LMFDB - Embedded newform 841.2.e.d.196.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,-2,6,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			196.1
Root			$0.974928 + 0.222521i$ of defining polynomial
Character	$\chi$	$=$	841.196
Dual form			841.2.e.d.236.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21572 + 0.277479i) q^{2} +(-0.781831 + 1.62349i) q^{3} +(-0.400969 + 0.193096i) q^{4} +(-0.900969 - 3.94740i) q^{5} +(0.500000 - 2.19064i) q^{6} +(-0.623490 - 0.300257i) q^{7} +(2.38374 - 1.90097i) q^{8} +(-0.153989 - 0.193096i) q^{9} +(2.19064 + 4.54892i) q^{10} +(2.22889 + 1.77748i) q^{11} -0.801938i q^{12} +(-0.914542 + 1.14680i) q^{13} +(0.841301 + 0.192021i) q^{14} +(7.11297 + 1.62349i) q^{15} +(-1.81551 + 2.27658i) q^{16} +1.60388i q^{17} +(0.240787 + 0.192021i) q^{18} +(-1.16802 - 2.42543i) q^{19} +(1.12349 + 1.40881i) q^{20} +(0.974928 - 0.777479i) q^{21} +(-3.20291 - 1.54244i) q^{22} +(1.14795 - 5.02949i) q^{23} +(1.22252 + 5.35621i) q^{24} +(-10.2654 + 4.94355i) q^{25} +(0.793610 - 1.64795i) q^{26} +(-4.83639 + 1.10388i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(1.90216 - 0.434157i) q^{31} +(-1.07031 + 2.22252i) q^{32} +(-4.62833 + 2.22889i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(-0.623490 + 2.73169i) q^{35} +(0.0990311 + 0.0476909i) q^{36} +(-2.22889 + 1.77748i) q^{37} +(2.09299 + 2.62453i) q^{38} +(-1.14680 - 2.38135i) q^{39} +(-9.65156 - 7.69687i) q^{40} +6.49396i q^{41} +(-0.969501 + 1.21572i) q^{42} +(0.648205 + 0.147948i) q^{43} +(-1.23694 - 0.282323i) q^{44} +(-0.623490 + 0.781831i) q^{45} +6.43296i q^{46} +(-3.71606 - 2.96346i) q^{47} +(-2.27658 - 4.72737i) q^{48} +(-4.06584 - 5.09841i) q^{49} +(11.1081 - 8.85839i) q^{50} +(-2.60388 - 1.25396i) q^{51} +(0.145260 - 0.636426i) q^{52} +(-0.0108851 - 0.0476909i) q^{53} +(5.57338 - 2.68400i) q^{54} +(5.00827 - 10.3998i) q^{55} +(-2.05702 + 0.469501i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(-3.16557 + 0.722521i) q^{60} +(0.567511 - 1.17845i) q^{61} +(-2.19202 + 1.05562i) q^{62} +(0.0380322 + 0.166630i) q^{63} +(1.98039 - 8.67664i) q^{64} +(5.35086 + 2.57684i) q^{65} +(5.00827 - 3.99396i) q^{66} +(-9.32036 - 11.6874i) q^{67} +(-0.309703 - 0.643104i) q^{68} +(7.26782 + 5.79590i) q^{69} -3.49396i q^{70} +(1.40850 - 1.76621i) q^{71} +(-0.734141 - 0.167563i) q^{72} +(-8.11437 - 1.85205i) q^{73} +(2.21648 - 2.77938i) q^{74} -20.5308i q^{75} +(0.936683 + 0.746980i) q^{76} +(-0.855989 - 1.77748i) q^{77} +(2.05496 + 2.57684i) q^{78} +(-7.61577 + 6.07338i) q^{79} +(10.6223 + 5.11543i) q^{80} +(2.15399 - 9.43724i) q^{81} +(-1.80194 - 7.89481i) q^{82} +(3.62349 - 1.74498i) q^{83} +(-0.240787 + 0.500000i) q^{84} +(6.33114 - 1.44504i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(-10.9744 + 2.50484i) q^{89} +(0.541044 - 1.12349i) q^{90} +(0.914542 - 0.440420i) q^{91} +(0.510885 + 2.23833i) q^{92} +(-0.782323 + 3.42758i) q^{93} +(5.33997 + 2.57159i) q^{94} +(-8.52179 + 6.79590i) q^{95} +(-2.77144 - 3.47527i) q^{96} +(1.98286 + 4.11745i) q^{97} +(6.35761 + 5.07002i) q^{98} -0.704103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

Coefficient data

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

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

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

$2$	−1.21572	+	0.277479i	−0.859640	+	0.196207i	−0.629548	−	0.776961i	$-0.716760\pi$
$2$	−1.21572	+	0.277479i	−0.859640	+	0.196207i	−0.230092	+	0.973169i	$0.573903\pi$
$3$	−0.781831	+	1.62349i	−0.451391	+	0.937322i	0.543786	+	0.839224i	$0.316990\pi$
$3$	−0.781831	+	1.62349i	−0.451391	+	0.937322i	−0.995177	+	0.0980984i	$0.968724\pi$
$4$	−0.400969	+	0.193096i	−0.200484	+	0.0965482i
$5$	−0.900969	−	3.94740i	−0.402926	−	1.76533i	−0.615450	−	0.788176i	$-0.711026\pi$
$5$	−0.900969	−	3.94740i	−0.402926	−	1.76533i	0.212524	−	0.977156i	$-0.431832\pi$
$6$	0.500000	−	2.19064i	0.204124	−	0.894326i
$7$	−0.623490	−	0.300257i	−0.235657	−	0.113486i	0.312329	−	0.949974i	$-0.398891\pi$
$7$	−0.623490	−	0.300257i	−0.235657	−	0.113486i	−0.547986	+	0.836488i	$0.684605\pi$
$8$	2.38374	−	1.90097i	0.842779	−	0.672094i
$9$	−0.153989	−	0.193096i	−0.0513298	−	0.0643655i
$10$	2.19064	+	4.54892i	0.692742	+	1.43849i
$11$	2.22889	+	1.77748i	0.672035	+	0.535930i	0.898987	−	0.437976i	$-0.144304\pi$
$11$	2.22889	+	1.77748i	0.672035	+	0.535930i	−0.226952	+	0.973906i	$0.572876\pi$
$12$		−	0.801938i		−	0.231499i
$13$	−0.914542	+	1.14680i	−0.253648	+	0.318065i	−0.892310	−	0.451422i	$-0.850917\pi$
$13$	−0.914542	+	1.14680i	−0.253648	+	0.318065i	0.638662	+	0.769487i	$0.279488\pi$
$14$	0.841301	+	0.192021i	0.224847	+	0.0513199i
$15$	7.11297	+	1.62349i	1.83656	+	0.419183i
$16$	−1.81551	+	2.27658i	−0.453878	+	0.569145i
$17$			1.60388i			0.388997i	0.980903	+	0.194498i	$0.0623079\pi$
$17$			1.60388i			0.388997i	−0.980903	+	0.194498i	$0.937692\pi$
$18$	0.240787	+	0.192021i	0.0567541	+	0.0452599i
$19$	−1.16802	−	2.42543i	−0.267963	−	0.556431i	0.722955	−	0.690895i	$-0.242783\pi$
$19$	−1.16802	−	2.42543i	−0.267963	−	0.556431i	−0.990919	+	0.134463i	$0.957069\pi$
$20$	1.12349	+	1.40881i	0.251220	+	0.315020i
$21$	0.974928	−	0.777479i	0.212747	−	0.169660i
$22$	−3.20291	−	1.54244i	−0.682862	−	0.328849i
$23$	1.14795	−	5.02949i	0.239364	−	1.04872i	−0.702225	−	0.711955i	$-0.747810\pi$
$23$	1.14795	−	5.02949i	0.239364	−	1.04872i	0.941588	−	0.336766i	$-0.109333\pi$
$24$	1.22252	+	5.35621i	0.249546	+	1.09333i
$25$	−10.2654	+	4.94355i	−2.05308	+	0.988711i
$26$	0.793610	−	1.64795i	0.155640	−	0.323189i
$27$	−4.83639	+	1.10388i	−0.930765	+	0.212441i
$28$	0.307979			0.0582025
$29$		0			0
$29$		0			0
$30$	−9.09783			−1.66103
$31$	1.90216	−	0.434157i	0.341639	−	0.0779769i	−0.0482592	−	0.998835i	$-0.515367\pi$
$31$	1.90216	−	0.434157i	0.341639	−	0.0779769i	0.389898	+	0.920858i	$0.372510\pi$
$32$	−1.07031	+	2.22252i	−0.189206	+	0.392890i
$33$	−4.62833	+	2.22889i	−0.805690	+	0.388000i
$34$	−0.445042	−	1.94986i	−0.0763241	−	0.334398i
$35$	−0.623490	+	2.73169i	−0.105389	+	0.461739i
$36$	0.0990311	+	0.0476909i	0.0165052	+	0.00794848i
$37$	−2.22889	+	1.77748i	−0.366427	+	0.292216i	−0.789342	−	0.613953i	$-0.789578\pi$
$37$	−2.22889	+	1.77748i	−0.366427	+	0.292216i	0.422915	+	0.906169i	$0.361007\pi$
$38$	2.09299	+	2.62453i	0.339528	+	0.425754i
$39$	−1.14680	−	2.38135i	−0.183635	−	0.381322i
$40$	−9.65156	−	7.69687i	−1.52605	−	1.21698i
$41$			6.49396i			1.01419i	0.861891	+	0.507093i	$0.169280\pi$
$41$			6.49396i			1.01419i	−0.861891	+	0.507093i	$0.830720\pi$
$42$	−0.969501	+	1.21572i	−0.149597	+	0.187589i
$43$	0.648205	+	0.147948i	0.0988503	+	0.0225619i	0.271660	−	0.962393i	$-0.412427\pi$
$43$	0.648205	+	0.147948i	0.0988503	+	0.0225619i	−0.172810	+	0.984955i	$0.555285\pi$
$44$	−1.23694	−	0.282323i	−0.186476	−	0.0425619i
$45$	−0.623490	+	0.781831i	−0.0929444	+	0.116549i
$46$			6.43296i			0.948488i
$47$	−3.71606	−	2.96346i	−0.542043	−	0.432265i	0.313809	−	0.949486i	$-0.398395\pi$
$47$	−3.71606	−	2.96346i	−0.542043	−	0.432265i	−0.855852	+	0.517221i	$0.826966\pi$
$48$	−2.27658	−	4.72737i	−0.328596	−	0.682336i
$49$	−4.06584	−	5.09841i	−0.580835	−	0.728344i
$50$	11.1081	−	8.85839i	1.57092	−	1.25277i
$51$	−2.60388	−	1.25396i	−0.364615	−	0.175590i
$52$	0.145260	−	0.636426i	0.0201439	−	0.0882564i
$53$	−0.0108851	−	0.0476909i	−0.00149519	−	0.00655085i	0.974175	−	0.225795i	$-0.0724980\pi$
$53$	−0.0108851	−	0.0476909i	−0.00149519	−	0.00655085i	−0.975670	+	0.219244i	$0.929641\pi$
$54$	5.57338	−	2.68400i	0.758440	−	0.365246i
$55$	5.00827	−	10.3998i	0.675315	−	1.40231i
$56$	−2.05702	+	0.469501i	−0.274880	+	0.0627396i
$57$	4.85086			0.642511
$58$		0			0
$59$	−6.39612			−0.832704			−0.416352	−	0.909203i	$-0.636692\pi$
$59$	−6.39612			−0.832704			−0.416352	+	0.909203i	$0.636692\pi$
$60$	−3.16557	+	0.722521i	−0.408673	+	0.0932771i
$61$	0.567511	−	1.17845i	0.0726623	−	0.150885i	−0.861474	−	0.507802i	$-0.830458\pi$
$61$	0.567511	−	1.17845i	0.0726623	−	0.150885i	0.934136	+	0.356918i	$0.116172\pi$
$62$	−2.19202	+	1.05562i	−0.278387	+	0.134064i
$63$	0.0380322	+	0.166630i	0.00479161	+	0.0209934i
$64$	1.98039	−	8.67664i	0.247548	−	1.08458i
$65$	5.35086	+	2.57684i	0.663692	+	0.319617i
$66$	5.00827	−	3.99396i	0.616475	−	0.491622i
$67$	−9.32036	−	11.6874i	−1.13866	−	1.42784i	−0.888048	−	0.459751i	$-0.847939\pi$
$67$	−9.32036	−	11.6874i	−1.13866	−	1.42784i	−0.250615	−	0.968087i	$-0.580633\pi$
$68$	−0.309703	−	0.643104i	−0.0375570	−	0.0779878i
$69$	7.26782	+	5.79590i	0.874943	+	0.697744i
$70$		−	3.49396i		−	0.417608i
$71$	1.40850	−	1.76621i	0.167158	−	0.209610i	−0.691196	−	0.722667i	$-0.742916\pi$
$71$	1.40850	−	1.76621i	0.167158	−	0.209610i	0.858354	+	0.513057i	$0.171487\pi$
$72$	−0.734141	−	0.167563i	−0.0865193	−	0.0197475i
$73$	−8.11437	−	1.85205i	−0.949715	−	0.216766i	−0.280516	−	0.959849i	$-0.590506\pi$
$73$	−8.11437	−	1.85205i	−0.949715	−	0.216766i	−0.669199	+	0.743083i	$0.733363\pi$
$74$	2.21648	−	2.77938i	0.257661	−	0.323096i
$75$		−	20.5308i		−	2.37069i
$76$	0.936683	+	0.746980i	0.107445	+	0.0856844i
$77$	−0.855989	−	1.77748i	−0.0975490	−	0.202563i
$78$	2.05496	+	2.57684i	0.232678	+	0.291769i
$79$	−7.61577	+	6.07338i	−0.856841	+	0.683308i	−0.949968	−	0.312346i	$-0.898885\pi$
