LMFDB - Embedded newform 315.2.k.b.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 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("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (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			256.1
Character	$\chi$	$=$	315.256
Dual form			315.2.k.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17004 + 2.02657i) q^{2} +(1.32145 - 1.11972i) q^{3} +(-1.73798 - 3.01027i) q^{4} -1.00000 q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.00344 - 2.44808i) q^{7} +3.45385 q^{8} +(0.492465 - 2.95930i) q^{9} +O(q^{10})$	\(q+(-1.17004 + 2.02657i) q^{2} +(1.32145 - 1.11972i) q^{3} +(-1.73798 - 3.01027i) q^{4} -1.00000 q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.00344 - 2.44808i) q^{7} +3.45385 q^{8} +(0.492465 - 2.95930i) q^{9} +(1.17004 - 2.02657i) q^{10} -3.25662 q^{11} +(-5.66730 - 2.03187i) q^{12} +(0.549485 - 0.951736i) q^{13} +(6.13526 + 0.830812i) q^{14} +(-1.32145 + 1.11972i) q^{15} +(-0.565177 + 0.978916i) q^{16} +(0.763940 - 1.32318i) q^{17} +(5.42102 + 4.46051i) q^{18} +(-3.06883 - 5.31536i) q^{19} +(1.73798 + 3.01027i) q^{20} +(-4.06716 - 2.11145i) q^{21} +(3.81036 - 6.59974i) q^{22} +4.30605 q^{23} +(4.56409 - 3.86733i) q^{24} +1.00000 q^{25} +(1.28584 + 2.22714i) q^{26} +(-2.66282 - 4.46200i) q^{27} +(-5.62542 + 7.27533i) q^{28} +(-1.48384 - 2.57008i) q^{29} +(-0.723033 - 3.98812i) q^{30} +(-2.04950 - 3.54983i) q^{31} +(2.13129 + 3.69150i) q^{32} +(-4.30346 + 3.64649i) q^{33} +(1.78768 + 3.09635i) q^{34} +(1.00344 + 2.44808i) q^{35} +(-9.76418 + 3.66075i) q^{36} +(4.94725 + 8.56889i) q^{37} +14.3626 q^{38} +(-0.339558 - 1.87294i) q^{39} -3.45385 q^{40} +(-0.222291 + 0.385018i) q^{41} +(9.03772 - 5.77188i) q^{42} +(2.84617 + 4.92971i) q^{43} +(5.65993 + 9.80328i) q^{44} +(-0.492465 + 2.95930i) q^{45} +(-5.03824 + 8.72650i) q^{46} +(-3.11646 + 5.39786i) q^{47} +(0.349255 + 1.92643i) q^{48} +(-4.98622 + 4.91301i) q^{49} +(-1.17004 + 2.02657i) q^{50} +(-0.472082 - 2.60392i) q^{51} -3.81997 q^{52} +(5.48563 - 9.50139i) q^{53} +(12.1581 - 0.175665i) q^{54} +3.25662 q^{55} +(-3.46573 - 8.45530i) q^{56} +(-10.0070 - 3.58777i) q^{57} +6.94459 q^{58} +(3.77646 + 6.54103i) q^{59} +(5.66730 + 2.03187i) q^{60} +(3.74286 - 6.48282i) q^{61} +9.59196 q^{62} +(-7.73878 + 1.76389i) q^{63} -12.2355 q^{64} +(-0.549485 + 0.951736i) q^{65} +(-2.35464 - 12.9878i) q^{66} +(-1.06964 - 1.85268i) q^{67} -5.31084 q^{68} +(5.69024 - 4.82156i) q^{69} +(-6.13526 - 0.830812i) q^{70} -15.7970 q^{71} +(1.70090 - 10.2210i) q^{72} +(4.96804 - 8.60490i) q^{73} -23.1539 q^{74} +(1.32145 - 1.11972i) q^{75} +(-10.6671 + 18.4760i) q^{76} +(3.26782 + 7.97246i) q^{77} +(4.19293 + 1.50328i) q^{78} +(-3.93113 + 6.80891i) q^{79} +(0.565177 - 0.978916i) q^{80} +(-8.51496 - 2.91471i) q^{81} +(-0.520177 - 0.900972i) q^{82} +(-8.19187 - 14.1887i) q^{83} +(0.712601 + 15.9129i) q^{84} +(-0.763940 + 1.32318i) q^{85} -13.3205 q^{86} +(-4.83859 - 1.73476i) q^{87} -11.2479 q^{88} +(0.440119 + 0.762308i) q^{89} +(-5.42102 - 4.46051i) q^{90} +(-2.88130 - 0.390175i) q^{91} +(-7.48382 - 12.9624i) q^{92} +(-6.68312 - 2.39607i) q^{93} +(-7.29275 - 12.6314i) q^{94} +(3.06883 + 5.31536i) q^{95} +(6.94983 + 2.49170i) q^{96} +(7.41446 + 12.8422i) q^{97} +(-4.12247 - 15.8533i) q^{98} +(-1.60377 + 9.63731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.17004	+	2.02657i	−0.827342	+	1.43300i	0.0727746	+	0.997348i	$0.476815\pi$
$2$	−1.17004	+	2.02657i	−0.827342	+	1.43300i	−0.900116	+	0.435650i	$0.856519\pi$
$3$	1.32145	−	1.11972i	0.762940	−	0.646469i
$3$	1.32145	−	1.11972i	0.762940	−	0.646469i
$4$	−1.73798	−	3.01027i	−0.868989	−	1.50513i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.723033	+	3.98812i	0.295177	+	1.62814i
$7$	−1.00344	−	2.44808i	−0.379265	−	0.925288i
$7$	−1.00344	−	2.44808i	−0.379265	−	0.925288i
$8$	3.45385			1.22112
$9$	0.492465	−	2.95930i	0.164155	−	0.986435i
$10$	1.17004	−	2.02657i	0.369998	−	0.640856i
$11$	−3.25662			−0.981907			−0.490953	−	0.871186i	$-0.663351\pi$
$11$	−3.25662			−0.981907			−0.490953	+	0.871186i	$0.663351\pi$
$12$	−5.66730	−	2.03187i	−1.63601	−	0.586552i
$13$	0.549485	−	0.951736i	0.152400	−	0.263964i	−0.779709	−	0.626142i	$-0.784633\pi$
$13$	0.549485	−	0.951736i	0.152400	−	0.263964i	0.932109	+	0.362177i	$0.117967\pi$
$14$	6.13526	+	0.830812i	1.63972	+	0.222044i
$15$	−1.32145	+	1.11972i	−0.341197	+	0.289110i
$16$	−0.565177	+	0.978916i	−0.141294	+	0.244729i
$17$	0.763940	−	1.32318i	0.185283	−	0.320919i	−0.758389	−	0.651802i	$-0.774013\pi$
$17$	0.763940	−	1.32318i	0.185283	−	0.320919i	0.943672	+	0.330883i	$0.107347\pi$
$18$	5.42102	+	4.46051i	1.27775	+	1.05135i
$19$	−3.06883	−	5.31536i	−0.704037	−	1.21943i	−0.967038	−	0.254632i	$-0.918046\pi$
$19$	−3.06883	−	5.31536i	−0.704037	−	1.21943i	0.263001	−	0.964796i	$-0.415288\pi$
$20$	1.73798	+	3.01027i	0.388624	+	0.673116i
$21$	−4.06716	−	2.11145i	−0.887527	−	0.460756i
$22$	3.81036	−	6.59974i	0.812372	−	1.40707i
$23$	4.30605			0.897874			0.448937	−	0.893563i	$-0.351803\pi$
$23$	4.30605			0.897874			0.448937	+	0.893563i	$0.351803\pi$
$24$	4.56409	−	3.86733i	0.931641	−	0.789416i
$25$	1.00000			0.200000
$26$	1.28584	+	2.22714i	0.252173	+	0.436777i
$27$	−2.66282	−	4.46200i	−0.512459	−	0.858712i
$28$	−5.62542	+	7.27533i	−1.06310	+	1.37491i
$29$	−1.48384	−	2.57008i	−0.275542	−	0.477253i	0.694730	−	0.719271i	$-0.255524\pi$
$29$	−1.48384	−	2.57008i	−0.275542	−	0.477253i	−0.970272	+	0.242018i	$0.922191\pi$
$30$	−0.723033	−	3.98812i	−0.132007	−	0.728127i
$31$	−2.04950	−	3.54983i	−0.368101	−	0.637569i	0.621168	−	0.783678i	$-0.286659\pi$
$31$	−2.04950	−	3.54983i	−0.368101	−	0.637569i	−0.989269	+	0.146108i	$0.953325\pi$
$32$	2.13129	+	3.69150i	0.376762	+	0.652572i
$33$	−4.30346	+	3.64649i	−0.749136	+	0.634772i
$34$	1.78768	+	3.09635i	0.306584	+	0.531019i
$35$	1.00344	+	2.44808i	0.169612	+	0.413801i
$36$	−9.76418	+	3.66075i	−1.62736	+	0.610125i
$37$	4.94725	+	8.56889i	0.813323	+	1.40872i	0.910526	+	0.413452i	$0.135677\pi$
$37$	4.94725	+	8.56889i	0.813323	+	1.40872i	−0.0972035	+	0.995265i	$0.530990\pi$
$38$	14.3626			2.32992
$39$	−0.339558	−	1.87294i	−0.0543728	−	0.299911i
$40$	−3.45385			−0.546101
$41$	−0.222291	+	0.385018i	−0.0347159	+	0.0601298i	−0.882861	−	0.469634i	$-0.844386\pi$
$41$	−0.222291	+	0.385018i	−0.0347159	+	0.0601298i	0.848145	+	0.529764i	$0.177719\pi$
$42$	9.03772	−	5.77188i	1.39455	−	0.890621i
$43$	2.84617	+	4.92971i	0.434037	+	0.751773i	0.997216	−	0.0745609i	$-0.0237555\pi$
$43$	2.84617	+	4.92971i	0.434037	+	0.751773i	−0.563180	+	0.826334i	$0.690422\pi$
$44$	5.65993	+	9.80328i	0.853266	+	1.47790i
$45$	−0.492465	+	2.95930i	−0.0734124	+	0.441147i
$46$	−5.03824	+	8.72650i	−0.742849	+	1.28665i
$47$	−3.11646	+	5.39786i	−0.454582	+	0.787359i	−0.998664	−	0.0516728i	$-0.983545\pi$
$47$	−3.11646	+	5.39786i	−0.454582	+	0.787359i	0.544082	+	0.839032i	$0.316878\pi$
$48$	0.349255	+	1.92643i	0.0504106	+	0.278056i
$49$	−4.98622	+	4.91301i	−0.712317	+	0.701858i
$50$	−1.17004	+	2.02657i	−0.165468	+	0.286600i
$51$	−0.472082	−	2.60392i	−0.0661047	−	0.364621i
$52$	−3.81997			−0.529735
$53$	5.48563	−	9.50139i	0.753509	−	1.30512i	−0.192603	−	0.981277i	$-0.561693\pi$
$53$	5.48563	−	9.50139i	0.753509	−	1.30512i	0.946112	−	0.323839i	$-0.104974\pi$
$54$	12.1581	−	0.175665i	1.65451	−	0.0239050i
$55$	3.25662			0.439122
$56$	−3.46573	−	8.45530i	−0.463128	−	1.12989i
$57$	−10.0070	−	3.58777i	−1.32546	−	0.475212i
$58$	6.94459			0.911869
$59$	3.77646	+	6.54103i	0.491654	+	0.851569i	0.999954	−	0.00961076i	$-0.00305925\pi$
$59$	3.77646	+	6.54103i	0.491654	+	0.851569i	−0.508300	+	0.861180i	$0.669726\pi$
$60$	5.66730	+	2.03187i	0.731645	+	0.262314i
$61$	3.74286	−	6.48282i	0.479224	−	0.830040i	−0.520492	−	0.853866i	$-0.674251\pi$
$61$	3.74286	−	6.48282i	0.479224	−	0.830040i	0.999716	+	0.0238261i	$0.00758481\pi$
$62$	9.59196			1.21818
$63$	−7.73878	+	1.76389i	−0.974994	+	0.222229i
$64$	−12.2355			−1.52943
$65$	−0.549485	+	0.951736i	−0.0681553	+	0.118048i
$66$	−2.35464	−	12.9878i	−0.289836	−	1.59868i
$67$	−1.06964	−	1.85268i	−0.130678	−	0.226340i	0.793260	−	0.608883i	$-0.208382\pi$
$67$	−1.06964	−	1.85268i	−0.130678	−	0.226340i	−0.923938	+	0.382542i	$0.875049\pi$
$68$	−5.31084			−0.644034
$69$	5.69024	−	4.82156i	0.685024	−	0.580448i
$70$	−6.13526	−	0.830812i	−0.733304	−	0.0993011i
$71$	−15.7970			−1.87476			−0.937380	−	0.348308i	$-0.886756\pi$
$71$	−15.7970			−1.87476			−0.937380	+	0.348308i	$0.886756\pi$
$72$	1.70090	−	10.2210i	0.200453	−	1.20455i
$73$	4.96804	−	8.60490i	0.581465	−	1.00713i	−0.413841	−	0.910349i	$-0.635813\pi$
$73$	4.96804	−	8.60490i	0.581465	−	1.00713i	0.995306	−	0.0967780i	$-0.0308537\pi$
$74$	−23.1539			−2.69158
