LMFDB - Embedded newform 315.2.be.c.236.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.13
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48159 - 0.855399i) q^{2} +(1.02526 - 1.39601i) q^{3} +(0.463416 - 0.802660i) q^{4} -1.00000 q^{5} +(0.324870 - 2.94533i) q^{6} +(1.20122 - 2.35734i) q^{7} +1.83597i q^{8} +(-0.897694 - 2.86254i) q^{9} +O(q^{10})$	\(q+(1.48159 - 0.855399i) q^{2} +(1.02526 - 1.39601i) q^{3} +(0.463416 - 0.802660i) q^{4} -1.00000 q^{5} +(0.324870 - 2.94533i) q^{6} +(1.20122 - 2.35734i) q^{7} +1.83597i q^{8} +(-0.897694 - 2.86254i) q^{9} +(-1.48159 + 0.855399i) q^{10} -0.574148i q^{11} +(-0.645401 - 1.46987i) q^{12} +(0.130417 - 0.0752961i) q^{13} +(-0.236742 - 4.52015i) q^{14} +(-1.02526 + 1.39601i) q^{15} +(2.49732 + 4.32549i) q^{16} +(0.586913 + 1.01656i) q^{17} +(-3.77864 - 3.47324i) q^{18} +(0.00148739 + 0.000858744i) q^{19} +(-0.463416 + 0.802660i) q^{20} +(-2.05931 - 4.09380i) q^{21} +(-0.491126 - 0.850655i) q^{22} +7.46725i q^{23} +(2.56304 + 1.88235i) q^{24} +1.00000 q^{25} +(0.128816 - 0.223117i) q^{26} +(-4.91651 - 1.68165i) q^{27} +(-1.33548 - 2.05660i) q^{28} +(5.81941 + 3.35984i) q^{29} +(-0.324870 + 2.94533i) q^{30} +(-5.74833 - 3.31880i) q^{31} +(4.22004 + 2.43644i) q^{32} +(-0.801517 - 0.588650i) q^{33} +(1.73914 + 1.00409i) q^{34} +(-1.20122 + 2.35734i) q^{35} +(-2.71365 - 0.606004i) q^{36} +(-0.718409 + 1.24432i) q^{37} +0.00293828 q^{38} +(0.0285965 - 0.259261i) q^{39} -1.83597i q^{40} +(5.37138 + 9.30350i) q^{41} +(-6.55290 - 4.30383i) q^{42} +(-3.00541 + 5.20553i) q^{43} +(-0.460846 - 0.266069i) q^{44} +(0.897694 + 2.86254i) q^{45} +(6.38748 + 11.0634i) q^{46} +(-4.22215 - 7.31298i) q^{47} +(8.59883 + 0.948451i) q^{48} +(-4.11412 - 5.66339i) q^{49} +(1.48159 - 0.855399i) q^{50} +(2.02087 + 0.222902i) q^{51} -0.139574i q^{52} +(-9.60845 + 5.54744i) q^{53} +(-8.72276 + 1.71405i) q^{54} +0.574148i q^{55} +(4.32802 + 2.20542i) q^{56} +(0.00272377 - 0.00119598i) q^{57} +11.4960 q^{58} +(5.13465 - 8.89348i) q^{59} +(0.645401 + 1.46987i) q^{60} +(6.36845 - 3.67682i) q^{61} -11.3556 q^{62} +(-7.82632 - 1.32238i) q^{63} -1.65277 q^{64} +(-0.130417 + 0.0752961i) q^{65} +(-1.69105 - 0.186523i) q^{66} +(4.10141 - 7.10384i) q^{67} +1.08794 q^{68} +(10.4244 + 7.65586i) q^{69} +(0.236742 + 4.52015i) q^{70} -0.0708560i q^{71} +(5.25555 - 1.64814i) q^{72} +(10.2405 - 5.91235i) q^{73} +2.45811i q^{74} +(1.02526 - 1.39601i) q^{75} +(0.00137856 - 0.000795911i) q^{76} +(-1.35346 - 0.689680i) q^{77} +(-0.179403 - 0.408581i) q^{78} +(-1.65540 - 2.86723i) q^{79} +(-2.49732 - 4.32549i) q^{80} +(-7.38829 + 5.13937i) q^{81} +(15.9164 + 9.18935i) q^{82} +(-4.47627 + 7.75313i) q^{83} +(-4.24025 - 0.244206i) q^{84} +(-0.586913 - 1.01656i) q^{85} +10.2833i q^{86} +(10.6568 - 4.67926i) q^{87} +1.05412 q^{88} +(-0.699730 + 1.21197i) q^{89} +(3.77864 + 3.47324i) q^{90} +(-0.0208391 - 0.397884i) q^{91} +(5.99366 + 3.46044i) q^{92} +(-10.5266 + 4.62211i) q^{93} +(-12.5110 - 7.22325i) q^{94} +(-0.00148739 - 0.000858744i) q^{95} +(7.72793 - 3.39324i) q^{96} +(-14.9143 - 8.61076i) q^{97} +(-10.9399 - 4.87163i) q^{98} +(-1.64352 + 0.515409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.48159	−	0.855399i	1.04765	−	0.604859i	0.125656	−	0.992074i	$-0.459896\pi$
$2$	1.48159	−	0.855399i	1.04765	−	0.604859i	0.921989	+	0.387215i	$0.126563\pi$
$3$	1.02526	−	1.39601i	0.591933	−	0.805987i
$3$	1.02526	−	1.39601i	0.591933	−	0.805987i
$4$	0.463416	−	0.802660i	0.231708	−	0.401330i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.324870	−	2.94533i	0.132627	−	1.20242i
$7$	1.20122	−	2.35734i	0.454020	−	0.890992i
$7$	1.20122	−	2.35734i	0.454020	−	0.890992i
$8$			1.83597i			0.649115i
$9$	−0.897694	−	2.86254i	−0.299231	−	0.954181i
$10$	−1.48159	+	0.855399i	−0.468521	+	0.270501i
$11$		−	0.574148i		−	0.173112i	−0.996247	−	0.0865561i	$-0.972414\pi$
$11$		−	0.574148i		−	0.173112i	0.996247	−	0.0865561i	$-0.0275862\pi$
$12$	−0.645401	−	1.46987i	−0.186311	−	0.424314i
$13$	0.130417	−	0.0752961i	0.0361711	−	0.0208834i	−0.481805	−	0.876278i	$-0.660019\pi$
$13$	0.130417	−	0.0752961i	0.0361711	−	0.0208834i	0.517976	+	0.855395i	$0.326685\pi$
$14$	−0.236742	−	4.52015i	−0.0632720	−	1.20806i
$15$	−1.02526	+	1.39601i	−0.264720	+	0.360449i
$16$	2.49732	+	4.32549i	0.624331	+	1.08137i
$17$	0.586913	+	1.01656i	0.142347	+	0.246553i	0.928380	−	0.371632i	$-0.121202\pi$
$17$	0.586913	+	1.01656i	0.142347	+	0.246553i	−0.786033	+	0.618185i	$0.787868\pi$
$18$	−3.77864	−	3.47324i	−0.890633	−	0.818651i
$19$	0.00148739		0.000858744i	0.000341230		0.000197009i	0.500171	−	0.865927i	$-0.333271\pi$
$19$	0.00148739		0.000858744i	0.000341230		0.000197009i	−0.499829	+	0.866124i	$0.666604\pi$
$20$	−0.463416	+	0.802660i	−0.103623	+	0.179480i
$21$	−2.05931	−	4.09380i	−0.449379	−	0.893341i
$22$	−0.491126	−	0.850655i	−0.104708	−	0.181360i
$23$			7.46725i			1.55703i	0.627626	+	0.778515i	$0.284027\pi$
$23$			7.46725i			1.55703i	−0.627626	+	0.778515i	$0.715973\pi$
$24$	2.56304	+	1.88235i	0.523179	+	0.384232i
$25$	1.00000			0.200000
$26$	0.128816	−	0.223117i	0.0252630	−	0.0437568i
$27$	−4.91651	−	1.68165i	−0.946182	−	0.323634i
$28$	−1.33548	−	2.05660i	−0.252382	−	0.388661i
$29$	5.81941	+	3.35984i	1.08064	+	0.623906i	0.931068	−	0.364845i	$-0.118878\pi$
$29$	5.81941	+	3.35984i	1.08064	+	0.623906i	0.149569	+	0.988751i	$0.452211\pi$
$30$	−0.324870	+	2.94533i	−0.0593128	+	0.537741i
$31$	−5.74833	−	3.31880i	−1.03243	−	0.596074i	−0.114750	−	0.993394i	$-0.536607\pi$
$31$	−5.74833	−	3.31880i	−1.03243	−	0.596074i	−0.917680	+	0.397321i	$0.869940\pi$
$32$	4.22004	+	2.43644i	0.746005	+	0.430706i
$33$	−0.801517	−	0.588650i	−0.139526	−	0.102471i
$34$	1.73914	+	1.00409i	0.298259	+	0.172200i
$35$	−1.20122	+	2.35734i	−0.203044	+	0.398464i
$36$	−2.71365	−	0.606004i	−0.452275	−	0.101001i
$37$	−0.718409	+	1.24432i	−0.118106	+	0.204565i	−0.919017	−	0.394218i	$-0.871015\pi$
$37$	−0.718409	+	1.24432i	−0.118106	+	0.204565i	0.800911	+	0.598783i	$0.204349\pi$
$38$	0.00293828			0.000476651
$39$	0.0285965	−	0.259261i	0.00457910	−	0.0415150i
$40$		−	1.83597i		−	0.290293i
$41$	5.37138	+	9.30350i	0.838869	+	1.45296i	0.890841	+	0.454315i	$0.150116\pi$
$41$	5.37138	+	9.30350i	0.838869	+	1.45296i	−0.0519726	+	0.998649i	$0.516551\pi$
$42$	−6.55290	−	4.30383i	−1.01114	−	0.664095i
$43$	−3.00541	+	5.20553i	−0.458321	+	0.793836i	−0.998872	−	0.0474753i	$-0.984882\pi$
$43$	−3.00541	+	5.20553i	−0.458321	+	0.793836i	0.540551	+	0.841311i	$0.318216\pi$
$44$	−0.460846	−	0.266069i	−0.0694751	−	0.0401115i
$45$	0.897694	+	2.86254i	0.133820	+	0.426723i
$46$	6.38748	+	11.0634i	0.941783	+	1.63122i
$47$	−4.22215	−	7.31298i	−0.615864	−	1.06671i	−0.990232	−	0.139428i	$-0.955474\pi$
$47$	−4.22215	−	7.31298i	−0.615864	−	1.06671i	0.374368	−	0.927280i	$-0.377860\pi$
$48$	8.59883	+	0.948451i	1.24113	+	0.136897i
$49$	−4.11412	−	5.66339i	−0.587732	−	0.809056i
$50$	1.48159	−	0.855399i	0.209529	−	0.120972i
$51$	2.02087	+	0.222902i	0.282979	+	0.0312125i
$52$		−	0.139574i		−	0.0193554i
$53$	−9.60845	+	5.54744i	−1.31982	+	0.762000i	−0.983700	−	0.179818i	$-0.942449\pi$
$53$	−9.60845	+	5.54744i	−1.31982	+	0.762000i	−0.336123	+	0.941818i	$0.609116\pi$
$54$	−8.72276	+	1.71405i	−1.18702	+	0.233253i
$55$			0.574148i			0.0774181i
$56$	4.32802	+	2.20542i	0.578356	+	0.294711i
$57$	0.00272377	−	0.00119598i	0.000360772	−	0.000158411i
$58$	11.4960			1.50950
$59$	5.13465	−	8.89348i	0.668475	−	1.15783i	−0.309856	−	0.950784i	$-0.600281\pi$
$59$	5.13465	−	8.89348i	0.668475	−	1.15783i	0.978331	−	0.207049i	$-0.0663860\pi$
$60$	0.645401	+	1.46987i	0.0833210	+	0.189759i
$61$	6.36845	−	3.67682i	0.815396	−	0.470769i	−0.0334303	−	0.999441i	$-0.510643\pi$
$61$	6.36845	−	3.67682i	0.815396	−	0.470769i	0.848826	+	0.528672i	$0.177310\pi$
$62$	−11.3556			−1.44216
$63$	−7.82632	−	1.32238i	−0.986024	−	0.166604i
$64$	−1.65277			−0.206596
$65$	−0.130417	+	0.0752961i	−0.0161762	+	0.00933933i
$66$	−1.69105	−	0.186523i	−0.208154	−	0.0229594i
$67$	4.10141	−	7.10384i	0.501066	−	0.867872i	−0.498933	−	0.866641i	$-0.666275\pi$
$67$	4.10141	−	7.10384i	0.501066	−	0.867872i	0.999999	−	0.00123183i	$-0.000392104\pi$
$68$	1.08794			0.131932
$69$	10.4244	+	7.65586i	1.25495	+	0.921657i
$70$	0.236742	+	4.52015i	0.0282961	+	0.540261i
$71$		−	0.0708560i		−	0.00840906i	−0.999991	−	0.00420453i	$-0.998662\pi$
$71$		−	0.0708560i		−	0.00840906i	0.999991	−	0.00420453i	$-0.00133835\pi$
$72$	5.25555	−	1.64814i	0.619373	−	0.194236i
$73$	10.2405	−	5.91235i	1.19856	−	0.691989i	0.238326	−	0.971185i	$-0.423401\pi$
$73$	10.2405	−	5.91235i	1.19856	−	0.691989i	0.960234	+	0.279197i	$0.0900681\pi$
$74$			2.45811i			0.285749i
$75$	1.02526	−	1.39601i	0.118387	−	0.161197i
$76$	0.00137856		0.000795911i	0.000158132		9.12973e-5i
$77$	−1.35346	−	0.689680i	−0.154242	−	0.0785964i
$78$	−0.179403	−	0.408581i	−0.0203134	−	0.0462627i
$79$	−1.65540	−	2.86723i	−0.186247	−	0.322589i	0.757749	−	0.652546i	$-0.226299\pi$