$79$	−7.61577	+	6.07338i	−0.856841	+	0.683308i	0.0931270	+	0.995654i	$0.470314\pi$
$80$	10.6223	+	5.11543i	1.18761	+	0.571922i
$81$	2.15399	−	9.43724i	0.239332	−	1.04858i
$82$	−1.80194	−	7.89481i	−0.198991	−	0.871835i
$83$	3.62349	−	1.74498i	0.397730	−	0.191537i	−0.224318	−	0.974516i	$-0.572015\pi$
$83$	3.62349	−	1.74498i	0.397730	−	0.191537i	0.622047	+	0.782980i	$0.286301\pi$
$84$	−0.240787	+	0.500000i	−0.0262720	+	0.0545545i
$85$	6.33114	−	1.44504i	0.686709	−	0.156737i
$86$	−0.829085			−0.0894025
$87$		0			0
$88$	8.69202			0.926573
$89$	−10.9744	+	2.50484i	−1.16329	+	0.265513i	−0.760225	−	0.649659i	$-0.774912\pi$
$89$	−10.9744	+	2.50484i	−1.16329	+	0.265513i	−0.403063	+	0.915172i	$0.632054\pi$
$90$	0.541044	−	1.12349i	0.0570311	−	0.118426i
$91$	0.914542	−	0.440420i	0.0958701	−	0.0461686i
$92$	0.510885	+	2.23833i	0.0532635	+	0.233362i
$93$	−0.782323	+	3.42758i	−0.0811232	+	0.355424i
$94$	5.33997	+	2.57159i	0.550776	+	0.265240i
$95$	−8.52179	+	6.79590i	−0.874317	+	0.697244i
$96$	−2.77144	−	3.47527i	−0.282859	−	0.354694i
$97$	1.98286	+	4.11745i	0.201329	+	0.418064i	0.977049	−	0.213013i	$-0.0683277\pi$
$97$	1.98286	+	4.11745i	0.201329	+	0.418064i	−0.775721	+	0.631077i	$0.782613\pi$
$98$	6.35761	+	5.07002i	0.642215	+	0.512150i
$99$		−	0.704103i		−	0.0707650i
$100$	3.16152	−	3.96442i	0.316152	−	0.396442i
$101$	3.13257	+	0.714988i	0.311702	+	0.0711440i	0.375510	−	0.926818i	$-0.377467\pi$
$101$	3.13257	+	0.714988i	0.311702	+	0.0711440i	−0.0638082	+	0.997962i	$0.520325\pi$
$102$	3.51352	+	0.801938i	0.347890	+	0.0794037i
$103$	−4.07338	+	5.10785i	−0.401362	+	0.503292i	−0.940907	−	0.338665i	$-0.890025\pi$
$103$	−4.07338	+	5.10785i	−0.401362	+	0.503292i	0.539545	+	0.841957i	$0.318596\pi$
$104$			4.47219i			0.438534i
$105$	−3.94740	−	3.14795i	−0.385227	−	0.307208i
$106$	0.0264664	+	0.0549581i	0.00257065	+	0.00533801i
$107$	−3.60656	−	4.52249i	−0.348660	−	0.437205i	0.576319	−	0.817225i	$-0.304489\pi$
$107$	−3.60656	−	4.52249i	−0.348660	−	0.437205i	−0.924978	+	0.380020i	$0.875917\pi$
$108$	1.72609	−	1.37651i	0.166093	−	0.132455i
$109$	8.27628	+	3.98565i	0.792724	+	0.381756i	0.786004	−	0.618222i	$-0.212147\pi$
$109$	8.27628	+	3.98565i	0.792724	+	0.381756i	0.00672026	+	0.999977i	$0.497861\pi$
$110$	−3.20291	+	14.0329i	−0.305385	+	1.33798i
$111$	−1.14310	−	5.00827i	−0.108499	−	0.475364i
$112$	1.81551	−	0.874304i	0.171550	−	0.0826140i
$113$	−3.89027	+	8.07822i	−0.365965	+	0.759935i	−0.999910	−	0.0134437i	$-0.995721\pi$
$113$	−3.89027	+	8.07822i	−0.365965	+	0.759935i	0.633944	+	0.773379i	$0.281435\pi$
$114$	−5.89726	+	1.34601i	−0.552329	+	0.126065i
$115$	−20.8877			−1.94779
$116$		0			0
$117$	0.362273			0.0334921
$118$	7.77587	−	1.77479i	0.715826	−	0.163383i
$119$	0.481575	−	1.00000i	0.0441459	−	0.0916698i
$120$	20.0417	−	9.65156i	1.82955	−	0.881063i
$121$	−0.639219	−	2.80060i	−0.0581108	−	0.254600i
$122$	−0.362937	+	1.59013i	−0.0328587	+	0.143964i
$123$	−10.5429	−	5.07718i	−0.950619	−	0.457794i
$124$	−0.678875	+	0.541385i	−0.0609648	+	0.0486178i
$125$	16.1407	+	20.2398i	1.44367	+	1.81030i
$126$	−0.0924727	−	0.192021i	−0.00823812	−	0.0171066i
$127$	−12.1689	−	9.70440i	−1.07982	−	0.861126i	−0.0889600	−	0.996035i	$-0.528354\pi$
$127$	−12.1689	−	9.70440i	−1.07982	−	0.861126i	−0.990858	+	0.134909i	$0.956926\pi$
$128$			6.16421i			0.544844i
$129$	−0.746980	+	0.936683i	−0.0657679	+	0.0824703i
$130$	−7.22013	−	1.64795i	−0.633248	−	0.144535i
$131$	−13.0962	−	2.98911i	−1.14422	−	0.261160i	−0.391930	−	0.919995i	$-0.628192\pi$
$131$	−13.0962	−	2.98911i	−1.14422	−	0.261160i	−0.752288	+	0.658835i	$0.771050\pi$
$132$	1.42543	−	1.78743i	0.124068	−	0.155576i
$133$			1.86294i			0.161537i
$134$	14.5739	+	11.6223i	1.25899	+	1.00401i
$135$	8.71488	+	18.0966i	0.750058	+	1.55751i
$136$	3.04892	+	3.82322i	0.261443	+	0.327839i
$137$	−13.2851	+	10.5945i	−1.13502	+	0.905148i	−0.996364	−	0.0851931i	$-0.972849\pi$
$137$	−13.2851	+	10.5945i	−1.13502	+	0.905148i	−0.138655	+	0.990341i	$0.544278\pi$
$138$	−10.4438	−	5.02949i	−0.889039	−	0.428139i
$139$	−2.77359	+	12.1519i	−0.235253	+	1.03071i	0.709956	+	0.704246i	$0.248715\pi$
$139$	−2.77359	+	12.1519i	−0.235253	+	1.03071i	−0.945209	+	0.326465i	$0.894142\pi$
$140$	−0.277479	−	1.21572i	−0.0234513	−	0.102747i
$141$	7.71648	−	3.71606i	0.649845	−	0.312949i
$142$	−1.22225	+	2.53803i	−0.102569	+	0.212987i
$143$	−4.07683	+	0.930509i	−0.340921	+	0.0778131i
$144$	0.719169			0.0599307
$145$		0			0
$146$	10.3787			0.858945
$147$	11.4560	−	2.61476i	0.944876	−	0.215662i
$148$	0.550490	−	1.14310i	0.0452500	−	0.0939626i
$149$	−16.5015	+	7.94670i	−1.35185	+	0.651019i	−0.962805	−	0.270198i	$-0.912911\pi$
$149$	−16.5015	+	7.94670i	−1.35185	+	0.651019i	−0.389050	+	0.921217i	$0.627197\pi$
$150$	5.69687	+	24.9596i	0.465147	+	2.03794i
$151$	−4.23609	+	18.5595i	−0.344728	+	1.51035i	0.444233	+	0.895911i	$0.353476\pi$
$151$	−4.23609	+	18.5595i	−0.344728	+	1.51035i	−0.788961	+	0.614443i	$0.789381\pi$
$152$	−7.39493	−	3.56121i	−0.599808	−	0.288852i
$153$	0.309703	−	0.246980i	0.0250380	−	0.0199671i
$154$	1.53385	+	1.92339i	0.123601	+	0.154991i
$155$	−3.42758	−	7.11745i	−0.275310	−	0.571687i
$156$	0.919662	+	0.733406i	0.0736319	+	0.0587195i
$157$		−	11.4383i		−	0.912879i	−0.889755	−	0.456439i	$-0.849125\pi$
$157$		−	11.4383i		−	0.912879i	0.889755	−	0.456439i	$-0.150875\pi$
$158$	7.57338	−	9.49671i	0.602505	−	0.755518i
$159$	0.0859360	+	0.0196143i	0.00681517	+	0.00155552i
$160$	9.73750	+	2.22252i	0.769817	+	0.175706i
$161$	−2.22587	+	2.79116i	−0.175423	+	0.219974i
$162$			12.0707i			0.948363i
$163$	−5.21838	−	4.16152i	−0.408735	−	0.325956i	0.397444	−	0.917626i	$-0.369897\pi$
$163$	−5.21838	−	4.16152i	−0.408735	−	0.325956i	−0.806180	+	0.591671i	$0.798469\pi$
$164$	−1.25396	−	2.60388i	−0.0979179	−	0.203329i
$165$	12.9683	+	16.2617i	1.00958	+	1.26597i
$166$	−3.92094	+	3.12684i	−0.304324	+	0.242690i
$167$	−13.2153	−	6.36415i	−1.02263	−	0.492472i	−0.154071	−	0.988060i	$-0.549239\pi$
$167$	−13.2153	−	6.36415i	−1.02263	−	0.492472i	−0.868558	+	0.495587i	$0.834953\pi$
$168$	0.846011	−	3.70662i	0.0652711	−	0.285972i
$169$	2.41401	+	10.5765i	0.185693	+	0.813575i
$170$	−7.29590	+	3.51352i	−0.559570	+	0.269475i
$171$	−0.288478	+	0.599031i	−0.0220605	+	0.0458091i
$172$	−0.288478	+	0.0658433i	−0.0219963	+	0.00502050i
$173$	23.3599			1.77602			0.888009	−	0.459825i	$-0.152088\pi$
$173$	23.3599			1.77602			0.888009	+	0.459825i	$0.152088\pi$
$174$		0			0
$175$	7.88471			0.596028
$176$	−8.09314	+	1.84721i	−0.610044	+	0.139238i
$177$	5.00069	−	10.3840i	0.375875	−	0.780512i
$178$	12.6468	−	6.09035i	0.947914	−	0.456491i
$179$	−0.147948	−	0.648205i	−0.0110582	−	0.0484491i	0.969098	−	0.246677i	$-0.0793386\pi$
$179$	−0.147948	−	0.648205i	−0.0110582	−	0.0484491i	−0.980156	+	0.198228i	$0.936481\pi$
$180$	0.0990311	−	0.433884i	0.00738134	−	0.0323398i
$181$	−9.88016	−	4.75803i	−0.734386	−	0.353662i	0.0290213	−	0.999579i	$-0.490761\pi$
$181$	−9.88016	−	4.75803i	−0.734386	−	0.353662i	−0.763408	+	0.645917i	$0.776475\pi$
$182$	−0.989616	+	0.789192i	−0.0733552	+	0.0584988i
$183$	1.46950	+	1.84270i	0.108629	+	0.136216i
$184$	−6.82450	−	14.1712i	−0.503108	−	1.04472i
$185$	9.02458	+	7.19687i	0.663501	+	0.529124i
$186$		−	4.38404i		−	0.321454i
$187$	−2.85086	+	3.57486i	−0.208475	+	0.261420i
$188$	2.06226	+	0.470697i	0.150406	+	0.0343291i
$189$	3.34689	+	0.763906i	0.243450	+	0.0555660i
$190$	8.47434	−	10.6265i	0.614794	−	0.770927i
$191$			0.518122i			0.0374900i	0.999824	+	0.0187450i	$0.00596707\pi$
$191$			0.518122i			0.0374900i	−0.999824	+	0.0187450i	$0.994033\pi$
$192$	12.5381	+	9.99880i	0.904860	+	0.721601i
$193$	0.601552	+	1.24914i	0.0433007	+	0.0899147i	0.921497	−	0.388386i	$-0.126967\pi$
$193$	0.601552	+	1.24914i	0.0433007	+	0.0899147i	−0.878196	+	0.478301i	$0.841253\pi$
$194$	−3.55310	−	4.45544i	−0.255098	−	0.319882i
$195$	−8.36693	+	6.67241i	−0.599169	+	0.477821i
$196$	2.61476	+	1.25920i	0.186769	+	0.0899430i
$197$	−2.88351	+	12.6335i	−0.205442	+	0.900099i	0.762114	+	0.647442i	$0.224161\pi$
$197$	−2.88351	+	12.6335i	−0.205442	+	0.900099i	−0.967556	+	0.252656i	$0.918696\pi$
$198$	0.195374	+	0.855989i	0.0138846	+	0.0608325i
$199$	17.5722	−	8.46232i	1.24566	−	0.599878i	0.309314	−	0.950960i	$-0.399901\pi$
$199$	17.5722	−	8.46232i	1.24566	−	0.599878i	0.936345	+	0.351082i	$0.114186\pi$
$200$	−15.0725	+	31.2983i	−1.06579	+	2.21313i
$201$	26.2613	−	5.99396i	1.85233	−	0.422781i
$202$	−4.00670			−0.281911
$203$		0			0
$204$	1.28621			0.0900526
$205$	25.6343	−	5.85086i	1.79038	−	0.408641i
$206$	3.53474	−	7.33997i	0.246277	−	0.511400i
$207$	−1.14795	+	0.552823i	−0.0797879	+	0.0384238i
$208$	−0.950419	−	4.16406i	−0.0658997	−	0.288725i
$209$	1.70775	−	7.48215i	0.118128	−	0.517551i
$210$	5.67241	+	2.73169i	0.391433	+	0.188504i
$211$	16.1300	−	12.8632i	1.11043	−	0.885541i	0.116248	−	0.993220i	$-0.462913\pi$
$211$	16.1300	−	12.8632i	1.11043	−	0.885541i	0.994186	+	0.107679i	$0.0343418\pi$
$212$	0.0135735	+	0.0170207i	0.000932234	+	0.00116898i
$213$	1.76621	+	3.66756i	0.121018	+	0.251297i
$214$	5.63945	+	4.49731i	0.385505	+	0.307430i
$215$		−	2.69202i		−	0.183594i
