LMFDB - Embedded newform 585.2.bt.b.376.16

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			376.16
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16682 - 0.673666i) q^{2} +(0.619932 - 1.61731i) q^{3} +(-0.0923480 - 0.159951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.81288 + 1.46949i) q^{6} +(-4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 - 2.00524i) q^{9} +O(q^{10})$	\(q+(-1.16682 - 0.673666i) q^{2} +(0.619932 - 1.61731i) q^{3} +(-0.0923480 - 0.159951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.81288 + 1.46949i) q^{6} +(-4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 - 2.00524i) q^{9} -1.34733 q^{10} +(-1.11056 - 0.641180i) q^{11} +(-0.315940 + 0.0501961i) q^{12} +(0.382510 + 3.58520i) q^{13} +(3.16872 + 5.48839i) q^{14} +(-0.271777 - 1.71060i) q^{15} +(1.79825 - 3.11466i) q^{16} -0.689981 q^{17} +(1.25275 + 3.84296i) q^{18} +6.46642i q^{19} +(-0.159951 - 0.0923480i) q^{20} +(-6.32897 + 5.13015i) q^{21} +(0.863882 + 1.49629i) q^{22} +(-2.10450 - 3.64510i) q^{23} +(4.76056 + 1.82478i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.96891 - 4.44099i) q^{26} +(-4.62639 + 2.36569i) q^{27} +0.868754i q^{28} +(2.78420 - 4.82237i) q^{29} +(-0.835255 + 2.17905i) q^{30} +(-0.646732 + 0.373391i) q^{31} +(0.901834 - 0.520674i) q^{32} +(-1.72545 + 1.39862i) q^{33} +(0.805086 + 0.464817i) q^{34} -4.70370 q^{35} +(-0.114679 + 0.542091i) q^{36} -8.06746i q^{37} +(4.35621 - 7.54517i) q^{38} +(6.03551 + 1.60395i) q^{39} +(1.47176 + 2.54916i) q^{40} +(6.39700 - 3.69331i) q^{41} +(10.8408 - 1.72237i) q^{42} +(-5.42456 + 9.39562i) q^{43} +0.236847i q^{44} +(-2.93504 - 0.620907i) q^{45} +5.67092i q^{46} +(-6.50187 - 3.75385i) q^{47} +(-3.92257 - 4.83920i) q^{48} +(7.56239 + 13.0984i) q^{49} +(-1.16682 + 0.673666i) q^{50} +(-0.427741 + 1.11591i) q^{51} +(0.538134 - 0.392269i) q^{52} -5.44121 q^{53} +(6.99187 + 0.356295i) q^{54} -1.28236 q^{55} +(6.92270 - 11.9905i) q^{56} +(10.4582 + 4.00874i) q^{57} +(-6.49733 + 3.75124i) q^{58} +(0.357947 - 0.206661i) q^{59} +(-0.248514 + 0.201441i) q^{60} +(-2.91595 + 5.05058i) q^{61} +1.00616 q^{62} +(4.37350 + 13.4162i) q^{63} -8.59603 q^{64} +(2.12387 + 2.91362i) q^{65} +(2.95551 - 0.469566i) q^{66} +(-9.45733 + 5.46019i) q^{67} +(0.0637184 + 0.110363i) q^{68} +(-7.19989 + 1.14391i) q^{69} +(5.48839 + 3.16872i) q^{70} +5.80266i q^{71} +(5.90245 - 6.56806i) q^{72} -9.51919i q^{73} +(-5.43478 + 9.41331i) q^{74} +(-1.09066 - 1.34553i) q^{75} +(1.03431 - 0.597161i) q^{76} +(3.01592 + 5.22372i) q^{77} +(-5.96185 - 5.93744i) q^{78} +(-2.41946 + 4.19062i) q^{79} -3.59650i q^{80} +(0.958005 + 8.94887i) q^{81} -9.95222 q^{82} +(-2.46941 - 1.42572i) q^{83} +(1.40504 + 0.538569i) q^{84} +(-0.597541 + 0.344990i) q^{85} +(12.6590 - 7.30869i) q^{86} +(-6.07324 - 7.49245i) q^{87} +(1.88732 - 3.26893i) q^{88} -10.7367i q^{89} +(3.00639 + 2.70173i) q^{90} +(6.87370 - 15.5040i) q^{91} +(-0.388693 + 0.673235i) q^{92} +(0.202958 + 1.27744i) q^{93} +(5.05769 + 8.76017i) q^{94} +(3.23321 + 5.60008i) q^{95} +(-0.283014 - 1.78133i) q^{96} +(-1.55060 - 0.895240i) q^{97} -20.3781i q^{98} +(1.19234 + 3.65764i) 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 $

$2$	−1.16682	−	0.673666i	−0.825069	−	0.476354i	0.0270923	−	0.999633i	$-0.491375\pi$
$2$	−1.16682	−	0.673666i	−0.825069	−	0.476354i	−0.852161	+	0.523279i	$0.824709\pi$
$3$	0.619932	−	1.61731i	0.357918	−	0.933753i
$3$	0.619932	−	1.61731i	0.357918	−	0.933753i
$4$	−0.0923480	−	0.159951i	−0.0461740	−	0.0799757i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.81288	+	1.46949i	−0.740104	+	0.599915i
$7$	−4.07352	−	2.35185i	−1.53965	−	0.888916i	−0.998859	−	0.0477566i	$-0.984793\pi$
$7$	−4.07352	−	2.35185i	−1.53965	−	0.888916i	−0.540788	−	0.841159i	$-0.681874\pi$
$8$			2.94351i			1.04069i
$9$	−2.23137	−	2.00524i	−0.743789	−	0.668414i
$10$	−1.34733			−0.426064
$11$	−1.11056	−	0.641180i	−0.334845	−	0.193323i	0.323145	−	0.946349i	$-0.395260\pi$
$11$	−1.11056	−	0.641180i	−0.334845	−	0.193323i	−0.657990	+	0.753027i	$0.728593\pi$
$12$	−0.315940	+	0.0501961i	−0.0912041	+	0.0144904i
$13$	0.382510	+	3.58520i	0.106089	+	0.994357i
$13$	0.382510	+	3.58520i	0.106089	+	0.994357i
$14$	3.16872	+	5.48839i	0.846877	+	1.46683i
$15$	−0.271777	−	1.71060i	−0.0701724	−	0.441674i
$16$	1.79825	−	3.11466i	0.449562	−	0.778664i
$17$	−0.689981			−0.167345			−0.0836725	−	0.996493i	$-0.526665\pi$
$17$	−0.689981			−0.167345			−0.0836725	+	0.996493i	$0.526665\pi$
$18$	1.25275	+	3.84296i	0.295276	+	0.905795i
$19$			6.46642i			1.48350i	0.670678	+	0.741749i	$0.266003\pi$
$19$			6.46642i			1.48350i	−0.670678	+	0.741749i	$0.733997\pi$
$20$	−0.159951	−	0.0923480i	−0.0357662	−	0.0206496i
$21$	−6.32897	+	5.13015i	−1.38110	+	1.11949i
$22$	0.863882	+	1.49629i	0.184180	+	0.319010i
$23$	−2.10450	−	3.64510i	−0.438818	−	0.760056i	0.558780	−	0.829316i	$-0.311270\pi$
$23$	−2.10450	−	3.64510i	−0.438818	−	0.760056i	−0.997599	+	0.0692600i	$0.977936\pi$
$24$	4.76056	+	1.82478i	0.971746	+	0.372481i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.96891	−	4.44099i	0.386135	−	0.870949i
$27$	−4.62639	+	2.36569i	−0.890349	+	0.455278i
$28$			0.868754i			0.164179i
$29$	2.78420	−	4.82237i	0.517012	−	0.895492i	−0.482792	−	0.875735i	$-0.660377\pi$
$29$	2.78420	−	4.82237i	0.517012	−	0.895492i	0.999805	−	0.0197568i	$-0.00628921\pi$
$30$	−0.835255	+	2.17905i	−0.152496	+	0.397838i
$31$	−0.646732	+	0.373391i	−0.116157	+	0.0670630i	−0.556953	−	0.830544i	$-0.688030\pi$
$31$	−0.646732	+	0.373391i	−0.116157	+	0.0670630i	0.440796	+	0.897607i	$0.354696\pi$
$32$	0.901834	−	0.520674i	0.159423	−	0.0920431i
$33$	−1.72545	+	1.39862i	−0.300363	+	0.243469i
$34$	0.805086	+	0.464817i	0.138071	+	0.0797154i
$35$	−4.70370			−0.795070
$36$	−0.114679	+	0.542091i	−0.0191132	+	0.0903484i
$37$		−	8.06746i		−	1.32628i	−0.748494	−	0.663141i	$-0.769223\pi$
$37$		−	8.06746i		−	1.32628i	0.748494	−	0.663141i	$-0.230777\pi$
$38$	4.35621	−	7.54517i	0.706670	−	1.22399i
$39$	6.03551	+	1.60395i	0.966455	+	0.256837i
$40$	1.47176	+	2.54916i	0.232705	+	0.403057i
$41$	6.39700	−	3.69331i	0.999043	−	0.576798i	0.0910779	−	0.995844i	$-0.470969\pi$
$41$	6.39700	−	3.69331i	0.999043	−	0.576798i	0.907965	+	0.419046i	$0.137635\pi$
$42$	10.8408	−	1.72237i	1.67277	−	0.265767i
$43$	−5.42456	+	9.39562i	−0.827238	+	1.43282i	0.0729590	+	0.997335i	$0.476756\pi$
$43$	−5.42456	+	9.39562i	−0.827238	+	1.43282i	−0.900197	+	0.435483i	$0.856578\pi$
$44$			0.236847i			0.0357060i
$45$	−2.93504	−	0.620907i	−0.437530	−	0.0925594i
$46$			5.67092i			0.836131i
$47$	−6.50187	−	3.75385i	−0.948394	−	0.547556i	−0.0558127	−	0.998441i	$-0.517775\pi$
$47$	−6.50187	−	3.75385i	−0.948394	−	0.547556i	−0.892582	+	0.450885i	$0.851108\pi$
$48$	−3.92257	−	4.83920i	−0.566174	−	0.698478i
$49$	7.56239	+	13.0984i	1.08034	+	1.87121i
$50$	−1.16682	+	0.673666i	−0.165014	+	0.0952708i
$51$	−0.427741	+	1.11591i	−0.0598958	+	0.156259i
$52$	0.538134	−	0.392269i	0.0746258	−	0.0543980i
$53$	−5.44121			−0.747407			−0.373704	−	0.927548i	$-0.621912\pi$
$53$	−5.44121			−0.747407			−0.373704	+	0.927548i	$0.621912\pi$
$54$	6.99187	+	0.356295i	0.951473	+	0.0484856i
$55$	−1.28236			−0.172913
$56$	6.92270	−	11.9905i	0.925084	−	1.60229i
$57$	10.4582	+	4.00874i	1.38522	+	0.530971i
$58$	−6.49733	+	3.75124i	−0.853142	+	0.492562i
$59$	0.357947	−	0.206661i	0.0466007	−	0.0269050i	−0.476519	−	0.879164i	$-0.658102\pi$
$59$	0.357947	−	0.206661i	0.0466007	−	0.0269050i	0.523119	+	0.852259i	$0.324768\pi$
$60$	−0.248514	+	0.201441i	−0.0320830	+	0.0260059i
$61$	−2.91595	+	5.05058i	−0.373350	+	0.646661i	−0.990079	−	0.140515i	$-0.955124\pi$
$61$	−2.91595	+	5.05058i	−0.373350	+	0.646661i	0.616729	+	0.787176i	$0.288457\pi$
$62$	1.00616			0.127783
$63$	4.37350	+	13.4162i	0.551009	+	1.69029i
$64$	−8.59603			−1.07450
$65$	2.12387	+	2.91362i	0.263433	+	0.361390i
$66$	2.95551	−	0.469566i	0.363798	−	0.0577996i
$67$	−9.45733	+	5.46019i	−1.15540	+	0.667068i	−0.950196	−	0.311652i	$-0.899118\pi$
$67$	−9.45733	+	5.46019i	−1.15540	+	0.667068i	−0.205200	+	0.978720i	$0.565784\pi$
$68$	0.0637184	+	0.110363i	0.00772699	+	0.0133835i
$69$	−7.19989	+	1.14391i	−0.866765	+	0.137710i
$70$	5.48839	+	3.16872i	0.655988	+	0.378735i
$71$			5.80266i			0.688649i	0.938851	+	0.344325i	$0.111892\pi$
$71$			5.80266i			0.688649i	−0.938851	+	0.344325i	$0.888108\pi$
$72$	5.90245	−	6.56806i	0.695611	−	0.774053i
$73$		−	9.51919i		−	1.11414i	−0.830467	−	0.557068i	$-0.811926\pi$
$73$		−	9.51919i		−	1.11414i	0.830467	−	0.557068i	$-0.188074\pi$
$74$	−5.43478	+	9.41331i	−0.631780	+	1.09427i
$75$	−1.09066	−	1.34553i	−0.125939	−	0.155369i
$76$	1.03431	−	0.597161i	0.118644	−	0.0684990i
$77$	3.01592	+	5.22372i	0.343695	+	0.595298i
$78$	−5.96185	−	5.93744i	−0.675047	−	0.672283i
