LMFDB - Embedded newform 429.2.n.b.313.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
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			313.3
Root			$0.169480 - 0.521606i$ of defining polynomial
Character	$\chi$	$=$	429.313
Dual form			429.2.n.b.196.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.169480 + 0.521606i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.37468 - 0.998767i) q^{4} +(-0.266070 + 0.818878i) q^{5} +(-0.169480 + 0.521606i) q^{6} +(2.33406 - 1.69579i) q^{7} +(1.64135 + 1.19251i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.169480 + 0.521606i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.37468 - 0.998767i) q^{4} +(-0.266070 + 0.818878i) q^{5} +(-0.169480 + 0.521606i) q^{6} +(2.33406 - 1.69579i) q^{7} +(1.64135 + 1.19251i) q^{8} +(0.309017 + 0.951057i) q^{9} -0.472225 q^{10} +(-2.07523 + 2.58716i) q^{11} +1.69920 q^{12} +(-0.309017 - 0.951057i) q^{13} +(1.28011 + 0.930055i) q^{14} +(-0.696579 + 0.506094i) q^{15} +(0.706320 - 2.17383i) q^{16} +(0.732462 - 2.25429i) q^{17} +(-0.443705 + 0.322370i) q^{18} +(-1.91727 - 1.39298i) q^{19} +(0.452106 + 1.39144i) q^{20} +2.88505 q^{21} +(-1.70119 - 0.643981i) q^{22} +1.81427 q^{23} +(0.626941 + 1.92953i) q^{24} +(3.44532 + 2.50317i) q^{25} +(0.443705 - 0.322370i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.51489 - 4.66236i) q^{28} +(-3.43067 + 2.49253i) q^{29} +(-0.382038 - 0.277567i) q^{30} +(-0.318476 - 0.980168i) q^{31} +5.31124 q^{32} +(-3.19959 + 0.873268i) q^{33} +1.29999 q^{34} +(0.767625 + 2.36251i) q^{35} +(1.37468 + 0.998767i) q^{36} +(-8.78740 + 6.38442i) q^{37} +(0.401647 - 1.23614i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-1.41324 + 1.02678i) q^{40} +(-1.61597 - 1.17407i) q^{41} +(0.488959 + 1.50486i) q^{42} +1.67092 q^{43} +(-0.268817 + 5.62921i) q^{44} -0.861019 q^{45} +(0.307483 + 0.946334i) q^{46} +(-2.12809 - 1.54615i) q^{47} +(1.84917 - 1.34350i) q^{48} +(0.408994 - 1.25875i) q^{49} +(-0.721756 + 2.22134i) q^{50} +(1.91761 - 1.39323i) q^{51} +(-1.37468 - 0.998767i) q^{52} +(-2.34937 - 7.23063i) q^{53} -0.548449 q^{54} +(-1.56641 - 2.38773i) q^{55} +5.85327 q^{56} +(-0.732333 - 2.25389i) q^{57} +(-1.88155 - 1.36703i) q^{58} +(-4.27373 + 3.10505i) q^{59} +(-0.452106 + 1.39144i) q^{60} +(0.526405 - 1.62011i) q^{61} +(0.457286 - 0.332238i) q^{62} +(2.33406 + 1.69579i) q^{63} +(-0.512491 - 1.57729i) q^{64} +0.861019 q^{65} +(-0.997769 - 1.52093i) q^{66} -7.33979 q^{67} +(-1.24460 - 3.83049i) q^{68} +(1.46777 + 1.06640i) q^{69} +(-1.10220 + 0.800795i) q^{70} +(-1.30904 + 4.02882i) q^{71} +(-0.626941 + 1.92953i) q^{72} +(8.36680 - 6.07883i) q^{73} +(-4.81944 - 3.50153i) q^{74} +(1.31599 + 4.05021i) q^{75} -4.02691 q^{76} +(-0.456421 + 9.55775i) q^{77} +0.548449 q^{78} +(-1.70314 - 5.24171i) q^{79} +(1.59217 + 1.15678i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.338528 - 1.04188i) q^{82} +(0.438561 - 1.34975i) q^{83} +(3.96604 - 2.88150i) q^{84} +(1.65110 + 1.19959i) q^{85} +(0.283188 + 0.871564i) q^{86} -4.24054 q^{87} +(-6.49142 + 1.77171i) q^{88} +6.01572 q^{89} +(-0.145926 - 0.449113i) q^{90} +(-2.33406 - 1.69579i) q^{91} +(2.49405 - 1.81203i) q^{92} +(0.318476 - 0.980168i) q^{93} +(0.445812 - 1.37207i) q^{94} +(1.65081 - 1.19938i) q^{95} +(4.29688 + 3.12187i) q^{96} +(-1.05099 - 3.23462i) q^{97} +0.725890 q^{98} +(-3.10182 - 1.17419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.169480	+	0.521606i	0.119841	+	0.368831i	0.992926	−	0.118736i	$-0.0378843\pi$
$2$	0.169480	+	0.521606i	0.119841	+	0.368831i	−0.873085	+	0.487567i	$0.837884\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	1.37468	−	0.998767i	0.687342	−	0.499383i
$5$	−0.266070	+	0.818878i	−0.118990	+	0.366213i	−0.992758	−	0.120129i	$-0.961669\pi$
$5$	−0.266070	+	0.818878i	−0.118990	+	0.366213i	0.873768	+	0.486342i	$0.161669\pi$
$6$	−0.169480	+	0.521606i	−0.0691899	+	0.212945i
$7$	2.33406	−	1.69579i	0.882191	−	0.640949i	−0.0516395	−	0.998666i	$-0.516445\pi$
$7$	2.33406	−	1.69579i	0.882191	−	0.640949i	0.933830	+	0.357717i	$0.116445\pi$
$8$	1.64135	+	1.19251i	0.580306	+	0.421617i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.472225			−0.149331
$11$	−2.07523	+	2.58716i	−0.625706	+	0.780059i
$11$	−2.07523	+	2.58716i	−0.625706	+	0.780059i
$12$	1.69920			0.490518
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$	1.28011	+	0.930055i	0.342124	+	0.248568i
$15$	−0.696579	+	0.506094i	−0.179856	+	0.130673i
$16$	0.706320	−	2.17383i	0.176580	−	0.543458i
$17$	0.732462	−	2.25429i	0.177648	−	0.546745i	−0.822096	−	0.569348i	$-0.807196\pi$
$17$	0.732462	−	2.25429i	0.177648	−	0.546745i	0.999745	+	0.0226037i	$0.00719561\pi$
$18$	−0.443705	+	0.322370i	−0.104582	+	0.0759834i
$19$	−1.91727	−	1.39298i	−0.439852	−	0.319571i	0.345724	−	0.938336i	$-0.387633\pi$
$19$	−1.91727	−	1.39298i	−0.439852	−	0.319571i	−0.785576	+	0.618765i	$0.787633\pi$
$20$	0.452106	+	1.39144i	0.101094	+	0.311135i
$21$	2.88505			0.629570
$22$	−1.70119	−	0.643981i	−0.362695	−	0.137297i
$23$	1.81427			0.378301			0.189151	−	0.981948i	$-0.439427\pi$
$23$	1.81427			0.378301			0.189151	+	0.981948i	$0.439427\pi$
$24$	0.626941	+	1.92953i	0.127974	+	0.393863i
$25$	3.44532	+	2.50317i	0.689063	+	0.500634i
$26$	0.443705	−	0.322370i	0.0870176	−	0.0632220i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.51489	−	4.66236i	0.286288	−	0.881103i
$29$	−3.43067	+	2.49253i	−0.637060	+	0.462851i	−0.858839	−	0.512246i	$-0.828814\pi$
$29$	−3.43067	+	2.49253i	−0.637060	+	0.462851i	0.221779	+	0.975097i	$0.428814\pi$
$30$	−0.382038	−	0.277567i	−0.0697503	−	0.0506766i
$31$	−0.318476	−	0.980168i	−0.0572000	−	0.176043i	0.918374	−	0.395712i	$-0.129502\pi$
$31$	−0.318476	−	0.980168i	−0.0572000	−	0.176043i	−0.975574	+	0.219669i	$0.929502\pi$
$32$	5.31124			0.938903
$33$	−3.19959	+	0.873268i	−0.556978	+	0.152016i
$34$	1.29999			0.222946
$35$	0.767625	+	2.36251i	0.129752	+	0.399336i
$36$	1.37468	+	0.998767i	0.229114	+	0.166461i
$37$	−8.78740	+	6.38442i	−1.44464	+	1.04959i	−0.457592	+	0.889162i	$0.651288\pi$
$37$	−8.78740	+	6.38442i	−1.44464	+	1.04959i	−0.987047	+	0.160429i	$0.948712\pi$
$38$	0.401647	−	1.23614i	0.0651558	−	0.200529i
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$	−1.41324	+	1.02678i	−0.223452	+	0.162348i
$41$	−1.61597	−	1.17407i	−0.252372	−	0.183359i	0.454405	−	0.890795i	$-0.349852\pi$
$41$	−1.61597	−	1.17407i	−0.252372	−	0.183359i	−0.706778	+	0.707436i	$0.749852\pi$
$42$	0.488959	+	1.50486i	0.0754480	+	0.232205i
$43$	1.67092			0.254814			0.127407	−	0.991851i	$-0.459335\pi$
$43$	1.67092			0.254814			0.127407	+	0.991851i	$0.459335\pi$
$44$	−0.268817	+	5.62921i	−0.0405257	+	0.848635i
$45$	−0.861019			−0.128353
$46$	0.307483	+	0.946334i	0.0453358	+	0.139529i
$47$	−2.12809	−	1.54615i	−0.310414	−	0.225529i	0.421660	−	0.906754i	$-0.361448\pi$
$47$	−2.12809	−	1.54615i	−0.310414	−	0.225529i	−0.732074	+	0.681225i	$0.761448\pi$
$48$	1.84917	−	1.34350i	0.266905	−	0.193918i
$49$	0.408994	−	1.25875i	0.0584277	−	0.179822i
$50$	−0.721756	+	2.22134i	−0.102072	+	0.314144i
$51$	1.91761	−	1.39323i	0.268519	−	0.195091i
$52$	−1.37468	−	0.998767i	−0.190634	−	0.138504i
$53$	−2.34937	−	7.23063i	−0.322711	−	0.993204i	−0.972463	−	0.233057i	$-0.925127\pi$
$53$	−2.34937	−	7.23063i	−0.322711	−	0.993204i	0.649752	−	0.760147i	$-0.274873\pi$
$54$	−0.548449			−0.0746345
$55$	−1.56641	−	2.38773i	−0.211215	−	0.321961i
$56$	5.85327			0.782176
$57$	−0.732333	−	2.25389i	−0.0969998	−	0.298535i
$58$	−1.88155	−	1.36703i	−0.247059	−	0.179499i
$59$	−4.27373	+	3.10505i	−0.556392	+	0.404242i	−0.830137	−	0.557560i	$-0.811738\pi$
$59$	−4.27373	+	3.10505i	−0.556392	+	0.404242i	0.273745	+	0.961802i	$0.411738\pi$
$60$	−0.452106	+	1.39144i	−0.0583667	+	0.179634i
$61$	0.526405	−	1.62011i	0.0673993	−	0.207434i	−0.911685	−	0.410891i	$-0.865218\pi$
$61$	0.526405	−	1.62011i	0.0673993	−	0.207434i	0.979084	+	0.203457i	$0.0652177\pi$
$62$	0.457286	−	0.332238i	0.0580754	−	0.0421943i
$63$	2.33406	+	1.69579i	0.294064	+	0.213650i
$64$	−0.512491	−	1.57729i	−0.0640614	−	0.197161i
$65$	0.861019			0.106796
$66$	−0.997769	−	1.52093i	−0.122817	−	0.187213i
$67$	−7.33979			−0.896698			−0.448349	−	0.893858i	$-0.647988\pi$
$67$	−7.33979			−0.896698			−0.448349	+	0.893858i	$0.647988\pi$
$68$	−1.24460	−	3.83049i	−0.150930	−	0.464515i
$69$	1.46777	+	1.06640i	0.176699	+	0.128380i
$70$	−1.10220	+	0.800795i	−0.131738	+	0.0957133i
$71$	−1.30904	+	4.02882i	−0.155355	+	0.478133i	−0.998197	−	0.0600283i	$-0.980881\pi$
$71$	−1.30904	+	4.02882i	−0.155355	+	0.478133i	0.842842	+	0.538161i	$0.180881\pi$
$72$	−0.626941	+	1.92953i	−0.0738857	+	0.227397i
$73$	8.36680	−	6.07883i	0.979259	−	0.711474i	0.0217165	−	0.999764i	$-0.493087\pi$
$73$	8.36680	−	6.07883i	0.979259	−	0.711474i	0.957543	+	0.288291i	$0.0930869\pi$
$74$	−4.81944	−	3.50153i	−0.560248	−	0.407044i
$75$	1.31599	+	4.05021i	0.151958	+	0.467678i
