LMFDB - Embedded newform 671.2.i.b.34.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(34,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("671.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.i (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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			34.18
Character	$\chi$	$=$	671.34
Dual form			671.2.i.b.375.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.729261 - 0.529839i) q^{2} +(-0.384786 + 0.279563i) q^{3} +(-0.366942 + 1.12933i) q^{4} +(0.465877 - 1.43382i) q^{5} +(-0.132486 + 0.407749i) q^{6} +(2.67691 + 1.94489i) q^{7} +(0.887873 + 2.73259i) q^{8} +(-0.857146 + 2.63803i) q^{9} +O(q^{10})$	\(q+(0.729261 - 0.529839i) q^{2} +(-0.384786 + 0.279563i) q^{3} +(-0.366942 + 1.12933i) q^{4} +(0.465877 - 1.43382i) q^{5} +(-0.132486 + 0.407749i) q^{6} +(2.67691 + 1.94489i) q^{7} +(0.887873 + 2.73259i) q^{8} +(-0.857146 + 2.63803i) q^{9} +(-0.419949 - 1.29247i) q^{10} -1.00000 q^{11} +(-0.174525 - 0.537134i) q^{12} -5.28661 q^{13} +2.98265 q^{14} +(0.221581 + 0.681957i) q^{15} +(0.173997 + 0.126416i) q^{16} +(-0.665826 + 2.04920i) q^{17} +(0.772646 + 2.37796i) q^{18} +(2.23070 - 1.62070i) q^{19} +(1.44831 + 1.05226i) q^{20} -1.57376 q^{21} +(-0.729261 + 0.529839i) q^{22} +(-1.35929 + 4.18347i) q^{23} +(-1.10557 - 0.803246i) q^{24} +(2.20628 + 1.60296i) q^{25} +(-3.85532 + 2.80106i) q^{26} +(-0.848603 - 2.61173i) q^{27} +(-3.17870 + 2.30946i) q^{28} +5.76381 q^{29} +(0.522918 + 0.379922i) q^{30} +(-2.52968 - 1.83792i) q^{31} -5.55257 q^{32} +(0.384786 - 0.279563i) q^{33} +(0.600186 + 1.84718i) q^{34} +(4.03574 - 2.93214i) q^{35} +(-2.66468 - 1.93600i) q^{36} +(2.31425 + 1.68140i) q^{37} +(0.768053 - 2.36383i) q^{38} +(2.03421 - 1.47794i) q^{39} +4.33169 q^{40} +(4.04625 + 2.93977i) q^{41} +(-1.14768 + 0.833839i) q^{42} +(2.13928 + 6.58401i) q^{43} +(0.366942 - 1.12933i) q^{44} +(3.38314 + 2.45799i) q^{45} +(1.22529 + 3.77105i) q^{46} +1.75317 q^{47} -0.102293 q^{48} +(1.22014 + 3.75522i) q^{49} +2.45826 q^{50} +(-0.316681 - 0.974644i) q^{51} +(1.93988 - 5.97033i) q^{52} +(1.73490 + 5.33946i) q^{53} +(-2.00265 - 1.45501i) q^{54} +(-0.465877 + 1.43382i) q^{55} +(-2.93784 + 9.04174i) q^{56} +(-0.405254 + 1.24724i) q^{57} +(4.20333 - 3.05390i) q^{58} +(1.65351 - 1.20134i) q^{59} -0.851461 q^{60} +(6.88003 - 3.69665i) q^{61} -2.81860 q^{62} +(-7.42518 + 5.39471i) q^{63} +(-4.39727 + 3.19480i) q^{64} +(-2.46291 + 7.58007i) q^{65} +(0.132486 - 0.407749i) q^{66} +(4.03288 - 12.4119i) q^{67} +(-2.06990 - 1.50387i) q^{68} +(-0.646509 - 1.98975i) q^{69} +(1.38955 - 4.27659i) q^{70} +(1.10013 + 3.38585i) q^{71} -7.96969 q^{72} +(-2.55560 - 7.86532i) q^{73} +2.57857 q^{74} -1.29707 q^{75} +(1.01177 + 3.11390i) q^{76} +(-2.67691 - 1.94489i) q^{77} +(0.700401 - 2.15561i) q^{78} +(-4.00355 - 12.3217i) q^{79} +(0.262320 - 0.190586i) q^{80} +(-5.67544 - 4.12345i) q^{81} +4.50838 q^{82} +(-2.48801 + 1.80764i) q^{83} +(0.577477 - 1.77729i) q^{84} +(2.62800 + 1.90935i) q^{85} +(5.04856 + 3.66800i) q^{86} +(-2.21783 + 1.61135i) q^{87} +(-0.887873 - 2.73259i) q^{88} +(-2.82647 + 2.05355i) q^{89} +3.76953 q^{90} +(-14.1518 - 10.2819i) q^{91} +(-4.22574 - 3.07018i) q^{92} +1.48720 q^{93} +(1.27852 - 0.928897i) q^{94} +(-1.28456 - 3.95347i) q^{95} +(2.13655 - 1.55229i) q^{96} +(-13.1541 - 9.55698i) q^{97} +(2.87947 + 2.09206i) q^{98} +(0.857146 - 2.63803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) $ 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.729261	−	0.529839i	0.515666	−	0.374653i	−0.299303	−	0.954158i	$-0.596754\pi$
$2$	0.729261	−	0.529839i	0.515666	−	0.374653i	0.814969	+	0.579505i	$0.196754\pi$
$3$	−0.384786	+	0.279563i	−0.222156	+	0.161406i	−0.693297	−	0.720652i	$-0.743842\pi$
$3$	−0.384786	+	0.279563i	−0.222156	+	0.161406i	0.471141	+	0.882058i	$0.343842\pi$
$4$	−0.366942	+	1.12933i	−0.183471	+	0.564665i
$5$	0.465877	−	1.43382i	0.208347	−	0.641225i	−0.791213	−	0.611541i	$-0.790550\pi$
$5$	0.465877	−	1.43382i	0.208347	−	0.641225i	0.999559	−	0.0296839i	$-0.00945006\pi$
$6$	−0.132486	+	0.407749i	−0.0540871	+	0.166463i
$7$	2.67691	+	1.94489i	1.01178	+	0.735100i	0.964581	−	0.263786i	$-0.0849712\pi$
$7$	2.67691	+	1.94489i	1.01178	+	0.735100i	0.0471970	+	0.998886i	$0.484971\pi$
$8$	0.887873	+	2.73259i	0.313911	+	0.966118i
$9$	−0.857146	+	2.63803i	−0.285715	+	0.879342i
$10$	−0.419949	−	1.29247i	−0.132800	−	0.408715i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−0.174525	−	0.537134i	−0.0503811	−	0.155057i
$13$	−5.28661			−1.46624			−0.733121	−	0.680098i	$-0.761937\pi$
$13$	−5.28661			−1.46624			−0.733121	+	0.680098i	$0.761937\pi$
$14$	2.98265			0.797147
$15$	0.221581	+	0.681957i	0.0572120	+	0.176080i
$16$	0.173997	+	0.126416i	0.0434992	+	0.0316041i
$17$	−0.665826	+	2.04920i	−0.161486	+	0.497004i	−0.998760	−	0.0497797i	$-0.984148\pi$
$17$	−0.665826	+	2.04920i	−0.161486	+	0.497004i	0.837274	+	0.546784i	$0.184148\pi$
$18$	0.772646	+	2.37796i	0.182114	+	0.560491i
$19$	2.23070	−	1.62070i	0.511758	−	0.371814i	−0.301732	−	0.953393i	$-0.597565\pi$
$19$	2.23070	−	1.62070i	0.511758	−	0.371814i	0.813490	+	0.581579i	$0.197565\pi$
$20$	1.44831	+	1.05226i	0.323852	+	0.235292i
$21$	−1.57376			−0.343422
$22$	−0.729261	+	0.529839i	−0.155479	+	0.112962i
$23$	−1.35929	+	4.18347i	−0.283432	+	0.872314i	0.703432	+	0.710762i	$0.251650\pi$
$23$	−1.35929	+	4.18347i	−0.283432	+	0.872314i	−0.986864	+	0.161552i	$0.948350\pi$
$24$	−1.10557	−	0.803246i	−0.225674	−	0.163962i
$25$	2.20628	+	1.60296i	0.441256	+	0.320591i
$26$	−3.85532	+	2.80106i	−0.756091	+	0.549332i
$27$	−0.848603	−	2.61173i	−0.163314	−	0.502628i
$28$	−3.17870	+	2.30946i	−0.600717	+	0.436446i
$29$	5.76381			1.07031			0.535157	−	0.844753i	$-0.320253\pi$
$29$	5.76381			1.07031			0.535157	+	0.844753i	$0.320253\pi$
$30$	0.522918	+	0.379922i	0.0954714	+	0.0693640i
$31$	−2.52968	−	1.83792i	−0.454343	−	0.330100i	0.336965	−	0.941517i	$-0.390600\pi$
$31$	−2.52968	−	1.83792i	−0.454343	−	0.330100i	−0.791308	+	0.611418i	$0.790600\pi$
$32$	−5.55257			−0.981565
$33$	0.384786	−	0.279563i	0.0669826	−	0.0486657i
$34$	0.600186	+	1.84718i	0.102931	+	0.316789i
$35$	4.03574	−	2.93214i	0.682165	−	0.495622i
$36$	−2.66468	−	1.93600i	−0.444113	−	0.322667i
$37$	2.31425	+	1.68140i	0.380461	+	0.276421i	0.761535	−	0.648123i	$-0.224446\pi$
$37$	2.31425	+	1.68140i	0.380461	+	0.276421i	−0.381074	+	0.924544i	$0.624446\pi$
$38$	0.768053	−	2.36383i	0.124595	−	0.383463i
$39$	2.03421	−	1.47794i	0.325735	−	0.236660i
$40$	4.33169			0.684901
$41$	4.04625	+	2.93977i	0.631917	+	0.459115i	0.857064	−	0.515210i	$-0.172286\pi$
$41$	4.04625	+	2.93977i	0.631917	+	0.459115i	−0.225147	+	0.974325i	$0.572286\pi$
$42$	−1.14768	+	0.833839i	−0.177091	+	0.128664i
$43$	2.13928	+	6.58401i	0.326237	+	1.00405i	0.970879	+	0.239569i	$0.0770061\pi$
$43$	2.13928	+	6.58401i	0.326237	+	1.00405i	−0.644643	+	0.764484i	$0.722994\pi$
$44$	0.366942	−	1.12933i	0.0553185	−	0.170253i
$45$	3.38314	+	2.45799i	0.504328	+	0.366416i
$46$	1.22529	+	3.77105i	0.180659	+	0.556011i
$47$	1.75317			0.255726			0.127863	−	0.991792i	$-0.459188\pi$
$47$	1.75317			0.255726			0.127863	+	0.991792i	$0.459188\pi$
$48$	−0.102293			−0.0147647
$49$	1.22014	+	3.75522i	0.174306	+	0.536460i
$50$	2.45826			0.347651
$51$	−0.316681	−	0.974644i	−0.0443442	−	0.136477i
$52$	1.93988	−	5.97033i	0.269013	−	0.827936i
$53$	1.73490	+	5.33946i	0.238306	+	0.733432i	0.996666	+	0.0815949i	$0.0260014\pi$
$53$	1.73490	+	5.33946i	0.238306	+	0.733432i	−0.758359	+	0.651837i	$0.773999\pi$
$54$	−2.00265	−	1.45501i	−0.272526	−	0.198002i
$55$	−0.465877	+	1.43382i	−0.0628189	+	0.193337i
$56$	−2.93784	+	9.04174i	−0.392585	+	1.20825i
$57$	−0.405254	+	1.24724i	−0.0536772	+	0.165201i
$58$	4.20333	−	3.05390i	0.551924	−	0.400996i
$59$	1.65351	−	1.20134i	0.215269	−	0.156402i	−0.474926	−	0.880026i	$-0.657525\pi$
$59$	1.65351	−	1.20134i	0.215269	−	0.156402i	0.690194	+	0.723624i	$0.257525\pi$
$60$	−0.851461			−0.109923
$61$	6.88003	−	3.69665i	0.880898	−	0.473307i
$61$	6.88003	−	3.69665i	0.880898	−	0.473307i
$62$	−2.81860			−0.357962
$63$	−7.42518	+	5.39471i	−0.935485	+	0.679670i
$64$	−4.39727	+	3.19480i	−0.549659	+	0.399350i
$65$	−2.46291	+	7.58007i	−0.305487	+	0.940191i
$66$	0.132486	−	0.407749i	0.0163079	−	0.0501905i
$67$	4.03288	−	12.4119i	0.492695	−	1.51636i	−0.327823	−	0.944739i	$-0.606315\pi$
$67$	4.03288	−	12.4119i	0.492695	−	1.51636i	0.820518	−	0.571621i	$-0.193685\pi$
$68$	−2.06990	−	1.50387i	−0.251013	−	0.182371i
$69$	−0.646509	−	1.98975i	−0.0778305	−	0.239538i
$70$	1.38955	−	4.27659i	0.166083	−	0.511150i
$71$	1.10013	+	3.38585i	0.130561	+	0.401826i	0.994873	−	0.101130i	$-0.0322458\pi$
$71$	1.10013	+	3.38585i	0.130561	+	0.401826i	−0.864312	+	0.502956i	$0.832246\pi$
$72$	−7.96969			−0.939237
