LMFDB - Embedded newform 315.2.bl.i.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 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("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.i.146.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.32000 - 1.33945i) q^{2} +(0.852012 + 1.50800i) q^{3} +(2.58825 - 4.48298i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.99656 + 2.35733i) q^{6} +(-1.06513 + 2.42188i) q^{7} -8.50953i q^{8} +(-1.54815 + 2.56968i) q^{9} +O(q^{10})$	\(q+(2.32000 - 1.33945i) q^{2} +(0.852012 + 1.50800i) q^{3} +(2.58825 - 4.48298i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.99656 + 2.35733i) q^{6} +(-1.06513 + 2.42188i) q^{7} -8.50953i q^{8} +(-1.54815 + 2.56968i) q^{9} -2.67890i q^{10} +(-4.13341 + 2.38643i) q^{11} +(8.96558 + 0.0835367i) q^{12} +(-3.81421 - 2.20214i) q^{13} +(0.772880 + 7.04544i) q^{14} +(1.73198 + 0.0161377i) q^{15} +(-6.22159 - 10.7761i) q^{16} +2.88443 q^{17} +(-0.149751 + 8.03530i) q^{18} -1.11998i q^{19} +(-2.58825 - 4.48298i) q^{20} +(-4.55971 + 0.457245i) q^{21} +(-6.39300 + 11.0730i) q^{22} +(0.0967696 + 0.0558700i) q^{23} +(12.8324 - 7.25022i) q^{24} +(-0.500000 - 0.866025i) q^{25} -11.7986 q^{26} +(-5.19412 - 0.145222i) q^{27} +(8.10040 + 11.0434i) q^{28} +(6.32673 - 3.65274i) q^{29} +(4.03979 - 2.28246i) q^{30} +(3.39714 + 1.96134i) q^{31} +(-14.1292 - 8.15748i) q^{32} +(-7.12046 - 4.19994i) q^{33} +(6.69186 - 3.86355i) q^{34} +(1.56484 + 2.13337i) q^{35} +(7.51281 + 13.5913i) q^{36} +0.197887 q^{37} +(-1.50016 - 2.59835i) q^{38} +(0.0710747 - 7.62810i) q^{39} +(-7.36947 - 4.25477i) q^{40} +(4.21652 - 7.30322i) q^{41} +(-9.96604 + 7.16830i) q^{42} +(-1.01753 - 1.76242i) q^{43} +24.7067i q^{44} +(1.45133 + 2.62558i) q^{45} +0.299340 q^{46} +(3.67167 + 6.35952i) q^{47} +(10.9495 - 18.5636i) q^{48} +(-4.73098 - 5.15924i) q^{49} +(-2.32000 - 1.33945i) q^{50} +(2.45757 + 4.34973i) q^{51} +(-19.7443 + 11.3994i) q^{52} +10.3981i q^{53} +(-12.2449 + 6.62035i) q^{54} +4.77285i q^{55} +(20.6090 + 9.06378i) q^{56} +(1.68894 - 0.954238i) q^{57} +(9.78532 - 16.9487i) q^{58} +(-2.59260 + 4.49051i) q^{59} +(4.55513 - 7.72265i) q^{60} +(-3.71337 + 2.14391i) q^{61} +10.5085 q^{62} +(-4.57445 - 6.48648i) q^{63} -18.8198 q^{64} +(-3.81421 + 2.20214i) q^{65} +(-22.1450 - 0.206336i) q^{66} +(-3.20591 + 5.55281i) q^{67} +(7.46562 - 12.9308i) q^{68} +(-0.00180322 + 0.193531i) q^{69} +(6.48797 + 2.85338i) q^{70} +0.343592i q^{71} +(21.8667 + 13.1740i) q^{72} -7.87210i q^{73} +(0.459097 - 0.265060i) q^{74} +(0.879963 - 1.49187i) q^{75} +(-5.02086 - 2.89879i) q^{76} +(-1.37700 - 12.5525i) q^{77} +(-10.0526 - 17.7923i) q^{78} +(-6.55399 - 11.3518i) q^{79} -12.4432 q^{80} +(-4.20646 - 7.95649i) q^{81} -22.5913i q^{82} +(3.77013 + 6.53006i) q^{83} +(-9.75185 + 21.6246i) q^{84} +(1.44221 - 2.49799i) q^{85} +(-4.72134 - 2.72587i) q^{86} +(10.8988 + 6.42855i) q^{87} +(20.3074 + 35.1734i) q^{88} -3.94862 q^{89} +(6.88390 + 4.14734i) q^{90} +(9.39595 - 6.89199i) q^{91} +(0.500928 - 0.289211i) q^{92} +(-0.0633029 + 6.79398i) q^{93} +(17.0365 + 9.83604i) q^{94} +(-0.969933 - 0.559991i) q^{95} +(0.263285 - 28.2571i) q^{96} +(14.8882 - 8.59573i) q^{97} +(-17.8864 - 5.63251i) q^{98} +(0.266803 - 14.3161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.32000	−	1.33945i	1.64048	−	0.947134i	0.659823	−	0.751421i	$-0.270631\pi$
$2$	2.32000	−	1.33945i	1.64048	−	0.947134i	0.980661	−	0.195713i	$-0.0627021\pi$
$3$	0.852012	+	1.50800i	0.491909	+	0.870646i
$3$	0.852012	+	1.50800i	0.491909	+	0.870646i
$4$	2.58825	−	4.48298i	1.29413	−	2.24149i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.99656	+	2.35733i	1.63159	+	0.962377i
$7$	−1.06513	+	2.42188i	−0.402582	+	0.915384i
$7$	−1.06513	+	2.42188i	−0.402582	+	0.915384i
$8$		−	8.50953i		−	3.00857i
$9$	−1.54815	+	2.56968i	−0.516050	+	0.856558i
$10$		−	2.67890i		−	0.847142i
$11$	−4.13341	+	2.38643i	−1.24627	+	0.719535i	−0.970364	−	0.241649i	$-0.922312\pi$
$11$	−4.13341	+	2.38643i	−1.24627	+	0.719535i	−0.275907	+	0.961184i	$0.588978\pi$
$12$	8.96558	+	0.0835367i	2.58814	+	0.0241150i
$13$	−3.81421	−	2.20214i	−1.05787	−	0.610763i	−0.133030	−	0.991112i	$-0.542471\pi$
$13$	−3.81421	−	2.20214i	−1.05787	−	0.610763i	−0.924843	+	0.380349i	$0.875804\pi$
$14$	0.772880	+	7.04544i	0.206561	+	1.88297i
$15$	1.73198	+	0.0161377i	0.447194	+	0.00416673i
$16$	−6.22159	−	10.7761i	−1.55540	−	2.69403i
$17$	2.88443			0.699577			0.349788	−	0.936829i	$-0.386254\pi$
$17$	2.88443			0.699577			0.349788	+	0.936829i	$0.386254\pi$
$18$	−0.149751	+	8.03530i	−0.0352966	+	1.89394i
$19$		−	1.11998i		−	0.256941i	−0.991713	−	0.128471i	$-0.958993\pi$
$19$		−	1.11998i		−	0.256941i	0.991713	−	0.128471i	$-0.0410068\pi$
$20$	−2.58825	−	4.48298i	−0.578751	−	1.00243i
$21$	−4.55971	+	0.457245i	−0.995010	+	0.0997790i
$22$	−6.39300	+	11.0730i	−1.36299	+	2.36077i
$23$	0.0967696	+	0.0558700i	0.0201779	+	0.0116497i	0.510055	−	0.860142i	$-0.329625\pi$
$23$	0.0967696	+	0.0558700i	0.0201779	+	0.0116497i	−0.489877	+	0.871791i	$0.662958\pi$
$24$	12.8324	−	7.25022i	2.61940	−	1.47995i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−11.7986			−2.31390
$27$	−5.19412	−	0.145222i	−0.999609	−	0.0279480i
$28$	8.10040	+	11.0434i	1.53083	+	2.08701i
$29$	6.32673	−	3.65274i	1.17484	−	0.678297i	0.220028	−	0.975494i	$-0.429385\pi$
$29$	6.32673	−	3.65274i	1.17484	−	0.678297i	0.954816	+	0.297197i	$0.0960518\pi$
$30$	4.03979	−	2.28246i	0.737561	−	0.416717i
$31$	3.39714	+	1.96134i	0.610144	+	0.352267i	0.773022	−	0.634379i	$-0.218744\pi$
$31$	3.39714	+	1.96134i	0.610144	+	0.352267i	−0.162878	+	0.986646i	$0.552078\pi$
$32$	−14.1292	−	8.15748i	−2.49771	−	1.44205i
$33$	−7.12046	−	4.19994i	−1.23951	−	0.731115i
$34$	6.69186	−	3.86355i	1.14764	−	0.662593i
$35$	1.56484	+	2.13337i	0.264506	+	0.360606i
$36$	7.51281	+	13.5913i	1.25213	+	2.26522i
$37$	0.197887			0.0325325			0.0162662	−	0.999868i	$-0.494822\pi$
$37$	0.197887			0.0325325			0.0162662	+	0.999868i	$0.494822\pi$
$38$	−1.50016	−	2.59835i	−0.243358	−	0.421508i
$39$	0.0710747	−	7.62810i	0.0113811	−	1.22147i
$40$	−7.36947	−	4.25477i	−1.16522	−	0.672738i
$41$	4.21652	−	7.30322i	0.658509	−	1.14057i	−0.322492	−	0.946572i	$-0.604521\pi$
$41$	4.21652	−	7.30322i	0.658509	−	1.14057i	0.981002	−	0.194000i	$-0.0621461\pi$
$42$	−9.96604	+	7.16830i	−1.53779	+	1.10609i
$43$	−1.01753	−	1.76242i	−0.155172	−	0.268766i	0.777949	−	0.628327i	$-0.216260\pi$
$43$	−1.01753	−	1.76242i	−0.155172	−	0.268766i	−0.933122	+	0.359560i	$0.882927\pi$
$44$			24.7067i			3.72467i
$45$	1.45133	+	2.62558i	0.216351	+	0.391398i
$46$	0.299340			0.0441353
$47$	3.67167	+	6.35952i	0.535568	+	0.927631i	0.999136	+	0.0415697i	$0.0132359\pi$
$47$	3.67167	+	6.35952i	0.535568	+	0.927631i	−0.463567	+	0.886062i	$0.653431\pi$
$48$	10.9495	−	18.5636i	1.58043	−	2.67942i
$49$	−4.73098	−	5.15924i	−0.675855	−	0.737035i
$50$	−2.32000	−	1.33945i	−0.328097	−	0.189427i
$51$	2.45757	+	4.34973i	0.344128	+	0.609084i
$52$	−19.7443	+	11.3994i	−2.73804	+	1.58081i
$53$			10.3981i			1.42828i	0.700002	+	0.714141i	$0.253183\pi$
$53$			10.3981i			1.42828i	−0.700002	+	0.714141i	$0.746817\pi$
$54$	−12.2449	+	6.62035i	−1.66631	+	0.900916i
$55$			4.77285i			0.643572i
$56$	20.6090	+	9.06378i	2.75400	+	1.21120i
$57$	1.68894	−	0.954238i	0.223705	−	0.126392i
$58$	9.78532	−	16.9487i	1.28488	−	2.22547i
$59$	−2.59260	+	4.49051i	−0.337527	+	0.584615i	−0.983967	−	0.178351i	$-0.942924\pi$
$59$	−2.59260	+	4.49051i	−0.337527	+	0.584615i	0.646440	+	0.762965i	$0.276257\pi$
$60$	4.55513	−	7.72265i	0.588065	−	0.996990i
$61$	−3.71337	+	2.14391i	−0.475448	+	0.274500i	−0.718517	−	0.695509i	$-0.755179\pi$
$61$	−3.71337	+	2.14391i	−0.475448	+	0.274500i	0.243070	+	0.970009i	$0.421846\pi$
$62$	10.5085			1.33458
$63$	−4.57445	−	6.48648i	−0.576327	−	0.817219i
$64$	−18.8198			−2.35247
$65$	−3.81421	+	2.20214i	−0.473095	+	0.273142i
$66$	−22.1450	−	0.206336i	−2.72587	−	0.0253982i
$67$	−3.20591	+	5.55281i	−0.391665	+	0.678383i	−0.992669	−	0.120862i	$-0.961434\pi$
$67$	−3.20591	+	5.55281i	−0.391665	+	0.678383i	0.601004	+	0.799246i	$0.294767\pi$
$68$	7.46562	−	12.9308i	0.905340	−	1.56809i
$69$	−0.00180322	+	0.193531i	−0.000217082	+	0.0232984i
$70$	6.48797	+	2.85338i	0.775460	+	0.341045i
$71$			0.343592i			0.0407768i	0.999792	+	0.0203884i	$0.00649028\pi$
$71$			0.343592i			0.0407768i	−0.999792	+	0.0203884i	$0.993510\pi$
$72$	21.8667	+	13.1740i	2.57702	+	1.55258i
$73$		−	7.87210i		−	0.921360i	−0.887566	−	0.460680i	$-0.847606\pi$
$73$		−	7.87210i		−	0.921360i	0.887566	−	0.460680i	$-0.152394\pi$
$74$	0.459097	−	0.265060i	0.0533690	−	0.0308126i
$75$	0.879963	−	1.49187i	0.101609	−	0.172266i
$76$	−5.02086	−	2.89879i	−0.575932	−	0.332514i
$77$	−1.37700	−	12.5525i	−0.156924	−	1.43049i
$78$	−10.0526	−	17.7923i	−1.13823	−	2.01459i
