LMFDB - Embedded newform 72.2.l.b.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(11,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.l (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:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.8
Root			$-0.409484 + 1.35363i$ of defining polynomial
Character	$\chi$	$=$	72.11
Dual form			72.2.l.b.59.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37702 - 0.322193i) q^{2} +(-1.12774 + 1.31461i) q^{3} +(1.79238 - 0.887333i) q^{4} +(0.565188 + 0.978934i) q^{5} +(-1.12936 + 2.17360i) q^{6} +(-3.71499 - 2.14485i) q^{7} +(2.18226 - 1.79937i) q^{8} +(-0.456412 - 2.96508i) q^{9} +(1.09368 + 1.16591i) q^{10} +(1.00953 + 0.582853i) q^{11} +(-0.854841 + 3.35697i) q^{12} +(-2.64466 + 1.52689i) q^{13} +(-5.80668 - 1.75656i) q^{14} +(-1.92430 - 0.360979i) q^{15} +(2.42528 - 3.18088i) q^{16} +1.49654i q^{17} +(-1.58382 - 3.93593i) q^{18} -3.42378 q^{19} +(1.88167 + 1.25312i) q^{20} +(7.00918 - 2.46494i) q^{21} +(1.57794 + 0.477339i) q^{22} +(3.85938 + 6.68464i) q^{23} +(-0.0955437 + 4.89805i) q^{24} +(1.86113 - 3.22356i) q^{25} +(-3.14980 + 2.95466i) q^{26} +(4.41264 + 2.74383i) q^{27} +(-8.56188 - 0.547960i) q^{28} +(0.709580 - 1.22903i) q^{29} +(-2.76611 + 0.122920i) q^{30} +(4.66408 - 2.69281i) q^{31} +(2.31481 - 5.16156i) q^{32} +(-1.90471 + 0.669837i) q^{33} +(0.482173 + 2.06077i) q^{34} -4.84897i q^{35} +(-3.44908 - 4.90957i) q^{36} +2.97201i q^{37} +(-4.71462 + 1.10312i) q^{38} +(0.975209 - 5.19864i) q^{39} +(2.99485 + 1.11931i) q^{40} +(-4.23339 + 2.44415i) q^{41} +(8.85761 - 5.65258i) q^{42} +(-1.74292 + 3.01882i) q^{43} +(2.32665 + 0.148906i) q^{44} +(2.64466 - 2.12262i) q^{45} +(7.46820 + 7.96144i) q^{46} +(1.77991 - 3.08289i) q^{47} +(1.44655 + 6.77551i) q^{48} +(5.70075 + 9.87399i) q^{49} +(1.52420 - 5.03856i) q^{50} +(-1.96737 - 1.68770i) q^{51} +(-3.38538 + 5.08347i) q^{52} -11.2786 q^{53} +(6.96035 + 2.35659i) q^{54} +1.31769i q^{55} +(-11.9665 + 2.00402i) q^{56} +(3.86113 - 4.50094i) q^{57} +(0.581124 - 1.92102i) q^{58} +(7.50935 - 4.33553i) q^{59} +(-3.76940 + 1.06049i) q^{60} +(3.16057 + 1.82476i) q^{61} +(5.55494 - 5.21079i) q^{62} +(-4.66408 + 11.9942i) q^{63} +(1.52453 - 7.85340i) q^{64} +(-2.98946 - 1.72596i) q^{65} +(-2.40702 + 1.53607i) q^{66} +(-5.58255 - 9.66925i) q^{67} +(1.32793 + 2.68237i) q^{68} +(-13.1401 - 2.46494i) q^{69} +(-1.56230 - 6.67714i) q^{70} -2.54954 q^{71} +(-6.33129 - 5.64932i) q^{72} -7.06491 q^{73} +(0.957560 + 4.09253i) q^{74} +(2.13887 + 6.08200i) q^{75} +(-6.13672 + 3.03803i) q^{76} +(-2.50026 - 4.33059i) q^{77} +(-0.332078 - 7.47285i) q^{78} +(2.24998 + 1.29902i) q^{79} +(4.48461 + 0.576391i) q^{80} +(-8.58338 + 2.70659i) q^{81} +(-5.04198 + 4.72961i) q^{82} +(-3.98482 - 2.30064i) q^{83} +(10.3759 - 10.6376i) q^{84} +(-1.46501 + 0.845824i) q^{85} +(-1.42740 + 4.71855i) q^{86} +(0.815476 + 2.31885i) q^{87} +(3.25183 - 0.544584i) q^{88} +8.63803i q^{89} +(2.95786 - 3.77499i) q^{90} +13.0998 q^{91} +(12.8490 + 8.55689i) q^{92} +(-1.71986 + 9.16824i) q^{93} +(1.45769 - 4.81869i) q^{94} +(-1.93508 - 3.35165i) q^{95} +(4.17495 + 8.86396i) q^{96} +(3.35869 - 5.81742i) q^{97} +(11.0314 + 11.7600i) q^{98} +(1.26744 - 3.25936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9} + 12 q^{11} - 6 q^{12} - 18 q^{14} + 7 q^{16} - 4 q^{19} + 18 q^{20} - q^{22} + 21 q^{24} - 14 q^{25} - 36 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 - 6 * q^3 - 5 * q^4 - 3 * q^6 - 6 * q^9 + 12 * q^11 - 6 * q^12 - 18 * q^14 + 7 * q^16 - 4 * q^19 + 18 * q^20 - q^22 + 21 * q^24 - 14 * q^25 - 36 * q^27 - 12 * q^28 + 12 * q^30 + 27 * q^32 + 12 * q^33 - 13 * q^34 + 27 * q^36 - 15 * q^38 - 12 * q^40 - 36 * q^41 + 42 * q^42 + 8 * q^43 + 12 * q^46 - 27 * q^48 + 10 * q^49 + 51 * q^50 + 18 * q^51 - 18 * q^52 + 39 * q^54 - 66 * q^56 + 18 * q^57 + 12 * q^58 + 12 * q^59 - 72 * q^60 + 34 * q^64 - 6 * q^65 - 24 * q^66 - 16 * q^67 - 9 * q^68 + 18 * q^70 - 21 * q^72 - 4 * q^73 - 60 * q^74 + 78 * q^75 - 7 * q^76 - 72 * q^78 - 6 * q^81 - 22 * q^82 + 54 * q^83 + 12 * q^84 - 51 * q^86 - 13 * q^88 - 66 * q^90 - 36 * q^91 + 84 * q^92 + 24 * q^94 + 42 * q^96 + 8 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.37702	−	0.322193i	0.973702	−	0.227825i
$2$	1.37702	−	0.322193i	0.973702	−	0.227825i
$3$	−1.12774	+	1.31461i	−0.651100	+	0.758992i
$3$	−1.12774	+	1.31461i	−0.651100	+	0.758992i
$4$	1.79238	−	0.887333i	0.896192	−	0.443667i
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	0.964285	−	0.264868i	$-0.0853285\pi$
$5$	0.565188	+	0.978934i	0.252760	+	0.437793i	−0.711525	+	0.702661i	$0.751995\pi$
$6$	−1.12936	+	2.17360i	−0.461061	+	0.887369i
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.409320	−	0.912391i	$-0.634234\pi$
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.994814	+	0.101714i	$0.967567\pi$
$8$	2.18226	−	1.79937i	0.771546	−	0.636174i
$9$	−0.456412	−	2.96508i	−0.152137	−	0.988359i
$10$	1.09368	+	1.16591i	0.345853	+	0.368695i
$11$	1.00953	+	0.582853i	0.304385	+	0.175737i	0.644411	−	0.764679i	$-0.277103\pi$
$11$	1.00953	+	0.582853i	0.304385	+	0.175737i	−0.340026	+	0.940416i	$0.610436\pi$
$12$	−0.854841	+	3.35697i	−0.246771	+	0.969074i
$13$	−2.64466	+	1.52689i	−0.733496	+	0.423484i	−0.819700	−	0.572793i	$-0.805860\pi$
$13$	−2.64466	+	1.52689i	−0.733496	+	0.423484i	0.0862038	+	0.996278i	$0.472526\pi$
$14$	−5.80668	−	1.75656i	−1.55190	−	0.469461i
$15$	−1.92430	−	0.360979i	−0.496853	−	0.0932043i
$16$	2.42528	−	3.18088i	0.606320	−	0.795221i
$17$			1.49654i			0.362963i	0.983394	+	0.181482i	$0.0580893\pi$
$17$			1.49654i			0.362963i	−0.983394	+	0.181482i	$0.941911\pi$
$18$	−1.58382	−	3.93593i	−0.373309	−	0.927707i
$19$	−3.42378			−0.785468			−0.392734	−	0.919652i	$-0.628471\pi$
$19$	−3.42378			−0.785468			−0.392734	+	0.919652i	$0.628471\pi$
$20$	1.88167	+	1.25312i	0.420755	+	0.280205i
$21$	7.00918	−	2.46494i	1.52953	−	0.537894i
$22$	1.57794	+	0.477339i	0.336418	+	0.101769i
$23$	3.85938	+	6.68464i	0.804736	+	1.39384i	0.916469	+	0.400106i	$0.131027\pi$
$23$	3.85938	+	6.68464i	0.804736	+	1.39384i	−0.111733	+	0.993738i	$0.535640\pi$
$24$	−0.0955437	+	4.89805i	−0.0195028	+	0.999810i
$25$	1.86113	−	3.22356i	0.372225	−	0.644713i
$26$	−3.14980	+	2.95466i	−0.617726	+	0.579456i
$27$	4.41264	+	2.74383i	0.849213	+	0.528050i
$28$	−8.56188	−	0.547960i	−1.61804	−	0.103555i
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	−0.792592	−	0.609753i	$-0.791269\pi$
$29$	0.709580	−	1.22903i	0.131766	−	0.228225i	0.924357	+	0.381528i	$0.124602\pi$
$30$	−2.76611	+	0.122920i	−0.505021	+	0.0224421i
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	−0.0187859	−	0.999824i	$-0.505980\pi$
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	0.856480	+	0.516181i	$0.172647\pi$
$32$	2.31481	−	5.16156i	0.409204	−	0.912443i
$33$	−1.90471	+	0.669837i	−0.331568	+	0.116604i
$34$	0.482173	+	2.06077i	0.0826920	+	0.353418i
$35$		−	4.84897i		−	0.819625i
$36$	−3.44908	−	4.90957i	−0.574846	−	0.818261i
$37$			2.97201i			0.488596i	0.969700	+	0.244298i	$0.0785575\pi$
$37$			2.97201i			0.488596i	−0.969700	+	0.244298i	$0.921443\pi$
$38$	−4.71462	+	1.10312i	−0.764812	+	0.178949i
$39$	0.975209	−	5.19864i	0.156158	−	0.832448i
$40$	2.99485	+	1.11931i	0.473528	+	0.176978i
$41$	−4.23339	+	2.44415i	−0.661144	+	0.381712i	−0.792713	−	0.609595i	$-0.791332\pi$
$41$	−4.23339	+	2.44415i	−0.661144	+	0.381712i	0.131569	+	0.991307i	$0.457999\pi$
$42$	8.85761	−	5.65258i	1.36676	−	0.872213i
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	−0.967771	−	0.251832i	$-0.918967\pi$
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	0.701978	+	0.712198i	$0.252300\pi$
$44$	2.32665	+	0.148906i	0.350756	+	0.0224484i
$45$	2.64466	−	2.12262i	0.394242	−	0.316422i
$46$	7.46820	+	7.96144i	1.10113	+	1.17385i
$47$	1.77991	−	3.08289i	0.259627	−	0.449686i	−0.706515	−	0.707698i	$-0.749734\pi$
$47$	1.77991	−	3.08289i	0.259627	−	0.449686i	0.966142	+	0.258011i	$0.0830672\pi$
$48$	1.44655	+	6.77551i	0.208791	+	0.977960i
$49$	5.70075	+	9.87399i	0.814393	+	1.41057i
$50$	1.52420	−	5.03856i	0.215555	−	0.712560i
$51$	−1.96737	−	1.68770i	−0.275486	−	0.236326i
$52$	−3.38538	+	5.08347i	−0.469467	+	0.704951i
$53$	−11.2786			−1.54923			−0.774616	−	0.632432i	$-0.782057\pi$
$53$	−11.2786			−1.54923			−0.774616	+	0.632432i	$0.782057\pi$
$54$	6.96035	+	2.35659i	0.947184	+	0.320692i
$55$			1.31769i			0.177677i
$56$	−11.9665	+	2.00402i	−1.59908	+	0.267799i
$57$	3.86113	−	4.50094i	0.511419	−	0.596164i
$58$	0.581124	−	1.92102i	0.0763053	−	0.252243i
$59$	7.50935	−	4.33553i	0.977634	−	0.564437i	0.0760791	−	0.997102i	$-0.475760\pi$
$59$	7.50935	−	4.33553i	0.977634	−	0.564437i	0.901555	+	0.432664i	$0.142427\pi$
$60$	−3.76940	+	1.06049i	−0.486627	+	0.136908i
$61$	3.16057	+	1.82476i	0.404670	+	0.233636i	0.688497	−	0.725239i	$-0.258271\pi$
$61$	3.16057	+	1.82476i	0.404670	+	0.233636i	−0.283827	+	0.958875i	$0.591604\pi$
$62$	5.55494	−	5.21079i	0.705478	−	0.661771i
$63$	−4.66408	+	11.9942i	−0.587619	+	1.51112i
$64$	1.52453	−	7.85340i	0.190566	−	0.981674i
$65$	−2.98946	−	1.72596i	−0.370796	−	0.214079i
$66$	−2.40702	+	1.53607i	−0.296283	+	0.189077i
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	−0.974364	−	0.224975i	$-0.927770\pi$
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	0.292348	−	0.956312i	$-0.405563\pi$
$68$	1.32793	+	2.68237i	0.161035	+	0.325285i
$69$	−13.1401	−	2.46494i	−1.58188	−	0.296744i
