LMFDB - Embedded newform 170.2.n.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			9.1
Root			$2.99334 - 1.23988i$ of defining polynomial
Character	$\chi$	$=$	170.9
Dual form			170.2.n.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.23988 + 2.99334i) q^{3} +1.00000i q^{4} +(-2.18859 - 0.458323i) q^{5} +(2.99334 - 1.23988i) q^{6} +(1.49921 - 0.620992i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-5.30145 - 5.30145i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.23988 + 2.99334i) q^{3} +1.00000i q^{4} +(-2.18859 - 0.458323i) q^{5} +(2.99334 - 1.23988i) q^{6} +(1.49921 - 0.620992i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-5.30145 - 5.30145i) q^{9} +(1.22349 + 1.87165i) q^{10} +(-4.11919 + 1.70622i) q^{11} +(-2.99334 - 1.23988i) q^{12} -1.78934 q^{13} +(-1.49921 - 0.620992i) q^{14} +(4.08551 - 5.98294i) q^{15} -1.00000 q^{16} +(-3.35446 - 2.39741i) q^{17} +7.49739i q^{18} +(-0.157527 + 0.157527i) q^{19} +(0.458323 - 2.18859i) q^{20} +5.25759i q^{21} +(4.11919 + 1.70622i) q^{22} +(2.07076 + 4.99927i) q^{23} +(1.23988 + 2.99334i) q^{24} +(4.57988 + 2.00616i) q^{25} +(1.26525 + 1.26525i) q^{26} +(13.4622 - 5.57623i) q^{27} +(0.620992 + 1.49921i) q^{28} +(-2.00418 + 4.83853i) q^{29} +(-7.11947 + 1.34168i) q^{30} +(-1.60817 - 0.666124i) q^{31} +(0.707107 + 0.707107i) q^{32} -14.4456i q^{33} +(0.676740 + 4.06719i) q^{34} +(-3.56577 + 0.671978i) q^{35} +(5.30145 - 5.30145i) q^{36} +(-3.91254 + 9.44570i) q^{37} +0.222777 q^{38} +(2.21857 - 5.35610i) q^{39} +(-1.87165 + 1.22349i) q^{40} +(0.657761 + 1.58798i) q^{41} +(3.71768 - 3.71768i) q^{42} +(3.65649 - 3.65649i) q^{43} +(-1.70622 - 4.11919i) q^{44} +(9.17295 + 14.0325i) q^{45} +(2.07076 - 4.99927i) q^{46} -5.48034 q^{47} +(1.23988 - 2.99334i) q^{48} +(-3.08775 + 3.08775i) q^{49} +(-1.81989 - 4.65704i) q^{50} +(11.3354 - 7.06855i) q^{51} -1.78934i q^{52} +(-1.42918 - 1.42918i) q^{53} +(-13.4622 - 5.57623i) q^{54} +(9.79722 - 1.84631i) q^{55} +(0.620992 - 1.49921i) q^{56} +(-0.276217 - 0.666847i) q^{57} +(4.83853 - 2.00418i) q^{58} +(1.74254 + 1.74254i) q^{59} +(5.98294 + 4.08551i) q^{60} +(-3.62231 - 8.74502i) q^{61} +(0.666124 + 1.60817i) q^{62} +(-11.2401 - 4.65582i) q^{63} -1.00000i q^{64} +(3.91614 + 0.820096i) q^{65} +(-10.2146 + 10.2146i) q^{66} +14.4344i q^{67} +(2.39741 - 3.35446i) q^{68} -17.5320 q^{69} +(2.99654 + 2.04622i) q^{70} +(7.59937 + 3.14776i) q^{71} -7.49739 q^{72} +(1.40695 + 0.582777i) q^{73} +(9.44570 - 3.91254i) q^{74} +(-11.6836 + 11.2217i) q^{75} +(-0.157527 - 0.157527i) q^{76} +(-5.11596 + 5.11596i) q^{77} +(-5.35610 + 2.21857i) q^{78} +(-2.76144 + 1.14383i) q^{79} +(2.18859 + 0.458323i) q^{80} +24.7186i q^{81} +(0.657761 - 1.58798i) q^{82} +(-10.0574 - 10.0574i) q^{83} -5.25759 q^{84} +(6.24277 + 6.78438i) q^{85} -5.17105 q^{86} +(-11.9984 - 11.9984i) q^{87} +(-1.70622 + 4.11919i) q^{88} -9.77020i q^{89} +(3.43622 - 16.4087i) q^{90} +(-2.68259 + 1.11117i) q^{91} +(-4.99927 + 2.07076i) q^{92} +(3.98787 - 3.98787i) q^{93} +(3.87519 + 3.87519i) q^{94} +(0.416961 - 0.272565i) q^{95} +(-2.99334 + 1.23988i) q^{96} +(4.59847 + 1.90475i) q^{97} +4.36674 q^{98} +(30.8831 + 12.7922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.23988	+	2.99334i	−0.715846	+	1.72821i	−0.0309978	+	0.999519i	$0.509868\pi$
$3$	−1.23988	+	2.99334i	−0.715846	+	1.72821i	−0.684848	+	0.728686i	$0.740132\pi$
$4$			1.00000i			0.500000i
$5$	−2.18859	−	0.458323i	−0.978769	−	0.204968i
$5$	−2.18859	−	0.458323i	−0.978769	−	0.204968i
$6$	2.99334	−	1.23988i	1.22203	−	0.506180i
$7$	1.49921	−	0.620992i	0.566647	−	0.234713i	−0.0809209	−	0.996721i	$-0.525786\pi$
$7$	1.49921	−	0.620992i	0.566647	−	0.234713i	0.647568	+	0.762008i	$0.275786\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−5.30145	−	5.30145i	−1.76715	−	1.76715i
$10$	1.22349	+	1.87165i	0.386900	+	0.591868i
$11$	−4.11919	+	1.70622i	−1.24198	+	0.514445i	−0.904333	−	0.426827i	$-0.859631\pi$
$11$	−4.11919	+	1.70622i	−1.24198	+	0.514445i	−0.337648	+	0.941272i	$0.609631\pi$
$12$	−2.99334	−	1.23988i	−0.864103	−	0.357923i
$13$	−1.78934			−0.496274			−0.248137	−	0.968725i	$-0.579818\pi$
$13$	−1.78934			−0.496274			−0.248137	+	0.968725i	$0.579818\pi$
$14$	−1.49921	−	0.620992i	−0.400680	−	0.165967i
$15$	4.08551	−	5.98294i	1.05487	−	1.54479i
$16$	−1.00000			−0.250000
$17$	−3.35446	−	2.39741i	−0.813577	−	0.581457i
$17$	−3.35446	−	2.39741i	−0.813577	−	0.581457i
$18$			7.49739i			1.76715i
$19$	−0.157527	+	0.157527i	−0.0361392	+	0.0361392i	−0.724945	−	0.688806i	$-0.758135\pi$
$19$	−0.157527	+	0.157527i	−0.0361392	+	0.0361392i	0.688806	+	0.724945i	$0.258135\pi$
$20$	0.458323	−	2.18859i	0.102484	−	0.489384i
$21$			5.25759i			1.14730i
$22$	4.11919	+	1.70622i	0.878213	+	0.363768i
$23$	2.07076	+	4.99927i	0.431784	+	1.04242i	0.978712	+	0.205239i	$0.0657973\pi$
$23$	2.07076	+	4.99927i	0.431784	+	1.04242i	−0.546928	+	0.837180i	$0.684203\pi$
$24$	1.23988	+	2.99334i	0.253090	+	0.611013i
$25$	4.57988	+	2.00616i	0.915976	+	0.401233i
$26$	1.26525	+	1.26525i	0.248137	+	0.248137i
$27$	13.4622	−	5.57623i	2.59080	−	1.07315i
$28$	0.620992	+	1.49921i	0.117356	+	0.283324i
$29$	−2.00418	+	4.83853i	−0.372168	+	0.898492i	0.621215	+	0.783640i	$0.286639\pi$
$29$	−2.00418	+	4.83853i	−0.372168	+	0.898492i	−0.993383	+	0.114852i	$0.963361\pi$
$30$	−7.11947	+	1.34168i	−1.29983	+	0.244956i
$31$	−1.60817	−	0.666124i	−0.288835	−	0.119639i	0.233561	−	0.972342i	$-0.424962\pi$
$31$	−1.60817	−	0.666124i	−0.288835	−	0.119639i	−0.522397	+	0.852703i	$0.674962\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		−	14.4456i		−	2.51466i
$34$	0.676740	+	4.06719i	0.116060	+	0.697517i
$35$	−3.56577	+	0.671978i	−0.602725	+	0.113585i
$36$	5.30145	−	5.30145i	0.883575	−	0.883575i
$37$	−3.91254	+	9.44570i	−0.643217	+	1.55286i	0.179098	+	0.983831i	$0.442682\pi$
$37$	−3.91254	+	9.44570i	−0.643217	+	1.55286i	−0.822315	+	0.569032i	$0.807318\pi$
$38$	0.222777			0.0361392
$39$	2.21857	−	5.35610i	0.355256	−	0.857663i
$40$	−1.87165	+	1.22349i	−0.295934	+	0.193450i
$41$	0.657761	+	1.58798i	0.102725	+	0.248000i	0.966883	−	0.255221i	$-0.0821482\pi$
$41$	0.657761	+	1.58798i	0.102725	+	0.248000i	−0.864158	+	0.503221i	$0.832148\pi$
$42$	3.71768	−	3.71768i	0.573651	−	0.573651i
$43$	3.65649	−	3.65649i	0.557609	−	0.557609i	−0.371017	−	0.928626i	$-0.620991\pi$
$43$	3.65649	−	3.65649i	0.557609	−	0.557609i	0.928626	+	0.371017i	$0.120991\pi$
$44$	−1.70622	−	4.11919i	−0.257223	−	0.620991i
$45$	9.17295	+	14.0325i	1.36742	+	2.09184i
$46$	2.07076	−	4.99927i	0.305318	−	0.737102i
$47$	−5.48034			−0.799390			−0.399695	−	0.916648i	$-0.630884\pi$
$47$	−5.48034			−0.799390			−0.399695	+	0.916648i	$0.630884\pi$
$48$	1.23988	−	2.99334i	0.178962	−	0.432051i
$49$	−3.08775	+	3.08775i	−0.441108	+	0.441108i
$50$	−1.81989	−	4.65704i	−0.257372	−	0.658605i
$51$	11.3354	−	7.06855i	1.58727	−	0.989794i
$52$		−	1.78934i		−	0.248137i
$53$	−1.42918	−	1.42918i	−0.196313	−	0.196313i	0.602105	−	0.798417i	$-0.294329\pi$
$53$	−1.42918	−	1.42918i	−0.196313	−	0.196313i	−0.798417	+	0.602105i	$0.794329\pi$
$54$	−13.4622	−	5.57623i	−1.83197	−	0.758828i
$55$	9.79722	−	1.84631i	1.32106	−	0.248956i
$56$	0.620992	−	1.49921i	0.0829836	−	0.200340i
$57$	−0.276217	−	0.666847i	−0.0365859	−	0.0883261i
$58$	4.83853	−	2.00418i	0.635330	−	0.263162i
$59$	1.74254	+	1.74254i	0.226859	+	0.226859i	0.811379	−	0.584520i	$-0.198717\pi$
$59$	1.74254	+	1.74254i	0.226859	+	0.226859i	−0.584520	+	0.811379i	$0.698717\pi$
$60$	5.98294	+	4.08551i	0.772394	+	0.527437i
$61$	−3.62231	−	8.74502i	−0.463789	−	1.11969i	−0.966830	−	0.255423i	$-0.917785\pi$
$61$	−3.62231	−	8.74502i	−0.463789	−	1.11969i	0.503041	−	0.864263i	$-0.332215\pi$
$62$	0.666124	+	1.60817i	0.0845979	+	0.204237i
$63$	−11.2401	−	4.65582i	−1.41612	−	0.586578i
$64$		−	1.00000i		−	0.125000i
$65$	3.91614	+	0.820096i	0.485737	+	0.101720i
$66$	−10.2146	+	10.2146i	−1.25733	+	1.25733i
$67$			14.4344i			1.76345i	0.471767	+	0.881723i	$0.343616\pi$
$67$			14.4344i			1.76345i	−0.471767	+	0.881723i	$0.656384\pi$
$68$	2.39741	−	3.35446i	0.290729	−	0.406789i
$69$	−17.5320			−2.11061
$70$	2.99654	+	2.04622i	0.358155	+	0.244570i
$71$	7.59937	+	3.14776i	0.901879	+	0.373571i	0.784942	−	0.619569i	$-0.212692\pi$
$71$	7.59937	+	3.14776i	0.901879	+	0.373571i	0.116937	+	0.993139i	$0.462692\pi$
$72$	−7.49739			−0.883575
$73$	1.40695	+	0.582777i	0.164671	+	0.0682089i	0.463496	−	0.886099i	$-0.346595\pi$
$73$	1.40695	+	0.582777i	0.164671	+	0.0682089i	−0.298825	+	0.954308i	$0.596595\pi$
$74$	9.44570	−	3.91254i	1.09804	−	0.454823i
$75$	−11.6836	+	11.2217i	−1.34911	+	1.29577i
$76$	−0.157527	−	0.157527i	−0.0180696	−	0.0180696i
$77$	−5.11596	+	5.11596i	−0.583018	+	0.583018i
$78$	−5.35610	+	2.21857i	−0.606459	+	0.251204i
$79$	−2.76144	+	1.14383i	−0.310687	+	0.128691i	−0.532578	−	0.846381i	$-0.678777\pi$
