LMFDB - Embedded newform 845.2.m.f.316.1

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)

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);

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")

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			316.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	845.316
Dual form			845.2.m.f.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.09077 - 1.20711i) q^{2} +(0.707107 - 1.22474i) q^{3} +(1.91421 + 3.31552i) q^{4} -1.00000i q^{5} +(-2.95680 + 1.70711i) q^{6} +(4.18154 - 2.41421i) q^{7} -4.41421i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.20711 + 2.09077i) q^{10} +(-2.95680 - 1.70711i) q^{11} +5.41421 q^{12} -11.6569 q^{14} +(-1.22474 - 0.707107i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.414214 + 0.717439i) q^{17} -2.41421i q^{18} +(-0.507306 + 0.292893i) q^{19} +(3.31552 - 1.91421i) q^{20} -6.82843i q^{21} +(4.12132 + 7.13834i) q^{22} +(0.707107 - 1.22474i) q^{23} +(-5.40629 - 3.12132i) q^{24} -1.00000 q^{25} +5.65685 q^{27} +(16.0087 + 9.24264i) q^{28} +(2.82843 - 4.89898i) q^{29} +(1.70711 + 2.95680i) q^{30} -1.75736i q^{31} +(-1.37333 + 0.792893i) q^{32} +(-4.18154 + 2.41421i) q^{33} -2.00000i q^{34} +(-2.41421 - 4.18154i) q^{35} +(-1.91421 + 3.31552i) q^{36} +(7.34847 + 4.24264i) q^{37} +1.41421 q^{38} -4.41421 q^{40} +(-2.74666 - 1.58579i) q^{41} +(-8.24264 + 14.2767i) q^{42} +(-5.53553 - 9.58783i) q^{43} -13.0711i q^{44} +(0.866025 - 0.500000i) q^{45} +(-2.95680 + 1.70711i) q^{46} -4.82843i q^{47} +(2.12132 + 3.67423i) q^{48} +(8.15685 - 14.1281i) q^{49} +(2.09077 + 1.20711i) q^{50} +1.17157 q^{51} +2.48528 q^{53} +(-11.8272 - 6.82843i) q^{54} +(-1.70711 + 2.95680i) q^{55} +(-10.6569 - 18.4582i) q^{56} +0.828427i q^{57} +(-11.8272 + 6.82843i) q^{58} +(1.52192 - 0.878680i) q^{59} -5.41421i q^{60} +(4.00000 + 6.92820i) q^{61} +(-2.12132 + 3.67423i) q^{62} +(4.18154 + 2.41421i) q^{63} +9.82843 q^{64} +11.6569 q^{66} +(-1.73205 - 1.00000i) q^{67} +(-1.58579 + 2.74666i) q^{68} +(-1.00000 - 1.73205i) q^{69} +11.6569i q^{70} +(-10.3053 + 5.94975i) q^{71} +(3.82282 - 2.20711i) q^{72} +8.48528i q^{73} +(-10.2426 - 17.7408i) q^{74} +(-0.707107 + 1.22474i) q^{75} +(-1.94218 - 1.12132i) q^{76} -16.4853 q^{77} -8.48528 q^{79} +(2.59808 + 1.50000i) q^{80} +(2.50000 - 4.33013i) q^{81} +(3.82843 + 6.63103i) q^{82} +3.17157i q^{83} +(22.6398 - 13.0711i) q^{84} +(0.717439 - 0.414214i) q^{85} +26.7279i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-7.53553 + 13.0519i) q^{88} +(-5.19615 - 3.00000i) q^{89} -2.41421 q^{90} +5.41421 q^{92} +(-2.15232 - 1.24264i) q^{93} +(-5.82843 + 10.0951i) q^{94} +(0.292893 + 0.507306i) q^{95} +2.24264i q^{96} +(6.63103 - 3.82843i) q^{97} +(-34.1082 + 19.6924i) q^{98} -3.41421i 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 $

$2$	−2.09077	−	1.20711i	−1.47840	−	0.853553i	−0.478696	−	0.877981i	$-0.658890\pi$
$2$	−2.09077	−	1.20711i	−1.47840	−	0.853553i	−0.999702	+	0.0244272i	$0.992224\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	−0.586445	−	0.809989i	$-0.699473\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	0.994694	+	0.102882i	$0.0328064\pi$
$4$	1.91421	+	3.31552i	0.957107	+	1.65776i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.95680	+	1.70711i	−1.20711	+	0.696923i
$7$	4.18154	−	2.41421i	1.58047	−	0.912487i	0.585684	−	0.810539i	$-0.300826\pi$
$7$	4.18154	−	2.41421i	1.58047	−	0.912487i	0.994790	−	0.101947i	$-0.0325074\pi$
$8$		−	4.41421i		−	1.56066i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.20711	+	2.09077i	−0.381721	+	0.661160i
$11$	−2.95680	−	1.70711i	−0.891507	−	0.514712i	−0.0170722	−	0.999854i	$-0.505435\pi$
$11$	−2.95680	−	1.70711i	−0.891507	−	0.514712i	−0.874435	+	0.485142i	$0.838768\pi$
$12$	5.41421			1.56295
$13$		0			0
$13$		0			0
$14$	−11.6569			−3.11543
$15$	−1.22474	−	0.707107i	−0.316228	−	0.182574i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	0.414214	+	0.717439i	0.100462	+	0.174005i	0.911875	−	0.410468i	$-0.134635\pi$
$17$	0.414214	+	0.717439i	0.100462	+	0.174005i	−0.811413	+	0.584473i	$0.801301\pi$
$18$		−	2.41421i		−	0.569036i
$19$	−0.507306	+	0.292893i	−0.116384	+	0.0671943i	−0.557062	−	0.830471i	$-0.688071\pi$
$19$	−0.507306	+	0.292893i	−0.116384	+	0.0671943i	0.440678	+	0.897665i	$0.354738\pi$
$20$	3.31552	−	1.91421i	0.741372	−	0.428031i
$21$		−	6.82843i		−	1.49008i
$22$	4.12132	+	7.13834i	0.878668	+	1.52190i
$23$	0.707107	−	1.22474i	0.147442	−	0.255377i	−0.782839	−	0.622224i	$-0.786229\pi$
$23$	0.707107	−	1.22474i	0.147442	−	0.255377i	0.930281	+	0.366847i	$0.119563\pi$
$24$	−5.40629	−	3.12132i	−1.10355	−	0.637137i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.65685			1.08866
$28$	16.0087	+	9.24264i	3.02536	+	1.74669i
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	−0.474343	−	0.880340i	$-0.657314\pi$
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	0.999568	−	0.0293774i	$-0.00935245\pi$
$30$	1.70711	+	2.95680i	0.311674	+	0.539835i
$31$		−	1.75736i		−	0.315631i	−0.987469	−	0.157816i	$-0.949555\pi$
$31$		−	1.75736i		−	0.315631i	0.987469	−	0.157816i	$-0.0504451\pi$
$32$	−1.37333	+	0.792893i	−0.242773	+	0.140165i
$33$	−4.18154	+	2.41421i	−0.727913	+	0.420261i
$34$		−	2.00000i		−	0.342997i
$35$	−2.41421	−	4.18154i	−0.408077	−	0.706809i
$36$	−1.91421	+	3.31552i	−0.319036	+	0.552586i
$37$	7.34847	+	4.24264i	1.20808	+	0.697486i	0.962340	−	0.271850i	$-0.0876353\pi$
$37$	7.34847	+	4.24264i	1.20808	+	0.697486i	0.245741	+	0.969335i	$0.420969\pi$
$38$	1.41421			0.229416
$39$		0			0
$40$	−4.41421			−0.697948
$41$	−2.74666	−	1.58579i	−0.428957	−	0.247658i	0.269945	−	0.962876i	$-0.412994\pi$
$41$	−2.74666	−	1.58579i	−0.428957	−	0.247658i	−0.698902	+	0.715217i	$0.746328\pi$
$42$	−8.24264	+	14.2767i	−1.27187	+	2.20294i
$43$	−5.53553	−	9.58783i	−0.844161	−	1.46213i	−0.886348	−	0.463020i	$-0.846766\pi$
$43$	−5.53553	−	9.58783i	−0.844161	−	1.46213i	0.0421868	−	0.999110i	$-0.486568\pi$
$44$		−	13.0711i		−	1.97054i
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$	−2.95680	+	1.70711i	−0.435956	+	0.251699i
$47$		−	4.82843i		−	0.704298i	−0.935944	−	0.352149i	$-0.885451\pi$
$47$		−	4.82843i		−	0.704298i	0.935944	−	0.352149i	$-0.114549\pi$
$48$	2.12132	+	3.67423i	0.306186	+	0.530330i
$49$	8.15685	−	14.1281i	1.16526	−	2.01830i
$50$	2.09077	+	1.20711i	0.295680	+	0.170711i
$51$	1.17157			0.164053
$52$		0			0
$53$	2.48528			0.341380			0.170690	−	0.985325i	$-0.445400\pi$
$53$	2.48528			0.341380			0.170690	+	0.985325i	$0.445400\pi$
$54$	−11.8272	−	6.82843i	−1.60948	−	0.929231i
$55$	−1.70711	+	2.95680i	−0.230186	+	0.398694i
$56$	−10.6569	−	18.4582i	−1.42408	−	2.46658i
$57$			0.828427i			0.109728i
$58$	−11.8272	+	6.82843i	−1.55299	+	0.896616i
$59$	1.52192	−	0.878680i	0.198137	−	0.114394i	−0.397649	−	0.917537i	$-0.630174\pi$
$59$	1.52192	−	0.878680i	0.198137	−	0.114394i	0.595786	+	0.803143i	$0.296841\pi$
$60$		−	5.41421i		−	0.698972i
$61$	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
$63$	4.18154	+	2.41421i	0.526825	+	0.304162i
$64$	9.82843			1.22855
$65$		0			0
$66$	11.6569			1.43486
$67$	−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	$0.705652\pi$
$68$	−1.58579	+	2.74666i	−0.192305	+	0.333082i
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$			11.6569i			1.39326i
$71$	−10.3053	+	5.94975i	−1.22301	+	0.706105i	−0.965558	−	0.260186i	$-0.916216\pi$
$71$	−10.3053	+	5.94975i	−1.22301	+	0.706105i	−0.257451	+	0.966291i	$0.582883\pi$
$72$	3.82282	−	2.20711i	0.450524	−	0.260110i
$73$			8.48528i			0.993127i	0.868000	+	0.496564i	$0.165405\pi$
$73$			8.48528i			0.993127i	−0.868000	+	0.496564i	$0.834595\pi$
$74$	−10.2426	−	17.7408i	−1.19068	−	2.06232i
$75$	−0.707107	+	1.22474i	−0.0816497	+	0.141421i
$76$	−1.94218	−	1.12132i	−0.222784	−	0.128624i
$77$	−16.4853			−1.87867
$78$		0			0
$79$	−8.48528			−0.954669			−0.477334	−	0.878722i	$-0.658397\pi$
$79$	−8.48528			−0.954669			−0.477334	+	0.878722i	$0.658397\pi$
$80$	2.59808	+	1.50000i	0.290474	+	0.167705i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	3.82843	+	6.63103i	0.422779	+	0.732275i
