LMFDB - Embedded newform 315.2.l.b.121.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, 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 $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.11
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32555 q^{2} +(-1.66925 - 0.462165i) q^{3} +3.40817 q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.88192 - 1.07479i) q^{6} +(2.02670 + 1.70073i) q^{7} +3.27475 q^{8} +(2.57281 + 1.54294i) q^{9} +O(q^{10})$	\(q+2.32555 q^{2} +(-1.66925 - 0.462165i) q^{3} +3.40817 q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.88192 - 1.07479i) q^{6} +(2.02670 + 1.70073i) q^{7} +3.27475 q^{8} +(2.57281 + 1.54294i) q^{9} +(1.16277 + 2.01398i) q^{10} +(1.47865 - 2.56109i) q^{11} +(-5.68909 - 1.57514i) q^{12} +(1.00448 - 1.73980i) q^{13} +(4.71318 + 3.95513i) q^{14} +(-0.434379 - 1.67670i) q^{15} +0.799261 q^{16} +(-1.98046 - 3.43026i) q^{17} +(5.98318 + 3.58818i) q^{18} +(-2.55847 + 4.43140i) q^{19} +(1.70408 + 2.95156i) q^{20} +(-2.59705 - 3.77562i) q^{21} +(3.43866 - 5.95593i) q^{22} +(-0.216531 - 0.375043i) q^{23} +(-5.46639 - 1.51348i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.33596 - 4.04599i) q^{26} +(-3.58157 - 3.76462i) q^{27} +(6.90732 + 5.79638i) q^{28} +(1.68214 + 2.91356i) q^{29} +(-1.01017 - 3.89924i) q^{30} -9.06536 q^{31} -4.69079 q^{32} +(-3.65188 + 3.59173i) q^{33} +(-4.60565 - 7.97722i) q^{34} +(-0.459529 + 2.60554i) q^{35} +(8.76855 + 5.25860i) q^{36} +(0.0400194 - 0.0693157i) q^{37} +(-5.94984 + 10.3054i) q^{38} +(-2.48080 + 2.43994i) q^{39} +(1.63738 + 2.83602i) q^{40} +(-0.435072 + 0.753568i) q^{41} +(-6.03956 - 8.78039i) q^{42} +(-1.02431 - 1.77416i) q^{43} +(5.03947 - 8.72862i) q^{44} +(-0.0498234 + 2.99959i) q^{45} +(-0.503553 - 0.872180i) q^{46} -3.84772 q^{47} +(-1.33417 - 0.369391i) q^{48} +(1.21501 + 6.89375i) q^{49} +(-1.16277 + 2.01398i) q^{50} +(1.72054 + 6.64127i) q^{51} +(3.42342 - 5.92954i) q^{52} +(-4.24749 - 7.35687i) q^{53} +(-8.32910 - 8.75480i) q^{54} +2.95729 q^{55} +(6.63694 + 5.56948i) q^{56} +(6.31877 - 6.21469i) q^{57} +(3.91190 + 6.77561i) q^{58} +11.7807 q^{59} +(-1.48044 - 5.71446i) q^{60} +15.0097 q^{61} -21.0819 q^{62} +(2.59017 + 7.50273i) q^{63} -12.5072 q^{64} +2.00895 q^{65} +(-8.49262 + 8.35273i) q^{66} -9.09400 q^{67} +(-6.74974 - 11.6909i) q^{68} +(0.188113 + 0.726115i) q^{69} +(-1.06866 + 6.05930i) q^{70} -2.95233 q^{71} +(8.42531 + 5.05275i) q^{72} +(-5.84200 - 10.1186i) q^{73} +(0.0930671 - 0.161197i) q^{74} +(1.23487 - 1.21453i) q^{75} +(-8.71969 + 15.1029i) q^{76} +(7.35250 - 2.67578i) q^{77} +(-5.76922 + 5.67419i) q^{78} -12.3024 q^{79} +(0.399631 + 0.692181i) q^{80} +(4.23866 + 7.93938i) q^{81} +(-1.01178 + 1.75246i) q^{82} +(-0.126085 - 0.218385i) q^{83} +(-8.85118 - 12.8679i) q^{84} +(1.98046 - 3.43026i) q^{85} +(-2.38208 - 4.12589i) q^{86} +(-1.46138 - 5.64089i) q^{87} +(4.84220 - 8.38694i) q^{88} +(8.58029 - 14.8615i) q^{89} +(-0.115867 + 6.97568i) q^{90} +(4.99471 - 1.81771i) q^{91} +(-0.737974 - 1.27821i) q^{92} +(15.1324 + 4.18969i) q^{93} -8.94806 q^{94} -5.11694 q^{95} +(7.83011 + 2.16792i) q^{96} +(7.67728 + 13.2974i) q^{97} +(2.82557 + 16.0317i) q^{98} +(7.75588 - 4.30773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.32555			1.64441			0.822205	−	0.569192i	$-0.192744\pi$
$2$	2.32555			1.64441			0.822205	+	0.569192i	$0.192744\pi$
$3$	−1.66925	−	0.462165i	−0.963743	−	0.266831i
$3$	−1.66925	−	0.462165i	−0.963743	−	0.266831i
$4$	3.40817			1.70408
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−3.88192	−	1.07479i	−1.58479	−	0.438780i
$7$	2.02670	+	1.70073i	0.766020	+	0.642817i
$7$	2.02670	+	1.70073i	0.766020	+	0.642817i
$8$	3.27475			1.15780
$9$	2.57281	+	1.54294i	0.857602	+	0.514314i
$10$	1.16277	+	2.01398i	0.367701	+	0.636877i
$11$	1.47865	−	2.56109i	0.445829	−	0.772198i	−0.552281	−	0.833658i	$-0.686242\pi$
$11$	1.47865	−	2.56109i	0.445829	−	0.772198i	0.998110	+	0.0614602i	$0.0195757\pi$
$12$	−5.68909	−	1.57514i	−1.64230	−	0.454703i
$13$	1.00448	−	1.73980i	0.278592	−	0.482535i	−0.692443	−	0.721472i	$-0.743466\pi$
$13$	1.00448	−	1.73980i	0.278592	−	0.482535i	0.971035	+	0.238937i	$0.0767991\pi$
$14$	4.71318	+	3.95513i	1.25965	+	1.05705i
$15$	−0.434379	−	1.67670i	−0.112156	−	0.432921i
$16$	0.799261			0.199815
$17$	−1.98046	−	3.43026i	−0.480332	−	0.831960i	0.519413	−	0.854523i	$-0.326151\pi$
$17$	−1.98046	−	3.43026i	−0.480332	−	0.831960i	−0.999745	+	0.0225634i	$0.992817\pi$
$18$	5.98318	+	3.58818i	1.41025	+	0.845743i
$19$	−2.55847	+	4.43140i	−0.586953	+	1.01663i	0.407676	+	0.913127i	$0.366339\pi$
$19$	−2.55847	+	4.43140i	−0.586953	+	1.01663i	−0.994629	+	0.103506i	$0.966994\pi$
$20$	1.70408	+	2.95156i	0.381044	+	0.659988i
$21$	−2.59705	−	3.77562i	−0.566723	−	0.823908i
$22$	3.43866	−	5.95593i	0.733125	−	1.26981i
$23$	−0.216531	−	0.375043i	−0.0451499	−	0.0782019i	0.842567	−	0.538591i	$-0.181043\pi$
$23$	−0.216531	−	0.375043i	−0.0451499	−	0.0782019i	−0.887717	+	0.460389i	$0.847710\pi$
$24$	−5.46639	−	1.51348i	−1.11582	−	0.308937i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.33596	−	4.04599i	0.458119	−	0.793485i
$27$	−3.58157	−	3.76462i	−0.689273	−	0.724502i
$28$	6.90732	+	5.79638i	1.30536	+	1.09541i
$29$	1.68214	+	2.91356i	0.312366	+	0.541034i	0.978874	−	0.204464i	$-0.0655451\pi$
$29$	1.68214	+	2.91356i	0.312366	+	0.541034i	−0.666508	+	0.745498i	$0.732212\pi$
$30$	−1.01017	−	3.89924i	−0.184431	−	0.711900i
$31$	−9.06536			−1.62819			−0.814093	−	0.580735i	$-0.802765\pi$
$31$	−9.06536			−1.62819			−0.814093	+	0.580735i	$0.802765\pi$
$32$	−4.69079			−0.829222
$33$	−3.65188	+	3.59173i	−0.635711	+	0.625239i
$34$	−4.60565	−	7.97722i	−0.789863	−	1.36808i
$35$	−0.459529	+	2.60554i	−0.0776746	+	0.440416i
$36$	8.76855	+	5.25860i	1.46142	+	0.876433i
$37$	0.0400194	−	0.0693157i	0.00657916	−	0.0113954i	−0.862717	−	0.505687i	$-0.831239\pi$
$37$	0.0400194	−	0.0693157i	0.00657916	−	0.0113954i	0.869296	+	0.494291i	$0.164572\pi$
$38$	−5.94984	+	10.3054i	−0.965191	+	1.67176i
$39$	−2.48080	+	2.43994i	−0.397246	+	0.390703i
$40$	1.63738	+	2.83602i	0.258892	+	0.448414i
$41$	−0.435072	+	0.753568i	−0.0679469	+	0.117687i	−0.897997	−	0.440001i	$-0.854978\pi$
$41$	−0.435072	+	0.753568i	−0.0679469	+	0.117687i	0.830051	+	0.557688i	$0.188312\pi$
$42$	−6.03956	−	8.78039i	−0.931925	−	1.35484i
$43$	−1.02431	−	1.77416i	−0.156206	−	0.270557i	0.777292	−	0.629141i	$-0.216593\pi$
$43$	−1.02431	−	1.77416i	−0.156206	−	0.270557i	−0.933497	+	0.358584i	$0.883260\pi$
$44$	5.03947	−	8.72862i	0.759729	−	1.31589i
$45$	−0.0498234	+	2.99959i	−0.00742723	+	0.447152i
$46$	−0.503553	−	0.872180i	−0.0742449	−	0.128596i
$47$	−3.84772			−0.561248			−0.280624	−	0.959818i	$-0.590541\pi$
$47$	−3.84772			−0.561248			−0.280624	+	0.959818i	$0.590541\pi$
$48$	−1.33417	−	0.369391i	−0.192571	−	0.0533170i
$49$	1.21501	+	6.89375i	0.173573	+	0.984821i
$50$	−1.16277	+	2.01398i	−0.164441	+	0.284820i
$51$	1.72054	+	6.64127i	0.240924	+	0.929963i
$52$	3.42342	−	5.92954i	0.474743	−	0.822279i
$53$	−4.24749	−	7.35687i	−0.583438	−	1.01054i	−0.995068	−	0.0991931i	$-0.968374\pi$
$53$	−4.24749	−	7.35687i	−0.583438	−	1.01054i	0.411630	−	0.911351i	$-0.364959\pi$
$54$	−8.32910	−	8.75480i	−1.13345	−	1.19138i
$55$	2.95729			0.398761
$56$	6.63694	+	5.56948i	0.886898	+	0.744254i
$57$	6.31877	−	6.21469i	0.836941	−	0.823155i
$58$	3.91190	+	6.77561i	0.513658	+	0.889681i
$59$	11.7807			1.53371			0.766857	−	0.641818i	$-0.221819\pi$
$59$	11.7807			1.53371			0.766857	+	0.641818i	$0.221819\pi$
$60$	−1.48044	−	5.71446i	−0.191123	−	0.737734i
$61$	15.0097			1.92180			0.960901	−	0.276894i	$-0.0893050\pi$
$61$	15.0097			1.92180			0.960901	+	0.276894i	$0.0893050\pi$
$62$	−21.0819			−2.67740
$63$	2.59017	+	7.50273i	0.326331	+	0.945256i
$64$	−12.5072			−1.56340
$65$	2.00895			0.249180
$66$	−8.49262	+	8.35273i	−1.04537	+	1.02815i
$67$	−9.09400			−1.11101			−0.555504	−	0.831514i	$-0.687475\pi$
$67$	−9.09400			−1.11101			−0.555504	+	0.831514i	$0.687475\pi$
$68$	−6.74974	−	11.6909i	−0.818526	−	1.41773i
$69$	0.188113	+	0.726115i	0.0226462	+	0.0874139i
$70$	−1.06866	+	6.05930i	−0.127729	+	0.724225i
$71$	−2.95233			−0.350377			−0.175189	−	0.984535i	$-0.556054\pi$
$71$	−2.95233			−0.350377			−0.175189	+	0.984535i	$0.556054\pi$
$72$	8.42531	+	5.05275i	0.992932	+	0.595473i
$73$	−5.84200	−	10.1186i	−0.683754	−	1.18430i	−0.973827	−	0.227292i	$-0.927013\pi$
$73$	−5.84200	−	10.1186i	−0.683754	−	1.18430i	0.290073	−	0.957005i	$-0.406320\pi$
$74$	0.0930671	−	0.161197i	0.0108188	−	0.0187388i
$75$	1.23487	−	1.21453i	0.142591	−	0.140242i
$76$	−8.71969	+	15.1029i	−1.00022	+	1.73243i
$77$	7.35250	−	2.67578i	0.837895	−	0.304933i
$78$	−5.76922	+	5.67419i	−0.653235	+	0.642475i
$79$	−12.3024			−1.38413			−0.692065	−	0.721835i	$-0.743299\pi$
