LMFDB - Embedded newform 585.2.bt.b.571.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.12
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62679 + 0.939229i) q^{2} +(-1.72455 - 0.161066i) q^{3} +(0.764302 - 1.32381i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.95676 - 1.35772i) q^{6} +(1.80641 - 1.04293i) q^{7} -0.885499i q^{8} +(2.94812 + 0.555532i) q^{9} +O(q^{10})$	\(q+(-1.62679 + 0.939229i) q^{2} +(-1.72455 - 0.161066i) q^{3} +(0.764302 - 1.32381i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.95676 - 1.35772i) q^{6} +(1.80641 - 1.04293i) q^{7} -0.885499i q^{8} +(2.94812 + 0.555532i) q^{9} +1.87846 q^{10} +(-4.07120 + 2.35051i) q^{11} +(-1.53129 + 2.15987i) q^{12} +(-0.125111 - 3.60338i) q^{13} +(-1.95910 + 3.39326i) q^{14} +(1.41297 + 1.00176i) q^{15} +(2.36029 + 4.08814i) q^{16} +4.67113 q^{17} +(-5.31774 + 1.86522i) q^{18} +4.04179i q^{19} +(-1.32381 + 0.764302i) q^{20} +(-3.28322 + 1.50763i) q^{21} +(4.41533 - 7.64758i) q^{22} +(-2.18398 + 3.78277i) q^{23} +(-0.142624 + 1.52708i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.58793 + 5.74444i) q^{26} +(-4.99468 - 1.43288i) q^{27} -3.18845i q^{28} +(-1.28426 - 2.22441i) q^{29} +(-3.23949 - 0.302556i) q^{30} +(-0.329654 - 0.190326i) q^{31} +(-6.14567 - 3.54820i) q^{32} +(7.39956 - 3.39783i) q^{33} +(-7.59895 + 4.38726i) q^{34} -2.08586 q^{35} +(2.98867 - 3.47815i) q^{36} -3.79577i q^{37} +(-3.79617 - 6.57516i) q^{38} +(-0.364623 + 6.23434i) q^{39} +(-0.442749 + 0.766865i) q^{40} +(-10.4550 - 6.03621i) q^{41} +(3.92510 - 5.53629i) q^{42} +(-2.00139 - 3.46651i) q^{43} +7.18599i q^{44} +(-2.27538 - 1.95516i) q^{45} -8.20503i q^{46} +(0.347660 - 0.200722i) q^{47} +(-3.41197 - 7.43035i) q^{48} +(-1.32459 + 2.29426i) q^{49} +(-1.62679 - 0.939229i) q^{50} +(-8.05557 - 0.752361i) q^{51} +(-4.86581 - 2.58845i) q^{52} -12.5055 q^{53} +(9.47111 - 2.36015i) q^{54} +4.70102 q^{55} +(-0.923514 - 1.59957i) q^{56} +(0.650996 - 6.97025i) q^{57} +(4.17845 + 2.41243i) q^{58} +(6.53793 + 3.77468i) q^{59} +(2.40607 - 1.10485i) q^{60} +(-1.68660 - 2.92128i) q^{61} +0.715038 q^{62} +(5.90488 - 2.07116i) q^{63} +3.88915 q^{64} +(-1.69334 + 3.18317i) q^{65} +(-8.84621 + 12.4774i) q^{66} +(-9.00690 - 5.20013i) q^{67} +(3.57015 - 6.18368i) q^{68} +(4.37565 - 6.17179i) q^{69} +(3.39326 - 1.95910i) q^{70} +5.42477i q^{71} +(0.491923 - 2.61055i) q^{72} +1.66754i q^{73} +(3.56510 + 6.17493i) q^{74} +(-0.722785 - 1.57403i) q^{75} +(5.35056 + 3.08915i) q^{76} +(-4.90284 + 8.49196i) q^{77} +(-5.26231 - 10.4844i) q^{78} +(-0.531415 - 0.920437i) q^{79} -4.72058i q^{80} +(8.38277 + 3.27555i) q^{81} +22.6775 q^{82} +(1.57473 - 0.909171i) q^{83} +(-0.513552 + 5.49863i) q^{84} +(-4.04531 - 2.33556i) q^{85} +(6.51170 + 3.75953i) q^{86} +(1.85649 + 4.04294i) q^{87} +(2.08137 + 3.60504i) q^{88} +7.99178i q^{89} +(5.53791 + 1.04354i) q^{90} +(-3.98408 - 6.37869i) q^{91} +(3.33844 + 5.78235i) q^{92} +(0.537849 + 0.381322i) q^{93} +(-0.377047 + 0.653065i) q^{94} +(2.02090 - 3.50029i) q^{95} +(10.0270 + 7.10890i) q^{96} +(-14.4483 + 8.34172i) q^{97} -4.97638i q^{98} +(-13.3082 + 4.66789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−1.62679	+	0.939229i	−1.15032	+	0.664135i	−0.948964	−	0.315384i	$-0.897867\pi$
$2$	−1.62679	+	0.939229i	−1.15032	+	0.664135i	−0.201352	+	0.979519i	$0.564533\pi$
$3$	−1.72455	−	0.161066i	−0.995667	−	0.0929916i
$3$	−1.72455	−	0.161066i	−0.995667	−	0.0929916i
$4$	0.764302	−	1.32381i	0.382151	−	0.661905i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	2.95676	−	1.35772i	1.20709	−	0.554288i
$7$	1.80641	−	1.04293i	0.682758	−	0.394191i	−0.118135	−	0.992998i	$-0.537692\pi$
$7$	1.80641	−	1.04293i	0.682758	−	0.394191i	0.800893	+	0.598807i	$0.204358\pi$
$8$		−	0.885499i		−	0.313071i
$9$	2.94812	+	0.555532i	0.982705	+	0.185177i
$10$	1.87846			0.594020
$11$	−4.07120	+	2.35051i	−1.22751	+	0.708705i	−0.966509	−	0.256632i	$-0.917387\pi$
$11$	−4.07120	+	2.35051i	−1.22751	+	0.708705i	−0.261004	+	0.965338i	$0.584054\pi$
$12$	−1.53129	+	2.15987i	−0.442046	+	0.623500i
$13$	−0.125111	−	3.60338i	−0.0346995	−	0.999398i
$13$	−0.125111	−	3.60338i	−0.0346995	−	0.999398i
$14$	−1.95910	+	3.39326i	−0.523592	+	0.906887i
$15$	1.41297	+	1.00176i	0.364827	+	0.258653i
$16$	2.36029	+	4.08814i	0.590072	+	1.02204i
$17$	4.67113			1.13291			0.566457	−	0.824091i	$-0.308314\pi$
$17$	4.67113			1.13291			0.566457	+	0.824091i	$0.308314\pi$
$18$	−5.31774	+	1.86522i	−1.25340	+	0.439636i
$19$			4.04179i			0.927251i	0.886031	+	0.463625i	$0.153452\pi$
$19$			4.04179i			0.927251i	−0.886031	+	0.463625i	$0.846548\pi$
$20$	−1.32381	+	0.764302i	−0.296013	+	0.170903i
$21$	−3.28322	+	1.50763i	−0.716456	+	0.328992i
$22$	4.41533	−	7.64758i	0.941352	−	1.63047i
$23$	−2.18398	+	3.78277i	−0.455392	+	0.788762i	−0.998711	−	0.0507648i	$-0.983834\pi$
$23$	−2.18398	+	3.78277i	−0.455392	+	0.788762i	0.543319	+	0.839526i	$0.317167\pi$
$24$	−0.142624	+	1.52708i	−0.0291130	+	0.311715i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	3.58793	+	5.74444i	0.703651	+	1.12658i
$27$	−4.99468	−	1.43288i	−0.961227	−	0.275758i
$28$		−	3.18845i		−	0.602561i
$29$	−1.28426	−	2.22441i	−0.238481	−	0.413062i	0.721797	−	0.692104i	$-0.243316\pi$
$29$	−1.28426	−	2.22441i	−0.238481	−	0.413062i	−0.960279	+	0.279043i	$0.909983\pi$
$30$	−3.23949	−	0.302556i	−0.591447	−	0.0552389i
$31$	−0.329654	−	0.190326i	−0.0592076	−	0.0341835i	0.470104	−	0.882611i	$-0.344216\pi$
$31$	−0.329654	−	0.190326i	−0.0592076	−	0.0341835i	−0.529312	+	0.848428i	$0.677550\pi$
$32$	−6.14567	−	3.54820i	−1.08641	−	0.627240i
$33$	7.39956	−	3.39783i	1.28810	−	0.591486i
$34$	−7.59895	+	4.38726i	−1.30321	+	0.752408i
$35$	−2.08586			−0.352575
$36$	2.98867	−	3.47815i	0.498111	−	0.579691i
$37$		−	3.79577i		−	0.624021i	−0.950079	−	0.312011i	$-0.898998\pi$
$37$		−	3.79577i		−	0.624021i	0.950079	−	0.312011i	$-0.101002\pi$
$38$	−3.79617	−	6.57516i	−0.615820	−	1.06663i
$39$	−0.364623	+	6.23434i	−0.0583865	+	0.998294i
$40$	−0.442749	+	0.766865i	−0.0700048	+	0.121252i
$41$	−10.4550	−	6.03621i	−1.63280	−	0.942698i	−0.983224	−	0.182401i	$-0.941613\pi$
$41$	−10.4550	−	6.03621i	−1.63280	−	0.942698i	−0.649576	−	0.760297i	$-0.725053\pi$
$42$	3.92510	−	5.53629i	0.605656	−	0.854268i
$43$	−2.00139	−	3.46651i	−0.305210	−	0.528639i	0.672098	−	0.740462i	$-0.265393\pi$
$43$	−2.00139	−	3.46651i	−0.305210	−	0.528639i	−0.977308	+	0.211823i	$0.932060\pi$
$44$			7.18599i			1.08333i
$45$	−2.27538	−	1.95516i	−0.339193	−	0.291458i
$46$		−	8.20503i		−	1.20977i
$47$	0.347660	−	0.200722i	0.0507114	−	0.0292783i	−0.474430	−	0.880293i	$-0.657346\pi$
$47$	0.347660	−	0.200722i	0.0507114	−	0.0292783i	0.525141	+	0.851015i	$0.324012\pi$
$48$	−3.41197	−	7.43035i	−0.492475	−	1.07248i
$49$	−1.32459	+	2.29426i	−0.189227	+	0.327751i
$50$	−1.62679	−	0.939229i	−0.230063	−	0.132827i
$51$	−8.05557	−	0.752361i	−1.12801	−	0.105352i
$52$	−4.86581	−	2.58845i	−0.674766	−	0.358953i
$53$	−12.5055			−1.71776			−0.858880	−	0.512178i	$-0.828839\pi$
$53$	−12.5055			−1.71776			−0.858880	+	0.512178i	$0.828839\pi$
$54$	9.47111	−	2.36015i	1.28886	−	0.321175i
$55$	4.70102			0.633885
$56$	−0.923514	−	1.59957i	−0.123410	−	0.213752i
$57$	0.650996	−	6.97025i	0.0862266	−	0.923233i
$58$	4.17845	+	2.41243i	0.548658	+	0.316768i
$59$	6.53793	+	3.77468i	0.851166	+	0.491421i	0.861044	−	0.508530i	$-0.169811\pi$
$59$	6.53793	+	3.77468i	0.851166	+	0.491421i	−0.00987778	+	0.999951i	$0.503144\pi$
$60$	2.40607	−	1.10485i	0.310623	−	0.142636i
$61$	−1.68660	−	2.92128i	−0.215947	−	0.374032i	0.737618	−	0.675218i	$-0.235951\pi$
$61$	−1.68660	−	2.92128i	−0.215947	−	0.374032i	−0.953565	+	0.301187i	$0.902617\pi$
$62$	0.715038			0.0908100
$63$	5.90488	−	2.07116i	0.743945	−	0.260942i
$64$	3.88915			0.486143
$65$	−1.69334	+	3.18317i	−0.210033	+	0.394824i
$66$	−8.84621	+	12.4774i	−1.08889	+	1.53587i
$67$	−9.00690	−	5.20013i	−1.10037	−	0.635297i	−0.164050	−	0.986452i	$-0.552456\pi$
$67$	−9.00690	−	5.20013i	−1.10037	−	0.635297i	−0.936318	+	0.351155i	$0.885789\pi$
$68$	3.57015	−	6.18368i	0.432944	−	0.749881i
$69$	4.37565	−	6.17179i	0.526767	−	0.742996i
$70$	3.39326	−	1.95910i	0.405572	−	0.234157i
$71$			5.42477i			0.643801i	0.946773	+	0.321901i	$0.104322\pi$
$71$			5.42477i			0.643801i	−0.946773	+	0.321901i	$0.895678\pi$
$72$	0.491923	−	2.61055i	0.0579737	−	0.307657i
$73$			1.66754i			0.195171i	0.995227	+	0.0975857i	$0.0311120\pi$
$73$			1.66754i			0.195171i	−0.995227	+	0.0975857i	$0.968888\pi$
$74$	3.56510	+	6.17493i	0.414434	+	0.717821i
$75$	−0.722785	−	1.57403i	−0.0834601	−	0.181754i
$76$	5.35056	+	3.08915i	0.613751	+	0.354350i
$77$	−4.90284	+	8.49196i	−0.558730	+	0.967749i
$78$	−5.26231	−	10.4844i	−0.595839	−	1.18713i
