LMFDB - Embedded newform 272.2.l.b.69.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.2
Character	$\chi$	$=$	272.69
Dual form			272.2.l.b.205.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36107 - 0.384035i) q^{2} +(-0.873530 + 0.873530i) q^{3} +(1.70503 + 1.04540i) q^{4} +(2.72140 + 2.72140i) q^{5} +(1.52440 - 0.853471i) q^{6} +0.811757i q^{7} +(-1.91920 - 2.07766i) q^{8} +1.47389i q^{9} +(-2.65891 - 4.74914i) q^{10} +(-2.22499 - 2.22499i) q^{11} +(-2.40259 + 0.576211i) q^{12} +(0.0925117 - 0.0925117i) q^{13} +(0.311743 - 1.10486i) q^{14} -4.75446 q^{15} +(1.81428 + 3.56488i) q^{16} -1.00000 q^{17} +(0.566025 - 2.00607i) q^{18} +(0.715398 - 0.715398i) q^{19} +(1.79513 + 7.48504i) q^{20} +(-0.709095 - 0.709095i) q^{21} +(2.17390 + 3.88284i) q^{22} +5.62465i q^{23} +(3.49138 + 0.138413i) q^{24} +9.81208i q^{25} +(-0.161443 + 0.0903873i) q^{26} +(-3.90808 - 3.90808i) q^{27} +(-0.848610 + 1.38407i) q^{28} +(-2.76319 + 2.76319i) q^{29} +(6.47116 + 1.82588i) q^{30} +6.95416 q^{31} +(-1.10033 - 5.54881i) q^{32} +3.88719 q^{33} +(1.36107 + 0.384035i) q^{34} +(-2.20912 + 2.20912i) q^{35} +(-1.54080 + 2.51303i) q^{36} +(2.51540 + 2.51540i) q^{37} +(-1.24845 + 0.698970i) q^{38} +0.161624i q^{39} +(0.431213 - 10.8771i) q^{40} +0.212724i q^{41} +(0.692812 + 1.23745i) q^{42} +(-3.62804 - 3.62804i) q^{43} +(-1.46768 - 6.11968i) q^{44} +(-4.01105 + 4.01105i) q^{45} +(2.16006 - 7.65556i) q^{46} -4.20905 q^{47} +(-4.69886 - 1.52920i) q^{48} +6.34105 q^{49} +(3.76818 - 13.3550i) q^{50} +(0.873530 - 0.873530i) q^{51} +(0.254447 - 0.0610239i) q^{52} +(-8.32206 - 8.32206i) q^{53} +(3.81834 + 6.82002i) q^{54} -12.1102i q^{55} +(1.68655 - 1.55793i) q^{56} +1.24984i q^{57} +(4.82206 - 2.69974i) q^{58} +(9.73007 + 9.73007i) q^{59} +(-8.10651 - 4.97031i) q^{60} +(10.6241 - 10.6241i) q^{61} +(-9.46512 - 2.67064i) q^{62} -1.19644 q^{63} +(-0.633312 + 7.97489i) q^{64} +0.503523 q^{65} +(-5.29074 - 1.49282i) q^{66} +(-6.49328 + 6.49328i) q^{67} +(-1.70503 - 1.04540i) q^{68} +(-4.91331 - 4.91331i) q^{69} +(3.85515 - 2.15839i) q^{70} -5.47999i q^{71} +(3.06224 - 2.82869i) q^{72} +5.67133i q^{73} +(-2.45764 - 4.38964i) q^{74} +(-8.57115 - 8.57115i) q^{75} +(1.96765 - 0.471901i) q^{76} +(1.80615 - 1.80615i) q^{77} +(0.0620691 - 0.219981i) q^{78} +9.75031 q^{79} +(-4.76409 + 14.6389i) q^{80} +2.40598 q^{81} +(0.0816934 - 0.289532i) q^{82} +(-1.06975 + 1.06975i) q^{83} +(-0.467744 - 1.95032i) q^{84} +(-2.72140 - 2.72140i) q^{85} +(3.54473 + 6.33132i) q^{86} -4.82746i q^{87} +(-0.352554 + 8.89297i) q^{88} -2.37255i q^{89} +(6.99971 - 3.91894i) q^{90} +(0.0750970 + 0.0750970i) q^{91} +(-5.88001 + 9.59022i) q^{92} +(-6.07467 + 6.07467i) q^{93} +(5.72882 + 1.61642i) q^{94} +3.89377 q^{95} +(5.80822 + 3.88588i) q^{96} +13.9030 q^{97} +(-8.63063 - 2.43519i) q^{98} +(3.27939 - 3.27939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−1.36107	−	0.384035i	−0.962423	−	0.271554i
$2$	−1.36107	−	0.384035i	−0.962423	−	0.271554i
$3$	−0.873530	+	0.873530i	−0.504333	+	0.504333i	−0.912781	−	0.408448i	$-0.866070\pi$
$3$	−0.873530	+	0.873530i	−0.504333	+	0.504333i	0.408448	+	0.912781i	$0.366070\pi$
$4$	1.70503	+	1.04540i	0.852517	+	0.522700i
$5$	2.72140	+	2.72140i	1.21705	+	1.21705i	0.968660	+	0.248389i	$0.0799010\pi$
$5$	2.72140	+	2.72140i	1.21705	+	1.21705i	0.248389	+	0.968660i	$0.420099\pi$
$6$	1.52440	−	0.853471i	0.622335	−	0.348428i
$7$			0.811757i			0.306815i	0.988163	+	0.153408i	$0.0490248\pi$
$7$			0.811757i			0.306815i	−0.988163	+	0.153408i	$0.950975\pi$
$8$	−1.91920	−	2.07766i	−0.678541	−	0.734562i
$9$			1.47389i			0.491296i
$10$	−2.65891	−	4.74914i	−0.840822	−	1.50181i
$11$	−2.22499	−	2.22499i	−0.670859	−	0.670859i	0.287055	−	0.957914i	$-0.407324\pi$
$11$	−2.22499	−	2.22499i	−0.670859	−	0.670859i	−0.957914	+	0.287055i	$0.907324\pi$
$12$	−2.40259	+	0.576211i	−0.693567	+	0.166338i
$13$	0.0925117	−	0.0925117i	0.0256581	−	0.0256581i	−0.694161	−	0.719819i	$-0.744225\pi$
$13$	0.0925117	−	0.0925117i	0.0256581	−	0.0256581i	0.719819	+	0.694161i	$0.244225\pi$
$14$	0.311743	−	1.10486i	0.0833169	−	0.295286i
$15$	−4.75446			−1.22760
$16$	1.81428	+	3.56488i	0.453570	+	0.891220i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	0.566025	−	2.00607i	0.133413	−	0.472835i
$19$	0.715398	−	0.715398i	0.164124	−	0.164124i	−0.620267	−	0.784391i	$-0.712976\pi$
$19$	0.715398	−	0.715398i	0.164124	−	0.164124i	0.784391	+	0.620267i	$0.212976\pi$
$20$	1.79513	+	7.48504i	0.401404	+	1.67371i
$21$	−0.709095	−	0.709095i	−0.154737	−	0.154737i
$22$	2.17390	+	3.88284i	0.463476	+	0.827825i
$23$			5.62465i			1.17282i	0.810014	+	0.586411i	$0.199459\pi$
$23$			5.62465i			1.17282i	−0.810014	+	0.586411i	$0.800541\pi$
$24$	3.49138	+	0.138413i	0.712675	+	0.0282534i
$25$			9.81208i			1.96242i
$26$	−0.161443	+	0.0903873i	−0.0316615	+	0.0177264i
$27$	−3.90808	−	3.90808i	−0.752110	−	0.752110i
$28$	−0.848610	+	1.38407i	−0.160372	+	0.261565i
$29$	−2.76319	+	2.76319i	−0.513111	+	0.513111i	−0.915478	−	0.402367i	$-0.868187\pi$
$29$	−2.76319	+	2.76319i	−0.513111	+	0.513111i	0.402367	+	0.915478i	$0.368187\pi$
$30$	6.47116	+	1.82588i	1.18147	+	0.333358i
$31$	6.95416			1.24900			0.624502	−	0.781023i	$-0.285302\pi$
$31$	6.95416			1.24900			0.624502	+	0.781023i	$0.285302\pi$
$32$	−1.10033	−	5.54881i	−0.194512	−	0.980900i
$33$	3.88719			0.676673
$34$	1.36107	+	0.384035i	0.233422	+	0.0658615i
$35$	−2.20912	+	2.20912i	−0.373409	+	0.373409i
$36$	−1.54080	+	2.51303i	−0.256800	+	0.418839i
$37$	2.51540	+	2.51540i	0.413529	+	0.413529i	0.882966	−	0.469437i	$-0.155543\pi$
$37$	2.51540	+	2.51540i	0.413529	+	0.413529i	−0.469437	+	0.882966i	$0.655543\pi$
$38$	−1.24845	+	0.698970i	−0.202525	+	0.113388i
$39$			0.161624i			0.0258805i
$40$	0.431213	−	10.8771i	0.0681807	−	1.71982i
$41$			0.212724i			0.0332219i	0.999862	+	0.0166109i	$0.00528767\pi$
$41$			0.212724i			0.0332219i	−0.999862	+	0.0166109i	$0.994712\pi$
$42$	0.692812	+	1.23745i	0.106903	+	0.190942i
$43$	−3.62804	−	3.62804i	−0.553271	−	0.553271i	0.374113	−	0.927383i	$-0.377947\pi$
$43$	−3.62804	−	3.62804i	−0.553271	−	0.553271i	−0.927383	+	0.374113i	$0.877947\pi$
$44$	−1.46768	−	6.11968i	−0.221261	−	0.922576i
$45$	−4.01105	+	4.01105i	−0.597932	+	0.597932i
$46$	2.16006	−	7.65556i	0.318484	−	1.12875i
$47$	−4.20905			−0.613953			−0.306977	−	0.951717i	$-0.599317\pi$
$47$	−4.20905			−0.613953			−0.306977	+	0.951717i	$0.599317\pi$
$48$	−4.69886	−	1.52920i	−0.678222	−	0.220721i
$49$	6.34105			0.905864
$50$	3.76818	−	13.3550i	0.532902	−	1.88868i
$51$	0.873530	−	0.873530i	0.122319	−	0.122319i
$52$	0.254447	−	0.0610239i	0.0352855	−	0.00846250i
$53$	−8.32206	−	8.32206i	−1.14312	−	1.14312i	−0.987876	−	0.155248i	$-0.950382\pi$
$53$	−8.32206	−	8.32206i	−1.14312	−	1.14312i	−0.155248	−	0.987876i	$-0.549618\pi$
$54$	3.81834	+	6.82002i	0.519610	+	0.928087i
$55$		−	12.1102i		−	1.63294i
$56$	1.68655	−	1.55793i	0.225375	−	0.208187i
$57$			1.24984i			0.165546i
$58$	4.82206	−	2.69974i	0.633167	−	0.354493i
$59$	9.73007	+	9.73007i	1.26675	+	1.26675i	0.947759	+	0.318988i	$0.103343\pi$
$59$	9.73007	+	9.73007i	1.26675	+	1.26675i	0.318988	+	0.947759i	$0.396657\pi$
$60$	−8.10651	−	4.97031i	−1.04655	−	0.641664i
$61$	10.6241	−	10.6241i	1.36028	−	1.36028i	0.486729	−	0.873553i	$-0.338190\pi$
$61$	10.6241	−	10.6241i	1.36028	−	1.36028i	0.873553	−	0.486729i	$-0.161810\pi$
$62$	−9.46512	−	2.67064i	−1.20207	−	0.339172i
$63$	−1.19644			−0.150737
$64$	−0.633312	+	7.97489i	−0.0791640	+	0.996862i
$65$	0.503523			0.0624544
$66$	−5.29074	−	1.49282i	−0.651246	−	0.183753i
$67$	−6.49328	+	6.49328i	−0.793280	+	0.793280i	−0.982026	−	0.188746i	$-0.939558\pi$
$67$	−6.49328	+	6.49328i	−0.793280	+	0.793280i	0.188746	+	0.982026i	$0.439558\pi$
$68$	−1.70503	−	1.04540i	−0.206766	−	0.126773i
$69$	−4.91331	−	4.91331i	−0.591492	−	0.591492i
$70$	3.85515	−	2.15839i	0.460779	−	0.257977i
$71$		−	5.47999i		−	0.650355i	−0.945653	−	0.325177i	$-0.894576\pi$
$71$		−	5.47999i		−	0.650355i	0.945653	−	0.325177i	$-0.105424\pi$
$72$	3.06224	−	2.82869i	0.360888	−	0.333365i
$73$			5.67133i			0.663779i	0.943318	+	0.331890i	$0.107686\pi$
$73$			5.67133i			0.663779i	−0.943318	+	0.331890i	$0.892314\pi$
$74$	−2.45764	−	4.38964i	−0.285695	−	0.510285i
$75$	−8.57115	−	8.57115i	−0.989711	−	0.989711i
$76$	1.96765	−	0.471901i	0.225705	−	0.0541308i
$77$	1.80615	−	1.80615i	0.205830	−	0.205830i
$78$	0.0620691	−	0.219981i	0.00702794	−	0.0249080i
$79$	9.75031			1.09700			0.548498	−	0.836152i	$-0.315200\pi$
$79$	9.75031			1.09700			0.548498	+	0.836152i	$0.315200\pi$