$79$	−2.76144	+	1.14383i	−0.310687	+	0.128691i	0.221892	+	0.975071i	$0.428777\pi$
$80$	2.18859	+	0.458323i	0.244692	+	0.0512421i
$81$			24.7186i			2.74652i
$82$	0.657761	−	1.58798i	0.0726376	−	0.175363i
$83$	−10.0574	−	10.0574i	−1.10394	−	1.10394i	−0.993930	−	0.110014i	$-0.964910\pi$
$83$	−10.0574	−	10.0574i	−1.10394	−	1.10394i	−0.110014	−	0.993930i	$-0.535090\pi$
$84$	−5.25759			−0.573651
$85$	6.24277	+	6.78438i	0.677123	+	0.735869i
$86$	−5.17105			−0.557609
$87$	−11.9984	−	11.9984i	−1.28636	−	1.28636i
$88$	−1.70622	+	4.11919i	−0.181884	+	0.439107i
$89$		−	9.77020i		−	1.03564i	−0.855490	−	0.517820i	$-0.826744\pi$
$89$		−	9.77020i		−	1.03564i	0.855490	−	0.517820i	$-0.173256\pi$
$90$	3.43622	−	16.4087i	0.362210	−	1.72963i
$91$	−2.68259	+	1.11117i	−0.281212	+	0.116482i
$92$	−4.99927	+	2.07076i	−0.521210	+	0.215892i
$93$	3.98787	−	3.98787i	0.413523	−	0.413523i
$94$	3.87519	+	3.87519i	0.399695	+	0.399695i
$95$	0.416961	−	0.272565i	0.0427793	−	0.0279645i
$96$	−2.99334	+	1.23988i	−0.305506	+	0.126545i
$97$	4.59847	+	1.90475i	0.466903	+	0.193398i	0.603716	−	0.797199i	$-0.293686\pi$
$97$	4.59847	+	1.90475i	0.466903	+	0.193398i	−0.136813	+	0.990597i	$0.543686\pi$
$98$	4.36674			0.441108
$99$	30.8831	+	12.7922i	3.10387	+	1.28567i
$100$	−2.00616	+	4.57988i	−0.200616	+	0.457988i
$101$	11.1039			1.10488			0.552438	−	0.833554i	$-0.313698\pi$
$101$	11.1039			1.10488			0.552438	+	0.833554i	$0.313698\pi$
$102$	−13.0136	−	3.01712i	−1.28853	−	0.298739i
$103$			3.86906i			0.381230i	0.981665	+	0.190615i	$0.0610481\pi$
$103$			3.86906i			0.381230i	−0.981665	+	0.190615i	$0.938952\pi$
$104$	−1.26525	+	1.26525i	−0.124068	+	0.124068i
$105$	2.40968	−	11.5067i	0.235160	−	1.12294i
$106$			2.02116i			0.196313i
$107$	11.1802	+	4.63098i	1.08083	+	0.447694i	0.850800	−	0.525490i	$-0.176118\pi$
$107$	11.1802	+	4.63098i	1.08083	+	0.447694i	0.230029	+	0.973184i	$0.426118\pi$
$108$	5.57623	+	13.4622i	0.536573	+	1.29540i
$109$	−4.89487	−	11.8173i	−0.468843	−	1.13189i	−0.964669	−	0.263466i	$-0.915134\pi$
$109$	−4.89487	−	11.8173i	−0.468843	−	1.13189i	0.495825	−	0.868422i	$-0.334866\pi$
$110$	−8.23322	−	5.62214i	−0.785007	−	0.536050i
$111$	−23.4231	−	23.4231i	−2.22322	−	2.22322i
$112$	−1.49921	+	0.620992i	−0.141662	+	0.0586782i
$113$	1.96861	+	4.75264i	0.185191	+	0.447091i	0.989022	−	0.147767i	$-0.0472084\pi$
$113$	1.96861	+	4.75264i	0.185191	+	0.447091i	−0.803831	+	0.594858i	$0.797208\pi$
$114$	−0.276217	+	0.666847i	−0.0258701	+	0.0624560i
$115$	−2.24078	−	11.8904i	−0.208954	−	1.10879i
$116$	−4.83853	−	2.00418i	−0.449246	−	0.186084i
$117$	9.48610	+	9.48610i	0.876991	+	0.876991i
$118$		−	2.46432i		−	0.226859i
$119$	−6.51781	−	1.51112i	−0.597487	−	0.138524i
$120$	−1.34168	−	7.11947i	−0.122478	−	0.649916i
$121$	6.27832	−	6.27832i	0.570756	−	0.570756i
$122$	−3.62231	+	8.74502i	−0.327948	+	0.791737i
$123$	−5.56890			−0.502130
$124$	0.666124	−	1.60817i	0.0598197	−	0.144418i
$125$	−9.10402	−	6.48974i	−0.814289	−	0.580460i
$126$	4.65582	+	11.2401i	0.414773	+	1.00135i
$127$	−0.920220	+	0.920220i	−0.0816564	+	0.0816564i	−0.746755	−	0.665099i	$-0.768389\pi$
$127$	−0.920220	+	0.920220i	−0.0816564	+	0.0816564i	0.665099	+	0.746755i	$0.268389\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	6.41149	+	15.4787i	0.564501	+	1.36283i
$130$	−2.18923	−	3.34902i	−0.192008	−	0.293729i
$131$	1.58915	−	3.83655i	0.138845	−	0.335201i	−0.839128	−	0.543934i	$-0.816934\pi$
$131$	1.58915	−	3.83655i	0.138845	−	0.335201i	0.977973	+	0.208733i	$0.0669341\pi$
$132$	14.4456			1.25733
$133$	−0.138343	+	0.333989i	−0.0119958	+	0.0289605i
$134$	10.2067	−	10.2067i	0.881723	−	0.881723i
$135$	−32.0190	+	6.03406i	−2.75576	+	0.519329i
$136$	−4.06719	+	0.676740i	−0.348759	+	0.0580300i
$137$		−	21.1172i		−	1.80417i	−0.431562	−	0.902083i	$-0.642037\pi$
$137$		−	21.1172i		−	1.80417i	0.431562	−	0.902083i	$-0.357963\pi$
$138$	12.3970	+	12.3970i	1.05530	+	1.05530i
$139$	9.90569	+	4.10307i	0.840190	+	0.348018i	0.760928	−	0.648836i	$-0.224744\pi$
$139$	9.90569	+	4.10307i	0.840190	+	0.348018i	0.0792614	+	0.996854i	$0.474744\pi$
$140$	−0.671978	−	3.56577i	−0.0567925	−	0.301363i
$141$	6.79498	−	16.4045i	0.572240	−	1.38151i
$142$	−3.14776	−	7.59937i	−0.264154	−	0.637725i
$143$	7.37063	−	3.05301i	0.616363	−	0.255306i
$144$	5.30145	+	5.30145i	0.441788	+	0.441788i
$145$	6.60395	−	9.67101i	0.548428	−	0.803133i
$146$	−0.582777	−	1.40695i	−0.0482310	−	0.116440i
$147$	−5.41425	−	13.0711i	−0.446560	−	1.07809i
$148$	−9.44570	−	3.91254i	−0.776432	−	0.321609i
$149$			8.46929i			0.693831i	0.937896	+	0.346915i	$0.112771\pi$
$149$			8.46929i			0.693831i	−0.937896	+	0.346915i	$0.887229\pi$
$150$	16.1965	+	0.326622i	1.32244	+	0.0266686i
$151$	1.27947	−	1.27947i	0.104121	−	0.104121i	−0.653127	−	0.757248i	$-0.726543\pi$
$151$	1.27947	−	1.27947i	0.104121	−	0.104121i	0.757248	+	0.653127i	$0.226543\pi$
$152$			0.222777i			0.0180696i
$153$	5.07378	+	30.4933i	0.410191	+	2.46524i
$154$	7.23507			0.583018
$155$	3.21432	+	2.19493i	0.258181	+	0.176301i
$156$	5.35610	+	2.21857i	0.428831	+	0.177628i
$157$	−2.07703			−0.165765			−0.0828824	−	0.996559i	$-0.526413\pi$
$157$	−2.07703			−0.165765			−0.0828824	+	0.996559i	$0.526413\pi$
$158$	2.76144	+	1.14383i	0.219689	+	0.0909980i
$159$	6.05003	−	2.50600i	0.479798	−	0.198739i
$160$	−1.22349	−	1.87165i	−0.0967250	−	0.147967i
$161$	6.20901	+	6.20901i	0.489339	+	0.489339i
$162$	17.4787	−	17.4787i	1.37326	−	1.37326i
$163$	−1.91410	+	0.792847i	−0.149924	+	0.0621006i	−0.456384	−	0.889783i	$-0.650856\pi$
$163$	−1.91410	+	0.792847i	−0.149924	+	0.0621006i	0.306460	+	0.951884i	$0.400856\pi$
$164$	−1.58798	+	0.657761i	−0.124000	+	0.0513625i
$165$	−6.62077	+	31.6156i	−0.515426	+	2.46127i
$166$			14.2233i			1.10394i
$167$	−6.65999	+	16.0786i	−0.515366	+	1.24420i	0.425357	+	0.905026i	$0.360149\pi$
$167$	−6.65999	+	16.0786i	−0.515366	+	1.24420i	−0.940723	+	0.339177i	$0.889851\pi$
$168$	3.71768	+	3.71768i	0.286825	+	0.286825i
$169$	−9.79826			−0.753712
$170$	0.382976	−	9.21159i	0.0293730	−	0.706496i
$171$	1.67025			0.127727
$172$	3.65649	+	3.65649i	0.278805	+	0.278805i
$173$	1.97254	−	4.76214i	0.149970	−	0.362059i	−0.830985	−	0.556295i	$-0.812223\pi$
$173$	1.97254	−	4.76214i	0.149970	−	0.362059i	0.980955	+	0.194236i	$0.0622226\pi$
$174$			16.9683i			1.28636i
$175$	8.11200	+	0.163588i	0.613210	+	0.0123661i
$176$	4.11919	−	1.70622i	0.310495	−	0.128611i
$177$	−7.37654	+	3.05546i	−0.554455	+	0.229663i
$178$	−6.90857	+	6.90857i	−0.517820	+	0.517820i
$179$	−2.09869	−	2.09869i	−0.156864	−	0.156864i	0.624312	−	0.781175i	$-0.285380\pi$
$179$	−2.09869	−	2.09869i	−0.156864	−	0.156864i	−0.781175	+	0.624312i	$0.785380\pi$
$180$	−14.0325	+	9.17295i	−1.04592	+	0.683711i
$181$	−10.0565	+	4.16552i	−0.747491	+	0.309621i	−0.723717	−	0.690096i	$-0.757568\pi$
$181$	−10.0565	+	4.16552i	−0.747491	+	0.309621i	−0.0237737	+	0.999717i	$0.507568\pi$
$182$	2.68259	+	1.11117i	0.198847	+	0.0823651i
$183$	30.6680			2.26705
$184$	4.99927	+	2.07076i	0.368551	+	0.152659i
$185$	12.8921	−	18.8796i	0.947848	−	1.38806i
$186$	−5.63970			−0.413523
$187$	17.9082	+	4.15191i	1.30958	+	0.303618i
$188$		−	5.48034i		−	0.399695i
$189$	16.7198	−	16.7198i	1.21619	−	1.21619i
$190$	−0.487568	−	0.102104i	−0.0353719	−	0.00740739i
$191$			24.0385i			1.73937i	0.493611	+	0.869683i	$0.335677\pi$
$191$			24.0385i			1.73937i	−0.493611	+	0.869683i	$0.664323\pi$
$192$	2.99334	+	1.23988i	0.216026	+	0.0894808i
$193$	−6.71939	−	16.2220i	−0.483672	−	1.16769i	−0.957852	−	0.287261i	$-0.907255\pi$
$193$	−6.71939	−	16.2220i	−0.483672	−	1.16769i	0.474180	−	0.880428i	$-0.342745\pi$
$194$	−1.90475	−	4.59847i	−0.136753	−	0.330151i
$195$	−7.31037	+	10.7055i	−0.523507	+	0.766637i
$196$	−3.08775	−	3.08775i	−0.220554	−	0.220554i
$197$	−14.0551	+	5.82183i	−1.00139	+	0.414788i	−0.822306	−	0.569046i	$-0.807313\pi$
$197$	−14.0551	+	5.82183i	−1.00139	+	0.414788i	−0.179082	+	0.983834i	$0.557313\pi$
$198$	−12.7922	−	30.8831i	−0.909103	−	2.19477i
$199$	−3.07405	+	7.42142i	−0.217914	+	0.526091i	−0.994598	−	0.103799i	$-0.966900\pi$
$199$	−3.07405	+	7.42142i	−0.217914	+	0.526091i	0.776684	+	0.629890i	$0.216900\pi$
$200$	4.65704	−	1.81989i	0.329302	−	0.128686i
$201$	−43.2071	−	17.8970i	−3.04760	−	1.26236i
$202$	−7.85162	−	7.85162i	−0.552438	−	0.552438i
$203$			8.49854i			0.596481i
$204$	7.06855	+	11.3354i	0.494897	+	0.793637i
$205$	−0.711766	−	3.77690i	−0.0497119	−	0.263790i
$206$	2.73584	−	2.73584i	0.190615	−	0.190615i
$207$	15.5253	−	37.4814i	1.07908	−	2.60514i
$208$	1.78934			0.124068
$209$	0.380107	−	0.917660i	0.0262926	−	0.0634759i
$210$	−9.84039	+	6.43259i	−0.679051	+	0.443891i
$211$	3.61423	+	8.72553i	0.248814	+	0.600690i	0.998104	−	0.0615519i	$-0.0196050\pi$
$211$	3.61423	+	8.72553i	0.248814	+	0.600690i	−0.749290	+	0.662242i	$0.769605\pi$
