LMFDB - Embedded newform 546.2.ch.a.137.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.9
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.238917 - 1.71549i) q^{3} -1.00000i q^{4} +(0.465027 + 0.124604i) q^{5} +(1.38198 + 1.04410i) q^{6} +(-1.66275 + 2.05797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.88584 + 0.819723i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.238917 - 1.71549i) q^{3} -1.00000i q^{4} +(0.465027 + 0.124604i) q^{5} +(1.38198 + 1.04410i) q^{6} +(-1.66275 + 2.05797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.88584 + 0.819723i) q^{9} +(-0.416932 + 0.240716i) q^{10} +(1.51809 - 5.66560i) q^{11} +(-1.71549 + 0.238917i) q^{12} +(-3.55655 - 0.592407i) q^{13} +(-0.279464 - 2.63095i) q^{14} +(0.102654 - 0.827520i) q^{15} -1.00000 q^{16} -0.466653 q^{17} +(1.46096 - 2.62023i) q^{18} +(1.43851 - 0.385448i) q^{19} +(0.124604 - 0.465027i) q^{20} +(3.92770 + 2.36075i) q^{21} +(2.93273 + 5.07964i) q^{22} -0.870719 q^{23} +(1.04410 - 1.38198i) q^{24} +(-4.12940 - 2.38411i) q^{25} +(2.93376 - 2.09597i) q^{26} +(2.09571 + 4.75479i) q^{27} +(2.05797 + 1.66275i) q^{28} +(-7.17817 - 4.14432i) q^{29} +(0.512558 + 0.657732i) q^{30} +(-3.20788 + 0.859548i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-10.0820 - 1.25067i) q^{33} +(0.329973 - 0.329973i) q^{34} +(-1.02965 + 0.749828i) q^{35} +(0.819723 + 2.88584i) q^{36} +(-3.74611 + 3.74611i) q^{37} +(-0.744629 + 1.28974i) q^{38} +(-0.166549 + 6.24278i) q^{39} +(0.240716 + 0.416932i) q^{40} +(-0.926123 - 3.45634i) q^{41} +(-4.44661 + 1.10800i) q^{42} +(-8.93046 + 5.15600i) q^{43} +(-5.66560 - 1.51809i) q^{44} +(-1.44413 + 0.0216075i) q^{45} +(0.615692 - 0.615692i) q^{46} +(1.59337 - 5.94655i) q^{47} +(0.238917 + 1.71549i) q^{48} +(-1.47051 - 6.84380i) q^{49} +(4.60575 - 1.23411i) q^{50} +(0.111492 + 0.800540i) q^{51} +(-0.592407 + 3.55655i) q^{52} +(7.10203 + 4.10036i) q^{53} +(-4.84403 - 1.88026i) q^{54} +(1.41191 - 2.44550i) q^{55} +(-2.63095 + 0.279464i) q^{56} +(-1.00492 - 2.37567i) q^{57} +(8.00621 - 2.14526i) q^{58} +(1.57951 + 1.57951i) q^{59} +(-0.827520 - 0.102654i) q^{60} +(4.06340 - 7.03801i) q^{61} +(1.66052 - 2.87610i) q^{62} +(3.11146 - 7.30197i) q^{63} +1.00000i q^{64} +(-1.58008 - 0.718644i) q^{65} +(8.01341 - 6.24469i) q^{66} +(-1.66153 + 6.20090i) q^{67} +0.466653i q^{68} +(0.208030 + 1.49371i) q^{69} +(0.197867 - 1.25828i) q^{70} +(-5.26585 - 1.41098i) q^{71} +(-2.62023 - 1.46096i) q^{72} +(-3.27021 - 12.2046i) q^{73} -5.29779i q^{74} +(-3.10334 + 7.65357i) q^{75} +(-0.385448 - 1.43851i) q^{76} +(9.13544 + 12.5447i) q^{77} +(-4.29654 - 4.53208i) q^{78} +(4.47389 + 7.74901i) q^{79} +(-0.465027 - 0.124604i) q^{80} +(7.65611 - 4.73117i) q^{81} +(3.09887 + 1.78913i) q^{82} +(10.5966 - 10.5966i) q^{83} +(2.36075 - 3.92770i) q^{84} +(-0.217006 - 0.0581466i) q^{85} +(2.66894 - 9.96064i) q^{86} +(-5.39456 + 13.3043i) q^{87} +(5.07964 - 2.93273i) q^{88} +(-4.10253 - 4.10253i) q^{89} +(1.00588 - 1.03643i) q^{90} +(7.13282 - 6.33426i) q^{91} +0.870719i q^{92} +(2.24097 + 5.29773i) q^{93} +(3.07816 + 5.33153i) q^{94} +0.716975 q^{95} +(-1.38198 - 1.04410i) q^{96} +(1.48697 - 5.54945i) q^{97} +(5.87911 + 3.79949i) q^{98} +(0.263252 + 17.5944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.238917	−	1.71549i	−0.137939	−	0.990441i
$3$	−0.238917	−	1.71549i	−0.137939	−	0.990441i
$4$		−	1.00000i		−	0.500000i
$5$	0.465027	+	0.124604i	0.207966	+	0.0557244i	0.361298	−	0.932450i	$-0.382334\pi$
$5$	0.465027	+	0.124604i	0.207966	+	0.0557244i	−0.153332	+	0.988175i	$0.549000\pi$
$6$	1.38198	+	1.04410i	0.564190	+	0.426251i
$7$	−1.66275	+	2.05797i	−0.628461	+	0.777841i
$7$	−1.66275	+	2.05797i	−0.628461	+	0.777841i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.88584	+	0.819723i	−0.961946	+	0.273241i
$10$	−0.416932	+	0.240716i	−0.131845	+	0.0761209i
$11$	1.51809	−	5.66560i	0.457722	−	1.70824i	−0.222237	−	0.974993i	$-0.571336\pi$
$11$	1.51809	−	5.66560i	0.457722	−	1.70824i	0.679959	−	0.733250i	$-0.261997\pi$
$12$	−1.71549	+	0.238917i	−0.495220	+	0.0689695i
$13$	−3.55655	−	0.592407i	−0.986410	−	0.164304i
$13$	−3.55655	−	0.592407i	−0.986410	−	0.164304i
$14$	−0.279464	−	2.63095i	−0.0746899	−	0.703151i
$15$	0.102654	−	0.827520i	0.0265050	−	0.213665i
$16$	−1.00000			−0.250000
$17$	−0.466653			−0.113180			−0.0565900	−	0.998398i	$-0.518023\pi$
$17$	−0.466653			−0.113180			−0.0565900	+	0.998398i	$0.518023\pi$
$18$	1.46096	−	2.62023i	0.344352	−	0.617593i
$19$	1.43851	−	0.385448i	0.330018	−	0.0884279i	−0.0900058	−	0.995941i	$-0.528689\pi$
$19$	1.43851	−	0.385448i	0.330018	−	0.0884279i	0.420023	+	0.907513i	$0.362022\pi$
$20$	0.124604	−	0.465027i	0.0278622	−	0.103983i
$21$	3.92770	+	2.36075i	0.857095	+	0.515159i
$22$	2.93273	+	5.07964i	0.625260	+	1.08298i
$23$	−0.870719			−0.181558			−0.0907788	−	0.995871i	$-0.528936\pi$
$23$	−0.870719			−0.181558			−0.0907788	+	0.995871i	$0.528936\pi$
$24$	1.04410	−	1.38198i	0.213125	−	0.282095i
$25$	−4.12940	−	2.38411i	−0.825881	−	0.476822i
$26$	2.93376	−	2.09597i	0.575357	−	0.411053i
$27$	2.09571	+	4.75479i	0.403319	+	0.915060i
$28$	2.05797	+	1.66275i	0.388920	+	0.314231i
$29$	−7.17817	−	4.14432i	−1.33295	−	0.769580i	−0.347201	−	0.937791i	$-0.612868\pi$
$29$	−7.17817	−	4.14432i	−1.33295	−	0.769580i	−0.985751	+	0.168210i	$0.946201\pi$
$30$	0.512558	+	0.657732i	0.0935799	+	0.120085i
$31$	−3.20788	+	0.859548i	−0.576152	+	0.154379i	−0.535116	−	0.844778i	$-0.679732\pi$
$31$	−3.20788	+	0.859548i	−0.576152	+	0.154379i	−0.0410352	+	0.999158i	$0.513066\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−10.0820	−	1.25067i	−1.75505	−	0.217713i
$34$	0.329973	−	0.329973i	0.0565900	−	0.0565900i
$35$	−1.02965	+	0.749828i	−0.174043	+	0.126744i
$36$	0.819723	+	2.88584i	0.136620	+	0.480973i
$37$	−3.74611	+	3.74611i	−0.615856	+	0.615856i	−0.944466	−	0.328610i	$-0.893420\pi$
$37$	−3.74611	+	3.74611i	−0.615856	+	0.615856i	0.328610	+	0.944466i	$0.393420\pi$
$38$	−0.744629	+	1.28974i	−0.120795	+	0.209223i
$39$	−0.166549	+	6.24278i	−0.0266692	+	0.999644i
$40$	0.240716	+	0.416932i	0.0380605	+	0.0659227i
$41$	−0.926123	−	3.45634i	−0.144636	−	0.539789i	−0.999771	−	0.0213843i	$-0.993193\pi$
$41$	−0.926123	−	3.45634i	−0.144636	−	0.539789i	0.855135	−	0.518405i	$-0.173474\pi$
$42$	−4.44661	+	1.10800i	−0.686127	+	0.170968i
$43$	−8.93046	+	5.15600i	−1.36188	+	0.786283i	−0.989874	−	0.141946i	$-0.954664\pi$
$43$	−8.93046	+	5.15600i	−1.36188	+	0.786283i	−0.372008	+	0.928229i	$0.621331\pi$
$44$	−5.66560	−	1.51809i	−0.854121	−	0.228861i
$45$	−1.44413	+	0.0216075i	−0.215278	+	0.00322105i
$46$	0.615692	−	0.615692i	0.0907788	−	0.0907788i
$47$	1.59337	−	5.94655i	0.232417	−	0.867393i	−0.746879	−	0.664960i	$-0.768449\pi$
$47$	1.59337	−	5.94655i	0.232417	−	0.867393i	0.979296	−	0.202433i	$-0.0648848\pi$
$48$	0.238917	+	1.71549i	0.0344848	+	0.247610i
$49$	−1.47051	−	6.84380i	−0.210073	−	0.977686i
$50$	4.60575	−	1.23411i	0.651352	−	0.174529i
$51$	0.111492	+	0.800540i	0.0156119	+	0.112098i
$52$	−0.592407	+	3.55655i	−0.0821521	+	0.493205i
$53$	7.10203	+	4.10036i	0.975538	+	0.563227i	0.900920	−	0.433985i	$-0.142893\pi$
$53$	7.10203	+	4.10036i	0.975538	+	0.563227i	0.0746181	+	0.997212i	$0.476226\pi$
$54$	−4.84403	−	1.88026i	−0.659189	−	0.255870i
$55$	1.41191	−	2.44550i	0.190382	−	0.329751i
$56$	−2.63095	+	0.279464i	−0.351576	+	0.0373450i
$57$	−1.00492	−	2.37567i	−0.133105	−	0.314665i
$58$	8.00621	−	2.14526i	1.05127	−	0.281686i
$59$	1.57951	+	1.57951i	0.205635	+	0.205635i	0.802409	−	0.596774i	$-0.203551\pi$
$59$	1.57951	+	1.57951i	0.205635	+	0.205635i	−0.596774	+	0.802409i	$0.703551\pi$
$60$	−0.827520	−	0.102654i	−0.106832	−	0.0132525i
$61$	4.06340	−	7.03801i	0.520265	−	0.901125i	−0.479458	−	0.877565i	$-0.659167\pi$
$61$	4.06340	−	7.03801i	0.520265	−	0.901125i	0.999722	−	0.0235600i	$-0.00750009\pi$
$62$	1.66052	−	2.87610i	0.210886	−	0.365265i
$63$	3.11146	−	7.30197i	0.392007	−	0.919962i
$64$			1.00000i			0.125000i
$65$	−1.58008	−	0.718644i	−0.195984	−	0.0891368i
$66$	8.01341	−	6.24469i	0.986382	−	0.768669i
$67$	−1.66153	+	6.20090i	−0.202988	+	0.757561i	0.787066	+	0.616869i	$0.211599\pi$
$67$	−1.66153	+	6.20090i	−0.202988	+	0.757561i	−0.990053	+	0.140691i	$0.955067\pi$
$68$			0.466653i			0.0565900i
$69$	0.208030	+	1.49371i	0.0250439	+	0.179822i
$70$	0.197867	−	1.25828i	0.0236497	−	0.150394i
$71$	−5.26585	−	1.41098i	−0.624941	−	0.167452i	−0.0675680	−	0.997715i	$-0.521524\pi$
$71$	−5.26585	−	1.41098i	−0.624941	−	0.167452i	−0.557373	+	0.830262i	$0.688191\pi$
$72$	−2.62023	−	1.46096i	−0.308797	−	0.172176i
$73$	−3.27021	−	12.2046i	−0.382750	−	1.42844i	−0.841684	−	0.539971i	$-0.818435\pi$
$73$	−3.27021	−	12.2046i	−0.382750	−	1.42844i	0.458934	−	0.888470i	$-0.348231\pi$
$74$		−	5.29779i		−	0.615856i
$75$	−3.10334	+	7.65357i	−0.358343	+	0.883758i
$76$	−0.385448	−	1.43851i	−0.0442140	−	0.165009i
$77$	9.13544	+	12.5447i	1.04108	+	1.42960i
$78$	−4.29654	−	4.53208i	−0.486488	−	0.513157i
$79$	4.47389	+	7.74901i	0.503352	+	0.871832i	0.999992	+	0.00387539i	$0.00123358\pi$
$79$	4.47389	+	7.74901i	0.503352	+	0.871832i	−0.496640	+	0.867957i	$0.665433\pi$
$80$	−0.465027	−	0.124604i	−0.0519916	−	0.0139311i
