - 0.414214i) q^{33} -2.00000i q^{34} +(0.414214 + 0.717439i) q^{35} +(0.914214 - 1.58346i) q^{36} +(-7.34847 - 4.24264i) q^{37} -1.41421 q^{38} -1.58579 q^{40} +(-7.64564 - 4.41421i) q^{41} +(0.242641 - 0.420266i) q^{42} +(1.53553 + 2.65962i) q^{43} +1.07107i q^{44} +(0.866025 - 0.500000i) q^{45} +(-0.507306 + 0.292893i) q^{46} +0.828427i q^{47} +(-2.12132 - 3.67423i) q^{48} +(-3.15685 + 5.46783i) q^{49} +(-0.358719 - 0.207107i) q^{50} +6.82843 q^{51} -14.4853 q^{53} +(-2.02922 - 1.17157i) q^{54} +(-0.292893 + 0.507306i) q^{55} +(0.656854 + 1.13770i) q^{56} -4.82843i q^{57} +(-2.02922 + 1.17157i) q^{58} +(8.87039 - 5.12132i) q^{59} -2.58579i q^{60} +(4.00000 + 6.92820i) q^{61} +(2.12132 - 3.67423i) q^{62} +(-0.717439 - 0.414214i) q^{63} +4.17157 q^{64} +0.343146 q^{66} +(-1.73205 - 1.00000i) q^{67} +(-4.41421 + 7.64564i) q^{68} +(-1.00000 - 1.73205i) q^{69} +0.343146i q^{70} +(6.84116 - 3.94975i) q^{71} +(1.37333 - 0.792893i) q^{72} -8.48528i q^{73} +(-1.75736 - 3.04384i) q^{74} +(0.707107 - 1.22474i) q^{75} +(5.40629 + 3.12132i) q^{76} +0.485281 q^{77} +8.48528 q^{79} +(2.59808 + 1.50000i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-1.82843 - 3.16693i) q^{82} +8.82843i q^{83} +(-1.85514 + 1.07107i) q^{84} +(-4.18154 + 2.41421i) q^{85} +1.27208i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.464466 + 0.804479i) q^{88} +(-5.19615 - 3.00000i) q^{89} +0.414214 q^{90} +2.58579 q^{92} +(12.5446 + 7.24264i) q^{93} +(-0.171573 + 0.297173i) q^{94} +(1.70711 + 2.95680i) q^{95} -6.24264i q^{96} +(-3.16693 + 1.82843i) q^{97} +(-2.26485 + 1.30761i) q^{98} -0.585786i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{9} - 4 q^{10} + 32 q^{12} - 48 q^{14} - 12 q^{16} - 8 q^{17} + 16 q^{22} - 8 q^{25} + 8 q^{30} - 8 q^{35} - 4 q^{36} - 24 q^{40} - 32 q^{42} - 16 q^{43} + 20 q^{49} + 32 q^{51} - 48 q^{53}+ \cdots + 8 q^{95}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^9 - 4 * q^10 + 32 * q^12 - 48 * q^14 - 12 * q^16 - 8 * q^17 + 16 * q^22 - 8 * q^25 + 8 * q^30 - 8 * q^35 - 4 * q^36 - 24 * q^40 - 32 * q^42 - 16 * q^43 + 20 * q^49 + 32 * q^51 - 48 * q^53 - 8 * q^55 - 40 * q^56 + 32 * q^61 + 56 * q^64 + 48 * q^66 - 24 * q^68 - 8 * q^69 - 48 * q^74 - 64 * q^77 + 20 * q^81 + 8 * q^82 - 32 * q^87 - 32 * q^88 - 8 * q^90 + 32 * q^92 - 24 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	0.621436	−	0.783465i	$-0.286550\pi$
$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	−0.367783	+	0.929912i	$0.619883\pi$
$3$	−0.707107	+	1.22474i	−0.408248	+	0.707107i	−0.994694	−	0.102882i	$-0.967194\pi$
$3$	−0.707107	+	1.22474i	−0.408248	+	0.707107i	0.586445	+	0.809989i	$0.300527\pi$
$4$	−0.914214	−	1.58346i	−0.457107	−	0.791732i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.507306	+	0.292893i	−0.207107	+	0.119573i
$7$	−0.717439	+	0.414214i	−0.271166	+	0.156558i	−0.629418	−	0.777067i	$-0.716706\pi$
$7$	−0.717439	+	0.414214i	−0.271166	+	0.156558i	0.358251	+	0.933625i	$0.383373\pi$
$8$		−	1.58579i		−	0.560660i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.207107	−	0.358719i	0.0654929	−	0.113437i
$11$	−0.507306	−	0.292893i	−0.152958	−	0.0883106i	0.421567	−	0.906797i	$-0.361480\pi$
$11$	−0.507306	−	0.292893i	−0.152958	−	0.0883106i	−0.574526	+	0.818487i	$0.694813\pi$
$12$	2.58579			0.746452
$13$		0			0
$13$		0			0
$14$	−0.343146			−0.0917096
$15$	1.22474	+	0.707107i	0.316228	+	0.182574i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−2.41421	−	4.18154i	−0.585533	−	1.01417i	−0.994809	−	0.101762i	$-0.967552\pi$
$17$	−2.41421	−	4.18154i	−0.585533	−	1.01417i	0.409276	−	0.912411i	$-0.365781\pi$
$18$			0.414214i			0.0976311i
$19$	−2.95680	+	1.70711i	−0.678335	+	0.391637i	−0.799228	−	0.601028i	$-0.794758\pi$
$19$	−2.95680	+	1.70711i	−0.678335	+	0.391637i	0.120892	+	0.992666i	$0.461424\pi$
$20$	−1.58346	+	0.914214i	−0.354073	+	0.204424i
$21$		−	1.17157i		−	0.255658i
$22$	−0.121320	−	0.210133i	−0.0258656	−	0.0448005i
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	−0.930281	−	0.366847i	$-0.880437\pi$
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	0.782839	+	0.622224i	$0.213771\pi$
$24$	1.94218	+	1.12132i	0.396447	+	0.228889i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.65685			−1.08866
$28$	1.31178	+	0.757359i	0.247904	+	0.143127i
$29$	−2.82843	+	4.89898i	−0.525226	+	0.909718i	0.474343	+	0.880340i	$0.342686\pi$
$29$	−2.82843	+	4.89898i	−0.525226	+	0.909718i	−0.999568	+	0.0293774i	$0.990648\pi$
$30$	0.292893	+	0.507306i	0.0534747	+	0.0926210i
$31$		−	10.2426i		−	1.83963i	−0.392349	−	0.919816i	$-0.628338\pi$
$31$		−	10.2426i		−	1.83963i	0.392349	−	0.919816i	$-0.371662\pi$
$32$	−3.82282	+	2.20711i	−0.675786	+	0.390165i
$33$	0.717439	−	0.414214i	0.124890	−	0.0721053i
$34$		−	2.00000i		−	0.342997i
$35$	0.414214	+	0.717439i	0.0700149	+	0.121269i
$36$	0.914214	−	1.58346i	0.152369	−	0.263911i
$37$	−7.34847	−	4.24264i	−1.20808	−	0.697486i	−0.245741	−	0.969335i	$-0.579031\pi$
$37$	−7.34847	−	4.24264i	−1.20808	−	0.697486i	−0.962340	+	0.271850i	$0.912365\pi$
$38$	−1.41421			−0.229416
$39$		0			0
$40$	−1.58579			−0.250735
$41$	−7.64564	−	4.41421i	−1.19405	−	0.689384i	−0.234826	−	0.972037i	$-0.575452\pi$
$41$	−7.64564	−	4.41421i	−1.19405	−	0.689384i	−0.959222	+	0.282653i	$0.908786\pi$
$42$	0.242641	−	0.420266i	0.0374403	−	0.0648485i
$43$	1.53553	+	2.65962i	0.234167	+	0.405589i	0.959030	−	0.283304i	$-0.0914305\pi$
$43$	1.53553	+	2.65962i	0.234167	+	0.405589i	−0.724863	+	0.688893i	$0.758097\pi$
$44$			1.07107i			0.161470i
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$	−0.507306	+	0.292893i	−0.0747982	+	0.0431847i
$47$			0.828427i			0.120839i	0.998173	+	0.0604193i	$0.0192438\pi$
$47$			0.828427i			0.120839i	−0.998173	+	0.0604193i	$0.980756\pi$
$48$	−2.12132	−	3.67423i	−0.306186	−	0.530330i
$49$	−3.15685	+	5.46783i	−0.450979	+	0.781119i
$50$	−0.358719	−	0.207107i	−0.0507306	−	0.0292893i
$51$	6.82843			0.956171
$52$		0			0
$53$	−14.4853			−1.98971			−0.994853	−	0.101327i	$-0.967691\pi$
$53$	−14.4853			−1.98971			−0.994853	+	0.101327i	$0.967691\pi$
$54$	−2.02922	−	1.17157i	−0.276142	−	0.159431i
$55$	−0.292893	+	0.507306i	−0.0394937	+	0.0684051i
$56$	0.656854	+	1.13770i	0.0877758	+	0.152032i
$57$		−	4.82843i		−	0.639541i
$58$	−2.02922	+	1.17157i	−0.266450	+	0.153835i
$59$	8.87039	−	5.12132i	1.15483	−	0.666739i	0.204767	−	0.978811i	$-0.434356\pi$
$59$	8.87039	−	5.12132i	1.15483	−	0.666739i	0.950059	+	0.312072i	$0.101023\pi$
$60$		−	2.58579i		−	0.333824i
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	2.12132	−	3.67423i	0.269408	−	0.466628i
$63$	−0.717439	−	0.414214i	−0.0903888	−	0.0521860i
$64$	4.17157			0.521447
$65$		0			0
$66$	0.343146			0.0422383
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	0.390453	−	0.920623i	$-0.372318\pi$
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	−0.602056	+	0.798454i	$0.705652\pi$
$68$	−4.41421	+	7.64564i	−0.535302	+	0.927170i
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$			0.343146i			0.0410138i
$71$	6.84116	−	3.94975i	0.811897	−	0.468749i	−0.0357174	−	0.999362i	$-0.511372\pi$
$71$	6.84116	−	3.94975i	0.811897	−	0.468749i	0.847614	+	0.530613i	$0.178038\pi$
$72$	1.37333	−	0.792893i	0.161849	−	0.0934434i
$73$		−	8.48528i		−	0.993127i	−0.868000	−	0.496564i	$-0.834595\pi$
$73$		−	8.48528i		−	0.993127i	0.868000	−	0.496564i	$-0.165405\pi$
$74$	−1.75736	−	3.04384i	−0.204289	−	0.353839i
$75$	0.707107	−	1.22474i	0.0816497	−	0.141421i
$76$	5.40629	+	3.12132i	0.620143	+	0.358040i
$77$	0.485281			0.0553029
$78$		0			0
$79$	8.48528			0.954669			0.477334	−	0.878722i	$-0.341603\pi$
$79$	8.48528			0.954669			0.477334	+	0.878722i	$0.341603\pi$
$80$	2.59808	+	1.50000i	0.290474	+	0.167705i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	−1.82843	−	3.16693i	−0.201916	−	0.349729i
$83$			8.82843i			0.969046i	0.874779	+	0.484523i	$0.161007\pi$
$83$			8.82843i			0.969046i	−0.874779	+	0.484523i	$0.838993\pi$
$84$	−1.85514	+	1.07107i	−0.202413	+	0.116863i
$85$	−4.18154	+	2.41421i	−0.453552	+	0.261858i
$86$			1.27208i			0.137172i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	−0.464466	+	0.804479i	−0.0495123	+	0.0857577i
$89$	−5.19615	−	3.00000i	−0.550791	−	0.317999i	0.198650	−	0.980071i	$-0.436344\pi$