$79$	−6.55399	−	11.3518i	−0.737381	−	1.27718i	−0.953671	−	0.300853i	$-0.902729\pi$
$79$	−6.55399	−	11.3518i	−0.737381	−	1.27718i	0.216289	−	0.976329i	$-0.430605\pi$
$80$	−12.4432			−1.39119
$81$	−4.20646	−	7.95649i	−0.467384	−	0.884054i
$82$		−	22.5913i		−	2.49479i
$83$	3.77013	+	6.53006i	0.413826	+	0.716767i	0.995304	−	0.0967944i	$-0.0308589\pi$
$83$	3.77013	+	6.53006i	0.413826	+	0.716767i	−0.581479	+	0.813562i	$0.697526\pi$
$84$	−9.75185	+	21.6246i	−1.06401	+	2.35943i
$85$	1.44221	−	2.49799i	0.156430	−	0.270945i
$86$	−4.72134	−	2.72587i	−0.509116	−	0.293938i
$87$	10.8988	+	6.42855i	1.16847	+	0.689213i
$88$	20.3074	+	35.1734i	2.16477	+	3.74950i
$89$	−3.94862			−0.418553			−0.209276	−	0.977857i	$-0.567111\pi$
$89$	−3.94862			−0.418553			−0.209276	+	0.977857i	$0.567111\pi$
$90$	6.88390	+	4.14734i	0.725627	+	0.437168i
$91$	9.39595	−	6.89199i	0.984964	−	0.722477i
$92$	0.500928	−	0.289211i	0.0522254	−	0.0301523i
$93$	−0.0633029	+	6.79398i	−0.00656420	+	0.704503i
$94$	17.0365	+	9.83604i	1.75718	+	1.01451i
$95$	−0.969933	−	0.559991i	−0.0995130	−	0.0574538i
$96$	0.263285	−	28.2571i	0.0268714	−	2.88398i
$97$	14.8882	−	8.59573i	1.51167	−	0.872764i	0.511764	−	0.859126i	$-0.328992\pi$
$97$	14.8882	−	8.59573i	1.51167	−	0.872764i	0.999907	−	0.0136381i	$-0.00434128\pi$
$98$	−17.8864	−	5.63251i	−1.80680	−	0.568969i
$99$	0.266803	−	14.3161i	0.0268147	−	1.43882i
$100$	−5.17650			−0.517650
$101$	8.04316	+	13.9312i	0.800325	+	1.38620i	0.919402	+	0.393318i	$0.128673\pi$
$101$	8.04316	+	13.9312i	0.800325	+	1.38620i	−0.119078	+	0.992885i	$0.537994\pi$
$102$	11.5278	+	6.79956i	1.14142	+	0.673257i
$103$	1.46398	+	0.845231i	0.144251	+	0.0832831i	0.570388	−	0.821375i	$-0.306793\pi$
$103$	1.46398	+	0.845231i	0.144251	+	0.0832831i	−0.426138	+	0.904658i	$0.640126\pi$
$104$	−18.7392	+	32.4572i	−1.83753	+	3.18269i
$105$	−1.88387	+	4.17744i	−0.183847	+	0.407677i
$106$	13.9277	+	24.1234i	1.35277	+	2.34307i
$107$			10.8276i			1.04674i	0.852106	+	0.523370i	$0.175325\pi$
$107$			10.8276i			1.04674i	−0.852106	+	0.523370i	$0.824675\pi$
$108$	−14.0947	+	22.9093i	−1.35627	+	2.20445i
$109$	−6.92264			−0.663069			−0.331534	−	0.943443i	$-0.607566\pi$
$109$	−6.92264			−0.663069			−0.331534	+	0.943443i	$0.607566\pi$
$110$	6.39300	+	11.0730i	0.609549	+	1.05577i
$111$	0.168602	+	0.298415i	0.0160030	+	0.0283243i
$112$	32.7252	−	3.58994i	3.09224	−	0.339217i
$113$	−9.26887	−	5.35138i	−0.871942	−	0.503416i	−0.00394864	−	0.999992i	$-0.501257\pi$
$113$	−9.26887	−	5.35138i	−0.871942	−	0.503416i	−0.867993	+	0.496576i	$0.834590\pi$
$114$	2.64017	−	4.47607i	0.247275	−	0.419223i
$115$	0.0967696	−	0.0558700i	0.00902381	−	0.00520990i
$116$		−	37.8168i		−	3.51120i
$117$	11.5638	−	6.39205i	1.06907	−	0.590945i
$118$			13.8906i			1.27873i
$119$	−3.07230	+	6.98573i	−0.281637	+	0.640381i
$120$	0.137324	−	14.7383i	0.0125359	−	1.34542i
$121$	5.89007	−	10.2019i	0.535461	−	0.927446i
$122$	−5.74333	+	9.94774i	−0.519976	+	0.900626i
$123$	14.6058	+	0.136090i	1.31696	+	0.0122708i
$124$	17.5853	−	10.1529i	1.57921	−	0.911756i
$125$	−1.00000			−0.0894427
$126$	−19.3010	−	8.92134i	−1.71947	−	0.794777i
$127$	11.1104			0.985892			0.492946	−	0.870060i	$-0.335920\pi$
$127$	11.1104			0.985892			0.492946	+	0.870060i	$0.335920\pi$
$128$	−15.4034	+	8.89318i	−1.36149	+	0.786054i
$129$	1.79078	−	3.03605i	0.157670	−	0.267309i
$130$	−5.89931	+	10.2179i	−0.517403	+	0.896169i
$131$	7.26824	−	12.5890i	0.635029	−	1.09990i	−0.351480	−	0.936196i	$-0.614321\pi$
$131$	7.26824	−	12.5890i	0.635029	−	1.09990i	0.986509	−	0.163708i	$-0.0523453\pi$
$132$	−37.2578	+	21.0504i	−3.24287	+	1.83220i
$133$	2.71246	+	1.19293i	0.235200	+	0.103440i
$134$			17.1766i			1.48384i
$135$	−2.72283	+	4.42563i	−0.234344	+	0.380898i
$136$		−	24.5451i		−	2.10473i
$137$	−0.868046	+	0.501167i	−0.0741622	+	0.0428175i	−0.536623	−	0.843822i	$-0.680300\pi$
$137$	−0.868046	+	0.501167i	−0.0741622	+	0.0428175i	0.462460	+	0.886640i	$0.346967\pi$
$138$	0.255041	+	0.451406i	0.0217106	+	0.0384262i
$139$	−18.3782	−	10.6107i	−1.55882	−	0.899986i	−0.997370	−	0.0724762i	$-0.976910\pi$
$139$	−18.3782	−	10.6107i	−1.55882	−	0.899986i	−0.561451	−	0.827510i	$-0.689757\pi$
$140$	13.6141	−	1.49346i	1.15060	−	0.126220i
$141$	−6.46187	+	10.9553i	−0.544188	+	0.922601i
$142$	0.460224	+	0.797131i	0.0386211	+	0.0668938i
$143$	21.0210			1.75786
$144$	37.3230	+	0.695575i	3.11025	+	0.0579646i
$145$		−	7.30548i		−	0.606687i
$146$	−10.5443	−	18.2632i	−0.872651	−	1.51148i
$147$	3.74930	−	11.5301i	0.309237	−	0.950985i
$148$	0.512182	−	0.887125i	0.0421011	−	0.0729212i
$149$	3.47516	+	2.00638i	0.284696	+	0.164369i	0.635548	−	0.772062i	$-0.280774\pi$
$149$	3.47516	+	2.00638i	0.284696	+	0.164369i	−0.350851	+	0.936431i	$0.614108\pi$
$150$	0.0432312	−	4.63979i	0.00352981	−	0.378837i
$151$	−5.32728	−	9.22712i	−0.433528	−	0.750892i	0.563646	−	0.826016i	$-0.309398\pi$
$151$	−5.32728	−	9.22712i	−0.433528	−	0.750892i	−0.997174	+	0.0751240i	$0.976065\pi$
$152$	−9.53052			−0.773027
$153$	−4.46553	+	7.41204i	−0.361017	+	0.599228i
$154$	−20.0081	−	27.2773i	−1.61230	−	2.19807i
$155$	3.39714	−	1.96134i	0.272865	−	0.157539i
$156$	−34.0127	−	20.0621i	−2.72319	−	1.60625i
$157$	−4.21199	−	2.43179i	−0.336153	−	0.194078i	0.322417	−	0.946598i	$-0.395505\pi$
$157$	−4.21199	−	2.43179i	−0.336153	−	0.194078i	−0.658570	+	0.752520i	$0.728838\pi$
$158$	−30.4104	−	17.5575i	−2.41933	−	1.39680i
$159$	−15.6803	+	8.85927i	−1.24353	+	0.702586i
$160$	−14.1292	+	8.15748i	−1.11701	+	0.644905i
$161$	−0.238383	+	0.174855i	−0.0187872	+	0.0137805i
$162$	−20.4163	−	12.8247i	−1.60405	−	1.00760i
$163$	−4.38054			−0.343110			−0.171555	−	0.985175i	$-0.554879\pi$
$163$	−4.38054			−0.343110			−0.171555	+	0.985175i	$0.554879\pi$
$164$	−21.8268	−	37.8052i	−1.70439	−	2.95209i
$165$	−7.19748	+	4.06653i	−0.560323	+	0.316579i
$166$	17.4934	+	10.0998i	1.35775	+	0.783897i
$167$	−2.78491	+	4.82361i	−0.215503	+	0.373262i	−0.953428	−	0.301620i	$-0.902472\pi$
$167$	−2.78491	+	4.82361i	−0.215503	+	0.373262i	0.737925	+	0.674883i	$0.235806\pi$
$168$	3.89094	+	38.8010i	0.300192	+	2.99356i
$169$	3.19882	+	5.54052i	0.246063	+	0.426194i
$170$		−	7.72709i		−	0.592641i
$171$	2.87799	+	1.73390i	0.220085	+	0.132595i
$172$	−10.5345			−0.803250
$173$	−4.99589	−	8.65314i	−0.379831	−	0.657886i	0.611207	−	0.791471i	$-0.290684\pi$
$173$	−4.99589	−	8.65314i	−0.379831	−	0.657886i	−0.991037	+	0.133585i	$0.957351\pi$
$174$	33.8959	+	0.315825i	2.56964	+	0.0239426i
$175$	2.62997	−	0.288507i	0.198807	−	0.0218090i
$176$	51.4328	+	29.6947i	3.87689	+	2.23832i
$177$	−8.98063	−	0.0836769i	−0.675025	−	0.00628954i
$178$	−9.16078	+	5.28898i	−0.686629	+	0.396426i
$179$		−	8.14256i		−	0.608604i	−0.952576	−	0.304302i	$-0.901577\pi$
$179$		−	8.14256i		−	0.608604i	0.952576	−	0.304302i	$-0.0984231\pi$
$180$	15.5268	+	0.289367i	1.15730	+	0.0215681i
$181$			6.20886i			0.461501i	0.973013	+	0.230750i	$0.0741181\pi$
$181$			6.20886i			0.461501i	−0.973013	+	0.230750i	$0.925882\pi$
$182$	12.5671	−	28.5748i	0.931535	−	2.11810i
$183$	−6.39686	−	3.77313i	−0.472870	−	0.278918i
$184$	0.475427	−	0.823464i	0.0350490	−	0.0607066i
$185$	0.0989436	−	0.171375i	0.00727448	−	0.0125998i
$186$	8.95334	+	15.8468i	0.656491	+	1.16194i
$187$	−11.9225	+	6.88348i	−0.871862	+	0.503370i
$188$	38.0128			2.77237
$189$	5.88414	−	12.4248i	0.428008	−	0.903775i
$190$	−3.00032			−0.217666
$191$	5.04943	−	2.91529i	0.365364	−	0.210943i	−0.306067	−	0.952010i	$-0.599013\pi$
$191$	5.04943	−	2.91529i	0.365364	−	0.210943i	0.671431	+	0.741067i	$0.265680\pi$
$192$	−16.0347	−	28.3803i	−1.15720	−	2.04817i
$193$	1.61443	−	2.79628i	0.116209	−	0.201280i	−0.802053	−	0.597253i	$-0.796259\pi$
$193$	1.61443	−	2.79628i	0.116209	−	0.201280i	0.918262	+	0.395972i	$0.129592\pi$
$194$	23.0271	−	39.8841i	1.65325	−	2.86351i
$195$	−6.57059	−	3.87560i	−0.470530	−	0.277538i
$196$	−35.3738	+	7.85550i	−2.52670	+	0.561107i
$197$			18.8417i			1.34241i	0.741270	+	0.671207i	$0.234224\pi$
$197$			18.8417i			1.34241i	−0.741270	+	0.671207i	$0.765776\pi$
$198$	−18.5567	−	33.5706i	−1.31877	−	2.38576i
$199$			19.6558i			1.39336i	0.717380	+	0.696682i	$0.245341\pi$
$199$			19.6558i			1.39336i	−0.717380	+	0.696682i	$0.754659\pi$
$200$	−7.36947	+	4.25477i	−0.521100	+	0.300857i
$201$	−11.1051	−	0.103472i	−0.783296	−	0.00729835i
$202$	37.3202	+	21.5468i	2.62584	+	1.51603i
$203$	2.10768	+	19.2132i	0.147930	+	1.34850i
$204$	25.8606	+	0.240956i	1.81060	+	0.0168703i
$205$	−4.21652	−	7.30322i	−0.294494	−	0.510079i
$206$	4.52858			0.315521
$207$	−0.293382	+	0.162171i	−0.0203914	+	0.0112717i
$208$			54.8032i			3.79992i
$209$	2.67275	+	4.62935i	0.184878	+	0.320219i
$210$	1.22491	+	12.2150i	0.0845270	+	0.842915i
$211$	4.89731	−	8.48239i	0.337145	−	0.583952i	−0.646750	−	0.762702i	$-0.723872\pi$
