LMFDB - Embedded newform 231.2.j.f.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.f.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43376 - 1.04169i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.352519 + 1.08494i) q^{4} +(-0.477260 + 0.346750i) q^{5} +(1.43376 - 1.04169i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.470553 + 1.44821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.43376 - 1.04169i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.352519 + 1.08494i) q^{4} +(-0.477260 + 0.346750i) q^{5} +(1.43376 - 1.04169i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.470553 + 1.44821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.04548 q^{10} +(-2.19098 + 2.48990i) q^{11} -1.14077 q^{12} +(1.24948 + 0.907802i) q^{13} +(-0.547647 + 1.68548i) q^{14} +(-0.182297 - 0.561053i) q^{15} +(4.02905 - 2.92728i) q^{16} +(-5.78051 + 4.19979i) q^{17} +(0.547647 + 1.68548i) q^{18} +(-1.91300 + 5.88760i) q^{19} +(-0.544446 - 0.395563i) q^{20} +1.00000 q^{21} +(5.73503 - 1.28760i) q^{22} +3.76314 q^{23} +(-1.23192 - 0.895044i) q^{24} +(-1.43754 + 4.42430i) q^{25} +(-0.845811 - 2.60314i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.922906 - 0.670530i) q^{28} +(0.187665 + 0.577574i) q^{29} +(-0.323071 + 0.994311i) q^{30} +(5.55914 + 4.03895i) q^{31} -5.78051 q^{32} +(-1.69098 - 2.85317i) q^{33} +12.6627 q^{34} +(0.477260 + 0.346750i) q^{35} +(0.352519 - 1.08494i) q^{36} +(-2.38157 - 7.32972i) q^{37} +(8.87581 - 6.44865i) q^{38} +(-1.24948 + 0.907802i) q^{39} +(-0.277591 - 0.854338i) q^{40} +(2.31233 - 7.11663i) q^{41} +(-1.43376 - 1.04169i) q^{42} -10.9537 q^{43} +(-3.47375 - 1.49935i) q^{44} +0.589926 q^{45} +(-5.39544 - 3.92001i) q^{46} +(-3.15419 + 9.70760i) q^{47} +(1.53896 + 4.73644i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.66983 - 4.84591i) q^{50} +(-2.20796 - 6.79540i) q^{51} +(-0.544446 + 1.67563i) q^{52} +(-5.69927 - 4.14076i) q^{53} -1.77222 q^{54} +(0.182297 - 1.94805i) q^{55} +1.52274 q^{56} +(-5.00829 - 3.63874i) q^{57} +(0.332585 - 1.02359i) q^{58} +(-1.03640 - 3.18971i) q^{59} +(0.544446 - 0.395563i) q^{60} +(2.72674 - 1.98109i) q^{61} +(-3.76314 - 11.5818i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(0.229756 + 0.166927i) q^{64} -0.911108 q^{65} +(-0.547647 + 5.85223i) q^{66} -2.19138 q^{67} +(-6.59426 - 4.79101i) q^{68} +(-1.16287 + 3.57896i) q^{69} +(-0.323071 - 0.994311i) q^{70} +(11.2801 - 8.19549i) q^{71} +(1.23192 - 0.895044i) q^{72} +(-0.800331 - 2.46317i) q^{73} +(-4.22067 + 12.9899i) q^{74} +(-3.76354 - 2.73437i) q^{75} -7.06206 q^{76} +(3.04508 + 1.31433i) q^{77} +2.73710 q^{78} +(3.77286 + 2.74114i) q^{79} +(-0.907873 + 2.79415i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-10.7286 + 7.79481i) q^{82} +(2.83941 - 2.06295i) q^{83} +(0.352519 + 1.08494i) q^{84} +(1.30253 - 4.00878i) q^{85} +(15.7050 + 11.4104i) q^{86} -0.607298 q^{87} +(-2.57493 - 4.34464i) q^{88} +8.15095 q^{89} +(-0.845811 - 0.614518i) q^{90} +(0.477260 - 1.46886i) q^{91} +(1.32658 + 4.08279i) q^{92} +(-5.55914 + 4.03895i) q^{93} +(14.6346 - 10.6327i) q^{94} +(-1.12853 - 3.47325i) q^{95} +(1.78628 - 5.49760i) q^{96} +(3.88093 + 2.81966i) q^{97} +1.77222 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.43376	−	1.04169i	−1.01382	−	0.736584i	−0.0488134	−	0.998808i	$-0.515544\pi$
$2$	−1.43376	−	1.04169i	−1.01382	−	0.736584i	−0.965007	+	0.262224i	$0.915544\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.352519	+	1.08494i	0.176259	+	0.542470i
$5$	−0.477260	+	0.346750i	−0.213437	+	0.155071i	−0.689367	−	0.724412i	$-0.742111\pi$
$5$	−0.477260	+	0.346750i	−0.213437	+	0.155071i	0.475930	+	0.879483i	$0.342111\pi$
$6$	1.43376	−	1.04169i	0.585329	−	0.425267i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.470553	+	1.44821i	−0.166365	+	0.512020i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.04548			0.330610
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$12$	−1.14077			−0.329313
$13$	1.24948	+	0.907802i	0.346544	+	0.251779i	0.747418	−	0.664354i	$-0.231293\pi$
$13$	1.24948	+	0.907802i	0.346544	+	0.251779i	−0.400874	+	0.916133i	$0.631293\pi$
$14$	−0.547647	+	1.68548i	−0.146365	+	0.450465i
$15$	−0.182297	−	0.561053i	−0.0470689	−	0.144863i
$16$	4.02905	−	2.92728i	1.00726	−	0.731819i
$17$	−5.78051	+	4.19979i	−1.40198	+	1.01860i	−0.407552	+	0.913182i	$0.633618\pi$
$17$	−5.78051	+	4.19979i	−1.40198	+	1.01860i	−0.994428	+	0.105417i	$0.966382\pi$
$18$	0.547647	+	1.68548i	0.129082	+	0.397272i
$19$	−1.91300	+	5.88760i	−0.438872	+	1.35071i	0.450195	+	0.892930i	$0.351354\pi$
$19$	−1.91300	+	5.88760i	−0.438872	+	1.35071i	−0.889067	+	0.457778i	$0.848646\pi$
$20$	−0.544446	−	0.395563i	−0.121742	−	0.0884506i
$21$	1.00000			0.218218
$22$	5.73503	−	1.28760i	1.22271	−	0.274516i
$23$	3.76314			0.784669			0.392335	−	0.919823i	$-0.371668\pi$
$23$	3.76314			0.784669			0.392335	+	0.919823i	$0.371668\pi$
$24$	−1.23192	−	0.895044i	−0.251465	−	0.182700i
$25$	−1.43754	+	4.42430i	−0.287509	+	0.884861i
$26$	−0.845811	−	2.60314i	−0.165877	−	0.510518i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.922906	−	0.670530i	0.174413	−	0.126718i
$29$	0.187665	+	0.577574i	0.0348486	+	0.107253i	0.966968	−	0.254899i	$-0.0820422\pi$
$29$	0.187665	+	0.577574i	0.0348486	+	0.107253i	−0.932119	+	0.362152i	$0.882042\pi$
$30$	−0.323071	+	0.994311i	−0.0589844	+	0.181535i
$31$	5.55914	+	4.03895i	0.998451	+	0.725417i	0.961755	−	0.273909i	$-0.0883169\pi$
$31$	5.55914	+	4.03895i	0.998451	+	0.725417i	0.0366954	+	0.999326i	$0.488317\pi$
$32$	−5.78051			−1.02186
$33$	−1.69098	−	2.85317i	−0.294362	−	0.496673i
$34$	12.6627			2.17164
$35$	0.477260	+	0.346750i	0.0806717	+	0.0586114i
$36$	0.352519	−	1.08494i	0.0587531	−	0.180823i
$37$	−2.38157	−	7.32972i	−0.391528	−	1.20500i	−0.931633	−	0.363401i	$-0.881615\pi$
$37$	−2.38157	−	7.32972i	−0.391528	−	1.20500i	0.540105	−	0.841598i	$-0.318385\pi$
$38$	8.87581	−	6.44865i	1.43985	−	1.04611i
$39$	−1.24948	+	0.907802i	−0.200077	+	0.145365i
$40$	−0.277591	−	0.854338i	−0.0438910	−	0.135083i
$41$	2.31233	−	7.11663i	0.361126	−	1.11143i	−0.591246	−	0.806492i	$-0.701364\pi$
$41$	2.31233	−	7.11663i	0.361126	−	1.11143i	0.952372	−	0.304940i	$-0.0986364\pi$
$42$	−1.43376	−	1.04169i	−0.221234	−	0.160736i
$43$	−10.9537			−1.67043			−0.835214	−	0.549925i	$-0.814656\pi$
$43$	−10.9537			−1.67043			−0.835214	+	0.549925i	$0.814656\pi$
$44$	−3.47375	−	1.49935i	−0.523688	−	0.226036i
$45$	0.589926			0.0879409
$46$	−5.39544	−	3.92001i	−0.795514	−	0.577975i
$47$	−3.15419	+	9.70760i	−0.460086	+	1.41600i	0.404973	+	0.914328i	$0.367281\pi$
$47$	−3.15419	+	9.70760i	−0.460086	+	1.41600i	−0.865059	+	0.501670i	$0.832719\pi$
$48$	1.53896	+	4.73644i	0.222130	+	0.683646i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	6.66983	−	4.84591i	0.943256	−	0.685316i
$51$	−2.20796	−	6.79540i	−0.309176	−	0.951547i
$52$	−0.544446	+	1.67563i	−0.0755010	+	0.232368i
$53$	−5.69927	−	4.14076i	−0.782855	−	0.568778i	0.122979	−	0.992409i	$-0.460755\pi$
$53$	−5.69927	−	4.14076i	−0.782855	−	0.568778i	−0.905835	+	0.423631i	$0.860755\pi$
$54$	−1.77222			−0.241169
$55$	0.182297	−	1.94805i	0.0245809	−	0.262675i
$56$	1.52274			0.203485
$57$	−5.00829	−	3.63874i	−0.663364	−	0.481962i
$58$	0.332585	−	1.02359i	0.0436705	−	0.134404i
$59$	−1.03640	−	3.18971i	−0.134928	−	0.415265i	0.860651	−	0.509195i	$-0.170057\pi$
$59$	−1.03640	−	3.18971i	−0.134928	−	0.415265i	−0.995579	+	0.0939305i	$0.970057\pi$
$60$	0.544446	−	0.395563i	0.0702876	−	0.0510670i
$61$	2.72674	−	1.98109i	0.349124	−	0.253653i	−0.399378	−	0.916787i	$-0.630774\pi$
$61$	2.72674	−	1.98109i	0.349124	−	0.253653i	0.748501	+	0.663133i	$0.230774\pi$
$62$	−3.76314	−	11.5818i	−0.477920	−	1.47088i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	0.229756	+	0.166927i	0.0287194	+	0.0208659i
$65$	−0.911108			−0.113009
$66$	−0.547647	+	5.85223i	−0.0674107	+	0.720360i
$67$	−2.19138			−0.267719			−0.133860	−	0.991000i	$-0.542737\pi$
$67$	−2.19138			−0.267719			−0.133860	+	0.991000i	$0.542737\pi$
$68$	−6.59426	−	4.79101i	−0.799671	−	0.580995i
$69$	−1.16287	+	3.57896i	−0.139994	+	0.430856i
$70$	−0.323071	−	0.994311i	−0.0386144	−	0.118843i
$71$	11.2801	−	8.19549i	1.33870	−	0.972625i	0.339213	−	0.940710i	$-0.389839\pi$
$71$	11.2801	−	8.19549i	1.33870	−	0.972625i	0.999491	−	0.0319157i	$-0.0101608\pi$
$72$	1.23192	−	0.895044i	0.145183	−	0.105482i
$73$	−0.800331	−	2.46317i	−0.0936717	−	0.288292i	0.893234	−	0.449593i	$-0.148431\pi$
$73$	−0.800331	−	2.46317i	−0.0936717	−	0.288292i	−0.986905	+	0.161301i	$0.948431\pi$
$74$	−4.22067	+	12.9899i	−0.490643	+	1.51005i
$75$	−3.76354	−	2.73437i	−0.434576	−	0.315738i
$76$	−7.06206			−0.810074
$77$	3.04508	+	1.31433i	0.347020	+	0.149782i
$78$	2.73710			0.309916
$79$	3.77286	+	2.74114i	0.424480	+	0.308403i	0.779438	−	0.626479i	$-0.215505\pi$