$73$	−2.55560	−	7.86532i	−0.299110	−	0.920566i	−0.981810	−	0.189867i	$-0.939194\pi$
$73$	−2.55560	−	7.86532i	−0.299110	−	0.920566i	0.682700	−	0.730699i	$-0.260806\pi$
$74$	2.57857			0.299753
$75$	−1.29707			−0.149773
$76$	1.01177	+	3.11390i	0.116058	+	0.357189i
$77$	−2.67691	−	1.94489i	−0.305063	−	0.221641i
$78$	0.700401	−	2.15561i	0.0793048	−	0.244075i
$79$	−4.00355	−	12.3217i	−0.450435	−	1.38630i	−0.876412	−	0.481563i	$-0.840069\pi$
$79$	−4.00355	−	12.3217i	−0.450435	−	1.38630i	0.425977	−	0.904734i	$-0.359931\pi$
$80$	0.262320	−	0.190586i	0.0293282	−	0.0213082i
$81$	−5.67544	−	4.12345i	−0.630605	−	0.458161i
$82$	4.50838			0.497867
$83$	−2.48801	+	1.80764i	−0.273094	+	0.198415i	−0.715900	−	0.698203i	$-0.753983\pi$
$83$	−2.48801	+	1.80764i	−0.273094	+	0.198415i	0.442805	+	0.896618i	$0.353983\pi$
$84$	0.577477	−	1.77729i	0.0630080	−	0.193919i
$85$	2.62800	+	1.90935i	0.285046	+	0.207098i
$86$	5.04856	+	3.66800i	0.544401	+	0.395530i
$87$	−2.21783	+	1.61135i	−0.237777	+	0.172755i
$88$	−0.887873	−	2.73259i	−0.0946476	−	0.291295i
$89$	−2.82647	+	2.05355i	−0.299605	+	0.217676i	−0.727423	−	0.686189i	$-0.759282\pi$
$89$	−2.82647	+	2.05355i	−0.299605	+	0.217676i	0.427818	+	0.903865i	$0.359282\pi$
$90$	3.76953			0.397343
$91$	−14.1518	−	10.2819i	−1.48351	−	1.07784i
$92$	−4.22574	−	3.07018i	−0.440564	−	0.320088i
$93$	1.48720			0.154215
$94$	1.27852	−	0.928897i	0.131869	−	0.0958084i
$95$	−1.28456	−	3.95347i	−0.131793	−	0.405618i
$96$	2.13655	−	1.55229i	0.218061	−	0.158430i
$97$	−13.1541	−	9.55698i	−1.33559	−	0.970365i	−0.999594	−	0.0285021i	$-0.990926\pi$
$97$	−13.1541	−	9.55698i	−1.33559	−	0.970365i	−0.335999	−	0.941862i	$-0.609074\pi$
$98$	2.87947	+	2.09206i	0.290870	+	0.211330i
$99$	0.857146	−	2.63803i	0.0861465	−	0.265132i
$100$	−2.61984	+	1.90343i	−0.261984	+	0.190343i
$101$	−8.89839			−0.885423			−0.442711	−	0.896664i	$-0.645983\pi$
$101$	−8.89839			−0.885423			−0.442711	+	0.896664i	$0.645983\pi$
$102$	−0.747348	−	0.542980i	−0.0739985	−	0.0537630i
$103$	8.51194	−	6.18429i	0.838707	−	0.609356i	−0.0833025	−	0.996524i	$-0.526547\pi$
$103$	8.51194	−	6.18429i	0.838707	−	0.609356i	0.922009	+	0.387168i	$0.126547\pi$
$104$	−4.69384	−	14.4462i	−0.460269	−	1.41656i
$105$	−0.733178	+	2.25649i	−0.0715509	+	0.220211i
$106$	4.09425	+	2.97465i	0.397669	+	0.288923i
$107$	5.50790	+	16.9516i	0.532468	+	1.63877i	0.749057	+	0.662506i	$0.230507\pi$
$107$	5.50790	+	16.9516i	0.532468	+	1.63877i	−0.216588	+	0.976263i	$0.569493\pi$
$108$	3.26089			0.313780
$109$	20.6408			1.97703			0.988513	−	0.151135i	$-0.0482929\pi$
$109$	20.6408			1.97703			0.988513	+	0.151135i	$0.0482929\pi$
$110$	0.419949	+	1.29247i	0.0400406	+	0.123232i
$111$	−1.36055			−0.129138
$112$	0.219909	+	0.676811i	0.0207795	+	0.0639526i
$113$	5.43807	−	16.7366i	0.511570	−	1.57445i	−0.277867	−	0.960620i	$-0.589627\pi$
$113$	5.43807	−	16.7366i	0.511570	−	1.57445i	0.789437	−	0.613832i	$-0.210373\pi$
$114$	0.365303	+	1.12429i	0.0342137	+	0.105299i
$115$	5.36509	+	3.89797i	0.500298	+	0.363487i
$116$	−2.11498	+	6.50925i	−0.196371	+	0.604368i
$117$	4.53140	−	13.9462i	0.418928	−	1.28933i
$118$	0.569321	−	1.75219i	0.0524102	−	0.161302i
$119$	−5.76783	+	4.19057i	−0.528736	+	0.384149i
$120$	−1.66677	+	1.21098i	−0.152155	+	0.110547i
$121$	1.00000			0.0909091
$122$	3.05871	−	6.34113i	0.276923	−	0.574099i
$123$	−2.37879			−0.214488
$124$	3.00386	−	2.18243i	0.269754	−	0.195988i
$125$	9.42462	−	6.84739i	0.842964	−	0.612449i
$126$	−2.55657	+	7.86831i	−0.227757	+	0.700965i
$127$	−4.47711	+	13.7791i	−0.397279	+	1.22270i	0.529894	+	0.848064i	$0.322232\pi$
$127$	−4.47711	+	13.7791i	−0.397279	+	1.22270i	−0.927173	+	0.374635i	$0.877768\pi$
$128$	1.91765	−	5.90192i	0.169498	−	0.521661i
$129$	−2.66381	−	1.93537i	−0.234536	−	0.170400i
$130$	2.22011	+	6.83280i	0.194717	+	0.599276i
$131$	1.69685	−	5.22237i	0.148255	−	0.456281i	−0.849161	−	0.528135i	$-0.822892\pi$
$131$	1.69685	−	5.22237i	0.148255	−	0.456281i	0.997415	+	0.0718541i	$0.0228916\pi$
$132$	0.174525	+	0.537134i	0.0151905	+	0.0467515i
$133$	9.12347			0.791105
$134$	−3.63531	−	11.1883i	−0.314043	−	0.966525i
$135$	−4.14010			−0.356323
$136$	−6.19080			−0.530857
$137$	5.05254	+	15.5501i	0.431668	+	1.32854i	0.896463	+	0.443118i	$0.146128\pi$
$137$	5.05254	+	15.5501i	0.431668	+	1.32854i	−0.464795	+	0.885418i	$0.653872\pi$
$138$	−1.52572	−	1.10850i	−0.129878	−	0.0943619i
$139$	3.27655	−	10.0842i	0.277914	−	0.855330i	−0.710520	−	0.703677i	$-0.751540\pi$
$139$	3.27655	−	10.0842i	0.277914	−	0.855330i	0.988434	−	0.151653i	$-0.0484598\pi$
$140$	1.83047	+	5.63361i	0.154703	+	0.476127i
$141$	−0.674593	+	0.490121i	−0.0568110	+	0.0412756i
$142$	2.59624	+	1.88628i	0.217871	+	0.158293i
$143$	5.28661			0.442089
$144$	−0.482630	+	0.350651i	−0.0402192	+	0.0292209i
$145$	2.68523	−	8.26429i	0.222996	−	0.686312i
$146$	−6.03105	−	4.38182i	−0.499134	−	0.362642i
$147$	−1.51932	−	1.10385i	−0.125311	−	0.0910438i
$148$	−2.74806	+	1.99658i	−0.225889	+	0.164118i
$149$	−2.28051	−	7.01868i	−0.186826	−	0.574993i	0.813149	−	0.582056i	$-0.197752\pi$
$149$	−2.28051	−	7.01868i	−0.186826	−	0.574993i	−0.999975	+	0.00706339i	$0.997752\pi$
$150$	−0.945905	+	0.687240i	−0.0772328	+	0.0561129i
$151$	−12.8804			−1.04819			−0.524095	−	0.851660i	$-0.675596\pi$
$151$	−12.8804			−1.04819			−0.524095	+	0.851660i	$0.675596\pi$
$152$	6.40929	+	4.65662i	0.519862	+	0.377702i
$153$	−4.83513	−	3.51293i	−0.390897	−	0.284004i
$154$	−2.98265			−0.240349
$155$	−3.81376	+	2.77086i	−0.306329	+	0.222561i
$156$	0.922648	+	2.83962i	0.0738709	+	0.227351i
$157$	12.3232	−	8.95333i	0.983499	−	0.714554i	0.0250108	−	0.999687i	$-0.492038\pi$
$157$	12.3232	−	8.95333i	0.983499	−	0.714554i	0.958488	+	0.285134i	$0.0920380\pi$
$158$	−9.44815	−	6.86448i	−0.751654	−	0.546109i
$159$	−2.16028	−	1.56954i	−0.171322	−	0.124472i
$160$	−2.58681	+	7.96140i	−0.204506	+	0.629404i
$161$	−11.7751	+	8.55512i	−0.928009	+	0.674238i
$162$	−6.32365			−0.496833
$163$	9.21295	+	6.69360i	0.721614	+	0.524283i	0.886899	−	0.461963i	$-0.152855\pi$
$163$	9.21295	+	6.69360i	0.721614	+	0.524283i	−0.165285	+	0.986246i	$0.552855\pi$
$164$	−4.80470	+	3.49082i	−0.375184	+	0.272587i
$165$	−0.221581	−	0.681957i	−0.0172501	−	0.0530903i
$166$	−0.856647	+	2.63649i	−0.0664887	+	0.204631i
$167$	−8.48525	−	6.16489i	−0.656608	−	0.477054i	0.208908	−	0.977935i	$-0.433009\pi$
$167$	−8.48525	−	6.16489i	−0.656608	−	0.477054i	−0.865516	+	0.500882i	$0.833009\pi$
$168$	−1.39730	−	4.30044i	−0.107804	−	0.331786i
$169$	14.9483			1.14987
$170$	2.92815			0.224579
$171$	2.36341	+	7.27382i	0.180734	+	0.556243i
$172$	−8.22051			−0.626808
$173$	−3.99505	−	12.2955i	−0.303738	−	0.934810i	−0.980145	−	0.198282i	$-0.936464\pi$
$173$	−3.99505	−	12.2955i	−0.303738	−	0.934810i	0.676407	−	0.736528i	$-0.263536\pi$
$174$	−0.763624	+	2.35019i	−0.0578902	+	0.178168i
$175$	2.78844	+	8.58195i	0.210787	+	0.648734i
$176$	−0.173997	−	0.126416i	−0.0131155	−	0.00952898i
$177$	−0.300395	+	0.924521i	−0.0225791	+	0.0694912i
$178$	−0.973184	+	2.99515i	−0.0729432	+	0.224496i
$179$	−0.949700	+	2.92287i	−0.0709839	+	0.218466i	−0.980255	−	0.197739i	$-0.936640\pi$
$179$	−0.949700	+	2.92287i	−0.0709839	+	0.218466i	0.909271	+	0.416205i	$0.136640\pi$
$180$	−4.01730	+	2.91874i	−0.299432	+	0.217550i
$181$	−15.5658	+	11.3092i	−1.15700	+	0.840607i	−0.989395	−	0.145248i	$-0.953602\pi$
$181$	−15.5658	+	11.3092i	−1.15700	+	0.840607i	−0.167601	+	0.985855i	$0.553602\pi$
$182$	−15.7681			−1.16881
$183$	−1.61389	+	3.34582i	−0.119302	+	0.247330i
$184$	−12.6386			−0.931731
$185$	3.48899	−	2.53490i	0.256516	−	0.186370i
$186$	1.08456	−	0.787976i	0.0795235	−	0.0577772i
$187$	0.665826	−	2.04920i	0.0486900	−	0.149852i
$188$	−0.643309	+	1.97990i	−0.0469182	+	0.144399i
$189$	2.80790	−	8.64182i	0.204244	−	0.628600i
$190$	−3.03149	−	2.20250i	−0.219927	−	0.159786i
$191$	3.99368	+	12.2913i	0.288972	+	0.889366i	0.985180	+	0.171525i	$0.0548694\pi$
$191$	3.99368	+	12.2913i	0.288972	+	0.889366i	−0.696207	+	0.717841i	$0.745131\pi$
$192$	0.798857	−	2.45863i	0.0576525	−	0.177436i
$193$	−5.77689	−	17.7794i	−0.415830	−	1.27979i	−0.911507	−	0.411285i	$-0.865080\pi$
$193$	−5.77689	−	17.7794i	−0.415830	−	1.27979i	0.495677	−	0.868507i	$-0.334920\pi$
$194$	−14.6564			−1.05227
$195$	−1.17141	−	3.60524i	−0.0838867	−	0.258177i
$196$	−4.68860			−0.334900
$197$	17.5169			1.24803			0.624015	−	0.781412i	$-0.285500\pi$
$197$	17.5169			1.24803			0.624015	+	0.781412i	$0.285500\pi$
$198$	−0.772646	−	2.37796i	−0.0549096	−	0.168994i
$199$	−1.94136	−	1.41048i	−0.137619	−	0.0999864i	0.516846	−	0.856079i	$-0.327106\pi$
$199$	−1.94136	−	1.41048i	−0.137619	−	0.0999864i	−0.654465	+	0.756092i	$0.727106\pi$
$200$	−2.42133	+	7.45209i	−0.171214	+	0.526942i
$201$	1.91813	+	5.90338i	0.135294	+	0.416393i
$202$	−6.48925	+	4.71472i	−0.456582	+	0.331726i
$203$	15.4292	+	11.2100i	1.08292	+	0.786787i