$76$	−4.02691			−0.461918
$77$	−0.456421	+	9.55775i	−0.0520140	+	1.08921i
$78$	0.548449			0.0620996
$79$	−1.70314	−	5.24171i	−0.191618	−	0.589739i	−0.999999	−	0.00108015i	$-0.999656\pi$
$79$	−1.70314	−	5.24171i	−0.191618	−	0.589739i	0.808382	−	0.588659i	$-0.200344\pi$
$80$	1.59217	+	1.15678i	0.178010	+	0.129332i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	0.338528	−	1.04188i	0.0373842	−	0.115057i
$83$	0.438561	−	1.34975i	0.0481384	−	0.148155i	−0.924098	−	0.382156i	$-0.875182\pi$
$83$	0.438561	−	1.34975i	0.0481384	−	0.148155i	0.972236	+	0.234001i	$0.0751819\pi$
$84$	3.96604	−	2.88150i	0.432730	−	0.314397i
$85$	1.65110	+	1.19959i	0.179087	+	0.130114i
$86$	0.283188	+	0.871564i	0.0305370	+	0.0939832i
$87$	−4.24054			−0.454634
$88$	−6.49142	+	1.77171i	−0.691987	+	0.188865i
$89$	6.01572			0.637665			0.318832	−	0.947811i	$-0.396709\pi$
$89$	6.01572			0.637665			0.318832	+	0.947811i	$0.396709\pi$
$90$	−0.145926	−	0.449113i	−0.0153819	−	0.0473406i
$91$	−2.33406	−	1.69579i	−0.244676	−	0.177767i
$92$	2.49405	−	1.81203i	0.260023	−	0.188917i
$93$	0.318476	−	0.980168i	0.0330244	−	0.101639i
$94$	0.445812	−	1.37207i	0.0459820	−	0.141518i
$95$	1.65081	−	1.19938i	0.169369	−	0.123054i
$96$	4.29688	+	3.12187i	0.438549	+	0.318624i
$97$	−1.05099	−	3.23462i	−0.106712	−	0.328426i	0.883416	−	0.468589i	$-0.155237\pi$
$97$	−1.05099	−	3.23462i	−0.106712	−	0.328426i	−0.990128	+	0.140163i	$0.955237\pi$
$98$	0.725890			0.0733260
$99$	−3.10182	−	1.17419i	−0.311745	−	0.118010i
$100$	7.23631			0.723631
$101$	−3.71677	−	11.4390i	−0.369832	−	1.13823i	−0.946899	−	0.321530i	$-0.895803\pi$
$101$	−3.71677	−	11.4390i	−0.369832	−	1.13823i	0.577067	−	0.816697i	$-0.304197\pi$
$102$	1.05171	+	0.764113i	0.104135	+	0.0756584i
$103$	−7.45807	+	5.41861i	−0.734866	+	0.533911i	−0.891099	−	0.453809i	$-0.850065\pi$
$103$	−7.45807	+	5.41861i	−0.734866	+	0.533911i	0.156233	+	0.987720i	$0.450065\pi$
$104$	0.626941	−	1.92953i	0.0614767	−	0.189206i
$105$	−0.767625	+	2.36251i	−0.0749125	+	0.230557i
$106$	3.37337	−	2.45090i	0.327651	−	0.238052i
$107$	−12.0751	−	8.77306i	−1.16734	−	0.848123i	−0.176653	−	0.984273i	$-0.556527\pi$
$107$	−12.0751	−	8.77306i	−1.16734	−	0.848123i	−0.990688	+	0.136150i	$0.956527\pi$
$108$	0.525083	+	1.61604i	0.0505261	+	0.155503i
$109$	−8.27227			−0.792340			−0.396170	−	0.918177i	$-0.629661\pi$
$109$	−8.27227			−0.792340			−0.396170	+	0.918177i	$0.629661\pi$
$110$	0.979977	−	1.22172i	0.0934371	−	0.116487i
$111$	−10.8618			−1.03096
$112$	−2.03777	−	6.27162i	−0.192551	−	0.592612i
$113$	−2.65827	−	1.93135i	−0.250069	−	0.181686i	0.455688	−	0.890139i	$-0.349393\pi$
$113$	−2.65827	−	1.93135i	−0.250069	−	0.181686i	−0.705757	+	0.708454i	$0.749393\pi$
$114$	1.05153	−	0.763978i	0.0984844	−	0.0715531i
$115$	−0.482722	+	1.48566i	−0.0450140	+	0.138539i
$116$	−2.22664	+	6.85288i	−0.206738	+	0.636274i
$117$	0.809017	−	0.587785i	0.0747936	−	0.0543408i
$118$	−2.34392	−	1.70296i	−0.215775	−	0.156770i
$119$	−2.11319	−	6.50373i	−0.193716	−	0.596196i
$120$	−1.74686			−0.159465
$121$	−2.38682	−	10.7379i	−0.216984	−	0.976175i
$122$	0.934274			0.0845852
$123$	−0.617246	−	1.89969i	−0.0556552	−	0.171289i
$124$	−1.41676	−	1.02934i	−0.127229	−	0.0924374i
$125$	−6.44938	+	4.68575i	−0.576850	+	0.419106i
$126$	−0.488959	+	1.50486i	−0.0435599	+	0.134064i
$127$	4.62472	−	14.2334i	0.410378	−	1.26301i	−0.505943	−	0.862567i	$-0.668855\pi$
$127$	4.62472	−	14.2334i	0.410378	−	1.26301i	0.916321	−	0.400445i	$-0.131145\pi$
$128$	9.32963	−	6.77837i	0.824631	−	0.599129i
$129$	1.35181	+	0.982145i	0.119020	+	0.0864730i
$130$	0.145926	+	0.449113i	0.0127985	+	0.0393898i
$131$	4.75880			0.415779			0.207889	−	0.978152i	$-0.433341\pi$
$131$	4.75880			0.415779			0.207889	+	0.978152i	$0.433341\pi$
$132$	−3.52624	+	4.39612i	−0.306920	+	0.382633i
$133$	−6.83723			−0.592863
$134$	−1.24395	−	3.82848i	−0.107461	−	0.330730i
$135$	−0.696579	−	0.506094i	−0.0599520	−	0.0435577i
$136$	3.89049	−	2.82661i	0.333607	−	0.242380i
$137$	−6.48027	+	19.9442i	−0.553647	+	1.70395i	0.145844	+	0.989308i	$0.453410\pi$
$137$	−6.48027	+	19.9442i	−0.553647	+	1.70395i	−0.699491	+	0.714641i	$0.746590\pi$
$138$	−0.307483	+	0.946334i	−0.0261746	+	0.0805573i
$139$	9.87558	−	7.17503i	0.837636	−	0.608578i	−0.0840734	−	0.996460i	$-0.526793\pi$
$139$	9.87558	−	7.17503i	0.837636	−	0.608578i	0.921709	+	0.387882i	$0.126793\pi$
$140$	3.41483	+	2.48102i	0.288606	+	0.209685i
$141$	−0.812859	−	2.50172i	−0.0684551	−	0.210683i
$142$	−2.32331			−0.194968
$143$	3.10182	+	1.17419i	0.259387	+	0.0981903i
$144$	2.28570			0.190475
$145$	−1.12828	−	3.47249i	−0.0936985	−	0.288374i
$146$	4.58876	+	3.33393i	0.379769	+	0.275918i
$147$	1.07076	−	0.777953i	0.0883148	−	0.0641645i
$148$	−5.70335	+	17.5531i	−0.468813	+	1.44286i
$149$	−1.82404	+	5.61381i	−0.149431	+	0.459901i	−0.997554	−	0.0698979i	$-0.977733\pi$
$149$	−1.82404	+	5.61381i	−0.149431	+	0.459901i	0.848123	+	0.529799i	$0.177733\pi$
$150$	−1.88958	+	1.37286i	−0.154284	+	0.112094i
$151$	−2.71948	−	1.97582i	−0.221308	−	0.160790i	0.471607	−	0.881809i	$-0.343674\pi$
$151$	−2.71948	−	1.97582i	−0.221308	−	0.160790i	−0.692915	+	0.721019i	$0.743674\pi$
$152$	−1.48577	−	4.57274i	−0.120512	−	0.370898i
$153$	2.37030			0.191627
$154$	−5.06273	+	1.38178i	−0.407967	+	0.111347i
$155$	0.887375			0.0712757
$156$	−0.525083	−	1.61604i	−0.0420403	−	0.129387i
$157$	10.5387	+	7.65679i	0.841077	+	0.611078i	0.922671	−	0.385587i	$-0.126001\pi$
$157$	10.5387	+	7.65679i	0.841077	+	0.611078i	−0.0815941	+	0.996666i	$0.526001\pi$
$158$	2.44546	−	1.77673i	0.194551	−	0.141349i
$159$	2.34937	−	7.23063i	0.186318	−	0.573426i
$160$	−1.41316	+	4.34926i	−0.111720	+	0.343839i
$161$	4.23461	−	3.07662i	0.333734	−	0.242472i
$162$	−0.443705	−	0.322370i	−0.0348607	−	0.0253278i
$163$	4.04880	+	12.4609i	0.317127	+	0.976015i	0.974870	+	0.222773i	$0.0715110\pi$
$163$	4.04880	+	12.4609i	0.317127	+	0.976015i	−0.657744	+	0.753242i	$0.728489\pi$
$164$	−3.39408			−0.265033
$165$	0.136215	−	2.85243i	0.0106043	−	0.222061i
$166$	0.778367			0.0604130
$167$	4.81141	+	14.8080i	0.372318	+	1.14588i	0.945270	+	0.326288i	$0.105798\pi$
$167$	4.81141	+	14.8080i	0.372318	+	1.14588i	−0.572953	+	0.819589i	$0.694202\pi$
$168$	4.73539	+	3.44046i	0.365343	+	0.265438i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−0.345887	+	1.06453i	−0.0265283	+	0.0816457i
$171$	0.732333	−	2.25389i	0.0560029	−	0.172359i
$172$	2.29699	−	1.66886i	0.175144	−	0.127250i
$173$	−1.23479	−	0.897126i	−0.0938792	−	0.0682072i	0.539855	−	0.841758i	$-0.318479\pi$
$173$	−1.23479	−	0.897126i	−0.0938792	−	0.0682072i	−0.633735	+	0.773550i	$0.718479\pi$
$174$	−0.718688	−	2.21189i	−0.0544836	−	0.167683i
$175$	12.2864			0.928766
$176$	4.15827	+	6.33857i	0.313442	+	0.477788i
$177$	−5.28262			−0.397066
$178$	1.01954	+	3.13783i	0.0764180	+	0.235191i
$179$	13.6531	+	9.91956i	1.02048	+	0.741423i	0.966381	−	0.257113i	$-0.0827712\pi$
$179$	13.6531	+	9.91956i	1.02048	+	0.741423i	0.0540993	+	0.998536i	$0.482771\pi$
$180$	−1.18363	+	0.859957i	−0.0882225	+	0.0640974i
$181$	−7.42763	+	22.8599i	−0.552091	+	1.69916i	0.151413	+	0.988471i	$0.451618\pi$
$181$	−7.42763	+	22.8599i	−0.552091	+	1.69916i	−0.703504	+	0.710691i	$0.748382\pi$
$182$	0.488959	−	1.50486i	0.0362441	−	0.111548i
$183$	1.37815	−	1.00128i	0.101876	−	0.0740169i
$184$	2.97786	+	2.16354i	0.219531	+	0.159498i
$185$	−2.89000	−	8.89450i	−0.212477	−	0.653937i
$186$	0.565237			0.0414452
$187$	4.31218	+	6.57316i	0.315337	+	0.480677i
$188$	−4.46970			−0.325986
$189$	0.891530	+	2.74385i	0.0648493	+	0.199586i
$190$	0.905384	+	0.657800i	0.0656834	+	0.0477218i
$191$	14.4595	−	10.5054i	1.04625	−	0.760145i	0.0747541	−	0.997202i	$-0.476183\pi$
$191$	14.4595	−	10.5054i	1.04625	−	0.760145i	0.971496	+	0.237057i	$0.0761828\pi$
$192$	0.512491	−	1.57729i	0.0369859	−	0.113831i
$193$	−4.95832	+	15.2601i	−0.356908	+	1.09845i	0.597988	+	0.801505i	$0.295967\pi$
$193$	−4.95832	+	15.2601i	−0.356908	+	1.09845i	−0.954895	+	0.296943i	$0.904033\pi$
$194$	1.50907	−	1.09641i	0.108345	−	0.0787174i
$195$	0.696579	+	0.506094i	0.0498831	+	0.0362422i
$196$	−0.694964	−	2.13888i	−0.0496403	−	0.152777i
$197$	−20.1579			−1.43619			−0.718097	−	0.695943i	$-0.754986\pi$
$197$	−20.1579			−1.43619			−0.718097	+	0.695943i	$0.754986\pi$
$198$	0.0867657	−	1.81693i	0.00616617	−	0.129124i
$199$	14.9087			1.05685			0.528423	−	0.848981i	$-0.322783\pi$
$199$	14.9087			1.05685			0.528423	+	0.848981i	$0.322783\pi$
$200$	2.66992	+	8.21717i	0.188792	+	0.581042i
$201$	−5.93802	−	4.31422i	−0.418835	−	0.304302i
$202$	5.33675	−	3.87738i	0.375492	−	0.272811i
$203$	−3.78057	+	11.6354i	−0.265344	+	0.816646i
$204$	1.24460	−	3.83049i	0.0871395	−	0.268188i
$205$	1.39138	−	1.01090i	0.0971784	−	0.0706042i
$206$	−4.09037	−	2.97183i	−0.284990	−	0.207057i
$207$	0.560640	+	1.72547i	0.0389672	+	0.119929i
$208$	−2.28570			−0.158485
$209$	7.58265	−	2.06954i	0.524503	−	0.143153i
