LMFDB - Embedded newform 605.2.j.j.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.3
Root			$-0.897801 - 1.48120i$ of defining polynomial
Character	$\chi$	$=$	605.9
Dual form			605.2.j.j.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.753510 + 0.244830i) q^{2} +(-1.48377 - 2.04223i) q^{3} +(-1.11020 - 0.806607i) q^{4} +(-1.12244 - 1.93394i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(2.03615 - 2.80252i) q^{7} +(-1.57045 - 2.16154i) q^{8} +(-1.04209 + 3.20723i) q^{9} +(-0.372281 - 1.73205i) q^{10} +3.46410i q^{12} +(2.22040 - 1.61321i) q^{14} +(-2.28412 + 5.16180i) q^{15} +(0.193976 + 0.596996i) q^{16} +(4.80158 - 1.56013i) q^{17} +(-1.57045 + 2.16154i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(-0.313800 + 3.05243i) q^{20} -8.74456 q^{21} -2.52434i q^{23} +(-2.08418 + 6.41446i) q^{24} +(-2.48026 + 4.34146i) q^{25} +(0.893769 - 0.290403i) q^{27} +(-4.52106 + 1.46898i) q^{28} +(2.22040 + 1.61321i) q^{29} +(-2.98487 + 3.33025i) q^{30} +(-0.733075 + 2.25617i) q^{31} +5.84096i q^{32} +4.00000 q^{34} +(-7.70536 - 0.792137i) q^{35} +(3.74390 - 2.72010i) q^{36} +(6.48745 - 8.92921i) q^{37} +(-3.01404 + 0.979321i) q^{38} +(-2.41756 + 5.46337i) q^{40} +(-2.22040 + 1.61321i) q^{41} +(-6.58911 - 2.14093i) q^{42} -3.46410i q^{43} +(7.37228 - 1.58457i) q^{45} +(0.618034 - 1.90211i) q^{46} +(3.89893 + 5.36641i) q^{47} +(0.931389 - 1.28195i) q^{48} +(-1.54508 - 4.75528i) q^{49} +(-2.93182 + 2.66409i) q^{50} +(-10.3106 - 7.49107i) q^{51} +(-3.01404 - 0.979321i) q^{53} +0.744563 q^{54} -9.25544 q^{56} +(9.60315 + 3.12025i) q^{57} +(1.27813 + 1.75919i) q^{58} +(-1.31685 - 0.956749i) q^{59} +(6.69937 - 3.88824i) q^{60} +(-3.32025 - 10.2187i) q^{61} +(-1.10476 + 1.52057i) q^{62} +(6.86646 + 9.45088i) q^{63} +(-1.04209 + 3.20723i) q^{64} +0.644810i q^{67} +(-6.58911 - 2.14093i) q^{68} +(-5.15528 + 3.74553i) q^{69} +(-5.61212 - 2.48339i) q^{70} +(2.19923 + 6.76852i) q^{71} +(8.56912 - 2.78428i) q^{72} +(4.07230 - 5.60503i) q^{73} +(7.07450 - 5.13992i) q^{74} +(12.5464 - 1.37646i) q^{75} +5.48913 q^{76} +(3.93829 - 12.1208i) q^{79} +(0.936830 - 1.04523i) q^{80} +(6.26548 + 4.55214i) q^{81} +(-2.06805 + 0.671952i) q^{82} +(-6.30860 + 2.04979i) q^{83} +(9.70820 + 7.05342i) q^{84} +(-8.40667 - 7.53482i) q^{85} +(0.848116 - 2.61023i) q^{86} -6.92820i q^{87} +4.37228 q^{89} +(5.94304 + 0.610965i) q^{90} +(-2.03615 + 2.80252i) q^{92} +(5.69534 - 1.85053i) q^{93} +(1.62402 + 4.99822i) q^{94} +(8.17926 + 3.61936i) q^{95} +(11.9286 - 8.66664i) q^{96} +(3.90781 + 1.26972i) q^{97} -3.96143i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.753510	+	0.244830i	0.532812	+	0.173121i	0.563052	−	0.826422i	$-0.309627\pi$
$2$	0.753510	+	0.244830i	0.532812	+	0.173121i	−0.0302400	+	0.999543i	$0.509627\pi$
$3$	−1.48377	−	2.04223i	−0.856654	−	1.17908i	−0.982357	−	0.187015i	$-0.940119\pi$
$3$	−1.48377	−	2.04223i	−0.856654	−	1.17908i	0.125703	−	0.992068i	$-0.459881\pi$
$4$	−1.11020	−	0.806607i	−0.555099	−	0.403303i
$5$	−1.12244	−	1.93394i	−0.501970	−	0.864885i
$5$	−1.12244	−	1.93394i	−0.501970	−	0.864885i
$6$	−0.618034	−	1.90211i	−0.252311	−	0.776534i
$7$	2.03615	−	2.80252i	0.769592	−	1.05925i	−0.226764	−	0.973950i	$-0.572814\pi$
$7$	2.03615	−	2.80252i	0.769592	−	1.05925i	0.996355	−	0.0853021i	$-0.0271855\pi$
$8$	−1.57045	−	2.16154i	−0.555239	−	0.764221i
$9$	−1.04209	+	3.20723i	−0.347364	+	1.06908i
$10$	−0.372281	−	1.73205i	−0.117726	−	0.547723i
$11$		0			0
$11$		0			0
$12$			3.46410i			1.00000i
$13$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$13$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$14$	2.22040	−	1.61321i	0.593426	−	0.431149i
$15$	−2.28412	+	5.16180i	−0.589757	+	1.33277i
$16$	0.193976	+	0.596996i	0.0484939	+	0.149249i
$17$	4.80158	−	1.56013i	1.16455	−	0.378386i	0.337946	−	0.941166i	$-0.390268\pi$
$17$	4.80158	−	1.56013i	1.16455	−	0.378386i	0.826607	+	0.562779i	$0.190268\pi$
$18$	−1.57045	+	2.16154i	−0.370159	+	0.509481i
$19$	−3.23607	+	2.35114i	−0.742405	+	0.539389i	−0.893463	−	0.449136i	$-0.851732\pi$
$19$	−3.23607	+	2.35114i	−0.742405	+	0.539389i	0.151058	+	0.988525i	$0.451732\pi$
$20$	−0.313800	+	3.05243i	−0.0701678	+	0.682543i
$21$	−8.74456			−1.90822
$22$		0			0
$23$		−	2.52434i		−	0.526361i	−0.964747	−	0.263180i	$-0.915229\pi$
$23$		−	2.52434i		−	0.526361i	0.964747	−	0.263180i	$-0.0847714\pi$
$24$	−2.08418	+	6.41446i	−0.425432	+	1.30935i
$25$	−2.48026	+	4.34146i	−0.496052	+	0.868293i
$26$		0			0
$27$	0.893769	−	0.290403i	0.172006	−	0.0558881i
$28$	−4.52106	+	1.46898i	−0.854400	+	0.277611i
$29$	2.22040	+	1.61321i	0.412318	+	0.299566i	0.774539	−	0.632526i	$-0.217982\pi$
$29$	2.22040	+	1.61321i	0.412318	+	0.299566i	−0.362222	+	0.932092i	$0.617982\pi$
$30$	−2.98487	+	3.33025i	−0.544960	+	0.608017i
$31$	−0.733075	+	2.25617i	−0.131664	+	0.405221i	−0.995056	−	0.0993129i	$-0.968336\pi$
$31$	−0.733075	+	2.25617i	−0.131664	+	0.405221i	0.863392	+	0.504534i	$0.168336\pi$
$32$			5.84096i			1.03255i
$33$		0			0
$34$	4.00000			0.685994
$35$	−7.70536	−	0.792137i	−1.30244	−	0.133896i
$36$	3.74390	−	2.72010i	0.623984	−	0.453351i
$37$	6.48745	−	8.92921i	1.06653	−	1.46795i	0.192991	−	0.981200i	$-0.438181\pi$
$37$	6.48745	−	8.92921i	1.06653	−	1.46795i	0.873540	−	0.486753i	$-0.161819\pi$
$38$	−3.01404	+	0.979321i	−0.488942	+	0.158867i
$39$		0			0
$40$	−2.41756	+	5.46337i	−0.382250	+	0.863834i
$41$	−2.22040	+	1.61321i	−0.346768	+	0.251942i	−0.747512	−	0.664248i	$-0.768752\pi$
$41$	−2.22040	+	1.61321i	−0.346768	+	0.251942i	0.400744	+	0.916190i	$0.368752\pi$
$42$	−6.58911	−	2.14093i	−1.01672	−	0.330353i
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$		0			0
$45$	7.37228	−	1.58457i	1.09899	−	0.236214i
$46$	0.618034	−	1.90211i	0.0911241	−	0.280451i
$47$	3.89893	+	5.36641i	0.568717	+	0.782772i	0.992402	−	0.123038i	$-0.0392637\pi$
$47$	3.89893	+	5.36641i	0.568717	+	0.782772i	−0.423685	+	0.905810i	$0.639264\pi$
$48$	0.931389	−	1.28195i	0.134434	−	0.185033i
$49$	−1.54508	−	4.75528i	−0.220726	−	0.679326i
$50$	−2.93182	+	2.66409i	−0.414622	+	0.376759i
$51$	−10.3106	−	7.49107i	−1.44377	−	1.04896i
$52$		0			0
$53$	−3.01404	−	0.979321i	−0.414010	−	0.134520i	0.0946033	−	0.995515i	$-0.469842\pi$
$53$	−3.01404	−	0.979321i	−0.414010	−	0.134520i	−0.508613	+	0.860995i	$0.669842\pi$
$54$	0.744563			0.101322
$55$		0			0
$56$	−9.25544			−1.23681
$57$	9.60315	+	3.12025i	1.27197	+	0.413288i
$58$	1.27813	+	1.75919i	0.167826	+	0.230993i
$59$	−1.31685	−	0.956749i	−0.171440	−	0.124558i	0.498757	−	0.866742i	$-0.333790\pi$
$59$	−1.31685	−	0.956749i	−0.171440	−	0.124558i	−0.670196	+	0.742184i	$0.733790\pi$
$60$	6.69937	−	3.88824i	0.864885	−	0.501970i
$61$	−3.32025	−	10.2187i	−0.425115	−	1.30837i	−0.902884	−	0.429884i	$-0.858555\pi$
$61$	−3.32025	−	10.2187i	−0.425115	−	1.30837i	0.477770	−	0.878485i	$-0.341445\pi$
$62$	−1.10476	+	1.52057i	−0.140304	+	0.193113i
$63$	6.86646	+	9.45088i	0.865093	+	1.19070i
$64$	−1.04209	+	3.20723i	−0.130262	+	0.400904i
$65$		0			0
$66$		0			0
$67$			0.644810i			0.0787761i	0.999224	+	0.0393880i	$0.0125408\pi$
$67$			0.644810i			0.0787761i	−0.999224	+	0.0393880i	$0.987459\pi$
$68$	−6.58911	−	2.14093i	−0.799047	−	0.259626i
$69$	−5.15528	+	3.74553i	−0.620623	+	0.450909i
$70$	−5.61212	−	2.48339i	−0.670777	−	0.296821i
$71$	2.19923	+	6.76852i	0.261000	+	0.803276i	0.992588	+	0.121528i	$0.0387796\pi$
$71$	2.19923	+	6.76852i	0.261000	+	0.803276i	−0.731588	+	0.681747i	$0.761220\pi$
$72$	8.56912	−	2.78428i	1.00988	−	0.328130i
$73$	4.07230	−	5.60503i	0.476626	−	0.656020i	−0.501226	−	0.865316i	$-0.667117\pi$
$73$	4.07230	−	5.60503i	0.476626	−	0.656020i	0.977852	+	0.209297i	$0.0671175\pi$
$74$	7.07450	−	5.13992i	0.822394	−	0.597504i
$75$	12.5464	−	1.37646i	1.44873	−	0.158939i
$76$	5.48913			0.629646
$77$		0			0
$78$		0			0
$79$	3.93829	−	12.1208i	0.443092	−	1.36370i	−0.441471	−	0.897276i	$-0.645543\pi$
$79$	3.93829	−	12.1208i	0.443092	−	1.36370i	0.884563	−	0.466421i	$-0.154457\pi$
$80$	0.936830	−	1.04523i	0.104741	−	0.116860i
$81$	6.26548	+	4.55214i	0.696165	+	0.505793i
$82$	−2.06805	+	0.671952i	−0.228378	+	0.0742046i
$83$	−6.30860	+	2.04979i	−0.692458	+	0.224993i	−0.634042	−	0.773299i	$-0.718605\pi$
$83$	−6.30860	+	2.04979i	−0.692458	+	0.224993i	−0.0584167	+	0.998292i	$0.518605\pi$
$84$	9.70820	+	7.05342i	1.05925	+	0.769592i
