LMFDB - Embedded newform 841.2.d.e.571.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] 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([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,5,2,5,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			571.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	841.571
Dual form			841.2.d.e.190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62349 - 0.781831i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.777479 - 0.974928i) q^{4} +(-0.321552 + 0.154851i) q^{5} +(0.722521 + 0.347948i) q^{6} +(-2.52446 - 3.16557i) q^{7} +(-0.301938 + 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +(-0.400969 + 0.502799i) q^{10} +(-0.647948 - 2.83885i) q^{11} +0.554958 q^{12} +(-1.15399 - 5.05596i) q^{13} +(-6.57338 - 3.16557i) q^{14} +(-0.143104 - 0.0689153i) q^{15} +(1.09903 + 4.81517i) q^{16} +1.10992 q^{17} +(-1.12349 - 4.92233i) q^{18} +(1.27748 - 1.60191i) q^{19} +(-0.0990311 + 0.433884i) q^{20} +(0.400969 - 1.75676i) q^{21} +(-3.27144 - 4.10225i) q^{22} +(3.72737 + 1.79500i) q^{23} +(-0.544073 + 0.262012i) q^{24} +(-3.03803 + 3.80957i) q^{25} +(-5.82640 - 7.30607i) q^{26} +(2.32640 - 1.12033i) q^{27} -5.04892 q^{28} -0.286208 q^{30} +(5.72737 - 2.75815i) q^{31} +(3.85690 + 4.83639i) q^{32} +(0.807979 - 1.01317i) q^{33} +(1.80194 - 0.867767i) q^{34} +(1.30194 + 0.626980i) q^{35} +(-2.17845 - 2.73169i) q^{36} +(0.647948 - 2.83885i) q^{37} +(0.821552 - 3.59945i) q^{38} +(1.43900 - 1.80445i) q^{39} +(-0.107760 - 0.472129i) q^{40} +0.396125 q^{41} +(-0.722521 - 3.16557i) q^{42} +(-5.17241 - 2.49090i) q^{43} +(-3.27144 - 1.57544i) q^{44} +(0.222521 + 0.974928i) q^{45} +7.45473 q^{46} +(1.73609 + 7.60633i) q^{47} +(-1.37047 + 1.71851i) q^{48} +(-2.09030 + 9.15821i) q^{49} +(-1.95377 + 8.56003i) q^{50} +(0.307979 + 0.386193i) q^{51} +(-5.82640 - 2.80584i) q^{52} +(3.92543 - 1.89039i) q^{53} +(2.90097 - 3.63770i) q^{54} +(0.647948 + 0.812502i) q^{55} +(4.94989 - 2.38374i) q^{56} +0.911854 q^{57} -9.10992 q^{59} +(-0.178448 + 0.0859360i) q^{60} +(-3.77144 - 4.72923i) q^{61} +(7.14191 - 8.95567i) q^{62} +(-10.2213 + 4.92233i) q^{63} +(1.14310 + 0.550490i) q^{64} +(1.15399 + 1.44706i) q^{65} +(0.519614 - 2.27658i) q^{66} +(-0.0833017 + 0.364968i) q^{67} +(0.862937 - 1.08209i) q^{68} +(0.409698 + 1.79500i) q^{69} +2.60388 q^{70} +(2.53803 + 11.1198i) q^{71} +(3.42543 + 1.64960i) q^{72} +(8.06249 + 3.88269i) q^{73} +(-1.16756 - 5.11543i) q^{74} -2.16852 q^{75} +(-0.568532 - 2.49090i) q^{76} +(-7.35086 + 9.21768i) q^{77} +(0.925428 - 4.05456i) q^{78} +(0.132219 - 0.579289i) q^{79} +(-1.09903 - 1.37814i) q^{80} +(-6.53803 - 3.14855i) q^{81} +(0.643104 - 0.309703i) q^{82} +(-5.88135 + 7.37499i) q^{83} +(-1.40097 - 1.75676i) q^{84} +(-0.356896 + 0.171872i) q^{85} -10.3448 q^{86} +3.95108 q^{88} +(-1.28232 + 0.617534i) q^{89} +(1.12349 + 1.40881i) q^{90} +(-13.0918 + 16.4166i) q^{91} +(4.64795 - 2.23833i) q^{92} +(2.54892 + 1.22749i) q^{93} +(8.76540 + 10.9915i) q^{94} +(-0.162718 + 0.712916i) q^{95} +(-0.612605 + 2.68400i) q^{96} +(9.82036 - 12.3143i) q^{97} +(3.76659 + 16.5025i) q^{98} -8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} + 7 q^{8} - q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{12} - 12 q^{13} - 12 q^{14} - 9 q^{15} + 11 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} - 5 q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 6 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 + 7 * q^8 - q^9 + 2 * q^10 + 10 * q^11 + 4 * q^12 - 12 * q^13 - 12 * q^14 - 9 * q^15 + 11 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 - 5 * q^20 - 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 - 17 * q^26 - 4 * q^27 - 12 * q^28 - 18 * q^30 + 12 * q^31 + 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 - 10 * q^37 + 9 * q^38 - 11 * q^39 - 21 * q^40 + 20 * q^41 - 4 * q^42 - 8 * q^43 - q^44 + q^45 + 4 * q^47 + 6 * q^48 - q^49 - 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 - 10 * q^55 + 7 * q^56 - 2 * q^57 - 56 * q^59 + 3 * q^60 - 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 + 16 * q^66 - 30 * q^67 + 16 * q^68 + 14 * q^69 - 2 * q^70 + 7 * q^72 + 24 * q^73 - 6 * q^74 + 48 * q^75 + 2 * q^76 - 17 * q^77 - 8 * q^78 + 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 - 4 * q^84 + 6 * q^85 - 16 * q^86 + 42 * q^88 + 14 * q^89 + 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 - 22 * q^95 - 2 * q^96 + 22 * q^97 + 26 * q^98 - 32 * q^99

Character values

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

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

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 $

$2$	1.62349	−	0.781831i	1.14798	−	0.552838i	0.239554	−	0.970883i	$-0.422999\pi$
$2$	1.62349	−	0.781831i	1.14798	−	0.552838i	0.908426	+	0.418045i	$0.137284\pi$
$3$	0.277479	+	0.347948i	0.160203	+	0.200888i	0.855454	−	0.517879i	$-0.173278\pi$
$3$	0.277479	+	0.347948i	0.160203	+	0.200888i	−0.695251	+	0.718767i	$0.744707\pi$
$4$	0.777479	−	0.974928i	0.388740	−	0.487464i
$5$	−0.321552	+	0.154851i	−0.143802	+	0.0692516i	−0.504401	−	0.863469i	$-0.668287\pi$
$5$	−0.321552	+	0.154851i	−0.143802	+	0.0692516i	0.360599	+	0.932721i	$0.382572\pi$
$6$	0.722521	+	0.347948i	0.294968	+	0.142049i
$7$	−2.52446	−	3.16557i	−0.954156	−	1.19647i	−0.980440	−	0.196819i	$-0.936939\pi$
$7$	−2.52446	−	3.16557i	−0.954156	−	1.19647i	0.0262842	−	0.999655i	$-0.491633\pi$
$8$	−0.301938	+	1.32288i	−0.106751	+	0.467707i
$9$	0.623490	−	2.73169i	0.207830	−	0.910562i
$10$	−0.400969	+	0.502799i	−0.126797	+	0.158999i
$11$	−0.647948	−	2.83885i	−0.195364	−	0.855945i	−0.973652	−	0.228038i	$-0.926769\pi$
$11$	−0.647948	−	2.83885i	−0.195364	−	0.855945i	0.778288	−	0.627907i	$-0.216088\pi$
$12$	0.554958			0.160203
$13$	−1.15399	−	5.05596i	−0.320059	−	1.40227i	−0.837447	−	0.546519i	$-0.815953\pi$
$13$	−1.15399	−	5.05596i	−0.320059	−	1.40227i	0.517388	−	0.855751i	$-0.326905\pi$
$14$	−6.57338	−	3.16557i	−1.75681	−	0.846034i
$15$	−0.143104	−	0.0689153i	−0.0369493	−	0.0177939i
$16$	1.09903	+	4.81517i	0.274758	+	1.20379i
$17$	1.10992			0.269194			0.134597	−	0.990900i	$-0.457026\pi$
$17$	1.10992			0.269194			0.134597	+	0.990900i	$0.457026\pi$
$18$	−1.12349	−	4.92233i	−0.264809	−	1.16020i
$19$	1.27748	−	1.60191i	0.293074	−	0.367503i	−0.613395	−	0.789777i	$-0.710196\pi$
$19$	1.27748	−	1.60191i	0.293074	−	0.367503i	0.906468	+	0.422274i	$0.138768\pi$
$20$	−0.0990311	+	0.433884i	−0.0221440	+	0.0970194i
$21$	0.400969	−	1.75676i	0.0874986	−	0.383356i
$22$	−3.27144	−	4.10225i	−0.697473	−	0.874603i
$23$	3.72737	+	1.79500i	0.777209	+	0.374284i	0.780054	−	0.625712i	$-0.215191\pi$
$23$	3.72737	+	1.79500i	0.777209	+	0.374284i	−0.00284506	+	0.999996i	$0.500906\pi$
$24$	−0.544073	+	0.262012i	−0.111058	+	0.0534829i
$25$	−3.03803	+	3.80957i	−0.607606	+	0.761914i
$26$	−5.82640	−	7.30607i	−1.14265	−	1.43284i
$27$	2.32640	−	1.12033i	0.447715	−	0.215608i
$28$	−5.04892			−0.954156
$29$		0			0
$29$		0			0
$30$	−0.286208			−0.0522542
$31$	5.72737	−	2.75815i	1.02867	−	0.495379i	0.158095	−	0.987424i	$-0.449465\pi$
$31$	5.72737	−	2.75815i	1.02867	−	0.495379i	0.870570	+	0.492045i	$0.163750\pi$
$32$	3.85690	+	4.83639i	0.681809	+	0.854962i
$33$	0.807979	−	1.01317i	0.140651	−	0.176371i
$34$	1.80194	−	0.867767i	0.309030	−	0.148821i
$35$	1.30194	+	0.626980i	0.220068	+	0.105979i
$36$	−2.17845	−	2.73169i	−0.363075	−	0.455281i
$37$	0.647948	−	2.83885i	0.106522	−	0.466704i	−0.893328	−	0.449405i	$-0.851636\pi$
$37$	0.647948	−	2.83885i	0.106522	−	0.466704i	0.999850	−	0.0172990i	$-0.00550672\pi$
$38$	0.821552	−	3.59945i	0.133273	−	0.583909i
$39$	1.43900	−	1.80445i	0.230425	−	0.288943i
$40$	−0.107760	−	0.472129i	−0.0170384	−	0.0746501i
$41$	0.396125			0.0618643			0.0309321	−	0.999521i	$-0.490152\pi$
$41$	0.396125			0.0618643			0.0309321	+	0.999521i	$0.490152\pi$
$42$	−0.722521	−	3.16557i	−0.111487	−	0.488458i
$43$	−5.17241	−	2.49090i	−0.788785	−	0.379859i	−0.00428731	−	0.999991i	$-0.501365\pi$
$43$	−5.17241	−	2.49090i	−0.788785	−	0.379859i	−0.784497	+	0.620132i	$0.787079\pi$
$44$	−3.27144	−	1.57544i	−0.493188	−	0.237507i
$45$	0.222521	+	0.974928i	0.0331715	+	0.145334i
$46$	7.45473			1.09914
$47$	1.73609	+	7.60633i	0.253235	+	1.10950i	0.928328	+	0.371763i	$0.121247\pi$
$47$	1.73609	+	7.60633i	0.253235	+	1.10950i	−0.675092	+	0.737733i	$0.735896\pi$
$48$	−1.37047	+	1.71851i	−0.197810	+	0.248046i
$49$	−2.09030	+	9.15821i	−0.298615	+	1.30832i
$50$	−1.95377	+	8.56003i	−0.276305	+	1.21057i
$51$	0.307979	+	0.386193i	0.0431256	+	0.0540778i
$52$	−5.82640	−	2.80584i	−0.807976	−	0.389101i
$53$	3.92543	−	1.89039i	0.539199	−	0.259665i	−0.144404	−	0.989519i	$-0.546126\pi$
$53$	3.92543	−	1.89039i	0.539199	−	0.259665i	0.683603	+	0.729854i	$0.260412\pi$
$54$	2.90097	−	3.63770i	0.394772	−	0.495028i
$55$	0.647948	+	0.812502i	0.0873694	+	0.109558i
$56$	4.94989	−	2.38374i	0.661456	−	0.318541i
$57$	0.911854			0.120778
$58$		0			0
$59$	−9.10992			−1.18601			−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992			−1.18601			−0.593005	+	0.805199i	$0.702059\pi$
$60$	−0.178448	+	0.0859360i	−0.0230375	+	0.0110943i
$61$	−3.77144	−	4.72923i	−0.482883	−	0.605516i	0.479390	−	0.877602i	$-0.340858\pi$
$61$	−3.77144	−	4.72923i	−0.482883	−	0.605516i	−0.962273	+	0.272086i	$0.912287\pi$
$62$	7.14191	−	8.95567i	0.907023	−	1.13737i
$63$	−10.2213	+	4.92233i	−1.28777	+	0.620155i
$64$	1.14310	+	0.550490i	0.142888	+	0.0688112i
