LMFDB - Embedded newform 403.2.k.c.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - 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			157.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	403.157
Dual form			403.2.k.c.326.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.224514i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +2.61803 q^{5} +0.618034 q^{6} +(-0.572949 - 1.76336i) q^{7} +(0.454915 - 1.40008i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.224514i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +2.61803 q^{5} +0.618034 q^{6} +(-0.572949 - 1.76336i) q^{7} +(0.454915 - 1.40008i) q^{8} +(-0.118034 + 0.363271i) q^{9} +(0.809017 + 0.587785i) q^{10} +(1.30902 + 4.02874i) q^{11} +(-2.42705 - 1.76336i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.218847 - 0.673542i) q^{14} +(3.42705 - 2.48990i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(0.309017 - 0.951057i) q^{17} +(-0.118034 + 0.0857567i) q^{18} +(-5.85410 - 4.25325i) q^{19} +(-1.50000 - 4.61653i) q^{20} +(-2.42705 - 1.76336i) q^{21} +(-0.500000 + 1.53884i) q^{22} +(0.763932 - 2.35114i) q^{23} +(-0.736068 - 2.26538i) q^{24} +1.85410 q^{25} +0.381966 q^{26} +(1.69098 + 5.20431i) q^{27} +(-2.78115 + 2.02063i) q^{28} +(4.73607 + 3.44095i) q^{29} +1.61803 q^{30} +(3.23607 + 4.53077i) q^{31} -4.14590 q^{32} +(5.54508 + 4.02874i) q^{33} +(0.309017 - 0.224514i) q^{34} +(-1.50000 - 4.61653i) q^{35} +0.708204 q^{36} -7.61803 q^{37} +(-0.854102 - 2.62866i) q^{38} +(0.500000 - 1.53884i) q^{39} +(1.19098 - 3.66547i) q^{40} +(2.92705 + 2.12663i) q^{41} +(-0.354102 - 1.08981i) q^{42} +(-2.73607 - 1.98787i) q^{43} +(6.35410 - 4.61653i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(0.763932 - 0.555029i) q^{46} +(4.16312 - 3.02468i) q^{47} +(-1.57295 + 4.84104i) q^{48} +(2.88197 - 2.09387i) q^{49} +(0.572949 + 0.416272i) q^{50} +(-0.500000 - 1.53884i) q^{51} +(-1.50000 - 1.08981i) q^{52} +(-3.64590 + 11.2209i) q^{53} +(-0.645898 + 1.98787i) q^{54} +(3.42705 + 10.5474i) q^{55} -2.72949 q^{56} -11.7082 q^{57} +(0.690983 + 2.12663i) q^{58} +(1.11803 - 0.812299i) q^{59} +(-6.35410 - 4.61653i) q^{60} +11.0000 q^{61} +(-0.0172209 + 2.12663i) q^{62} +0.708204 q^{63} +(3.80902 + 2.76741i) q^{64} +(2.11803 - 1.53884i) q^{65} +(0.809017 + 2.48990i) q^{66} -5.61803 q^{67} -1.85410 q^{68} +(-1.23607 - 3.80423i) q^{69} +(0.572949 - 1.76336i) q^{70} +(-2.85410 + 8.78402i) q^{71} +(0.454915 + 0.330515i) q^{72} +(-1.16312 - 3.57971i) q^{73} +(-2.35410 - 1.71036i) q^{74} +(2.42705 - 1.76336i) q^{75} +(-4.14590 + 12.7598i) q^{76} +(6.35410 - 4.61653i) q^{77} +(0.500000 - 0.363271i) q^{78} +(-0.545085 + 1.67760i) q^{79} +(-6.66312 + 4.84104i) q^{80} +(6.23607 + 4.53077i) q^{81} +(0.427051 + 1.31433i) q^{82} +(-4.61803 - 3.35520i) q^{83} +(-1.71885 + 5.29007i) q^{84} +(0.809017 - 2.48990i) q^{85} +(-0.399187 - 1.22857i) q^{86} +9.47214 q^{87} +6.23607 q^{88} +(1.16312 + 3.57971i) q^{89} +(-0.309017 + 0.224514i) q^{90} +(-1.50000 - 1.08981i) q^{91} -4.58359 q^{92} +(8.54508 + 2.85317i) q^{93} +1.96556 q^{94} +(-15.3262 - 11.1352i) q^{95} +(-5.42705 + 3.94298i) q^{96} +(3.70820 + 11.4127i) q^{97} +1.36068 q^{98} -1.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{3} - 9 q^{4} + 6 q^{5} - 2 q^{6} - 9 q^{7} + 13 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 + 3 * q^3 - 9 * q^4 + 6 * q^5 - 2 * q^6 - 9 * q^7 + 13 * q^8 + 4 * q^9	\( 4 q - q^{2} + 3 q^{3} - 9 q^{4} + 6 q^{5} - 2 q^{6} - 9 q^{7} + 13 q^{8} + 4 q^{9} + q^{10} + 3 q^{11} - 3 q^{12} + q^{13} + 21 q^{14} + 7 q^{15} + q^{16} - q^{17} + 4 q^{18} - 10 q^{19} - 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} + 6 q^{24} - 6 q^{25} + 6 q^{26} + 9 q^{27} + 9 q^{28} + 10 q^{29} + 2 q^{30} + 4 q^{31} - 30 q^{32} + 11 q^{33} - q^{34} - 6 q^{35} - 24 q^{36} - 26 q^{37} + 10 q^{38} + 2 q^{39} + 7 q^{40} + 5 q^{41} + 12 q^{42} - 2 q^{43} + 12 q^{44} + q^{45} + 12 q^{46} + q^{47} - 13 q^{48} + 16 q^{49} + 9 q^{50} - 2 q^{51} - 6 q^{52} - 28 q^{53} - 16 q^{54} + 7 q^{55} - 78 q^{56} - 20 q^{57} + 5 q^{58} - 12 q^{60} + 44 q^{61} + 29 q^{62} - 24 q^{63} + 13 q^{64} + 4 q^{65} + q^{66} - 18 q^{67} + 6 q^{68} + 4 q^{69} + 9 q^{70} + 2 q^{71} + 13 q^{72} + 11 q^{73} + 4 q^{74} + 3 q^{75} - 30 q^{76} + 12 q^{77} + 2 q^{78} + 9 q^{79} - 11 q^{80} + 16 q^{81} - 5 q^{82} - 14 q^{83} - 27 q^{84} + q^{85} + 23 q^{86} + 20 q^{87} + 16 q^{88} - 11 q^{89} + q^{90} - 6 q^{91} - 72 q^{92} + 23 q^{93} + 66 q^{94} - 30 q^{95} - 15 q^{96} - 12 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^3 - 9 * q^4 + 6 * q^5 - 2 * q^6 - 9 * q^7 + 13 * q^8 + 4 * q^9 + q^10 + 3 * q^11 - 3 * q^12 + q^13 + 21 * q^14 + 7 * q^15 + q^16 - q^17 + 4 * q^18 - 10 * q^19 - 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 + 6 * q^24 - 6 * q^25 + 6 * q^26 + 9 * q^27 + 9 * q^28 + 10 * q^29 + 2 * q^30 + 4 * q^31 - 30 * q^32 + 11 * q^33 - q^34 - 6 * q^35 - 24 * q^36 - 26 * q^37 + 10 * q^38 + 2 * q^39 + 7 * q^40 + 5 * q^41 + 12 * q^42 - 2 * q^43 + 12 * q^44 + q^45 + 12 * q^46 + q^47 - 13 * q^48 + 16 * q^49 + 9 * q^50 - 2 * q^51 - 6 * q^52 - 28 * q^53 - 16 * q^54 + 7 * q^55 - 78 * q^56 - 20 * q^57 + 5 * q^58 - 12 * q^60 + 44 * q^61 + 29 * q^62 - 24 * q^63 + 13 * q^64 + 4 * q^65 + q^66 - 18 * q^67 + 6 * q^68 + 4 * q^69 + 9 * q^70 + 2 * q^71 + 13 * q^72 + 11 * q^73 + 4 * q^74 + 3 * q^75 - 30 * q^76 + 12 * q^77 + 2 * q^78 + 9 * q^79 - 11 * q^80 + 16 * q^81 - 5 * q^82 - 14 * q^83 - 27 * q^84 + q^85 + 23 * q^86 + 20 * q^87 + 16 * q^88 - 11 * q^89 + q^90 - 6 * q^91 - 72 * q^92 + 23 * q^93 + 66 * q^94 - 30 * q^95 - 15 * q^96 - 12 * q^97 - 84 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.309017	+	0.224514i	0.218508	+	0.158755i	0.691655	−	0.722228i	$-0.256882\pi$
$2$	0.309017	+	0.224514i	0.218508	+	0.158755i	−0.473147	+	0.880984i	$0.656882\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$	−0.572949	−	1.76336i	−0.286475	−	0.881678i
$5$	2.61803			1.17082			0.585410	−	0.810737i	$-0.300933\pi$
$5$	2.61803			1.17082			0.585410	+	0.810737i	$0.300933\pi$
$6$	0.618034			0.252311
$7$	−0.572949	−	1.76336i	−0.216554	−	0.666486i	−0.999040	−	0.0438167i	$-0.986048\pi$
$7$	−0.572949	−	1.76336i	−0.216554	−	0.666486i	0.782485	−	0.622669i	$-0.213952\pi$
$8$	0.454915	−	1.40008i	0.160837	−	0.495005i
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	0.929208	+	0.369558i	$0.120491\pi$
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	−0.534524	+	0.845153i	$0.679509\pi$
$12$	−2.42705	−	1.76336i	−0.700629	−	0.509037i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	0.218847	−	0.673542i	0.0584893	−	0.180012i
$15$	3.42705	−	2.48990i	0.884861	−	0.642889i
$16$	−2.54508	+	1.84911i	−0.636271	+	0.462278i
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i	−0.906564	−	0.422069i	$-0.861304\pi$
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i	0.981511	+	0.191404i	$0.0613040\pi$
$18$	−0.118034	+	0.0857567i	−0.0278209	+	0.0202131i
$19$	−5.85410	−	4.25325i	−1.34302	−	0.975763i	−0.999327	−	0.0366825i	$-0.988321\pi$
$19$	−5.85410	−	4.25325i	−1.34302	−	0.975763i	−0.343696	−	0.939081i	$-0.611679\pi$
$20$	−1.50000	−	4.61653i	−0.335410	−	1.03229i
$21$	−2.42705	−	1.76336i	−0.529626	−	0.384796i
$22$	−0.500000	+	1.53884i	−0.106600	+	0.328082i
$23$	0.763932	−	2.35114i	0.159291	−	0.490247i	−0.839280	−	0.543700i	$-0.817023\pi$
$23$	0.763932	−	2.35114i	0.159291	−	0.490247i	0.998570	+	0.0534534i	$0.0170229\pi$
$24$	−0.736068	−	2.26538i	−0.150249	−	0.462420i
$25$	1.85410			0.370820
$26$	0.381966			0.0749097
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−2.78115	+	2.02063i	−0.525589	+	0.381862i
$29$	4.73607	+	3.44095i	0.879466	+	0.638969i	0.933110	−	0.359591i	$-0.117084\pi$
$29$	4.73607	+	3.44095i	0.879466	+	0.638969i	−0.0536443	+	0.998560i	$0.517084\pi$
$30$	1.61803			0.295411
$31$	3.23607	+	4.53077i	0.581215	+	0.813750i
$31$	3.23607	+	4.53077i	0.581215	+	0.813750i
$32$	−4.14590			−0.732898
$33$	5.54508	+	4.02874i	0.965275	+	0.701314i
$34$	0.309017	−	0.224514i	0.0529960	−	0.0385038i
$35$	−1.50000	−	4.61653i	−0.253546	−	0.780335i
$36$	0.708204			0.118034
$37$	−7.61803			−1.25240			−0.626199	−	0.779664i	$-0.715390\pi$
$37$	−7.61803			−1.25240			−0.626199	+	0.779664i	$0.715390\pi$
$38$	−0.854102	−	2.62866i	−0.138554	−	0.426424i
$39$	0.500000	−	1.53884i	0.0800641	−	0.246412i
$40$	1.19098	−	3.66547i	0.188311	−	0.579562i
$41$	2.92705	+	2.12663i	0.457129	+	0.332123i	0.792404	−	0.609997i	$-0.208829\pi$
$41$	2.92705	+	2.12663i	0.457129	+	0.332123i	−0.335275	+	0.942120i	$0.608829\pi$
$42$	−0.354102	−	1.08981i	−0.0546391	−	0.168162i
$43$	−2.73607	−	1.98787i	−0.417246	−	0.303147i	0.359283	−	0.933229i	$-0.383021\pi$
$43$	−2.73607	−	1.98787i	−0.417246	−	0.303147i	−0.776529	+	0.630082i	$0.783021\pi$
$44$	6.35410	−	4.61653i	0.957917	−	0.695967i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	0.763932	−	0.555029i	0.112636	−	0.0818346i
$47$	4.16312	−	3.02468i	0.607253	−	0.441195i	−0.241193	−	0.970477i	$-0.577539\pi$
$47$	4.16312	−	3.02468i	0.607253	−	0.441195i	0.848446	+	0.529282i	$0.177539\pi$
$48$	−1.57295	+	4.84104i	−0.227036	+	0.698744i
$49$	2.88197	−	2.09387i	0.411709	−	0.299124i
$50$	0.572949	+	0.416272i	0.0810272	+	0.0588697i
$51$	−0.500000	−	1.53884i	−0.0700140	−	0.215481i
$52$	−1.50000	−	1.08981i	−0.208013	−	0.151130i