$80$	−4.76409	+	14.6389i	−0.532641	+	1.63668i
$81$	2.40598			0.267331
$82$	0.0816934	−	0.289532i	0.00902152	−	0.0319735i
$83$	−1.06975	+	1.06975i	−0.117420	+	0.117420i	−0.763375	−	0.645955i	$-0.776459\pi$
$83$	−1.06975	+	1.06975i	−0.117420	+	0.117420i	0.645955	+	0.763375i	$0.276459\pi$
$84$	−0.467744	−	1.95032i	−0.0510350	−	0.212797i
$85$	−2.72140	−	2.72140i	−0.295178	−	0.295178i
$86$	3.54473	+	6.33132i	0.382238	+	0.682723i
$87$		−	4.82746i		−	0.517558i
$88$	−0.352554	+	8.89297i	−0.0375824	+	0.947993i
$89$		−	2.37255i		−	0.251490i	−0.992063	−	0.125745i	$-0.959868\pi$
$89$		−	2.37255i		−	0.251490i	0.992063	−	0.125745i	$-0.0401321\pi$
$90$	6.99971	−	3.91894i	0.737834	−	0.413093i
$91$	0.0750970	+	0.0750970i	0.00787231	+	0.00787231i
$92$	−5.88001	+	9.59022i	−0.613033	+	0.999850i
$93$	−6.07467	+	6.07467i	−0.629914	+	0.629914i
$94$	5.72882	+	1.61642i	0.590883	+	0.166721i
$95$	3.89377			0.399493
$96$	5.80822	+	3.88588i	0.592799	+	0.396601i
$97$	13.9030			1.41164			0.705819	−	0.708392i	$-0.250579\pi$
$97$	13.9030			1.41164			0.705819	+	0.708392i	$0.250579\pi$
$98$	−8.63063	−	2.43519i	−0.871825	−	0.245991i
$99$	3.27939	−	3.27939i	0.329591	−	0.329591i
$100$	−10.2575	+	16.7299i	−1.02575	+	1.67299i
$101$	−5.43609	−	5.43609i	−0.540911	−	0.540911i	0.382885	−	0.923796i	$-0.374931\pi$
$101$	−5.43609	−	5.43609i	−0.540911	−	0.540911i	−0.923796	+	0.382885i	$0.874931\pi$
$102$	−1.52440	+	0.853471i	−0.150938	+	0.0845063i
$103$		−	11.8030i		−	1.16298i	−0.813553	−	0.581491i	$-0.802470\pi$
$103$		−	11.8030i		−	1.16298i	0.813553	−	0.581491i	$-0.197530\pi$
$104$	−0.369756	−	0.0146587i	−0.0362576	−	0.00143740i
$105$		−	3.85947i		−	0.376645i
$106$	8.13096	+	14.5229i	0.789749	+	1.41059i
$107$	2.55367	+	2.55367i	0.246872	+	0.246872i	0.819686	−	0.572814i	$-0.194148\pi$
$107$	2.55367	+	2.55367i	0.246872	+	0.246872i	−0.572814	+	0.819686i	$0.694148\pi$
$108$	−2.57791	−	10.7489i	−0.248059	−	1.03431i
$109$	11.7765	−	11.7765i	1.12798	−	1.12798i	0.137476	−	0.990505i	$-0.456101\pi$
$109$	11.7765	−	11.7765i	1.12798	−	1.12798i	0.990505	−	0.137476i	$-0.0438989\pi$
$110$	−4.65074	+	16.4828i	−0.443430	+	1.57158i
$111$	−4.39455			−0.417113
$112$	−2.89382	+	1.47276i	−0.273440	+	0.139162i
$113$	17.8118			1.67559			0.837795	−	0.545984i	$-0.183844\pi$
$113$	17.8118			1.67559			0.837795	+	0.545984i	$0.183844\pi$
$114$	0.479984	−	1.70113i	0.0449546	−	0.159325i
$115$	−15.3070	+	15.3070i	−1.42738	+	1.42738i
$116$	−7.59996	+	1.82269i	−0.705639	+	0.169233i
$117$	0.136352	+	0.136352i	0.0126057	+	0.0126057i
$118$	−9.50664	−	16.9800i	−0.875157	−	1.56314i
$119$		−	0.811757i		−	0.0744137i
$120$	9.12478	+	9.87813i	0.832974	+	0.901746i
$121$		−	1.09886i		−	0.0998962i
$122$	−18.5403	+	10.3802i	−1.67856	+	0.939777i
$123$	−0.185821	−	0.185821i	−0.0167549	−	0.0167549i
$124$	11.8571	+	7.26987i	1.06480	+	0.652854i
$125$	−13.0956	+	13.0956i	−1.17131	+	1.17131i
$126$	1.62844	+	0.459475i	0.145073	+	0.0409333i
$127$	9.04244			0.802386			0.401193	−	0.915993i	$-0.368596\pi$
$127$	9.04244			0.802386			0.401193	+	0.915993i	$0.368596\pi$
$128$	3.92462	−	10.6112i	0.346891	−	0.937906i
$129$	6.33840			0.558065
$130$	−0.685332	−	0.193371i	−0.0601076	−	0.0169597i
$131$	−11.6300	+	11.6300i	−1.01612	+	1.01612i	−0.0162519	+	0.999868i	$0.505173\pi$
$131$	−11.6300	+	11.6300i	−1.01612	+	1.01612i	−0.999868	+	0.0162519i	$0.994827\pi$
$132$	6.62779	+	4.06366i	0.576875	+	0.353696i
$133$	0.580729	+	0.580729i	0.0503556	+	0.0503556i
$134$	11.3315	−	6.34417i	0.978889	−	0.548053i
$135$		−	21.2709i		−	1.83071i
$136$	1.91920	+	2.07766i	0.164570	+	0.178158i
$137$		−	2.50865i		−	0.214328i	−0.994241	−	0.107164i	$-0.965823\pi$
$137$		−	2.50865i		−	0.214328i	0.994241	−	0.107164i	$-0.0341771\pi$
$138$	4.80048	+	8.57424i	0.408644	+	0.729888i
$139$	−6.56319	−	6.56319i	−0.556682	−	0.556682i	0.371679	−	0.928361i	$-0.378782\pi$
$139$	−6.56319	−	6.56319i	−0.556682	−	0.556682i	−0.928361	+	0.371679i	$0.878782\pi$
$140$	−6.07604	+	1.45721i	−0.513519	+	0.123157i
$141$	3.67673	−	3.67673i	0.309637	−	0.309637i
$142$	−2.10451	+	7.45866i	−0.176606	+	0.625917i
$143$	−0.411675			−0.0344260
$144$	−5.25424	+	2.67405i	−0.437853	+	0.222838i
$145$	−15.0395			−1.24896
$146$	2.17799	−	7.71909i	0.180252	−	0.638836i
$147$	−5.53910	+	5.53910i	−0.456857	+	0.456857i
$148$	1.65925	+	6.91844i	0.136389	+	0.568692i
$149$	3.99916	+	3.99916i	0.327624	+	0.327624i	0.851682	−	0.524059i	$-0.175583\pi$
$149$	3.99916	+	3.99916i	0.327624	+	0.327624i	−0.524059	+	0.851682i	$0.675583\pi$
$150$	8.37433	+	14.9576i	0.683761	+	1.22128i
$151$			19.3467i			1.57442i	0.616688	+	0.787208i	$0.288474\pi$
$151$			19.3467i			1.57442i	−0.616688	+	0.787208i	$0.711526\pi$
$152$	−2.85935	−	0.113356i	−0.231924	−	0.00919442i
$153$		−	1.47389i		−	0.119157i
$154$	−3.15193	+	1.76468i	−0.253989	+	0.142202i
$155$	18.9251	+	18.9251i	1.52010	+	1.52010i
$156$	−0.168961	+	0.275574i	−0.0135277	+	0.0220635i
$157$	−7.55371	+	7.55371i	−0.602852	+	0.602852i	−0.941068	−	0.338217i	$-0.890176\pi$
$157$	−7.55371	+	7.55371i	−0.602852	+	0.602852i	0.338217	+	0.941068i	$0.390176\pi$
$158$	−13.2709	−	3.74446i	−1.05577	−	0.297893i
$159$	14.5391			1.15303
$160$	12.1061	−	18.0950i	0.957072	−	1.43053i
$161$	−4.56585			−0.359840
$162$	−3.27471	−	0.923981i	−0.257286	−	0.0725948i
$163$	8.28277	−	8.28277i	0.648756	−	0.648756i	−0.303936	−	0.952692i	$-0.598301\pi$
$163$	8.28277	−	8.28277i	0.648756	−	0.648756i	0.952692	+	0.303936i	$0.0983009\pi$
$164$	−0.222381	+	0.362701i	−0.0173650	+	0.0283222i
$165$	10.5786	+	10.5786i	0.823544	+	0.823544i
$166$	1.86683	−	1.04519i	0.144894	−	0.0811221i
$167$		−	8.56391i		−	0.662695i	−0.943509	−	0.331348i	$-0.892497\pi$
$167$		−	8.56391i		−	0.662695i	0.943509	−	0.331348i	$-0.107503\pi$
$168$	−0.112358	+	2.83415i	−0.00866858	+	0.218660i
$169$			12.9829i			0.998683i
$170$	2.65891	+	4.74914i	0.203929	+	0.364243i
$171$	1.05442	+	1.05442i	0.0806333	+	0.0806333i
$172$	−2.39318	−	9.97868i	−0.182478	−	0.760867i
$173$	13.6850	−	13.6850i	1.04045	−	1.04045i	0.0413075	−	0.999146i	$-0.486848\pi$
$173$	13.6850	−	13.6850i	1.04045	−	1.04045i	0.999146	−	0.0413075i	$-0.0131523\pi$
$174$	−1.85391	+	6.57051i	−0.140545	+	0.498109i
$175$	−7.96503			−0.602100
$176$	3.89506	−	11.9686i	0.293601	−	0.902165i
$177$	−16.9990			−1.27772
$178$	−0.911144	+	3.22922i	−0.0682931	+	0.242040i
$179$	13.4675	−	13.4675i	1.00661	−	1.00661i	0.00663069	−	0.999978i	$-0.497889\pi$
$179$	13.4675	−	13.4675i	1.00661	−	1.00661i	0.999978	−	0.00663069i	$-0.00211063\pi$
$180$	−11.0321	+	2.64583i	−0.822286	+	0.197208i
$181$	−15.2556	−	15.2556i	−1.13394	−	1.13394i	−0.989515	−	0.144428i	$-0.953866\pi$
$181$	−15.2556	−	15.2556i	−1.13394	−	1.13394i	−0.144428	−	0.989515i	$-0.546134\pi$
$182$	−0.0733726	−	0.131052i	−0.00543874	−	0.00971425i
$183$			18.5610i			1.37207i
$184$	11.6861	−	10.7949i	0.861510	−	0.795807i
$185$			13.6908i			1.00657i
$186$	10.6010	−	5.93518i	0.777300	−	0.435188i
$187$	2.22499	+	2.22499i	0.162707	+	0.162707i
$188$	−7.17657	−	4.40014i	−0.523405	−	0.320913i
$189$	3.17241	−	3.17241i	0.230759	−	0.230759i
$190$	−5.29971	−	1.49535i	−0.384481	−	0.108484i
$191$	4.20985			0.304614			0.152307	−	0.988333i	$-0.451330\pi$
$191$	4.20985			0.304614			0.152307	+	0.988333i	$0.451330\pi$
$192$	−6.41309	−	7.51953i	−0.462825	−	0.542675i
$193$	−22.8254			−1.64301			−0.821505	−	0.570201i	$-0.806865\pi$
$193$	−22.8254			−1.64301			−0.821505	+	0.570201i	$0.806865\pi$
$194$	−18.9230	−	5.33925i	−1.35859	−	0.383336i
$195$	−0.439843	+	0.439843i	−0.0314978	+	0.0314978i
$196$	10.8117	+	6.62893i	0.772265	+	0.473495i
$197$	−6.67328	−	6.67328i	−0.475452	−	0.475452i	0.428222	−	0.903674i	$-0.359140\pi$
$197$	−6.67328	−	6.67328i	−0.475452	−	0.475452i	−0.903674	+	0.428222i	$0.859140\pi$
$198$	−5.72288	+	3.20408i	−0.406707	+	0.227704i
$199$			14.3844i			1.01968i	0.860268	+	0.509842i	$0.170296\pi$
$199$			14.3844i			1.01968i	−0.860268	+	0.509842i	$0.829704\pi$
$200$	20.3861	−	18.8314i	1.44152	−	1.33158i
$201$		−	11.3441i		−	0.800155i
$202$	5.31126	+	9.48656i	0.373699	+	0.667472i
$203$	−2.24304	−	2.24304i	−0.157430	−	0.157430i
$204$	2.40259	−	0.576211i	0.168215	−	0.0403429i
$205$	−0.578907	+	0.578907i	−0.0404326	+	0.0404326i
$206$	−4.53276	+	16.0647i	−0.315812	+	1.11928i
$207$	−8.29012			−0.576203
$208$	0.497635	+	0.161951i	0.0345048	+	0.0112293i
$209$	−3.18350			−0.220208
$210$	−1.48217	+	5.25301i	−0.102279	+	0.362492i
$211$	−1.78440	+	1.78440i	−0.122843	+	0.122843i	−0.765856	−	0.643012i	$-0.777684\pi$
