LMFDB - Embedded newform 273.2.l.c.256.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [273,2,Mod(16,273)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("273.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.8
Root			$0.904928 - 1.56738i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.c.16.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.80986 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.27558 q^{4} +(1.98776 + 3.44291i) q^{5} +(-0.904928 - 1.56738i) q^{6} +(1.70815 - 2.02045i) q^{7} -1.31110 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.59756 + 6.23116i) q^{10} +(0.143327 + 0.248250i) q^{11} +(-0.637789 - 1.10468i) q^{12} +(3.60075 - 0.185985i) q^{13} +(3.09151 - 3.65672i) q^{14} +(1.98776 - 3.44291i) q^{15} -4.92406 q^{16} -4.60182 q^{17} +(-0.904928 + 1.56738i) q^{18} +(3.48374 - 6.03402i) q^{19} +(2.53555 + 4.39170i) q^{20} +(-2.60384 - 0.469078i) q^{21} +(0.259402 + 0.449297i) q^{22} -7.23857 q^{23} +(0.655549 + 1.13544i) q^{24} +(-5.40240 + 9.35723i) q^{25} +(6.51684 - 0.336606i) q^{26} +1.00000 q^{27} +(2.17888 - 2.57724i) q^{28} +(0.421754 - 0.730500i) q^{29} +(3.59756 - 6.23116i) q^{30} +(-0.212854 + 0.368675i) q^{31} -6.28963 q^{32} +(0.143327 - 0.248250i) q^{33} -8.32864 q^{34} +(10.3516 + 1.86483i) q^{35} +(-0.637789 + 1.10468i) q^{36} -4.36416 q^{37} +(6.30507 - 10.9207i) q^{38} +(-1.96144 - 3.02535i) q^{39} +(-2.60615 - 4.51399i) q^{40} +(-0.509885 + 0.883147i) q^{41} +(-4.71257 - 0.848963i) q^{42} +(0.585291 + 1.01375i) q^{43} +(0.182825 + 0.316662i) q^{44} -3.97552 q^{45} -13.1008 q^{46} +(2.71264 + 4.69843i) q^{47} +(2.46203 + 4.26436i) q^{48} +(-1.16444 - 6.90247i) q^{49} +(-9.77756 + 16.9352i) q^{50} +(2.30091 + 3.98530i) q^{51} +(4.59304 - 0.237238i) q^{52} +(-0.574226 + 0.994589i) q^{53} +1.80986 q^{54} +(-0.569801 + 0.986924i) q^{55} +(-2.23956 + 2.64901i) q^{56} -6.96749 q^{57} +(0.763315 - 1.32210i) q^{58} -4.85854 q^{59} +(2.53555 - 4.39170i) q^{60} +(-4.08424 + 7.07411i) q^{61} +(-0.385236 + 0.667248i) q^{62} +(0.895685 + 2.48953i) q^{63} -1.53522 q^{64} +(7.79777 + 12.0274i) q^{65} +(0.259402 - 0.449297i) q^{66} +(-0.786937 - 1.36302i) q^{67} -5.86999 q^{68} +(3.61929 + 6.26879i) q^{69} +(18.7349 + 3.37507i) q^{70} +(-3.22369 - 5.58359i) q^{71} +(0.655549 - 1.13544i) q^{72} +(8.24845 - 14.2867i) q^{73} -7.89851 q^{74} +10.8048 q^{75} +(4.44379 - 7.69686i) q^{76} +(0.746401 + 0.134463i) q^{77} +(-3.54993 - 5.47545i) q^{78} +(-3.84412 - 6.65821i) q^{79} +(-9.78785 - 16.9531i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.922819 + 1.59837i) q^{82} +13.3888 q^{83} +(-3.32140 - 0.598345i) q^{84} +(-9.14733 - 15.8436i) q^{85} +(1.05929 + 1.83475i) q^{86} -0.843509 q^{87} +(-0.187916 - 0.325480i) q^{88} -2.21571 q^{89} -7.19513 q^{90} +(5.77486 - 7.59283i) q^{91} -9.23336 q^{92} +0.425709 q^{93} +(4.90949 + 8.50349i) q^{94} +27.6994 q^{95} +(3.14482 + 5.44698i) q^{96} +(9.52241 + 16.4933i) q^{97} +(-2.10746 - 12.4925i) q^{98} -0.286654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.80986			1.27976			0.639881	−	0.768474i	$-0.278984\pi$
$2$	1.80986			1.27976			0.639881	+	0.768474i	$0.278984\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.27558			0.637789
$5$	1.98776	+	3.44291i	0.888954	+	1.53971i	0.841113	+	0.540859i	$0.181901\pi$
$5$	1.98776	+	3.44291i	0.888954	+	1.53971i	0.0478412	+	0.998855i	$0.484766\pi$
$6$	−0.904928	−	1.56738i	−0.369435	−	0.639881i
$7$	1.70815	−	2.02045i	0.645621	−	0.763658i
$7$	1.70815	−	2.02045i	0.645621	−	0.763658i
$8$	−1.31110			−0.463543
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.59756	+	6.23116i	1.13765	+	1.97047i
$11$	0.143327	+	0.248250i	0.0432148	+	0.0748502i	0.886824	−	0.462108i	$-0.152907\pi$
$11$	0.143327	+	0.248250i	0.0432148	+	0.0748502i	−0.843609	+	0.536958i	$0.819573\pi$
$12$	−0.637789	−	1.10468i	−0.184114	−	0.318895i
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$14$	3.09151	−	3.65672i	0.826240	−	0.977300i
$15$	1.98776	−	3.44291i	0.513238	−	0.888954i
$16$	−4.92406			−1.23101
$17$	−4.60182			−1.11611			−0.558053	−	0.829805i	$-0.688452\pi$
$17$	−4.60182			−1.11611			−0.558053	+	0.829805i	$0.688452\pi$
$18$	−0.904928	+	1.56738i	−0.213294	+	0.369435i
$19$	3.48374	−	6.03402i	0.799225	−	1.38430i	−0.120896	−	0.992665i	$-0.538577\pi$
$19$	3.48374	−	6.03402i	0.799225	−	1.38430i	0.920121	−	0.391634i	$-0.128090\pi$
$20$	2.53555	+	4.39170i	0.566965	+	0.982013i
$21$	−2.60384	−	0.469078i	−0.568204	−	0.102361i
$22$	0.259402	+	0.449297i	0.0553046	+	0.0957904i
$23$	−7.23857			−1.50935			−0.754673	−	0.656101i	$-0.772205\pi$
$23$	−7.23857			−1.50935			−0.754673	+	0.656101i	$0.772205\pi$
$24$	0.655549	+	1.13544i	0.133813	+	0.231772i
$25$	−5.40240	+	9.35723i	−1.08048	+	1.87145i
$26$	6.51684	−	0.336606i	1.27806	−	0.0660139i
$27$	1.00000			0.192450
$28$	2.17888	−	2.57724i	0.411770	−	0.487053i
$29$	0.421754	−	0.730500i	0.0783178	−	0.135650i	−0.824206	−	0.566289i	$-0.808378\pi$
$29$	0.421754	−	0.730500i	0.0783178	−	0.135650i	0.902524	+	0.430639i	$0.141712\pi$
$30$	3.59756	−	6.23116i	0.656822	−	1.13765i
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	−0.884507	−	0.466527i	$-0.845505\pi$
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	0.846277	+	0.532742i	$0.178839\pi$
$32$	−6.28963			−1.11186
$33$	0.143327	−	0.248250i	0.0249501	−	0.0432148i
$34$	−8.32864			−1.42835
$35$	10.3516	+	1.86483i	1.74974	+	0.315214i
$36$	−0.637789	+	1.10468i	−0.106298	+	0.184114i
$37$	−4.36416			−0.717464			−0.358732	−	0.933441i	$-0.616791\pi$
$37$	−4.36416			−0.717464			−0.358732	+	0.933441i	$0.616791\pi$
$38$	6.30507	−	10.9207i	1.02282	−	1.77157i
$39$	−1.96144	−	3.02535i	−0.314082	−	0.484444i
$40$	−2.60615	−	4.51399i	−0.412069	−	0.713724i
$41$	−0.509885	+	0.883147i	−0.0796307	+	0.137924i	−0.903091	−	0.429450i	$-0.858707\pi$
$41$	−0.509885	+	0.883147i	−0.0796307	+	0.137924i	0.823460	+	0.567374i	$0.192041\pi$
$42$	−4.71257	−	0.848963i	−0.727165	−	0.130998i
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	0.907197	−	0.420706i	$-0.138218\pi$
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	−0.817941	+	0.575302i	$0.804884\pi$
$44$	0.182825	+	0.316662i	0.0275619	+	0.0477386i
$45$	−3.97552			−0.592636
$46$	−13.1008			−1.93160
$47$	2.71264	+	4.69843i	0.395680	+	0.685337i	0.993188	−	0.116526i	$-0.0371758\pi$
$47$	2.71264	+	4.69843i	0.395680	+	0.685337i	−0.597508	+	0.801863i	$0.703842\pi$
$48$	2.46203	+	4.26436i	0.355363	+	0.615507i
$49$	−1.16444	−	6.90247i	−0.166348	−	0.986067i
$50$	−9.77756	+	16.9352i	−1.38276	+	2.39500i
$51$	2.30091	+	3.98530i	0.322192	+	0.558053i
$52$	4.59304	−	0.237238i	0.636940	−	0.0328991i
$53$	−0.574226	+	0.994589i	−0.0788760	+	0.136617i	−0.902765	−	0.430134i	$-0.858466\pi$
$53$	−0.574226	+	0.994589i	−0.0788760	+	0.136617i	0.823889	+	0.566751i	$0.191800\pi$
$54$	1.80986			0.246290
$55$	−0.569801	+	0.986924i	−0.0768319	+	0.133077i
$56$	−2.23956	+	2.64901i	−0.299273	+	0.353989i
$57$	−6.96749			−0.922866
$58$	0.763315	−	1.32210i	0.100228	−	0.173600i
$59$	−4.85854			−0.632528			−0.316264	−	0.948671i	$-0.602429\pi$
$59$	−4.85854			−0.632528			−0.316264	+	0.948671i	$0.602429\pi$
$60$	2.53555	−	4.39170i	0.327338	−	0.566965i
$61$	−4.08424	+	7.07411i	−0.522933	+	0.905747i	0.476710	+	0.879060i	$0.341829\pi$
$61$	−4.08424	+	7.07411i	−0.522933	+	0.905747i	−0.999644	+	0.0266869i	$0.991504\pi$
$62$	−0.385236	+	0.667248i	−0.0489250	+	0.0847406i
$63$	0.895685	+	2.48953i	0.112846	+	0.313651i
$64$	−1.53522			−0.191902
$65$	7.79777	+	12.0274i	0.967194	+	1.49181i
$66$	0.259402	−	0.449297i	0.0319301	−	0.0553046i
$67$	−0.786937	−	1.36302i	−0.0961397	−	0.166519i	0.813944	−	0.580943i	$-0.197316\pi$
$67$	−0.786937	−	1.36302i	−0.0961397	−	0.166519i	−0.910084	+	0.414425i	$0.863983\pi$
$68$	−5.86999			−0.711841
$69$	3.61929	+	6.26879i	0.435711	+	0.754673i
$70$	18.7349	+	3.37507i	2.23925	+	0.403399i
$71$	−3.22369	−	5.58359i	−0.382581	−	0.662650i	0.608849	−	0.793286i	$-0.291631\pi$
$71$	−3.22369	−	5.58359i	−0.382581	−	0.662650i	−0.991430	+	0.130636i	$0.958298\pi$
$72$	0.655549	−	1.13544i	0.0772572	−	0.133813i
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.256893	−	0.966440i	$-0.417301\pi$
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.708515	−	0.705696i	$-0.249365\pi$
$74$	−7.89851			−0.918183
$75$	10.8048			1.24763
$76$	4.44379	−	7.69686i	0.509737	−	0.882891i
$77$	0.746401	+	0.134463i	0.0850603	+	0.0153235i
$78$	−3.54993	−	5.47545i	−0.401950	−	0.619972i
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	0.564590	−	0.825371i	$-0.309034\pi$