$70$	−1.56230	−	6.67714i	−0.186731	−	0.798071i
$71$	−2.54954			−0.302574			−0.151287	−	0.988490i	$-0.548342\pi$
$71$	−2.54954			−0.302574			−0.151287	+	0.988490i	$0.548342\pi$
$72$	−6.33129	−	5.64932i	−0.746149	−	0.665779i
$73$	−7.06491			−0.826885			−0.413442	−	0.910530i	$-0.635674\pi$
$73$	−7.06491			−0.826885			−0.413442	+	0.910530i	$0.635674\pi$
$74$	0.957560	+	4.09253i	0.111314	+	0.475747i
$75$	2.13887	+	6.08200i	0.246976	+	0.702288i
$76$	−6.13672	+	3.03803i	−0.703930	+	0.348486i
$77$	−2.50026	−	4.33059i	−0.284932	−	0.493516i
$78$	−0.332078	−	7.47285i	−0.0376004	−	0.846133i
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	0.621202	−	0.783650i	$-0.286645\pi$
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	−0.368060	+	0.929802i	$0.619978\pi$
$80$	4.48461	+	0.576391i	0.501395	+	0.0644424i
$81$	−8.58338	+	2.70659i	−0.953709	+	0.300732i
$82$	−5.04198	+	4.72961i	−0.556794	+	0.522298i
$83$	−3.98482	−	2.30064i	−0.437391	−	0.252528i	0.265099	−	0.964221i	$-0.414595\pi$
$83$	−3.98482	−	2.30064i	−0.437391	−	0.252528i	−0.702490	+	0.711693i	$0.747929\pi$
$84$	10.3759	−	10.6376i	1.13211	−	1.16066i
$85$	−1.46501	+	0.845824i	−0.158903	+	0.0917425i
$86$	−1.42740	+	4.71855i	−0.153920	+	0.508814i
$87$	0.815476	+	2.31885i	0.0874282	+	0.248606i
$88$	3.25183	−	0.544584i	0.346646	−	0.0580529i
$89$			8.63803i			0.915630i	0.889048	+	0.457815i	$0.151368\pi$
$89$			8.63803i			0.915630i	−0.889048	+	0.457815i	$0.848632\pi$
$90$	2.95786	−	3.77499i	0.311786	−	0.397919i
$91$	13.0998			1.37323
$92$	12.8490	+	8.55689i	1.33960	+	0.892117i
$93$	−1.71986	+	9.16824i	−0.178342	+	0.950702i
$94$	1.45769	−	4.81869i	0.150349	−	0.497010i
$95$	−1.93508	−	3.35165i	−0.198535	−	0.343872i
$96$	4.17495	+	8.86396i	0.426104	+	0.904674i
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	−0.643600	−	0.765362i	$-0.722560\pi$
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	0.984623	+	0.174693i	$0.0558931\pi$
$98$	11.0314	+	11.7600i	1.11434	+	1.18794i
$99$	1.26744	−	3.25936i	0.127383	−	0.327578i
$100$	0.475475	−	7.42930i	0.0475475	−	0.742930i
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	−0.290967	−	0.956733i	$-0.593977\pi$
$101$	6.86479	−	11.8902i	0.683072	−	1.18312i	0.974039	−	0.226382i	$-0.0726897\pi$
$102$	−3.25287	−	1.69013i	−0.322082	−	0.167348i
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	−0.205022	−	0.978757i	$-0.565727\pi$
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	0.745118	+	0.666933i	$0.232393\pi$
$104$	−3.02388	+	8.09080i	−0.296516	+	0.793368i
$105$	6.37451	+	5.46837i	0.622089	+	0.533658i
$106$	−15.5309	+	3.63388i	−1.50849	+	0.352953i
$107$			10.4483i			1.01007i	0.863097	+	0.505037i	$0.168521\pi$
$107$			10.4483i			1.01007i	−0.863097	+	0.505037i	$0.831479\pi$
$108$	10.3438	+	1.00251i	0.995336	+	0.0964665i
$109$		−	9.67531i		−	0.926727i	−0.886168	−	0.463364i	$-0.846642\pi$
$109$		−	9.67531i		−	0.926727i	0.886168	−	0.463364i	$-0.153358\pi$
$110$	0.424549	+	1.81448i	0.0404792	+	0.173004i
$111$	−3.90704	−	3.35165i	−0.370840	−	0.318125i
$112$	−15.8324	+	6.61509i	−1.49602	+	0.625067i
$113$	7.15149	−	4.12891i	0.672756	−	0.388416i	−0.124364	−	0.992237i	$-0.539689\pi$
$113$	7.15149	−	4.12891i	0.672756	−	0.388416i	0.797120	+	0.603821i	$0.206356\pi$
$114$	3.86669	−	7.44192i	0.362149	−	0.697000i
$115$	−4.36255	+	7.55615i	−0.406810	+	0.704615i
$116$	0.181281	−	2.83253i	0.0168316	−	0.262993i
$117$	5.73441	+	7.14472i	0.530146	+	0.660530i
$118$	8.94367	−	8.38958i	0.823332	−	0.772323i
$119$	3.20984	−	5.55961i	0.294246	−	0.509649i
$120$	−4.84887	+	2.67479i	−0.442639	+	0.244173i
$121$	−4.82056	−	8.34946i	−0.438233	−	0.759042i
$122$	4.94011	+	1.49442i	0.447256	+	0.135298i
$123$	1.56105	−	8.32162i	0.140755	−	0.750335i
$124$	5.97040	−	8.96514i	0.536158	−	0.805093i
$125$	9.85942			0.881853
$126$	−2.55811	+	18.0190i	−0.227895	+	1.60526i
$127$			2.78757i			0.247357i	0.992322	+	0.123678i	$0.0394691\pi$
$127$			2.78757i			0.247357i	−0.992322	+	0.123678i	$0.960531\pi$
$128$	−0.431001	−	11.3055i	−0.0380955	−	0.999274i
$129$	−2.00303	−	5.69571i	−0.176357	−	0.501479i
$130$	−4.67264	−	1.41351i	−0.409818	−	0.123973i
$131$	−13.0529	+	7.53612i	−1.14044	+	0.658434i	−0.946540	−	0.322587i	$-0.895447\pi$
$131$	−13.0529	+	7.53612i	−1.14044	+	0.658434i	−0.193901	+	0.981021i	$0.562114\pi$
$132$	−2.81961	+	2.89072i	−0.245416	+	0.251605i
$133$	12.7193	+	7.34348i	1.10290	+	0.636761i
$134$	−10.8027	−	11.5161i	−0.933207	−	0.994842i
$135$	−0.192056	+	5.87046i	−0.0165295	+	0.505249i
$136$	2.69283	+	3.26583i	0.230908	+	0.280043i
$137$	7.55211	+	4.36021i	0.645220	+	0.372518i	0.786623	−	0.617434i	$-0.211828\pi$
$137$	7.55211	+	4.36021i	0.645220	+	0.372518i	−0.141402	+	0.989952i	$0.545161\pi$
$138$	−18.8884	+	0.839361i	−1.60789	+	0.0714512i
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	0.912034	−	0.410115i	$-0.134511\pi$
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	−0.811187	+	0.584787i	$0.801178\pi$
$140$	−4.30265	−	8.69121i	−0.363641	−	0.734542i
$141$	2.04554	+	5.81659i	0.172265	+	0.489845i
$142$	−3.51077	+	0.821442i	−0.294617	+	0.0689339i
$143$	−3.55982			−0.297687
$144$	−10.5385	−	5.73935i	−0.878208	−	0.478279i
$145$	1.60418			0.133220
$146$	−9.72854	+	2.27626i	−0.805139	+	0.188385i
$147$	−19.4094	−	3.64100i	−1.60086	−	0.300305i
$148$	2.63717	+	5.32698i	0.216774	+	0.437875i
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	0.955707	+	0.294320i	$0.0950931\pi$
$149$	8.94426	+	15.4919i	0.732742	+	1.26915i	−0.222965	+	0.974826i	$0.571574\pi$
$150$	4.90485	+	7.68592i	0.400480	+	0.627553i
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	0.399520	−	0.916725i	$-0.369177\pi$
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	−0.594147	+	0.804357i	$0.702510\pi$
$152$	−7.47158	+	6.16065i	−0.606025	+	0.499694i
$153$	4.43735	−	0.683037i	0.358738	−	0.0552202i
$154$	−4.83820	−	5.15775i	−0.389874	−	0.415623i
$155$	5.27216	+	3.04388i	0.423470	+	0.244491i
$156$	−2.86498	−	10.1833i	−0.229382	−	0.815315i
$157$	−2.21148	+	1.27680i	−0.176495	+	0.101900i	−0.585645	−	0.810568i	$-0.699159\pi$
$157$	−2.21148	+	1.27680i	−0.176495	+	0.101900i	0.409150	+	0.912467i	$0.365825\pi$
$158$	3.51681	+	1.06386i	0.279782	+	0.0846362i
$159$	12.7193	−	14.8270i	1.00871	−	1.17585i
$160$	6.36112	−	0.651206i	0.502891	−	0.0514824i
$161$		−	33.1111i		−	2.60952i
$162$	−10.9475	+	6.49254i	−0.860114	+	0.510102i
$163$	6.93355			0.543077			0.271539	−	0.962428i	$-0.412468\pi$
$163$	6.93355			0.543077			0.271539	+	0.962428i	$0.412468\pi$
$164$	−5.41908	+	8.13728i	−0.423159	+	0.635414i
$165$	−1.73225	−	1.48601i	−0.134855	−	0.115685i
$166$	−6.22844	−	1.88415i	−0.483421	−	0.146239i
$167$	−8.36829	−	14.4943i	−0.647558	−	1.12160i	−0.983704	−	0.179794i	$-0.942457\pi$
$167$	−8.36829	−	14.4943i	−0.647558	−	1.12160i	0.336146	−	0.941810i	$-0.390876\pi$
$168$	10.8605	−	17.9913i	0.837907	−	1.38806i
$169$	−1.83719	+	3.18211i	−0.141322	+	0.244778i
$170$	−1.74483	+	1.63673i	−0.133823	+	0.125532i
$171$	1.56265	+	10.1518i	0.119499	+	0.776325i
$172$	−0.445276	+	6.95744i	−0.0339520	+	0.530500i
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	0.156761	+	0.987637i	$0.449895\pi$
$173$	−10.2190	+	17.6999i	−0.776938	+	1.34570i	−0.933699	+	0.358059i	$0.883438\pi$
$174$	1.87004	+	2.93036i	0.141768	+	0.222150i
$175$	−13.8281	+	7.98367i	−1.04531	+	0.603508i
$176$	4.30238	−	1.79762i	0.324304	−	0.135501i
$177$	−2.76905	+	14.7612i	−0.208134	+	1.10952i
$178$	2.78311	+	11.8948i	0.208603	+	0.891550i
$179$		−	4.07982i		−	0.304940i	−0.988308	−	0.152470i	$-0.951277\pi$
$179$		−	4.07982i		−	0.304940i	0.988308	−	0.152470i	$-0.0487227\pi$
$180$	2.85677	−	6.15125i	0.212931	−	0.458487i
$181$		−	22.3226i		−	1.65923i	−0.558337	−	0.829614i	$-0.688560\pi$
$181$		−	22.3226i		−	1.65923i	0.558337	−	0.829614i	$-0.311440\pi$
$182$	18.0388	−	4.22067i	1.33712	−	0.312857i
$183$	−5.96315	+	2.09708i	−0.440809	+	0.155021i
$184$	20.4503	+	7.64317i	1.50762	+	0.563462i
$185$	−2.90940	+	1.67974i	−0.213904	+	0.123497i
$186$	0.585648	+	13.1790i	0.0429418	+	0.966332i
$187$	−0.872261	+	1.51080i	−0.0637861	+	0.110481i
$188$	0.454726	−	7.10510i	0.0331643	−	0.518193i
$189$	−10.5078	−	19.6577i	−0.764331	−	1.42989i
$190$	−3.74452	−	3.99183i	−0.271656	−	0.289598i
$191$	−7.27481	+	12.6003i	−0.526387	+	0.911728i	0.473141	+	0.880987i	$0.343120\pi$
$191$	−7.27481	+	12.6003i	−0.526387	+	0.911728i	−0.999527	+	0.0307415i	$0.990213\pi$
$192$	8.60491	+	10.8607i	0.621006	+	0.783806i
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	0.934154	−	0.356870i	$-0.116156\pi$
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	−0.776136	+	0.630566i	$0.782823\pi$
$194$	2.75066	−	9.09287i	0.197486	−	0.652830i
$195$	5.64030	−	1.98354i	0.403910	−	0.142044i
$196$	18.9795	+	12.6395i	1.35568	+	0.902823i
$197$	7.69721			0.548404			0.274202	−	0.961672i	$-0.411586\pi$
$197$	7.69721			0.548404			0.274202	+	0.961672i	$0.411586\pi$
$198$	0.695157	−	4.89658i	0.0494026	−	0.347985i
$199$			20.9790i			1.48716i	0.668646	+	0.743580i	$0.266874\pi$
$199$			20.9790i			1.48716i	−0.668646	+	0.743580i	$0.733126\pi$
$200$	−1.73893	−	10.3835i	−0.122961	−	0.734225i
$201$	19.0070	+	3.56551i	1.34065	+	0.251491i
$202$	5.62204	−	18.5848i	0.395566	−	1.30762i
$203$	−5.27216	+	3.04388i	−0.370033	+	0.213639i
$204$	−5.02383	−	1.27930i	−0.351738	−	0.0895689i
$205$	−4.78532	−	2.76280i	−0.334221	−	0.192963i
$206$	6.52834	−	6.12388i	0.454851	−	0.426671i
