LMFDB - Embedded newform 585.2.bt.b.376.12

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			376.12
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.12

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	−0.201352	−	0.979519i	$-0.564533\pi$
$2$	−1.62679	−	0.939229i	−1.15032	−	0.664135i	−0.948964	+	0.315384i	$0.897867\pi$
$3$	−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	0.800893	−	0.598807i	$-0.204358\pi$
$7$	1.80641	+	1.04293i	0.682758	+	0.394191i	−0.118135	+	0.992998i	$0.537692\pi$
$8$			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	−0.261004	−	0.965338i	$-0.584054\pi$
$11$	−4.07120	−	2.35051i	−1.22751	−	0.708705i	−0.966509	+	0.256632i	$0.917387\pi$
$12$	−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	$-0.846548\pi$
$19$		−	4.04179i		−	0.927251i	0.886031	−	0.463625i	$-0.153452\pi$
$20$	−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	0.543319	−	0.839526i	$-0.317167\pi$
$23$	−2.18398	−	3.78277i	−0.455392	−	0.788762i	−0.998711	+	0.0507648i	$0.983834\pi$
$24$	−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	−0.960279	−	0.279043i	$-0.909983\pi$
$29$	−1.28426	+	2.22441i	−0.238481	+	0.413062i	0.721797	+	0.692104i	$0.243316\pi$
$30$	−3.23949	+	0.302556i	−0.591447	+	0.0552389i
$31$	−0.329654	+	0.190326i	−0.0592076	+	0.0341835i	−0.529312	−	0.848428i	$-0.677550\pi$
$31$	−0.329654	+	0.190326i	−0.0592076	+	0.0341835i	0.470104	+	0.882611i	$0.344216\pi$
$32$	−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	$0.101002\pi$
$37$			3.79577i			0.624021i	−0.950079	+	0.312011i	$0.898998\pi$
$38$	−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	−0.649576	+	0.760297i	$0.725053\pi$
$41$	−10.4550	+	6.03621i	−1.63280	+	0.942698i	−0.983224	+	0.182401i	$0.941613\pi$
$42$	3.92510	+	5.53629i	0.605656	+	0.854268i
$43$	−2.00139	+	3.46651i	−0.305210	+	0.528639i	−0.977308	−	0.211823i	$-0.932060\pi$
$43$	−2.00139	+	3.46651i	−0.305210	+	0.528639i	0.672098	+	0.740462i	$0.265393\pi$
$44$		−	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	0.525141	−	0.851015i	$-0.324012\pi$
$47$	0.347660	+	0.200722i	0.0507114	+	0.0292783i	−0.474430	+	0.880293i	$0.657346\pi$
$48$	−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	−0.00987778	−	0.999951i	$-0.503144\pi$
$59$	6.53793	−	3.77468i	0.851166	−	0.491421i	0.861044	+	0.508530i	$0.169811\pi$
$60$	2.40607	+	1.10485i	0.310623	+	0.142636i
$61$	−1.68660	+	2.92128i	−0.215947	+	0.374032i	−0.953565	−	0.301187i	$-0.902617\pi$
$61$	−1.68660	+	2.92128i	−0.215947	+	0.374032i	0.737618	+	0.675218i	$0.235951\pi$
$62$	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	−0.936318	−	0.351155i	$-0.885789\pi$
$67$	−9.00690	+	5.20013i	−1.10037	+	0.635297i	−0.164050	+	0.986452i	$0.552456\pi$
$68$	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	$-0.895678\pi$
$71$		−	5.42477i		−	0.643801i	0.946773	−	0.321901i	$-0.104322\pi$
$72$	0.491923	+	2.61055i	0.0579737	+	0.307657i
$73$		−	1.66754i		−	0.195171i	−0.995227	−	0.0975857i	$-0.968888\pi$
$73$		−	1.66754i		−	0.195171i	0.995227	−	0.0975857i	$-0.0311120\pi$
$74$	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	−0.894371	−	0.447327i	$-0.852376\pi$