$204$	1.21690			0.0851999
$205$	6.10016	−	4.43203i	0.426054	−	0.309546i
$206$	2.93075	−	9.01993i	0.204195	−	0.628448i
$207$	−9.87100	−	7.17170i	−0.686082	−	0.498467i
$208$	−0.919855	−	0.668314i	−0.0637805	−	0.0463392i
$209$	−2.23070	+	1.62070i	−0.154301	+	0.112106i
$210$	0.660899	+	2.03404i	0.0456064	+	0.140362i
$211$	−8.33409	+	6.05507i	−0.573742	+	0.416848i	−0.836463	−	0.548024i	$-0.815380\pi$
$211$	−8.33409	+	6.05507i	−0.573742	+	0.416848i	0.262720	+	0.964872i	$0.415380\pi$
$212$	−6.66662			−0.457866
$213$	−1.36987	−	0.995270i	−0.0938621	−	0.0681948i
$214$	12.9983	+	9.44382i	0.888546	+	0.645566i
$215$	10.4369			0.711794
$216$	6.38334	−	4.63777i	0.434332	−	0.315560i
$217$	−3.19717	−	9.83989i	−0.217038	−	0.667975i
$218$	15.0525	−	10.9363i	1.01948	−	0.740699i
$219$	3.18221	+	2.31201i	0.215034	+	0.156231i
$220$	−1.44831	−	1.05226i	−0.0976450	−	0.0709432i
$221$	3.51996	−	10.8333i	0.236778	−	0.728729i
$222$	−0.992197	+	0.720874i	−0.0665919	+	0.0483819i
$223$	2.22965			0.149308			0.0746542	−	0.997209i	$-0.476215\pi$
$223$	2.22965			0.149308			0.0746542	+	0.997209i	$0.476215\pi$
$224$	−14.8637	−	10.7991i	−0.993126	−	0.721548i
$225$	−6.11974	+	4.44625i	−0.407983	+	0.296417i
$226$	−4.90196	−	15.0867i	−0.326074	−	1.00355i
$227$	−6.83409	+	21.0332i	−0.453594	+	1.39602i	0.419183	+	0.907902i	$0.362316\pi$
$227$	−6.83409	+	21.0332i	−0.453594	+	1.39602i	−0.872778	+	0.488118i	$0.837684\pi$
$228$	−1.25984	−	0.915331i	−0.0834353	−	0.0606193i
$229$	3.42064	+	10.5276i	0.226042	+	0.695686i	0.998184	+	0.0602359i	$0.0191853\pi$
$229$	3.42064	+	10.5276i	0.226042	+	0.695686i	−0.772142	+	0.635450i	$0.780815\pi$
$230$	5.97785			0.394168
$231$	1.57376			0.103546
$232$	5.11754	+	15.7502i	0.335983	+	1.03405i
$233$	−2.35927			−0.154561			−0.0772805	−	0.997009i	$-0.524624\pi$
$233$	−2.35927			−0.154561			−0.0772805	+	0.997009i	$0.524624\pi$
$234$	−4.08468	−	12.5714i	−0.267024	−	0.821816i
$235$	0.816760	−	2.51373i	0.0532795	−	0.163978i
$236$	0.749973	+	2.30818i	0.0488191	+	0.150250i
$237$	4.98520	+	3.62196i	0.323823	+	0.235272i
$238$	−1.98593	+	6.11205i	−0.128728	+	0.396185i
$239$	−0.810849	+	2.49554i	−0.0524495	+	0.161423i	−0.973850	−	0.227191i	$-0.927046\pi$
$239$	−0.810849	+	2.49554i	−0.0524495	+	0.161423i	0.921401	+	0.388614i	$0.127046\pi$
$240$	−0.0476559	+	0.146670i	−0.00307618	+	0.00946750i
$241$	5.81556	−	4.22525i	0.374613	−	0.272172i	−0.384508	−	0.923122i	$-0.625629\pi$
$241$	5.81556	−	4.22525i	0.374613	−	0.272172i	0.759121	+	0.650949i	$0.225629\pi$
$242$	0.729261	−	0.529839i	0.0468787	−	0.0340594i
$243$	11.5750			0.742537
$244$	1.65016	+	9.12628i	0.105641	+	0.584250i
$245$	5.95276			0.380308
$246$	−1.73476	+	1.26038i	−0.110604	+	0.0803587i
$247$	−11.7928	+	8.56801i	−0.750361	+	0.545169i
$248$	2.77625	−	8.54441i	0.176292	−	0.542571i
$249$	0.451999	−	1.39111i	0.0286443	−	0.0881581i
$250$	3.24500	−	9.98707i	0.205232	−	0.631638i
$251$	20.5942	+	14.9625i	1.29989	+	0.944427i	0.999955	−	0.00953219i	$-0.00303424\pi$
$251$	20.5942	+	14.9625i	1.29989	+	0.944427i	0.299937	+	0.953959i	$0.403034\pi$
$252$	−3.36780	−	10.3650i	−0.212151	−	0.652935i
$253$	1.35929	−	4.18347i	0.0854580	−	0.263013i
$254$	4.03574	+	12.4207i	0.253225	+	0.779346i
$255$	−1.54500			−0.0967517
$256$	−5.08782	−	15.6587i	−0.317988	−	0.978668i
$257$	23.0095			1.43529			0.717647	−	0.696407i	$-0.245219\pi$
$257$	23.0095			1.43529			0.717647	+	0.696407i	$0.245219\pi$
$258$	−2.96805			−0.184783
$259$	2.92491	+	9.00195i	0.181745	+	0.559354i
$260$	−7.65665	−	5.56288i	−0.474845	−	0.344995i
$261$	−4.94043	+	15.2051i	−0.305805	+	0.941171i
$262$	−1.52957	−	4.70753i	−0.0944971	−	0.290832i
$263$	−18.0261	+	13.0967i	−1.11154	+	0.807580i	−0.982905	−	0.184113i	$-0.941059\pi$
$263$	−18.0261	+	13.0967i	−1.11154	+	0.807580i	−0.128633	+	0.991692i	$0.541059\pi$
$264$	1.10557	+	0.803246i	0.0680434	+	0.0494364i
$265$	8.46409			0.519945
$266$	6.65340	−	4.83398i	0.407946	−	0.296390i
$267$	0.513488	−	1.58035i	0.0314250	−	0.0967161i
$268$	12.5373	+	9.10891i	0.765840	+	0.556415i
$269$	−7.53261	−	5.47276i	−0.459271	−	0.333680i	0.333974	−	0.942582i	$-0.391610\pi$
$269$	−7.53261	−	5.47276i	−0.459271	−	0.333680i	−0.793245	+	0.608902i	$0.791610\pi$
$270$	−3.01922	+	2.19359i	−0.183744	+	0.133498i
$271$	−2.66793	−	8.21106i	−0.162065	−	0.498786i	0.836743	−	0.547596i	$-0.184457\pi$
$271$	−2.66793	−	8.21106i	−0.162065	−	0.498786i	−0.998808	+	0.0488102i	$0.984457\pi$
$272$	−0.374904	+	0.272384i	−0.0227319	+	0.0165157i
$273$	8.31986			0.503541
$274$	11.9237	+	8.66307i	0.720337	+	0.523355i
$275$	−2.20628	−	1.60296i	−0.133044	−	0.0966619i
$276$	2.48431			0.149538
$277$	26.4359	−	19.2068i	1.58838	−	1.15403i	0.682178	−	0.731186i	$-0.261033\pi$
$277$	26.4359	−	19.2068i	1.58838	−	1.15403i	0.906204	−	0.422841i	$-0.138967\pi$
$278$	−2.95354	−	9.09006i	−0.177142	−	0.545186i
$279$	7.01677	−	5.09798i	0.420083	−	0.305208i
$280$	11.5956	+	8.42468i	0.692968	+	0.503471i
$281$	−22.1485	−	16.0918i	−1.32127	−	0.959958i	−0.999916	−	0.0129983i	$-0.995862\pi$
$281$	−22.1485	−	16.0918i	−1.32127	−	0.959958i	−0.321353	−	0.946959i	$-0.604138\pi$
$282$	−0.232270	+	0.714852i	−0.0138315	+	0.0425688i
$283$	−10.4380	+	7.58365i	−0.620475	+	0.450801i	−0.853087	−	0.521768i	$-0.825273\pi$
$283$	−10.4380	+	7.58365i	−0.620475	+	0.450801i	0.232613	+	0.972569i	$0.425273\pi$
$284$	−4.22742			−0.250851
$285$	1.59953	+	1.16212i	0.0947478	+	0.0688383i
$286$	3.85532	−	2.80106i	0.227970	−	0.165630i
$287$	5.11392	+	15.7390i	0.301865	+	0.929045i
$288$	4.75936	−	14.6478i	0.280448	−	0.863131i
$289$	9.99739	+	7.26353i	0.588082	+	0.427266i
$290$	−2.42051	−	7.44957i	−0.142137	−	0.437454i
$291$	7.73328			0.453333
$292$	9.82029			0.574689
$293$	1.94000	+	5.97069i	0.113336	+	0.348812i	0.991596	−	0.129371i	$-0.0412958\pi$
$293$	1.94000	+	5.97069i	0.113336	+	0.348812i	−0.878261	+	0.478182i	$0.841296\pi$
$294$	−1.69284			−0.0987285
$295$	−0.952183	−	2.93052i	−0.0554382	−	0.170621i
$296$	−2.53983	+	7.81679i	−0.147625	+	0.454342i
$297$	0.848603	+	2.61173i	0.0492409	+	0.151548i
$298$	−5.38186	−	3.91015i	−0.311763	−	0.226509i
$299$	7.18606	−	22.1164i	0.415580	−	1.27902i
$300$	0.475950	−	1.46482i	0.0274790	−	0.0845716i
$301$	−7.07854	+	21.7855i	−0.408000	+	1.25570i
$302$	−9.39316	+	6.82453i	−0.540516	+	0.392708i
$303$	3.42397	−	2.48766i	0.196702	−	0.142913i
$304$	0.593018			0.0340119
$305$	−2.09509	−	11.5869i	−0.119964	−	0.663465i
$306$	−5.38737			−0.307975
$307$	−17.1179	+	12.4368i	−0.976968	+	0.709808i	−0.957029	−	0.289993i	$-0.906347\pi$
$307$	−17.1179	+	12.4368i	−0.976968	+	0.709808i	−0.0199387	+	0.999801i	$0.506347\pi$
$308$	3.17870	−	2.30946i	0.181123	−	0.131594i
$309$	−1.54637	+	4.75925i	−0.0879702	+	0.270744i
$310$	−1.31312	+	4.04137i	−0.0745802	+	0.229534i
$311$	1.85021	−	5.69435i	0.104916	−	0.322897i	−0.884795	−	0.465980i	$-0.845702\pi$
$311$	1.85021	−	5.69435i	0.104916	−	0.322897i	0.989711	+	0.143083i	$0.0457017\pi$
$312$	5.84474	+	4.24645i	0.330893	+	0.240408i
$313$	9.04046	+	27.8237i	0.510997	+	1.57269i	0.790449	+	0.612528i	$0.209847\pi$
$313$	9.04046	+	27.8237i	0.510997	+	1.57269i	−0.279452	+	0.960160i	$0.590153\pi$
$314$	4.24301	−	13.0586i	0.239447	−	0.736942i
$315$	4.27583	+	13.1597i	0.240916	+	0.741463i
$316$	15.3843			0.865435
$317$	−2.33520	−	7.18701i	−0.131158	−	0.403663i	0.863815	−	0.503810i	$-0.168069\pi$
$317$	−2.33520	−	7.18701i	−0.131158	−	0.403663i	−0.994973	+	0.100147i	$0.968069\pi$
$318$	−2.40701			−0.134979
$319$	−5.76381			−0.322712
$320$	2.53219	+	7.79329i	0.141554	+	0.435658i
$321$	−6.85839	−	4.98291i	−0.382798	−	0.278119i
$322$	−4.05430	+	12.4778i	−0.225937	+	0.695363i
$323$	1.83588	+	5.65025i	0.102151	+	0.314389i
$324$	6.73929	−	4.89638i	0.374405	−	0.272021i
$325$	−11.6638	−	8.47421i	−0.646988	−	0.470065i
$326$	10.2652			0.568536
$327$	−7.94227	+	5.77040i	−0.439209	+	0.319104i
$328$	−4.44064	+	13.6669i	−0.245193	+	0.754628i
$329$	4.69307	+	3.40972i	0.258738	+	0.187984i
$330$	−0.522918	−	0.379922i	−0.0287857	−	0.0209140i
$331$	2.63835	−	1.91687i	0.145017	−	0.105361i	−0.512911	−	0.858442i	$-0.671433\pi$
$331$	2.63835	−	1.91687i	0.145017	−	0.105361i	0.657928	+	0.753081i	$0.271433\pi$
$332$	−1.12847	−	3.47308i	−0.0619330	−	0.190610i
$333$	−6.41924	+	4.66385i	−0.351772	+	0.255578i
$334$	−9.45437			−0.517320
$335$	−15.9177	−	11.5649i	−0.869676	−	0.631857i
$336$	−0.273829	−	0.198949i	−0.0149386	−	0.0108535i
$337$	−0.460644			−0.0250929			−0.0125464	−	0.999921i	$-0.503994\pi$
$337$	−0.460644			−0.0250929			−0.0125464	+	0.999921i	$0.503994\pi$
$338$	10.9012	−	7.92019i	0.592948	−	0.430802i
$339$	2.58646	+	7.96031i	0.140477	+	0.432345i
$340$	−3.12061	+	2.26726i	−0.169239	+	0.122959i
$341$	2.52968	+	1.83792i	0.136990	+	0.0995288i
$342$	5.57750	+	4.05229i	0.301597	+	0.219123i
$343$	3.12016	−	9.60286i	0.168473	−	0.518506i
$344$	−16.0920	+	11.6915i	−0.867624	+	0.630366i
