LMFDB - Embedded newform 310.2.k.a.129.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(129,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("310.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.k (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:	$2.47536246266$
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			129.16
Character	$\chi$	$=$	310.129
Dual form			310.2.k.a.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(-2.05774 + 0.875053i) q^{5} +(-1.34467 + 2.32904i) q^{6} +(2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 + 3.66553i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(-2.05774 + 0.875053i) q^{5} +(-1.34467 + 2.32904i) q^{6} +(2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 + 3.66553i) q^{9} +(-0.875053 - 2.05774i) q^{10} +(-1.25570 - 2.17494i) q^{11} +(-2.32904 - 1.34467i) q^{12} +(0.925785 - 0.534502i) q^{13} +(-1.66997 + 2.89246i) q^{14} +(-5.96922 - 0.728949i) q^{15} +1.00000 q^{16} +(-0.979392 - 0.565452i) q^{17} +(-3.66553 + 2.11630i) q^{18} +(-3.42647 + 5.93482i) q^{19} +(2.05774 - 0.875053i) q^{20} +(4.49112 + 7.77885i) q^{21} +(2.17494 - 1.25570i) q^{22} -4.55942i q^{23} +(1.34467 - 2.32904i) q^{24} +(3.46856 - 3.60126i) q^{25} +(0.534502 + 0.925785i) q^{26} +3.31488i q^{27} +(-2.89246 - 1.66997i) q^{28} +2.14564 q^{29} +(0.728949 - 5.96922i) q^{30} +(0.527107 - 5.54276i) q^{31} +1.00000i q^{32} -6.75404i q^{33} +(0.565452 - 0.979392i) q^{34} +(-7.41324 - 0.905290i) q^{35} +(-2.11630 - 3.66553i) q^{36} +(9.97382 + 5.75839i) q^{37} +(-5.93482 - 3.42647i) q^{38} +2.87493 q^{39} +(0.875053 + 2.05774i) q^{40} +(-3.61032 - 6.25326i) q^{41} +(-7.77885 + 4.49112i) q^{42} +(0.400075 + 0.230984i) q^{43} +(1.25570 + 2.17494i) q^{44} +(-7.56232 - 5.69083i) q^{45} +4.55942 q^{46} +6.54587i q^{47} +(2.32904 + 1.34467i) q^{48} +(2.07757 + 3.59845i) q^{49} +(3.60126 + 3.46856i) q^{50} +(-1.52070 - 2.63393i) q^{51} +(-0.925785 + 0.534502i) q^{52} +(8.42860 - 4.86625i) q^{53} -3.31488 q^{54} +(4.48709 + 3.37665i) q^{55} +(1.66997 - 2.89246i) q^{56} +(-15.9608 + 9.21497i) q^{57} +2.14564i q^{58} +(4.93480 - 8.54733i) q^{59} +(5.96922 + 0.728949i) q^{60} -1.86761 q^{61} +(5.54276 + 0.527107i) q^{62} +14.1366i q^{63} -1.00000 q^{64} +(-1.43731 + 1.90998i) q^{65} +6.75404 q^{66} +(-13.8308 + 7.98521i) q^{67} +(0.979392 + 0.565452i) q^{68} +(6.13094 - 10.6191i) q^{69} +(0.905290 - 7.41324i) q^{70} +(1.50751 + 2.61109i) q^{71} +(3.66553 - 2.11630i) q^{72} +(-3.62147 + 2.09086i) q^{73} +(-5.75839 + 9.97382i) q^{74} +(12.9210 - 3.72340i) q^{75} +(3.42647 - 5.93482i) q^{76} -8.38791i q^{77} +2.87493i q^{78} +(2.71853 - 4.70863i) q^{79} +(-2.05774 + 0.875053i) q^{80} +(1.89146 - 3.27611i) q^{81} +(6.25326 - 3.61032i) q^{82} +(11.7770 - 6.79944i) q^{83} +(-4.49112 - 7.77885i) q^{84} +(2.51013 + 0.306532i) q^{85} +(-0.230984 + 0.400075i) q^{86} +(4.99729 + 2.88519i) q^{87} +(-2.17494 + 1.25570i) q^{88} -13.9990 q^{89} +(5.69083 - 7.56232i) q^{90} +3.57040 q^{91} +4.55942i q^{92} +(8.68086 - 12.2005i) q^{93} -6.54587 q^{94} +(1.85749 - 15.2106i) q^{95} +(-1.34467 + 2.32904i) q^{96} -10.0509i q^{97} +(-3.59845 + 2.07757i) q^{98} +(5.31487 - 9.20563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9	$ 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} + 8 q^{15} + 32 q^{16} - 8 q^{19} + 2 q^{20} + 16 q^{21} - 4 q^{24} + 22 q^{25} + 12 q^{26} - 8 q^{29} + 28 q^{30} + 12 q^{31} - 12 q^{34} - 32 q^{35} - 8 q^{36} - 64 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{44} - 24 q^{45} - 8 q^{46} + 20 q^{49} - 40 q^{51} + 8 q^{54} - 8 q^{55} + 16 q^{59} - 8 q^{60} - 40 q^{61} - 32 q^{64} - 6 q^{65} - 24 q^{66} + 36 q^{69} + 36 q^{70} + 48 q^{71} - 28 q^{74} + 8 q^{75} + 8 q^{76} + 4 q^{79} - 2 q^{80} - 32 q^{81} - 16 q^{84} - 84 q^{85} + 12 q^{86} + 72 q^{89} + 40 q^{90} + 24 q^{91} + 16 q^{94} - 48 q^{95} + 4 q^{96} + 64 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 + 8 * q^15 + 32 * q^16 - 8 * q^19 + 2 * q^20 + 16 * q^21 - 4 * q^24 + 22 * q^25 + 12 * q^26 - 8 * q^29 + 28 * q^30 + 12 * q^31 - 12 * q^34 - 32 * q^35 - 8 * q^36 - 64 * q^39 + 4 * q^40 - 16 * q^41 - 4 * q^44 - 24 * q^45 - 8 * q^46 + 20 * q^49 - 40 * q^51 + 8 * q^54 - 8 * q^55 + 16 * q^59 - 8 * q^60 - 40 * q^61 - 32 * q^64 - 6 * q^65 - 24 * q^66 + 36 * q^69 + 36 * q^70 + 48 * q^71 - 28 * q^74 + 8 * q^75 + 8 * q^76 + 4 * q^79 - 2 * q^80 - 32 * q^81 - 16 * q^84 - 84 * q^85 + 12 * q^86 + 72 * q^89 + 40 * q^90 + 24 * q^91 + 16 * q^94 - 48 * q^95 + 4 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	2.32904	+	1.34467i	1.34467	+	0.776348i	0.987489	−	0.157686i	$-0.0504033\pi$
$3$	2.32904	+	1.34467i	1.34467	+	0.776348i	0.357185	+	0.934034i	$0.383737\pi$
$4$	−1.00000			−0.500000
$5$	−2.05774	+	0.875053i	−0.920248	+	0.391336i
$5$	−2.05774	+	0.875053i	−0.920248	+	0.391336i
$6$	−1.34467	+	2.32904i	−0.548961	+	0.950828i
$7$	2.89246	+	1.66997i	1.09325	+	0.631188i	0.934440	−	0.356122i	$-0.115901\pi$
$7$	2.89246	+	1.66997i	1.09325	+	0.631188i	0.158809	+	0.987309i	$0.449234\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.11630	+	3.66553i	0.705432	+	1.22184i
$10$	−0.875053	−	2.05774i	−0.276716	−	0.650714i
$11$	−1.25570	−	2.17494i	−0.378608	−	0.655769i	0.612252	−	0.790663i	$-0.290264\pi$
$11$	−1.25570	−	2.17494i	−0.378608	−	0.655769i	−0.990860	+	0.134894i	$0.956931\pi$
$12$	−2.32904	−	1.34467i	−0.672337	−	0.388174i
$13$	0.925785	−	0.534502i	0.256767	−	0.148244i	−0.366092	−	0.930579i	$-0.619304\pi$
$13$	0.925785	−	0.534502i	0.256767	−	0.148244i	0.622859	+	0.782334i	$0.285971\pi$
$14$	−1.66997	+	2.89246i	−0.446317	+	0.773044i
$15$	−5.96922	−	0.728949i	−1.54125	−	0.188214i
$16$	1.00000			0.250000
$17$	−0.979392	−	0.565452i	−0.237537	−	0.137142i	0.376507	−	0.926414i	$-0.377125\pi$
$17$	−0.979392	−	0.565452i	−0.237537	−	0.137142i	−0.614044	+	0.789271i	$0.710458\pi$
$18$	−3.66553	+	2.11630i	−0.863975	+	0.498816i
$19$	−3.42647	+	5.93482i	−0.786086	+	1.36154i	0.142262	+	0.989829i	$0.454562\pi$
$19$	−3.42647	+	5.93482i	−0.786086	+	1.36154i	−0.928348	+	0.371712i	$0.878771\pi$
$20$	2.05774	−	0.875053i	0.460124	−	0.195668i
$21$	4.49112	+	7.77885i	0.980042	+	1.69748i
$22$	2.17494	−	1.25570i	0.463698	−	0.267716i
$23$		−	4.55942i		−	0.950705i	−0.879795	−	0.475353i	$-0.842321\pi$
$23$		−	4.55942i		−	0.950705i	0.879795	−	0.475353i	$-0.157679\pi$
$24$	1.34467	−	2.32904i	0.274480	−	0.475414i
$25$	3.46856	−	3.60126i	0.693713	−	0.720252i
$26$	0.534502	+	0.925785i	0.104825	+	0.181561i
$27$			3.31488i			0.637948i
$28$	−2.89246	−	1.66997i	−0.546624	−	0.315594i
$29$	2.14564			0.398436			0.199218	−	0.979955i	$-0.436160\pi$
$29$	2.14564			0.398436			0.199218	+	0.979955i	$0.436160\pi$
$30$	0.728949	−	5.96922i	0.133087	−	1.08983i
$31$	0.527107	−	5.54276i	0.0946712	−	0.995509i
$31$	0.527107	−	5.54276i	0.0946712	−	0.995509i
$32$			1.00000i			0.176777i
$33$		−	6.75404i		−	1.17573i
$34$	0.565452	−	0.979392i	0.0969743	−	0.167964i
$35$	−7.41324	−	0.905290i	−1.25307	−	0.153022i
$36$	−2.11630	−	3.66553i	−0.352716	−	0.610922i
$37$	9.97382	+	5.75839i	1.63969	+	0.946673i	0.980941	+	0.194306i	$0.0622456\pi$
$37$	9.97382	+	5.75839i	1.63969	+	0.946673i	0.658745	+	0.752367i	$0.271088\pi$
$38$	−5.93482	−	3.42647i	−0.962755	−	0.555847i
$39$	2.87493			0.460357
$40$	0.875053	+	2.05774i	0.138358	+	0.325357i
$41$	−3.61032	−	6.25326i	−0.563838	−	0.976595i	−0.997157	−	0.0753549i	$-0.975991\pi$
$41$	−3.61032	−	6.25326i	−0.563838	−	0.976595i	0.433319	−	0.901241i	$-0.357342\pi$
$42$	−7.77885	+	4.49112i	−1.20030	+	0.692995i
$43$	0.400075	+	0.230984i	0.0610109	+	0.0352247i	0.530195	−	0.847876i	$-0.322119\pi$
$43$	0.400075	+	0.230984i	0.0610109	+	0.0352247i	−0.469184	+	0.883100i	$0.655452\pi$
$44$	1.25570	+	2.17494i	0.189304	+	0.327884i
$45$	−7.56232	−	5.69083i	−1.12732	−	0.848340i
$46$	4.55942			0.672250
$47$			6.54587i			0.954813i	0.878683	+	0.477406i	$0.158423\pi$
$47$			6.54587i			0.954813i	−0.878683	+	0.477406i	$0.841577\pi$
$48$	2.32904	+	1.34467i	0.336169	+	0.194087i
$49$	2.07757	+	3.59845i	0.296796	+	0.514065i
$50$	3.60126	+	3.46856i	0.509295	+	0.490529i
$51$	−1.52070	−	2.63393i	−0.212940	−	0.368823i
$52$	−0.925785	+	0.534502i	−0.128383	+	0.0741222i
$53$	8.42860	−	4.86625i	1.15776	−	0.668431i	0.206992	−	0.978343i	$-0.433633\pi$
$53$	8.42860	−	4.86625i	1.15776	−	0.668431i	0.950765	+	0.309911i	$0.100299\pi$
$54$	−3.31488			−0.451098
$55$	4.48709	+	3.37665i	0.605039	+	0.455307i
$56$	1.66997	−	2.89246i	0.223159	−	0.386522i
$57$	−15.9608	+	9.21497i	−2.11406	+	1.22055i
$58$			2.14564i			0.281737i
$59$	4.93480	−	8.54733i	0.642457	−	1.11277i	−0.342426	−	0.939545i	$-0.611249\pi$
$59$	4.93480	−	8.54733i	0.642457	−	1.11277i	0.984883	−	0.173223i	$-0.0554180\pi$
$60$	5.96922	+	0.728949i	0.770623	+	0.0941070i
$61$	−1.86761			−0.239123			−0.119562	−	0.992827i	$-0.538149\pi$
$61$	−1.86761			−0.239123			−0.119562	+	0.992827i	$0.538149\pi$