$211$	−1.78440	+	1.78440i	−0.122843	+	0.122843i	0.643012	+	0.765856i	$0.277684\pi$
$212$	−5.48952	−	22.8893i	−0.377022	−	1.57204i
$213$	4.78693	+	4.78693i	0.327995	+	0.327995i
$214$	−2.49503	−	4.45642i	−0.170556	−	0.304635i
$215$		−	19.7467i		−	1.34672i
$216$	−0.619244	+	15.6200i	−0.0421342	+	1.06281i
$217$			5.64509i			0.383214i
$218$	−20.5512	+	11.5060i	−1.39190	+	0.779287i
$219$	−4.95408	−	4.95408i	−0.334766	−	0.334766i
$220$	12.6600	−	20.6483i	0.853535	−	1.39211i
$221$	−0.0925117	+	0.0925117i	−0.00622301	+	0.00622301i
$222$	5.98131	+	1.68766i	0.401439	+	0.113269i
$223$	11.0194			0.737915			0.368958	−	0.929446i	$-0.379715\pi$
$223$	11.0194			0.737915			0.368958	+	0.929446i	$0.379715\pi$
$224$	4.50429	−	0.893199i	0.300955	−	0.0596794i
$225$	−14.4619			−0.964128
$226$	−24.2431	−	6.84035i	−1.61263	−	0.455013i
$227$	10.5447	−	10.5447i	0.699876	−	0.699876i	−0.264508	−	0.964384i	$-0.585209\pi$
$227$	10.5447	−	10.5447i	0.699876	−	0.699876i	0.964384	+	0.264508i	$0.0852095\pi$
$228$	−1.30659	+	2.13103i	−0.0865307	+	0.141131i
$229$	−12.0869	−	12.0869i	−0.798723	−	0.798723i	0.184171	−	0.982894i	$-0.441040\pi$
$229$	−12.0869	−	12.0869i	−0.798723	−	0.798723i	−0.982894	+	0.184171i	$0.941040\pi$
$230$	26.7123	−	14.9555i	1.76136	−	0.986134i
$231$			3.15545i			0.207614i
$232$	11.0441	+	0.437833i	0.725079	+	0.0287452i
$233$			4.07680i			0.267080i	0.991043	+	0.133540i	$0.0426345\pi$
$233$			4.07680i			0.267080i	−0.991043	+	0.133540i	$0.957365\pi$
$234$	−0.133221	−	0.237949i	−0.00870892	−	0.0155552i
$235$	−11.4545	−	11.4545i	−0.747211	−	0.747211i
$236$	6.41829	+	26.7619i	0.417795	+	1.74205i
$237$	−8.51719	+	8.51719i	−0.553251	+	0.553251i
$238$	−0.311743	+	1.10486i	−0.0202073	+	0.0716174i
$239$	22.2734			1.44075			0.720374	−	0.693585i	$-0.243970\pi$
$239$	22.2734			1.44075			0.720374	+	0.693585i	$0.243970\pi$
$240$	−8.62593	−	16.9491i	−0.556801	−	1.09406i
$241$	−12.5002			−0.805206			−0.402603	−	0.915375i	$-0.631895\pi$
$241$	−12.5002			−0.805206			−0.402603	+	0.915375i	$0.631895\pi$
$242$	−0.422000	+	1.49563i	−0.0271272	+	0.0961424i
$243$	9.62254	−	9.62254i	0.617286	−	0.617286i
$244$	29.2210	−	7.00806i	1.87068	−	0.448645i
$245$	17.2566	+	17.2566i	1.10248	+	1.10248i
$246$	0.181554	+	0.324277i	0.0115754	+	0.0206751i
$247$		−	0.132365i		−	0.00842220i
$248$	−13.3465	−	14.4484i	−0.847501	−	0.917472i
$249$		−	1.86892i		−	0.118438i
$250$	22.8533	−	12.7949i	1.44537	−	0.809221i
$251$	8.13968	+	8.13968i	0.513772	+	0.513772i	0.915680	−	0.401908i	$-0.131653\pi$
$251$	8.13968	+	8.13968i	0.513772	+	0.513772i	−0.401908	+	0.915680i	$0.631653\pi$
$252$	−2.03997	−	1.25076i	−0.128506	−	0.0787903i
$253$	12.5148	−	12.5148i	0.786798	−	0.786798i
$254$	−12.3074	−	3.47261i	−0.772235	−	0.217891i
$255$	4.75446			0.297736
$256$	−9.41676	+	12.9354i	−0.588548	+	0.808462i
$257$	−12.8905			−0.804085			−0.402042	−	0.915621i	$-0.631700\pi$
$257$	−12.8905			−0.804085			−0.402042	+	0.915621i	$0.631700\pi$
$258$	−8.62702	−	2.43417i	−0.537095	−	0.151545i
$259$	−2.04189	+	2.04189i	−0.126877	+	0.126877i
$260$	0.858524	+	0.526383i	0.0532434	+	0.0326449i
$261$	−4.07263	−	4.07263i	−0.252090	−	0.252090i
$262$	20.2956	−	11.3630i	1.25387	−	0.702006i
$263$			0.308956i			0.0190510i	0.999955	+	0.00952552i	$0.00303211\pi$
$263$			0.308956i			0.0190510i	−0.999955	+	0.00952552i	$0.996968\pi$
$264$	−7.46031	−	8.07624i	−0.459150	−	0.497058i
$265$		−	45.2954i		−	2.78247i
$266$	−0.567394	−	1.01343i	−0.0347892	−	0.0621377i
$267$	2.07250	+	2.07250i	0.126835	+	0.126835i
$268$	−17.8593	+	4.28319i	−1.09093	+	0.261638i
$269$	−8.79905	+	8.79905i	−0.536488	+	0.536488i	−0.922496	−	0.386008i	$-0.873854\pi$
$269$	−8.79905	+	8.79905i	−0.536488	+	0.536488i	0.386008	+	0.922496i	$0.373854\pi$
$270$	−8.16878	+	28.9513i	−0.497136	+	1.76192i
$271$	−30.5971			−1.85864			−0.929322	−	0.369271i	$-0.879608\pi$
$271$	−30.5971			−1.85864			−0.929322	+	0.369271i	$0.879608\pi$
$272$	−1.81428	−	3.56488i	−0.110007	−	0.216153i
$273$	−0.131199			−0.00794053
$274$	−0.963410	+	3.41445i	−0.0582017	+	0.206275i
$275$	21.8318	−	21.8318i	1.31650	−	1.31650i
$276$	−3.24099	−	13.5137i	−0.195085	−	0.813430i
$277$	−8.58238	−	8.58238i	−0.515665	−	0.515665i	0.400592	−	0.916257i	$-0.368805\pi$
$277$	−8.58238	−	8.58238i	−0.515665	−	0.515665i	−0.916257	+	0.400592i	$0.868805\pi$
$278$	6.41248	+	11.4535i	0.384595	+	0.686933i
$279$			10.2497i			0.613631i
$280$	8.82954	+	0.350040i	0.527666	+	0.0209189i
$281$		−	14.0187i		−	0.836284i	−0.908382	−	0.418142i	$-0.862681\pi$
$281$		−	14.0187i		−	0.836284i	0.908382	−	0.418142i	$-0.137319\pi$
$282$	−6.41629	+	3.59230i	−0.382085	+	0.213919i
$283$	17.7439	+	17.7439i	1.05477	+	1.05477i	0.998411	+	0.0563557i	$0.0179481\pi$
$283$	17.7439	+	17.7439i	1.05477	+	1.05477i	0.0563557	+	0.998411i	$0.482052\pi$
$284$	5.72877	−	9.34356i	0.339940	−	0.554438i
$285$	−3.40133	+	3.40133i	−0.201477	+	0.201477i
$286$	0.560319	+	0.158098i	0.0331324	+	0.00934851i
$287$	−0.172680			−0.0101930
$288$	8.17833	−	1.62176i	0.481913	−	0.0955633i
$289$	1.00000			0.0588235
$290$	20.4698	+	5.77570i	1.20203	+	0.339161i
$291$	−12.1447	+	12.1447i	−0.711936	+	0.711936i
$292$	−5.92880	+	9.66981i	−0.346957	+	0.565883i
$293$	15.6639	+	15.6639i	0.915093	+	0.915093i	0.996667	−	0.0815747i	$-0.0259949\pi$
$293$	15.6639	+	15.6639i	0.915093	+	0.915093i	−0.0815747	+	0.996667i	$0.525995\pi$
$294$	9.66632	−	5.41190i	0.563751	−	0.315629i
$295$			52.9589i			3.08339i
$296$	0.398571	−	10.0537i	0.0231665	−	0.584359i
$297$			17.3909i			1.00912i
$298$	−3.90732	−	6.97896i	−0.226345	−	0.404280i
$299$	0.520346	+	0.520346i	0.0300924	+	0.0300924i
$300$	−5.65383	−	23.5744i	−0.326424	−	1.36107i
$301$	2.94509	−	2.94509i	0.169752	−	0.169752i
$302$	7.42983	−	26.3323i	0.427539	−	1.51525i
$303$	9.49717			0.545598
$304$	3.84824	+	1.25238i	0.220712	+	0.0718287i
$305$	57.8252			3.31106
$306$	−0.566025	+	2.00607i	−0.0323575	+	0.114679i
$307$	−24.2750	+	24.2750i	−1.38545	+	1.38545i	−0.550830	+	0.834618i	$0.685689\pi$
$307$	−24.2750	+	24.2750i	−1.38545	+	1.38545i	−0.834618	+	0.550830i	$0.814311\pi$
$308$	4.96769	−	1.19140i	0.283061	−	0.0678863i
$309$	10.3103	+	10.3103i	0.586530	+	0.586530i
$310$	−18.4905	−	33.0263i	−1.05019	−	1.87577i
$311$		−	9.11346i		−	0.516777i	−0.966041	−	0.258388i	$-0.916809\pi$
$311$		−	9.11346i		−	0.516777i	0.966041	−	0.258388i	$-0.0831914\pi$
$312$	0.335798	−	0.310189i	0.0190108	−	0.0175610i
$313$			23.9198i			1.35203i	0.736889	+	0.676014i	$0.236294\pi$
$313$			23.9198i			1.35203i	−0.736889	+	0.676014i	$0.763706\pi$
$314$	13.1820	−	7.38025i	0.743905	−	0.416492i
$315$	−3.25600	−	3.25600i	−0.183455	−	0.183455i
$316$	16.6246	+	10.1930i	0.935208	+	0.573399i
$317$	−2.76228	+	2.76228i	−0.155145	+	0.155145i	−0.780411	−	0.625266i	$-0.784990\pi$
$317$	−2.76228	+	2.76228i	−0.155145	+	0.155145i	0.625266	+	0.780411i	$0.284990\pi$
$318$	−19.7888	−	5.58354i	−1.10970	−	0.313110i
$319$	12.2961			0.688450
$320$	−23.4264	+	19.9794i	−1.30958	+	1.11688i
$321$	−4.46141			−0.249012
$322$	6.21445	+	1.75345i	0.346318	+	0.0977158i
$323$	−0.715398	+	0.715398i	−0.0398058	+	0.0398058i
$324$	4.10228	+	2.51521i	0.227904	+	0.139734i
$325$	0.907732	+	0.907732i	0.0503519	+	0.0503519i
$326$	−14.4543	+	8.09257i	−0.800550	+	0.448206i
$327$			20.5742i			1.13776i
$328$	0.441967	−	0.408260i	0.0244035	−	0.0225424i
$329$		−	3.41673i		−	0.188370i
$330$	−10.3357	−	18.4608i	−0.568961	−	1.01623i
$331$	−14.0750	−	14.0750i	−0.773633	−	0.773633i	0.205107	−	0.978740i	$-0.434246\pi$
$331$	−14.0750	−	14.0750i	−0.773633	−	0.773633i	−0.978740	+	0.205107i	$0.934246\pi$
$332$	−2.94228	+	0.705645i	−0.161478	+	0.0387273i
$333$	−3.70742	+	3.70742i	−0.203165	+	0.203165i
$334$	−3.28884	+	11.6561i	−0.179957	+	0.637793i
$335$	−35.3417			−1.93092
$336$	1.24134	−	3.81434i	0.0677207	−	0.208089i
$337$	10.1722			0.554117			0.277059	−	0.960853i	$-0.410640\pi$
$337$	10.1722			0.554117			0.277059	+	0.960853i	$0.410640\pi$
$338$	4.98588	−	17.6706i	0.271196	−	0.961156i
$339$	−15.5591	+	15.5591i	−0.845056	+	0.845056i
$340$	−1.79513	−	7.48504i	−0.0973548	−	0.405933i
$341$	−15.4729	−	15.4729i	−0.837906	−	0.837906i
$342$	−1.03020	−	1.84007i	−0.0557071	−	0.0994997i
$343$			10.8297i			0.584749i
$344$	−0.574871	+	14.5008i	−0.0309950	+	0.781829i
$345$		−	26.7422i		−	1.43975i
$346$	−23.8819	+	13.3708i	−1.28390	+	0.718818i
$347$	7.47499	+	7.47499i	0.401278	+	0.401278i	0.878683	−	0.477405i	$-0.158423\pi$
$347$	7.47499	+	7.47499i	0.401278	+	0.401278i	−0.477405	+	0.878683i	$0.658423\pi$
$348$	5.04662	−	8.23098i	0.270527	−	0.441227i