$210$	−1.36239			−0.0940141
$211$	−1.97745	−	6.08595i	−0.136133	−	0.418974i	0.859632	−	0.510914i	$-0.170693\pi$
$211$	−1.97745	−	6.08595i	−0.136133	−	0.418974i	−0.995765	+	0.0919403i	$0.970693\pi$
$212$	−10.4514	−	7.59336i	−0.717803	−	0.521514i
$213$	−3.42712	+	2.48995i	−0.234822	+	0.170608i
$214$	2.52959	−	7.78529i	0.172919	−	0.532191i
$215$	−0.444582	+	1.36828i	−0.0303202	+	0.0933161i
$216$	−1.64135	+	1.19251i	−0.111680	+	0.0811402i
$217$	−2.40550	−	1.74770i	−0.163296	−	0.118642i
$218$	−1.40198	−	4.31487i	−0.0949544	−	0.292240i
$219$	10.3419			0.698843
$220$	−4.53811	−	1.71789i	−0.305959	−	0.115820i
$221$	−2.37030			−0.159443
$222$	−1.84086	−	5.66559i	−0.123551	−	0.380249i
$223$	21.0317	+	15.2804i	1.40839	+	1.02325i	0.993555	+	0.113354i	$0.0361595\pi$
$223$	21.0317	+	15.2804i	1.40839	+	1.02325i	0.414831	+	0.909898i	$0.363841\pi$
$224$	12.3967	−	9.00676i	0.828292	−	0.601789i
$225$	−1.31599	+	4.05021i	−0.0877329	+	0.270014i
$226$	0.556878	−	1.71389i	0.0370430	−	0.114006i
$227$	21.6386	−	15.7213i	1.43620	−	1.04346i	0.447383	−	0.894343i	$-0.352356\pi$
$227$	21.6386	−	15.7213i	1.43620	−	1.04346i	0.988819	−	0.149119i	$-0.0476437\pi$
$228$	−3.25784	−	2.36696i	−0.215755	−	0.156755i
$229$	−0.755999	−	2.32673i	−0.0499578	−	0.153754i	0.922965	−	0.384883i	$-0.125758\pi$
$229$	−0.755999	−	2.32673i	−0.0499578	−	0.153754i	−0.972923	+	0.231129i	$0.925758\pi$
$230$	−0.856743			−0.0564920
$231$	−5.98716	+	7.46410i	−0.393926	+	0.491102i
$232$	−8.60332			−0.564836
$233$	5.71402	+	17.5859i	0.374338	+	1.15209i	0.943924	+	0.330162i	$0.107103\pi$
$233$	5.71402	+	17.5859i	0.374338	+	1.15209i	−0.569586	+	0.821932i	$0.692897\pi$
$234$	0.443705	+	0.322370i	0.0290059	+	0.0210740i
$235$	1.83233	−	1.33126i	0.119528	−	0.0868421i
$236$	−2.77381	+	8.53692i	−0.180560	+	0.555706i
$237$	1.70314	−	5.24171i	0.110631	−	0.340486i
$238$	3.03424	−	2.20451i	0.196681	−	0.142897i
$239$	−16.9174	−	12.2912i	−1.09429	−	0.795051i	−0.114175	−	0.993461i	$-0.536422\pi$
$239$	−16.9174	−	12.2912i	−1.09429	−	0.795051i	−0.980119	+	0.198410i	$0.936422\pi$
$240$	0.608155	+	1.87171i	0.0392562	+	0.120818i
$241$	23.3711			1.50546			0.752731	−	0.658328i	$-0.228736\pi$
$241$	23.3711			1.50546			0.752731	+	0.658328i	$0.228736\pi$
$242$	5.19645	−	3.06485i	0.334040	−	0.197016i
$243$	−1.00000			−0.0641500
$244$	−0.894470	−	2.75289i	−0.0572626	−	0.176236i
$245$	0.921945	+	0.669832i	0.0589009	+	0.0427940i
$246$	0.886278	−	0.643919i	0.0565070	−	0.0410548i
$247$	−0.732333	+	2.25389i	−0.0465972	+	0.143411i
$248$	0.646132	−	1.98859i	0.0410294	−	0.126276i
$249$	1.14817	−	0.834193i	0.0727622	−	0.0528649i
$250$	−3.53716	−	2.56989i	−0.223709	−	0.162534i
$251$	−8.11719	−	24.9821i	−0.512353	−	1.57686i	−0.788048	−	0.615614i	$-0.788908\pi$
$251$	−8.11719	−	24.9821i	−0.512353	−	1.57686i	0.275695	−	0.961245i	$-0.411092\pi$
$252$	4.90229			0.308815
$253$	−3.76503	+	4.69381i	−0.236705	+	0.295097i
$254$	8.20804			0.515018
$255$	0.630663	+	1.94098i	0.0394937	+	0.121549i
$256$	2.43339	+	1.76796i	0.152087	+	0.110497i
$257$	−6.89518	+	5.00964i	−0.430109	+	0.312493i	−0.781693	−	0.623664i	$-0.785643\pi$
$257$	−6.89518	+	5.00964i	−0.430109	+	0.312493i	0.351583	+	0.936157i	$0.385643\pi$
$258$	−0.283188	+	0.871564i	−0.0176305	+	0.0542612i
$259$	−9.68364	+	29.8032i	−0.601712	+	1.85188i
$260$	1.18363	−	0.859957i	0.0734056	−	0.0533323i
$261$	−3.43067	−	2.49253i	−0.212353	−	0.154284i
$262$	0.806522	+	2.48222i	0.0498271	+	0.153352i
$263$	25.4425			1.56885			0.784427	−	0.620221i	$-0.212957\pi$
$263$	25.4425			1.56885			0.784427	+	0.620221i	$0.212957\pi$
$264$	−6.29305	−	2.38222i	−0.387310	−	0.146615i
$265$	6.54610			0.402124
$266$	−1.15877	−	3.56634i	−0.0710490	−	0.218666i
$267$	4.86682	+	3.53595i	0.297844	+	0.216397i
$268$	−10.0899	+	7.33074i	−0.616339	+	0.447796i
$269$	6.08164	−	18.7173i	0.370804	−	1.14122i	−0.575462	−	0.817828i	$-0.695178\pi$
$269$	6.08164	−	18.7173i	0.370804	−	1.14122i	0.946266	−	0.323389i	$-0.104822\pi$
$270$	0.145926	−	0.449113i	0.00888075	−	0.0273321i
$271$	8.61902	−	6.26208i	0.523568	−	0.380395i	−0.294378	−	0.955689i	$-0.595113\pi$
$271$	8.61902	−	6.26208i	0.523568	−	0.380395i	0.817946	+	0.575294i	$0.195113\pi$
$272$	−4.38308	−	3.18450i	−0.265763	−	0.193088i
$273$	−0.891530	−	2.74385i	−0.0539579	−	0.166065i
$274$	−11.5013			−0.694819
$275$	−13.6259	+	3.71894i	−0.821675	+	0.224260i
$276$	3.08281			0.185564
$277$	3.32125	+	10.2217i	0.199554	+	0.614165i	0.999893	+	0.0146171i	$0.00465292\pi$
$277$	3.32125	+	10.2217i	0.199554	+	0.614165i	−0.800339	+	0.599548i	$0.795347\pi$
$278$	5.41625	+	3.93514i	0.324845	+	0.236014i
$279$	0.833781	−	0.605777i	0.0499172	−	0.0362669i
$280$	−1.55738	+	4.79311i	−0.0930710	+	0.286443i
$281$	1.19919	−	3.69072i	0.0715376	−	0.220170i	−0.908895	−	0.417025i	$-0.863073\pi$
$281$	1.19919	−	3.69072i	0.0715376	−	0.220170i	0.980433	+	0.196855i	$0.0630728\pi$
$282$	1.16715	−	0.847984i	0.0695028	−	0.0504967i
$283$	18.3333	+	13.3199i	1.08980	+	0.791786i	0.979365	−	0.202098i	$-0.0647758\pi$
$283$	18.3333	+	13.3199i	1.08980	+	0.791786i	0.110434	+	0.993883i	$0.464776\pi$
$284$	2.22433	+	6.84579i	0.131990	+	0.406223i
$285$	2.04051			0.120869
$286$	−0.0867657	+	1.81693i	−0.00513056	+	0.107437i
$287$	−5.76275			−0.340165
$288$	1.64126	+	5.05129i	0.0967124	+	0.297650i
$289$	9.20799	+	6.68999i	0.541646	+	0.393529i
$290$	1.62005	−	1.17703i	0.0951326	−	0.0691179i
$291$	1.05099	−	3.23462i	0.0616102	−	0.189617i
$292$	5.43037	−	16.7130i	0.317788	−	0.978052i
$293$	−21.0141	+	15.2676i	−1.22766	+	0.891944i	−0.996712	−	0.0810236i	$-0.974181\pi$
$293$	−21.0141	+	15.2676i	−1.22766	+	0.891944i	−0.230943	+	0.972967i	$0.574181\pi$
$294$	0.587257	+	0.426668i	0.0342495	+	0.0248838i
$295$	−1.40554	−	4.32582i	−0.0818339	−	0.251859i
$296$	−22.0367			−1.28086
$297$	−1.81926	−	2.77314i	−0.105564	−	0.160914i
$298$	−3.23733			−0.187534
$299$	−0.560640	−	1.72547i	−0.0324227	−	0.0997867i
$300$	5.85430	+	4.25339i	0.337998	+	0.245570i
$301$	3.90003	−	2.83354i	0.224794	−	0.163323i
$302$	0.569702	−	1.75336i	0.0327826	−	0.100895i
$303$	3.71677	−	11.4390i	0.213523	−	0.657155i
$304$	−4.38231	+	3.18393i	−0.251343	+	0.182611i
$305$	1.18661	+	0.862123i	0.0679451	+	0.0493650i
$306$	0.401718	+	1.23636i	0.0229647	+	0.0706780i
$307$	23.7938			1.35798			0.678991	−	0.734146i	$-0.262417\pi$
$307$	23.7938			1.35798			0.678991	+	0.734146i	$0.262417\pi$
$308$	8.91853	+	13.5947i	0.508180	+	0.774633i
$309$	−9.21869			−0.524433
$310$	0.150392	+	0.462860i	0.00854171	+	0.0262887i
$311$	0.260256	+	0.189087i	0.0147578	+	0.0107221i	0.595140	−	0.803622i	$-0.297097\pi$
$311$	0.260256	+	0.189087i	0.0147578	+	0.0107221i	−0.580382	+	0.814344i	$0.697097\pi$
$312$	1.64135	−	1.19251i	0.0929233	−	0.0675128i
$313$	−9.45290	+	29.0930i	−0.534309	+	1.64444i	0.210827	+	0.977523i	$0.432384\pi$
$313$	−9.45290	+	29.0930i	−0.534309	+	1.64444i	−0.745136	+	0.666912i	$0.767616\pi$
$314$	−2.20773	+	6.79471i	−0.124590	+	0.383447i
$315$	−2.00967	+	1.46011i	−0.113232	+	0.0822678i
$316$	−7.57653	−	5.50467i	−0.426213	−	0.309662i
$317$	−7.91864	−	24.3711i	−0.444755	−	1.36882i	−0.882752	−	0.469840i	$-0.844312\pi$
$317$	−7.91864	−	24.3711i	−0.444755	−	1.36882i	0.437996	−	0.898977i	$-0.355688\pi$
$318$	4.16971			0.233826
$319$	0.670862	−	14.0483i	0.0375611	−	0.786553i
$320$	1.42796			0.0798256
$321$	−4.61227	−	14.1951i	−0.257432	−	0.792293i
$322$	2.32247	+	1.68737i	0.129426	+	0.0940335i
$323$	−4.54450	+	3.30177i	−0.252863	+	0.183716i
$324$	−0.525083	+	1.61604i	−0.0291713	+	0.0897799i
$325$	1.31599	−	4.05021i	0.0729982	−	0.224665i
$326$	−5.81350	+	4.22376i	−0.321980	+	0.233932i
$327$	−6.69241	−	4.86232i	−0.370091	−	0.268887i
$328$	−1.25228	−	3.85414i	−0.0691459	−	0.212809i
$329$	−7.58904			−0.418397
$330$	1.51093	−	0.412379i	0.0831739	−	0.0227007i
$331$	6.92200			0.380467			0.190234	−	0.981739i	$-0.439075\pi$
$331$	6.92200			0.380467			0.190234	+	0.981739i	$0.439075\pi$
$332$	−0.745205	−	2.29351i	−0.0408984	−	0.125872i
$333$	−8.78740	−	6.38442i	−0.481546	−	0.349864i
$334$	−6.90850	+	5.01932i	−0.378016	+	0.274645i
$335$	1.95290	−	6.01039i	0.106698	−	0.328383i
$336$	2.03777	−	6.27162i	0.111170	−	0.342145i
$337$	−24.0335	+	17.4613i	−1.30919	+	0.951180i	−0.309187	+	0.951001i	$0.600057\pi$
$337$	−24.0335	+	17.4613i	−1.30919	+	0.951180i	−1.00000		0.000178979i	$0.999943\pi$
$338$	−0.443705	−	0.322370i	−0.0241343	−	0.0175346i
$339$	−1.01537	−	3.12498i	−0.0551472	−	0.169726i
$340$	3.46785			0.188071
$341$	3.19677	+	1.21013i	0.173115	+	0.0655321i
$342$	1.29976			0.0702828
$343$	5.06074	+	15.5754i	0.273254	+	0.840991i
$344$	2.74258	+	1.99260i	0.147870	+	0.107434i
$345$	−1.26378	+	0.918191i	−0.0680397	+	0.0494338i
$346$	0.258674	−	0.796118i	0.0139064	−	0.0427996i
$347$	−7.00782	+	21.5679i	−0.376200	+	1.15782i	0.566466	+	0.824085i	$0.308310\pi$
$347$	−7.00782	+	21.5679i	−0.376200	+	1.15782i	−0.942666	+	0.333739i	$0.891690\pi$