$83$			3.17157i			0.348125i	0.984735	+	0.174063i	$0.0556895\pi$
$83$			3.17157i			0.348125i	−0.984735	+	0.174063i	$0.944310\pi$
$84$	22.6398	−	13.0711i	2.47020	−	1.42617i
$85$	0.717439	−	0.414214i	0.0778172	−	0.0449278i
$86$			26.7279i			2.88215i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	−7.53553	+	13.0519i	−0.803291	+	1.39134i
$89$	−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	$0.769678\pi$
$90$	−2.41421			−0.254480
$91$		0			0
$92$	5.41421			0.564471
$93$	−2.15232	−	1.24264i	−0.223185	−	0.128856i
$94$	−5.82843	+	10.0951i	−0.601156	+	1.04123i
$95$	0.292893	+	0.507306i	0.0300502	+	0.0520485i
$96$			2.24264i			0.228889i
$97$	6.63103	−	3.82843i	0.673279	−	0.388718i	−0.124039	−	0.992277i	$-0.539585\pi$
$97$	6.63103	−	3.82843i	0.673279	−	0.388718i	0.797318	+	0.603559i	$0.206251\pi$
$98$	−34.1082	+	19.6924i	−3.44545	+	1.98923i
$99$		−	3.41421i		−	0.343141i
$100$	−1.91421	−	3.31552i	−0.191421	−	0.331552i
$101$	−1.82843	+	3.16693i	−0.181935	+	0.315121i	−0.942540	−	0.334095i	$-0.891569\pi$
$101$	−1.82843	+	3.16693i	−0.181935	+	0.315121i	0.760604	+	0.649216i	$0.224903\pi$
$102$	−2.44949	−	1.41421i	−0.242536	−	0.140028i
$103$	−14.5858			−1.43718			−0.718590	−	0.695434i	$-0.755212\pi$
$103$	−14.5858			−1.43718			−0.718590	+	0.695434i	$0.755212\pi$
$104$		0			0
$105$	−6.82843			−0.666386
$106$	−5.19615	−	3.00000i	−0.504695	−	0.291386i
$107$	4.70711	−	8.15295i	0.455053	−	0.788175i	−0.543638	−	0.839320i	$-0.682954\pi$
$107$	4.70711	−	8.15295i	0.455053	−	0.788175i	0.998691	+	0.0511445i	$0.0162869\pi$
$108$	10.8284	+	18.7554i	1.04197	+	1.80474i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	7.13834	−	4.12132i	0.680614	−	0.392952i
$111$	10.3923	−	6.00000i	0.986394	−	0.569495i
$112$			14.4853i			1.36873i
$113$	4.41421	+	7.64564i	0.415254	+	0.719242i	0.995455	−	0.0952319i	$-0.0303593\pi$
$113$	4.41421	+	7.64564i	0.415254	+	0.719242i	−0.580201	+	0.814473i	$0.697026\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	−1.22474	−	0.707107i	−0.114208	−	0.0659380i
$116$	21.6569			2.01079
$117$		0			0
$118$	−4.24264			−0.390567
$119$	3.46410	+	2.00000i	0.317554	+	0.183340i
$120$	−3.12132	+	5.40629i	−0.284936	+	0.493524i
$121$	0.328427	+	0.568852i	0.0298570	+	0.0517139i
$122$		−	19.3137i		−	1.74858i
$123$	−3.88437	+	2.24264i	−0.350242	+	0.202212i
$124$	5.82655	−	3.36396i	0.523240	−	0.302093i
$125$			1.00000i			0.0894427i
$126$	−5.82843	−	10.0951i	−0.519238	−	0.899346i
$127$	−3.29289	+	5.70346i	−0.292197	+	0.506100i	−0.974329	−	0.225129i	$-0.927720\pi$
$127$	−3.29289	+	5.70346i	−0.292197	+	0.506100i	0.682132	+	0.731229i	$0.261053\pi$
$128$	−17.8023	−	10.2782i	−1.57352	−	0.908471i
$129$	−15.6569			−1.37851
$130$		0			0
$131$	−16.9706			−1.48272			−0.741362	−	0.671105i	$-0.765820\pi$
$131$	−16.9706			−1.48272			−0.741362	+	0.671105i	$0.765820\pi$
$132$	−16.0087	−	9.24264i	−1.39338	−	0.804469i
$133$	−1.41421	+	2.44949i	−0.122628	+	0.212398i
$134$	2.41421	+	4.18154i	0.208556	+	0.361230i
$135$		−	5.65685i		−	0.486864i
$136$	3.16693	−	1.82843i	0.271562	−	0.156786i
$137$	−14.9941	+	8.65685i	−1.28103	+	0.739605i	−0.977037	−	0.213068i	$-0.931654\pi$
$137$	−14.9941	+	8.65685i	−1.28103	+	0.739605i	−0.303996	+	0.952673i	$0.598321\pi$
$138$			4.82843i			0.411023i
$139$	−2.24264	−	3.88437i	−0.190218	−	0.329468i	0.755104	−	0.655605i	$-0.227586\pi$
$139$	−2.24264	−	3.88437i	−0.190218	−	0.329468i	−0.945323	+	0.326137i	$0.894253\pi$
$140$	9.24264	−	16.0087i	0.781146	−	1.35298i
$141$	−5.91359	−	3.41421i	−0.498014	−	0.287529i
$142$	28.7279			2.41079
$143$		0			0
$144$	−3.00000			−0.250000
$145$	−4.89898	−	2.82843i	−0.406838	−	0.234888i
$146$	10.2426	−	17.7408i	0.847687	−	1.46824i
$147$	−11.5355	−	19.9801i	−0.951435	−	1.64793i
$148$			32.4853i			2.67027i
$149$	10.0951	−	5.82843i	0.827025	−	0.477483i	−0.0258077	−	0.999667i	$-0.508216\pi$
$149$	10.0951	−	5.82843i	0.827025	−	0.477483i	0.852833	+	0.522184i	$0.174882\pi$
$150$	2.95680	−	1.70711i	0.241421	−	0.139385i
$151$			9.75736i			0.794043i	0.917809	+	0.397021i	$0.129956\pi$
$151$			9.75736i			0.794043i	−0.917809	+	0.397021i	$0.870044\pi$
$152$	1.29289	+	2.23936i	0.104867	+	0.181636i
$153$	−0.414214	+	0.717439i	−0.0334872	+	0.0580015i
$154$	34.4669	+	19.8995i	2.77742	+	1.60355i
$155$	−1.75736			−0.141154
$156$		0			0
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$	17.7408	+	10.2426i	1.41138	+	0.814861i
$159$	1.75736	−	3.04384i	0.139368	−	0.241392i
$160$	0.792893	+	1.37333i	0.0626837	+	0.108571i
$161$		−	6.82843i		−	0.538155i
$162$	−10.4539	+	6.03553i	−0.821332	+	0.474196i
$163$	16.4290	−	9.48528i	1.28682	−	0.742945i	0.308732	−	0.951149i	$-0.400095\pi$
$163$	16.4290	−	9.48528i	1.28682	−	0.742945i	0.978085	+	0.208204i	$0.0667619\pi$
$164$		−	12.1421i		−	0.948141i
$165$	2.41421	+	4.18154i	0.187946	+	0.325532i
$166$	3.82843	−	6.63103i	0.297144	−	0.514668i
$167$	2.74666	+	1.58579i	0.212543	+	0.122712i	0.602493	−	0.798124i	$-0.294174\pi$
$167$	2.74666	+	1.58579i	0.212543	+	0.122712i	−0.389950	+	0.920836i	$0.627508\pi$
$168$	−30.1421			−2.32552
$169$		0			0
$170$	−2.00000			−0.153393
$171$	−0.507306	−	0.292893i	−0.0387947	−	0.0223981i
$172$	21.1924	−	36.7063i	1.61590	−	2.79883i
$173$	8.41421	+	14.5738i	0.639721	+	1.10803i	0.985494	+	0.169711i	$0.0542834\pi$
$173$	8.41421	+	14.5738i	0.639721	+	1.10803i	−0.345773	+	0.938318i	$0.612383\pi$
$174$			19.3137i			1.46417i
$175$	−4.18154	+	2.41421i	−0.316095	+	0.182497i
$176$	8.87039	−	5.12132i	0.668631	−	0.386034i
$177$		−	2.48528i		−	0.186805i
$178$	7.24264	+	12.5446i	0.542859	+	0.940259i
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	−0.740748	−	0.671783i	$-0.765529\pi$
$179$	2.82843	−	4.89898i	0.211407	−	0.366167i	0.952155	+	0.305616i	$0.0988623\pi$
$180$	3.31552	+	1.91421i	0.247124	+	0.142677i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	11.3137			0.836333
$184$	−5.40629	−	3.12132i	−0.398557	−	0.230107i
$185$	4.24264	−	7.34847i	0.311925	−	0.540270i
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$		−	2.82843i		−	0.206835i
$188$	16.0087	−	9.24264i	1.16756	−	0.674089i
$189$	23.6544	−	13.6569i	1.72060	−	0.993390i
$190$		−	1.41421i		−	0.102598i
$191$	−1.17157	−	2.02922i	−0.0847720	−	0.146829i	0.820522	−	0.571615i	$-0.193683\pi$
$191$	−1.17157	−	2.02922i	−0.0847720	−	0.146829i	−0.905294	+	0.424785i	$0.860350\pi$
$192$	6.94975	−	12.0373i	0.501555	−	0.868718i
$193$	−3.76127	−	2.17157i	−0.270742	−	0.156313i	0.358483	−	0.933536i	$-0.383294\pi$
$193$	−3.76127	−	2.17157i	−0.270742	−	0.156313i	−0.629225	+	0.777223i	$0.716628\pi$
$194$	−18.4853			−1.32717
$195$		0			0
$196$	62.4558			4.46113
$197$	9.50079	+	5.48528i	0.676903	+	0.390810i	0.798687	−	0.601746i	$-0.205528\pi$
$197$	9.50079	+	5.48528i	0.676903	+	0.390810i	−0.121784	+	0.992557i	$0.538862\pi$
$198$	−4.12132	+	7.13834i	−0.292889	+	0.507299i
$199$	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	$0.788052\pi$
$200$			4.41421i			0.312132i
$201$	−2.44949	+	1.41421i	−0.172774	+	0.0997509i
$202$	7.64564	−	4.41421i	0.537946	−	0.310583i
$203$		−	27.3137i		−	1.91705i
$204$	2.24264	+	3.88437i	0.157016	+	0.271960i
$205$	−1.58579	+	2.74666i	−0.110756	+	0.191835i
$206$	30.4955	+	17.6066i	2.12472	+	1.22671i
$207$	1.41421			0.0982946
$208$		0			0
$209$	2.00000			0.138343
$210$	14.2767	+	8.24264i	0.985184	+	0.568796i
$211$	−1.65685	+	2.86976i	−0.114063	+	0.197562i	−0.917405	−	0.397956i	$-0.869720\pi$
$211$	−1.65685	+	2.86976i	−0.114063	+	0.197562i	0.803342	+	0.595518i	$0.203053\pi$
$212$	4.75736	+	8.23999i	0.326737	+	0.565925i
$213$			16.8284i			1.15306i
$214$	−19.6830	+	11.3640i	−1.34550	+	0.776824i
$215$	−9.58783	+	5.53553i	−0.653884	+	0.377520i
$216$		−	24.9706i		−	1.69903i
$217$	−4.24264	−	7.34847i	−0.288009	−	0.498847i
$218$	2.41421	−	4.18154i	0.163511	−	0.283210i
$219$	10.3923	+	6.00000i	0.702247	+	0.405442i
$220$	−13.0711			−0.881251
$221$		0			0
$222$	−28.9706			−1.94438
$223$	8.23999	+	4.75736i	0.551790	+	0.318576i	0.749844	−	0.661615i	$-0.230129\pi$