$207$	18.0590	−	14.4943i	1.25519	−	1.00742i
$208$	−1.55716	+	12.1155i	−0.107970	+	0.840058i
$209$	−3.45641	−	1.99556i	−0.239085	−	0.138036i
$210$	10.5397	+	5.47625i	0.727310	+	0.377897i
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	0.936363	−	0.351033i	$-0.114170\pi$
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	−0.772185	+	0.635397i	$0.780836\pi$
$212$	−20.2155	+	10.0079i	−1.38841	+	0.687343i
$213$	2.87521	−	3.35165i	0.197006	−	0.229651i
$214$	3.36636	+	14.3875i	0.230120	+	0.983512i
$215$	−3.94031			−0.268727
$216$	14.5667	−	1.95223i	0.991138	−	0.132833i
$217$	−23.1027			−1.56831
$218$	−3.11732	−	13.3231i	−0.211131	−	0.902356i
$219$	7.96737	−	9.28761i	0.538385	−	0.627599i
$220$	1.16923	+	2.36180i	0.0788293	+	0.159232i
$221$	−2.28505	−	3.95783i	−0.153709	−	0.266232i
$222$	−6.45997	−	3.35648i	−0.433564	−	0.225272i
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	0.0179997	−	0.999838i	$-0.494270\pi$
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	−0.856885	+	0.515507i	$0.827604\pi$
$224$	−19.6702	+	14.2102i	−1.31427	+	0.949459i
$225$	−10.4076	−	4.04711i	−0.693837	−	0.269807i
$226$	8.51746	−	7.98977i	0.566573	−	0.531471i
$227$	0.561821	+	0.324367i	0.0372894	+	0.0215290i	0.518529	−	0.855060i	$-0.326480\pi$
$227$	0.561821	+	0.324367i	0.0372894	+	0.0215290i	−0.481239	+	0.876589i	$0.659813\pi$
$228$	2.92678	−	11.4935i	0.193831	−	0.761177i
$229$	−12.0007	+	6.92863i	−0.793032	+	0.457857i	−0.841029	−	0.540990i	$-0.818050\pi$
$229$	−12.0007	+	6.92863i	−0.793032	+	0.457857i	0.0479971	+	0.998847i	$0.484716\pi$
$230$	−3.57279	+	11.8106i	−0.235583	+	0.778767i
$231$	8.51269	+	1.59689i	0.560094	+	0.105068i
$232$	−0.662990	−	3.95886i	−0.0435275	−	0.259912i
$233$			23.1276i			1.51514i	0.652755	+	0.757569i	$0.273613\pi$
$233$			23.1276i			1.51514i	−0.652755	+	0.757569i	$0.726387\pi$
$234$	10.1984	+	7.99086i	0.666690	+	0.522379i
$235$	4.02393			0.262492
$236$	9.61258	−	14.4342i	0.625726	−	0.939588i
$237$	−4.24510	+	1.49289i	−0.275749	+	0.0969734i
$238$	2.62876	−	8.68990i	0.170397	−	0.563283i
$239$	7.44075	+	12.8878i	0.481302	+	0.833640i	0.999770	−	0.0214576i	$-0.00683070\pi$
$239$	7.44075	+	12.8878i	0.481302	+	0.833640i	−0.518468	+	0.855097i	$0.673497\pi$
$240$	−5.81520	+	5.24551i	−0.375370	+	0.338596i
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	−0.990879	−	0.134755i	$-0.956975\pi$
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	0.612141	+	0.790749i	$0.290309\pi$
$242$	−9.32816	−	9.94425i	−0.599637	−	0.639241i
$243$	6.12169	−	14.3361i	0.392706	−	0.919664i
$244$	7.28413	+	0.466184i	0.466319	+	0.0298444i
$245$	−6.44399	+	11.1613i	−0.411691	+	0.713071i
$246$	−0.531568	−	11.9620i	−0.0338915	−	0.762671i
$247$	9.05472	−	5.22774i	0.576138	−	0.332633i
$248$	5.33288	−	14.2688i	0.338638	−	0.906071i
$249$	7.51829	−	2.64398i	0.476452	−	0.167555i
$250$	13.5766	−	3.17663i	0.858662	−	0.200908i
$251$			5.51619i			0.348179i	0.984730	+	0.174089i	$0.0556981\pi$
$251$			5.51619i			0.348179i	−0.984730	+	0.174089i	$0.944302\pi$
$252$	2.28300	+	25.6367i	0.143815	+	1.61496i
$253$			8.99781i			0.565687i
$254$	0.898134	+	3.83854i	0.0563539	+	0.240852i
$255$	0.540218	−	2.87979i	0.0338298	−	0.180339i
$256$	−4.23605	−	15.4291i	−0.264753	−	0.964316i
$257$	16.9194	−	9.76841i	1.05540	−	0.609337i	0.131245	−	0.991350i	$-0.458102\pi$
$257$	16.9194	−	9.76841i	1.05540	−	0.609337i	0.924157	+	0.382013i	$0.124769\pi$
$258$	−4.59333	−	7.19776i	−0.285968	−	0.448113i
$259$	6.37451	−	11.0410i	0.396093	−	0.686053i
$260$	−6.88976	−	0.440944i	−0.427285	−	0.0273462i
$261$	−3.96803	−	1.54302i	−0.245615	−	0.0955104i
$262$	−15.5461	+	14.5830i	−0.960442	+	0.900939i
$263$	−5.62576	+	9.74411i	−0.346899	+	0.600847i	−0.985697	−	0.168527i	$-0.946099\pi$
$263$	−5.62576	+	9.74411i	−0.346899	+	0.600847i	0.638798	+	0.769375i	$0.279432\pi$
$264$	−2.95130	+	4.88905i	−0.181640	+	0.300900i
$265$	−6.37451	−	11.0410i	−0.391583	−	0.678242i
$266$	19.8808	+	6.01408i	1.21897	+	0.368747i
$267$	−11.3557	−	9.74144i	−0.694955	−	0.596167i
$268$	−18.5859	−	12.3774i	−1.13532	−	0.756072i
$269$	14.1600			0.863350			0.431675	−	0.902029i	$-0.357923\pi$
$269$	14.1600			0.863350			0.431675	+	0.902029i	$0.357923\pi$
$270$	1.62696	+	8.14564i	0.0990133	+	0.495728i
$271$		−	3.91574i		−	0.237864i	−0.992902	−	0.118932i	$-0.962053\pi$
$271$		−	3.91574i		−	0.237864i	0.992902	−	0.118932i	$-0.0379471\pi$
$272$	4.76031	+	3.62952i	0.288636	+	0.220072i
$273$	−14.7732	+	17.2212i	−0.894113	+	1.04227i
$274$	11.8043	+	3.57088i	0.713121	+	0.215725i
$275$	3.75773	−	2.16953i	0.226600	−	0.130827i
$276$	−25.7393	+	7.24152i	−1.54932	+	0.435888i
$277$	−22.9537	−	13.2523i	−1.37915	−	0.796253i	−0.387094	−	0.922040i	$-0.626521\pi$
$277$	−22.9537	−	13.2523i	−1.37915	−	0.796253i	−0.992057	+	0.125787i	$0.959854\pi$
$278$	2.30074	+	2.45270i	0.137989	+	0.147103i
$279$	−10.1131	−	12.6003i	−0.605457	−	0.754362i
$280$	−8.72510	−	10.5817i	−0.521424	−	0.632378i
$281$	−0.923368	−	0.533106i	−0.0550835	−	0.0318025i	0.472205	−	0.881489i	$-0.343458\pi$
$281$	−0.923368	−	0.533106i	−0.0550835	−	0.0318025i	−0.527289	+	0.849686i	$0.676791\pi$
$282$	4.69082	+	7.35052i	0.279334	+	0.437717i
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	0.914030	−	0.405647i	$-0.132954\pi$
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	−0.808315	+	0.588750i	$0.799620\pi$
$284$	−4.56975	+	2.26229i	−0.271165	+	0.134242i
$285$	6.58838	+	1.23591i	0.390262	+	0.0732090i
$286$	−4.90195	+	1.14695i	−0.289859	+	0.0678205i
$287$	20.9693			1.23778
$288$	−16.3609	−	4.50779i	−0.964077	−	0.265624i
$289$	14.7604			0.868258
$290$	2.20900	−	0.516856i	0.129717	−	0.0303509i
$291$	3.85993	+	10.9759i	0.226273	+	0.643419i
$292$	−12.6630	+	6.26893i	−0.741047	+	0.366861i
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	0.543620	−	0.839331i	$-0.317053\pi$
$293$	−7.78958	−	13.4919i	−0.455072	−	0.788208i	−0.998692	+	0.0511233i	$0.983720\pi$
$294$	−27.9003	+	1.23983i	−1.62718	+	0.0723086i
$295$	8.48839	+	4.90077i	0.494213	+	0.285334i
$296$	5.34775	+	6.48570i	0.310832	+	0.376974i
$297$	2.85545	+	5.34190i	0.165690	+	0.309969i
$298$	17.3078	+	18.4509i	1.00262	+	1.06883i
$299$	−20.4135	−	11.7857i	−1.18054	−	0.681586i
$300$	9.23044	+	9.00338i	0.532920	+	0.519810i
$301$	12.9498	−	7.47659i	0.746416	−	0.430944i
$302$	−3.73819	−	1.13083i	−0.215109	−	0.0650721i
$303$	7.88927	+	22.4335i	0.453227	+	1.28877i
$304$	−8.30361	+	10.8906i	−0.476245	+	0.624621i
$305$			4.12532i			0.236215i
$306$	5.89026	−	2.37024i	0.336724	−	0.135498i
$307$	−0.960690			−0.0548295			−0.0274147	−	0.999624i	$-0.508727\pi$
$307$	−0.960690			−0.0548295			−0.0274147	+	0.999624i	$0.508727\pi$
$308$	−8.32411	−	5.54350i	−0.474310	−	0.315870i
$309$	−2.02124	+	10.7748i	−0.114984	+	0.612957i
$310$	8.24061	+	2.49285i	0.468035	+	0.141584i
$311$	−4.49539	−	7.78624i	−0.254910	−	0.441517i	0.709961	−	0.704241i	$-0.248713\pi$
$311$	−4.49539	−	7.78624i	−0.254910	−	0.441517i	−0.964871	+	0.262724i	$0.915379\pi$
$312$	−7.22612	−	13.0995i	−0.409098	−	0.741616i
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	−0.516051	−	0.856558i	$-0.672599\pi$
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	0.999826	+	0.0186349i	$0.00593201\pi$
$314$	−2.63388	+	2.47070i	−0.148639	+	0.139430i
$315$	−14.3776	+	2.21313i	−0.810084	+	0.124696i
$316$	5.18549	+	0.331871i	0.291707	+	0.0186692i
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	−0.732919	−	0.680316i	$-0.761842\pi$
$317$	3.96528	−	6.86806i	0.222712	−	0.385749i	0.955631	+	0.294568i	$0.0951757\pi$
$318$	12.7376	−	24.5151i	0.714290	−	1.37474i
$319$	1.43269	−	0.827162i	0.0802151	−	0.0463122i
$320$	8.54960	−	2.94623i	0.477937	−	0.164699i
$321$	−13.7355	−	11.7829i	−0.766639	−	0.657660i
$322$	−10.6682	−	45.5948i	−0.594514	−	2.54090i
$323$		−	5.12381i		−	0.285096i
$324$	−12.9831	+	12.4676i	−0.721281	+	0.692643i
$325$			11.3670i			0.630526i
$326$	9.54765	−	2.23394i	0.528796	−	0.123726i
$327$	12.7193	+	10.9112i	0.703378	+	0.603392i
$328$	−4.84043	+	12.9512i	−0.267268	+	0.715111i
$329$	−13.2247	+	7.63528i	−0.729101	+	0.420946i
$330$	−2.86412	−	1.48815i	−0.157665	−	0.0819198i
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	−0.704094	−	0.710107i	$-0.748647\pi$
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	0.967018	+	0.254710i	$0.0819799\pi$
$332$	−9.18377	−	0.587761i	−0.504025	−	0.0322576i
$333$	8.81225	−	1.35646i	0.482908	−	0.0743336i
$334$	−16.1933	−	17.2628i	−0.886058	−	0.944578i
$335$	6.31037	−	10.9299i	0.344773	−	0.597164i
$336$	9.15853	−	28.2736i	0.499639	−	1.54245i
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.783305	+	0.621638i	$0.213532\pi$
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.146702	+	0.989181i	$0.453134\pi$
$338$	−1.50460	+	4.97377i	−0.0818396	+	0.270537i
$339$	−2.63709	+	14.0578i	−0.143227	+	0.763514i
$340$	−1.87533	+	2.81599i	−0.101704	+	0.152719i
$341$	6.27805			0.339975
$342$	5.42263	+	13.4757i	0.293222	+	0.728685i
$343$		−	18.8811i		−	1.01949i
$344$	1.62848	+	9.72402i	0.0878019	+	0.524284i
$345$	−5.01360	−	14.2564i	−0.269923	−	0.767540i
$346$	−8.36906	+	27.6656i	−0.449923	+	1.48731i
$347$	20.9431	−	12.0915i	1.12428	−	0.649105i	0.181792	−	0.983337i	$-0.441810\pi$
$347$	20.9431	−	12.0915i	1.12428	−	0.649105i	0.942491	+	0.334232i	$0.108477\pi$
$348$	3.51924	+	3.43266i	0.188651	+	0.184010i
$349$	9.71845	+	5.61095i	0.520217	+	0.300347i	0.737023	−	0.675867i	$-0.236231\pi$