$65$	1.15399	+	1.44706i	0.143135	+	0.179485i
$66$	0.519614	−	2.27658i	0.0639601	−	0.280228i
$67$	−0.0833017	+	0.364968i	−0.0101769	+	0.0445880i	−0.979761	−	0.200169i	$-0.935851\pi$
$67$	−0.0833017	+	0.364968i	−0.0101769	+	0.0445880i	0.969585	+	0.244757i	$0.0787081\pi$
$68$	0.862937	−	1.08209i	0.104646	−	0.131222i
$69$	0.409698	+	1.79500i	0.0493219	+	0.216093i
$70$	2.60388			0.311223
$71$	2.53803	+	11.1198i	0.301209	+	1.31968i	0.868305	+	0.496031i	$0.165210\pi$
$71$	2.53803	+	11.1198i	0.301209	+	1.31968i	−0.567096	+	0.823652i	$0.691933\pi$
$72$	3.42543	+	1.64960i	0.403691	+	0.194407i
$73$	8.06249	+	3.88269i	0.943643	+	0.454435i	0.841453	−	0.540330i	$-0.181701\pi$
$73$	8.06249	+	3.88269i	0.943643	+	0.454435i	0.102190	+	0.994765i	$0.467415\pi$
$74$	−1.16756	−	5.11543i	−0.135726	−	0.594656i
$75$	−2.16852			−0.250399
$76$	−0.568532	−	2.49090i	−0.0652151	−	0.285726i
$77$	−7.35086	+	9.21768i	−0.837708	+	1.05045i
$78$	0.925428	−	4.05456i	0.104784	−	0.459089i
$79$	0.132219	−	0.579289i	0.0148758	−	0.0651751i	−0.966945	−	0.254984i	$-0.917930\pi$
$79$	0.132219	−	0.579289i	0.0148758	−	0.0651751i	0.981821	+	0.189809i	$0.0607869\pi$
$80$	−1.09903	−	1.37814i	−0.122875	−	0.154081i
$81$	−6.53803	−	3.14855i	−0.726448	−	0.349839i
$82$	0.643104	−	0.309703i	0.0710190	−	0.0342009i
$83$	−5.88135	+	7.37499i	−0.645563	+	0.809510i	−0.991686	−	0.128679i	$-0.958926\pi$
$83$	−5.88135	+	7.37499i	−0.645563	+	0.809510i	0.346124	+	0.938189i	$0.387498\pi$
$84$	−1.40097	−	1.75676i	−0.152858	−	0.191678i
$85$	−0.356896	+	0.171872i	−0.0387108	+	0.0186421i
$86$	−10.3448			−1.11551
$87$		0			0
$88$	3.95108			0.421187
$89$	−1.28232	+	0.617534i	−0.135926	+	0.0654585i	−0.500611	−	0.865673i	$-0.666891\pi$
$89$	−1.28232	+	0.617534i	−0.135926	+	0.0654585i	0.364685	+	0.931131i	$0.381177\pi$
$90$	1.12349	+	1.40881i	0.118426	+	0.148502i
$91$	−13.0918	+	16.4166i	−1.37239	+	1.72093i
$92$	4.64795	−	2.23833i	0.484582	−	0.233362i
$93$	2.54892	+	1.22749i	0.264310	+	0.127285i
$94$	8.76540	+	10.9915i	0.904082	+	1.13368i
$95$	−0.162718	+	0.712916i	−0.0166946	+	0.0731437i
$96$	−0.612605	+	2.68400i	−0.0625237	+	0.273934i
$97$	9.82036	−	12.3143i	0.997106	−	1.25033i	0.0290551	−	0.999578i	$-0.490750\pi$
$97$	9.82036	−	12.3143i	0.997106	−	1.25033i	0.968051	−	0.250754i	$-0.0806784\pi$
$98$	3.76659	+	16.5025i	0.380483	+	1.66701i
$99$	−8.15883			−0.819994
$100$	1.35205	+	5.92372i	0.135205	+	0.592372i
$101$	15.7153	+	7.56808i	1.56373	+	0.753052i	0.997464	−	0.0711709i	$-0.0226736\pi$
$101$	15.7153	+	7.56808i	1.56373	+	0.753052i	0.566265	+	0.824223i	$0.308388\pi$
$102$	0.801938	+	0.386193i	0.0794037	+	0.0382388i
$103$	0.626178	+	2.74347i	0.0616992	+	0.270322i	0.996363	−	0.0852112i	$-0.0271565\pi$
$103$	0.626178	+	2.74347i	0.0616992	+	0.270322i	−0.934664	+	0.355533i	$0.884299\pi$
$104$	7.03684			0.690019
$105$	0.143104	+	0.626980i	0.0139655	+	0.0611870i
$106$	4.89493	−	6.13805i	0.475437	−	0.596180i
$107$	1.66003	−	7.27307i	0.160481	−	0.703114i	−0.829096	−	0.559107i	$-0.811144\pi$
$107$	1.66003	−	7.27307i	0.160481	−	0.703114i	0.989577	−	0.144007i	$-0.0459988\pi$
$108$	0.716480	−	3.13910i	0.0689433	−	0.302060i
$109$	−1.03050	−	1.29221i	−0.0987039	−	0.123771i	0.730026	−	0.683419i	$-0.239508\pi$
$109$	−1.03050	−	1.29221i	−0.0987039	−	0.123771i	−0.828730	+	0.559648i	$0.810936\pi$
$110$	1.68718	+	0.812502i	0.160866	+	0.0774690i
$111$	1.16756	−	0.562269i	0.110820	−	0.0533682i
$112$	12.4683	−	15.6348i	1.17814	−	1.47735i
$113$	5.38740	+	6.75558i	0.506804	+	0.635512i	0.967749	−	0.251917i	$-0.0810610\pi$
$113$	5.38740	+	6.75558i	0.506804	+	0.635512i	−0.460945	+	0.887429i	$0.652490\pi$
$114$	1.48039	−	0.712916i	0.138651	−	0.0667707i
$115$	−1.47650			−0.137684
$116$		0			0
$117$	−14.5308			−1.34337
$118$	−14.7899	+	7.12242i	−1.36152	+	0.655672i
$119$	−2.80194	−	3.51352i	−0.256853	−	0.322084i
$120$	0.134375	−	0.168501i	0.0122667	−	0.0153820i
$121$	2.27144	−	1.09387i	0.206494	−	0.0994425i
$122$	−9.82036	−	4.72923i	−0.889093	−	0.428165i
$123$	0.109916	+	0.137831i	0.00991082	+	0.0124278i
$124$	1.76391	−	7.72818i	0.158403	−	0.694011i
$125$	0.784052	−	3.43516i	0.0701278	−	0.307250i
$126$	−12.7458	+	15.9827i	−1.13548	+	1.42385i
$127$	−2.33028	−	10.2096i	−0.206779	−	0.905958i	−0.966694	−	0.255935i	$-0.917617\pi$
$127$	−2.33028	−	10.2096i	−0.206779	−	0.905958i	0.759915	−	0.650023i	$-0.225241\pi$
$128$	−10.0858			−0.891463
$129$	−0.568532	−	2.49090i	−0.0500564	−	0.219312i
$130$	3.00484	+	1.44706i	0.263542	+	0.126915i
$131$	0.409698	+	0.197300i	0.0357955	+	0.0172382i	0.451696	−	0.892172i	$-0.350819\pi$
$131$	0.409698	+	0.197300i	0.0357955	+	0.0172382i	−0.415900	+	0.909410i	$0.636534\pi$
$132$	−0.359584	−	1.57544i	−0.0312978	−	0.137125i
$133$	−8.29590			−0.719345
$134$	0.150104	+	0.657650i	0.0129670	+	0.0568123i
$135$	−0.574572	+	0.720491i	−0.0494513	+	0.0620100i
$136$	−0.335126	+	1.46828i	−0.0287368	+	0.125904i
$137$	2.94624	−	12.9083i	0.251714	−	1.10283i	−0.678149	−	0.734925i	$-0.737217\pi$
$137$	2.94624	−	12.9083i	0.251714	−	1.10283i	0.929863	−	0.367907i	$-0.119925\pi$
$138$	2.06853	+	2.59386i	0.176085	+	0.220804i
$139$	2.51961	+	1.21338i	0.213711	+	0.102918i	0.537677	−	0.843151i	$-0.319302\pi$
$139$	2.51961	+	1.21338i	0.213711	+	0.102918i	−0.323966	+	0.946069i	$0.605016\pi$
$140$	1.62349	−	0.781831i	0.137210	−	0.0660768i
$141$	−2.16487	+	2.71467i	−0.182315	+	0.228616i
$142$	12.8143	+	16.0686i	1.07535	+	1.34845i
$143$	−13.6054	+	6.55200i	−1.13774	+	0.547906i
$144$	13.8388			1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	−3.76659	+	1.81390i	−0.310663	+	0.149608i
$148$	−2.26391	−	2.83885i	−0.186092	−	0.233352i
$149$	1.68867	−	2.11752i	0.138341	−	0.173474i	−0.707835	−	0.706378i	$-0.750328\pi$
$149$	1.68867	−	2.11752i	0.138341	−	0.173474i	0.846176	+	0.532904i	$0.178899\pi$
$150$	−3.52057	+	1.69542i	−0.287454	+	0.138430i
$151$	2.19418	+	1.05666i	0.178560	+	0.0859898i	0.521028	−	0.853540i	$-0.325549\pi$
$151$	2.19418	+	1.05666i	0.178560	+	0.0859898i	−0.342468	+	0.939529i	$0.611263\pi$
$152$	1.73341	+	2.17362i	0.140598	+	0.176304i
$153$	0.692021	−	3.03194i	0.0559466	−	0.245118i
$154$	−4.72737	+	20.7119i	−0.380942	+	1.66902i
$155$	−1.41454	+	1.77378i	−0.113619	+	0.142473i
$156$	−0.640416	−	2.80584i	−0.0512743	−	0.224647i
$157$	17.6775			1.41082			0.705411	−	0.708799i	$-0.250762\pi$
$157$	17.6775			1.41082			0.705411	+	0.708799i	$0.250762\pi$
$158$	−0.238250	−	1.04384i	−0.0189542	−	0.0830437i
$159$	1.74698	+	0.841301i	0.138544	+	0.0667195i
$160$	−1.98911	−	0.957907i	−0.157253	−	0.0757292i
$161$	−3.72737	−	16.3307i	−0.293758	−	1.28704i
$162$	−13.0761			−1.02735
$163$	1.10507	+	4.84164i	0.0865559	+	0.379226i	0.999589	−	0.0286587i	$-0.00912360\pi$
$163$	1.10507	+	4.84164i	0.0865559	+	0.379226i	−0.913033	+	0.407885i	$0.866266\pi$
$164$	0.307979	−	0.386193i	0.0240491	−	0.0301566i
$165$	−0.102916	+	0.450904i	−0.00801200	+	0.0351029i
$166$	−3.78232	+	16.5714i	−0.293565	+	1.28619i
$167$	9.01842	+	11.3087i	0.697866	+	0.875096i	0.996862	−	0.0791579i	$-0.0252231\pi$
$167$	9.01842	+	11.3087i	0.697866	+	0.875096i	−0.298996	+	0.954254i	$0.596652\pi$
$168$	2.20291	+	1.06086i	0.169958	+	0.0818474i
$169$	−12.5184	+	6.02855i	−0.962955	+	0.463735i
$170$	−0.445042	+	0.558065i	−0.0341332	+	0.0428016i
$171$	−3.57942	−	4.48845i	−0.273725	−	0.343240i
$172$	−6.44989	+	3.10610i	−0.491799	+	0.236838i
$173$	10.5133			0.799314			0.399657	−	0.916665i	$-0.369129\pi$
$173$	10.5133			0.799314			0.399657	+	0.916665i	$0.369129\pi$
$174$		0			0
$175$	19.7289			1.49136
$176$	12.9574	−	6.23996i	0.976702	−	0.470355i
$177$	−2.52781	−	3.16977i	−0.190002	−	0.238255i
$178$	−1.59903	+	2.00512i	−0.119852	+	0.150290i
$179$	5.17241	−	2.49090i	0.386604	−	0.186179i	−0.230478	−	0.973078i	$-0.574029\pi$
$179$	5.17241	−	2.49090i	0.386604	−	0.186179i	0.617082	+	0.786899i	$0.288315\pi$
$180$	1.12349	+	0.541044i	0.0837400	+	0.0403271i
$181$	−4.14042	−	5.19192i	−0.307755	−	0.385912i	0.603769	−	0.797159i	$-0.293665\pi$
$181$	−4.14042	−	5.19192i	−0.307755	−	0.385912i	−0.911524	+	0.411247i	$0.865093\pi$
$182$	−8.41939	+	36.8877i	−0.624086	+	2.73430i
$183$	0.599031	−	2.62453i	0.0442817	−	0.194011i
$184$	−3.50000	+	4.38886i	−0.258023	+	0.323551i
$185$	0.231250	+	1.01317i	0.0170018	+	0.0744900i
$186$	5.09783			0.373791
$187$	−0.719169	−	3.15088i	−0.0525908	−	0.230415i
$188$	8.76540	+	4.22119i	0.639282	+	0.307862i
$189$	−9.41939	−	4.53614i	−0.685160	−	0.329955i
$190$	0.293209	+	1.28463i	0.0212716	+	0.0931969i
$191$	−18.8116			−1.36116			−0.680581	−	0.732673i	$-0.738272\pi$
$191$	−18.8116			−1.36116			−0.680581	+	0.732673i	$0.738272\pi$
$192$	0.125646	+	0.550490i	0.00906770	+	0.0397282i
$193$	6.78650	−	8.51001i	0.488503	−	0.612564i	−0.475090	−	0.879937i	$-0.657584\pi$
$193$	6.78650	−	8.51001i	0.488503	−	0.612564i	0.963593	+	0.267374i	$0.0861558\pi$
$194$	6.31551	−	27.6701i	0.453427	−	1.98659i
$195$	−0.183292	+	0.803056i	−0.0131258	+	0.0575080i
$196$	7.30343	+	9.15821i	0.521674	+	0.654158i
$197$	7.56853	+	3.64481i	0.539236	+	0.259682i	0.683618	−	0.729840i	$-0.260405\pi$
$197$	7.56853	+	3.64481i	0.539236	+	0.259682i	−0.144383	+	0.989522i	$0.546120\pi$
$198$	−13.2458	+	6.37883i	−0.941337	+	0.453324i
$199$	−4.12833	+	5.17677i	−0.292650	+	0.366971i	−0.906321	−	0.422591i	$-0.861121\pi$
$199$	−4.12833	+	5.17677i	−0.292650	+	0.366971i	0.613671	+	0.789562i	$0.289692\pi$
$200$	−4.12229	−	5.16919i	−0.291490	−	0.365517i