$349$	0.208207	−	0.208207i	0.0111451	−	0.0111451i	−0.701512	−	0.712657i	$-0.747491\pi$
$349$	0.208207	−	0.208207i	0.0111451	−	0.0111451i	0.712657	+	0.701512i	$0.247491\pi$
$350$	10.8410	+	3.05885i	0.579475	+	0.163502i
$351$	−0.723086			−0.0385955
$352$	−9.89781	+	14.7942i	−0.527555	+	0.788536i
$353$	−23.9216			−1.27322			−0.636610	−	0.771186i	$-0.719664\pi$
$353$	−23.9216			−1.27322			−0.636610	+	0.771186i	$0.719664\pi$
$354$	23.1369	+	6.52822i	1.22971	+	0.346971i
$355$	14.9133	−	14.9133i	0.791514	−	0.791514i
$356$	2.48026	−	4.04528i	0.131454	−	0.214400i
$357$	0.709095	+	0.709095i	0.0375293	+	0.0375293i
$358$	−23.5022	+	13.1583i	−1.24213	+	0.695435i
$359$			17.0909i			0.902022i	0.892518	+	0.451011i	$0.148937\pi$
$359$			17.0909i			0.902022i	−0.892518	+	0.451011i	$0.851063\pi$
$360$	16.0316	+	0.635560i	0.844940	+	0.0334969i
$361$			17.9764i			0.946127i
$362$	14.9053	+	26.6227i	0.783407	+	1.39926i
$363$	0.959886	+	0.959886i	0.0503810	+	0.0503810i
$364$	0.0495366	+	0.206549i	0.00259642	+	0.0108261i
$365$	−15.4340	+	15.4340i	−0.807852	+	0.807852i
$366$	7.12808	−	25.2629i	0.372591	−	1.32051i
$367$	−8.51104			−0.444273			−0.222136	−	0.975016i	$-0.571303\pi$
$367$	−8.51104			−0.444273			−0.222136	+	0.975016i	$0.571303\pi$
$368$	−20.0512	+	10.2047i	−1.04524	+	0.531957i
$369$	−0.313531			−0.0163218
$370$	5.25776	−	18.6342i	0.273338	−	0.968747i
$371$	6.75549	−	6.75549i	0.350728	−	0.350728i
$372$	−16.7080	+	4.00707i	−0.866268	+	0.207757i
$373$	−6.22310	−	6.22310i	−0.322220	−	0.322220i	0.527398	−	0.849618i	$-0.323168\pi$
$373$	−6.22310	−	6.22310i	−0.322220	−	0.322220i	−0.849618	+	0.527398i	$0.823168\pi$
$374$	−2.17390	−	3.88284i	−0.112409	−	0.200777i
$375$		−	22.8788i		−	1.18146i
$376$	8.07803	+	8.74496i	0.416592	+	0.450987i
$377$			0.511254i			0.0263309i
$378$	−5.53620	+	3.09956i	−0.284751	+	0.159424i
$379$	−14.2314	−	14.2314i	−0.731020	−	0.731020i	0.239802	−	0.970822i	$-0.422918\pi$
$379$	−14.2314	−	14.2314i	−0.731020	−	0.731020i	−0.970822	+	0.239802i	$0.922918\pi$
$380$	6.63902	+	4.07055i	0.340574	+	0.208815i
$381$	−7.89884	+	7.89884i	−0.404670	+	0.404670i
$382$	−5.72991	−	1.61673i	−0.293168	−	0.0827192i
$383$	−10.1004			−0.516106			−0.258053	−	0.966131i	$-0.583081\pi$
$383$	−10.1004			−0.516106			−0.258053	+	0.966131i	$0.583081\pi$
$384$	5.84092	+	12.6975i	0.298068	+	0.647965i
$385$	9.83053			0.501010
$386$	31.0670	+	8.76577i	1.58127	+	0.446166i
$387$	5.34733	−	5.34733i	0.271820	−	0.271820i
$388$	23.7051	+	14.5342i	1.20345	+	0.737863i
$389$	5.23187	+	5.23187i	0.265266	+	0.265266i	0.827189	−	0.561923i	$-0.189938\pi$
$389$	5.23187	+	5.23187i	0.265266	+	0.265266i	−0.561923	+	0.827189i	$0.689938\pi$
$390$	0.767573	−	0.429743i	0.0388676	−	0.0217609i
$391$		−	5.62465i		−	0.284451i
$392$	−12.1698	−	13.1745i	−0.614666	−	0.665414i
$393$		−	20.3184i		−	1.02493i
$394$	6.52004	+	11.6456i	0.328475	+	0.586696i
$395$	26.5345	+	26.5345i	1.33510	+	1.33510i
$396$	9.01973	−	2.16320i	0.453259	−	0.108705i
$397$	8.77244	−	8.77244i	0.440276	−	0.440276i	−0.451829	−	0.892105i	$-0.649228\pi$
$397$	8.77244	−	8.77244i	0.440276	−	0.440276i	0.892105	+	0.451829i	$0.149228\pi$
$398$	5.52412	−	19.5782i	0.276899	−	0.981368i
$399$	−1.01457			−0.0507920
$400$	−34.9789	+	17.8019i	−1.74895	+	0.890094i
$401$	−6.72905			−0.336033			−0.168016	−	0.985784i	$-0.553736\pi$
$401$	−6.72905			−0.336033			−0.168016	+	0.985784i	$0.553736\pi$
$402$	−4.35655	+	15.4402i	−0.217285	+	0.770087i
$403$	0.643341	−	0.643341i	0.0320471	−	0.0320471i
$404$	−3.58583	−	14.9516i	−0.178402	−	0.743870i
$405$	6.54765	+	6.54765i	0.325355	+	0.325355i
$406$	2.19153	+	3.91434i	0.108764	+	0.194265i
$407$		−	11.1935i		−	0.554839i
$408$	−3.49138	−	0.138413i	−0.172849	−	0.00685246i
$409$			0.690736i			0.0341547i	0.999854	+	0.0170773i	$0.00543615\pi$
$409$			0.690736i			0.0341547i	−0.999854	+	0.0170773i	$0.994564\pi$
$410$	1.01026	−	0.565614i	0.0498929	−	0.0279337i
$411$	2.19138	+	2.19138i	0.108093	+	0.108093i
$412$	12.3388	−	20.1245i	0.607890	−	0.991462i
$413$	−7.89845	+	7.89845i	−0.388657	+	0.388657i
$414$	11.2834	+	3.18370i	0.554551	+	0.156470i
$415$	−5.82245			−0.285813
$416$	−0.615123	−	0.411536i	−0.0301589	−	0.0201772i
$417$	11.4663			0.561506
$418$	4.33298	+	1.22258i	0.211933	+	0.0597982i
$419$	3.54963	−	3.54963i	0.173411	−	0.173411i	−0.615065	−	0.788476i	$-0.710870\pi$
$419$	3.54963	−	3.54963i	0.173411	−	0.173411i	0.788476	+	0.615065i	$0.210870\pi$
$420$	4.03468	−	6.58052i	0.196872	−	0.321097i
$421$	−7.89011	−	7.89011i	−0.384540	−	0.384540i	0.488194	−	0.872735i	$-0.337656\pi$
$421$	−7.89011	−	7.89011i	−0.384540	−	0.384540i	−0.872735	+	0.488194i	$0.837656\pi$
$422$	3.11398	−	1.74343i	0.151586	−	0.0848688i
$423$		−	6.20368i		−	0.301633i
$424$	−1.31865	+	33.2621i	−0.0640393	+	1.61535i
$425$		−	9.81208i		−	0.475956i
$426$	−4.67701	−	8.35371i	−0.226602	−	0.404739i
$427$	8.62422	+	8.62422i	0.417355	+	0.417355i
$428$	1.68449	+	7.02369i	0.0814228	+	0.339503i
$429$	0.359610	−	0.359610i	0.0173622	−	0.0173622i
$430$	−7.58343	+	26.8767i	−0.365706	+	1.29611i
$431$	−17.5928			−0.847417			−0.423708	−	0.905799i	$-0.639272\pi$
$431$	−17.5928			−0.847417			−0.423708	+	0.905799i	$0.639272\pi$
$432$	6.84148	−	21.0222i	0.329161	−	1.01143i
$433$	32.0867			1.54199			0.770993	−	0.636843i	$-0.219760\pi$
$433$	32.0867			1.54199			0.770993	+	0.636843i	$0.219760\pi$
$434$	2.16791	−	7.68338i	0.104063	−	0.368814i
$435$	13.1375	−	13.1375i	0.629893	−	0.629893i
$436$	32.3904	−	7.76817i	1.55122	−	0.372028i
$437$	4.02386	+	4.02386i	0.192488	+	0.192488i
$438$	4.84032	+	8.64540i	0.231279	+	0.413093i
$439$		−	21.5068i		−	1.02646i	−0.858250	−	0.513232i	$-0.828448\pi$
$439$		−	21.5068i		−	1.02646i	0.858250	−	0.513232i	$-0.171552\pi$
$440$	−25.1608	+	23.2419i	−1.19949	+	1.10801i
$441$			9.34601i			0.445048i
$442$	0.161443	−	0.0903873i	0.00767905	−	0.00429929i
$443$	−0.629680	−	0.629680i	−0.0299170	−	0.0299170i	0.691990	−	0.721907i	$-0.256734\pi$
$443$	−0.629680	−	0.629680i	−0.0299170	−	0.0299170i	−0.721907	+	0.691990i	$0.756734\pi$
$444$	−7.49286	−	4.59406i	−0.355596	−	0.218025i
$445$	6.45668	−	6.45668i	0.306076	−	0.306076i
$446$	−14.9982	−	4.23185i	−0.710187	−	0.200384i
$447$	−6.98677			−0.330463
$448$	−6.47368	−	0.514095i	−0.305852	−	0.0242887i
$449$	−21.0975			−0.995655			−0.497827	−	0.867276i	$-0.665869\pi$
$449$	−21.0975			−0.995655			−0.497827	+	0.867276i	$0.665869\pi$
$450$	19.6837	+	5.55389i	0.927900	+	0.261813i
$451$	0.473308	−	0.473308i	0.0222872	−	0.0222872i
$452$	30.3697	+	18.6204i	1.42847	+	0.875831i
$453$	−16.9000	−	16.9000i	−0.794030	−	0.794030i
$454$	−18.4016	+	10.3026i	−0.863631	+	0.483523i
$455$			0.408739i			0.0191620i
$456$	2.59675	−	2.39870i	0.121604	−	0.112330i
$457$		−	21.3677i		−	0.999538i	−0.866159	−	0.499769i	$-0.833418\pi$
$457$		−	21.3677i		−	0.999538i	0.866159	−	0.499769i	$-0.166582\pi$
$458$	11.8093	+	21.0929i	0.551814	+	0.985606i
$459$	3.90808	+	3.90808i	0.182413	+	0.182413i
$460$	−42.1008	+	10.0970i	−1.96296	+	0.470775i
$461$	−16.5235	+	16.5235i	−0.769576	+	0.769576i	−0.978032	−	0.208456i	$-0.933156\pi$
$461$	−16.5235	+	16.5235i	−0.769576	+	0.769576i	0.208456	+	0.978032i	$0.433156\pi$
$462$	1.21181	−	4.29480i	0.0563783	−	0.199812i
$463$	−24.3235			−1.13041			−0.565204	−	0.824951i	$-0.691203\pi$
$463$	−24.3235			−1.13041			−0.565204	+	0.824951i	$0.691203\pi$
$464$	−14.8636	−	4.83723i	−0.690027	−	0.224563i
$465$	−33.0633			−1.53327
$466$	1.56564	−	5.54882i	0.0725267	−	0.257044i
$467$	3.03762	−	3.03762i	0.140564	−	0.140564i	−0.633323	−	0.773887i	$-0.718310\pi$
$467$	3.03762	−	3.03762i	0.140564	−	0.140564i	0.773887	+	0.633323i	$0.218310\pi$
$468$	0.0899425	+	0.375027i	0.00415760	+	0.0173356i
$469$	−5.27096	−	5.27096i	−0.243391	−	0.243391i
$470$	11.1915	+	19.9894i	0.516225	+	0.922041i
$471$		−	13.1968i		−	0.608076i
$472$	1.54175	−	38.8897i	0.0709649	−	1.79004i
$473$			16.1447i			0.742333i
$474$	14.8634	−	8.32161i	0.682699	−	0.382224i
$475$	7.01954	+	7.01954i	0.322079	+	0.322079i
$476$	0.848610	−	1.38407i	0.0388960	−	0.0634389i
$477$	12.2658	−	12.2658i	0.561612	−	0.561612i
$478$	−30.3158	−	8.55378i	−1.38661	−	0.391241i
$479$	30.9555			1.41440			0.707198	−	0.707016i	$-0.249959\pi$
$479$	30.9555			1.41440			0.707198	+	0.707016i	$0.249959\pi$
$480$	5.23146	+	26.3816i	0.238783	+	1.20415i
$481$	0.465408			0.0212208
$482$	17.0136	+	4.80050i	0.774949	+	0.218657i
$483$	3.98841	−	3.98841i	0.181479	−	0.181479i
$484$	1.14875	−	1.87359i	0.0522157	−	0.0851632i
$485$	37.8358	+	37.8358i	1.71803	+	1.71803i
$486$	−16.7924	+	9.40157i	−0.761717	+	0.426464i
