LMFDB - Embedded newform 154.2.f.e.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.1
Root			$-0.357358 - 1.86824i$ of defining polynomial
Character	$\chi$	$=$	154.15
Dual form			154.2.f.e.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.02988 + 3.16963i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.47539 - 1.79848i) q^{5} +(-2.69625 + 1.95894i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.55888 - 4.76530i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.02988 + 3.16963i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.47539 - 1.79848i) q^{5} +(-2.69625 + 1.95894i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.55888 - 4.76530i) q^{9} +3.05975 q^{10} +(-2.60809 - 2.04887i) q^{11} -3.33275 q^{12} +(1.62656 + 1.18176i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(3.15117 + 9.69829i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.13182 - 2.27540i) q^{17} +(-2.50527 - 7.71042i) q^{18} +(0.0995695 - 0.306444i) q^{19} +(2.47539 + 1.79848i) q^{20} -3.33275 q^{21} +(-0.905698 - 3.19057i) q^{22} +0.774467 q^{23} +(-2.69625 - 1.95894i) q^{24} +(1.34796 - 4.14859i) q^{25} +(0.621290 + 1.91213i) q^{26} +(13.7703 - 10.0047i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(0.0934255 + 0.287534i) q^{29} +(-3.15117 + 9.69829i) q^{30} +(3.86263 + 2.80636i) q^{31} -1.00000 q^{32} +(9.18017 - 6.15662i) q^{33} +3.87115 q^{34} +(2.47539 + 1.79848i) q^{35} +(2.50527 - 7.71042i) q^{36} +(-1.66023 - 5.10966i) q^{37} +(0.260676 - 0.189393i) q^{38} +(-5.42091 + 3.93852i) q^{39} +(0.945515 + 2.91000i) q^{40} +(-1.88723 + 5.80831i) q^{41} +(-2.69625 - 1.95894i) q^{42} -8.28353 q^{43} +(1.14264 - 3.11358i) q^{44} -24.8061 q^{45} +(0.626557 + 0.455220i) q^{46} +(0.376698 - 1.15936i) q^{47} +(-1.02988 - 3.16963i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.52900 - 2.56397i) q^{50} +(3.98680 + 12.2701i) q^{51} +(-0.621290 + 1.91213i) q^{52} +(2.52988 + 1.83806i) q^{53} +17.0211 q^{54} +(-10.1409 - 0.381150i) q^{55} -1.00000 q^{56} +(0.868769 + 0.631198i) q^{57} +(-0.0934255 + 0.287534i) q^{58} +(-4.16784 - 12.8273i) q^{59} +(-8.24986 + 5.99387i) q^{60} +(-9.57408 + 6.95598i) q^{61} +(1.47539 + 4.54079i) q^{62} +(2.50527 - 7.71042i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.15174 q^{65} +(11.0457 + 0.415157i) q^{66} -2.22378 q^{67} +(3.13182 + 2.27540i) q^{68} +(-0.797605 + 2.45478i) q^{69} +(0.945515 + 2.91000i) q^{70} +(11.0020 - 7.99343i) q^{71} +(6.55888 - 4.76530i) q^{72} +(1.70999 + 5.26281i) q^{73} +(1.66023 - 5.10966i) q^{74} +(11.7613 + 8.54506i) q^{75} +0.322214 q^{76} +(1.14264 - 3.11358i) q^{77} -6.70061 q^{78} +(-14.2059 - 10.3212i) q^{79} +(-0.945515 + 2.91000i) q^{80} +(10.0138 + 30.8193i) q^{81} +(-4.94084 + 3.58973i) q^{82} +(0.249265 - 0.181101i) q^{83} +(-1.02988 - 3.16963i) q^{84} +(3.66023 - 11.2650i) q^{85} +(-6.70152 - 4.86894i) q^{86} -1.00759 q^{87} +(2.75453 - 1.84731i) q^{88} +4.69483 q^{89} +(-20.0685 - 14.5806i) q^{90} +(-0.621290 + 1.91213i) q^{91} +(0.239324 + 0.736562i) q^{92} +(-12.8732 + 9.35290i) q^{93} +(0.986209 - 0.716523i) q^{94} +(-0.304658 - 0.937641i) q^{95} +(1.02988 - 3.16963i) q^{96} +(-8.33334 - 6.05453i) q^{97} -1.00000 q^{98} +(7.34269 + 25.8666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20} - 6 q^{21} - 20 q^{23} - 4 q^{24} - 25 q^{25} + 17 q^{26} + 32 q^{27} - 2 q^{28} - 23 q^{29} - 30 q^{30} + 3 q^{31} - 8 q^{32} + 40 q^{33} + 2 q^{34} + 5 q^{35} - 2 q^{36} + 6 q^{37} - q^{38} - 21 q^{39} - 2 q^{41} - 4 q^{42} - 16 q^{43} + 15 q^{44} - 40 q^{45} - 5 q^{46} + 34 q^{47} - q^{48} - 2 q^{49} - 10 q^{50} + 4 q^{51} - 17 q^{52} + 13 q^{53} + 48 q^{54} - 25 q^{55} - 8 q^{56} - 12 q^{57} + 23 q^{58} - 3 q^{59} - 25 q^{60} - 16 q^{61} - 3 q^{62} - 2 q^{63} - 2 q^{64} + 10 q^{65} + 15 q^{66} + 18 q^{67} - 7 q^{68} - 15 q^{69} + 45 q^{71} + 7 q^{72} + q^{73} - 6 q^{74} + 40 q^{75} + 26 q^{76} + 15 q^{77} - 4 q^{78} - 21 q^{79} + 57 q^{81} - 3 q^{82} + 12 q^{83} - q^{84} + 10 q^{85} - 14 q^{86} - 4 q^{87} + 10 q^{88} + 12 q^{89} - 40 q^{90} - 17 q^{91} + 5 q^{92} - 31 q^{93} + 31 q^{94} - 30 q^{95} + q^{96} + 5 q^{97} - 8 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.02988	+	3.16963i	−0.594599	+	1.82999i	−0.0378884	+	0.999282i	$0.512063\pi$
$3$	−1.02988	+	3.16963i	−0.594599	+	1.82999i	−0.556711	+	0.830706i	$0.687937\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	2.47539	−	1.79848i	1.10703	−	0.804303i	0.124836	−	0.992177i	$-0.460160\pi$
$5$	2.47539	−	1.79848i	1.10703	−	0.804303i	0.982193	+	0.187874i	$0.0601597\pi$
$6$	−2.69625	+	1.95894i	−1.10074	+	0.799734i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−6.55888	−	4.76530i	−2.18629	−	1.58843i
$10$	3.05975			0.967579
$11$	−2.60809	−	2.04887i	−0.786370	−	0.617756i
$11$	−2.60809	−	2.04887i	−0.786370	−	0.617756i
$12$	−3.33275			−0.962082
$13$	1.62656	+	1.18176i	0.451126	+	0.327762i	0.790040	−	0.613055i	$-0.210060\pi$
$13$	1.62656	+	1.18176i	0.451126	+	0.327762i	−0.338914	+	0.940817i	$0.610060\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	3.15117	+	9.69829i	0.813627	+	2.50409i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.13182	−	2.27540i	0.759579	−	0.551867i	−0.139202	−	0.990264i	$-0.544454\pi$
$17$	3.13182	−	2.27540i	0.759579	−	0.551867i	0.898781	+	0.438397i	$0.144454\pi$
$18$	−2.50527	−	7.71042i	−0.590497	−	1.81736i
$19$	0.0995695	−	0.306444i	0.0228428	−	0.0703030i	−0.938985	−	0.343957i	$-0.888232\pi$
$19$	0.0995695	−	0.306444i	0.0228428	−	0.0703030i	0.961828	+	0.273654i	$0.0882324\pi$
$20$	2.47539	+	1.79848i	0.553514	+	0.402152i
$21$	−3.33275			−0.727265
$22$	−0.905698	−	3.19057i	−0.193095	−	0.680231i
$23$	0.774467			0.161488			0.0807438	−	0.996735i	$-0.474270\pi$
$23$	0.774467			0.161488			0.0807438	+	0.996735i	$0.474270\pi$
$24$	−2.69625	−	1.95894i	−0.550370	−	0.399867i
$25$	1.34796	−	4.14859i	0.269592	−	0.829718i
$26$	0.621290	+	1.91213i	0.121845	+	0.375000i
$27$	13.7703	−	10.0047i	2.65010	−	1.92541i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	0.0934255	+	0.287534i	0.0173487	+	0.0533938i	0.959356	−	0.282198i	$-0.0910636\pi$
$29$	0.0934255	+	0.287534i	0.0173487	+	0.0533938i	−0.942007	+	0.335592i	$0.891064\pi$
$30$	−3.15117	+	9.69829i	−0.575322	+	1.77066i
$31$	3.86263	+	2.80636i	0.693748	+	0.504037i	0.877890	−	0.478862i	$-0.158951\pi$
$31$	3.86263	+	2.80636i	0.693748	+	0.504037i	−0.184142	+	0.982900i	$0.558951\pi$
$32$	−1.00000			−0.176777
$33$	9.18017	−	6.15662i	1.59806	−	1.07173i
$34$	3.87115			0.663896
$35$	2.47539	+	1.79848i	0.418418	+	0.303998i
$36$	2.50527	−	7.71042i	0.417545	−	1.28507i
$37$	−1.66023	−	5.10966i	−0.272940	−	0.840024i	−0.989757	−	0.142762i	$-0.954402\pi$
$37$	−1.66023	−	5.10966i	−0.272940	−	0.840024i	0.716817	−	0.697262i	$-0.245598\pi$
$38$	0.260676	−	0.189393i	0.0422873	−	0.0307235i
$39$	−5.42091	+	3.93852i	−0.868040	+	0.630668i
$40$	0.945515	+	2.91000i	0.149499	+	0.460111i
$41$	−1.88723	+	5.80831i	−0.294736	+	0.907105i	0.688573	+	0.725167i	$0.258237\pi$
$41$	−1.88723	+	5.80831i	−0.294736	+	0.907105i	−0.983310	+	0.181939i	$0.941763\pi$
$42$	−2.69625	−	1.95894i	−0.416041	−	0.302271i
$43$	−8.28353			−1.26323			−0.631613	−	0.775284i	$-0.717607\pi$
$43$	−8.28353			−1.26323			−0.631613	+	0.775284i	$0.717607\pi$
$44$	1.14264	−	3.11358i	0.172260	−	0.469390i
$45$	−24.8061			−3.69787
$46$	0.626557	+	0.455220i	0.0923808	+	0.0671186i
$47$	0.376698	−	1.15936i	0.0549471	−	0.169110i	−0.919817	−	0.392348i	$-0.871663\pi$
$47$	0.376698	−	1.15936i	0.0549471	−	0.169110i	0.974764	+	0.223238i	$0.0716628\pi$
$48$	−1.02988	−	3.16963i	−0.148650	−	0.457497i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	3.52900	−	2.56397i	0.499076	−	0.362600i
$51$	3.98680	+	12.2701i	0.558264	+	1.71816i
$52$	−0.621290	+	1.91213i	−0.0861574	+	0.265165i
$53$	2.52988	+	1.83806i	0.347505	+	0.252477i	0.747822	−	0.663900i	$-0.231100\pi$
$53$	2.52988	+	1.83806i	0.347505	+	0.252477i	−0.400316	+	0.916377i	$0.631100\pi$
$54$	17.0211			2.31627
$55$	−10.1409	−	0.381150i	−1.36740	−	0.0513943i
$56$	−1.00000			−0.133631
$57$	0.868769	+	0.631198i	0.115071	+	0.0836042i
$58$	−0.0934255	+	0.287534i	−0.0122674	+	0.0377551i
$59$	−4.16784	−	12.8273i	−0.542607	−	1.66997i	−0.726612	−	0.687048i	$-0.758906\pi$
$59$	−4.16784	−	12.8273i	−0.542607	−	1.66997i	0.184005	−	0.982925i	$-0.441094\pi$
$60$	−8.24986	+	5.99387i	−1.06505	+	0.773806i
$61$	−9.57408	+	6.95598i	−1.22584	+	0.890622i	−0.996571	−	0.0827421i	$-0.973632\pi$
$61$	−9.57408	+	6.95598i	−1.22584	+	0.890622i	−0.229265	+	0.973364i	$0.573632\pi$
$62$	1.47539	+	4.54079i	0.187375	+	0.576681i
$63$	2.50527	−	7.71042i	0.315634	−	0.971422i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.15174			0.763029
$66$	11.0457	+	0.415157i	1.35963	+	0.0511023i
$67$	−2.22378			−0.271678			−0.135839	−	0.990731i	$-0.543373\pi$
$67$	−2.22378			−0.271678			−0.135839	+	0.990731i	$0.543373\pi$
$68$	3.13182	+	2.27540i	0.379790	+	0.275933i
$69$	−0.797605	+	2.45478i	−0.0960204	+	0.295520i
$70$	0.945515	+	2.91000i	0.113011	+	0.347811i