$79$	−12.3024			−1.38413			−0.692065	+	0.721835i	$0.743299\pi$
$80$	0.399631	+	0.692181i	0.0446801	+	0.0773881i
$81$	4.23866	+	7.93938i	0.470963	+	0.882153i
$82$	−1.01178	+	1.75246i	−0.111733	+	0.193526i
$83$	−0.126085	−	0.218385i	−0.0138396	−	0.0239709i	0.859023	−	0.511938i	$-0.171072\pi$
$83$	−0.126085	−	0.218385i	−0.0138396	−	0.0239709i	−0.872862	+	0.487967i	$0.837739\pi$
$84$	−8.85118	−	12.8679i	−0.965743	−	1.40401i
$85$	1.98046	−	3.43026i	0.214811	−	0.372064i
$86$	−2.38208	−	4.12589i	−0.256867	−	0.444906i
$87$	−1.46138	−	5.64089i	−0.156676	−	0.604767i
$88$	4.84220	−	8.38694i	0.516181	−	0.894051i
$89$	8.58029	−	14.8615i	0.909508	−	1.57531i	0.0947600	−	0.995500i	$-0.469792\pi$
$89$	8.58029	−	14.8615i	0.909508	−	1.57531i	0.814748	−	0.579815i	$-0.196875\pi$
$90$	−0.115867	+	6.97568i	−0.0122134	+	0.735301i
$91$	4.99471	−	1.81771i	0.523588	−	0.190548i
$92$	−0.737974	−	1.27821i	−0.0769391	−	0.133262i
$93$	15.1324	+	4.18969i	1.56915	+	0.434451i
$94$	−8.94806			−0.922922
$95$	−5.11694			−0.524987
$96$	7.83011	+	2.16792i	0.799157	+	0.221262i
$97$	7.67728	+	13.2974i	0.779510	+	1.35015i	0.932224	+	0.361881i	$0.117865\pi$
$97$	7.67728	+	13.2974i	0.779510	+	1.35015i	−0.152714	+	0.988270i	$0.548801\pi$
$98$	2.82557	+	16.0317i	0.285426	+	1.61945i
$99$	7.75588	−	4.30773i	0.779496	−	0.432943i
$100$	−1.70408	+	2.95156i	−0.170408	+	0.295156i
$101$	2.84503	−	4.92774i	0.283091	−	0.490328i	−0.689053	−	0.724711i	$-0.741973\pi$
$101$	2.84503	−	4.92774i	0.283091	−	0.490328i	0.972144	+	0.234382i	$0.0753068\pi$
$102$	4.00120	+	15.4446i	0.396178	+	1.52924i
$103$	8.40122	+	14.5513i	0.827796	+	1.43379i	0.899763	+	0.436378i	$0.143739\pi$
$103$	8.40122	+	14.5513i	0.827796	+	1.43379i	−0.0719668	+	0.997407i	$0.522928\pi$
$104$	3.28941	−	5.69743i	0.322553	−	0.558679i
$105$	1.97126	−	4.13692i	0.192375	−	0.403722i
$106$	−9.87774	−	17.1087i	−0.959411	−	1.66175i
$107$	7.47266	−	12.9430i	0.722409	−	1.25125i	−0.237623	−	0.971358i	$-0.576368\pi$
$107$	7.47266	−	12.9430i	0.722409	−	1.25125i	0.960032	−	0.279892i	$-0.0902985\pi$
$108$	−12.2066	−	12.8305i	−1.17458	−	1.23461i
$109$	8.06216	+	13.9641i	0.772215	+	1.33752i	0.936346	+	0.351077i	$0.114185\pi$
$109$	8.06216	+	13.9641i	0.772215	+	1.33752i	−0.164131	+	0.986439i	$0.552482\pi$
$110$	6.87732			0.655727
$111$	−0.0988379	+	0.0972098i	−0.00938128	+	0.00922675i
$112$	1.61986	+	1.35933i	0.153063	+	0.128445i
$113$	5.41997	−	9.38766i	0.509868	−	0.883117i	−0.490067	−	0.871685i	$-0.663028\pi$
$113$	5.41997	−	9.38766i	0.509868	−	0.883117i	0.999935	−	0.0114319i	$-0.00363896\pi$
$114$	14.6946	−	14.4525i	1.37627	−	1.35360i
$115$	0.216531	−	0.375043i	0.0201916	−	0.0349729i
$116$	5.73302	+	9.92988i	0.532298	+	0.921966i
$117$	5.26874	−	2.92633i	0.487095	−	0.270539i
$118$	27.3965			2.52205
$119$	1.82016	−	10.3203i	0.166854	−	0.946063i
$120$	−1.42248	−	5.49077i	−0.129855	−	0.501237i
$121$	1.12721	+	1.95238i	0.102474	+	0.177490i
$122$	34.9059			3.16023
$123$	1.07452	−	1.05682i	0.0968861	−	0.0952902i
$124$	−30.8962			−2.77456
$125$	−1.00000			−0.0894427
$126$	6.02356	+	17.4480i	0.536621	+	1.55439i
$127$	−6.40805			−0.568623			−0.284311	−	0.958732i	$-0.591765\pi$
$127$	−6.40805			−0.568623			−0.284311	+	0.958732i	$0.591765\pi$
$128$	−19.7044			−1.74164
$129$	0.889879	+	3.43492i	0.0783494	+	0.302428i
$130$	4.67191			0.409754
$131$	−0.0560766	−	0.0971274i	−0.00489943	−	0.00848606i	0.863565	−	0.504237i	$-0.168226\pi$
$131$	−0.0560766	−	0.0971274i	−0.00489943	−	0.00848606i	−0.868465	+	0.495751i	$0.834893\pi$
$132$	−12.4462	+	12.2412i	−1.08330	+	1.06546i
$133$	−12.7219	+	4.62983i	−1.10313	+	0.401458i
$134$	−21.1485			−1.82695
$135$	1.46947	−	4.98404i	0.126472	−	0.428958i
$136$	−6.48552	−	11.2333i	−0.556129	−	0.963243i
$137$	−9.61419	+	16.6523i	−0.821396	+	1.42270i	0.0832467	+	0.996529i	$0.473471\pi$
$137$	−9.61419	+	16.6523i	−0.821396	+	1.42270i	−0.904643	+	0.426171i	$0.859862\pi$
$138$	0.437466	+	1.68861i	0.0372396	+	0.143744i
$139$	−6.94402	+	12.0274i	−0.588984	+	1.02015i	0.405381	+	0.914148i	$0.367139\pi$
$139$	−6.94402	+	12.0274i	−0.588984	+	1.02015i	−0.994366	+	0.106003i	$0.966195\pi$
$140$	−1.56615	+	8.88011i	−0.132364	+	0.750506i
$141$	6.42282	+	1.77828i	0.540899	+	0.149759i
$142$	−6.86578			−0.576164
$143$	−2.97053	−	5.14511i	−0.248408	−	0.430256i
$144$	2.05634	+	1.23321i	0.171362	+	0.102768i
$145$	−1.68214	+	2.91356i	−0.139694	+	0.241958i
$146$	−13.5858	−	23.5313i	−1.12437	−	1.94747i
$147$	1.15789	−	12.0689i	0.0955011	−	0.995429i
$148$	0.136393	−	0.236239i	0.0112114	−	0.0194188i
$149$	5.65469	+	9.79421i	0.463250	+	0.802373i	0.999121	−	0.0419272i	$-0.0133498\pi$
$149$	5.65469	+	9.79421i	0.463250	+	0.802373i	−0.535870	+	0.844300i	$0.680016\pi$
$150$	2.87175	−	2.82445i	0.234478	−	0.230615i
$151$	−5.25717	+	9.10568i	−0.427822	+	0.741010i	−0.996679	−	0.0814266i	$-0.974052\pi$
$151$	−5.25717	+	9.10568i	−0.427822	+	0.741010i	0.568857	+	0.822436i	$0.307386\pi$
$152$	−8.37836	+	14.5117i	−0.679575	+	1.17706i
$153$	0.197346	−	11.8811i	0.0159545	−	0.960532i
$154$	17.0986	−	6.22264i	1.37784	−	0.501435i
$155$	−4.53268	−	7.85083i	−0.364073	−	0.630594i
$156$	−8.45498	+	8.31571i	−0.676940	+	0.665790i
$157$	2.08796			0.166637			0.0833187	−	0.996523i	$-0.473448\pi$
$157$	2.08796			0.166637			0.0833187	+	0.996523i	$0.473448\pi$
$158$	−28.6098			−2.27608
$159$	3.69004	+	14.2435i	0.292639	+	1.12958i
$160$	−2.34539	−	4.06234i	−0.185420	−	0.321156i
$161$	0.199005	−	1.12836i	0.0156838	−	0.0889273i
$162$	9.85721	+	18.4634i	0.774455	+	1.45062i
$163$	9.73811	−	16.8669i	0.762748	−	1.32112i	−0.178681	−	0.983907i	$-0.557183\pi$
$163$	9.73811	−	16.8669i	0.762748	−	1.32112i	0.941429	−	0.337211i	$-0.109484\pi$
$164$	−1.48280	+	2.56828i	−0.115787	+	0.200549i
$165$	−4.93647	−	1.36676i	−0.384303	−	0.106402i
$166$	−0.293216	−	0.507865i	−0.0227580	−	0.0394180i
$167$	0.328916	−	0.569700i	0.0254523	−	0.0440847i	−0.853019	−	0.521880i	$-0.825231\pi$
$167$	0.328916	−	0.569700i	0.0254523	−	0.0440847i	0.878471	+	0.477796i	$0.158564\pi$
$168$	−8.50470	−	12.3642i	−0.656152	−	0.953922i
$169$	4.48205	+	7.76315i	0.344773	+	0.597165i
$170$	4.60565	−	7.97722i	0.353237	−	0.611825i
$171$	−13.4198	+	7.45356i	−1.02624	+	0.569988i
$172$	−3.49102	−	6.04663i	−0.266188	−	0.461051i
$173$	−12.2995			−0.935116			−0.467558	−	0.883962i	$-0.654866\pi$
$173$	−12.2995			−0.935116			−0.467558	+	0.883962i	$0.654866\pi$
$174$	−3.39850	−	13.1181i	−0.257639	−	0.994484i
$175$	−2.48623	+	0.904806i	−0.187941	+	0.0683969i
$176$	1.18182	−	2.04698i	0.0890834	−	0.154297i
$177$	−19.6649	−	5.44463i	−1.47811	−	0.409243i
$178$	19.9539	−	34.5611i	1.49560	−	2.59046i
$179$	10.3534	+	17.9326i	0.773849	+	1.34035i	0.935439	+	0.353488i	$0.115004\pi$
$179$	10.3534	+	17.9326i	0.773849	+	1.34035i	−0.161590	+	0.986858i	$0.551662\pi$
$180$	−0.169806	+	10.2231i	−0.0126566	+	0.761984i
$181$	9.89856			0.735754			0.367877	−	0.929874i	$-0.380085\pi$
$181$	9.89856			0.735754			0.367877	+	0.929874i	$0.380085\pi$
$182$	11.6154	−	4.22717i	0.860993	−	0.313339i
$183$	−25.0551	−	6.93699i	−1.85212	−	0.512797i
$184$	−0.709086	−	1.22817i	−0.0522745	−	0.0905422i
$185$	0.0800389			0.00588458
$186$	35.1910	+	9.74333i	2.58033	+	0.714415i
$187$	−11.7136			−0.856583
$188$	−13.1137			−0.956413
$189$	−0.856143	−	13.7210i	−0.0622753	−	0.998059i
$190$	−11.8997			−0.863293
$191$	−14.3165			−1.03590			−0.517951	−	0.855410i	$-0.673305\pi$
$191$	−14.3165			−1.03590			−0.517951	+	0.855410i	$0.673305\pi$
$192$	20.8776	+	5.78038i	1.50671	+	0.417163i
$193$	−5.88311			−0.423476			−0.211738	−	0.977327i	$-0.567912\pi$
$193$	−5.88311			−0.423476			−0.211738	+	0.977327i	$0.567912\pi$
$194$	17.8539	+	30.9238i	1.28183	+	2.22020i
$195$	−3.35345	−	0.928469i	−0.240145	−	0.0664890i
$196$	4.14096	+	23.4950i	0.295783	+	1.67822i
$197$	21.2370			1.51307			0.756536	−	0.653952i	$-0.226890\pi$
$197$	21.2370			1.51307			0.756536	+	0.653952i	$0.226890\pi$
$198$	18.0367	−	10.0178i	1.28181	−	0.711935i
$199$	−1.38845	−	2.40486i	−0.0984246	−	0.170476i	0.812608	−	0.582810i	$-0.198047\pi$
$199$	−1.38845	−	2.40486i	−0.0984246	−	0.170476i	−0.911033	+	0.412334i	$0.864714\pi$
$200$	−1.63738	+	2.83602i	−0.115780	+	0.200537i
$201$	15.1802	+	4.20293i	1.07073	+	0.296452i
$202$	6.61625	−	11.4597i	0.465518	−	0.806300i
$203$	−1.54599	+	8.76577i	−0.108507	+	0.615237i
$204$	5.86389	+	22.6345i	0.410554	+	1.58473i
$205$	−0.870145			−0.0607736
$206$	19.5374	+	33.8398i	1.36124	+	2.35773i
$207$	0.0215766	−	1.29901i	0.00149968	−	0.0902873i
$208$	0.802839	−	1.39056i	0.0556669	−	0.0964179i
$209$	7.56614	+	13.1049i	0.523361	+	0.906488i
$210$	4.58426	−	9.62061i	0.316344	−	0.663885i
$211$	12.9601	−	22.4476i	0.892212	−	1.54536i	0.0549949	−	0.998487i	$-0.482486\pi$