$79$	−0.531415	+	0.920437i	−0.0597888	+	0.103557i	0.834582	+	0.550884i	$0.185709\pi$
$80$			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	0.583929	−	0.811805i	$-0.301515\pi$
$83$	1.57473	+	0.909171i	0.172849	+	0.0997945i	−0.411079	+	0.911600i	$0.634848\pi$
$84$	−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	$-0.860779\pi$
$89$		−	7.99178i		−	0.847127i	0.905866	−	0.423564i	$-0.139221\pi$
$90$	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	−0.467684	−	0.883896i	$-0.654911\pi$
$97$	−14.4483	−	8.34172i	−1.46700	−	0.846974i	−0.999318	+	0.0369221i	$0.988245\pi$
$98$			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	0.100842	+	0.994902i	$0.467846\pi$
$101$	−8.15236	+	14.1203i	−0.811190	+	1.40502i	−0.912032	+	0.410119i	$0.865487\pi$
$102$	13.8114	+	6.34209i	1.36753	+	0.627961i
$103$	−3.55530	−	6.15796i	−0.350314	−	0.606761i	0.635990	−	0.771697i	$-0.280592\pi$
$103$	−3.55530	−	6.15796i	−0.350314	−	0.606761i	−0.986304	+	0.164935i	$0.947258\pi$
$104$	−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	$0.0207981\pi$
$109$			1.36335i			0.130586i	−0.997866	+	0.0652928i	$0.979202\pi$
$110$	−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	−0.852764	−	0.522296i	$-0.825076\pi$
$113$	−9.34075	−	16.1787i	−0.878704	−	1.52196i	−0.0259397	−	0.999664i	$-0.508258\pi$
$114$	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	0.977159	−	0.212507i	$-0.0681630\pi$
$131$	3.48565	+	6.03733i	0.304543	+	0.527484i	−0.672617	+	0.739991i	$0.734830\pi$
$132$	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	0.955752	−	0.294174i	$-0.0950445\pi$
$137$	13.7983	+	7.96643i	1.17887	+	0.680618i	0.223114	+	0.974792i	$0.428378\pi$
$138$	−1.32155	−	14.1500i	−0.112498	−	1.20452i
$139$	−8.56894	−	14.8418i	−0.726808	−	1.25887i	−0.958226	−	0.286014i	$-0.907670\pi$
$139$	−8.56894	−	14.8418i	−0.726808	−	1.25887i	0.231418	−	0.972854i	$-0.425664\pi$
$140$	−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	0.0243629	−	0.999703i	$-0.492244\pi$
$149$	11.0141	−	6.35901i	0.902313	−	0.520950i	0.877950	+	0.478753i	$0.158911\pi$
$150$	2.65420	−	1.88176i	0.216714	−	0.153645i
$151$	−1.42753	−	0.824184i	−0.116171	−	0.0670711i	0.440789	−	0.897611i	$-0.354699\pi$
$151$	−1.42753	−	0.824184i	−0.116171	−	0.0670711i	−0.556959	+	0.830540i	$0.688032\pi$
$152$	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	0.561904	−	0.827203i	$-0.310069\pi$
$157$	−5.45588	−	9.44986i	−0.435427	−	0.754181i	−0.997330	+	0.0730217i	$0.976736\pi$
$158$	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	$-0.885294\pi$
$163$		−	9.00367i		−	0.705222i	0.935770	−	0.352611i	$-0.114706\pi$
$164$	−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	0.124613	−	0.992205i	$-0.460231\pi$
$167$	13.5198	−	7.80567i	1.04619	−	0.604021i	0.921581	+	0.388185i	$0.126898\pi$
$168$	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	0.0794956	+	0.996835i	$0.474669\pi$
$173$	−10.8319	+	18.7615i	−0.823537	+	1.42641i	−0.903032	+	0.429572i	$0.858664\pi$
$174$	−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	0.493720	+	0.869621i	$0.335637\pi$
$191$	−6.99657	+	12.1184i	−0.506254	+	0.876857i	−0.999974	+	0.00723635i	$0.997697\pi$