$211$	4.89731	−	8.48239i	0.337145	−	0.583952i	0.983894	+	0.178750i	$0.0572054\pi$
$212$	46.6143	+	26.9128i	3.20148	+	1.84838i
$213$	−0.518138	+	0.292744i	−0.0355022	+	0.0200585i
$214$	14.5030	+	25.1199i	0.991403	+	1.71716i
$215$	−2.03507			−0.138790
$216$	−1.23577	+	44.1996i	−0.0840837	+	3.00740i
$217$	−8.36853	+	6.13837i	−0.568093	+	0.416700i
$218$	−16.0605	+	9.27253i	−1.08775	+	0.628015i
$219$	11.8712	−	6.70713i	0.802179	−	0.453226i
$220$	21.3966	+	12.3533i	1.44256	+	0.832863i
$221$	−11.0018	−	6.35191i	−0.740063	−	0.427276i
$222$	0.790868	+	0.466486i	0.0530796	+	0.0313085i
$223$	−15.4577	+	8.92452i	−1.03513	+	0.597630i	−0.918449	−	0.395540i	$-0.870558\pi$
$223$	−15.4577	+	8.92452i	−1.03513	+	0.597630i	−0.116677	+	0.993170i	$0.537224\pi$
$224$	34.8059	−	25.5303i	2.32556	−	1.70582i
$225$	2.99948	+	0.0559001i	0.199965	+	0.00372667i
$226$	−28.6716			−1.90721
$227$	4.96556	+	8.60060i	0.329576	+	0.570842i	0.982428	−	0.186644i	$-0.0597610\pi$
$227$	4.96556	+	8.60060i	0.329576	+	0.570842i	−0.652852	+	0.757485i	$0.726428\pi$
$228$	0.0935595	−	10.0413i	0.00619613	−	0.665000i
$229$	−20.7768	−	11.9955i	−1.37297	−	0.792685i	−0.381670	−	0.924299i	$-0.624651\pi$
$229$	−20.7768	−	11.9955i	−1.37297	−	0.792685i	−0.991301	+	0.131613i	$0.957984\pi$
$230$	0.149670	−	0.259236i	0.00986895	−	0.0170935i
$231$	17.7560	−	12.7714i	1.16826	−	0.840296i
$232$	−31.0831	−	53.8375i	−2.04071	−	3.53461i
$233$		−	5.27832i		−	0.345794i	−0.984940	−	0.172897i	$-0.944687\pi$
$233$		−	5.27832i		−	0.345794i	0.984940	−	0.172897i	$-0.0553128\pi$
$234$	18.2660	−	30.3186i	1.19409	−	1.98199i
$235$	7.34334			0.479027
$236$	13.4206	+	23.2451i	0.873606	+	1.51313i
$237$	11.5345	−	19.5553i	0.749249	−	1.27026i
$238$	2.22932	+	20.3221i	0.144505	+	1.31728i
$239$	−5.72405	−	3.30478i	−0.370258	−	0.213769i	0.303313	−	0.952891i	$-0.401907\pi$
$239$	−5.72405	−	3.30478i	−0.370258	−	0.213769i	−0.673571	+	0.739122i	$0.735240\pi$
$240$	−10.6017	−	18.7644i	−0.684339	−	1.21123i
$241$	7.01537	−	4.05033i	0.451900	−	0.260904i	−0.256733	−	0.966482i	$-0.582646\pi$
$241$	7.01537	−	4.05033i	0.451900	−	0.260904i	0.708632	+	0.705578i	$0.249313\pi$
$242$		−	31.5578i		−	2.02861i
$243$	8.41446	−	13.1224i	0.539788	−	0.841801i
$244$			22.1959i			1.42095i
$245$	−6.83353	+	1.51753i	−0.436578	+	0.0969514i
$246$	34.0677	−	19.2480i	2.17208	−	1.22721i
$247$	−2.46635	+	4.27185i	−0.156930	+	0.271811i
$248$	16.6901	−	28.9081i	1.05982	−	1.83566i
$249$	−6.63516	+	11.2491i	−0.420486	+	0.712880i
$250$	−2.32000	+	1.33945i	−0.146729	+	0.0847142i
$251$	−7.06403			−0.445877			−0.222939	−	0.974832i	$-0.571565\pi$
$251$	−7.06403			−0.445877			−0.222939	+	0.974832i	$0.571565\pi$
$252$	−40.9186	+	3.71856i	−2.57763	+	0.234247i
$253$	−0.533318			−0.0335294
$254$	25.7762	−	14.8819i	1.61734	−	0.933772i
$255$	4.99576	+	0.0465479i	0.312847	+	0.00291494i
$256$	−5.00418	+	8.66749i	−0.312761	+	0.541718i
$257$	−12.8485	+	22.2542i	−0.801467	+	1.38818i	0.117184	+	0.993110i	$0.462613\pi$
$257$	−12.8485	+	22.2542i	−0.801467	+	1.38818i	−0.918651	+	0.395071i	$0.870720\pi$
$258$	0.0879783	−	9.44228i	0.00547729	−	0.587851i
$259$	−0.210776	+	0.479259i	−0.0130970	+	0.0297797i
$260$			22.7987i			1.41392i
$261$	−0.408377	+	21.9126i	−0.0252779	+	1.35636i
$262$		−	38.9418i		−	2.40583i
$263$	25.0269	−	14.4493i	1.54323	−	0.890983i	0.544595	−	0.838699i	$-0.316683\pi$
$263$	25.0269	−	14.4493i	1.54323	−	0.890983i	0.998632	−	0.0522836i	$-0.0166500\pi$
$264$	−35.7395	+	60.5918i	−2.19961	+	3.72917i
$265$	9.00498	+	5.19903i	0.553171	+	0.319374i
$266$	7.89076	−	0.865612i	0.483814	−	0.0530741i
$267$	−3.36427	−	5.95453i	−0.205890	−	0.364411i
$268$	16.5954	+	28.7441i	1.01373	+	1.75583i
$269$	−13.5862			−0.828367			−0.414184	−	0.910193i	$-0.635933\pi$
$269$	−13.5862			−0.828367			−0.414184	+	0.910193i	$0.635933\pi$
$270$	−0.389036	+	13.9145i	−0.0236760	+	0.846812i
$271$			16.0421i			0.974486i	0.873266	+	0.487243i	$0.161997\pi$
$271$			16.0421i			0.974486i	−0.873266	+	0.487243i	$0.838003\pi$
$272$	−17.9457	−	31.0829i	−1.08812	−	1.88468i
$273$	18.3986	+	8.29707i	1.11353	+	0.502162i
$274$	−1.34257	+	2.32541i	−0.0811079	+	0.140483i
$275$	4.13341	+	2.38643i	0.249254	+	0.143907i
$276$	0.862928	+	0.508990i	0.0519422	+	0.0306376i
$277$	5.54140	+	9.59798i	0.332950	+	0.576687i	0.983089	−	0.183129i	$-0.0586226\pi$
$277$	5.54140	+	9.59798i	0.332950	+	0.576687i	−0.650139	+	0.759816i	$0.725289\pi$
$278$	−56.8499			−3.40963
$279$	−10.2993	+	5.69310i	−0.616602	+	0.340837i
$280$	18.1540	−	13.3161i	1.08491	−	0.795787i
$281$	−21.2489	+	12.2681i	−1.26760	+	0.731852i	−0.974534	−	0.224239i	$-0.928010\pi$
$281$	−21.2489	+	12.2681i	−1.26760	+	0.731852i	−0.293071	+	0.956091i	$0.594677\pi$
$282$	−0.317461	+	34.0716i	−0.0189046	+	2.02893i
$283$	12.2369	+	7.06499i	0.727409	+	0.419970i	0.817474	−	0.575966i	$-0.195374\pi$
$283$	12.2369	+	7.06499i	0.727409	+	0.419970i	−0.0900643	+	0.995936i	$0.528707\pi$
$284$	1.54032	+	0.889302i	0.0914009	+	0.0527703i
$285$	0.0180739	−	1.93978i	0.00107060	−	0.114903i
$286$	48.7685	−	28.1565i	2.88374	−	1.66493i
$287$	13.1964	+	17.9908i	0.778957	+	1.06196i
$288$	42.8361	−	23.6784i	2.52414	−	1.39526i
$289$	−8.68008			−0.510593
$290$	−9.78532	−	16.9487i	−0.574614	−	0.995260i
$291$	25.6473	+	15.1279i	1.50347	+	0.886810i
$292$	−35.2905	−	20.3750i	−2.06522	−	1.19236i
$293$	−0.810575	+	1.40396i	−0.0473543	+	0.0820200i	−0.888731	−	0.458429i	$-0.848412\pi$
$293$	−0.810575	+	1.40396i	−0.0473543	+	0.0820200i	0.841377	+	0.540449i	$0.181746\pi$
$294$	−6.74560	−	31.7717i	−0.393411	−	1.85296i
$295$	2.59260	+	4.49051i	0.150947	+	0.261448i
$296$		−	1.68393i		−	0.0978763i
$297$	21.8160	−	11.7951i	1.26589	−	0.684423i
$298$	10.7498			0.622719
$299$	−0.246067	−	0.426200i	−0.0142304	−	0.0246478i
$300$	−4.41044	−	7.80619i	−0.254637	−	0.450690i
$301$	5.35217	−	0.587130i	0.308494	−	0.0338416i
$302$	−24.7185	−	14.2712i	−1.42239	−	0.821218i
$303$	−14.1554	+	23.9986i	−0.813205	+	1.37869i
$304$	−12.0690	+	6.96806i	−0.692207	+	0.399646i
$305$			4.28783i			0.245520i
$306$	−0.431945	+	23.1773i	−0.0246927	+	1.32496i
$307$			14.8744i			0.848928i	0.905445	+	0.424464i	$0.139537\pi$
$307$			14.8744i			0.848928i	−0.905445	+	0.424464i	$0.860463\pi$
$308$	−59.8366	−	26.3159i	−3.40951	−	1.49949i
$309$	−0.0272801	+	2.92784i	−0.00155191	+	0.166559i
$310$	5.25423	−	9.10060i	0.298420	−	0.516879i
$311$	10.2022	−	17.6707i	0.578513	−	1.00201i	−0.417138	−	0.908843i	$-0.636967\pi$
$311$	10.2022	−	17.6707i	0.578513	−	1.00201i	0.995650	−	0.0931699i	$-0.0297000\pi$
$312$	−64.9115	−	0.604813i	−3.67489	−	0.0342408i
$313$	0.879452	−	0.507752i	0.0497096	−	0.0286998i	−0.474939	−	0.880019i	$-0.657530\pi$
$313$	0.879452	−	0.507752i	0.0497096	−	0.0286998i	0.524649	+	0.851319i	$0.324197\pi$
$314$	−13.0290			−0.735272
$315$	−7.90468	+	0.718354i	−0.445378	+	0.0404746i
$316$	−67.8535			−3.81706
$317$	26.7930	−	15.4690i	1.50485	−	0.868824i	0.504863	−	0.863200i	$-0.331543\pi$
$317$	26.7930	−	15.4690i	1.50485	−	0.868824i	0.999984	−	0.00562430i	$-0.00179028\pi$
$318$	−24.5117	+	41.5564i	−1.37455	+	2.33037i
$319$	−17.4340	+	30.1966i	−0.976116	+	1.69068i
$320$	−9.40989	+	16.2984i	−0.526029	+	0.911108i
$321$	−16.3280	+	9.22522i	−0.911340	+	0.514901i
$322$	−0.318837	+	0.724965i	−0.0177681	+	0.0404007i
$323$		−	3.23051i		−	0.179750i
$324$	−46.5562	−	1.73590i	−2.58645	−	0.0964389i
$325$			4.40428i			0.244305i
$326$	−10.1628	+	5.86751i	−0.562867	+	0.324971i
$327$	−5.89818	−	10.4394i	−0.326170	−	0.577299i
$328$	−62.1470	−	35.8806i	−3.43149	−	1.98117i
$329$	−19.3128	+	2.11860i	−1.06475	+	0.116802i
$330$	−11.2512	+	19.0750i	−0.619359	+	1.05004i
$331$	−8.80119	−	15.2441i	−0.483757	−	0.837892i	0.516069	−	0.856547i	$-0.327395\pi$
$331$	−8.80119	−	15.2441i	−0.483757	−	0.837892i	−0.999826	+	0.0186549i	$0.994062\pi$
$332$	39.0322			2.14217
$333$	−0.306359	+	0.508506i	−0.0167884	+	0.0278659i
$334$			14.9210i			0.816441i
$335$	3.20591	+	5.55281i	0.175158	+	0.303382i
$336$	33.2959	+	46.2911i	1.81644	+	2.52539i
$337$	−8.85656	+	15.3400i	−0.482447	+	0.835624i	−0.999797	−	0.0201507i	$-0.993585\pi$
$337$	−8.85656	+	15.3400i	−0.482447	+	0.835624i	0.517349	+	0.855774i	$0.326919\pi$
$338$	14.8425	+	8.56932i	0.807325	+	0.466109i
$339$	0.172718	−	18.5369i	0.00938074	−	1.00679i
$340$	−7.46562	−	12.9308i	−0.404880	−	0.701273i
$341$	−18.7224			−1.01387
$342$	8.99939	+	0.167718i	0.486631	+	0.00906915i
$343$	17.5342	−	5.96258i	0.946757	−	0.321949i
$344$	−14.9974	+	8.65873i	−0.808604	+	0.466848i
$345$	0.166701	+	0.0983270i	0.00897488	+	0.00529375i
$346$	−23.1809	−	13.3835i	−1.24621	−	0.719501i
$347$	26.9193	+	15.5418i	1.44510	+	0.834330i	0.998184	−	0.0602447i	$-0.0191881\pi$
$347$	26.9193	+	15.5418i	1.44510	+	0.834330i	0.446918	+	0.894575i	$0.352521\pi$
$348$	57.0279	−	32.2204i	3.05702	−	1.72719i
$349$	−13.5634	+	7.83084i	−0.726033	+	0.419175i	−0.816969	−	0.576682i	$-0.804347\pi$