$211$	12.9601	−	22.4476i	0.892212	−	1.54536i	0.837217	−	0.546870i	$-0.184181\pi$
$212$	−14.4762	−	25.0734i	−0.994226	−	1.72205i
$213$	4.92819	+	1.36447i	0.337674	+	0.0934916i
$214$	17.3780	−	30.0996i	1.18794	−	2.05757i
$215$	1.02431	−	1.77416i	0.0698574	−	0.120997i
$216$	−11.7288	−	12.3282i	−0.798041	−	0.838828i
$217$	−18.3727	−	15.4178i	−1.24722	−	1.04663i
$218$	18.7489	+	32.4741i	1.26984	+	2.19942i
$219$	5.07528	+	19.5905i	0.342956	+	1.32380i
$220$	10.0789			0.679522
$221$	−7.95730			−0.535266
$222$	−0.229852	+	0.226066i	−0.0154267	+	0.0151725i
$223$	7.06550	+	12.2378i	0.473141	+	0.819504i	0.999527	−	0.0307411i	$-0.00978674\pi$
$223$	7.06550	+	12.2378i	0.473141	+	0.819504i	−0.526386	+	0.850246i	$0.676453\pi$
$224$	−9.50681	−	7.97778i	−0.635201	−	0.533038i
$225$	−2.62263	+	1.45664i	−0.174842	+	0.0971097i
$226$	12.6044	−	21.8314i	0.838431	−	1.45221i
$227$	2.16066	−	3.74238i	0.143408	−	0.248390i	−0.785370	−	0.619027i	$-0.787527\pi$
$227$	2.16066	−	3.74238i	0.143408	−	0.248390i	0.928778	+	0.370637i	$0.120860\pi$
$228$	21.5354	−	21.1807i	1.42622	−	1.40272i
$229$	−3.63846	−	6.30199i	−0.240436	−	0.416447i	0.720403	−	0.693556i	$-0.243957\pi$
$229$	−3.63846	−	6.30199i	−0.240436	−	0.416447i	−0.960839	+	0.277109i	$0.910624\pi$
$230$	0.503553	−	0.872180i	0.0332033	−	0.0575098i
$231$	−13.5098	+	1.06847i	−0.888882	+	0.0703003i
$232$	5.50860	+	9.54118i	0.361657	+	0.626409i
$233$	1.98252	−	3.43383i	0.129879	−	0.224958i	−0.793750	−	0.608244i	$-0.791874\pi$
$233$	1.98252	−	3.43383i	0.129879	−	0.224958i	0.923630	+	0.383286i	$0.125208\pi$
$234$	12.2527	−	6.80532i	0.800984	−	0.444877i
$235$	−1.92386	−	3.33223i	−0.125499	−	0.217370i
$236$	40.1505			2.61358
$237$	20.5358	+	5.68575i	1.33395	+	0.369329i
$238$	4.23286	−	24.0004i	0.274376	−	1.55572i
$239$	−8.06282	+	13.9652i	−0.521540	+	0.903334i	0.478146	+	0.878280i	$0.341309\pi$
$239$	−8.06282	+	13.9652i	−0.521540	+	0.903334i	−0.999686	+	0.0250538i	$0.992024\pi$
$240$	−0.347182	−	1.34012i	−0.0224105	−	0.0865043i
$241$	0.770016	−	1.33371i	0.0496011	−	0.0859116i	−0.840159	−	0.542340i	$-0.817538\pi$
$241$	0.770016	−	1.33371i	0.0496011	−	0.0859116i	0.889760	+	0.456429i	$0.150872\pi$
$242$	2.62138	+	4.54036i	0.168509	+	0.291865i
$243$	−3.40609	−	15.2118i	−0.218501	−	0.975837i
$244$	51.1557			3.27491
$245$	−5.36265	+	4.49911i	−0.342607	+	0.287437i
$246$	2.49884	−	2.45768i	0.159320	−	0.156696i
$247$	5.13984	+	8.90247i	0.327040	+	0.566451i
$248$	−29.6868			−1.88511
$249$	0.109537	+	0.422812i	0.00694164	+	0.0267946i
$250$	−2.32555			−0.147080
$251$	−6.88146			−0.434354			−0.217177	−	0.976132i	$-0.569685\pi$
$251$	−6.88146			−0.434354			−0.217177	+	0.976132i	$0.569685\pi$
$252$	8.82773	+	25.5706i	0.556095	+	1.61079i
$253$	−1.28069			−0.0805164
$254$	−14.9022			−0.935049
$255$	−4.89123	+	4.81067i	−0.306301	+	0.301256i
$256$	−20.8092			−1.30058
$257$	−6.40026	−	11.0856i	−0.399237	−	0.691499i	0.594395	−	0.804174i	$-0.297392\pi$
$257$	−6.40026	−	11.0856i	−0.399237	−	0.691499i	−0.993632	+	0.112674i	$0.964058\pi$
$258$	2.06945	+	7.98806i	0.128839	+	0.497315i
$259$	0.198995	−	0.0724196i	0.0123649	−	0.00449994i
$260$	6.84684			0.424623
$261$	−0.167620	+	10.0915i	−0.0103754	+	0.624646i
$262$	−0.130409	−	0.225874i	−0.00805667	−	0.0139546i
$263$	3.83388	−	6.64047i	0.236407	−	0.409469i	−0.723274	−	0.690562i	$-0.757363\pi$
$263$	3.83388	−	6.64047i	0.236407	−	0.409469i	0.959681	+	0.281093i	$0.0906968\pi$
$264$	−11.9590	+	11.7620i	−0.736026	+	0.723902i
$265$	4.24749	−	7.35687i	0.260921	−	0.451929i
$266$	−29.5853	+	10.7669i	−1.81399	+	0.660161i
$267$	−21.1911	+	20.8421i	−1.29688	+	1.27551i
$268$	−30.9938			−1.89325
$269$	−3.44232	−	5.96227i	−0.209882	−	0.363526i	0.741795	−	0.670626i	$-0.233975\pi$
$269$	−3.44232	−	5.96227i	−0.209882	−	0.363526i	−0.951677	+	0.307100i	$0.900641\pi$
$270$	3.41733	−	11.5906i	0.207972	−	0.705382i
$271$	−2.16184	+	3.74442i	−0.131322	+	0.227457i	−0.924187	−	0.381941i	$-0.875256\pi$
$271$	−2.16184	+	3.74442i	−0.131322	+	0.227457i	0.792864	+	0.609398i	$0.208589\pi$
$272$	−1.58291	−	2.74167i	−0.0959777	−	0.166238i
$273$	−9.17752	+	0.725836i	−0.555449	+	0.0439296i
$274$	−22.3583	+	38.7256i	−1.35071	+	2.33950i
$275$	1.47865	+	2.56109i	0.0891657	+	0.154440i
$276$	0.641121	+	2.47472i	0.0385910	+	0.148961i
$277$	5.40863	−	9.36802i	0.324973	−	0.562870i	−0.656534	−	0.754296i	$-0.727978\pi$
$277$	5.40863	−	9.36802i	0.324973	−	0.562870i	0.981507	+	0.191427i	$0.0613115\pi$
$278$	−16.1486	+	27.9703i	−0.968532	+	1.67755i
$279$	−23.3234	−	13.9873i	−1.39634	−	0.837399i
$280$	−1.50484	+	8.53250i	−0.0899317	+	0.509914i
$281$	−7.45465	−	12.9118i	−0.444707	−	0.770255i	0.553325	−	0.832966i	$-0.313359\pi$
$281$	−7.45465	−	12.9118i	−0.444707	−	0.770255i	−0.998032	+	0.0627106i	$0.980026\pi$
$282$	14.9366	+	4.13548i	0.889460	+	0.246264i
$283$	13.7151			0.815277			0.407638	−	0.913143i	$-0.366352\pi$
$283$	13.7151			0.815277			0.407638	+	0.913143i	$0.366352\pi$
$284$	−10.0620			−0.597072
$285$	8.54146	+	2.36487i	0.505952	+	0.140083i
$286$	−6.90811	−	11.9652i	−0.408485	−	0.707517i
$287$	−2.16338	+	0.787312i	−0.127700	+	0.0464736i
$288$	−12.0685	−	7.23761i	−0.711143	−	0.426480i
$289$	0.655553	−	1.13545i	0.0385620	−	0.0667913i
$290$	−3.91190	+	6.77561i	−0.229715	+	0.397877i
$291$	−6.66970	−	25.7450i	−0.390985	−	1.50920i
$292$	−19.9105	−	34.4860i	−1.16517	−	2.01814i
$293$	−4.89324	+	8.47534i	−0.285866	+	0.495135i	−0.972819	−	0.231568i	$-0.925615\pi$
$293$	−4.89324	+	8.47534i	−0.285866	+	0.495135i	0.686953	+	0.726702i	$0.258948\pi$
$294$	2.69272	−	28.0669i	0.157043	−	1.63689i
$295$	5.89034	+	10.2024i	0.342949	+	0.594005i
$296$	0.131054	−	0.226992i	0.00761735	−	0.0131936i
$297$	−14.9374	+	3.60618i	−0.866756	+	0.209252i
$298$	13.1502	+	22.7769i	0.761773	+	1.31943i
$299$	−0.870002			−0.0503135
$300$	4.20865	−	4.13933i	0.242987	−	0.238984i
$301$	0.941401	−	5.33776i	0.0542615	−	0.307664i
$302$	−12.2258	+	21.1757i	−0.703515	+	1.21852i
$303$	−7.02650	+	6.91076i	−0.403662	+	0.397013i
$304$	−2.04489	+	3.54185i	−0.117282	+	0.203139i
$305$	7.50487	+	12.9988i	0.429728	+	0.744310i
$306$	0.458938	−	27.6301i	0.0262358	−	1.57951i
$307$	−11.5120			−0.657025			−0.328513	−	0.944500i	$-0.606547\pi$
$307$	−11.5120			−0.657025			−0.328513	+	0.944500i	$0.606547\pi$
$308$	25.0585	−	9.11949i	1.42784	−	0.519631i
$309$	−7.29863	−	28.1726i	−0.415204	−	1.60268i
$310$	−10.5410	−	18.2575i	−0.598686	−	1.03695i
$311$	16.6973			0.946816			0.473408	−	0.880843i	$-0.343024\pi$
$311$	16.6973			0.946816			0.473408	+	0.880843i	$0.343024\pi$
$312$	−8.12402	+	7.99020i	−0.459932	+	0.452356i
$313$	4.49036			0.253810			0.126905	−	0.991915i	$-0.459496\pi$
$313$	4.49036			0.253810			0.126905	+	0.991915i	$0.459496\pi$
$314$	4.85565			0.274020
$315$	−5.20247	+	5.99452i	−0.293126	+	0.337753i
$316$	−41.9287			−2.35867
$317$	−11.6864			−0.656372			−0.328186	−	0.944613i	$-0.606437\pi$
$317$	−11.6864			−0.656372			−0.328186	+	0.944613i	$0.606437\pi$
$318$	8.58137	+	33.1240i	0.481219	+	1.85750i
$319$	9.94917			0.557047
$320$	−6.25358	−	10.8315i	−0.349586	−	0.605501i
$321$	−18.4556	+	18.1516i	−1.03009	+	1.01312i
$322$	0.462795	−	2.62406i	0.0257905	−	0.146233i
$323$	20.2678			1.12773
$324$	14.4461	+	27.0587i	0.802559	+	1.50326i
$325$	1.00448	+	1.73980i	0.0557183	+	0.0965070i
$326$	22.6464	−	39.2248i	1.25427	−	2.17246i
$327$	−7.00407	−	27.0356i	−0.387326	−	1.49507i
$328$	−1.42476	+	2.46775i	−0.0786690	+	0.136259i
$329$	−7.79818	−	6.54395i	−0.429927	−	0.360780i
$330$	−11.4800	−	3.17846i	−0.631952	−	0.174968i
$331$	−7.25961			−0.399024			−0.199512	−	0.979895i	$-0.563936\pi$
$331$	−7.25961			−0.399024			−0.199512	+	0.979895i	$0.563936\pi$
$332$	−0.429718	−	0.744293i	−0.0235838	−	0.0408484i
$333$	0.209912	−	0.116588i	0.0115031	−	0.00638900i
$334$	0.764910	−	1.32486i	0.0418540	−	0.0724933i
$335$	−4.54700	−	7.87563i	−0.248429	−	0.430292i
$336$	−2.07572	−	3.01771i	−0.113240	−	0.164630i
$337$	3.31859	−	5.74796i	0.180775	−	0.313111i	−0.761370	−	0.648318i	$-0.775473\pi$
$337$	3.31859	−	5.74796i	0.180775	−	0.313111i	0.942145	+	0.335207i	$0.108806\pi$
$338$	10.4232	+	18.0536i	0.566949	+	0.981984i
$339$	−13.3859	+	13.1654i	−0.727025	+	0.715049i
$340$	6.74974	−	11.6909i	0.366056	−	0.634027i
$341$	−13.4045	+	23.2172i	−0.725892	+	1.25728i
$342$	−31.2084	+	17.3336i	−1.68756	+	0.937294i
$343$	−9.26196	+	16.0380i	−0.500099	+	0.865968i
$344$	−3.35437	−	5.80993i	−0.180855	−	0.313251i
$345$	−0.534777	+	0.525968i	−0.0287914	+	0.0283172i
$346$	−28.6031			−1.53771
$347$	2.90093			0.155730			0.0778649	−	0.996964i	$-0.475190\pi$
$347$	2.90093			0.155730			0.0778649	+	0.996964i	$0.475190\pi$
$348$	−4.98061	−	19.2251i	−0.266989	−	1.03057i
$349$	−3.58299	−	6.20592i	−0.191793	−	0.332195i	0.754051	−	0.656815i	$-0.228097\pi$
