LMFDB - Embedded newform 546.2.bu.a.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.3
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.703834 + 1.58260i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.95010 - 2.95010i) q^{5} +(-1.34651 - 1.08946i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.00924 - 2.22777i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.703834 + 1.58260i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.95010 - 2.95010i) q^{5} +(-1.34651 - 1.08946i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.00924 - 2.22777i) q^{9} +(3.61312 - 2.08604i) q^{10} +(4.57939 + 1.22704i) q^{11} +(1.40084 - 1.01865i) q^{12} +(-0.0551355 + 3.60513i) q^{13} +1.00000i q^{14} +(6.74521 - 2.59245i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0517866 + 0.0896970i) q^{17} +(2.67189 - 1.36418i) q^{18} +(-0.467589 - 1.74507i) q^{19} +(1.07981 + 4.02992i) q^{20} +(-0.270245 + 1.71084i) q^{21} +(-2.37046 + 4.10576i) q^{22} +(3.68789 + 6.38760i) q^{23} +(0.621380 + 1.61675i) q^{24} +12.4062i q^{25} +(-3.46802 - 0.986333i) q^{26} +(4.93984 - 1.61183i) q^{27} +(-0.965926 - 0.258819i) q^{28} +(5.86255 - 3.38474i) q^{29} +(0.758322 + 7.18635i) q^{30} +(5.59482 - 5.59482i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.16504 + 6.38369i) q^{33} +(-0.0732373 - 0.0732373i) q^{34} +(-3.61312 - 2.08604i) q^{35} +(0.626163 + 2.93393i) q^{36} +(1.73995 - 6.49360i) q^{37} +1.80663 q^{38} +(-5.66667 - 2.62467i) q^{39} -4.17208 q^{40} +(-0.610064 + 2.27679i) q^{41} +(-1.58260 - 0.703834i) q^{42} +(-1.27879 - 0.738312i) q^{43} +(-3.35234 - 3.35234i) q^{44} +(-0.644706 + 12.4996i) q^{45} +(-7.12445 + 1.90899i) q^{46} +(-1.05070 + 1.05070i) q^{47} +(-1.72249 + 0.181761i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-11.9835 - 3.21097i) q^{50} +(-0.105505 - 0.145089i) q^{51} +(1.85031 - 3.09457i) q^{52} +7.03011i q^{53} +(0.278386 + 5.18869i) q^{54} +(-9.88976 - 17.1296i) q^{55} +(0.500000 - 0.866025i) q^{56} +(3.09084 + 0.488231i) q^{57} +(1.75207 + 6.53883i) q^{58} +(2.57322 + 9.60340i) q^{59} +(-7.13775 - 1.12748i) q^{60} +(4.05054 - 7.01575i) q^{61} +(3.95613 + 6.85222i) q^{62} +(-2.51736 - 1.63183i) q^{63} -1.00000i q^{64} +(10.7982 - 10.4729i) q^{65} +(-4.82936 - 6.64127i) q^{66} +(4.97185 + 1.33220i) q^{67} +(0.0896970 - 0.0517866i) q^{68} +(-12.7047 + 1.34063i) q^{69} +(2.95010 - 2.95010i) q^{70} +(13.4294 - 3.59839i) q^{71} +(-2.99602 - 0.154529i) q^{72} +(3.07999 + 3.07999i) q^{73} +(5.82200 + 3.36133i) q^{74} +(-19.6341 - 8.73192i) q^{75} +(-0.467589 + 1.74507i) q^{76} +4.74093 q^{77} +(4.00188 - 4.79427i) q^{78} -1.08752 q^{79} +(1.07981 - 4.02992i) q^{80} +(-0.925943 + 8.95224i) q^{81} +(-2.04131 - 1.17855i) q^{82} +(-8.79180 - 8.79180i) q^{83} +(1.08946 - 1.34651i) q^{84} +(0.417391 - 0.111840i) q^{85} +(1.04413 - 1.04413i) q^{86} +(1.23043 + 11.6604i) q^{87} +(4.10576 - 2.37046i) q^{88} +(10.0049 + 2.68079i) q^{89} +(-11.9068 - 3.85788i) q^{90} +(0.879819 + 3.49656i) q^{91} -7.37577i q^{92} +(4.91653 + 12.7922i) q^{93} +(-0.742959 - 1.28684i) q^{94} +(-3.76869 + 6.52756i) q^{95} +(0.270245 - 1.71084i) q^{96} +(0.420957 + 1.57103i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-6.46749 - 12.6672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.703834	+	1.58260i	−0.406359	+	0.913714i