$71$	11.0020	−	7.99343i	1.30570	−	0.948646i	0.305705	−	0.952126i	$-0.401108\pi$
$71$	11.0020	−	7.99343i	1.30570	−	0.948646i	0.999994	+	0.00348082i	$0.00110798\pi$
$72$	6.55888	−	4.76530i	0.772971	−	0.561596i
$73$	1.70999	+	5.26281i	0.200139	+	0.615965i	0.999878	+	0.0156169i	$0.00497121\pi$
$73$	1.70999	+	5.26281i	0.200139	+	0.615965i	−0.799739	+	0.600348i	$0.795029\pi$
$74$	1.66023	−	5.10966i	0.192998	−	0.593986i
$75$	11.7613	+	8.54506i	1.35807	+	0.986699i
$76$	0.322214			0.0369605
$77$	1.14264	−	3.11358i	0.130216	−	0.354825i
$78$	−6.70061			−0.758695
$79$	−14.2059	−	10.3212i	−1.59829	−	1.16123i	−0.890689	−	0.454613i	$-0.849778\pi$
$79$	−14.2059	−	10.3212i	−1.59829	−	1.16123i	−0.707600	−	0.706613i	$-0.750222\pi$
$80$	−0.945515	+	2.91000i	−0.105712	+	0.325348i
$81$	10.0138	+	30.8193i	1.11264	+	3.42436i
$82$	−4.94084	+	3.58973i	−0.545625	+	0.396420i
$83$	0.249265	−	0.181101i	0.0273604	−	0.0198785i	−0.574021	−	0.818841i	$-0.694617\pi$
$83$	0.249265	−	0.181101i	0.0273604	−	0.0198785i	0.601381	+	0.798962i	$0.294617\pi$
$84$	−1.02988	−	3.16963i	−0.112369	−	0.345835i
$85$	3.66023	−	11.2650i	0.397008	−	1.22186i
$86$	−6.70152	−	4.86894i	−0.722643	−	0.525031i
$87$	−1.00759			−0.108025
$88$	2.75453	−	1.84731i	0.293634	−	0.196924i
$89$	4.69483			0.497651			0.248826	−	0.968548i	$-0.419955\pi$
$89$	4.69483			0.497651			0.248826	+	0.968548i	$0.419955\pi$
$90$	−20.0685	−	14.5806i	−2.11541	−	1.53693i
$91$	−0.621290	+	1.91213i	−0.0651288	+	0.200446i
$92$	0.239324	+	0.736562i	0.0249512	+	0.0767919i
$93$	−12.8732	+	9.35290i	−1.33488	+	0.969850i
$94$	0.986209	−	0.716523i	0.101720	−	0.0739037i
$95$	−0.304658	−	0.937641i	−0.0312573	−	0.0962000i
$96$	1.02988	−	3.16963i	0.105111	−	0.323499i
$97$	−8.33334	−	6.05453i	−0.846123	−	0.614744i	0.0779515	−	0.996957i	$-0.475162\pi$
$97$	−8.33334	−	6.05453i	−0.846123	−	0.614744i	−0.924074	+	0.382213i	$0.875162\pi$
$98$	−1.00000			−0.101015
$99$	7.34269	+	25.8666i	0.737968	+	2.59969i
$100$	4.36208			0.436208
$101$	−1.60951	−	1.16938i	−0.160152	−	0.116357i	0.504823	−	0.863223i	$-0.331558\pi$
$101$	−1.60951	−	1.16938i	−0.160152	−	0.116357i	−0.664975	+	0.746866i	$0.731558\pi$
$102$	−3.98680	+	12.2701i	−0.394752	+	1.21492i
$103$	0.537471	+	1.65416i	0.0529585	+	0.162990i	0.974038	−	0.226386i	$-0.0726909\pi$
$103$	0.537471	+	1.65416i	0.0529585	+	0.162990i	−0.921079	+	0.389375i	$0.872691\pi$
$104$	−1.62656	+	1.18176i	−0.159497	+	0.115881i
$105$	−8.24986	+	5.99387i	−0.805104	+	0.584942i
$106$	0.966327	+	2.97405i	0.0938579	+	0.288865i
$107$	−4.38344	+	13.4908i	−0.423763	+	1.30421i	0.480411	+	0.877043i	$0.340487\pi$
$107$	−4.38344	+	13.4908i	−0.423763	+	1.30421i	−0.904174	+	0.427164i	$0.859513\pi$
$108$	13.7703	+	10.0047i	1.32505	+	0.962706i
$109$	0.831279			0.0796221			0.0398110	−	0.999207i	$-0.487324\pi$
$109$	0.831279			0.0796221			0.0398110	+	0.999207i	$0.487324\pi$
$110$	−7.98012	−	6.26902i	−0.760874	−	0.597728i
$111$	17.9056			1.69952
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	3.30196	−	10.1624i	0.310623	−	0.955998i	−0.666896	−	0.745151i	$-0.732378\pi$
$113$	3.30196	−	10.1624i	0.310623	−	0.955998i	0.977519	−	0.210848i	$-0.0676224\pi$
$114$	0.331840	+	1.02130i	0.0310797	+	0.0956535i
$115$	1.91711	−	1.39286i	0.178771	−	0.129885i
$116$	−0.244591	+	0.177706i	−0.0227097	+	0.0164996i
$117$	−5.03693	−	15.5021i	−0.465664	−	1.43317i
$118$	4.16784	−	12.8273i	0.383681	−	1.18085i
$119$	3.13182	+	2.27540i	0.287094	+	0.208586i
$120$	−10.1974			−0.930890
$121$	2.60430	+	10.6873i	0.236754	+	0.971570i
$122$	−11.8342			−1.07142
$123$	−16.4666	−	11.9637i	−1.48474	−	1.07873i
$124$	−1.47539	+	4.54079i	−0.132494	+	0.407775i
$125$	0.603160	+	1.85634i	0.0539483	+	0.166036i
$126$	6.55888	−	4.76530i	0.584311	−	0.424527i
$127$	−1.51609	+	1.10150i	−0.134531	+	0.0977424i	−0.653015	−	0.757345i	$-0.726496\pi$
$127$	−1.51609	+	1.10150i	−0.134531	+	0.0977424i	0.518485	+	0.855087i	$0.326496\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	8.53101	−	26.2558i	0.751114	−	2.31169i
$130$	4.97686	+	3.61590i	0.436500	+	0.317136i
$131$	−1.78676			−0.156110			−0.0780548	−	0.996949i	$-0.524871\pi$
$131$	−1.78676			−0.156110			−0.0780548	+	0.996949i	$0.524871\pi$
$132$	8.69212	+	6.82836i	0.756552	+	0.594332i
$133$	0.322214			0.0279395
$134$	−1.79908	−	1.30711i	−0.155416	−	0.112917i
$135$	16.0937	−	49.5313i	1.38512	−	4.26297i
$136$	1.19625	+	3.68168i	0.102578	+	0.315702i
$137$	7.84416	−	5.69912i	0.670172	−	0.486908i	−0.199911	−	0.979814i	$-0.564065\pi$
$137$	7.84416	−	5.69912i	0.670172	−	0.486908i	0.870083	+	0.492906i	$0.164065\pi$
$138$	−2.08816	+	1.51714i	−0.177756	+	0.129147i
$139$	6.18685	+	19.0412i	0.524762	+	1.61505i	0.764786	+	0.644284i	$0.222845\pi$
$139$	6.18685	+	19.0412i	0.524762	+	1.61505i	−0.240024	+	0.970767i	$0.577155\pi$
$140$	−0.945515	+	2.91000i	−0.0799106	+	0.245940i
$141$	3.28679	+	2.38799i	0.276797	+	0.201105i
$142$	13.5992			1.14122
$143$	−1.82094	−	6.41475i	−0.152274	−	0.536428i
$144$	8.10722			0.675601
$145$	0.748388	+	0.543736i	0.0621503	+	0.0451548i
$146$	−1.70999	+	5.26281i	−0.141520	+	0.435553i
$147$	−1.02988	−	3.16963i	−0.0849427	−	0.261427i
$148$	4.34654	−	3.15795i	0.357283	−	0.259582i
$149$	−11.6745	+	8.48204i	−0.956415	+	0.694876i	−0.952315	−	0.305116i	$-0.901305\pi$
$149$	−11.6745	+	8.48204i	−0.956415	+	0.694876i	−0.00409948	+	0.999992i	$0.501305\pi$
$150$	4.49241	+	13.8262i	0.366803	+	1.12890i
$151$	1.10897	−	3.41306i	0.0902466	−	0.277751i	−0.895739	−	0.444580i	$-0.853353\pi$
$151$	1.10897	−	3.41306i	0.0902466	−	0.277751i	0.985986	+	0.166829i	$0.0533529\pi$
$152$	0.260676	+	0.189393i	0.0211437	+	0.0153618i
$153$	−31.3842			−2.53727
$154$	2.75453	−	1.84731i	0.221967	−	0.148860i
$155$	14.6087			1.17340
$156$	−5.42091	−	3.93852i	−0.434020	−	0.315334i
$157$	−3.31721	+	10.2093i	−0.264742	+	0.814792i	0.727011	+	0.686626i	$0.240909\pi$
$157$	−3.31721	+	10.2093i	−0.264742	+	0.814792i	−0.991753	+	0.128166i	$0.959091\pi$
$158$	−5.42617	−	16.7000i	−0.431683	−	1.32858i
$159$	−8.43144	+	6.12580i	−0.668657	+	0.485808i
$160$	−2.47539	+	1.79848i	−0.195697	+	0.142182i
$161$	0.239324	+	0.736562i	0.0188613	+	0.0580492i
$162$	−10.0138	+	30.8193i	−0.786758	+	2.42139i
$163$	1.84980	+	1.34396i	0.144887	+	0.105267i	0.657868	−	0.753134i	$-0.271459\pi$
$163$	1.84980	+	1.34396i	0.144887	+	0.105267i	−0.512980	+	0.858400i	$0.671459\pi$
$164$	−6.10722			−0.476893
$165$	11.6520	−	31.7504i	0.907104	−	2.47176i
$166$	0.308108			0.0239138
$167$	11.2197	+	8.15159i	0.868206	+	0.630789i	0.930105	−	0.367294i	$-0.119716\pi$
$167$	11.2197	+	8.15159i	0.868206	+	0.630789i	−0.0618986	+	0.998082i	$0.519716\pi$
$168$	1.02988	−	3.16963i	0.0794567	−	0.244542i
$169$	−2.76810	−	8.51932i	−0.212930	−	0.655333i
$170$	9.58261	−	6.96217i	0.734952	−	0.533974i
$171$	−2.11336	+	1.53545i	−0.161613	+	0.117419i
$172$	−2.55975	−	7.87811i	−0.195179	−	0.600700i
$173$	2.63182	−	8.09992i	0.200094	−	0.615826i	−0.799785	−	0.600286i	$-0.795053\pi$
$173$	2.63182	−	8.09992i	0.200094	−	0.615826i	0.999879	−	0.0155397i	$-0.00494663\pi$
$174$	−0.815161	−	0.592249i	−0.0617972	−	0.0448983i
$175$	4.36208			0.329743
$176$	3.31428	+	0.124569i	0.249824	+	0.00938974i
$177$	44.9502			3.37867
$178$	3.79820	+	2.75955i	0.284687	+	0.206837i
$179$	−5.38109	+	16.5613i	−0.402202	+	1.23785i	0.521008	+	0.853552i	$0.325556\pi$
$179$	−5.38109	+	16.5613i	−0.402202	+	1.23785i	−0.923209	+	0.384297i	$0.874444\pi$
$180$	−7.66550	−	23.5920i	−0.571352	−	1.75844i
$181$	−7.80205	+	5.66852i	−0.579922	+	0.421338i	−0.838696	−	0.544600i	$-0.816681\pi$
$181$	−7.80205	+	5.66852i	−0.579922	+	0.421338i	0.258774	+	0.965938i	$0.416681\pi$
$182$	−1.62656	+	1.18176i	−0.120568	+	0.0875981i
$183$	−12.1878	−	37.5101i	−0.900947	−	2.77283i
$184$	−0.239324	+	0.736562i	−0.0176432	+	0.0543001i
$185$	−13.2993	−	9.66253i	−0.977787	−	0.710404i
$186$	−15.9121			−1.16673
$187$	−12.8301	−	0.482225i	−0.938229	−	0.0352638i
$188$	1.21902			0.0889063
$189$	13.7703	+	10.0047i	1.00164	+	0.727737i
$190$	0.304658	−	0.937641i	0.0221022	−	0.0680237i
$191$	−0.556270	−	1.71202i	−0.0402503	−	0.123878i	0.928912	−	0.370300i	$-0.120745\pi$
$191$	−0.556270	−	1.71202i	−0.0402503	−	0.123878i	−0.969163	+	0.246422i	$0.920745\pi$
$192$	2.69625	−	1.95894i	0.194585	−	0.141374i
$193$	8.32423	−	6.04790i	0.599191	−	0.435338i	−0.246401	−	0.969168i	$-0.579248\pi$
$193$	8.32423	−	6.04790i	0.599191	−	0.435338i	0.845592	+	0.533830i	$0.179248\pi$
$194$	−3.18305	−	9.79643i	−0.228530	−	0.703343i
$195$	−6.33553	+	19.4988i	−0.453697	+	1.39633i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	9.53189			0.679119			0.339559	−	0.940585i	$-0.389722\pi$
$197$	9.53189			0.679119			0.339559	+	0.940585i	$0.389722\pi$
$198$	−9.26365	+	25.2425i	−0.658339	+	1.79390i
$199$	3.25714			0.230892			0.115446	−	0.993314i	$-0.463170\pi$
$199$	3.25714			0.230892			0.115446	+	0.993314i	$0.463170\pi$
$200$	3.52900	+	2.56397i	0.249538	+	0.181300i
$201$	2.29022	−	7.04857i	0.161540	−	0.497167i
$202$	−0.614778	−	1.89209i	−0.0432557	−	0.133127i