$79$	−2.41946	+	4.19062i	−0.272210	+	0.471482i	−0.969427	−	0.245378i	$-0.921088\pi$
$79$	−2.41946	+	4.19062i	−0.272210	+	0.471482i	0.697217	+	0.716860i	$0.254421\pi$
$80$		−	3.59650i		−	0.402100i
$81$	0.958005	+	8.94887i	0.106445	+	0.994319i
$82$	−9.95222			−1.09904
$83$	−2.46941	−	1.42572i	−0.271053	−	0.156493i	0.358313	−	0.933602i	$-0.383352\pi$
$83$	−2.46941	−	1.42572i	−0.271053	−	0.156493i	−0.629366	+	0.777109i	$0.716685\pi$
$84$	1.40504	+	0.538569i	0.153303	+	0.0587627i
$85$	−0.597541	+	0.344990i	−0.0648124	+	0.0374195i
$86$	12.6590	−	7.30869i	1.36506	−	0.788116i
$87$	−6.07324	−	7.49245i	−0.651120	−	0.803274i
$88$	1.88732	−	3.26893i	0.201189	−	0.348469i
$89$		−	10.7367i		−	1.13809i	−0.822306	−	0.569045i	$-0.807313\pi$
$89$		−	10.7367i		−	1.13809i	0.822306	−	0.569045i	$-0.192687\pi$
$90$	3.00639	+	2.70173i	0.316902	+	0.284787i
$91$	6.87370	−	15.5040i	0.720559	−	1.62526i
$92$	−0.388693	+	0.673235i	−0.0405240	+	0.0701896i
$93$	0.202958	+	1.27744i	0.0210458	+	0.132465i
$94$	5.05769	+	8.76017i	0.521661	+	0.903543i
$95$	3.23321	+	5.60008i	0.331720	+	0.574556i
$96$	−0.283014	−	1.78133i	−0.0288850	−	0.181806i
$97$	−1.55060	−	0.895240i	−0.157440	−	0.0908979i	0.419210	−	0.907889i	$-0.362307\pi$
$97$	−1.55060	−	0.895240i	−0.157440	−	0.0908979i	−0.576650	+	0.816991i	$0.695640\pi$
$98$		−	20.3781i		−	2.05850i
$99$	1.19234	+	3.65764i	0.119834	+	0.367607i
$100$	−0.184696			−0.0184696
$101$	−1.85667	+	3.21584i	−0.184745	+	0.319988i	−0.943491	−	0.331399i	$-0.892479\pi$
$101$	−1.85667	+	3.21584i	−0.184745	+	0.319988i	0.758746	+	0.651387i	$0.225813\pi$
$102$	1.25085	−	1.01392i	0.123853	−	0.100393i
$103$	−5.29740	−	9.17537i	−0.521969	−	0.904076i	−0.999673	−	0.0255558i	$-0.991864\pi$
$103$	−5.29740	−	9.17537i	−0.521969	−	0.904076i	0.477705	−	0.878520i	$-0.341469\pi$
$104$	−10.5531	+	1.12592i	−1.03482	+	0.110406i
$105$	−2.91598	+	7.60733i	−0.284570	+	0.742399i
$106$	6.34893	+	3.66556i	0.616663	+	0.356030i
$107$	−14.5036			−1.40211			−0.701056	−	0.713106i	$-0.747288\pi$
$107$	−14.5036			−1.40211			−0.701056	+	0.713106i	$0.747288\pi$
$108$	0.805634	+	0.521531i	0.0775222	+	0.0501843i
$109$			4.43511i			0.424806i	0.977182	+	0.212403i	$0.0681290\pi$
$109$			4.43511i			0.424806i	−0.977182	+	0.212403i	$0.931871\pi$
$110$	1.49629	+	0.863882i	0.142665	+	0.0823679i
$111$	−13.0476	−	5.00128i	−1.23842	−	0.474701i
$112$	−14.6504	+	8.45842i	−1.38433	+	0.799245i
$113$	3.57608	+	6.19396i	0.336409	+	0.582678i	0.983755	−	0.179519i	$-0.0574540\pi$
$113$	3.57608	+	6.19396i	0.336409	+	0.582678i	−0.647345	+	0.762197i	$0.724121\pi$
$114$	−9.50231	−	11.7228i	−0.889973	−	1.09794i
$115$	−3.64510	−	2.10450i	−0.339907	−	0.196246i
$116$	−1.02846			−0.0954901
$117$	6.33568	−	8.76693i	0.585734	−	0.810503i
$118$	−0.556882			−0.0512651
$119$	2.81065	+	1.62273i	0.257652	+	0.148756i
$120$	5.03516	−	0.799978i	0.459645	−	0.0730276i
$121$	−4.67778	−	8.10215i	−0.425253	−	0.736559i
$122$	6.80481	−	3.92876i	0.616078	−	0.355693i
$123$	−2.00751	−	12.6355i	−0.181011	−	1.13931i
$124$	0.119449	+	0.0689638i	0.0107268	+	0.00619313i
$125$		−	1.00000i		−	0.0894427i
$126$	3.93496	−	18.6007i	0.350554	−	1.65708i
$127$	10.7582			0.954634			0.477317	−	0.878731i	$-0.341609\pi$
$127$	10.7582			0.954634			0.477317	+	0.878731i	$0.341609\pi$
$128$	8.22639	+	4.74951i	0.727117	+	0.419801i
$129$	11.8327	+	14.5978i	1.04181	+	1.28527i
$130$	−0.515368	−	4.83046i	−0.0452008	−	0.423659i
$131$	−8.92688	−	15.4618i	−0.779945	−	1.35090i	−0.931973	−	0.362528i	$-0.881914\pi$
$131$	−8.92688	−	15.4618i	−0.779945	−	1.35090i	0.152028	−	0.988376i	$-0.451420\pi$
$132$	0.383054	+	0.146829i	0.0333406	+	0.0127798i
$133$	15.2080	−	26.3411i	1.31870	−	2.28406i
$134$	14.7134			1.27104
$135$	−2.82373	+	4.36195i	−0.243028	+	0.375417i
$136$		−	2.03097i		−	0.174154i
$137$	3.72175	+	2.14875i	0.317970	+	0.183580i	0.650488	−	0.759517i	$-0.274565\pi$
$137$	3.72175	+	2.14875i	0.317970	+	0.183580i	−0.332517	+	0.943097i	$0.607898\pi$
$138$	9.17162	+	3.51559i	0.780740	+	0.299267i
$139$	0.0771951	+	0.133706i	0.00654761	+	0.0113408i	0.869281	−	0.494319i	$-0.164582\pi$
$139$	0.0771951	+	0.133706i	0.00654761	+	0.0113408i	−0.862733	+	0.505660i	$0.831249\pi$
$140$	0.434377	+	0.752363i	0.0367116	+	0.0635863i
$141$	−10.1019	+	8.18838i	−0.850729	+	0.689586i
$142$	3.90906	−	6.77068i	0.328041	−	0.568183i
$143$	1.87396	−	4.22683i	0.156708	−	0.353465i
$144$	−10.2582	+	3.34402i	−0.854849	+	0.278668i
$145$		−	5.56839i		−	0.462430i
$146$	−6.41276	+	11.1072i	−0.530723	+	0.919240i
$147$	25.8724	−	4.11056i	2.13392	−	0.339034i
$148$	−1.29040	+	0.745014i	−0.106070	+	0.0612398i
$149$	8.04826	−	4.64667i	0.659339	−	0.380670i	−0.132686	−	0.991158i	$-0.542360\pi$
$149$	8.04826	−	4.64667i	0.659339	−	0.380670i	0.792025	+	0.610488i	$0.209027\pi$
$150$	0.366173	+	2.30474i	0.0298979	+	0.188181i
$151$	−6.14219	−	3.54620i	−0.499845	−	0.288585i	0.228805	−	0.973472i	$-0.426518\pi$
$151$	−6.14219	−	3.54620i	−0.499845	−	0.288585i	−0.728649	+	0.684887i	$0.759852\pi$
$152$	−19.0340			−1.54386
$153$	1.53960	+	1.38358i	0.124469	+	0.111856i
$154$		−	8.12688i		−	0.654883i
$155$	−0.373391	+	0.646732i	−0.0299915	+	0.0519468i
$156$	−0.300813	−	1.11351i	−0.0240843	−	0.0891521i
$157$	−6.72039	−	11.6401i	−0.536345	−	0.928978i	−0.999097	−	0.0424895i	$-0.986471\pi$
$157$	−6.72039	−	11.6401i	−0.536345	−	0.928978i	0.462751	−	0.886488i	$-0.346862\pi$
$158$	5.64616	−	3.25981i	0.449184	−	0.259337i
$159$	−3.37318	+	8.80011i	−0.267511	+	0.697894i
$160$	0.520674	−	0.901834i	0.0411629	−	0.0712963i
$161$			19.7979i			1.56029i
$162$	4.91073	−	11.0871i	0.385823	−	0.871087i
$163$		−	4.64686i		−	0.363970i	−0.983301	−	0.181985i	$-0.941748\pi$
$163$		−	4.64686i		−	0.363970i	0.983301	−	0.181985i	$-0.0582523\pi$
$164$	−1.18150	−	0.682139i	−0.0922596	−	0.0532661i
$165$	−0.794976	+	2.07397i	−0.0618888	+	0.161458i
$166$	1.92091	+	3.32712i	0.149092	+	0.258234i
$167$	10.9080	−	6.29773i	0.844086	−	0.487333i	−0.0145650	−	0.999894i	$-0.504636\pi$
$167$	10.9080	−	6.29773i	0.844086	−	0.487333i	0.858651	+	0.512561i	$0.171303\pi$
$168$	−15.1007	−	18.6294i	−1.16504	−	1.43729i
$169$	−12.7074	+	2.74275i	−0.977490	+	0.210981i
$170$	0.929633			0.0712996
$171$	12.9667	−	14.4290i	0.991591	−	1.10341i
$172$	2.00379			0.152788
$173$	10.8444	−	18.7831i	0.824485	−	1.42805i	−0.0778279	−	0.996967i	$-0.524798\pi$
$173$	10.8444	−	18.7831i	0.824485	−	1.42805i	0.902313	−	0.431082i	$-0.141868\pi$
$174$	2.03900	+	12.8337i	0.154576	+	0.972920i
$175$	−4.07352	+	2.35185i	−0.307929	+	0.177783i
$176$	−3.99411	+	2.30600i	−0.301067	+	0.173821i
$177$	−0.112331	−	0.707026i	−0.00844333	−	0.0531434i
$178$	−7.23297	+	12.5279i	−0.542134	+	0.939004i
$179$	−15.5830			−1.16473			−0.582364	−	0.812928i	$-0.697872\pi$
$179$	−15.5830			−1.16473			−0.582364	+	0.812928i	$0.697872\pi$
$180$	0.171730	+	0.526804i	0.0128000	+	0.0392656i
$181$	−23.6483			−1.75776			−0.878882	−	0.477040i	$-0.841710\pi$
$181$	−23.6483			−1.75776			−0.878882	+	0.477040i	$0.841710\pi$
$182$	−18.4649	+	13.4599i	−1.36871	+	0.997713i
$183$	6.36065	+	7.84701i	0.470193	+	0.580068i
$184$	10.7294	−	6.19462i	0.790981	−	0.456673i
$185$	−4.03373	−	6.98663i	−0.296566	−	0.513667i
$186$	0.623753	−	1.62728i	0.0457358	−	0.119318i
$187$	0.766262	+	0.442402i	0.0560346	+	0.0323516i
$188$			1.38664i			0.101131i
$189$	24.4095	+	1.24387i	1.77553	+	0.0904781i
$190$		−	8.71241i		−	0.632065i
$191$	−0.337619	+	0.584773i	−0.0244292	+	0.0423127i	−0.877982	−	0.478694i	$-0.841110\pi$
$191$	−0.337619	+	0.584773i	−0.0244292	+	0.0423127i	0.853552	+	0.521007i	$0.174444\pi$
$192$	−5.32896	+	13.9024i	−0.384584	+	1.00332i
$193$	−12.7236	+	7.34599i	−0.915867	+	0.528776i	−0.882314	−	0.470661i	$-0.844015\pi$
$193$	−12.7236	+	7.34599i	−0.915867	+	0.528776i	−0.0335526	+	0.999437i	$0.510682\pi$
$194$	1.20619	+	2.08918i	0.0865991	+	0.149994i
$195$	6.02888	−	1.62869i	0.431737	−	0.116633i
$196$	1.39674	−	2.41923i	0.0997674	−	0.172802i
$197$		−	2.61631i		−	0.186404i	−0.995647	−	0.0932021i	$-0.970290\pi$
$197$		−	2.61631i		−	0.186404i	0.995647	−	0.0932021i	$-0.0297103\pi$
$198$	1.07278	−	5.07106i	0.0762392	−	0.360385i
$199$	25.9577			1.84009			0.920045	−	0.391813i	$-0.128152\pi$
$199$	25.9577			1.84009			0.920045	+	0.391813i	$0.128152\pi$
$200$	2.54916	+	1.47176i	0.180253	+	0.104069i
$201$	2.96790	+	18.6804i	0.209340	+	1.31761i
$202$	4.33280	−	2.50154i	0.304855	−	0.176008i
$203$	−22.6830	+	13.0960i	−1.59203	+	0.919161i
$204$	0.217993	−	0.0346343i	0.0152625	−	0.00242489i
$205$	3.69331	−	6.39700i	0.257952	−	0.446786i
$206$			14.2747i			0.994567i
$207$	−2.61340	+	12.3536i	−0.181644	+	0.858634i
$208$	11.8545	+	5.25570i	0.821963	+	0.364417i
$209$	4.14613	−	7.18132i	0.286794	−	0.496742i
$210$	8.52723	−	6.91202i	0.588435	−	0.476975i