$53$	−3.64590	+	11.2209i	−0.500803	+	1.54131i	0.306912	+	0.951738i	$0.400704\pi$
$53$	−3.64590	+	11.2209i	−0.500803	+	1.54131i	−0.807714	+	0.589574i	$0.799296\pi$
$54$	−0.645898	+	1.98787i	−0.0878956	+	0.270515i
$55$	3.42705	+	10.5474i	0.462103	+	1.42221i
$56$	−2.72949			−0.364743
$57$	−11.7082			−1.55079
$58$	0.690983	+	2.12663i	0.0907305	+	0.279240i
$59$	1.11803	−	0.812299i	0.145556	−	0.105752i	−0.512624	−	0.858613i	$-0.671327\pi$
$59$	1.11803	−	0.812299i	0.145556	−	0.105752i	0.658180	+	0.752861i	$0.271327\pi$
$60$	−6.35410	−	4.61653i	−0.820311	−	0.595991i
$61$	11.0000			1.40841			0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000			1.40841			0.704203	+	0.709999i	$0.251305\pi$
$62$	−0.0172209	+	2.12663i	−0.00218706	+	0.270082i
$63$	0.708204			0.0892253
$64$	3.80902	+	2.76741i	0.476127	+	0.345927i
$65$	2.11803	−	1.53884i	0.262710	−	0.190870i
$66$	0.809017	+	2.48990i	0.0995831	+	0.306485i
$67$	−5.61803			−0.686352			−0.343176	−	0.939271i	$-0.611503\pi$
$67$	−5.61803			−0.686352			−0.343176	+	0.939271i	$0.611503\pi$
$68$	−1.85410			−0.224843
$69$	−1.23607	−	3.80423i	−0.148805	−	0.457975i
$70$	0.572949	−	1.76336i	0.0684805	−	0.210761i
$71$	−2.85410	+	8.78402i	−0.338720	+	1.04247i	0.626141	+	0.779710i	$0.284633\pi$
$71$	−2.85410	+	8.78402i	−0.338720	+	1.04247i	−0.964861	+	0.262762i	$0.915367\pi$
$72$	0.454915	+	0.330515i	0.0536123	+	0.0389516i
$73$	−1.16312	−	3.57971i	−0.136133	−	0.418974i	0.859632	−	0.510914i	$-0.170693\pi$
$73$	−1.16312	−	3.57971i	−0.136133	−	0.418974i	−0.995764	+	0.0919406i	$0.970693\pi$
$74$	−2.35410	−	1.71036i	−0.273659	−	0.198825i
$75$	2.42705	−	1.76336i	0.280252	−	0.203615i
$76$	−4.14590	+	12.7598i	−0.475567	+	1.46365i
$77$	6.35410	−	4.61653i	0.724117	−	0.526102i
$78$	0.500000	−	0.363271i	0.0566139	−	0.0411324i
$79$	−0.545085	+	1.67760i	−0.0613269	+	0.188745i	−0.977026	−	0.213120i	$-0.931638\pi$
$79$	−0.545085	+	1.67760i	−0.0613269	+	0.188745i	0.915699	+	0.401864i	$0.131638\pi$
$80$	−6.66312	+	4.84104i	−0.744959	+	0.541245i
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$	0.427051	+	1.31433i	0.0471599	+	0.145143i
$83$	−4.61803	−	3.35520i	−0.506895	−	0.368281i	0.304749	−	0.952433i	$-0.401427\pi$
$83$	−4.61803	−	3.35520i	−0.506895	−	0.368281i	−0.811644	+	0.584152i	$0.801427\pi$
$84$	−1.71885	+	5.29007i	−0.187542	+	0.577194i
$85$	0.809017	−	2.48990i	0.0877502	−	0.270067i
$86$	−0.399187	−	1.22857i	−0.0430454	−	0.132480i
$87$	9.47214			1.01552
$88$	6.23607			0.664767
$89$	1.16312	+	3.57971i	0.123290	+	0.379449i	0.993586	−	0.113081i	$-0.0360721\pi$
$89$	1.16312	+	3.57971i	0.123290	+	0.379449i	−0.870295	+	0.492530i	$0.836072\pi$
$90$	−0.309017	+	0.224514i	−0.0325733	+	0.0236659i
$91$	−1.50000	−	1.08981i	−0.157243	−	0.114244i
$92$	−4.58359			−0.477873
$93$	8.54508	+	2.85317i	0.886084	+	0.295860i
$94$	1.96556			0.202732
$95$	−15.3262	−	11.1352i	−1.57244	−	1.14244i
$96$	−5.42705	+	3.94298i	−0.553896	+	0.402429i
$97$	3.70820	+	11.4127i	0.376511	+	1.15878i	0.942454	+	0.334337i	$0.108512\pi$
$97$	3.70820	+	11.4127i	0.376511	+	1.15878i	−0.565942	+	0.824445i	$0.691488\pi$
$98$	1.36068			0.137449
$99$	−1.61803			−0.162619
$100$	−1.06231	−	3.26944i	−0.106231	−	0.326944i
$101$	−2.66312	+	8.19624i	−0.264990	+	0.815556i	0.726705	+	0.686949i	$0.241051\pi$
$101$	−2.66312	+	8.19624i	−0.264990	+	0.815556i	−0.991696	+	0.128607i	$0.958949\pi$
$102$	0.190983	−	0.587785i	0.0189101	−	0.0581994i
$103$	−14.6353	−	10.6331i	−1.44205	−	1.04771i	−0.987608	−	0.156940i	$-0.949837\pi$
$103$	−14.6353	−	10.6331i	−1.44205	−	1.04771i	−0.454446	−	0.890774i	$-0.650163\pi$
$104$	−0.454915	−	1.40008i	−0.0446081	−	0.137290i
$105$	−6.35410	−	4.61653i	−0.620097	−	0.450527i
$106$	−3.64590	+	2.64890i	−0.354121	+	0.257284i
$107$	0.409830	−	1.26133i	0.0396198	−	0.121937i	−0.929290	−	0.369350i	$-0.879580\pi$
$107$	0.409830	−	1.26133i	0.0396198	−	0.121937i	0.968910	+	0.247413i	$0.0795804\pi$
$108$	8.20820	−	5.96361i	0.789835	−	0.573849i
$109$	−7.85410	+	5.70634i	−0.752287	+	0.546568i	−0.896535	−	0.442973i	$-0.853924\pi$
$109$	−7.85410	+	5.70634i	−0.752287	+	0.546568i	0.144248	+	0.989542i	$0.453924\pi$
$110$	−1.30902	+	4.02874i	−0.124810	+	0.384125i
$111$	−9.97214	+	7.24518i	−0.946513	+	0.687682i
$112$	4.71885	+	3.42844i	0.445889	+	0.323957i
$113$	−2.69098	−	8.28199i	−0.253146	−	0.779104i	−0.994189	−	0.107647i	$-0.965668\pi$
$113$	−2.69098	−	8.28199i	−0.253146	−	0.779104i	0.741043	−	0.671458i	$-0.234332\pi$
$114$	−3.61803	−	2.62866i	−0.338860	−	0.246196i
$115$	2.00000	−	6.15537i	0.186501	−	0.573991i
$116$	3.35410	−	10.3229i	0.311421	−	0.958454i
$117$	0.118034	+	0.363271i	0.0109122	+	0.0335844i
$118$	0.527864			0.0485938
$119$	−1.85410			−0.169965
$120$	−1.92705	−	5.93085i	−0.175915	−	0.541410i
$121$	−5.61803	+	4.08174i	−0.510730	+	0.371067i
$122$	3.39919	+	2.46965i	0.307748	+	0.223592i
$123$	5.85410			0.527847
$124$	6.13525	−	8.30224i	0.550962	−	0.745563i
$125$	−8.23607			−0.736656
$126$	0.218847	+	0.159002i	0.0194964	+	0.0141650i
$127$	5.85410	−	4.25325i	0.519468	−	0.377415i	−0.296936	−	0.954897i	$-0.595965\pi$
$127$	5.85410	−	4.25325i	0.519468	−	0.377415i	0.816403	+	0.577482i	$0.195965\pi$
$128$	3.11803	+	9.59632i	0.275598	+	0.848203i
$129$	−5.47214			−0.481795
$130$	1.00000			0.0877058
$131$	−5.47214	−	16.8415i	−0.478103	−	1.47145i	−0.841727	−	0.539903i	$-0.818461\pi$
$131$	−5.47214	−	16.8415i	−0.478103	−	1.47145i	0.363624	−	0.931546i	$-0.381539\pi$
$132$	3.92705	−	12.0862i	0.341806	−	1.05197i
$133$	−4.14590	+	12.7598i	−0.359495	+	1.10641i
$134$	−1.73607	−	1.26133i	−0.149973	−	0.108962i
$135$	4.42705	+	13.6251i	0.381020	+	1.17266i
$136$	−1.19098	−	0.865300i	−0.102126	−	0.0741988i
$137$	−0.354102	+	0.257270i	−0.0302530	+	0.0219801i	−0.602809	−	0.797886i	$-0.705952\pi$
$137$	−0.354102	+	0.257270i	−0.0302530	+	0.0219801i	0.572556	+	0.819866i	$0.305952\pi$
$138$	0.472136	−	1.45309i	0.0401909	−	0.123695i
$139$	7.80902	−	5.67358i	0.662352	−	0.481227i	−0.205104	−	0.978740i	$-0.565753\pi$
$139$	7.80902	−	5.67358i	0.662352	−	0.481227i	0.867456	+	0.497513i	$0.165753\pi$
$140$	−7.28115	+	5.29007i	−0.615370	+	0.447092i
$141$	2.57295	−	7.91872i	0.216681	−	0.666877i
$142$	−2.85410	+	2.07363i	−0.239511	+	0.174015i
$143$	3.42705	+	2.48990i	0.286584	+	0.208216i
$144$	−0.371323	−	1.14281i	−0.0309436	−	0.0952345i
$145$	12.3992	+	9.00854i	1.02970	+	0.748118i
$146$	0.444272	−	1.36733i	0.0367682	−	0.113161i
$147$	1.78115	−	5.48183i	0.146907	−	0.452133i
$148$	4.36475	+	13.4333i	0.358780	+	1.10421i
$149$	7.76393			0.636046			0.318023	−	0.948083i	$-0.396981\pi$
$149$	7.76393			0.636046			0.318023	+	0.948083i	$0.396981\pi$
$150$	1.14590			0.0935622
$151$	6.01722	+	18.5191i	0.489674	+	1.50706i	0.825095	+	0.564994i	$0.191122\pi$
$151$	6.01722	+	18.5191i	0.489674	+	1.50706i	−0.335420	+	0.942069i	$0.608878\pi$
$152$	−8.61803	+	6.26137i	−0.699015	+	0.507864i
$153$	0.309017	+	0.224514i	0.0249825	+	0.0181509i
$154$	3.00000			0.241747
$155$	8.47214	+	11.8617i	0.680498	+	0.952755i
$156$	−3.00000			−0.240192
$157$	−6.19098	−	4.49801i	−0.494094	−	0.358980i	0.312662	−	0.949864i	$-0.398779\pi$
$157$	−6.19098	−	4.49801i	−0.494094	−	0.358980i	−0.806757	+	0.590884i	$0.798779\pi$
$158$	−0.545085	+	0.396027i	−0.0433646	+	0.0315062i
$159$	5.89919	+	18.1558i	0.467836	+	1.43985i
$160$	−10.8541			−0.858092
$161$	−4.58359			−0.361238
$162$	0.909830	+	2.80017i	0.0714830	+	0.220002i
$163$	0.826238	−	2.54290i	0.0647159	−	0.199175i	−0.913470	−	0.406906i	$-0.866608\pi$
$163$	0.826238	−	2.54290i	0.0647159	−	0.199175i	0.978186	+	0.207731i	$0.0666077\pi$
$164$	2.07295	−	6.37988i	0.161870	−	0.498185i
$165$	14.5172	+	10.5474i	1.13016	+	0.821112i
$166$	−0.673762	−	2.07363i	−0.0522941	−	0.160945i
$167$	−15.2812	−	11.1024i	−1.18249	−	0.859130i	−0.190041	−	0.981776i	$-0.560862\pi$
$167$	−15.2812	−	11.1024i	−1.18249	−	0.859130i	−0.992450	+	0.122646i	$0.960862\pi$
$168$	−3.57295	+	2.59590i	−0.275659	+	0.200278i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	0.809017	−	0.587785i	0.0620488	−	0.0450811i
$171$	2.23607	−	1.62460i	0.170996	−	0.124236i
$172$	−1.93769	+	5.96361i	−0.147748	+	0.454721i
$173$	18.1353	−	13.1760i	1.37880	−	1.00176i	0.381807	−	0.924242i	$-0.375302\pi$
$173$	18.1353	−	13.1760i	1.37880	−	1.00176i	0.996991	−	0.0775131i	$-0.0246979\pi$
$174$	2.92705	+	2.12663i	0.221899	+	0.161219i
$175$	−1.06231	−	3.26944i	−0.0803028	−	0.247147i
$176$	−10.7812	−	7.83297i	−0.812660	−	0.590432i
$177$	0.690983	−	2.12663i	0.0519375	−	0.159847i
$178$	−0.444272	+	1.36733i	−0.0332996	+	0.102486i
$179$	−1.28115	−	3.94298i	−0.0957579	−	0.294712i	0.891693	−	0.452641i	$-0.149518\pi$
$179$	−1.28115	−	3.94298i	−0.0957579	−	0.294712i	−0.987450	+	0.157929i	$0.949518\pi$
$180$	1.85410			0.138197
$181$	19.2361			1.42981			0.714903	−	0.699224i	$-0.246471\pi$
$181$	19.2361			1.42981			0.714903	+	0.699224i	$0.246471\pi$
$182$	−0.218847	−	0.673542i	−0.0162220	−	0.0499263i
$183$	14.3992	−	10.4616i	1.06442	−	0.773345i
$184$	−2.94427	−	2.13914i	−0.217055	−	0.157699i
$185$	−19.9443			−1.46633
$186$	2.00000	+	2.80017i	0.146647	+	0.205318i
$187$	4.23607			0.309772
$188$	−7.71885	−	5.60807i	−0.562955	−	0.409011i
$189$	8.20820	−	5.96361i	0.597059	−	0.433789i
$190$	−2.23607	−	6.88191i	−0.162221	−	0.499266i
$191$	−20.2361			−1.46423			−0.732115	−	0.681181i	$-0.761467\pi$
$191$	−20.2361			−1.46423			−0.732115	+	0.681181i	$0.761467\pi$
$192$	7.61803			0.549784
