LMFDB - Embedded newform 841.2.d.a.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)

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);

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")

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:	$1$
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.a.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	−0.908426	−	0.418045i	$-0.862716\pi$
$2$	−1.62349	+	0.781831i	−1.14798	+	0.552838i	−0.239554	+	0.970883i	$0.577001\pi$
$3$	−0.277479	−	0.347948i	−0.160203	−	0.200888i	0.695251	−	0.718767i	$-0.255293\pi$
$3$	−0.277479	−	0.347948i	−0.160203	−	0.200888i	−0.855454	+	0.517879i	$0.826722\pi$
$4$	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	$0.0732310\pi$
$11$	0.647948	+	2.83885i	0.195364	+	0.855945i	−0.778288	+	0.627907i	$0.783912\pi$
$12$	−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	$-0.542974\pi$
$17$	−1.10992			−0.269194			−0.134597	+	0.990900i	$0.542974\pi$
$18$	1.12349	+	4.92233i	0.264809	+	1.16020i
$19$	−1.27748	+	1.60191i	−0.293074	+	0.367503i	−0.906468	−	0.422274i	$-0.861232\pi$
$19$	−1.27748	+	1.60191i	−0.293074	+	0.367503i	0.613395	+	0.789777i	$0.289804\pi$
$20$	−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	−0.870570	−	0.492045i	$-0.836250\pi$
$31$	−5.72737	+	2.75815i	−1.02867	+	0.495379i	−0.158095	+	0.987424i	$0.550535\pi$
$32$	−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	$0.148364\pi$
$37$	−0.647948	+	2.83885i	−0.106522	+	0.466704i	−0.999850	+	0.0172990i	$0.994493\pi$
$38$	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	$-0.509848\pi$
$41$	−0.396125			−0.0618643			−0.0309321	+	0.999521i	$0.509848\pi$
$42$	−0.722521	−	3.16557i	−0.111487	−	0.488458i
$43$	5.17241	+	2.49090i	0.788785	+	0.379859i	0.784497	−	0.620132i	$-0.212921\pi$
$43$	5.17241	+	2.49090i	0.788785	+	0.379859i	0.00428731	+	0.999991i	$0.498635\pi$
$44$	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	$-0.878753\pi$
$47$	−1.73609	−	7.60633i	−0.253235	−	1.10950i	0.675092	−	0.737733i	$-0.264104\pi$
$48$	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	0.962273	−	0.272086i	$-0.0877134\pi$
$61$	3.77144	+	4.72923i	0.482883	+	0.605516i	−0.479390	+	0.877602i	$0.659142\pi$
$62$	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	−0.102190	−	0.994765i	$-0.532585\pi$
$73$	−8.06249	−	3.88269i	−0.943643	−	0.454435i	−0.841453	+	0.540330i	$0.818299\pi$
$74$	−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	−0.981821	−	0.189809i	$-0.939213\pi$
$79$	−0.132219	+	0.579289i	−0.0148758	+	0.0651751i	0.966945	+	0.254984i	$0.0820703\pi$
$80$	−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	−0.364685	−	0.931131i	$-0.618823\pi$
$89$	1.28232	−	0.617534i	0.135926	−	0.0654585i	0.500611	+	0.865673i	$0.333109\pi$
$90$	−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	$0.509250\pi$
$97$	−9.82036	+	12.3143i	−0.997106	+	1.25033i	−0.968051	+	0.250754i	$0.919322\pi$
$98$	−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	−0.566265	−	0.824223i	$-0.691612\pi$
$101$	−15.7153	−	7.56808i	−1.56373	−	0.753052i	−0.997464	+	0.0711709i	$0.977326\pi$
$102$	−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	0.460945	−	0.887429i	$-0.347510\pi$
$113$	−5.38740	−	6.75558i	−0.506804	−	0.635512i	−0.967749	+	0.251917i	$0.918939\pi$
$114$	−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	$0.0823835\pi$
$127$	2.33028	+	10.2096i	0.206779	+	0.905958i	−0.759915	+	0.650023i	$0.774759\pi$
$128$	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	0.415900	−	0.909410i	$-0.363466\pi$
$131$	−0.409698	−	0.197300i	−0.0357955	−	0.0172382i	−0.451696	+	0.892172i	$0.649181\pi$
$132$	−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	$0.262783\pi$