$62$	5.54276	+	0.527107i	0.703931	+	0.0669426i
$63$			14.1366i			1.78104i
$64$	−1.00000			−0.125000
$65$	−1.43731	+	1.90998i	−0.178276	+	0.236903i
$66$	6.75404			0.831364
$67$	−13.8308	+	7.98521i	−1.68970	+	0.975549i	−0.734958	+	0.678113i	$0.762798\pi$
$67$	−13.8308	+	7.98521i	−1.68970	+	0.975549i	−0.954742	+	0.297436i	$0.903869\pi$
$68$	0.979392	+	0.565452i	0.118769	+	0.0685712i
$69$	6.13094	−	10.6191i	0.738078	−	1.27839i
$70$	0.905290	−	7.41324i	0.108203	−	0.886052i
$71$	1.50751	+	2.61109i	0.178909	+	0.309879i	0.941507	−	0.336993i	$-0.109410\pi$
$71$	1.50751	+	2.61109i	0.178909	+	0.309879i	−0.762598	+	0.646872i	$0.776077\pi$
$72$	3.66553	−	2.11630i	0.431987	−	0.249408i
$73$	−3.62147	+	2.09086i	−0.423861	+	0.244716i	−0.696728	−	0.717336i	$-0.745361\pi$
$73$	−3.62147	+	2.09086i	−0.423861	+	0.244716i	0.272867	+	0.962052i	$0.412028\pi$
$74$	−5.75839	+	9.97382i	−0.669399	+	1.15943i
$75$	12.9210	−	3.72340i	1.49198	−	0.429941i
$76$	3.42647	−	5.93482i	0.393043	−	0.680770i
$77$		−	8.38791i		−	0.955891i
$78$			2.87493i			0.325521i
$79$	2.71853	−	4.70863i	0.305859	−	0.529763i	−0.671594	−	0.740920i	$-0.734390\pi$
$79$	2.71853	−	4.70863i	0.305859	−	0.529763i	0.977452	+	0.211157i	$0.0677232\pi$
$80$	−2.05774	+	0.875053i	−0.230062	+	0.0978339i
$81$	1.89146	−	3.27611i	0.210163	−	0.364012i
$82$	6.25326	−	3.61032i	0.690557	−	0.398693i
$83$	11.7770	−	6.79944i	1.29269	−	0.746336i	0.313561	−	0.949568i	$-0.398478\pi$
$83$	11.7770	−	6.79944i	1.29269	−	0.746336i	0.979130	+	0.203233i	$0.0651447\pi$
$84$	−4.49112	−	7.77885i	−0.490021	−	0.848742i
$85$	2.51013	+	0.306532i	0.272262	+	0.0332481i
$86$	−0.230984	+	0.400075i	−0.0249076	+	0.0431412i
$87$	4.99729	+	2.88519i	0.535766	+	0.309325i
$88$	−2.17494	+	1.25570i	−0.231849	+	0.133858i
$89$	−13.9990			−1.48389			−0.741947	−	0.670459i	$-0.766097\pi$
$89$	−13.9990			−1.48389			−0.741947	+	0.670459i	$0.766097\pi$
$90$	5.69083	−	7.56232i	0.599867	−	0.797139i
$91$	3.57040			0.374280
$92$			4.55942i			0.475353i
$93$	8.68086	−	12.2005i	0.900163	−	1.26514i
$94$	−6.54587			−0.675155
$95$	1.85749	−	15.2106i	0.190575	−	1.56058i
$96$	−1.34467	+	2.32904i	−0.137240	+	0.237707i
$97$		−	10.0509i		−	1.02052i	−0.860021	−	0.510259i	$-0.829550\pi$
$97$		−	10.0509i		−	1.02052i	0.860021	−	0.510259i	$-0.170450\pi$
$98$	−3.59845	+	2.07757i	−0.363499	+	0.209866i
$99$	5.31487	−	9.20563i	0.534165	−	0.925201i
$100$	−3.46856	+	3.60126i	−0.346856	+	0.360126i
$101$	−14.8784			−1.48045			−0.740227	−	0.672357i	$-0.765282\pi$
$101$	−14.8784			−1.48045			−0.740227	+	0.672357i	$0.765282\pi$
$102$	2.63393	−	1.52070i	0.260798	−	0.150572i
$103$	−3.70015	+	2.13628i	−0.364587	+	0.210494i	−0.671091	−	0.741375i	$-0.734174\pi$
$103$	−3.70015	+	2.13628i	−0.364587	+	0.210494i	0.306504	+	0.951869i	$0.400841\pi$
$104$	−0.534502	−	0.925785i	−0.0524123	−	0.0907807i
$105$	−16.0484	−	12.0769i	−1.56617	−	1.17858i
$106$	4.86625	+	8.42860i	0.472652	+	0.818658i
$107$	8.51540	+	4.91637i	0.823215	+	0.475283i	0.851524	−	0.524316i	$-0.175679\pi$
$107$	8.51540	+	4.91637i	0.823215	+	0.475283i	−0.0283088	+	0.999599i	$0.509012\pi$
$108$		−	3.31488i		−	0.318974i
$109$	12.2368			1.17207			0.586037	−	0.810284i	$-0.300687\pi$
$109$	12.2368			1.17207			0.586037	+	0.810284i	$0.300687\pi$
$110$	−3.37665	+	4.48709i	−0.321951	+	0.427827i
$111$	15.4863	+	26.8231i	1.46990	+	2.54593i
$112$	2.89246	+	1.66997i	0.273312	+	0.157797i
$113$	−11.9249	+	6.88486i	−1.12180	+	0.647673i	−0.941860	−	0.336004i	$-0.890924\pi$
$113$	−11.9249	+	6.88486i	−1.12180	+	0.647673i	−0.179942	+	0.983677i	$0.557591\pi$
$114$	−9.21497	−	15.9608i	−0.863061	−	1.49487i
$115$	3.98974	+	9.38209i	0.372045	+	0.874885i
$116$	−2.14564			−0.199218
$117$	3.91847	+	2.26233i	0.362263	+	0.209153i
$118$	8.54733	+	4.93480i	0.786845	+	0.454285i
$119$	−1.88857	−	3.27110i	−0.173125	−	0.299861i
$120$	−0.728949	+	5.96922i	−0.0665437	+	0.544913i
$121$	2.34643	−	4.06414i	0.213312	−	0.369467i
$122$		−	1.86761i		−	0.169086i
$123$		−	19.4188i		−	1.75094i
$124$	−0.527107	+	5.54276i	−0.0473356	+	0.497754i
$125$	−3.98610	+	10.4456i	−0.356528	+	0.934285i
$126$	−14.1366			−1.25939
$127$	−1.09323	−	0.631179i	−0.0970088	−	0.0560081i	0.450711	−	0.892670i	$-0.351171\pi$
$127$	−1.09323	−	0.631179i	−0.0970088	−	0.0560081i	−0.547720	+	0.836662i	$0.684504\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.621195	+	1.07594i	0.0546932	+	0.0947314i
$130$	−1.90998	−	1.43731i	−0.167516	−	0.126060i
$131$	−2.00041	+	3.46482i	−0.174777	+	0.302723i	−0.940084	−	0.340943i	$-0.889254\pi$
$131$	−2.00041	+	3.46482i	−0.174777	+	0.302723i	0.765307	+	0.643665i	$0.222587\pi$
$132$			6.75404i			0.587863i
$133$	−19.8219	+	11.4442i	−1.71878	+	0.992335i
$134$	−7.98521	−	13.8308i	−0.689817	−	1.19480i
$135$	−2.90069	−	6.82115i	−0.249652	−	0.587071i
$136$	−0.565452	+	0.979392i	−0.0484871	+	0.0839822i
$137$	−9.42943	+	5.44408i	−0.805611	+	0.465119i	−0.845429	−	0.534087i	$-0.820655\pi$
$137$	−9.42943	+	5.44408i	−0.805611	+	0.465119i	0.0398187	+	0.999207i	$0.487322\pi$
$138$	10.6191	+	6.13094i	0.903957	+	0.521900i
$139$	−10.7590			−0.912569			−0.456285	−	0.889834i	$-0.650820\pi$
$139$	−10.7590			−0.912569			−0.456285	+	0.889834i	$0.650820\pi$
$140$	7.41324	+	0.905290i	0.626533	+	0.0765110i
$141$	−8.80206	+	15.2456i	−0.741267	+	1.28391i
$142$	−2.61109	+	1.50751i	−0.219118	+	0.126508i
$143$	−2.32502	−	1.34235i	−0.194428	−	0.112253i
$144$	2.11630	+	3.66553i	0.176358	+	0.305461i
$145$	−4.41517	+	1.87755i	−0.366660	+	0.155922i
$146$	−2.09086	−	3.62147i	−0.173040	−	0.299715i
$147$			11.1746i			0.921666i
$148$	−9.97382	−	5.75839i	−0.819843	−	0.473336i
$149$	−5.86843	+	10.1644i	−0.480761	+	0.832702i	−0.999756	−	0.0220752i	$-0.992973\pi$
$149$	−5.86843	+	10.1644i	−0.480761	+	0.832702i	0.518996	+	0.854777i	$0.326306\pi$
$150$	3.72340	+	12.9210i	0.304014	+	1.05499i
$151$	5.08955			0.414182			0.207091	−	0.978322i	$-0.433600\pi$
$151$	5.08955			0.414182			0.207091	+	0.978322i	$0.433600\pi$
$152$	5.93482	+	3.42647i	0.481377	+	0.277923i
$153$		−	4.78666i		−	0.386979i
$154$	8.38791			0.675917
$155$	3.76556	+	11.8668i	0.302457	+	0.953163i
$156$	−2.87493			−0.230178
$157$		−	5.04463i		−	0.402605i	−0.979529	−	0.201303i	$-0.935483\pi$
$157$		−	5.04463i		−	0.402605i	0.979529	−	0.201303i	$-0.0645175\pi$
$158$	4.70863	+	2.71853i	0.374599	+	0.216275i
$159$	26.1741			2.07574
$160$	−0.875053	−	2.05774i	−0.0691790	−	0.162678i
$161$	7.61408	−	13.1880i	0.600073	−	1.03936i
$162$	3.27611	+	1.89146i	0.257395	+	0.148607i
$163$			12.4987i			0.978972i	0.872011	+	0.489486i	$0.162816\pi$
$163$			12.4987i			0.978972i	−0.872011	+	0.489486i	$0.837184\pi$
$164$	3.61032	+	6.25326i	0.281919	+	0.488298i
$165$	5.91014	+	13.8980i	0.460104	+	1.08196i
$166$	6.79944	+	11.7770i	0.527739	+	0.914071i
$167$	−15.4460	−	8.91775i	−1.19525	−	0.690076i	−0.235755	−	0.971812i	$-0.575756\pi$
$167$	−15.4460	−	8.91775i	−1.19525	−	0.690076i	−0.959492	+	0.281736i	$0.909090\pi$
$168$	7.77885	−	4.49112i	0.600151	−	0.346497i
$169$	−5.92861	+	10.2687i	−0.456047	+	0.789897i
$170$	−0.306532	+	2.51013i	−0.0235100	+	0.192518i
$171$	−29.0057			−2.21812
$172$	−0.400075	−	0.230984i	−0.0305055	−	0.0176123i
$173$	−7.01810	+	4.05190i	−0.533576	+	0.308060i	−0.742472	−	0.669878i	$-0.766347\pi$
$173$	−7.01810	+	4.05190i	−0.533576	+	0.308060i	0.208895	+	0.977938i	$0.433013\pi$
$174$	−2.88519	+	4.99729i	−0.218726	+	0.378844i
$175$	16.0467	−	4.62413i	1.21301	−	0.349551i
$176$	−1.25570	−	2.17494i	−0.0946520	−	0.163942i
$177$	22.9867	−	13.2714i	1.72779	−	0.997540i
$178$		−	13.9990i		−	1.04927i
$179$	−9.47460	+	16.4105i	−0.708165	+	1.22658i	0.257373	+	0.966312i	$0.417143\pi$
$179$	−9.47460	+	16.4105i	−0.708165	+	1.22658i	−0.965537	+	0.260265i	$0.916190\pi$
$180$	7.56232	+	5.69083i	0.563662	+	0.424170i
$181$	−6.25755	−	10.8384i	−0.465120	−	0.805612i	0.534087	−	0.845430i	$-0.320656\pi$
$181$	−6.25755	−	10.8384i	−0.465120	−	0.805612i	−0.999207	+	0.0398180i	$0.987322\pi$
$182$			3.57040i			0.264656i
$183$	−4.34975	−	2.51133i	−0.321543	−	0.185643i
$184$	−4.55942			−0.336125
$185$	−25.5624	−	3.12163i	−1.87938	−	0.229507i
$186$	12.2005	+	8.68086i	0.894587	+	0.636511i
$187$			2.84016i			0.207693i
$188$		−	6.54587i		−	0.477406i
$189$	−5.53573	+	9.58817i	−0.402665	+	0.697436i
$190$	15.2106	+	1.85749i	1.10350	+	0.134757i
$191$	−0.719583	−	1.24636i	−0.0520672	−	0.0901831i	0.838817	−	0.544413i	$-0.183248\pi$
$191$	−0.719583	−	1.24636i	−0.0520672	−	0.0901831i	−0.890884	+	0.454230i	$0.849914\pi$
$192$	−2.32904	−	1.34467i	−0.168084	−	0.0970435i
$193$	−15.8380	−	9.14408i	−1.14005	−	0.658205i	−0.193603	−	0.981080i	$-0.562018\pi$
$193$	−15.8380	−	9.14408i	−1.14005	−	0.658205i	−0.946442	+	0.322874i	$0.895351\pi$
$194$	10.0509			0.721615
$195$	−5.91584	+	2.51571i	−0.423642	+	0.180154i
$196$	−2.07757	−	3.59845i	−0.148398	−	0.257032i
$197$	−2.76140	+	1.59430i	−0.196742	+	0.113589i	−0.595135	−	0.803626i	$-0.702901\pi$
$197$	−2.76140	+	1.59430i	−0.196742	+	0.113589i	0.398393	+	0.917215i	$0.369568\pi$