$192$	−6.70701	+	0.626410i	−0.484037	+	0.0452073i
$193$	−16.5377	+	9.54803i	−1.19041	+	0.687282i	−0.958399	−	0.285431i	$-0.907863\pi$
$193$	−16.5377	+	9.54803i	−1.19041	+	0.687282i	−0.232009	+	0.972714i	$0.574530\pi$
$194$	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	$0.101089\pi$
$197$			8.76577i			0.624535i	−0.949994	+	0.312268i	$0.898911\pi$
$198$	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	0.556107	−	0.831111i	$-0.312295\pi$
$211$	−6.41620	−	11.1132i	−0.441710	−	0.765064i	−0.997817	+	0.0660471i	$0.978961\pi$
$212$	−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	0.913211	−	0.407487i	$-0.133595\pi$
$223$	15.1859	+	8.76758i	1.01692	+	0.587121i	0.103712	+	0.994607i	$0.466928\pi$
$224$	−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	−0.996287	−	0.0860927i	$-0.972562\pi$
$227$	−23.6392	−	13.6481i	−1.56899	−	0.905856i	−0.572702	−	0.819764i	$-0.694105\pi$
$228$	−8.72973	+	6.18917i	−0.578140	+	0.409888i
$229$	−5.68727	+	3.28354i	−0.375825	+	0.216983i	−0.676000	−	0.736901i	$-0.736288\pi$
$229$	−5.68727	+	3.28354i	−0.375825	+	0.216983i	0.300175	+	0.953884i	$0.402955\pi$
$230$	−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	−0.613480	−	0.789710i	$-0.710231\pi$
$239$	−3.65328	+	2.10922i	−0.236311	+	0.136434i	0.377169	+	0.926144i	$0.376898\pi$
$240$	−0.760326	−	8.14085i	−0.0490788	−	0.525490i
$241$	−9.40687	−	5.43106i	−0.605950	−	0.349845i	0.165429	−	0.986222i	$-0.447099\pi$
$241$	−9.40687	−	5.43106i	−0.605950	−	0.349845i	−0.771379	+	0.636376i	$0.780433\pi$
$242$		−	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	0.877817	−	0.478997i	$-0.158999\pi$
$257$	0.386111	+	0.668764i	0.0240849	+	0.0417163i	−0.853732	+	0.520713i	$0.825666\pi$
$258$	−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	−0.389970	+	0.920828i	$0.627515\pi$
$263$	−16.0948	+	27.8769i	−0.992445	+	1.71897i	−0.602475	+	0.798138i	$0.705819\pi$
$264$	−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	$0.0928539\pi$
$271$			9.46865i			0.575179i	−0.957754	+	0.287590i	$0.907146\pi$
$272$	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	0.0495043	+	0.998774i	$0.484236\pi$
$277$	−13.9839	+	24.2208i	−0.840211	+	1.45529i	−0.889716	+	0.456515i	$0.849097\pi$
$278$			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	0.834431	−	0.551113i	$-0.185797\pi$
$281$	12.9808	+	7.49445i	0.774368	+	0.447082i	−0.0600625	+	0.998195i	$0.519130\pi$
$282$	0.755421	+	1.06551i	0.0449847	+	0.0634502i
$283$	9.64098	+	16.6987i	0.573097	+	0.992632i	0.996246	+	0.0865723i	$0.0275914\pi$
$283$	9.64098	+	16.6987i	0.573097	+	0.992632i	−0.423149	+	0.906060i	$0.639075\pi$
$284$	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	−0.475737	−	0.879587i	$-0.657819\pi$
$293$	0.824006	−	0.475740i	0.0481390	−	0.0277930i	0.523876	+	0.851794i	$0.324485\pi$
$294$	−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	$-0.889220\pi$
$307$		−	11.9511i		−	0.682084i	0.940048	−	0.341042i	$-0.110780\pi$
$308$	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	0.580329	−	0.814382i	$-0.302924\pi$
$311$	−7.32057	−	12.6796i	−0.415111	−	0.718994i	−0.995440	+	0.0953883i	$0.969591\pi$
$312$	5.52051	−	0.322874i	0.312537	−	0.0182791i