$349$	9.71845	+	5.61095i	0.520217	+	0.300347i	−0.216807	+	0.976215i	$0.569564\pi$
$350$	−16.4694	+	15.4490i	−0.880324	+	0.825784i
$351$	−15.8595	−	0.518852i	−0.846515	−	0.0276943i
$352$	5.34530	−	3.86156i	0.284906	−	0.205822i
$353$	−5.85176	−	3.37852i	−0.311458	−	0.179820i	0.336121	−	0.941819i	$-0.390885\pi$
$353$	−5.85176	−	3.37852i	−0.311458	−	0.179820i	−0.647579	+	0.761999i	$0.724218\pi$
$354$	0.942916	+	21.2187i	0.0501154	+	1.12776i
$355$	−1.44097	−	2.49583i	−0.0764786	−	0.132465i
$356$	7.66481	+	15.4827i	0.406234	+	0.820580i
$357$	3.68887	+	10.4895i	0.195236	+	0.555163i
$358$	−1.31449	−	5.61800i	−0.0694728	−	0.296921i
$359$	20.3395			1.07348			0.536739	−	0.843748i	$-0.319656\pi$
$359$	20.3395			1.07348			0.536739	+	0.843748i	$0.319656\pi$
$360$	1.95195	−	9.39084i	0.102877	−	0.494941i
$361$	−7.27775			−0.383039
$362$	−7.19219	−	30.7388i	−0.378013	−	1.61559i
$363$	16.4126	+	3.07884i	0.861440	+	0.161597i
$364$	23.4799	−	11.6239i	1.23068	−	0.609259i
$365$	−3.99300	−	6.91608i	−0.209003	−	0.362004i
$366$	−7.53573	+	4.80901i	−0.393899	+	0.251371i
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	0.773657	−	0.633605i	$-0.218425\pi$
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	−0.161889	+	0.986809i	$0.551759\pi$
$368$	30.6231	+	3.93588i	1.59634	+	0.205172i
$369$	9.17925	+	11.4368i	0.477853	+	0.595375i
$370$	−3.46511	+	3.25043i	−0.180143	+	0.168982i
$371$	41.8998	+	24.1908i	2.17533	+	1.25593i
$372$	5.05263	+	17.9591i	0.261967	+	0.931136i
$373$	23.0364	−	13.3001i	1.19278	−	0.688651i	0.233843	−	0.972274i	$-0.424870\pi$
$373$	23.0364	−	13.3001i	1.19278	−	0.688651i	0.958936	+	0.283623i	$0.0915364\pi$
$374$	−0.714355	+	2.36144i	−0.0369384	+	0.122107i
$375$	−11.1188	+	12.9613i	−0.574175	+	0.669319i
$376$	−1.66304	−	9.93040i	−0.0857650	−	0.512121i
$377$			4.33381i			0.223203i
$378$	−20.8031	−	23.6836i	−1.06999	−	1.21815i
$379$	−28.5030			−1.46410			−0.732050	−	0.681251i	$-0.761436\pi$
$379$	−28.5030			−1.46410			−0.732050	+	0.681251i	$0.761436\pi$
$380$	−6.44243	−	4.29039i	−0.330490	−	0.220092i
$381$	−3.66457	−	3.14365i	−0.187742	−	0.161054i
$382$	−5.95784	+	19.6948i	−0.304830	+	1.00768i
$383$	−10.0515	−	17.4097i	−0.513606	−	0.889592i	−0.999875	−	0.0157832i	$-0.994976\pi$
$383$	−10.0515	−	17.4097i	−0.513606	−	0.889592i	0.486269	−	0.873809i	$-0.338357\pi$
$384$	15.3484	+	12.1830i	0.783245	+	0.621713i
$385$	2.82624	−	4.89519i	0.144038	−	0.249482i
$386$	4.24800	+	4.52856i	0.216217	+	0.230498i
$387$	9.74654	+	3.79006i	0.495444	+	0.192660i
$388$	0.858068	−	13.4073i	0.0435618	−	0.680654i
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	−0.892130	−	0.451778i	$-0.850790\pi$
$389$	−1.08110	+	1.87253i	−0.0548142	+	0.0949409i	0.837316	+	0.546719i	$0.184123\pi$
$390$	7.12774	−	4.54864i	0.360927	−	0.230330i
$391$	−10.0038	+	5.77570i	−0.505914	+	0.292090i
$392$	30.2075	+	11.2899i	1.52571	+	0.570224i
$393$	4.81323	−	25.6583i	0.242795	−	1.29429i
$394$	10.5992	−	2.47999i	0.533982	−	0.124940i
$395$			2.93677i			0.147765i
$396$	−0.620395	−	6.96667i	−0.0311760	−	0.350088i
$397$			18.8504i			0.946076i	0.881042	+	0.473038i	$0.156843\pi$
$397$			18.8504i			0.946076i	−0.881042	+	0.473038i	$0.843157\pi$
$398$	6.75928	+	28.8885i	0.338812	+	1.44805i
$399$	−23.9979	+	8.43940i	−1.20140	+	0.422499i
$400$	−5.74004	−	13.7381i	−0.287002	−	0.686903i
$401$	−15.0668	+	8.69883i	−0.752401	+	0.434399i	−0.826561	−	0.562848i	$-0.809706\pi$
$401$	−15.0668	+	8.69883i	−0.752401	+	0.434399i	0.0741601	+	0.997246i	$0.476372\pi$
$402$	27.3218	−	1.21413i	1.36269	−	0.0605551i
$403$	−8.22326	+	14.2431i	−0.409630	+	0.709500i
$404$	1.75380	−	27.4031i	0.0872546	−	1.36335i
$405$	−7.50079	−	6.87283i	−0.372717	−	0.341513i
$406$	−6.27917	+	5.89015i	−0.311630	+	0.292323i
$407$	−1.73225	+	3.00034i	−0.0858643	+	0.148721i
$408$	−7.33011	−	0.142985i	−0.362894	−	0.00707879i
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	−0.999950	−	0.0100370i	$-0.996805\pi$
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	0.491282	−	0.871000i	$-0.336528\pi$
$410$	−7.47965	−	2.26265i	−0.369393	−	0.111744i
$411$	−14.2488	+	5.01092i	−0.702841	+	0.247170i
$412$	7.01660	−	10.5361i	0.345683	−	0.519077i
$413$	−37.1962			−1.83030
$414$	20.1977	−	25.7775i	0.992664	−	1.26689i
$415$		−	5.20117i		−	0.255316i
$416$	1.75928	+	17.1850i	0.0862557	+	0.842565i
$417$	−4.04810	−	0.759379i	−0.198236	−	0.0371870i
$418$	−5.40251	−	1.63430i	−0.264246	−	0.0799363i
$419$	−24.1959	+	13.9695i	−1.18205	+	0.682455i	−0.956487	−	0.291774i	$-0.905755\pi$
$419$	−24.1959	+	13.9695i	−1.18205	+	0.682455i	−0.225560	+	0.974229i	$0.572421\pi$
$420$	16.2778	+	4.14510i	0.794277	+	0.202260i
$421$	6.27826	+	3.62475i	0.305983	+	0.176660i	0.645128	−	0.764075i	$-0.276804\pi$
$421$	6.27826	+	3.62475i	0.305983	+	0.176660i	−0.339144	+	0.940734i	$0.610137\pi$
$422$	4.61481	+	4.91960i	0.224645	+	0.239482i
$423$	−9.95340	−	3.87050i	−0.483951	−	0.188190i
$424$	−24.6128	+	20.2944i	−1.19530	+	0.985581i
$425$	4.82418	+	2.78524i	0.234007	+	0.135104i
$426$	2.87935	−	5.54167i	0.139505	−	0.268495i
$427$	−7.82766	−	13.5579i	−0.378807	−	0.656113i
$428$	9.27112	+	18.7274i	0.448137	+	0.905221i
$429$	4.01455	−	4.67978i	0.193824	−	0.225942i
$430$	−5.42589	+	1.26954i	−0.261660	+	0.0612225i
$431$	−37.7004			−1.81596			−0.907982	−	0.419009i	$-0.862377\pi$
$431$	−37.7004			−1.81596			−0.907982	+	0.419009i	$0.862377\pi$
$432$	19.4297	−	7.38155i	0.934811	−	0.355145i
$433$	36.1185			1.73575			0.867873	−	0.496787i	$-0.165487\pi$
$433$	36.1185			1.73575			0.867873	+	0.496787i	$0.165487\pi$
$434$	−31.8129	+	7.44351i	−1.52707	+	0.357300i
$435$	−1.80910	+	2.10888i	−0.0867397	+	0.101113i
$436$	−8.58523	−	17.3419i	−0.411158	−	0.830525i
$437$	−13.2137	−	22.8867i	−0.632095	−	1.09482i
$438$	7.97884	−	15.3563i	0.381244	−	0.733751i
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	0.268993	−	0.963142i	$-0.413309\pi$
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	−0.699609	+	0.714526i	$0.746642\pi$
$440$	2.37101	+	2.87554i	0.113033	+	0.137086i
$441$	26.6753	−	21.4098i	1.27025	−	1.01951i
$442$	−4.42175	−	4.71379i	−0.210321	−	0.224212i
$443$	−30.7905	−	17.7769i	−1.46290	−	0.844606i	−0.463756	−	0.885963i	$-0.653498\pi$
$443$	−30.7905	−	17.7769i	−1.46290	−	0.844606i	−0.999144	+	0.0413574i	$0.986832\pi$
$444$	−9.97695	−	2.54060i	−0.473485	−	0.120571i
$445$	−8.45606	+	4.88211i	−0.400856	+	0.231434i
$446$	−19.5806	−	5.92327i	−0.927167	−	0.280475i
$447$	−30.4526	−	5.71259i	−1.44036	−	0.270196i
$448$	−22.5079	+	25.9054i	−1.06340	+	1.22391i
$449$		−	16.7750i		−	0.791662i	−0.918323	−	0.395831i	$-0.870457\pi$
$449$		−	16.7750i		−	0.791662i	0.918323	−	0.395831i	$-0.129543\pi$
$450$	−15.6354	−	2.21972i	−0.737060	−	0.104639i
$451$	−5.69832			−0.268323
$452$	9.15449	−	13.7464i	0.430591	−	0.646574i
$453$	4.51234	−	1.58687i	0.212008	−	0.0745575i
$454$	0.878149	+	0.265647i	0.0412136	+	0.0124674i
$455$	7.40386	+	12.8239i	0.347098	+	0.601192i
$456$	0.327120	−	16.7698i	0.0153188	−	0.785319i
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	−0.881479	−	0.472223i	$-0.843452\pi$
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	0.849697	+	0.527272i	$0.176785\pi$
$458$	−14.2929	+	13.4074i	−0.667866	+	0.626489i
$459$	−4.10624	+	6.60368i	−0.191663	+	0.308233i
$460$	−1.11453	+	17.4146i	−0.0519653	+	0.811958i
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	−0.723332	−	0.690500i	$-0.757391\pi$
$461$	5.07410	−	8.78860i	0.236324	−	0.409326i	0.959657	+	0.281174i	$0.0907238\pi$
$462$	12.2367	−	0.543773i	0.569301	−	0.0252986i
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.150012	−	0.988684i	$-0.452069\pi$
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.931232	+	0.364428i	$0.118735\pi$
$464$	−2.18847	−	5.23783i	−0.101597	−	0.243160i
$465$	−9.94715	+	3.49814i	−0.461288	+	0.162223i
$466$	7.45153	+	31.8472i	0.345186	+	1.47529i
$467$		−	31.4118i		−	1.45356i	−0.686868	−	0.726782i	$-0.741015\pi$
$467$		−	31.4118i		−	1.45356i	0.686868	−	0.726782i	$-0.258985\pi$
$468$	16.6180	+	7.71775i	0.768168	+	0.356753i
$469$			47.8949i			2.21158i
$470$	5.54105	−	1.29648i	0.255590	−	0.0598023i
$471$	0.815476	−	4.34713i	0.0375751	−	0.200305i
$472$	8.58614	−	22.9734i	0.395209	−	1.05743i
$473$	−3.51906	+	2.03173i	−0.161807	+	0.0934191i
$474$	−5.36460	+	3.42348i	−0.246404	+	0.157246i
$475$	−6.37208	+	11.0368i	−0.292371	+	0.506402i
$476$	0.820042	−	12.8132i	0.0375866	−	0.587290i
$477$	5.14767	+	33.4419i	0.235696	+	1.53120i
$478$	14.3984	+	15.3494i	0.658568	+	0.702064i
$479$	−2.42488	+	4.20001i	−0.110796	+	0.191904i	−0.916091	−	0.400970i	$-0.868673\pi$
$479$	−2.42488	+	4.20001i	−0.110796	+	0.191904i	0.805296	+	0.592873i	$0.202007\pi$
$480$	−6.31760	+	9.09680i	−0.288358	+	0.415210i
$481$	−4.53794	−	7.85995i	−0.206912	−	0.358383i
$482$	−4.81521	+	15.9176i	−0.219327	+	0.725028i
$483$	43.5283	+	37.3407i	1.98061	+	1.69906i
$484$	−16.0491	−	10.6880i	−0.729503	−	0.485818i
$485$	7.59316			0.344788
$486$	3.81070	−	21.7136i	0.172857	−	0.984947i
$487$		−	23.2664i		−	1.05430i	−0.849772	−	0.527150i	$-0.823261\pi$
$487$		−	23.2664i		−	1.05430i	0.849772	−	0.527150i	$-0.176739\pi$
$488$	10.1806	−	1.70495i	0.460855	−	0.0771794i
$489$	−7.81923	+	9.11493i	−0.353598	+	0.412191i
$490$	−5.27743	+	17.4456i	−0.238410	+	0.788112i
$491$	9.48139	−	5.47408i	0.427889	−	0.247042i	−0.270558	−	0.962704i	$-0.587208\pi$
$491$	9.48139	−	5.47408i	0.427889	−	0.247042i	0.698447	+	0.715662i	$0.253875\pi$