$203$	−0.244591	+	0.177706i	−0.0171669	+	0.0124725i
$204$	−10.4376	+	7.58335i	−0.730777	+	0.530941i
$205$	5.77447	+	17.7720i	0.403306	+	1.24125i
$206$	−0.537471	+	1.65416i	−0.0374473	+	0.115251i
$207$	−5.07963	−	3.69057i	−0.353059	−	0.256512i
$208$	−2.01054			−0.139406
$209$	−0.887548	+	0.595229i	−0.0613930	+	0.0411728i
$210$	−10.1974			−0.703687
$211$	−4.90015	−	3.56017i	−0.337340	−	0.245092i	0.406199	−	0.913785i	$-0.366854\pi$
$211$	−4.90015	−	3.56017i	−0.337340	−	0.245092i	−0.743539	+	0.668693i	$0.766854\pi$
$212$	−0.966327	+	2.97405i	−0.0663676	+	0.204258i
$213$	14.0055	+	43.1046i	0.959643	+	2.95348i
$214$	−11.4760	+	8.33779i	−0.784482	+	0.569960i
$215$	−20.5050	+	14.8977i	−1.39843	+	1.01602i
$216$	5.25980	+	16.1880i	0.357884	+	1.10145i
$217$	−1.47539	+	4.54079i	−0.100156	+	0.308249i
$218$	0.672519	+	0.488613i	0.0455487	+	0.0330931i
$219$	−18.4422			−1.24621
$220$	−2.77121	−	9.76234i	−0.186835	−	0.658177i
$221$	7.78308			0.523547
$222$	14.4859	+	10.5246i	0.972232	+	0.706368i
$223$	−5.07405	+	15.6163i	−0.339784	+	1.04575i	0.624534	+	0.780998i	$0.285289\pi$
$223$	−5.07405	+	15.6163i	−0.339784	+	1.04575i	−0.964317	+	0.264749i	$0.914711\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	−28.6104	+	20.7866i	−1.90736	+	1.38578i
$226$	8.64465	−	6.28071i	0.575034	−	0.417787i
$227$	−1.89485	−	5.83174i	−0.125765	−	0.387066i	0.868274	−	0.496084i	$-0.165229\pi$
$227$	−1.89485	−	5.83174i	−0.125765	−	0.387066i	−0.994040	+	0.109018i	$0.965229\pi$
$228$	−0.331840	+	1.02130i	−0.0219767	+	0.0676372i
$229$	0.563549	+	0.409443i	0.0372404	+	0.0270567i	0.606250	−	0.795274i	$-0.292673\pi$
$229$	0.563549	+	0.409443i	0.0372404	+	0.0270567i	−0.569009	+	0.822331i	$0.692673\pi$
$230$	2.36968			0.156252
$231$	8.69212	+	6.82836i	0.571899	+	0.449273i
$232$	−0.302331			−0.0198490
$233$	−11.0159	−	8.00351i	−0.721675	−	0.524327i	0.165244	−	0.986253i	$-0.447159\pi$
$233$	−11.0159	−	8.00351i	−0.721675	−	0.524327i	−0.886919	+	0.461925i	$0.847159\pi$
$234$	5.03693	−	15.5021i	0.329274	−	1.01340i
$235$	−1.15260	−	3.54735i	−0.0751876	−	0.231404i
$236$	10.9116	−	7.92771i	0.710282	−	0.516050i
$237$	47.3447	−	34.3980i	3.07537	−	2.23439i
$238$	1.19625	+	3.68168i	0.0775414	+	0.238648i
$239$	−7.37495	+	22.6977i	−0.477046	+	1.46820i	0.366133	+	0.930562i	$0.380681\pi$
$239$	−7.37495	+	22.6977i	−0.477046	+	1.46820i	−0.843179	+	0.537633i	$0.819319\pi$
$240$	−8.24986	−	5.99387i	−0.532526	−	0.386903i
$241$	23.6818			1.52548			0.762740	−	0.646706i	$-0.223854\pi$
$241$	23.6818			1.52548			0.762740	+	0.646706i	$0.223854\pi$
$242$	−4.17490	+	10.1769i	−0.268373	+	0.654199i
$243$	−56.9355			−3.65242
$244$	−9.57408	−	6.95598i	−0.612918	−	0.445311i
$245$	−0.945515	+	2.91000i	−0.0604068	+	0.185913i
$246$	−6.28968	−	19.3576i	−0.401015	−	1.23420i
$247$	0.524099	−	0.380780i	0.0333476	−	0.0242285i
$248$	−3.86263	+	2.80636i	−0.245277	+	0.178204i
$249$	0.317313	+	0.976590i	0.0201089	+	0.0618889i
$250$	−0.603160	+	1.85634i	−0.0381472	+	0.117405i
$251$	−3.56598	−	2.59084i	−0.225083	−	0.163532i	0.469529	−	0.882917i	$-0.344424\pi$
$251$	−3.56598	−	2.59084i	−0.225083	−	0.163532i	−0.694612	+	0.719385i	$0.744424\pi$
$252$	8.10722			0.510707
$253$	−2.01988	−	1.58678i	−0.126989	−	0.0997600i
$254$	−1.87398			−0.117584
$255$	31.9364	+	23.2032i	1.99994	+	1.45304i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.80434	+	24.0193i	0.486822	+	1.49828i	0.829325	+	0.558766i	$0.188725\pi$
$257$	7.80434	+	24.0193i	0.486822	+	1.49828i	−0.342504	+	0.939516i	$0.611275\pi$
$258$	22.3345	−	16.2269i	1.39048	−	1.01025i
$259$	4.34654	−	3.15795i	0.270081	−	0.196225i
$260$	1.90099	+	5.85065i	0.117895	+	0.362842i
$261$	0.757421	−	2.33110i	0.0468832	−	0.144292i
$262$	−1.44552	−	1.05023i	−0.0893042	−	0.0648833i
$263$	28.5654			1.76142			0.880710	−	0.473657i	$-0.157066\pi$
$263$	28.5654			1.76142			0.880710	+	0.473657i	$0.157066\pi$
$264$	3.01846	+	10.6334i	0.185774	+	0.654438i
$265$	9.56815			0.587767
$266$	0.260676	+	0.189393i	0.0159831	+	0.0116124i
$267$	−4.83510	+	14.8809i	−0.295903	+	0.910696i
$268$	−0.687186	−	2.11494i	−0.0419766	−	0.129191i
$269$	−3.51810	+	2.55605i	−0.214502	+	0.155845i	−0.689848	−	0.723954i	$-0.742323\pi$
$269$	−3.51810	+	2.55605i	−0.214502	+	0.155845i	0.475346	+	0.879799i	$0.342323\pi$
$270$	42.1338	−	30.6120i	2.56418	−	1.86299i
$271$	3.45602	+	10.6365i	0.209938	+	0.646123i	0.999474	+	0.0324192i	$0.0103212\pi$
$271$	3.45602	+	10.6365i	0.209938	+	0.646123i	−0.789536	+	0.613704i	$0.789679\pi$
$272$	−1.19625	+	3.68168i	−0.0725333	+	0.223235i
$273$	−5.42091	−	3.93852i	−0.328088	−	0.238370i
$274$	9.69592			0.585752
$275$	−12.0155	+	8.05812i	−0.724562	+	0.485923i
$276$	−2.58111			−0.155364
$277$	2.63508	+	1.91450i	0.158327	+	0.115031i	0.664128	−	0.747619i	$-0.268803\pi$
$277$	2.63508	+	1.91450i	0.158327	+	0.115031i	−0.505801	+	0.862650i	$0.668803\pi$
$278$	−6.18685	+	19.0412i	−0.371063	+	1.14201i
$279$	−11.9613	−	36.8132i	−0.716105	−	2.20395i
$280$	−2.47539	+	1.79848i	−0.147933	+	0.107480i
$281$	−2.05214	+	1.49097i	−0.122420	+	0.0889435i	−0.647311	−	0.762226i	$-0.724106\pi$
$281$	−2.05214	+	1.49097i	−0.122420	+	0.0889435i	0.524890	+	0.851170i	$0.324106\pi$
$282$	1.25544	+	3.86385i	0.0747604	+	0.230089i
$283$	6.37871	−	19.6317i	0.379175	−	1.16698i	−0.561444	−	0.827515i	$-0.689754\pi$
$283$	6.37871	−	19.6317i	0.379175	−	1.16698i	0.940618	−	0.339466i	$-0.110246\pi$
$284$	11.0020	+	7.99343i	0.652849	+	0.474323i
$285$	3.28574			0.194630
$286$	2.29732	−	6.25996i	0.135844	−	0.370159i
$287$	−6.10722			−0.360498
$288$	6.55888	+	4.76530i	0.386485	+	0.280798i
$289$	−0.622425	+	1.91563i	−0.0366132	+	0.112684i
$290$	0.285859	+	0.879783i	0.0167862	+	0.0516627i
$291$	27.7729	−	20.1782i	1.62808	−	1.18287i
$292$	−4.47681	+	3.25259i	−0.261985	+	0.190344i
$293$	−4.79636	−	14.7617i	−0.280206	−	0.862387i	−0.987795	−	0.155762i	$-0.950217\pi$
$293$	−4.79636	−	14.7617i	−0.280206	−	0.862387i	0.707588	−	0.706625i	$-0.249783\pi$
$294$	1.02988	−	3.16963i	0.0600636	−	0.184857i
$295$	−33.3867	−	24.2568i	−1.94385	−	1.41229i
$296$	5.37262			0.312277
$297$	−56.4127	−	2.12030i	−3.27340	−	0.123032i
$298$	−14.4305			−0.835937
$299$	1.25972	+	0.915237i	0.0728512	+	0.0529295i
$300$	−4.49241	+	13.8262i	−0.259369	+	0.798256i
$301$	−2.55975	−	7.87811i	−0.147542	−	0.454087i
$302$	2.90332	−	2.10938i	0.167067	−	0.121381i
$303$	5.36410	−	3.89724i	0.308159	−	0.223891i
$304$	0.0995695	+	0.306444i	0.00571070	+	0.0175757i
$305$	−11.1894	+	34.4375i	−0.640705	+	1.97189i
$306$	−25.3904	−	18.4472i	−1.45147	−	1.05456i
$307$	5.31405			0.303289			0.151645	−	0.988435i	$-0.451543\pi$
$307$	5.31405			0.303289			0.151645	+	0.988435i	$0.451543\pi$
$308$	3.31428	+	0.124569i	0.188849	+	0.00709798i
$309$	−5.79662			−0.329758
$310$	11.8187	+	8.58677i	0.671256	+	0.487696i
$311$	5.07354	−	15.6148i	0.287694	−	0.885432i	−0.697884	−	0.716211i	$-0.745875\pi$
$311$	5.07354	−	15.6148i	0.287694	−	0.885432i	0.985578	−	0.169221i	$-0.0541251\pi$
$312$	−2.07060	−	6.37266i	−0.117225	−	0.360781i
$313$	3.36180	−	2.44249i	0.190020	−	0.138058i	−0.488708	−	0.872448i	$-0.662532\pi$
$313$	3.36180	−	2.44249i	0.190020	−	0.138058i	0.678728	+	0.734390i	$0.262532\pi$
$314$	−8.68456	+	6.30970i	−0.490098	+	0.356077i
$315$	−7.66550	−	23.5920i	−0.431902	−	1.32926i
$316$	5.42617	−	16.7000i	0.305246	−	0.939451i
$317$	−17.0296	−	12.3727i	−0.956477	−	0.694921i	−0.00414734	−	0.999991i	$-0.501320\pi$
$317$	−17.0296	−	12.3727i	−0.956477	−	0.694921i	−0.952330	+	0.305070i	$0.901320\pi$
$318$	−10.4218			−0.584428
$319$	0.345457	−	0.941332i	0.0193419	−	0.0527045i
$320$	−3.05975			−0.171045
$321$	−38.2466	−	27.7878i	−2.13472	−	1.55096i
$322$	−0.239324	+	0.736562i	−0.0133370	+	0.0410470i
$323$	−0.385448	−	1.18629i	−0.0214469	−	0.0660069i
$324$	−26.2164	+	19.0474i	−1.45647	+	1.05819i
$325$	7.09518	−	5.15495i	0.393570	−	0.285945i
$326$	0.706559	+	2.17456i	0.0391327	+	0.120438i
$327$	−0.856114	+	2.63485i	−0.0473432	+	0.145707i
$328$	−4.94084	−	3.58973i	−0.272812	−	0.198210i
$329$	1.21902			0.0672068
$330$	28.0890	−	18.8377i	1.54625	−	1.03698i
$331$	7.08558			0.389459			0.194729	−	0.980857i	$-0.437617\pi$
$331$	7.08558			0.389459			0.194729	+	0.980857i	$0.437617\pi$
$332$	0.249265	+	0.181101i	0.0136802	+	0.00993923i
$333$	−13.4598	+	41.4252i	−0.737595	+	2.27008i
$334$	4.28554	+	13.1895i	0.234495	+	0.721700i
$335$	−5.50473	+	3.99942i	−0.300755	+	0.218512i
$336$	2.69625	−	1.95894i	0.147093	−	0.106869i
$337$	5.78770	+	17.8127i	0.315276	+	0.970319i	0.975641	+	0.219375i	$0.0704017\pi$
$337$	5.78770	+	17.8127i	0.315276	+	0.970319i	−0.660365	+	0.750945i	$0.729598\pi$
$338$	2.76810	−	8.51932i	0.150565	−	0.463390i
$339$	28.8105	+	20.9320i	1.56477	+	1.13687i
$340$	11.8448			0.642372
$341$	−4.32423	−	15.2333i	−0.234170	−	0.824927i
$342$	−2.61226			−0.141255
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	2.55975	−	7.87811i	0.138013	−	0.424759i
$345$	2.44047	+	7.51101i	0.131391	+	0.404379i
$346$	6.89021	−	5.00603i	0.370420	−	0.269126i
$347$	−20.4259	+	14.8403i	−1.09652	+	0.796668i	−0.980488	−	0.196578i	$-0.937017\pi$