$348$	−5.82941	+	4.23531i	−0.312489	+	0.227037i
$349$	3.69218	+	2.68253i	0.197638	+	0.143592i	0.682203	−	0.731163i	$-0.261022\pi$
$349$	3.69218	+	2.68253i	0.197638	+	0.143592i	−0.484565	+	0.874755i	$0.661022\pi$
$350$	2.08230	+	6.40867i	0.111304	+	0.342558i
$351$	1.00000			0.0533761
$352$	−11.0221	+	13.7410i	−0.587477	+	0.732400i
$353$	9.80944			0.522104			0.261052	−	0.965325i	$-0.415931\pi$
$353$	9.80944			0.522104			0.261052	+	0.965325i	$0.415931\pi$
$354$	−0.895298	−	2.75545i	−0.0475846	−	0.146450i
$355$	−2.95082	−	2.14389i	−0.156613	−	0.113786i
$356$	8.26971	−	6.00830i	0.438294	−	0.318439i
$357$	2.11319	−	6.50373i	0.111842	−	0.344214i
$358$	−2.86017	+	8.80271i	−0.151165	+	0.465238i
$359$	−0.0584317	+	0.0424531i	−0.00308391	+	0.00224059i	−0.589326	−	0.807895i	$-0.700607\pi$
$359$	−0.0584317	+	0.0424531i	−0.00308391	+	0.00224059i	0.586242	+	0.810136i	$0.300607\pi$
$360$	−1.41324	−	1.02678i	−0.0744841	−	0.0541159i
$361$	−4.13578	−	12.7286i	−0.217673	−	0.669928i
$362$	−13.1827			−0.692867
$363$	4.38061	−	10.0901i	0.229923	−	0.529593i
$364$	−4.90229			−0.256950
$365$	2.75167	+	8.46878i	0.144029	+	0.443276i
$366$	0.755843	+	0.549152i	0.0395086	+	0.0287047i
$367$	11.8065	−	8.57791i	0.616293	−	0.447763i	−0.235331	−	0.971915i	$-0.575618\pi$
$367$	11.8065	−	8.57791i	0.616293	−	0.447763i	0.851625	+	0.524152i	$0.175618\pi$
$368$	1.28146	−	3.94391i	0.0668005	−	0.205591i
$369$	0.617246	−	1.89969i	0.0321326	−	0.0988939i
$370$	4.14963	−	3.01488i	0.215729	−	0.156736i
$371$	−17.7452	−	12.8927i	−0.921286	−	0.669353i
$372$	−0.541156	−	1.66551i	−0.0280576	−	0.0863525i
$373$	−12.0924			−0.626122			−0.313061	−	0.949733i	$-0.601354\pi$
$373$	−12.0924			−0.626122			−0.313061	+	0.949733i	$0.601354\pi$
$374$	−2.69777	+	3.36328i	−0.139499	+	0.173911i
$375$	−7.97187			−0.411666
$376$	−1.64915	−	5.07556i	−0.0850483	−	0.261752i
$377$	3.43067	+	2.49253i	0.176689	+	0.128372i
$378$	−1.28011	+	0.930055i	−0.0658418	+	0.0478369i
$379$	6.13245	−	18.8737i	0.315003	−	0.969479i	−0.660751	−	0.750606i	$-0.729762\pi$
$379$	6.13245	−	18.8737i	0.315003	−	0.969479i	0.975753	−	0.218873i	$-0.0702381\pi$
$380$	1.07144	−	3.29754i	0.0549635	−	0.169160i
$381$	12.1077	−	8.79674i	0.620295	−	0.450671i
$382$	7.93028	+	5.76168i	0.405748	+	0.294793i
$383$	−11.6345	−	35.8072i	−0.594493	−	1.82966i	−0.557235	−	0.830355i	$-0.688138\pi$
$383$	−11.6345	−	35.8072i	−0.594493	−	1.82966i	−0.0372574	−	0.999306i	$-0.511862\pi$
$384$	11.5321			0.588493
$385$	−7.70519	−	2.91678i	−0.392693	−	0.148653i
$386$	−8.80012			−0.447914
$387$	0.516344	+	1.58914i	0.0262472	+	0.0807807i
$388$	−4.67541	−	3.39689i	−0.237358	−	0.172451i
$389$	26.5462	−	19.2869i	1.34595	−	0.977887i	0.346743	−	0.937960i	$-0.387287\pi$
$389$	26.5462	−	19.2869i	1.34595	−	0.977887i	0.999203	−	0.0399270i	$-0.0127125\pi$
$390$	−0.145926	+	0.449113i	−0.00738923	+	0.0227417i
$391$	1.32888	−	4.08988i	0.0672045	−	0.206834i
$392$	2.17238	−	1.57833i	0.109722	−	0.0797177i
$393$	3.84995	+	2.79715i	0.194204	+	0.141098i
$394$	−3.41637	−	10.5145i	−0.172114	−	0.529713i
$395$	4.74548			0.238771
$396$	−5.43676	+	1.48386i	−0.273208	+	0.0745668i
$397$	−6.97595			−0.350113			−0.175057	−	0.984558i	$-0.556011\pi$
$397$	−6.97595			−0.350113			−0.175057	+	0.984558i	$0.556011\pi$
$398$	2.52672	+	7.77644i	0.126653	+	0.389798i
$399$	−5.53143	−	4.01882i	−0.276918	−	0.201193i
$400$	7.87496	−	5.72150i	0.393748	−	0.286075i
$401$	−5.88124	+	18.1006i	−0.293695	+	0.903900i	0.689962	+	0.723846i	$0.257627\pi$
$401$	−5.88124	+	18.1006i	−0.293695	+	0.903900i	−0.983657	+	0.180054i	$0.942373\pi$
$402$	1.24395	−	3.82848i	0.0620425	−	0.190947i
$403$	−0.833781	+	0.605777i	−0.0415336	+	0.0301759i
$404$	−16.5343	−	12.0129i	−0.822613	−	0.597663i
$405$	−0.266070	−	0.818878i	−0.0132211	−	0.0406904i
$406$	−6.70983			−0.333003
$407$	1.71836	−	35.9836i	0.0851760	−	1.78364i
$408$	4.80891			0.238077
$409$	−5.94251	−	18.2892i	−0.293838	−	0.904341i	−0.983609	−	0.180314i	$-0.942289\pi$
$409$	−5.94251	−	18.2892i	−0.293838	−	0.904341i	0.689771	−	0.724028i	$-0.257711\pi$
$410$	0.763102	+	0.554426i	0.0376869	+	0.0273812i
$411$	−16.9656	+	12.3262i	−0.836849	+	0.608007i
$412$	−4.84057	+	14.8978i	−0.238478	+	0.733960i
$413$	−4.70962	+	14.4947i	−0.231745	+	0.713238i
$414$	−0.805000	+	0.584866i	−0.0395636	+	0.0287446i
$415$	0.988595	+	0.718256i	0.0485282	+	0.0352578i
$416$	−1.64126	−	5.05129i	−0.0804696	−	0.247660i
$417$	12.2069			0.597774
$418$	2.36459	+	3.60441i	0.115656	+	0.176297i
$419$	−7.92185			−0.387008			−0.193504	−	0.981100i	$-0.561985\pi$
$419$	−7.92185			−0.387008			−0.193504	+	0.981100i	$0.561985\pi$
$420$	1.30435	+	4.01438i	0.0636458	+	0.195882i
$421$	−11.2643	−	8.18398i	−0.548987	−	0.398863i	0.278425	−	0.960458i	$-0.410188\pi$
$421$	−11.2643	−	8.18398i	−0.548987	−	0.398863i	−0.827412	+	0.561595i	$0.810188\pi$
$422$	2.83933	−	2.06289i	0.138216	−	0.100420i
$423$	0.812859	−	2.50172i	0.0395226	−	0.121638i
$424$	4.76647	−	14.6697i	0.231480	−	0.712423i
$425$	8.16642	−	5.93325i	0.396130	−	0.287805i
$426$	−1.87960	−	1.36561i	−0.0910669	−	0.0661640i
$427$	−1.51871	−	4.67410i	−0.0734954	−	0.226196i
$428$	−25.3617			−1.22590
$429$	1.81926	+	2.77314i	0.0878345	+	0.133888i
$430$	−0.789052			−0.0380515
$431$	−4.12564	−	12.6974i	−0.198725	−	0.611613i	−0.999913	−	0.0131998i	$-0.995798\pi$
$431$	−4.12564	−	12.6974i	−0.198725	−	0.611613i	0.801188	−	0.598413i	$-0.204202\pi$
$432$	1.84917	+	1.34350i	0.0889683	+	0.0646392i
$433$	−21.4217	+	15.5638i	−1.02946	+	0.747949i	−0.968201	−	0.250173i	$-0.919512\pi$
$433$	−21.4217	+	15.5638i	−1.02946	+	0.747949i	−0.0612619	+	0.998122i	$0.519512\pi$
$434$	0.503926	−	1.55093i	0.0241892	−	0.0744468i
$435$	1.12828	−	3.47249i	0.0540969	−	0.166493i
$436$	−11.3718	+	8.26207i	−0.544609	+	0.395681i
$437$	−3.47845	−	2.52724i	−0.166397	−	0.120894i
$438$	1.75275	+	5.39441i	0.0837497	+	0.257755i
$439$	33.1329			1.58134			0.790672	−	0.612240i	$-0.209731\pi$
$439$	33.1329			1.58134			0.790672	+	0.612240i	$0.209731\pi$
$440$	0.276356	−	5.78707i	0.0131748	−	0.275888i
$441$	1.32353			0.0630254
$442$	−0.401718	−	1.23636i	−0.0191078	−	0.0588077i
$443$	−2.21514	−	1.60939i	−0.105244	−	0.0764646i	0.533918	−	0.845536i	$-0.320719\pi$
$443$	−2.21514	−	1.60939i	−0.105244	−	0.0764646i	−0.639163	+	0.769071i	$0.720719\pi$
$444$	−14.9316	+	10.8484i	−0.708621	+	0.514843i
$445$	−1.60060	+	4.92614i	−0.0758756	+	0.233521i
$446$	−4.40591	+	13.5600i	−0.208626	+	0.642084i
$447$	−4.77539	+	3.46952i	−0.225868	+	0.164103i
$448$	−3.87093	−	2.81240i	−0.182884	−	0.132873i
$449$	8.30204	+	25.5510i	0.391797	+	1.20583i	0.931428	+	0.363926i	$0.118564\pi$
$449$	8.30204	+	25.5510i	0.391797	+	1.20583i	−0.539630	+	0.841902i	$0.681436\pi$
$450$	−2.33565			−0.110104
$451$	6.39103	−	1.74431i	0.300942	−	0.0821364i
$452$	−5.58324			−0.262614
$453$	−1.03875	−	3.19694i	−0.0488047	−	0.150206i
$454$	11.8676	+	8.62235i	0.556976	+	0.404667i
$455$	2.00967	−	1.46011i	0.0942147	−	0.0684510i
$456$	1.48577	−	4.57274i	0.0695778	−	0.214138i
$457$	1.49423	−	4.59878i	0.0698973	−	0.215122i	−0.910006	−	0.414595i	$-0.863923\pi$
$457$	1.49423	−	4.59878i	0.0698973	−	0.215122i	0.979903	+	0.199474i	$0.0639232\pi$
$458$	1.08551	−	0.788668i	0.0507224	−	0.0368520i
$459$	1.91761	+	1.39323i	0.0895064	+	0.0650302i
$460$	0.820243	+	2.52445i	0.0382440	+	0.117703i
$461$	−2.49419			−0.116166			−0.0580829	−	0.998312i	$-0.518499\pi$
$461$	−2.49419			−0.116166			−0.0580829	+	0.998312i	$0.518499\pi$
$462$	−4.90802	−	1.85792i	−0.228342	−	0.0864382i
$463$	38.3608			1.78278			0.891389	−	0.453239i	$-0.149731\pi$
$463$	38.3608			1.78278			0.891389	+	0.453239i	$0.149731\pi$
$464$	2.99518	+	9.21822i	0.139048	+	0.427945i
$465$	0.717901	+	0.521586i	0.0332919	+	0.0241880i
$466$	−8.20452	+	5.96094i	−0.380067	+	0.276135i
$467$	0.510228	−	1.57032i	0.0236105	−	0.0726658i	−0.938557	−	0.345124i	$-0.887837\pi$
$467$	0.510228	−	1.57032i	0.0236105	−	0.0726658i	0.962168	+	0.272459i	$0.0878368\pi$
$468$	0.525083	−	1.61604i	0.0242720	−	0.0747014i
$469$	−17.1315	+	12.4468i	−0.791059	+	0.574738i
$470$	1.00494	+	0.730131i	0.0463544	+	0.0336784i
$471$	4.02541	+	12.3889i	0.185481	+	0.570853i
$472$	−10.7175			−0.493313
$473$	−3.46756	+	4.32295i	−0.159438	+	0.198770i
$474$	3.02276			0.138840
$475$	−3.11875	−	9.59851i	−0.143098	−	0.440410i
$476$	−9.40069	−	6.83000i	−0.430880	−	0.313052i
$477$	6.15074	−	4.46878i	0.281623	−	0.204611i
$478$	3.54400	−	10.9073i	0.162099	−	0.498889i
$479$	−5.30948	+	16.3409i	−0.242596	+	0.746635i	0.753426	+	0.657533i	$0.228400\pi$
$479$	−5.30948	+	16.3409i	−0.242596	+	0.746635i	−0.996022	+	0.0891023i	$0.971600\pi$
$480$	−3.69970	+	2.68799i	−0.168867	+	0.122689i
$481$	8.78740	+	6.38442i	0.400671	+	0.291104i
$482$	3.96093	+	12.1905i	0.180415	+	0.555261i
$483$	5.23426			0.238167
$484$	−14.0058	−	12.3774i	−0.636628	−	0.562608i
$485$	2.92839			0.132972