$81$	7.65611	−	4.73117i	0.850679	−	0.525686i
$82$	3.09887	+	1.78913i	0.342213	+	0.197577i
$83$	10.5966	−	10.5966i	1.16313	−	1.16313i	0.179341	−	0.983787i	$-0.442604\pi$
$83$	10.5966	−	10.5966i	1.16313	−	1.16313i	0.983787	−	0.179341i	$-0.0573965\pi$
$84$	2.36075	−	3.92770i	0.257579	−	0.428547i
$85$	−0.217006	−	0.0581466i	−0.0235376	−	0.00630689i
$86$	2.66894	−	9.96064i	0.287800	−	1.07408i
$87$	−5.39456	+	13.3043i	−0.578358	+	1.42637i
$88$	5.07964	−	2.93273i	0.541491	−	0.312630i
$89$	−4.10253	−	4.10253i	−0.434867	−	0.434867i	0.455413	−	0.890280i	$-0.349492\pi$
$89$	−4.10253	−	4.10253i	−0.434867	−	0.434867i	−0.890280	+	0.455413i	$0.849492\pi$
$90$	1.00588	−	1.03643i	0.106029	−	0.109250i
$91$	7.13282	−	6.33426i	0.747723	−	0.664011i
$92$			0.870719i			0.0907788i
$93$	2.24097	+	5.29773i	0.232377	+	0.549349i
$94$	3.07816	+	5.33153i	0.317488	+	0.549905i
$95$	0.716975			0.0735601
$96$	−1.38198	−	1.04410i	−0.141047	−	0.106563i
$97$	1.48697	−	5.54945i	0.150979	−	0.563462i	−0.848437	−	0.529296i	$-0.822456\pi$
$97$	1.48697	−	5.54945i	0.150979	−	0.563462i	0.999416	−	0.0341654i	$-0.0108773\pi$
$98$	5.87911	+	3.79949i	0.593879	+	0.383806i
$99$	0.263252	+	17.5944i	0.0264578	+	1.76830i
$100$	−2.38411	+	4.12940i	−0.238411	+	0.412940i
$101$	5.17260	+	8.95921i	0.514693	+	0.891474i	0.999855	+	0.0170499i	$0.00542740\pi$
$101$	5.17260	+	8.95921i	0.514693	+	0.891474i	−0.485162	+	0.874424i	$0.661239\pi$
$102$	−0.644904	−	0.487231i	−0.0638550	−	0.0482431i
$103$	4.27173	−	2.46629i	0.420906	−	0.243010i	−0.274559	−	0.961570i	$-0.588532\pi$
$103$	4.27173	−	2.46629i	0.420906	−	0.243010i	0.695465	+	0.718560i	$0.255198\pi$
$104$	−2.09597	−	2.93376i	−0.205526	−	0.287678i
$105$	1.53233	+	1.58722i	0.149540	+	0.154897i
$106$	−7.92128	+	2.12250i	−0.769383	+	0.206155i
$107$			9.69164i			0.936926i	0.883483	+	0.468463i	$0.155192\pi$
$107$			9.69164i			0.936926i	−0.883483	+	0.468463i	$0.844808\pi$
$108$	4.75479	−	2.09571i	0.457530	−	0.201659i
$109$	−2.62265	+	0.702737i	−0.251204	+	0.0673100i	−0.382224	−	0.924070i	$-0.624842\pi$
$109$	−2.62265	+	0.702737i	−0.251204	+	0.0673100i	0.131019	+	0.991380i	$0.458175\pi$
$110$	0.730857	+	2.72760i	0.0696845	+	0.260066i
$111$	7.32143	+	5.53141i	0.694919	+	0.525018i
$112$	1.66275	−	2.05797i	0.157115	−	0.194460i
$113$	−2.25886	+	1.30415i	−0.212496	+	0.122684i	−0.602471	−	0.798141i	$-0.705817\pi$
$113$	−2.25886	+	1.30415i	−0.212496	+	0.122684i	0.389975	+	0.920825i	$0.372484\pi$
$114$	2.39044	+	0.969266i	0.223885	+	0.0907801i
$115$	−0.404908	−	0.108495i	−0.0377578	−	0.0101172i
$116$	−4.14432	+	7.17817i	−0.384790	+	0.666476i
$117$	10.7492	−	1.20579i	0.993767	−	0.111476i
$118$	−2.23377			−0.205635
$119$	0.775928	−	0.960360i	0.0711292	−	0.0880360i
$120$	0.657732	−	0.512558i	0.0600425	−	0.0467900i
$121$	−20.2681	−	11.7018i	−1.84256	−	1.06380i
$122$	2.10337	+	7.84988i	0.190430	+	0.710695i
$123$	−5.70806	+	2.41454i	−0.514678	+	0.217712i
$124$	0.859548	+	3.20788i	0.0771897	+	0.288076i
$125$	−3.32533	−	3.32533i	−0.297427	−	0.297427i
$126$	2.96314	+	7.36341i	0.263977	+	0.655985i
$127$	18.5098	+	10.6866i	1.64248	+	0.948286i	0.979948	+	0.199252i	$0.0638511\pi$
$127$	18.5098	+	10.6866i	1.64248	+	0.948286i	0.662531	+	0.749034i	$0.269482\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	10.9787	+	14.0883i	0.966624	+	1.24040i
$130$	1.62544	−	0.609124i	0.142561	−	0.0534237i
$131$	14.4191	−	8.32490i	1.25981	−	0.727350i	0.286770	−	0.957999i	$-0.407418\pi$
$131$	14.4191	−	8.32490i	1.25981	−	0.727350i	0.973037	+	0.230650i	$0.0740851\pi$
$132$	−1.25067	+	10.0820i	−0.108857	+	0.877525i
$133$	−1.59865	+	3.60133i	−0.138620	+	0.312275i
$134$	−3.20982	−	5.55958i	−0.277286	−	0.480274i
$135$	0.382096	+	2.47224i	0.0328856	+	0.212776i
$136$	−0.329973	−	0.329973i	−0.0282950	−	0.0282950i
$137$	−9.42959	−	9.42959i	−0.805624	−	0.805624i	0.178344	−	0.983968i	$-0.442926\pi$
$137$	−9.42959	−	9.42959i	−0.805624	−	0.805624i	−0.983968	+	0.178344i	$0.942926\pi$
$138$	−1.20331	−	0.909116i	−0.102433	−	0.0773891i
$139$	−0.972392	−	1.68423i	−0.0824772	−	0.142855i	0.821836	−	0.569724i	$-0.192950\pi$
$139$	−0.972392	−	1.68423i	−0.0824772	−	0.142855i	−0.904313	+	0.426869i	$0.859617\pi$
$140$	0.749828	+	1.02965i	0.0633720	+	0.0870217i
$141$	−10.5819	−	1.31269i	−0.891161	−	0.110548i
$142$	4.72123	−	2.72580i	0.396197	−	0.228744i
$143$	−8.75552	+	19.2507i	−0.732173	+	1.60982i
$144$	2.88584	−	0.819723i	0.240486	−	0.0683102i
$145$	−2.82164	−	2.82164i	−0.234325	−	0.234325i
$146$	10.9424	+	6.31757i	0.905595	+	0.522846i
$147$	−11.3892	+	4.15776i	−0.939362	+	0.342926i
$148$	3.74611	+	3.74611i	0.307928	+	0.307928i
$149$	−0.773564	−	2.88698i	−0.0633728	−	0.236511i	0.926973	−	0.375127i	$-0.122401\pi$
$149$	−0.773564	−	2.88698i	−0.0633728	−	0.236511i	−0.990346	+	0.138617i	$0.955734\pi$
$150$	−3.21750	−	7.60629i	−0.262708	−	0.621051i
$151$	−2.87663	−	10.7357i	−0.234097	−	0.873661i	−0.978554	−	0.205991i	$-0.933958\pi$
$151$	−2.87663	−	10.7357i	−0.234097	−	0.873661i	0.744457	−	0.667670i	$-0.232708\pi$
$152$	1.28974	+	0.744629i	0.104611	+	0.0603974i
$153$	1.34668	−	0.382526i	0.108873	−	0.0309254i
$154$	−15.3302	−	2.41070i	−1.23534	−	0.194259i
$155$	−1.59885			−0.128423
$156$	6.24278	+	0.166549i	0.499822	+	0.0133346i
$157$	2.47257	−	4.28261i	0.197332	−	0.341790i	−0.750330	−	0.661063i	$-0.770106\pi$
$157$	2.47257	−	4.28261i	0.197332	−	0.341790i	0.947663	+	0.319274i	$0.103439\pi$
$158$	−8.64290	−	2.31586i	−0.687592	−	0.184240i
$159$	5.33734	−	13.1631i	0.423278	−	1.04390i
$160$	0.416932	−	0.240716i	0.0329613	−	0.0190302i
$161$	1.44779	−	1.79192i	0.114102	−	0.141223i
$162$	−2.06824	+	8.75913i	−0.162497	+	0.688182i
$163$	−0.247423	−	0.923396i	−0.0193797	−	0.0723260i	0.955559	−	0.294801i	$-0.0952532\pi$
$163$	−0.247423	−	0.923396i	−0.0193797	−	0.0723260i	−0.974938	+	0.222475i	$0.928587\pi$
$164$	−3.45634	+	0.926123i	−0.269895	+	0.0723181i
$165$	−4.53256	−	1.83785i	−0.352859	−	0.143076i
$166$			14.9859i			1.16313i
$167$	21.7807	−	5.83613i	1.68544	−	0.451614i	0.716237	−	0.697857i	$-0.245863\pi$
$167$	21.7807	−	5.83613i	1.68544	−	0.451614i	0.969208	+	0.246244i	$0.0791964\pi$
$168$	1.10800	+	4.44661i	0.0854840	+	0.343063i
$169$	12.2981	+	4.21385i	0.946008	+	0.324143i
$170$	0.194562	−	0.112331i	0.0149223	−	0.00861537i
$171$	−3.83535	+	2.29152i	−0.293297	+	0.175237i
$172$	5.15600	+	8.93046i	0.393142	+	0.680941i
$173$	−0.155408	+	0.269175i	−0.0118155	+	0.0204650i	−0.871873	−	0.489733i	$-0.837094\pi$
$173$	−0.155408	+	0.269175i	−0.0118155	+	0.0204650i	0.860057	+	0.510198i	$0.170428\pi$
$174$	−5.59300	−	13.2221i	−0.424004	−	1.00236i
$175$	11.7726	−	4.53402i	0.889926	−	0.342739i
$176$	−1.51809	+	5.66560i	−0.114431	+	0.427061i
$177$	2.33227	−	3.08702i	0.175304	−	0.232035i
$178$	5.80185			0.434867
$179$	6.50022	+	11.2587i	0.485849	+	0.841515i	0.999868	−	0.0162637i	$-0.00517712\pi$
$179$	6.50022	+	11.2587i	0.485849	+	0.841515i	−0.514019	+	0.857779i	$0.671844\pi$
$180$	0.0216075	+	1.44413i	0.00161052	+	0.107639i
$181$			20.2009i			1.50152i	0.660576	+	0.750759i	$0.270312\pi$
$181$			20.2009i			1.50152i	−0.660576	+	0.750759i	$0.729688\pi$
$182$	−0.564666	+	9.52267i	−0.0418558	+	0.705867i
$183$	−13.0445	−	5.28923i	−0.964276	−	0.390991i
$184$	−0.615692	−	0.615692i	−0.0453894	−	0.0453894i
$185$	−2.20882	+	1.27526i	−0.162395	+	0.0937591i
$186$	−5.33066	−	2.16146i	−0.390863	−	0.158486i
$187$	−0.708423	+	2.64387i	−0.0518050	+	0.193339i
$188$	−5.94655	−	1.59337i	−0.433697	−	0.116209i
$189$	−13.2699	−	3.59313i	−0.965241	−	0.261362i
$190$	−0.506978	+	0.506978i	−0.0367801	+	0.0367801i
$191$	−23.2797	−	13.4406i	−1.68446	−	0.972524i	−0.958631	−	0.284650i	$-0.908123\pi$
$191$	−23.2797	−	13.4406i	−1.68446	−	0.972524i	−0.725830	−	0.687874i	$-0.758544\pi$
$192$	1.71549	−	0.238917i	0.123805	−	0.0172424i
$193$	11.6471	+	3.12084i	0.838378	+	0.224643i	0.652365	−	0.757905i	$-0.273777\pi$
$193$	11.6471	+	3.12084i	0.838378	+	0.224643i	0.186013	+	0.982547i	$0.440443\pi$
$194$	2.87261	+	4.97550i	0.206241	+	0.357220i
$195$	−0.855322	+	2.88231i	−0.0612509	+	0.206406i
$196$	−6.84380	+	1.47051i	−0.488843	+	0.105037i
$197$	1.82790	+	6.82183i	0.130233	+	0.486035i	0.999972	−	0.00747630i	$-0.00237980\pi$
$197$	1.82790	+	6.82183i	0.130233	+	0.486035i	−0.869739	+	0.493511i	$0.835713\pi$
$198$	−12.6273	−	12.2550i	−0.897381	−	0.870924i
$199$			17.8369i			1.26442i	0.774796	+	0.632211i	$0.217852\pi$
$199$			17.8369i			1.26442i	−0.774796	+	0.632211i	$0.782148\pi$
$200$	−1.23411	−	4.60575i	−0.0872646	−	0.325676i
$201$	11.0346	+	1.36883i	0.778319	+	0.0965502i
$202$	−9.99270	−	2.67753i	−0.703084	−	0.188391i
$203$	20.4644	−	7.88151i	1.43632	−	0.553174i
$204$	0.800540	−	0.111492i	0.0560490	−	0.00780597i
$205$		−	1.72269i		−	0.120318i
$206$	−1.27664	+	4.76450i	−0.0889480	+	0.331958i
$207$	2.51275	−	0.713748i	0.174648	−	0.0496089i
$208$	3.55655	+	0.592407i	0.246602	+	0.0410761i
$209$		−	8.73519i		−	0.604226i
$210$	−2.20585	−	0.0388143i	−0.152218	−	0.00267844i
$211$	13.3383	−	23.1026i	0.918246	−	1.59045i	0.116167	−	0.993230i	$-0.462939\pi$
$211$	13.3383	−	23.1026i	0.918246	−	1.59045i	0.802079	−	0.597218i	$-0.203727\pi$
$212$	4.10036	−	7.10203i	0.281614	−	0.487769i
$213$	−1.16242	+	9.37063i	−0.0796479	+	0.642065i