$211$	−5.16589	−	8.94758i	−0.355634	−	0.615977i	0.631592	−	0.775301i	$-0.282402\pi$
$211$	−5.16589	−	8.94758i	−0.355634	−	0.615977i	−0.987226	+	0.159324i	$0.949069\pi$
$212$	0.502485	+	0.870329i	0.0345108	+	0.0597744i
$213$	9.38469	+	3.59726i	0.643028	+	0.246480i
$214$	16.9231	+	9.77056i	1.15684	+	0.667902i
$215$			10.8491i			0.739904i
$216$	−6.96345	−	13.6178i	−0.473802	−	0.926576i
$217$	3.51264			0.238453
$218$	2.98778	−	5.17499i	0.202358	−	0.350494i
$219$	−15.3955	−	5.90125i	−1.04033	−	0.398770i
$220$	0.118423	+	0.205115i	0.00798410	+	0.0138289i
$221$	−0.263925	−	2.47372i	−0.0177535	−	0.166401i
$222$	11.8550	+	14.6253i	0.795657	+	0.981587i
$223$	15.3886	+	8.88463i	1.03050	+	0.594959i	0.917128	−	0.398594i	$-0.130502\pi$
$223$	15.3886	+	8.88463i	1.03050	+	0.594959i	0.113371	+	0.993553i	$0.463835\pi$
$224$	−4.89819			−0.327274
$225$	−2.85227	+	0.929800i	−0.190152	+	0.0619867i
$226$		−	9.63634i		−	0.641000i
$227$	−24.6734	−	14.2452i	−1.63763	−	0.945485i	−0.981647	−	0.190707i	$-0.938922\pi$
$227$	−24.6734	−	14.2452i	−1.63763	−	0.945485i	−0.655981	−	0.754777i	$-0.727745\pi$
$228$	−0.324589	−	2.04300i	−0.0214964	−	0.135301i
$229$	−5.24154	+	3.02620i	−0.346371	+	0.199977i	−0.663086	−	0.748544i	$-0.730753\pi$
$229$	−5.24154	+	3.02620i	−0.346371	+	0.199977i	0.316715	+	0.948521i	$0.397420\pi$
$230$	2.83546	+	4.91116i	0.186965	+	0.323832i
$231$	10.3180	−	1.63931i	0.678876	−	0.107859i
$232$	14.1947	+	8.19531i	0.931928	+	0.538049i
$233$	8.75020			0.573244			0.286622	−	0.958044i	$-0.407468\pi$
$233$	8.75020			0.573244			0.286622	+	0.958044i	$0.407468\pi$
$234$	−13.2986	+	5.96133i	−0.869357	+	0.389705i
$235$	−7.50771			−0.489749
$236$	−0.0661114	−	0.0381694i	−0.00430349	−	0.00248462i
$237$	5.27763	+	6.51091i	0.342819	+	0.422929i
$238$	−2.18636	−	3.78688i	−0.141721	−	0.245467i
$239$	24.3851	−	14.0788i	1.57734	−	0.910679i	0.582114	−	0.813107i	$-0.302226\pi$
$239$	24.3851	−	14.0788i	1.57734	−	0.910679i	0.995229	−	0.0975716i	$-0.0311075\pi$
$240$	−5.81664	−	2.22958i	−0.375462	−	0.143919i
$241$	−2.53789	−	1.46525i	−0.163480	−	0.0943852i	0.416028	−	0.909352i	$-0.363422\pi$
$241$	−2.53789	−	1.46525i	−0.163480	−	0.0943852i	−0.579508	+	0.814967i	$0.696755\pi$
$242$			12.6050i			0.810283i
$243$	15.0670	+	3.99830i	0.966547	+	0.256491i
$244$	1.07713			0.0689562
$245$	13.0984	+	7.56239i	0.836829	+	0.483143i
$246$	−6.16970	+	16.0958i	−0.393366	+	1.02623i
$247$	−23.1834	+	2.47347i	−1.47513	+	0.157383i
$248$	−1.09908	−	1.90366i	−0.0697917	−	0.120883i
$249$	−3.83669	+	3.10995i	−0.243140	+	0.197085i
$250$	−0.673666	+	1.16682i	−0.0426064	+	0.0737964i
$251$	14.7686			0.932185			0.466093	−	0.884736i	$-0.345661\pi$
$251$	14.7686			0.932185			0.466093	+	0.884736i	$0.345661\pi$
$252$	1.74206	−	1.93851i	0.109740	−	0.122115i
$253$			5.39745i			0.339335i
$254$	−12.5529	−	7.24742i	−0.787639	−	0.454744i
$255$	0.187521	+	1.18028i	0.0117430	+	0.0739119i
$256$	2.19687	+	3.80509i	0.137304	+	0.237818i
$257$	−8.52231	−	14.7611i	−0.531607	−	0.920771i	−0.999319	−	0.0368900i	$-0.988255\pi$
$257$	−8.52231	−	14.7611i	−0.531607	−	0.920771i	0.467712	−	0.883881i	$-0.345078\pi$
$258$	−3.97266	−	25.0044i	−0.247327	−	1.55671i
$259$	−18.9735	+	32.8630i	−1.17895	+	2.04201i
$260$	0.269903	−	0.608783i	0.0167387	−	0.0377551i
$261$	−15.8826	+	5.17749i	−0.983108	+	0.320479i
$262$			24.0549i			1.48612i
$263$	−6.10773	+	10.5789i	−0.376619	+	0.652323i	−0.990568	−	0.137023i	$-0.956247\pi$
$263$	−6.10773	+	10.5789i	−0.376619	+	0.652323i	0.613949	+	0.789346i	$0.289580\pi$
$264$	−4.11686	−	5.07889i	−0.253375	−	0.312584i
$265$	−4.71222	+	2.72060i	−0.289470	+	0.167125i
$266$	−35.4902	+	20.4903i	−2.17604	+	1.25634i
$267$	−17.3646	−	6.65604i	−1.06270	−	0.407343i
$268$	1.74673	+	1.00848i	0.106699	+	0.0616024i
$269$	14.2974			0.871727			0.435863	−	0.900013i	$-0.356443\pi$
$269$	14.2974			0.871727			0.435863	+	0.900013i	$0.356443\pi$
$270$	6.23329	−	3.18738i	0.379346	−	0.193977i
$271$		−	3.84476i		−	0.233553i	−0.993158	−	0.116776i	$-0.962744\pi$
$271$		−	3.84476i		−	0.233553i	0.993158	−	0.116776i	$-0.0372561\pi$
$272$	−1.24076	+	2.14905i	−0.0752319	+	0.130306i
$273$	−20.8135	−	20.7283i	−1.25969	−	1.25454i
$274$	−2.89508	−	5.01443i	−0.174898	−	0.302933i
$275$	−1.11056	+	0.641180i	−0.0669690	+	0.0386646i
$276$	0.847865	+	1.04600i	0.0510355	+	0.0629615i
$277$	13.5454	−	23.4614i	0.813865	−	1.40966i	−0.0962743	−	0.995355i	$-0.530693\pi$
$277$	13.5454	−	23.4614i	0.813865	−	1.40966i	0.910140	−	0.414301i	$-0.135974\pi$
$278$		−	0.208015i		−	0.0124759i
$279$	2.19184	+	0.463682i	0.131222	+	0.0277599i
$280$		−	13.8454i		−	0.827420i
$281$	7.02708	+	4.05709i	0.419201	+	0.242026i	0.694735	−	0.719266i	$-0.255522\pi$
$281$	7.02708	+	4.05709i	0.419201	+	0.242026i	−0.275535	+	0.961291i	$0.588855\pi$
$282$	17.3033	−	2.74912i	1.03040	−	0.163708i
$283$	12.1427	+	21.0317i	0.721807	+	1.25021i	0.960275	+	0.279056i	$0.0900215\pi$
$283$	12.1427	+	21.0317i	0.721807	+	1.25021i	−0.238468	+	0.971150i	$0.576645\pi$
$284$	0.928144	−	0.535864i	0.0550752	−	0.0317977i
$285$	11.0614	−	1.75742i	0.655222	−	0.104101i
$286$	−5.03405	+	3.66954i	−0.297670	+	0.216984i
$287$	−34.7444			−2.05090
$288$	−3.05640	−	0.646581i	−0.180100	−	0.0381001i
$289$	−16.5239			−0.971996
$290$	−3.75124	+	6.49733i	−0.220280	+	0.381537i
$291$	−2.40915	+	1.95281i	−0.141227	+	0.114476i
$292$	−1.52261	+	0.879078i	−0.0891039	+	0.0514442i
$293$	−22.8249	+	13.1779i	−1.33344	+	0.769864i	−0.985826	−	0.167773i	$-0.946342\pi$
$293$	−22.8249	+	13.1779i	−1.33344	+	0.769864i	−0.347617	+	0.937637i	$0.613009\pi$
$294$	−32.9577	−	12.6330i	−1.92213	−	0.736774i
$295$	0.206661	−	0.357947i	0.0120323	−	0.0208405i
$296$	23.7467			1.38025
$297$	6.65470	+	0.339113i	0.386145	+	0.0196773i
$298$	−12.5212			−0.725334
$299$	12.2634	−	8.93934i	0.709213	−	0.516976i
$300$	−0.114499	+	0.298710i	−0.00661060	+	0.0172460i
$301$	44.1941	−	25.5155i	2.54731	−	1.47069i
$302$	4.77791	+	8.27557i	0.274938	+	0.476206i
$303$	4.04999	+	4.99640i	0.232666	+	0.287036i
$304$	20.1407	+	11.6282i	1.15515	+	0.666924i
$305$			5.83191i			0.333934i
$306$	−0.864373	−	2.65157i	−0.0494129	−	0.151580i
$307$			17.8331i			1.01779i	0.860828	+	0.508896i	$0.169946\pi$
$307$			17.8331i			1.01779i	−0.860828	+	0.508896i	$0.830054\pi$
$308$	0.557028	−	0.964800i	0.0317396	−	0.0549746i
$309$	−18.1234	+	2.87942i	−1.03101	+	0.163805i
$310$	0.871363	−	0.503082i	0.0494901	−	0.0285731i
$311$	12.4668	+	21.5932i	0.706929	+	1.22444i	0.965991	+	0.258576i	$0.0832533\pi$
$311$	12.4668	+	21.5932i	0.706929	+	1.22444i	−0.259062	+	0.965861i	$0.583413\pi$
$312$	−4.72124	+	17.7656i	−0.267287	+	1.00578i
$313$	0.556344	−	0.963617i	0.0314464	−	0.0544668i	−0.849874	−	0.526986i	$-0.823322\pi$
$313$	0.556344	−	0.963617i	0.0314464	−	0.0544668i	0.881320	+	0.472519i	$0.156655\pi$
$314$			18.1092i			1.02196i
$315$	10.4957	+	9.43206i	0.591365	+	0.531436i
$316$	0.893728			0.0502761
$317$	23.8124	+	13.7481i	1.33744	+	0.772169i	0.986427	−	0.164203i	$-0.0525051\pi$
$317$	23.8124	+	13.7481i	1.33744	+	0.772169i	0.351010	+	0.936372i	$0.385838\pi$
$318$	9.86424	−	7.99578i	0.553159	−	0.448381i
$319$	−6.18401	+	3.57034i	−0.346238	+	0.199901i
$320$	−7.44438	+	4.29802i	−0.416154	+	0.240266i
$321$	−8.99123	+	23.4567i	−0.501841	+	1.30923i
$322$	13.3371	−	23.1006i	0.743250	−	1.28735i
$323$		−	4.46170i		−	0.248256i
$324$	1.34291	−	0.979644i	0.0746064	−	0.0544247i
$325$	3.29613	+	1.46134i	0.182837	+	0.0810605i
$326$	−3.13043	+	5.42207i	−0.173379	+	0.300301i
$327$	7.17293	+	2.74947i	0.396664	+	0.152046i
$328$	10.8713	+	18.8296i	0.600267	+	1.03969i
$329$	17.6570	+	30.5828i	0.973462	+	1.68609i
$330$	2.32476	−	1.88441i	0.127974	−	0.103733i
$331$	−10.6947	−	6.17460i	−0.587835	−	0.339387i	0.176406	−	0.984317i	$-0.443553\pi$
$331$	−10.6947	−	6.17460i	−0.587835	−	0.339387i	−0.764241	+	0.644931i	$0.776886\pi$
$332$			0.526648i			0.0289036i
$333$	−16.1772	+	18.0015i	−0.886506	+	0.986475i
$334$	−16.9703			−0.928572
$335$	−5.46019	+	9.45733i	−0.298322	+	0.516709i
$336$	4.59760	+	28.9379i	0.250820	+	1.57869i
$337$	−0.663331	−	1.14892i	−0.0361339	−	0.0625858i	0.847393	−	0.530966i	$-0.178171\pi$
$337$	−0.663331	−	1.14892i	−0.0361339	−	0.0625858i	−0.883527	+	0.468381i	$0.844838\pi$
$338$	16.6750	+	5.36022i	0.906999	+	0.291557i
$339$	12.2345	−	1.94379i	0.664485	−	0.105572i
$340$	0.110363	+	0.0637184i	0.00598530	+	0.00345561i
$341$	0.957643			0.0518593
$342$	−24.8502	+	8.10080i	−1.34374	+	0.438041i
$343$		−	38.2165i		−	2.06350i
$344$	−27.6561	−	15.9673i	−1.49112	−	0.860897i
$345$	−5.66334	+	4.59060i	−0.304904	+	0.247150i
$346$	−25.3070	+	14.6110i	−1.36051	+	0.785493i
$347$	12.6904	+	21.9804i	0.681256	+	1.17997i	0.974598	+	0.223963i	$0.0718993\pi$
$347$	12.6904	+	21.9804i	0.681256	+	1.17997i	−0.293342	+	0.956008i	$0.594767\pi$
$348$	−0.637576	+	1.66334i	−0.0341776	+	0.0891642i