$223$	8.23999	+	4.75736i	0.551790	+	0.318576i	−0.198053	+	0.980191i	$0.563462\pi$
$224$	−3.82843	+	6.63103i	−0.255798	+	0.443054i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		−	21.3137i		−	1.41777i
$227$	14.1536	−	8.17157i	0.939406	−	0.542366i	0.0496320	−	0.998768i	$-0.484195\pi$
$227$	14.1536	−	8.17157i	0.939406	−	0.542366i	0.889774	+	0.456401i	$0.150862\pi$
$228$	−2.74666	+	1.58579i	−0.181902	+	0.105021i
$229$		−	4.82843i		−	0.319071i	−0.987192	−	0.159536i	$-0.949000\pi$
$229$		−	4.82843i		−	0.319071i	0.987192	−	0.159536i	$-0.0509997\pi$
$230$	1.70711	+	2.95680i	0.112563	+	0.194965i
$231$	−11.6569	+	20.1903i	−0.766965	+	1.32842i
$232$	−21.6251	−	12.4853i	−1.41976	−	0.819699i
$233$	20.6274			1.35135			0.675674	−	0.737201i	$-0.263853\pi$
$233$	20.6274			1.35135			0.675674	+	0.737201i	$0.263853\pi$
$234$		0			0
$235$	−4.82843			−0.314972
$236$	5.82655	+	3.36396i	0.379276	+	0.218975i
$237$	−6.00000	+	10.3923i	−0.389742	+	0.675053i
$238$	−4.82843	−	8.36308i	−0.312980	−	0.542098i
$239$			3.41421i			0.220847i	0.993885	+	0.110424i	$0.0352207\pi$
$239$			3.41421i			0.220847i	−0.993885	+	0.110424i	$0.964779\pi$
$240$	3.67423	−	2.12132i	0.237171	−	0.136931i
$241$	−12.5446	+	7.24264i	−0.808070	+	0.466539i	−0.846285	−	0.532730i	$-0.821166\pi$
$241$	−12.5446	+	7.24264i	−0.808070	+	0.466539i	0.0382151	+	0.999270i	$0.487833\pi$
$242$		−	1.58579i		−	0.101938i
$243$	4.94975	+	8.57321i	0.317526	+	0.549972i
$244$	−15.3137	+	26.5241i	−0.980360	+	1.69803i
$245$	−14.1281	−	8.15685i	−0.902610	−	0.521122i
$246$	10.8284			0.690395
$247$		0			0
$248$	−7.75736			−0.492593
$249$	3.88437	+	2.24264i	0.246162	+	0.142122i
$250$	1.20711	−	2.09077i	0.0763441	−	0.132232i
$251$	9.89949	+	17.1464i	0.624851	+	1.08227i	0.988570	+	0.150764i	$0.0481735\pi$
$251$	9.89949	+	17.1464i	0.624851	+	1.08227i	−0.363719	+	0.931509i	$0.618493\pi$
$252$			18.4853i			1.16446i
$253$	−4.18154	+	2.41421i	−0.262891	+	0.151780i
$254$	13.7694	−	7.94975i	0.863967	−	0.498812i
$255$		−	1.17157i		−	0.0733667i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	13.8284	−	23.9515i	0.862594	−	1.49406i	−0.00682332	−	0.999977i	$-0.502172\pi$
$257$	13.8284	−	23.9515i	0.862594	−	1.49406i	0.869417	−	0.494079i	$-0.164495\pi$
$258$	32.7349	+	18.8995i	2.03798	+	1.17663i
$259$	40.9706			2.54579
$260$		0			0
$261$	5.65685			0.350150
$262$	35.4815	+	20.4853i	2.19206	+	1.26558i
$263$	5.29289	−	9.16756i	0.326374	−	0.565296i	−0.655416	−	0.755268i	$-0.727507\pi$
$263$	5.29289	−	9.16756i	0.326374	−	0.565296i	0.981789	+	0.189972i	$0.0608399\pi$
$264$	10.6569	+	18.4582i	0.655884	+	1.13602i
$265$		−	2.48528i		−	0.152670i
$266$	5.91359	−	3.41421i	0.362586	−	0.209339i
$267$	−7.34847	+	4.24264i	−0.449719	+	0.259645i
$268$		−	7.65685i		−	0.467717i
$269$	12.6569	+	21.9223i	0.771702	+	1.33663i	0.936630	+	0.350321i	$0.113928\pi$
$269$	12.6569	+	21.9223i	0.771702	+	1.33663i	−0.164928	+	0.986306i	$0.552739\pi$
$270$	−6.82843	+	11.8272i	−0.415565	+	0.719779i
$271$	−23.1471	−	13.3640i	−1.40608	−	0.811803i	−0.411076	−	0.911601i	$-0.634847\pi$
$271$	−23.1471	−	13.3640i	−1.40608	−	0.811803i	−0.995008	+	0.0997982i	$0.968180\pi$
$272$	−2.48528			−0.150692
$273$		0			0
$274$	41.7990			2.52517
$275$	2.95680	+	1.70711i	0.178301	+	0.102942i
$276$	3.82843	−	6.63103i	0.230444	−	0.399141i
$277$	−6.41421	−	11.1097i	−0.385393	−	0.667520i	0.606431	−	0.795136i	$-0.292601\pi$
$277$	−6.41421	−	11.1097i	−0.385393	−	0.667520i	−0.991824	+	0.127616i	$0.959267\pi$
$278$			10.8284i			0.649446i
$279$	1.52192	−	0.878680i	0.0911148	−	0.0526052i
$280$	−18.4582	+	10.6569i	−1.10309	+	0.636869i
$281$			21.7990i			1.30042i	0.759755	+	0.650209i	$0.225319\pi$
$281$			21.7990i			1.30042i	−0.759755	+	0.650209i	$0.774681\pi$
$282$	8.24264	+	14.2767i	0.490842	+	0.850163i
$283$	−8.36396	+	14.4868i	−0.497186	+	0.861151i	−0.999995	−	0.00324643i	$-0.998967\pi$
$283$	−8.36396	+	14.4868i	−0.497186	+	0.861151i	0.502809	+	0.864398i	$0.332300\pi$
$284$	−39.4530	−	22.7782i	−2.34110	−	1.35164i
$285$	0.828427			0.0490718
$286$		0			0
$287$	−15.3137			−0.903940
$288$	−1.37333	−	0.792893i	−0.0809243	−	0.0467217i
$289$	8.15685	−	14.1281i	0.479815	−	0.831064i
$290$	6.82843	+	11.8272i	0.400979	+	0.694516i
$291$		−	10.8284i		−	0.634774i
$292$	−28.1331	+	16.2426i	−1.64636	+	0.950529i
$293$	22.6398	−	13.0711i	1.32263	−	0.763620i	0.338481	−	0.940973i	$-0.390087\pi$
$293$	22.6398	−	13.0711i	1.32263	−	0.763620i	0.984147	+	0.177353i	$0.0567535\pi$
$294$			55.6985i			3.24840i
$295$	−0.878680	−	1.52192i	−0.0511587	−	0.0886095i
$296$	18.7279	−	32.4377i	1.08854	−	1.88540i
$297$	−16.7262	−	9.65685i	−0.970550	−	0.560348i
$298$	−28.1421			−1.63023
$299$		0			0
$300$	−5.41421			−0.312590
$301$	−46.2941	−	26.7279i	−2.66835	−	1.54057i
$302$	11.7782	−	20.4004i	0.677758	−	1.17391i
$303$	2.58579	+	4.47871i	0.148550	+	0.257295i
$304$		−	1.75736i		−	0.100791i
$305$	6.92820	−	4.00000i	0.396708	−	0.229039i
$306$	1.73205	−	1.00000i	0.0990148	−	0.0571662i
$307$			24.8284i			1.41703i	0.705694	+	0.708517i	$0.250635\pi$
$307$			24.8284i			1.41703i	−0.705694	+	0.708517i	$0.749365\pi$
$308$	−31.5563	−	54.6572i	−1.79809	−	3.11438i
$309$	−10.3137	+	17.8639i	−0.586726	+	1.01624i
$310$	3.67423	+	2.12132i	0.208683	+	0.120483i
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		0			0
$313$	−4.82843			−0.272919			−0.136459	−	0.990646i	$-0.543572\pi$
$313$	−4.82843			−0.272919			−0.136459	+	0.990646i	$0.543572\pi$
$314$	−37.6339	−	21.7279i	−2.12380	−	1.22618i
$315$	2.41421	−	4.18154i	0.136026	−	0.235603i
$316$	−16.2426	−	28.1331i	−0.913720	−	1.58261i
$317$			2.14214i			0.120314i	0.998189	+	0.0601572i	$0.0191602\pi$
$317$			2.14214i			0.120314i	−0.998189	+	0.0601572i	$0.980840\pi$
$318$	−7.34847	+	4.24264i	−0.412082	+	0.237915i
$319$	−16.7262	+	9.65685i	−0.936485	+	0.540680i
$320$		−	9.82843i		−	0.549426i
$321$	−6.65685	−	11.5300i	−0.371549	−	0.643542i
$322$	−8.24264	+	14.2767i	−0.459344	+	0.795608i
$323$	−0.420266	−	0.242641i	−0.0233842	−	0.0135009i
$324$	19.1421			1.06345
$325$		0			0
$326$	−45.7990			−2.53657
$327$	2.44949	+	1.41421i	0.135457	+	0.0782062i
$328$	−7.00000	+	12.1244i	−0.386510	+	0.669456i
$329$	−11.6569	−	20.1903i	−0.642663	−	1.11313i
$330$		−	11.6569i		−	0.641689i
$331$	22.5527	−	13.0208i	1.23961	−	0.715689i	0.270595	−	0.962693i	$-0.412780\pi$
$331$	22.5527	−	13.0208i	1.23961	−	0.715689i	0.969014	+	0.247005i	$0.0794463\pi$
$332$	−10.5154	+	6.07107i	−0.577107	+	0.333193i
$333$			8.48528i			0.464991i
$334$	−3.82843	−	6.63103i	−0.209482	−	0.362834i
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	17.7408	+	10.2426i	0.967839	+	0.558782i
$337$	−12.8284			−0.698809			−0.349404	−	0.936972i	$-0.613616\pi$
$337$	−12.8284			−0.698809			−0.349404	+	0.936972i	$0.613616\pi$
$338$		0			0
$339$	12.4853			0.678107
$340$	2.74666	+	1.58579i	0.148959	+	0.0860013i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	0.707107	+	1.22474i	0.0382360	+	0.0662266i
$343$		−	44.9706i		−	2.42818i
$344$	−42.3227	+	24.4350i	−2.28189	+	1.31745i
$345$	−1.73205	+	1.00000i	−0.0932505	+	0.0538382i
$346$		−	40.6274i		−	2.18414i
$347$	2.12132	+	3.67423i	0.113878	+	0.197243i	0.917331	−	0.398126i	$-0.130339\pi$
$347$	2.12132	+	3.67423i	0.113878	+	0.197243i	−0.803452	+	0.595369i	$0.797006\pi$
$348$	15.3137	−	26.5241i	0.820901	−	1.42184i
$349$	−16.0087	−	9.24264i	−0.856927	−	0.494747i	0.00605481	−	0.999982i	$-0.498073\pi$
$349$	−16.0087	−	9.24264i	−0.856927	−	0.494747i	−0.862982	+	0.505234i	$0.831406\pi$
$350$	11.6569			0.623085
$351$		0			0
$352$	5.41421			0.288579
$353$	12.8418	+	7.41421i	0.683500	+	0.394619i	0.801172	−	0.598434i	$-0.204210\pi$
$353$	12.8418	+	7.41421i	0.683500	+	0.394619i	−0.117673	+	0.993052i	$0.537543\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	5.94975	+	10.3053i	0.315780	+	0.546947i
$356$		−	22.9706i		−	1.21744i
$357$	4.89898	−	2.82843i	0.259281	−	0.149696i
$358$	−11.8272	+	6.82843i	−0.625086	+	0.360894i
$359$		−	8.10051i		−	0.427528i	−0.976885	−	0.213764i	$-0.931428\pi$
$359$		−	8.10051i		−	0.427528i	0.976885	−	0.213764i	$-0.0685724\pi$
$360$	−2.20711	−	3.82282i	−0.116325	−	0.201480i