$486$	−0.169480	−	0.521606i	−0.00768777	−	0.0236605i
$487$	−18.3025	−	13.2975i	−0.829365	−	0.602569i	0.0900145	−	0.995940i	$-0.471309\pi$
$487$	−18.3025	−	13.2975i	−0.829365	−	0.602569i	−0.919380	+	0.393371i	$0.871309\pi$
$488$	2.79602	−	2.03143i	0.126570	−	0.0919583i
$489$	−4.04880	+	12.4609i	−0.183093	+	0.563503i
$490$	−0.193137	+	0.594415i	−0.00872505	+	0.0268529i
$491$	−14.0339	+	10.1962i	−0.633340	+	0.460148i	−0.857556	−	0.514391i	$-0.828018\pi$
$491$	−14.0339	+	10.1962i	−0.633340	+	0.460148i	0.224216	+	0.974540i	$0.428018\pi$
$492$	−2.74587	−	1.99499i	−0.123793	−	0.0899410i
$493$	3.10604	+	9.55940i	0.139889	+	0.430534i
$494$	−1.29976			−0.0584788
$495$	1.78681	−	2.22760i	0.0803113	−	0.100123i
$496$	−2.35567			−0.105773
$497$	3.77666	+	11.6234i	0.169406	+	0.521379i
$498$	0.629712	+	0.457513i	0.0282181	+	0.0205016i
$499$	−18.2528	+	13.2614i	−0.817107	+	0.593663i	−0.915882	−	0.401447i	$-0.868507\pi$
$499$	−18.2528	+	13.2614i	−0.817107	+	0.593663i	0.0987757	+	0.995110i	$0.468507\pi$
$500$	−4.18589	+	12.8829i	−0.187199	+	0.576139i
$501$	−4.81141	+	14.8080i	−0.214958	+	0.661572i
$502$	11.6551	−	8.46795i	0.520194	−	0.377943i
$503$	−0.311011	−	0.225963i	−0.0138673	−	0.0100752i	0.580830	−	0.814025i	$-0.302728\pi$
$503$	−0.311011	−	0.225963i	−0.0138673	−	0.0100752i	−0.594697	+	0.803950i	$0.702728\pi$
$504$	1.80876	+	5.56679i	0.0805685	+	0.247964i
$505$	10.3561			0.460840
$506$	−3.08642	−	1.16836i	−0.137208	−	0.0519397i
$507$	−1.00000			−0.0444116
$508$	−7.85834	−	24.1855i	−0.348658	−	1.07306i
$509$	21.1729	+	15.3830i	0.938472	+	0.681840i	0.948052	−	0.318114i	$-0.103050\pi$
$509$	21.1729	+	15.3830i	0.938472	+	0.681840i	−0.00958015	+	0.999954i	$0.503050\pi$
$510$	−0.905543	+	0.657916i	−0.0400981	+	0.0291330i
$511$	9.22015	−	28.3767i	0.407875	−	1.25531i
$512$	6.61744	−	20.3664i	0.292452	−	0.900075i
$513$	1.91727	−	1.39298i	0.0846496	−	0.0615015i
$514$	−3.78165	−	2.74753i	−0.166802	−	0.121188i
$515$	−2.45281	−	7.54898i	−0.108084	−	0.332648i
$516$	2.83924			0.124991
$517$	8.41643	−	2.29710i	0.370154	−	0.101026i
$518$	−17.1867			−0.755140
$519$	−0.471647	−	1.45158i	−0.0207030	−	0.0637173i
$520$	1.41324	+	1.02678i	0.0619745	+	0.0450271i
$521$	19.8204	−	14.4004i	0.868347	−	0.630891i	−0.0617957	−	0.998089i	$-0.519683\pi$
$521$	19.8204	−	14.4004i	0.868347	−	0.630891i	0.930143	+	0.367198i	$0.119683\pi$
$522$	0.718688	−	2.21189i	0.0314561	−	0.0968119i
$523$	−3.25528	+	10.0187i	−0.142343	+	0.438088i	−0.996660	−	0.0816653i	$-0.973976\pi$
$523$	−3.25528	+	10.0187i	−0.142343	+	0.438088i	0.854316	+	0.519753i	$0.173976\pi$
$524$	6.54185	−	4.75294i	0.285782	−	0.207633i
$525$	9.93992	+	7.22178i	0.433814	+	0.315184i
$526$	4.31200	+	13.2710i	0.188012	+	0.578642i
$527$	−2.44285			−0.106412
$528$	−0.361602	+	7.57218i	−0.0157367	+	0.329537i
$529$	−19.7084			−0.856888
$530$	1.10943	+	3.41449i	0.0481907	+	0.148316i
$531$	−4.27373	−	3.10505i	−0.185464	−	0.134747i
$532$	−9.39903	+	6.82879i	−0.407500	+	0.296066i
$533$	−0.617246	+	1.89969i	−0.0267359	+	0.0822847i
$534$	−1.01954	+	3.13783i	−0.0441200	+	0.135787i
$535$	10.3969	−	7.55377i	0.449496	−	0.326578i
$536$	−12.0472	−	8.75280i	−0.520360	−	0.378063i
$537$	5.21502	+	16.0502i	0.225045	+	0.692617i
$538$	10.7938			0.465354
$539$	2.40784	+	3.67034i	0.103713	+	0.158093i
$540$	−1.46305			−0.0629595
$541$	−9.94607	−	30.6108i	−0.427615	−	1.31606i	−0.900468	−	0.434922i	$-0.856776\pi$
$541$	−9.94607	−	30.6108i	−0.427615	−	1.31606i	0.472853	−	0.881141i	$-0.343224\pi$
$542$	4.72709	+	3.43443i	0.203046	+	0.147522i
$543$	−19.4458	+	14.1282i	−0.834498	+	0.606298i
$544$	3.89028	−	11.9730i	0.166794	−	0.513340i
$545$	2.20100	−	6.77398i	0.0942804	−	0.290165i
$546$	1.28011	−	0.930055i	0.0547837	−	0.0398027i
$547$	2.19772	+	1.59674i	0.0939679	+	0.0682716i	0.633777	−	0.773516i	$-0.281504\pi$
$547$	2.19772	+	1.59674i	0.0939679	+	0.0682716i	−0.539809	+	0.841787i	$0.681504\pi$
$548$	11.0113	+	33.8893i	0.470379	+	1.44768i
$549$	1.70348			0.0727029
$550$	−4.24915	−	6.47709i	−0.181184	−	0.276184i
$551$	10.0496			0.428126
$552$	1.13744	+	3.50068i	0.0484127	+	0.148999i
$553$	−12.8641	−	9.34630i	−0.547036	−	0.397445i
$554$	−4.76884	+	3.46476i	−0.202608	+	0.147204i
$555$	2.89000	−	8.89450i	0.122674	−	0.377551i
$556$	6.40963	−	19.7268i	0.271829	−	0.836603i
$557$	21.0858	−	15.3197i	0.893433	−	0.649117i	−0.0433378	−	0.999060i	$-0.513799\pi$
$557$	21.0858	−	15.3197i	0.893433	−	0.649117i	0.936771	+	0.349943i	$0.113799\pi$
$558$	0.457286	+	0.332238i	0.0193585	+	0.0140648i
$559$	−0.516344	−	1.58914i	−0.0218390	−	0.0672136i
$560$	5.67788			0.239934
$561$	−0.374985	+	7.85243i	−0.0158319	+	0.331530i
$562$	2.12834			0.0897787
$563$	6.27595	+	19.3154i	0.264500	+	0.814047i	0.991808	+	0.127736i	$0.0407710\pi$
$563$	6.27595	+	19.3154i	0.264500	+	0.814047i	−0.727308	+	0.686311i	$0.759229\pi$
$564$	−3.61606	−	2.62722i	−0.152264	−	0.110626i
$565$	2.28882	−	1.66292i	0.0962914	−	0.0699598i
$566$	−3.84062	+	11.8202i	−0.161433	+	0.496840i
$567$	−0.891530	+	2.74385i	−0.0374408	+	0.115231i
$568$	−6.95302	+	5.05167i	−0.291742	+	0.211963i
$569$	8.31780	+	6.04324i	0.348700	+	0.253346i	0.748324	−	0.663334i	$-0.230859\pi$
$569$	8.31780	+	6.04324i	0.348700	+	0.253346i	−0.399623	+	0.916679i	$0.630859\pi$
$570$	0.345826	+	1.06434i	0.0144850	+	0.0445804i
$571$	−7.56987			−0.316789			−0.158395	−	0.987376i	$-0.550632\pi$
$571$	−7.56987			−0.316789			−0.158395	+	0.987376i	$0.550632\pi$
$572$	5.43676	−	1.48386i	0.227322	−	0.0620433i
$573$	17.8729			0.746650
$574$	−0.976672	−	3.00589i	−0.0407655	−	0.125463i
$575$	6.25073	+	4.54142i	0.260674	+	0.189390i
$576$	1.34172	−	0.974817i	0.0559050	−	0.0406174i
$577$	2.68657	−	8.26841i	0.111843	−	0.344218i	−0.879432	−	0.476024i	$-0.842078\pi$
$577$	2.68657	−	8.26841i	0.111843	−	0.344218i	0.991276	+	0.131806i	$0.0420775\pi$
$578$	−1.92897	+	5.93676i	−0.0802346	+	0.246937i
$579$	−12.9810	+	9.43128i	−0.539474	+	0.391951i
$580$	−5.01923	−	3.64669i	−0.208412	−	0.151420i
$581$	−1.26527	−	3.89411i	−0.0524924	−	0.161555i
$582$	1.86532			0.0773199
$583$	23.5823	+	8.92702i	0.976680	+	0.369720i
$584$	20.9820			0.868240
$585$	0.266070	+	0.818878i	0.0110006	+	0.0338564i
$586$	−11.5251	−	8.37351i	−0.476099	−	0.345906i
$587$	13.4552	−	9.77576i	0.555355	−	0.403489i	−0.274401	−	0.961615i	$-0.588480\pi$
$587$	13.4552	−	9.77576i	0.555355	−	0.403489i	0.829756	+	0.558126i	$0.188480\pi$
$588$	0.694964	−	2.13888i	0.0286598	−	0.0882059i
$589$	−0.754749	+	2.32288i	−0.0310989	+	0.0957126i
$590$	2.01816	−	1.46628i	0.0830864	−	0.0603658i
$591$	−16.3081	−	11.8485i	−0.670826	−	0.487384i
$592$	7.67192	+	23.6118i	0.315314	+	0.970437i
$593$	13.8633			0.569297			0.284649	−	0.958632i	$-0.408123\pi$
$593$	13.8633			0.569297			0.284649	+	0.958632i	$0.408123\pi$
$594$	1.13816	−	1.41893i	0.0466992	−	0.0582193i
$595$	5.88802			0.241385
$596$	3.09941	+	9.53900i	0.126957	+	0.390733i
$597$	12.0614	+	8.76309i	0.493638	+	0.358649i
$598$	0.805000	−	0.584866i	0.0329189	−	0.0239170i
$599$	−12.8816	+	39.6455i	−0.526329	+	1.61987i	0.235345	+	0.971912i	$0.424378\pi$
$599$	−12.8816	+	39.6455i	−0.526329	+	1.61987i	−0.761674	+	0.647961i	$0.775622\pi$
$600$	−2.66992	+	8.21717i	−0.108999	+	0.335465i
$601$	−15.3781	+	11.1729i	−0.627287	+	0.455751i	−0.855459	−	0.517870i	$-0.826725\pi$
$601$	−15.3781	+	11.1729i	−0.627287	+	0.455751i	0.228172	+	0.973621i	$0.426725\pi$
$602$	2.13897	+	1.55405i	0.0871779	+	0.0633384i
$603$	−2.26812	−	6.98056i	−0.0923650	−	0.284270i
$604$	−5.71182			−0.232410
$605$	9.42811	+	0.902519i	0.383307	+	0.0366926i
$606$	6.59659			0.267968
$607$	−13.3917	−	41.2154i	−0.543552	−	1.67288i	−0.724408	−	0.689372i	$-0.757887\pi$
$607$	−13.3917	−	41.2154i	−0.543552	−	1.67288i	0.180855	−	0.983510i	$-0.442113\pi$
$608$	−10.1831	−	7.39845i	−0.412979	−	0.300047i
$609$	−9.89767	+	7.19108i	−0.401074	+	0.291397i
$610$	−0.248582	+	0.765056i	−0.0100648	+	0.0309762i
$611$	−0.812859	+	2.50172i	−0.0328848	+	0.101209i
$612$	3.25841	−	2.36737i	0.131713	−	0.0956954i
$613$	5.58239	+	4.05584i	0.225471	+	0.163814i	0.694786	−	0.719217i	$-0.255499\pi$
$613$	5.58239	+	4.05584i	0.225471	+	0.163814i	−0.469315	+	0.883031i	$0.655499\pi$
$614$	4.03257	+	12.4110i	0.162741	+	0.500866i
$615$	1.71984			0.0693508
$616$	−12.1469	+	15.1434i	−0.489412	+	0.610143i
$617$	−26.7547			−1.07710			−0.538552	−	0.842592i	$-0.681029\pi$
$617$	−26.7547			−1.07710			−0.538552	+	0.842592i	$0.681029\pi$
$618$	−1.56238	−	4.80852i	−0.0628483	−	0.193427i
$619$	6.30059	+	4.57765i	0.253242	+	0.183991i	0.707162	−	0.707051i	$-0.249975\pi$
$619$	6.30059	+	4.57765i	0.253242	+	0.183991i	−0.453920	+	0.891042i	$0.649975\pi$
$620$	1.21986	−	0.886281i	0.0489908	−	0.0355939i
$621$	−0.560640	+	1.72547i	−0.0224977	+	0.0692408i
$622$	−0.0545207	+	0.167797i	−0.00218608	+	0.00672806i
$623$	14.0410	−	10.2014i	0.562542	−	0.408710i
$624$	−1.84917	−	1.34350i	−0.0740261	−	0.0537831i
$625$	4.45890	+	13.7231i	0.178356	+	0.548923i