$345$	−3.15414			−0.169813
$346$	−9.42809	−	6.84991i	−0.506857	−	0.368253i
$347$	19.1475	−	13.9115i	1.02789	−	0.746809i	0.0600078	−	0.998198i	$-0.480887\pi$
$347$	19.1475	−	13.9115i	1.02789	−	0.746809i	0.967886	+	0.251389i	$0.0808874\pi$
$348$	−1.00593	−	3.09594i	−0.0539236	−	0.165960i
$349$	7.88472	−	24.2667i	0.422059	−	1.29896i	−0.483723	−	0.875221i	$-0.660716\pi$
$349$	7.88472	−	24.2667i	0.422059	−	1.29896i	0.905782	−	0.423744i	$-0.139284\pi$
$350$	6.58056	+	4.78106i	0.351746	+	0.255558i
$351$	4.48623	+	13.8072i	0.239457	+	0.736974i
$352$	5.55257			0.295953
$353$	−30.9493			−1.64726			−0.823632	−	0.567124i	$-0.808056\pi$
$353$	−30.9493			−1.64726			−0.823632	+	0.567124i	$0.808056\pi$
$354$	0.270781	+	0.833378i	0.0143919	+	0.0442936i
$355$	5.36723			0.284863
$356$	−1.28199	−	3.94555i	−0.0679452	−	0.209114i
$357$	1.04785	−	3.22495i	0.0554580	−	0.170682i
$358$	0.856075	+	2.63473i	0.0452450	+	0.139250i
$359$	11.3034	+	8.21239i	0.596570	+	0.433434i	0.844660	−	0.535304i	$-0.179803\pi$
$359$	11.3034	+	8.21239i	0.596570	+	0.433434i	−0.248090	+	0.968737i	$0.579803\pi$
$360$	−3.71290	+	11.4271i	−0.195687	+	0.602262i
$361$	−3.52196	+	10.8395i	−0.185367	+	0.570500i
$362$	−5.35947	+	16.4947i	−0.281687	+	0.866945i
$363$	−0.384786	+	0.279563i	−0.0201960	+	0.0146733i
$364$	16.8045	−	12.2092i	0.880797	−	0.639937i
$365$	−12.4681			−0.652608
$366$	0.595799	+	3.29508i	0.0311429	+	0.172237i
$367$	12.8767			0.672159			0.336080	−	0.941834i	$-0.390899\pi$
$367$	12.8767			0.672159			0.336080	+	0.941834i	$0.390899\pi$
$368$	−0.765372	+	0.556075i	−0.0398978	+	0.0289874i
$369$	−11.2234	+	8.15429i	−0.584267	+	0.424495i
$370$	1.20130	−	3.69721i	0.0624525	−	0.192209i
$371$	−5.74051	+	17.6675i	−0.298032	+	0.917250i
$372$	−0.545714	+	1.67954i	−0.0282940	+	0.0870799i
$373$	−6.82448	−	4.95827i	−0.353358	−	0.256730i	0.396918	−	0.917854i	$-0.370080\pi$
$373$	−6.82448	−	4.95827i	−0.353358	−	0.256730i	−0.750276	+	0.661124i	$0.770080\pi$
$374$	−0.600186	−	1.84718i	−0.0310349	−	0.0955156i
$375$	−1.71218	+	5.26956i	−0.0884167	+	0.272119i
$376$	1.55659	+	4.79069i	0.0802750	+	0.247061i
$377$	−30.4711			−1.56934
$378$	−2.53108	−	7.78988i	−0.130185	−	0.400668i
$379$	17.2204			0.884552			0.442276	−	0.896879i	$-0.354171\pi$
$379$	17.2204			0.884552			0.442276	+	0.896879i	$0.354171\pi$
$380$	4.93613			0.253218
$381$	−2.12941	−	6.55364i	−0.109093	−	0.335753i
$382$	9.42484	+	6.84755i	0.482217	+	0.350351i
$383$	1.82335	−	5.61171i	0.0931690	−	0.286745i	−0.893603	−	0.448858i	$-0.851831\pi$
$383$	1.82335	−	5.61171i	0.0931690	−	0.286745i	0.986772	+	0.162113i	$0.0518309\pi$
$384$	0.912075	+	2.80708i	0.0465442	+	0.143248i
$385$	−4.03574	+	2.93214i	−0.205680	+	0.149436i
$386$	−13.6331	−	9.90504i	−0.693907	−	0.504153i
$387$	−19.2025			−0.976117
$388$	15.6198	−	11.3484i	0.792973	−	0.576129i
$389$	2.25096	−	6.92775i	0.114128	−	0.351251i	−0.877636	−	0.479328i	$-0.840880\pi$
$389$	2.25096	−	6.92775i	0.114128	−	0.351251i	0.991764	+	0.128077i	$0.0408804\pi$
$390$	−2.76447	−	2.00850i	−0.139984	−	0.101704i
$391$	−7.66772	−	5.57093i	−0.387773	−	0.281734i
$392$	−9.17815	+	6.66832i	−0.463567	+	0.336801i
$393$	0.807059	+	2.48387i	0.0407107	+	0.125295i
$394$	12.7744	−	9.28117i	0.643566	−	0.467578i
$395$	−19.5323			−0.982775
$396$	2.66468	+	1.93600i	0.133905	+	0.0972878i
$397$	27.8354	+	20.2236i	1.39702	+	1.01499i	0.995053	+	0.0993407i	$0.0316734\pi$
$397$	27.8354	+	20.2236i	1.39702	+	1.01499i	0.401967	+	0.915654i	$0.368327\pi$
$398$	−2.16309			−0.108426
$399$	−3.51058	+	2.55059i	−0.175749	+	0.127689i
$400$	0.181246	+	0.557819i	0.00906232	+	0.0278910i
$401$	15.1350	−	10.9962i	0.755805	−	0.549125i	−0.141816	−	0.989893i	$-0.545294\pi$
$401$	15.1350	−	10.9962i	0.755805	−	0.549125i	0.897621	+	0.440768i	$0.145294\pi$
$402$	4.52666	+	3.28881i	0.225769	+	0.164031i
$403$	13.3734	+	9.71636i	0.666177	+	0.484006i
$404$	3.26519	−	10.0492i	0.162449	−	0.499967i
$405$	−8.55635	+	6.21655i	−0.425169	+	0.308903i
$406$	17.1914			0.853197
$407$	−2.31425	−	1.68140i	−0.114713	−	0.0833441i
$408$	2.38213	−	1.73072i	0.117933	−	0.0856834i
$409$	−5.60682	−	17.2560i	−0.277239	−	0.853255i	−0.988618	−	0.150446i	$-0.951929\pi$
$409$	−5.60682	−	17.2560i	−0.277239	−	0.853255i	0.711379	−	0.702809i	$-0.248071\pi$
$410$	2.10035	−	6.46421i	0.103729	−	0.319245i
$411$	−6.29139	−	4.57096i	−0.310331	−	0.225469i
$412$	3.86072	+	11.8821i	0.190204	+	0.585387i
$413$	6.76279			0.332775
$414$	−10.9984			−0.540541
$415$	1.43273	+	4.40950i	0.0703301	+	0.216454i
$416$	29.3543			1.43921
$417$	1.55840	+	4.79626i	0.0763151	+	0.234874i
$418$	−0.768053	+	2.36383i	−0.0375667	+	0.115618i
$419$	0.364171	+	1.12080i	0.0177909	+	0.0547548i	0.959558	−	0.281512i	$-0.0908358\pi$
$419$	0.364171	+	1.12080i	0.0177909	+	0.0547548i	−0.941767	+	0.336266i	$0.890836\pi$
$420$	−2.27929	−	1.65600i	−0.111218	−	0.0808045i
$421$	1.54781	−	4.76368i	0.0754357	−	0.232167i	−0.906228	−	0.422790i	$-0.861051\pi$
$421$	1.54781	−	4.76368i	0.0754357	−	0.232167i	0.981663	+	0.190623i	$0.0610507\pi$
$422$	−2.86951	+	8.83146i	−0.139686	+	0.429909i
$423$	−1.50272	+	4.62490i	−0.0730647	+	0.224870i
$424$	−13.0502	+	9.48154i	−0.633775	+	0.460464i
$425$	−4.75378	+	3.45382i	−0.230592	+	0.167535i
$426$	−1.52633			−0.0739508
$427$	25.6068	+	3.48531i	1.23920	+	0.168666i
$428$	−21.1650			−1.02305
$429$	−2.03421	+	1.47794i	−0.0982128	+	0.0713558i
$430$	7.61126	−	5.52991i	0.367048	−	0.266676i
$431$	−1.48040	+	4.55620i	−0.0713084	+	0.219465i	−0.980359	−	0.197221i	$-0.936808\pi$
$431$	−1.48040	+	4.55620i	−0.0713084	+	0.219465i	0.909051	+	0.416686i	$0.136808\pi$
$432$	0.182511	−	0.561710i	0.00878105	−	0.0270253i
$433$	−1.61953	+	4.98439i	−0.0778295	+	0.239535i	−0.982400	−	0.186790i	$-0.940192\pi$
$433$	−1.61953	+	4.98439i	−0.0778295	+	0.239535i	0.904570	+	0.426324i	$0.140192\pi$
$434$	−7.54514	−	5.48186i	−0.362178	−	0.263138i
$435$	1.27715	+	3.93067i	0.0612348	+	0.188461i
$436$	−7.57395	+	23.3102i	−0.362727	+	1.11636i
$437$	3.74797	+	11.5351i	0.179290	+	0.551797i
$438$	3.54566			0.169418
$439$	−0.443320	−	1.36440i	−0.0211585	−	0.0651193i	0.939920	−	0.341395i	$-0.110900\pi$
$439$	−0.443320	−	1.36440i	−0.0211585	−	0.0651193i	−0.961078	+	0.276276i	$0.910900\pi$
$440$	−4.33169			−0.206505
$441$	−10.9522			−0.521534
$442$	−3.17295	−	9.76535i	−0.150922	−	0.464490i
$443$	−12.6527	−	9.19270i	−0.601147	−	0.436759i	0.245139	−	0.969488i	$-0.421166\pi$
$443$	−12.6527	−	9.19270i	−0.601147	−	0.436759i	−0.846286	+	0.532729i	$0.821166\pi$
$444$	0.499243	−	1.53651i	0.0236930	−	0.0729196i
$445$	1.62764	+	5.00936i	0.0771575	+	0.237466i
$446$	1.62600	−	1.18136i	0.0769932	−	0.0559388i
$447$	2.83967	+	2.06314i	0.134312	+	0.0975833i
$448$	−17.9847			−0.849695
$449$	−2.93930	+	2.13553i	−0.138714	+	0.100782i	−0.654978	−	0.755648i	$-0.727322\pi$
$449$	−2.93930	+	2.13553i	−0.138714	+	0.100782i	0.516264	+	0.856429i	$0.327322\pi$
$450$	−2.10709	+	6.48496i	−0.0993293	+	0.305704i
$451$	−4.04625	−	2.93977i	−0.190530	−	0.138428i
$452$	16.9057	+	12.2827i	0.795179	+	0.577732i
$453$	4.95619	−	3.60088i	0.232862	−	0.169184i
$454$	6.16036	+	18.9596i	0.289120	+	0.889820i
$455$	−21.3354	+	15.5011i	−1.00022	+	0.726702i
$456$	−3.76802			−0.176454
$457$	20.6542	+	15.0061i	0.966162	+	0.701958i	0.954574	−	0.297975i	$-0.0963112\pi$
$457$	20.6542	+	15.0061i	0.966162	+	0.701958i	0.0115883	+	0.999933i	$0.496311\pi$
$458$	8.07250	+	5.86501i	0.377203	+	0.274054i
$459$	5.91698			0.276181
$460$	−6.37077	+	4.62863i	−0.297039	+	0.215811i
$461$	−4.52534	−	13.9276i	−0.210766	−	0.648671i	−0.999427	−	0.0338431i	$-0.989225\pi$
$461$	−4.52534	−	13.9276i	−0.210766	−	0.648671i	0.788661	−	0.614828i	$-0.210775\pi$
$462$	1.14768	−	0.833839i	0.0533950	−	0.0387937i
$463$	7.40411	+	5.37940i	0.344098	+	0.250002i	0.746389	−	0.665510i	$-0.231786\pi$
$463$	7.40411	+	5.37940i	0.344098	+	0.250002i	−0.402291	+	0.915512i	$0.631786\pi$
$464$	1.00289	+	0.728640i	0.0465578	+	0.0338262i
$465$	0.692851	−	2.13238i	0.0321302	−	0.0988866i
$466$	−1.72053	+	1.25004i	−0.0797019	+	0.0579068i
$467$	2.85971			0.132332			0.0661659	−	0.997809i	$-0.478923\pi$
$467$	2.85971			0.132332			0.0661659	+	0.997809i	$0.478923\pi$
$468$	14.0871	+	10.2349i	0.651178	+	0.473108i
$469$	34.9356	−	25.3822i	1.61317	−	1.17204i
$470$	−0.736241	−	2.26592i	−0.0339603	−	0.104519i
$471$	−2.23877	+	6.89023i	−0.103157	+	0.317485i
$472$	4.75089	+	3.45173i	0.218678	+	0.158879i
$473$	−2.13928	−	6.58401i	−0.0983640	−	0.302733i
$474$	5.55457			0.255130
$475$	7.51946			0.345016
$476$	−2.61608	−	8.05148i	−0.119908	−	0.369039i
$477$	−15.5727			−0.713025
$478$	0.730913	+	2.24952i	0.0334312	+	0.102891i
$479$	0.571754	−	1.75968i	0.0261241	−	0.0804017i	−0.937144	−	0.348942i	$-0.886541\pi$
$479$	0.571754	−	1.75968i	0.0261241	−	0.0804017i	0.963269	+	0.268540i	$0.0865411\pi$
