LMFDB - Embedded newform 61.2.g.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.1
Root			$-2.53165i$ of defining polynomial
Character	$\chi$	$=$	61.3
Dual form			61.2.g.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40774 - 0.782322i) q^{2} +(-0.277331 + 0.853536i) q^{3} +(3.56715 + 2.59169i) q^{4} +(0.429180 + 0.311818i) q^{5} +(1.33548 - 1.83813i) q^{6} +(3.57843 - 1.16270i) q^{7} +(-3.58511 - 4.93448i) q^{8} +(1.77544 + 1.28993i) q^{9} +O(q^{10})$	\(q+(-2.40774 - 0.782322i) q^{2} +(-0.277331 + 0.853536i) q^{3} +(3.56715 + 2.59169i) q^{4} +(0.429180 + 0.311818i) q^{5} +(1.33548 - 1.83813i) q^{6} +(3.57843 - 1.16270i) q^{7} +(-3.58511 - 4.93448i) q^{8} +(1.77544 + 1.28993i) q^{9} +(-0.789413 - 1.08653i) q^{10} +3.16134i q^{11} +(-3.20138 + 2.32594i) q^{12} -4.65275 q^{13} -9.52554 q^{14} +(-0.385172 + 0.279844i) q^{15} +(2.04660 + 6.29878i) q^{16} +(3.59169 - 4.94354i) q^{17} +(-3.26566 - 4.49479i) q^{18} +(-0.859497 + 2.64526i) q^{19} +(0.722817 + 2.22460i) q^{20} +3.37677i q^{21} +(2.47319 - 7.61169i) q^{22} +(-1.52188 + 2.09469i) q^{23} +(5.20601 - 1.69154i) q^{24} +(-1.45812 - 4.48763i) q^{25} +(11.2026 + 3.63995i) q^{26} +(-3.77157 + 2.74021i) q^{27} +(15.7782 + 5.12664i) q^{28} -9.86410i q^{29} +(1.14632 - 0.372463i) q^{30} +(-0.188112 + 0.0611214i) q^{31} -4.56821i q^{32} +(-2.69832 - 0.876737i) q^{33} +(-12.5153 + 9.09290i) q^{34} +(1.89834 + 0.616809i) q^{35} +(2.99016 + 9.20277i) q^{36} +(-4.45796 + 1.44848i) q^{37} +(4.13889 - 5.69669i) q^{38} +(1.29035 - 3.97129i) q^{39} -3.23568i q^{40} +(0.929659 + 2.86120i) q^{41} +(2.64172 - 8.13039i) q^{42} +(0.0652075 + 0.0897504i) q^{43} +(-8.19321 + 11.2770i) q^{44} +(0.359760 + 1.10723i) q^{45} +(5.30302 - 3.85287i) q^{46} -7.12344 q^{47} -5.94381 q^{48} +(5.79017 - 4.20680i) q^{49} +11.9458i q^{50} +(3.22340 + 4.43663i) q^{51} +(-16.5971 - 12.0585i) q^{52} +(1.18709 + 1.63388i) q^{53} +(11.2247 - 3.64712i) q^{54} +(-0.985763 + 1.35679i) q^{55} +(-18.5664 - 13.4893i) q^{56} +(-2.01946 - 1.46722i) q^{57} +(-7.71690 + 23.7502i) q^{58} +(2.39011 + 0.776593i) q^{59} -2.09924 q^{60} +(-5.20167 - 5.82603i) q^{61} +0.500742 q^{62} +(7.85310 + 2.55163i) q^{63} +(0.519377 - 1.59848i) q^{64} +(-1.99687 - 1.45081i) q^{65} +(5.81096 + 4.22191i) q^{66} +(5.54456 - 7.63144i) q^{67} +(25.6242 - 8.32581i) q^{68} +(-1.36583 - 1.87990i) q^{69} +(-4.08818 - 2.97023i) q^{70} +(2.69434 + 3.70844i) q^{71} -13.3854i q^{72} +(-2.80969 + 2.04136i) q^{73} +11.8668 q^{74} +4.23473 q^{75} +(-9.92164 + 7.20849i) q^{76} +(3.67570 + 11.3126i) q^{77} +(-6.21366 + 8.55237i) q^{78} +(-3.93268 - 5.41286i) q^{79} +(-1.08571 + 3.34148i) q^{80} +(0.741582 + 2.28235i) q^{81} -7.61631i q^{82} +(0.572819 - 1.76296i) q^{83} +(-8.75153 + 12.0455i) q^{84} +(3.08297 - 1.00172i) q^{85} +(-0.0867890 - 0.267109i) q^{86} +(8.41936 + 2.73562i) q^{87} +(15.5996 - 11.3338i) q^{88} +(-11.9477 - 3.88203i) q^{89} -2.94737i q^{90} +(-16.6496 + 5.40977i) q^{91} +(-10.8576 + 3.52784i) q^{92} -0.177511i q^{93} +(17.1514 + 5.57282i) q^{94} +(-1.19372 + 0.867287i) q^{95} +(3.89913 + 1.26691i) q^{96} +(1.87366 + 5.76654i) q^{97} +(-17.2323 + 5.59911i) q^{98} +(-4.07792 + 5.61277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−2.40774	−	0.782322i	−1.70253	−	0.553185i	−0.713468	−	0.700688i	$-0.752876\pi$
$2$	−2.40774	−	0.782322i	−1.70253	−	0.553185i	−0.989062	+	0.147503i	$0.952876\pi$
$3$	−0.277331	+	0.853536i	−0.160117	+	0.492789i	−0.998643	−	0.0520718i	$-0.983418\pi$
$3$	−0.277331	+	0.853536i	−0.160117	+	0.492789i	0.838526	+	0.544861i	$0.183418\pi$
$4$	3.56715	+	2.59169i	1.78358	+	1.29584i
$5$	0.429180	+	0.311818i	0.191935	+	0.139449i	0.679603	−	0.733580i	$-0.262152\pi$
$5$	0.429180	+	0.311818i	0.191935	+	0.139449i	−0.487667	+	0.873029i	$0.662152\pi$
$6$	1.33548	−	1.83813i	0.545207	−	0.750414i
$7$	3.57843	−	1.16270i	1.35252	−	0.439460i	0.458981	−	0.888446i	$-0.348215\pi$
$7$	3.57843	−	1.16270i	1.35252	−	0.439460i	0.893539	+	0.448986i	$0.148215\pi$
$8$	−3.58511	−	4.93448i	−1.26753	−	1.74460i
$9$	1.77544	+	1.28993i	0.591813	+	0.429978i
$10$	−0.789413	−	1.08653i	−0.249634	−	0.343592i
$11$			3.16134i			0.953181i	0.879126	+	0.476590i	$0.158127\pi$
$11$			3.16134i			0.953181i	−0.879126	+	0.476590i	$0.841873\pi$
$12$	−3.20138	+	2.32594i	−0.924158	+	0.671440i
$13$	−4.65275			−1.29044			−0.645221	−	0.763996i	$-0.723235\pi$
$13$	−4.65275			−1.29044			−0.645221	+	0.763996i	$0.723235\pi$
$14$	−9.52554			−2.54581
$15$	−0.385172	+	0.279844i	−0.0994511	+	0.0722555i
$16$	2.04660	+	6.29878i	0.511649	+	1.57469i
$17$	3.59169	−	4.94354i	0.871113	−	1.19898i	−0.107691	−	0.994184i	$-0.534346\pi$
$17$	3.59169	−	4.94354i	0.871113	−	1.19898i	0.978804	−	0.204800i	$-0.0656544\pi$
$18$	−3.26566	−	4.49479i	−0.769722	−	1.05943i
$19$	−0.859497	+	2.64526i	−0.197182	+	0.606864i	0.802762	+	0.596299i	$0.203363\pi$
$19$	−0.859497	+	2.64526i	−0.197182	+	0.606864i	−0.999944	+	0.0105647i	$0.996637\pi$
$20$	0.722817	+	2.22460i	0.161627	+	0.497436i
$21$			3.37677i			0.736872i
$22$	2.47319	−	7.61169i	0.527286	−	1.62282i
$23$	−1.52188	+	2.09469i	−0.317334	+	0.436773i	−0.937651	−	0.347578i	$-0.887004\pi$
$23$	−1.52188	+	2.09469i	−0.317334	+	0.436773i	0.620317	+	0.784351i	$0.287004\pi$
$24$	5.20601	−	1.69154i	1.06267	−	0.345283i
$25$	−1.45812	−	4.48763i	−0.291624	−	0.897526i
$26$	11.2026	+	3.63995i	2.19701	+	0.713853i
$27$	−3.77157	+	2.74021i	−0.725839	+	0.527353i
$28$	15.7782	+	5.12664i	2.98179	+	0.968843i
$29$		−	9.86410i		−	1.83172i	−0.401501	−	0.915859i	$-0.631511\pi$
$29$		−	9.86410i		−	1.83172i	0.401501	−	0.915859i	$-0.368489\pi$
$30$	1.14632	−	0.372463i	0.209289	−	0.0680021i
$31$	−0.188112	+	0.0611214i	−0.0337860	+	0.0109777i	−0.325861	−	0.945418i	$-0.605654\pi$
$31$	−0.188112	+	0.0611214i	−0.0337860	+	0.0109777i	0.292075	+	0.956395i	$0.405654\pi$
$32$		−	4.56821i		−	0.807554i
$33$	−2.69832	−	0.876737i	−0.469717	−	0.152620i
$34$	−12.5153	+	9.09290i	−2.14636	+	1.55942i
$35$	1.89834	+	0.616809i	0.320879	+	0.104260i
$36$	2.99016	+	9.20277i	0.498360	+	1.53380i
$37$	−4.45796	+	1.44848i	−0.732884	+	0.238128i	−0.651600	−	0.758563i	$-0.725902\pi$
$37$	−4.45796	+	1.44848i	−0.732884	+	0.238128i	−0.0812838	+	0.996691i	$0.525902\pi$
$38$	4.13889	−	5.69669i	0.671417	−	0.924126i
$39$	1.29035	−	3.97129i	0.206621	−	0.635915i
$40$		−	3.23568i		−	0.511606i
$41$	0.929659	+	2.86120i	0.145188	+	0.446844i	0.997035	−	0.0769472i	$-0.0245173\pi$
$41$	0.929659	+	2.86120i	0.145188	+	0.446844i	−0.851847	+	0.523791i	$0.824517\pi$
$42$	2.64172	−	8.13039i	0.407627	−	1.25455i
$43$	0.0652075	+	0.0897504i	0.00994405	+	0.0136868i	0.813960	−	0.580921i	$-0.197307\pi$
$43$	0.0652075	+	0.0897504i	0.00994405	+	0.0136868i	−0.804016	+	0.594608i	$0.797307\pi$
$44$	−8.19321	+	11.2770i	−1.23517	+	1.70007i
$45$	0.359760	+	1.10723i	0.0536299	+	0.165056i
$46$	5.30302	−	3.85287i	0.781887	−	0.568074i
$47$	−7.12344			−1.03906			−0.519530	−	0.854452i	$-0.673893\pi$
$47$	−7.12344			−1.03906			−0.519530	+	0.854452i	$0.673893\pi$
$48$	−5.94381			−0.857916
$49$	5.79017	−	4.20680i	0.827167	−	0.600972i
$50$			11.9458i			1.68939i
$51$	3.22340	+	4.43663i	0.451366	+	0.621253i
$52$	−16.5971	−	12.0585i	−2.30160	−	1.67221i
$53$	1.18709	+	1.63388i	0.163059	+	0.224431i	0.882726	−	0.469888i	$-0.155706\pi$
$53$	1.18709	+	1.63388i	0.163059	+	0.224431i	−0.719667	+	0.694319i	$0.755706\pi$
$54$	11.2247	−	3.64712i	1.52749	−	0.496310i
$55$	−0.985763	+	1.35679i	−0.132920	+	0.182949i
$56$	−18.5664	−	13.4893i	−2.48104	−	1.80258i
$57$	−2.01946	−	1.46722i	−0.267484	−	0.194338i
$58$	−7.71690	+	23.7502i	−1.01328	+	3.11855i
$59$	2.39011	+	0.776593i	0.311165	+	0.101104i	0.460437	−	0.887693i	$-0.347693\pi$
$59$	2.39011	+	0.776593i	0.311165	+	0.101104i	−0.149271	+	0.988796i	$0.547693\pi$
$60$	−2.09924			−0.271010
$61$	−5.20167	−	5.82603i	−0.666006	−	0.745947i
$61$	−5.20167	−	5.82603i	−0.666006	−	0.745947i
$62$	0.500742			0.0635943
$63$	7.85310	+	2.55163i	0.989397	+	0.321475i
$64$	0.519377	−	1.59848i	0.0649222	−	0.199810i
$65$	−1.99687	−	1.45081i	−0.247681	−	0.179951i
$66$	5.81096	+	4.22191i	0.715280	+	0.519681i
$67$	5.54456	−	7.63144i	0.677376	−	0.932329i	−0.322522	−	0.946562i	$-0.604531\pi$
$67$	5.54456	−	7.63144i	0.677376	−	0.932329i	0.999899	+	0.0142333i	$0.00453076\pi$
$68$	25.6242	−	8.32581i	3.10739	−	1.00965i
$69$	−1.36583	−	1.87990i	−0.164426	−	0.226314i
$70$	−4.08818	−	2.97023i	−0.488630	−	0.355011i
$71$	2.69434	+	3.70844i	0.319760	+	0.440111i	0.938394	−	0.345568i	$-0.112314\pi$
$71$	2.69434	+	3.70844i	0.319760	+	0.440111i	−0.618634	+	0.785679i	$0.712314\pi$
$72$		−	13.3854i		−	1.57749i
$73$	−2.80969	+	2.04136i	−0.328850	+	0.238923i	−0.739942	−	0.672670i	$-0.765147\pi$
$73$	−2.80969	+	2.04136i	−0.328850	+	0.238923i	0.411093	+	0.911594i	$0.365147\pi$
$74$	11.8668			1.37949
$75$	4.23473			0.488985
$76$	−9.92164	+	7.20849i	−1.13809	+	0.826871i
