LMFDB - Embedded newform 315.2.bl.i.146.2

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			146.2
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.i.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21303 - 1.27769i) q^{2} +(-0.920618 - 1.46713i) q^{3} +(2.26501 + 3.92311i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.162815 + 4.42307i) q^{6} +(1.57885 - 2.12303i) q^{7} -6.46517i q^{8} +(-1.30493 + 2.70133i) q^{9} +O(q^{10})$	\(q+(-2.21303 - 1.27769i) q^{2} +(-0.920618 - 1.46713i) q^{3} +(2.26501 + 3.92311i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.162815 + 4.42307i) q^{6} +(1.57885 - 2.12303i) q^{7} -6.46517i q^{8} +(-1.30493 + 2.70133i) q^{9} -2.55539i q^{10} +(-3.67950 - 2.12436i) q^{11} +(3.67049 - 6.93474i) q^{12} +(-3.06147 + 1.76754i) q^{13} +(-6.20662 + 2.68104i) q^{14} +(0.810261 - 1.53084i) q^{15} +(-3.73050 + 6.46141i) q^{16} -7.46750 q^{17} +(6.33931 - 4.31083i) q^{18} -0.474051i q^{19} +(-2.26501 + 3.92311i) q^{20} +(-4.56826 - 0.361877i) q^{21} +(5.42856 + 9.40254i) q^{22} +(3.79725 - 2.19235i) q^{23} +(-9.48523 + 5.95195i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.03349 q^{26} +(5.16453 - 0.572396i) q^{27} +(11.9050 + 1.38532i) q^{28} +(3.03806 + 1.75402i) q^{29} +(-3.74908 + 2.35254i) q^{30} +(-6.18566 + 3.57129i) q^{31} +(5.31342 - 3.06771i) q^{32} +(0.270705 + 7.35401i) q^{33} +(16.5258 + 9.54118i) q^{34} +(2.62802 + 0.305810i) q^{35} +(-13.5533 + 0.999159i) q^{36} -6.01728 q^{37} +(-0.605693 + 1.04909i) q^{38} +(5.41164 + 2.86433i) q^{39} +(5.59900 - 3.23258i) q^{40} +(-0.648068 - 1.12249i) q^{41} +(9.64735 + 6.63769i) q^{42} +(0.406148 - 0.703468i) q^{43} -19.2467i q^{44} +(-2.99188 + 0.220564i) q^{45} -11.2046 q^{46} +(-6.34775 + 10.9946i) q^{47} +(12.9141 - 0.475374i) q^{48} +(-2.01447 - 6.70387i) q^{49} +(2.21303 - 1.27769i) q^{50} +(6.87471 + 10.9558i) q^{51} +(-13.8685 - 8.00697i) q^{52} +2.09014i q^{53} +(-12.1606 - 5.33196i) q^{54} -4.24872i q^{55} +(-13.7257 - 10.2075i) q^{56} +(-0.695494 + 0.436420i) q^{57} +(-4.48222 - 7.76342i) q^{58} +(-2.03206 - 3.51963i) q^{59} +(7.84090 - 0.288628i) q^{60} +(-2.27474 - 1.31332i) q^{61} +18.2521 q^{62} +(3.67471 + 7.03538i) q^{63} -0.756369 q^{64} +(-3.06147 - 1.76754i) q^{65} +(8.79710 - 16.6205i) q^{66} +(-3.57579 - 6.19345i) q^{67} +(-16.9139 - 29.2958i) q^{68} +(-6.71227 - 3.55274i) q^{69} +(-5.42516 - 4.03457i) q^{70} +11.1585i q^{71} +(17.4645 + 8.43657i) q^{72} -1.75510i q^{73} +(13.3164 + 7.68825i) q^{74} +(1.73088 - 0.0637145i) q^{75} +(1.85975 - 1.07373i) q^{76} +(-10.3194 + 4.45762i) q^{77} +(-8.31639 - 13.2533i) q^{78} +(0.917777 - 1.58964i) q^{79} -7.46100 q^{80} +(-5.59434 - 7.05006i) q^{81} +3.31213i q^{82} +(2.79791 - 4.84613i) q^{83} +(-8.92747 - 18.7414i) q^{84} +(-3.73375 - 6.46704i) q^{85} +(-1.79764 + 1.03787i) q^{86} +(-0.223514 - 6.07201i) q^{87} +(-13.7343 + 23.7886i) q^{88} +14.3932 q^{89} +(6.90294 + 3.33459i) q^{90} +(-1.08106 + 9.29024i) q^{91} +(17.2016 + 9.93135i) q^{92} +(10.9342 + 5.78735i) q^{93} +(28.0955 - 16.2210i) q^{94} +(0.410541 - 0.237026i) q^{95} +(-9.39235 - 4.97128i) q^{96} +(-7.56815 - 4.36947i) q^{97} +(-4.10740 + 17.4098i) q^{98} +(10.5401 - 7.16739i) 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.21303	−	1.27769i	−1.56485	−	0.903466i	−0.996754	−	0.0805039i	$-0.974347\pi$
$2$	−2.21303	−	1.27769i	−1.56485	−	0.903466i	−0.568096	−	0.822963i	$-0.692320\pi$
$3$	−0.920618	−	1.46713i	−0.531519	−	0.847046i
$3$	−0.920618	−	1.46713i	−0.531519	−	0.847046i
$4$	2.26501	+	3.92311i	1.13250	+	1.96155i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.162815	+	4.42307i	0.0664691	+	1.80571i
$7$	1.57885	−	2.12303i	0.596749	−	0.802428i
$7$	1.57885	−	2.12303i	0.596749	−	0.802428i
$8$		−	6.46517i		−	2.28578i
$9$	−1.30493	+	2.70133i	−0.434975	+	0.900442i
$10$		−	2.55539i		−	0.808085i
$11$	−3.67950	−	2.12436i	−1.10941	−	0.640518i	−0.170733	−	0.985317i	$-0.554614\pi$
$11$	−3.67950	−	2.12436i	−1.10941	−	0.640518i	−0.938676	+	0.344799i	$0.887947\pi$
$12$	3.67049	−	6.93474i	1.05958	−	2.00189i
$13$	−3.06147	+	1.76754i	−0.849098	+	0.490227i	−0.860346	−	0.509710i	$-0.829753\pi$
$13$	−3.06147	+	1.76754i	−0.849098	+	0.490227i	0.0112486	+	0.999937i	$0.496419\pi$
$14$	−6.20662	+	2.68104i	−1.65879	+	0.716537i
$15$	0.810261	−	1.53084i	0.209208	−	0.395262i
$16$	−3.73050	+	6.46141i	−0.932625	+	1.61535i
$17$	−7.46750			−1.81113			−0.905567	−	0.424202i	$-0.860555\pi$
$17$	−7.46750			−1.81113			−0.905567	+	0.424202i	$0.860555\pi$
$18$	6.33931	−	4.31083i	1.49419	−	1.01607i
$19$		−	0.474051i		−	0.108755i	−0.998520	−	0.0543774i	$-0.982683\pi$
$19$		−	0.474051i		−	0.108755i	0.998520	−	0.0543774i	$-0.0173174\pi$
$20$	−2.26501	+	3.92311i	−0.506471	+	0.877233i
$21$	−4.56826	−	0.361877i	−0.996877	−	0.0789681i
$22$	5.42856	+	9.40254i	1.15737	+	2.00463i
$23$	3.79725	−	2.19235i	0.791782	−	0.457136i	−0.0488075	−	0.998808i	$-0.515542\pi$
$23$	3.79725	−	2.19235i	0.791782	−	0.457136i	0.840590	+	0.541673i	$0.182209\pi$
$24$	−9.48523	+	5.95195i	−1.93616	+	1.21494i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	9.03349			1.77161
$27$	5.16453	−	0.572396i	0.993914	−	0.110158i
$28$	11.9050	+	1.38532i	2.24983	+	0.261802i
$29$	3.03806	+	1.75402i	0.564154	+	0.325714i	0.754811	−	0.655942i	$-0.227729\pi$
$29$	3.03806	+	1.75402i	0.564154	+	0.325714i	−0.190657	+	0.981657i	$0.561062\pi$
$30$	−3.74908	+	2.35254i	−0.684486	+	0.429512i
$31$	−6.18566	+	3.57129i	−1.11098	+	0.641423i	−0.939082	−	0.343693i	$-0.888322\pi$
$31$	−6.18566	+	3.57129i	−1.11098	+	0.641423i	−0.171894	+	0.985115i	$0.554989\pi$
$32$	5.31342	−	3.06771i	0.939289	−	0.542299i
$33$	0.270705	+	7.35401i	0.0471237	+	1.28017i
$34$	16.5258	+	9.54118i	2.83415	+	1.63630i
$35$	2.62802	+	0.305810i	0.444216	+	0.0516914i
$36$	−13.5533	+	0.999159i	−2.25888	+	0.166527i
$37$	−6.01728			−0.989235			−0.494617	−	0.869111i	$-0.664692\pi$
$37$	−6.01728			−0.989235			−0.494617	+	0.869111i	$0.664692\pi$
$38$	−0.605693	+	1.04909i	−0.0982564	+	0.170185i
$39$	5.41164	+	2.86433i	0.866556	+	0.458660i
$40$	5.59900	−	3.23258i	0.885280	−	0.511117i
$41$	−0.648068	−	1.12249i	−0.101211	−	0.175303i	0.810973	−	0.585084i	$-0.198938\pi$
$41$	−0.648068	−	1.12249i	−0.101211	−	0.175303i	−0.912184	+	0.409781i	$0.865605\pi$
$42$	9.64735	+	6.63769i	1.48862	+	1.02422i
$43$	0.406148	−	0.703468i	0.0619369	−	0.107278i	−0.833394	−	0.552679i	$-0.813606\pi$
$43$	0.406148	−	0.703468i	0.0619369	−	0.107278i	0.895331	+	0.445401i	$0.146939\pi$
$44$		−	19.2467i		−	2.90156i
$45$	−2.99188	+	0.220564i	−0.446003	+	0.0328798i
$46$	−11.2046			−1.65203
$47$	−6.34775	+	10.9946i	−0.925915	+	1.60373i	−0.135831	+	0.990732i	$0.543370\pi$
$47$	−6.34775	+	10.9946i	−0.925915	+	1.60373i	−0.790084	+	0.612999i	$0.789963\pi$
$48$	12.9141	−	0.475374i	1.86399	−	0.0686143i
$49$	−2.01447	−	6.70387i	−0.287782	−	0.957696i
$50$	2.21303	−	1.27769i	0.312970	−	0.180693i
$51$	6.87471	+	10.9558i	0.962652	+	1.53412i
$52$	−13.8685	−	8.00697i	−1.92321	−	1.11037i
$53$			2.09014i			0.287102i	0.989643	+	0.143551i	$0.0458522\pi$
$53$			2.09014i			0.287102i	−0.989643	+	0.143551i	$0.954148\pi$
$54$	−12.1606	−	5.33196i	−1.65485	−	0.725588i
$55$		−	4.24872i		−	0.572897i
$56$	−13.7257	−	10.2075i	−1.83418	−	1.36404i
$57$	−0.695494	+	0.436420i	−0.0921204	+	0.0578053i
$58$	−4.48222	−	7.76342i	−0.588544	−	1.01939i
$59$	−2.03206	−	3.51963i	−0.264552	−	0.458217i	0.702894	−	0.711294i	$-0.251891\pi$
$59$	−2.03206	−	3.51963i	−0.264552	−	0.458217i	−0.967446	+	0.253077i	$0.918557\pi$
$60$	7.84090	−	0.288628i	1.01226	−	0.0372617i
$61$	−2.27474	−	1.31332i	−0.291251	−	0.168154i	0.347255	−	0.937771i	$-0.387114\pi$
$61$	−2.27474	−	1.31332i	−0.291251	−	0.168154i	−0.638506	+	0.769617i	$0.720447\pi$
$62$	18.2521			2.31802
$63$	3.67471	+	7.03538i	0.462969	+	0.886374i
$64$	−0.756369			−0.0945462
$65$	−3.06147	−	1.76754i	−0.379728	−	0.219236i
$66$	8.79710	−	16.6205i	1.08285	−	2.04585i
$67$	−3.57579	−	6.19345i	−0.436853	−	0.756651i	0.560592	−	0.828092i	$-0.310574\pi$
$67$	−3.57579	−	6.19345i	−0.436853	−	0.756651i	−0.997445	+	0.0714412i	$0.977240\pi$
$68$	−16.9139	−	29.2958i	−2.05112	−	3.55264i
$69$	−6.71227	−	3.55274i	−0.808062	−	0.427700i
$70$	−5.42516	−	4.03457i	−0.648430	−	0.482224i
$71$			11.1585i			1.32427i	0.749383	+	0.662137i	$0.230350\pi$
$71$			11.1585i			1.32427i	−0.749383	+	0.662137i	$0.769650\pi$
$72$	17.4645	+	8.43657i	2.05822	+	0.994259i
$73$		−	1.75510i		−	0.205419i	−0.994711	−	0.102709i	$-0.967249\pi$
$73$		−	1.75510i		−	0.205419i	0.994711	−	0.102709i	$-0.0327511\pi$
$74$	13.3164	+	7.68825i	1.54800	+	0.893740i
$75$	1.73088	−	0.0637145i	0.199865	−	0.00735712i
$76$	1.85975	−	1.07373i	0.213328	−	0.123165i
$77$	−10.3194	+	4.45762i	−1.17601	+	0.507993i
$78$	−8.31639	−	13.2533i	−0.941646	−	1.50064i