$89$	−5.19615	−	3.00000i	−0.550791	−	0.317999i	−0.749441	+	0.662071i	$0.769678\pi$
$90$	0.414214			0.0436619
$91$		0			0
$92$	2.58579			0.269587
$93$	12.5446	+	7.24264i	1.30082	+	0.751027i
$94$	−0.171573	+	0.297173i	−0.0176964	+	0.0306510i
$95$	1.70711	+	2.95680i	0.175145	+	0.303361i
$96$		−	6.24264i		−	0.637137i
$97$	−3.16693	+	1.82843i	−0.321553	+	0.185649i	−0.652085	−	0.758146i	$-0.726105\pi$
$97$	−3.16693	+	1.82843i	−0.321553	+	0.185649i	0.330532	+	0.943795i	$0.392772\pi$
$98$	−2.26485	+	1.30761i	−0.228784	+	0.132089i
$99$		−	0.585786i		−	0.0588738i
$100$	0.914214	+	1.58346i	0.0914214	+	0.158346i
$101$	3.82843	−	6.63103i	0.380943	−	0.659812i	−0.610255	−	0.792205i	$-0.708933\pi$
$101$	3.82843	−	6.63103i	0.380943	−	0.659812i	0.991197	+	0.132393i	$0.0422662\pi$
$102$	2.44949	+	1.41421i	0.242536	+	0.140028i
$103$	−17.4142			−1.71587			−0.857937	−	0.513755i	$-0.828254\pi$
$103$	−17.4142			−1.71587			−0.857937	+	0.513755i	$0.828254\pi$
$104$		0			0
$105$	−1.17157			−0.114334
$106$	−5.19615	−	3.00000i	−0.504695	−	0.291386i
$107$	3.29289	−	5.70346i	0.318336	−	0.551374i	−0.661805	−	0.749676i	$-0.730209\pi$
$107$	3.29289	−	5.70346i	0.318336	−	0.551374i	0.980141	+	0.198302i	$0.0635426\pi$
$108$	5.17157	+	8.95743i	0.497635	+	0.861929i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	−0.210133	+	0.121320i	−0.0200354	+	0.0115674i
$111$	10.3923	−	6.00000i	0.986394	−	0.569495i
$112$		−	2.48528i		−	0.234837i
$113$	1.58579	+	2.74666i	0.149178	+	0.258384i	0.930924	−	0.365213i	$-0.119004\pi$
$113$	1.58579	+	2.74666i	0.149178	+	0.258384i	−0.781746	+	0.623597i	$0.785671\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	1.22474	+	0.707107i	0.114208	+	0.0659380i
$116$	10.3431			0.960337
$117$		0			0
$118$	4.24264			0.390567
$119$	3.46410	+	2.00000i	0.317554	+	0.183340i
$120$	1.12132	−	1.94218i	0.102362	−	0.177296i
$121$	−5.32843	−	9.22911i	−0.484402	−	0.839010i
$122$			3.31371i			0.300009i
$123$	10.8126	−	6.24264i	0.974937	−	0.562880i
$124$	−16.2189	+	9.36396i	−1.45650	+	0.840909i
$125$			1.00000i			0.0894427i
$126$	−0.171573	−	0.297173i	−0.0152849	−	0.0264743i
$127$	−4.70711	+	8.15295i	−0.417688	+	0.723457i	−0.995706	−	0.0925666i	$-0.970493\pi$
$127$	−4.70711	+	8.15295i	−0.417688	+	0.723457i	0.578018	+	0.816024i	$0.303826\pi$
$128$	9.14207	+	5.27817i	0.808052	+	0.466529i
$129$	−4.34315			−0.382393
$130$		0			0
$131$	16.9706			1.48272			0.741362	−	0.671105i	$-0.234180\pi$
$131$	16.9706			1.48272			0.741362	+	0.671105i	$0.234180\pi$
$132$	−1.31178	−	0.757359i	−0.114176	−	0.0659197i
$133$	1.41421	−	2.44949i	0.122628	−	0.212398i
$134$	−0.414214	−	0.717439i	−0.0357826	−	0.0619773i
$135$			5.65685i			0.486864i
$136$	−6.63103	+	3.82843i	−0.568606	+	0.328285i
$137$	4.60181	−	2.65685i	0.393159	−	0.226990i	−0.290369	−	0.956915i	$-0.593778\pi$
$137$	4.60181	−	2.65685i	0.393159	−	0.226990i	0.683528	+	0.729924i	$0.260445\pi$
$138$		−	0.828427i		−	0.0705204i
$139$	6.24264	+	10.8126i	0.529494	+	0.917110i	0.999408	+	0.0343983i	$0.0109515\pi$
$139$	6.24264	+	10.8126i	0.529494	+	0.917110i	−0.469914	+	0.882712i	$0.655715\pi$
$140$	0.757359	−	1.31178i	0.0640085	−	0.110866i
$141$	−1.01461	−	0.585786i	−0.0854457	−	0.0493321i
$142$	3.27208			0.274587
$143$		0			0
$144$	−3.00000			−0.250000
$145$	4.89898	+	2.82843i	0.406838	+	0.234888i
$146$	1.75736	−	3.04384i	0.145440	−	0.251910i
$147$	−4.46447	−	7.73268i	−0.368223	−	0.637781i
$148$			15.5147i			1.27530i
$149$	0.297173	−	0.171573i	0.0243454	−	0.0140558i	−0.487778	−	0.872968i	$-0.662192\pi$
$149$	0.297173	−	0.171573i	0.0243454	−	0.0140558i	0.512123	+	0.858912i	$0.328859\pi$
$150$	0.507306	−	0.292893i	0.0414214	−	0.0239146i
$151$			18.2426i			1.48457i	0.670087	+	0.742283i	$0.266257\pi$
$151$			18.2426i			1.48457i	−0.670087	+	0.742283i	$0.733743\pi$
$152$	2.70711	+	4.68885i	0.219575	+	0.380316i
$153$	2.41421	−	4.18154i	0.195178	−	0.338058i
$154$	0.174080	+	0.100505i	0.0140278	+	0.00809893i
$155$	−10.2426			−0.822709
$156$		0			0
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$	3.04384	+	1.75736i	0.242155	+	0.139808i
$159$	10.2426	−	17.7408i	0.812294	−	1.40693i
$160$	2.20711	+	3.82282i	0.174487	+	0.302221i
$161$		−	1.17157i		−	0.0923329i
$162$	1.79360	−	1.03553i	0.140918	−	0.0813592i
$163$	−12.9649	+	7.48528i	−1.01549	+	0.586292i	−0.912794	−	0.408420i	$-0.866080\pi$
$163$	−12.9649	+	7.48528i	−1.01549	+	0.586292i	−0.102694	+	0.994713i	$0.532746\pi$
$164$			16.1421i			1.26049i
$165$	−0.414214	−	0.717439i	−0.0322465	−	0.0558525i
$166$	−1.82843	+	3.16693i	−0.141913	+	0.245801i
$167$	7.64564	+	4.41421i	0.591638	+	0.341582i	0.765745	−	0.643145i	$-0.222371\pi$
$167$	7.64564	+	4.41421i	0.591638	+	0.341582i	−0.174107	+	0.984727i	$0.555704\pi$
$168$	−1.85786			−0.143337
$169$		0			0
$170$	−2.00000			−0.153393
$171$	−2.95680	−	1.70711i	−0.226112	−	0.130546i
$172$	2.80761	−	4.86293i	0.214078	−	0.370795i
$173$	5.58579	+	9.67487i	0.424679	+	0.735566i	0.996390	−	0.0848887i	$-0.0270535\pi$
$173$	5.58579	+	9.67487i	0.424679	+	0.735566i	−0.571711	+	0.820455i	$0.693720\pi$
$174$		−	3.31371i		−	0.251212i
$175$	0.717439	−	0.414214i	0.0542333	−	0.0313116i
$176$	1.52192	−	0.878680i	0.114719	−	0.0662330i
$177$			14.4853i			1.08878i
$178$	−1.24264	−	2.15232i	−0.0931399	−	0.161323i
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	−0.952155	−	0.305616i	$-0.901138\pi$
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	0.740748	+	0.671783i	$0.234471\pi$
$180$	−1.58346	−	0.914214i	−0.118024	−	0.0681415i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	−11.3137			−0.836333
$184$	1.94218	+	1.12132i	0.143180	+	0.0826648i
$185$	−4.24264	+	7.34847i	−0.311925	+	0.540270i
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$			2.82843i			0.206835i
$188$	1.31178	−	0.757359i	0.0956717	−	0.0552361i
$189$	4.05845	−	2.34315i	0.295209	−	0.170439i
$190$			1.41421i			0.102598i
$191$	−6.82843	−	11.8272i	−0.494088	−	0.855785i	0.505889	−	0.862599i	$-0.331164\pi$
$191$	−6.82843	−	11.8272i	−0.494088	−	0.855785i	−0.999977	+	0.00681360i	$0.997831\pi$
$192$	−2.94975	+	5.10911i	−0.212880	+	0.368718i
$193$	−13.5592	−	7.82843i	−0.976015	−	0.563503i	−0.0749503	−	0.997187i	$-0.523880\pi$
$193$	−13.5592	−	7.82843i	−0.976015	−	0.563503i	−0.901065	+	0.433685i	$0.857213\pi$
$194$	−1.51472			−0.108750
$195$		0			0
$196$	11.5442			0.824583
$197$	−19.8931	−	11.4853i	−1.41732	−	0.818292i	−0.421261	−	0.906939i	$-0.638412\pi$
$197$	−19.8931	−	11.4853i	−1.41732	−	0.818292i	−0.996063	+	0.0886471i	$0.971746\pi$
$198$	0.121320	−	0.210133i	0.00862186	−	0.0149335i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$			1.58579i			0.112132i
$201$	2.44949	−	1.41421i	0.172774	−	0.0997509i
$202$	2.74666	−	1.58579i	0.193255	−	0.111576i
$203$		−	4.68629i		−	0.328913i
$204$	−6.24264	−	10.8126i	−0.437072	−	0.757031i
$205$	−4.41421	+	7.64564i	−0.308302	+	0.533995i
$206$	−6.24682	−	3.60660i	−0.435236	−	0.251284i
$207$	−1.41421			−0.0982946
$208$		0			0
$209$	2.00000			0.138343
$210$	−0.420266	−	0.242641i	−0.0290011	−	0.0167438i
$211$	9.65685	−	16.7262i	0.664805	−	1.15148i	−0.314533	−	0.949247i	$-0.601848\pi$
$211$	9.65685	−	16.7262i	0.664805	−	1.15148i	0.979338	−	0.202230i	$-0.0648188\pi$
$212$	13.2426	+	22.9369i	0.909508	+	1.57531i
$213$			11.1716i			0.765464i
$214$	2.36245	−	1.36396i	0.161494	−	0.0932385i
$215$	2.65962	−	1.53553i	0.181385	−	0.104723i
$216$			8.97056i			0.610369i
$217$	4.24264	+	7.34847i	0.288009	+	0.498847i
$218$	−0.414214	+	0.717439i	−0.0280541	+	0.0485911i
$219$	10.3923	+	6.00000i	0.702247	+	0.405442i
$220$	1.07107			0.0722114
$221$		0			0
$222$	4.97056			0.333602
$223$	22.9369	+	13.2426i	1.53597	+	0.886793i	0.999069	+	0.0431479i	$0.0137387\pi$
$223$	22.9369	+	13.2426i	1.53597	+	0.886793i	0.536902	+	0.843645i	$0.319595\pi$
$224$	1.82843	−	3.16693i	0.122167	−	0.211599i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$			1.31371i			0.0873866i
$227$	23.9515	−	13.8284i	1.58972	−	0.917825i	0.596367	−	0.802712i	$-0.296610\pi$
$227$	23.9515	−	13.8284i	1.58972	−	0.917825i	0.993352	−	0.115113i	$-0.0367230\pi$
$228$	−7.64564	+	4.41421i	−0.506345	+	0.292338i
$229$			0.828427i			0.0547440i	0.999625	+	0.0273720i	$0.00871387\pi$
$229$			0.828427i			0.0547440i	−0.999625	+	0.0273720i	$0.991286\pi$