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	−0.997088	+	0.0762639i	$0.975701\pi$
$80$	−9.78785	−	16.9531i	−1.09432	−	1.89541i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.922819	+	1.59837i	−0.101908	+	0.176510i
$83$	13.3888			1.46961			0.734805	−	0.678279i	$-0.237274\pi$
$83$	13.3888			1.46961			0.734805	+	0.678279i	$0.237274\pi$
$84$	−3.32140	−	0.598345i	−0.362394	−	0.0652848i
$85$	−9.14733	−	15.8436i	−0.992168	−	1.71848i
$86$	1.05929	+	1.83475i	0.114226	+	0.197846i
$87$	−0.843509			−0.0904336
$88$	−0.187916	−	0.325480i	−0.0200319	−	0.0346963i
$89$	−2.21571			−0.234865			−0.117433	−	0.993081i	$-0.537466\pi$
$89$	−2.21571			−0.234865			−0.117433	+	0.993081i	$0.537466\pi$
$90$	−7.19513			−0.758433
$91$	5.77486	−	7.59283i	0.605369	−	0.795945i
$92$	−9.23336			−0.962645
$93$	0.425709			0.0441439
$94$	4.90949	+	8.50349i	0.506375	+	0.877068i
$95$	27.6994			2.84190
$96$	3.14482	+	5.44698i	0.320967	+	0.555930i
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.704549	+	0.709656i	$0.251150\pi$
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.262306	+	0.964985i	$0.415517\pi$
$98$	−2.10746	−	12.4925i	−0.212886	−	1.26193i
$99$	−0.286654			−0.0288098
$100$	−6.89118	+	11.9359i	−0.689118	+	1.19359i
$101$	4.54427	+	7.87091i	0.452172	+	0.783185i	0.998521	−	0.0543727i	$-0.0173159\pi$
$101$	4.54427	+	7.87091i	0.452172	+	0.783185i	−0.546348	+	0.837558i	$0.683983\pi$
$102$	4.16432	+	7.21281i	0.412329	+	0.714175i
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	0.958097	−	0.286443i	$-0.0924729\pi$
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	−0.727116	+	0.686515i	$0.759140\pi$
$104$	−4.72094	+	0.243845i	−0.462926	+	0.0239109i
$105$	−3.56082	−	9.89718i	−0.347500	−	0.965866i
$106$	−1.03927	+	1.80006i	−0.100943	+	0.174838i
$107$	14.5056			1.40231			0.701154	−	0.713010i	$-0.252669\pi$
$107$	14.5056			1.40231			0.701154	+	0.713010i	$0.252669\pi$
$108$	1.27558			0.122743
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	−0.747952	−	0.663752i	$-0.768963\pi$
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	0.948803	+	0.315870i	$0.102296\pi$
$110$	−1.03126	+	1.78619i	−0.0983265	+	0.170307i
$111$	2.18208	+	3.77948i	0.207114	+	0.358732i
$112$	−8.41104	+	9.94881i	−0.794768	+	0.940074i
$113$	4.12305	+	7.14133i	0.387864	+	0.671800i	0.992162	−	0.124958i	$-0.0398797\pi$
$113$	4.12305	+	7.14133i	0.387864	+	0.671800i	−0.604298	+	0.796758i	$0.706546\pi$
$114$	−12.6101			−1.18105
$115$	−14.3886	−	24.9217i	−1.34174	−	2.32396i
$116$	0.537981	−	0.931810i	0.0499503	−	0.0865164i
$117$	−1.63931	+	3.21133i	−0.151554	+	0.296888i
$118$	−8.79326			−0.809485
$119$	−7.86061	+	9.29776i	−0.720581	+	0.852324i
$120$	−2.60615	+	4.51399i	−0.237908	+	0.412069i
$121$	5.45891	−	9.45512i	0.496265	−	0.859556i
$122$	−7.39189	+	12.8031i	−0.669230	+	1.15914i
$123$	1.01977			0.0919496
$124$	−0.271512	+	0.470273i	−0.0243825	+	0.0422318i
$125$	−23.0771			−2.06408
$126$	1.62106	+	4.50569i	0.144416	+	0.401398i
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	−0.985894	−	0.167374i	$-0.946471\pi$
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	0.637897	+	0.770122i	$0.279805\pi$
$128$	9.80074			0.866272
$129$	0.585291	−	1.01375i	0.0515320	−	0.0892560i
$130$	14.1128	+	21.7678i	1.23778	+	1.90916i
$131$	−4.04277	−	7.00228i	−0.353218	−	0.611792i	0.633593	−	0.773666i	$-0.281579\pi$
$131$	−4.04277	−	7.00228i	−0.353218	−	0.611792i	−0.986811	+	0.161874i	$0.948246\pi$
$132$	0.182825	−	0.316662i	0.0159129	−	0.0275619i
$133$	−6.24067	−	17.3457i	−0.541135	−	1.50407i
$134$	−1.42424	−	2.46686i	−0.123036	−	0.213104i
$135$	1.98776	+	3.44291i	0.171079	+	0.296318i
$136$	6.03345			0.517364
$137$	1.50968			0.128981			0.0644904	−	0.997918i	$-0.479458\pi$
$137$	1.50968			0.128981			0.0644904	+	0.997918i	$0.479458\pi$
$138$	6.55039	+	11.3456i	0.557606	+	0.965802i
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	0.938926	−	0.344120i	$-0.111823\pi$
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	−0.767479	+	0.641074i	$0.778489\pi$
$140$	13.2043	+	2.37874i	1.11597	+	0.201040i
$141$	2.71264	−	4.69843i	0.228446	−	0.395680i
$142$	−5.83441	−	10.1055i	−0.489613	−	0.848034i
$143$	0.562256	+	0.867230i	0.0470182	+	0.0725214i
$144$	2.46203	−	4.26436i	0.205169	−	0.355363i
$145$	3.35339			0.278484
$146$	14.9285	−	25.8569i	1.23549	−	2.13993i
$147$	−5.39550	+	4.45967i	−0.445013	+	0.367827i
$148$	−5.56683			−0.457591
$149$	9.59737	−	16.6231i	0.786247	−	1.36182i	−0.142004	−	0.989866i	$-0.545355\pi$
$149$	9.59737	−	16.6231i	0.786247	−	1.36182i	0.928251	−	0.371954i	$-0.121312\pi$
$150$	19.5551			1.59667
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	0.166125	+	0.986105i	$0.446874\pi$
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	−0.937054	+	0.349184i	$0.886459\pi$
$152$	−4.56753	+	7.91120i	−0.370476	+	0.641683i
$153$	2.30091	−	3.98530i	0.186018	−	0.322192i
$154$	1.35088	+	0.243359i	0.108857	+	0.0196104i
$155$	−1.69242			−0.135938
$156$	−2.50197	−	3.85907i	−0.200318	−	0.308973i
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	0.207197	+	0.978299i	$0.433566\pi$
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	−0.950831	+	0.309711i	$0.899768\pi$
$158$	−6.95730	−	12.0504i	−0.553493	−	0.958679i
$159$	1.14845			0.0910782
$160$	−12.5023	−	21.6546i	−0.988394	−	1.71195i
$161$	−12.3646	+	14.6252i	−0.974465	+	1.15262i
$162$	−0.904928	−	1.56738i	−0.0710979	−	0.123145i
$163$	−5.35262	+	9.27102i	−0.419250	+	0.726162i	−0.995864	−	0.0908544i	$-0.971040\pi$
$163$	−5.35262	+	9.27102i	−0.419250	+	0.726162i	0.576614	+	0.817016i	$0.304374\pi$
$164$	−0.650398	+	1.12652i	−0.0507876	+	0.0879667i
$165$	1.13960			0.0887179
$166$	24.2318			1.88075
$167$	0.0240620	−	0.0416766i	0.00186197	−	0.00322503i	−0.865093	−	0.501612i	$-0.832741\pi$
$167$	0.0240620	−	0.0416766i	0.00186197	−	0.00322503i	0.866955	+	0.498387i	$0.166074\pi$
$168$	3.41389	+	0.615007i	0.263387	+	0.0474489i
$169$	12.9308	−	1.33937i	0.994678	−	0.103029i
$170$	−16.5554	−	28.6747i	−1.26974	−	2.19925i
$171$	3.48374	+	6.03402i	0.266408	+	0.461433i
$172$	0.746584	+	1.29312i	0.0569265	+	0.0985996i
$173$	7.01486	−	12.1501i	0.533330	−	0.923755i	−0.465912	−	0.884831i	$-0.654274\pi$
$173$	7.01486	−	12.1501i	0.533330	−	0.923755i	0.999242	−	0.0389240i	$-0.0123930\pi$
$174$	−1.52663			−0.115733
$175$	9.67770	+	26.8988i	0.731565	+	2.03336i
$176$	−0.705751	−	1.22240i	−0.0531980	−	0.0921416i
$177$	2.42927	+	4.20762i	0.182595	+	0.316264i
$178$	−4.01012			−0.300571
$179$	−2.34931	−	4.06913i	−0.175596	−	0.304141i	0.764771	−	0.644302i	$-0.222852\pi$
$179$	−2.34931	−	4.06913i	−0.175596	−	0.304141i	−0.940367	+	0.340161i	$0.889519\pi$
$180$	−5.07109			−0.377977
$181$	−22.0382			−1.63809			−0.819044	−	0.573730i	$-0.805496\pi$
$181$	−22.0382			−1.63809			−0.819044	+	0.573730i	$0.805496\pi$
$182$	10.4517	−	13.7419i	0.774728	−	1.01862i
$183$	8.16848			0.603832
$184$	9.49048			0.699648
$185$	−8.67492	−	15.0254i	−0.637793	−	1.10469i
$186$	0.770472			0.0564937
$187$	−0.659567	−	1.14240i	−0.0482323	−	0.0835408i
$188$	3.46019	+	5.99322i	0.252360	+	0.437101i
$189$	1.70815	−	2.02045i	0.124250	−	0.146966i
$190$	50.1319			3.63695
$191$	−5.54871	+	9.61065i	−0.401491	+	0.695402i	−0.993906	−	0.110230i	$-0.964841\pi$
$191$	−5.54871	+	9.61065i	−0.401491	+	0.695402i	0.592415	+	0.805633i	$0.298174\pi$
$192$	0.767610	+	1.32954i	0.0553975	+	0.0959512i
$193$	0.243115	+	0.421088i	0.0174998	+	0.0303106i	0.874643	−	0.484768i	$-0.161096\pi$
$193$	0.243115	+	0.421088i	0.0174998	+	0.0303106i	−0.857143	+	0.515079i	$0.827763\pi$
$194$	17.2342	+	29.8505i	1.23734	+	2.14314i
$195$	6.51711	−	12.7667i	0.466700	−	0.914245i
$196$	−1.48533	−	8.80464i	−0.106095	−	0.628903i
$197$	−8.53814	+	14.7885i	−0.608317	+	1.05364i	0.383200	+	0.923665i	$0.374822\pi$
$197$	−8.53814	+	14.7885i	−0.608317	+	1.05364i	−0.991518	+	0.129971i	$0.958511\pi$
$198$	−0.518803			−0.0368697
$199$	23.1698			1.64246			0.821230	−	0.570597i	$-0.193288\pi$
$199$	23.1698			1.64246			0.821230	+	0.570597i	$0.193288\pi$
$200$	7.08308	−	12.2683i	0.500849	−	0.867497i
$201$	−0.786937	+	1.36302i	−0.0555063	+	0.0961397i
$202$	8.22448	+	14.2452i	0.578673	+	1.00229i
$203$	−0.755518	−	2.09994i	−0.0530270	−	0.147387i
$204$	2.93499	+	5.08356i	0.205491	+	0.355920i
$205$	−4.05412			−0.283152
$206$	4.24268	+	7.34853i	0.295601	+	0.511997i
$207$	3.61929	−	6.26879i	0.251558	−	0.435711i
$208$	−17.7303	+	0.915801i	−1.22938	+	0.0634994i
$209$	1.99726			0.138153
$210$	−6.44457	−	17.9125i	−0.444717	−	1.23608i
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	−0.813487	−	0.581583i	$-0.802433\pi$