$212$	1.42918	−	1.42918i	0.0981564	−	0.0981564i
$213$	−18.8446	+	18.8446i	−1.29121	+	1.29121i
$214$	−4.63098	−	11.1802i	−0.316567	−	0.764262i
$215$	−9.67841	+	6.32671i	−0.660062	+	0.431478i
$216$	5.57623	−	13.4622i	0.379414	−	0.915987i
$217$	−2.82463			−0.191749
$218$	−4.89487	+	11.8173i	−0.331522	+	0.800366i
$219$	−3.48890	+	3.48890i	−0.235758	+	0.235758i
$220$	1.84631	+	9.79722i	0.124478	+	0.660529i
$221$	6.00228	+	4.28978i	0.403757	+	0.288562i
$222$			33.1253i			2.22322i
$223$	1.52869	+	1.52869i	0.102369	+	0.102369i	0.756436	−	0.654067i	$-0.226939\pi$
$223$	1.52869	+	1.52869i	0.102369	+	0.102369i	−0.654067	+	0.756436i	$0.726939\pi$
$224$	1.49921	+	0.620992i	0.100170	+	0.0414918i
$225$	−13.6444	−	34.9156i	−0.909629	−	2.32771i
$226$	1.96861	−	4.75264i	0.130950	−	0.316141i
$227$	0.146890	+	0.354624i	0.00974943	+	0.0235372i	0.928679	−	0.370884i	$-0.120945\pi$
$227$	0.146890	+	0.354624i	0.00974943	+	0.0235372i	−0.918930	+	0.394421i	$0.870945\pi$
$228$	0.666847	−	0.276217i	0.0441631	−	0.0182929i
$229$	−6.36165	−	6.36165i	−0.420390	−	0.420390i	0.464948	−	0.885338i	$-0.346073\pi$
$229$	−6.36165	−	6.36165i	−0.420390	−	0.420390i	−0.885338	+	0.464948i	$0.846073\pi$
$230$	−6.82334	+	9.99228i	−0.449918	+	0.658872i
$231$	−8.97063	−	21.6570i	−0.590224	−	1.42493i
$232$	2.00418	+	4.83853i	0.131581	+	0.317665i
$233$	11.4366	+	4.73720i	0.749238	+	0.310344i	0.724430	−	0.689348i	$-0.242103\pi$
$233$	11.4366	+	4.73720i	0.749238	+	0.310344i	0.0248072	+	0.999692i	$0.492103\pi$
$234$		−	13.4154i		−	0.876991i
$235$	11.9942	+	2.51177i	0.782418	+	0.163850i
$236$	−1.74254	+	1.74254i	−0.113429	+	0.113429i
$237$		−	9.68415i		−	0.629053i
$238$	3.54027	+	5.67731i	0.229481	+	0.368005i
$239$	−8.64334			−0.559091			−0.279545	−	0.960132i	$-0.590184\pi$
$239$	−8.64334			−0.559091			−0.279545	+	0.960132i	$0.590184\pi$
$240$	−4.08551	+	5.98294i	−0.263719	+	0.386197i
$241$	−20.1931	−	8.36424i	−1.30075	−	0.538788i	−0.378578	−	0.925569i	$-0.623587\pi$
$241$	−20.1931	−	8.36424i	−1.30075	−	0.538788i	−0.922171	+	0.386781i	$0.873587\pi$
$242$	−8.87889			−0.570756
$243$	−33.6047	−	13.9195i	−2.15574	−	0.892937i
$244$	8.74502	−	3.62231i	0.559843	−	0.231894i
$245$	8.17303	−	5.34265i	0.522156	−	0.341329i
$246$	3.93780	+	3.93780i	0.251065	+	0.251065i
$247$	0.281870	−	0.281870i	0.0179349	−	0.0179349i
$248$	−1.60817	+	0.666124i	−0.102119	+	0.0422989i
$249$	42.5752	−	17.6352i	2.69810	−	1.11759i
$250$	1.84858	+	11.0265i	0.116914	+	0.697374i
$251$			21.7468i			1.37264i	0.727298	+	0.686322i	$0.240776\pi$
$251$			21.7468i			1.37264i	−0.727298	+	0.686322i	$0.759224\pi$
$252$	4.65582	−	11.2401i	0.293289	−	0.708062i
$253$	−17.0597	−	17.0597i	−1.07254	−	1.07254i
$254$	1.30139			0.0816564
$255$	−28.0482	+	10.2749i	−1.75645	+	0.643439i
$256$	1.00000			0.0625000
$257$	13.9606	+	13.9606i	0.870840	+	0.870840i	0.992564	−	0.121724i	$-0.0388423\pi$
$257$	13.9606	+	13.9606i	0.870840	+	0.870840i	−0.121724	+	0.992564i	$0.538842\pi$
$258$	6.41149	−	15.4787i	0.399162	−	0.963663i
$259$			16.5907i			1.03090i
$260$	−0.820096	+	3.91614i	−0.0508602	+	0.242869i
$261$	36.2763	−	15.0261i	2.24545	−	0.930095i
$262$	−3.83655	+	1.58915i	−0.237023	+	0.0981780i
$263$	13.2397	−	13.2397i	0.816392	−	0.816392i	−0.169191	−	0.985583i	$-0.554115\pi$
$263$	13.2397	−	13.2397i	0.816392	−	0.816392i	0.985583	+	0.169191i	$0.0541154\pi$
$264$	−10.2146	−	10.2146i	−0.628666	−	0.628666i
$265$	2.47286	+	3.78292i	0.151907	+	0.232383i
$266$	0.333989	−	0.138343i	0.0204782	−	0.00848234i
$267$	29.2455	+	12.1139i	1.78980	+	0.741358i
$268$	−14.4344			−0.881723
$269$	9.51404	+	3.94085i	0.580081	+	0.240278i	0.653377	−	0.757033i	$-0.273352\pi$
$269$	9.51404	+	3.94085i	0.580081	+	0.240278i	−0.0732956	+	0.997310i	$0.523352\pi$
$270$	26.9076	+	18.3741i	1.63754	+	1.11821i
$271$	18.9442			1.15078			0.575390	−	0.817879i	$-0.304850\pi$
$271$	18.9442			1.15078			0.575390	+	0.817879i	$0.304850\pi$
$272$	3.35446	+	2.39741i	0.203394	+	0.145364i
$273$		−	9.40763i		−	0.569376i
$274$	−14.9321	+	14.9321i	−0.902083	+	0.902083i
$275$	−22.2883	−	0.449471i	−1.34404	−	0.0271041i
$276$		−	17.5320i		−	1.05530i
$277$	−21.1959	−	8.77965i	−1.27354	−	0.527518i	−0.359502	−	0.933144i	$-0.617053\pi$
$277$	−21.1959	−	8.77965i	−1.27354	−	0.527518i	−0.914039	+	0.405626i	$0.867053\pi$
$278$	−4.10307	−	9.90569i	−0.246086	−	0.594104i
$279$	4.99419	+	12.0570i	0.298994	+	0.721836i
$280$	−2.04622	+	2.99654i	−0.122285	+	0.179078i
$281$	16.9895	+	16.9895i	1.01351	+	1.01351i	0.999907	+	0.0136041i	$0.00433046\pi$
$281$	16.9895	+	16.9895i	1.01351	+	1.01351i	0.0136041	+	0.999907i	$0.495670\pi$
$282$	−16.4045	+	6.79498i	−0.976875	+	0.404635i
$283$	−6.03994	−	14.5817i	−0.359037	−	0.866792i	−0.995436	−	0.0954321i	$-0.969577\pi$
$283$	−6.03994	−	14.5817i	−0.359037	−	0.866792i	0.636399	−	0.771360i	$-0.280423\pi$
$284$	−3.14776	+	7.59937i	−0.186785	+	0.450940i
$285$	0.298896	+	1.58605i	0.0177051	+	0.0939498i
$286$	−7.37063	−	3.05301i	−0.435834	−	0.180528i
$287$	1.97224	+	1.97224i	0.116418	+	0.116418i
$288$		−	7.49739i		−	0.441788i
$289$	5.50486	+	16.0840i	0.323815	+	0.946120i
$290$	−11.5081	+	2.16874i	−0.675781	+	0.127353i
$291$	−11.4031	+	11.4031i	−0.668462	+	0.668462i
$292$	−0.582777	+	1.40695i	−0.0341044	+	0.0823354i
$293$	7.54899			0.441017			0.220508	−	0.975385i	$-0.429228\pi$
$293$	7.54899			0.441017			0.220508	+	0.975385i	$0.429228\pi$
$294$	−5.41425	+	13.0711i	−0.315765	+	0.762325i
$295$	−3.01506	−	4.61235i	−0.175543	−	0.268541i
$296$	3.91254	+	9.44570i	0.227412	+	0.549020i
$297$	−45.9390	+	45.9390i	−2.66565	+	2.66565i
$298$	5.98869	−	5.98869i	0.346915	−	0.346915i
$299$	−3.70530	−	8.94539i	−0.214283	−	0.517325i
$300$	−11.2217	−	11.6836i	−0.647887	−	0.674555i
$301$	3.21118	−	7.75248i	0.185090	−	0.446846i
$302$	−1.80944			−0.104121
$303$	−13.7675	+	33.2376i	−0.790921	+	1.90945i
$304$	0.157527	−	0.157527i	0.00903480	−	0.00903480i
$305$	3.91971	+	20.7995i	0.224442	+	1.19097i
$306$	17.9743	−	25.1497i	1.02752	−	1.43771i
$307$		−	12.4976i		−	0.713278i	−0.934242	−	0.356639i	$-0.883923\pi$
$307$		−	12.4976i		−	0.713278i	0.934242	−	0.356639i	$-0.116077\pi$
$308$	−5.11596	−	5.11596i	−0.291509	−	0.291509i
$309$	−11.5814	−	4.79717i	−0.658843	−	0.272902i
$310$	−0.720816	−	3.82492i	−0.0409396	−	0.217241i
$311$	−6.67803	+	16.1222i	−0.378677	+	0.914206i	0.613538	+	0.789665i	$0.289746\pi$
$311$	−6.67803	+	16.1222i	−0.378677	+	0.914206i	−0.992214	+	0.124541i	$0.960254\pi$
$312$	−2.21857	−	5.35610i	−0.125602	−	0.303230i
$313$	−7.99415	+	3.31129i	−0.451856	+	0.187165i	−0.596993	−	0.802247i	$-0.703638\pi$
$313$	−7.99415	+	3.31129i	−0.451856	+	0.187165i	0.145137	+	0.989412i	$0.453638\pi$
$314$	1.46868	+	1.46868i	0.0828824	+	0.0828824i
$315$	22.4662	+	15.3413i	1.26583	+	0.864385i
$316$	−1.14383	−	2.76144i	−0.0643453	−	0.155343i
$317$	−1.60449	−	3.87358i	−0.0901171	−	0.217562i	0.872394	−	0.488802i	$-0.162566\pi$
$317$	−1.60449	−	3.87358i	−0.0901171	−	0.217562i	−0.962512	+	0.271241i	$0.912566\pi$
$318$	−6.05003	−	2.50600i	−0.339269	−	0.140530i
$319$		−	23.3504i		−	1.30737i
$320$	−0.458323	+	2.18859i	−0.0256210	+	0.122346i
$321$	−27.7242	+	27.7242i	−1.54741	+	1.54741i
$322$		−	8.78087i		−	0.489339i
$323$	0.906076	−	0.150762i	0.0504154	−	0.00838864i
$324$	−24.7186			−1.37326
$325$	−8.19497	−	3.58971i	−0.454575	−	0.199121i
$326$	1.91410	+	0.792847i	0.106012	+	0.0439118i
$327$	41.4421			2.29175
$328$	1.58798	+	0.657761i	0.0876813	+	0.0363188i
$329$	−8.21617	+	3.40325i	−0.452972	+	0.187627i
$330$	27.0372	−	17.6740i	1.48835	−	0.972923i
$331$	−4.95608	−	4.95608i	−0.272411	−	0.272411i	0.557659	−	0.830070i	$-0.311700\pi$
$331$	−4.95608	−	4.95608i	−0.272411	−	0.272411i	−0.830070	+	0.557659i	$0.811700\pi$
$332$	10.0574	−	10.0574i	0.551972	−	0.551972i
$333$	70.8181	−	29.3338i	3.88081	−	1.60748i
$334$	16.0786	−	6.65999i	0.879784	−	0.364419i
$335$	6.61563	−	31.5911i	0.361450	−	1.72601i
$336$		−	5.25759i		−	0.286825i
$337$	0.581083	−	1.40286i	0.0316536	−	0.0764186i	−0.907262	−	0.420565i	$-0.861832\pi$
$337$	0.581083	−	1.40286i	0.0316536	−	0.0764186i	0.938916	+	0.344147i	$0.111832\pi$
$338$	6.92842	+	6.92842i	0.376856	+	0.376856i
$339$	−16.6671			−0.905233
$340$	−6.78438	+	6.24277i	−0.367935	+	0.338562i
$341$	7.76089			0.420276
$342$	−1.18104	−	1.18104i	−0.0638635	−	0.0638635i
$343$	−7.05866	+	17.0411i	−0.381132	+	0.920134i
$344$		−	5.17105i		−	0.278805i
$345$	38.3704	+	8.03532i	2.06579	+	0.432607i
$346$	−4.76214	+	1.97254i	−0.256014	+	0.106045i
$347$	6.53872	−	2.70843i	0.351017	−	0.145396i	−0.200206	−	0.979754i	$-0.564161\pi$
$347$	6.53872	−	2.70843i	0.351017	−	0.145396i	0.551223	+	0.834358i	$0.314161\pi$
$348$	11.9984	−	11.9984i	0.643182	−	0.643182i
$349$	6.15710	+	6.15710i	0.329582	+	0.329582i	0.852427	−	0.522845i	$-0.175130\pi$
$349$	6.15710	+	6.15710i	0.329582	+	0.329582i	−0.522845	+	0.852427i	$0.675130\pi$