$193$	6.64590	+	20.4540i	0.478382	+	1.47231i	0.841341	+	0.540504i	$0.181766\pi$
$193$	6.64590	+	20.4540i	0.478382	+	1.47231i	−0.362959	+	0.931805i	$0.618234\pi$
$194$	−1.41641	+	4.35926i	−0.101692	+	0.312976i
$195$	1.30902	−	4.02874i	0.0937407	−	0.288504i
$196$	−5.34346	−	3.88225i	−0.381676	−	0.277304i
$197$	−7.26393	−	22.3561i	−0.517534	−	1.59281i	−0.778624	−	0.627491i	$-0.784082\pi$
$197$	−7.26393	−	22.3561i	−0.517534	−	1.59281i	0.261090	−	0.965314i	$-0.415918\pi$
$198$	−0.500000	−	0.363271i	−0.0355335	−	0.0258166i
$199$	15.8262	−	11.4984i	1.12189	−	0.815102i	0.137397	−	0.990516i	$-0.456126\pi$
$199$	15.8262	−	11.4984i	1.12189	−	0.815102i	0.984495	+	0.175414i	$0.0561263\pi$
$200$	0.843459	−	2.59590i	0.0596415	−	0.183558i
$201$	−7.35410	+	5.34307i	−0.518718	+	0.376871i
$202$	−2.66312	+	1.93487i	−0.187376	+	0.136137i
$203$	3.35410	−	10.3229i	0.235412	−	0.724523i
$204$	−2.42705	+	1.76336i	−0.169928	+	0.123460i
$205$	7.66312	+	5.56758i	0.535215	+	0.388857i
$206$	−2.13525	−	6.57164i	−0.148770	−	0.457868i
$207$	0.763932	+	0.555029i	0.0530969	+	0.0385772i
$208$	−0.972136	+	2.99193i	−0.0674055	+	0.207453i
$209$	9.47214	−	29.1522i	0.655201	−	2.01650i
$210$	−0.927051	−	2.85317i	−0.0639726	−	0.196887i
$211$	1.94427			0.133849			0.0669246	−	0.997758i	$-0.478681\pi$
$211$	1.94427			0.133849			0.0669246	+	0.997758i	$0.478681\pi$
$212$	21.8754			1.50241
$213$	4.61803	+	14.2128i	0.316422	+	0.973848i
$214$	0.409830	−	0.297759i	0.0280154	−	0.0203544i
$215$	−7.16312	−	5.20431i	−0.488521	−	0.354931i
$216$	8.05573			0.548123
$217$	6.13525	−	8.30224i	0.416488	−	0.563593i
$218$	−3.70820			−0.251151
$219$	−4.92705	−	3.57971i	−0.332939	−	0.241895i
$220$	16.6353	−	12.0862i	1.12155	−	0.814853i
$221$	−0.309017	−	0.951057i	−0.0207867	−	0.0639750i
$222$	−4.70820			−0.315994
$223$	−16.2361			−1.08725			−0.543624	−	0.839329i	$-0.682948\pi$
$223$	−16.2361			−1.08725			−0.543624	+	0.839329i	$0.682948\pi$
$224$	2.37539	+	7.31069i	0.158712	+	0.488466i
$225$	−0.218847	+	0.673542i	−0.0145898	+	0.0449028i
$226$	1.02786	−	3.16344i	0.0683725	−	0.210429i
$227$	17.3713	+	12.6210i	1.15298	+	0.837686i	0.988874	−	0.148758i	$-0.0475275\pi$
$227$	17.3713	+	12.6210i	1.15298	+	0.837686i	0.164102	+	0.986443i	$0.447528\pi$
$228$	6.70820	+	20.6457i	0.444262	+	1.36730i
$229$	−14.4443	−	10.4944i	−0.954504	−	0.693488i	−0.00263644	−	0.999997i	$-0.500839\pi$
$229$	−14.4443	−	10.4944i	−0.954504	−	0.693488i	−0.951868	+	0.306509i	$0.900839\pi$
$230$	2.00000	−	1.45309i	0.131876	−	0.0958136i
$231$	3.92705	−	12.0862i	0.258381	−	0.795215i
$232$	6.97214	−	5.06555i	0.457743	−	0.332570i
$233$	1.54508	−	1.12257i	0.101222	−	0.0735420i	−0.536023	−	0.844203i	$-0.680074\pi$
$233$	1.54508	−	1.12257i	0.101222	−	0.0735420i	0.637245	+	0.770661i	$0.280074\pi$
$234$	−0.0450850	+	0.138757i	−0.00294730	+	0.00907085i
$235$	10.8992	−	7.91872i	0.710985	−	0.516561i
$236$	−2.07295	−	1.50609i	−0.134937	−	0.0980378i
$237$	0.881966	+	2.71441i	0.0572898	+	0.176320i
$238$	−0.572949	−	0.416272i	−0.0371388	−	0.0269829i
$239$	−0.798374	+	2.45714i	−0.0516425	+	0.158939i	−0.973552	−	0.228467i	$-0.926629\pi$
$239$	−0.798374	+	2.45714i	−0.0516425	+	0.158939i	0.921909	+	0.387406i	$0.126629\pi$
$240$	−4.11803	+	12.6740i	−0.265818	+	0.818104i
$241$	−4.66312	−	14.3516i	−0.300378	−	0.924468i	−0.981362	−	0.192170i	$-0.938448\pi$
$241$	−4.66312	−	14.3516i	−0.300378	−	0.924468i	0.680984	−	0.732298i	$-0.261552\pi$
$242$	−2.65248			−0.170508
$243$	−3.94427			−0.253025
$244$	−6.30244	−	19.3969i	−0.403472	−	1.24176i
$245$	7.54508	−	5.48183i	0.482038	−	0.350221i
$246$	1.80902	+	1.31433i	0.115339	+	0.0837985i
$247$	−7.23607			−0.460420
$248$	7.81559	−	2.46965i	0.496291	−	0.156823i
$249$	−9.23607			−0.585312
$250$	−2.54508	−	1.84911i	−0.160965	−	0.116948i
$251$	−16.3992	+	11.9147i	−1.03511	+	0.752050i	−0.969325	−	0.245784i	$-0.920954\pi$
$251$	−16.3992	+	11.9147i	−1.03511	+	0.752050i	−0.0657830	+	0.997834i	$0.520954\pi$
$252$	−0.405765	−	1.24882i	−0.0255608	−	0.0786680i
$253$	10.4721			0.658378
$254$	2.76393			0.173425
$255$	−1.30902	−	4.02874i	−0.0819738	−	0.252289i
$256$	1.71885	−	5.29007i	0.107428	−	0.330629i
$257$	−0.0450850	+	0.138757i	−0.00281232	+	0.00865544i	−0.952453	−	0.304686i	$-0.901448\pi$
$257$	−0.0450850	+	0.138757i	−0.00281232	+	0.00865544i	0.949641	+	0.313342i	$0.101448\pi$
$258$	−1.69098	−	1.22857i	−0.105276	−	0.0764875i
$259$	4.36475	+	13.4333i	0.271212	+	0.834705i
$260$	−3.92705	−	2.85317i	−0.243545	−	0.176946i
$261$	−1.80902	+	1.31433i	−0.111975	+	0.0813548i
$262$	2.09017	−	6.43288i	0.129131	−	0.397425i
$263$	3.54508	−	2.57565i	0.218599	−	0.158822i	−0.473097	−	0.881011i	$-0.656864\pi$
$263$	3.54508	−	2.57565i	0.218599	−	0.158822i	0.691696	+	0.722189i	$0.256864\pi$
$264$	8.16312	−	5.93085i	0.502405	−	0.365019i
$265$	−9.54508	+	29.3768i	−0.586350	+	1.80460i
$266$	−4.14590	+	3.01217i	−0.254201	+	0.184688i
$267$	4.92705	+	3.57971i	0.301531	+	0.219075i
$268$	3.21885	+	9.90659i	0.196622	+	0.605141i
$269$	−12.1353	−	8.81678i	−0.739900	−	0.537568i	0.152780	−	0.988260i	$-0.451177\pi$
$269$	−12.1353	−	8.81678i	−0.739900	−	0.537568i	−0.892680	+	0.450692i	$0.851177\pi$
$270$	−1.69098	+	5.20431i	−0.102910	+	0.316724i
$271$	8.26393	−	25.4338i	0.501998	−	1.54499i	−0.303761	−	0.952748i	$-0.598242\pi$
$271$	8.26393	−	25.4338i	0.501998	−	1.54499i	0.805759	−	0.592243i	$-0.201758\pi$
$272$	0.972136	+	2.99193i	0.0589444	+	0.181412i
$273$	−3.00000			−0.181568
$274$	−0.167184			−0.0101000
$275$	2.42705	+	7.46969i	0.146357	+	0.450440i
$276$	−6.00000	+	4.35926i	−0.361158	+	0.262396i
$277$	−7.04508	−	5.11855i	−0.423298	−	0.307544i	0.355665	−	0.934613i	$-0.384254\pi$
$277$	−7.04508	−	5.11855i	−0.423298	−	0.307544i	−0.778963	+	0.627069i	$0.784254\pi$
$278$	3.68692			0.221127
$279$	−2.02786	+	0.640786i	−0.121405	+	0.0383628i
$280$	−7.14590			−0.427049
$281$	−4.57295	−	3.32244i	−0.272799	−	0.198200i	0.442971	−	0.896536i	$-0.353924\pi$
$281$	−4.57295	−	3.32244i	−0.272799	−	0.198200i	−0.715771	+	0.698336i	$0.753924\pi$
$282$	2.57295	−	1.86936i	0.153217	−	0.111319i
$283$	−0.854102	−	2.62866i	−0.0507711	−	0.156257i	0.922456	−	0.386101i	$-0.126178\pi$
$283$	−0.854102	−	2.62866i	−0.0507711	−	0.156257i	−0.973228	+	0.229844i	$0.926178\pi$
$284$	17.1246			1.01616
$285$	−30.6525			−1.81570
$286$	0.500000	+	1.53884i	0.0295656	+	0.0909936i
$287$	2.07295	−	6.37988i	0.122362	−	0.376592i
$288$	0.489357	−	1.50609i	0.0288356	−	0.0887469i
$289$	12.9443	+	9.40456i	0.761428	+	0.553210i
$290$	1.80902	+	5.56758i	0.106229	+	0.326940i
$291$	15.7082	+	11.4127i	0.920831	+	0.669023i
$292$	−5.64590	+	4.10199i	−0.330401	+	0.240051i
$293$	−4.91641	+	15.1311i	−0.287220	+	0.883971i	0.698505	+	0.715605i	$0.253849\pi$
$293$	−4.91641	+	15.1311i	−0.287220	+	0.883971i	−0.985725	+	0.168366i	$0.946151\pi$
$294$	1.78115	−	1.29408i	0.103879	−	0.0754725i
$295$	2.92705	−	2.12663i	0.170419	−	0.123817i
$296$	−3.46556	+	10.6659i	−0.201431	+	0.619942i
$297$	−18.7533	+	13.6251i	−1.08818	+	0.790606i
$298$	2.39919	+	1.74311i	0.138981	+	0.100976i
$299$	−0.763932	−	2.35114i	−0.0441793	−	0.135970i
$300$	−4.50000	−	3.26944i	−0.259808	−	0.188761i
$301$	−1.93769	+	5.96361i	−0.111687	+	0.343737i
$302$	−2.29837	+	7.07367i	−0.132257	+	0.407044i
$303$	4.30902	+	13.2618i	0.247547	+	0.761870i
$304$	22.7639			1.30560
$305$	28.7984			1.64899
$306$	0.0450850	+	0.138757i	0.00257734	+	0.00793223i
$307$	19.8713	−	14.4374i	1.13412	−	0.823984i	0.147828	−	0.989013i	$-0.452772\pi$
$307$	19.8713	−	14.4374i	1.13412	−	0.823984i	0.986289	+	0.165029i	$0.0527719\pi$
$308$	−11.7812	−	8.55951i	−0.671293	−	0.487723i
$309$	−29.2705			−1.66514
$310$	−0.0450850	+	5.56758i	−0.00256065	+	0.316217i
$311$	−28.6525			−1.62473			−0.812366	−	0.583147i	$-0.801821\pi$
$311$	−28.6525			−1.62473			−0.812366	+	0.583147i	$0.801821\pi$
$312$	−1.92705	−	1.40008i	−0.109098	−	0.0792642i
$313$	−9.85410	+	7.15942i	−0.556987	+	0.404675i	−0.830355	−	0.557235i	$-0.811862\pi$
$313$	−9.85410	+	7.15942i	−0.556987	+	0.404675i	0.273368	+	0.961909i	$0.411862\pi$
$314$	−0.903252	−	2.77992i	−0.0509735	−	0.156880i
$315$	1.85410			0.104467
$316$	3.27051			0.183981
$317$	−0.781153	−	2.40414i	−0.0438739	−	0.135030i	0.926720	−	0.375752i	$-0.122616\pi$
$317$	−0.781153	−	2.40414i	−0.0438739	−	0.135030i	−0.970594	+	0.240722i	$0.922616\pi$
$318$	−2.25329	+	6.93491i	−0.126358	+	0.388890i
$319$	−7.66312	+	23.5847i	−0.429052	+	1.32049i
$320$	9.97214	+	7.24518i	0.557459	+	0.405018i
$321$	−0.663119	−	2.04087i	−0.0370117	−	0.113910i
$322$	−1.41641	−	1.02908i	−0.0789333	−	0.0573484i
$323$	−5.85410	+	4.25325i	−0.325731	+	0.236657i
$324$	4.41641	−	13.5923i	0.245356	−	0.755128i
$325$	1.50000	−	1.08981i	0.0832050	−	0.0604520i
$326$	0.826238	−	0.600297i	0.0457611	−	0.0332474i
$327$	−4.85410	+	14.9394i	−0.268432	+	0.826150i
$328$	4.30902	−	3.13068i	0.237926	−	0.172863i
$329$	−7.71885	−	5.60807i	−0.425554	−	0.309183i
$330$	2.11803	+	6.51864i	0.116594	+	0.358839i
$331$	−13.1180	−	9.53081i	−0.721032	−	0.523861i	0.165682	−	0.986179i	$-0.447018\pi$
$331$	−13.1180	−	9.53081i	−0.721032	−	0.523861i	−0.886714	+	0.462319i	$0.847018\pi$
$332$	−3.27051	+	10.0656i	−0.179493	+	0.552421i
$333$	0.899187	−	2.76741i	0.0492751	−	0.151653i
$334$	−2.22949	−	6.86167i	−0.121992	−	0.375454i
$335$	−14.7082			−0.803595
$336$	9.43769			0.514868
$337$	−1.89919	−	5.84510i	−0.103455	−	0.318403i	0.885909	−	0.463858i	$-0.153535\pi$