$480$	−1.23034	−	3.78661i	−0.0561573	−	0.172834i
$481$	−12.2346	−	8.88894i	−0.557848	−	0.405301i
$482$	2.00236	−	6.16262i	0.0912049	−	0.280700i
$483$	2.13920	−	6.58378i	0.0973369	−	0.299572i
$484$	−0.366942	+	1.12933i	−0.0166792	+	0.0513332i
$485$	−19.8312	+	14.4082i	−0.900488	+	0.654243i
$486$	8.44120	−	6.13289i	0.382901	−	0.278194i
$487$	−4.00710			−0.181579			−0.0907896	−	0.995870i	$-0.528939\pi$
$487$	−4.00710			−0.181579			−0.0907896	+	0.995870i	$0.528939\pi$
$488$	16.2100	+	15.5182i	0.733793	+	0.702475i
$489$	−5.41630			−0.244933
$490$	4.34112	−	3.15400i	0.196112	−	0.142483i
$491$	−32.0287	+	23.2702i	−1.44544	+	1.05017i	−0.458564	+	0.888661i	$0.651636\pi$
$491$	−32.0287	+	23.2702i	−1.44544	+	1.05017i	−0.986871	+	0.161509i	$0.948364\pi$
$492$	0.872877	−	2.68644i	0.0393523	−	0.121114i
$493$	−3.83770	+	11.8112i	−0.172841	+	0.531950i
$494$	−4.06040	+	12.4966i	−0.182686	+	0.562250i
$495$	−3.38314	−	2.45799i	−0.152061	−	0.110479i
$496$	−0.207813	−	0.639584i	−0.00933110	−	0.0287182i
$497$	−3.64016	+	11.2032i	−0.163283	+	0.502534i
$498$	−0.407440	−	1.25397i	−0.0182578	−	0.0561918i
$499$	6.27675			0.280986			0.140493	−	0.990082i	$-0.455131\pi$
$499$	6.27675			0.280986			0.140493	+	0.990082i	$0.455131\pi$
$500$	4.27468	+	13.1561i	0.191169	+	0.588359i
$501$	4.98848			0.222869
$502$	22.9463			1.02414
$503$	7.23971	+	22.2815i	0.322803	+	0.993484i	0.972423	+	0.233225i	$0.0749279\pi$
$503$	7.23971	+	22.2815i	0.322803	+	0.993484i	−0.649620	+	0.760259i	$0.725072\pi$
$504$	−21.3342	−	15.5002i	−0.950300	−	0.690433i
$505$	−4.14556	+	12.7587i	−0.184475	+	0.567755i
$506$	−1.22529	−	3.77105i	−0.0544707	−	0.167644i
$507$	−5.75189	+	4.17899i	−0.255450	+	0.185596i
$508$	−13.9183	−	10.1123i	−0.617526	−	0.448659i
$509$	−12.3113			−0.545691			−0.272845	−	0.962058i	$-0.587965\pi$
$509$	−12.3113			−0.545691			−0.272845	+	0.962058i	$0.587965\pi$
$510$	−1.12671	+	0.818602i	−0.0498915	+	0.0362483i
$511$	8.45608	−	26.0251i	0.374075	−	1.15128i
$512$	−1.96599	−	1.42838i	−0.0868854	−	0.0631260i
$513$	−6.12580	−	4.45066i	−0.270461	−	0.196501i
$514$	16.7800	−	12.1914i	0.740132	−	0.537737i
$515$	−4.90165	−	15.0857i	−0.215993	−	0.664757i
$516$	3.16314	−	2.29815i	0.139249	−	0.101171i
$517$	−1.75317			−0.0771041
$518$	6.90261	+	5.01504i	0.303283	+	0.220348i
$519$	4.97461	+	3.61427i	0.218361	+	0.158649i
$520$	−22.9000			−1.00423
$521$	18.8732	−	13.7122i	0.826852	−	0.600743i	−0.0918149	−	0.995776i	$-0.529267\pi$
$521$	18.8732	−	13.7122i	0.826852	−	0.600743i	0.918667	+	0.395033i	$0.129267\pi$
$522$	4.45339	+	13.7061i	0.194920	+	0.599901i
$523$	9.85455	−	7.15975i	0.430909	−	0.313074i	−0.351103	−	0.936337i	$-0.614193\pi$
$523$	9.85455	−	7.15975i	0.430909	−	0.313074i	0.782012	+	0.623263i	$0.214193\pi$
$524$	5.27513	+	3.83261i	0.230445	+	0.167428i
$525$	−3.47215	−	2.52267i	−0.151537	−	0.110098i
$526$	−6.20658	+	19.1019i	−0.270620	+	0.832882i
$527$	5.45058	−	3.96008i	0.237431	−	0.172504i
$528$	0.102293			0.00445173
$529$	2.95362	+	2.14593i	0.128418	+	0.0933015i
$530$	6.17254	−	4.48461i	0.268118	−	0.194799i
$531$	1.75188	+	5.39173i	0.0760250	+	0.233981i
$532$	−3.34778	+	10.3034i	−0.145145	+	0.446710i
$533$	−21.3909	−	15.5414i	−0.926544	−	0.673174i
$534$	−0.462867	−	1.42456i	−0.0200302	−	0.0616466i
$535$	26.8715			1.16176
$536$	37.4975			1.61964
$537$	−0.451697	−	1.39018i	−0.0194922	−	0.0599908i
$538$	−8.39293			−0.361845
$539$	−1.22014	−	3.75522i	−0.0525554	−	0.161749i
$540$	1.51918	−	4.67554i	0.0653749	−	0.201203i
$541$	−6.93064	−	21.3303i	−0.297972	−	0.917062i	−0.982207	−	0.187801i	$-0.939864\pi$
$541$	−6.93064	−	21.3303i	−0.297972	−	0.917062i	0.684235	−	0.729261i	$-0.260136\pi$
$542$	−6.29616	−	4.57443i	−0.270443	−	0.196489i
$543$	2.82786	−	8.70325i	0.121355	−	0.373492i
$544$	3.69704	−	11.3783i	0.158509	−	0.487842i
$545$	9.61606	−	29.5952i	0.411907	−	1.26772i
$546$	6.06735	−	4.40819i	0.259659	−	0.188653i
$547$	−12.9433	+	9.40384i	−0.553414	+	0.402079i	−0.829043	−	0.559185i	$-0.811114\pi$
$547$	−12.9433	+	9.40384i	−0.553414	+	0.402079i	0.275628	+	0.961264i	$0.411114\pi$
$548$	−19.4152			−0.829376
$549$	3.85465	+	21.3183i	0.164513	+	0.909841i
$550$	−2.45826			−0.104821
$551$	12.8573	−	9.34140i	0.547741	−	0.397957i
$552$	4.86316	−	3.53329i	0.206990	−	0.150387i
$553$	13.2472	−	40.7705i	0.563326	−	1.73374i
$554$	9.10217	−	28.0136i	0.386714	−	1.19018i
$555$	−0.633850	+	1.95079i	−0.0269054	+	0.0828064i
$556$	10.1861	+	7.40062i	0.431986	+	0.313856i
$557$	−13.5903	−	41.8266i	−0.575839	−	1.77225i	−0.633304	−	0.773903i	$-0.718302\pi$
$557$	−13.5903	−	41.8266i	−0.575839	−	1.77225i	0.0574653	−	0.998348i	$-0.481698\pi$
$558$	2.41595	−	7.43553i	0.102275	−	0.314771i
$559$	−11.3095	−	34.8071i	−0.478342	−	1.47219i
$560$	1.07288			0.0453373
$561$	0.316681	+	0.974644i	0.0133703	+	0.0411495i
$562$	−24.6781			−1.04098
$563$	−26.7156			−1.12593			−0.562965	−	0.826481i	$-0.690339\pi$
$563$	−26.7156			−1.12593			−0.562965	+	0.826481i	$0.690339\pi$
$564$	−0.305972	−	0.941684i	−0.0128837	−	0.0396521i
$565$	−21.4639	−	15.5944i	−0.902994	−	0.656063i
$566$	−3.59391	+	11.0609i	−0.151063	+	0.464925i
$567$	−7.17301	−	22.0762i	−0.301238	−	0.927115i
$568$	−8.27537	+	6.01240i	−0.347227	+	0.252275i
$569$	−1.91859	−	1.39394i	−0.0804316	−	0.0584369i	0.546843	−	0.837235i	$-0.315830\pi$
$569$	−1.91859	−	1.39394i	−0.0804316	−	0.0584369i	−0.627274	+	0.778798i	$0.715830\pi$
$570$	1.78221			0.0746487
$571$	−0.619667	+	0.450214i	−0.0259322	+	0.0188409i	−0.600676	−	0.799493i	$-0.705102\pi$
$571$	−0.619667	+	0.450214i	−0.0259322	+	0.0188409i	0.574744	+	0.818334i	$0.305102\pi$
$572$	−1.93988	+	5.97033i	−0.0811104	+	0.249632i
$573$	−4.97290	−	3.61302i	−0.207746	−	0.150936i
$574$	12.0685	+	8.76830i	0.503731	+	0.365982i
$575$	−9.70490	+	7.05102i	−0.404722	+	0.294048i
$576$	−4.65887	−	14.3385i	−0.194119	−	0.597438i
$577$	−29.9505	+	21.7603i	−1.24686	+	0.905893i	−0.998035	−	0.0626565i	$-0.980043\pi$
$577$	−29.9505	+	21.7603i	−1.24686	+	0.905893i	−0.248820	+	0.968550i	$0.580043\pi$
$578$	11.1392			0.463330
$579$	7.19334	+	5.22627i	0.298945	+	0.217196i
$580$	8.34778	+	6.06502i	0.346623	+	0.251836i
$581$	−10.1759			−0.422165
$582$	5.63958	−	4.09740i	0.233768	−	0.169842i
$583$	−1.73490	−	5.33946i	−0.0718521	−	0.221138i
$584$	19.2237	−	13.9668i	0.795481	−	0.577951i
$585$	−17.8853	−	12.9945i	−0.739467	−	0.537255i
$586$	4.57827	+	3.32631i	0.189127	+	0.137409i
$587$	−12.9646	+	39.9009i	−0.535106	+	1.64689i	0.208314	+	0.978062i	$0.433202\pi$
$587$	−12.9646	+	39.9009i	−0.535106	+	1.64689i	−0.743420	+	0.668825i	$0.766798\pi$
$588$	1.80411	−	1.31076i	0.0744002	−	0.0540549i
$589$	−8.62165			−0.355249
$590$	−2.24709	−	1.63261i	−0.0925114	−	0.0672135i
$591$	−6.74027	+	4.89709i	−0.277258	+	0.201439i
$592$	0.190117	+	0.585119i	0.00781374	+	0.0240482i
$593$	3.15471	−	9.70921i	0.129549	−	0.398709i	−0.865154	−	0.501507i	$-0.832779\pi$
$593$	3.15471	−	9.70921i	0.129549	−	0.398709i	0.994702	+	0.102797i	$0.0327793\pi$
$594$	2.00265	+	1.45501i	0.0821698	+	0.0596998i
$595$	3.32144	+	10.2223i	0.136166	+	0.419075i
$596$	8.76322			0.358955
$597$	1.14133			0.0467114
$598$	−6.47763	−	19.9361i	−0.264890	−	0.815248i
$599$	−1.93943			−0.0792430			−0.0396215	−	0.999215i	$-0.512615\pi$
$599$	−1.93943			−0.0792430			−0.0396215	+	0.999215i	$0.512615\pi$
$600$	−1.15164	−	3.54437i	−0.0470154	−	0.144698i
$601$	2.10096	−	6.46609i	0.0857000	−	0.263757i	−0.899019	−	0.437910i	$-0.855719\pi$
$601$	2.10096	−	6.46609i	0.0857000	−	0.263757i	0.984719	+	0.174153i	$0.0557187\pi$
$602$	6.38071	+	19.6378i	0.260058	+	0.800378i
$603$	29.2862	+	21.2777i	1.19263	+	0.866495i
$604$	4.72635	−	14.5462i	0.192312	−	0.591876i
$605$	0.465877	−	1.43382i	0.0189406	−	0.0582932i
$606$	1.17891	−	3.62831i	0.0478900	−	0.147390i
$607$	3.29209	−	2.39185i	0.133622	−	0.0970821i	−0.518967	−	0.854795i	$-0.673683\pi$
$607$	3.29209	−	2.39185i	0.133622	−	0.0970821i	0.652588	+	0.757713i	$0.273683\pi$
$608$	−12.3861	+	8.99904i	−0.502323	+	0.364959i
$609$	−9.07085			−0.367569
$610$	−7.66708	−	7.33984i	−0.310431	−	0.297181i
$611$	−9.26831			−0.374956
$612$	5.74147	−	4.17142i	0.232085	−	0.168620i
$613$	0.528996	−	0.384338i	0.0213659	−	0.0155233i	−0.577051	−	0.816708i	$-0.695797\pi$
$613$	0.528996	−	0.384338i	0.0213659	−	0.0155233i	0.598417	+	0.801185i	$0.295797\pi$
$614$	−5.89386	+	18.1394i	−0.237857	+	0.732048i
$615$	−1.10822	+	3.41076i	−0.0446879	+	0.137535i
$616$	2.93784	−	9.04174i	0.118369	−	0.364302i
$617$	−10.8471	−	7.88087i	−0.436687	−	0.317272i	0.347630	−	0.937632i	$-0.386987\pi$
$617$	−10.8471	−	7.88087i	−0.436687	−	0.317272i	−0.784317	+	0.620360i	$0.786987\pi$
$618$	1.39393	+	4.29007i	0.0560720	+	0.172572i
$619$	2.56434	−	7.89222i	0.103069	−	0.317215i	−0.886203	−	0.463297i	$-0.846666\pi$
$619$	2.56434	−	7.89222i	0.103069	−	0.317215i	0.989273	+	0.146082i	$0.0466663\pi$
$620$	−1.72979	−	5.32374i	−0.0694700	−	0.213807i