$85$	−8.40667	−	7.53482i	−0.911831	−	0.817266i
$86$	0.848116	−	2.61023i	0.0914548	−	0.281469i
$87$		−	6.92820i		−	0.742781i
$88$		0			0
$89$	4.37228			0.463461			0.231730	−	0.972780i	$-0.425561\pi$
$89$	4.37228			0.463461			0.231730	+	0.972780i	$0.425561\pi$
$90$	5.94304	+	0.610965i	0.626451	+	0.0644013i
$91$		0			0
$92$	−2.03615	+	2.80252i	−0.212283	+	0.292183i
$93$	5.69534	−	1.85053i	0.590580	−	0.191891i
$94$	1.62402	+	4.99822i	0.167505	+	0.515527i
$95$	8.17926	+	3.61936i	0.839174	+	0.371338i
$96$	11.9286	−	8.66664i	1.21746	−	0.884535i
$97$	3.90781	+	1.26972i	0.396778	+	0.128921i	0.500608	−	0.865674i	$-0.333110\pi$
$97$	3.90781	+	1.26972i	0.396778	+	0.128921i	−0.103830	+	0.994595i	$0.533110\pi$
$98$		−	3.96143i		−	0.400165i
$99$		0			0
$100$	6.25544	−	2.81929i	0.625544	−	0.281929i
$101$	−1.85410	+	5.70634i	−0.184490	+	0.567802i	−0.999939	−	0.0110267i	$-0.996490\pi$
$101$	−1.85410	+	5.70634i	−0.184490	+	0.567802i	0.815449	+	0.578829i	$0.196490\pi$
$102$	−5.93507	−	8.16893i	−0.587660	−	0.808844i
$103$	−6.10844	+	8.40755i	−0.601883	+	0.828421i	−0.995879	−	0.0906914i	$-0.971092\pi$
$103$	−6.10844	+	8.40755i	−0.601883	+	0.828421i	0.393996	+	0.919112i	$0.371092\pi$
$104$		0			0
$105$	9.81524	+	16.9115i	0.957869	+	1.65039i
$106$	−2.03134	−	1.47586i	−0.197301	−	0.143348i
$107$	−3.89893	−	5.36641i	−0.376923	−	0.518791i	0.577843	−	0.816148i	$-0.303895\pi$
$107$	−3.89893	−	5.36641i	−0.376923	−	0.518791i	−0.954766	+	0.297358i	$0.903895\pi$
$108$	−1.22650	−	0.398515i	−0.118020	−	0.0383471i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−27.8614			−2.64449
$112$	2.06805	+	0.671952i	0.195413	+	0.0634935i
$113$	−9.45499	−	13.0137i	−0.889451	−	1.22422i	−0.973713	−	0.227780i	$-0.926853\pi$
$113$	−9.45499	−	13.0137i	−0.889451	−	1.22422i	0.0842619	−	0.996444i	$-0.473147\pi$
$114$	6.47214	+	4.70228i	0.606171	+	0.440409i
$115$	−4.88192	+	2.83341i	−0.455242	+	0.264217i
$116$	−1.16385	−	3.58198i	−0.108061	−	0.332578i
$117$		0			0
$118$	−0.758020	−	1.04332i	−0.0697814	−	0.0960458i
$119$	5.40444	−	16.6331i	0.495424	−	1.52476i
$120$	14.7446	−	3.16915i	1.34599	−	0.289302i
$121$		0			0
$122$		−	8.51278i		−	0.770711i
$123$	6.58911	+	2.14093i	0.594120	+	0.193041i
$124$	2.63370	−	1.91350i	0.236514	−	0.171837i
$125$	11.1801	−	0.0763444i	0.999977	−	0.00682845i
$126$	2.86009	+	8.80244i	0.254797	+	0.784184i
$127$	−11.1102	+	3.60991i	−0.985868	+	0.320328i	−0.757205	−	0.653178i	$-0.773436\pi$
$127$	−11.1102	+	3.60991i	−0.985868	+	0.320328i	−0.228663	+	0.973506i	$0.573436\pi$
$128$	5.29601	−	7.28933i	0.468106	−	0.644292i
$129$	−7.07450	+	5.13992i	−0.622875	+	0.452545i
$130$		0			0
$131$	−8.74456			−0.764016			−0.382008	−	0.924159i	$-0.624767\pi$
$131$	−8.74456			−0.764016			−0.382008	+	0.924159i	$0.624767\pi$
$132$		0			0
$133$			13.8564i			1.20150i
$134$	−0.157869	+	0.485871i	−0.0136378	+	0.0419728i
$135$	−1.56482	−	1.40254i	−0.134679	−	0.120711i
$136$	−10.9129	−	7.92871i	−0.935776	−	0.679881i
$137$	−2.12027	+	0.688918i	−0.181147	+	0.0588582i	−0.398186	−	0.917305i	$-0.630360\pi$
$137$	−2.12027	+	0.688918i	−0.181147	+	0.0588582i	0.217039	+	0.976163i	$0.430360\pi$
$138$	−4.80158	+	1.56013i	−0.408737	+	0.132807i
$139$	−14.7514	−	10.7175i	−1.25119	−	0.909046i	−0.252904	−	0.967491i	$-0.581386\pi$
$139$	−14.7514	−	10.7175i	−1.25119	−	0.909046i	−0.998291	+	0.0584456i	$0.981386\pi$
$140$	7.91554	+	7.09462i	0.668985	+	0.599605i
$141$	5.17435	−	15.9250i	0.435759	−	1.34113i
$142$			5.63858i			0.473179i
$143$		0			0
$144$	−2.11684			−0.176404
$145$	0.627600	−	6.10485i	0.0521194	−	0.506981i
$146$	4.44080	−	3.22643i	0.367523	−	0.267021i
$147$	−7.41884	+	10.2112i	−0.611896	+	0.842202i
$148$	−14.4047	+	4.68038i	−1.18406	+	0.384725i
$149$	3.55033	+	10.9268i	0.290855	+	0.895159i	0.984582	+	0.174921i	$0.0559672\pi$
$149$	3.55033	+	10.9268i	0.290855	+	0.895159i	−0.693728	+	0.720237i	$0.744033\pi$
$150$	9.79084	+	2.03457i	0.799419	+	0.166122i
$151$	17.9874	−	13.0686i	1.46380	−	1.06351i	0.481443	−	0.876478i	$-0.340113\pi$
$151$	17.9874	−	13.0686i	1.46380	−	1.06351i	0.982354	−	0.187033i	$-0.0598871\pi$
$152$	10.1642	+	3.30254i	0.824424	+	0.267872i
$153$			17.0256i			1.37643i
$154$		0			0
$155$	5.18614	−	1.11469i	0.416561	−	0.0895342i
$156$		0			0
$157$	3.17318	+	4.36750i	0.253247	+	0.348565i	0.916645	−	0.399702i	$-0.130886\pi$
$157$	3.17318	+	4.36750i	0.253247	+	0.348565i	−0.663398	+	0.748267i	$0.730886\pi$
$158$	5.93507	−	8.16893i	0.472169	−	0.649885i
$159$	2.47214	+	7.60845i	0.196053	+	0.603390i
$160$	11.2961	−	6.55612i	0.893034	−	0.518307i
$161$	−7.07450	−	5.13992i	−0.557549	−	0.405083i
$162$	3.60660	+	4.96406i	0.283361	+	0.390013i
$163$	−3.29456	−	1.07047i	−0.258050	−	0.0838454i	0.177135	−	0.984187i	$-0.443317\pi$
$163$	−3.29456	−	1.07047i	−0.258050	−	0.0838454i	−0.435185	+	0.900341i	$0.643317\pi$
$164$	3.76631			0.294100
$165$		0			0
$166$	−5.25544			−0.407901
$167$	−21.2744	−	6.91246i	−1.64626	−	0.534902i	−0.668335	−	0.743861i	$-0.732993\pi$
$167$	−21.2744	−	6.91246i	−1.64626	−	0.534902i	−0.977924	+	0.208959i	$0.932993\pi$
$168$	13.7329	+	18.9018i	1.05952	+	1.45830i
$169$	−10.5172	−	7.64121i	−0.809017	−	0.587785i
$170$	−4.48976	−	7.73577i	−0.344349	−	0.593306i
$171$	−4.16837	−	12.8289i	−0.318763	−	0.981052i
$172$	−2.79417	+	3.84584i	−0.213053	+	0.293243i
$173$	−1.10476	−	1.52057i	−0.0839932	−	0.115607i	0.764953	−	0.644086i	$-0.222762\pi$
$173$	−1.10476	−	1.52057i	−0.0839932	−	0.115607i	−0.848946	+	0.528480i	$0.822762\pi$
$174$	1.69623	−	5.22047i	0.128591	−	0.395763i
$175$	7.11684	+	15.7908i	0.537983	+	1.19368i
$176$		0			0
$177$			4.10891i			0.308845i
$178$	3.29456	+	1.07047i	0.246937	+	0.0802348i
$179$	−12.8321	+	9.32310i	−0.959120	+	0.696841i	−0.952946	−	0.303140i	$-0.901965\pi$
$179$	−12.8321	+	9.32310i	−0.959120	+	0.696841i	−0.00617360	+	0.999981i	$0.501965\pi$
$180$	−9.46283	−	4.18734i	−0.705317	−	0.312106i
$181$	2.12701	+	6.54627i	0.158100	+	0.486580i	0.998462	−	0.0554448i	$-0.0176577\pi$
$181$	2.12701	+	6.54627i	0.158100	+	0.486580i	−0.840362	+	0.542025i	$0.817658\pi$
$182$		0			0
$183$	−15.9424	+	21.9429i	−1.17850	+	1.62207i
$184$	−5.45647	+	3.96435i	−0.402256	+	0.292256i
$185$	−24.5503	−	2.52386i	−1.80498	−	0.185558i
$186$	4.74456			0.347888
$187$		0			0
$188$		−	9.10268i		−	0.663881i
$189$	1.00599	−	3.09610i	0.0731747	−	0.225208i
$190$	5.27702	+	4.72975i	0.382836	+	0.343132i
$191$	11.0251	+	8.01017i	0.797745	+	0.579596i	0.910252	−	0.414055i	$-0.135888\pi$
$191$	11.0251	+	8.01017i	0.797745	+	0.579596i	−0.112507	+	0.993651i	$0.535888\pi$
$192$	8.09613	−	2.63059i	0.584288	−	0.189847i
$193$	22.2203	−	7.21983i	1.59946	−	0.519695i	0.632483	−	0.774575i	$-0.282036\pi$
$193$	22.2203	−	7.21983i	1.59946	−	0.519695i	0.966973	+	0.254880i	$0.0820360\pi$
$194$	2.63370	+	1.91350i	0.189089	+	0.137381i
$195$		0			0
$196$	−2.12029	+	6.52559i	−0.151449	+	0.466113i
$197$			1.87953i			0.133911i	0.997756	+	0.0669554i	$0.0213285\pi$
$197$			1.87953i			0.133911i	−0.997756	+	0.0669554i	$0.978671\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	13.2794	−	1.45687i	0.938995	−	0.103016i
$201$	1.31685	−	0.956749i	0.0928836	−	0.0674839i
$202$	−2.79417	+	3.84584i	−0.196597	+	0.270592i
$203$	9.04212	−	2.93796i	0.634632	−	0.206204i
$204$	5.40444	+	16.6331i	0.378386	+	1.16455i
$205$	5.61212	+	2.48339i	0.391968	+	0.173447i
$206$	−6.66119	+	4.83964i	−0.464107	+	0.337194i
$207$	8.09613	+	2.63059i	0.562720	+	0.182839i
$208$		0			0
$209$		0			0
$210$	3.25544	+	15.1460i	0.224647	+	1.04518i
$211$	6.64050	−	20.4374i	0.457151	−	1.40697i	−0.411440	−	0.911437i	$-0.634974\pi$
$211$	6.64050	−	20.4374i	0.457151	−	1.40697i	0.868591	−	0.495530i	$-0.165026\pi$
$212$	2.55626	+	3.51838i	0.175564	+	0.241644i
$213$	10.5597	−	14.5342i	0.723542	−	0.995870i
$214$	−1.62402	−	4.99822i	−0.111016	−	0.341671i
$215$	−6.69937	+	3.88824i	−0.456893	+	0.265176i
$216$	−2.03134	−	1.47586i	−0.138215	−	0.100419i
$217$	4.83032	+	6.64836i	0.327903	+	0.451320i
$218$	7.53510	+	2.44830i	0.510341	+	0.165820i
$219$	−17.4891			−1.18181
$220$		0			0
$221$		0			0
$222$	−20.9938	−	6.82131i	−1.40901	−	0.457816i
$223$	−4.45131	−	6.12670i	−0.298081	−	0.410274i	0.633537	−	0.773713i	$-0.281603\pi$
$223$	−4.45131	−	6.12670i	−0.298081	−	0.410274i	−0.931618	+	0.363439i	$0.881603\pi$