$79$	−1.65540	−	2.86723i	−0.186247	−	0.322589i	−0.943996	+	0.329957i	$0.892966\pi$
$80$	−2.49732	−	4.32549i	−0.279209	−	0.483605i
$81$	−7.38829	+	5.13937i	−0.820921	+	0.571042i
$82$	15.9164	+	9.18935i	1.75767	+	1.01479i
$83$	−4.47627	+	7.75313i	−0.491334	+	0.851016i	−0.999950	−	0.00997747i	$-0.996824\pi$
$83$	−4.47627	+	7.75313i	−0.491334	+	0.851016i	0.508616	+	0.860994i	$0.330157\pi$
$84$	−4.24025	−	0.244206i	−0.462649	−	0.0266451i
$85$	−0.586913	−	1.01656i	−0.0636597	−	0.110262i
$86$			10.2833i			1.10888i
$87$	10.6568	−	4.67926i	1.14253	−	0.501670i
$88$	1.05412			0.112370
$89$	−0.699730	+	1.21197i	−0.0741713	+	0.128468i	−0.900726	−	0.434389i	$-0.856964\pi$
$89$	−0.699730	+	1.21197i	−0.0741713	+	0.128468i	0.826554	+	0.562857i	$0.190298\pi$
$90$	3.77864	+	3.47324i	0.398303	+	0.366112i
$91$	−0.0208391	−	0.397884i	−0.00218453	−	0.0417096i
$92$	5.99366	+	3.46044i	0.624883	+	0.360776i
$93$	−10.5266	+	4.62211i	−1.09156	+	0.479290i
$94$	−12.5110	−	7.22325i	−1.29042	−	0.745022i
$95$	−0.00148739		0.000858744i	−0.000152603		8.81053e-5i
$96$	7.72793	−	3.39324i	0.788728	−	0.346322i
$97$	−14.9143	−	8.61076i	−1.51432	−	0.874291i	−0.999859	−	0.0167742i	$-0.994660\pi$
$97$	−14.9143	−	8.61076i	−1.51432	−	0.874291i	−0.514457	−	0.857516i	$-0.672006\pi$
$98$	−10.9399	−	4.87163i	−1.10510	−	0.492109i
$99$	−1.64352	+	0.515409i	−0.165180	+	0.0518006i
$100$	0.463416	−	0.802660i	0.0463416	−	0.0802660i
$101$	−13.3497			−1.32834			−0.664171	−	0.747580i	$-0.731215\pi$
$101$	−13.3497			−1.32834			−0.664171	+	0.747580i	$0.731215\pi$
$102$	3.18478	−	1.39840i	0.315341	−	0.138462i
$103$		−	4.44340i		−	0.437822i	−0.975745	−	0.218911i	$-0.929750\pi$
$103$		−	4.44340i		−	0.437822i	0.975745	−	0.218911i	$-0.0702504\pi$
$104$	0.138242	+	0.239442i	0.0135557	+	0.0234792i
$105$	2.05931	+	4.09380i	0.200968	+	0.399514i
$106$	−9.49056	+	16.4381i	−0.921805	+	1.59661i
$107$	5.21803	+	3.01263i	0.504446	+	0.291242i	0.730548	−	0.682862i	$-0.239265\pi$
$107$	5.21803	+	3.01263i	0.504446	+	0.291242i	−0.226102	+	0.974104i	$0.572598\pi$
$108$	−3.62818	+	3.16698i	−0.349122	+	0.304743i
$109$	2.58035	+	4.46930i	0.247153	+	0.428082i	0.962735	−	0.270447i	$-0.0871716\pi$
$109$	2.58035	+	4.46930i	0.247153	+	0.428082i	−0.715582	+	0.698529i	$0.753838\pi$
$110$	0.491126	+	0.850655i	0.0468270	+	0.0811068i
$111$	1.00053	+	2.27866i	0.0949662	+	0.216280i
$112$	13.1965	−	0.691165i	1.24695	−	0.0653089i
$113$	−7.32830	+	4.23100i	−0.689389	+	0.398019i	−0.803383	−	0.595463i	$-0.796969\pi$
$113$	−7.32830	+	4.23100i	−0.689389	+	0.398019i	0.113994	+	0.993481i	$0.463635\pi$
$114$	0.00301249	−	0.00410187i	0.000282146	−	0.000384175i
$115$		−	7.46725i		−	0.696325i
$116$	5.39361	−	3.11400i	0.500785	−	0.289128i
$117$	−0.332613	−	0.305730i	−0.0307500	−	0.0282648i
$118$		−	17.5687i		−	1.61733i
$119$	3.10140	−	0.162435i	0.284305	−	0.0148904i
$120$	−2.56304	−	1.88235i	−0.233973	−	0.171834i
$121$	10.6704			0.970032
$122$	6.29030	−	10.8951i	0.569497	−	0.986398i
$123$	18.4948	+	2.03998i	1.66762	+	0.183939i
$124$	−5.32773	+	3.07597i	−0.478444	+	0.276230i
$125$	−1.00000			−0.0894427
$126$	−12.7266	+	4.73540i	−1.13378	+	0.421863i
$127$	−6.42212			−0.569871			−0.284936	−	0.958547i	$-0.591972\pi$
$127$	−6.42212			−0.569871			−0.284936	+	0.958547i	$0.591972\pi$
$128$	−10.8888	+	6.28666i	−0.962445	+	0.555668i
$129$	4.18565	+	9.53260i	0.368526	+	0.839299i
$130$	−0.128816	+	0.223117i	−0.0112980	+	0.0195686i
$131$	−13.3497			−1.16637			−0.583185	−	0.812340i	$-0.698194\pi$
$131$	−13.3497			−1.16637			−0.583185	+	0.812340i	$0.698194\pi$
$132$	−0.843921	+	0.370556i	−0.0734539	+	0.0322528i
$133$	0.00381104	−	0.00247474i	0.000330459	−	0.000214587i
$134$		−	14.0334i		−	1.21230i
$135$	4.91651	+	1.68165i	0.423146	+	0.144734i
$136$	−1.86639	+	1.07756i	−0.160041	+	0.0923998i
$137$		−	18.2872i		−	1.56238i	−0.624295	−	0.781189i	$-0.714614\pi$
$137$		−	18.2872i		−	1.56238i	0.624295	−	0.781189i	$-0.285386\pi$
$138$	21.9935	+	2.42588i	1.87221	+	0.206505i
$139$	−4.60943	+	2.66125i	−0.390967	+	0.225725i	−0.682579	−	0.730812i	$-0.739142\pi$
$139$	−4.60943	+	2.66125i	−0.390967	+	0.225725i	0.291612	+	0.956537i	$0.405808\pi$
$140$	1.33548	+	2.05660i	0.112868	+	0.173815i
$141$	−14.5378	−	1.60352i	−1.22430	−	0.135041i
$142$	−0.0606101	−	0.104980i	−0.00508629	−	0.00880971i
$143$	−0.0432311	−	0.0748785i	−0.00361517	−	0.00626166i
$144$	10.1401	−	11.0317i	0.845005	−	0.919305i
$145$	−5.81941	−	3.35984i	−0.483276	−	0.279019i
$146$	10.1148	−	17.5194i	0.837111	−	1.44992i
$147$	−12.1242	−	0.0630688i	−0.999986	−	0.00520182i
$148$	0.665844	+	1.15328i	0.0547320	+	0.0947987i
$149$		−	0.724628i		−	0.0593638i	−0.999559	−	0.0296819i	$-0.990551\pi$
$149$		−	0.724628i		−	0.0593638i	0.999559	−	0.0296819i	$-0.00944943\pi$
$150$	0.324870	−	2.94533i	0.0265255	−	0.240485i
$151$	−3.86372			−0.314425			−0.157213	−	0.987565i	$-0.550251\pi$
$151$	−3.86372			−0.314425			−0.157213	+	0.987565i	$0.550251\pi$
$152$	−0.00157663	+	0.00273081i	−0.000127882	+	0.000221498i
$153$	2.38309	−	2.59263i	0.192661	−	0.209601i
$154$	−2.59524	+	0.135925i	−0.209130	+	0.0109532i
$155$	5.74833	+	3.31880i	0.461717	+	0.266572i
$156$	−0.194846	−	0.143099i	−0.0156002	−	0.0114571i
$157$	5.67491	+	3.27641i	0.452907	+	0.261486i	0.709057	−	0.705151i	$-0.249121\pi$
$157$	5.67491	+	3.27641i	0.452907	+	0.261486i	−0.256150	+	0.966637i	$0.582454\pi$
$158$	−4.90526	−	2.83205i	−0.390242	−	0.225306i
$159$	−2.10685	+	19.1011i	−0.167084	+	1.51481i
$160$	−4.22004	−	2.43644i	−0.333624	−	0.192618i
$161$	17.6029	+	8.96984i	1.38730	+	0.706922i
$162$	−6.55024	+	13.9344i	−0.514635	+	1.09479i
$163$	9.53391	−	16.5132i	0.746753	−	1.29341i	−0.202618	−	0.979258i	$-0.564945\pi$
$163$	9.53391	−	16.5132i	0.746753	−	1.29341i	0.949371	−	0.314157i	$-0.101722\pi$
$164$	9.95673			0.777490
$165$	0.801517	+	0.588650i	0.0623980	+	0.0458263i
$166$			15.3160i			1.18875i
$167$	3.03835	+	5.26258i	0.235115	+	0.407231i	0.959306	−	0.282368i	$-0.0911200\pi$
$167$	3.03835	+	5.26258i	0.235115	+	0.407231i	−0.724191	+	0.689599i	$0.757787\pi$
$168$	7.51612	−	3.78085i	0.579881	−	0.291699i
$169$	−6.48866	+	11.2387i	−0.499128	+	0.864515i
$170$	−1.73914	−	1.00409i	−0.133386	−	0.0770102i
$171$	0.00112297	−	0.00502860i	8.58757e−5	−	0.000384547i
$172$	2.78551	+	4.82465i	0.212393	+	0.367876i
$173$	−9.82533	−	17.0180i	−0.747006	−	1.29385i	−0.949252	−	0.314518i	$-0.898157\pi$
$173$	−9.82533	−	17.0180i	−0.747006	−	1.29385i	0.202246	−	0.979335i	$-0.435176\pi$
$174$	11.7864	−	16.0486i	0.893523	−	1.21664i
$175$	1.20122	−	2.35734i	0.0908040	−	0.178198i
$176$	2.48347	−	1.43383i	0.187199	−	0.108079i
$177$	−7.15106	−	16.2861i	−0.537506	−	1.22414i
$178$			2.39420i			0.179453i
$179$	11.5181	−	6.64999i	0.860905	−	0.497044i	−0.00341036	−	0.999994i	$-0.501086\pi$
$179$	11.5181	−	6.64999i	0.860905	−	0.497044i	0.864315	+	0.502951i	$0.167752\pi$
$180$	2.71365	+	0.606004i	0.202264	+	0.0451689i
$181$			7.87417i			0.585282i	0.956222	+	0.292641i	$0.0945341\pi$
$181$			7.87417i			0.585282i	−0.956222	+	0.292641i	$0.905466\pi$
$182$	−0.371225	−	0.571677i	−0.0275170	−	0.0423755i
$183$	1.39641	−	12.6601i	0.103226	−	0.935862i
$184$	−13.7097			−1.01069
$185$	0.718409	−	1.24432i	0.0528185	−	0.0914843i
$186$	−11.6424	+	15.8525i	−0.853662	+	1.16236i
$187$	0.583658	−	0.336975i	0.0426813	−	0.0246421i
$188$	−7.82645			−0.570803
$189$	−9.87005	+	9.56985i	−0.717941	+	0.696104i
$190$	−0.00293828			−0.000213165
$191$	5.74756	−	3.31835i	0.415879	−	0.240108i	−0.277434	−	0.960745i	$-0.589484\pi$
$191$	5.74756	−	3.31835i	0.415879	−	0.240108i	0.693312	+	0.720637i	$0.256151\pi$
$192$	−1.69452	+	2.30729i	−0.122291	+	0.166514i
$193$	5.42222	−	9.39156i	0.390300	−	0.676020i	−0.602189	−	0.798354i	$-0.705705\pi$
$193$	5.42222	−	9.39156i	0.390300	−	0.676020i	0.992489	+	0.122334i	$0.0390379\pi$
$194$	−29.4626			−2.11529
$195$	−0.0285965	+	0.259261i	−0.00204784	+	0.0185661i
$196$	−6.45232	+	0.677738i	−0.460880	+	0.0484099i
$197$			11.0578i			0.787838i	0.919145	+	0.393919i	$0.128881\pi$
$197$			11.0578i			0.787838i	−0.919145	+	0.393919i	$0.871119\pi$
$198$	−1.99416	+	2.16950i	−0.141718	+	0.154179i
$199$	0.779269	−	0.449911i	0.0552409	−	0.0318933i	−0.472125	−	0.881532i	$-0.656513\pi$
$199$	0.779269	−	0.449911i	0.0552409	−	0.0318933i	0.527366	+	0.849638i	$0.323180\pi$
$200$			1.83597i			0.129823i
$201$	−5.71205	−	13.0089i	−0.402897	−	0.917575i
$202$	−19.7788	+	11.4193i	−1.39163	+	0.803459i
$203$	14.9107	−	9.68243i	1.04653	−	0.679573i
$204$	1.11542	−	1.51878i	0.0780949	−	0.106336i
$205$	−5.37138	−	9.30350i	−0.375153	−	0.649785i
$206$	−3.80088	−	6.58333i	−0.264820	−	0.458682i
$207$	21.3753	−	6.70331i	1.48569	−	0.465912i
$208$	0.651385	+	0.376077i	0.0451654	+	0.0260763i
$209$	0.000493046	0	0.000853981i	3.41047e−5	0	5.90711e-5i
$210$	6.55290	+	4.30383i	0.452193	+	0.296992i
$211$	−9.71550	−	16.8277i	−0.668842	−	1.15847i	−0.978228	−	0.207532i	$-0.933457\pi$