$492$	−4.58606	−	16.3007i	−0.206755	−	0.734893i
$493$	1.83929	+	1.06191i	0.0828373	+	0.0478262i
$494$	10.7842	−	10.1161i	0.485205	−	0.455144i
$495$	3.90704	−	0.601407i	0.175609	−	0.0270312i
$496$	2.74618	−	21.3667i	0.123307	−	0.959394i
$497$	9.47149	+	5.46837i	0.424855	+	0.245290i
$498$	9.50099	−	6.06316i	0.425749	−	0.271697i
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.861694	+	0.507429i	$0.169404\pi$
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.00859924	+	0.999963i	$0.497263\pi$
$500$	17.6719	−	8.74859i	0.790310	−	0.391249i
$501$	28.4916	+	5.34473i	1.27291	+	0.238785i
$502$	1.77727	+	7.59591i	0.0793237	+	0.339022i
$503$	9.97588			0.444803			0.222401	−	0.974955i	$-0.428610\pi$
$503$	9.97588			0.444803			0.222401	+	0.974955i	$0.428610\pi$
$504$	11.4037	+	34.5668i	0.507962	+	1.53973i
$505$	15.5196			0.690612
$506$	2.89903	+	12.3902i	0.128878	+	0.550811i
$507$	−2.11137	−	6.00378i	−0.0937692	−	0.266637i
$508$	2.47350	+	4.99639i	0.109744	+	0.221679i
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	0.985719	−	0.168396i	$-0.0538589\pi$
$509$	7.82922	+	13.5606i	0.347024	+	0.601063i	−0.638695	+	0.769460i	$0.720526\pi$
$510$	−0.183955	−	4.13959i	−0.00814566	−	0.183304i
$511$	26.2460	+	15.1532i	1.16106	+	0.670336i
$512$	−10.8043	−	19.8813i	−0.477486	−	0.878640i
$513$	−15.1079	−	9.39426i	−0.667030	−	0.414767i
$514$	20.1511	−	18.9026i	0.888826	−	0.833759i
$515$	6.19601	+	3.57727i	0.273029	+	0.157633i
$516$	−8.64418	−	8.43154i	−0.380539	−	0.371178i
$517$	3.59375	−	2.07485i	0.158053	−	0.0912519i
$518$	5.22053	−	17.2575i	0.229377	−	0.758251i
$519$	−11.7441	−	33.3949i	−0.515508	−	1.46587i
$520$	−9.62942	+	1.61264i	−0.422278	+	0.0707189i
$521$			9.78813i			0.428826i	0.976743	+	0.214413i	$0.0687838\pi$
$521$			9.78813i			0.428826i	−0.976743	+	0.214413i	$0.931216\pi$
$522$	−5.96121	−	0.846301i	−0.260915	−	0.0370416i
$523$	−32.9015			−1.43868			−0.719342	−	0.694656i	$-0.755557\pi$
$523$	−32.9015			−1.43868			−0.719342	+	0.694656i	$0.755557\pi$
$524$	−16.7088	+	25.0899i	−0.729928	+	1.09606i
$525$	5.09907	−	27.1821i	0.222542	−	1.18632i
$526$	−4.60732	+	15.2304i	−0.200889	+	0.664079i
$527$	4.02989	+	6.97997i	0.175545	+	0.304052i
$528$	−2.48879	+	7.68322i	−0.108311	+	0.334369i
$529$	−18.2896	+	31.6786i	−0.795201	+	1.37733i
$530$	−12.3352	−	13.1499i	−0.535806	−	0.571194i
$531$	−16.2825	−	20.2870i	−0.706601	−	0.880382i
$532$	29.3140	+	1.87609i	1.27092	+	0.0813389i
$533$	7.46391	−	12.9279i	0.323298	−	0.559968i
$534$	−18.7756	−	9.75547i	−0.812501	−	0.422161i
$535$	−10.2282	+	5.90525i	−0.442203	+	0.255306i
$536$	−29.5811	−	11.0558i	−1.27771	−	0.477536i
$537$	5.36338	+	4.60097i	0.231447	+	0.198546i
$538$	19.4986	−	4.56225i	0.840646	−	0.196692i
$539$			13.2908i			0.572476i
$540$	4.86482	+	10.6925i	0.209349	+	0.460134i
$541$		−	26.4228i		−	1.13601i	−0.823027	−	0.568003i	$-0.807716\pi$
$541$		−	26.4228i		−	1.13601i	0.823027	−	0.568003i	$-0.192284\pi$
$542$	−1.26162	−	5.39206i	−0.0541913	−	0.231609i
$543$	29.3456	+	25.1741i	1.25934	+	1.08032i
$544$	7.72446	+	3.46419i	0.331183	+	0.148526i
$545$	9.47149	−	5.46837i	0.405714	−	0.234239i
$546$	−14.7945	+	28.4738i	−0.633144	+	1.21857i
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	−0.182674	−	0.983174i	$-0.558475\pi$
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	0.942790	−	0.333387i	$-0.108191\pi$
$548$	17.4052	+	1.11393i	0.743515	+	0.0475849i
$549$	3.96803	−	10.2042i	0.169351	−	0.435504i
$550$	4.47547	−	4.19820i	0.190835	−	0.179012i
$551$	−2.42944	+	4.20792i	−0.103498	+	0.179263i
$552$	−33.1104	+	18.2648i	−1.40927	+	0.777399i
$553$	−5.57242	−	9.65172i	−0.236964	−	0.410433i
$554$	−35.8775	−	10.8532i	−1.52429	−	0.461109i
$555$	1.07283	−	5.71905i	0.0455392	−	0.242760i
$556$	3.95842	+	2.63614i	0.167874	+	0.111797i
$557$	−18.4413			−0.781384			−0.390692	−	0.920522i	$-0.627764\pi$
$557$	−18.4413			−0.781384			−0.390692	+	0.920522i	$0.627764\pi$
$558$	−17.9857	−	14.0926i	−0.761397	−	0.596586i
$559$		−	10.6450i		−	0.450236i
$560$	−15.4240	−	11.7601i	−0.651783	−	0.496955i
$561$	−1.00244	−	2.85047i	−0.0423228	−	0.120347i
$562$	−1.44326	−	0.436597i	−0.0608803	−	0.0184168i
$563$	35.4943	−	20.4926i	1.49591	−	0.863661i	0.495917	−	0.868370i	$-0.334832\pi$
$563$	35.4943	−	20.4926i	1.49591	−	0.863661i	0.999989	+	0.00470871i	$0.00149884\pi$
$564$	8.82765	+	8.61049i	0.371711	+	0.362567i
$565$	8.08387	+	4.66722i	0.340091	+	0.196352i
$566$	3.44134	+	3.66862i	0.144650	+	0.154204i
$567$	37.6924	+	8.35509i	1.58293	+	0.350881i
$568$	−5.56375	+	4.58756i	−0.233450	+	0.192490i
$569$	−3.72340	−	2.14971i	−0.156093	−	0.0901205i	0.419919	−	0.907562i	$-0.362059\pi$
$569$	−3.72340	−	2.14971i	−0.156093	−	0.0901205i	−0.576012	+	0.817441i	$0.695392\pi$
$570$	9.47056	−	0.420852i	0.396678	−	0.0176276i
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	0.816929	−	0.576738i	$-0.195675\pi$
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	−0.907934	+	0.419112i	$0.862341\pi$
$572$	−6.38056	+	3.15875i	−0.266785	+	0.132074i
$573$	−8.36048	−	23.7734i	−0.349264	−	0.993150i
$574$	28.8752	−	6.75616i	1.20523	−	0.281997i
$575$	28.7312			1.19817
$576$	−23.9817	−	0.935955i	−0.999239	−	0.0389981i
$577$	12.5475			0.522361			0.261180	−	0.965290i	$-0.415888\pi$
$577$	12.5475			0.522361			0.261180	+	0.965290i	$0.415888\pi$
$578$	20.3254	−	4.75569i	0.845424	−	0.197810i
$579$	−7.47423	−	1.40209i	−0.310619	−	0.0582687i
$580$	2.87531	−	1.42345i	0.119391	−	0.0591054i
$581$	9.86905	+	17.0937i	0.409437	+	0.709166i
$582$	8.85157	+	13.8704i	0.366909	+	0.574948i
$583$	−11.3861	−	6.57376i	−0.471563	−	0.272257i
$584$	−15.4175	+	12.7124i	−0.637979	+	0.526042i
$585$	−3.75319	+	9.65172i	−0.155175	+	0.399049i
$586$	−15.0734	−	16.0690i	−0.622678	−	0.663803i
$587$	−8.02388	−	4.63259i	−0.331181	−	0.191207i	0.325184	−	0.945651i	$-0.394574\pi$
$587$	−8.02388	−	4.63259i	−0.331181	−	0.191207i	−0.656365	+	0.754443i	$0.727907\pi$
$588$	−38.0199	+	10.6966i	−1.56792	+	0.441119i
$589$	−15.9688	+	9.21958i	−0.657982	+	0.379886i
$590$	13.2677	+	4.01358i	0.546222	+	0.165236i
$591$	−8.68044	+	10.1188i	−0.357066	+	0.416234i
$592$	9.45362	+	7.20796i	0.388542	+	0.296245i
$593$			11.1342i			0.457228i	0.973517	+	0.228614i	$0.0734193\pi$
$593$			11.1342i			0.457228i	−0.973517	+	0.228614i	$0.926581\pi$
$594$	5.65314	+	6.43592i	0.231951	+	0.264069i
$595$	7.25666			0.297494
$596$	29.7780	+	19.8309i	1.21976	+	0.812305i
$597$	−27.5792	−	23.6588i	−1.12874	−	0.968291i
$598$	−31.9071	−	9.65214i	−1.30478	−	0.394705i
$599$	22.8693	+	39.6108i	0.934415	+	1.61845i	0.775675	+	0.631133i	$0.217410\pi$
$599$	22.8693	+	39.6108i	0.934415	+	1.61845i	0.158740	+	0.987320i	$0.449257\pi$
$600$	15.6114	+	9.42387i	0.637331	+	0.384728i
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	−0.998907	−	0.0467325i	$-0.985119\pi$
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	0.539925	+	0.841713i	$0.318453\pi$
$602$	15.4233	−	14.4678i	0.628608	−	0.589663i
$603$	−26.1222	+	20.9658i	−1.06378	+	0.853795i
$604$	−5.51192	−	0.352763i	−0.224277	−	0.0143537i
$605$	5.44905	−	9.43803i	0.221535	−	0.383710i
$606$	18.0916	+	28.3496i	0.734922	+	1.15162i
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.909366	−	0.415997i	$-0.863433\pi$
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.0944185	+	0.995533i	$0.530099\pi$
$608$	−7.92538	+	17.6720i	−0.321417	+	0.716695i
$609$	1.94409	−	10.3636i	0.0787786	−	0.419953i
$610$	1.32915	+	5.68066i	0.0538157	+	0.230003i
$611$			10.8709i			0.439791i
$612$	7.34735	−	5.16167i	0.296999	−	0.208648i
$613$		−	40.4574i		−	1.63406i	−0.576596	−	0.817030i	$-0.695619\pi$
$613$		−	40.4574i		−	1.63406i	0.576596	−	0.817030i	$-0.304381\pi$
$614$	−1.32289	+	0.309527i	−0.0533876	+	0.0124915i
$615$	9.02860	−	3.17512i	0.364068	−	0.128033i
$616$	−13.2486	−	4.95156i	−0.533800	−	0.199504i
$617$	−31.6715	+	18.2855i	−1.27505	+	0.736148i	−0.975933	−	0.218070i	$-0.930024\pi$
$617$	−31.6715	+	18.2855i	−1.27505	+	0.736148i	−0.299112	+	0.954218i	$0.596691\pi$
$618$	0.688272	+	15.4884i	0.0276864	+	0.623034i
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	−0.0878927	−	0.996130i	$-0.528013\pi$
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	0.906620	−	0.421948i	$-0.138653\pi$
$620$	12.1507	+	0.777643i	0.487983	+	0.0312309i
$621$	−1.31145	+	40.0864i	−0.0526267	+	1.60861i
$622$	−8.69892	−	9.27345i	−0.348795	−	0.371831i
$623$	18.5273	−	32.0902i	0.742279	−	1.28567i
$624$	−14.1711	−	15.7102i	−0.567298	−	0.628910i
$625$	−3.73321	−	6.46610i	−0.149328	−	0.258644i
$626$	7.00943	−	23.1711i	0.280153	−	0.926103i
$627$	6.52132	−	2.29337i	0.260436	−	0.0915884i
$628$	−2.83087	+	4.25083i	−0.112964	+	0.169627i
$629$	−4.44772			−0.177342
$630$	−19.0852	+	7.67987i	−0.760372	+	0.305973i
$631$			15.0916i			0.600788i	0.953815	+	0.300394i	$0.0971182\pi$
$631$			15.0916i			0.600788i	−0.953815	+	0.300394i	$0.902882\pi$
$632$	7.24746	−	1.21373i	0.288289	−	0.0482797i
$633$	−8.11963	−	1.52316i	−0.322726	−	0.0605400i
$634$	3.24744	−	10.7351i	0.128972	−	0.426344i
$635$	−2.72884	+	1.57550i	−0.108291	+	0.0625218i
$636$	9.64139	−	37.8619i	0.382306	−	1.50132i
$637$	−30.1531	−	17.4089i	−1.19471	−	0.689765i
$638$	1.70634	−	1.60062i	0.0675546	−	0.0633693i
$639$	1.16364	+	7.55957i	0.0460328	+	0.299052i
$640$	10.8237	−	6.81165i	0.427846	−	0.269254i
$641$	−26.9377	−	15.5525i	−1.06398	−	0.614287i	−0.137447	−	0.990509i	$-0.543890\pi$