$224$	16.3694	+	11.8931i	1.09373	+	0.794639i
$225$	−11.3394	−	12.4790i	−0.755961	−	0.831932i
$226$	−3.93829	−	12.1208i	−0.261971	−	0.806264i
$227$	−5.76170	+	7.93031i	−0.382418	+	0.526353i	−0.956223	−	0.292639i	$-0.905467\pi$
$227$	−5.76170	+	7.93031i	−0.382418	+	0.526353i	0.573805	+	0.818992i	$0.305467\pi$
$228$	−8.14459	−	11.2101i	−0.539389	−	0.742405i
$229$	−6.29538	+	19.3752i	−0.416010	+	1.28035i	0.495333	+	0.868703i	$0.335046\pi$
$229$	−6.29538	+	19.3752i	−0.416010	+	1.28035i	−0.911344	+	0.411646i	$0.864954\pi$
$230$	−4.37228	+	0.939764i	−0.288300	+	0.0619662i
$231$		0			0
$232$		−	7.33296i		−	0.481433i
$233$	16.1923	+	5.26119i	1.06079	+	0.344672i	0.786894	−	0.617088i	$-0.211688\pi$
$233$	16.1923	+	5.26119i	1.06079	+	0.344672i	0.273896	+	0.961759i	$0.411688\pi$
$234$		0			0
$235$	6.00202	−	13.5638i	0.391529	−	0.884803i
$236$	0.690248	+	2.12436i	0.0449313	+	0.138284i
$237$	−30.5970	+	9.94157i	−1.98749	+	0.645774i
$238$	8.14459	−	11.2101i	0.527935	−	0.726641i
$239$	2.63370	−	1.91350i	0.170360	−	0.123774i	−0.499338	−	0.866407i	$-0.666423\pi$
$239$	2.63370	−	1.91350i	0.170360	−	0.123774i	0.669698	+	0.742633i	$0.266423\pi$
$240$	−3.52464	−	0.362345i	−0.227514	−	0.0233893i
$241$	−5.25544			−0.338532			−0.169266	−	0.985570i	$-0.554140\pi$
$241$	−5.25544			−0.338532			−0.169266	+	0.985570i	$0.554140\pi$
$242$		0			0
$243$		−	22.3692i		−	1.43498i
$244$	−4.55632	+	14.0229i	−0.291689	+	0.897725i
$245$	−7.46218	+	8.32562i	−0.476741	+	0.531904i
$246$	4.44080	+	3.22643i	0.283135	+	0.205709i
$247$		0			0
$248$	6.02808	−	1.95864i	0.382783	−	0.124374i
$249$	13.5466	+	9.84221i	0.858483	+	0.623725i
$250$	8.44299	+	2.67969i	0.533982	+	0.169479i
$251$	−1.50898	+	4.64416i	−0.0952459	+	0.293137i	−0.987318	−	0.158757i	$-0.949251\pi$
$251$	−1.50898	+	4.64416i	−0.0952459	+	0.293137i	0.892072	+	0.451894i	$0.149251\pi$
$252$		−	16.0309i		−	1.00985i
$253$		0			0
$254$	−9.25544			−0.580738
$255$	−2.91430	+	28.3483i	−0.182501	+	1.77524i
$256$	11.2317	−	8.16031i	0.701982	−	0.510020i
$257$	−14.0797	+	19.3790i	−0.878265	+	1.20883i	0.0986329	+	0.995124i	$0.468553\pi$
$257$	−14.0797	+	19.3790i	−0.878265	+	1.20883i	−0.976898	+	0.213705i	$0.931447\pi$
$258$	−6.58911	+	2.14093i	−0.410220	+	0.133289i
$259$	−11.8149	−	36.3624i	−0.734140	−	2.25945i
$260$		0			0
$261$	−7.48781	+	5.44021i	−0.463484	+	0.336741i
$262$	−6.58911	−	2.14093i	−0.407077	−	0.132267i
$263$		−	14.1514i		−	0.872610i	−0.899799	−	0.436305i	$-0.856287\pi$
$263$		−	14.1514i		−	0.872610i	0.899799	−	0.436305i	$-0.143713\pi$
$264$		0			0
$265$	1.48913	+	6.92820i	0.0914762	+	0.425596i
$266$	−3.39247	+	10.4409i	−0.208005	+	0.640175i
$267$	−6.48745	−	8.92921i	−0.397026	−	0.546459i
$268$	0.520108	−	0.715868i	0.0317707	−	0.0437286i
$269$	−3.55033	−	10.9268i	−0.216468	−	0.666219i	−0.999046	−	0.0436672i	$-0.986096\pi$
$269$	−3.55033	−	10.9268i	−0.216468	−	0.666219i	0.782578	−	0.622552i	$-0.213904\pi$
$270$	−0.835726	−	1.43994i	−0.0508607	−	0.0876320i
$271$	−7.67686	−	5.57757i	−0.466336	−	0.338813i	0.329675	−	0.944094i	$-0.393061\pi$
$271$	−7.67686	−	5.57757i	−0.466336	−	0.338813i	−0.796012	+	0.605281i	$0.793061\pi$
$272$	1.86278	+	2.56389i	0.112948	+	0.155459i
$273$		0			0
$274$	−1.76631			−0.106707
$275$		0			0
$276$	8.74456			0.526361
$277$	7.81561	+	2.53945i	0.469595	+	0.152581i	0.534249	−	0.845327i	$-0.320594\pi$
$277$	7.81561	+	2.53945i	0.469595	+	0.152581i	−0.0646543	+	0.997908i	$0.520594\pi$
$278$	−8.49133	−	11.6873i	−0.509276	−	0.700958i
$279$	−6.47214	−	4.70228i	−0.387477	−	0.281518i
$280$	10.3887	+	17.8995i	0.620841	+	1.06970i
$281$	7.25854	+	22.3395i	0.433008	+	1.33266i	0.895114	+	0.445837i	$0.147094\pi$
$281$	7.25854	+	22.3395i	0.433008	+	1.33266i	−0.462106	+	0.886825i	$0.652906\pi$
$282$	7.79785	−	10.7328i	0.464355	−	0.639130i
$283$	−2.79417	−	3.84584i	−0.166096	−	0.228612i	0.717853	−	0.696195i	$-0.245125\pi$
$283$	−2.79417	−	3.84584i	−0.166096	−	0.228612i	−0.883949	+	0.467583i	$0.845125\pi$
$284$	3.01796	−	9.28831i	0.179083	−	0.551160i
$285$	−4.74456	−	22.0742i	−0.281044	−	1.30756i
$286$		0			0
$287$			9.50744i			0.561207i
$288$	−18.7333	−	6.08682i	−1.10387	−	0.358669i
$289$	6.86785	−	4.98978i	0.403991	−	0.293517i
$290$	1.96756	−	4.44641i	0.115539	−	0.261102i
$291$	−3.20521	−	9.86463i	−0.187893	−	0.578275i
$292$	−9.04212	+	2.93796i	−0.529150	+	0.171931i
$293$	5.93507	−	8.16893i	0.346731	−	0.477234i	−0.599661	−	0.800254i	$-0.704698\pi$
$293$	5.93507	−	8.16893i	0.346731	−	0.477234i	0.946392	+	0.323020i	$0.104698\pi$
$294$	−8.09017	+	5.87785i	−0.471828	+	0.342803i
$295$	−0.372211	+	3.62061i	−0.0216710	+	0.210800i
$296$	−29.4891			−1.71402
$297$		0			0
$298$			9.10268i			0.527304i
$299$		0			0
$300$	−15.0393	−	8.59188i	−0.868293	−	0.496052i
$301$	−9.70820	−	7.05342i	−0.559572	−	0.406553i
$302$	16.7533	−	5.44348i	0.964044	−	0.313237i
$303$	14.4047	−	4.68038i	0.827530	−	0.268881i
$304$	−2.03134	−	1.47586i	−0.116505	−	0.0846461i
$305$	−16.0356	+	17.8910i	−0.918194	+	1.02444i
$306$	−4.16837	+	12.8289i	−0.238290	+	0.733381i
$307$		−	28.1176i		−	1.60475i	−0.596817	−	0.802377i	$-0.703568\pi$
$307$		−	28.1176i		−	1.60475i	0.596817	−	0.802377i	$-0.296432\pi$
$308$		0			0
$309$	26.2337			1.49238
$310$	4.18072	+	0.429792i	0.237449	+	0.0244106i
$311$	14.1490	−	10.2798i	0.802316	−	0.582917i	−0.109277	−	0.994011i	$-0.534853\pi$
$311$	14.1490	−	10.2798i	0.802316	−	0.582917i	0.911593	+	0.411095i	$0.134853\pi$
$312$		0			0
$313$	30.2643	−	9.83345i	1.71064	−	0.555820i	0.720198	−	0.693769i	$-0.244051\pi$
$313$	30.2643	−	9.83345i	1.71064	−	0.555820i	0.990439	+	0.137949i	$0.0440511\pi$
$314$	1.32172	+	4.06785i	0.0745892	+	0.229562i
$315$	10.5703	−	23.8874i	0.595567	−	1.34590i
$316$	−14.1490	+	10.2798i	−0.795943	+	0.578287i
$317$	3.34677	+	1.08743i	0.187973	+	0.0610763i	0.401491	−	0.915863i	$-0.368492\pi$
$317$	3.34677	+	1.08743i	0.187973	+	0.0610763i	−0.213518	+	0.976939i	$0.568492\pi$
$318$			6.33830i			0.355434i
$319$		0			0
$320$	7.37228	−	1.58457i	0.412123	−	0.0885804i
$321$	−5.17435	+	15.9250i	−0.288804	+	0.888848i
$322$	−4.07230	−	5.60503i	−0.226940	−	0.312356i
$323$	−11.8701	+	16.3379i	−0.660473	+	0.909063i
$324$	−3.28415	−	10.1076i	−0.182453	−	0.561531i
$325$		0			0
$326$	−2.22040	−	1.61321i	−0.122976	−	0.0893476i
$327$	−14.8377	−	20.4223i	−0.820526	−	1.12936i
$328$	6.97406	+	2.26601i	0.385078	+	0.125119i
$329$	22.9783			1.26683
$330$		0			0
$331$	3.11684			0.171317			0.0856586	−	0.996325i	$-0.472701\pi$
$331$	3.11684			0.171317			0.0856586	+	0.996325i	$0.472701\pi$
$332$	8.65717	+	2.81288i	0.475124	+	0.154377i
$333$	21.8775	+	30.1118i	1.19888	+	1.65012i
$334$	−14.3381	−	10.4172i	−0.784544	−	0.570004i
$335$	1.24703	−	0.723760i	0.0681323	−	0.0395432i
$336$	−1.69623	−	5.22047i	−0.0925371	−	0.284800i
$337$	−7.38657	+	10.1667i	−0.402372	+	0.553818i	−0.961337	−	0.275373i	$-0.911199\pi$
$337$	−7.38657	+	10.1667i	−0.402372	+	0.553818i	0.558965	+	0.829191i	$0.311199\pi$
$338$	−6.05403	−	8.33266i	−0.329296	−	0.453237i
$339$	−12.5479	+	38.6186i	−0.681510	+	2.09747i
$340$	3.25544	+	15.1460i	0.176551	+	0.821409i
$341$		0			0
$342$		−	10.6873i		−	0.577901i
$343$	6.58911	+	2.14093i	0.355779	+	0.115599i
$344$	−7.48781	+	5.44021i	−0.403715	+	0.293316i
$345$	13.0301	+	5.76589i	0.701519	+	0.310425i
$346$	−0.460165	−	1.41624i	−0.0247386	−	0.0761377i
$347$	27.8635	−	9.05339i	1.49579	−	0.486011i	0.557003	−	0.830511i	$-0.311951\pi$
$347$	27.8635	−	9.05339i	1.49579	−	0.486011i	0.938787	+	0.344499i	$0.111951\pi$
$348$	−5.58834	+	7.69168i	−0.299566	+	0.412318i
$349$	6.05883	−	4.40200i	0.324322	−	0.235634i	−0.413696	−	0.910415i	$-0.635762\pi$
$349$	6.05883	−	4.40200i	0.324322	−	0.235634i	0.738017	+	0.674782i	$0.235762\pi$
$350$	1.49654	+	13.6410i	0.0799933	+	0.729140i
$351$		0			0
$352$		0			0
$353$			21.7244i			1.15627i	0.815941	+	0.578136i	$0.196220\pi$
$353$			21.7244i			1.15627i	−0.815941	+	0.578136i	$0.803780\pi$
$354$	−1.00599	+	3.09610i	−0.0534675	+	0.164556i
$355$	10.6214	−	11.8504i	0.563727	−	0.628955i
$356$	−4.85410	−	3.52671i	−0.257267	−	0.186915i
$357$	−41.9877	+	13.6426i	−2.22222	+	0.722044i
$358$	−11.9517	+	3.88335i	−0.631668	+	0.205241i
$359$	−5.26741	−	3.82700i	−0.278003	−	0.201981i	0.440043	−	0.897977i	$-0.354963\pi$
$359$	−5.26741	−	3.82700i	−0.278003	−	0.201981i	−0.718046	+	0.695996i	$0.754963\pi$