$79$	−0.531415	−	0.920437i	−0.0597888	−	0.103557i	0.834582	−	0.550884i	$-0.185709\pi$
$79$	−0.531415	−	0.920437i	−0.0597888	−	0.103557i	−0.894371	+	0.447327i	$0.852376\pi$
$80$		−	4.72058i		−	0.527777i
$81$	8.38277	+	3.27555i	0.931419	+	0.363950i
$82$	22.6775			2.50431
$83$	1.57473	−	0.909171i	0.172849	−	0.0997945i	−0.411079	−	0.911600i	$-0.634848\pi$
$83$	1.57473	−	0.909171i	0.172849	−	0.0997945i	0.583929	+	0.811805i	$0.301515\pi$
$84$	−0.513552	+	5.49863i	−0.0560331	+	0.599950i
$85$	−4.04531	−	2.33556i	−0.438776	−	0.253327i
$86$	6.51170	+	3.75953i	0.702175	+	0.405401i
$87$	1.85649	+	4.04294i	0.199037	+	0.433449i
$88$	2.08137	+	3.60504i	0.221875	+	0.384299i
$89$			7.99178i			0.847127i	0.905866	+	0.423564i	$0.139221\pi$
$89$			7.99178i			0.847127i	−0.905866	+	0.423564i	$0.860779\pi$
$90$	5.53791	+	1.04354i	0.583747	+	0.109999i
$91$	−3.98408	−	6.37869i	−0.417645	−	0.668669i
$92$	3.33844	+	5.78235i	0.348057	+	0.602852i
$93$	0.537849	+	0.381322i	0.0557723	+	0.0395412i
$94$	−0.377047	+	0.653065i	−0.0388894	+	0.0673585i
$95$	2.02090	−	3.50029i	0.207340	−	0.359123i
$96$	10.0270	+	7.10890i	1.02338	+	0.725549i
$97$	−14.4483	+	8.34172i	−1.46700	+	0.846974i	−0.999318	−	0.0369221i	$-0.988245\pi$
$97$	−14.4483	+	8.34172i	−1.46700	+	0.846974i	−0.467684	+	0.883896i	$0.654911\pi$
$98$		−	4.97638i		−	0.502690i
$99$	−13.3082	+	4.66789i	−1.33752	+	0.469140i
$100$	1.52860			0.152860
$101$	−8.15236	−	14.1203i	−0.811190	−	1.40502i	−0.912032	−	0.410119i	$-0.865487\pi$
$101$	−8.15236	−	14.1203i	−0.811190	−	1.40502i	0.100842	−	0.994902i	$-0.467846\pi$
$102$	13.8114	−	6.34209i	1.36753	−	0.627961i
$103$	−3.55530	+	6.15796i	−0.350314	+	0.606761i	−0.986304	−	0.164935i	$-0.947258\pi$
$103$	−3.55530	+	6.15796i	−0.350314	+	0.606761i	0.635990	+	0.771697i	$0.280592\pi$
$104$	−3.19079	+	0.110786i	−0.312883	+	0.0108634i
$105$	3.59716	+	0.335962i	0.351047	+	0.0327865i
$106$	20.3438	−	11.7455i	1.97597	−	1.14082i
$107$	−7.92209			−0.765857			−0.382929	−	0.923778i	$-0.625085\pi$
$107$	−7.92209			−0.765857			−0.382929	+	0.923778i	$0.625085\pi$
$108$	−5.71431	+	5.51685i	−0.549859	+	0.530859i
$109$		−	1.36335i		−	0.130586i	−0.997866	−	0.0652928i	$-0.979202\pi$
$109$		−	1.36335i		−	0.130586i	0.997866	−	0.0652928i	$-0.0207981\pi$
$110$	−7.64758	+	4.41533i	−0.729168	+	0.420985i
$111$	−0.611371	+	6.54598i	−0.0580287	+	0.621317i
$112$	8.52729	+	4.92324i	0.805754	+	0.465202i
$113$	−9.34075	+	16.1787i	−0.878704	+	1.52196i	−0.0259397	+	0.999664i	$0.508258\pi$
$113$	−9.34075	+	16.1787i	−0.878704	+	1.52196i	−0.852764	+	0.522296i	$0.825076\pi$
$114$	5.48763	+	11.9506i	0.513964	+	1.11928i
$115$	3.78277	−	2.18398i	0.352745	−	0.203657i
$116$	−3.92625			−0.364543
$117$	1.63295	−	10.6927i	0.150966	−	0.988539i
$118$	−14.1811			−1.30548
$119$	8.43796	−	4.87166i	0.773507	−	0.446584i
$120$	0.887058	−	1.25118i	0.0809769	−	0.114217i
$121$	5.54979	−	9.61251i	0.504526	−	0.873865i
$122$	5.48750	+	3.16821i	0.496815	+	0.286836i
$123$	17.0579	+	12.0937i	1.53806	+	1.09045i
$124$	−0.503910	+	0.290933i	−0.0452525	+	0.0261265i
$125$		−	1.00000i		−	0.0894427i
$126$	−7.66072	+	8.91539i	−0.682471	+	0.794246i
$127$	−12.7088			−1.12773			−0.563864	−	0.825868i	$-0.690686\pi$
$127$	−12.7088			−1.12773			−0.563864	+	0.825868i	$0.690686\pi$
$128$	5.96451	−	3.44361i	0.527193	−	0.304375i
$129$	2.89316	+	6.30052i	0.254728	+	0.554730i
$130$	−0.235016	−	6.76880i	−0.0206122	−	0.593663i
$131$	3.48565	−	6.03733i	0.304543	−	0.527484i	−0.672617	−	0.739991i	$-0.734830\pi$
$131$	3.48565	−	6.03733i	0.304543	−	0.527484i	0.977159	+	0.212507i	$0.0681630\pi$
$132$	1.15742	−	12.3926i	0.100741	−	1.07863i
$133$	4.21531	+	7.30113i	0.365514	+	0.633088i
$134$	19.5365			1.68769
$135$	3.60908	+	3.73825i	0.310620	+	0.321738i
$136$		−	4.13628i		−	0.354683i
$137$	13.7983	−	7.96643i	1.17887	−	0.680618i	0.223114	−	0.974792i	$-0.428378\pi$
$137$	13.7983	−	7.96643i	1.17887	−	0.680618i	0.955752	+	0.294174i	$0.0950445\pi$
$138$	−1.32155	+	14.1500i	−0.112498	+	1.20452i
$139$	−8.56894	+	14.8418i	−0.726808	+	1.25887i	0.231418	+	0.972854i	$0.425664\pi$
$139$	−8.56894	+	14.8418i	−0.726808	+	1.25887i	−0.958226	+	0.286014i	$0.907670\pi$
$140$	−1.59423	+	2.76128i	−0.134737	+	0.233371i
$141$	−0.631885	+	0.290157i	−0.0532143	+	0.0244356i
$142$	−5.09510	−	8.82497i	−0.427571	−	0.740575i
$143$	8.97913	+	14.3760i	0.750873	+	1.20218i
$144$	4.68731	+	13.3635i	0.390609	+	1.11363i
$145$			2.56852i			0.213304i
$146$	−1.56621	−	2.71275i	−0.129620	−	0.224509i
$147$	2.65385	−	3.74321i	0.218886	−	0.308735i
$148$	−5.02488	−	2.90111i	−0.413042	−	0.238470i
$149$	11.0141	+	6.35901i	0.902313	+	0.520950i	0.877950	−	0.478753i	$-0.158911\pi$
$149$	11.0141	+	6.35901i	0.902313	+	0.520950i	0.0243629	+	0.999703i	$0.492244\pi$
$150$	2.65420	+	1.88176i	0.216714	+	0.153645i
$151$	−1.42753	+	0.824184i	−0.116171	+	0.0670711i	−0.556959	−	0.830540i	$-0.688032\pi$
$151$	−1.42753	+	0.824184i	−0.116171	+	0.0670711i	0.440789	+	0.897611i	$0.354699\pi$
$152$	3.57900			0.290295
$153$	13.7710	+	2.59496i	1.11332	+	0.209790i
$154$		−	18.4195i		−	1.48429i
$155$	0.190326	+	0.329654i	0.0152873	+	0.0264785i
$156$	7.97440	+	5.24761i	0.638463	+	0.420145i
$157$	−5.45588	+	9.44986i	−0.435427	+	0.754181i	−0.997330	−	0.0730217i	$-0.976736\pi$
$157$	−5.45588	+	9.44986i	−0.435427	+	0.754181i	0.561904	+	0.827203i	$0.310069\pi$
$158$	1.72900	+	0.998240i	0.137552	+	0.0794157i
$159$	21.5663	+	2.01421i	1.71032	+	0.159737i
$160$	3.54820	+	6.14567i	0.280510	+	0.485858i
$161$			9.11097i			0.718045i
$162$	−16.7135	+	2.54471i	−1.31314	+	0.199931i
$163$			9.00367i			0.705222i	0.935770	+	0.352611i	$0.114706\pi$
$163$			9.00367i			0.705222i	−0.935770	+	0.352611i	$0.885294\pi$
$164$	−15.9816	+	9.22697i	−1.24795	+	0.720505i
$165$	−8.10712	−	0.757175i	−0.631138	−	0.0589460i
$166$	−1.70784	+	2.95806i	−0.132554	+	0.229590i
$167$	13.5198	+	7.80567i	1.04619	+	0.604021i	0.921581	−	0.388185i	$-0.126898\pi$
$167$	13.5198	+	7.80567i	1.04619	+	0.604021i	0.124613	+	0.992205i	$0.460231\pi$
$168$	1.33500	+	2.90728i	0.102998	+	0.224302i
$169$	−12.9687	+	0.901644i	−0.997592	+	0.0693573i
$170$	8.77451			0.672975
$171$	−2.24535	+	11.9157i	−0.171706	+	0.911214i
$172$	−6.11867			−0.466544
$173$	−10.8319	−	18.7615i	−0.823537	−	1.42641i	−0.903032	−	0.429572i	$-0.858664\pi$
$173$	−10.8319	−	18.7615i	−0.823537	−	1.42641i	0.0794956	−	0.996835i	$-0.474669\pi$
$174$	−6.81737	−	4.83335i	−0.516824	−	0.366416i
$175$	1.80641	+	1.04293i	0.136552	+	0.0788381i
$176$	−19.2184	−	11.0958i	−1.44864	−	0.836375i
$177$	−10.6670	−	7.56264i	−0.801780	−	0.568443i
$178$	−7.50611	−	13.0010i	−0.562607	−	0.974463i
$179$	−1.48557			−0.111037			−0.0555184	−	0.998458i	$-0.517681\pi$
$179$	−1.48557			−0.111037			−0.0555184	+	0.998458i	$0.517681\pi$
$180$	−4.32734	+	1.51783i	−0.322541	+	0.113132i
$181$	12.1657			0.904266			0.452133	−	0.891951i	$-0.350663\pi$
$181$	12.1657			0.904266			0.452133	+	0.891951i	$0.350663\pi$
$182$	12.4723	+	6.63485i	0.924510	+	0.491808i
$183$	2.43810	+	5.30954i	0.180230	+	0.392492i
$184$	3.34964	+	1.93391i	0.246938	+	0.142570i
$185$	−1.89789	+	3.28724i	−0.139535	+	0.241682i
$186$	−1.23312	−	0.115169i	−0.0904165	−	0.00844457i
$187$	−19.0171	+	10.9795i	−1.39067	+	0.802902i
$188$		−	0.613647i		−	0.0447548i
$189$	−10.5168	+	2.62074i	−0.764987	+	0.190630i
$190$			7.59234i			0.550806i
$191$	−6.99657	−	12.1184i	−0.506254	−	0.876857i	−0.999974	−	0.00723635i	$-0.997697\pi$
$191$	−6.99657	−	12.1184i	−0.506254	−	0.876857i	0.493720	−	0.869621i	$-0.335637\pi$
$192$	−6.70701	−	0.626410i	−0.484037	−	0.0452073i
$193$	−16.5377	−	9.54803i	−1.19041	−	0.687282i	−0.232009	−	0.972714i	$-0.574530\pi$
$193$	−16.5377	−	9.54803i	−1.19041	−	0.687282i	−0.958399	+	0.285431i	$0.907863\pi$
$194$	15.6696	−	27.1405i	1.12501	−	1.94857i
$195$	3.43295	−	5.21679i	0.245838	−	0.373582i
$196$	2.02478	+	3.50701i	0.144627	+	0.250501i
$197$		−	8.76577i		−	0.624535i	−0.949994	−	0.312268i	$-0.898911\pi$
$197$		−	8.76577i		−	0.624535i	0.949994	−	0.312268i	$-0.101089\pi$
$198$	17.2654	−	20.0931i	1.22700	−	1.42795i
$199$	5.62103			0.398464			0.199232	−	0.979952i	$-0.436155\pi$
$199$	5.62103			0.398464			0.199232	+	0.979952i	$0.436155\pi$
$200$	0.766865	−	0.442749i	0.0542255	−	0.0313071i
$201$	14.6952	+	10.4186i	1.03652	+	0.734870i
$202$	26.5244	+	15.3139i	1.86625	+	1.07748i
$203$	−4.63980	−	2.67879i	−0.325650	−	0.188014i
$204$	−7.15287	+	10.0890i	−0.500801	+	0.706372i
$205$	6.03621	+	10.4550i	0.421587	+	0.730210i
$206$		−	13.3570i		−	0.930623i
$207$	−8.54008	+	9.93876i	−0.593577	+	0.690792i
$208$	14.4358	−	9.01649i	1.00094	−	0.625181i
$209$	−9.50027	−	16.4549i	−0.657147	−	1.13821i
$210$	−6.16738	+	2.83202i	−0.425590	+	0.195428i
$211$	−6.41620	+	11.1132i	−0.441710	+	0.765064i	−0.997817	−	0.0660471i	$-0.978961\pi$
