LMFDB - Embedded newform 585.2.bt.b.571.16

Newspace parameters

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

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

Embedding invariants

Embedding label			571.16
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.16

$q$-expansion

$f(q)$	$=$	$q+(-1.16682 + 0.673666i) q^{2} +(0.619932 + 1.61731i) q^{3} +(-0.0923480 + 0.159951i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.81288 - 1.46949i) q^{6} +(-4.07352 + 2.35185i) q^{7} -2.94351i q^{8} +(-2.23137 + 2.00524i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.16682	+	0.673666i	−0.825069	+	0.476354i	−0.852161	−	0.523279i	$-0.824709\pi$
$2$	−1.16682	+	0.673666i	−0.825069	+	0.476354i	0.0270923	+	0.999633i	$0.491375\pi$
$3$	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	−0.540788	+	0.841159i	$0.681874\pi$
$7$	−4.07352	+	2.35185i	−1.53965	+	0.888916i	−0.998859	+	0.0477566i	$0.984793\pi$
$8$		−	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	−0.657990	−	0.753027i	$-0.728593\pi$
$11$	−1.11056	+	0.641180i	−0.334845	+	0.193323i	0.323145	+	0.946349i	$0.395260\pi$
$12$	−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	$-0.733997\pi$
$19$		−	6.46642i		−	1.48350i	0.670678	−	0.741749i	$-0.266003\pi$
$20$	−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	−0.997599	−	0.0692600i	$-0.977936\pi$
$23$	−2.10450	+	3.64510i	−0.438818	+	0.760056i	0.558780	+	0.829316i	$0.311270\pi$
$24$	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	0.999805	+	0.0197568i	$0.00628921\pi$
$29$	2.78420	+	4.82237i	0.517012	+	0.895492i	−0.482792	+	0.875735i	$0.660377\pi$
$30$	−0.835255	−	2.17905i	−0.152496	−	0.397838i
$31$	−0.646732	−	0.373391i	−0.116157	−	0.0670630i	0.440796	−	0.897607i	$-0.354696\pi$
$31$	−0.646732	−	0.373391i	−0.116157	−	0.0670630i	−0.556953	+	0.830544i	$0.688030\pi$
$32$	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	$0.230777\pi$
$37$			8.06746i			1.32628i	−0.748494	+	0.663141i	$0.769223\pi$
$38$	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	0.907965	−	0.419046i	$-0.137635\pi$
$41$	6.39700	+	3.69331i	0.999043	+	0.576798i	0.0910779	+	0.995844i	$0.470969\pi$
$42$	10.8408	+	1.72237i	1.67277	+	0.265767i
$43$	−5.42456	−	9.39562i	−0.827238	−	1.43282i	−0.900197	−	0.435483i	$-0.856578\pi$
$43$	−5.42456	−	9.39562i	−0.827238	−	1.43282i	0.0729590	−	0.997335i	$-0.476756\pi$
$44$		−	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	−0.892582	−	0.450885i	$-0.851108\pi$
$47$	−6.50187	+	3.75385i	−0.948394	+	0.547556i	−0.0558127	+	0.998441i	$0.517775\pi$
$48$	−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	0.523119	−	0.852259i	$-0.324768\pi$
$59$	0.357947	+	0.206661i	0.0466007	+	0.0269050i	−0.476519	+	0.879164i	$0.658102\pi$
$60$	−0.248514	−	0.201441i	−0.0320830	−	0.0260059i
$61$	−2.91595	−	5.05058i	−0.373350	−	0.646661i	0.616729	−	0.787176i	$-0.288457\pi$
$61$	−2.91595	−	5.05058i	−0.373350	−	0.646661i	−0.990079	+	0.140515i	$0.955124\pi$
$62$	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	−0.205200	−	0.978720i	$-0.565784\pi$
$67$	−9.45733	−	5.46019i	−1.15540	−	0.667068i	−0.950196	+	0.311652i	$0.899118\pi$
$68$	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	$-0.888108\pi$
$71$		−	5.80266i		−	0.688649i	0.938851	−	0.344325i	$-0.111892\pi$
$72$	5.90245	+	6.56806i	0.695611	+	0.774053i
$73$			9.51919i			1.11414i	0.830467	+	0.557068i	$0.188074\pi$
$73$			9.51919i			1.11414i	−0.830467	+	0.557068i	$0.811926\pi$
$74$	−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	0.697217	−	0.716860i	$-0.254421\pi$