$360$	−15.0029	−	13.4470i	−0.790725	−	0.708719i
$361$	−0.927051	+	2.85317i	−0.0487922	+	0.150167i
$362$			5.45343i			0.286626i
$363$		0			0
$364$		0			0
$365$	−15.4107	−	1.58427i	−0.806634	−	0.0829247i
$366$	−17.3851	+	12.6310i	−0.908732	+	0.660232i
$367$	14.1119	−	19.4234i	0.736637	−	1.01389i	−0.262168	−	0.965022i	$-0.584437\pi$
$367$	14.1119	−	19.4234i	0.736637	−	1.01389i	0.998805	−	0.0488717i	$-0.0155626\pi$
$368$	1.50702	−	0.489660i	0.0785588	−	0.0255253i
$369$	−2.86009	−	8.80244i	−0.148890	−	0.458237i
$370$	−17.8810	−	7.91242i	−0.929589	−	0.411347i
$371$	−8.88159	+	6.45285i	−0.461109	+	0.335015i
$372$	−7.81561	−	2.53945i	−0.405221	−	0.131664i
$373$		−	8.21782i		−	0.425503i	−0.977106	−	0.212751i	$-0.931758\pi$
$373$		−	8.21782i		−	0.425503i	0.977106	−	0.212751i	$-0.0682424\pi$
$374$		0			0
$375$	−16.7446	−	22.7190i	−0.864685	−	1.17321i
$376$	5.47665	−	16.8554i	0.282437	−	0.869251i
$377$		0			0
$378$	1.51604	−	2.08665i	0.0779767	−	0.107326i
$379$	1.96914	+	6.06040i	0.101148	+	0.311302i	0.988807	−	0.149199i	$-0.0476697\pi$
$379$	1.96914	+	6.06040i	0.101148	+	0.311302i	−0.887659	+	0.460501i	$0.847670\pi$
$380$	−6.16121	−	10.6156i	−0.316063	−	0.544571i
$381$	23.8572	+	17.3333i	1.22224	+	0.888010i
$382$	6.34636	+	8.73501i	0.324708	+	0.446922i
$383$	5.41483	+	1.75938i	0.276685	+	0.0899003i	0.444073	−	0.895991i	$-0.353533\pi$
$383$	5.41483	+	1.75938i	0.276685	+	0.0899003i	−0.167388	+	0.985891i	$0.553533\pi$
$384$	−22.7446			−1.16068
$385$		0			0
$386$	18.5109			0.942179
$387$	11.1102	+	3.60991i	0.564762	+	0.183502i
$388$	−3.31428	−	4.56171i	−0.168257	−	0.231586i
$389$	−7.97805	−	5.79639i	−0.404503	−	0.293889i	0.366870	−	0.930272i	$-0.380429\pi$
$389$	−7.97805	−	5.79639i	−0.404503	−	0.293889i	−0.771373	+	0.636384i	$0.780429\pi$
$390$		0			0
$391$	−3.93829	−	12.1208i	−0.199168	−	0.612975i
$392$	−7.85227	+	10.8077i	−0.396599	+	0.545872i
$393$	12.9749	+	17.8584i	0.654497	+	0.900838i
$394$	−0.460165	+	1.41624i	−0.0231828	+	0.0713493i
$395$	−27.8614	+	5.98844i	−1.40186	+	0.301311i
$396$		0			0
$397$		−	23.3639i		−	1.17260i	−0.810095	−	0.586299i	$-0.800584\pi$
$397$		−	23.3639i		−	1.17260i	0.810095	−	0.586299i	$-0.199416\pi$
$398$	6.02808	+	1.95864i	0.302160	+	0.0981778i
$399$	28.2980	−	20.5597i	1.41667	−	1.02927i
$400$	−3.07295	−	0.638568i	−0.153647	−	0.0319284i
$401$	3.55033	+	10.9268i	0.177295	+	0.545659i	0.999731	−	0.0231995i	$-0.00738530\pi$
$401$	3.55033	+	10.9268i	0.177295	+	0.545659i	−0.822436	+	0.568858i	$0.807385\pi$
$402$	1.22650	−	0.398515i	0.0611724	−	0.0198761i
$403$		0			0
$404$	6.66119	−	4.83964i	0.331407	−	0.240781i
$405$	1.77095	−	17.2266i	0.0879993	−	0.855996i
$406$	7.53262			0.373838
$407$		0			0
$408$			34.0511i			1.68578i
$409$	1.39394	−	4.29010i	0.0689257	−	0.212132i	−0.910661	−	0.413155i	$-0.864427\pi$
$409$	1.39394	−	4.29010i	0.0689257	−	0.212132i	0.979586	+	0.201023i	$0.0644267\pi$
$410$	3.62078	+	3.24527i	0.178818	+	0.160273i
$411$	4.55292	+	3.30789i	0.224579	+	0.163166i
$412$	13.5632	−	4.40694i	0.668210	−	0.217114i
$413$	−5.36261	+	1.74242i	−0.263877	+	0.0857388i
$414$	5.45647	+	3.96435i	0.268171	+	0.194837i
$415$	11.0452	+	9.89970i	0.542187	+	0.485957i
$416$		0			0
$417$			46.0280i			2.25400i
$418$		0			0
$419$	−22.9783			−1.12256			−0.561280	−	0.827626i	$-0.689691\pi$
$419$	−22.9783			−1.12256			−0.561280	+	0.827626i	$0.689691\pi$
$420$	2.74404	−	26.6921i	0.133896	−	1.30244i
$421$	−25.4752	+	18.5088i	−1.24159	+	0.902066i	−0.997703	−	0.0677386i	$-0.978422\pi$
$421$	−25.4752	+	18.5088i	−1.24159	+	0.902066i	−0.243884	+	0.969804i	$0.578422\pi$
$422$	10.0074	−	13.7740i	0.487151	−	0.670506i
$423$	−21.2744	+	6.91246i	−1.03439	+	0.336095i
$424$	2.61656	+	8.05295i	0.127072	+	0.391086i
$425$	−5.13593	+	24.7154i	−0.249129	+	1.19887i
$426$	11.5153	−	8.36635i	0.557918	−	0.405351i
$427$	−35.3986	−	11.5017i	−1.71306	−	0.556606i
$428$			9.10268i			0.439995i
$429$		0			0
$430$	−6.00000	+	1.28962i	−0.289346	+	0.0621910i
$431$	−9.80289	+	30.1702i	−0.472189	+	1.45325i	0.377524	+	0.926000i	$0.376776\pi$
$431$	−9.80289	+	30.1702i	−0.472189	+	1.45325i	−0.849712	+	0.527247i	$0.823224\pi$
$432$	0.346739	+	0.477245i	0.0166825	+	0.0229615i
$433$	−12.0758	+	16.6209i	−0.580325	+	0.798749i	−0.993731	−	0.111798i	$-0.964339\pi$
$433$	−12.0758	+	16.6209i	−0.580325	+	0.798749i	0.413406	+	0.910547i	$0.364339\pi$
$434$	2.01197	+	6.19221i	0.0965777	+	0.297236i
$435$	−13.3987	+	7.77648i	−0.642421	+	0.372854i
$436$	−11.1020	−	8.06607i	−0.531689	−	0.386295i
$437$	5.93507	+	8.16893i	0.283913	+	0.390773i
$438$	−13.1782	−	4.28187i	−0.629680	−	0.204595i
$439$	−1.48913			−0.0710721			−0.0355360	−	0.999368i	$-0.511314\pi$
$439$	−1.48913			−0.0710721			−0.0355360	+	0.999368i	$0.511314\pi$
$440$		0			0
$441$	16.8614			0.802924
$442$		0			0
$443$	8.87034	+	12.2090i	0.421443	+	0.580066i	0.965963	−	0.258682i	$-0.0832881\pi$
$443$	8.87034	+	12.2090i	0.421443	+	0.580066i	−0.544520	+	0.838748i	$0.683288\pi$
$444$	30.9317	+	22.4732i	1.46795	+	1.06653i
$445$	−4.90762	−	8.45574i	−0.232643	−	0.400840i
$446$	−1.85410	−	5.70634i	−0.0877943	−	0.270203i
$447$	17.0472	−	23.4635i	0.806305	−	1.10978i
$448$	6.86646	+	9.45088i	0.324410	+	0.446512i
$449$	6.75555	−	20.7914i	0.318814	−	0.981208i	−0.655342	−	0.755332i	$-0.727476\pi$
$449$	6.75555	−	20.7914i	0.318814	−	0.981208i	0.974156	−	0.225876i	$-0.0725245\pi$
$450$	−5.48913	−	12.1793i	−0.258760	−	0.574136i
$451$		0			0
$452$			22.0742i			1.03828i
$453$	−53.3784	−	17.3437i	−2.50793	−	0.814877i
$454$	−6.28308	+	4.56492i	−0.294879	+	0.214242i
$455$		0			0
$456$	−8.33674	−	25.6578i	−0.390404	−	1.20154i
$457$	19.7673	−	6.42280i	0.924677	−	0.300446i	0.192293	−	0.981338i	$-0.438408\pi$
$457$	19.7673	−	6.42280i	0.924677	−	0.300446i	0.732384	+	0.680892i	$0.238408\pi$
$458$	−9.48726	+	13.0581i	−0.443311	+	0.610165i
$459$	3.83843	−	2.78878i	0.179163	−	0.130169i
$460$	7.70536	+	0.792137i	0.359264	+	0.0369336i
$461$	32.2337			1.50127			0.750636	−	0.660716i	$-0.229747\pi$
$461$	32.2337			1.50127			0.750636	+	0.660716i	$0.229747\pi$
$462$		0			0
$463$		−	20.1398i		−	0.935976i	−0.883735	−	0.467988i	$-0.844979\pi$
$463$		−	20.1398i		−	0.935976i	0.883735	−	0.467988i	$-0.155021\pi$
$464$	−0.532379	+	1.63849i	−0.0247151	+	0.0760651i
$465$	−9.97149	−	8.93736i	−0.462417	−	0.414460i
$466$	10.9129	+	7.92871i	0.505532	+	0.367290i
$467$	−4.18832	+	1.36087i	−0.193813	+	0.0629735i	−0.404315	−	0.914620i	$-0.632490\pi$
$467$	−4.18832	+	1.36087i	−0.193813	+	0.0629735i	0.210502	+	0.977593i	$0.432490\pi$
$468$		0			0
$469$	1.80709	+	1.31293i	0.0834437	+	0.0606254i
$470$	7.84340	−	8.75095i	0.361789	−	0.403651i
$471$	4.21120	−	12.9607i	0.194042	−	0.597199i
$472$			4.34896i			0.200177i
$473$		0			0
$474$	−25.4891			−1.17075
$475$	−2.18110	−	19.8807i	−0.100076	−	0.912190i
$476$	−19.4164	+	14.1068i	−0.889950	+	0.646586i
$477$	6.28181	−	8.64617i	0.287624	−	0.395881i
$478$	2.45300	−	0.797029i	0.112198	−	0.0364553i
$479$	5.40444	+	16.6331i	0.246935	+	0.759988i	0.995312	+	0.0967144i	$0.0308334\pi$
$479$	5.40444	+	16.6331i	0.246935	+	0.759988i	−0.748377	+	0.663273i	$0.769167\pi$
$480$	−30.1499	−	13.3415i	−1.37615	−	0.608951i
$481$		0			0
$482$	−3.96002	−	1.28669i	−0.180374	−	0.0586071i
$483$			22.0742i			1.00441i
$484$		0			0
$485$	−1.93070	−	8.98266i	−0.0876687	−	0.407882i
$486$	5.47665	−	16.8554i	0.248426	−	0.764576i
$487$	13.3539	+	18.3801i	0.605124	+	0.832881i	0.996165	−	0.0874917i	$-0.0278851\pi$
$487$	13.3539	+	18.3801i	0.605124	+	0.832881i	−0.391042	+	0.920373i	$0.627885\pi$
$488$	−16.8738	+	23.2248i	−0.763843	+	1.05134i
$489$	2.70222	+	8.31657i	0.122199	+	0.376088i
$490$	−7.66118	+	4.44647i	−0.346097	+	0.200871i
$491$	23.8572	+	17.3333i	1.07666	+	0.782240i	0.977098	−	0.212792i	$-0.0682555\pi$
$491$	23.8572	+	17.3333i	1.07666	+	0.782240i	0.0995629	+	0.995031i	$0.468256\pi$
$492$	−5.58834	−	7.69168i	−0.251942	−	0.346768i
$493$	13.1782	+	4.28187i	0.593517	+	0.192846i
$494$		0			0
$495$		0			0
$496$	−1.48913			−0.0668637
$497$	23.4468	+	7.61834i	1.05173	+	0.341729i
$498$	7.79785	+	10.7328i	0.349430	+	0.480949i
$499$	−16.1803	−	11.7557i	−0.724331	−	0.526258i	0.163434	−	0.986554i	$-0.447743\pi$
$499$	−16.1803	−	11.7557i	−0.724331	−	0.526258i	−0.887765	+	0.460297i	$0.847743\pi$
$500$	−12.4737	−	8.93317i	−0.557840	−	0.399503i