$214$	−6.85302	−	6.85302i	−0.468463	−	0.468463i
$215$	−4.79536	+	1.28491i	−0.327041	+	0.0876303i
$216$	−1.88026	+	4.84403i	−0.127935	+	0.329595i
$217$	3.56497	−	8.03094i	0.242006	−	0.545176i
$218$	1.35758	−	2.35140i	0.0919472	−	0.159257i
$219$	−20.1556	+	8.52593i	−1.36199	+	0.576129i
$220$	−2.44550	−	1.41191i	−0.164875	−	0.0951908i
$221$	1.65967	+	0.276449i	0.111642	+	0.0185959i
$222$	−9.08833	+	1.26574i	−0.609969	+	0.0849506i
$223$	9.10841	−	2.44059i	0.609944	−	0.163434i	0.0593918	−	0.998235i	$-0.481084\pi$
$223$	9.10841	−	2.44059i	0.609944	−	0.163434i	0.550552	+	0.834801i	$0.314417\pi$
$224$	0.279464	+	2.63095i	0.0186725	+	0.175788i
$225$	13.8711	+	3.49519i	0.924740	+	0.233013i
$226$	0.675079	−	2.51943i	0.0449056	−	0.167590i
$227$	−2.60795	+	2.60795i	−0.173096	+	0.173096i	−0.788338	−	0.615242i	$-0.789058\pi$
$227$	−2.60795	+	2.60795i	−0.173096	+	0.173096i	0.615242	+	0.788338i	$0.289058\pi$
$228$	−2.37567	+	1.00492i	−0.157333	+	0.0665525i
$229$	−11.6394	−	3.11877i	−0.769154	−	0.206094i	−0.147156	−	0.989113i	$-0.547012\pi$
$229$	−11.6394	−	3.11877i	−0.769154	−	0.206094i	−0.621998	+	0.783019i	$0.713679\pi$
$230$	0.363030	−	0.209596i	0.0239375	−	0.0138203i
$231$	19.3377	−	18.6689i	1.27233	−	1.22833i
$232$	−2.14526	−	8.00621i	−0.140843	−	0.525633i
$233$	4.38097	+	7.58807i	0.287007	+	0.497111i	0.973094	−	0.230409i	$-0.0740063\pi$
$233$	4.38097	+	7.58807i	0.287007	+	0.497111i	−0.686087	+	0.727520i	$0.740673\pi$
$234$	−6.74823	+	8.45348i	−0.441146	+	0.552621i
$235$	1.48192	−	2.56676i	0.0966699	−	0.167437i
$236$	1.57951	−	1.57951i	0.102818	−	0.102818i
$237$	12.2245	−	9.52631i	0.794066	−	0.618800i
$238$	0.130413	+	1.22774i	0.00845340	+	0.0795826i
$239$	−4.62329	+	4.62329i	−0.299056	+	0.299056i	−0.840644	−	0.541588i	$-0.817823\pi$
$239$	−4.62329	+	4.62329i	−0.299056	+	0.299056i	0.541588	+	0.840644i	$0.317823\pi$
$240$	−0.102654	+	0.827520i	−0.00662626	+	0.0534162i
$241$	15.2624	−	15.2624i	0.983136	−	0.983136i	−0.0167243	−	0.999860i	$-0.505324\pi$
$241$	15.2624	−	15.2624i	0.983136	−	0.983136i	0.999860	+	0.0167243i	$0.00532374\pi$
$242$	22.6062	−	6.05730i	1.45318	−	0.389378i
$243$	−9.94547	−	12.0036i	−0.638002	−	0.770034i
$244$	−7.03801	−	4.06340i	−0.450563	−	0.260132i
$245$	0.168934	−	3.36578i	0.0107928	−	0.215032i
$246$	2.32887	−	5.74354i	0.148483	−	0.366195i
$247$	−5.34449	+	0.518681i	−0.340062	+	0.0330029i
$248$	−2.87610	−	1.66052i	−0.182633	−	0.105443i
$249$	−20.7101	−	15.6467i	−1.31245	−	0.991568i
$250$	4.70273			0.297427
$251$	−5.29381	−	9.16914i	−0.334142	−	0.578751i	0.649177	−	0.760637i	$-0.275113\pi$
$251$	−5.29381	−	9.16914i	−0.334142	−	0.578751i	−0.983320	+	0.181886i	$0.941780\pi$
$252$	−7.30197	−	3.11146i	−0.459981	−	0.196004i
$253$	−1.32183	+	4.93315i	−0.0831029	+	0.310144i
$254$	−20.6450	+	5.53181i	−1.29538	+	0.347097i
$255$	−0.0479036	+	0.386165i	−0.00299984	+	0.0241826i
$256$	1.00000			0.0625000
$257$	−29.5740			−1.84478			−0.922389	−	0.386263i	$-0.873766\pi$
$257$	−29.5740			−1.84478			−0.922389	+	0.386263i	$0.873766\pi$
$258$	−17.7251	−	2.19879i	−1.10351	−	0.136891i
$259$	−1.48054	−	13.9382i	−0.0919965	−	0.866080i
$260$	−0.718644	+	1.58008i	−0.0445684	+	0.0979921i
$261$	24.1122	+	6.07572i	1.49251	+	0.376077i
$262$	−4.30928	+	16.0825i	−0.266229	+	0.993578i
$263$	6.83072	−	3.94372i	0.421200	−	0.243180i	−0.274390	−	0.961618i	$-0.588476\pi$
$263$	6.83072	−	3.94372i	0.421200	−	0.243180i	0.695591	+	0.718438i	$0.255143\pi$
$264$	−6.24469	−	8.01341i	−0.384334	−	0.493191i
$265$	2.79171	+	2.79171i	0.171494	+	0.171494i
$266$	−1.41611	−	3.67694i	−0.0868272	−	0.225448i
$267$	−6.05769	+	8.01802i	−0.370725	+	0.490695i
$268$	6.20090	+	1.66153i	0.378780	+	0.101494i
$269$		−	29.7845i		−	1.81599i	−0.418980	−	0.907995i	$-0.637612\pi$
$269$		−	29.7845i		−	1.81599i	0.418980	−	0.907995i	$-0.362388\pi$
$270$	−2.01832	−	1.47795i	−0.122831	−	0.0899453i
$271$	−6.07406	+	6.07406i	−0.368973	+	0.368973i	−0.867103	−	0.498130i	$-0.834020\pi$
$271$	−6.07406	+	6.07406i	−0.368973	+	0.368973i	0.498130	+	0.867103i	$0.334020\pi$
$272$	0.466653			0.0282950
$273$	−12.5705	−	10.7229i	−0.760804	−	0.648982i
$274$	13.3355			0.805624
$275$	−19.7762	+	19.7762i	−1.19255	+	1.19255i
$276$	1.49371	−	0.208030i	0.0899110	−	0.0125219i
$277$			6.35459i			0.381810i	0.981608	+	0.190905i	$0.0611423\pi$
$277$			6.35459i			0.381810i	−0.981608	+	0.190905i	$0.938858\pi$
$278$	1.87852	+	0.503347i	0.112666	+	0.0301888i
$279$	8.55282	−	5.11008i	0.512044	−	0.305933i
$280$	−1.25828	−	0.197867i	−0.0751969	−	0.0118248i
$281$	0.464005	+	0.464005i	0.0276802	+	0.0276802i	0.720811	−	0.693131i	$-0.243769\pi$
$281$	0.464005	+	0.464005i	0.0276802	+	0.0276802i	−0.693131	+	0.720811i	$0.743769\pi$
$282$	8.41078	−	6.55436i	0.500854	−	0.390306i
$283$	−16.8193	+	9.71061i	−0.999802	+	0.577236i	−0.908190	−	0.418559i	$-0.862535\pi$
$283$	−16.8193	+	9.71061i	−0.999802	+	0.577236i	−0.0916124	+	0.995795i	$0.529202\pi$
$284$	−1.41098	+	5.26585i	−0.0837262	+	0.312470i
$285$	−0.171298	−	1.22997i	−0.0101468	−	0.0728569i
$286$	−7.42119	−	19.8034i	−0.438824	−	1.17100i
$287$	8.65297	+	3.84110i	0.510768	+	0.226733i
$288$	−1.46096	+	2.62023i	−0.0860881	+	0.154398i
$289$	−16.7822			−0.987190
$290$	3.99041			0.234325
$291$	−9.87531	−	1.22503i	−0.578901	−	0.0718125i
$292$	−12.2046	+	3.27021i	−0.714221	+	0.191375i
$293$	3.42855	−	12.7955i	0.200298	−	0.747523i	−0.790533	−	0.612419i	$-0.790197\pi$
$293$	3.42855	−	12.7955i	0.200298	−	0.747523i	0.990831	−	0.135104i	$-0.0431368\pi$
$294$	5.11338	−	10.9933i	0.298218	−	0.641144i
$295$	0.537703	+	0.931330i	0.0313063	+	0.0542241i
$296$	−5.29779			−0.307928
$297$	30.1202	−	4.65522i	1.74775	−	0.270123i
$298$	2.58840	+	1.49441i	0.149942	+	0.0865689i
$299$	3.09676	+	0.515820i	0.179090	+	0.0298307i
$300$	7.65357	+	3.10334i	0.441879	+	0.179172i
$301$	4.23822	−	26.9518i	0.244287	−	1.55348i
$302$	9.62539	+	5.55722i	0.553879	+	0.319782i
$303$	14.1336	−	11.0141i	0.811956	−	0.632742i
$304$	−1.43851	+	0.385448i	−0.0825044	+	0.0221070i
$305$	2.76655	−	2.76655i	0.158412	−	0.158412i
$306$	−0.681763	+	1.22274i	−0.0389738	+	0.0698992i
$307$	−2.72810	+	2.72810i	−0.155701	+	0.155701i	−0.780659	−	0.624958i	$-0.785116\pi$
$307$	−2.72810	+	2.72810i	−0.155701	+	0.155701i	0.624958	+	0.780659i	$0.285116\pi$
$308$	12.5447	−	9.13544i	0.714800	−	0.520540i
$309$	−5.25149	−	6.73889i	−0.298747	−	0.383362i
$310$	1.13056	−	1.13056i	0.0642114	−	0.0642114i
$311$	−15.3393	+	26.5685i	−0.869814	+	1.50656i	−0.00762716	+	0.999971i	$0.502428\pi$
$311$	−15.3393	+	26.5685i	−0.869814	+	1.50656i	−0.862187	+	0.506591i	$0.830906\pi$
$312$	−4.53208	+	4.29654i	−0.256578	+	0.243244i
$313$	−9.21751	−	15.9652i	−0.521005	−	0.902406i	−0.999702	−	0.0244263i	$-0.992224\pi$
$313$	−9.21751	−	15.9652i	−0.521005	−	0.902406i	0.478697	−	0.877980i	$-0.341109\pi$
$314$	1.27989	+	4.77663i	0.0722286	+	0.269561i
$315$	2.35677	−	3.00791i	0.132789	−	0.169477i
$316$	7.74901	−	4.47389i	0.435916	−	0.251676i
$317$	−29.7506	−	7.97165i	−1.67096	−	0.447733i	−0.705592	−	0.708619i	$-0.749319\pi$
$317$	−29.7506	−	7.97165i	−1.67096	−	0.447733i	−0.965370	+	0.260886i	$0.915985\pi$
$318$	5.53367	+	13.0818i	0.310313	+	0.733591i
$319$	−34.3772	+	34.3772i	−1.92475	+	1.92475i
$320$	−0.124604	+	0.465027i	−0.00696555	+	0.0259958i
$321$	16.6259	−	2.31550i	0.927970	−	0.129239i
$322$	0.243335	+	2.29082i	0.0135605	+	0.127662i
$323$	−0.671286	+	0.179871i	−0.0373514	+	0.0100083i
$324$	−4.73117	−	7.65611i	−0.262843	−	0.425339i
$325$	13.2741	+	10.9255i	0.736313	+	0.606038i
$326$	0.827894	+	0.477985i	0.0458528	+	0.0264731i
$327$	1.83214	+	4.33124i	0.101317	+	0.239518i
$328$	1.78913	−	3.09887i	0.0987883	−	0.171106i
$329$	9.58846	+	13.1668i	0.528629	+	0.725906i
$330$	4.50456	−	1.90545i	0.247968	−	0.104892i
$331$	10.2561	−	2.74812i	0.563727	−	0.151050i	0.0343091	−	0.999411i	$-0.489077\pi$
$331$	10.2561	−	2.74812i	0.563727	−	0.151050i	0.529418	+	0.848361i	$0.322410\pi$
$332$	−10.5966	−	10.5966i	−0.581564	−	0.581564i
$333$	7.73988	−	13.8814i	0.424143	−	0.760697i
$334$	−11.2745	+	19.5281i	−0.616916	+	1.06853i
$335$	−1.54531	+	2.67655i	−0.0844292	+	0.146236i
$336$	−3.92770	−	2.36075i	−0.214274	−	0.128790i
$337$		−	17.3642i		−	0.945889i	−0.881092	−	0.472944i	$-0.843191\pi$
$337$		−	17.3642i		−	0.945889i	0.881092	−	0.472944i	$-0.156809\pi$
$338$	−11.6757	+	5.71643i	−0.635075	+	0.310933i
$339$	2.77695	+	3.56347i	0.150823	+	0.193541i
$340$	−0.0581466	+	0.217006i	−0.00315344	+	0.0117688i
$341$			19.4794i			1.05487i
$342$	1.09165	−	4.33236i	0.0590298	−	0.234267i
$343$	16.5295	+	8.35326i	0.892507	+	0.451034i
$344$	−9.96064	−	2.66894i	−0.537041	−	0.143900i
$345$	−0.0893825	+	0.720538i	−0.00481219	+	0.0387925i
$346$	−0.0804451	−	0.300225i	−0.00432476	−	0.0161402i
$347$			0.197192i			0.0105858i	0.999986	+	0.00529292i	$0.00168480\pi$
$347$			0.197192i			0.0105858i	−0.999986	+	0.00529292i	$0.998315\pi$
$348$	13.3043	+	5.39456i	0.713183	+	0.289179i
$349$	4.40329	+	16.4333i	0.235703	+	0.879654i	0.977831	+	0.209396i	$0.0671498\pi$
$349$	4.40329	+	16.4333i	0.235703	+	0.879654i	−0.742128	+	0.670258i	$0.766184\pi$
$350$	−5.11846	+	11.5305i	−0.273593	+	0.616333i
$351$	−4.63671	−	18.1522i	−0.247489	−	0.968891i