$3$	−0.703834	+	1.58260i	−0.406359	+	0.913714i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.95010	−	2.95010i	−1.31933	−	1.31933i	−0.914309	−	0.405018i	$-0.867265\pi$
$5$	−2.95010	−	2.95010i	−1.31933	−	1.31933i	−0.405018	−	0.914309i	$-0.632735\pi$
$6$	−1.34651	−	1.08946i	−0.549709	−	0.444769i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$7$	0.965926	−	0.258819i	0.365086	−	0.0978244i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.00924	−	2.22777i	−0.669745	−	0.742591i
$10$	3.61312	−	2.08604i	1.14257	−	0.659663i
$11$	4.57939	+	1.22704i	1.38074	+	0.369967i	0.871389	−	0.490593i	$-0.163220\pi$
$11$	4.57939	+	1.22704i	1.38074	+	0.369967i	0.509348	+	0.860561i	$0.329887\pi$
$12$	1.40084	−	1.01865i	0.404387	−	0.294060i
$13$	−0.0551355	+	3.60513i	−0.0152918	+	0.999883i
$13$	−0.0551355	+	3.60513i	−0.0152918	+	0.999883i
$14$			1.00000i			0.267261i
$15$	6.74521	−	2.59245i	1.74161	−	0.669367i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.0517866	+	0.0896970i	−0.0125601	+	0.0217547i	−0.872237	−	0.489083i	$-0.837331\pi$
$17$	−0.0517866	+	0.0896970i	−0.0125601	+	0.0217547i	0.859677	+	0.510838i	$0.170665\pi$
$18$	2.67189	−	1.36418i	0.629771	−	0.321541i
$19$	−0.467589	−	1.74507i	−0.107272	−	0.400346i	0.891321	−	0.453373i	$-0.149780\pi$
$19$	−0.467589	−	1.74507i	−0.107272	−	0.400346i	−0.998593	+	0.0530276i	$0.983113\pi$
$20$	1.07981	+	4.02992i	0.241454	+	0.901117i
$21$	−0.270245	+	1.71084i	−0.0589722	+	0.373336i
$22$	−2.37046	+	4.10576i	−0.505385	+	0.875352i
$23$	3.68789	+	6.38760i	0.768977	+	1.33191i	0.938118	+	0.346316i	$0.112567\pi$
$23$	3.68789	+	6.38760i	0.768977	+	1.33191i	−0.169141	+	0.985592i	$0.554099\pi$
$24$	0.621380	+	1.61675i	0.126839	+	0.330018i
$25$			12.4062i			2.48124i
$26$	−3.46802	−	0.986333i	−0.680134	−	0.193436i
$27$	4.93984	−	1.61183i	0.950672	−	0.310197i
$28$	−0.965926	−	0.258819i	−0.182543	−	0.0489122i
$29$	5.86255	−	3.38474i	1.08865	−	0.628531i	0.155432	−	0.987847i	$-0.450323\pi$
$29$	5.86255	−	3.38474i	1.08865	−	0.628531i	0.933216	+	0.359315i	$0.116990\pi$
$30$	0.758322	+	7.18635i	0.138450	+	1.31204i
$31$	5.59482	−	5.59482i	1.00486	−	1.00486i	0.00487084	−	0.999988i	$-0.498450\pi$
$31$	5.59482	−	5.59482i	1.00486	−	1.00486i	0.999988	−	0.00487084i	$-0.00155044\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−5.16504	+	6.38369i	−0.899119	+	1.11126i
$34$	−0.0732373	−	0.0732373i	−0.0125601	−	0.0125601i
$35$	−3.61312	−	2.08604i	−0.610729	−	0.352605i
$36$	0.626163	+	2.93393i	0.104360	+	0.488988i
$37$	1.73995	−	6.49360i	0.286047	−	1.06754i	−0.662024	−	0.749482i	$-0.730302\pi$
$37$	1.73995	−	6.49360i	0.286047	−	1.06754i	0.948071	−	0.318059i	$-0.103031\pi$
$38$	1.80663			0.293073
$39$	−5.66667	−	2.62467i	−0.907393	−	0.420283i
$40$	−4.17208			−0.659663
$41$	−0.610064	+	2.27679i	−0.0952760	+	0.355575i	−0.997061	−	0.0766097i	$-0.975590\pi$