$211$	−6.41620	+	11.1132i	−0.441710	+	0.765064i	0.556107	+	0.831111i	$0.312295\pi$
$212$	−9.55795	+	16.5549i	−0.656443	+	1.13699i
$213$	0.873747	−	9.35526i	0.0598681	−	0.641012i
$214$	12.8876	−	7.44066i	0.880978	−	0.508633i
$215$			4.00279i			0.272988i
$216$	−1.26882	+	4.42279i	−0.0863320	+	0.300932i
$217$	−0.793987			−0.0538993
$218$	1.28050	+	2.21789i	0.0867264	+	0.150215i
$219$	0.268585	−	2.87576i	0.0181493	−	0.194326i
$220$	3.59300	−	6.22325i	0.242240	−	0.419572i
$221$	−0.584409	−	16.8318i	−0.0393116	−	1.13223i
$222$	−5.15360	−	11.2232i	−0.345887	−	0.753250i
$223$	15.1859	−	8.76758i	1.01692	−	0.587121i	0.103712	−	0.994607i	$-0.466928\pi$
$223$	15.1859	−	8.76758i	1.01692	−	0.587121i	0.913211	+	0.407487i	$0.133595\pi$
$224$	−14.8021			−0.989009
$225$	0.992953	+	2.83091i	0.0661968	+	0.188727i
$226$		−	35.0924i		−	2.33431i
$227$	−23.6392	+	13.6481i	−1.56899	+	0.905856i	−0.572702	+	0.819764i	$0.694105\pi$
$227$	−23.6392	+	13.6481i	−1.56899	+	0.905856i	−0.996287	+	0.0860927i	$0.972562\pi$
$228$	−8.72973	−	6.18917i	−0.578140	−	0.409888i
$229$	−5.68727	−	3.28354i	−0.375825	−	0.216983i	0.300175	−	0.953884i	$-0.402955\pi$
$229$	−5.68727	−	3.28354i	−0.375825	−	0.216983i	−0.676000	+	0.736901i	$0.736288\pi$
$230$	−4.10252	+	7.10577i	−0.270512	+	0.468540i
$231$	9.82293	−	13.8551i	0.646301	−	0.911598i
$232$	−1.96971	+	1.13721i	−0.129318	+	0.0746616i
$233$	28.4893			1.86640			0.933198	−	0.359364i	$-0.117006\pi$
$233$	28.4893			1.86640			0.933198	+	0.359364i	$0.117006\pi$
$234$	7.38640	+	18.9285i	0.482864	+	1.23739i
$235$	−0.401443			−0.0261873
$236$	9.99391	−	5.76998i	0.650548	−	0.375594i
$237$	0.768198	+	1.67293i	0.0498998	+	0.108668i
$238$	−9.15121	+	15.8504i	−0.593185	+	1.02743i
$239$	−3.65328	−	2.10922i	−0.236311	−	0.136434i	0.377169	−	0.926144i	$-0.376898\pi$
$239$	−3.65328	−	2.10922i	−0.236311	−	0.136434i	−0.613480	+	0.789710i	$0.710231\pi$
$240$	−0.760326	+	8.14085i	−0.0490788	+	0.525490i
$241$	−9.40687	+	5.43106i	−0.605950	+	0.349845i	−0.771379	−	0.636376i	$-0.780433\pi$
$241$	−9.40687	+	5.43106i	−0.605950	+	0.349845i	0.165429	+	0.986222i	$0.447099\pi$
$242$			20.8501i			1.34029i
$243$	−13.9289	−	6.99901i	−0.893538	−	0.448987i
$244$	−5.15629			−0.330098
$245$	2.29426	−	1.32459i	0.146575	−	0.0846251i
$246$	−39.1084	−	3.65258i	−2.49346	−	0.232880i
$247$	14.5641	−	0.505672i	0.926692	−	0.0321752i
$248$	−0.168533	+	0.291908i	−0.0107019	+	0.0185362i
$249$	−2.86213	+	1.31427i	−0.181380	+	0.0832885i
$250$	0.939229	+	1.62679i	0.0594020	+	0.102887i
$251$	17.3204			1.09325			0.546626	−	0.837377i	$-0.315912\pi$
$251$	17.3204			1.09325			0.546626	+	0.837377i	$0.315912\pi$
$252$	1.77129	−	9.39993i	0.111581	−	0.592140i
$253$		−	20.5339i		−	1.29095i
$254$	20.6746	−	11.9365i	1.29724	−	0.748963i
$255$	6.60015	+	4.67935i	0.413317	+	0.293032i
$256$	−10.3578	+	17.9403i	−0.647364	+	1.12127i
$257$	0.386111	−	0.668764i	0.0240849	−	0.0417163i	−0.853732	−	0.520713i	$-0.825666\pi$
$257$	0.386111	−	0.668764i	0.0240849	−	0.0417163i	0.877817	+	0.478997i	$0.158999\pi$
$258$	−10.6242	−	7.53230i	−0.661433	−	0.468941i
$259$	−3.95873	−	6.85672i	−0.245983	−	0.426056i
$260$	2.91969	+	4.67457i	0.181072	+	0.289904i
$261$	−2.55042	−	7.27125i	−0.157867	−	0.450079i
$262$			13.0953i			0.809031i
$263$	−16.0948	−	27.8769i	−0.992445	−	1.71897i	−0.602475	−	0.798138i	$-0.705819\pi$
$263$	−16.0948	−	27.8769i	−0.992445	−	1.71897i	−0.389970	−	0.920828i	$-0.627515\pi$
$264$	−3.00877	−	6.55230i	−0.185177	−	0.403266i
$265$	10.8301	+	6.25274i	0.665285	+	0.384103i
$266$	−13.7149	−	7.91828i	−0.840912	−	0.485501i
$267$	1.28721	−	13.7822i	0.0787757	−	0.843456i
$268$	−13.7680	+	7.94894i	−0.841013	+	0.485559i
$269$	−1.91487			−0.116752			−0.0583758	−	0.998295i	$-0.518592\pi$
$269$	−1.91487			−0.116752			−0.0583758	+	0.998295i	$0.518592\pi$
$270$	−9.38230	−	2.69161i	−0.570989	−	0.163806i
$271$		−	9.46865i		−	0.575179i	−0.957754	−	0.287590i	$-0.907146\pi$
$271$		−	9.46865i		−	0.575179i	0.957754	−	0.287590i	$-0.0928539\pi$
$272$	11.0252	+	19.0962i	0.668502	+	1.15788i
$273$	5.84333	+	11.6421i	0.353654	+	0.704609i
$274$	−14.9646	+	25.9195i	−0.904045	+	1.56585i
$275$	−4.07120	−	2.35051i	−0.245503	−	0.141741i
$276$	−4.82595	−	10.5096i	−0.290488	−	0.632606i
$277$	−13.9839	−	24.2208i	−0.840211	−	1.45529i	−0.889716	−	0.456515i	$-0.849097\pi$
$277$	−13.9839	−	24.2208i	−0.840211	−	1.45529i	0.0495043	−	0.998774i	$-0.484236\pi$
$278$		−	32.1928i		−	1.93079i
$279$	−0.866126	−	0.744236i	−0.0518536	−	0.0445563i
$280$			1.84703i			0.110381i
$281$	12.9808	−	7.49445i	0.774368	−	0.447082i	−0.0600625	−	0.998195i	$-0.519130\pi$
$281$	12.9808	−	7.49445i	0.774368	−	0.447082i	0.834431	+	0.551113i	$0.185797\pi$
$282$	0.755421	−	1.06551i	0.0449847	−	0.0634502i
$283$	9.64098	−	16.6987i	0.573097	−	0.992632i	−0.423149	−	0.906060i	$-0.639075\pi$
$283$	9.64098	−	16.6987i	0.573097	−	0.992632i	0.996246	−	0.0865723i	$-0.0275914\pi$
$284$	7.18136	+	4.14616i	0.426135	+	0.246029i
$285$	−4.04891	+	5.71092i	−0.239837	+	0.338286i
$286$	−28.1095	−	14.9533i	−1.66215	−	0.884208i
$287$	−25.1814			−1.48641
$288$	−16.1470	−	13.8746i	−0.951471	−	0.817571i
$289$	4.81943			0.283496
$290$	−2.41243	−	4.17845i	−0.141663	−	0.245367i
$291$	26.2603	−	12.0586i	1.53941	−	0.706885i
$292$	2.20751	+	1.27451i	0.129185	+	0.0745849i
$293$	0.824006	+	0.475740i	0.0481390	+	0.0277930i	0.523876	−	0.851794i	$-0.324485\pi$
$293$	0.824006	+	0.475740i	0.0481390	+	0.0277930i	−0.475737	+	0.879587i	$0.657819\pi$
$294$	−0.801527	+	8.58199i	−0.0467460	+	0.500512i
$295$	−3.77468	−	6.53793i	−0.219770	−	0.380653i
$296$	−3.36115			−0.195363
$297$	23.7024	−	5.90649i	1.37535	−	0.342729i
$298$	−23.8903			−1.38393
$299$	13.9040	+	7.39645i	0.804088	+	0.427748i
$300$	−2.63615	−	0.246206i	−0.152198	−	0.0142147i
$301$	−7.23067	−	4.17463i	−0.416769	−	0.240622i
$302$	1.54819	−	2.68155i	0.0890886	−	0.154306i
$303$	11.7848	+	25.6642i	0.677019	+	1.47437i
$304$	−16.5234	+	9.53980i	−0.947683	+	0.547145i
$305$			3.37320i			0.193149i
$306$	−24.8398	+	8.71268i	−1.42000	+	0.498071i
$307$			11.9511i			0.682084i	0.940048	+	0.341042i	$0.110780\pi$
$307$			11.9511i			0.682084i	−0.940048	+	0.341042i	$0.889220\pi$
$308$	7.49449	+	12.9808i	0.427038	+	0.739652i
$309$	7.12311	−	10.0470i	0.405220	−	0.571556i
$310$	−0.619241	−	0.357519i	−0.0351705	−	0.0203057i
$311$	−7.32057	+	12.6796i	−0.415111	+	0.718994i	−0.995440	−	0.0953883i	$-0.969591\pi$
$311$	−7.32057	+	12.6796i	−0.415111	+	0.718994i	0.580329	+	0.814382i	$0.302924\pi$
$312$	5.52051	+	0.322874i	0.312537	+	0.0182791i
$313$	5.11270	+	8.85546i	0.288987	+	0.500540i	0.973568	−	0.228396i	$-0.0733482\pi$
$313$	5.11270	+	8.85546i	0.288987	+	0.500540i	−0.684581	+	0.728937i	$0.740015\pi$
$314$		−	20.4973i		−	1.15673i
$315$	−6.14936	−	1.15876i	−0.346477	−	0.0652889i
$316$	−1.62464			−0.0913934
$317$	13.3955	−	7.73390i	0.752367	−	0.434379i	−0.0741816	−	0.997245i	$-0.523634\pi$
$317$	13.3955	−	7.73390i	0.752367	−	0.434379i	0.826548	+	0.562866i	$0.190301\pi$
$318$	−36.9756	+	16.9790i	−2.07349	+	0.952133i
$319$	10.4570	+	6.03734i	0.585478	+	0.338026i
$320$	−3.36810	−	1.94457i	−0.188283	−	0.108705i
$321$	13.6620	+	1.27598i	0.762539	+	0.0712183i
$322$	−8.55728	−	14.8216i	−0.476879	−	0.825978i
$323$			18.8797i			1.05050i
$324$	10.7432	−	8.59368i	0.596842	−	0.477427i
$325$	3.05806	−	1.91004i	0.169631	−	0.105950i
$326$	−8.45650	−	14.6471i	−0.468362	−	0.811227i
$327$	−0.219590	+	2.35116i	−0.0121434	+	0.130020i
$328$	−5.34506	+	9.25791i	−0.295131	+	0.511183i
$329$	0.418677	−	0.725170i	0.0230824	−	0.0399799i
$330$	13.8998	−	6.38267i	0.765157	−	0.351355i
$331$	0.0867959	−	0.0501116i	0.00477073	−	0.00275438i	−0.497613	−	0.867399i	$-0.665790\pi$
$331$	0.0867959	−	0.0501116i	0.00477073	−	0.00275438i	0.502383	+	0.864645i	$0.332457\pi$
$332$		−	2.77952i		−	0.152546i
$333$	2.10867	−	11.1904i	0.115555	−	0.613229i
$334$	−29.3252			−1.60460
$335$	5.20013	+	9.00690i	0.284114	+	0.492099i
$336$	−13.9127	−	9.86380i	−0.759002	−	0.538115i
$337$	4.34329	−	7.52280i	0.236594	−	0.409793i	−0.723141	−	0.690701i	$-0.757302\pi$
$337$	4.34329	−	7.52280i	0.236594	−	0.409793i	0.959735	+	0.280908i	$0.0906355\pi$
$338$	20.2505	−	13.6474i	1.10148	−	0.742319i
$339$	18.7144	−	26.3963i	1.01643	−	1.43365i
$340$	−6.18368	+	3.57015i	−0.335357	+	0.193619i
$341$	1.78945			0.0969042
$342$	−7.53883	−	21.4932i	−0.407653	−	1.16222i
$343$			20.1269i			1.08675i
$344$	−3.06960	+	1.77223i	−0.165501	+	0.0955523i
$345$	−6.87532	+	3.15710i	−0.370155	+	0.169973i
$346$	35.2426	+	20.3473i	1.89465	+	1.09388i
$347$	−13.9147	+	24.1010i	−0.746982	+	1.29381i	0.202281	+	0.979327i	$0.435164\pi$
$347$	−13.9147	+	24.1010i	−0.746982	+	1.29381i	−0.949263	+	0.314483i	$0.898169\pi$
$348$	6.77100	+	0.632387i	0.362964	+	0.0338995i