$216$	−9.43027	+	11.8252i	−0.641649	+	0.804602i
$217$	−1.31634	−	0.300446i	−0.0893589	−	0.0203956i
$218$	−11.1675	−	2.54892i	−0.756361	−	0.172634i
$219$	9.35086	−	11.7256i	0.631872	−	0.792343i
$220$			5.13706i			0.346341i
$221$	−1.83932	−	1.46681i	−0.123726	−	0.0986685i
$222$	2.77938	+	5.77144i	0.186540	+	0.387354i
$223$	−13.1561	−	16.4973i	−0.881001	−	1.10474i	−0.993807	−	0.111123i	$-0.964555\pi$
$223$	−13.1561	−	16.4973i	−0.881001	−	1.10474i	0.112806	−	0.993617i	$-0.464016\pi$
$224$	1.33465	−	1.06435i	0.0891753	−	0.0711150i
$225$	2.53534	+	1.22096i	0.169023	+	0.0813971i
$226$	2.48792	−	10.9003i	0.165494	−	0.725076i
$227$	−1.58761	−	6.95579i	−0.105374	−	0.461672i	−0.999893	−	0.0146424i	$-0.995339\pi$
$227$	−1.58761	−	6.95579i	−0.105374	−	0.461672i	0.894519	−	0.447030i	$-0.147518\pi$
$228$	−1.94504	+	0.936683i	−0.128814	+	0.0620333i
$229$	−0.977261	+	2.02930i	−0.0645792	+	0.134100i	−0.930760	−	0.365631i	$-0.880853\pi$
$229$	−0.977261	+	2.02930i	−0.0645792	+	0.134100i	0.866181	+	0.499731i	$0.166568\pi$
$230$	25.3935	−	5.79590i	1.67440	−	0.382170i
$231$	3.55496			0.233899
$232$		0			0
$233$	18.9095			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$233$	18.9095			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$234$	−0.440420	+	0.100523i	−0.0287912	+	0.00657140i
$235$	−8.34991	+	17.3388i	−0.544688	+	1.13106i
$236$	2.56465	−	1.23507i	0.166944	−	0.0803961i
$237$	−3.90581	−	17.1125i	−0.253710	−	1.11158i
$238$	−0.307979	+	1.34934i	−0.0199633	+	0.0874649i
$239$	18.4448	+	8.88255i	1.19310	+	0.574564i	0.921700	−	0.387904i	$-0.126801\pi$
$239$	18.4448	+	8.88255i	1.19310	+	0.574564i	0.271395	+	0.962468i	$0.412515\pi$
$240$	−16.6097	+	13.2458i	−1.07215	+	0.855012i
$241$	−4.59448	−	5.76130i	−0.295957	−	0.371118i	0.611514	−	0.791234i	$-0.290561\pi$
$241$	−4.59448	−	5.76130i	−0.295957	−	0.371118i	−0.907470	+	0.420116i	$0.861989\pi$
$242$	1.55422	+	3.22737i	0.0999089	+	0.207463i
$243$	2.00175	+	1.59634i	0.128412	+	0.102405i
$244$			0.582105i			0.0372655i
$245$	−16.4623	+	20.6430i	−1.05174	+	1.31883i
$246$	14.2259	+	3.24698i	0.907013	+	0.207020i
$247$	3.84969	+	0.878666i	0.244950	+	0.0559082i
$248$	3.70895	−	4.65087i	0.235518	−	0.295331i
$249$			7.24698i			0.459259i
$250$	−25.2386	−	20.1271i	−1.59623	−	1.27295i
$251$	5.62114	+	11.6724i	0.354803	+	0.736756i	0.999620	−	0.0275815i	$-0.00878057\pi$
$251$	5.62114	+	11.6724i	0.354803	+	0.736756i	−0.644817	+	0.764337i	$0.723066\pi$
$252$	−0.0474254	−	0.0594696i	−0.00298752	−	0.00374623i
$253$	11.4985	−	9.16972i	0.722902	−	0.576495i
$254$	17.4867	+	8.42116i	1.09721	+	0.528391i
$255$	−2.60388	+	11.4083i	−0.163061	+	0.714417i
$256$	2.25033	+	9.85935i	0.140646	+	0.616209i
$257$	−15.0390	+	7.24240i	−0.938107	+	0.451768i	−0.839501	−	0.543358i	$-0.817153\pi$
$257$	−15.0390	+	7.24240i	−0.938107	+	0.451768i	−0.0986056	+	0.995127i	$0.531438\pi$
$258$	0.648205	−	1.34601i	0.0403555	−	0.0837990i
$259$	1.92339	−	0.439001i	0.119514	−	0.0272782i
$260$	−2.64310			−0.163918
$261$		0			0
$262$	16.7506			1.03486
$263$	−17.1678	+	3.91843i	−1.05861	+	0.241621i	−0.716175	−	0.697921i	$-0.754109\pi$
$263$	−17.1678	+	3.91843i	−1.05861	+	0.241621i	−0.342434	+	0.939542i	$0.611251\pi$
$264$	−6.79570	+	14.1114i	−0.418246	+	0.868497i
$265$	−0.178448	+	0.0859360i	−0.0109620	+	0.00527901i
$266$	−0.516926	−	2.26480i	−0.0316948	−	0.138864i
$267$	4.51357	−	19.7753i	0.276226	−	1.21023i
$268$	5.99396	+	2.88654i	0.366139	+	0.176323i
$269$	−5.24568	+	4.18329i	−0.319835	+	0.255060i	−0.770225	−	0.637772i	$-0.779856\pi$
$269$	−5.24568	+	4.18329i	−0.319835	+	0.255060i	0.450390	+	0.892832i	$0.351285\pi$
$270$	−15.6163	−	19.5822i	−0.950375	−	1.19173i
$271$	−5.49638	−	11.4133i	−0.333881	−	0.693311i	0.664669	−	0.747138i	$-0.268573\pi$
$271$	−5.49638	−	11.4133i	−0.333881	−	0.693311i	−0.998550	+	0.0538264i	$0.982858\pi$
$272$	−3.65135	−	2.91185i	−0.221396	−	0.176557i
$273$			1.82908i			0.110701i
$274$	13.2111	−	16.5662i	0.798112	−	1.00080i
$275$	−31.6675	−	7.22790i	−1.90962	−	0.435859i
$276$	−4.03334	−	0.920583i	−0.242778	−	0.0554126i
$277$	9.81431	−	12.3068i	0.589685	−	0.739442i	−0.394046	−	0.919091i	$-0.628925\pi$
$277$	9.81431	−	12.3068i	0.589685	−	0.739442i	0.983731	+	0.179649i	$0.0574963\pi$
$278$		−	15.5429i		−	0.932200i
$279$	−0.376747	−	0.300446i	−0.0225553	−	0.0179872i
$280$	3.70662	+	7.69687i	0.221513	+	0.459976i
$281$	7.36629	+	9.23703i	0.439436	+	0.551035i	0.951394	−	0.307975i	$-0.0996513\pi$
$281$	7.36629	+	9.23703i	0.439436	+	0.551035i	−0.511959	+	0.859010i	$0.671080\pi$
$282$	−8.34991	+	6.65883i	−0.497230	+	0.396528i
$283$	−1.98039	−	0.953703i	−0.117722	−	0.0566918i	0.374096	−	0.927390i	$-0.377953\pi$
$283$	−1.98039	−	0.953703i	−0.117722	−	0.0566918i	−0.491818	+	0.870698i	$0.663667\pi$
$284$	−0.223717	+	0.980170i	−0.0132752	+	0.0581624i
$285$	−4.37047	−	19.1483i	−0.258884	−	1.13425i
$286$	4.69806	−	2.26247i	0.277802	−	0.133783i
$287$	1.94986	−	4.04892i	0.115096	−	0.239000i
$288$	0.593977	−	0.135571i	0.0350004	−	0.00798862i
$289$	14.4276			0.848681
$290$		0			0
$291$	−8.23490			−0.482738
$292$	3.61123	−	0.824240i	0.211331	−	0.0482350i
$293$	8.95696	−	18.5993i	0.523271	−	1.08658i	−0.457098	−	0.889416i	$-0.651111\pi$
$293$	8.95696	−	18.5993i	0.523271	−	1.08658i	0.980370	−	0.197168i	$-0.0631745\pi$
$294$	−13.2017	+	6.35761i	−0.769939	+	0.370783i
$295$	5.76271	+	25.2481i	0.335518	+	1.47000i
$296$	−1.93416	+	8.47409i	−0.112421	+	0.492547i
$297$	−12.7419	−	6.13617i	−0.739360	−	0.356057i
$298$	17.8561	−	14.2397i	1.03437	−	0.824886i
$299$	4.71797	+	5.91615i	0.272847	+	0.342140i
$300$	3.96442	+	8.23221i	0.228886	+	0.475287i
$301$	−0.359726	−	0.286872i	−0.0207343	−	0.0165350i
$302$		−	23.7385i		−	1.36600i
$303$	−3.60992	+	4.52669i	−0.207384	+	0.260052i
$304$	7.64224	+	1.74429i	0.438312	+	0.100042i
$305$	−5.16312	−	1.17845i	−0.295639	−	0.0674777i
$306$	−0.307979	+	0.386193i	−0.0176060	+	0.0220772i
$307$		−	22.8116i		−	1.30193i	−0.759108	−	0.650964i	$-0.774365\pi$
$307$		−	22.8116i		−	1.30193i	0.759108	−	0.650964i	$-0.225635\pi$
$308$	0.686450	+	0.547425i	0.0391141	+	0.0311925i
$309$	−5.10785	−	10.6066i	−0.290576	−	0.603386i
$310$	6.14191	+	7.70171i	0.348837	+	0.437428i
$311$	24.3072	−	19.3843i	1.37833	−	1.09918i	0.394740	−	0.918793i	$-0.370835\pi$
$311$	24.3072	−	19.3843i	1.37833	−	1.09918i	0.983595	−	0.180392i	$-0.0577366\pi$
$312$	−7.26055	−	3.49650i	−0.411048	−	0.197950i
$313$	2.49947	−	10.9509i	0.141278	−	0.618980i	−0.853861	−	0.520501i	$-0.825745\pi$
$313$	2.49947	−	10.9509i	0.141278	−	0.618980i	0.995139	−	0.0984792i	$-0.0313978\pi$
$314$	3.17390	+	13.9058i	0.179113	+	0.784747i
$315$	0.623490	−	0.300257i	0.0351297	−	0.0169176i
$316$	1.88094	−	3.90581i	0.105811	−	0.219719i
$317$	−5.77832	+	1.31886i	−0.324543	+	0.0740748i	−0.381688	−	0.924291i	$-0.624657\pi$
$317$	−5.77832	+	1.31886i	−0.324543	+	0.0740748i	0.0571456	+	0.998366i	$0.481800\pi$
$318$	−0.109916			−0.00616380
$319$		0			0
$320$	−36.0344			−2.01439
$321$	10.1619	−	2.31940i	0.567184	−	0.129456i
$322$	1.93154	−	4.01089i	0.107641	−	0.223518i
$323$	3.89008	−	1.87337i	0.216450	−	0.104237i
$324$	0.958615	+	4.19997i	0.0532564	+	0.233332i
$325$	3.71887	−	16.2934i	0.206286	−	0.903798i
$326$	7.49880	+	3.61123i	0.415320	+	0.200008i
$327$	−12.9413	+	10.3204i	−0.715656	+	0.570717i
$328$	12.3448	+	15.4799i	0.681628	+	0.854735i
$329$	1.42713	+	2.96346i	0.0786801	+	0.163381i
$330$	−20.2781	−	16.1712i	−1.11627	−	0.890196i
$331$			30.9095i			1.69894i	0.527639	+	0.849469i	$0.323077\pi$
$331$			30.9095i			1.69894i	−0.527639	+	0.849469i	$0.676923\pi$
$332$	−1.11596	+	1.39937i	−0.0612461	+	0.0768002i
$333$	0.686450	+	0.156678i	0.0376172	+	0.00858588i
$334$	17.8319	+	4.07002i	0.975720	+	0.222702i
$335$	−37.7373	+	47.3211i	−2.06181	+	2.58543i
$336$			3.63102i			0.198089i
$337$	6.26643	+	4.99731i	0.341354	+	0.272221i	0.779129	−	0.626864i	$-0.215662\pi$
$337$	6.26643	+	4.99731i	0.341354	+	0.272221i	−0.437775	+	0.899085i	$0.644233\pi$
$338$	−5.86950	−	12.1881i	−0.319259	−	0.662947i
$339$	−10.0734	−	12.6316i	−0.547111	−	0.686055i
$340$	−2.25956	+	1.80194i	−0.122542	+	0.0977238i
$341$	5.01142	+	2.41337i	0.271383	+	0.130691i
$342$	0.184489	−	0.808298i	0.00997601	−	0.0437077i
$343$	2.08211	+	9.12230i	0.112423	+	0.492558i
$344$	1.82640	−	0.879546i	0.0984727	−	0.0474220i
$345$	16.3307	−	33.9110i	0.879213	−	1.82570i
$346$	−28.3990	+	6.48188i	−1.52674	+	0.348468i
$347$	2.26337			0.121504			0.0607521	−	0.998153i	$-0.480650\pi$
$347$	2.26337			0.121504			0.0607521	+	0.998153i	$0.480650\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$	−9.58556	+	2.18784i	−0.512370	+	0.116945i
$351$	3.15716	−	6.55592i	0.168517	−	0.349929i
$352$	−6.33609	+	3.05130i	−0.337714	+	0.162635i
$353$	−0.218636	−	0.957907i	−0.0116368	−	0.0509843i	0.968776	−	0.247937i	$-0.0797526\pi$
$353$	−0.218636	−	0.957907i	−0.0116368	−	0.0509843i	−0.980413	+	0.196953i	$0.936895\pi$
$354$	−3.19806	+	14.0116i	−0.169975	+	0.744710i
$355$	−8.24094	−	3.96863i	−0.437384	−	0.210633i
$356$	3.91673	−	3.12349i	0.207586	−	0.165545i
$357$	1.24698	+	1.56366i	0.0659972	+	0.0827578i
$358$	0.359726	+	0.746980i	0.0190121	+	0.0394791i
$359$	6.16264	+	4.91454i	0.325252	+	0.259380i	0.772478	−	0.635041i	$-0.219017\pi$