$487$		−	27.2411i		−	1.23441i	−0.786801	−	0.617206i	$-0.788264\pi$
$487$		−	27.2411i		−	1.23441i	0.786801	−	0.617206i	$-0.211736\pi$
$488$	−42.4632	−	1.68342i	−1.92222	−	0.0762048i
$489$			14.4705i			0.654378i
$490$	−16.8603	−	30.1145i	−0.761671	−	1.36044i
$491$	−29.4747	−	29.4747i	−1.33017	−	1.33017i	−0.905211	−	0.424963i	$-0.860287\pi$
$491$	−29.4747	−	29.4747i	−1.33017	−	1.33017i	−0.424963	−	0.905211i	$-0.639713\pi$
$492$	−0.122574	−	0.511087i	−0.00552605	−	0.0230416i
$493$	2.76319	−	2.76319i	0.124448	−	0.124448i
$494$	−0.0508329	+	0.180159i	−0.00228708	+	0.00810572i
$495$	17.8491			0.802256
$496$	12.6168	+	24.7908i	0.566511	+	1.11314i
$497$	4.44842			0.199539
$498$	−0.717731	+	2.54373i	−0.0321623	+	0.113987i
$499$	13.5201	−	13.5201i	0.605241	−	0.605241i	−0.336458	−	0.941699i	$-0.609229\pi$
$499$	13.5201	−	13.5201i	0.605241	−	0.605241i	0.941699	+	0.336458i	$0.109229\pi$
$500$	−36.0186	+	8.63833i	−1.61080	+	0.386318i
$501$	7.48084	+	7.48084i	0.334219	+	0.334219i
$502$	−7.95277	−	14.2046i	−0.354949	−	0.633983i
$503$		−	3.49145i		−	0.155676i	−0.996966	−	0.0778380i	$-0.975198\pi$
$503$		−	3.49145i		−	0.155676i	0.996966	−	0.0778380i	$-0.0248017\pi$
$504$	2.29621	+	2.48579i	0.102281	+	0.110726i
$505$		−	29.5876i		−	1.31663i
$506$	−21.8396	+	12.2274i	−0.970890	+	0.543574i
$507$	−11.3409	−	11.3409i	−0.503669	−	0.503669i
$508$	15.4177	+	9.45295i	0.684048	+	0.419407i
$509$	−18.3706	+	18.3706i	−0.814264	+	0.814264i	−0.985270	−	0.171006i	$-0.945298\pi$
$509$	−18.3706	+	18.3706i	−0.814264	+	0.814264i	0.171006	+	0.985270i	$0.445298\pi$
$510$	−6.47116	−	1.82588i	−0.286548	−	0.0808513i
$511$	−4.60374			−0.203658
$512$	17.7845	−	13.9896i	0.785973	−	0.618261i
$513$	−5.59166			−0.246878
$514$	17.5448	+	4.95039i	0.773870	+	0.218352i
$515$	32.1207	−	32.1207i	1.41541	−	1.41541i
$516$	10.8072	+	6.62616i	0.475760	+	0.291700i
$517$	9.36509	+	9.36509i	0.411876	+	0.411876i
$518$	3.56332	−	1.99500i	0.156563	−	0.0876555i
$519$			23.9086i			1.04947i
$520$	−0.966364	−	1.04615i	−0.0423779	−	0.0458766i
$521$			12.1710i			0.533219i	0.963805	+	0.266610i	$0.0859035\pi$
$521$			12.1710i			0.533219i	−0.963805	+	0.266610i	$0.914097\pi$
$522$	3.97911	+	7.10718i	0.174161	+	0.311073i
$523$	3.67520	+	3.67520i	0.160705	+	0.160705i	0.782879	−	0.622174i	$-0.213750\pi$
$523$	3.67520	+	3.67520i	0.160705	+	0.160705i	−0.622174	+	0.782879i	$0.713750\pi$
$524$	−31.9876	+	7.67157i	−1.39738	+	0.335134i
$525$	6.95769	−	6.95769i	0.303659	−	0.303659i
$526$	0.118650	−	0.420511i	0.00517338	−	0.0183352i
$527$	−6.95416			−0.302928
$528$	7.05246	+	13.8574i	0.306919	+	0.603065i
$529$	−8.63672			−0.375510
$530$	−17.3950	+	61.6503i	−0.755592	+	2.67792i
$531$	−14.3410	+	14.3410i	−0.622348	+	0.622348i
$532$	0.383069	+	1.59726i	0.0166082	+	0.0692499i
$533$	0.0196794	+	0.0196794i	0.000852411	+	0.000852411i
$534$	−2.02491	−	3.61673i	−0.0876263	−	0.156511i
$535$			13.8991i			0.600911i
$536$	25.9527	+	1.02887i	1.12099	+	0.0444406i
$537$			23.5286i			1.01533i
$538$	15.3553	−	8.59700i	0.662014	−	0.370643i
$539$	−14.1088	−	14.1088i	−0.607707	−	0.607707i
$540$	22.2366	−	36.2676i	0.956911	−	1.56071i
$541$	27.5044	−	27.5044i	1.18250	−	1.18250i	0.203411	−	0.979093i	$-0.434797\pi$
$541$	27.5044	−	27.5044i	1.18250	−	1.18250i	0.979093	−	0.203411i	$-0.0652029\pi$
$542$	41.6449	+	11.7504i	1.78880	+	0.504722i
$543$	26.6525			1.14377
$544$	1.10033	+	5.54881i	0.0471762	+	0.237903i
$545$	64.0970			2.74562
$546$	0.178571	+	0.0503851i	0.00764215	+	0.00215628i
$547$	12.1518	−	12.1518i	0.519572	−	0.519572i	−0.397870	−	0.917442i	$-0.630250\pi$
$547$	12.1518	−	12.1518i	0.519572	−	0.519572i	0.917442	+	0.397870i	$0.130250\pi$
$548$	2.62254	−	4.27733i	0.112029	−	0.182719i
$549$	15.6588	+	15.6588i	0.668302	+	0.668302i
$550$	−38.0988	+	21.3304i	−1.62454	+	0.909533i
$551$			3.95356i			0.168427i
$552$	−0.778524	+	19.6378i	−0.0331362	+	0.835840i
$553$			7.91489i			0.336575i
$554$	8.38530	+	14.9772i	0.356257	+	0.636319i
$555$	−11.9594	−	11.9594i	−0.507647	−	0.507647i
$556$	−4.32931	−	18.0516i	−0.183604	−	0.765559i
$557$	−0.112971	+	0.112971i	−0.00478672	+	0.00478672i	−0.709496	−	0.704709i	$-0.751077\pi$
$557$	−0.112971	+	0.112971i	−0.00478672	+	0.00478672i	0.704709	+	0.709496i	$0.251077\pi$
$558$	3.93623	−	13.9505i	0.166634	−	0.590573i
$559$	−0.671272			−0.0283918
$560$	−11.8832	−	3.86728i	−0.502158	−	0.163423i
$561$	−3.88719			−0.164117
$562$	−5.38366	+	19.0804i	−0.227096	+	0.804859i
$563$	−21.9841	+	21.9841i	−0.926520	+	0.926520i	−0.997479	−	0.0709594i	$-0.977394\pi$
$563$	−21.9841	+	21.9841i	−0.926520	+	0.926520i	0.0709594	+	0.997479i	$0.477394\pi$
$564$	10.1126	−	2.42530i	0.425818	−	0.102124i
$565$	48.4730	+	48.4730i	2.03928	+	2.03928i
$566$	−17.3365	−	30.9650i	−0.728706	−	1.30156i
$567$			1.95307i			0.0820214i
$568$	−11.3855	+	10.5172i	−0.477726	+	0.441292i
$569$		−	20.7631i		−	0.870434i	−0.900326	−	0.435217i	$-0.856672\pi$
$569$		−	20.7631i		−	0.870434i	0.900326	−	0.435217i	$-0.143328\pi$
$570$	5.93568	−	3.32322i	0.248618	−	0.139195i
$571$	−5.28870	−	5.28870i	−0.221325	−	0.221325i	0.587731	−	0.809056i	$-0.300021\pi$
$571$	−5.28870	−	5.28870i	−0.221325	−	0.221325i	−0.809056	+	0.587731i	$0.800021\pi$
$572$	−0.701919	−	0.430364i	−0.0293487	−	0.0179944i
$573$	−3.67744	+	3.67744i	−0.153627	+	0.153627i
$574$	0.235030	+	0.0663152i	0.00980996	+	0.00276794i
$575$	−55.1896			−2.30156
$576$	−11.7541	−	0.933431i	−0.489755	−	0.0388930i
$577$	−13.9901			−0.582416			−0.291208	−	0.956660i	$-0.594057\pi$
$577$	−13.9901			−0.582416			−0.291208	+	0.956660i	$0.594057\pi$
$578$	−1.36107	−	0.384035i	−0.0566131	−	0.0159738i
$579$	19.9387	−	19.9387i	0.828624	−	0.828624i
$580$	−25.6429	−	15.7223i	−1.06476	−	0.652832i
$581$	−0.868378	−	0.868378i	−0.0360264	−	0.0360264i
$582$	21.1938	−	11.8658i	0.878512	−	0.491855i
$583$			37.0330i			1.53375i
$584$	11.7831	−	10.8844i	0.487587	−	0.450401i
$585$			0.742138i			0.0306836i
$586$	−15.3042	−	27.3351i	−0.632209	−	1.12920i
$587$	−19.7296	−	19.7296i	−0.814328	−	0.814328i	0.170951	−	0.985280i	$-0.445316\pi$
$587$	−19.7296	−	19.7296i	−0.814328	−	0.814328i	−0.985280	+	0.170951i	$0.945316\pi$
$588$	−15.2349	+	3.65378i	−0.628278	+	0.150680i
$589$	4.97499	−	4.97499i	0.204991	−	0.204991i
$590$	20.3381	−	72.0809i	0.837305	−	2.96752i
$591$	11.6586			0.479572
$592$	−4.40346	+	13.5307i	−0.180981	+	0.556110i
$593$	−2.88528			−0.118484			−0.0592422	−	0.998244i	$-0.518868\pi$
$593$	−2.88528			−0.118484			−0.0592422	+	0.998244i	$0.518868\pi$
$594$	6.67870	−	23.6702i	0.274030	−	0.971200i
$595$	2.20912	−	2.20912i	0.0905651	−	0.0905651i
$596$	2.63798	+	10.9994i	0.108056	+	0.450554i
$597$	−12.5652	−	12.5652i	−0.514260	−	0.514260i
$598$	−0.508397	−	0.908060i	−0.0207899	−	0.0371333i
$599$		−	41.6385i		−	1.70130i	−0.525729	−	0.850652i	$-0.676207\pi$
$599$		−	41.6385i		−	1.70130i	0.525729	−	0.850652i	$-0.323793\pi$
$600$	−1.35812	+	34.2577i	−0.0554450	+	1.39856i
$601$		−	28.7151i		−	1.17131i	−0.810560	−	0.585656i	$-0.800837\pi$
$601$		−	28.7151i		−	1.17131i	0.810560	−	0.585656i	$-0.199163\pi$
$602$	−5.13949	+	2.87746i	−0.209470	+	0.117276i
$603$	−9.57037	−	9.57037i	−0.389736	−	0.389736i
$604$	−20.2251	+	32.9869i	−0.822947	+	1.34222i
$605$	2.99044	−	2.99044i	0.121579	−	0.121579i
$606$	−12.9263	−	3.64725i	−0.525097	−	0.148159i
$607$	−5.66264			−0.229839			−0.114920	−	0.993375i	$-0.536661\pi$
$607$	−5.66264			−0.229839			−0.114920	+	0.993375i	$0.536661\pi$
$608$	−4.75678	−	3.18243i	−0.192913	−	0.129065i
$609$	3.91872			0.158795
$610$	−78.7042	−	22.2069i	−3.18664	−	0.899131i
$611$	−0.389386	+	0.389386i	−0.0157529	+	0.0157529i
$612$	1.54080	−	2.51303i	0.0622833	−	0.101583i
$613$	12.5195	+	12.5195i	0.505656	+	0.505656i	0.913190	−	0.407534i	$-0.133611\pi$
$613$	12.5195	+	12.5195i	0.505656	+	0.505656i	−0.407534	+	0.913190i	$0.633611\pi$
$614$	42.3625	−	23.7176i	1.70961	−	0.957163i
$615$		−	1.01139i		−	0.0407830i
$616$	−7.21893	−	0.286189i	−0.290859	−	0.0115309i
$617$		−	31.2165i		−	1.25673i	−0.777918	−	0.628365i	$-0.783724\pi$
$617$		−	31.2165i		−	1.25673i	0.777918	−	0.628365i	$-0.216276\pi$
$618$	−10.0735	−	17.9925i	−0.405216	−	0.723765i
$619$	−12.3212	−	12.3212i	−0.495232	−	0.495232i	0.414718	−	0.909950i	$-0.363880\pi$
$619$	−12.3212	−	12.3212i	−0.495232	−	0.495232i	−0.909950	+	0.414718i	$0.863880\pi$
$620$	12.4836	+	52.0522i	0.501355	+	2.09047i
$621$	21.9816	−	21.9816i	0.882091	−	0.882091i
$622$	−3.49989	+	12.4041i	−0.140333	+	0.497358i
$623$	1.92594			0.0771610
$624$	−0.576169	+	0.293231i	−0.0230652	+	0.0117386i