$211$	−9.71550	−	16.8277i	−0.668842	−	1.15847i	0.309386	−	0.950937i	$-0.399877\pi$
$212$			10.2831i			0.706246i
$213$	−0.0989157	−	0.0726456i	−0.00677759	−	0.00497760i
$214$	10.3080			0.704640
$215$	3.00541	−	5.20553i	0.204968	−	0.355014i
$216$	3.08747	−	9.02659i	0.210076	−	0.614181i
$217$	−14.7286	+	9.56416i	−0.999840	+	0.649257i
$218$	7.64608	+	4.41447i	0.517858	+	0.298985i
$219$	2.24544	−	20.3575i	0.151732	−	1.37563i
$220$	0.460846	+	0.266069i	0.0310702	+	0.0179384i
$221$	0.153087	+	0.0883846i	0.0102977	+	0.00594539i
$222$	3.43154	+	2.52019i	0.230310	+	0.169144i
$223$	2.12653	+	1.22775i	0.142403	+	0.0822164i	0.569509	−	0.821985i	$-0.307133\pi$
$223$	2.12653	+	1.22775i	0.142403	+	0.0822164i	−0.427106	+	0.904202i	$0.640467\pi$
$224$	10.8127	−	7.02137i	0.722457	−	0.469135i
$225$	−0.897694	−	2.86254i	−0.0598463	−	0.190836i
$226$	−7.23839	+	12.5373i	−0.481490	+	0.833966i
$227$	1.85806			0.123324			0.0616618	−	0.998097i	$-0.480360\pi$
$227$	1.85806			0.123324			0.0616618	+	0.998097i	$0.480360\pi$
$228$	0.000302277	−	0.00274050i	2.00188e−5	−	0.000181494i
$229$			27.2093i			1.79804i	0.437909	+	0.899019i	$0.355719\pi$
$229$			27.2093i			1.79804i	−0.437909	+	0.899019i	$0.644281\pi$
$230$	−6.38748	−	11.0634i	−0.421178	−	0.729502i
$231$	−2.35045	+	1.18235i	−0.154648	+	0.0777930i
$232$	−6.16858	+	10.6843i	−0.404987	+	0.701458i
$233$	4.27773	+	2.46975i	0.280244	+	0.161799i	0.633534	−	0.773715i	$-0.281604\pi$
$233$	4.27773	+	2.46975i	0.280244	+	0.161799i	−0.353290	+	0.935514i	$0.614937\pi$
$234$	−0.754318	−	0.168452i	−0.0493113	−	0.0110121i
$235$	4.22215	+	7.31298i	0.275423	+	0.477046i
$236$	−4.75896	−	8.24276i	−0.309782	−	0.536558i
$237$	−5.69990	−	0.628699i	−0.370248	−	0.0408384i
$238$	4.45608	−	2.89360i	0.288844	−	0.187564i
$239$	16.7127	−	9.64908i	1.08105	−	0.624147i	0.149874	−	0.988705i	$-0.452113\pi$
$239$	16.7127	−	9.64908i	1.08105	−	0.624147i	0.931181	+	0.364558i	$0.118780\pi$
$240$	−8.59883	−	0.948451i	−0.555052	−	0.0612222i
$241$		−	17.1792i		−	1.10661i	−0.832979	−	0.553305i	$-0.813366\pi$
$241$		−	17.1792i		−	1.10661i	0.832979	−	0.553305i	$-0.186634\pi$
$242$	15.8091	−	9.12741i	1.01625	−	0.586732i
$243$	−0.400278	+	15.5833i	−0.0256778	+	0.999670i
$244$		−	6.81559i		−	0.436324i
$245$	4.11412	+	5.66339i	0.262842	+	0.361821i
$246$	29.1469	−	12.7981i	1.85834	−	0.815974i
$247$	0.000258640	0		1.64569e−5	0
$248$	6.09323	−	10.5538i	0.386921	−	0.670166i
$249$	6.23412	+	14.1979i	0.395071	+	0.899754i
$250$	−1.48159	+	0.855399i	−0.0937043	+	0.0541002i
$251$	14.8491			0.937268			0.468634	−	0.883392i	$-0.344746\pi$
$251$	14.8491			0.937268			0.468634	+	0.883392i	$0.344746\pi$
$252$	−4.68826	+	5.66906i	−0.295333	+	0.357117i
$253$	4.28731			0.269541
$254$	−9.51499	+	5.49348i	−0.597023	+	0.344692i
$255$	−2.02087	−	0.222902i	−0.126552	−	0.0139587i
$256$	−9.10244	+	15.7659i	−0.568903	+	0.985368i
$257$	−13.9053			−0.867391			−0.433695	−	0.901060i	$-0.642791\pi$
$257$	−13.9053			−0.867391			−0.433695	+	0.901060i	$0.642791\pi$
$258$	14.3556	+	10.5430i	0.893742	+	0.656382i
$259$	2.07032	+	3.18824i	0.128643	+	0.198108i
$260$			0.139574i			0.00865599i
$261$	4.39363	−	19.6744i	0.271959	−	1.21782i
$262$	−19.7789	+	11.4193i	−1.22194	+	0.705488i
$263$			3.75524i			0.231558i	0.993275	+	0.115779i	$0.0369364\pi$
$263$			3.75524i			0.231558i	−0.993275	+	0.115779i	$0.963064\pi$
$264$	1.08075	−	1.47157i	0.0665153	−	0.0905686i
$265$	9.60845	−	5.54744i	0.590243	−	0.340777i
$266$	0.00352953	−	0.00692652i	0.000216409	−	0.000424692i
$267$	0.974518	+	2.21941i	0.0596395	+	0.135826i
$268$	−3.80131	−	6.58407i	−0.232202	−	0.402186i
$269$	11.2443	+	19.4757i	0.685578	+	1.18746i	0.973255	+	0.229729i	$0.0737838\pi$
$269$	11.2443	+	19.4757i	0.685578	+	1.18746i	−0.287677	+	0.957728i	$0.592883\pi$
$270$	8.72276	−	1.71405i	0.530850	−	0.104314i
$271$	19.6597	+	11.3506i	1.19424	+	0.689497i	0.959266	−	0.282504i	$-0.0911650\pi$
$271$	19.6597	+	11.3506i	1.19424	+	0.689497i	0.234978	+	0.972001i	$0.424498\pi$
$272$	−2.93142	+	5.07738i	−0.177744	+	0.307861i
$273$	−0.576816	−	0.378842i	−0.0349105	−	0.0229286i
$274$	−15.6428	−	27.0942i	−0.945017	−	1.63682i
$275$		−	0.574148i		−	0.0346224i
$276$	10.9759	−	4.81938i	0.660669	−	0.290092i
$277$	−24.4942			−1.47171			−0.735856	−	0.677138i	$-0.763220\pi$
$277$	−24.4942			−1.47171			−0.735856	+	0.677138i	$0.763220\pi$
$278$	−4.55287	+	7.88580i	−0.273063	+	0.472959i
$279$	−4.33996	+	19.4341i	−0.259827	+	1.16349i
$280$	−4.32802	−	2.20542i	−0.258649	−	0.131799i
$281$	13.9234	+	8.03869i	0.830602	+	0.479548i	0.854059	−	0.520177i	$-0.174134\pi$
$281$	13.9234	+	8.03869i	0.830602	+	0.479548i	−0.0234571	+	0.999725i	$0.507467\pi$
$282$	−22.9108	+	10.0599i	−1.36432	+	0.599056i
$283$	−4.49698	−	2.59633i	−0.267318	−	0.154336i	0.360350	−	0.932817i	$-0.382657\pi$
$283$	−4.49698	−	2.59633i	−0.267318	−	0.154336i	−0.627668	+	0.778481i	$0.715991\pi$
$284$	−0.0568732	−	0.0328358i	−0.00337481	−	0.00194844i
$285$	−0.00272377	+	0.00119598i	−0.000161342	+	7.08436e-5i
$286$	−0.128102	−	0.0739597i	−0.00757483	−	0.00437333i
$287$	28.3838	−	1.48660i	1.67544	−	0.0877509i
$288$	3.18611	−	14.2672i	0.187743	−	0.840704i
$289$	7.81107	−	13.5292i	0.459474	−	0.795833i
$290$	−11.4960			−0.675069
$291$	−27.3117	+	11.9923i	−1.60104	+	0.702998i
$292$		−	10.9595i		−	0.641357i
$293$	1.24041	+	2.14845i	0.0724655	+	0.125514i	0.899981	−	0.435928i	$-0.143580\pi$
$293$	1.24041	+	2.14845i	0.0724655	+	0.125514i	−0.827516	+	0.561442i	$0.810247\pi$
$294$	−18.0171	+	10.2776i	−1.05078	+	0.599401i
$295$	−5.13465	+	8.89348i	−0.298951	+	0.517799i
$296$	−2.28454	−	1.31898i	−0.132786	−	0.0766642i
$297$	−0.965517	+	2.82280i	−0.0560250	+	0.163796i
$298$	−0.619846	−	1.07360i	−0.0359067	−	0.0621923i
$299$	0.562255	+	0.973854i	0.0325160	+	0.0563194i
$300$	−0.645401	−	1.46987i	−0.0372623	−	0.0848628i
$301$	8.66104	+	13.3378i	0.499214	+	0.768778i
$302$	−5.72448	+	3.30503i	−0.329407	+	0.190183i
$303$	−13.6869	+	18.6363i	−0.786289	+	1.07063i
$304$			0.00857825i			0.000491996i
$305$	−6.36845	+	3.67682i	−0.364656	+	0.210534i
$306$	1.31304	−	5.87971i	0.0750614	−	0.336121i
$307$			16.2261i			0.926071i	0.886340	+	0.463035i	$0.153240\pi$
$307$			16.2261i			0.926071i	−0.886340	+	0.463035i	$0.846760\pi$
$308$	−1.18080	+	0.766762i	−0.0672820	+	0.0436903i
$309$	−6.20304	−	4.55563i	−0.352879	−	0.259161i
$310$	11.3556			0.644954
$311$	7.90912	−	13.6990i	0.448485	−	0.776799i	−0.549802	−	0.835295i	$-0.685297\pi$
$311$	7.90912	−	13.6990i	0.448485	−	0.776799i	0.998288	+	0.0584954i	$0.0186303\pi$
$312$	0.475997	+	0.0525024i	0.0269480	+	0.00297236i
$313$	−26.2426	+	15.1512i	−1.48332	+	0.856396i	−0.999820	−	0.0189481i	$-0.993968\pi$
$313$	−26.2426	+	15.1512i	−1.48332	+	0.856396i	−0.483501	+	0.875344i	$0.660635\pi$
$314$	11.2106			0.632649
$315$	7.82632	+	1.32238i	0.440963	+	0.0745077i
$316$	−3.06855			−0.172620
$317$	−23.0201	+	13.2907i	−1.29294	+	0.746479i	−0.979174	−	0.203022i	$-0.934924\pi$
$317$	−23.0201	+	13.2907i	−1.29294	+	0.746479i	−0.313765	+	0.949501i	$0.601590\pi$
$318$	13.2175	+	30.1022i	0.741203	+	1.68805i
$319$	1.92905	−	3.34121i	0.108006	−	0.187072i
$320$	1.65277			0.0923927
$321$	9.55548	−	4.19570i	0.533335	−	0.234181i
$322$	33.7531	−	1.76781i	1.88099	−	0.0985164i
$323$			0.00201603i			0.000112175i
$324$	0.701317	+	8.31195i	0.0389621	+	0.461775i
$325$	0.130417	−	0.0752961i	0.00723422	−	0.00417668i
$326$		−	32.6212i		−	1.80672i
$327$	8.88473	+	0.979985i	0.491326	+	0.0541933i
$328$	−17.0810	+	9.86172i	−0.943140	+	0.544522i
$329$	−22.3110	+	1.16853i	−1.23004	+	0.0644233i
$330$	1.69105	+	0.186523i	0.0930895	+	0.0102678i
$331$	6.52587	+	11.3031i	0.358694	+	0.621276i	0.987743	−	0.156089i	$-0.0498888\pi$
$331$	6.52587	+	11.3031i	0.358694	+	0.621276i	−0.629049	+	0.777366i	$0.716555\pi$
$332$	4.14875	+	7.18584i	0.227692	+	0.394374i
$333$	4.20683	+	0.939456i	0.230533	+	0.0514819i
$334$	9.00322	+	5.19801i	0.492634	+	0.284423i
$335$	−4.10141	+	7.10384i	−0.224084	+	0.388124i
$336$	12.5649	−	19.1311i	0.685474	−	1.04369i
$337$	12.2635	+	21.2411i	0.668038	+	1.15708i	0.978452	+	0.206474i	$0.0661989\pi$
$337$	12.2635	+	21.2411i	0.668038	+	1.15708i	−0.310414	+	0.950601i	$0.600468\pi$
$338$			22.2016i			1.20761i
$339$	−1.60688	+	14.5683i	−0.0872736	+	0.791239i
$340$	−1.08794			−0.0590018
$341$	−1.90548	+	3.30039i	−0.103188	+	0.178726i
$342$	−0.00263767	−	0.00841094i	−0.000142629	−	0.000454811i
$343$	−18.2925	+	2.89540i	−0.987704	+	0.156337i
$344$	−9.55722	−	5.51787i	−0.515291	−	0.297503i
$345$	−10.4244	−	7.65586i	−0.561229	−	0.412177i
$346$	−29.1143	−	16.8092i	−1.56520	−	0.903666i
$347$	17.0470	+	9.84207i	0.915129	+	0.528350i	0.882078	−	0.471103i	$-0.156144\pi$
$347$	17.0470	+	9.84207i	0.915129	+	0.528350i	0.0330514	+	0.999454i	$0.489477\pi$
$348$	1.18266	−	10.7222i	0.0633971	−	0.574770i
$349$	25.4274	+	14.6805i	1.36110	+	0.785831i	0.989770	−	0.142671i	$-0.0455690\pi$