$77$	3.67570	+	11.3126i	0.418885	+	1.28920i
$78$	−6.21366	+	8.55237i	−0.703558	+	0.968365i
$79$	−3.93268	−	5.41286i	−0.442461	−	0.608995i	0.528296	−	0.849060i	$-0.322831\pi$
$79$	−3.93268	−	5.41286i	−0.442461	−	0.608995i	−0.970757	+	0.240065i	$0.922831\pi$
$80$	−1.08571	+	3.34148i	−0.121386	+	0.373588i
$81$	0.741582	+	2.28235i	0.0823980	+	0.253595i
$82$		−	7.61631i		−	0.841081i
$83$	0.572819	−	1.76296i	0.0628751	−	0.193510i	−0.914685	−	0.404168i	$-0.867561\pi$
$83$	0.572819	−	1.76296i	0.0628751	−	0.193510i	0.977560	+	0.210659i	$0.0675609\pi$
$84$	−8.75153	+	12.0455i	−0.954871	+	1.31427i
$85$	3.08297	−	1.00172i	0.334395	−	0.108651i
$86$	−0.0867890	−	0.267109i	−0.00935870	−	0.0288031i
$87$	8.41936	+	2.73562i	0.902650	+	0.293289i
$88$	15.5996	−	11.3338i	1.66292	−	1.20818i
$89$	−11.9477	−	3.88203i	−1.26645	−	0.411495i	−0.402662	−	0.915349i	$-0.631915\pi$
$89$	−11.9477	−	3.88203i	−1.26645	−	0.411495i	−0.863789	+	0.503854i	$0.831915\pi$
$90$		−	2.94737i		−	0.310680i
$91$	−16.6496	+	5.40977i	−1.74535	+	0.567098i
$92$	−10.8576	+	3.52784i	−1.13198	+	0.367802i
$93$		−	0.177511i		−	0.0184071i
$94$	17.1514	+	5.57282i	1.76903	+	0.574793i
$95$	−1.19372	+	0.867287i	−0.122473	+	0.0889818i
$96$	3.89913	+	1.26691i	0.397954	+	0.129303i
$97$	1.87366	+	5.76654i	0.190242	+	0.585503i	0.999999	−	0.00126112i	$-0.000401426\pi$
$97$	1.87366	+	5.76654i	0.190242	+	0.585503i	−0.809758	+	0.586765i	$0.800401\pi$
$98$	−17.2323	+	5.59911i	−1.74073	+	0.565596i
$99$	−4.07792	+	5.61277i	−0.409846	+	0.564105i
$100$	6.42920	−	19.7870i	0.642920	−	1.97870i
$101$		−	7.37615i		−	0.733954i	−0.930230	−	0.366977i	$-0.880393\pi$
$101$		−	7.37615i		−	0.733954i	0.930230	−	0.366977i	$-0.119607\pi$
$102$	−4.29024	−	13.2040i	−0.424797	−	1.30739i
$103$	0.752231	−	2.31513i	0.0741195	−	0.228116i	−0.907133	−	0.420845i	$-0.861734\pi$
$103$	0.752231	−	2.31513i	0.0741195	−	0.228116i	0.981252	+	0.192728i	$0.0617337\pi$
$104$	16.6806	+	22.9589i	1.63567	+	2.25131i
$105$	−1.05294	+	1.44924i	−0.102756	+	0.141432i
$106$	−1.57997	−	4.86265i	−0.153460	−	0.472303i
$107$	−3.50231	+	2.54458i	−0.338581	+	0.245993i	−0.744063	−	0.668110i	$-0.767104\pi$
$107$	−3.50231	+	2.54458i	−0.338581	+	0.245993i	0.405482	+	0.914103i	$0.367104\pi$
$108$	−20.5555			−1.97796
$109$	9.94823			0.952867			0.476434	−	0.879210i	$-0.341929\pi$
$109$	9.94823			0.952867			0.476434	+	0.879210i	$0.341929\pi$
$110$	3.43491	−	2.49560i	0.327505	−	0.237947i
$111$		−	4.20674i		−	0.399286i
$112$	14.6472	+	20.1602i	1.38403	+	1.90496i
$113$	9.29626	+	6.75413i	0.874518	+	0.635375i	0.931796	−	0.362984i	$-0.118242\pi$
$113$	9.29626	+	6.75413i	0.874518	+	0.635375i	−0.0572773	+	0.998358i	$0.518242\pi$
$114$	3.71449	+	5.11256i	0.347894	+	0.478835i
$115$	−1.30632	+	0.424450i	−0.121815	+	0.0395802i
$116$	25.5647	−	35.1867i	2.37362	−	3.26701i
$117$	−8.26069	−	6.00174i	−0.763701	−	0.554861i
$118$	−5.14721	−	3.73967i	−0.473839	−	0.344264i
$119$	7.10475	−	21.8662i	0.651292	−	2.00447i
$120$	2.76177	+	0.897353i	0.252114	+	0.0819168i
$121$	1.00591			0.0914468
$122$	7.96644	+	18.0970i	0.721247	+	1.63842i
$123$	−2.69996			−0.243447
$124$	−0.829433	−	0.269499i	−0.0744853	−	0.0242017i
$125$	1.59319	−	4.90333i	0.142499	−	0.438567i
$126$	−16.9120	−	12.2873i	−1.50664	−	1.09464i
$127$	13.7617	+	9.99846i	1.22115	+	0.887220i	0.996195	−	0.0871481i	$-0.0277753\pi$
$127$	13.7617	+	9.99846i	1.22115	+	0.887220i	0.224959	+	0.974368i	$0.427775\pi$
$128$	−7.87131	+	10.8339i	−0.695732	+	0.957593i
$129$	−0.0946892	+	0.0307664i	−0.00833692	+	0.00270883i
$130$	3.67294	+	5.05537i	0.322138	+	0.443386i
$131$	−3.87602	−	2.81609i	−0.338649	−	0.246043i	0.405442	−	0.914121i	$-0.367118\pi$
$131$	−3.87602	−	2.81609i	−0.338649	−	0.246043i	−0.744092	+	0.668077i	$0.767118\pi$
$132$	−7.35308	−	10.1206i	−0.640004	−	0.880889i
$133$			10.4652i			0.907449i
$134$	−19.3201	+	14.0369i	−1.66900	+	1.21260i
$135$	−2.47313			−0.212853
$136$	−37.2704			−3.19591
$137$	−13.6664	+	9.92923i	−1.16760	+	0.848311i	−0.990720	−	0.135921i	$-0.956601\pi$
$137$	−13.6664	+	9.92923i	−1.16760	+	0.848311i	−0.176881	+	0.984232i	$0.556601\pi$
$138$	1.81787	+	5.59483i	0.154747	+	0.476264i
$139$	−10.6797	+	14.6994i	−0.905844	+	1.24679i	0.0627214	+	0.998031i	$0.480022\pi$
$139$	−10.6797	+	14.6994i	−0.905844	+	1.24679i	−0.968566	+	0.248757i	$0.919978\pi$
$140$	5.17310	+	7.12016i	0.437207	+	0.601764i
$141$	1.97555	−	6.08011i	0.166371	−	0.512037i
$142$	−3.58608	−	11.0368i	−0.300937	−	0.926189i
$143$		−	14.7089i		−	1.23002i
$144$	−4.49139	+	13.8231i	−0.374282	+	1.15192i
$145$	3.07580	−	4.23348i	0.255431	−	0.351571i
$146$	8.36202	−	2.71698i	0.692045	−	0.224859i
$147$	1.98487	+	6.10879i	0.163709	+	0.503845i
$148$	−19.6562	−	6.38669i	−1.61573	−	0.524983i
$149$	8.15641	−	5.92598i	0.668199	−	0.485475i	−0.201223	−	0.979545i	$-0.564492\pi$
$149$	8.15641	−	5.92598i	0.668199	−	0.485475i	0.869422	+	0.494071i	$0.164492\pi$
$150$	−10.1961	−	3.31293i	−0.832511	−	0.270499i
$151$			5.38328i			0.438085i	0.975715	+	0.219043i	$0.0702933\pi$
$151$			5.38328i			0.438085i	−0.975715	+	0.219043i	$0.929707\pi$
$152$	16.1344	−	5.24237i	1.30867	−	0.425213i
$153$	12.7537	−	4.14392i	1.03107	−	0.335016i
$154$		−	30.1135i		−	2.42661i
$155$	−0.0997929	−	0.0324247i	−0.00801556	−	0.00260441i
$156$	14.8952	−	10.8220i	1.19257	−	0.866454i
$157$	−1.87482	−	0.609167i	−0.149627	−	0.0486168i	0.233246	−	0.972418i	$-0.425065\pi$
$157$	−1.87482	−	0.609167i	−0.149627	−	0.0486168i	−0.382873	+	0.923801i	$0.625065\pi$
$158$	5.23426	+	16.1094i	0.416415	+	1.28159i
$159$	−1.72379	+	0.560095i	−0.136706	+	0.0444184i
$160$	1.42445	−	1.96059i	0.112613	−	0.154998i
$161$	−3.01045	+	9.26520i	−0.237256	+	0.730200i
$162$		−	6.07547i		−	0.477334i
$163$	6.00025	+	18.4669i	0.469976	+	1.44644i	0.852615	+	0.522540i	$0.175015\pi$
$163$	6.00025	+	18.4669i	0.469976	+	1.44644i	−0.382639	+	0.923898i	$0.624985\pi$
$164$	−4.09909	+	12.6157i	−0.320085	+	0.985121i
$165$	−0.884683	−	1.21766i	−0.0688725	−	0.0947949i
$166$	−2.75840	+	3.79661i	−0.214093	+	0.294674i
$167$	−1.61829	−	4.98057i	−0.125227	−	0.385408i	0.868716	−	0.495311i	$-0.164946\pi$
$167$	−1.61829	−	4.98057i	−0.125227	−	0.385408i	−0.993942	+	0.109903i	$0.964946\pi$
$168$	16.6626	−	12.1061i	1.28555	−	0.934005i
$169$	8.64811			0.665239
$170$	−8.20665			−0.629421
$171$	−4.93819	+	3.58781i	−0.377633	+	0.274366i
$172$			0.489151i			0.0372974i
$173$	1.42513	+	1.96152i	0.108350	+	0.149132i	0.859749	−	0.510718i	$-0.170620\pi$
$173$	1.42513	+	1.96152i	0.108350	+	0.149132i	−0.751398	+	0.659849i	$0.770620\pi$
$174$	−18.1315	−	13.1733i	−1.37455	−	0.998666i
$175$	−10.4356	−	14.3633i	−0.788854	−	1.08576i
$176$	−19.9126	+	6.46999i	−1.50097	+	0.487694i
$177$	−1.32570	+	1.82467i	−0.0996456	+	0.137150i
$178$	25.7299	+	18.6939i	1.92854	+	1.40116i
$179$	10.0650	+	7.31264i	0.752293	+	0.546573i	0.896537	−	0.442969i	$-0.146075\pi$
$179$	10.0650	+	7.31264i	0.752293	+	0.546573i	−0.144244	+	0.989542i	$0.546075\pi$
$180$	−1.58627	+	4.88203i	−0.118234	+	0.363885i
$181$	19.4109	+	6.30699i	1.44280	+	0.468795i	0.922770	−	0.385352i	$-0.125920\pi$
$181$	19.4109	+	6.30699i	1.44280	+	0.468795i	0.520032	+	0.854147i	$0.325920\pi$
$182$	44.3200			3.28522
$183$	6.41531	−	2.82407i	0.474233	−	0.208762i
$184$	15.7923			1.16422
$185$	−2.36493	−	0.768413i	−0.173873	−	0.0564948i
$186$	−0.138871	+	0.427401i	−0.0101825	+	0.0313386i
$187$	15.6282	+	11.3546i	1.14285	+	0.830328i
$188$	−25.4104	−	18.4617i	−1.85324	−	1.34646i
$189$	−10.3103	+	14.1909i	−0.749961	+	1.03223i
$190$	3.55266	−	1.15433i	0.257737	−	0.0837439i
$191$	−4.58970	−	6.31718i	−0.332099	−	0.457095i	0.610014	−	0.792391i	$-0.291164\pi$
$191$	−4.58970	−	6.31718i	−0.332099	−	0.457095i	−0.942113	+	0.335296i	$0.891164\pi$
$192$	1.22032	+	0.886614i	0.0880690	+	0.0639859i
$193$	2.92631	+	4.02772i	0.210640	+	0.289922i	0.901244	−	0.433312i	$-0.142655\pi$
$193$	2.92631	+	4.02772i	0.210640	+	0.289922i	−0.690604	+	0.723233i	$0.742655\pi$
$194$		−	15.3501i		−	1.10208i
$195$	1.79211	−	1.30205i	0.128336	−	0.0932414i
$196$	31.5571			2.25408
$197$	−0.0686580			−0.00489168			−0.00244584	−	0.999997i	$-0.500779\pi$
$197$	−0.0686580			−0.00489168			−0.00244584	+	0.999997i	$0.500779\pi$
$198$	14.2096	−	10.3239i	1.00983	−	0.733684i
$199$	−7.67995	−	23.6365i	−0.544417	−	1.67554i	−0.722372	−	0.691505i	$-0.756948\pi$
$199$	−7.67995	−	23.6365i	−0.544417	−	1.67554i	0.177954	−	0.984039i	$-0.443052\pi$
$200$	−16.9166	+	23.2837i	−1.19618	+	1.64641i
$201$	4.97603	+	6.84891i	0.350982	+	0.483085i
$202$	−5.77052	+	17.7598i	−0.406013	+	1.24958i
$203$	−11.4690	−	35.2980i	−0.804967	−	2.47743i
$204$			24.1802i			1.69295i
$205$	−0.493181	+	1.51785i	−0.0344452	+	0.106011i
$206$	−3.62235	+	4.98574i	−0.252381	+	0.347373i
$207$	−5.40402	+	1.75587i	−0.375605	+	0.122042i
$208$	−9.52231	−	29.3067i	−0.660253	−	2.03205i
$209$	−8.36257	−	2.71716i	−0.578451	−	0.187950i