$79$	3.77286	+	2.74114i	0.424480	+	0.308403i	−0.354958	+	0.934882i	$0.615505\pi$
$80$	−0.907873	+	2.79415i	−0.101503	+	0.312395i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−10.7286	+	7.79481i	−1.18478	+	0.860792i
$83$	2.83941	−	2.06295i	0.311666	−	0.226438i	−0.420945	−	0.907086i	$-0.638302\pi$
$83$	2.83941	−	2.06295i	0.311666	−	0.226438i	0.732611	+	0.680648i	$0.238302\pi$
$84$	0.352519	+	1.08494i	0.0384629	+	0.118377i
$85$	1.30253	−	4.00878i	0.141279	−	0.434814i
$86$	15.7050	+	11.4104i	1.69351	+	1.23041i
$87$	−0.607298			−0.0651091
$88$	−2.57493	−	4.34464i	−0.274488	−	0.463140i
$89$	8.15095			0.863999			0.432000	−	0.901874i	$-0.357808\pi$
$89$	8.15095			0.863999			0.432000	+	0.901874i	$0.357808\pi$
$90$	−0.845811	−	0.614518i	−0.0891563	−	0.0647759i
$91$	0.477260	−	1.46886i	0.0500304	−	0.153978i
$92$	1.32658	+	4.08279i	0.138305	+	0.425660i
$93$	−5.55914	+	4.03895i	−0.576456	+	0.418820i
$94$	14.6346	−	10.6327i	1.50945	−	1.09668i
$95$	−1.12853	−	3.47325i	−0.115784	−	0.356348i
$96$	1.78628	−	5.49760i	0.182311	−	0.561096i
$97$	3.88093	+	2.81966i	0.394049	+	0.286293i	0.767113	−	0.641512i	$-0.221693\pi$
$97$	3.88093	+	2.81966i	0.394049	+	0.286293i	−0.373064	+	0.927806i	$0.621693\pi$
$98$	1.77222			0.179022
$99$	3.23607	−	0.726543i	0.325237	−	0.0730203i
$100$	−5.30687			−0.530687
$101$	1.15419	+	0.838567i	0.114846	+	0.0834406i	0.643726	−	0.765256i	$-0.277388\pi$
$101$	1.15419	+	0.838567i	0.114846	+	0.0834406i	−0.528880	+	0.848697i	$0.677388\pi$
$102$	−3.91300	+	12.0430i	−0.387444	+	1.19243i
$103$	5.44403	+	16.7550i	0.536416	+	1.65092i	0.740569	+	0.671980i	$0.234556\pi$
$103$	5.44403	+	16.7550i	0.536416	+	1.65092i	−0.204153	+	0.978939i	$0.565444\pi$
$104$	−1.90264	+	1.38235i	−0.186569	+	0.135550i
$105$	−0.477260	+	0.346750i	−0.0465758	+	0.0338393i
$106$	3.85800	+	11.8737i	0.374722	+	1.15328i
$107$	−2.22494	+	6.84765i	−0.215093	+	0.661987i	0.784054	+	0.620692i	$0.213148\pi$
$107$	−2.22494	+	6.84765i	−0.215093	+	0.661987i	−0.999147	+	0.0412951i	$0.986852\pi$
$108$	0.922906	+	0.670530i	0.0888066	+	0.0645218i
$109$	−8.88678			−0.851199			−0.425599	−	0.904912i	$-0.639937\pi$
$109$	−8.88678			−0.851199			−0.425599	+	0.904912i	$0.639937\pi$
$110$	−2.29063	+	2.60314i	−0.218403	+	0.248200i
$111$	7.70693			0.731509
$112$	−4.02905	−	2.92728i	−0.380710	−	0.276602i
$113$	−2.41300	+	7.42644i	−0.226996	+	0.698621i	0.771087	+	0.636730i	$0.219713\pi$
$113$	−2.41300	+	7.42644i	−0.226996	+	0.698621i	−0.998083	+	0.0618913i	$0.980287\pi$
$114$	3.39026	+	10.4341i	0.317527	+	0.977247i
$115$	−1.79600	+	1.30487i	−0.167478	+	0.121680i
$116$	−0.560478	+	0.407211i	−0.0520391	+	0.0378086i
$117$	−0.477260	−	1.46886i	−0.0441227	−	0.135796i
$118$	−1.83673	+	5.65287i	−0.169085	+	0.520389i
$119$	5.78051	+	4.19979i	0.529899	+	0.384994i
$120$	0.898304			0.0820035
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	−5.97317			−0.540785
$123$	6.05377	+	4.39832i	0.545850	+	0.396583i
$124$	−2.42232	+	7.45514i	−0.217531	+	0.669491i
$125$	−1.75953	−	5.41527i	−0.157377	−	0.484357i
$126$	1.43376	−	1.04169i	0.127729	−	0.0928008i
$127$	−6.67589	+	4.85032i	−0.592390	+	0.430396i	−0.843170	−	0.537648i	$-0.819313\pi$
$127$	−6.67589	+	4.85032i	−0.592390	+	0.430396i	0.250780	+	0.968044i	$0.419313\pi$
$128$	3.41703	+	10.5165i	0.302025	+	0.929538i
$129$	3.38489	−	10.4176i	0.298023	−	0.917220i
$130$	1.30631	+	0.949089i	0.114571	+	0.0832406i
$131$	12.1162			1.05860			0.529299	−	0.848435i	$-0.322455\pi$
$131$	12.1162			1.05860			0.529299	+	0.848435i	$0.322455\pi$
$132$	2.49942	−	2.84041i	0.217546	−	0.247226i
$133$	6.19059			0.536792
$134$	3.14191	+	2.28273i	0.271419	+	0.197198i
$135$	−0.182297	+	0.561053i	−0.0156896	+	0.0482877i
$136$	−3.36215	−	10.3476i	−0.288302	−	0.887302i
$137$	14.1212	−	10.2597i	1.20646	−	0.876541i	0.211551	−	0.977367i	$-0.432148\pi$
$137$	14.1212	−	10.2597i	1.20646	−	0.876541i	0.994904	+	0.100826i	$0.0321484\pi$
$138$	5.39544	−	3.92001i	0.459290	−	0.333694i
$139$	4.56182	+	14.0398i	0.386928	+	1.19084i	0.935072	+	0.354459i	$0.115335\pi$
$139$	4.56182	+	14.0398i	0.386928	+	1.19084i	−0.548143	+	0.836384i	$0.684665\pi$
$140$	−0.207960	+	0.640034i	−0.0175758	+	0.0540928i
$141$	−8.25777	−	5.99962i	−0.695430	−	0.505259i
$142$	−24.7101			−2.07362
$143$	−4.99793	+	1.12211i	−0.417948	+	0.0938352i
$144$	−4.98018			−0.415015
$145$	−0.289839	−	0.210580i	−0.0240698	−	0.0174877i
$146$	−1.41837	+	4.36528i	−0.117385	+	0.361273i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	7.11276	−	5.16773i	0.584666	−	0.424784i
$149$	−10.1336	+	7.36248i	−0.830175	+	0.603158i	−0.919609	−	0.392835i	$-0.871494\pi$
$149$	−10.1336	+	7.36248i	−0.830175	+	0.603158i	0.0894336	+	0.995993i	$0.471494\pi$
$150$	2.54765	+	7.84085i	0.208015	+	0.640203i
$151$	0.101534	−	0.312491i	0.00826275	−	0.0254301i	−0.946840	−	0.321704i	$-0.895744\pi$
$151$	0.101534	−	0.312491i	0.00826275	−	0.0254301i	0.955103	+	0.296274i	$0.0957443\pi$
$152$	−7.62632	−	5.54085i	−0.618577	−	0.449422i
$153$	7.14511			0.577648
$154$	−2.99680	−	5.05645i	−0.241489	−	0.407461i
$155$	−4.05366			−0.325598
$156$	−1.42538	−	1.03560i	−0.114122	−	0.0829142i
$157$	−0.828439	+	2.54967i	−0.0661167	+	0.203486i	−0.978657	−	0.205501i	$-0.934118\pi$
$157$	−0.828439	+	2.54967i	−0.0661167	+	0.203486i	0.912540	+	0.408987i	$0.134118\pi$
$158$	−2.55396	−	7.86028i	−0.203182	−	0.625330i
$159$	5.69927	−	4.14076i	0.451982	−	0.328384i
$160$	2.75881	−	2.00439i	0.218103	−	0.158461i
$161$	−1.16287	−	3.57896i	−0.0916474	−	0.282062i
$162$	0.547647	−	1.68548i	0.0430272	−	0.132424i
$163$	0.721375	+	0.524109i	0.0565024	+	0.0410514i	0.615678	−	0.787998i	$-0.288882\pi$
$163$	0.721375	+	0.524109i	0.0565024	+	0.0410514i	−0.559176	+	0.829049i	$0.688882\pi$
$164$	8.53627			0.666570
$165$	1.79637	+	0.775356i	0.139848	+	0.0603614i
$166$	−6.21997			−0.482764
$167$	−9.35307	−	6.79540i	−0.723762	−	0.525844i	0.163822	−	0.986490i	$-0.447618\pi$
$167$	−9.35307	−	6.79540i	−0.723762	−	0.525844i	−0.887584	+	0.460646i	$0.847618\pi$
$168$	−0.470553	+	1.44821i	−0.0363039	+	0.111732i
$169$	−3.28012	−	10.0952i	−0.252317	−	0.776551i
$170$	−6.04341	+	4.39080i	−0.463509	+	0.336759i
$171$	5.00829	−	3.63874i	0.382994	−	0.278261i
$172$	−3.86139	−	11.8841i	−0.294428	−	0.906158i
$173$	2.77784	−	8.54930i	0.211195	−	0.649991i	−0.788207	−	0.615410i	$-0.788990\pi$
$173$	2.77784	−	8.54930i	0.211195	−	0.649991i	0.999402	−	0.0345809i	$-0.0110096\pi$
$174$	0.870718	+	0.632614i	0.0660090	+	0.0479583i
$175$	4.65199			0.351657
$176$	−1.53896	+	16.4455i	−0.116004	+	1.23963i
$177$	3.35386			0.252091
$178$	−11.6865	−	8.49074i	−0.875940	−	0.636408i
$179$	−1.89919	+	5.84510i	−0.141952	+	0.436883i	−0.996606	−	0.0823141i	$-0.973769\pi$
$179$	−1.89919	+	5.84510i	−0.141952	+	0.436883i	0.854655	+	0.519197i	$0.173769\pi$
$180$	0.207960	+	0.640034i	0.0155004	+	0.0477053i
$181$	−12.1079	+	8.79692i	−0.899975	+	0.653870i	−0.938459	−	0.345389i	$-0.887747\pi$
$181$	−12.1079	+	8.79692i	−0.899975	+	0.653870i	0.0384849	+	0.999259i	$0.487747\pi$
$182$	−2.21436	+	1.60883i	−0.164139	+	0.119254i
$183$	1.04152	+	3.20548i	0.0769916	+	0.236956i
$184$	−1.77076	+	5.44983i	−0.130542	+	0.401767i
$185$	3.67821	+	2.67237i	0.270427	+	0.196477i
$186$	12.1778			0.892918
$187$	2.20796	−	23.5946i	0.161462	−	1.72540i
$188$	−11.6441			−0.849231
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	−2.00000	+	6.15537i	−0.145095	+	0.446557i
$191$	3.05108	+	9.39026i	0.220768	+	0.679456i	0.998694	+	0.0510986i	$0.0162723\pi$
$191$	3.05108	+	9.39026i	0.220768	+	0.679456i	−0.777925	+	0.628357i	$0.783728\pi$
$192$	−0.229756	+	0.166927i	−0.0165812	+	0.0120469i
$193$	5.00064	−	3.63318i	0.359954	−	0.261522i	−0.393079	−	0.919505i	$-0.628590\pi$
$193$	5.00064	−	3.63318i	0.359954	−	0.261522i	0.753033	+	0.657983i	$0.228590\pi$
$194$	−2.62711	−	8.08543i	−0.188616	−	0.580500i
$195$	0.281548	−	0.866516i	0.0201621	−	0.0620525i
$196$	−0.922906	−	0.670530i	−0.0659218	−	0.0478950i
$197$	−19.0720			−1.35882			−0.679412	−	0.733757i	$-0.737765\pi$
$197$	−19.0720			−1.35882			−0.679412	+	0.733757i	$0.737765\pi$
$198$	−5.39657	−	2.32928i	−0.383517	−	0.165535i
$199$	−11.8479			−0.839878			−0.419939	−	0.907552i	$-0.637948\pi$
$199$	−11.8479			−0.839878			−0.419939	+	0.907552i	$0.637948\pi$
$200$	−5.73089	−	4.16373i	−0.405235	−	0.294420i
$201$	0.677173	−	2.08412i	0.0477641	−	0.147003i
$202$	−0.781304	−	2.40461i	−0.0549723	−	0.169187i
$203$	0.491314	−	0.356961i	0.0344835	−	0.0250537i
$204$	6.59426	−	4.79101i	0.461691	−	0.335438i
$205$	1.36411	+	4.19829i	0.0952733	+	0.293221i
$206$	9.64803	−	29.6936i	0.672210	−	2.06885i
$207$	−3.04445	−	2.21192i	−0.211604	−	0.153739i
$208$	7.69162			0.533318
$209$	−10.4682	−	17.6628i	−0.724099	−	1.22176i
$210$	1.04548			0.0721450
$211$	16.9740	+	12.3324i	1.16854	+	0.848994i	0.990833	−	0.135089i	$-0.0431322\pi$
$211$	16.9740	+	12.3324i	1.16854	+	0.848994i	0.177707	+	0.984084i	$0.443132\pi$