$621$	12.0796			0.484738
$622$	−1.66781	−	5.13298i	−0.0668730	−	0.205814i
$623$	−11.5602			−0.463148
$624$	0.540783			0.0216486
$625$	−1.21360	−	3.73509i	−0.0485441	−	0.149403i
$626$	21.3349	+	15.5007i	0.852716	+	0.619534i
$627$	0.405254	−	1.24724i	0.0161843	−	0.0498101i
$628$	5.58937	+	17.2023i	0.223040	+	0.686447i
$629$	−4.98642	+	3.62285i	−0.198822	+	0.144452i
$630$	10.0907	+	7.33133i	0.402024	+	0.292087i
$631$	−32.5113			−1.29425			−0.647127	−	0.762382i	$-0.724030\pi$
$631$	−32.5113			−1.29425			−0.647127	+	0.762382i	$0.724030\pi$
$632$	30.1155	−	21.8802i	1.19793	−	0.870347i
$633$	1.51406	−	4.65981i	0.0601786	−	0.185211i
$634$	−5.51093	−	4.00393i	−0.218867	−	0.159016i
$635$	17.6710	+	12.8387i	0.701253	+	0.509490i
$636$	2.56522	−	1.86374i	0.101718	−	0.0739022i
$637$	−6.45043	−	19.8524i	−0.255576	−	0.786581i
$638$	−4.20333	+	3.05390i	−0.166411	+	0.120905i
$639$	−9.87492			−0.390646
$640$	−7.56892	−	5.49914i	−0.299188	−	0.217373i
$641$	15.4868	+	11.2518i	0.611692	+	0.444421i	0.850010	−	0.526767i	$-0.176596\pi$
$641$	15.4868	+	11.2518i	0.611692	+	0.444421i	−0.238317	+	0.971187i	$0.576596\pi$
$642$	−7.64171			−0.301594
$643$	−19.2573	+	13.9912i	−0.759434	+	0.551761i	−0.898737	−	0.438489i	$-0.855514\pi$
$643$	−19.2573	+	13.9912i	−0.759434	+	0.551761i	0.139303	+	0.990250i	$0.455514\pi$
$644$	−5.34077	−	16.4372i	−0.210456	−	0.647717i
$645$	−4.01599	+	2.91779i	−0.158129	+	0.114888i
$646$	4.33256	+	3.14779i	0.170462	+	0.123848i
$647$	16.3821	+	11.9023i	0.644047	+	0.467928i	0.861238	−	0.508201i	$-0.169689\pi$
$647$	16.3821	+	11.9023i	0.644047	+	0.467928i	−0.217191	+	0.976129i	$0.569689\pi$
$648$	6.22864	−	19.1698i	0.244684	−	0.753060i
$649$	−1.65351	+	1.20134i	−0.0649059	+	0.0471569i
$650$	−12.9959			−0.509741
$651$	3.98110	+	2.89244i	0.156032	+	0.113364i
$652$	−10.9399	+	7.94830i	−0.428439	+	0.311279i
$653$	11.9013	+	36.6284i	0.465733	+	1.43338i	0.858058	+	0.513553i	$0.171671\pi$
$653$	11.9013	+	36.6284i	0.465733	+	1.43338i	−0.392325	+	0.919827i	$0.628329\pi$
$654$	−2.73461	+	8.41626i	−0.106932	+	0.329102i
$655$	−6.69743	−	4.86597i	−0.261690	−	0.190129i
$656$	0.332400	+	1.02302i	0.0129780	+	0.0399423i
$657$	22.9394			0.894952
$658$	5.22908			0.203851
$659$	−6.51177	−	20.0412i	−0.253663	−	0.780693i	−0.994090	−	0.108557i	$-0.965377\pi$
$659$	−6.51177	−	20.0412i	−0.253663	−	0.780693i	0.740428	−	0.672136i	$-0.234623\pi$
$660$	0.851461			0.0331431
$661$	−4.49235	−	13.8260i	−0.174732	−	0.537770i	0.824889	−	0.565295i	$-0.191238\pi$
$661$	−4.49235	−	13.8260i	−0.174732	−	0.537770i	−0.999621	+	0.0275244i	$0.991238\pi$
$662$	0.908412	−	2.79580i	0.0353064	−	0.108662i
$663$	1.67417	+	5.15257i	0.0650194	+	0.200109i
$664$	−7.14859	−	5.19375i	−0.277419	−	0.201557i
$665$	4.25042	−	13.0814i	0.164824	−	0.507276i
$666$	−2.21021	+	6.80234i	−0.0856440	+	0.263585i
$667$	−7.83471	+	24.1128i	−0.303361	+	0.933650i
$668$	10.0758	−	7.32049i	0.389844	−	0.283238i
$669$	−0.857938	+	0.623328i	−0.0331698	+	0.0240993i
$670$	−17.7357			−0.685189
$671$	−6.88003	+	3.69665i	−0.265601	+	0.142707i
$672$	8.73840			0.337091
$673$	−9.05127	+	6.57613i	−0.348901	+	0.253491i	−0.748408	−	0.663239i	$-0.769181\pi$
$673$	−9.05127	+	6.57613i	−0.348901	+	0.253491i	0.399507	+	0.916730i	$0.369181\pi$
$674$	−0.335930	+	0.244067i	−0.0129395	+	0.00940112i
$675$	2.31423	−	7.12248i	0.0890749	−	0.274144i
$676$	−5.48515	+	16.8816i	−0.210967	+	0.649290i
$677$	−15.4506	+	47.5520i	−0.593814	+	1.82757i	−0.0332724	+	0.999446i	$0.510593\pi$
$677$	−15.4506	+	47.5520i	−0.593814	+	1.82757i	−0.560542	+	0.828126i	$0.689407\pi$
$678$	6.10389	+	4.43474i	0.234419	+	0.170315i
$679$	−16.6250	−	51.1664i	−0.638008	−	1.96359i
$680$	−2.88415	+	8.87651i	−0.110602	+	0.340399i
$681$	−3.25044	−	10.0038i	−0.124557	−	0.383347i
$682$	2.81860			0.107930
$683$	2.12373	+	6.53618i	0.0812624	+	0.250100i	0.983431	−	0.181284i	$-0.0580254\pi$
$683$	2.12373	+	6.53618i	0.0812624	+	0.250100i	−0.902168	+	0.431384i	$0.858025\pi$
$684$	−9.08177			−0.347250
$685$	24.6500			0.941827
$686$	−2.81256	−	8.65618i	−0.107384	−	0.330494i
$687$	−4.25935	−	3.09460i	−0.162504	−	0.118066i
$688$	−0.460099	+	1.41604i	−0.0175411	+	0.0539859i
$689$	−9.17173	−	28.2277i	−0.349415	−	1.07539i
$690$	−2.30019	+	1.67119i	−0.0875669	+	0.0636210i
$691$	−39.2742	−	28.5344i	−1.49406	−	1.08550i	−0.972672	−	0.232182i	$-0.925414\pi$
$691$	−39.2742	−	28.5344i	−1.49406	−	1.08550i	−0.521390	−	0.853318i	$-0.674586\pi$
$692$	15.3516			0.583582
$693$	7.42518	−	5.39471i	0.282059	−	0.204928i
$694$	6.59270	−	20.2902i	0.250256	−	0.770207i
$695$	−12.9325	−	9.39599i	−0.490557	−	0.356410i
$696$	−6.37232	−	4.62976i	−0.241542	−	0.175491i
$697$	−8.71827	+	6.33419i	−0.330228	+	0.239925i
$698$	−7.10742	−	21.8744i	−0.269020	−	0.827957i
$699$	0.907815	−	0.659566i	0.0343367	−	0.0249471i
$700$	−10.7151			−0.404991
$701$	−26.2677	−	19.0846i	−0.992119	−	0.720817i	−0.0317349	−	0.999496i	$-0.510103\pi$
$701$	−26.2677	−	19.0846i	−0.992119	−	0.720817i	−0.960384	+	0.278680i	$0.910103\pi$
$702$	10.5872	+	7.69208i	0.399590	+	0.290319i
$703$	7.88745			0.297481
$704$	4.39727	−	3.19480i	0.165728	−	0.120409i
$705$	0.388469	+	1.19558i	0.0146306	+	0.0450283i
$706$	−22.5701	+	16.3982i	−0.849438	+	0.617153i
$707$	−23.8202	−	17.3064i	−0.895852	−	0.650874i
$708$	−0.933861	−	0.678490i	−0.0350967	−	0.0254992i
$709$	12.6350	−	38.8866i	0.474518	−	1.46042i	−0.372089	−	0.928197i	$-0.621358\pi$
$709$	12.6350	−	38.8866i	0.474518	−	1.46042i	0.846607	−	0.532219i	$-0.178642\pi$
$710$	3.91411	−	2.84377i	0.146894	−	0.106725i
$711$	35.9365			1.34773
$712$	−8.12107	−	5.90030i	−0.304350	−	0.221123i
$713$	11.1274	−	8.08456i	0.416726	−	0.302769i
$714$	−0.944549	−	2.90702i	−0.0353488	−	0.108793i
$715$	2.46291	−	7.58007i	0.0921077	−	0.283478i
$716$	−2.95241	−	2.14505i	−0.110337	−	0.0801642i
$717$	−0.385657	−	1.18693i	−0.0144026	−	0.0443268i
$718$	12.5944			0.470018
$719$	32.9996			1.23068			0.615339	−	0.788263i	$-0.289019\pi$
$719$	32.9996			1.23068			0.615339	+	0.788263i	$0.289019\pi$
$720$	0.277925	+	0.855366i	0.0103577	+	0.0318776i
$721$	34.8135			1.29652
$722$	3.17476	+	9.77090i	0.118152	+	0.363635i
$723$	−1.05652	+	3.25163i	−0.0392924	+	0.120929i
$724$	−7.06009	−	21.7287i	−0.262386	−	0.807542i
$725$	12.7166	+	9.23914i	0.472282	+	0.343133i
$726$	−0.132486	+	0.407749i	−0.00491701	+	0.0151330i
$727$	−9.52757	+	29.3228i	−0.353358	+	1.08752i	0.603598	+	0.797289i	$0.293733\pi$
$727$	−9.52757	+	29.3228i	−0.353358	+	1.08752i	−0.956955	+	0.290235i	$0.906267\pi$
$728$	15.5312	−	47.8002i	0.575625	−	1.77159i
$729$	12.5724	−	9.13440i	0.465646	−	0.338311i
$730$	−9.09248	+	6.60607i	−0.336528	+	0.244502i
$731$	−14.9164			−0.551701
$732$	−3.18633	−	3.05034i	−0.117770	−	0.112744i
$733$	7.38610			0.272812			0.136406	−	0.990653i	$-0.456445\pi$
$733$	7.38610			0.272812			0.136406	+	0.990653i	$0.456445\pi$
$734$	9.39049	−	6.82259i	0.346609	−	0.251826i
$735$	−2.29054	+	1.66417i	−0.0844877	+	0.0613839i
$736$	7.54757	−	23.2290i	0.278207	−	0.856233i
$737$	−4.03288	+	12.4119i	−0.148553	+	0.457200i
$738$	−3.86434	+	11.8932i	−0.142248	+	0.437795i
$739$	−18.3253	−	13.3141i	−0.674106	−	0.489767i	0.197291	−	0.980345i	$-0.436786\pi$
$739$	−18.3253	−	13.3141i	−0.674106	−	0.489767i	−0.871397	+	0.490578i	$0.836786\pi$
$740$	1.58248	+	4.87039i	0.0581733	+	0.179039i
$741$	2.14242	−	6.59369i	0.0787038	−	0.242225i
$742$	5.17459	+	15.9258i	0.189965	+	0.584653i
$743$	−42.0158			−1.54141			−0.770705	−	0.637192i	$-0.780096\pi$
$743$	−42.0158			−1.54141			−0.770705	+	0.637192i	$0.780096\pi$
$744$	1.32044	+	4.06391i	0.0484098	+	0.148990i
$745$	−11.1260			−0.407624
$746$	−7.60391			−0.278399
$747$	−2.63602	−	8.11284i	−0.0964470	−	0.296833i
$748$	2.06990	+	1.50387i	0.0756832	+	0.0549871i
$749$	−18.2248	+	56.0901i	−0.665919	+	2.04949i
$750$	1.54339	+	4.75007i	0.0563566	+	0.173448i
$751$	−2.84472	+	2.06681i	−0.103805	+	0.0754190i	−0.638477	−	0.769641i	$-0.720435\pi$
$751$	−2.84472	+	2.06681i	−0.103805	+	0.0754190i	0.534672	+	0.845060i	$0.320435\pi$
$752$	0.305046	+	0.221629i	0.0111239	+	0.00808196i
$753$	−12.1073			−0.441215
$754$	−22.2214	+	16.1448i	−0.809255	+	0.587958i
$755$	−6.00067	+	18.4682i	−0.218387	+	0.672126i
$756$	8.72913	+	6.34208i	0.317475	+	0.230659i
$757$	1.33821	+	0.972263i	0.0486379	+	0.0353375i	0.611839	−	0.790983i	$-0.290430\pi$
$757$	1.33821	+	0.972263i	0.0486379	+	0.0353375i	−0.563201	+	0.826320i	$0.690430\pi$
$758$	12.5582	−	9.12404i	0.456133	−	0.331400i
$759$	0.646509	+	1.98975i	0.0234668	+	0.0722233i
$760$	9.66271	−	7.02037i	0.350503	−	0.254656i
$761$	23.3450			0.846254			0.423127	−	0.906070i	$-0.360932\pi$
$761$	23.3450			0.846254			0.423127	+	0.906070i	$0.360932\pi$
$762$	−5.02527	−	3.65107i	−0.182046	−	0.132264i
$763$	55.2535	+	40.1440i	2.00031	+	1.45331i
$764$	−15.3464			−0.555212