$75$	1.32145	−	1.11972i	0.152588	−	0.129294i
$76$	−10.6671	+	18.4760i	−1.22360	+	2.11934i
$77$	3.26782	+	7.97246i	0.372403	+	0.908547i
$78$	4.19293	+	1.50328i	0.474756	+	0.170212i
$79$	−3.93113	+	6.80891i	−0.442286	+	0.766062i	−0.997859	−	0.0654059i	$-0.979166\pi$
$79$	−3.93113	+	6.80891i	−0.442286	+	0.766062i	0.555573	+	0.831468i	$0.312499\pi$
$80$	0.565177	−	0.978916i	0.0631887	−	0.109446i
$81$	−8.51496	−	2.91471i	−0.946106	−	0.323856i
$82$	−0.520177	−	0.900972i	−0.0574439	−	0.0994958i
$83$	−8.19187	−	14.1887i	−0.899174	−	1.55742i	−0.828552	−	0.559912i	$-0.810835\pi$
$83$	−8.19187	−	14.1887i	−0.899174	−	1.55742i	−0.0706223	−	0.997503i	$-0.522499\pi$
$84$	0.712601	+	15.9129i	0.0777511	+	1.73624i
$85$	−0.763940	+	1.32318i	−0.0828609	+	0.143519i
$86$	−13.3205			−1.43639
$87$	−4.83859	−	1.73476i	−0.518751	−	0.185986i
$88$	−11.2479			−1.19903
$89$	0.440119	+	0.762308i	0.0466525	+	0.0808045i	0.888409	−	0.459053i	$-0.151811\pi$
$89$	0.440119	+	0.762308i	0.0466525	+	0.0808045i	−0.841756	+	0.539858i	$0.818478\pi$
$90$	−5.42102	−	4.46051i	−0.571426	−	0.470179i
$91$	−2.88130	−	0.390175i	−0.302043	−	0.0409014i
$92$	−7.48382	−	12.9624i	−0.780242	−	1.35142i
$93$	−6.68312	−	2.39607i	−0.693008	−	0.248461i
$94$	−7.29275	−	12.6314i	−0.752190	−	1.30283i
$95$	3.06883	+	5.31536i	0.314855	+	0.545345i
$96$	6.94983	+	2.49170i	0.709315	+	0.254308i
$97$	7.41446	+	12.8422i	0.752824	+	1.30393i	0.946449	+	0.322854i	$0.104642\pi$
$97$	7.41446	+	12.8422i	0.752824	+	1.30393i	−0.193624	+	0.981076i	$0.562024\pi$
$98$	−4.12247	−	15.8533i	−0.416432	−	1.60142i
$99$	−1.60377	+	9.63731i	−0.161185	+	0.968587i
$100$	−1.73798	−	3.01027i	−0.173798	−	0.301027i
$101$	15.0759			1.50011			0.750053	−	0.661378i	$-0.230028\pi$
$101$	15.0759			1.50011			0.750053	+	0.661378i	$0.230028\pi$
$102$	5.82936	+	2.08998i	0.577193	+	0.206939i
$103$	8.91340			0.878263			0.439132	−	0.898423i	$-0.355286\pi$
$103$	8.91340			0.878263			0.439132	+	0.898423i	$0.355286\pi$
$104$	1.89784	−	3.28715i	0.186098	−	0.322332i
$105$	4.06716	+	2.11145i	0.396914	+	0.206057i
$106$	12.8368	+	22.2340i	1.24682	+	2.15955i
$107$	−1.52574	−	2.64266i	−0.147499	−	0.255476i	0.782803	−	0.622269i	$-0.213789\pi$
$107$	−1.52574	−	2.64266i	−0.147499	−	0.255476i	−0.930302	+	0.366793i	$0.880456\pi$
$108$	−8.80388	+	15.7706i	−0.847154	+	1.51753i
$109$	9.98551	−	17.2954i	0.956438	−	1.65660i	0.225396	−	0.974267i	$-0.427632\pi$
$109$	9.98551	−	17.2954i	0.956438	−	1.65660i	0.731042	−	0.682332i	$-0.239034\pi$
$110$	−3.81036	+	6.59974i	−0.363304	+	0.629261i
$111$	16.1323	+	5.78384i	1.53121	+	0.548978i
$112$	2.96359	+	0.401317i	0.280033	+	0.0379209i
$113$	−4.49399	+	7.78382i	−0.422759	+	0.732240i	−0.996208	−	0.0870011i	$-0.972272\pi$
$113$	−4.49399	+	7.78382i	−0.422759	+	0.732240i	0.573449	+	0.819241i	$0.305605\pi$
$114$	18.9794	−	16.0820i	1.77759	−	1.50622i
$115$	−4.30605			−0.401541
$116$	−5.15776	+	8.93350i	−0.478886	+	0.829454i
$117$	−2.54587	−	2.09479i	−0.235366	−	0.193663i
$118$	−17.6744			−1.62706
$119$	−4.00583	−	0.542453i	−0.367214	−	0.0497266i
$120$	−4.56409	+	3.86733i	−0.416642	+	0.353038i
$121$	−0.394454			−0.0358595
$122$	8.75857	+	15.1703i	0.792964	+	1.37345i
$123$	0.137366	+	0.757686i	0.0123859	+	0.0683182i
$124$	−7.12396	+	12.3391i	−0.639751	+	1.10808i
$125$	−1.00000			−0.0894427
$126$	5.48003	−	17.7470i	0.488200	−	1.58102i
$127$	14.1353			1.25431			0.627154	−	0.778895i	$-0.284220\pi$
$127$	14.1353			1.25431			0.627154	+	0.778895i	$0.284220\pi$
$128$	10.0534	−	17.4130i	0.888602	−	1.53910i
$129$	9.28095	+	3.32746i	0.817142	+	0.292967i
$130$	−1.28584	−	2.22714i	−0.112775	−	0.195333i
$131$	5.67427			0.495763			0.247882	−	0.968790i	$-0.420266\pi$
$131$	5.67427			0.495763			0.247882	+	0.968790i	$0.420266\pi$
$132$	18.4562	+	6.61703i	1.60641	+	0.575939i
$133$	−9.93306	+	12.8464i	−0.861306	+	1.11392i
$134$	5.00609			0.432460
$135$	2.66282	+	4.46200i	0.229179	+	0.384028i
$136$	2.63853	−	4.57007i	0.226252	−	0.391880i
$137$	−21.6440			−1.84917			−0.924585	−	0.380976i	$-0.875588\pi$
$137$	−21.6440			−1.84917			−0.924585	+	0.380976i	$0.875588\pi$
$138$	3.11342	+	17.1730i	0.265032	+	1.46187i
$139$	1.27376	−	2.20622i	0.108039	−	0.187129i	−0.806937	−	0.590638i	$-0.798876\pi$
$139$	1.27376	−	2.20622i	0.108039	−	0.187129i	0.914976	+	0.403509i	$0.132210\pi$
$140$	5.62542	−	7.27533i	0.475435	−	0.614878i
$141$	1.92584	+	10.6226i	0.162185	+	0.894581i
$142$	18.4831	−	32.0137i	1.55107	−	2.68653i
$143$	−1.78946	+	3.09944i	−0.149642	+	0.259188i
$144$	2.61858	+	2.15461i	0.218215	+	0.179551i
$145$	1.48384	+	2.57008i	0.123226	+	0.213434i
$146$	11.6256	+	20.1361i	0.962141	+	1.66648i
$147$	−1.08786	+	12.0755i	−0.0897249	+	0.995967i
$148$	17.1964	−	29.7851i	1.41354	−	2.44832i
$149$	6.41030			0.525152			0.262576	−	0.964911i	$-0.415428\pi$
$149$	6.41030			0.525152			0.262576	+	0.964911i	$0.415428\pi$
$150$	0.723033	+	3.98812i	0.0590354	+	0.325629i
$151$	1.86661			0.151903			0.0759513	−	0.997112i	$-0.475801\pi$
$151$	1.86661			0.151903			0.0759513	+	0.997112i	$0.475801\pi$
$152$	−10.5993	−	18.3585i	−0.859713	−	1.48907i
$153$	−3.53949	−	2.91235i	−0.286150	−	0.235450i
$154$	−19.9802	−	2.70564i	−1.61005	−	0.218026i
$155$	2.04950	+	3.54983i	0.164620	+	0.285130i
$156$	−5.04791	+	4.27729i	−0.404156	+	0.342457i
$157$	9.64355	+	16.7031i	0.769639	+	1.33305i	0.937759	+	0.347287i	$0.112897\pi$
$157$	9.64355	+	16.7031i	0.769639	+	1.33305i	−0.168120	+	0.985767i	$0.553770\pi$
$158$	−9.19913	−	15.9334i	−0.731844	−	1.26759i
$159$	−3.38988	−	18.6980i	−0.268835	−	1.48285i
$160$	−2.13129	−	3.69150i	−0.168493	−	0.291839i
$161$	−4.32087	−	10.5416i	−0.340532	−	0.830792i
$162$	15.8697	−	13.8458i	1.24684	−	1.08783i
$163$	4.41723	+	7.65086i	0.345984	+	0.599262i	0.985532	−	0.169489i	$-0.0542119\pi$
$163$	4.41723	+	7.65086i	0.345984	+	0.599262i	−0.639548	+	0.768751i	$0.720879\pi$
$164$	1.54534			0.120671
$165$	4.30346	−	3.64649i	0.335024	−	0.283879i
$166$	38.3392			2.97570
$167$	10.1846	−	17.6402i	0.788105	−	1.36504i	−0.139022	−	0.990289i	$-0.544396\pi$
$167$	10.1846	−	17.6402i	0.788105	−	1.36504i	0.927127	−	0.374748i	$-0.122271\pi$
$168$	−14.0473	−	7.29263i	−1.08378	−	0.562639i
$169$	5.89613	+	10.2124i	0.453549	+	0.785569i
$170$	−1.78768	−	3.09635i	−0.137109	−	0.237479i
$171$	−17.2411	+	6.46396i	−1.31846	+	0.494311i
$172$	9.89315	−	17.1354i	0.754346	−	1.30657i
$173$	−2.74542	+	4.75520i	−0.208730	+	0.361531i	−0.951315	−	0.308221i	$-0.900266\pi$
$173$	−2.74542	+	4.75520i	−0.208730	+	0.361531i	0.742585	+	0.669752i	$0.233600\pi$
$174$	9.17693	−	7.77598i	0.695702	−	0.589495i
$175$	−1.00344	−	2.44808i	−0.0758529	−	0.185058i
$176$	1.84057	−	3.18795i	0.138738	−	0.240301i
$177$	12.3145	+	4.41507i	0.925616	+	0.331857i
$178$	−2.05982			−0.154390
$179$	−2.96012	+	5.12708i	−0.221250	+	0.383216i	−0.955188	−	0.296001i	$-0.904347\pi$
$179$	−2.96012	+	5.12708i	−0.221250	+	0.383216i	0.733938	+	0.679216i	$0.237680\pi$
$180$	9.76418	−	3.66075i	0.727779	−	0.272856i
$181$	−1.20377			−0.0894752			−0.0447376	−	0.998999i	$-0.514245\pi$
$181$	−1.20377			−0.0894752			−0.0447376	+	0.998999i	$0.514245\pi$
$182$	4.16195	−	5.38263i	0.308504	−	0.398987i
$183$	−2.31293	−	12.7577i	−0.170976	−	0.943075i
$184$	14.8724			1.09641
$185$	−4.94725	−	8.56889i	−0.363729	−	0.629997i
$186$	12.6753	−	10.7403i	0.929399	−	0.787516i
$187$	−2.48786	+	4.30910i	−0.181930	+	0.315112i
$188$	21.6653			1.58011
$189$	−8.25136	+	10.9961i	−0.600198	+	0.799851i
$190$	−14.3626			−1.04197
$191$	−1.48151	+	2.56605i	−0.107198	+	0.185673i	−0.914634	−	0.404282i	$-0.867521\pi$
$191$	−1.48151	+	2.56605i	−0.107198	+	0.185673i	0.807436	+	0.589955i	$0.200855\pi$
$192$	−16.1686	+	13.7003i	−1.16687	+	0.988732i
$193$	2.75661	+	4.77459i	0.198425	+	0.343682i	0.948018	−	0.318217i	$-0.103084\pi$
$193$	2.75661	+	4.77459i	0.198425	+	0.343682i	−0.749593	+	0.661899i	$0.769751\pi$
$194$	−34.7008			−2.49137
$195$	0.339558	+	1.87294i	0.0243163	+	0.134124i
$196$	23.4554	+	6.47113i	1.67539	+	0.462224i
$197$	10.8939			0.776157			0.388078	−	0.921626i	$-0.373139\pi$
$197$	10.8939			0.776157			0.388078	+	0.921626i	$0.373139\pi$
$198$	−17.6542	−	14.5262i	−1.25463	−	1.03233i
$199$	7.03715	−	12.1887i	0.498850	−	0.864034i	−0.501149	−	0.865361i	$-0.667089\pi$
$199$	7.03715	−	12.1887i	0.498850	−	0.864034i	0.999999	+	0.00132701i	$0.000422399\pi$
$200$	3.45385			0.244224
$201$	−3.48795	−	1.25052i	−0.246021	−	0.0882050i
$202$	−17.6393	+	30.5522i	−1.24110	+	2.14965i
$203$	−4.80283	+	6.21148i	−0.337093	+	0.435961i
$204$	−7.01802	+	5.94664i	−0.491359	+	0.416348i
$205$	0.222291	−	0.385018i	0.0155254	−	0.0268909i
$206$	−10.4290	+	18.0636i	−0.726624	+	1.25855i
$207$	2.12058	−	12.7429i	0.147391	−	0.885694i
$208$	0.621113	+	1.07580i	0.0430664	+	0.0745933i
$209$	9.99399	+	17.3101i	0.691299	+	1.19736i