$626$	−16.7772			−0.670551
$627$	7.35094	+	2.78268i	0.293568	+	0.111129i
$628$	22.1347			0.883270
$629$	7.95587	+	24.4856i	0.317221	+	0.976306i
$630$	−1.10220	−	0.800795i	−0.0439127	−	0.0319044i
$631$	4.68114	−	3.40104i	0.186353	−	0.135393i	−0.490697	−	0.871330i	$-0.663258\pi$
$631$	4.68114	−	3.40104i	0.186353	−	0.135393i	0.677050	+	0.735937i	$0.263258\pi$
$632$	3.45536	−	10.6345i	0.137447	−	0.423018i
$633$	1.97745	−	6.08595i	0.0785964	−	0.241895i
$634$	11.3701	−	8.26083i	0.451562	−	0.328079i
$635$	10.4249	+	7.57416i	0.413701	+	0.300571i
$636$	−3.99207	−	12.2863i	−0.158296	−	0.487184i
$637$	−1.32353			−0.0524403
$638$	7.44137	−	2.03098i	0.294607	−	0.0804072i
$639$	−4.23615			−0.167580
$640$	3.06833	+	9.44335i	0.121286	+	0.373281i
$641$	19.6740	+	14.2940i	0.777077	+	0.564580i	0.904100	−	0.427320i	$-0.140542\pi$
$641$	19.6740	+	14.2940i	0.777077	+	0.564580i	−0.127023	+	0.991900i	$0.540542\pi$
$642$	6.62256	−	4.81157i	0.261372	−	0.189898i
$643$	−3.62688	+	11.1624i	−0.143030	+	0.440201i	−0.996752	−	0.0805273i	$-0.974340\pi$
$643$	−3.62688	+	11.1624i	−0.143030	+	0.440201i	0.853722	+	0.520728i	$0.174340\pi$
$644$	2.74842	−	8.45877i	0.108303	−	0.333322i
$645$	−1.16393	+	0.845645i	−0.0458297	+	0.0332973i
$646$	−2.49243	−	1.81085i	−0.0980632	−	0.0712471i
$647$	−7.43368	−	22.8785i	−0.292248	−	0.899447i	−0.984132	−	0.177438i	$-0.943219\pi$
$647$	−7.43368	−	22.8785i	−0.292248	−	0.899447i	0.691884	−	0.722009i	$-0.256781\pi$
$648$	−2.02882			−0.0796998
$649$	0.835720	−	17.5005i	0.0328049	−	0.686955i
$650$	2.33565			0.0916117
$651$	−0.918820	−	2.82784i	−0.0360114	−	0.110832i
$652$	18.0114	+	13.0860i	0.705380	+	0.512489i
$653$	15.8385	−	11.5073i	0.619808	−	0.450317i	−0.233046	−	0.972466i	$-0.574869\pi$
$653$	15.8385	−	11.5073i	0.619808	−	0.450317i	0.852855	+	0.522149i	$0.174869\pi$
$654$	1.40198	−	4.31487i	0.0548219	−	0.168725i
$655$	−1.26617	+	3.89688i	−0.0494735	+	0.152264i
$656$	−3.69363	+	2.68358i	−0.144212	+	0.104776i
$657$	8.36680	+	6.07883i	0.326420	+	0.237158i
$658$	−1.28619	−	3.95849i	−0.0501409	−	0.154318i
$659$	9.76928			0.380557			0.190279	−	0.981730i	$-0.439061\pi$
$659$	9.76928			0.380557			0.190279	+	0.981730i	$0.439061\pi$
$660$	−2.66166	−	4.05723i	−0.103605	−	0.157928i
$661$	7.70930			0.299857			0.149929	−	0.988697i	$-0.452096\pi$
$661$	7.70930			0.299857			0.149929	+	0.988697i	$0.452096\pi$
$662$	1.17314	+	3.61056i	0.0455954	+	0.140328i
$663$	−1.91761	−	1.39323i	−0.0744738	−	0.0541084i
$664$	2.32943	−	1.69243i	0.0903995	−	0.0656791i
$665$	1.81918	−	5.59885i	0.0705447	−	0.217114i
$666$	1.84086	−	5.66559i	0.0713319	−	0.219537i
$667$	−6.22416	+	4.52212i	−0.241001	+	0.175097i
$668$	21.4039	+	15.5508i	0.828142	+	0.601680i
$669$	8.03339	+	24.7242i	0.310589	+	0.955894i
$670$	3.46603			0.133905
$671$	3.09907	+	4.72400i	0.119638	+	0.182368i
$672$	15.3232			0.591106
$673$	−8.99157	−	27.6732i	−0.346599	−	1.06672i	−0.960722	−	0.277513i	$-0.910490\pi$
$673$	−8.99157	−	27.6732i	−0.346599	−	1.06672i	0.614123	−	0.789211i	$-0.289510\pi$
$674$	−13.1811	−	9.57666i	−0.507719	−	0.368879i
$675$	−3.44532	+	2.50317i	−0.132610	+	0.0963470i
$676$	−0.525083	+	1.61604i	−0.0201955	+	0.0621553i
$677$	11.8305	−	36.4106i	0.454683	−	1.39937i	−0.416823	−	0.908988i	$-0.636857\pi$
$677$	11.8305	−	36.4106i	0.454683	−	1.39937i	0.871506	−	0.490384i	$-0.163143\pi$
$678$	1.45792	−	1.05924i	0.0559913	−	0.0406800i
$679$	−7.93831	−	5.76752i	−0.304645	−	0.221337i
$680$	1.27951	+	3.93791i	0.0490668	+	0.151012i
$681$	26.7467			1.02494
$682$	−0.0894216	+	1.87255i	−0.00342413	+	0.0717035i
$683$	20.9870			0.803046			0.401523	−	0.915849i	$-0.368481\pi$
$683$	20.9870			0.803046			0.401523	+	0.915849i	$0.368481\pi$
$684$	−1.24438	−	3.82982i	−0.0475801	−	0.146437i
$685$	−14.6077	−	10.6131i	−0.558130	−	0.405505i
$686$	−7.26651	+	5.27943i	−0.277437	+	0.201570i
$687$	0.755999	−	2.32673i	0.0288432	−	0.0887702i
$688$	1.18021	−	3.63231i	0.0449950	−	0.138480i
$689$	−6.15074	+	4.46878i	−0.234325	+	0.170247i
$690$	−0.693120	−	0.503581i	−0.0263866	−	0.0191710i
$691$	0.814167	+	2.50575i	0.0309724	+	0.0953232i	0.965348	−	0.260967i	$-0.0840414\pi$
$691$	0.814167	+	2.50575i	0.0309724	+	0.0953232i	−0.934375	+	0.356290i	$0.884041\pi$
$692$	−2.59346			−0.0985887
$693$	−9.23100	+	2.51942i	−0.350657	+	0.0957050i
$694$	−12.4376			−0.472125
$695$	3.24788	+	9.99595i	0.123199	+	0.379168i
$696$	−6.96023	−	5.05690i	−0.263827	−	0.191681i
$697$	−3.83033	+	2.78290i	−0.145084	+	0.105410i
$698$	−0.773472	+	2.38050i	−0.0292763	+	0.0901033i
$699$	−5.71402	+	17.5859i	−0.216124	+	0.665162i
$700$	16.8900	−	12.2713i	0.638380	−	0.463810i
$701$	13.6947	+	9.94975i	0.517240	+	0.375797i	0.815563	−	0.578668i	$-0.196427\pi$
$701$	13.6947	+	9.94975i	0.517240	+	0.375797i	−0.298323	+	0.954465i	$0.596427\pi$
$702$	0.169480	+	0.521606i	0.00639661	+	0.0196868i
$703$	25.7412			0.970847
$704$	5.14424	+	1.94734i	0.193881	+	0.0733930i
$705$	2.26488			0.0853004
$706$	1.66250	+	5.11666i	0.0625692	+	0.192568i
$707$	−28.0734	−	20.3965i	−1.05581	−	0.767089i
$708$	−7.26193	+	5.27610i	−0.272920	+	0.198288i
$709$	12.8151	−	39.4409i	0.481283	−	1.48124i	−0.356011	−	0.934482i	$-0.615863\pi$
$709$	12.8151	−	39.4409i	0.481283	−	1.48124i	0.837293	−	0.546754i	$-0.184137\pi$
$710$	0.618163	−	1.90251i	0.0231992	−	0.0713999i
$711$	4.45887	−	3.23956i	0.167221	−	0.121493i
$712$	9.87392	+	7.17382i	0.370041	+	0.268850i
$713$	−0.577801	−	1.77829i	−0.0216388	−	0.0665975i
$714$	3.75053			0.140360
$715$	−1.78681	+	2.22760i	−0.0668231	+	0.0833074i
$716$	28.6760			1.07167
$717$	−6.46186	−	19.8876i	−0.241323	−	0.742715i
$718$	−0.0320468	−	0.0232834i	−0.00119598	−	0.000868928i
$719$	21.0968	−	15.3277i	0.786777	−	0.571627i	−0.120228	−	0.992746i	$-0.538363\pi$
$719$	21.0968	−	15.3277i	0.786777	−	0.571627i	0.907005	+	0.421119i	$0.138363\pi$
$720$	−0.608155	+	1.87171i	−0.0226646	+	0.0697545i
$721$	−8.21874	+	25.2947i	−0.306082	+	0.942023i
$722$	5.93840	−	4.31450i	0.221004	−	0.160569i
$723$	18.9076	+	13.7372i	0.703180	+	0.510891i
$724$	12.6210	+	38.8436i	0.469058	+	1.44361i
$725$	−18.0590			−0.670694
$726$	6.00549	+	0.574883i	0.222884	+	0.0213359i
$727$	−48.9788			−1.81652			−0.908261	−	0.418403i	$-0.862590\pi$
$727$	−48.9788			−1.81652			−0.908261	+	0.418403i	$0.862590\pi$
$728$	−1.80876	−	5.56679i	−0.0670371	−	0.206319i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−3.95101	+	2.87058i	−0.146233	+	0.106245i
$731$	1.22389	−	3.76674i	0.0452671	−	0.139318i
$732$	0.894470	−	2.75289i	0.0330606	−	0.101750i
$733$	−41.5744	+	30.2056i	−1.53559	+	1.11567i	−0.582559	+	0.812789i	$0.697948\pi$
$733$	−41.5744	+	30.2056i	−1.53559	+	1.11567i	−0.953028	+	0.302881i	$0.902052\pi$
$734$	6.47525	+	4.70455i	0.239006	+	0.173648i
$735$	0.352152	+	1.08381i	0.0129893	+	0.0399770i
$736$	9.63602			0.355188
$737$	15.2318	−	18.9892i	0.561070	−	0.699478i
$738$	1.09550			0.0403259
$739$	−0.611781	−	1.88287i	−0.0225047	−	0.0692624i	0.939173	−	0.343443i	$-0.111593\pi$
$739$	−0.611781	−	1.88287i	−0.0225047	−	0.0692624i	−0.961678	+	0.274181i	$0.911593\pi$
$740$	−12.8564	−	9.34070i	−0.472610	−	0.343371i
$741$	−1.91727	+	1.39298i	−0.0704327	+	0.0511724i
$742$	3.71743	−	11.4411i	0.136471	−	0.420015i
$743$	−6.53858	+	20.1237i	−0.239877	+	0.738267i	0.756560	+	0.653925i	$0.226879\pi$
$743$	−6.53858	+	20.1237i	−0.239877	+	0.738267i	−0.996437	+	0.0843418i	$0.973121\pi$
$744$	1.69160	−	1.22902i	0.0620169	−	0.0450579i
$745$	−4.11170	−	2.98733i	−0.150641	−	0.109447i
$746$	−2.04943	−	6.30748i	−0.0750348	−	0.230933i
$747$	1.41921			0.0519263
$748$	12.4929	+	4.72917i	0.456787	+	0.172916i
$749$	−43.0612			−1.57342
$750$	−1.35107	−	4.15818i	−0.0493342	−	0.151835i
$751$	6.84228	+	4.97121i	0.249678	+	0.181402i	0.705584	−	0.708626i	$-0.250685\pi$
$751$	6.84228	+	4.97121i	0.249678	+	0.181402i	−0.455906	+	0.890028i	$0.650685\pi$
$752$	−4.86418	+	3.53403i	−0.177378	+	0.128873i
$753$	8.11719	−	24.9821i	0.295807	−	0.910400i
$754$	−0.718688	+	2.21189i	−0.0261731	+	0.0805524i
$755$	2.34153	−	1.70122i	0.0852169	−	0.0619137i
$756$	3.96604	+	2.88150i	0.144243	+	0.104799i
$757$	9.41677	+	28.9818i	0.342258	+	1.05336i	0.963035	+	0.269375i	$0.0868172\pi$
$757$	9.41677	+	28.9818i	0.342258	+	1.05336i	−0.620777	+	0.783987i	$0.713183\pi$
$758$	10.8840			0.395324
$759$	−5.80493	+	1.58434i	−0.210705	+	0.0575080i
$760$	4.13984			0.150168
$761$	−4.00923	−	12.3391i	−0.145334	−	0.447293i	0.851719	−	0.523998i	$-0.175560\pi$
$761$	−4.00923	−	12.3391i	−0.145334	−	0.447293i	−0.997054	+	0.0767048i	$0.975560\pi$
$762$	6.64044	+	4.82456i	0.240558	+	0.174776i
$763$	−19.3079	+	14.0280i	−0.698995	+	0.507849i
$764$	9.38474	−	28.8833i	0.339528	−	1.04496i
$765$	−0.630663	+	1.94098i	−0.0228017	+	0.0701764i
$766$	16.7054	−	12.1372i	0.603591	−	0.438535i
$767$	4.27373	+	3.10505i	0.154315	+	0.112117i
$768$	0.929471	+	2.86062i	0.0335394	+	0.103224i