$201$	−0.150104	+	0.0722865i	−0.0105875	+	0.00509869i
$202$	31.4306			2.21145
$203$		0			0
$204$	0.615957			0.0431256
$205$	−0.127375	+	0.0613404i	−0.00889623	+	0.00428420i
$206$	3.16152	+	3.96442i	0.220274	+	0.276214i
$207$	7.22737	−	9.06283i	0.502337	−	0.629910i
$208$	23.0770	−	11.1133i	1.60010	−	0.770569i
$209$	−5.37531	−	2.58861i	−0.371818	−	0.179058i
$210$	0.722521	+	0.906013i	0.0498587	+	0.0625208i
$211$	1.80247	−	7.89714i	0.124087	−	0.543661i	−0.874222	−	0.485527i	$-0.838628\pi$
$211$	1.80247	−	7.89714i	0.124087	−	0.543661i	0.998309	−	0.0581343i	$-0.0185152\pi$
$212$	1.20895	−	5.29674i	0.0830308	−	0.363782i
$213$	−3.16487	+	3.96863i	−0.216854	+	0.271926i
$214$	−2.99127	−	13.1056i	−0.204479	−	0.895881i
$215$	2.04892			0.139735
$216$	0.779635	+	3.41580i	0.0530474	+	0.232416i
$217$	−23.1896	−	11.1675i	−1.57421	−	0.758102i
$218$	−2.68329	−	1.29221i	−0.181735	−	0.0875192i
$219$	0.886199	+	3.88269i	0.0598838	+	0.262368i
$220$	1.29590			0.0873694
$221$	−1.28083	−	5.61169i	−0.0861580	−	0.377483i
$222$	1.45593	−	1.82567i	0.0977154	−	0.122531i
$223$	−4.87747	+	21.3696i	−0.326620	+	1.43101i	0.498910	+	0.866654i	$0.333734\pi$
$223$	−4.87747	+	21.3696i	−0.326620	+	1.43101i	−0.825529	+	0.564360i	$0.809123\pi$
$224$	5.57338	−	24.4186i	0.372387	−	1.63153i
$225$	8.51238	+	10.6742i	0.567492	+	0.711612i
$226$	14.0281	+	6.75558i	0.933136	+	0.449375i
$227$	16.4683	−	7.93072i	1.09304	−	0.526380i	0.201576	−	0.979473i	$-0.435394\pi$
$227$	16.4683	−	7.93072i	1.09304	−	0.526380i	0.891463	+	0.453093i	$0.149679\pi$
$228$	0.708947	−	0.888992i	0.0469512	−	0.0588749i
$229$	9.99127	+	12.5287i	0.660242	+	0.827917i	0.993370	−	0.114965i	$-0.0366755\pi$
$229$	9.99127	+	12.5287i	0.660242	+	0.827917i	−0.333128	+	0.942882i	$0.608104\pi$
$230$	−2.39708	+	1.15437i	−0.158059	+	0.0761172i
$231$	−5.24698			−0.345226
$232$		0			0
$233$	1.95646			0.128172			0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646			0.128172			0.0640860	+	0.997944i	$0.479587\pi$
$234$	−23.5906	+	11.3606i	−1.54217	+	0.742668i
$235$	−1.73609	−	2.17699i	−0.113250	−	0.142011i
$236$	−7.08277	+	8.88151i	−0.461049	+	0.578137i
$237$	0.238250	−	0.114735i	0.0154760	−	0.00745286i
$238$	−7.29590	−	3.51352i	−0.472923	−	0.227748i
$239$	−5.58844	−	7.00768i	−0.361486	−	0.453289i	0.567517	−	0.823362i	$-0.307904\pi$
$239$	−5.58844	−	7.00768i	−0.361486	−	0.453289i	−0.929003	+	0.370073i	$0.879333\pi$
$240$	0.174563	−	0.764811i	0.0112680	−	0.0493683i
$241$	−4.42812	+	19.4008i	−0.285240	+	1.24972i	0.605735	+	0.795666i	$0.292879\pi$
$241$	−4.42812	+	19.4008i	−0.285240	+	1.24972i	−0.890975	+	0.454052i	$0.849978\pi$
$242$	2.83244	−	3.55176i	0.182076	−	0.228316i
$243$	−2.44235	−	10.7006i	−0.156677	−	0.686447i
$244$	−7.54288			−0.482883
$245$	−0.746020	−	3.26853i	−0.0476615	−	0.208819i
$246$	0.286208	+	0.137831i	0.0182480	+	0.00878776i
$247$	−9.57338	−	4.61029i	−0.609139	−	0.293346i
$248$	1.91939	+	8.40938i	0.121881	+	0.533996i
$249$	−4.19806			−0.266041
$250$	−1.41281	−	6.18994i	−0.0893542	−	0.391486i
$251$	16.0891	−	20.1751i	1.01554	−	1.27344i	0.0540635	−	0.998537i	$-0.482783\pi$
$251$	16.0891	−	20.1751i	1.01554	−	1.27344i	0.961472	−	0.274904i	$-0.0886459\pi$
$252$	−3.14795	+	13.7921i	−0.198302	+	0.868818i
$253$	2.68060	−	11.7445i	0.168528	−	0.738370i
$254$	−11.7654	−	14.7533i	−0.738227	−	0.925707i
$255$	−0.158834	−	0.0764902i	−0.00994655	−	0.00479000i
$256$	−18.6603	+	8.98634i	−1.16627	+	0.561646i
$257$	7.45138	−	9.34373i	0.464804	−	0.582846i	−0.493086	−	0.869981i	$-0.664131\pi$
$257$	7.45138	−	9.34373i	0.464804	−	0.582846i	0.957890	+	0.287134i	$0.0927027\pi$
$258$	−2.87047	−	3.59945i	−0.178708	−	0.224092i
$259$	−10.6223	+	5.11543i	−0.660037	+	0.317857i
$260$	2.30798			0.143135
$261$		0			0
$262$	0.819396			0.0506225
$263$	0.299782	−	0.144367i	0.0184853	−	0.00890207i	−0.424618	−	0.905372i	$-0.639592\pi$
$263$	0.299782	−	0.144367i	0.0184853	−	0.00890207i	0.443104	+	0.896470i	$0.353877\pi$
$264$	1.09634	+	1.37477i	0.0674752	+	0.0846113i
$265$	−0.969501	+	1.21572i	−0.0595559	+	0.0746808i
$266$	−13.4683	+	6.48599i	−0.825795	+	0.397682i
$267$	−0.570688	−	0.274829i	−0.0349255	−	0.0168192i
$268$	0.291053	+	0.364968i	0.0177789	+	0.0222940i
$269$	0.236758	−	1.03731i	0.0144354	−	0.0632457i	−0.967197	−	0.254027i	$-0.918245\pi$
$269$	0.236758	−	1.03731i	0.0144354	−	0.0632457i	0.981633	+	0.190781i	$0.0611020\pi$
$270$	−0.369510	+	1.61893i	−0.0224877	+	0.0985249i
$271$	−10.2654	+	12.8724i	−0.623578	+	0.781943i	−0.988843	−	0.148961i	$-0.952407\pi$
$271$	−10.2654	+	12.8724i	−0.623578	+	0.781943i	0.365265	+	0.930904i	$0.380979\pi$
$272$	1.21983	+	5.34444i	0.0739632	+	0.324054i
$273$	−9.34481			−0.565574
$274$	−5.30894	−	23.2600i	−0.320725	−	1.40519i
$275$	12.7833	+	6.15610i	0.770861	+	0.371227i
$276$	2.06853	+	0.996152i	0.124511	+	0.0599613i
$277$	−1.46734	−	6.42886i	−0.0881642	−	0.386273i	0.911524	−	0.411247i	$-0.134907\pi$
$277$	−1.46734	−	6.42886i	−0.0881642	−	0.386273i	−0.999688	+	0.0249745i	$0.992050\pi$
$278$	5.03923			0.302233
$279$	−3.96346	−	17.3651i	−0.237286	−	1.03962i
$280$	−1.22252	+	1.53299i	−0.0730596	+	0.0916138i
$281$	6.79470	−	29.7695i	0.405338	−	1.77590i	−0.199858	−	0.979825i	$-0.564048\pi$
$281$	6.79470	−	29.7695i	0.405338	−	1.77590i	0.605196	−	0.796076i	$-0.293095\pi$
$282$	−1.39224	+	6.09980i	−0.0829067	+	0.363238i
$283$	−2.21648	−	2.77938i	−0.131756	−	0.165217i	0.711577	−	0.702608i	$-0.247981\pi$
$283$	−2.21648	−	2.77938i	−0.131756	−	0.165217i	−0.843333	+	0.537391i	$0.819410\pi$
$284$	12.8143	+	6.17105i	0.760390	+	0.366184i
$285$	−0.293209	+	0.141202i	−0.0173682	+	0.00836407i
$286$	−16.9656	+	21.2742i	−1.00320	+	1.25797i
$287$	−1.00000	−	1.25396i	−0.0590281	−	0.0740189i
$288$	15.6163	−	7.52039i	0.920197	−	0.443143i
$289$	−15.7681			−0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	10.0538	−	4.84164i	0.588352	−	0.283335i
$293$	20.5003	+	25.7066i	1.19764	+	1.50179i	0.816569	+	0.577247i	$0.195873\pi$
$293$	20.5003	+	25.7066i	1.19764	+	1.50179i	0.381071	+	0.924546i	$0.375555\pi$
$294$	−4.69687	+	5.88968i	−0.273927	+	0.343493i
$295$	2.92931	−	1.41068i	0.170551	−	0.0821331i
$296$	3.55980	+	1.71431i	0.206909	+	0.0996423i
$297$	−4.68784	−	5.87837i	−0.272016	−	0.341097i
$298$	1.08599	−	4.75803i	0.0629097	−	0.275625i
$299$	4.77413	−	20.9168i	0.276095	−	1.20965i
$300$	−1.68598	+	2.11415i	−0.0973401	+	0.122061i
$301$	5.17241	+	22.6618i	0.298133	+	1.30620i
$302$	4.38835			0.252521
$303$	1.72737	+	7.56808i	0.0992345	+	0.434775i
$304$	9.11745	+	4.39073i	0.522922	+	0.251826i
$305$	1.94504	+	0.936683i	0.111373	+	0.0536343i
$306$	−1.24698	−	5.46337i	−0.0712851	−	0.312320i
$307$	14.6703			0.837275			0.418638	−	0.908153i	$-0.362508\pi$
$307$	14.6703			0.837275			0.418638	+	0.908153i	$0.362508\pi$
$308$	3.27144	+	14.3331i	0.186407	+	0.816705i
$309$	−0.780831	+	0.979132i	−0.0444199	+	0.0557009i
$310$	−0.909698	+	3.98565i	−0.0516674	+	0.226370i
$311$	−4.12253	+	18.0620i	−0.233767	+	1.02420i	0.712717	+	0.701452i	$0.247464\pi$
$311$	−4.12253	+	18.0620i	−0.233767	+	1.02420i	−0.946484	+	0.322750i	$0.895393\pi$
$312$	1.95257	+	2.44845i	0.110543	+	0.138616i
$313$	−20.7153	−	9.97595i	−1.17090	−	0.563874i	−0.255651	−	0.966769i	$-0.582290\pi$
$313$	−20.7153	−	9.97595i	−1.17090	−	0.563874i	−0.915246	+	0.402895i	$0.868004\pi$
$314$	28.6993	−	13.8209i	1.61960	−	0.779956i
$315$	2.52446	−	3.16557i	0.142237	−	0.178360i
$316$	−0.461968	−	0.579289i	−0.0259877	−	0.0325876i
$317$	−12.6664	+	6.09980i	−0.711414	+	0.342599i	−0.754344	−	0.656479i	$-0.772045\pi$
$317$	−12.6664	+	6.09980i	−0.711414	+	0.342599i	0.0429302	+	0.999078i	$0.486331\pi$
$318$	3.49396			0.195932
$319$		0			0
$320$	−0.452812			−0.0253129
$321$	2.99127	−	1.44052i	0.166956	−	0.0804020i
$322$	−18.8192	−	23.5985i	−1.04875	−	1.31509i
$323$	1.41789	−	1.77798i	0.0788938	−	0.0989297i
$324$	−8.15279	+	3.92618i	−0.452933	+	0.218121i
$325$	22.7669	+	10.9640i	1.26288	+	0.608171i
$326$	5.57942	+	6.99637i	0.309015	+	0.387493i
$327$	0.163678	−	0.717120i	0.00905141	−	0.0396568i
$328$	−0.119605	+	0.524023i	−0.00660408	+	0.0289344i
$329$	19.6957	−	24.6976i	1.08586	−	1.36162i
$330$	0.185448	+	0.812502i	0.0102086	+	0.0447267i
$331$	13.9565			0.767116			0.383558	−	0.923517i	$-0.374699\pi$
$331$	13.9565			0.767116			0.383558	+	0.923517i	$0.374699\pi$
$332$	2.61745	+	11.4678i	0.143651	+	0.629377i
$333$	−7.35086	−	3.53999i	−0.402824	−	0.193990i
$334$	23.4828	+	11.3087i	1.28492	+	0.618787i
$335$	−0.0297300	−	0.130256i	−0.00162432	−	0.00711663i
$336$	8.89977			0.485522
$337$	3.11476	+	13.6467i	0.169672	+	0.743381i	0.986130	+	0.165976i	$0.0530774\pi$
$337$	3.11476	+	13.6467i	0.169672	+	0.743381i	−0.816458	+	0.577405i	$0.804065\pi$
$338$	−15.6102	+	19.5746i	−0.849084	+	1.06472i
$339$	−0.855699	+	3.74906i	−0.0464752	+	0.203621i
$340$	−0.109916	+	0.481575i	−0.00596105	+	0.0261171i
$341$	−11.5410	−	14.4720i	−0.624981	−	0.783701i
$342$	−9.32036	−	4.48845i	−0.503987	−	0.242707i
$343$	8.73221	−	4.20521i	0.471495	−	0.227060i
$344$	4.85690	−	6.09035i	0.261866	−	0.328370i
$345$	−0.409698	−	0.513745i	−0.0220574	−	0.0276591i
$346$	17.0683	−	8.21966i	0.917597	−	0.441892i
$347$	−19.8538			−1.06581			−0.532905	−	0.846175i	$-0.678900\pi$
$347$	−19.8538			−1.06581			−0.532905	+	0.846175i	$0.678900\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	32.0296	−	15.4246i	1.71205	−	0.824482i
$351$	−8.34899	−	10.4693i	−0.445636	−	0.558810i
$352$	11.2307	−	14.0829i	0.598599	−	0.750620i