$349$	−3.58299	−	6.20592i	−0.191793	−	0.332195i	−0.945845	+	0.324620i	$0.894764\pi$
$350$	−5.78184	+	2.10417i	−0.309052	+	0.112472i
$351$	−10.1473	+	2.44975i	−0.541623	+	0.130758i
$352$	−6.93602	+	12.0135i	−0.369691	+	0.640324i
$353$	−0.866059	+	1.50006i	−0.0460956	+	0.0798400i	−0.888153	−	0.459549i	$-0.848011\pi$
$353$	−0.866059	+	1.50006i	−0.0460956	+	0.0798400i	0.842057	+	0.539389i	$0.181345\pi$
$354$	−45.7317	−	12.6617i	−2.43061	−	0.672963i
$355$	−1.47617	−	2.55679i	−0.0783467	−	0.135701i
$356$	29.2430	−	50.6504i	1.54988	−	2.68447i
$357$	−7.80800	+	16.3860i	−0.413243	+	0.867240i
$358$	24.0773	+	41.7031i	1.27252	+	2.20408i
$359$	2.90961	−	5.03960i	0.153564	−	0.265980i	−0.778972	−	0.627059i	$-0.784258\pi$
$359$	2.90961	−	5.03960i	0.153564	−	0.265980i	0.932535	+	0.361079i	$0.117592\pi$
$360$	−0.163159	+	9.82291i	−0.00859925	+	0.517713i
$361$	−3.59153	−	6.22071i	−0.189028	−	0.327406i
$362$	23.0196			1.20988
$363$	−0.979273	−	3.77998i	−0.0513985	−	0.198397i
$364$	17.0228	−	6.19506i	0.892238	−	0.324710i
$365$	5.84200	−	10.1186i	0.305784	−	0.529633i
$366$	−58.2667	−	16.1323i	−3.04565	−	0.843248i
$367$	2.11692	−	3.66662i	0.110502	−	0.191396i	−0.805470	−	0.592636i	$-0.798087\pi$
$367$	2.11692	−	3.66662i	0.110502	−	0.191396i	0.915973	+	0.401240i	$0.131421\pi$
$368$	−0.173065	−	0.299757i	−0.00902164	−	0.0156259i
$369$	−2.28207	+	1.26749i	−0.118800	+	0.0659830i
$370$	0.186134			0.00967665
$371$	3.90369	−	22.1340i	0.202670	−	1.14914i
$372$	51.5736	+	14.2792i	2.67397	+	0.740341i
$373$	2.70674	+	4.68820i	0.140149	+	0.242746i	0.927553	−	0.373692i	$-0.121908\pi$
$373$	2.70674	+	4.68820i	0.140149	+	0.242746i	−0.787403	+	0.616438i	$0.788575\pi$
$374$	−27.2405			−1.40857
$375$	1.66925	+	0.462165i	0.0861998	+	0.0238661i
$376$	−12.6003			−0.649813
$377$	6.75869			0.348090
$378$	−1.99100	−	31.9089i	−0.102406	−	1.64122i
$379$	16.3583			0.840268			0.420134	−	0.907462i	$-0.361983\pi$
$379$	16.3583			0.840268			0.420134	+	0.907462i	$0.361983\pi$
$380$	−17.4394			−0.894621
$381$	10.6967	+	2.96158i	0.548006	+	0.151726i
$382$	−33.2936			−1.70345
$383$	1.25957	+	2.18164i	0.0643611	+	0.111477i	0.896410	−	0.443225i	$-0.146166\pi$
$383$	1.25957	+	2.18164i	0.0643611	+	0.111477i	−0.832049	+	0.554702i	$0.812832\pi$
$384$	32.8917	+	9.10670i	1.67850	+	0.464725i
$385$	5.99354	+	5.02957i	0.305459	+	0.256330i
$386$	−13.6814			−0.696367
$387$	0.102069	−	6.14502i	0.00518847	−	0.312369i
$388$	26.1655	+	45.3199i	1.32835	+	2.30077i
$389$	−17.6491	+	30.5692i	−0.894847	+	1.54992i	−0.0608531	+	0.998147i	$0.519382\pi$
$389$	−17.6491	+	30.5692i	−0.894847	+	1.54992i	−0.833994	+	0.551774i	$0.813951\pi$
$390$	−7.79860	−	2.15920i	−0.394897	−	0.109335i
$391$	−0.857663	+	1.48552i	−0.0433739	+	0.0751258i
$392$	3.97887	+	22.5753i	0.200963	+	1.14023i
$393$	0.0487170	+	0.188047i	0.00245745	+	0.00948571i
$394$	49.3876			2.48811
$395$	−6.15121	−	10.6542i	−0.309501	−	0.536071i
$396$	26.4333	−	14.6814i	1.32833	−	0.737770i
$397$	−7.06116	+	12.2303i	−0.354390	+	0.613821i	−0.987013	−	0.160639i	$-0.948645\pi$
$397$	−7.06116	+	12.2303i	−0.354390	+	0.613821i	0.632624	+	0.774459i	$0.281978\pi$
$398$	−3.22890	−	5.59262i	−0.161850	−	0.280333i
$399$	23.3758	−	1.84875i	1.17025	−	0.0925534i
$400$	−0.399631	+	0.692181i	−0.0199815	+	0.0346090i
$401$	−0.924439	−	1.60117i	−0.0461643	−	0.0799589i	0.842020	−	0.539446i	$-0.181366\pi$
$401$	−0.924439	−	1.60117i	−0.0461643	−	0.0799589i	−0.888184	+	0.459488i	$0.848033\pi$
$402$	35.3022	+	9.77411i	1.76071	+	0.487488i
$403$	−9.10594	+	15.7719i	−0.453599	+	0.785656i
$404$	9.69633	−	16.7945i	0.482411	−	0.835560i
$405$	−4.75637	+	7.64048i	−0.236346	+	0.379658i
$406$	−3.59526	+	20.3852i	−0.178430	+	1.01170i
$407$	−0.118349	−	0.204987i	−0.00586635	−	0.0101608i
$408$	5.63435	+	21.7485i	0.278942	+	1.07671i
$409$	−23.8400			−1.17881			−0.589406	−	0.807837i	$-0.700638\pi$
$409$	−23.8400			−1.17881			−0.589406	+	0.807837i	$0.700638\pi$
$410$	−2.02356			−0.0999366
$411$	23.7446	−	23.3535i	1.17124	−	1.15194i
$412$	28.6327	+	49.5934i	1.41063	+	2.44329i
$413$	23.8759	+	20.0358i	1.17486	+	0.985897i
$414$	0.0501775	−	3.02090i	0.00246609	−	0.148469i
$415$	0.126085	−	0.218385i	0.00618926	−	0.0107201i
$416$	−4.71179	+	8.16105i	−0.231014	+	0.400129i
$417$	17.1500	−	16.8675i	0.839838	−	0.826004i
$418$	17.5954	+	30.4762i	0.860620	+	1.49064i
$419$	13.9024	−	24.0796i	0.679175	−	1.17637i	−0.296054	−	0.955171i	$-0.595671\pi$
$419$	13.9024	−	24.0796i	0.679175	−	1.17637i	0.975230	−	0.221195i	$-0.0709957\pi$
$420$	6.71838	−	14.0993i	0.327823	−	0.687976i
$421$	−15.7054	−	27.2025i	−0.765434	−	1.32577i	−0.940017	−	0.341128i	$-0.889191\pi$
$421$	−15.7054	−	27.2025i	−0.765434	−	1.32577i	0.174583	−	0.984643i	$-0.444142\pi$
$422$	30.1394	−	52.2029i	1.46716	−	2.54120i
$423$	−9.89945	−	5.93681i	−0.481328	−	0.288658i
$424$	−13.9095	−	24.0919i	−0.675505	−	1.17001i
$425$	3.96092			0.192133
$426$	11.4607	+	3.17313i	0.555274	+	0.153739i
$427$	30.4202	+	25.5276i	1.47214	+	1.23537i
$428$	25.4681	−	44.1120i	1.23104	−	2.13223i
$429$	2.58067	+	9.96136i	0.124596	+	0.480939i
$430$	2.38208	−	4.12589i	0.114874	−	0.198968i
$431$	−17.5172	−	30.3406i	−0.843772	−	1.46146i	−0.886683	−	0.462378i	$-0.846996\pi$
$431$	−17.5172	−	30.3406i	−0.843772	−	1.46146i	0.0429109	−	0.999079i	$-0.486337\pi$
$432$	−2.86261	−	3.00892i	−0.137727	−	0.144767i
$433$	−28.3872			−1.36420			−0.682101	−	0.731258i	$-0.738933\pi$
$433$	−28.3872			−1.36420			−0.682101	+	0.731258i	$0.738933\pi$
$434$	−42.7267	−	35.8547i	−2.05095	−	1.72108i
$435$	4.15446	−	4.08603i	0.199191	−	0.195910i
$436$	27.4772	+	47.5919i	1.31592	+	2.27924i
$437$	2.21595			0.106003
$438$	11.8028	+	45.5587i	0.563960	+	2.17688i
$439$	−10.3905			−0.495910			−0.247955	−	0.968772i	$-0.579759\pi$
$439$	−10.3905			−0.495910			−0.247955	+	0.968772i	$0.579759\pi$
$440$	9.68441			0.461686
$441$	−7.51066	+	19.6110i	−0.357650	+	0.933856i
$442$	−18.5051			−0.880197
$443$	14.2769			0.678318			0.339159	−	0.940729i	$-0.389858\pi$
$443$	14.2769			0.678318			0.339159	+	0.940729i	$0.389858\pi$
$444$	−0.336856	+	0.331307i	−0.0159865	+	0.0157231i
$445$	17.1606			0.813489
$446$	16.4312	+	28.4596i	0.778038	+	1.34760i
$447$	−4.91256	−	18.9624i	−0.232356	−	0.896891i
$448$	−25.3483	−	21.2714i	−1.19759	−	1.00498i
$449$	7.89891			0.372773			0.186386	−	0.982477i	$-0.440322\pi$
$449$	7.89891			0.372773			0.186386	+	0.982477i	$0.440322\pi$
$450$	−6.09905	+	3.38749i	−0.287512	+	0.159688i
$451$	1.28664	+	2.22852i	0.0605854	+	0.104937i
$452$	18.4721	−	31.9947i	0.868857	−	1.50490i
$453$	12.9839	−	12.7700i	0.610035	−	0.599987i
$454$	5.02472	−	8.70307i	0.235822	−	0.408456i
$455$	4.07154	+	3.41669i	0.190877	+	0.160177i
$456$	20.6924	−	20.3516i	0.969011	−	0.953050i
$457$	27.3852			1.28103			0.640513	−	0.767948i	$-0.278722\pi$
$457$	27.3852			1.28103			0.640513	+	0.767948i	$0.278722\pi$
$458$	−8.46140	−	14.6556i	−0.395375	−	0.684810i
$459$	−5.82047	+	19.7414i	−0.271676	+	0.921449i
$460$	0.737974	−	1.27821i	0.0344082	−	0.0595968i
$461$	16.7801	+	29.0640i	0.781528	+	1.35365i	0.931052	+	0.364888i	$0.118893\pi$
$461$	16.7801	+	29.0640i	0.781528	+	1.35365i	−0.149524	+	0.988758i	$0.547774\pi$
$462$	−31.4177	+	2.48478i	−1.46169	+	0.115602i
$463$	3.99562	−	6.92062i	0.185692	−	0.321629i	−0.758117	−	0.652118i	$-0.773881\pi$
$463$	3.99562	−	6.92062i	0.185692	−	0.321629i	0.943810	+	0.330490i	$0.107214\pi$
$464$	1.34447	+	2.32869i	0.0624155	+	0.108107i
$465$	3.93780	+	15.1999i	0.182611	+	0.704877i
$466$	4.61045	−	7.98554i	0.213575	−	0.369923i
$467$	−17.7951	+	30.8220i	−0.823460	+	1.42627i	0.0796308	+	0.996824i	$0.474626\pi$
$467$	−17.7951	+	30.8220i	−0.823460	+	1.42627i	−0.903091	+	0.429450i	$0.858707\pi$
$468$	17.9567	−	9.97342i	0.830050	−	0.461021i
$469$	−18.4308	−	15.4665i	−0.851055	−	0.714175i
$470$	−4.47403	−	7.74925i	−0.206372	−	0.357446i
$471$	−3.48533	−	0.964983i	−0.160596	−	0.0444641i
$472$	38.5788			1.77574
$473$	−6.05837			−0.278564
$474$	47.7570	+	13.2225i	2.19355	+	0.607329i
$475$	−2.55847	−	4.43140i	−0.117391	−	0.203327i
$476$	6.20340	−	35.1734i	0.284332	−	1.61217i
$477$	0.423249	−	25.4814i	0.0193792	−	1.16671i
$478$	−18.7505	+	32.4767i	−0.857626	+	1.48545i
$479$	2.09591	−	3.63023i	0.0957647	−	0.165869i	−0.814163	−	0.580637i	$-0.802804\pi$
$479$	2.09591	−	3.63023i	0.0957647	−	0.165869i	0.909927	+	0.414767i	$0.136137\pi$
$480$	2.03758	+	7.86503i	0.0930024	+	0.358988i
$481$	−0.0803972	−	0.139252i	−0.00366580	−	0.00634934i
$482$	1.79071	−	3.10160i	0.0815645	−	0.141274i
$483$	−0.853679	+	1.79155i	−0.0388437	+	0.0815182i
$484$	3.84172	+	6.65405i	0.174624	+	0.302457i
$485$	−7.67728	+	13.2974i	−0.348608	+	0.603806i
$486$	−7.92102	−	35.3757i	−0.359305	−	1.60468i
$487$	−2.62050	−	4.53883i	−0.118746	−	0.205674i	0.800525	−	0.599299i	$-0.204554\pi$