$361$	−9.32843	+	16.1573i	−0.490970	+	0.850385i
$362$		0			0
$363$	0.928932			0.0487563
$364$		0			0
$365$	8.48528			0.444140
$366$	−23.6544	−	13.6569i	−1.23643	−	0.713855i
$367$	−17.7782	+	30.7927i	−0.928013	+	1.60737i	−0.141371	+	0.989957i	$0.545151\pi$
$367$	−17.7782	+	30.7927i	−0.928013	+	1.60737i	−0.786642	+	0.617409i	$0.788182\pi$
$368$	2.12132	+	3.67423i	0.110581	+	0.191533i
$369$		−	3.17157i		−	0.165105i
$370$	−17.7408	+	10.2426i	−0.922299	+	0.532490i
$371$	10.3923	−	6.00000i	0.539542	−	0.311504i
$372$		−	9.51472i		−	0.493315i
$373$	1.34315	+	2.32640i	0.0695455	+	0.120456i	0.898701	−	0.438561i	$-0.144512\pi$
$373$	1.34315	+	2.32640i	0.0695455	+	0.120456i	−0.829156	+	0.559018i	$0.811178\pi$
$374$	−3.41421	+	5.91359i	−0.176545	+	0.305785i
$375$	1.22474	+	0.707107i	0.0632456	+	0.0365148i
$376$	−21.3137			−1.09917
$377$		0			0
$378$	−65.9411			−3.39165
$379$	25.1763	+	14.5355i	1.29322	+	0.746640i	0.979223	−	0.202784i	$-0.0649990\pi$
$379$	25.1763	+	14.5355i	1.29322	+	0.746640i	0.313995	+	0.949425i	$0.398332\pi$
$380$	−1.12132	+	1.94218i	−0.0575225	+	0.0996319i
$381$	4.65685	+	8.06591i	0.238578	+	0.413229i
$382$			5.65685i			0.289430i
$383$	25.2123	−	14.5563i	1.28829	−	0.743795i	0.309941	−	0.950756i	$-0.399691\pi$
$383$	25.2123	−	14.5563i	1.28829	−	0.743795i	0.978349	+	0.206961i	$0.0663574\pi$
$384$	−25.1763	+	14.5355i	−1.28477	+	0.741763i
$385$			16.4853i			0.840168i
$386$	5.24264	+	9.08052i	0.266843	+	0.462186i
$387$	5.53553	−	9.58783i	0.281387	−	0.487377i
$388$	25.3864	+	14.6569i	1.28880	+	0.744089i
$389$	−28.6274			−1.45147			−0.725734	−	0.687976i	$-0.758500\pi$
$389$	−28.6274			−1.45147			−0.725734	+	0.687976i	$0.758500\pi$
$390$		0			0
$391$	1.17157			0.0592490
$392$	−62.3644	−	36.0061i	−3.14988	−	1.81858i
$393$	−12.0000	+	20.7846i	−0.605320	+	1.04844i
$394$	−13.2426	−	22.9369i	−0.667155	−	1.15555i
$395$			8.48528i			0.426941i
$396$	11.3199	−	6.53553i	0.568845	−	0.328423i
$397$	10.2182	−	5.89949i	0.512838	−	0.296087i	−0.221161	−	0.975237i	$-0.570985\pi$
$397$	10.2182	−	5.89949i	0.512838	−	0.296087i	0.733999	+	0.679150i	$0.237651\pi$
$398$		−	9.65685i		−	0.484054i
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$	1.50000	−	2.59808i	0.0750000	−	0.129904i
$401$	4.60181	+	2.65685i	0.229803	+	0.132677i	0.610481	−	0.792031i	$-0.290976\pi$
$401$	4.60181	+	2.65685i	0.229803	+	0.132677i	−0.380678	+	0.924708i	$0.624309\pi$
$402$	6.82843			0.340571
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−4.33013	−	2.50000i	−0.215166	−	0.124226i
$406$	−32.9706	+	57.1067i	−1.63630	+	2.83416i
$407$	−14.4853	−	25.0892i	−0.718009	−	1.24363i
$408$		−	5.17157i		−	0.256031i
$409$	−6.21076	+	3.58579i	−0.307103	+	0.177306i	−0.645629	−	0.763651i	$-0.723405\pi$
$409$	−6.21076	+	3.58579i	−0.307103	+	0.177306i	0.338527	+	0.940957i	$0.390071\pi$
$410$	6.63103	−	3.82843i	0.327483	−	0.189073i
$411$			24.4853i			1.20777i
$412$	−27.9203	−	48.3594i	−1.37553	−	2.38250i
$413$	4.24264	−	7.34847i	0.208767	−	0.361595i
$414$	−2.95680	−	1.70711i	−0.145319	−	0.0838997i
$415$	3.17157			0.155686
$416$		0			0
$417$	−6.34315			−0.310625
$418$	−4.18154	−	2.41421i	−0.204526	−	0.118083i
$419$	−5.41421	+	9.37769i	−0.264502	+	0.458130i	−0.967433	−	0.253127i	$-0.918541\pi$
$419$	−5.41421	+	9.37769i	−0.264502	+	0.458130i	0.702931	+	0.711258i	$0.251874\pi$
$420$	−13.0711	−	22.6398i	−0.637803	−	1.10471i
$421$			34.9706i			1.70436i	0.523248	+	0.852180i	$0.324720\pi$
$421$			34.9706i			1.70436i	−0.523248	+	0.852180i	$0.675280\pi$
$422$	6.92820	−	4.00000i	0.337260	−	0.194717i
$423$	4.18154	−	2.41421i	0.203313	−	0.117383i
$424$		−	10.9706i		−	0.532778i
$425$	−0.414214	−	0.717439i	−0.0200923	−	0.0348009i
$426$	20.3137	−	35.1844i	0.984202	−	1.70469i
$427$	33.4523	+	19.3137i	1.61887	+	0.934656i
$428$	36.0416			1.74214
$429$		0			0
$430$	26.7279			1.28893
$431$	34.9742	+	20.1924i	1.68465	+	0.972633i	0.958498	+	0.285099i	$0.0920264\pi$
$431$	34.9742	+	20.1924i	1.68465	+	0.972633i	0.726152	+	0.687534i	$0.241307\pi$
$432$	−8.48528	+	14.6969i	−0.408248	+	0.707107i
$433$	3.82843	+	6.63103i	0.183982	+	0.318667i	0.943233	−	0.332131i	$-0.107768\pi$
$433$	3.82843	+	6.63103i	0.183982	+	0.318667i	−0.759251	+	0.650798i	$0.774434\pi$
$434$			20.4853i			0.983325i
$435$	−6.92820	+	4.00000i	−0.332182	+	0.191785i
$436$	−6.63103	+	3.82843i	−0.317569	+	0.183348i
$437$			0.828427i			0.0396290i
$438$	−14.4853	−	25.0892i	−0.692134	−	1.19881i
$439$	0.485281	−	0.840532i	0.0231612	−	0.0401164i	−0.854212	−	0.519924i	$-0.825960\pi$
$439$	0.485281	−	0.840532i	0.0231612	−	0.0401164i	0.877374	+	0.479808i	$0.159294\pi$
$440$	13.0519	+	7.53553i	0.622226	+	0.359242i
$441$	16.3137			0.776843
$442$		0			0
$443$	−9.41421			−0.447283			−0.223641	−	0.974671i	$-0.571794\pi$
$443$	−9.41421			−0.447283			−0.223641	+	0.974671i	$0.571794\pi$
$444$	39.7862	+	22.9706i	1.88817	+	1.09013i
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	−11.4853	−	19.8931i	−0.543844	−	0.941965i
$447$		−	16.4853i		−	0.779727i
$448$	41.0980	−	23.7279i	1.94170	−	1.12104i
$449$	−28.6764	+	16.5563i	−1.35332	+	0.781342i	−0.988714	−	0.149817i	$-0.952131\pi$
$449$	−28.6764	+	16.5563i	−1.35332	+	0.781342i	−0.364611	+	0.931160i	$0.618798\pi$
$450$			2.41421i			0.113807i
$451$	5.41421	+	9.37769i	0.254945	+	0.441578i
$452$	−16.8995	+	29.2708i	−0.794885	+	1.37678i
$453$	11.9503	+	6.89949i	0.561473	+	0.324167i
$454$	−39.4558			−1.85175
$455$		0			0
$456$	3.65685			0.171248
$457$	−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	$0.804988\pi$
$458$	−5.82843	+	10.0951i	−0.272345	+	0.471715i
$459$	2.34315	+	4.05845i	0.109369	+	0.189432i
$460$		−	5.41421i		−	0.252439i
$461$	−8.23999	+	4.75736i	−0.383775	+	0.221572i	−0.679459	−	0.733713i	$-0.737786\pi$
$461$	−8.23999	+	4.75736i	−0.383775	+	0.221572i	0.295685	+	0.955286i	$0.404452\pi$
$462$	48.7436	−	28.1421i	2.26776	−	1.30929i
$463$		−	4.34315i		−	0.201843i	−0.994894	−	0.100922i	$-0.967821\pi$
$463$		−	4.34315i		−	0.201843i	0.994894	−	0.100922i	$-0.0321791\pi$
$464$	8.48528	+	14.6969i	0.393919	+	0.682288i
$465$	−1.24264	+	2.15232i	−0.0576261	+	0.0998113i
$466$	−43.1272	−	24.8995i	−1.99783	−	1.15345i
$467$	13.4142			0.620736			0.310368	−	0.950617i	$-0.399548\pi$
$467$	13.4142			0.620736			0.310368	+	0.950617i	$0.399548\pi$
$468$		0			0
$469$	−9.65685			−0.445912
$470$	10.0951	+	5.82843i	0.465654	+	0.268845i
$471$	12.7279	−	22.0454i	0.586472	−	1.01580i
$472$	−3.87868	−	6.71807i	−0.178531	−	0.309224i
$473$			37.7990i			1.73800i
$474$	25.0892	−	14.4853i	1.15239	−	0.665331i
$475$	0.507306	−	0.292893i	0.0232768	−	0.0134389i
$476$			15.3137i			0.701903i
$477$	1.24264	+	2.15232i	0.0568966	+	0.0985478i
$478$	4.12132	−	7.13834i	0.188505	−	0.326500i
$479$	26.6112	+	15.3640i	1.21589	+	0.701997i	0.964037	−	0.265767i	$-0.0856252\pi$
$479$	26.6112	+	15.3640i	1.21589	+	0.701997i	0.251858	+	0.967764i	$0.418959\pi$
$480$	2.24264			0.102362
$481$		0			0
$482$	34.9706			1.59287
$483$	−8.36308	−	4.82843i	−0.380533	−	0.219701i
$484$	−1.25736	+	2.17781i	−0.0571527	+	0.0989914i
$485$	−3.82843	−	6.63103i	−0.173840	−	0.301100i
$486$		−	23.8995i		−	1.08410i
$487$	9.50079	−	5.48528i	0.430522	−	0.248562i	−0.269047	−	0.963127i	$-0.586709\pi$
$487$	9.50079	−	5.48528i	0.430522	−	0.248562i	0.699569	+	0.714565i	$0.253375\pi$
$488$	30.5826	−	17.6569i	1.38441	−	0.799288i
$489$		−	26.8284i		−	1.21322i
$490$	19.6924	+	34.1082i	0.889611	+	1.54085i
$491$	2.58579	−	4.47871i	0.116695	−	0.202122i	−0.801761	−	0.597645i	$-0.796103\pi$
$491$	2.58579	−	4.47871i	0.116695	−	0.202122i	0.918456	+	0.395523i	$0.129437\pi$
$492$	−14.8710	−	8.58579i	−0.670437	−	0.387077i
$493$	4.68629			0.211060
$494$		0			0
$495$	−3.41421			−0.153457
$496$	4.56575	+	2.63604i	0.205008	+	0.118362i
$497$	−28.7279	+	49.7582i	−1.28862	+	2.23196i
$498$	−5.41421	−	9.37769i	−0.242617	−	0.420224i
$499$		−	41.5563i		−	1.86032i	−0.367157	−	0.930159i	$-0.619669\pi$
$499$		−	41.5563i		−	1.86032i	0.367157	−	0.930159i	$-0.380331\pi$
$500$	−3.31552	+	1.91421i	−0.148274	+	0.0856062i
$501$	3.88437	−	2.24264i	0.173541	−	0.100194i