$79$	0.917777	−	1.58964i	0.103258	−	0.178848i	−0.809767	−	0.586751i	$-0.800407\pi$
$79$	0.917777	−	1.58964i	0.103258	−	0.178848i	0.913025	+	0.407903i	$0.133740\pi$
$80$	−7.46100			−0.834165
$81$	−5.59434	−	7.05006i	−0.621593	−	0.783341i
$82$			3.31213i			0.365764i
$83$	2.79791	−	4.84613i	0.307111	−	0.531931i	−0.670618	−	0.741803i	$-0.733971\pi$
$83$	2.79791	−	4.84613i	0.307111	−	0.531931i	0.977729	+	0.209871i	$0.0673045\pi$
$84$	−8.92747	−	18.7414i	−0.974067	−	2.04486i
$85$	−3.73375	−	6.46704i	−0.404982	−	0.701449i
$86$	−1.79764	+	1.03787i	−0.193844	+	0.111916i
$87$	−0.223514	−	6.07201i	−0.0239632	−	0.650987i
$88$	−13.7343	+	23.7886i	−1.46409	+	2.53587i
$89$	14.3932			1.52568			0.762840	−	0.646587i	$-0.223804\pi$
$89$	14.3932			1.52568			0.762840	+	0.646587i	$0.223804\pi$
$90$	6.90294	+	3.33459i	0.727634	+	0.351497i
$91$	−1.08106	+	9.29024i	−0.113326	+	0.973882i
$92$	17.2016	+	9.93135i	1.79339	+	1.03542i
$93$	10.9342	+	5.78735i	1.13382	+	0.600121i
$94$	28.0955	−	16.2210i	2.89783	−	1.67307i
$95$	0.410541	−	0.237026i	0.0421206	−	0.0243183i
$96$	−9.39235	−	4.97128i	−0.958602	−	0.507379i
$97$	−7.56815	−	4.36947i	−0.768429	−	0.443653i	0.0638848	−	0.997957i	$-0.479651\pi$
$97$	−7.56815	−	4.36947i	−0.768429	−	0.443653i	−0.832314	+	0.554304i	$0.812984\pi$
$98$	−4.10740	+	17.4098i	−0.414911	+	1.75865i
$99$	10.5401	−	7.16739i	1.05932	−	0.720350i
$100$	−4.53001			−0.453001
$101$	4.67664	−	8.10018i	0.465343	−	0.805999i	−0.533874	−	0.845564i	$-0.679264\pi$
$101$	4.67664	−	8.10018i	0.465343	−	0.805999i	0.999217	+	0.0395658i	$0.0125975\pi$
$102$	−1.21582	−	33.0293i	−0.120385	−	3.27038i
$103$	0.668174	−	0.385771i	0.0658372	−	0.0380111i	−0.466720	−	0.884405i	$-0.654564\pi$
$103$	0.668174	−	0.385771i	0.0658372	−	0.0380111i	0.532557	+	0.846394i	$0.321231\pi$
$104$	11.4274	+	19.7929i	1.12055	+	1.94085i
$105$	−1.97074	−	4.13717i	−0.192324	−	0.403747i
$106$	2.67056	−	4.62554i	0.259387	−	0.449272i
$107$		−	13.4458i		−	1.29985i	−0.759997	−	0.649927i	$-0.774800\pi$
$107$		−	13.4458i		−	1.29985i	0.759997	−	0.649927i	$-0.225200\pi$
$108$	13.9433	+	18.9645i	1.34169	+	1.82486i
$109$	−4.75379			−0.455330			−0.227665	−	0.973740i	$-0.573109\pi$
$109$	−4.75379			−0.455330			−0.227665	+	0.973740i	$0.573109\pi$
$110$	−5.42856	+	9.40254i	−0.517593	+	0.896497i
$111$	5.53961	+	8.82812i	0.525797	+	0.837928i
$112$	7.82785	+	18.1215i	0.739662	+	1.71232i
$113$	−9.15660	+	5.28657i	−0.861381	+	0.497318i	−0.864474	−	0.502677i	$-0.832349\pi$
$113$	−9.15660	+	5.28657i	−0.861381	+	0.497318i	0.00309376	+	0.999995i	$0.499015\pi$
$114$	2.09676	−	0.0771829i	0.196380	−	0.00722884i
$115$	3.79725	+	2.19235i	0.354096	+	0.204437i
$116$			15.8915i			1.47549i
$117$	−0.779711	−	10.5765i	−0.0720843	−	0.977800i
$118$			10.3854i			0.956054i
$119$	−11.7901	+	15.8537i	−1.08079	+	1.45331i
$120$	−9.89715	−	5.23847i	−0.903482	−	0.478205i
$121$	3.52579	+	6.10685i	0.320527	+	0.555169i
$122$	3.35605	+	5.81285i	0.303843	+	0.526271i
$123$	−1.05021	+	1.98418i	−0.0946941	+	0.178907i
$124$	−28.0211	−	16.1780i	−2.51637	−	1.45283i
$125$	−1.00000			−0.0894427
$126$	0.856825	−	20.2647i	0.0763320	−	1.80532i
$127$	−11.2674			−0.999820			−0.499910	−	0.866077i	$-0.666634\pi$
$127$	−11.2674			−0.999820			−0.499910	+	0.866077i	$0.666634\pi$
$128$	−8.95297	−	5.16900i	−0.791339	−	0.456880i
$129$	−1.40598	+	0.0517550i	−0.123790	+	0.00455678i
$130$	4.51675	+	7.82324i	0.396145	+	0.686143i
$131$	−7.79640	−	13.5038i	−0.681174	−	1.17983i	−0.974623	−	0.223854i	$-0.928136\pi$
$131$	−7.79640	−	13.5038i	−0.681174	−	1.17983i	0.293448	−	0.955975i	$-0.405197\pi$
$132$	−28.2374	+	17.7189i	−2.45775	+	1.54223i
$133$	−1.00642	−	0.748455i	−0.0872680	−	0.0648993i
$134$			18.2751i			1.57873i
$135$	3.07797	+	4.18642i	0.264910	+	0.360309i
$136$			48.2787i			4.13986i
$137$	3.25657	+	1.88018i	0.278227	+	0.160635i	0.632621	−	0.774462i	$-0.281979\pi$
$137$	3.25657	+	1.88018i	0.278227	+	0.160635i	−0.354393	+	0.935096i	$0.615313\pi$
$138$	10.3151	+	16.4386i	0.878083	+	1.39934i
$139$	4.71277	−	2.72092i	0.399732	−	0.230786i	−0.286636	−	0.958040i	$-0.592537\pi$
$139$	4.71277	−	2.72092i	0.399732	−	0.230786i	0.686368	+	0.727254i	$0.259204\pi$
$140$	4.75275	+	11.0027i	0.401681	+	0.929894i
$141$	21.9744	−	0.808888i	1.85058	−	0.0681207i
$142$	14.2572	−	24.6942i	1.19644	−	2.07229i
$143$	15.0195			1.25600
$144$	−12.5864	−	18.5090i	−1.04886	−	1.54241i
$145$			3.50805i			0.291328i
$146$	−2.24248	+	3.88409i	−0.185589	+	0.321449i
$147$	−7.98087	+	9.12719i	−0.658251	+	0.752798i
$148$	−13.6292	−	23.6064i	−1.12031	−	1.94044i
$149$	−6.68258	+	3.85819i	−0.547458	+	0.316075i	−0.748096	−	0.663590i	$-0.769032\pi$
$149$	−6.68258	+	3.85819i	−0.547458	+	0.316075i	0.200638	+	0.979665i	$0.435698\pi$
$150$	−3.91190	−	2.07053i	−0.319405	−	0.169058i
$151$	−0.605580	+	1.04889i	−0.0492814	+	0.0853578i	−0.889614	−	0.456714i	$-0.849026\pi$
$151$	−0.605580	+	1.04889i	−0.0492814	+	0.0853578i	0.840332	+	0.542071i	$0.182360\pi$
$152$	−3.06482			−0.248590
$153$	9.74454	−	20.1722i	0.787799	−	1.63082i
$154$	28.5327	+	3.32022i	2.29923	+	0.267551i
$155$	−6.18566	−	3.57129i	−0.496844	−	0.286853i
$156$	1.02032	+	27.7182i	0.0816910	+	2.21923i
$157$	15.1908	−	8.77042i	1.21236	−	0.699956i	0.249086	−	0.968481i	$-0.419870\pi$
$157$	15.1908	−	8.77042i	1.21236	−	0.699956i	0.963273	+	0.268526i	$0.0865364\pi$
$158$	−4.06214	+	2.34528i	−0.323167	+	0.186580i
$159$	3.06650	−	1.92422i	0.243189	−	0.152600i
$160$	5.31342	+	3.06771i	0.420063	+	0.242523i
$161$	1.34088	−	11.5230i	0.105676	−	0.908143i
$162$	3.37261	+	22.7499i	0.264977	+	1.78740i
$163$	6.32828			0.495669			0.247835	−	0.968802i	$-0.420281\pi$
$163$	6.32828			0.495669			0.247835	+	0.968802i	$0.420281\pi$
$164$	2.93576	−	5.08488i	0.229244	−	0.397062i
$165$	−6.23341	+	3.91144i	−0.485270	+	0.304505i
$166$	−12.3837	+	7.14975i	−0.961164	+	0.554929i
$167$	0.976158	+	1.69076i	0.0755374	+	0.130835i	0.901320	−	0.433154i	$-0.142599\pi$
$167$	0.976158	+	1.69076i	0.0755374	+	0.130835i	−0.825782	+	0.563989i	$0.809266\pi$
$168$	−2.33960	+	29.5346i	−0.180504	+	2.27864i
$169$	−0.251619	+	0.435817i	−0.0193553	+	0.0335244i
$170$			19.0824i			1.46355i
$171$	1.28057	+	0.618602i	0.0979275	+	0.0473057i
$172$	3.67971			0.280575
$173$	−2.81618	+	4.87777i	−0.214110	+	0.370850i	−0.952997	−	0.302980i	$-0.902019\pi$
$173$	−2.81618	+	4.87777i	−0.214110	+	0.370850i	0.738887	+	0.673830i	$0.235352\pi$
$174$	−7.26353	+	13.7231i	−0.550647	+	1.04035i
$175$	1.04917	+	2.42884i	0.0793098	+	0.183603i
$176$	27.4527	−	15.8498i	2.06933	−	1.19473i
$177$	−3.29300	+	6.22152i	−0.247517	+	0.467638i
$178$	−31.8527	−	18.3902i	−2.38746	−	1.37840i
$179$		−	8.09586i		−	0.605113i	−0.953131	−	0.302557i	$-0.902160\pi$
$179$		−	8.09586i		−	0.605113i	0.953131	−	0.302557i	$-0.0978401\pi$
$180$	−7.64193	−	11.2379i	−0.569596	−	0.837623i
$181$		−	13.8016i		−	1.02587i	−0.858429	−	0.512933i	$-0.828559\pi$
$181$		−	13.8016i		−	1.02587i	0.858429	−	0.512933i	$-0.171441\pi$
$182$	14.2625	−	19.1783i	1.05721	−	1.42159i
$183$	0.167355	+	4.54640i	0.0123713	+	0.336080i
$184$	−14.1739	−	24.5499i	−1.04491	−	1.80984i
$185$	−3.00864	−	5.21112i	−0.221200	−	0.383129i
$186$	−16.8032	−	26.7781i	−1.23207	−	1.96347i
$187$	27.4766	+	15.8636i	2.00929	+	1.16006i
$188$	−57.5108			−4.19441
$189$	6.93880	−	11.8682i	0.504723	−	0.863281i
$190$	−1.21139			−0.0878832
$191$	−0.566372	−	0.326995i	−0.0409813	−	0.0236605i	0.479369	−	0.877613i	$-0.340865\pi$
$191$	−0.566372	−	0.326995i	−0.0409813	−	0.0236605i	−0.520351	+	0.853953i	$0.674199\pi$
$192$	0.696327	+	1.10969i	0.0502531	+	0.0800850i
$193$	7.14304	+	12.3721i	0.514167	+	0.890564i	0.999865	+	0.0164367i	$0.00523222\pi$
$193$	7.14304	+	12.3721i	0.514167	+	0.890564i	−0.485698	+	0.874127i	$0.661434\pi$
$194$	11.1657	+	19.3396i	0.801651	+	1.38850i
$195$	0.225236	+	6.11879i	0.0161295	+	0.438175i
$196$	21.7372	−	23.0873i	1.55266	−	1.64909i
$197$			3.36821i			0.239975i	0.992775	+	0.119988i	$0.0382855\pi$
$197$			3.36821i			0.239975i	−0.992775	+	0.119988i	$0.961715\pi$
$198$	−32.4832	+	2.39469i	−2.30848	+	0.170183i
$199$		−	5.86209i		−	0.415552i	−0.978176	−	0.207776i	$-0.933377\pi$
$199$		−	5.86209i		−	0.415552i	0.978176	−	0.207776i	$-0.0666226\pi$
$200$	5.59900	+	3.23258i	0.395909	+	0.228578i
$201$	−5.79465	+	10.9479i	−0.408723	+	0.772209i
$202$	−20.6991	+	11.9506i	−1.45639	+	0.840844i
$203$	8.52048	−	3.68054i	0.598020	−	0.258323i
$204$	−27.4094	+	51.7851i	−1.91904	+	3.62568i
$205$	0.648068	−	1.12249i	0.0452630	−	0.0783979i
$206$	−1.97159			−0.137367
$207$	0.967106	+	13.1185i	0.0672185	+	0.911797i
$208$		−	26.3752i		−	1.82879i
$209$	−1.00705	+	1.74427i	−0.0696594	+	0.120654i
$210$	−0.924738	+	11.6737i	−0.0638130	+	0.805561i
$211$	−10.7413	−	18.6045i	−0.739463	−	1.28079i	−0.952737	−	0.303796i	$-0.901746\pi$