$337$	−1.89919	−	5.84510i	−0.103455	−	0.318403i	−0.989365	+	0.145455i	$0.953535\pi$
$338$	0.309017	−	0.224514i	0.0168083	−	0.0122120i
$339$	−11.3992	−	8.28199i	−0.619119	−	0.449816i
$340$	−4.85410			−0.263251
$341$	−14.0172	+	18.9681i	−0.759075	+	1.02718i
$342$	1.05573			0.0570872
$343$	−15.8435	−	11.5109i	−0.855466	−	0.621533i
$344$	−4.02786	+	2.92641i	−0.217168	+	0.157782i
$345$	−3.23607	−	9.95959i	−0.174224	−	0.536206i
$346$	8.56231			0.460312
$347$	27.4164			1.47179			0.735895	−	0.677096i	$-0.236762\pi$
$347$	27.4164			1.47179			0.735895	+	0.677096i	$0.236762\pi$
$348$	−5.42705	−	16.7027i	−0.290920	−	0.895361i
$349$	−10.4164	+	32.0584i	−0.557578	+	1.71605i	0.131460	+	0.991321i	$0.458034\pi$
$349$	−10.4164	+	32.0584i	−0.557578	+	1.71605i	−0.689037	+	0.724726i	$0.741966\pi$
$350$	0.405765	−	1.24882i	0.0216890	−	0.0667520i
$351$	4.42705	+	3.21644i	0.236299	+	0.171681i
$352$	−5.42705	−	16.7027i	−0.289263	−	0.890259i
$353$	14.8541	+	10.7921i	0.790604	+	0.574407i	0.908143	−	0.418661i	$-0.137500\pi$
$353$	14.8541	+	10.7921i	0.790604	+	0.574407i	−0.117539	+	0.993068i	$0.537500\pi$
$354$	0.690983	−	0.502029i	0.0367253	−	0.0266825i
$355$	−7.47214	+	22.9969i	−0.396580	+	1.22055i
$356$	5.64590	−	4.10199i	0.299232	−	0.217405i
$357$	−2.42705	+	1.76336i	−0.128453	+	0.0933267i
$358$	0.489357	−	1.50609i	0.0258633	−	0.0795991i
$359$	−2.85410	+	2.07363i	−0.150634	+	0.109442i	−0.660549	−	0.750783i	$-0.729677\pi$
$359$	−2.85410	+	2.07363i	−0.150634	+	0.109442i	0.509916	+	0.860224i	$0.329677\pi$
$360$	1.19098	+	0.865300i	0.0627703	+	0.0456053i
$361$	10.3090	+	31.7279i	0.542580	+	1.66989i
$362$	5.94427	+	4.31877i	0.312424	+	0.226989i
$363$	−3.47214	+	10.6861i	−0.182240	+	0.560877i
$364$	−1.06231	+	3.26944i	−0.0556800	+	0.171365i
$365$	−3.04508	−	9.37181i	−0.159387	−	0.490543i
$366$	6.79837			0.355357
$367$	19.8328			1.03526			0.517632	−	0.855603i	$-0.326814\pi$
$367$	19.8328			1.03526			0.517632	+	0.855603i	$0.326814\pi$
$368$	2.40325	+	7.39645i	0.125278	+	0.385567i
$369$	−1.11803	+	0.812299i	−0.0582025	+	0.0422866i
$370$	−6.16312	−	4.47777i	−0.320405	−	0.232788i
$371$	21.8754			1.13571
$372$	0.135255	−	16.7027i	0.00701264	−	0.865997i
$373$	−20.3262			−1.05245			−0.526226	−	0.850345i	$-0.676394\pi$
$373$	−20.3262			−1.05245			−0.526226	+	0.850345i	$0.676394\pi$
$374$	1.30902	+	0.951057i	0.0676877	+	0.0491780i
$375$	−10.7812	+	7.83297i	−0.556736	+	0.404493i
$376$	−2.34095	−	7.20469i	−0.120725	−	0.371554i
$377$	5.85410			0.301502
$378$	3.87539			0.199328
$379$	−11.0172	−	33.9075i	−0.565917	−	1.74171i	−0.665212	−	0.746654i	$-0.731659\pi$
$379$	−11.0172	−	33.9075i	−0.565917	−	1.74171i	0.0992956	−	0.995058i	$-0.468341\pi$
$380$	−10.8541	+	33.4055i	−0.556804	+	1.71367i
$381$	3.61803	−	11.1352i	0.185357	−	0.570472i
$382$	−6.25329	−	4.54328i	−0.319946	−	0.232454i
$383$	−7.65248	−	23.5519i	−0.391023	−	1.20345i	−0.932016	−	0.362418i	$-0.881951\pi$
$383$	−7.65248	−	23.5519i	−0.391023	−	1.20345i	0.540992	−	0.841028i	$-0.318049\pi$
$384$	13.2082	+	9.59632i	0.674028	+	0.489710i
$385$	16.6353	−	12.0862i	0.847811	−	0.615971i
$386$	−2.53851	+	7.81272i	−0.129207	+	0.397657i
$387$	1.04508	−	0.759299i	0.0531247	−	0.0385973i
$388$	18.0000	−	13.0778i	0.913812	−	0.663923i
$389$	8.98278	−	27.6462i	0.455445	−	1.40172i	−0.415167	−	0.909745i	$-0.636277\pi$
$389$	8.98278	−	27.6462i	0.455445	−	1.40172i	0.870612	−	0.491970i	$-0.163723\pi$
$390$	1.30902	−	0.951057i	0.0662847	−	0.0481586i
$391$	−2.00000	−	1.45309i	−0.101144	−	0.0734857i
$392$	−1.62055	−	4.98753i	−0.0818500	−	0.251908i
$393$	−23.1803	−	16.8415i	−1.16929	−	0.849541i
$394$	2.77458	−	8.53926i	0.139781	−	0.430202i
$395$	−1.42705	+	4.39201i	−0.0718027	+	0.220986i
$396$	0.927051	+	2.85317i	0.0465861	+	0.143377i
$397$	−17.1246			−0.859460			−0.429730	−	0.902958i	$-0.641391\pi$
$397$	−17.1246			−0.859460			−0.429730	+	0.902958i	$0.641391\pi$
$398$	7.47214			0.374544
$399$	6.70820	+	20.6457i	0.335830	+	1.03358i
$400$	−4.71885	+	3.42844i	−0.235942	+	0.171422i
$401$	9.50000	+	6.90215i	0.474407	+	0.344677i	0.799156	−	0.601123i	$-0.205280\pi$
$401$	9.50000	+	6.90215i	0.474407	+	0.344677i	−0.324749	+	0.945800i	$0.605280\pi$
$402$	−3.47214			−0.173174
$403$	5.28115	+	1.76336i	0.263073	+	0.0878390i
$404$	15.9787			0.794971
$405$	16.3262	+	11.8617i	0.811257	+	0.589413i
$406$	3.35410	−	2.43690i	0.166461	−	0.120941i
$407$	−9.97214	−	30.6911i	−0.494300	−	1.52130i
$408$	−2.38197			−0.117925
$409$	−14.1246			−0.698417			−0.349209	−	0.937045i	$-0.613550\pi$
$409$	−14.1246			−0.698417			−0.349209	+	0.937045i	$0.613550\pi$
$410$	1.11803	+	3.44095i	0.0552158	+	0.169937i
$411$	−0.218847	+	0.673542i	−0.0107949	+	0.0332234i
$412$	−10.3647	+	31.8994i	−0.510634	+	1.57157i
$413$	−2.07295	−	1.50609i	−0.102003	−	0.0741096i
$414$	0.111456	+	0.343027i	0.00547777	+	0.0168588i
$415$	−12.0902	−	8.78402i	−0.593483	−	0.431191i
$416$	−3.35410	+	2.43690i	−0.164448	+	0.119479i
$417$	4.82624	−	14.8536i	0.236342	−	0.727386i
$418$	9.47214	−	6.88191i	0.463297	−	0.336605i
$419$	9.82624	−	7.13918i	0.480043	−	0.348772i	−0.321299	−	0.946978i	$-0.604120\pi$
$419$	9.82624	−	7.13918i	0.480043	−	0.348772i	0.801342	+	0.598206i	$0.204120\pi$
$420$	−4.50000	+	13.8496i	−0.219578	+	0.675790i
$421$	−32.3156	+	23.4787i	−1.57497	+	1.14428i	−0.652770	+	0.757556i	$0.726393\pi$
$421$	−32.3156	+	23.4787i	−1.57497	+	1.14428i	−0.922196	+	0.386723i	$0.873607\pi$
$422$	0.600813	+	0.436516i	0.0292471	+	0.0212493i
$423$	0.607391	+	1.86936i	0.0295324	+	0.0908912i
$424$	14.0517	+	10.2091i	0.682409	+	0.495799i
$425$	0.572949	−	1.76336i	0.0277921	−	0.0855353i
$426$	−1.76393	+	5.42882i	−0.0854628	+	0.263027i
$427$	−6.30244	−	19.3969i	−0.304996	−	0.938682i
$428$	−2.45898			−0.118859
$429$	6.85410			0.330919
$430$	−1.04508	−	3.21644i	−0.0503985	−	0.155111i
$431$	−4.47214	+	3.24920i	−0.215415	+	0.156508i	−0.690260	−	0.723561i	$-0.742504\pi$
$431$	−4.47214	+	3.24920i	−0.215415	+	0.156508i	0.474845	+	0.880069i	$0.342504\pi$
$432$	−13.9271	−	10.1186i	−0.670066	−	0.486831i
$433$	−11.7984			−0.566994			−0.283497	−	0.958973i	$-0.591495\pi$
$433$	−11.7984			−0.566994			−0.283497	+	0.958973i	$0.591495\pi$
$434$	3.75987	−	1.18808i	0.180479	−	0.0570298i
$435$	24.7984			1.18899
$436$	14.5623	+	10.5801i	0.697408	+	0.506697i
$437$	−14.4721	+	10.5146i	−0.692296	+	0.502983i
$438$	−0.718847	−	2.21238i	−0.0343478	−	0.105712i
$439$	−0.763932			−0.0364605			−0.0182302	−	0.999834i	$-0.505803\pi$
$439$	−0.763932			−0.0364605			−0.0182302	+	0.999834i	$0.505803\pi$
$440$	16.3262			0.778323
$441$	0.420473	+	1.29408i	0.0200225	+	0.0616230i
$442$	0.118034	−	0.363271i	0.00561430	−	0.0172791i
$443$	3.51064	−	10.8046i	0.166796	−	0.513344i	−0.832368	−	0.554223i	$-0.813016\pi$
$443$	3.51064	−	10.8046i	0.166796	−	0.513344i	0.999164	+	0.0408783i	$0.0130156\pi$
$444$	18.4894	+	13.4333i	0.877466	+	0.637516i
$445$	3.04508	+	9.37181i	0.144351	+	0.444266i
$446$	−5.01722	−	3.64522i	−0.237572	−	0.172606i
$447$	10.1631	−	7.38394i	0.480699	−	0.349248i
$448$	2.69756	−	8.30224i	0.127448	−	0.392244i
$449$	−22.3992	+	16.2740i	−1.05708	+	0.768016i	−0.973547	−	0.228489i	$-0.926622\pi$
$449$	−22.3992	+	16.2740i	−1.05708	+	0.768016i	−0.0835365	+	0.996505i	$0.526622\pi$
$450$	−0.218847	+	0.159002i	−0.0103165	+	0.00749541i
$451$	−4.73607	+	14.5761i	−0.223013	+	0.686363i
$452$	−13.0623	+	9.49032i	−0.614399	+	0.446387i
$453$	25.4894	+	18.5191i	1.19759	+	0.870103i
$454$	2.53444	+	7.80021i	0.118947	+	0.366082i
$455$	−3.92705	−	2.85317i	−0.184103	−	0.133759i
$456$	−5.32624	+	16.3925i	−0.249424	+	0.767648i
$457$	1.44427	−	4.44501i	0.0675602	−	0.207929i	−0.911577	−	0.411130i	$-0.865134\pi$
$457$	1.44427	−	4.44501i	0.0675602	−	0.207929i	0.979137	+	0.203201i	$0.0651344\pi$
$458$	−2.10739	−	6.48588i	−0.0984719	−	0.303065i
$459$	5.47214			0.255417
$460$	−12.0000			−0.559503
$461$	12.3992	+	38.1608i	0.577488	+	1.77732i	0.627548	+	0.778578i	$0.284059\pi$
$461$	12.3992	+	38.1608i	0.577488	+	1.77732i	−0.0500599	+	0.998746i	$0.515941\pi$
$462$	3.92705	−	2.85317i	0.182703	−	0.132741i
$463$	−4.70820	−	3.42071i	−0.218809	−	0.158974i	0.472981	−	0.881072i	$-0.343178\pi$
$463$	−4.70820	−	3.42071i	−0.218809	−	0.158974i	−0.691790	+	0.722098i	$0.743178\pi$
$464$	−18.4164			−0.854960
$465$	22.3713	+	7.46969i	1.03745	+	0.346399i
$466$	0.729490			0.0337930
$467$	0.763932	+	0.555029i	0.0353506	+	0.0256837i	0.605320	−	0.795982i	$-0.293045\pi$
$467$	0.763932	+	0.555029i	0.0353506	+	0.0256837i	−0.569970	+	0.821666i	$0.693045\pi$
$468$	0.572949	−	0.416272i	0.0264846	−	0.0192422i
$469$	3.21885	+	9.90659i	0.148633	+	0.457444i
$470$	5.14590			0.237363
$471$	−12.3820			−0.570531
$472$	−0.628677	−	1.93487i	−0.0289372	−	0.0890596i
$473$	4.42705	−	13.6251i	0.203556	−	0.626481i
$474$	−0.336881	+	1.03681i	−0.0154735	+	0.0476224i
$475$	−10.8541	−	7.88597i	−0.498020	−	0.361833i
$476$	1.06231	+	3.26944i	0.0486907	+	0.149855i
$477$	−3.64590	−	2.64890i	−0.166934	−	0.121285i
$478$	−0.798374	+	0.580053i	−0.0365168	+	0.0265310i
$479$	−5.47214	+	16.8415i	−0.250028	+	0.769508i	0.744740	+	0.667354i	$0.232573\pi$
$479$	−5.47214	+	16.8415i	−0.250028	+	0.769508i	−0.994769	+	0.102154i	$0.967427\pi$
$480$	−14.2082	+	10.3229i	−0.648513	+	0.471172i
$481$	−6.16312	+	4.47777i	−0.281014	+	0.204169i
$482$	1.78115	−	5.48183i	0.0811293	−	0.249690i