$210$	3.66898	−	2.66567i	0.253183	−	0.183948i
$211$	2.53343	+	0.823160i	0.174408	+	0.0566687i	0.394919	−	0.918716i	$-0.370773\pi$
$211$	2.53343	+	0.823160i	0.174408	+	0.0566687i	−0.220511	+	0.975384i	$0.570773\pi$
$212$			8.90487i			0.611589i
$213$	−3.91251	+	1.27125i	−0.268081	+	0.0871048i
$214$	10.4233	−	3.38674i	0.712524	−	0.231513i
$215$			0.0588520i			0.00401367i
$216$	27.0430	+	8.78679i	1.84004	+	0.597866i
$217$	−0.602081	+	0.437437i	−0.0408719	+	0.0296952i
$218$	−23.9527	−	7.78272i	−1.62228	−	0.527112i
$219$	−0.963161	−	2.96431i	−0.0650844	−	0.200309i
$220$	−7.03273	+	2.28507i	−0.474147	+	0.154060i
$221$	−16.7113	+	23.0011i	−1.12412	+	1.54722i
$222$	−3.29102	+	10.1287i	−0.220879	+	0.679796i
$223$		−	19.0396i		−	1.27499i	−0.770455	−	0.637494i	$-0.779971\pi$
$223$		−	19.0396i		−	1.27499i	0.770455	−	0.637494i	$-0.220029\pi$
$224$	−5.31147	−	16.3470i	−0.354888	−	1.09223i
$225$	3.19994	−	9.84840i	0.213329	−	0.656560i
$226$	−17.0991	−	23.5348i	−1.13741	−	1.56551i
$227$	9.01726	−	12.4112i	0.598497	−	0.823760i	−0.397073	−	0.917787i	$-0.629974\pi$
$227$	9.01726	−	12.4112i	0.598497	−	0.823760i	0.995570	+	0.0940268i	$0.0299739\pi$
$228$	−3.40113	−	10.4676i	−0.225245	−	0.693234i
$229$	−0.992434	+	0.721046i	−0.0655819	+	0.0476480i	−0.620093	−	0.784528i	$-0.712905\pi$
$229$	−0.992434	+	0.721046i	−0.0655819	+	0.0476480i	0.554511	+	0.832176i	$0.312905\pi$
$230$	3.47734			0.229289
$231$	−10.6751			−0.702372
$232$	−48.6742	+	35.3639i	−3.19562	+	2.32175i
$233$			12.5184i			0.820109i	0.912061	+	0.410054i	$0.134490\pi$
$233$			12.5184i			0.820109i	−0.912061	+	0.410054i	$0.865510\pi$
$234$	15.1943	+	20.9131i	0.993282	+	1.36714i
$235$	−3.05724	−	2.22121i	−0.199432	−	0.144896i
$236$	6.51319	+	8.96463i	0.423972	+	0.583548i
$237$	5.71072	−	1.85553i	0.370951	−	0.120529i
$238$	−34.2128	+	47.0899i	−2.21769	+	3.05238i
$239$	10.9540	+	7.95854i	0.708555	+	0.514795i	0.882707	−	0.469923i	$-0.155718\pi$
$239$	10.9540	+	7.95854i	0.708555	+	0.514795i	−0.174152	+	0.984719i	$0.555718\pi$
$240$	−2.55097	−	1.85339i	−0.164664	−	0.119636i
$241$	−2.25285	+	6.93357i	−0.145119	+	0.446630i	−0.997026	−	0.0770624i	$-0.975446\pi$
$241$	−2.25285	+	6.93357i	−0.145119	+	0.446630i	0.851907	+	0.523693i	$0.175446\pi$
$242$	−2.42198	−	0.786949i	−0.155691	−	0.0505870i
$243$	−16.1395			−1.03535
$244$	−3.45589	−	34.2634i	−0.221241	−	2.19349i
$245$	3.79678			0.242568
$246$	6.50079	+	2.11224i	0.414475	+	0.134671i
$247$	3.99903	−	12.3077i	0.254452	−	0.783123i
$248$	0.976005	+	0.709109i	0.0619764	+	0.0450285i
$249$	1.34589	+	0.977843i	0.0852920	+	0.0619683i
$250$	−7.67197	+	10.5596i	−0.485218	+	0.667845i
$251$	−15.9793	+	5.19197i	−1.00860	+	0.327714i	−0.766297	−	0.642486i	$-0.777903\pi$
$251$	−15.9793	+	5.19197i	−1.00860	+	0.327714i	−0.242304	+	0.970200i	$0.577903\pi$
$252$	21.4002	+	29.4548i	1.34808	+	1.85548i
$253$	−6.62203	−	4.81119i	−0.416324	−	0.302477i
$254$	−25.3126	−	34.8398i	−1.58825	−	2.18604i
$255$			2.90923i			0.182183i
$256$	24.7082	−	17.9516i	1.54426	−	1.12197i
$257$	−9.47405			−0.590975			−0.295488	−	0.955347i	$-0.595482\pi$
$257$	−9.47405			−0.590975			−0.295488	+	0.955347i	$0.595482\pi$
$258$	0.252056			0.0156923
$259$	−14.2684	+	10.3666i	−0.886592	+	0.644147i
$260$	−3.36309	−	10.3505i	−0.208570	−	0.641912i
$261$	12.7240	−	17.5131i	0.787597	−	1.08403i
$262$	7.12936	+	9.81272i	0.440453	+	0.606232i
$263$	3.83905	−	11.8154i	0.236726	−	0.728568i	−0.760162	−	0.649734i	$-0.774880\pi$
$263$	3.83905	−	11.8154i	0.236726	−	0.728568i	0.996888	−	0.0788339i	$-0.0251197\pi$
$264$	5.34752	+	16.4580i	0.329117	+	1.01292i
$265$			1.07139i			0.0658147i
$266$	8.18717	−	25.1975i	0.501988	−	1.54496i
$267$	6.62691	−	9.12115i	0.405560	−	0.558206i
$268$	39.5566	−	12.8527i	2.41630	−	0.785105i
$269$	5.63856	+	17.3537i	0.343789	+	1.05807i	0.962229	+	0.272242i	$0.0877650\pi$
$269$	5.63856	+	17.3537i	0.343789	+	1.05807i	−0.618440	+	0.785832i	$0.712235\pi$
$270$	5.95465	+	1.93478i	0.362389	+	0.117747i
$271$	−19.1985	+	13.9485i	−1.16623	+	0.847313i	−0.990552	−	0.137136i	$-0.956210\pi$
$271$	−19.1985	+	13.9485i	−1.16623	+	0.847313i	−0.175674	+	0.984448i	$0.556210\pi$
$272$	38.4890	+	12.5058i	2.33374	+	0.758277i
$273$		−	15.7113i		−	0.950890i
$274$	40.6730	−	13.2155i	2.45715	−	0.798376i
$275$	14.1869	−	4.60961i	0.855504	−	0.277970i
$276$		−	10.2457i		−	0.616718i
$277$	−13.4238	−	4.36167i	−0.806560	−	0.262067i	−0.123420	−	0.992355i	$-0.539386\pi$
$277$	−13.4238	−	4.36167i	−0.806560	−	0.262067i	−0.683140	+	0.730287i	$0.739386\pi$
$278$	37.2137	−	27.0374i	2.23193	−	1.62159i
$279$	−0.412825	−	0.134135i	−0.0247152	−	0.00803045i
$280$	−3.76214	−	11.5787i	−0.224831	−	0.691958i
$281$	9.26325	−	3.00981i	0.552599	−	0.179550i	−0.0193894	−	0.999812i	$-0.506172\pi$
$281$	9.26325	−	3.00981i	0.552599	−	0.179550i	0.571988	+	0.820262i	$0.306172\pi$
$282$	−9.51320	+	13.0938i	−0.566503	+	0.779725i
$283$	−7.27337	+	22.3851i	−0.432357	+	1.33066i	0.463414	+	0.886142i	$0.346624\pi$
$283$	−7.27337	+	22.3851i	−0.432357	+	1.33066i	−0.895771	+	0.444516i	$0.853376\pi$
$284$			20.2115i			1.19933i
$285$	−0.409206	−	1.25941i	−0.0242393	−	0.0746008i
$286$	−11.5071	+	35.4153i	−0.680431	+	2.09415i
$287$	6.65344	+	9.15767i	0.392740	+	0.540560i
$288$	5.89269	−	8.11059i	0.347230	−	0.477921i
$289$	−6.28505	−	19.3434i	−0.369709	−	1.13785i
$290$	−10.7177	+	7.78685i	−0.629364	+	0.457259i
$291$	−5.44157			−0.318991
$292$	−15.3132			−0.896136
$293$	4.41318	−	3.20637i	0.257821	−	0.187318i	−0.451365	−	0.892339i	$-0.649063\pi$
$293$	4.41318	−	3.20637i	0.257821	−	0.187318i	0.709186	+	0.705022i	$0.249063\pi$
$294$		−	16.2612i		−	0.948372i
$295$	0.783632	+	1.07858i	0.0456248	+	0.0627971i
$296$	23.1298	+	16.8048i	1.34439	+	0.976756i
$297$	−8.66273	−	11.9232i	−0.502662	−	0.691856i
$298$	−24.2745	+	7.88727i	−1.40619	+	0.456898i
$299$	7.08094	−	9.74607i	0.409501	−	0.563630i
$300$	15.1059	+	10.9751i	0.872141	+	0.633648i
$301$	0.337694	+	0.245349i	0.0194643	+	0.0141417i
$302$	4.21146	−	12.9615i	0.242342	−	0.745853i
$303$	6.29580	+	2.04563i	0.361684	+	0.117518i
$304$	−18.4209			−1.05651
$305$	−0.415794	−	4.12239i	−0.0238083	−	0.236047i
$306$	−33.9494			−1.94076
$307$	−25.7750	−	8.37480i	−1.47106	−	0.477975i	−0.539628	−	0.841903i	$-0.681435\pi$
$307$	−25.7750	−	8.37480i	−1.47106	−	0.477975i	−0.931427	+	0.363929i	$0.881435\pi$
$308$	−16.2071	+	49.8802i	−0.923483	+	2.84219i
$309$	1.76743	+	1.28411i	0.100545	+	0.0730506i
$310$	0.214909	+	0.156140i	0.0122060	+	0.00886818i
$311$	−3.04878	+	4.19628i	−0.172880	+	0.237949i	−0.886661	−	0.462420i	$-0.846981\pi$
$311$	−3.04878	+	4.19628i	−0.172880	+	0.237949i	0.713781	+	0.700369i	$0.246981\pi$
$312$	−24.2223	+	7.87030i	−1.37132	+	0.445568i
$313$	5.77734	+	7.95182i	0.326554	+	0.449463i	0.940454	−	0.339920i	$-0.110400\pi$
$313$	5.77734	+	7.95182i	0.326554	+	0.449463i	−0.613900	+	0.789384i	$0.710400\pi$
$314$	4.03752	+	2.93343i	0.227851	+	0.165543i
$315$	2.57475	+	3.54384i	0.145071	+	0.199673i
$316$		−	29.5008i		−	1.65955i
$317$	−15.8812	+	11.5384i	−0.891977	+	0.648059i	−0.936393	−	0.350954i	$-0.885857\pi$
$317$	−15.8812	+	11.5384i	−0.891977	+	0.648059i	0.0444155	+	0.999013i	$0.485857\pi$
$318$	4.58862			0.257317
$319$	31.1838			1.74596
$320$	0.721341	−	0.524085i	0.0403242	−	0.0292972i
$321$	−1.20059	−	3.69503i	−0.0670103	−	0.206237i
$322$	14.4967	−	19.9531i	0.807872	−	1.11194i
$323$	9.98990	+	13.7499i	0.555853	+	0.765066i
$324$	−3.26981	+	10.0634i	−0.181656	+	0.559080i
$325$	6.78427	+	20.8798i	0.376324	+	1.15820i
$326$		−	49.1576i		−	2.72259i
$327$	−2.75895	+	8.49117i	−0.152570	+	0.469563i
$328$	10.7856	−	14.8451i	0.595534	−	0.819682i
$329$	−25.4907	+	8.28244i	−1.40535	+	0.456626i
$330$	1.17748	+	3.62392i	0.0648183	+	0.199490i
$331$	31.0282	+	10.0817i	1.70546	+	0.554139i	0.989568	−	0.144067i	$-0.0460180\pi$
$331$	31.0282	+	10.0817i	1.70546	+	0.554139i	0.715897	+	0.698206i	$0.246018\pi$
$332$	6.61236	−	4.80416i	0.362901	−	0.263663i
$333$	−9.78328	−	3.17878i	−0.536121	−	0.174196i
$334$			13.2579i			0.725442i
$335$	4.75924	−	1.54637i	0.260025	−	0.0844872i
$336$	−21.2695	+	6.91089i	−1.16035	+	0.377020i
$337$		−	13.0597i		−	0.711409i	−0.934599	−	0.355704i	$-0.884241\pi$
$337$		−	13.0597i		−	0.711409i	0.934599	−	0.355704i	$-0.115759\pi$
$338$	−20.8224	−	6.76561i	−1.13259	−	0.368001i
$339$	−8.34302	+	6.06156i	−0.453131	+	0.329219i
$340$	13.5935	+	4.41681i	0.737214	+	0.239535i
$341$	−0.193226	−	0.594688i	−0.0104638	−	0.0322041i
$342$	14.6967	−	4.77525i	0.794707	−	0.258216i
$343$	0.347316	−	0.478040i	0.0187533	−	0.0258117i
$344$	0.209096	−	0.643530i	0.0112737	−	0.0346968i
$345$		−	1.23271i		−	0.0663667i
$346$	−1.89680	−	5.83774i	−0.101972	−	0.313839i
$347$	5.38821	−	16.5832i	0.289254	−	0.890233i	−0.695837	−	0.718200i	$-0.744966\pi$
$347$	5.38821	−	16.5832i	0.289254	−	0.890233i	0.985091	−	0.172033i	$-0.0550336\pi$