$502$		−	47.7990i		−	2.13337i
$503$	−18.9497	−	32.8219i	−0.844927	−	1.46346i	−0.885684	−	0.464288i	$-0.846310\pi$
$503$	−18.9497	−	32.8219i	−0.844927	−	1.46346i	0.0407567	−	0.999169i	$-0.487023\pi$
$504$	10.6569	−	18.4582i	0.474694	−	0.822194i
$505$	3.16693	+	1.82843i	0.140926	+	0.0813639i
$506$	11.6569			0.518210
$507$		0			0
$508$	−25.2132			−1.11866
$509$	35.6046	+	20.5563i	1.57815	+	0.911144i	0.995118	+	0.0986936i	$0.0314664\pi$
$509$	35.6046	+	20.5563i	1.57815	+	0.911144i	0.583030	+	0.812451i	$0.301867\pi$
$510$	−1.41421	+	2.44949i	−0.0626224	+	0.108465i
$511$	20.4853	+	35.4815i	0.906215	+	1.56961i
$512$		−	31.2426i		−	1.38074i
$513$	−2.86976	+	1.65685i	−0.126703	+	0.0731519i
$514$	−57.8241	+	33.3848i	−2.55051	+	1.47254i
$515$			14.5858i			0.642727i
$516$	−29.9706	−	51.9105i	−1.31938	−	2.28523i
$517$	−8.24264	+	14.2767i	−0.362511	+	0.627887i
$518$	−85.6600	−	49.4558i	−3.76369	−	2.17297i
$519$	23.7990			1.04466
$520$		0			0
$521$	−17.6569			−0.773561			−0.386780	−	0.922172i	$-0.626413\pi$
$521$	−17.6569			−0.773561			−0.386780	+	0.922172i	$0.626413\pi$
$522$	−11.8272	−	6.82843i	−0.517662	−	0.298872i
$523$	9.87868	−	17.1104i	0.431965	−	0.748184i	−0.565078	−	0.825038i	$-0.691154\pi$
$523$	9.87868	−	17.1104i	0.431965	−	0.748184i	0.997042	+	0.0768531i	$0.0244872\pi$
$524$	−32.4853	−	56.2662i	−1.41913	−	2.45800i
$525$			6.82843i			0.298017i
$526$	−22.1324	+	12.7782i	−0.965021	+	0.557155i
$527$	1.26080	−	0.727922i	0.0549212	−	0.0317088i
$528$		−	14.4853i		−	0.630391i
$529$	10.5000	+	18.1865i	0.456522	+	0.790719i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	1.52192	+	0.878680i	0.0660456	+	0.0381314i
$532$	−10.8284			−0.469472
$533$		0			0
$534$	20.4853			0.886485
$535$	−8.15295	−	4.70711i	−0.352483	−	0.203506i
$536$	−4.41421	+	7.64564i	−0.190665	+	0.330241i
$537$	−4.00000	−	6.92820i	−0.172613	−	0.298974i
$538$		−	61.1127i		−	2.63476i
$539$	−48.2363	+	27.8492i	−2.07768	+	1.19955i
$540$	18.7554	−	10.8284i	0.807103	−	0.465981i
$541$		−	7.17157i		−	0.308330i	−0.988045	−	0.154165i	$-0.950731\pi$
$541$		−	7.17157i		−	0.308330i	0.988045	−	0.154165i	$-0.0492687\pi$
$542$	32.2635	+	55.8819i	1.38583	+	2.40034i
$543$		0			0
$544$	−1.13770	−	0.656854i	−0.0487787	−	0.0281624i
$545$	2.00000			0.0856706
$546$		0			0
$547$	13.2132			0.564956			0.282478	−	0.959274i	$-0.408844\pi$
$547$	13.2132			0.564956			0.282478	+	0.959274i	$0.408844\pi$
$548$	−57.4039	−	33.1421i	−2.45217	−	1.41576i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$	−4.12132	−	7.13834i	−0.175734	−	0.304380i
$551$			3.31371i			0.141169i
$552$	−7.64564	+	4.41421i	−0.325420	+	0.187881i
$553$	−35.4815	+	20.4853i	−1.50883	+	0.871123i
$554$			30.9706i			1.31581i
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	8.58579	−	14.8710i	0.364118	−	0.630672i
$557$	31.0028	+	17.8995i	1.31363	+	0.758426i	0.982696	−	0.185227i	$-0.0593021\pi$
$557$	31.0028	+	17.8995i	1.31363	+	0.758426i	0.330937	+	0.943653i	$0.392635\pi$
$558$	−4.24264			−0.179605
$559$		0			0
$560$	14.4853			0.612115
$561$	−3.46410	−	2.00000i	−0.146254	−	0.0844401i
$562$	26.3137	−	45.5767i	1.10998	−	1.92254i
$563$	−3.87868	−	6.71807i	−0.163467	−	0.283133i	0.772643	−	0.634841i	$-0.218934\pi$
$563$	−3.87868	−	6.71807i	−0.163467	−	0.283133i	−0.936110	+	0.351708i	$0.885601\pi$
$564$		−	26.1421i		−	1.10078i
$565$	7.64564	−	4.41421i	0.321655	−	0.185707i
$566$	34.9742	−	20.1924i	1.47008	−	0.848749i
$567$		−	24.1421i		−	1.01387i
$568$	26.2635	+	45.4896i	1.10199	+	1.90870i
$569$	−5.17157	+	8.95743i	−0.216804	+	0.375515i	−0.953829	−	0.300350i	$-0.902896\pi$
$569$	−5.17157	+	8.95743i	−0.216804	+	0.375515i	0.737025	+	0.675865i	$0.236230\pi$
$570$	−1.73205	−	1.00000i	−0.0725476	−	0.0418854i
$571$	11.5147			0.481876			0.240938	−	0.970541i	$-0.422545\pi$
$571$	11.5147			0.481876			0.240938	+	0.970541i	$0.422545\pi$
$572$		0			0
$573$	−3.31371			−0.138432
$574$	32.0174	+	18.4853i	1.33638	+	0.771561i
$575$	−0.707107	+	1.22474i	−0.0294884	+	0.0510754i
$576$	4.91421	+	8.51167i	0.204759	+	0.354653i
$577$			34.8284i			1.44993i	0.688788	+	0.724963i	$0.258143\pi$
$577$			34.8284i			1.44993i	−0.688788	+	0.724963i	$0.741857\pi$
$578$	−34.1082	+	19.6924i	−1.41871	+	0.819095i
$579$	−5.31925	+	3.07107i	−0.221060	+	0.127629i
$580$		−	21.6569i		−	0.899252i
$581$	7.65685	+	13.2621i	0.317660	+	0.550203i
$582$	−13.0711	+	22.6398i	−0.541813	+	0.938448i
$583$	−7.34847	−	4.24264i	−0.304342	−	0.175712i
$584$	37.4558			1.54993
$585$		0			0
$586$	−63.1127			−2.60716
$587$	17.6177	+	10.1716i	0.727160	+	0.419826i	0.817382	−	0.576096i	$-0.195425\pi$
$587$	17.6177	+	10.1716i	0.727160	+	0.419826i	−0.0902226	+	0.995922i	$0.528758\pi$
$588$	44.1630	−	76.4925i	1.82125	−	3.15450i
$589$	0.514719	+	0.891519i	0.0212086	+	0.0367344i
$590$			4.24264i			0.174667i
$591$	13.4361	−	7.75736i	0.552689	−	0.319095i
$592$	−22.0454	+	12.7279i	−0.906061	+	0.523114i
$593$		−	24.6274i		−	1.01133i	−0.862731	−	0.505663i	$-0.831248\pi$
$593$		−	24.6274i		−	1.01133i	0.862731	−	0.505663i	$-0.168752\pi$
$594$	23.3137	+	40.3805i	0.956573	+	1.65683i
$595$	2.00000	−	3.46410i	0.0819920	−	0.142014i
$596$	38.6485	+	22.3137i	1.58310	+	0.914005i
$597$	5.65685			0.231520
$598$		0			0
$599$	25.4558			1.04010			0.520049	−	0.854137i	$-0.325914\pi$
$599$	25.4558			1.04010			0.520049	+	0.854137i	$0.325914\pi$
$600$	5.40629	+	3.12132i	0.220711	+	0.127427i
$601$	22.3137	−	38.6485i	0.910195	−	1.57650i	0.0964075	−	0.995342i	$-0.469265\pi$
$601$	22.3137	−	38.6485i	0.910195	−	1.57650i	0.813788	−	0.581162i	$-0.197402\pi$
$602$	64.5269	+	111.764i	2.62992	+	4.55516i
$603$		−	2.00000i		−	0.0814463i
$604$	−32.3507	+	18.6777i	−1.31633	+	0.759984i
$605$	0.568852	−	0.328427i	0.0231271	−	0.0133525i
$606$		−	12.4853i		−	0.507180i
$607$	−15.8787	−	27.5027i	−0.644496	−	1.11630i	−0.984418	−	0.175846i	$-0.943734\pi$
$607$	−15.8787	−	27.5027i	−0.644496	−	1.11630i	0.339922	−	0.940454i	$-0.389599\pi$
$608$	0.464466	−	0.804479i	0.0188366	−	0.0326259i
$609$	−33.4523	−	19.3137i	−1.35556	−	0.782631i
$610$	−19.3137			−0.781989
$611$		0			0
$612$	−3.17157			−0.128203
$613$	−12.7187	−	7.34315i	−0.513704	−	0.296587i	0.220651	−	0.975353i	$-0.429182\pi$
$613$	−12.7187	−	7.34315i	−0.513704	−	0.296587i	−0.734355	+	0.678766i	$0.762515\pi$
$614$	29.9706	−	51.9105i	1.20951	−	2.09494i
$615$	2.24264	+	3.88437i	0.0904320	+	0.156633i
$616$			72.7696i			2.93197i
$617$	−9.50079	+	5.48528i	−0.382487	+	0.220829i	−0.678900	−	0.734231i	$-0.737543\pi$
$617$	−9.50079	+	5.48528i	−0.382487	+	0.220829i	0.296413	+	0.955060i	$0.404210\pi$
$618$	43.1272	−	24.8995i	1.73483	−	1.00160i
$619$			1.75736i			0.0706342i	0.999376	+	0.0353171i	$0.0112441\pi$
$619$			1.75736i			0.0706342i	−0.999376	+	0.0353171i	$0.988756\pi$
$620$	−3.36396	−	5.82655i	−0.135100	−	0.234000i
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$	17.7408	+	10.2426i	0.711340	+	0.410692i
$623$	−28.9706			−1.16068
$624$		0			0
$625$	1.00000			0.0400000
$626$	10.0951	+	5.82843i	0.403483	+	0.232951i
$627$	1.41421	−	2.44949i	0.0564782	−	0.0978232i
$628$	34.4558	+	59.6793i	1.37494	+	2.38146i
$629$			7.02944i			0.280282i
$630$	−10.0951	+	5.82843i	−0.402200	+	0.232210i
$631$	−8.45012	+	4.87868i	−0.336394	+	0.194217i	−0.658676	−	0.752426i	$-0.728883\pi$
$631$	−8.45012	+	4.87868i	−0.336394	+	0.194217i	0.322282	+	0.946644i	$0.395550\pi$
$632$			37.4558i			1.48991i
$633$	2.34315	+	4.05845i	0.0931317	+	0.161309i
$634$	2.58579	−	4.47871i	0.102695	−	0.177872i
$635$	5.70346	+	3.29289i	0.226335	+	0.130674i
$636$	13.4558			0.533559
$637$		0			0
$638$	46.6274			1.84600
$639$	−10.3053	−	5.94975i	−0.407670	−	0.235368i
$640$	−10.2782	+	17.8023i	−0.406281	+	0.703699i
$641$	23.8284	+	41.2720i	0.941166	+	1.63015i	0.763251	+	0.646102i	$0.223602\pi$
$641$	23.8284	+	41.2720i	0.941166	+	1.63015i	0.177915	+	0.984046i	$0.443065\pi$
$642$			32.1421i			1.26855i
$643$	−8.23999	+	4.75736i	−0.324953	+	0.187612i	−0.653598	−	0.756842i	$-0.726741\pi$
$643$	−8.23999	+	4.75736i	−0.324953	+	0.187612i	0.328645	+	0.944454i	$0.393408\pi$