$353$	3.61745	−	1.74207i	0.192537	−	0.0927211i	−0.335131	−	0.942171i	$-0.608781\pi$
$353$	3.61745	−	1.74207i	0.192537	−	0.0927211i	0.527669	+	0.849450i	$0.323066\pi$
$354$	−6.58211	−	3.16977i	−0.349835	−	0.168472i
$355$	−2.53803	−	3.18259i	−0.134705	−	0.168914i
$356$	−0.394928	+	1.73029i	−0.0209311	+	0.0917053i
$357$	0.445042	−	1.94986i	0.0235541	−	0.103197i
$358$	6.44989	−	8.08790i	0.340887	−	0.427459i
$359$	0.166071	+	0.727604i	0.00876488	+	0.0384015i	0.979121	−	0.203277i	$-0.0651592\pi$
$359$	0.166071	+	0.727604i	0.00876488	+	0.0384015i	−0.970356	+	0.241679i	$0.922302\pi$
$360$	−1.35690			−0.0715147
$361$	3.29374	+	14.4308i	0.173355	+	0.759517i
$362$	−10.7811	−	5.19192i	−0.566643	−	0.272881i
$363$	1.01089	+	0.486817i	0.0530577	+	0.0255512i
$364$	5.82640	+	25.5271i	0.305386	+	1.33798i
$365$	−3.19375			−0.167169
$366$	−1.07942	−	4.72923i	−0.0564220	−	0.247201i
$367$	−21.2292	+	26.6205i	−1.10815	+	1.38958i	−0.195569	+	0.980690i	$0.562655\pi$
$367$	−21.2292	+	26.6205i	−1.10815	+	1.38958i	−0.912584	+	0.408890i	$0.865916\pi$
$368$	−4.54676	+	19.9207i	−0.237016	+	1.03844i
$369$	0.246980	−	1.08209i	0.0128572	−	0.0563313i
$370$	1.16756	+	1.46408i	0.0606987	+	0.0761138i
$371$	−15.8937	−	7.65402i	−0.825161	−	0.397377i
$372$	3.17845	−	1.53066i	0.164795	−	0.0793610i
$373$	17.4581	−	21.8917i	0.903945	−	1.13351i	−0.0865888	−	0.996244i	$-0.527597\pi$
$373$	17.4581	−	21.8917i	0.903945	−	1.13351i	0.990534	−	0.137267i	$-0.0438320\pi$
$374$	−3.63102	−	4.55316i	−0.187756	−	0.235438i
$375$	1.41281	−	0.680375i	0.0729574	−	0.0351344i
$376$	−10.5864			−0.545953
$377$		0			0
$378$	−18.8388			−0.968962
$379$	−20.6151	+	9.92769i	−1.05892	+	0.509951i	−0.880521	−	0.474006i	$-0.842807\pi$
$379$	−20.6151	+	9.92769i	−1.05892	+	0.509951i	−0.178403	+	0.983958i	$0.557093\pi$
$380$	0.568532	+	0.712916i	0.0291651	+	0.0365718i
$381$	2.90581	−	3.64377i	0.148869	−	0.186676i
$382$	−30.5405	+	14.7075i	−1.56259	+	0.752502i
$383$	−10.6838	−	5.14506i	−0.545918	−	0.262900i	0.140533	−	0.990076i	$-0.455118\pi$
$383$	−10.6838	−	5.14506i	−0.545918	−	0.262900i	−0.686451	+	0.727176i	$0.740833\pi$
$384$	−2.79859	−	3.50932i	−0.142815	−	0.179084i
$385$	0.936313	−	4.10225i	0.0477189	−	0.209070i
$386$	4.36443	−	19.1218i	0.222144	−	0.973275i
$387$	−10.0293	+	12.5763i	−0.509818	+	0.639292i
$388$	−4.37047	−	19.1483i	−0.221877	−	0.972107i
$389$	−10.3913			−0.526862			−0.263431	−	0.964678i	$-0.584854\pi$
$389$	−10.3913			−0.526862			−0.263431	+	0.964678i	$0.584854\pi$
$390$	0.330281	+	1.44706i	0.0167244	+	0.0732746i
$391$	4.13706	+	1.99230i	0.209220	+	0.100755i
$392$	−11.4840	−	5.53042i	−0.580031	−	0.279328i
$393$	0.0450325	+	0.197300i	0.00227159	+	0.00995248i
$394$	15.1371			0.762594
$395$	0.0471884	+	0.206746i	0.00237431	+	0.0104025i
$396$	−6.34332	+	7.95427i	−0.318764	+	0.399717i
$397$	−1.82855	+	8.01141i	−0.0917724	+	0.402081i	−0.999861	−	0.0166978i	$-0.994685\pi$
$397$	−1.82855	+	8.01141i	−0.0917724	+	0.402081i	0.908088	+	0.418779i	$0.137542\pi$
$398$	−2.65495	+	11.6321i	−0.133081	+	0.583064i
$399$	−2.30194	−	2.88654i	−0.115241	−	0.144508i
$400$	−21.6826	−	10.4418i	−1.08413	−	0.522090i
$401$	−22.4170	+	10.7955i	−1.11945	+	0.539099i	−0.899723	−	0.436462i	$-0.856231\pi$
$401$	−22.4170	+	10.7955i	−1.11945	+	0.539099i	−0.219728	+	0.975561i	$0.570517\pi$
$402$	−0.187177	+	0.234713i	−0.00933555	+	0.0117064i
$403$	−20.5544	−	25.7744i	−1.02389	−	1.28392i
$404$	19.5966	−	9.43724i	0.974969	−	0.469520i
$405$	2.58987			0.128692
$406$		0			0
$407$	−8.47889			−0.420283
$408$	−0.603875	+	0.290811i	−0.0298963	+	0.0143973i
$409$	11.7811	+	14.7731i	0.582539	+	0.730481i	0.982544	−	0.186032i	$-0.0595628\pi$
$409$	11.7811	+	14.7731i	0.582539	+	0.730481i	−0.400004	+	0.916513i	$0.630991\pi$
$410$	−0.158834	+	0.199171i	−0.00784423	+	0.00983636i
$411$	5.30894	−	2.55665i	0.261871	−	0.126110i
$412$	3.16152	+	1.52251i	0.155757	+	0.0750086i
$413$	22.9976	+	28.8381i	1.13164	+	1.41903i
$414$	4.64795	−	20.3640i	0.228434	−	1.00084i
$415$	0.749136	−	3.28218i	0.0367736	−	0.161116i
$416$	20.0018	−	25.0814i	0.980668	−	1.22972i
$417$	0.276947	+	1.21338i	0.0135621	+	0.0594196i
$418$	−10.7506			−0.525830
$419$	2.42380	+	10.6194i	0.118411	+	0.518791i	0.998992	+	0.0448952i	$0.0142954\pi$
$419$	2.42380	+	10.6194i	0.118411	+	0.518791i	−0.880581	+	0.473895i	$0.842847\pi$
$420$	0.722521	+	0.347948i	0.0352554	+	0.0169781i
$421$	17.9840	+	8.66065i	0.876488	+	0.422094i	0.817341	−	0.576155i	$-0.195447\pi$
$421$	17.9840	+	8.66065i	0.876488	+	0.422094i	0.0591476	+	0.998249i	$0.481162\pi$
$422$	−3.24794	−	14.2302i	−0.158107	−	0.692713i
$423$	21.8605			1.06290
$424$	1.31551	+	5.76363i	0.0638869	+	0.279907i
$425$	−3.37196	+	4.22831i	−0.163564	+	0.205103i
$426$	−2.03534	+	8.91742i	−0.0986127	+	0.432051i
$427$	−5.44989	+	23.8775i	−0.263738	+	1.15551i
$428$	−5.80008	−	7.27307i	−0.280357	−	0.351557i
$429$	−6.05496	−	2.91591i	−0.292336	−	0.140782i
$430$	3.32640	−	1.60191i	0.160413	−	0.0772509i
$431$	−18.8233	+	23.6037i	−0.906688	+	1.13695i	0.0834015	+	0.996516i	$0.473422\pi$
$431$	−18.8233	+	23.6037i	−0.906688	+	1.13695i	−0.990090	+	0.140435i	$0.955150\pi$
$432$	7.95138	+	9.97071i	0.382561	+	0.479716i
$433$	18.1918	−	8.76070i	0.874241	−	0.421012i	0.0577235	−	0.998333i	$-0.481616\pi$
$433$	18.1918	−	8.76070i	0.874241	−	0.421012i	0.816518	+	0.577320i	$0.195902\pi$
$434$	−46.3793			−2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	7.63706	−	3.67782i	0.365330	−	0.175934i
$438$	4.47434	+	5.61065i	0.213792	+	0.268087i
$439$	−6.64944	+	8.33813i	−0.317360	+	0.397957i	−0.914767	−	0.403981i	$-0.867626\pi$
$439$	−6.64944	+	8.33813i	−0.317360	+	0.397957i	0.597407	+	0.801938i	$0.296198\pi$
$440$	−1.27048	+	0.611830i	−0.0605677	+	0.0291679i
$441$	23.7141	+	11.4201i	1.12924	+	0.543814i
$442$	−6.46681	−	8.10913i	−0.307595	−	0.385712i
$443$	4.52834	−	19.8400i	0.215148	−	0.942625i	−0.745859	−	0.666103i	$-0.767961\pi$
$443$	4.52834	−	19.8400i	0.215148	−	0.942625i	0.961008	−	0.276522i	$-0.0891819\pi$
$444$	0.359584	−	1.57544i	0.0170651	−	0.0747672i
$445$	0.316708	−	0.397139i	0.0150134	−	0.0188262i
$446$	8.78890	+	38.5067i	0.416166	+	1.82334i
$447$	1.20536			0.0570115
$448$	−1.14310	−	5.00827i	−0.0540066	−	0.236618i
$449$	−17.4998	−	8.42744i	−0.825865	−	0.397716i	−0.0273022	−	0.999627i	$-0.508692\pi$
$449$	−17.4998	−	8.42744i	−0.825865	−	0.397716i	−0.798563	+	0.601912i	$0.794406\pi$
$450$	22.1652	+	10.6742i	1.04488	+	0.503186i
$451$	−0.256668	−	1.12454i	−0.0120860	−	0.0529524i
$452$	10.7748			0.506804
$453$	0.241176	+	1.05666i	0.0113314	+	0.0496462i
$454$	20.5356	−	25.7509i	0.963785	−	1.20855i
$455$	1.66756	−	7.30607i	0.0781765	−	0.342514i
$456$	−0.275323	+	1.20627i	−0.0128932	+	0.0564887i
$457$	−7.74429	−	9.71103i	−0.362263	−	0.454263i	0.566981	−	0.823731i	$-0.308111\pi$
$457$	−7.74429	−	9.71103i	−0.362263	−	0.454263i	−0.929243	+	0.369468i	$0.879540\pi$
$458$	26.0160	+	12.5287i	1.21565	+	0.585426i
$459$	2.58211	−	1.24348i	0.120522	−	0.0580405i
$460$	−1.14795	+	1.43948i	−0.0535234	+	0.0671162i
$461$	−13.6833	−	17.1583i	−0.637294	−	0.799142i	0.353367	−	0.935485i	$-0.385037\pi$
$461$	−13.6833	−	17.1583i	−0.637294	−	0.799142i	−0.990662	+	0.136343i	$0.956465\pi$
$462$	−8.51842	+	4.10225i	−0.396313	+	0.190854i
$463$	−33.0073			−1.53398			−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073			−1.53398			−0.766990	+	0.641660i	$0.778246\pi$
$464$		0			0
$465$	−1.00969			−0.0468232
$466$	3.17629	−	1.52962i	0.147139	−	0.0708584i
$467$	−16.2751	−	20.4083i	−0.753121	−	0.944384i	0.246573	−	0.969124i	$-0.420696\pi$
$467$	−16.2751	−	20.4083i	−0.753121	−	0.944384i	−0.999694	+	0.0247402i	$0.992124\pi$
$468$	−11.2974	+	14.1665i	−0.522222	+	0.654846i
$469$	1.36563	−	0.657650i	0.0630587	−	0.0303675i
$470$	−4.52057	−	2.17699i	−0.208519	−	0.100417i
$471$	4.90515	+	6.15086i	0.226017	+	0.283417i
$472$	2.75063	−	12.0513i	0.126608	−	0.554705i
$473$	−3.71983	+	16.2977i	−0.171038	+	0.749367i
$474$	0.297093	−	0.372543i	0.0136460	−	0.0171115i
$475$	2.22156	+	9.73330i	0.101932	+	0.446594i
$476$	−5.60388			−0.256853
$477$	−2.71648	−	11.9017i	−0.124379	−	0.544940i
$478$	−14.5516	−	7.00768i	−0.665575	−	0.320524i
$479$	−29.7913	−	14.3468i	−1.36120	−	0.655520i	−0.396297	−	0.918122i	$-0.629705\pi$
$479$	−29.7913	−	14.3468i	−1.36120	−	0.655520i	−0.964904	+	0.262602i	$0.915419\pi$
$480$	−0.218636	−	0.957907i	−0.00997933	−	0.0437223i
$481$	−15.1008			−0.688538
$482$	7.97919	+	34.9591i	0.363442	+	1.59234i
$483$	4.64795	−	5.82834i	0.211489	−	0.265199i
$484$	0.699554	−	3.06495i	0.0317979	−	0.139316i
$485$	−1.25086	+	5.48040i	−0.0567988	+	0.248852i
$486$	−12.3312	−	15.4629i	−0.559356	−	0.701411i
$487$	9.15064	+	4.40671i	0.414655	+	0.199687i	0.629567	−	0.776946i	$-0.283232\pi$
$487$	9.15064	+	4.40671i	0.414655	+	0.199687i	−0.214912	+	0.976633i	$0.568947\pi$
$488$	7.39493	−	3.56121i	0.334753	−	0.161208i
$489$	−1.37800	+	1.72796i	−0.0623154	+	0.0781411i
$490$	−3.76659	−	4.72316i	−0.170157	−	0.213371i
$491$	17.7327	−	8.53964i	0.800267	−	0.385388i	0.0113870	−	0.999935i	$-0.496375\pi$
$491$	17.7327	−	8.53964i	0.800267	−	0.385388i	0.788880	+	0.614547i	$0.210661\pi$
$492$	0.219833			0.00991082
$493$		0			0
$494$	−19.1468			−0.861453
$495$	2.62349	−	1.26341i	0.117917	−	0.0567859i
$496$	19.5755	+	24.5469i	0.878967	+	1.10219i
$497$	28.7935	−	36.1059i	1.29157	−	1.61957i
$498$	−6.81551	+	3.28218i	−0.305410	+	0.147078i