$348$	22.9433	+	31.5787i	1.22989	+	1.69280i
$349$	0.496216	−	0.682983i	0.0265618	−	0.0365592i	−0.795530	−	0.605915i	$-0.792807\pi$
$349$	0.496216	−	0.682983i	0.0265618	−	0.0365592i	0.822091	+	0.569356i	$0.192807\pi$
$350$	13.8894	+	42.7471i	0.742418	+	2.28493i
$351$	17.5482	−	12.7495i	0.936653	−	0.680518i
$352$	14.4417			0.769745
$353$	25.9163			1.37939			0.689693	−	0.724102i	$-0.257745\pi$
$353$	25.9163			1.37939			0.689693	+	0.724102i	$0.257745\pi$
$354$	4.61942	−	3.35620i	0.245519	−	0.178380i
$355$			2.43174i			0.129063i
$356$	−32.5581	−	44.8124i	−1.72558	−	2.37505i
$357$	16.6932	+	12.1283i	0.883498	+	0.641899i
$358$	−18.5130	−	25.4810i	−0.978445	−	1.34671i
$359$	−19.3532	+	6.28825i	−1.02142	+	0.331881i	−0.771395	−	0.636357i	$-0.780441\pi$
$359$	−19.3532	+	6.28825i	−1.02142	+	0.331881i	−0.250030	+	0.968238i	$0.580441\pi$
$360$	4.17381	−	5.74476i	0.219979	−	0.302775i
$361$	9.11266	+	6.62074i	0.479614	+	0.348460i
$362$	−41.8023	−	30.3712i	−2.19708	−	1.59627i
$363$	−0.278971	+	0.858584i	−0.0146422	+	0.0450640i
$364$	−73.4119	−	23.8530i	−3.84783	−	1.25024i
$365$	−1.84240			−0.0964356
$366$	−17.6557	+	1.78080i	−0.922880	+	0.0930839i
$367$	34.4146			1.79643			0.898215	−	0.439557i	$-0.144865\pi$
$367$	34.4146			1.79643			0.898215	+	0.439557i	$0.144865\pi$
$368$	−16.3087	−	5.29900i	−0.850148	−	0.276230i
$369$	−2.04020	+	6.27908i	−0.106208	+	0.326876i
$370$	5.09299	+	3.70028i	0.264772	+	0.192368i
$371$	6.14763	+	4.46651i	0.319169	+	0.231890i
$372$	0.460054	−	0.633210i	0.0238527	−	0.0328304i
$373$	21.7662	−	7.07225i	1.12701	−	0.366187i	0.314570	−	0.949234i	$-0.398140\pi$
$373$	21.7662	−	7.07225i	1.12701	−	0.366187i	0.812438	+	0.583047i	$0.198140\pi$
$374$	−28.7458	−	39.5652i	−1.48641	−	2.04587i
$375$	3.74333	+	2.71969i	0.193305	+	0.140444i
$376$	25.5383	+	35.1504i	1.31704	+	1.81275i
$377$			45.8952i			2.36372i
$378$	35.9262	−	26.1019i	1.84785	−	1.34254i
$379$	5.42658			0.278745			0.139372	−	0.990240i	$-0.455491\pi$
$379$	5.42658			0.278745			0.139372	+	0.990240i	$0.455491\pi$
$380$	−6.50591			−0.333746
$381$	−12.3506	+	8.97323i	−0.632740	+	0.459712i
$382$	6.10873	+	18.8007i	0.312550	+	0.961930i
$383$	−8.67325	+	11.9377i	−0.443182	+	0.609988i	−0.970916	−	0.239422i	$-0.923042\pi$
$383$	−8.67325	+	11.9377i	−0.443182	+	0.609988i	0.527733	+	0.849410i	$0.323042\pi$
$384$	−7.06419	−	9.72302i	−0.360493	−	0.496176i
$385$	−1.94995	+	6.00131i	−0.0993784	+	0.305855i
$386$	−3.89482	−	11.9870i	−0.198241	−	0.610123i
$387$			0.243460i			0.0123758i
$388$	−8.26143	+	25.4261i	−0.419411	+	1.29081i
$389$	21.2100	−	29.1931i	1.07539	−	1.48015i	0.210894	−	0.977509i	$-0.432363\pi$
$389$	21.2100	−	29.1931i	1.07539	−	1.48015i	0.864496	−	0.502639i	$-0.167637\pi$
$390$	−5.33356	+	1.73298i	−0.270075	+	0.0877528i
$391$	4.88905	+	15.0470i	0.247250	+	0.760958i
$392$	−41.5168	−	13.4896i	−2.09691	−	0.681329i
$393$	3.47857	−	2.52733i	0.175471	−	0.127487i
$394$	0.165311	+	0.0537127i	0.00832823	+	0.00270601i
$395$		−	3.54937i		−	0.178588i
$396$	−29.0931	+	9.45292i	−1.46198	+	0.475027i
$397$	−3.48135	+	1.13116i	−0.174724	+	0.0567713i	−0.395073	−	0.918650i	$-0.629281\pi$
$397$	−3.48135	+	1.13116i	−0.174724	+	0.0567713i	0.220349	+	0.975421i	$0.429281\pi$
$398$			62.9186i			3.15383i
$399$	−8.93244	−	2.90232i	−0.447181	−	0.145298i
$400$	25.2824	−	18.3687i	1.26412	−	0.918437i
$401$	18.4107	+	5.98201i	0.919388	+	0.298727i	0.730216	−	0.683217i	$-0.239420\pi$
$401$	18.4107	+	5.98201i	0.919388	+	0.298727i	0.189172	+	0.981944i	$0.439420\pi$
$402$	−6.62292	−	20.3833i	−0.330321	−	1.01662i
$403$	0.875240	−	0.284383i	0.0435988	−	0.0141661i
$404$	19.1167	−	26.3118i	0.951090	−	1.30906i
$405$	−0.393406	+	1.21078i	−0.0195485	+	0.0601641i
$406$			93.9609i			4.66320i
$407$	−4.57914	−	14.0931i	−0.226979	−	0.698571i
$408$	10.3362	−	31.8116i	0.511719	−	1.57491i
$409$	−16.6434	−	22.9076i	−0.822961	−	1.13271i	−0.989193	−	0.146622i	$-0.953160\pi$
$409$	−16.6434	−	22.9076i	−0.822961	−	1.13271i	0.166232	−	0.986087i	$-0.446840\pi$
$410$	2.37490	−	3.26877i	0.117288	−	0.161433i
$411$	−4.68484	−	14.4185i	−0.231086	−	0.711210i
$412$	8.68341	−	6.30887i	0.427801	−	0.310816i
$413$	9.45578			0.465288
$414$	14.3851			0.706991
$415$	0.795564	−	0.578011i	0.0390527	−	0.0283734i
$416$			21.2548i			1.04210i
$417$	−9.58465	−	13.1921i	−0.469362	−	0.646022i
$418$	18.0092	+	13.0845i	0.880859	+	0.639981i
$419$	8.58592	+	11.8175i	0.419450	+	0.577323i	0.965491	−	0.260435i	$-0.0838660\pi$
$419$	8.58592	+	11.8175i	0.419450	+	0.577323i	−0.546042	+	0.837758i	$0.683866\pi$
$420$	−7.51197	+	2.44079i	−0.366547	+	0.119098i
$421$	−4.58896	+	6.31617i	−0.223652	+	0.307831i	−0.906067	−	0.423134i	$-0.860930\pi$
$421$	−4.58896	+	6.31617i	−0.223652	+	0.307831i	0.682415	+	0.730965i	$0.260930\pi$
$422$	−5.45585	−	3.96391i	−0.265587	−	0.192960i
$423$	−12.6472	−	9.18875i	−0.614930	−	0.446772i
$424$	3.80653	−	11.7153i	0.184862	−	0.568945i
$425$	−27.4219	−	8.90991i	−1.33016	−	0.432194i
$426$	10.4148			0.504601
$427$	−25.3878	−	14.8001i	−1.22860	−	0.716225i
$428$	−19.0880			−0.922653
$429$	12.5546	+	4.07924i	0.606142	+	0.196948i
$430$	0.0460412	−	0.141700i	0.00222030	−	0.00683340i
$431$	−25.9728	−	18.8704i	−1.25107	−	0.908954i	−0.252784	−	0.967523i	$-0.581346\pi$
$431$	−25.9728	−	18.8704i	−1.25107	−	0.908954i	−0.998283	+	0.0585689i	$0.981346\pi$
$432$	−24.9788	−	18.1482i	−1.20179	−	0.873155i
$433$	20.6530	−	28.4265i	0.992521	−	1.36609i	0.0627178	−	0.998031i	$-0.480023\pi$
$433$	20.6530	−	28.4265i	0.992521	−	1.36609i	0.929803	−	0.368057i	$-0.119977\pi$
$434$	1.79187	−	0.582214i	0.0860126	−	0.0279472i
$435$	2.76041	+	3.79938i	0.132352	+	0.182166i
$436$	35.4868	+	25.7827i	1.69951	+	1.23477i
$437$	−4.23295	−	5.82615i	−0.202489	−	0.278703i
$438$			7.89078i			0.377036i
$439$	−17.6268	+	12.8066i	−0.841280	+	0.611226i	−0.922728	−	0.385452i	$-0.874046\pi$
$439$	−17.6268	+	12.8066i	−0.841280	+	0.611226i	0.0814476	+	0.996678i	$0.474046\pi$
$440$	10.2291			0.487653
$441$	15.7066			0.747933
$442$	58.2306	−	42.3070i	2.76975	−	2.01234i
$443$	1.09670	+	3.37530i	0.0521058	+	0.160365i	0.973723	−	0.227734i	$-0.0731317\pi$
$443$	1.09670	+	3.37530i	0.0521058	+	0.160365i	−0.921618	+	0.388099i	$0.873132\pi$
$444$	10.9025	−	15.0061i	0.517412	−	0.712156i
$445$	−3.91722	−	5.39159i	−0.185694	−	0.255586i
$446$	−14.8951	+	45.8425i	−0.705305	+	2.17071i
$447$	2.79601	+	8.60524i	0.132247	+	0.407014i
$448$		−	6.32393i		−	0.298778i
$449$	−0.608084	+	1.87149i	−0.0286973	+	0.0883211i	−0.964379	−	0.264523i	$-0.914785\pi$
$449$	−0.608084	+	1.87149i	−0.0286973	+	0.0883211i	0.935682	+	0.352844i	$0.114785\pi$
$450$	−15.4092	+	21.2090i	−0.726398	+	0.999802i
$451$	−9.04522	+	2.93897i	−0.425923	+	0.138391i
$452$	15.6566	+	48.1860i	0.736423	+	2.26648i
$453$	−4.59482	−	1.49295i	−0.215883	−	0.0701448i
$454$	−31.4208	+	22.8285i	−1.47465	+	1.07140i
$455$	−8.83253	−	2.86986i	−0.414075	−	0.134541i
$456$			15.2251i			0.712982i
$457$	−33.3620	+	10.8400i	−1.56061	+	0.507073i	−0.956970	−	0.290185i	$-0.906283\pi$
$457$	−33.3620	+	10.8400i	−1.56061	+	0.507073i	−0.603639	+	0.797258i	$0.706283\pi$
$458$	2.95361	−	0.959687i	0.138013	−	0.0448433i
$459$			28.4869i			1.32965i
$460$	−5.75989	−	1.87150i	−0.268556	−	0.0872593i
$461$	−8.13830	+	5.91282i	−0.379039	+	0.275388i	−0.760949	−	0.648812i	$-0.775266\pi$
$461$	−8.13830	+	5.91282i	−0.379039	+	0.275388i	0.381910	+	0.924199i	$0.375266\pi$
$462$	25.7029	+	8.35139i	1.19581	+	0.388542i
$463$	8.25122	+	25.3947i	0.383467	+	1.18019i	0.937586	+	0.347752i	$0.113055\pi$
$463$	8.25122	+	25.3947i	0.383467	+	1.18019i	−0.554120	+	0.832437i	$0.686945\pi$
$464$	62.1318	−	20.1878i	2.88439	−	0.937197i
$465$	0.0553512	−	0.0761844i	0.00256685	−	0.00353297i
$466$	9.79344	−	30.1411i	0.453672	−	1.39626i
$467$			19.3294i			0.894459i	0.894419	+	0.447229i	$0.147589\pi$
$467$			19.3294i			0.894459i	−0.894419	+	0.447229i	$0.852411\pi$
$468$	−13.9125	−	42.8182i	−0.643105	−	1.97927i
$469$	10.9677	−	33.7553i	0.506443	−	1.55867i
$470$	5.62333	+	7.73985i	0.259385	+	0.357013i
$471$	1.03989	−	1.43129i	0.0479157	−	0.0659503i
$472$	−4.73671	−	14.5781i	−0.218025	−	0.671011i
$473$	−0.283732	+	0.206143i	−0.0130460	+	0.00947848i
$474$	−15.2016			−0.698231
$475$	13.1242			0.602179
$476$	82.0140	−	59.5867i	3.75911	−	2.73115i
$477$			4.43213i			0.202933i
$478$	−20.1482	−	27.7317i	−0.921559	−	1.26842i
$479$	30.0533	+	21.8350i	1.37317	+	0.997668i	0.997482	+	0.0709231i	$0.0225945\pi$
$479$	30.0533	+	21.8350i	1.37317	+	0.997668i	0.375691	+	0.926745i	$0.377406\pi$
$480$	1.27839	+	1.75955i	0.0583502	+	0.0803121i
$481$	20.7418	−	6.73942i	0.945744	−	0.307291i
$482$	10.8486	−	14.9318i	0.494139	−	0.680123i
$483$	−7.07329	−	5.13904i	−0.321846	−	0.233835i
$484$	3.58825	+	2.60702i	0.163102	+	0.118501i
$485$	−0.993971	+	3.05913i	−0.0451339	+	0.138908i
$486$	38.8597	+	12.6263i	1.76271	+	0.572740i