$347$	−20.4259	+	14.8403i	−1.09652	+	0.796668i	−0.116031	+	0.993246i	$0.537017\pi$
$348$	−0.311364	−	0.958279i	−0.0166909	−	0.0513692i
$349$	−0.337443	+	1.03854i	−0.0180629	+	0.0555919i	−0.959682	−	0.281089i	$-0.909304\pi$
$349$	−0.337443	+	1.03854i	−0.0180629	+	0.0555919i	0.941619	+	0.336681i	$0.109304\pi$
$350$	3.52900	+	2.56397i	0.188633	+	0.137050i
$351$	34.2215			1.82661
$352$	2.60809	+	2.04887i	0.139012	+	0.109205i
$353$	20.6496			1.09907			0.549535	−	0.835471i	$-0.314805\pi$
$353$	20.6496			1.09907			0.549535	+	0.835471i	$0.314805\pi$
$354$	36.3655	+	26.4211i	1.93280	+	1.40426i
$355$	12.8583	−	39.5737i	0.682447	−	2.10036i
$356$	1.45078	+	4.46505i	0.0768913	+	0.236647i
$357$	−10.4376	+	7.58335i	−0.552416	+	0.401353i
$358$	−14.0879	+	10.2354i	−0.744567	+	0.540960i
$359$	−4.33074	−	13.3286i	−0.228568	−	0.703459i	−0.997910	−	0.0646218i	$-0.979416\pi$
$359$	−4.33074	−	13.3286i	−0.228568	−	0.703459i	0.769342	−	0.638837i	$-0.220584\pi$
$360$	7.66550	−	23.5920i	0.404007	−	1.24341i
$361$	15.2873	+	11.1069i	0.804596	+	0.584573i
$362$	−9.64386			−0.506870
$363$	−36.5568	−	2.75190i	−1.91873	−	0.144437i
$364$	−2.01054			−0.105381
$365$	13.6979	+	9.95213i	0.716982	+	0.520918i
$366$	12.1878	−	37.5101i	0.637065	−	1.96069i
$367$	−8.51991	−	26.2216i	−0.444736	−	1.36876i	−0.882773	−	0.469800i	$-0.844326\pi$
$367$	−8.51991	−	26.2216i	−0.444736	−	1.36876i	0.438037	−	0.898957i	$-0.355674\pi$
$368$	−0.626557	+	0.455220i	−0.0326616	+	0.0237300i
$369$	40.0565	−	29.1027i	2.08526	−	1.51503i
$370$	−5.07989	−	15.6343i	−0.264091	−	0.812789i
$371$	−0.966327	+	2.97405i	−0.0501692	+	0.154405i
$372$	−12.8732	−	9.35290i	−0.667442	−	0.484925i
$373$	26.1779			1.35544			0.677719	−	0.735321i	$-0.262969\pi$
$373$	26.1779			1.35544			0.677719	+	0.735321i	$0.262969\pi$
$374$	−10.0963	−	7.93146i	−0.522068	−	0.410126i
$375$	−6.50508			−0.335921
$376$	0.986209	+	0.716523i	0.0508599	+	0.0369518i
$377$	−0.187835	+	0.578098i	−0.00967401	+	0.0297735i
$378$	5.25980	+	16.1880i	0.270535	+	0.832621i
$379$	2.44789	−	1.77850i	0.125740	−	0.0913554i	−0.523138	−	0.852248i	$-0.675239\pi$
$379$	2.44789	−	1.77850i	0.125740	−	0.0913554i	0.648878	+	0.760893i	$0.275239\pi$
$380$	0.797605	−	0.579494i	0.0409163	−	0.0297274i
$381$	−1.92997	−	5.93984i	−0.0988755	−	0.304307i
$382$	0.556270	−	1.71202i	0.0284612	−	0.0875947i
$383$	25.7800	+	18.7303i	1.31730	+	0.957072i	0.999962	+	0.00875802i	$0.00278780\pi$
$383$	25.7800	+	18.7303i	1.31730	+	0.957072i	0.317335	+	0.948314i	$0.397212\pi$
$384$	3.33275			0.170074
$385$	−2.77121	−	9.76234i	−0.141234	−	0.497535i
$386$	10.2893			0.523712
$387$	54.3307	+	39.4735i	2.76178	+	2.00655i
$388$	3.18305	−	9.79643i	0.161595	−	0.497338i
$389$	−8.91261	−	27.4302i	−0.451887	−	1.39077i	−0.874751	−	0.484573i	$-0.838975\pi$
$389$	−8.91261	−	27.4302i	−0.451887	−	1.39077i	0.422864	−	0.906193i	$-0.361025\pi$
$390$	−16.5866	+	12.0509i	−0.839897	+	0.610221i
$391$	2.42550	−	1.76223i	0.122663	−	0.0891196i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	1.84014	−	5.66336i	0.0928226	−	0.285679i
$394$	7.71146	+	5.60270i	0.388498	+	0.282260i
$395$	−53.7276			−2.70333
$396$	−22.3316	+	14.9765i	−1.12220	+	0.752599i
$397$	−9.97644			−0.500703			−0.250352	−	0.968155i	$-0.580546\pi$
$397$	−9.97644			−0.500703			−0.250352	+	0.968155i	$0.580546\pi$
$398$	2.63508	+	1.91450i	0.132085	+	0.0959651i
$399$	−0.331840	+	1.02130i	−0.0166128	+	0.0511289i
$400$	1.34796	+	4.14859i	0.0673979	+	0.207429i
$401$	−15.8168	+	11.4916i	−0.789855	+	0.573863i	−0.907920	−	0.419142i	$-0.862331\pi$
$401$	−15.8168	+	11.4916i	−0.789855	+	0.573863i	0.118065	+	0.993006i	$0.462331\pi$
$402$	5.99587	−	4.35625i	0.299047	−	0.217270i
$403$	2.96633	+	9.12941i	0.147763	+	0.454769i
$404$	0.614778	−	1.89209i	0.0305864	−	0.0941352i
$405$	80.2158	+	58.2802i	3.98596	+	2.89597i
$406$	−0.302331			−0.0150045
$407$	−6.13898	+	16.7281i	−0.304298	+	0.829180i
$408$	−12.9016			−0.638723
$409$	21.9007	+	15.9118i	1.08292	+	0.786789i	0.978190	−	0.207712i	$-0.0666016\pi$
$409$	21.9007	+	15.9118i	1.08292	+	0.786789i	0.104732	+	0.994500i	$0.466602\pi$
$410$	−5.77447	+	17.7720i	−0.285181	+	0.877696i
$411$	9.98559	+	30.7325i	0.492553	+	1.51592i
$412$	−1.40712	+	1.02233i	−0.0693236	+	0.0503666i
$413$	10.9116	−	7.92771i	0.536923	−	0.390097i
$414$	−1.94025	−	5.97147i	−0.0953580	−	0.293482i
$415$	0.291321	−	0.896594i	0.0143004	−	0.0440121i
$416$	−1.62656	−	1.18176i	−0.0797485	−	0.0579407i
$417$	−66.7252			−3.26755
$418$	−1.06791	−	0.0401379i	−0.0522331	−	0.00196321i
$419$	17.2021			0.840377			0.420188	−	0.907437i	$-0.361964\pi$
$419$	17.2021			0.840377			0.420188	+	0.907437i	$0.361964\pi$
$420$	−8.24986	−	5.99387i	−0.402552	−	0.292471i
$421$	−2.13035	+	6.55656i	−0.103827	+	0.319547i	−0.989453	−	0.144852i	$-0.953730\pi$
$421$	−2.13035	+	6.55656i	−0.103827	+	0.319547i	0.885626	+	0.464399i	$0.153730\pi$
$422$	−1.87169	−	5.76047i	−0.0911124	−	0.280415i
$423$	−7.99541	+	5.80901i	−0.388750	+	0.282444i
$424$	−2.52988	+	1.83806i	−0.122862	+	0.0892642i
$425$	−5.21815	−	16.0598i	−0.253117	−	0.779015i
$426$	−14.0055	+	43.1046i	−0.678570	+	2.08842i
$427$	−9.57408	−	6.95598i	−0.463322	−	0.336623i
$428$	−14.1851			−0.685663
$429$	22.2077	+	0.834688i	1.07220	+	0.0402991i
$430$	−25.3456			−1.22227
$431$	−9.93767	−	7.22014i	−0.478681	−	0.347782i	0.322134	−	0.946694i	$-0.395600\pi$
$431$	−9.93767	−	7.22014i	−0.478681	−	0.347782i	−0.800815	+	0.598912i	$0.795600\pi$
$432$	−5.25980	+	16.1880i	−0.253062	+	0.778846i
$433$	1.38485	+	4.26214i	0.0665519	+	0.204826i	0.978802	−	0.204807i	$-0.0656568\pi$
$433$	1.38485	+	4.26214i	0.0665519	+	0.204826i	−0.912250	+	0.409633i	$0.865657\pi$
$434$	−3.86263	+	2.80636i	−0.185412	+	0.134710i
$435$	−2.49419	+	1.81214i	−0.119587	+	0.0868853i
$436$	0.256879	+	0.790593i	0.0123023	+	0.0378625i
$437$	0.0771134	−	0.237330i	0.00368883	−	0.0113531i
$438$	−14.9201	−	10.8401i	−0.712909	−	0.517959i
$439$	−28.4158			−1.35621			−0.678107	−	0.734963i	$-0.737199\pi$
$439$	−28.4158			−1.35621			−0.678107	+	0.734963i	$0.737199\pi$
$440$	3.49620	−	9.52678i	0.166675	−	0.454171i
$441$	8.10722			0.386058
$442$	6.29664	+	4.57478i	0.299501	+	0.217600i
$443$	−1.53010	+	4.70917i	−0.0726974	+	0.223740i	−0.980803	−	0.195002i	$-0.937529\pi$
$443$	−1.53010	+	4.70917i	−0.0726974	+	0.223740i	0.908105	+	0.418742i	$0.137529\pi$
$444$	5.53313	+	17.0292i	0.262591	+	0.808171i
$445$	11.6215	−	8.44355i	0.550914	−	0.400263i
$446$	−13.2840	+	9.65142i	−0.629018	+	0.457008i
$447$	−14.8616	−	45.7394i	−0.702931	−	2.16340i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−20.2670	−	14.7249i	−0.956460	−	0.694909i	−0.00413422	−	0.999991i	$-0.501316\pi$
$449$	−20.2670	−	14.7249i	−0.956460	−	0.694909i	−0.952326	+	0.305082i	$0.901316\pi$
$450$	−35.3644			−1.66709
$451$	16.8225	−	11.2819i	0.792142	−	0.531245i
$452$	10.6854			0.502598
$453$	9.67603	+	7.03005i	0.454620	+	0.330301i
$454$	1.89485	−	5.83174i	0.0889296	−	0.273697i
$455$	1.90099	+	5.85065i	0.0891199	+	0.274283i
$456$	−0.868769	+	0.631198i	−0.0406838	+	0.0295585i
$457$	−12.2964	+	8.93387i	−0.575202	+	0.417909i	−0.836991	−	0.547216i	$-0.815687\pi$
$457$	−12.2964	+	8.93387i	−0.575202	+	0.417909i	0.261789	+	0.965125i	$0.415687\pi$
$458$	0.215257	+	0.662492i	0.0100583	+	0.0309562i
$459$	20.3615	−	62.6661i	0.950392	−	2.92501i
$460$	1.91711	+	1.39286i	0.0893857	+	0.0649425i
$461$	−12.0838			−0.562797			−0.281398	−	0.959591i	$-0.590798\pi$
$461$	−12.0838			−0.562797			−0.281398	+	0.959591i	$0.590798\pi$
$462$	3.01846	+	10.6334i	0.140432	+	0.494708i
$463$	−17.6430			−0.819941			−0.409970	−	0.912099i	$-0.634461\pi$
$463$	−17.6430			−0.819941			−0.409970	+	0.912099i	$0.634461\pi$
$464$	−0.244591	−	0.177706i	−0.0113549	−	0.00824979i
$465$	−15.0451	+	46.3042i	−0.697702	+	2.14730i
$466$	−4.20769	−	12.9500i	−0.194918	−	0.599895i
$467$	−7.61721	+	5.53423i	−0.352482	+	0.256093i	−0.749910	−	0.661540i	$-0.769903\pi$
$467$	−7.61721	+	5.53423i	−0.352482	+	0.256093i	0.397427	+	0.917634i	$0.369903\pi$
$468$	13.1869	−	9.58081i	0.609562	−	0.442873i
$469$	−0.687186	−	2.11494i	−0.0317313	−	0.0976589i
$470$	1.15260	−	3.54735i	0.0531656	−	0.163627i
$471$	−28.9434	−	21.0286i	−1.33364	−	0.968949i
$472$	13.4874			0.620809
$473$	21.6042	+	16.9718i	0.993363	+	0.780366i
$474$	58.5213			2.68797
$475$	−1.13709	−	0.826146i	−0.0521734	−	0.0379062i
$476$	−1.19625	+	3.68168i	−0.0548301	+	0.168750i
$477$	−7.83422	−	24.1112i	−0.358704	−	1.10398i
$478$	−19.3079	+	14.0280i	−0.883121	+	0.641625i
$479$	−13.1869	+	9.58081i	−0.602523	+	0.437758i	−0.846773	−	0.531954i	$-0.821458\pi$
$479$	−13.1869	+	9.58081i	−0.602523	+	0.437758i	0.244251	+	0.969712i	$0.421458\pi$
$480$	−3.15117	−	9.69829i	−0.143830	−	0.442664i
$481$	3.33795	−	10.2732i	0.152198	−	0.468416i
$482$	19.1590	+	13.9198i	0.872668	+	0.634030i
$483$	−2.58111			−0.117444
$484$	−9.35942	+	5.77938i	−0.425428	+	0.262699i
$485$	−31.5172			−1.43112
$486$	−46.0618	−	33.4659i	−2.08941	−	1.51804i
$487$	7.25280	−	22.3218i	0.328656	−	1.01150i	−0.641108	−	0.767451i	$-0.721525\pi$