$349$	−26.2928	+	15.1801i	−1.40742	+	0.812574i	−0.995139	−	0.0984825i	$-0.968601\pi$
$349$	−26.2928	+	15.1801i	−1.40742	+	0.812574i	−0.412281	+	0.911057i	$0.635268\pi$
$350$	−3.91820			−0.209437
$351$	−4.53833	+	18.1770i	−0.242238	+	0.970217i
$352$	33.3603			1.77811
$353$	26.9341	−	15.5504i	1.43356	−	0.827665i	0.436168	−	0.899865i	$-0.356335\pi$
$353$	26.9341	−	15.5504i	1.43356	−	0.827665i	0.997390	+	0.0721999i	$0.0230019\pi$
$354$	24.4560	+	2.28410i	1.29982	+	0.121399i
$355$	2.71238	−	4.69799i	0.143958	−	0.249343i
$356$	10.5796	+	6.10813i	0.560717	+	0.323730i
$357$	−15.3363	+	7.04233i	−0.811684	+	0.372720i
$358$	2.41672	−	1.39529i	0.127727	−	0.0737435i
$359$		−	21.7248i		−	1.14659i	−0.819349	−	0.573295i	$-0.805665\pi$
$359$		−	21.7248i		−	1.14659i	0.819349	−	0.573295i	$-0.194335\pi$
$360$	−1.73129	+	2.01484i	−0.0912472	+	0.106192i
$361$	2.66392			0.140206
$362$	−19.7910	+	11.4263i	−1.04019	+	0.600555i
$363$	−11.1191	+	15.6833i	−0.583602	+	0.823161i
$364$	−11.4892	+	0.398910i	−0.602198	+	0.0209086i
$365$	0.833772	−	1.44414i	0.0436416	−	0.0755895i
$366$	−8.95316	−	6.34758i	−0.467989	−	0.331793i
$367$	17.0523	+	29.5354i	0.890121	+	1.54173i	0.839730	+	0.543004i	$0.182713\pi$
$367$	17.0523	+	29.5354i	0.890121	+	1.54173i	0.0503907	+	0.998730i	$0.483953\pi$
$368$	−20.6193			−1.07486
$369$	−27.4693	−	23.6035i	−1.42999	−	1.22875i
$370$		−	7.13020i		−	0.370681i
$371$	−22.5900	+	13.0423i	−1.17281	+	0.677125i
$372$	0.915876	−	0.420564i	0.0474860	−	0.0218052i
$373$	15.8612	−	27.4724i	0.821260	−	1.42246i	−0.0834837	−	0.996509i	$-0.526605\pi$
$373$	15.8612	−	27.4724i	0.821260	−	1.42246i	0.904744	−	0.425956i	$-0.140062\pi$
$374$	20.6246	−	35.7228i	1.06647	−	1.84718i
$375$	−0.161066	+	1.72455i	−0.00831742	+	0.0890552i
$376$	−0.177739	−	0.307853i	−0.00916618	−	0.0158763i
$377$	−7.85470	+	4.90598i	−0.404538	+	0.252671i
$378$	14.6472	−	14.1411i	0.753372	−	0.727340i
$379$		−	22.1785i		−	1.13923i	−0.821910	−	0.569617i	$-0.807092\pi$
$379$		−	22.1785i		−	1.13923i	0.821910	−	0.569617i	$-0.192908\pi$
$380$	−3.08915	−	5.35056i	−0.158470	−	0.274478i
$381$	21.9170	+	2.04697i	1.12284	+	0.104869i
$382$	22.7639	+	13.1428i	1.16470	+	0.672442i
$383$	1.82956	+	1.05630i	0.0934863	+	0.0539744i	0.546014	−	0.837776i	$-0.316144\pi$
$383$	1.82956	+	1.05630i	0.0934863	+	0.0539744i	−0.452528	+	0.891750i	$0.649478\pi$
$384$	−10.8407	+	4.97798i	−0.553213	+	0.254032i
$385$	8.49196	−	4.90284i	0.432790	−	0.249872i
$386$	35.8711			1.82579
$387$	−3.97458	−	11.3315i	−0.202039	−	0.576014i
$388$			25.5024i			1.29469i
$389$	17.8558	+	30.9271i	0.905324	+	1.56807i	0.820482	+	0.571672i	$0.193705\pi$
$389$	17.8558	+	30.9271i	0.905324	+	1.56807i	0.0848416	+	0.996394i	$0.472962\pi$
$390$	−0.684929	+	11.7110i	−0.0346828	+	0.593007i
$391$	−10.2017	+	17.6698i	−0.515920	+	0.893600i
$392$	2.03157	+	1.17292i	0.102610	+	0.0592416i
$393$	−6.98358	+	9.85023i	−0.352275	+	0.496878i
$394$	8.23306	+	14.2601i	0.414776	+	0.718413i
$395$			1.06283i			0.0534768i
$396$	−3.99205	+	21.1851i	−0.200608	+	1.06459i
$397$			13.7712i			0.691159i	0.938389	+	0.345580i	$0.112318\pi$
$397$			13.7712i			0.691159i	−0.938389	+	0.345580i	$0.887682\pi$
$398$	−9.14424	+	5.27943i	−0.458359	+	0.264634i
$399$	−6.09353	−	13.2701i	−0.305058	−	0.664335i
$400$	−2.36029	+	4.08814i	−0.118014	+	0.204407i
$401$	−1.45703	−	0.841215i	−0.0727605	−	0.0420083i	0.463178	−	0.886265i	$-0.346709\pi$
$401$	−1.45703	−	0.841215i	−0.0727605	−	0.0420083i	−0.535939	+	0.844257i	$0.680042\pi$
$402$	−33.6915	−	3.14666i	−1.68038	−	0.156941i
$403$	−0.644573	+	1.21168i	−0.0321085	+	0.0603581i
$404$	−24.9234			−1.23999
$405$	−5.62192	−	7.02809i	−0.279355	−	0.349229i
$406$	10.0640			0.499467
$407$	8.92200	+	15.4534i	0.442247	+	0.765994i
$408$	−0.666215	+	7.13320i	−0.0329825	+	0.353146i
$409$	6.83235	+	3.94466i	0.337838	+	0.195051i	0.659315	−	0.751866i	$-0.270846\pi$
$409$	6.83235	+	3.94466i	0.337838	+	0.195051i	−0.321478	+	0.946917i	$0.604180\pi$
$410$	−19.6393	−	11.3388i	−0.969917	−	0.559982i
$411$	−25.0789	+	11.5160i	−1.23705	+	0.568045i
$412$	5.43464	+	9.41307i	0.267745	+	0.463749i
$413$	15.7469			0.774855
$414$	4.55816	−	24.1894i	0.224021	−	1.18884i
$415$	−1.81834			−0.0892589
$416$	−12.0166	+	22.5891i	−0.589164	+	1.10752i
$417$	17.1680	−	24.2153i	0.840723	−	1.18583i
$418$	30.9099	+	17.8459i	1.51185	+	0.872869i
$419$	−4.92218	+	8.52547i	−0.240464	+	0.416497i	−0.960847	−	0.277081i	$-0.910633\pi$
$419$	−4.92218	+	8.52547i	−0.240464	+	0.416497i	0.720382	+	0.693577i	$0.243966\pi$
$420$	3.19407	−	4.50518i	0.155854	−	0.219830i
$421$	7.00463	−	4.04412i	0.341385	−	0.197098i	−0.319500	−	0.947586i	$-0.603515\pi$
$421$	7.00463	−	4.04412i	0.341385	−	0.197098i	0.660884	+	0.750488i	$0.270181\pi$
$422$		−	24.1051i		−	1.17342i
$423$	1.13645	−	0.398614i	0.0552560	−	0.0193813i
$424$			11.0736i			0.537781i
$425$	2.33556	+	4.04531i	0.113291	+	0.196227i
$426$	7.36532	+	16.0397i	0.356851	+	0.777126i
$427$	−6.09339	−	3.51802i	−0.294880	−	0.170249i
$428$	−6.05487	+	10.4873i	−0.292673	+	0.506925i
$429$	−13.1694	−	26.2383i	−0.635826	−	1.26680i
$430$	−3.75953	−	6.51170i	−0.181301	−	0.314022i
$431$			5.33973i			0.257206i	0.991696	+	0.128603i	$0.0410492\pi$
$431$			5.33973i			0.257206i	−0.991696	+	0.128603i	$0.958951\pi$
$432$	−5.93107	−	23.8010i	−0.285359	−	1.14513i
$433$	−29.5532			−1.42023			−0.710117	−	0.704084i	$-0.751358\pi$
$433$	−29.5532			−1.42023			−0.710117	+	0.704084i	$0.751358\pi$
$434$	1.29165	−	0.745735i	0.0620013	−	0.0357964i
$435$	0.413702	−	4.42953i	0.0198355	−	0.212380i
$436$	−1.80482	−	1.04201i	−0.0864352	−	0.0499034i
$437$	−15.2892	−	8.82720i	−0.731380	−	0.422262i
$438$	2.26406	+	4.93052i	0.108181	+	0.235589i
$439$	−3.22427	−	5.58459i	−0.153886	−	0.266538i	0.778767	−	0.627313i	$-0.215845\pi$
$439$	−3.22427	−	5.58459i	−0.153886	−	0.266538i	−0.932653	+	0.360775i	$0.882512\pi$
$440$		−	4.16275i		−	0.198451i
$441$	−5.17958	+	6.02789i	−0.246647	+	0.287042i
$442$	16.7597	+	26.8330i	0.797176	+	1.27632i
$443$	14.2674	+	24.7119i	0.677867	+	1.17410i	0.975622	+	0.219457i	$0.0704287\pi$
$443$	14.2674	+	24.7119i	0.677867	+	1.17410i	−0.297755	+	0.954642i	$0.596238\pi$
$444$	8.19836	+	5.81244i	0.389077	+	0.275846i
$445$	3.99589	−	6.92108i	0.189423	−	0.328091i
$446$	−16.4695	+	28.5261i	−0.779855	+	1.35075i
$447$	−17.9701	−	12.7404i	−0.849959	−	0.602601i
$448$	7.02539	−	4.05611i	0.331918	−	0.191633i
$449$		−	18.4800i		−	0.872124i	−0.899917	−	0.436062i	$-0.856373\pi$
$449$		−	18.4800i		−	0.872124i	0.899917	−	0.436062i	$-0.143627\pi$
$450$	−4.27420	−	3.67269i	−0.201488	−	0.173132i
$451$	56.7527			2.67238
$452$	14.2783	+	24.7307i	0.671595	+	1.16324i
$453$	2.59459	−	1.19142i	0.121904	−	0.0559776i
$454$	25.6374	−	44.4052i	1.20322	−	2.08404i
$455$	0.260964	+	7.51615i	0.0122342	+	0.352363i
$456$	−6.17215	−	0.576456i	−0.289038	−	0.0269950i
$457$	25.2930	−	14.6029i	1.18316	−	0.683096i	0.226414	−	0.974031i	$-0.427300\pi$
$457$	25.2930	−	14.6029i	1.18316	−	0.683096i	0.956743	+	0.290935i	$0.0939665\pi$
$458$	12.3360			0.576423
$459$	−23.3308	−	6.69318i	−1.08899	−	0.312411i
$460$		−	6.67688i		−	0.311311i
$461$	25.8926	−	14.9491i	1.20594	−	0.696249i	0.244069	−	0.969758i	$-0.421518\pi$
$461$	25.8926	−	14.9491i	1.20594	−	0.696249i	0.961869	+	0.273509i	$0.0881844\pi$
$462$	−2.96677	+	31.7653i	−0.138026	+	1.47786i
$463$	−24.4237	−	14.1010i	−1.13507	−	0.655331i	−0.189862	−	0.981811i	$-0.560804\pi$
$463$	−24.4237	−	14.1010i	−1.13507	−	0.655331i	−0.945204	+	0.326480i	$0.894138\pi$
$464$	6.06246	−	10.5005i	0.281442	−	0.487473i
$465$	−0.275130	−	0.599159i	−0.0127588	−	0.0277853i
$466$	−46.3461	+	26.7580i	−2.14694	+	1.23954i
$467$	−3.97634			−0.184003			−0.0920015	−	0.995759i	$-0.529326\pi$
$467$	−3.97634			−0.184003			−0.0920015	+	0.995759i	$0.529326\pi$
$468$	−12.9070	−	10.3342i	−0.596626	−	0.477696i
$469$	−21.6935			−1.00171
$470$	0.653065	−	0.377047i	0.0301236	−	0.0173919i
$471$	10.9310	−	15.4180i	0.503672	−	0.710422i
$472$	3.34247	−	5.78933i	0.153850	−	0.266476i
$473$	16.2961	+	9.40859i	0.749298	+	0.432607i
$474$	−2.82096	−	1.99999i	−0.129571	−	0.0918628i
$475$	−3.50029	+	2.02090i	−0.160605	+	0.0927251i
$476$		−	14.8937i		−	0.682650i
$477$	−36.8676	−	6.94719i	−1.68805	−	0.318090i
$478$	7.92417			0.362443
$479$	−1.88124	+	1.08613i	−0.0859561	+	0.0496268i	−0.542362	−	0.840145i	$-0.682470\pi$
$479$	−1.88124	+	1.08613i	−0.0859561	+	0.0496268i	0.456406	+	0.889772i	$0.349137\pi$
$480$	−5.12918	−	11.1700i	−0.234114	−	0.509838i
$481$	−13.6776	+	0.474893i	−0.623645	+	0.0216532i
$482$	10.2020	−	17.6704i	0.464689	−	0.804865i
$483$	1.46747	−	15.7123i	0.0667721	−	0.714933i
$484$	−8.48342	−	14.6937i	−0.385610	−	0.667896i
$485$	16.6834			0.757556