$359$	6.16264	+	4.91454i	0.325252	+	0.259380i	−0.447227	+	0.894421i	$0.647588\pi$
$360$			3.04892i			0.160692i
$361$	7.32789	−	9.18888i	0.385678	−	0.483625i
$362$	13.3317	+	3.04288i	0.700699	+	0.159930i
$363$	5.04651	+	1.15183i	0.264873	+	0.0604556i
$364$	−0.281659	+	0.353190i	−0.0147630	+	0.0185122i
$365$			33.6993i			1.76390i
$366$	−2.29780	−	1.83244i	−0.120108	−	0.0957830i
$367$	−12.7163	−	26.4056i	−0.663783	−	1.37836i	−0.912216	−	0.409711i	$-0.865630\pi$
$367$	−12.7163	−	26.4056i	−0.663783	−	1.37836i	0.248432	−	0.968649i	$-0.420085\pi$
$368$	9.36592	+	11.7445i	0.488232	+	0.612224i
$369$	1.25396	−	1.00000i	0.0652786	−	0.0520579i
$370$	−12.9683	−	6.24521i	−0.674190	−	0.324673i
$371$	−0.00753275	+	0.0330031i	−0.000391081	+	0.00171344i
$372$	−0.348167	−	1.52542i	−0.0180516	−	0.0790892i
$373$	3.43512	−	1.65426i	0.177864	−	0.0856546i	−0.342833	−	0.939396i	$-0.611387\pi$
$373$	3.43512	−	1.65426i	0.177864	−	0.0856546i	0.520697	+	0.853742i	$0.325672\pi$
$374$	2.47388	−	5.13706i	0.127921	−	0.265631i
$375$	−45.4784	+	10.3802i	−2.34850	+	0.536029i
$376$	−14.4916			−0.747345
$377$		0			0
$378$	−4.28083			−0.220182
$379$	−8.79978	+	2.00849i	−0.452014	+	0.103169i	−0.442466	−	0.896785i	$-0.645896\pi$
$379$	−8.79978	+	2.00849i	−0.452014	+	0.103169i	−0.00954794	+	0.999954i	$0.503039\pi$
$380$	2.10471	−	4.37047i	0.107969	−	0.224200i
$381$	25.2690	−	12.1689i	1.29457	−	0.623433i
$382$	−0.143768	−	0.629889i	−0.00735582	−	0.0322279i
$383$	−7.38524	+	32.3568i	−0.377368	+	1.65336i	0.328120	+	0.944636i	$0.393585\pi$
$383$	−7.38524	+	32.3568i	−0.377368	+	1.65336i	−0.705488	+	0.708722i	$0.749272\pi$
$384$	−10.0075	−	4.81937i	−0.510695	−	0.245938i
$385$	−6.24521	+	4.98039i	−0.318285	+	0.253824i
$386$	−1.07792	−	1.35168i	−0.0548649	−	0.0687984i
$387$	−0.0712482	−	0.147948i	−0.00362175	−	0.00752064i
$388$	−1.59013	−	1.26809i	−0.0807266	−	0.0643773i
$389$			27.5362i			1.39614i	0.716030	+	0.698070i	$0.245957\pi$
$389$			27.5362i			1.39614i	−0.716030	+	0.698070i	$0.754043\pi$
$390$	8.32036	−	10.4334i	0.421318	−	0.528316i
$391$	8.06668	+	1.84117i	0.407949	+	0.0931118i
$392$	−19.3838	−	4.42423i	−0.979031	−	0.223457i
$393$	15.0918	−	18.9245i	0.761280	−	0.954615i
$394$		−	16.1588i		−	0.814070i
$395$	30.8356	+	24.5906i	1.55151	+	1.23729i
$396$	0.135960	+	0.282323i	0.00683224	+	0.0141873i
$397$	−11.9852	−	15.0290i	−0.601521	−	0.754284i	0.384093	−	0.923294i	$-0.374514\pi$
$397$	−11.9852	−	15.0290i	−0.601521	−	0.754284i	−0.985614	+	0.169010i	$0.945943\pi$
$398$	−19.0147	+	15.1637i	−0.953118	+	0.760086i
$399$	−3.02446	−	1.45650i	−0.151412	−	0.0729163i
$400$	7.38255	−	32.3451i	0.369128	−	1.61725i
$401$	−2.45353	−	10.7496i	−0.122524	−	0.536811i	−0.998515	−	0.0544837i	$-0.982649\pi$
$401$	−2.45353	−	10.7496i	−0.122524	−	0.536811i	0.875991	−	0.482327i	$-0.160208\pi$
$402$	−30.2630	+	14.5739i	−1.50938	+	0.726880i
$403$	−1.24172	+	2.57846i	−0.0618545	+	0.128442i
$404$	−1.39412	+	0.318200i	−0.0693603	+	0.0158310i
$405$	−39.1933			−1.94753
$406$		0			0
$407$	−8.12737			−0.402859
$408$	−8.59070	+	1.96077i	−0.425303	+	0.0970726i
$409$	−14.6745	+	30.4720i	−0.725608	+	1.50674i	0.131339	+	0.991337i	$0.458072\pi$
$409$	−14.6745	+	30.4720i	−0.725608	+	1.50674i	−0.856948	+	0.515404i	$0.827642\pi$
$410$	−29.5405	+	14.2259i	−1.45890	+	0.702569i
$411$	−6.81336	−	29.8513i	−0.336078	−	1.47245i
$412$	0.646989	−	2.83464i	0.0318749	−	0.139653i
$413$	3.98792	+	1.92048i	0.196233	+	0.0945007i
$414$	1.24218	−	0.990607i	0.0610499	−	0.0486857i
$415$	−10.1528	−	12.7312i	−0.498381	−	0.624950i
$416$	−1.56994	−	3.26002i	−0.0769728	−	0.159836i
$417$	−17.5600	−	14.0036i	−0.859918	−	0.685762i
$418$			9.57002i			0.468085i
$419$	22.2080	−	27.8480i	1.08493	−	1.36046i	0.157052	−	0.987590i	$-0.449801\pi$
$419$	22.2080	−	27.8480i	1.08493	−	1.36046i	0.927882	−	0.372874i	$-0.121628\pi$
$420$	2.19064	+	0.500000i	0.106892	+	0.0243975i
$421$	9.22001	+	2.10441i	0.449356	+	0.102563i	0.441209	−	0.897404i	$-0.354550\pi$
$421$	9.22001	+	2.10441i	0.449356	+	0.102563i	0.00814670	+	0.999967i	$0.497407\pi$
$422$	−16.0402	+	20.1138i	−0.780824	+	0.979123i
$423$			1.17390i			0.0570769i
$424$	−0.116606	−	0.0929903i	−0.00566290	−	0.00451601i
$425$	−7.92885	−	16.4644i	−0.384606	−	0.798642i
$426$	−3.16487	−	3.96863i	−0.153339	−	0.192281i
$427$	−0.707674	+	0.564351i	−0.0342468	+	0.0273109i
$428$	2.31940	+	1.11696i	0.112112	+	0.0539904i
$429$	1.67672	−	7.34619i	0.0809528	−	0.354677i
$430$	0.746980	+	3.27273i	0.0360226	+	0.157825i
$431$	−0.887928	+	0.427603i	−0.0427700	+	0.0205969i	−0.455146	−	0.890417i	$-0.650413\pi$
$431$	−0.887928	+	0.427603i	−0.0427700	+	0.0205969i	0.412377	+	0.911014i	$0.364699\pi$
$432$	6.26747	−	13.0145i	0.301544	−	0.626162i
$433$	−27.9651	+	6.38285i	−1.34392	+	0.306740i	−0.833182	−	0.552999i	$-0.813483\pi$
$433$	−27.9651	+	6.38285i	−1.34392	+	0.306740i	−0.510734	+	0.859739i	$0.670626\pi$
$434$	1.68366			0.0808183
$435$		0			0
$436$	−4.08815			−0.195787
$437$	−13.5395	+	3.09030i	−0.647682	+	0.147829i
$438$	−8.11437	+	16.8497i	−0.387719	+	0.805108i
$439$	−5.94116	+	2.86111i	−0.283556	+	0.136553i	−0.570256	−	0.821467i	$-0.693156\pi$
$439$	−5.94116	+	2.86111i	−0.283556	+	0.136553i	0.286700	+	0.958020i	$0.407442\pi$
$440$	−7.83124	−	34.3109i	−0.373340	−	1.63571i
$441$	−0.358388	+	1.57020i	−0.0170661	+	0.0747714i
$442$	2.64310	+	1.27285i	0.125720	+	0.0605434i
$443$	16.7221	−	13.3354i	0.794490	−	0.633585i	−0.139767	−	0.990184i	$-0.544635\pi$
$443$	16.7221	−	13.3354i	0.794490	−	0.633585i	0.934257	+	0.356599i	$0.116064\pi$
$444$	1.42543	+	1.78743i	0.0676478	+	0.0848277i
$445$	19.7753	+	41.0637i	0.937437	+	1.94661i
$446$	20.5718	+	16.4054i	0.974102	+	0.776820i
$447$		−	33.0030i		−	1.56099i
$448$	−3.83997	+	4.81517i	−0.181422	+	0.227495i
$449$	28.5231	+	6.51022i	1.34609	+	0.307236i	0.834033	−	0.551715i	$-0.186026\pi$
$449$	28.5231	+	6.51022i	1.34609	+	0.307236i	0.512058	+	0.858951i	$0.328883\pi$
$450$	−3.42105	−	0.780831i	−0.161270	−	0.0368087i
$451$	−11.5429	+	14.4743i	−0.543533	+	0.681569i
$452$		−	3.99031i		−	0.187688i
$453$	−26.8193	−	21.3877i	−1.26008	−	1.00488i
$454$	3.86017	+	8.01573i	0.181167	+	0.376197i
$455$	−2.56249	−	3.21326i	−0.120131	−	0.150640i
$456$	11.5632	−	9.22132i	0.541495	−	0.431828i
$457$	−0.217677	−	0.104828i	−0.0101825	−	0.00490362i	0.428786	−	0.903406i	$-0.358942\pi$
$457$	−0.217677	−	0.104828i	−0.0101825	−	0.00490362i	−0.438968	+	0.898503i	$0.644656\pi$
$458$	0.624982	−	2.73822i	0.0292035	−	0.127949i
$459$	−1.77048	−	7.75697i	−0.0826389	−	0.362065i
$460$	8.37531	−	4.03334i	0.390501	−	0.188055i
$461$	7.52272	−	15.6211i	0.350368	−	0.727547i	−0.649081	−	0.760719i	$-0.724847\pi$
$461$	7.52272	−	15.6211i	0.350368	−	0.727547i	0.999450	+	0.0331719i	$0.0105609\pi$
$462$	−4.32182	+	0.986426i	−0.201069	+	0.0458927i
$463$	−4.24996			−0.197513			−0.0987563	−	0.995112i	$-0.531486\pi$
$463$	−4.24996			−0.197513			−0.0987563	+	0.995112i	$0.531486\pi$
$464$		0			0
$465$	14.2349			0.660128
$466$	−22.9885	+	5.24698i	−1.06492	+	0.243062i
$467$	12.5103	−	25.9780i	0.578910	−	1.20212i	−0.381718	−	0.924279i	$-0.624667\pi$
$467$	12.5103	−	25.9780i	0.578910	−	1.20212i	0.960628	−	0.277839i	$-0.0896183\pi$
$468$	−0.145260	+	0.0699536i	−0.00671465	+	0.00323360i
$469$	2.30194	+	10.0854i	0.106294	+	0.465703i
$470$	5.33997	−	23.3959i	0.246314	−	1.07917i
$471$	18.5700	+	8.94285i	0.855662	+	0.412065i
$472$	−15.2467	+	12.1588i	−0.701786	+	0.559656i
$473$	1.18180	+	1.48193i	0.0543392	+	0.0681392i
$474$	9.49671	+	19.7201i	0.436198	+	0.905775i
$475$	23.9805	+	19.1238i	1.10030	+	0.877459i
$476$			0.493959i			0.0226406i
$477$	−0.00753275	+	0.00944576i	−0.000344901	+	0.000432492i
$478$	−24.8884	−	5.68060i	−1.13837	−	0.259825i
$479$	23.5707	+	5.37986i	1.07697	+	0.245812i	0.723985	−	0.689816i	$-0.242308\pi$
$479$	23.5707	+	5.37986i	1.07697	+	0.245812i	0.352988	+	0.935628i	$0.385166\pi$
$480$	−11.2213	+	14.0711i	−0.512181	+	0.642255i
$481$		−	4.18167i		−	0.190668i
$482$	7.18422	+	5.72923i	0.327232	+	0.260959i
$483$	−2.79116	−	5.79590i	−0.127002	−	0.263722i
$484$	0.797093	+	0.999524i	0.0362315	+	0.0454329i
$485$	14.4667	−	11.5368i	0.656901	−	0.523861i
$486$	−2.87651	−	1.38525i	−0.130481	−	0.0628364i
$487$	−4.29709	+	18.8268i	−0.194720	+	0.853124i	0.779298	+	0.626653i	$0.215576\pi$
$487$	−4.29709	+	18.8268i	−0.194720	+	0.853124i	−0.974018	+	0.226470i	$0.927281\pi$
$488$	−0.887395	−	3.88793i	−0.0401705	−	0.175998i
$489$	10.8361	−	5.21838i	0.490025	−	0.235983i
$490$	14.2854	−	29.6640i	0.645349	−	1.34008i
$491$	35.9657	−	8.20895i	1.62311	−	0.370465i	0.688249	−	0.725475i	$-0.258380\pi$
$491$	35.9657	−	8.20895i	1.62311	−	0.370465i	0.934863	+	0.355010i	$0.115523\pi$
$492$	5.20775			0.234784
$493$		0			0
$494$	−4.92394			−0.221538
$495$	−2.77938	+	0.634375i	−0.124924	+	0.0285130i
$496$	−2.46501	+	5.11865i	−0.110682	+	0.229834i
$497$	−1.40850	+	0.678299i	−0.0631799	+	0.0304259i
$498$	−2.01089	−	8.81026i	−0.0901099	−	0.394797i
$499$	8.39254	−	36.7701i	0.375701	−	1.64606i	−0.334748	−	0.942308i	$-0.608651\pi$
$499$	8.39254	−	36.7701i	0.375701	−	1.64606i	0.710450	−	0.703748i	$-0.248492\pi$
$500$	−10.3802	−	4.99882i	−0.464215	−	0.223554i