$350$	−5.62038	−	5.85173i	−0.300422	−	0.312788i
$351$	−24.0885	+	9.97777i	−1.28575	+	0.532574i
$352$	−4.11919	−	1.70622i	−0.219553	−	0.0909420i
$353$	−2.63910			−0.140465			−0.0702325	−	0.997531i	$-0.522374\pi$
$353$	−2.63910			−0.140465			−0.0702325	+	0.997531i	$0.522374\pi$
$354$	7.37654	+	3.05546i	0.392059	+	0.162396i
$355$	−15.1892	−	10.3721i	−0.806161	−	0.550496i
$356$	9.77020			0.517820
$357$	12.6046	−	17.6364i	0.667106	−	0.933418i
$358$			2.96800i			0.156864i
$359$	−5.56265	+	5.56265i	−0.293585	+	0.293585i	−0.838495	−	0.544909i	$-0.816564\pi$
$359$	−5.56265	+	5.56265i	−0.293585	+	0.293585i	0.544909	+	0.838495i	$0.316564\pi$
$360$	16.4087	+	3.43622i	0.864816	+	0.181105i
$361$			18.9504i			0.997388i
$362$	10.0565	+	4.16552i	0.528556	+	0.218935i
$363$	11.0088	+	26.5775i	0.577811	+	1.39496i
$364$	−1.11117	−	2.68259i	−0.0582410	−	0.140606i
$365$	−2.81214	−	1.92030i	−0.147194	−	0.100513i
$366$	−21.6856	−	21.6856i	−1.13352	−	1.13352i
$367$	−21.5147	+	8.91170i	−1.12306	+	0.465187i	−0.865417	−	0.501053i	$-0.832946\pi$
$367$	−21.5147	+	8.91170i	−1.12306	+	0.465187i	−0.257644	+	0.966240i	$0.582946\pi$
$368$	−2.07076	−	4.99927i	−0.107946	−	0.260605i
$369$	4.93149	−	11.9057i	0.256723	−	0.619784i
$370$	−22.4660	+	4.23377i	−1.16795	+	0.220103i
$371$	−3.03014	−	1.25513i	−0.157317	−	0.0651629i
$372$	3.98787	+	3.98787i	0.206762	+	0.206762i
$373$			22.8229i			1.18173i	0.806772	+	0.590863i	$0.201213\pi$
$373$			22.8229i			1.18173i	−0.806772	+	0.590863i	$0.798787\pi$
$374$	−9.72715	−	15.5988i	−0.502979	−	0.806597i
$375$	30.7139	−	19.2049i	1.58606	−	0.991738i
$376$	−3.87519	+	3.87519i	−0.199848	+	0.199848i
$377$	3.58617	−	8.65778i	0.184697	−	0.445898i
$378$	−23.6454			−1.21619
$379$	7.07822	−	17.0883i	0.363583	−	0.877768i	−0.631187	−	0.775631i	$-0.717432\pi$
$379$	7.07822	−	17.0883i	0.363583	−	0.877768i	0.994770	−	0.102137i	$-0.0325681\pi$
$380$	0.272565	+	0.416961i	0.0139823	+	0.0213897i
$381$	−1.61357	−	3.89550i	−0.0826656	−	0.199572i
$382$	16.9978	−	16.9978i	0.869683	−	0.869683i
$383$	−13.2517	+	13.2517i	−0.677130	+	0.677130i	−0.959350	−	0.282220i	$-0.908929\pi$
$383$	−13.2517	+	13.2517i	−0.677130	+	0.677130i	0.282220	+	0.959350i	$0.408929\pi$
$384$	−1.23988	−	2.99334i	−0.0632724	−	0.152753i
$385$	13.5415	−	8.85200i	0.690140	−	0.451140i
$386$	−6.71939	+	16.2220i	−0.342008	+	0.825680i
$387$	−38.7694			−1.97076
$388$	−1.90475	+	4.59847i	−0.0966989	+	0.233452i
$389$	−1.12576	+	1.12576i	−0.0570785	+	0.0570785i	−0.735070	−	0.677991i	$-0.762851\pi$
$389$	−1.12576	+	1.12576i	−0.0570785	+	0.0570785i	0.677991	+	0.735070i	$0.262851\pi$
$390$	12.7392	−	2.40072i	0.645072	−	0.121565i
$391$	5.03898	−	21.7343i	0.254832	−	1.09915i
$392$			4.36674i			0.220554i
$393$	9.51373	+	9.51373i	0.479904	+	0.479904i
$394$	14.0551	+	5.82183i	0.708088	+	0.293300i
$395$	6.56792	−	1.23774i	0.330468	−	0.0622775i
$396$	−12.7922	+	30.8831i	−0.642833	+	1.55194i
$397$	2.73922	+	6.61306i	0.137478	+	0.331900i	0.977592	−	0.210509i	$-0.0675122\pi$
$397$	2.73922	+	6.61306i	0.137478	+	0.331900i	−0.840114	+	0.542409i	$0.817512\pi$
$398$	7.42142	−	3.07405i	0.372002	−	0.154088i
$399$	−0.828214	−	0.828214i	−0.0414626	−	0.0414626i
$400$	−4.57988	−	2.00616i	−0.228994	−	0.100308i
$401$	1.34092	+	3.23726i	0.0669621	+	0.161661i	0.953818	−	0.300386i	$-0.0971153\pi$
$401$	1.34092	+	3.23726i	0.0669621	+	0.161661i	−0.886856	+	0.462046i	$0.847115\pi$
$402$	17.8970	+	43.2071i	0.892620	+	2.15498i
$403$	2.87756	+	1.19192i	0.143341	+	0.0593739i
$404$			11.1039i			0.552438i
$405$	11.3291	−	54.0991i	0.562949	−	2.68820i
$406$	6.00938	−	6.00938i	0.298240	−	0.298240i
$407$		−	45.5843i		−	2.25953i
$408$	3.01712	−	13.0136i	0.149370	−	0.644267i
$409$	−1.87972			−0.0929461			−0.0464730	−	0.998920i	$-0.514798\pi$
$409$	−1.87972			−0.0929461			−0.0464730	+	0.998920i	$0.514798\pi$
$410$	−2.16738	+	3.17397i	−0.107039	+	0.156751i
$411$	63.2110	+	26.1829i	3.11797	+	1.29151i
$412$	−3.86906			−0.190615
$413$	3.69452	+	1.53032i	0.181796	+	0.0753022i
$414$	−37.4814	+	15.5253i	−1.84211	+	0.763028i
$415$	17.4020	+	26.6211i	0.854233	+	1.30678i
$416$	−1.26525	−	1.26525i	−0.0620342	−	0.0620342i
$417$	−24.5638	+	24.5638i	−1.20289	+	1.20289i
$418$	−0.917660	+	0.380107i	−0.0448842	+	0.0185917i
$419$	−30.1244	+	12.4779i	−1.47167	+	0.609586i	−0.967240	−	0.253865i	$-0.918298\pi$
$419$	−30.1244	+	12.4779i	−1.47167	+	0.609586i	−0.504432	+	0.863451i	$0.668298\pi$
$420$	11.5067	+	2.40968i	0.561471	+	0.117580i
$421$		−	27.3895i		−	1.33488i	−0.744661	−	0.667442i	$-0.767389\pi$
$421$		−	27.3895i		−	1.33488i	0.744661	−	0.667442i	$-0.232611\pi$
$422$	3.61423	−	8.72553i	0.175938	−	0.424752i
$423$	29.0538	+	29.0538i	1.41264	+	1.41264i
$424$	−2.02116			−0.0981564
$425$	−10.5534	−	17.7095i	−0.511917	−	0.859035i
$426$	26.6503			1.29121
$427$	−10.8612	−	10.8612i	−0.525609	−	0.525609i
$428$	−4.63098	+	11.1802i	−0.223847	+	0.540415i
$429$			25.8482i			1.24796i
$430$	11.3173	+	2.37001i	0.545770	+	0.114292i
$431$	−16.7310	+	6.93020i	−0.805903	+	0.333816i	−0.747318	−	0.664466i	$-0.768659\pi$
$431$	−16.7310	+	6.93020i	−0.805903	+	0.333816i	−0.0585849	+	0.998282i	$0.518659\pi$
$432$	−13.4622	+	5.57623i	−0.647701	+	0.268286i
$433$	22.9117	−	22.9117i	1.10107	−	1.10107i	0.106786	−	0.994282i	$-0.465944\pi$
$433$	22.9117	−	22.9117i	1.10107	−	1.10107i	0.994282	−	0.106786i	$-0.0340559\pi$
$434$	1.99732	+	1.99732i	0.0958743	+	0.0958743i
$435$	20.7605	+	31.7588i	0.995389	+	1.52272i
$436$	11.8173	−	4.89487i	0.565944	−	0.234422i
$437$	−1.11372	−	0.461319i	−0.0532766	−	0.0220679i
$438$	4.93405			0.235758
$439$	−20.5501	−	8.51214i	−0.980804	−	0.406262i	−0.166081	−	0.986112i	$-0.553111\pi$
$439$	−20.5501	−	8.51214i	−0.980804	−	0.406262i	−0.814723	+	0.579850i	$0.803111\pi$
$440$	5.62214	−	8.23322i	0.268025	−	0.392503i
$441$	32.7392			1.55901
$442$	−1.21092	−	7.27759i	−0.0575975	−	0.346159i
$443$			9.63914i			0.457969i	0.973430	+	0.228985i	$0.0735406\pi$
$443$			9.63914i			0.457969i	−0.973430	+	0.228985i	$0.926459\pi$
$444$	23.4231	−	23.4231i	1.11161	−	1.11161i
$445$	−4.47791	+	21.3830i	−0.212273	+	1.01365i
$446$		−	2.16190i		−	0.102369i
$447$	−25.3514	−	10.5009i	−1.19908	−	0.496676i
$448$	−0.620992	−	1.49921i	−0.0293391	−	0.0708309i
$449$	−14.9247	−	36.0315i	−0.704341	−	1.70043i	−0.713678	−	0.700474i	$-0.752972\pi$
$449$	−14.9247	−	36.0315i	−0.704341	−	1.70043i	0.00933673	−	0.999956i	$-0.497028\pi$
$450$	−15.0410	+	34.3371i	−0.709039	+	1.61867i
$451$	−5.41888	−	5.41888i	−0.255165	−	0.255165i
$452$	−4.75264	+	1.96861i	−0.223546	+	0.0925956i
$453$	2.24349	+	5.41626i	0.105408	+	0.254478i
$454$	0.146890	−	0.354624i	0.00689389	−	0.0166433i
$455$	6.38038	−	1.20240i	0.299117	−	0.0563693i
$456$	−0.666847	−	0.276217i	−0.0312280	−	0.0129351i
$457$	−2.77769	−	2.77769i	−0.129935	−	0.129935i	0.639149	−	0.769083i	$-0.279287\pi$
$457$	−2.77769	−	2.77769i	−0.129935	−	0.129935i	−0.769083	+	0.639149i	$0.779287\pi$
$458$			8.99673i			0.420390i
$459$	−58.5270	−	13.5692i	−2.73181	−	0.633354i
$460$	11.8904	−	2.24078i	0.554395	−	0.104477i
$461$	26.6343	−	26.6343i	1.24048	−	1.24048i	0.280681	−	0.959801i	$-0.409440\pi$
$461$	26.6343	−	26.6343i	1.24048	−	1.24048i	0.959801	−	0.280681i	$-0.0905603\pi$
$462$	−8.97063	+	21.6570i	−0.417351	+	1.00758i
$463$	−5.27399			−0.245103			−0.122551	−	0.992462i	$-0.539108\pi$
$463$	−5.27399			−0.245103			−0.122551	+	0.992462i	$0.539108\pi$
$464$	2.00418	−	4.83853i	0.0930419	−	0.224623i
$465$	−10.5556	+	6.90010i	−0.489503	+	0.319984i
$466$	−4.73720	−	11.4366i	−0.219447	−	0.529791i
$467$	4.54550	−	4.54550i	0.210340	−	0.210340i	−0.594072	−	0.804412i	$-0.702480\pi$
$467$	4.54550	−	4.54550i	0.210340	−	0.210340i	0.804412	+	0.594072i	$0.202480\pi$
$468$	−9.48610	+	9.48610i	−0.438495	+	0.438495i
$469$	8.96367	+	21.6402i	0.413904	+	0.999252i
$470$	−6.70512	−	10.2573i	−0.309284	−	0.473134i
$471$	2.57527	−	6.21725i	0.118662	−	0.286476i
$472$	2.46432			0.113429
$473$	−8.82297	+	21.3005i	−0.405681	+	0.979399i
$474$	−6.84773	+	6.84773i	−0.314527	+	0.314527i
$475$	−1.03748	+	0.405430i	−0.0476029	+	0.0186024i
$476$	1.51112	−	6.51781i	0.0692620	−	0.298743i
$477$			15.1534i			0.693829i
$478$	6.11176	+	6.11176i	0.279545	+	0.279545i
$479$	−37.2765	−	15.4404i	−1.70321	−	0.705492i	−0.703222	−	0.710970i	$-0.748256\pi$
$479$	−37.2765	−	15.4404i	−1.70321	−	0.705492i	−0.999985	+	0.00547848i	$0.998256\pi$
$480$	7.11947	−	1.34168i	0.324958	−	0.0612391i
$481$	7.00086	−	16.9016i	0.319212	−	0.770646i
$482$	8.36424	+	20.1931i	0.380981	+	0.919769i
$483$	−26.2841	+	10.8872i	−1.19597	+	0.495387i
$484$	6.27832	+	6.27832i	0.285378	+	0.285378i
$485$	−9.19118	−	6.27630i	−0.417350	−	0.284992i
$486$	13.9195	+	33.6047i	0.631402	+	1.52434i
$487$	6.35893	+	15.3518i	0.288151	+	0.695657i	0.999978	−	0.00669763i	$-0.00213194\pi$