$644$	22.6398	−	13.0711i	0.892131	−	0.515072i
$645$			15.6569i			0.616488i
$646$	0.585786	+	1.01461i	0.0230475	+	0.0399194i
$647$	4.70711	−	8.15295i	0.185055	−	0.320525i	−0.758540	−	0.651627i	$-0.774087\pi$
$647$	4.70711	−	8.15295i	0.185055	−	0.320525i	0.943595	+	0.331101i	$0.107420\pi$
$648$	−19.1141	−	11.0355i	−0.750873	−	0.433517i
$649$	−6.00000			−0.235521
$650$		0			0
$651$	−12.0000			−0.470317
$652$	62.8972	+	36.3137i	2.46324	+	1.42215i
$653$	−23.4853	+	40.6777i	−0.919050	+	1.59184i	−0.118189	+	0.992991i	$0.537709\pi$
$653$	−23.4853	+	40.6777i	−0.919050	+	1.59184i	−0.800861	+	0.598850i	$0.795624\pi$
$654$	−3.41421	−	5.91359i	−0.133506	−	0.231240i
$655$			16.9706i			0.663095i
$656$	8.23999	−	4.75736i	0.321717	−	0.185744i
$657$	−7.34847	+	4.24264i	−0.286691	+	0.165521i
$658$			56.2843i			2.19419i
$659$	−8.92893	−	15.4654i	−0.347822	−	0.602445i	0.638040	−	0.770003i	$-0.279745\pi$
$659$	−8.92893	−	15.4654i	−0.347822	−	0.602445i	−0.985862	+	0.167558i	$0.946412\pi$
$660$	−9.24264	+	16.0087i	−0.359769	+	0.623139i
$661$	−25.6326	−	14.7990i	−0.996993	−	0.575614i	−0.0896356	−	0.995975i	$-0.528570\pi$
$661$	−25.6326	−	14.7990i	−0.996993	−	0.575614i	−0.907357	+	0.420361i	$0.861904\pi$
$662$	−62.8701			−2.44351
$663$		0			0
$664$	14.0000			0.543305
$665$	2.44949	+	1.41421i	0.0949871	+	0.0548408i
$666$	10.2426	−	17.7408i	0.396894	−	0.687441i
$667$	−4.00000	−	6.92820i	−0.154881	−	0.268261i
$668$			12.1421i			0.469793i
$669$	11.6531	−	6.72792i	0.450535	−	0.260116i
$670$	4.18154	−	2.41421i	0.161547	−	0.0932692i
$671$		−	27.3137i		−	1.05443i
$672$	5.41421	+	9.37769i	0.208858	+	0.361752i
$673$	3.24264	−	5.61642i	0.124995	−	0.216497i	−0.796736	−	0.604327i	$-0.793442\pi$
$673$	3.24264	−	5.61642i	0.124995	−	0.216497i	0.921731	+	0.387830i	$0.126775\pi$
$674$	26.8213	+	15.4853i	1.03312	+	0.596471i
$675$	−5.65685			−0.217732
$676$		0			0
$677$	−20.1421			−0.774125			−0.387063	−	0.922053i	$-0.626510\pi$
$677$	−20.1421			−0.774125			−0.387063	+	0.922053i	$0.626510\pi$
$678$	−26.1039	−	15.0711i	−1.00251	−	0.578801i
$679$	18.4853	−	32.0174i	0.709400	−	1.22872i
$680$	−1.82843	−	3.16693i	−0.0701170	−	0.121446i
$681$		−	23.1127i		−	0.885681i
$682$	12.5446	−	7.24264i	0.480358	−	0.277335i
$683$	9.25460	−	5.34315i	0.354117	−	0.204450i	−0.312380	−	0.949957i	$-0.601126\pi$
$683$	9.25460	−	5.34315i	0.354117	−	0.204450i	0.666497	+	0.745507i	$0.267793\pi$
$684$		−	2.24264i		−	0.0857495i
$685$	8.65685	+	14.9941i	0.330761	+	0.572896i
$686$	−54.2843	+	94.0231i	−2.07258	+	3.58982i
$687$	−5.91359	−	3.41421i	−0.225618	−	0.130260i
$688$	33.2132			1.26624
$689$		0			0
$690$	4.82843			0.183815
$691$	6.00063	+	3.46447i	0.228275	+	0.131795i	0.609776	−	0.792574i	$-0.291259\pi$
$691$	6.00063	+	3.46447i	0.228275	+	0.131795i	−0.381501	+	0.924368i	$0.624593\pi$
$692$	−32.2132	+	55.7949i	−1.22456	+	2.12100i
$693$	−8.24264	−	14.2767i	−0.313112	−	0.542326i
$694$		−	10.2426i		−	0.388805i
$695$	−3.88437	+	2.24264i	−0.147342	+	0.0850682i
$696$	−30.5826	+	17.6569i	−1.15923	+	0.669281i
$697$		−	2.62742i		−	0.0995205i
$698$	22.3137	+	38.6485i	0.844586	+	1.46287i
$699$	14.5858	−	25.2633i	0.551685	−	0.955547i
$700$	−16.0087	−	9.24264i	−0.605073	−	0.349339i
$701$	−14.6863			−0.554694			−0.277347	−	0.960770i	$-0.589455\pi$
$701$	−14.6863			−0.554694			−0.277347	+	0.960770i	$0.589455\pi$
$702$		0			0
$703$	−4.97056			−0.187468
$704$	−29.0607	−	16.7782i	−1.09526	−	0.632351i
$705$	−3.41421	+	5.91359i	−0.128587	+	0.222719i
$706$	−17.8995	−	31.0028i	−0.673656	−	1.16681i
$707$			17.6569i			0.664054i
$708$	8.23999	−	4.75736i	0.309678	−	0.178793i
$709$	39.0687	−	22.5563i	1.46726	−	0.847121i	0.467929	−	0.883766i	$-0.345000\pi$
$709$	39.0687	−	22.5563i	1.46726	−	0.847121i	0.999328	+	0.0366445i	$0.0116669\pi$
$710$		−	28.7279i		−	1.07814i
$711$	−4.24264	−	7.34847i	−0.159111	−	0.275589i
$712$	−13.2426	+	22.9369i	−0.496289	+	0.859598i
$713$	−2.15232	−	1.24264i	−0.0806049	−	0.0465373i
$714$	−13.6569			−0.511095
$715$		0			0
$716$	21.6569			0.809355
$717$	4.18154	+	2.41421i	0.156162	+	0.0901605i
$718$	−9.77817	+	16.9363i	−0.364918	+	0.632057i
$719$	14.4853	+	25.0892i	0.540210	+	0.935671i	0.998892	+	0.0470703i	$0.0149885\pi$
$719$	14.4853	+	25.0892i	0.540210	+	0.935671i	−0.458682	+	0.888601i	$0.651678\pi$
$720$			3.00000i			0.111803i
$721$	−60.9911	+	35.2132i	−2.27143	+	1.31141i
$722$	39.0072	−	22.5208i	1.45170	−	0.838138i
$723$			20.4853i			0.761856i
$724$		0			0
$725$	−2.82843	+	4.89898i	−0.105045	+	0.181944i
$726$	−1.94218	−	1.12132i	−0.0720812	−	0.0416161i
$727$	51.3553			1.90466			0.952332	−	0.305063i	$-0.0986777\pi$
$727$	51.3553			1.90466			0.952332	+	0.305063i	$0.0986777\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−17.7408	−	10.2426i	−0.656616	−	0.379097i
$731$	4.58579	−	7.94282i	0.169611	−	0.293776i
$732$	21.6569	+	37.5108i	0.800460	+	1.38644i
$733$		−	21.3137i		−	0.787240i	−0.919273	−	0.393620i	$-0.871223\pi$
$733$		−	21.3137i		−	0.787240i	0.919273	−	0.393620i	$-0.128777\pi$
$734$	74.3402	−	42.9203i	2.74395	−	1.58422i
$735$	−19.9801	+	11.5355i	−0.736978	+	0.425495i
$736$			2.24264i			0.0826648i
$737$	3.41421	+	5.91359i	0.125764	+	0.217830i
$738$	−3.82843	+	6.63103i	−0.140926	+	0.244092i
$739$	−4.56575	−	2.63604i	−0.167954	−	0.0969683i	0.413667	−	0.910428i	$-0.364248\pi$
$739$	−4.56575	−	2.63604i	−0.167954	−	0.0969683i	−0.581621	+	0.813460i	$0.697581\pi$
$740$	32.4853			1.19418
$741$		0			0
$742$	−28.9706			−1.06354
$743$	−18.6323	−	10.7574i	−0.683553	−	0.394649i	0.117640	−	0.993056i	$-0.462467\pi$
$743$	−18.6323	−	10.7574i	−0.683553	−	0.394649i	−0.801192	+	0.598407i	$0.795801\pi$
$744$	−5.48528	+	9.50079i	−0.201100	+	0.348316i
$745$	−5.82843	−	10.0951i	−0.213537	−	0.369857i
$746$		−	6.48528i		−	0.237443i
$747$	−2.74666	+	1.58579i	−0.100495	+	0.0580209i
$748$	9.37769	−	5.41421i	0.342882	−	0.197963i
$749$		−	45.4558i		−	1.66092i
$750$	−1.70711	−	2.95680i	−0.0623347	−	0.107967i
$751$	−13.7574	+	23.8284i	−0.502013	+	0.869512i	0.497984	+	0.867186i	$0.334074\pi$
$751$	−13.7574	+	23.8284i	−0.502013	+	0.869512i	−0.999997	+	0.00232617i	$0.999260\pi$
$752$	12.5446	+	7.24264i	0.457455	+	0.264112i
$753$	28.0000			1.02038
$754$		0			0
$755$	9.75736			0.355107
$756$	90.5590	+	52.2843i	3.29360	+	1.90156i
$757$	12.0711	−	20.9077i	0.438730	−	0.759903i	−0.558861	−	0.829261i	$-0.688762\pi$
$757$	12.0711	−	20.9077i	0.438730	−	0.759903i	0.997592	+	0.0693577i	$0.0220950\pi$
$758$	−35.0919	−	60.7809i	−1.27459	−	2.20766i
$759$			6.82843i			0.247856i
$760$	2.23936	−	1.29289i	0.0812300	−	0.0468982i
$761$	7.47156	−	4.31371i	0.270844	−	0.156372i	−0.358427	−	0.933558i	$-0.616687\pi$
$761$	7.47156	−	4.31371i	0.270844	−	0.156372i	0.629271	+	0.777186i	$0.283354\pi$
$762$		−	22.4853i		−	0.814556i
$763$	4.82843	+	8.36308i	0.174801	+	0.302764i
$764$	4.48528	−	7.76874i	0.162272	−	0.281063i
$765$	0.717439	+	0.414214i	0.0259391	+	0.0149759i
$766$	−70.2843			−2.53947
$767$		0			0
$768$	42.3848			1.52943
$769$	−19.8931	−	11.4853i	−0.717363	−	0.414170i	0.0964182	−	0.995341i	$-0.469261\pi$
$769$	−19.8931	−	11.4853i	−0.717363	−	0.414170i	−0.813781	+	0.581171i	$0.802595\pi$
$770$	19.8995	−	34.4669i	0.717128	−	1.24210i
$771$	−19.5563	−	33.8726i	−0.704305	−	1.21989i
$772$		−	16.6274i		−	0.598434i
$773$	19.1757	−	11.0711i	0.689700	−	0.398199i	−0.113799	−	0.993504i	$-0.536302\pi$
$773$	19.1757	−	11.0711i	0.689700	−	0.398199i	0.803500	+	0.595305i	$0.202969\pi$
$774$	−23.1471	+	13.3640i	−0.832004	+	0.480358i
$775$			1.75736i			0.0631262i
$776$	−16.8995	−	29.2708i	−0.606657	−	1.05076i
$777$	28.9706	−	50.1785i	1.03931	−	1.80014i
$778$	59.8534	+	34.5563i	2.14585	+	1.23891i
$779$	1.85786			0.0665649
$780$		0			0
$781$	40.6274			1.45376
$782$	−2.44949	−	1.41421i	−0.0875936	−	0.0505722i
$783$	16.0000	−	27.7128i	0.571793	−	0.990375i
$784$	24.4706	+	42.3843i	0.873949	+	1.51372i
$785$		−	18.0000i		−	0.642448i
$786$	50.1785	−	28.9706i	1.78981	−	1.03335i
$787$	19.4728	−	11.2426i	0.694131	−	0.400757i	−0.111027	−	0.993817i	$-0.535414\pi$
$787$	19.4728	−	11.2426i	0.694131	−	0.400757i	0.805158	+	0.593061i	$0.202081\pi$