$211$	−10.7413	−	18.6045i	−0.739463	−	1.28079i	0.213274	−	0.976992i	$-0.431587\pi$
$212$	−8.19983	+	4.73417i	−0.563166	+	0.325144i
$213$	16.3710	−	10.2727i	1.12172	−	0.703876i
$214$	−17.1796	+	29.7560i	−1.17437	+	2.03408i
$215$	0.812295			0.0553981
$216$	−3.70064	−	33.3896i	−0.251797	−	2.27187i
$217$	−2.18427	+	18.7708i	−0.148278	+	1.27425i
$218$	10.5203	+	6.07389i	0.712523	+	0.411376i
$219$	−2.57495	+	1.61577i	−0.173999	+	0.109184i
$220$	16.6682	−	9.62337i	1.12377	−	0.648808i
$221$	22.8615	−	13.1991i	1.53783	−	0.887867i
$222$	−0.979706	−	26.6148i	−0.0657536	−	1.78627i
$223$	6.87624	+	3.97000i	0.460467	+	0.265851i	0.712241	−	0.701935i	$-0.247680\pi$
$223$	6.87624	+	3.97000i	0.460467	+	0.265851i	−0.251773	+	0.967786i	$0.581014\pi$
$224$	1.87627	−	16.1240i	0.125364	−	1.07733i
$225$	−1.68695	−	2.48076i	−0.112464	−	0.165384i
$226$	27.0185			1.79724
$227$	1.52350	−	2.63878i	0.101118	−	0.175142i	−0.811027	−	0.585008i	$-0.801091\pi$
$227$	1.52350	−	2.63878i	0.101118	−	0.175142i	0.912146	+	0.409866i	$0.134425\pi$
$228$	−3.28742	−	1.74000i	−0.217715	−	0.115234i
$229$	−20.4678	+	11.8171i	−1.35255	+	0.780896i	−0.988606	−	0.150524i	$-0.951904\pi$
$229$	−20.4678	+	11.8171i	−1.35255	+	0.780896i	−0.363945	+	0.931420i	$0.618570\pi$
$230$	−5.60230	−	9.70346i	−0.369404	−	0.639827i
$231$	16.0402	+	11.0362i	1.05536	+	0.726126i
$232$	11.3401	−	19.6416i	0.744512	−	1.28953i
$233$		−	8.34677i		−	0.546815i	−0.961898	−	0.273408i	$-0.911849\pi$
$233$		−	8.34677i		−	0.546815i	0.961898	−	0.273408i	$-0.0881508\pi$
$234$	−11.7880	+	24.4024i	−0.770609	+	1.59524i
$235$	−12.6955			−0.828163
$236$	9.20525	−	15.9440i	0.599211	−	1.03786i
$237$	−3.17712	+	0.116951i	−0.206376	+	0.00759681i
$238$	46.3479	−	20.0206i	3.00429	−	1.29775i
$239$	20.4410	−	11.8016i	1.32222	−	0.763381i	0.338134	−	0.941098i	$-0.390204\pi$
$239$	20.4410	−	11.8016i	1.32222	−	0.763381i	0.984082	+	0.177717i	$0.0568711\pi$
$240$	6.86873	+	10.9462i	0.443374	+	0.706576i
$241$	−17.4442	−	10.0714i	−1.12368	−	0.648758i	−0.181343	−	0.983420i	$-0.558044\pi$
$241$	−17.4442	−	10.0714i	−1.12368	−	0.648758i	−0.942338	+	0.334662i	$0.891378\pi$
$242$		−	18.0196i		−	1.15834i
$243$	−5.19310	+	14.6980i	−0.333138	+	0.942878i
$244$		−	11.8987i		−	0.761739i
$245$	4.79849	−	5.09652i	0.306564	−	0.325605i
$246$	4.85932	−	3.04921i	0.309819	−	0.194410i
$247$	0.837904	+	1.45129i	0.0533145	+	0.0923435i
$248$	23.0890	+	39.9913i	1.46615	+	2.53945i
$249$	−9.68569	+	0.356535i	−0.613806	+	0.0225945i
$250$	2.21303	+	1.27769i	0.139964	+	0.0808085i
$251$	26.8096			1.69221			0.846104	−	0.533018i	$-0.178942\pi$
$251$	26.8096			1.69221			0.846104	+	0.533018i	$0.178942\pi$
$252$	−19.2773	+	30.3514i	−1.21436	+	1.91196i
$253$	−18.6293			−1.17121
$254$	24.9351	+	14.3963i	1.56457	+	0.903304i
$255$	−6.05062	+	11.4316i	−0.378905	+	0.715872i
$256$	13.9652	+	24.1884i	0.872824	+	1.51178i
$257$	−9.42879	−	16.3311i	−0.588152	−	1.01871i	−0.994474	−	0.104979i	$-0.966522\pi$
$257$	−9.42879	−	16.3311i	−0.588152	−	1.01871i	0.406323	−	0.913730i	$-0.366811\pi$
$258$	3.17762	+	1.68188i	0.197830	+	0.104709i
$259$	−9.50037	+	12.7748i	−0.590325	+	0.793790i
$260$		−	16.0139i		−	0.993143i
$261$	−8.70264	+	5.91792i	−0.538680	+	0.366310i
$262$			39.8457i			2.46167i
$263$	23.7292	+	13.7000i	1.46320	+	0.844781i	0.999158	−	0.0410303i	$-0.0130640\pi$
$263$	23.7292	+	13.7000i	1.46320	+	0.844781i	0.464046	+	0.885811i	$0.346397\pi$
$264$	47.5449	−	1.75015i	2.92619	−	0.107715i
$265$	−1.81011	+	1.04507i	−0.111194	+	0.0641980i
$266$	1.27095	+	2.94226i	0.0779269	+	0.180401i
$267$	−13.2507	−	21.1167i	−0.810928	−	1.29232i
$268$	16.1984	−	28.0564i	0.989474	−	1.71382i
$269$	−21.8704			−1.33346			−0.666731	−	0.745299i	$-0.732307\pi$
$269$	−21.8704			−1.33346			−0.666731	+	0.745299i	$0.732307\pi$
$270$	−1.46270	−	13.1974i	−0.0890168	−	0.803167i
$271$		−	22.2347i		−	1.35066i	−0.737514	−	0.675331i	$-0.764001\pi$
$271$		−	22.2347i		−	1.35066i	0.737514	−	0.675331i	$-0.235999\pi$
$272$	27.8575	−	48.2506i	1.68911	−	2.92562i
$273$	14.6252	−	6.96671i	0.885158	−	0.421644i
$274$	−4.80459	−	8.32180i	−0.290256	−	0.502738i
$275$	3.67950	−	2.12436i	0.221882	−	0.128104i
$276$	−1.26554	−	34.3799i	−0.0761767	−	2.06943i
$277$	1.79176	−	3.10342i	0.107657	−	0.186467i	−0.807164	−	0.590327i	$-0.798999\pi$
$277$	1.79176	−	3.10342i	0.107657	−	0.186467i	0.914820	+	0.403861i	$0.132332\pi$
$278$	−13.9060			−0.834028
$279$	−1.57540	−	21.3698i	−0.0943166	−	1.27937i
$280$	1.97712	−	16.9906i	0.118155	−	1.01538i
$281$	−7.90601	−	4.56453i	−0.471633	−	0.272297i	0.245290	−	0.969450i	$-0.421117\pi$
$281$	−7.90601	−	4.56453i	−0.471633	−	0.272297i	−0.716923	+	0.697152i	$0.754450\pi$
$282$	−49.6635	−	26.2864i	−2.95742	−	1.56533i
$283$	−14.3529	+	8.28664i	−0.853190	+	0.492589i	−0.861726	−	0.507374i	$-0.830616\pi$
$283$	−14.3529	+	8.28664i	−0.853190	+	0.492589i	0.00853598	+	0.999964i	$0.497283\pi$
$284$	−43.7761	+	25.2741i	−2.59763	+	1.49974i
$285$	−0.725698	−	0.384105i	−0.0429866	−	0.0227524i
$286$	−33.2387	−	19.1904i	−1.96545	−	1.13475i
$287$	−3.40627	−	0.396372i	−0.201066	−	0.0233971i
$288$	1.35325	+	18.3564i	0.0797412	+	1.08166i
$289$	38.7636			2.28021
$290$	4.48222	−	7.76342i	0.263205	−	0.455884i
$291$	0.556798	+	15.1261i	0.0326401	+	0.886705i
$292$	6.88544	−	3.97531i	0.402940	−	0.232637i
$293$	−11.7759	−	20.3965i	−0.687956	−	1.19157i	−0.972498	−	0.232911i	$-0.925175\pi$
$293$	−11.7759	−	20.3965i	−0.687956	−	1.19157i	0.284543	−	0.958663i	$-0.408158\pi$
$294$	29.3237	−	10.0017i	1.71019	−	0.583308i
$295$	2.03206	−	3.51963i	0.118311	−	0.204921i
$296$			38.9027i			2.26118i
$297$	−20.2188	−	8.86518i	−1.17322	−	0.514410i
$298$	19.7183			1.14225
$299$	−7.75011	+	13.4236i	−0.448200	+	0.776306i
$300$	4.17041	+	6.64611i	0.240779	+	0.383713i
$301$	−0.852236	−	1.97293i	−0.0491220	−	0.113718i
$302$	2.68033	−	1.54749i	0.154236	−	0.0890481i
$303$	−16.1894	+	0.595940i	−0.930057	+	0.0342359i
$304$	3.06304	+	1.76845i	0.175677	+	0.101427i
$305$		−	2.62665i		−	0.150401i
$306$	−47.3388	+	32.1911i	−2.70618	+	1.84024i
$307$		−	12.6259i		−	0.720598i	−0.932837	−	0.360299i	$-0.882675\pi$
$307$		−	12.6259i		−	0.720598i	0.932837	−	0.360299i	$-0.117325\pi$
$308$	−40.8613	−	30.3877i	−2.32829	−	1.73150i
$309$	−1.18111	−	0.625150i	−0.0671909	−	0.0355635i
$310$	9.12604	+	15.8068i	0.518324	+	0.897764i
$311$	4.20710	+	7.28691i	0.238563	+	0.413203i	0.960302	−	0.278962i	$-0.0899904\pi$
$311$	4.20710	+	7.28691i	0.238563	+	0.413203i	−0.721739	+	0.692165i	$0.756657\pi$
$312$	18.5184	−	34.9872i	1.04840	−	1.98076i
$313$	16.2566	+	9.38575i	0.918877	+	0.530514i	0.883277	−	0.468852i	$-0.155332\pi$
$313$	16.2566	+	9.38575i	0.918877	+	0.530514i	0.0356003	+	0.999366i	$0.488666\pi$
$314$	−44.8237			−2.52955
$315$	−4.25546	+	6.70008i	−0.239768	+	0.377507i
$316$	8.31509			0.467760
$317$	−24.4557	−	14.1195i	−1.37357	−	0.793030i	−0.382192	−	0.924083i	$-0.624831\pi$
$317$	−24.4557	−	14.1195i	−1.37357	−	0.793030i	−0.991375	+	0.131053i	$0.958164\pi$
$318$	−9.24481	+	0.340306i	−0.518423	+	0.0190834i
$319$	−7.45235	−	12.9079i	−0.417252	−	0.722701i
$320$	−0.378185	−	0.655035i	−0.0211412	−	0.0366176i
$321$	−19.7267	+	12.3784i	−1.10104	+	0.690897i
$322$	−17.6904	+	23.7876i	−0.985845	+	1.32563i
$323$			3.53998i			0.196970i
$324$	14.9870	−	37.9156i	0.832608	−	2.10642i
$325$		−	3.53508i		−	0.196091i
$326$	−14.0047	−	8.08561i	−0.775648	−	0.447821i
$327$	4.37642	+	6.97441i	0.242017	+	0.385686i
$328$	−7.25707	+	4.18987i	−0.400704	+	0.231347i
$329$	13.3197	+	30.8353i	0.734341	+	1.70000i
$330$	18.7924	−	0.691757i	1.03449	−	0.0380799i
$331$	−12.7702	+	22.1187i	−0.701916	+	1.21575i	0.265877	+	0.964007i	$0.414338\pi$
$331$	−12.7702	+	22.1187i	−0.701916	+	1.21575i	−0.967793	+	0.251747i	$0.918995\pi$
$332$	25.3492			1.39122
$333$	7.85211	−	16.2546i	0.430293	−	0.890749i
$334$		−	4.98893i		−	0.272982i
$335$	3.57579	−	6.19345i	0.195366	−	0.338385i
$336$	19.3801	−	28.1675i	1.05727	−	1.53666i
$337$	9.08840	+	15.7416i	0.495077	+	0.857498i	0.999984	−	0.00567555i	$-0.00180659\pi$
$337$	9.08840	+	15.7416i	0.495077	+	0.857498i	−0.504907	+	0.863174i	$0.668473\pi$
$338$	1.11368	−	0.642985i	0.0605764	−	0.0349738i
$339$	16.1858	+	8.56700i	0.879092	+	0.465295i
$340$	16.9139	−	29.2958i	0.917287	−	1.58879i
$341$	30.3468			1.64337
$342$	−2.04355	−	3.00516i	−0.110503	−	0.162500i
$343$	−17.4130	−	6.30762i	−0.940216	−	0.340579i
$344$	−4.54804	−	2.62581i	−0.245214	−	0.141574i
$345$	−0.279369	−	7.58937i	−0.0150407	−	0.408598i
$346$	12.4646	−	7.19644i	0.670101	−	0.386883i
$347$	−1.12031	+	0.646813i	−0.0601415	+	0.0347227i	−0.529769	−	0.848142i	$-0.677721\pi$
$347$	−1.12031	+	0.646813i	−0.0601415	+	0.0347227i	0.469628	+	0.882865i	$0.344388\pi$
$348$	23.3149	−	14.6300i	1.24981	−	0.784251i
$349$	20.3812	+	11.7671i	1.09098	+	0.629879i	0.933838	−	0.357697i	$-0.116438\pi$