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	0.910409	+	0.413709i	$0.135767\pi$
$212$	−0.732470	+	1.26868i	−0.0503063	+	0.0871330i
$213$	−3.22369	+	5.58359i	−0.220883	+	0.382581i
$214$	26.2530			1.79462
$215$	−2.32684	+	4.03020i	−0.158689	+	0.274857i
$216$	−1.31110			−0.0892090
$217$	0.381301	+	1.05981i	0.0258844	+	0.0719449i
$218$	3.79515	−	6.57340i	0.257040	−	0.445207i
$219$	−16.4969			−1.11476
$220$	−0.726825	+	1.25890i	−0.0490026	+	0.0848749i
$221$	−16.5700	+	0.855871i	−1.11462	+	0.0575721i
$222$	3.94925	+	6.84031i	0.265057	+	0.459092i
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	0.451916	+	0.892061i	$0.350741\pi$
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	−0.998505	+	0.0546597i	$0.982593\pi$
$224$	−10.7437	+	12.7079i	−0.717840	+	0.849082i
$225$	−5.40240	−	9.35723i	−0.360160	−	0.623815i
$226$	7.46213	+	12.9248i	0.496373	+	0.859744i
$227$	−6.20577			−0.411892			−0.205946	−	0.978563i	$-0.566027\pi$
$227$	−6.20577			−0.411892			−0.205946	+	0.978563i	$0.566027\pi$
$228$	−8.88757			−0.588594
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	0.874535	−	0.484962i	$-0.161167\pi$
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	−0.857257	+	0.514889i	$0.827833\pi$
$230$	−26.0412	−	45.1047i	−1.71711	−	2.97412i
$231$	−0.256752	−	0.713634i	−0.0168930	−	0.0469537i
$232$	−0.552962	+	0.957758i	−0.0363037	+	0.0628799i
$233$	−6.48273	−	11.2284i	−0.424697	−	0.735598i	0.571695	−	0.820466i	$-0.306286\pi$
$233$	−6.48273	−	11.2284i	−0.424697	−	0.735598i	−0.996392	+	0.0848689i	$0.972953\pi$
$234$	−2.96691	+	5.81205i	−0.193953	+	0.379946i
$235$	−10.7842	+	18.6787i	−0.703482	+	1.21847i
$236$	−6.19745			−0.403419
$237$	−3.84412	+	6.65821i	−0.249702	+	0.432497i
$238$	−14.2266	+	16.8276i	−0.922172	+	1.09077i
$239$	−4.79605			−0.310231			−0.155116	−	0.987896i	$-0.549575\pi$
$239$	−4.79605			−0.310231			−0.155116	+	0.987896i	$0.549575\pi$
$240$	−9.78785	+	16.9531i	−0.631803	+	1.09432i
$241$	10.4195			0.671179			0.335589	−	0.942008i	$-0.391065\pi$
$241$	10.4195			0.671179			0.335589	+	0.942008i	$0.391065\pi$
$242$	9.87985	−	17.1124i	0.635101	−	1.10003i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.20977	+	9.02358i	−0.333521	+	0.577676i
$245$	21.4499	−	17.7295i	1.37039	−	1.13270i
$246$	1.84564			0.117674
$247$	11.4219	−	22.3749i	0.726755	−	1.42368i
$248$	0.279073	−	0.483369i	0.0177212	−	0.0306940i
$249$	−6.69439	−	11.5950i	−0.424240	−	0.734805i
$250$	−41.7663			−2.64153
$251$	−5.10645	−	8.84463i	−0.322316	−	0.558268i	0.658649	−	0.752450i	$-0.271128\pi$
$251$	−5.10645	−	8.84463i	−0.322316	−	0.558268i	−0.980966	+	0.194182i	$0.937795\pi$
$252$	1.14252	+	3.17559i	0.0719718	+	0.200043i
$253$	−1.03748	−	1.79698i	−0.0652261	−	0.112975i
$254$	−7.09776	+	12.2937i	−0.445353	+	0.771374i
$255$	−9.14733	+	15.8436i	−0.572828	+	0.992168i
$256$	20.8084			1.30052
$257$	−6.36280			−0.396901			−0.198450	−	0.980111i	$-0.563591\pi$
$257$	−6.36280			−0.396901			−0.198450	+	0.980111i	$0.563591\pi$
$258$	1.05929	−	1.83475i	0.0659486	−	0.114226i
$259$	−7.45466	+	8.81758i	−0.463210	+	0.547898i
$260$	9.94666	+	15.3418i	0.616866	+	0.951460i
$261$	0.421754	+	0.730500i	0.0261059	+	0.0452168i
$262$	−7.31683	−	12.6731i	−0.452035	−	0.782948i
$263$	8.50677	+	14.7342i	0.524550	+	0.908547i	0.999591	+	0.0285838i	$0.00909974\pi$
$263$	8.50677	+	14.7342i	0.524550	+	0.908547i	−0.475041	+	0.879963i	$0.657567\pi$
$264$	−0.187916	+	0.325480i	−0.0115654	+	0.0200319i
$265$	−4.56570			−0.280469
$266$	−11.2947	−	31.3933i	−0.692524	−	1.92485i
$267$	1.10786	+	1.91886i	0.0677997	+	0.117433i
$268$	−1.00380	−	1.73863i	−0.0613168	−	0.106204i
$269$	−9.06039			−0.552422			−0.276211	−	0.961097i	$-0.589079\pi$
$269$	−9.06039			−0.552422			−0.276211	+	0.961097i	$0.589079\pi$
$270$	3.59756	+	6.23116i	0.218941	+	0.379216i
$271$	2.22796			0.135339			0.0676696	−	0.997708i	$-0.478444\pi$
$271$	2.22796			0.135339			0.0676696	+	0.997708i	$0.478444\pi$
$272$	22.6596			1.37394
$273$	−9.46301	−	1.20476i	−0.572727	−	0.0729153i
$274$	2.73231			0.165065
$275$	−3.09724			−0.186771
$276$	4.61668	+	7.99633i	0.277892	+	0.481322i
$277$	−7.80754			−0.469110			−0.234555	−	0.972103i	$-0.575363\pi$
$277$	−7.80754			−0.469110			−0.234555	+	0.972103i	$0.575363\pi$
$278$	3.65830	+	6.33637i	0.219411	+	0.380030i
$279$	−0.212854	−	0.368675i	−0.0127433	−	0.0220720i
$280$	−13.5720	−	2.44498i	−0.811082	−	0.146115i
$281$	−12.7531			−0.760789			−0.380394	−	0.924824i	$-0.624212\pi$
$281$	−12.7531			−0.760789			−0.380394	+	0.924824i	$0.624212\pi$
$282$	4.90949	−	8.50349i	0.292356	−	0.506375i
$283$	−8.17193	−	14.1542i	−0.485771	−	0.841380i	0.514095	−	0.857733i	$-0.328128\pi$
$283$	−8.17193	−	14.1542i	−0.485771	−	0.841380i	−0.999866	+	0.0163530i	$0.994794\pi$
$284$	−4.11206	−	7.12230i	−0.244006	−	0.422631i
$285$	−13.8497	−	23.9884i	−0.820386	−	1.42095i
$286$	1.01760	+	1.56956i	0.0601721	+	0.0928101i
$287$	0.913393	+	2.53875i	0.0539159	+	0.149857i
$288$	3.14482	−	5.44698i	0.185310	−	0.320967i
$289$	4.17679			0.245694
$290$	6.06915			0.356393
$291$	9.52241	−	16.4933i	0.558214	−	0.966854i
$292$	10.5215	−	18.2238i	0.615727	−	1.06647i
$293$	11.8319	+	20.4935i	0.691227	+	1.19724i	0.971436	+	0.237302i	$0.0762630\pi$
$293$	11.8319	+	20.4935i	0.691227	+	1.19724i	−0.280209	+	0.959939i	$0.590404\pi$
$294$	−9.76507	+	8.07135i	−0.569511	+	0.470731i
$295$	−9.65762	−	16.7275i	−0.562288	−	0.973912i
$296$	5.72185			0.332576
$297$	0.143327	+	0.248250i	0.00831669	+	0.0144049i
$298$	17.3699	−	30.0855i	1.00621	−	1.74280i
$299$	−26.0643	+	1.34627i	−1.50734	+	0.0778566i
$300$	13.7824			0.795725
$301$	3.04800	+	0.549094i	0.175684	+	0.0316492i
$302$	−17.1454	+	29.6967i	−0.986605	+	1.70885i
$303$	4.54427	−	7.87091i	0.261062	−	0.452172i
$304$	−17.1541	+	29.7119i	−0.983858	+	1.70409i
$305$	−32.4740			−1.85946
$306$	4.16432	−	7.21281i	0.238058	−	0.412329i
$307$	8.99691			0.513481			0.256740	−	0.966480i	$-0.417351\pi$
$307$	8.99691			0.513481			0.256740	+	0.966480i	$0.417351\pi$
$308$	0.952093	+	0.171518i	0.0542505	+	0.00977316i
$309$	2.34421	−	4.06029i	0.133357	−	0.230982i
$310$	−3.06303			−0.173968
$311$	15.4498	−	26.7598i	0.876077	−	1.51741i	0.0204655	−	0.999791i	$-0.493485\pi$
$311$	15.4498	−	26.7598i	0.876077	−	1.51741i	0.855611	−	0.517619i	$-0.173181\pi$
$312$	2.57165	+	3.96653i	0.145591	+	0.224561i
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	0.952254	−	0.305308i	$-0.0987595\pi$
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	−0.740532	+	0.672022i	$0.765426\pi$
$314$	−16.8637	+	29.2088i	−0.951673	+	1.64835i
$315$	−6.79080	+	8.03235i	−0.382618	+	0.452572i
$316$	−4.90348	−	8.49307i	−0.275842	−	0.477773i
$317$	8.11402	+	14.0539i	0.455729	+	0.789346i	0.998730	−	0.0503864i	$-0.0160453\pi$
$317$	8.11402	+	14.0539i	0.455729	+	0.789346i	−0.543001	+	0.839732i	$0.682712\pi$
$318$	2.07853			0.116558
$319$	0.241796			0.0135379
$320$	−3.05165	−	5.28562i	−0.170593	−	0.295475i
$321$	−7.25279	−	12.5622i	−0.404811	−	0.701154i
$322$	−22.3781	+	26.4695i	−1.24708	+	1.47508i
$323$	−16.0316	+	27.7675i	−0.892021	+	1.54503i
$324$	−0.637789	−	1.10468i	−0.0354327	−	0.0613713i
$325$	−17.7124	+	34.6978i	−0.982507	+	1.92469i
$326$	−9.68748	+	16.7792i	−0.536540	+	0.929314i
$327$	−4.19387			−0.231922
$328$	0.668510	−	1.15789i	0.0369123	−	0.0639340i
$329$	14.1266	+	2.54488i	0.778822	+	0.140304i
$330$	2.06251			0.113538
$331$	−2.79217	+	4.83618i	−0.153472	+	0.265821i	−0.932501	−	0.361166i	$-0.882379\pi$
$331$	−2.79217	+	4.83618i	−0.153472	+	0.265821i	0.779030	+	0.626987i	$0.215712\pi$
$332$	17.0784			0.937301
$333$	2.18208	−	3.77948i	0.119577	−	0.207114i
$334$	0.0435488	−	0.0754287i	0.00238288	−	0.00412727i
$335$	3.12849	−	5.41870i	0.170928	−	0.296055i
$336$	12.8214	+	2.30977i	0.699467	+	0.126008i
$337$	−0.504097			−0.0274599			−0.0137299	−	0.999906i	$-0.504371\pi$
$337$	−0.504097			−0.0274599			−0.0137299	+	0.999906i	$0.504371\pi$
$338$	23.4029	−	2.42407i	1.27295	−	0.131852i
$339$	4.12305	−	7.14133i	0.223933	−	0.387864i
$340$	−11.6681	−	20.2098i	−0.632794	−	1.09603i
$341$	−0.122031			−0.00660836
$342$	6.30507	+	10.9207i	0.340939	+	0.590524i
$343$	−15.9351	−	9.43778i	−0.860416	−	0.509592i
$344$	−0.767374	−	1.32913i	−0.0413740	−	0.0716619i
$345$	−14.3886	+	24.9217i	−0.774654	+	1.34174i
$346$	12.6959	−	21.9899i	0.682535	−	1.18219i
$347$	−12.1334			−0.651357			−0.325678	−	0.945481i	$-0.605593\pi$
$347$	−12.1334			−0.651357			−0.325678	+	0.945481i	$0.605593\pi$
$348$	−1.07596			−0.0576776