$212$	2.48338	−	7.64307i	0.170560	−	0.524928i
$213$	4.30862	+	13.2606i	0.295222	+	0.908600i
$214$	10.3231	−	7.50019i	0.705674	−	0.512702i
$215$	5.22778	−	3.79820i	0.356531	−	0.259035i
$216$	0.470553	+	1.44821i	0.0320170	+	0.0985383i
$217$	2.12340	−	6.53516i	0.144146	−	0.443636i
$218$	12.7415	+	9.25724i	0.862963	+	0.626979i
$219$	2.58993			0.175011
$220$	2.17778	−	0.488943i	0.146826	−	0.0329645i
$221$	−11.0352			−0.742310
$222$	−11.0499	−	8.02820i	−0.741619	−	0.538818i
$223$	1.04714	−	3.22275i	0.0701214	−	0.215811i	−0.909855	−	0.414927i	$-0.863807\pi$
$223$	1.04714	−	3.22275i	0.0701214	−	0.215811i	0.979976	+	0.199116i	$0.0638070\pi$
$224$	1.78628	+	5.49760i	0.119351	+	0.367324i
$225$	3.76354	−	2.73437i	0.250902	−	0.182291i
$226$	11.1957	−	8.13414i	0.744725	−	0.541075i
$227$	5.99409	+	18.4479i	0.397841	+	1.22443i	0.926726	+	0.375737i	$0.122610\pi$
$227$	5.99409	+	18.4479i	0.397841	+	1.22443i	−0.528885	+	0.848693i	$0.677390\pi$
$228$	2.18230	−	6.71642i	0.144526	−	0.444806i
$229$	7.98018	+	5.79794i	0.527345	+	0.383139i	0.819364	−	0.573274i	$-0.194327\pi$
$229$	7.98018	+	5.79794i	0.527345	+	0.383139i	−0.292019	+	0.956413i	$0.594327\pi$
$230$	3.93429			0.259419
$231$	−2.19098	+	2.48990i	−0.144156	+	0.163823i
$232$	−0.924756			−0.0607132
$233$	−5.76521	−	4.18867i	−0.377691	−	0.274409i	0.382702	−	0.923872i	$-0.374994\pi$
$233$	−5.76521	−	4.18867i	−0.377691	−	0.274409i	−0.760393	+	0.649463i	$0.774994\pi$
$234$	−0.845811	+	2.60314i	−0.0552924	+	0.170173i
$235$	−1.86074	−	5.72676i	−0.121381	−	0.373573i
$236$	3.09529	−	2.24886i	0.201486	−	0.146388i
$237$	−3.77286	+	2.74114i	−0.245074	+	0.178056i
$238$	−3.91300	−	12.0430i	−0.253642	−	0.780630i
$239$	6.88781	−	21.1985i	0.445535	−	1.37122i	−0.436360	−	0.899772i	$-0.643733\pi$
$239$	6.88781	−	21.1985i	0.445535	−	1.37122i	0.881895	−	0.471445i	$-0.156267\pi$
$240$	−2.37684	−	1.72688i	−0.153424	−	0.111469i
$241$	14.8753			0.958199			0.479100	−	0.877761i	$-0.340963\pi$
$241$	14.8753			0.958199			0.479100	+	0.877761i	$0.340963\pi$
$242$	−9.35938	+	17.1008i	−0.601644	+	1.09928i
$243$	−1.00000			−0.0641500
$244$	3.11060	+	2.25998i	0.199136	+	0.144680i
$245$	0.182297	−	0.561053i	0.0116465	−	0.0358443i
$246$	−4.09797	−	12.6123i	−0.261277	−	0.804128i
$247$	−7.73503	+	5.61983i	−0.492168	+	0.357581i
$248$	−8.46512	+	6.15027i	−0.537536	+	0.390543i
$249$	1.08456	+	3.33793i	0.0687310	+	0.211532i
$250$	−3.11828	+	9.59707i	−0.197217	+	0.606972i
$251$	20.9724	+	15.2373i	1.32376	+	0.961771i	0.999877	+	0.0156760i	$0.00499002\pi$
$251$	20.9724	+	15.2373i	1.32376	+	0.961771i	0.323888	+	0.946096i	$0.395010\pi$
$252$	−1.14077			−0.0718620
$253$	−8.24498	+	9.36984i	−0.518357	+	0.589077i
$254$	14.6241			0.917600
$255$	3.41007	+	2.47756i	0.213547	+	0.155151i
$256$	6.23125	−	19.1778i	0.389453	−	1.19861i
$257$	0.269300	+	0.828821i	0.0167985	+	0.0517004i	0.959104	−	0.283053i	$-0.0913471\pi$
$257$	0.269300	+	0.828821i	0.0167985	+	0.0517004i	−0.942306	+	0.334753i	$0.891347\pi$
$258$	−15.7050	+	11.4104i	−0.977751	+	0.710378i
$259$	−6.23503	+	4.53002i	−0.387426	+	0.281482i
$260$	−0.321183	−	0.988498i	−0.0199189	−	0.0613041i
$261$	0.187665	−	0.577574i	0.0116162	−	0.0357510i
$262$	−17.3717	−	12.6213i	−1.07323	−	0.779746i
$263$	26.8873			1.65794			0.828970	−	0.559293i	$-0.188927\pi$
$263$	26.8873			1.65794			0.828970	+	0.559293i	$0.188927\pi$
$264$	4.92769	−	1.10634i	0.303278	−	0.0680902i
$265$	4.15584			0.255291
$266$	−8.87581	−	6.44865i	−0.544211	−	0.395392i
$267$	−2.51878	+	7.75202i	−0.154147	+	0.474416i
$268$	−0.772501	−	2.37751i	−0.0471880	−	0.145230i
$269$	0.803010	−	0.583421i	0.0489604	−	0.0355718i	−0.563036	−	0.826432i	$-0.690367\pi$
$269$	0.803010	−	0.583421i	0.0489604	−	0.0355718i	0.611996	+	0.790861i	$0.290367\pi$
$270$	0.845811	−	0.614518i	0.0514744	−	0.0373984i
$271$	8.30174	+	25.5501i	0.504295	+	1.55206i	0.801953	+	0.597388i	$0.203795\pi$
$271$	8.30174	+	25.5501i	0.504295	+	1.55206i	−0.297658	+	0.954673i	$0.596205\pi$
$272$	−10.9960	+	33.8423i	−0.666733	+	2.05199i
$273$	1.24948	+	0.907802i	0.0756221	+	0.0549427i
$274$	−30.9337			−1.86878
$275$	−7.86643	−	13.2729i	−0.474364	−	0.800387i
$276$	−4.29289			−0.258402
$277$	22.3533	+	16.2406i	1.34308	+	0.975805i	0.999325	+	0.0367459i	$0.0116992\pi$
$277$	22.3533	+	16.2406i	1.34308	+	0.975805i	0.343756	+	0.939059i	$0.388301\pi$
$278$	8.08456	−	24.8817i	0.484880	−	1.49231i
$279$	−2.12340	−	6.53516i	−0.127125	−	0.391250i
$280$	−0.726743	+	0.528010i	−0.0434312	+	0.0315546i
$281$	−19.2884	+	14.0138i	−1.15065	+	0.835996i	−0.988567	−	0.150781i	$-0.951821\pi$
$281$	−19.2884	+	14.0138i	−1.15065	+	0.835996i	−0.162083	+	0.986777i	$0.551821\pi$
$282$	5.58993	+	17.2040i	0.332875	+	1.02448i
$283$	2.70308	−	8.31922i	0.160681	−	0.494527i	−0.838011	−	0.545654i	$-0.816281\pi$
$283$	2.70308	−	8.31922i	0.160681	−	0.494527i	0.998692	+	0.0511272i	$0.0162814\pi$
$284$	12.8681	+	9.34920i	0.763579	+	0.554773i
$285$	3.65199			0.216325
$286$	8.33471	+	3.59745i	0.492842	+	0.212722i
$287$	−7.48287			−0.441700
$288$	4.67653	+	3.39770i	0.275567	+	0.200211i
$289$	10.5228	−	32.3859i	0.618990	−	1.90505i
$290$	0.196200	+	0.603842i	0.0115213	+	0.0354588i
$291$	−3.88093	+	2.81966i	−0.227504	+	0.165292i
$292$	2.39026	−	1.73662i	0.139879	−	0.101628i
$293$	−6.06451	−	18.6646i	−0.354292	−	1.09040i	−0.956419	−	0.291999i	$-0.905680\pi$
$293$	−6.06451	−	18.6646i	−0.354292	−	1.09040i	0.602126	−	0.798401i	$-0.294320\pi$
$294$	−0.547647	+	1.68548i	−0.0319394	+	0.0982994i
$295$	1.60066	+	1.16295i	0.0931942	+	0.0677095i
$296$	11.7356			0.682120
$297$	−0.309017	+	3.30220i	−0.0179310	+	0.191613i
$298$	22.1985			1.28592
$299$	4.70198	+	3.41619i	0.271923	+	0.197563i
$300$	1.63991	−	5.04713i	0.0946804	−	0.291396i
$301$	3.38489	+	10.4176i	0.195102	+	0.600461i
$302$	−0.471093	+	0.342269i	−0.0271084	+	0.0196954i
$303$	−1.15419	+	0.838567i	−0.0663064	+	0.0481744i
$304$	9.52707	+	29.3213i	0.546415	+	1.68169i
$305$	−0.614421	+	1.89099i	−0.0351817	+	0.108278i
$306$	−10.2444	−	7.44296i	−0.585631	−	0.425486i
$307$	−17.0835			−0.975009			−0.487504	−	0.873121i	$-0.662093\pi$
$307$	−17.0835			−0.975009			−0.487504	+	0.873121i	$0.662093\pi$
$308$	−0.352519	+	3.76706i	−0.0200866	+	0.214648i
$309$	−17.6172			−1.00221
$310$	5.81197	+	4.22264i	0.330098	+	0.239830i
$311$	−2.23528	+	6.87948i	−0.126751	+	0.390099i	−0.994216	−	0.107399i	$-0.965748\pi$
$311$	−2.23528	+	6.87948i	−0.126751	+	0.390099i	0.867465	+	0.497498i	$0.165748\pi$
$312$	−0.726743	−	2.23668i	−0.0411437	−	0.126627i
$313$	−11.1470	+	8.09877i	−0.630065	+	0.457769i	−0.856423	−	0.516275i	$-0.827318\pi$
$313$	−11.1470	+	8.09877i	−0.630065	+	0.457769i	0.226357	+	0.974044i	$0.427318\pi$
$314$	3.84374	−	2.79264i	0.216915	−	0.157598i
$315$	−0.182297	−	0.561053i	−0.0102713	−	0.0316117i
$316$	−1.64398	+	5.05964i	−0.0924808	+	0.284627i
$317$	5.62775	+	4.08880i	0.316086	+	0.229650i	0.734504	−	0.678605i	$-0.237415\pi$
$317$	5.62775	+	4.08880i	0.316086	+	0.229650i	−0.418417	+	0.908255i	$0.637415\pi$
$318$	−12.4848			−0.700111
$319$	−1.84927	−	0.798188i	−0.103539	−	0.0446900i
$320$	−0.167535			−0.00936550
$321$	−5.82496	−	4.23208i	−0.325118	−	0.236212i
$322$	−2.06087	+	6.34272i	−0.114848	+	0.353466i
$323$	−13.6686	−	42.0675i	−0.760540	−	2.34070i
$324$	−0.922906	+	0.670530i	−0.0512725	+	0.0372517i
$325$	−5.81258	+	4.22309i	−0.322424	+	0.234255i
$326$	−0.488319	−	1.50289i	−0.0270455	−	0.0832375i
$327$	2.74617	−	8.45183i	0.151863	−	0.467387i
$328$	9.21832	+	6.69750i	0.508997	+	0.369808i
$329$	10.2072			0.562739
$330$	−1.76789	−	2.98293i	−0.0973191	−	0.164205i
$331$	−29.6698			−1.63080			−0.815401	−	0.578896i	$-0.803484\pi$
$331$	−29.6698			−1.63080			−0.815401	+	0.578896i	$0.803484\pi$
$332$	3.23912	+	2.35336i	0.177770	+	0.129157i
$333$	−2.38157	+	7.32972i	−0.130509	+	0.401666i
$334$	6.33136	+	19.4859i	0.346437	+	1.06622i
$335$	1.04586	−	0.759860i	0.0571413	−	0.0415156i
$336$	4.02905	−	2.92728i	0.219803	−	0.159696i
$337$	6.04791	+	18.6135i	0.329451	+	1.01394i	0.969391	+	0.245520i	$0.0789588\pi$
$337$	6.04791	+	18.6135i	0.329451	+	1.01394i	−0.639941	+	0.768424i	$0.721041\pi$
$338$	−5.81310	+	17.8909i	−0.316191	+	0.973136i
$339$	−6.31731	−	4.58979i	−0.343109	−	0.249283i
$340$	4.80846			0.260775
$341$	−22.2366	+	4.99242i	−1.20418	+	0.270355i
$342$	−10.9711			−0.593249
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	5.15431	−	15.8633i	0.277902	−	0.855293i
$345$	−0.686010	−	2.11132i	−0.0369335	−	0.113670i
$346$	−12.8884	+	9.36399i	−0.692886	+	0.503411i
$347$	5.25201	−	3.81581i	0.281943	−	0.204843i	−0.437822	−	0.899062i	$-0.644250\pi$
$347$	5.25201	−	3.81581i	0.281943	−	0.204843i	0.719764	+	0.694218i	$0.244250\pi$
$348$	−0.214084	−	0.658882i	−0.0114761	−	0.0353198i
$349$	2.43495	−	7.49400i	0.130340	−	0.401144i	−0.864496	−	0.502639i	$-0.832362\pi$
$349$	2.43495	−	7.49400i	0.130340	−	0.401144i	0.994836	+	0.101495i	$0.0323625\pi$