$349$	−13.5634	+	7.83084i	−0.726033	+	0.419175i	0.0909365	+	0.995857i	$0.471014\pi$
$350$	5.71509	−	4.19205i	0.305484	−	0.224075i
$351$	19.4917	+	11.9921i	1.04039	+	0.640090i
$352$	77.8689			4.15043
$353$	0.634698	+	1.09933i	0.0337816	+	0.0585114i	0.882422	−	0.470459i	$-0.155912\pi$
$353$	0.634698	+	1.09933i	0.0337816	+	0.0585114i	−0.848640	+	0.528970i	$0.822578\pi$
$354$	−20.9471	+	11.8350i	−1.11333	+	0.629022i
$355$	0.297559	+	0.171796i	0.0157928	+	0.00911798i
$356$	−10.2200	+	17.7016i	−0.541660	+	0.938182i
$357$	−13.1521	+	1.31889i	−0.696085	+	0.0698030i
$358$	−10.9066	−	18.8907i	−0.576429	−	0.998405i
$359$		−	3.58764i		−	0.189349i	−0.995508	−	0.0946743i	$-0.969819\pi$
$359$		−	3.58764i		−	0.189349i	0.995508	−	0.0946743i	$-0.0301810\pi$
$360$	22.3424	−	12.3501i	1.17755	−	0.650909i
$361$	17.7456			0.933981
$362$	8.31645	+	14.4045i	0.437103	+	0.757085i
$363$	20.4029	+	0.190104i	1.07088	+	0.00997787i
$364$	−6.57759	−	59.9601i	−0.344759	−	3.14276i
$365$	−6.81744	−	3.93605i	−0.356841	−	0.206022i
$366$	−19.8946	−	0.185368i	−1.03991	−	0.00968933i
$367$	−1.21329	+	0.700496i	−0.0633334	+	0.0365656i	−0.531332	−	0.847163i	$-0.678308\pi$
$367$	−1.21329	+	0.700496i	−0.0633334	+	0.0365656i	0.467999	+	0.883729i	$0.344975\pi$
$368$		−	1.39040i		−	0.0724796i
$369$	12.2391	+	22.1416i	0.637142	+	1.15264i
$370$		−	0.530120i		−	0.0275596i
$371$	−25.1828	−	11.0753i	−1.30743	−	0.575001i
$372$	30.2935	+	17.8683i	1.57064	+	0.926430i
$373$	−15.6757	+	27.1511i	−0.811656	+	1.40583i	0.100048	+	0.994983i	$0.468100\pi$
$373$	−15.6757	+	27.1511i	−0.811656	+	1.40583i	−0.911704	+	0.410847i	$0.865233\pi$
$374$	−18.4401	+	31.9393i	−0.953517	+	1.65154i
$375$	−0.852012	−	1.50800i	−0.0439977	−	0.0778730i
$376$	54.1165	−	31.2442i	2.79085	−	1.61130i
$377$	−32.1753			−1.65711
$378$	−2.99128	−	36.7071i	−0.153855	−	1.88801i
$379$	6.57225			0.337594			0.168797	−	0.985651i	$-0.446012\pi$
$379$	6.57225			0.337594			0.168797	+	0.985651i	$0.446012\pi$
$380$	−5.02086	+	2.89879i	−0.257565	+	0.148705i
$381$	9.46623	+	16.7546i	0.484970	+	0.858363i
$382$	7.80976	−	13.5269i	0.399582	−	0.692097i
$383$	12.6072	−	21.8362i	0.644196	−	1.11578i	−0.340291	−	0.940320i	$-0.610525\pi$
$383$	12.6072	−	21.8362i	0.644196	−	1.11578i	0.984487	−	0.175460i	$-0.0561412\pi$
$384$	−26.5349	−	15.6514i	−1.35410	−	0.798705i
$385$	−11.5593	−	5.08373i	−0.589115	−	0.259091i
$386$		−	8.64979i		−	0.440263i
$387$	6.10414	+	0.113760i	0.310291	+	0.00578277i
$388$		−	88.9916i		−	4.51786i
$389$	11.5344	−	6.65938i	0.584816	−	0.337644i	−0.178229	−	0.983989i	$-0.557037\pi$
$389$	11.5344	−	6.65938i	0.584816	−	0.337644i	0.763045	+	0.646345i	$0.223703\pi$
$390$	−20.4349	−	0.190402i	−1.03476	−	0.00964138i
$391$	0.279125	+	0.161153i	0.0141160	+	0.00814985i
$392$	−43.9028	+	40.2585i	−2.21742	+	2.03336i
$393$	25.1768	+	0.234585i	1.27000	+	0.0118332i
$394$	25.2375	+	43.7126i	1.27145	+	2.20221i
$395$	−13.1080			−0.659534
$396$	−63.4882	−	38.2497i	−3.19040	−	1.92212i
$397$			8.28898i			0.416012i	0.978128	+	0.208006i	$0.0666973\pi$
$397$			8.28898i			0.416012i	−0.978128	+	0.208006i	$0.933303\pi$
$398$	26.3280	+	45.6014i	1.31970	+	2.28579i
$399$	0.512106	+	5.10679i	0.0256374	+	0.255659i
$400$	−6.22159	+	10.7761i	−0.311079	+	0.538805i
$401$	−13.6087	−	7.85697i	−0.679585	−	0.392358i	0.120114	−	0.992760i	$-0.461674\pi$
$401$	−13.6087	−	7.85697i	−0.679585	−	0.392358i	−0.799699	+	0.600402i	$0.795007\pi$
$402$	−25.9024	+	14.6347i	−1.29190	+	0.729913i
$403$	−8.63828	−	14.9619i	−0.430303	−	0.745307i
$404$	83.2709			4.14288
$405$	−8.99375	−	0.335342i	−0.446903	−	0.0166633i
$406$	30.6249	+	41.7514i	1.51989	+	2.07209i
$407$	−0.817950	+	0.472243i	−0.0405443	+	0.0234082i
$408$	37.0142	−	20.9128i	1.83247	−	1.03534i
$409$	15.7651	+	9.10196i	0.779532	+	0.450063i	0.836264	−	0.548326i	$-0.184735\pi$
$409$	15.7651	+	9.10196i	0.779532	+	0.450063i	−0.0567323	+	0.998389i	$0.518068\pi$
$410$	−19.5646	−	11.2956i	−0.966227	−	0.557851i
$411$	−1.49535	−	0.882016i	−0.0737600	−	0.0435067i
$412$	7.57831	−	4.37534i	0.373357	−	0.215558i
$413$	−8.11400	−	11.0619i	−0.399264	−	0.544323i
$414$	−0.463423	+	0.769207i	−0.0227760	+	0.0378044i
$415$	7.54026			0.370137
$416$	35.9278	+	62.2287i	1.76150	+	3.05101i
$417$	0.342463	−	36.7549i	0.0167705	−	1.79989i
$418$	12.4016	+	7.16004i	0.606580	+	0.350209i
$419$	9.61867	−	16.6600i	0.469903	−	0.813896i	−0.529505	−	0.848307i	$-0.677622\pi$
$419$	9.61867	−	16.6600i	0.469903	−	0.813896i	0.999408	+	0.0344111i	$0.0109556\pi$
$420$	13.8515	+	19.2576i	0.675883	+	0.939676i
$421$	9.60976	+	16.6446i	0.468351	+	0.811208i	0.999346	−	0.0361672i	$-0.0115149\pi$
$421$	9.60976	+	16.6446i	0.468351	+	0.811208i	−0.530995	+	0.847375i	$0.678182\pi$
$422$		−	26.2388i		−	1.27729i
$423$	−22.0262	−	0.410493i	−1.07095	−	0.0199589i
$424$	88.4825			4.29709
$425$	−1.44221	−	2.49799i	−0.0699577	−	0.121170i
$426$	−0.809960	+	1.37318i	−0.0392427	+	0.0665310i
$427$	−1.23707	−	11.2769i	−0.0598658	−	0.545726i
$428$	48.5398	+	28.0245i	2.34626	+	1.35461i
$429$	17.9101	+	31.6997i	0.864709	+	1.53048i
$430$	−4.72134	+	2.72587i	−0.227683	+	0.131453i
$431$			15.2248i			0.733353i	0.930348	+	0.366677i	$0.119504\pi$
$431$			15.2248i			0.733353i	−0.930348	+	0.366677i	$0.880496\pi$
$432$	30.7508	+	56.8759i	1.47950	+	2.73644i
$433$		−	18.8465i		−	0.905703i	−0.891586	−	0.452851i	$-0.850407\pi$
$433$		−	18.8465i		−	0.905703i	0.891586	−	0.452851i	$-0.149593\pi$
$434$	−11.1929	+	25.4502i	−0.537277	+	1.22165i
$435$	11.0167	−	6.22436i	0.528210	−	0.298435i
$436$	−17.9175	+	31.0341i	−0.858095	+	1.48626i
$437$	0.0625733	−	0.108380i	0.00299329	−	0.00518453i
$438$	18.5572	−	31.4613i	0.886696	−	1.50328i
$439$	25.3210	−	14.6191i	1.20851	−	0.697731i	0.246073	−	0.969251i	$-0.420860\pi$
$439$	25.3210	−	14.6191i	1.20851	−	0.697731i	0.962433	+	0.271521i	$0.0875265\pi$
$440$	40.6148			1.93623
$441$	20.5819	−	4.16980i	0.980088	−	0.198562i
$442$	−34.0322			−1.61875
$443$	4.02381	−	2.32315i	0.191177	−	0.110376i	−0.401356	−	0.915922i	$-0.631461\pi$
$443$	4.02381	−	2.32315i	0.191177	−	0.110376i	0.592533	+	0.805546i	$0.298128\pi$
$444$	1.77417	+	0.0165308i	0.0841985	+	0.000784519i
$445$	−1.97431	+	3.41960i	−0.0935912	+	0.162105i
$446$	−23.9079	+	41.4097i	−1.13207	+	1.96081i
$447$	−0.0647567	+	6.95002i	−0.00306289	+	0.328725i
$448$	20.0456	−	45.5792i	0.947064	−	2.15341i
$449$		−	19.9936i		−	0.943557i	−0.881717	−	0.471778i	$-0.843612\pi$
$449$		−	19.9936i		−	0.943557i	0.881717	−	0.471778i	$-0.156388\pi$
$450$	7.03365	−	3.88796i	0.331570	−	0.183280i
$451$			40.2497i			1.89528i
$452$	−47.9803	+	27.7014i	−2.25680	+	1.30297i
$453$	9.37562	−	15.8952i	0.440505	−	0.746820i
$454$	23.0401	+	13.3022i	1.08133	+	0.624305i
$455$	−1.27066	−	11.5831i	−0.0595696	−	0.543026i
$456$	−8.12012	−	14.3721i	−0.380259	−	0.673033i
$457$	−3.03236	−	5.25221i	−0.141848	−	0.245688i	0.786345	−	0.617788i	$-0.211971\pi$
$457$	−3.03236	−	5.25221i	−0.141848	−	0.245688i	−0.928193	+	0.372100i	$0.878638\pi$
$458$	−64.2695			−3.00312
$459$	−14.9821	−	0.418883i	−0.699303	−	0.0195518i
$460$		−	0.578422i		−	0.0269691i
$461$	−1.76833	−	3.06284i	−0.0823595	−	0.142651i	0.821903	−	0.569627i	$-0.192912\pi$
$461$	−1.76833	−	3.06284i	−0.0823595	−	0.142651i	−0.904263	+	0.426976i	$0.859579\pi$
$462$	24.0871	−	53.4128i	1.12063	−	2.48499i
$463$	−18.1889	+	31.5042i	−0.845312	+	1.46412i	0.0400379	+	0.999198i	$0.487252\pi$
$463$	−18.1889	+	31.5042i	−0.845312	+	1.46412i	−0.885350	+	0.464925i	$0.846081\pi$
$464$	−78.7246	−	45.4517i	−3.65470	−	2.11004i
$465$	5.85211	+	3.45181i	0.271385	+	0.160074i
$466$	−7.07005	−	12.2457i	−0.327514	−	0.567270i
$467$	−8.34838			−0.386317			−0.193159	−	0.981168i	$-0.561873\pi$
$467$	−8.34838			−0.386317			−0.193159	+	0.981168i	$0.561873\pi$
$468$	1.27445	−	68.3844i	0.0589116	−	3.16107i
$469$	−10.0335	−	13.6788i	−0.463304	−	0.631629i
$470$	17.0365	−	9.83604i	0.785836	−	0.453703i
$471$	0.0784869	−	8.42361i	0.00361648	−	0.388139i
$472$	38.2121	+	22.0618i	1.75886	+	1.01548i
$473$	8.41177	+	4.85654i	0.386774	+	0.223304i
$474$	0.566673	−	60.8183i	0.0260282	−	2.79347i
$475$	−0.969933	+	0.559991i	−0.0445036	+	0.0256941i
$476$	23.3650	+	31.8539i	1.07093	+	1.46002i
$477$	−26.7196	−	16.0977i	−1.22341	−	0.737065i
$478$	−17.7064			−0.809870
$479$	7.06408	+	12.2353i	0.322766	+	0.559047i	0.981058	−	0.193716i	$-0.0620540\pi$
$479$	7.06408	+	12.2353i	0.322766	+	0.559047i	−0.658292	+	0.752763i	$0.728721\pi$
$480$	−24.3397	−	14.3566i	−1.11095	−	0.655284i
$481$	−0.754784	−	0.435775i	−0.0344152	−	0.0198696i
$482$	10.8504	−	18.7935i	0.494223	−	0.856019i
$483$	−0.466787	−	0.210503i	−0.0212396	−	0.00957823i
$484$	−30.4900	−	52.8102i	−1.38591	−	2.40046i
$485$		−	17.1915i		−	0.780624i
$486$	1.94473	−	41.7146i	0.0882146	−	1.89221i