$230$	0.292893	+	0.507306i	0.0193128	+	0.0334508i
$231$	−0.343146	+	0.594346i	−0.0225773	+	0.0391051i
$232$	7.76874	+	4.48528i	0.510042	+	0.294473i
$233$	−24.6274			−1.61340			−0.806698	−	0.590964i	$-0.798747\pi$
$233$	−24.6274			−1.61340			−0.806698	+	0.590964i	$0.798747\pi$
$234$		0			0
$235$	0.828427			0.0540406
$236$	−16.2189	−	9.36396i	−1.05576	−	0.609542i
$237$	−6.00000	+	10.3923i	−0.389742	+	0.675053i
$238$	0.828427	+	1.43488i	0.0536990	+	0.0930093i
$239$			0.585786i			0.0378914i	0.999821	+	0.0189457i	$0.00603096\pi$
$239$			0.585786i			0.0378914i	−0.999821	+	0.0189457i	$0.993969\pi$
$240$	−3.67423	+	2.12132i	−0.237171	+	0.136931i
$241$	2.15232	−	1.24264i	0.138643	−	0.0800455i	−0.429074	−	0.903269i	$-0.641160\pi$
$241$	2.15232	−	1.24264i	0.138643	−	0.0800455i	0.567717	+	0.823224i	$0.307827\pi$
$242$		−	4.41421i		−	0.283756i
$243$	−4.94975	−	8.57321i	−0.317526	−	0.549972i
$244$	7.31371	−	12.6677i	0.468212	−	0.810967i
$245$	5.46783	+	3.15685i	0.349327	+	0.201684i
$246$	5.17157			0.329727
$247$		0			0
$248$	−16.2426			−1.03141
$249$	−10.8126	−	6.24264i	−0.685219	−	0.395611i
$250$	−0.207107	+	0.358719i	−0.0130986	+	0.0226874i
$251$	−9.89949	−	17.1464i	−0.624851	−	1.08227i	−0.988570	−	0.150764i	$-0.951827\pi$
$251$	−9.89949	−	17.1464i	−0.624851	−	1.08227i	0.363719	−	0.931509i	$-0.381507\pi$
$252$			1.51472i			0.0954183i
$253$	0.717439	−	0.414214i	0.0451050	−	0.0260414i
$254$	−3.37706	+	1.94975i	−0.211896	+	0.122338i
$255$		−	6.82843i		−	0.427613i
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	8.17157	−	14.1536i	0.509729	−	0.882876i	−0.490208	−	0.871606i	$-0.663079\pi$
$257$	8.17157	−	14.1536i	0.509729	−	0.882876i	0.999936	−	0.0112704i	$-0.00358756\pi$
$258$	−1.55797	−	0.899495i	−0.0969950	−	0.0560001i
$259$	7.02944			0.436788
$260$		0			0
$261$	−5.65685			−0.350150
$262$	6.08767	+	3.51472i	0.376098	+	0.217140i
$263$	6.70711	−	11.6170i	0.413578	−	0.716338i	−0.581700	−	0.813403i	$-0.697612\pi$
$263$	6.70711	−	11.6170i	0.413578	−	0.716338i	0.995278	+	0.0970654i	$0.0309456\pi$
$264$	−0.656854	−	1.13770i	−0.0404266	−	0.0700209i
$265$			14.4853i			0.889824i
$266$	1.01461	−	0.585786i	0.0622098	−	0.0359169i
$267$	7.34847	−	4.24264i	0.449719	−	0.259645i
$268$			3.65685i			0.223378i
$269$	1.34315	+	2.32640i	0.0818930	+	0.141843i	0.904063	−	0.427399i	$-0.140570\pi$
$269$	1.34315	+	2.32640i	0.0818930	+	0.141843i	−0.822170	+	0.569242i	$0.807237\pi$
$270$	−1.17157	+	2.02922i	−0.0712997	+	0.123495i
$271$	−1.10165	−	0.636039i	−0.0669206	−	0.0386366i	0.466166	−	0.884697i	$-0.345635\pi$
$271$	−1.10165	−	0.636039i	−0.0669206	−	0.0386366i	−0.533087	+	0.846060i	$0.678968\pi$
$272$	14.4853			0.878299
$273$		0			0
$274$	2.20101			0.132968
$275$	0.507306	+	0.292893i	0.0305917	+	0.0176621i
$276$	−1.82843	+	3.16693i	−0.110058	+	0.190627i
$277$	−3.58579	−	6.21076i	−0.215449	−	0.373169i	0.737962	−	0.674842i	$-0.235788\pi$
$277$	−3.58579	−	6.21076i	−0.215449	−	0.373169i	−0.953411	+	0.301673i	$0.902455\pi$
$278$			5.17157i			0.310170i
$279$	8.87039	−	5.12132i	0.531056	−	0.306605i
$280$	1.13770	−	0.656854i	0.0679909	−	0.0392545i
$281$		−	17.7990i		−	1.06180i	−0.847435	−	0.530899i	$-0.821854\pi$
$281$		−	17.7990i		−	1.06180i	0.847435	−	0.530899i	$-0.178146\pi$
$282$	−0.242641	−	0.420266i	−0.0144490	−	0.0250265i
$283$	4.36396	−	7.55860i	0.259411	−	0.449312i	−0.706674	−	0.707540i	$-0.749805\pi$
$283$	4.36396	−	7.55860i	0.259411	−	0.449312i	0.966084	+	0.258227i	$0.0831384\pi$
$284$	−12.5086	−	7.22183i	−0.742247	−	0.428536i
$285$	−4.82843			−0.286011
$286$		0			0
$287$	7.31371			0.431715
$288$	−3.82282	−	2.20711i	−0.225262	−	0.130055i
$289$	−3.15685	+	5.46783i	−0.185697	+	0.321637i
$290$	1.17157	+	2.02922i	0.0687971	+	0.119160i
$291$		−	5.17157i		−	0.303163i
$292$	−13.4361	+	7.75736i	−0.786291	+	0.453965i
$293$	−1.85514	+	1.07107i	−0.108379	+	0.0625724i	−0.553210	−	0.833042i	$-0.686597\pi$
$293$	−1.85514	+	1.07107i	−0.108379	+	0.0625724i	0.444831	+	0.895615i	$0.353264\pi$
$294$		−	3.69848i		−	0.215700i
$295$	−5.12132	−	8.87039i	−0.298175	−	0.516454i
$296$	−6.72792	+	11.6531i	−0.391053	+	0.677323i
$297$	2.86976	+	1.65685i	0.166520	+	0.0961404i
$298$	0.142136			0.00823370
$299$		0			0
$300$	−2.58579			−0.149290
$301$	−2.20330	−	1.27208i	−0.126996	−	0.0733214i
$302$	−3.77817	+	6.54399i	−0.217410	+	0.376564i
$303$	5.41421	+	9.37769i	0.311038	+	0.538734i
$304$		−	10.2426i		−	0.587456i
$305$	6.92820	−	4.00000i	0.396708	−	0.229039i
$306$	1.73205	−	1.00000i	0.0990148	−	0.0571662i
$307$			19.1716i			1.09418i	0.837074	+	0.547090i	$0.184264\pi$
$307$			19.1716i			1.09418i	−0.837074	+	0.547090i	$0.815736\pi$
$308$	−0.443651	−	0.768426i	−0.0252794	−	0.0437851i
$309$	12.3137	−	21.3280i	0.700502	−	1.21331i
$310$	−3.67423	−	2.12132i	−0.208683	−	0.120483i
$311$	8.48528			0.481156			0.240578	−	0.970630i	$-0.422663\pi$
$311$	8.48528			0.481156			0.240578	+	0.970630i	$0.422663\pi$
$312$		0			0
$313$	0.828427			0.0468255			0.0234127	−	0.999726i	$-0.492547\pi$
$313$	0.828427			0.0468255			0.0234127	+	0.999726i	$0.492547\pi$
$314$	6.45695	+	3.72792i	0.364387	+	0.210379i
$315$	−0.414214	+	0.717439i	−0.0233383	+	0.0404231i
$316$	−7.75736	−	13.4361i	−0.436386	−	0.755842i
$317$		−	26.1421i		−	1.46829i	−0.678993	−	0.734144i	$-0.737584\pi$
$317$		−	26.1421i		−	1.46829i	0.678993	−	0.734144i	$-0.262416\pi$
$318$	7.34847	−	4.24264i	0.412082	−	0.237915i
$319$	2.86976	−	1.65685i	0.160675	−	0.0927660i
$320$		−	4.17157i		−	0.233198i
$321$	4.65685	+	8.06591i	0.259920	+	0.450195i
$322$	0.242641	−	0.420266i	0.0135218	−	0.0234205i
$323$	14.2767	+	8.24264i	0.794375	+	0.458633i
$324$	−9.14214			−0.507896
$325$		0			0
$326$	−6.20101			−0.343442
$327$	−2.44949	−	1.41421i	−0.135457	−	0.0782062i
$328$	−7.00000	+	12.1244i	−0.386510	+	0.669456i
$329$	−0.343146	−	0.594346i	−0.0189182	−	0.0327673i
$330$		−	0.343146i		−	0.0188896i
$331$	−19.0886	+	11.0208i	−1.04921	+	0.605759i	−0.922427	−	0.386172i	$-0.873797\pi$
$331$	−19.0886	+	11.0208i	−1.04921	+	0.605759i	−0.126778	+	0.991931i	$0.540464\pi$
$332$	13.9795	−	8.07107i	0.767225	−	0.442957i
$333$		−	8.48528i		−	0.464991i
$334$	1.82843	+	3.16693i	0.100047	+	0.173287i
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	3.04384	+	1.75736i	0.166055	+	0.0958718i
$337$	−7.17157			−0.390660			−0.195330	−	0.980738i	$-0.562578\pi$
$337$	−7.17157			−0.390660			−0.195330	+	0.980738i	$0.562578\pi$
$338$		0			0
$339$	−4.48528			−0.243607
$340$	7.64564	+	4.41421i	0.414643	+	0.239394i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	−0.707107	−	1.22474i	−0.0382360	−	0.0662266i
$343$		−	11.0294i		−	0.595534i
$344$	4.21759	−	2.43503i	0.227397	−	0.131288i
$345$	−1.73205	+	1.00000i	−0.0932505	+	0.0538382i
$346$			4.62742i			0.248771i
$347$	−2.12132	−	3.67423i	−0.113878	−	0.197243i	0.803452	−	0.595369i	$-0.202994\pi$
$347$	−2.12132	−	3.67423i	−0.113878	−	0.197243i	−0.917331	+	0.398126i	$0.869661\pi$
$348$	−7.31371	+	12.6677i	−0.392056	+	0.679061i
$349$	−1.31178	−	0.757359i	−0.0702182	−	0.0405405i	0.464480	−	0.885584i	$-0.346241\pi$
$349$	−1.31178	−	0.757359i	−0.0702182	−	0.0405405i	−0.534698	+	0.845043i	$0.679575\pi$
$350$	0.343146			0.0183419
$351$		0			0
$352$	2.58579			0.137823
$353$	7.94282	+	4.58579i	0.422753	+	0.244077i	0.696255	−	0.717795i	$-0.254848\pi$
$353$	7.94282	+	4.58579i	0.422753	+	0.244077i	−0.273501	+	0.961872i	$0.588182\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	−3.94975	−	6.84116i	−0.209631	−	0.363091i
$356$			10.9706i			0.581439i
$357$	−4.89898	+	2.82843i	−0.259281	+	0.149696i
$358$	−2.02922	+	1.17157i	−0.107248	+	0.0619196i
$359$		−	27.8995i		−	1.47248i	−0.676721	−	0.736240i	$-0.736600\pi$
$359$		−	27.8995i		−	1.47248i	0.676721	−	0.736240i	$-0.263400\pi$
$360$	−0.792893	−	1.37333i	−0.0417891	−	0.0723809i
$361$	−3.67157	+	6.35935i	−0.193241	+	0.334703i
$362$		0			0
$363$	15.0711			0.791026
$364$		0			0
$365$	−8.48528			−0.444140
$366$	−4.05845	−	2.34315i	−0.212138	−	0.122478i
$367$	−2.22183	+	3.84831i	−0.115978	+	0.200880i	−0.918170	−	0.396186i	$-0.870334\pi$
$367$	−2.22183	+	3.84831i	−0.115978	+	0.200880i	0.802192	+	0.597066i	$0.203667\pi$
$368$	−2.12132	−	3.67423i	−0.110581	−	0.191533i
$369$		−	8.82843i		−	0.459590i