$352$	−2.93273	−	5.07964i	−0.156315	−	0.270746i
$353$	−17.2258	−	4.61564i	−0.916838	−	0.245666i	−0.230605	−	0.973048i	$-0.574070\pi$
$353$	−17.2258	−	4.61564i	−0.916838	−	0.245666i	−0.686233	+	0.727382i	$0.740737\pi$
$354$	0.533687	+	3.83202i	0.0283651	+	0.203670i
$355$	−2.27295	−	1.31229i	−0.120635	−	0.0696489i
$356$	−4.10253	+	4.10253i	−0.217433	+	0.217433i
$357$	−1.83287	−	1.10165i	−0.0970059	−	0.0583057i
$358$	−12.5575	−	3.36476i	−0.663682	−	0.177833i
$359$	6.36070	−	23.7385i	0.335705	−	1.25287i	−0.567398	−	0.823444i	$-0.692050\pi$
$359$	6.36070	−	23.7385i	0.335705	−	1.25287i	0.903103	−	0.429424i	$-0.141284\pi$
$360$	−1.03643	−	1.00588i	−0.0546249	−	0.0530143i
$361$	−14.5337	+	8.39105i	−0.764933	+	0.441634i
$362$	−14.2842	−	14.2842i	−0.750759	−	0.750759i
$363$	−15.2320	+	37.5656i	−0.799471	+	1.97168i
$364$	−6.33426	−	7.13282i	−0.332006	−	0.373861i
$365$		−	6.08295i		−	0.318396i
$366$	12.9639	−	5.48379i	0.677633	−	0.286642i
$367$	−4.06185	−	7.03533i	−0.212027	−	0.367241i	0.740322	−	0.672253i	$-0.234673\pi$
$367$	−4.06185	−	7.03533i	−0.212027	−	0.367241i	−0.952349	+	0.305011i	$0.901340\pi$
$368$	0.870719			0.0453894
$369$	5.50588	+	9.21526i	0.286625	+	0.479728i
$370$	0.660124	−	2.46362i	0.0343182	−	0.128077i
$371$	−20.2473	+	7.79791i	−1.05119	+	0.404847i
$372$	5.29773	−	2.24097i	0.274675	−	0.116189i
$373$	−9.04553	+	15.6673i	−0.468360	+	0.811223i	−0.999346	−	0.0361573i	$-0.988488\pi$
$373$	−9.04553	+	15.6673i	−0.468360	+	0.811223i	0.530986	+	0.847380i	$0.321822\pi$
$374$	−1.36857	−	2.37043i	−0.0707669	−	0.122572i
$375$	−4.91010	+	6.49906i	−0.253557	+	0.335610i
$376$	5.33153	−	3.07816i	0.274953	−	0.158744i
$377$	23.0744	+	18.9919i	1.18839	+	0.978131i
$378$	11.9239	−	6.84249i	0.613301	−	0.351940i
$379$	−12.9182	+	3.46143i	−0.663564	+	0.177802i	−0.574854	−	0.818256i	$-0.694941\pi$
$379$	−12.9182	+	3.46143i	−0.663564	+	0.177802i	−0.0887102	+	0.996057i	$0.528275\pi$
$380$		−	0.716975i		−	0.0367801i
$381$	13.9105	−	34.3067i	0.712659	−	1.75758i
$382$	25.9652	−	6.95734i	1.32849	−	0.355969i
$383$	4.08601	+	15.2492i	0.208785	+	0.779197i	0.988262	+	0.152766i	$0.0488182\pi$
$383$	4.08601	+	15.2492i	0.208785	+	0.779197i	−0.779477	+	0.626431i	$0.784515\pi$
$384$	−1.04410	+	1.38198i	−0.0532814	+	0.0705237i
$385$	2.68511	+	6.97192i	0.136846	+	0.355322i
$386$	−10.4425	+	6.02899i	−0.531510	+	0.306868i
$387$	21.5454	−	22.1999i	1.09521	−	1.12848i
$388$	−5.54945	−	1.48697i	−0.281731	−	0.0754895i
$389$	3.18974	−	5.52480i	0.161726	−	0.280118i	−0.773762	−	0.633477i	$-0.781627\pi$
$389$	3.18974	−	5.52480i	0.161726	−	0.280118i	0.935488	+	0.353359i	$0.114960\pi$
$390$	−1.43329	−	2.64290i	−0.0725777	−	0.133829i
$391$	0.406324			0.0205487
$392$	3.79949	−	5.87911i	0.191903	−	0.296940i
$393$	−17.7263	−	22.7470i	−0.894173	−	1.14743i
$394$	−6.11628	−	3.53124i	−0.308134	−	0.177901i
$395$	1.11493	+	4.16096i	0.0560980	+	0.209361i
$396$	17.5944	−	0.263252i	0.884152	−	0.0132289i
$397$	5.03000	+	18.7722i	0.252448	+	0.942150i	0.969492	+	0.245122i	$0.0788279\pi$
$397$	5.03000	+	18.7722i	0.252448	+	0.942150i	−0.717044	+	0.697028i	$0.754505\pi$
$398$	−12.6126	−	12.6126i	−0.632211	−	0.632211i
$399$	6.56000	+	1.88205i	0.328411	+	0.0942204i
$400$	4.12940	+	2.38411i	0.206470	+	0.119206i
$401$	2.87242	+	2.87242i	0.143442	+	0.143442i	0.775181	−	0.631739i	$-0.217659\pi$
$401$	2.87242	+	2.87242i	0.143442	+	0.143442i	−0.631739	+	0.775181i	$0.717659\pi$
$402$	−8.77053	+	6.83471i	−0.437434	+	0.340884i
$403$	11.9182	−	1.15666i	0.593687	−	0.0576172i
$404$	8.95921	−	5.17260i	0.445737	−	0.257346i
$405$	4.14982	−	1.24614i	0.206206	−	0.0619213i
$406$	−8.89745	+	20.0436i	−0.441573	+	0.994747i
$407$	15.5370	+	26.9109i	0.770140	+	1.33392i
$408$	−0.487231	+	0.644904i	−0.0241215	+	0.0319275i
$409$	18.0574	+	18.0574i	0.892881	+	0.892881i	0.994793	−	0.101912i	$-0.0324961\pi$
$409$	18.0574	+	18.0574i	0.892881	+	0.892881i	−0.101912	+	0.994793i	$0.532496\pi$
$410$	1.21812	+	1.21812i	0.0601589	+	0.0601589i
$411$	−13.9235	+	18.4293i	−0.686796	+	0.909050i
$412$	−2.46629	−	4.27173i	−0.121505	−	0.210453i
$413$	−5.87694	+	0.624259i	−0.289185	+	0.0307178i
$414$	−1.27209	+	2.28148i	−0.0625198	+	0.112129i
$415$	6.24808	−	3.60733i	0.306706	−	0.177077i
$416$	−2.93376	+	2.09597i	−0.143839	+	0.102763i
$417$	−2.65697	+	2.07053i	−0.130112	+	0.101394i
$418$	6.17671	+	6.17671i	0.302113	+	0.302113i
$419$	−18.9200	−	10.9234i	−0.924301	−	0.533645i	−0.0392960	−	0.999228i	$-0.512512\pi$
$419$	−18.9200	−	10.9234i	−0.924301	−	0.533645i	−0.885005	+	0.465582i	$0.845845\pi$
$420$	1.58722	−	1.53233i	0.0774484	−	0.0747699i
$421$	−1.86668	−	1.86668i	−0.0909765	−	0.0909765i	0.660154	−	0.751130i	$-0.270491\pi$
$421$	−1.86668	−	1.86668i	−0.0909765	−	0.0909765i	−0.751130	+	0.660154i	$0.770491\pi$
$422$	6.90441	+	25.7676i	0.336101	+	1.25435i
$423$	0.276306	+	18.4669i	0.0134345	+	0.897891i
$424$	2.12250	+	7.92128i	0.103078	+	0.384691i
$425$	1.92700	+	1.11255i	0.0934731	+	0.0539667i
$426$	−5.80408	−	7.44799i	−0.281209	−	0.360857i
$427$	7.72762	+	20.0648i	0.373966	+	0.971005i
$428$	9.69164			0.468463
$429$	35.1162	+	10.4207i	1.69543	+	0.503117i
$430$	2.48226	−	4.29940i	0.119705	−	0.207336i
$431$	−13.9236	−	3.73082i	−0.670676	−	0.179707i	−0.0926167	−	0.995702i	$-0.529523\pi$
$431$	−13.9236	−	3.73082i	−0.670676	−	0.179707i	−0.578059	+	0.815995i	$0.696190\pi$
$432$	−2.09571	−	4.75479i	−0.100830	−	0.228765i
$433$	−7.36962	+	4.25485i	−0.354161	+	0.204475i	−0.666516	−	0.745490i	$-0.732215\pi$
$433$	−7.36962	+	4.25485i	−0.354161	+	0.204475i	0.312355	+	0.949965i	$0.398882\pi$
$434$	3.15791	+	8.19955i	0.151585	+	0.393591i
$435$	−4.16637	+	5.51465i	−0.199762	+	0.264407i
$436$	0.702737	+	2.62265i	0.0336550	+	0.125602i
$437$	−1.25254	+	0.335617i	−0.0599172	+	0.0160548i
$438$	8.22343	−	20.2809i	0.392931	−	0.969059i
$439$		−	3.00234i		−	0.143294i	−0.997430	−	0.0716469i	$-0.977175\pi$
$439$		−	3.00234i		−	0.143294i	0.997430	−	0.0716469i	$-0.0228255\pi$
$440$	2.72760	−	0.730857i	0.130033	−	0.0348422i
$441$	9.85368	+	18.5447i	0.469223	+	0.883080i
$442$	−1.36905	+	0.978089i	−0.0651189	+	0.0465229i
$443$	0.930017	−	0.536946i	0.0441865	−	0.0255111i	−0.477744	−	0.878499i	$-0.658545\pi$
$443$	0.930017	−	0.536946i	0.0441865	−	0.0255111i	0.521930	+	0.852988i	$0.325212\pi$
$444$	5.53141	−	7.32143i	0.262509	−	0.347460i
$445$	−1.39660	−	2.41897i	−0.0662050	−	0.114670i
$446$	−4.71486	+	8.16637i	−0.223255	+	0.386689i
$447$	−4.76778	+	2.01679i	−0.225508	+	0.0953911i
$448$	−2.05797	−	1.66275i	−0.0972301	−	0.0785576i
$449$	4.71841	−	17.6094i	0.222676	−	0.831037i	−0.760647	−	0.649166i	$-0.775118\pi$
$449$	4.71841	−	17.6094i	0.222676	−	0.831037i	0.983322	−	0.181871i	$-0.0582153\pi$
$450$	−12.2798	+	7.33687i	−0.578876	+	0.345863i
$451$	−20.9882			−0.988294
$452$	1.30415	+	2.25886i	0.0613422	+	0.106248i
$453$	−17.7298	+	7.49979i	−0.833018	+	0.352371i
$454$		−	3.68820i		−	0.173096i
$455$	4.10622	−	2.05683i	0.192503	−	0.0964255i
$456$	0.969266	−	2.39044i	0.0453901	−	0.111943i
$457$	15.2810	+	15.2810i	0.714817	+	0.714817i	0.967539	−	0.252722i	$-0.0813257\pi$
$457$	15.2810	+	15.2810i	0.714817	+	0.714817i	−0.252722	+	0.967539i	$0.581326\pi$
$458$	10.4356	−	6.02500i	0.487624	−	0.281530i
$459$	−0.977967	−	2.21884i	−0.0456476	−	0.103566i
$460$	−0.108495	+	0.404908i	−0.00505859	+	0.0188789i
$461$	−3.51205	−	0.941050i	−0.163572	−	0.0438291i	0.176103	−	0.984372i	$-0.443651\pi$
$461$	−3.51205	−	0.941050i	−0.163572	−	0.0438291i	−0.339676	+	0.940543i	$0.610317\pi$
$462$	−0.472889	+	26.8748i	−0.0220008	+	1.25033i
$463$	11.6333	−	11.6333i	0.540645	−	0.540645i	−0.383073	−	0.923718i	$-0.625134\pi$
$463$	11.6333	−	11.6333i	0.540645	−	0.540645i	0.923718	+	0.383073i	$0.125134\pi$
$464$	7.17817	+	4.14432i	0.333238	+	0.192395i
$465$	0.381993	+	2.74282i	0.0177145	+	0.127195i
$466$	−8.46339	−	2.26776i	−0.392059	−	0.105052i
$467$	18.1640	+	31.4610i	0.840532	+	1.45584i	0.889446	+	0.457040i	$0.151091\pi$
$467$	18.1640	+	31.4610i	0.840532	+	1.45584i	−0.0489144	+	0.998803i	$0.515576\pi$
$468$	−1.20579	−	10.7492i	−0.0557379	−	0.496884i
$469$	−9.99859	−	13.7299i	−0.461692	−	0.633990i
$470$	0.767099	+	2.86285i	0.0353836	+	0.132054i
$471$	−7.93753	−	3.21848i	−0.365742	−	0.148300i
$472$			2.23377i			0.102818i
$473$	15.6546	+	58.4237i	0.719799	+	2.68633i
$474$	−1.90790	+	15.3801i	−0.0876328	+	0.706433i
$475$	−6.85915	−	1.83790i	−0.314720	−	0.0843289i
$476$	−0.960360	−	0.775928i	−0.0440180	−	0.0355646i
$477$	−23.8564	−	6.01127i	−1.09231	−	0.275237i
$478$		−	6.53831i		−	0.299056i
$479$	5.88949	−	21.9799i	0.269098	−	1.00429i	−0.690596	−	0.723240i	$-0.742652\pi$
$479$	5.88949	−	21.9799i	0.269098	−	1.00429i	0.959694	−	0.281046i	$-0.0906815\pi$
$480$	−0.512558	−	0.657732i	−0.0233950	−	0.0300212i
$481$	15.5424	−	11.1040i	0.708674	−	0.506299i
$482$			21.5843i			0.983136i
$483$	−3.41993	−	2.05555i	−0.155612	−	0.0935310i
$484$	−11.7018	+	20.2681i	−0.531901	+	0.921279i
$485$	1.38296	−	2.39536i	0.0627971	−	0.108768i
$486$	15.5204	+	1.45535i	0.704018	+	0.0660160i
$487$	−26.5260	−	26.5260i	−1.20201	−	1.20201i	−0.973555	−	0.228451i	$-0.926634\pi$
$487$	−26.5260	−	26.5260i	−1.20201	−	1.20201i	−0.228451	−	0.973555i	$-0.573366\pi$
$488$	7.84988	−	2.10337i	0.355347	−	0.0952151i