$313$	5.11270	−	8.85546i	0.288987	−	0.500540i	−0.684581	−	0.728937i	$-0.740015\pi$
$313$	5.11270	−	8.85546i	0.288987	−	0.500540i	0.973568	+	0.228396i	$0.0733482\pi$
$314$			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	0.826548	−	0.562866i	$-0.190301\pi$
$317$	13.3955	+	7.73390i	0.752367	+	0.434379i	−0.0741816	+	0.997245i	$0.523634\pi$
$318$	−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	0.502383	−	0.864645i	$-0.332457\pi$
$331$	0.0867959	+	0.0501116i	0.00477073	+	0.00275438i	−0.497613	+	0.867399i	$0.665790\pi$
$332$			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	0.959735	−	0.280908i	$-0.0906355\pi$
$337$	4.34329	+	7.52280i	0.236594	+	0.409793i	−0.723141	+	0.690701i	$0.757302\pi$
$338$	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	−0.949263	−	0.314483i	$-0.898169\pi$
$347$	−13.9147	−	24.1010i	−0.746982	−	1.29381i	0.202281	−	0.979327i	$-0.435164\pi$
$348$	6.77100	−	0.632387i	0.362964	−	0.0338995i
$349$	−26.2928	−	15.1801i	−1.40742	−	0.812574i	−0.412281	−	0.911057i	$-0.635268\pi$
$349$	−26.2928	−	15.1801i	−1.40742	−	0.812574i	−0.995139	+	0.0984825i	$0.968601\pi$
$350$	−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	0.997390	−	0.0721999i	$-0.0230019\pi$
$353$	26.9341	+	15.5504i	1.43356	+	0.827665i	0.436168	+	0.899865i	$0.356335\pi$
$354$	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	$0.194335\pi$
$359$			21.7248i			1.14659i	−0.819349	+	0.573295i	$0.805665\pi$
$360$	−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	0.0503907	−	0.998730i	$-0.483953\pi$
$367$	17.0523	−	29.5354i	0.890121	−	1.54173i	0.839730	−	0.543004i	$-0.182713\pi$
$368$	−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	0.904744	+	0.425956i	$0.140062\pi$
$373$	15.8612	+	27.4724i	0.821260	+	1.42246i	−0.0834837	+	0.996509i	$0.526605\pi$
$374$	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	$0.192908\pi$
$379$			22.1785i			1.13923i	−0.821910	+	0.569617i	$0.807092\pi$
$380$	−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	−0.452528	−	0.891750i	$-0.649478\pi$
$383$	1.82956	−	1.05630i	0.0934863	−	0.0539744i	0.546014	+	0.837776i	$0.316144\pi$
$384$	−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	0.0848416	−	0.996394i	$-0.472962\pi$
$389$	17.8558	−	30.9271i	0.905324	−	1.56807i	0.820482	−	0.571672i	$-0.193705\pi$
$390$	−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	$-0.887682\pi$
$397$		−	13.7712i		−	0.691159i	0.938389	−	0.345580i	$-0.112318\pi$
$398$	−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	−0.535939	−	0.844257i	$-0.680042\pi$
$401$	−1.45703	+	0.841215i	−0.0727605	+	0.0420083i	0.463178	+	0.886265i	$0.346709\pi$
$402$	−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	−0.321478	−	0.946917i	$-0.604180\pi$
$409$	6.83235	−	3.94466i	0.337838	−	0.195051i	0.659315	+	0.751866i	$0.270846\pi$
$410$	−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	0.720382	−	0.693577i	$-0.243966\pi$
$419$	−4.92218	−	8.52547i	−0.240464	−	0.416497i	−0.960847	+	0.277081i	$0.910633\pi$
$420$	3.19407	+	4.50518i	0.155854	+	0.219830i
$421$	7.00463	+	4.04412i	0.341385	+	0.197098i	0.660884	−	0.750488i	$-0.270181\pi$