$487$	−25.5677			−1.15858			−0.579292	−	0.815120i	$-0.696671\pi$
$487$	−25.5677			−1.15858			−0.579292	+	0.815120i	$0.696671\pi$
$488$	18.2437	+	31.5990i	0.825853	+	1.43042i
$489$	−3.73227	−	6.60587i	−0.168779	−	0.298728i
$490$	−13.8211	+	12.6738i	−0.624373	+	0.572545i
$491$	−17.2005	−	9.93072i	−0.776248	−	0.448167i	0.0588510	−	0.998267i	$-0.481256\pi$
$491$	−17.2005	−	9.93072i	−0.776248	−	0.448167i	−0.835099	+	0.550100i	$0.814590\pi$
$492$	38.4136	−	65.1254i	1.73182	−	2.93608i
$493$	18.2490	−	10.5361i	0.821894	−	0.474520i
$494$			13.2142i			0.594536i
$495$	−12.2647	−	7.38910i	−0.551257	−	0.332115i
$496$		−	48.8106i		−	2.19166i
$497$	−0.832137	−	0.365971i	−0.0373264	−	0.0164160i
$498$	−0.325975	+	34.9852i	−0.0146073	+	1.56773i
$499$	14.1695	−	24.5422i	0.634312	−	1.09866i	−0.352349	−	0.935869i	$-0.614617\pi$
$499$	14.1695	−	24.5422i	0.634312	−	1.09866i	0.986660	−	0.162791i	$-0.0520498\pi$
$500$	−2.58825	+	4.48298i	−0.115750	+	0.200485i
$501$	−9.64680	−	0.0898840i	−0.430987	−	0.00401572i
$502$	−16.3885	+	9.46191i	−0.731455	+	0.422306i
$503$	0.446489			0.0199080			0.00995398	−	0.999950i	$-0.496831\pi$
$503$	0.446489			0.0199080			0.00995398	+	0.999950i	$0.496831\pi$
$504$	−55.1969	+	38.9265i	−2.45866	+	1.73392i
$505$	16.0863			0.715832
$506$	−1.23730	+	0.714353i	−0.0550045	+	0.0317569i
$507$	−5.62969	+	9.54442i	−0.250023	+	0.423883i
$508$	28.7566	−	49.8079i	1.27587	−	2.20987i
$509$	−14.2688	+	24.7143i	−0.632454	+	1.09544i	0.354595	+	0.935020i	$0.384619\pi$
$509$	−14.2688	+	24.7143i	−0.632454	+	1.09544i	−0.987049	+	0.160422i	$0.948715\pi$
$510$	11.6525	−	6.58358i	0.515981	−	0.291526i
$511$	19.0653	+	8.38484i	0.843398	+	0.370923i
$512$		−	8.76137i		−	0.387201i
$513$	−0.162646	+	5.81732i	−0.00718100	+	0.256841i
$514$			68.8396i			3.03639i
$515$	1.46398	−	0.845231i	0.0645108	−	0.0372453i
$516$	−8.97555	−	15.8861i	−0.395126	−	0.699347i
$517$	−30.3531	−	17.5244i	−1.33493	−	0.770720i
$518$	0.152943	+	1.39420i	0.00671993	+	0.0612577i
$519$	8.79240	−	14.9064i	0.385944	−	0.654318i
$520$	18.7392	+	32.4572i	0.821767	+	1.42334i
$521$	19.4253			0.851037			0.425518	−	0.904950i	$-0.360092\pi$
$521$	19.4253			0.851037			0.425518	+	0.904950i	$0.360092\pi$
$522$	28.4034	+	51.3842i	1.24318	+	2.24903i
$523$			2.85907i			0.125018i	0.998044	+	0.0625091i	$0.0199102\pi$
$523$			2.85907i			0.125018i	−0.998044	+	0.0625091i	$0.980090\pi$
$524$	−37.6241	−	65.1668i	−1.64362	−	2.84683i
$525$	2.67584	+	3.72020i	0.116783	+	0.162363i
$526$	38.7083	−	67.0447i	1.68776	−	2.92329i
$527$	9.79881	+	5.65734i	0.426843	+	0.246438i
$528$	−0.958407	+	102.861i	−0.0417093	+	4.47646i
$529$	−11.4938	−	19.9078i	−0.499729	−	0.865555i
$530$	27.8553			1.20996
$531$	−7.52542	−	13.6141i	−0.326575	−	0.590802i
$532$	12.3684	−	9.07230i	0.536238	−	0.393334i
$533$	−32.1654	+	18.5707i	−1.39324	+	0.804387i
$534$	−15.7809	−	9.30821i	−0.682906	−	0.402806i
$535$	9.37694	+	5.41378i	0.405401	+	0.234058i
$536$	47.2518	+	27.2808i	2.04097	+	1.17835i
$537$	12.2790	−	6.93756i	0.529879	−	0.299378i
$538$	−31.5200	+	18.1981i	−1.35892	+	0.784575i
$539$	31.8673	+	10.0351i	1.37262	+	0.432244i
$540$	12.7927	+	23.6610i	0.550509	+	1.01821i
$541$	−4.33301			−0.186290			−0.0931452	−	0.995653i	$-0.529692\pi$
$541$	−4.33301			−0.186290			−0.0931452	+	0.995653i	$0.529692\pi$
$542$	21.4875	+	37.2175i	0.922969	+	1.59863i
$543$	−9.36298	+	5.29002i	−0.401804	+	0.227017i
$544$	−40.7546	−	23.5297i	−1.74734	−	1.00883i
$545$	−3.46132	+	5.99518i	−0.148267	+	0.256805i
$546$	53.7982	−	5.39485i	2.30235	−	0.230878i
$547$	−5.30628	−	9.19074i	−0.226880	−	0.392968i	0.730002	−	0.683445i	$-0.239519\pi$
$547$	−5.30628	−	9.19074i	−0.226880	−	0.392968i	−0.956882	+	0.290477i	$0.906186\pi$
$548$			5.18858i			0.221645i
$549$	0.239690	−	12.8612i	0.0102297	−	0.548905i
$550$	12.7860			0.545197
$551$	−4.09100	−	7.08582i	−0.174283	−	0.301866i
$552$	1.64686	+	0.0153446i	0.0700949	+	0.000653108i
$553$	34.4736	−	3.78174i	1.46597	−	0.160816i
$554$	25.7120	+	14.8448i	1.09240	+	0.630697i
$555$	0.342736	+	0.00319344i	0.0145483	+	0.000135554i
$556$	−95.1350	+	54.9262i	−4.03462	+	2.32939i
$557$		−	1.93280i		−	0.0818953i	−0.999161	−	0.0409476i	$-0.986962\pi$
$557$		−	1.93280i		−	0.0818953i	0.999161	−	0.0409476i	$-0.0130377\pi$
$558$	−16.2687	+	27.0033i	−0.688708	+	1.14314i
$559$			8.96299i			0.379094i
$560$	13.2536	−	30.1358i	0.560068	−	1.27347i
$561$	−20.5385	−	12.1144i	−0.867134	−	0.511471i
$562$	−32.8649	+	56.9238i	−1.38632	+	2.40118i
$563$	−5.96641	+	10.3341i	−0.251454	+	0.435532i	−0.963926	−	0.266169i	$-0.914242\pi$
$563$	−5.96641	+	10.3341i	−0.251454	+	0.435532i	0.712472	+	0.701700i	$0.247575\pi$
$564$	32.3874	+	57.3235i	1.36376	+	2.41375i
$565$	−9.26887	+	5.35138i	−0.389944	+	0.225134i
$566$	37.8528			1.59107
$567$	23.7501	−	1.71281i	0.997410	−	0.0719315i
$568$	2.92380			0.122680
$569$	38.5178	−	22.2383i	1.61475	−	0.932276i	0.626501	−	0.779421i	$-0.284486\pi$
$569$	38.5178	−	22.2383i	1.61475	−	0.932276i	0.988249	−	0.152856i	$-0.0488469\pi$
$570$	−2.55631	−	4.52449i	−0.107072	−	0.189510i
$571$	−13.5056	+	23.3923i	−0.565190	+	0.978937i	0.431842	+	0.901949i	$0.357864\pi$
$571$	−13.5056	+	23.3923i	−0.565190	+	0.978937i	−0.997032	+	0.0769882i	$0.975470\pi$
$572$	54.4075	−	94.2366i	2.27489	−	3.94023i
$573$	8.69844	+	5.13069i	0.363382	+	0.214338i
$574$	54.7133	+	24.0627i	2.28369	+	1.00436i
$575$		−	0.111740i		−	0.00465988i
$576$	29.1358	−	48.3607i	1.21399	−	2.01503i
$577$		−	30.1225i		−	1.25402i	−0.779012	−	0.627009i	$-0.784279\pi$
$577$		−	30.1225i		−	1.25402i	0.779012	−	0.627009i	$-0.215721\pi$
$578$	−20.1377	+	11.6265i	−0.837619	+	0.483600i
$579$	5.59231	+	0.0521063i	0.232408	+	0.00216546i
$580$	−32.7503	−	18.9084i	−1.35988	−	0.785129i
$581$	−19.8307	+	2.17542i	−0.822716	+	0.0902515i
$582$	79.7647	+	0.743207i	3.30635	+	0.0308069i
$583$	−24.8142	−	42.9794i	−1.02770	−	1.78003i
$584$	−66.9879			−2.77198
$585$	0.246199	−	13.2105i	0.0101791	−	0.546188i
$586$			4.34290i			0.179403i
$587$	−5.16411	−	8.94450i	−0.213145	−	0.369179i	0.739552	−	0.673100i	$-0.235038\pi$
$587$	−5.16411	−	8.94450i	−0.213145	−	0.369179i	−0.952697	+	0.303921i	$0.901704\pi$
$588$	−41.9850	−	46.6508i	−1.73143	−	1.92385i
$589$	2.19666	−	3.80473i	0.0905120	−	0.156771i
$590$	12.0296	+	6.94531i	0.495252	+	0.285934i
$591$	−28.4133	+	16.0533i	−1.16877	+	0.660346i
$592$	−1.23117	−	2.13245i	−0.0506009	−	0.0876433i
$593$	−1.55021			−0.0636595			−0.0318298	−	0.999493i	$-0.510133\pi$
$593$	−1.55021			−0.0636595			−0.0318298	+	0.999493i	$0.510133\pi$
$594$	34.8141	−	56.5861i	1.42844	−	2.32176i
$595$	4.51367	+	6.15356i	0.185042	+	0.252271i
$596$	17.9892	−	10.3861i	0.736865	−	0.425429i
$597$	−29.6411	+	16.7470i	−1.21313	+	0.685409i
$598$	−1.14175	−	0.659188i	−0.0466895	−	0.0269562i
$599$	5.69617	+	3.28869i	0.232739	+	0.134372i	0.611835	−	0.790985i	$-0.290432\pi$
$599$	5.69617	+	3.28869i	0.232739	+	0.134372i	−0.379096	+	0.925357i	$0.623765\pi$
$600$	−12.6951	−	7.48808i	−0.518275	−	0.305699i
$601$	24.1429	−	13.9389i	0.984808	−	0.568579i	0.0810897	−	0.996707i	$-0.474160\pi$
$601$	24.1429	−	13.9389i	0.984808	−	0.568579i	0.903718	+	0.428128i	$0.140827\pi$
$602$	11.6306	−	8.53111i	0.474027	−	0.347702i
$603$	−9.30567	−	16.8347i	−0.378956	−	0.685564i
$604$	−55.1534			−2.24416
$605$	−5.89007	−	10.2019i	−0.239465	−	0.414766i
$606$	−0.695431	+	74.6372i	−0.0282500	+	3.03193i
$607$	31.1956	+	18.0108i	1.26619	+	0.731035i	0.974265	−	0.225406i	$-0.0723709\pi$
$607$	31.1956	+	18.0108i	1.26619	+	0.731035i	0.291925	+	0.956441i	$0.405704\pi$
$608$	−9.13622	+	15.8244i	−0.370523	+	0.641764i
$609$	−27.1778	+	19.5483i	−1.10130	+	0.792137i
$610$	5.74333	+	9.94774i	0.232541	+	0.402772i
$611$		−	32.3421i		−	1.30842i
$612$	21.6702	+	39.2031i	0.875964	+	1.58469i
$613$	−16.6484			−0.672422			−0.336211	−	0.941787i	$-0.609146\pi$
$613$	−16.6484			−0.672422			−0.336211	+	0.941787i	$0.609146\pi$
$614$	19.9235	+	34.5086i	0.804048	+	1.39265i
$615$	7.42076	−	12.5810i	0.299234	−	0.507313i
$616$	−106.816	+	11.7176i	−4.30373	+	0.472117i
$617$	3.16751	+	1.82876i	0.127519	+	0.0736232i	0.562403	−	0.826864i	$-0.309877\pi$
$617$	3.16751	+	1.82876i	0.127519	+	0.0736232i	−0.434884	+	0.900487i	$0.643210\pi$
$618$	3.85840	+	6.82911i	0.155208	+	0.274707i
$619$	−8.83611	+	5.10153i	−0.355153	+	0.205048i	−0.666953	−	0.745100i	$-0.732402\pi$
$619$	−8.83611	+	5.10153i	−0.355153	+	0.205048i	0.311799	+	0.950148i	$0.399068\pi$
$620$		−	20.3058i		−	0.815499i
$621$	−0.494520	−	0.304249i	−0.0198444	−	0.0122091i
$622$		−	54.6612i		−	2.19172i
$623$	4.20580	−	9.56307i	0.168502	−	0.383136i
$624$	−82.6434	+	46.6930i	−3.30838	+	1.86921i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.36022	−	2.35596i	0.0543652	−	0.0941633i
$627$	−4.70385	+	7.97478i	−0.187854	+	0.318482i
$628$	−21.8034	+	12.5882i	−0.870049	+	0.502323i
$629$	0.570791			0.0227589