$210$	−9.03772	+	5.77188i	−0.623662	+	0.398298i
$211$	5.77175	−	9.99696i	0.397343	−	0.688219i	−0.596054	−	0.802945i	$-0.703266\pi$
$211$	5.77175	−	9.99696i	0.397343	−	0.688219i	0.993397	+	0.114725i	$0.0365988\pi$
$212$	−38.1356			−2.61916
$213$	−20.8750	+	17.6882i	−1.43033	+	1.21197i
$214$	7.14070			0.488128
$215$	−2.84617	−	4.92971i	−0.194107	−	0.336203i
$216$	−9.19696	−	15.4111i	−0.625774	−	1.04859i
$217$	−6.63374	+	8.57939i	−0.450328	+	0.582407i
$218$	23.3668	+	40.4726i	1.58260	+	2.74115i
$219$	−3.07003	−	16.9338i	−0.207454	−	1.14428i
$220$	−5.65993	−	9.80328i	−0.381592	−	0.660937i
$221$	−0.839547	−	1.45414i	−0.0564741	−	0.0978160i
$222$	−30.5967	+	25.9258i	−2.05352	+	1.74003i
$223$	−10.7665	−	18.6481i	−0.720976	−	1.24877i	−0.960609	−	0.277903i	$-0.910361\pi$
$223$	−10.7665	−	18.6481i	−0.720976	−	1.24877i	0.239634	−	0.970863i	$-0.422973\pi$
$224$	6.89848	−	8.92177i	0.460924	−	0.596111i
$225$	0.492465	−	2.95930i	0.0328310	−	0.197287i
$226$	−10.5163	−	18.2147i	−0.699532	−	1.21163i
$227$	9.17769			0.609145			0.304572	−	0.952489i	$-0.401486\pi$
$227$	9.17769			0.609145			0.304572	+	0.952489i	$0.401486\pi$
$228$	6.59181	+	36.3592i	0.436553	+	2.40795i
$229$	8.98648			0.593843			0.296922	−	0.954902i	$-0.404040\pi$
$229$	8.98648			0.593843			0.296922	+	0.954902i	$0.404040\pi$
$230$	5.03824	−	8.72650i	0.332212	−	0.575408i
$231$	13.2452	+	6.87619i	0.871468	+	0.452420i
$232$	−5.12495	−	8.87668i	−0.336470	−	0.582782i
$233$	4.70726	+	8.15321i	0.308383	+	0.534134i	0.978009	−	0.208564i	$-0.0668790\pi$
$233$	4.70726	+	8.15321i	0.308383	+	0.534134i	−0.669626	+	0.742698i	$0.733546\pi$
$234$	7.22400	−	2.70840i	0.472248	−	0.177053i
$235$	3.11646	−	5.39786i	0.203295	−	0.352118i
$236$	13.1268	−	22.7363i	0.854483	−	1.48001i
$237$	2.42927	+	13.3994i	0.157798	+	0.870384i
$238$	5.78629	−	7.48338i	0.375069	−	0.485076i
$239$	7.36865	−	12.7629i	0.476638	−	0.825562i	−0.523003	−	0.852331i	$-0.675188\pi$
$239$	7.36865	−	12.7629i	0.476638	−	0.825562i	0.999642	+	0.0267687i	$0.00852177\pi$
$240$	−0.349255	−	1.92643i	−0.0225443	−	0.124350i
$241$	−7.13567			−0.459649			−0.229825	−	0.973232i	$-0.573815\pi$
$241$	−7.13567			−0.459649			−0.229825	+	0.973232i	$0.573815\pi$
$242$	0.461526	−	0.799387i	0.0296680	−	0.0513865i
$243$	−14.5157	+	5.68270i	−0.931186	+	0.364546i
$244$	−26.0200			−1.66576
$245$	4.98622	−	4.91301i	0.318558	−	0.313881i
$246$	−1.69622	−	0.608140i	−0.108147	−	0.0387736i
$247$	−6.74510			−0.429180
$248$	−7.07865	−	12.2606i	−0.449495	−	0.778548i
$249$	−26.7125	−	9.57713i	−1.69284	−	0.606926i
$250$	1.17004	−	2.02657i	0.0739997	−	0.128171i
$251$	−13.5593			−0.855853			−0.427927	−	0.903813i	$-0.640756\pi$
$251$	−13.5593			−0.855853			−0.427927	+	0.903813i	$0.640756\pi$
$252$	18.7596	+	20.2302i	1.18174	+	1.27438i
$253$	−14.0232			−0.881628
$254$	−16.5389	+	28.6462i	−1.03774	+	1.79742i
$255$	0.472082	+	2.60392i	0.0295629	+	0.163064i
$256$	11.2902	+	19.5552i	0.705638	+	1.22220i
$257$	21.2148			1.32334			0.661672	−	0.749793i	$-0.269847\pi$
$257$	21.2148			1.32334			0.661672	+	0.749793i	$0.269847\pi$
$258$	−17.6024	+	14.9152i	−1.09588	+	0.928580i
$259$	16.0131	−	20.7096i	0.995004	−	1.28683i
$260$	3.81997			0.236905
$261$	−8.33640	+	3.12545i	−0.516010	+	0.193461i
$262$	−6.63911	+	11.4993i	−0.410166	+	0.710428i
$263$	7.50395			0.462713			0.231357	−	0.972869i	$-0.425684\pi$
$263$	7.50395			0.462713			0.231357	+	0.972869i	$0.425684\pi$
$264$	−14.8635	+	12.5944i	−0.914784	+	0.775133i
$265$	−5.48563	+	9.50139i	−0.336980	+	0.583666i
$266$	−14.4120	−	35.1608i	−0.883655	−	2.15585i
$267$	1.43516	+	0.514544i	0.0878307	+	0.0314896i
$268$	−3.71803	+	6.43982i	−0.227115	+	0.393374i
$269$	13.5820	−	23.5247i	0.828110	−	1.43433i	−0.0714097	−	0.997447i	$-0.522750\pi$
$269$	13.5820	−	23.5247i	0.828110	−	1.43433i	0.899519	−	0.436881i	$-0.143917\pi$
$270$	−12.1581	+	0.175665i	−0.739920	+	0.0106906i
$271$	1.65552	+	2.86744i	0.100566	+	0.174185i	0.911918	−	0.410373i	$-0.134601\pi$
$271$	1.65552	+	2.86744i	0.100566	+	0.174185i	−0.811352	+	0.584558i	$0.801268\pi$
$272$	0.863523	+	1.49567i	0.0523588	+	0.0906880i
$273$	−4.24439	+	2.71065i	−0.256882	+	0.164056i
$274$	25.3243	−	43.8629i	1.52990	−	2.64986i
$275$	−3.25662			−0.196381
$276$	−24.4037	−	8.74936i	−1.46893	−	0.526649i
$277$	−28.2844			−1.69945			−0.849724	−	0.527228i	$-0.823231\pi$
$277$	−28.2844			−1.69945			−0.849724	+	0.527228i	$0.823231\pi$
$278$	2.98069	+	5.16271i	0.178770	+	0.309639i
$279$	−11.5143	+	4.31692i	−0.689346	+	0.258447i
$280$	3.46573	+	8.45530i	0.207117	+	0.505301i
$281$	−3.32484	−	5.75879i	−0.198343	−	0.343540i	0.749648	−	0.661837i	$-0.230223\pi$
$281$	−3.32484	−	5.75879i	−0.198343	−	0.343540i	−0.947991	+	0.318296i	$0.896889\pi$
$282$	−23.7806	−	8.52597i	−1.41612	−	0.507714i
$283$	−4.46173	−	7.72795i	−0.265223	−	0.459379i	0.702399	−	0.711783i	$-0.252112\pi$
$283$	−4.46173	−	7.72795i	−0.265223	−	0.459379i	−0.967622	+	0.252404i	$0.918779\pi$
$284$	27.4549	+	47.5532i	1.62915	+	2.82176i
$285$	10.0070	+	3.58777i	0.592764	+	0.212521i
$286$	−4.18748	−	7.25292i	−0.247611	−	0.428874i
$287$	1.16561	+	0.157843i	0.0688039	+	0.00931715i
$288$	11.9739	−	4.48920i	0.705567	−	0.264529i
$289$	7.33279	+	12.7008i	0.431341	+	0.747104i
$290$	−6.94459			−0.407800
$291$	24.1775	+	8.66826i	1.41731	+	0.508143i
$292$	−34.5374			−2.02115
$293$	5.91498	−	10.2450i	0.345557	−	0.598522i	−0.639898	−	0.768460i	$-0.721023\pi$
$293$	5.91498	−	10.2450i	0.345557	−	0.598522i	0.985455	+	0.169938i	$0.0543567\pi$
$294$	−23.1989	−	16.3334i	−1.35298	−	0.952580i
$295$	−3.77646	−	6.54103i	−0.219874	−	0.380833i
$296$	17.0870	+	29.5956i	0.993164	+	1.72021i
$297$	8.67177	+	14.5310i	0.503187	+	0.843175i
$298$	−7.50029	+	12.9909i	−0.434480	+	0.752542i
$299$	2.36611	−	4.09823i	0.136836	−	0.237007i
$300$	−5.66730	−	2.03187i	−0.327202	−	0.117310i
$301$	9.21237	−	11.9143i	0.530992	−	0.686730i
$302$	−2.18401	+	3.78281i	−0.125675	+	0.217676i
$303$	19.9220	−	16.8807i	1.14449	−	0.969772i
$304$	6.93772			0.397906
$305$	−3.74286	+	6.48282i	−0.214315	+	0.371205i
$306$	10.0434	−	3.76544i	0.574143	−	0.215256i
$307$	−1.60111			−0.0913799			−0.0456900	−	0.998956i	$-0.514549\pi$
$307$	−1.60111			−0.0913799			−0.0456900	+	0.998956i	$0.514549\pi$
$308$	18.3198	−	23.6930i	1.04387	−	1.35003i
$309$	11.7786	−	9.98049i	0.670062	−	0.567770i
$310$	−9.59196			−0.544787
$311$	−2.33135	−	4.03802i	−0.132199	−	0.228975i	0.792325	−	0.610099i	$-0.208870\pi$
$311$	−2.33135	−	4.03802i	−0.132199	−	0.228975i	−0.924524	+	0.381124i	$0.875537\pi$
$312$	−1.17278	−	6.46885i	−0.0663957	−	0.366227i
$313$	11.8023	−	20.4423i	0.667108	−	1.15547i	−0.311601	−	0.950213i	$-0.600865\pi$
$313$	11.8023	−	20.4423i	0.667108	−	1.15547i	0.978709	−	0.205252i	$-0.0658014\pi$
$314$	−45.1333			−2.54702
$315$	7.73878	−	1.76389i	0.436031	−	0.0993839i
$316$	27.3288			1.53737
$317$	4.30054	−	7.44876i	0.241542	−	0.418364i	−0.719611	−	0.694377i	$-0.755680\pi$
$317$	4.30054	−	7.44876i	0.241542	−	0.418364i	0.961154	+	0.276013i	$0.0890134\pi$
$318$	41.8590	+	15.0075i	2.34733	+	0.841580i
$319$	4.83229	+	8.36977i	0.270556	+	0.468617i
$320$	12.2355			0.683983
$321$	−4.97523	−	1.78375i	−0.277690	−	0.0995591i
$322$	26.4188	+	3.57752i	1.47226	+	0.199367i
$323$	−9.37760			−0.521783
$324$	6.02476	+	30.6980i	0.334709	+	1.70544i
$325$	0.549485	−	0.951736i	0.0304800	−	0.0527928i
$326$	−20.6733			−1.14499
$327$	−6.17061	−	34.0360i	−0.341236	−	1.88219i
$328$	−0.767758	+	1.32980i	−0.0423923	+	0.0734256i
$329$	16.3416	+	2.21291i	0.900941	+	0.122002i
$330$	2.35464	+	12.9878i	0.129619	+	0.714953i
$331$	11.4828	−	19.8889i	0.631154	−	1.09319i	−0.356162	−	0.934424i	$-0.615915\pi$
$331$	11.4828	−	19.8889i	0.631154	−	1.09319i	0.987316	−	0.158767i	$-0.0507518\pi$
$332$	−28.4746	+	49.3194i	−1.56274	+	2.70675i
$333$	27.7943	−	10.4205i	1.52312	−	0.571042i
$334$	23.8326	+	41.2793i	1.30406	+	2.25871i
$335$	1.06964	+	1.85268i	0.0584408	+	0.101222i
$336$	4.36560	−	2.78806i	0.238163	−	0.152101i
$337$	−15.1857	+	26.3025i	−0.827220	+	1.43279i	0.0729904	+	0.997333i	$0.476746\pi$
$337$	−15.1857	+	26.3025i	−0.827220	+	1.43279i	−0.900211	+	0.435455i	$0.856588\pi$
$338$	−27.5948			−1.50096
$339$	2.77709	+	15.3179i	0.150831	+	0.831956i
$340$	5.31084			0.288021
$341$	6.67443	+	11.5604i	0.361441	+	0.626033i
$342$	7.07307	−	42.5032i	0.382468	−	2.29831i
$343$	17.0308	+	7.27676i	0.919578	+	0.392908i
$344$	9.83023	+	17.0265i	0.530010	+	0.918005i
$345$	−5.69024	+	4.82156i	−0.306352	+	0.259584i
$346$	−6.42449	−	11.1275i	−0.345383	−	0.598220i
$347$	−3.89837	−	6.75217i	−0.209275	−	0.362476i	0.742211	−	0.670166i	$-0.233777\pi$
$347$	−3.89837	−	6.75217i	−0.209275	−	0.362476i	−0.951486	+	0.307691i	$0.900444\pi$
$348$	3.18727	+	17.5804i	0.170856	+	0.942409i