$79$	−2.41946	−	4.19062i	−0.272210	−	0.471482i	−0.969427	+	0.245378i	$0.921088\pi$
$80$			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	−0.629366	−	0.777109i	$-0.716685\pi$
$83$	−2.46941	+	1.42572i	−0.271053	+	0.156493i	0.358313	+	0.933602i	$0.383352\pi$
$84$	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	$0.192687\pi$
$89$			10.7367i			1.13809i	−0.822306	+	0.569045i	$0.807313\pi$
$90$	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	−0.576650	−	0.816991i	$-0.695640\pi$
$97$	−1.55060	+	0.895240i	−0.157440	+	0.0908979i	0.419210	+	0.907889i	$0.362307\pi$
$98$			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	0.758746	−	0.651387i	$-0.225813\pi$
$101$	−1.85667	−	3.21584i	−0.184745	−	0.319988i	−0.943491	+	0.331399i	$0.892479\pi$
$102$	1.25085	+	1.01392i	0.123853	+	0.100393i
$103$	−5.29740	+	9.17537i	−0.521969	+	0.904076i	0.477705	+	0.878520i	$0.341469\pi$
$103$	−5.29740	+	9.17537i	−0.521969	+	0.904076i	−0.999673	+	0.0255558i	$0.991864\pi$
$104$	−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	$-0.931871\pi$
$109$		−	4.43511i		−	0.424806i	0.977182	−	0.212403i	$-0.0681290\pi$
$110$	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	−0.647345	−	0.762197i	$-0.724121\pi$
$113$	3.57608	−	6.19396i	0.336409	−	0.582678i	0.983755	+	0.179519i	$0.0574540\pi$
$114$	−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	0.152028	+	0.988376i	$0.451420\pi$
$131$	−8.92688	+	15.4618i	−0.779945	+	1.35090i	−0.931973	+	0.362528i	$0.881914\pi$
$132$	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	−0.332517	−	0.943097i	$-0.607898\pi$
$137$	3.72175	−	2.14875i	0.317970	−	0.183580i	0.650488	+	0.759517i	$0.274565\pi$
$138$	9.17162	−	3.51559i	0.780740	−	0.299267i
$139$	0.0771951	−	0.133706i	0.00654761	−	0.0113408i	−0.862733	−	0.505660i	$-0.831249\pi$
$139$	0.0771951	−	0.133706i	0.00654761	−	0.0113408i	0.869281	+	0.494319i	$0.164582\pi$
$140$	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	0.792025	−	0.610488i	$-0.209027\pi$
$149$	8.04826	+	4.64667i	0.659339	+	0.380670i	−0.132686	+	0.991158i	$0.542360\pi$
$150$	0.366173	−	2.30474i	0.0298979	−	0.188181i
$151$	−6.14219	+	3.54620i	−0.499845	+	0.288585i	−0.728649	−	0.684887i	$-0.759852\pi$
$151$	−6.14219	+	3.54620i	−0.499845	+	0.288585i	0.228805	+	0.973472i	$0.426518\pi$
$152$	−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	0.462751	+	0.886488i	$0.346862\pi$
$157$	−6.72039	+	11.6401i	−0.536345	+	0.928978i	−0.999097	+	0.0424895i	$0.986471\pi$
$158$	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	$0.0582523\pi$
$163$			4.64686i			0.363970i	−0.983301	+	0.181985i	$0.941748\pi$
$164$	−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	0.858651	−	0.512561i	$-0.171303\pi$
$167$	10.9080	+	6.29773i	0.844086	+	0.487333i	−0.0145650	+	0.999894i	$0.504636\pi$
$168$	−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	0.902313	+	0.431082i	$0.141868\pi$
$173$	10.8444	+	18.7831i	0.824485	+	1.42805i	−0.0778279	+	0.996967i	$0.524798\pi$
$174$	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	0.853552	−	0.521007i	$-0.174444\pi$
$191$	−0.337619	−	0.584773i	−0.0244292	−	0.0423127i	−0.877982	+	0.478694i	$0.841110\pi$
$192$	−5.32896	−	13.9024i	−0.384584	−	1.00332i
$193$	−12.7236	−	7.34599i	−0.915867	−	0.528776i	−0.0335526	−	0.999437i	$-0.510682\pi$
$193$	−12.7236	−	7.34599i	−0.915867	−	0.528776i	−0.882314	+	0.470661i	$0.844015\pi$
$194$	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	$0.0297103\pi$
$197$			2.61631i			0.186404i	−0.995647	+	0.0932021i	$0.970290\pi$
$198$	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	−0.987226	−	0.159324i	$-0.949069\pi$