$625$	−22.2166			−0.888662
$626$	9.18604	−	32.5566i	0.367148	−	1.30122i
$627$	2.78089	−	2.78089i	0.111058	−	0.111058i
$628$	−20.7760	+	4.98269i	−0.829051	+	0.198831i
$629$	−2.51540	−	2.51540i	−0.100296	−	0.100296i
$630$	3.18123	+	5.68207i	0.126743	+	0.226379i
$631$			9.77095i			0.388975i	0.980905	+	0.194488i	$0.0623044\pi$
$631$			9.77095i			0.388975i	−0.980905	+	0.194488i	$0.937696\pi$
$632$	−18.7128	−	20.2578i	−0.744357	−	0.805812i
$633$		−	3.11746i		−	0.123908i
$634$	4.82047	−	2.69885i	0.191445	−	0.107185i
$635$	24.6081	+	24.6081i	0.976544	+	0.976544i
$636$	24.7897	+	15.1992i	0.982977	+	0.602688i
$637$	0.586621	−	0.586621i	0.0232428	−	0.0232428i
$638$	−16.7359	−	4.72214i	−0.662581	−	0.186951i
$639$	8.07689			0.319517
$640$	39.5578	−	18.1969i	1.56366	−	0.719294i
$641$	−17.6626			−0.697630			−0.348815	−	0.937192i	$-0.613416\pi$
$641$	−17.6626			−0.697630			−0.348815	+	0.937192i	$0.613416\pi$
$642$	6.07230	+	1.71334i	0.239655	+	0.0676201i
$643$	9.25773	−	9.25773i	0.365089	−	0.365089i	−0.500593	−	0.865683i	$-0.666885\pi$
$643$	9.25773	−	9.25773i	0.365089	−	0.365089i	0.865683	+	0.500593i	$0.166885\pi$
$644$	−7.78493	−	4.77314i	−0.306769	−	0.188088i
$645$	17.2494	+	17.2494i	0.679193	+	0.679193i
$646$	1.24845	−	0.698970i	0.0491194	−	0.0275006i
$647$		−	26.8152i		−	1.05421i	−0.849799	−	0.527107i	$-0.823277\pi$
$647$		−	26.8152i		−	1.05421i	0.849799	−	0.527107i	$-0.176723\pi$
$648$	−4.61757	−	4.99880i	−0.181395	−	0.196372i
$649$		−	43.2986i		−	1.69962i
$650$	−0.886888	−	1.58409i	−0.0347866	−	0.0621331i
$651$	−4.93116	−	4.93116i	−0.193267	−	0.193267i
$652$	22.7812	−	5.46360i	0.892180	−	0.213971i
$653$	16.4726	−	16.4726i	0.644624	−	0.644624i	−0.307065	−	0.951689i	$-0.599347\pi$
$653$	16.4726	−	16.4726i	0.644624	−	0.644624i	0.951689	+	0.307065i	$0.0993467\pi$
$654$	7.90122	−	28.0030i	0.308962	−	1.09500i
$655$	−63.3000			−2.47334
$656$	−0.758335	+	0.385941i	−0.0296080	+	0.0150685i
$657$	−8.35891			−0.326112
$658$	−1.31214	+	4.65041i	−0.0511527	+	0.181292i
$659$	−16.2172	+	16.2172i	−0.631733	+	0.631733i	−0.948503	−	0.316770i	$-0.897402\pi$
$659$	−16.2172	+	16.2172i	−0.631733	+	0.631733i	0.316770	+	0.948503i	$0.397402\pi$
$660$	6.97802	+	29.0958i	0.271619	+	1.13255i
$661$	−9.31196	−	9.31196i	−0.362193	−	0.362193i	0.502427	−	0.864620i	$-0.332441\pi$
$661$	−9.31196	−	9.31196i	−0.362193	−	0.362193i	−0.864620	+	0.502427i	$0.832441\pi$
$662$	13.7518	+	24.5624i	0.534479	+	0.954645i
$663$		−	0.161624i		−	0.00627694i
$664$	4.27564	+	0.169504i	0.165927	+	0.00657805i
$665$			3.16080i			0.122571i
$666$	6.46984	−	3.62229i	0.250701	−	0.140361i
$667$	−15.5420	−	15.5420i	−0.601787	−	0.601787i
$668$	8.95270	−	14.6018i	0.346390	−	0.564959i
$669$	−9.62580	+	9.62580i	−0.372155	+	0.372155i
$670$	48.1026	+	13.5724i	1.85836	+	0.524349i
$671$	−47.2772			−1.82511
$672$	−3.15439	+	4.71487i	−0.121683	+	0.181880i
$673$	−31.3729			−1.20934			−0.604669	−	0.796477i	$-0.706695\pi$
$673$	−31.3729			−1.20934			−0.604669	+	0.796477i	$0.706695\pi$
$674$	−13.8451	−	3.90650i	−0.533295	−	0.150473i
$675$	38.3464	−	38.3464i	1.47595	−	1.47595i
$676$	−13.5723	+	22.1363i	−0.522011	+	0.851395i
$677$	−1.04818	−	1.04818i	−0.0402849	−	0.0402849i	0.686677	−	0.726962i	$-0.259069\pi$
$677$	−1.04818	−	1.04818i	−0.0402849	−	0.0402849i	−0.726962	+	0.686677i	$0.759069\pi$
$678$	27.1523	−	15.2018i	1.04278	−	0.583823i
$679$			11.2859i			0.433112i
$680$	−0.431213	+	10.8771i	−0.0165363	+	0.417117i
$681$			18.4222i			0.705941i
$682$	15.1176	+	27.0019i	0.578884	+	1.03396i
$683$	10.7141	+	10.7141i	0.409963	+	0.409963i	0.881726	−	0.471763i	$-0.156382\pi$
$683$	10.7141	+	10.7141i	0.409963	+	0.409963i	−0.471763	+	0.881726i	$0.656382\pi$
$684$	0.695531	+	2.90010i	0.0265943	+	0.110888i
$685$	6.82705	−	6.82705i	0.260848	−	0.260848i
$686$	4.15898	−	14.7400i	0.158791	−	0.562776i
$687$	21.1165			0.805645
$688$	6.35124	−	19.5158i	0.242139	−	0.744033i
$689$	−1.53978			−0.0586608
$690$	−10.2699	+	36.3980i	−0.390970	+	1.38565i
$691$	−26.5363	+	26.5363i	−1.00949	+	1.00949i	−0.00953274	+	0.999955i	$0.503034\pi$
$691$	−26.5363	+	26.5363i	−1.00949	+	1.00949i	−0.999955	+	0.00953274i	$0.996966\pi$
$692$	37.6398	−	9.02713i	1.43085	−	0.343160i
$693$	2.66207	+	2.66207i	0.101124	+	0.101124i
$694$	−7.30334	−	13.0447i	−0.277231	−	0.495168i
$695$		−	35.7222i		−	1.35502i
$696$	−10.0298	+	9.26487i	−0.380178	+	0.351184i
$697$		−	0.212724i		−	0.00805748i
$698$	−0.363343	+	0.203426i	−0.0137528	+	0.00769978i
$699$	−3.56121	−	3.56121i	−0.134697	−	0.134697i
$700$	−13.5806	−	8.32663i	−0.513300	−	0.314717i
$701$	16.6425	−	16.6425i	0.628578	−	0.628578i	−0.319132	−	0.947710i	$-0.603391\pi$
$701$	16.6425	−	16.6425i	0.628578	−	0.628578i	0.947710	+	0.319132i	$0.103391\pi$
$702$	0.984172	+	0.277690i	0.0371452	+	0.0104807i
$703$	3.59902			0.135740
$704$	19.1532	−	16.3349i	0.721862	−	0.615646i
$705$	20.0118			0.753686
$706$	32.5591	+	9.18675i	1.22538	+	0.345748i
$707$	4.41278	−	4.41278i	0.165960	−	0.165960i
$708$	−28.9839	−	17.7708i	−1.08928	−	0.667866i
$709$	19.2677	+	19.2677i	0.723614	+	0.723614i	0.969339	−	0.245726i	$-0.0790262\pi$
$709$	19.2677	+	19.2677i	0.723614	+	0.723614i	−0.245726	+	0.969339i	$0.579026\pi$
$710$	−26.0252	+	14.5708i	−0.976710	+	0.546832i
$711$			14.3709i			0.538950i
$712$	−4.92935	+	4.55341i	−0.184735	+	0.170646i
$713$			39.1147i			1.46486i
$714$	−0.692812	−	1.23745i	−0.0259278	−	0.0463103i
$715$	−1.12033	−	1.12033i	−0.0418981	−	0.0418981i
$716$	37.0415	−	8.88364i	1.38430	−	0.331997i
$717$	−19.4565	+	19.4565i	−0.726617	+	0.726617i
$718$	6.56350	−	23.2619i	0.244948	−	0.868127i
$719$	28.8748			1.07685			0.538425	−	0.842674i	$-0.319020\pi$
$719$	28.8748			1.07685			0.538425	+	0.842674i	$0.319020\pi$
$720$	−21.5761	−	7.02174i	−0.804093	−	0.261685i
$721$	9.58115			0.356821
$722$	6.90357	−	24.4672i	0.256924	−	0.910575i
$723$	10.9193	−	10.9193i	0.406092	−	0.406092i
$724$	−10.0632	−	41.9596i	−0.373994	−	1.55942i
$725$	−27.1126	−	27.1126i	−1.00694	−	1.00694i
$726$	−0.937844	−	1.67510i	−0.0348067	−	0.0621689i
$727$		−	11.8252i		−	0.438573i	−0.975660	−	0.219287i	$-0.929627\pi$
$727$		−	11.8252i		−	0.438573i	0.975660	−	0.219287i	$-0.0703730\pi$
$728$	0.0118993	−	0.300152i	0.000441017	−	0.0111244i
$729$			24.0291i			0.889967i
$730$	26.9340	−	15.0796i	0.996870	−	0.558120i
$731$	3.62804	+	3.62804i	0.134188	+	0.134188i
$732$	−19.4037	+	31.6472i	−0.717180	+	1.16971i
$733$	4.55382	−	4.55382i	0.168199	−	0.168199i	−0.617988	−	0.786187i	$-0.712052\pi$
$733$	4.55382	−	4.55382i	0.168199	−	0.168199i	0.786187	+	0.617988i	$0.212052\pi$
$734$	11.5841	+	3.26854i	0.427579	+	0.120644i
$735$	−30.1483			−1.11204
$736$	31.2101	−	6.18896i	1.15042	−	0.228128i
$737$	28.8949			1.06436
$738$	0.426739	+	0.120407i	0.0157085	+	0.00443224i
$739$	−35.7680	+	35.7680i	−1.31575	+	1.31575i	−0.398638	+	0.917108i	$0.630517\pi$
$739$	−35.7680	+	35.7680i	−1.31575	+	1.31575i	−0.917108	+	0.398638i	$0.869483\pi$
$740$	−14.3124	+	23.3433i	−0.526134	+	0.858118i
$741$	0.115625	+	0.115625i	0.00424759	+	0.00424759i
$742$	−11.7891	+	6.60037i	−0.432790	+	0.242307i
$743$			17.7070i			0.649607i	0.945781	+	0.324804i	$0.105298\pi$
$743$			17.7070i			0.649607i	−0.945781	+	0.324804i	$0.894702\pi$
$744$	24.2796	+	0.962546i	0.890134	+	0.0352886i
$745$			21.7667i			0.797468i
$746$	6.08020	+	10.8600i	0.222612	+	0.397612i
$747$	−1.57669	−	1.57669i	−0.0576882	−	0.0576882i
$748$	1.46768	+	6.11968i	0.0536637	+	0.223758i
$749$	−2.07296	+	2.07296i	−0.0757442	+	0.0757442i
$750$	−8.78628	+	31.1398i	−0.320830	+	1.13706i
$751$	−16.5193			−0.602799			−0.301400	−	0.953498i	$-0.597454\pi$
$751$	−16.5193			−0.602799			−0.301400	+	0.953498i	$0.597454\pi$
$752$	−7.63640	−	15.0048i	−0.278471	−	0.547168i
$753$	−14.2205			−0.518224
$754$	0.196340	−	0.695854i	0.00715027	−	0.0253415i
$755$	−52.6503	+	52.6503i	−1.91614	+	1.91614i
$756$	8.72550	−	2.09263i	0.317343	−	0.0761083i
$757$	33.5735	+	33.5735i	1.22025	+	1.22025i	0.967543	+	0.252705i	$0.0813201\pi$
$757$	33.5735	+	33.5735i	1.22025	+	1.22025i	0.252705	+	0.967543i	$0.418680\pi$
$758$	13.9046	+	24.8354i	0.505040	+	0.902062i
$759$			21.8641i			0.793616i
$760$	−7.47295	−	8.08992i	−0.271072	−	0.293452i
$761$		−	0.227331i		−	0.00824075i	−0.999992	−	0.00412037i	$-0.998688\pi$
$761$		−	0.227331i		−	0.00824075i	0.999992	−	0.00412037i	$-0.00131156\pi$
$762$	13.7843	−	7.71746i	0.499353	−	0.279574i
$763$	9.55963	+	9.55963i	0.346082	+	0.346082i
$764$	7.17794	+	4.40098i	0.259689	+	0.159222i
$765$	4.01105	−	4.01105i	0.145020	−	0.145020i