$788$			42.0000i			1.49619i
$789$	−7.48528	−	12.9649i	−0.266483	−	0.461562i
$790$	10.2426	−	17.7408i	0.364417	−	0.631188i
$791$	36.9164	+	21.3137i	1.31260	+	0.757828i
$792$	−15.0711			−0.535527
$793$		0			0
$794$	−28.4853			−1.01090
$795$	−3.04384	−	1.75736i	−0.107954	−	0.0623271i
$796$	−7.65685	+	13.2621i	−0.271390	+	0.470061i
$797$	−11.4853	−	19.8931i	−0.406830	−	0.704649i	0.587703	−	0.809077i	$-0.300032\pi$
$797$	−11.4853	−	19.8931i	−0.406830	−	0.704649i	−0.994533	+	0.104427i	$0.966699\pi$
$798$		−	9.65685i		−	0.341849i
$799$	3.46410	−	2.00000i	0.122551	−	0.0707549i
$800$	1.37333	−	0.792893i	0.0485546	−	0.0280330i
$801$		−	6.00000i		−	0.212000i
$802$	−6.41421	−	11.1097i	−0.226494	−	0.392299i
$803$	14.4853	−	25.0892i	0.511174	−	0.885380i
$804$	−9.37769	−	5.41421i	−0.330726	−	0.190945i
$805$	−6.82843			−0.240670
$806$		0			0
$807$	35.7990			1.26018
$808$	13.9795	+	8.07107i	0.491797	+	0.283939i
$809$	−22.6274	+	39.1918i	−0.795538	+	1.37791i	0.126960	+	0.991908i	$0.459478\pi$
$809$	−22.6274	+	39.1918i	−0.795538	+	1.37791i	−0.922497	+	0.386004i	$0.873855\pi$
$810$	6.03553	+	10.4539i	0.212067	+	0.367311i
$811$			28.3848i			0.996724i	0.866969	+	0.498362i	$0.166065\pi$
$811$			28.3848i			0.996724i	−0.866969	+	0.498362i	$0.833935\pi$
$812$	90.5590	−	52.2843i	3.17800	−	1.83482i
$813$	−32.7349	+	18.8995i	−1.14806	+	0.662834i
$814$			69.9411i			2.45144i
$815$	−9.48528	−	16.4290i	−0.332255	−	0.575482i
$816$	−1.75736	+	3.04384i	−0.0615199	+	0.106556i
$817$	5.61642	+	3.24264i	0.196494	+	0.113446i
$818$	17.3137			0.605360
$819$		0			0
$820$	−12.1421			−0.424022
$821$	−44.3880	−	25.6274i	−1.54915	−	0.894403i	−0.998207	−	0.0598613i	$-0.980934\pi$
$821$	−44.3880	−	25.6274i	−1.54915	−	0.894403i	−0.550945	−	0.834542i	$-0.685733\pi$
$822$	29.5563	−	51.1931i	1.03090	−	1.78556i
$823$	−1.19239	−	2.06528i	−0.0415640	−	0.0719910i	0.844495	−	0.535563i	$-0.179901\pi$
$823$	−1.19239	−	2.06528i	−0.0415640	−	0.0719910i	−0.886059	+	0.463572i	$0.846567\pi$
$824$			64.3848i			2.24295i
$825$	4.18154	−	2.41421i	0.145583	−	0.0840521i
$826$	−17.7408	+	10.2426i	−0.617280	+	0.356387i
$827$			56.1421i			1.95225i	0.217202	+	0.976127i	$0.430307\pi$
$827$			56.1421i			1.95225i	−0.217202	+	0.976127i	$0.569693\pi$
$828$	2.70711	+	4.68885i	0.0940785	+	0.162949i
$829$	20.4853	−	35.4815i	0.711483	−	1.23233i	−0.252817	−	0.967514i	$-0.581357\pi$
$829$	20.4853	−	35.4815i	0.711483	−	1.23233i	0.964300	−	0.264811i	$-0.0853096\pi$
$830$	−6.63103	−	3.82843i	−0.230166	−	0.132887i
$831$	−18.1421			−0.629344
$832$		0			0
$833$	13.5147			0.468257
$834$	13.2621	+	7.65685i	0.459228	+	0.265135i
$835$	1.58579	−	2.74666i	0.0548784	−	0.0950522i
$836$	3.82843	+	6.63103i	0.132409	+	0.229339i
$837$		−	9.94113i		−	0.343616i
$838$	22.6398	−	13.0711i	0.782077	−	0.451533i
$839$	5.82655	−	3.36396i	0.201155	−	0.116137i	−0.396039	−	0.918234i	$-0.629616\pi$
$839$	5.82655	−	3.36396i	0.201155	−	0.116137i	0.597194	+	0.802097i	$0.296282\pi$
$840$			30.1421i			1.04000i
$841$	−1.50000	−	2.59808i	−0.0517241	−	0.0895888i
$842$	42.2132	−	73.1154i	1.45476	−	2.51972i
$843$	26.6982	+	15.4142i	0.919535	+	0.530894i
$844$	−12.6863			−0.436680
$845$		0			0
$846$	−11.6569			−0.400771
$847$	2.74666	+	1.58579i	0.0943764	+	0.0544883i
$848$	−3.72792	+	6.45695i	−0.128017	+	0.221733i
$849$	11.8284	+	20.4874i	0.405951	+	0.703127i
$850$			2.00000i			0.0685994i
$851$	10.3923	−	6.00000i	0.356244	−	0.205677i
$852$	−55.7949	+	32.2132i	−1.91150	+	1.10361i
$853$		−	13.4558i		−	0.460719i	−0.973106	−	0.230360i	$-0.926010\pi$
$853$		−	13.4558i		−	0.460719i	0.973106	−	0.230360i	$-0.0739903\pi$
$854$	−46.6274	−	80.7611i	−1.59556	−	2.76359i
$855$	−0.292893	+	0.507306i	−0.0100167	+	0.0173495i
$856$	−35.9889	−	20.7782i	−1.23007	−	0.710183i
$857$	−11.6569			−0.398191			−0.199095	−	0.979980i	$-0.563800\pi$
$857$	−11.6569			−0.398191			−0.199095	+	0.979980i	$0.563800\pi$
$858$		0			0
$859$	−27.7990			−0.948489			−0.474245	−	0.880393i	$-0.657279\pi$
$859$	−27.7990			−0.948489			−0.474245	+	0.880393i	$0.657279\pi$
$860$	−36.7063	−	21.1924i	−1.25167	−	0.722654i
$861$	−10.8284	+	18.7554i	−0.369032	+	0.639182i
$862$	−48.7487	−	84.4353i	−1.66039	−	2.87588i
$863$			31.4558i			1.07077i	0.844608	+	0.535385i	$0.179833\pi$
$863$			31.4558i			1.07077i	−0.844608	+	0.535385i	$0.820167\pi$
$864$	−7.76874	+	4.48528i	−0.264298	+	0.152592i
$865$	14.5738	−	8.41421i	0.495526	−	0.286092i
$866$		−	18.4853i		−	0.628155i
$867$	−11.5355	−	19.9801i	−0.391767	−	0.678561i
$868$	16.2426	−	28.1331i	0.551311	−	0.954899i
$869$	25.0892	+	14.4853i	0.851094	+	0.491380i
$870$	19.3137			0.654796
$871$		0			0
$872$	8.82843			0.298968
$873$	6.63103	+	3.82843i	0.224426	+	0.129573i
$874$	1.00000	−	1.73205i	0.0338255	−	0.0585875i
$875$	2.41421	+	4.18154i	0.0816153	+	0.141362i
$876$			45.9411i			1.55221i
$877$	−21.9223	+	12.6569i	−0.740264	+	0.427392i	−0.822165	−	0.569249i	$-0.807234\pi$
$877$	−21.9223	+	12.6569i	−0.740264	+	0.427392i	0.0819013	+	0.996640i	$0.473901\pi$
$878$	−2.02922	+	1.17157i	−0.0684830	+	0.0395387i
$879$		−	36.9706i		−	1.24699i
$880$	−5.12132	−	8.87039i	−0.172640	−	0.299021i
$881$	9.51472	−	16.4800i	0.320559	−	0.555225i	−0.660044	−	0.751227i	$-0.729463\pi$
$881$	9.51472	−	16.4800i	0.320559	−	0.555225i	0.980603	+	0.196002i	$0.0627959\pi$
$882$	−34.1082	−	19.6924i	−1.14848	−	0.663077i
$883$	23.7574			0.799499			0.399749	−	0.916624i	$-0.369097\pi$
$883$	23.7574			0.799499			0.399749	+	0.916624i	$0.369097\pi$
$884$		0			0
$885$	−2.48528			−0.0835418
$886$	19.6830	+	11.3640i	0.661262	+	0.381780i
$887$	11.1924	−	19.3858i	0.375804	−	0.650911i	−0.614643	−	0.788805i	$-0.710700\pi$
$887$	11.1924	−	19.3858i	0.375804	−	0.650911i	0.990447	+	0.137894i	$0.0440334\pi$
$888$	−26.4853	−	45.8739i	−0.888788	−	1.53943i
$889$			31.7990i			1.06650i
$890$	12.5446	−	7.24264i	0.420497	−	0.242774i
$891$	−14.7840	+	8.53553i	−0.495282	+	0.285951i
$892$			36.4264i			1.21965i
$893$	1.41421	+	2.44949i	0.0473249	+	0.0819690i
$894$	−19.8995	+	34.4669i	−0.665539	+	1.15275i
$895$	−4.89898	−	2.82843i	−0.163755	−	0.0945439i
$896$	−99.2548			−3.31587
$897$		0			0
$898$	79.9411			2.66767
$899$	−8.60927	−	4.97056i	−0.287135	−	0.165778i
$900$	1.91421	−	3.31552i	0.0638071	−	0.110517i
$901$	1.02944	+	1.78304i	0.0342955	+	0.0594016i
$902$		−	26.1421i		−	0.870438i
$903$	−65.4698	+	37.7990i	−2.17870	+	1.25787i
$904$	33.7495	−	19.4853i	1.12249	−	0.648071i
$905$		0			0
$906$	−16.6569	−	28.8505i	−0.553387	−	0.958494i
$907$	4.60660	−	7.97887i	0.152960	−	0.264934i	−0.779355	−	0.626583i	$-0.784453\pi$
$907$	4.60660	−	7.97887i	0.152960	−	0.264934i	0.932314	+	0.361649i	$0.117786\pi$
$908$	54.1859	+	31.2843i	1.79822	+	1.03821i
$909$	−3.65685			−0.121290
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−2.15232	−	1.24264i	−0.0712703	−	0.0411479i
$913$	5.41421	−	9.37769i	0.179184	−	0.310356i
$914$	21.7279	+	37.6339i	0.718696	+	1.24482i
$915$		−	11.3137i		−	0.374020i
$916$	16.0087	−	9.24264i	0.528943	−	0.305385i
$917$	−70.9631	+	40.9706i	−2.34341	+	1.35297i
$918$		−	11.3137i		−	0.373408i
$919$	−0.242641	−	0.420266i	−0.00800398	−	0.0138633i	0.861996	−	0.506916i	$-0.169214\pi$
$919$	−0.242641	−	0.420266i	−0.00800398	−	0.0138633i	−0.870000	+	0.493052i	$0.835881\pi$
$920$	−3.12132	+	5.40629i	−0.102907	+	0.178240i
$921$	30.4085	+	17.5563i	1.00199	+	0.578501i
$922$	22.9706			0.756495
$923$		0			0
$924$	−89.2548			−2.93627
$925$	−7.34847	−	4.24264i	−0.241616	−	0.139497i
$926$	−5.24264	+	9.08052i	−0.172284	+	0.298404i
$927$	−7.29289	−	12.6317i	−0.239530	−	0.414878i
$928$			8.97056i			0.294473i
$929$	−14.5738	+	8.41421i	−0.478152	+	0.276061i	−0.719646	−	0.694341i	$-0.755696\pi$
$929$	−14.5738	+	8.41421i	−0.478152	+	0.276061i	0.241494	+	0.970402i	$0.422363\pi$
$930$	5.19615	−	3.00000i	0.170389	−	0.0983739i
$931$			9.55635i			0.313197i
$932$	39.4853	+	68.3905i	1.29338	+	2.24021i
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$	−28.0460	−	16.1924i	−0.917694	−	0.529831i
$935$	−2.82843			−0.0924995
$936$		0			0
$937$	−22.9706			−0.750416			−0.375208	−	0.926941i	$-0.622429\pi$