$137$	−2.94624	+	12.9083i	−0.251714	+	1.10283i	−0.929863	+	0.367907i	$0.880075\pi$
$138$	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	$-0.749238\pi$
$157$	−17.6775			−1.41082			−0.705411	+	0.708799i	$0.749238\pi$
$158$	−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	0.913033	−	0.407885i	$-0.133734\pi$
$163$	−1.10507	−	4.84164i	−0.0865559	−	0.379226i	−0.999589	+	0.0286587i	$0.990876\pi$
$164$	−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	$-0.261728\pi$
$191$	18.8116			1.36116			0.680581	+	0.732673i	$0.261728\pi$
$192$	−0.125646	−	0.550490i	−0.00906770	−	0.0397282i
$193$	−6.78650	+	8.51001i	−0.488503	+	0.612564i	−0.963593	−	0.267374i	$-0.913844\pi$
$193$	−6.78650	+	8.51001i	−0.488503	+	0.612564i	0.475090	+	0.879937i	$0.342416\pi$
$194$	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	$0.161372\pi$
$211$	−1.80247	+	7.89714i	−0.124087	+	0.543661i	−0.998309	+	0.0581343i	$0.981485\pi$
$212$	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	0.333128	−	0.942882i	$-0.391896\pi$
$229$	−9.99127	−	12.5287i	−0.660242	−	0.827917i	−0.993370	+	0.114965i	$0.963325\pi$
$230$	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	$0.517217\pi$
$251$	−16.0891	+	20.1751i	−1.01554	+	1.27344i	−0.961472	+	0.274904i	$0.911354\pi$
$252$	−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	−0.443104	−	0.896470i	$-0.646123\pi$
$263$	−0.299782	+	0.144367i	−0.0184853	+	0.00890207i	0.424618	+	0.905372i	$0.360408\pi$
$264$	−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	−0.981633	−	0.190781i	$-0.938898\pi$
$269$	−0.236758	+	1.03731i	−0.0144354	+	0.0632457i	0.967197	+	0.254027i	$0.0817551\pi$
$270$	−0.369510	+	1.61893i	−0.0224877	+	0.0985249i
$271$	10.2654	−	12.8724i	0.623578	−	0.781943i	−0.365265	−	0.930904i	$-0.619021\pi$
$271$	10.2654	−	12.8724i	0.623578	−	0.781943i	0.988843	+	0.148961i	$0.0475929\pi$
$272$	−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	$-0.804127\pi$
$293$	−20.5003	−	25.7066i	−1.19764	−	1.50179i	−0.381071	−	0.924546i	$-0.624445\pi$
$294$	−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	$-0.637492\pi$
$307$	−14.6703			−0.837275			−0.418638	+	0.908153i	$0.637492\pi$
$308$	−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	$-0.752536\pi$
$311$	4.12253	−	18.0620i	0.233767	−	1.02420i	0.946484	−	0.322750i	$-0.104607\pi$
$312$	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	−0.0429302	−	0.999078i	$-0.513669\pi$
$317$	12.6664	−	6.09980i	0.711414	−	0.342599i	0.754344	+	0.656479i	$0.227955\pi$
$318$	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	$-0.625301\pi$
$331$	−13.9565			−0.767116			−0.383558	+	0.923517i	$0.625301\pi$
$332$	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	$-0.946923\pi$
$337$	−3.11476	−	13.6467i	−0.169672	−	0.743381i	0.816458	−	0.577405i	$-0.195935\pi$
$338$	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	0.970356	−	0.241679i	$-0.0776979\pi$
$359$	−0.166071	−	0.727604i	−0.00876488	−	0.0384015i	−0.979121	+	0.203277i	$0.934841\pi$
$360$	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	$-0.437345\pi$
$367$	21.2292	−	26.6205i	1.10815	−	1.38958i	0.912584	−	0.408890i	$-0.134084\pi$
$368$	−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	0.178403	−	0.983958i	$-0.442907\pi$
$379$	20.6151	−	9.92769i	1.05892	−	0.509951i	0.880521	+	0.474006i	$0.157193\pi$
$380$	−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	$-0.415146\pi$
$389$	10.3913			0.526862			0.263431	+	0.964678i	$0.415146\pi$
$390$	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	0.400004	−	0.916513i	$-0.369009\pi$
$409$	−11.7811	−	14.7731i	−0.582539	−	0.730481i	−0.982544	+	0.186032i	$0.940437\pi$