$489$	−1.52497	+	0.645068i	−0.0689614	+	0.0291710i
$490$	2.26051	+	2.49942i	0.102120	+	0.112912i
$491$	3.62316	−	6.27551i	0.163511	−	0.283210i	−0.772614	−	0.634876i	$-0.781051\pi$
$491$	3.62316	−	6.27551i	0.163511	−	0.283210i	0.936126	+	0.351666i	$0.114385\pi$
$492$	2.41454	+	5.70806i	0.108856	+	0.257339i
$493$	3.34971	+	1.93396i	0.150864	+	0.0871011i
$494$	3.41236	−	4.14589i	0.153529	−	0.186532i
$495$	−2.06991	+	8.21467i	−0.0930354	+	0.369222i
$496$	3.20788	−	0.859548i	0.144038	−	0.0385948i
$497$	11.6596	−	8.49086i	0.523002	−	0.380867i
$498$	25.7081	−	3.58038i	1.15201	−	0.160441i
$499$	9.52261	−	35.5389i	0.426291	−	1.59094i	−0.334797	−	0.942290i	$-0.608668\pi$
$499$	9.52261	−	35.5389i	0.426291	−	1.59094i	0.761088	−	0.648649i	$-0.224665\pi$
$500$	−3.32533	+	3.32533i	−0.148713	+	0.148713i
$501$	−15.2156	−	35.9704i	−0.679785	−	1.60704i
$502$	10.2269	+	2.74028i	0.456447	+	0.122305i
$503$	0.459527	−	0.265308i	0.0204893	−	0.0118295i	−0.489720	−	0.871880i	$-0.662901\pi$
$503$	0.459527	−	0.265308i	0.0204893	−	0.0118295i	0.510210	+	0.860050i	$0.329568\pi$
$504$	7.36341	−	2.96314i	0.327992	−	0.131989i
$505$	1.28905	+	4.81079i	0.0573619	+	0.214078i
$506$	−2.55359	−	4.42294i	−0.113521	−	0.196624i
$507$	4.29061	−	22.1041i	0.190552	−	0.981677i
$508$	10.6866	−	18.5098i	0.474143	−	0.821240i
$509$	28.0159	−	28.0159i	1.24178	−	1.24178i	0.282525	−	0.959260i	$-0.408828\pi$
$509$	28.0159	−	28.0159i	1.24178	−	1.24178i	0.959260	−	0.282525i	$-0.0911719\pi$
$510$	−0.239187	−	0.306933i	−0.0105914	−	0.0135912i
$511$	30.5543	+	13.5632i	1.35164	+	0.600001i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.84743	+	6.03204i	0.214019	+	0.266321i
$514$	20.9120	−	20.9120i	0.922389	−	0.922389i
$515$	2.29378	−	0.614616i	0.101076	−	0.0270832i
$516$	14.0883	−	10.9787i	0.620202	−	0.483312i
$517$	−31.2719	−	18.0548i	−1.37534	−	0.794050i
$518$	10.9027	+	8.80892i	0.479038	+	0.387042i
$519$	0.498897	+	0.202291i	0.0218992	+	0.00887959i
$520$	−0.609124	−	1.62544i	−0.0267118	−	0.0712803i
$521$	11.2528	+	6.49681i	0.492995	+	0.284631i	0.725816	−	0.687889i	$-0.241462\pi$
$521$	11.2528	+	6.49681i	0.492995	+	0.284631i	−0.232821	+	0.972520i	$0.574796\pi$
$522$	−21.3461	+	12.7537i	−0.934293	+	0.558216i
$523$	−7.25129			−0.317077			−0.158538	−	0.987353i	$-0.550678\pi$
$523$	−7.25129			−0.317077			−0.158538	+	0.987353i	$0.550678\pi$
$524$	−8.32490	−	14.4191i	−0.363675	−	0.629903i
$525$	−10.5908	−	19.1126i	−0.462219	−	0.834142i
$526$	−2.04142	+	7.61868i	−0.0890101	+	0.332190i
$527$	1.49696	−	0.401110i	0.0652088	−	0.0174726i
$528$	10.0820	+	1.25067i	0.438763	+	0.0544283i
$529$	−22.2418			−0.967037
$530$	−3.94808			−0.171494
$531$	−5.85299	−	3.26346i	−0.253998	−	0.141622i
$532$	3.60133	+	1.59865i	0.156137	+	0.0693102i
$533$	1.24624	+	12.8413i	0.0539808	+	0.556218i
$534$	−1.38616	−	9.95303i	−0.0599851	−	0.430710i
$535$	−1.20761	+	4.50687i	−0.0522096	+	0.194849i
$536$	−5.55958	+	3.20982i	−0.240137	+	0.138643i
$537$	17.7612	−	13.8410i	0.766453	−	0.597283i
$538$	21.0608	+	21.0608i	0.907995	+	0.907995i
$539$	−41.0066	−	2.05819i	−1.76628	−	0.0886525i
$540$	2.47224	−	0.382096i	0.106388	−	0.0164428i
$541$	−0.991173	−	0.265584i	−0.0426139	−	0.0114184i	0.237449	−	0.971400i	$-0.423689\pi$
$541$	−0.991173	−	0.265584i	−0.0426139	−	0.0114184i	−0.280063	+	0.959982i	$0.590355\pi$
$542$		−	8.59002i		−	0.368973i
$543$	34.6544	−	4.82634i	1.48716	−	0.207118i
$544$	−0.329973	+	0.329973i	−0.0141475	+	0.0141475i
$545$	−1.30717			−0.0559928
$546$	16.4710	−	1.30645i	0.704893	−	0.0559109i
$547$	−23.9034			−1.02203			−0.511017	−	0.859570i	$-0.670731\pi$
$547$	−23.9034			−1.02203			−0.511017	+	0.859570i	$0.670731\pi$
$548$	−9.42959	+	9.42959i	−0.402812	+	0.402812i
$549$	−5.95709	+	23.6414i	−0.254242	+	1.00899i
$550$		−	27.9678i		−	1.19255i
$551$	−11.9233	−	3.19484i	−0.507950	−	0.136105i
$552$	−0.909116	+	1.20331i	−0.0386945	+	0.0512165i
$553$	−23.3862	−	3.67753i	−0.994484	−	0.156384i
$554$	−4.49337	−	4.49337i	−0.190905	−	0.190905i
$555$	2.71543	+	3.48453i	0.115263	+	0.147910i
$556$	−1.68423	+	0.972392i	−0.0714274	+	0.0412386i
$557$	−6.64730	+	24.8081i	−0.281655	+	1.05115i	0.669594	+	0.742728i	$0.266468\pi$
$557$	−6.64730	+	24.8081i	−0.281655	+	1.05115i	−0.951249	+	0.308424i	$0.900198\pi$
$558$	−2.43438	+	9.66113i	−0.103056	+	0.408988i
$559$	34.8161	−	13.0471i	1.47256	−	0.551834i
$560$	1.02965	−	0.749828i	0.0435109	−	0.0316860i
$561$	4.70479	+	0.583628i	0.198637	+	0.0246408i
$562$	−0.656203			−0.0276802
$563$	31.3743			1.32227			0.661134	−	0.750268i	$-0.270076\pi$
$563$	31.3743			1.32227			0.661134	+	0.750268i	$0.270076\pi$
$564$	−1.31269	+	10.5819i	−0.0552741	+	0.445580i
$565$	−1.21293	+	0.325004i	−0.0510284	+	0.0136730i
$566$	5.02658	−	18.7595i	0.211283	−	0.788519i
$567$	−2.99358	+	23.6228i	−0.125719	+	0.992066i
$568$	−2.72580	−	4.72123i	−0.114372	−	0.198098i
$569$	−16.4690			−0.690417			−0.345209	−	0.938526i	$-0.612192\pi$
$569$	−16.4690			−0.690417			−0.345209	+	0.938526i	$0.612192\pi$
$570$	0.990844	+	0.748592i	0.0415019	+	0.0313551i
$571$	−15.4274	−	8.90703i	−0.645618	−	0.372748i	0.141157	−	0.989987i	$-0.454918\pi$
$571$	−15.4274	−	8.90703i	−0.645618	−	0.372748i	−0.786775	+	0.617239i	$0.788251\pi$
$572$	19.2507	+	8.75552i	0.804911	+	0.366087i
$573$	−17.4953	+	43.1474i	−0.730875	+	1.80251i
$574$	−8.83464	+	3.40251i	−0.368751	+	0.142018i
$575$	3.59555	+	2.07589i	0.149945	+	0.0865707i
$576$	−0.819723	−	2.88584i	−0.0341551	−	0.120243i
$577$	−3.56574	+	0.955437i	−0.148444	+	0.0397754i	−0.332276	−	0.943182i	$-0.607816\pi$
$577$	−3.56574	+	0.955437i	−0.148444	+	0.0397754i	0.183832	+	0.982958i	$0.441150\pi$
$578$	11.8668	−	11.8668i	0.493595	−	0.493595i
$579$	2.57108	−	20.7262i	0.106850	−	0.861351i
$580$	−2.82164	+	2.82164i	−0.117162	+	0.117162i
$581$	4.18801	+	39.4270i	0.173748	+	1.63571i
$582$	7.84913	−	6.11668i	0.325357	−	0.253544i
$583$	34.0125	−	34.0125i	1.40865	−	1.40865i
$584$	6.31757	−	10.9424i	0.261423	−	0.452798i
$585$	5.14893	+	0.778666i	0.212882	+	0.0321939i
$586$	6.62345	+	11.4722i	0.273612	+	0.473911i
$587$	6.15789	+	22.9816i	0.254163	+	0.948551i	0.968554	+	0.248803i	$0.0800373\pi$
$587$	6.15789	+	22.9816i	0.254163	+	0.948551i	−0.714391	+	0.699747i	$0.753296\pi$
$588$	4.15776	+	11.3892i	0.171463	+	0.469681i
$589$	−4.28326	+	2.47294i	−0.176489	+	0.101896i
$590$	−1.03876	−	0.278336i	−0.0427652	−	0.0114589i
$591$	11.2661	−	4.76561i	0.463425	−	0.196031i
$592$	3.74611	−	3.74611i	0.153964	−	0.153964i
$593$	9.26825	−	34.5896i	0.380601	−	1.42042i	−0.464384	−	0.885634i	$-0.653724\pi$
$593$	9.26825	−	34.5896i	0.380601	−	1.42042i	0.844985	−	0.534789i	$-0.179609\pi$
$594$	−18.0065	+	24.5899i	−0.738814	+	1.00894i
$595$	0.480492	−	0.349909i	0.0196982	−	0.0143449i
$596$	−2.88698	+	0.773564i	−0.118255	+	0.0316864i
$597$	30.5990	−	4.26154i	1.25234	−	0.174413i
$598$	−2.55448	+	1.82500i	−0.104460	+	0.0746297i
$599$	40.7319	+	23.5166i	1.66426	+	0.960862i	0.970645	+	0.240517i	$0.0773171\pi$
$599$	40.7319	+	23.5166i	1.66426	+	0.960862i	0.693617	+	0.720344i	$0.256016\pi$
$600$	−7.60629	+	3.21750i	−0.310525	+	0.131354i
$601$	−6.85225	+	11.8684i	−0.279509	+	0.484124i	−0.971263	−	0.238010i	$-0.923505\pi$
$601$	−6.85225	+	11.8684i	−0.279509	+	0.484124i	0.691754	+	0.722134i	$0.256838\pi$
$602$	16.0609	+	22.0547i	0.654595	+	0.898882i
$603$	−0.288125	−	19.2568i	−0.0117333	−	0.784197i
$604$	−10.7357	+	2.87663i	−0.436830	+	0.117048i
$605$	−7.96714	−	7.96714i	−0.323910	−	0.323910i
$606$	−2.20586	+	17.7821i	−0.0896071	+	0.722349i
$607$	7.56657	−	13.1057i	0.307118	−	0.531944i	−0.670613	−	0.741808i	$-0.733969\pi$
$607$	7.56657	−	13.1057i	0.307118	−	0.531944i	0.977731	+	0.209864i	$0.0673021\pi$
$608$	0.744629	−	1.28974i	0.0301987	−	0.0523057i
$609$	−18.4100	−	33.2235i	−0.746010	−	1.34629i
$610$			3.91249i			0.158412i
$611$	−9.18969	+	20.2053i	−0.371775	+	0.817418i
$612$	−0.382526	−	1.34668i	−0.0154627	−	0.0544365i
$613$	−5.62343	+	20.9869i	−0.227128	+	0.847654i	0.754412	+	0.656401i	$0.227922\pi$
$613$	−5.62343	+	20.9869i	−0.227128	+	0.847654i	−0.981541	+	0.191254i	$0.938745\pi$
$614$		−	3.85812i		−	0.155701i
$615$	−2.95526	+	0.411580i	−0.119168	+	0.0165965i
$616$	−2.41070	+	15.3302i	−0.0971297	+	0.617670i
$617$	−15.3782	−	4.12058i	−0.619104	−	0.165888i	−0.0643837	−	0.997925i	$-0.520508\pi$
$617$	−15.3782	−	4.12058i	−0.619104	−	0.165888i	−0.554721	+	0.832037i	$0.687175\pi$
$618$	8.47848	+	1.05175i	0.341055	+	0.0423077i
$619$	−1.51716	−	5.66211i	−0.0609797	−	0.227579i	0.928710	−	0.370807i	$-0.120919\pi$
$619$	−1.51716	−	5.66211i	−0.0609797	−	0.227579i	−0.989690	+	0.143227i	$0.954252\pi$
$620$			1.59885i			0.0642114i
$621$	−1.82477	−	4.14009i	−0.0732256	−	0.166136i
$622$	−7.94022	−	29.6333i	−0.318374	−	1.18819i
$623$	15.2644	−	1.62141i	0.611554	−	0.0649604i
$624$	0.166549	−	6.24278i	0.00666729	−	0.249911i
$625$	10.7885	+	18.6863i	0.431542	+	0.747452i
$626$	17.8069	+	4.77134i	0.711705	+	0.190701i
$627$	−14.9852	+	2.08699i	−0.598450	+	0.0833463i
$628$	−4.28261	−	2.47257i	−0.170895	−	0.0986661i
$629$	1.74813	−	1.74813i	0.0697026	−	0.0697026i
$630$	0.460431	+	3.79340i	0.0183440	+	0.151133i
$631$	37.1184	+	9.94585i	1.47766	+	0.395938i	0.905551	−	0.424238i	$-0.139458\pi$