$766$	13.7474	+	3.87891i	0.496713	+	0.140151i
$767$	1.80029			0.0650047
$768$	−3.07364	−	19.5253i	−0.110910	−	0.704558i
$769$	−32.8784			−1.18563			−0.592813	−	0.805340i	$-0.701983\pi$
$769$	−32.8784			−1.18563			−0.592813	+	0.805340i	$0.701983\pi$
$770$	−13.3801	−	3.77527i	−0.482184	−	0.136051i
$771$	11.2602	−	11.2602i	0.405527	−	0.405527i
$772$	−38.9181	−	23.8617i	−1.40069	−	0.858800i
$773$	2.07623	+	2.07623i	0.0746768	+	0.0746768i	0.743459	−	0.668782i	$-0.233184\pi$
$773$	2.07623	+	2.07623i	0.0746768	+	0.0746768i	−0.668782	+	0.743459i	$0.733184\pi$
$774$	−9.33166	+	5.22454i	−0.335420	+	0.187792i
$775$			68.2348i			2.45107i
$776$	−26.6827	−	28.8857i	−0.957855	−	1.03694i
$777$		−	3.56731i		−	0.127977i
$778$	−5.11173	−	9.13017i	−0.183264	−	0.327333i
$779$	0.152182	+	0.152182i	0.00545249	+	0.00545249i
$780$	−1.20976	+	0.290136i	−0.0433163	+	0.0103885i
$781$	−12.1929	+	12.1929i	−0.436296	+	0.436296i
$782$	−2.16006	+	7.65556i	−0.0772437	+	0.273762i
$783$	21.5975			0.771832
$784$	11.5045	+	22.6051i	0.410873	+	0.807325i
$785$	−41.1134			−1.46740
$786$	−7.80296	+	27.6547i	−0.278322	+	0.986412i
$787$	−15.0473	+	15.0473i	−0.536378	+	0.536378i	−0.922463	−	0.386085i	$-0.873827\pi$
$787$	−15.0473	+	15.0473i	−0.536378	+	0.536378i	0.386085	+	0.922463i	$0.373827\pi$
$788$	−4.40193	−	18.3544i	−0.156812	−	0.653849i
$789$	−0.269882	−	0.269882i	−0.00960807	−	0.00960807i
$790$	−25.9252	−	46.3056i	−0.922378	−	1.64748i
$791$			14.4588i			0.514097i
$792$	−13.1072	−	0.519626i	−0.465746	−	0.0184641i
$793$		−	1.96571i		−	0.0698046i
$794$	−15.3088	+	8.57100i	−0.543291	+	0.304173i
$795$	39.5669	+	39.5669i	1.40329	+	1.40329i
$796$	−15.0375	+	24.5259i	−0.532988	+	0.869298i
$797$	−21.2974	+	21.2974i	−0.754393	+	0.754393i	−0.975296	−	0.220903i	$-0.929100\pi$
$797$	−21.2974	+	21.2974i	−0.754393	+	0.754393i	0.220903	+	0.975296i	$0.429100\pi$
$798$	1.38090	+	0.389630i	0.0488834	+	0.0137928i
$799$	4.20905			0.148906
$800$	54.4454	−	10.7965i	1.92493	−	0.381714i
$801$	3.49688			0.123556
$802$	9.15872	+	2.58419i	0.323406	+	0.0912510i
$803$	12.6186	−	12.6186i	0.445302	−	0.445302i
$804$	11.8592	−	19.3422i	0.418240	−	0.682145i
$805$	−12.4255	−	12.4255i	−0.437942	−	0.437942i
$806$	−1.12270	+	0.628568i	−0.0395454	+	0.0221404i
$807$		−	15.3725i		−	0.541137i
$808$	−0.861360	+	21.7273i	−0.0303026	+	0.764363i
$809$			33.6407i			1.18275i	0.806398	+	0.591373i	$0.201414\pi$
$809$			33.6407i			1.18275i	−0.806398	+	0.591373i	$0.798586\pi$
$810$	−6.39729	−	11.4263i	−0.224778	−	0.401481i
$811$	35.7605	+	35.7605i	1.25572	+	1.25572i	0.953116	+	0.302606i	$0.0978568\pi$
$811$	35.7605	+	35.7605i	1.25572	+	1.25572i	0.302606	+	0.953116i	$0.402143\pi$
$812$	−1.47959	−	6.16932i	−0.0519233	−	0.216501i
$813$	26.7275	−	26.7275i	0.937375	−	0.937375i
$814$	−4.29868	+	15.2351i	−0.150669	+	0.533990i
$815$	45.0815			1.57914
$816$	4.69886	+	1.52920i	0.164493	+	0.0535328i
$817$	−5.19098			−0.181609
$818$	0.265267	−	0.940141i	0.00927484	−	0.0328713i
$819$	−0.110685	+	0.110685i	−0.00386764	+	0.00386764i
$820$	−1.59225	+	0.381867i	−0.0556036	+	0.0133354i
$821$	5.98243	+	5.98243i	0.208788	+	0.208788i	0.803752	−	0.594964i	$-0.202834\pi$
$821$	5.98243	+	5.98243i	0.208788	+	0.208788i	−0.594964	+	0.803752i	$0.702834\pi$
$822$	−2.14106	−	3.82420i	−0.0746781	−	0.133384i
$823$		−	33.4648i		−	1.16651i	−0.812290	−	0.583254i	$-0.801779\pi$
$823$		−	33.4648i		−	1.16651i	0.812290	−	0.583254i	$-0.198221\pi$
$824$	−24.5225	+	22.6523i	−0.854283	+	0.789131i
$825$			38.1414i			1.32791i
$826$	13.7836	−	7.71708i	0.479594	−	0.268512i
$827$	26.0067	+	26.0067i	0.904342	+	0.904342i	0.995808	−	0.0914660i	$-0.0291553\pi$
$827$	26.0067	+	26.0067i	0.904342	+	0.904342i	−0.0914660	+	0.995808i	$0.529155\pi$
$828$	−14.1349	−	8.66648i	−0.491223	−	0.301181i
$829$	−9.35752	+	9.35752i	−0.325000	+	0.325000i	−0.850682	−	0.525681i	$-0.823810\pi$
$829$	−9.35752	+	9.35752i	−0.325000	+	0.325000i	0.525681	+	0.850682i	$0.323810\pi$
$830$	7.92477	+	2.23602i	0.275073	+	0.0776135i
$831$	14.9939			0.520134
$832$	0.679182	+	0.796359i	0.0235464	+	0.0276088i
$833$	−6.34105			−0.219704
$834$	−15.6064	−	4.40346i	−0.540407	−	0.152479i
$835$	23.3059	−	23.3059i	0.806533	−	0.806533i
$836$	−5.42798	−	3.32803i	−0.187731	−	0.115102i
$837$	−27.1774	−	27.1774i	−0.939389	−	0.939389i
$838$	−6.19449	+	3.46812i	−0.213985	+	0.119804i
$839$			34.6276i			1.19548i	0.801691	+	0.597739i	$0.203934\pi$
$839$			34.6276i			1.19548i	−0.801691	+	0.597739i	$0.796066\pi$
$840$	−8.01864	+	7.40710i	−0.276670	+	0.255569i
$841$			13.7296i			0.473434i
$842$	7.70893	+	13.7691i	0.265667	+	0.474514i
$843$	12.2457	+	12.2457i	0.421766	+	0.421766i
$844$	−4.90788	+	1.17706i	−0.168936	+	0.0405159i
$845$	−35.3317	+	35.3317i	−1.21545	+	1.21545i
$846$	−2.38243	+	8.44365i	−0.0819096	+	0.290299i
$847$	0.892006			0.0306497
$848$	14.5686	−	44.7657i	0.500288	−	1.53726i
$849$	−30.9997			−1.06391
$850$	−3.76818	+	13.3550i	−0.129248	+	0.458071i
$851$	−14.1482	+	14.1482i	−0.484996	+	0.484996i
$852$	3.15763	+	13.1661i	0.108179	+	0.451065i
$853$	−14.2493	−	14.2493i	−0.487888	−	0.487888i	0.419751	−	0.907639i	$-0.362117\pi$
$853$	−14.2493	−	14.2493i	−0.487888	−	0.487888i	−0.907639	+	0.419751i	$0.862117\pi$
$854$	−8.42618	−	15.0502i	−0.288338	−	0.515007i
$855$			5.73899i			0.196269i
$856$	0.404634	−	10.2066i	0.0138301	−	0.348856i
$857$			0.0617597i			0.00210967i	0.999999	+	0.00105484i	$0.000335765\pi$
$857$			0.0617597i			0.00210967i	−0.999999	+	0.00105484i	$0.999664\pi$
$858$	−0.627559	+	0.351353i	−0.0214245	+	0.0119950i
$859$	−18.9964	−	18.9964i	−0.648147	−	0.648147i	0.304398	−	0.952545i	$-0.401545\pi$
$859$	−18.9964	−	18.9964i	−0.648147	−	0.648147i	−0.952545	+	0.304398i	$0.901545\pi$
$860$	20.6432	−	33.6688i	0.703927	−	1.14810i
$861$	0.150841	−	0.150841i	0.00514065	−	0.00514065i
$862$	23.9451	+	6.75627i	0.815574	+	0.230119i
$863$	20.2347			0.688797			0.344398	−	0.938824i	$-0.388083\pi$
$863$	20.2347			0.688797			0.344398	+	0.938824i	$0.388083\pi$
$864$	−17.3850	+	25.9853i	−0.591450	+	0.884039i
$865$	74.4850			2.53257
$866$	−43.6723	−	12.3224i	−1.48404	−	0.418732i
$867$	−0.873530	+	0.873530i	−0.0296666	+	0.0296666i
$868$	−5.90137	+	9.62507i	−0.200306	+	0.326696i
$869$	−21.6943	−	21.6943i	−0.735930	−	0.735930i
$870$	−22.9263	+	12.8358i	−0.777273	+	0.435174i
$871$			1.20141i			0.0407082i
$872$	−47.0689	−	1.86601i	−1.59395	−	0.0631910i
$873$			20.4915i			0.693533i
$874$	−3.93146	−	7.02207i	−0.132984	−	0.237525i
$875$	−10.6305	−	10.6305i	−0.359375	−	0.359375i
$876$	−3.26788	−	13.6259i	−0.110412	−	0.460375i
$877$	−40.0949	+	40.0949i	−1.35391	+	1.35391i	−0.472666	+	0.881242i	$0.656708\pi$
$877$	−40.0949	+	40.0949i	−1.35391	+	1.35391i	−0.881242	+	0.472666i	$0.843292\pi$
$878$	−8.25937	+	29.2723i	−0.278740	+	0.987893i
$879$	−27.3657			−0.923023
$880$	43.1714	−	21.9713i	1.45531	−	0.740652i
$881$	25.1953			0.848852			0.424426	−	0.905463i	$-0.360476\pi$
$881$	25.1953			0.848852			0.424426	+	0.905463i	$0.360476\pi$
$882$	3.58920	−	12.7206i	0.120854	−	0.428324i
$883$	1.57982	−	1.57982i	0.0531652	−	0.0531652i	−0.680024	−	0.733190i	$-0.738031\pi$
$883$	1.57982	−	1.57982i	0.0531652	−	0.0531652i	0.733190	+	0.680024i	$0.238031\pi$
$884$	−0.254447	+	0.0610239i	−0.00855798	+	0.00205246i
$885$	−46.2612	−	46.2612i	−1.55505	−	1.55505i
$886$	0.615221	+	1.09886i	0.0206688	+	0.0369169i
$887$		−	33.9153i		−	1.13876i	−0.822073	−	0.569382i	$-0.807182\pi$
$887$		−	33.9153i		−	1.13876i	0.822073	−	0.569382i	$-0.192818\pi$
$888$	8.43405	+	9.13037i	0.283028	+	0.306395i
$889$			7.34026i			0.246185i
$890$	−11.2676	+	6.30841i	−0.377691	+	0.211458i
$891$	−5.35328	−	5.35328i	−0.179342	−	0.179342i
$892$	18.7885	+	11.5197i	0.629085	+	0.385708i
$893$	−3.01115	+	3.01115i	−0.100764	+	0.100764i
$894$	9.50950	+	2.68317i	0.318045	+	0.0897385i
$895$	73.3011			2.45018
$896$	8.61371	+	3.18584i	0.287764	+	0.106431i
$897$	−0.909076			−0.0303532
$898$	28.7153	+	8.10220i	0.958241	+	0.270374i
$899$	−19.2156	+	19.2156i	−0.640878	+	0.640878i
$900$	−24.6581	−	15.1185i	−0.821936	−	0.503949i
$901$	8.32206	+	8.32206i	0.277248	+	0.277248i
$902$	−0.825973	+	0.462439i	−0.0275019	+	0.0153975i
$903$			5.14524i			0.171223i
$904$	−34.1844	−	37.0067i	−1.13696	−	1.23083i
$905$		−	83.0336i		−	2.76013i
$906$	16.5119	+	29.4923i	0.548571	+	0.979815i
$907$	25.3392	+	25.3392i	0.841374	+	0.841374i	0.989038	−	0.147664i	$-0.0471754\pi$
$907$	25.3392	+	25.3392i	0.841374	+	0.841374i	−0.147664	+	0.989038i	$0.547175\pi$
$908$	29.0025	−	6.95565i	0.962481	−	0.230831i