$501$	17.4494	+	53.7037i	0.779581	+	2.39930i
$502$	−2.27406	+	3.12997i	−0.101496	+	0.139698i
$503$	0.173369	+	0.238623i	0.00773016	+	0.0106397i	0.812865	−	0.582453i	$-0.197907\pi$
$503$	0.173369	+	0.238623i	0.00773016	+	0.0106397i	−0.805134	+	0.593092i	$0.797907\pi$
$504$	9.64502	−	29.6843i	0.429623	−	1.32224i
$505$	13.1168	−	2.81929i	0.583692	−	0.125457i
$506$		0			0
$507$			32.8164i			1.45743i
$508$	15.2463	+	4.95382i	0.676444	+	0.219790i
$509$	22.9537	−	16.6768i	1.01740	−	0.739187i	0.0516541	−	0.998665i	$-0.483551\pi$
$509$	22.9537	−	16.6768i	1.01740	−	0.739187i	0.965749	+	0.259478i	$0.0835507\pi$
$510$	−9.13648	+	20.6472i	−0.404570	+	0.914274i
$511$	−7.41641	−	22.8254i	−0.328083	−	1.00973i
$512$	−6.67716	+	2.16954i	−0.295091	+	0.0958810i
$513$	−2.20952	+	3.04114i	−0.0975526	+	0.134270i
$514$	−15.3537	+	11.1551i	−0.677224	+	0.492032i
$515$	23.1161	+	2.37641i	1.01862	+	0.104717i
$516$	12.0000			0.528271
$517$		0			0
$518$		−	30.2921i		−	1.33096i
$519$	−1.46615	+	4.51235i	−0.0643569	+	0.198070i
$520$		0			0
$521$	−15.0525	−	10.9363i	−0.659464	−	0.479129i	0.207018	−	0.978337i	$-0.433624\pi$
$521$	−15.0525	−	10.9363i	−0.659464	−	0.479129i	−0.866482	+	0.499209i	$0.833624\pi$
$522$	−6.97406	+	2.26601i	−0.305246	+	0.0991806i
$523$	8.65717	−	2.81288i	0.378552	−	0.122999i	−0.113560	−	0.993531i	$-0.536225\pi$
$523$	8.65717	−	2.81288i	0.378552	−	0.122999i	0.492111	+	0.870532i	$0.336225\pi$
$524$	9.70820	+	7.05342i	0.424105	+	0.308130i
$525$	21.6888	−	37.9642i	0.946577	−	1.65689i
$526$	3.46468	−	10.6632i	0.151067	−	0.464937i
$527$			11.9769i			0.521721i
$528$		0			0
$529$	16.6277			0.722944
$530$	−0.574163	+	5.58505i	−0.0249400	+	0.242599i
$531$	4.44080	−	3.22643i	0.192714	−	0.140015i
$532$	11.1767	−	15.3834i	0.484570	−	0.666954i
$533$		0			0
$534$	−2.70222	−	8.31657i	−0.116936	−	0.359893i
$535$	−6.00202	+	13.5638i	−0.259490	+	0.586413i
$536$	1.39379	−	1.01264i	0.0602024	−	0.0437396i
$537$	38.0799	+	12.3729i	1.64327	+	0.533930i
$538$		−	9.10268i		−	0.392445i
$539$		0			0
$540$	0.605969	+	2.81929i	0.0260768	+	0.121323i
$541$	0.0722135	−	0.222250i	0.00310470	−	0.00955529i	−0.949492	−	0.313791i	$-0.898401\pi$
$541$	0.0722135	−	0.222250i	0.00310470	−	0.00955529i	0.952597	+	0.304235i	$0.0984010\pi$
$542$	−4.41903	−	6.08228i	−0.189814	−	0.261256i
$543$	10.2130	−	14.0570i	0.438282	−	0.603244i
$544$	9.11264	+	28.0458i	0.390701	+	1.20245i
$545$	−11.2244	−	19.3394i	−0.480800	−	0.828410i
$546$		0			0
$547$	5.35042	+	7.36423i	0.228768	+	0.314872i	0.907934	−	0.419112i	$-0.137659\pi$
$547$	5.35042	+	7.36423i	0.228768	+	0.314872i	−0.679167	+	0.733984i	$0.737659\pi$
$548$	2.90961	+	0.945389i	0.124292	+	0.0403850i
$549$	36.2337			1.54642
$550$		0			0
$551$	−10.9783			−0.467689
$552$	16.1923	+	5.26119i	0.689189	+	0.223931i
$553$	−25.9498	−	35.7169i	−1.10350	−	1.51884i
$554$	5.26741	+	3.82700i	0.223791	+	0.162593i
$555$	31.2727	+	53.8823i	1.32745	+	2.28718i
$556$	7.73215	+	23.7971i	0.327916	+	1.00922i
$557$	18.9100	−	26.0274i	0.801242	−	1.10281i	−0.191375	−	0.981517i	$-0.561295\pi$
$557$	18.9100	−	26.0274i	0.801242	−	1.10281i	0.992616	−	0.121297i	$-0.0387055\pi$
$558$	−3.72556	−	5.12779i	−0.157715	−	0.217077i
$559$		0			0
$560$	−1.02175	−	4.75372i	−0.0431768	−	0.200881i
$561$		0			0
$562$			18.6101i			0.785021i
$563$	11.6712	+	3.79220i	0.491883	+	0.159822i	0.544447	−	0.838795i	$-0.316739\pi$
$563$	11.6712	+	3.79220i	0.491883	+	0.159822i	−0.0525644	+	0.998618i	$0.516739\pi$
$564$	−18.5898	+	13.5063i	−0.782772	+	0.568717i
$565$	−14.5550	+	32.8925i	−0.612335	+	1.38380i
$566$	−1.16385	−	3.58198i	−0.0489205	−	0.150562i
$567$	25.5149	−	8.29029i	1.07153	−	0.348160i
$568$	11.1767	−	15.3834i	0.468963	−	0.645472i
$569$	31.3450	−	22.7735i	1.31405	−	0.954714i	0.314065	−	0.949401i	$-0.398309\pi$
$569$	31.3450	−	22.7735i	1.31405	−	0.954714i	0.999986	−	0.00531266i	$-0.00169108\pi$
$570$	1.82936	−	17.7948i	0.0766236	−	0.745340i
$571$	21.4891			0.899292			0.449646	−	0.893207i	$-0.351550\pi$
$571$	21.4891			0.899292			0.449646	+	0.893207i	$0.351550\pi$
$572$		0			0
$573$		−	34.4010i		−	1.43712i
$574$	−2.32771	+	7.16395i	−0.0971567	+	0.299018i
$575$	10.9593	+	6.26102i	0.457035	+	0.261103i
$576$	−9.20037	−	6.68446i	−0.383349	−	0.278519i
$577$	30.2643	−	9.83345i	1.25992	−	0.409372i	0.398453	−	0.917189i	$-0.369547\pi$
$577$	30.2643	−	9.83345i	1.25992	−	0.409372i	0.861465	+	0.507817i	$0.169547\pi$
$578$	6.39664	−	2.07839i	0.266065	−	0.0864498i
$579$	−47.7144	−	34.6665i	−1.98294	−	1.44069i
$580$	−5.62098	+	6.27138i	−0.233398	+	0.260405i
$581$	−7.10067	+	21.8536i	−0.294585	+	0.906641i
$582$		−	8.21782i		−	0.340640i
$583$		0			0
$584$	−18.5109			−0.765985
$585$		0			0
$586$	6.47214	−	4.70228i	0.267361	−	0.194249i
$587$	16.4626	−	22.6588i	0.679482	−	0.935227i	−0.320445	−	0.947267i	$-0.603833\pi$
$587$	16.4626	−	22.6588i	0.679482	−	0.935227i	0.999928	+	0.0120400i	$0.00383253\pi$
$588$	16.4728	−	5.35233i	0.679326	−	0.220726i
$589$	−2.93230	−	9.02469i	−0.120823	−	0.371856i
$590$	−1.16690	+	2.63703i	−0.0480405	+	0.108565i
$591$	3.83843	−	2.78878i	0.157892	−	0.114715i
$592$	6.58911	+	2.14093i	0.270811	+	0.0879918i
$593$		−	43.5586i		−	1.78874i	−0.447333	−	0.894368i	$-0.647626\pi$
$593$		−	43.5586i		−	1.78874i	0.447333	−	0.894368i	$-0.352374\pi$
$594$		0			0
$595$	−38.2337	+	8.21782i	−1.56743	+	0.336898i
$596$	4.87206	−	14.9947i	0.199567	−	0.614205i
$597$	−11.8701	−	16.3379i	−0.485813	−	0.668664i
$598$		0			0
$599$	10.8089	+	33.2663i	0.441639	+	1.35922i	0.886128	+	0.463440i	$0.153385\pi$
$599$	10.8089	+	33.2663i	0.441639	+	1.35922i	−0.444490	+	0.895784i	$0.646615\pi$
$600$	−22.6788	−	24.9580i	−0.925859	−	1.01890i
$601$	24.6486	+	17.9083i	1.00544	+	0.730494i	0.963247	−	0.268616i	$-0.0865662\pi$
$601$	24.6486	+	17.9083i	1.00544	+	0.730494i	0.0421910	+	0.999110i	$0.486566\pi$
$602$	−5.58834	−	7.69168i	−0.227764	−	0.313490i
$603$	−2.06805	−	0.671952i	−0.0842177	−	0.0273640i
$604$	−30.5109			−1.24147
$605$		0			0
$606$	12.0000			0.487467
$607$	3.29456	+	1.07047i	0.133722	+	0.0434489i	0.375113	−	0.926979i	$-0.377604\pi$
$607$	3.29456	+	1.07047i	0.133722	+	0.0434489i	−0.241391	+	0.970428i	$0.577604\pi$
$608$	−13.7329	−	18.9018i	−0.556944	−	0.766567i
$609$	−19.4164	−	14.1068i	−0.786793	−	0.571638i
$610$	−16.4632	+	9.55507i	−0.666576	+	0.386874i
$611$		0			0
$612$	13.7329	−	18.9018i	0.555121	−	0.764058i
$613$	−25.9498	−	35.7169i	−1.04810	−	1.44259i	−0.890442	−	0.455097i	$-0.849605\pi$
$613$	−25.9498	−	35.7169i	−1.04810	−	1.44259i	−0.157661	−	0.987493i	$-0.550395\pi$
$614$	6.88403	−	21.1869i	0.277817	−	0.855032i
$615$	−3.25544	−	15.1460i	−0.131272	−	0.610747i
$616$		0			0
$617$			3.75906i			0.151334i	0.997133	+	0.0756669i	$0.0241086\pi$
$617$			3.75906i			0.151334i	−0.997133	+	0.0756669i	$0.975891\pi$
$618$	19.7673	+	6.42280i	0.795159	+	0.258363i
$619$	−2.52158	+	1.83203i	−0.101351	+	0.0736357i	−0.637306	−	0.770610i	$-0.719951\pi$
$619$	−2.52158	+	1.83203i	−0.101351	+	0.0736357i	0.535956	+	0.844246i	$0.319951\pi$
$620$	−6.65677	−	2.94565i	−0.267342	−	0.118300i
$621$	−0.733075	−	2.25617i	−0.0294173	−	0.0905371i
$622$	13.1782	−	4.28187i	0.528399	−	0.171687i
$623$	8.90261	−	12.2534i	0.356676	−	0.490922i
$624$		0			0
$625$	−12.6966	−	21.5359i	−0.507864	−	0.861437i
$626$	25.2119			1.00767
$627$		0			0
$628$		−	7.40830i		−	0.295624i
$629$	17.2193	−	52.9955i	0.686578	−	2.11307i
$630$	13.8131	−	15.4114i	0.550329	−	0.614007i
$631$	13.4345	+	9.76074i	0.534819	+	0.388569i	0.822157	−	0.569260i	$-0.192770\pi$
$631$	13.4345	+	9.76074i	0.534819	+	0.388569i	−0.287338	+	0.957829i	$0.592770\pi$
$632$	−32.3845	+	10.5224i	−1.28819	+	0.418557i
$633$	−51.5908	+	16.7629i	−2.05055	+	0.666265i
$634$	2.25559	+	1.63878i	0.0895809	+	0.0650843i
$635$	19.4519	+	17.4345i	0.771923	+	0.691868i
$636$	3.39247	−	10.4409i	0.134520	−	0.414010i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−20.0416	−	2.06035i	−0.792214	−	0.0814423i
$641$	15.8792	−	11.5369i	0.627189	−	0.455680i	−0.228236	−	0.973606i	$-0.573296\pi$
$641$	15.8792	−	11.5369i	0.627189	−	0.455680i	0.855425	+	0.517926i	$0.173296\pi$
$642$	−7.79785	+	10.7328i	−0.307757	+	0.423591i
$643$	−37.2383	+	12.0995i	−1.46854	+	0.477156i	−0.930665	−	0.365871i	$-0.880771\pi$
$643$	−37.2383	+	12.0995i	−1.46854	+	0.477156i	−0.537871	+	0.843027i	$0.680771\pi$