$641$	−26.9377	−	15.5525i	−1.06398	−	0.614287i	−0.926529	+	0.376222i	$0.877223\pi$
$642$	−22.7104	−	11.7999i	−0.896309	−	0.465706i
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	0.825429	−	0.564505i	$-0.190933\pi$
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	−0.901591	+	0.432590i	$0.857600\pi$
$644$	−29.3806	−	59.3479i	−1.15776	−	2.33863i
$645$	4.44363	−	5.17997i	0.174968	−	0.203961i
$646$	−1.65085	−	7.05560i	−0.0649520	−	0.277599i
$647$	−24.1359			−0.948879			−0.474440	−	0.880288i	$-0.657349\pi$
$647$	−24.1359			−0.948879			−0.474440	+	0.880288i	$0.657349\pi$
$648$	−13.8610	+	21.3512i	−0.544512	+	0.838753i
$649$	10.1079			0.396770
$650$	3.66235	+	15.6526i	0.143649	+	0.613944i
$651$	26.0538	−	30.3711i	1.02113	−	1.19034i
$652$	12.4276	−	6.15237i	0.486702	−	0.240945i
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	0.986667	+	0.162750i	$0.0520364\pi$
$653$	16.2083	+	28.0736i	0.634279	+	1.09860i	−0.352388	+	0.935854i	$0.614630\pi$
$654$	21.0303	+	10.9269i	0.822349	+	0.427277i
$655$	−14.7547	−	8.51864i	−0.576515	−	0.332851i
$656$	−2.49259	+	19.3937i	−0.0973195	+	0.757195i
$657$	3.22450	+	20.9480i	0.125800	+	0.817259i
$658$	−15.7507	+	14.7748i	−0.614025	+	0.575984i
$659$	19.7202	+	11.3855i	0.768191	+	0.443515i	0.832229	−	0.554432i	$-0.187064\pi$
$659$	19.7202	+	11.3855i	0.768191	+	0.443515i	−0.0640377	+	0.997947i	$0.520398\pi$
$660$	−4.42343	−	1.12641i	−0.172182	−	0.0438455i
$661$	−25.6004	+	14.7804i	−0.995740	+	0.574891i	−0.906985	−	0.421163i	$-0.861622\pi$
$661$	−25.6004	+	14.7804i	−0.995740	+	0.574891i	−0.0887549	+	0.996053i	$0.528289\pi$
$662$	3.91752	−	12.9502i	0.152259	−	0.503322i
$663$	7.77995	+	1.45944i	0.302148	+	0.0566798i
$664$	−12.8356	+	2.14958i	−0.498119	+	0.0834200i
$665$			16.6018i			0.643790i
$666$	11.6976	−	4.70712i	0.453274	−	0.182397i
$667$	10.9542			0.424147
$668$	−27.8605	−	18.5539i	−1.07795	−	0.717872i
$669$	23.6355	−	8.31197i	0.913802	−	0.321359i
$670$	5.16800	−	17.0839i	0.199657	−	0.660007i
$671$	2.12713	+	3.68430i	0.0821171	+	0.142231i
$672$	3.50197	−	41.8841i	0.135091	−	1.61572i
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	−0.641961	−	0.766738i	$-0.721879\pi$
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	0.984995	+	0.172585i	$0.0552121\pi$
$674$	33.0369	+	35.2188i	1.27253	+	1.35658i
$675$	17.0574	−	9.11782i	0.656539	−	0.350945i
$676$	−0.469360	+	7.33376i	−0.0180523	+	0.282068i
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.0320192	+	0.999487i	$0.510194\pi$
$677$	−22.9383	+	39.7303i	−0.881591	+	1.52696i	−0.849572	+	0.527473i	$0.823140\pi$
$678$	0.897982	+	20.2075i	0.0344868	+	0.776065i
$679$	−24.9550	+	14.4078i	−0.957684	+	0.552919i
$680$	−1.67508	+	4.48191i	−0.0642365	+	0.171873i
$681$	−1.06000	+	0.372775i	−0.0406195	+	0.0142848i
$682$	8.64502	−	2.02274i	0.331035	−	0.0774548i
$683$			2.20513i			0.0843769i	0.999110	+	0.0421884i	$0.0134330\pi$
$683$			2.20513i			0.0843769i	−0.999110	+	0.0421884i	$0.986567\pi$
$684$	11.8089	+	16.8093i	0.451524	+	0.642718i
$685$			9.85735i			0.376630i
$686$	−6.08336	−	25.9997i	−0.232264	−	0.992675i
$687$	4.42524	−	23.5900i	0.168833	−	0.900015i
$688$	5.37546	+	12.8655i	0.204938	+	0.490493i
$689$	29.8280	−	17.2212i	1.13636	−	0.656075i
$690$	−11.4972	−	18.0161i	−0.437689	−	0.685860i
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	−0.992446	−	0.122684i	$-0.960850\pi$
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	0.602471	+	0.798141i	$0.294183\pi$
$692$	−2.61073	+	40.7926i	−0.0992449	+	1.55070i
$693$	−11.6994	+	9.39001i	−0.444422	+	0.356697i
$694$	24.9433	−	23.3980i	0.946835	−	0.888175i
$695$	−1.34398	+	2.32784i	−0.0509801	+	0.0883001i
$696$	5.95205	+	3.59298i	0.225612	+	0.136192i
$697$	−3.65776	−	6.33542i	−0.138547	−	0.239971i
$698$	15.1903	+	4.59519i	0.574963	+	0.173931i
$699$	−30.4038	−	26.0819i	−1.14998	−	0.986506i
$700$	−17.7011	+	26.5799i	−0.669039	+	1.00463i
$701$	26.6854			1.00789			0.503947	−	0.863734i	$-0.331881\pi$
$701$	26.6854			1.00789			0.503947	+	0.863734i	$0.331881\pi$
$702$	−22.0060	+	4.39533i	−0.830563	+	0.165891i
$703$		−	10.1755i		−	0.383776i
$704$	6.11643	−	7.03968i	0.230522	−	0.265318i
$705$	−4.53794	+	5.28991i	−0.170909	+	0.199230i
$706$	−9.14655	−	2.76690i	−0.344235	−	0.104134i
$707$	−51.0052	+	29.4479i	−1.91825	+	1.10750i
$708$	8.13493	+	28.9148i	0.305729	+	1.08669i
$709$	−37.8684	−	21.8633i	−1.42218	−	0.821095i	−0.425693	−	0.904868i	$-0.639970\pi$
$709$	−37.8684	−	21.8633i	−1.42218	−	0.821095i	−0.996485	+	0.0837727i	$0.973303\pi$
$710$	−2.78838	−	2.97254i	−0.104646	−	0.111558i
$711$	2.82479	−	7.26425i	0.105938	−	0.272431i
$712$	15.5430	+	18.8504i	0.582500	+	0.706450i
$713$	36.0009	+	20.7851i	1.34825	+	0.778410i
$714$	8.45930	+	13.2557i	0.316581	+	0.496084i
$715$	−2.01197	−	3.48483i	−0.0752433	−	0.130325i
$716$	−3.62016	−	7.31260i	−0.135292	−	0.273285i
$717$	−25.3336	−	4.75232i	−0.946101	−	0.177479i
$718$	28.0080	−	6.55324i	1.04525	−	0.244565i
$719$	−13.9253			−0.519327			−0.259663	−	0.965699i	$-0.583612\pi$
$719$	−13.9253			−0.519327			−0.259663	+	0.965699i	$0.583612\pi$
$720$	−0.337786	−	13.5603i	−0.0125885	−	0.505363i
$721$	−27.1510			−1.01115
$722$	−10.0216	+	2.34484i	−0.372966	+	0.0872658i
$723$	−6.75705	−	19.2140i	−0.251297	−	0.714577i
$724$	−19.8076	−	40.0107i	−0.736145	−	1.48699i
$725$	−2.64124	−	4.57475i	−0.0980930	−	0.169902i
$726$	23.5926	−	1.04841i	0.875602	−	0.0389100i
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.948259	−	0.317497i	$-0.102842\pi$
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.199169	+	0.979965i	$0.436176\pi$
$728$	28.5872	−	23.5714i	1.05951	−	0.873616i
$729$	11.9428	+	24.2151i	0.442326	+	0.896854i
$730$	−7.72676	−	8.23708i	−0.285980	−	0.304868i
$731$	−4.51778	−	2.60834i	−0.167096	−	0.0964730i
$732$	−8.82744	+	9.05007i	−0.326272	+	0.334500i
$733$	30.2141	−	17.4441i	1.11598	−	0.644312i	0.175610	−	0.984460i	$-0.443810\pi$
$733$	30.2141	−	17.4441i	1.11598	−	0.644312i	0.940372	+	0.340148i	$0.110477\pi$
$734$	18.3185	+	5.54148i	0.676148	+	0.204540i
$735$	−7.40567	−	21.0584i	−0.273162	−	0.776751i
$736$	43.4369	−	4.44676i	1.60110	−	0.163910i
$737$		−	13.0152i		−	0.479422i
$738$	16.3249	+	12.7912i	0.600928	+	0.470852i
$739$	13.1128			0.482361			0.241181	−	0.970480i	$-0.422465\pi$
$739$	13.1128			0.482361			0.241181	+	0.970480i	$0.422465\pi$
$740$	−3.72427	+	5.59236i	−0.136907	+	0.205579i
$741$	−3.33890	+	17.7990i	−0.122657	+	0.653862i
$742$	65.4911	+	19.8115i	2.40425	+	0.727305i
$743$	−11.1665	−	19.3410i	−0.409660	−	0.709551i	0.585192	−	0.810895i	$-0.301019\pi$
$743$	−11.1665	−	19.3410i	−0.409660	−	0.709551i	−0.994851	+	0.101344i	$0.967686\pi$
$744$	12.7439	+	23.1022i	0.467213	+	0.846967i
$745$	−10.1104	+	17.5117i	−0.370415	+	0.641578i
$746$	27.4365	−	25.7367i	1.00452	−	0.942286i
$747$	−5.00286	+	12.8654i	−0.183045	+	0.470719i
$748$	−0.222843	+	3.48192i	−0.00814794	+	0.127312i
$749$	22.4100	−	38.8153i	0.818844	−	1.41828i
$750$	−11.1349	+	21.4304i	−0.406588	+	0.782529i
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	−0.622174	−	0.782879i	$-0.713750\pi$
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	0.366906	+	0.930258i	$0.380417\pi$
$752$	−5.48955	−	13.1386i	−0.200183	−	0.479114i
$753$	−7.25165	−	6.22082i	−0.264265	−	0.226699i
$754$	1.39632	+	5.96776i	0.0508511	+	0.217333i
$755$		−	3.12165i		−	0.113608i
$756$	−36.2770	−	25.9103i	−1.31938	−	0.942348i
$757$			12.7751i			0.464319i	0.972678	+	0.232160i	$0.0745792\pi$
$757$			12.7751i			0.464319i	−0.972678	+	0.232160i	$0.925421\pi$
$758$	−39.2493	+	9.18346i	−1.42560	+	0.333558i
$759$	−11.8286	−	10.1472i	−0.429352	−	0.368319i
$760$	−10.2537	−	3.83226i	−0.371941	−	0.139011i
$761$	43.2325	−	24.9603i	1.56718	−	0.904809i	0.570679	−	0.821173i	$-0.306680\pi$
$761$	43.2325	−	24.9603i	1.56718	−	0.904809i	0.996496	−	0.0836361i	$-0.0266533\pi$
$762$	−6.05906	−	3.14818i	−0.219497	−	0.114046i
$763$	−20.7521	+	35.9437i	−0.751276	+	1.30125i
$764$	−1.85855	+	29.0398i	−0.0672399	+	1.05062i
$765$	3.17658	+	3.95783i	0.114850	+	0.143096i
$766$	−19.4504	−	20.7350i	−0.702771	−	0.749186i
$767$	−13.2398	+	22.9320i	−0.478060	+	0.828025i
$768$	25.0604	+	11.8312i	0.904289	+	0.426921i
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	−0.999869	−	0.0161588i	$-0.994856\pi$
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	0.485941	−	0.873992i	$-0.338477\pi$
$770$	2.31460	−	7.65138i	0.0834124	−	0.275737i
$771$	−6.23897	+	33.2586i	−0.224691	+	1.19778i
$772$	7.30866	+	4.86726i	0.263044	+	0.175176i
$773$	−20.8254			−0.749037			−0.374518	−	0.927220i	$-0.622192\pi$
$773$	−20.8254			−0.749037			−0.374518	+	0.927220i	$0.622192\pi$
$774$	14.6423	+	2.07874i	0.526308	+	0.0747188i
$775$		−	20.0466i		−	0.720096i
$776$	−3.13817	−	18.7387i	−0.112654	−	0.672679i
$777$	7.32583	+	20.8314i	0.262813	+	0.747321i
$778$	−0.885390	+	2.92684i	−0.0317428	+	0.104932i
$779$	14.4942	−	8.36822i	0.519308	−	0.299822i
$780$	8.34951	−	8.56009i	0.298961	−	0.306500i
$781$	−2.57384	−	1.48601i	−0.0920991	−	0.0531735i
$782$	−11.9146	+	11.1764i	−0.426065	+	0.399668i
$783$	6.50337	−	3.47630i	0.232411	−	0.124233i
$784$	45.2339	+	5.81375i	1.61550	+	0.207634i
$785$	−2.49980	−	1.44326i	−0.0892218	−	0.0515122i
$786$	−1.63900	−	36.8829i	−0.0584612	−	1.31557i
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	0.989888	−	0.141853i	$-0.0453060\pi$
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	−0.617792	+	0.786341i	$0.711973\pi$