$350$	−6.66983	−	4.84591i	−0.356517	−	0.259025i
$351$	1.54445			0.0824364
$352$	12.6650	−	14.3929i	0.675047	−	0.767144i
$353$	−5.34594			−0.284536			−0.142268	−	0.989828i	$-0.545439\pi$
$353$	−5.34594			−0.284536			−0.142268	+	0.989828i	$0.545439\pi$
$354$	−4.80862	−	3.49367i	−0.255575	−	0.185686i
$355$	−2.54177	+	7.82276i	−0.134903	+	0.415189i
$356$	2.87336	+	8.84330i	0.152288	+	0.468694i
$357$	−5.78051	+	4.19979i	−0.305937	+	0.222276i
$358$	8.81173	−	6.40210i	0.465715	−	0.338361i
$359$	−5.51643	−	16.9778i	−0.291146	−	0.896056i	−0.984489	−	0.175448i	$-0.943863\pi$
$359$	−5.51643	−	16.9778i	−0.291146	−	0.896056i	0.693343	−	0.720608i	$-0.256137\pi$
$360$	−0.277591	+	0.854338i	−0.0146303	+	0.0450275i
$361$	−15.6329	−	11.3580i	−0.822786	−	0.597789i
$362$	26.5235			1.39404
$363$	10.8090	+	2.04087i	0.567326	+	0.107118i
$364$	1.76186			0.0923467
$365$	1.23607	+	0.898056i	0.0646988	+	0.0470064i
$366$	1.84581	−	5.68082i	0.0964821	−	0.296941i
$367$	−9.25065	−	28.4706i	−0.482880	−	1.48615i	−0.835028	−	0.550207i	$-0.814549\pi$
$367$	−9.25065	−	28.4706i	−0.482880	−	1.48615i	0.352148	−	0.935944i	$-0.385451\pi$
$368$	15.1619	−	11.0158i	0.790368	−	0.574236i
$369$	−6.05377	+	4.39832i	−0.315147	+	0.228967i
$370$	−2.48988	−	7.66308i	−0.129443	−	0.398384i
$371$	−2.17693	+	6.69990i	−0.113021	+	0.347841i
$372$	−6.34172	−	4.60753i	−0.328803	−	0.238889i
$373$	23.4915			1.21635			0.608173	−	0.793805i	$-0.291903\pi$
$373$	23.4915			1.21635			0.608173	+	0.793805i	$0.291903\pi$
$374$	−27.7438	+	31.5289i	−1.43460	+	1.63032i
$375$	5.69396			0.294035
$376$	−12.5744	−	9.13587i	−0.648477	−	0.471146i
$377$	−0.289839	+	0.892032i	−0.0149275	+	0.0459420i
$378$	0.547647	+	1.68548i	0.0281679	+	0.0866919i
$379$	25.4462	−	18.4877i	1.30708	−	0.949650i	0.307084	−	0.951683i	$-0.400647\pi$
$379$	25.4462	−	18.4877i	1.30708	−	0.949650i	0.999998	+	0.00203230i	$0.000646901\pi$
$380$	3.37044	−	2.44877i	0.172900	−	0.125619i
$381$	−2.54996	−	7.84798i	−0.130639	−	0.402064i
$382$	5.40720	−	16.6416i	0.276656	−	0.851460i
$383$	4.55274	+	3.30776i	0.232634	+	0.169018i	0.697995	−	0.716102i	$-0.254076\pi$
$383$	4.55274	+	3.30776i	0.232634	+	0.169018i	−0.465361	+	0.885121i	$0.654076\pi$
$384$	−11.0577			−0.564287
$385$	−1.90904	+	0.428606i	−0.0972937	+	0.0218438i
$386$	−10.9543			−0.557561
$387$	8.86175	+	6.43844i	0.450468	+	0.327284i
$388$	−1.69107	+	5.20456i	−0.0858508	+	0.264222i
$389$	8.06758	+	24.8295i	0.409043	+	1.25890i	0.917472	+	0.397800i	$0.130226\pi$
$389$	8.06758	+	24.8295i	0.409043	+	1.25890i	−0.508430	+	0.861104i	$0.669774\pi$
$390$	−1.30631	+	0.949089i	−0.0661475	+	0.0480590i
$391$	−21.7529	+	15.8044i	−1.10009	+	0.799263i
$392$	−0.470553	−	1.44821i	−0.0237665	−	0.0731457i
$393$	−3.74411	+	11.5232i	−0.188866	+	0.581269i
$394$	27.3447	+	19.8671i	1.37760	+	1.00089i
$395$	−2.75113			−0.138424
$396$	1.92903	+	3.25482i	0.0969374	+	0.163561i
$397$	10.3828			0.521096			0.260548	−	0.965461i	$-0.416097\pi$
$397$	10.3828			0.521096			0.260548	+	0.965461i	$0.416097\pi$
$398$	16.9871	+	12.3418i	0.851485	+	0.618640i
$399$	−1.91300	+	5.88760i	−0.0957696	+	0.294749i
$400$	7.15923	+	22.0338i	0.357961	+	1.10169i
$401$	−2.98427	+	2.16820i	−0.149027	+	0.108275i	−0.659801	−	0.751441i	$-0.729359\pi$
$401$	−2.98427	+	2.16820i	−0.149027	+	0.108275i	0.510773	+	0.859716i	$0.329359\pi$
$402$	−3.14191	+	2.28273i	−0.156704	+	0.113852i
$403$	3.27948	+	10.0932i	0.163363	+	0.502778i
$404$	−0.502923	+	1.54784i	−0.0250213	+	0.0770078i
$405$	−0.477260	−	0.346750i	−0.0237152	−	0.0172301i
$406$	−1.07627			−0.0534142
$407$	23.4682	+	10.1294i	1.16328	+	0.502097i
$408$	10.8801			0.538647
$409$	−0.873919	−	0.634940i	−0.0432125	−	0.0313957i	0.565969	−	0.824426i	$-0.308502\pi$
$409$	−0.873919	−	0.634940i	−0.0432125	−	0.0313957i	−0.609182	+	0.793031i	$0.708502\pi$
$410$	2.41750	−	7.44030i	0.119392	−	0.367450i
$411$	5.39382	+	16.6005i	0.266057	+	0.818841i
$412$	−16.2591	+	11.8129i	−0.801026	+	0.581979i
$413$	−2.71333	+	1.97135i	−0.133514	+	0.0970037i
$414$	2.06087	+	6.34272i	0.101286	+	0.311727i
$415$	−0.639809	+	1.96913i	−0.0314070	+	0.0966607i
$416$	−7.22265	−	5.24756i	−0.354120	−	0.257283i
$417$	−14.7624			−0.722915
$418$	−3.39026	+	36.2287i	−0.165823	+	1.77201i
$419$	10.0766			0.492273			0.246136	−	0.969235i	$-0.420839\pi$
$419$	10.0766			0.492273			0.246136	+	0.969235i	$0.420839\pi$
$420$	−0.544446	−	0.395563i	−0.0265662	−	0.0193015i
$421$	3.70069	−	11.3895i	0.180360	−	0.555092i	−0.819477	−	0.573112i	$-0.805736\pi$
$421$	3.70069	−	11.3895i	0.180360	−	0.555092i	0.999838	+	0.0180196i	$0.00573612\pi$
$422$	−11.4902	−	35.3632i	−0.559335	−	1.72145i
$423$	8.25777	−	5.99962i	0.401507	−	0.291712i
$424$	8.67851	−	6.30531i	0.421466	−	0.306213i
$425$	−10.2714	−	31.6121i	−0.498236	−	1.53341i
$426$	7.63584	−	23.5007i	0.369958	−	1.13861i
$427$	−2.72674	−	1.98109i	−0.131956	−	0.0958719i
$428$	−8.21363			−0.397021
$429$	0.477260	−	5.10007i	0.0230423	−	0.246233i
$430$	−11.4519			−0.552260
$431$	0.443784	+	0.322428i	0.0213763	+	0.0155308i	0.598422	−	0.801181i	$-0.295795\pi$
$431$	0.443784	+	0.322428i	0.0213763	+	0.0155308i	−0.577046	+	0.816712i	$0.695795\pi$
$432$	1.53896	−	4.73644i	0.0740433	−	0.227882i
$433$	6.05298	+	18.6292i	0.290888	+	0.895260i	0.984572	+	0.174981i	$0.0559864\pi$
$433$	6.05298	+	18.6292i	0.290888	+	0.895260i	−0.693684	+	0.720279i	$0.744014\pi$
$434$	−9.85203	+	7.15792i	−0.472913	+	0.343591i
$435$	0.289839	−	0.210580i	0.0138967	−	0.0100966i
$436$	−3.13275	−	9.64162i	−0.150032	−	0.461750i
$437$	−7.19888	+	22.1559i	−0.344369	+	1.05986i
$438$	−3.71333	−	2.69789i	−0.177430	−	0.128910i
$439$	37.4069			1.78533			0.892667	−	0.450716i	$-0.148831\pi$
$439$	37.4069			1.78533			0.892667	+	0.450716i	$0.148831\pi$
$440$	2.73541	+	1.18067i	0.130406	+	0.0562860i
$441$	1.00000			0.0476190
$442$	15.8219	+	11.4953i	0.752569	+	0.546773i
$443$	6.62774	−	20.3981i	0.314893	−	0.969142i	−0.660905	−	0.750469i	$-0.729827\pi$
$443$	6.62774	−	20.3981i	0.314893	−	0.969142i	0.975798	−	0.218672i	$-0.0701726\pi$
$444$	2.71683	+	8.36156i	0.128935	+	0.396822i
$445$	−3.89012	+	2.82634i	−0.184410	+	0.133981i
$446$	−4.85844	+	3.52986i	−0.230054	+	0.167144i
$447$	−3.87068	−	11.9127i	−0.183077	−	0.563453i
$448$	0.0877588	−	0.270094i	0.00414621	−	0.0127607i
$449$	−5.17693	−	3.76126i	−0.244314	−	0.177505i	0.458889	−	0.888494i	$-0.348248\pi$
$449$	−5.17693	−	3.76126i	−0.244314	−	0.177505i	−0.703203	+	0.710989i	$0.748248\pi$
$450$	−8.24436			−0.388643
$451$	12.6534	+	21.3499i	0.595826	+	1.00533i
$452$	−8.90787			−0.418991
$453$	0.265820	+	0.193130i	0.0124893	+	0.00907403i
$454$	10.6229	−	32.6938i	0.498555	−	1.53440i
$455$	0.281548	+	0.866516i	0.0131992	+	0.0406229i
$456$	7.62632	−	5.54085i	0.357135	−	0.259474i
$457$	29.8875	−	21.7145i	1.39808	−	1.01576i	0.403155	−	0.915132i	$-0.367914\pi$
$457$	29.8875	−	21.7145i	1.39808	−	1.01576i	0.994924	−	0.100632i	$-0.0320865\pi$
$458$	−5.40202	−	16.6257i	−0.252420	−	0.776868i
$459$	−2.20796	+	6.79540i	−0.103059	+	0.317182i
$460$	−2.04883	−	1.48856i	−0.0955270	−	0.0694045i
$461$	7.39825			0.344571			0.172285	−	0.985047i	$-0.444885\pi$
$461$	7.39825			0.344571			0.172285	+	0.985047i	$0.444885\pi$
$462$	5.73503	−	1.28760i	0.266818	−	0.0599044i
$463$	−14.3717			−0.667910			−0.333955	−	0.942589i	$-0.608383\pi$
$463$	−14.3717			−0.667910			−0.333955	+	0.942589i	$0.608383\pi$
$464$	2.44683	+	1.77773i	0.113591	+	0.0825290i
$465$	1.25265	−	3.85526i	0.0580902	−	0.178783i
$466$	3.90264	+	12.0111i	0.180786	+	0.556403i
$467$	−29.2562	+	21.2559i	−1.35382	+	0.983604i	−0.355004	+	0.934865i	$0.615520\pi$
$467$	−29.2562	+	21.2559i	−1.35382	+	0.983604i	−0.998812	+	0.0487394i	$0.984480\pi$
$468$	1.42538	−	1.03560i	0.0658881	−	0.0478705i
$469$	0.677173	+	2.08412i	0.0312689	+	0.0962359i
$470$	−3.29764	+	10.1491i	−0.152109	+	0.468143i
$471$	−2.16888	−	1.57579i	−0.0999368	−	0.0726083i
$472$	5.10705			0.235071
$473$	23.9994	−	27.2737i	1.10350	−	1.25404i
$474$	8.26479			0.379614
$475$	−23.2985	−	16.9274i	−1.06901	−	0.776680i
$476$	−2.51878	+	7.75202i	−0.115448	+	0.355313i
$477$	2.17693	+	6.69990i	0.0996747	+	0.306767i
$478$	−31.9577	+	23.2186i	−1.46171	+	1.06199i
$479$	−12.9647	+	9.41941i	−0.592372	+	0.430384i	−0.843163	−	0.537658i	$-0.819309\pi$
$479$	−12.9647	+	9.41941i	−0.592372	+	0.430384i	0.250791	+	0.968041i	$0.419309\pi$
$480$	1.05377	+	3.24317i	0.0480978	+	0.148030i
$481$	3.67821	−	11.3204i	0.167712	−	0.516164i
$482$	−21.3275	−	15.4953i	−0.971442	−	0.705794i
$483$	3.76314			0.171229
$484$	11.3442	−	5.36424i	0.515644	−	0.243829i
$485$	−2.82993			−0.128501
$486$	1.43376	+	1.04169i	0.0650366	+	0.0472519i
$487$	0.479160	−	1.47470i	0.0217128	−	0.0668251i	−0.939613	−	0.342239i	$-0.888815\pi$
$487$	0.479160	−	1.47470i	0.0217128	−	0.0668251i	0.961326	+	0.275414i	$0.0888148\pi$
$488$	1.58597	+	4.88111i	0.0717934	+	0.220957i