$486$	29.2331	−	1.69648i	1.32604	−	0.0769539i
$487$			18.0177i			0.816458i	0.912880	+	0.408229i	$0.133853\pi$
$487$			18.0177i			0.816458i	−0.912880	+	0.408229i	$0.866147\pi$
$488$	−2.58679	+	1.49348i	−0.117099	+	0.0676069i
$489$	1.45019	−	15.5272i	0.0655797	−	0.702166i
$490$	−2.48819	+	4.30967i	−0.112405	+	0.194691i
$491$	−10.4359	+	18.0756i	−0.470967	+	0.815739i	−0.999449	−	0.0332061i	$-0.989428\pi$
$491$	−10.4359	+	18.0756i	−0.470967	+	0.815739i	0.528482	+	0.848945i	$0.322762\pi$
$492$	29.0471	−	13.3382i	1.30955	−	0.601334i
$493$	−5.99895	−	10.3905i	−0.270179	−	0.467964i
$494$	−23.2178	+	14.5017i	−1.04462	+	0.652460i
$495$	13.8591	+	2.61157i	0.622922	+	0.117381i
$496$		−	1.79690i		−	0.0806830i
$497$	5.65766	+	9.79935i	0.253781	+	0.439561i
$498$	3.42169	−	4.82624i	0.153330	−	0.216269i
$499$	11.0473	+	6.37814i	0.494544	+	0.285525i	0.726458	−	0.687211i	$-0.241165\pi$
$499$	11.0473	+	6.37814i	0.494544	+	0.285525i	−0.231914	+	0.972736i	$0.574499\pi$
$500$	−1.32381	−	0.764302i	−0.0592025	−	0.0341806i
$501$	−22.0583	−	15.6388i	−0.985492	−	0.698691i
$502$	−28.1766	+	16.2678i	−1.25759	+	0.726067i
$503$	−1.56661			−0.0698517			−0.0349258	−	0.999390i	$-0.511119\pi$
$503$	−1.56661			−0.0698517			−0.0349258	+	0.999390i	$0.511119\pi$
$504$	−1.83401	−	5.22877i	−0.0816934	−	0.232908i
$505$			16.3047i			0.725550i
$506$	19.2860	+	33.4043i	0.857368	+	1.48500i
$507$	22.5103	+	0.533892i	0.999719	+	0.0237110i
$508$	−9.71339	+	16.8241i	−0.430962	+	0.746448i
$509$	11.6920	+	6.75038i	0.518239	+	0.299205i	0.736214	−	0.676749i	$-0.236612\pi$
$509$	11.6920	+	6.75038i	0.518239	+	0.299205i	−0.217975	+	0.975954i	$0.569945\pi$
$510$	−15.1321	−	1.41328i	−0.670058	−	0.0625810i
$511$	1.73913	+	3.01227i	0.0769347	+	0.133255i
$512$		−	25.1390i		−	1.11100i
$513$	5.79141	−	20.1875i	0.255697	−	0.891298i
$514$			1.45059i			0.0639826i
$515$	6.15796	−	3.55530i	0.271352	−	0.156665i
$516$	10.5519	+	0.985511i	0.464523	+	0.0433847i
$517$	−0.943596	+	1.63436i	−0.0414993	+	0.0718789i
$518$	12.8801	+	7.43630i	0.565917	+	0.326732i
$519$	15.6583	+	34.0997i	0.687324	+	1.49681i
$520$	2.81870	+	1.49945i	0.123608	+	0.0657553i
$521$	−20.7529			−0.909203			−0.454602	−	0.890695i	$-0.650218\pi$
$521$	−20.7529			−0.909203			−0.454602	+	0.890695i	$0.650218\pi$
$522$	10.9784	+	9.43339i	0.480510	+	0.412888i
$523$	−23.5812			−1.03113			−0.515567	−	0.856849i	$-0.672419\pi$
$523$	−23.5812			−1.03113			−0.515567	+	0.856849i	$0.672419\pi$
$524$	−5.32818	−	9.22868i	−0.232763	−	0.403157i
$525$	−2.94725	−	2.08953i	−0.128629	−	0.0911947i
$526$	52.3656	+	30.2333i	2.28325	+	1.31824i
$527$	−1.53986	−	0.889036i	−0.0670772	−	0.0387270i
$528$	31.3559	+	22.2306i	1.36459	+	0.967462i
$529$	1.96045	+	3.39559i	0.0852368	+	0.147635i
$530$	−23.4910			−1.02038
$531$	17.1776	+	14.7602i	0.745446	+	0.640539i
$532$	12.8871			0.558725
$533$	−20.4427	+	38.4286i	−0.885472	+	1.66453i
$534$	10.8506	+	23.6297i	0.469552	+	1.02256i
$535$	6.86073	+	3.96105i	0.296615	+	0.171251i
$536$	−4.60471	+	7.97560i	−0.198893	+	0.344493i
$537$	2.56194	+	0.239275i	0.110556	+	0.0103255i
$538$	3.11510	−	1.79850i	0.134301	−	0.0775389i
$539$		−	12.4539i		−	0.536426i
$540$	7.70716	−	1.92058i	0.331663	−	0.0826486i
$541$			31.0090i			1.33318i	0.745424	+	0.666591i	$0.232247\pi$
$541$			31.0090i			1.33318i	−0.745424	+	0.666591i	$0.767753\pi$
$542$	8.89323	+	15.4035i	0.381997	+	0.661638i
$543$	−20.9802	−	1.95948i	−0.900348	−	0.0840892i
$544$	−28.7072	−	16.5741i	−1.23081	−	0.710609i
$545$	−0.681677	+	1.18070i	−0.0291998	+	0.0505756i
$546$	−20.4404	−	13.4510i	−0.874770	−	0.575648i
$547$	12.5202	+	21.6857i	0.535326	+	0.927212i	0.999147	+	0.0412834i	$0.0131446\pi$
$547$	12.5202	+	21.6857i	0.535326	+	0.927212i	−0.463821	+	0.885929i	$0.653522\pi$
$548$		−	24.3550i		−	1.04040i
$549$	−3.34943	−	9.54923i	−0.142950	−	0.407551i
$550$	8.83066			0.376541
$551$	8.99059	−	5.19072i	0.383012	−	0.221132i
$552$	−5.46511	−	3.87464i	−0.232611	−	0.164915i
$553$	−1.91990	−	1.10846i	−0.0816426	−	0.0471364i
$554$	45.4978	+	26.2682i	1.93302	+	1.11603i
$555$	3.80245	−	5.36330i	0.161405	−	0.227659i
$556$	13.0985	+	22.6873i	0.555500	+	0.962155i
$557$			9.29754i			0.393949i	0.980409	+	0.196975i	$0.0631117\pi$
$557$			9.29754i			0.393949i	−0.980409	+	0.196975i	$0.936888\pi$
$558$	2.10802	+	0.397227i	0.0892394	+	0.0168159i
$559$	−12.2408	+	7.64548i	−0.517730	+	0.323369i
$560$	−4.92324	−	8.52729i	−0.208045	−	0.360344i
$561$	34.5643	−	15.8717i	1.45931	−	0.670103i
$562$	−14.0780	+	24.3838i	−0.593845	+	1.02857i
$563$	9.25094	−	16.0231i	0.389881	−	0.675293i	−0.602553	−	0.798079i	$-0.705850\pi$
$563$	9.25094	−	16.0231i	0.389881	−	0.675293i	0.992433	+	0.122786i	$0.0391830\pi$
$564$	−0.0988379	+	1.05826i	−0.00416182	+	0.0445609i
$565$	16.1787	−	9.34075i	0.680641	−	0.392968i
$566$			36.2203i			1.52245i
$567$	18.5589	−	2.82567i	0.779399	−	0.118667i
$568$	4.80363			0.201556
$569$	10.2225	+	17.7060i	0.428551	+	0.742272i	0.996745	−	0.0806227i	$-0.0256909\pi$
$569$	10.2225	+	17.7060i	0.428551	+	0.742272i	−0.568194	+	0.822895i	$0.692358\pi$
$570$	1.22287	−	13.0933i	0.0512203	−	0.548419i
$571$	12.4042	−	21.4846i	0.519098	−	0.899104i	−0.480656	−	0.876909i	$-0.659601\pi$
$571$	12.4042	−	21.4846i	0.519098	−	0.899104i	0.999754	−	0.0221945i	$-0.00706532\pi$
$572$	25.8939	−	0.899046i	1.08268	−	0.0375910i
$573$	10.1140	+	22.0257i	0.422520	+	0.920135i
$574$	40.9649	−	23.6511i	1.70984	−	0.987177i
$575$	−4.36796			−0.182157
$576$	11.4657	+	2.16055i	0.477736	+	0.0900228i
$577$		−	32.7191i		−	1.36211i	−0.732230	−	0.681057i	$-0.761520\pi$
$577$		−	32.7191i		−	1.36211i	0.732230	−	0.681057i	$-0.238480\pi$
$578$	−7.84021	+	4.52654i	−0.326110	+	0.188279i
$579$	26.9821	+	19.1297i	1.12134	+	0.795002i
$580$	3.40023	+	1.96313i	0.141187	+	0.0815144i
$581$	1.89640	−	3.28467i	0.0786761	−	0.136271i
$582$	−31.3943	+	44.2812i	−1.30134	+	1.83551i
$583$	50.9123	−	29.3942i	2.10857	−	1.21738i
$584$	1.47661			0.0611025
$585$	−6.76052	+	8.44366i	−0.279513	+	0.349102i
$586$	−1.78732			−0.0738333
$587$	−25.5311	+	14.7404i	−1.05378	+	0.608401i	−0.923705	−	0.383103i	$-0.874855\pi$
$587$	−25.5311	+	14.7404i	−1.05378	+	0.608401i	−0.130075	+	0.991504i	$0.541522\pi$
$588$	−2.92696	−	6.37413i	−0.120706	−	0.262865i
$589$	0.769258	−	1.33239i	0.0316967	−	0.0549003i
$590$	12.2812	+	7.09057i	0.505610	+	0.291914i
$591$	−1.41187	+	15.1170i	−0.0580765	+	0.621829i
$592$	15.5177	−	8.95912i	0.637772	−	0.368218i
$593$			25.4261i			1.04413i	0.852907	+	0.522063i	$0.174837\pi$
$593$			25.4261i			1.04413i	−0.852907	+	0.522063i	$0.825163\pi$
$594$	−33.0113	+	31.8706i	−1.35447	+	1.30767i
$595$	−9.74332			−0.399437
$596$	16.8362	−	9.72040i	0.689639	−	0.398163i
$597$	−9.69372	−	0.905358i	−0.396738	−	0.0370538i
$598$	−29.5659	+	1.02654i	−1.20904	+	0.0419783i
$599$	14.8405	−	25.7045i	0.606367	−	1.05026i	−0.385467	−	0.922722i	$-0.625960\pi$
$599$	14.8405	−	25.7045i	0.606367	−	1.05026i	0.991834	−	0.127537i	$-0.0407071\pi$
$600$	−1.39380	+	0.640026i	−0.0569019	+	0.0261289i
$601$	3.28435	+	5.68866i	0.133971	+	0.232045i	0.925204	−	0.379470i	$-0.123894\pi$
$601$	3.28435	+	5.68866i	0.133971	+	0.232045i	−0.791233	+	0.611515i	$0.790560\pi$
$602$	15.6837			0.639221
$603$	−23.6645	−	20.3342i	−0.963694	−	0.828073i
$604$			2.51970i			0.102525i
$605$	−9.61251	+	5.54979i	−0.390804	+	0.225631i
$606$	−43.2759	−	30.6816i	−1.75797	−	1.24636i
$607$	21.3033	−	36.8985i	0.864676	−	1.49766i	−0.00269327	−	0.999996i	$-0.500857\pi$
$607$	21.3033	−	36.8985i	0.864676	−	1.49766i	0.867369	−	0.497666i	$-0.165809\pi$
$608$	14.3411	−	24.8395i	0.581609	−	1.00738i
$609$	7.57009	+	5.36701i	0.306755	+	0.217482i
$610$	−3.16821	−	5.48750i	−0.128277	−	0.222182i
$611$	−0.766772	−	1.22764i	−0.0310203	−	0.0496649i
$612$	13.9604	−	16.2469i	0.564318	−	0.656741i
$613$			11.7258i			0.473603i	0.971558	+	0.236801i	$0.0760990\pi$
$613$			11.7258i			0.473603i	−0.971558	+	0.236801i	$0.923901\pi$
$614$	−11.2248	−	19.4419i	−0.452996	−	0.784612i
$615$	−8.72577	−	19.0024i	−0.351857	−	0.766250i
$616$	7.51962	+	4.34146i	0.302974	+	0.174922i
$617$	−24.2780	−	14.0169i	−0.977396	−	0.564300i	−0.0759130	−	0.997114i	$-0.524187\pi$
$617$	−24.2780	−	14.0169i	−0.977396	−	0.564300i	−0.901483	+	0.432815i	$0.857520\pi$
$618$	−2.15135	+	23.0347i	−0.0865401	+	0.926590i
$619$	28.9581	−	16.7190i	1.16393	−	0.671993i	0.211684	−	0.977338i	$-0.432105\pi$
$619$	28.9581	−	16.7190i	1.16393	−	0.671993i	0.952242	+	0.305345i	$0.0987719\pi$
$620$	0.581866			0.0233683
$621$	16.3286	−	15.7643i	0.655242	−	0.632601i
$622$		−	27.5028i		−	1.10276i
$623$	8.33487	+	14.4364i	0.333930	+	0.578383i
$624$	−26.3475	+	13.2242i	−1.05474	+	0.529393i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−16.6346	−	9.60399i	−0.664853	−	0.383853i