$631$	37.1184	+	9.94585i	1.47766	+	0.395938i	0.572111	+	0.820177i	$0.306125\pi$
$632$	−2.31586	+	8.64290i	−0.0921199	+	0.343796i
$633$	−42.8191	−	17.3621i	−1.70191	−	0.690083i
$634$	26.6737	−	15.4001i	1.05935	−	0.611614i
$635$	7.27596	+	7.27596i	0.288738	+	0.288738i
$636$	−13.1631	−	5.33734i	−0.521952	−	0.211639i
$637$	1.17564	+	25.2115i	0.0465804	+	0.998915i
$638$		−	48.6167i		−	1.92475i
$639$	16.3530	−	0.244677i	0.646914	−	0.00967929i
$640$	−0.240716	−	0.416932i	−0.00951512	−	0.0164807i
$641$	−18.1190			−0.715658			−0.357829	−	0.933787i	$-0.616483\pi$
$641$	−18.1190			−0.715658			−0.357829	+	0.933787i	$0.616483\pi$
$642$	−10.1190	+	13.3936i	−0.399366	+	0.528604i
$643$	−3.36696	+	12.5657i	−0.132780	+	0.495542i	−0.999997	−	0.00238837i	$-0.999240\pi$
$643$	−3.36696	+	12.5657i	−0.132780	+	0.495542i	0.867217	+	0.497930i	$0.165906\pi$
$644$	−1.79192	−	1.44779i	−0.0706114	−	0.0570509i
$645$	3.34995	+	7.91942i	0.131904	+	0.311827i
$646$	0.347483	−	0.601859i	0.0136716	−	0.0236798i
$647$	−21.4208	−	37.1019i	−0.842137	−	1.45862i	−0.888084	−	0.459681i	$-0.847964\pi$
$647$	−21.4208	−	37.1019i	−0.842137	−	1.45862i	0.0459471	−	0.998944i	$-0.485369\pi$
$648$	8.75913	+	2.06824i	0.344091	+	0.0812483i
$649$	11.3467	−	6.55105i	0.445399	−	0.257151i
$650$	−17.1117	+	1.66068i	−0.671175	+	0.0651374i
$651$	−14.6288	−	4.19696i	−0.573346	−	0.164492i
$652$	−0.923396	+	0.247423i	−0.0361630	+	0.00968984i
$653$			35.2103i			1.37789i	0.724815	+	0.688943i	$0.241925\pi$
$653$			35.2103i			1.37789i	−0.724815	+	0.688943i	$0.758075\pi$
$654$	−4.35817	−	1.76714i	−0.170418	−	0.0691004i
$655$	7.74260	−	2.07462i	0.302528	−	0.0810623i
$656$	0.926123	+	3.45634i	0.0361590	+	0.134947i
$657$	19.4417	+	32.5398i	0.758493	+	1.26950i
$658$	−16.0904	−	2.53024i	−0.627268	−	0.0986389i
$659$	16.8702	−	9.74000i	0.657168	−	0.379416i	−0.134029	−	0.990977i	$-0.542791\pi$
$659$	16.8702	−	9.74000i	0.657168	−	0.379416i	0.791197	+	0.611561i	$0.209458\pi$
$660$	−1.83785	+	4.53256i	−0.0715381	+	0.176430i
$661$	−17.4835	−	4.68469i	−0.680030	−	0.182213i	−0.0977613	−	0.995210i	$-0.531168\pi$
$661$	−17.4835	−	4.68469i	−0.680030	−	0.182213i	−0.582269	+	0.812996i	$0.697835\pi$
$662$	−5.30896	+	9.19538i	−0.206338	+	0.357389i
$663$	0.0777205	−	2.91321i	0.00301842	−	0.113140i
$664$	14.9859			0.581564
$665$	−1.19215	+	1.47552i	−0.0462297	+	0.0572181i
$666$	4.34272	+	15.2886i	0.168277	+	0.592420i
$667$	6.25017	+	3.60854i	0.242008	+	0.139723i
$668$	−5.83613	−	21.7807i	−0.225807	−	0.842722i
$669$	−6.36297	−	15.0423i	−0.246007	−	0.581570i
$670$	−0.799910	−	2.98531i	−0.0309032	−	0.115332i
$671$	−33.7059	−	33.7059i	−1.30120	−	1.30120i
$672$	4.44661	−	1.10800i	0.171532	−	0.0427420i
$673$	−29.6917	−	17.1425i	−1.14453	−	0.660795i	−0.196982	−	0.980407i	$-0.563114\pi$
$673$	−29.6917	−	17.1425i	−1.14453	−	0.660795i	−0.947548	+	0.319612i	$0.896447\pi$
$674$	12.2783	+	12.2783i	0.472944	+	0.472944i
$675$	2.68194	−	24.6308i	0.103228	−	0.948041i
$676$	4.21385	−	12.2981i	0.162071	−	0.473004i
$677$	−11.9245	+	6.88461i	−0.458296	+	0.264597i	−0.711327	−	0.702861i	$-0.751906\pi$
$677$	−11.9245	+	6.88461i	−0.458296	+	0.264597i	0.253032	+	0.967458i	$0.418572\pi$
$678$	−4.48336	−	0.556159i	−0.172182	−	0.0213591i
$679$	8.94816	+	12.2875i	0.343399	+	0.471551i
$680$	−0.112331	−	0.194562i	−0.00430768	−	0.00746113i
$681$	5.09701	+	3.85084i	0.195318	+	0.147564i
$682$	−13.7740	−	13.7740i	−0.527435	−	0.527435i
$683$	−17.9960	−	17.9960i	−0.688598	−	0.688598i	0.273324	−	0.961922i	$-0.411877\pi$
$683$	−17.9960	−	17.9960i	−0.688598	−	0.688598i	−0.961922	+	0.273324i	$0.911877\pi$
$684$	2.29152	+	3.83535i	0.0876186	+	0.146648i
$685$	−3.21005	−	5.55997i	−0.122650	−	0.212436i
$686$	−17.5947	+	5.78144i	−0.671770	+	0.220736i
$687$	−2.56937	+	20.7125i	−0.0980277	+	0.790230i
$688$	8.93046	−	5.15600i	0.340471	−	0.196571i
$689$	−22.8296	−	18.7904i	−0.869740	−	0.715858i
$690$	−0.446294	−	0.572700i	−0.0169901	−	0.0218023i
$691$	−28.1654	−	28.1654i	−1.07146	−	1.07146i	−0.997242	−	0.0742205i	$-0.976353\pi$
$691$	−28.1654	−	28.1654i	−1.07146	−	1.07146i	−0.0742205	−	0.997242i	$-0.523647\pi$
$692$	0.269175	+	0.155408i	0.0102325	+	0.00590773i
$693$	−36.6466	−	28.7134i	−1.39209	−	1.09073i
$694$	−0.139436	−	0.139436i	−0.00529292	−	0.00529292i
$695$	−0.242327	−	0.904377i	−0.00919199	−	0.0343050i
$696$	−13.2221	+	5.59300i	−0.501181	+	0.212002i
$697$	0.432178	+	1.61291i	0.0163699	+	0.0610933i
$698$	−14.7337	−	8.50650i	−0.557678	−	0.321976i
$699$	11.9706	−	9.32846i	0.452770	−	0.352835i
$700$	−4.53402	−	11.7726i	−0.171370	−	0.444963i
$701$	−2.29061			−0.0865150			−0.0432575	−	0.999064i	$-0.513774\pi$
$701$	−2.29061			−0.0865150			−0.0432575	+	0.999064i	$0.513774\pi$
$702$	16.1142	+	9.55686i	0.608190	+	0.360701i
$703$	−3.94489	+	6.83275i	−0.148784	+	0.257702i
$704$	5.66560	+	1.51809i	0.213530	+	0.0572153i
$705$	−4.75732	−	1.92898i	−0.179171	−	0.0726497i
$706$	15.4442	−	8.91674i	0.581252	−	0.335586i
$707$	−27.0386	−	4.25186i	−1.01689	−	0.159908i
$708$	−3.08702	−	2.33227i	−0.116017	−	0.0876522i
$709$	−0.0690207	−	0.257589i	−0.00259213	−	0.00967395i	0.964618	−	0.263653i	$-0.0849273\pi$
$709$	−0.0690207	−	0.257589i	−0.00259213	−	0.00967395i	−0.967210	+	0.253979i	$0.918261\pi$
$710$	2.53514	−	0.679289i	0.0951422	−	0.0254933i
$711$	−19.2630	−	18.6950i	−0.722418	−	0.701119i
$712$		−	5.80185i		−	0.217433i
$713$	2.79316	−	0.748425i	0.104605	−	0.0280287i
$714$	2.07502	−	0.517051i	0.0776558	−	0.0193501i
$715$	−6.47025	+	7.86111i	−0.241974	+	0.293989i
$716$	11.2587	−	6.50022i	0.420758	−	0.242925i
$717$	9.03580	+	6.82663i	0.337448	+	0.254945i
$718$	12.2879	+	21.2833i	0.458582	+	0.794287i
$719$	18.9931	−	32.8971i	0.708324	−	1.22685i	−0.257154	−	0.966370i	$-0.582785\pi$
$719$	18.9931	−	32.8971i	0.708324	−	1.22685i	0.965478	−	0.260483i	$-0.0838819\pi$
$720$	1.44413	−	0.0216075i	0.0538196	−	0.000805262i
$721$	−2.02728	+	12.8919i	−0.0754999	+	0.480121i
$722$	4.34353	−	16.2103i	0.161649	−	0.603284i
$723$	−29.8290	−	22.5361i	−1.10935	−	0.838125i
$724$	20.2009			0.750759
$725$	19.7610	+	34.2271i	0.733906	+	1.27116i
$726$	−15.7923	−	37.3335i	−0.586106	−	1.38558i
$727$			27.5446i			1.02157i	0.859708	+	0.510786i	$0.170645\pi$
$727$			27.5446i			1.02157i	−0.859708	+	0.510786i	$0.829355\pi$
$728$	9.52267	+	0.564666i	0.352933	+	0.0209279i
$729$	−18.2160	+	19.9293i	−0.674668	+	0.738121i
$730$	4.30129	+	4.30129i	0.159198	+	0.159198i
$731$	4.16743	−	2.40606i	0.154138	−	0.0889915i
$732$	−5.28923	+	13.0445i	−0.195496	+	0.482138i
$733$	−3.91907	+	14.6262i	−0.144754	+	0.540229i	0.855012	+	0.518608i	$0.173550\pi$
$733$	−3.91907	+	14.6262i	−0.144754	+	0.540229i	−0.999766	+	0.0216214i	$0.993117\pi$
$734$	7.84689	+	2.10257i	0.289634	+	0.0776072i
$735$	−5.81434	+	0.514338i	−0.214465	+	0.0189717i
$736$	−0.615692	+	0.615692i	−0.0226947	+	0.0226947i
$737$	32.6095	+	18.8271i	1.20119	+	0.693505i
$738$	−10.4094	−	2.62293i	−0.383176	−	0.0965515i
$739$	40.0390	+	10.7284i	1.47286	+	0.394651i	0.903910	−	0.427722i	$-0.140684\pi$
$739$	40.0390	+	10.7284i	1.47286	+	0.394651i	0.568948	+	0.822373i	$0.307350\pi$
$740$	1.27526	+	2.20882i	0.0468795	+	0.0811977i
$741$	2.16669	+	9.04451i	0.0795952	+	0.332259i
$742$	8.80307	−	19.8310i	0.323171	−	0.728018i
$743$	−9.63013	−	35.9401i	−0.353295	−	1.31852i	−0.882616	−	0.470094i	$-0.844220\pi$
$743$	−9.63013	−	35.9401i	−0.353295	−	1.31852i	0.529321	−	0.848422i	$-0.322447\pi$
$744$	−2.16146	+	5.33066i	−0.0792429	+	0.195432i
$745$		−	1.43891i		−	0.0527176i
$746$	−4.68231	−	17.4746i	−0.171432	−	0.639792i
$747$	−21.8938	+	39.2663i	−0.801052	+	1.43668i
$748$	2.64387	+	0.708423i	0.0966694	+	0.0259025i
$749$	−19.9451	−	16.1148i	−0.728780	−	0.588822i
$750$	−1.12356	−	8.06750i	−0.0410267	−	0.294583i
$751$			39.6042i			1.44518i	0.691278	+	0.722588i	$0.257048\pi$
$751$			39.6042i			1.44518i	−0.691278	+	0.722588i	$0.742952\pi$
$752$	−1.59337	+	5.94655i	−0.0581043	+	0.216848i
$753$	−14.4648	+	11.2722i	−0.527128	+	0.410780i
$754$	−29.7453	+	2.88678i	−1.08326	+	0.105130i
$755$		−	5.35084i		−	0.194737i
$756$	−3.59313	+	13.2699i	−0.130681	+	0.482620i
$757$	−10.9136	+	18.9029i	−0.396660	+	0.687036i	−0.993312	−	0.115465i	$-0.963164\pi$
$757$	−10.9136	+	18.9029i	−0.396660	+	0.687036i	0.596651	+	0.802501i	$0.296498\pi$
$758$	6.68696	−	11.5822i	0.242881	−	0.420683i
$759$	8.77859	+	1.08898i	0.318643	+	0.0395275i
$760$	0.506978	+	0.506978i	0.0183900	+	0.0183900i
$761$	15.1010	−	4.04630i	0.547411	−	0.146678i	0.0254944	−	0.999675i	$-0.491884\pi$
$761$	15.1010	−	4.04630i	0.547411	−	0.146678i	0.521916	+	0.852997i	$0.325217\pi$
$762$	14.4222	+	34.0947i	0.522463	+	1.23512i
$763$	2.91460	−	6.56582i	0.105516	−	0.237699i
$764$	−13.4406	+	23.2797i	−0.486262	+	0.842231i
$765$	0.673908	−	0.0100832i	0.0243652	−	0.000364558i
$766$	−13.6721	−	7.89356i	−0.493991	−	0.285206i
$767$	−4.68191	−	6.55334i	−0.169054	−	0.236627i
$768$	−0.238917	−	1.71549i	−0.00862119	−	0.0619025i
$769$	23.8156	−	6.38138i	0.858814	−	0.230119i	0.197569	−	0.980289i	$-0.436695\pi$
$769$	23.8156	−	6.38138i	0.858814	−	0.230119i	0.661245	+	0.750170i	$0.270029\pi$
$770$	−6.82856	−	3.03123i	−0.246084	−	0.109238i
$771$	7.06575	+	50.7341i	0.254467	+	1.82714i