$198$	9.20563	+	5.31487i	0.654216	+	0.377712i
$199$	−7.53070	−	13.0436i	−0.533837	−	0.924633i	−0.999219	−	0.0395230i	$-0.987416\pi$
$199$	−7.53070	−	13.0436i	−0.533837	−	0.924633i	0.465381	−	0.885110i	$-0.345917\pi$
$200$	−3.60126	−	3.46856i	−0.254647	−	0.245265i
$201$	−42.9500			−3.02946
$202$		−	14.8784i		−	1.04684i
$203$	6.20619	+	3.58315i	0.435589	+	0.251488i
$204$	1.52070	+	2.63393i	0.106470	+	0.184412i
$205$	12.9010	+	9.70835i	0.901047	+	0.678060i
$206$	−2.13628	−	3.70015i	−0.148842	−	0.257802i
$207$	16.7127	−	9.64909i	1.16161	−	0.670658i
$208$	0.925785	−	0.534502i	0.0641917	−	0.0370611i
$209$	17.2105			1.19047
$210$	12.0769	−	16.0484i	0.833382	−	1.10745i
$211$	9.05661	−	15.6865i	0.623483	−	1.07990i	−0.365350	−	0.930870i	$-0.619051\pi$
$211$	9.05661	−	15.6865i	0.623483	−	1.07990i	0.988832	−	0.149033i	$-0.0476161\pi$
$212$	−8.42860	+	4.86625i	−0.578879	+	0.334216i
$213$			8.10845i			0.555582i
$214$	−4.91637	+	8.51540i	−0.336076	+	0.582101i
$215$	−1.02537	−	0.125216i	−0.0699298	−	0.00853969i
$216$	3.31488			0.225549
$217$	10.7809	−	15.1520i	0.731852	−	1.02858i
$218$			12.2368i			0.828782i
$219$	−11.2461			−0.759940
$220$	−4.48709	−	3.37665i	−0.302519	−	0.227653i
$221$	−1.20894			−0.0813223
$222$	−26.8231	+	15.4863i	−1.80025	+	1.03937i
$223$	5.50332	+	3.17734i	0.368529	+	0.212770i	0.672816	−	0.739810i	$-0.265085\pi$
$223$	5.50332	+	3.17734i	0.368529	+	0.212770i	−0.304286	+	0.952581i	$0.598418\pi$
$224$	−1.66997	+	2.89246i	−0.111579	+	0.193261i
$225$	20.5411	+	5.09281i	1.36940	+	0.339521i
$226$	−6.88486	−	11.9249i	−0.457974	−	0.793234i
$227$	−20.3941	+	11.7745i	−1.35360	+	0.781503i	−0.988752	−	0.149562i	$-0.952214\pi$
$227$	−20.3941	+	11.7745i	−1.35360	+	0.781503i	−0.364851	+	0.931066i	$0.618880\pi$
$228$	15.9608	−	9.21497i	1.05703	−	0.610276i
$229$	11.2948	−	19.5632i	0.746384	−	1.29278i	−0.203161	−	0.979145i	$-0.565122\pi$
$229$	11.2948	−	19.5632i	0.746384	−	1.29278i	0.949545	−	0.313630i	$-0.101545\pi$
$230$	−9.38209	+	3.98974i	−0.618637	+	0.263075i
$231$	11.2790	−	19.5358i	0.742104	−	1.28536i
$232$		−	2.14564i		−	0.140868i
$233$		−	11.4137i		−	0.747735i	−0.927482	−	0.373867i	$-0.878032\pi$
$233$		−	11.4137i		−	0.747735i	0.927482	−	0.373867i	$-0.121968\pi$
$234$	−2.26233	+	3.91847i	−0.147893	+	0.256159i
$235$	−5.72798	−	13.4697i	−0.373652	−	0.878665i
$236$	−4.93480	+	8.54733i	−0.321228	+	0.556384i
$237$	12.6632	−	7.31108i	0.822560	−	0.474905i
$238$	3.27110	−	1.88857i	0.212034	−	0.122418i
$239$	7.99093	+	13.8407i	0.516890	+	0.895280i	0.999808	+	0.0196140i	$0.00624373\pi$
$239$	7.99093	+	13.8407i	0.516890	+	0.895280i	−0.482918	+	0.875666i	$0.660423\pi$
$240$	−5.96922	−	0.728949i	−0.385312	−	0.0470535i
$241$	−3.42853	+	5.93840i	−0.220851	+	0.382526i	−0.955067	−	0.296391i	$-0.904217\pi$
$241$	−3.42853	+	5.93840i	−0.220851	+	0.382526i	0.734215	+	0.678917i	$0.237550\pi$
$242$	4.06414	+	2.34643i	0.261253	+	0.150834i
$243$	17.4229	−	10.0591i	1.11768	−	0.645293i
$244$	1.86761			0.119562
$245$	−7.42393	−	5.58669i	−0.474297	−	0.356921i
$246$	19.4188			1.23810
$247$			7.32582i			0.466131i
$248$	−5.54276	−	0.527107i	−0.351965	−	0.0334713i
$249$	36.5721			2.31766
$250$	−10.4456	−	3.98610i	−0.660639	−	0.252103i
$251$	−0.519274	+	0.899409i	−0.0327763	+	0.0567702i	−0.881948	−	0.471346i	$-0.843768\pi$
$251$	−0.519274	+	0.899409i	−0.0327763	+	0.0567702i	0.849172	+	0.528116i	$0.177102\pi$
$252$		−	14.1366i		−	0.890520i
$253$	−9.91646	+	5.72527i	−0.623443	+	0.359945i
$254$	0.631179	−	1.09323i	0.0396037	−	0.0685956i
$255$	5.43402	+	4.08924i	0.340292	+	0.256078i
$256$	1.00000			0.0625000
$257$	9.99457	−	5.77037i	0.623444	−	0.359946i	−0.154765	−	0.987951i	$-0.549462\pi$
$257$	9.99457	−	5.77037i	0.623444	−	0.359946i	0.778209	+	0.628006i	$0.216129\pi$
$258$	−1.07594	+	0.621195i	−0.0669852	+	0.0386739i
$259$	19.2326	+	33.3119i	1.19506	+	2.06990i
$260$	1.43731	−	1.90998i	0.0891379	−	0.118452i
$261$	4.54082	+	7.86492i	0.281069	+	0.486827i
$262$	−3.46482	−	2.00041i	−0.214057	−	0.123586i
$263$			27.8728i			1.71871i	0.511377	+	0.859356i	$0.329136\pi$
$263$			27.8728i			1.71871i	−0.511377	+	0.859356i	$0.670864\pi$
$264$	−6.75404			−0.415682
$265$	−13.0856	+	17.3889i	−0.803843	+	1.06819i
$266$	−11.4442	−	19.8219i	−0.701687	−	1.21536i
$267$	−32.6043	−	18.8241i	−1.99535	−	1.15202i
$268$	13.8308	−	7.98521i	0.844850	−	0.487774i
$269$	−3.72020	−	6.44358i	−0.226825	−	0.392872i	0.730040	−	0.683404i	$-0.239501\pi$
$269$	−3.72020	−	6.44358i	−0.226825	−	0.392872i	−0.956865	+	0.290532i	$0.906168\pi$
$270$	6.82115	−	2.90069i	0.415122	−	0.176531i
$271$	12.3624			0.750962			0.375481	−	0.926830i	$-0.377478\pi$
$271$	12.3624			0.750962			0.375481	+	0.926830i	$0.377478\pi$
$272$	−0.979392	−	0.565452i	−0.0593844	−	0.0342856i
$273$	8.31562	+	4.80103i	0.503284	+	0.290571i
$274$	−5.44408	−	9.42943i	−0.328889	−	0.569653i
$275$	−12.1880	−	3.02181i	−0.734964	−	0.182222i
$276$	−6.13094	+	10.6191i	−0.369039	+	0.639194i
$277$			11.1581i			0.670423i	0.942143	+	0.335211i	$0.108808\pi$
$277$			11.1581i			0.670423i	−0.942143	+	0.335211i	$0.891192\pi$
$278$		−	10.7590i		−	0.645284i
$279$	21.4327	−	9.79800i	1.28314	−	0.586591i
$280$	−0.905290	+	7.41324i	−0.0541014	+	0.443026i
$281$	3.11884			0.186055			0.0930273	−	0.995664i	$-0.470346\pi$
$281$	3.11884			0.186055			0.0930273	+	0.995664i	$0.470346\pi$
$282$	−15.2456	−	8.80206i	−0.907863	−	0.524155i
$283$			22.2481i			1.32251i	0.750161	+	0.661255i	$0.229976\pi$
$283$			22.2481i			1.32251i	−0.750161	+	0.661255i	$0.770024\pi$
$284$	−1.50751	−	2.61109i	−0.0894544	−	0.154940i
$285$	24.7795	−	32.9285i	1.46781	−	1.95052i
$286$	1.34235	−	2.32502i	0.0793749	−	0.137481i
$287$		−	24.1165i		−	1.42355i
$288$	−3.66553	+	2.11630i	−0.215994	+	0.124704i
$289$	−7.86053	−	13.6148i	−0.462384	−	0.800873i
$290$	−1.87755	−	4.41517i	−0.110254	−	0.259268i
$291$	13.5152	−	23.4091i	0.792277	−	1.37226i
$292$	3.62147	−	2.09086i	0.211930	−	0.122358i
$293$	26.5745	+	15.3428i	1.55250	+	0.896335i	0.997938	+	0.0641905i	$0.0204465\pi$
$293$	26.5745	+	15.3428i	1.55250	+	0.896335i	0.554559	+	0.832144i	$0.312887\pi$
$294$	−11.1746			−0.651717
$295$	−2.67516	+	21.9064i	−0.155754	+	1.27544i
$296$	5.75839	−	9.97382i	0.334699	−	0.579716i
$297$	7.20965	−	4.16249i	0.418346	−	0.241532i
$298$	−10.1644	−	5.86843i	−0.588809	−	0.339949i
$299$	−2.43702	−	4.22105i	−0.140937	−	0.244109i
$300$	−12.9210	+	3.72340i	−0.745992	+	0.214971i
$301$	0.771469	+	1.33622i	0.0444667	+	0.0770187i
$302$			5.08955i			0.292871i
$303$	−34.6524	−	20.0066i	−1.99073	−	1.14935i
$304$	−3.42647	+	5.93482i	−0.196521	+	0.340385i
$305$	3.84305	−	1.63426i	0.220053	−	0.0935773i
$306$	4.78666			0.273635
$307$	11.7719	+	6.79649i	0.671855	+	0.387896i	0.796779	−	0.604270i	$-0.206535\pi$
$307$	11.7719	+	6.79649i	0.671855	+	0.387896i	−0.124924	+	0.992166i	$0.539869\pi$
$308$			8.38791i			0.477945i
$309$	−11.4904			−0.653667
$310$	−11.8668	+	3.76556i	−0.673988	+	0.213869i
$311$	8.28787			0.469962			0.234981	−	0.972000i	$-0.424497\pi$
$311$	8.28787			0.469962			0.234981	+	0.972000i	$0.424497\pi$
$312$		−	2.87493i		−	0.162761i
$313$	−8.61486	−	4.97379i	−0.486940	−	0.281135i	0.236364	−	0.971665i	$-0.424044\pi$
$313$	−8.61486	−	4.97379i	−0.486940	−	0.281135i	−0.723304	+	0.690529i	$0.757378\pi$
$314$	5.04463			0.284685
$315$	−12.3702	−	29.0894i	−0.696985	−	1.63900i
$316$	−2.71853	+	4.70863i	−0.152929	+	0.264881i
$317$	1.94235	+	1.12141i	0.109093	+	0.0629849i	0.553554	−	0.832813i	$-0.313271\pi$
$317$	1.94235	+	1.12141i	0.109093	+	0.0629849i	−0.444461	+	0.895798i	$0.646605\pi$
$318$			26.1741i			1.46777i
$319$	−2.69428	−	4.66664i	−0.150851	−	0.261282i
$320$	2.05774	−	0.875053i	0.115031	−	0.0489169i
$321$	13.2218	+	22.9009i	0.737971	+	1.27820i
$322$	13.1880	+	7.61408i	0.734937	+	0.424316i
$323$	6.71171	−	3.87501i	0.373450	−	0.215611i
$324$	−1.89146	+	3.27611i	−0.105081	+	0.182006i
$325$	1.28627	−	5.18795i	0.0713492	−	0.287776i
$326$	−12.4987			−0.692238
$327$	28.5001	+	16.4545i	1.57606	+	0.909938i
$328$	−6.25326	+	3.61032i	−0.345279	+	0.199347i
$329$	−10.9314	+	18.9337i	−0.602666	+	1.04385i
$330$	−13.8980	+	5.91014i	−0.765061	+	0.325342i
$331$	11.7477	+	20.3476i	0.645712	+	1.11841i	0.984137	+	0.177413i	$0.0567727\pi$
$331$	11.7477	+	20.3476i	0.645712	+	1.11841i	−0.338424	+	0.940994i	$0.609894\pi$
$332$	−11.7770	+	6.79944i	−0.646346	+	0.373168i
$333$			48.7458i			2.67126i
$334$	8.91775	−	15.4460i	0.487958	−	0.845167i
$335$	21.4726	−	28.5341i	1.17318	−	1.55899i
$336$	4.49112	+	7.77885i	0.245011	+	0.424371i
$337$		−	5.10345i		−	0.278003i	−0.990292	−	0.139001i	$-0.955611\pi$
$337$		−	5.10345i		−	0.278003i	0.990292	−	0.139001i	$-0.0443893\pi$
$338$	−10.2687	−	5.92861i	−0.558542	−	0.322474i
$339$	−37.0316			−2.01128
$340$	−2.51013	−	0.306532i	−0.136131	−	0.0166240i
$341$	−12.7170	+	5.81362i	−0.688666	+	0.314825i
$342$		−	29.0057i		−	1.56845i
$343$		−	9.50164i		−	0.513041i