$627$	13.7333	+	29.9075i	0.548456	+	1.19439i
$628$	8.33987	+	14.4451i	0.332797	+	0.576422i
$629$		−	17.7305i		−	0.706963i
$630$	11.0921	−	3.89059i	0.441919	−	0.155005i
$631$		−	27.9073i		−	1.11097i	−0.831526	−	0.555485i	$-0.812532\pi$
$631$		−	27.9073i		−	1.11097i	0.831526	−	0.555485i	$-0.187468\pi$
$632$	−0.815046	+	0.470567i	−0.0324208	+	0.0187182i
$633$	12.8550	−	18.1318i	0.510940	−	0.720673i
$634$	−14.5278	+	25.1629i	−0.576973	+	0.999346i
$635$	11.0062	+	6.35442i	0.436767	+	0.252167i
$636$	19.1496	−	27.0102i	0.759329	−	1.07102i
$637$	8.43281	+	4.48597i	0.334120	+	0.177741i
$638$	−22.6818			−0.897979
$639$	−3.01363	+	15.9928i	−0.119217	+	0.632667i
$640$	−6.88722			−0.272241
$641$	−23.8045	−	41.2305i	−0.940220	−	1.62851i	−0.765050	−	0.643970i	$-0.777286\pi$
$641$	−23.8045	−	41.2305i	−0.940220	−	1.62851i	−0.175169	−	0.984538i	$-0.556047\pi$
$642$	−23.4237	+	10.7560i	−0.924459	+	0.424505i
$643$	−2.16175	−	1.24809i	−0.0852512	−	0.0492198i	0.456768	−	0.889586i	$-0.349007\pi$
$643$	−2.16175	−	1.24809i	−0.0852512	−	0.0492198i	−0.542020	+	0.840366i	$0.682340\pi$
$644$	12.0612	+	6.96353i	0.475277	+	0.274401i
$645$	0.644714	−	6.90299i	0.0253856	−	0.271805i
$646$	−17.7324	−	30.7134i	−0.697671	−	1.20840i
$647$	−38.9234			−1.53024			−0.765118	−	0.643890i	$-0.777320\pi$
$647$	−38.9234			−1.53024			−0.765118	+	0.643890i	$0.777320\pi$
$648$	2.90049	−	7.42293i	0.113942	−	0.291600i
$649$	−35.4897			−1.39309
$650$	−3.18087	+	5.97946i	−0.124764	+	0.234534i
$651$	1.36927	+	0.127884i	0.0536658	+	0.00501219i
$652$	11.9191	+	6.88152i	0.466789	+	0.269501i
$653$	−6.00474	+	10.4005i	−0.234984	+	0.407004i	−0.959268	−	0.282498i	$-0.908837\pi$
$653$	−6.00474	+	10.4005i	−0.234984	+	0.407004i	0.724284	+	0.689502i	$0.242170\pi$
$654$	−1.85105	−	4.03110i	−0.0723819	−	0.157629i
$655$	−6.03733	+	3.48565i	−0.235898	+	0.136196i
$656$		−	56.9888i		−	2.22504i
$657$	−0.926375	+	4.91611i	−0.0361413	+	0.191796i
$658$			1.57294i			0.0613194i
$659$	−20.7848	−	36.0003i	−0.809660	−	1.40237i	−0.913100	−	0.407736i	$-0.866318\pi$
$659$	−20.7848	−	36.0003i	−0.809660	−	1.40237i	0.103440	−	0.994636i	$-0.467015\pi$
$660$	−7.19864	+	10.1536i	−0.280207	+	0.395227i
$661$	−2.37517	−	1.37130i	−0.0923834	−	0.0533376i	0.453097	−	0.891461i	$-0.350319\pi$
$661$	−2.37517	−	1.37130i	−0.0923834	−	0.0533376i	−0.545480	+	0.838124i	$0.683653\pi$
$662$	−0.0941325	+	0.163042i	−0.00365857	+	0.00633682i
$663$	−1.70320	+	29.1214i	−0.0661469	+	1.13098i
$664$	−0.805070	−	1.39442i	−0.0312428	−	0.0541141i
$665$		−	8.43062i		−	0.326925i
$666$	7.07995	+	20.1849i	0.274342	+	0.782150i
$667$	11.2192			0.434410
$668$	20.6664	−	11.9318i	0.799608	−	0.461654i
$669$	−27.6009	+	12.6742i	−1.06711	+	0.490011i
$670$	−16.9191	−	9.76823i	−0.653641	−	0.377380i
$671$	13.7330	+	7.92875i	0.530156	+	0.306086i
$672$	25.5269	+	2.38412i	0.984723	+	0.0919695i
$673$	3.91211	+	6.77598i	0.150801	+	0.261195i	0.931522	−	0.363685i	$-0.118481\pi$
$673$	3.91211	+	6.77598i	0.150801	+	0.261195i	−0.780721	+	0.624879i	$0.785148\pi$
$674$			16.3174i			0.628522i
$675$	−1.25643	−	5.04196i	−0.0483600	−	0.194065i
$676$	−8.71839	+	17.8572i	−0.335323	+	0.686816i
$677$	2.99863	+	5.19378i	0.115247	+	0.199613i	0.917878	−	0.396862i	$-0.129901\pi$
$677$	2.99863	+	5.19378i	0.115247	+	0.199613i	−0.802632	+	0.596475i	$0.796567\pi$
$678$	−5.65220	+	60.5185i	−0.217072	+	2.32420i
$679$	−17.3997	+	30.1371i	−0.667738	+	1.15656i
$680$	−2.06814	+	3.58212i	−0.0793095	+	0.137368i
$681$	42.9651	−	19.7293i	1.64643	−	0.756028i
$682$	−2.91106	+	1.68070i	−0.111470	+	0.0643575i
$683$		−	23.2955i		−	0.891377i	−0.895188	−	0.445688i	$-0.852959\pi$
$683$		−	23.2955i		−	0.891377i	0.895188	−	0.445688i	$-0.147041\pi$
$684$	14.0580	+	12.0796i	0.537519	+	0.461874i
$685$	−15.9329			−0.608764
$686$	−18.9037	−	32.7422i	−0.721748	−	1.25010i
$687$	9.27908	+	6.57865i	0.354019	+	0.250991i
$688$	9.44773	−	16.3640i	0.360191	−	0.623870i
$689$	1.56457	+	45.0620i	0.0596054	+	1.71672i
$690$	8.21948	−	11.5934i	0.312910	−	0.441355i
$691$	−29.8998	+	17.2626i	−1.13744	+	0.656701i	−0.945795	−	0.324763i	$-0.894715\pi$
$691$	−29.8998	+	17.2626i	−1.13744	+	0.656701i	−0.191645	+	0.981464i	$0.561382\pi$
$692$	−33.1155			−1.25886
$693$	−19.1717	+	22.3116i	−0.728272	+	0.847547i
$694$		−	52.2765i		−	1.98439i
$695$	14.8418	−	8.56894i	0.562983	−	0.325038i
$696$	3.58002	−	1.64392i	0.135700	−	0.0623126i
$697$	−48.8367	−	28.1959i	−1.84982	−	1.06800i
$698$	28.5152	−	49.3899i	1.07932	−	1.86943i
$699$	−49.1311	−	4.58866i	−1.85831	−	0.173559i
$700$	2.76128	−	1.59423i	0.104367	−	0.0602561i
$701$	34.9294			1.31926			0.659632	−	0.751589i	$-0.270712\pi$
$701$	34.9294			1.31926			0.659632	+	0.751589i	$0.270712\pi$
$702$	−9.68945	−	33.8327i	−0.365705	−	1.27693i
$703$	15.3417			0.578624
$704$	−15.8335	+	9.14148i	−0.596747	+	0.344532i
$705$	0.692307	+	0.0646589i	0.0260738	+	0.00243520i
$706$	−29.2108	+	50.5946i	−1.09936	+	1.90415i
$707$	−29.4530	−	17.0047i	−1.10769	−	0.639527i
$708$	−18.1643	+	8.34092i	−0.682656	+	0.313471i
$709$	3.49355	−	2.01700i	0.131203	−	0.0757501i	−0.432962	−	0.901412i	$-0.642532\pi$
$709$	3.49355	−	2.01700i	0.131203	−	0.0757501i	0.564165	+	0.825662i	$0.309198\pi$
$710$			10.1902i			0.382431i
$711$	−1.05534	−	3.00877i	−0.0395783	−	0.112838i
$712$	7.07671			0.265211
$713$	1.43992	−	0.831337i	0.0539253	−	0.0311338i
$714$	18.3346	−	25.8607i	0.686156	−	0.967813i
$715$	−0.588149	−	16.9396i	−0.0219955	−	0.633503i
$716$	−1.13542	+	1.96661i	−0.0424328	+	0.0734958i
$717$	5.96052	+	4.22587i	0.222600	+	0.157818i
$718$	20.4045	+	35.3417i	0.761490	+	1.31894i
$719$	0.0970774			0.00362038			0.00181019	−	0.999998i	$-0.499424\pi$
$719$	0.0970774			0.00362038			0.00181019	+	0.999998i	$0.499424\pi$
$720$	2.62243	−	13.9168i	0.0977323	−	0.518649i
$721$			14.8317i			0.552362i
$722$	−4.33364	+	2.50203i	−0.161281	+	0.0931158i
$723$	17.0973	−	7.85098i	0.635857	−	0.291981i
$724$	9.29823	−	16.1050i	0.345566	−	0.598538i
$725$	1.28426	−	2.22441i	0.0476963	−	0.0826124i
$726$	3.35824	−	35.9569i	0.124636	−	1.33449i
$727$	−16.7239	−	28.9666i	−0.620255	−	1.07431i	−0.989438	−	0.144957i	$-0.953696\pi$
$727$	−16.7239	−	28.9666i	−0.620255	−	1.07431i	0.369183	−	0.929357i	$-0.379638\pi$
$728$	−5.64833	+	3.52790i	−0.209341	+	0.130753i
$729$	22.8937	+	14.3136i	0.847915	+	0.530133i
$730$			3.13241i			0.115936i
$731$	−9.34876	−	16.1925i	−0.345776	−	0.598902i
$732$	8.89226	+	0.830504i	0.328667	+	0.0306963i
$733$	−19.0031	−	10.9715i	−0.701897	−	0.405240i	0.106157	−	0.994349i	$-0.466145\pi$
$733$	−19.0031	−	10.9715i	−0.701897	−	0.405240i	−0.808053	+	0.589109i	$0.799479\pi$
$734$	−55.4809	−	32.0319i	−2.04784	−	1.18232i
$735$	−4.16990	+	1.91479i	−0.153809	+	0.0706281i
$736$	26.8441	−	15.4984i	0.989485	−	0.571280i
$737$	48.8918			1.80095
$738$	66.8560	+	12.5981i	2.46100	+	0.463742i
$739$			9.00066i			0.331094i	0.986202	+	0.165547i	$0.0529390\pi$
$739$			9.00066i			0.331094i	−0.986202	+	0.165547i	$0.947061\pi$
$740$	2.90111	+	5.02488i	0.106647	+	0.184718i
$741$	−25.1979	−	1.47373i	−0.925669	−	0.0541389i
$742$	24.4995	−	42.4344i	0.899404	−	1.55781i
$743$	−40.2399	−	23.2325i	−1.47626	−	0.852319i	−0.476619	−	0.879110i	$-0.658138\pi$
$743$	−40.2399	−	23.2325i	−1.47626	−	0.852319i	−0.999641	+	0.0267903i	$0.991471\pi$
$744$	0.337660	−	0.476264i	0.0123792	−	0.0174607i
$745$	−6.35901	−	11.0141i	−0.232976	−	0.403526i
$746$			59.5891i			2.18171i
$747$	5.14756	−	1.80553i	0.188339	−	0.0660608i
$748$			33.5667i			1.22732i
$749$	−14.3105	+	8.26219i	−0.522895	+	0.301894i
$750$	−1.35772	−	2.95676i	−0.0495770	−	0.107965i
$751$	−1.53198	+	2.65346i	−0.0559027	+	0.0968263i	−0.892622	−	0.450805i	$-0.851137\pi$
$751$	−1.53198	+	2.65346i	−0.0559027	+	0.0968263i	0.836720	+	0.547631i	$0.184470\pi$
$752$	1.64116	+	0.947522i	0.0598468	+	0.0345526i
$753$	−29.8698	−	2.78973i	−1.08852	−	0.101663i
$754$	8.17013	−	15.3584i	0.297539	−	0.559319i
$755$	1.64837			0.0599903
$756$	−4.56868	+	15.9253i	−0.166161	+	0.579198i
$757$	0.0667874			0.00242743			0.00121371	−	0.999999i	$-0.499614\pi$
$757$	0.0667874			0.00242743			0.00121371	+	0.999999i	$0.499614\pi$
$758$	20.8307	+	36.0798i	0.756605	+	1.31048i
$759$	−3.30731	+	35.4116i	−0.120048	+	1.28536i
$760$	−3.09951	−	1.78950i	−0.112431	−	0.0649120i
$761$	12.7798	+	7.37842i	0.463267	+	0.267467i	0.713417	−	0.700740i	$-0.247147\pi$
$761$	12.7798	+	7.37842i	0.463267	+	0.267467i	−0.250150	+	0.968207i	$0.580480\pi$
$762$	−37.5769	+	17.2551i	−1.36127	+	0.625085i
$763$	−1.42188	−	2.46277i	−0.0514756	−	0.0891584i
$764$	−21.3899			−0.773861
$765$	−10.6286	−	9.13281i	−0.384277	−	0.330198i
$766$	−3.96843			−0.143385
$767$	12.7836	−	24.0309i	0.461590	−	0.867706i
$768$	20.7521	−	29.2705i	0.748827	−	1.05621i
$769$	1.81074	+	1.04543i	0.0652968	+	0.0376991i	0.532293	−	0.846560i	$-0.321330\pi$