$349$	25.4274	+	14.6805i	1.36110	+	0.785831i	0.371329	+	0.928501i	$0.378902\pi$
$350$	−0.236742	−	4.52015i	−0.0126544	−	0.241612i
$351$	−0.767816	+	0.150878i	−0.0409830	+	0.00805330i
$352$	1.39888	−	2.42293i	0.0745605	−	0.129143i
$353$	−15.3147			−0.815119			−0.407560	−	0.913179i	$-0.633620\pi$
$353$	−15.3147			−0.815119			−0.407560	+	0.913179i	$0.633620\pi$
$354$	−24.5261	−	18.0125i	−1.30355	−	0.957351i
$355$			0.0708560i			0.00376064i
$356$	0.648532	+	1.12329i	0.0343721	+	0.0595343i
$357$	2.95297	−	4.49613i	0.156288	−	0.237960i
$358$	11.3768	−	19.7052i	0.601282	−	1.04145i
$359$	−2.96529	−	1.71201i	−0.156502	−	0.0903564i	0.419704	−	0.907661i	$-0.362134\pi$
$359$	−2.96529	−	1.71201i	−0.156502	−	0.0903564i	−0.576206	+	0.817305i	$0.695467\pi$
$360$	−5.25555	+	1.64814i	−0.276992	+	0.0868648i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	6.73556	+	11.6663i	0.354013	+	0.613168i
$363$	10.9399	−	14.8959i	0.574194	−	0.781834i
$364$	−0.329023	−	0.167659i	−0.0172455	−	0.00878772i
$365$	−10.2405	+	5.91235i	−0.536012	+	0.309467i
$366$	−8.76054	−	19.9516i	−0.457921	−	1.04289i
$367$			0.649932i			0.0339262i	0.999856	+	0.0169631i	$0.00539978\pi$
$367$			0.649932i			0.0339262i	−0.999856	+	0.0169631i	$0.994600\pi$
$368$	−32.2995	+	18.6481i	−1.68373	+	0.972102i
$369$	21.8098	−	23.7275i	1.13537	−	1.23520i
$370$		−	2.45811i		−	0.127791i
$371$	1.53532	+	29.3141i	0.0797100	+	1.52191i
$372$	−1.16821	+	10.5912i	−0.0605690	+	0.549130i
$373$	17.6606			0.914433			0.457217	−	0.889355i	$-0.348846\pi$
$373$	17.6606			0.914433			0.457217	+	0.889355i	$0.348846\pi$
$374$	0.576497	−	0.998522i	0.0298099	−	0.0516323i
$375$	−1.02526	+	1.39601i	−0.0529441	+	0.0720897i
$376$	13.4265	−	7.75177i	0.692417	−	0.399767i
$377$	1.01193			0.0521171
$378$	−6.43738	+	22.6215i	−0.331103	+	1.16352i
$379$	34.7390			1.78442			0.892210	−	0.451620i	$-0.149154\pi$
$379$	34.7390			1.78442			0.892210	+	0.451620i	$0.149154\pi$
$380$	−0.00137856		0.000795911i	−7.07186e−5		4.08294e-5i
$381$	−6.58433	+	8.96536i	−0.337325	+	0.459309i
$382$	5.67703	−	9.83291i	0.290462	−	0.503096i
$383$	2.44225			0.124793			0.0623965	−	0.998051i	$-0.480126\pi$
$383$	2.44225			0.124793			0.0623965	+	0.998051i	$0.480126\pi$
$384$	−2.38759	+	21.6464i	−0.121841	+	1.10464i
$385$	1.35346	+	0.689680i	0.0689789	+	0.0351494i
$386$		−	18.5527i		−	0.944306i
$387$	17.5990	+	3.93015i	0.894607	+	0.199781i
$388$	−13.8230	+	7.98073i	−0.701758	+	0.405160i
$389$			15.9430i			0.808345i	0.914683	+	0.404172i	$0.132440\pi$
$389$			15.9430i			0.808345i	−0.914683	+	0.404172i	$0.867560\pi$
$390$	0.179403	+	0.408581i	0.00908444	+	0.0206893i
$391$	−7.59094	+	4.38263i	−0.383890	+	0.221639i
$392$	10.3978	−	7.55343i	0.525170	−	0.381506i
$393$	−13.6869	+	18.6363i	−0.690412	+	0.940079i
$394$	9.45886	+	16.3832i	0.476531	+	0.825375i
$395$	1.65540	+	2.86723i	0.0832921	+	0.144266i
$396$	−0.347936	+	1.55804i	−0.0174845	+	0.0782944i
$397$	12.0664	+	6.96657i	0.605598	+	0.349642i	0.771241	−	0.636544i	$-0.219637\pi$
$397$	12.0664	+	6.96657i	0.605598	+	0.349642i	−0.165643	+	0.986186i	$0.552970\pi$
$398$	0.769707	−	1.33317i	0.0385819	−	0.0668258i
$399$	0.000452532	−	0.00785750i	2.26550e−5	−	0.000393367i
$400$	2.49732	+	4.32549i	0.124866	+	0.216275i
$401$		−	28.5774i		−	1.42709i	−0.700610	−	0.713545i	$-0.747089\pi$
$401$		−	28.5774i		−	1.42709i	0.700610	−	0.713545i	$-0.252911\pi$
$402$	−19.5907	−	14.3878i	−0.977096	−	0.717598i
$403$	−0.999570			−0.0497921
$404$	−6.18645	+	10.7152i	−0.307787	+	0.533104i
$405$	7.38829	−	5.13937i	0.367127	−	0.255378i
$406$	13.8093	−	27.1000i	0.685343	−	1.34495i
$407$	0.714425	+	0.412473i	0.0354127	+	0.0204455i
$408$	−0.409243	+	3.71027i	−0.0202605	+	0.183686i
$409$	29.9432	+	17.2877i	1.48060	+	0.854822i	0.999758	−	0.0219878i	$-0.00699950\pi$
$409$	29.9432	+	17.2877i	1.48060	+	0.854822i	0.480837	+	0.876810i	$0.340333\pi$
$410$	−15.9164	−	9.18935i	−0.786056	−	0.453830i
$411$	−25.5291	−	18.7490i	−1.25926	−	0.924822i
$412$	−3.56654	−	2.05914i	−0.175711	−	0.101447i
$413$	−14.7971	−	22.7872i	−0.728118	−	1.12128i
$414$	25.9356	−	28.2160i	1.27466	−	1.38674i
$415$	4.47627	−	7.75313i	0.219731	−	0.380586i
$416$	0.733818			0.0359784
$417$	−1.01071	+	9.16328i	−0.0494947	+	0.448728i
$418$		−	0.00168701i		−	8.25142e-5i
$419$	−3.74166	−	6.48074i	−0.182792	−	0.316605i	0.760038	−	0.649878i	$-0.225180\pi$
$419$	−3.74166	−	6.48074i	−0.182792	−	0.316605i	−0.942830	+	0.333273i	$0.891847\pi$
$420$	4.24025	+	0.244206i	0.206903	+	0.0119160i
$421$	4.74302	−	8.21515i	0.231161	−	0.400382i	−0.726989	−	0.686649i	$-0.759081\pi$
$421$	4.74302	−	8.21515i	0.231161	−	0.400382i	0.958150	+	0.286267i	$0.0924144\pi$
$422$	−28.7889	−	16.6213i	−1.40142	−	0.809110i
$423$	−17.1435	+	18.6509i	−0.833546	+	0.906838i
$424$	−10.1850	−	17.6409i	−0.494626	−	0.856717i
$425$	0.586913	+	1.01656i	0.0284695	+	0.0493106i
$426$	−0.208694	−	0.0230189i	−0.0101113	−	0.00111527i
$427$	−1.01761	−	19.4293i	−0.0492454	−	0.940249i
$428$	4.83623	−	2.79220i	0.233768	−	0.134966i
$429$	−0.148854	−	0.0164186i	−0.00718675	−	0.000792698i
$430$		−	10.2833i		−	0.495906i
$431$	−25.2973	+	14.6054i	−1.21853	+	0.703519i	−0.964603	−	0.263705i	$-0.915056\pi$
$431$	−25.2973	+	14.6054i	−1.21853	+	0.703519i	−0.253927	+	0.967223i	$0.581722\pi$
$432$	−5.00414	−	25.4659i	−0.240762	−	1.22523i
$433$			12.2560i			0.588987i	0.955654	+	0.294493i	$0.0951509\pi$
$433$			12.2560i			0.588987i	−0.955654	+	0.294493i	$0.904849\pi$
$434$	−13.6406	+	26.7690i	−0.654770	+	1.28495i
$435$	−10.6568	+	4.67926i	−0.510953	+	0.224354i
$436$	4.78311			0.229069
$437$	−0.00641246	+	0.0111067i	−0.000306750	+	0.000531306i
$438$	−14.0870	−	32.0824i	−0.673103	−	1.53295i
$439$	0.651289	−	0.376022i	0.0310843	−	0.0179465i	−0.484377	−	0.874859i	$-0.660954\pi$
$439$	0.651289	−	0.376022i	0.0310843	−	0.0179465i	0.515462	+	0.856913i	$0.327620\pi$
$440$	−1.05412			−0.0502533
$441$	−12.5185	+	16.8608i	−0.596117	+	0.802897i
$442$	0.302416			0.0143845
$443$	25.2094	−	14.5547i	1.19773	−	0.691513i	0.237685	−	0.971342i	$-0.423611\pi$
$443$	25.2094	−	14.5547i	1.19773	−	0.691513i	0.960050	+	0.279830i	$0.0902780\pi$
$444$	2.29265	+	0.252879i	0.108804	+	0.0120011i
$445$	0.699730	−	1.21197i	0.0331704	−	0.0574528i
$446$	4.20088			0.198917
$447$	−1.01159	−	0.742930i	−0.0478465	−	0.0351394i
$448$	−1.98535	+	3.89615i	−0.0937988	+	0.184076i
$449$		−	33.1131i		−	1.56270i	−0.624091	−	0.781352i	$-0.714531\pi$
$449$		−	33.1131i		−	1.56270i	0.624091	−	0.781352i	$-0.285469\pi$
$450$	−3.77864	−	3.47324i	−0.178127	−	0.163730i
$451$	5.34159	−	3.08397i	0.251526	−	0.145218i
$452$			7.84285i			0.368896i
$453$	−3.96131	+	5.39380i	−0.186119	+	0.253423i
$454$	2.75289	−	1.58938i	0.129199	−	0.0745933i
$455$	0.0208391	+	0.397884i	0.000976953	+	0.0186531i
$456$	0.00219578	+	0.00500078i	0.000102827	+	0.000234183i
$457$	−11.2360	−	19.4613i	−0.525597	−	0.910361i	−0.999555	−	0.0298136i	$-0.990509\pi$
$457$	−11.2360	−	19.4613i	−0.525597	−	0.910361i	0.473958	−	0.880547i	$-0.342825\pi$
$458$	23.2748	+	40.3131i	1.08756	+	1.88371i
$459$	−1.17606	−	5.98493i	−0.0548937	−	0.279352i
$460$	−5.99366	−	3.46044i	−0.279456	−	0.161344i
$461$	4.42868	−	7.67071i	0.206264	−	0.357260i	−0.744270	−	0.667878i	$-0.767203\pi$
$461$	4.42868	−	7.67071i	0.206264	−	0.357260i	0.950535	+	0.310618i	$0.100536\pi$
$462$	−2.47103	+	3.76234i	−0.114963	+	0.175040i
$463$	−18.4035	−	31.8758i	−0.855283	−	1.48139i	−0.876382	−	0.481616i	$-0.840050\pi$
$463$	−18.4035	−	31.8758i	−0.855283	−	1.48139i	0.0210995	−	0.999777i	$-0.493283\pi$
$464$			33.5624i			1.55810i
$465$	10.5266	−	4.62211i	0.488159	−	0.214345i
$466$	8.45049			0.391461
$467$	6.27600	−	10.8703i	0.290418	−	0.503020i	−0.683490	−	0.729960i	$-0.739539\pi$
$467$	6.27600	−	10.8703i	0.290418	−	0.503020i	0.973909	+	0.226940i	$0.0728722\pi$
$468$	−0.399535	+	0.125294i	−0.0184685	+	0.00579174i
$469$	−11.8195	−	18.2017i	−0.545773	−	0.840477i
$470$	12.5110	+	7.22325i	0.577091	+	0.333184i
$471$	10.3922	−	4.56308i	0.478845	−	0.210255i
$472$	16.3282	+	9.42710i	0.751567	+	0.433917i
$473$	2.98875	+	1.72555i	0.137423	+	0.0793410i
$474$	−8.98273	+	3.94421i	−0.412591	+	0.181164i
$475$	0.00148739		0.000858744i	6.82461e−5		3.94019e-5i
$476$	1.30686	−	2.56465i	0.0598998	−	0.117550i
$477$	24.5052	+	22.5247i	1.12202	+	1.03133i
$478$	16.5076	−	28.5921i	0.755041	−	1.30777i
$479$	−17.9790			−0.821483			−0.410741	−	0.911752i	$-0.634730\pi$
$479$	−17.9790			−0.821483			−0.410741	+	0.911752i	$0.634730\pi$
$480$	−7.72793	+	3.39324i	−0.352730	+	0.154880i
$481$			0.216374i			0.00986578i
$482$	−14.6951	−	25.4526i	−0.669343	−	1.15934i
$483$	30.5695	−	15.3774i	1.39096	−	0.699696i
$484$	4.94481	−	8.56466i	0.224764	−	0.389303i
$485$	14.9143	+	8.61076i	0.677223	+	0.390995i
$486$	12.7369	+	23.4306i	0.577758	+	1.06283i
$487$	−1.00935	−	1.74825i	−0.0457382	−	0.0792208i	0.842250	−	0.539087i	$-0.181231\pi$
$487$	−1.00935	−	1.74825i	−0.0457382	−	0.0792208i	−0.887988	+	0.459866i	$0.847897\pi$