$370$	−3.04384	+	1.75736i	−0.158241	+	0.0913608i
$371$	10.3923	−	6.00000i	0.539542	−	0.311504i
$372$		−	26.4853i		−	1.37320i
$373$	12.6569	+	21.9223i	0.655347	+	1.13509i	0.981807	+	0.189883i	$0.0608110\pi$
$373$	12.6569	+	21.9223i	0.655347	+	1.13509i	−0.326460	+	0.945211i	$0.605856\pi$
$374$	−0.585786	+	1.01461i	−0.0302903	+	0.0524643i
$375$	−1.22474	−	0.707107i	−0.0632456	−	0.0365148i
$376$	1.31371			0.0677493
$377$		0			0
$378$	1.94113			0.0998407
$379$	12.9288	+	7.46447i	0.664110	+	0.383424i	0.793841	−	0.608125i	$-0.208078\pi$
$379$	12.9288	+	7.46447i	0.664110	+	0.383424i	−0.129731	+	0.991549i	$0.541412\pi$
$380$	3.12132	−	5.40629i	0.160120	−	0.277337i
$381$	−6.65685	−	11.5300i	−0.341041	−	0.590700i
$382$		−	5.65685i		−	0.289430i
$383$	−28.6764	+	16.5563i	−1.46530	+	0.845990i	−0.999248	−	0.0387688i	$-0.987656\pi$
$383$	−28.6764	+	16.5563i	−1.46530	+	0.845990i	−0.466049	+	0.884759i	$0.654323\pi$
$384$	−12.9288	+	7.46447i	−0.659772	+	0.380919i
$385$		−	0.485281i		−	0.0247322i
$386$	−3.24264	−	5.61642i	−0.165046	−	0.285868i
$387$	−1.53553	+	2.65962i	−0.0780556	+	0.135196i
$388$	5.79050	+	3.34315i	0.293968	+	0.169723i
$389$	16.6274			0.843044			0.421522	−	0.906818i	$-0.361496\pi$
$389$	16.6274			0.843044			0.421522	+	0.906818i	$0.361496\pi$
$390$		0			0
$391$	6.82843			0.345328
$392$	8.67081	+	5.00610i	0.437942	+	0.252846i
$393$	−12.0000	+	20.7846i	−0.605320	+	1.04844i
$394$	−4.75736	−	8.23999i	−0.239672	−	0.415125i
$395$		−	8.48528i		−	0.426941i
$396$	−0.927572	+	0.535534i	−0.0466122	+	0.0269116i
$397$	−24.0746	+	13.8995i	−1.20827	+	0.697596i	−0.962381	−	0.271702i	$-0.912413\pi$
$397$	−24.0746	+	13.8995i	−1.20827	+	0.697596i	−0.245890	+	0.969298i	$0.579080\pi$
$398$			1.65685i			0.0830506i
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$	1.50000	−	2.59808i	0.0750000	−	0.129904i
$401$	−14.9941	−	8.65685i	−0.748770	−	0.432303i	0.0764792	−	0.997071i	$-0.475632\pi$
$401$	−14.9941	−	8.65685i	−0.748770	−	0.432303i	−0.825249	+	0.564769i	$0.808965\pi$
$402$	1.17157			0.0584327
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−4.33013	−	2.50000i	−0.215166	−	0.124226i
$406$	0.970563	−	1.68106i	0.0481682	−	0.0834298i
$407$	2.48528	+	4.30463i	0.123191	+	0.213373i
$408$		−	10.8284i		−	0.536087i
$409$	−11.1097	+	6.41421i	−0.549341	+	0.317162i	−0.748856	−	0.662732i	$-0.769397\pi$
$409$	−11.1097	+	6.41421i	−0.549341	+	0.317162i	0.199515	+	0.979895i	$0.436063\pi$
$410$	−3.16693	+	1.82843i	−0.156403	+	0.0902996i
$411$			7.51472i			0.370674i
$412$	15.9203	+	27.5748i	0.784337	+	1.35851i
$413$	−4.24264	+	7.34847i	−0.208767	+	0.361595i
$414$	−0.507306	−	0.292893i	−0.0249327	−	0.0143949i
$415$	8.82843			0.433370
$416$		0			0
$417$	−17.6569			−0.864660
$418$	0.717439	+	0.414214i	0.0350911	+	0.0202598i
$419$	−2.58579	+	4.47871i	−0.126324	+	0.218799i	−0.922250	−	0.386595i	$-0.873651\pi$
$419$	−2.58579	+	4.47871i	−0.126324	+	0.218799i	0.795926	+	0.605394i	$0.206985\pi$
$420$	1.07107	+	1.85514i	0.0522628	+	0.0905218i
$421$			1.02944i			0.0501717i	0.999685	+	0.0250859i	$0.00798591\pi$
$421$			1.02944i			0.0501717i	−0.999685	+	0.0250859i	$0.992014\pi$
$422$	6.92820	−	4.00000i	0.337260	−	0.194717i
$423$	−0.717439	+	0.414214i	−0.0348831	+	0.0201398i
$424$			22.9706i			1.11555i
$425$	2.41421	+	4.18154i	0.117107	+	0.202835i
$426$	−2.31371	+	4.00746i	−0.112100	+	0.194162i
$427$	−5.73951	−	3.31371i	−0.277754	−	0.160362i
$428$	−12.0416			−0.582054
$429$		0			0
$430$	1.27208			0.0613450
$431$	3.13088	+	1.80761i	0.150809	+	0.0870696i	0.573506	−	0.819202i	$-0.305583\pi$
$431$	3.13088	+	1.80761i	0.150809	+	0.0870696i	−0.422697	+	0.906271i	$0.638916\pi$
$432$	8.48528	−	14.6969i	0.408248	−	0.707107i
$433$	−1.82843	−	3.16693i	−0.0878686	−	0.152193i	0.818741	−	0.574162i	$-0.194672\pi$
$433$	−1.82843	−	3.16693i	−0.0878686	−	0.152193i	−0.906610	+	0.421970i	$0.861339\pi$
$434$			3.51472i			0.168712i
$435$	−6.92820	+	4.00000i	−0.332182	+	0.191785i
$436$	3.16693	−	1.82843i	0.151668	−	0.0875658i
$437$		−	4.82843i		−	0.230975i
$438$	2.48528	+	4.30463i	0.118751	+	0.205683i
$439$	−16.4853	+	28.5533i	−0.786800	+	1.36278i	0.141119	+	0.989993i	$0.454930\pi$
$439$	−16.4853	+	28.5533i	−0.786800	+	1.36278i	−0.927918	+	0.372784i	$0.878403\pi$
$440$	0.804479	+	0.464466i	0.0383520	+	0.0221426i
$441$	−6.31371			−0.300653
$442$		0			0
$443$	−6.58579			−0.312900			−0.156450	−	0.987686i	$-0.550005\pi$
$443$	−6.58579			−0.312900			−0.156450	+	0.987686i	$0.550005\pi$
$444$	−19.0016	−	10.9706i	−0.901775	−	0.520640i
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	5.48528	+	9.50079i	0.259736	+	0.449875i
$447$			0.485281i			0.0229530i
$448$	−2.99285	+	1.72792i	−0.141399	+	0.0816366i
$449$	25.2123	−	14.5563i	1.18984	−	0.686957i	0.231573	−	0.972818i	$-0.425613\pi$
$449$	25.2123	−	14.5563i	1.18984	−	0.686957i	0.958271	+	0.285861i	$0.0922796\pi$
$450$		−	0.414214i		−	0.0195262i
$451$	2.58579	+	4.47871i	0.121760	+	0.210894i
$452$	2.89949	−	5.02207i	0.136381	−	0.236218i
$453$	−22.3426	−	12.8995i	−1.04975	−	0.606071i
$454$	11.4558			0.537649
$455$		0			0
$456$	−7.65685			−0.358565
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	0.0889312	−	0.996038i	$-0.471655\pi$
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	−0.818128	+	0.575036i	$0.804988\pi$
$458$	−0.171573	+	0.297173i	−0.00801707	+	0.0138860i
$459$	13.6569	+	23.6544i	0.637447	+	1.10409i
$460$		−	2.58579i		−	0.120563i
$461$	−22.9369	+	13.2426i	−1.06828	+	0.616771i	−0.927711	−	0.373300i	$-0.878226\pi$
$461$	−22.9369	+	13.2426i	−1.06828	+	0.616771i	−0.140568	+	0.990071i	$0.544893\pi$
$462$	−0.246186	+	0.142136i	−0.0114536	+	0.00661275i
$463$		−	15.6569i		−	0.727636i	−0.931470	−	0.363818i	$-0.881473\pi$
$463$		−	15.6569i		−	0.727636i	0.931470	−	0.363818i	$-0.118527\pi$
$464$	−8.48528	−	14.6969i	−0.393919	−	0.682288i
$465$	7.24264	−	12.5446i	0.335869	−	0.581743i
$466$	−8.83433	−	5.10051i	−0.409243	−	0.236276i
$467$	10.5858			0.489852			0.244926	−	0.969542i	$-0.421236\pi$
$467$	10.5858			0.489852			0.244926	+	0.969542i	$0.421236\pi$
$468$		0			0
$469$	1.65685			0.0765064
$470$	0.297173	+	0.171573i	0.0137076	+	0.00791407i
$471$	−12.7279	+	22.0454i	−0.586472	+	1.01580i
$472$	−8.12132	−	14.0665i	−0.373814	−	0.647465i
$473$		−	1.79899i		−	0.0827176i
$474$	−4.30463	+	2.48528i	−0.197718	+	0.114153i
$475$	2.95680	−	1.70711i	0.135667	−	0.0783274i
$476$		−	7.31371i		−	0.335223i
$477$	−7.24264	−	12.5446i	−0.331618	−	0.574379i
$478$	−0.121320	+	0.210133i	−0.00554906	+	0.00961126i
$479$	4.56575	+	2.63604i	0.208615	+	0.120444i	0.600667	−	0.799499i	$-0.294902\pi$
$479$	4.56575	+	2.63604i	0.208615	+	0.120444i	−0.392053	+	0.919943i	$0.628235\pi$
$480$	−6.24264			−0.284936
$481$		0			0
$482$	1.02944			0.0468896
$483$	1.43488	+	0.828427i	0.0652892	+	0.0376947i
$484$	−9.74264	+	16.8747i	−0.442847	+	0.767034i
$485$	1.82843	+	3.16693i	0.0830246	+	0.143803i
$486$		−	4.10051i		−	0.186003i
$487$	−19.8931	+	11.4853i	−0.901442	+	0.520448i	−0.877668	−	0.479270i	$-0.840902\pi$
$487$	−19.8931	+	11.4853i	−0.901442	+	0.520448i	−0.0237742	+	0.999717i	$0.507568\pi$
$488$	10.9867	−	6.34315i	0.497342	−	0.287141i
$489$		−	21.1716i		−	0.957412i
$490$	1.30761	+	2.26485i	0.0590719	+	0.102316i
$491$	5.41421	−	9.37769i	0.244340	−	0.423209i	−0.717606	−	0.696449i	$-0.754762\pi$
$491$	5.41421	−	9.37769i	0.244340	−	0.423209i	0.961946	+	0.273240i	$0.0880954\pi$
$492$	−19.7700	−	11.4142i	−0.891300	−	0.514592i
$493$	27.3137			1.23015
$494$		0			0
$495$	−0.585786			−0.0263291
$496$	26.6112	+	15.3640i	1.19488	+	0.689862i
$497$	−3.27208	+	5.66741i	−0.146773	+	0.254218i
$498$	−2.58579	−	4.47871i	−0.115872	−	0.200696i
$499$		−	10.4437i		−	0.467522i	−0.972294	−	0.233761i	$-0.924897\pi$
$499$		−	10.4437i		−	0.467522i	0.972294	−	0.233761i	$-0.0751033\pi$
$500$	1.58346	−	0.914214i	0.0708147	−	0.0408849i
$501$	−10.8126	+	6.24264i	−0.483070	+	0.278901i
$502$		−	8.20101i		−	0.366029i
$503$	−9.05025	−	15.6755i	−0.403531	−	0.698936i	0.590618	−	0.806951i	$-0.298884\pi$
$503$	−9.05025	−	15.6755i	−0.403531	−	0.698936i	−0.994149	+	0.108015i	$0.965551\pi$
$504$	−0.656854	+	1.13770i	−0.0292586	+	0.0506774i
$505$	−6.63103	−	3.82843i	−0.295077	−	0.170363i
$506$	0.343146			0.0152547
$507$		0			0