$483$	−6.00000	+	4.35926i	−0.273009	+	0.198353i
$484$	10.4164	+	7.56796i	0.473473	+	0.343998i
$485$	9.70820	+	29.8788i	0.440827	+	1.35673i
$486$	−1.21885	−	0.885544i	−0.0552880	−	0.0401691i
$487$	5.44427	−	16.7557i	0.246704	−	0.759275i	−0.748648	−	0.662968i	$-0.769297\pi$
$487$	5.44427	−	16.7557i	0.246704	−	0.759275i	0.995352	−	0.0963077i	$-0.0307033\pi$
$488$	5.00407	−	15.4009i	0.226523	−	0.697167i
$489$	−1.33688	−	4.11450i	−0.0604559	−	0.186064i
$490$	3.56231			0.160929
$491$	−18.6525			−0.841774			−0.420887	−	0.907113i	$-0.638281\pi$
$491$	−18.6525			−0.841774			−0.420887	+	0.907113i	$0.638281\pi$
$492$	−3.35410	−	10.3229i	−0.151215	−	0.465391i
$493$	4.73607	−	3.44095i	0.213302	−	0.154973i
$494$	−2.23607	−	1.62460i	−0.100605	−	0.0730941i
$495$	−4.23607			−0.190397
$496$	−16.6140	−	5.54734i	−0.745989	−	0.249083i
$497$	17.1246			0.768144
$498$	−2.85410	−	2.07363i	−0.127895	−	0.0929214i
$499$	−14.8992	+	10.8249i	−0.666979	+	0.484589i	−0.869013	−	0.494790i	$-0.835245\pi$
$499$	−14.8992	+	10.8249i	−0.666979	+	0.484589i	0.202033	+	0.979379i	$0.435245\pi$
$500$	4.71885	+	14.5231i	0.211033	+	0.649494i
$501$	−30.5623			−1.36542
$502$	−7.74265			−0.345571
$503$	−6.30902	−	19.4172i	−0.281305	−	0.865768i	−0.987482	−	0.157733i	$-0.949582\pi$
$503$	−6.30902	−	19.4172i	−0.281305	−	0.865768i	0.706177	−	0.708036i	$-0.250418\pi$
$504$	0.322173	−	0.991545i	0.0143507	−	0.0441669i
$505$	−6.97214	+	21.4580i	−0.310256	+	0.954870i
$506$	3.23607	+	2.35114i	0.143861	+	0.104521i
$507$	−0.500000	−	1.53884i	−0.0222058	−	0.0683424i
$508$	−10.8541	−	7.88597i	−0.481573	−	0.349883i
$509$	21.0902	−	15.3229i	0.934805	−	0.679176i	−0.0123593	−	0.999924i	$-0.503934\pi$
$509$	21.0902	−	15.3229i	0.934805	−	0.679176i	0.947165	+	0.320748i	$0.103934\pi$
$510$	0.500000	−	1.53884i	0.0221404	−	0.0681411i
$511$	−5.64590	+	4.10199i	−0.249760	+	0.181461i
$512$	18.0451	−	13.1105i	0.797488	−	0.579409i
$513$	12.2361	−	37.6587i	0.540236	−	1.66267i
$514$	−0.0450850	+	0.0327561i	−0.00198861	+	0.00144481i
$515$	−38.3156	−	27.8379i	−1.68839	−	1.22668i
$516$	3.13525	+	9.64932i	0.138022	+	0.424788i
$517$	17.6353	+	12.8128i	0.775598	+	0.563505i
$518$	−1.66718	+	5.13107i	−0.0732519	+	0.225446i
$519$	11.2082	−	34.4953i	0.491986	−	1.51418i
$520$	−1.19098	−	3.66547i	−0.0522281	−	0.160741i
$521$	39.1246			1.71408			0.857040	−	0.515250i	$-0.172301\pi$
$521$	39.1246			1.71408			0.857040	+	0.515250i	$0.172301\pi$
$522$	−0.854102			−0.0373830
$523$	−1.10739	−	3.40820i	−0.0484228	−	0.149030i	0.923921	−	0.382582i	$-0.124965\pi$
$523$	−1.10739	−	3.40820i	−0.0484228	−	0.149030i	−0.972344	+	0.233552i	$0.924965\pi$
$524$	−26.5623	+	19.2986i	−1.16038	+	0.843065i
$525$	−4.50000	−	3.26944i	−0.196396	−	0.142690i
$526$	1.67376			0.0729795
$527$	5.30902	−	1.67760i	0.231264	−	0.0730774i
$528$	−21.5623			−0.938379
$529$	13.6631	+	9.92684i	0.594049	+	0.431602i
$530$	−9.54508	+	6.93491i	−0.414612	+	0.301233i
$531$	0.163119	+	0.502029i	0.00707876	+	0.0217862i
$532$	24.8754			1.07848
$533$	3.61803			0.156714
$534$	0.718847	+	2.21238i	0.0311076	+	0.0957392i
$535$	1.07295	−	3.30220i	0.0463876	−	0.142766i
$536$	−2.55573	+	7.86572i	−0.110391	+	0.339747i
$537$	−5.42705	−	3.94298i	−0.234195	−	0.170152i
$538$	−1.77051	−	5.44907i	−0.0763321	−	0.234926i
$539$	12.2082	+	8.86978i	0.525845	+	0.382048i
$540$	21.4894	−	15.6129i	0.924755	−	0.671874i
$541$	3.87132	−	11.9147i	0.166441	−	0.512253i	−0.832698	−	0.553727i	$-0.813205\pi$
$541$	3.87132	−	11.9147i	0.166441	−	0.512253i	0.999140	+	0.0414735i	$0.0132052\pi$
$542$	8.26393	−	6.00410i	0.354966	−	0.257898i
$543$	25.1803	−	18.2946i	1.08059	−	0.785096i
$544$	−1.28115	+	3.94298i	−0.0549290	+	0.169054i
$545$	−20.5623	+	14.9394i	−0.880792	+	0.639933i
$546$	−0.927051	−	0.673542i	−0.0396741	−	0.0288249i
$547$	8.32624	+	25.6255i	0.356004	+	1.09567i	0.955425	+	0.295234i	$0.0953977\pi$
$547$	8.32624	+	25.6255i	0.356004	+	1.09567i	−0.599421	+	0.800434i	$0.704602\pi$
$548$	0.656541	+	0.477005i	0.0280460	+	0.0203766i
$549$	−1.29837	+	3.99598i	−0.0554132	+	0.170544i
$550$	−0.927051	+	2.85317i	−0.0395296	+	0.121660i
$551$	−13.0902	−	40.2874i	−0.557660	−	1.71630i
$552$	−5.88854			−0.250633
$553$	3.27051			0.139076
$554$	−1.02786	−	3.16344i	−0.0436698	−	0.134402i
$555$	−26.1074	+	18.9681i	−1.10820	+	0.805152i
$556$	−14.4787	−	10.5194i	−0.614034	−	0.446122i
$557$	0.944272			0.0400101			0.0200050	−	0.999800i	$-0.493632\pi$
$557$	0.944272			0.0400101			0.0200050	+	0.999800i	$0.493632\pi$
$558$	−0.770510	−	0.257270i	−0.0326183	−	0.0108911i
$559$	−3.38197			−0.143042
$560$	12.3541	+	8.97578i	0.522056	+	0.379296i
$561$	5.54508	−	4.02874i	0.234114	−	0.170094i
$562$	−0.667184	−	2.05338i	−0.0281435	−	0.0866167i
$563$	34.0000			1.43293			0.716465	−	0.697623i	$-0.245759\pi$
$563$	34.0000			1.43293			0.716465	+	0.697623i	$0.245759\pi$
$564$	−15.4377			−0.650044
$565$	−7.04508	−	21.6825i	−0.296389	−	0.912191i
$566$	0.326238	−	1.00406i	0.0137128	−	0.0422037i
$567$	4.41641	−	13.5923i	0.185472	−	0.570823i
$568$	11.0000	+	7.99197i	0.461550	+	0.335336i
$569$	0.510643	+	1.57160i	0.0214073	+	0.0658848i	0.961189	−	0.275889i	$-0.0889723\pi$
$569$	0.510643	+	1.57160i	0.0214073	+	0.0658848i	−0.939782	+	0.341774i	$0.888972\pi$
$570$	−9.47214	−	6.88191i	−0.396744	−	0.288251i
$571$	1.66312	−	1.20833i	0.0695994	−	0.0505669i	−0.552442	−	0.833552i	$-0.686304\pi$
$571$	1.66312	−	1.20833i	0.0695994	−	0.0505669i	0.622041	+	0.782985i	$0.286304\pi$
$572$	2.42705	−	7.46969i	0.101480	−	0.312324i
$573$	−26.4894	+	19.2456i	−1.10661	+	0.803998i
$574$	2.07295	−	1.50609i	0.0865232	−	0.0628628i
$575$	1.41641	−	4.35926i	0.0590683	−	0.181794i
$576$	−1.45492	+	1.05706i	−0.0606215	+	0.0440441i
$577$	29.0795	+	21.1275i	1.21060	+	0.879550i	0.995285	−	0.0969955i	$-0.0309232\pi$
$577$	29.0795	+	21.1275i	1.21060	+	0.879550i	0.215312	+	0.976545i	$0.430923\pi$
$578$	1.88854	+	5.81234i	0.0785531	+	0.241761i
$579$	28.1525	+	20.4540i	1.16998	+	0.850038i
$580$	8.78115	−	27.0256i	0.364618	−	1.12218i
$581$	−3.27051	+	10.0656i	−0.135684	+	0.417591i
$582$	2.29180	+	7.05342i	0.0949980	+	0.292374i
$583$	−49.9787			−2.06991
$584$	−5.54102			−0.229289
$585$	0.309017	+	0.951057i	0.0127763	+	0.0393213i
$586$	−4.91641	+	3.57198i	−0.203095	+	0.147557i
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.993437	−	0.114377i	$-0.0364873\pi$
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.198210	+	0.980160i	$0.436487\pi$
$588$	−10.6869			−0.440721
$589$	0.326238	−	40.2874i	0.0134424	−	1.66001i
$590$	1.38197			0.0568946
$591$	−30.7705	−	22.3561i	−1.26573	−	0.919606i
$592$	19.3885	−	14.0866i	0.796864	−	0.578956i
$593$	−3.81559	−	11.7432i	−0.156688	−	0.482235i	0.841640	−	0.540039i	$-0.181590\pi$
$593$	−3.81559	−	11.7432i	−0.156688	−	0.482235i	−0.998328	+	0.0578034i	$0.981590\pi$
$594$	−8.85410			−0.363288
$595$	−4.85410			−0.198999
$596$	−4.44834	−	13.6906i	−0.182211	−	0.560788i
$597$	9.78115	−	30.1033i	0.400316	−	1.23205i
$598$	0.291796	−	0.898056i	0.0119324	−	0.0367242i
$599$	22.4443	+	16.3067i	0.917048	+	0.666274i	0.942788	−	0.333394i	$-0.108194\pi$
$599$	22.4443	+	16.3067i	0.917048	+	0.666274i	−0.0257394	+	0.999669i	$0.508194\pi$
$600$	−1.36475	−	4.20025i	−0.0557155	−	0.171475i
$601$	30.1976	+	21.9398i	1.23178	+	0.894944i	0.997023	−	0.0771094i	$-0.0245691\pi$
$601$	30.1976	+	21.9398i	1.23178	+	0.894944i	0.234762	+	0.972053i	$0.424569\pi$
$602$	−1.93769	+	1.40782i	−0.0789745	+	0.0573783i
$603$	0.663119	−	2.04087i	0.0270043	−	0.0831107i
$604$	29.2082	−	21.2210i	1.18846	−	0.863470i
$605$	−14.7082	+	10.6861i	−0.597974	+	0.434453i
$606$	−1.64590	+	5.06555i	−0.0668600	+	0.205774i
$607$	24.4894	−	17.7926i	0.993992	−	0.722178i	0.0332006	−	0.999449i	$-0.489430\pi$
$607$	24.4894	−	17.7926i	0.993992	−	0.722178i	0.960792	+	0.277271i	$0.0894300\pi$
$608$	24.2705	+	17.6336i	0.984299	+	0.715135i
$609$	−5.42705	−	16.7027i	−0.219915	−	0.676829i
$610$	8.89919	+	6.46564i	0.360318	+	0.261786i
$611$	1.59017	−	4.89404i	0.0643314	−	0.197992i
$612$	0.218847	−	0.673542i	0.00884637	−	0.0272263i
$613$	−8.48278	−	26.1073i	−0.342616	−	1.05446i	−0.962848	−	0.270045i	$-0.912961\pi$
$613$	−8.48278	−	26.1073i	−0.342616	−	1.05446i	0.620231	−	0.784419i	$-0.287039\pi$
$614$	9.38197			0.378625
$615$	15.3262			0.618014
$616$	−3.57295	−	10.9964i	−0.143958	−	0.443058i
$617$	13.2812	−	9.64932i	0.534679	−	0.388467i	−0.287426	−	0.957803i	$-0.592800\pi$
$617$	13.2812	−	9.64932i	0.534679	−	0.388467i	0.822105	+	0.569336i	$0.192800\pi$
$618$	−9.04508	−	6.57164i	−0.363847	−	0.264350i
$619$	−7.20163			−0.289458			−0.144729	−	0.989471i	$-0.546231\pi$
$619$	−7.20163			−0.289458			−0.144729	+	0.989471i	$0.546231\pi$
$620$	16.0623	−	21.7355i	0.645078	−	0.872920i
$621$	13.5279			0.542854
$622$	−8.85410	−	6.43288i	−0.355017	−	0.257935i
$623$	5.64590	−	4.10199i	0.226198	−	0.164343i
$624$	1.57295	+	4.84104i	0.0629684	+	0.193797i
$625$	−30.8328			−1.23331
$626$	−4.65248			−0.185950
$627$	−15.3262	−	47.1693i	−0.612071	−	1.88376i
$628$	−4.38448	+	13.4940i	−0.174960	+	0.538471i
$629$	−2.35410	+	7.24518i	−0.0938642	+	0.288884i
$630$	0.572949	+	0.416272i	0.0228268	+	0.0165847i
$631$	1.94427	+	5.98385i	0.0774002	+	0.238213i	0.982269	−	0.187477i	$-0.0600311\pi$
$631$	1.94427	+	5.98385i	0.0774002	+	0.238213i	−0.904869	+	0.425691i	$0.860031\pi$
$632$	2.10081	+	1.52633i	0.0835659	+	0.0607141i
$633$	2.54508	−	1.84911i	0.101158	−	0.0734956i