$487$	−2.62050	−	4.53883i	−0.118746	−	0.205674i	−0.919271	+	0.393625i	$0.871221\pi$
$488$	49.1532			2.22506
$489$	−24.0507	+	23.6545i	−1.08761	+	1.06969i
$490$	−12.4711	+	10.4629i	−0.563387	+	0.472665i
$491$	−1.74427	+	3.02116i	−0.0787177	+	0.136343i	−0.902697	−	0.430277i	$-0.858416\pi$
$491$	−1.74427	+	3.02116i	−0.0787177	+	0.136343i	0.823979	+	0.566620i	$0.191749\pi$
$492$	3.66214	−	3.60181i	0.165102	−	0.162382i
$493$	6.66283	−	11.5404i	0.300079	−	0.519752i
$494$	11.9529	+	20.7031i	0.537788	+	0.931477i
$495$	7.60854	+	4.56293i	0.341978	+	0.205088i
$496$	−7.24559			−0.325337
$497$	−5.98349	−	5.02113i	−0.268396	−	0.225228i
$498$	0.254734	+	0.983270i	0.0114149	+	0.0440614i
$499$	3.53333	+	6.11990i	0.158173	+	0.273964i	0.934210	−	0.356723i	$-0.116106\pi$
$499$	3.53333	+	6.11990i	0.158173	+	0.273964i	−0.776037	+	0.630688i	$0.782773\pi$
$500$	−3.40817			−0.152418
$501$	−0.812340	+	0.798959i	−0.0362927	+	0.0356948i
$502$	−16.0031			−0.714255
$503$	−4.16784			−0.185835			−0.0929174	−	0.995674i	$-0.529619\pi$
$503$	−4.16784			−0.185835			−0.0929174	+	0.995674i	$0.529619\pi$
$504$	8.48217	+	24.5696i	0.377826	+	1.09442i
$505$	5.69006			0.253204
$506$	−2.97831			−0.132402
$507$	−3.89382	−	15.0301i	−0.172931	−	0.667510i
$508$	−21.8397			−0.968980
$509$	−9.99813	−	17.3173i	−0.443159	−	0.767575i	0.554762	−	0.832009i	$-0.312809\pi$
$509$	−9.99813	−	17.3173i	−0.443159	−	0.767575i	−0.997922	+	0.0644340i	$0.979476\pi$
$510$	−11.3748	+	11.1874i	−0.503684	+	0.495388i
$511$	5.36913	−	30.4431i	0.237516	−	1.34672i
$512$	−8.98394			−0.397038
$513$	25.8459	−	6.23969i	1.14112	−	0.275489i
$514$	−14.8841	−	25.7800i	−0.656510	−	1.13711i
$515$	−8.40122	+	14.5513i	−0.370202	+	0.641208i
$516$	3.03285	+	11.7068i	0.133514	+	0.515362i
$517$	−5.68942	+	9.85437i	−0.250221	+	0.433395i
$518$	0.462772	−	0.168415i	0.0203330	−	0.00739974i
$519$	20.5310	+	5.68442i	0.901212	+	0.249518i
$520$	6.57883			0.288501
$521$	−9.66649	−	16.7429i	−0.423497	−	0.733518i	0.572782	−	0.819708i	$-0.305864\pi$
$521$	−9.66649	−	16.7429i	−0.423497	−	0.733518i	−0.996279	+	0.0861898i	$0.972531\pi$
$522$	−0.389808	+	23.4682i	−0.0170614	+	1.02717i
$523$	3.14491	−	5.44714i	0.137517	−	0.238187i	−0.789039	−	0.614343i	$-0.789421\pi$
$523$	3.14491	−	5.44714i	0.137517	−	0.238187i	0.926556	+	0.376156i	$0.122754\pi$
$524$	−0.191118	−	0.331026i	−0.00834904	−	0.0144610i
$525$	4.56831	−	0.361301i	0.199377	−	0.0157684i
$526$	8.91586	−	15.4427i	0.388750	−	0.673335i
$527$	17.9536	+	31.0965i	0.782070	+	1.35459i
$528$	−2.91881	+	2.87073i	−0.127025	+	0.124932i
$529$	11.4062	−	19.7562i	0.495923	−	0.858964i
$530$	9.87774	−	17.1087i	0.429062	−	0.743156i
$531$	30.3094	+	18.1769i	1.31532	+	0.788811i
$532$	−43.3582	+	15.7792i	−1.87982	+	0.684117i
$533$	0.874040	+	1.51388i	0.0378589	+	0.0655735i
$534$	−49.2809	+	48.4692i	−2.13260	+	2.09747i
$535$	14.9453			0.646142
$536$	−29.7806			−1.28633
$537$	−8.99460	−	34.7190i	−0.388146	−	1.49824i
$538$	−8.00527	−	13.8655i	−0.345132	−	0.597786i
$539$	19.4521	+	7.08166i	0.837861	+	0.305029i
$540$	5.00821	−	16.9864i	0.215519	−	0.730980i
$541$	13.1057	−	22.6998i	0.563460	−	0.975941i	−0.433732	−	0.901042i	$-0.642803\pi$
$541$	13.1057	−	22.6998i	0.563460	−	0.975941i	0.997191	−	0.0748985i	$-0.0238633\pi$
$542$	−5.02746	+	8.70782i	−0.215948	+	0.374033i
$543$	−16.5232	−	4.57477i	−0.709078	−	0.196322i
$544$	9.28992	+	16.0906i	0.398302	+	0.689880i
$545$	−8.06216	+	13.9641i	−0.345345	+	0.598155i
$546$	−21.3427	+	1.68796i	−0.913385	+	0.0722382i
$547$	13.7438	+	23.8049i	0.587642	+	1.01783i	0.994540	+	0.104353i	$0.0332770\pi$
$547$	13.7438	+	23.8049i	0.587642	+	1.01783i	−0.406898	+	0.913474i	$0.633390\pi$
$548$	−32.7668	+	56.7537i	−1.39973	+	2.42440i
$549$	38.6172	+	23.1592i	1.64814	+	0.988409i
$550$	3.43866	+	5.95593i	0.146625	+	0.253962i
$551$	−17.2148			−0.733377
$552$	0.616025	+	2.37785i	0.0262198	+	0.101208i
$553$	−24.9333	−	20.9231i	−1.06027	−	0.889742i
$554$	12.5780	−	21.7858i	0.534389	−	0.925588i
$555$	−0.133605	−	0.0369912i	−0.00567122	−	0.00157019i
$556$	−23.6664	+	40.9914i	−1.00368	+	1.73842i
$557$	10.3852	+	17.9877i	0.440035	+	0.762162i	0.997692	−	0.0679092i	$-0.0216328\pi$
$557$	10.3852	+	17.9877i	0.440035	+	0.762162i	−0.557657	+	0.830072i	$0.688299\pi$
$558$	−54.2397	−	32.5281i	−2.29615	−	1.37703i
$559$	−4.11558			−0.174071
$560$	−0.367284	+	2.08251i	−0.0155206	+	0.0880020i
$561$	19.5530	+	5.41362i	0.825527	+	0.228563i
$562$	−17.3361	−	30.0271i	−0.731280	−	1.26661i
$563$	−28.4633			−1.19959			−0.599794	−	0.800155i	$-0.704751\pi$
$563$	−28.4633			−1.19959			−0.599794	+	0.800155i	$0.704751\pi$
$564$	21.8900	+	6.06069i	0.921737	+	0.255201i
$565$	10.8399			0.456039
$566$	31.8950			1.34065
$567$	−4.91227	+	23.2996i	−0.206296	+	0.978490i
$568$	−9.66816			−0.405667
$569$	−3.94111			−0.165220			−0.0826101	−	0.996582i	$-0.526326\pi$
$569$	−3.94111			−0.165220			−0.0826101	+	0.996582i	$0.526326\pi$
$570$	19.8636	+	5.49962i	0.831993	+	0.230354i
$571$	0.731159			0.0305980			0.0152990	−	0.999883i	$-0.495130\pi$
$571$	0.731159			0.0305980			0.0152990	+	0.999883i	$0.495130\pi$
$572$	−10.1241	−	17.5354i	−0.423308	−	0.733191i
$573$	23.8978	+	6.61657i	0.998344	+	0.276411i
$574$	−5.03104	+	1.83093i	−0.209991	+	0.0764216i
$575$	0.433062			0.0180600
$576$	−32.1785	−	19.2978i	−1.34077	−	0.804076i
$577$	5.81896	+	10.0787i	0.242247	+	0.419583i	0.961354	−	0.275316i	$-0.0887824\pi$
$577$	5.81896	+	10.0787i	0.242247	+	0.419583i	−0.719107	+	0.694899i	$0.755449\pi$
$578$	1.52452	−	2.64054i	0.0634116	−	0.109832i
$579$	9.82040	+	2.71897i	0.408122	+	0.112997i
$580$	−5.73302	+	9.92988i	−0.238051	+	0.412316i
$581$	0.115879	−	0.657038i	0.00480748	−	0.0272585i
$582$	−15.5107	−	59.8711i	−0.642939	−	2.48174i
$583$	−25.1222			−1.04045
$584$	−19.1311	−	33.1360i	−0.791650	−	1.37118i
$585$	5.16865	+	3.09970i	0.213697	+	0.128157i
$586$	−11.3795	+	19.7098i	−0.470081	+	0.814204i
$587$	12.2189	+	21.1637i	0.504327	+	0.873520i	0.999987	+	0.00500395i	$0.00159281\pi$
$587$	12.2189	+	21.1637i	0.504327	+	0.873520i	−0.495660	+	0.868517i	$0.665074\pi$
$588$	3.94628	−	41.1329i	0.162742	−	1.69629i
$589$	23.1934	−	40.1722i	0.955669	−	1.65527i
$590$	13.6983	+	23.7261i	0.563949	+	0.976788i
$591$	−35.4499	−	9.81500i	−1.45821	−	0.403735i
$592$	0.0319860	−	0.0554014i	0.00131462	−	0.00227698i
$593$	13.2758	−	22.9944i	0.545174	−	0.944268i	−0.453422	−	0.891296i	$-0.649797\pi$
$593$	13.2758	−	22.9944i	0.545174	−	0.944268i	0.998596	−	0.0529726i	$-0.0168696\pi$
$594$	−34.7376	+	8.38634i	−1.42530	+	0.344096i
$595$	9.84775	−	3.58386i	0.403718	−	0.146924i
$596$	19.2721	+	33.3803i	0.789417	+	1.36731i
$597$	1.20623	+	4.65602i	0.0493676	+	0.190558i
$598$	−2.02323			−0.0827360
$599$	26.3662			1.07729			0.538647	−	0.842531i	$-0.318936\pi$
$599$	26.3662			1.07729			0.538647	+	0.842531i	$0.318936\pi$
$600$	4.04391	−	3.97729i	0.165092	−	0.162372i
$601$	8.67608	+	15.0274i	0.353905	+	0.612981i	0.986930	−	0.161150i	$-0.0515204\pi$
$601$	8.67608	+	15.0274i	0.353905	+	0.612981i	−0.633025	+	0.774131i	$0.718187\pi$
$602$	2.18927	−	12.4132i	0.0892281	−	0.505925i
$603$	−23.3971	−	14.0315i	−0.952803	−	0.571407i
$604$	−17.9173	+	31.0337i	−0.729044	+	1.26274i
$605$	−1.12721	+	1.95238i	−0.0458276	+	0.0793757i
$606$	−16.3405	+	16.0713i	−0.663786	+	0.652852i
$607$	13.4702	+	23.3311i	0.546738	+	0.946979i	0.998495	+	0.0548377i	$0.0174641\pi$
$607$	13.4702	+	23.3311i	0.546738	+	0.946979i	−0.451757	+	0.892141i	$0.649203\pi$
$608$	12.0012	−	20.7868i	0.486715	−	0.843014i
$609$	6.63188	−	13.9178i	0.268737	−	0.563977i
$610$	17.4529	+	30.2294i	0.706648	+	1.22395i
$611$	−3.86495	+	6.69429i	−0.156359	+	0.270822i
$612$	0.672589	−	40.4928i	0.0271878	−	1.63683i
$613$	−11.9877	−	20.7633i	−0.484179	−	0.838623i	0.515655	−	0.856796i	$-0.327548\pi$
$613$	−11.9877	−	20.7633i	−0.484179	−	0.838623i	−0.999835	+	0.0181727i	$0.994215\pi$
$614$	−26.7717			−1.08042
$615$	1.45249	+	0.402151i	0.0585701	+	0.0162163i
$616$	24.0776	−	8.76251i	0.970116	−	0.353051i
$617$	−23.1081	+	40.0243i	−0.930295	+	1.61132i	−0.147480	+	0.989065i	$0.547116\pi$
$617$	−23.1081	+	40.0243i	−0.930295	+	1.61132i	−0.782816	+	0.622254i	$0.786217\pi$
$618$	−16.9733	−	65.5167i	−0.682766	−	2.63547i
$619$	−17.1411	+	29.6892i	−0.688958	+	1.19331i	0.283218	+	0.959056i	$0.408598\pi$
$619$	−17.1411	+	29.6892i	−0.688958	+	1.19331i	−0.972175	+	0.234254i	$0.924735\pi$
$620$	−15.4481	−	26.7569i	−0.620411	−	1.07458i
$621$	−0.636373	+	2.15840i	−0.0255368	+	0.0866136i
$622$	38.8303			1.55695
$623$	42.6651	−	15.5270i	1.70934	−	0.622075i
$624$	−1.98281	+	1.95015i	−0.0793759	+	0.0780684i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.4425			0.417368
$627$	−6.57315	−	25.3723i	−0.262506	−	1.01327i
$628$	7.11612			0.283964
$629$	−0.317028			−0.0126407