$765$	−7.28950	+	5.29613i	−0.263552	+	0.191482i
$766$	−1.64360	−	5.05849i	−0.0593857	−	0.182770i
$767$	−8.74146	+	6.35104i	−0.315636	+	0.229323i
$768$	6.33531	+	4.60287i	0.228606	+	0.166092i
$769$	3.69697	+	2.68600i	0.133316	+	0.0968598i	0.652445	−	0.757836i	$-0.273743\pi$
$769$	3.69697	+	2.68600i	0.133316	+	0.0968598i	−0.519129	+	0.854696i	$0.673743\pi$
$770$	−1.38955	+	4.27659i	−0.0500759	+	0.154118i
$771$	−8.85374	+	6.43262i	−0.318859	+	0.231665i
$772$	22.1986			0.798946
$773$	28.5800	+	20.7646i	1.02795	+	0.746851i	0.967898	−	0.251344i	$-0.0808724\pi$
$773$	28.5800	+	20.7646i	1.02795	+	0.746851i	0.0600550	+	0.998195i	$0.480872\pi$
$774$	−14.0036	+	10.1742i	−0.503350	+	0.365705i
$775$	−2.63507	−	8.10992i	−0.0946546	−	0.291317i
$776$	14.4362	−	44.4301i	0.518230	−	1.59495i
$777$	−3.64208	−	2.64612i	−0.130659	−	0.0949292i
$778$	−2.02906	−	6.24479i	−0.0727452	−	0.223887i
$779$	13.7904			0.494094
$780$	4.50135			0.161174
$781$	−1.10013	−	3.38585i	−0.0393657	−	0.121155i
$782$	−8.54347			−0.305514
$783$	−4.89119	−	15.0535i	−0.174797	−	0.537969i
$784$	−0.262419	+	0.807643i	−0.00937211	+	0.0288444i
$785$	−7.09639	−	21.8404i	−0.253281	−	0.779519i
$786$	1.90461	+	1.38378i	0.0679352	+	0.0493578i
$787$	15.6491	−	48.1630i	0.557830	−	1.71683i	−0.130519	−	0.991446i	$-0.541664\pi$
$787$	15.6491	−	48.1630i	0.557830	−	1.71683i	0.688349	−	0.725379i	$-0.258336\pi$
$788$	−6.42769	+	19.7824i	−0.228977	+	0.704719i
$789$	3.27483	−	10.0789i	0.116587	−	0.358818i
$790$	−14.2441	+	10.3490i	−0.506783	+	0.368200i
$791$	47.1082	−	34.2261i	1.67497	−	1.21694i
$792$	7.96969			0.283191
$793$	−36.3721	+	19.5427i	−1.29161	+	0.693983i
$794$	31.0146			1.10067
$795$	−3.25686	+	2.36625i	−0.115509	+	0.0839222i
$796$	2.30526	−	1.67487i	0.0817079	−	0.0593643i
$797$	2.57199	−	7.91576i	0.0911044	−	0.280391i	−0.895114	−	0.445836i	$-0.852906\pi$
$797$	2.57199	−	7.91576i	0.0911044	−	0.280391i	0.986219	+	0.165446i	$0.0529063\pi$
$798$	−1.20873	+	3.72009i	−0.0427886	+	0.131690i
$799$	−1.16730	+	3.59259i	−0.0412962	+	0.127097i
$800$	−12.2505	−	8.90052i	−0.433121	−	0.314681i
$801$	−2.99462	−	9.21649i	−0.105810	−	0.325649i
$802$	5.21114	−	16.0382i	0.184012	−	0.566330i
$803$	2.55560	+	7.86532i	0.0901850	+	0.277561i
$804$	−7.37071			−0.259945
$805$	6.78077	+	20.8691i	0.238991	+	0.735537i
$806$	14.9008			0.524859
$807$	4.42842			0.155888
$808$	−7.90064	−	24.3157i	−0.277944	−	0.855423i
$809$	−11.9759	−	8.70098i	−0.421049	−	0.305910i	0.357011	−	0.934100i	$-0.383796\pi$
$809$	−11.9759	−	8.70098i	−0.421049	−	0.305910i	−0.778060	+	0.628190i	$0.783796\pi$
$810$	−2.94604	+	9.06699i	−0.103513	+	0.318581i
$811$	−12.4369	−	38.2767i	−0.436717	−	1.34408i	−0.891316	−	0.453382i	$-0.850217\pi$
$811$	−12.4369	−	38.2767i	−0.436717	−	1.34408i	0.454599	−	0.890696i	$-0.349783\pi$
$812$	−18.3214	+	13.3113i	−0.642955	+	0.467134i
$813$	3.32209	+	2.41364i	0.116511	+	0.0846501i
$814$	−2.57857			−0.0903789
$815$	13.8895	−	10.0913i	0.486529	−	0.353484i
$816$	0.0681092	−	0.209619i	0.00238430	−	0.00733812i
$817$	15.4428	+	11.2198i	0.540275	+	0.392532i
$818$	−13.2318	−	9.61344i	−0.462638	−	0.336126i
$819$	39.2541	−	28.5198i	1.37165	−	0.996561i
$820$	2.76682	+	8.51539i	0.0966215	+	0.297370i
$821$	−40.1516	+	29.1718i	−1.40130	+	1.01810i	−0.406784	+	0.913524i	$0.633350\pi$
$821$	−40.1516	+	29.1718i	−1.40130	+	1.01810i	−0.994516	+	0.104580i	$0.966650\pi$
$822$	−7.00994			−0.244500
$823$	31.0269	+	22.5424i	1.08153	+	0.785778i	0.977949	−	0.208843i	$-0.0669697\pi$
$823$	31.0269	+	22.5424i	1.08153	+	0.785778i	0.103582	+	0.994621i	$0.466970\pi$
$824$	24.4567	+	17.7688i	0.851989	+	0.619006i
$825$	1.29707			0.0451583
$826$	4.93184	−	3.58319i	0.171601	−	0.124675i
$827$	−9.76698	−	30.0597i	−0.339631	−	1.04528i	−0.964396	−	0.264464i	$-0.914805\pi$
$827$	−9.76698	−	30.0597i	−0.339631	−	1.04528i	0.624765	−	0.780813i	$-0.285195\pi$
$828$	11.7213	−	8.51602i	0.407343	−	0.295952i
$829$	17.7247	+	12.8778i	0.615605	+	0.447263i	0.851384	−	0.524543i	$-0.175764\pi$
$829$	17.7247	+	12.8778i	0.615605	+	0.447263i	−0.235778	+	0.971807i	$0.575764\pi$
$830$	3.38116	+	2.45656i	0.117362	+	0.0852684i
$831$	−4.80265	+	14.7810i	−0.166602	+	0.512748i
$832$	23.2467	−	16.8897i	0.805933	−	0.585545i
$833$	−8.50760			−0.294771
$834$	3.67773	+	2.67203i	0.127349	+	0.0925247i
$835$	−12.7924	+	9.29426i	−0.442701	+	0.321641i
$836$	−1.01177	−	3.11390i	−0.0349927	−	0.107696i
$837$	−2.65345	+	8.16649i	−0.0917168	+	0.282275i
$838$	0.859421	+	0.624406i	0.0296882	+	0.0215698i
$839$	−9.90727	−	30.4914i	−0.342037	−	1.05268i	−0.963151	−	0.268961i	$-0.913320\pi$
$839$	−9.90727	−	30.4914i	−0.342037	−	1.05268i	0.621114	−	0.783720i	$-0.286680\pi$
$840$	−6.81704			−0.235210
$841$	4.22155			0.145571
$842$	−1.39522	−	4.29406i	−0.0480826	−	0.147983i
$843$	13.0211			0.448471
$844$	−3.78005	−	11.6338i	−0.130115	−	0.400452i
$845$	6.96407	−	21.4332i	0.239571	−	0.737324i
$846$	1.35458	+	4.16896i	0.0465713	+	0.143332i
$847$	2.67691	+	1.94489i	0.0919798	+	0.0668273i
$848$	−0.373128	+	1.14837i	−0.0128133	+	0.0394352i
$849$	1.89628	−	5.83616i	0.0650803	−	0.200297i
$850$	−1.63678	+	5.03748i	−0.0561409	+	0.172784i
$851$	−10.1799	+	7.39610i	−0.348961	+	0.253535i
$852$	1.62665	−	1.18183i	0.0557281	−	0.0404889i
$853$	11.5305			0.394797			0.197399	−	0.980323i	$-0.436751\pi$
$853$	11.5305			0.394797			0.197399	+	0.980323i	$0.436751\pi$
$854$	20.5207	−	11.0258i	0.702205	−	0.377295i
$855$	11.5304			0.394332
$856$	−41.4314	+	30.1017i	−1.41610	+	1.02885i
$857$	−9.51475	+	6.91287i	−0.325018	+	0.236139i	−0.738314	−	0.674458i	$-0.764378\pi$
$857$	−9.51475	+	6.91287i	−0.325018	+	0.236139i	0.413296	+	0.910597i	$0.364378\pi$
$858$	−0.700401	+	2.15561i	−0.0239113	+	0.0735914i
$859$	−4.60204	+	14.1636i	−0.157020	+	0.483256i	−0.998360	−	0.0572492i	$-0.981767\pi$
$859$	−4.60204	+	14.1636i	−0.157020	+	0.483256i	0.841340	+	0.540506i	$0.181767\pi$
$860$	−3.82975	+	11.7868i	−0.130593	+	0.401925i
$861$	−6.36781	−	4.62649i	−0.217015	−	0.157670i
$862$	1.33446	+	4.10704i	0.0454518	+	0.139886i
$863$	0.0605427	−	0.186331i	0.00206090	−	0.00634279i	−0.950021	−	0.312187i	$-0.898939\pi$
$863$	0.0605427	−	0.186331i	0.00206090	−	0.00634279i	0.952082	+	0.305844i	$0.0989386\pi$
$864$	4.71192	+	14.5018i	0.160303	+	0.493362i
$865$	−19.4908			−0.662707
$866$	1.45987	+	4.49301i	0.0496084	+	0.152679i
$867$	−5.87747			−0.199609
$868$	12.2857			0.417002
$869$	4.00355	+	12.3217i	0.135811	+	0.417984i
$870$	3.01400	+	2.18980i	0.102184	+	0.0742412i
$871$	−21.3203	+	65.6171i	−0.722411	+	2.22335i
$872$	18.3264	+	56.4028i	0.620610	+	1.91004i
$873$	36.4865	−	26.5090i	1.23488	−	0.897194i
$874$	8.84499	+	6.42626i	0.299186	+	0.217372i
$875$	38.5463			1.30310
$876$	−3.77871	+	2.74539i	−0.127671	+	0.0927582i
$877$	16.9775	−	52.2514i	0.573290	−	1.76441i	−0.0686392	−	0.997642i	$-0.521866\pi$
$877$	16.9775	−	52.2514i	0.573290	−	1.76441i	0.641929	−	0.766764i	$-0.278134\pi$
$878$	−1.04621	−	0.760116i	−0.0353079	−	0.0256527i
$879$	−2.41567	−	1.75509i	−0.0814785	−	0.0591976i
$880$	−0.262320	+	0.190586i	−0.00884279	+	0.00642466i
$881$	1.61385	+	4.96691i	0.0543718	+	0.167339i	0.974555	−	0.224149i	$-0.0719603\pi$
$881$	1.61385	+	4.96691i	0.0543718	+	0.167339i	−0.920183	+	0.391488i	$0.871960\pi$
$882$	−7.98702	+	5.80291i	−0.268937	+	0.195394i
$883$	−44.4786			−1.49682			−0.748412	−	0.663235i	$-0.769183\pi$
$883$	−44.4786			−1.49682			−0.748412	+	0.663235i	$0.769183\pi$
$884$	10.9428	+	7.95040i	0.368046	+	0.267401i
$885$	1.18565	+	0.861426i	0.0398552	+	0.0289565i
$886$	−14.0978			−0.473624
$887$	−18.1203	+	13.1652i	−0.608420	+	0.442043i	−0.848858	−	0.528621i	$-0.822709\pi$
$887$	−18.1203	+	13.1652i	−0.608420	+	0.442043i	0.240437	+	0.970665i	$0.422709\pi$
$888$	−1.20800	−	3.71783i	−0.0405377	−	0.124762i
$889$	−38.7837	+	28.1780i	−1.30076	+	0.945060i
$890$	3.84113	+	2.79074i	0.128755	+	0.0935460i
$891$	5.67544	+	4.12345i	0.190134	+	0.138141i
$892$	−0.818151	+	2.51801i	−0.0273937	+	0.0843092i
$893$	3.91079	−	2.84135i	0.130869	−	0.0950822i
$894$	3.16400			0.105820
$895$	3.74844	+	2.72340i	0.125297	+	0.0910333i
$896$	16.6120	−	12.0693i	0.554967	−	0.403207i
$897$	3.41784	+	10.5190i	0.114118	+	0.351220i
$898$	−1.01203	+	3.11472i	−0.0337720	+	0.103939i
$899$	−14.5806	−	10.5934i	−0.486290	−	0.353310i
$900$	−2.77570	−	8.54273i	−0.0925233	−	0.284758i
$901$	−12.0968			−0.403002
$902$	−4.50838			−0.150113
$903$	−3.36670	−	10.3617i	−0.112037	−	0.344814i
$904$	50.5628			1.68169
$905$	8.96365	+	27.5873i	0.297962	+	0.917032i
$906$	1.70647	−	5.25197i	0.0566936	−	0.174485i
$907$	2.52782	+	7.77982i	0.0839348	+	0.258325i	0.984212	−	0.176992i	$-0.0566366\pi$
$907$	2.52782	+	7.77982i	0.0839348	+	0.258325i	−0.900278	+	0.435316i	$0.856637\pi$
$908$	−21.2457	−	15.4359i	−0.705062	−	0.512258i
$909$	7.62722	−	23.4742i	0.252979	−	0.778589i
$910$	−7.34601	+	22.6087i	−0.243518	+	0.749471i