$487$	7.25280	−	22.3218i	0.328656	−	1.01150i	0.969763	−	0.244047i	$-0.0784752\pi$
$488$	−3.65697	−	11.2550i	−0.165543	−	0.509490i
$489$	−6.16490	+	4.47907i	−0.278787	+	0.202550i
$490$	−2.47539	+	1.79848i	−0.111827	+	0.0812469i
$491$	5.85708	+	18.0262i	0.264326	+	0.813512i	0.991848	+	0.127428i	$0.0406720\pi$
$491$	5.85708	+	18.0262i	0.264326	+	0.813512i	−0.727522	+	0.686085i	$0.759328\pi$
$492$	6.28968	−	19.3576i	0.283560	−	0.872709i
$493$	0.946849	+	0.687926i	0.0426439	+	0.0309826i
$494$	0.647822			0.0291469
$495$	64.6965	+	50.8243i	2.90789	+	2.28438i
$496$	−4.77447			−0.214380
$497$	11.0020	+	7.99343i	0.493508	+	0.358554i
$498$	−0.317313	+	0.976590i	−0.0142191	+	0.0437620i
$499$	2.69537	+	8.29551i	0.120662	+	0.371358i	0.993086	−	0.117391i	$-0.0374532\pi$
$499$	2.69537	+	8.29551i	0.120662	+	0.371358i	−0.872424	+	0.488749i	$0.837453\pi$
$500$	−1.57909	+	1.14728i	−0.0706192	+	0.0513078i
$501$	−37.3924	+	27.1672i	−1.67057	+	1.21374i
$502$	−1.36208	−	4.19206i	−0.0607928	−	0.187101i
$503$	13.1890	−	40.5916i	0.588069	−	1.80989i	0.00149168	−	0.999999i	$-0.499525\pi$
$503$	13.1890	−	40.5916i	0.588069	−	1.80989i	0.586578	−	0.809893i	$-0.300475\pi$
$504$	6.55888	+	4.76530i	0.292156	+	0.212263i
$505$	−6.08727			−0.270880
$506$	−0.701434	−	2.47099i	−0.0311825	−	0.109849i
$507$	29.8539			1.32586
$508$	−1.51609	−	1.10150i	−0.0672654	−	0.0488712i
$509$	8.92796	−	27.4774i	0.395725	−	1.21792i	−0.532671	−	0.846323i	$-0.678812\pi$
$509$	8.92796	−	27.4774i	0.395725	−	1.21792i	0.928396	−	0.371593i	$-0.121188\pi$
$510$	12.1986	+	37.5435i	0.540164	+	1.66246i
$511$	−4.47681	+	3.25259i	−0.198042	+	0.143886i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.69478	−	5.21600i	−0.0748264	−	0.230292i
$514$	−7.80434	+	24.0193i	−0.344235	+	1.05945i
$515$	4.30543	+	3.12808i	0.189720	+	0.137839i
$516$	27.6069			1.21533
$517$	−3.35783	+	2.25191i	−0.147677	+	0.0990389i
$518$	5.37262			0.236059
$519$	22.9633	+	16.6838i	1.00798	+	0.732339i
$520$	−1.90099	+	5.85065i	−0.0833640	+	0.256568i
$521$	−10.2349	−	31.4997i	−0.448398	−	1.38003i	−0.878714	−	0.477349i	$-0.841598\pi$
$521$	−10.2349	−	31.4997i	−0.448398	−	1.38003i	0.430316	−	0.902678i	$-0.358402\pi$
$522$	1.98295	−	1.44070i	0.0867915	−	0.0630577i
$523$	31.5084	−	22.8922i	1.37776	−	1.00100i	0.380679	−	0.924707i	$-0.375690\pi$
$523$	31.5084	−	22.8922i	1.37776	−	1.00100i	0.997085	−	0.0762974i	$-0.0243099\pi$
$524$	−0.552138	−	1.69931i	−0.0241203	−	0.0742345i
$525$	−4.49241	+	13.8262i	−0.196065	+	0.603425i
$526$	23.1099	+	16.7903i	1.00764	+	0.732093i
$527$	18.4827			0.805118
$528$	−3.80814	+	10.3768i	−0.165728	+	0.451591i
$529$	−22.4002			−0.973922
$530$	7.74079	+	5.62402i	0.336239	+	0.244292i
$531$	−33.7896	+	103.994i	−1.46634	+	4.51294i
$532$	0.0995695	+	0.306444i	0.00431689	+	0.0132860i
$533$	−9.93374	+	7.21728i	−0.430278	+	0.312615i
$534$	−12.6584	+	9.19690i	−0.547785	+	0.397989i
$535$	13.4122	+	41.2786i	0.579861	+	1.78463i
$536$	0.687186	−	2.11494i	0.0296819	−	0.0913515i
$537$	−46.9514	−	34.1122i	−2.02610	−	1.47205i
$538$	−4.34861			−0.187482
$539$	3.31428	+	0.124569i	0.142756	+	0.00536557i
$540$	52.0803			2.24118
$541$	−27.3721	−	19.8870i	−1.17682	−	0.855007i	−0.185008	−	0.982737i	$-0.559231\pi$
$541$	−27.3721	−	19.8870i	−1.17682	−	0.855007i	−0.991809	+	0.127730i	$0.959231\pi$
$542$	−3.45602	+	10.6365i	−0.148449	+	0.456878i
$543$	−9.93198	−	30.5675i	−0.426222	−	1.31178i
$544$	−3.13182	+	2.27540i	−0.134276	+	0.0975571i
$545$	2.05774	−	1.49504i	0.0881439	−	0.0640403i
$546$	−2.07060	−	6.37266i	−0.0886136	−	0.272725i
$547$	9.96602	−	30.6723i	0.426116	−	1.31145i	−0.475805	−	0.879551i	$-0.657843\pi$
$547$	9.96602	−	30.6723i	0.426116	−	1.31145i	0.901921	−	0.431901i	$-0.142157\pi$
$548$	7.84416	+	5.69912i	0.335086	+	0.243454i
$549$	95.9426			4.09473
$550$	−14.4572	−	0.543381i	−0.616456	−	0.0231698i
$551$	0.0974153			0.00415003
$552$	−2.08816	−	1.51714i	−0.0888779	−	0.0645736i
$553$	5.42617	−	16.7000i	0.230744	−	0.710158i
$554$	1.00651	+	3.09772i	0.0427626	+	0.131610i
$555$	44.3233	−	32.2028i	1.88142	−	1.36693i
$556$	−16.1974	+	11.7681i	−0.686922	+	0.499078i
$557$	−1.33198	−	4.09941i	−0.0564378	−	0.173698i	0.918864	−	0.394575i	$-0.129108\pi$
$557$	−1.33198	−	4.09941i	−0.0564378	−	0.173698i	−0.975302	+	0.220877i	$0.929108\pi$
$558$	11.9613	−	36.8132i	0.506363	−	1.55843i
$559$	−13.4736	−	9.78917i	−0.569874	−	0.414038i
$560$	−3.05975			−0.129298
$561$	14.7419	−	40.1700i	0.622403	−	1.69598i
$562$	−2.53658			−0.106999
$563$	−35.1289	−	25.5226i	−1.48051	−	1.07565i	−0.977393	−	0.211430i	$-0.932188\pi$
$563$	−35.1289	−	25.5226i	−1.48051	−	1.07565i	−0.503113	−	0.864221i	$-0.667812\pi$
$564$	−1.25544	+	3.86385i	−0.0528636	+	0.162697i
$565$	−10.1032	−	31.0944i	−0.425044	−	1.30815i
$566$	16.6997	−	12.1330i	0.701940	−	0.509989i
$567$	−26.2164	+	19.0474i	−1.10099	+	0.799914i
$568$	4.20239	+	12.9336i	0.176329	+	0.542684i
$569$	4.97273	−	15.3045i	0.208468	−	0.641598i	−0.791085	−	0.611706i	$-0.790484\pi$
$569$	4.97273	−	15.3045i	0.208468	−	0.641598i	0.999553	−	0.0298919i	$-0.00951631\pi$
$570$	2.65822	+	1.93131i	0.111341	+	0.0808936i
$571$	−7.23141			−0.302625			−0.151313	−	0.988486i	$-0.548350\pi$
$571$	−7.23141			−0.302625			−0.151313	+	0.988486i	$0.548350\pi$
$572$	5.53808	−	3.71408i	0.231559	−	0.155293i
$573$	5.99937			0.250627
$574$	−4.94084	−	3.58973i	−0.206227	−	0.149833i
$575$	1.04395	−	3.21295i	0.0435357	−	0.133989i
$576$	2.50527	+	7.71042i	0.104386	+	0.321268i
$577$	−36.4417	+	26.4764i	−1.51709	+	1.10223i	−0.554180	+	0.832397i	$0.686968\pi$
$577$	−36.4417	+	26.4764i	−1.51709	+	1.10223i	−0.962907	+	0.269832i	$0.913032\pi$
$578$	−1.62953	+	1.18392i	−0.0677795	+	0.0492447i
$579$	10.5967	+	32.6133i	0.440384	+	1.35536i
$580$	−0.285859	+	0.879783i	−0.0118696	+	0.0365310i
$581$	0.249265	+	0.181101i	0.0103412	+	0.00751336i
$582$	34.3292			1.42299
$583$	−2.83221	−	9.97722i	−0.117298	−	0.413214i
$584$	−5.53364			−0.228984
$585$	−40.3485	−	29.3149i	−1.66821	−	1.21202i
$586$	4.79636	−	14.7617i	0.198136	−	0.609800i
$587$	5.80963	+	17.8802i	0.239789	+	0.737995i	0.996450	+	0.0841874i	$0.0268294\pi$
$587$	5.80963	+	17.8802i	0.239789	+	0.737995i	−0.756661	+	0.653808i	$0.773171\pi$
$588$	2.69625	−	1.95894i	0.111192	−	0.0807854i
$589$	1.24459	−	0.904248i	0.0512825	−	0.0372589i
$590$	−12.7526	−	39.2484i	−0.525015	−	1.61583i
$591$	−9.81666	+	30.2126i	−0.403804	+	1.24278i
$592$	4.34654	+	3.15795i	0.178642	+	0.129791i
$593$	21.1599			0.868933			0.434466	−	0.900688i	$-0.356937\pi$
$593$	21.1599			0.868933			0.434466	+	0.900688i	$0.356937\pi$
$594$	−44.3925	−	34.8739i	−1.82145	−	1.43089i
$595$	11.8448			0.485588
$596$	−11.6745	−	8.48204i	−0.478207	−	0.347438i
$597$	−3.35445	+	10.3239i	−0.137288	+	0.422530i
$598$	0.481168	+	1.48088i	0.0196764	+	0.0605579i
$599$	17.7765	−	12.9154i	0.726327	−	0.527708i	−0.162072	−	0.986779i	$-0.551818\pi$
$599$	17.7765	−	12.9154i	0.726327	−	0.527708i	0.888399	+	0.459071i	$0.151818\pi$
$600$	−11.7613	+	8.54506i	−0.480152	+	0.348851i
$601$	13.6783	+	42.0976i	0.557951	+	1.71720i	0.688021	+	0.725691i	$0.258480\pi$
$601$	13.6783	+	42.0976i	0.557951	+	1.71720i	−0.130070	+	0.991505i	$0.541520\pi$
$602$	2.55975	−	7.87811i	0.104328	−	0.321088i
$603$	14.5855	+	10.5970i	0.593967	+	0.431543i
$604$	3.58870			0.146022
$605$	25.6675	+	21.7714i	1.04353	+	0.885133i
$606$	6.63039			0.269341
$607$	19.4482	+	14.1299i	0.789377	+	0.573516i	0.907779	−	0.419450i	$-0.137777\pi$
$607$	19.4482	+	14.1299i	0.789377	+	0.573516i	−0.118401	+	0.992966i	$0.537777\pi$
$608$	−0.0995695	+	0.306444i	−0.00403808	+	0.0124279i
$609$	−0.311364	−	0.958279i	−0.0126171	−	0.0388314i
$610$	−29.2943	+	21.2836i	−1.18609	+	0.861747i
$611$	1.98281	−	1.44059i	0.0802158	−	0.0582802i
$612$	−9.69826	−	29.8482i	−0.392029	−	1.20654i
$613$	−13.1570	+	40.4931i	−0.531407	+	1.63550i	0.219881	+	0.975527i	$0.429433\pi$
$613$	−13.1570	+	40.4931i	−0.531407	+	1.63550i	−0.751288	+	0.659975i	$0.770567\pi$
$614$	4.29916	+	3.12352i	0.173500	+	0.126055i
$615$	−62.2776			−2.51128
$616$	2.60809	+	2.04887i	0.105083	+	0.0825512i
$617$	46.8952			1.88793			0.943964	−	0.330048i	$-0.107065\pi$
$617$	46.8952			1.88793			0.943964	+	0.330048i	$0.107065\pi$
$618$	−4.68956	−	3.40717i	−0.188642	−	0.137056i
$619$	−4.16459	+	12.8173i	−0.167389	+	0.515170i	−0.999204	−	0.0398820i	$-0.987302\pi$
$619$	−4.16459	+	12.8173i	−0.167389	+	0.515170i	0.831815	+	0.555052i	$0.187302\pi$
$620$	4.51433	+	13.8937i	0.181300	+	0.557984i
$621$	10.6647	−	7.74834i	0.427959	−	0.310930i
$622$	13.2827	−	9.65045i	0.532588	−	0.386948i
$623$	1.45078	+	4.46505i	0.0581244	+	0.178888i
$624$	2.07060	−	6.37266i	0.0828904	−	0.255111i
$625$	22.4766	+	16.3302i	0.899065	+	0.653209i
$626$	4.15541			0.166084
$627$	−0.972591	−	3.42621i	−0.0388415	−	0.136830i
$628$	−10.7347			−0.428361
$629$	−16.8261	−	12.2249i	−0.670901	−	0.487438i
$630$	7.66550	−	23.5920i	0.305401	−	0.939927i
$631$	10.1386	+	31.2033i	0.403610	+	1.24218i	0.922050	+	0.387070i	$0.126513\pi$