$630$	−17.3766	+	12.2545i	−0.692301	+	0.488231i
$631$	−16.4023			−0.652967			−0.326484	−	0.945203i	$-0.605864\pi$
$631$	−16.4023			−0.652967			−0.326484	+	0.945203i	$0.605864\pi$
$632$	−96.5989	+	55.7714i	−3.84250	+	2.21847i
$633$	16.9641	+	0.158062i	0.674261	+	0.00628242i
$634$	41.4398	−	71.7759i	1.64579	−	2.85058i
$635$	5.55522	−	9.62192i	0.220452	−	0.381834i
$636$	−0.868619	+	93.2245i	−0.0344430	+	3.69659i
$637$	6.68362	+	30.0967i	0.264815	+	1.19248i
$638$			93.4078i			3.69805i
$639$	−0.882919	−	0.531932i	−0.0349277	−	0.0210429i
$640$			17.7864i			0.703068i
$641$	39.4627	−	22.7838i	1.55868	−	0.899907i	0.561301	−	0.827611i	$-0.310301\pi$
$641$	39.4627	−	22.7838i	1.55868	−	0.899907i	0.997383	−	0.0722956i	$-0.0230325\pi$
$642$	−25.5242	+	43.2730i	−1.00736	+	1.70785i
$643$	6.60629	+	3.81414i	0.260527	+	0.150415i	0.624575	−	0.780965i	$-0.285272\pi$
$643$	6.60629	+	3.81414i	0.260527	+	0.150415i	−0.364048	+	0.931380i	$0.618606\pi$
$644$	0.166879	+	1.52123i	0.00657594	+	0.0599451i
$645$	−1.73390	−	3.06889i	−0.0682723	−	0.120837i
$646$	−4.32710	−	7.49476i	−0.170248	−	0.294877i
$647$	−39.6762			−1.55983			−0.779915	−	0.625885i	$-0.784738\pi$
$647$	−39.6762			−1.55983			−0.779915	+	0.625885i	$0.784738\pi$
$648$	−67.7060	+	35.7950i	−2.65974	+	1.40616i
$649$		−	24.7482i		−	0.971451i
$650$	5.89931	+	10.2179i	0.231390	+	0.400779i
$651$	−16.3868	−	7.38981i	−0.642248	−	0.289629i
$652$	−11.3379	+	19.6379i	−0.444028	+	0.769079i
$653$	−5.64232	−	3.25759i	−0.220801	−	0.127479i	0.385520	−	0.922699i	$-0.374022\pi$
$653$	−5.64232	−	3.25759i	−0.220801	−	0.127479i	−0.606321	+	0.795220i	$0.707355\pi$
$654$	−27.6668	−	16.3190i	−1.08186	−	0.638123i
$655$	−7.26824	−	12.5890i	−0.283994	−	0.491892i
$656$	−104.934			−4.09697
$657$	20.2287	+	12.1872i	0.789199	+	0.475468i
$658$	−41.9678	+	30.7837i	−1.63608	+	1.20007i
$659$	5.73510	−	3.31116i	0.223408	−	0.128985i	−0.384119	−	0.923283i	$-0.625495\pi$
$659$	5.73510	−	3.31116i	0.223408	−	0.128985i	0.607527	+	0.794299i	$0.292162\pi$
$660$	−0.398708	+	42.7914i	−0.0155197	+	1.66565i
$661$	−10.3518	−	5.97662i	−0.402639	−	0.232464i	0.284983	−	0.958533i	$-0.408012\pi$
$661$	−10.3518	−	5.97662i	−0.402639	−	0.232464i	−0.687622	+	0.726069i	$0.741345\pi$
$662$	−40.8375	−	23.5775i	−1.58719	−	0.916366i
$663$	0.205010	−	22.0027i	0.00796193	−	0.854514i
$664$	55.5678	−	32.0821i	2.15645	−	1.24503i
$665$	2.38934	−	1.75259i	0.0926545	−	0.0679627i
$666$	−0.0296337	+	1.59008i	−0.00114828	+	0.0616145i
$667$	0.816314			0.0316078
$668$	14.4161	+	24.9694i	0.557776	+	0.966097i
$669$	−26.6284	−	15.7065i	−1.02951	−	0.607248i
$670$	14.8754	+	8.58832i	0.574687	+	0.331796i
$671$	10.2326	−	17.7234i	0.395025	−	0.684203i
$672$	68.1548	+	30.7352i	2.62913	+	1.18564i
$673$	16.9701	+	29.3931i	0.654150	+	1.13302i	0.982106	+	0.188328i	$0.0603067\pi$
$673$	16.9701	+	29.3931i	0.654150	+	1.13302i	−0.327957	+	0.944693i	$0.606360\pi$
$674$			47.4517i			1.82777i
$675$	2.47130	+	4.57085i	0.0951202	+	0.175932i
$676$	33.1174			1.27375
$677$	−7.25420	−	12.5646i	−0.278801	−	0.482898i	0.692286	−	0.721624i	$-0.256604\pi$
$677$	−7.25420	−	12.5646i	−0.278801	−	0.482898i	−0.971087	+	0.238725i	$0.923270\pi$
$678$	−24.4286	−	43.2369i	−0.938174	−	1.66050i
$679$	4.95985	+	45.2131i	0.190342	+	1.73512i
$680$	−21.2567	−	12.2726i	−0.815158	−	0.470631i
$681$	−8.73902	+	14.8159i	−0.334880	+	0.567746i
$682$	−43.4358	+	25.0777i	−1.66324	+	0.960274i
$683$			8.56717i			0.327814i	0.986476	+	0.163907i	$0.0524096\pi$
$683$			8.56717i			0.327814i	−0.986476	+	0.163907i	$0.947590\pi$
$684$	15.2220	−	8.41421i	0.582028	−	0.321725i
$685$			1.00233i			0.0382972i
$686$	32.6926	−	37.3193i	1.24821	−	1.42486i
$687$	0.387159	−	41.5518i	0.0147710	−	1.58530i
$688$	−12.6613	+	21.9301i	−0.482709	+	0.836077i
$689$	22.8979	−	39.6604i	0.872342	−	1.51094i
$690$	0.518450	+	0.00483065i	0.0197370	+	0.000183900i
$691$	25.2639	−	14.5861i	0.961085	−	0.554883i	0.0645780	−	0.997913i	$-0.479430\pi$
$691$	25.2639	−	14.5861i	0.961085	−	0.554883i	0.896507	+	0.443030i	$0.146097\pi$
$692$	−51.7225			−1.96619
$693$	34.3876	+	15.8947i	1.30628	+	0.603789i
$694$	83.2701			3.16089
$695$	−18.3782	+	10.6107i	−0.697126	+	0.402486i
$696$	54.7040	−	92.7437i	2.07355	−	3.51544i
$697$	12.1622	−	21.0656i	0.460678	−	0.797917i
$698$	−20.9780	+	36.3350i	−0.794030	+	1.37530i
$699$	7.95973	−	4.49719i	0.301065	−	0.170100i
$700$	5.51366	−	12.5369i	0.208397	−	0.473849i
$701$			24.0871i			0.909757i	0.890553	+	0.454879i	$0.150317\pi$
$701$			24.0871i			0.909757i	−0.890553	+	0.454879i	$0.849683\pi$
$702$	61.2834	+	1.71342i	2.31299	+	0.0646689i
$703$		−	0.221630i		−	0.00835893i
$704$	77.7899	−	44.9120i	2.93182	−	1.69269i
$705$	6.25662	+	11.0738i	0.235638	+	0.417063i
$706$	2.94499	+	1.70029i	0.110836	+	0.0639914i
$707$	−42.3066	+	4.64101i	−1.59110	+	0.174543i
$708$	−23.6192	+	40.0434i	−0.887666	+	1.50492i
$709$	9.39512	+	16.2728i	0.352841	+	0.611139i	0.986746	−	0.162272i	$-0.0518823\pi$
$709$	9.39512	+	16.2728i	0.352841	+	0.611139i	−0.633905	+	0.773411i	$0.718549\pi$
$710$	0.920448			0.0345438
$711$	39.3171	+	0.732737i	1.47451	+	0.0274798i
$712$			33.6009i			1.25925i
$713$	0.219160	+	0.379596i	0.00820760	+	0.0142160i
$714$	−28.7463	+	20.6765i	−1.07580	+	0.773797i
$715$	10.5105	−	18.2047i	0.393070	−	0.680817i
$716$	−36.5030	−	21.0750i	−1.36418	−	0.787610i
$717$	0.106663	−	11.4476i	0.00398340	−	0.427518i
$718$	−4.80547	−	8.32332i	−0.179338	−	0.310623i
$719$	−14.7915			−0.551630			−0.275815	−	0.961211i	$-0.588948\pi$
$719$	−14.7915			−0.551630			−0.275815	+	0.961211i	$0.588948\pi$
$720$	19.2639	−	31.9749i	0.717923	−	1.19163i
$721$	−3.60638	+	2.64531i	−0.134309	+	0.0985163i
$722$	41.1698	−	23.7694i	1.53218	−	0.884605i
$723$	12.0851	+	7.12828i	0.449449	+	0.265103i
$724$	27.8342	+	16.0701i	1.03445	+	0.597240i
$725$	−6.32673	−	3.65274i	−0.234969	−	0.135659i
$726$	47.5893	−	26.8876i	1.76620	−	0.997894i
$727$	−10.5875	+	6.11269i	−0.392668	+	0.226707i	−0.683316	−	0.730123i	$-0.739463\pi$
$727$	−10.5875	+	6.11269i	−0.392668	+	0.226707i	0.290647	+	0.956830i	$0.406129\pi$
$728$	−58.6476	−	79.9552i	−2.17363	−	2.96334i
$729$	26.9578	+	1.50860i	0.998438	+	0.0558742i
$730$	−21.0886			−0.780523
$731$	−2.93500	−	5.08357i	−0.108555	−	0.188023i
$732$	−33.4716	+	18.9112i	−1.23714	+	0.698979i
$733$	−14.7962	−	8.54257i	−0.546509	−	0.315527i	0.201204	−	0.979549i	$-0.435515\pi$
$733$	−14.7962	−	8.54257i	−0.546509	−	0.315527i	−0.747713	+	0.664022i	$0.768848\pi$
$734$	−1.87656	+	3.25029i	−0.0692650	+	0.119971i
$735$	−8.11069	−	9.01203i	−0.299167	−	0.332414i
$736$	−0.911516	−	1.57879i	−0.0335989	−	0.0581950i
$737$		−	30.6027i		−	1.12727i
$738$	58.0522	+	34.9747i	2.13693	+	1.28744i
$739$	−32.1643			−1.18318			−0.591591	−	0.806238i	$-0.701500\pi$
$739$	−32.1643			−1.18318			−0.591591	+	0.806238i	$0.701500\pi$
$740$	−0.512182	−	0.887125i	−0.0188282	−	0.0326114i
$741$	−8.54333	−	0.0796024i	−0.313847	−	0.00292427i
$742$	−73.2588	+	8.03645i	−2.68942	+	0.295027i
$743$	2.83545	+	1.63705i	0.104022	+	0.0600574i	0.551109	−	0.834433i	$-0.314205\pi$
$743$	2.83545	+	1.63705i	0.104022	+	0.0600574i	−0.447086	+	0.894491i	$0.647538\pi$
$744$	57.8136	+	0.538678i	2.11955	+	0.0197489i
$745$	3.47516	−	2.00638i	0.127320	−	0.0735082i
$746$			83.9872i			3.07499i
$747$	−22.6169	−	0.421501i	−0.827508	−	0.0154219i
$748$			71.2647i			2.60569i
$749$	−26.2230	−	11.5328i	−0.958169	−	0.421399i
$750$	−3.99656	−	2.35733i	−0.145934	−	0.0860777i
$751$	16.9210	−	29.3080i	0.617455	−	1.06946i	−0.372493	−	0.928035i	$-0.621497\pi$
$751$	16.9210	−	29.3080i	0.617455	−	1.06946i	0.989948	−	0.141429i	$-0.0451697\pi$
$752$	45.6872	−	79.1326i	1.66604	−	2.88567i
$753$	−6.01864	−	10.6526i	−0.219331	−	0.388202i
$754$	−74.6466	+	43.0973i	−2.71847	+	1.56951i
$755$	−10.6546			−0.387759
$756$	−40.4707	−	58.5371i	−1.47191	−	2.12898i
$757$	44.0486			1.60097			0.800486	−	0.599351i	$-0.204575\pi$
$757$	44.0486			1.60097			0.800486	+	0.599351i	$0.204575\pi$
$758$	15.2476	−	8.80320i	0.553817	−	0.319747i
$759$	−0.454394	−	0.804246i	−0.0164935	−	0.0291923i
$760$	−4.76526	+	8.25367i	−0.172854	+	0.299392i
$761$	3.23646	−	5.60570i	0.117321	−	0.203207i	−0.801384	−	0.598150i	$-0.795903\pi$
$761$	3.23646	−	5.60570i	0.117321	−	0.203207i	0.918705	+	0.394944i	$0.129236\pi$
$762$	44.4035	+	26.1910i	1.60857	+	0.948800i
$763$	7.37354	−	16.7658i	0.266940	−	0.606962i
$764$		−	30.1820i		−	1.09195i
$765$	4.18625	+	7.57328i	0.151354	+	0.273813i
$766$		−	67.5466i		−	2.44056i
$767$	19.7774	−	11.4185i	0.714122	−	0.412299i
$768$	−17.3342	−	0.161511i	−0.625495	−	0.00582804i
$769$	25.9367	+	14.9746i	0.935302	+	0.539997i	0.888485	−	0.458906i	$-0.151759\pi$
$769$	25.9367	+	14.9746i	0.935302	+	0.539997i	0.0468178	+	0.998903i	$0.485092\pi$
$770$	−33.6268	+	3.68884i	−1.21183	+	0.132937i