$349$	−11.4337	−	6.60123i	−0.612030	−	0.353355i	0.161730	−	0.986835i	$-0.448293\pi$
$349$	−11.4337	−	6.60123i	−0.612030	−	0.353355i	−0.773759	+	0.633480i	$0.781626\pi$
$350$	6.33744			0.338751
$351$	−10.2511	−	15.6817i	−0.547165	−	0.837025i
$352$	−1.33538			−0.0711761
$353$	8.09353	+	4.67280i	0.430775	+	0.248708i	0.699677	−	0.714460i	$-0.253327\pi$
$353$	8.09353	+	4.67280i	0.430775	+	0.248708i	−0.268902	+	0.963168i	$0.586661\pi$
$354$	−0.345229	+	0.900649i	−0.0183487	+	0.0478689i
$355$	2.90133	+	5.02525i	0.153987	+	0.266713i
$356$	−1.71736	+	0.991515i	−0.0910196	+	0.0525502i
$357$	4.36687	−	3.53971i	0.231119	−	0.187341i
$358$	18.1826	+	10.4977i	0.960981	+	0.554823i
$359$		−	29.6022i		−	1.56234i	−0.624315	−	0.781172i	$-0.714622\pi$
$359$		−	29.6022i		−	1.56234i	0.624315	−	0.781172i	$-0.285378\pi$
$360$	1.82765	−	8.63933i	0.0963254	−	0.455333i
$361$	−22.8145			−1.20077
$362$	27.5934	+	15.9311i	1.45028	+	0.837318i
$363$	−16.0036	+	2.54262i	−0.839970	+	0.133453i
$364$	−3.11466	+	0.332307i	−0.163253	+	0.0174176i
$365$	−4.75959	−	8.24386i	−0.249129	−	0.431503i
$366$	−2.13549	−	13.4410i	−0.111624	−	0.702574i
$367$	9.36803	−	16.2259i	0.489007	−	0.846985i	−0.510913	−	0.859633i	$-0.670693\pi$
$367$	9.36803	−	16.2259i	0.489007	−	0.846985i	0.999920	+	0.0126473i	$0.00402586\pi$
$368$	−15.1376			−0.789104
$369$	−21.6800	−	4.58640i	−1.12862	−	0.238758i
$370$			10.8696i			0.565081i
$371$	22.1649	+	12.7969i	1.15074	+	0.664382i
$372$	0.185586	−	0.150433i	0.00962218	−	0.00779957i
$373$	7.12935	+	12.3484i	0.369144	+	0.639375i	0.989432	−	0.144998i	$-0.0463177\pi$
$373$	7.12935	+	12.3484i	0.369144	+	0.639375i	−0.620288	+	0.784374i	$0.712984\pi$
$374$	−0.596062	−	1.03241i	−0.0308216	−	0.0533846i
$375$	−1.61731	−	0.619932i	−0.0835174	−	0.0320132i
$376$	11.0495	−	19.1383i	0.569835	−	0.986983i
$377$	18.3542	+	8.13731i	0.945287	+	0.419093i
$378$	−27.6436	−	17.8952i	−1.42183	−	0.920430i
$379$		−	2.12905i		−	0.109362i	−0.998504	−	0.0546811i	$-0.982586\pi$
$379$		−	2.12905i		−	0.109362i	0.998504	−	0.0546811i	$-0.0174142\pi$
$380$	0.597161	−	1.03431i	0.0306337	−	0.0530591i
$381$	6.66934	−	17.3993i	0.341681	−	0.891392i
$382$	0.787883	−	0.454885i	0.0403116	−	0.0232739i
$383$	−10.5441	+	6.08761i	−0.538776	+	0.311063i	−0.744583	−	0.667530i	$-0.767352\pi$
$383$	−10.5441	+	6.08761i	−0.538776	+	0.311063i	0.205807	+	0.978593i	$0.434018\pi$
$384$	12.7812	−	10.3602i	0.652239	−	0.528693i
$385$	5.22372	+	3.01592i	0.266225	+	0.153705i
$386$	19.7950			1.00754
$387$	30.9447	−	10.0875i	1.57301	−	0.512777i
$388$			0.330695i			0.0167885i
$389$	12.7383	−	22.0634i	0.645858	−	1.11866i	−0.338245	−	0.941058i	$-0.609833\pi$
$389$	12.7383	−	22.0634i	0.645858	−	1.11866i	0.984103	−	0.177600i	$-0.0568333\pi$
$390$	−8.13183	−	2.16105i	−0.411771	−	0.109429i
$391$	1.45206	+	2.51505i	0.0734340	+	0.127191i
$392$	−38.5554	+	22.2600i	−1.94734	+	1.12430i
$393$	−30.5406	+	4.85223i	−1.54057	+	0.244763i
$394$	−1.76252	+	3.05277i	−0.0887943	+	0.153796i
$395$			4.83891i			0.243472i
$396$	0.474935	−	0.528492i	0.0238664	−	0.0265577i
$397$			18.5900i			0.933004i	0.884520	+	0.466502i	$0.154486\pi$
$397$			18.5900i			0.933004i	−0.884520	+	0.466502i	$0.845514\pi$
$398$	−30.2880	−	17.4868i	−1.51820	−	0.876534i
$399$	−33.1737	−	40.9258i	−1.66076	−	2.04885i
$400$	−1.79825	−	3.11466i	−0.0899124	−	0.155733i
$401$	3.02411	−	1.74597i	0.151017	−	0.0871897i	−0.422587	−	0.906322i	$-0.638878\pi$
$401$	3.02411	−	1.74597i	0.151017	−	0.0871897i	0.573604	+	0.819132i	$0.305545\pi$
$402$	9.12130	−	23.7961i	0.454929	−	1.18684i
$403$	−1.58606	−	2.17584i	−0.0790075	−	0.108386i
$404$	0.685837			0.0341217
$405$	5.30409	+	7.27094i	0.263562	+	0.361296i
$406$	35.2894			1.75138
$407$	−5.17269	+	8.95937i	−0.256401	+	0.444099i
$408$	−3.28470	−	1.25906i	−0.162617	−	0.0623328i
$409$	6.29168	−	3.63250i	0.311103	−	0.179616i	−0.336317	−	0.941749i	$-0.609181\pi$
$409$	6.29168	−	3.63250i	0.311103	−	0.179616i	0.647420	+	0.762133i	$0.275848\pi$
$410$	−8.61888	+	4.97611i	−0.425656	+	0.245753i
$411$	5.78242	−	4.68713i	0.285226	−	0.231199i
$412$	−0.978409	+	1.69465i	−0.0482028	+	0.0834896i
$413$	−1.94414			−0.0956649
$414$	11.3716	−	12.6539i	0.558882	−	0.621906i
$415$	−2.85143			−0.139971
$416$	2.21168	+	3.03410i	0.108437	+	0.148759i
$417$	0.264099	−	0.0419597i	0.0129330	−	0.00205477i
$418$	−9.67562	+	5.58622i	−0.473250	+	0.273231i
$419$	−8.78209	−	15.2110i	−0.429033	−	0.743107i	0.567755	−	0.823198i	$-0.307812\pi$
$419$	−8.78209	−	15.2110i	−0.429033	−	0.743107i	−0.996788	+	0.0800910i	$0.974479\pi$
$420$	1.48609	−	0.236107i	0.0725136	−	0.0115209i
$421$	13.8198	+	7.97886i	0.673536	+	0.388866i	0.797415	−	0.603431i	$-0.206200\pi$
$421$	13.8198	+	7.97886i	0.673536	+	0.388866i	−0.123879	+	0.992297i	$0.539534\pi$
$422$			13.9203i			0.677631i
$423$	6.98067	+	21.4140i	0.339412	+	1.04119i
$424$		−	16.0163i		−	0.777818i
$425$	−0.344990	+	0.597541i	−0.0167345	+	0.0289850i
$426$	−8.52693	−	10.5195i	−0.413131	−	0.509672i
$427$	23.7564	−	13.7158i	1.14965	−	0.663753i
$428$	1.33938	+	2.31987i	0.0647412	+	0.112135i
$429$	−5.67435	−	5.65112i	−0.273960	−	0.272838i
$430$	7.30869	−	12.6590i	0.352456	−	0.610472i
$431$		−	2.36438i		−	0.113888i	−0.998377	−	0.0569440i	$-0.981864\pi$
$431$		−	2.36438i		−	0.113888i	0.998377	−	0.0569440i	$-0.0181356\pi$
$432$	−0.951075	+	18.6637i	−0.0457586	+	0.897959i
$433$	−15.9227			−0.765194			−0.382597	−	0.923915i	$-0.624970\pi$
$433$	−15.9227			−0.765194			−0.382597	+	0.923915i	$0.624970\pi$
$434$	−4.09863	−	2.36634i	−0.196741	−	0.113588i
$435$	−9.00580	−	3.45203i	−0.431795	−	0.165512i
$436$	0.709402	−	0.409573i	0.0339742	−	0.0196150i
$437$	23.5707	−	13.6086i	1.12754	−	0.650986i
$438$	13.9883	+	17.2571i	0.668387	+	0.824577i
$439$	12.2763	−	21.2632i	0.585916	−	1.01484i	−0.408844	−	0.912604i	$-0.634068\pi$
$439$	12.2763	−	21.2632i	0.585916	−	1.01484i	0.994761	−	0.102233i	$-0.0325986\pi$
$440$		−	3.77464i		−	0.179949i
$441$	9.39108	−	44.3919i	0.447195	−	2.11390i
$442$	−1.35851	+	3.06420i	−0.0646177	+	0.145749i
$443$	10.9342	−	18.9386i	0.519501	−	0.899802i	−0.480242	−	0.877136i	$-0.659451\pi$
$443$	10.9342	−	18.9386i	0.519501	−	0.899802i	0.999743	−	0.0226659i	$-0.00721539\pi$
$444$	0.404955	+	2.54884i	0.0192183	+	0.120962i
$445$	−5.36836	−	9.29828i	−0.254485	−	0.440781i
$446$	−11.9705	−	20.7336i	−0.566822	−	0.981764i
$447$	−2.52571	−	15.8971i	−0.119462	−	0.751909i
$448$	35.0161	+	20.2166i	1.65436	+	0.955143i
$449$			13.2031i			0.623092i	0.950231	+	0.311546i	$0.100847\pi$
$449$			13.2031i			0.623092i	−0.950231	+	0.311546i	$0.899153\pi$
$450$	3.95448	+	0.836568i	0.186416	+	0.0394362i
$451$	−9.47229			−0.446033
$452$	0.660488	−	1.14400i	0.0310667	−	0.0538092i
$453$	−9.54304	+	7.73541i	−0.448371	+	0.363441i
$454$	19.1930	+	33.2432i	0.900771	+	1.56018i
$455$	−1.79921	−	16.8637i	−0.0843483	−	0.790583i
$456$	−11.7998	+	30.7838i	−0.552575	+	1.44158i
$457$	14.3166	+	8.26571i	0.669704	+	0.386654i	0.795964	−	0.605344i	$-0.206964\pi$
$457$	14.3166	+	8.26571i	0.669704	+	0.386654i	−0.126261	+	0.991997i	$0.540298\pi$
$458$	8.15460			0.381039
$459$	3.19212	−	1.63228i	0.148995	−	0.0761885i
$460$			0.777385i			0.0362458i
$461$	−30.1732	−	17.4205i	−1.40531	−	0.811354i	−0.410375	−	0.911917i	$-0.634602\pi$
$461$	−30.1732	−	17.4205i	−1.40531	−	0.811354i	−0.994931	+	0.100563i	$0.967935\pi$
$462$	−13.1437	−	5.03812i	−0.611499	−	0.234394i
$463$	28.0327	−	16.1847i	1.30279	−	0.752167i	0.321910	−	0.946770i	$-0.395675\pi$
$463$	28.0327	−	16.1847i	1.30279	−	0.752167i	0.980882	+	0.194603i	$0.0623419\pi$
$464$	−10.0134	−	17.3436i	−0.464858	−	0.805158i
$465$	0.814488	+	1.00482i	0.0377710	+	0.0465973i
$466$	−10.2099	−	5.89471i	−0.472966	−	0.273067i
$467$	8.15829			0.377521			0.188760	−	0.982023i	$-0.439553\pi$
$467$	8.15829			0.377521			0.188760	+	0.982023i	$0.439553\pi$
$468$	−1.98737	−	0.203793i	−0.0918663	−	0.00942032i
$469$	51.3662			2.37187
$470$	8.76017	+	5.05769i	0.404077	+	0.233294i
$471$	−22.9917	+	3.65289i	−1.05940	+	0.168316i
$472$	0.608309	+	1.05362i	0.0279997	+	0.0484969i
$473$	12.0486	−	6.95624i	0.553993	−	0.319848i
$474$	−1.77188	−	11.1524i	−0.0813852	−	0.512249i
$475$	5.60008	+	3.23321i	0.256949	+	0.148350i
$476$		−	0.599424i		−	0.0274746i
$477$	12.1413	+	10.9109i	0.555914	+	0.499578i
$478$	−37.9375			−1.73522
$479$	−15.9891	−	9.23132i	−0.730561	−	0.421790i	0.0880661	−	0.996115i	$-0.471931\pi$
$479$	−15.9891	−	9.23132i	−0.730561	−	0.421790i	−0.818628	+	0.574325i	$0.805265\pi$
$480$	−1.13576	−	1.40117i	−0.0518401	−	0.0639542i
$481$	28.9235	−	3.08588i	1.31880	−	0.140704i
$482$	1.97418	+	3.41938i	0.0899215	+	0.155749i
$483$	32.0192	+	12.2733i	1.45693	+	0.558456i
$484$	−0.863967	+	1.49643i	−0.0392712	+	0.0680197i
$485$	−1.79048			−0.0813015
$486$	−14.8870	−	14.8154i	−0.675287	−	0.672041i