$769$	1.81074	+	1.04543i	0.0652968	+	0.0376991i	−0.466996	+	0.884259i	$0.654664\pi$
$770$	−9.20977	+	15.9518i	−0.331897	+	0.574863i
$771$	−0.773581	+	1.09112i	−0.0278598	+	0.0392959i
$772$	−25.2795	+	14.5952i	−0.909831	+	0.525291i
$773$			42.5945i			1.53202i	0.642831	+	0.766008i	$0.277760\pi$
$773$			42.5945i			1.53202i	−0.642831	+	0.766008i	$0.722240\pi$
$774$	17.1087	+	14.7010i	0.614960	+	0.528416i
$775$		−	0.380652i		−	0.0136734i
$776$	7.38659	+	12.7939i	0.265163	+	0.459276i
$777$	5.72262	+	12.4623i	0.205298	+	0.447084i
$778$	−58.0953	−	33.5413i	−2.08282	−	1.20251i
$779$	24.3971	−	42.2570i	0.874117	−	1.51401i
$780$	−4.28223	−	8.53176i	−0.153328	−	0.305486i
$781$	−12.7510	−	22.0853i	−0.456265	−	0.790275i
$782$		−	38.3268i		−	1.37056i
$783$	3.22717	+	12.9504i	0.115329	+	0.462809i
$784$	−12.5057			−0.446631
$785$	9.44986	−	5.45588i	0.337280	−	0.194729i
$786$	2.10921	−	22.5834i	0.0752331	−	0.805525i
$787$	1.46148	+	0.843783i	0.0520960	+	0.0300776i	0.525822	−	0.850595i	$-0.323758\pi$
$787$	1.46148	+	0.843783i	0.0520960	+	0.0300776i	−0.473726	+	0.880672i	$0.657091\pi$
$788$	−11.6042	−	6.69969i	−0.413383	−	0.238667i
$789$	23.2661	+	50.6674i	0.828295	+	1.80381i
$790$	−0.998240	−	1.72900i	−0.0355158	−	0.0615152i
$791$			38.9670i			1.38551i
$792$	4.13341	+	11.7844i	0.146874	+	0.418739i
$793$	−10.3155	+	6.44295i	−0.366313	+	0.228796i
$794$	−12.9344	−	22.4030i	−0.459023	−	0.795051i
$795$	−17.6698	−	12.5275i	−0.626684	−	0.444304i
$796$	4.29616	−	7.44117i	0.152273	−	0.263745i
$797$	9.26032	−	16.0393i	0.328017	−	0.568143i	−0.654101	−	0.756407i	$-0.726953\pi$
$797$	9.26032	−	16.0393i	0.328017	−	0.568143i	0.982118	+	0.188265i	$0.0602862\pi$
$798$	22.3765	+	15.8644i	0.792121	+	0.561595i
$799$	1.62396	−	0.937596i	0.0574517	−	0.0331698i
$800$		−	7.09641i		−	0.250896i
$801$	−4.43969	+	23.5607i	−0.156869	+	0.832476i
$802$	3.16037			0.111597
$803$	−3.91958	−	6.78891i	−0.138319	−	0.239575i
$804$	25.0238	−	11.4908i	0.882521	−	0.405248i
$805$	4.55548	−	7.89033i	0.160560	−	0.278097i
$806$	−0.0894591	−	2.57655i	−0.00315106	−	0.0907553i
$807$	3.30228	+	0.308421i	0.116246	+	0.0108569i
$808$	−12.5035	+	7.21890i	−0.439872	+	0.253960i
$809$	−32.0323			−1.12619			−0.563097	−	0.826391i	$-0.690390\pi$
$809$	−32.0323			−1.12619			−0.563097	+	0.826391i	$0.690390\pi$
$810$	15.7467	+	6.15297i	0.553282	+	0.216193i
$811$		−	44.7077i		−	1.56990i	−0.619560	−	0.784949i	$-0.712689\pi$
$811$		−	44.7077i		−	1.56990i	0.619560	−	0.784949i	$-0.287311\pi$
$812$	−7.09242	+	4.09481i	−0.248895	+	0.143700i
$813$	−1.52508	+	16.3291i	−0.0534869	+	0.572687i
$814$	−29.0285	−	16.7596i	−1.01745	−	0.587423i
$815$	4.50183	−	7.79740i	0.157692	−	0.273131i
$816$	−15.9377	−	34.7081i	−0.557932	−	1.21503i
$817$	14.0109	−	8.08922i	0.490180	−	0.283006i
$818$	−14.8197			−0.518160
$819$	−8.20195	−	21.0184i	−0.286599	−	0.734443i
$820$	18.4539			0.644439
$821$	−41.1519	+	23.7590i	−1.43621	+	0.829196i	−0.997584	−	0.0694730i	$-0.977868\pi$
$821$	−41.1519	+	23.7590i	−1.43621	+	0.829196i	−0.438626	+	0.898669i	$0.644535\pi$
$822$	29.9819	−	42.2890i	1.04574	−	1.47500i
$823$	15.7245	−	27.2357i	0.548123	−	0.949377i	−0.450280	−	0.892887i	$-0.648676\pi$
$823$	15.7245	−	27.2357i	0.548123	−	0.949377i	0.998403	−	0.0564895i	$-0.0179907\pi$
$824$	5.45286	+	3.14821i	0.189959	+	0.109673i
$825$	6.64238	+	4.70929i	0.231258	+	0.163957i
$826$	−25.6169	+	14.7899i	−0.891327	+	0.514608i
$827$			10.8827i			0.378430i	0.981936	+	0.189215i	$0.0605942\pi$
$827$			10.8827i			0.378430i	−0.981936	+	0.189215i	$0.939406\pi$
$828$	6.62983	+	18.9016i	0.230402	+	0.656878i
$829$	17.2048			0.597549			0.298774	−	0.954324i	$-0.403422\pi$
$829$	17.2048			0.597549			0.298774	+	0.954324i	$0.403422\pi$
$830$	2.95806	−	1.70784i	0.102676	−	0.0592800i
$831$	20.2147	+	44.0223i	0.701241	+	1.52712i
$832$	−0.486575	−	14.0141i	−0.0168689	−	0.485851i
$833$	−6.18734	+	10.7168i	−0.214378	+	0.371314i
$834$	−5.18517	+	55.5179i	−0.179548	+	1.92243i
$835$	−7.80567	−	13.5198i	−0.270126	−	0.467872i
$836$	−29.0443			−1.00452
$837$	1.37380	+	1.42297i	0.0474856	+	0.0491851i
$838$		−	18.4922i		−	0.638803i
$839$	−3.72891	+	2.15288i	−0.128736	+	0.0743258i	−0.562985	−	0.826467i	$-0.690347\pi$
$839$	−3.72891	+	2.15288i	−0.128736	+	0.0743258i	0.434249	+	0.900793i	$0.357014\pi$
$840$	0.297494	−	3.18528i	0.0102645	−	0.109903i
$841$	11.2013	−	19.4013i	0.386253	−	0.669010i
$842$	−7.59671	+	13.1579i	−0.261800	+	0.453451i
$843$	−23.5930	+	10.8338i	−0.812588	+	0.373135i
$844$	9.80783	+	16.9877i	0.337599	+	0.584739i
$845$	11.6820	+	5.70350i	0.401874	+	0.196206i
$846$	−1.47438	+	1.71585i	−0.0506901	+	0.0589921i
$847$		−	23.1522i		−	0.795518i
$848$	−29.5165	−	51.1241i	−1.01360	−	1.75561i
$849$	−19.3159	+	27.2448i	−0.662920	+	0.935038i
$850$	−7.59895	−	4.38726i	−0.260642	−	0.150482i
$851$	14.3585	+	8.28990i	0.492204	+	0.284174i
$852$	−11.7168	−	8.30691i	−0.401410	−	0.284590i
$853$	−5.97945	+	3.45224i	−0.204732	+	0.118202i	−0.598861	−	0.800853i	$-0.704380\pi$
$853$	−5.97945	+	3.45224i	−0.204732	+	0.118202i	0.394129	+	0.919055i	$0.371046\pi$
$854$	13.2169			0.452273
$855$	7.90236	−	9.19660i	0.270255	−	0.314517i
$856$			7.01500i			0.239768i
$857$	−3.68263	−	6.37850i	−0.125796	−	0.217885i	0.796248	−	0.604971i	$-0.206815\pi$
$857$	−3.68263	−	6.37850i	−0.125796	−	0.217885i	−0.922044	+	0.387085i	$0.873482\pi$
$858$	46.0677	+	30.3152i	1.57273	+	1.03494i
$859$	−20.4592	+	35.4363i	−0.698058	+	1.20907i	0.271081	+	0.962557i	$0.412619\pi$
$859$	−20.4592	+	35.4363i	−0.698058	+	1.20907i	−0.969139	+	0.246515i	$0.920714\pi$
$860$	5.29893	+	3.05934i	0.180692	+	0.104322i
$861$	43.4265	+	4.05587i	1.47997	+	0.138224i
$862$	−5.01523	−	8.68663i	−0.170819	−	0.295868i
$863$			19.6031i			0.667298i	0.942697	+	0.333649i	$0.108280\pi$
$863$			19.6031i			0.667298i	−0.942697	+	0.333649i	$0.891720\pi$
$864$	25.6115	+	26.5282i	0.871321	+	0.902507i
$865$			21.6639i			0.736594i
$866$	48.0768	−	27.7572i	1.63372	−	0.943227i
$867$	−8.31132	−	0.776247i	−0.282267	−	0.0263627i
$868$	−0.606845	+	1.05109i	−0.0205977	+	0.0356762i
$869$	4.32699	+	2.49819i	0.146783	+	0.0847453i
$870$	3.48734	+	7.59449i	0.118232	+	0.257477i
$871$	−17.6112	+	33.1059i	−0.596733	+	1.12175i
$872$	−1.20725			−0.0408826
$873$	−47.2293	+	16.5659i	−1.59847	+	0.560670i
$874$	33.1630			1.12176
$875$	−1.04293	−	1.80641i	−0.0352575	−	0.0610678i
$876$	−3.60167	−	2.55350i	−0.121689	−	0.0862748i
$877$	36.9812	+	21.3511i	1.24877	+	0.720976i	0.970863	−	0.239634i	$-0.0770273\pi$
$877$	36.9812	+	21.3511i	1.24877	+	0.720976i	0.277903	+	0.960609i	$0.410361\pi$
$878$	10.4904	+	6.05665i	0.354035	+	0.204402i
$879$	−1.34441	−	0.953155i	−0.0453459	−	0.0321491i
$880$	11.0958	+	19.2184i	0.374038	+	0.647853i
$881$	−15.2667			−0.514348			−0.257174	−	0.966365i	$-0.582791\pi$
$881$	−15.2667			−0.514348			−0.257174	+	0.966365i	$0.582791\pi$
$882$	2.76454	−	14.6709i	0.0930869	−	0.493996i
$883$	35.7154			1.20192			0.600959	−	0.799280i	$-0.294786\pi$
$883$	35.7154			1.20192			0.600959	+	0.799280i	$0.294786\pi$
$884$	−22.7288	−	12.0910i	−0.764453	−	0.406663i
$885$	5.45656	+	11.8829i	0.183420	+	0.399441i
$886$	−46.4203	−	26.8008i	−1.55952	−	0.900390i
$887$	−1.30726	+	2.26423i	−0.0438933	+	0.0760255i	−0.887137	−	0.461505i	$-0.847310\pi$
$887$	−1.30726	+	2.26423i	−0.0438933	+	0.0760255i	0.843244	+	0.537531i	$0.180643\pi$
$888$	5.79646	+	0.541368i	0.194516	+	0.0181671i
$889$	−22.9574	+	13.2544i	−0.769965	+	0.444540i
$890$			15.0122i			0.503211i
$891$	−41.8271	+	6.36837i	−1.40126	+	0.213348i
$892$		−	26.8043i		−	0.897474i
$893$	0.811275	+	1.40517i	0.0271483	+	0.0470222i
$894$	41.1999	+	3.84791i	1.37793	+	0.128694i
$895$	1.28654	+	0.742786i	0.0430044	+	0.0248286i
$896$	7.18289	−	12.4411i	0.239964	−	0.415629i
$897$	−22.7867	−	14.9950i	−0.760827	−	0.500668i
$898$	17.3569	+	30.0631i	0.579208	+	1.00322i
$899$			0.977713i			0.0326085i
$900$	4.50650	+	0.849188i	0.150217	+	0.0283063i
$901$	−58.4147			−1.94607
$902$	−92.3248	+	53.3037i	−3.07408	+	1.77482i
$903$	11.7972	+	8.36395i	0.392587	+	0.278335i
$904$	14.3262	+	8.27122i	0.476482	+	0.275097i
$905$	−10.5358	−	6.08283i	−0.350221	−	0.202200i
$906$	−3.10184	+	4.37510i	−0.103052	+	0.145353i
$907$	15.8682	+	27.4846i	0.526896	+	0.912610i	0.999509	+	0.0313403i	$0.00997755\pi$
$907$	15.8682	+	27.4846i	0.526896	+	0.912610i	−0.472613	+	0.881270i	$0.656689\pi$
$908$			41.7251i			1.38469i
$909$	−16.1898	−	46.1571i	−0.536982	−	1.53094i
$910$	−7.48392	−	11.9821i	−0.248090	−	0.397203i
$911$	18.0266	+	31.2229i	0.597247	+	1.03446i	0.993226	+	0.116203i	$0.0370722\pi$
$911$	18.0266	+	31.2229i	0.597247	+	1.03446i	−0.395978	+	0.918260i	$0.629595\pi$
$912$	30.0319	−	13.7905i	0.994456	−	0.456648i