$508$	17.2132			0.763712
$509$	−18.2841	−	10.5563i	−0.810430	−	0.467902i	0.0366752	−	0.999327i	$-0.488323\pi$
$509$	−18.2841	−	10.5563i	−0.810430	−	0.467902i	−0.847105	+	0.531425i	$0.821657\pi$
$510$	1.41421	−	2.44949i	0.0626224	−	0.108465i
$511$	3.51472	+	6.08767i	0.155482	+	0.269303i
$512$		−	22.7574i		−	1.00574i
$513$	16.7262	−	9.65685i	0.738478	−	0.426361i
$514$	5.86260	−	3.38478i	0.258588	−	0.149296i
$515$			17.4142i			0.767362i
$516$	3.97056	+	6.87722i	0.174794	+	0.302753i
$517$	0.242641	−	0.420266i	0.0106713	−	0.0184833i
$518$	2.52160	+	1.45584i	0.110793	+	0.0639661i
$519$	−15.7990			−0.693499
$520$		0			0
$521$	−6.34315			−0.277898			−0.138949	−	0.990300i	$-0.544372\pi$
$521$	−6.34315			−0.277898			−0.138949	+	0.990300i	$0.544372\pi$
$522$	−2.02922	−	1.17157i	−0.0888167	−	0.0512784i
$523$	14.1213	−	24.4588i	0.617482	−	1.06951i	−0.372461	−	0.928048i	$-0.621486\pi$
$523$	14.1213	−	24.4588i	0.617482	−	1.06951i	0.989944	−	0.141463i	$-0.0451806\pi$
$524$	−15.5147	−	26.8723i	−0.677764	−	1.17392i
$525$			1.17157i			0.0511316i
$526$	4.81194	−	2.77817i	0.209811	−	0.121134i
$527$	−42.8300	+	24.7279i	−1.86570	+	1.07717i
$528$			2.48528i			0.108158i
$529$	10.5000	+	18.1865i	0.456522	+	0.790719i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	8.87039	+	5.12132i	0.384942	+	0.222246i
$532$	−5.17157			−0.224216
$533$		0			0
$534$	3.51472			0.152097
$535$	−5.70346	−	3.29289i	−0.246582	−	0.142364i
$536$	−1.58579	+	2.74666i	−0.0684955	+	0.118638i
$537$	−4.00000	−	6.92820i	−0.172613	−	0.298974i
$538$			1.11270i			0.0479718i
$539$	3.20298	−	1.84924i	0.137962	−	0.0796525i
$540$	8.95743	−	5.17157i	0.385466	−	0.222549i
$541$		−	12.8284i		−	0.551537i	−0.961224	−	0.275769i	$-0.911068\pi$
$541$		−	12.8284i		−	0.551537i	0.961224	−	0.275769i	$-0.0889323\pi$
$542$	−0.263456	−	0.456319i	−0.0113164	−	0.0196006i
$543$		0			0
$544$	18.4582	+	10.6569i	0.791389	+	0.456909i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−29.2132			−1.24907			−0.624533	−	0.780998i	$-0.714711\pi$
$547$	−29.2132			−1.24907			−0.624533	+	0.780998i	$0.714711\pi$
$548$	−8.41407	−	4.85786i	−0.359431	−	0.207518i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$	0.121320	+	0.210133i	0.00517312	+	0.00896010i
$551$		−	19.3137i		−	0.822792i
$552$	−2.74666	+	1.58579i	−0.116906	+	0.0674956i
$553$	−6.08767	+	3.51472i	−0.258874	+	0.149461i
$554$		−	2.97056i		−	0.126207i
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	11.4142	−	19.7700i	0.484070	−	0.838435i
$557$	−3.29002	−	1.89949i	−0.139403	−	0.0804842i	0.428677	−	0.903458i	$-0.358980\pi$
$557$	−3.29002	−	1.89949i	−0.139403	−	0.0804842i	−0.568079	+	0.822974i	$0.692313\pi$
$558$	4.24264			0.179605
$559$		0			0
$560$	−2.48528			−0.105022
$561$	−3.46410	−	2.00000i	−0.146254	−	0.0844401i
$562$	3.68629	−	6.38484i	0.155497	−	0.269328i
$563$	−8.12132	−	14.0665i	−0.342273	−	0.592834i	0.642582	−	0.766217i	$-0.277863\pi$
$563$	−8.12132	−	14.0665i	−0.342273	−	0.592834i	−0.984854	+	0.173383i	$0.944530\pi$
$564$			2.14214i			0.0902002i
$565$	2.74666	−	1.58579i	0.115553	−	0.0667145i
$566$	3.13088	−	1.80761i	0.131601	−	0.0759796i
$567$			4.14214i			0.173953i
$568$	−6.26346	−	10.8486i	−0.262809	−	0.455198i
$569$	−10.8284	+	18.7554i	−0.453951	+	0.786267i	−0.998627	−	0.0523799i	$-0.983319\pi$
$569$	−10.8284	+	18.7554i	−0.453951	+	0.786267i	0.544676	+	0.838647i	$0.316653\pi$
$570$	−1.73205	−	1.00000i	−0.0725476	−	0.0418854i
$571$	28.4853			1.19207			0.596036	−	0.802958i	$-0.296742\pi$
$571$	28.4853			1.19207			0.596036	+	0.802958i	$0.296742\pi$
$572$		0			0
$573$	19.3137			0.806842
$574$	2.62357	+	1.51472i	0.109506	+	0.0632231i
$575$	0.707107	−	1.22474i	0.0294884	−	0.0510754i
$576$	2.08579	+	3.61269i	0.0869078	+	0.150529i
$577$			29.1716i			1.21443i	0.794538	+	0.607214i	$0.207713\pi$
$577$			29.1716i			1.21443i	−0.794538	+	0.607214i	$0.792287\pi$
$578$	−2.26485	+	1.30761i	−0.0942053	+	0.0543895i
$579$	19.1757	−	11.0711i	0.796913	−	0.460098i
$580$		−	10.3431i		−	0.429476i
$581$	−3.65685	−	6.33386i	−0.151712	−	0.262773i
$582$	1.07107	−	1.85514i	0.0443972	−	0.0768982i
$583$	7.34847	+	4.24264i	0.304342	+	0.175712i
$584$	−13.4558			−0.556807
$585$		0			0
$586$	−0.887302			−0.0366541
$587$	27.4156	+	15.8284i	1.13156	+	0.653309i	0.944328	−	0.329006i	$-0.106714\pi$
$587$	27.4156	+	15.8284i	1.13156	+	0.653309i	0.187237	+	0.982315i	$0.440047\pi$
$588$	−8.16295	+	14.1386i	−0.336634	+	0.583068i
$589$	17.4853	+	30.2854i	0.720468	+	1.24789i
$590$		−	4.24264i		−	0.174667i
$591$	28.1331	−	16.2426i	1.15724	−	0.668133i
$592$	22.0454	−	12.7279i	0.906061	−	0.523114i
$593$			20.6274i			0.847066i	0.905881	+	0.423533i	$0.139210\pi$
$593$			20.6274i			0.847066i	−0.905881	+	0.423533i	$0.860790\pi$
$594$	0.686292	+	1.18869i	0.0281589	+	0.0487726i
$595$	2.00000	−	3.46410i	0.0819920	−	0.142014i
$596$	−0.543359	−	0.313708i	−0.0222569	−	0.0128500i
$597$	−5.65685			−0.231520
$598$		0			0
$599$	−25.4558			−1.04010			−0.520049	−	0.854137i	$-0.674086\pi$
$599$	−25.4558			−1.04010			−0.520049	+	0.854137i	$0.674086\pi$
$600$	−1.94218	−	1.12132i	−0.0792893	−	0.0457777i
$601$	−0.313708	+	0.543359i	−0.0127964	+	0.0221641i	−0.872353	−	0.488877i	$-0.837407\pi$
$601$	−0.313708	+	0.543359i	−0.0127964	+	0.0221641i	0.859556	+	0.511041i	$0.170740\pi$
$602$	−0.526912	−	0.912638i	−0.0214753	−	0.0371964i
$603$		−	2.00000i		−	0.0814463i
$604$	28.8866	−	16.6777i	1.17538	−	0.678605i
$605$	−9.22911	+	5.32843i	−0.375217	+	0.216631i
$606$			4.48528i			0.182202i
$607$	−20.1213	−	34.8511i	−0.816699	−	1.41456i	−0.908101	−	0.418750i	$-0.862468\pi$
$607$	−20.1213	−	34.8511i	−0.816699	−	1.41456i	0.0914022	−	0.995814i	$-0.470865\pi$
$608$	7.53553	−	13.0519i	0.305606	−	0.529326i
$609$	5.73951	+	3.31371i	0.232577	+	0.134278i
$610$	3.31371			0.134168
$611$		0			0
$612$	−8.82843			−0.356868
$613$	−32.3146	−	18.6569i	−1.30518	−	0.753543i	−0.323888	−	0.946095i	$-0.604990\pi$
$613$	−32.3146	−	18.6569i	−1.30518	−	0.753543i	−0.981287	+	0.192552i	$0.938324\pi$
$614$	−3.97056	+	6.87722i	−0.160239	+	0.277542i
$615$	−6.24264	−	10.8126i	−0.251728	−	0.436005i
$616$		−	0.769553i		−	0.0310062i
$617$	19.8931	−	11.4853i	0.800866	−	0.462380i	−0.0429081	−	0.999079i	$-0.513662\pi$
$617$	19.8931	−	11.4853i	0.800866	−	0.462380i	0.843774	+	0.536699i	$0.180329\pi$
$618$	8.83433	−	5.10051i	0.355369	−	0.205172i
$619$			10.2426i			0.411686i	0.978585	+	0.205843i	$0.0659937\pi$
$619$			10.2426i			0.411686i	−0.978585	+	0.205843i	$0.934006\pi$
$620$	9.36396	+	16.2189i	0.376066	+	0.651365i
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$	3.04384	+	1.75736i	0.122047	+	0.0704637i
$623$	4.97056			0.199141
$624$		0			0
$625$	1.00000			0.0400000
$626$	0.297173	+	0.171573i	0.0118774	+	0.00685743i
$627$	−1.41421	+	2.44949i	−0.0564782	+	0.0978232i
$628$	−16.4558	−	28.5024i	−0.656660	−	1.13737i
$629$			40.9706i			1.63360i
$630$	−0.297173	+	0.171573i	−0.0118397	+	0.00683563i
$631$	−15.7986	+	9.12132i	−0.628932	+	0.363114i	−0.780338	−	0.625358i	$-0.784953\pi$
$631$	−15.7986	+	9.12132i	−0.628932	+	0.363114i	0.151406	+	0.988472i	$0.451620\pi$
$632$		−	13.4558i		−	0.535245i
$633$	13.6569	+	23.6544i	0.542811	+	0.940177i
$634$	5.41421	−	9.37769i	0.215026	−	0.372436i
$635$	8.15295	+	4.70711i	0.323540	+	0.186796i
$636$	−37.4558			−1.48522
$637$		0			0
$638$	1.37258			0.0543411
$639$	6.84116	+	3.94975i	0.270632	+	0.156250i
$640$	5.27817	−	9.14207i	0.208638	−	0.361372i
$641$	18.1716	+	31.4741i	0.717734	+	1.24315i	0.961896	+	0.273417i	$0.0881539\pi$
$641$	18.1716	+	31.4741i	0.717734	+	1.24315i	−0.244162	+	0.969735i	$0.578513\pi$
$642$			3.85786i			0.152258i
$643$	−22.9369	+	13.2426i	−0.904544	+	0.522239i	−0.878672	−	0.477426i	$-0.841570\pi$
$643$	−22.9369	+	13.2426i	−0.904544	+	0.522239i	−0.0258724	+	0.999665i	$0.508236\pi$
$644$	−1.85514	+	1.07107i	−0.0731029	+	0.0422060i
$645$			4.34315i			0.171011i
$646$	3.41421	+	5.91359i	0.134330	+	0.232667i
$647$	3.29289	−	5.70346i	0.129457	−	0.224226i	−0.794009	−	0.607906i	$-0.792010\pi$
$647$	3.29289	−	5.70346i	0.129457	−	0.224226i	0.923466	+	0.383679i	$0.125343\pi$
$648$	−6.86666	−	3.96447i	−0.269748	−	0.155739i
$649$	−6.00000			−0.235521
$650$		0			0
$651$	−12.0000			−0.470317
$652$	23.7054	+	13.6863i	0.928373	+	0.535997i