$349$	10.4057	+	18.0232i	0.557004	+	0.964760i	0.997745	+	0.0671252i	$0.0213827\pi$
$349$	10.4057	+	18.0232i	0.557004	+	0.964760i	−0.440740	+	0.897635i	$0.645284\pi$
$350$	6.13526	+	0.830812i	0.327944	+	0.0444088i
$351$	−5.70982	+	0.0824975i	−0.304768	+	0.00440339i
$352$	−6.94079	−	12.0218i	−0.369945	−	0.640764i
$353$	−12.1046			−0.644260			−0.322130	−	0.946695i	$-0.604399\pi$
$353$	−12.1046			−0.644260			−0.322130	+	0.946695i	$0.604399\pi$
$354$	−23.3559	+	19.7904i	−1.24135	+	1.05185i
$355$	15.7970			0.838418
$356$	1.52983	−	2.64975i	0.0810810	−	0.140436i
$357$	−5.90090	+	3.76857i	−0.312309	+	0.199454i
$358$	−6.92690	−	11.9977i	−0.366098	−	0.634101i
$359$	5.74290	+	9.94699i	0.303099	+	0.524982i	0.976836	−	0.213988i	$-0.0686455\pi$
$359$	5.74290	+	9.94699i	0.303099	+	0.524982i	−0.673738	+	0.738971i	$0.735312\pi$
$360$	−1.70090	+	10.2210i	−0.0896453	+	0.538693i
$361$	−9.33540	+	16.1694i	−0.491337	+	0.851020i
$362$	1.40845	−	2.43951i	0.0740266	−	0.128218i
$363$	−0.521252	+	0.441677i	−0.0273586	+	0.0231820i
$364$	3.83311	+	9.35161i	0.200910	+	0.490157i
$365$	−4.96804	+	8.60490i	−0.260039	+	0.450401i
$366$	28.5605	+	10.2397i	1.49288	+	0.535236i
$367$	−3.89545			−0.203341			−0.101670	−	0.994818i	$-0.532419\pi$
$367$	−3.89545			−0.203341			−0.101670	+	0.994818i	$0.532419\pi$
$368$	−2.43368	+	4.21526i	−0.126864	+	0.219736i
$369$	1.02992	+	0.847433i	0.0536153	+	0.0441156i
$370$	23.1539			1.20371
$371$	−28.7647	−	3.89520i	−1.49339	−	0.202229i
$372$	4.40230	+	24.2823i	0.228249	+	1.25898i
$373$	−22.8314			−1.18217			−0.591084	−	0.806610i	$-0.701300\pi$
$373$	−22.8314			−1.18217			−0.591084	+	0.806610i	$0.701300\pi$
$374$	−5.82178	−	10.0836i	−0.301037	−	0.521411i
$375$	−1.32145	+	1.11972i	−0.0682394	+	0.0578220i
$376$	−10.7638	+	18.6434i	−0.555099	+	0.961460i
$377$	−3.26139			−0.167970
$378$	−12.6300	−	29.5878i	−0.649617	−	1.52183i
$379$	−30.0012			−1.54106			−0.770530	−	0.637403i	$-0.780008\pi$
$379$	−30.0012			−1.54106			−0.770530	+	0.637403i	$0.780008\pi$
$380$	10.6671	−	18.4760i	0.547211	−	0.947797i
$381$	18.6791	−	15.8276i	0.956962	−	0.810871i
$382$	−3.46685	−	6.00476i	−0.177379	−	0.307230i
$383$	22.2774			1.13832			0.569162	−	0.822225i	$-0.307268\pi$
$383$	22.2774			1.13832			0.569162	+	0.822225i	$0.307268\pi$
$384$	−6.21256	−	34.2673i	−0.317033	−	1.74870i
$385$	−3.26782	−	7.97246i	−0.166543	−	0.406314i
$386$	−12.9014			−0.656662
$387$	15.9901	−	5.99497i	0.812825	−	0.304741i
$388$	25.7723	−	44.6390i	1.30839	−	2.26620i
$389$	6.09373			0.308964			0.154482	−	0.987996i	$-0.450629\pi$
$389$	6.09373			0.308964			0.154482	+	0.987996i	$0.450629\pi$
$390$	−4.19293	−	1.50328i	−0.212317	−	0.0761213i
$391$	3.28956	−	5.69769i	0.166360	−	0.288145i
$392$	−17.2216	+	16.9688i	−0.869824	+	0.857053i
$393$	7.49827	−	6.35358i	0.378238	−	0.320496i
$394$	−12.7463	+	22.0772i	−0.642147	+	1.11223i
$395$	3.93113	−	6.80891i	0.197796	−	0.342593i
$396$	31.7982	−	11.9217i	1.59792	−	0.599086i
$397$	12.8751	+	22.3002i	0.646180	+	1.11922i	0.984028	+	0.178016i	$0.0569679\pi$
$397$	12.8751	+	22.3002i	0.646180	+	1.11922i	−0.337847	+	0.941201i	$0.609699\pi$
$398$	16.4675	+	28.5225i	0.825439	+	1.42970i
$399$	1.25827	+	28.0981i	0.0629924	+	1.40666i
$400$	−0.565177	+	0.978916i	−0.0282589	+	0.0489458i
$401$	−11.2228			−0.560440			−0.280220	−	0.959936i	$-0.590407\pi$
$401$	−11.2228			−0.560440			−0.280220	+	0.959936i	$0.590407\pi$
$402$	6.61530	−	5.60541i	0.329941	−	0.279572i
$403$	−4.50468			−0.224394
$404$	−26.2015	−	45.3824i	−1.30358	−	2.25786i
$405$	8.51496	+	2.91471i	0.423112	+	0.144833i
$406$	−6.96848	−	17.0009i	−0.345840	−	0.843742i
$407$	−16.1113	−	27.9056i	−0.798607	−	1.38323i
$408$	−1.63050	−	8.99353i	−0.0807217	−	0.445246i
$409$	2.28525	+	3.95817i	0.112999	+	0.195719i	0.916978	−	0.398938i	$-0.130621\pi$
$409$	2.28525	+	3.95817i	0.112999	+	0.195719i	−0.803979	+	0.594657i	$0.797288\pi$
$410$	0.520177	+	0.900972i	0.0256897	+	0.0444959i
$411$	−28.6015	+	24.2351i	−1.41081	+	1.19543i
$412$	−15.4913	−	26.8317i	−0.763201	−	1.32190i
$413$	12.2235	−	15.8086i	0.601480	−	0.777892i
$414$	23.3432	+	19.2072i	1.14726	+	0.943982i
$415$	8.19187	+	14.1887i	0.402123	+	0.696497i
$416$	4.68445			0.229674
$417$	−0.787128	−	4.34166i	−0.0385458	−	0.212612i
$418$	−46.7734			−2.28776
$419$	1.10806	−	1.91922i	0.0541324	−	0.0937601i	−0.837689	−	0.546147i	$-0.816094\pi$
$419$	1.10806	−	1.91922i	0.0541324	−	0.0937601i	0.891822	+	0.452387i	$0.149427\pi$
$420$	−0.712601	−	15.9129i	−0.0347713	−	0.776469i
$421$	6.75580	+	11.7014i	0.329257	+	0.570290i	0.982365	−	0.186975i	$-0.0598683\pi$
$421$	6.75580	+	11.7014i	0.329257	+	0.570290i	−0.653107	+	0.757265i	$0.726535\pi$
$422$	13.5063	+	23.3936i	0.657478	+	1.13878i
$423$	14.4392	+	11.8808i	0.702057	+	0.577664i
$424$	18.9465	−	32.8163i	0.920125	−	1.59370i
$425$	0.763940	−	1.32318i	0.0370565	−	0.0641838i
$426$	−11.4218	−	63.0004i	−0.553386	−	3.05238i
$427$	−19.6262	−	2.65770i	−0.949779	−	0.128615i
$428$	−5.30341	+	9.18577i	−0.256350	+	0.444011i
$429$	1.10581	+	6.09945i	0.0533890	+	0.294484i
$430$	13.3205			0.642371
$431$	−3.41681	+	5.91809i	−0.164582	+	0.285064i	−0.936507	−	0.350650i	$-0.885961\pi$
$431$	−3.41681	+	5.91809i	−0.164582	+	0.285064i	0.771925	+	0.635714i	$0.219294\pi$
$432$	5.87288	−	0.0848535i	0.282559	−	0.00408251i
$433$	−9.28532			−0.446224			−0.223112	−	0.974793i	$-0.571622\pi$
$433$	−9.28532			−0.446224			−0.223112	+	0.974793i	$0.571622\pi$
$434$	−9.62496	−	23.4819i	−0.462013	−	1.12717i
$435$	4.83859	+	1.73476i	0.231993	+	0.0831753i
$436$	−69.4184			−3.32454
$437$	−13.2145	−	22.8882i	−0.632137	−	1.09489i
$438$	37.9094	+	13.5915i	1.81138	+	0.649428i
$439$	−9.31979	+	16.1424i	−0.444809	+	0.770433i	−0.998039	−	0.0625964i	$-0.980062\pi$
$439$	−9.31979	+	16.1424i	−0.444809	+	0.770433i	0.553229	+	0.833029i	$0.313395\pi$
$440$	11.2479			0.536220
$441$	12.0835	+	17.1752i	0.575407	+	0.817867i
$442$	3.92921			0.186893
$443$	−1.63289	+	2.82825i	−0.0775809	+	0.134374i	−0.902206	−	0.431306i	$-0.858053\pi$
$443$	−1.63289	+	2.82825i	−0.0775809	+	0.134374i	0.824625	+	0.565680i	$0.191386\pi$
$444$	−10.6266	−	58.6146i	−0.504318	−	2.78173i
$445$	−0.440119	−	0.762308i	−0.0208636	−	0.0361369i
$446$	50.3887			2.38597
$447$	8.47089	−	7.17772i	0.400659	−	0.339495i
$448$	12.2776	+	29.9534i	0.580060	+	1.41517i
$449$	−18.4183			−0.869215			−0.434607	−	0.900620i	$-0.643113\pi$
$449$	−18.4183			−0.869215			−0.434607	+	0.900620i	$0.643113\pi$
$450$	5.42102	+	4.46051i	0.255549	+	0.210270i
$451$	0.723915	−	1.25386i	0.0340878	−	0.0590418i
$452$	31.2418			1.46949
$453$	2.46664	−	2.09008i	0.115893	−	0.0982004i
$454$	−10.7382	+	18.5992i	−0.503971	+	0.872903i
$455$	2.88130	+	0.390175i	0.135078	+	0.0182917i
$456$	−34.5627	−	12.3916i	−1.61855	−	0.580291i
$457$	−8.38139	+	14.5170i	−0.392065	+	0.679076i	−0.992722	−	0.120431i	$-0.961572\pi$
$457$	−8.38139	+	14.5170i	−0.392065	+	0.679076i	0.600657	+	0.799507i	$0.294906\pi$
$458$	−10.5145	+	18.2117i	−0.491311	+	0.850976i
$459$	−7.93827	+	0.114695i	−0.370527	+	0.00535350i
$460$	7.48382	+	12.9624i	0.348935	+	0.604373i
$461$	5.98073	+	10.3589i	0.278550	+	0.482463i	0.971025	−	0.238979i	$-0.0768128\pi$
$461$	5.98073	+	10.3589i	0.278550	+	0.482463i	−0.692474	+	0.721442i	$0.743479\pi$
$462$	−29.4324	+	18.7968i	−1.36932	+	0.874506i
$463$	−11.7397	+	20.3338i	−0.545592	+	0.944993i	0.452977	+	0.891522i	$0.350362\pi$
$463$	−11.7397	+	20.3338i	−0.545592	+	0.944993i	−0.998569	+	0.0534711i	$0.982971\pi$
$464$	3.35453			0.155730
$465$	6.68312	+	2.39607i	0.309922	+	0.111115i
$466$	−22.0307			−1.02055
$467$	−15.1457	−	26.2331i	−0.700858	−	1.21392i	−0.968166	−	0.250311i	$-0.919467\pi$
$467$	−15.1457	−	26.2331i	−0.700858	−	1.21392i	0.267307	−	0.963611i	$-0.413866\pi$
$468$	−1.88120	+	11.3045i	−0.0869586	+	0.522549i
$469$	−3.46218	+	4.47762i	−0.159869	+	0.206757i
$470$	7.29275	+	12.6314i	0.336389	+	0.582644i
$471$	31.4462	+	11.2743i	1.44897	+	0.519492i
$472$	13.0433	+	22.5917i	0.600368	+	1.03987i
$473$	−9.26888	−	16.0542i	−0.426183	−	0.738171i
$474$	−29.9971	−	10.7547i	−1.37781	−	0.493981i
$475$	−3.06883	−	5.31536i	−0.140807	−	0.243886i
$476$	5.32911	+	13.0014i	0.244259	+	0.595917i
$477$	−25.4160	−	20.9127i	−1.16372	−	0.957529i
$478$	17.2432	+	29.8661i	0.788686	+	1.36604i
$479$	−0.289900			−0.0132459			−0.00662293	−	0.999978i	$-0.502108\pi$
$479$	−0.289900			−0.0132459			−0.00662293	+	0.999978i	$0.502108\pi$
$480$	−6.94983	−	2.49170i	−0.317215	−	0.113730i
$481$	10.8738			0.495801
$482$	8.34901	−	14.4609i	0.380287	−	0.658676i
$483$	−17.5134	−	9.09202i	−0.796887	−	0.413701i
$484$	0.685552	+	1.18741i	0.0311615	+	0.0539732i
$485$	−7.41446	−	12.8422i	−0.336673	−	0.583135i
$486$	5.46761	−	36.0661i	0.248016	−	1.63599i