$630$	−12.0986	+	13.9405i	−0.482019	+	0.555404i
$631$	26.8165			1.06755			0.533774	−	0.845627i	$-0.320773\pi$
$631$	26.8165			1.06755			0.533774	+	0.845627i	$0.320773\pi$
$632$	−40.2874			−1.60255
$633$	−32.0082	+	31.4810i	−1.27221	+	1.25126i
$634$	−27.1772			−1.07934
$635$	−3.20403	−	5.54954i	−0.127148	−	0.220227i
$636$	12.5763	+	48.5443i	0.498682	+	1.92491i
$637$	13.2142	+	4.81072i	0.523566	+	0.190608i
$638$	23.1373			0.916013
$639$	−7.59578	−	4.55527i	−0.300484	−	0.180204i
$640$	−9.85221	−	17.0645i	−0.389443	−	0.674535i
$641$	−7.96623	+	13.7979i	−0.314647	+	0.544985i	−0.979362	−	0.202112i	$-0.935220\pi$
$641$	−7.96623	+	13.7979i	−0.314647	+	0.544985i	0.664715	+	0.747097i	$0.268553\pi$
$642$	−42.9193	+	42.2123i	−1.69389	+	1.66599i
$643$	18.2048	−	31.5317i	0.717929	−	1.24349i	−0.243890	−	0.969803i	$-0.578424\pi$
$643$	18.2048	−	31.5317i	0.717929	−	1.24349i	0.961819	−	0.273686i	$-0.0882430\pi$
$644$	0.678241	−	3.84564i	0.0267264	−	0.151539i
$645$	−2.52979	+	2.48812i	−0.0996103	+	0.0979695i
$646$	47.1337			1.85445
$647$	2.57737	+	4.46414i	0.101327	+	0.175503i	0.912232	−	0.409675i	$-0.134358\pi$
$647$	2.57737	+	4.46414i	0.101327	+	0.175503i	−0.810905	+	0.585178i	$0.801025\pi$
$648$	13.8806	+	25.9995i	0.545281	+	1.02136i
$649$	17.4195	−	30.1714i	0.683774	−	1.18433i
$650$	2.33596	+	4.04599i	0.0916237	+	0.158697i
$651$	23.5432	+	34.2274i	0.922730	+	1.34148i
$652$	33.1891	−	57.4852i	1.29979	−	2.25129i
$653$	14.4922	+	25.1012i	0.567124	+	0.982287i	0.996849	+	0.0793272i	$0.0252772\pi$
$653$	14.4922	+	25.1012i	0.567124	+	0.982287i	−0.429725	+	0.902960i	$0.641389\pi$
$654$	−16.2883	−	62.8726i	−0.636923	−	2.45851i
$655$	0.0560766	−	0.0971274i	0.00219109	−	0.00379508i
$656$	−0.347737	+	0.602297i	−0.0135768	+	0.0235158i
$657$	0.582136	−	35.0471i	0.0227113	−	1.36732i
$658$	−18.1350	−	15.2183i	−0.706977	−	0.593270i
$659$	6.18409	+	10.7112i	0.240898	+	0.417248i	0.960970	−	0.276651i	$-0.0892247\pi$
$659$	6.18409	+	10.7112i	0.240898	+	0.417248i	−0.720072	+	0.693899i	$0.755891\pi$
$660$	−16.8243	−	4.65814i	−0.654885	−	0.181318i
$661$	4.91215			0.191061			0.0955303	−	0.995427i	$-0.469545\pi$
$661$	4.91215			0.191061			0.0955303	+	0.995427i	$0.469545\pi$
$662$	−16.8826			−0.656159
$663$	13.2827	+	3.67759i	0.515859	+	0.142826i
$664$	−0.412897	−	0.715158i	−0.0160235	−	0.0277535i
$665$	−10.3705	−	8.70255i	−0.402150	−	0.337470i
$666$	0.488161	−	0.271131i	0.0189159	−	0.0105061i
$667$	0.728473	−	1.26175i	0.0282066	−	0.0488552i
$668$	1.12100	−	1.94163i	0.0433728	−	0.0751239i
$669$	−6.13821	−	23.6934i	−0.237317	−	0.916041i
$670$	−10.5743	−	18.3151i	−0.408519	−	0.707576i
$671$	22.1941	−	38.4413i	0.856794	−	1.48401i
$672$	12.1822	+	17.7107i	0.469939	+	0.683203i
$673$	−14.0727	−	24.3746i	−0.542461	−	0.939570i	−0.998762	−	0.0497447i	$-0.984159\pi$
$673$	−14.0727	−	24.3746i	−0.542461	−	0.939570i	0.456301	−	0.889826i	$-0.349174\pi$
$674$	7.71753	−	13.3672i	0.297268	−	0.514884i
$675$	5.05104	−	1.21942i	0.194415	−	0.0469355i
$676$	15.2756	+	26.4581i	0.587522	+	1.01762i
$677$	20.4664			0.786587			0.393294	−	0.919413i	$-0.371336\pi$
$677$	20.4664			0.786587			0.393294	+	0.919413i	$0.371336\pi$
$678$	−31.1296	+	30.6169i	−1.19553	+	1.17583i
$679$	−7.05587	+	40.0069i	−0.270779	+	1.53532i
$680$	6.48552	−	11.2333i	0.248708	−	0.430776i
$681$	−5.33629	+	5.24839i	−0.204487	+	0.201119i
$682$	−31.1727	+	53.9927i	−1.19366	+	2.06749i
$683$	−9.41989	−	16.3157i	−0.360442	−	0.624304i	0.627592	−	0.778543i	$-0.284041\pi$
$683$	−9.41989	−	16.3157i	−0.360442	−	0.624304i	−0.988034	+	0.154239i	$0.950707\pi$
$684$	−45.7370	+	25.4030i	−1.74880	+	0.971307i
$685$	−19.2284			−0.734679
$686$	−21.5391	+	37.2970i	−0.822367	+	1.42401i
$687$	3.16094	+	12.2012i	0.120597	+	0.465504i
$688$	−0.818692	−	1.41802i	−0.0312123	−	0.0540614i
$689$	−17.0660			−0.650164
$690$	−1.24365	+	1.22316i	−0.0473449	+	0.0465650i
$691$	−34.0384			−1.29488			−0.647442	−	0.762115i	$-0.724161\pi$
$691$	−34.0384			−1.29488			−0.647442	+	0.762115i	$0.724161\pi$
$692$	−41.9189			−1.59352
$693$	23.0451	+	4.46023i	0.875412	+	0.169430i
$694$	6.74624			0.256084
$695$	−13.8880			−0.526804
$696$	−4.78564	−	18.4725i	−0.181399	−	0.700199i
$697$	3.44657			0.130548
$698$	−8.33241	−	14.4322i	−0.315386	−	0.546265i
$699$	−4.89633	+	4.81568i	−0.185196	+	0.182146i
$700$	−8.47347	+	3.08373i	−0.320267	+	0.116554i
$701$	−44.6921			−1.68800			−0.843998	−	0.536346i	$-0.819804\pi$
$701$	−44.6921			−1.68800			−0.843998	+	0.536346i	$0.819804\pi$
$702$	−23.5980	+	5.69702i	−0.890650	+	0.215020i
$703$	0.204777	+	0.354684i	0.00772331	+	0.0133772i
$704$	−18.4937	+	32.0320i	−0.697007	+	1.20725i
$705$	1.67137	+	6.45147i	0.0629475	+	0.242976i
$706$	−2.01406	+	3.48845i	−0.0758001	+	0.131290i
$707$	14.1468	−	5.14840i	0.532045	−	0.193625i
$708$	−67.0214	−	18.5562i	−2.51882	−	0.697384i
$709$	−31.3158			−1.17609			−0.588045	−	0.808828i	$-0.700102\pi$
$709$	−31.3158			−1.17609			−0.588045	+	0.808828i	$0.700102\pi$
$710$	−3.43289	−	5.94594i	−0.128834	−	0.223147i
$711$	−31.6517	−	18.9819i	−1.18703	−	0.711877i
$712$	28.0983	−	48.6677i	1.05303	−	1.82390i
$713$	1.96293	+	3.39990i	0.0735124	+	0.127327i
$714$	−18.1579	+	38.1065i	−0.679541	+	1.42610i
$715$	2.97053	−	5.14511i	0.111092	−	0.192416i
$716$	35.2861	+	61.1173i	1.31870	+	2.28406i
$717$	19.9131	−	19.5851i	0.743669	−	0.731419i
$718$	6.76644	−	11.7198i	0.252521	−	0.437380i
$719$	21.5997	−	37.4118i	0.805533	−	1.39522i	−0.110398	−	0.993887i	$-0.535213\pi$
$719$	21.5997	−	37.4118i	0.805533	−	1.39522i	0.915931	−	0.401336i	$-0.131454\pi$
$720$	−0.0398219	+	2.39745i	−0.00148407	+	0.0893478i
$721$	−7.72120	+	43.7794i	−0.287553	+	1.63043i
$722$	−8.35227	−	14.4665i	−0.310839	−	0.538389i
$723$	−1.90174	+	1.87042i	−0.0707266	+	0.0695616i
$724$	33.7359			1.25379
$725$	−3.36428			−0.124946
$726$	−2.27734	−	8.79052i	−0.0845202	−	0.326247i
$727$	−0.462646	−	0.801327i	−0.0171586	−	0.0297196i	0.857319	−	0.514786i	$-0.172129\pi$
$727$	−0.462646	−	0.801327i	−0.0171586	−	0.0297196i	−0.874477	+	0.485067i	$0.838795\pi$
$728$	16.3565	−	5.95256i	0.606211	−	0.220617i
$729$	−1.34474	+	26.9665i	−0.0498051	+	0.998759i
$730$	13.5858	−	23.5313i	0.502834	−	0.870934i
$731$	−4.05721	+	7.02730i	−0.150062	+	0.259914i
$732$	−85.3918	−	23.6424i	−3.15617	−	0.873848i
$733$	16.1042	+	27.8934i	0.594824	+	1.03027i	0.993572	+	0.113205i	$0.0361116\pi$
$733$	16.1042	+	27.8934i	0.594824	+	1.03027i	−0.398748	+	0.917061i	$0.630555\pi$
$734$	4.92300	−	8.52689i	0.181711	−	0.314733i
$735$	11.0310	−	5.03171i	0.406883	−	0.185597i
$736$	1.01570	+	1.75925i	0.0374393	+	0.0648467i
$737$	−13.4468	+	23.2905i	−0.495319	+	0.857918i
$738$	−5.30705	+	2.94761i	−0.195355	+	0.108503i
$739$	3.96081	+	6.86033i	0.145701	+	0.252361i	0.929634	−	0.368484i	$-0.120123\pi$
$739$	3.96081	+	6.86033i	0.145701	+	0.252361i	−0.783933	+	0.620845i	$0.786790\pi$
$740$	0.272786			0.0100278
$741$	−4.46528	−	17.2359i	−0.164036	−	0.633178i
$742$	9.07821	−	51.4737i	0.333272	−	1.88966i
$743$	−9.01322	+	15.6114i	−0.330663	+	0.572725i	−0.982642	−	0.185512i	$-0.940606\pi$
$743$	−9.01322	+	15.6114i	−0.330663	+	0.572725i	0.651979	+	0.758237i	$0.273939\pi$
$744$	49.5548	+	13.7202i	1.81677	+	0.503008i
$745$	−5.65469	+	9.79421i	−0.207172	+	0.358832i
$746$	6.29464	+	10.9026i	0.230463	+	0.399174i
$747$	0.0125639	−	0.756405i	0.000459691	−	0.0276754i
$748$	−39.9219			−1.45969
$749$	37.1574	−	13.5226i	1.35770	−	0.494105i
$750$	3.88192	+	1.07479i	0.141748	+	0.0392457i
$751$	−6.30612	−	10.9225i	−0.230113	−	0.398568i	0.727728	−	0.685866i	$-0.240576\pi$
$751$	−6.30612	−	10.9225i	−0.230113	−	0.398568i	−0.957841	+	0.287298i	$0.907243\pi$
$752$	−3.07534			−0.112146
$753$	11.4869	+	3.18037i	0.418606	+	0.115899i
$754$	15.7176			0.572403
$755$	−10.5143			−0.382656
$756$	−2.91788	−	46.7636i	−0.106122	−	1.70078i
$757$	31.5254			1.14581			0.572905	−	0.819622i	$-0.305816\pi$
$757$	31.5254			1.14581			0.572905	+	0.819622i	$0.305816\pi$
$758$	38.0419			1.38174
$759$	2.13780	+	0.591892i	0.0775972	+	0.0214843i
$760$	−16.7567			−0.607830
$761$	−5.04134	−	8.73186i	−0.182748	−	0.316530i	0.760067	−	0.649845i	$-0.225166\pi$
$761$	−5.04134	−	8.73186i	−0.182748	−	0.316530i	−0.942816	+	0.333315i	$0.891833\pi$
$762$	24.8756	+	6.88729i	0.901147	+	0.249500i
$763$	−7.40960	+	42.0126i	−0.268245	+	1.52096i
$764$	−48.7928			−1.76526
$765$	10.3880	−	5.76965i	0.375580	−	0.208602i
$766$	2.92919	+	5.07351i	0.105836	+	0.183313i
$767$	11.8334	−	20.4961i	0.427280	−	0.740071i
$768$	34.7358	+	9.61730i	1.25342	+	0.347034i
$769$	4.49619	−	7.78763i	0.162137	−	0.280829i	−0.773498	−	0.633799i	$-0.781495\pi$
$769$	4.49619	−	7.78763i	0.162137	−	0.280829i	0.935635	+	0.352970i	$0.114828\pi$
$770$	13.9383	+	11.6965i	0.502300	+	0.421512i
$771$	5.56028	+	21.4626i	0.200249	+	0.772957i