$653$	−6.51472	+	11.2838i	−0.254941	+	0.441570i	−0.964879	−	0.262693i	$-0.915389\pi$
$653$	−6.51472	+	11.2838i	−0.254941	+	0.441570i	0.709939	+	0.704263i	$0.248723\pi$
$654$	−0.585786	−	1.01461i	−0.0229061	−	0.0396745i
$655$		−	16.9706i		−	0.663095i
$656$	22.9369	−	13.2426i	0.895537	−	0.517038i
$657$	7.34847	−	4.24264i	0.286691	−	0.165521i
$658$		−	0.284271i		−	0.0110820i
$659$	−23.0711	−	39.9603i	−0.898721	−	1.55663i	−0.829130	−	0.559055i	$-0.811164\pi$
$659$	−23.0711	−	39.9603i	−0.898721	−	1.55663i	−0.0695907	−	0.997576i	$-0.522169\pi$
$660$	−0.757359	+	1.31178i	−0.0294802	+	0.0510612i
$661$	42.9531	+	24.7990i	1.67068	+	0.964569i	0.967257	+	0.253800i	$0.0816805\pi$
$661$	42.9531	+	24.7990i	1.67068	+	0.964569i	0.703426	+	0.710769i	$0.251653\pi$
$662$	−9.12994			−0.354845
$663$		0			0
$664$	14.0000			0.543305
$665$	−2.44949	−	1.41421i	−0.0949871	−	0.0548408i
$666$	1.75736	−	3.04384i	0.0680963	−	0.117946i
$667$	−4.00000	−	6.92820i	−0.154881	−	0.268261i
$668$		−	16.1421i		−	0.624558i
$669$	−32.4377	+	18.7279i	−1.25411	+	0.724063i
$670$	−0.717439	+	0.414214i	−0.0277171	+	0.0160025i
$671$		−	4.68629i		−	0.180912i
$672$	2.58579	+	4.47871i	0.0997489	+	0.172770i
$673$	−5.24264	+	9.08052i	−0.202089	+	0.350028i	−0.949201	−	0.314669i	$-0.898106\pi$
$673$	−5.24264	+	9.08052i	−0.202089	+	0.350028i	0.747112	+	0.664698i	$0.231440\pi$
$674$	−2.57258	−	1.48528i	−0.0990922	−	0.0572109i
$675$	5.65685			0.217732
$676$		0			0
$677$	8.14214			0.312928			0.156464	−	0.987684i	$-0.449991\pi$
$677$	8.14214			0.312928			0.156464	+	0.987684i	$0.449991\pi$
$678$	−1.60896	−	0.928932i	−0.0617916	−	0.0356754i
$679$	1.51472	−	2.62357i	0.0581296	−	0.100683i
$680$	3.82843	+	6.63103i	0.146813	+	0.254288i
$681$			39.1127i			1.49880i
$682$	−2.15232	+	1.24264i	−0.0824165	+	0.0475832i
$683$	28.8505	−	16.6569i	1.10393	−	0.637357i	0.166683	−	0.986011i	$-0.446694\pi$
$683$	28.8505	−	16.6569i	1.10393	−	0.637357i	0.937252	+	0.348654i	$0.113361\pi$
$684$			6.24264i			0.238693i
$685$	−2.65685	−	4.60181i	−0.101513	−	0.175826i
$686$	2.28427	−	3.95647i	0.0872139	−	0.151059i
$687$	−1.01461	−	0.585786i	−0.0387099	−	0.0223491i
$688$	−9.21320			−0.351250
$689$		0			0
$690$	−0.828427			−0.0315377
$691$	18.2481	+	10.5355i	0.694190	+	0.400791i	0.805180	−	0.593031i	$-0.202069\pi$
$691$	18.2481	+	10.5355i	0.694190	+	0.400791i	−0.110990	+	0.993822i	$0.535402\pi$
$692$	10.2132	−	17.6898i	0.388248	−	0.672465i
$693$	0.242641	+	0.420266i	0.00921716	+	0.0159646i
$694$		−	1.75736i		−	0.0667084i
$695$	10.8126	−	6.24264i	0.410144	−	0.236797i
$696$	−10.9867	+	6.34315i	−0.416448	+	0.240436i
$697$			42.6274i			1.61463i
$698$	−0.313708	−	0.543359i	−0.0118740	−	0.0205664i
$699$	17.4142	−	30.1623i	0.658666	−	1.14084i
$700$	−1.31178	−	0.757359i	−0.0495808	−	0.0286255i
$701$	−37.3137			−1.40932			−0.704660	−	0.709545i	$-0.748900\pi$
$701$	−37.3137			−1.40932			−0.704660	+	0.709545i	$0.748900\pi$
$702$		0			0
$703$	28.9706			1.09265
$704$	−2.11626	−	1.22183i	−0.0797597	−	0.0460493i
$705$	−0.585786	+	1.01461i	−0.0220620	+	0.0382125i
$706$	1.89949	+	3.29002i	0.0714884	+	0.123822i
$707$			6.34315i			0.238559i
$708$	22.9369	−	13.2426i	0.862022	−	0.497689i
$709$	−14.8200	+	8.55635i	−0.556578	+	0.321340i	−0.751771	−	0.659424i	$-0.770800\pi$
$709$	−14.8200	+	8.55635i	−0.556578	+	0.321340i	0.195193	+	0.980765i	$0.437467\pi$
$710$		−	3.27208i		−	0.122799i
$711$	4.24264	+	7.34847i	0.159111	+	0.275589i
$712$	−4.75736	+	8.23999i	−0.178290	+	0.308807i
$713$	12.5446	+	7.24264i	0.469800	+	0.271239i
$714$	−2.34315			−0.0876900
$715$		0			0
$716$	10.3431			0.386542
$717$	−0.717439	−	0.414214i	−0.0267932	−	0.0154691i
$718$	5.77817	−	10.0081i	0.215640	−	0.373499i
$719$	−2.48528	−	4.30463i	−0.0926854	−	0.160536i	0.815955	−	0.578116i	$-0.196212\pi$
$719$	−2.48528	−	4.30463i	−0.0926854	−	0.160536i	−0.908640	+	0.417580i	$0.862878\pi$
$720$			3.00000i			0.111803i
$721$	12.4936	−	7.21320i	0.465287	−	0.268634i
$722$	−2.63413	+	1.52082i	−0.0980321	+	0.0565989i
$723$			3.51472i			0.130714i
$724$		0			0
$725$	2.82843	−	4.89898i	0.105045	−	0.181944i
$726$	5.40629	+	3.12132i	0.200646	+	0.115843i
$727$	−19.3553			−0.717850			−0.358925	−	0.933366i	$-0.616857\pi$
$727$	−19.3553			−0.717850			−0.358925	+	0.933366i	$0.616857\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−3.04384	−	1.75736i	−0.112657	−	0.0650428i
$731$	7.41421	−	12.8418i	0.274225	−	0.474971i
$732$	10.3431	+	17.9149i	0.382294	+	0.662152i
$733$			1.31371i			0.0485229i	0.999706	+	0.0242615i	$0.00772342\pi$
$733$			1.31371i			0.0485229i	−0.999706	+	0.0242615i	$0.992277\pi$
$734$	−1.59402	+	0.920310i	−0.0588365	+	0.0339693i
$735$	−7.73268	+	4.46447i	−0.285224	+	0.164674i
$736$		−	6.24264i		−	0.230107i
$737$	0.585786	+	1.01461i	0.0215777	+	0.0373737i
$738$	1.82843	−	3.16693i	0.0673053	−	0.116576i
$739$	−26.6112	−	15.3640i	−0.978907	−	0.565172i	−0.0769673	−	0.997034i	$-0.524524\pi$
$739$	−26.6112	−	15.3640i	−0.978907	−	0.565172i	−0.901940	+	0.431861i	$0.857857\pi$
$740$	15.5147			0.570332
$741$		0			0
$742$	4.97056			0.182475
$743$	−33.3292	−	19.2426i	−1.22273	−	0.705944i	−0.257232	−	0.966350i	$-0.582810\pi$
$743$	−33.3292	−	19.2426i	−1.22273	−	0.705944i	−0.965499	+	0.260406i	$0.916144\pi$
$744$	11.4853	−	19.8931i	0.421071	−	0.729316i
$745$	−0.171573	−	0.297173i	−0.00628594	−	0.0108876i
$746$			10.4853i			0.383893i
$747$	−7.64564	+	4.41421i	−0.279739	+	0.161508i
$748$	4.47871	−	2.58579i	0.163758	−	0.0945457i
$749$			5.45584i			0.199352i
$750$	−0.292893	−	0.507306i	−0.0106949	−	0.0185242i
$751$	−22.2426	+	38.5254i	−0.811645	+	1.40581i	0.100066	+	0.994981i	$0.468095\pi$
$751$	−22.2426	+	38.5254i	−0.811645	+	1.40581i	−0.911712	+	0.410830i	$0.865239\pi$
$752$	−2.15232	−	1.24264i	−0.0784869	−	0.0453144i
$753$	28.0000			1.02038
$754$		0			0
$755$	18.2426			0.663918
$756$	−7.42058	−	4.28427i	−0.269884	−	0.155817i
$757$	−2.07107	+	3.58719i	−0.0752742	+	0.130379i	−0.901205	−	0.433392i	$-0.857317\pi$
$757$	−2.07107	+	3.58719i	−0.0752742	+	0.130379i	0.825931	+	0.563771i	$0.190650\pi$
$758$	3.09188	+	5.35530i	0.112302	+	0.194513i
$759$			1.17157i			0.0425254i
$760$	4.68885	−	2.70711i	0.170082	−	0.0981971i
$761$	−31.7203	+	18.3137i	−1.14986	+	0.663871i	−0.948853	−	0.315719i	$-0.897754\pi$
$761$	−31.7203	+	18.3137i	−1.14986	+	0.663871i	−0.201006	+	0.979590i	$0.564421\pi$
$762$		−	5.51472i		−	0.199777i
$763$	−0.828427	−	1.43488i	−0.0299911	−	0.0519461i
$764$	−12.4853	+	21.6251i	−0.451702	+	0.782370i
$765$	−4.18154	−	2.41421i	−0.151184	−	0.0872861i
$766$	−13.7157			−0.495569
$767$		0			0
$768$	5.61522			0.202622
$769$	9.50079	+	5.48528i	0.342607	+	0.197804i	0.661424	−	0.750012i	$-0.269952\pi$
$769$	9.50079	+	5.48528i	0.342607	+	0.197804i	−0.318817	+	0.947816i	$0.603286\pi$
$770$	0.100505	−	0.174080i	0.00362195	−	0.00627340i
$771$	11.5563	+	20.0162i	0.416192	+	0.720865i
$772$			28.6274i			1.03032i
$773$	−5.31925	+	3.07107i	−0.191320	+	0.110459i	−0.592600	−	0.805497i	$-0.701899\pi$
$773$	−5.31925	+	3.07107i	−0.191320	+	0.110459i	0.401280	+	0.915955i	$0.368565\pi$
$774$	−1.10165	+	0.636039i	−0.0395981	+	0.0228619i
$775$			10.2426i			0.367927i
$776$	2.89949	+	5.02207i	0.104086	+	0.180282i
$777$	−4.97056	+	8.60927i	−0.178318	+	0.308856i
$778$	5.96458	+	3.44365i	0.213840	+	0.123461i
$779$	30.1421			1.07995
$780$		0			0
$781$	−4.62742			−0.165582
$782$	2.44949	+	1.41421i	0.0875936	+	0.0505722i
$783$	16.0000	−	27.7128i	0.571793	−	0.990375i
$784$	−9.47056	−	16.4035i	−0.338234	−	0.585839i
$785$		−	18.0000i		−	0.642448i
$786$	−8.60927	+	4.97056i	−0.307082	+	0.177294i
$787$	4.77589	−	2.75736i	0.170242	−	0.0982892i	−0.412458	−	0.910977i	$-0.635330\pi$
$787$	4.77589	−	2.75736i	0.170242	−	0.0982892i	0.582700	+	0.812687i	$0.301996\pi$
$788$			42.0000i			1.49619i
$789$	9.48528	+	16.4290i	0.337685	+	0.584888i
$790$	1.75736	−	3.04384i	0.0625240	−	0.108295i
$791$	−2.27541	−	1.31371i	−0.0809043	−	0.0467101i
$792$	−0.928932			−0.0330082
$793$		0			0
$794$	−11.5147			−0.408642
$795$	−17.7408	−	10.2426i	−0.629200	−	0.363269i
$796$	3.65685	−	6.33386i	0.129614	−	0.224498i
$797$	5.48528	+	9.50079i	0.194299	+	0.336535i	0.946670	−	0.322204i	$-0.104424\pi$
$797$	5.48528	+	9.50079i	0.194299	+	0.336535i	−0.752372	+	0.658739i	$0.771090\pi$