$487$	13.3737	−	23.1640i	0.606021	−	1.04966i	−0.385868	−	0.922554i	$-0.626098\pi$
$487$	13.3737	−	23.1640i	0.606021	−	1.04966i	0.991889	−	0.127106i	$-0.0405687\pi$
$488$	12.9273	−	22.3907i	0.585190	−	1.01358i
$489$	14.4040	+	5.16419i	0.651369	+	0.233533i
$490$	4.12247	+	15.8533i	0.186234	+	0.716179i
$491$	−1.84307	+	3.19229i	−0.0831767	+	0.144066i	−0.904613	−	0.426234i	$-0.859840\pi$
$491$	−1.84307	+	3.19229i	−0.0831767	+	0.144066i	0.821436	+	0.570301i	$0.193173\pi$
$492$	2.04210	−	1.73035i	0.0920648	−	0.0780101i
$493$	−4.53425			−0.204213
$494$	7.89202	−	13.6694i	0.355079	−	0.615015i
$495$	1.60377	−	9.63731i	0.0720841	−	0.433165i
$496$	4.63332			0.208042
$497$	15.8514	+	38.6724i	0.711031	+	1.73469i
$498$	50.6633	−	42.9291i	2.27028	−	1.92370i
$499$	3.36109			0.150463			0.0752315	−	0.997166i	$-0.476030\pi$
$499$	3.36109			0.150463			0.0752315	+	0.997166i	$0.476030\pi$
$500$	1.73798	+	3.01027i	0.0777247	+	0.134623i
$501$	−6.29362	−	34.7144i	−0.281178	−	1.55093i
$502$	15.8649	−	27.4787i	0.708083	−	1.22644i
$503$	−7.93752			−0.353916			−0.176958	−	0.984218i	$-0.556626\pi$
$503$	−7.93752			−0.353916			−0.176958	+	0.984218i	$0.556626\pi$
$504$	−26.7286	+	6.09220i	−1.19058	+	0.271368i
$505$	−15.0759			−0.670868
$506$	16.4076	−	28.4188i	0.729408	−	1.26337i
$507$	19.2265	+	6.89318i	0.853877	+	0.306137i
$508$	−24.5669	−	42.5511i	−1.08998	−	1.88790i
$509$	13.4473			0.596042			0.298021	−	0.954559i	$-0.403673\pi$
$509$	13.4473			0.596042			0.298021	+	0.954559i	$0.403673\pi$
$510$	−5.82936	−	2.08998i	−0.258129	−	0.0925458i
$511$	−26.0506	−	3.52767i	−1.15241	−	0.156055i
$512$	−12.6264			−0.558012
$513$	−15.5454	+	27.8469i	−0.686347	+	1.22947i
$514$	−24.8221	+	42.9932i	−1.09486	+	1.89635i
$515$	−8.91340			−0.392771
$516$	−6.11354	−	33.7212i	−0.269134	−	1.48449i
$517$	10.1491	−	17.5788i	0.446357	−	0.773113i
$518$	23.2335	+	56.6826i	1.02082	+	2.49049i
$519$	1.69655	+	9.35786i	0.0744703	+	0.410764i
$520$	−1.89784	+	3.28715i	−0.0832257	+	0.144151i
$521$	9.26516	−	16.0477i	0.405914	−	0.703064i	−0.588513	−	0.808487i	$-0.700287\pi$
$521$	9.26516	−	16.0477i	0.405914	−	0.703064i	0.994427	+	0.105424i	$0.0336199\pi$
$522$	3.41997	−	20.5511i	0.149688	−	0.899499i
$523$	−18.3171	−	31.7262i	−0.800952	−	1.38729i	−0.918990	−	0.394280i	$-0.870994\pi$
$523$	−18.3171	−	31.7262i	−0.800952	−	1.38729i	0.118038	−	0.993009i	$-0.462339\pi$
$524$	−9.86176	−	17.0811i	−0.430813	−	0.746190i
$525$	−4.06716	−	2.11145i	−0.177505	−	0.0921513i
$526$	−8.77990	+	15.2072i	−0.382822	+	0.663067i
$527$	−6.26277			−0.272811
$528$	−1.13739	−	6.27364i	−0.0494985	−	0.273025i
$529$	−4.45792			−0.193822
$530$	−12.8368	−	22.2340i	−0.557595	−	0.965782i
$531$	21.2167	−	7.95448i	0.920725	−	0.345195i
$532$	55.9345	+	7.57442i	2.42507	+	0.328393i
$533$	0.244291	+	0.423124i	0.0105814	+	0.0183275i
$534$	−2.72195	+	2.30642i	−0.117790	+	0.0998085i
$535$	1.52574	+	2.64266i	0.0659636	+	0.114252i
$536$	−3.69438	−	6.39886i	−0.159573	−	0.276389i
$537$	1.82923	+	10.0897i	0.0789369	+	0.435402i
$538$	31.7829	+	55.0497i	1.37026	+	2.37336i
$539$	16.2382	−	15.9998i	0.699428	−	0.689159i
$540$	8.80388	−	15.7706i	0.378859	−	0.678660i
$541$	−4.11892	−	7.13418i	−0.177086	−	0.306722i	0.763795	−	0.645459i	$-0.223334\pi$
$541$	−4.11892	−	7.13418i	−0.177086	−	0.306722i	−0.940881	+	0.338737i	$0.890000\pi$
$542$	−7.74808			−0.332809
$543$	−1.59072	+	1.34788i	−0.0682642	+	0.0578430i
$544$	6.51271			0.279230
$545$	−9.98551	+	17.2954i	−0.427732	+	0.740854i
$546$	−0.527215	−	11.7731i	−0.0225627	−	0.503842i
$547$	9.35515	+	16.2036i	0.399997	+	0.692816i	0.993725	−	0.111850i	$-0.0356777\pi$
$547$	9.35515	+	16.2036i	0.399997	+	0.692816i	−0.593728	+	0.804666i	$0.702344\pi$
$548$	37.6168	+	65.1541i	1.60691	+	2.78325i
$549$	−17.3414	−	14.2688i	−0.740113	−	0.608978i
$550$	3.81036	−	6.59974i	0.162474	−	0.281414i
$551$	−9.10729	+	15.7743i	−0.387983	+	0.672007i
$552$	19.6532	−	16.6529i	0.836496	−	0.708796i
$553$	20.6134	+	2.79139i	0.876572	+	0.118702i
$554$	33.0939	−	57.3203i	1.40602	−	2.43531i
$555$	−16.1323	−	5.78384i	−0.684777	−	0.245510i
$556$	−8.85506			−0.375538
$557$	8.91417	−	15.4398i	0.377706	−	0.654205i	−0.613022	−	0.790066i	$-0.710046\pi$
$557$	8.91417	−	15.4398i	0.377706	−	0.654205i	0.990728	+	0.135860i	$0.0433798\pi$
$558$	4.72371	−	28.3855i	0.199970	−	1.20166i
$559$	6.25571			0.264588
$560$	−2.96359	−	0.401317i	−0.125234	−	0.0169587i
$561$	1.53739	+	8.47996i	0.0649086	+	0.358024i
$562$	15.5607			0.656390
$563$	−16.3816	−	28.3738i	−0.690404	−	1.19581i	−0.971706	−	0.236195i	$-0.924100\pi$
$563$	−16.3816	−	28.3738i	−0.690404	−	1.19581i	0.281302	−	0.959619i	$-0.409234\pi$
$564$	28.6297	−	24.2591i	1.20553	−	1.02149i
$565$	4.49399	−	7.78382i	0.189064	−	0.327468i
$566$	20.8816			0.877719
$567$	1.40881	+	23.7700i	0.0591642	+	0.998248i
$568$	−54.5605			−2.28931
$569$	4.01861	−	6.96043i	0.168469	−	0.291796i	−0.769413	−	0.638752i	$-0.779451\pi$
$569$	4.01861	−	6.96043i	0.168469	−	0.291796i	0.937882	+	0.346955i	$0.112784\pi$
$570$	−18.9794	+	16.0820i	−0.794961	+	0.673602i
$571$	4.11422	+	7.12604i	0.172175	+	0.298216i	0.939180	−	0.343425i	$-0.111587\pi$
$571$	4.11422	+	7.12604i	0.172175	+	0.298216i	−0.767005	+	0.641641i	$0.778254\pi$
$572$	12.4402			0.520150
$573$	0.915510	+	5.04979i	0.0382460	+	0.210958i
$574$	−1.68369	+	2.17751i	−0.0702758	+	0.0908874i
$575$	4.30605			0.179575
$576$	−6.02554	+	36.2085i	−0.251064	+	1.50869i
$577$	−10.2344	+	17.7266i	−0.426065	+	0.737966i	−0.996519	−	0.0833630i	$-0.973434\pi$
$577$	−10.2344	+	17.7266i	−0.426065	+	0.737966i	0.570454	+	0.821329i	$0.306767\pi$
$578$	−34.3186			−1.42746
$579$	8.98892	+	3.22276i	0.373567	+	0.133933i
$580$	5.15776	−	8.93350i	0.214164	−	0.370943i
$581$	−26.5151	+	34.2919i	−1.10003	+	1.42267i
$582$	−45.8554	+	38.8551i	−1.90077	+	1.61060i
$583$	−17.8646	+	30.9424i	−0.739876	+	1.28150i
$584$	17.1589	−	29.7200i	0.710038	−	1.22982i
$585$	2.54587	+	2.09479i	0.105259	+	0.0866089i
$586$	13.8415	+	23.9742i	0.571787	+	0.990365i
$587$	12.9160	+	22.3712i	0.533101	+	0.923359i	0.999253	+	0.0386538i	$0.0123069\pi$
$587$	12.9160	+	22.3712i	0.533101	+	0.923359i	−0.466151	+	0.884705i	$0.654360\pi$
$588$	38.2410	−	17.7121i	1.57703	−	0.730436i
$589$	−12.5791	+	21.7877i	−0.518313	+	0.897745i
$590$	17.6744			0.727645
$591$	14.3957	−	12.1981i	0.592161	−	0.501762i
$592$	−11.1843			−0.459671
$593$	22.2664	+	38.5665i	0.914370	+	1.58373i	0.807822	+	0.589427i	$0.200646\pi$
$593$	22.2664	+	38.5665i	0.914370	+	1.58373i	0.106548	+	0.994308i	$0.466020\pi$
$594$	−39.5943	+	0.572073i	−1.62458	+	0.0234724i
$595$	4.00583	+	0.542453i	0.164223	+	0.0222384i
$596$	−11.1409	−	19.2967i	−0.456351	−	0.790423i
$597$	−4.34865	−	23.9864i	−0.177979	−	0.981698i
$598$	5.53688	+	9.59016i	0.226420	+	0.392171i
$599$	13.0436	+	22.5922i	0.532946	+	0.923090i	0.999260	+	0.0384707i	$0.0122486\pi$
$599$	13.0436	+	22.5922i	0.532946	+	0.923090i	−0.466313	+	0.884620i	$0.654418\pi$
$600$	4.56409	−	3.86733i	0.186328	−	0.157883i
$601$	−21.7328	−	37.6424i	−0.886500	−	1.53546i	−0.843984	−	0.536368i	$-0.819796\pi$
$601$	−21.7328	−	37.6424i	−0.886500	−	1.53546i	−0.0425160	−	0.999096i	$-0.513537\pi$
$602$	13.3663	+	32.6097i	0.544771	+	1.32907i
$603$	−6.00939	+	2.25302i	−0.244721	+	0.0917500i
$604$	−3.24413	−	5.61900i	−0.132002	−	0.228634i
$605$	0.394454			0.0160368
$606$	10.9004	+	60.1244i	0.442797	+	2.44239i
$607$	−7.72077			−0.313377			−0.156688	−	0.987648i	$-0.550082\pi$
$607$	−7.72077			−0.313377			−0.156688	+	0.987648i	$0.550082\pi$
$608$	13.0811	−	22.6572i	0.530509	−	0.918869i
$609$	0.608399	+	13.5860i	0.0246536	+	0.550532i
$610$	−8.75857	−	15.1703i	−0.354624	−	0.614227i
$611$	3.42490	+	5.93209i	0.138556	+	0.239987i
$612$	−2.61540	+	15.7164i	−0.105721	+	0.635298i
$613$	3.51912	−	6.09529i	0.142136	−	0.246186i	−0.786165	−	0.618017i	$-0.787936\pi$
$613$	3.51912	−	6.09529i	0.142136	−	0.246186i	0.928301	+	0.371830i	$0.121270\pi$
$614$	1.87335	−	3.24474i	0.0756024	−	0.130947i
$615$	−0.137366	−	0.757686i	−0.00553913	−	0.0305528i
$616$	11.2865	+	27.5357i	0.454748	+	1.10944i
$617$	−9.98197	+	17.2893i	−0.401859	+	0.696040i	−0.993950	−	0.109831i	$-0.964969\pi$
$617$	−9.98197	+	17.2893i	−0.401859	+	0.696040i	0.592091	+	0.805871i	$0.298302\pi$
$618$	6.44468	+	35.5477i	0.259243	+	1.42994i
$619$	11.1269			0.447229			0.223614	−	0.974678i	$-0.428214\pi$
$619$	11.1269			0.447229			0.223614	+	0.974678i	$0.428214\pi$
$620$	7.12396	−	12.3391i	0.286105	−	0.495549i
$621$	−11.4662	−	19.2136i	−0.460124	−	0.771015i
$622$	10.9111			0.437495
$623$	1.42456	−	1.84238i	0.0570738	−	0.0738133i
$624$	2.02536	+	0.726145i	0.0810794	+	0.0290691i
$625$	1.00000			0.0400000
$626$	27.6184	+	47.8364i	1.10385	+	1.91193i
$627$	32.5890	+	11.6840i	1.30148	+	0.466614i
$628$	33.5205	−	58.0593i	1.33761	−	2.31682i