$634$	0.298374	−	0.918300i	0.0118499	−	0.0364704i
$635$	15.3262	−	11.1352i	0.608203	−	0.441885i
$636$	28.6353	−	20.8047i	1.13546	−	0.824961i
$637$	1.10081	−	3.38795i	0.0436158	−	0.134236i
$638$	−7.66312	+	5.56758i	−0.303386	+	0.220423i
$639$	−2.85410	−	2.07363i	−0.112907	−	0.0820314i
$640$	8.16312	+	25.1235i	0.322676	+	0.993093i
$641$	−6.66312	−	4.84104i	−0.263177	−	0.191210i	0.448369	−	0.893848i	$-0.352005\pi$
$641$	−6.66312	−	4.84104i	−0.263177	−	0.191210i	−0.711547	+	0.702639i	$0.752005\pi$
$642$	0.253289	−	0.779543i	0.00999652	−	0.0307661i
$643$	−7.31559	+	22.5151i	−0.288499	+	0.887908i	0.696829	+	0.717237i	$0.254594\pi$
$643$	−7.31559	+	22.5151i	−0.288499	+	0.887908i	−0.985328	+	0.170671i	$0.945406\pi$
$644$	2.62616	+	8.08250i	0.103485	+	0.318495i
$645$	−14.3262			−0.564095
$646$	−2.76393			−0.108745
$647$	−10.6525	−	32.7849i	−0.418792	−	1.28891i	−0.908815	−	0.417200i	$-0.863012\pi$
$647$	−10.6525	−	32.7849i	−0.418792	−	1.28891i	0.490023	−	0.871710i	$-0.336988\pi$
$648$	9.18034	−	6.66991i	0.360638	−	0.262019i
$649$	4.73607	+	3.44095i	0.185907	+	0.135069i
$650$	0.708204			0.0277780
$651$	0.135255	−	16.7027i	0.00530106	−	0.654632i
$652$	−4.95743			−0.194148
$653$	1.80902	+	1.31433i	0.0707923	+	0.0514336i	0.622619	−	0.782525i	$-0.286069\pi$
$653$	1.80902	+	1.31433i	0.0707923	+	0.0514336i	−0.551826	+	0.833959i	$0.686069\pi$
$654$	−4.85410	+	3.52671i	−0.189810	+	0.137905i
$655$	−14.3262	−	44.0916i	−0.559772	−	1.72280i
$656$	−11.3820			−0.444391
$657$	1.43769			0.0560898
$658$	−1.12616	−	3.46598i	−0.0439025	−	0.135118i
$659$	−0.218847	+	0.673542i	−0.00852507	+	0.0262375i	−0.955229	−	0.295869i	$-0.904391\pi$
$659$	−0.218847	+	0.673542i	−0.00852507	+	0.0262375i	0.946703	+	0.322106i	$0.104391\pi$
$660$	10.2812	−	31.6421i	0.400193	−	1.23167i
$661$	5.00000	+	3.63271i	0.194477	+	0.141296i	0.680763	−	0.732504i	$-0.261648\pi$
$661$	5.00000	+	3.63271i	0.194477	+	0.141296i	−0.486285	+	0.873800i	$0.661648\pi$
$662$	−1.91390	−	5.89036i	−0.0743857	−	0.228936i
$663$	−1.30902	−	0.951057i	−0.0508380	−	0.0369360i
$664$	−6.79837	+	4.93931i	−0.263828	+	0.191682i
$665$	−10.8541	+	33.4055i	−0.420904	+	1.29541i
$666$	0.899187	−	0.653298i	0.0348428	−	0.0253148i
$667$	11.7082	−	8.50651i	0.453343	−	0.329373i
$668$	−10.8222	+	33.3072i	−0.418722	+	1.28870i
$669$	−21.2533	+	15.4414i	−0.821700	+	0.597000i
$670$	−4.54508	−	3.30220i	−0.175592	−	0.127575i
$671$	14.3992	+	44.3161i	0.555874	+	1.71081i
$672$	10.0623	+	7.31069i	0.388162	+	0.282016i
$673$	4.35410	−	13.4005i	0.167838	−	0.516553i	−0.831396	−	0.555680i	$-0.812458\pi$
$673$	4.35410	−	13.4005i	0.167838	−	0.516553i	0.999234	+	0.0391273i	$0.0124578\pi$
$674$	0.725425	−	2.23263i	0.0279423	−	0.0859976i
$675$	3.13525	+	9.64932i	0.120676	+	0.371403i
$676$	−1.85410			−0.0713116
$677$	29.5066			1.13403			0.567015	−	0.823707i	$-0.308098\pi$
$677$	29.5066			1.13403			0.567015	+	0.823707i	$0.308098\pi$
$678$	−1.66312	−	5.11855i	−0.0638717	−	0.196577i
$679$	18.0000	−	13.0778i	0.690777	−	0.501879i
$680$	−3.11803	−	2.26538i	−0.119571	−	0.0868735i
$681$	34.7426			1.33134
$682$	−8.59017	+	2.71441i	−0.328935	+	0.103940i
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$	−4.14590	−	3.01217i	−0.158522	−	0.115173i
$685$	−0.927051	+	0.673542i	−0.0354208	+	0.0257347i
$686$	−2.31153	−	7.11416i	−0.0882546	−	0.271620i
$687$	−28.8885			−1.10217
$688$	10.6393			0.405620
$689$	3.64590	+	11.2209i	0.138898	+	0.427483i
$690$	1.23607	−	3.80423i	0.0470563	−	0.144824i
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	−0.761995	−	0.647582i	$-0.775780\pi$
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	0.997107	−	0.0760155i	$-0.0242198\pi$
$692$	−33.6246	−	24.4297i	−1.27822	−	0.928678i
$693$	0.927051	+	2.85317i	0.0352158	+	0.108383i
$694$	8.47214	+	6.15537i	0.321598	+	0.233655i
$695$	20.4443	−	14.8536i	0.775495	−	0.563430i
$696$	4.30902	−	13.2618i	0.163333	−	0.502687i
$697$	2.92705	−	2.12663i	0.110870	−	0.0805517i
$698$	−10.4164	+	7.56796i	−0.394267	+	0.286452i
$699$	0.954915	−	2.93893i	0.0361182	−	0.111160i
$700$	−5.15654	+	3.74645i	−0.194899	+	0.141602i
$701$	3.66312	+	2.66141i	0.138354	+	0.100520i	0.654810	−	0.755794i	$-0.272749\pi$
$701$	3.66312	+	2.66141i	0.138354	+	0.100520i	−0.516455	+	0.856314i	$0.672749\pi$
$702$	0.645898	+	1.98787i	0.0243779	+	0.0750273i
$703$	44.5967	+	32.4014i	1.68200	+	1.22204i
$704$	−6.16312	+	18.9681i	−0.232281	+	0.714888i
$705$	6.73607	−	20.7315i	0.253695	−	0.780793i
$706$	2.16718	+	6.66991i	0.0815631	+	0.251025i
$707$	15.9787			0.600941
$708$	−4.14590			−0.155812
$709$	−0.472136	−	1.45309i	−0.0177314	−	0.0545718i	0.941799	−	0.336176i	$-0.109134\pi$
$709$	−0.472136	−	1.45309i	−0.0177314	−	0.0545718i	−0.959531	+	0.281604i	$0.909134\pi$
$710$	−7.47214	+	5.42882i	−0.280424	+	0.203740i
$711$	−0.545085	−	0.396027i	−0.0204423	−	0.0148522i
$712$	5.54102			0.207658
$713$	13.1246	−	4.14725i	0.491521	−	0.155316i
$714$	−1.14590			−0.0428842
$715$	8.97214	+	6.51864i	0.335539	+	0.243783i
$716$	−6.21885	+	4.51826i	−0.232409	+	0.168855i
$717$	1.29180	+	3.97574i	0.0482430	+	0.148477i
$718$	−1.34752			−0.0502892
$719$	27.5623			1.02790			0.513950	−	0.857820i	$-0.328182\pi$
$719$	27.5623			1.02790			0.513950	+	0.857820i	$0.328182\pi$
$720$	−0.972136	−	2.99193i	−0.0362294	−	0.111503i
$721$	−10.3647	+	31.8994i	−0.386003	+	1.18800i
$722$	−3.93769	+	12.1190i	−0.146546	+	0.451022i
$723$	−19.7533	−	14.3516i	−0.734633	−	0.533742i
$724$	−11.0213	−	33.9200i	−0.409603	−	1.26063i
$725$	8.78115	+	6.37988i	0.326124	+	0.236943i
$726$	−3.47214	+	2.52265i	−0.128863	+	0.0936245i
$727$	−15.6353	+	48.1204i	−0.579880	+	1.78469i	0.0390478	+	0.999237i	$0.487568\pi$
$727$	−15.6353	+	48.1204i	−0.579880	+	1.78469i	−0.618927	+	0.785448i	$0.712432\pi$
$728$	−2.20820	+	1.60435i	−0.0818415	+	0.0594613i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	1.16312	−	3.57971i	0.0430490	−	0.132491i
$731$	−2.73607	+	1.98787i	−0.101197	+	0.0735240i
$732$	−26.6976	−	19.3969i	−0.986770	−	0.716931i
$733$	5.13525	+	15.8047i	0.189675	+	0.583760i	0.999998	−	0.00222456i	$-0.000708101\pi$
$733$	5.13525	+	15.8047i	0.189675	+	0.583760i	−0.810323	+	0.585984i	$0.800708\pi$
$734$	6.12868	+	4.45274i	0.226214	+	0.164354i
$735$	4.66312	−	14.3516i	0.172002	−	0.529367i
$736$	−3.16718	+	9.74759i	−0.116744	+	0.359301i
$737$	−7.35410	−	22.6336i	−0.270892	−	0.833719i
$738$	−0.527864			−0.0194309
$739$	−19.0902			−0.702243			−0.351122	−	0.936330i	$-0.614200\pi$
$739$	−19.0902			−0.702243			−0.351122	+	0.936330i	$0.614200\pi$
$740$	11.4271	+	35.1688i	0.420067	+	1.29283i
$741$	−9.47214	+	6.88191i	−0.347968	+	0.252813i
$742$	6.75987	+	4.91133i	0.248163	+	0.180301i
$743$	23.5279			0.863154			0.431577	−	0.902076i	$-0.357957\pi$
$743$	23.5279			0.863154			0.431577	+	0.902076i	$0.357957\pi$
$744$	7.88197	−	10.6659i	0.288967	−	0.391031i
$745$	20.3262			0.744696
$746$	−6.28115	−	4.56352i	−0.229969	−	0.167083i
$747$	1.76393	−	1.28157i	0.0645389	−	0.0468903i
$748$	−2.42705	−	7.46969i	−0.0887418	−	0.273119i
$749$	−2.45898			−0.0898492
$750$	−5.09017			−0.185867
$751$	15.1246	+	46.5488i	0.551905	+	1.69859i	0.703980	+	0.710220i	$0.251404\pi$
$751$	15.1246	+	46.5488i	0.551905	+	1.69859i	−0.152075	+	0.988369i	$0.548596\pi$
$752$	−5.00251	+	15.3962i	−0.182423	+	0.561440i
$753$	−10.1353	+	31.1931i	−0.369349	+	1.13674i
$754$	1.80902	+	1.31433i	0.0658805	+	0.0478650i
$755$	15.7533	+	48.4836i	0.573321	+	1.76450i
$756$	−15.2188	−	11.0571i	−0.553504	−	0.402144i
$757$	21.8885	−	15.9030i	0.795553	−	0.578003i	−0.114053	−	0.993475i	$-0.536384\pi$
$757$	21.8885	−	15.9030i	0.795553	−	0.578003i	0.909606	+	0.415472i	$0.136384\pi$
$758$	4.20820	−	12.9515i	0.152849	−	0.470420i
$759$	13.7082	−	9.95959i	0.497576	−	0.361510i
$760$	−22.5623	+	16.3925i	−0.818421	+	0.594618i
$761$	−2.04508	+	6.29412i	−0.0741343	+	0.228162i	−0.981257	−	0.192705i	$-0.938274\pi$
$761$	−2.04508	+	6.29412i	−0.0741343	+	0.228162i	0.907122	+	0.420867i	$0.138274\pi$
$762$	3.61803	−	2.62866i	0.131068	−	0.0952261i
$763$	14.5623	+	10.5801i	0.527191	+	0.383027i
$764$	11.5942	+	35.6834i	0.419465	+	1.29098i
$765$	0.809017	+	0.587785i	0.0292501	+	0.0212514i
$766$	2.92299	−	8.99602i	0.105612	−	0.325040i
$767$	0.427051	−	1.31433i	0.0154199	−	0.0474576i
$768$	−2.78115	−	8.55951i	−0.100356	−	0.308865i
$769$	−29.7639			−1.07331			−0.536657	−	0.843800i	$-0.680313\pi$
$769$	−29.7639			−1.07331			−0.536657	+	0.843800i	$0.680313\pi$
$770$	7.85410			0.283042
$771$	0.0729490	+	0.224514i	0.00262719	+	0.00808567i
$772$	32.2599	−	23.4382i	1.16106	−	0.843558i
$773$	−28.8435	−	20.9560i	−1.03743	−	0.753735i	−0.0676455	−	0.997709i	$-0.521549\pi$
$773$	−28.8435	−	20.9560i	−1.03743	−	0.753735i	−0.969782	+	0.243975i	$0.921549\pi$
$774$	0.493422			0.0177357
$775$	6.00000	+	8.40051i	0.215526	+	0.301755i
$776$	17.6656			0.634159
$777$	18.4894	+	13.4333i	0.663302	+	0.481917i
$778$	8.98278	−	6.52637i	0.322048	−	0.233982i
$779$	−8.09017	−	24.8990i	−0.289860	−	0.892099i
$780$	−7.85410			−0.281222
$781$	−39.1246			−1.39999
$782$	−0.291796	−	0.898056i	−0.0104346	−	0.0321144i
$783$	−9.89919	+	30.4666i	−0.353768	+	1.08879i
$784$	−3.46305	+	10.6582i	−0.123680	+	0.380649i
$785$	−16.2082	−	11.7759i	−0.578496	−	0.420302i
$786$	−3.38197	−	10.4086i	−0.120631	−	0.371263i
$787$	12.8090	+	9.30630i	0.456592	+	0.331734i	0.792193	−	0.610271i	$-0.208939\pi$