$501$	20.6642	−	16.4792i	0.923211	−	0.736236i
$502$	−10.0725	−	12.6306i	−0.449560	−	0.563730i
$503$	3.04139	+	6.31551i	0.135609	+	0.281595i	0.957704	−	0.287756i	$-0.0929091\pi$
$503$	3.04139	+	6.31551i	0.135609	+	0.281595i	−0.822095	+	0.569350i	$0.807195\pi$
$504$	0.407417	+	0.324904i	0.0181478	+	0.0144724i
$505$		−	13.0097i		−	0.578924i
$506$	−11.4345	+	14.3383i	−0.508323	+	0.637417i
$507$	−19.0581	−	4.34990i	−0.846402	−	0.193186i
$508$	6.75325	+	1.54138i	0.299627	+	0.0683879i
$509$	11.4641	−	14.3756i	0.508138	−	0.637185i	−0.459905	−	0.887968i	$-0.652117\pi$
$509$	11.4641	−	14.3756i	0.508138	−	0.637185i	0.968043	+	0.250783i	$0.0806880\pi$
$510$		−	14.5918i		−	0.646135i
$511$	4.50313	+	3.59113i	0.199207	+	0.158862i
$512$	−10.8206	−	22.4693i	−0.478209	−	0.993011i
$513$	8.32640	+	10.4410i	0.367619	+	0.460980i
$514$	16.2735	−	12.9777i	0.717794	−	0.572422i
$515$	23.8327	+	11.4772i	1.05020	+	0.505748i
$516$	0.118645	−	0.519820i	0.00522308	−	0.0228838i
$517$	−3.01520	−	13.2104i	−0.132608	−	0.580995i
$518$	−2.21648	+	1.06740i	−0.0973865	+	0.0468989i
$519$	−18.2635	+	37.9245i	−0.801678	+	1.66470i
$520$	17.6535	−	4.02930i	0.774159	−	0.176697i
$521$	−3.94571			−0.172865			−0.0864323	−	0.996258i	$-0.527547\pi$
$521$	−3.94571			−0.172865			−0.0864323	+	0.996258i	$0.527547\pi$
$522$		0			0
$523$	−33.9952			−1.48651			−0.743253	−	0.669010i	$-0.766718\pi$
$523$	−33.9952			−1.48651			−0.743253	+	0.669010i	$0.766718\pi$
$524$	5.82834	−	1.33028i	0.254612	−	0.0581136i
$525$	−6.16451	+	12.8007i	−0.269041	+	0.558670i
$526$	19.7838	−	9.52738i	0.862615	−	0.415414i
$527$	0.696333	+	3.05084i	0.0303328	+	0.132896i
$528$	3.32855	−	14.5833i	0.144857	−	0.634658i
$529$	−3.25571	−	1.56787i	−0.141553	−	0.0681681i
$530$	0.193096	−	0.153989i	0.00838757	−	0.00668887i
$531$	0.984935	+	1.23507i	0.0427425	+	0.0535974i
$532$	−0.359726	−	0.746980i	−0.0155961	−	0.0323857i
$533$	−7.44727	−	5.93900i	−0.322577	−	0.257247i
$534$			25.2935i			1.09456i
$535$	−14.6027	+	18.3112i	−0.631329	+	0.791661i
$536$	−44.4346	−	10.1419i	−1.91928	−	0.438064i
$537$	1.16802	+	0.266594i	0.0504040	+	0.0115044i
$538$	5.21648	−	6.54126i	0.224898	−	0.282014i
$539$		−	18.5907i		−	0.800759i
$540$	−6.98879	−	5.57338i	−0.300750	−	0.239840i
$541$	10.1685	+	21.1151i	0.437177	+	0.907807i	0.996866	+	0.0791047i	$0.0252061\pi$
$541$	10.1685	+	21.1151i	0.437177	+	0.907807i	−0.559689	+	0.828702i	$0.689080\pi$
$542$	9.84899	+	12.3502i	0.423051	+	0.530489i
$543$	15.4492	−	12.3204i	0.662990	−	0.528717i
$544$	−3.56465	−	1.71664i	−0.152833	−	0.0736005i
$545$	8.27628	−	36.2608i	0.354517	−	1.55324i
$546$	−0.507533	−	2.22365i	−0.0217204	−	0.0951633i
$547$	−29.0976	+	14.0127i	−1.24412	+	0.599138i	−0.935930	−	0.352186i	$-0.885439\pi$
$547$	−29.0976	+	14.0127i	−1.24412	+	0.599138i	−0.308193	+	0.951324i	$0.599724\pi$
$548$	3.28114	−	6.81336i	0.140163	−	0.291052i
$549$	−0.314945	+	0.0718841i	−0.0134415	+	0.00306794i
$550$	40.5042			1.72711
$551$		0			0
$552$	28.3424			1.20633
$553$	6.57193	−	1.50000i	0.279467	−	0.0637865i
$554$	−8.51654	+	17.6848i	−0.361833	+	0.751354i
$555$	−18.7397	+	9.02458i	−0.795458	+	0.383072i
$556$	−1.23437	−	5.40811i	−0.0523488	−	0.229355i
$557$	3.61045	−	15.8184i	0.152980	−	0.670248i	−0.839030	−	0.544085i	$-0.816877\pi$
$557$	3.61045	−	15.8184i	0.152980	−	0.670248i	0.992010	−	0.126162i	$-0.0402660\pi$
$558$	0.541385	+	0.260717i	0.0229186	+	0.0110370i
$559$	−0.762478	+	0.608056i	−0.0322494	+	0.0257180i
$560$	−5.08695	−	6.37883i	−0.214963	−	0.269555i
$561$	−3.57486	−	7.42327i	−0.150931	−	0.313411i
$562$	−11.5184	−	9.18561i	−0.485874	−	0.387472i
$563$		−	21.9168i		−	0.923681i	−0.886963	−	0.461841i	$-0.847189\pi$
$563$		−	21.9168i		−	0.923681i	0.886963	−	0.461841i	$-0.152811\pi$
$564$	−2.37651	+	2.98005i	−0.100069	+	0.125483i
$565$	35.3930	+	8.07822i	1.48899	+	0.339853i
$566$	2.67222	+	0.609916i	0.112322	+	0.0256367i
$567$	−4.17659	+	5.23728i	−0.175400	+	0.219945i
$568$		−	6.88769i		−	0.289001i
$569$	−29.3163	−	23.3790i	−1.22900	−	0.980097i	−0.999978	−	0.00667655i	$-0.997875\pi$
$569$	−29.3163	−	23.3790i	−1.22900	−	0.980097i	−0.229025	−	0.973421i	$-0.573554\pi$
$570$	10.6265	+	22.0661i	0.445095	+	0.924249i
$571$	17.2201	+	21.5934i	0.720640	+	0.903654i	0.998374	−	0.0570041i	$-0.0181548\pi$
$571$	17.2201	+	21.5934i	0.720640	+	0.903654i	−0.277734	+	0.960658i	$0.589583\pi$
$572$	1.45500	−	1.16033i	0.0608367	−	0.0485156i
$573$	−0.841166	−	0.405084i	−0.0351402	−	0.0169226i
$574$	−1.24698	+	5.46337i	−0.0520479	+	0.228037i
$575$	13.0794	+	57.3047i	0.545449	+	2.38977i
$576$	−1.98039	+	0.953703i	−0.0825161	+	0.0397376i
$577$	−2.74684	+	5.70387i	−0.114352	+	0.237455i	−0.950288	−	0.311372i	$-0.899211\pi$
$577$	−2.74684	+	5.70387i	−0.114352	+	0.237455i	0.835936	+	0.548827i	$0.184926\pi$
$578$	−17.5398	+	4.00335i	−0.729561	+	0.166518i
$579$	−2.49827			−0.103825
$580$		0			0
$581$	−2.78315			−0.115465
$582$	10.0113	−	2.28501i	0.414981	−	0.0947168i
$583$	0.0605078	−	0.125646i	0.00250598	−	0.00520371i
$584$	−22.8632	+	11.0104i	−0.946087	+	0.455612i
$585$	−0.326396	−	1.43004i	−0.0134948	−	0.0591247i
$586$	−5.72819	+	25.0969i	−0.236629	+	1.03674i
$587$	17.5939	+	8.47280i	0.726180	+	0.349710i	0.760180	−	0.649712i	$-0.225110\pi$
$587$	17.5939	+	8.47280i	0.726180	+	0.349710i	−0.0340005	+	0.999422i	$0.510825\pi$
$588$	−4.08860	+	3.26055i	−0.168611	+	0.134463i
$589$	−3.27479	−	4.10646i	−0.134935	−	0.169204i
$590$	−14.0116	−	29.0954i	−0.576850	−	1.19784i
$591$	−18.2559	−	14.5586i	−0.750948	−	0.598861i
$592$		−	8.30127i		−	0.341180i
$593$	1.53720	−	1.92759i	0.0631254	−	0.0791568i	−0.749266	−	0.662269i	$-0.769594\pi$
$593$	1.53720	−	1.92759i	0.0631254	−	0.0791568i	0.812392	+	0.583112i	$0.198165\pi$
$594$	17.1932	+	3.92423i	0.705445	+	0.161013i
$595$	−4.38129	−	1.00000i	−0.179615	−	0.0409960i
$596$	5.08211	−	6.37276i	0.208171	−	0.261038i
$597$			35.1444i			1.43836i
$598$	−7.37732	−	5.88321i	−0.301681	−	0.240583i
$599$	−2.23963	−	4.65064i	−0.0915087	−	0.190020i	0.850191	−	0.526474i	$-0.176486\pi$
$599$	−2.23963	−	4.65064i	−0.0915087	−	0.190020i	−0.941700	+	0.336455i	$0.890772\pi$
$600$	−39.0284	−	48.9401i	−1.59333	−	1.99797i
$601$	−23.0381	+	18.3723i	−0.939743	+	0.749420i	−0.968201	−	0.250175i	$-0.919512\pi$
$601$	−23.0381	+	18.3723i	−0.939743	+	0.749420i	0.0284577	+	0.999595i	$0.490940\pi$
$602$	0.516926	+	0.248938i	0.0210683	+	0.0101460i
$603$	−0.821552	+	3.59945i	−0.0334562	+	0.146581i
$604$	−1.88524	−	8.25977i	−0.0767093	−	0.336085i
$605$	−10.4792	+	5.04651i	−0.426040	+	0.205170i
$606$	3.13257	−	6.50484i	0.127252	−	0.264241i
$607$	33.7827	−	7.71068i	1.37120	−	0.312967i	0.527394	−	0.849621i	$-0.323169\pi$
$607$	33.7827	−	7.71068i	1.37120	−	0.312967i	0.843802	+	0.536654i	$0.180312\pi$
$608$	6.64071			0.269316
$609$		0			0
$610$	6.60388			0.267383
$611$	6.79699	−	1.55137i	0.274977	−	0.0627617i
$612$	−0.0764902	+	0.158834i	−0.00309193	+	0.00642047i
$613$	24.7407	−	11.9145i	0.999268	−	0.481222i	0.138578	−	0.990352i	$-0.455747\pi$
$613$	24.7407	−	11.9145i	0.999268	−	0.481222i	0.860690	+	0.509130i	$0.170033\pi$
$614$	6.32975	+	27.7324i	0.255448	+	1.11919i
$615$	−10.5429	+	46.1914i	−0.425130	+	1.86262i
$616$	−5.41939	−	2.60984i	−0.218353	−	0.105153i
$617$	−26.8000	+	21.3723i	−1.07893	+	0.860415i	−0.990751	−	0.135690i	$-0.956675\pi$
$617$	−26.8000	+	21.3723i	−1.07893	+	0.860415i	−0.0881746	+	0.996105i	$0.528103\pi$
$618$	9.15279	+	11.4772i	0.368179	+	0.461682i
$619$	−11.1363	−	23.1247i	−0.447605	−	0.929462i	−0.995664	−	0.0930221i	$-0.970347\pi$
$619$	−11.1363	−	23.1247i	−0.447605	−	0.929462i	0.548059	−	0.836440i	$-0.315367\pi$
$620$	2.74871	+	2.19202i	0.110391	+	0.0880337i
$621$			25.5918i			1.02696i
$622$	−24.1719	+	30.3106i	−0.969204	+	1.21534i
$623$	7.59455	+	1.73341i	0.304269	+	0.0694474i
$624$	7.50337	+	1.71260i	0.300375	+	0.0685587i
$625$	29.8330	−	37.4094i	1.19332	−	1.49638i
$626$			14.0067i			0.559821i
$627$	10.8120	+	8.62229i	0.431790	+	0.344341i
$628$	2.20870	+	4.58642i	0.0881368	+	0.183018i
$629$	−2.85086	−	3.57486i	−0.113671	−	0.142539i
$630$	−0.674671	+	0.538032i	−0.0268795	+	0.0214357i
$631$	−26.4894	−	12.7566i	−1.05453	−	0.507833i	−0.175438	−	0.984491i	$-0.556134\pi$
$631$	−26.4894	−	12.7566i	−1.05453	−	0.507833i	−0.879089	+	0.476657i	$0.841848\pi$
$632$	−6.60872	+	28.9547i	−0.262881	+	1.15176i
$633$	8.27240	+	36.2437i	0.328798	+	1.44056i
$634$	6.65883	−	3.20673i	0.264456	−	0.127355i
$635$	−27.3433	+	56.7790i	−1.08509	+	2.25321i
$636$	−0.0382451	+	0.00872920i	−0.00151652	+	0.000346135i
$637$	9.56524			0.378989
$638$		0			0
$639$	−0.557942			−0.0220718
$640$	24.3326	−	5.55376i	0.961831	−	0.219532i
$641$	4.54164	−	9.43080i	0.179384	−	0.372494i	−0.791816	−	0.610759i	$-0.790864\pi$
$641$	4.54164	−	9.43080i	0.179384	−	0.372494i	0.971200	+	0.238265i	$0.0765786\pi$
$642$	−11.7104	+	5.63945i	−0.462174	+	0.222571i
$643$	0.678743	+	2.97377i	0.0267670	+	0.117274i	0.986546	−	0.163481i	$-0.0522723\pi$
$643$	0.678743	+	2.97377i	0.0267670	+	0.117274i	−0.959779	+	0.280755i	$0.909415\pi$
$644$	0.353543	−	1.54898i	0.0139316	−	0.0610382i
$645$	4.37047	+	2.10471i	0.172087	+	0.0828728i
$646$	−4.20941	+	3.35690i	−0.165617	+	0.132075i