$629$	15.1176			0.602778
$630$	−5.48003	+	17.7470i	−0.218330	+	0.707056i
$631$	3.94010			0.156853			0.0784265	−	0.996920i	$-0.475010\pi$
$631$	3.94010			0.156853			0.0784265	+	0.996920i	$0.475010\pi$
$632$	−13.5775	+	23.5169i	−0.540084	+	0.935453i
$633$	−3.56669	−	19.6732i	−0.141763	−	0.781940i
$634$	10.0636	+	17.4307i	0.399676	+	0.692260i
$635$	−14.1353			−0.560943
$636$	−50.3943	+	42.7011i	−1.99827	+	1.69321i
$637$	1.93604	+	7.44519i	0.0767086	+	0.294989i
$638$	−22.6159			−0.895370
$639$	−7.77948	+	46.7482i	−0.307751	+	1.84933i
$640$	−10.0534	+	17.4130i	−0.397395	+	0.688308i
$641$	9.45310			0.373375			0.186687	−	0.982419i	$-0.440225\pi$
$641$	9.45310			0.373375			0.186687	+	0.982419i	$0.440225\pi$
$642$	9.43609	−	7.99557i	0.372413	−	0.315560i
$643$	2.84191	−	4.92233i	0.112074	−	0.194118i	−0.804532	−	0.593909i	$-0.797584\pi$
$643$	2.84191	−	4.92233i	0.112074	−	0.194118i	0.916606	+	0.399791i	$0.130917\pi$
$644$	−24.2234	+	31.3280i	−0.954534	+	1.23449i
$645$	−9.28095	−	3.32746i	−0.365437	−	0.131019i
$646$	10.9721	−	19.0043i	0.431693	−	0.747715i
$647$	−1.00965	+	1.74877i	−0.0396935	+	0.0687512i	−0.885190	−	0.465230i	$-0.845972\pi$
$647$	−1.00965	+	1.74877i	−0.0396935	+	0.0687512i	0.845496	+	0.533982i	$0.179305\pi$
$648$	−29.4094	−	10.0670i	−1.15531	−	0.395467i
$649$	−12.2985	−	21.3016i	−0.482758	−	0.836161i
$650$	1.28584	+	2.22714i	0.0504347	+	0.0873554i
$651$	0.840329	+	18.7652i	0.0329351	+	0.735464i
$652$	15.3541	−	26.5940i	0.601312	−	1.04150i
$653$	46.5020			1.81976			0.909882	−	0.414867i	$-0.136172\pi$
$653$	46.5020			1.81976			0.909882	+	0.414867i	$0.136172\pi$
$654$	76.1960	+	27.3182i	2.97950	+	1.06823i
$655$	−5.67427			−0.221712
$656$	−0.251267	−	0.435207i	−0.00981033	−	0.0169920i
$657$	−23.0179	−	18.9396i	−0.898015	−	0.738902i
$658$	−23.6049	+	30.5281i	−0.920215	+	1.19011i
$659$	−14.4190	−	24.9744i	−0.561685	−	0.972866i	−0.997350	−	0.0727574i	$-0.976820\pi$
$659$	−14.4190	−	24.9744i	−0.561685	−	0.972866i	0.435665	−	0.900109i	$-0.356513\pi$
$660$	−18.4562	−	6.61703i	−0.718407	−	0.257568i
$661$	−3.63059	−	6.28836i	−0.141213	−	0.244589i	0.786740	−	0.617284i	$-0.211767\pi$
$661$	−3.63059	−	6.28836i	−0.141213	−	0.244589i	−0.927954	+	0.372695i	$0.878434\pi$
$662$	26.8707	+	46.5415i	1.04436	+	1.80889i
$663$	−2.73765	−	0.981517i	−0.106321	−	0.0381190i
$664$	−28.2935	−	49.0057i	−1.09800	−	1.90179i
$665$	9.93306	−	12.8464i	0.385188	−	0.498162i
$666$	−11.4025	+	68.5193i	−0.441837	+	2.65507i
$667$	−6.38949	−	11.0669i	−0.247402	−	0.428513i
$668$	−70.8021			−2.73942
$669$	−35.1079	−	12.5871i	−1.35735	−	0.486645i
$670$	−5.00609			−0.193402
$671$	−12.1891	+	21.1121i	−0.470553	+	0.815022i
$672$	−0.873865	−	19.5140i	−0.0337101	−	0.752770i
$673$	−14.3678	−	24.8857i	−0.553837	−	0.959274i	−0.997993	−	0.0633242i	$-0.979830\pi$
$673$	−14.3678	−	24.8857i	−0.553837	−	0.959274i	0.444156	−	0.895949i	$-0.353504\pi$
$674$	−35.5358	−	61.5498i	−1.36879	−	2.37081i
$675$	−2.66282	−	4.46200i	−0.102492	−	0.171742i
$676$	20.4947	−	35.4978i	0.788257	−	1.36530i
$677$	−10.8513	+	18.7950i	−0.417048	+	0.722349i	−0.995641	−	0.0932677i	$-0.970269\pi$
$677$	−10.8513	+	18.7950i	−0.417048	+	0.722349i	0.578593	+	0.815617i	$0.303602\pi$
$678$	−34.2921	−	12.2946i	−1.31698	−	0.472171i
$679$	23.9988	−	31.0376i	0.920991	−	1.19111i
$680$	−2.63853	+	4.57007i	−0.101183	+	0.175254i
$681$	12.1279	−	10.2764i	0.464741	−	0.393793i
$682$	−31.2373			−1.19614
$683$	−21.1996	+	36.7188i	−0.811180	+	1.40501i	0.100858	+	0.994901i	$0.467841\pi$
$683$	−21.1996	+	36.7188i	−0.811180	+	1.40501i	−0.912038	+	0.410105i	$0.865492\pi$
$684$	49.4228	+	40.6660i	1.88973	+	1.55490i
$685$	21.6440			0.826974
$686$	−34.6735	+	26.0000i	−1.32384	+	0.992684i
$687$	11.8752	−	10.0623i	0.453067	−	0.383901i
$688$	−6.43436			−0.245308
$689$	−6.02855	−	10.4417i	−0.229669	−	0.397799i
$690$	−3.11342	−	17.1730i	−0.118526	−	0.653767i
$691$	−3.44009	+	5.95842i	−0.130867	+	0.226669i	−0.924011	−	0.382366i	$-0.875110\pi$
$691$	−3.44009	+	5.95842i	−0.130867	+	0.226669i	0.793144	+	0.609034i	$0.208443\pi$
$692$	19.0859			0.725537
$693$	25.2022	−	5.74431i	0.957353	−	0.218208i
$694$	18.2450			0.692569
$695$	−1.27376	+	2.20622i	−0.0483164	+	0.0836865i
$696$	−16.7117	−	5.99159i	−0.633457	−	0.227111i
$697$	0.339633	+	0.588262i	0.0128645	+	0.0222820i
$698$	−48.7003			−1.84333
$699$	15.3497	+	5.50327i	0.580579	+	0.208153i
$700$	−5.62542	+	7.27533i	−0.212621	+	0.274982i
$701$	10.0762			0.380572			0.190286	−	0.981729i	$-0.439059\pi$
$701$	10.0762			0.380572			0.190286	+	0.981729i	$0.439059\pi$
$702$	6.51352	−	11.6679i	0.245837	−	0.440375i
$703$	30.3645	−	52.5928i	1.14522	−	1.98358i
$704$	39.8462			1.50176
$705$	−1.92584	−	10.6226i	−0.0725312	−	0.400069i
$706$	14.1628	−	24.5307i	0.533024	−	0.923224i
$707$	−15.1277	−	36.9070i	−0.568937	−	1.38803i
$708$	−8.11181	−	44.7433i	−0.304860	−	1.68155i
$709$	2.60348	−	4.50936i	0.0977758	−	0.169353i	−0.812988	−	0.582281i	$-0.802161\pi$
$709$	2.60348	−	4.50936i	0.0977758	−	0.169353i	0.910764	+	0.412928i	$0.135494\pi$
$710$	−18.4831	+	32.0137i	−0.693659	+	1.20145i
$711$	18.2137	+	14.9865i	0.683067	+	0.562039i
$712$	1.52010	+	2.63290i	0.0569683	+	0.0986719i
$713$	−8.82525	−	15.2858i	−0.330508	−	0.572457i
$714$	−0.732978	−	16.3679i	−0.0274310	−	0.612554i
$715$	1.78946	−	3.09944i	0.0669221	−	0.115912i
$716$	20.5785			0.769054
$717$	−4.55351	−	25.1163i	−0.170054	−	0.937986i
$718$	−26.8776			−1.00306
$719$	10.9108	+	18.8980i	0.406902	+	0.704776i	0.994541	−	0.104348i	$-0.0332756\pi$
$719$	10.9108	+	18.8980i	0.406902	+	0.704776i	−0.587638	+	0.809124i	$0.699942\pi$
$720$	−2.61858	−	2.15461i	−0.0975887	−	0.0802977i
$721$	−8.94406	−	21.8207i	−0.333094	−	0.812646i
$722$	−21.8455	−	37.8376i	−0.813007	−	1.40817i
$723$	−9.42944	+	7.98994i	−0.350685	+	0.297149i
$724$	2.09212	+	3.62365i	0.0777529	+	0.134672i
$725$	−1.48384	−	2.57008i	−0.0551084	−	0.0954505i
$726$	−0.285203	−	1.57313i	−0.0105849	−	0.0583843i
$727$	−9.27100	−	16.0578i	−0.343842	−	0.595553i	0.641300	−	0.767290i	$-0.278395\pi$
$727$	−9.27100	−	16.0578i	−0.343842	−	0.595553i	−0.985143	+	0.171737i	$0.945062\pi$
$728$	−9.95159	−	1.34760i	−0.368830	−	0.0499455i
$729$	−12.8188	+	23.7629i	−0.474771	+	0.880109i
$730$	−11.6256	−	20.1361i	−0.430283	−	0.745271i
$731$	8.69721			0.321678
$732$	−34.3842	+	29.1351i	−1.27088	+	1.07686i
$733$	−11.3482			−0.419156			−0.209578	−	0.977792i	$-0.567209\pi$
$733$	−11.3482			−0.419156			−0.209578	+	0.977792i	$0.567209\pi$
$734$	4.55782	−	7.89438i	0.168232	−	0.291387i
$735$	1.08786	−	12.0755i	0.0401262	−	0.445410i
$736$	9.17744	+	15.8958i	0.338285	+	0.585927i
$737$	3.48341	+	6.03345i	0.128313	+	0.222245i
$738$	−2.92242	+	1.09566i	−0.107576	+	0.0403319i
$739$	1.73717	−	3.00887i	0.0639029	−	0.110683i	−0.832304	−	0.554320i	$-0.812979\pi$
$739$	1.73717	−	3.00887i	0.0639029	−	0.110683i	0.896207	+	0.443637i	$0.146312\pi$
$740$	−17.1964	+	29.7851i	−0.632153	+	1.09492i
$741$	−8.91332	+	7.55261i	−0.327439	+	0.277452i
$742$	41.5496	−	53.7360i	1.52534	−	1.97271i
$743$	−20.7664	+	35.9685i	−0.761846	+	1.31956i	0.180051	+	0.983657i	$0.442374\pi$
$743$	−20.7664	+	35.9685i	−0.761846	+	1.31956i	−0.941898	+	0.335899i	$0.890960\pi$
$744$	−23.0825	−	8.27567i	−0.846245	−	0.303401i
$745$	−6.41030			−0.234855
$746$	26.7137	−	46.2694i	0.978057	−	1.69404i
$747$	−46.0230	+	17.2548i	−1.68389	+	0.631319i
$748$	17.2954			0.632381
$749$	−4.93846	+	6.38689i	−0.180448	+	0.233372i
$750$	−0.723033	−	3.98812i	−0.0264014	−	0.145625i
$751$	−33.2413			−1.21299			−0.606497	−	0.795086i	$-0.707426\pi$
$751$	−33.2413			−1.21299			−0.606497	+	0.795086i	$0.707426\pi$
$752$	−3.52270	−	6.10150i	−0.128460	−	0.222499i
$753$	−17.9179	+	15.1826i	−0.652965	+	0.553283i
$754$	3.81595	−	6.60942i	0.138969	−	0.240701i
$755$	−1.86661			−0.0679329
$756$	47.4420	+	5.72774i	1.72545	+	0.208316i
$757$	13.7487			0.499705			0.249853	−	0.968284i	$-0.419618\pi$
$757$	13.7487			0.499705			0.249853	+	0.968284i	$0.419618\pi$
$758$	35.1026	−	60.7995i	1.27498	−	2.20834i
$759$	−18.5309	+	15.7020i	−0.672630	+	0.569946i
$760$	10.5993	+	18.3585i	0.384476	+	0.665931i
$761$	−52.4798			−1.90239			−0.951197	−	0.308586i	$-0.900144\pi$
$761$	−52.4798			−1.90239			−0.951197	+	0.308586i	$0.900144\pi$
$762$	10.2203	+	56.3734i	0.370243	+	2.04219i
$763$	−52.3604	−	7.09044i	−1.89558	−	0.256691i
$764$	10.2993			0.372617
$765$	3.53949	+	2.91235i	0.127970	+	0.105296i
$766$	−26.0654	+	45.1467i	−0.941783	+	1.63122i
$767$	8.30045			0.299712
$768$	36.8158	+	13.1994i	1.32848	+	0.476293i
$769$	−17.0666	+	29.5602i	−0.615436	+	1.06597i	0.374872	+	0.927077i	$0.377687\pi$
$769$	−17.0666	+	29.5602i	−0.615436	+	1.06597i	−0.990308	+	0.138890i	$0.955647\pi$
$770$	19.9802	+	2.70564i	0.720036	+	0.0975044i