$344$	0.230984	−	0.400075i	0.0124538	−	0.0215706i
$345$	−3.32359	+	27.2162i	−0.178936	+	1.46527i
$346$	−4.05190	−	7.01810i	−0.217832	−	0.377296i
$347$	−26.2194	−	15.1378i	−1.40753	−	0.812639i	−0.412382	−	0.911011i	$-0.635303\pi$
$347$	−26.2194	−	15.1378i	−1.40753	−	0.812639i	−0.995150	+	0.0983723i	$0.968636\pi$
$348$	−4.99729	−	2.88519i	−0.267883	−	0.154662i
$349$	11.9756			0.641038			0.320519	−	0.947242i	$-0.396143\pi$
$349$	11.9756			0.641038			0.320519	+	0.947242i	$0.396143\pi$
$350$	4.62413	+	16.0467i	0.247170	+	0.857731i
$351$	1.77181	+	3.06886i	0.0945722	+	0.163804i
$352$	2.17494	−	1.25570i	0.115925	−	0.0669291i
$353$	−14.7949	−	8.54181i	−0.787450	−	0.454635i	0.0516138	−	0.998667i	$-0.483564\pi$
$353$	−14.7949	−	8.54181i	−0.787450	−	0.454635i	−0.839064	+	0.544032i	$0.816897\pi$
$354$	13.2714	+	22.9867i	0.705367	+	1.22173i
$355$	−5.38691	−	4.05378i	−0.285907	−	0.215152i
$356$	13.9990			0.741947
$357$		−	10.1581i		−	0.537621i
$358$	−16.4105	−	9.47460i	−0.867321	−	0.500748i
$359$	14.7258	+	25.5058i	0.777198	+	1.34615i	0.933551	+	0.358446i	$0.116693\pi$
$359$	14.7258	+	25.5058i	0.777198	+	1.34615i	−0.156352	+	0.987701i	$0.549974\pi$
$360$	−5.69083	+	7.56232i	−0.299933	+	0.398569i
$361$	−13.9814	−	24.2165i	−0.735862	−	1.27455i
$362$	10.8384	−	6.25755i	0.569653	−	0.328890i
$363$	10.9299	−	6.31037i	0.573670	−	0.331208i
$364$	−3.57040			−0.187140
$365$	5.62242	−	7.47141i	0.294291	−	0.391071i
$366$	2.51133	−	4.34975i	0.131269	−	0.227365i
$367$	27.0994	−	15.6459i	1.41458	−	0.816707i	0.418763	−	0.908096i	$-0.362464\pi$
$367$	27.0994	−	15.6459i	1.41458	−	0.816707i	0.995815	+	0.0913882i	$0.0291304\pi$
$368$		−	4.55942i		−	0.237676i
$369$	15.2810	−	26.4675i	0.795499	−	1.37784i
$370$	3.12163	−	25.5624i	0.162286	−	1.32893i
$371$	32.5059			1.68762
$372$	−8.68086	+	12.2005i	−0.450082	+	0.632568i
$373$		−	19.9316i		−	1.03202i	−0.856583	−	0.516009i	$-0.827417\pi$
$373$		−	19.9316i		−	1.03202i	0.856583	−	0.516009i	$-0.172583\pi$
$374$	−2.84016			−0.146861
$375$	−23.3298	+	18.9683i	−1.20474	+	0.979519i
$376$	6.54587			0.337577
$377$	1.98640	−	1.14685i	0.102305	−	0.0590658i
$378$	−9.58817	−	5.53573i	−0.493162	−	0.284727i
$379$	7.41755	−	12.8476i	0.381014	−	0.659936i	−0.610193	−	0.792252i	$-0.708908\pi$
$379$	7.41755	−	12.8476i	0.381014	−	0.659936i	0.991207	+	0.132317i	$0.0422416\pi$
$380$	−1.85749	+	15.2106i	−0.0952874	+	0.780289i
$381$	−1.69746	−	2.94009i	−0.0869635	−	0.150625i
$382$	1.24636	−	0.719583i	0.0637691	−	0.0368171i
$383$	4.20151	−	2.42574i	0.214687	−	0.123950i	−0.388801	−	0.921322i	$-0.627111\pi$
$383$	4.20151	−	2.42574i	0.214687	−	0.123950i	0.603488	+	0.797372i	$0.293777\pi$
$384$	1.34467	−	2.32904i	0.0686201	−	0.118854i
$385$	7.33986	+	17.2601i	0.374074	+	0.879657i
$386$	9.14408	−	15.8380i	0.465422	−	0.806134i
$387$			1.95532i			0.0993945i
$388$			10.0509i			0.510259i
$389$	1.13556	−	1.96685i	0.0575752	−	0.0997232i	−0.835801	−	0.549032i	$-0.814996\pi$
$389$	1.13556	−	1.96685i	0.0575752	−	0.0997232i	0.893376	+	0.449309i	$0.148330\pi$
$390$	−2.51571	−	5.91584i	−0.127388	−	0.299560i
$391$	−2.57814	+	4.46546i	−0.130382	+	0.225828i
$392$	3.59845	−	2.07757i	0.181749	−	0.104933i
$393$	−9.31811	+	5.37981i	−0.470036	+	0.271376i
$394$	−1.59430	−	2.76140i	−0.0803194	−	0.139117i
$395$	−1.47372	+	12.0680i	−0.0741508	+	0.607206i
$396$	−5.31487	+	9.20563i	−0.267082	+	0.462600i
$397$	−8.18167	−	4.72369i	−0.410626	−	0.237075i	0.280432	−	0.959874i	$-0.409522\pi$
$397$	−8.18167	−	4.72369i	−0.410626	−	0.237075i	−0.691059	+	0.722799i	$0.742855\pi$
$398$	13.0436	−	7.53070i	0.653814	−	0.377480i
$399$	−61.5547			−3.08159
$400$	3.46856	−	3.60126i	0.173428	−	0.180063i
$401$	20.3650			1.01698			0.508490	−	0.861068i	$-0.330204\pi$
$401$	20.3650			1.01698			0.508490	+	0.861068i	$0.330204\pi$
$402$		−	42.9500i		−	2.14215i
$403$	−2.47463	−	5.41314i	−0.123270	−	0.269648i
$404$	14.8784			0.740227
$405$	−1.02536	+	8.39650i	−0.0509507	+	0.417226i
$406$	−3.58315	+	6.20619i	−0.177829	+	0.308008i
$407$		−	28.9232i		−	1.43367i
$408$	−2.63393	+	1.52070i	−0.130399	+	0.0752858i
$409$	6.41855	−	11.1173i	0.317377	−	0.549713i	−0.662563	−	0.749006i	$-0.730531\pi$
$409$	6.41855	−	11.1173i	0.317377	−	0.549713i	0.979940	+	0.199293i	$0.0638646\pi$
$410$	−9.70835	+	12.9010i	−0.479461	+	0.637136i
$411$	−29.2821			−1.44438
$412$	3.70015	−	2.13628i	0.182293	−	0.105247i
$413$	28.5475	−	16.4819i	1.40473	−	0.811021i
$414$	9.64909	+	16.7127i	0.474227	+	0.821385i
$415$	−18.2841	+	24.2969i	−0.897529	+	1.19269i
$416$	0.534502	+	0.925785i	0.0262061	+	0.0453904i
$417$	−25.0583	−	14.4674i	−1.22711	−	0.708471i
$418$			17.2105i			0.841792i
$419$	−16.9178			−0.826488			−0.413244	−	0.910620i	$-0.635604\pi$
$419$	−16.9178			−0.826488			−0.413244	+	0.910620i	$0.635604\pi$
$420$	16.0484	+	12.0769i	0.783084	+	0.589290i
$421$	4.96613	+	8.60160i	0.242035	+	0.419216i	0.961294	−	0.275526i	$-0.0888519\pi$
$421$	4.96613	+	8.60160i	0.242035	+	0.419216i	−0.719259	+	0.694742i	$0.755519\pi$
$422$	15.6865	+	9.05661i	0.763607	+	0.440869i
$423$	−23.9941	+	13.8530i	−1.16663	+	0.673556i
$424$	−4.86625	−	8.42860i	−0.236326	−	0.409329i
$425$	−5.43342	+	1.56574i	−0.263560	+	0.0759493i
$426$	−8.10845			−0.392856
$427$	−5.40200	−	3.11885i	−0.261421	−	0.150931i
$428$	−8.51540	−	4.91637i	−0.411608	−	0.237642i
$429$	−3.61005	−	6.25279i	−0.174295	−	0.301887i
$430$	0.125216	−	1.02537i	0.00603847	−	0.0494479i
$431$	0.257626	−	0.446222i	0.0124094	−	0.0214938i	−0.859754	−	0.510708i	$-0.829383\pi$
$431$	0.257626	−	0.446222i	0.0124094	−	0.0214938i	0.872163	+	0.489215i	$0.162717\pi$
$432$			3.31488i			0.159487i
$433$			37.7395i			1.81365i	0.421511	+	0.906823i	$0.361500\pi$
$433$			37.7395i			1.81365i	−0.421511	+	0.906823i	$0.638500\pi$
$434$	15.1520	+	10.7809i	0.727318	+	0.517497i
$435$	−12.8078	−	1.56406i	−0.614088	−	0.0749911i
$436$	−12.2368			−0.586037
$437$	27.0593	+	15.6227i	1.29442	+	0.747336i
$438$		−	11.2461i		−	0.537358i
$439$	−7.16777	−	12.4149i	−0.342099	−	0.592533i	0.642723	−	0.766098i	$-0.277804\pi$
$439$	−7.16777	−	12.4149i	−0.342099	−	0.592533i	−0.984822	+	0.173566i	$0.944471\pi$
$440$	3.37665	−	4.48709i	0.160975	−	0.213914i
$441$	−8.79351	+	15.2308i	−0.418738	+	0.725276i
$442$		−	1.20894i		−	0.0575035i
$443$	23.7485	−	13.7112i	1.12833	−	0.651440i	0.184813	−	0.982774i	$-0.440832\pi$
$443$	23.7485	−	13.7112i	1.12833	−	0.651440i	0.943514	+	0.331334i	$0.107499\pi$
$444$	−15.4863	−	26.8231i	−0.734948	−	1.27297i
$445$	28.8063	−	12.2499i	1.36555	−	0.580700i
$446$	−3.17734	+	5.50332i	−0.150451	+	0.260590i
$447$	−27.3357	+	15.7823i	−1.29293	+	0.746475i
$448$	−2.89246	−	1.66997i	−0.136656	−	0.0788984i
$449$	39.8495			1.88062			0.940308	−	0.340326i	$-0.110537\pi$
$449$	39.8495			1.88062			0.940308	+	0.340326i	$0.110537\pi$
$450$	−5.09281	+	20.5411i	−0.240077	+	0.968314i
$451$	−9.06697	+	15.7045i	−0.426947	+	0.739494i
$452$	11.9249	−	6.88486i	0.560901	−	0.323836i
$453$	11.8538	+	6.84379i	0.556940	+	0.321549i
$454$	−11.7745	−	20.3941i	−0.552606	−	0.957142i
$455$	−7.34695	+	3.12429i	−0.344430	+	0.146469i
$456$	9.21497	+	15.9608i	0.431530	+	0.747433i
$457$		−	17.5445i		−	0.820696i	−0.911929	−	0.410348i	$-0.865407\pi$
$457$		−	17.5445i		−	0.820696i	0.911929	−	0.410348i	$-0.134593\pi$
$458$	19.5632	+	11.2948i	0.914130	+	0.527773i
$459$	1.87440	−	3.24656i	0.0874897	−	0.151537i
$460$	−3.98974	−	9.38209i	−0.186022	−	0.437442i
$461$	−9.00321			−0.419321			−0.209661	−	0.977774i	$-0.567236\pi$
$461$	−9.00321			−0.419321			−0.209661	+	0.977774i	$0.567236\pi$
$462$	19.5358	+	11.2790i	0.908888	+	0.524747i
$463$			23.2104i			1.07868i	0.842088	+	0.539340i	$0.181326\pi$
$463$			23.2104i			1.07868i	−0.842088	+	0.539340i	$0.818674\pi$
$464$	2.14564			0.0996089
$465$	−7.18681	+	32.7017i	−0.333280	+	1.51651i
$466$	11.4137			0.528728
$467$		−	6.78086i		−	0.313781i	−0.987616	−	0.156890i	$-0.949853\pi$
$467$		−	6.78086i		−	0.313781i	0.987616	−	0.156890i	$-0.0501470\pi$
$468$	−3.91847	−	2.26233i	−0.181132	−	0.104576i
$469$	−53.3401			−2.46302
$470$	13.4697	−	5.72798i	0.621310	−	0.264212i
$471$	6.78338	−	11.7492i	0.312562	−	0.541373i
$472$	−8.54733	−	4.93480i	−0.393423	−	0.227143i
$473$		−	1.16019i		−	0.0533454i
$474$	7.31108	+	12.6632i	0.335809	+	0.581638i
$475$	9.48788	+	32.9249i	0.435334	+	1.51070i
$476$	1.88857	+	3.27110i	0.0865625	+	0.149931i
$477$	35.6748	+	20.5969i	1.63344	+	0.943066i
$478$	−13.8407	+	7.99093i	−0.633058	+	0.365496i
$479$	−6.75903	+	11.7070i	−0.308828	+	0.534906i	−0.978106	−	0.208106i	$-0.933270\pi$
$479$	−6.75903	+	11.7070i	−0.308828	+	0.534906i	0.669278	+	0.743012i	$0.266603\pi$
$480$	0.728949	−	5.96922i	0.0332718	−	0.272456i
$481$	12.3115			0.561355
$482$	−5.93840	−	3.42853i	−0.270487	−	0.156165i
$483$	35.4670	−	20.4769i	1.61381	−	0.931731i
$484$	−2.34643	+	4.06414i	−0.106656	+	0.184733i
$485$	8.79510	+	20.6822i	0.399365	+	0.939130i
$486$	10.0591	+	17.4229i	0.456291	+	0.790319i