$421$	7.00463	+	4.04412i	0.341385	+	0.197098i	−0.319500	+	0.947586i	$0.603515\pi$
$422$			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	$-0.958951\pi$
$431$		−	5.33973i		−	0.257206i	0.991696	−	0.128603i	$-0.0410492\pi$
$432$	−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	−0.932653	−	0.360775i	$-0.882512\pi$
$439$	−3.22427	+	5.58459i	−0.153886	+	0.266538i	0.778767	+	0.627313i	$0.215845\pi$
$440$			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	−0.297755	−	0.954642i	$-0.596238\pi$
$443$	14.2674	−	24.7119i	0.677867	−	1.17410i	0.975622	−	0.219457i	$-0.0704287\pi$
$444$	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	$0.143627\pi$
$449$			18.4800i			0.872124i	−0.899917	+	0.436062i	$0.856373\pi$
$450$	−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	0.956743	−	0.290935i	$-0.0939665\pi$
$457$	25.2930	+	14.6029i	1.18316	+	0.683096i	0.226414	+	0.974031i	$0.427300\pi$
$458$	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	0.961869	−	0.273509i	$-0.0881844\pi$
$461$	25.8926	+	14.9491i	1.20594	+	0.696249i	0.244069	+	0.969758i	$0.421518\pi$
$462$	−2.96677	−	31.7653i	−0.138026	−	1.47786i
$463$	−24.4237	+	14.1010i	−1.13507	+	0.655331i	−0.945204	−	0.326480i	$-0.894138\pi$
$463$	−24.4237	+	14.1010i	−1.13507	+	0.655331i	−0.189862	+	0.981811i	$0.560804\pi$
$464$	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	0.456406	−	0.889772i	$-0.349137\pi$
$479$	−1.88124	−	1.08613i	−0.0859561	−	0.0496268i	−0.542362	+	0.840145i	$0.682470\pi$
$480$	−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	$-0.866147\pi$
$487$		−	18.0177i		−	0.816458i	0.912880	−	0.408229i	$-0.133853\pi$
$488$	−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	0.528482	−	0.848945i	$-0.322762\pi$
$491$	−10.4359	−	18.0756i	−0.470967	−	0.815739i	−0.999449	+	0.0332061i	$0.989428\pi$
$492$	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	−0.231914	−	0.972736i	$-0.574499\pi$
$499$	11.0473	−	6.37814i	0.494544	−	0.285525i	0.726458	+	0.687211i	$0.241165\pi$
$500$	−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	−0.217975	−	0.975954i	$-0.569945\pi$
$509$	11.6920	−	6.75038i	0.518239	−	0.299205i	0.736214	+	0.676749i	$0.236612\pi$
$510$	−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	$-0.767753\pi$
$541$		−	31.0090i		−	1.33318i	0.745424	−	0.666591i	$-0.232247\pi$
$542$	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	−0.463821	−	0.885929i	$-0.653522\pi$
$547$	12.5202	−	21.6857i	0.535326	−	0.927212i	0.999147	−	0.0412834i	$-0.0131446\pi$
$548$			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	$-0.936888\pi$
$557$		−	9.29754i		−	0.393949i	0.980409	−	0.196975i	$-0.0631117\pi$
$558$	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	0.992433	−	0.122786i	$-0.0391830\pi$
$563$	9.25094	+	16.0231i	0.389881	+	0.675293i	−0.602553	+	0.798079i	$0.705850\pi$
$564$	−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	−0.568194	−	0.822895i	$-0.692358\pi$
$569$	10.2225	−	17.7060i	0.428551	−	0.742272i	0.996745	+	0.0806227i	$0.0256909\pi$
$570$	1.22287	+	13.0933i	0.0512203	+	0.548419i
$571$	12.4042	+	21.4846i	0.519098	+	0.899104i	0.999754	+	0.0221945i	$0.00706532\pi$