$644$	3.70820	+	11.4127i	0.146124	+	0.449723i
$645$	17.8810	+	7.91242i	0.704064	+	0.311551i
$646$	−12.9443	+	9.40456i	−0.509286	+	0.370018i
$647$	−39.0259	−	12.6803i	−1.53426	−	0.498513i	−0.584478	−	0.811410i	$-0.698701\pi$
$647$	−39.0259	−	12.6803i	−1.53426	−	0.498513i	−0.949787	+	0.312897i	$0.898701\pi$
$648$		−	20.6920i		−	0.812860i
$649$		0			0
$650$		0			0
$651$	6.41042	−	19.7293i	0.251244	−	0.773250i
$652$	2.79417	+	3.84584i	0.109428	+	0.150615i
$653$	15.0433	−	20.7054i	0.588691	−	0.810263i	−0.405924	−	0.913907i	$-0.633050\pi$
$653$	15.0433	−	20.7054i	0.588691	−	0.810263i	0.994615	+	0.103644i	$0.0330501\pi$
$654$	−6.18034	−	19.0211i	−0.241670	−	0.743785i
$655$	9.81524	+	16.9115i	0.383513	+	0.660786i
$656$	−1.39379	−	1.01264i	−0.0544182	−	0.0395371i
$657$	13.7329	+	18.9018i	0.535772	+	0.737428i
$658$	17.3143	+	5.62577i	0.674983	+	0.219315i
$659$	32.7446			1.27555			0.637774	−	0.770224i	$-0.279856\pi$
$659$	32.7446			1.27555			0.637774	+	0.770224i	$0.279856\pi$
$660$		0			0
$661$	35.3505			1.37498			0.687488	−	0.726196i	$-0.258713\pi$
$661$	35.3505			1.37498			0.687488	+	0.726196i	$0.258713\pi$
$662$	2.34857	+	0.763097i	0.0912799	+	0.0296586i
$663$		0			0
$664$	14.3381	+	10.4172i	0.556425	+	0.404266i
$665$	26.7975	−	15.5530i	1.03916	−	0.603118i
$666$	9.11264	+	28.0458i	0.353108	+	1.08675i
$667$	4.07230	−	5.60503i	0.157680	−	0.217028i
$668$	18.0431	+	24.8342i	0.698110	+	0.960866i
$669$	−5.90743	+	18.1812i	−0.228394	+	0.702926i
$670$	1.11684	−	0.240051i	0.0431474	−	0.00927397i
$671$		0			0
$672$		−	51.0767i		−	1.97033i
$673$	1.22650	+	0.398515i	0.0472782	+	0.0153616i	0.332561	−	0.943082i	$-0.392087\pi$
$673$	1.22650	+	0.398515i	0.0472782	+	0.0153616i	−0.285282	+	0.958443i	$0.592087\pi$
$674$	−8.05498	+	5.85228i	−0.310266	+	0.225422i
$675$	−0.956006	+	4.60054i	−0.0367967	+	0.177075i
$676$	5.51276	+	16.9665i	0.212029	+	0.652559i
$677$	−41.3222	+	13.4264i	−1.58814	+	0.516019i	−0.964138	−	0.265403i	$-0.914495\pi$
$677$	−41.3222	+	13.4264i	−1.58814	+	0.516019i	−0.624004	+	0.781421i	$0.714495\pi$
$678$	−18.9100	+	26.0274i	−0.726233	+	0.999575i
$679$	11.5153	−	8.36635i	0.441916	−	0.321071i
$680$	−3.08456	+	30.0045i	−0.118288	+	1.15062i
$681$	24.7446			0.948214
$682$		0			0
$683$			44.4434i			1.70058i	0.526314	+	0.850290i	$0.323573\pi$
$683$			44.4434i			1.70058i	−0.526314	+	0.850290i	$0.676427\pi$
$684$	−5.72017	+	17.6049i	−0.218716	+	0.673140i
$685$	3.71220	+	3.32721i	0.141836	+	0.127126i
$686$	4.44080	+	3.22643i	0.169550	+	0.123186i
$687$	48.9095	−	15.8917i	1.86601	−	0.606305i
$688$	2.06805	−	0.671952i	0.0788438	−	0.0256179i
$689$		0			0
$690$	8.40667	+	7.53482i	0.320036	+	0.286846i
$691$	4.98710	−	15.3487i	0.189718	−	0.583893i	−0.810279	−	0.586044i	$-0.800685\pi$
$691$	4.98710	−	15.3487i	0.189718	−	0.583893i	0.999998	+	0.00215105i	$0.000684700\pi$
$692$			2.57924i			0.0980480i
$693$		0			0
$694$	23.2119			0.881113
$695$	−4.16950	+	40.5580i	−0.158158	+	1.53845i
$696$	−14.9756	+	10.8804i	−0.567649	+	0.412421i
$697$	−8.14459	+	11.2101i	−0.308498	+	0.424612i
$698$	5.64313	−	1.83356i	0.213596	−	0.0694014i
$699$	−13.2810	−	40.8747i	−0.502334	−	1.54602i
$700$	4.83588	−	23.2715i	0.182779	−	0.879579i
$701$	−28.7113	+	20.8600i	−1.08441	+	0.787871i	−0.978447	−	0.206499i	$-0.933793\pi$
$701$	−28.7113	+	20.8600i	−1.08441	+	0.787871i	−0.105964	+	0.994370i	$0.533793\pi$
$702$		0			0
$703$			44.1485i			1.66509i
$704$		0			0
$705$	−36.6060	+	7.86797i	−1.37866	+	0.296325i
$706$	−5.31878	+	16.3695i	−0.200175	+	0.616075i
$707$	12.2169	+	16.8151i	0.459463	+	0.632397i
$708$	3.31428	−	4.56171i	0.124558	−	0.171440i
$709$	−12.7058	−	39.1044i	−0.477176	−	1.46860i	−0.843000	−	0.537914i	$-0.819213\pi$
$709$	−12.7058	−	39.1044i	−0.477176	−	1.46860i	0.365823	−	0.930684i	$-0.380787\pi$
$710$	10.9047	−	6.32896i	0.409246	−	0.237522i
$711$	34.7701	+	25.2620i	1.30398	+	0.947398i
$712$	−6.86646	−	9.45088i	−0.257332	−	0.354187i
$713$	5.69534	+	1.85053i	0.213292	+	0.0693029i
$714$	−34.9783			−1.30903
$715$		0			0
$716$	21.7663			0.813445
$717$	−7.81561	−	2.53945i	−0.291879	−	0.0948374i
$718$	−3.03208	−	4.17330i	−0.113156	−	0.155746i
$719$	17.2729	+	12.5495i	0.644172	+	0.468018i	0.861281	−	0.508129i	$-0.169663\pi$
$719$	17.2729	+	12.5495i	0.644172	+	0.468018i	−0.217109	+	0.976147i	$0.569663\pi$
$720$	2.37603	+	4.09385i	0.0885493	+	0.152569i
$721$	11.1246	+	34.2380i	0.414302	+	1.27509i
$722$	−1.39708	+	1.92292i	−0.0519941	+	0.0715637i
$723$	7.79785	+	10.7328i	0.290005	+	0.399158i
$724$	2.91886	−	8.98332i	0.108479	−	0.333863i
$725$	−12.5109	+	5.63858i	−0.464642	+	0.209412i
$726$		0			0
$727$			15.7908i			0.585650i	0.956166	+	0.292825i	$0.0945953\pi$
$727$			15.7908i			0.585650i	−0.956166	+	0.292825i	$0.905405\pi$
$728$		0			0
$729$	−26.8866	+	19.5343i	−0.995801	+	0.723492i
$730$	−11.2242	−	4.96677i	−0.415428	−	0.183829i
$731$	−5.40444	−	16.6331i	−0.199890	−	0.615199i
$732$	35.3986	−	11.5017i	1.30837	−	0.425115i
$733$	−17.8052	+	24.5068i	−0.657651	+	0.905179i	−0.999401	−	0.0346121i	$-0.988980\pi$
$733$	−17.8052	+	24.5068i	−0.657651	+	0.905179i	0.341750	+	0.939791i	$0.388980\pi$
$734$	15.3889	−	11.1807i	0.568015	−	0.412687i
$735$	28.0750	+	2.88621i	1.03556	+	0.106459i
$736$	14.7446			0.543492
$737$		0			0
$738$		−	7.33296i		−	0.269930i
$739$	0.230083	−	0.708121i	0.00846372	−	0.0260487i	−0.946735	−	0.322012i	$-0.895641\pi$
$739$	0.230083	−	0.708121i	0.00846372	−	0.0260487i	0.955199	+	0.295964i	$0.0956407\pi$
$740$	25.2200	+	22.6045i	0.927106	+	0.830957i
$741$		0			0
$742$	−8.27222	+	2.68781i	−0.303683	+	0.0986725i
$743$	−20.7133	+	6.73017i	−0.759898	+	0.246906i	−0.663235	−	0.748411i	$-0.730817\pi$
$743$	−20.7133	+	6.73017i	−0.759898	+	0.246906i	−0.0966632	+	0.995317i	$0.530817\pi$
$744$	−12.9443	−	9.40456i	−0.474560	−	0.344788i
$745$	17.1468	−	19.1308i	0.628209	−	0.700899i
$746$	2.01197	−	6.19221i	0.0736635	−	0.226713i
$747$		−	22.3692i		−	0.818446i
$748$		0			0
$749$	−22.9783			−0.839607
$750$	−7.05488	−	21.2186i	−0.257608	−	0.774793i
$751$	−17.4972	+	12.7125i	−0.638482	+	0.463884i	−0.859328	−	0.511425i	$-0.829118\pi$
$751$	−17.4972	+	12.7125i	−0.638482	+	0.463884i	0.220847	+	0.975309i	$0.429118\pi$
$752$	−2.44743	+	3.36860i	−0.0892485	+	0.122840i
$753$	11.7234	−	3.80917i	0.427225	−	0.138814i
$754$		0			0
$755$	−45.4638	−	20.1179i	−1.65460	−	0.732165i
$756$	−3.61418	+	2.62586i	−0.131447	+	0.0955015i
$757$	37.8516	+	12.2987i	1.37574	+	0.447005i	0.901266	−	0.433266i	$-0.142639\pi$
$757$	37.8516	+	12.2987i	1.37574	+	0.447005i	0.474473	+	0.880270i	$0.342639\pi$
$758$			5.04868i			0.183376i
$759$		0			0
$760$	−5.02175	−	23.3639i	−0.182158	−	0.847496i
$761$	−6.56829	+	20.2151i	−0.238100	+	0.732798i	0.758595	+	0.651563i	$0.225886\pi$
$761$	−6.56829	+	20.2151i	−0.238100	+	0.732798i	−0.996695	+	0.0812347i	$0.974114\pi$
$762$	13.7329	+	18.9018i	0.497491	+	0.684738i
$763$	20.3615	−	28.0252i	0.737135	−	1.01458i
$764$	−5.77895	−	17.7858i	−0.209075	−	0.643467i
$765$	32.9264	−	19.1101i	1.19046	−	0.690929i
$766$	3.64937	+	2.65143i	0.131857	+	0.0957999i
$767$		0			0
$768$	−33.3305	−	10.8297i	−1.20271	−	0.390785i
$769$	−51.2119			−1.84675			−0.923375	−	0.383900i	$-0.874581\pi$
$769$	−51.2119			−1.84675			−0.923375	+	0.383900i	$0.874581\pi$
$770$		0			0
$771$	60.4674			2.17768
$772$	−30.4926	−	9.90763i	−1.09745	−	0.356584i
$773$	18.1520	+	24.9840i	0.652881	+	0.898613i	0.999220	−	0.0394963i	$-0.0125753\pi$
$773$	18.1520	+	24.9840i	0.652881	+	0.898613i	−0.346339	+	0.938109i	$0.612575\pi$
$774$	7.48781	+	5.44021i	0.269144	+	0.195544i
$775$	−7.97688	−	8.77852i	−0.286538	−	0.315334i
$776$	−3.39247	−	10.4409i	−0.121782	−	0.374808i
$777$	−56.7299	+	78.0821i	−2.03518	+	2.80118i
$778$	−4.59240	−	6.32090i	−0.164646	−	0.226615i
$779$	3.39247	−	10.4409i	0.121548	−	0.374085i
$780$		0			0
$781$		0			0
$782$		−	10.0974i		−	0.361081i
$783$	2.45300	+	0.797029i	0.0876632	+	0.0284835i
$784$	2.53918	−	1.84482i	0.0906848	−	0.0658864i
$785$	4.88480	−	11.0390i	0.174346	−	0.393999i
$786$	5.40444	+	16.6331i	0.192770	+	0.593285i
$787$	−4.52106	+	1.46898i	−0.161158	+	0.0523635i	−0.388485	−	0.921455i	$-0.627001\pi$
$787$	−4.52106	+	1.46898i	−0.161158	+	0.0523635i	0.227327	+	0.973819i	$0.427001\pi$
$788$	1.51604	−	2.08665i	0.0540067	−	0.0743338i
$789$	−28.9004	+	20.9973i	−1.02888	+	0.747525i