$771$	−44.5065	−	0.414689i	−1.60286	−	0.0149347i
$772$	−8.35710	−	14.4749i	−0.300779	−	0.520964i
$773$	34.6458			1.24612			0.623061	−	0.782173i	$-0.285889\pi$
$773$	34.6458			1.24612			0.623061	+	0.782173i	$0.285889\pi$
$774$	14.3140	−	7.91227i	0.514504	−	0.284401i
$775$		−	3.92268i		−	0.140907i
$776$	−73.1456	−	126.692i	−2.62577	−	4.54798i
$777$	−0.902308	+	0.0904829i	−0.0323701	+	0.00324605i
$778$	17.8398	−	30.8995i	0.639588	−	1.10780i
$779$	−8.17948	−	4.72242i	−0.293060	−	0.169198i
$780$	−34.3806	+	19.4248i	−1.23102	+	0.695520i
$781$	−0.819957	−	1.42021i	−0.0293404	−	0.0508190i
$782$	0.863425			0.0308760
$783$	−33.3923	+	18.0540i	−1.19334	+	0.645197i
$784$	−26.1623	+	83.0803i	−0.934369	+	2.96715i
$785$	−4.21199	+	2.43179i	−0.150332	+	0.0867943i
$786$	58.7244	−	33.1789i	2.09463	−	1.18345i
$787$	−35.7131	−	20.6190i	−1.27303	−	0.734987i	−0.297477	−	0.954729i	$-0.596145\pi$
$787$	−35.7131	−	20.6190i	−1.27303	−	0.734987i	−0.975558	+	0.219742i	$0.929478\pi$
$788$	84.4669	+	48.7670i	3.00901	+	1.73725i
$789$	43.1129	+	25.4297i	1.53486	+	0.905322i
$790$	−30.4104	+	17.5575i	−1.08196	+	0.624667i
$791$	22.8330	−	16.7481i	0.811847	−	0.595495i
$792$	−121.823	−	2.27037i	−4.32880	−	0.0806740i
$793$	18.8848			0.670618
$794$	11.1027	+	19.2304i	0.394019	+	0.682461i
$795$	−0.167800	+	18.0092i	−0.00595126	+	0.638719i
$796$	88.1167	+	50.8742i	3.12321	+	1.80319i
$797$	−7.94712	+	13.7648i	−0.281501	+	0.487575i	−0.971755	−	0.235993i	$-0.924166\pi$
$797$	−7.94712	+	13.7648i	−0.281501	+	0.487575i	0.690253	+	0.723568i	$0.257499\pi$
$798$	8.02837	+	11.1618i	0.284201	+	0.395123i
$799$	10.5907	+	18.3436i	0.374671	+	0.648949i
$800$			16.3150i			0.576821i
$801$	6.11306	−	10.1467i	0.215994	−	0.358515i
$802$	−42.0961			−1.48646
$803$	18.7862	+	32.5387i	0.662951	+	1.14826i
$804$	−29.2067	+	49.5163i	−1.03004	+	1.74631i
$805$	0.0322377	+	0.293873i	0.00113623	+	0.0103577i
$806$	−40.0815	−	23.1411i	−1.41181	−	0.815110i
$807$	−11.5756	−	20.4881i	−0.407482	−	0.721215i
$808$	118.548	−	68.4436i	4.17049	−	2.40784i
$809$			5.04800i			0.177478i	0.996055	+	0.0887391i	$0.0282837\pi$
$809$			5.04800i			0.177478i	−0.996055	+	0.0887391i	$0.971716\pi$
$810$	−21.3146	+	11.2687i	−0.748920	+	0.395941i
$811$		−	33.3788i		−	1.17209i	−0.810279	−	0.586045i	$-0.800684\pi$
$811$		−	33.3788i		−	1.17209i	0.810279	−	0.586045i	$-0.199316\pi$
$812$	91.5877	+	40.2800i	3.21410	+	1.41355i
$813$	−24.1915	+	13.6680i	−0.848432	+	0.479359i
$814$	−1.26509	+	2.19120i	−0.0443415	+	0.0768017i
$815$	−2.19027	+	3.79366i	−0.0767218	+	0.132886i
$816$	31.5832	−	53.5452i	1.10563	−	1.87446i
$817$	−1.97388	+	1.13962i	−0.0690572	+	0.0398702i
$818$	48.7665			1.70508
$819$	3.16383	+	34.8144i	0.110553	+	1.21651i
$820$	−43.6536			−1.52445
$821$	−4.73913	+	2.73614i	−0.165397	+	0.0954918i	−0.580413	−	0.814322i	$-0.697109\pi$
$821$	−4.73913	+	2.73614i	−0.165397	+	0.0954918i	0.415017	+	0.909814i	$0.363776\pi$
$822$	−4.65061	−	0.0433320i	−0.162209	−	0.00151138i
$823$	−5.19296	+	8.99447i	−0.181015	+	0.313528i	−0.942227	−	0.334976i	$-0.891272\pi$
$823$	−5.19296	+	8.99447i	−0.181015	+	0.313528i	0.761211	+	0.648504i	$0.224605\pi$
$824$	7.19252	−	12.4578i	0.250563	−	0.433989i
$825$	−0.0770227	+	8.26647i	−0.00268159	+	0.287801i
$826$	−33.6414	−	14.7954i	−1.17053	−	0.514796i
$827$			11.3895i			0.396053i	0.980197	+	0.198027i	$0.0634533\pi$
$827$			11.3895i			0.396053i	−0.980197	+	0.198027i	$0.936547\pi$
$828$	−0.0323338	+	1.73496i	−0.00112368	+	0.0602942i
$829$		−	12.0807i		−	0.419581i	−0.977746	−	0.209790i	$-0.932722\pi$
$829$		−	12.0807i		−	0.419581i	0.977746	−	0.209790i	$-0.0672782\pi$
$830$	17.4934	−	10.0998i	0.607204	−	0.350569i
$831$	−9.75245	+	16.5340i	−0.338309	+	0.573559i
$832$	71.7826	+	41.4437i	2.48862	+	1.43680i
$833$	−13.6462	−	14.8815i	−0.472812	−	0.515612i
$834$	−48.4368	−	85.7298i	−1.67723	−	2.96858i
$835$	2.78491	+	4.82361i	0.0963759	+	0.166928i
$836$	27.6710			0.957023
$837$	−17.3603	−	10.6808i	−0.600061	−	0.369182i
$838$		−	51.5349i		−	1.78024i
$839$	16.4502	+	28.4925i	0.567923	+	0.983671i	0.996771	+	0.0802946i	$0.0255861\pi$
$839$	16.4502	+	28.4925i	0.567923	+	0.983671i	−0.428848	+	0.903376i	$0.641081\pi$
$840$	35.5481	+	16.0308i	1.22653	+	0.553116i
$841$	12.1850	−	21.1051i	0.420173	−	0.727761i
$842$	44.5892	+	25.7436i	1.53665	+	0.887183i
$843$	−36.6047	−	21.5909i	−1.26073	−	0.743631i
$844$	−25.3510	−	43.9091i	−0.872616	−	1.51141i
$845$	6.39764			0.220086
$846$	−51.6505	+	28.5506i	−1.77578	+	0.981591i
$847$	18.4341	+	25.1314i	0.633402	+	0.863526i
$848$	112.051	−	64.6924i	3.84783	−	2.22155i
$849$	−0.228025	+	24.4728i	−0.00782579	+	0.839904i
$850$	−6.69186	−	3.86355i	−0.229529	−	0.132519i
$851$	0.0191495	+	0.0110559i	0.000656435	+	0.000378993i
$852$	−0.0287025	+	3.08050i	−0.000983332	+	0.105536i
$853$	−24.3894	+	14.0812i	−0.835077	+	0.482132i	−0.855588	−	0.517658i	$-0.826804\pi$
$853$	−24.3894	+	14.0812i	−0.835077	+	0.482132i	0.0205111	+	0.999790i	$0.493471\pi$
$854$	−17.9748	−	24.5053i	−0.615085	−	0.838554i
$855$	2.94060	−	1.62546i	0.100566	−	0.0555896i
$856$	92.1375			3.14919
$857$	−27.6980	−	47.9743i	−0.946144	−	1.63877i	−0.753444	−	0.657512i	$-0.771609\pi$
$857$	−27.6980	−	47.9743i	−0.946144	−	1.63877i	−0.192700	−	0.981258i	$-0.561724\pi$
$858$	84.0115	+	49.5534i	2.86811	+	1.69173i
$859$	−34.0795	−	19.6758i	−1.16278	−	0.671330i	−0.210809	−	0.977527i	$-0.567610\pi$
$859$	−34.0795	−	19.6758i	−1.16278	−	0.671330i	−0.951968	+	0.306197i	$0.900943\pi$
$860$	−5.26726	+	9.12317i	−0.179612	+	0.311097i
$861$	−15.8867	+	35.2285i	−0.541418	+	1.20059i
$862$	20.3929	+	35.3215i	0.694584	+	1.20305i
$863$			38.5883i			1.31356i	0.754081	+	0.656781i	$0.228082\pi$
$863$			38.5883i			1.31356i	−0.754081	+	0.656781i	$0.771918\pi$
$864$	72.2040	+	44.4228i	2.45643	+	1.51129i
$865$	−9.99178			−0.339731
$866$	−25.2439	−	43.7237i	−0.857822	−	1.48579i
$867$	−7.39553	−	13.0896i	−0.251165	−	0.444546i
$868$	5.85835	+	53.4036i	0.198845	+	1.81264i
$869$	54.1807	+	31.2812i	1.83795	+	1.06114i
$870$	17.2215	−	29.1968i	0.583862	−	0.989864i
$871$	24.4561	−	14.1197i	0.828663	−	0.478429i
$872$			58.9084i			1.99489i
$873$	−0.961004	+	51.5654i	−0.0325251	+	1.74522i
$874$		−	0.335255i		−	0.0113402i
$875$	1.06513	−	2.42188i	0.0360081	−	0.0818744i
$876$	0.657609	−	70.5779i	0.0222186	−	2.38461i
$877$	27.8234	−	48.1915i	0.939529	−	1.62731i	0.173177	−	0.984891i	$-0.444597\pi$
$877$	27.8234	−	48.1915i	0.939529	−	1.62731i	0.766352	−	0.642421i	$-0.222070\pi$
$878$	39.1631	−	67.8324i	1.32169	−	2.28923i
$879$	−2.80779	−	0.0261616i	−0.0947044	−	0.000882408i
$880$	51.4328	−	29.6947i	1.73380	−	1.00101i
$881$	−53.6708			−1.80822			−0.904108	−	0.427305i	$-0.859463\pi$
$881$	−53.6708			−1.80822			−0.904108	+	0.427305i	$0.859463\pi$
$882$	42.1646	−	37.2423i	1.41975	−	1.25401i
$883$	−8.28126			−0.278687			−0.139343	−	0.990244i	$-0.544499\pi$
$883$	−8.28126			−0.278687			−0.139343	+	0.990244i	$0.544499\pi$
$884$	−56.9510	+	32.8807i	−1.91547	+	1.10590i
$885$	−4.56278	+	7.73561i	−0.153376	+	0.260030i
$886$	6.22348	−	10.7794i	0.209082	−	0.362141i
$887$	26.6830	−	46.2163i	0.895928	−	1.55179i	0.0632764	−	0.997996i	$-0.479845\pi$
$887$	26.6830	−	46.2163i	0.895928	−	1.55179i	0.832652	−	0.553797i	$-0.186822\pi$
$888$	2.53937	−	1.43473i	0.0852156	−	0.0481463i
$889$	−11.8341	+	26.9081i	−0.396903	+	0.902470i
$890$			10.5780i			0.354574i
$891$	36.3746	+	22.8490i	1.21860	+	0.765472i
$892$			92.3956i			3.09363i
$893$	7.12255	−	4.11220i	0.238347	−	0.137610i
$894$	9.15896	+	16.2107i	0.306322	+	0.542168i
$895$	−7.05167	−	4.07128i	−0.235711	−	0.136088i
$896$	−5.13148	−	46.7777i	−0.171431	−	1.56273i
$897$	0.433059	−	0.734197i	0.0144594	−	0.0245141i
$898$	−26.7804	−	46.3851i	−0.893675	−	1.54789i
$899$	28.6571			0.955766
$900$	8.01401	−	13.3019i	0.267134	−	0.443398i
$901$			29.9924i			0.999193i
$902$	53.9124	+	93.3790i	1.79509	+	3.10918i
$903$	5.44551	+	7.57085i	0.181215	+	0.251942i
$904$	−45.5378	+	78.8737i	−1.51456	+	2.62330i
$905$	5.37703	+	3.10443i	0.178739	+	0.103195i
$906$	0.460609	−	49.4349i	0.0153027	−	1.64236i
$907$	6.11754	+	10.5959i	0.203130	+	0.351831i	0.949535	−	0.313660i	$-0.101555\pi$
$907$	6.11754	+	10.5959i	0.203130	+	0.351831i	−0.746406	+	0.665491i	$0.768222\pi$
$908$	51.4084			1.70605
$909$	−48.2506	−	0.899227i	−1.60037	−	0.0298255i
$910$	−18.4630	−	25.1708i	−0.612041	−	0.834404i
$911$	−7.39685	+	4.27058i	−0.245069	+	0.141491i	−0.617504	−	0.786568i	$-0.711856\pi$
$911$	−7.39685	+	4.27058i	−0.245069	+	0.141491i	0.372435	+	0.928058i	$0.378523\pi$
$912$	−20.7908	−	12.2633i	−0.688453	−	0.406078i
$913$	−31.1670	−	17.9943i	−1.03148	−	0.595524i
$914$	−14.0701	−	8.12340i	−0.465399	−	0.268698i
$915$	−6.46606	+	3.65328i	−0.213761	+	0.120774i
$916$	−107.551	+	62.0948i	−3.55359	+	2.05167i
$917$	22.7473	+	31.0117i	0.751182	+	1.02410i