$487$	−7.94228			−0.359899			−0.179949	−	0.983676i	$-0.557593\pi$
$487$	−7.94228			−0.359899			−0.179949	+	0.983676i	$0.557593\pi$
$488$	−10.0999	+	46.5545i	−0.457200	+	2.10742i
$489$	−17.4262			−0.788040
$490$	−9.14167	−	2.97031i	−0.412979	−	0.134185i
$491$	6.93607	−	21.3470i	0.313020	−	0.963378i	−0.663541	−	0.748140i	$-0.730947\pi$
$491$	6.93607	−	21.3470i	0.313020	−	0.963378i	0.976562	−	0.215238i	$-0.0690528\pi$
$492$	−9.63115	−	6.99744i	−0.434206	−	0.315469i
$493$	−48.7636	−	35.4288i	−2.19620	−	1.59563i
$494$	−19.2572	+	26.5053i	−0.866424	+	1.19253i
$495$	−3.50033	+	1.13732i	−0.157328	+	0.0511190i
$496$	−0.769980	−	1.05979i	−0.0345731	−	0.0475858i
$497$	13.9533	+	10.1377i	0.625893	+	0.454738i
$498$	−2.47555	−	3.40731i	−0.110932	−	0.152685i
$499$		−	24.3041i		−	1.08800i	−0.839085	−	0.544000i	$-0.816909\pi$
$499$		−	24.3041i		−	1.08800i	0.839085	−	0.544000i	$-0.183091\pi$
$500$	18.3910	−	13.3619i	0.822472	−	0.597561i
$501$	4.69989			0.209976
$502$	42.5357			1.89846
$503$	−4.13079	+	3.00119i	−0.184183	+	0.133817i	−0.676056	−	0.736850i	$-0.736312\pi$
$503$	−4.13079	+	3.00119i	−0.184183	+	0.133817i	0.491873	+	0.870667i	$0.336312\pi$
$504$	−15.5633	−	47.8988i	−0.693243	−	2.13358i
$505$	2.30001	−	3.16570i	0.102349	−	0.140872i
$506$	12.1802	+	16.7647i	0.541477	+	0.745280i
$507$	−2.39839	+	7.38147i	−0.106516	+	0.327823i
$508$	23.1772	+	71.3321i	1.02832	+	3.16485i
$509$			15.8065i			0.700613i	0.936635	+	0.350306i	$0.113923\pi$
$509$			15.8065i			0.700613i	−0.936635	+	0.350306i	$0.886077\pi$
$510$	2.27595	−	7.00467i	0.100781	−	0.310172i
$511$	−7.68080	+	10.5717i	−0.339779	+	0.467665i
$512$	−48.0627	+	15.6165i	−2.12409	+	0.690159i
$513$	−4.00690	−	12.3320i	−0.176909	−	0.544470i
$514$	22.8111	+	7.41176i	1.00615	+	0.326919i
$515$	1.04474	−	0.759049i	0.0460368	−	0.0334477i
$516$	−0.417508	−	0.135656i	−0.0183797	−	0.00597194i
$517$		−	22.5196i		−	0.990412i
$518$	42.4645	−	13.7975i	1.86578	−	0.606229i
$519$	−2.06946	+	0.672408i	−0.0908391	+	0.0295154i
$520$			15.0548i			0.660198i
$521$	−25.0387	−	8.13557i	−1.09697	−	0.356426i	−0.296031	−	0.955178i	$-0.595663\pi$
$521$	−25.0387	−	8.13557i	−1.09697	−	0.356426i	−0.800934	+	0.598752i	$0.795663\pi$
$522$	−44.3371	+	32.2128i	−1.94058	+	1.40991i
$523$	−18.1070	−	5.88331i	−0.791762	−	0.257259i	−0.114908	−	0.993376i	$-0.536657\pi$
$523$	−18.1070	−	5.88331i	−0.791762	−	0.257259i	−0.676854	+	0.736117i	$0.736657\pi$
$524$	−6.52792	−	20.0909i	−0.285173	−	0.877673i
$525$	15.1537	−	4.92374i	0.661362	−	0.214889i
$526$	−18.4869	+	25.4450i	−0.806066	+	1.10945i
$527$	−0.373486	+	1.14947i	−0.0162693	+	0.0500717i
$528$		−	18.7904i		−	0.817748i
$529$	5.03579	+	15.4986i	0.218947	+	0.673851i
$530$	0.838169	−	2.57962i	0.0364077	−	0.112051i
$531$	3.24174	+	4.46187i	0.140679	+	0.193629i
$532$	−27.1226	+	37.3310i	−1.17591	+	1.61850i
$533$	−4.32547	−	13.3124i	−0.187357	−	0.576626i
$534$	−23.0915	+	16.7770i	−0.999269	+	0.726011i
$535$	−2.29657			−0.0992892
$536$	−57.5350			−2.48513
$537$	−9.03293	+	6.56281i	−0.389800	+	0.283206i
$538$		−	46.1944i		−	1.99158i
$539$	13.2991	+	18.3047i	0.572835	+	0.788440i
$540$	−8.82202	−	6.40958i	−0.379639	−	0.275824i
$541$	−11.8478	−	16.3070i	−0.509375	−	0.701094i	0.474439	−	0.880288i	$-0.342651\pi$
$541$	−11.8478	−	16.3070i	−0.509375	−	0.701094i	−0.983814	+	0.179194i	$0.942651\pi$
$542$	57.1373	−	18.5650i	2.45426	−	0.797436i
$543$	−10.7665	+	14.8188i	−0.462034	+	0.635935i
$544$	−22.5831	−	16.4076i	−0.968245	−	0.703471i
$545$	4.26958	+	3.10203i	0.182889	+	0.132877i
$546$	−12.2913	+	37.8287i	−0.526018	+	1.61892i
$547$	−16.6767	−	5.41857i	−0.713042	−	0.231681i	−0.0700382	−	0.997544i	$-0.522312\pi$
$547$	−16.6767	−	5.41857i	−0.713042	−	0.231681i	−0.643004	+	0.765863i	$0.722312\pi$
$548$	−74.4836			−3.18178
$549$	−1.72006	−	17.0536i	−0.0734106	−	0.727829i
$550$	−37.7647			−1.61029
$551$	26.0931	+	8.47816i	1.11160	+	0.361182i
$552$	−4.37969	+	13.4793i	−0.186412	+	0.573717i
$553$	−20.3664	−	14.7970i	−0.866066	−	0.629233i
$554$	28.9089	+	21.0035i	1.22822	+	0.892354i
$555$	1.31174	−	1.80545i	0.0556801	−	0.0766370i
$556$	−76.1926	+	24.7565i	−3.23128	+	1.04991i
$557$	−7.13668	−	9.82280i	−0.302391	−	0.416206i	0.630598	−	0.776109i	$-0.282810\pi$
$557$	−7.13668	−	9.82280i	−0.302391	−	0.416206i	−0.932989	+	0.359904i	$0.882810\pi$
$558$	0.889038	+	0.645924i	0.0376360	+	0.0273441i
$559$	−0.303394	−	0.417587i	−0.0128322	−	0.0176620i
$560$			13.2196i			0.558630i
$561$	−14.0257	+	10.1903i	−0.592166	+	0.430234i
$562$	−24.6581			−1.04014
$563$	0.405968			0.0171095			0.00855476	−	0.999963i	$-0.497277\pi$
$563$	0.405968			0.0171095			0.00855476	+	0.999963i	$0.497277\pi$
$564$	22.8048	−	16.5687i	0.960255	−	0.697666i
$565$	1.88371	+	5.79748i	0.0792485	+	0.243902i
$566$	35.0248	−	48.2075i	1.47220	−	2.02631i
$567$	5.30740	+	7.30500i	0.222890	+	0.306781i
$568$	8.63973	−	26.5903i	0.362515	−	1.11571i
$569$	0.433911	+	1.33544i	0.0181905	+	0.0559845i	0.959740	−	0.280891i	$-0.0906299\pi$
$569$	0.433911	+	1.33544i	0.0181905	+	0.0559845i	−0.941549	+	0.336875i	$0.890630\pi$
$570$			3.35245i			0.140419i
$571$	0.500444	−	1.54021i	0.0209429	−	0.0644557i	−0.940039	−	0.341067i	$-0.889212\pi$
$571$	0.500444	−	1.54021i	0.0209429	−	0.0644557i	0.960982	+	0.276612i	$0.0892116\pi$
$572$	38.1210	−	52.4690i	1.59392	−	2.19384i
$573$	6.66480	−	2.16552i	0.278426	−	0.0904661i
$574$	−8.85550	−	27.2544i	−0.369622	−	1.13758i
$575$	11.6193	+	3.77533i	0.484557	+	0.157442i
$576$	2.98405	−	2.16804i	0.124336	−	0.0903351i
$577$	44.8170	+	14.5619i	1.86575	+	0.606220i	0.993008	+	0.118047i	$0.0376634\pi$
$577$	44.8170	+	14.5619i	1.86575	+	0.606220i	0.872747	+	0.488173i	$0.162337\pi$
$578$			51.4908i			2.14173i
$579$	−4.24936	+	1.38070i	−0.176597	+	0.0573799i
$580$	21.9437	−	7.12994i	0.911163	−	0.296055i
$581$		−	6.97464i		−	0.289357i
$582$	13.1019	+	4.25706i	0.543091	+	0.176461i
$583$	−5.16527	+	3.75279i	−0.213924	+	0.155425i
$584$	20.1461	+	6.54587i	0.833652	+	0.270870i
$585$	−1.67388	−	5.15166i	−0.0692062	−	0.212995i
$586$	−13.1342	+	4.26756i	−0.542569	+	0.176291i
$587$	−0.725235	+	0.998201i	−0.0299337	+	0.0412002i	−0.823722	−	0.566995i	$-0.808106\pi$
$587$	−0.725235	+	0.998201i	−0.0299337	+	0.0412002i	0.793788	+	0.608195i	$0.208106\pi$
$588$	−8.75176	+	26.9351i	−0.360916	+	1.11079i
$589$		−	0.550140i		−	0.0226681i
$590$	−1.04299	−	3.20998i	−0.0429391	−	0.132153i
$591$	0.0190410	−	0.0586021i	0.000783241	−	0.00241057i
$592$	−18.2473	−	25.1152i	−0.749959	−	1.03223i
$593$	10.8021	−	14.8678i	0.443588	−	0.610546i	−0.527417	−	0.849607i	$-0.676839\pi$
$593$	10.8021	−	14.8678i	0.443588	−	0.610546i	0.971005	+	0.239060i	$0.0768394\pi$
$594$	11.5298	+	35.4851i	0.473073	+	1.45597i
$595$	9.86749	−	7.16915i	0.404528	−	0.293906i
$596$	44.4534			1.82088
$597$	22.3044			0.912860
$598$	−24.6736	+	17.9264i	−1.00898	+	0.733067i
$599$			28.0735i			1.14705i	0.819188	+	0.573526i	$0.194425\pi$
$599$			28.0735i			1.14705i	−0.819188	+	0.573526i	$0.805575\pi$
$600$	−15.1820	−	20.8962i	−0.619802	−	0.853084i
$601$	−10.0730	−	7.31846i	−0.410886	−	0.298526i	0.363074	−	0.931760i	$-0.381727\pi$
$601$	−10.0730	−	7.31846i	−0.410886	−	0.298526i	−0.773960	+	0.633234i	$0.781727\pi$
$602$	−0.621137	−	0.854921i	−0.0253156	−	0.0348440i
$603$	19.6881	−	6.39705i	0.801761	−	0.260508i
$604$	−13.9518	+	19.2030i	−0.567690	+	0.781358i
$605$	0.431719	+	0.313662i	0.0175519	+	0.0127522i
$606$	−13.5583	−	9.85069i	−0.550769	−	0.400157i
$607$	11.9284	−	36.7118i	0.484158	−	1.49009i	−0.349038	−	0.937109i	$-0.613492\pi$
$607$	11.9284	−	36.7118i	0.484158	−	1.49009i	0.833196	−	0.552978i	$-0.186508\pi$
$608$	12.0841	+	3.92637i	0.490075	+	0.159235i
$609$	33.3088			1.34974
$610$	−2.22391	+	10.2509i	−0.0900436	+	0.415048i
$611$	33.1436			1.34085
$612$	56.2340	+	18.2715i	2.27312	+	0.738583i
$613$	3.71363	−	11.4294i	0.149992	−	0.461628i	−0.847627	−	0.530592i	$-0.821970\pi$
$613$	3.71363	−	11.4294i	0.149992	−	0.461628i	0.997619	+	0.0689645i	$0.0219695\pi$
$614$	55.5076	+	40.3287i	2.24011	+	1.62753i
$615$	−1.15877	−	0.841894i	−0.0467260	−	0.0339485i
$616$	42.6442	−	58.6947i	1.71818	−	2.36488i
$617$	29.6357	−	9.62923i	1.19309	−	0.387658i	0.355875	−	0.934534i	$-0.384183\pi$
$617$	29.6357	−	9.62923i	1.19309	−	0.387658i	0.837214	+	0.546875i	$0.184183\pi$
$618$	−3.25092	−	4.47451i	−0.130771	−	0.179991i
$619$	−8.30424	−	6.03338i	−0.333776	−	0.242502i	0.408255	−	0.912868i	$-0.366137\pi$
$619$	−8.30424	−	6.03338i	−0.333776	−	0.242502i	−0.742031	+	0.670366i	$0.766137\pi$
$620$	−0.271942	−	0.374296i	−0.0109214	−	0.0150321i
$621$		−	12.0705i		−	0.484374i
$622$	10.6235	−	7.71843i	0.425964	−	0.309481i
$623$	−47.2675			−1.89373
$624$	27.6551			1.10709
$625$	−16.8743	+	12.2599i	−0.674973	+	0.490396i
$626$	−7.68944	−	23.6657i	−0.307332	−	0.945870i
$627$	4.63839	−	6.38420i	0.185240	−	0.254960i
$628$	−5.10901	−	7.03195i	−0.203872	−	0.280605i