$487$	−13.1954	+	7.61835i	−0.597939	+	0.345220i	−0.768230	−	0.640173i	$-0.778863\pi$
$487$	−13.1954	+	7.61835i	−0.597939	+	0.345220i	0.170291	+	0.985394i	$0.445529\pi$
$488$			1.86761i			0.0845428i
$489$	−16.8066	+	29.1100i	−0.760023	+	1.31640i
$490$	5.58669	−	7.42393i	0.252381	−	0.335379i
$491$	13.4117	+	23.2298i	0.605262	+	1.04834i	0.992010	+	0.126159i	$0.0402651\pi$
$491$	13.4117	+	23.2298i	0.605262	+	1.04834i	−0.386748	+	0.922186i	$0.626402\pi$
$492$			19.4188i			0.875468i
$493$	−2.10142	−	1.21326i	−0.0946434	−	0.0546424i
$494$	−7.32582			−0.329604
$495$	−2.88120	+	23.5936i	−0.129500	+	1.06045i
$496$	0.527107	−	5.54276i	0.0236678	−	0.248877i
$497$			10.0700i			0.451700i
$498$			36.5721i			1.63884i
$499$	−12.6708	+	21.9465i	−0.567224	+	0.982461i	0.429615	+	0.903012i	$0.358649\pi$
$499$	−12.6708	+	21.9465i	−0.567224	+	0.982461i	−0.996839	+	0.0794487i	$0.974684\pi$
$500$	3.98610	−	10.4456i	0.178264	−	0.467142i
$501$	−23.9829	−	41.5397i	−1.07148	−	1.85586i
$502$	−0.899409	−	0.519274i	−0.0401426	−	0.0231763i
$503$	18.8555	+	10.8862i	0.840723	+	0.485392i	0.857510	−	0.514467i	$-0.172010\pi$
$503$	18.8555	+	10.8862i	0.840723	+	0.485392i	−0.0167866	+	0.999859i	$0.505344\pi$
$504$	14.1366			0.629693
$505$	30.6158	−	13.0194i	1.36238	−	0.579354i
$506$	−5.72527	−	9.91646i	−0.254519	−	0.440840i
$507$	−27.6160	+	15.9441i	−1.22647	+	0.708103i
$508$	1.09323	+	0.631179i	0.0485044	+	0.0280040i
$509$	−6.84283	−	11.8521i	−0.303303	−	0.525337i	0.673579	−	0.739115i	$-0.264756\pi$
$509$	−6.84283	−	11.8521i	−0.303303	−	0.525337i	−0.976882	+	0.213779i	$0.931423\pi$
$510$	−4.08924	+	5.43402i	−0.181074	+	0.240623i
$511$	−13.9666			−0.617847
$512$			1.00000i			0.0441942i
$513$	−19.6732	−	11.3583i	−0.868593	−	0.501482i
$514$	5.77037	+	9.99457i	0.254520	+	0.440842i
$515$	5.74458	−	7.63374i	0.253136	−	0.336383i
$516$	−0.621195	−	1.07594i	−0.0273466	−	0.0473657i
$517$	14.2369	−	8.21965i	0.626136	−	0.361500i
$518$	−33.3119	+	19.2326i	−1.46364	+	0.845032i
$519$	−21.7940			−0.956649
$520$	1.90998	+	1.43731i	0.0837580	+	0.0630300i
$521$	9.85190	−	17.0640i	0.431620	−	0.747587i	−0.565393	−	0.824821i	$-0.691276\pi$
$521$	9.85190	−	17.0640i	0.431620	−	0.747587i	0.997013	+	0.0772342i	$0.0246089\pi$
$522$	−7.86492	+	4.54082i	−0.344238	+	0.198746i
$523$			2.63019i			0.115010i	0.998345	+	0.0575050i	$0.0183145\pi$
$523$			2.63019i			0.115010i	−0.998345	+	0.0575050i	$0.981685\pi$
$524$	2.00041	−	3.46482i	0.0873885	−	0.151361i
$525$	43.5914	+	10.8078i	1.90248	+	0.471689i
$526$	−27.8728			−1.21531
$527$	−3.65041	+	5.13048i	−0.159014	+	0.223487i
$528$		−	6.75404i		−	0.293932i
$529$	2.21167			0.0961597
$530$	−17.3889	−	13.0856i	−0.755327	−	0.568403i
$531$	41.7740			1.81284
$532$	19.8219	−	11.4442i	0.859388	−	0.496168i
$533$	−6.68477	−	3.85945i	−0.289549	−	0.167171i
$534$	18.8241	−	32.6043i	0.814600	−	1.41093i
$535$	−21.8245	−	2.66517i	−0.943557	−	0.115225i
$536$	7.98521	+	13.8308i	0.344909	+	0.597399i
$537$	−44.1335	+	25.4805i	−1.90450	+	1.09956i
$538$	6.44358	−	3.72020i	0.277803	−	0.160389i
$539$	5.21761	−	9.03717i	0.224738	−	0.389258i
$540$	2.90069	+	6.82115i	0.124826	+	0.293535i
$541$	−3.36443	+	5.82736i	−0.144648	+	0.250538i	−0.929242	−	0.369473i	$-0.879538\pi$
$541$	−3.36443	+	5.82736i	−0.144648	+	0.250538i	0.784594	+	0.620010i	$0.212872\pi$
$542$			12.3624i			0.531010i
$543$		−	33.6575i		−	1.44438i
$544$	0.565452	−	0.979392i	0.0242436	−	0.0419911i
$545$	−25.1802	+	10.7079i	−1.07860	+	0.458675i
$546$	−4.80103	+	8.31562i	−0.205465	+	0.355876i
$547$	−7.58550	+	4.37949i	−0.324333	+	0.187254i	−0.653322	−	0.757080i	$-0.726625\pi$
$547$	−7.58550	+	4.37949i	−0.324333	+	0.187254i	0.328989	+	0.944334i	$0.393292\pi$
$548$	9.42943	−	5.44408i	0.402805	−	0.232560i
$549$	−3.95242	−	6.84579i	−0.168685	−	0.292171i
$550$	3.02181	−	12.1880i	0.128850	−	0.519698i
$551$	−7.35198	+	12.7340i	−0.313205	+	0.542486i
$552$	−10.6191	−	6.13094i	−0.451979	−	0.260950i
$553$	15.7265	−	9.07970i	0.668759	−	0.386108i
$554$	−11.1581			−0.474060
$555$	−55.3384	−	41.6435i	−2.34898	−	1.76767i
$556$	10.7590			0.456285
$557$			26.2133i			1.11069i	0.831619	+	0.555347i	$0.187414\pi$
$557$			26.2133i			1.11069i	−0.831619	+	0.555347i	$0.812586\pi$
$558$	9.79800	+	21.4327i	0.414782	+	0.907318i
$559$	0.493845			0.0208874
$560$	−7.41324	−	0.905290i	−0.313267	−	0.0382555i
$561$	−3.81908	+	6.61485i	−0.161242	+	0.279279i
$562$			3.11884i			0.131560i
$563$	28.2023	−	16.2826i	1.18858	−	0.686230i	0.230600	−	0.973049i	$-0.425931\pi$
$563$	28.2023	−	16.2826i	1.18858	−	0.686230i	0.957985	+	0.286819i	$0.0925978\pi$
$564$	8.80206	−	15.2456i	0.370634	−	0.641956i
$565$	18.5137	−	24.6022i	0.778879	−	1.03502i
$566$	−22.2481			−0.935156
$567$	10.9420	−	6.31735i	0.459520	−	0.265304i
$568$	2.61109	−	1.50751i	0.109559	−	0.0632538i
$569$	−6.76602	−	11.7191i	−0.283646	−	0.491290i	0.688634	−	0.725109i	$-0.258211\pi$
$569$	−6.76602	−	11.7191i	−0.283646	−	0.491290i	−0.972280	+	0.233820i	$0.924877\pi$
$570$	32.9285	+	24.7795i	1.37922	+	1.03790i
$571$	5.51144	+	9.54610i	0.230647	+	0.399492i	0.957999	−	0.286773i	$-0.0925825\pi$
$571$	5.51144	+	9.54610i	0.230647	+	0.399492i	−0.727352	+	0.686265i	$0.759249\pi$
$572$	2.32502	+	1.34235i	0.0972139	+	0.0561265i
$573$		−	3.87042i		−	0.161689i
$574$	24.1165			1.00660
$575$	−16.4197	−	15.8147i	−0.684747	−	0.659517i
$576$	−2.11630	−	3.66553i	−0.0881791	−	0.152731i
$577$	−31.6666	−	18.2827i	−1.31830	−	0.761119i	−0.334842	−	0.942274i	$-0.608683\pi$
$577$	−31.6666	−	18.2827i	−1.31830	−	0.761119i	−0.983455	+	0.181155i	$0.942016\pi$
$578$	13.6148	−	7.86053i	0.566302	−	0.326955i
$579$	−24.5916	−	42.5939i	−1.02199	−	1.77014i
$580$	4.41517	−	1.87755i	0.183330	−	0.0779610i
$581$	45.4193			1.88431
$582$	23.4091	+	13.5152i	0.970337	+	0.560225i
$583$	−21.1676	−	12.2211i	−0.876672	−	0.506147i
$584$	2.09086	+	3.62147i	0.0865202	+	0.149857i
$585$	−10.0429	−	1.22641i	−0.415221	−	0.0507059i
$586$	−15.3428	+	26.5745i	−0.633804	+	1.09778i
$587$			4.97632i			0.205395i	0.994713	+	0.102697i	$0.0327473\pi$
$587$			4.97632i			0.205395i	−0.994713	+	0.102697i	$0.967253\pi$
$588$		−	11.1746i		−	0.460833i
$589$	31.0891	+	22.1204i	1.28101	+	0.911454i
$590$	−21.9064	−	2.67516i	−0.901871	−	0.110135i
$591$	−8.57523			−0.352738
$592$	9.97382	+	5.75839i	0.409921	+	0.236668i
$593$			4.23391i			0.173866i	0.996214	+	0.0869330i	$0.0277066\pi$
$593$			4.23391i			0.173866i	−0.996214	+	0.0869330i	$0.972293\pi$
$594$	4.16249	+	7.20965i	0.170789	+	0.295816i
$595$	6.74857	+	5.07847i	0.276664	+	0.208197i
$596$	5.86843	−	10.1644i	0.240380	−	0.416351i
$597$		−	40.5054i		−	1.65777i
$598$	4.22105	−	2.43702i	0.172611	−	0.0996572i
$599$	−15.3524	−	26.5911i	−0.627282	−	1.08648i	−0.988095	−	0.153845i	$-0.950834\pi$
$599$	−15.3524	−	26.5911i	−0.627282	−	1.08648i	0.360813	−	0.932638i	$-0.382499\pi$
$600$	−3.72340	−	12.9210i	−0.152007	−	0.527496i
$601$	−9.18723	+	15.9128i	−0.374755	+	0.649095i	−0.990290	−	0.139015i	$-0.955607\pi$
$601$	−9.18723	+	15.9128i	−0.374755	+	0.649095i	0.615535	+	0.788109i	$0.288940\pi$
$602$	−1.33622	+	0.771469i	−0.0544604	+	0.0314427i
$603$	−58.5401	−	33.7982i	−2.38394	−	1.37637i
$604$	−5.08955			−0.207091
$605$	−1.27200	+	10.4162i	−0.0517142	+	0.423478i
$606$	20.0066	−	34.6524i	0.812711	−	1.40766i
$607$	−32.5339	+	18.7835i	−1.32051	+	0.762398i	−0.983810	−	0.179214i	$-0.942645\pi$
$607$	−32.5339	+	18.7835i	−1.32051	+	0.762398i	−0.336701	+	0.941612i	$0.609311\pi$
$608$	−5.93482	−	3.42647i	−0.240689	−	0.138962i
$609$	9.63633	+	16.6906i	0.390484	+	0.676338i
$610$	1.63426	+	3.84305i	0.0661692	+	0.155601i
$611$	3.49878	+	6.06007i	0.141546	+	0.245164i
$612$			4.78666i			0.193489i
$613$	23.5128	+	13.5751i	0.949674	+	0.548295i	0.892980	−	0.450097i	$-0.148611\pi$
$613$	23.5128	+	13.5751i	0.949674	+	0.548295i	0.0566946	+	0.998392i	$0.481944\pi$
$614$	−6.79649	+	11.7719i	−0.274284	+	0.475074i
$615$	16.9925	+	39.9589i	0.685204	+	1.61130i
$616$	−8.38791			−0.337958
$617$	5.08011	+	2.93300i	0.204518	+	0.118078i	0.598761	−	0.800928i	$-0.295660\pi$
$617$	5.08011	+	2.93300i	0.204518	+	0.118078i	−0.394243	+	0.919006i	$0.628993\pi$
$618$		−	11.4904i		−	0.462213i
$619$	23.8518			0.958683			0.479342	−	0.877628i	$-0.340876\pi$
$619$	23.8518			0.958683			0.479342	+	0.877628i	$0.340876\pi$
$620$	−3.76556	−	11.8668i	−0.151228	−	0.476582i
$621$	15.1139			0.606501
$622$			8.28787i			0.332313i
$623$	−40.4917	−	23.3779i	−1.62227	−	0.936615i
$624$	2.87493			0.115089
$625$	−0.938115	−	24.9824i	−0.0375246	−	0.999296i
$626$	4.97379	−	8.61486i	0.198793	−	0.344319i
$627$	40.0840	+	23.1425i	1.60080	+	0.924222i
$628$			5.04463i			0.201303i
$629$	−6.51219	−	11.2794i	−0.259658	−	0.449741i
$630$	29.0894	−	12.3702i	1.15895	−	0.492843i
$631$	−21.9338	−	37.9904i	−0.873170	−	1.51238i	−0.858699	−	0.512480i	$-0.828727\pi$
$631$	−21.9338	−	37.9904i	−0.873170	−	1.51238i	−0.0144711	−	0.999895i	$-0.504606\pi$
$632$	−4.70863	−	2.71853i	−0.187299	−	0.108137i