$487$		−	36.5271i		−	1.65520i	−0.561317	−	0.827601i	$-0.689705\pi$
$487$		−	36.5271i		−	1.65520i	0.561317	−	0.827601i	$-0.310295\pi$
$488$	−14.8664	−	8.58314i	−0.672972	−	0.388541i
$489$	−7.51540	−	2.88074i	−0.339858	−	0.130272i
$490$	−10.1891	−	17.6480i	−0.460295	−	0.797254i
$491$	−12.3472	−	21.3859i	−0.557220	−	0.965133i	−0.997727	−	0.0673836i	$-0.978535\pi$
$491$	−12.3472	−	21.3859i	−0.557220	−	0.965133i	0.440508	−	0.897749i	$-0.354798\pi$
$492$	−1.83568	+	1.48797i	−0.0827588	+	0.0670828i
$493$	−1.92104	+	3.32734i	−0.0865194	+	0.149856i
$494$	28.7173	+	12.7318i	1.29205	+	0.572830i
$495$	2.86141	+	2.57144i	0.128611	+	0.115578i
$496$			2.68580i			0.120596i
$497$	13.6470	−	23.6373i	0.612151	−	1.06028i
$498$	6.57181	−	1.04412i	0.294490	−	0.0467881i
$499$	6.04869	−	3.49221i	0.270776	−	0.156333i	−0.358464	−	0.933544i	$-0.616699\pi$
$499$	6.04869	−	3.49221i	0.270776	−	0.156333i	0.629240	+	0.777211i	$0.283366\pi$
$500$	−0.159951	+	0.0923480i	−0.00715325	+	0.00412993i
$501$	−3.42315	−	21.5458i	−0.152935	−	0.962593i
$502$	−17.2323	−	9.94910i	−0.769117	−	0.444050i
$503$	10.0965			0.450179			0.225089	−	0.974338i	$-0.427733\pi$
$503$	10.0965			0.450179			0.225089	+	0.974338i	$0.427733\pi$
$504$	−39.4909	+	12.8734i	−1.75906	+	0.573429i
$505$			3.71333i			0.165241i
$506$	3.63608	−	6.29787i	0.161643	−	0.279974i
$507$	−3.44184	+	22.2521i	−0.152857	+	0.988248i
$508$	−0.993496	−	1.72079i	−0.0440793	−	0.0763475i
$509$	−25.1392	+	14.5141i	−1.11427	+	0.643326i	−0.939933	−	0.341359i	$-0.889113\pi$
$509$	−25.1392	+	14.5141i	−1.11427	+	0.643326i	−0.174341	+	0.984685i	$0.555779\pi$
$510$	0.576310	−	1.50350i	0.0255194	−	0.0665762i
$511$	−22.3877	+	38.7766i	−0.990374	+	1.71538i
$512$		−	24.9179i		−	1.10122i
$513$	−15.2976	−	29.9162i	−0.675404	−	1.32083i
$514$			22.9648i			1.01293i
$515$	−9.17537	−	5.29740i	−0.404315	−	0.233431i
$516$	1.24221	−	3.24074i	0.0546854	−	0.142666i
$517$	4.81379	+	8.33773i	0.211710	+	0.366693i
$518$	44.2774	−	25.5636i	1.94544	−	1.12320i
$519$	−23.6552	−	29.1830i	−1.03835	−	1.28099i
$520$	−8.57628	+	6.25162i	−0.376095	+	0.274152i
$521$	11.5657			0.506701			0.253350	−	0.967375i	$-0.418467\pi$
$521$	11.5657			0.506701			0.253350	+	0.967375i	$0.418467\pi$
$522$	22.0201	+	4.65834i	0.963793	+	0.203890i
$523$	6.17284			0.269919			0.134960	−	0.990851i	$-0.456910\pi$
$523$	6.17284			0.269919			0.134960	+	0.990851i	$0.456910\pi$
$524$	−1.64876	+	2.85573i	−0.0720264	+	0.124753i
$525$	1.27836	+	8.04613i	0.0557920	+	0.351162i
$526$	14.2533	−	8.22914i	0.621473	−	0.358808i
$527$	0.446233	−	0.257633i	0.0194382	−	0.0112227i
$528$	1.25343	+	7.88926i	0.0545487	+	0.343336i
$529$	2.64217	−	4.57637i	0.114877	−	0.198973i
$530$	7.33111			0.318443
$531$	−1.21312	−	0.256634i	−0.0526448	−	0.0111370i
$532$	−5.61773			−0.243559
$533$	15.6882	+	21.5218i	0.679530	+	0.932213i
$534$	15.7775	+	19.4644i	0.682758	+	0.842306i
$535$	−12.5605	+	7.25178i	−0.543036	+	0.313522i
$536$	−16.0721	−	27.8377i	−0.694210	−	1.20241i
$537$	−9.66040	+	25.2025i	−0.416877	+	1.08757i
$538$	−16.6825	−	9.63166i	−0.719235	−	0.415250i
$539$		−	19.3954i		−	0.835419i
$540$	0.958465	+	0.0488419i	0.0412458	+	0.00210182i
$541$			10.6019i			0.455811i	0.973683	+	0.227905i	$0.0731877\pi$
$541$			10.6019i			0.455811i	−0.973683	+	0.227905i	$0.926812\pi$
$542$	−2.59009	+	4.48616i	−0.111254	+	0.192697i
$543$	−14.6603	+	38.2466i	−0.629135	+	1.64132i
$544$	−0.622248	+	0.359255i	−0.0266787	+	0.0154029i
$545$	2.21755	+	3.84091i	0.0949895	+	0.164527i
$546$	10.3218	+	38.2077i	0.441731	+	1.63514i
$547$	−13.0254	+	22.5607i	−0.556926	+	0.964624i	0.440825	+	0.897593i	$0.354686\pi$
$547$	−13.0254	+	22.5607i	−0.556926	+	0.964624i	−0.997751	+	0.0670308i	$0.978647\pi$
$548$		−	0.793732i		−	0.0339065i
$549$	16.6342	−	5.42251i	0.709931	−	0.231427i
$550$	1.72776			0.0736721
$551$	31.1835	+	18.0038i	1.32846	+	0.766987i
$552$	−3.36710	−	21.1930i	−0.143313	−	0.902033i
$553$	19.7114	−	11.3804i	0.838215	−	0.483944i
$554$	−31.6102	+	18.2502i	−1.34299	+	0.775376i
$555$	−13.8002	+	2.19255i	−0.585784	+	0.0930685i
$556$	0.0142576	−	0.0246949i	0.000604658	−	0.00104730i
$557$			33.4373i			1.41678i	0.705819	+	0.708392i	$0.250579\pi$
$557$			33.4373i			1.41678i	−0.705819	+	0.708392i	$0.749421\pi$
$558$	−2.24512	−	2.01760i	−0.0950435	−	0.0854119i
$559$	−35.7601	−	15.8542i	−1.51249	−	0.670563i
$560$	−8.45842	+	14.6504i	−0.357433	+	0.619093i
$561$	1.19053	−	0.965023i	0.0502642	−	0.0407433i
$562$	−5.46625	−	9.46782i	−0.230580	−	0.399376i
$563$	−6.04230	−	10.4656i	−0.254653	−	0.441071i	0.710148	−	0.704052i	$-0.248628\pi$
$563$	−6.04230	−	10.4656i	−0.254653	−	0.441071i	−0.964801	+	0.262981i	$0.915294\pi$
$564$	2.24263	+	0.859625i	0.0944317	+	0.0361967i
$565$	6.19396	+	3.57608i	0.260582	+	0.150447i
$566$		−	32.7204i		−	1.37534i
$567$	17.1439	−	38.7065i	0.719978	−	1.62552i
$568$	−17.0802			−0.716669
$569$	−2.87574	+	4.98094i	−0.120557	+	0.208812i	−0.919988	−	0.391947i	$-0.871802\pi$
$569$	−2.87574	+	4.98094i	−0.120557	+	0.208812i	0.799430	+	0.600759i	$0.205135\pi$
$570$	−14.0906	−	5.40111i	−0.590192	−	0.226227i
$571$	3.34805	+	5.79900i	0.140112	+	0.242681i	0.927539	−	0.373728i	$-0.121921\pi$
$571$	3.34805	+	5.79900i	0.140112	+	0.242681i	−0.787427	+	0.616408i	$0.788587\pi$
$572$	−0.849143	+	0.0905962i	−0.0355045	+	0.00378802i
$573$	0.736457	+	0.908553i	0.0307659	+	0.0379553i
$574$	40.5406	+	23.4061i	1.69213	+	0.976953i
$575$	−4.20900			−0.175527
$576$	19.1809	+	17.2371i	0.799205	+	0.718214i
$577$		−	21.0568i		−	0.876607i	−0.898827	−	0.438304i	$-0.855579\pi$
$577$		−	21.0568i		−	0.876607i	0.898827	−	0.438304i	$-0.144421\pi$
$578$	19.2805	+	11.1316i	0.801964	+	0.463014i
$579$	3.99294	+	25.1320i	0.165941	+	1.04445i
$580$	−0.890673	+	0.514230i	−0.0369832	+	0.0213522i
$581$	6.70614	+	11.6154i	0.278217	+	0.481887i
$582$	4.12659	−	0.655627i	0.171053	−	0.0271766i
$583$	6.04276	+	3.48879i	0.250266	+	0.144491i
$584$	28.0198			1.15947
$585$	1.10340	−	10.7602i	0.0456198	−	0.444881i
$586$	35.5101			1.46691
$587$	−13.1797	−	7.60928i	−0.543983	−	0.314069i	0.202709	−	0.979239i	$-0.435026\pi$
$587$	−13.1797	−	7.60928i	−0.543983	−	0.314069i	−0.746692	+	0.665170i	$0.768359\pi$
$588$	−3.04675	−	3.75872i	−0.125646	−	0.155007i
$589$	−2.41450	−	4.18204i	−0.0994878	−	0.172318i
$590$	−0.482274	+	0.278441i	−0.0198549	+	0.0114632i
$591$	−4.23137	−	1.62193i	−0.174055	−	0.0667174i
$592$	−25.1274	−	14.5073i	−1.03273	−	0.596246i
$593$			31.4829i			1.29285i	0.762979	+	0.646423i	$0.223736\pi$
$593$			31.4829i			1.29285i	−0.762979	+	0.646423i	$0.776264\pi$
$594$	−7.53641	−	4.87873i	−0.309223	−	0.200177i
$595$	3.24546			0.133051
$596$	−1.48648	−	0.858221i	−0.0608887	−	0.0351541i
$597$	16.0920	−	41.9815i	0.658601	−	1.71819i
$598$	−20.3314	+	2.16918i	−0.831413	+	0.0887045i
$599$	−3.53079	−	6.11551i	−0.144264	−	0.249873i	0.784834	−	0.619706i	$-0.212748\pi$
$599$	−3.53079	−	6.11551i	−0.144264	−	0.249873i	−0.929098	+	0.369833i	$0.879415\pi$
$600$	3.96059	−	3.21038i	0.161690	−	0.131063i
$601$	−0.0378043	+	0.0654790i	−0.00154207	+	0.00267094i	−0.866795	−	0.498664i	$-0.833824\pi$
$601$	−0.0378043	+	0.0654790i	−0.00154207	+	0.00267094i	0.865253	+	0.501335i	$0.167158\pi$
$602$	−68.7557			−2.80227
$603$	32.0518	+	6.78054i	1.30525	+	0.276125i
$604$			1.30994i			0.0533006i
$605$	−8.10215	−	4.67778i	−0.329399	−	0.190179i
$606$	−1.35972	−	8.55826i	−0.0552350	−	0.347656i
$607$	−22.5595	−	39.0742i	−0.915663	−	1.58597i	−0.805928	−	0.592014i	$-0.798333\pi$
$607$	−22.5595	−	39.0742i	−0.915663	−	1.58597i	−0.109735	−	0.993961i	$-0.535000\pi$
$608$	3.36690	+	5.83164i	0.136546	+	0.236504i
$609$	7.11839	+	44.8040i	0.288452	+	1.81555i
$610$	3.92876	−	6.80481i	0.159071	−	0.275519i
$611$	10.9713	−	24.7464i	0.443851	−	1.00113i
$612$	0.0791264	−	0.374032i	0.00319849	−	0.0151194i
$613$			18.2482i			0.737039i	0.929620	+	0.368519i	$0.120135\pi$
$613$			18.2482i			0.737039i	−0.929620	+	0.368519i	$0.879865\pi$
$614$	12.0136	−	20.8081i	0.484829	−	0.839748i
$615$	−8.05631	−	9.93892i	−0.324862	−	0.400776i
$616$	−15.3761	+	8.87738i	−0.619520	+	0.357680i
$617$	−6.90824	+	3.98847i	−0.278115	+	0.160570i	−0.632570	−	0.774503i	$-0.718000\pi$
$617$	−6.90824	+	3.98847i	−0.278115	+	0.160570i	0.354455	+	0.935073i	$0.384667\pi$
$618$	23.0866	+	8.84936i	0.928680	+	0.355974i
$619$	−3.59308	−	2.07447i	−0.144418	−	0.0833799i	0.426050	−	0.904700i	$-0.359905\pi$
$619$	−3.59308	−	2.07447i	−0.144418	−	0.0833799i	−0.570468	+	0.821320i	$0.693238\pi$
$620$	0.137928			0.00553931
$621$	18.3594	+	11.8851i	0.736738	+	0.476931i
$622$		−	33.5939i		−	1.34699i
$623$	−25.2512	+	43.7363i	−1.01167	+	1.75226i
$624$	15.8491	−	15.9142i	0.634471	−	0.637079i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.29831	+	0.749581i	−0.0518910	+	0.0299593i