$211$	−5.16589	+	8.94758i	−0.355634	+	0.615977i	0.631592	+	0.775301i	$0.282402\pi$
$212$	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	0.113371	−	0.993553i	$-0.463835\pi$
$223$	15.3886	−	8.88463i	1.03050	−	0.594959i	0.917128	+	0.398594i	$0.130502\pi$
$224$	−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	−0.655981	+	0.754777i	$0.727745\pi$
$227$	−24.6734	+	14.2452i	−1.63763	+	0.945485i	−0.981647	+	0.190707i	$0.938922\pi$
$228$	−0.324589	+	2.04300i	−0.0214964	+	0.135301i
$229$	−5.24154	−	3.02620i	−0.346371	−	0.199977i	0.316715	−	0.948521i	$-0.397420\pi$
$229$	−5.24154	−	3.02620i	−0.346371	−	0.199977i	−0.663086	+	0.748544i	$0.730753\pi$
$230$	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	0.995229	+	0.0975716i	$0.0311075\pi$
$239$	24.3851	+	14.0788i	1.57734	+	0.910679i	0.582114	+	0.813107i	$0.302226\pi$
$240$	−5.81664	+	2.22958i	−0.375462	+	0.143919i
$241$	−2.53789	+	1.46525i	−0.163480	+	0.0943852i	−0.579508	−	0.814967i	$-0.696755\pi$
$241$	−2.53789	+	1.46525i	−0.163480	+	0.0943852i	0.416028	+	0.909352i	$0.363422\pi$
$242$		−	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	0.467712	+	0.883881i	$0.345078\pi$
$257$	−8.52231	+	14.7611i	−0.531607	+	0.920771i	−0.999319	+	0.0368900i	$0.988255\pi$
$258$	−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	0.613949	−	0.789346i	$-0.289580\pi$
$263$	−6.10773	−	10.5789i	−0.376619	−	0.652323i	−0.990568	+	0.137023i	$0.956247\pi$
$264$	−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	$0.0372561\pi$
$271$			3.84476i			0.233553i	−0.993158	+	0.116776i	$0.962744\pi$
$272$	−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	0.910140	+	0.414301i	$0.135974\pi$
$277$	13.5454	+	23.4614i	0.813865	+	1.40966i	−0.0962743	+	0.995355i	$0.530693\pi$
$278$			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	−0.275535	−	0.961291i	$-0.588855\pi$
$281$	7.02708	−	4.05709i	0.419201	−	0.242026i	0.694735	+	0.719266i	$0.255522\pi$
$282$	17.3033	+	2.74912i	1.03040	+	0.163708i
$283$	12.1427	−	21.0317i	0.721807	−	1.25021i	−0.238468	−	0.971150i	$-0.576645\pi$
$283$	12.1427	−	21.0317i	0.721807	−	1.25021i	0.960275	−	0.279056i	$-0.0900215\pi$
$284$	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	−0.347617	−	0.937637i	$-0.613009\pi$
$293$	−22.8249	−	13.1779i	−1.33344	−	0.769864i	−0.985826	+	0.167773i	$0.946342\pi$
$294$	−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	$-0.830054\pi$
$307$		−	17.8331i		−	1.01779i	0.860828	−	0.508896i	$-0.169946\pi$
$308$	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	−0.259062	−	0.965861i	$-0.583413\pi$
$311$	12.4668	−	21.5932i	0.706929	−	1.22444i	0.965991	−	0.258576i	$-0.0832533\pi$
$312$	−4.72124	−	17.7656i	−0.267287	−	1.00578i
$313$	0.556344	+	0.963617i	0.0314464	+	0.0544668i	0.881320	−	0.472519i	$-0.156655\pi$
$313$	0.556344	+	0.963617i	0.0314464	+	0.0544668i	−0.849874	+	0.526986i	$0.823322\pi$
$314$		−	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	0.351010	−	0.936372i	$-0.385838\pi$
$317$	23.8124	−	13.7481i	1.33744	−	0.772169i	0.986427	+	0.164203i	$0.0525051\pi$
$318$	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	−0.764241	−	0.644931i	$-0.776886\pi$
$331$	−10.6947	+	6.17460i	−0.587835	+	0.339387i	0.176406	+	0.984317i	$0.443553\pi$
$332$		−	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	−0.883527	−	0.468381i	$-0.844838\pi$
$337$	−0.663331	+	1.14892i	−0.0361339	+	0.0625858i	0.847393	+	0.530966i	$0.178171\pi$
$338$	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	−0.293342	−	0.956008i	$-0.594767\pi$