$487$	6.35893	+	15.3518i	0.288151	+	0.695657i	−0.711827	+	0.702355i	$0.752132\pi$
$488$	−8.74502	−	3.62231i	−0.395869	−	0.163974i
$489$		−	6.71260i		−	0.303554i
$490$	−9.55703	−	2.00138i	−0.431742	−	0.0904131i
$491$	15.7923	−	15.7923i	0.712696	−	0.712696i	−0.254403	−	0.967098i	$-0.581879\pi$
$491$	15.7923	−	15.7923i	0.712696	−	0.712696i	0.967098	+	0.254403i	$0.0818789\pi$
$492$		−	5.56890i		−	0.251065i
$493$	18.3229	−	11.4258i	0.825222	−	0.514593i
$494$	−0.398624			−0.0179349
$495$	−61.7276	−	42.1514i	−2.77445	−	1.89456i
$496$	1.60817	+	0.666124i	0.0722088	+	0.0299099i
$497$	13.3478			0.598729
$498$	−42.5752	−	17.6352i	−1.90784	−	0.790254i
$499$	18.1465	−	7.51654i	0.812350	−	0.336486i	0.0624588	−	0.998048i	$-0.480106\pi$
$499$	18.1465	−	7.51654i	0.812350	−	0.336486i	0.749891	+	0.661561i	$0.230106\pi$
$500$	6.48974	−	9.10402i	0.290230	−	0.407144i
$501$	−39.8712	−	39.8712i	−1.78132	−	1.78132i
$502$	15.3773	−	15.3773i	0.686322	−	0.686322i
$503$	−11.7306	+	4.85898i	−0.523042	+	0.216651i	−0.628553	−	0.777767i	$-0.716352\pi$
$503$	−11.7306	+	4.85898i	−0.523042	+	0.216651i	0.105510	+	0.994418i	$0.466352\pi$
$504$	−11.2401	+	4.65582i	−0.500676	+	0.207387i
$505$	−24.3018	−	5.08915i	−1.08142	−	0.226464i
$506$			24.1261i			1.07254i
$507$	12.1487	−	29.3295i	0.539542	−	1.30257i
$508$	−0.920220	−	0.920220i	−0.0408282	−	0.0408282i
$509$	2.65410			0.117641			0.0588204	−	0.998269i	$-0.481266\pi$
$509$	2.65410			0.117641			0.0588204	+	0.998269i	$0.481266\pi$
$510$	27.0986	+	12.5677i	1.19994	+	0.556505i
$511$	2.47121			0.109320
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.24226	+	2.99907i	−0.0548469	+	0.132412i
$514$		−	19.7433i		−	0.870840i
$515$	1.77328	−	8.46779i	0.0781399	−	0.373136i
$516$	−15.4787	+	6.41149i	−0.681413	+	0.282250i
$517$	22.5745	−	9.35068i	0.992827	−	0.411243i
$518$	11.7314	−	11.7314i	0.515449	−	0.515449i
$519$	11.8090	+	11.8090i	0.518357	+	0.518357i
$520$	3.34902	−	2.18923i	0.146864	−	0.0960042i
$521$	−16.7528	+	6.93925i	−0.733955	+	0.304014i	−0.718176	−	0.695862i	$-0.755023\pi$
$521$	−16.7528	+	6.93925i	−0.733955	+	0.304014i	−0.0157786	+	0.999876i	$0.505023\pi$
$522$	−36.2763	−	15.0261i	−1.58777	−	0.657676i
$523$	−33.8690			−1.48099			−0.740494	−	0.672063i	$-0.765408\pi$
$523$	−33.8690			−1.48099			−0.740494	+	0.672063i	$0.765408\pi$
$524$	3.83655	+	1.58915i	0.167600	+	0.0694224i
$525$	−10.5476	+	24.0792i	−0.460335	+	1.05090i
$526$	−18.7237			−0.816392
$527$	3.79756	+	6.08992i	0.165425	+	0.265281i
$528$			14.4456i			0.628666i
$529$	−4.44116	+	4.44116i	−0.193094	+	0.193094i
$530$	0.926346	−	4.42350i	0.0402379	−	0.192145i
$531$		−	18.4759i		−	0.801787i
$532$	−0.333989	−	0.138343i	−0.0144803	−	0.00599792i
$533$	−1.17696	−	2.84143i	−0.0509797	−	0.123076i
$534$	−12.1139	−	29.2455i	−0.524219	−	1.26558i
$535$	−22.3464	−	15.2595i	−0.966118	−	0.659725i
$536$	10.2067	+	10.2067i	0.440862	+	0.440862i
$537$	8.88422	−	3.67997i	0.383383	−	0.158802i
$538$	−3.94085	−	9.51404i	−0.169902	−	0.410179i
$539$	7.45064	−	17.9874i	0.320922	−	0.774774i
$540$	−6.03406	−	32.0190i	−0.259664	−	1.37788i
$541$	4.21829	+	1.74727i	0.181359	+	0.0751212i	0.471515	−	0.881858i	$-0.343707\pi$
$541$	4.21829	+	1.74727i	0.181359	+	0.0751212i	−0.290156	+	0.956979i	$0.593707\pi$
$542$	−13.3956	−	13.3956i	−0.575390	−	0.575390i
$543$		−	35.2672i		−	1.51346i
$544$	−0.676740	−	4.06719i	−0.0290150	−	0.174379i
$545$	5.29676	+	28.1066i	0.226888	+	1.20395i
$546$	−6.65220	+	6.65220i	−0.284688	+	0.284688i
$547$	−8.73921	+	21.0983i	−0.373662	+	0.902099i	0.619462	+	0.785027i	$0.287351\pi$
$547$	−8.73921	+	21.0983i	−0.373662	+	0.902099i	−0.993123	+	0.117072i	$0.962649\pi$
$548$	21.1172			0.902083
$549$	−27.1578	+	65.5648i	−1.15907	+	2.79824i
$550$	15.4424	+	16.0781i	0.658467	+	0.685571i
$551$	−0.446486	−	1.07791i	−0.0190210	−	0.0459207i
$552$	−12.3970	+	12.3970i	−0.527651	+	0.527651i
$553$	−3.42967	+	3.42967i	−0.145844	+	0.145844i
$554$	8.77965	+	21.1959i	0.373012	+	0.900530i
$555$	40.5283	+	61.9990i	1.72033	+	2.63171i
$556$	−4.10307	+	9.90569i	−0.174009	+	0.420095i
$557$	−24.3785			−1.03295			−0.516476	−	0.856302i	$-0.672756\pi$
$557$	−24.3785			−1.03295			−0.516476	+	0.856302i	$0.672756\pi$
$558$	4.99419	−	12.0570i	0.211421	−	0.510415i
$559$	−6.54270	+	6.54270i	−0.276727	+	0.276727i
$560$	3.56577	−	0.671978i	0.150681	−	0.0283963i
$561$	−34.6321	+	48.4574i	−1.46217	+	2.04587i
$562$		−	24.0269i		−	1.01351i
$563$	13.5026	+	13.5026i	0.569068	+	0.569068i	0.931867	−	0.362799i	$-0.118179\pi$
$563$	13.5026	+	13.5026i	0.569068	+	0.569068i	−0.362799	+	0.931867i	$0.618179\pi$
$564$	16.4045	+	6.79498i	0.690755	+	0.286120i
$565$	−2.13024	−	11.3039i	−0.0896198	−	0.475557i
$566$	−6.03994	+	14.5817i	−0.253878	+	0.612915i
$567$	15.3501	+	37.0584i	0.644643	+	1.55631i
$568$	7.59937	−	3.14776i	0.318863	−	0.132077i
$569$	32.8960	+	32.8960i	1.37907	+	1.37907i	0.846189	+	0.532883i	$0.178892\pi$
$569$	32.8960	+	32.8960i	1.37907	+	1.37907i	0.532883	+	0.846189i	$0.321108\pi$
$570$	0.910159	−	1.33286i	0.0381224	−	0.0558274i
$571$	3.84418	+	9.28068i	0.160874	+	0.388384i	0.983677	−	0.179942i	$-0.0575910\pi$
$571$	3.84418	+	9.28068i	0.160874	+	0.388384i	−0.822803	+	0.568327i	$0.807591\pi$
$572$	3.05301	+	7.37063i	0.127653	+	0.308181i
$573$	−71.9554	−	29.8049i	−3.00598	−	1.24512i
$574$		−	2.78917i		−	0.116418i
$575$	−0.545502	+	27.0503i	−0.0227490	+	1.12808i
$576$	−5.30145	+	5.30145i	−0.220894	+	0.220894i
$577$			19.1206i			0.796002i	0.917385	+	0.398001i	$0.130296\pi$
$577$			19.1206i			0.796002i	−0.917385	+	0.398001i	$0.869704\pi$
$578$	7.48061	−	15.2657i	0.311152	−	0.634968i
$579$	56.8893			2.36424
$580$	9.67101	+	6.60395i	0.401567	+	0.274214i
$581$	−21.3237	−	8.83258i	−0.884657	−	0.366437i
$582$	16.1264			0.668462
$583$	8.32555	+	3.44855i	0.344809	+	0.142825i
$584$	1.40695	−	0.582777i	0.0582199	−	0.0241155i
$585$	−16.4135	−	25.1089i	−0.678616	−	1.03813i
$586$	−5.33794	−	5.33794i	−0.220508	−	0.220508i
$587$	1.31962	−	1.31962i	0.0544667	−	0.0544667i	−0.679349	−	0.733815i	$-0.737738\pi$
$587$	1.31962	−	1.31962i	0.0544667	−	0.0544667i	0.733815	+	0.679349i	$0.237738\pi$
$588$	13.0711	−	5.41425i	0.539045	−	0.223280i
$589$	0.358263	−	0.148397i	0.0147620	−	0.00611460i
$590$	−1.12945	+	5.39339i	−0.0464989	+	0.222042i
$591$		−	49.2902i		−	2.02753i
$592$	3.91254	−	9.44570i	0.160804	−	0.388216i
$593$	−6.22387	−	6.22387i	−0.255584	−	0.255584i	0.567671	−	0.823255i	$-0.307844\pi$
$593$	−6.22387	−	6.22387i	−0.255584	−	0.255584i	−0.823255	+	0.567671i	$0.807844\pi$
$594$	64.9676			2.66565
$595$	13.5723	+	6.29448i	0.556408	+	0.258049i
$596$	−8.46929			−0.346915
$597$	−18.4034	−	18.4034i	−0.753200	−	0.753200i
$598$	−3.70530	+	8.94539i	−0.151521	+	0.365804i
$599$		−	4.79224i		−	0.195806i	−0.995196	−	0.0979028i	$-0.968787\pi$
$599$		−	4.79224i		−	0.195806i	0.995196	−	0.0979028i	$-0.0312134\pi$
$600$	−0.326622	+	16.1965i	−0.0133343	+	0.661221i
$601$	−12.0035	+	4.97202i	−0.489634	+	0.202813i	−0.613820	−	0.789446i	$-0.710368\pi$
$601$	−12.0035	+	4.97202i	−0.489634	+	0.202813i	0.124186	+	0.992259i	$0.460368\pi$
$602$	−7.75248	+	3.21118i	−0.315968	+	0.130878i
$603$	76.5234	−	76.5234i	3.11628	−	3.11628i
$604$	1.27947	+	1.27947i	0.0520607	+	0.0520607i
$605$	−16.6182	+	10.8632i	−0.675625	+	0.441652i
$606$	33.2376	−	13.7675i	1.35019	−	0.559265i
$607$	35.5125	+	14.7098i	1.44141	+	0.597051i	0.960139	−	0.279522i	$-0.0901761\pi$
$607$	35.5125	+	14.7098i	1.44141	+	0.597051i	0.481269	+	0.876573i	$0.340176\pi$
$608$	−0.222777			−0.00903480
$609$	−25.4390	−	10.5372i	−1.03084	−	0.426988i
$610$	11.9358	−	17.4791i	0.483266	−	0.707708i
$611$	9.80620			0.396716
$612$	−30.4933	+	5.07378i	−1.23262	+	0.205096i
$613$			20.7647i			0.838678i	0.907830	+	0.419339i	$0.137738\pi$
$613$			20.7647i			0.838678i	−0.907830	+	0.419339i	$0.862262\pi$
$614$	−8.83717	+	8.83717i	−0.356639	+	0.356639i
$615$	12.1880	+	2.55235i	0.491470	+	0.102921i
$616$			7.23507i			0.291509i
$617$	44.8083	+	18.5602i	1.80391	+	0.747206i	0.984828	+	0.173535i	$0.0555190\pi$
$617$	44.8083	+	18.5602i	1.80391	+	0.747206i	0.819086	+	0.573671i	$0.194481\pi$
$618$	4.79717	+	11.5814i	0.192971	+	0.465872i
$619$	4.87259	+	11.7635i	0.195846	+	0.472814i	0.991044	−	0.133536i	$-0.0426331\pi$
$619$	4.87259	+	11.7635i	0.195846	+	0.472814i	−0.795198	+	0.606350i	$0.792633\pi$
$620$	−2.19493	+	3.21432i	−0.0881507	+	0.129090i
$621$	55.7541	+	55.7541i	2.23734	+	2.23734i
$622$	16.1222	−	6.67803i	0.646441	−	0.267765i
$623$	−6.06722	−	14.6476i	−0.243078	−	0.586842i
$624$	−2.21857	+	5.35610i	−0.0888139	+	0.214416i
$625$	16.9506	+	18.3760i	0.678024	+	0.735040i
$626$	7.99415	+	3.31129i	0.319510	+	0.132346i
$627$	2.27558	+	2.27558i	0.0908779	+	0.0908779i
$628$		−	2.07703i		−	0.0828824i
$629$	35.7697	−	22.3053i	1.42623	−	0.889371i
$630$	−5.03808	−	26.7340i	−0.200722	−	1.06511i