$349$	20.3812	+	11.7671i	1.09098	+	0.629879i	0.157145	+	0.987576i	$0.449771\pi$
$350$	0.781464	−	6.71561i	0.0417710	−	0.358964i
$351$	−14.7993	+	10.8809i	−0.789928	+	0.580778i
$352$	−26.0676			−1.38941
$353$	−16.0281	+	27.7615i	−0.853091	+	1.47760i	0.0253130	+	0.999680i	$0.491942\pi$
$353$	−16.0281	+	27.7615i	−0.853091	+	1.47760i	−0.878404	+	0.477918i	$0.841392\pi$
$354$	15.2367	−	9.56099i	0.809822	−	0.508161i
$355$	−9.66357	+	5.57926i	−0.512889	+	0.296117i
$356$	32.6008	+	56.4662i	1.72784	+	2.99270i
$357$	34.1135	+	2.70232i	1.80548	+	0.143022i
$358$	−10.3440	+	17.9164i	−0.546700	+	0.946911i
$359$		−	26.4174i		−	1.39426i	−0.716946	−	0.697128i	$-0.754461\pi$
$359$		−	26.4174i		−	1.39426i	0.716946	−	0.697128i	$-0.245539\pi$
$360$	1.42599	+	19.3430i	0.0751560	+	1.01947i
$361$	18.7753			0.988172
$362$	−17.6343	+	30.5434i	−0.926836	+	1.60533i
$363$	5.71363	−	10.7949i	0.299888	−	0.566584i
$364$	−38.8952	+	16.8013i	−2.03866	+	0.880630i
$365$	1.51996	−	0.877549i	0.0795583	−	0.0459330i
$366$	5.43855	−	10.2752i	0.284278	−	0.537092i
$367$	29.7815	+	17.1943i	1.55458	+	0.897537i	0.997759	+	0.0669043i	$0.0213122\pi$
$367$	29.7815	+	17.1943i	1.55458	+	0.897537i	0.556821	+	0.830633i	$0.312021\pi$
$368$			32.7142i			1.70534i
$369$	3.87788	−	0.285881i	0.201875	−	0.0148824i
$370$			15.3765i			0.799386i
$371$	4.43741	+	3.30001i	0.230379	+	0.171328i
$372$	2.06155	+	56.0043i	0.106886	+	2.90369i
$373$	16.3414	+	28.3041i	0.846124	+	1.46553i	0.884642	+	0.466271i	$0.154403\pi$
$373$	16.3414	+	28.3041i	0.846124	+	1.46553i	−0.0385184	+	0.999258i	$0.512264\pi$
$374$	−40.5378	−	70.2135i	−2.09616	−	3.63065i
$375$	0.920618	+	1.46713i	0.0475405	+	0.0757621i
$376$	71.0821	+	41.0393i	3.66578	+	2.11644i
$377$	−12.4012			−0.638695
$378$	−30.5197	+	17.3989i	−1.56976	+	0.894905i
$379$	−20.0049			−1.02758			−0.513792	−	0.857915i	$-0.671760\pi$
$379$	−20.0049			−1.02758			−0.513792	+	0.857915i	$0.671760\pi$
$380$	1.85975	+	1.07373i	0.0954034	+	0.0550812i
$381$	10.3730	+	16.5307i	0.531423	+	0.846894i
$382$	0.835600	+	1.44730i	0.0427530	+	0.0740504i
$383$	7.12122	+	12.3343i	0.363878	+	0.630254i	0.988595	−	0.150596i	$-0.0481193\pi$
$383$	7.12122	+	12.3343i	0.363878	+	0.630254i	−0.624718	+	0.780851i	$0.714786\pi$
$384$	0.658681	+	17.8938i	0.0336132	+	0.913141i
$385$	−9.02013	−	6.70808i	−0.459709	−	0.341875i
$386$		−	36.5065i		−	1.85813i
$387$	1.37031	+	2.01511i	0.0696565	+	0.102434i
$388$		−	39.5875i		−	2.00975i
$389$	−2.04713	−	1.18191i	−0.103793	−	0.0599251i	0.447205	−	0.894432i	$-0.352420\pi$
$389$	−2.04713	−	1.18191i	−0.103793	−	0.0599251i	−0.550998	+	0.834506i	$0.685753\pi$
$390$	7.31949	−	13.8289i	0.370637	−	0.700251i
$391$	−28.3560	+	16.3713i	−1.43402	+	0.827934i
$392$	−43.3417	+	13.0239i	−2.18908	+	0.657807i
$393$	−12.6342	+	23.8701i	−0.637313	+	1.20409i
$394$	4.30355	−	7.45396i	0.216809	−	0.375525i
$395$	1.83555			0.0923568
$396$	51.9917	+	25.1156i	2.61268	+	1.26211i
$397$		−	15.4381i		−	0.774818i	−0.921908	−	0.387409i	$-0.873370\pi$
$397$		−	15.4381i		−	0.774818i	0.921908	−	0.387409i	$-0.126630\pi$
$398$	−7.48996	+	12.9730i	−0.375438	+	0.650277i
$399$	−0.171549	+	2.16559i	−0.00858817	+	0.108415i
$400$	−3.73050	−	6.46141i	−0.186525	−	0.323071i
$401$	−15.0901	+	8.71225i	−0.753562	+	0.435069i	−0.826979	−	0.562232i	$-0.809943\pi$
$401$	−15.0901	+	8.71225i	−0.753562	+	0.435069i	0.0734175	+	0.997301i	$0.476609\pi$
$402$	26.8119	−	16.8244i	1.33725	−	0.839123i
$403$	12.6248	−	21.8668i	0.628885	−	1.08926i
$404$	42.3705			2.10801
$405$	3.30837	−	8.36987i	0.164394	−	0.415902i
$406$	−23.5587	−	2.74141i	−1.16920	−	0.136054i
$407$	22.1406	+	12.7829i	1.09747	+	0.633623i
$408$	70.8309	−	44.4462i	3.50665	−	2.20041i
$409$	−1.65618	+	0.956195i	−0.0818927	+	0.0472808i	−0.540387	−	0.841416i	$-0.681722\pi$
$409$	−1.65618	+	0.956195i	−0.0818927	+	0.0472808i	0.458494	+	0.888697i	$0.348389\pi$
$410$	−2.86839	+	1.65607i	−0.141660	+	0.0817873i
$411$	−0.239590	−	6.50873i	−0.0118181	−	0.321052i
$412$	3.02684	+	1.74755i	0.149122	+	0.0860954i
$413$	−10.6806	−	1.24285i	−0.525557	−	0.0611566i
$414$	14.6212	−	30.2673i	0.718591	−	1.48755i
$415$	5.59582			0.274688
$416$	−10.8446	+	18.7833i	−0.531699	+	0.920929i
$417$	−8.33060	−	4.40931i	−0.407951	−	0.215925i
$418$	4.45729	−	2.57342i	0.218013	−	0.125870i
$419$	−5.98450	−	10.3655i	−0.292362	−	0.506385i	0.682006	−	0.731347i	$-0.261108\pi$
$419$	−5.98450	−	10.3655i	−0.292362	−	0.506385i	−0.974368	+	0.224961i	$0.927774\pi$
$420$	11.7668	−	17.1021i	0.574163	−	0.834499i
$421$	−17.3379	+	30.0302i	−0.845000	+	1.46358i	0.0406220	+	0.999175i	$0.487066\pi$
$421$	−17.3379	+	30.0302i	−0.845000	+	1.46358i	−0.885622	+	0.464408i	$0.846267\pi$
$422$			54.8965i			2.67232i
$423$	−21.4167	−	31.4945i	−1.04132	−	1.53132i
$424$	13.5131			0.656253
$425$	3.73375	−	6.46704i	0.181113	−	0.313698i
$426$	−49.3549	+	1.81678i	−2.39125	+	0.0880233i
$427$	−6.37969	+	2.75580i	−0.308735	+	0.133362i
$428$	52.7493	−	30.4548i	2.54973	−	1.47209i
$429$	−13.8272	−	22.0356i	−0.667586	−	1.06389i
$430$	−1.79764	−	1.03787i	−0.0866897	−	0.0500503i
$431$			33.2887i			1.60346i	0.597687	+	0.801729i	$0.296087\pi$
$431$			33.2887i			1.60346i	−0.597687	+	0.801729i	$0.703913\pi$
$432$	−15.5678	+	35.5055i	−0.749005	+	1.70826i
$433$		−	1.40309i		−	0.0674283i	−0.999432	−	0.0337142i	$-0.989266\pi$
$433$		−	1.40309i		−	0.0674283i	0.999432	−	0.0337142i	$-0.0107336\pi$
$434$	28.8173	−	38.7496i	1.38327	−	1.86004i
$435$	5.14676	−	3.22957i	0.246768	−	0.154846i
$436$	−10.7674	−	18.6496i	−0.515663	−	0.893154i
$437$	−1.03928	−	1.80009i	−0.0497157	−	0.0861101i
$438$	7.76292	−	0.285757i	0.370926	−	0.0136540i
$439$	−7.50463	−	4.33280i	−0.358177	−	0.206793i	0.310104	−	0.950703i	$-0.399636\pi$
$439$	−7.50463	−	4.33280i	−0.358177	−	0.206793i	−0.668281	+	0.743909i	$0.732969\pi$
$440$	−27.4687			−1.30952
$441$	20.7381	+	3.30630i	0.987528	+	0.157443i
$442$	−67.4576			−3.20863
$443$	1.22623	+	0.707967i	0.0582601	+	0.0336365i	0.528847	−	0.848717i	$-0.322624\pi$
$443$	1.22623	+	0.707967i	0.0582601	+	0.0336365i	−0.470587	+	0.882354i	$0.655958\pi$
$444$	−22.0864	+	41.7282i	−1.04817	+	1.98033i
$445$	7.19662	+	12.4649i	0.341152	+	0.590893i
$446$	−10.1449	−	17.5715i	−0.480375	−	0.832033i
$447$	11.8126	+	6.25228i	0.558714	+	0.295723i
$448$	−1.19419	+	1.60579i	−0.0564203	+	0.0758665i
$449$		−	7.67349i		−	0.362134i	−0.983471	−	0.181067i	$-0.942045\pi$
$449$		−	7.67349i		−	0.362134i	0.983471	−	0.181067i	$-0.0579551\pi$
$450$	0.563627	+	7.64542i	0.0265697	+	0.360409i
$451$			5.50691i			0.259310i
$452$	−41.4795	−	23.9482i	−1.95103	−	1.12643i
$453$	2.09637	−	0.0771684i	0.0984960	−	0.00362569i
$454$	−6.74310	+	3.89313i	−0.316470	+	0.182714i
$455$	−8.58612	+	3.70889i	−0.402523	+	0.173876i
$456$	2.82153	+	4.49649i	0.132130	+	0.210567i
$457$	−5.32319	+	9.22004i	−0.249008	+	0.431295i	−0.963251	−	0.268603i	$-0.913438\pi$
$457$	−5.32319	+	9.22004i	−0.249008	+	0.431295i	0.714243	+	0.699898i	$0.246771\pi$
$458$	60.3946			2.82205
$459$	−38.5661	+	4.27437i	−1.80011	+	0.199510i
$460$			19.8627i			0.926104i
$461$	6.44303	−	11.1597i	0.300082	−	0.519757i	−0.676072	−	0.736835i	$-0.736319\pi$
$461$	6.44303	−	11.1597i	0.300082	−	0.519757i	0.976154	+	0.217078i	$0.0696527\pi$
$462$	−21.3965	−	44.9178i	−0.995457	−	2.08976i
$463$	6.82413	+	11.8197i	0.317144	+	0.549310i	0.979891	−	0.199534i	$-0.0639427\pi$
$463$	6.82413	+	11.8197i	0.317144	+	0.549310i	−0.662747	+	0.748844i	$0.730609\pi$
$464$	−22.6670	+	13.0868i	−1.05229	+	0.607538i
$465$	0.455086	+	12.3629i	0.0211041	+	0.573318i
$466$	−10.6646	+	18.4717i	−0.494029	+	0.855683i
$467$	−19.9617			−0.923719			−0.461859	−	0.886953i	$-0.652818\pi$
$467$	−19.9617			−0.923719			−0.461859	+	0.886953i	$0.652818\pi$
$468$	39.7268	−	27.0148i	1.83637	−	1.24876i
$469$	−18.7945	−	2.18703i	−0.867849	−	0.100988i
$470$	28.0955	+	16.2210i	1.29595	+	0.748218i
$471$	−26.8523	−	14.2127i	−1.23729	−	0.654885i
$472$	−22.7550	+	13.1376i	−1.04738	+	0.604707i
$473$	−2.98884	+	1.72561i	−0.137427	+	0.0793434i
$474$	7.18050	+	3.80057i	0.329811	+	0.174566i
$475$	0.410541	+	0.237026i	0.0188369	+	0.0108755i
$476$	−88.9003	−	10.3449i	−4.07474	−	0.474158i
$477$	−5.64614	−	2.72747i	−0.258519	−	0.124882i
$478$	−60.3153			−2.75876
$479$	12.7288	−	22.0469i	0.581594	−	1.00735i	−0.413697	−	0.910415i	$-0.635763\pi$
$479$	12.7288	−	22.0469i	0.581594	−	1.00735i	0.995291	−	0.0969357i	$-0.0309041\pi$
$480$	−0.390915	−	10.6197i	−0.0178427	−	0.484719i
$481$	18.4217	−	10.6358i	0.839957	−	0.484949i
$482$	25.7364	+	44.5768i	1.17226	+	2.03042i
$483$	−18.1402	+	8.64107i	−0.825409	+	0.393182i
$484$	−15.9719	+	27.6641i	−0.725995	+	1.25746i
$485$		−	8.73895i		−	0.396815i
$486$	30.2721	−	25.8920i	1.37317	−	1.17448i
$487$	11.3891			0.516088			0.258044	−	0.966133i	$-0.416922\pi$