$788$	13.7964	−	6.82999i	0.491475	−	0.243308i
$789$	−6.46533	−	18.3845i	−0.230172	−	0.654506i
$790$	0.946206	+	4.04400i	0.0336645	+	0.143879i
$791$	−35.4236			−1.25952
$792$	−3.09891	−	9.39338i	−0.110115	−	0.333779i
$793$	−11.1448			−0.395765
$794$	6.07347	+	25.9575i	0.215540	+	0.921197i
$795$	21.7034	+	4.07133i	0.769740	+	0.144395i
$796$	18.6154	+	37.6024i	0.659804	+	1.33278i
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	0.999920	+	0.0126529i	$0.00402764\pi$
$797$	14.4238	+	24.9828i	0.510918	+	0.884935i	−0.489002	+	0.872283i	$0.662639\pi$
$798$	−30.3265	+	19.3532i	−1.07355	+	0.685096i
$799$	4.61367	+	2.66370i	0.163220	+	0.0942350i
$800$	−12.3305	−	17.0682i	−0.435948	−	0.603453i
$801$	25.6124	−	3.94250i	0.904971	−	0.139301i
$802$	−17.9446	+	16.8329i	−0.633647	+	0.594390i
$803$	−7.13225	−	4.11780i	−0.251691	−	0.145314i
$804$	37.2316	−	10.4748i	1.31306	−	0.369417i
$805$	32.4136	−	18.7140i	1.14243	−	0.659582i
$806$	−6.73460	+	22.2626i	−0.237216	+	0.784165i
$807$	−15.9688	+	18.6149i	−0.562128	+	0.655276i
$808$	−6.41406	−	38.2997i	−0.225646	−	1.34738i
$809$		−	43.6746i		−	1.53552i	−0.640739	−	0.767759i	$-0.721372\pi$
$809$		−	43.6746i		−	1.53552i	0.640739	−	0.767759i	$-0.278628\pi$
$810$	−12.5431	−	7.04734i	−0.440721	−	0.247618i
$811$	42.3445			1.48692			0.743458	−	0.668782i	$-0.233184\pi$
$811$	42.3445			1.48692			0.743458	+	0.668782i	$0.233184\pi$
$812$	−6.74880	+	10.1340i	−0.236836	+	0.355633i
$813$	5.14767	+	4.41593i	0.180537	+	0.154873i
$814$	−1.41866	+	4.68965i	−0.0497239	+	0.164372i
$815$	3.91876	+	6.78749i	0.137268	+	0.237755i
$816$	−10.1398	+	2.16481i	−0.354964	+	0.0757837i
$817$	5.96737	−	10.3358i	0.208772	−	0.361603i
$818$	−19.9064	−	21.2212i	−0.696012	−	0.741981i
$819$	−5.97891	−	38.8420i	−0.208920	−	1.35725i
$820$	−11.0287	−	0.705833i	−0.385137	−	0.0246488i
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	−0.840380	−	0.541997i	$-0.817668\pi$
$821$	1.40953	−	2.44138i	0.0491930	−	0.0852047i	0.889573	+	0.456792i	$0.151002\pi$
$822$	−18.0064	+	11.4910i	−0.628046	+	0.400795i
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	−0.575841	−	0.817562i	$-0.695325\pi$
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	0.420109	+	0.907474i	$0.361992\pi$
$824$	6.26736	−	16.7692i	0.218334	−	0.584181i
$825$	−1.38565	+	7.38662i	−0.0482422	+	0.257169i
$826$	−51.2200	+	11.9843i	−1.78217	+	0.416989i
$827$			21.8630i			0.760251i	0.924935	+	0.380125i	$0.124119\pi$
$827$			21.8630i			0.760251i	−0.924935	+	0.380125i	$0.875881\pi$
$828$	19.5074	−	42.0037i	0.677929	−	1.45973i
$829$			22.0815i			0.766924i	0.923557	+	0.383462i	$0.125268\pi$
$829$			22.0815i			0.766924i	−0.923557	+	0.383462i	$0.874732\pi$
$830$	−1.67578	−	7.16213i	−0.0581672	−	0.248601i
$831$	43.3074	−	15.2300i	1.50232	−	0.528324i
$832$	7.95945	+	23.0973i	0.275944	+	0.800756i
$833$	−14.7768	+	8.53139i	−0.511986	+	0.295595i
$834$	−5.81899	+	0.258584i	−0.201495	+	0.00895403i
$835$	9.45931	−	16.3840i	0.327353	−	0.566992i
$836$	−7.96594	−	0.509820i	−0.275508	−	0.0176325i
$837$	27.9695	+	0.915040i	0.966768	+	0.0316284i
$838$	−28.8174	+	27.0321i	−0.995482	+	0.933808i
$839$	25.4035	−	44.0002i	0.877026	−	1.51905i	0.0224378	−	0.999748i	$-0.492857\pi$
$839$	25.4035	−	44.0002i	0.877026	−	1.51905i	0.854588	−	0.519306i	$-0.173809\pi$
$840$	23.7505	+	0.463288i	0.819469	+	0.0159850i
$841$	13.4930	+	23.3705i	0.465276	+	0.805881i
$842$	9.81317	+	2.96856i	0.338184	+	0.102303i
$843$	1.74215	−	0.612666i	0.0600027	−	0.0211013i
$844$	7.93976	+	5.28754i	0.273298	+	0.182005i
$845$	−4.15343			−0.142882
$846$	−14.9531	−	2.12286i	−0.514098	−	0.0729854i
$847$			41.3575i			1.42106i
$848$	−27.3537	+	35.8759i	−0.939330	+	1.23198i
$849$	−6.05494	−	1.13584i	−0.207805	−	0.0389820i
$850$	7.54039	+	2.28103i	0.258633	+	0.0782386i
$851$	−19.8668	+	11.4701i	−0.681026	+	0.393191i
$852$	2.17945	−	8.55872i	0.0746666	−	0.293217i
$853$	45.4891	+	26.2631i	1.55752	+	0.899233i	0.997494	+	0.0707558i	$0.0225411\pi$
$853$	45.4891	+	26.2631i	1.55752	+	0.899233i	0.560023	+	0.828477i	$0.310792\pi$
$854$	−15.1471	−	16.1475i	−0.518324	−	0.552557i
$855$	−9.05472	+	7.26739i	−0.309665	+	0.248539i
$856$	18.8004	+	22.8009i	0.642583	+	0.779319i
$857$	−48.4564	−	27.9763i	−1.65524	−	0.955653i	−0.974867	−	0.222786i	$-0.928485\pi$
$857$	−48.4564	−	27.9763i	−1.65524	−	0.955653i	−0.680372	−	0.732867i	$-0.738182\pi$
$858$	4.02033	−	7.73763i	0.137252	−	0.264158i
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	0.999552	+	0.0299443i	$0.00953300\pi$
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	−0.473843	+	0.880609i	$0.657134\pi$
$860$	−7.06254	+	3.49636i	−0.240831	+	0.119225i
$861$	−23.6479	+	27.5665i	−0.805918	+	0.939464i
$862$	−51.9143	+	12.1468i	−1.76821	+	0.413721i
$863$	−25.1750			−0.856966			−0.428483	−	0.903550i	$-0.640952\pi$
$863$	−25.1750			−0.856966			−0.428483	+	0.903550i	$0.640952\pi$
$864$	24.3768	−	16.4247i	0.829317	−	0.558779i
$865$	−23.1027			−0.785514
$866$	49.7360	−	11.6371i	1.69010	−	0.395446i
$867$	−16.6458	+	19.4042i	−0.565323	+	0.659000i
$868$	−41.4088	+	20.4998i	−1.40551	+	0.695808i
$869$	1.51428	+	2.62281i	0.0513685	+	0.0889728i
$870$	−1.81171	+	3.48686i	−0.0614226	+	0.118215i
$871$	29.5278	+	17.0479i	1.00051	+	0.577646i
$872$	−17.4095	−	21.1141i	−0.589560	−	0.715012i
$873$	−18.7821	−	7.30364i	−0.635676	−	0.247191i
$874$	−25.5694	−	27.2582i	−0.864899	−	0.922022i
$875$	−36.6276	−	21.1470i	−1.23824	−	0.714898i
$876$	6.03937	−	23.7167i	0.204051	−	0.801312i
$877$	31.8486	−	18.3878i	1.07545	−	0.620913i	0.145786	−	0.989316i	$-0.453429\pi$
$877$	31.8486	−	18.3878i	1.07545	−	0.620913i	0.929666	+	0.368404i	$0.120096\pi$
$878$	−14.1024	−	4.26607i	−0.475932	−	0.143973i
$879$	26.5213	+	4.97511i	0.894541	+	0.167806i
$880$	4.19141	+	3.19576i	0.141292	+	0.107729i
$881$		−	8.15439i		−	0.274728i	−0.990521	−	0.137364i	$-0.956137\pi$
$881$		−	8.15439i		−	0.274728i	0.990521	−	0.137364i	$-0.0438631\pi$
$882$	29.8344	−	38.0763i	1.00458	−	1.28210i
$883$	−20.3792			−0.685814			−0.342907	−	0.939369i	$-0.611412\pi$
$883$	−20.3792			−0.685814			−0.342907	+	0.939369i	$0.611412\pi$
$884$	−7.60760	−	5.06634i	−0.255871	−	0.170399i
$885$	−16.0153	+	5.63215i	−0.538348	+	0.189323i
$886$	−48.1268	−	14.5587i	−1.61685	−	0.489110i
$887$	−22.3561	−	38.7220i	−0.750646	−	1.30016i	−0.947510	−	0.319726i	$-0.896409\pi$
$887$	−22.3561	−	38.7220i	−0.750646	−	1.30016i	0.196864	−	0.980431i	$-0.436924\pi$
$888$	−14.5571	−	0.283957i	−0.488503	−	0.00952897i
$889$	5.97891	−	10.3558i	0.200526	−	0.347322i
$890$	−10.0712	+	9.44726i	−0.337588	+	0.316673i
$891$	−10.2427	−	2.27046i	−0.343145	−	0.0760633i
$892$	−28.8713	−	1.84776i	−0.966684	−	0.0618677i
$893$	−6.09402	+	10.5551i	−0.203928	+	0.353214i
$894$	−43.7745	+	1.94525i	−1.46404	+	0.0650589i
$895$	3.99387	−	2.30586i	0.133500	−	0.0770765i
$896$	−22.6474	+	42.9242i	−0.756597	+	1.43400i
$897$	38.5147	−	13.5446i	1.28597	−	0.452241i
$898$	−5.40479	−	23.0996i	−0.180360	−	0.770843i
$899$		−	7.64305i		−	0.254910i
$900$	−22.2455	+	1.98100i	−0.741516	+	0.0660333i
$901$		−	16.8788i		−	0.562315i
$902$	−7.84671	+	1.83596i	−0.261267	+	0.0611307i
$903$	−4.77521	+	25.4557i	−0.158909	+	0.847112i
$904$	8.17697	−	21.8786i	0.271962	−	0.727670i
$905$	21.8524	−	12.6165i	0.726398	−	0.419386i
$906$	5.70231	−	3.63899i	0.189447	−	0.120897i
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	−0.702212	−	0.711968i	$-0.747804\pi$
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	0.967688	+	0.252150i	$0.0811376\pi$
$908$	1.29482	+	0.0828684i	0.0429701	+	0.00275009i
$909$	−38.3884	−	14.9278i	−1.27326	−	0.495125i
$910$	14.3270	+	15.2733i	0.474937	+	0.506304i
$911$	−14.1609	+	24.5275i	−0.469173	+	0.812631i	−0.999379	−	0.0352377i	$-0.988781\pi$
$911$	−14.1609	+	24.5275i	−0.469173	+	0.812631i	0.530206	+	0.847869i	$0.322115\pi$
$912$	−4.95266	−	23.1978i	−0.163999	−	0.768157i
$913$	−2.68187	−	4.64514i	−0.0887570	−	0.153732i
$914$	−0.556437	+	1.83941i	−0.0184053	+	0.0608424i
$915$	−5.42320	−	4.65229i	−0.179286	−	0.153800i
$916$	−15.3619	+	23.0674i	−0.507573	+	0.762170i
$917$	64.6553			2.13511
$918$	−3.52673	+	10.4164i	−0.116399	+	0.343793i
$919$			17.1474i			0.565642i	0.959173	+	0.282821i	$0.0912702\pi$
$919$			17.1474i			0.565642i	−0.959173	+	0.282821i	$0.908730\pi$
$920$	4.07611	+	24.3393i	0.134385	+	0.802444i
$921$	1.08341	−	1.26294i	0.0356995	−	0.0416151i
$922$	4.15553	−	13.7369i	0.136855	−	0.452402i
$923$	6.74265	−	3.89287i	0.221937	−	0.128135i
$924$	16.6750	−	4.69135i	0.548566	−	0.154334i
$925$	9.58047	+	5.53129i	0.315004	+	0.181868i
$926$	27.7094	−	25.9927i	0.910589	−	0.854174i
$927$	−11.8853	−	14.8083i	−0.390363	−	0.486368i
$928$	−4.70116	−	6.50750i	−0.154323	−	0.213619i
$929$	38.0670	+	21.9780i	1.24894	+	0.721075i	0.970898	−	0.239495i	$-0.0769818\pi$
$929$	38.0670	+	21.9780i	1.24894	+	0.721075i	0.278040	+	0.960569i	$0.410315\pi$
$930$	−12.5704	+	8.02192i	−0.412199	+	0.263049i
$931$	−19.5181	−	33.8064i	−0.639680	−	1.10796i
$932$	20.5219	+	41.4535i	0.672216	+	1.35785i
$933$	15.3055	+	2.87115i	0.501080	+	0.0939972i
$934$	−10.1207	−	43.2548i	−0.331158	−	1.41534i
$935$	−1.97197			−0.0644902
$936$	25.3700	+	5.27332i	0.829244	+	0.172364i
$937$	−13.5845			−0.443786			−0.221893	−	0.975071i	$-0.571223\pi$
$937$	−13.5845			−0.443786			−0.221893	+	0.975071i	$0.571223\pi$
$938$	15.4314	+	65.9523i	0.503852	+	2.15342i
$939$	9.83615	+	27.9696i	0.320991	+	0.912753i