$499$	−25.0916	−	12.0835i	−1.12325	−	0.540930i	−0.222357	−	0.974965i	$-0.571375\pi$
$499$	−25.0916	−	12.0835i	−1.12325	−	0.540930i	−0.900896	+	0.434036i	$0.857089\pi$
$500$	−2.73945	−	3.43516i	−0.122512	−	0.153625i
$501$	−1.43243	+	6.27588i	−0.0639962	+	0.280385i
$502$	10.3470	−	45.3330i	0.461808	−	2.02331i
$503$	−0.140416	+	0.176076i	−0.00626083	+	0.00785083i	−0.784952	−	0.619557i	$-0.787312\pi$
$503$	−0.140416	+	0.176076i	−0.00626083	+	0.00785083i	0.778691	+	0.627407i	$0.215884\pi$
$504$	−3.42543	−	15.0078i	−0.152581	−	0.668500i
$505$	−6.22521			−0.277018
$506$	−4.83028	−	21.1628i	−0.214732	−	0.940803i
$507$	−5.57122	−	2.68296i	−0.247427	−	0.119154i
$508$	−11.7654	−	5.66592i	−0.522005	−	0.251384i
$509$	5.63049	+	24.6688i	0.249567	+	1.09342i	0.931995	+	0.362472i	$0.118067\pi$
$509$	5.63049	+	24.6688i	0.249567	+	1.09342i	−0.682428	+	0.730953i	$0.739076\pi$
$510$	−0.317667			−0.0140665
$511$	−8.06249	−	35.3241i	−0.356664	−	1.56265i
$512$	−10.6923	+	13.4077i	−0.472538	+	0.592544i
$513$	1.17725	−	5.15788i	0.0519769	−	0.227726i
$514$	4.79201	−	20.9952i	0.211367	−	0.926058i
$515$	−0.626178	−	0.785203i	−0.0275927	−	0.0346002i
$516$	−2.87047	−	1.38235i	−0.126365	−	0.0608544i
$517$	20.4683	−	9.85702i	0.900195	−	0.433511i
$518$	−13.2458	+	16.6097i	−0.581986	+	0.729788i
$519$	2.91723	+	3.65809i	0.128052	+	0.160572i
$520$	−2.26271	+	1.08966i	−0.0992264	+	0.0477849i
$521$	23.5797			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$522$		0			0
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	0.510885	−	0.246029i	0.0223181	−	0.0107478i
$525$	5.47434	+	6.86461i	0.238920	+	0.299596i
$526$	0.373822	−	0.468758i	0.0162994	−	0.0204388i
$527$	6.35690	−	3.06132i	0.276911	−	0.133353i
$528$	5.76659	+	2.77705i	0.250959	+	0.120855i
$529$	−3.66905	−	4.60085i	−0.159524	−	0.200037i
$530$	−0.623490	+	2.73169i	−0.0270827	+	0.118657i
$531$	−5.67994	+	24.8854i	−0.246488	+	1.07994i
$532$	−6.44989	+	8.08790i	−0.279638	+	0.350655i
$533$	−0.457123	−	2.00279i	−0.0198002	−	0.0867504i
$534$	−1.14138			−0.0493921
$535$	0.592458	+	2.59573i	0.0256142	+	0.112223i
$536$	−0.457656	−	0.220395i	−0.0197677	−	0.00951963i
$537$	2.30194	+	1.10855i	0.0993359	+	0.0478377i
$538$	−0.426624	−	1.86916i	−0.0183931	−	0.0805853i
$539$	27.3532			1.17818
$540$	0.255709	+	1.12033i	0.0110040	+	0.0482115i
$541$	−15.3753	+	19.2800i	−0.661036	+	0.828913i	−0.993456	−	0.114218i	$-0.963564\pi$
$541$	−15.3753	+	19.2800i	−0.661036	+	0.828913i	0.332419	+	0.943132i	$0.392135\pi$
$542$	−6.60172	+	28.9240i	−0.283568	+	1.24239i
$543$	0.657637	−	2.88130i	0.0282219	−	0.123648i
$544$	4.28083	+	5.36799i	0.183539	+	0.230151i
$545$	0.531459	+	0.255937i	0.0227652	+	0.0109631i
$546$	−15.1712	+	7.30607i	−0.649268	+	0.312671i
$547$	15.4882	−	19.4216i	0.662228	−	0.830408i	−0.331356	−	0.943506i	$-0.607506\pi$
$547$	15.4882	−	19.4216i	0.662228	−	0.830408i	0.993584	+	0.113098i	$0.0360774\pi$
$548$	−10.2940	−	12.9083i	−0.439739	−	0.551416i
$549$	−15.2702	+	7.35376i	−0.651718	+	0.313851i
$550$	25.5666			1.09016
$551$		0			0
$552$	−2.49827			−0.106333
$553$	−2.16756	+	1.04384i	−0.0921741	+	0.0443887i
$554$	−7.40850	−	9.28997i	−0.314757	−	0.394693i
$555$	−0.288364	+	0.361597i	−0.0122404	+	0.0153489i
$556$	3.14191	−	1.51306i	0.133247	−	0.0641682i
$557$	−6.99612	−	3.36915i	−0.296435	−	0.142756i	0.279755	−	0.960071i	$-0.409747\pi$
$557$	−6.99612	−	3.36915i	−0.296435	−	0.142756i	−0.576190	+	0.817316i	$0.695461\pi$
$558$	−20.0112	−	25.0932i	−0.847141	−	1.06228i
$559$	−6.62498	+	29.0259i	−0.280207	+	1.22767i
$560$	−1.58815	+	6.95812i	−0.0671114	+	0.294034i
$561$	0.896789	−	1.12454i	0.0378624	−	0.0474780i
$562$	−12.2436	−	53.6428i	−0.516466	−	2.26279i
$563$	20.8009			0.876652			0.438326	−	0.898816i	$-0.355571\pi$
$563$	20.8009			0.876652			0.438326	+	0.898816i	$0.355571\pi$
$564$	0.963460	+	4.22119i	0.0405690	+	0.177744i
$565$	−2.77844	−	1.33803i	−0.116890	−	0.0562912i
$566$	−5.77144	−	2.77938i	−0.242592	−	0.116826i
$567$	6.53803	+	28.6450i	0.274572	+	1.20298i
$568$	−15.4765			−0.649380
$569$	−0.625113	−	2.73880i	−0.0262061	−	0.114816i	0.960133	−	0.279543i	$-0.0901830\pi$
$569$	−0.625113	−	2.73880i	−0.0262061	−	0.114816i	−0.986339	+	0.164727i	$0.947326\pi$
$570$	−0.365625	+	0.458479i	−0.0153143	+	0.0192036i
$571$	−0.643637	+	2.81996i	−0.0269354	+	0.118011i	−0.986608	−	0.163107i	$-0.947848\pi$
$571$	−0.643637	+	2.81996i	−0.0269354	+	0.118011i	0.959673	+	0.281119i	$0.0907055\pi$
$572$	−4.19016	+	18.3583i	−0.175199	+	0.767599i
$573$	−5.21983	−	6.54546i	−0.218062	−	0.273441i
$574$	−2.60388	−	1.25396i	−0.108684	−	0.0523393i
$575$	−18.1621	+	8.74638i	−0.757410	+	0.364749i
$576$	2.21648	−	2.77938i	0.0923533	−	0.115807i
$577$	4.48225	+	5.62056i	0.186598	+	0.233987i	0.866328	−	0.499476i	$-0.166474\pi$
$577$	4.48225	+	5.62056i	0.186598	+	0.233987i	−0.679729	+	0.733463i	$0.737903\pi$
$578$	−25.5993	+	12.3280i	−1.06479	+	0.512777i
$579$	4.84415			0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	11.3802	−	5.48040i	0.471723	−	0.227170i
$583$	−7.90999	−	9.91882i	−0.327598	−	0.410795i
$584$	−7.57069	+	9.49334i	−0.313277	+	0.392837i
$585$	4.67241	−	2.25011i	0.193180	−	0.0930307i
$586$	53.3802	+	25.7066i	2.20512	+	1.06193i
$587$	−19.3512	−	24.2656i	−0.798707	−	1.00155i	−0.999759	−	0.0219668i	$-0.993007\pi$
$587$	−19.3512	−	24.2656i	−0.798707	−	1.00155i	0.201051	−	0.979581i	$-0.435564\pi$
$588$	−1.16003	+	5.08242i	−0.0478388	+	0.209596i
$589$	2.89828	−	12.6982i	0.119422	−	0.523220i
$590$	3.65279	−	4.58046i	0.150383	−	0.188574i
$591$	0.831905	+	3.64481i	0.0342200	+	0.149928i
$592$	14.3817			0.591082
$593$	−8.11476	−	35.5531i	−0.333233	−	1.45999i	−0.812830	−	0.582501i	$-0.802074\pi$
$593$	−8.11476	−	35.5531i	−0.333233	−	1.45999i	0.479597	−	0.877489i	$-0.340783\pi$
$594$	−12.2066	−	5.87837i	−0.500841	−	0.241192i
$595$	1.44504	+	0.695895i	0.0592409	+	0.0285289i
$596$	−0.751528	−	3.29266i	−0.0307838	−	0.134873i
$597$	−2.94677			−0.120603
$598$	−8.60268	−	37.6908i	−0.351790	−	1.54129i
$599$	18.7473	−	23.5083i	0.765993	−	0.960525i	−0.233938	−	0.972251i	$-0.575161\pi$
$599$	18.7473	−	23.5083i	0.765993	−	0.960525i	0.999931	+	0.0117267i	$0.00373282\pi$
$600$	0.654759	−	2.86869i	0.0267304	−	0.117114i
$601$	7.38458	−	32.3539i	0.301223	−	1.31974i	−0.567060	−	0.823676i	$-0.691919\pi$
$601$	7.38458	−	32.3539i	0.301223	−	1.31974i	0.868283	−	0.496068i	$-0.165223\pi$
$602$	26.1151	+	32.7472i	1.06437	+	1.33468i
$603$	0.945042	+	0.455108i	0.0384851	+	0.0185334i
$604$	2.73609	−	1.31763i	0.111330	−	0.0536138i
$605$	−0.560999	+	0.703470i	−0.0228078	+	0.0286001i
$606$	8.72132	+	10.9362i	0.354280	+	0.444253i
$607$	13.6228	−	6.56041i	0.552933	−	0.266279i	−0.136485	−	0.990642i	$-0.543581\pi$
$607$	13.6228	−	6.56041i	0.552933	−	0.266279i	0.689418	+	0.724363i	$0.257866\pi$
$608$	12.6746			0.514021
$609$		0			0
$610$	3.89008			0.157505
$611$	36.4538	−	17.5552i	1.47476	−	0.710209i
$612$	−2.41789	−	3.03194i	−0.0977376	−	0.122559i
$613$	2.34146	−	2.93610i	0.0945708	−	0.118588i	−0.732294	−	0.680988i	$-0.761551\pi$
$613$	2.34146	−	2.93610i	0.0945708	−	0.118588i	0.826865	+	0.562400i	$0.190122\pi$
$614$	23.8170	−	11.4697i	0.961176	−	0.462878i
$615$	−0.0566871	−	0.0272990i	−0.00228584	−	0.00110080i
$616$	−9.97434	−	12.5074i	−0.401878	−	0.503939i
$617$	−6.64364	+	29.1077i	−0.267463	+	1.17183i	0.645491	+	0.763768i	$0.276653\pi$
$617$	−6.64364	+	29.1077i	−0.267463	+	1.17183i	−0.912954	+	0.408063i	$0.866204\pi$
$618$	−0.502156	+	2.20009i	−0.0201997	+	0.0885006i
$619$	−28.7540	+	36.0564i	−1.15572	+	1.44923i	−0.284269	+	0.958745i	$0.591751\pi$
$619$	−28.7540	+	36.0564i	−1.15572	+	1.44923i	−0.871451	+	0.490483i	$0.836821\pi$
$620$	0.629531	+	2.75815i	0.0252826	+	0.110770i
$621$	10.6823			0.428667
$622$	7.42854	+	32.5466i	0.297857	+	1.30500i
$623$	5.19202	+	2.50035i	0.208014	+	0.100174i
$624$	10.2702	+	4.94589i	0.411139	+	0.197994i
$625$	−5.14148	−	22.5263i	−0.205659	−	0.901052i
$626$	−41.4306			−1.65590
$627$	−0.590834	−	2.58861i	−0.0235957	−	0.103379i
$628$	13.7439	−	17.2343i	0.548442	−	0.687725i
$629$	0.719169	−	3.15088i	0.0286751	−	0.125634i
$630$	1.62349	−	7.11297i	0.0646814	−	0.283388i
$631$	7.87465	+	9.87450i	0.313485	+	0.393098i	0.913465	−	0.406917i	$-0.133396\pi$
$631$	7.87465	+	9.87450i	0.313485	+	0.393098i	−0.599980	+	0.800015i	$0.704825\pi$
$632$	0.726406	+	0.349819i	0.0288949	+	0.0139150i
$633$	3.24794	−	1.56413i	0.129094	−	0.0621684i
$634$	−15.7947	+	19.8059i	−0.627288	+	0.786594i
$635$	2.33028	+	2.92208i	0.0924744	+	0.115959i
$636$	2.17845	−	1.04909i	0.0863811	−	0.0415989i
$637$	48.7157			1.93019
$638$		0			0
$639$	31.9584			1.26425
$640$	3.24309	−	1.56179i	0.128195	−	0.0617353i
$641$	24.3173	+	30.4929i	0.960476	+	1.20440i	0.978853	+	0.204567i	$0.0655787\pi$
$641$	24.3173	+	30.4929i	0.960476	+	1.20440i	−0.0183770	+	0.999831i	$0.505850\pi$
$642$	3.73005	−	4.67734i	0.147213	−	0.184600i
$643$	−37.2068	+	17.9179i	−1.46729	+	0.706612i	−0.985501	−	0.169672i	$-0.945729\pi$
$643$	−37.2068	+	17.9179i	−1.46729	+	0.706612i	−0.481794	+	0.876284i	$0.660015\pi$
$644$	−18.8192	−	9.06283i	−0.741579	−	0.357126i
$645$	0.568532	+	0.712916i	0.0223859	+	0.0280710i
$646$	0.911854	−	3.99509i	0.0358764	−	0.157185i
$647$	3.98547	−	17.4615i	0.156685	−	0.686481i	−0.834165	−	0.551515i	$-0.814050\pi$
$647$	3.98547	−	17.4615i	0.156685	−	0.686481i	0.990850	−	0.134967i	$-0.0430928\pi$
$648$	6.13922	−	7.69834i	0.241171	−	0.302419i
$649$	5.90276	+	25.8617i	0.231703	+	1.01516i
$650$	45.5338			1.78598