$787$	12.8090	+	9.30630i	0.456592	+	0.331734i	−0.335601	+	0.942004i	$0.608939\pi$
$788$	−35.2599	+	25.6178i	−1.25608	+	0.912596i
$789$	2.19098	−	6.74315i	0.0780011	−	0.240063i
$790$	−1.42705	+	1.03681i	−0.0507722	+	0.0368882i
$791$	−13.0623	+	9.49032i	−0.464442	+	0.337437i
$792$	−0.736068	+	2.26538i	−0.0261550	+	0.0804969i
$793$	8.89919	−	6.46564i	0.316019	−	0.229602i
$794$	−5.29180	−	3.84471i	−0.187799	−	0.136444i
$795$	15.4443	+	47.5326i	0.547752	+	1.68581i
$796$	−29.3435	−	21.3193i	−1.04005	−	0.755642i
$797$	−12.9098	+	39.7324i	−0.457290	+	1.40739i	0.411136	+	0.911574i	$0.365132\pi$
$797$	−12.9098	+	39.7324i	−0.457290	+	1.40739i	−0.868426	+	0.495819i	$0.834868\pi$
$798$	−2.56231	+	7.88597i	−0.0907046	+	0.279160i
$799$	−1.59017	−	4.89404i	−0.0562562	−	0.173139i
$800$	−7.68692			−0.271774
$801$	−1.43769			−0.0507984
$802$	1.38603	+	4.26577i	0.0489425	+	0.150629i
$803$	12.8992	−	9.37181i	0.455202	−	0.330724i
$804$	13.6353	+	9.90659i	0.480878	+	0.349379i
$805$	−12.0000			−0.422944
$806$	1.23607	+	1.73060i	0.0435386	+	0.0609578i
$807$	−24.2705			−0.854362
$808$	10.2639	+	7.45718i	0.361084	+	0.262343i
$809$	31.3156	−	22.7521i	1.10100	−	0.799922i	0.119775	−	0.992801i	$-0.461783\pi$
$809$	31.3156	−	22.7521i	1.10100	−	0.799922i	0.981222	+	0.192879i	$0.0617826\pi$
$810$	2.38197	+	7.33094i	0.0836938	+	0.257583i
$811$	−13.5410			−0.475490			−0.237745	−	0.971328i	$-0.576408\pi$
$811$	−13.5410			−0.475490			−0.237745	+	0.971328i	$0.576408\pi$
$812$	−20.1246			−0.706235
$813$	−13.3713	−	41.1527i	−0.468953	−	1.44329i
$814$	3.80902	−	11.7229i	0.133506	−	0.410889i
$815$	2.16312	−	6.65740i	0.0757708	−	0.233198i
$816$	4.11803	+	2.99193i	0.144160	+	0.104738i
$817$	7.56231	+	23.2744i	0.264572	+	0.814268i
$818$	−4.36475	−	3.17117i	−0.152610	−	0.110877i
$819$	0.572949	−	0.416272i	0.0200205	−	0.0145457i
$820$	5.42705	−	16.7027i	0.189521	−	0.583285i
$821$	−28.4443	+	20.6660i	−0.992712	+	0.721247i	−0.960513	−	0.278234i	$-0.910251\pi$
$821$	−28.4443	+	20.6660i	−0.992712	+	0.721247i	−0.0321986	+	0.999481i	$0.510251\pi$
$822$	−0.218847	+	0.159002i	−0.00763317	+	0.00554582i
$823$	0.281153	−	0.865300i	0.00980038	−	0.0301625i	−0.946037	−	0.324059i	$-0.894952\pi$
$823$	0.281153	−	0.865300i	0.00980038	−	0.0301625i	0.955837	+	0.293897i	$0.0949522\pi$
$824$	−21.5451	+	15.6534i	−0.750559	+	0.545313i
$825$	10.2812	+	7.46969i	0.357944	+	0.260061i
$826$	−0.302439	−	0.930812i	−0.0105232	−	0.0323871i
$827$	19.8992	+	14.4576i	0.691963	+	0.502740i	0.877305	−	0.479934i	$-0.159339\pi$
$827$	19.8992	+	14.4576i	0.691963	+	0.502740i	−0.185342	+	0.982674i	$0.559339\pi$
$828$	0.541020	−	1.66509i	0.0188017	−	0.0578658i
$829$	2.25329	−	6.93491i	0.0782600	−	0.240859i	−0.904271	−	0.426959i	$-0.859585\pi$
$829$	2.25329	−	6.93491i	0.0782600	−	0.240859i	0.982531	+	0.186100i	$0.0595848\pi$
$830$	−1.76393	−	5.42882i	−0.0612270	−	0.188437i
$831$	−14.0902			−0.488783
$832$	4.70820			0.163228
$833$	−1.10081	−	3.38795i	−0.0381409	−	0.117386i
$834$	4.82624	−	3.50647i	0.167119	−	0.121419i
$835$	−40.0066	−	29.0665i	−1.38448	−	1.00589i
$836$	−56.8328			−1.96560
$837$	−18.1074	+	24.5030i	−0.625883	+	0.846946i
$838$	4.63932			0.160263
$839$	−13.8090	−	10.0328i	−0.476740	−	0.346372i	0.323322	−	0.946289i	$-0.395200\pi$
$839$	−13.8090	−	10.0328i	−0.476740	−	0.346372i	−0.800062	+	0.599917i	$0.795200\pi$
$840$	−9.35410	+	6.79615i	−0.322747	+	0.234490i
$841$	1.62868	+	5.01255i	0.0561613	+	0.172847i
$842$	−15.2574			−0.525803
$843$	−9.14590			−0.315001
$844$	−1.11397	−	3.42844i	−0.0383444	−	0.118012i
$845$	0.809017	−	2.48990i	0.0278310	−	0.0856551i
$846$	−0.232003	+	0.714031i	−0.00797642	+	0.0245489i
$847$	10.4164	+	7.56796i	0.357912	+	0.260038i
$848$	−11.4696	−	35.2999i	−0.393868	−	1.21220i
$849$	−3.61803	−	2.62866i	−0.124171	−	0.0902152i
$850$	0.572949	−	0.416272i	0.0196520	−	0.0142780i
$851$	−5.81966	+	17.9111i	−0.199495	+	0.613984i
$852$	22.4164	−	16.2865i	0.767973	−	0.557965i
$853$	−7.57295	+	5.50207i	−0.259293	+	0.188387i	−0.709835	−	0.704368i	$-0.751231\pi$
$853$	−7.57295	+	5.50207i	−0.259293	+	0.188387i	0.450542	+	0.892755i	$0.351231\pi$
$854$	2.40732	−	7.40896i	0.0823767	−	0.253529i
$855$	5.85410	−	4.25325i	0.200206	−	0.145458i
$856$	−1.57953	−	1.14759i	−0.0539871	−	0.0392239i
$857$	0.517221	+	1.59184i	0.0176679	+	0.0543763i	0.959502	−	0.281703i	$-0.0908991\pi$
$857$	0.517221	+	1.59184i	0.0176679	+	0.0543763i	−0.941834	+	0.336079i	$0.890899\pi$
$858$	2.11803	+	1.53884i	0.0723085	+	0.0525352i
$859$	−3.79837	+	11.6902i	−0.129599	+	0.398864i	−0.994711	−	0.102714i	$-0.967247\pi$
$859$	−3.79837	+	11.6902i	−0.129599	+	0.398864i	0.865112	+	0.501579i	$0.167247\pi$
$860$	−5.07295	+	15.6129i	−0.172986	+	0.532397i
$861$	−3.35410	−	10.3229i	−0.114307	−	0.351802i
$862$	−2.11146			−0.0719165
$863$	38.7426			1.31881			0.659407	−	0.751786i	$-0.270807\pi$
$863$	38.7426			1.31881			0.659407	+	0.751786i	$0.270807\pi$
$864$	−7.01064	−	21.5765i	−0.238507	−	0.734049i
$865$	47.4787	−	34.4953i	1.61432	−	1.17288i
$866$	−3.64590	−	2.64890i	−0.123893	−	0.0900133i
$867$	25.8885			0.879221
$868$	−18.1550	−	6.06188i	−0.616220	−	0.205754i
$869$	−7.47214			−0.253475
$870$	7.66312	+	5.56758i	0.259804	+	0.188759i
$871$	−4.54508	+	3.30220i	−0.154004	+	0.111891i
$872$	4.41641	+	13.5923i	0.149558	+	0.460294i
$873$	−4.58359			−0.155131
$874$	−6.83282			−0.231123
$875$	4.71885	+	14.5231i	0.159526	+	0.490971i
$876$	−3.48936	+	10.7391i	−0.117894	+	0.362842i
$877$	2.44834	−	7.53521i	0.0826745	−	0.254446i	−0.901172	−	0.433463i	$-0.857292\pi$
$877$	2.44834	−	7.53521i	0.0826745	−	0.254446i	0.983846	+	0.179017i	$0.0572916\pi$
$878$	−0.236068	−	0.171513i	−0.00796691	−	0.00578830i
$879$	7.95492	+	24.4827i	0.268313	+	0.825781i
$880$	−28.2254	−	20.5070i	−0.951479	−	0.691290i
$881$	37.8885	−	27.5276i	1.27650	−	0.927430i	0.277056	−	0.960854i	$-0.410641\pi$
$881$	37.8885	−	27.5276i	1.27650	−	0.927430i	0.999441	+	0.0334240i	$0.0106412\pi$
$882$	−0.160606	+	0.494296i	−0.00540790	+	0.0166438i
$883$	−22.0344	+	16.0090i	−0.741518	+	0.538744i	−0.893186	−	0.449687i	$-0.851535\pi$
$883$	−22.0344	+	16.0090i	−0.741518	+	0.538744i	0.151668	+	0.988431i	$0.451535\pi$
$884$	−1.50000	+	1.08981i	−0.0504505	+	0.0366544i
$885$	1.80902	−	5.56758i	0.0608094	−	0.187152i
$886$	3.51064	−	2.55063i	0.117942	−	0.0856901i
$887$	−14.1631	−	10.2901i	−0.475551	−	0.345508i	0.324050	−	0.946040i	$-0.394955\pi$
$887$	−14.1631	−	10.2901i	−0.475551	−	0.345508i	−0.799601	+	0.600532i	$0.794955\pi$
$888$	5.60739	+	17.2578i	0.188172	+	0.579133i
$889$	−10.8541	−	7.88597i	−0.364035	−	0.264487i
$890$	−1.16312	+	3.57971i	−0.0389878	+	0.119992i
$891$	−10.0902	+	31.0543i	−0.338033	+	1.04036i
$892$	9.30244	+	28.6300i	0.311469	+	0.958602i
$893$	−37.2361			−1.24606
$894$	4.79837			0.160482
$895$	−3.35410	−	10.3229i	−0.112115	−	0.345055i
$896$	15.1353	−	10.9964i	0.505633	−	0.367364i
$897$	−3.23607	−	2.35114i	−0.108049	−	0.0785023i
$898$	−10.5755			−0.352908
$899$	−0.263932	+	32.5932i	−0.00880263	+	1.08704i
$900$	1.31308			0.0437694
$901$	9.54508	+	6.93491i	0.317993	+	0.231035i
$902$	−4.73607	+	3.44095i	−0.157694	+	0.114571i
$903$	3.13525	+	9.64932i	0.104335	+	0.321109i
$904$	−12.8197			−0.426376
$905$	50.3607			1.67405
$906$	3.71885	+	11.4454i	0.123550	+	0.380249i
$907$	−6.40983	+	19.7274i	−0.212835	+	0.655039i	0.786465	+	0.617634i	$0.211909\pi$
$907$	−6.40983	+	19.7274i	−0.212835	+	0.655039i	−0.999300	+	0.0374041i	$0.988091\pi$
$908$	12.3024	−	37.8630i	0.408271	−	1.25653i
$909$	−2.66312	−	1.93487i	−0.0883301	−	0.0641756i
$910$	−0.572949	−	1.76336i	−0.0189931	−	0.0584547i
$911$	39.8328	+	28.9402i	1.31972	+	0.958833i	0.999936	+	0.0113424i	$0.00361048\pi$
$911$	39.8328	+	28.9402i	1.31972	+	0.958833i	0.319784	+	0.947490i	$0.396390\pi$
$912$	29.7984	−	21.6498i	0.986723	−	0.716896i
$913$	7.47214	−	22.9969i	0.247292	−	0.761085i
$914$	1.44427	−	1.04932i	0.0477723	−	0.0347086i
$915$	37.6976	−	27.3889i	1.24624	−	0.905448i
$916$	−10.2295	+	31.4831i	−0.337992	+	1.04023i
$917$	−26.5623	+	19.2986i	−0.877165	+	0.637297i
$918$	1.69098	+	1.22857i	0.0558108	+	0.0405489i
$919$	−6.33688	−	19.5029i	−0.209034	−	0.643342i	−0.999524	−	0.0308657i	$-0.990174\pi$
$919$	−6.33688	−	19.5029i	−0.209034	−	0.643342i	0.790489	−	0.612476i	$-0.209826\pi$
$920$	−7.70820	−	5.60034i	−0.254132	−	0.184638i
$921$	12.2812	−	37.7975i	0.404678	−	1.24547i
$922$	−4.73607	+	14.5761i	−0.155974	+	0.480039i
$923$	2.85410	+	8.78402i	0.0939439	+	0.289130i
$924$	−23.5623			−0.775143
$925$	−14.1246			−0.464414
$926$	−0.686918	−	2.11412i	−0.0225735	−	0.0694741i
$927$	5.59017	−	4.06150i	0.183605	−	0.133397i
$928$	−19.6353	−	14.2658i	−0.644559	−	0.468299i
$929$	28.5279			0.935969			0.467984	−	0.883737i	$-0.344980\pi$
$929$	28.5279			0.935969			0.467984	+	0.883737i	$0.344980\pi$
$930$	5.23607	+	7.33094i	0.171697	+	0.240391i
$931$	−25.7771			−0.844810
$932$	−2.86475	−	2.08136i	−0.0938378	−	0.0681772i
$933$	−37.5066	+	27.2501i	−1.22791	+	0.892129i
$934$	0.111456	+	0.343027i	0.00364696	+	0.0112242i
$935$	11.0902			0.362687
$936$	0.562306			0.0183795
$937$	−4.01722	−	12.3637i	−0.131237	−	0.403906i	0.863749	−	0.503923i	$-0.168110\pi$
$937$	−4.01722	−	12.3637i	−0.131237	−	0.403906i	−0.994986	+	0.100017i	$0.968110\pi$
$938$	−1.22949	+	3.78398i	−0.0401443	+	0.123551i
$939$	−6.09017	+	18.7436i	−0.198745	+	0.611675i
$940$	−20.2082	−	14.6821i	−0.659119	−	0.478878i