$772$	−20.0506			−0.721637
$773$	−17.8964	−	30.9974i	−0.643688	−	1.11490i	−0.984603	−	0.174806i	$-0.944070\pi$
$773$	−17.8964	−	30.9974i	−0.643688	−	1.11490i	0.340915	−	0.940094i	$-0.389263\pi$
$774$	0.237367	−	14.2905i	0.00853197	−	0.513662i
$775$	4.53268	−	7.85083i	0.162819	−	0.282010i
$776$	25.1412	+	43.5459i	0.902517	+	1.56321i
$777$	−0.365643	+	0.0289181i	−0.0131174	+	0.00103743i
$778$	−41.0439	+	71.0901i	−1.47149	+	2.54870i
$779$	−2.22624	−	3.85596i	−0.0797633	−	0.138154i
$780$	−11.4291	−	3.16437i	−0.409228	−	0.113303i
$781$	−4.36545	+	7.56119i	−0.156208	+	0.270561i
$782$	−1.99453	+	3.45464i	−0.0713244	+	0.123538i
$783$	4.94373	−	16.7677i	0.176674	−	0.599230i
$784$	0.971113	+	5.50991i	0.0346826	+	0.196782i
$785$	1.04398	+	1.80823i	0.0372613	+	0.0645384i
$786$	0.113294	+	0.437312i	0.00404105	+	0.0155984i
$787$	−12.5609			−0.447747			−0.223874	−	0.974618i	$-0.571870\pi$
$787$	−12.5609			−0.447747			−0.223874	+	0.974618i	$0.571870\pi$
$788$	72.3792			2.57840
$789$	−9.46871	+	9.31274i	−0.337095	+	0.331542i
$790$	−14.3049	−	24.7769i	−0.508946	−	0.881521i
$791$	26.9505	−	9.80803i	0.958251	−	0.348734i
$792$	25.3986	−	14.1067i	0.902500	−	0.501261i
$793$	15.0769	−	26.1140i	0.535398	−	0.927336i
$794$	−16.4211	+	28.4421i	−0.582762	+	1.00937i
$795$	−10.4902	+	10.3174i	−0.372050	+	0.365922i
$796$	−4.73206	−	8.19618i	−0.167724	−	0.290506i
$797$	−3.44704	+	5.97045i	−0.122101	+	0.211484i	−0.920596	−	0.390517i	$-0.872296\pi$
$797$	−3.44704	+	5.97045i	−0.122101	+	0.211484i	0.798495	+	0.602001i	$0.205630\pi$
$798$	54.3614	−	4.29936i	1.92437	−	0.152196i
$799$	7.62026	+	13.1987i	0.269586	+	0.466936i
$800$	2.34539	−	4.06234i	0.0829222	−	0.143625i
$801$	45.0058	−	24.9969i	1.59020	−	0.883220i
$802$	−2.14982	−	3.72361i	−0.0759130	−	0.131485i
$803$	−34.5530			−1.21935
$804$	51.7365	+	14.3243i	1.82461	+	0.505179i
$805$	1.07669	−	0.391837i	0.0379484	−	0.0138105i
$806$	−21.1763	+	36.6784i	−0.745902	+	1.29194i
$807$	2.99054	+	11.5435i	0.105272	+	0.406349i
$808$	9.31678	−	16.1371i	0.327763	−	0.567702i
$809$	−8.42797	−	14.5977i	−0.296312	−	0.513227i	0.678977	−	0.734159i	$-0.262423\pi$
$809$	−8.42797	−	14.5977i	−0.296312	−	0.513227i	−0.975289	+	0.220932i	$0.929090\pi$
$810$	−11.0612	+	17.7683i	−0.388650	+	0.624314i
$811$	6.95388			0.244184			0.122092	−	0.992519i	$-0.461040\pi$
$811$	6.95388			0.244184			0.122092	+	0.992519i	$0.461040\pi$
$812$	−5.26898	+	29.8752i	−0.184905	+	1.04841i
$813$	5.33920	−	5.25125i	0.187254	−	0.184169i
$814$	−0.275227	−	0.476706i	−0.00964669	−	0.0167086i
$815$	19.4762			0.682222
$816$	1.37516	+	5.30811i	0.0481403	+	0.185821i
$817$	10.4827			0.366742
$818$	−55.4410			−1.93845
$819$	15.6551	+	3.02993i	0.547032	+	0.105874i
$820$	−2.96560			−0.103563
$821$	23.8541			0.832515			0.416258	−	0.909247i	$-0.363341\pi$
$821$	23.8541			0.832515			0.416258	+	0.909247i	$0.363341\pi$
$822$	55.2192	−	54.3096i	1.92599	−	1.89427i
$823$	30.1713			1.05171			0.525853	−	0.850576i	$-0.323746\pi$
$823$	30.1713			1.05171			0.525853	+	0.850576i	$0.323746\pi$
$824$	27.5119	+	47.6520i	0.958423	+	1.66004i
$825$	−1.28459	−	4.95849i	−0.0447236	−	0.172632i
$826$	55.5245	+	46.5942i	1.93194	+	1.62122i
$827$	−21.2692			−0.739603			−0.369802	−	0.929111i	$-0.620574\pi$
$827$	−21.2692			−0.739603			−0.369802	+	0.929111i	$0.620574\pi$
$828$	0.0735367	−	4.42723i	0.00255558	−	0.153857i
$829$	−5.63065	−	9.75257i	−0.195561	−	0.338721i	0.751524	−	0.659706i	$-0.229319\pi$
$829$	−5.63065	−	9.75257i	−0.195561	−	0.338721i	−0.947084	+	0.320985i	$0.895986\pi$
$830$	0.293216	−	0.507865i	0.0101777	−	0.0176283i
$831$	−13.3579	+	13.1379i	−0.463382	+	0.455749i
$832$	−12.5632	+	21.7600i	−0.435549	+	0.754393i
$833$	21.2410	−	17.8206i	0.735959	−	0.617447i
$834$	39.8831	−	39.2261i	1.38104	−	1.35829i
$835$	0.657832			0.0227652
$836$	25.7867	+	44.6638i	0.891850	+	1.54473i
$837$	32.4682	+	34.1276i	1.12226	+	1.17962i
$838$	32.3306	−	55.9982i	1.11684	−	1.93443i
$839$	−16.5892	−	28.7333i	−0.572722	−	0.991984i	−0.996285	−	0.0861170i	$-0.972554\pi$
$839$	−16.5892	−	28.7333i	−0.572722	−	0.991984i	0.423563	−	0.905867i	$-0.360779\pi$
$840$	6.45539	−	13.5474i	0.222732	−	0.467430i
$841$	8.84079	−	15.3127i	0.304855	−	0.528024i
$842$	−36.5236	−	63.2608i	−1.25869	−	2.18011i
$843$	6.47629	+	24.9984i	0.223055	+	0.860990i
$844$	44.1703	−	76.5052i	1.52040	−	2.63342i
$845$	−4.48205	+	7.76315i	−0.154187	+	0.267060i
$846$	−23.0216	−	13.8063i	−0.791500	−	0.474671i
$847$	−1.03597	+	5.87398i	−0.0355964	+	0.201832i
$848$	−3.39486	−	5.88006i	−0.116580	−	0.201922i
$849$	−22.8939	−	6.33863i	−0.785717	−	0.217541i
$850$	9.21130			0.315945
$851$	−0.0346618			−0.00118819
$852$	16.7961	+	4.65032i	0.575424	+	0.159317i
$853$	−1.95782	−	3.39105i	−0.0670346	−	0.116107i	0.830560	−	0.556929i	$-0.188020\pi$
$853$	−1.95782	−	3.39105i	−0.0670346	−	0.116107i	−0.897595	+	0.440822i	$0.854687\pi$
$854$	70.7436	+	59.3656i	2.42080	+	2.03145i
$855$	−13.1649	−	7.89514i	−0.450230	−	0.270008i
$856$	24.4711	−	42.3852i	0.836405	−	1.44870i
$857$	−8.97868	+	15.5515i	−0.306706	+	0.531230i	−0.977640	−	0.210287i	$-0.932560\pi$
$857$	−8.97868	+	15.5515i	−0.306706	+	0.531230i	0.670934	+	0.741517i	$0.265894\pi$
$858$	6.00147	+	23.1656i	0.204887	+	0.790861i
$859$	−24.0869	−	41.7198i	−0.821835	−	1.42346i	−0.904314	−	0.426867i	$-0.859617\pi$
$859$	−24.0869	−	41.7198i	−0.821835	−	1.42346i	0.0824792	−	0.996593i	$-0.473716\pi$
$860$	3.49102	−	6.04663i	0.119043	−	0.206188i
$861$	3.97509	−	0.314384i	0.135471	−	0.0107142i
$862$	−40.7370	−	70.5585i	−1.38751	−	2.40323i
$863$	−22.0723	+	38.2303i	−0.751349	+	1.30137i	0.195821	+	0.980640i	$0.437263\pi$
$863$	−22.0723	+	38.2303i	−0.751349	+	1.30137i	−0.947169	+	0.320734i	$0.896070\pi$
$864$	16.8004	+	17.6590i	0.571561	+	0.600773i
$865$	−6.14977	−	10.6517i	−0.209098	−	0.362169i
$866$	−66.0157			−2.24331
$867$	−1.61905	+	1.59238i	−0.0549858	+	0.0540801i
$868$	−62.6173	−	52.5463i	−2.12537	−	1.78354i
$869$	−18.1909	+	31.5076i	−0.617085	+	1.06882i
$870$	9.66140	−	9.50226i	0.327552	−	0.322157i
$871$	−9.13470	+	15.8218i	−0.309518	+	0.536100i
$872$	26.4016	+	45.7289i	0.894071	+	1.54858i
$873$	−0.765016	+	46.0574i	−0.0258919	+	1.55881i
$874$	5.15330			0.174313
$875$	−2.02670	−	1.70073i	−0.0685149	−	0.0574953i
$876$	17.2974	+	66.7677i	0.584425	+	2.25587i
$877$	−14.2930	−	24.7563i	−0.482641	−	0.835959i	0.517160	−	0.855889i	$-0.326989\pi$
$877$	−14.2930	−	24.7563i	−0.482641	−	0.835959i	−0.999801	+	0.0199294i	$0.993656\pi$
$878$	−24.1635			−0.815479
$879$	12.0851	−	11.8860i	0.407619	−	0.400905i
$880$	2.36365			0.0796786
$881$	−25.1883			−0.848615			−0.424308	−	0.905518i	$-0.639482\pi$
$881$	−25.1883			−0.848615			−0.424308	+	0.905518i	$0.639482\pi$
$882$	−17.4664	+	45.6062i	−0.588123	+	1.53564i
$883$	−0.466663			−0.0157044			−0.00785222	−	0.999969i	$-0.502499\pi$
$883$	−0.466663			−0.0157044			−0.00785222	+	0.999969i	$0.502499\pi$
$884$	−27.1198			−0.912138
$885$	−5.11728	−	19.7526i	−0.172016	−	0.663978i
$886$	33.2017			1.11543
$887$	−2.51863	−	4.36240i	−0.0845673	−	0.146475i	0.820639	−	0.571446i	$-0.193617\pi$
$887$	−2.51863	−	4.36240i	−0.0845673	−	0.146475i	−0.905207	+	0.424971i	$0.860284\pi$
$888$	−0.323670	+	0.318338i	−0.0108616	+	0.0106827i
$889$	−12.9872	−	10.8984i	−0.435577	−	0.365520i
$890$	39.9077			1.33771
$891$	26.6010	+	0.883932i	0.891165	+	0.0296128i
$892$	24.0804	+	41.7085i	0.806272	+	1.39650i
$893$	9.84428	−	17.0508i	0.329426	−	0.570583i
$894$	−11.4244	−	44.0980i	−0.382089	−	1.47486i
$895$	−10.3534	+	17.9326i	−0.346076	+	0.599421i
$896$	−39.9349	−	33.5120i	−1.33413	−	1.11956i
$897$	1.45225	+	0.402085i	0.0484893	+	0.0134252i
$898$	18.3693			0.612991
$899$	−15.2492	−	26.4124i	−0.508590	−	0.880904i
$900$	−8.93836	+	4.96449i	−0.297945	+	0.165483i
$901$	−16.8240	+	29.1400i	−0.560488	+	0.970794i
$902$	2.99213	+	5.18253i	0.0996271	+	0.172559i
$903$	−4.03837	+	8.47499i	−0.134388	+	0.282030i
$904$	17.7491	−	30.7423i	0.590325	−	1.02247i
$905$	4.94928	+	8.57240i	0.164520	+	0.284956i
$906$	30.1946	−	29.6972i	1.00315	−	0.986624i
$907$	29.7457	−	51.5211i	0.987691	−	1.71073i	0.358384	−	0.933574i	$-0.383328\pi$
$907$	29.7457	−	51.5211i	0.987691	−	1.71073i	0.629307	−	0.777157i	$-0.283339\pi$
$908$	7.36390	−	12.7546i	0.244380	−	0.423278i
$909$	14.9229	−	8.28840i	0.494962	−	0.274909i
$910$	9.46856	+	7.94568i	0.313880	+	0.263397i
$911$	24.2229	+	41.9552i	0.802540	+	1.39004i	0.917940	+	0.396720i	$0.129852\pi$
$911$	24.2229	+	41.9552i	0.802540	+	1.39004i	−0.115400	+	0.993319i	$0.536815\pi$
$912$	5.05035	−	4.96716i	0.167234	−	0.164479i
$913$	−0.745740			−0.0246804
$914$	63.6855			2.10653
$915$	−6.51992	−	25.1668i	−0.215542	−	0.831989i
$916$	−12.4005	−	21.4782i	−0.409723	−	0.709661i
$917$	0.0515376	−	0.292219i	0.00170192	−	0.00964993i