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	−0.411084	−	0.911597i	$-0.634850\pi$
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	0.995009	−	0.0997893i	$-0.0318169\pi$
$350$	17.5152	+	48.6830i	0.936229	+	2.60222i
$351$	3.60075	−	0.185985i	0.192194	−	0.00992715i
$352$	−0.901476	−	1.56140i	−0.0480488	−	0.0832230i
$353$	6.04396	+	10.4684i	0.321688	+	0.557179i	0.980836	−	0.194833i	$-0.0624166\pi$
$353$	6.04396	+	10.4684i	0.321688	+	0.557179i	−0.659149	+	0.752013i	$0.729083\pi$
$354$	4.39663	+	7.61518i	0.233678	+	0.404742i
$355$	12.8158	−	22.1977i	0.680194	−	1.17813i
$356$	−2.82631			−0.149794
$357$	11.9824	+	2.15861i	0.634176	+	0.114246i
$358$	−4.25192	−	7.36454i	−0.224721	−	0.389228i
$359$	−7.22027	−	12.5059i	−0.381071	−	0.660035i	0.610144	−	0.792290i	$-0.291111\pi$
$359$	−7.22027	−	12.5059i	−0.381071	−	0.660035i	−0.991216	+	0.132255i	$0.957778\pi$
$360$	5.21231			0.274713
$361$	−14.7729	−	25.5875i	−0.777523	−	1.34671i
$362$	−39.8860			−2.09636
$363$	−10.9178			−0.573037
$364$	7.36628	−	9.68525i	0.386098	−	0.507645i
$365$	65.5838			3.43281
$366$	14.7838			0.772760
$367$	−12.1894	−	21.1126i	−0.636280	−	1.10207i	−0.986242	−	0.165305i	$-0.947139\pi$
$367$	−12.1894	−	21.1126i	−0.636280	−	1.10207i	0.349963	−	0.936764i	$-0.386194\pi$
$368$	35.6431			1.85803
$369$	−0.509885	−	0.883147i	−0.0265436	−	0.0459748i
$370$	−15.7004	−	27.1938i	−0.816223	−	1.41374i
$371$	1.02865	+	2.85910i	0.0534049	+	0.148437i
$372$	0.543025			0.0281545
$373$	4.20017	−	7.27490i	0.217476	−	0.376680i	−0.736559	−	0.676373i	$-0.763551\pi$
$373$	4.20017	−	7.27490i	0.217476	−	0.376680i	0.954036	+	0.299693i	$0.0968842\pi$
$374$	−1.19372	−	2.06758i	−0.0617258	−	0.106912i
$375$	11.5386	+	19.9854i	0.595849	+	1.03204i
$376$	−3.55654	−	6.16011i	−0.183415	−	0.317684i
$377$	1.38277	−	2.70879i	0.0712163	−	0.139510i
$378$	3.09151	−	3.65672i	0.159010	−	0.188082i
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	−0.909169	−	0.416428i	$-0.863282\pi$
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	0.815222	+	0.579149i	$0.196615\pi$
$380$	35.3328			1.81253
$381$	7.84345			0.401832
$382$	−10.0424	+	17.3939i	−0.513812	+	0.889949i
$383$	15.3526	−	26.5915i	0.784481	−	1.35876i	−0.144827	−	0.989457i	$-0.546263\pi$
$383$	15.3526	−	26.5915i	0.784481	−	1.35876i	0.929308	−	0.369305i	$-0.120404\pi$
$384$	−4.90037	−	8.48769i	−0.250071	−	0.433136i
$385$	1.02072	+	2.83707i	0.0520209	+	0.144590i
$386$	0.440003	+	0.762108i	0.0223956	+	0.0387903i
$387$	−1.17058			−0.0595040
$388$	12.1466	+	21.0385i	0.616649	+	1.06807i
$389$	−9.21889	+	15.9676i	−0.467416	+	0.809589i	−0.999307	−	0.0372241i	$-0.988148\pi$
$389$	−9.21889	+	15.9676i	−0.467416	+	0.809589i	0.531890	+	0.846813i	$0.321482\pi$
$390$	11.7950	−	23.1060i	0.597264	−	1.17002i
$391$	33.3106			1.68459
$392$	1.52669	+	9.04982i	0.0771095	+	0.457085i
$393$	−4.04277	+	7.00228i	−0.203931	+	0.353218i
$394$	−15.4528	+	26.7650i	−0.778501	+	1.34840i
$395$	15.2824	−	26.4699i	0.768941	−	1.33184i
$396$	−0.365650			−0.0183746
$397$	1.13032	−	1.95777i	0.0567290	−	0.0982576i	−0.836266	−	0.548324i	$-0.815266\pi$
$397$	1.13032	−	1.95777i	0.0567290	−	0.0982576i	0.892995	+	0.450066i	$0.148600\pi$
$398$	41.9339			2.10196
$399$	−11.9015	+	14.0775i	−0.595821	+	0.704754i
$400$	26.6017	−	46.0755i	1.33009	−	2.30378i
$401$	28.5217			1.42431			0.712153	−	0.702024i	$-0.247720\pi$
$401$	28.5217			1.42431			0.712153	+	0.702024i	$0.247720\pi$
$402$	−1.42424	+	2.46686i	−0.0710348	+	0.123036i
$403$	−0.697868	+	1.36709i	−0.0347633	+	0.0680998i
$404$	5.79658	+	10.0400i	0.288391	+	0.499507i
$405$	1.98776	−	3.44291i	0.0987727	−	0.171079i
$406$	−1.36738	−	3.80059i	−0.0678619	−	0.188620i
$407$	−0.625503	−	1.08340i	−0.0310051	−	0.0537023i
$408$	−3.01672	−	5.22512i	−0.149350	−	0.258682i
$409$	10.8540			0.536695			0.268348	−	0.963322i	$-0.413522\pi$
$409$	10.8540			0.536695			0.268348	+	0.963322i	$0.413522\pi$
$410$	−7.33738			−0.362367
$411$	−0.754841	−	1.30742i	−0.0372335	−	0.0644904i
$412$	2.99022	+	5.17921i	0.147318	+	0.255162i
$413$	−8.29912	+	9.81643i	−0.408373	+	0.483035i
$414$	6.55039	−	11.3456i	0.321934	−	0.557606i
$415$	26.6137	+	46.0963i	1.30642	+	2.26278i
$416$	−22.6474	+	1.16978i	−1.11038	+	0.0573531i
$417$	2.02132	−	3.50104i	0.0989846	−	0.171446i
$418$	3.61475			0.176803
$419$	−7.68279	+	13.3070i	−0.375329	+	0.650089i	−0.990376	−	0.138401i	$-0.955804\pi$
$419$	−7.68279	+	13.3070i	−0.375329	+	0.650089i	0.615047	+	0.788490i	$0.289137\pi$
$420$	−4.54210	−	12.6246i	−0.221632	−	0.616019i
$421$	−3.33695			−0.162633			−0.0813166	−	0.996688i	$-0.525912\pi$
$421$	−3.33695			−0.162633			−0.0813166	+	0.996688i	$0.525912\pi$
$422$	2.54806	−	4.41337i	0.124038	−	0.214839i
$423$	−5.42528			−0.263786
$424$	0.752867	−	1.30400i	0.0365625	−	0.0633281i
$425$	24.8609	−	43.0603i	1.20593	−	2.08873i
$426$	−5.83441	+	10.1055i	−0.282678	+	0.489613i
$427$	7.31639	+	20.3357i	0.354065	+	0.984112i
$428$	18.5030			0.894377
$429$	0.469915	−	0.920543i	0.0226877	−	0.0444442i
$430$	−4.21124	+	7.29408i	−0.203084	+	0.351752i
$431$	2.13047	+	3.69008i	0.102621	+	0.177745i	0.912764	−	0.408488i	$-0.133944\pi$
$431$	2.13047	+	3.69008i	0.102621	+	0.177745i	−0.810143	+	0.586233i	$0.800610\pi$
$432$	−4.92406			−0.236909
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	0.700792	−	0.713365i	$-0.252830\pi$
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	−0.968189	+	0.250221i	$0.919497\pi$
$434$	0.690100	+	1.91811i	0.0331259	+	0.0920722i
$435$	−1.67670	−	2.90412i	−0.0803914	−	0.139242i
$436$	2.67481	−	4.63290i	0.128100	−	0.221876i
$437$	−25.2173	+	43.6777i	−1.20631	+	2.08939i
$438$	−29.8570			−1.42662
$439$	41.0024			1.95694			0.978470	−	0.206389i	$-0.0661712\pi$
$439$	41.0024			1.95694			0.978470	+	0.206389i	$0.0661712\pi$
$440$	0.747065	−	1.29395i	0.0356149	−	0.0616869i
$441$	6.55993	+	2.44280i	0.312378	+	0.116324i
$442$	−29.9894	+	1.54900i	−1.42645	+	0.0736785i
$443$	−7.92693	−	13.7298i	−0.376620	−	0.652325i	0.613948	−	0.789346i	$-0.289580\pi$
$443$	−7.92693	−	13.7298i	−0.376620	−	0.652325i	−0.990568	+	0.137022i	$0.956247\pi$
$444$	2.78342	+	4.82102i	0.132095	+	0.228795i
$445$	−4.40431	−	7.62849i	−0.208784	−	0.361625i
$446$	−14.7726	+	25.5869i	−0.699504	+	1.21158i
$447$	−19.1947			−0.907880
$448$	−2.62239	+	3.10183i	−0.123896	+	0.146548i
$449$	−7.54997	−	13.0769i	−0.356305	−	0.617139i	0.631035	−	0.775754i	$-0.282630\pi$
$449$	−7.54997	−	13.0769i	−0.356305	−	0.617139i	−0.987340	+	0.158616i	$0.949297\pi$
$450$	−9.77756	−	16.9352i	−0.460919	−	0.798335i
$451$	−0.292322			−0.0137649
$452$	5.25927	+	9.10933i	0.247375	+	0.428467i
$453$	18.9467			0.890192
$454$	−11.2316			−0.527123
$455$	37.6204	+	4.78954i	1.76367	+	0.224537i
$456$	9.13506			0.427789
$457$	−0.0278479			−0.00130267			−0.000651335	−	1.00000i	$-0.500207\pi$
$457$	−0.0278479			−0.00130267			−0.000651335		1.00000i	$0.500207\pi$
$458$	0.473210	+	0.819624i	0.0221116	+	0.0382985i
$459$	−4.60182			−0.214795
$460$	−18.3537	−	31.7896i	−0.855747	−	1.48220i
$461$	14.0543	+	24.3428i	0.654575	+	1.13376i	0.982000	+	0.188880i	$0.0604859\pi$
$461$	14.0543	+	24.3428i	0.654575	+	1.13376i	−0.327425	+	0.944877i	$0.606181\pi$
$462$	−0.464684	−	1.29157i	−0.0216191	−	0.0600895i
$463$	−0.266538			−0.0123871			−0.00619354	−	0.999981i	$-0.501971\pi$
$463$	−0.266538			−0.0123871			−0.00619354	+	0.999981i	$0.501971\pi$
$464$	−2.07674	+	3.59702i	−0.0964104	+	0.166988i
$465$	0.846208	+	1.46568i	0.0392420	+	0.0679691i
$466$	−11.7328	−	20.3218i	−0.543511	−	0.941389i
$467$	−18.5400	−	32.1123i	−0.857931	−	1.48598i	−0.873899	−	0.486107i	$-0.838417\pi$
$467$	−18.5400	−	32.1123i	−0.857931	−	1.48598i	0.0159687	−	0.999872i	$-0.494917\pi$
$468$	−2.09107	+	4.09631i	−0.0966595	+	0.189352i
$469$	−4.09811	−	0.738270i	−0.189233	−	0.0340901i
$470$	−19.5178	+	33.8058i	−0.900289	+	1.55935i
$471$	18.6354			0.858674
$472$	6.37002			0.293204
$473$	−0.167776	+	0.290597i	−0.00771436	+	0.0133617i
$474$	−6.95730	+	12.0504i	−0.319560	+	0.553493i
$475$	37.6411	+	65.1964i	1.72709	+	2.99141i
$476$	−10.0268	+	11.8600i	−0.459579	+	0.543603i
$477$	−0.574226	−	0.994589i	−0.0262920	−	0.0455391i
$478$	−8.68017			−0.397022
$479$	−14.3993	−	24.9404i	−0.657922	−	1.13955i	−0.981153	−	0.193234i	$-0.938102\pi$
$479$	−14.3993	−	24.9404i	−0.657922	−	1.13955i	0.323231	−	0.946320i	$-0.395231\pi$
$480$	−12.5023	+	21.6546i	−0.570649	+	0.988394i
$481$	−15.7143	+	0.811669i	−0.716509	+	0.0370089i
$482$	18.8578			0.858949
$483$	18.8481	+	3.39545i	0.857616	+	0.154498i
$484$	6.96327	−	12.0607i	0.316512	−	0.548216i
$485$	−37.8566	+	65.5695i	−1.71898	+	2.97736i