$627$	−9.04407	−	11.1575i	−0.361186	−	0.445588i
$628$	−1.24123	+	2.14987i	−0.0495304	+	0.0857892i
$629$			5.56640i			0.221947i
$630$	−5.89256	−	18.0761i	−0.234765	−	0.720170i
$631$			47.5878i			1.89444i	0.320586	+	0.947219i	$0.396120\pi$
$631$			47.5878i			1.89444i	−0.320586	+	0.947219i	$0.603880\pi$
$632$	−12.3351	−	7.12170i	−0.490666	−	0.283286i
$633$	−17.6735	+	2.80794i	−0.702458	+	0.111605i
$634$	−18.5232	−	32.0832i	−0.735652	−	1.27419i
$635$	9.31686	−	5.37909i	0.369728	−	0.213463i
$636$	1.71910	−	0.273127i	0.0681666	−	0.0108302i
$637$	−44.0679	+	32.1230i	−1.74603	+	1.27276i
$638$	9.62087			0.380894
$639$	11.6357	−	12.9479i	0.460303	−	0.512210i
$640$	9.49901			0.375482
$641$	−22.3444	+	38.7016i	−0.882549	+	1.52862i	−0.0340518	+	0.999420i	$0.510841\pi$
$641$	−22.3444	+	38.7016i	−0.882549	+	1.52862i	−0.848497	+	0.529200i	$0.822492\pi$
$642$	26.2932	−	21.3128i	1.03771	−	0.841148i
$643$	−40.3294	+	23.2842i	−1.59043	+	0.918238i	−0.597203	+	0.802090i	$0.703721\pi$
$643$	−40.3294	+	23.2842i	−1.59043	+	0.918238i	−0.993232	+	0.116148i	$0.962945\pi$
$644$	3.16670	−	1.82829i	0.124785	−	0.0720448i
$645$	17.5464	+	6.72572i	0.690888	+	0.264825i
$646$	−3.00570	+	5.20602i	−0.118258	+	0.204828i
$647$	9.01192			0.354295			0.177148	−	0.984184i	$-0.443313\pi$
$647$	9.01192			0.354295			0.177148	+	0.984184i	$0.443313\pi$
$648$	−26.3411	+	2.81990i	−1.03478	+	0.110776i
$649$	−0.530027			−0.0208054
$650$	−2.86155	−	3.92562i	−0.112239	−	0.153975i
$651$	2.17760	−	5.68102i	0.0853468	−	0.222657i
$652$	−0.743272	+	0.429128i	−0.0291088	+	0.0168060i
$653$	−1.39222	−	2.41140i	−0.0544820	−	0.0943655i	0.837498	−	0.546440i	$-0.184017\pi$
$653$	−1.39222	−	2.41140i	−0.0544820	−	0.0943655i	−0.891980	+	0.452075i	$0.850684\pi$
$654$	−6.51732	−	8.04030i	−0.254848	−	0.314401i
$655$	−15.4618	−	8.92688i	−0.604143	−	0.348802i
$656$		−	26.5659i		−	1.03722i
$657$	−19.0883	+	21.2408i	−0.744705	+	0.828683i
$658$		−	47.5797i		−	1.85485i
$659$	24.3369	−	42.1528i	0.948033	−	1.64204i	0.198471	−	0.980107i	$-0.436402\pi$
$659$	24.3369	−	42.1528i	0.948033	−	1.64204i	0.749562	−	0.661934i	$-0.230264\pi$
$660$	0.405149	−	0.0643694i	0.0157704	−	0.00250557i
$661$	17.4542	−	10.0772i	0.678889	−	0.391957i	−0.120547	−	0.992708i	$-0.538465\pi$
$661$	17.4542	−	10.0772i	0.678889	−	0.391957i	0.799436	+	0.600751i	$0.205132\pi$
$662$	8.31923	+	14.4093i	0.323336	+	0.560035i
$663$	−4.16439	−	1.10669i	−0.161731	−	0.0429804i
$664$	4.19661	−	7.26874i	0.162860	−	0.282082i
$665$		−	30.4161i		−	1.17948i
$666$	31.0030	−	10.1065i	1.20134	−	0.391619i
$667$	−23.4374			−0.907498
$668$	−2.01466	−	1.16317i	−0.0779497	−	0.0450043i
$669$	23.9091	−	19.3803i	0.924379	−	0.749285i
$670$	12.7422	−	7.35669i	0.492273	−	0.284214i
$671$	6.47666	−	3.73930i	0.250029	−	0.144354i
$672$	−3.03655	+	7.92188i	−0.117137	+	0.305593i
$673$	−6.19480	+	10.7297i	−0.238792	+	0.413600i	−0.960368	−	0.278735i	$-0.910085\pi$
$673$	−6.19480	+	10.7297i	−0.238792	+	0.413600i	0.721576	+	0.692335i	$0.243418\pi$
$674$			1.78745i			0.0688502i
$675$	−0.264445	+	5.18942i	−0.0101785	+	0.199741i
$676$	1.61221	+	1.77927i	0.0620080	+	0.0684336i
$677$	−23.2146	+	40.2088i	−0.892208	+	1.54535i	−0.0549850	+	0.998487i	$0.517511\pi$
$677$	−23.2146	+	40.2088i	−0.892208	+	1.54535i	−0.837223	+	0.546862i	$0.815822\pi$
$678$	−15.5849	−	5.97388i	−0.598536	−	0.229425i
$679$	4.21094	+	7.29356i	0.161601	+	0.279901i
$680$	−1.01548	−	1.75887i	−0.0389420	−	0.0674495i
$681$	−38.3346	+	31.0734i	−1.46899	+	1.19073i
$682$	−1.11740	−	0.645131i	−0.0427875	−	0.0247034i
$683$			19.0750i			0.729884i	0.931030	+	0.364942i	$0.118911\pi$
$683$			19.0750i			0.729884i	−0.931030	+	0.364942i	$0.881089\pi$
$684$	−3.50538	−	0.741563i	−0.134032	−	0.0283544i
$685$	4.29750			0.164199
$686$	−25.7452	+	44.5920i	−0.982956	+	1.70253i
$687$	1.64490	+	10.3532i	0.0627570	+	0.395000i
$688$	19.5094	+	33.7913i	0.743789	+	1.28828i
$689$	−2.08132	−	19.5078i	−0.0792918	−	0.743189i
$690$	9.70065	−	1.54122i	0.369297	−	0.0586734i
$691$	14.9252	+	8.61704i	0.567779	+	0.327808i	0.756262	−	0.654269i	$-0.227024\pi$
$691$	14.9252	+	8.61704i	0.567779	+	0.327808i	−0.188483	+	0.982077i	$0.560357\pi$
$692$	−4.00584			−0.152279
$693$	3.74521	−	17.7037i	0.142269	−	0.672507i
$694$		−	34.1964i		−	1.29808i
$695$	0.133706	+	0.0771951i	0.00507175	+	0.00292818i
$696$	22.0541	−	17.8767i	0.835958	−	0.677613i
$697$	−4.41380	+	2.54831i	−0.167185	+	0.0965242i
$698$	8.89404	+	15.4049i	0.336645	+	0.583085i
$699$	5.42453	−	14.1518i	0.205175	−	0.535269i
$700$	0.752363	+	0.434377i	0.0284367	+	0.0164179i
$701$	−37.1790			−1.40423			−0.702116	−	0.712063i	$-0.747761\pi$
$701$	−37.1790			−1.40423			−0.702116	+	0.712063i	$0.747761\pi$
$702$	1.39707	+	25.2036i	0.0527290	+	0.951247i
$703$	52.1676			1.96754
$704$	9.54637	+	5.51160i	0.359792	+	0.207726i
$705$	−4.65427	+	12.1423i	−0.175290	+	0.457304i
$706$	−6.29581	−	10.9047i	−0.236946	−	0.410403i
$707$	15.1263	−	8.73319i	0.568884	−	0.328446i
$708$	−0.102716	+	0.0832600i	−0.00386032	+	0.00312910i
$709$	−4.67297	−	2.69794i	−0.175497	−	0.101323i	0.409678	−	0.912230i	$-0.365641\pi$
$709$	−4.67297	−	2.69794i	−0.175497	−	0.101323i	−0.585175	+	0.810907i	$0.698974\pi$
$710$		−	7.81811i		−	0.293409i
$711$	13.8019	−	4.49922i	0.517612	−	0.168734i
$712$	31.6037			1.18440
$713$	2.72209	+	1.57160i	0.101943	+	0.0588570i
$714$	−7.47995	+	1.18840i	−0.279930	+	0.0444748i
$715$	−0.490515	−	4.59752i	−0.0183442	−	0.171937i
$716$	1.43906	+	2.49252i	0.0537801	+	0.0931499i
$717$	−7.65255	−	48.1661i	−0.285790	−	1.79880i
$718$	−19.9420	+	34.5406i	−0.744229	+	1.28904i
$719$	−13.0486			−0.486630			−0.243315	−	0.969947i	$-0.578235\pi$
$719$	−13.0486			−0.486630			−0.243315	+	0.969947i	$0.578235\pi$
$720$	−7.21185	+	8.02510i	−0.268770	+	0.299078i
$721$			49.8348i			1.85594i
$722$	26.6206	+	15.3694i	0.990715	+	0.571989i
$723$	−3.94308	+	3.19619i	−0.146645	+	0.118868i
$724$	2.18387	+	3.78258i	0.0811630	+	0.140578i
$725$	−2.78420	−	4.82237i	−0.103402	−	0.179098i
$726$	20.3862	+	7.81427i	0.756604	+	0.290015i
$727$	13.1337	−	22.7482i	0.487102	−	0.843685i	−0.512788	−	0.858515i	$-0.671387\pi$
$727$	13.1337	−	22.7482i	0.487102	−	0.843685i	0.999890	+	0.0148298i	$0.00472065\pi$
$728$	45.6362	+	20.2328i	1.69139	+	0.749878i
$729$	15.8070	−	21.8892i	0.585444	−	0.810713i
$730$			12.8255i			0.474693i
$731$	3.74284	−	6.48280i	0.138434	−	0.239775i
$732$	0.667748	−	1.74205i	0.0246807	−	0.0643880i
$733$	−0.173348	+	0.100083i	−0.00640277	+	0.00369664i	−0.503198	−	0.864171i	$-0.667843\pi$
$733$	−0.173348	+	0.100083i	−0.00640277	+	0.00369664i	0.496795	+	0.867868i	$0.334510\pi$
$734$	−21.8617	+	12.6218i	−0.806929	+	0.465881i
$735$	20.3509	−	16.4960i	0.750653	−	0.608466i
$736$	−3.79582	−	2.19152i	−0.139916	−	0.0807804i
$737$	14.0038			0.515838
$738$	22.2071	+	19.9566i	0.817453	+	0.734613i
$739$			18.4711i			0.679469i	0.940521	+	0.339734i	$0.110337\pi$
$739$			18.4711i			0.679469i	−0.940521	+	0.339734i	$0.889663\pi$
$740$	−0.745014	+	1.29040i	−0.0273873	+	0.0474361i
$741$	−10.3718	+	39.0281i	−0.381017	+	1.43373i
$742$	−17.2417	−	29.8635i	−0.632962	−	1.09632i
$743$	39.2169	−	22.6419i	1.43873	−	0.830651i	0.440969	−	0.897523i	$-0.354635\pi$
$743$	39.2169	−	22.6419i	1.43873	−	0.830651i	0.997762	+	0.0668712i	$0.0213017\pi$
$744$	−3.76017	+	0.597409i	−0.137854	+	0.0219021i
$745$	4.64667	−	8.04826i	0.170241	−	0.294865i
$746$		−	19.2112i		−	0.703372i
$747$	2.65126	+	8.13306i	0.0970045	+	0.297573i
$748$		−	0.163420i		−	0.00597521i
$749$	59.0806	+	34.1102i	2.15876	+	1.24636i
$750$	1.46949	+	1.81288i	0.0536580	+	0.0661969i
$751$	1.17321	+	2.03207i	0.0428112	+	0.0741511i	0.886637	−	0.462466i	$-0.153035\pi$
$751$	1.17321	+	2.03207i	0.0428112	+	0.0741511i	−0.843826	+	0.536617i	$0.819702\pi$
$752$	−23.3839	+	13.5007i	−0.852724	+	0.492320i
$753$	9.15553	−	23.8854i	0.333646	−	0.870431i
$754$	−15.9342	−	21.8594i	−0.580291	−	0.796072i
$755$	−7.09239			−0.258119
$756$	−2.05521	−	4.01920i	−0.0747471	−	0.146177i
$757$	16.5812			0.602655			0.301328	−	0.953521i	$-0.402570\pi$
$757$	16.5812			0.602655			0.301328	+	0.953521i	$0.402570\pi$
$758$	−1.43427	+	2.48423i	−0.0520951	+	0.0902313i
$759$	8.72933	+	3.34605i	0.316855	+	0.121454i
$760$	−16.4839	+	9.51699i	−0.597934	+	0.345217i
$761$	33.9243	−	19.5862i	1.22976	−	0.709999i	0.262776	−	0.964857i	$-0.415362\pi$
$761$	33.9243	−	19.5862i	1.22976	−	0.709999i	0.966979	+	0.254857i	$0.0820285\pi$
$762$	−19.5033	+	15.8090i	−0.706528	+	0.572699i
$763$	10.4307	−	18.0665i	0.377617	−	0.654051i
$764$	0.124714			0.00451198
$765$	2.02512	+	0.428414i	0.0732185	+	0.0154893i
$766$	16.4041			0.592703
$767$	0.877840	+	1.20426i	0.0316970	+	0.0434834i
$768$	7.51591	−	1.19412i	0.271207	−	0.0430889i
$769$	−11.5984	+	6.69637i	−0.418251	+	0.241477i	−0.694329	−	0.719658i	$-0.744299\pi$