$769$	−46.6018			−1.68050			−0.840252	−	0.542196i	$-0.817593\pi$
$769$	−46.6018			−1.68050			−0.840252	+	0.542196i	$0.817593\pi$
$770$	0.215533	−	4.51341i	0.00776728	−	0.162652i
$771$	−8.52291			−0.306945
$772$	8.42519	+	25.9301i	0.303229	+	0.933244i
$773$	16.4000	+	11.9153i	0.589866	+	0.428563i	0.842268	−	0.539060i	$-0.181220\pi$
$773$	16.4000	+	11.9153i	0.589866	+	0.428563i	−0.252401	+	0.967623i	$0.581220\pi$
$774$	−0.741397	+	0.538656i	−0.0266490	+	0.0193616i
$775$	1.35628	−	4.17419i	0.0487189	−	0.149941i
$776$	2.13228	−	6.56247i	0.0765443	−	0.235579i
$777$	−25.3521	+	18.4194i	−0.909502	+	0.660792i
$778$	14.5592	+	10.5779i	0.521974	+	0.379236i
$779$	1.46280	+	4.50203i	0.0524102	+	0.161302i
$780$	1.46305			0.0523855
$781$	−7.70665	−	11.7474i	−0.275765	−	0.420357i
$782$	2.35853			0.0843407
$783$	−1.31040	−	4.03300i	−0.0468299	−	0.144128i
$784$	−2.44744	−	1.77817i	−0.0874085	−	0.0635060i
$785$	−9.07399	+	6.59264i	−0.323865	+	0.235301i
$786$	−0.806522	+	2.48222i	−0.0287677	+	0.0885379i
$787$	14.0965	−	43.3847i	0.502487	−	1.54650i	−0.302466	−	0.953160i	$-0.597810\pi$
$787$	14.0965	−	43.3847i	0.502487	−	1.54650i	0.804954	−	0.593337i	$-0.202190\pi$
$788$	−27.7108	+	20.1331i	−0.987157	+	0.717211i
$789$	20.5834	+	14.9548i	0.732790	+	0.532403i
$790$	0.804263	+	2.47527i	0.0286144	+	0.0880661i
$791$	−9.47971			−0.337060
$792$	−3.69095	−	5.62622i	−0.131152	−	0.199919i
$793$	−1.70348			−0.0604925
$794$	−1.18229	−	3.63870i	−0.0419577	−	0.129133i
$795$	5.29591	+	3.84770i	0.187826	+	0.136464i
$796$	20.4947	−	14.8903i	0.726415	−	0.527772i
$797$	−5.38118	+	16.5616i	−0.190611	+	0.586641i	−1.00000		0.000632438i	$-0.999799\pi$
$797$	−5.38118	+	16.5616i	−0.190611	+	0.586641i	0.809389	+	0.587273i	$0.199799\pi$
$798$	1.15877	−	3.56634i	0.0410201	−	0.126247i
$799$	−5.04421	+	3.66483i	−0.178451	+	0.129652i
$800$	18.2989	+	13.2949i	0.646964	+	0.470047i
$801$	1.85896	+	5.72129i	0.0656831	+	0.202152i
$802$	−10.4381			−0.368583
$803$	−1.63611	+	34.2613i	−0.0577372	+	1.20905i
$804$	−12.4718			−0.439847
$805$	1.39268	+	4.28622i	0.0490855	+	0.151069i
$806$	−0.457286	−	0.332238i	−0.0161072	−	0.0117026i
$807$	15.9219	−	11.5680i	0.560478	−	0.407211i
$808$	7.54067	−	23.2078i	0.265280	−	0.816447i
$809$	−12.5402	+	38.5946i	−0.440889	+	1.35692i	0.446042	+	0.895012i	$0.352833\pi$
$809$	−12.5402	+	38.5946i	−0.440889	+	1.35692i	−0.886930	+	0.461903i	$0.847167\pi$
$810$	0.382038	−	0.277567i	0.0134234	−	0.00975271i
$811$	−10.4341	−	7.58083i	−0.366391	−	0.266199i	0.389322	−	0.921102i	$-0.372710\pi$
$811$	−10.4341	−	7.58083i	−0.366391	−	0.266199i	−0.755713	+	0.654903i	$0.772710\pi$
$812$	6.42397	+	19.7709i	0.225437	+	0.693824i
$813$	10.6537			0.373641
$814$	19.0605	−	5.20219i	0.668069	−	0.182337i
$815$	−11.2812			−0.395165
$816$	−1.67419	−	5.15262i	−0.0586083	−	0.180378i
$817$	−3.20362	−	2.32756i	−0.112080	−	0.0814311i
$818$	8.53261	−	6.19930i	0.298336	−	0.216753i
$819$	0.891530	−	2.74385i	0.0311526	−	0.0958778i
$820$	0.903060	−	2.77933i	0.0315362	−	0.0970586i
$821$	12.9638	−	9.41874i	0.452439	−	0.328716i	−0.338119	−	0.941103i	$-0.609791\pi$
$821$	12.9638	−	9.41874i	0.452439	−	0.328716i	0.790558	+	0.612387i	$0.209791\pi$
$822$	−9.30474	−	6.76029i	−0.324540	−	0.235792i
$823$	14.7850	+	45.5037i	0.515374	+	1.58616i	0.782600	+	0.622524i	$0.213893\pi$
$823$	14.7850	+	45.5037i	0.515374	+	1.58616i	−0.267226	+	0.963634i	$0.586107\pi$
$824$	−18.7031			−0.651553
$825$	−13.2096	−	5.00044i	−0.459898	−	0.174093i
$826$	−8.35871			−0.290837
$827$	13.7889	+	42.4379i	0.479488	+	1.47571i	0.839809	+	0.542882i	$0.182667\pi$
$827$	13.7889	+	42.4379i	0.479488	+	1.47571i	−0.360321	+	0.932828i	$0.617333\pi$
$828$	2.49405	+	1.81203i	0.0866742	+	0.0629725i
$829$	22.2096	−	16.1362i	0.771370	−	0.560433i	−0.131007	−	0.991382i	$-0.541821\pi$
$829$	22.2096	−	16.1362i	0.771370	−	0.560433i	0.902377	+	0.430948i	$0.141821\pi$
$830$	−0.207100	+	0.637387i	−0.00718853	+	0.0221240i
$831$	−3.32125	+	10.2217i	−0.115213	+	0.354588i
$832$	−1.34172	+	0.974817i	−0.0465158	+	0.0337957i
$833$	−2.53802	−	1.84398i	−0.0879371	−	0.0638901i
$834$	2.06882	+	6.36719i	0.0716375	+	0.220478i
$835$	−13.4061			−0.463937
$836$	8.35676	−	10.4183i	0.289025	−	0.360323i
$837$	1.03061			0.0356231
$838$	−1.34260	−	4.13209i	−0.0463792	−	0.142741i
$839$	−35.7959	−	26.0072i	−1.23581	−	0.897869i	−0.238498	−	0.971143i	$-0.576655\pi$
$839$	−35.7959	−	26.0072i	−1.23581	−	0.897869i	−0.997312	+	0.0732743i	$0.976655\pi$
$840$	−4.07726	+	2.96230i	−0.140679	+	0.102209i
$841$	−3.40468	+	10.4785i	−0.117403	+	0.361329i
$842$	2.35974	−	7.26254i	0.0813221	−	0.250284i
$843$	3.13952	−	2.28099i	0.108131	−	0.0785615i
$844$	−8.79681	−	6.39126i	−0.302799	−	0.219996i
$845$	−0.266070	−	0.818878i	−0.00915307	−	0.0281703i
$846$	1.44268			0.0496003
$847$	−23.7803	−	21.0154i	−0.817100	−	0.722097i
$848$	−17.3776			−0.596748
$849$	7.00269	+	21.5521i	0.240332	+	0.739664i
$850$	4.47887	+	3.25409i	0.153624	+	0.111614i
$851$	−15.9427	+	11.5831i	−0.546509	+	0.397062i
$852$	−2.22433	+	6.84579i	−0.0762043	+	0.234533i
$853$	4.46809	−	13.7514i	0.152985	−	0.470838i	−0.844966	−	0.534819i	$-0.820380\pi$
$853$	4.46809	−	13.7514i	0.152985	−	0.470838i	0.997951	+	0.0639810i	$0.0203797\pi$
$854$	2.18065	−	1.58433i	0.0746202	−	0.0542148i
$855$	1.65081	+	1.19938i	0.0564564	+	0.0410180i
$856$	−9.35748	−	28.7994i	−0.319832	−	0.984342i
$857$	−57.2894			−1.95697			−0.978483	−	0.206325i	$-0.933850\pi$
$857$	−57.2894			−1.95697			−0.978483	+	0.206325i	$0.933850\pi$
$858$	−1.13816	+	1.41893i	−0.0388561	+	0.0484414i
$859$	−6.09124			−0.207830			−0.103915	−	0.994586i	$-0.533137\pi$
$859$	−6.09124			−0.207830			−0.103915	+	0.994586i	$0.533137\pi$
$860$	0.755435	+	2.32499i	0.0257601	+	0.0792815i
$861$	−4.66217	−	3.38726i	−0.158886	−	0.115438i
$862$	5.92383	−	4.30392i	0.201767	−	0.146592i
$863$	1.91899	−	5.90605i	0.0653232	−	0.201044i	−0.913068	−	0.407808i	$-0.866293\pi$
$863$	1.91899	−	5.90605i	0.0653232	−	0.201044i	0.978391	+	0.206764i	$0.0662932\pi$
$864$	−1.64126	+	5.05129i	−0.0558369	+	0.171848i
$865$	1.06318	−	0.772443i	0.0361491	−	0.0262638i
$866$	−11.7487	−	8.53595i	−0.399238	−	0.290063i
$867$	3.51714	+	10.8246i	0.119448	+	0.367624i
$868$	−5.05235			−0.171488
$869$	17.0956	+	6.47148i	0.579928	+	0.219530i
$870$	2.00249			0.0678908
$871$	2.26812	+	6.98056i	0.0768523	+	0.236527i
$872$	−13.5777	−	9.86479i	−0.459800	−	0.334064i
$873$	2.75153	−	1.99910i	0.0931252	−	0.0676594i
$874$	0.728696	−	2.24270i	0.0246485	−	0.0758603i
$875$	−7.10717	+	21.8736i	−0.240266	+	0.739463i
$876$	14.2169	−	10.3292i	0.480344	−	0.348991i
$877$	−31.7252	−	23.0497i	−1.07128	−	0.778333i	−0.0951408	−	0.995464i	$-0.530330\pi$
$877$	−31.7252	−	23.0497i	−1.07128	−	0.778333i	−0.976142	+	0.217131i	$0.930330\pi$
$878$	5.61536	+	17.2823i	0.189509	+	0.583249i
$879$	−25.9748			−0.876109
$880$	−6.29690	+	1.71862i	−0.212269	+	0.0579346i
$881$	−28.7305			−0.967956			−0.483978	−	0.875080i	$-0.660808\pi$
$881$	−28.7305			−0.967956			−0.483978	+	0.875080i	$0.660808\pi$
$882$	0.224312	+	0.690363i	0.00755299	+	0.0232457i
$883$	−3.70137	−	2.68920i	−0.124561	−	0.0904988i	0.523760	−	0.851866i	$-0.324529\pi$
$883$	−3.70137	−	2.68920i	−0.124561	−	0.0904988i	−0.648321	+	0.761367i	$0.724529\pi$
$884$	−3.25841	+	2.36737i	−0.109592	+	0.0796234i
$885$	1.40554	−	4.32582i	0.0472468	−	0.145411i
$886$	0.464047	−	1.42819i	0.0155900	−	0.0479810i
$887$	−35.1359	+	25.5277i	−1.17975	+	0.857137i	−0.992143	−	0.125108i	$-0.960072\pi$
$887$	−35.1359	+	25.5277i	−1.17975	+	0.857137i	−0.187605	+	0.982245i	$0.560072\pi$
$888$	−17.8281	−	12.9529i	−0.598271	−	0.434670i
$889$	−13.3426	−	41.0642i	−0.447495	−	1.37725i
$890$	−2.84077			−0.0952229
$891$	0.158202	−	3.31285i	0.00529996	−	0.110985i
$892$	44.1735			1.47904
$893$	1.92638	+	5.92878i	0.0644637	+	0.198399i
$894$	−2.61906	−	1.90286i	−0.0875944	−	0.0636411i
$895$	−11.7556	+	8.54093i	−0.392946	+	0.285492i
$896$	10.2812	−	31.6422i	0.343470	−	1.05709i
$897$	0.560640	−	1.72547i	0.0187192	−	0.0576119i
$898$	−11.9206	+	8.66079i	−0.397794	+	0.289014i
$899$	3.53569	+	2.56883i	0.117922	+	0.0856751i
$900$	2.23614	+	6.88214i	0.0745381	+	0.229405i
$901$	−18.0207			−0.600358
$902$	1.99300	+	3.03798i	0.0663595	+	0.101154i
$903$	4.82071			0.160423
$904$	−2.06000	−	6.34004i	−0.0685147	−	0.210867i
$905$	−16.7432	−	12.1646i	−0.556562	−	0.404366i
$906$	1.49150	−	1.08364i	0.0495517	−	0.0360014i
$907$	8.94713	−	27.5364i	0.297085	−	0.914332i	−0.685429	−	0.728140i	$-0.740385\pi$
$907$	8.94713	−	27.5364i	0.297085	−	0.914332i	0.982513	−	0.186193i	$-0.0596149\pi$
$908$	14.0442	−	43.2238i	0.466075	−	1.43443i
$909$	9.73062	−	7.06971i	0.322744	−	0.234488i
$910$	1.10220	+	0.800795i	0.0365376	+	0.0265461i
$911$	−17.4709	−	53.7699i	−0.578837	−	1.78148i	−0.622726	−	0.782440i	$-0.713975\pi$
$911$	−17.4709	−	53.7699i	−0.578837	−	1.78148i	0.0438890	−	0.999036i	$-0.486025\pi$
$912$	−5.41683			−0.179369