$486$	−0.904928	+	1.56738i	−0.0410484	+	0.0710979i
$487$	−13.7303			−0.622181			−0.311090	−	0.950380i	$-0.600694\pi$
$487$	−13.7303			−0.622181			−0.311090	+	0.950380i	$0.600694\pi$
$488$	5.35484	−	9.27486i	0.242402	−	0.419853i
$489$	10.7052			0.484108
$490$	38.8213	−	32.0879i	1.75377	−	1.44958i
$491$	13.7632	−	23.8386i	0.621126	−	1.07582i	−0.368150	−	0.929766i	$-0.620009\pi$
$491$	13.7632	−	23.8386i	0.621126	−	1.07582i	0.989276	−	0.146056i	$-0.0466579\pi$
$492$	1.30080			0.0586445
$493$	−1.94084	+	3.36163i	−0.0874110	+	0.151400i
$494$	20.6719	−	40.4954i	0.930073	−	1.82197i
$495$	−0.569801	−	0.986924i	−0.0256106	−	0.0443589i
$496$	1.04811	−	1.81537i	0.0470614	−	0.0815127i
$497$	−16.7879	−	3.02432i	−0.753041	−	0.135659i
$498$	−12.1159	−	20.9853i	−0.542925	−	0.940375i
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	0.906284	−	0.422669i	$-0.138907\pi$
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	−0.819184	+	0.573531i	$0.805573\pi$
$500$	−29.4367			−1.31645
$501$	−0.0481240			−0.00215002
$502$	−9.24194	−	16.0075i	−0.412488	−	0.714450i
$503$	−1.87991	−	3.25610i	−0.0838212	−	0.145183i	0.821067	−	0.570832i	$-0.193379\pi$
$503$	−1.87991	−	3.25610i	−0.0838212	−	0.145183i	−0.904888	+	0.425649i	$0.860046\pi$
$504$	−1.17433	−	3.26402i	−0.0523089	−	0.145391i
$505$	−18.0659	+	31.2910i	−0.803921	+	1.39243i
$506$	−1.87770	−	3.25227i	−0.0834738	−	0.144581i
$507$	−7.62534	−	10.5287i	−0.338653	−	0.467597i
$508$	−5.00247	+	8.66453i	−0.221949	+	0.384426i
$509$	−38.5481			−1.70861			−0.854307	−	0.519769i	$-0.826018\pi$
$509$	−38.5481			−1.70861			−0.854307	+	0.519769i	$0.826018\pi$
$510$	−16.5554	+	28.6747i	−0.733084	+	1.26974i
$511$	−14.7760	−	41.0695i	−0.653653	−	1.81681i
$512$	18.0587			0.798088
$513$	3.48374	−	6.03402i	0.153811	−	0.266408i
$514$	−11.5158			−0.507938
$515$	−9.31946	+	16.1418i	−0.410664	+	0.711291i
$516$	0.746584	−	1.29312i	0.0328665	−	0.0569265i
$517$	−0.777591	+	1.34683i	−0.0341984	+	0.0592334i
$518$	−13.4919	+	15.9585i	−0.592798	+	0.701178i
$519$	−14.0297			−0.615837
$520$	−10.2236	−	15.7690i	−0.448336	−	0.691519i
$521$	−6.92277	+	11.9906i	−0.303292	+	0.525318i	−0.976880	−	0.213790i	$-0.931419\pi$
$521$	−6.92277	+	11.9906i	−0.303292	+	0.525318i	0.673587	+	0.739108i	$0.264753\pi$
$522$	0.763315	+	1.32210i	0.0334094	+	0.0578667i
$523$	20.0671			0.877472			0.438736	−	0.898616i	$-0.355426\pi$
$523$	20.0671			0.877472			0.438736	+	0.898616i	$0.355426\pi$
$524$	−5.15687	−	8.93196i	−0.225279	−	0.390194i
$525$	18.4562	−	21.8306i	0.805496	−	0.952763i
$526$	15.3960	+	26.6667i	0.671299	+	1.16272i
$527$	0.979519	−	1.69658i	0.0426685	−	0.0739040i
$528$	−0.705751	+	1.22240i	−0.0307139	+	0.0531980i
$529$	29.3969			1.27813
$530$	−8.26326			−0.358933
$531$	2.42927	−	4.20762i	0.105421	−	0.182595i
$532$	−7.96047	−	22.1259i	−0.345130	−	0.959278i
$533$	−1.67172	+	3.27482i	−0.0724101	+	0.141848i
$534$	2.00506	+	3.47287i	0.0867674	+	0.150286i
$535$	28.8337	+	49.9414i	1.24659	+	2.15915i
$536$	1.03175	+	1.78705i	0.0445649	+	0.0771887i
$537$	−2.34931	+	4.06913i	−0.101380	+	0.175596i
$538$	−16.3980			−0.706968
$539$	1.54664	−	1.27838i	0.0666186	−	0.0550638i
$540$	2.53555	+	4.39170i	0.109113	+	0.188988i
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	−0.909788	−	0.415072i	$-0.863756\pi$
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	0.0954310	−	0.995436i	$-0.469577\pi$
$542$	4.03229			0.173202
$543$	11.0191	+	19.0857i	0.472876	+	0.819044i
$544$	28.9438			1.24096
$545$	16.6728			0.714186
$546$	−17.1267	−	2.18044i	−0.732954	−	0.0933141i
$547$	29.3783			1.25613			0.628063	−	0.778162i	$-0.283848\pi$
$547$	29.3783			1.25613			0.628063	+	0.778162i	$0.283848\pi$
$548$	1.92572			0.0822625
$549$	−4.08424	−	7.07411i	−0.174311	−	0.301916i
$550$	−5.60556			−0.239022
$551$	−2.93857	−	5.08975i	−0.125187	−	0.216831i
$552$	−4.74524	−	8.21900i	−0.201971	−	0.349824i
$553$	−20.0189	−	3.60638i	−0.851291	−	0.153359i
$554$	−14.1305			−0.600349
$555$	−8.67492	+	15.0254i	−0.368230	+	0.637793i
$556$	2.57836	+	4.46584i	0.109347	+	0.189394i
$557$	−0.513038	−	0.888609i	−0.0217381	−	0.0376516i	0.854952	−	0.518708i	$-0.173587\pi$
$557$	−0.513038	−	0.888609i	−0.0217381	−	0.0376516i	−0.876690	+	0.481056i	$0.840253\pi$
$558$	−0.385236	−	0.667248i	−0.0163083	−	0.0282469i
$559$	2.29603	+	3.54142i	0.0971117	+	0.149786i
$560$	−50.9720	−	9.18253i	−2.15396	−	0.388033i
$561$	−0.659567	+	1.14240i	−0.0278469	+	0.0482323i
$562$	−23.0814			−0.973628
$563$	−36.2249			−1.52670			−0.763348	−	0.645988i	$-0.776446\pi$
$563$	−36.2249			−1.52670			−0.763348	+	0.645988i	$0.776446\pi$
$564$	3.46019	−	5.99322i	0.145700	−	0.252360i
$565$	−16.3913	+	28.3905i	−0.689587	+	1.19440i
$566$	−14.7900	−	25.6171i	−0.621671	−	1.07677i
$567$	−2.60384	−	0.469078i	−0.109351	−	0.0196994i
$568$	4.22657	+	7.32064i	0.177343	+	0.307167i
$569$	2.83671			0.118921			0.0594605	−	0.998231i	$-0.481062\pi$
$569$	2.83671			0.118921			0.0594605	+	0.998231i	$0.481062\pi$
$570$	−25.0660	−	43.4155i	−1.04990	−	1.81848i
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	−0.813921	−	0.580975i	$-0.802671\pi$
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	0.910100	+	0.414389i	$0.136005\pi$
$572$	0.717202	+	1.10622i	0.0299877	+	0.0462534i
$573$	11.0974			0.463602
$574$	1.65311	+	4.59477i	0.0689995	+	0.191782i
$575$	39.1057	−	67.7330i	1.63082	−	2.82466i
$576$	0.767610	−	1.32954i	0.0319837	−	0.0553975i
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	−0.624329	−	0.781161i	$-0.714628\pi$
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	0.988670	+	0.150105i	$0.0479611\pi$
$578$	7.55939			0.314429
$579$	0.243115	−	0.421088i	0.0101035	−	0.0174998i
$580$	4.27751			0.177614
$581$	22.8701	−	27.0514i	0.948810	−	1.12228i
$582$	17.2342	−	29.8505i	0.714380	−	1.23734i
$583$	−0.329209			−0.0136344
$584$	−10.8145	+	18.7313i	−0.447509	+	0.775108i
$585$	−14.3149	+	0.739388i	−0.591847	+	0.0305699i
$586$	21.4140	+	37.0902i	0.884606	+	1.53218i
$587$	−0.671155	+	1.16247i	−0.0277015	+	0.0479805i	−0.879544	−	0.475818i	$-0.842152\pi$
$587$	−0.671155	+	1.16247i	−0.0277015	+	0.0479805i	0.851842	+	0.523798i	$0.175485\pi$
$588$	−6.88238	+	5.68865i	−0.283824	+	0.234596i
$589$	1.48306	+	2.56874i	0.0611084	+	0.105843i
$590$	−17.4789	−	30.2743i	−0.719595	−	1.24638i
$591$	17.0763			0.702424
$592$	21.4894			0.883209
$593$	22.0843	+	38.2512i	0.906895	+	1.57079i	0.818353	+	0.574716i	$0.194888\pi$
$593$	22.0843	+	38.2512i	0.906895	+	1.57079i	0.0885427	+	0.996072i	$0.471779\pi$
$594$	0.259402	+	0.449297i	0.0106434	+	0.0184349i
$595$	−47.6363	−	8.58162i	−1.95290	−	0.351812i
$596$	12.2422	−	21.2041i	0.501460	−	0.868554i
$597$	−11.5849	−	20.0656i	−0.474138	−	0.821230i
$598$	−47.1726	+	2.43655i	−1.92903	+	0.0996378i
$599$	8.46583	−	14.6632i	0.345904	−	0.599124i	−0.639613	−	0.768697i	$-0.720905\pi$
$599$	8.46583	−	14.6632i	0.345904	−	0.599124i	0.985518	+	0.169573i	$0.0542388\pi$
$600$	−14.1662			−0.578331
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	−0.669530	−	0.742785i	$-0.733504\pi$
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	0.978036	+	0.208437i	$0.0668378\pi$
$602$	5.51645	+	0.993781i	0.224834	+	0.0405035i
$603$	1.57387			0.0640931
$604$	−12.0840	+	20.9301i	−0.491690	+	0.851633i
$605$	43.4041			1.76463
$606$	8.22448	−	14.2452i	0.334097	−	0.578673i
$607$	−23.8620	+	41.3301i	−0.968527	+	1.67754i	−0.268701	+	0.963224i	$0.586594\pi$
$607$	−23.8620	+	41.3301i	−0.968527	+	1.67754i	−0.699825	+	0.714314i	$0.746739\pi$
$608$	−21.9115	+	37.9518i	−0.888628	+	1.53915i
$609$	−1.44084	+	1.70427i	−0.0583858	+	0.0690604i
$610$	−58.7733			−2.37966
$611$	10.6414	+	16.4134i	0.430505	+	0.664014i
$612$	2.93499	−	5.08356i	0.118640	−	0.205491i
$613$	−11.9854	−	20.7593i	−0.484086	−	0.838462i	0.515747	−	0.856741i	$-0.327515\pi$
$613$	−11.9854	−	20.7593i	−0.484086	−	0.838462i	−0.999833	+	0.0182791i	$0.994181\pi$
$614$	16.2831			0.657133
$615$	2.02706	+	3.51097i	0.0817390	+	0.141576i
$616$	−0.978606	−	0.176295i	−0.0394292	−	0.00710311i
$617$	−1.41810	−	2.45623i	−0.0570907	−	0.0988839i	0.836068	−	0.548626i	$-0.184849\pi$
$617$	−1.41810	−	2.45623i	−0.0570907	−	0.0988839i	−0.893158	+	0.449743i	$0.851516\pi$
$618$	4.24268	−	7.34853i	0.170666	−	0.295601i
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	−0.852488	−	0.522746i	$-0.824908\pi$
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	0.878956	+	0.476904i	$0.158241\pi$
$620$	−2.15881			−0.0866999
$621$	−7.23857			−0.290474
$622$	27.9619	−	48.4314i	1.12117	−	1.94192i
$623$	−3.78477	+	4.47674i	−0.151634	+	0.179357i