$489$	−0.721375	+	0.524109i	−0.0326217	+	0.0237010i
$490$	−0.845811	+	0.614518i	−0.0382099	+	0.0277611i
$491$	−0.0102481	−	0.0315404i	−0.000462490	−	0.00142340i	0.950825	−	0.309729i	$-0.100238\pi$
$491$	−0.0102481	−	0.0315404i	−0.000462490	−	0.00142340i	−0.951287	+	0.308305i	$0.900238\pi$
$492$	−2.63785	+	8.11847i	−0.118924	+	0.366009i
$493$	−3.51049	−	2.55052i	−0.158105	−	0.114870i
$494$	16.9443			0.762359
$495$	−1.29252	+	1.46886i	−0.0580943	+	0.0660201i
$496$	34.2212			1.53658
$497$	−11.2801	−	8.19549i	−0.505982	−	0.367618i
$498$	1.92208	−	5.91555i	0.0861304	−	0.265082i
$499$	−8.35317	−	25.7084i	−0.373939	−	1.15087i	−0.944192	−	0.329397i	$-0.893155\pi$
$499$	−8.35317	−	25.7084i	−0.373939	−	1.15087i	0.570252	−	0.821470i	$-0.306845\pi$
$500$	5.25498	−	3.81797i	0.235010	−	0.170745i
$501$	9.35307	−	6.79540i	0.417864	−	0.303596i
$502$	−14.1968	−	43.6933i	−0.633635	−	1.95013i
$503$	−9.06474	+	27.8984i	−0.404177	+	1.24393i	0.517404	+	0.855741i	$0.326899\pi$
$503$	−9.06474	+	27.8984i	−0.404177	+	1.24393i	−0.921581	+	0.388187i	$0.873101\pi$
$504$	−1.23192	−	0.895044i	−0.0548742	−	0.0398684i
$505$	−0.841621			−0.0374516
$506$	21.5817	−	4.84540i	0.959426	−	0.215404i
$507$	10.6147			0.471415
$508$	−7.61569	−	5.53312i	−0.337891	−	0.245493i
$509$	−5.13984	+	15.8188i	−0.227819	+	0.701156i	0.770174	+	0.637834i	$0.220169\pi$
$509$	−5.13984	+	15.8188i	−0.227819	+	0.701156i	−0.997993	+	0.0633219i	$0.979831\pi$
$510$	−2.30838	−	7.10446i	−0.102217	−	0.314591i
$511$	−2.09529	+	1.52232i	−0.0926903	+	0.0673435i
$512$	−11.0196	+	8.00620i	−0.487002	+	0.353828i
$513$	1.91300	+	5.88760i	0.0844609	+	0.259944i
$514$	0.477260	−	1.46886i	0.0210510	−	0.0647884i
$515$	−8.40801	−	6.10877i	−0.370501	−	0.269185i
$516$	12.4957			0.550094
$517$	−17.2602	−	29.1228i	−0.759101	−	1.28082i
$518$	13.6584			0.600115
$519$	7.27247	+	5.28376i	0.319226	+	0.231931i
$520$	0.428724	−	1.31948i	0.0188008	−	0.0578629i
$521$	11.0913	+	34.1356i	0.485920	+	1.49551i	0.830644	+	0.556805i	$0.187973\pi$
$521$	11.0913	+	34.1356i	0.485920	+	1.49551i	−0.344723	+	0.938704i	$0.612027\pi$
$522$	−0.870718	+	0.632614i	−0.0381103	+	0.0276888i
$523$	−5.88861	+	4.27833i	−0.257491	+	0.187078i	−0.709040	−	0.705168i	$-0.750872\pi$
$523$	−5.88861	+	4.27833i	−0.257491	+	0.187078i	0.451549	+	0.892246i	$0.350872\pi$
$524$	4.27119	+	13.1454i	0.186588	+	0.574258i
$525$	−1.43754	+	4.42430i	−0.0627395	+	0.193092i
$526$	−38.5498	−	28.0081i	−1.68085	−	1.22121i
$527$	−49.0974			−2.13872
$528$	−15.1651	−	6.54559i	−0.659975	−	0.284860i
$529$	−8.83876			−0.384294
$530$	−5.95848	−	4.32909i	−0.258820	−	0.188044i
$531$	−1.03640	+	3.18971i	−0.0449759	+	0.138422i
$532$	2.18230	+	6.71642i	0.0946146	+	0.291194i
$533$	9.34972	−	6.79297i	0.404981	−	0.294236i
$534$	11.6865	−	8.49074i	0.505724	−	0.367430i
$535$	−1.31255	−	4.03961i	−0.0567464	−	0.174647i
$536$	1.03116	−	3.17358i	0.0445393	−	0.137078i
$537$	−4.97214	−	3.61247i	−0.214564	−	0.155890i
$538$	−1.75906			−0.0758386
$539$	0.309017	−	3.30220i	0.0133103	−	0.142236i
$540$	−0.672972			−0.0289601
$541$	8.47110	+	6.15462i	0.364201	+	0.264608i	0.754802	−	0.655952i	$-0.227733\pi$
$541$	8.47110	+	6.15462i	0.364201	+	0.264608i	−0.390601	+	0.920560i	$0.627733\pi$
$542$	14.7125	−	45.2805i	0.631958	−	1.94497i
$543$	−4.62481	−	14.2337i	−0.198470	−	0.610827i
$544$	33.4143	−	24.2769i	1.43263	−	1.04087i
$545$	4.24130	−	3.08149i	0.181677	−	0.131996i
$546$	−0.845811	−	2.60314i	−0.0361974	−	0.111404i
$547$	2.52346	−	7.76642i	0.107895	−	0.332068i	−0.882504	−	0.470305i	$-0.844144\pi$
$547$	2.52346	−	7.76642i	0.107895	−	0.332068i	0.990399	+	0.138238i	$0.0441437\pi$
$548$	16.1091	+	11.7039i	0.688147	+	0.499968i
$549$	−3.37044			−0.143847
$550$	−2.54765	+	27.2245i	−0.108632	+	1.16086i
$551$	−3.75953			−0.160161
$552$	−4.63590	−	3.36818i	−0.197317	−	0.143359i
$553$	1.44111	−	4.43527i	0.0612820	−	0.188607i
$554$	−15.1316	−	46.5703i	−0.642880	−	1.97858i
$555$	−3.67821	+	2.67237i	−0.156131	+	0.113436i
$556$	−13.6243	+	9.89860i	−0.577797	+	0.419794i
$557$	3.67005	+	11.2953i	0.155505	+	0.478595i	0.998212	−	0.0597778i	$-0.0190392\pi$
$557$	3.67005	+	11.2953i	0.155505	+	0.478595i	−0.842707	+	0.538373i	$0.819039\pi$
$558$	−3.76314	+	11.5818i	−0.159307	+	0.490295i
$559$	−13.6865	−	9.94382i	−0.578877	−	0.420579i
$560$	2.93794			0.124151
$561$	21.7575	+	9.39101i	0.918601	+	0.396489i
$562$	42.2530			1.78233
$563$	−3.91507	−	2.84446i	−0.165000	−	0.119880i	0.502221	−	0.864739i	$-0.332516\pi$
$563$	−3.91507	−	2.84446i	−0.165000	−	0.119880i	−0.667221	+	0.744860i	$0.732516\pi$
$564$	3.59822	−	11.0742i	0.151512	−	0.466307i
$565$	−1.42349	−	4.38105i	−0.0598866	−	0.184312i
$566$	−12.5416	+	9.11200i	−0.527162	+	0.383006i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	6.56091	+	20.1924i	0.275290	+	0.847255i
$569$	2.01786	−	6.21033i	0.0845931	−	0.260351i	−0.899809	−	0.436284i	$-0.856294\pi$
$569$	2.01786	−	6.21033i	0.0845931	−	0.260351i	0.984402	+	0.175933i	$0.0562943\pi$
$570$	−5.23607	−	3.80423i	−0.219315	−	0.159341i
$571$	−33.8691			−1.41738			−0.708689	−	0.705521i	$-0.750713\pi$
$571$	−33.8691			−1.41738			−0.708689	+	0.705521i	$0.750713\pi$
$572$	−2.97928	−	5.02690i	−0.124570	−	0.210185i
$573$	−9.87351			−0.412472
$574$	10.7286	+	7.79481i	0.447804	+	0.325349i
$575$	−5.40968	+	16.6493i	−0.225599	+	0.694323i
$576$	−0.0877588	−	0.270094i	−0.00365662	−	0.0112539i
$577$	30.2256	−	21.9602i	1.25831	−	0.914216i	0.259636	−	0.965706i	$-0.416397\pi$
$577$	30.2256	−	21.9602i	1.25831	−	0.914216i	0.998673	+	0.0514908i	$0.0163973\pi$
$578$	−48.8232	+	35.4721i	−2.03078	+	1.47544i
$579$	1.91007	+	5.87860i	0.0793800	+	0.244306i
$580$	0.126293	−	0.388691i	0.00524405	−	0.0161395i
$581$	−2.83941	−	2.06295i	−0.117799	−	0.0855856i
$582$	8.50152			0.352399
$583$	22.7971	−	5.11827i	0.944159	−	0.211977i
$584$	3.94378			0.163195
$585$	0.737102	+	0.535536i	0.0304754	+	0.0221417i
$586$	−10.7477	+	33.0779i	−0.443982	+	1.36644i
$587$	−0.642674	−	1.97795i	−0.0265260	−	0.0816386i	0.936917	−	0.349552i	$-0.113666\pi$
$587$	−0.642674	−	1.97795i	−0.0265260	−	0.0816386i	−0.963443	+	0.267913i	$0.913666\pi$
$588$	0.922906	−	0.670530i	0.0380600	−	0.0276522i
$589$	−34.4143	+	25.0035i	−1.41802	+	1.03025i
$590$	−1.08353	−	3.33478i	−0.0446084	−	0.137291i
$591$	5.89357	−	18.1386i	0.242429	−	0.746121i
$592$	−31.0516	−	22.5603i	−1.27621	−	0.927223i
$593$	6.54983			0.268969			0.134485	−	0.990916i	$-0.457062\pi$
$593$	6.54983			0.268969			0.134485	+	0.990916i	$0.457062\pi$
$594$	3.88291	−	4.41265i	0.159318	−	0.181053i
$595$	−4.21508			−0.172802
$596$	−11.5601	−	8.39892i	−0.473521	−	0.344033i
$597$	3.66121	−	11.2681i	0.149843	−	0.461171i
$598$	−3.18291	−	9.79598i	−0.130159	−	0.400587i
$599$	4.03042	−	2.92827i	0.164679	−	0.119646i	−0.502394	−	0.864639i	$-0.667547\pi$
$599$	4.03042	−	2.92827i	0.164679	−	0.119646i	0.667072	+	0.744993i	$0.267547\pi$
$600$	5.73089	−	4.16373i	0.233963	−	0.169984i
$601$	−10.0342	−	30.8821i	−0.409303	−	1.25971i	−0.917248	−	0.398316i	$-0.869595\pi$
$601$	−10.0342	−	30.8821i	−0.409303	−	1.25971i	0.507945	−	0.861389i	$-0.330405\pi$
$602$	5.99878	−	18.4623i	0.244492	−	0.752469i
$603$	1.77286	+	1.28806i	0.0721965	+	0.0524538i
$604$	0.374827			0.0152515
$605$	4.45104	+	4.72205i	0.180961	+	0.191979i
$606$	2.52835			0.102707
$607$	−2.53536	−	1.84205i	−0.102907	−	0.0747665i	0.535142	−	0.844762i	$-0.320258\pi$
$607$	−2.53536	−	1.84205i	−0.102907	−	0.0747665i	−0.638049	+	0.769996i	$0.720258\pi$
$608$	11.0581	−	34.0333i	0.448465	−	1.38023i
$609$	0.187665	+	0.577574i	0.00760458	+	0.0234045i
$610$	2.85076	−	2.07119i	0.115424	−	0.0838602i
$611$	−12.7537	+	9.26609i	−0.515959	+	0.374866i
$612$	2.51878	+	7.75202i	0.101816	+	0.313357i
$613$	14.4769	−	44.5555i	0.584718	−	1.79958i	−0.0156800	−	0.999877i	$-0.504991\pi$
$613$	14.4769	−	44.5555i	0.584718	−	1.79958i	0.600398	−	0.799701i	$-0.295009\pi$
$614$	24.4937	+	17.7957i	0.988484	+	0.718175i
$615$	−4.41434			−0.178003
$616$	−3.33630	+	3.79147i	−0.134423	+	0.152763i
$617$	26.5924			1.07057			0.535286	−	0.844671i	$-0.320204\pi$
$617$	26.5924			1.07057			0.535286	+	0.844671i	$0.320204\pi$
$618$	25.2589	+	18.3516i	1.01606	+	0.738211i
$619$	−10.1903	+	31.3625i	−0.409582	+	1.26056i	0.507426	+	0.861695i	$0.330597\pi$
$619$	−10.1903	+	31.3625i	−0.409582	+	1.26056i	−0.917008	+	0.398869i	$0.869403\pi$
$620$	−1.42899	−	4.39798i	−0.0573896	−	0.176627i
$621$	3.04445	−	2.21192i	0.122169	−	0.0887613i
$622$	10.3711	−	7.53505i	0.415844	−	0.302128i
$623$	−2.51878	−	7.75202i	−0.100913	−	0.310578i
$624$	−2.37684	+	7.31517i	−0.0951498	+	0.292841i
$625$	−16.1002	−	11.6975i	−0.644007	−	0.467899i
$626$	24.4185			0.975959
$627$	20.0332	−	4.49773i	0.800047	−	0.179622i
$628$	−3.05828			−0.122039
$629$	44.5500	+	32.3675i	1.77632	+	1.29058i
$630$	−0.323071	+	0.994311i	−0.0128715	+	0.0396143i