$769$	−11.5984	+	6.69637i	−0.418251	+	0.241477i	0.276078	+	0.961135i	$0.410965\pi$
$770$	−4.06344	−	7.03808i	−0.146436	−	0.253635i
$771$	−29.1565	+	4.63233i	−1.05004	+	0.166829i
$772$	2.35000	+	1.35677i	0.0845785	+	0.0488314i
$773$			1.74544i			0.0627792i	0.999507	+	0.0313896i	$0.00999327\pi$
$773$			1.74544i			0.0627792i	−0.999507	+	0.0313896i	$0.990007\pi$
$774$	−42.9026	−	9.07603i	−1.54210	−	0.326231i
$775$			0.746782i			0.0268252i
$776$	2.63515	−	4.56421i	0.0945964	−	0.163846i
$777$	41.3873	+	51.0587i	1.48476	+	1.83172i
$778$	−29.7267	+	17.1627i	−1.06575	+	0.615313i
$779$	23.8825	+	41.3656i	0.855678	+	1.48208i
$780$	−0.817267	−	0.813921i	−0.0292628	−	0.0291430i
$781$	3.72055	−	6.44418i	0.133132	−	0.230591i
$782$		−	3.91283i		−	0.139922i
$783$	−1.47253	+	28.8967i	−0.0526240	+	1.03268i
$784$	54.3962			1.94272
$785$	−11.6401	−	6.72039i	−0.415451	−	0.239861i
$786$	38.9042	+	14.9124i	1.38767	+	0.531909i
$787$	6.26287	−	3.61587i	0.223247	−	0.128892i	−0.384206	−	0.923248i	$-0.625525\pi$
$787$	6.26287	−	3.61587i	0.223247	−	0.128892i	0.607453	+	0.794356i	$0.292191\pi$
$788$	−0.418482	+	0.241611i	−0.0149078	+	0.00860702i
$789$	13.3230	+	16.4363i	0.474310	+	0.585147i
$790$	3.25981	−	5.64616i	0.115979	−	0.200881i
$791$		−	33.6416i		−	1.19616i
$792$	−10.7663	+	3.50966i	−0.382564	+	0.124710i
$793$	−19.2227	−	8.52239i	−0.682620	−	0.302639i
$794$	12.5234	−	21.6912i	0.444440	−	0.769792i
$795$	1.47879	+	9.30771i	0.0524474	+	0.330110i
$796$	−2.39714	−	4.15196i	−0.0849643	−	0.147162i
$797$	−0.166846	−	0.288986i	−0.00590999	−	0.0102364i	0.863055	−	0.505109i	$-0.168548\pi$
$797$	−0.166846	−	0.288986i	−0.00590999	−	0.0102364i	−0.868965	+	0.494873i	$0.835215\pi$
$798$	11.1376	+	70.1012i	0.394265	+	2.48155i
$799$	4.48616	+	2.59009i	0.158709	+	0.0916307i
$800$		−	1.04135i		−	0.0368172i
$801$	−21.5297	+	23.9576i	−0.760716	+	0.846500i
$802$	−4.70481			−0.166133
$803$	−6.10351	+	10.5716i	−0.215388	+	0.373063i
$804$	2.71387	−	2.19981i	0.0957108	−	0.0775814i
$805$	9.89893	+	17.1454i	0.348891	+	0.604298i
$806$	0.384867	+	3.60730i	0.0135564	+	0.127062i
$807$	8.86341	−	23.1233i	0.312007	−	0.813977i
$808$	−9.46586	−	5.46511i	−0.333008	−	0.192262i
$809$	−21.5481			−0.757589			−0.378795	−	0.925481i	$-0.623661\pi$
$809$	−21.5481			−0.757589			−0.378795	+	0.925481i	$0.623661\pi$
$810$	−1.29075	−	12.0571i	−0.0453524	−	0.423643i
$811$			38.3145i			1.34540i	0.739913	+	0.672702i	$0.234867\pi$
$811$			38.3145i			1.34540i	−0.739913	+	0.672702i	$0.765133\pi$
$812$	4.18946	+	2.41878i	0.147021	+	0.0848826i
$813$	−6.21816	−	2.38349i	−0.218081	−	0.0835927i
$814$	12.0712	−	6.96933i	0.423097	−	0.244275i
$815$	−2.32343	−	4.02430i	−0.0813862	−	0.140965i
$816$	2.70650	+	3.33895i	0.0947463	+	0.116887i
$817$	−60.7560	−	35.0775i	−2.12558	−	1.22721i
$818$	−9.78837			−0.342242
$819$	−46.4271	+	20.8117i	−1.62229	+	0.727221i
$820$	−1.36428			−0.0476427
$821$	−2.80704	−	1.62065i	−0.0979665	−	0.0565610i	0.450216	−	0.892920i	$-0.351347\pi$
$821$	−2.80704	−	1.62065i	−0.0979665	−	0.0565610i	−0.548183	+	0.836359i	$0.684680\pi$
$822$	−9.90463	+	1.57363i	−0.345464	+	0.0548867i
$823$	−10.2808	−	17.8069i	−0.358367	−	0.620711i	0.629321	−	0.777146i	$-0.283333\pi$
$823$	−10.2808	−	17.8069i	−0.358367	−	0.620711i	−0.987688	+	0.156435i	$0.950000\pi$
$824$	27.0078	−	15.5930i	0.940862	−	0.543207i
$825$	0.348515	+	2.19360i	0.0121337	+	0.0763713i
$826$	2.26847	+	1.30970i	0.0789302	+	0.0455704i
$827$		−	15.8002i		−	0.549426i	−0.961526	−	0.274713i	$-0.911417\pi$
$827$		−	15.8002i		−	0.549426i	0.961526	−	0.274713i	$-0.0885828\pi$
$828$	2.21732	−	0.722813i	0.0770571	−	0.0251195i
$829$	−36.2323			−1.25840			−0.629201	−	0.777243i	$-0.716618\pi$
$829$	−36.2323			−1.25840			−0.629201	+	0.777243i	$0.716618\pi$
$830$	3.32712	+	1.92091i	0.115486	+	0.0666758i
$831$	−29.5470	−	36.4516i	−1.02497	−	1.26449i
$832$	−3.28807	−	30.8185i	−0.113993	−	1.06844i
$833$	−5.21791	−	9.03768i	−0.180790	−	0.313137i
$834$	−0.336424	−	0.128955i	−0.0116494	−	0.00446535i
$835$	6.29773	−	10.9080i	0.217942	−	0.377487i
$836$	−1.53155			−0.0529697
$837$	2.10871	−	3.25742i	0.0728876	−	0.112593i
$838$			23.6648i			0.817486i
$839$	−38.1830	−	22.0450i	−1.31822	−	0.761077i	−0.334781	−	0.942296i	$-0.608662\pi$
$839$	−38.1830	−	22.0450i	−1.31822	−	0.761077i	−0.983443	+	0.181219i	$0.941996\pi$
$840$	−22.3923	−	8.58321i	−0.772606	−	0.296149i
$841$	−1.00350	−	1.73812i	−0.0346035	−	0.0599350i
$842$	−10.7502	−	18.6199i	−0.370476	−	0.641683i
$843$	10.9179	−	8.84984i	0.376032	−	0.304805i
$844$	−0.954119	+	1.65258i	−0.0328421	+	0.0568842i
$845$	−9.63353	+	8.72898i	−0.331404	+	0.300286i
$846$	6.28071	−	29.6891i	0.215935	−	1.02073i
$847$			44.0057i			1.51205i
$848$	−9.78464	+	16.9475i	−0.336006	+	0.581979i
$849$	41.5424	−	6.60019i	1.42573	−	0.226518i
$850$	0.805086	−	0.464817i	0.0276142	−	0.0159431i
$851$	−29.4067	+	16.9780i	−1.00805	+	0.581997i
$852$	−0.291271	−	1.83329i	−0.00997877	−	0.0628076i
$853$	24.3692	+	14.0696i	0.834386	+	0.481733i	0.855352	−	0.518047i	$-0.173341\pi$
$853$	24.3692	+	14.0696i	0.834386	+	0.481733i	−0.0209659	+	0.999780i	$0.506674\pi$
$854$	−36.9594			−1.26472
$855$	4.01504	−	18.9792i	0.137312	−	0.649075i
$856$		−	42.6914i		−	1.45916i
$857$	22.0174	−	38.1353i	0.752100	−	1.30268i	−0.194703	−	0.980862i	$-0.562374\pi$
$857$	22.0174	−	38.1353i	0.752100	−	1.30268i	0.946803	−	0.321813i	$-0.104292\pi$
$858$	2.81400	+	10.4165i	0.0960684	+	0.355613i
$859$	1.83197	+	3.17306i	0.0625060	+	0.108263i	0.895585	−	0.444891i	$-0.146757\pi$
$859$	1.83197	+	3.17306i	0.0625060	+	0.108263i	−0.833079	+	0.553154i	$0.813424\pi$
$860$	1.73533	−	1.00189i	0.0591744	−	0.0341643i
$861$	−21.5392	+	56.1924i	−0.734053	+	1.91503i
$862$	−1.59280	+	2.75881i	−0.0542510	+	0.0939654i
$863$		−	27.1013i		−	0.922539i	−0.887260	−	0.461269i	$-0.847394\pi$
$863$		−	27.1013i		−	0.922539i	0.887260	−	0.461269i	$-0.152606\pi$
$864$	−2.94048	+	4.54231i	−0.100037	+	0.154532i
$865$		−	21.6888i		−	0.737441i
$866$	18.5789	+	10.7266i	0.631338	+	0.364503i
$867$	−10.2437	+	26.7243i	−0.347895	+	0.907604i
$868$	−0.324385	−	0.561851i	−0.0110103	−	0.0190705i
$869$	5.37388	−	3.10261i	0.182296	−	0.105249i
$870$	8.18267	+	10.0948i	0.277419	+	0.342246i
$871$	−23.1934	−	31.8179i	−0.785879	−	1.07811i
$872$	−13.0548			−0.442091
$873$	1.66479	+	5.10694i	0.0563446	+	0.172844i
$874$	−36.6705			−1.24040
$875$	−2.35185	+	4.07352i	−0.0795070	+	0.137710i
$876$	0.477826	+	3.00749i	0.0161442	+	0.101614i
$877$	21.1948	−	12.2368i	0.715697	−	0.413208i	−0.0974701	−	0.995238i	$-0.531075\pi$
$877$	21.1948	−	12.2368i	0.715697	−	0.413208i	0.813167	+	0.582031i	$0.197742\pi$
$878$	−28.6486	+	16.5403i	−0.966843	+	0.558207i
$879$	7.16291	+	45.0843i	0.241599	+	1.52065i
$880$	−2.30600	+	3.99411i	−0.0777352	+	0.134641i
$881$	39.3187			1.32468			0.662341	−	0.749203i	$-0.269563\pi$
$881$	39.3187			1.32468			0.662341	+	0.749203i	$0.269563\pi$
$882$	−40.8630	+	45.4711i	−1.37593	+	1.53109i
$883$	−19.4346			−0.654027			−0.327014	−	0.945020i	$-0.606042\pi$
$883$	−19.4346			−0.654027			−0.327014	+	0.945020i	$0.606042\pi$
$884$	−0.371303	+	0.270658i	−0.0124883	+	0.00910323i
$885$	−0.450795	−	0.556137i	−0.0151533	−	0.0186943i
$886$	−25.5166	+	14.7320i	−0.857248	+	0.494932i
$887$	18.3946	+	31.8604i	0.617631	+	1.06977i	0.989917	+	0.141650i	$0.0452409\pi$
$887$	18.3946	+	31.8604i	0.617631	+	1.06977i	−0.372285	+	0.928118i	$0.621426\pi$
$888$	14.7213	−	38.4057i	0.494015	−	1.28881i
$889$	−43.8237	−	25.3016i	−1.46980	−	0.848589i
$890$			14.4659i			0.484899i
$891$	4.67391	−	10.5525i	0.156582	−	0.353521i
$892$		−	3.28191i		−	0.109887i
$893$	24.2740	−	42.0438i	0.812298	−	1.40694i
$894$	−7.76230	+	20.2506i	−0.259610	+	0.677283i
$895$	−13.4953	+	7.79150i	−0.451097	+	0.260441i
$896$	−22.3403	−	38.6945i	−0.746335	−	1.29269i
$897$	−6.85517	−	25.3755i	−0.228888	−	0.847264i
$898$	8.89447	−	15.4057i	0.296812	−	0.514094i
$899$			4.15838i			0.138690i
$900$	0.412125	+	0.370360i	0.0137375	+	0.0123453i
$901$	3.75433			0.125075
$902$	11.0525	+	6.38116i	0.368008	+	0.212469i
$903$	−13.8690	−	87.2934i	−0.461533	−	2.90494i
$904$	−18.2320	+	10.5262i	−0.606387	+	0.350097i
$905$	−20.4800	+	11.8241i	−0.680779	+	0.393048i
$906$	16.3461	−	2.59705i	0.543064	−	0.0862811i
$907$	7.55603	−	13.0874i	0.250894	−	0.434561i	−0.712878	−	0.701288i	$-0.752609\pi$
$907$	7.55603	−	13.0874i	0.250894	−	0.434561i	0.963772	+	0.266727i	$0.0859421\pi$
$908$			5.26205i			0.174627i
$909$	10.5914	−	3.45265i	0.351296	−	0.114517i
$910$	−9.26115	+	20.8891i	−0.307004	+	0.692466i
$911$	1.15976	−	2.00877i	0.0384247	−	0.0665535i	−0.846174	−	0.532907i	$-0.821099\pi$
$911$	1.15976	−	2.00877i	0.0384247	−	0.0665535i	0.884598	+	0.466354i	$0.154433\pi$
$912$	31.2923	−	25.3649i	1.03619	−	0.839917i
$913$	1.82828	+	3.16667i	0.0605072	+	0.104802i