$772$	3.12084	−	11.6471i	0.112321	−	0.419189i
$773$	13.2371	−	13.2371i	0.476105	−	0.476105i	−0.427778	−	0.903884i	$-0.640704\pi$
$773$	13.2371	−	13.2371i	0.476105	−	0.476105i	0.903884	+	0.427778i	$0.140704\pi$
$774$	0.462821	+	30.9326i	0.0166357	+	1.11185i
$775$	15.2959	+	4.09852i	0.549444	+	0.147223i
$776$	4.97550	−	2.87261i	0.178610	−	0.103121i
$777$	−23.5572	+	5.86995i	−0.845111	+	0.210583i
$778$	1.65113	+	6.16211i	0.0591960	+	0.220922i
$779$	−2.66448	−	4.61502i	−0.0954649	−	0.165350i
$780$	2.88231	+	0.855322i	0.103203	+	0.0306254i
$781$	−15.9881	+	27.6922i	−0.572099	+	0.990904i
$782$	−0.287314	+	0.287314i	−0.0102743	+	0.0102743i
$783$	4.66203	−	42.8159i	0.166607	−	1.53012i
$784$	1.47051	+	6.84380i	0.0525183	+	0.244421i
$785$	1.68344	−	1.68344i	0.0600845	−	0.0600845i
$786$	28.6189	+	3.55017i	1.02080	+	0.126630i
$787$	−37.8053	+	37.8053i	−1.34761	+	1.34761i	−0.459365	+	0.888248i	$0.651923\pi$
$787$	−37.8053	+	37.8053i	−1.34761	+	1.34761i	−0.888248	+	0.459365i	$0.848077\pi$
$788$	6.82183	−	1.82790i	0.243018	−	0.0651164i
$789$	−8.39741	−	10.7758i	−0.298956	−	0.383630i
$790$	−3.73062	−	2.15387i	−0.132729	−	0.0766313i
$791$	1.07201	−	6.81716i	0.0381163	−	0.242390i
$792$	−12.2550	+	12.6273i	−0.435462	+	0.448691i
$793$	−18.6211	+	22.6239i	−0.661253	+	0.803397i
$794$	−16.8307	−	9.71720i	−0.597299	−	0.344851i
$795$	4.12218	−	5.45615i	0.146199	−	0.193510i
$796$	17.8369			0.632211
$797$	−10.9261	−	18.9246i	−0.387023	−	0.670344i	0.605024	−	0.796207i	$-0.293163\pi$
$797$	−10.9261	−	18.9246i	−0.387023	−	0.670344i	−0.992048	+	0.125863i	$0.959830\pi$
$798$	−5.96943	+	3.30781i	−0.211316	+	0.117095i
$799$	−0.743552	+	2.77497i	−0.0263050	+	0.0981715i
$800$	−4.60575	+	1.23411i	−0.162838	+	0.0436323i
$801$	15.2022	+	8.47629i	0.537142	+	0.299495i
$802$	−4.06222			−0.143442
$803$	−74.1109			−2.61532
$804$	1.36883	−	11.0346i	0.0482751	−	0.389159i
$805$	0.896541	−	0.652890i	0.0315989	−	0.0230113i
$806$	−7.60954	+	9.24530i	−0.268035	+	0.325652i
$807$	−51.0951	+	7.11603i	−1.79863	+	0.250496i
$808$	−2.67753	+	9.99270i	−0.0941953	+	0.351542i
$809$	36.2255	−	20.9148i	1.27362	−	0.735325i	0.297953	−	0.954581i	$-0.403696\pi$
$809$	36.2255	−	20.9148i	1.27362	−	0.735325i	0.975668	+	0.219255i	$0.0703628\pi$
$810$	−2.05321	+	3.81552i	−0.0721423	+	0.134064i
$811$	21.9874	+	21.9874i	0.772081	+	0.772081i	0.978470	−	0.206389i	$-0.0661712\pi$
$811$	21.9874	+	21.9874i	0.772081	+	0.772081i	−0.206389	+	0.978470i	$0.566171\pi$
$812$	−7.88151	−	20.4644i	−0.276587	−	0.718160i
$813$	11.8712	+	8.96882i	0.416342	+	0.314550i
$814$	−30.0152	−	8.04254i	−1.05203	−	0.281891i
$815$		−	0.460234i		−	0.0161213i
$816$	−0.111492	−	0.800540i	−0.00390298	−	0.0280245i
$817$	−10.8592	+	10.8592i	−0.379916	+	0.379916i
$818$	−25.5370			−0.892881
$819$	−15.3918	+	24.1266i	−0.537834	+	0.843051i
$820$	−1.72269			−0.0601589
$821$	2.74997	−	2.74997i	0.0959746	−	0.0959746i	−0.657489	−	0.753464i	$-0.728382\pi$
$821$	2.74997	−	2.74997i	0.0959746	−	0.0959746i	0.753464	+	0.657489i	$0.228382\pi$
$822$	−3.18607	−	22.8769i	−0.111127	−	0.797923i
$823$			8.67690i			0.302458i	0.988499	+	0.151229i	$0.0483231\pi$
$823$			8.67690i			0.302458i	−0.988499	+	0.151229i	$0.951677\pi$
$824$	4.76450	+	1.27664i	0.165979	+	0.0444740i
$825$	38.6509	+	29.2011i	1.34565	+	1.01665i
$826$	3.71421	−	4.59704i	0.129234	−	0.159952i
$827$	3.53129	+	3.53129i	0.122795	+	0.122795i	0.765834	−	0.643039i	$-0.222327\pi$
$827$	3.53129	+	3.53129i	0.122795	+	0.122795i	−0.643039	+	0.765834i	$0.722327\pi$
$828$	−0.713748	−	2.51275i	−0.0248045	−	0.0873242i
$829$	34.5746	−	19.9617i	1.20083	−	0.693297i	0.240087	−	0.970751i	$-0.422824\pi$
$829$	34.5746	−	19.9617i	1.20083	−	0.693297i	0.960739	+	0.277454i	$0.0894905\pi$
$830$	−1.86729	+	6.96882i	−0.0648146	+	0.241891i
$831$	10.9013	−	1.51822i	0.378160	−	0.0526665i
$832$	0.592407	−	3.55655i	0.0205380	−	0.123301i
$833$	0.686219	+	3.19368i	0.0237761	+	0.110654i
$834$	0.414679	−	3.34284i	0.0143591	−	0.115753i
$835$	10.8558			0.375682
$836$	−8.73519			−0.302113
$837$	−10.8097	−	13.4514i	−0.373639	−	0.464949i
$838$	21.1025	−	5.65439i	0.728973	−	0.195328i
$839$	9.12451	−	34.0532i	0.315013	−	1.17565i	−0.608964	−	0.793198i	$-0.708415\pi$
$839$	9.12451	−	34.0532i	0.315013	−	1.17565i	0.923977	−	0.382448i	$-0.124919\pi$
$840$	−0.0388143	+	2.20585i	−0.00133922	+	0.0761092i
$841$	19.8507	+	34.3825i	0.684508	+	1.18560i
$842$	2.63989			0.0909765
$843$	0.685139	−	0.906857i	0.0235974	−	0.0312338i
$844$	−23.1026	−	13.3383i	−0.795224	−	0.459123i
$845$	5.19389	+	3.49194i	0.178675	+	0.120126i
$846$	−13.2534	−	12.8627i	−0.455663	−	0.442228i
$847$	57.7829	−	22.2541i	1.98544	−	0.764659i
$848$	−7.10203	−	4.10036i	−0.243885	−	0.140807i
$849$	20.6769	+	26.5333i	0.709630	+	0.910621i
$850$	−2.14929	+	0.575900i	−0.0737199	+	0.0197532i
$851$	3.26181	−	3.26181i	0.111813	−	0.111813i
$852$	9.37063	+	1.16242i	0.321033	+	0.0398240i
$853$	14.6506	−	14.6506i	0.501628	−	0.501628i	−0.410315	−	0.911944i	$-0.634581\pi$
$853$	14.6506	−	14.6506i	0.501628	−	0.501628i	0.911944	+	0.410315i	$0.134581\pi$
$854$	−19.6522	−	8.72373i	−0.672486	−	0.298520i
$855$	−2.06907	+	0.587721i	−0.0707608	+	0.0200996i
$856$	−6.85302	+	6.85302i	−0.234232	+	0.234232i
$857$	23.6057	−	40.8863i	0.806357	−	1.39665i	−0.109015	−	0.994040i	$-0.534770\pi$
$857$	23.6057	−	40.8863i	0.806357	−	1.39665i	0.915371	−	0.402611i	$-0.131897\pi$
$858$	−32.1995	+	17.4624i	−1.09927	+	0.596156i
$859$	−5.12900	−	8.88369i	−0.174999	−	0.303108i	0.765162	−	0.643838i	$-0.222659\pi$
$859$	−5.12900	−	8.88369i	−0.174999	−	0.303108i	−0.940161	+	0.340730i	$0.889326\pi$
$860$	1.28491	+	4.79536i	0.0438152	+	0.163520i
$861$	4.52203	−	15.7618i	0.154110	−	0.537161i
$862$	12.4836	−	7.20738i	0.425192	−	0.245484i
$863$	5.58401	+	1.49623i	0.190082	+	0.0509323i	0.352604	−	0.935773i	$-0.385296\pi$
$863$	5.58401	+	1.49623i	0.190082	+	0.0509323i	−0.162522	+	0.986705i	$0.551963\pi$
$864$	4.84403	+	1.88026i	0.164797	+	0.0639676i
$865$	−0.105809	+	0.105809i	−0.00359762	+	0.00359762i
$866$	2.20247	−	8.21974i	0.0748431	−	0.279318i
$867$	4.00957	+	28.7898i	0.136172	+	0.977753i
$868$	−8.03094	−	3.56497i	−0.272588	−	0.121003i
$869$	50.6946	−	13.5836i	1.71970	−	0.460791i
$870$	−0.953378	−	6.84552i	−0.0323225	−	0.232085i
$871$	9.58276	−	21.0695i	0.324699	−	0.713913i
$872$	−2.35140	−	1.35758i	−0.0796286	−	0.0459736i
$873$	0.257855	+	17.2337i	0.00872708	+	0.583273i
$874$	0.648363	−	1.12300i	0.0219312	−	0.0379860i
$875$	12.3726	−	1.31424i	0.418272	−	0.0444295i
$876$	8.52593	+	20.1556i	0.288064	+	0.680995i
$877$	−14.5117	+	3.88840i	−0.490025	+	0.131302i	−0.495367	−	0.868684i	$-0.664966\pi$
$877$	−14.5117	+	3.88840i	−0.490025	+	0.131302i	0.00534172	+	0.999986i	$0.498300\pi$
$878$	2.12297	+	2.12297i	0.0716469	+	0.0716469i
$879$	−22.7698	−	2.82458i	−0.768006	−	0.0952709i
$880$	−1.41191	+	2.44550i	−0.0475954	+	0.0824376i
$881$	−9.97554	+	17.2781i	−0.336084	+	0.582115i	−0.983693	−	0.179858i	$-0.942436\pi$
$881$	−9.97554	+	17.2781i	−0.336084	+	0.582115i	0.647608	+	0.761974i	$0.275769\pi$
$882$	−20.0807	−	6.14547i	−0.676151	−	0.206929i
$883$		−	23.3363i		−	0.785328i	−0.919682	−	0.392664i	$-0.871553\pi$
$883$		−	23.3363i		−	0.785328i	0.919682	−	0.392664i	$-0.128447\pi$
$884$	0.276449	−	1.65967i	0.00929797	−	0.0558209i
$885$	1.46922	−	1.14494i	0.0493874	−	0.0384867i
$886$	−0.277944	+	1.03730i	−0.00933770	+	0.0348488i
$887$			24.8633i			0.834828i	0.908716	+	0.417414i	$0.137064\pi$
$887$			24.8633i			0.834828i	−0.908716	+	0.417414i	$0.862936\pi$
$888$	1.26574	+	9.08833i	0.0424753	+	0.304984i
$889$	−52.7700	+	20.3235i	−1.76985	+	0.681627i
$890$	2.69801	+	0.722931i	0.0904377	+	0.0242327i
$891$	−15.1822	−	50.5588i	−0.508624	−	1.69378i
$892$	−2.44059	−	9.10841i	−0.0817170	−	0.304972i
$893$		−	9.16835i		−	0.306807i
$894$	1.94524	−	4.79742i	0.0650585	−	0.160450i
$895$	1.61990	+	6.04555i	0.0541473	+	0.202080i
$896$	2.63095	−	0.279464i	0.0878939	−	0.00933624i
$897$	0.145017	−	5.43571i	0.00484199	−	0.181493i
$898$	9.11527	+	15.7881i	0.304181	+	0.526856i
$899$	26.5889	+	7.12448i	0.886790	+	0.237615i
$900$	3.49519	−	13.8711i	0.116506	−	0.462370i
$901$	−3.31418	−	1.91344i	−0.110411	−	0.0637460i
$902$	14.8409	−	14.8409i	0.494147	−	0.494147i
$903$	−47.2482	−	0.831382i	−1.57232	−	0.0276666i
$904$	−2.51943	−	0.675079i	−0.0837950	−	0.0224528i
$905$	−2.51710	+	9.39394i	−0.0836712	+	0.312265i
$906$	7.23370	−	17.8400i	0.240324	−	0.592695i
$907$	33.1332	−	19.1295i	1.10017	−	0.635184i	0.163905	−	0.986476i	$-0.447591\pi$
$907$	33.1332	−	19.1295i	1.10017	−	0.635184i	0.936266	+	0.351292i	$0.114258\pi$
$908$	2.60795	+	2.60795i	0.0865479	+	0.0865479i
$909$	−22.2713	−	21.6147i	−0.738694	−	0.716915i
$910$	−1.44914	+	4.35793i	−0.0480386	+	0.144464i
$911$		−	53.2100i		−	1.76293i	−0.472254	−	0.881463i	$-0.656559\pi$
$911$		−	53.2100i		−	1.76293i	0.472254	−	0.881463i	$-0.343441\pi$
$912$	1.00492	+	2.37567i	0.0332762	+	0.0786663i
$913$	−43.9495	−	76.1227i	−1.45452	−	2.51929i
$914$	−21.6107			−0.714817
$915$	−5.40698	−	4.08502i	−0.178749	−	0.135047i
$916$	−3.11877	+	11.6394i	−0.103047	+	0.384577i
$917$	−6.84304	+	43.5165i	−0.225977	+	1.43704i
$918$	2.26048	+	0.877427i	0.0746070	+	0.0289594i