$488$	6.75056	+	11.6923i	0.305583	+	0.529286i
$489$	−13.2779	−	30.2397i	−0.600448	−	1.36749i
$490$	10.9399	+	4.87163i	0.494215	+	0.220078i
$491$	29.4591	−	17.0082i	1.32947	−	0.767570i	0.344253	−	0.938877i	$-0.388132\pi$
$491$	29.4591	−	17.0082i	1.32947	−	0.767570i	0.985218	+	0.171307i	$0.0547989\pi$
$492$	10.2082	−	13.8997i	0.460222	−	0.626647i
$493$			7.88774i			0.355246i
$494$	0.000383200	0	0.000221241i	1.72410e−5	0	9.95409e-6i
$495$	1.64352	−	0.515409i	0.0738709	−	0.0231659i
$496$		−	33.1524i		−	1.48859i
$497$	−0.167032	−	0.0851138i	−0.00749240	−	0.00381788i
$498$	21.3813	+	15.7028i	0.958119	+	0.703661i
$499$	33.4923			1.49932			0.749660	−	0.661823i	$-0.230217\pi$
$499$	33.4923			1.49932			0.749660	+	0.661823i	$0.230217\pi$
$500$	−0.463416	+	0.802660i	−0.0207246	+	0.0358960i
$501$	10.4617	+	1.15393i	0.467395	+	0.0515537i
$502$	22.0004	−	12.7019i	0.981925	−	0.566915i
$503$	−28.8478			−1.28626			−0.643129	−	0.765758i	$-0.722364\pi$
$503$	−28.8478			−1.28626			−0.643129	+	0.765758i	$0.722364\pi$
$504$	2.42786	−	14.3689i	0.108145	−	0.640043i
$505$	13.3497			0.594053
$506$	6.35206	−	3.66736i	0.282383	−	0.163034i
$507$	9.03679	+	20.5808i	0.401338	+	0.914025i
$508$	−2.97611	+	5.15478i	−0.132044	+	0.228706i
$509$	−9.08722			−0.402784			−0.201392	−	0.979511i	$-0.564546\pi$
$509$	−9.08722			−0.402784			−0.201392	+	0.979511i	$0.564546\pi$
$510$	−3.18478	+	1.39840i	−0.141025	+	0.0619223i
$511$	−1.63632	−	31.2424i	−0.0723864	−	1.38208i
$512$			5.99824i			0.265087i
$513$	−0.00586865	−	0.00672329i	−0.000259107	−	0.000296841i
$514$	−20.6021	+	11.8946i	−0.908718	+	0.524649i
$515$			4.44340i			0.195800i
$516$	9.59113	+	1.05790i	0.422226	+	0.0465715i
$517$	−4.19874	+	2.42414i	−0.184660	+	0.106614i
$518$	5.79460	+	2.95273i	0.254600	+	0.129736i
$519$	−33.8308	−	3.73153i	−1.48501	−	0.163796i
$520$	−0.138242	−	0.239442i	−0.00606230	−	0.0105002i
$521$	−5.10354	−	8.83959i	−0.223590	−	0.387269i	0.732305	−	0.680976i	$-0.238444\pi$
$521$	−5.10354	−	8.83959i	−0.223590	−	0.387269i	−0.955896	+	0.293707i	$0.905111\pi$
$522$	−10.3199	−	32.9078i	−0.451690	−	1.44034i
$523$	−29.5981	−	17.0885i	−1.29423	−	0.747226i	−0.314832	−	0.949147i	$-0.601948\pi$
$523$	−29.5981	−	17.0885i	−1.29423	−	0.747226i	−0.979402	+	0.201921i	$0.935282\pi$
$524$	−6.18646	+	10.7153i	−0.270257	+	0.468099i
$525$	−2.05931	−	4.09380i	−0.0898758	−	0.178668i
$526$	3.21223	+	5.56374i	0.140060	+	0.242591i
$527$		−	7.79139i		−	0.339398i
$528$	0.544551	−	4.93700i	0.0236986	−	0.214856i
$529$	−32.7599			−1.42434
$530$	9.49056	−	16.4381i	0.412244	−	0.714027i
$531$	−30.0673	−	6.71454i	−1.30481	−	0.291386i
$532$	−0.000220278	−	0.00420580i	−9.55027e−6	−	0.000182345i
$533$	1.40104	+	0.808888i	0.0606856	+	0.0350368i
$534$	3.34232	+	2.45467i	0.144636	+	0.106224i
$535$	−5.21803	−	3.01263i	−0.225595	−	0.130247i
$536$	13.0425	+	7.53008i	0.563349	+	0.325250i
$537$	2.52558	−	22.8974i	0.108987	−	0.988095i
$538$	33.3190	+	19.2368i	1.43649	+	0.829356i
$539$	−3.25163	+	2.36212i	−0.140057	+	0.101744i
$540$	3.62818	−	3.16698i	0.156132	−	0.136285i
$541$	−21.3930	+	37.0537i	−0.919756	+	1.59306i	−0.119970	+	0.992778i	$0.538280\pi$
$541$	−21.3930	+	37.0537i	−0.919756	+	1.59306i	−0.799786	+	0.600286i	$0.795054\pi$
$542$	38.8370			1.66819
$543$	10.9924	+	8.07305i	0.471730	+	0.346448i
$544$			5.71992i			0.245240i
$545$	−2.58035	−	4.46930i	−0.110530	−	0.191444i
$546$	−1.17867	−	0.0678824i	−0.0504424	−	0.00290510i
$547$	17.5337	−	30.3692i	0.749685	−	1.29849i	−0.198288	−	0.980144i	$-0.563538\pi$
$547$	17.5337	−	30.3692i	0.749685	−	1.29849i	0.947973	−	0.318350i	$-0.103129\pi$
$548$	−14.6784	−	8.47456i	−0.627029	−	0.362015i
$549$	−16.2420	−	14.9293i	−0.693191	−	0.637166i
$550$	−0.491126	−	0.850655i	−0.0209417	−	0.0362721i
$551$	0.00577048	+	0.00999477i	0.000245831	+	0.000425792i
$552$	−14.0560	+	19.1389i	−0.598261	+	0.814605i
$553$	−8.74756	+	0.458152i	−0.371984	+	0.0194826i
$554$	−36.2904	+	20.9523i	−1.54183	+	0.890177i
$555$	−1.00053	−	2.27866i	−0.0424702	−	0.0967236i
$556$			4.93307i			0.209209i
$557$	−22.7389	+	13.1283i	−0.963477	+	0.556263i	−0.897241	−	0.441541i	$-0.854432\pi$
$557$	−22.7389	+	13.1283i	−0.963477	+	0.556263i	−0.0662353	+	0.997804i	$0.521099\pi$
$558$	10.1938	+	32.5059i	0.431540	+	1.37608i
$559$			0.905184i			0.0382852i
$560$	−13.1965	+	0.691165i	−0.557654	+	0.0292070i
$561$	0.127979	−	1.16028i	0.00540327	−	0.0489871i
$562$	27.5052			1.16024
$563$	19.5646	−	33.8869i	0.824550	−	1.42816i	−0.0777130	−	0.996976i	$-0.524762\pi$
$563$	19.5646	−	33.8869i	0.824550	−	1.42816i	0.902263	−	0.431186i	$-0.141905\pi$
$564$	−8.02413	+	10.9258i	−0.337877	+	0.460060i
$565$	7.32830	−	4.23100i	0.308304	−	0.177999i
$566$	−8.88361			−0.373406
$567$	3.24027	+	23.5903i	0.136079	+	0.990698i
$568$	0.130090			0.00545845
$569$	−8.66998	+	5.00561i	−0.363464	+	0.209846i	−0.670599	−	0.741820i	$-0.733963\pi$
$569$	−8.66998	+	5.00561i	−0.363464	+	0.209846i	0.307135	+	0.951666i	$0.400630\pi$
$570$	−0.00301249	+	0.00410187i	−0.000126179	+	0.000171808i
$571$	8.59567	−	14.8881i	0.359717	−	0.623049i	−0.628196	−	0.778055i	$-0.716206\pi$
$571$	8.59567	−	14.8881i	0.359717	−	0.623049i	0.987914	+	0.155006i	$0.0495397\pi$
$572$	−0.0801359			−0.00335065
$573$	1.26027	−	11.4258i	0.0526484	−	0.477320i
$574$	40.7816	−	26.4820i	1.70219	−	1.10534i
$575$			7.46725i			0.311406i
$576$	1.48368	+	4.73112i	0.0618201	+	0.197130i
$577$	−21.9901	+	12.6960i	−0.915458	+	0.528540i	−0.882183	−	0.470906i	$-0.843927\pi$
$577$	−21.9901	+	12.6960i	−0.915458	+	0.528540i	−0.0332750	+	0.999446i	$0.510594\pi$
$578$		−	26.7263i		−	1.11167i
$579$	−7.55155	−	17.1983i	−0.313832	−	0.714735i
$580$	−5.39361	+	3.11400i	−0.223958	+	0.129302i
$581$	12.8998	+	19.8653i	0.535173	+	0.824153i
$582$	−30.2067	+	41.1301i	−1.25211	+	1.70490i
$583$	3.18506	+	5.51668i	0.131912	+	0.228477i
$584$	10.8549	+	18.8013i	0.449180	+	0.778003i
$585$	0.332613	+	0.305730i	0.0137518	+	0.0126404i
$586$	3.67557	+	2.12209i	0.151836	+	0.0876628i
$587$	−2.12974	+	3.68882i	−0.0879038	+	0.152254i	−0.906625	−	0.421938i	$-0.861350\pi$
$587$	−2.12974	+	3.68882i	−0.0879038	+	0.152254i	0.818721	+	0.574191i	$0.194683\pi$
$588$	−5.66916	+	9.70237i	−0.233792	+	0.400119i
$589$	−0.00570000	−	0.00987268i	−0.000234864	−	0.000406797i
$590$			17.5687i			0.723293i
$591$	15.4369	+	11.3371i	0.634987	+	0.466347i
$592$	−7.17640			−0.294948
$593$	16.9948	−	29.4359i	0.697894	−	1.20879i	−0.271301	−	0.962494i	$-0.587454\pi$
$593$	16.9948	−	29.4359i	0.697894	−	1.20879i	0.969195	−	0.246293i	$-0.0792127\pi$
$594$	0.984119	+	5.00816i	0.0403789	+	0.205487i
$595$	−3.10140	+	0.162435i	−0.127145	+	0.00665920i
$596$	−0.581630	−	0.335804i	−0.0238245	−	0.0137551i
$597$	0.170870	−	1.54914i	0.00699326	−	0.0634022i
$598$	1.66607	+	0.961905i	0.0681306	+	0.0393352i
$599$	0.419567	+	0.242237i	0.0171430	+	0.00989753i	0.508547	−	0.861034i	$-0.330183\pi$
$599$	0.419567	+	0.242237i	0.0171430	+	0.00989753i	−0.491404	+	0.870932i	$0.663516\pi$
$600$	2.56304	+	1.88235i	0.104636	+	0.0768465i
$601$	33.2908	+	19.2204i	1.35796	+	0.784018i	0.989349	−	0.145565i	$-0.0465001\pi$
$601$	33.2908	+	19.2204i	1.35796	+	0.784018i	0.368611	+	0.929584i	$0.379833\pi$
$602$	24.2413	+	12.3526i	0.988002	+	0.503453i
$603$	−24.0169	−	5.36337i	−0.978042	−	0.218413i
$604$	−1.79051	+	3.10126i	−0.0728549	+	0.126188i
$605$	−10.6704			−0.433812
$606$	−4.33690	+	39.3192i	−0.176175	+	1.59723i
$607$			5.34382i			0.216899i	0.994102	+	0.108449i	$0.0345886\pi$
$607$			5.34382i			0.216899i	−0.994102	+	0.108449i	$0.965411\pi$
$608$	0.00418456	+	0.00724787i	0.000169706	+	0.000293940i
$609$	1.77053	−	30.7425i	0.0717457	−	1.24575i
$610$	−6.29030	+	10.8951i	−0.254687	+	0.441131i
$611$	−1.10128	−	0.635823i	−0.0445530	−	0.0257227i
$612$	−0.976637	−	3.11427i	−0.0394782	−	0.125887i
$613$	22.9643	+	39.7754i	0.927520	+	1.60651i	0.787457	+	0.616370i	$0.211397\pi$
$613$	22.9643	+	39.7754i	0.927520	+	1.60651i	0.140064	+	0.990142i	$0.455269\pi$
$614$	13.8798	+	24.0405i	0.560142	+	0.970194i
$615$	−18.4948	−	2.03998i	−0.745784	−	0.0822599i
$616$	1.26624	−	2.48493i	0.0510181	−	0.100121i
$617$	−34.3802	+	19.8494i	−1.38409	+	0.799107i	−0.992641	−	0.121092i	$-0.961360\pi$
$617$	−34.3802	+	19.8494i	−1.38409	+	0.799107i	−0.391452	+	0.920199i	$0.628027\pi$
$618$	−13.0873	−	1.44353i	−0.526448	−	0.0580672i
$619$			35.7655i			1.43754i	0.695249	+	0.718769i	$0.255294\pi$
$619$			35.7655i			1.43754i	−0.695249	+	0.718769i	$0.744706\pi$
$620$	5.32773	−	3.07597i	0.213967	−	0.123534i
$621$	12.5573	−	36.7128i	0.503908	−	1.47323i
$622$		−	27.0618i		−	1.08508i
$623$	2.01649	+	3.10535i	0.0807891	+	0.124413i
$624$	1.19285	−	0.523765i	0.0477520	−	0.0209674i
$625$	1.00000			0.0400000
$626$	−25.9206	+	44.8959i	−1.03600	+	1.79440i
$627$	−0.000686668	−	0.00156385i	−2.74229e−5	−	6.24541e-5i
$628$	5.25969	−	3.03668i	0.209884	−	0.121177i
$629$	−1.68657			−0.0672481
$630$	12.7266	−	4.73540i	0.507040	−	0.188663i