$41$	−0.610064	+	2.27679i	−0.0952760	+	0.355575i	0.901785	+	0.432185i	$0.142257\pi$
$42$	−1.58260	−	0.703834i	−0.244200	−	0.108604i
$43$	−1.27879	−	0.738312i	−0.195014	−	0.112591i	0.399314	−	0.916814i	$-0.369248\pi$
$43$	−1.27879	−	0.738312i	−0.195014	−	0.112591i	−0.594328	+	0.804223i	$0.702582\pi$
$44$	−3.35234	−	3.35234i	−0.505385	−	0.505385i
$45$	−0.644706	+	12.4996i	−0.0961072	+	1.86333i
$46$	−7.12445	+	1.90899i	−1.05044	+	0.281465i
$47$	−1.05070	+	1.05070i	−0.153261	+	0.153261i	−0.779573	−	0.626312i	$-0.784564\pi$
$47$	−1.05070	+	1.05070i	−0.153261	+	0.153261i	0.626312	+	0.779573i	$0.284564\pi$
$48$	−1.72249	+	0.181761i	−0.248620	+	0.0262350i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−11.9835	−	3.21097i	−1.69472	−	0.454099i
$51$	−0.105505	−	0.145089i	−0.0147737	−	0.0203166i
$52$	1.85031	−	3.09457i	0.256592	−	0.429139i
$53$			7.03011i			0.965660i	0.875714	+	0.482830i	$0.160391\pi$
$53$			7.03011i			0.965660i	−0.875714	+	0.482830i	$0.839609\pi$
$54$	0.278386	+	5.18869i	0.0378835	+	0.706091i
$55$	−9.88976	−	17.1296i	−1.33353	−	2.30975i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	3.09084	+	0.488231i	0.409392	+	0.0646678i
$58$	1.75207	+	6.53883i	0.230058	+	0.858590i
$59$	2.57322	+	9.60340i	0.335005	+	1.25026i	0.903863	+	0.427821i	$0.140719\pi$
$59$	2.57322	+	9.60340i	0.335005	+	1.25026i	−0.568858	+	0.822436i	$0.692615\pi$
$60$	−7.13775	−	1.12748i	−0.921479	−	0.145557i
$61$	4.05054	−	7.01575i	0.518619	−	0.898274i	−0.481147	−	0.876640i	$-0.659780\pi$
$61$	4.05054	−	7.01575i	0.518619	−	0.898274i	0.999766	−	0.0216343i	$-0.00688695\pi$
$62$	3.95613	+	6.85222i	0.502429	+	0.870233i
$63$	−2.51736	−	1.63183i	−0.317158	−	0.205592i
$64$		−	1.00000i		−	0.125000i
$65$	10.7982	−	10.4729i	1.33935	−	1.29900i
$66$	−4.82936	−	6.64127i	−0.594454	−	0.817484i
$67$	4.97185	+	1.33220i	0.607408	+	0.162755i	0.549397	−	0.835561i	$-0.314857\pi$
$67$	4.97185	+	1.33220i	0.607408	+	0.162755i	0.0580111	+	0.998316i	$0.481524\pi$
$68$	0.0896970	−	0.0517866i	0.0108774	−	0.00628005i
$69$	−12.7047	+	1.34063i	−1.52946	+	0.161393i
$70$	2.95010	−	2.95010i	0.352605	−	0.352605i
$71$	13.4294	−	3.59839i	1.59377	−	0.427051i	0.650620	−	0.759404i	$-0.274509\pi$
$71$	13.4294	−	3.59839i	1.59377	−	0.427051i	0.943155	+	0.332353i	$0.107843\pi$
$72$	−2.99602	−	0.154529i	−0.353084	−	0.0182114i
$73$	3.07999	+	3.07999i	0.360486	+	0.360486i	0.863992	−	0.503506i	$-0.167957\pi$
$73$	3.07999	+	3.07999i	0.360486	+	0.360486i	−0.503506	+	0.863992i	$0.667957\pi$
$74$	5.82200	+	3.36133i	0.676794	+	0.390747i
$75$	−19.6341	−	8.73192i	−2.26715	−	1.00828i
$76$	−0.467589	+	1.74507i	−0.0536361	+	0.200173i
$77$	4.74093			0.540279
$78$	4.00188	−	4.79427i	0.453123	−	0.542844i
$79$	−1.08752			−0.122356			−0.0611779	−	0.998127i	$-0.519486\pi$
$79$	−1.08752			−0.122356			−0.0611779	+	0.998127i	$0.519486\pi$
$80$	1.07981	−	4.02992i	0.120727	−	0.450558i
$81$	−0.925943	+	8.95224i	−0.102883	+	0.994694i
$82$	−2.04131	−	1.17855i	−0.225425	−	0.130149i
$83$	−8.79180	−	8.79180i	−0.965026	−	0.965026i	0.0343828	−	0.999409i	$-0.489053\pi$
$83$	−8.79180	−	8.79180i	−0.965026	−	0.965026i	−0.999409	+	0.0343828i	$0.989053\pi$