$631$	−28.6219	+	28.6219i	−1.13942	+	1.13942i	−0.150867	+	0.988554i	$0.548206\pi$
$631$	−28.6219	+	28.6219i	−1.13942	+	1.13942i	−0.988554	+	0.150867i	$0.951794\pi$
$632$	−1.14383	+	2.76144i	−0.0454990	+	0.109844i
$633$	−30.5997			−1.21623
$634$	−1.60449	+	3.87358i	−0.0637224	+	0.153840i
$635$	2.43575	−	1.59223i	0.0966596	−	0.0631857i
$636$	2.50600	+	6.05003i	0.0993695	+	0.239899i
$637$	5.52504	−	5.52504i	0.218910	−	0.218910i
$638$	−16.5112	+	16.5112i	−0.653685	+	0.653685i
$639$	−23.6000	−	56.9754i	−0.933601	−	2.25391i
$640$	1.87165	−	1.22349i	0.0739836	−	0.0483625i
$641$	13.2912	−	32.0879i	0.524973	−	1.26740i	−0.409808	−	0.912172i	$-0.634404\pi$
$641$	13.2912	−	32.0879i	0.524973	−	1.26740i	0.934781	−	0.355225i	$-0.115596\pi$
$642$	39.2079			1.54741
$643$	5.51999	−	13.3264i	0.217687	−	0.525543i	−0.776879	−	0.629650i	$-0.783198\pi$
$643$	5.51999	−	13.3264i	0.217687	−	0.525543i	0.994566	+	0.104107i	$0.0331983\pi$
$644$	−6.20901	+	6.20901i	−0.244669	+	0.244669i
$645$	−6.93790	−	36.8151i	−0.273180	−	1.44960i
$646$	−0.747298	−	0.534088i	−0.0294020	−	0.0210134i
$647$		−	38.3237i		−	1.50666i	−0.657644	−	0.753329i	$-0.728447\pi$
$647$		−	38.3237i		−	1.50666i	0.657644	−	0.753329i	$-0.271553\pi$
$648$	17.4787	+	17.4787i	0.686629	+	0.686629i
$649$	−10.1510	−	4.20467i	−0.398461	−	0.165048i
$650$	3.25641	+	8.33303i	0.127727	+	0.326848i
$651$	3.50221	−	8.45509i	0.137263	−	0.331381i
$652$	−0.792847	−	1.91410i	−0.0310503	−	0.0749621i
$653$	−28.2020	+	11.6817i	−1.10363	+	0.457139i	−0.858740	−	0.512412i	$-0.828752\pi$
$653$	−28.2020	+	11.6817i	−1.10363	+	0.457139i	−0.244891	+	0.969551i	$0.578752\pi$
$654$	−29.3040	−	29.3040i	−1.14588	−	1.14588i
$655$	−5.23638	+	7.66830i	−0.204602	+	0.299625i
$656$	−0.657761	−	1.58798i	−0.0256813	−	0.0620000i
$657$	−4.36930	−	10.5484i	−0.170463	−	0.411534i
$658$	8.21617	+	3.40325i	0.320300	+	0.132672i
$659$		−	32.1026i		−	1.25054i	−0.780408	−	0.625271i	$-0.784989\pi$
$659$		−	32.1026i		−	1.25054i	0.780408	−	0.625271i	$-0.215011\pi$
$660$	−31.6156	−	6.62077i	−1.23064	−	0.257713i
$661$	−1.48757	+	1.48757i	−0.0578597	+	0.0578597i	−0.735445	−	0.677585i	$-0.763027\pi$
$661$	−1.48757	+	1.48757i	−0.0578597	+	0.0578597i	0.677585	+	0.735445i	$0.263027\pi$
$662$			7.00895i			0.272411i
$663$	−20.2829	+	12.6480i	−0.787722	+	0.491209i
$664$	−14.2233			−0.551972
$665$	0.455851	−	0.667561i	0.0176771	−	0.0258869i
$666$	−70.8181	−	29.3338i	−2.74414	−	1.13666i
$667$	−28.3393			−1.09730
$668$	−16.0786	−	6.65999i	−0.622101	−	0.257683i
$669$	−6.47129	+	2.68049i	−0.250194	+	0.103634i
$670$	−27.0162	+	17.6603i	−1.04373	+	0.682278i
$671$	29.8419	+	29.8419i	1.15203	+	1.15203i
$672$	−3.71768	+	3.71768i	−0.143413	+	0.143413i
$673$	28.5802	−	11.8383i	1.10169	−	0.456334i	0.243620	−	0.969871i	$-0.421665\pi$
$673$	28.5802	−	11.8383i	1.10169	−	0.456334i	0.858067	+	0.513537i	$0.171665\pi$
$674$	−1.40286	+	0.581083i	−0.0540361	+	0.0223825i
$675$	72.8421	+	1.46895i	2.80369	+	0.0565398i
$676$		−	9.79826i		−	0.376856i
$677$	−0.866714	+	2.09243i	−0.0333105	+	0.0804188i	−0.939659	−	0.342111i	$-0.888858\pi$
$677$	−0.866714	+	2.09243i	−0.0333105	+	0.0804188i	0.906349	+	0.422530i	$0.138858\pi$
$678$	11.7854	+	11.7854i	0.452617	+	0.452617i
$679$	8.07689			0.309963
$680$	9.21159	+	0.382976i	0.353248	+	0.0146865i
$681$	−1.24364			−0.0476562
$682$	−5.48778	−	5.48778i	−0.210138	−	0.210138i
$683$	2.62081	−	6.32720i	0.100283	−	0.242103i	−0.865773	−	0.500436i	$-0.833173\pi$
$683$	2.62081	−	6.32720i	0.100283	−	0.242103i	0.966056	+	0.258333i	$0.0831730\pi$
$684$			1.67025i			0.0638635i
$685$	−9.67851	+	46.2170i	−0.369797	+	1.76586i
$686$	17.0411	−	7.05866i	0.650633	−	0.269501i
$687$	26.9303	−	11.1549i	1.02745	−	0.425585i
$688$	−3.65649	+	3.65649i	−0.139402	+	0.139402i
$689$	2.55729	+	2.55729i	0.0974249	+	0.0974249i
$690$	−21.4502	−	32.8138i	−0.816594	−	1.24920i
$691$	21.4601	−	8.88906i	0.816380	−	0.338156i	0.0648836	−	0.997893i	$-0.479332\pi$
$691$	21.4601	−	8.88906i	0.816380	−	0.338156i	0.751496	+	0.659737i	$0.229332\pi$
$692$	4.76214	+	1.97254i	0.181030	+	0.0749849i
$693$	54.2441			2.06056
$694$	−6.53872	−	2.70843i	−0.248206	−	0.102810i
$695$	−19.7990	−	13.5200i	−0.751019	−	0.512841i
$696$	−16.9683			−0.643182
$697$	1.60059	−	6.90373i	0.0606267	−	0.261497i
$698$		−	8.70745i		−	0.329582i
$699$	−28.3601	+	28.3601i	−1.07268	+	1.07268i
$700$	−0.163588	+	8.11200i	−0.00618305	+	0.306605i
$701$		−	44.0844i		−	1.66505i	−0.553991	−	0.832523i	$-0.686896\pi$
$701$		−	44.0844i		−	1.66505i	0.553991	−	0.832523i	$-0.313104\pi$
$702$	24.0885	+	9.97777i	0.909161	+	0.376587i
$703$	−0.871624	−	2.10429i	−0.0328739	−	0.0793646i
$704$	1.70622	+	4.11919i	0.0643057	+	0.155248i
$705$	−22.3900	+	32.7885i	−0.843256	+	1.23489i
$706$	1.86612	+	1.86612i	0.0702325	+	0.0702325i
$707$	16.6470	−	6.89541i	0.626075	−	0.259329i
$708$	−3.05546	−	7.37654i	−0.114831	−	0.277227i
$709$	−7.50658	+	18.1225i	−0.281916	+	0.680605i	−0.999880	−	0.0154750i	$-0.995074\pi$
$709$	−7.50658	+	18.1225i	−0.281916	+	0.680605i	0.717965	+	0.696080i	$0.245074\pi$
$710$	3.40621	+	18.0746i	0.127833	+	0.678328i
$711$	20.7036	+	8.57572i	0.776446	+	0.321615i
$712$	−6.90857	−	6.90857i	−0.258910	−	0.258910i
$713$		−	9.41904i		−	0.352746i
$714$	−21.3836	+	3.55803i	−0.800262	+	0.133156i
$715$	−17.5306	+	3.30368i	−0.655606	+	0.123551i
$716$	2.09869	−	2.09869i	0.0784318	−	0.0784318i
$717$	10.7167	−	25.8724i	0.400223	−	0.966224i
$718$	7.86678			0.293585
$719$	−16.5133	+	39.8667i	−0.615844	+	1.48678i	0.240645	+	0.970613i	$0.422641\pi$
$719$	−16.5133	+	39.8667i	−0.615844	+	1.48678i	−0.856489	+	0.516165i	$0.827359\pi$
$720$	−9.17295	−	14.0325i	−0.341856	−	0.522960i
$721$	2.40265	+	5.80052i	0.0894795	+	0.216023i
$722$	13.3999	−	13.3999i	0.498694	−	0.498694i
$723$	50.0740	−	50.0740i	1.86227	−	1.86227i
$724$	−4.16552	−	10.0565i	−0.154810	−	0.373746i
$725$	−18.8858	+	18.1392i	−0.701401	+	0.673671i
$726$	11.0088	−	26.5775i	0.408574	−	0.986384i
$727$	32.8765			1.21932			0.609661	−	0.792663i	$-0.291306\pi$
$727$	32.8765			1.21932			0.609661	+	0.792663i	$0.291306\pi$
$728$	−1.11117	+	2.68259i	−0.0411826	+	0.0994235i
$729$	30.8955	−	30.8955i	1.14428	−	1.14428i
$730$	0.630625	+	3.34634i	0.0233405	+	0.123853i
$731$	−21.0316	+	3.49946i	−0.777884	+	0.129432i
$732$			30.6680i			1.13352i
$733$	28.5557	+	28.5557i	1.05473	+	1.05473i	0.998413	+	0.0563160i	$0.0179354\pi$
$733$	28.5557	+	28.5557i	1.05473	+	1.05473i	0.0563160	+	0.998413i	$0.482065\pi$
$734$	21.5147	+	8.91170i	0.794124	+	0.328937i
$735$	5.85878	+	31.0889i	0.216104	+	1.14673i
$736$	−2.07076	+	4.99927i	−0.0763294	+	0.184275i
$737$	−24.6283	−	59.4581i	−0.907197	−	2.19017i
$738$	−11.9057	+	4.93149i	−0.438254	+	0.181531i
$739$	17.2306	+	17.2306i	0.633838	+	0.633838i	0.949028	−	0.315191i	$-0.102068\pi$
$739$	17.2306	+	17.2306i	0.633838	+	0.633838i	−0.315191	+	0.949028i	$0.602068\pi$
$740$	18.8796	+	12.8921i	0.694028	+	0.473924i
$741$	0.494247	+	1.19322i	0.0181566	+	0.0438339i
$742$	1.25513	+	3.03014i	0.0460772	+	0.111240i
$743$	−23.4641	−	9.71915i	−0.860815	−	0.356561i	−0.0917885	−	0.995779i	$-0.529258\pi$
$743$	−23.4641	−	9.71915i	−0.860815	−	0.356561i	−0.769026	+	0.639217i	$0.779258\pi$
$744$		−	5.63970i		−	0.206762i
$745$	3.88167	−	18.5358i	0.142213	−	0.679100i
$746$	16.1382	−	16.1382i	0.590863	−	0.590863i
$747$			106.638i			3.90167i
$748$	−4.15191	+	17.9082i	−0.151809	+	0.654788i
$749$	19.6372			0.717528
$750$	−35.2979	−	8.13809i	−1.28890	−	0.297161i
$751$	14.8511	+	6.15152i	0.541924	+	0.224472i	0.636817	−	0.771015i	$-0.280251\pi$
$751$	14.8511	+	6.15152i	0.541924	+	0.224472i	−0.0948927	+	0.995488i	$0.530251\pi$
$752$	5.48034			0.199848
$753$	−65.0955	−	26.9634i	−2.37221	−	0.982602i
$754$	−8.65778	+	3.58617i	−0.315298	+	0.130601i
$755$	−3.38664	+	2.21382i	−0.123252	+	0.0805692i
$756$	16.7198	+	16.7198i	0.608095	+	0.608095i
$757$	−23.3000	+	23.3000i	−0.846853	+	0.846853i	−0.989739	−	0.142886i	$-0.954362\pi$
$757$	−23.3000	+	23.3000i	−0.846853	+	0.846853i	0.142886	+	0.989739i	$0.454362\pi$
$758$	−17.0883	+	7.07822i	−0.620676	+	0.257092i
$759$	72.2176	−	29.9135i	2.62133	−	1.08579i
$760$	0.102104	−	0.487568i	0.00370370	−	0.0176860i
$761$			3.29371i			0.119397i	0.998216	+	0.0596985i	$0.0190139\pi$
$761$			3.29371i			0.119397i	−0.998216	+	0.0596985i	$0.980986\pi$
$762$	−1.61357	+	3.89550i	−0.0584534	+	0.141119i
$763$	−14.6769	−	14.6769i	−0.531338	−	0.531338i
$764$	−24.0385			−0.869683
$765$	2.87132	−	69.0628i	0.103813	−	2.49697i
$766$	18.7407			0.677130
$767$	−3.11799	−	3.11799i	−0.112584	−	0.112584i
$768$	−1.23988	+	2.99334i	−0.0447404	+	0.108013i
$769$			11.8679i			0.427966i	0.976837	+	0.213983i	$0.0686437\pi$
$769$			11.8679i			0.427966i	−0.976837	+	0.213983i	$0.931356\pi$
$770$	−15.8346	−	3.31600i	−0.570640	−	0.119500i
$771$	−59.0984	+	24.4794i	−2.12838	+	0.881603i