$624$	9.65826	+	14.8970i	0.386640	+	0.596357i
$625$	−18.8598	−	32.6662i	−0.754393	−	1.30665i
$626$	6.77926	+	11.7420i	0.270954	+	0.469305i
$627$	−0.998630	−	1.72968i	−0.0398814	−	0.0690767i
$628$	−11.8855	+	20.5862i	−0.474281	+	0.821479i
$629$	20.0831			0.800766
$630$	−12.2904	+	14.5374i	−0.489660	+	0.579184i
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	0.538489	−	0.842633i	$-0.318995\pi$
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	−0.998986	+	0.0450286i	$0.985662\pi$
$632$	5.04002	+	8.72957i	0.200481	+	0.347244i
$633$	−2.81576			−0.111916
$634$	14.6852	+	25.4355i	0.583224	+	1.01017i
$635$	−31.1818			−1.23741
$636$	1.46494			0.0580887
$637$	−5.47660	−	24.6375i	−0.216991	−	0.976174i
$638$	0.437615			0.0173253
$639$	6.44737			0.255054
$640$	19.4816	+	33.7430i	0.770076	+	1.33381i
$641$	−36.6525			−1.44769			−0.723843	−	0.689965i	$-0.757626\pi$
$641$	−36.6525			−1.44769			−0.723843	+	0.689965i	$0.757626\pi$
$642$	−13.1265	−	22.7358i	−0.518062	−	0.897310i
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	0.826813	−	0.562477i	$-0.190151\pi$
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	−0.900526	+	0.434803i	$0.856818\pi$
$644$	−15.7720	+	18.6556i	−0.621503	+	0.735132i
$645$	4.65368			0.183238
$646$	−29.0148	+	50.2552i	−1.14157	+	1.97726i
$647$	0.763093	+	1.32172i	0.0300003	+	0.0519620i	0.880636	−	0.473794i	$-0.157116\pi$
$647$	0.763093	+	1.32172i	0.0300003	+	0.0519620i	−0.850635	+	0.525756i	$0.823783\pi$
$648$	0.655549	+	1.13544i	0.0257524	+	0.0446045i
$649$	−0.696361	−	1.20613i	−0.0273345	−	0.0473448i
$650$	−32.0569	+	62.7981i	−1.25737	+	2.46314i
$651$	0.727175	−	0.860123i	0.0285002	−	0.0337109i
$652$	−6.82769	+	11.8259i	−0.267393	+	0.463138i
$653$	8.95092			0.350277			0.175138	−	0.984544i	$-0.443963\pi$
$653$	8.95092			0.350277			0.175138	+	0.984544i	$0.443963\pi$
$654$	−7.59031			−0.296804
$655$	16.0721	−	27.8377i	0.627990	−	1.08771i
$656$	2.51070	−	4.34867i	0.0980265	−	0.169787i
$657$	8.24845	+	14.2867i	0.321803	+	0.557379i
$658$	25.5670	+	4.60587i	0.996707	+	0.179555i
$659$	4.30599	+	7.45819i	0.167737	+	0.290530i	0.937624	−	0.347651i	$-0.113021\pi$
$659$	4.30599	+	7.45819i	0.167737	+	0.290530i	−0.769887	+	0.638181i	$0.779687\pi$
$660$	1.45365			0.0565833
$661$	20.0392	+	34.7088i	0.779433	+	1.35002i	0.932269	+	0.361765i	$0.117826\pi$
$661$	20.0392	+	34.7088i	0.779433	+	1.35002i	−0.152837	+	0.988251i	$0.548841\pi$
$662$	−5.05343	+	8.75279i	−0.196407	+	0.340187i
$663$	9.02622	+	13.9221i	0.350549	+	0.540691i
$664$	−17.5540			−0.681228
$665$	47.3148	−	55.9653i	1.83479	−	2.17024i
$666$	3.94925	−	6.84031i	0.153031	−	0.265057i
$667$	−3.05290	+	5.28778i	−0.118209	+	0.204744i
$668$	0.0306930	−	0.0531618i	0.00118755	−	0.00205689i
$669$	16.3246			0.631147
$670$	5.66211	−	9.80707i	0.218747	−	0.378880i
$671$	−2.34153			−0.0903938
$672$	16.3772	+	2.95033i	0.631764	+	0.113811i
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	0.0339689	+	0.999423i	$0.489185\pi$
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	−0.882510	+	0.470294i	$0.844148\pi$
$674$	−0.912342			−0.0351421
$675$	−5.40240	+	9.35723i	−0.207938	+	0.360160i
$676$	16.4943	−	1.70847i	0.634395	−	0.0657105i
$677$	−12.0556	−	20.8809i	−0.463334	−	0.802518i	0.535791	−	0.844351i	$-0.320014\pi$
$677$	−12.0556	−	20.8809i	−0.463334	−	0.802518i	−0.999125	+	0.0418328i	$0.986680\pi$
$678$	7.46213	−	12.9248i	0.286581	−	0.496373i
$679$	49.5896	+	8.93350i	1.90307	+	0.342836i
$680$	11.9931	+	20.7726i	0.459913	+	0.796592i
$681$	3.10289	+	5.37436i	0.118903	+	0.205946i
$682$	−0.220859			−0.00845713
$683$	−18.5855			−0.711155			−0.355578	−	0.934647i	$-0.615716\pi$
$683$	−18.5855			−0.711155			−0.355578	+	0.934647i	$0.615716\pi$
$684$	4.44379	+	7.69686i	0.169912	+	0.294297i
$685$	3.00089	+	5.19769i	0.114658	+	0.198594i
$686$	−28.8403	−	17.0810i	−1.10113	−	0.652157i
$687$	0.261463	−	0.452867i	0.00997543	−	0.0172779i
$688$	−2.88201	−	4.99178i	−0.109875	−	0.190310i
$689$	−1.88267	+	3.68807i	−0.0717239	+	0.140504i
$690$	−26.0412	+	45.1047i	−0.991372	+	1.71711i
$691$	−22.6374			−0.861166			−0.430583	−	0.902551i	$-0.641692\pi$
$691$	−22.6374			−0.861166			−0.430583	+	0.902551i	$0.641692\pi$
$692$	8.94801	−	15.4984i	0.340152	−	0.589161i
$693$	−0.489649	+	0.579171i	−0.0186002	+	0.0220009i
$694$	−21.9598			−0.833581
$695$	−8.03582	+	13.9185i	−0.304816	+	0.527957i
$696$	1.10592			0.0419199
$697$	2.34640	−	4.06409i	0.0888763	−	0.153938i
$698$	19.7430	−	34.1959i	0.747284	−	1.29433i
$699$	−6.48273	+	11.2284i	−0.245199	+	0.424697i
$700$	12.3447	+	34.3116i	0.466584	+	1.29686i
$701$	50.1432			1.89388			0.946941	−	0.321407i	$-0.104156\pi$
$701$	50.1432			1.89388			0.946941	+	0.321407i	$0.104156\pi$
$702$	6.51684	−	0.336606i	0.245962	−	0.0127044i
$703$	−15.2036	+	26.3335i	−0.573416	+	0.993185i
$704$	−0.220039	−	0.381118i	−0.00829302	−	0.0143639i
$705$	21.5684			0.812311
$706$	10.9387	+	18.9464i	0.411683	+	0.713056i
$707$	23.6651	+	4.26324i	0.890018	+	0.160336i
$708$	3.09872	+	5.36715i	0.116457	+	0.201710i
$709$	14.8556	−	25.7306i	0.557913	−	0.966334i	−0.439757	−	0.898117i	$-0.644936\pi$
$709$	14.8556	−	25.7306i	0.557913	−	0.966334i	0.997670	−	0.0682172i	$-0.0217311\pi$
$710$	23.1948	−	40.1746i	0.870487	−	1.50773i
$711$	7.68824			0.288332
$712$	2.90502			0.108870
$713$	1.54076	−	2.66868i	0.0577020	−	0.0999428i
$714$	21.6864	+	3.90678i	0.811594	+	0.146208i
$715$	−1.86816	+	3.65964i	−0.0698651	+	0.136863i
$716$	−2.99673	−	5.19049i	−0.111993	−	0.193978i
$717$	2.39803	+	4.15351i	0.0895560	+	0.155116i
$718$	−13.0677	−	22.6338i	−0.487681	−	0.844687i
$719$	14.9346	−	25.8675i	0.556968	−	0.964697i	−0.440780	−	0.897615i	$-0.645298\pi$
$719$	14.9346	−	25.8675i	0.556968	−	0.964697i	0.997748	−	0.0670813i	$-0.0213687\pi$
$720$	19.5757			0.729544
$721$	12.2079	+	2.19923i	0.454645	+	0.0819037i
$722$	−26.7369	−	46.3096i	−0.995044	−	1.72347i
$723$	−5.20975	−	9.02355i	−0.193753	−	0.335589i
$724$	−28.1115			−1.04476
$725$	4.55697	+	7.89291i	0.169242	+	0.293135i
$726$	−19.7597			−0.733351
$727$	36.0210			1.33594			0.667972	−	0.744186i	$-0.267163\pi$
$727$	36.0210			1.33594			0.667972	+	0.744186i	$0.267163\pi$
$728$	−7.57141	+	9.95495i	−0.280615	+	0.368955i
$729$	1.00000			0.0370370
$730$	118.697			4.39318
$731$	−2.69341	−	4.66512i	−0.0996192	−	0.172546i
$732$	10.4195			0.385117
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	0.982816	−	0.184586i	$-0.0590945\pi$
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	−0.651265	+	0.758851i	$0.725761\pi$
$734$	−22.0610	−	38.2108i	−0.814286	−	1.41038i
$735$	−26.0792	−	9.71143i	−0.961945	−	0.358211i
$736$	45.5280			1.67818
$737$	0.225579	−	0.390714i	0.00830931	−	0.0143921i
$738$	−0.922819	−	1.59837i	−0.0339694	−	0.0588368i
$739$	−22.2469	−	38.5328i	−0.818366	−	1.41745i	−0.906886	−	0.421377i	$-0.861547\pi$
$739$	−22.2469	−	38.5328i	−0.818366	−	1.41745i	0.0885201	−	0.996074i	$-0.471786\pi$
$740$	−11.0655	−	19.1661i	−0.406777	−	0.704559i
$741$	−25.0882	+	1.29585i	−0.921637	+	0.0476042i
$742$	1.86171	+	5.17457i	0.0683456	+	0.189964i
$743$	−10.7390	+	18.6004i	−0.393975	+	0.682384i	−0.992970	−	0.118368i	$-0.962234\pi$
$743$	−10.7390	+	18.6004i	−0.393975	+	0.682384i	0.598995	+	0.800753i	$0.295567\pi$
$744$	−0.558146			−0.0204626
$745$	76.3092			2.79575
$746$	7.60169	−	13.1665i	0.278318	−	0.482061i
$747$	−6.69439	+	11.5950i	−0.244935	+	0.424240i
$748$	−0.841329	−	1.45722i	−0.0307620	−	0.0532814i
$749$	24.7777	−	29.3078i	0.905359	−	1.07088i
$750$	20.8831	+	36.1706i	0.762544	+	1.32077i
$751$	3.20035			0.116783			0.0583913	−	0.998294i	$-0.481403\pi$
$751$	3.20035			0.116783			0.0583913	+	0.998294i	$0.481403\pi$
$752$	−13.3572	−	23.1354i	−0.487087	−	0.843660i
$753$	−5.10645	+	8.84463i	−0.186089	+	0.322316i
$754$	2.50262	−	4.90252i	0.0911399	−	0.178539i
$755$	−75.3230			−2.74128
$756$	2.17888	−	2.57724i	0.0792451	−	0.0937334i
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	−0.999313	−	0.0370727i	$-0.988197\pi$
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	0.531762	+	0.846894i	$0.321530\pi$
$758$	−3.31013	+	5.73331i	−0.120229	+	0.208243i
$759$	−1.03748	+	1.79698i	−0.0376583	+	0.0652261i
$760$	−36.3167			−1.31734
$761$	−14.3748	+	24.8979i	−0.521087	+	0.902548i	0.478613	+	0.878026i	$0.341140\pi$
$761$	−14.3748	+	24.8979i	−0.521087	+	0.902548i	−0.999699	+	0.0245222i	$0.992194\pi$
$762$	14.1955			0.514249
$763$	−3.75639	−	10.4408i	−0.135990	−	0.377981i
$764$	−7.07782	+	12.2591i	−0.256066	+	0.443520i
$765$	18.2947			0.661445
$766$	27.7860	−	48.1268i	1.00395	−	1.73889i
$767$	−17.4944	+	0.903616i	−0.631686	+	0.0326277i