$571$	12.4042	+	21.4846i	0.519098	+	0.899104i	−0.480656	+	0.876909i	$0.659601\pi$
$572$	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	$0.238480\pi$
$577$			32.7191i			1.36211i	−0.732230	+	0.681057i	$0.761520\pi$
$578$	−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	−0.130075	−	0.991504i	$-0.541522\pi$
$587$	−25.5311	−	14.7404i	−1.05378	−	0.608401i	−0.923705	+	0.383103i	$0.874855\pi$
$588$	−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	$-0.825163\pi$
$593$		−	25.4261i		−	1.04413i	0.852907	−	0.522063i	$-0.174837\pi$
$594$	−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	0.991834	+	0.127537i	$0.0407071\pi$
$599$	14.8405	+	25.7045i	0.606367	+	1.05026i	−0.385467	+	0.922722i	$0.625960\pi$
$600$	−1.39380	−	0.640026i	−0.0569019	−	0.0261289i
$601$	3.28435	−	5.68866i	0.133971	−	0.232045i	−0.791233	−	0.611515i	$-0.790560\pi$
$601$	3.28435	−	5.68866i	0.133971	−	0.232045i	0.925204	+	0.379470i	$0.123894\pi$
$602$	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	0.867369	+	0.497666i	$0.165809\pi$
$607$	21.3033	+	36.8985i	0.864676	+	1.49766i	−0.00269327	+	0.999996i	$0.500857\pi$
$608$	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	$-0.923901\pi$
$613$		−	11.7258i		−	0.473603i	0.971558	−	0.236801i	$-0.0760990\pi$
$614$	−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	−0.901483	−	0.432815i	$-0.857520\pi$
$617$	−24.2780	+	14.0169i	−0.977396	+	0.564300i	−0.0759130	+	0.997114i	$0.524187\pi$
$618$	−2.15135	−	23.0347i	−0.0865401	−	0.926590i
$619$	28.9581	+	16.7190i	1.16393	+	0.671993i	0.952242	−	0.305345i	$-0.0987719\pi$
$619$	28.9581	+	16.7190i	1.16393	+	0.671993i	0.211684	+	0.977338i	$0.432105\pi$
$620$	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	$0.187468\pi$
$631$			27.9073i			1.11097i	−0.831526	+	0.555485i	$0.812532\pi$
$632$	−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	−0.175169	+	0.984538i	$0.556047\pi$
$641$	−23.8045	+	41.2305i	−0.940220	+	1.62851i	−0.765050	+	0.643970i	$0.777286\pi$
$642$	−23.4237	−	10.7560i	−0.924459	−	0.424505i
$643$	−2.16175	+	1.24809i	−0.0852512	+	0.0492198i	−0.542020	−	0.840366i	$-0.682340\pi$
$643$	−2.16175	+	1.24809i	−0.0852512	+	0.0492198i	0.456768	+	0.889586i	$0.349007\pi$
$644$	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	0.724284	−	0.689502i	$-0.242170\pi$
$653$	−6.00474	−	10.4005i	−0.234984	−	0.407004i	−0.959268	+	0.282498i	$0.908837\pi$
$654$	−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	0.103440	+	0.994636i	$0.467015\pi$
$659$	−20.7848	+	36.0003i	−0.809660	+	1.40237i	−0.913100	+	0.407736i	$0.866318\pi$
$660$	−7.19864	−	10.1536i	−0.280207	−	0.395227i
$661$	−2.37517	+	1.37130i	−0.0923834	+	0.0533376i	−0.545480	−	0.838124i	$-0.683653\pi$
$661$	−2.37517	+	1.37130i	−0.0923834	+	0.0533376i	0.453097	+	0.891461i	$0.350319\pi$
$662$	−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	−0.780721	−	0.624879i	$-0.785148\pi$
$673$	3.91211	−	6.77598i	0.150801	−	0.261195i	0.931522	+	0.363685i	$0.118481\pi$
$674$		−	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	−0.802632	−	0.596475i	$-0.796567\pi$
$677$	2.99863	−	5.19378i	0.115247	−	0.199613i	0.917878	+	0.396862i	$0.129901\pi$