$410$	−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	−0.0591476	−	0.998249i	$-0.518838\pi$
$421$	−17.9840	−	8.66065i	−0.876488	−	0.422094i	−0.817341	+	0.576155i	$0.804553\pi$
$422$	−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	−0.816518	−	0.577320i	$-0.804098\pi$
$433$	−18.1918	+	8.76070i	−0.874241	+	0.421012i	−0.0577235	+	0.998333i	$0.518384\pi$
$434$	−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	$0.232039\pi$
$443$	−4.52834	+	19.8400i	−0.215148	+	0.942625i	−0.961008	+	0.276522i	$0.910818\pi$
$444$	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	0.798563	−	0.601912i	$-0.205594\pi$
$449$	17.4998	+	8.42744i	0.825865	+	0.397716i	0.0273022	+	0.999627i	$0.491308\pi$
$450$	−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	0.990662	−	0.136343i	$-0.0435348\pi$
$461$	13.6833	+	17.1583i	0.637294	+	0.799142i	−0.353367	+	0.935485i	$0.614963\pi$
$462$	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	0.999694	−	0.0247402i	$-0.00787586\pi$
$467$	16.2751	+	20.4083i	0.753121	+	0.944384i	−0.246573	+	0.969124i	$0.579304\pi$
$468$	−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	0.964904	−	0.262602i	$-0.0845807\pi$
$479$	29.7913	+	14.3468i	1.36120	+	0.655520i	0.396297	+	0.918122i	$0.370295\pi$
$480$	−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	−0.788880	−	0.614547i	$-0.789339\pi$
$491$	−17.7327	+	8.53964i	−0.800267	+	0.385388i	−0.0113870	+	0.999935i	$0.503625\pi$
$492$	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	−0.778691	−	0.627407i	$-0.784116\pi$
$503$	0.140416	−	0.176076i	0.00626083	−	0.00785083i	0.784952	+	0.619557i	$0.212688\pi$
$504$	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	−0.332419	−	0.943132i	$-0.607865\pi$
$541$	15.3753	−	19.2800i	0.661036	−	0.828913i	0.993456	+	0.114218i	$0.0364363\pi$
$542$	−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	$-0.644429\pi$
$563$	−20.8009			−0.876652			−0.438326	+	0.898816i	$0.644429\pi$
$564$	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	0.986339	−	0.164727i	$-0.0526742\pi$
$569$	0.625113	+	2.73880i	0.0262061	+	0.114816i	−0.960133	+	0.279543i	$0.909817\pi$
$570$	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	0.679729	−	0.733463i	$-0.262097\pi$
$577$	−4.48225	−	5.62056i	−0.186598	−	0.233987i	−0.866328	+	0.499476i	$0.833526\pi$
$578$	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	−0.999931	−	0.0117267i	$-0.996267\pi$
$599$	−18.7473	+	23.5083i	−0.765993	+	0.960525i	0.233938	+	0.972251i	$0.424839\pi$
$600$	0.654759	−	2.86869i	0.0267304	−	0.117114i
$601$	−7.38458	+	32.3539i	−0.301223	+	1.31974i	0.567060	+	0.823676i	$0.308081\pi$
$601$	−7.38458	+	32.3539i	−0.301223	+	1.31974i	−0.868283	+	0.496068i	$0.834777\pi$
$602$	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	−0.689418	−	0.724363i	$-0.742134\pi$
$607$	−13.6228	+	6.56041i	−0.552933	+	0.266279i	0.136485	+	0.990642i	$0.456419\pi$
$608$	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	$-0.723347\pi$
$617$	6.64364	−	29.1077i	0.267463	−	1.17183i	0.912954	−	0.408063i	$-0.133796\pi$
$618$	−0.502156	+	2.20009i	−0.0201997	+	0.0885006i
$619$	28.7540	−	36.0564i	1.15572	−	1.44923i	0.284269	−	0.958745i	$-0.408249\pi$
$619$	28.7540	−	36.0564i	1.15572	−	1.44923i	0.871451	−	0.490483i	$-0.163179\pi$
$620$	−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	$-0.934421\pi$
$641$	−24.3173	−	30.4929i	−0.960476	−	1.20440i	0.0183770	−	0.999831i	$-0.494150\pi$
$642$	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	0.184060	−	0.982915i	$-0.441076\pi$
$653$	−12.0015	−	5.77961i	−0.469655	−	0.226174i	−0.653714	+	0.756741i	$0.726790\pi$
$654$	−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	$-0.809468\pi$