$629$	−8.85101	+	27.2406i	−0.352913	+	1.08615i
$630$	−3.42691	−	10.5469i	−0.136531	−	0.420200i
$631$			45.8007i			1.82330i	0.410969	+	0.911649i	$0.365191\pi$
$631$			45.8007i			1.82330i	−0.410969	+	0.911649i	$0.634809\pi$
$632$	−12.6106	+	38.8114i	−0.501622	+	1.54383i
$633$	−1.40519	+	1.93408i	−0.0558514	+	0.0768728i
$634$	47.2645	−	15.3572i	1.87711	−	0.609911i
$635$	2.78856	+	8.58229i	0.110660	+	0.340578i
$636$	−7.60062	−	2.46959i	−0.301384	−	0.0979257i
$637$	−26.9402	+	19.5732i	−1.06741	+	0.775519i
$638$	−75.0825	−	24.3958i	−2.97254	−	0.965838i
$639$			10.0596i			0.397953i
$640$	−6.75642	+	2.19530i	−0.267071	+	0.0867767i
$641$	−15.5799	+	5.06222i	−0.615369	+	0.199946i	−0.600083	−	0.799938i	$-0.704866\pi$
$641$	−15.5799	+	5.06222i	−0.615369	+	0.199946i	−0.0152861	+	0.999883i	$0.504866\pi$
$642$			9.83593i			0.388193i
$643$	3.47394	+	1.12875i	0.136999	+	0.0445137i	0.376714	−	0.926330i	$-0.377054\pi$
$643$	3.47394	+	1.12875i	0.136999	+	0.0445137i	−0.239715	+	0.970843i	$0.577054\pi$
$644$	−34.7512	+	25.2482i	−1.36939	+	0.994920i
$645$	−0.0502323	−	0.0163215i	−0.00197789	−	0.000642657i
$646$	−13.2962	−	40.9215i	−0.523133	−	1.61004i
$647$	1.62855	−	0.529147i	0.0640248	−	0.0208029i	−0.276829	−	0.960919i	$-0.589284\pi$
$647$	1.62855	−	0.529147i	0.0640248	−	0.0208029i	0.340854	+	0.940116i	$0.389284\pi$
$648$	8.60357	−	11.8418i	0.337980	−	0.465190i
$649$	−2.45508	+	7.55595i	−0.0963701	+	0.296597i
$650$		−	55.5807i		−	2.18005i
$651$	−0.206393	−	0.635212i	−0.00808918	−	0.0248959i
$652$	−26.4566	+	81.4249i	−1.03612	+	3.18885i
$653$	13.6936	+	18.8477i	0.535874	+	0.737567i	0.988011	−	0.154381i	$-0.0493385\pi$
$653$	13.6936	+	18.8477i	0.535874	+	0.737567i	−0.452138	+	0.891948i	$0.649338\pi$
$654$	13.2857	−	18.2861i	0.519510	−	0.715044i
$655$	−0.785404	−	2.41722i	−0.0306883	−	0.0944488i
$656$	−16.1194	+	11.7114i	−0.629357	+	0.457254i
$657$	−7.62166			−0.297349
$658$	67.8546			2.64525
$659$	−7.08082	+	5.14451i	−0.275829	+	0.200402i	−0.717096	−	0.696974i	$-0.754529\pi$
$659$	−7.08082	+	5.14451i	−0.275829	+	0.200402i	0.441267	+	0.897376i	$0.354529\pi$
$660$		−	6.63641i		−	0.258322i
$661$	−5.14712	−	7.08440i	−0.200200	−	0.275551i	0.697099	−	0.716975i	$-0.254474\pi$
$661$	−5.14712	−	7.08440i	−0.200200	−	0.275551i	−0.897299	+	0.441423i	$0.854474\pi$
$662$	−66.8208	−	48.5481i	−2.59706	−	1.88688i
$663$	−14.9977	−	20.6426i	−0.582462	−	0.801690i
$664$	−10.7529	+	3.49383i	−0.417293	+	0.135587i
$665$	−3.26324	+	4.49147i	−0.126543	+	0.174172i
$666$	21.0688	+	15.3074i	0.816398	+	0.593148i
$667$	20.6622	+	15.0120i	0.800045	+	0.581267i
$668$	7.13541	−	21.9605i	0.276077	−	0.849679i
$669$	16.2510	+	5.28027i	0.628300	+	0.204147i
$670$	−12.6688			−0.489437
$671$	18.4181	−	16.4443i	0.711022	−	0.634824i
$672$	15.4258			0.595064
$673$	2.95881	+	0.961376i	0.114054	+	0.0370583i	0.365488	−	0.930816i	$-0.380902\pi$
$673$	2.95881	+	0.961376i	0.114054	+	0.0370583i	−0.251434	+	0.967874i	$0.580902\pi$
$674$	−10.2169	+	31.4444i	−0.393541	+	1.21119i
$675$	17.7964	+	12.9299i	0.684985	+	0.497671i
$676$	30.8491	+	22.4132i	1.18650	+	0.862046i
$677$	1.17051	−	1.61107i	0.0449863	−	0.0619184i	−0.785931	−	0.618314i	$-0.787816\pi$
$677$	1.17051	−	1.61107i	0.0449863	−	0.0619184i	0.830918	+	0.556396i	$0.187816\pi$
$678$	24.8299	−	8.06773i	0.953588	−	0.309839i
$679$	13.4095	+	18.4567i	0.514611	+	0.708301i
$680$	−15.9957	−	11.6216i	−0.613408	−	0.445667i
$681$	8.09264	+	11.1386i	0.310111	+	0.426831i
$682$			1.58302i			0.0606169i
$683$	27.0855	−	19.6787i	1.03640	−	0.752986i	0.0668175	−	0.997765i	$-0.478715\pi$
$683$	27.0855	−	19.6787i	1.03640	−	0.752986i	0.969579	+	0.244779i	$0.0787155\pi$
$684$	−26.9137			−1.02907
$685$	−8.96147			−0.342400
$686$	−1.21023	+	0.879282i	−0.0462067	+	0.0335711i
$687$	−0.340206	−	1.04705i	−0.0129797	−	0.0399473i
$688$	−0.431864	+	0.594410i	−0.0164647	+	0.0226617i
$689$	−5.52322	−	7.60206i	−0.210418	−	0.289615i
$690$	−0.964374	+	2.96804i	−0.0367131	+	0.112991i
$691$	−12.3993	−	38.1610i	−0.471690	−	1.45171i	−0.850370	−	0.526186i	$-0.823622\pi$
$691$	−12.3993	−	38.1610i	−0.471690	−	1.45171i	0.378679	−	0.925528i	$-0.376378\pi$
$692$			10.6905i			0.406393i
$693$	−8.06656	+	24.8263i	−0.306423	+	0.943074i
$694$	−25.9468	+	35.7127i	−0.984928	+	1.35564i
$695$	−9.16708	+	2.97856i	−0.347727	+	0.112983i
$696$	−16.6855	−	51.3526i	−0.632462	−	1.94652i
$697$	17.4835	+	5.68073i	0.662234	+	0.215173i
$698$	−1.72907	+	1.25624i	−0.0654464	+	0.0475496i
$699$	−10.6849	−	3.47174i	−0.404141	−	0.131313i
$700$		−	78.2818i		−	2.95877i
$701$	−16.4311	+	5.33879i	−0.620594	+	0.201643i	−0.602404	−	0.798191i	$-0.705790\pi$
$701$	−16.4311	+	5.33879i	−0.620594	+	0.201643i	−0.0181902	+	0.999835i	$0.505790\pi$
$702$	−52.2257	+	16.9692i	−1.97113	+	0.640459i
$703$		−	13.0374i		−	0.491716i
$704$	5.05334	+	1.64193i	0.190455	+	0.0618826i
$705$	2.74375	−	1.99345i	0.103336	−	0.0750778i
$706$	−62.3997	−	20.2749i	−2.34845	−	0.763056i
$707$	−8.57626	−	26.3950i	−0.322544	−	0.992687i
$708$	−9.45794	+	3.07307i	−0.355451	+	0.115493i
$709$	−0.663776	+	0.913609i	−0.0249286	+	0.0343113i	−0.821299	−	0.570497i	$-0.806750\pi$
$709$	−0.663776	+	0.913609i	−0.0249286	+	0.0343113i	0.796371	+	0.604809i	$0.206750\pi$
$710$	1.90240	−	5.85499i	0.0713958	−	0.219734i
$711$		−	14.6831i		−	0.550659i
$712$	23.6779	+	72.8730i	0.887366	+	2.73103i
$713$	0.158254	−	0.487057i	0.00592667	−	0.0182404i
$714$	−30.7046	−	42.2613i	−1.14909	−	1.58159i
$715$	4.58651	−	6.31279i	0.171526	−	0.236085i
$716$	16.9513	+	52.1706i	0.633498	+	1.94971i
$717$	−9.83078	+	7.14248i	−0.367137	+	0.266741i
$718$	51.5170			1.92260
$719$	−33.8749			−1.26332			−0.631660	−	0.775245i	$-0.717626\pi$
$719$	−33.8749			−1.26332			−0.631660	+	0.775245i	$0.717626\pi$
$720$	−6.23790	+	4.53210i	−0.232473	+	0.168901i
$721$		−	9.15915i		−	0.341105i
$722$	−16.7614	−	23.0700i	−0.623794	−	0.858578i
$723$	−5.29326	−	3.84578i	−0.196858	−	0.143026i
$724$	52.8959	+	72.8050i	1.96586	+	2.70578i
$725$	−44.2664	+	14.3830i	−1.64401	+	0.534173i
$726$	1.34338	−	1.84900i	0.0498575	−	0.0686229i
$727$	−15.8197	−	11.4937i	−0.586720	−	0.426277i	0.254420	−	0.967094i	$-0.418115\pi$
$727$	−15.8197	−	11.4937i	−0.586720	−	0.426277i	−0.841141	+	0.540817i	$0.818115\pi$
$728$	86.3848	+	62.7623i	3.20164	+	2.32612i
$729$	2.25123	−	6.92856i	0.0833788	−	0.256613i
$730$	4.43602	+	1.44135i	0.164184	+	0.0533467i
$731$	0.677890			0.0250727
$732$	30.2035	+	6.55257i	1.11635	+	0.242190i
$733$	35.6696			1.31749			0.658743	−	0.752368i	$-0.271089\pi$
$733$	35.6696			1.31749			0.658743	+	0.752368i	$0.271089\pi$
$734$	−82.8615	−	26.9233i	−3.05847	−	0.993758i
$735$	−1.05296	+	3.24069i	−0.0388392	+	0.119535i
$736$	9.56899	+	6.95228i	0.352718	+	0.256264i
$737$	24.1256	+	17.5283i	0.888677	+	0.645662i
$738$	9.82453	−	13.5223i	0.361646	−	0.497763i
$739$	−36.5237	+	11.8673i	−1.34355	+	0.436545i	−0.890517	−	0.454951i	$-0.849657\pi$
$739$	−36.5237	+	11.8673i	−1.34355	+	0.436545i	−0.453030	+	0.891495i	$0.649657\pi$
$740$	−6.44458	−	8.87020i	−0.236907	−	0.326075i
$741$	9.39604	+	6.82662i	0.345172	+	0.250782i
$742$	−11.3076	−	15.5636i	−0.415117	−	0.571359i
$743$			35.7621i			1.31198i	0.754768	+	0.655992i	$0.227749\pi$
$743$			35.7621i			1.31198i	−0.754768	+	0.655992i	$0.772251\pi$
$744$	−0.875926	+	0.636398i	−0.0321130	+	0.0233315i
$745$	5.34840			0.195950
$746$	−57.9400			−2.12133
$747$	3.29110	−	2.39113i	0.120415	−	0.0874867i
$748$	26.3207	+	81.0069i	0.962382	+	2.96191i
$749$	−9.57418	+	13.1777i	−0.349833	+	0.481504i
$750$	−6.88529	−	9.47679i	−0.251415	−	0.346043i
$751$	12.6196	−	38.8391i	0.460495	−	1.41726i	−0.404065	−	0.914730i	$-0.632403\pi$
$751$	12.6196	−	38.8391i	0.460495	−	1.41726i	0.864560	−	0.502529i	$-0.167597\pi$
$752$	−14.5788	−	44.8689i	−0.531634	−	1.63620i
$753$		−	15.0788i		−	0.549500i
$754$	35.9049	−	110.504i	1.30758	−	4.02431i
$755$	−1.67860	+	2.31040i	−0.0610906	+	0.0840840i
$756$	−73.5565	+	23.8999i	−2.67522	+	0.869233i
$757$	−2.44415	−	7.52232i	−0.0888341	−	0.273403i	0.896764	−	0.442510i	$-0.145912\pi$
$757$	−2.44415	−	7.52232i	−0.0888341	−	0.273403i	−0.985598	+	0.169107i	$0.945912\pi$
$758$	−13.0658	−	4.24534i	−0.474571	−	0.154198i
$759$	5.94301	−	4.31785i	0.215718	−	0.156728i
$760$	8.55922	+	2.78106i	0.310476	+	0.100880i
$761$			11.7695i			0.426643i	0.976982	+	0.213322i	$0.0684283\pi$
$761$			11.7695i			0.426643i	−0.976982	+	0.213322i	$0.931572\pi$
$762$	36.7570	−	11.9431i	1.33156	−	0.432651i
$763$	35.5990	−	11.5668i	1.28877	−	0.418747i
$764$		−	34.4294i		−	1.24561i
$765$	6.76577	+	2.19833i	0.244617	+	0.0794809i
$766$	30.2221	−	21.9576i	1.09197	−	0.793361i
$767$	−11.1206	−	3.61329i	−0.401541	−	0.130468i
$768$	8.46995	+	26.0678i	0.305633	+	0.940642i
$769$	−16.7493	+	5.44219i	−0.603996	+	0.196250i	−0.595022	−	0.803709i	$-0.702857\pi$
$769$	−16.7493	+	5.44219i	−0.603996	+	0.196250i	−0.00897422	+	0.999960i	$0.502857\pi$