$678$	−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	$0.147041\pi$
$683$			23.2955i			0.891377i	−0.895188	+	0.445688i	$0.852959\pi$
$684$	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	−0.191645	−	0.981464i	$-0.561382\pi$
$691$	−29.8998	−	17.2626i	−1.13744	−	0.656701i	−0.945795	+	0.324763i	$0.894715\pi$
$692$	−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	0.564165	−	0.825662i	$-0.309198\pi$
$709$	3.49355	+	2.01700i	0.131203	+	0.0757501i	−0.432962	+	0.901412i	$0.642532\pi$
$710$		−	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	0.369183	+	0.929357i	$0.379638\pi$
$727$	−16.7239	+	28.9666i	−0.620255	+	1.07431i	−0.989438	+	0.144957i	$0.953696\pi$
$728$	−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	−0.808053	−	0.589109i	$-0.799479\pi$
$733$	−19.0031	+	10.9715i	−0.701897	+	0.405240i	0.106157	+	0.994349i	$0.466145\pi$
$734$	−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	$-0.947061\pi$
$739$		−	9.00066i		−	0.331094i	0.986202	−	0.165547i	$-0.0529390\pi$
$740$	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	−0.999641	−	0.0267903i	$-0.991471\pi$
$743$	−40.2399	+	23.2325i	−1.47626	+	0.852319i	−0.476619	+	0.879110i	$0.658138\pi$
$744$	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	0.836720	−	0.547631i	$-0.184470\pi$
$751$	−1.53198	−	2.65346i	−0.0559027	−	0.0968263i	−0.892622	+	0.450805i	$0.851137\pi$
$752$	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	−0.250150	−	0.968207i	$-0.580480\pi$
$761$	12.7798	−	7.37842i	0.463267	−	0.267467i	0.713417	+	0.700740i	$0.247147\pi$
$762$	−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	−0.466996	−	0.884259i	$-0.654664\pi$
$769$	1.81074	−	1.04543i	0.0652968	−	0.0376991i	0.532293	+	0.846560i	$0.321330\pi$
$770$	−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	$-0.722240\pi$
$773$		−	42.5945i		−	1.53202i	0.642831	−	0.766008i	$-0.277760\pi$
$774$	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	−0.473726	−	0.880672i	$-0.657091\pi$
$787$	1.46148	−	0.843783i	0.0520960	−	0.0300776i	0.525822	+	0.850595i	$0.323758\pi$
$788$	−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	0.982118	−	0.188265i	$-0.0602862\pi$
$797$	9.26032	+	16.0393i	0.328017	+	0.568143i	−0.654101	+	0.756407i	$0.726953\pi$
$798$	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	$0.287311\pi$
$811$			44.7077i			1.56990i	−0.619560	+	0.784949i	$0.712689\pi$
$812$	−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	−0.438626	−	0.898669i	$-0.644535\pi$
$821$	−41.1519	−	23.7590i	−1.43621	−	0.829196i	−0.997584	+	0.0694730i	$0.977868\pi$
$822$	29.9819	+	42.2890i	1.04574	+	1.47500i
$823$	15.7245	+	27.2357i	0.548123	+	0.949377i	0.998403	+	0.0564895i	$0.0179907\pi$
$823$	15.7245	+	27.2357i	0.548123	+	0.949377i	−0.450280	+	0.892887i	$0.648676\pi$
$824$	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	$-0.939406\pi$
$827$		−	10.8827i		−	0.378430i	0.981936	−	0.189215i	$-0.0605942\pi$
$828$	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	0.434249	−	0.900793i	$-0.357014\pi$
$839$	−3.72891	−	2.15288i	−0.128736	−	0.0743258i	−0.562985	+	0.826467i	$0.690347\pi$
$840$	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	0.394129	−	0.919055i	$-0.371046\pi$