$647$	18.5824	+	23.3016i	0.730550	+	0.916080i	0.998883	−	0.0472458i	$-0.0150444\pi$
$647$	18.5824	+	23.3016i	0.730550	+	0.916080i	−0.268334	+	0.963326i	$0.586473\pi$
$648$	−12.8054	−	26.5906i	−0.503042	−	1.04458i
$649$	−14.2562	−	11.3690i	−0.559607	−	0.446271i
$650$			20.8401i			0.817416i
$651$	1.51693	−	1.90216i	0.0594530	−	0.0745517i
$652$	2.89598	+	0.660990i	0.113416	+	0.0258863i
$653$	−11.1039	−	2.53438i	−0.434528	−	0.0991781i	−0.000338791	−	1.00000i	$-0.500108\pi$
$653$	−11.1039	−	2.53438i	−0.434528	−	0.0991781i	−0.434189	+	0.900822i	$0.642965\pi$
$654$	12.8693	−	16.1376i	0.503228	−	0.631028i
$655$			54.3889i			2.12515i
$656$	−14.7840	−	11.7899i	−0.577219	−	0.460317i
$657$	0.891901	+	1.85205i	0.0347964	+	0.0722554i
$658$	−2.55728	−	3.20673i	−0.0996931	−	0.125011i
$659$	−3.58664	+	2.86025i	−0.139716	+	0.111419i	−0.690854	−	0.722995i	$-0.742765\pi$
$659$	−3.58664	+	2.86025i	−0.139716	+	0.111419i	0.551138	+	0.834414i	$0.314194\pi$
$660$	−8.33997	−	4.01632i	−0.324633	−	0.156335i
$661$	2.86712	−	12.5617i	0.111518	−	0.488592i	−0.888065	−	0.459718i	$-0.847951\pi$
$661$	2.86712	−	12.5617i	0.111518	−	0.488592i	0.999583	−	0.0288743i	$-0.00919225\pi$
$662$	−8.57673	−	37.5771i	−0.333344	−	1.46048i
$663$	3.81940	−	1.83932i	0.148333	−	0.0714334i
$664$	5.32030	−	11.0477i	0.206468	−	0.428735i
$665$	7.35376	−	1.67845i	0.285167	−	0.0650874i
$666$	−0.878002			−0.0340219
$667$		0			0
$668$	6.52781			0.252569
$669$	37.0691	−	8.46077i	1.43317	−	0.327112i
$670$	32.7472	−	68.0004i	1.26514	−	2.62708i
$671$	3.35958	−	1.61789i	0.129695	−	0.0624580i
$672$	0.684489	+	2.99894i	0.0264047	+	0.115687i
$673$	1.06518	−	4.66686i	0.0410596	−	0.179894i	−0.950240	−	0.311519i	$-0.899162\pi$
$673$	1.06518	−	4.66686i	0.0410596	−	0.179894i	0.991300	+	0.131625i	$0.0420194\pi$
$674$	−9.00484	−	4.33650i	−0.346854	−	0.167036i
$675$	44.1904	−	35.2407i	1.70089	−	1.35642i
$676$	−3.01022	−	3.77470i	−0.115778	−	0.145181i
$677$	13.2449	+	27.5034i	0.509045	+	1.05704i	0.984187	+	0.177133i	$0.0566823\pi$
$677$	13.2449	+	27.5034i	0.509045	+	1.05704i	−0.475142	+	0.879909i	$0.657603\pi$
$678$	15.7514	+	12.5613i	0.604928	+	0.482414i
$679$		−	3.16255i		−	0.121368i
$680$	12.3448	−	15.4799i	0.473402	−	0.593627i
$681$	12.5339	+	2.86078i	0.480300	+	0.109625i
$682$	−6.76212	−	1.54341i	−0.258935	−	0.0591002i
$683$	5.95138	−	7.46279i	0.227723	−	0.285556i	−0.654822	−	0.755783i	$-0.727257\pi$
$683$	5.95138	−	7.46279i	0.227723	−	0.285556i	0.882545	+	0.470227i	$0.155828\pi$
$684$		−	0.295897i		−	0.0113139i
$685$	53.7901	+	42.8962i	2.05521	+	1.63898i
$686$	−5.06249	−	10.5124i	−0.193287	−	0.401364i
$687$	−2.53050	−	3.17315i	−0.0965446	−	0.121063i
$688$	−1.51364	+	1.20709i	−0.0577070	+	0.0460198i
$689$	0.0646468	+	0.0311323i	0.00246285	+	0.00118604i
$690$	−10.4438	+	45.7575i	−0.397590	+	1.74196i
$691$	3.66799	+	16.0705i	0.139537	+	0.611351i	0.995537	+	0.0943750i	$0.0300853\pi$
$691$	3.66799	+	16.0705i	0.139537	+	0.611351i	−0.856000	+	0.516976i	$0.827058\pi$
$692$	−9.36658	+	4.51071i	−0.356064	+	0.171471i
$693$	−0.211412	+	0.439001i	−0.00803087	+	0.0166763i
$694$	−2.75162	+	0.628039i	−0.104450	+	0.0238400i
$695$	50.4674			1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$	28.6531	−	6.53989i	1.08454	−	0.247539i
$699$	−14.7840	+	30.6993i	−0.559183	+	1.16115i
$700$	−3.16152	+	1.52251i	−0.119494	+	0.0575454i
$701$	10.4288	+	45.6915i	0.393890	+	1.72574i	0.650748	+	0.759294i	$0.274456\pi$
$701$	10.4288	+	45.6915i	0.393890	+	1.72574i	−0.256858	+	0.966449i	$0.582687\pi$
$702$	−2.01908	+	8.84618i	−0.0762053	+	0.333877i
$703$	6.91454	+	3.32987i	0.260787	+	0.125588i
$704$	19.8366	−	15.8192i	0.747620	−	0.596207i
$705$	−21.6211	−	27.1120i	−0.814298	−	1.02110i
$706$	0.531598	+	1.10388i	0.0200070	+	0.0415449i
$707$	−1.73844	−	1.38636i	−0.0653809	−	0.0521395i
$708$			5.12929i			0.192771i
$709$	−6.60955	+	8.28811i	−0.248227	+	0.311267i	−0.890298	−	0.455379i	$-0.849504\pi$
$709$	−6.60955	+	8.28811i	−0.248227	+	0.311267i	0.642071	+	0.766645i	$0.278075\pi$
$710$	11.1198	+	2.53803i	0.417320	+	0.0952507i
$711$	2.34549	+	0.535344i	0.0879629	+	0.0200770i
$712$	−21.3986	+	26.8330i	−0.801946	+	1.00561i
$713$		−	10.0653i		−	0.376949i
$714$	−1.94986	−	1.55496i	−0.0729715	−	0.0581928i
$715$	7.34619	+	15.2545i	0.274732	+	0.570486i
$716$	0.184489	+	0.231342i	0.00689467	+	0.00864564i
$717$	−28.8415	+	23.0003i	−1.07710	+	0.858962i
$718$	−8.85570	−	4.26468i	−0.330492	−	0.159156i
$719$	2.96064	−	12.9714i	0.110413	−	0.483752i	−0.889241	−	0.457440i	$-0.848766\pi$
$719$	2.96064	−	12.9714i	0.110413	−	0.483752i	0.999654	−	0.0263121i	$-0.00837637\pi$
$720$	−0.647948	−	2.83885i	−0.0241476	−	0.105798i
$721$	4.07338	−	1.96163i	0.151700	−	0.0730551i
$722$	−6.35890	+	13.2044i	−0.236654	+	0.491417i
$723$	12.9455	−	2.95473i	0.481449	−	0.109888i
$724$	4.88040			0.181378
$725$		0			0
$726$	−6.45473			−0.239558
$727$	−32.1896	+	7.34708i	−1.19385	+	0.272488i	−0.772859	−	0.634578i	$-0.781174\pi$
$727$	−32.1896	+	7.34708i	−1.19385	+	0.272488i	−0.420989	+	0.907066i	$0.638317\pi$
$728$	1.34281	−	2.78836i	0.0497677	−	0.103344i
$729$	22.0073	−	10.5982i	0.815085	−	0.392524i
$730$	−9.35086	−	40.9688i	−0.346091	−	1.51632i
$731$	−0.237291	+	1.03964i	−0.00877652	+	0.0384525i
$732$	−0.945042	−	0.455108i	−0.0349298	−	0.0168213i
$733$	−24.8585	+	19.8240i	−0.918170	+	0.732216i	−0.963768	−	0.266744i	$-0.914052\pi$
$733$	−24.8585	+	19.8240i	−0.918170	+	0.732216i	0.0455974	+	0.998960i	$0.485481\pi$
$734$	22.7863	+	28.5732i	0.841059	+	1.05465i
$735$	−20.6430	−	42.8657i	−0.761429	−	1.58112i
$736$	9.94949	+	7.93445i	0.366743	+	0.292468i
$737$		−	42.6165i		−	1.56980i
$738$	−1.24698	+	1.56366i	−0.0459020	+	0.0575592i
$739$	−23.3354	−	5.32616i	−0.858408	−	0.195926i	−0.229407	−	0.973331i	$-0.573679\pi$
$739$	−23.3354	−	5.32616i	−0.858408	−	0.195926i	−0.629001	+	0.777405i	$0.716536\pi$
$740$	−5.00827	−	1.14310i	−0.184108	−	0.0420213i
$741$	−4.43631	+	5.56296i	−0.162972	+	0.204360i
$742$		−	0.0422126i		−	0.00154967i
$743$	−5.79534	−	4.62163i	−0.212610	−	0.169551i	0.511394	−	0.859346i	$-0.329129\pi$
$743$	−5.79534	−	4.62163i	−0.212610	−	0.169551i	−0.724005	+	0.689795i	$0.757701\pi$
$744$	4.65087	+	9.65764i	0.170509	+	0.354066i
$745$	46.2362	+	57.9783i	1.69396	+	2.12416i
$746$	−3.71710	+	2.96429i	−0.136093	+	0.108530i
$747$	−0.894928	−	0.430975i	−0.0327437	−	0.0157685i
$748$	0.452812	−	1.98390i	0.0165564	−	0.0725385i
$749$	0.890748	+	3.90262i	0.0325472	+	0.142599i
$750$	52.4086	−	25.2386i	1.91369	−	0.921585i
$751$	−8.40098	+	17.4448i	−0.306556	+	0.636570i	−0.996154	−	0.0876226i	$-0.972073\pi$
$751$	−8.40098	+	17.4448i	−0.306556	+	0.636570i	0.689598	+	0.724193i	$0.257787\pi$
$752$	13.4931	−	3.07971i	0.492043	−	0.112306i
$753$	−23.3448			−0.850732
$754$		0			0
$755$	77.0786			2.80518
$756$	−1.48951	+	0.339970i	−0.0541728	+	0.0123646i
$757$	14.8548	−	30.8463i	0.539907	−	1.12113i	−0.435393	−	0.900241i	$-0.643390\pi$
$757$	14.8548	−	30.8463i	0.539907	−	1.12113i	0.975299	−	0.220887i	$-0.0708953\pi$
$758$	10.1407	−	4.88351i	0.368327	−	0.177377i
$759$	5.89708	+	25.8368i	0.214051	+	0.937817i
$760$	−7.39493	+	32.3993i	−0.268242	+	1.17525i
$761$	−13.1174	−	6.31703i	−0.475507	−	0.228992i	0.180751	−	0.983529i	$-0.442147\pi$
$761$	−13.1174	−	6.31703i	−0.475507	−	0.228992i	−0.656258	+	0.754537i	$0.727862\pi$
$762$	−27.3433	+	21.8056i	−0.990545	+	0.789933i
$763$	−3.96346	−	4.97002i	−0.143487	−	0.179927i
$764$	−0.100048	−	0.207751i	−0.00361959	−	0.00751617i
$765$	−1.25396	−	1.00000i	−0.0453370	−	0.0361551i
$766$		−	41.3860i		−	1.49534i
$767$	5.84953	−	7.33507i	0.211214	−	0.264854i
$768$	−17.7659	−	4.05496i	−0.641073	−	0.146321i
$769$	−11.2737	−	2.57314i	−0.406539	−	0.0927898i	0.0143613	−	0.999897i	$-0.495428\pi$
$769$	−11.2737	−	2.57314i	−0.406539	−	0.0927898i	−0.420900	+	0.907107i	$0.638286\pi$
$770$	6.21044	−	7.78764i	0.223809	−	0.280647i
$771$		−	30.0780i		−	1.08323i
$772$	−0.482407	−	0.384707i	−0.0173622	−	0.0138459i
$773$	3.63350	+	7.54503i	0.130688	+	0.271376i	0.956037	−	0.293247i	$-0.0947359\pi$
$773$	3.63350	+	7.54503i	0.130688	+	0.271376i	−0.825349	+	0.564623i	$0.809022\pi$
$774$	0.127670	+	0.160093i	0.00458901	+	0.00575444i
$775$	−17.3802	+	13.8602i	−0.624315	+	0.497875i
$776$	12.5538	+	6.04557i	0.450654	+	0.217023i
$777$	−0.791053	+	3.46583i	−0.0283789	+	0.124336i
$778$	−7.64071	−	33.4761i	−0.273933	−	1.20018i
$779$	15.7506	−	7.58510i	0.564325	−	0.271764i
$780$	2.06646	−	4.29105i	0.0739912	−	0.153644i
$781$	6.27879	−	1.43309i	0.224673	−	0.0512801i
$782$	−10.3177			−0.368959
$783$		0			0
$784$	18.9885			0.678161
$785$	−45.1517	+	10.3056i	−1.61153	+	0.367822i
$786$	−13.0962	+	27.1945i	−0.467125	+	0.969995i
$787$	−8.76055	+	4.21886i	−0.312280	+	0.150386i	−0.583458	−	0.812143i	$-0.698301\pi$
$787$	−8.76055	+	4.21886i	−0.312280	+	0.150386i	0.271179	+	0.962529i	$0.412587\pi$
$788$	−1.28328	−	5.62243i	−0.0457151	−	0.200291i
$789$	7.06076	−	30.9352i	0.251370	−	1.10132i
$790$	−44.3107	−	21.3389i	−1.57650	−	0.759205i
$791$	4.85108	−	3.86861i	0.172485	−	0.137552i
$792$	−1.33848	−	1.67840i	−0.0475607	−	0.0596393i
$793$	0.832431	+	1.72856i	0.0295605	+	0.0613830i
$794$	18.7409	+	14.9453i	0.665088	+	0.530390i
$795$		−	0.356896i		−	0.0126578i