$914$	−11.1367	−	19.2893i	−0.368368	−	0.638032i
$915$	9.43199	+	3.61539i	0.311812	+	0.119521i
$916$	0.968091	+	0.558928i	0.0319866	+	0.0184675i
$917$			83.9787i			2.77322i
$918$	−4.82426	−	0.245837i	−0.159224	−	0.00811382i
$919$	−2.41646			−0.0797116			−0.0398558	−	0.999205i	$-0.512690\pi$
$919$	−2.41646			−0.0797116			−0.0398558	+	0.999205i	$0.512690\pi$
$920$	6.19462	−	10.7294i	0.204230	−	0.353738i
$921$	28.8417	+	11.0553i	0.950366	+	0.364286i
$922$	23.4712	+	40.6533i	0.772983	+	1.33885i
$923$	−20.8037	+	2.21958i	−0.684763	+	0.0730582i
$924$	−1.21506	−	1.49900i	−0.0399725	−	0.0493133i
$925$	−6.98663	−	4.03373i	−0.229719	−	0.132628i
$926$	−43.6124			−1.43319
$927$	−6.57839	+	31.0962i	−0.216063	+	1.02133i
$928$		−	5.79864i		−	0.190350i
$929$	14.6055	+	8.43250i	0.479191	+	0.276661i	0.720079	−	0.693892i	$-0.244105\pi$
$929$	14.6055	+	8.43250i	0.479191	+	0.276661i	−0.240888	+	0.970553i	$0.577439\pi$
$930$	−0.273452	−	1.72114i	−0.00896684	−	0.0564384i
$931$	−84.7000	+	48.9016i	−2.77593	+	1.60268i
$932$	−0.808063	−	1.39961i	−0.0264690	−	0.0458456i
$933$	42.6514	−	6.77639i	1.39634	−	0.221849i
$934$	−9.51929	−	5.49596i	−0.311481	−	0.179833i
$935$	0.884803			0.0289362
$936$	25.8056	+	18.6492i	0.843481	+	0.609567i
$937$	7.73841			0.252803			0.126401	−	0.991979i	$-0.459657\pi$
$937$	7.73841			0.252803			0.126401	+	0.991979i	$0.459657\pi$
$938$	−59.9353	−	34.6036i	−1.95696	−	1.12985i
$939$	−1.21357	−	1.49716i	−0.0396033	−	0.0488579i
$940$	0.693322	+	1.20087i	0.0226137	+	0.0391680i
$941$	−50.6505	+	29.2431i	−1.65116	+	0.953298i	−0.674564	+	0.738216i	$0.735668\pi$
$941$	−50.6505	+	29.2431i	−1.65116	+	0.953298i	−0.976596	+	0.215082i	$0.930998\pi$
$942$	29.2881	+	11.2265i	0.954259	+	0.365778i
$943$	−26.9249	−	15.5451i	−0.876797	−	0.506219i
$944$		−	1.48651i		−	0.0483818i
$945$	21.7612	−	11.1275i	0.707890	−	0.361978i
$946$	−18.7447			−0.609443
$947$	−4.70833	−	2.71836i	−0.153000	−	0.0883347i	0.421545	−	0.906807i	$-0.361488\pi$
$947$	−4.70833	−	2.71836i	−0.153000	−	0.0883347i	−0.574546	+	0.818473i	$0.694821\pi$
$948$	0.554051	−	1.44543i	0.0179947	−	0.0469455i
$949$	34.1282	−	3.64118i	1.10785	−	0.118198i
$950$	−4.35621	−	7.54517i	−0.141334	−	0.244798i
$951$	36.9969	−	29.9891i	1.19971	−	0.972462i
$952$	−4.77653	+	8.27319i	−0.154808	+	0.268136i
$953$	−4.08765			−0.132412			−0.0662059	−	0.997806i	$-0.521089\pi$
$953$	−4.08765			−0.132412			−0.0662059	+	0.997806i	$0.521089\pi$
$954$	−6.81647	−	20.9104i	−0.220691	−	0.676998i
$955$			0.675237i			0.0218502i
$956$	−4.50383	−	2.60029i	−0.145664	−	0.0840994i
$957$	1.94067	+	12.2148i	0.0627330	+	0.394849i
$958$	12.4377	+	21.5427i	0.401842	+	0.696011i
$959$	−10.1071	−	17.5060i	−0.326375	−	0.565297i
$960$	2.33620	+	14.7043i	0.0754006	+	0.474580i
$961$	−15.2212	+	26.3638i	−0.491005	+	0.850446i
$962$	−35.8275	−	15.8841i	−1.15512	−	0.512124i
$963$	32.3628	+	29.0832i	1.04288	+	0.937192i
$964$			0.541253i			0.0174326i
$965$	−7.34599	+	12.7236i	−0.236476	+	0.409588i
$966$	−29.0927	−	35.8911i	−0.936041	−	1.15478i
$967$	22.6264	−	13.0634i	0.727616	−	0.420089i	−0.0899337	−	0.995948i	$-0.528666\pi$
$967$	22.6264	−	13.0634i	0.727616	−	0.420089i	0.817549	+	0.575859i	$0.195332\pi$
$968$	23.8488	−	13.7691i	0.766528	−	0.442555i
$969$	−7.21595	−	2.76595i	−0.231810	−	0.0888553i
$970$	2.08918	+	1.20619i	0.0670794	+	0.0387283i
$971$	17.6665			0.566945			0.283473	−	0.958980i	$-0.408513\pi$
$971$	17.6665			0.566945			0.283473	+	0.958980i	$0.408513\pi$
$972$	−0.751870	−	2.77922i	−0.0241162	−	0.0891435i
$973$		−	0.726205i		−	0.0232811i
$974$	−24.6071	+	42.6207i	−0.788462	+	1.36566i
$975$	4.40681	−	4.42493i	0.141131	−	0.141711i
$976$	10.4872	+	18.1644i	0.335688	+	0.581428i
$977$	4.95084	−	2.85837i	0.158391	−	0.0914473i	−0.418709	−	0.908120i	$-0.637517\pi$
$977$	4.95084	−	2.85837i	0.158391	−	0.0914473i	0.577101	+	0.816673i	$0.304184\pi$
$978$	6.82850	+	8.42419i	0.218351	+	0.269376i
$979$	−6.88417	+	11.9237i	−0.220019	+	0.381084i
$980$		−	2.79349i		−	0.0892347i
$981$	8.89346	−	9.89635i	0.283946	−	0.315966i
$982$			33.2715i			1.06173i
$983$	−23.1189	−	13.3477i	−0.737380	−	0.425726i	0.0837361	−	0.996488i	$-0.473315\pi$
$983$	−23.1189	−	13.3477i	−0.737380	−	0.425726i	−0.821116	+	0.570762i	$0.806648\pi$
$984$	37.1928	−	5.90913i	1.18566	−	0.188376i
$985$	−1.30815	−	2.26579i	−0.0416812	−	0.0721940i
$986$	4.48304	−	2.58828i	0.142769	−	0.0824277i
$987$	60.4080	−	9.59752i	1.92281	−	0.305492i
$988$	2.53658	+	3.47980i	0.0806993	+	0.110707i
$989$	45.6639			1.45203
$990$	−1.60647	−	4.92806i	−0.0510571	−	0.156624i
$991$	16.9888			0.539668			0.269834	−	0.962907i	$-0.413031\pi$
$991$	16.9888			0.539668			0.269834	+	0.962907i	$0.413031\pi$
$992$	−0.388830	+	0.673474i	−0.0123454	+	0.0213828i
$993$	−16.6162	+	13.4688i	−0.527300	+	0.427420i
$994$	−31.8473	+	18.3870i	−1.01013	+	0.583201i
$995$	22.4800	−	12.9788i	0.712664	−	0.411457i
$996$	0.851752	+	0.326486i	0.0269888	+	0.0103451i
$997$	−6.32338	+	10.9524i	−0.200263	+	0.346867i	−0.948613	−	0.316438i	$-0.897513\pi$
$997$	−6.32338	+	10.9524i	−0.200263	+	0.346867i	0.748350	+	0.663304i	$0.230846\pi$
$998$	−9.41034			−0.297879
$999$	19.0851	+	37.3232i	0.603827	+	1.18085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.16	✓	108
9.4	even	3	inner	585.2.bt.b.571.39	yes	108
13.12	even	2	inner	585.2.bt.b.376.39	yes	108
117.103	even	6	inner	585.2.bt.b.571.16	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.16	✓	108	1.1	even	1	trivial
585.2.bt.b.376.39	yes	108	13.12	even	2	inner
585.2.bt.b.571.16	yes	108	117.103	even	6	inner
585.2.bt.b.571.39	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)

\(f(q)\)	\(=\)	\(q+(-1.16682 - 0.673666i) q^{2} +(0.619932 - 1.61731i) q^{3} +(-0.0923480 - 0.159951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.81288 + 1.46949i) q^{6} +(-4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 - 2.00524i) q^{9} +O(q^{10})\)	\(q+(-1.16682 - 0.673666i) q^{2} +(0.619932 - 1.61731i) q^{3} +(-0.0923480 - 0.159951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.81288 + 1.46949i) q^{6} +(-4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 - 2.00524i) q^{9} -1.34733 q^{10} +(-1.11056 - 0.641180i) q^{11} +(-0.315940 + 0.0501961i) q^{12} +(0.382510 + 3.58520i) q^{13} +(3.16872 + 5.48839i) q^{14} +(-0.271777 - 1.71060i) q^{15} +(1.79825 - 3.11466i) q^{16} -0.689981 q^{17} +(1.25275 + 3.84296i) q^{18} +6.46642i q^{19} +(-0.159951 - 0.0923480i) q^{20} +(-6.32897 + 5.13015i) q^{21} +(0.863882 + 1.49629i) q^{22} +(-2.10450 - 3.64510i) q^{23} +(4.76056 + 1.82478i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.96891 - 4.44099i) q^{26} +(-4.62639 + 2.36569i) q^{27} +0.868754i q^{28} +(2.78420 - 4.82237i) q^{29} +(-0.835255 + 2.17905i) q^{30} +(-0.646732 + 0.373391i) q^{31} +(0.901834 - 0.520674i) q^{32} +(-1.72545 + 1.39862i) q^{33} +(0.805086 + 0.464817i) q^{34} -4.70370 q^{35} +(-0.114679 + 0.542091i) q^{36} -8.06746i q^{37} +(4.35621 - 7.54517i) q^{38} +(6.03551 + 1.60395i) q^{39} +(1.47176 + 2.54916i) q^{40} +(6.39700 - 3.69331i) q^{41} +(10.8408 - 1.72237i) q^{42} +(-5.42456 + 9.39562i) q^{43} +0.236847i q^{44} +(-2.93504 - 0.620907i) q^{45} +5.67092i q^{46} +(-6.50187 - 3.75385i) q^{47} +(-3.92257 - 4.83920i) q^{48} +(7.56239 + 13.0984i) q^{49} +(-1.16682 + 0.673666i) q^{50} +(-0.427741 + 1.11591i) q^{51} +(0.538134 - 0.392269i) q^{52} -5.44121 q^{53} +(6.99187 + 0.356295i) q^{54} -1.28236 q^{55} +(6.92270 - 11.9905i) q^{56} +(10.4582 + 4.00874i) q^{57} +(-6.49733 + 3.75124i) q^{58} +(0.357947 - 0.206661i) q^{59} +(-0.248514 + 0.201441i) q^{60} +(-2.91595 + 5.05058i) q^{61} +1.00616 q^{62} +(4.37350 + 13.4162i) q^{63} -8.59603 q^{64} +(2.12387 + 2.91362i) q^{65} +(2.95551 - 0.469566i) q^{66} +(-9.45733 + 5.46019i) q^{67} +(0.0637184 + 0.110363i) q^{68} +(-7.19989 + 1.14391i) q^{69} +(5.48839 + 3.16872i) q^{70} +5.80266i q^{71} +(5.90245 - 6.56806i) q^{72} -9.51919i q^{73} +(-5.43478 + 9.41331i) q^{74} +(-1.09066 - 1.34553i) q^{75} +(1.03431 - 0.597161i) q^{76} +(3.01592 + 5.22372i) q^{77} +(-5.96185 - 5.93744i) q^{78} +(-2.41946 + 4.19062i) q^{79} -3.59650i q^{80} +(0.958005 + 8.94887i) q^{81} -9.95222 q^{82} +(-2.46941 - 1.42572i) q^{83} +(1.40504 + 0.538569i) q^{84} +(-0.597541 + 0.344990i) q^{85} +(12.6590 - 7.30869i) q^{86} +(-6.07324 - 7.49245i) q^{87} +(1.88732 - 3.26893i) q^{88} -10.7367i q^{89} +(3.00639 + 2.70173i) q^{90} +(6.87370 - 15.5040i) q^{91} +(-0.388693 + 0.673235i) q^{92} +(0.202958 + 1.27744i) q^{93} +(5.05769 + 8.76017i) q^{94} +(3.23321 + 5.60008i) q^{95} +(-0.283014 - 1.78133i) q^{96} +(-1.55060 - 0.895240i) q^{97} -20.3781i q^{98} +(1.19234 + 3.65764i) 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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