$909$	8.01219	−	8.01219i	0.265748	−	0.265748i
$910$	0.156970	−	0.556323i	0.00520351	−	0.0184419i
$911$	23.5612			0.780619			0.390309	−	0.920684i	$-0.372368\pi$
$911$	23.5612			0.780619			0.390309	+	0.920684i	$0.372368\pi$
$912$	−4.45554	+	2.26757i	−0.147538	+	0.0750867i
$913$	4.76036			0.157545
$914$	−8.20594	+	29.0830i	−0.271428	+	0.961979i
$915$	−50.5120	+	50.5120i	−1.66988	+	1.66988i
$916$	−7.97293	−	33.2441i	−0.263433	−	1.09842i
$917$	−9.44075	−	9.44075i	−0.311761	−	0.311761i
$918$	−3.81834	−	6.82002i	−0.126024	−	0.225094i
$919$		−	33.2708i		−	1.09750i	−0.835986	−	0.548751i	$-0.815103\pi$
$919$		−	33.2708i		−	1.09750i	0.835986	−	0.548751i	$-0.184897\pi$
$920$	61.1798	+	2.42542i	2.01704	+	0.0799638i
$921$		−	42.4099i		−	1.39745i
$922$	28.8353	−	16.1441i	0.949639	−	0.531676i
$923$	−0.506963	−	0.506963i	−0.0166869	−	0.0166869i
$924$	−3.29871	+	5.38016i	−0.108520	+	0.176994i
$925$	−24.6813	+	24.6813i	−0.811516	+	0.811516i
$926$	33.1060	+	9.34108i	1.08793	+	0.306967i
$927$	17.3963			0.571369
$928$	18.3728	+	12.2920i	0.603117	+	0.403504i
$929$	−27.4656			−0.901117			−0.450559	−	0.892747i	$-0.648775\pi$
$929$	−27.4656			−0.901117			−0.450559	+	0.892747i	$0.648775\pi$
$930$	45.0015	+	12.6975i	1.47566	+	0.416366i
$931$	4.53637	−	4.53637i	0.148674	−	0.148674i
$932$	−4.26189	+	6.95109i	−0.139603	+	0.227691i
$933$	7.96088	+	7.96088i	0.260628	+	0.260628i
$934$	−5.30097	+	2.96786i	−0.173453	+	0.0971114i
$935$			12.1102i			0.396045i
$936$	0.0216053	−	0.544980i	0.000706191	−	0.0178132i
$937$			11.8041i			0.385624i	0.981236	+	0.192812i	$0.0617608\pi$
$937$			11.8041i			0.385624i	−0.981236	+	0.192812i	$0.938239\pi$
$938$	5.14993	+	9.19840i	0.168151	+	0.300338i
$939$	−20.8947	−	20.8947i	−0.681872	−	0.681872i
$940$	−7.55581	−	31.5049i	−0.246443	−	1.02758i
$941$	2.19292	−	2.19292i	0.0714872	−	0.0714872i	−0.670459	−	0.741946i	$-0.733903\pi$
$941$	2.19292	−	2.19292i	0.0714872	−	0.0714872i	0.741946	+	0.670459i	$0.233903\pi$
$942$	−5.06803	+	17.9618i	−0.165125	+	0.585226i
$943$	−1.19650			−0.0389633
$944$	−17.0335	+	52.3396i	−0.554392	+	1.70351i
$945$	17.2668			0.561690
$946$	6.20013	−	21.9741i	0.201583	−	0.714439i
$947$	32.5828	−	32.5828i	1.05880	−	1.05880i	0.0606402	−	0.998160i	$-0.480686\pi$
$947$	32.5828	−	32.5828i	1.05880	−	1.05880i	0.998160	−	0.0606402i	$-0.0193142\pi$
$948$	−23.4260	+	5.61824i	−0.760840	+	0.182472i
$949$	0.524664	+	0.524664i	0.0170313	+	0.0170313i
$950$	−6.85835	−	12.2499i	−0.222514	−	0.397438i
$951$		−	4.82587i		−	0.156489i
$952$	−1.68655	+	1.55793i	−0.0546615	+	0.0504927i
$953$		−	2.40271i		−	0.0778315i	−0.999242	−	0.0389157i	$-0.987610\pi$
$953$		−	2.40271i		−	0.0778315i	0.999242	−	0.0389157i	$-0.0123904\pi$
$954$	−21.4051	+	11.9841i	−0.693017	+	0.388001i
$955$	11.4567	+	11.4567i	0.370731	+	0.370731i
$956$	37.9770	+	23.2846i	1.22826	+	0.753079i
$957$	−10.7410	+	10.7410i	−0.347208	+	0.347208i
$958$	−42.1327	−	11.8880i	−1.36125	−	0.384084i
$959$	2.03641			0.0657592
$960$	3.01105	−	37.9163i	0.0971814	−	1.22374i
$961$	17.3604			0.560012
$962$	−0.633453	−	0.178733i	−0.0204234	−	0.00576258i
$963$	−3.76382	+	3.76382i	−0.121287	+	0.121287i
$964$	−21.3132	−	13.0677i	−0.686452	−	0.420881i
$965$	−62.1172	−	62.1172i	−1.99962	−	1.99962i
$966$	−6.96020	+	3.89682i	−0.223941	+	0.125378i
$967$		−	8.14895i		−	0.262052i	−0.991379	−	0.131026i	$-0.958173\pi$
$967$		−	8.14895i		−	0.262052i	0.991379	−	0.131026i	$-0.0418272\pi$
$968$	−2.28305	+	2.10893i	−0.0733800	+	0.0677837i
$969$		−	1.24984i		−	0.0401508i
$970$	−36.9669	−	66.0274i	−1.18694	−	2.12001i
$971$	11.9241	+	11.9241i	0.382663	+	0.382663i	0.872061	−	0.489398i	$-0.162783\pi$
$971$	11.9241	+	11.9241i	0.382663	+	0.382663i	−0.489398	+	0.872061i	$0.662783\pi$
$972$	26.4661	−	6.34736i	0.848902	−	0.203592i
$973$	5.32771	−	5.32771i	0.170799	−	0.170799i
$974$	−10.4615	+	37.0771i	−0.335210	+	1.18803i
$975$	−1.58586			−0.0507883
$976$	57.1490	+	18.5986i	1.82929	+	0.595327i
$977$	43.3574			1.38713			0.693563	−	0.720396i	$-0.256040\pi$
$977$	43.3574			1.38713			0.693563	+	0.720396i	$0.256040\pi$
$978$	5.55718	−	19.6954i	0.177699	−	0.629789i
$979$	−5.27890	+	5.27890i	−0.168714	+	0.168714i
$980$	11.3830	+	47.4630i	0.363618	+	1.51615i
$981$	17.3572	+	17.3572i	0.554173	+	0.554173i
$982$	28.7978	+	51.4365i	0.918976	+	1.64140i
$983$		−	27.5984i		−	0.880252i	−0.897936	−	0.440126i	$-0.854934\pi$
$983$		−	27.5984i		−	0.880252i	0.897936	−	0.440126i	$-0.145066\pi$
$984$	−0.0294437	+	0.742699i	−0.000938631	+	0.0236764i
$985$		−	36.3214i		−	1.15730i
$986$	−4.82206	+	2.69974i	−0.153566	+	0.0859771i
$987$	2.98461	+	2.98461i	0.0950013	+	0.0950013i
$988$	0.138375	−	0.225687i	0.00440228	−	0.00718007i
$989$	20.4065	−	20.4065i	0.648888	−	0.648888i
$990$	−24.2939	−	6.85467i	−0.772110	−	0.217856i
$991$	−1.61847			−0.0514124			−0.0257062	−	0.999670i	$-0.508183\pi$
$991$	−1.61847			−0.0514124			−0.0257062	+	0.999670i	$0.508183\pi$
$992$	−7.65186	−	38.5873i	−0.242947	−	1.22515i
$993$	24.5899			0.780337
$994$	−6.05462	−	1.70835i	−0.192041	−	0.0541855i
$995$	−39.1458	+	39.1458i	−1.24101	+	1.24101i
$996$	1.95377	−	3.18657i	0.0619074	−	0.100970i
$997$	−5.16110	−	5.16110i	−0.163454	−	0.163454i	0.620641	−	0.784095i	$-0.286872\pi$
$997$	−5.16110	−	5.16110i	−0.163454	−	0.163454i	−0.784095	+	0.620641i	$0.786872\pi$
$998$	−23.5940	+	13.2096i	−0.746853	+	0.418142i
$999$		−	19.6608i		−	0.622039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.69.2	✓	30
4.3	odd	2		1088.2.l.b.817.10		30
16.3	odd	4		1088.2.l.b.273.10		30
16.13	even	4	inner	272.2.l.b.205.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.2	✓	30	1.1	even	1	trivial
272.2.l.b.205.2	yes	30	16.13	even	4	inner
1088.2.l.b.273.10		30	16.3	odd	4
1088.2.l.b.817.10		30	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36107 - 0.384035i) q^{2} +(-0.873530 + 0.873530i) q^{3} +(1.70503 + 1.04540i) q^{4} +(2.72140 + 2.72140i) q^{5} +(1.52440 - 0.853471i) q^{6} +0.811757i q^{7} +(-1.91920 - 2.07766i) q^{8} +1.47389i q^{9} +(-2.65891 - 4.74914i) q^{10} +(-2.22499 - 2.22499i) q^{11} +(-2.40259 + 0.576211i) q^{12} +(0.0925117 - 0.0925117i) q^{13} +(0.311743 - 1.10486i) q^{14} -4.75446 q^{15} +(1.81428 + 3.56488i) q^{16} -1.00000 q^{17} +(0.566025 - 2.00607i) q^{18} +(0.715398 - 0.715398i) q^{19} +(1.79513 + 7.48504i) q^{20} +(-0.709095 - 0.709095i) q^{21} +(2.17390 + 3.88284i) q^{22} +5.62465i q^{23} +(3.49138 + 0.138413i) q^{24} +9.81208i q^{25} +(-0.161443 + 0.0903873i) q^{26} +(-3.90808 - 3.90808i) q^{27} +(-0.848610 + 1.38407i) q^{28} +(-2.76319 + 2.76319i) q^{29} +(6.47116 + 1.82588i) q^{30} +6.95416 q^{31} +(-1.10033 - 5.54881i) q^{32} +3.88719 q^{33} +(1.36107 + 0.384035i) q^{34} +(-2.20912 + 2.20912i) q^{35} +(-1.54080 + 2.51303i) q^{36} +(2.51540 + 2.51540i) q^{37} +(-1.24845 + 0.698970i) q^{38} +0.161624i q^{39} +(0.431213 - 10.8771i) q^{40} +0.212724i q^{41} +(0.692812 + 1.23745i) q^{42} +(-3.62804 - 3.62804i) q^{43} +(-1.46768 - 6.11968i) q^{44} +(-4.01105 + 4.01105i) q^{45} +(2.16006 - 7.65556i) q^{46} -4.20905 q^{47} +(-4.69886 - 1.52920i) q^{48} +6.34105 q^{49} +(3.76818 - 13.3550i) q^{50} +(0.873530 - 0.873530i) q^{51} +(0.254447 - 0.0610239i) q^{52} +(-8.32206 - 8.32206i) q^{53} +(3.81834 + 6.82002i) q^{54} -12.1102i q^{55} +(1.68655 - 1.55793i) q^{56} +1.24984i q^{57} +(4.82206 - 2.69974i) q^{58} +(9.73007 + 9.73007i) q^{59} +(-8.10651 - 4.97031i) q^{60} +(10.6241 - 10.6241i) q^{61} +(-9.46512 - 2.67064i) q^{62} -1.19644 q^{63} +(-0.633312 + 7.97489i) q^{64} +0.503523 q^{65} +(-5.29074 - 1.49282i) q^{66} +(-6.49328 + 6.49328i) q^{67} +(-1.70503 - 1.04540i) q^{68} +(-4.91331 - 4.91331i) q^{69} +(3.85515 - 2.15839i) q^{70} -5.47999i q^{71} +(3.06224 - 2.82869i) q^{72} +5.67133i q^{73} +(-2.45764 - 4.38964i) q^{74} +(-8.57115 - 8.57115i) q^{75} +(1.96765 - 0.471901i) q^{76} +(1.80615 - 1.80615i) q^{77} +(0.0620691 - 0.219981i) q^{78} +9.75031 q^{79} +(-4.76409 + 14.6389i) q^{80} +2.40598 q^{81} +(0.0816934 - 0.289532i) q^{82} +(-1.06975 + 1.06975i) q^{83} +(-0.467744 - 1.95032i) q^{84} +(-2.72140 - 2.72140i) q^{85} +(3.54473 + 6.33132i) q^{86} -4.82746i q^{87} +(-0.352554 + 8.89297i) q^{88} -2.37255i q^{89} +(6.99971 - 3.91894i) q^{90} +(0.0750970 + 0.0750970i) q^{91} +(-5.88001 + 9.59022i) q^{92} +(-6.07467 + 6.07467i) q^{93} +(5.72882 + 1.61642i) q^{94} +3.89377 q^{95} +(5.80822 + 3.88588i) q^{96} +13.9030 q^{97} +(-8.63063 - 2.43519i) q^{98} +(3.27939 - 3.27939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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