$631$	−42.2092			−1.68032			−0.840162	−	0.542336i	$-0.817540\pi$
$631$	−42.2092			−1.68032			−0.840162	+	0.542336i	$0.817540\pi$
$632$	5.26417	−	3.03927i	0.209397	−	0.120896i
$633$	−33.4526	−	3.68982i	−1.32962	−	0.146657i
$634$	−22.7377	+	39.3828i	−0.903028	+	1.56409i
$635$	6.42212			0.254854
$636$	14.3553	+	10.5428i	0.569225	+	0.418050i
$637$	−0.962982	−	0.428823i	−0.0381547	−	0.0169906i
$638$		−	6.60042i		−	0.261313i
$639$	−0.202828	+	0.0636070i	−0.00802376	+	0.00251625i
$640$	10.8888	−	6.28666i	0.430418	−	0.248502i
$641$		−	16.5845i		−	0.655047i	−0.944843	−	0.327524i	$-0.893786\pi$
$641$		−	16.5845i		−	0.655047i	0.944843	−	0.327524i	$-0.106214\pi$
$642$	10.5684	−	14.3901i	0.417100	−	0.567931i
$643$	−16.8290	+	9.71622i	−0.663670	+	0.383170i	−0.793674	−	0.608343i	$-0.791834\pi$
$643$	−16.8290	+	9.71622i	−0.663670	+	0.383170i	0.130004	+	0.991514i	$0.458501\pi$
$644$	15.3572	−	9.97235i	0.605158	−	0.392966i
$645$	−4.18565	−	9.53260i	−0.164810	−	0.375346i
$646$	0.00172451	+	0.00298694i	6.78501e−5	+	0.000117520i
$647$	−12.3390	−	21.3718i	−0.485098	−	0.840214i	0.514756	−	0.857337i	$-0.327883\pi$
$647$	−12.3390	−	21.3718i	−0.485098	−	0.840214i	−0.999853	+	0.0171232i	$0.994549\pi$
$648$	−9.43576	−	13.5647i	−0.370672	−	0.532872i
$649$	−5.10618	−	2.94805i	−0.200435	−	0.115721i
$650$	0.128816	−	0.223117i	0.00505260	−	0.00875135i
$651$	−1.74891	+	30.3670i	−0.0685451	+	1.19018i
$652$	−8.83633	−	15.3050i	−0.346057	−	0.599389i
$653$			23.9903i			0.938815i	0.882982	+	0.469407i	$0.155532\pi$
$653$			23.9903i			0.938815i	−0.882982	+	0.469407i	$0.844468\pi$
$654$	14.0018	−	6.14805i	0.547515	−	0.240408i
$655$	13.3497			0.521616
$656$	−26.8281	+	46.4677i	−1.04746	+	1.81426i
$657$	−26.1172	−	24.0064i	−1.01893	−	0.936578i
$658$	−32.0562	+	20.8161i	−1.24968	+	0.811495i
$659$	5.35052	+	3.08912i	0.208427	+	0.120335i	0.600580	−	0.799565i	$-0.294936\pi$
$659$	5.35052	+	3.08912i	0.208427	+	0.120335i	−0.392153	+	0.919900i	$0.628270\pi$
$660$	0.843921	−	0.370556i	0.0328496	−	0.0144239i
$661$	10.4500	+	6.03334i	0.406460	+	0.234670i	0.689267	−	0.724507i	$-0.257933\pi$
$661$	10.4500	+	6.03334i	0.406460	+	0.234670i	−0.282808	+	0.959177i	$0.591266\pi$
$662$	19.3374	+	11.1644i	0.751569	+	0.433918i
$663$	0.280339	−	0.123094i	0.0108875	−	0.00478056i
$664$	−14.2345	−	8.21832i	−0.552407	−	0.318933i
$665$	−0.00381104	+	0.00247474i	−0.000147786	+	9.59663e-5i
$666$	7.03643	−	2.20663i	0.272656	−	0.0855051i
$667$	−25.0888	+	43.4550i	−0.971441	+	1.68259i
$668$	5.63209			0.217912
$669$	3.89420	−	1.70990i	0.150558	−	0.0661085i
$670$			14.0334i			0.542156i
$671$	−2.11104	−	3.65643i	−0.0814959	−	0.141155i
$672$	1.28393	−	22.2934i	0.0495287	−	0.859987i
$673$	21.8014	−	37.7611i	0.840382	−	1.45558i	−0.0491906	−	0.998789i	$-0.515664\pi$
$673$	21.8014	−	37.7611i	0.840382	−	1.45558i	0.889572	−	0.456794i	$-0.151003\pi$
$674$	36.3392	+	20.9805i	1.39973	+	0.808137i
$675$	−4.91651	−	1.68165i	−0.189236	−	0.0647268i
$676$	6.01390	+	10.4164i	0.231304	+	0.400630i
$677$	−7.09308	−	12.2856i	−0.272609	−	0.472173i	0.696920	−	0.717149i	$-0.254553\pi$
$677$	−7.09308	−	12.2856i	−0.272609	−	0.472173i	−0.969529	+	0.244976i	$0.921220\pi$
$678$	10.0809	+	22.9588i	0.387156	+	0.881727i
$679$	−38.2139	+	24.8146i	−1.46652	+	0.952297i
$680$	1.86639	−	1.07756i	0.0715726	−	0.0413225i
$681$	1.90499	−	2.59387i	0.0729993	−	0.0993972i
$682$			6.51979i			0.249656i
$683$	−35.8109	+	20.6754i	−1.37026	+	0.791123i	−0.990961	−	0.134150i	$-0.957170\pi$
$683$	−35.8109	+	20.6754i	−1.37026	+	0.791123i	−0.379303	+	0.925272i	$0.623836\pi$
$684$	−0.00351585	−	0.00323170i	−0.000134432	−	0.000123567i
$685$			18.2872i			0.698716i
$686$	−24.6254	+	19.9372i	−0.940202	+	0.761207i
$687$	37.9844	+	27.8965i	1.44920	+	1.06432i
$688$	−30.0220			−1.14458
$689$	−0.835402	+	1.44696i	−0.0318263	+	0.0551247i
$690$	−21.9935	−	2.42588i	−0.837278	−	0.0923518i
$691$	−12.4578	+	7.19254i	−0.473919	+	0.273617i	−0.717879	−	0.696168i	$-0.754887\pi$
$691$	−12.4578	+	7.19254i	−0.473919	+	0.273617i	0.243960	+	0.969785i	$0.421553\pi$
$692$	−18.2129			−0.692349
$693$	−0.759242	+	4.49347i	−0.0288412	+	0.170693i
$694$	33.6756			1.27831
$695$	4.60943	−	2.66125i	0.174846	−	0.100947i
$696$	8.59101	+	19.5656i	0.325641	+	0.741631i
$697$	−6.30507	+	10.9207i	−0.238822	+	0.413651i
$698$	50.2309			1.90127
$699$	7.83358	−	3.43963i	0.296293	−	0.130099i
$700$	−1.33548	−	2.05660i	−0.0504763	−	0.0777323i
$701$			18.3839i			0.694349i	0.937801	+	0.347174i	$0.112859\pi$
$701$			18.3839i			0.694349i	−0.937801	+	0.347174i	$0.887141\pi$
$702$	−1.00853	+	0.880330i	−0.0380646	+	0.0332259i
$703$	−0.00213711	+	0.00123386i	−8.06025e−5	+	4.65359e-5i
$704$			0.948935i			0.0357643i
$705$	14.5378	+	1.60352i	0.547525	+	0.0603920i
$706$	−22.6902	+	13.1002i	−0.853956	+	0.493032i
$707$	−16.0359	+	31.4698i	−0.603094	+	1.18354i
$708$	−16.3861	−	1.80739i	−0.615829	−	0.0679259i
$709$	−8.28047	−	14.3422i	−0.310980	−	0.538632i	0.667595	−	0.744524i	$-0.267324\pi$
$709$	−8.28047	−	14.3422i	−0.310980	−	0.538632i	−0.978575	+	0.205892i	$0.933990\pi$
$710$	0.0606101	+	0.104980i	0.00227466	+	0.00393982i
$711$	−6.72154	+	7.31255i	−0.252077	+	0.274242i
$712$	−2.22514	−	1.28469i	−0.0833908	−	0.0481457i
$713$	24.7823	−	42.9242i	0.928105	−	1.60752i
$714$	0.529126	−	9.18742i	0.0198020	−	0.343830i
$715$	0.0432311	+	0.0748785i	0.00161675	+	0.00280030i
$716$		−	12.3268i		−	0.460676i
$717$	3.66459	−	33.2239i	0.136857	−	1.24077i
$718$	−5.85781			−0.218611
$719$	16.2728	−	28.1854i	0.606875	−	1.05114i	−0.384878	−	0.922968i	$-0.625756\pi$
$719$	16.2728	−	28.1854i	0.606875	−	1.05114i	0.991752	−	0.128170i	$-0.0409103\pi$
$720$	−10.1401	+	11.0317i	−0.377898	+	0.411126i
$721$	−10.4746	−	5.33752i	−0.390095	−	0.198780i
$722$	−28.1503	−	16.2526i	−1.04765	−	0.604859i
$723$	−23.9824	−	17.6131i	−0.891914	−	0.655039i
$724$	6.32028	+	3.64901i	0.234891	+	0.135615i
$725$	5.81941	+	3.35984i	0.216128	+	0.124781i
$726$	3.46647	−	31.4277i	0.128653	−	1.16639i
$727$	−1.88292	−	1.08711i	−0.0698338	−	0.0403185i	0.464677	−	0.885480i	$-0.346171\pi$
$727$	−1.88292	−	1.08711i	−0.0698338	−	0.0403185i	−0.534510	+	0.845162i	$0.679504\pi$
$728$	0.730505	−	0.0382601i	0.0270743	−	0.00141801i
$729$	21.3441	+	16.5357i	0.790522	+	0.612434i
$730$	−10.1148	+	17.5194i	−0.374367	+	0.648423i
$731$	−7.05567			−0.260963
$732$	−9.51464	−	6.98774i	−0.351671	−	0.258274i
$733$			11.8589i			0.438017i	0.975723	+	0.219009i	$0.0702823\pi$
$733$			11.8589i			0.438017i	−0.975723	+	0.219009i	$0.929718\pi$
$734$	0.555951	+	0.962936i	0.0205205	+	0.0355426i
$735$	12.1242	+	0.0630688i	0.447208	+	0.00232633i
$736$	−18.1935	+	31.5121i	−0.670622	+	1.16155i
$737$	−4.07866	−	2.35481i	−0.150239	−	0.0867407i
$738$	12.0168	−	53.8106i	0.442345	−	1.98080i
$739$	−9.10025	−	15.7621i	−0.334758	−	0.579818i	0.648680	−	0.761061i	$-0.275321\pi$
$739$	−9.10025	−	15.7621i	−0.334758	−	0.579818i	−0.983438	+	0.181243i	$0.941988\pi$
$740$	−0.665844	−	1.15328i	−0.0244769	−	0.0423953i
$741$	0.000265173	0	0.000361065i	9.74137e−6	0	1.32640e-5i
$742$	27.3500	+	42.1184i	1.00405	+	1.54621i
$743$	8.54475	−	4.93331i	0.313476	−	0.180986i	−0.335005	−	0.942216i	$-0.608738\pi$
$743$	8.54475	−	4.93331i	0.313476	−	0.180986i	0.648481	+	0.761231i	$0.275405\pi$
$744$	−8.48607	−	19.3266i	−0.311114	−	0.708546i
$745$			0.724628i			0.0265483i
$746$	26.1659	−	15.1069i	0.958002	−	0.553103i
$747$	26.2120	+	5.85357i	0.959046	+	0.214171i
$748$		−	0.624639i		−	0.0228390i
$749$	13.3698	−	8.68183i	0.488522	−	0.317227i
$750$	−0.324870	+	2.94533i	−0.0118626	+	0.107548i
$751$	8.12561			0.296508			0.148254	−	0.988949i	$-0.452635\pi$
$751$	8.12561			0.296508			0.148254	+	0.988949i	$0.452635\pi$
$752$	21.0882	−	36.5258i	0.769006	−	1.33196i
$753$	15.2242	−	20.7295i	0.554800	−	0.755426i
$754$	1.49927	−	0.865605i	0.0546003	−	0.0315235i
$755$	3.86372			0.140615
$756$	3.10740	+	12.3571i	0.113015	+	0.449424i
$757$	27.0462			0.983009			0.491505	−	0.870875i	$-0.336447\pi$
$757$	27.0462			0.983009			0.491505	+	0.870875i	$0.336447\pi$
$758$	51.4691	−	29.7157i	1.86944	−	1.07932i
$759$	4.39560	−	5.98513i	0.159550	−	0.217247i
$760$	0.00157663	−	0.00273081i	5.71905e−5	−	9.90568e-5i
$761$	5.88456			0.213315			0.106658	−	0.994296i	$-0.465985\pi$
$761$	5.88456			0.213315			0.106658	+	0.994296i	$0.465985\pi$
$762$	−2.08635	+	18.9153i	−0.0755806	+	0.685228i
$763$	13.6353	−	0.714145i	0.493630	−	0.0258538i
$764$		−	6.15111i		−	0.222539i
$765$	−2.38309	+	2.59263i	−0.0861607	+	0.0937366i
$766$	3.61842	−	2.08910i	0.130739	−	0.0754822i
$767$		−	1.54648i		−	0.0558401i
$768$	12.6770	+	28.8712i	0.457442	+	1.04180i
$769$	37.1384	−	21.4419i	1.33925	−	0.773214i	0.352550	−	0.935793i	$-0.385314\pi$
$769$	37.1384	−	21.4419i	1.33925	−	0.773214i	0.986696	+	0.162579i	$0.0519811\pi$
$770$	2.59524	−	0.135925i	0.0935259	−	0.00489840i
$771$	−14.2565	+	19.4120i	−0.513437	+	0.699106i
$772$	−5.02549	−	8.70440i	−0.180871	−	0.313278i