$633$	42.1865	−	24.3564i	1.67676	−	0.968079i
$634$	−1.12141	+	1.94235i	−0.0445371	+	0.0771404i
$635$	2.80190	+	0.342163i	0.111190	+	0.0135783i
$636$	−26.1741			−1.03787
$637$	3.84677	+	2.22093i	0.152414	+	0.0879965i
$638$	4.66664	−	2.69428i	0.184754	−	0.106668i
$639$	−6.38069	+	11.0517i	−0.252416	+	0.437198i
$640$	0.875053	+	2.05774i	0.0345895	+	0.0813392i
$641$	2.13146	+	3.69179i	0.0841874	+	0.145817i	0.905045	−	0.425317i	$-0.139837\pi$
$641$	2.13146	+	3.69179i	0.0841874	+	0.145817i	−0.820857	+	0.571133i	$0.806504\pi$
$642$	−22.9009	+	13.2218i	−0.903826	+	0.521824i
$643$			22.7470i			0.897055i	0.893769	+	0.448528i	$0.148051\pi$
$643$			22.7470i			0.897055i	−0.893769	+	0.448528i	$0.851949\pi$
$644$	−7.61408	+	13.1880i	−0.300037	+	0.519679i
$645$	−2.21976	−	1.67043i	−0.0874031	−	0.0657730i
$646$	3.87501	+	6.71171i	0.152460	+	0.264069i
$647$		−	21.1723i		−	0.832368i	−0.909280	−	0.416184i	$-0.863367\pi$
$647$		−	21.1723i		−	0.832368i	0.909280	−	0.416184i	$-0.136633\pi$
$648$	−3.27611	−	1.89146i	−0.128698	−	0.0743037i
$649$	−24.7865			−0.972957
$650$	5.18795	+	1.28627i	0.203488	+	0.0504515i
$651$	45.4836	−	20.7929i	1.78264	−	0.814938i
$652$		−	12.4987i		−	0.489486i
$653$		−	7.50358i		−	0.293638i	−0.989163	−	0.146819i	$-0.953097\pi$
$653$		−	7.50358i		−	0.293638i	0.989163	−	0.146819i	$-0.0469035\pi$
$654$	−16.4545	+	28.5001i	−0.643423	+	1.11444i
$655$	1.08443	−	8.88016i	0.0423721	−	0.346976i
$656$	−3.61032	−	6.25326i	−0.140959	−	0.244149i
$657$	−15.3282	−	8.84975i	−0.598010	−	0.345261i
$658$	−18.9337	−	10.9314i	−0.738112	−	0.426149i
$659$	41.7093			1.62476			0.812382	−	0.583126i	$-0.198171\pi$
$659$	41.7093			1.62476			0.812382	+	0.583126i	$0.198171\pi$
$660$	−5.91014	−	13.8980i	−0.230052	−	0.540980i
$661$	−18.3974	−	31.8652i	−0.715576	−	1.23941i	−0.962737	−	0.270439i	$-0.912831\pi$
$661$	−18.3974	−	31.8652i	−0.715576	−	1.23941i	0.247161	−	0.968974i	$-0.420502\pi$
$662$	−20.3476	+	11.7477i	−0.790833	+	0.456587i
$663$	−2.81568	−	1.62563i	−0.109352	−	0.0631344i
$664$	−6.79944	−	11.7770i	−0.263869	−	0.457035i
$665$	30.7740	−	40.8943i	1.19336	−	1.58581i
$666$	−48.7458			−1.88886
$667$		−	9.78289i		−	0.378795i
$668$	15.4460	+	8.91775i	0.597624	+	0.345038i
$669$	8.54498	+	14.8003i	0.330368	+	0.572214i
$670$	28.5341	+	21.4726i	1.10237	+	0.829561i
$671$	2.34516	+	4.06194i	0.0905339	+	0.156809i
$672$	−7.77885	+	4.49112i	−0.300075	+	0.173249i
$673$	4.09110	−	2.36200i	0.157700	−	0.0910483i	−0.419073	−	0.907952i	$-0.637645\pi$
$673$	4.09110	−	2.36200i	0.157700	−	0.0910483i	0.576773	+	0.816904i	$0.304312\pi$
$674$	5.10345			0.196578
$675$	11.9377	+	11.4979i	0.459483	+	0.442553i
$676$	5.92861	−	10.2687i	0.228024	−	0.394949i
$677$	−9.66900	+	5.58240i	−0.371610	+	0.214549i	−0.674162	−	0.738584i	$-0.735495\pi$
$677$	−9.66900	+	5.58240i	−0.371610	+	0.214549i	0.302552	+	0.953133i	$0.402162\pi$
$678$		−	37.0316i		−	1.42219i
$679$	16.7847	−	29.0720i	0.644138	−	1.11568i
$680$	0.306532	−	2.51013i	0.0117550	−	0.0962592i
$681$	−63.3317			−2.42687
$682$	−5.81362	−	12.7170i	−0.222615	−	0.486961i
$683$		−	27.2295i		−	1.04191i	−0.853585	−	0.520954i	$-0.825576\pi$
$683$		−	27.2295i		−	1.04191i	0.853585	−	0.520954i	$-0.174424\pi$
$684$	29.0057			1.10906
$685$	14.6394	−	19.4537i	0.559344	−	0.743289i
$686$	9.50164			0.362774
$687$	52.6124	−	30.3758i	2.00729	−	1.15891i
$688$	0.400075	+	0.230984i	0.0152527	+	0.00880617i
$689$	5.20205	−	9.01021i	0.198182	−	0.343262i
$690$	−27.2162	−	3.32359i	−1.03610	−	0.126527i
$691$	18.4515	+	31.9589i	0.701927	+	1.21577i	0.967789	+	0.251762i	$0.0810101\pi$
$691$	18.4515	+	31.9589i	0.701927	+	1.21577i	−0.265862	+	0.964011i	$0.585657\pi$
$692$	7.01810	−	4.05190i	0.266788	−	0.154030i
$693$	30.7462	−	17.7513i	1.16795	−	0.674317i
$694$	15.1378	−	26.2194i	0.574622	−	0.995275i
$695$	22.1393	−	9.41472i	0.839790	−	0.357121i
$696$	2.88519	−	4.99729i	0.109363	−	0.189422i
$697$			8.16586i			0.309304i
$698$			11.9756i			0.453282i
$699$	15.3477	−	26.5829i	0.580502	−	1.00546i
$700$	−16.0467	+	4.62413i	−0.606507	+	0.174776i
$701$	−15.2412	+	26.3985i	−0.575652	+	0.997058i	0.420319	+	0.907377i	$0.361918\pi$
$701$	−15.2412	+	26.3985i	−0.575652	+	0.997058i	−0.995970	+	0.0896816i	$0.971415\pi$
$702$	−3.06886	+	1.77181i	−0.115827	+	0.0668727i
$703$	−68.3500	+	39.4619i	−2.57787	+	1.48833i
$704$	1.25570	+	2.17494i	0.0473260	+	0.0819711i
$705$	4.77161	−	39.0737i	0.179709	−	1.47160i
$706$	8.54181	−	14.7949i	0.321475	−	0.556812i
$707$	−43.0352	−	24.8464i	−1.61850	−	0.934444i
$708$	−22.9867	+	13.2714i	−0.863895	+	0.498770i
$709$	−30.1272			−1.13145			−0.565726	−	0.824593i	$-0.691404\pi$
$709$	−30.1272			−1.13145			−0.565726	+	0.824593i	$0.691404\pi$
$710$	4.05378	−	5.38691i	0.152136	−	0.202167i
$711$	23.0129			0.863050
$712$			13.9990i			0.524636i
$713$	−25.2718	−	2.40330i	−0.946435	−	0.0900044i
$714$	10.1581			0.380156
$715$	5.95891	+	0.727690i	0.222850	+	0.0272141i
$716$	9.47460	−	16.4105i	0.354082	−	0.613289i
$717$			42.9808i			1.60515i
$718$	−25.5058	+	14.7258i	−0.951870	+	0.549562i
$719$	−14.7187	+	25.4936i	−0.548917	+	0.950752i	0.449432	+	0.893314i	$0.351626\pi$
$719$	−14.7187	+	25.4936i	−0.548917	+	0.950752i	−0.998349	+	0.0574372i	$0.981707\pi$
$720$	−7.56232	−	5.69083i	−0.281831	−	0.212085i
$721$	−14.2701			−0.531446
$722$	24.2165	−	13.9814i	0.901244	−	0.520333i
$723$	−15.9704	+	9.22052i	−0.593946	+	0.342915i
$724$	6.25755	+	10.8384i	0.232560	+	0.402806i
$725$	7.44230	−	7.72701i	0.276400	−	0.286974i
$726$	6.31037	+	10.9299i	0.234200	+	0.405646i
$727$	9.81546	+	5.66696i	0.364035	+	0.210176i	0.670849	−	0.741594i	$-0.265930\pi$
$727$	9.81546	+	5.66696i	0.364035	+	0.210176i	−0.306814	+	0.951769i	$0.599263\pi$
$728$		−	3.57040i		−	0.132328i
$729$	42.7562			1.58356
$730$	7.47141	+	5.62242i	0.276529	+	0.208095i
$731$	−0.261220	−	0.452447i	−0.00966159	−	0.0167344i
$732$	4.34975	+	2.51133i	0.160771	+	0.0928213i
$733$	−5.22234	+	3.01512i	−0.192891	+	0.111366i	−0.593335	−	0.804955i	$-0.702189\pi$
$733$	−5.22234	+	3.01512i	−0.192891	+	0.111366i	0.400444	+	0.916321i	$0.368856\pi$
$734$	15.6459	+	27.0994i	0.577499	+	1.00026i
$735$	−9.77838	−	22.9944i	−0.360681	−	0.848162i
$736$	4.55942			0.168063
$737$	34.7347	+	20.0541i	1.27947	+	0.738701i
$738$	26.4675	+	15.2810i	0.974283	+	0.562503i
$739$	4.45863	+	7.72257i	0.164013	+	0.284079i	0.936304	−	0.351189i	$-0.114223\pi$
$739$	4.45863	+	7.72257i	0.164013	+	0.284079i	−0.772291	+	0.635269i	$0.780889\pi$
$740$	25.5624	+	3.12163i	0.939692	+	0.114753i
$741$	−9.85085	+	17.0622i	−0.361880	+	0.626794i
$742$			32.5059i			1.19333i
$743$			33.6977i			1.23625i	0.786081	+	0.618124i	$0.212107\pi$
$743$			33.6977i			1.23625i	−0.786081	+	0.618124i	$0.787893\pi$
$744$	−12.2005	−	8.68086i	−0.447293	−	0.318256i
$745$	3.18128	−	26.0509i	0.116553	−	0.954431i
$746$	19.9316			0.729747
$747$	49.8472	+	28.7793i	1.82381	+	1.05298i
$748$		−	2.84016i		−	0.103846i
$749$	16.4203	+	28.4409i	0.599986	+	1.03921i
$750$	−18.9683	−	23.3298i	−0.692624	−	0.851883i
$751$	15.1183	−	26.1857i	0.551675	−	0.955529i	−0.446479	−	0.894794i	$-0.647322\pi$
$751$	15.1183	−	26.1857i	0.551675	−	0.955529i	0.998154	−	0.0607351i	$-0.0193445\pi$
$752$			6.54587i			0.238703i
$753$	−2.41882	+	1.39651i	−0.0881468	+	0.0508916i
$754$	1.14685	+	1.98640i	0.0417658	+	0.0723406i
$755$	−10.4730	+	4.45363i	−0.381150	+	0.162084i
$756$	5.53573	−	9.58817i	0.201333	−	0.348718i
$757$	−17.9791	+	10.3803i	−0.653463	+	0.377277i	−0.789782	−	0.613388i	$-0.789806\pi$
$757$	−17.9791	+	10.3803i	−0.653463	+	0.377277i	0.136319	+	0.990665i	$0.456473\pi$
$758$	12.8476	+	7.41755i	0.466645	+	0.269418i
$759$	−30.7945			−1.11777
$760$	−15.2106	−	1.85749i	−0.551748	−	0.0673783i
$761$	−18.2860	+	31.6722i	−0.662866	+	1.14812i	0.316993	+	0.948428i	$0.397327\pi$
$761$	−18.2860	+	31.6722i	−0.662866	+	1.14812i	−0.979859	+	0.199690i	$0.936007\pi$
$762$	2.94009	−	1.69746i	0.106508	−	0.0614925i
$763$	35.3946	+	20.4351i	1.28137	+	0.739799i
$764$	0.719583	+	1.24636i	0.0260336	+	0.0450915i
$765$	4.18858	+	9.84969i	0.151438	+	0.356116i
$766$	2.42574	+	4.20151i	0.0876457	+	0.151807i
$767$		−	10.5507i		−	0.380962i
$768$	2.32904	+	1.34467i	0.0840421	+	0.0485218i
$769$	−4.76428	+	8.25198i	−0.171804	+	0.297574i	−0.939051	−	0.343779i	$-0.888293\pi$
$769$	−4.76428	+	8.25198i	−0.171804	+	0.297574i	0.767246	+	0.641353i	$0.221626\pi$
$770$	−17.2601	+	7.33986i	−0.622011	+	0.264510i
$771$	31.0371			1.11777
$772$	15.8380	+	9.14408i	0.570023	+	0.329103i
$773$		−	3.33060i		−	0.119793i	−0.998205	−	0.0598966i	$-0.980923\pi$
$773$		−	3.33060i		−	0.119793i	0.998205	−	0.0598966i	$-0.0190771\pi$
$774$	−1.95532			−0.0702825
$775$	−18.1326	−	21.1237i	−0.651342	−	0.758784i
$776$	−10.0509			−0.360808
$777$			103.446i			3.71112i
$778$	1.96685	+	1.13556i	0.0705149	+	0.0407118i
$779$	49.4826			1.77290
$780$	5.91584	−	2.51571i	0.211821	−	0.0900770i
$781$	3.78597	−	6.55749i	0.135473	−	0.234646i
$782$	−4.46546	−	2.57814i	−0.159685	−	0.0921939i