$770$	9.38992	−	12.9241i	0.338389	−	0.465753i
$771$	2.62744	−	8.08644i	0.0946251	−	0.291226i
$772$			21.9516i			0.790054i
$773$	6.55823	+	20.1842i	0.235883	+	0.725974i	0.997003	+	0.0773624i	$0.0246499\pi$
$773$	6.55823	+	20.1842i	0.235883	+	0.725974i	−0.761120	+	0.648611i	$0.775350\pi$
$774$	0.190464	−	0.586188i	0.00684609	−	0.0210701i
$775$	0.548581	+	0.755056i	0.0197056	+	0.0271224i
$776$	21.7376	−	29.9192i	0.780334	−	1.07404i
$777$	−4.89118	−	15.0535i	−0.175470	−	0.540042i
$778$	−73.9066	+	53.6963i	−2.64968	+	1.92511i
$779$	−8.36765			−0.299802
$780$	9.76723			0.349723
$781$	−11.7237	+	8.51774i	−0.419506	+	0.304789i
$782$		−	40.0540i		−	1.43233i
$783$	27.0297	+	37.2031i	0.965961	+	1.32953i
$784$	38.3479	+	27.8614i	1.36957	+	0.995048i
$785$	−0.614688	−	0.846046i	−0.0219392	−	0.0301967i
$786$	−10.3527	+	3.36379i	−0.369268	+	0.119983i
$787$	6.73565	−	9.27082i	0.240100	−	0.330469i	−0.671913	−	0.740630i	$-0.734527\pi$
$787$	6.73565	−	9.27082i	0.240100	−	0.330469i	0.912013	+	0.410161i	$0.134527\pi$
$788$	−0.244914	−	0.177940i	−0.00872468	−	0.00633885i
$789$	9.02016	+	6.55353i	0.321126	+	0.233312i
$790$	−2.77675	+	8.54597i	−0.0987925	+	0.304052i
$791$	41.1190	+	13.3604i	1.46203	+	0.475041i
$792$	42.3159			1.50363
$793$	24.2021	+	27.1071i	0.859441	+	0.962601i
$794$	9.26712			0.328878
$795$	−0.914466	−	0.297128i	−0.0324328	−	0.0105380i
$796$	33.8627	−	104.219i	1.20023	−	3.69394i
$797$	−6.19205	−	4.49879i	−0.219334	−	0.159355i	0.472693	−	0.881227i	$-0.343282\pi$
$797$	−6.19205	−	4.49879i	−0.219334	−	0.159355i	−0.692027	+	0.721872i	$0.743282\pi$
$798$	19.2364	+	13.9761i	0.680962	+	0.494748i
$799$	−25.5852	+	35.2150i	−0.905139	+	1.24582i
$800$	−20.5005	+	6.66100i	−0.724801	+	0.235502i
$801$	−16.2048	−	22.3040i	−0.572569	−	0.788073i
$802$	−39.6484	−	28.8063i	−1.40003	−	1.01718i
$803$	−6.45345	−	8.88241i	−0.227737	−	0.313453i
$804$			37.3274i			1.31644i
$805$	−4.18108	+	3.03773i	−0.147364	+	0.107066i
$806$	−2.32983			−0.0820648
$807$	−16.3757			−0.576454
$808$	−36.3974	+	26.4443i	−1.28046	+	0.930307i
$809$	−2.25437	−	6.93824i	−0.0792595	−	0.243936i	0.903574	−	0.428433i	$-0.140934\pi$
$809$	−2.25437	−	6.93824i	−0.0792595	−	0.243936i	−0.982833	+	0.184498i	$0.940934\pi$
$810$	1.89444	−	2.60747i	0.0665638	−	0.0916173i
$811$	−2.98135	−	4.10348i	−0.104689	−	0.144093i	0.753458	−	0.657496i	$-0.228384\pi$
$811$	−2.98135	−	4.10348i	−0.104689	−	0.144093i	−0.858147	+	0.513404i	$0.828384\pi$
$812$	50.5697	−	155.637i	1.77465	−	5.46180i
$813$	−6.58123	−	20.2550i	−0.230814	−	0.710372i
$814$			37.5150i			1.31490i
$815$	−3.18311	+	9.79661i	−0.111500	+	0.343160i
$816$	−21.3483	+	29.3835i	−0.747342	+	1.02863i
$817$	−0.293459	+	0.0953505i	−0.0102668	+	0.00333589i
$818$	22.1517	+	68.1760i	0.774517	+	2.38372i
$819$	−36.5385	−	11.8721i	−1.27676	−	0.414844i
$820$	−5.69305	+	4.13624i	−0.198810	+	0.144444i
$821$	16.1994	+	5.26351i	0.565364	+	0.183698i	0.577733	−	0.816226i	$-0.303937\pi$
$821$	16.1994	+	5.26351i	0.565364	+	0.183698i	−0.0123694	+	0.999923i	$0.503937\pi$
$822$			38.3809i			1.33869i
$823$	24.5724	−	7.98405i	0.856539	−	0.278306i	0.152357	−	0.988326i	$-0.451314\pi$
$823$	24.5724	−	7.98405i	0.856539	−	0.278306i	0.704182	+	0.710019i	$0.251314\pi$
$824$	−14.1208	+	4.58812i	−0.491921	+	0.159835i
$825$			13.3874i			0.466091i
$826$	−22.7671	−	7.39746i	−0.792167	−	0.257391i
$827$	7.75548	−	5.63469i	0.269685	−	0.195937i	−0.444721	−	0.895669i	$-0.646697\pi$
$827$	7.75548	−	5.63469i	0.269685	−	0.195937i	0.714406	+	0.699732i	$0.246697\pi$
$828$	−23.8276	−	7.74206i	−0.828067	−	0.269055i
$829$	9.08875	+	27.9723i	0.315665	+	0.971518i	0.975480	+	0.220089i	$0.0706349\pi$
$829$	9.08875	+	27.9723i	0.315665	+	0.971518i	−0.659814	+	0.751429i	$0.729365\pi$
$830$	−2.36770	+	0.769313i	−0.0821842	+	0.0267032i
$831$	7.44568	−	10.2481i	0.258288	−	0.355503i
$832$	−2.41653	+	7.43733i	−0.0837783	+	0.257843i
$833$		−	43.7335i		−	1.51528i
$834$	12.7568	+	39.2615i	0.441734	+	1.35952i
$835$	0.858494	−	2.64217i	0.0297094	−	0.0914362i
$836$	−22.7885	−	31.3657i	−0.788157	−	1.08481i
$837$	0.541994	−	0.745990i	0.0187340	−	0.0257852i
$838$	−11.4276	−	35.1704i	−0.394759	−	1.21494i
$839$	20.7543	−	15.0789i	0.716519	−	0.520581i	−0.168751	−	0.985659i	$-0.553973\pi$
$839$	20.7543	−	15.0789i	0.716519	−	0.520581i	0.885270	+	0.465077i	$0.153973\pi$
$840$	10.9262			0.376988
$841$	−68.3005			−2.35519
$842$	15.9903	−	11.6176i	0.551062	−	0.400370i
$843$			8.74122i			0.301064i
$844$	6.90374	+	9.50218i	0.237636	+	0.327079i
$845$	3.71160	+	2.69664i	0.127683	+	0.0927671i
$846$	23.2627	+	32.0183i	0.799788	+	1.10081i
$847$	3.59960	−	1.16958i	0.123684	−	0.0401872i
$848$	−7.86199	+	10.8211i	−0.269982	+	0.371598i
$849$	−17.0894	−	12.4162i	−0.586506	−	0.426122i
$850$	59.0544	+	42.9055i	2.02555	+	1.47165i
$851$	3.75037	−	11.5425i	0.128561	−	0.395670i
$852$	−17.2512	−	5.60526i	−0.591017	−	0.192033i
$853$	4.23309			0.144938			0.0724691	−	0.997371i	$-0.476912\pi$
$853$	4.23309			0.144938			0.0724691	+	0.997371i	$0.476912\pi$
$854$	49.5487	+	55.4961i	1.69552	+	1.89904i
$855$	−3.23812			−0.110741
$856$	25.1123	+	8.15948i	0.858321	+	0.278885i
$857$	−11.7213	+	36.0745i	−0.400393	+	1.23228i	0.524289	+	0.851541i	$0.324331\pi$
$857$	−11.7213	+	36.0745i	−0.400393	+	1.23228i	−0.924681	+	0.380742i	$0.875669\pi$
$858$	−27.0370	−	19.6435i	−0.923027	−	0.670618i
$859$	−6.87189	−	4.99272i	−0.234466	−	0.170350i	0.464348	−	0.885653i	$-0.346289\pi$
$859$	−6.87189	−	4.99272i	−0.234466	−	0.170350i	−0.698814	+	0.715303i	$0.746289\pi$
$860$	−0.152526	+	0.209934i	−0.00520109	+	0.00715869i
$861$	−9.66160	+	3.13925i	−0.329267	+	0.106985i
$862$	47.7731	+	65.7541i	1.62716	+	2.23959i
$863$	−39.3965	−	28.6233i	−1.34107	−	0.974347i	−0.999404	−	0.0345275i	$-0.989007\pi$
$863$	−39.3965	−	28.6233i	−1.34107	−	0.974347i	−0.341670	−	0.939820i	$-0.610993\pi$
$864$	12.5178	+	17.2293i	0.425866	+	0.586154i
$865$			1.28623i			0.0437330i
$866$	−71.9658	+	52.2862i	−2.44550	+	1.77676i
$867$	18.2533			0.619915
$868$	−3.28142			−0.111378
$869$	17.1119	−	12.4325i	0.580482	−	0.421745i
$870$	−3.67401	−	11.3075i	−0.124561	−	0.383358i
$871$	−25.7975	+	35.5072i	−0.874115	+	1.20312i
$872$	−35.6655	−	49.0893i	−1.20779	−	1.66237i
$873$	−4.11187	+	12.6550i	−0.139166	+	0.428308i
$874$	5.63391	+	17.3394i	0.190570	+	0.586513i
$875$		−	19.3986i		−	0.655793i
$876$	4.24681	−	13.0703i	0.143486	−	0.441606i
$877$	4.33905	−	5.97219i	0.146519	−	0.201666i	−0.729449	−	0.684035i	$-0.760223\pi$
$877$	4.33905	−	5.97219i	0.146519	−	0.201666i	0.875968	+	0.482369i	$0.160223\pi$
$878$	52.4596	−	17.0452i	1.77043	−	0.575246i
$879$	1.51284	+	4.65603i	0.0510267	+	0.157044i
$880$	−10.5636	−	3.43231i	−0.356097	−	0.115703i
$881$	41.8422	−	30.4001i	1.40970	−	1.02421i	0.416334	−	0.909212i	$-0.363315\pi$
$881$	41.8422	−	30.4001i	1.40970	−	1.02421i	0.993366	−	0.114995i	$-0.0366852\pi$
$882$	−37.8174	−	12.2876i	−1.27338	−	0.413746i
$883$		−	35.3584i		−	1.18990i	−0.803761	−	0.594952i	$-0.797171\pi$
$883$		−	35.3584i		−	1.18990i	0.803761	−	0.594952i	$-0.202829\pi$
$884$	−119.223	+	38.7380i	−4.00991	+	1.30290i
$885$	−1.13793	+	0.369735i	−0.0382510	+	0.0124285i
$886$		−	8.98481i		−	0.301851i
$887$	5.93562	+	1.92860i	0.199299	+	0.0647560i	0.406965	−	0.913444i	$-0.366587\pi$
$887$	5.93562	+	1.92860i	0.199299	+	0.0647560i	−0.207667	+	0.978200i	$0.566587\pi$
$888$	−20.7580	+	15.0816i	−0.696594	+	0.506105i
$889$	60.8706	+	19.7780i	2.04153	+	0.663334i
$890$	5.21368	+	16.0461i	0.174763	+	0.537865i
$891$	−7.21530	+	2.34439i	−0.241722	+	0.0785401i
$892$	49.3448	−	67.9173i	1.65219	−	2.27404i
$893$	6.12257	−	18.8433i	0.204884	−	0.630568i
$894$		−	22.9066i		−	0.766110i
$895$	2.03948	+	6.27689i	0.0681724	+	0.209813i
$896$	−15.5703	+	47.9205i	−0.520167	+	1.60091i
$897$	6.35486	+	8.74672i	0.212183	+	0.292044i
$898$	2.92822	−	4.03035i	0.0977159	−	0.134494i
$899$	0.602908	+	1.85556i	0.0201081	+	0.0618864i
$900$	36.9386	−	26.8375i	1.23129	−	0.894583i
$901$	12.3408			0.411132
$902$	24.0778			0.801702
$903$	−0.303067	+	0.220191i	−0.0100854	+	0.00732749i
$904$		−	70.0864i		−	2.33104i
$905$	6.36415	+	8.75951i	0.211552	+	0.291176i
$906$	9.89517	+	7.18926i	0.328745	+	0.238847i
$907$	34.4871	+	47.4674i	1.14512	+	1.57613i	0.755493	+	0.655157i	$0.227398\pi$
$907$	34.4871	+	47.4674i	1.14512	+	1.57613i	0.389631	+	0.920971i	$0.372602\pi$
$908$	64.3319	−	20.9027i	2.13493	−	0.693680i
$909$	9.51473	−	13.0959i	0.315584	−	0.434364i
$910$	19.0213	+	13.8198i	0.630549	+	0.458121i
$911$	−20.5507	−	14.9310i	−0.680875	−	0.494685i	0.192773	−	0.981243i	$-0.438252\pi$
$911$	−20.5507	−	14.9310i	−0.680875	−	0.494685i	−0.873648	+	0.486559i	$0.838252\pi$
$912$	5.10869	−	15.7229i	0.169166	−	0.520638i
$913$	5.57331	+	1.81088i	0.184450	+	0.0599313i
$914$	88.8074			2.93749
$915$	3.63392	+	0.788370i	0.120134	+	0.0260627i