$487$	11.3891			0.516088			0.258044	+	0.966133i	$0.416922\pi$
$488$	−8.49085	+	14.7066i	−0.384363	+	0.665736i
$489$	−5.82593	−	9.28440i	−0.263458	−	0.419855i
$490$	−17.1310	+	5.14777i	−0.773900	+	0.232552i
$491$	17.8295	−	10.2939i	0.804636	−	0.464557i	−0.0404536	−	0.999181i	$-0.512880\pi$
$491$	17.8295	−	10.2939i	0.804636	−	0.464557i	0.845090	+	0.534625i	$0.179547\pi$
$492$	−10.1629	+	0.374101i	−0.458178	+	0.0168658i
$493$	−22.6867	−	13.0982i	−1.02176	−	0.589912i
$494$		−	4.28234i		−	0.192672i
$495$	11.4772	+	5.54426i	0.515860	+	0.249196i
$496$		−	53.2908i		−	2.39283i
$497$	23.6898	+	17.6176i	1.06263	+	0.790258i
$498$	21.8903	+	11.5863i	0.980927	+	0.519196i
$499$	−4.00243	−	6.93242i	−0.179173	−	0.310338i	0.762424	−	0.647078i	$-0.224009\pi$
$499$	−4.00243	−	6.93242i	−0.179173	−	0.310338i	−0.941598	+	0.336740i	$0.890676\pi$
$500$	−2.26501	−	3.92311i	−0.101294	−	0.175447i
$501$	1.58189	−	2.98869i	0.0706734	−	0.133525i
$502$	−59.3305	−	34.2545i	−2.64805	−	1.52885i
$503$	−1.54015			−0.0686721			−0.0343360	−	0.999410i	$-0.510932\pi$
$503$	−1.54015			−0.0686721			−0.0343360	+	0.999410i	$0.510932\pi$
$504$	45.4849	−	23.7576i	2.02606	−	1.05825i
$505$	9.35329			0.416216
$506$	41.2272	+	23.8026i	1.83277	+	1.05815i
$507$	0.871045	−	0.0320636i	0.0386845	−	0.00142399i
$508$	−25.5207	−	44.2032i	−1.13230	−	1.96120i
$509$	−3.03402	−	5.25508i	−0.134481	−	0.232927i	0.790918	−	0.611922i	$-0.209603\pi$
$509$	−3.03402	−	5.25508i	−0.134481	−	0.232927i	−0.925399	+	0.378994i	$0.876270\pi$
$510$	27.9963	−	17.5676i	1.23970	−	0.777905i
$511$	−3.72612	−	2.77103i	−0.164834	−	0.122583i
$512$		−	50.6969i		−	2.24051i
$513$	−0.271345	−	2.44825i	−0.0119802	−	0.108093i
$514$			48.1885i			2.12550i
$515$	0.668174	+	0.385771i	0.0294433	+	0.0169991i
$516$	−3.38760	−	5.39860i	−0.149131	−	0.237660i
$517$	46.7130	−	26.9698i	2.05444	−	1.18613i
$518$	37.3470	−	16.1325i	1.64093	−	0.708824i
$519$	9.74893	−	0.358863i	0.427931	−	0.0157523i
$520$	−11.4274	+	19.7929i	−0.501126	+	0.867976i
$521$	−7.79260			−0.341400			−0.170700	−	0.985323i	$-0.554603\pi$
$521$	−7.79260			−0.341400			−0.170700	+	0.985323i	$0.554603\pi$
$522$	26.8205	−	1.97723i	1.17390	−	0.0865411i
$523$			9.16498i			0.400757i	0.979719	+	0.200378i	$0.0642171\pi$
$523$			9.16498i			0.400757i	−0.979719	+	0.200378i	$0.935783\pi$
$524$	35.3178	−	61.1722i	1.54286	−	2.67232i
$525$	2.59753	−	3.77529i	0.113365	−	0.164767i
$526$	−35.0089	−	60.6373i	−1.52646	−	2.64391i
$527$	46.1914	−	26.6686i	2.01213	−	1.16170i
$528$	−48.5272	−	25.6850i	−2.11187	−	1.11780i
$529$	−1.88724	+	3.26880i	−0.0820541	+	0.142122i
$530$	5.34111			0.232003
$531$	12.1594	−	0.896399i	0.527671	−	0.0389004i
$532$	0.656715	−	5.64356i	0.0284722	−	0.244679i
$533$	3.96808	+	2.29097i	0.171876	+	0.0992329i
$534$	2.34344	+	63.6623i	0.101411	+	2.75494i
$535$	11.6444	−	6.72289i	0.503431	−	0.290656i
$536$	−40.0417	+	23.1181i	−1.72954	+	0.998550i
$537$	−11.8777	+	7.45319i	−0.512559	+	0.321629i
$538$	48.3999	+	27.9437i	2.08667	+	1.20474i
$539$	−6.82917	+	28.9463i	−0.294153	+	1.24681i
$540$	−9.45212	+	21.5575i	−0.406755	+	0.927686i
$541$	11.5112			0.494907			0.247453	−	0.968900i	$-0.420406\pi$
$541$	11.5112			0.494907			0.247453	+	0.968900i	$0.420406\pi$
$542$	−28.4092	+	49.2061i	−1.22028	+	2.11358i
$543$	−20.2487	+	12.7060i	−0.868956	+	0.545267i
$544$	−39.6780	+	22.9081i	−1.70118	+	0.982176i
$545$	−2.37689	−	4.11690i	−0.101815	−	0.176349i
$546$	−41.2674	−	3.26902i	−1.76608	−	0.139901i
$547$	14.7106	−	25.4795i	0.628980	−	1.08943i	−0.358776	−	0.933424i	$-0.616806\pi$
$547$	14.7106	−	25.4795i	0.628980	−	1.08943i	0.987757	−	0.156002i	$-0.0498607\pi$
$548$			17.0345i			0.727677i
$549$	6.51608	−	4.43103i	0.278100	−	0.189112i
$550$	−10.8571			−0.462949
$551$	0.831498	−	1.44020i	0.0354230	−	0.0613544i
$552$	−22.9691	+	43.3960i	−0.977629	+	1.84705i
$553$	−1.92581	−	4.45826i	−0.0818937	−	0.189584i
$554$	−7.93045	+	4.57865i	−0.336933	+	0.194528i
$555$	−4.87557	+	9.21151i	−0.206956	+	0.391007i
$556$	21.3489	+	12.3258i	0.905396	+	0.522731i
$557$		−	2.45245i		−	0.103914i	−0.998649	−	0.0519568i	$-0.983454\pi$
$557$		−	2.45245i		−	0.103914i	0.998649	−	0.0519568i	$-0.0165458\pi$
$558$	−23.8176	+	49.3048i	−1.00828	+	2.08724i
$559$			2.87153i			0.121453i
$560$	−11.7798	+	15.8399i	−0.497787	+	0.669357i
$561$	−2.02149	−	54.9161i	−0.0853473	−	2.31856i
$562$	11.6642	+	20.2029i	0.492023	+	0.852209i
$563$	12.4793	+	21.6148i	0.525939	+	0.910953i	0.999543	+	0.0302157i	$0.00961941\pi$
$563$	12.4793	+	21.6148i	0.525939	+	0.910953i	−0.473604	+	0.880738i	$0.657047\pi$
$564$	52.9455	+	84.3757i	2.22941	+	3.55286i
$565$	−9.15660	−	5.28657i	−0.385221	−	0.222408i
$566$	42.3512			1.78015
$567$	−23.8001	+	0.745931i	−0.999509	+	0.0313262i
$568$	72.1418			3.02700
$569$	−11.6289	−	6.71395i	−0.487509	−	0.281463i	0.236032	−	0.971745i	$-0.424153\pi$
$569$	−11.6289	−	6.71395i	−0.487509	−	0.281463i	−0.723540	+	0.690282i	$0.757486\pi$
$570$	1.11522	+	1.77726i	0.0467116	+	0.0744411i
$571$	1.77883	+	3.08102i	0.0744416	+	0.128937i	0.900843	−	0.434144i	$-0.142949\pi$
$571$	1.77883	+	3.08102i	0.0744416	+	0.128937i	−0.826402	+	0.563081i	$0.809616\pi$
$572$	34.0193	+	58.9232i	1.42242	+	2.46370i
$573$	0.0416687	+	1.13198i	0.00174073	+	0.0472890i
$574$	7.03174	+	5.22935i	0.293499	+	0.218269i
$575$			4.38469i			0.182854i
$576$	0.987006	−	2.04320i	0.0411253	−	0.0851334i
$577$		−	12.8669i		−	0.535656i	−0.963467	−	0.267828i	$-0.913694\pi$
$577$		−	12.8669i		−	0.535656i	0.963467	−	0.267828i	$-0.0863059\pi$
$578$	−85.7850	−	49.5280i	−3.56819	−	2.06009i
$579$	11.5754	−	21.8697i	0.481059	−	0.908875i
$580$	−13.7625	+	7.94576i	−0.571455	+	0.329930i
$581$	−5.87097	−	13.5913i	−0.243569	−	0.563864i
$582$	18.0943	−	34.1859i	0.750031	−	1.41705i
$583$	4.44020	−	7.69065i	0.183894	−	0.318514i
$584$	−11.3470			−0.469542
$585$	8.76968	−	5.96351i	0.362582	−	0.246561i
$586$			60.1840i			2.48618i
$587$	−11.5624	+	20.0267i	−0.477233	+	0.826591i	−0.999660	−	0.0260930i	$-0.991693\pi$
$587$	−11.5624	+	20.0267i	−0.477233	+	0.826591i	0.522427	+	0.852684i	$0.325027\pi$
$588$	−53.8837	−	10.6367i	−2.22213	−	0.438649i
$589$	1.69298	+	2.93232i	0.0697578	+	0.120824i
$590$	−8.99402	+	5.19270i	−0.370278	+	0.213780i
$591$	4.94160	−	3.10083i	0.203270	−	0.127551i
$592$	22.4475	−	38.8801i	0.922585	−	1.59796i
$593$	−8.68451			−0.356630			−0.178315	−	0.983973i	$-0.557065\pi$
$593$	−8.68451			−0.356630			−0.178315	+	0.983973i	$0.557065\pi$
$594$	33.4179	+	45.4524i	1.37115	+	1.86494i
$595$	−19.6247	−	2.28364i	−0.804535	−	0.0936200i
$596$	−30.2722	−	17.4776i	−1.24000	−	0.715912i
$597$	−8.60043	+	5.39674i	−0.351992	+	0.220874i
$598$	34.3025	−	19.8045i	1.40273	−	0.809868i
$599$	−18.0483	+	10.4202i	−0.737435	+	0.425758i	−0.821136	−	0.570732i	$-0.806659\pi$
$599$	−18.0483	+	10.4202i	−0.737435	+	0.425758i	0.0837008	+	0.996491i	$0.473326\pi$
$600$	−0.411925	−	11.1904i	−0.0168168	−	0.456847i
$601$	2.85200	+	1.64660i	0.116335	+	0.0671663i	0.557039	−	0.830487i	$-0.311938\pi$
$601$	2.85200	+	1.64660i	0.116335	+	0.0671663i	−0.440703	+	0.897653i	$0.645271\pi$
$602$	−0.634780	+	5.45506i	−0.0258717	+	0.222332i
$603$	21.3967	−	1.57738i	0.871340	−	0.0642360i
$604$	−5.48657			−0.223245
$605$	−3.52579	+	6.10685i	−0.143344	+	0.248279i
$606$	36.5891	+	19.3663i	1.48633	+	0.786701i
$607$	−19.4942	+	11.2550i	−0.791244	+	0.456825i	−0.840400	−	0.541966i	$-0.817680\pi$
$607$	−19.4942	+	11.2550i	−0.791244	+	0.456825i	0.0491565	+	0.998791i	$0.484347\pi$
$608$	−1.45425	−	2.51884i	−0.0589776	−	0.102152i
$609$	−13.2439	−	9.11225i	−0.536671	−	0.369247i
$610$	−3.35605	+	5.81285i	−0.135883	+	0.235355i
$611$		−	44.8796i		−	1.81563i
$612$	101.209	−	7.46122i	4.09113	−	0.301602i
$613$	11.2370			0.453858			0.226929	−	0.973911i	$-0.427132\pi$
$613$	11.2370			0.453858			0.226929	+	0.973911i	$0.427132\pi$
$614$	−16.1320	+	27.9415i	−0.651036	+	1.12763i
$615$	−2.24345	+	0.0825827i	−0.0904648	+	0.00333006i
$616$	28.8193	+	66.7169i	1.16116	+	2.68810i
$617$	−35.1572	+	20.2980i	−1.41538	+	0.817167i	−0.995888	−	0.0905937i	$-0.971124\pi$
$617$	−35.1572	+	20.2980i	−1.41538	+	0.817167i	−0.419488	+	0.907761i	$0.637790\pi$
$618$	1.81508	+	2.89257i	0.0730132	+	0.116356i
$619$	10.5155	+	6.07113i	0.422654	+	0.244019i	0.696212	−	0.717836i	$-0.254867\pi$
$619$	10.5155	+	6.07113i	0.422654	+	0.244019i	−0.273558	+	0.961855i	$0.588201\pi$
$620$		−	32.3560i		−	1.29945i
$621$	18.3561	−	13.4960i	0.736606	−	0.541574i
$622$		−	21.5016i		−	0.862134i
$623$	22.7247	−	30.5572i	0.910447	−	1.22425i
$624$	−38.6958	+	24.2815i	−1.54907	+	0.972037i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−23.9842	−	41.5419i	−0.958603	−	1.66035i
$627$	3.48618	−	0.128328i	0.139225	−	0.00512493i
$628$	68.8146	+	39.7301i	2.74600	+	1.58540i
$629$	44.9340			1.79164