$913$	2.58191	+	3.93568i	0.0854489	+	0.130252i
$914$	2.65199			0.0877201
$915$	0.453245	+	1.39494i	0.0149838	+	0.0461154i
$916$	−3.36312	−	2.44345i	−0.111121	−	0.0807338i
$917$	11.1073	−	8.06994i	0.366796	−	0.266493i
$918$	−0.401718	+	1.23636i	−0.0132587	+	0.0408060i
$919$	7.67772	−	23.6296i	0.253265	−	0.779468i	−0.740902	−	0.671613i	$-0.765602\pi$
$919$	7.67772	−	23.6296i	0.253265	−	0.779468i	0.994167	−	0.107855i	$-0.0343982\pi$
$920$	−2.56399	+	1.86285i	−0.0845323	+	0.0614163i
$921$	19.2496	+	13.9856i	0.634295	+	0.460842i
$922$	−0.422715	−	1.30098i	−0.0139214	−	0.0428456i
$923$	4.23615			0.139435
$924$	−0.775552	+	16.2406i	−0.0255138	+	0.534275i
$925$	−46.2566			−1.52091
$926$	6.50139	+	20.0092i	0.213649	+	0.657544i
$927$	−7.45807	−	5.41861i	−0.244955	−	0.177970i
$928$	−18.2211	+	13.2384i	−0.598138	+	0.434572i
$929$	−7.01059	+	21.5764i	−0.230010	+	0.707898i	0.767734	+	0.640769i	$0.221384\pi$
$929$	−7.01059	+	21.5764i	−0.230010	+	0.707898i	−0.997744	+	0.0671299i	$0.978616\pi$
$930$	−0.150392	+	0.462860i	−0.00493156	+	0.0151778i
$931$	−2.53757	+	1.84365i	−0.0831655	+	0.0604233i
$932$	25.4192	+	18.4682i	0.832635	+	0.604945i
$933$	0.0994089	+	0.305949i	0.00325450	+	0.0100163i
$934$	0.905562			0.0296309
$935$	−6.52996	+	1.78223i	−0.213552	+	0.0582850i
$936$	2.02882			0.0663142
$937$	8.96952	+	27.6054i	0.293022	+	0.901828i	0.983879	+	0.178836i	$0.0572333\pi$
$937$	8.96952	+	27.6054i	0.293022	+	0.901828i	−0.690857	+	0.722991i	$0.742767\pi$
$938$	−9.39575	−	6.82641i	−0.306782	−	0.222890i
$939$	−24.7480	+	17.9805i	−0.807621	+	0.586771i
$940$	1.18925	−	3.66014i	0.0387891	−	0.119381i
$941$	17.6921	−	54.4508i	0.576747	−	1.77504i	−0.0534048	−	0.998573i	$-0.517007\pi$
$941$	17.6921	−	54.4508i	0.576747	−	1.77504i	0.630152	−	0.776472i	$-0.282993\pi$
$942$	−5.77992	+	4.19936i	−0.188320	+	0.136823i
$943$	−2.93181	−	2.13008i	−0.0954728	−	0.0693651i
$944$	3.73122	+	11.4835i	0.121441	+	0.373757i
$945$	−2.48409			−0.0808073
$946$	−2.84256	−	1.07604i	−0.0924196	−	0.0349852i
$947$	18.8001			0.610922			0.305461	−	0.952205i	$-0.401190\pi$
$947$	18.8001			0.610922			0.305461	+	0.952205i	$0.401190\pi$
$948$	−2.89398	−	8.90674i	−0.0939919	−	0.289277i
$949$	−8.36680	−	6.07883i	−0.271598	−	0.197327i
$950$	4.47808	−	3.25351i	0.145288	−	0.105558i
$951$	7.91864	−	24.3711i	0.256780	−	0.790287i
$952$	4.28729	−	13.1949i	0.138952	−	0.427650i
$953$	−36.3494	+	26.4094i	−1.17747	+	0.855484i	−0.991884	−	0.127143i	$-0.959419\pi$
$953$	−36.3494	+	26.4094i	−1.17747	+	0.855484i	−0.185589	+	0.982628i	$0.559419\pi$
$954$	3.37337	+	2.45090i	0.109217	+	0.0793507i
$955$	4.75543	+	14.6357i	0.153882	+	0.473600i
$956$	−35.5321			−1.14919
$957$	8.80011	−	10.9710i	0.284467	−	0.354641i
$958$	−9.42337			−0.304455
$959$	18.6959	+	57.5401i	0.603723	+	1.85807i
$960$	1.15525	+	0.839336i	0.0372854	+	0.0270894i
$961$	24.2202	−	17.5970i	0.781298	−	0.567646i
$962$	−1.84086	+	5.66559i	−0.0593518	+	0.182666i
$963$	4.61227	−	14.1951i	0.148628	−	0.457431i
$964$	32.1278	−	23.3422i	1.03477	−	0.751803i
$965$	−11.1769	−	8.12051i	−0.359798	−	0.261409i
$966$	0.887103	+	2.73022i	0.0285421	+	0.0878435i
$967$	2.82220			0.0907560			0.0453780	−	0.998970i	$-0.485551\pi$
$967$	2.82220			0.0907560			0.0453780	+	0.998970i	$0.485551\pi$
$968$	8.88750	−	20.4711i	0.285655	−	0.657965i
$969$	−5.61731			−0.180454
$970$	0.496304	+	1.52747i	0.0159354	+	0.0490440i
$971$	−39.0446	−	28.3676i	−1.25300	−	0.910359i	−0.254609	−	0.967044i	$-0.581947\pi$
$971$	−39.0446	−	28.3676i	−1.25300	−	0.910359i	−0.998392	+	0.0566855i	$0.981947\pi$
$972$	−1.37468	+	0.998767i	−0.0440930	+	0.0320355i
$973$	10.8828	−	33.4939i	0.348887	−	1.07376i
$974$	3.83417	−	11.8004i	0.122855	−	0.378108i
$975$	3.44532	−	2.50317i	0.110338	−	0.0801656i
$976$	−3.15003	−	2.28863i	−0.100830	−	0.0732573i
$977$	−11.0552	−	34.0243i	−0.353687	−	1.08854i	−0.956767	−	0.290855i	$-0.906060\pi$
$977$	−11.0552	−	34.0243i	−0.353687	−	1.08854i	0.603081	−	0.797680i	$-0.293940\pi$
$978$	−7.18589			−0.229779
$979$	−12.4840	+	15.5636i	−0.398991	+	0.497416i
$980$	1.93639			0.0618557
$981$	−2.55627	−	7.86740i	−0.0816155	−	0.251187i
$982$	−7.69687	−	5.59210i	−0.245617	−	0.178451i
$983$	29.5985	−	21.5046i	0.944047	−	0.685890i	−0.00534449	−	0.999986i	$-0.501701\pi$
$983$	29.5985	−	21.5046i	0.944047	−	0.685890i	0.949391	+	0.314095i	$0.101701\pi$
$984$	1.25228	−	3.85414i	0.0399214	−	0.122865i
$985$	5.36341	−	16.5069i	0.170893	−	0.525953i
$986$	−4.45983	+	3.24025i	−0.142030	+	0.103191i
$987$	−6.13966	−	4.46072i	−0.195428	−	0.141986i
$988$	1.24438	+	3.82982i	0.0395891	+	0.121843i
$989$	3.03151			0.0963963
$990$	1.46476	+	0.554480i	0.0465530	+	0.0176225i
$991$	34.4494			1.09432			0.547161	−	0.837027i	$-0.315709\pi$
$991$	34.4494			1.09432			0.547161	+	0.837027i	$0.315709\pi$
$992$	−1.69150	−	5.20591i	−0.0537053	−	0.165288i
$993$	5.60001	+	4.06865i	0.177711	+	0.129115i
$994$	−5.42275	+	3.93986i	−0.171999	+	0.124965i
$995$	−3.96674	+	12.2084i	−0.125754	+	0.387031i
$996$	0.745205	−	2.29351i	0.0236127	−	0.0726725i
$997$	−32.8352	+	23.8562i	−1.03990	+	0.755532i	−0.970266	−	0.242041i	$-0.922183\pi$
$997$	−32.8352	+	23.8562i	−1.03990	+	0.755532i	−0.0696345	+	0.997573i	$0.522183\pi$
$998$	−10.0107	−	7.27321i	−0.316884	−	0.230230i
$999$	−3.35649	−	10.3302i	−0.106195	−	0.326833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.313.3	yes	20
11.3	even	5		4719.2.a.bn.1.6		10
11.8	odd	10		4719.2.a.bi.1.5		10
11.9	even	5	inner	429.2.n.b.196.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.196.3	✓	20	11.9	even	5	inner
429.2.n.b.313.3	yes	20	1.1	even	1	trivial
4719.2.a.bi.1.5		10	11.8	odd	10
4719.2.a.bn.1.6		10	11.3	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.169480 + 0.521606i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.37468 - 0.998767i) q^{4} +(-0.266070 + 0.818878i) q^{5} +(-0.169480 + 0.521606i) q^{6} +(2.33406 - 1.69579i) q^{7} +(1.64135 + 1.19251i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.169480 + 0.521606i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.37468 - 0.998767i) q^{4} +(-0.266070 + 0.818878i) q^{5} +(-0.169480 + 0.521606i) q^{6} +(2.33406 - 1.69579i) q^{7} +(1.64135 + 1.19251i) q^{8} +(0.309017 + 0.951057i) q^{9} -0.472225 q^{10} +(-2.07523 + 2.58716i) q^{11} +1.69920 q^{12} +(-0.309017 - 0.951057i) q^{13} +(1.28011 + 0.930055i) q^{14} +(-0.696579 + 0.506094i) q^{15} +(0.706320 - 2.17383i) q^{16} +(0.732462 - 2.25429i) q^{17} +(-0.443705 + 0.322370i) q^{18} +(-1.91727 - 1.39298i) q^{19} +(0.452106 + 1.39144i) q^{20} +2.88505 q^{21} +(-1.70119 - 0.643981i) q^{22} +1.81427 q^{23} +(0.626941 + 1.92953i) q^{24} +(3.44532 + 2.50317i) q^{25} +(0.443705 - 0.322370i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.51489 - 4.66236i) q^{28} +(-3.43067 + 2.49253i) q^{29} +(-0.382038 - 0.277567i) q^{30} +(-0.318476 - 0.980168i) q^{31} +5.31124 q^{32} +(-3.19959 + 0.873268i) q^{33} +1.29999 q^{34} +(0.767625 + 2.36251i) q^{35} +(1.37468 + 0.998767i) q^{36} +(-8.78740 + 6.38442i) q^{37} +(0.401647 - 1.23614i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-1.41324 + 1.02678i) q^{40} +(-1.61597 - 1.17407i) q^{41} +(0.488959 + 1.50486i) q^{42} +1.67092 q^{43} +(-0.268817 + 5.62921i) q^{44} -0.861019 q^{45} +(0.307483 + 0.946334i) q^{46} +(-2.12809 - 1.54615i) q^{47} +(1.84917 - 1.34350i) q^{48} +(0.408994 - 1.25875i) q^{49} +(-0.721756 + 2.22134i) q^{50} +(1.91761 - 1.39323i) q^{51} +(-1.37468 - 0.998767i) q^{52} +(-2.34937 - 7.23063i) q^{53} -0.548449 q^{54} +(-1.56641 - 2.38773i) q^{55} +5.85327 q^{56} +(-0.732333 - 2.25389i) q^{57} +(-1.88155 - 1.36703i) q^{58} +(-4.27373 + 3.10505i) q^{59} +(-0.452106 + 1.39144i) q^{60} +(0.526405 - 1.62011i) q^{61} +(0.457286 - 0.332238i) q^{62} +(2.33406 + 1.69579i) q^{63} +(-0.512491 - 1.57729i) q^{64} +0.861019 q^{65} +(-0.997769 - 1.52093i) q^{66} -7.33979 q^{67} +(-1.24460 - 3.83049i) q^{68} +(1.46777 + 1.06640i) q^{69} +(-1.10220 + 0.800795i) q^{70} +(-1.30904 + 4.02882i) q^{71} +(-0.626941 + 1.92953i) q^{72} +(8.36680 - 6.07883i) q^{73} +(-4.81944 - 3.50153i) q^{74} +(1.31599 + 4.05021i) q^{75} -4.02691 q^{76} +(-0.456421 + 9.55775i) q^{77} +0.548449 q^{78} +(-1.70314 - 5.24171i) q^{79} +(1.59217 + 1.15678i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.338528 - 1.04188i) q^{82} +(0.438561 - 1.34975i) q^{83} +(3.96604 - 2.88150i) q^{84} +(1.65110 + 1.19959i) q^{85} +(0.283188 + 0.871564i) q^{86} -4.24054 q^{87} +(-6.49142 + 1.77171i) q^{88} +6.01572 q^{89} +(-0.145926 - 0.449113i) q^{90} +(-2.33406 - 1.69579i) q^{91} +(2.49405 - 1.81203i) q^{92} +(0.318476 - 0.980168i) q^{93} +(0.445812 - 1.37207i) q^{94} +(1.65081 - 1.19938i) q^{95} +(4.29688 + 3.12187i) q^{96} +(-1.05099 - 3.23462i) q^{97} +0.725890 q^{98} +(-3.10182 - 1.17419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

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