$772$	16.2220	−	6.71939i	0.583844	−	0.241836i
$773$	−32.2433	+	32.2433i	−1.15971	+	1.15971i	−0.175173	+	0.984538i	$0.556048\pi$
$773$	−32.2433	+	32.2433i	−1.15971	+	1.15971i	−0.984538	+	0.175173i	$0.943952\pi$
$774$	27.4141	+	27.4141i	0.985379	+	0.985379i
$775$	−6.02885	−	6.27702i	−0.216563	−	0.225477i
$776$	4.59847	−	1.90475i	0.165075	−	0.0683764i
$777$	−49.6617	−	20.5705i	−1.78160	−	0.737964i
$778$	1.59207			0.0570785
$779$	−0.353765	−	0.146534i	−0.0126749	−	0.00525013i
$780$	−10.7055	−	7.31037i	−0.383319	−	0.261753i
$781$	−36.6740			−1.31230
$782$	−18.9316	+	11.8054i	−0.676992	+	0.422160i
$783$			76.3130i			2.72721i
$784$	3.08775	−	3.08775i	0.110277	−	0.110277i
$785$	4.54577	+	0.951949i	0.162245	+	0.0339765i
$786$		−	13.4544i		−	0.479904i
$787$	−8.98074	−	3.71995i	−0.320129	−	0.132602i	0.216832	−	0.976209i	$-0.430428\pi$
$787$	−8.98074	−	3.71995i	−0.320129	−	0.132602i	−0.536961	+	0.843607i	$0.680428\pi$
$788$	−5.82183	−	14.0551i	−0.207394	−	0.500694i
$789$	23.2152	+	56.0464i	0.826482	+	1.99530i
$790$	−5.51944	−	3.76901i	−0.196373	−	0.134095i
$791$	5.90271	+	5.90271i	0.209876	+	0.209876i
$792$	30.8831	−	12.7922i	1.09738	−	0.454551i
$793$	6.48154	+	15.6478i	0.230166	+	0.555670i
$794$	2.73922	−	6.61306i	0.0972113	−	0.234689i
$795$	−14.3896	+	2.71176i	−0.510347	+	0.0961761i
$796$	−7.42142	−	3.07405i	−0.263045	−	0.108957i
$797$	27.3910	+	27.3910i	0.970240	+	0.970240i	0.999570	−	0.0293297i	$-0.00933729\pi$
$797$	27.3910	+	27.3910i	0.970240	+	0.970240i	−0.0293297	+	0.999570i	$0.509337\pi$
$798$			1.17127i			0.0414626i
$799$	18.3836	+	13.1386i	0.650365	+	0.464811i
$800$	1.81989	+	4.65704i	0.0643429	+	0.164651i
$801$	−51.7962	+	51.7962i	−1.83013	+	1.83013i
$802$	1.34092	−	3.23726i	0.0473494	−	0.114311i
$803$	−6.78983			−0.239608
$804$	17.8970	−	43.2071i	0.631178	−	1.52380i
$805$	−10.7433	−	16.4347i	−0.378651	−	0.579248i
$806$	−1.19192	−	2.87756i	−0.0419837	−	0.101358i
$807$	−23.5926	+	23.5926i	−0.830498	+	0.830498i
$808$	7.85162	−	7.85162i	0.276219	−	0.276219i
$809$	7.24919	+	17.5011i	0.254868	+	0.615306i	0.998584	−	0.0531895i	$-0.0169387\pi$
$809$	7.24919	+	17.5011i	0.254868	+	0.615306i	−0.743716	+	0.668495i	$0.766939\pi$
$810$	−46.2647	+	30.2429i	−1.62558	+	1.06263i
$811$	−16.6667	+	40.2369i	−0.585245	+	1.41291i	0.302757	+	0.953068i	$0.402093\pi$
$811$	−16.6667	+	40.2369i	−0.585245	+	1.41291i	−0.888002	+	0.459840i	$0.847907\pi$
$812$	−8.49854			−0.298240
$813$	−23.4886	+	56.7065i	−0.823781	+	1.98878i
$814$	−32.2329	+	32.2329i	−1.12976	+	1.12976i
$815$	4.55257	−	0.857943i	0.159470	−	0.0300524i
$816$	−11.3354	+	7.06855i	−0.396818	+	0.247449i
$817$			1.15199i			0.0403031i
$818$	1.32916	+	1.32916i	0.0464730	+	0.0464730i
$819$	20.1124	+	8.33085i	0.702786	+	0.291103i
$820$	3.77690	−	0.711766i	0.131895	−	0.0248559i
$821$	−6.20858	+	14.9888i	−0.216681	+	0.523114i	−0.994422	−	0.105470i	$-0.966365\pi$
$821$	−6.20858	+	14.9888i	−0.216681	+	0.523114i	0.777741	+	0.628584i	$0.216365\pi$
$822$	−26.1829	−	63.2110i	−0.913232	−	2.20474i
$823$	9.99366	−	4.13951i	0.348357	−	0.144294i	−0.201642	−	0.979459i	$-0.564628\pi$
$823$	9.99366	−	4.13951i	0.348357	−	0.144294i	0.550000	+	0.835165i	$0.314628\pi$
$824$	2.73584	+	2.73584i	0.0953074	+	0.0953074i
$825$	28.9803	−	66.1593i	1.00897	−	2.30337i
$826$	−1.53032	−	3.69452i	−0.0532467	−	0.128549i
$827$	−16.7142	−	40.3516i	−0.581210	−	1.40316i	−0.891717	−	0.452593i	$-0.850499\pi$
$827$	−16.7142	−	40.3516i	−0.581210	−	1.40316i	0.310507	−	0.950571i	$-0.399501\pi$
$828$	37.4814	+	15.5253i	1.30257	+	0.539542i
$829$		−	38.5554i		−	1.33909i	−0.742774	−	0.669543i	$-0.766490\pi$
$829$		−	38.5554i		−	1.33909i	0.742774	−	0.669543i	$-0.233510\pi$
$830$	6.51888	−	31.1291i	0.226274	−	1.08051i
$831$	52.5609	−	52.5609i	1.82332	−	1.82332i
$832$			1.78934i			0.0620342i
$833$	17.7604	−	2.95515i	0.615360	−	0.102390i
$834$	34.7384			1.20289
$835$	21.9452	−	32.1372i	0.759446	−	1.11215i
$836$	0.917660	+	0.380107i	0.0317379	+	0.0131463i
$837$	−25.3639			−0.876706
$838$	30.1244	+	12.4779i	1.04063	+	0.431043i
$839$	39.2712	−	16.2667i	1.35579	−	0.561588i	0.417894	−	0.908496i	$-0.362768\pi$
$839$	39.2712	−	16.2667i	1.35579	−	0.561588i	0.937899	+	0.346908i	$0.112768\pi$
$840$	−6.43259	−	9.84039i	−0.221946	−	0.339526i
$841$	1.11149	+	1.11149i	0.0383273	+	0.0383273i
$842$	−19.3673	+	19.3673i	−0.667442	+	0.667442i
$843$	−71.9205	+	29.7905i	−2.47707	+	1.02604i
$844$	−8.72553	+	3.61423i	−0.300345	+	0.124407i
$845$	21.4444	+	4.49077i	0.737710	+	0.154487i
$846$		−	41.0882i		−	1.41264i
$847$	5.51372	−	13.3113i	0.189454	−	0.457382i
$848$	1.42918	+	1.42918i	0.0490782	+	0.0490782i
$849$	51.1368			1.75501
$850$	−5.06006	+	19.9849i	−0.173559	+	0.685476i
$851$	−55.3235			−1.89647
$852$	−18.8446	−	18.8446i	−0.645607	−	0.645607i
$853$	2.19607	−	5.30178i	0.0751920	−	0.181530i	−0.881814	−	0.471597i	$-0.843678\pi$
$853$	2.19607	−	5.30178i	0.0751920	−	0.181530i	0.957006	+	0.290067i	$0.0936777\pi$
$854$			15.3600i			0.525609i
$855$	−3.65549	−	0.765512i	−0.125015	−	0.0261800i
$856$	11.1802	−	4.63098i	0.382131	−	0.158284i
$857$	7.83237	−	3.24428i	0.267549	−	0.110822i	−0.244876	−	0.969554i	$-0.578747\pi$
$857$	7.83237	−	3.24428i	0.267549	−	0.110822i	0.512425	+	0.858732i	$0.328747\pi$
$858$	18.2774	−	18.2774i	0.623980	−	0.623980i
$859$	−25.6691	−	25.6691i	−0.875818	−	0.875818i	0.117281	−	0.993099i	$-0.462582\pi$
$859$	−25.6691	−	25.6691i	−0.875818	−	0.875818i	−0.993099	+	0.117281i	$0.962582\pi$
$860$	−6.32671	−	9.67841i	−0.215739	−	0.330031i
$861$	−8.34893	+	3.45824i	−0.284531	+	0.117857i
$862$	16.7310	+	6.93020i	0.569860	+	0.236044i
$863$	37.1792			1.26560			0.632798	−	0.774317i	$-0.281906\pi$
$863$	37.1792			1.26560			0.632798	+	0.774317i	$0.281906\pi$
$864$	13.4622	+	5.57623i	0.457993	+	0.189707i
$865$	−6.49970	+	9.51833i	−0.220996	+	0.323633i
$866$	−32.4021			−1.10107
$867$	−54.9704	−	3.46440i	−1.86689	−	0.117657i
$868$		−	2.82463i		−	0.0958743i
$869$	9.42328	−	9.42328i	0.319663	−	0.319663i
$870$	7.77697	−	37.1367i	0.263664	−	1.25905i
$871$		−	25.8281i		−	0.875152i
$872$	−11.8173	−	4.89487i	−0.400183	−	0.165761i
$873$	−14.2806	−	34.4765i	−0.483326	−	1.16685i
$874$	0.461319	+	1.11372i	0.0156043	+	0.0376722i
$875$	−17.6789	−	4.07595i	−0.597656	−	0.137792i
$876$	−3.48890	−	3.48890i	−0.117879	−	0.117879i
$877$	−23.2054	+	9.61198i	−0.783590	+	0.324573i	−0.738363	−	0.674403i	$-0.764401\pi$
$877$	−23.2054	+	9.61198i	−0.783590	+	0.324573i	−0.0452265	+	0.998977i	$0.514401\pi$
$878$	8.51214	+	20.5501i	0.287271	+	0.693533i
$879$	−9.35985	+	22.5967i	−0.315700	+	0.762167i
$880$	−9.79722	+	1.84631i	−0.330264	+	0.0622391i
$881$	9.88865	+	4.09601i	0.333157	+	0.137998i	0.542990	−	0.839739i	$-0.317292\pi$
$881$	9.88865	+	4.09601i	0.333157	+	0.137998i	−0.209833	+	0.977737i	$0.567292\pi$
$882$	−23.1501	−	23.1501i	−0.779504	−	0.779504i
$883$			3.61322i			0.121595i	0.998150	+	0.0607973i	$0.0193643\pi$
$883$			3.61322i			0.121595i	−0.998150	+	0.0607973i	$0.980636\pi$
$884$	−4.28978	+	6.00228i	−0.144281	+	0.201878i
$885$	17.5446	−	3.30633i	0.589756	−	0.111141i
$886$	6.81590	−	6.81590i	0.228985	−	0.228985i
$887$	−12.4793	+	30.1276i	−0.419013	+	1.01159i	0.563621	+	0.826033i	$0.309408\pi$
$887$	−12.4793	+	30.1276i	−0.419013	+	1.01159i	−0.982634	+	0.185553i	$0.940592\pi$
$888$	−33.1253			−1.11161
$889$	−0.808152	+	1.95105i	−0.0271045	+	0.0654362i
$890$	18.2864	−	11.9537i	0.612962	−	0.400689i
$891$	−42.1755	−	101.821i	−1.41293	−	3.41112i
$892$	−1.52869	+	1.52869i	−0.0511844	+	0.0511844i
$893$	0.863303	−	0.863303i	0.0288893	−	0.0288893i
$894$	10.5009	+	25.3514i	0.351203	+	0.847879i
$895$	3.63130	+	5.55506i	0.121381	+	0.185685i
$896$	−0.620992	+	1.49921i	−0.0207459	+	0.0500850i
$897$	31.3707			1.04744
$898$	−14.9247	+	36.0315i	−0.498045	+	1.20239i
$899$	6.44612	−	6.44612i	0.214990	−	0.214990i
$900$	34.9156	−	13.6444i	1.16385	−	0.454814i
$901$	1.36780	+	8.22045i	0.0455681	+	0.273863i
$902$			7.66345i			0.255165i
$903$	19.2243	+	19.2243i	0.639745	+	0.639745i
$904$	4.75264	+	1.96861i	0.158071	+	0.0654750i
$905$	23.9187	−	4.50753i	0.795083	−	0.149835i
$906$	2.24349	−	5.41626i	0.0745350	−	0.179943i
$907$	6.13159	+	14.8030i	0.203596	+	0.491525i	0.992390	−	0.123133i	$-0.0392942\pi$
$907$	6.13159	+	14.8030i	0.203596	+	0.491525i	−0.788794	+	0.614658i	$0.789294\pi$
$908$	−0.354624	+	0.146890i	−0.0117686	+	0.00487472i
$909$	−58.8666	−	58.8666i	−1.95248	−	1.95248i
$910$	−5.36183	−	3.66139i	−0.177743	−	0.121374i
$911$	13.9350	+	33.6421i	0.461687	+	1.11461i	0.967704	+	0.252088i	$0.0811174\pi$
$911$	13.9350	+	33.6421i	0.461687	+	1.11461i	−0.506017	+	0.862524i	$0.668883\pi$
$912$	0.276217	+	0.666847i	0.00914647	+	0.0220815i
$913$	58.5885	+	24.2682i	1.93900	+	0.803159i
$914$			3.92824i			0.129935i
$915$	−67.1199	−	14.0559i	−2.21891	−	0.464673i
$916$	6.36165	−	6.36165i	0.210195	−	0.210195i