$790$	−22.4600	−	2.30896i	−0.799091	−	0.0821493i
$791$	−55.7228			−1.98128
$792$		0			0
$793$		0			0
$794$	5.72017	−	17.6049i	0.203001	−	0.624774i
$795$	11.9395	−	13.3210i	0.423450	−	0.472447i
$796$	−8.88159	−	6.45285i	−0.314800	−	0.228715i
$797$	−29.7032	+	9.65116i	−1.05214	+	0.341862i	−0.783509	−	0.621381i	$-0.786572\pi$
$797$	−29.7032	+	9.65116i	−1.05214	+	0.341862i	−0.268633	+	0.963242i	$0.586572\pi$
$798$	26.3565	−	8.56373i	0.933008	−	0.303153i
$799$	27.0933	+	19.6844i	0.958491	+	0.696385i
$800$	−25.3583	−	14.4871i	−0.896552	−	0.512197i
$801$	−4.55632	+	14.0229i	−0.160990	+	0.495475i
$802$			9.10268i			0.321427i
$803$		0			0
$804$	−2.23369			−0.0787761
$805$	−1.99962	+	19.4509i	−0.0704774	+	0.685555i
$806$		0			0
$807$	−17.0472	+	23.4635i	−0.600090	+	0.825953i
$808$	15.2463	−	4.95382i	0.536362	−	0.174275i
$809$	−6.56829	−	20.2151i	−0.230929	−	0.710726i	−0.997635	−	0.0687282i	$-0.978106\pi$
$809$	−6.56829	−	20.2151i	−0.230929	−	0.710726i	0.766707	−	0.641998i	$-0.221894\pi$
$810$	5.55202	−	12.5468i	0.195078	−	0.440850i
$811$	27.6956	−	20.1221i	0.972525	−	0.706581i	0.0164996	−	0.999864i	$-0.494748\pi$
$811$	27.6956	−	20.1221i	0.972525	−	0.706581i	0.956026	+	0.293283i	$0.0947478\pi$
$812$	−12.4083	−	4.03171i	−0.435447	−	0.141485i
$813$			23.9538i			0.840095i
$814$		0			0
$815$	1.62772	+	7.57301i	0.0570165	+	0.265271i
$816$	2.47214	−	7.60845i	0.0865421	−	0.266349i
$817$	8.14459	+	11.2101i	0.284943	+	0.392191i
$818$	2.10069	−	2.89135i	0.0734489	−	0.101094i
$819$		0			0
$820$	−4.22746	−	7.28383i	−0.147629	−	0.254362i
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	0.303923	−	0.952697i	$-0.401703\pi$
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	−0.812151	+	0.583447i	$0.801703\pi$
$822$	2.62080	+	3.60722i	0.0914108	+	0.125816i
$823$	−31.8757	−	10.3570i	−1.11112	−	0.361024i	−0.304746	−	0.952434i	$-0.598572\pi$
$823$	−31.8757	−	10.3570i	−1.11112	−	0.361024i	−0.806371	+	0.591410i	$0.798572\pi$
$824$	27.7663			0.967285
$825$		0			0
$826$	−4.46738			−0.155440
$827$	−17.1382	−	5.56855i	−0.595955	−	0.193638i	−0.00451961	−	0.999990i	$-0.501439\pi$
$827$	−17.1382	−	5.56855i	−0.595955	−	0.193638i	−0.591436	+	0.806352i	$0.701439\pi$
$828$	−6.86646	−	9.45088i	−0.238626	−	0.328441i
$829$	25.3631	+	18.4274i	0.880897	+	0.640009i	0.933489	−	0.358607i	$-0.116748\pi$
$829$	25.3631	+	18.4274i	0.880897	+	0.640009i	−0.0525914	+	0.998616i	$0.516748\pi$
$830$	5.89891	+	10.1637i	0.204754	+	0.352788i
$831$	−6.41042	−	19.7293i	−0.222375	−	0.684400i
$832$		0			0
$833$	−14.8377	−	20.4223i	−0.514095	−	0.707592i
$834$	−11.2690	+	34.6825i	−0.390215	+	1.20096i
$835$	10.5109	+	48.9022i	0.363744	+	1.69233i
$836$		0			0
$837$			2.22938i			0.0770588i
$838$	−17.3143	−	5.62577i	−0.598114	−	0.194339i
$839$	5.75765	−	4.18318i	0.198776	−	0.144419i	−0.483945	−	0.875098i	$-0.660796\pi$
$839$	5.75765	−	4.18318i	0.198776	−	0.144419i	0.682721	+	0.730679i	$0.260796\pi$
$840$	21.1405	−	47.7747i	0.729417	−	1.64839i
$841$	−6.63378	−	20.4167i	−0.228751	−	0.704024i
$842$	−23.7274	+	7.70949i	−0.817699	+	0.265686i
$843$	34.8524	−	47.9702i	1.20038	−	1.65218i
$844$	−23.8572	+	17.3333i	−0.821199	+	0.596636i
$845$	−2.97271	+	28.9165i	−0.102264	+	0.994757i
$846$	−17.7228			−0.609323
$847$		0			0
$848$		−	1.98933i		−	0.0683140i
$849$	−3.70820	+	11.4127i	−0.127265	+	0.391682i
$850$	−9.92105	+	17.3659i	−0.340289	+	0.595644i
$851$	−22.5404	−	16.3765i	−0.772673	−	0.561380i
$852$	−23.4468	+	7.61834i	−0.803276	+	0.261000i
$853$	−23.4468	+	7.61834i	−0.802805	+	0.260847i	−0.681547	−	0.731774i	$-0.738693\pi$
$853$	−23.4468	+	7.61834i	−0.802805	+	0.260847i	−0.121257	+	0.992621i	$0.538693\pi$
$854$	−23.8572	−	17.3333i	−0.816377	−	0.593132i
$855$	−20.1316	+	22.4611i	−0.688488	+	0.768152i
$856$	−5.47665	+	16.8554i	−0.187188	+	0.576106i
$857$		−	10.6873i		−	0.365070i	−0.983199	−	0.182535i	$-0.941570\pi$
$857$		−	10.6873i		−	0.365070i	0.983199	−	0.182535i	$-0.0584303\pi$
$858$		0			0
$859$	−11.1168			−0.379302			−0.189651	−	0.981852i	$-0.560736\pi$
$859$	−11.1168			−0.379302			−0.189651	+	0.981852i	$0.560736\pi$
$860$	10.5739	+	1.08704i	0.360568	+	0.0370676i
$861$	19.4164	−	14.1068i	0.661709	−	0.480760i
$862$	−14.7731	+	20.3335i	−0.503175	+	0.692561i
$863$	−22.5009	+	7.31097i	−0.765938	+	0.248868i	−0.665825	−	0.746108i	$-0.731920\pi$
$863$	−22.5009	+	7.31097i	−0.765938	+	0.248868i	−0.100113	+	0.994976i	$0.531920\pi$
$864$	1.69623	+	5.22047i	0.0577070	+	0.177604i
$865$	−1.70067	+	3.84329i	−0.0578245	+	0.130676i
$866$	−13.1685	+	9.56749i	−0.447485	+	0.325117i
$867$	−20.3806	−	6.62205i	−0.692161	−	0.224897i
$868$		−	11.2772i		−	0.382772i
$869$		0			0
$870$	−12.0000	+	2.57924i	−0.406838	+	0.0874444i
$871$		0			0
$872$	−15.7045	−	21.6154i	−0.531823	−	0.731991i
$873$	−8.14459	+	11.2101i	−0.275653	+	0.379403i
$874$	2.47214	+	7.60845i	0.0836212	+	0.257360i
$875$	22.5503	−	31.4878i	0.762341	−	1.06448i
$876$	19.4164	+	14.1068i	0.656020	+	0.476626i
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$	−1.12207	−	0.364583i	−0.0378680	−	0.0123041i
$879$	−25.4891			−0.859727
$880$		0			0
$881$	21.8614			0.736530			0.368265	−	0.929721i	$-0.379952\pi$
$881$	21.8614			0.736530			0.368265	+	0.929721i	$0.379952\pi$
$882$	12.7052	+	4.12818i	0.427807	+	0.139003i
$883$	−14.2530	−	19.6176i	−0.479653	−	0.660185i	0.498785	−	0.866726i	$-0.333780\pi$
$883$	−14.2530	−	19.6176i	−0.479653	−	0.660185i	−0.978438	+	0.206540i	$0.933780\pi$
$884$		0			0
$885$	7.94640	−	4.61200i	0.267115	−	0.155031i
$886$	3.69476	+	11.3713i	0.124128	+	0.382027i
$887$	−8.31796	+	11.4487i	−0.279290	+	0.384409i	−0.925498	−	0.378751i	$-0.876354\pi$
$887$	−8.31796	+	11.4487i	−0.279290	+	0.384409i	0.646209	+	0.763161i	$0.276354\pi$
$888$	43.7550	+	60.2236i	1.46832	+	2.02097i
$889$	−12.5051	+	38.4868i	−0.419408	+	1.29080i
$890$	−1.62772	−	7.57301i	−0.0545613	−	0.253848i
$891$		0			0
$892$			10.3923i			0.347960i
$893$	−25.2344	−	8.19915i	−0.844436	−	0.274374i
$894$	18.5898	−	13.5063i	0.621736	−	0.451717i
$895$	32.4336	+	14.3520i	1.08414	+	0.479735i
$896$	−9.64502	−	29.6843i	−0.322217	−	0.991683i
$897$		0			0
$898$	10.1807	−	14.0126i	0.339736	−	0.467606i
$899$	−5.26741	+	3.82700i	−0.175678	+	0.127637i
$900$	2.52337	+	23.0006i	0.0841125	+	0.766686i
$901$	−16.0000			−0.533037
$902$		0			0
$903$			30.2921i			1.00806i
$904$	−13.2810	+	40.8747i	−0.441720	+	1.35947i
$905$	10.2727	−	11.4613i	0.341475	−	0.380987i
$906$	−35.9749	−	26.1373i	−1.19518	−	0.868353i
$907$	18.9258	−	6.14936i	0.628420	−	0.204186i	0.0225451	−	0.999746i	$-0.492823\pi$
$907$	18.9258	−	6.14936i	0.628420	−	0.204186i	0.605875	+	0.795560i	$0.292823\pi$
$908$	12.7933	−	4.15679i	0.424560	−	0.137948i
$909$	−16.3694	−	11.8931i	−0.542939	−	0.394468i
$910$		0			0
$911$	−9.42838	+	29.0176i	−0.312376	+	0.961395i	0.664445	+	0.747337i	$0.268668\pi$
$911$	−9.42838	+	29.0176i	−0.312376	+	0.961395i	−0.976821	+	0.214058i	$0.931332\pi$
$912$			6.33830i			0.209882i
$913$		0			0
$914$	16.4674			0.544692
$915$	60.3307	+	6.20220i	1.99447	+	0.205039i
$916$	22.6173	−	16.4324i	0.747296	−	0.542942i
$917$	−17.8052	+	24.5068i	−0.587980	+	0.809285i
$918$	3.57507	−	1.16161i	0.117995	−	0.0383389i
$919$	1.92632	+	5.92859i	0.0635433	+	0.195566i	0.977788	−	0.209596i	$-0.0672150\pi$
$919$	1.92632	+	5.92859i	0.0635433	+	0.195566i	−0.914245	+	0.405162i	$0.867215\pi$
$920$	13.7914	+	6.10274i	0.454688	+	0.201201i
$921$	−57.4226	+	41.7200i	−1.89214	+	1.37472i
$922$	24.2884	+	7.89178i	0.799896	+	0.259902i
$923$		0			0
$924$		0			0
$925$	22.6753	+	50.3118i	0.745558	+	1.65424i
$926$	4.93083	−	15.1755i	0.162037	−	0.498699i
$927$	−20.5994	−	28.3526i	−0.676573	−	0.931222i
$928$	−9.42272	+	12.9693i	−0.309316	+	0.425737i
$929$	16.3712	+	50.3853i	0.537121	+	1.65309i	0.739021	+	0.673682i	$0.235288\pi$
$929$	16.3712	+	50.3853i	0.537121	+	1.65309i	−0.201900	+	0.979406i	$0.564712\pi$
$930$	−5.32548	−	9.17571i	−0.174629	−	0.300883i
$931$	16.1803	+	11.7557i	0.530289	+	0.385278i
$932$	−13.7329	−	18.9018i	−0.449837	−	0.619147i
$933$	−41.9877	−	13.6426i	−1.37461	−	0.446639i
$934$	−3.48913			−0.114168
$935$		0			0
$936$		0			0
$937$	−24.6733	−	8.01686i	−0.806043	−	0.261899i	−0.123122	−	0.992392i	$-0.539291\pi$
$937$	−24.6733	−	8.01686i	−0.806043	−	0.261899i	−0.682921	+	0.730492i	$0.739291\pi$