$631$	10.1386	+	31.2033i	0.403610	+	1.24218i	−0.518441	+	0.855114i	$0.673487\pi$
$632$	14.2059	−	10.3212i	0.565081	−	0.410555i
$633$	16.3310	−	11.8651i	0.649098	−	0.471597i
$634$	−6.50473	−	20.0195i	−0.258336	−	0.795075i
$635$	−1.77188	+	5.45329i	−0.0703150	+	0.216407i
$636$	−8.43144	−	6.12580i	−0.334328	−	0.242904i
$637$	−2.01054			−0.0796603
$638$	0.832781	−	0.558499i	0.0329701	−	0.0221112i
$639$	−110.252			−4.36150
$640$	−2.47539	−	1.79848i	−0.0978484	−	0.0710911i
$641$	12.2168	−	37.5994i	0.482534	−	1.48509i	−0.352986	−	0.935629i	$-0.614834\pi$
$641$	12.2168	−	37.5994i	0.482534	−	1.48509i	0.835521	−	0.549459i	$-0.185166\pi$
$642$	−14.6089	−	44.9616i	−0.576567	−	1.77449i
$643$	3.55494	−	2.58282i	0.140193	−	0.101856i	−0.515478	−	0.856903i	$-0.672386\pi$
$643$	3.55494	−	2.58282i	0.140193	−	0.101856i	0.655671	+	0.755046i	$0.272386\pi$
$644$	−0.626557	+	0.455220i	−0.0246898	+	0.0179382i
$645$	−26.1028	−	80.3361i	−1.02780	−	3.16323i
$646$	0.385448	−	1.18629i	0.0151653	−	0.0466739i
$647$	10.1755	+	7.39293i	0.400040	+	0.290646i	0.769557	−	0.638578i	$-0.220477\pi$
$647$	10.1755	+	7.39293i	0.400040	+	0.290646i	−0.369517	+	0.929224i	$0.620477\pi$
$648$	−32.4053			−1.27300
$649$	−15.4113	+	41.9942i	−0.604947	+	1.64842i
$650$	8.77012			0.343993
$651$	−12.8732	−	9.35290i	−0.504539	−	0.366569i
$652$	−0.706559	+	2.17456i	−0.0276710	+	0.0851625i
$653$	−7.90626	−	24.3330i	−0.309396	−	0.952223i	−0.978000	−	0.208604i	$-0.933108\pi$
$653$	−7.90626	−	24.3330i	−0.309396	−	0.952223i	0.668604	−	0.743618i	$-0.266892\pi$
$654$	−2.24134	+	1.62843i	−0.0876432	+	0.0636765i
$655$	−4.42292	+	3.21344i	−0.172818	+	0.125559i
$656$	−1.88723	−	5.80831i	−0.0736841	−	0.226776i
$657$	13.8633	−	42.6667i	0.540857	−	1.66459i
$658$	0.986209	+	0.716523i	0.0384464	+	0.0279330i
$659$	−0.107281			−0.00417908			−0.00208954	−	0.999998i	$-0.500665\pi$
$659$	−0.107281			−0.00417908			−0.00208954	+	0.999998i	$0.500665\pi$
$660$	33.7970	+	1.27028i	1.31555	+	0.0494455i
$661$	−5.56598			−0.216492			−0.108246	−	0.994124i	$-0.534523\pi$
$661$	−5.56598			−0.216492			−0.108246	+	0.994124i	$0.534523\pi$
$662$	5.73236	+	4.16480i	0.222794	+	0.161870i
$663$	−8.01561	+	24.6695i	−0.311300	+	0.958084i
$664$	0.0952107	+	0.293028i	0.00369489	+	0.0113717i
$665$	0.797605	−	0.579494i	0.0309298	−	0.0224718i
$666$	−35.2383	+	25.6022i	−1.36546	+	0.992063i
$667$	0.0723550	+	0.222686i	0.00280160	+	0.00862243i
$668$	−4.28554	+	13.1895i	−0.165813	+	0.510319i
$669$	−44.2724	−	32.1658i	−1.71167	−	1.24360i
$670$	−6.80422			−0.262870
$671$	39.2220	+	1.47418i	1.51415	+	0.0569100i
$672$	3.33275			0.128564
$673$	35.7399	+	25.9666i	1.37767	+	1.00094i	0.997093	+	0.0761907i	$0.0242758\pi$
$673$	35.7399	+	25.9666i	1.37767	+	1.00094i	0.380580	+	0.924748i	$0.375724\pi$
$674$	−5.78770	+	17.8127i	−0.222934	+	0.686119i
$675$	−22.9437	−	70.6134i	−0.883103	−	2.71791i
$676$	7.24697	−	5.26523i	0.278730	−	0.202509i
$677$	−6.87115	+	4.99218i	−0.264080	+	0.191865i	−0.711944	−	0.702237i	$-0.752185\pi$
$677$	−6.87115	+	4.99218i	−0.264080	+	0.191865i	0.447864	+	0.894102i	$0.352185\pi$
$678$	11.0046	+	33.8687i	0.422630	+	1.30072i
$679$	3.18305	−	9.79643i	0.122154	−	0.375953i
$680$	9.58261	+	6.96217i	0.367476	+	0.266987i
$681$	20.4359			0.783107
$682$	5.45551	−	14.8657i	0.208902	−	0.569236i
$683$	30.8407			1.18009			0.590043	−	0.807372i	$-0.299111\pi$
$683$	30.8407			1.18009			0.590043	+	0.807372i	$0.299111\pi$
$684$	−2.11336	−	1.53545i	−0.0808064	−	0.0587093i
$685$	9.16764	−	28.2151i	0.350277	−	1.07804i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−1.87817	+	1.36457i	−0.0716566	+	0.0520616i
$688$	6.70152	−	4.86894i	0.255493	−	0.185627i
$689$	1.94283	+	5.97943i	0.0740161	+	0.227798i
$690$	−2.44047	+	7.51101i	−0.0929073	+	0.285939i
$691$	17.7724	+	12.9124i	0.676095	+	0.491212i	0.872060	−	0.489399i	$-0.162784\pi$
$691$	17.7724	+	12.9124i	0.676095	+	0.491212i	−0.195965	+	0.980611i	$0.562784\pi$
$692$	8.51676			0.323759
$693$	−22.3316	+	14.9765i	−0.848307	+	0.568912i
$694$	−25.2478			−0.958393
$695$	49.5600	+	36.0074i	1.87992	+	1.36584i
$696$	0.311364	−	0.958279i	0.0118022	−	0.0363235i
$697$	7.30576	+	22.4848i	0.276725	+	0.851673i
$698$	−0.883436	+	0.641854i	−0.0334386	+	0.0242945i
$699$	36.7132	−	26.6737i	1.38862	−	1.00889i
$700$	1.34796	+	4.14859i	0.0509480	+	0.156802i
$701$	−13.8794	+	42.7164i	−0.524218	+	1.61338i	0.241639	+	0.970366i	$0.422315\pi$
$701$	−13.8794	+	42.7164i	−0.524218	+	1.61338i	−0.765857	+	0.643011i	$0.777685\pi$
$702$	27.6857	+	20.1149i	1.04493	+	0.759187i
$703$	−1.73113			−0.0652909
$704$	0.905698	+	3.19057i	0.0341348	+	0.120249i
$705$	12.4308			0.468172
$706$	16.7059	+	12.1376i	0.628735	+	0.456803i
$707$	0.614778	−	1.89209i	0.0231211	−	0.0711595i
$708$	13.8904	+	42.7502i	0.522032	+	1.60665i
$709$	−12.5342	+	9.10664i	−0.470732	+	0.342007i	−0.797727	−	0.603019i	$-0.793964\pi$
$709$	−12.5342	+	9.10664i	−0.470732	+	0.342007i	0.326994	+	0.945026i	$0.393964\pi$
$710$	33.6634	−	24.4579i	1.26337	−	0.917889i
$711$	43.9912	+	135.391i	1.64980	+	5.07756i
$712$	−1.45078	+	4.46505i	−0.0543704	+	0.167335i
$713$	2.99148	+	2.17344i	0.112032	+	0.0813958i
$714$	−12.9016			−0.482829
$715$	−16.0443	−	12.6041i	−0.600023	−	0.471366i
$716$	−17.4136			−0.650776
$717$	−64.3482	−	46.7517i	−2.40313	−	1.74598i
$718$	4.33074	−	13.3286i	0.161622	−	0.497420i
$719$	−4.18960	−	12.8943i	−0.156246	−	0.480875i	0.842039	−	0.539416i	$-0.181355\pi$
$719$	−4.18960	−	12.8943i	−0.156246	−	0.480875i	−0.998285	+	0.0585415i	$0.981355\pi$
$720$	20.0685	−	14.5806i	0.747910	−	0.543389i
$721$	−1.40712	+	1.02233i	−0.0524037	+	0.0380735i
$722$	5.83924	+	17.9713i	0.217314	+	0.668824i
$723$	−24.3893	+	75.0626i	−0.907049	+	2.79161i
$724$	−7.80205	−	5.66852i	−0.289961	−	0.210669i
$725$	1.31879			0.0489788
$726$	−27.9576	−	23.7139i	−1.03760	−	0.880105i
$727$	−16.5544			−0.613967			−0.306984	−	0.951715i	$-0.599320\pi$
$727$	−16.5544			−0.613967			−0.306984	+	0.951715i	$0.599320\pi$
$728$	−1.62656	−	1.18176i	−0.0602842	−	0.0437990i
$729$	28.5952	−	88.0069i	1.05908	−	3.25952i
$730$	5.23214	+	16.1029i	0.193650	+	0.595994i
$731$	−25.9426	+	18.8484i	−0.959521	+	0.697133i
$732$	31.9080	−	23.1825i	1.17935	−	0.856851i
$733$	0.274240	+	0.844025i	0.0101293	+	0.0311748i	0.955993	−	0.293388i	$-0.0947828\pi$
$733$	0.274240	+	0.844025i	0.0101293	+	0.0311748i	−0.945864	+	0.324563i	$0.894783\pi$
$734$	8.51991	−	26.2216i	0.314476	−	0.967857i
$735$	−8.24986	−	5.99387i	−0.304301	−	0.221087i
$736$	−0.774467			−0.0285472
$737$	5.79982	+	4.55623i	0.213639	+	0.167831i
$738$	49.5125			1.82258
$739$	−11.6324	−	8.45141i	−0.427904	−	0.310890i	0.352907	−	0.935659i	$-0.385193\pi$
$739$	−11.6324	−	8.45141i	−0.427904	−	0.310890i	−0.780810	+	0.624768i	$0.785193\pi$
$740$	5.07989	−	15.6343i	0.186741	−	0.574729i
$741$	0.667177	+	2.05336i	0.0245093	+	0.0754320i
$742$	−2.52988	+	1.83806i	−0.0928747	+	0.0674774i
$743$	5.18008	−	3.76355i	0.190039	−	0.138071i	−0.488698	−	0.872453i	$-0.662528\pi$
$743$	5.18008	−	3.76355i	0.190039	−	0.138071i	0.678736	+	0.734382i	$0.262528\pi$
$744$	−4.91711	−	15.1333i	−0.180270	−	0.554814i
$745$	−13.6443	+	41.9928i	−0.499887	+	1.53850i
$746$	21.1783	+	15.3870i	0.775394	+	0.563356i
$747$	−2.49790			−0.0913934
$748$	−3.50609	−	12.3512i	−0.128195	−	0.451603i
$749$	−14.1851			−0.518312
$750$	−5.26272	−	3.82359i	−0.192167	−	0.139618i
$751$	8.91385	−	27.4340i	0.325271	−	1.00108i	−0.646047	−	0.763298i	$-0.723579\pi$
$751$	8.91385	−	27.4340i	0.325271	−	1.00108i	0.971318	−	0.237784i	$-0.0764210\pi$
$752$	0.376698	+	1.15936i	0.0137368	+	0.0422775i
$753$	11.8845	−	8.63461i	0.433096	−	0.314663i
$754$	−0.491759	+	0.357284i	−0.0179088	+	0.0130115i
$755$	−3.39317	−	10.4431i	−0.123490	−	0.380064i
$756$	−5.25980	+	16.1880i	−0.191297	+	0.588752i
$757$	18.5864	+	13.5038i	0.675533	+	0.490804i	0.871873	−	0.489732i	$-0.162906\pi$
$757$	18.5864	+	13.5038i	0.675533	+	0.490804i	−0.196340	+	0.980536i	$0.562906\pi$
$758$	3.02576			0.109901
$759$	7.10974	−	4.76810i	0.258067	−	0.173071i
$760$	0.985894			0.0357621
$761$	−17.2012	−	12.4974i	−0.623542	−	0.453030i	0.230615	−	0.973045i	$-0.425926\pi$
$761$	−17.2012	−	12.4974i	−0.623542	−	0.453030i	−0.854157	+	0.520015i	$0.825926\pi$
$762$	1.92997	−	5.93984i	0.0699155	−	0.215178i
$763$	0.256879	+	0.790593i	0.00929965	+	0.0286214i
$764$	1.45633	−	1.05809i	0.0526883	−	0.0382803i
$765$	−77.6883	+	56.4438i	−2.80883	+	2.04073i
$766$	9.84708	+	30.3062i	0.355790	+	1.09501i
$767$	8.37960	−	25.7898i	0.302570	−	0.931214i
$768$	2.69625	+	1.95894i	0.0972926	+	0.0706872i
$769$	31.1522			1.12338			0.561688	−	0.827349i	$-0.310152\pi$
$769$	31.1522			1.12338			0.561688	+	0.827349i	$0.310152\pi$
$770$	3.49620	−	9.52678i	0.125994	−	0.343321i
$771$	−84.1699			−3.03130
$772$	8.32423	+	6.04790i	0.299595	+	0.217669i
$773$	11.0246	−	33.9304i	0.396529	−	1.22039i	−0.531236	−	0.847224i	$-0.678272\pi$
$773$	11.0246	−	33.9304i	0.396529	−	1.22039i	0.927765	−	0.373166i	$-0.121728\pi$
$774$	20.7525	+	63.8695i	0.745932	+	2.29574i
$775$	16.8491	−	12.2416i	0.605237	−	0.439731i