$651$	−2.54892	−	11.1675i	−0.0998999	−	0.437690i
$652$	5.57942	+	2.68691i	0.218507	+	0.105227i
$653$	12.0015	+	5.77961i	0.469655	+	0.226174i	0.653714	−	0.756741i	$-0.273210\pi$
$653$	12.0015	+	5.77961i	0.469655	+	0.226174i	−0.184060	+	0.982915i	$0.558924\pi$
$654$	−0.294937	−	1.29221i	−0.0115330	−	0.0505292i
$655$	−0.162291			−0.00634125
$656$	0.435353	+	1.90741i	0.0169977	+	0.0744717i
$657$	15.6332	−	19.6034i	0.609908	−	0.764801i
$658$	12.6664	−	55.4950i	0.493786	−	2.16342i
$659$	−4.17576	+	18.2952i	−0.162664	+	0.712680i	0.826140	+	0.563465i	$0.190532\pi$
$659$	−4.17576	+	18.2952i	−0.162664	+	0.712680i	−0.988805	+	0.149215i	$0.952325\pi$
$660$	0.359584	+	0.450904i	0.0139968	+	0.0175514i
$661$	22.2799	+	10.7294i	0.866589	+	0.417327i	0.813708	−	0.581274i	$-0.197445\pi$
$661$	22.2799	+	10.7294i	0.866589	+	0.417327i	0.0528807	+	0.998601i	$0.483160\pi$
$662$	22.6582	−	10.9116i	0.880635	−	0.424091i
$663$	1.59717	−	2.00279i	0.0620290	−	0.0777819i
$664$	−7.98039	−	10.0071i	−0.309699	−	0.388350i
$665$	2.66756	−	1.28463i	0.103444	−	0.0498158i
$666$	−14.7017			−0.569680
$667$		0			0
$668$	18.0368			0.697866
$669$	−8.78890	+	4.23251i	−0.339798	+	0.163638i
$670$	−0.150104	−	0.188225i	−0.00579904	−	0.00727177i
$671$	−10.9819	+	13.7708i	−0.423951	+	0.531617i
$672$	10.0429	−	4.83639i	0.387412	−	0.186568i
$673$	−22.9230	−	11.0392i	−0.883618	−	0.425528i	−0.0636734	−	0.997971i	$-0.520282\pi$
$673$	−22.9230	−	11.0392i	−0.883618	−	0.425528i	−0.819945	+	0.572443i	$0.805996\pi$
$674$	15.7262	+	19.7200i	0.605749	+	0.759586i
$675$	−2.79968	+	12.2662i	−0.107760	+	0.472126i
$676$	−3.85540	+	16.8916i	−0.148285	+	0.649678i
$677$	0.384411	−	0.482037i	0.0147741	−	0.0185262i	−0.774390	−	0.632709i	$-0.781943\pi$
$677$	0.384411	−	0.482037i	0.0147741	−	0.0185262i	0.789164	+	0.614183i	$0.210514\pi$
$678$	1.54192	+	6.75558i	0.0592170	+	0.259446i
$679$	−63.7730			−2.44738
$680$	−0.119605	−	0.524023i	−0.00458664	−	0.0200954i
$681$	7.32908	+	3.52950i	0.280851	+	0.135251i
$682$	−30.0514	−	14.4720i	−1.15073	−	0.554161i
$683$	−4.01022	−	17.5699i	−0.153447	−	0.672295i	−0.991868	−	0.127272i	$-0.959378\pi$
$683$	−4.01022	−	17.5699i	−0.153447	−	0.672295i	0.838421	−	0.545023i	$-0.183479\pi$
$684$	−7.15883			−0.273725
$685$	1.05150	+	4.60692i	0.0401758	+	0.176022i
$686$	10.8889	−	13.6542i	0.415740	−	0.521321i
$687$	−1.58695	+	6.95288i	−0.0605459	+	0.265269i
$688$	6.30947	−	27.6436i	0.240546	−	1.05390i
$689$	−14.0876	−	17.6653i	−0.536695	−	0.672995i
$690$	−1.06680	−	0.513745i	−0.0406125	−	0.0195579i
$691$	−11.1235	+	5.35679i	−0.423157	+	0.203782i	−0.633329	−	0.773883i	$-0.718312\pi$
$691$	−11.1235	+	5.35679i	−0.423157	+	0.203782i	0.210172	+	0.977665i	$0.432598\pi$
$692$	8.17390	−	10.2497i	0.310725	−	0.389637i
$693$	20.5966	+	25.8274i	0.782402	+	0.981101i
$694$	−32.2325	+	15.5224i	−1.22353	+	0.589221i
$695$	−0.998081			−0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$	−43.7047	+	21.0471i	−1.65425	+	0.796643i
$699$	0.542877	+	0.680746i	0.0205335	+	0.0257482i
$700$	15.3388	−	19.2342i	0.579751	−	0.726985i
$701$	30.7207	−	14.7943i	1.16030	−	0.558773i	0.248190	−	0.968711i	$-0.420164\pi$
$701$	30.7207	−	14.7943i	1.16030	−	0.558773i	0.912113	+	0.409939i	$0.134450\pi$
$702$	−21.7397	−	10.4693i	−0.820514	−	0.395139i
$703$	−3.71983	−	4.66452i	−0.140296	−	0.175926i
$704$	0.822085	−	3.60179i	0.0309835	−	0.135747i
$705$	0.275750	−	1.20814i	0.0103854	−	0.0455012i
$706$	4.51089	−	5.65647i	0.169769	−	0.212884i
$707$	−15.7153	−	68.8532i	−0.591034	−	2.58949i
$708$	−5.05562			−0.190002
$709$	−9.36712	−	41.0400i	−0.351789	−	1.54129i	−0.773047	−	0.634349i	$-0.781268\pi$
$709$	−9.36712	−	41.0400i	−0.351789	−	1.54129i	0.421257	−	0.906941i	$-0.361589\pi$
$710$	−6.60872	−	3.18259i	−0.248021	−	0.119441i
$711$	−1.50000	−	0.722362i	−0.0562544	−	0.0270907i
$712$	−0.429739	−	1.88281i	−0.0161052	−	0.0705613i
$713$	26.2989			0.984901
$714$	−0.801938	−	3.51352i	−0.0300118	−	0.131490i
$715$	3.36025	−	4.21362i	0.125666	−	0.157580i
$716$	1.59299	−	6.97935i	0.0595328	−	0.260830i
$717$	0.887632	−	3.88897i	0.0331492	−	0.145236i
$718$	0.838478	+	1.05142i	0.0312917	+	0.0392386i
$719$	47.0795	+	22.6723i	1.75577	+	0.845533i	0.975472	+	0.220123i	$0.0706459\pi$
$719$	47.0795	+	22.6723i	1.75577	+	0.845533i	0.780296	+	0.625410i	$0.215068\pi$
$720$	−4.44989	+	2.14295i	−0.165837	+	0.0798631i
$721$	7.10388	−	8.90798i	0.264562	−	0.331750i
$722$	16.6298	+	20.8531i	0.618898	+	0.776074i
$723$	−7.97919	+	3.84258i	−0.296749	+	0.142907i
$724$	−8.28083			−0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	−27.0155	+	13.0100i	−1.00195	+	0.482513i	−0.861599	−	0.507589i	$-0.830537\pi$
$727$	−27.0155	+	13.0100i	−1.00195	+	0.482513i	−0.140350	+	0.990102i	$0.544823\pi$
$728$	−17.7642	−	22.2756i	−0.658385	−	0.825589i
$729$	−10.5278	+	13.2015i	−0.389919	+	0.488943i
$730$	−5.18502	+	2.49697i	−0.191906	+	0.0924172i
$731$	−5.74094	−	2.76469i	−0.212336	−	0.102256i
$732$	−2.09299	−	2.62453i	−0.0773591	−	0.0970053i
$733$	−0.670784	+	2.93890i	−0.0247760	+	0.108551i	−0.985804	−	0.167901i	$-0.946301\pi$
$733$	−0.670784	+	2.93890i	−0.0247760	+	0.108551i	0.961028	+	0.276451i	$0.0891584\pi$
$734$	−13.6526	+	59.8158i	−0.503925	+	2.20784i
$735$	0.930272	−	1.16652i	0.0343136	−	0.0430279i
$736$	5.69471	+	24.9502i	0.209910	+	0.919675i
$737$	1.09006			0.0401531
$738$	−0.445042	−	1.94986i	−0.0163822	−	0.0717752i
$739$	18.7739	+	9.04103i	0.690609	+	0.332580i	0.746057	−	0.665882i	$-0.231945\pi$
$739$	18.7739	+	9.04103i	0.690609	+	0.332580i	−0.0554484	+	0.998462i	$0.517659\pi$
$740$	1.16756	+	0.562269i	0.0429205	+	0.0206694i
$741$	−1.05227	−	4.61029i	−0.0386561	−	0.169363i
$742$	−31.7875			−1.16695
$743$	6.84601	+	29.9943i	0.251156	+	1.10039i	0.930421	+	0.366492i	$0.119441\pi$
$743$	6.84601	+	29.9943i	0.251156	+	1.10039i	−0.679265	+	0.733893i	$0.737701\pi$
$744$	−2.39344	+	3.00127i	−0.0877476	+	0.110032i
$745$	−0.215094	+	0.942387i	−0.00788042	+	0.0345264i
$746$	11.2274	−	49.1903i	0.411063	−	1.80098i
$747$	16.4792	+	20.6642i	0.602942	+	0.756065i
$748$	−3.63102	−	1.74861i	−0.132763	−	0.0639355i
$749$	−27.2141	+	13.1056i	−0.994381	+	0.478869i
$750$	1.76175	−	2.20916i	0.0643300	−	0.0806673i
$751$	−2.78650	−	3.49417i	−0.101681	−	0.127504i	0.728387	−	0.685165i	$-0.240270\pi$
$751$	−2.78650	−	3.49417i	−0.101681	−	0.127504i	−0.830068	+	0.557662i	$0.811699\pi$
$752$	−34.7177	+	16.7192i	−1.26603	+	0.609686i
$753$	11.4843			0.418510
$754$		0			0
$755$	−0.869167			−0.0316322
$756$	−11.7458	+	5.65647i	−0.427190	+	0.205724i
$757$	−5.27210	−	6.61101i	−0.191618	−	0.240281i	0.676737	−	0.736225i	$-0.263394\pi$
$757$	−5.27210	−	6.61101i	−0.191618	−	0.240281i	−0.868355	+	0.495944i	$0.834822\pi$
$758$	−25.7066	+	32.2350i	−0.933704	+	1.17083i
$759$	4.83028	−	2.32614i	0.175328	−	0.0844336i
$760$	−0.893969	−	0.430513i	−0.0324276	−	0.0156163i
$761$	15.3971	+	19.3073i	0.558144	+	0.699890i	0.978213	−	0.207602i	$-0.0665658\pi$
$761$	15.3971	+	19.3073i	0.558144	+	0.699890i	−0.420070	+	0.907492i	$0.637994\pi$
$762$	1.86874	−	8.18749i	0.0676973	−	0.296601i
$763$	−1.48911	+	6.52424i	−0.0539096	+	0.236193i
$764$	−14.6256	+	18.3400i	−0.529137	+	0.663517i
$765$	0.246980	+	1.08209i	0.00892957	+	0.0391230i
$766$	−21.3676			−0.772045
$767$	10.5127	+	46.0593i	0.379593	+	1.66311i
$768$	−8.30463	−	3.99930i	−0.299667	−	0.144312i
$769$	−27.1579	−	13.0786i	−0.979340	−	0.471625i	−0.125462	−	0.992098i	$-0.540041\pi$
$769$	−27.1579	−	13.0786i	−0.979340	−	0.471625i	−0.853878	+	0.520473i	$0.825756\pi$
$770$	−1.68718	−	7.39201i	−0.0608016	−	0.266389i
$771$	5.31873			0.191549
$772$	−3.02028	−	13.2327i	−0.108702	−	0.476255i
$773$	3.53952	−	4.43842i	0.127308	−	0.159639i	−0.714092	−	0.700051i	$-0.753160\pi$
$773$	3.53952	−	4.43842i	0.127308	−	0.159639i	0.841400	+	0.540412i	$0.181732\pi$
$774$	−6.44989	+	28.2588i	−0.231836	+	1.01574i
$775$	−6.89254	+	30.1982i	−0.247587	+	1.08475i
$776$	13.3252	+	16.7093i	0.478347	+	0.599828i
$777$	−4.72737	−	2.27658i	−0.169593	−	0.0816718i
$778$	−16.8702	+	8.12428i	−0.604827	+	0.291269i
$779$	0.506041	−	0.634555i	0.0181308	−	0.0227353i
$780$	0.640416	+	0.803056i	0.0229306	+	0.0287540i
$781$	29.9230	−	14.4102i	1.07073	−	0.515637i
$782$	8.27413			0.295882
$783$		0			0
$784$	−46.3957			−1.65699
$785$	−5.68425	+	2.73739i	−0.202880	+	0.0977017i
$786$	0.227365	+	0.285107i	0.00810985	+	0.0101694i
$787$	−2.25033	+	2.82183i	−0.0802157	+	0.100587i	−0.820320	−	0.571905i	$-0.806205\pi$
$787$	−2.25033	+	2.82183i	−0.0802157	+	0.100587i	0.740104	+	0.672492i	$0.234776\pi$
$788$	9.43780	−	4.54501i	0.336208	−	0.161909i
$789$	0.133415	+	0.0642495i	0.00474972	+	0.00228734i
$790$	0.238250	+	0.298757i	0.00847657	+	0.0106293i
$791$	7.78501	−	34.1084i	0.276803	−	1.21275i
$792$	2.46346	−	10.7931i	0.0875352	−	0.383517i
$793$	−19.5586	+	24.5257i	−0.694546	+	0.870934i
$794$	3.29494	+	14.4361i	0.116933	+	0.512317i
$795$	−0.692021			−0.0245435
$796$	1.83728	+	8.04966i	0.0651207	+	0.285313i
$797$	27.7347	+	13.3563i	0.982412	+	0.473105i	0.854934	−	0.518737i	$-0.173597\pi$
$797$	27.7347	+	13.3563i	0.982412	+	0.473105i	0.127478	+	0.991841i	$0.459312\pi$
$798$	−5.99396	−	2.88654i	−0.212184	−	0.102182i
$799$	1.92692	+	8.44239i	0.0681695	+	0.298670i
$800$	−30.1420			−1.06568
$801$	0.887395	+	3.88793i	0.0313546	+	0.137373i
$802$	−27.9535	+	35.0526i	−0.987074	+	1.23775i
$803$	5.79829	−	25.4040i	0.204617	−	0.896487i
$804$	−0.0462289	+	0.202542i	−0.00163037	+	0.00714311i