$937$	−22.9706			−0.750416			−0.375208	+	0.926941i	$0.622429\pi$
$938$	20.1903	+	11.6569i	0.659235	+	0.380610i
$939$	−3.41421	+	5.91359i	−0.111419	+	0.192983i
$940$	−9.24264	−	16.0087i	−0.301462	−	0.522147i
$941$		−	18.7696i		−	0.611870i	−0.952052	−	0.305935i	$-0.901031\pi$
$941$		−	18.7696i		−	0.611870i	0.952052	−	0.305935i	$-0.0989690\pi$
$942$	−53.2223	+	30.7279i	−1.73408	+	1.00117i
$943$	−3.88437	+	2.24264i	−0.126492	+	0.0730304i
$944$			5.27208i			0.171592i
$945$	−13.6569	−	23.6544i	−0.444258	−	0.769477i
$946$	45.6274	−	79.0290i	1.48348	−	2.56945i
$947$	−14.8200	−	8.55635i	−0.481586	−	0.278044i	0.239491	−	0.970899i	$-0.423019\pi$
$947$	−14.8200	−	8.55635i	−0.481586	−	0.278044i	−0.721077	+	0.692855i	$0.756353\pi$
$948$	−45.9411			−1.49210
$949$		0			0
$950$	−1.41421			−0.0458831
$951$	2.62357	+	1.51472i	0.0850751	+	0.0491181i
$952$	8.82843	−	15.2913i	0.286131	−	0.495593i
$953$	17.6274	+	30.5316i	0.571008	+	0.989015i	0.996463	+	0.0840352i	$0.0267808\pi$
$953$	17.6274	+	30.5316i	0.571008	+	0.989015i	−0.425455	+	0.904980i	$0.639886\pi$
$954$		−	6.00000i		−	0.194257i
$955$	−2.02922	+	1.17157i	−0.0656641	+	0.0379112i
$956$	−11.3199	+	6.53553i	−0.366111	+	0.211374i
$957$			27.3137i			0.882927i
$958$	−37.0919	−	64.2450i	−1.19838	−	2.07566i
$959$	−41.7990	+	72.3980i	−1.34976	+	2.33785i
$960$	−12.0373	−	6.94975i	−0.388503	−	0.224302i
$961$	27.9117			0.900377
$962$		0			0
$963$	9.41421			0.303369
$964$	−48.0262	−	27.7279i	−1.54682	−	0.893056i
$965$	−2.17157	+	3.76127i	−0.0699054	+	0.121080i
$966$	11.6569	+	20.1903i	0.375053	+	0.649611i
$967$		−	47.9411i		−	1.54168i	−0.637027	−	0.770841i	$-0.719836\pi$
$967$		−	47.9411i		−	1.54168i	0.637027	−	0.770841i	$-0.280164\pi$
$968$	2.51104	−	1.44975i	0.0807078	−	0.0465966i
$969$	−0.594346	+	0.343146i	−0.0190931	+	0.0110234i
$970$			18.4853i			0.593527i
$971$	−22.1421	−	38.3513i	−0.710575	−	1.23075i	−0.964642	−	0.263565i	$-0.915102\pi$
$971$	−22.1421	−	38.3513i	−0.710575	−	1.23075i	0.254067	−	0.967187i	$-0.418232\pi$
$972$	−18.9497	+	32.8219i	−0.607813	+	1.05276i
$973$	−18.7554	−	10.8284i	−0.601270	−	0.347143i
$974$	−26.4853			−0.848643
$975$		0			0
$976$	−24.0000			−0.768221
$977$	−34.2208	−	19.7574i	−1.09482	−	0.632094i	−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−34.2208	−	19.7574i	−1.09482	−	0.632094i	−0.934855	+	0.355029i	$0.884471\pi$
$978$	−32.3848	+	56.0921i	−1.03555	+	1.79363i
$979$	10.2426	+	17.7408i	0.327356	+	0.566998i
$980$		−	62.4558i		−	1.99508i
$981$	−1.73205	+	1.00000i	−0.0553001	+	0.0319275i
$982$	−10.8126	+	6.24264i	−0.345043	+	0.199211i
$983$		−	1.02944i		−	0.0328339i	−0.999865	−	0.0164170i	$-0.994774\pi$
$983$		−	1.02944i		−	0.0328339i	0.999865	−	0.0164170i	$-0.00522592\pi$
$984$	9.89949	+	17.1464i	0.315584	+	0.546608i
$985$	5.48528	−	9.50079i	0.174776	−	0.302720i
$986$	−9.79796	−	5.65685i	−0.312031	−	0.180151i
$987$	−32.9706			−1.04946
$988$		0			0
$989$	−15.6569			−0.497859
$990$	7.13834	+	4.12132i	0.226871	+	0.130984i
$991$	−24.4853	+	42.4098i	−0.777801	+	1.34719i	0.155406	+	0.987851i	$0.450331\pi$
$991$	−24.4853	+	42.4098i	−0.777801	+	1.34719i	−0.933207	+	0.359340i	$0.883002\pi$
$992$	1.39340	+	2.41344i	0.0442404	+	0.0766267i
$993$		−	36.8284i		−	1.16871i
$994$	120.127	−	69.3553i	3.81020	−	2.19982i
$995$	3.46410	−	2.00000i	0.109819	−	0.0634043i
$996$			17.1716i			0.544102i
$997$	−14.4142	−	24.9662i	−0.456503	−	0.790686i	0.542271	−	0.840204i	$-0.317565\pi$
$997$	−14.4142	−	24.9662i	−0.456503	−	0.790686i	−0.998773	+	0.0495181i	$0.984231\pi$
$998$	−50.1630	+	86.8848i	−1.58788	+	2.75029i
$999$	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.316.1		8
13.2	odd	12		845.2.e.c.146.1		4
13.3	even	3	inner	845.2.m.f.361.4		8
13.4	even	6		845.2.c.b.506.1		4
13.5	odd	4		845.2.e.c.191.1		4
13.6	odd	12		845.2.a.g.1.2		2
13.7	odd	12		65.2.a.b.1.1	✓	2
13.8	odd	4		845.2.e.h.191.2		4
13.9	even	3		845.2.c.b.506.4		4
13.10	even	6	inner	845.2.m.f.361.1		8
13.11	odd	12		845.2.e.h.146.2		4
13.12	even	2	inner	845.2.m.f.316.4		8
39.20	even	12		585.2.a.m.1.2		2
39.32	even	12		7605.2.a.x.1.1		2
52.7	even	12		1040.2.a.j.1.2		2
65.7	even	12		325.2.b.f.274.1		4
65.19	odd	12		4225.2.a.r.1.1		2
65.33	even	12		325.2.b.f.274.4		4
65.59	odd	12		325.2.a.i.1.2		2
91.20	even	12		3185.2.a.j.1.1		2
104.59	even	12		4160.2.a.z.1.1		2
104.85	odd	12		4160.2.a.bf.1.2		2
143.98	even	12		7865.2.a.j.1.2		2
156.59	odd	12		9360.2.a.cd.1.1		2
195.59	even	12		2925.2.a.u.1.1		2
195.98	odd	12		2925.2.c.r.2224.1		4
195.137	odd	12		2925.2.c.r.2224.4		4
260.59	even	12		5200.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.b.1.1	✓	2	13.7	odd	12
325.2.a.i.1.2		2	65.59	odd	12
325.2.b.f.274.1		4	65.7	even	12
325.2.b.f.274.4		4	65.33	even	12
585.2.a.m.1.2		2	39.20	even	12
845.2.a.g.1.2		2	13.6	odd	12
845.2.c.b.506.1		4	13.4	even	6
845.2.c.b.506.4		4	13.9	even	3
845.2.e.c.146.1		4	13.2	odd	12
845.2.e.c.191.1		4	13.5	odd	4
845.2.e.h.146.2		4	13.11	odd	12
845.2.e.h.191.2		4	13.8	odd	4
845.2.m.f.316.1		8	1.1	even	1	trivial
845.2.m.f.316.4		8	13.12	even	2	inner
845.2.m.f.361.1		8	13.10	even	6	inner
845.2.m.f.361.4		8	13.3	even	3	inner
1040.2.a.j.1.2		2	52.7	even	12
2925.2.a.u.1.1		2	195.59	even	12
2925.2.c.r.2224.1		4	195.98	odd	12
2925.2.c.r.2224.4		4	195.137	odd	12
3185.2.a.j.1.1		2	91.20	even	12
4160.2.a.z.1.1		2	104.59	even	12
4160.2.a.bf.1.2		2	104.85	odd	12
4225.2.a.r.1.1		2	65.19	odd	12
5200.2.a.bu.1.1		2	260.59	even	12
7605.2.a.x.1.1		2	39.32	even	12
7865.2.a.j.1.2		2	143.98	even	12
9360.2.a.cd.1.1		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+(-2.09077 - 1.20711i) q^{2} +(0.707107 - 1.22474i) q^{3} +(1.91421 + 3.31552i) q^{4} -1.00000i q^{5} +(-2.95680 + 1.70711i) q^{6} +(4.18154 - 2.41421i) q^{7} -4.41421i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.20711 + 2.09077i) q^{10} +(-2.95680 - 1.70711i) q^{11} +5.41421 q^{12} -11.6569 q^{14} +(-1.22474 - 0.707107i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.414214 + 0.717439i) q^{17} -2.41421i q^{18} +(-0.507306 + 0.292893i) q^{19} +(3.31552 - 1.91421i) q^{20} -6.82843i q^{21} +(4.12132 + 7.13834i) q^{22} +(0.707107 - 1.22474i) q^{23} +(-5.40629 - 3.12132i) q^{24} -1.00000 q^{25} +5.65685 q^{27} +(16.0087 + 9.24264i) q^{28} +(2.82843 - 4.89898i) q^{29} +(1.70711 + 2.95680i) q^{30} -1.75736i q^{31} +(-1.37333 + 0.792893i) q^{32} +(-4.18154 + 2.41421i) q^{33} -2.00000i q^{34} +(-2.41421 - 4.18154i) q^{35} +(-1.91421 + 3.31552i) q^{36} +(7.34847 + 4.24264i) q^{37} +1.41421 q^{38} -4.41421 q^{40} +(-2.74666 - 1.58579i) q^{41} +(-8.24264 + 14.2767i) q^{42} +(-5.53553 - 9.58783i) q^{43} -13.0711i q^{44} +(0.866025 - 0.500000i) q^{45} +(-2.95680 + 1.70711i) q^{46} -4.82843i q^{47} +(2.12132 + 3.67423i) q^{48} +(8.15685 - 14.1281i) q^{49} +(2.09077 + 1.20711i) q^{50} +1.17157 q^{51} +2.48528 q^{53} +(-11.8272 - 6.82843i) q^{54} +(-1.70711 + 2.95680i) q^{55} +(-10.6569 - 18.4582i) q^{56} +0.828427i q^{57} +(-11.8272 + 6.82843i) q^{58} +(1.52192 - 0.878680i) q^{59} -5.41421i q^{60} +(4.00000 + 6.92820i) q^{61} +(-2.12132 + 3.67423i) q^{62} +(4.18154 + 2.41421i) q^{63} +9.82843 q^{64} +11.6569 q^{66} +(-1.73205 - 1.00000i) q^{67} +(-1.58579 + 2.74666i) q^{68} +(-1.00000 - 1.73205i) q^{69} +11.6569i q^{70} +(-10.3053 + 5.94975i) q^{71} +(3.82282 - 2.20711i) q^{72} +8.48528i q^{73} +(-10.2426 - 17.7408i) q^{74} +(-0.707107 + 1.22474i) q^{75} +(-1.94218 - 1.12132i) q^{76} -16.4853 q^{77} -8.48528 q^{79} +(2.59808 + 1.50000i) q^{80} +(2.50000 - 4.33013i) q^{81} +(3.82843 + 6.63103i) q^{82} +3.17157i q^{83} +(22.6398 - 13.0711i) q^{84} +(0.717439 - 0.414214i) q^{85} +26.7279i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-7.53553 + 13.0519i) q^{88} +(-5.19615 - 3.00000i) q^{89} -2.41421 q^{90} +5.41421 q^{92} +(-2.15232 - 1.24264i) q^{93} +(-5.82843 + 10.0951i) q^{94} +(0.292893 + 0.507306i) q^{95} +2.24264i q^{96} +(6.63103 - 3.82843i) q^{97} +(-34.1082 + 19.6924i) q^{98} -3.41421i 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

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