$776$	8.33334	−	6.05453i	0.299150	−	0.217345i
$777$	5.53313	+	17.0292i	0.198500	+	0.610920i
$778$	8.91261	−	27.4302i	0.319533	−	0.983420i
$779$	1.59201	+	1.15666i	0.0570396	+	0.0414417i
$780$	−20.5022			−0.734097
$781$	−45.0717	−	1.69404i	−1.61279	−	0.0606176i
$782$	2.99808			0.107211
$783$	4.16320	+	3.02474i	0.148781	+	0.108096i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	10.1498	+	31.2380i	0.362263	+	1.11493i
$786$	4.81754	−	3.50015i	0.171836	−	0.124846i
$787$	38.2229	−	27.7706i	1.36250	−	0.989914i	0.364219	−	0.931313i	$-0.381336\pi$
$787$	38.2229	−	27.7706i	1.36250	−	0.989914i	0.998281	−	0.0586011i	$-0.0186640\pi$
$788$	2.94552	+	9.06536i	0.104930	+	0.322940i
$789$	−29.4188	+	90.5419i	−1.04734	+	3.22338i
$790$	−43.4666	−	31.5803i	−1.54647	−	1.12358i
$791$	10.6854			0.379928
$792$	−26.8696	−	1.00991i	−0.954770	−	0.0358855i
$793$	−23.7931			−0.844918
$794$	−8.07111	−	5.86401i	−0.286433	−	0.208106i
$795$	−9.85401	+	30.3275i	−0.349486	+	1.07561i
$796$	1.00651	+	3.09772i	0.0356748	+	0.109796i
$797$	−23.2912	+	16.9221i	−0.825018	+	0.599410i	−0.918145	−	0.396244i	$-0.870314\pi$
$797$	−23.2912	+	16.9221i	−0.825018	+	0.599410i	0.0931276	+	0.995654i	$0.470314\pi$
$798$	−0.868769	+	0.631198i	−0.0307541	+	0.0223442i
$799$	−1.45826	−	4.48805i	−0.0515894	−	0.158776i
$800$	−1.34796	+	4.14859i	−0.0476575	+	0.146675i
$801$	−30.7928	−	22.3723i	−1.08801	−	0.790486i
$802$	−19.5507			−0.690359
$803$	6.32297	−	17.2294i	0.223133	−	0.608013i
$804$	7.41130			0.261376
$805$	1.91711	+	1.39286i	0.0675692	+	0.0490919i
$806$	−2.96633	+	9.12941i	−0.104484	+	0.321570i
$807$	−4.47853	−	13.7835i	−0.157652	−	0.485202i
$808$	1.60951	−	1.16938i	0.0566224	−	0.0411386i
$809$	−9.87871	+	7.17730i	−0.347317	+	0.252341i	−0.747743	−	0.663989i	$-0.768862\pi$
$809$	−9.87871	+	7.17730i	−0.347317	+	0.252341i	0.400426	+	0.916329i	$0.368862\pi$
$810$	30.6397	+	94.2994i	1.07657	+	3.31334i
$811$	0.555728	−	1.71036i	0.0195143	−	0.0600587i	−0.940825	−	0.338892i	$-0.889948\pi$
$811$	0.555728	−	1.71036i	0.0195143	−	0.0600587i	0.960339	+	0.278834i	$0.0899478\pi$
$812$	−0.244591	−	0.177706i	−0.00858347	−	0.00623625i
$813$	−37.2732			−1.30723
$814$	−14.7991	+	9.92489i	−0.518707	+	0.347867i
$815$	6.99604			0.245061
$816$	−10.4376	−	7.58335i	−0.365389	−	0.265470i
$817$	−0.824788	+	2.53843i	−0.0288557	+	0.0888086i
$818$	8.36534	+	25.7459i	0.292487	+	0.900183i
$819$	13.1869	−	9.58081i	0.460786	−	0.334781i
$820$	−15.1178	+	10.9837i	−0.527935	+	0.383567i
$821$	−9.44105	−	29.0566i	−0.329495	−	1.01408i	−0.969371	−	0.245603i	$-0.921014\pi$
$821$	−9.44105	−	29.0566i	−0.329495	−	1.01408i	0.639876	−	0.768478i	$-0.278986\pi$
$822$	−9.98559	+	30.7325i	−0.348288	+	1.07192i
$823$	23.7167	+	17.2312i	0.826713	+	0.600642i	0.918628	−	0.395125i	$-0.129299\pi$
$823$	23.7167	+	17.2312i	0.826713	+	0.600642i	−0.0919144	+	0.995767i	$0.529299\pi$
$824$	−1.73929			−0.0605911
$825$	−13.1668	−	46.3836i	−0.458409	−	1.61487i
$826$	13.4874			0.469288
$827$	−13.4912	−	9.80190i	−0.469134	−	0.340846i	0.327970	−	0.944688i	$-0.393636\pi$
$827$	−13.4912	−	9.80190i	−0.469134	−	0.340846i	−0.797104	+	0.603843i	$0.793636\pi$
$828$	1.94025	−	5.97147i	0.0674283	−	0.207523i
$829$	5.41858	+	16.6767i	0.188195	+	0.579205i	0.999989	−	0.00473947i	$-0.00150863\pi$
$829$	5.41858	+	16.6767i	0.188195	+	0.579205i	−0.811794	+	0.583944i	$0.801509\pi$
$830$	0.762689	−	0.554126i	0.0264733	−	0.0192340i
$831$	−8.78206	+	6.38054i	−0.304646	+	0.221339i
$832$	−0.621290	−	1.91213i	−0.0215393	−	0.0662913i
$833$	−1.19625	+	3.68168i	−0.0414476	+	0.127563i
$834$	−53.9818	−	39.2201i	−1.86924	−	1.35808i
$835$	42.4336			1.46848
$836$	−0.840364	−	0.660173i	−0.0290646	−	0.0228326i
$837$	81.2665			2.80898
$838$	13.9168	+	10.1111i	0.480747	+	0.349283i
$839$	−9.52988	+	29.3299i	−0.329008	+	1.01258i	0.640591	+	0.767882i	$0.278689\pi$
$839$	−9.52988	+	29.3299i	−0.329008	+	1.01258i	−0.969599	+	0.244700i	$0.921311\pi$
$840$	−3.15117	−	9.69829i	−0.108726	−	0.334623i
$841$	23.3875	−	16.9920i	0.806467	−	0.585933i
$842$	−5.57734	+	4.05217i	−0.192208	+	0.139647i
$843$	−2.61236	−	8.04003i	−0.0899746	−	0.276913i
$844$	1.87169	−	5.76047i	0.0644262	−	0.198284i
$845$	−22.1739	−	16.1103i	−0.762807	−	0.554211i
$846$	−9.88287			−0.339780
$847$	−9.35942	+	5.77938i	−0.321594	+	0.198582i
$848$	−3.12710			−0.107385
$849$	55.6558	+	40.4363i	1.91010	+	1.38777i
$850$	5.21815	−	16.0598i	0.178981	−	0.550847i
$851$	−1.28579	−	3.95727i	−0.0440765	−	0.135653i
$852$	−36.6669	+	26.6401i	−1.25619	+	0.912675i
$853$	−9.67997	+	7.03291i	−0.331436	+	0.240802i	−0.741040	−	0.671461i	$-0.765667\pi$
$853$	−9.67997	+	7.03291i	−0.331436	+	0.240802i	0.409604	+	0.912264i	$0.365667\pi$
$854$	−3.65697	−	11.2550i	−0.125139	−	0.385139i
$855$	−2.46993	+	7.60166i	−0.0844698	+	0.259971i
$856$	−11.4760	−	8.33779i	−0.392241	−	0.284980i
$857$	−13.3349			−0.455512			−0.227756	−	0.973718i	$-0.573139\pi$
$857$	−13.3349			−0.455512			−0.227756	+	0.973718i	$0.573139\pi$
$858$	17.4758	+	13.7287i	0.596614	+	0.468688i
$859$	30.0728			1.02607			0.513035	−	0.858368i	$-0.328521\pi$
$859$	30.0728			1.02607			0.513035	+	0.858368i	$0.328521\pi$
$860$	−20.5050	−	14.8977i	−0.699214	−	0.508009i
$861$	6.28968	−	19.3576i	0.214352	−	0.659706i
$862$	−3.79585	−	11.6824i	−0.129287	−	0.397905i
$863$	28.4378	−	20.6613i	0.968034	−	0.703318i	0.0130311	−	0.999915i	$-0.495852\pi$
$863$	28.4378	−	20.6613i	0.968034	−	0.703318i	0.955003	+	0.296597i	$0.0958519\pi$
$864$	−13.7703	+	10.0047i	−0.468476	+	0.340368i
$865$	−8.05273	−	24.7838i	−0.273801	−	0.842673i
$866$	−1.38485	+	4.26214i	−0.0470593	+	0.144834i
$867$	−5.43082	−	3.94572i	−0.184440	−	0.134004i
$868$	−4.77447			−0.162056
$869$	15.9036	+	56.0246i	0.539492	+	1.90051i
$870$	−3.08299			−0.104523
$871$	−3.61711	−	2.62798i	−0.122561	−	0.0890457i
$872$	−0.256879	+	0.790593i	−0.00869903	+	0.0267729i
$873$	25.8057	+	79.4218i	0.873391	+	2.68802i
$874$	0.201885	−	0.146678i	0.00682887	−	0.00496147i
$875$	−1.57909	+	1.14728i	−0.0533831	+	0.0387851i
$876$	−5.69896	−	17.5396i	−0.192550	−	0.592608i
$877$	11.8955	−	36.6105i	0.401682	−	1.23625i	−0.521953	−	0.852974i	$-0.674796\pi$
$877$	11.8955	−	36.6105i	0.401682	−	1.23625i	0.923634	−	0.383275i	$-0.125204\pi$
$878$	−22.9889	−	16.7024i	−0.775838	−	0.563679i
$879$	51.7288			1.74477
$880$	8.42819	−	5.65231i	0.284114	−	0.190539i
$881$	−32.9695			−1.11077			−0.555385	−	0.831593i	$-0.687429\pi$
$881$	−32.9695			−1.11077			−0.555385	+	0.831593i	$0.687429\pi$
$882$	6.55888	+	4.76530i	0.220849	+	0.160456i
$883$	2.63769	−	8.11797i	0.0887653	−	0.273192i	−0.896813	−	0.442409i	$-0.854124\pi$
$883$	2.63769	−	8.11797i	0.0887653	−	0.273192i	0.985579	+	0.169217i	$0.0541240\pi$
$884$	2.40510	+	7.40215i	0.0808924	+	0.248961i
$885$	111.269	−	80.8419i	3.74028	−	2.71747i
$886$	−4.00586	+	2.91043i	−0.134580	+	0.0977778i
$887$	−11.2699	−	34.6852i	−0.378406	−	1.16461i	−0.941152	−	0.337984i	$-0.890255\pi$
$887$	−11.2699	−	34.6852i	−0.378406	−	1.16461i	0.562745	−	0.826630i	$-0.309745\pi$
$888$	−5.53313	+	17.0292i	−0.185680	+	0.571463i
$889$	−1.51609	−	1.10150i	−0.0508479	−	0.0369431i
$890$	14.3650			0.481517
$891$	37.0277	−	100.896i	1.24047	−	3.38016i
$892$	−16.4200			−0.549782
$893$	−0.317770	−	0.230874i	−0.0106338	−	0.00772589i
$894$	14.8616	−	45.7394i	0.497048	−	1.52976i
$895$	16.4648	+	50.6734i	0.550358	+	1.69383i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−4.19832	+	3.05025i	−0.140178	+	0.101845i
$898$	−7.74132	−	23.8253i	−0.258331	−	0.795061i
$899$	−0.446057	+	1.37282i	−0.0148768	+	0.0457862i
$900$	−28.6104	−	20.7866i	−0.953679	−	0.692888i
$901$	12.1055			0.403291
$902$	20.2411	+	0.760770i	0.673953	+	0.0253309i
$903$	27.6069			0.918701
$904$	8.64465	+	6.28071i	0.287517	+	0.208893i
$905$	−9.11842	+	28.0636i	−0.303107	+	0.932866i
$906$	3.69592	+	11.3749i	0.122789	+	0.377904i
$907$	−8.53042	+	6.19771i	−0.283248	+	0.205792i	−0.720333	−	0.693629i	$-0.756011\pi$
$907$	−8.53042	+	6.19771i	−0.283248	+	0.205792i	0.437085	+	0.899420i	$0.356011\pi$
$908$	4.96078	−	3.60422i	0.164629	−	0.119610i
$909$	4.98414	+	15.3396i	0.165314	+	0.508783i
$910$	−1.90099	+	5.85065i	−0.0630173	+	0.193947i
$911$	−34.5934	−	25.1336i	−1.14613	−	0.832713i	−0.158169	−	0.987412i	$-0.550559\pi$
$911$	−34.5934	−	25.1336i	−1.14613	−	0.832713i	−0.987962	+	0.154699i	$0.950559\pi$
$912$	−1.07386			−0.0355590
$913$	−1.02116	−	0.0383807i	−0.0337954	−	0.00127022i
$914$	−15.1992			−0.502745
$915$	−97.6306	−	70.9328i	−3.22757	−	2.34497i
$916$	−0.215257	+	0.662492i	−0.00711228	+	0.0218894i
$917$	−0.552138	−	1.69931i	−0.0182332	−	0.0561160i
$918$	53.3070	−	38.7298i	1.75939	−	1.27827i
$919$	11.1064	−	8.06927i	0.366366	−	0.266181i	−0.389336	−	0.921096i	$-0.627296\pi$
$919$	11.1064	−	8.06927i	0.366366	−	0.266181i	0.755702	+	0.654915i	$0.227296\pi$
$920$	0.732271	+	2.25370i	0.0241423	+	0.0743022i
$921$	−5.47282	+	16.8436i	−0.180335	+	0.555016i
$922$	−9.77597	−	7.10266i	−0.321954	−	0.233914i
$923$	27.3417			0.899964
$924$	−3.80814	+	10.3768i	−0.125279	+	0.341371i
$925$	−23.4358			−0.770565