$630$	17.9781	−	9.39030i	0.716266	−	0.374119i
$631$	22.4079			0.892046			0.446023	−	0.895022i	$-0.352840\pi$
$631$	22.4079			0.892046			0.446023	+	0.895022i	$0.352840\pi$
$632$	−10.2773	−	5.93358i	−0.408808	−	0.236025i
$633$	−17.4066	+	32.8865i	−0.691848	+	1.30712i
$634$	36.0808	+	62.4938i	1.43295	+	2.48194i
$635$	−5.63370	−	9.75786i	−0.223567	−	0.387229i
$636$	14.4945	+	7.67183i	0.574746	+	0.304208i
$637$	18.0166	+	16.9630i	0.713843	+	0.672099i
$638$			38.0873i			1.50789i
$639$	−30.1428	−	14.5611i	−1.19243	−	0.576026i
$640$		−	10.3380i		−	0.408645i
$641$	−19.0012	−	10.9703i	−0.750502	−	0.433302i	0.0753736	−	0.997155i	$-0.475985\pi$
$641$	−19.0012	−	10.9703i	−0.750502	−	0.433302i	−0.825875	+	0.563853i	$0.809318\pi$
$642$	59.4716	−	2.18918i	2.34716	−	0.0864001i
$643$	−1.23157	+	0.711050i	−0.0485686	+	0.0280411i	−0.524088	−	0.851664i	$-0.675594\pi$
$643$	−1.23157	+	0.711050i	−0.0485686	+	0.0280411i	0.475519	+	0.879705i	$0.342260\pi$
$644$	48.2433	−	20.8394i	1.90105	−	0.821186i
$645$	−0.747813	−	1.19174i	−0.0294451	−	0.0469247i
$646$	4.52301	−	7.83409i	0.177956	−	0.308228i
$647$	−1.82171			−0.0716186			−0.0358093	−	0.999359i	$-0.511401\pi$
$647$	−1.82171			−0.0716186			−0.0358093	+	0.999359i	$0.511401\pi$
$648$	−45.5799	+	36.1683i	−1.79055	+	1.42083i
$649$			17.2673i			0.677800i
$650$	−4.51675	+	7.82324i	−0.177161	+	0.306853i
$651$	29.5501	−	14.0762i	1.15816	−	0.551688i
$652$	14.3336	+	24.8265i	0.561347	+	0.972282i
$653$	−4.13529	+	2.38751i	−0.161827	+	0.0934306i	−0.578726	−	0.815522i	$-0.696450\pi$
$653$	−4.13529	+	2.38751i	−0.161827	+	0.0934306i	0.416900	+	0.908953i	$0.363117\pi$
$654$	−0.773990	−	21.0263i	−0.0302654	−	0.822194i
$655$	7.79640	−	13.5038i	0.304630	−	0.527635i
$656$	9.67047			0.377568
$657$	4.74109	+	2.29027i	0.184968	+	0.0893521i
$658$	9.92108	−	85.2580i	0.386764	−	3.32370i
$659$	6.24797	+	3.60727i	0.243386	+	0.140519i	0.616732	−	0.787173i	$-0.288456\pi$
$659$	6.24797	+	3.60727i	0.243386	+	0.140519i	−0.373346	+	0.927692i	$0.621789\pi$
$660$	−29.4637	−	15.5949i	−1.14687	−	0.607030i
$661$	−39.7860	+	22.9705i	−1.54750	+	0.893448i	−0.549165	+	0.835714i	$0.685054\pi$
$661$	−39.7860	+	22.9705i	−1.54750	+	0.893448i	−0.998332	+	0.0577339i	$0.981613\pi$
$662$	56.5219	−	32.6329i	2.19679	−	1.26832i
$663$	−40.4114	−	21.3894i	−1.56945	−	0.830696i
$664$	−31.3310	−	18.0890i	−1.21588	−	0.701988i
$665$	0.144970	−	1.24582i	0.00562169	−	0.0483107i
$666$	−38.1454	+	25.9394i	−1.47811	+	1.00513i
$667$	15.3817			0.595582
$668$	−4.42201	+	7.65915i	−0.171093	+	0.296341i
$669$	−0.505893	−	13.7432i	−0.0195590	−	0.531342i
$670$	−15.8267	+	9.13754i	−0.611438	+	0.353014i
$671$	5.57993	+	9.66473i	0.215411	+	0.373103i
$672$	−25.3833	+	12.0913i	−0.979180	+	0.466431i
$673$	−3.92869	+	6.80469i	−0.151440	+	0.262302i	−0.931757	−	0.363082i	$-0.881724\pi$
$673$	−3.92869	+	6.80469i	−0.151440	+	0.262302i	0.780317	+	0.625384i	$0.215058\pi$
$674$		−	46.4488i		−	1.78914i
$675$	−2.08655	+	4.75881i	−0.0803115	+	0.183167i
$676$	−2.27968			−0.0876799
$677$	7.33822	−	12.7102i	0.282031	−	0.488491i	−0.689854	−	0.723948i	$-0.742325\pi$
$677$	7.33822	−	12.7102i	0.282031	−	0.488491i	0.971885	+	0.235457i	$0.0756587\pi$
$678$	−24.8737	−	39.6395i	−0.955268	−	1.52235i
$679$	−21.2255	+	9.16864i	−0.814559	+	0.351860i
$680$	−41.8105	+	24.1393i	−1.60336	+	0.925701i
$681$	−5.27398	+	0.194138i	−0.202100	+	0.00743939i
$682$	−67.1584	−	38.7739i	−2.57163	−	1.48473i
$683$		−	35.8729i		−	1.37264i	−0.727300	−	0.686319i	$-0.759225\pi$
$683$		−	35.8729i		−	1.37264i	0.727300	−	0.686319i	$-0.240775\pi$
$684$	0.473653	+	6.42494i	0.0181106	+	0.245664i
$685$			3.76036i			0.143676i
$686$	30.4764	+	36.2075i	1.16359	+	1.38241i
$687$	36.1802	+	19.1499i	1.38036	+	0.730613i
$688$	3.03027	+	5.24858i	0.115528	+	0.200100i
$689$	−3.69440	−	6.39888i	−0.140745	−	0.243778i
$690$	−9.07864	+	17.1525i	−0.345618	+	0.652983i
$691$	−27.2999	−	15.7616i	−1.03854	−	0.599600i	−0.119119	−	0.992880i	$-0.538007\pi$
$691$	−27.2999	−	15.7616i	−1.03854	−	0.599600i	−0.919419	+	0.393280i	$0.871340\pi$
$692$	−25.5147			−0.969922
$693$	1.42460	−	33.6930i	0.0541160	−	1.27989i
$694$	3.30572			0.125483
$695$	4.71277	+	2.72092i	0.178766	+	0.103210i
$696$	−39.2566	+	1.44505i	−1.48802	+	0.0547746i
$697$	4.83945	+	8.38217i	0.183307	+	0.317497i
$698$	−30.0695	−	52.0820i	−1.13815	−	1.97133i
$699$	−12.2458	+	7.68418i	−0.463178	+	0.290643i
$700$	−7.15221	+	9.61733i	−0.270328	+	0.363501i
$701$			26.3154i			0.993918i	0.867774	+	0.496959i	$0.165550\pi$
$701$			26.3154i			0.993918i	−0.867774	+	0.496959i	$0.834450\pi$
$702$	46.6537	−	5.17074i	1.76083	−	0.195157i
$703$			2.85250i			0.107584i
$704$	2.78306	+	1.60680i	0.104890	+	0.0605585i
$705$	11.6877	+	18.6259i	0.440184	+	0.701493i
$706$	70.9415	−	40.9581i	2.66992	−	1.54148i
$707$	−9.81319	−	22.7176i	−0.369063	−	0.854383i
$708$	−31.8664	+	1.17302i	−1.19761	+	0.0440847i
$709$	−14.9552	+	25.9032i	−0.561655	+	0.972816i	0.435697	+	0.900094i	$0.356502\pi$
$709$	−14.9552	+	25.9032i	−0.561655	+	0.972816i	−0.997352	+	0.0727223i	$0.976831\pi$
$710$	28.5144			1.07013
$711$	3.09650	+	4.55357i	0.116128	+	0.170772i
$712$		−	93.0547i		−	3.48737i
$713$	−15.6590	+	27.1222i	−0.586434	+	1.01573i
$714$	−72.0416	−	49.5670i	−2.69609	−	1.85500i
$715$	7.50977	+	13.0073i	0.280849	+	0.486445i
$716$	31.7609	−	18.3372i	1.18696	−	0.685293i
$717$	−36.1327	−	19.1247i	−1.34940	−	0.714226i
$718$	−33.7534	+	58.4625i	−1.25966	+	2.18180i
$719$	5.15995			0.192434			0.0962168	−	0.995360i	$-0.469326\pi$
$719$	5.15995			0.192434			0.0962168	+	0.995360i	$0.469326\pi$
$720$	9.73605	−	20.1546i	0.362841	−	0.751117i
$721$	0.235945	−	2.02762i	0.00878706	−	0.0755127i
$722$	−41.5503	−	23.9891i	−1.54634	−	0.892781i
$723$	1.28339	+	34.8648i	0.0477299	+	1.29664i
$724$	54.1452	−	31.2608i	2.01229	−	1.16180i
$725$	−3.03806	+	1.75402i	−0.112831	+	0.0651428i
$726$	−26.4370	+	16.5891i	−0.981168	+	0.615680i
$727$	18.9436	+	10.9371i	0.702581	+	0.405635i	0.808308	−	0.588760i	$-0.200384\pi$
$727$	18.9436	+	10.9371i	0.702581	+	0.405635i	−0.105727	+	0.994395i	$0.533717\pi$
$728$	60.0630	+	6.98925i	2.22608	+	0.259039i
$729$	26.3447	−	5.91231i	0.975731	−	0.218975i
$730$	−4.48496			−0.165996
$731$	−3.03291	+	5.25315i	−0.112176	+	0.194295i
$732$	−17.4570	+	10.9542i	−0.645228	+	0.404878i
$733$	29.8581	−	17.2386i	1.10284	−	0.636722i	0.165871	−	0.986147i	$-0.446956\pi$
$733$	29.8581	−	17.2386i	1.10284	−	0.636722i	0.936964	+	0.349425i	$0.113623\pi$
$734$	−43.9382	−	76.1032i	−1.62179	−	2.80902i
$735$	−11.8948	−	2.34804i	−0.438747	−	0.0866089i
$736$	13.4509	−	23.2977i	0.495808	−	0.858765i
$737$			30.3850i			1.11925i
$738$	−8.94715	−	4.32209i	−0.329349	−	0.159098i
$739$	9.11445			0.335280			0.167640	−	0.985848i	$-0.446385\pi$
$739$	9.11445			0.335280			0.167640	+	0.985848i	$0.446385\pi$
$740$	13.6292	−	23.6064i	0.501019	−	0.867790i
$741$	1.35784	−	2.56540i	0.0498815	−	0.0942422i
$742$	−5.60373	−	12.9727i	−0.205719	−	0.476242i
$743$	−44.7080	+	25.8122i	−1.64018	+	0.946956i	−0.659407	+	0.751786i	$0.729193\pi$
$743$	−44.7080	+	25.8122i	−1.64018	+	0.946956i	−0.980769	+	0.195170i	$0.937474\pi$
$744$	37.4162	−	70.6912i	1.37175	−	2.59167i
$745$	−6.68258	−	3.85819i	−0.244831	−	0.141353i
$746$		−	83.5171i		−	3.05778i
$747$	9.43990	+	13.8819i	0.345388	+	0.507913i
$748$			143.725i			5.25511i
$749$	−28.5457	−	21.2289i	−1.04304	−	0.775686i
$750$	−0.162815	−	4.42307i	−0.00594518	−	0.161508i
$751$	1.41105	+	2.44401i	0.0514900	+	0.0891833i	0.890622	−	0.454745i	$-0.150270\pi$
$751$	1.41105	+	2.44401i	0.0514900	+	0.0891833i	−0.839132	+	0.543928i	$0.816936\pi$
$752$	−47.3605	−	82.0309i	−1.72706	−	2.99136i
$753$	−24.6814	−	39.3331i	−0.899441	−	1.43338i
$754$	27.4443	+	15.8450i	0.999462	+	0.577040i
$755$	−1.21116			−0.0440786
$756$	62.2765	+	0.340196i	2.26497	+	0.0123728i
$757$	14.7361			0.535592			0.267796	−	0.963476i	$-0.413705\pi$
$757$	14.7361			0.535592			0.267796	+	0.963476i	$0.413705\pi$
$758$	44.2715	+	25.5602i	1.60801	+	0.928388i
$759$	17.1505	+	27.3316i	0.622523	+	0.992073i
$760$	−1.53241	−	2.65421i	−0.0555864	−	0.0962785i
$761$	−2.10497	−	3.64591i	−0.0763050	−	0.132164i	0.825348	−	0.564624i	$-0.190979\pi$
$761$	−2.10497	−	3.64591i	−0.0763050	−	0.132164i	−0.901653	+	0.432460i	$0.857646\pi$
$762$	−1.83451	−	49.8365i	−0.0664572	−	1.80539i
$763$	−7.50551	+	10.0924i	−0.271718	+	0.365370i
$764$		−	2.96259i		−	0.107183i
$765$	22.3419	−	1.64706i	0.807772	−	0.0595497i
$766$		−	36.3950i		−	1.31500i
$767$	12.4422	+	7.18348i	0.449260	+	0.259381i
$768$	22.6309	−	42.7570i	0.816622	−	1.54286i
$769$	−24.9362	+	14.3969i	−0.899221	+	0.519165i	−0.876947	−	0.480586i	$-0.840424\pi$
$769$	−24.9362	+	14.3969i	−0.899221	+	0.519165i	−0.0222736	+	0.999752i	$0.507090\pi$
$770$	11.3910	+	26.3702i	0.410502	+	0.950315i