$631$	3.45237	+	10.6253i	0.137437	+	0.422987i	0.995961	−	0.0897862i	$-0.0286184\pi$
$631$	3.45237	+	10.6253i	0.137437	+	0.422987i	−0.858524	+	0.512773i	$0.828618\pi$
$632$	−5.74509	+	4.17405i	−0.228527	+	0.166035i
$633$	−16.9740	+	12.3324i	−0.674657	+	0.490167i
$634$	−3.80959	−	11.7247i	−0.151298	−	0.465648i
$635$	1.50429	−	4.62973i	0.0596959	−	0.183725i
$636$	6.50158	+	4.72368i	0.257805	+	0.187306i
$637$	−1.54445			−0.0611932
$638$	1.81995	+	3.07077i	0.0720525	+	0.121573i
$639$	−13.9430			−0.551576
$640$	−5.27741	−	3.83426i	−0.208608	−	0.151563i
$641$	−12.9526	+	39.8639i	−0.511595	+	1.57453i	0.277798	+	0.960640i	$0.410395\pi$
$641$	−12.9526	+	39.8639i	−0.511595	+	1.57453i	−0.789393	+	0.613888i	$0.789605\pi$
$642$	3.94308	+	12.1356i	0.155621	+	0.478952i
$643$	−23.5321	+	17.0971i	−0.928017	+	0.674244i	−0.945506	−	0.325604i	$-0.894433\pi$
$643$	−23.5321	+	17.0971i	−0.928017	+	0.674244i	0.0174898	+	0.999847i	$0.494433\pi$
$644$	3.47302	−	2.52330i	0.136856	−	0.0994320i
$645$	1.99683	+	6.14562i	0.0786252	+	0.241984i
$646$	−24.2238	+	74.5530i	−0.953071	+	2.93325i
$647$	−1.53554	−	1.11564i	−0.0603685	−	0.0438603i	0.557192	−	0.830384i	$-0.311879\pi$
$647$	−1.53554	−	1.11564i	−0.0603685	−	0.0438603i	−0.617560	+	0.786524i	$0.711879\pi$
$648$	−1.52274			−0.0598189
$649$	10.2128	+	4.40807i	0.400887	+	0.173032i
$650$	12.7330			0.499428
$651$	5.55914	+	4.03895i	0.217880	+	0.158299i
$652$	−0.314330	+	0.967407i	−0.0123101	+	0.0378866i
$653$	6.25817	+	19.2607i	0.244901	+	0.753728i	0.995653	+	0.0931434i	$0.0296915\pi$
$653$	6.25817	+	19.2607i	0.244901	+	0.753728i	−0.750752	+	0.660585i	$0.770308\pi$
$654$	−12.7415	+	9.25724i	−0.498232	+	0.361987i
$655$	−5.78258	+	4.20129i	−0.225944	+	0.164158i
$656$	−11.5158	−	35.4421i	−0.449618	−	1.38378i
$657$	−0.800331	+	2.46317i	−0.0312239	+	0.0960973i
$658$	−14.6346	−	10.6327i	−0.570517	−	0.414505i
$659$	−11.5620			−0.450392			−0.225196	−	0.974314i	$-0.572302\pi$
$659$	−11.5620			−0.450392			−0.225196	+	0.974314i	$0.572302\pi$
$660$	−0.207960	+	2.22229i	−0.00809482	+	0.0865024i
$661$	−32.6894			−1.27147			−0.635735	−	0.771907i	$-0.719303\pi$
$661$	−32.6894			−1.27147			−0.635735	+	0.771907i	$0.719303\pi$
$662$	42.5394	+	30.9067i	1.65334	+	1.20122i
$663$	3.41007	−	10.4951i	0.132436	−	0.407597i
$664$	1.65150	+	5.08279i	0.0640906	+	0.197251i
$665$	−2.95452	+	2.14658i	−0.114571	+	0.0832410i
$666$	11.0499	−	8.02820i	0.428174	−	0.311086i
$667$	0.706211	+	2.17349i	0.0273446	+	0.0841580i
$668$	4.07548	−	12.5430i	0.157685	−	0.485304i
$669$	2.74144	+	1.99177i	0.105990	+	0.0770063i
$670$	−2.29104			−0.0885107
$671$	−1.04152	+	11.1299i	−0.0402076	+	0.429663i
$672$	−5.78051			−0.222988
$673$	16.2814	+	11.8291i	0.627602	+	0.455979i	0.855569	−	0.517690i	$-0.173208\pi$
$673$	16.2814	+	11.8291i	0.627602	+	0.455979i	−0.227967	+	0.973669i	$0.573208\pi$
$674$	10.7182	−	32.9874i	0.412851	−	1.27063i
$675$	1.43754	+	4.42430i	0.0553311	+	0.170292i
$676$	9.79635	−	7.11747i	0.376783	−	0.273749i
$677$	−19.0722	+	13.8568i	−0.733006	+	0.532560i	−0.890513	−	0.454958i	$-0.849654\pi$
$677$	−19.0722	+	13.8568i	−0.733006	+	0.532560i	0.157507	+	0.987518i	$0.449654\pi$
$678$	4.27637	+	13.1613i	0.164233	+	0.505457i
$679$	1.48238	−	4.56231i	0.0568887	−	0.175085i
$680$	5.19266	+	3.77269i	0.199129	+	0.144676i
$681$	−19.3973			−0.743305
$682$	37.0824	+	16.0056i	1.41996	+	0.612886i
$683$	11.5812			0.443143			0.221572	−	0.975144i	$-0.428881\pi$
$683$	11.5812			0.443143			0.221572	+	0.975144i	$0.428881\pi$
$684$	5.71333	+	4.15098i	0.218455	+	0.158717i
$685$	−3.18195	+	9.79304i	−0.121576	+	0.374173i
$686$	−0.547647	−	1.68548i	−0.0209093	−	0.0643521i
$687$	−7.98018	+	5.79794i	−0.304463	+	0.221205i
$688$	−44.1332	+	32.0646i	−1.68256	+	1.22245i
$689$	−3.36215	−	10.3476i	−0.128088	−	0.394213i
$690$	−1.21576	+	3.74173i	−0.0462833	+	0.142445i
$691$	−35.4482	−	25.7546i	−1.34851	−	0.979752i	−0.999084	−	0.0427885i	$-0.986376\pi$
$691$	−35.4482	−	25.7546i	−1.34851	−	0.979752i	−0.349428	−	0.936963i	$-0.613624\pi$
$692$	10.2547			0.389826
$693$	−1.69098	−	2.85317i	−0.0642351	−	0.108383i
$694$	−11.5050			−0.436723
$695$	−7.04548	−	5.11884i	−0.267250	−	0.194169i
$696$	0.285765	−	0.879496i	0.0108319	−	0.0333372i
$697$	16.5219	+	50.8491i	0.625811	+	1.92605i
$698$	−11.2975	+	8.20813i	−0.427617	+	0.310682i
$699$	5.76521	−	4.18867i	0.218060	−	0.158430i
$700$	1.63991	+	5.04713i	0.0619828	+	0.190764i
$701$	−7.05070	+	21.6998i	−0.266301	+	0.819591i	0.725090	+	0.688655i	$0.241798\pi$
$701$	−7.05070	+	21.6998i	−0.266301	+	0.819591i	−0.991391	+	0.130936i	$0.958202\pi$
$702$	−2.21436	−	1.60883i	−0.0835757	−	0.0607213i
$703$	47.7104			1.79943
$704$	−0.919022	+	0.206333i	−0.0346370	+	0.00777648i
$705$	6.02147			0.226782
$706$	7.66479	+	5.56880i	0.288468	+	0.209584i
$707$	0.440861	−	1.35683i	0.0165803	−	0.0510289i
$708$	1.18230	+	3.63874i	0.0444334	+	0.136752i
$709$	−32.3401	+	23.4965i	−1.21456	+	0.882428i	−0.995637	−	0.0933141i	$-0.970254\pi$
$709$	−32.3401	+	23.4965i	−1.21456	+	0.882428i	−0.218922	+	0.975742i	$0.570254\pi$
$710$	11.7931	−	8.56822i	0.442589	−	0.321559i
$711$	−1.44111	−	4.43527i	−0.0540457	−	0.166335i
$712$	−3.83545	+	11.8043i	−0.143740	+	0.442385i
$713$	20.9198	+	15.1991i	0.783454	+	0.569212i
$714$	12.6627			0.473891
$715$	1.99622	−	2.26857i	0.0746545	−	0.0848396i
$716$	−7.01108			−0.262016
$717$	18.0325	+	13.1014i	0.673437	+	0.489281i
$718$	−9.77635	+	30.0885i	−0.364850	+	1.12289i
$719$	−8.10242	−	24.9367i	−0.302169	−	0.929981i	−0.980718	−	0.195426i	$-0.937391\pi$
$719$	−8.10242	−	24.9367i	−0.302169	−	0.929981i	0.678549	−	0.734555i	$-0.262609\pi$
$720$	2.37684	−	1.72688i	0.0885797	−	0.0643569i
$721$	14.2526	−	10.3552i	0.530796	−	0.385646i
$722$	10.5824	+	32.5692i	0.393836	+	1.21210i
$723$	−4.59671	+	14.1472i	−0.170953	+	0.526140i
$724$	−13.8124	−	10.0353i	−0.513334	−	0.372959i
$725$	−2.82514			−0.104923
$726$	−13.3716	−	14.1857i	−0.496266	−	0.526482i
$727$	−22.2366			−0.824708			−0.412354	−	0.911024i	$-0.635293\pi$
$727$	−22.2366			−0.824708			−0.412354	+	0.911024i	$0.635293\pi$
$728$	1.90264	+	1.38235i	0.0705164	+	0.0512332i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.836730	−	2.57519i	−0.0309688	−	0.0953121i
$731$	63.3182	−	46.0034i	2.34191	−	1.70150i
$732$	−3.11060	+	2.25998i	−0.114971	+	0.0835313i
$733$	−6.52903	−	20.0943i	−0.241155	−	0.742200i	−0.996245	−	0.0865782i	$-0.972407\pi$
$733$	−6.52903	−	20.0943i	−0.241155	−	0.742200i	0.755090	−	0.655621i	$-0.227593\pi$
$734$	−16.3942	+	50.4562i	−0.605121	+	1.86237i
$735$	0.477260	+	0.346750i	0.0176040	+	0.0127901i
$736$	−21.7529			−0.801822
$737$	4.80127	−	5.45631i	0.176857	−	0.200986i
$738$	13.2613			0.488156
$739$	−30.3410	−	22.0440i	−1.11611	−	0.810903i	−0.132497	−	0.991183i	$-0.542299\pi$
$739$	−30.3410	−	22.0440i	−1.11611	−	0.810903i	−0.983615	+	0.180280i	$0.942299\pi$
$740$	−1.60273	+	4.93270i	−0.0589175	+	0.181330i
$741$	−2.95452	−	9.09308i	−0.108537	−	0.334043i
$742$	10.1004	−	7.33836i	0.370797	−	0.269400i
$743$	29.2430	−	21.2463i	1.07282	−	0.779452i	0.0964055	−	0.995342i	$-0.469265\pi$
$743$	29.2430	−	21.2463i	1.07282	−	0.779452i	0.976418	+	0.215891i	$0.0692654\pi$
$744$	−3.23339	−	9.95135i	−0.118542	−	0.364834i
$745$	2.28342	−	7.02763i	0.0836579	−	0.257473i
$746$	−33.6812	−	24.4708i	−1.23316	−	0.895940i
$747$	−3.50970			−0.128413
$748$	26.3770	−	5.92201i	0.964440	−	0.216530i
$749$	7.20005			0.263084
$750$	−8.16376	−	5.93132i	−0.298098	−	0.216581i
$751$	−13.4587	+	41.4216i	−0.491115	+	1.51150i	0.331810	+	0.943346i	$0.392341\pi$
$751$	−13.4587	+	41.4216i	−0.491115	+	1.51150i	−0.822925	+	0.568150i	$0.807659\pi$
$752$	15.7084	+	48.3456i	0.572828	+	1.76298i
$753$	−20.9724	+	15.2373i	−0.764276	+	0.555279i
$754$	1.34478	−	0.977038i	0.0489739	−	0.0355816i
$755$	0.0598978	+	0.184346i	0.00217990	+	0.00670905i
$756$	0.352519	−	1.08494i	0.0128210	−	0.0394589i
$757$	35.9561	+	26.1236i	1.30685	+	0.949479i	0.999997	−	0.00227928i	$-0.000725518\pi$
$757$	35.9561	+	26.1236i	1.30685	+	0.949479i	0.306848	+	0.951758i	$0.400726\pi$
$758$	−55.7421			−2.02464
$759$	−6.36341	−	10.7369i	−0.230977	−	0.389724i
$760$	5.56103			0.201720
$761$	12.9130	+	9.38184i	0.468096	+	0.340091i	0.796699	−	0.604377i	$-0.206578\pi$
$761$	12.9130	+	9.38184i	0.468096	+	0.340091i	−0.328603	+	0.944468i	$0.606578\pi$
$762$	−4.51911	+	13.9084i	−0.163710	+	0.503847i
$763$	2.74617	+	8.45183i	0.0994179	+	0.305977i
$764$	−9.11231	+	6.62048i	−0.329672	+	0.239521i
$765$	−3.41007	+	2.47756i	−0.123291	+	0.0895765i
$766$	−3.08188	−	9.48505i	−0.111353	−	0.342709i
$767$	1.60066	−	4.92633i	0.0577966	−	0.177880i
$768$	16.3136	+	11.8525i	0.588667	+	0.427692i
$769$	5.19899			0.187480			0.0937402	−	0.995597i	$-0.470118\pi$
$769$	5.19899			0.187480			0.0937402	+	0.995597i	$0.470118\pi$
$770$	3.18358	+	1.37410i	0.114728	+	0.0495192i
$771$	−0.871474			−0.0313854
$772$	5.70460	+	4.14463i	0.205313	+	0.149169i