$783$			7.11254i			0.254181i
$784$	2.07757	+	3.59845i	0.0741989	+	0.128516i
$785$	4.41432	+	10.3805i	0.157554	+	0.370497i
$786$	−5.37981	−	9.31811i	−0.191892	−	0.332366i
$787$	23.2991	+	13.4518i	0.830524	+	0.479503i	0.854032	−	0.520220i	$-0.174150\pi$
$787$	23.2991	+	13.4518i	0.830524	+	0.479503i	−0.0235082	+	0.999724i	$0.507484\pi$
$788$	2.76140	−	1.59430i	0.0983708	−	0.0567944i
$789$	−37.4799	+	64.9171i	−1.33432	+	2.31111i
$790$	−12.0680	−	1.47372i	−0.429360	−	0.0524325i
$791$	−45.9899			−1.63521
$792$	−9.20563	−	5.31487i	−0.327108	−	0.188856i
$793$	−1.72901	+	0.998242i	−0.0613988	+	0.0354486i
$794$	4.72369	−	8.18167i	0.167637	−	0.290357i
$795$	−53.8594	+	22.9037i	−1.91020	+	0.812311i
$796$	7.53070	+	13.0436i	0.266919	+	0.462317i
$797$	−17.0397	+	9.83785i	−0.603576	+	0.348474i	−0.770447	−	0.637504i	$-0.779967\pi$
$797$	−17.0397	+	9.83785i	−0.603576	+	0.348474i	0.166871	+	0.985979i	$0.446634\pi$
$798$		−	61.5547i		−	2.17901i
$799$	3.70138	−	6.41097i	0.130945	−	0.226804i
$800$	3.60126	+	3.46856i	0.127324	+	0.122632i
$801$	−29.6261	−	51.3139i	−1.04679	−	1.81309i
$802$			20.3650i			0.719113i
$803$	9.09496	+	5.25098i	0.320954	+	0.185303i
$804$	42.9500			1.51473
$805$	−4.12760	+	33.8001i	−0.145479	+	1.19130i
$806$	5.41314	−	2.47463i	0.190670	−	0.0871651i
$807$		−	20.0099i		−	0.704380i
$808$			14.8784i			0.523419i
$809$	19.5953	−	33.9401i	0.688936	−	1.19327i	−0.283247	−	0.959047i	$-0.591412\pi$
$809$	19.5953	−	33.9401i	0.688936	−	1.19327i	0.972183	−	0.234225i	$-0.0752551\pi$
$810$	−8.39650	−	1.02536i	−0.295023	−	0.0360276i
$811$	−6.00390	−	10.3991i	−0.210825	−	0.365160i	0.741148	−	0.671342i	$-0.234282\pi$
$811$	−6.00390	−	10.3991i	−0.210825	−	0.365160i	−0.951973	+	0.306182i	$0.900948\pi$
$812$	−6.20619	−	3.58315i	−0.217795	−	0.125744i
$813$	28.7926	+	16.6234i	1.00980	+	0.583008i
$814$	28.9232			1.01376
$815$	−10.9370	−	25.7190i	−0.383106	−	0.900897i
$816$	−1.52070	−	2.63393i	−0.0532351	−	0.0922059i
$817$	−2.74169	+	1.58292i	−0.0959197	+	0.0553792i
$818$	11.1173	+	6.41855i	0.388706	+	0.224419i
$819$	7.55603	+	13.0874i	0.264029	+	0.457312i
$820$	−12.9010	−	9.70835i	−0.450524	−	0.339030i
$821$	−45.3721			−1.58350			−0.791748	−	0.610848i	$-0.790829\pi$
$821$	−45.3721			−1.58350			−0.791748	+	0.610848i	$0.790829\pi$
$822$		−	29.2821i		−	1.02133i
$823$	34.4620	+	19.8966i	1.20127	+	0.693553i	0.960838	−	0.277112i	$-0.0893774\pi$
$823$	34.4620	+	19.8966i	1.20127	+	0.693553i	0.240432	+	0.970666i	$0.422711\pi$
$824$	2.13628	+	3.70015i	0.0744210	+	0.128901i
$825$	−24.3230	−	23.4268i	−0.846819	−	0.815617i
$826$	16.4819	+	28.5475i	0.573479	+	0.993294i
$827$	10.8815	−	6.28245i	0.378387	−	0.218462i	−0.298729	−	0.954338i	$-0.596563\pi$
$827$	10.8815	−	6.28245i	0.378387	−	0.218462i	0.677116	+	0.735876i	$0.263229\pi$
$828$	−16.7127	+	9.64909i	−0.580807	+	0.335329i
$829$	−48.2511			−1.67583			−0.837914	−	0.545802i	$-0.816225\pi$
$829$	−48.2511			−1.67583			−0.837914	+	0.545802i	$0.816225\pi$
$830$	−24.2969	−	18.2841i	−0.843359	−	0.634649i
$831$	−15.0040	+	25.9876i	−0.520481	+	0.901500i
$832$	−0.925785	+	0.534502i	−0.0320958	+	0.0185305i
$833$		−	4.69906i		−	0.162813i
$834$	14.4674	−	25.0583i	0.500965	−	0.867696i
$835$	39.5873	+	4.83432i	1.36998	+	0.167299i
$836$	−17.2105			−0.595237
$837$	18.3736	+	1.74729i	0.635083	+	0.0603953i
$838$		−	16.9178i		−	0.584415i
$839$	−32.2788			−1.11439			−0.557193	−	0.830383i	$-0.688122\pi$
$839$	−32.2788			−1.11439			−0.557193	+	0.830383i	$0.688122\pi$
$840$	−12.0769	+	16.0484i	−0.416691	+	0.553724i
$841$	−24.3962			−0.841249
$842$	−8.60160	+	4.96613i	−0.296431	+	0.171144i
$843$	7.26392	+	4.19383i	0.250183	+	0.144443i
$844$	−9.05661	+	15.6865i	−0.311741	+	0.539952i
$845$	3.21391	−	26.3181i	0.110562	−	0.905369i
$846$	−13.8530	−	23.9941i	−0.476276	−	0.824934i
$847$	13.5739	−	7.83691i	0.466406	−	0.269279i
$848$	8.42860	−	4.86625i	0.289439	−	0.167108i
$849$	−29.9164	+	51.8167i	−1.02673	+	1.77834i
$850$	−1.56574	−	5.43342i	−0.0537043	−	0.186365i
$851$	26.2549	−	45.4748i	0.900007	−	1.55886i
$852$		−	8.10845i		−	0.277791i
$853$		−	3.23296i		−	0.110694i	−0.998467	−	0.0553472i	$-0.982373\pi$
$853$		−	3.23296i		−	0.110694i	0.998467	−	0.0553472i	$-0.0176266\pi$
$854$	3.11885	−	5.40200i	0.106725	−	0.184853i
$855$	59.6861	−	25.3815i	2.04122	−	0.868030i
$856$	4.91637	−	8.51540i	0.168038	−	0.291050i
$857$	2.10784	−	1.21696i	0.0720025	−	0.0415707i	−0.463567	−	0.886062i	$-0.653430\pi$
$857$	2.10784	−	1.21696i	0.0720025	−	0.0415707i	0.535569	+	0.844491i	$0.320097\pi$
$858$	6.25279	−	3.61005i	0.213467	−	0.123245i
$859$	4.93095	+	8.54066i	0.168242	+	0.291403i	0.937802	−	0.347171i	$-0.112858\pi$
$859$	4.93095	+	8.54066i	0.168242	+	0.291403i	−0.769560	+	0.638575i	$0.779524\pi$
$860$	1.02537	+	0.125216i	0.0349649	+	0.00426985i
$861$	32.4288	−	56.1683i	1.10517	−	1.91421i
$862$	0.446222	+	0.257626i	0.0151984	+	0.00877479i
$863$	−6.80650	+	3.92974i	−0.231696	+	0.133770i	−0.611354	−	0.791357i	$-0.709375\pi$
$863$	−6.80650	+	3.92974i	−0.231696	+	0.133770i	0.379658	+	0.925127i	$0.376042\pi$
$864$	−3.31488			−0.112774
$865$	10.8958	−	14.4790i	0.370468	−	0.492299i
$866$	−37.7395			−1.28244
$867$		−	42.2794i		−	1.43588i
$868$	−10.7809	+	15.1520i	−0.365926	+	0.514292i
$869$	−13.6546			−0.463202
$870$	1.56406	−	12.8078i	0.0530267	−	0.434225i
$871$	−8.53623	+	14.7852i	−0.289239	+	0.500977i
$872$		−	12.2368i		−	0.414391i
$873$	36.8421	−	21.2708i	1.24691	−	0.719907i
$874$	−15.6227	+	27.0593i	−0.528446	+	0.915296i
$875$	−28.9735	+	23.5569i	−0.979483	+	0.796370i
$876$	11.2461			0.379970
$877$	−46.5201	+	26.8584i	−1.57087	+	0.906943i	−0.574808	+	0.818288i	$0.694923\pi$
$877$	−46.5201	+	26.8584i	−1.57087	+	0.906943i	−0.996062	+	0.0886546i	$0.971743\pi$
$878$	12.4149	−	7.16777i	0.418984	−	0.241900i
$879$	41.2621	+	71.4680i	1.39174	+	2.41056i
$880$	4.48709	+	3.37665i	0.151260	+	0.113827i
$881$	15.3470	+	26.5818i	0.517054	+	0.895564i	0.999804	+	0.0198057i	$0.00630477\pi$
$881$	15.3470	+	26.5818i	0.517054	+	0.895564i	−0.482750	+	0.875758i	$0.660362\pi$
$882$	−15.2308	−	8.79351i	−0.512848	−	0.296093i
$883$		−	47.7407i		−	1.60660i	−0.595573	−	0.803301i	$-0.703075\pi$
$883$		−	47.7407i		−	1.60660i	0.595573	−	0.803301i	$-0.296925\pi$
$884$	1.20894			0.0406611
$885$	−35.6875	+	47.4237i	−1.19962	+	1.59413i
$886$	13.7112	+	23.7485i	0.460637	+	0.797847i
$887$	18.4652	+	10.6609i	0.620001	+	0.357958i	0.776869	−	0.629662i	$-0.216807\pi$
$887$	18.4652	+	10.6609i	0.620001	+	0.357958i	−0.156868	+	0.987620i	$0.550140\pi$
$888$	26.8231	−	15.4863i	0.900123	−	0.519686i
$889$	−2.10809	−	3.65132i	−0.0707032	−	0.122461i
$890$	12.2499	+	28.8063i	0.410617	+	0.965590i
$891$	−9.50045			−0.318277
$892$	−5.50332	−	3.17734i	−0.184265	−	0.106385i
$893$	−38.8485	−	22.4292i	−1.30002	−	0.750565i
$894$	−15.7823	−	27.3357i	−0.527837	−	0.914241i
$895$	5.13619	−	42.0592i	0.171684	−	1.40589i
$896$	1.66997	−	2.89246i	0.0557896	−	0.0966305i
$897$		−	13.1080i		−	0.437663i
$898$			39.8495i			1.32980i
$899$	1.13098	−	11.8928i	0.0377204	−	0.396646i
$900$	−20.5411	−	5.09281i	−0.684702	−	0.169760i
$901$	−11.0065			−0.366681
$902$	−15.7045	−	9.06697i	−0.522901	−	0.301897i
$903$			4.14950i			0.138087i
$904$	6.88486	+	11.9249i	0.228987	+	0.396617i
$905$	22.3606	+	16.8269i	0.743290	+	0.559344i
$906$	−6.84379	+	11.8538i	−0.227370	+	0.393816i
$907$			3.01352i			0.100062i	0.998748	+	0.0500311i	$0.0159321\pi$
$907$			3.01352i			0.100062i	−0.998748	+	0.0500311i	$0.984068\pi$
$908$	20.3941	−	11.7745i	0.676802	−	0.390752i
$909$	−31.4871	−	54.5372i	−1.04436	−	1.80888i
$910$	−3.12429	−	7.34695i	−0.103569	−	0.243549i
$911$	9.27333	−	16.0619i	0.307239	−	0.532154i	−0.670518	−	0.741893i	$-0.733928\pi$
$911$	9.27333	−	16.0619i	0.307239	−	0.532154i	0.977757	+	0.209739i	$0.0672615\pi$
$912$	−15.9608	+	9.21497i	−0.528515	+	0.305138i
$913$	−29.5767	−	17.0761i	−0.978847	−	0.565137i
$914$	17.5445			0.580319
$915$	11.1482	+	1.36139i	0.368548	+	0.0450063i
$916$	−11.2948	+	19.5632i	−0.373192	+	0.646388i
$917$	−11.5723	+	6.68125i	−0.382150	+	0.220634i
$918$	3.24656	+	1.87440i	0.107153	+	0.0618646i
$919$	5.30786	+	9.19349i	0.175090	+	0.303265i	0.940192	−	0.340644i	$-0.110645\pi$
$919$	5.30786	+	9.19349i	0.175090	+	0.303265i	−0.765102	+	0.643909i	$0.777312\pi$
$920$	9.38209	−	3.98974i	0.309318	−	0.131538i
$921$	18.2781	+	31.6586i	0.602285	+	1.04319i
$922$		−	9.00321i		−	0.296505i
$923$	2.79127	+	1.61154i	0.0918757	+	0.0530444i
$924$	−11.2790	+	19.5358i	−0.371052	+	0.642681i
$925$	55.3323	−	15.9450i	1.81931	−	0.524267i
$926$	−23.2104			−0.762742
$927$	−15.6612	−	9.04202i	−0.514383	−	0.296979i
$928$			2.14564i			0.0704341i
$929$	28.8336			0.945999			0.473000	−	0.881063i	$-0.343171\pi$
$929$	28.8336			0.945999			0.473000	+	0.881063i	$0.343171\pi$
$930$	−32.7017	−	7.18681i	−1.07233	−	0.235665i
$931$	−28.4749			−0.933227
$932$			11.4137i			0.373867i
$933$	19.3028	+	11.1445i	0.631946	+	0.364854i