$913$	−4.27403	+	7.40284i	−0.141450	+	0.244998i
$914$	−27.4310	+	47.5118i	−0.907336	+	1.57155i
$915$	0.543309	−	5.81724i	0.0179613	−	0.192312i
$916$	−8.69357	+	5.01924i	−0.287244	+	0.165840i
$917$		−	14.5412i		−	0.480192i
$918$	44.2408	−	11.0245i	1.46016	−	0.363864i
$919$	−9.50481			−0.313535			−0.156767	−	0.987636i	$-0.550107\pi$
$919$	−9.50481			−0.313535			−0.156767	+	0.987636i	$0.550107\pi$
$920$	−1.93391	−	3.34964i	−0.0637592	−	0.110434i
$921$	1.92491	−	20.6102i	0.0634281	−	0.679128i
$922$	−28.0812	+	48.6381i	−0.924806	+	1.60181i
$923$	19.5475	−	0.678698i	0.643414	−	0.0223396i
$924$	−10.8338	−	23.5932i	−0.356406	−	0.776158i
$925$	3.28724	−	1.89789i	0.108084	−	0.0624021i
$926$	52.9764			1.74091
$927$	−13.9024	+	16.1793i	−0.456614	+	0.531397i
$928$			18.2273i			0.598340i
$929$	5.71773	−	3.30114i	0.187593	−	0.108307i	−0.403262	−	0.915084i	$-0.632124\pi$
$929$	5.71773	−	3.30114i	0.187593	−	0.108307i	0.590855	+	0.806778i	$0.298790\pi$
$930$	1.01033	+	0.716297i	0.0331299	+	0.0234883i
$931$	−9.27292	−	5.35372i	−0.303908	−	0.175461i
$932$	21.7744	−	37.7144i	0.713244	−	1.23538i
$933$	14.6669	−	20.6874i	0.480173	−	0.677277i
$934$	6.46867	−	3.73469i	0.211662	−	0.122203i
$935$	21.9591			0.718138
$936$	−9.46836	−	1.44598i	−0.309483	−	0.0472632i
$937$	24.2497			0.792204			0.396102	−	0.918206i	$-0.370363\pi$
$937$	24.2497			0.792204			0.396102	+	0.918206i	$0.370363\pi$
$938$	35.2908	−	20.3752i	1.15229	−	0.665273i
$939$	−7.39077	−	16.0951i	−0.241189	−	0.525245i
$940$	−0.306824	+	0.531434i	−0.0100075	+	0.0173335i
$941$	44.4919	+	25.6874i	1.45039	+	0.837385i	0.998503	−	0.0546890i	$-0.0174167\pi$
$941$	44.4919	+	25.6874i	1.45039	+	0.837385i	0.451890	+	0.892074i	$0.350750\pi$
$942$	−3.30142	+	35.3485i	−0.107566	+	1.15172i
$943$	45.6672	−	26.3659i	1.48713	−	0.858593i
$944$			35.6373i			1.15990i
$945$	10.4182	+	2.98879i	0.338904	+	0.0972255i
$946$	−35.3473			−1.14924
$947$	−14.3005	+	8.25642i	−0.464705	+	0.268297i	−0.714020	−	0.700125i	$-0.753128\pi$
$947$	−14.3005	+	8.25642i	−0.464705	+	0.268297i	0.249316	+	0.968422i	$0.419794\pi$
$948$	2.80177	+	0.261675i	0.0909974	+	0.00849882i
$949$	6.00880	−	0.208628i	0.195054	−	0.00677236i
$950$	3.79617	−	6.57516i	0.123164	−	0.213326i
$951$	−24.3468	+	11.1799i	−0.789500	+	0.362533i
$952$	−4.31385	−	7.47181i	−0.139813	−	0.242163i
$953$	−12.6301			−0.409129			−0.204564	−	0.978853i	$-0.565578\pi$
$953$	−12.6301			−0.409129			−0.204564	+	0.978853i	$0.565578\pi$
$954$	66.5009	−	23.3255i	2.15305	−	0.755190i
$955$			13.9931i			0.452807i
$956$	−5.58441	+	3.22416i	−0.180613	+	0.104277i
$957$	−17.0611	−	12.0959i	−0.551508	−	0.391006i
$958$	2.04026	−	3.53383i	0.0659177	−	0.114173i
$959$	16.6169	−	28.7813i	0.536587	−	0.929396i
$960$	5.49524	+	3.89599i	0.177358	+	0.125743i
$961$	−15.4276	−	26.7213i	−0.497663	−	0.861978i
$962$	21.8046	−	13.6190i	0.703008	−	0.439093i
$963$	−23.3552	−	4.40098i	−0.752612	−	0.141819i
$964$			16.6039i			0.534775i
$965$	9.54803	+	16.5377i	0.307362	+	0.532367i
$966$	12.3702	+	26.9389i	0.398003	+	0.866745i
$967$	−37.5789	−	21.6962i	−1.20846	−	0.697702i	−0.246034	−	0.969261i	$-0.579128\pi$
$967$	−37.5789	−	21.6962i	−1.20846	−	0.697702i	−0.962422	+	0.271559i	$0.912461\pi$
$968$	−8.51187	−	4.91433i	−0.273582	−	0.157953i
$969$	3.04089	−	32.5589i	0.0976873	−	1.04594i
$970$	−27.1405	+	15.6696i	−0.871429	+	0.503120i
$971$	3.03908			0.0975288			0.0487644	−	0.998810i	$-0.484472\pi$
$971$	3.03908			0.0975288			0.0487644	+	0.998810i	$0.484472\pi$
$972$	−19.9112	+	13.0898i	−0.638653	+	0.419857i
$973$			35.7472i			1.14600i
$974$	−16.9227	−	29.3110i	−0.542238	−	0.939184i
$975$	−5.58141	+	2.80140i	−0.178748	+	0.0897166i
$976$	7.96174	−	13.7901i	0.254849	−	0.441411i
$977$	21.7380	+	12.5504i	0.695459	+	0.401524i	0.805654	−	0.592386i	$-0.201814\pi$
$977$	21.7380	+	12.5504i	0.695459	+	0.401524i	−0.110195	+	0.993910i	$0.535147\pi$
$978$	12.2245	+	26.6216i	0.390896	+	0.851266i
$979$	−18.7848	−	32.5361i	−0.600363	−	1.03986i
$980$		−	4.04955i		−	0.129358i
$981$	0.757387	−	4.01932i	0.0241815	−	0.128327i
$982$		−	39.2069i		−	1.25114i
$983$	−45.9699	+	26.5407i	−1.46621	+	0.846518i	−0.999286	−	0.0377782i	$-0.987972\pi$
$983$	−45.9699	+	26.5407i	−1.46621	+	0.846518i	−0.466926	+	0.884296i	$0.654639\pi$
$984$	10.7089	−	15.1048i	0.341388	−	0.481523i
$985$	−4.38288	+	7.59138i	−0.139650	+	0.241881i
$986$	19.5181	+	11.2688i	0.621582	+	0.358871i
$987$	−0.838829	+	1.18315i	−0.0267002	+	0.0376602i
$988$	10.4620	−	19.6666i	0.332839	−	0.625678i
$989$	17.4840			0.555960
$990$	−24.9988	+	8.76843i	−0.794514	+	0.278679i
$991$	−13.9997			−0.444715			−0.222358	−	0.974965i	$-0.571375\pi$
$991$	−13.9997			−0.444715			−0.222358	+	0.974965i	$0.571375\pi$
$992$	1.35063	+	2.33936i	0.0428826	+	0.0742748i
$993$	−0.157755	+	0.0724399i	−0.00500619	+	0.00229881i
$994$	−18.4077	−	10.6277i	−0.583855	−	0.337089i
$995$	−4.86795	−	2.81051i	−0.154324	−	0.0890993i
$996$	−0.447687	+	4.79342i	−0.0141855	+	0.151885i
$997$	10.3102	+	17.8578i	0.326528	+	0.565563i	0.981820	−	0.189812i	$-0.0607880\pi$
$997$	10.3102	+	17.8578i	0.326528	+	0.565563i	−0.655293	+	0.755375i	$0.727455\pi$
$998$	−23.9621			−0.758509
$999$	−5.43889	+	18.9587i	−0.172079	+	0.599826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.12	yes	108
9.7	even	3	inner	585.2.bt.b.376.43	yes	108
13.12	even	2	inner	585.2.bt.b.571.43	yes	108
117.25	even	6	inner	585.2.bt.b.376.12	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.12	✓	108	117.25	even	6	inner
585.2.bt.b.376.43	yes	108	9.7	even	3	inner
585.2.bt.b.571.12	yes	108	1.1	even	1	trivial
585.2.bt.b.571.43	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62679 + 0.939229i) q^{2} +(-1.72455 - 0.161066i) q^{3} +(0.764302 - 1.32381i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.95676 - 1.35772i) q^{6} +(1.80641 - 1.04293i) q^{7} -0.885499i q^{8} +(2.94812 + 0.555532i) q^{9} +O(q^{10})\)	\(q+(-1.62679 + 0.939229i) q^{2} +(-1.72455 - 0.161066i) q^{3} +(0.764302 - 1.32381i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.95676 - 1.35772i) q^{6} +(1.80641 - 1.04293i) q^{7} -0.885499i q^{8} +(2.94812 + 0.555532i) q^{9} +1.87846 q^{10} +(-4.07120 + 2.35051i) q^{11} +(-1.53129 + 2.15987i) q^{12} +(-0.125111 - 3.60338i) q^{13} +(-1.95910 + 3.39326i) q^{14} +(1.41297 + 1.00176i) q^{15} +(2.36029 + 4.08814i) q^{16} +4.67113 q^{17} +(-5.31774 + 1.86522i) q^{18} +4.04179i q^{19} +(-1.32381 + 0.764302i) q^{20} +(-3.28322 + 1.50763i) q^{21} +(4.41533 - 7.64758i) q^{22} +(-2.18398 + 3.78277i) q^{23} +(-0.142624 + 1.52708i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.58793 + 5.74444i) q^{26} +(-4.99468 - 1.43288i) q^{27} -3.18845i q^{28} +(-1.28426 - 2.22441i) q^{29} +(-3.23949 - 0.302556i) q^{30} +(-0.329654 - 0.190326i) q^{31} +(-6.14567 - 3.54820i) q^{32} +(7.39956 - 3.39783i) q^{33} +(-7.59895 + 4.38726i) q^{34} -2.08586 q^{35} +(2.98867 - 3.47815i) q^{36} -3.79577i q^{37} +(-3.79617 - 6.57516i) q^{38} +(-0.364623 + 6.23434i) q^{39} +(-0.442749 + 0.766865i) q^{40} +(-10.4550 - 6.03621i) q^{41} +(3.92510 - 5.53629i) q^{42} +(-2.00139 - 3.46651i) q^{43} +7.18599i q^{44} +(-2.27538 - 1.95516i) q^{45} -8.20503i q^{46} +(0.347660 - 0.200722i) q^{47} +(-3.41197 - 7.43035i) q^{48} +(-1.32459 + 2.29426i) q^{49} +(-1.62679 - 0.939229i) q^{50} +(-8.05557 - 0.752361i) q^{51} +(-4.86581 - 2.58845i) q^{52} -12.5055 q^{53} +(9.47111 - 2.36015i) q^{54} +4.70102 q^{55} +(-0.923514 - 1.59957i) q^{56} +(0.650996 - 6.97025i) q^{57} +(4.17845 + 2.41243i) q^{58} +(6.53793 + 3.77468i) q^{59} +(2.40607 - 1.10485i) q^{60} +(-1.68660 - 2.92128i) q^{61} +0.715038 q^{62} +(5.90488 - 2.07116i) q^{63} +3.88915 q^{64} +(-1.69334 + 3.18317i) q^{65} +(-8.84621 + 12.4774i) q^{66} +(-9.00690 - 5.20013i) q^{67} +(3.57015 - 6.18368i) q^{68} +(4.37565 - 6.17179i) q^{69} +(3.39326 - 1.95910i) q^{70} +5.42477i q^{71} +(0.491923 - 2.61055i) q^{72} +1.66754i q^{73} +(3.56510 + 6.17493i) q^{74} +(-0.722785 - 1.57403i) q^{75} +(5.35056 + 3.08915i) q^{76} +(-4.90284 + 8.49196i) q^{77} +(-5.26231 - 10.4844i) q^{78} +(-0.531415 - 0.920437i) q^{79} -4.72058i q^{80} +(8.38277 + 3.27555i) q^{81} +22.6775 q^{82} +(1.57473 - 0.909171i) q^{83} +(-0.513552 + 5.49863i) q^{84} +(-4.04531 - 2.33556i) q^{85} +(6.51170 + 3.75953i) q^{86} +(1.85649 + 4.04294i) q^{87} +(2.08137 + 3.60504i) q^{88} +7.99178i q^{89} +(5.53791 + 1.04354i) q^{90} +(-3.98408 - 6.37869i) q^{91} +(3.33844 + 5.78235i) q^{92} +(0.537849 + 0.381322i) q^{93} +(-0.377047 + 0.653065i) q^{94} +(2.02090 - 3.50029i) q^{95} +(10.0270 + 7.10890i) q^{96} +(-14.4483 + 8.34172i) q^{97} -4.97638i q^{98} +(-13.3082 + 4.66789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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