$926$	−14.2735	−	10.3703i	−0.469057	−	0.340790i
$927$	4.35739	−	13.4107i	0.143115	−	0.440464i
$928$	−0.0934255	−	0.287534i	−0.00306684	−	0.00943877i
$929$	6.82289	−	4.95712i	0.223852	−	0.162638i	−0.470207	−	0.882556i	$-0.655821\pi$
$929$	6.82289	−	4.95712i	0.223852	−	0.162638i	0.694059	+	0.719918i	$0.255821\pi$
$930$	−39.3887	+	28.6176i	−1.29161	+	0.938406i
$931$	0.0995695	+	0.306444i	0.00326326	+	0.0100433i
$932$	4.20769	−	12.9500i	0.137828	−	0.424190i
$933$	44.2679	+	32.1625i	1.44927	+	1.05295i
$934$	−9.41539			−0.308081
$935$	−32.6268	+	21.8809i	−1.06701	+	0.715583i
$936$	16.2998			0.532777
$937$	−21.4855	−	15.6101i	−0.701900	−	0.509960i	0.178651	−	0.983913i	$-0.442827\pi$
$937$	−21.4855	−	15.6101i	−0.701900	−	0.509960i	−0.880550	+	0.473952i	$0.842827\pi$
$938$	0.687186	−	2.11494i	0.0224374	−	0.0690553i
$939$	4.27956	+	13.1711i	0.139658	+	0.429824i
$940$	3.01756	−	2.19238i	0.0984218	−	0.0715076i
$941$	−8.53973	+	6.20448i	−0.278387	+	0.202260i	−0.718214	−	0.695823i	$-0.755040\pi$
$941$	−8.53973	+	6.20448i	−0.278387	+	0.202260i	0.439826	+	0.898083i	$0.355040\pi$
$942$	−11.0554	−	34.0251i	−0.360205	−	1.10860i
$943$	−1.46160	+	4.49834i	−0.0475963	+	0.146486i
$944$	10.9116	+	7.92771i	0.355141	+	0.258025i
$945$	52.0803			1.69417
$946$	7.50238	+	26.4292i	0.243923	+	0.859286i
$947$	−0.676703			−0.0219899			−0.0109949	−	0.999940i	$-0.503500\pi$
$947$	−0.676703			−0.0219899			−0.0109949	+	0.999940i	$0.503500\pi$
$948$	47.3447	+	34.3980i	1.53769	+	1.11719i
$949$	−3.43799	+	10.5811i	−0.111602	+	0.343476i
$950$	−0.434331	−	1.33673i	−0.0140915	−	0.0433693i
$951$	56.7554	−	41.2352i	1.84042	−	1.33714i
$952$	−3.13182	+	2.27540i	−0.101503	+	0.0737463i
$953$	−0.319759	−	0.984117i	−0.0103580	−	0.0318787i	0.945744	−	0.324913i	$-0.105335\pi$
$953$	−0.319759	−	0.984117i	−0.0103580	−	0.0318787i	−0.956102	+	0.293034i	$0.905335\pi$
$954$	7.83422	−	24.1112i	0.253642	−	0.780630i
$955$	−4.45602	−	3.23749i	−0.144193	−	0.104763i
$956$	−23.8658			−0.771876
$957$	2.62790	+	2.06443i	0.0849479	+	0.0667334i
$958$	−16.2998			−0.526624
$959$	7.84416	+	5.69912i	0.253301	+	0.184034i
$960$	3.15117	−	9.69829i	0.101703	−	0.313011i
$961$	−2.53532	−	7.80291i	−0.0817845	−	0.251707i
$962$	8.73887	−	6.34916i	0.281753	−	0.204705i
$963$	93.0383	−	67.5963i	2.99812	−	2.17826i
$964$	7.31808	+	22.5227i	0.235700	+	0.725409i
$965$	9.72870	−	29.9419i	0.313178	−	0.963863i
$966$	−2.08816	−	1.51714i	−0.0671854	−	0.0488130i
$967$	−52.3366			−1.68303			−0.841516	−	0.540232i	$-0.818336\pi$
$967$	−52.3366			−1.68303			−0.841516	+	0.540232i	$0.818336\pi$
$968$	−10.9690	−	0.825714i	−0.352556	−	0.0265395i
$969$	4.15706			0.133544
$970$	−25.4980	−	18.5254i	−0.818690	−	0.594813i
$971$	5.11248	−	15.7346i	0.164067	−	0.504948i	−0.834899	−	0.550403i	$-0.814474\pi$
$971$	5.11248	−	15.7346i	0.164067	−	0.504948i	0.998966	+	0.0454557i	$0.0144740\pi$
$972$	−17.5941	−	54.1489i	−0.564329	−	1.73683i
$973$	−16.1974	+	11.7681i	−0.519264	+	0.377268i
$974$	18.9881	−	13.7956i	0.608417	−	0.442041i
$975$	9.03214	+	27.7981i	0.289260	+	0.890251i
$976$	3.65697	−	11.2550i	0.117057	−	0.360264i
$977$	27.2537	+	19.8010i	0.871924	+	0.633490i	0.931103	−	0.364757i	$-0.118848\pi$
$977$	27.2537	+	19.8010i	0.871924	+	0.633490i	−0.0591783	+	0.998247i	$0.518848\pi$
$978$	−7.62024			−0.243668
$979$	−12.2446	−	9.61908i	−0.391338	−	0.307427i
$980$	−3.05975			−0.0977402
$981$	−5.45225	−	3.96129i	−0.174077	−	0.126474i
$982$	−5.85708	+	18.0262i	−0.186907	+	0.575240i
$983$	11.7698	+	36.2238i	0.375399	+	1.15536i	0.943209	+	0.332199i	$0.107791\pi$
$983$	11.7698	+	36.2238i	0.375399	+	1.15536i	−0.567810	+	0.823159i	$0.692209\pi$
$984$	16.4666	−	11.9637i	0.524936	−	0.381388i
$985$	23.5952	−	17.1429i	0.751804	−	0.546218i
$986$	0.361664	+	1.11309i	0.0115177	+	0.0354479i
$987$	−1.25544	+	3.86385i	−0.0399611	+	0.122988i
$988$	0.524099	+	0.380780i	0.0166738	+	0.0121142i
$989$	−6.41532			−0.203995
$990$	22.4668	+	79.1454i	0.714042	+	2.51541i
$991$	−30.0647			−0.955036			−0.477518	−	0.878622i	$-0.658463\pi$
$991$	−30.0647			−0.955036			−0.477518	+	0.878622i	$0.658463\pi$
$992$	−3.86263	−	2.80636i	−0.122638	−	0.0891021i
$993$	−7.29727	+	22.4587i	−0.231572	+	0.712705i
$994$	4.20239	+	12.9336i	0.133292	+	0.410230i
$995$	8.06269	−	5.85789i	0.255605	−	0.185708i
$996$	−0.830737	+	0.603566i	−0.0263229	+	0.0191247i
$997$	0.824928	+	2.53887i	0.0261257	+	0.0804067i	0.963269	−	0.268537i	$-0.0865403\pi$
$997$	0.824928	+	2.53887i	0.0261257	+	0.0804067i	−0.937144	+	0.348944i	$0.886540\pi$
$998$	−2.69537	+	8.29551i	−0.0853206	+	0.262590i
$999$	−73.9828	−	53.7516i	−2.34071	−	1.70063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.e.15.1	✓	8
11.3	even	5	inner	154.2.f.e.113.1	yes	8
11.5	even	5		1694.2.a.x.1.1		4
11.6	odd	10		1694.2.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.e.15.1	✓	8	1.1	even	1	trivial
154.2.f.e.113.1	yes	8	11.3	even	5	inner
1694.2.a.x.1.1		4	11.5	even	5
1694.2.a.z.1.1		4	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.02988 + 3.16963i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.47539 - 1.79848i) q^{5} +(-2.69625 + 1.95894i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.55888 - 4.76530i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.02988 + 3.16963i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.47539 - 1.79848i) q^{5} +(-2.69625 + 1.95894i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-6.55888 - 4.76530i) q^{9} +3.05975 q^{10} +(-2.60809 - 2.04887i) q^{11} -3.33275 q^{12} +(1.62656 + 1.18176i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(3.15117 + 9.69829i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.13182 - 2.27540i) q^{17} +(-2.50527 - 7.71042i) q^{18} +(0.0995695 - 0.306444i) q^{19} +(2.47539 + 1.79848i) q^{20} -3.33275 q^{21} +(-0.905698 - 3.19057i) q^{22} +0.774467 q^{23} +(-2.69625 - 1.95894i) q^{24} +(1.34796 - 4.14859i) q^{25} +(0.621290 + 1.91213i) q^{26} +(13.7703 - 10.0047i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(0.0934255 + 0.287534i) q^{29} +(-3.15117 + 9.69829i) q^{30} +(3.86263 + 2.80636i) q^{31} -1.00000 q^{32} +(9.18017 - 6.15662i) q^{33} +3.87115 q^{34} +(2.47539 + 1.79848i) q^{35} +(2.50527 - 7.71042i) q^{36} +(-1.66023 - 5.10966i) q^{37} +(0.260676 - 0.189393i) q^{38} +(-5.42091 + 3.93852i) q^{39} +(0.945515 + 2.91000i) q^{40} +(-1.88723 + 5.80831i) q^{41} +(-2.69625 - 1.95894i) q^{42} -8.28353 q^{43} +(1.14264 - 3.11358i) q^{44} -24.8061 q^{45} +(0.626557 + 0.455220i) q^{46} +(0.376698 - 1.15936i) q^{47} +(-1.02988 - 3.16963i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.52900 - 2.56397i) q^{50} +(3.98680 + 12.2701i) q^{51} +(-0.621290 + 1.91213i) q^{52} +(2.52988 + 1.83806i) q^{53} +17.0211 q^{54} +(-10.1409 - 0.381150i) q^{55} -1.00000 q^{56} +(0.868769 + 0.631198i) q^{57} +(-0.0934255 + 0.287534i) q^{58} +(-4.16784 - 12.8273i) q^{59} +(-8.24986 + 5.99387i) q^{60} +(-9.57408 + 6.95598i) q^{61} +(1.47539 + 4.54079i) q^{62} +(2.50527 - 7.71042i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.15174 q^{65} +(11.0457 + 0.415157i) q^{66} -2.22378 q^{67} +(3.13182 + 2.27540i) q^{68} +(-0.797605 + 2.45478i) q^{69} +(0.945515 + 2.91000i) q^{70} +(11.0020 - 7.99343i) q^{71} +(6.55888 - 4.76530i) q^{72} +(1.70999 + 5.26281i) q^{73} +(1.66023 - 5.10966i) q^{74} +(11.7613 + 8.54506i) q^{75} +0.322214 q^{76} +(1.14264 - 3.11358i) q^{77} -6.70061 q^{78} +(-14.2059 - 10.3212i) q^{79} +(-0.945515 + 2.91000i) q^{80} +(10.0138 + 30.8193i) q^{81} +(-4.94084 + 3.58973i) q^{82} +(0.249265 - 0.181101i) q^{83} +(-1.02988 - 3.16963i) q^{84} +(3.66023 - 11.2650i) q^{85} +(-6.70152 - 4.86894i) q^{86} -1.00759 q^{87} +(2.75453 - 1.84731i) q^{88} +4.69483 q^{89} +(-20.0685 - 14.5806i) q^{90} +(-0.621290 + 1.91213i) q^{91} +(0.239324 + 0.736562i) q^{92} +(-12.8732 + 9.35290i) q^{93} +(0.986209 - 0.716523i) q^{94} +(-0.304658 - 0.937641i) q^{95} +(1.02988 - 3.16963i) q^{96} +(-8.33334 - 6.05453i) q^{97} -1.00000 q^{98} +(7.34269 + 25.8666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20} - 6 q^{21} - 20 q^{23} - 4 q^{24} - 25 q^{25} + 17 q^{26} + 32 q^{27} - 2 q^{28} - 23 q^{29} - 30 q^{30} + 3 q^{31} - 8 q^{32} + 40 q^{33} + 2 q^{34} + 5 q^{35} - 2 q^{36} + 6 q^{37} - q^{38} - 21 q^{39} - 2 q^{41} - 4 q^{42} - 16 q^{43} + 15 q^{44} - 40 q^{45} - 5 q^{46} + 34 q^{47} - q^{48} - 2 q^{49} - 10 q^{50} + 4 q^{51} - 17 q^{52} + 13 q^{53} + 48 q^{54} - 25 q^{55} - 8 q^{56} - 12 q^{57} + 23 q^{58} - 3 q^{59} - 25 q^{60} - 16 q^{61} - 3 q^{62} - 2 q^{63} - 2 q^{64} + 10 q^{65} + 15 q^{66} + 18 q^{67} - 7 q^{68} - 15 q^{69} + 45 q^{71} + 7 q^{72} + q^{73} - 6 q^{74} + 40 q^{75} + 26 q^{76} + 15 q^{77} - 4 q^{78} - 21 q^{79} + 57 q^{81} - 3 q^{82} + 12 q^{83} - q^{84} + 10 q^{85} - 14 q^{86} - 4 q^{87} + 10 q^{88} + 12 q^{89} - 40 q^{90} - 17 q^{91} + 5 q^{92} - 31 q^{93} + 31 q^{94} - 30 q^{95} + q^{96} + 5 q^{97} - 8 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

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