$796$	−5.41185	+	6.78625i	−0.191818	+	0.240532i
$797$	−25.7480	−	5.87681i	−0.912040	−	0.208167i	−0.259342	−	0.965786i	$-0.583506\pi$
$797$	−25.7480	−	5.87681i	−0.912040	−	0.208167i	−0.652698	+	0.757618i	$0.726363\pi$
$798$	4.08103	+	0.931468i	0.144467	+	0.0329736i
$799$	4.75302	−	5.96010i	0.168150	−	0.210853i
$800$		−	28.1062i		−	0.993704i
$801$	2.17362	+	1.73341i	0.0768012	+	0.0612469i
$802$	5.96560	+	12.3877i	0.210653	+	0.437425i
$803$	−14.7940	−	18.5511i	−0.522070	−	0.654655i
$804$	−9.37253	+	7.47434i	−0.330544	+	0.263600i
$805$	13.0233	+	6.27167i	0.459010	+	0.221047i
$806$	0.794109	−	3.47922i	0.0279713	−	0.122550i
$807$	−2.69029	−	11.7869i	−0.0947028	−	0.414920i
$808$	8.82640	−	4.25057i	0.310512	−	0.149534i
$809$	8.15261	−	16.9291i	0.286631	−	0.595195i	−0.707085	−	0.707129i	$-0.749990\pi$
$809$	8.15261	−	16.9291i	0.286631	−	0.595195i	0.993716	+	0.111934i	$0.0357045\pi$
$810$	47.6479	−	10.8753i	1.67418	−	0.382120i
$811$	−48.6983			−1.71003			−0.855013	−	0.518606i	$-0.826451\pi$
$811$	−48.6983			−1.71003			−0.855013	+	0.518606i	$0.826451\pi$
$812$		0			0
$813$	22.8267			0.800567
$814$	9.88057	−	2.25518i	0.346314	−	0.0790439i
$815$	−11.7256	+	24.3485i	−0.410730	+	0.852889i
$816$	7.58211	−	3.65135i	0.265427	−	0.127823i
$817$	−0.398280	−	1.74498i	−0.0139341	−	0.0610491i
$818$	9.38471	−	41.1171i	0.328129	−	1.43763i
$819$	−0.225873	−	0.108775i	−0.00789265	−	0.00380090i
$820$	−9.14877	+	7.29590i	−0.319489	+	0.254784i
$821$	−3.90246	−	4.89353i	−0.136197	−	0.170785i	0.709056	−	0.705152i	$-0.249121\pi$
$821$	−3.90246	−	4.89353i	−0.136197	−	0.170785i	−0.845253	+	0.534367i	$0.820550\pi$
$822$	16.5662	+	34.4001i	0.577813	+	1.19984i
$823$	11.7403	+	9.36257i	0.409241	+	0.326359i	0.806378	−	0.591401i	$-0.201425\pi$
$823$	11.7403	+	9.36257i	0.409241	+	0.326359i	−0.397137	+	0.917759i	$0.629996\pi$
$824$			19.9191i			0.693916i
$825$	36.4931	−	45.7608i	1.27053	−	1.59319i
$826$	−5.38107	−	1.22819i	−0.187231	−	0.0427343i
$827$	−11.6573	−	2.66069i	−0.405363	−	0.0925214i	0.0149778	−	0.999888i	$-0.495232\pi$
$827$	−11.6573	−	2.66069i	−0.405363	−	0.0925214i	−0.420341	+	0.907366i	$0.638089\pi$
$828$	0.353543	−	0.443330i	0.0122865	−	0.0154068i
$829$		−	28.6305i		−	0.994380i	−0.867642	−	0.497190i	$-0.834365\pi$
$829$		−	28.6305i		−	0.994380i	0.867642	−	0.497190i	$-0.165635\pi$
$830$	15.8755	+	12.6603i	0.551048	+	0.439446i
$831$	12.3068	+	25.5553i	0.426917	+	0.886502i
$832$	8.13922	+	10.2063i	0.282177	+	0.353838i
$833$	8.17721	−	6.52111i	0.283323	−	0.225943i
$834$	25.2337	+	12.1519i	0.873772	+	0.420786i
$835$	−13.2153	+	57.8999i	−0.457334	+	2.00371i
$836$	0.760021	+	3.32987i	0.0262859	+	0.115166i
$837$	−8.72037	+	4.19951i	−0.301420	+	0.145156i
$838$	−19.2714	+	40.0175i	−0.665720	+	1.38238i
$839$	−47.1115	+	10.7529i	−1.62647	+	0.371231i	−0.935964	−	0.352096i	$-0.885469\pi$
$839$	−47.1115	+	10.7529i	−1.62647	+	0.371231i	−0.690505	+	0.723327i	$0.742612\pi$
$840$	−15.3937			−0.531134
$841$		0			0
$842$	−11.7928			−0.406408
$843$	−20.7554	+	4.73729i	−0.714855	+	0.163161i
$844$	−3.98378	+	8.27240i	−0.137127	+	0.284748i
$845$	39.5746	−	19.0581i	1.36141	−	0.655620i
$846$	−0.325732	−	1.42713i	−0.0111989	−	0.0490656i
$847$	−0.442353	+	1.93808i	−0.0151994	+	0.0665931i
$848$	0.128334	+	0.0618025i	0.00440701	+	0.00212231i
$849$	3.09666	−	2.46950i	0.106277	−	0.0847530i
$850$	14.2078	+	17.8160i	0.487322	+	0.611082i
$851$	6.38117	+	13.2506i	0.218744	+	0.454226i
$852$	−1.41639	−	1.12953i	−0.0485246	−	0.0386971i
$853$		−	6.40688i		−	0.219367i	−0.993967	−	0.109684i	$-0.965016\pi$
$853$		−	6.40688i		−	0.219367i	0.993967	−	0.109684i	$-0.0349838\pi$
$854$	0.703735	−	0.882455i	0.0240813	−	0.0301970i
$855$	2.62453	+	0.599031i	0.0897569	+	0.0204864i
$856$	−17.1942	−	3.92447i	−0.587686	−	0.134136i
$857$	−0.447730	+	0.561436i	−0.0152942	+	0.0191783i	−0.789420	−	0.613854i	$-0.789618\pi$
$857$	−0.447730	+	0.561436i	−0.0152942	+	0.0191783i	0.774126	+	0.633032i	$0.218190\pi$
$858$			9.39612i			0.320778i
$859$	−12.1946	−	9.72484i	−0.416073	−	0.331807i	0.392975	−	0.919549i	$-0.371446\pi$
$859$	−12.1946	−	9.72484i	−0.416073	−	0.331807i	−0.809049	+	0.587742i	$0.800017\pi$
$860$	0.519820	+	1.07942i	0.0177257	+	0.0368078i
$861$	5.04892	+	6.33114i	0.172067	+	0.215765i
$862$	0.960816	−	0.766225i	0.0327255	−	0.0260977i
$863$	12.1586	+	5.85527i	0.413883	+	0.199316i	0.629225	−	0.777223i	$-0.283372\pi$
$863$	12.1586	+	5.85527i	0.413883	+	0.199316i	−0.215342	+	0.976539i	$0.569087\pi$
$864$	2.72305	−	11.9305i	0.0926402	−	0.405883i
$865$	−21.0465	−	92.2108i	−0.715603	−	3.13526i
$866$	32.2265	−	15.5194i	1.09510	−	0.527372i
$867$	−11.2799	+	23.4230i	−0.383087	+	0.795488i
$868$	0.585826	−	0.133711i	0.0198842	−	0.00453845i
$869$	−27.7700			−0.942033
$870$		0			0
$871$	21.9269			0.742965
$872$	27.3051	−	6.23221i	0.924667	−	0.211049i
$873$	0.489726	−	1.01693i	0.0165747	−	0.0344177i
$874$	15.6027	−	7.51385i	0.527768	−	0.254160i
$875$	−3.98643	−	17.4657i	−0.134766	−	0.590448i
$876$	−1.48523	+	6.50722i	−0.0501813	+	0.219859i
$877$	14.1446	+	6.81168i	0.477629	+	0.230014i	0.657179	−	0.753735i	$-0.271750\pi$
$877$	14.1446	+	6.81168i	0.477629	+	0.230014i	−0.179550	+	0.983749i	$0.557464\pi$
$878$	6.42886	−	5.12684i	0.216963	−	0.173023i
$879$	23.1930	+	29.0831i	0.782280	+	0.980948i
$880$	14.5833	+	30.2826i	0.491604	+	1.02083i
$881$	8.46839	+	6.75332i	0.285307	+	0.227525i	0.755677	−	0.654944i	$-0.227308\pi$
$881$	8.46839	+	6.75332i	0.285307	+	0.227525i	−0.470370	+	0.882469i	$0.655879\pi$
$882$		−	2.00836i		−	0.0676250i
$883$	10.2744	−	12.8837i	0.345762	−	0.433572i	−0.578294	−	0.815828i	$-0.696281\pi$
$883$	10.2744	−	12.8837i	0.345762	−	0.433572i	0.924056	+	0.382257i	$0.124853\pi$
$884$	1.02075	+	0.232979i	0.0343315	+	0.00783593i
$885$	−45.4955	−	10.3840i	−1.52931	−	0.349056i
$886$	−16.6290	+	20.8521i	−0.558662	+	0.700540i
$887$			28.5763i			0.959497i	0.877406	+	0.479748i	$0.159272\pi$
$887$			28.5763i			0.959497i	−0.877406	+	0.479748i	$0.840728\pi$
$888$	−12.2454	−	9.76540i	−0.410929	−	0.327705i
$889$	4.67339	+	9.70440i	0.156741	+	0.325475i
$890$	−35.4354	−	44.4346i	−1.18780	−	1.48945i
$891$	21.5755	−	17.2059i	0.722807	−	0.576419i
$892$	8.46077	+	4.07449i	0.283288	+	0.136424i
$893$	−2.84721	+	12.4744i	−0.0952782	+	0.417441i
$894$	9.15764	+	40.1222i	0.306277	+	1.34189i
$895$	−2.42543	+	1.16802i	−0.0810731	+	0.0390427i
$896$	1.85085	−	3.84332i	0.0618324	−	0.128396i
$897$	−13.2935	+	3.03415i	−0.443856	+	0.101307i
$898$	−36.4825			−1.21744
$899$		0			0
$900$	−1.25236			−0.0417452
$901$	0.0764902	−	0.0174584i	0.00254826	−	0.000581624i
$902$	10.0165	−	20.7995i	0.333514	−	0.692549i
$903$	0.746980	−	0.359726i	0.0248579	−	0.0119709i
$904$	6.08306	+	26.6516i	0.202320	+	0.886421i
$905$	−9.88016	+	43.2878i	−0.328428	+	1.43894i
$906$	38.5393	+	18.5595i	1.28038	+	0.616600i
$907$	−25.6906	+	20.4875i	−0.853042	+	0.680278i	−0.949058	−	0.315102i	$-0.897961\pi$
$907$	−25.6906	+	20.4875i	−0.853042	+	0.680278i	0.0960163	+	0.995380i	$0.469390\pi$
$908$	1.97972	+	2.48249i	0.0656994	+	0.0823844i
$909$	−0.344320	−	0.714988i	−0.0114204	−	0.0237147i
$910$	4.00687	+	3.19537i	0.132827	+	0.105926i
$911$			10.9638i			0.363245i	0.983368	+	0.181623i	$0.0581350\pi$
$911$			10.9638i			0.363245i	−0.983368	+	0.181623i	$0.941865\pi$
$912$	−8.80678	+	11.0434i	−0.291622	+	0.365682i
$913$	11.1780	+	2.55131i	0.369938	+	0.0844360i
$914$	0.293720	+	0.0670397i	0.00971540	+	0.00221748i
$915$	5.94989	−	7.46092i	0.196697	−	0.246650i
$916$		−	1.00239i		−	0.0331200i
$917$	7.26782	+	5.79590i	0.240005	+	0.191397i
$918$	4.30480	+	8.93900i	0.142079	+	0.295031i
$919$	4.77748	+	5.99077i	0.157594	+	0.197617i	0.854360	−	0.519682i	$-0.173950\pi$
$919$	4.77748	+	5.99077i	0.157594	+	0.197617i	−0.696765	+	0.717299i	$0.745378\pi$
$920$	−49.7908	+	39.7068i	−1.64155	+	1.30910i
$921$	37.0344	+	17.8348i	1.22033	+	0.587678i
$922$	−4.81096	+	21.0782i	−0.158441	+	0.694174i
$923$	0.737349	+	3.23054i	0.0242702	+	0.106334i
$924$	−1.42543	+	0.686450i	−0.0468931	+	0.0225825i
$925$	14.0934	−	29.2652i	0.463387	−	0.962233i
$926$	5.16675	−	1.17928i	0.169790	−	0.0387534i
$927$	1.61356			0.0529964
$928$		0			0
$929$	9.35988			0.307088			0.153544	−	0.988142i	$-0.450931\pi$
$929$	9.35988			0.307088			0.153544	+	0.988142i	$0.450931\pi$
$930$	−17.3056	+	3.94989i	−0.567472	+	0.129522i
$931$	−7.61681	+	15.8165i	−0.249631	+	0.518364i
$932$	−7.58211	+	3.65135i	−0.248360	+	0.119604i
$933$	12.4661	+	54.6178i	0.408123	+	1.78811i
$934$	−8.00066	+	35.0532i	−0.261790	+	1.14698i
$935$	16.6799	+	8.03264i	0.545492	+	0.262695i
$936$	0.863564	−	0.688669i	0.0282265	−	0.0225099i
$937$	−4.86563	−	6.10130i	−0.158953	−	0.199321i	0.695977	−	0.718064i	$-0.254972\pi$
$937$	−4.86563	−	6.10130i	−0.158953	−	0.199321i	−0.854930	+	0.518743i	$0.826400\pi$
$938$	−5.59700	−	11.6223i	−0.182749	−	0.379481i
$939$	15.8245	+	12.6196i	0.516413	+	0.411825i
$940$		−	8.56465i		−	0.279348i
$941$	17.9242	−	22.4763i	0.584313	−	0.732706i	−0.398529	−	0.917156i	$-0.630479\pi$
$941$	17.9242	−	22.4763i	0.584313	−	0.732706i	0.982842	+	0.184450i	$0.0590505\pi$
$942$	−25.0573	−	5.71917i	−0.816411	−	0.186341i
$943$	32.6613	+	7.45473i	1.06360	+	0.242759i
$944$	11.6122	−	14.5613i	0.377946	−	0.473929i