$911$	−1.65284	+	5.08692i	−0.0547610	+	0.168537i	−0.974696	−	0.223533i	$-0.928241\pi$
$911$	−1.65284	+	5.08692i	−0.0547610	+	0.168537i	0.919935	+	0.392070i	$0.128241\pi$
$912$	−0.228185	+	0.165786i	−0.00755595	+	0.00548972i
$913$	2.48801	−	1.80764i	0.0823410	−	0.0598243i
$914$	23.0131			0.761207
$915$	4.04544	+	3.87277i	0.133738	+	0.128030i
$916$	−13.1443			−0.434302
$917$	14.6993	−	10.6796i	0.485413	−	0.352673i
$918$	4.31503	−	3.13505i	0.142417	−	0.103472i
$919$	−8.76015	+	26.9610i	−0.288971	+	0.889360i	0.696210	+	0.717838i	$0.254868\pi$
$919$	−8.76015	+	26.9610i	−0.288971	+	0.889360i	−0.985180	+	0.171522i	$0.945132\pi$
$920$	−5.88804	+	18.1215i	−0.194123	+	0.597449i
$921$	3.10982	−	9.57105i	0.102472	−	0.315377i
$922$	−10.6795	−	7.75913i	−0.351712	−	0.255533i
$923$	−5.81595	−	17.8997i	−0.191434	−	0.589174i
$924$	−0.577477	+	1.77729i	−0.0189976	+	0.0584686i
$925$	2.41068	+	7.41930i	0.0792625	+	0.243945i
$926$	8.24975			0.271104
$927$	9.01833	+	27.7556i	0.296201	+	0.911612i
$928$	−32.0040			−1.05058
$929$	18.0911			0.593550			0.296775	−	0.954947i	$-0.404089\pi$
$929$	18.0911			0.593550			0.296775	+	0.954947i	$0.404089\pi$
$930$	−0.624548	−	1.92216i	−0.0204797	−	0.0630301i
$931$	8.80785	+	6.39928i	0.288666	+	0.209728i
$932$	0.865715	−	2.66440i	0.0283574	−	0.0872752i
$933$	0.879998	+	2.70835i	0.0288098	+	0.0886675i
$934$	2.08548	−	1.51519i	0.0682390	−	0.0495785i
$935$	−2.62800	−	1.90935i	−0.0859447	−	0.0624425i
$936$	42.1327			1.37715
$937$	−34.3196	+	24.9346i	−1.12117	+	0.814579i	−0.984386	−	0.176022i	$-0.943677\pi$
$937$	−34.3196	+	24.9346i	−1.12117	+	0.814579i	−0.136786	+	0.990601i	$0.543677\pi$
$938$	12.0287	−	37.0205i	0.392750	−	1.20876i
$939$	−11.2571	−	8.17878i	−0.367362	−	0.266904i
$940$	2.53913	+	1.84478i	0.0828172	+	0.0601702i
$941$	−10.8661	+	7.89470i	−0.354226	+	0.257360i	−0.750640	−	0.660712i	$-0.770254\pi$
$941$	−10.8661	+	7.89470i	−0.354226	+	0.257360i	0.396414	+	0.918072i	$0.370254\pi$
$942$	2.01807	+	6.21097i	0.0657521	+	0.202364i
$943$	−17.7985	+	12.9313i	−0.579598	+	0.421103i
$944$	0.439575			0.0143069
$945$	−11.0827	−	8.05205i	−0.360520	−	0.261933i
$946$	−5.04856	−	3.66800i	−0.164143	−	0.119257i
$947$	−37.8336			−1.22943			−0.614713	−	0.788751i	$-0.710728\pi$
$947$	−37.8336			−1.22943			−0.614713	+	0.788751i	$0.710728\pi$
$948$	−5.91966	+	4.30089i	−0.192262	+	0.139686i
$949$	13.5105	+	41.5809i	0.438568	+	1.34977i
$950$	5.48365	−	3.98410i	0.177913	−	0.129261i
$951$	2.90778	+	2.11262i	0.0942911	+	0.0685065i
$952$	−16.5722	−	12.0404i	−0.537109	−	0.390233i
$953$	−10.4085	+	32.0342i	−0.337165	+	1.03769i	0.628480	+	0.777826i	$0.283677\pi$
$953$	−10.4085	+	32.0342i	−0.337165	+	1.03769i	−0.965646	+	0.259863i	$0.916323\pi$
$954$	−11.3566	+	8.25103i	−0.367683	+	0.267137i
$955$	19.4841			0.630490
$956$	−2.52075	−	1.83143i	−0.0815269	−	0.0592328i
$957$	2.21783	−	1.61135i	0.0716924	−	0.0520876i
$958$	−0.515388	−	1.58620i	−0.0166514	−	0.0512479i
$959$	−16.7181	+	51.4530i	−0.539855	+	1.66150i
$960$	−3.15307	−	2.29084i	−0.101765	−	0.0739365i
$961$	−6.55821	−	20.1841i	−0.211555	−	0.651100i
$962$	−13.6319			−0.439510
$963$	−49.4397			−1.59317
$964$	2.63773	+	8.11810i	0.0849556	+	0.261466i
$965$	−28.1839			−0.907271
$966$	−1.92831	−	5.93473i	−0.0620423	−	0.190947i
$967$	1.59709	−	4.91535i	0.0513590	−	0.158067i	−0.922087	−	0.386982i	$-0.873518\pi$
$967$	1.59709	−	4.91535i	0.0513590	−	0.158067i	0.973446	+	0.228915i	$0.0735177\pi$
$968$	0.887873	+	2.73259i	0.0285373	+	0.0878289i
$969$	−2.28602	−	1.66089i	−0.0734377	−	0.0533556i
$970$	−6.82809	+	21.0147i	−0.219237	+	0.674741i
$971$	11.4048	−	35.1004i	0.365998	−	1.12643i	−0.583356	−	0.812217i	$-0.698261\pi$
$971$	11.4048	−	35.1004i	0.365998	−	1.12643i	0.949354	−	0.314209i	$-0.101739\pi$
$972$	−4.24735	+	13.0720i	−0.136234	+	0.419284i
$973$	28.3837	−	20.6220i	0.909940	−	0.661110i
$974$	−2.92223	+	2.12312i	−0.0936342	+	0.0680292i
$975$	6.85712			0.219604
$976$	1.66442	+	0.226542i	0.0532768	+	0.00725143i
$977$	23.7020			0.758294			0.379147	−	0.925336i	$-0.376218\pi$
$977$	23.7020			0.758294			0.379147	+	0.925336i	$0.376218\pi$
$978$	−3.94990	+	2.86977i	−0.126304	+	0.0917651i
$979$	2.82647	−	2.05355i	0.0903344	−	0.0656318i
$980$	−2.18431	+	6.72262i	−0.0697753	+	0.214746i
$981$	−17.6922	+	54.4509i	−0.564867	+	1.73848i
$982$	−11.0278	+	33.9401i	−0.351912	+	1.08307i
$983$	29.9421	+	21.7542i	0.955006	+	0.693852i	0.951986	−	0.306143i	$-0.0990386\pi$
$983$	29.9421	+	21.7542i	0.955006	+	0.693852i	0.00302043	+	0.999995i	$0.499039\pi$
$984$	−2.11206	−	6.50026i	−0.0673301	−	0.207221i
$985$	8.16074	−	25.1162i	0.260023	−	0.800268i
$986$	3.45936	+	10.6468i	0.110169	+	0.339064i
$987$	−2.75906			−0.0878218
$988$	−5.34882	−	16.4620i	−0.170169	−	0.523725i
$989$	−30.4519			−0.968316
$990$	−3.76953			−0.119804
$991$	4.09585	+	12.6057i	0.130109	+	0.400434i	0.994797	−	0.101875i	$-0.0324840\pi$
$991$	4.09585	+	12.6057i	0.130109	+	0.400434i	−0.864688	+	0.502309i	$0.832484\pi$
$992$	14.0462	+	10.2052i	0.445967	+	0.324014i
$993$	−0.479312	+	1.47517i	−0.0152105	+	0.0468132i
$994$	3.28130	+	10.0988i	0.104076	+	0.320314i
$995$	−2.92682	+	2.12646i	−0.0927863	+	0.0674132i
$996$	1.40517	+	1.02091i	0.0445244	+	0.0323489i
$997$	14.2731			0.452034			0.226017	−	0.974123i	$-0.427429\pi$
$997$	14.2731			0.452034			0.226017	+	0.974123i	$0.427429\pi$
$998$	4.57739	−	3.32567i	0.144895	−	0.105272i
$999$	2.42749	−	7.47105i	0.0768024	−	0.236374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.i.b.34.18	✓	108
61.9	even	5	inner	671.2.i.b.375.18	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.i.b.34.18	✓	108	1.1	even	1	trivial
671.2.i.b.375.18	yes	108	61.9	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.729261 - 0.529839i) q^{2} +(-0.384786 + 0.279563i) q^{3} +(-0.366942 + 1.12933i) q^{4} +(0.465877 - 1.43382i) q^{5} +(-0.132486 + 0.407749i) q^{6} +(2.67691 + 1.94489i) q^{7} +(0.887873 + 2.73259i) q^{8} +(-0.857146 + 2.63803i) q^{9} +O(q^{10})\)	\(q+(0.729261 - 0.529839i) q^{2} +(-0.384786 + 0.279563i) q^{3} +(-0.366942 + 1.12933i) q^{4} +(0.465877 - 1.43382i) q^{5} +(-0.132486 + 0.407749i) q^{6} +(2.67691 + 1.94489i) q^{7} +(0.887873 + 2.73259i) q^{8} +(-0.857146 + 2.63803i) q^{9} +(-0.419949 - 1.29247i) q^{10} -1.00000 q^{11} +(-0.174525 - 0.537134i) q^{12} -5.28661 q^{13} +2.98265 q^{14} +(0.221581 + 0.681957i) q^{15} +(0.173997 + 0.126416i) q^{16} +(-0.665826 + 2.04920i) q^{17} +(0.772646 + 2.37796i) q^{18} +(2.23070 - 1.62070i) q^{19} +(1.44831 + 1.05226i) q^{20} -1.57376 q^{21} +(-0.729261 + 0.529839i) q^{22} +(-1.35929 + 4.18347i) q^{23} +(-1.10557 - 0.803246i) q^{24} +(2.20628 + 1.60296i) q^{25} +(-3.85532 + 2.80106i) q^{26} +(-0.848603 - 2.61173i) q^{27} +(-3.17870 + 2.30946i) q^{28} +5.76381 q^{29} +(0.522918 + 0.379922i) q^{30} +(-2.52968 - 1.83792i) q^{31} -5.55257 q^{32} +(0.384786 - 0.279563i) q^{33} +(0.600186 + 1.84718i) q^{34} +(4.03574 - 2.93214i) q^{35} +(-2.66468 - 1.93600i) q^{36} +(2.31425 + 1.68140i) q^{37} +(0.768053 - 2.36383i) q^{38} +(2.03421 - 1.47794i) q^{39} +4.33169 q^{40} +(4.04625 + 2.93977i) q^{41} +(-1.14768 + 0.833839i) q^{42} +(2.13928 + 6.58401i) q^{43} +(0.366942 - 1.12933i) q^{44} +(3.38314 + 2.45799i) q^{45} +(1.22529 + 3.77105i) q^{46} +1.75317 q^{47} -0.102293 q^{48} +(1.22014 + 3.75522i) q^{49} +2.45826 q^{50} +(-0.316681 - 0.974644i) q^{51} +(1.93988 - 5.97033i) q^{52} +(1.73490 + 5.33946i) q^{53} +(-2.00265 - 1.45501i) q^{54} +(-0.465877 + 1.43382i) q^{55} +(-2.93784 + 9.04174i) q^{56} +(-0.405254 + 1.24724i) q^{57} +(4.20333 - 3.05390i) q^{58} +(1.65351 - 1.20134i) q^{59} -0.851461 q^{60} +(6.88003 - 3.69665i) q^{61} -2.81860 q^{62} +(-7.42518 + 5.39471i) q^{63} +(-4.39727 + 3.19480i) q^{64} +(-2.46291 + 7.58007i) q^{65} +(0.132486 - 0.407749i) q^{66} +(4.03288 - 12.4119i) q^{67} +(-2.06990 - 1.50387i) q^{68} +(-0.646509 - 1.98975i) q^{69} +(1.38955 - 4.27659i) q^{70} +(1.10013 + 3.38585i) q^{71} -7.96969 q^{72} +(-2.55560 - 7.86532i) q^{73} +2.57857 q^{74} -1.29707 q^{75} +(1.01177 + 3.11390i) q^{76} +(-2.67691 - 1.94489i) q^{77} +(0.700401 - 2.15561i) q^{78} +(-4.00355 - 12.3217i) q^{79} +(0.262320 - 0.190586i) q^{80} +(-5.67544 - 4.12345i) q^{81} +4.50838 q^{82} +(-2.48801 + 1.80764i) q^{83} +(0.577477 - 1.77729i) q^{84} +(2.62800 + 1.90935i) q^{85} +(5.04856 + 3.66800i) q^{86} +(-2.21783 + 1.61135i) q^{87} +(-0.887873 - 2.73259i) q^{88} +(-2.82647 + 2.05355i) q^{89} +3.76953 q^{90} +(-14.1518 - 10.2819i) q^{91} +(-4.22574 - 3.07018i) q^{92} +1.48720 q^{93} +(1.27852 - 0.928897i) q^{94} +(-1.28456 - 3.95347i) q^{95} +(2.13655 - 1.55229i) q^{96} +(-13.1541 - 9.55698i) q^{97} +(2.87947 + 2.09206i) q^{98} +(0.857146 - 2.63803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

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