$805$	3.72737	+	4.67397i	0.131372	+	0.164736i
$806$	−53.5212	−	25.7744i	−1.88520	−	0.907866i
$807$	0.426624	−	0.205451i	0.0150179	−	0.00723223i
$808$	−14.7567	+	18.5043i	−0.519138	+	0.650978i
$809$	3.26540	+	4.09468i	0.114805	+	0.143961i	0.835914	−	0.548861i	$-0.184938\pi$
$809$	3.26540	+	4.09468i	0.114805	+	0.143961i	−0.721108	+	0.692822i	$0.756367\pi$
$810$	4.20464	−	2.02485i	0.147736	−	0.0711458i
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$		0			0
$813$	−7.32736			−0.256982
$814$	−13.7654	+	6.62907i	−0.482477	+	0.232349i
$815$	−1.10507	−	1.38572i	−0.0387090	−	0.0485395i
$816$	−1.52111	+	1.90741i	−0.0532494	+	0.0667726i
$817$	−10.5978	+	5.10365i	−0.370771	+	0.178554i
$818$	30.6766	+	14.7731i	1.07258	+	0.516528i
$819$	36.6824	+	45.9983i	1.28179	+	1.60731i
$820$	−0.0392287	+	0.171872i	−0.00136992	+	0.00600203i
$821$	−3.42812	+	15.0196i	−0.119642	+	0.524186i	0.879217	+	0.476422i	$0.158067\pi$
$821$	−3.42812	+	15.0196i	−0.119642	+	0.524186i	−0.998859	+	0.0477639i	$0.984791\pi$
$822$	6.62014	−	8.30139i	0.230904	−	0.289544i
$823$	7.93416	+	34.7618i	0.276567	+	1.21172i	0.902102	+	0.431524i	$0.142024\pi$
$823$	7.93416	+	34.7618i	0.276567	+	1.21172i	−0.625534	+	0.780197i	$0.715119\pi$
$824$	−3.81833			−0.133018
$825$	1.40509	+	6.15610i	0.0489190	+	0.214328i
$826$	59.8829	+	28.8381i	2.08359	+	1.00341i
$827$	46.8989	+	22.5853i	1.63083	+	0.785368i	0.999955	+	0.00948645i	$0.00301967\pi$
$827$	46.8989	+	22.5853i	1.63083	+	0.785368i	0.630879	+	0.775882i	$0.282695\pi$
$828$	−3.21648	−	14.0923i	−0.111780	−	0.489742i
$829$	−13.4168			−0.465986			−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168			−0.465986			−0.232993	+	0.972478i	$0.574852\pi$
$830$	−1.34990	−	5.91428i	−0.0468556	−	0.205288i
$831$	1.82975	−	2.29443i	0.0634733	−	0.0795930i
$832$	1.46412	−	6.41475i	0.0507594	−	0.222391i
$833$	−2.32006	+	10.1648i	−0.0803853	+	0.352191i
$834$	1.39828	+	1.75339i	0.0484185	+	0.0607149i
$835$	−4.65106	−	2.23983i	−0.160957	−	0.0775127i
$836$	−6.70291	+	3.22795i	−0.231825	+	0.111641i
$837$	10.2341	−	12.8331i	0.353741	−	0.443577i
$838$	12.2376	+	15.3454i	0.422740	+	0.530100i
$839$	27.9763	−	13.4727i	0.965848	−	0.465128i	0.116633	−	0.993175i	$-0.462790\pi$
$839$	27.9763	−	13.4727i	0.965848	−	0.465128i	0.849215	+	0.528047i	$0.177076\pi$
$840$	−0.872625			−0.0301084
$841$		0			0
$842$	35.9681			1.23954
$843$	12.2436	−	5.89622i	0.421693	−	0.203077i
$844$	−6.29776	−	7.89714i	−0.216778	−	0.271831i
$845$	3.09179	−	3.87699i	0.106361	−	0.133372i
$846$	35.4904	−	17.0913i	1.22018	−	0.587610i
$847$	−9.19687	−	4.42898i	−0.316008	−	0.152181i
$848$	13.4167	+	16.8240i	0.460731	+	0.577739i
$849$	0.352052	−	1.54244i	0.0120824	−	0.0529364i
$850$	−2.16852	+	9.50092i	−0.0743797	+	0.325879i
$851$	7.51089	−	9.41835i	0.257470	−	0.322857i
$852$	1.40850	+	6.17105i	0.0482545	+	0.211417i
$853$	21.3357			0.730521			0.365261	−	0.930905i	$-0.380980\pi$
$853$	21.3357			0.730521			0.365261	+	0.930905i	$0.380980\pi$
$854$	9.82036	+	43.0258i	0.336046	+	1.47231i
$855$	1.84601	+	0.888992i	0.0631322	+	0.0304029i
$856$	9.12014	+	4.39203i	0.311720	+	0.150116i
$857$	2.18784	+	9.58556i	0.0747352	+	0.327436i	0.998451	−	0.0556427i	$-0.0177208\pi$
$857$	2.18784	+	9.58556i	0.0747352	+	0.327436i	−0.923716	+	0.383079i	$0.874864\pi$
$858$	−12.1099			−0.413426
$859$	11.5230	+	50.4854i	0.393159	+	1.72254i	0.653414	+	0.757000i	$0.273336\pi$
$859$	11.5230	+	50.4854i	0.393159	+	1.72254i	−0.260256	+	0.965540i	$0.583807\pi$
$860$	1.59299	−	1.99755i	0.0543205	−	0.0681158i
$861$	0.158834	−	0.695895i	0.00541303	−	0.0237161i
$862$	−12.1054	+	53.0371i	−0.412310	+	1.80645i
$863$	−10.1471	−	12.7241i	−0.345412	−	0.433133i	0.578533	−	0.815659i	$-0.303626\pi$
$863$	−10.1471	−	12.7241i	−0.345412	−	0.433133i	−0.923945	+	0.382526i	$0.875054\pi$
$864$	14.3910	+	6.93036i	0.489593	+	0.235776i
$865$	−3.38059	+	1.62800i	−0.114943	+	0.0553538i
$866$	22.6848	−	28.4458i	0.770860	−	0.966628i
$867$	−4.37531	−	5.48647i	−0.148593	−	0.186330i
$868$	−28.9170	+	13.9257i	−0.981507	+	0.472669i
$869$	−1.73019			−0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	2.02057	−	0.973057i	0.0684253	−	0.0329519i
$873$	−27.5160	−	34.5040i	−0.931276	−	1.16778i
$874$	9.52326	−	11.9418i	0.322129	−	0.403937i
$875$	−12.8535	+	6.18994i	−0.434529	+	0.209258i
$876$	4.47434	+	2.15473i	0.151174	+	0.0728016i
$877$	9.23155	+	11.5760i	0.311727	+	0.390893i	0.912872	−	0.408247i	$-0.133860\pi$
$877$	9.23155	+	11.5760i	0.311727	+	0.390893i	−0.601144	+	0.799140i	$0.705288\pi$
$878$	−4.27628	+	18.7356i	−0.144318	+	0.632296i
$879$	−3.25614	+	14.2661i	−0.109827	+	0.481182i
$880$	−3.20022	+	4.01295i	−0.107879	+	0.135276i
$881$	4.14728	+	18.1704i	0.139726	+	0.612178i	0.995494	+	0.0948195i	$0.0302274\pi$
$881$	4.14728	+	18.1704i	0.139726	+	0.612178i	−0.855769	+	0.517358i	$0.826915\pi$
$882$	47.4282			1.59699
$883$	7.20828	+	31.5816i	0.242578	+	1.06280i	0.938661	+	0.344842i	$0.112068\pi$
$883$	7.20828	+	31.5816i	0.242578	+	1.06280i	−0.696083	+	0.717962i	$0.745075\pi$
$884$	−6.46681	−	3.11425i	−0.217502	−	0.104744i
$885$	1.30367	+	0.627813i	0.0438223	+	0.0211037i
$886$	−8.15979	−	35.7504i	−0.274134	−	1.20106i
$887$	−6.16288			−0.206929			−0.103465	−	0.994633i	$-0.532993\pi$
$887$	−6.16288			−0.206929			−0.103465	+	0.994633i	$0.532993\pi$
$888$	0.391280	+	1.71431i	0.0131305	+	0.0575285i
$889$	−26.4366	+	33.1505i	−0.886655	+	1.11183i
$890$	0.203676	−	0.892363i	0.00682724	−	0.0299121i
$891$	−4.70195	+	20.6006i	−0.157521	+	0.690145i
$892$	17.0417	+	21.3696i	0.570598	+	0.715507i
$893$	14.4025	+	6.93586i	0.481960	+	0.232100i
$894$	1.95689	−	0.942387i	0.0654481	−	0.0315181i
$895$	−1.27748	+	1.60191i	−0.0427014	+	0.0535459i
$896$	25.4611	+	31.9272i	0.850595	+	1.06661i
$897$	8.60268	−	4.14283i	0.287235	−	0.138325i
$898$	−34.9995			−1.16795
$899$		0			0
$900$	17.0248			0.567492
$901$	4.35690	−	2.09817i	0.145149	−	0.0699002i
$902$	−1.29590	−	1.62500i	−0.0431486	−	0.0541067i
$903$	−6.44989	+	8.08790i	−0.214639	+	0.269149i
$904$	−10.5635	+	5.08709i	−0.351335	+	0.169194i
$905$	2.13533	+	1.02832i	0.0709809	+	0.0341826i
$906$	1.21768	+	1.52692i	0.0404546	+	0.0507285i
$907$	−9.78740	+	42.8814i	−0.324985	+	1.42385i	0.503573	+	0.863952i	$0.332018\pi$
$907$	−9.78740	+	42.8814i	−0.324985	+	1.42385i	−0.828559	+	0.559902i	$0.810839\pi$
$908$	5.07188	−	22.2214i	0.168316	−	0.737442i
$909$	30.4720	−	38.2106i	1.01069	−	1.26737i
$910$	−3.00484	−	13.1651i	−0.0996096	−	0.436418i
$911$	−25.6233			−0.848936			−0.424468	−	0.905443i	$-0.639539\pi$
$911$	−25.6233			−0.848936			−0.424468	+	0.905443i	$0.639539\pi$
$912$	1.00216	+	4.39073i	0.0331847	+	0.145392i
$913$	24.7473	+	11.9177i	0.819015	+	0.394417i
$914$	−20.1652	−	9.71103i	−0.667005	−	0.321212i
$915$	0.213792	+	0.936683i	0.00706774	+	0.0309658i
$916$	19.9825			0.660242
$917$	−0.409698	−	1.79500i	−0.0135294	−	0.0592763i
$918$	3.21983	−	4.03754i	0.106270	−	0.133259i
$919$	1.38889	−	6.08511i	0.0458152	−	0.200729i	−0.946841	−	0.321703i	$-0.895745\pi$
$919$	1.38889	−	6.08511i	0.0458152	−	0.200729i	0.992656	+	0.120974i	$0.0386018\pi$
$920$	0.445811	−	1.95323i	0.0146980	−	0.0643960i
$921$	4.07069	+	5.10448i	0.134134	+	0.168198i
$922$	−35.6296	−	17.1583i	−1.17340	−	0.565079i
$923$	53.2926	−	25.6644i	1.75415	−	0.844753i
$924$	−4.07942	+	5.11543i	−0.134203	+	0.168285i
$925$	8.84631	+	11.0929i	0.290865	+	0.364733i
$926$	−53.5870	+	25.8061i	−1.76098	+	0.848042i
$927$	7.88471			0.258968
$928$		0			0
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$	−1.63922	+	0.789406i	−0.0537521	+	0.0258857i
$931$	12.0003	+	15.0479i	0.393294	+	0.493175i
$932$	1.52111	−	1.90741i	0.0498255	−	0.0624792i
$933$	−7.42854	+	3.57740i	−0.243200	+	0.117119i
$934$	−42.3783	−	20.4083i	−1.38666	−	0.667780i
$935$	0.719169	+	0.901809i	0.0235193	+	0.0294923i
$936$	4.38740	−	19.2224i	0.143407	−	0.628305i
$937$	0.909994	−	3.98694i	0.0297282	−	0.130248i	−0.957886	−	0.287148i	$-0.907293\pi$
$937$	0.909994	−	3.98694i	0.0297282	−	0.130248i	0.987614	+	0.156900i	$0.0501501\pi$
$938$	1.70291	−	2.13538i	0.0556019	−	0.0697225i
$939$	−2.27695	−	9.97595i	−0.0743053	−	0.325553i
$940$	−3.47219			−0.113250
$941$	−1.37143	−	6.00862i	−0.0447073	−	0.195875i	0.947643	−	0.319333i	$-0.103459\pi$
$941$	−1.37143	−	6.00862i	−0.0447073	−	0.195875i	−0.992350	+	0.123458i	$0.960602\pi$
$942$	12.7724	+	6.15086i	0.416147	+	0.200406i
$943$	1.47650	+	0.711045i	0.0480815	+	0.0231548i
$944$	−10.0121	−	43.8658i	−0.325865	−	1.42771i
$945$	3.73125			0.121378
$946$	6.70291	+	29.3674i	0.217930	+	0.954815i
$947$	−30.9889	+	38.8588i	−1.00700	+	1.26274i	−0.0423823	+	0.999101i	$0.513495\pi$
$947$	−30.9889	+	38.8588i	−1.00700	+	1.26274i	−0.964621	+	0.263641i	$0.915077\pi$
$948$	0.0733760	−	0.321481i	0.00238314	−	0.0104412i
$949$	10.3267	−	45.2442i	0.335219	−	1.46869i
$950$	11.2165	+	14.0650i	0.363911	+	0.456330i
$951$	−5.63706	−	2.71467i	−0.182794	−	0.0880291i
$952$	5.49396	−	2.64575i	0.178060	−	0.0857493i
$953$	11.0268	−	13.8271i	0.357192	−	0.447905i	−0.570474	−	0.821316i	$-0.693240\pi$
$953$	11.0268	−	13.8271i	0.357192	−	0.447905i	0.927666	+	0.373411i	$0.121812\pi$
$954$	−13.7153	−	17.1984i	−0.444049	−	0.556819i
$955$	6.04892	−	2.91301i	0.195738	−	0.0942626i
$956$	−11.1769			−0.361486
$957$		0			0
$958$	−59.5827			−1.92503
$959$	−48.2998	+	23.2600i	−1.55968	+	0.751104i
$960$	−0.125646	−	0.157555i	−0.00405520	−	0.00508506i
$961$	5.86712	−	7.35713i	0.189262	−	0.237327i