$940$	7.21243	−	3.57057i	0.235244	−	0.116459i
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	0.557258	−	0.830339i	$-0.311853\pi$
$941$	−13.5116	−	23.4028i	−0.440466	−	0.762909i	−0.997724	+	0.0674301i	$0.978520\pi$
$942$	−0.277686	−	6.24884i	−0.00904750	−	0.203598i
$943$	−32.6765	−	18.8658i	−1.06409	−	0.614354i
$944$	4.42146	−	34.4012i	0.143906	−	1.11966i
$945$	13.3047	−	21.3968i	0.432803	−	0.696037i
$946$	−4.19122	+	3.93156i	−0.136268	+	0.127826i
$947$	34.5376	+	19.9403i	1.12232	+	0.647972i	0.941992	−	0.335634i	$-0.108951\pi$
$947$	34.5376	+	19.9403i	1.12232	+	0.647972i	0.180328	+	0.983607i	$0.442284\pi$
$948$	−6.28416	+	6.44265i	−0.204100	+	0.209247i
$949$	18.6843	−	10.7874i	0.606516	−	0.350172i
$950$	−5.21853	+	17.2509i	−0.169312	+	0.559694i
$951$	4.55704	+	12.9582i	0.147772	+	0.420198i
$952$	−2.99909	−	17.9082i	−0.0972011	−	0.580409i
$953$			14.0999i			0.456741i	0.973574	+	0.228371i	$0.0733398\pi$
$953$			14.0999i			0.456741i	−0.973574	+	0.228371i	$0.926660\pi$
$954$	17.8632	+	44.3917i	0.578342	+	1.43723i
$955$	−16.4465			−0.532197
$956$	24.7724	+	16.4974i	0.801197	+	0.533563i
$957$	−0.528299	+	2.81625i	−0.0170775	+	0.0910365i
$958$	−1.98590	+	6.56479i	−0.0641615	+	0.212099i
$959$	−18.7040	−	32.3963i	−0.603983	−	1.04613i
$960$	−5.76856	+	14.5620i	−0.186179	+	0.469986i
$961$	−0.997565	+	1.72783i	−0.0321795	+	0.0557366i
$962$	−8.78127	−	9.36124i	−0.283120	−	0.301818i
$963$	30.9800	−	4.76872i	0.998317	−	0.153670i
$964$	−1.50210	+	23.4704i	−0.0483795	+	0.755930i
$965$	−2.48147	+	4.29803i	−0.0798813	+	0.138358i
$966$	71.9704	+	37.3945i	2.31561	+	1.20315i
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.463063	−	0.886326i	$-0.346750\pi$
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.999112	+	0.0421387i	$0.0134171\pi$
$968$	−25.5435	−	9.54672i	−0.821000	−	0.306843i
$969$	6.73582	+	5.77832i	0.216386	+	0.185626i
$970$	10.4560	−	2.44646i	0.335721	−	0.0785512i
$971$			61.3864i			1.96998i	0.172599	+	0.984992i	$0.444784\pi$
$971$			61.3864i			1.96998i	−0.172599	+	0.984992i	$0.555216\pi$
$972$	−1.74853	−	31.1278i	−0.0560841	−	0.998426i
$973$		−	10.2006i		−	0.327017i
$974$	−7.49625	−	32.0383i	−0.240195	−	1.02657i
$975$	−14.9432	−	12.8190i	−0.478564	−	0.410535i
$976$	13.4696	−	5.62787i	0.431152	−	0.180144i
$977$	−25.9568	+	14.9862i	−0.830431	+	0.479450i	−0.854000	−	0.520273i	$-0.825830\pi$
$977$	−25.9568	+	14.9862i	−0.830431	+	0.479450i	0.0235691	+	0.999722i	$0.492497\pi$
$978$	−7.83049	+	15.0708i	−0.250392	+	0.481910i
$979$	−5.03471	+	8.72037i	−0.160910	+	0.278704i
$980$	−1.64629	+	25.7233i	−0.0525889	+	0.821702i
$981$	−28.6881	+	4.41593i	−0.915939	+	0.140990i
$982$	11.2924	−	10.5928i	0.360354	−	0.338029i
$983$	21.1703	−	36.6681i	0.675228	−	1.16953i	−0.301174	−	0.953569i	$-0.597378\pi$
$983$	21.1703	−	36.6681i	0.675228	−	1.16953i	0.976402	−	0.215961i	$-0.0692883\pi$
$984$	−11.5671	−	20.9689i	−0.368745	−	0.668463i
$985$	4.35037	+	7.53506i	0.138614	+	0.240087i
$986$	2.87488	+	0.869673i	0.0915549	+	0.0276960i
$987$	4.87656	−	25.9959i	0.155223	−	0.827460i
$988$	11.5908	−	17.4047i	0.368752	−	0.553717i
$989$	−26.9063			−0.855572
$990$	5.18632	−	2.08697i	0.164832	−	0.0663283i
$991$			12.3787i			0.393222i	0.980482	+	0.196611i	$0.0629937\pi$
$991$			12.3787i			0.393222i	−0.980482	+	0.196611i	$0.937006\pi$
$992$	−3.10264	−	30.3073i	−0.0985089	−	0.962256i
$993$	5.49735	+	15.6320i	0.174453	+	0.496066i
$994$	14.8043	+	4.47842i	0.469565	+	0.142047i
$995$	−20.5370	+	11.8571i	−0.651068	+	0.375894i
$996$	11.1296	−	11.4103i	0.352654	−	0.361548i
$997$	6.20535	+	3.58266i	0.196525	+	0.113464i	0.595034	−	0.803701i	$-0.297139\pi$
$997$	6.20535	+	3.58266i	0.196525	+	0.113464i	−0.398508	+	0.917165i	$0.630472\pi$
$998$	37.6196	+	40.1042i	1.19083	+	1.26948i
$999$	−8.15469	+	13.1144i	−0.258003	+	0.414922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.l.b.11.8	yes	16
3.2	odd	2		216.2.l.b.35.1		16
4.3	odd	2		288.2.p.b.47.6		16
8.3	odd	2	inner	72.2.l.b.11.6	✓	16
8.5	even	2		288.2.p.b.47.5		16
9.2	odd	6		648.2.f.b.323.12		16
9.4	even	3		216.2.l.b.179.3		16
9.5	odd	6	inner	72.2.l.b.59.6	yes	16
9.7	even	3		648.2.f.b.323.5		16
12.11	even	2		864.2.p.b.143.4		16
24.5	odd	2		864.2.p.b.143.5		16
24.11	even	2		216.2.l.b.35.3		16
36.7	odd	6		2592.2.f.b.1295.7		16
36.11	even	6		2592.2.f.b.1295.9		16
36.23	even	6		288.2.p.b.239.5		16
36.31	odd	6		864.2.p.b.719.5		16
72.5	odd	6		288.2.p.b.239.6		16
72.11	even	6		648.2.f.b.323.6		16
72.13	even	6		864.2.p.b.719.4		16
72.29	odd	6		2592.2.f.b.1295.8		16
72.43	odd	6		648.2.f.b.323.11		16
72.59	even	6	inner	72.2.l.b.59.8	yes	16
72.61	even	6		2592.2.f.b.1295.10		16
72.67	odd	6		216.2.l.b.179.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.6	✓	16	8.3	odd	2	inner
72.2.l.b.11.8	yes	16	1.1	even	1	trivial
72.2.l.b.59.6	yes	16	9.5	odd	6	inner
72.2.l.b.59.8	yes	16	72.59	even	6	inner
216.2.l.b.35.1		16	3.2	odd	2
216.2.l.b.35.3		16	24.11	even	2
216.2.l.b.179.1		16	72.67	odd	6
216.2.l.b.179.3		16	9.4	even	3
288.2.p.b.47.5		16	8.5	even	2
288.2.p.b.47.6		16	4.3	odd	2
288.2.p.b.239.5		16	36.23	even	6
288.2.p.b.239.6		16	72.5	odd	6
648.2.f.b.323.5		16	9.7	even	3
648.2.f.b.323.6		16	72.11	even	6
648.2.f.b.323.11		16	72.43	odd	6
648.2.f.b.323.12		16	9.2	odd	6
864.2.p.b.143.4		16	12.11	even	2
864.2.p.b.143.5		16	24.5	odd	2
864.2.p.b.719.4		16	72.13	even	6
864.2.p.b.719.5		16	36.31	odd	6
2592.2.f.b.1295.7		16	36.7	odd	6
2592.2.f.b.1295.8		16	72.29	odd	6
2592.2.f.b.1295.9		16	36.11	even	6
2592.2.f.b.1295.10		16	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37702 - 0.322193i) q^{2} +(-1.12774 + 1.31461i) q^{3} +(1.79238 - 0.887333i) q^{4} +(0.565188 + 0.978934i) q^{5} +(-1.12936 + 2.17360i) q^{6} +(-3.71499 - 2.14485i) q^{7} +(2.18226 - 1.79937i) q^{8} +(-0.456412 - 2.96508i) q^{9} +(1.09368 + 1.16591i) q^{10} +(1.00953 + 0.582853i) q^{11} +(-0.854841 + 3.35697i) q^{12} +(-2.64466 + 1.52689i) q^{13} +(-5.80668 - 1.75656i) q^{14} +(-1.92430 - 0.360979i) q^{15} +(2.42528 - 3.18088i) q^{16} +1.49654i q^{17} +(-1.58382 - 3.93593i) q^{18} -3.42378 q^{19} +(1.88167 + 1.25312i) q^{20} +(7.00918 - 2.46494i) q^{21} +(1.57794 + 0.477339i) q^{22} +(3.85938 + 6.68464i) q^{23} +(-0.0955437 + 4.89805i) q^{24} +(1.86113 - 3.22356i) q^{25} +(-3.14980 + 2.95466i) q^{26} +(4.41264 + 2.74383i) q^{27} +(-8.56188 - 0.547960i) q^{28} +(0.709580 - 1.22903i) q^{29} +(-2.76611 + 0.122920i) q^{30} +(4.66408 - 2.69281i) q^{31} +(2.31481 - 5.16156i) q^{32} +(-1.90471 + 0.669837i) q^{33} +(0.482173 + 2.06077i) q^{34} -4.84897i q^{35} +(-3.44908 - 4.90957i) q^{36} +2.97201i q^{37} +(-4.71462 + 1.10312i) q^{38} +(0.975209 - 5.19864i) q^{39} +(2.99485 + 1.11931i) q^{40} +(-4.23339 + 2.44415i) q^{41} +(8.85761 - 5.65258i) q^{42} +(-1.74292 + 3.01882i) q^{43} +(2.32665 + 0.148906i) q^{44} +(2.64466 - 2.12262i) q^{45} +(7.46820 + 7.96144i) q^{46} +(1.77991 - 3.08289i) q^{47} +(1.44655 + 6.77551i) q^{48} +(5.70075 + 9.87399i) q^{49} +(1.52420 - 5.03856i) q^{50} +(-1.96737 - 1.68770i) q^{51} +(-3.38538 + 5.08347i) q^{52} -11.2786 q^{53} +(6.96035 + 2.35659i) q^{54} +1.31769i q^{55} +(-11.9665 + 2.00402i) q^{56} +(3.86113 - 4.50094i) q^{57} +(0.581124 - 1.92102i) q^{58} +(7.50935 - 4.33553i) q^{59} +(-3.76940 + 1.06049i) q^{60} +(3.16057 + 1.82476i) q^{61} +(5.55494 - 5.21079i) q^{62} +(-4.66408 + 11.9942i) q^{63} +(1.52453 - 7.85340i) q^{64} +(-2.98946 - 1.72596i) q^{65} +(-2.40702 + 1.53607i) q^{66} +(-5.58255 - 9.66925i) q^{67} +(1.32793 + 2.68237i) q^{68} +(-13.1401 - 2.46494i) q^{69} +(-1.56230 - 6.67714i) q^{70} -2.54954 q^{71} +(-6.33129 - 5.64932i) q^{72} -7.06491 q^{73} +(0.957560 + 4.09253i) q^{74} +(2.13887 + 6.08200i) q^{75} +(-6.13672 + 3.03803i) q^{76} +(-2.50026 - 4.33059i) q^{77} +(-0.332078 - 7.47285i) q^{78} +(2.24998 + 1.29902i) q^{79} +(4.48461 + 0.576391i) q^{80} +(-8.58338 + 2.70659i) q^{81} +(-5.04198 + 4.72961i) q^{82} +(-3.98482 - 2.30064i) q^{83} +(10.3759 - 10.6376i) q^{84} +(-1.46501 + 0.845824i) q^{85} +(-1.42740 + 4.71855i) q^{86} +(0.815476 + 2.31885i) q^{87} +(3.25183 - 0.544584i) q^{88} +8.63803i q^{89} +(2.95786 - 3.77499i) q^{90} +13.0998 q^{91} +(12.8490 + 8.55689i) q^{92} +(-1.71986 + 9.16824i) q^{93} +(1.45769 - 4.81869i) q^{94} +(-1.93508 - 3.35165i) q^{95} +(4.17495 + 8.86396i) q^{96} +(3.35869 - 5.81742i) q^{97} +(11.0314 + 11.7600i) q^{98} +(1.26744 - 3.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9} + 12 q^{11} - 6 q^{12} - 18 q^{14} + 7 q^{16} - 4 q^{19} + 18 q^{20} - q^{22} + 21 q^{24} - 14 q^{25} - 36 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 6 * q^3 - 5 * q^4 - 3 * q^6 - 6 * q^9 + 12 * q^11 - 6 * q^12 - 18 * q^14 + 7 * q^16 - 4 * q^19 + 18 * q^20 - q^22 + 21 * q^24 - 14 * q^25 - 36 * q^27 - 12 * q^28 + 12 * q^30 + 27 * q^32 + 12 * q^33 - 13 * q^34 + 27 * q^36 - 15 * q^38 - 12 * q^40 - 36 * q^41 + 42 * q^42 + 8 * q^43 + 12 * q^46 - 27 * q^48 + 10 * q^49 + 51 * q^50 + 18 * q^51 - 18 * q^52 + 39 * q^54 - 66 * q^56 + 18 * q^57 + 12 * q^58 + 12 * q^59 - 72 * q^60 + 34 * q^64 - 6 * q^65 - 24 * q^66 - 16 * q^67 - 9 * q^68 + 18 * q^70 - 21 * q^72 - 4 * q^73 - 60 * q^74 + 78 * q^75 - 7 * q^76 - 72 * q^78 - 6 * q^81 - 22 * q^82 + 54 * q^83 + 12 * q^84 - 51 * q^86 - 13 * q^88 - 66 * q^90 - 36 * q^91 + 84 * q^92 + 24 * q^94 + 42 * q^96 + 8 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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