$771$	−15.2796	+	28.8680i	−0.550280	+	1.03965i
$772$	−32.3581	+	56.0458i	−1.16459	+	2.01713i
$773$	23.0284			0.828275			0.414137	−	0.910214i	$-0.364083\pi$
$773$	23.0284			0.828275			0.414137	+	0.910214i	$0.364083\pi$
$774$	−0.457832	−	6.21034i	−0.0164564	−	0.223226i
$775$		−	7.14258i		−	0.256569i
$776$	−28.2494	+	48.9294i	−1.01409	+	1.75646i
$777$	27.4885	+	2.17752i	0.986146	+	0.0781180i
$778$	3.02024	+	5.23120i	0.108281	+	0.187548i
$779$	−0.532116	+	0.307218i	−0.0190650	+	0.0110072i
$780$	−23.4945	+	14.7427i	−0.841238	+	0.527874i
$781$	23.7047	−	41.0578i	0.848221	−	1.46916i
$782$	83.6703			2.99204
$783$	16.6941	+	7.31974i	0.596600	+	0.261586i
$784$	50.8315	+	11.9924i	1.81541	+	0.428301i
$785$	15.1908	+	8.77042i	0.542183	+	0.313030i
$786$	58.4587	−	36.6826i	2.08515	−	1.30843i
$787$	5.85487	−	3.38031i	0.208704	−	0.120495i	−0.392005	−	0.919963i	$-0.628218\pi$
$787$	5.85487	−	3.38031i	0.208704	−	0.120495i	0.600709	+	0.799468i	$0.294885\pi$
$788$	−13.2139	+	7.62902i	−0.470724	+	0.271773i
$789$	−1.74578	−	47.4262i	−0.0621516	−	1.68842i
$790$	−4.06214	−	2.34528i	−0.144524	−	0.0834412i
$791$	−3.23337	+	27.7864i	−0.114965	+	0.987970i
$792$	−46.3384	−	68.1433i	−1.64656	−	2.42137i
$793$	9.28539			0.329734
$794$	−19.7252	+	34.1651i	−0.700022	+	1.21247i
$795$	3.19967	+	1.69356i	0.113481	+	0.0600642i
$796$	22.9976	−	13.2777i	0.815128	−	0.470615i
$797$	−3.18883	−	5.52322i	−0.112954	−	0.195642i	0.804006	−	0.594621i	$-0.202698\pi$
$797$	−3.18883	−	5.52322i	−0.112954	−	0.195642i	−0.916960	+	0.398979i	$0.869365\pi$
$798$	3.14661	−	4.57334i	0.111389	−	0.161894i
$799$	47.4018	−	82.1024i	1.67696	−	2.90457i
$800$			6.13541i			0.216920i
$801$	−18.7821	+	38.8808i	−0.663633	+	1.37379i
$802$	44.5264			1.57228
$803$	−3.72846	+	6.45787i	−0.131574	+	0.227893i
$804$	−56.0749	+	2.06415i	−1.97761	+	0.0727968i
$805$	10.6497	−	4.60028i	0.375352	−	0.162139i
$806$	−55.8781	+	32.2612i	−1.96822	+	1.13635i
$807$	20.1343	+	32.0867i	0.708760	+	1.12950i
$808$	−52.3691	−	30.2353i	−1.84234	−	1.06367i
$809$			24.8244i			0.872781i	0.899757	+	0.436390i	$0.143743\pi$
$809$			24.8244i			0.872781i	−0.899757	+	0.436390i	$0.856257\pi$
$810$	−18.0157	+	14.2957i	−0.633006	+	0.502300i
$811$		−	52.6052i		−	1.84722i	−0.383336	−	0.923609i	$-0.625225\pi$
$811$		−	52.6052i		−	1.84722i	0.383336	−	0.923609i	$-0.374775\pi$
$812$	33.7381	+	25.0903i	1.18397	+	0.880497i
$813$	−32.6212	+	20.4697i	−1.14407	+	0.717903i
$814$	−32.6652	−	56.5777i	−1.14491	−	1.98305i
$815$	3.16414	+	5.48045i	0.110835	+	0.191972i
$816$	−96.4359	+	3.54985i	−3.37593	+	0.124270i
$817$	−0.333480	−	0.192535i	−0.0116670	−	0.00673594i
$818$	4.88690			0.170866
$819$	−23.6853	−	15.0434i	−0.827631	−	0.525658i
$820$	5.87151			0.205042
$821$	−23.1200	−	13.3483i	−0.806892	−	0.465859i	0.0389833	−	0.999240i	$-0.487588\pi$
$821$	−23.1200	−	13.3483i	−0.806892	−	0.465859i	−0.845875	+	0.533380i	$0.820921\pi$
$822$	−7.78595	+	14.7101i	−0.271566	+	0.513075i
$823$	−20.6957	−	35.8460i	−0.721406	−	1.24951i	−0.960436	−	0.278500i	$-0.910163\pi$
$823$	−20.6957	−	35.8460i	−0.721406	−	1.24951i	0.239030	−	0.971012i	$-0.423171\pi$
$824$	−2.49407	−	4.31986i	−0.0868852	−	0.150489i
$825$	−6.50411	−	3.44257i	−0.226444	−	0.119855i
$826$	22.0485	+	16.3970i	0.767165	+	0.570524i
$827$			27.3917i			0.952502i	0.879309	+	0.476251i	$0.158005\pi$
$827$			27.3917i			0.952502i	−0.879309	+	0.476251i	$0.841995\pi$
$828$	−49.2747	+	33.5075i	−1.71241	+	1.16447i
$829$			19.1296i			0.664398i	0.943209	+	0.332199i	$0.107790\pi$
$829$			19.1296i			0.664398i	−0.943209	+	0.332199i	$0.892210\pi$
$830$	−12.3837	−	7.14975i	−0.429846	−	0.248172i
$831$	−6.20264	+	0.228322i	−0.215167	+	0.00792042i
$832$	2.31560	−	1.33691i	0.0802790	−	0.0463491i
$833$	15.0431	+	50.0612i	0.521212	+	1.73452i
$834$	12.8021	+	20.4019i	0.443302	+	0.706461i
$835$	−0.976158	+	1.69076i	−0.0337814	+	0.0585110i
$836$	−9.12395			−0.315558
$837$	−29.9018	+	21.9847i	−1.03356	+	0.759902i
$838$			30.5854i			1.05656i
$839$	−9.71201	+	16.8217i	−0.335296	+	0.580749i	−0.983542	−	0.180682i	$-0.942170\pi$
$839$	−9.71201	+	16.8217i	−0.335296	+	0.580749i	0.648246	+	0.761431i	$0.275503\pi$
$840$	−26.7475	+	12.7412i	−0.922877	+	0.439611i
$841$	−8.34680	−	14.4571i	−0.287821	−	0.498520i
$842$	76.7388	−	44.3052i	2.64460	−	1.52686i
$843$	0.581654	+	15.8013i	0.0200332	+	0.544226i
$844$	48.6584	−	84.2787i	1.67489	−	2.90099i
$845$	−0.503239			−0.0173119
$846$	7.15553	+	97.0624i	0.246012	+	3.33708i
$847$	18.5317	+	2.15645i	0.636757	+	0.0740964i
$848$	−13.5052	−	7.79725i	−0.463772	−	0.267759i
$849$	25.3711	+	13.4287i	0.870733	+	0.460871i
$850$	−16.5258	+	9.54118i	−0.566831	+	0.327260i
$851$	−22.8491	+	13.1920i	−0.783258	+	0.452214i
$852$	77.3814	+	40.9573i	2.65104	+	1.40317i
$853$	−33.1978	−	19.1667i	−1.13667	−	0.656257i	−0.191066	−	0.981577i	$-0.561195\pi$
$853$	−33.1978	−	19.1667i	−1.13667	−	0.656257i	−0.945604	+	0.325320i	$0.894528\pi$
$854$	17.6395	+	2.05263i	0.603612	+	0.0702395i
$855$	0.104559	+	1.41831i	0.00357584	+	0.0485050i
$856$	−86.9293			−2.97118
$857$	−10.1058	+	17.5038i	−0.345208	+	0.597918i	−0.985392	−	0.170304i	$-0.945525\pi$
$857$	−10.1058	+	17.5038i	−0.345208	+	0.597918i	0.640183	+	0.768222i	$0.278858\pi$
$858$	2.44541	+	66.4324i	0.0834850	+	2.26797i
$859$	18.2808	−	10.5544i	0.623732	−	0.360112i	−0.154589	−	0.987979i	$-0.549405\pi$
$859$	18.2808	−	10.5544i	0.623732	−	0.360112i	0.778320	+	0.627867i	$0.216072\pi$
$860$	1.83985	+	3.18672i	0.0627385	+	0.108666i
$861$	2.55434	+	5.36234i	0.0870518	+	0.182748i
$862$	42.5328	−	73.6689i	1.44867	−	2.50917i
$863$		−	28.8274i		−	0.981295i	−0.871358	−	0.490648i	$-0.836760\pi$
$863$		−	28.8274i		−	0.981295i	0.871358	−	0.490648i	$-0.163240\pi$
$864$	25.6854	−	18.8846i	0.873834	−	0.642468i
$865$	−5.63236			−0.191506
$866$	−1.79272	+	3.10509i	−0.0609192	+	0.105515i
$867$	−35.6864	−	56.8711i	−1.21197	−	1.93144i
$868$	−78.5874	+	33.9469i	−2.66743	+	1.15223i
$869$	−6.75391	+	3.89937i	−0.229111	+	0.132277i
$870$	−15.5163	+	0.571165i	−0.526053	+	0.0193643i
$871$	21.8943	+	12.6407i	0.741861	+	0.428314i
$872$			30.7340i			1.04079i
$873$	21.6793	−	14.7422i	0.733732	−	0.498948i
$874$			5.31155i			0.179666i
$875$	−1.57885	+	2.12303i	−0.0533748	+	0.0717714i
$876$	−12.1711	−	6.44207i	−0.411225	−	0.217657i
$877$	1.70318	+	2.94999i	0.0575123	+	0.0996142i	0.893348	−	0.449365i	$-0.148350\pi$
$877$	1.70318	+	2.94999i	0.0575123	+	0.0996142i	−0.835836	+	0.548979i	$0.815017\pi$
$878$	11.0720	+	19.1773i	0.373662	+	0.647201i
$879$	−19.0831	+	36.0541i	−0.643657	+	1.21607i
$880$	27.4527	+	15.8498i	0.925431	+	0.534298i
$881$	−13.9772			−0.470904			−0.235452	−	0.971886i	$-0.575657\pi$
$881$	−13.9772			−0.470904			−0.235452	+	0.971886i	$0.575657\pi$
$882$	−41.6696	−	33.8139i	−1.40309	−	1.13857i
$883$	−35.5207			−1.19537			−0.597684	−	0.801732i	$-0.703912\pi$
$883$	−35.5207			−1.19537			−0.597684	+	0.801732i	$0.703912\pi$
$884$	103.563	+	59.7921i	3.48320	+	2.01102i
$885$	−7.03449	+	0.258943i	−0.236462	+	0.00870429i
$886$	−1.80913	−	3.13351i	−0.0607789	−	0.105272i
$887$	−21.5923	−	37.3989i	−0.724997	−	1.25573i	−0.958975	−	0.283490i	$-0.908508\pi$
$887$	−21.5923	−	37.3989i	−0.724997	−	1.25573i	0.233978	−	0.972242i	$-0.424826\pi$
$888$	57.0753	−	35.8145i	1.91532	−	1.20186i
$889$	−17.7895	+	23.9210i	−0.596641	+	0.802284i
$890$		−	36.7803i		−	1.23288i
$891$	5.60747	+	37.8251i	0.187857	+	1.26719i
$892$			35.9683i			1.20431i
$893$	5.21202	+	3.00916i	0.174414	+	0.100698i
$894$	−18.1531	−	28.9293i	−0.607129	−	0.967541i
$895$	7.01122	−	4.04793i	0.234359	−	0.135307i
$896$	−25.1093	+	10.8463i	−0.838843	+	0.362350i
$897$	26.8290	−	0.987589i	0.895794	−	0.0329746i
$898$	−9.80437	+	16.9817i	−0.327176	+	0.566686i
$899$	−25.0565			−0.835682
$900$	5.91133	−	12.2370i	0.197044	−	0.407902i
$901$		−	15.6081i		−	0.519981i
$902$	7.03615	−	12.1870i	0.234278	−	0.405782i
$903$	−2.10996	+	3.06665i	−0.0702151	+	0.102052i
$904$	34.1785	+	59.1990i	1.13676	+	1.96893i
$905$	11.9526	−	6.90081i	0.397316	−	0.229391i
$906$	−4.73793	−	2.50774i	−0.157407	−	0.0833142i
$907$	3.24606	−	5.62234i	0.107784	−	0.186687i	−0.807088	−	0.590431i	$-0.798958\pi$
$907$	3.24606	−	5.62234i	0.107784	−	0.186687i	0.914872	+	0.403744i	$0.132291\pi$
$908$	13.8029			0.458067
$909$	15.7786	+	23.2033i	0.523342	+	0.769604i
$910$	23.7402	+	2.76254i	0.786980	+	0.0915772i
$911$	27.1552	+	15.6781i	0.899691	+	0.519437i	0.877100	−	0.480308i	$-0.159475\pi$
$911$	27.1552	+	15.6781i	0.899691	+	0.519437i	0.0225913	+	0.999745i	$0.492808\pi$
$912$	−0.225352	−	6.12194i	−0.00746214	−	0.202718i
$913$	−20.5898	+	11.8875i	−0.681423	+	0.393420i
$914$	23.5608	−	13.6028i	0.779321	−	0.449941i
$915$	−3.85362	+	2.41814i	−0.127397	+	0.0799411i
$916$	−92.7195	−	53.5316i	−3.06354	−	1.76873i
$917$	−40.9781	−	4.76844i	−1.35322	−	0.157468i