$962$	−24.5160	+	11.8063i	−0.790428	+	0.380650i
$963$	−18.8327	−	9.06937i	−0.606876	−	0.292256i
$964$	15.4717	+	19.4008i	0.498309	+	0.624859i
$965$	−0.864429	+	3.78731i	−0.0278269	+	0.121918i
$966$	2.98911	−	13.0962i	0.0961732	−	0.421362i
$967$	−8.03886	+	10.0804i	−0.258512	+	0.324164i	−0.894102	−	0.447862i	$-0.852185\pi$
$967$	−8.03886	+	10.0804i	−0.258512	+	0.324164i	0.635590	+	0.772027i	$0.280757\pi$
$968$	0.761217	+	3.33511i	0.0244664	+	0.107194i
$969$	1.01208			0.0325127
$970$	2.25398	+	9.87533i	0.0723709	+	0.317078i
$971$	−4.35839	−	2.09889i	−0.139867	−	0.0673566i	0.362641	−	0.931929i	$-0.381875\pi$
$971$	−4.35839	−	2.09889i	−0.139867	−	0.0673566i	−0.502508	+	0.864572i	$0.667589\pi$
$972$	−12.3312	−	5.93841i	−0.395525	−	0.190475i
$973$	−2.51961	−	11.0392i	−0.0807751	−	0.353899i
$974$	18.3013			0.586411
$975$	2.50245	+	10.9640i	0.0801426	+	0.351128i
$976$	18.6271	−	23.3577i	0.596240	−	0.747661i
$977$	−3.65870	+	16.0298i	−0.117052	+	0.512839i	0.882077	+	0.471106i	$0.156145\pi$
$977$	−3.65870	+	16.0298i	−0.117052	+	0.512839i	−0.999129	+	0.0417333i	$0.986712\pi$
$978$	−0.886199	+	3.88269i	−0.0283375	+	0.124155i
$979$	2.58397	+	3.24019i	0.0825839	+	0.103557i
$980$	−3.76659	−	1.81390i	−0.120319	−	0.0579428i
$981$	−4.17241	+	2.00933i	−0.133215	+	0.0641528i
$982$	22.1124	−	27.7280i	0.705634	−	0.884837i
$983$	16.5221	+	20.7180i	0.526972	+	0.660802i	0.972073	−	0.234678i	$-0.0754037\pi$
$983$	16.5221	+	20.7180i	0.526972	+	0.660802i	−0.445101	+	0.895480i	$0.646832\pi$
$984$	−0.215521	+	0.103789i	−0.00687055	+	0.00330868i
$985$	−2.99808			−0.0955268
$986$		0			0
$987$	14.0586			0.447490
$988$	−11.9378	+	5.74894i	−0.379792	+	0.182898i
$989$	−14.8083	−	18.5690i	−0.470876	−	0.590459i
$990$	3.27144	−	4.10225i	0.103973	−	0.130378i
$991$	−36.4049	+	17.5317i	−1.15644	+	0.556912i	−0.910962	−	0.412490i	$-0.864659\pi$
$991$	−36.4049	+	17.5317i	−1.15644	+	0.556912i	−0.245478	+	0.969402i	$0.578945\pi$
$992$	35.4294	+	17.0619i	1.12488	+	0.541715i
$993$	3.87263	+	4.85612i	0.122894	+	0.154104i
$994$	18.5172	−	81.1292i	0.587331	−	2.57326i
$995$	0.525845	−	2.30388i	0.0166704	−	0.0730378i
$996$	−3.26391	+	4.09281i	−0.103421	+	0.129686i
$997$	5.21930	+	22.8672i	0.165297	+	0.724213i	0.987835	+	0.155503i	$0.0497000\pi$
$997$	5.21930	+	22.8672i	0.165297	+	0.724213i	−0.822538	+	0.568710i	$0.807443\pi$
$998$	−50.1831			−1.58852
$999$	−1.67307	−	7.33020i	−0.0529336	−	0.231917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.e.571.1		6
29.2	odd	28		841.2.e.c.196.2		12
29.3	odd	28		841.2.e.d.267.2		12
29.4	even	14		841.2.a.f.1.3		3
29.5	even	14		841.2.d.c.645.1		6
29.6	even	14		841.2.d.d.778.1		6
29.7	even	7		29.2.d.a.23.1	✓	6
29.8	odd	28		841.2.e.c.236.2		12
29.9	even	14		841.2.d.c.605.1		6
29.10	odd	28		841.2.b.c.840.1		6
29.11	odd	28		841.2.e.b.651.2		12
29.12	odd	4		841.2.e.b.270.2		12
29.13	even	14		841.2.d.a.190.1		6
29.14	odd	28		841.2.e.d.63.1		12
29.15	odd	28		841.2.e.d.63.2		12
29.16	even	7	inner	841.2.d.e.190.1		6
29.17	odd	4		841.2.e.b.270.1		12
29.18	odd	28		841.2.e.b.651.1		12
29.19	odd	28		841.2.b.c.840.6		6
29.20	even	7		841.2.d.b.605.1		6
29.21	odd	28		841.2.e.c.236.1		12
29.22	even	14		841.2.d.d.574.1		6
29.23	even	7		29.2.d.a.24.1	yes	6
29.24	even	7		841.2.d.b.645.1		6
29.25	even	7		841.2.a.e.1.1		3
29.26	odd	28		841.2.e.d.267.1		12
29.27	odd	28		841.2.e.c.196.1		12
29.28	even	2		841.2.d.a.571.1		6
87.23	odd	14		261.2.k.a.82.1		6
87.62	odd	14		7569.2.a.p.1.1		3
87.65	odd	14		261.2.k.a.226.1		6
87.83	odd	14		7569.2.a.r.1.3		3
116.7	odd	14		464.2.u.f.81.1		6
116.23	odd	14		464.2.u.f.401.1		6
145.7	odd	28		725.2.r.b.574.1		12
145.23	odd	28		725.2.r.b.24.1		12
145.52	odd	28		725.2.r.b.24.2		12
145.94	even	14		725.2.l.b.226.1		6
145.123	odd	28		725.2.r.b.574.2		12
145.139	even	14		725.2.l.b.401.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.7	even	7
29.2.d.a.24.1	yes	6	29.23	even	7
261.2.k.a.82.1		6	87.23	odd	14
261.2.k.a.226.1		6	87.65	odd	14
464.2.u.f.81.1		6	116.7	odd	14
464.2.u.f.401.1		6	116.23	odd	14
725.2.l.b.226.1		6	145.94	even	14
725.2.l.b.401.1		6	145.139	even	14
725.2.r.b.24.1		12	145.23	odd	28
725.2.r.b.24.2		12	145.52	odd	28
725.2.r.b.574.1		12	145.7	odd	28
725.2.r.b.574.2		12	145.123	odd	28
841.2.a.e.1.1		3	29.25	even	7
841.2.a.f.1.3		3	29.4	even	14
841.2.b.c.840.1		6	29.10	odd	28
841.2.b.c.840.6		6	29.19	odd	28
841.2.d.a.190.1		6	29.13	even	14
841.2.d.a.571.1		6	29.28	even	2
841.2.d.b.605.1		6	29.20	even	7
841.2.d.b.645.1		6	29.24	even	7
841.2.d.c.605.1		6	29.9	even	14
841.2.d.c.645.1		6	29.5	even	14
841.2.d.d.574.1		6	29.22	even	14
841.2.d.d.778.1		6	29.6	even	14
841.2.d.e.190.1		6	29.16	even	7	inner
841.2.d.e.571.1		6	1.1	even	1	trivial
841.2.e.b.270.1		12	29.17	odd	4
841.2.e.b.270.2		12	29.12	odd	4
841.2.e.b.651.1		12	29.18	odd	28
841.2.e.b.651.2		12	29.11	odd	28
841.2.e.c.196.1		12	29.27	odd	28
841.2.e.c.196.2		12	29.2	odd	28
841.2.e.c.236.1		12	29.21	odd	28
841.2.e.c.236.2		12	29.8	odd	28
841.2.e.d.63.1		12	29.14	odd	28
841.2.e.d.63.2		12	29.15	odd	28
841.2.e.d.267.1		12	29.26	odd	28
841.2.e.d.267.2		12	29.3	odd	28
7569.2.a.p.1.1		3	87.62	odd	14
7569.2.a.r.1.3		3	87.83	odd	14

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.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62349 - 0.781831i) q^{2} +(0.277479 + 0.347948i) q^{3} +(0.777479 - 0.974928i) q^{4} +(-0.321552 + 0.154851i) q^{5} +(0.722521 + 0.347948i) q^{6} +(-2.52446 - 3.16557i) q^{7} +(-0.301938 + 1.32288i) q^{8} +(0.623490 - 2.73169i) q^{9} +(-0.400969 + 0.502799i) q^{10} +(-0.647948 - 2.83885i) q^{11} +0.554958 q^{12} +(-1.15399 - 5.05596i) q^{13} +(-6.57338 - 3.16557i) q^{14} +(-0.143104 - 0.0689153i) q^{15} +(1.09903 + 4.81517i) q^{16} +1.10992 q^{17} +(-1.12349 - 4.92233i) q^{18} +(1.27748 - 1.60191i) q^{19} +(-0.0990311 + 0.433884i) q^{20} +(0.400969 - 1.75676i) q^{21} +(-3.27144 - 4.10225i) q^{22} +(3.72737 + 1.79500i) q^{23} +(-0.544073 + 0.262012i) q^{24} +(-3.03803 + 3.80957i) q^{25} +(-5.82640 - 7.30607i) q^{26} +(2.32640 - 1.12033i) q^{27} -5.04892 q^{28} -0.286208 q^{30} +(5.72737 - 2.75815i) q^{31} +(3.85690 + 4.83639i) q^{32} +(0.807979 - 1.01317i) q^{33} +(1.80194 - 0.867767i) q^{34} +(1.30194 + 0.626980i) q^{35} +(-2.17845 - 2.73169i) q^{36} +(0.647948 - 2.83885i) q^{37} +(0.821552 - 3.59945i) q^{38} +(1.43900 - 1.80445i) q^{39} +(-0.107760 - 0.472129i) q^{40} +0.396125 q^{41} +(-0.722521 - 3.16557i) q^{42} +(-5.17241 - 2.49090i) q^{43} +(-3.27144 - 1.57544i) q^{44} +(0.222521 + 0.974928i) q^{45} +7.45473 q^{46} +(1.73609 + 7.60633i) q^{47} +(-1.37047 + 1.71851i) q^{48} +(-2.09030 + 9.15821i) q^{49} +(-1.95377 + 8.56003i) q^{50} +(0.307979 + 0.386193i) q^{51} +(-5.82640 - 2.80584i) q^{52} +(3.92543 - 1.89039i) q^{53} +(2.90097 - 3.63770i) q^{54} +(0.647948 + 0.812502i) q^{55} +(4.94989 - 2.38374i) q^{56} +0.911854 q^{57} -9.10992 q^{59} +(-0.178448 + 0.0859360i) q^{60} +(-3.77144 - 4.72923i) q^{61} +(7.14191 - 8.95567i) q^{62} +(-10.2213 + 4.92233i) q^{63} +(1.14310 + 0.550490i) q^{64} +(1.15399 + 1.44706i) q^{65} +(0.519614 - 2.27658i) q^{66} +(-0.0833017 + 0.364968i) q^{67} +(0.862937 - 1.08209i) q^{68} +(0.409698 + 1.79500i) q^{69} +2.60388 q^{70} +(2.53803 + 11.1198i) q^{71} +(3.42543 + 1.64960i) q^{72} +(8.06249 + 3.88269i) q^{73} +(-1.16756 - 5.11543i) q^{74} -2.16852 q^{75} +(-0.568532 - 2.49090i) q^{76} +(-7.35086 + 9.21768i) q^{77} +(0.925428 - 4.05456i) q^{78} +(0.132219 - 0.579289i) q^{79} +(-1.09903 - 1.37814i) q^{80} +(-6.53803 - 3.14855i) q^{81} +(0.643104 - 0.309703i) q^{82} +(-5.88135 + 7.37499i) q^{83} +(-1.40097 - 1.75676i) q^{84} +(-0.356896 + 0.171872i) q^{85} -10.3448 q^{86} +3.95108 q^{88} +(-1.28232 + 0.617534i) q^{89} +(1.12349 + 1.40881i) q^{90} +(-13.0918 + 16.4166i) q^{91} +(4.64795 - 2.23833i) q^{92} +(2.54892 + 1.22749i) q^{93} +(8.76540 + 10.9915i) q^{94} +(-0.162718 + 0.712916i) q^{95} +(-0.612605 + 2.68400i) q^{96} +(9.82036 - 12.3143i) q^{97} +(3.76659 + 16.5025i) q^{98} -8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} + 7 q^{8} - q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{12} - 12 q^{13} - 12 q^{14} - 9 q^{15} + 11 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} - 5 q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 6 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 + 7 * q^8 - q^9 + 2 * q^10 + 10 * q^11 + 4 * q^12 - 12 * q^13 - 12 * q^14 - 9 * q^15 + 11 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 - 5 * q^20 - 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 - 17 * q^26 - 4 * q^27 - 12 * q^28 - 18 * q^30 + 12 * q^31 + 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 - 10 * q^37 + 9 * q^38 - 11 * q^39 - 21 * q^40 + 20 * q^41 - 4 * q^42 - 8 * q^43 - q^44 + q^45 + 4 * q^47 + 6 * q^48 - q^49 - 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 - 10 * q^55 + 7 * q^56 - 2 * q^57 - 56 * q^59 + 3 * q^60 - 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 + 16 * q^66 - 30 * q^67 + 16 * q^68 + 14 * q^69 - 2 * q^70 + 7 * q^72 + 24 * q^73 - 6 * q^74 + 48 * q^75 + 2 * q^76 - 17 * q^77 - 8 * q^78 + 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 - 4 * q^84 + 6 * q^85 - 16 * q^86 + 42 * q^88 + 14 * q^89 + 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 - 22 * q^95 - 2 * q^96 + 22 * q^97 + 26 * q^98 - 32 * q^99

Introduction

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