$919$	18.1613	−	31.4564i	0.599088	−	1.03765i	−0.393869	−	0.919167i	$-0.628863\pi$
$919$	18.1613	−	31.4564i	0.599088	−	1.03765i	0.992956	−	0.118483i	$-0.0378032\pi$
$920$	−0.209596	−	0.363030i	−0.00691017	−	0.0119688i
$921$	5.33184	+	4.02825i	0.175690	+	0.132735i
$922$	3.14882	−	1.81797i	0.103701	−	0.0598716i
$923$	17.8924	+	8.13774i	0.588935	+	0.267857i
$924$	−18.6689	−	19.3377i	−0.614163	−	0.636164i
$925$	24.4003	−	6.53804i	0.802277	−	0.214970i
$926$			16.4520i			0.540645i
$927$	−10.3059	+	10.6189i	−0.338489	+	0.348772i
$928$	−8.00621	+	2.14526i	−0.262817	+	0.0704215i
$929$	−1.14671	−	4.27958i	−0.0376223	−	0.140409i	0.944560	−	0.328339i	$-0.106489\pi$
$929$	−1.14671	−	4.27958i	−0.0376223	−	0.140409i	−0.982182	+	0.187930i	$0.939822\pi$
$930$	−2.20958	−	1.66936i	−0.0724548	−	0.0547403i
$931$	−4.75328	−	9.27809i	−0.155783	−	0.304077i
$932$	7.58807	−	4.38097i	0.248556	−	0.143504i
$933$	49.2429	+	19.9669i	1.61214	+	0.653685i
$934$	−35.0902	−	9.40240i	−1.14819	−	0.307656i
$935$	−0.658871	+	1.14120i	−0.0215474	+	0.0373212i
$936$	8.45348	+	6.74823i	0.276311	+	0.220573i
$937$	−29.5180			−0.964311			−0.482156	−	0.876086i	$-0.660146\pi$
$937$	−29.5180			−0.964311			−0.482156	+	0.876086i	$0.660146\pi$
$938$	16.7786	+	2.63846i	0.547841	+	0.0861489i
$939$	−25.1860	+	19.6269i	−0.821913	+	0.640501i
$940$	−2.56676	−	1.48192i	−0.0837186	−	0.0483350i
$941$	−9.38958	−	35.0424i	−0.306091	−	1.14235i	−0.932002	−	0.362454i	$-0.881939\pi$
$941$	−9.38958	−	35.0424i	−0.306091	−	1.14235i	0.625910	−	0.779895i	$-0.284728\pi$
$942$	7.88849	−	3.33687i	0.257021	−	0.108721i
$943$	0.806393	+	3.00950i	0.0262598	+	0.0980028i
$944$	−1.57951	−	1.57951i	−0.0514088	−	0.0514088i
$945$	−5.72313	−	3.32437i	−0.186173	−	0.108142i
$946$	−52.3813	−	30.2423i	−1.70306	−	0.983263i
$947$	2.50579	+	2.50579i	0.0814273	+	0.0814273i	0.746647	−	0.665220i	$-0.231662\pi$
$947$	2.50579	+	2.50579i	0.0814273	+	0.0814273i	−0.665220	+	0.746647i	$0.731662\pi$
$948$	−9.52631	−	12.2245i	−0.309400	−	0.397033i
$949$	4.40059	+	45.3436i	0.142849	+	1.47192i
$950$	6.14975	−	3.55056i	0.199524	−	0.115195i
$951$	−6.56738	+	52.9416i	−0.212962	+	1.71675i
$952$	1.22774	−	0.130413i	0.0397913	−	0.00422670i
$953$	−16.1085	−	27.9007i	−0.521805	−	0.903792i	−0.999678	−	0.0253634i	$-0.991926\pi$
$953$	−16.1085	−	27.9007i	−0.521805	−	0.903792i	0.477874	−	0.878429i	$-0.341408\pi$
$954$	21.1197	−	12.6184i	0.683774	−	0.408537i
$955$	−9.15095	−	9.15095i	−0.296118	−	0.296118i
$956$	4.62329	+	4.62329i	0.149528	+	0.149528i
$957$	67.1871	+	50.7605i	2.17185	+	1.64085i
$958$	11.3776	+	19.7066i	0.367594	+	0.636692i
$959$	35.0849	−	3.72678i	1.13295	−	0.120344i
$960$	0.827520	+	0.102654i	0.0267081	+	0.00331313i
$961$	−17.2951	+	9.98535i	−0.557908	+	0.322108i
$962$	−3.13845	+	18.8419i	−0.101188	+	0.607486i
$963$	−7.94446	−	27.9685i	−0.256007	−	0.901272i
$964$	−15.2624	−	15.2624i	−0.491568	−	0.491568i
$965$	5.02736	+	2.90255i	0.161836	+	0.0934362i
$966$	3.87175	−	0.964756i	0.124571	−	0.0310405i
$967$	−18.5890	−	18.5890i	−0.597783	−	0.597783i	0.341939	−	0.939722i	$-0.388916\pi$
$967$	−18.5890	−	18.5890i	−0.597783	−	0.597783i	−0.939722	+	0.341939i	$0.888916\pi$
$968$	−6.05730	−	22.6062i	−0.194689	−	0.726590i
$969$	0.468949	+	1.10861i	0.0150648	+	0.0356138i
$970$	0.715874	+	2.67168i	0.0229853	+	0.0857824i
$971$	22.1365	+	12.7805i	0.710394	+	0.410146i	0.811207	−	0.584759i	$-0.198811\pi$
$971$	22.1365	+	12.7805i	0.710394	+	0.410146i	−0.100813	+	0.994905i	$0.532144\pi$
$972$	−12.0036	+	9.94547i	−0.385017	+	0.319001i
$973$	5.08295	+	0.799304i	0.162952	+	0.0256245i
$974$	37.5134			1.20201
$975$	15.5712	−	25.3819i	0.498678	−	0.812870i
$976$	−4.06340	+	7.03801i	−0.130066	+	0.225281i
$977$	−33.5143	−	8.98014i	−1.07222	−	0.287300i	−0.320814	−	0.947142i	$-0.603957\pi$
$977$	−33.5143	−	8.98014i	−1.07222	−	0.287300i	−0.751404	+	0.659842i	$0.770623\pi$
$978$	0.622182	−	1.53445i	0.0198952	−	0.0490662i
$979$	−29.4713	+	17.0153i	−0.941907	+	0.543810i
$980$	−3.36578	−	0.168934i	−0.107516	−	0.00539640i
$981$	6.99249	−	4.17783i	0.223253	−	0.133388i
$982$	1.87549	+	6.99942i	0.0598492	+	0.223360i
$983$	−3.33974	+	0.894882i	−0.106521	+	0.0285423i	−0.311686	−	0.950185i	$-0.600894\pi$
$983$	−3.33974	+	0.894882i	−0.106521	+	0.0285423i	0.205165	+	0.978727i	$0.434227\pi$
$984$	−5.74354	−	2.32887i	−0.183097	−	0.0742417i
$985$			3.40010i			0.108336i
$986$	−3.73612	+	1.00109i	−0.118982	+	0.0318812i
$987$	20.2966	−	19.5947i	0.646049	−	0.623706i
$988$	0.518681	+	5.34449i	0.0165015	+	0.170031i
$989$	7.77593	−	4.48943i	0.247260	−	0.142756i
$990$	−4.34501	−	7.27230i	−0.138093	−	0.231129i
$991$	0.592908	+	1.02695i	0.0188344	+	0.0326221i	0.875289	−	0.483600i	$-0.160671\pi$
$991$	0.592908	+	1.02695i	0.0188344	+	0.0326221i	−0.856455	+	0.516222i	$0.827338\pi$
$992$	−1.66052	+	2.87610i	−0.0527215	+	0.0913164i
$993$	−7.16475	−	16.9377i	−0.227366	−	0.537503i
$994$	−2.24060	+	14.2485i	−0.0710675	+	0.451935i
$995$	−2.22254	+	8.29462i	−0.0704592	+	0.262957i
$996$	−15.6467	+	20.7101i	−0.495784	+	0.656225i
$997$	45.2664			1.43360			0.716801	−	0.697278i	$-0.245606\pi$
$997$	45.2664			1.43360			0.716801	+	0.697278i	$0.245606\pi$
$998$	18.3963	+	31.8633i	0.582324	+	1.00861i
$999$	−25.6627	−	9.96121i	−0.811931	−	0.315159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.9	yes	152
3.2	odd	2	inner	546.2.ch.a.137.24	yes	152
7.2	even	3		546.2.bw.a.527.37	yes	152
13.2	odd	12		546.2.bw.a.431.18	✓	152
21.2	odd	6		546.2.bw.a.527.18	yes	152
39.2	even	12		546.2.bw.a.431.37	yes	152
91.2	odd	12	inner	546.2.ch.a.275.24	yes	152
273.2	even	12	inner	546.2.ch.a.275.9	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.18	✓	152	13.2	odd	12
546.2.bw.a.431.37	yes	152	39.2	even	12
546.2.bw.a.527.18	yes	152	21.2	odd	6
546.2.bw.a.527.37	yes	152	7.2	even	3
546.2.ch.a.137.9	yes	152	1.1	even	1	trivial
546.2.ch.a.137.24	yes	152	3.2	odd	2	inner
546.2.ch.a.275.9	yes	152	273.2	even	12	inner
546.2.ch.a.275.24	yes	152	91.2	odd	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.238917 - 1.71549i) q^{3} -1.00000i q^{4} +(0.465027 + 0.124604i) q^{5} +(1.38198 + 1.04410i) q^{6} +(-1.66275 + 2.05797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.88584 + 0.819723i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.238917 - 1.71549i) q^{3} -1.00000i q^{4} +(0.465027 + 0.124604i) q^{5} +(1.38198 + 1.04410i) q^{6} +(-1.66275 + 2.05797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.88584 + 0.819723i) q^{9} +(-0.416932 + 0.240716i) q^{10} +(1.51809 - 5.66560i) q^{11} +(-1.71549 + 0.238917i) q^{12} +(-3.55655 - 0.592407i) q^{13} +(-0.279464 - 2.63095i) q^{14} +(0.102654 - 0.827520i) q^{15} -1.00000 q^{16} -0.466653 q^{17} +(1.46096 - 2.62023i) q^{18} +(1.43851 - 0.385448i) q^{19} +(0.124604 - 0.465027i) q^{20} +(3.92770 + 2.36075i) q^{21} +(2.93273 + 5.07964i) q^{22} -0.870719 q^{23} +(1.04410 - 1.38198i) q^{24} +(-4.12940 - 2.38411i) q^{25} +(2.93376 - 2.09597i) q^{26} +(2.09571 + 4.75479i) q^{27} +(2.05797 + 1.66275i) q^{28} +(-7.17817 - 4.14432i) q^{29} +(0.512558 + 0.657732i) q^{30} +(-3.20788 + 0.859548i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-10.0820 - 1.25067i) q^{33} +(0.329973 - 0.329973i) q^{34} +(-1.02965 + 0.749828i) q^{35} +(0.819723 + 2.88584i) q^{36} +(-3.74611 + 3.74611i) q^{37} +(-0.744629 + 1.28974i) q^{38} +(-0.166549 + 6.24278i) q^{39} +(0.240716 + 0.416932i) q^{40} +(-0.926123 - 3.45634i) q^{41} +(-4.44661 + 1.10800i) q^{42} +(-8.93046 + 5.15600i) q^{43} +(-5.66560 - 1.51809i) q^{44} +(-1.44413 + 0.0216075i) q^{45} +(0.615692 - 0.615692i) q^{46} +(1.59337 - 5.94655i) q^{47} +(0.238917 + 1.71549i) q^{48} +(-1.47051 - 6.84380i) q^{49} +(4.60575 - 1.23411i) q^{50} +(0.111492 + 0.800540i) q^{51} +(-0.592407 + 3.55655i) q^{52} +(7.10203 + 4.10036i) q^{53} +(-4.84403 - 1.88026i) q^{54} +(1.41191 - 2.44550i) q^{55} +(-2.63095 + 0.279464i) q^{56} +(-1.00492 - 2.37567i) q^{57} +(8.00621 - 2.14526i) q^{58} +(1.57951 + 1.57951i) q^{59} +(-0.827520 - 0.102654i) q^{60} +(4.06340 - 7.03801i) q^{61} +(1.66052 - 2.87610i) q^{62} +(3.11146 - 7.30197i) q^{63} +1.00000i q^{64} +(-1.58008 - 0.718644i) q^{65} +(8.01341 - 6.24469i) q^{66} +(-1.66153 + 6.20090i) q^{67} +0.466653i q^{68} +(0.208030 + 1.49371i) q^{69} +(0.197867 - 1.25828i) q^{70} +(-5.26585 - 1.41098i) q^{71} +(-2.62023 - 1.46096i) q^{72} +(-3.27021 - 12.2046i) q^{73} -5.29779i q^{74} +(-3.10334 + 7.65357i) q^{75} +(-0.385448 - 1.43851i) q^{76} +(9.13544 + 12.5447i) q^{77} +(-4.29654 - 4.53208i) q^{78} +(4.47389 + 7.74901i) q^{79} +(-0.465027 - 0.124604i) q^{80} +(7.65611 - 4.73117i) q^{81} +(3.09887 + 1.78913i) q^{82} +(10.5966 - 10.5966i) q^{83} +(2.36075 - 3.92770i) q^{84} +(-0.217006 - 0.0581466i) q^{85} +(2.66894 - 9.96064i) q^{86} +(-5.39456 + 13.3043i) q^{87} +(5.07964 - 2.93273i) q^{88} +(-4.10253 - 4.10253i) q^{89} +(1.00588 - 1.03643i) q^{90} +(7.13282 - 6.33426i) q^{91} +0.870719i q^{92} +(2.24097 + 5.29773i) q^{93} +(3.07816 + 5.33153i) q^{94} +0.716975 q^{95} +(-1.38198 - 1.04410i) q^{96} +(1.48697 - 5.54945i) q^{97} +(5.87911 + 3.79949i) q^{98} +(0.263252 + 17.5944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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