$347$	12.6904	−	21.9804i	0.681256	−	1.17997i	0.974598	−	0.223963i	$-0.0718993\pi$
$348$	−0.637576	−	1.66334i	−0.0341776	−	0.0891642i
$349$	−11.4337	+	6.60123i	−0.612030	+	0.353355i	−0.773759	−	0.633480i	$-0.781626\pi$
$349$	−11.4337	+	6.60123i	−0.612030	+	0.353355i	0.161730	+	0.986835i	$0.448293\pi$
$350$	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	−0.268902	−	0.963168i	$-0.586661\pi$
$353$	8.09353	−	4.67280i	0.430775	−	0.248708i	0.699677	+	0.714460i	$0.253327\pi$
$354$	−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	$0.285378\pi$
$359$			29.6022i			1.56234i	−0.624315	+	0.781172i	$0.714622\pi$
$360$	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	0.999920	−	0.0126473i	$-0.00402586\pi$
$367$	9.36803	+	16.2259i	0.489007	+	0.846985i	−0.510913	+	0.859633i	$0.670693\pi$
$368$	−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	−0.620288	−	0.784374i	$-0.712984\pi$
$373$	7.12935	−	12.3484i	0.369144	−	0.639375i	0.989432	+	0.144998i	$0.0463177\pi$
$374$	−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	$0.0174142\pi$
$379$			2.12905i			0.109362i	−0.998504	+	0.0546811i	$0.982586\pi$
$380$	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	0.205807	−	0.978593i	$-0.434018\pi$
$383$	−10.5441	−	6.08761i	−0.538776	−	0.311063i	−0.744583	+	0.667530i	$0.767352\pi$
$384$	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	0.984103	+	0.177600i	$0.0568333\pi$
$389$	12.7383	+	22.0634i	0.645858	+	1.11866i	−0.338245	+	0.941058i	$0.609833\pi$
$390$	−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	$-0.845514\pi$
$397$		−	18.5900i		−	0.933004i	0.884520	−	0.466502i	$-0.154486\pi$
$398$	−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	0.573604	−	0.819132i	$-0.305545\pi$
$401$	3.02411	+	1.74597i	0.151017	+	0.0871897i	−0.422587	+	0.906322i	$0.638878\pi$
$402$	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	0.647420	−	0.762133i	$-0.275848\pi$
$409$	6.29168	+	3.63250i	0.311103	+	0.179616i	−0.336317	+	0.941749i	$0.609181\pi$
$410$	−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	−0.996788	−	0.0800910i	$-0.974479\pi$
$419$	−8.78209	+	15.2110i	−0.429033	+	0.743107i	0.567755	+	0.823198i	$0.307812\pi$
$420$	1.48609	+	0.236107i	0.0725136	+	0.0115209i
$421$	13.8198	−	7.97886i	0.673536	−	0.388866i	−0.123879	−	0.992297i	$-0.539534\pi$
$421$	13.8198	−	7.97886i	0.673536	−	0.388866i	0.797415	+	0.603431i	$0.206200\pi$
$422$		−	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	$0.0181356\pi$
$431$			2.36438i			0.113888i	−0.998377	+	0.0569440i	$0.981864\pi$
$432$	−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	0.994761	+	0.102233i	$0.0325986\pi$
$439$	12.2763	+	21.2632i	0.585916	+	1.01484i	−0.408844	+	0.912604i	$0.634068\pi$
$440$			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	0.999743	+	0.0226659i	$0.00721539\pi$
$443$	10.9342	+	18.9386i	0.519501	+	0.899802i	−0.480242	+	0.877136i	$0.659451\pi$
$444$	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	$-0.899153\pi$
$449$		−	13.2031i		−	0.623092i	0.950231	−	0.311546i	$-0.100847\pi$
$450$	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	−0.126261	−	0.991997i	$-0.540298\pi$
$457$	14.3166	−	8.26571i	0.669704	−	0.386654i	0.795964	+	0.605344i	$0.206964\pi$
$458$	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	−0.994931	−	0.100563i	$-0.967935\pi$
$461$	−30.1732	+	17.4205i	−1.40531	+	0.811354i	−0.410375	+	0.911917i	$0.634602\pi$
$462$	−13.1437	+	5.03812i	−0.611499	+	0.234394i
$463$	28.0327	+	16.1847i	1.30279	+	0.752167i	0.980882	−	0.194603i	$-0.0623419\pi$