$798$			1.65685i			0.0586520i
$799$	3.46410	−	2.00000i	0.122551	−	0.0707549i
$800$	3.82282	−	2.20711i	0.135157	−	0.0780330i
$801$		−	6.00000i		−	0.212000i
$802$	−3.58579	−	6.21076i	−0.126619	−	0.219310i
$803$	−2.48528	+	4.30463i	−0.0877037	+	0.151907i
$804$	−4.47871	−	2.58579i	−0.157952	−	0.0911937i
$805$	−1.17157			−0.0412925
$806$		0			0
$807$	−3.79899			−0.133731
$808$	−10.5154	−	6.07107i	−0.369930	−	0.213579i
$809$	22.6274	−	39.1918i	0.795538	−	1.37791i	−0.126960	−	0.991908i	$-0.540522\pi$
$809$	22.6274	−	39.1918i	0.795538	−	1.37791i	0.922497	−	0.386004i	$-0.126145\pi$
$810$	−1.03553	−	1.79360i	−0.0363850	−	0.0630206i
$811$		−	8.38478i		−	0.294429i	−0.989105	−	0.147215i	$-0.952969\pi$
$811$		−	8.38478i		−	0.294429i	0.989105	−	0.147215i	$-0.0470308\pi$
$812$	−7.42058	+	4.28427i	−0.260411	+	0.150348i
$813$	1.55797	−	0.899495i	0.0546404	−	0.0315467i
$814$			2.05887i			0.0721635i
$815$	7.48528	+	12.9649i	0.262198	+	0.454140i
$816$	−10.2426	+	17.7408i	−0.358564	+	0.621051i
$817$	−9.08052	−	5.24264i	−0.317687	−	0.183417i
$818$	−5.31371			−0.185789
$819$		0			0
$820$	16.1421			0.563708
$821$	33.9957	+	19.6274i	1.18646	+	0.685002i	0.957500	−	0.288435i	$-0.0931348\pi$
$821$	33.9957	+	19.6274i	1.18646	+	0.685002i	0.228958	+	0.973436i	$0.426468\pi$
$822$	−1.55635	+	2.69568i	−0.0542839	+	0.0940225i
$823$	17.1924	+	29.7781i	0.599289	+	1.03800i	0.992926	+	0.118733i	$0.0378833\pi$
$823$	17.1924	+	29.7781i	0.599289	+	1.03800i	−0.393637	+	0.919266i	$0.628783\pi$
$824$			27.6152i			0.962022i
$825$	−0.717439	+	0.414214i	−0.0249780	+	0.0144211i
$826$	−3.04384	+	1.75736i	−0.105909	+	0.0611464i
$827$			27.8579i			0.968713i	0.874871	+	0.484356i	$0.160946\pi$
$827$			27.8579i			0.968713i	−0.874871	+	0.484356i	$0.839054\pi$
$828$	1.29289	+	2.23936i	0.0449311	+	0.0778230i
$829$	3.51472	−	6.08767i	0.122071	−	0.211434i	−0.798513	−	0.601977i	$-0.794380\pi$
$829$	3.51472	−	6.08767i	0.122071	−	0.211434i	0.920584	+	0.390544i	$0.127713\pi$
$830$	3.16693	+	1.82843i	0.109926	+	0.0634656i
$831$	10.1421			0.351827
$832$		0			0
$833$	30.4853			1.05625
$834$	−6.33386	−	3.65685i	−0.219324	−	0.126627i
$835$	4.41421	−	7.64564i	0.152760	−	0.264588i
$836$	−1.82843	−	3.16693i	−0.0632375	−	0.109531i
$837$			57.9411i			2.00274i
$838$	−1.85514	+	1.07107i	−0.0640849	+	0.0369994i
$839$	−16.2189	+	9.36396i	−0.559937	+	0.323280i	−0.753120	−	0.657883i	$-0.771452\pi$
$839$	−16.2189	+	9.36396i	−0.559937	+	0.323280i	0.193183	+	0.981163i	$0.438119\pi$
$840$			1.85786i			0.0641024i
$841$	−1.50000	−	2.59808i	−0.0517241	−	0.0895888i
$842$	−0.213203	+	0.369279i	−0.00734748	+	0.0127262i
$843$	21.7992	+	12.5858i	0.750805	+	0.433478i
$844$	−35.3137			−1.21555
$845$		0			0
$846$	−0.343146			−0.0117976
$847$	7.64564	+	4.41421i	0.262707	+	0.151674i
$848$	21.7279	−	37.6339i	0.746140	−	1.29235i
$849$	6.17157	+	10.6895i	0.211808	+	0.366862i
$850$			2.00000i			0.0685994i
$851$	10.3923	−	6.00000i	0.356244	−	0.205677i
$852$	17.6898	−	10.2132i	0.606042	−	0.349899i
$853$			37.4558i			1.28246i	0.767347	+	0.641232i	$0.221576\pi$
$853$			37.4558i			1.28246i	−0.767347	+	0.641232i	$0.778424\pi$
$854$	−1.37258	−	2.37738i	−0.0469688	−	0.0813524i
$855$	−1.70711	+	2.95680i	−0.0583818	+	0.101120i
$856$	−9.04447	−	5.22183i	−0.309134	−	0.178478i
$857$	−0.343146			−0.0117216			−0.00586082	−	0.999983i	$-0.501866\pi$
$857$	−0.343146			−0.0117216			−0.00586082	+	0.999983i	$0.501866\pi$
$858$		0			0
$859$	11.7990			0.402576			0.201288	−	0.979532i	$-0.435487\pi$
$859$	11.7990			0.402576			0.201288	+	0.979532i	$0.435487\pi$
$860$	−4.86293	−	2.80761i	−0.165824	−	0.0957388i
$861$	−5.17157	+	8.95743i	−0.176247	+	0.305268i
$862$	0.748737	+	1.29685i	0.0255021	+	0.0441709i
$863$		−	19.4558i		−	0.662285i	−0.943581	−	0.331142i	$-0.892566\pi$
$863$		−	19.4558i		−	0.662285i	0.943581	−	0.331142i	$-0.107434\pi$
$864$	21.6251	−	12.4853i	0.735702	−	0.424758i
$865$	9.67487	−	5.58579i	0.328955	−	0.189922i
$866$		−	1.51472i		−	0.0514722i
$867$	−4.46447	−	7.73268i	−0.151621	−	0.262616i
$868$	7.75736	−	13.4361i	0.263302	−	0.456052i
$869$	−4.30463	−	2.48528i	−0.146025	−	0.0843074i
$870$	−3.31371			−0.112345
$871$		0			0
$872$	3.17157			0.107403
$873$	−3.16693	−	1.82843i	−0.107184	−	0.0618829i
$874$	1.00000	−	1.73205i	0.0338255	−	0.0585875i
$875$	−0.414214	−	0.717439i	−0.0140030	−	0.0242539i
$876$		−	21.9411i		−	0.741322i
$877$	−2.32640	+	1.34315i	−0.0785568	+	0.0453548i	−0.538764	−	0.842457i	$-0.681109\pi$
$877$	−2.32640	+	1.34315i	−0.0785568	+	0.0453548i	0.460207	+	0.887812i	$0.347775\pi$
$878$	−11.8272	+	6.82843i	−0.399148	+	0.230448i
$879$		−	3.02944i		−	0.102180i
$880$	−0.878680	−	1.52192i	−0.0296203	−	0.0513038i
$881$	26.4853	−	45.8739i	0.892312	−	1.54553i	0.0552151	−	0.998474i	$-0.482416\pi$
$881$	26.4853	−	45.8739i	0.892312	−	1.54553i	0.837097	−	0.547055i	$-0.184251\pi$
$882$	−2.26485	−	1.30761i	−0.0762615	−	0.0440296i
$883$	32.2426			1.08505			0.542526	−	0.840039i	$-0.317468\pi$
$883$	32.2426			1.08505			0.542526	+	0.840039i	$0.317468\pi$
$884$		0			0
$885$	14.4853			0.486917
$886$	−2.36245	−	1.36396i	−0.0793681	−	0.0458232i
$887$	−7.19239	+	12.4576i	−0.241497	+	0.418285i	−0.961141	−	0.276058i	$-0.910972\pi$
$887$	−7.19239	+	12.4576i	−0.241497	+	0.418285i	0.719644	+	0.694343i	$0.244305\pi$
$888$	−9.51472	−	16.4800i	−0.319293	−	0.553032i
$889$		−	7.79899i		−	0.261570i
$890$	−2.15232	+	1.24264i	−0.0721458	+	0.0416534i
$891$	−2.53653	+	1.46447i	−0.0849769	+	0.0490615i
$892$		−	48.4264i		−	1.62144i
$893$	−1.41421	−	2.44949i	−0.0473249	−	0.0819690i
$894$	−0.100505	+	0.174080i	−0.00336139	+	0.00582210i
$895$	4.89898	+	2.82843i	0.163755	+	0.0945439i
$896$	−8.74517			−0.292155
$897$		0			0
$898$	12.0589			0.402410
$899$	50.1785	+	28.9706i	1.67355	+	0.966222i
$900$	−0.914214	+	1.58346i	−0.0304738	+	0.0527821i
$901$	34.9706	+	60.5708i	1.16504	+	2.01791i
$902$			2.14214i			0.0713253i
$903$	3.11594	−	1.79899i	0.103692	−	0.0598666i
$904$	4.35562	−	2.51472i	0.144866	−	0.0836383i
$905$		0			0
$906$	−5.34315	−	9.25460i	−0.177514	−	0.307463i
$907$	−16.6066	+	28.7635i	−0.551413	+	0.955076i	0.446760	+	0.894654i	$0.352578\pi$
$907$	−16.6066	+	28.7635i	−0.551413	+	0.955076i	−0.998173	+	0.0604217i	$0.980755\pi$
$908$	−43.7936	−	25.2843i	−1.45334	−	0.839088i
$909$	7.65685			0.253962
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	12.5446	+	7.24264i	0.415394	+	0.239828i
$913$	2.58579	−	4.47871i	0.0855770	−	0.148224i
$914$	−3.72792	−	6.45695i	−0.123309	−	0.213577i
$915$			11.3137i			0.374020i
$916$	1.31178	−	0.757359i	0.0433426	−	0.0250239i
$917$	−12.1753	+	7.02944i	−0.402065	+	0.232132i
$918$			11.3137i			0.373408i
$919$	8.24264	+	14.2767i	0.271900	+	0.470944i	0.969348	−	0.245691i	$-0.0790148\pi$
$919$	8.24264	+	14.2767i	0.271900	+	0.470944i	−0.697449	+	0.716635i	$0.745681\pi$
$920$	1.12132	−	1.94218i	0.0369688	−	0.0640319i
$921$	−23.4803	−	13.5563i	−0.773702	−	0.446697i
$922$	−10.9706			−0.361296
$923$		0			0
$924$	1.25483			0.0412810
$925$	7.34847	+	4.24264i	0.241616	+	0.139497i
$926$	3.24264	−	5.61642i	0.106560	−	0.184567i
$927$	−8.70711	−	15.0812i	−0.285979	−	0.495330i
$928$		−	24.9706i		−	0.819699i
$929$	−9.67487	+	5.58579i	−0.317422	+	0.183264i	−0.650243	−	0.759726i	$-0.725333\pi$
$929$	−9.67487	+	5.58579i	−0.317422	+	0.183264i	0.332821	+	0.942990i	$0.392000\pi$
$930$	5.19615	−	3.00000i	0.170389	−	0.0983739i
$931$		−	21.5563i		−	0.706481i
$932$	22.5147	+	38.9966i	0.737494	+	1.27738i
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$	3.79733	+	2.19239i	0.124252	+	0.0717371i
$935$	2.82843			0.0924995
$936$		0			0
$937$	10.9706			0.358393			0.179196	−	0.983813i	$-0.442650\pi$
$937$	10.9706			0.358393			0.179196	+	0.983813i	$0.442650\pi$
$938$	0.594346	+	0.343146i	0.0194061	+	0.0112041i
$939$	−0.585786	+	1.01461i	−0.0191164	+	0.0331106i
$940$	−0.757359	−	1.31178i	−0.0247023	−	0.0427857i
$941$			54.7696i			1.78544i	0.450615	+	0.892718i	$0.351205\pi$
$941$			54.7696i			1.78544i	−0.450615	+	0.892718i	$0.648795\pi$
$942$	−9.13151	+	5.27208i	−0.297521	+	0.171774i
$943$	10.8126	−	6.24264i	0.352106	−	0.203288i
$944$			30.7279i			1.00011i
$945$	−2.34315	−	4.05845i	−0.0762225	−	0.132021i
$946$	0.372583	−	0.645333i	0.0121137	−	0.0209816i