$917$		−	6.73863i		−	0.222529i
$918$	31.7900	+	50.9797i	1.04923	+	1.68258i
$919$	21.8170			0.719678			0.359839	−	0.933014i	$-0.382832\pi$
$919$	21.8170			0.719678			0.359839	+	0.933014i	$0.382832\pi$
$920$	−9.99228	−	6.82334i	−0.329436	−	0.224959i
$921$	37.4097	+	15.4956i	1.23269	+	0.510597i
$922$	−37.6666			−1.24048
$923$	−13.5979	−	5.63242i	−0.447579	−	0.185393i
$924$	21.6570	−	8.97063i	0.712463	−	0.295112i
$925$	−36.8686	+	35.4110i	−1.21223	+	1.16431i
$926$	3.72927	+	3.72927i	0.122551	+	0.122551i
$927$	20.5116	−	20.5116i	0.673690	−	0.673690i
$928$	−4.83853	+	2.00418i	−0.158832	+	0.0657906i
$929$	−44.7381	+	18.5311i	−1.46781	+	0.607986i	−0.966358	−	0.257200i	$-0.917200\pi$
$929$	−44.7381	+	18.5311i	−1.46781	+	0.607986i	−0.501450	+	0.865186i	$0.667200\pi$
$930$	12.3430	+	2.58481i	0.404743	+	0.0847591i
$931$		−	0.972811i		−	0.0318826i
$932$	−4.73720	+	11.4366i	−0.155172	+	0.374619i
$933$	−39.9792	−	39.9792i	−1.30886	−	1.30886i
$934$	−6.42830			−0.210340
$935$	−37.2908	−	17.2946i	−1.21954	−	0.565593i
$936$	13.4154			0.438495
$937$	33.7018	+	33.7018i	1.10099	+	1.10099i	0.994291	+	0.106699i	$0.0340280\pi$
$937$	33.7018	+	33.7018i	1.10099	+	1.10099i	0.106699	+	0.994291i	$0.465972\pi$
$938$	8.96367	−	21.6402i	0.292674	−	0.706578i
$939$		−	28.0348i		−	0.914881i
$940$	−2.51177	+	11.9942i	−0.0819248	+	0.391209i
$941$	−5.67849	+	2.35211i	−0.185113	+	0.0766765i	−0.473315	−	0.880893i	$-0.656943\pi$
$941$	−5.67849	+	2.35211i	−0.185113	+	0.0766765i	0.288201	+	0.957570i	$0.406943\pi$
$942$	−6.21725	+	2.57527i	−0.202569	+	0.0839068i
$943$	−6.57665	+	6.57665i	−0.214165	+	0.214165i
$944$	−1.74254	−	1.74254i	−0.0567147	−	0.0567147i
$945$	−44.2560	+	28.9299i	−1.43965	+	0.941088i
$946$	21.3005	−	8.82297i	0.692540	−	0.286859i
$947$	11.7699	+	4.87526i	0.382471	+	0.158425i	0.565631	−	0.824658i	$-0.308633\pi$
$947$	11.7699	+	4.87526i	0.382471	+	0.158425i	−0.183160	+	0.983083i	$0.558633\pi$
$948$	9.68415			0.314527
$949$	−2.51751	−	1.04279i	−0.0817218	−	0.0338503i
$950$	1.02029	+	0.446928i	0.0331027	+	0.0145002i
$951$	13.5843			0.440502
$952$	−5.67731	+	3.54027i	−0.184003	+	0.114741i
$953$		−	24.9800i		−	0.809180i	−0.914498	−	0.404590i	$-0.867414\pi$
$953$		−	24.9800i		−	0.809180i	0.914498	−	0.404590i	$-0.132586\pi$
$954$	10.7151	−	10.7151i	0.346914	−	0.346914i
$955$	11.0174	−	52.6105i	0.356515	−	1.70244i
$956$		−	8.64334i		−	0.279545i
$957$	69.8956	+	28.9517i	2.25940	+	0.935876i
$958$	15.4404	+	37.2765i	0.498858	+	1.20435i
$959$	−13.1136	−	31.6591i	−0.423461	−	1.02233i
$960$	−5.98294	−	4.08551i	−0.193098	−	0.131859i
$961$	−19.7778	−	19.7778i	−0.637995	−	0.637995i
$962$	−16.9016	+	7.00086i	−0.544929	+	0.225717i
$963$	−34.7203	−	83.8221i	−1.11885	−	2.70113i
$964$	8.36424	−	20.1931i	0.269394	−	0.650375i
$965$	7.27108	+	38.5831i	0.234064	+	1.24203i
$966$	26.2841	+	10.8872i	0.845678	+	0.350291i
$967$	−18.0041	−	18.0041i	−0.578973	−	0.578973i	0.355647	−	0.934620i	$-0.384260\pi$
$967$	−18.0041	−	18.0041i	−0.578973	−	0.578973i	−0.934620	+	0.355647i	$0.884260\pi$
$968$		−	8.87889i		−	0.285378i
$969$	−0.672145	+	2.89912i	−0.0215924	+	0.0931332i
$970$	2.06113	+	10.9372i	0.0661790	+	0.351171i
$971$	22.2438	−	22.2438i	0.713837	−	0.713837i	−0.253499	−	0.967336i	$-0.581581\pi$
$971$	22.2438	−	22.2438i	0.713837	−	0.713837i	0.967336	+	0.253499i	$0.0815814\pi$
$972$	13.9195	−	33.6047i	0.446469	−	1.07787i
$973$	17.3987			0.557776
$974$	6.35893	−	15.3518i	0.203753	−	0.491904i
$975$	20.9060	−	20.0795i	0.669528	−	0.643058i
$976$	3.62231	+	8.74502i	0.115947	+	0.279921i
$977$	1.83787	−	1.83787i	0.0587988	−	0.0587988i	−0.677096	−	0.735895i	$-0.736762\pi$
$977$	1.83787	−	1.83787i	0.0587988	−	0.0587988i	0.735895	+	0.677096i	$0.236762\pi$
$978$	−4.74652	+	4.74652i	−0.151777	+	0.151777i
$979$	16.6701	+	40.2453i	0.532780	+	1.28624i
$980$	5.34265	+	8.17303i	0.170665	+	0.261078i
$981$	−36.6987	+	88.5986i	−1.17170	+	2.82873i
$982$	−22.3337			−0.712696
$983$	9.13417	−	22.0518i	0.291335	−	0.703345i	−0.708663	−	0.705547i	$-0.750701\pi$
$983$	9.13417	−	22.0518i	0.291335	−	0.703345i	0.999998	+	0.00220274i	$0.000701155\pi$
$984$	−3.93780	+	3.93780i	−0.125533	+	0.125533i
$985$	33.4293	−	6.29983i	1.06515	−	0.200729i
$986$	−21.0355	−	4.87697i	−0.669907	−	0.155314i
$987$		−	28.8134i		−	0.917141i
$988$	0.281870	+	0.281870i	0.00896747	+	0.00896747i
$989$	25.8515	+	10.7080i	0.822029	+	0.340496i
$990$	13.8425	+	73.4536i	0.439943	+	2.33451i
$991$	1.36367	−	3.29218i	0.0433183	−	0.104580i	−0.900739	−	0.434360i	$-0.856975\pi$
$991$	1.36367	−	3.29218i	0.0433183	−	0.104580i	0.944058	+	0.329780i	$0.106975\pi$
$992$	−0.666124	−	1.60817i	−0.0211495	−	0.0510593i
$993$	20.9802	−	8.69027i	0.665785	−	0.275777i
$994$	−9.43830	−	9.43830i	−0.299365	−	0.299365i
$995$	10.1293	−	14.8336i	0.321119	−	0.470256i
$996$	17.6352	+	42.5752i	0.558794	+	1.34905i
$997$	6.90834	+	16.6782i	0.218789	+	0.528204i	0.994721	−	0.102612i	$-0.0327202\pi$
$997$	6.90834	+	16.6782i	0.218789	+	0.528204i	−0.775932	+	0.630816i	$0.782720\pi$
$998$	−18.1465	−	7.51654i	−0.574418	−	0.237932i
$999$			148.977i			4.71343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.9.1	✓	20
5.2	odd	4		850.2.l.i.451.5		20
5.3	odd	4		850.2.l.h.451.1		20
5.4	even	2		170.2.n.b.9.5	yes	20
17.2	even	8		170.2.n.b.19.5	yes	20
85.2	odd	8		850.2.l.i.801.5		20
85.19	even	8	inner	170.2.n.a.19.1	yes	20
85.53	odd	8		850.2.l.h.801.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.9.1	✓	20	1.1	even	1	trivial
170.2.n.a.19.1	yes	20	85.19	even	8	inner
170.2.n.b.9.5	yes	20	5.4	even	2
170.2.n.b.19.5	yes	20	17.2	even	8
850.2.l.h.451.1		20	5.3	odd	4
850.2.l.h.801.1		20	85.53	odd	8
850.2.l.i.451.5		20	5.2	odd	4
850.2.l.i.801.5		20	85.2	odd	8

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.23988 + 2.99334i) q^{3} +1.00000i q^{4} +(-2.18859 - 0.458323i) q^{5} +(2.99334 - 1.23988i) q^{6} +(1.49921 - 0.620992i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-5.30145 - 5.30145i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.23988 + 2.99334i) q^{3} +1.00000i q^{4} +(-2.18859 - 0.458323i) q^{5} +(2.99334 - 1.23988i) q^{6} +(1.49921 - 0.620992i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-5.30145 - 5.30145i) q^{9} +(1.22349 + 1.87165i) q^{10} +(-4.11919 + 1.70622i) q^{11} +(-2.99334 - 1.23988i) q^{12} -1.78934 q^{13} +(-1.49921 - 0.620992i) q^{14} +(4.08551 - 5.98294i) q^{15} -1.00000 q^{16} +(-3.35446 - 2.39741i) q^{17} +7.49739i q^{18} +(-0.157527 + 0.157527i) q^{19} +(0.458323 - 2.18859i) q^{20} +5.25759i q^{21} +(4.11919 + 1.70622i) q^{22} +(2.07076 + 4.99927i) q^{23} +(1.23988 + 2.99334i) q^{24} +(4.57988 + 2.00616i) q^{25} +(1.26525 + 1.26525i) q^{26} +(13.4622 - 5.57623i) q^{27} +(0.620992 + 1.49921i) q^{28} +(-2.00418 + 4.83853i) q^{29} +(-7.11947 + 1.34168i) q^{30} +(-1.60817 - 0.666124i) q^{31} +(0.707107 + 0.707107i) q^{32} -14.4456i q^{33} +(0.676740 + 4.06719i) q^{34} +(-3.56577 + 0.671978i) q^{35} +(5.30145 - 5.30145i) q^{36} +(-3.91254 + 9.44570i) q^{37} +0.222777 q^{38} +(2.21857 - 5.35610i) q^{39} +(-1.87165 + 1.22349i) q^{40} +(0.657761 + 1.58798i) q^{41} +(3.71768 - 3.71768i) q^{42} +(3.65649 - 3.65649i) q^{43} +(-1.70622 - 4.11919i) q^{44} +(9.17295 + 14.0325i) q^{45} +(2.07076 - 4.99927i) q^{46} -5.48034 q^{47} +(1.23988 - 2.99334i) q^{48} +(-3.08775 + 3.08775i) q^{49} +(-1.81989 - 4.65704i) q^{50} +(11.3354 - 7.06855i) q^{51} -1.78934i q^{52} +(-1.42918 - 1.42918i) q^{53} +(-13.4622 - 5.57623i) q^{54} +(9.79722 - 1.84631i) q^{55} +(0.620992 - 1.49921i) q^{56} +(-0.276217 - 0.666847i) q^{57} +(4.83853 - 2.00418i) q^{58} +(1.74254 + 1.74254i) q^{59} +(5.98294 + 4.08551i) q^{60} +(-3.62231 - 8.74502i) q^{61} +(0.666124 + 1.60817i) q^{62} +(-11.2401 - 4.65582i) q^{63} -1.00000i q^{64} +(3.91614 + 0.820096i) q^{65} +(-10.2146 + 10.2146i) q^{66} +14.4344i q^{67} +(2.39741 - 3.35446i) q^{68} -17.5320 q^{69} +(2.99654 + 2.04622i) q^{70} +(7.59937 + 3.14776i) q^{71} -7.49739 q^{72} +(1.40695 + 0.582777i) q^{73} +(9.44570 - 3.91254i) q^{74} +(-11.6836 + 11.2217i) q^{75} +(-0.157527 - 0.157527i) q^{76} +(-5.11596 + 5.11596i) q^{77} +(-5.35610 + 2.21857i) q^{78} +(-2.76144 + 1.14383i) q^{79} +(2.18859 + 0.458323i) q^{80} +24.7186i q^{81} +(0.657761 - 1.58798i) q^{82} +(-10.0574 - 10.0574i) q^{83} -5.25759 q^{84} +(6.24277 + 6.78438i) q^{85} -5.17105 q^{86} +(-11.9984 - 11.9984i) q^{87} +(-1.70622 + 4.11919i) q^{88} -9.77020i q^{89} +(3.43622 - 16.4087i) q^{90} +(-2.68259 + 1.11117i) q^{91} +(-4.99927 + 2.07076i) q^{92} +(3.98787 - 3.98787i) q^{93} +(3.87519 + 3.87519i) q^{94} +(0.416961 - 0.272565i) q^{95} +(-2.99334 + 1.23988i) q^{96} +(4.59847 + 1.90475i) q^{97} +4.36674 q^{98} +(30.8831 + 12.7922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Introduction

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