$941$	−1.88197	−	5.79210i	−0.0613503	−	0.188817i	0.915684	−	0.401899i	$-0.131650\pi$
$941$	−1.88197	−	5.79210i	−0.0613503	−	0.188817i	−0.977034	+	0.213082i	$0.931650\pi$
$942$	−3.82624	−	2.77992i	−0.124666	−	0.0905748i
$943$	7.23607	−	5.25731i	0.235639	−	0.171202i
$944$	−1.34346	+	4.13474i	−0.0437259	+	0.134574i
$945$	21.4894	−	15.6129i	0.699049	−	0.507889i
$946$	4.42705	−	3.21644i	0.143936	−	0.104576i
$947$	−5.54508	+	17.0660i	−0.180191	+	0.554571i	−0.999832	−	0.0183059i	$-0.994173\pi$
$947$	−5.54508	+	17.0660i	−0.180191	+	0.554571i	0.819641	+	0.572877i	$0.194173\pi$
$948$	4.28115	−	3.11044i	0.139045	−	0.101022i
$949$	−3.04508	−	2.21238i	−0.0988476	−	0.0718170i
$950$	−1.58359	−	4.87380i	−0.0513785	−	0.158127i
$951$	−3.30902	−	2.40414i	−0.107302	−	0.0779596i
$952$	−0.843459	+	2.59590i	−0.0273367	+	0.0841336i
$953$	9.57953	−	29.4828i	0.310311	−	0.955040i	−0.667330	−	0.744762i	$-0.732563\pi$
$953$	9.57953	−	29.4828i	0.310311	−	0.955040i	0.977642	−	0.210278i	$-0.0674370\pi$
$954$	−0.531929	−	1.63711i	−0.0172218	−	0.0530034i
$955$	−52.9787			−1.71435
$956$	4.79024			0.154928
$957$	12.3992	+	38.1608i	0.400809	+	1.23356i
$958$	−5.47214	+	3.97574i	−0.176797	+	0.128450i
$959$	0.656541	+	0.477005i	0.0212008	+	0.0154033i
$960$	19.9443			0.643699
$961$	−10.0557	+	29.3238i	−0.324378	+	0.945927i
$962$	−2.90983			−0.0938167
$963$	0.409830	+	0.297759i	0.0132066	+	0.00959515i
$964$	−22.6353	+	16.4455i	−0.729032	+	0.529673i
$965$	17.3992	+	53.5492i	0.560100	+	1.72381i
$966$	−2.83282			−0.0911444
$967$	−3.18034			−0.102273			−0.0511364	−	0.998692i	$-0.516284\pi$
$967$	−3.18034			−0.102273			−0.0511364	+	0.998692i	$0.516284\pi$
$968$	3.15905	+	9.72257i	0.101536	+	0.312495i
$969$	−3.61803	+	11.1352i	−0.116228	+	0.357713i
$970$	−3.70820	+	11.4127i	−0.119063	+	0.366439i
$971$	7.19098	+	5.22455i	0.230770	+	0.167664i	0.697161	−	0.716914i	$-0.254446\pi$
$971$	7.19098	+	5.22455i	0.230770	+	0.167664i	−0.466392	+	0.884578i	$0.654446\pi$
$972$	2.25987	+	6.95515i	0.0724853	+	0.223087i
$973$	−14.4787	−	10.5194i	−0.464166	−	0.337237i
$974$	5.44427	−	3.95550i	0.174446	−	0.126742i
$975$	0.927051	−	2.85317i	0.0296894	−	0.0913746i
$976$	−27.9959	+	20.3402i	−0.896128	+	0.651075i
$977$	11.9549	−	8.68575i	0.382472	−	0.277882i	−0.379892	−	0.925031i	$-0.624039\pi$
$977$	11.9549	−	8.68575i	0.382472	−	0.277882i	0.762364	+	0.647149i	$0.224039\pi$
$978$	0.510643	−	1.57160i	0.0163286	−	0.0502542i
$979$	−12.8992	+	9.37181i	−0.412260	+	0.299524i
$980$	−13.9894	−	10.1639i	−0.446874	−	0.324673i
$981$	−1.14590	−	3.52671i	−0.0365857	−	0.112599i
$982$	−5.76393	−	4.18774i	−0.183934	−	0.133636i
$983$	−16.9058	+	52.0306i	−0.539210	+	1.65952i	0.195162	+	0.980771i	$0.437477\pi$
$983$	−16.9058	+	52.0306i	−0.539210	+	1.65952i	−0.734372	+	0.678747i	$0.762523\pi$
$984$	2.66312	−	8.19624i	0.0848971	−	0.261287i
$985$	−19.0172	−	58.5290i	−0.605939	−	1.86489i
$986$	2.23607			0.0712109
$987$	−15.4377			−0.491387
$988$	4.14590	+	12.7598i	0.131899	+	0.405942i
$989$	−6.76393	+	4.91428i	−0.215081	+	0.156265i
$990$	−1.30902	−	0.951057i	−0.0416033	−	0.0302266i
$991$	36.9787			1.17467			0.587334	−	0.809345i	$-0.300178\pi$
$991$	36.9787			1.17467			0.587334	+	0.809345i	$0.300178\pi$
$992$	−13.4164	−	18.7841i	−0.425971	−	0.596396i
$993$	−26.2361			−0.832576
$994$	5.29180	+	3.84471i	0.167846	+	0.121947i
$995$	41.4336	−	30.1033i	1.31353	−	0.954339i
$996$	5.29180	+	16.2865i	0.167677	+	0.516057i
$997$	21.1803			0.670788			0.335394	−	0.942078i	$-0.391131\pi$
$997$	21.1803			0.670788			0.335394	+	0.942078i	$0.391131\pi$
$998$	−7.03444			−0.222671
$999$	−12.8820	−	39.6466i	−0.407567	−	1.25436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.c.157.1	✓	4
31.16	even	5	inner	403.2.k.c.326.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.c.157.1	✓	4	1.1	even	1	trivial
403.2.k.c.326.1	yes	4	31.16	even	5	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.224514i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +2.61803 q^{5} +0.618034 q^{6} +(-0.572949 - 1.76336i) q^{7} +(0.454915 - 1.40008i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.224514i) q^{2} +(1.30902 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +2.61803 q^{5} +0.618034 q^{6} +(-0.572949 - 1.76336i) q^{7} +(0.454915 - 1.40008i) q^{8} +(-0.118034 + 0.363271i) q^{9} +(0.809017 + 0.587785i) q^{10} +(1.30902 + 4.02874i) q^{11} +(-2.42705 - 1.76336i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.218847 - 0.673542i) q^{14} +(3.42705 - 2.48990i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(0.309017 - 0.951057i) q^{17} +(-0.118034 + 0.0857567i) q^{18} +(-5.85410 - 4.25325i) q^{19} +(-1.50000 - 4.61653i) q^{20} +(-2.42705 - 1.76336i) q^{21} +(-0.500000 + 1.53884i) q^{22} +(0.763932 - 2.35114i) q^{23} +(-0.736068 - 2.26538i) q^{24} +1.85410 q^{25} +0.381966 q^{26} +(1.69098 + 5.20431i) q^{27} +(-2.78115 + 2.02063i) q^{28} +(4.73607 + 3.44095i) q^{29} +1.61803 q^{30} +(3.23607 + 4.53077i) q^{31} -4.14590 q^{32} +(5.54508 + 4.02874i) q^{33} +(0.309017 - 0.224514i) q^{34} +(-1.50000 - 4.61653i) q^{35} +0.708204 q^{36} -7.61803 q^{37} +(-0.854102 - 2.62866i) q^{38} +(0.500000 - 1.53884i) q^{39} +(1.19098 - 3.66547i) q^{40} +(2.92705 + 2.12663i) q^{41} +(-0.354102 - 1.08981i) q^{42} +(-2.73607 - 1.98787i) q^{43} +(6.35410 - 4.61653i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(0.763932 - 0.555029i) q^{46} +(4.16312 - 3.02468i) q^{47} +(-1.57295 + 4.84104i) q^{48} +(2.88197 - 2.09387i) q^{49} +(0.572949 + 0.416272i) q^{50} +(-0.500000 - 1.53884i) q^{51} +(-1.50000 - 1.08981i) q^{52} +(-3.64590 + 11.2209i) q^{53} +(-0.645898 + 1.98787i) q^{54} +(3.42705 + 10.5474i) q^{55} -2.72949 q^{56} -11.7082 q^{57} +(0.690983 + 2.12663i) q^{58} +(1.11803 - 0.812299i) q^{59} +(-6.35410 - 4.61653i) q^{60} +11.0000 q^{61} +(-0.0172209 + 2.12663i) q^{62} +0.708204 q^{63} +(3.80902 + 2.76741i) q^{64} +(2.11803 - 1.53884i) q^{65} +(0.809017 + 2.48990i) q^{66} -5.61803 q^{67} -1.85410 q^{68} +(-1.23607 - 3.80423i) q^{69} +(0.572949 - 1.76336i) q^{70} +(-2.85410 + 8.78402i) q^{71} +(0.454915 + 0.330515i) q^{72} +(-1.16312 - 3.57971i) q^{73} +(-2.35410 - 1.71036i) q^{74} +(2.42705 - 1.76336i) q^{75} +(-4.14590 + 12.7598i) q^{76} +(6.35410 - 4.61653i) q^{77} +(0.500000 - 0.363271i) q^{78} +(-0.545085 + 1.67760i) q^{79} +(-6.66312 + 4.84104i) q^{80} +(6.23607 + 4.53077i) q^{81} +(0.427051 + 1.31433i) q^{82} +(-4.61803 - 3.35520i) q^{83} +(-1.71885 + 5.29007i) q^{84} +(0.809017 - 2.48990i) q^{85} +(-0.399187 - 1.22857i) q^{86} +9.47214 q^{87} +6.23607 q^{88} +(1.16312 + 3.57971i) q^{89} +(-0.309017 + 0.224514i) q^{90} +(-1.50000 - 1.08981i) q^{91} -4.58359 q^{92} +(8.54508 + 2.85317i) q^{93} +1.96556 q^{94} +(-15.3262 - 11.1352i) q^{95} +(-5.42705 + 3.94298i) q^{96} +(3.70820 + 11.4127i) q^{97} +1.36068 q^{98} -1.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{3} - 9 q^{4} + 6 q^{5} - 2 q^{6} - 9 q^{7} + 13 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 + 3 * q^3 - 9 * q^4 + 6 * q^5 - 2 * q^6 - 9 * q^7 + 13 * q^8 + 4 * q^9	\( 4 q - q^{2} + 3 q^{3} - 9 q^{4} + 6 q^{5} - 2 q^{6} - 9 q^{7} + 13 q^{8} + 4 q^{9} + q^{10} + 3 q^{11} - 3 q^{12} + q^{13} + 21 q^{14} + 7 q^{15} + q^{16} - q^{17} + 4 q^{18} - 10 q^{19} - 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} + 6 q^{24} - 6 q^{25} + 6 q^{26} + 9 q^{27} + 9 q^{28} + 10 q^{29} + 2 q^{30} + 4 q^{31} - 30 q^{32} + 11 q^{33} - q^{34} - 6 q^{35} - 24 q^{36} - 26 q^{37} + 10 q^{38} + 2 q^{39} + 7 q^{40} + 5 q^{41} + 12 q^{42} - 2 q^{43} + 12 q^{44} + q^{45} + 12 q^{46} + q^{47} - 13 q^{48} + 16 q^{49} + 9 q^{50} - 2 q^{51} - 6 q^{52} - 28 q^{53} - 16 q^{54} + 7 q^{55} - 78 q^{56} - 20 q^{57} + 5 q^{58} - 12 q^{60} + 44 q^{61} + 29 q^{62} - 24 q^{63} + 13 q^{64} + 4 q^{65} + q^{66} - 18 q^{67} + 6 q^{68} + 4 q^{69} + 9 q^{70} + 2 q^{71} + 13 q^{72} + 11 q^{73} + 4 q^{74} + 3 q^{75} - 30 q^{76} + 12 q^{77} + 2 q^{78} + 9 q^{79} - 11 q^{80} + 16 q^{81} - 5 q^{82} - 14 q^{83} - 27 q^{84} + q^{85} + 23 q^{86} + 20 q^{87} + 16 q^{88} - 11 q^{89} + q^{90} - 6 q^{91} - 72 q^{92} + 23 q^{93} + 66 q^{94} - 30 q^{95} - 15 q^{96} - 12 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^3 - 9 * q^4 + 6 * q^5 - 2 * q^6 - 9 * q^7 + 13 * q^8 + 4 * q^9 + q^10 + 3 * q^11 - 3 * q^12 + q^13 + 21 * q^14 + 7 * q^15 + q^16 - q^17 + 4 * q^18 - 10 * q^19 - 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 + 6 * q^24 - 6 * q^25 + 6 * q^26 + 9 * q^27 + 9 * q^28 + 10 * q^29 + 2 * q^30 + 4 * q^31 - 30 * q^32 + 11 * q^33 - q^34 - 6 * q^35 - 24 * q^36 - 26 * q^37 + 10 * q^38 + 2 * q^39 + 7 * q^40 + 5 * q^41 + 12 * q^42 - 2 * q^43 + 12 * q^44 + q^45 + 12 * q^46 + q^47 - 13 * q^48 + 16 * q^49 + 9 * q^50 - 2 * q^51 - 6 * q^52 - 28 * q^53 - 16 * q^54 + 7 * q^55 - 78 * q^56 - 20 * q^57 + 5 * q^58 - 12 * q^60 + 44 * q^61 + 29 * q^62 - 24 * q^63 + 13 * q^64 + 4 * q^65 + q^66 - 18 * q^67 + 6 * q^68 + 4 * q^69 + 9 * q^70 + 2 * q^71 + 13 * q^72 + 11 * q^73 + 4 * q^74 + 3 * q^75 - 30 * q^76 + 12 * q^77 + 2 * q^78 + 9 * q^79 - 11 * q^80 + 16 * q^81 - 5 * q^82 - 14 * q^83 - 27 * q^84 + q^85 + 23 * q^86 + 20 * q^87 + 16 * q^88 - 11 * q^89 + q^90 - 6 * q^91 - 72 * q^92 + 23 * q^93 + 66 * q^94 - 30 * q^95 - 15 * q^96 - 12 * q^97 - 84 * q^98 - 2 * q^99

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