$771$	28.0343	−	23.7546i	1.00963	−	0.855501i
$772$	9.58186	−	16.5963i	0.344859	−	0.597312i
$773$	2.36364	−	4.09395i	0.0850143	−	0.147249i	−0.820383	−	0.571814i	$-0.806240\pi$
$773$	2.36364	−	4.09395i	0.0850143	−	0.147249i	0.905397	+	0.424565i	$0.139573\pi$
$774$	−6.55988	+	39.4194i	−0.235790	+	1.41690i
$775$	−2.04950	−	3.54983i	−0.0736201	−	0.127514i
$776$	25.6084	+	44.3551i	0.919288	+	1.59225i
$777$	−2.02846	−	45.2969i	−0.0727705	−	1.62502i
$778$	−7.12989	+	12.3493i	−0.255619	+	0.442745i
$779$	2.72868			0.0977653
$780$	5.04791	−	4.27729i	0.180744	−	0.153152i
$781$	51.4448			1.84084
$782$	7.69783	+	13.3330i	0.275274	+	0.476788i
$783$	−7.51652	+	13.4645i	−0.268618	+	0.481183i
$784$	−1.99133	−	7.65781i	−0.0711188	−	0.273493i
$785$	−9.64355	−	16.7031i	−0.344193	−	0.596160i
$786$	4.10269	+	22.6297i	0.146338	+	0.807173i
$787$	−1.68905	−	2.92553i	−0.0602082	−	0.104284i	0.834350	−	0.551235i	$-0.185843\pi$
$787$	−1.68905	−	2.92553i	−0.0602082	−	0.104284i	−0.894558	+	0.446951i	$0.852510\pi$
$788$	−18.9333	−	32.7935i	−0.674472	−	1.16822i
$789$	9.91610	−	8.40230i	0.353022	−	0.299130i
$790$	9.19913	+	15.9334i	0.327290	+	0.566884i
$791$	23.5649	+	3.19106i	0.837871	+	0.113461i
$792$	−5.53918	+	33.2858i	−0.196826	+	1.18276i
$793$	−4.11329	−	7.12443i	−0.146067	−	0.252996i
$794$	−60.2572			−2.13845
$795$	3.38988	+	18.6980i	0.120227	+	0.663149i
$796$	−48.9216			−1.73398
$797$	1.93096	−	3.34453i	0.0683982	−	0.118469i	−0.829798	−	0.558064i	$-0.811544\pi$
$797$	1.93096	−	3.34453i	0.0683982	−	0.118469i	0.898196	+	0.439594i	$0.144878\pi$
$798$	−58.4149	−	30.3259i	−2.06786	−	1.07352i
$799$	4.76157	+	8.24729i	0.168452	+	0.291768i
$800$	2.13129	+	3.69150i	0.0753525	+	0.130514i
$801$	2.47264	−	0.927035i	0.0873666	−	0.0327552i
$802$	13.1311	−	22.7437i	0.463675	−	0.803109i
$803$	−16.1790	+	28.0229i	−0.570945	+	0.988905i
$804$	2.29758	+	12.6730i	0.0810295	+	0.446944i
$805$	4.32087	+	10.5416i	0.152291	+	0.371542i
$806$	5.27064	−	9.12902i	0.185650	−	0.321556i
$807$	−8.39309	−	46.2948i	−0.295451	−	1.62965i
$808$	52.0698			1.83181
$809$	−24.9768	+	43.2610i	−0.878137	+	1.52098i	−0.0247531	+	0.999694i	$0.507880\pi$
$809$	−24.9768	+	43.2610i	−0.878137	+	1.52098i	−0.853383	+	0.521284i	$0.825453\pi$
$810$	−15.8697	+	13.8458i	−0.557603	+	0.486492i
$811$	−1.93538			−0.0679603			−0.0339801	−	0.999423i	$-0.510818\pi$
$811$	−1.93538			−0.0679603			−0.0339801	+	0.999423i	$0.510818\pi$
$812$	27.0454	+	3.66238i	0.949109	+	0.128524i
$813$	5.39842	+	1.93547i	0.189331	+	0.0678800i
$814$	75.4033			2.64288
$815$	−4.41723	−	7.65086i	−0.154729	−	0.267998i
$816$	2.81583	+	1.00955i	0.0985736	+	0.0353412i
$817$	17.4688	−	30.2568i	0.611156	−	1.05855i
$818$	−10.6953			−0.373954
$819$	−2.57359	+	8.33451i	−0.0899284	+	0.291231i
$820$	−1.54534			−0.0539657
$821$	−1.49737	+	2.59351i	−0.0522584	+	0.0905142i	−0.890971	−	0.454060i	$-0.849975\pi$
$821$	−1.49737	+	2.59351i	−0.0522584	+	0.0905142i	0.838713	+	0.544574i	$0.183309\pi$
$822$	−15.6493	−	86.3188i	−0.545832	−	3.01071i
$823$	22.1143	+	38.3030i	0.770855	+	1.33516i	0.937095	+	0.349074i	$0.113504\pi$
$823$	22.1143	+	38.3030i	0.770855	+	1.33516i	−0.166240	+	0.986085i	$0.553163\pi$
$824$	30.7855			1.07246
$825$	−4.30346	+	3.64649i	−0.149827	+	0.126954i
$826$	17.7352	+	43.2685i	0.617088	+	1.50550i
$827$	23.1676			0.805618			0.402809	−	0.915284i	$-0.368034\pi$
$827$	23.1676			0.805618			0.402809	+	0.915284i	$0.368034\pi$
$828$	−42.0451	+	15.7634i	−1.46117	+	0.547816i
$829$	−26.9945	+	46.7558i	−0.937556	+	1.62389i	−0.167545	+	0.985864i	$0.553584\pi$
$829$	−26.9945	+	46.7558i	−0.937556	+	1.62389i	−0.770011	+	0.638030i	$0.779749\pi$
$830$	−38.3392			−1.33077
$831$	−37.3765	+	31.6706i	−1.29658	+	1.09864i
$832$	−6.72321	+	11.6449i	−0.233085	+	0.403716i
$833$	2.69164	+	10.3509i	0.0932598	+	0.358638i
$834$	9.71962	+	3.48474i	0.336563	+	0.120667i
$835$	−10.1846	+	17.6402i	−0.352451	+	0.610463i
$836$	34.7387	−	60.1691i	1.20146	−	2.08099i
$837$	−10.3819	+	18.5974i	−0.358851	+	0.642821i
$838$	2.59295	+	4.49112i	0.0895720	+	0.155143i
$839$	19.6127	+	33.9702i	0.677106	+	1.17278i	0.975849	+	0.218448i	$0.0700994\pi$
$839$	19.6127	+	33.9702i	0.677106	+	1.17278i	−0.298743	+	0.954334i	$0.596567\pi$
$840$	14.0473	+	7.29263i	0.484679	+	0.251620i
$841$	10.0964	−	17.4876i	0.348153	−	0.603019i
$842$	−31.6181			−1.08963
$843$	−10.8418	−	3.88708i	−0.373412	−	0.133878i
$844$	−40.1247			−1.38115
$845$	−5.89613	−	10.2124i	−0.202833	−	0.351317i
$846$	−40.9716	+	15.3609i	−1.40863	+	0.528120i
$847$	0.395811	+	0.965656i	0.0136002	+	0.0331803i
$848$	6.20071	+	10.7399i	0.212933	+	0.368811i
$849$	−14.5491	−	5.21623i	−0.499323	−	0.179020i
$850$	1.78768	+	3.09635i	0.0613168	+	0.106204i
$851$	21.3031	+	36.8981i	0.730261	+	1.26485i
$852$	89.5264	+	32.0975i	3.06712	+	1.09964i
$853$	2.50400	+	4.33705i	0.0857353	+	0.148498i	0.905704	−	0.423910i	$-0.139343\pi$
$853$	2.50400	+	4.33705i	0.0857353	+	0.148498i	−0.819969	+	0.572408i	$0.806009\pi$
$854$	28.3494	−	36.6642i	0.970098	−	1.25462i
$855$	17.2411	−	6.46396i	0.589632	−	0.221063i
$856$	−5.26968	−	9.12735i	−0.180114	−	0.311966i
$857$	49.2192			1.68129			0.840647	−	0.541583i	$-0.182175\pi$
$857$	49.2192			1.68129			0.840647	+	0.541583i	$0.182175\pi$
$858$	−13.6548	−	4.89559i	−0.466166	−	0.167133i
$859$	−3.11324			−0.106222			−0.0531111	−	0.998589i	$-0.516914\pi$
$859$	−3.11324			−0.106222			−0.0531111	+	0.998589i	$0.516914\pi$
$860$	−9.89315	+	17.1354i	−0.337354	+	0.584314i
$861$	1.71704	−	1.09658i	0.0585165	−	0.0373712i
$862$	−7.99559	−	13.8488i	−0.272331	−	0.471691i
$863$	−10.0338	−	17.3790i	−0.341554	−	0.591589i	0.643167	−	0.765726i	$-0.277620\pi$
$863$	−10.0338	−	17.3790i	−0.341554	−	0.591589i	−0.984722	+	0.174136i	$0.944287\pi$
$864$	10.7962	−	19.3396i	0.367295	−	0.657946i
$865$	2.74542	−	4.75520i	0.0933470	−	0.161682i
$866$	10.8642	−	18.8173i	0.369180	−	0.639438i
$867$	23.9112	+	8.57279i	0.812067	+	0.291147i
$868$	37.3555	+	5.05854i	1.26793	+	0.171698i
$869$	12.8022	−	22.1740i	0.434284	−	0.752202i
$870$	−9.17693	+	7.77598i	−0.311127	+	0.263630i
$871$	−2.35101			−0.0796610
$872$	34.4884	−	59.7357i	1.16793	−	2.02291i
$873$	41.6554	−	15.6173i	1.40982	−	0.528565i
$874$	61.8460			2.09197
$875$	1.00344	+	2.44808i	0.0339225	+	0.0827603i
$876$	−45.6394	+	38.6721i	−1.54201	+	1.30661i
$877$	−21.4546			−0.724472			−0.362236	−	0.932086i	$-0.617987\pi$
$877$	−21.4546			−0.724472			−0.362236	+	0.932086i	$0.617987\pi$
$878$	−21.8090	−	37.7743i	−0.736019	−	1.27482i
$879$	−3.65520	−	20.1614i	−0.123287	−	0.680028i
$880$	−1.84057	+	3.18795i	−0.0620454	+	0.107466i
$881$	−10.5582			−0.355715			−0.177857	−	0.984056i	$-0.556917\pi$
$881$	−10.5582			−0.355715			−0.177857	+	0.984056i	$0.556917\pi$
$882$	−48.9449	+	4.39245i	−1.64806	+	0.147901i
$883$	38.3077			1.28916			0.644578	−	0.764539i	$-0.277033\pi$
$883$	38.3077			1.28916			0.644578	+	0.764539i	$0.277033\pi$
$884$	−2.91823	+	5.05452i	−0.0981507	+	0.170002i
$885$	−12.3145	−	4.41507i	−0.413948	−	0.148411i
$886$	−3.82109	−	6.61831i	−0.128372	−	0.222347i
$887$	−13.9057			−0.466908			−0.233454	−	0.972368i	$-0.575003\pi$
$887$	−13.9057			−0.466908			−0.233454	+	0.972368i	$0.575003\pi$
$888$	55.7184	+	19.9765i	1.86979	+	0.670368i
$889$	−14.1840	−	34.6045i	−0.475715	−	1.16060i
$890$	2.05982			0.0690454
$891$	27.7299	+	9.49208i	0.928988	+	0.317997i
$892$	−37.4237	+	64.8198i	−1.25304	+	2.17033i
$893$	38.2555			1.28017
$894$	4.63485	+	25.5650i	0.155013	+	0.855022i
$895$	2.96012	−	5.12708i	0.0989458	−	0.171379i
$896$	−52.7164	−	7.13864i	−1.76113	−	0.238485i
$897$	−1.46216	−	8.06498i	−0.0488199	−	0.269282i
$898$	21.5501	−	37.3259i	0.719138	−	1.24558i
$899$	−6.08225	+	10.5348i	−0.202854	+	0.351354i
$900$	−9.76418	+	3.66075i	−0.325473	+	0.122025i
$901$	−8.38138	−	14.5170i	−0.279224	−	0.483631i
$902$	1.69402	+	2.93412i	0.0564045	+	0.0976955i
$903$	−1.16698	−	26.0594i	−0.0388346	−	0.867204i
$904$	−15.5216	+	26.8841i	−0.516239	+	0.894153i
$905$	1.20377			0.0400145
$906$	1.34962	+	7.44427i	0.0448382	+	0.247319i
$907$	14.8599			0.493415			0.246708	−	0.969090i	$-0.420651\pi$
$907$	14.8599			0.493415			0.246708	+	0.969090i	$0.420651\pi$
$908$	−15.9506	−	27.6273i	−0.529340	−	0.916844i
$909$	7.42434	−	44.6141i	0.246250	−	1.47976i
$910$	−4.16195	+	5.38263i	−0.137967	+	0.178433i
$911$	−23.6254	−	40.9204i	−0.782744	−	1.35575i	−0.930338	−	0.366704i	$-0.880486\pi$
$911$	−23.6254	−	40.9204i	−0.782744	−	1.35575i	0.147594	−	0.989048i	$-0.452847\pi$
$912$	9.16786	−	7.76829i	0.303578	−	0.257234i
$913$	26.6778	+	46.2072i	0.882905	+	1.52924i
$914$	−19.6131	−	33.9709i	−0.648743	−	1.12366i
$915$	2.31293	+	12.7577i	0.0764630	+	0.421756i
$916$	−15.6183	−	27.0517i	−0.516043	−	0.893813i
$917$	−5.69379	−	13.8911i	−0.188026	−	0.458724i