$463$	28.0327	+	16.1847i	1.30279	+	0.752167i	0.321910	+	0.946770i	$0.395675\pi$
$464$	−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	−0.818628	−	0.574325i	$-0.805265\pi$
$479$	−15.9891	+	9.23132i	−0.730561	+	0.421790i	0.0880661	+	0.996115i	$0.471931\pi$
$480$	−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	$0.310295\pi$
$487$			36.5271i			1.65520i	−0.561317	+	0.827601i	$0.689705\pi$
$488$	−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	0.440508	+	0.897749i	$0.354798\pi$
$491$	−12.3472	+	21.3859i	−0.557220	+	0.965133i	−0.997727	+	0.0673836i	$0.978535\pi$
$492$	−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	0.629240	−	0.777211i	$-0.283366\pi$
$499$	6.04869	+	3.49221i	0.270776	+	0.156333i	−0.358464	+	0.933544i	$0.616699\pi$
$500$	−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	−0.174341	−	0.984685i	$-0.555779\pi$
$509$	−25.1392	−	14.5141i	−1.11427	−	0.643326i	−0.939933	+	0.341359i	$0.889113\pi$
$510$	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	$-0.926812\pi$
$541$		−	10.6019i		−	0.455811i	0.973683	−	0.227905i	$-0.0731877\pi$
$542$	−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	−0.997751	−	0.0670308i	$-0.978647\pi$
$547$	−13.0254	−	22.5607i	−0.556926	−	0.964624i	0.440825	−	0.897593i	$-0.354686\pi$
$548$			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	$-0.749421\pi$
$557$		−	33.4373i		−	1.41678i	0.705819	−	0.708392i	$-0.250579\pi$
$558$	−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	−0.964801	−	0.262981i	$-0.915294\pi$
$563$	−6.04230	+	10.4656i	−0.254653	+	0.441071i	0.710148	+	0.704052i	$0.248628\pi$
$564$	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	0.799430	−	0.600759i	$-0.205135\pi$
$569$	−2.87574	−	4.98094i	−0.120557	−	0.208812i	−0.919988	+	0.391947i	$0.871802\pi$
$570$	−14.0906	+	5.40111i	−0.590192	+	0.226227i
$571$	3.34805	−	5.79900i	0.140112	−	0.242681i	−0.787427	−	0.616408i	$-0.788587\pi$
$571$	3.34805	−	5.79900i	0.140112	−	0.242681i	0.927539	+	0.373728i	$0.121921\pi$
$572$	−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	$0.144421\pi$
$577$			21.0568i			0.876607i	−0.898827	+	0.438304i	$0.855579\pi$
$578$	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	−0.746692	−	0.665170i	$-0.768359\pi$
$587$	−13.1797	+	7.60928i	−0.543983	+	0.314069i	0.202709	+	0.979239i	$0.435026\pi$
$588$	−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	$-0.776264\pi$
$593$		−	31.4829i		−	1.29285i	0.762979	−	0.646423i	$-0.223736\pi$
$594$	−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	−0.929098	−	0.369833i	$-0.879415\pi$
$599$	−3.53079	+	6.11551i	−0.144264	+	0.249873i	0.784834	+	0.619706i	$0.212748\pi$
$600$	3.96059	+	3.21038i	0.161690	+	0.131063i
$601$	−0.0378043	−	0.0654790i	−0.00154207	−	0.00267094i	0.865253	−	0.501335i	$-0.167158\pi$
$601$	−0.0378043	−	0.0654790i	−0.00154207	−	0.00267094i	−0.866795	+	0.498664i	$0.833824\pi$
$602$	−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	−0.109735	+	0.993961i	$0.535000\pi$
$607$	−22.5595	+	39.0742i	−0.915663	+	1.58597i	−0.805928	+	0.592014i	$0.798333\pi$
$608$	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	$-0.879865\pi$
$613$		−	18.2482i		−	0.737039i	0.929620	−	0.368519i	$-0.120135\pi$
$614$	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	0.354455	−	0.935073i	$-0.384667\pi$
$617$	−6.90824	−	3.98847i	−0.278115	−	0.160570i	−0.632570	+	0.774503i	$0.718000\pi$
$618$	23.0866	−	8.84936i	0.928680	−	0.355974i
$619$	−3.59308	+	2.07447i	−0.144418	+	0.0833799i	−0.570468	−	0.821320i	$-0.693238\pi$
$619$	−3.59308	+	2.07447i	−0.144418	+	0.0833799i	0.426050	+	0.904700i	$0.359905\pi$