$659$	4.17576	−	18.2952i	0.162664	−	0.712680i	0.988805	−	0.149215i	$-0.0476747\pi$
$660$	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	−0.789164	−	0.614183i	$-0.789486\pi$
$677$	−0.384411	+	0.482037i	−0.0147741	+	0.0185262i	0.774390	+	0.632709i	$0.218057\pi$
$678$	−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	0.140350	−	0.990102i	$-0.455177\pi$
$727$	27.0155	−	13.0100i	1.00195	−	0.482513i	0.861599	+	0.507589i	$0.169463\pi$
$728$	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	−0.961028	−	0.276451i	$-0.910842\pi$
$733$	0.670784	−	2.93890i	0.0247760	−	0.108551i	0.985804	+	0.167901i	$0.0536988\pi$
$734$	−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	0.0554484	−	0.998462i	$-0.482341\pi$
$739$	−18.7739	−	9.04103i	−0.690609	−	0.332580i	−0.746057	+	0.665882i	$0.768055\pi$
$740$	−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	$-0.880559\pi$
$743$	−6.84601	−	29.9943i	−0.251156	−	1.10039i	0.679265	−	0.733893i	$-0.262299\pi$
$744$	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	0.830068	−	0.557662i	$-0.188301\pi$
$751$	2.78650	+	3.49417i	0.101681	+	0.127504i	−0.728387	+	0.685165i	$0.759730\pi$
$752$	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	0.868355	−	0.495944i	$-0.165178\pi$
$757$	5.27210	+	6.61101i	0.191618	+	0.240281i	−0.676737	+	0.736225i	$0.736606\pi$
$758$	−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	0.853878	−	0.520473i	$-0.174244\pi$
$769$	27.1579	+	13.0786i	0.979340	+	0.471625i	0.125462	+	0.992098i	$0.459959\pi$
$770$	−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	−0.841400	−	0.540412i	$-0.818268\pi$
$773$	−3.53952	+	4.43842i	−0.127308	+	0.159639i	0.714092	+	0.700051i	$0.246840\pi$
$774$	−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	−0.127478	−	0.991841i	$-0.540688\pi$
$797$	−27.7347	−	13.3563i	−0.982412	−	0.473105i	−0.854934	+	0.518737i	$0.826403\pi$
$798$	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	0.721108	−	0.692822i	$-0.243633\pi$
$809$	−3.26540	−	4.09468i	−0.114805	−	0.143961i	−0.835914	+	0.548861i	$0.815062\pi$
$810$	−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	$-0.857976\pi$
$823$	−7.93416	−	34.7618i	−0.276567	−	1.21172i	0.625534	−	0.780197i	$-0.284881\pi$
$824$	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	$-0.996980\pi$
$827$	−46.8989	−	22.5853i	−1.63083	−	0.785368i	−0.630879	−	0.775882i	$-0.717305\pi$
$828$	−3.21648	−	14.0923i	−0.111780	−	0.489742i
$829$	13.4168			0.465986			0.232993	−	0.972478i	$-0.425148\pi$
$829$	13.4168			0.465986			0.232993	+	0.972478i	$0.425148\pi$
$830$	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	−0.849215	−	0.528047i	$-0.822924\pi$
$839$	−27.9763	+	13.4727i	−0.965848	+	0.465128i	−0.116633	+	0.993175i	$0.537210\pi$
$840$	−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	$-0.619020\pi$
$853$	−21.3357			−0.730521			−0.365261	+	0.930905i	$0.619020\pi$
$854$	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	$-0.726664\pi$
$859$	−11.5230	−	50.4854i	−0.393159	−	1.72254i	0.260256	−	0.965540i	$-0.416193\pi$
$860$	−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	$-0.969773\pi$
$881$	−4.14728	−	18.1704i	−0.139726	−	0.612178i	0.855769	−	0.517358i	$-0.173085\pi$
$882$	−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	$-0.467007\pi$
$887$	6.16288			0.206929			0.103465	+	0.994633i	$0.467007\pi$
$888$	−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	$-0.667982\pi$
$907$	9.78740	−	42.8814i	0.324985	−	1.42385i	0.828559	−	0.559902i	$-0.189161\pi$
$908$	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	$-0.360461\pi$
$911$	25.6233			0.848936			0.424468	+	0.905443i	$0.360461\pi$