$918$	9.05564	−	16.2216i	0.298881	−	0.535393i
$919$	−17.4778	−	30.2724i	−0.576539	−	0.998595i	−0.995873	−	0.0907626i	$-0.971070\pi$
$919$	−17.4778	−	30.2724i	−0.576539	−	0.998595i	0.419334	−	0.907832i	$-0.362264\pi$
$920$	−14.8724			−0.490330
$921$	−2.11578	+	1.79279i	−0.0697174	+	0.0590743i
$922$	−27.9907			−0.921825
$923$	−8.68023	+	15.0346i	−0.285713	+	0.494870i
$924$	−2.32067	−	51.8221i	−0.0763443	−	1.70482i
$925$	4.94725	+	8.56889i	0.162665	+	0.281743i
$926$	−27.4719	−	47.5827i	−0.902782	−	1.56366i
$927$	4.38954	−	26.3774i	0.144171	−	0.866349i
$928$	6.32498	−	10.9552i	0.207628	−	0.359622i
$929$	2.17775	−	3.77197i	0.0714497	−	0.123754i	−0.828087	−	0.560599i	$-0.810571\pi$
$929$	2.17775	−	3.77197i	0.0714497	−	0.123754i	0.899537	+	0.436845i	$0.143904\pi$
$930$	−12.6753	+	10.7403i	−0.415640	+	0.352188i
$931$	41.4163	+	11.4264i	1.35736	+	0.374484i
$932$	16.3622	−	28.3402i	0.535962	−	0.928314i
$933$	−7.60221	−	2.72559i	−0.248885	−	0.0892318i
$934$	70.8841			2.31940
$935$	2.48786	−	4.30910i	0.0813617	−	0.140923i
$936$	−8.79306	−	7.23509i	−0.287410	−	0.236486i
$937$	−24.6433			−0.805063			−0.402531	−	0.915406i	$-0.631870\pi$
$937$	−24.6433			−0.805063			−0.402531	+	0.915406i	$0.631870\pi$
$938$	−5.02331	−	12.2553i	−0.164017	−	0.400150i
$939$	−7.29334	−	40.2287i	−0.238009	−	1.31282i
$940$	−21.6653			−0.706645
$941$	3.56832	+	6.18051i	0.116324	+	0.201479i	0.918308	−	0.395866i	$-0.129556\pi$
$941$	3.56832	+	6.18051i	0.116324	+	0.201479i	−0.801984	+	0.597345i	$0.796222\pi$
$942$	−59.6414	+	50.5365i	−1.94322	+	1.64657i
$943$	−0.957195	+	1.65791i	−0.0311705	+	0.0539890i
$944$	−8.53749			−0.277871
$945$	8.25136	−	10.9961i	0.268417	−	0.357704i
$946$	43.3797			1.41040
$947$	15.1396	−	26.2225i	0.491970	−	0.852117i	−0.507987	−	0.861365i	$-0.669610\pi$
$947$	15.1396	−	26.2225i	0.491970	−	0.852117i	0.999957	+	0.00924769i	$0.00294367\pi$
$948$	36.1137	−	30.6006i	1.17292	−	0.993861i
$949$	−5.45973	−	9.45653i	−0.177230	−	0.306972i
$950$	14.3626			0.465983
$951$	−2.65755	−	14.6586i	−0.0861769	−	0.475336i
$952$	−13.8355	−	1.87355i	−0.448412	−	0.0607221i
$953$	8.57407			0.277741			0.138871	−	0.990311i	$-0.455653\pi$
$953$	8.57407			0.277741			0.138871	+	0.990311i	$0.455653\pi$
$954$	72.1187	−	27.0385i	2.33493	−	0.875404i
$955$	1.48151	−	2.56605i	0.0479406	−	0.0830355i
$956$	−51.2262			−1.65677
$957$	15.7574	+	5.64944i	0.509365	+	0.182621i
$958$	0.339194	−	0.587501i	0.0109589	−	0.0189813i
$959$	21.7184	+	52.9863i	0.701325	+	1.71102i
$960$	16.1686	−	13.7003i	0.521838	−	0.442174i
$961$	7.09911	−	12.2960i	0.229004	−	0.396646i
$962$	−12.7227	+	22.0364i	−0.410197	+	0.710482i
$963$	−8.57181	+	3.21371i	−0.276223	+	0.103560i
$964$	12.4016	+	21.4803i	0.399430	+	0.691833i
$965$	−2.75661	−	4.77459i	−0.0887384	−	0.153699i
$966$	38.9169	−	24.8540i	1.25213	−	0.799665i
$967$	−20.7447	+	35.9309i	−0.667105	+	1.15546i	0.311605	+	0.950212i	$0.399133\pi$
$967$	−20.7447	+	35.9309i	−0.667105	+	1.15546i	−0.978710	+	0.205248i	$0.934200\pi$
$968$	−1.36238			−0.0437887
$969$	−12.3920	+	10.5003i	−0.398089	+	0.337317i
$970$	34.7008			1.11418
$971$	1.84056	+	3.18794i	0.0590664	+	0.102306i	0.894047	−	0.447974i	$-0.147854\pi$
$971$	1.84056	+	3.18794i	0.0590664	+	0.102306i	−0.834980	+	0.550280i	$0.814521\pi$
$972$	42.3345	+	33.8198i	1.35788	+	1.08477i
$973$	−6.67914	−	0.904462i	−0.214123	−	0.0289957i
$974$	31.2955	+	54.2055i	1.00277	+	1.73685i
$975$	−0.339558	−	1.87294i	−0.0108746	−	0.0599821i
$976$	4.23076	+	7.32789i	0.135423	+	0.234560i
$977$	3.22078	+	5.57856i	0.103042	+	0.178474i	0.912937	−	0.408102i	$-0.133809\pi$
$977$	3.22078	+	5.57856i	0.103042	+	0.178474i	−0.809895	+	0.586575i	$0.800476\pi$
$978$	−27.3187	+	23.1482i	−0.873557	+	0.740199i
$979$	−1.43330	−	2.48254i	−0.0458084	−	0.0793425i
$980$	−23.4554	−	6.47113i	−0.749255	−	0.206713i
$981$	−46.2648	−	38.0675i	−1.47712	−	1.21540i
$982$	−4.31293	−	7.47021i	−0.137631	−	0.238384i
$983$	−7.52769			−0.240096			−0.120048	−	0.992768i	$-0.538305\pi$
$983$	−7.52769			−0.240096			−0.120048	+	0.992768i	$0.538305\pi$
$984$	0.474441	+	2.61693i	0.0151246	+	0.0834247i
$985$	−10.8939			−0.347108
$986$	5.30525	−	9.18896i	0.168954	−	0.292636i
$987$	24.0725	−	15.3737i	0.766235	−	0.489351i
$988$	11.7228	+	20.3045i	0.372953	+	0.645974i
$989$	12.2557	+	21.2276i	0.389710	+	0.674998i
$990$	17.6542	+	14.5262i	0.561087	+	0.461672i
$991$	−21.8853	+	37.9064i	−0.695209	+	1.20414i	0.274902	+	0.961472i	$0.411355\pi$
$991$	−21.8853	+	37.9064i	−0.695209	+	1.20414i	−0.970110	+	0.242664i	$0.921979\pi$
$992$	8.73615	−	15.1315i	0.277373	−	0.480424i
$993$	−7.09590	−	39.1397i	−0.225182	−	1.24206i
$994$	−96.9188	−	13.1244i	−3.07408	−	0.416279i
$995$	−7.03715	+	12.1887i	−0.223093	+	0.386408i
$996$	17.5960	+	97.0566i	0.557552	+	3.07536i
$997$	10.6581			0.337544			0.168772	−	0.985655i	$-0.446020\pi$
$997$	10.6581			0.337544			0.168772	+	0.985655i	$0.446020\pi$
$998$	−3.93260	+	6.81147i	−0.124484	+	0.215613i
$999$	25.0607	−	44.8920i	0.792886	−	1.42032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.256.1	yes	24
3.2	odd	2		945.2.k.b.361.12		24
7.2	even	3		315.2.l.b.121.12	yes	24
9.2	odd	6		945.2.l.b.46.1		24
9.7	even	3		315.2.l.b.151.12	yes	24
21.2	odd	6		945.2.l.b.226.1		24
63.2	odd	6		945.2.k.b.856.12		24
63.16	even	3	inner	315.2.k.b.16.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.1	✓	24	63.16	even	3	inner
315.2.k.b.256.1	yes	24	1.1	even	1	trivial
315.2.l.b.121.12	yes	24	7.2	even	3
315.2.l.b.151.12	yes	24	9.7	even	3
945.2.k.b.361.12		24	3.2	odd	2
945.2.k.b.856.12		24	63.2	odd	6
945.2.l.b.46.1		24	9.2	odd	6
945.2.l.b.226.1		24	21.2	odd	6

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17004 + 2.02657i) q^{2} +(1.32145 - 1.11972i) q^{3} +(-1.73798 - 3.01027i) q^{4} -1.00000 q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.00344 - 2.44808i) q^{7} +3.45385 q^{8} +(0.492465 - 2.95930i) q^{9} +O(q^{10})\)	\(q+(-1.17004 + 2.02657i) q^{2} +(1.32145 - 1.11972i) q^{3} +(-1.73798 - 3.01027i) q^{4} -1.00000 q^{5} +(0.723033 + 3.98812i) q^{6} +(-1.00344 - 2.44808i) q^{7} +3.45385 q^{8} +(0.492465 - 2.95930i) q^{9} +(1.17004 - 2.02657i) q^{10} -3.25662 q^{11} +(-5.66730 - 2.03187i) q^{12} +(0.549485 - 0.951736i) q^{13} +(6.13526 + 0.830812i) q^{14} +(-1.32145 + 1.11972i) q^{15} +(-0.565177 + 0.978916i) q^{16} +(0.763940 - 1.32318i) q^{17} +(5.42102 + 4.46051i) q^{18} +(-3.06883 - 5.31536i) q^{19} +(1.73798 + 3.01027i) q^{20} +(-4.06716 - 2.11145i) q^{21} +(3.81036 - 6.59974i) q^{22} +4.30605 q^{23} +(4.56409 - 3.86733i) q^{24} +1.00000 q^{25} +(1.28584 + 2.22714i) q^{26} +(-2.66282 - 4.46200i) q^{27} +(-5.62542 + 7.27533i) q^{28} +(-1.48384 - 2.57008i) q^{29} +(-0.723033 - 3.98812i) q^{30} +(-2.04950 - 3.54983i) q^{31} +(2.13129 + 3.69150i) q^{32} +(-4.30346 + 3.64649i) q^{33} +(1.78768 + 3.09635i) q^{34} +(1.00344 + 2.44808i) q^{35} +(-9.76418 + 3.66075i) q^{36} +(4.94725 + 8.56889i) q^{37} +14.3626 q^{38} +(-0.339558 - 1.87294i) q^{39} -3.45385 q^{40} +(-0.222291 + 0.385018i) q^{41} +(9.03772 - 5.77188i) q^{42} +(2.84617 + 4.92971i) q^{43} +(5.65993 + 9.80328i) q^{44} +(-0.492465 + 2.95930i) q^{45} +(-5.03824 + 8.72650i) q^{46} +(-3.11646 + 5.39786i) q^{47} +(0.349255 + 1.92643i) q^{48} +(-4.98622 + 4.91301i) q^{49} +(-1.17004 + 2.02657i) q^{50} +(-0.472082 - 2.60392i) q^{51} -3.81997 q^{52} +(5.48563 - 9.50139i) q^{53} +(12.1581 - 0.175665i) q^{54} +3.25662 q^{55} +(-3.46573 - 8.45530i) q^{56} +(-10.0070 - 3.58777i) q^{57} +6.94459 q^{58} +(3.77646 + 6.54103i) q^{59} +(5.66730 + 2.03187i) q^{60} +(3.74286 - 6.48282i) q^{61} +9.59196 q^{62} +(-7.73878 + 1.76389i) q^{63} -12.2355 q^{64} +(-0.549485 + 0.951736i) q^{65} +(-2.35464 - 12.9878i) q^{66} +(-1.06964 - 1.85268i) q^{67} -5.31084 q^{68} +(5.69024 - 4.82156i) q^{69} +(-6.13526 - 0.830812i) q^{70} -15.7970 q^{71} +(1.70090 - 10.2210i) q^{72} +(4.96804 - 8.60490i) q^{73} -23.1539 q^{74} +(1.32145 - 1.11972i) q^{75} +(-10.6671 + 18.4760i) q^{76} +(3.26782 + 7.97246i) q^{77} +(4.19293 + 1.50328i) q^{78} +(-3.93113 + 6.80891i) q^{79} +(0.565177 - 0.978916i) q^{80} +(-8.51496 - 2.91471i) q^{81} +(-0.520177 - 0.900972i) q^{82} +(-8.19187 - 14.1887i) q^{83} +(0.712601 + 15.9129i) q^{84} +(-0.763940 + 1.32318i) q^{85} -13.3205 q^{86} +(-4.83859 - 1.73476i) q^{87} -11.2479 q^{88} +(0.440119 + 0.762308i) q^{89} +(-5.42102 - 4.46051i) q^{90} +(-2.88130 - 0.390175i) q^{91} +(-7.48382 - 12.9624i) q^{92} +(-6.68312 - 2.39607i) q^{93} +(-7.29275 - 12.6314i) q^{94} +(3.06883 + 5.31536i) q^{95} +(6.94983 + 2.49170i) q^{96} +(7.41446 + 12.8422i) q^{97} +(-4.12247 - 15.8533i) q^{98} +(-1.60377 + 9.63731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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