$620$	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	$-0.603880\pi$
$631$		−	47.5878i		−	1.89444i	0.320586	−	0.947219i	$-0.396120\pi$
$632$	−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	−0.848497	−	0.529200i	$-0.822492\pi$
$641$	−22.3444	−	38.7016i	−0.882549	−	1.52862i	−0.0340518	−	0.999420i	$-0.510841\pi$
$642$	26.2932	+	21.3128i	1.03771	+	0.841148i
$643$	−40.3294	−	23.2842i	−1.59043	−	0.918238i	−0.993232	−	0.116148i	$-0.962945\pi$
$643$	−40.3294	−	23.2842i	−1.59043	−	0.918238i	−0.597203	−	0.802090i	$-0.703721\pi$
$644$	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	−0.891980	−	0.452075i	$-0.850684\pi$
$653$	−1.39222	+	2.41140i	−0.0544820	+	0.0943655i	0.837498	+	0.546440i	$0.184017\pi$
$654$	−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	0.749562	+	0.661934i	$0.230264\pi$
$659$	24.3369	+	42.1528i	0.948033	+	1.64204i	0.198471	+	0.980107i	$0.436402\pi$
$660$	0.405149	+	0.0643694i	0.0157704	+	0.00250557i
$661$	17.4542	+	10.0772i	0.678889	+	0.391957i	0.799436	−	0.600751i	$-0.205132\pi$
$661$	17.4542	+	10.0772i	0.678889	+	0.391957i	−0.120547	+	0.992708i	$0.538465\pi$
$662$	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	0.721576	−	0.692335i	$-0.243418\pi$
$673$	−6.19480	−	10.7297i	−0.238792	−	0.413600i	−0.960368	+	0.278735i	$0.910085\pi$
$674$		−	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	−0.837223	−	0.546862i	$-0.815822\pi$
$677$	−23.2146	−	40.2088i	−0.892208	−	1.54535i	−0.0549850	−	0.998487i	$-0.517511\pi$
$678$	−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	$-0.881089\pi$
$683$		−	19.0750i		−	0.729884i	0.931030	−	0.364942i	$-0.118911\pi$
$684$	−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	−0.188483	−	0.982077i	$-0.560357\pi$
$691$	14.9252	−	8.61704i	0.567779	−	0.327808i	0.756262	+	0.654269i	$0.227024\pi$
$692$	−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	−0.585175	−	0.810907i	$-0.698974\pi$
$709$	−4.67297	+	2.69794i	−0.175497	+	0.101323i	0.409678	+	0.912230i	$0.365641\pi$
$710$			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	0.999890	−	0.0148298i	$-0.00472065\pi$
$727$	13.1337	+	22.7482i	0.487102	+	0.843685i	−0.512788	+	0.858515i	$0.671387\pi$
$728$	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	0.496795	−	0.867868i	$-0.334510\pi$
$733$	−0.173348	−	0.100083i	−0.00640277	−	0.00369664i	−0.503198	+	0.864171i	$0.667843\pi$
$734$	−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	$-0.889663\pi$
$739$		−	18.4711i		−	0.679469i	0.940521	−	0.339734i	$-0.110337\pi$
$740$	−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	0.997762	−	0.0668712i	$-0.0213017\pi$
$743$	39.2169	+	22.6419i	1.43873	+	0.830651i	0.440969	+	0.897523i	$0.354635\pi$
$744$	−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	−0.843826	−	0.536617i	$-0.819702\pi$
$751$	1.17321	−	2.03207i	0.0428112	−	0.0741511i	0.886637	+	0.462466i	$0.153035\pi$
$752$	−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	0.966979	−	0.254857i	$-0.0820285\pi$
$761$	33.9243	+	19.5862i	1.22976	+	0.709999i	0.262776	+	0.964857i	$0.415362\pi$
$762$	−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	0.276078	−	0.961135i	$-0.410965\pi$
$769$	−11.5984	−	6.69637i	−0.418251	−	0.241477i	−0.694329	+	0.719658i	$0.744299\pi$
$770$	−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	$-0.990007\pi$
$773$		−	1.74544i		−	0.0627792i	0.999507	−	0.0313896i	$-0.00999327\pi$
$774$	−42.9026	+	9.07603i	−1.54210	+

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

Introduction

L-functions

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