$938$	1.04022	+	1.43174i	0.0339643	+	0.0467478i
$939$	−64.9874	−	47.2161i	−2.12078	−	1.54084i
$940$	−17.6041	+	10.2172i	−0.574181	+	0.333249i
$941$	−3.23460	−	9.95507i	−0.105445	−	0.324526i	0.884390	−	0.466749i	$-0.154575\pi$
$941$	−3.23460	−	9.95507i	−0.105445	−	0.324526i	−0.989835	+	0.142223i	$0.954575\pi$
$942$	6.34636	−	8.73501i	0.206775	−	0.284602i
$943$	4.07230	+	5.60503i	0.132612	+	0.182525i
$944$	0.315738	−	0.971741i	0.0102764	−	0.0316275i
$945$	−7.11684	+	1.52967i	−0.231511	+	0.0497602i
$946$		0			0
$947$		−	56.1802i		−	1.82561i	−0.408393	−	0.912806i	$-0.633911\pi$
$947$		−	56.1802i		−	1.82561i	0.408393	−	0.912806i	$-0.366089\pi$
$948$	41.9877	+	13.6426i	1.36370	+	0.443092i
$949$		0			0
$950$	3.22392	−	15.5143i	0.104598	−	0.503351i
$951$	−2.74505	−	8.44838i	−0.0890142	−	0.273958i
$952$	−44.4407	+	14.4397i	−1.44033	+	0.467992i
$953$	24.4983	−	33.7190i	0.793578	−	1.09227i	−0.200075	−	0.979781i	$-0.564119\pi$
$953$	24.4983	−	33.7190i	0.793578	−	1.09227i	0.993653	−	0.112486i	$-0.0358814\pi$
$954$	6.85025	−	4.97700i	0.221785	−	0.161136i
$955$	3.11626	−	30.3127i	0.100840	−	0.980897i
$956$	−4.46738			−0.144485
$957$		0			0
$958$			13.8564i			0.447680i
$959$	−2.38648	+	7.34483i	−0.0770635	+	0.237177i
$960$	−14.1748	−	12.7048i	−0.457491	−	0.410045i
$961$	20.5266	+	14.9135i	0.662149	+	0.481079i
$962$		0			0
$963$	21.2744	−	6.91246i	0.685557	−	0.222751i
$964$	5.83458	+	4.23907i	0.187919	+	0.136531i
$965$	−38.9037	−	34.8690i	−1.25235	−	1.12247i
$966$	−5.40444	+	16.6331i	−0.173885	+	0.535163i
$967$		−	46.3229i		−	1.48965i	−0.667262	−	0.744823i	$-0.732534\pi$
$967$		−	46.3229i		−	1.48965i	0.667262	−	0.744823i	$-0.267466\pi$
$968$		0			0
$969$	50.9783			1.63766
$970$	0.744422	−	7.24122i	0.0239020	−	0.232501i
$971$	−43.7639	+	31.7963i	−1.40445	+	1.02039i	−0.410348	+	0.911929i	$0.634593\pi$
$971$	−43.7639	+	31.7963i	−1.40445	+	1.02039i	−0.994100	+	0.108463i	$0.965407\pi$
$972$	−18.0431	+	24.8342i	−0.578734	+	0.796559i
$973$	−60.0719	+	19.5185i	−1.92582	+	0.625736i
$974$	5.56231	+	17.1190i	0.178228	+	0.548529i
$975$		0			0
$976$	5.45647	−	3.96435i	0.174657	−	0.126896i
$977$	26.0237	+	8.45562i	0.832573	+	0.270519i	0.694129	−	0.719851i	$-0.255790\pi$
$977$	26.0237	+	8.45562i	0.832573	+	0.270519i	0.138444	+	0.990370i	$0.455790\pi$
$978$			6.92820i			0.221540i
$979$		0			0
$980$	15.0000	−	3.22405i	0.479157	−	0.102989i
$981$	−10.4209	+	32.0723i	−0.332714	+	1.02399i
$982$	13.7329	+	18.9018i	0.438235	+	0.603179i
$983$	−4.79804	+	6.60394i	−0.153034	+	0.210633i	−0.878650	−	0.477467i	$-0.841555\pi$
$983$	−4.79804	+	6.60394i	−0.153034	+	0.210633i	0.725616	+	0.688100i	$0.241555\pi$
$984$	−5.72017	−	17.6049i	−0.182353	−	0.561223i
$985$	3.63490	−	2.10965i	0.115817	−	0.0672192i
$986$	8.88159	+	6.45285i	0.282847	+	0.205501i
$987$	−34.0944	−	46.9269i	−1.08524	−	1.49370i
$988$		0			0
$989$	−8.74456			−0.278061
$990$		0			0
$991$	−26.9783			−0.856992			−0.428496	−	0.903544i	$-0.640956\pi$
$991$	−26.9783			−0.856992			−0.428496	+	0.903544i	$0.640956\pi$
$992$	−13.1782	−	4.28187i	−0.418409	−	0.135949i
$993$	−4.62467	−	6.36532i	−0.146760	−	0.201997i
$994$	15.8022	+	11.4810i	0.501216	+	0.364155i
$995$	−8.97951	−	15.4715i	−0.284670	−	0.490481i
$996$	−7.10067	−	21.8536i	−0.224993	−	0.692458i
$997$	12.9749	−	17.8584i	0.410919	−	0.565582i	−0.552523	−	0.833498i	$-0.686335\pi$
$997$	12.9749	−	17.8584i	0.410919	−	0.565582i	0.963442	+	0.267916i	$0.0863348\pi$
$998$	−9.31389	−	12.8195i	−0.294826	−	0.405793i
$999$	3.20521	−	9.86463i	0.101408	−	0.312103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.j.9.3		16
5.4	even	2	inner	605.2.j.j.9.2		16
11.2	odd	10		605.2.j.i.124.3		16
11.3	even	5	inner	605.2.j.j.444.3		16
11.4	even	5		605.2.b.c.364.3		4
11.5	even	5	inner	605.2.j.j.269.2		16
11.6	odd	10		605.2.j.i.269.3		16
11.7	odd	10		55.2.b.a.34.2	✓	4
11.8	odd	10		605.2.j.i.444.2		16
11.9	even	5	inner	605.2.j.j.124.2		16
11.10	odd	2		605.2.j.i.9.2		16
33.29	even	10		495.2.c.a.199.3		4
44.7	even	10		880.2.b.h.529.1		4
55.4	even	10		605.2.b.c.364.2		4
55.7	even	20		275.2.a.h.1.3		4
55.9	even	10	inner	605.2.j.j.124.3		16
55.14	even	10	inner	605.2.j.j.444.2		16
55.18	even	20		275.2.a.h.1.2		4
55.19	odd	10		605.2.j.i.444.3		16
55.24	odd	10		605.2.j.i.124.2		16
55.29	odd	10		55.2.b.a.34.3	yes	4
55.37	odd	20		3025.2.a.ba.1.2		4
55.39	odd	10		605.2.j.i.269.2		16
55.48	odd	20		3025.2.a.ba.1.3		4
55.49	even	10	inner	605.2.j.j.269.3		16
55.54	odd	2		605.2.j.i.9.3		16
165.29	even	10		495.2.c.a.199.2		4
165.62	odd	20		2475.2.a.bi.1.2		4
165.128	odd	20		2475.2.a.bi.1.3		4
220.7	odd	20		4400.2.a.cc.1.1		4
220.139	even	10		880.2.b.h.529.4		4
220.183	odd	20		4400.2.a.cc.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.2	✓	4	11.7	odd	10
55.2.b.a.34.3	yes	4	55.29	odd	10
275.2.a.h.1.2		4	55.18	even	20
275.2.a.h.1.3		4	55.7	even	20
495.2.c.a.199.2		4	165.29	even	10
495.2.c.a.199.3		4	33.29	even	10
605.2.b.c.364.2		4	55.4	even	10
605.2.b.c.364.3		4	11.4	even	5
605.2.j.i.9.2		16	11.10	odd	2
605.2.j.i.9.3		16	55.54	odd	2
605.2.j.i.124.2		16	55.24	odd	10
605.2.j.i.124.3		16	11.2	odd	10
605.2.j.i.269.2		16	55.39	odd	10
605.2.j.i.269.3		16	11.6	odd	10
605.2.j.i.444.2		16	11.8	odd	10
605.2.j.i.444.3		16	55.19	odd	10
605.2.j.j.9.2		16	5.4	even	2	inner
605.2.j.j.9.3		16	1.1	even	1	trivial
605.2.j.j.124.2		16	11.9	even	5	inner
605.2.j.j.124.3		16	55.9	even	10	inner
605.2.j.j.269.2		16	11.5	even	5	inner
605.2.j.j.269.3		16	55.49	even	10	inner
605.2.j.j.444.2		16	55.14	even	10	inner
605.2.j.j.444.3		16	11.3	even	5	inner
880.2.b.h.529.1		4	44.7	even	10
880.2.b.h.529.4		4	220.139	even	10
2475.2.a.bi.1.2		4	165.62	odd	20
2475.2.a.bi.1.3		4	165.128	odd	20
3025.2.a.ba.1.2		4	55.37	odd	20
3025.2.a.ba.1.3		4	55.48	odd	20
4400.2.a.cc.1.1		4	220.7	odd	20
4400.2.a.cc.1.4		4	220.183	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.753510 + 0.244830i) q^{2} +(-1.48377 - 2.04223i) q^{3} +(-1.11020 - 0.806607i) q^{4} +(-1.12244 - 1.93394i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(2.03615 - 2.80252i) q^{7} +(-1.57045 - 2.16154i) q^{8} +(-1.04209 + 3.20723i) q^{9} +(-0.372281 - 1.73205i) q^{10} +3.46410i q^{12} +(2.22040 - 1.61321i) q^{14} +(-2.28412 + 5.16180i) q^{15} +(0.193976 + 0.596996i) q^{16} +(4.80158 - 1.56013i) q^{17} +(-1.57045 + 2.16154i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(-0.313800 + 3.05243i) q^{20} -8.74456 q^{21} -2.52434i q^{23} +(-2.08418 + 6.41446i) q^{24} +(-2.48026 + 4.34146i) q^{25} +(0.893769 - 0.290403i) q^{27} +(-4.52106 + 1.46898i) q^{28} +(2.22040 + 1.61321i) q^{29} +(-2.98487 + 3.33025i) q^{30} +(-0.733075 + 2.25617i) q^{31} +5.84096i q^{32} +4.00000 q^{34} +(-7.70536 - 0.792137i) q^{35} +(3.74390 - 2.72010i) q^{36} +(6.48745 - 8.92921i) q^{37} +(-3.01404 + 0.979321i) q^{38} +(-2.41756 + 5.46337i) q^{40} +(-2.22040 + 1.61321i) q^{41} +(-6.58911 - 2.14093i) q^{42} -3.46410i q^{43} +(7.37228 - 1.58457i) q^{45} +(0.618034 - 1.90211i) q^{46} +(3.89893 + 5.36641i) q^{47} +(0.931389 - 1.28195i) q^{48} +(-1.54508 - 4.75528i) q^{49} +(-2.93182 + 2.66409i) q^{50} +(-10.3106 - 7.49107i) q^{51} +(-3.01404 - 0.979321i) q^{53} +0.744563 q^{54} -9.25544 q^{56} +(9.60315 + 3.12025i) q^{57} +(1.27813 + 1.75919i) q^{58} +(-1.31685 - 0.956749i) q^{59} +(6.69937 - 3.88824i) q^{60} +(-3.32025 - 10.2187i) q^{61} +(-1.10476 + 1.52057i) q^{62} +(6.86646 + 9.45088i) q^{63} +(-1.04209 + 3.20723i) q^{64} +0.644810i q^{67} +(-6.58911 - 2.14093i) q^{68} +(-5.15528 + 3.74553i) q^{69} +(-5.61212 - 2.48339i) q^{70} +(2.19923 + 6.76852i) q^{71} +(8.56912 - 2.78428i) q^{72} +(4.07230 - 5.60503i) q^{73} +(7.07450 - 5.13992i) q^{74} +(12.5464 - 1.37646i) q^{75} +5.48913 q^{76} +(3.93829 - 12.1208i) q^{79} +(0.936830 - 1.04523i) q^{80} +(6.26548 + 4.55214i) q^{81} +(-2.06805 + 0.671952i) q^{82} +(-6.30860 + 2.04979i) q^{83} +(9.70820 + 7.05342i) q^{84} +(-8.40667 - 7.53482i) q^{85} +(0.848116 - 2.61023i) q^{86} -6.92820i q^{87} +4.37228 q^{89} +(5.94304 + 0.610965i) q^{90} +(-2.03615 + 2.80252i) q^{92} +(5.69534 - 1.85053i) q^{93} +(1.62402 + 4.99822i) q^{94} +(8.17926 + 3.61936i) q^{95} +(11.9286 - 8.66664i) q^{96} +(3.90781 + 1.26972i) q^{97} -3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Introduction

L-functions

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