$912$	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	$-0.486505\pi$
$947$	30.9889	−	38.8588i	1.00700	−	1.26274i	0.964621	−	0.263641i	$-0.0849233\pi$
$948$	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	−0.635590	−	0.772027i	$-0.719243\pi$
$967$	8.03886	−	10.0804i	0.258512	−	0.324164i	0.894102	+	0.447862i	$0.147815\pi$
$968$	−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	0.502508	−	0.864572i	$-0.332411\pi$
$971$	4.35839	+	2.09889i	0.139867	+	0.0673566i	−0.362641	+	0.931929i	$0.618125\pi$
$972$	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	0.445101	−	0.895480i	$-0.353168\pi$
$983$	−16.5221	−	20.7180i	−0.526972	−	0.660802i	−0.972073	+	0.234678i	$0.924596\pi$
$984$	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	$-0.950300\pi$
$997$	−5.21930	−	22.8672i	−0.165297	−	0.724213i	0.822538	−	0.568710i	$-0.192557\pi$
$998$	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.a.571.1		6
29.2	odd	28		841.2.e.c.196.1		12
29.3	odd	28		841.2.e.d.267.1		12
29.4	even	14		841.2.a.e.1.1		3
29.5	even	14		841.2.d.b.645.1		6
29.6	even	14		29.2.d.a.24.1	yes	6
29.7	even	7		841.2.d.d.574.1		6
29.8	odd	28		841.2.e.c.236.1		12
29.9	even	14		841.2.d.b.605.1		6
29.10	odd	28		841.2.b.c.840.6		6
29.11	odd	28		841.2.e.b.651.1		12
29.12	odd	4		841.2.e.b.270.1		12
29.13	even	14		841.2.d.e.190.1		6
29.14	odd	28		841.2.e.d.63.2		12
29.15	odd	28		841.2.e.d.63.1		12
29.16	even	7	inner	841.2.d.a.190.1		6
29.17	odd	4		841.2.e.b.270.2		12
29.18	odd	28		841.2.e.b.651.2		12
29.19	odd	28		841.2.b.c.840.1		6
29.20	even	7		841.2.d.c.605.1		6
29.21	odd	28		841.2.e.c.236.2		12
29.22	even	14		29.2.d.a.23.1	✓	6
29.23	even	7		841.2.d.d.778.1		6
29.24	even	7		841.2.d.c.645.1		6
29.25	even	7		841.2.a.f.1.3		3
29.26	odd	28		841.2.e.d.267.2		12
29.27	odd	28		841.2.e.c.196.2		12
29.28	even	2		841.2.d.e.571.1		6
87.35	odd	14		261.2.k.a.82.1		6
87.62	odd	14		7569.2.a.r.1.3		3
87.80	odd	14		261.2.k.a.226.1		6
87.83	odd	14		7569.2.a.p.1.1		3
116.35	odd	14		464.2.u.f.401.1		6
116.51	odd	14		464.2.u.f.81.1		6
145.22	odd	28		725.2.r.b.574.1		12
145.64	even	14		725.2.l.b.401.1		6
145.93	odd	28		725.2.r.b.24.1		12
145.109	even	14		725.2.l.b.226.1		6
145.122	odd	28		725.2.r.b.24.2		12
145.138	odd	28		725.2.r.b.574.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.22	even	14
29.2.d.a.24.1	yes	6	29.6	even	14
261.2.k.a.82.1		6	87.35	odd	14
261.2.k.a.226.1		6	87.80	odd	14
464.2.u.f.81.1		6	116.51	odd	14
464.2.u.f.401.1		6	116.35	odd	14
725.2.l.b.226.1		6	145.109	even	14
725.2.l.b.401.1		6	145.64	even	14
725.2.r.b.24.1		12	145.93	odd	28
725.2.r.b.24.2		12	145.122	odd	28
725.2.r.b.574.1		12	145.22	odd	28
725.2.r.b.574.2		12	145.138	odd	28
841.2.a.e.1.1		3	29.4	even	14
841.2.a.f.1.3		3	29.25	even	7
841.2.b.c.840.1		6	29.19	odd	28
841.2.b.c.840.6		6	29.10	odd	28
841.2.d.a.190.1		6	29.16	even	7	inner
841.2.d.a.571.1		6	1.1	even	1	trivial
841.2.d.b.605.1		6	29.9	even	14
841.2.d.b.645.1		6	29.5	even	14
841.2.d.c.605.1		6	29.20	even	7
841.2.d.c.645.1		6	29.24	even	7
841.2.d.d.574.1		6	29.7	even	7
841.2.d.d.778.1		6	29.23	even	7
841.2.d.e.190.1		6	29.13	even	14
841.2.d.e.571.1		6	29.28	even	2
841.2.e.b.270.1		12	29.12	odd	4
841.2.e.b.270.2		12	29.17	odd	4
841.2.e.b.651.1		12	29.11	odd	28
841.2.e.b.651.2		12	29.18	odd	28
841.2.e.c.196.1		12	29.2	odd	28
841.2.e.c.196.2		12	29.27	odd	28
841.2.e.c.236.1		12	29.8	odd	28
841.2.e.c.236.2		12	29.21	odd	28
841.2.e.d.63.1		12	29.15	odd	28
841.2.e.d.63.2		12	29.14	odd	28
841.2.e.d.267.1		12	29.3	odd	28
841.2.e.d.267.2		12	29.26	odd	28
7569.2.a.p.1.1		3	87.83	odd	14
7569.2.a.r.1.3		3	87.62	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

L-functions

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