$773$	−3.75809	+	11.5662i	−0.135169	+	0.416007i	−0.995616	−	0.0935321i	$-0.970184\pi$
$773$	−3.75809	+	11.5662i	−0.135169	+	0.416007i	0.860447	+	0.509539i	$0.170184\pi$
$774$	−5.99878	−	18.4623i	−0.215622	−	0.663615i
$775$	−25.8610	+	18.7891i	−0.928956	+	0.674926i
$776$	−5.90965	+	4.29361i	−0.212144	+	0.154132i
$777$	−2.38157	−	7.32972i	−0.0854384	−	0.262952i
$778$	14.2976	−	44.0033i	0.512592	−	1.57760i
$779$	37.4764	+	27.2282i	1.34273	+	0.975551i
$780$	1.03937			0.0372154
$781$	−4.30862	+	46.0425i	−0.154175	+	1.64753i
$782$	47.6516			1.70402
$783$	0.491314	+	0.356961i	0.0175581	+	0.0127567i
$784$	−1.53896	+	4.73644i	−0.0549629	+	0.169158i
$785$	−0.488718	−	1.50412i	−0.0174431	−	0.0536843i
$786$	17.3717	−	12.6213i	0.619629	−	0.450187i
$787$	32.0718	−	23.3015i	1.14324	−	0.830610i	0.155670	−	0.987809i	$-0.450246\pi$
$787$	32.0718	−	23.3015i	1.14324	−	0.830610i	0.987567	+	0.157199i	$0.0502463\pi$
$788$	−6.72324	−	20.6920i	−0.239505	−	0.737122i
$789$	−8.30862	+	25.5713i	−0.295795	+	0.910363i
$790$	3.94445	+	2.86581i	0.140337	+	0.101961i
$791$	7.80862			0.277643
$792$	−0.470553	+	5.02839i	−0.0167204	+	0.178676i
$793$	5.20546			0.184851
$794$	−14.8864	−	10.8156i	−0.528297	−	0.383830i
$795$	−1.28423	+	3.95244i	−0.0455468	+	0.140179i
$796$	−4.17662	−	12.8543i	−0.148036	−	0.455609i
$797$	28.4060	−	20.6382i	1.00619	−	0.731043i	0.0427865	−	0.999084i	$-0.486376\pi$
$797$	28.4060	−	20.6382i	1.00619	−	0.731043i	0.963407	+	0.268042i	$0.0863765\pi$
$798$	8.87581	−	6.44865i	0.314200	−	0.228280i
$799$	−22.5370	−	69.3618i	−0.797302	−	2.45384i
$800$	8.30974	−	25.5747i	0.293794	−	0.904204i
$801$	−6.59426	−	4.79101i	−0.232997	−	0.169282i
$802$	6.53731			0.230840
$803$	7.88654	+	3.40401i	0.278310	+	0.120125i
$804$	2.49987			0.0881635
$805$	1.79600	+	1.30487i	0.0633006	+	0.0459906i
$806$	5.81197	−	17.8874i	0.204718	−	0.630057i
$807$	0.306722	+	0.943994i	0.0107971	+	0.0332302i
$808$	−1.75753	+	1.27692i	−0.0618297	+	0.0449219i
$809$	33.8066	−	24.5619i	1.18858	−	0.863552i	0.195464	−	0.980711i	$-0.437379\pi$
$809$	33.8066	−	24.5619i	1.18858	−	0.863552i	0.993113	+	0.117159i	$0.0373787\pi$
$810$	0.323071	+	0.994311i	0.0113516	+	0.0349365i
$811$	−3.05889	+	9.41431i	−0.107412	+	0.330581i	−0.990289	−	0.139024i	$-0.955604\pi$
$811$	−3.05889	+	9.41431i	−0.107412	+	0.330581i	0.882877	+	0.469605i	$0.155604\pi$
$812$	0.560478	+	0.407211i	0.0196689	+	0.0142903i
$813$	−26.8650			−0.942197
$814$	−23.0961	−	38.9697i	−0.809518	−	1.36589i
$815$	−0.526018			−0.0184256
$816$	−28.7880	−	20.9157i	−1.00778	−	0.732197i
$817$	20.9545	−	64.4912i	0.733103	−	2.25626i
$818$	0.591581	+	1.82070i	0.0206842	+	0.0636593i
$819$	−1.24948	+	0.907802i	−0.0436605	+	0.0317212i
$820$	−4.07402	+	2.95995i	−0.142271	+	0.103366i
$821$	5.00410	+	15.4010i	0.174644	+	0.537500i	0.999617	−	0.0276726i	$-0.00880958\pi$
$821$	5.00410	+	15.4010i	0.174644	+	0.537500i	−0.824973	+	0.565173i	$0.808810\pi$
$822$	9.55905	−	29.4197i	0.333410	−	1.02613i
$823$	3.12800	+	2.27262i	0.109035	+	0.0792187i	0.640967	−	0.767569i	$-0.278534\pi$
$823$	3.12800	+	2.27262i	0.109035	+	0.0792187i	−0.531932	+	0.846787i	$0.678534\pi$
$824$	−26.8265			−0.934545
$825$	15.0541	−	3.37987i	0.524118	−	0.117672i
$826$	5.94378			0.206811
$827$	37.8765	+	27.5189i	1.31709	+	0.956925i	0.999964	+	0.00854365i	$0.00271956\pi$
$827$	37.8765	+	27.5189i	1.31709	+	0.956925i	0.317131	+	0.948382i	$0.397280\pi$
$828$	1.32658	−	4.08279i	0.0461017	−	0.141887i
$829$	−12.8427	−	39.5258i	−0.446046	−	1.37279i	−0.881332	−	0.472497i	$-0.843353\pi$
$829$	−12.8427	−	39.5258i	−0.446046	−	1.37279i	0.435286	−	0.900292i	$-0.356647\pi$
$830$	2.96855	−	2.15677i	0.103040	−	0.0748627i
$831$	−22.3533	+	16.2406i	−0.775428	+	0.563381i
$832$	0.135539	+	0.417145i	0.00469896	+	0.0144619i
$833$	2.20796	−	6.79540i	0.0765013	−	0.235447i
$834$	21.1656	+	15.3777i	0.732906	+	0.532488i
$835$	6.82015			0.236021
$836$	15.4729	−	17.5838i	0.535140	−	0.608149i
$837$	6.87147			0.237513
$838$	−14.4474	−	10.4966i	−0.499076	−	0.362600i
$839$	1.58872	−	4.88957i	0.0548486	−	0.168807i	−0.919880	−	0.392201i	$-0.871714\pi$
$839$	1.58872	−	4.88957i	0.0548486	−	0.168807i	0.974728	+	0.223394i	$0.0717138\pi$
$840$	−0.277591	−	0.854338i	−0.00957780	−	0.0294774i
$841$	23.1631	−	16.8290i	0.798728	−	0.580310i
$842$	−17.1702	+	12.4749i	−0.591725	+	0.429913i
$843$	−7.36752	−	22.6749i	−0.253751	−	0.780965i
$844$	−7.39621	+	22.7632i	−0.254588	+	0.783541i
$845$	5.06597	+	3.68064i	0.174275	+	0.126618i
$846$	−18.0894			−0.621926
$847$	−9.94427	+	4.70228i	−0.341689	+	0.161572i
$848$	−35.0838			−1.20478
$849$	7.07676	+	5.14156i	0.242874	+	0.176458i
$850$	−18.2032	+	56.0237i	−0.624365	+	1.92160i
$851$	−8.96219	−	27.5828i	−0.307220	−	0.945526i
$852$	−12.8681	+	9.34920i	−0.440853	+	0.320298i
$853$	−5.41758	+	3.93610i	−0.185494	+	0.134769i	−0.676657	−	0.736298i	$-0.736572\pi$
$853$	−5.41758	+	3.93610i	−0.185494	+	0.134769i	0.491163	+	0.871068i	$0.336572\pi$
$854$	1.84581	+	5.68082i	0.0631624	+	0.194394i
$855$	−1.12853	+	3.47325i	−0.0385948	+	0.118783i
$856$	−8.86990	−	6.44436i	−0.303167	−	0.220264i
$857$	−36.1064			−1.23337			−0.616686	−	0.787209i	$-0.711525\pi$
$857$	−36.1064			−1.23337			−0.616686	+	0.787209i	$0.711525\pi$
$858$	−5.99694	+	6.81511i	−0.204732	+	0.232664i
$859$	−37.1034			−1.26595			−0.632976	−	0.774171i	$-0.718167\pi$
$859$	−37.1034			−1.26595			−0.632976	+	0.774171i	$0.718167\pi$
$860$	5.96371	+	4.33289i	0.203361	+	0.147750i
$861$	2.31233	−	7.11663i	0.0788042	−	0.242534i
$862$	−0.300410	−	0.924567i	−0.0102320	−	0.0314909i
$863$	−31.0439	+	22.5547i	−1.05675	+	0.767771i	−0.973484	−	0.228756i	$-0.926534\pi$
$863$	−31.0439	+	22.5547i	−1.05675	+	0.767771i	−0.0832629	+	0.996528i	$0.526534\pi$
$864$	−4.67653	+	3.39770i	−0.159099	+	0.115592i
$865$	1.63872	+	5.04345i	0.0557180	+	0.171482i
$866$	10.7272	−	33.0150i	0.364526	−	1.12190i
$867$	27.5491	+	20.0156i	0.935617	+	0.679765i
$868$	7.83880			0.266066
$869$	−15.0914	+	3.38824i	−0.511942	+	0.114938i
$870$	−0.634918			−0.0215257
$871$	−2.73809	−	1.98934i	−0.0927766	−	0.0674062i
$872$	4.18170	−	12.8699i	0.141610	−	0.435831i
$873$	−1.48238	−	4.56231i	−0.0501711	−	0.154411i
$874$	33.4009	−	24.2672i	1.12980	−	0.820850i
$875$	−4.60651	+	3.34682i	−0.155728	+	0.113143i
$876$	0.912997	+	2.80992i	0.0308473	+	0.0949382i
$877$	−0.250661	+	0.771456i	−0.00846423	+	0.0260502i	−0.955199	−	0.295963i	$-0.904360\pi$
$877$	−0.250661	+	0.771456i	−0.00846423	+	0.0260502i	0.946735	+	0.322013i	$0.104360\pi$
$878$	−53.6325	−	38.9663i	−1.81001	−	1.31505i
$879$	19.6252			0.661940
$880$	−4.96800	−	8.38244i	−0.167471	−	0.282572i
$881$	−32.5076			−1.09521			−0.547605	−	0.836737i	$-0.684460\pi$
$881$	−32.5076			−1.09521			−0.547605	+	0.836737i	$0.684460\pi$
$882$	−1.43376	−	1.04169i	−0.0482772	−	0.0350754i
$883$	14.8636	−	45.7453i	0.500199	−	1.53945i	−0.308497	−	0.951225i	$-0.599826\pi$
$883$	14.8636	−	45.7453i	0.500199	−	1.53945i	0.808695	−	0.588228i	$-0.200174\pi$
$884$	−3.89012	−	11.9726i	−0.130839	−	0.402681i
$885$	−1.60066	+	1.16295i	−0.0538057	+	0.0390921i
$886$	−30.7510	+	22.3419i	−1.03310	+	0.750590i
$887$	3.51806	+	10.8275i	0.118125	+	0.363551i	0.992586	−	0.121545i	$-0.0387847\pi$
$887$	3.51806	+	10.8275i	0.118125	+	0.363551i	−0.874461	+	0.485096i	$0.838785\pi$
$888$	−3.62651	+	11.1613i	−0.121698	+	0.374547i
$889$	6.67589	+	4.85032i	0.223902	+	0.162675i
$890$	8.52166			0.285647
$891$	−3.04508	−	1.31433i	−0.102014	−	0.0440316i
$892$	3.86563			0.129431
$893$	−51.1205	−	37.1412i	−1.71068	−	1.24288i
$894$	−6.85971	+	21.1120i	−0.229423	+	0.706092i
$895$	−1.12038	−	3.44817i	−0.0374502	−	0.115260i
$896$	8.94589	−	6.49957i	0.298861	−	0.217135i
$897$	−4.70198	+	3.41619i	−0.156995	+	0.114063i
$898$	3.50441	+	10.7855i	0.116944	+	0.359916i
$899$	−1.28954	+	3.96879i	−0.0430085	+	0.132366i
$900$	4.29335	+	3.11930i	0.143112	+	0.103977i
$901$	50.3351			1.67690
$902$	4.09797	−	43.7915i	0.136448	−	1.45810i
$903$	−10.9537			−0.364517
$904$	−9.61962	−	6.98906i	−0.319944	−	0.232453i
$905$	2.72830	−	8.39683i	0.0906917	−	0.279120i
$906$	−0.179942	−	0.553803i	−0.00597816	−	0.0183989i
$907$	−10.8618	+	7.89153i	−0.360659	+	0.262034i	−0.753327	−	0.657646i	$-0.771552\pi$
$907$	−10.8618	+	7.89153i	−0.360659	+	0.262034i	0.392668	+	0.919680i	$0.371552\pi$
$908$	−17.9018	+	13.0065i	−0.594094	+	0.431634i
$909$	−0.440861	−	1.35683i	−0.0146224	−	0.0450032i
$910$	0.498966	−	1.53566i	0.0165406	−	0.0509066i
$911$	−2.74502	−	1.99437i	−0.0909464	−	0.0660765i	0.541383	−	0.840776i	$-0.317901\pi$
$911$	−2.74502	−	1.99437i	−0.0909464	−	0.0660765i	−0.632329	+	0.774700i	$0.717901\pi$
$912$	−30.8303			−1.02089
$913$	−1.08456	+	11.5897i	−0.0358936	+	0.383564i
$914$	−65.4712			−2.16560
$915$	−1.60858	−	1.16870i	−0.0531779	−	0.0386360i
$916$	−3.47726	+	10.7019i	−0.114892	+	0.353601i
$917$	−3.74411	−	11.5232i	−0.123642	−	0.380530i