$945$		−	13.8998i		−	0.452160i
$946$	−1.84794	−	1.47368i	−0.0600816	−	0.0479135i
$947$	−1.00197	−	2.08061i	−0.0325597	−	0.0676108i	0.884055	−	0.467384i	$-0.154803\pi$
$947$	−1.00197	−	2.08061i	−0.0325597	−	0.0676108i	−0.916614	+	0.399773i	$0.869089\pi$
$948$	4.87047	+	6.10738i	0.158185	+	0.198358i
$949$	9.54487	−	7.61178i	0.309839	−	0.247089i
$950$	−34.4599	−	16.5950i	−1.11803	−	0.538413i
$951$	2.37651	−	10.4122i	0.0770636	−	0.337638i
$952$	−0.753020	−	3.29920i	−0.0244055	−	0.106928i
$953$	31.1107	−	14.9821i	1.00778	−	0.485319i	0.144206	−	0.989548i	$-0.453937\pi$
$953$	31.1107	−	14.9821i	1.00778	−	0.485319i	0.863570	+	0.504228i	$0.168223\pi$
$954$	0.00653667	−	0.0135735i	0.000211633	−	0.000439460i
$955$	2.04524	−	0.466812i	0.0661823	−	0.0151057i
$956$	−9.11098			−0.294670
$957$		0			0
$958$	−30.1481			−0.974040
$959$	11.4642	−	2.61662i	0.370197	−	0.0844951i
$960$	28.1729	−	58.5016i	0.909275	−	1.88813i
$961$	−24.5003	+	11.7987i	−0.790332	+	0.380604i
$962$	1.16033	+	5.08372i	0.0374104	+	0.163906i
$963$	−0.317904	+	1.39283i	−0.0102443	+	0.0448833i
$964$	2.95473	+	1.42292i	0.0951655	+	0.0458293i
$965$	4.38886	−	3.50000i	0.141282	−	0.112669i
$966$	5.00149	+	6.27167i	0.160920	+	0.201788i
$967$	−22.3529	−	46.4163i	−0.718822	−	1.49265i	−0.864134	−	0.503263i	$-0.832133\pi$
$967$	−22.3529	−	46.4163i	−0.718822	−	1.49265i	0.145312	−	0.989386i	$-0.453581\pi$
$968$	−6.84759	−	5.46077i	−0.220090	−	0.175516i
$969$			7.78017i			0.249935i
$970$	−14.3862	+	18.0397i	−0.461913	+	0.579221i
$971$	7.73658	+	1.76582i	0.248279	+	0.0566680i	0.344849	−	0.938658i	$-0.387930\pi$
$971$	7.73658	+	1.76582i	0.248279	+	0.0566680i	−0.0965703	+	0.995326i	$0.530787\pi$
$972$	−1.11089	−	0.253553i	−0.0356317	−	0.00813271i
$973$	5.37800	−	6.74380i	0.172411	−	0.216196i
$974$		−	24.0804i		−	0.771585i
$975$	23.5447	+	18.7763i	0.754034	+	0.601322i
$976$	1.65251	+	3.43147i	0.0528955	+	0.109839i
$977$	17.2080	+	21.5782i	0.550534	+	0.690348i	0.976776	−	0.214261i	$-0.0687343\pi$
$977$	17.2080	+	21.5782i	0.550534	+	0.690348i	−0.426242	+	0.904609i	$0.640163\pi$
$978$	−11.7256	+	9.35086i	−0.374943	+	0.299007i
$979$	−28.9131	−	13.9238i	−0.924067	−	0.445007i
$980$	2.61476	−	11.4560i	0.0835255	−	0.365949i
$981$	−0.504844	−	2.21187i	−0.0161184	−	0.0706195i
$982$	−41.4463	+	19.9595i	−1.32260	+	0.636933i
$983$	15.3280	−	31.8288i	0.488886	−	1.01518i	−0.499933	−	0.866064i	$-0.666642\pi$
$983$	15.3280	−	31.8288i	0.488886	−	1.01518i	0.988819	−	0.149119i	$-0.0476436\pi$
$984$	−34.7830	+	7.93900i	−1.10884	+	0.253086i
$985$	52.4674			1.67175
$986$		0			0
$987$	−5.92692			−0.188656
$988$	−1.71327	+	0.391043i	−0.0545065	+	0.0124407i
$989$	1.48821	−	3.09030i	0.0473224	−	0.0982659i
$990$	3.20291	−	1.54244i	0.101795	−	0.0490219i
$991$	−0.123194	−	0.539750i	−0.00391340	−	0.0171457i	0.972934	−	0.231085i	$-0.0742276\pi$
$991$	−0.123194	−	0.539750i	−0.00391340	−	0.0171457i	−0.976847	+	0.213939i	$0.931370\pi$
$992$	−1.07098	+	4.69228i	−0.0340037	+	0.148980i
$993$	−50.1812	−	24.1660i	−1.59245	−	0.766885i
$994$	1.52412	−	1.21545i	0.0483423	−	0.0385517i
$995$	−49.2362	−	61.7402i	−1.56089	−	1.95730i
$996$	−1.39937	−	2.90581i	−0.0443406	−	0.0920742i
$997$	−17.3924	−	13.8699i	−0.550821	−	0.439265i	0.308114	−	0.951349i	$-0.400302\pi$
$997$	−17.3924	−	13.8699i	−0.550821	−	0.439265i	−0.858935	+	0.512084i	$0.828874\pi$
$998$			47.0307i			1.48873i
$999$	8.81767	−	11.0570i	0.278979	−	0.349828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.d.196.1		12
29.2	odd	28		841.2.a.f.1.1		3
29.3	odd	28		841.2.d.a.778.1		6
29.4	even	14	inner	841.2.e.d.236.1		12
29.5	even	14		841.2.b.c.840.5		6
29.6	even	14		841.2.e.c.270.1		12
29.7	even	7		841.2.e.b.63.2		12
29.8	odd	28		841.2.d.b.190.1		6
29.9	even	14		841.2.e.c.651.2		12
29.10	odd	28		29.2.d.a.25.1	yes	6
29.11	odd	28		841.2.d.a.574.1		6
29.12	odd	4		29.2.d.a.7.1	✓	6
29.13	even	14		841.2.e.b.267.2		12
29.14	odd	28		841.2.d.c.571.1		6
29.15	odd	28		841.2.d.b.571.1		6
29.16	even	7		841.2.e.b.267.1		12
29.17	odd	4		841.2.d.d.645.1		6
29.18	odd	28		841.2.d.e.574.1		6
29.19	odd	28		841.2.d.d.605.1		6
29.20	even	7		841.2.e.c.651.1		12
29.21	odd	28		841.2.d.c.190.1		6
29.22	even	14		841.2.e.b.63.1		12
29.23	even	7		841.2.e.c.270.2		12
29.24	even	7		841.2.b.c.840.2		6
29.25	even	7	inner	841.2.e.d.236.2		12
29.26	odd	28		841.2.d.e.778.1		6
29.27	odd	28		841.2.a.e.1.3		3
29.28	even	2	inner	841.2.e.d.196.2		12
87.2	even	28		7569.2.a.p.1.3		3
87.41	even	4		261.2.k.a.181.1		6
87.56	even	28		7569.2.a.r.1.1		3
87.68	even	28		261.2.k.a.199.1		6
116.39	even	28		464.2.u.f.257.1		6
116.99	even	4		464.2.u.f.65.1		6
145.12	even	4		725.2.r.b.674.2		12
145.39	odd	28		725.2.l.b.576.1		6
145.68	even	28		725.2.r.b.199.2		12
145.97	even	28		725.2.r.b.199.1		12
145.99	odd	4		725.2.l.b.326.1		6
145.128	even	4		725.2.r.b.674.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	29.12	odd	4
29.2.d.a.25.1	yes	6	29.10	odd	28
261.2.k.a.181.1		6	87.41	even	4
261.2.k.a.199.1		6	87.68	even	28
464.2.u.f.65.1		6	116.99	even	4
464.2.u.f.257.1		6	116.39	even	28
725.2.l.b.326.1		6	145.99	odd	4
725.2.l.b.576.1		6	145.39	odd	28
725.2.r.b.199.1		12	145.97	even	28
725.2.r.b.199.2		12	145.68	even	28
725.2.r.b.674.1		12	145.128	even	4
725.2.r.b.674.2		12	145.12	even	4
841.2.a.e.1.3		3	29.27	odd	28
841.2.a.f.1.1		3	29.2	odd	28
841.2.b.c.840.2		6	29.24	even	7
841.2.b.c.840.5		6	29.5	even	14
841.2.d.a.574.1		6	29.11	odd	28
841.2.d.a.778.1		6	29.3	odd	28
841.2.d.b.190.1		6	29.8	odd	28
841.2.d.b.571.1		6	29.15	odd	28
841.2.d.c.190.1		6	29.21	odd	28
841.2.d.c.571.1		6	29.14	odd	28
841.2.d.d.605.1		6	29.19	odd	28
841.2.d.d.645.1		6	29.17	odd	4
841.2.d.e.574.1		6	29.18	odd	28
841.2.d.e.778.1		6	29.26	odd	28
841.2.e.b.63.1		12	29.22	even	14
841.2.e.b.63.2		12	29.7	even	7
841.2.e.b.267.1		12	29.16	even	7
841.2.e.b.267.2		12	29.13	even	14
841.2.e.c.270.1		12	29.6	even	14
841.2.e.c.270.2		12	29.23	even	7
841.2.e.c.651.1		12	29.20	even	7
841.2.e.c.651.2		12	29.9	even	14
841.2.e.d.196.1		12	1.1	even	1	trivial
841.2.e.d.196.2		12	29.28	even	2	inner
841.2.e.d.236.1		12	29.4	even	14	inner
841.2.e.d.236.2		12	29.25	even	7	inner
7569.2.a.p.1.3		3	87.2	even	28
7569.2.a.r.1.1		3	87.56	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21572 + 0.277479i) q^{2} +(-0.781831 + 1.62349i) q^{3} +(-0.400969 + 0.193096i) q^{4} +(-0.900969 - 3.94740i) q^{5} +(0.500000 - 2.19064i) q^{6} +(-0.623490 - 0.300257i) q^{7} +(2.38374 - 1.90097i) q^{8} +(-0.153989 - 0.193096i) q^{9} +(2.19064 + 4.54892i) q^{10} +(2.22889 + 1.77748i) q^{11} -0.801938i q^{12} +(-0.914542 + 1.14680i) q^{13} +(0.841301 + 0.192021i) q^{14} +(7.11297 + 1.62349i) q^{15} +(-1.81551 + 2.27658i) q^{16} +1.60388i q^{17} +(0.240787 + 0.192021i) q^{18} +(-1.16802 - 2.42543i) q^{19} +(1.12349 + 1.40881i) q^{20} +(0.974928 - 0.777479i) q^{21} +(-3.20291 - 1.54244i) q^{22} +(1.14795 - 5.02949i) q^{23} +(1.22252 + 5.35621i) q^{24} +(-10.2654 + 4.94355i) q^{25} +(0.793610 - 1.64795i) q^{26} +(-4.83639 + 1.10388i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(1.90216 - 0.434157i) q^{31} +(-1.07031 + 2.22252i) q^{32} +(-4.62833 + 2.22889i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(-0.623490 + 2.73169i) q^{35} +(0.0990311 + 0.0476909i) q^{36} +(-2.22889 + 1.77748i) q^{37} +(2.09299 + 2.62453i) q^{38} +(-1.14680 - 2.38135i) q^{39} +(-9.65156 - 7.69687i) q^{40} +6.49396i q^{41} +(-0.969501 + 1.21572i) q^{42} +(0.648205 + 0.147948i) q^{43} +(-1.23694 - 0.282323i) q^{44} +(-0.623490 + 0.781831i) q^{45} +6.43296i q^{46} +(-3.71606 - 2.96346i) q^{47} +(-2.27658 - 4.72737i) q^{48} +(-4.06584 - 5.09841i) q^{49} +(11.1081 - 8.85839i) q^{50} +(-2.60388 - 1.25396i) q^{51} +(0.145260 - 0.636426i) q^{52} +(-0.0108851 - 0.0476909i) q^{53} +(5.57338 - 2.68400i) q^{54} +(5.00827 - 10.3998i) q^{55} +(-2.05702 + 0.469501i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(-3.16557 + 0.722521i) q^{60} +(0.567511 - 1.17845i) q^{61} +(-2.19202 + 1.05562i) q^{62} +(0.0380322 + 0.166630i) q^{63} +(1.98039 - 8.67664i) q^{64} +(5.35086 + 2.57684i) q^{65} +(5.00827 - 3.99396i) q^{66} +(-9.32036 - 11.6874i) q^{67} +(-0.309703 - 0.643104i) q^{68} +(7.26782 + 5.79590i) q^{69} -3.49396i q^{70} +(1.40850 - 1.76621i) q^{71} +(-0.734141 - 0.167563i) q^{72} +(-8.11437 - 1.85205i) q^{73} +(2.21648 - 2.77938i) q^{74} -20.5308i q^{75} +(0.936683 + 0.746980i) q^{76} +(-0.855989 - 1.77748i) q^{77} +(2.05496 + 2.57684i) q^{78} +(-7.61577 + 6.07338i) q^{79} +(10.6223 + 5.11543i) q^{80} +(2.15399 - 9.43724i) q^{81} +(-1.80194 - 7.89481i) q^{82} +(3.62349 - 1.74498i) q^{83} +(-0.240787 + 0.500000i) q^{84} +(6.33114 - 1.44504i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(-10.9744 + 2.50484i) q^{89} +(0.541044 - 1.12349i) q^{90} +(0.914542 - 0.440420i) q^{91} +(0.510885 + 2.23833i) q^{92} +(-0.782323 + 3.42758i) q^{93} +(5.33997 + 2.57159i) q^{94} +(-8.52179 + 6.79590i) q^{95} +(-2.77144 - 3.47527i) q^{96} +(1.98286 + 4.11745i) q^{97} +(6.35761 + 5.07002i) q^{98} -0.704103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

Introduction

L-functions

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