$918$	−13.5358	+	45.9095i	−0.446747	+	1.51524i
$919$	−7.16949	+	12.4179i	−0.236500	+	0.409630i	−0.959707	−	0.281001i	$-0.909334\pi$
$919$	−7.16949	+	12.4179i	−0.236500	+	0.409630i	0.723208	+	0.690631i	$0.242667\pi$
$920$	0.709086	−	1.22817i	0.0233779	−	0.0404917i
$921$	19.2164	+	5.32045i	0.633203	+	0.175315i
$922$	39.0229	+	67.5897i	1.28515	+	2.22595i
$923$	−2.96555	+	5.13648i	−0.0976122	+	0.169069i
$924$	−46.0437	+	3.64153i	−1.51473	+	0.119797i
$925$	0.0400194	+	0.0693157i	0.00131583	+	0.00227909i
$926$	9.29200	−	16.0942i	0.305354	−	0.528889i
$927$	−0.837154	+	50.4003i	−0.0274957	+	1.65536i
$928$	−7.89058	−	13.6669i	−0.259021	−	0.448637i
$929$	−46.5124			−1.52602			−0.763011	−	0.646386i	$-0.776280\pi$
$929$	−46.5124			−1.52602			−0.763011	+	0.646386i	$0.776280\pi$
$930$	9.15754	+	35.3480i	0.300288	+	1.15911i
$931$	−33.6575	−	12.2532i	−1.10308	−	0.401583i
$932$	6.75677	−	11.7031i	0.221325	−	0.383347i
$933$	−27.8720	−	7.71691i	−0.912488	−	0.252640i
$934$	−41.3834	+	71.6781i	−1.35411	+	2.34538i
$935$	−5.85680	−	10.1443i	−0.191538	−	0.331753i
$936$	17.2538	−	9.58301i	0.563959	−	0.313231i
$937$	−53.0098			−1.73175			−0.865877	−	0.500256i	$-0.833239\pi$
$937$	−53.0098			−1.73175			−0.865877	+	0.500256i	$0.833239\pi$
$938$	−42.8616	−	35.9680i	−1.39948	−	1.17440i
$939$	−7.49554	−	2.07529i	−0.244608	−	0.0677245i
$940$	−6.55684	−	11.3568i	−0.213861	−	0.370417i
$941$	51.4877			1.67845			0.839225	−	0.543785i	$-0.183009\pi$
$941$	51.4877			1.67845			0.839225	+	0.543785i	$0.183009\pi$
$942$	−8.10530	−	2.24411i	−0.264085	−	0.0731172i
$943$	0.376827			0.0122712
$944$	9.41585			0.306460
$945$	11.4547	−	7.60196i	0.372621	−	0.247292i
$946$	−14.0890			−0.458074
$947$	−30.9123			−1.00452			−0.502258	−	0.864718i	$-0.667497\pi$
$947$	−30.9123			−1.00452			−0.502258	+	0.864718i	$0.667497\pi$
$948$	69.9895	+	19.3780i	2.27315	+	0.629368i
$949$	−23.4726			−0.761952
$950$	−5.94984	−	10.3054i	−0.193038	−	0.334352i
$951$	19.5075	+	5.40104i	0.632574	+	0.175141i
$952$	5.96057	−	33.7966i	0.193183	−	1.09535i
$953$	−19.2506			−0.623588			−0.311794	−	0.950150i	$-0.600930\pi$
$953$	−19.2506			−0.623588			−0.311794	+	0.950150i	$0.600930\pi$
$954$	0.984285	−	59.2583i	0.0318674	−	1.91856i
$955$	−7.15823	−	12.3984i	−0.231635	−	0.401203i
$956$	−27.4794	+	47.5957i	−0.888748	+	1.53936i
$957$	−16.6077	−	4.59816i	−0.536850	−	0.148638i
$958$	4.87414	−	8.44226i	0.157476	−	0.272757i
$959$	−47.8061	+	17.3980i	−1.54374	+	0.561809i
$960$	5.43285	+	20.9707i	0.175345	+	0.676828i
$961$	51.1807			1.65099
$962$	−0.186967	−	0.323837i	−0.00602807	−	0.0104409i
$963$	39.1960	−	21.7700i	1.26307	−	0.701529i
$964$	2.62434	−	4.54550i	0.0845244	−	0.146401i
$965$	−2.94156	−	5.09492i	−0.0946920	−	0.164011i
$966$	−1.98527	+	4.16632i	−0.0638750	+	0.134049i
$967$	−9.18403	+	15.9072i	−0.295338	+	0.511541i	−0.975064	−	0.221926i	$-0.928766\pi$
$967$	−9.18403	+	15.9072i	−0.295338	+	0.511541i	0.679725	+	0.733467i	$0.262099\pi$
$968$	3.69133	+	6.39358i	0.118644	+	0.205497i
$969$	−33.8320	−	9.36707i	−1.08684	−	0.300914i
$970$	−17.8539	+	30.9238i	−0.573254	+	0.992904i
$971$	−9.62981	+	16.6793i	−0.309035	+	0.535265i	−0.978152	−	0.207893i	$-0.933339\pi$
$971$	−9.62981	+	16.6793i	−0.309035	+	0.535265i	0.669116	+	0.743158i	$0.266673\pi$
$972$	−11.6085	−	51.8443i	−0.372344	−	1.66291i
$973$	−34.5288	+	12.5660i	−1.10694	+	0.402847i
$974$	−6.09409	−	10.5553i	−0.195267	−	0.338213i
$975$	−0.872647	−	3.36841i	−0.0279471	−	0.107875i
$976$	11.9967			0.384005
$977$	−59.5430			−1.90495			−0.952475	−	0.304618i	$-0.901471\pi$
$977$	−59.5430			−1.90495			−0.952475	+	0.304618i	$0.901471\pi$
$978$	−55.9309	+	55.0096i	−1.78847	+	1.75901i
$979$	−25.3744	−	43.9498i	−0.810970	−	1.40464i
$980$	−18.2768	+	15.3337i	−0.583831	+	0.489817i
$981$	−0.803368	+	48.3663i	−0.0256496	+	1.54422i
$982$	−4.05638	+	7.02585i	−0.129444	+	0.224204i
$983$	4.78401	−	8.28614i	0.152586	−	0.264287i	−0.779591	−	0.626289i	$-0.784573\pi$
$983$	4.78401	−	8.28614i	0.152586	−	0.264287i	0.932177	+	0.362002i	$0.117907\pi$
$984$	3.51878	−	3.46082i	0.112175	−	0.110327i
$985$	10.6185	+	18.3918i	0.338333	+	0.586010i
$986$	15.4947	−	26.8377i	0.493453	−	0.854685i
$987$	9.99273	+	14.5276i	0.318072	+	0.462417i
$988$	17.5174	+	30.3411i	0.557304	+	0.965279i
$989$	−0.443591	+	0.768321i	−0.0141054	+	0.0244312i
$990$	17.6940	+	10.6113i	0.562353	+	0.337249i
$991$	7.44111	+	12.8884i	0.236375	+	0.409413i	0.959671	−	0.281125i	$-0.0907074\pi$
$991$	7.44111	+	12.8884i	0.236375	+	0.409413i	−0.723297	+	0.690537i	$0.757374\pi$
$992$	42.5237			1.35013
$993$	12.1181	+	3.35514i	0.384557	+	0.106472i
$994$	−13.9149	−	11.6769i	−0.441353	−	0.370368i
$995$	1.38845	−	2.40486i	0.0440168	−	0.0762393i
$996$	0.373321	+	1.44101i	0.0118291	+	0.0456603i
$997$	−3.58004	+	6.20081i	−0.113381	+	0.196382i	−0.917131	−	0.398585i	$-0.869501\pi$
$997$	−3.58004	+	6.20081i	−0.113381	+	0.196382i	0.803750	+	0.594967i	$0.202835\pi$
$998$	8.21692	+	14.2321i	0.260102	+	0.450510i
$999$	−0.404280	+	0.0976009i	−0.0127908	+	0.00308796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.11	yes	24
3.2	odd	2		945.2.l.b.226.2		24
7.4	even	3		315.2.k.b.256.2	yes	24
9.2	odd	6		945.2.k.b.856.11		24
9.7	even	3		315.2.k.b.16.2	✓	24
21.11	odd	6		945.2.k.b.361.11		24
63.11	odd	6		945.2.l.b.46.2		24
63.25	even	3	inner	315.2.l.b.151.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.2	✓	24	9.7	even	3
315.2.k.b.256.2	yes	24	7.4	even	3
315.2.l.b.121.11	yes	24	1.1	even	1	trivial
315.2.l.b.151.11	yes	24	63.25	even	3	inner
945.2.k.b.361.11		24	21.11	odd	6
945.2.k.b.856.11		24	9.2	odd	6
945.2.l.b.46.2		24	63.11	odd	6
945.2.l.b.226.2		24	3.2	odd	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.32555 q^{2} +(-1.66925 - 0.462165i) q^{3} +3.40817 q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.88192 - 1.07479i) q^{6} +(2.02670 + 1.70073i) q^{7} +3.27475 q^{8} +(2.57281 + 1.54294i) q^{9} +O(q^{10})\)	\(q+2.32555 q^{2} +(-1.66925 - 0.462165i) q^{3} +3.40817 q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.88192 - 1.07479i) q^{6} +(2.02670 + 1.70073i) q^{7} +3.27475 q^{8} +(2.57281 + 1.54294i) q^{9} +(1.16277 + 2.01398i) q^{10} +(1.47865 - 2.56109i) q^{11} +(-5.68909 - 1.57514i) q^{12} +(1.00448 - 1.73980i) q^{13} +(4.71318 + 3.95513i) q^{14} +(-0.434379 - 1.67670i) q^{15} +0.799261 q^{16} +(-1.98046 - 3.43026i) q^{17} +(5.98318 + 3.58818i) q^{18} +(-2.55847 + 4.43140i) q^{19} +(1.70408 + 2.95156i) q^{20} +(-2.59705 - 3.77562i) q^{21} +(3.43866 - 5.95593i) q^{22} +(-0.216531 - 0.375043i) q^{23} +(-5.46639 - 1.51348i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.33596 - 4.04599i) q^{26} +(-3.58157 - 3.76462i) q^{27} +(6.90732 + 5.79638i) q^{28} +(1.68214 + 2.91356i) q^{29} +(-1.01017 - 3.89924i) q^{30} -9.06536 q^{31} -4.69079 q^{32} +(-3.65188 + 3.59173i) q^{33} +(-4.60565 - 7.97722i) q^{34} +(-0.459529 + 2.60554i) q^{35} +(8.76855 + 5.25860i) q^{36} +(0.0400194 - 0.0693157i) q^{37} +(-5.94984 + 10.3054i) q^{38} +(-2.48080 + 2.43994i) q^{39} +(1.63738 + 2.83602i) q^{40} +(-0.435072 + 0.753568i) q^{41} +(-6.03956 - 8.78039i) q^{42} +(-1.02431 - 1.77416i) q^{43} +(5.03947 - 8.72862i) q^{44} +(-0.0498234 + 2.99959i) q^{45} +(-0.503553 - 0.872180i) q^{46} -3.84772 q^{47} +(-1.33417 - 0.369391i) q^{48} +(1.21501 + 6.89375i) q^{49} +(-1.16277 + 2.01398i) q^{50} +(1.72054 + 6.64127i) q^{51} +(3.42342 - 5.92954i) q^{52} +(-4.24749 - 7.35687i) q^{53} +(-8.32910 - 8.75480i) q^{54} +2.95729 q^{55} +(6.63694 + 5.56948i) q^{56} +(6.31877 - 6.21469i) q^{57} +(3.91190 + 6.77561i) q^{58} +11.7807 q^{59} +(-1.48044 - 5.71446i) q^{60} +15.0097 q^{61} -21.0819 q^{62} +(2.59017 + 7.50273i) q^{63} -12.5072 q^{64} +2.00895 q^{65} +(-8.49262 + 8.35273i) q^{66} -9.09400 q^{67} +(-6.74974 - 11.6909i) q^{68} +(0.188113 + 0.726115i) q^{69} +(-1.06866 + 6.05930i) q^{70} -2.95233 q^{71} +(8.42531 + 5.05275i) q^{72} +(-5.84200 - 10.1186i) q^{73} +(0.0930671 - 0.161197i) q^{74} +(1.23487 - 1.21453i) q^{75} +(-8.71969 + 15.1029i) q^{76} +(7.35250 - 2.67578i) q^{77} +(-5.76922 + 5.67419i) q^{78} -12.3024 q^{79} +(0.399631 + 0.692181i) q^{80} +(4.23866 + 7.93938i) q^{81} +(-1.01178 + 1.75246i) q^{82} +(-0.126085 - 0.218385i) q^{83} +(-8.85118 - 12.8679i) q^{84} +(1.98046 - 3.43026i) q^{85} +(-2.38208 - 4.12589i) q^{86} +(-1.46138 - 5.64089i) q^{87} +(4.84220 - 8.38694i) q^{88} +(8.58029 - 14.8615i) q^{89} +(-0.115867 + 6.97568i) q^{90} +(4.99471 - 1.81771i) q^{91} +(-0.737974 - 1.27821i) q^{92} +(15.1324 + 4.18969i) q^{93} -8.94806 q^{94} -5.11694 q^{95} +(7.83011 + 2.16792i) q^{96} +(7.67728 + 13.2974i) q^{97} +(2.82557 + 16.0317i) q^{98} +(7.75588 - 4.30773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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