$916$	−5.40889			−0.178715
$917$	−17.1443	−	5.57054i	−0.566156	−	0.183955i
$918$	22.2859	−	68.5890i	0.735545	−	2.26377i
$919$	9.90706	+	7.19790i	0.326804	+	0.237437i	0.739073	−	0.673625i	$-0.235264\pi$
$919$	9.90706	+	7.19790i	0.326804	+	0.237437i	−0.412269	+	0.911062i	$0.635264\pi$
$920$	6.77775	+	4.92432i	0.223456	+	0.162350i
$921$	14.2964	−	19.6773i	0.471081	−	0.648388i
$922$	24.2207	−	7.86977i	0.797665	−	0.259177i
$923$	−12.5361	−	17.2545i	−0.412631	−	0.567938i
$924$	−38.0798	−	27.6666i	−1.25273	−	0.910164i
$925$	13.0005	+	17.8936i	0.427453	+	0.588339i
$926$		−	67.5988i		−	2.22144i
$927$	4.32190	−	3.14005i	0.141950	−	0.103133i
$928$	−45.0613			−1.47921
$929$	58.8018			1.92923			0.964613	−	0.263671i	$-0.0849334\pi$
$929$	58.8018			1.92923			0.964613	+	0.263671i	$0.0849334\pi$
$930$	−0.192872	+	0.140130i	−0.00632453	+	0.00459504i
$931$	6.15146	+	18.9322i	0.201606	+	0.620479i
$932$	−32.4438	+	44.6551i	−1.06273	+	1.46273i
$933$	−2.73616	−	3.76600i	−0.0895777	−	0.123293i
$934$	15.1218	−	46.5402i	0.494802	−	1.52284i
$935$	3.16677	+	9.74632i	0.103564	+	0.318739i
$936$			62.2791i			2.03565i
$937$	0.371792	−	1.14426i	0.0121459	−	0.0373813i	−0.944800	−	0.327648i	$-0.893744\pi$
$937$	0.371792	−	1.14426i	0.0121459	−	0.0373813i	0.956946	+	0.290267i	$0.0937440\pi$
$938$	−52.8150	+	72.6936i	−1.72447	+	2.37353i
$939$	−8.38939	+	2.72588i	−0.273778	+	0.0889557i
$940$	−5.14894	−	15.8468i	−0.167940	−	0.516866i
$941$	−17.5239	−	5.69386i	−0.571263	−	0.185614i	0.00911996	−	0.999958i	$-0.497097\pi$
$941$	−17.5239	−	5.69386i	−0.571263	−	0.185614i	−0.580383	+	0.814344i	$0.697097\pi$
$942$	−3.62352	+	2.63264i	−0.118061	+	0.0857760i
$943$	−7.40815	−	2.40705i	−0.241243	−	0.0783844i
$944$			16.6441i			0.541720i
$945$	−8.84992	+	2.87551i	−0.287888	+	0.0935405i
$946$	0.844423	−	0.274370i	0.0274546	−	0.00892053i
$947$		−	45.8350i		−	1.48944i	−0.667379	−	0.744718i	$-0.732584\pi$
$947$		−	45.8350i		−	1.48944i	0.667379	−	0.744718i	$-0.267416\pi$
$948$	25.1800	+	8.18146i	0.817807	+	0.265722i
$949$	13.0728	−	9.49796i	0.424361	−	0.308317i
$950$	−31.5997	−	10.2674i	−1.02523	−	0.333117i
$951$	−5.44407	−	16.7551i	−0.176536	−	0.543322i
$952$	−133.370	+	43.3344i	−4.32253	+	1.40448i
$953$	10.7312	−	14.7702i	0.347617	−	0.478453i	−0.599030	−	0.800727i	$-0.704447\pi$
$953$	10.7312	−	14.7702i	0.347617	−	0.478453i	0.946647	+	0.322273i	$0.104447\pi$
$954$	3.46735	−	10.6714i	0.112260	−	0.345500i
$955$		−	4.14236i		−	0.134044i
$956$	18.4485	+	56.7787i	0.596667	+	1.83635i
$957$	−8.64822	+	26.6165i	−0.279557	+	0.860389i
$958$	−55.2786	−	76.0845i	−1.78597	−	2.45818i
$959$	−37.3596	+	51.4210i	−1.20640	+	1.66047i
$960$	0.247275	+	0.761035i	0.00798077	+	0.0245623i
$961$	−25.0479	+	18.1983i	−0.807996	+	0.587043i
$962$	−55.2132			−1.78015
$963$	−9.50047			−0.306148
$964$	−26.0059	+	18.8944i	−0.837593	+	0.608547i
$965$			2.64109i			0.0850199i
$966$	13.0103	+	17.9071i	0.418598	+	0.576151i
$967$	−3.27906	−	2.38238i	−0.105447	−	0.0766121i	0.533812	−	0.845603i	$-0.320759\pi$
$967$	−3.27906	−	2.38238i	−0.105447	−	0.0766121i	−0.639259	+	0.768991i	$0.720759\pi$
$968$	−3.60631	−	4.96366i	−0.115911	−	0.159538i
$969$	−14.5065	+	4.71346i	−0.466017	+	0.151418i
$970$	4.78645	−	6.58798i	0.153684	−	0.211527i
$971$	−1.50356	−	1.09240i	−0.0482517	−	0.0350569i	0.563398	−	0.826186i	$-0.309494\pi$
$971$	−1.50356	−	1.09240i	−0.0482517	−	0.0350569i	−0.611650	+	0.791129i	$0.709494\pi$
$972$	−57.5720	−	41.8285i	−1.84662	−	1.34165i
$973$	−21.1257	+	65.0182i	−0.677259	+	2.08439i
$974$	19.1229	+	6.21342i	0.612739	+	0.199091i
$975$	−19.7032			−0.631006
$976$	26.0511	−	44.6877i	0.833877	−	1.43042i
$977$	−45.7198			−1.46270			−0.731352	−	0.682000i	$-0.761110\pi$
$977$	−45.7198			−1.46270			−0.731352	+	0.682000i	$0.761110\pi$
$978$	41.9577	+	13.6329i	1.34166	+	0.435932i
$979$	12.2724	−	37.7707i	0.392229	−	1.20716i
$980$	13.5437	+	9.84008i	0.432638	+	0.314330i
$981$	17.6625	+	12.8325i	0.563920	+	0.409712i
$982$	−33.4005	+	45.9719i	−1.06585	+	1.46702i
$983$	−35.9808	+	11.6909i	−1.14761	+	0.372881i	−0.820243	−	0.572016i	$-0.806162\pi$
$983$	−35.9808	+	11.6909i	−1.14761	+	0.372881i	−0.327368	+	0.944897i	$0.606162\pi$
$984$	9.67963	+	13.3229i	0.308575	+	0.424718i
$985$	−0.0294667	−	0.0214088i	−0.000938886	−	0.000682141i
$986$	89.6933	+	123.452i	2.85642	+	3.93152i
$987$		−	24.0542i		−	0.765654i
$988$	46.1629	−	33.5393i	1.46864	−	1.06703i
$989$	−0.287237			−0.00913362
$990$	9.31763			0.296134
$991$	−20.9777	+	15.2412i	−0.666379	+	0.484153i	−0.868811	−	0.495143i	$-0.835116\pi$
$991$	−20.9777	+	15.2412i	−0.666379	+	0.484153i	0.202432	+	0.979296i	$0.435116\pi$
$992$	0.279216	+	0.859338i	0.00886511	+	0.0272840i
$993$	−17.2101	+	23.6877i	−0.546147	+	0.751707i
$994$	−25.6651	−	35.3249i	−0.814046	−	1.12044i
$995$	4.07418	−	12.5390i	0.129160	−	0.397515i
$996$	2.26671	+	6.97623i	0.0718236	+	0.221050i
$997$		−	21.4590i		−	0.679614i	−0.940495	−	0.339807i	$-0.889638\pi$
$997$		−	21.4590i		−	0.679614i	0.940495	−	0.339807i	$-0.110362\pi$
$998$	−19.0136	+	58.5179i	−0.601865	+	1.85235i
$999$	12.8444	−	17.6788i	0.406378	−	0.559331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.3.1	✓	16
3.2	odd	2		549.2.y.b.64.4		16
4.3	odd	2		976.2.bd.b.369.3		16
61.23	odd	20		3721.2.a.k.1.1		16
61.38	odd	20		3721.2.a.k.1.16		16
61.41	even	10	inner	61.2.g.a.41.1	yes	16
183.41	odd	10		549.2.y.b.163.4		16
244.163	odd	10		976.2.bd.b.529.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.1	✓	16	1.1	even	1	trivial
61.2.g.a.41.1	yes	16	61.41	even	10	inner
549.2.y.b.64.4		16	3.2	odd	2
549.2.y.b.163.4		16	183.41	odd	10
976.2.bd.b.369.3		16	4.3	odd	2
976.2.bd.b.529.3		16	244.163	odd	10
3721.2.a.k.1.1		16	61.23	odd	20
3721.2.a.k.1.16		16	61.38	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.40774 - 0.782322i) q^{2} +(-0.277331 + 0.853536i) q^{3} +(3.56715 + 2.59169i) q^{4} +(0.429180 + 0.311818i) q^{5} +(1.33548 - 1.83813i) q^{6} +(3.57843 - 1.16270i) q^{7} +(-3.58511 - 4.93448i) q^{8} +(1.77544 + 1.28993i) q^{9} +O(q^{10})\)	\(q+(-2.40774 - 0.782322i) q^{2} +(-0.277331 + 0.853536i) q^{3} +(3.56715 + 2.59169i) q^{4} +(0.429180 + 0.311818i) q^{5} +(1.33548 - 1.83813i) q^{6} +(3.57843 - 1.16270i) q^{7} +(-3.58511 - 4.93448i) q^{8} +(1.77544 + 1.28993i) q^{9} +(-0.789413 - 1.08653i) q^{10} +3.16134i q^{11} +(-3.20138 + 2.32594i) q^{12} -4.65275 q^{13} -9.52554 q^{14} +(-0.385172 + 0.279844i) q^{15} +(2.04660 + 6.29878i) q^{16} +(3.59169 - 4.94354i) q^{17} +(-3.26566 - 4.49479i) q^{18} +(-0.859497 + 2.64526i) q^{19} +(0.722817 + 2.22460i) q^{20} +3.37677i q^{21} +(2.47319 - 7.61169i) q^{22} +(-1.52188 + 2.09469i) q^{23} +(5.20601 - 1.69154i) q^{24} +(-1.45812 - 4.48763i) q^{25} +(11.2026 + 3.63995i) q^{26} +(-3.77157 + 2.74021i) q^{27} +(15.7782 + 5.12664i) q^{28} -9.86410i q^{29} +(1.14632 - 0.372463i) q^{30} +(-0.188112 + 0.0611214i) q^{31} -4.56821i q^{32} +(-2.69832 - 0.876737i) q^{33} +(-12.5153 + 9.09290i) q^{34} +(1.89834 + 0.616809i) q^{35} +(2.99016 + 9.20277i) q^{36} +(-4.45796 + 1.44848i) q^{37} +(4.13889 - 5.69669i) q^{38} +(1.29035 - 3.97129i) q^{39} -3.23568i q^{40} +(0.929659 + 2.86120i) q^{41} +(2.64172 - 8.13039i) q^{42} +(0.0652075 + 0.0897504i) q^{43} +(-8.19321 + 11.2770i) q^{44} +(0.359760 + 1.10723i) q^{45} +(5.30302 - 3.85287i) q^{46} -7.12344 q^{47} -5.94381 q^{48} +(5.79017 - 4.20680i) q^{49} +11.9458i q^{50} +(3.22340 + 4.43663i) q^{51} +(-16.5971 - 12.0585i) q^{52} +(1.18709 + 1.63388i) q^{53} +(11.2247 - 3.64712i) q^{54} +(-0.985763 + 1.35679i) q^{55} +(-18.5664 - 13.4893i) q^{56} +(-2.01946 - 1.46722i) q^{57} +(-7.71690 + 23.7502i) q^{58} +(2.39011 + 0.776593i) q^{59} -2.09924 q^{60} +(-5.20167 - 5.82603i) q^{61} +0.500742 q^{62} +(7.85310 + 2.55163i) q^{63} +(0.519377 - 1.59848i) q^{64} +(-1.99687 - 1.45081i) q^{65} +(5.81096 + 4.22191i) q^{66} +(5.54456 - 7.63144i) q^{67} +(25.6242 - 8.32581i) q^{68} +(-1.36583 - 1.87990i) q^{69} +(-4.08818 - 2.97023i) q^{70} +(2.69434 + 3.70844i) q^{71} -13.3854i q^{72} +(-2.80969 + 2.04136i) q^{73} +11.8668 q^{74} +4.23473 q^{75} +(-9.92164 + 7.20849i) q^{76} +(3.67570 + 11.3126i) q^{77} +(-6.21366 + 8.55237i) q^{78} +(-3.93268 - 5.41286i) q^{79} +(-1.08571 + 3.34148i) q^{80} +(0.741582 + 2.28235i) q^{81} -7.61631i q^{82} +(0.572819 - 1.76296i) q^{83} +(-8.75153 + 12.0455i) q^{84} +(3.08297 - 1.00172i) q^{85} +(-0.0867890 - 0.267109i) q^{86} +(8.41936 + 2.73562i) q^{87} +(15.5996 - 11.3338i) q^{88} +(-11.9477 - 3.88203i) q^{89} -2.94737i q^{90} +(-16.6496 + 5.40977i) q^{91} +(-10.8576 + 3.52784i) q^{92} -0.177511i q^{93} +(17.1514 + 5.57282i) q^{94} +(-1.19372 + 0.867287i) q^{95} +(3.89913 + 1.26691i) q^{96} +(1.87366 + 5.76654i) q^{97} +(-17.2323 + 5.59911i) q^{98} +(-4.07792 + 5.61277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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