$773$	−4.16275	−	7.21009i	−0.149724	−	0.259329i	0.781402	−	0.624028i	$-0.214505\pi$
$773$	−4.16275	−	7.21009i	−0.149724	−	0.259329i	−0.931125	+	0.364700i	$0.881172\pi$
$774$	29.4364	−	9.23127i	1.05807	−	0.331811i
$775$	−5.74833	−	3.31880i	−0.206486	−	0.119215i
$776$	15.8091	−	27.3822i	0.567515	−	0.982965i
$777$	6.57343	+	0.378580i	0.235821	+	0.0135815i
$778$	13.6377	+	23.6211i	0.488934	+	0.846859i
$779$			0.0184506i			0.000661060i
$780$	0.194846	+	0.143099i	0.00697662	+	0.00512376i
$781$	−0.0406818			−0.00145571
$782$	−7.49780	+	12.9866i	−0.268121	+	0.464399i
$783$	−22.9611	−	26.3049i	−0.820563	−	0.940060i
$784$	14.2226	−	31.9389i	0.507951	−	1.14068i
$785$	−5.67491	−	3.27641i	−0.202546	−	0.116940i
$786$	−4.33691	+	39.3193i	−0.154693	+	1.40247i
$787$	−20.2301	−	11.6798i	−0.721124	−	0.416341i	0.0940421	−	0.995568i	$-0.470021\pi$
$787$	−20.2301	−	11.6798i	−0.721124	−	0.416341i	−0.815166	+	0.579227i	$0.803355\pi$
$788$	8.87568	+	5.12437i	0.316183	+	0.182548i
$789$	5.24235	+	3.85009i	0.186633	+	0.137067i
$790$	4.90526	+	2.83205i	0.174521	+	0.100760i
$791$	1.17098	+	22.3577i	0.0416353	+	0.794948i
$792$	−0.946279	−	3.01747i	−0.0336246	−	0.107221i
$793$	0.553701	−	0.959038i	0.0196625	−	0.0340564i
$794$	23.8368			0.845936
$795$	2.10685	−	19.1011i	0.0747222	−	0.677445i
$796$		−	0.833983i		−	0.0295598i
$797$	5.30395	+	9.18672i	0.187876	+	0.325410i	0.944542	−	0.328391i	$-0.106506\pi$
$797$	5.30395	+	9.18672i	0.187876	+	0.325410i	−0.756666	+	0.653802i	$0.773173\pi$
$798$	−0.00605083	−	0.0120287i	−0.000214197	−	0.000425812i
$799$	4.95608	−	8.58418i	0.175333	−	0.303686i
$800$	4.22004	+	2.43644i	0.149201	+	0.0861412i
$801$	4.09745	+	0.915030i	0.144776	+	0.0323310i
$802$	−24.4451	−	42.3402i	−0.863187	−	1.49508i
$803$	−3.39457	−	5.87956i	−0.119792	−	0.207485i
$804$	−13.0888	−	1.44369i	−0.461605	−	0.0509150i
$805$	−17.6029	−	8.96984i	−0.620420	−	0.316145i
$806$	−1.48096	+	0.855032i	−0.0521645	+	0.0301172i
$807$	38.7167	+	4.27045i	1.36289	+	0.150327i
$808$		−	24.5097i		−	0.862247i
$809$	−15.8894	+	9.17377i	−0.558643	+	0.322533i	−0.752601	−	0.658477i	$-0.771201\pi$
$809$	−15.8894	+	9.17377i	−0.558643	+	0.322533i	0.193958	+	0.981010i	$0.437868\pi$
$810$	6.55024	−	13.9344i	0.230152	−	0.489605i
$811$			0.983192i			0.0345245i	0.999851	+	0.0172623i	$0.00549502\pi$
$811$			0.983192i			0.0345245i	−0.999851	+	0.0172623i	$0.994505\pi$
$812$	−0.861839	−	16.4552i	−0.0302446	−	0.577465i
$813$	36.0018	−	15.8080i	1.26264	−	0.554410i
$814$	1.41132			0.0494666
$815$	−9.53391	+	16.5132i	−0.333958	+	0.578433i
$816$	4.08261	+	9.29792i	0.142920	+	0.325492i
$817$	−0.00894044	+	0.00516176i	−0.000312786	+	0.000180587i
$818$	59.1516			2.06819
$819$	−1.12025	+	0.416831i	−0.0391448	+	0.0145653i
$820$	−9.95673			−0.347704
$821$	−27.5607	+	15.9122i	−0.961876	+	0.555340i	−0.896750	−	0.442537i	$-0.854078\pi$
$821$	−27.5607	+	15.9122i	−0.961876	+	0.555340i	−0.0651263	+	0.997877i	$0.520745\pi$
$822$	−53.8617	−	5.94094i	−1.87864	−	0.207214i
$823$	−4.25568	+	7.37106i	−0.148344	+	0.256939i	−0.930615	−	0.365998i	$-0.880728\pi$
$823$	−4.25568	+	7.37106i	−0.148344	+	0.256939i	0.782272	+	0.622937i	$0.214061\pi$
$824$	8.15798			0.284197
$825$	−0.801517	−	0.588650i	−0.0279053	−	0.0204942i
$826$	−41.4155	−	21.1040i	−1.44103	−	0.734300i
$827$		−	34.2983i		−	1.19267i	−0.802736	−	0.596334i	$-0.796623\pi$
$827$		−	34.2983i		−	1.19267i	0.802736	−	0.596334i	$-0.203377\pi$
$828$	4.52519	−	20.2635i	0.157261	−	0.704206i
$829$	−16.1048	+	9.29811i	−0.559343	+	0.322937i	−0.752882	−	0.658156i	$-0.771337\pi$
$829$	−16.1048	+	9.29811i	−0.559343	+	0.322937i	0.193539	+	0.981093i	$0.438003\pi$
$830$		−	15.3160i		−	0.531626i
$831$	−25.1128	+	34.1941i	−0.871154	+	1.18618i
$832$	−0.215549	+	0.124447i	−0.00747281	+	0.00431443i
$833$	3.34256	−	7.50619i	0.115813	−	0.260074i
$834$	6.34080	+	14.4408i	0.219564	+	0.500045i
$835$	−3.03835	−	5.26258i	−0.105147	−	0.182119i
$836$	−0.000456971	0	0.000791497i	−1.58047e−5	0	2.73745e-5i
$837$	22.6806	+	25.9836i	0.783957	+	0.898124i
$838$	−11.0872	−	6.40122i	−0.383003	−	0.221127i
$839$	19.7247	−	34.1643i	0.680974	−	1.17948i	−0.293710	−	0.955895i	$-0.594890\pi$
$839$	19.7247	−	34.1643i	0.680974	−	1.17948i	0.974684	−	0.223587i	$-0.0717766\pi$
$840$	−7.51612	+	3.78085i	−0.259331	+	0.130452i
$841$	8.07704	+	13.9898i	0.278518	+	0.482408i
$842$		−	16.2287i		−	0.559278i
$843$	25.4972	−	11.1955i	0.878170	−	0.385594i
$844$	−18.0093			−0.619904
$845$	6.48866	−	11.2387i	0.223217	−	0.386623i
$846$	−9.44578	+	42.2977i	−0.324752	+	1.45422i
$847$	12.8175	−	25.1537i	0.440414	−	0.864291i
$848$	−47.9908	−	27.7075i	−1.64801	−	0.951480i
$849$	−8.23508	+	3.61593i	−0.282627	+	0.124098i
$850$	1.73914	+	1.00409i	0.0596519	+	0.0344400i
$851$	−9.29166	−	5.36454i	−0.318514	−	0.183894i
$852$	−0.104149	+	0.0457305i	−0.00356808	+	0.00156670i
$853$	23.0814	+	13.3260i	0.790291	+	0.456275i	0.840065	−	0.542486i	$-0.182517\pi$
$853$	23.0814	+	13.3260i	0.790291	+	0.456275i	−0.0497738	+	0.998761i	$0.515850\pi$
$854$	−18.1275	−	27.9159i	−0.620310	−	0.955262i
$855$	−0.00112297	+	0.00502860i	−3.84048e−5	+	0.000171975i
$856$	−5.53111	+	9.58017i	−0.189049	+	0.327443i
$857$	13.9323			0.475920			0.237960	−	0.971275i	$-0.423521\pi$
$857$	13.9323			0.475920			0.237960	+	0.971275i	$0.423521\pi$
$858$	−0.234586	+	0.103004i	−0.00800864	+	0.00351650i
$859$		−	17.7196i		−	0.604585i	−0.953215	−	0.302292i	$-0.902248\pi$
$859$		−	17.7196i		−	0.604585i	0.953215	−	0.302292i	$-0.0977519\pi$
$860$	−2.78551	−	4.82465i	−0.0949852	−	0.164519i
$861$	27.0254	−	41.1482i	0.921022	−	1.40233i
$862$	−24.9869	+	43.2787i	−0.851059	+	1.47408i
$863$	31.5079	+	18.1911i	1.07254	+	0.619233i	0.928875	−	0.370393i	$-0.120777\pi$
$863$	31.5079	+	18.1911i	1.07254	+	0.619233i	0.143668	+	0.989626i	$0.454110\pi$
$864$	−16.6506	−	19.0754i	−0.566466	−	0.648959i
$865$	9.82533	+	17.0180i	0.334071	+	0.578628i
$866$	10.4838	+	18.1585i	0.356254	+	0.617049i
$867$	−10.8785	−	24.7752i	−0.369453	−	0.841410i
$868$	0.851311	+	16.2542i	0.0288954	+	0.551704i
$869$	−1.64622	+	0.950444i	−0.0558441	+	0.0322416i
$870$	−11.7864	+	16.0486i	−0.399596	+	0.544097i
$871$		−	1.23528i		−	0.0418558i
$872$	−8.20553	+	4.73747i	−0.277874	+	0.160431i
$873$	−11.2602	+	50.4226i	−0.381100	+	1.70655i
$874$			0.0219409i			0.000742160i
$875$	−1.20122	+	2.35734i	−0.0406088	+	0.0796927i
$876$	−15.2996	−	11.2363i	−0.516926	−	0.379640i
$877$	−24.4989			−0.827271			−0.413635	−	0.910443i	$-0.635741\pi$
$877$	−24.4989			−0.827271			−0.413635	+	0.910443i	$0.635741\pi$
$878$	0.643297	−	1.11422i	0.0217102	−	0.0376032i
$879$	4.27100	+	0.471091i	0.144057	+	0.0158895i
$880$	−2.48347	+	1.43383i	−0.0837179	+	0.0483345i
$881$	−23.4938			−0.791527			−0.395763	−	0.918353i	$-0.629520\pi$
$881$	−23.4938			−0.791527			−0.395763	+	0.918353i	$0.629520\pi$
$882$	−4.12454	+	35.6892i	−0.138880	+	1.20172i
$883$	26.9871			0.908189			0.454094	−	0.890954i	$-0.349963\pi$
$883$	26.9871			0.908189			0.454094	+	0.890954i	$0.349963\pi$
$884$	0.141885	−	0.0819176i	0.00477212	−	0.00275519i
$885$	7.15106	+	16.2861i	0.240380	+	0.547453i
$886$	24.9001	−	43.1282i	0.836535	−	1.44892i
$887$	−15.4073			−0.517328			−0.258664	−	0.965967i	$-0.583282\pi$
$887$	−15.4073			−0.517328			−0.258664	+	0.965967i	$0.583282\pi$
$888$	−4.18356	+	1.83695i	−0.140391	+	0.0616440i
$889$	−7.71441	+	15.1391i	−0.258733	+	0.507751i
$890$		−	2.39420i		−	0.0802536i
$891$	2.95076	+	4.24197i	0.0988543	+	0.142111i
$892$	1.97094	−	1.13792i	0.0659918	−	0.0381004i
$893$		−	0.0145030i		−	0.000485324i
$894$	−2.13427	−	0.235409i	−0.0713805	−	0.00787327i
$895$	−11.5181	+	6.64999i	−0.385008	+	0.222285i
$896$	1.73991	+	33.2204i	0.0581263	+	1.10981i
$897$	1.93597	+	0.213537i	0.0646401	+	0.00712980i
$898$	−28.3249	−	49.0602i	−0.945214	−	1.63716i
$899$	−22.3013	−	38.6269i	−0.743788	−	1.28828i
$900$	−2.71365	−	0.606004i	−0.0904551	−	0.0202001i
$901$	−11.2787	−	6.51174i	−0.375747	−	0.216937i
$902$	5.27605	−	9.13839i	0.175673	−	0.304275i
$903$	27.4995	+	1.58376i	0.915126	+	0.0527043i
$904$	−7.76801	−	13.4546i	−0.258360	−	0.447493i
$905$		−	7.87417i		−	0.261746i
$906$	−1.25521	+	11.3799i	−0.0417014	+	0.378073i
$907$	−13.1474			−0.436552			−0.218276	−	0.975887i	$-0.570043\pi$
$907$	−13.1474			−0.436552			−0.218276	+	0.975887i	$0.570043\pi$
$908$	0.861053	−	1.49139i	0.0285750	−	0.0494934i
$909$	11.9839	+	38.2140i	0.397482	+	1.26748i
$910$	0.371225	+	0.571677i	0.0123060	+	0.0189509i
$911$	−18.4987	−	10.6802i	−0.612889	−	0.353852i	0.161206	−	0.986921i	$-0.448462\pi$
$911$	−18.4987	−	10.6802i	−0.612889	−	0.353852i	−0.774095	+	0.633069i	$0.781795\pi$
$912$	0.0119753	+	0.00879491i	0.000396543	+	0.000291229i
$913$	4.45144	+	2.57004i	0.147321	+	0.0850560i
$914$	−33.2943	−	19.2225i	−1.10128	−	0.635824i
$915$	−1.39641	+	12.6601i	−0.0461639	+	0.418530i
$916$	21.8398	+	12.6092i	0.721606	+	0.416620i
$917$	−16.0360	+	31.4698i	−0.529555	+	1.03923i