$768$	−10.4042	−	18.0206i	−0.375429	−	0.650262i
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	−0.657386	−	0.753554i	$-0.728338\pi$
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	0.981290	+	0.192536i	$0.0616712\pi$
$770$	1.84736	+	5.13469i	0.0665744	+	0.185041i
$771$	3.18140	+	5.51035i	0.114575	+	0.198450i
$772$	0.310112	+	0.537131i	0.0111612	+	0.0193318i
$773$	39.6652			1.42666			0.713329	−	0.700829i	$-0.247187\pi$
$773$	39.6652			1.42666			0.713329	+	0.700829i	$0.247187\pi$
$774$	−2.11858			−0.0761509
$775$	−2.29985	−	3.98345i	−0.0826130	−	0.143090i
$776$	−12.4848	−	21.6243i	−0.448179	−	0.776269i
$777$	11.3636	+	2.04713i	0.407666	+	0.0734405i
$778$	−16.6849	+	28.8990i	−0.598182	+	1.03608i
$779$	3.55262	+	6.15331i	0.127286	+	0.220465i
$780$	8.31308	−	16.2850i	0.297656	−	0.583096i
$781$	0.924084	−	1.60056i	0.0330663	−	0.0572725i
$782$	60.2875			2.15587
$783$	0.421754	−	0.730500i	0.0150723	−	0.0261059i
$784$	5.73375	+	33.9882i	0.204777	+	1.21386i
$785$	−74.0855			−2.64422
$786$	−7.31683	+	12.6731i	−0.260983	+	0.452035i
$787$	−39.5666			−1.41040			−0.705199	−	0.709010i	$-0.749142\pi$
$787$	−39.5666			−1.41040			−0.705199	+	0.709010i	$0.749142\pi$
$788$	−10.8911	+	18.8639i	−0.387978	+	0.671998i
$789$	8.50677	−	14.7342i	0.302849	−	0.524550i
$790$	27.6589	−	47.9067i	0.984061	−	1.70444i
$791$	21.4715	+	3.86806i	0.763439	+	0.137533i
$792$	0.375832			0.0133546
$793$	−13.3907	+	26.2317i	−0.475516	+	0.931516i
$794$	2.04571	−	3.54328i	0.0725996	−	0.125746i
$795$	2.28285	+	3.95401i	0.0809644	+	0.140234i
$796$	29.5548			1.04754
$797$	−9.72309	−	16.8409i	−0.344409	−	0.596535i	0.640837	−	0.767677i	$-0.278588\pi$
$797$	−9.72309	−	16.8409i	−0.344409	−	0.596535i	−0.985246	+	0.171142i	$0.945254\pi$
$798$	−21.5400	+	25.4782i	−0.762509	+	0.901917i
$799$	−12.4831	−	21.6214i	−0.441621	−	0.764909i
$800$	33.9791	−	58.8536i	1.20134	−	2.08079i
$801$	1.10786	−	1.91886i	0.0391442	−	0.0677997i
$802$	51.6202			1.82277
$803$	4.72891			0.166880
$804$	−1.00380	+	1.73863i	−0.0354013	+	0.0613168i
$805$	−74.9309	−	13.4987i	−2.64097	−	0.475767i
$806$	−1.26304	+	2.47424i	−0.0444887	+	0.0871515i
$807$	4.53019	+	7.84653i	0.159470	+	0.276211i
$808$	−5.95799	−	10.3195i	−0.209601	−	0.363040i
$809$	8.65420	+	14.9895i	0.304265	+	0.527003i	0.977098	−	0.212792i	$-0.0682557\pi$
$809$	8.65420	+	14.9895i	0.304265	+	0.527003i	−0.672832	+	0.739795i	$0.734922\pi$
$810$	3.59756	−	6.23116i	0.126405	−	0.218941i
$811$	−2.62646			−0.0922275			−0.0461138	−	0.998936i	$-0.514684\pi$
$811$	−2.62646			−0.0922275			−0.0461138	+	0.998936i	$0.514684\pi$
$812$	−0.963723	−	2.67864i	−0.0338200	−	0.0940017i
$813$	−1.11398	−	1.92947i	−0.0390690	−	0.0676696i
$814$	−1.13207	−	1.96080i	−0.0396791	−	0.0687262i
$815$	−42.5590			−1.49078
$816$	−11.3298	−	19.6238i	−0.396623	−	0.686971i
$817$	8.15601			0.285343
$818$	19.6442			0.686842
$819$	3.68815	+	8.79759i	0.128875	+	0.307413i
$820$	−5.17135			−0.180591
$821$	−32.3955			−1.13061			−0.565305	−	0.824882i	$-0.691242\pi$
$821$	−32.3955			−1.13061			−0.565305	+	0.824882i	$0.691242\pi$
$822$	−1.36615	−	2.36625i	−0.0476501	−	0.0825323i
$823$	−41.0161			−1.42973			−0.714866	−	0.699261i	$-0.753512\pi$
$823$	−41.0161			−1.42973			−0.714866	+	0.699261i	$0.753512\pi$
$824$	−3.07349	−	5.32344i	−0.107070	−	0.185451i
$825$	1.54862	+	2.68229i	0.0539161	+	0.0933854i
$826$	−15.0202	+	17.7663i	−0.522620	+	0.618170i
$827$	−44.2260			−1.53789			−0.768944	−	0.639316i	$-0.779218\pi$
$827$	−44.2260			−1.53789			−0.768944	+	0.639316i	$0.779218\pi$
$828$	4.61668	−	7.99633i	0.160441	−	0.277892i
$829$	2.74781	+	4.75935i	0.0954354	+	0.165299i	0.909790	−	0.415068i	$-0.136242\pi$
$829$	2.74781	+	4.75935i	0.0954354	+	0.165299i	−0.814355	+	0.580367i	$0.802909\pi$
$830$	48.1670	+	83.4276i	1.67190	+	2.89582i
$831$	3.90377	+	6.76153i	0.135420	+	0.234555i
$832$	−5.52794	+	0.285528i	−0.191647	+	0.00989890i
$833$	5.35853	+	31.7640i	0.185662	+	1.10056i
$834$	3.65830	−	6.33637i	0.126677	−	0.219411i
$835$	0.191318			0.00662084
$836$	2.54766			0.0881127
$837$	−0.212854	+	0.368675i	−0.00735732	+	0.0127433i
$838$	−13.9047	+	24.0837i	−0.480332	+	0.831959i
$839$	−21.4269	−	37.1125i	−0.739739	−	1.28127i	−0.952612	−	0.304186i	$-0.901615\pi$
$839$	−21.4269	−	37.1125i	−0.739739	−	1.28127i	0.212873	−	0.977080i	$-0.431718\pi$
$840$	4.66858	+	12.9762i	0.161081	+	0.447721i
$841$	14.1442	+	24.4986i	0.487733	+	0.844778i
$842$	−6.03941			−0.208132
$843$	6.37657	+	11.0445i	0.219621	+	0.380394i
$844$	1.79586	−	3.11052i	0.0618160	−	0.107069i
$845$	30.3147	+	41.8572i	1.04286	+	1.43993i
$846$	−9.81898			−0.337584
$847$	−9.77894	−	27.1802i	−0.336008	−	0.933924i
$848$	2.82752	−	4.89741i	0.0970975	−	0.168178i
$849$	−8.17193	+	14.1542i	−0.280460	+	0.485771i
$850$	44.9946	−	77.9330i	1.54330	−	2.67308i
$851$	31.5903			1.08290
$852$	−4.11206	+	7.12230i	−0.140877	+	0.244006i
$853$	−46.0876			−1.57801			−0.789004	−	0.614388i	$-0.789403\pi$
$853$	−46.0876			−1.57801			−0.789004	+	0.614388i	$0.789403\pi$
$854$	13.2416	+	36.8046i	0.453118	+	1.25943i
$855$	−13.8497	+	23.9884i	−0.473650	+	0.820386i
$856$	−19.0183			−0.650031
$857$	3.33662	−	5.77919i	0.113977	−	0.197413i	−0.803394	−	0.595448i	$-0.796974\pi$
$857$	3.33662	−	5.77919i	0.113977	−	0.197413i	0.917370	+	0.398035i	$0.130308\pi$
$858$	0.850478	−	1.66605i	0.0290348	−	0.0568780i
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	0.971409	−	0.237411i	$-0.0762987\pi$
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	−0.691308	+	0.722560i	$0.742965\pi$
$860$	−2.96806	+	5.14084i	−0.101210	+	0.175301i
$861$	1.74192	−	2.06039i	0.0593646	−	0.0702181i
$862$	3.85584	+	6.67851i	0.131330	+	0.227471i
$863$	4.92500	+	8.53035i	0.167649	+	0.290377i	0.937593	−	0.347735i	$-0.113049\pi$
$863$	4.92500	+	8.53035i	0.167649	+	0.290377i	−0.769944	+	0.638112i	$0.779716\pi$
$864$	−6.28963			−0.213978
$865$	55.7755			1.89643
$866$	−10.0703	−	17.4423i	−0.342204	−	0.592714i
$867$	−2.08840	−	3.61721i	−0.0709256	−	0.122847i
$868$	0.486379	+	1.35188i	0.0165088	+	0.0458856i
$869$	1.10193	−	1.90861i	0.0373805	−	0.0647450i
$870$	−3.03458	−	5.25604i	−0.102882	−	0.178196i
$871$	−3.08707	−	4.76152i	−0.104601	−	0.161338i
$872$	−2.74929	+	4.76191i	−0.0931027	+	0.161259i
$873$	−19.0448			−0.644569
$874$	−45.6397	+	79.0503i	−1.54379	+	2.67392i
$875$	−39.4192	+	46.6262i	−1.33261	+	1.57625i
$876$	−21.0431			−0.710980
$877$	−3.02056	+	5.23177i	−0.101997	+	0.176664i	−0.912507	−	0.409060i	$-0.865857\pi$
$877$	−3.02056	+	5.23177i	−0.101997	+	0.176664i	0.810510	+	0.585724i	$0.199190\pi$
$878$	74.2085			2.50442
$879$	11.8319	−	20.4935i	0.399080	−	0.691227i
$880$	2.80573	−	4.85967i	0.0945812	−	0.163819i
$881$	15.5861	−	26.9959i	0.525109	−	0.909516i	−0.474463	−	0.880275i	$-0.657358\pi$
$881$	15.5861	−	26.9959i	0.525109	−	0.909516i	0.999572	−	0.0292404i	$-0.00930885\pi$
$882$	11.8725	+	4.42112i	0.399769	+	0.148867i
$883$	−18.2205			−0.613169			−0.306584	−	0.951844i	$-0.599186\pi$
$883$	−18.2205			−0.613169			−0.306584	+	0.951844i	$0.599186\pi$
$884$	−21.1364	+	1.09173i	−0.710893	+	0.0367189i
$885$	−9.65762	+	16.7275i	−0.324637	+	0.562288i
$886$	−14.3466	−	24.8490i	−0.481984	−	0.834820i
$887$	7.41684			0.249033			0.124517	−	0.992218i	$-0.460262\pi$
$887$	7.41684			0.249033			0.124517	+	0.992218i	$0.460262\pi$
$888$	−2.86093	−	4.95527i	−0.0960064	−	0.166288i
$889$	7.02526	+	19.5265i	0.235620	+	0.654898i
$890$	−7.97117	−	13.8065i	−0.267194	−	0.462794i
$891$	0.143327	−	0.248250i	0.00480164	−	0.00831669i
$892$	−10.4117	+	18.0336i	−0.348609	+	0.603808i
$893$	37.8006			1.26495
$894$	−34.7397			−1.16187
$895$	9.33975	−	16.1769i	0.312194	−	0.540735i
$896$	16.7412	−	19.8019i	0.559283	−	0.661535i
$897$	14.1980	+	21.8992i	0.474059	+	0.731193i
$898$	−13.6644	−	23.6674i	−0.455986	−	0.789790i
$899$	0.179545	+	0.310980i	0.00598815	+	0.0103718i
$900$	−6.89118	−	11.9359i	−0.229706	−	0.397863i
$901$	2.64249	−	4.57692i	0.0880341	−	0.152479i
$902$	−0.529060			−0.0176158
$903$	−1.04847	−	2.91420i	−0.0348910	−	0.0969783i
$904$	−5.40573	−	9.36299i	−0.179792	−	0.311409i
$905$	−43.8068	−	75.8756i	−1.45619	−	2.52219i
$906$	34.2907			1.13923
$907$	8.70718	+	15.0813i	0.289117	+	0.500766i	0.973599	−	0.228264i	$-0.0733049\pi$
$907$	8.70718	+	15.0813i	0.289117	+	0.500766i	−0.684482	+	0.729030i	$0.739972\pi$
$908$	−7.91595			−0.262700
$909$	−9.08855			−0.301448
$910$	68.0876	+	8.66839i	2.25708	+	0.287354i
$911$	−40.5753			−1.34432			−0.672159	−	0.740407i	$-0.734633\pi$
$911$	−40.5753			−1.34432			−0.672159	+	0.740407i	$0.734633\pi$