$853$	−5.97945	−	3.45224i	−0.204732	−	0.118202i	−0.598861	+	0.800853i	$0.704380\pi$
$854$	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	−0.922044	−	0.387085i	$-0.873482\pi$
$857$	−3.68263	+	6.37850i	−0.125796	+	0.217885i	0.796248	+	0.604971i	$0.206815\pi$
$858$	46.0677	−	30.3152i	1.57273	−	1.03494i
$859$	−20.4592	−	35.4363i	−0.698058	−	1.20907i	−0.969139	−	0.246515i	$-0.920714\pi$
$859$	−20.4592	−	35.4363i	−0.698058	−	1.20907i	0.271081	−	0.962557i	$-0.412619\pi$
$860$	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	$-0.891720\pi$
$863$		−	19.6031i		−	0.667298i	0.942697	−	0.333649i	$-0.108280\pi$
$864$	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	0.277903	−	0.960609i	$-0.410361\pi$
$877$	36.9812	−	21.3511i	1.24877	−	0.720976i	0.970863	+	0.239634i	$0.0770273\pi$
$878$	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	0.843244	−	0.537531i	$-0.180643\pi$
$887$	−1.30726	−	2.26423i	−0.0438933	−	0.0760255i	−0.887137	+	0.461505i	$0.847310\pi$
$888$	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	−0.472613	−	0.881270i	$-0.656689\pi$
$907$	15.8682	−	27.4846i	0.526896	−	0.912610i	0.999509	−	0.0313403i	$-0.00997755\pi$
$908$		−	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	−0.395978	−	0.918260i	$-0.629595\pi$
$911$	18.0266	−	31.2229i	0.597247	−	1.03446i	0.993226	−	0.116203i	$-0.0370722\pi$
$912$	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	0.590855	−	0.806778i	$-0.298790\pi$
$929$	5.71773	+	3.30114i	0.187593	+	0.108307i	−0.403262	+	0.915084i	$0.632124\pi$
$930$	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	0.451890	−	0.892074i	$-0.350750\pi$
$941$	44.4919	−	25.6874i	1.45039	−	0.837385i	0.998503	+	0.0546890i	$0.0174167\pi$
$942$	−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	0.249316	−	0.968422i	$-0.419794\pi$
$947$	−14.3005	−	8.25642i	−0.464705	−	0.268297i	−0.714020	+	0.700125i	$0.753128\pi$
$948$	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	−0.962422	−	0.271559i	$-0.912461\pi$
$967$	−37.5789	+	21.6962i	−1.20846	+	0.697702i	−0.246034	+	0.969261i	$0.579128\pi$
$968$	−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	−0.110195	−	0.993910i	$-0.535147\pi$
$977$	21.7380	−	12.5504i	0.695459	−	0.401524i	0.805654	+	0.592386i	$0.201814\pi$
$978$	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	−0.466926	−	0.884296i	$-0.654639\pi$
$983$	−45.9699	−	26.5407i	−1.46621	−	0.846518i	−0.999286	+	0.0377782i	$0.987972\pi$
$984$	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	−0.655293	−	0.755375i	$-0.727455\pi$
$997$	10.3102	−	17.8578i	0.326528	−	0.565563i	0.981820	+	0.189812i	$0.0607880\pi$
$998$	−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.376.12	✓	108
9.4	even	3	inner	585.2.bt.b.571.43	yes	108
13.12	even	2	inner	585.2.bt.b.376.43	yes	108
117.103	even	6	inner	585.2.bt.b.571.12	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.12	✓	108	1.1	even	1	trivial
585.2.bt.b.376.43	yes	108	13.12	even	2	inner
585.2.bt.b.571.12	yes	108	117.103	even	6	inner
585.2.bt.b.571.43	yes	108	9.4	even	3	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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