$918$	−6.86194	−	7.86124i	−0.226478	−	0.259460i
$919$	−12.2951	+	21.2957i	−0.405576	+	0.702479i	−0.994388	−	0.105791i	$-0.966263\pi$
$919$	−12.2951	+	21.2957i	−0.405576	+	0.702479i	0.588812	+	0.808270i	$0.299596\pi$
$920$	13.7097			0.451995
$921$	22.6518	+	16.6359i	0.746401	+	0.548172i
$922$		−	15.1532i		−	0.499043i
$923$	−0.00533518	−	0.00924080i	−0.000175610	−	0.000304165i
$924$	−0.140211	+	2.43453i	−0.00461259	+	0.0800902i
$925$	−0.718409	+	1.24432i	−0.0236211	+	0.0409130i
$926$	−54.5330	−	31.4847i	−1.79207	−	1.03465i
$927$	−12.7194	+	3.98882i	−0.417761	+	0.131010i
$928$	16.3721	+	28.3573i	0.537441	+	0.930875i
$929$	5.90781	+	10.2326i	0.193829	+	0.335722i	0.946516	−	0.322657i	$-0.104576\pi$
$929$	5.90781	+	10.2326i	0.193829	+	0.335722i	−0.752687	+	0.658378i	$0.771243\pi$
$930$	11.6424	−	15.8525i	0.381769	−	0.519825i
$931$	−0.00125590	−	0.0119566i	−4.11604e−5	−	0.000391863i
$932$	3.96474	−	2.28904i	0.129869	−	0.0749801i
$933$	−11.0151	−	25.0862i	−0.360617	−	0.821286i
$934$		−	21.4739i		−	0.702648i
$935$	−0.583658	+	0.336975i	−0.0190877	+	0.0110203i
$936$	0.561313	−	0.610668i	0.0183471	−	0.0199603i
$937$		−	45.3542i		−	1.48166i	−0.671694	−	0.740829i	$-0.734433\pi$
$937$		−	45.3542i		−	1.48166i	0.671694	−	0.740829i	$-0.265567\pi$
$938$	−33.0814	−	16.8572i	−1.08015	−	0.550407i
$939$	−5.75422	+	52.1689i	−0.187782	+	1.70247i
$940$	7.82645			0.255271
$941$	5.02943	−	8.71123i	0.163955	−	0.283978i	−0.772329	−	0.635223i	$-0.780908\pi$
$941$	5.02943	−	8.71123i	0.163955	−	0.283978i	0.936284	+	0.351245i	$0.114242\pi$
$942$	11.4937	−	15.6501i	0.374485	−	0.509907i
$943$	−69.4716	+	40.1095i	−2.26231	+	1.30614i
$944$	51.2916			1.66940
$945$	9.87005	−	9.56985i	0.321073	−	0.311307i
$946$	5.90415			0.191960
$947$	13.4544	−	7.76788i	0.437208	−	0.252422i	−0.265205	−	0.964192i	$-0.585439\pi$
$947$	13.4544	−	7.76788i	0.437208	−	0.252422i	0.702413	+	0.711770i	$0.252106\pi$
$948$	−3.14606	+	4.28373i	−0.102179	+	0.139129i
$949$	0.890354	−	1.54214i	0.0289021	−	0.0500600i
$950$	0.00293828			9.53303e−5
$951$	−5.04763	+	45.7627i	−0.163681	+	1.48396i
$952$	0.298227	+	5.69410i	0.00966560	+	0.184547i
$953$			31.4136i			1.01759i	0.860889	+	0.508793i	$0.169908\pi$
$953$			31.4136i			1.01759i	−0.860889	+	0.508793i	$0.830092\pi$
$954$	55.5744	+	12.4107i	1.79929	+	0.401812i
$955$	−5.74756	+	3.31835i	−0.185987	+	0.107379i
$956$		−	17.8861i		−	0.578479i
$957$	−2.68659	−	6.11856i	−0.0868452	−	0.197785i
$958$	−26.6376	+	15.3793i	−0.860623	+	0.496881i
$959$	−43.1091	−	21.9670i	−1.39207	−	0.709350i
$960$	1.69452	−	2.30729i	0.0546902	−	0.0744673i
$961$	6.52884	+	11.3083i	0.210608	+	0.364783i
$962$	0.185086	+	0.320578i	0.00596740	+	0.0103358i
$963$	3.93958	−	17.6412i	0.126951	−	0.568481i
$964$	−13.7891	−	7.96112i	−0.444116	−	0.256410i
$965$	−5.42222	+	9.39156i	−0.174548	+	0.302325i
$966$	32.1378	−	48.9322i	1.03402	−	1.57437i
$967$	−13.5686	−	23.5016i	−0.436338	−	0.755760i	0.561065	−	0.827771i	$-0.310392\pi$
$967$	−13.5686	−	23.5016i	−0.436338	−	0.755760i	−0.997404	+	0.0720113i	$0.977058\pi$
$968$			19.5905i			0.629663i
$969$	0.00281440	+	0.00206695i	9.04117e−5	+	6.64001e-5i
$970$	29.4626			0.945986
$971$	−24.3180	+	42.1200i	−0.780402	+	1.35170i	0.151306	+	0.988487i	$0.451652\pi$
$971$	−24.3180	+	42.1200i	−0.780402	+	1.35170i	−0.931708	+	0.363209i	$0.881681\pi$
$972$	12.3226	+	7.54284i	0.395248	+	0.241937i
$973$	0.736535	+	14.0628i	0.0236122	+	0.450831i
$974$	−2.99091	−	1.72680i	−0.0958348	−	0.0553302i
$975$	0.0285965	−	0.259261i	0.000915820	−	0.00830300i
$976$	31.8081	+	18.3644i	1.01815	+	0.587831i
$977$	49.9346	+	28.8297i	1.59755	+	0.922345i	0.991958	+	0.126569i	$0.0403965\pi$
$977$	49.9346	+	28.8297i	1.59755	+	0.922345i	0.605591	+	0.795776i	$0.292937\pi$
$978$	−45.5396	−	33.4451i	−1.45619	−	1.06946i
$979$	0.695850	+	0.401749i	0.0222395	+	0.0128400i
$980$	6.45232	−	0.677738i	0.206112	−	0.0216495i
$981$	10.4772	−	11.3984i	0.334511	−	0.363924i
$982$	29.0976	−	50.3986i	0.928543	−	1.60828i
$983$	−10.4508			−0.333330			−0.166665	−	0.986014i	$-0.553300\pi$
$983$	−10.4508			−0.333330			−0.166665	+	0.986014i	$0.553300\pi$
$984$	−3.74535	+	33.9561i	−0.119397	+	1.08248i
$985$		−	11.0578i		−	0.352332i
$986$	6.74716	+	11.6864i	0.214873	+	0.372172i
$987$	−21.2432	+	32.3444i	−0.676178	+	1.02953i
$988$	0.000119858	0	0.000207600i	3.81319e−6	0	6.60464e-6i
$989$	−38.8710	−	22.4422i	−1.23603	−	0.713620i
$990$	1.99416	−	2.16950i	0.0633784	−	0.0689511i
$991$	−1.42712	−	2.47185i	−0.0453341	−	0.0785209i	0.842468	−	0.538746i	$-0.181102\pi$
$991$	−1.42712	−	2.47185i	−0.0453341	−	0.0785209i	−0.887802	+	0.460225i	$0.847769\pi$
$992$	−16.1721	−	28.0109i	−0.513465	−	0.889348i
$993$	22.4700	+	2.47844i	0.713063	+	0.0786509i
$994$	−0.320280	+	0.0167746i	−0.0101587	+	0.000532058i
$995$	−0.779269	+	0.449911i	−0.0247045	+	0.0142631i
$996$	14.2850	+	1.57564i	0.452639	+	0.0499261i
$997$		−	8.15563i		−	0.258291i	−0.991626	−	0.129146i	$-0.958777\pi$
$997$		−	8.15563i		−	0.258291i	0.991626	−	0.129146i	$-0.0412235\pi$
$998$	49.6220	−	28.6493i	1.57076	−	0.906877i
$999$	5.62458	−	4.90960i	0.177954	−	0.155333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.13	yes	32
3.2	odd	2		945.2.be.c.656.4		32
7.3	odd	6		315.2.t.c.101.13	✓	32
9.4	even	3		945.2.t.c.341.13		32
9.5	odd	6		315.2.t.c.131.4	yes	32
21.17	even	6		945.2.t.c.521.4		32
63.31	odd	6		945.2.be.c.206.4		32
63.59	even	6	inner	315.2.be.c.311.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.13	✓	32	7.3	odd	6
315.2.t.c.131.4	yes	32	9.5	odd	6
315.2.be.c.236.13	yes	32	1.1	even	1	trivial
315.2.be.c.311.13	yes	32	63.59	even	6	inner
945.2.t.c.341.13		32	9.4	even	3
945.2.t.c.521.4		32	21.17	even	6
945.2.be.c.206.4		32	63.31	odd	6
945.2.be.c.656.4		32	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48159 - 0.855399i) q^{2} +(1.02526 - 1.39601i) q^{3} +(0.463416 - 0.802660i) q^{4} -1.00000 q^{5} +(0.324870 - 2.94533i) q^{6} +(1.20122 - 2.35734i) q^{7} +1.83597i q^{8} +(-0.897694 - 2.86254i) q^{9} +O(q^{10})\)	\(q+(1.48159 - 0.855399i) q^{2} +(1.02526 - 1.39601i) q^{3} +(0.463416 - 0.802660i) q^{4} -1.00000 q^{5} +(0.324870 - 2.94533i) q^{6} +(1.20122 - 2.35734i) q^{7} +1.83597i q^{8} +(-0.897694 - 2.86254i) q^{9} +(-1.48159 + 0.855399i) q^{10} -0.574148i q^{11} +(-0.645401 - 1.46987i) q^{12} +(0.130417 - 0.0752961i) q^{13} +(-0.236742 - 4.52015i) q^{14} +(-1.02526 + 1.39601i) q^{15} +(2.49732 + 4.32549i) q^{16} +(0.586913 + 1.01656i) q^{17} +(-3.77864 - 3.47324i) q^{18} +(0.00148739 + 0.000858744i) q^{19} +(-0.463416 + 0.802660i) q^{20} +(-2.05931 - 4.09380i) q^{21} +(-0.491126 - 0.850655i) q^{22} +7.46725i q^{23} +(2.56304 + 1.88235i) q^{24} +1.00000 q^{25} +(0.128816 - 0.223117i) q^{26} +(-4.91651 - 1.68165i) q^{27} +(-1.33548 - 2.05660i) q^{28} +(5.81941 + 3.35984i) q^{29} +(-0.324870 + 2.94533i) q^{30} +(-5.74833 - 3.31880i) q^{31} +(4.22004 + 2.43644i) q^{32} +(-0.801517 - 0.588650i) q^{33} +(1.73914 + 1.00409i) q^{34} +(-1.20122 + 2.35734i) q^{35} +(-2.71365 - 0.606004i) q^{36} +(-0.718409 + 1.24432i) q^{37} +0.00293828 q^{38} +(0.0285965 - 0.259261i) q^{39} -1.83597i q^{40} +(5.37138 + 9.30350i) q^{41} +(-6.55290 - 4.30383i) q^{42} +(-3.00541 + 5.20553i) q^{43} +(-0.460846 - 0.266069i) q^{44} +(0.897694 + 2.86254i) q^{45} +(6.38748 + 11.0634i) q^{46} +(-4.22215 - 7.31298i) q^{47} +(8.59883 + 0.948451i) q^{48} +(-4.11412 - 5.66339i) q^{49} +(1.48159 - 0.855399i) q^{50} +(2.02087 + 0.222902i) q^{51} -0.139574i q^{52} +(-9.60845 + 5.54744i) q^{53} +(-8.72276 + 1.71405i) q^{54} +0.574148i q^{55} +(4.32802 + 2.20542i) q^{56} +(0.00272377 - 0.00119598i) q^{57} +11.4960 q^{58} +(5.13465 - 8.89348i) q^{59} +(0.645401 + 1.46987i) q^{60} +(6.36845 - 3.67682i) q^{61} -11.3556 q^{62} +(-7.82632 - 1.32238i) q^{63} -1.65277 q^{64} +(-0.130417 + 0.0752961i) q^{65} +(-1.69105 - 0.186523i) q^{66} +(4.10141 - 7.10384i) q^{67} +1.08794 q^{68} +(10.4244 + 7.65586i) q^{69} +(0.236742 + 4.52015i) q^{70} -0.0708560i q^{71} +(5.25555 - 1.64814i) q^{72} +(10.2405 - 5.91235i) q^{73} +2.45811i q^{74} +(1.02526 - 1.39601i) q^{75} +(0.00137856 - 0.000795911i) q^{76} +(-1.35346 - 0.689680i) q^{77} +(-0.179403 - 0.408581i) q^{78} +(-1.65540 - 2.86723i) q^{79} +(-2.49732 - 4.32549i) q^{80} +(-7.38829 + 5.13937i) q^{81} +(15.9164 + 9.18935i) q^{82} +(-4.47627 + 7.75313i) q^{83} +(-4.24025 - 0.244206i) q^{84} +(-0.586913 - 1.01656i) q^{85} +10.2833i q^{86} +(10.6568 - 4.67926i) q^{87} +1.05412 q^{88} +(-0.699730 + 1.21197i) q^{89} +(3.77864 + 3.47324i) q^{90} +(-0.0208391 - 0.397884i) q^{91} +(5.99366 + 3.46044i) q^{92} +(-10.5266 + 4.62211i) q^{93} +(-12.5110 - 7.22325i) q^{94} +(-0.00148739 - 0.000858744i) q^{95} +(7.72793 - 3.39324i) q^{96} +(-14.9143 - 8.61076i) q^{97} +(-10.9399 - 4.87163i) q^{98} +(-1.64352 + 0.515409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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