$947$	39.0687	+	22.5563i	1.26956	+	0.732983i	0.974905	−	0.222620i	$-0.0714609\pi$
$947$	39.0687	+	22.5563i	1.26956	+	0.732983i	0.294658	+	0.955603i	$0.404794\pi$
$948$	21.9411			0.712615
$949$		0			0
$950$	1.41421			0.0458831
$951$	32.0174	+	18.4853i	1.03824	+	0.599426i
$952$	3.17157	−	5.49333i	0.102791	−	0.178040i
$953$	−27.6274	−	47.8521i	−0.894940	−	1.55008i	−0.833879	−	0.551947i	$-0.813885\pi$
$953$	−27.6274	−	47.8521i	−0.894940	−	1.55008i	−0.0610608	−	0.998134i	$-0.519448\pi$
$954$		−	6.00000i		−	0.194257i
$955$	−11.8272	+	6.82843i	−0.382719	+	0.220963i
$956$	0.927572	−	0.535534i	0.0299998	−	0.0173204i
$957$			4.68629i			0.151486i
$958$	1.09188	+	1.89120i	0.0352771	+	0.0611018i
$959$	−2.20101	+	3.81226i	−0.0710743	+	0.123104i
$960$	5.10911	+	2.94975i	0.164896	+	0.0952027i
$961$	−73.9117			−2.38425
$962$		0			0
$963$	6.58579			0.212224
$964$	−3.93535	−	2.27208i	−0.126749	−	0.0731787i
$965$	−7.82843	+	13.5592i	−0.252006	+	0.436487i
$966$	0.343146	+	0.594346i	0.0110405	+	0.0191228i
$967$			19.9411i			0.641263i	0.947204	+	0.320632i	$0.103895\pi$
$967$			19.9411i			0.641263i	−0.947204	+	0.320632i	$0.896105\pi$
$968$	−14.6354	+	8.44975i	−0.470399	+	0.271585i
$969$	−20.1903	+	11.6569i	−0.648605	+	0.374472i
$970$			1.51472i			0.0486347i
$971$	6.14214	+	10.6385i	0.197111	+	0.341405i	0.947590	−	0.319488i	$-0.103511\pi$
$971$	6.14214	+	10.6385i	0.197111	+	0.341405i	−0.750480	+	0.660893i	$0.770178\pi$
$972$	−9.05025	+	15.6755i	−0.290287	+	0.502792i
$973$	−8.95743	−	5.17157i	−0.287162	−	0.165793i
$974$	−9.51472			−0.304871
$975$		0			0
$976$	−24.0000			−0.768221
$977$	−48.9177	−	28.2426i	−1.56502	−	0.903562i	−0.996736	−	0.0807263i	$-0.974276\pi$
$977$	−48.9177	−	28.2426i	−1.56502	−	0.903562i	−0.568279	−	0.822836i	$-0.692391\pi$
$978$	4.38478	−	7.59466i	0.140210	−	0.242850i
$979$	1.75736	+	3.04384i	0.0561654	+	0.0972814i
$980$		−	11.5442i		−	0.368765i
$981$	−1.73205	+	1.00000i	−0.0553001	+	0.0319275i
$982$	3.88437	−	2.24264i	0.123955	−	0.0715655i
$983$		−	34.9706i		−	1.11539i	−0.830047	−	0.557694i	$-0.811686\pi$
$983$		−	34.9706i		−	1.11539i	0.830047	−	0.557694i	$-0.188314\pi$
$984$	−9.89949	−	17.1464i	−0.315584	−	0.546608i
$985$	−11.4853	+	19.8931i	−0.365951	+	0.633847i
$986$	9.79796	+	5.65685i	0.312031	+	0.180151i
$987$	0.970563			0.0308934
$988$		0			0
$989$	−4.34315			−0.138104
$990$	−0.210133	−	0.121320i	−0.00667847	−	0.00385581i
$991$	−7.51472	+	13.0159i	−0.238713	+	0.413463i	−0.960345	−	0.278814i	$-0.910059\pi$
$991$	−7.51472	+	13.0159i	−0.238713	+	0.413463i	0.721632	+	0.692277i	$0.243392\pi$
$992$	22.6066	+	39.1558i	0.717760	+	1.24320i
$993$		−	31.1716i		−	0.989200i
$994$	−2.34752	+	1.35534i	−0.0744587	+	0.0429887i
$995$	3.46410	−	2.00000i	0.109819	−	0.0634043i
$996$			22.8284i			0.723346i
$997$	−11.5858	−	20.0672i	−0.366926	−	0.635534i	0.622158	−	0.782892i	$-0.286256\pi$
$997$	−11.5858	−	20.0672i	−0.366926	−	0.635534i	−0.989083	+	0.147358i	$0.952923\pi$
$998$	2.16295	−	3.74634i	0.0684670	−	0.118588i
$999$	41.5692	+	24.0000i	1.31519	+	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.f.316.3		8
13.2	odd	12		845.2.e.c.146.2		4
13.3	even	3	inner	845.2.m.f.361.2		8
13.4	even	6		845.2.c.b.506.3		4
13.5	odd	4		845.2.e.c.191.2		4
13.6	odd	12		845.2.a.g.1.1		2
13.7	odd	12		65.2.a.b.1.2	✓	2
13.8	odd	4		845.2.e.h.191.1		4
13.9	even	3		845.2.c.b.506.2		4
13.10	even	6	inner	845.2.m.f.361.3		8
13.11	odd	12		845.2.e.h.146.1		4
13.12	even	2	inner	845.2.m.f.316.2		8
39.20	even	12		585.2.a.m.1.1		2
39.32	even	12		7605.2.a.x.1.2		2
52.7	even	12		1040.2.a.j.1.1		2
65.7	even	12		325.2.b.f.274.3		4
65.19	odd	12		4225.2.a.r.1.2		2
65.33	even	12		325.2.b.f.274.2		4
65.59	odd	12		325.2.a.i.1.1		2
91.20	even	12		3185.2.a.j.1.2		2
104.59	even	12		4160.2.a.z.1.2		2
104.85	odd	12		4160.2.a.bf.1.1		2
143.98	even	12		7865.2.a.j.1.1		2
156.59	odd	12		9360.2.a.cd.1.2		2
195.59	even	12		2925.2.a.u.1.2		2
195.98	odd	12		2925.2.c.r.2224.3		4
195.137	odd	12		2925.2.c.r.2224.2		4
260.59	even	12		5200.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.b.1.2	✓	2	13.7	odd	12
325.2.a.i.1.1		2	65.59	odd	12
325.2.b.f.274.2		4	65.33	even	12
325.2.b.f.274.3		4	65.7	even	12
585.2.a.m.1.1		2	39.20	even	12
845.2.a.g.1.1		2	13.6	odd	12
845.2.c.b.506.2		4	13.9	even	3
845.2.c.b.506.3		4	13.4	even	6
845.2.e.c.146.2		4	13.2	odd	12
845.2.e.c.191.2		4	13.5	odd	4
845.2.e.h.146.1		4	13.11	odd	12
845.2.e.h.191.1		4	13.8	odd	4
845.2.m.f.316.2		8	13.12	even	2	inner
845.2.m.f.316.3		8	1.1	even	1	trivial
845.2.m.f.361.2		8	13.3	even	3	inner
845.2.m.f.361.3		8	13.10	even	6	inner
1040.2.a.j.1.1		2	52.7	even	12
2925.2.a.u.1.2		2	195.59	even	12
2925.2.c.r.2224.2		4	195.137	odd	12
2925.2.c.r.2224.3		4	195.98	odd	12
3185.2.a.j.1.2		2	91.20	even	12
4160.2.a.z.1.2		2	104.59	even	12
4160.2.a.bf.1.1		2	104.85	odd	12
4225.2.a.r.1.2		2	65.19	odd	12
5200.2.a.bu.1.2		2	260.59	even	12
7605.2.a.x.1.2		2	39.32	even	12
7865.2.a.j.1.1		2	143.98	even	12
9360.2.a.cd.1.2		2	156.59	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.358719 + 0.207107i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000i q^{5} +(-0.507306 + 0.292893i) q^{6} +(-0.717439 + 0.414214i) q^{7} -1.58579i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.207107 - 0.358719i) q^{10} +(-0.507306 - 0.292893i) q^{11} +2.58579 q^{12} -0.343146 q^{14} +(1.22474 + 0.707107i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-2.41421 - 4.18154i) q^{17} +0.414214i q^{18} +(-2.95680 + 1.70711i) q^{19} +(-1.58346 + 0.914214i) q^{20} -1.17157i q^{21} +(-0.121320 - 0.210133i) q^{22} +(-0.707107 + 1.22474i) q^{23} +(1.94218 + 1.12132i) q^{24} -1.00000 q^{25} -5.65685 q^{27} +(1.31178 + 0.757359i) q^{28} +(-2.82843 + 4.89898i) q^{29} +(0.292893 + 0.507306i) q^{30} -10.2426i q^{31} +(-3.82282 + 2.20711i) q^{32} +(0.717439 - 0.414214i) q^{33} -2.00000i q^{34} +(0.414214 + 0.717439i) q^{35} +(0.914214 - 1.58346i) q^{36} +(-7.34847 - 4.24264i) q^{37} -1.41421 q^{38} -1.58579 q^{40} +(-7.64564 - 4.41421i) q^{41} +(0.242641 - 0.420266i) q^{42} +(1.53553 + 2.65962i) q^{43} +1.07107i q^{44} +(0.866025 - 0.500000i) q^{45} +(-0.507306 + 0.292893i) q^{46} +0.828427i q^{47} +(-2.12132 - 3.67423i) q^{48} +(-3.15685 + 5.46783i) q^{49} +(-0.358719 - 0.207107i) q^{50} +6.82843 q^{51} -14.4853 q^{53} +(-2.02922 - 1.17157i) q^{54} +(-0.292893 + 0.507306i) q^{55} +(0.656854 + 1.13770i) q^{56} -4.82843i q^{57} +(-2.02922 + 1.17157i) q^{58} +(8.87039 - 5.12132i) q^{59} -2.58579i q^{60} +(4.00000 + 6.92820i) q^{61} +(2.12132 - 3.67423i) q^{62} +(-0.717439 - 0.414214i) q^{63} +4.17157 q^{64} +0.343146 q^{66} +(-1.73205 - 1.00000i) q^{67} +(-4.41421 + 7.64564i) q^{68} +(-1.00000 - 1.73205i) q^{69} +0.343146i q^{70} +(6.84116 - 3.94975i) q^{71} +(1.37333 - 0.792893i) q^{72} -8.48528i q^{73} +(-1.75736 - 3.04384i) q^{74} +(0.707107 - 1.22474i) q^{75} +(5.40629 + 3.12132i) q^{76} +0.485281 q^{77} +8.48528 q^{79} +(2.59808 + 1.50000i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-1.82843 - 3.16693i) q^{82} +8.82843i q^{83} +(-1.85514 + 1.07107i) q^{84} +(-4.18154 + 2.41421i) q^{85} +1.27208i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.464466 + 0.804479i) q^{88} +(-5.19615 - 3.00000i) q^{89} +0.414214 q^{90} +2.58579 q^{92} +(12.5446 + 7.24264i) q^{93} +(-0.171573 + 0.297173i) q^{94} +(1.70711 + 2.95680i) q^{95} -6.24264i q^{96} +(-3.16693 + 1.82843i) q^{97} +(-2.26485 + 1.30761i) q^{98} -0.585786i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{9} - 4 q^{10} + 32 q^{12} - 48 q^{14} - 12 q^{16} - 8 q^{17} + 16 q^{22} - 8 q^{25} + 8 q^{30} - 8 q^{35} - 4 q^{36} - 24 q^{40} - 32 q^{42} - 16 q^{43} + 20 q^{49} + 32 q^{51} - 48 q^{53}+ \cdots + 8 q^{95}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^9 - 4 * q^10 + 32 * q^12 - 48 * q^14 - 12 * q^16 - 8 * q^17 + 16 * q^22 - 8 * q^25 + 8 * q^30 - 8 * q^35 - 4 * q^36 - 24 * q^40 - 32 * q^42 - 16 * q^43 + 20 * q^49 + 32 * q^51 - 48 * q^53 - 8 * q^55 - 40 * q^56 + 32 * q^61 + 56 * q^64 + 48 * q^66 - 24 * q^68 - 8 * q^69 - 48 * q^74 - 64 * q^77 + 20 * q^81 + 8 * q^82 - 32 * q^87 - 32 * q^88 - 8 * q^90 + 32 * q^92 - 24 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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