$918$	10.2444	−	7.44296i	0.338114	−	0.245654i
$919$	36.0553	−	26.1957i	1.18936	−	0.864117i	0.196160	−	0.980572i	$-0.437153\pi$
$919$	36.0553	−	26.1957i	1.18936	−	0.864117i	0.993196	+	0.116455i	$0.0371530\pi$
$920$	−1.04461	−	3.21499i	−0.0344399	−	0.105995i
$921$	5.27910	−	16.2474i	0.173952	−	0.535370i
$922$	−10.6073	−	7.70665i	−0.349333	−	0.253805i
$923$	21.5342			0.708807
$924$	−3.47375	−	1.49935i	−0.114278	−	0.0493250i
$925$	35.8525			1.17882
$926$	20.6056	+	14.9708i	0.677141	+	0.491972i
$927$	5.44403	−	16.7550i	0.178805	−	0.550306i
$928$	−1.08480	−	3.33868i	−0.0356104	−	0.109597i
$929$	5.78613	−	4.20387i	0.189837	−	0.137924i	−0.488807	−	0.872392i	$-0.662568\pi$
$929$	5.78613	−	4.20387i	0.189837	−	0.137924i	0.678644	+	0.734467i	$0.262568\pi$
$930$	−5.81197	+	4.22264i	−0.190582	+	0.138466i
$931$	−1.91300	−	5.88760i	−0.0626959	−	0.192958i
$932$	2.51211	−	7.73149i	0.0822871	−	0.253254i
$933$	−5.85203	−	4.25175i	−0.191587	−	0.139196i
$934$	64.0883			2.09703
$935$	7.12763	+	12.0263i	0.233099	+	0.393304i
$936$	2.35179			0.0768706
$937$	1.05828	+	0.768889i	0.0345727	+	0.0251185i	0.604937	−	0.796273i	$-0.293198\pi$
$937$	1.05828	+	0.768889i	0.0345727	+	0.0251185i	−0.570365	+	0.821392i	$0.693198\pi$
$938$	1.20010	−	3.69353i	0.0391847	−	0.120598i
$939$	−4.25777	−	13.1041i	−0.138947	−	0.427635i
$940$	5.55725	−	4.03758i	0.181258	−	0.131691i
$941$	17.8975	−	13.0033i	0.583442	−	0.423896i	−0.256521	−	0.966539i	$-0.582576\pi$
$941$	17.8975	−	13.0033i	0.583442	−	0.423896i	0.839963	+	0.542643i	$0.182576\pi$
$942$	1.46818	+	4.51859i	0.0478359	+	0.147224i
$943$	8.70164	−	26.7809i	0.283365	−	0.872106i
$944$	−13.5129	−	9.81767i	−0.439806	−	0.319538i
$945$	0.589926			0.0191903
$946$	−62.8200	+	14.1040i	−2.04245	+	0.458560i
$947$	−17.6842			−0.574658			−0.287329	−	0.957832i	$-0.592767\pi$
$947$	−17.6842			−0.574658			−0.287329	+	0.957832i	$0.592767\pi$
$948$	−4.30398	−	3.12703i	−0.139787	−	0.101561i
$949$	1.23607	−	3.80423i	0.0401245	−	0.123490i
$950$	15.7714	+	48.5395i	0.511693	+	1.57483i
$951$	−5.62775	+	4.08880i	−0.182492	+	0.132589i
$952$	−8.80222	+	6.39519i	−0.285282	+	0.207269i
$953$	−7.34659	−	22.6105i	−0.237980	−	0.732426i	−0.996712	−	0.0810235i	$-0.974181\pi$
$953$	−7.34659	−	22.6105i	−0.237980	−	0.732426i	0.758733	−	0.651402i	$-0.225819\pi$
$954$	3.85800	−	11.8737i	0.124907	−	0.384426i
$955$	−4.71223	−	3.42364i	−0.152484	−	0.110786i
$956$	25.4272			0.822374
$957$	1.33058	−	1.51211i	0.0430115	−	0.0488796i
$958$	28.4003			0.917573
$959$	−14.1212	−	10.2597i	−0.455997	−	0.331301i
$960$	0.0517712	−	0.159335i	0.00167091	−	0.00514253i
$961$	5.01138	+	15.4234i	0.161657	+	0.497530i
$962$	−17.0659	+	12.3991i	−0.550227	+	0.399764i
$963$	5.82496	−	4.23208i	0.187707	−	0.136377i
$964$	5.24380	+	16.1388i	0.168891	+	0.519795i
$965$	−1.12680	+	3.46794i	−0.0362730	+	0.111637i
$966$	−5.39544	−	3.92001i	−0.173595	−	0.126124i
$967$	21.1829			0.681195			0.340597	−	0.940209i	$-0.389371\pi$
$967$	21.1829			0.681195			0.340597	+	0.940209i	$0.389371\pi$
$968$	16.4593	+	3.10771i	0.529023	+	0.0998857i
$969$	44.2324			1.42095
$970$	4.05744	+	2.94790i	0.130276	+	0.0946514i
$971$	−14.6585	+	45.1143i	−0.470415	+	1.44779i	0.381628	+	0.924316i	$0.375363\pi$
$971$	−14.6585	+	45.1143i	−0.470415	+	1.44779i	−0.852043	+	0.523472i	$0.824637\pi$
$972$	−0.352519	−	1.08494i	−0.0113070	−	0.0347995i
$973$	11.9430	−	8.67709i	0.382875	−	0.278175i
$974$	−2.22318	+	1.61523i	−0.0712351	+	0.0517554i
$975$	−2.22021	−	6.83310i	−0.0711035	−	0.218834i
$976$	5.18698	−	15.9639i	0.166031	−	0.510991i
$977$	10.6677	+	7.75055i	0.341290	+	0.247962i	0.745206	−	0.666834i	$-0.232351\pi$
$977$	10.6677	+	7.75055i	0.341290	+	0.247962i	−0.403916	+	0.914796i	$0.632351\pi$
$978$	1.58023			0.0505303
$979$	−17.8586	+	20.2950i	−0.570763	+	0.648632i
$980$	0.672972			0.0214973
$981$	7.18955	+	5.22352i	0.229545	+	0.166774i
$982$	−0.0181619	+	0.0558965i	−0.000579569	+	0.00178373i
$983$	−1.25999	−	3.87784i	−0.0401873	−	0.123684i	0.928950	−	0.370205i	$-0.120713\pi$
$983$	−1.25999	−	3.87784i	−0.0401873	−	0.123684i	−0.969137	+	0.246521i	$0.920713\pi$
$984$	−9.21832	+	6.69750i	−0.293869	+	0.213509i
$985$	9.10231	−	6.61321i	0.290024	−	0.210714i
$986$	2.37635	+	7.31366i	0.0756785	+	0.232915i
$987$	−3.15419	+	9.70760i	−0.100399	+	0.308996i
$988$	−8.82393	−	6.41096i	−0.280726	−	0.203960i
$989$	−41.2204			−1.31073
$990$	3.38324	−	0.759586i	0.107527	−	0.0241412i
$991$	−5.49154			−0.174445			−0.0872223	−	0.996189i	$-0.527799\pi$
$991$	−5.49154			−0.174445			−0.0872223	+	0.996189i	$0.527799\pi$
$992$	−32.1347	−	23.3472i	−1.02028	−	0.741275i
$993$	9.16849	−	28.2177i	0.290953	−	0.895462i
$994$	7.63584	+	23.5007i	0.242194	+	0.745397i
$995$	5.65454	−	4.10827i	0.179261	−	0.130241i
$996$	−3.23912	+	2.35336i	−0.102636	+	0.0745691i
$997$	7.09891	+	21.8482i	0.224825	+	0.691939i	0.998309	+	0.0581241i	$0.0185119\pi$
$997$	7.09891	+	21.8482i	0.224825	+	0.691939i	−0.773485	+	0.633815i	$0.781488\pi$
$998$	−14.8037	+	45.5610i	−0.468602	+	1.44221i
$999$	−6.23503	−	4.53002i	−0.197268	−	0.143323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.f.169.1	✓	8
3.2	odd	2		693.2.m.f.631.2		8
11.3	even	5	inner	231.2.j.f.190.1	yes	8
11.5	even	5		2541.2.a.bn.1.4		4
11.6	odd	10		2541.2.a.bm.1.1		4
33.5	odd	10		7623.2.a.ci.1.1		4
33.14	odd	10		693.2.m.f.190.2		8
33.17	even	10		7623.2.a.cl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.169.1	✓	8	1.1	even	1	trivial
231.2.j.f.190.1	yes	8	11.3	even	5	inner
693.2.m.f.190.2		8	33.14	odd	10
693.2.m.f.631.2		8	3.2	odd	2
2541.2.a.bm.1.1		4	11.6	odd	10
2541.2.a.bn.1.4		4	11.5	even	5
7623.2.a.ci.1.1		4	33.5	odd	10
7623.2.a.cl.1.4		4	33.17	even	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43376 - 1.04169i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.352519 + 1.08494i) q^{4} +(-0.477260 + 0.346750i) q^{5} +(1.43376 - 1.04169i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.470553 + 1.44821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.43376 - 1.04169i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.352519 + 1.08494i) q^{4} +(-0.477260 + 0.346750i) q^{5} +(1.43376 - 1.04169i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.470553 + 1.44821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.04548 q^{10} +(-2.19098 + 2.48990i) q^{11} -1.14077 q^{12} +(1.24948 + 0.907802i) q^{13} +(-0.547647 + 1.68548i) q^{14} +(-0.182297 - 0.561053i) q^{15} +(4.02905 - 2.92728i) q^{16} +(-5.78051 + 4.19979i) q^{17} +(0.547647 + 1.68548i) q^{18} +(-1.91300 + 5.88760i) q^{19} +(-0.544446 - 0.395563i) q^{20} +1.00000 q^{21} +(5.73503 - 1.28760i) q^{22} +3.76314 q^{23} +(-1.23192 - 0.895044i) q^{24} +(-1.43754 + 4.42430i) q^{25} +(-0.845811 - 2.60314i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.922906 - 0.670530i) q^{28} +(0.187665 + 0.577574i) q^{29} +(-0.323071 + 0.994311i) q^{30} +(5.55914 + 4.03895i) q^{31} -5.78051 q^{32} +(-1.69098 - 2.85317i) q^{33} +12.6627 q^{34} +(0.477260 + 0.346750i) q^{35} +(0.352519 - 1.08494i) q^{36} +(-2.38157 - 7.32972i) q^{37} +(8.87581 - 6.44865i) q^{38} +(-1.24948 + 0.907802i) q^{39} +(-0.277591 - 0.854338i) q^{40} +(2.31233 - 7.11663i) q^{41} +(-1.43376 - 1.04169i) q^{42} -10.9537 q^{43} +(-3.47375 - 1.49935i) q^{44} +0.589926 q^{45} +(-5.39544 - 3.92001i) q^{46} +(-3.15419 + 9.70760i) q^{47} +(1.53896 + 4.73644i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.66983 - 4.84591i) q^{50} +(-2.20796 - 6.79540i) q^{51} +(-0.544446 + 1.67563i) q^{52} +(-5.69927 - 4.14076i) q^{53} -1.77222 q^{54} +(0.182297 - 1.94805i) q^{55} +1.52274 q^{56} +(-5.00829 - 3.63874i) q^{57} +(0.332585 - 1.02359i) q^{58} +(-1.03640 - 3.18971i) q^{59} +(0.544446 - 0.395563i) q^{60} +(2.72674 - 1.98109i) q^{61} +(-3.76314 - 11.5818i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(0.229756 + 0.166927i) q^{64} -0.911108 q^{65} +(-0.547647 + 5.85223i) q^{66} -2.19138 q^{67} +(-6.59426 - 4.79101i) q^{68} +(-1.16287 + 3.57896i) q^{69} +(-0.323071 - 0.994311i) q^{70} +(11.2801 - 8.19549i) q^{71} +(1.23192 - 0.895044i) q^{72} +(-0.800331 - 2.46317i) q^{73} +(-4.22067 + 12.9899i) q^{74} +(-3.76354 - 2.73437i) q^{75} -7.06206 q^{76} +(3.04508 + 1.31433i) q^{77} +2.73710 q^{78} +(3.77286 + 2.74114i) q^{79} +(-0.907873 + 2.79415i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-10.7286 + 7.79481i) q^{82} +(2.83941 - 2.06295i) q^{83} +(0.352519 + 1.08494i) q^{84} +(1.30253 - 4.00878i) q^{85} +(15.7050 + 11.4104i) q^{86} -0.607298 q^{87} +(-2.57493 - 4.34464i) q^{88} +8.15095 q^{89} +(-0.845811 - 0.614518i) q^{90} +(0.477260 - 1.46886i) q^{91} +(1.32658 + 4.08279i) q^{92} +(-5.55914 + 4.03895i) q^{93} +(14.6346 - 10.6327i) q^{94} +(-1.12853 - 3.47325i) q^{95} +(1.78628 - 5.49760i) q^{96} +(3.88093 + 2.81966i) q^{97} +1.77222 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more