$934$	6.78086			0.221877
$935$	−2.48529	−	5.84429i	−0.0812776	−	0.191129i
$936$	2.26233	−	3.91847i	0.0739466	−	0.128079i
$937$	−19.2047	−	11.0878i	−0.627390	−	0.362224i	0.152350	−	0.988327i	$-0.451316\pi$
$937$	−19.2047	−	11.0878i	−0.627390	−	0.362224i	−0.779741	+	0.626103i	$0.784649\pi$
$938$		−	53.3401i		−	1.74162i
$939$	−13.3763	−	23.1683i	−0.436517	−	0.756070i
$940$	5.72798	+	13.4697i	0.186826	+	0.439332i
$941$	5.67462	+	9.82873i	0.184987	+	0.320407i	0.943572	−	0.331167i	$-0.107442\pi$
$941$	5.67462	+	9.82873i	0.184987	+	0.320407i	−0.758585	+	0.651574i	$0.774109\pi$
$942$	11.7492	+	6.78338i	0.382808	+	0.221015i
$943$	−28.5113	+	16.4610i	−0.928454	+	0.536043i
$944$	4.93480	−	8.54733i	0.160614	−	0.278192i
$945$	3.00093	−	24.5740i	0.0976201	−	0.799392i
$946$	1.16019			0.0377209
$947$	1.41654	+	0.817838i	0.0460313	+	0.0265762i	0.522839	−	0.852431i	$-0.324873\pi$
$947$	1.41654	+	0.817838i	0.0460313	+	0.0265762i	−0.476808	+	0.879008i	$0.658206\pi$
$948$	−12.6632	+	7.31108i	−0.411280	+	0.237453i
$949$	−2.23514	+	3.87137i	−0.0725556	+	0.125670i
$950$	−32.9249	+	9.48788i	−1.06822	+	0.307828i
$951$	3.01587	+	5.22365i	0.0977964	+	0.169388i
$952$	−3.27110	+	1.88857i	−0.106017	+	0.0612090i
$953$			2.67046i			0.0865047i	0.999064	+	0.0432524i	$0.0137719\pi$
$953$			2.67046i			0.0865047i	−0.999064	+	0.0432524i	$0.986228\pi$
$954$	−20.5969	+	35.6748i	−0.666849	+	1.15502i
$955$	2.57134	+	1.93500i	0.0832066	+	0.0626151i
$956$	−7.99093	−	13.8407i	−0.258445	−	0.447640i
$957$		−	14.4917i		−	0.468451i
$958$	−11.7070	−	6.75903i	−0.378235	−	0.218374i
$959$	−36.3657			−1.17431
$960$	5.96922	+	0.728949i	0.192656	+	0.0235267i
$961$	−30.4443	−	5.84325i	−0.982075	−	0.188492i
$962$			12.3115i			0.396938i
$963$			41.6180i			1.34112i
$964$	3.42853	−	5.93840i	0.110426	−	0.191263i
$965$	40.5920	+	4.95702i	1.30670	+	0.159572i
$966$	20.4769	+	35.4670i	0.658834	+	1.14113i
$967$	52.6039	+	30.3709i	1.69163	+	0.976662i	0.953205	+	0.302326i	$0.0977630\pi$
$967$	52.6039	+	30.3709i	1.69163	+	0.976662i	0.738424	+	0.674337i	$0.235570\pi$
$968$	−4.06414	−	2.34643i	−0.130626	−	0.0754171i
$969$	20.8425			0.669558
$970$	−20.6822	+	8.79510i	−0.664065	+	0.282394i
$971$	23.2342	+	40.2428i	0.745621	+	1.29145i	0.949904	+	0.312542i	$0.101180\pi$
$971$	23.2342	+	40.2428i	0.745621	+	1.29145i	−0.204283	+	0.978912i	$0.565486\pi$
$972$	−17.4229	+	10.0591i	−0.558840	+	0.322646i
$973$	−31.1201	−	17.9672i	−0.997665	−	0.576002i
$974$	−7.61835	−	13.1954i	−0.244108	−	0.422807i
$975$	9.97187	−	10.3534i	0.319355	−	0.331573i
$976$	−1.86761			−0.0597808
$977$			1.40935i			0.0450891i	0.999746	+	0.0225445i	$0.00717675\pi$
$977$			1.40935i			0.0450891i	−0.999746	+	0.0225445i	$0.992823\pi$
$978$	−29.1100	−	16.8066i	−0.930834	−	0.537417i
$979$	17.5786	+	30.4470i	0.561814	+	0.973091i
$980$	7.42393	+	5.58669i	0.237149	+	0.178460i
$981$	25.8968	+	44.8545i	0.826820	+	1.43209i
$982$	−23.2298	+	13.4117i	−0.741292	+	0.427985i
$983$	17.0388	−	9.83737i	0.543454	−	0.313763i	−0.203024	−	0.979174i	$-0.565077\pi$
$983$	17.0388	−	9.83737i	0.543454	−	0.313763i	0.746478	+	0.665410i	$0.231743\pi$
$984$	−19.4188			−0.619050
$985$	4.28714	−	5.69701i	0.136600	−	0.181522i
$986$	1.21326	−	2.10142i	0.0386380	−	0.0669230i
$987$	−50.9193	+	29.3983i	−1.62078	+	0.935757i
$988$		−	7.32582i		−	0.233066i
$989$	1.05315	−	1.82411i	0.0334883	−	0.0580034i
$990$	−23.5936	−	2.88120i	−0.749853	−	0.0915705i
$991$	28.9565			0.919834			0.459917	−	0.887962i	$-0.347879\pi$
$991$	28.9565			0.919834			0.459917	+	0.887962i	$0.347879\pi$
$992$	5.54276	+	0.527107i	0.175983	+	0.0167357i
$993$			63.1873i			2.00519i
$994$	−10.0700			−0.319400
$995$	26.9100	+	20.2505i	0.853105	+	0.641982i
$996$	−36.5721			−1.15883
$997$	26.1902	−	15.1209i	0.829451	−	0.478884i	−0.0242137	−	0.999707i	$-0.507708\pi$
$997$	26.1902	−	15.1209i	0.829451	−	0.478884i	0.853665	+	0.520823i	$0.174375\pi$
$998$	−21.9465	−	12.6708i	−0.694705	−	0.401088i
$999$	−19.0883	+	33.0620i	−0.603928	+	1.04603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.k.a.129.16	yes	32
5.2	odd	4		1550.2.e.q.501.8		16
5.3	odd	4		1550.2.e.r.501.1		16
5.4	even	2	inner	310.2.k.a.129.1	✓	32
31.25	even	3	inner	310.2.k.a.149.9	yes	32
155.87	odd	12		1550.2.e.q.1451.8		16
155.118	odd	12		1550.2.e.r.1451.1		16
155.149	even	6	inner	310.2.k.a.149.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.k.a.129.1	✓	32	5.4	even	2	inner
310.2.k.a.129.16	yes	32	1.1	even	1	trivial
310.2.k.a.149.8	yes	32	155.149	even	6	inner
310.2.k.a.149.9	yes	32	31.25	even	3	inner
1550.2.e.q.501.8		16	5.2	odd	4
1550.2.e.q.1451.8		16	155.87	odd	12
1550.2.e.r.501.1		16	5.3	odd	4
1550.2.e.r.1451.1		16	155.118	odd	12

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(-2.05774 + 0.875053i) q^{5} +(-1.34467 + 2.32904i) q^{6} +(2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 + 3.66553i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(2.32904 + 1.34467i) q^{3} -1.00000 q^{4} +(-2.05774 + 0.875053i) q^{5} +(-1.34467 + 2.32904i) q^{6} +(2.89246 + 1.66997i) q^{7} -1.00000i q^{8} +(2.11630 + 3.66553i) q^{9} +(-0.875053 - 2.05774i) q^{10} +(-1.25570 - 2.17494i) q^{11} +(-2.32904 - 1.34467i) q^{12} +(0.925785 - 0.534502i) q^{13} +(-1.66997 + 2.89246i) q^{14} +(-5.96922 - 0.728949i) q^{15} +1.00000 q^{16} +(-0.979392 - 0.565452i) q^{17} +(-3.66553 + 2.11630i) q^{18} +(-3.42647 + 5.93482i) q^{19} +(2.05774 - 0.875053i) q^{20} +(4.49112 + 7.77885i) q^{21} +(2.17494 - 1.25570i) q^{22} -4.55942i q^{23} +(1.34467 - 2.32904i) q^{24} +(3.46856 - 3.60126i) q^{25} +(0.534502 + 0.925785i) q^{26} +3.31488i q^{27} +(-2.89246 - 1.66997i) q^{28} +2.14564 q^{29} +(0.728949 - 5.96922i) q^{30} +(0.527107 - 5.54276i) q^{31} +1.00000i q^{32} -6.75404i q^{33} +(0.565452 - 0.979392i) q^{34} +(-7.41324 - 0.905290i) q^{35} +(-2.11630 - 3.66553i) q^{36} +(9.97382 + 5.75839i) q^{37} +(-5.93482 - 3.42647i) q^{38} +2.87493 q^{39} +(0.875053 + 2.05774i) q^{40} +(-3.61032 - 6.25326i) q^{41} +(-7.77885 + 4.49112i) q^{42} +(0.400075 + 0.230984i) q^{43} +(1.25570 + 2.17494i) q^{44} +(-7.56232 - 5.69083i) q^{45} +4.55942 q^{46} +6.54587i q^{47} +(2.32904 + 1.34467i) q^{48} +(2.07757 + 3.59845i) q^{49} +(3.60126 + 3.46856i) q^{50} +(-1.52070 - 2.63393i) q^{51} +(-0.925785 + 0.534502i) q^{52} +(8.42860 - 4.86625i) q^{53} -3.31488 q^{54} +(4.48709 + 3.37665i) q^{55} +(1.66997 - 2.89246i) q^{56} +(-15.9608 + 9.21497i) q^{57} +2.14564i q^{58} +(4.93480 - 8.54733i) q^{59} +(5.96922 + 0.728949i) q^{60} -1.86761 q^{61} +(5.54276 + 0.527107i) q^{62} +14.1366i q^{63} -1.00000 q^{64} +(-1.43731 + 1.90998i) q^{65} +6.75404 q^{66} +(-13.8308 + 7.98521i) q^{67} +(0.979392 + 0.565452i) q^{68} +(6.13094 - 10.6191i) q^{69} +(0.905290 - 7.41324i) q^{70} +(1.50751 + 2.61109i) q^{71} +(3.66553 - 2.11630i) q^{72} +(-3.62147 + 2.09086i) q^{73} +(-5.75839 + 9.97382i) q^{74} +(12.9210 - 3.72340i) q^{75} +(3.42647 - 5.93482i) q^{76} -8.38791i q^{77} +2.87493i q^{78} +(2.71853 - 4.70863i) q^{79} +(-2.05774 + 0.875053i) q^{80} +(1.89146 - 3.27611i) q^{81} +(6.25326 - 3.61032i) q^{82} +(11.7770 - 6.79944i) q^{83} +(-4.49112 - 7.77885i) q^{84} +(2.51013 + 0.306532i) q^{85} +(-0.230984 + 0.400075i) q^{86} +(4.99729 + 2.88519i) q^{87} +(-2.17494 + 1.25570i) q^{88} -13.9990 q^{89} +(5.69083 - 7.56232i) q^{90} +3.57040 q^{91} +4.55942i q^{92} +(8.68086 - 12.2005i) q^{93} -6.54587 q^{94} +(1.85749 - 15.2106i) q^{95} +(-1.34467 + 2.32904i) q^{96} -10.0509i q^{97} +(-3.59845 + 2.07757i) q^{98} +(5.31487 - 9.20563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9	\( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} + 8 q^{15} + 32 q^{16} - 8 q^{19} + 2 q^{20} + 16 q^{21} - 4 q^{24} + 22 q^{25} + 12 q^{26} - 8 q^{29} + 28 q^{30} + 12 q^{31} - 12 q^{34} - 32 q^{35} - 8 q^{36} - 64 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{44} - 24 q^{45} - 8 q^{46} + 20 q^{49} - 40 q^{51} + 8 q^{54} - 8 q^{55} + 16 q^{59} - 8 q^{60} - 40 q^{61} - 32 q^{64} - 6 q^{65} - 24 q^{66} + 36 q^{69} + 36 q^{70} + 48 q^{71} - 28 q^{74} + 8 q^{75} + 8 q^{76} + 4 q^{79} - 2 q^{80} - 32 q^{81} - 16 q^{84} - 84 q^{85} + 12 q^{86} + 72 q^{89} + 40 q^{90} + 24 q^{91} + 16 q^{94} - 48 q^{95} + 4 q^{96} + 64 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 + 8 * q^15 + 32 * q^16 - 8 * q^19 + 2 * q^20 + 16 * q^21 - 4 * q^24 + 22 * q^25 + 12 * q^26 - 8 * q^29 + 28 * q^30 + 12 * q^31 - 12 * q^34 - 32 * q^35 - 8 * q^36 - 64 * q^39 + 4 * q^40 - 16 * q^41 - 4 * q^44 - 24 * q^45 - 8 * q^46 + 20 * q^49 - 40 * q^51 + 8 * q^54 - 8 * q^55 + 16 * q^59 - 8 * q^60 - 40 * q^61 - 32 * q^64 - 6 * q^65 - 24 * q^66 + 36 * q^69 + 36 * q^70 + 48 * q^71 - 28 * q^74 + 8 * q^75 + 8 * q^76 + 4 * q^79 - 2 * q^80 - 32 * q^81 - 16 * q^84 - 84 * q^85 + 12 * q^86 + 72 * q^89 + 40 * q^90 + 24 * q^91 + 16 * q^94 - 48 * q^95 + 4 * q^96 + 64 * q^99

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