$918$	90.8094	+	39.8164i	2.99716	+	1.31414i
$919$	−29.6866			−0.979269			−0.489635	−	0.871928i	$-0.662870\pi$
$919$	−29.6866			−0.979269			−0.489635	+	0.871928i	$0.662870\pi$
$920$	14.1739	−	24.5499i	0.467299	−	0.809386i
$921$	−18.5238	+	11.6236i	−0.610380	+	0.383011i
$922$	−28.5173	+	16.4644i	−0.939166	+	0.542228i
$923$	−19.7231	−	34.1614i	−0.649194	−	1.12444i
$924$	−6.96496	+	87.9242i	−0.229130	+	2.89249i
$925$	3.00864	−	5.21112i	0.0989235	−	0.171340i
$926$		−	34.8766i		−	1.14612i
$927$	0.170174	+	2.30836i	0.00558926	+	0.0758165i
$928$	21.5233			0.706538
$929$	−17.0653	+	29.5579i	−0.559894	+	0.969765i	0.437611	+	0.899165i	$0.355825\pi$
$929$	−17.0653	+	29.5579i	−0.559894	+	0.969765i	−0.997505	+	0.0706002i	$0.977509\pi$
$930$	14.7889	−	27.9410i	0.484948	−	0.916223i
$931$	−3.17798	+	0.954964i	−0.104154	+	0.0312977i
$932$	32.7453	−	18.9055i	1.07261	−	0.619270i
$933$	6.81770	−	12.8808i	0.223201	−	0.421699i
$934$	44.1760	+	25.5050i	1.44548	+	0.834549i
$935$			31.7273i			1.03759i
$936$	−68.3790	+	5.04097i	−2.23504	+	0.164769i
$937$			54.1542i			1.76914i	0.466407	+	0.884570i	$0.345548\pi$
$937$			54.1542i			1.76914i	−0.466407	+	0.884570i	$0.654452\pi$
$938$	38.7985	+	28.8536i	1.26681	+	0.942103i
$939$	−1.19602	−	32.4912i	−0.0390305	−	1.06031i
$940$	−28.7554	−	49.8058i	−0.937898	−	1.62449i
$941$	18.8053	+	32.5717i	0.613035	+	1.06181i	0.990726	+	0.135876i	$0.0433850\pi$
$941$	18.8053	+	32.5717i	0.613035	+	1.06181i	−0.377691	+	0.925932i	$0.623282\pi$
$942$	41.2655	+	65.7620i	1.34450	+	2.14264i
$943$	−4.92176	−	2.84158i	−0.160274	−	0.0925345i
$944$	30.3224			0.986909
$945$	13.7475	+	0.0750983i	0.447207	+	0.00244295i
$946$	8.81919			0.286737
$947$	−34.9044	−	20.1521i	−1.13424	−	0.654854i	−0.189243	−	0.981930i	$-0.560603\pi$
$947$	−34.9044	−	20.1521i	−1.13424	−	0.654854i	−0.944998	+	0.327076i	$0.893937\pi$
$948$	−7.65501	−	12.1993i	−0.248623	−	0.396215i
$949$	3.10220	+	5.37317i	0.100702	+	0.174420i
$950$	−0.605693	−	1.04909i	−0.0196513	−	0.0340370i
$951$	1.79923	+	48.8783i	0.0583442	+	1.58499i
$952$	102.497	+	76.2247i	3.32194	+	2.47046i
$953$			52.4874i			1.70023i	0.526595	+	0.850117i	$0.323469\pi$
$953$			52.4874i			1.70023i	−0.526595	+	0.850117i	$0.676531\pi$
$954$	9.01021	+	13.2500i	0.291716	+	0.428986i
$955$		−	0.653990i		−	0.0211626i
$956$	92.5978	+	53.4614i	2.99483	+	1.72906i
$957$	−12.0767	+	22.8167i	−0.390384	+	0.737561i
$958$	−56.3385	+	32.5271i	−1.82021	+	1.05090i
$959$	9.13330	−	3.94526i	0.294930	−	0.127399i
$960$	−0.612857	+	1.15788i	−0.0197799	+	0.0373705i
$961$	10.0082	−	17.3348i	0.322846	−	0.559186i
$962$	−54.3571			−1.75254
$963$	36.3215	+	17.5458i	1.17044	+	0.565404i
$964$		−	91.2474i		−	2.93888i
$965$	−7.14304	+	12.3721i	−0.229943	+	0.398272i
$966$	51.1855	+	4.05469i	1.64687	+	0.130457i
$967$	−27.2636	−	47.2220i	−0.876740	−	1.51856i	−0.854898	−	0.518796i	$-0.826380\pi$
$967$	−27.2636	−	47.2220i	−0.876740	−	1.51856i	−0.0218418	−	0.999761i	$-0.506953\pi$
$968$	39.4819	−	22.7949i	1.26899	−	0.732654i
$969$	5.19360	−	3.25897i	0.166842	−	0.104693i
$970$	−11.1657	+	19.3396i	−0.358509	+	0.620956i
$971$	3.64784			0.117065			0.0585324	−	0.998286i	$-0.481358\pi$
$971$	3.64784			0.117065			0.0585324	+	0.998286i	$0.481358\pi$
$972$	−69.4243	+	12.9180i	−2.22679	+	0.414346i
$973$	1.66417	−	14.3013i	0.0533509	−	0.458477i
$974$	−25.2044	−	14.5517i	−0.807600	−	0.466268i
$975$	−5.18641	+	3.25445i	−0.166098	+	0.104226i
$976$	16.9718	−	9.79870i	0.543255	−	0.313649i
$977$	−20.5740	+	11.8784i	−0.658222	+	0.380025i	−0.791599	−	0.611041i	$-0.790751\pi$
$977$	−20.5740	+	11.8784i	−0.658222	+	0.380025i	0.133377	+	0.991065i	$0.457418\pi$
$978$	1.03034	+	27.9904i	0.0329467	+	0.895035i
$979$	−52.9599	−	30.5764i	−1.69260	−	0.977225i
$980$	30.8628	+	7.28132i	0.985876	+	0.232593i
$981$	6.20334	−	12.8415i	0.198057	−	0.409999i
$982$	−52.6098			−1.67885
$983$	30.9587	−	53.6221i	0.987430	−	1.71028i	0.356835	−	0.934167i	$-0.383856\pi$
$983$	30.9587	−	53.6221i	0.987430	−	1.71028i	0.630595	−	0.776112i	$-0.282811\pi$
$984$	12.8281	+	6.78977i	0.408943	+	0.216450i
$985$	−2.91696	+	1.68411i	−0.0929420	+	0.0536601i
$986$	33.4709	+	57.9734i	1.06593	+	1.84625i
$987$	32.9769	−	47.9293i	1.04967	−	1.52561i
$988$	−3.79572	+	6.57437i	−0.120758	+	0.209159i
$989$		−	3.56166i		−	0.113254i
$990$	−18.3155	−	26.9339i	−0.582104	−	0.856017i
$991$	−13.7346			−0.436295			−0.218147	−	0.975916i	$-0.570001\pi$
$991$	−13.7346			−0.436295			−0.218147	+	0.975916i	$0.570001\pi$
$992$	−21.9113	+	37.9515i	−0.695686	+	1.20496i
$993$	44.2075	−	1.62730i	1.40288	−	0.0516408i
$994$	−29.9164	−	69.2567i	−0.948891	−	2.19669i
$995$	5.07672	−	2.93104i	0.160943	−	0.0929204i
$996$	−23.3369	−	37.1905i	−0.739458	−	1.17842i
$997$	41.3771	+	23.8891i	1.31043	+	0.756575i	0.982167	−	0.188012i	$-0.0602043\pi$
$997$	41.3771	+	23.8891i	1.31043	+	0.756575i	0.328260	+	0.944587i	$0.393538\pi$
$998$			20.4555i			0.647509i
$999$	−31.0764	+	3.44427i	−0.983214	+	0.108972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.i.146.2	yes	24
3.2	odd	2		945.2.bl.i.251.11		24
7.6	odd	2		315.2.bl.j.146.2	yes	24
9.4	even	3		945.2.bl.j.881.11		24
9.5	odd	6		315.2.bl.j.41.2	yes	24
21.20	even	2		945.2.bl.j.251.11		24
63.13	odd	6		945.2.bl.i.881.11		24
63.41	even	6	inner	315.2.bl.i.41.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.2	✓	24	63.41	even	6	inner
315.2.bl.i.146.2	yes	24	1.1	even	1	trivial
315.2.bl.j.41.2	yes	24	9.5	odd	6
315.2.bl.j.146.2	yes	24	7.6	odd	2
945.2.bl.i.251.11		24	3.2	odd	2
945.2.bl.i.881.11		24	63.13	odd	6
945.2.bl.j.251.11		24	21.20	even	2
945.2.bl.j.881.11		24	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-2.21303 - 1.27769i) q^{2} +(-0.920618 - 1.46713i) q^{3} +(2.26501 + 3.92311i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.162815 + 4.42307i) q^{6} +(1.57885 - 2.12303i) q^{7} -6.46517i q^{8} +(-1.30493 + 2.70133i) q^{9} +O(q^{10})\)	\(q+(-2.21303 - 1.27769i) q^{2} +(-0.920618 - 1.46713i) q^{3} +(2.26501 + 3.92311i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.162815 + 4.42307i) q^{6} +(1.57885 - 2.12303i) q^{7} -6.46517i q^{8} +(-1.30493 + 2.70133i) q^{9} -2.55539i q^{10} +(-3.67950 - 2.12436i) q^{11} +(3.67049 - 6.93474i) q^{12} +(-3.06147 + 1.76754i) q^{13} +(-6.20662 + 2.68104i) q^{14} +(0.810261 - 1.53084i) q^{15} +(-3.73050 + 6.46141i) q^{16} -7.46750 q^{17} +(6.33931 - 4.31083i) q^{18} -0.474051i q^{19} +(-2.26501 + 3.92311i) q^{20} +(-4.56826 - 0.361877i) q^{21} +(5.42856 + 9.40254i) q^{22} +(3.79725 - 2.19235i) q^{23} +(-9.48523 + 5.95195i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.03349 q^{26} +(5.16453 - 0.572396i) q^{27} +(11.9050 + 1.38532i) q^{28} +(3.03806 + 1.75402i) q^{29} +(-3.74908 + 2.35254i) q^{30} +(-6.18566 + 3.57129i) q^{31} +(5.31342 - 3.06771i) q^{32} +(0.270705 + 7.35401i) q^{33} +(16.5258 + 9.54118i) q^{34} +(2.62802 + 0.305810i) q^{35} +(-13.5533 + 0.999159i) q^{36} -6.01728 q^{37} +(-0.605693 + 1.04909i) q^{38} +(5.41164 + 2.86433i) q^{39} +(5.59900 - 3.23258i) q^{40} +(-0.648068 - 1.12249i) q^{41} +(9.64735 + 6.63769i) q^{42} +(0.406148 - 0.703468i) q^{43} -19.2467i q^{44} +(-2.99188 + 0.220564i) q^{45} -11.2046 q^{46} +(-6.34775 + 10.9946i) q^{47} +(12.9141 - 0.475374i) q^{48} +(-2.01447 - 6.70387i) q^{49} +(2.21303 - 1.27769i) q^{50} +(6.87471 + 10.9558i) q^{51} +(-13.8685 - 8.00697i) q^{52} +2.09014i q^{53} +(-12.1606 - 5.33196i) q^{54} -4.24872i q^{55} +(-13.7257 - 10.2075i) q^{56} +(-0.695494 + 0.436420i) q^{57} +(-4.48222 - 7.76342i) q^{58} +(-2.03206 - 3.51963i) q^{59} +(7.84090 - 0.288628i) q^{60} +(-2.27474 - 1.31332i) q^{61} +18.2521 q^{62} +(3.67471 + 7.03538i) q^{63} -0.756369 q^{64} +(-3.06147 - 1.76754i) q^{65} +(8.79710 - 16.6205i) q^{66} +(-3.57579 - 6.19345i) q^{67} +(-16.9139 - 29.2958i) q^{68} +(-6.71227 - 3.55274i) q^{69} +(-5.42516 - 4.03457i) q^{70} +11.1585i q^{71} +(17.4645 + 8.43657i) q^{72} -1.75510i q^{73} +(13.3164 + 7.68825i) q^{74} +(1.73088 - 0.0637145i) q^{75} +(1.85975 - 1.07373i) q^{76} +(-10.3194 + 4.45762i) q^{77} +(-8.31639 - 13.2533i) q^{78} +(0.917777 - 1.58964i) q^{79} -7.46100 q^{80} +(-5.59434 - 7.05006i) q^{81} +3.31213i q^{82} +(2.79791 - 4.84613i) q^{83} +(-8.92747 - 18.7414i) q^{84} +(-3.73375 - 6.46704i) q^{85} +(-1.79764 + 1.03787i) q^{86} +(-0.223514 - 6.07201i) q^{87} +(-13.7343 + 23.7886i) q^{88} +14.3932 q^{89} +(6.90294 + 3.33459i) q^{90} +(-1.08106 + 9.29024i) q^{91} +(17.2016 + 9.93135i) q^{92} +(10.9342 + 5.78735i) q^{93} +(28.0955 - 16.2210i) q^{94} +(0.410541 - 0.237026i) q^{95} +(-9.39235 - 4.97128i) q^{96} +(-7.56815 - 4.36947i) q^{97} +(-4.10740 + 17.4098i) q^{98} +(10.5401 - 7.16739i) 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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