$918$	−35.3194	+	19.0959i	−1.16571	+	0.630260i
$919$	−36.6803			−1.20997			−0.604985	−	0.796237i	$-0.706821\pi$
$919$	−36.6803			−1.20997			−0.604985	+	0.796237i	$0.706821\pi$
$920$	−0.475427	−	0.823464i	−0.0156744	−	0.0271488i
$921$	−22.4307	+	12.6732i	−0.739116	+	0.417596i
$922$	−8.20505	−	4.73719i	−0.270219	−	0.156011i
$923$	0.756636	−	1.31053i	0.0249050	−	0.0431367i
$924$	−11.2970	−	112.655i	−0.371644	−	3.70609i
$925$	−0.0989436	−	0.171375i	−0.00325325	−	0.00563479i
$926$			97.4527i			3.20250i
$927$	−4.43844	+	2.45342i	−0.145777	+	0.0805808i
$928$	−119.189			−3.91256
$929$	23.9156	+	41.4230i	0.784644	+	1.35904i	0.929211	+	0.369549i	$0.120488\pi$
$929$	23.9156	+	41.4230i	0.784644	+	1.35904i	−0.144567	+	0.989495i	$0.546179\pi$
$930$	18.2004	+	0.169582i	0.596815	+	0.00556082i
$931$	−5.77826	+	5.29861i	−0.189375	+	0.173655i
$932$	−23.6626	−	13.6616i	−0.775095	−	0.447501i
$933$	35.3399	+	0.329279i	1.15697	+	0.0107801i
$934$	−19.3682	+	11.1822i	−0.633747	+	0.365894i
$935$			13.7670i			0.450228i
$936$	−54.3934	−	98.4021i	−1.77790	−	3.21637i
$937$		−	29.0466i		−	0.948912i	−0.880279	−	0.474456i	$-0.842645\pi$
$937$		−	29.0466i		−	0.948912i	0.880279	−	0.474456i	$-0.157355\pi$
$938$	−41.5997	−	18.2954i	−1.35828	−	0.597366i
$939$	1.51500	+	0.893606i	0.0494400	+	0.0291617i
$940$	19.0064	−	32.9201i	0.619921	−	1.07373i
$941$	−22.2389	+	38.5189i	−0.724968	+	1.25568i	0.234020	+	0.972232i	$0.424812\pi$
$941$	−22.2389	+	38.5189i	−0.724968	+	1.25568i	−0.958987	+	0.283449i	$0.908521\pi$
$942$	−11.1009	−	19.6479i	−0.361687	−	0.640162i
$943$	0.816062	−	0.471153i	0.0265746	−	0.0153429i
$944$	64.5203			2.09996
$945$	−7.81816	−	11.3082i	−0.254325	−	0.367857i
$946$	26.0204			0.845995
$947$	−42.9852	+	24.8175i	−1.39683	+	0.806461i	−0.994059	−	0.108839i	$-0.965287\pi$
$947$	−42.9852	+	24.8175i	−1.39683	+	0.806461i	−0.402773	+	0.915300i	$0.631954\pi$
$948$	−57.8120	−	102.323i	−1.87765	−	3.32331i
$949$	−17.3355	+	30.0259i	−0.562733	+	0.974682i
$950$	−1.50016	+	2.59835i	−0.0486716	+	0.0843017i
$951$	46.1553	+	27.2243i	1.49669	+	0.882807i
$952$	59.4453	+	26.1438i	1.92663	+	0.847326i
$953$		−	37.0022i		−	1.19862i	−0.800518	−	0.599309i	$-0.795442\pi$
$953$		−	37.0022i		−	1.19862i	0.800518	−	0.599309i	$-0.204558\pi$
$954$	−83.5515	−	1.55712i	−2.70508	−	0.0504135i
$955$		−	5.83057i		−	0.188673i
$956$	−29.6306	+	17.1072i	−0.958321	+	0.553287i
$957$	−60.3905	−	0.562688i	−1.95215	−	0.0181891i
$958$	32.7772	+	18.9240i	1.05898	+	0.611405i
$959$	−0.289180	−	2.63611i	−0.00933810	−	0.0851244i
$960$	−32.5954	−	0.303707i	−1.05201	−	0.00980211i
$961$	−7.80629	−	13.5209i	−0.251816	−	0.436158i
$962$	−2.33479			−0.0752768
$963$	−27.8233	−	16.7627i	−0.896594	−	0.540170i
$964$		−	41.9330i		−	1.35057i
$965$	−1.61443	−	2.79628i	−0.0519703	−	0.0900153i
$966$	−1.36490	+	0.136872i	−0.0439150	+	0.00440377i
$967$	−23.0611	+	39.9431i	−0.741596	+	1.28448i	0.210172	+	0.977664i	$0.432598\pi$
$967$	−23.0611	+	39.9431i	−0.741596	+	1.28448i	−0.951768	+	0.306818i	$0.900736\pi$
$968$	−86.8134	−	50.1218i	−2.79029	−	1.61097i
$969$	4.87162	−	2.75243i	0.156499	−	0.0884208i
$970$	−23.0271	−	39.8841i	−0.739355	−	1.28060i
$971$	41.0969			1.31886			0.659431	−	0.751765i	$-0.270797\pi$
$971$	41.0969			1.31886			0.659431	+	0.751765i	$0.270797\pi$
$972$	−37.0487	−	71.6859i	−1.18834	−	2.29933i
$973$	45.2730	−	33.2081i	1.45139	−	1.06460i
$974$	−59.3170	+	34.2467i	−1.90064	+	1.09733i
$975$	−6.64166	+	3.75250i	−0.212703	+	0.120176i
$976$	46.2061	+	26.6771i	1.47902	+	0.853913i
$977$	47.6579	+	27.5153i	1.52471	+	0.880292i	0.999571	+	0.0292754i	$0.00931998\pi$
$977$	47.6579	+	27.5153i	1.52471	+	0.880292i	0.525139	+	0.851017i	$0.324013\pi$
$978$	−17.5071	−	10.3264i	−0.559815	−	0.330202i
$979$	16.3213	−	9.42309i	0.521630	−	0.301163i
$980$	−10.8838	+	34.5623i	−0.347671	+	1.10405i
$981$	10.7173	−	17.7889i	0.342177	−	0.567957i
$982$	−53.2068			−1.69790
$983$	−23.2722	−	40.3086i	−0.742266	−	1.28564i	−0.951461	−	0.307769i	$-0.900418\pi$
$983$	−23.2722	−	40.3086i	−0.742266	−	1.28564i	0.209195	−	0.977874i	$-0.432916\pi$
$984$	1.15806	−	124.289i	0.0369175	−	3.96218i
$985$	16.3174	+	9.42084i	0.519915	+	0.300173i
$986$	28.2251	−	48.8872i	0.898869	−	1.55689i
$987$	−19.6496	−	27.3187i	−0.625454	−	0.869564i
$988$	12.7671	+	22.1132i	0.406175	+	0.703516i
$989$		−	0.227398i		−	0.00723084i
$990$	−38.3513	−	0.714738i	−1.21889	−	0.0227159i
$991$	6.69760			0.212756			0.106378	−	0.994326i	$-0.466075\pi$
$991$	6.69760			0.212756			0.106378	+	0.994326i	$0.466075\pi$
$992$	−31.9992	−	55.4242i	−1.01597	−	1.75972i
$993$	15.4895	−	26.2604i	0.491543	−	0.833349i
$994$	−2.42075	+	0.265555i	−0.0767816	+	0.00842290i
$995$	17.0224	+	9.82791i	0.539648	+	0.311566i
$996$	33.2559	+	58.8607i	1.05375	+	1.86507i
$997$	50.0803	−	28.9139i	1.58606	−	0.915712i	0.592112	−	0.805856i	$-0.298294\pi$
$997$	50.0803	−	28.9139i	1.58606	−	0.915712i	0.993948	−	0.109856i	$-0.0350389\pi$
$998$		−	75.9171i		−	2.40311i
$999$	−1.02785	−	0.0287376i	−0.0325197	−	0.000909218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.i.41.12	✓	24
3.2	odd	2		945.2.bl.i.881.1		24
7.6	odd	2		315.2.bl.j.41.12	yes	24
9.2	odd	6		315.2.bl.j.146.12	yes	24
9.7	even	3		945.2.bl.j.251.1		24
21.20	even	2		945.2.bl.j.881.1		24
63.20	even	6	inner	315.2.bl.i.146.12	yes	24
63.34	odd	6		945.2.bl.i.251.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.12	✓	24	1.1	even	1	trivial
315.2.bl.i.146.12	yes	24	63.20	even	6	inner
315.2.bl.j.41.12	yes	24	7.6	odd	2
315.2.bl.j.146.12	yes	24	9.2	odd	6
945.2.bl.i.251.1		24	63.34	odd	6
945.2.bl.i.881.1		24	3.2	odd	2
945.2.bl.j.251.1		24	9.7	even	3
945.2.bl.j.881.1		24	21.20	even	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.32000 - 1.33945i) q^{2} +(0.852012 + 1.50800i) q^{3} +(2.58825 - 4.48298i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.99656 + 2.35733i) q^{6} +(-1.06513 + 2.42188i) q^{7} -8.50953i q^{8} +(-1.54815 + 2.56968i) q^{9} +O(q^{10})\)	\(q+(2.32000 - 1.33945i) q^{2} +(0.852012 + 1.50800i) q^{3} +(2.58825 - 4.48298i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.99656 + 2.35733i) q^{6} +(-1.06513 + 2.42188i) q^{7} -8.50953i q^{8} +(-1.54815 + 2.56968i) q^{9} -2.67890i q^{10} +(-4.13341 + 2.38643i) q^{11} +(8.96558 + 0.0835367i) q^{12} +(-3.81421 - 2.20214i) q^{13} +(0.772880 + 7.04544i) q^{14} +(1.73198 + 0.0161377i) q^{15} +(-6.22159 - 10.7761i) q^{16} +2.88443 q^{17} +(-0.149751 + 8.03530i) q^{18} -1.11998i q^{19} +(-2.58825 - 4.48298i) q^{20} +(-4.55971 + 0.457245i) q^{21} +(-6.39300 + 11.0730i) q^{22} +(0.0967696 + 0.0558700i) q^{23} +(12.8324 - 7.25022i) q^{24} +(-0.500000 - 0.866025i) q^{25} -11.7986 q^{26} +(-5.19412 - 0.145222i) q^{27} +(8.10040 + 11.0434i) q^{28} +(6.32673 - 3.65274i) q^{29} +(4.03979 - 2.28246i) q^{30} +(3.39714 + 1.96134i) q^{31} +(-14.1292 - 8.15748i) q^{32} +(-7.12046 - 4.19994i) q^{33} +(6.69186 - 3.86355i) q^{34} +(1.56484 + 2.13337i) q^{35} +(7.51281 + 13.5913i) q^{36} +0.197887 q^{37} +(-1.50016 - 2.59835i) q^{38} +(0.0710747 - 7.62810i) q^{39} +(-7.36947 - 4.25477i) q^{40} +(4.21652 - 7.30322i) q^{41} +(-9.96604 + 7.16830i) q^{42} +(-1.01753 - 1.76242i) q^{43} +24.7067i q^{44} +(1.45133 + 2.62558i) q^{45} +0.299340 q^{46} +(3.67167 + 6.35952i) q^{47} +(10.9495 - 18.5636i) q^{48} +(-4.73098 - 5.15924i) q^{49} +(-2.32000 - 1.33945i) q^{50} +(2.45757 + 4.34973i) q^{51} +(-19.7443 + 11.3994i) q^{52} +10.3981i q^{53} +(-12.2449 + 6.62035i) q^{54} +4.77285i q^{55} +(20.6090 + 9.06378i) q^{56} +(1.68894 - 0.954238i) q^{57} +(9.78532 - 16.9487i) q^{58} +(-2.59260 + 4.49051i) q^{59} +(4.55513 - 7.72265i) q^{60} +(-3.71337 + 2.14391i) q^{61} +10.5085 q^{62} +(-4.57445 - 6.48648i) q^{63} -18.8198 q^{64} +(-3.81421 + 2.20214i) q^{65} +(-22.1450 - 0.206336i) q^{66} +(-3.20591 + 5.55281i) q^{67} +(7.46562 - 12.9308i) q^{68} +(-0.00180322 + 0.193531i) q^{69} +(6.48797 + 2.85338i) q^{70} +0.343592i q^{71} +(21.8667 + 13.1740i) q^{72} -7.87210i q^{73} +(0.459097 - 0.265060i) q^{74} +(0.879963 - 1.49187i) q^{75} +(-5.02086 - 2.89879i) q^{76} +(-1.37700 - 12.5525i) q^{77} +(-10.0526 - 17.7923i) q^{78} +(-6.55399 - 11.3518i) q^{79} -12.4432 q^{80} +(-4.20646 - 7.95649i) q^{81} -22.5913i q^{82} +(3.77013 + 6.53006i) q^{83} +(-9.75185 + 21.6246i) q^{84} +(1.44221 - 2.49799i) q^{85} +(-4.72134 - 2.72587i) q^{86} +(10.8988 + 6.42855i) q^{87} +(20.3074 + 35.1734i) q^{88} -3.94862 q^{89} +(6.88390 + 4.14734i) q^{90} +(9.39595 - 6.89199i) q^{91} +(0.500928 - 0.289211i) q^{92} +(-0.0633029 + 6.79398i) q^{93} +(17.0365 + 9.83604i) q^{94} +(-0.969933 - 0.559991i) q^{95} +(0.263285 - 28.2571i) q^{96} +(14.8882 - 8.59573i) q^{97} +(-17.8864 - 5.63251i) q^{98} +(0.266803 - 14.3161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

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