$912$	34.3083			1.13606
$913$	1.91898	+	3.32376i	0.0635088	+	0.110001i
$914$	−0.0504007			−0.00166711
$915$	16.2370	+	28.1233i	0.536779	+	0.929728i
$916$	0.333516	+	0.577667i	0.0110197	+	0.0190867i
$917$	−21.0534	−	3.79275i	−0.695245	−	0.125247i
$918$	−8.32864			−0.274886
$919$	24.2733	−	42.0426i	0.800702	−	1.38686i	−0.118452	−	0.992960i	$-0.537793\pi$
$919$	24.2733	−	42.0426i	0.800702	−	1.38686i	0.919154	−	0.393898i	$-0.128874\pi$
$920$	18.8648	+	32.6748i	0.621955	+	1.07726i
$921$	−4.49845	−	7.79155i	−0.148229	−	0.256740i
$922$	25.4363	+	44.0570i	0.837700	+	1.45094i
$923$	−12.6462	−	19.5056i	−0.416253	−	0.642033i
$924$	−0.327507	−	0.910296i	−0.0107742	−	0.0299465i
$925$	23.5770	−	40.8365i	0.775206	−	1.34270i
$926$	−0.482395			−0.0158525
$927$	−4.68842			−0.153988
$928$	−2.65268	+	4.59458i	−0.0870785	+	0.150824i
$929$	4.06964	−	7.04883i	0.133521	−	0.231264i	−0.791511	−	0.611155i	$-0.790705\pi$
$929$	4.06964	−	7.04883i	0.133521	−	0.231264i	0.925031	+	0.379891i	$0.124038\pi$
$930$	1.53151	+	2.65266i	0.0502203	+	0.0869842i
$931$	−45.7062	−	17.0202i	−1.49796	−	0.557815i
$932$	−8.26922	−	14.3227i	−0.270867	−	0.469156i
$933$	−30.8996			−1.01161
$934$	−33.5548	−	58.1186i	−1.09795	−	1.90170i
$935$	2.62212	−	4.54165i	0.0857526	−	0.148528i
$936$	2.14929	−	4.21038i	0.0702519	−	0.137620i
$937$	30.6536			1.00141			0.500705	−	0.865618i	$-0.333074\pi$
$937$	30.6536			1.00141			0.500705	+	0.865618i	$0.333074\pi$
$938$	−7.41699	−	1.33616i	−0.242173	−	0.0436272i
$939$	3.74574	−	6.48782i	0.122238	−	0.211722i
$940$	−13.7561	+	23.8262i	−0.448673	+	0.777125i
$941$	4.34815	−	7.53122i	0.141746	−	0.245511i	−0.786408	−	0.617707i	$-0.788062\pi$
$941$	4.34815	−	7.53122i	0.141746	−	0.245511i	0.928154	+	0.372196i	$0.121395\pi$
$942$	33.7274			1.09890
$943$	3.69084	−	6.39272i	0.120190	−	0.208176i
$944$	23.9237			0.778651
$945$	10.3516	+	1.86483i	0.336738	+	0.0606629i
$946$	−0.303651	+	0.525938i	−0.00987254	+	0.0170997i
$947$	−11.4722			−0.372796			−0.186398	−	0.982474i	$-0.559681\pi$
$947$	−11.4722			−0.372796			−0.186398	+	0.982474i	$0.559681\pi$
$948$	−4.90348	+	8.49307i	−0.159258	+	0.275842i
$949$	27.0435	−	52.9771i	0.877869	−	1.71971i
$950$	68.1250	+	117.996i	2.21027	+	3.82830i
$951$	8.11402	−	14.0539i	0.263115	−	0.455729i
$952$	10.3060	−	12.1903i	0.334021	−	0.395089i
$953$	−23.1731	−	40.1370i	−0.750650	−	1.30016i	−0.947508	−	0.319731i	$-0.896407\pi$
$953$	−23.1731	−	40.1370i	−0.750650	−	1.30016i	0.196859	−	0.980432i	$-0.436926\pi$
$954$	−1.03927	−	1.80006i	−0.0336475	−	0.0582792i
$955$	−44.1181			−1.42763
$956$	−6.11774			−0.197862
$957$	−0.120898	−	0.209401i	−0.00390807	−	0.00676897i
$958$	−26.0607	−	45.1384i	−0.841983	−	1.45836i
$959$	2.57876	−	3.05024i	0.0832727	−	0.0984972i
$960$	−3.05165	+	5.28562i	−0.0984916	+	0.170593i
$961$	15.4094	+	26.6898i	0.497077	+	0.860963i
$962$	−28.4406	+	1.46900i	−0.916961	+	0.0473626i
$963$	−7.25279	+	12.5622i	−0.233718	+	0.404811i
$964$	13.2909			0.428071
$965$	−0.966511	+	1.67405i	−0.0311131	+	0.0538894i
$966$	34.1123	+	6.14528i	1.09754	+	0.197721i
$967$	8.71419			0.280229			0.140115	−	0.990135i	$-0.455253\pi$
$967$	8.71419			0.280229			0.140115	+	0.990135i	$0.455253\pi$
$968$	−7.15718	+	12.3966i	−0.230040	+	0.398442i
$969$	32.0632			1.03002
$970$	−68.5149	+	118.671i	−2.19988	+	3.81031i
$971$	−20.0281	+	34.6897i	−0.642733	+	1.11325i	0.342087	+	0.939668i	$0.388866\pi$
$971$	−20.0281	+	34.6897i	−0.642733	+	1.11325i	−0.984820	+	0.173578i	$0.944467\pi$
$972$	−0.637789	+	1.10468i	−0.0204571	+	0.0354327i
$973$	10.5264	+	1.89632i	0.337461	+	0.0607931i
$974$	−24.8499			−0.796243
$975$	38.9054	−	2.00953i	1.24597	−	0.0643565i
$976$	20.1110	−	34.8333i	0.643738	−	1.11499i
$977$	21.1533	+	36.6387i	0.676755	+	1.17217i	0.975953	+	0.217983i	$0.0699478\pi$
$977$	21.1533	+	36.6387i	0.676755	+	1.17217i	−0.299197	+	0.954191i	$0.596719\pi$
$978$	19.3750			0.619543
$979$	−0.317572	−	0.550050i	−0.0101496	−	0.0175797i
$980$	27.3611	−	22.6154i	0.874017	−	0.722422i
$981$	2.09694	+	3.63200i	0.0669500	+	0.115961i
$982$	24.9095	−	43.1445i	0.794893	−	1.37680i
$983$	2.44395	−	4.23305i	0.0779501	−	0.135013i	−0.824415	−	0.565985i	$-0.808496\pi$
$983$	2.44395	−	4.23305i	0.0779501	−	0.135013i	0.902365	+	0.430972i	$0.141829\pi$
$984$	−1.33702			−0.0426226
$985$	−67.8872			−2.16307
$986$	−3.51264	+	6.08407i	−0.111865	+	0.193756i
$987$	−4.85935	−	13.5064i	−0.154675	−	0.429913i
$988$	14.5695	−	28.5410i	0.463517	−	0.908009i
$989$	−4.23667	−	7.33813i	−0.134718	−	0.233339i
$990$	−1.03126	−	1.78619i	−0.0327755	−	0.0567688i
$991$	9.29795	+	16.1045i	0.295359	+	0.511577i	0.975068	−	0.221905i	$-0.0712273\pi$
$991$	9.29795	+	16.1045i	0.295359	+	0.511577i	−0.679709	+	0.733482i	$0.737894\pi$
$992$	1.33878	−	2.31883i	0.0425062	−	0.0736229i
$993$	5.58434			0.177214
$994$	−30.3837	−	5.47358i	−0.963712	−	0.173612i
$995$	46.0560	+	79.7713i	1.46007	+	2.52892i
$996$	−8.53922	−	14.7904i	−0.270575	−	0.468650i
$997$	−25.6363			−0.811909			−0.405954	−	0.913893i	$-0.633061\pi$
$997$	−25.6363			−0.811909			−0.405954	+	0.913893i	$0.633061\pi$
$998$	3.52138	+	6.09921i	0.111467	+	0.193067i
$999$	−4.36416			−0.138076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.256.8	yes	20
3.2	odd	2		819.2.s.f.802.3		20
7.2	even	3		273.2.j.c.100.3	✓	20
13.3	even	3		273.2.j.c.172.3	yes	20
21.2	odd	6		819.2.n.f.100.8		20
39.29	odd	6		819.2.n.f.172.8		20
91.16	even	3	inner	273.2.l.c.16.8	yes	20
273.107	odd	6		819.2.s.f.289.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.3	✓	20	7.2	even	3
273.2.j.c.172.3	yes	20	13.3	even	3
273.2.l.c.16.8	yes	20	91.16	even	3	inner
273.2.l.c.256.8	yes	20	1.1	even	1	trivial
819.2.n.f.100.8		20	21.2	odd	6
819.2.n.f.172.8		20	39.29	odd	6
819.2.s.f.289.3		20	273.107	odd	6
819.2.s.f.802.3		20	3.2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.80986 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.27558 q^{4} +(1.98776 + 3.44291i) q^{5} +(-0.904928 - 1.56738i) q^{6} +(1.70815 - 2.02045i) q^{7} -1.31110 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.59756 + 6.23116i) q^{10} +(0.143327 + 0.248250i) q^{11} +(-0.637789 - 1.10468i) q^{12} +(3.60075 - 0.185985i) q^{13} +(3.09151 - 3.65672i) q^{14} +(1.98776 - 3.44291i) q^{15} -4.92406 q^{16} -4.60182 q^{17} +(-0.904928 + 1.56738i) q^{18} +(3.48374 - 6.03402i) q^{19} +(2.53555 + 4.39170i) q^{20} +(-2.60384 - 0.469078i) q^{21} +(0.259402 + 0.449297i) q^{22} -7.23857 q^{23} +(0.655549 + 1.13544i) q^{24} +(-5.40240 + 9.35723i) q^{25} +(6.51684 - 0.336606i) q^{26} +1.00000 q^{27} +(2.17888 - 2.57724i) q^{28} +(0.421754 - 0.730500i) q^{29} +(3.59756 - 6.23116i) q^{30} +(-0.212854 + 0.368675i) q^{31} -6.28963 q^{32} +(0.143327 - 0.248250i) q^{33} -8.32864 q^{34} +(10.3516 + 1.86483i) q^{35} +(-0.637789 + 1.10468i) q^{36} -4.36416 q^{37} +(6.30507 - 10.9207i) q^{38} +(-1.96144 - 3.02535i) q^{39} +(-2.60615 - 4.51399i) q^{40} +(-0.509885 + 0.883147i) q^{41} +(-4.71257 - 0.848963i) q^{42} +(0.585291 + 1.01375i) q^{43} +(0.182825 + 0.316662i) q^{44} -3.97552 q^{45} -13.1008 q^{46} +(2.71264 + 4.69843i) q^{47} +(2.46203 + 4.26436i) q^{48} +(-1.16444 - 6.90247i) q^{49} +(-9.77756 + 16.9352i) q^{50} +(2.30091 + 3.98530i) q^{51} +(4.59304 - 0.237238i) q^{52} +(-0.574226 + 0.994589i) q^{53} +1.80986 q^{54} +(-0.569801 + 0.986924i) q^{55} +(-2.23956 + 2.64901i) q^{56} -6.96749 q^{57} +(0.763315 - 1.32210i) q^{58} -4.85854 q^{59} +(2.53555 - 4.39170i) q^{60} +(-4.08424 + 7.07411i) q^{61} +(-0.385236 + 0.667248i) q^{62} +(0.895685 + 2.48953i) q^{63} -1.53522 q^{64} +(7.79777 + 12.0274i) q^{65} +(0.259402 - 0.449297i) q^{66} +(-0.786937 - 1.36302i) q^{67} -5.86999 q^{68} +(3.61929 + 6.26879i) q^{69} +(18.7349 + 3.37507i) q^{70} +(-3.22369 - 5.58359i) q^{71} +(0.655549 - 1.13544i) q^{72} +(8.24845 - 14.2867i) q^{73} -7.89851 q^{74} +10.8048 q^{75} +(4.44379 - 7.69686i) q^{76} +(0.746401 + 0.134463i) q^{77} +(-3.54993 - 5.47545i) q^{78} +(-3.84412 - 6.65821i) q^{79} +(-9.78785 - 16.9531i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.922819 + 1.59837i) q^{82} +13.3888 q^{83} +(-3.32140 - 0.598345i) q^{84} +(-9.14733 - 15.8436i) q^{85} +(1.05929 + 1.83475i) q^{86} -0.843509 q^{87} +(-0.187916 - 0.325480i) q^{88} -2.21571 q^{89} -7.19513 q^{90} +(5.77486 - 7.59283i) q^{91} -9.23336 q^{92} +0.425709 q^{93} +(4.90949 + 8.50349i) q^{94} +27.6994 q^{95} +(3.14482 + 5.44698i) q^{96} +(9.52241 + 16.4933i) q^{97} +(-2.10746 - 12.4925i) q^{98} -0.286654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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