$84$	1.08946	−	1.34651i	0.118870	−	0.146916i
$85$	0.417391	−	0.111840i	0.0452725	−	0.0121307i
$86$	1.04413	−	1.04413i	0.112591	−	0.112591i
$87$	1.23043	+	11.6604i	0.131916	+	1.25012i
$88$	4.10576	−	2.37046i	0.437676	−	0.252692i
$89$	10.0049	+	2.68079i	1.06051	+	0.284163i	0.746589	−	0.665285i	$-0.231690\pi$
$89$	10.0049	+	2.68079i	1.06051	+	0.284163i	0.313923	+	0.949448i	$0.398357\pi$
$90$	−11.9068	−	3.85788i	−1.25509	−	0.406656i
$91$	0.879819	+	3.49656i	0.0922301	+	0.366539i
$92$		−	7.37577i		−	0.768977i
$93$	4.91653	+	12.7922i	0.509820	+	1.32649i
$94$	−0.742959	−	1.28684i	−0.0766304	−	0.132728i
$95$	−3.76869	+	6.52756i	−0.386659	+	0.669714i
$96$	0.270245	−	1.71084i	0.0275817	−	0.174612i
$97$	0.420957	+	1.57103i	0.0427417	+	0.159514i	0.983998	−	0.178178i	$-0.0570203\pi$
$97$	0.420957	+	1.57103i	0.0427417	+	0.159514i	−0.941257	+	0.337692i	$0.890354\pi$
$98$	0.258819	+	0.965926i	0.0261447	+	0.0975732i
$99$	−6.46749	−	12.6672i	−0.650008	−	1.27311i
$100$	6.20311	−	10.7441i	0.620311	−	1.07441i
$101$	−3.56624	−	6.17691i	−0.354854	−	0.614626i	0.632239	−	0.774774i	$-0.282136\pi$
$101$	−3.56624	−	6.17691i	−0.354854	−	0.614626i	−0.987093	+	0.160148i	$0.948803\pi$
$102$	0.167452	−	0.0643584i	0.0165802	−	0.00637243i
$103$			13.8569i			1.36536i	0.730717	+	0.682680i	$0.239186\pi$
$103$			13.8569i			1.36536i	−0.730717	+	0.682680i	$0.760814\pi$
$104$	2.51022	+	2.58820i	0.246148	+	0.253794i
$105$	5.84440	−	4.24990i	0.570355	−	0.414748i
$106$	−6.79057	−	1.81953i	−0.659558	−	0.176728i
$107$	3.53028	−	2.03821i	0.341285	−	0.197041i	−0.319555	−	0.947568i	$-0.603533\pi$
$107$	3.53028	−	2.03821i	0.341285	−	0.197041i	0.660840	+	0.750527i	$0.270200\pi$
$108$	−5.08394	−	1.07403i	−0.489202	−	0.103349i
$109$	1.84962	−	1.84962i	0.177161	−	0.177161i	−0.612956	−	0.790117i	$-0.710020\pi$
$109$	1.84962	−	1.84962i	0.177161	−	0.177161i	0.790117	+	0.612956i	$0.210020\pi$
$110$	19.1055	−	5.11932i	1.82164	−	0.488108i
$111$	9.05212	+	7.32406i	0.859189	+	0.695169i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−6.04528	−	3.49024i	−0.568692	−	0.328335i	0.187935	−	0.982182i	$-0.439821\pi$
$113$	−6.04528	−	3.49024i	−0.568692	−	0.328335i	−0.756627	+	0.653847i	$0.773154\pi$
$114$	−1.27156	+	2.85916i	−0.119093	+	0.267785i
$115$	7.96445	−	29.7237i	0.742689	−	2.77175i
$116$	−6.76949			−0.628531
$117$	8.14219	−	7.12073i	0.752746	−	0.658311i
$118$	−9.94217			−0.915251
$119$	−0.0268067	+	0.100044i	−0.00245737	+	0.00917102i
$120$	2.93645	−	6.60272i	0.268060	−	0.602743i
$121$	9.93886	+	5.73820i	0.903533	+	0.521655i
$122$	5.72833	+	5.72833i	0.518619	+	0.518619i
$123$	−3.17386	−	2.56797i	−0.286177	−	0.231546i
$124$	−7.64266	+	2.04785i	−0.686331	+	0.183902i
$125$	21.8491	−	21.8491i	1.95425	−	1.95425i
$126$	2.22777	−	2.00924i	0.198466	−	0.178997i
$127$	−2.38397	+	1.37639i	−0.211543	+	0.122135i	−0.602028	−	0.798475i	$-0.705641\pi$
$127$	−2.38397	+	1.37639i	−0.211543	+	0.122135i	0.390485	+	0.920609i	$0.372307\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	2.06851	−	1.50417i	0.182122	−	0.132435i
$130$	7.32123	+	13.1408i	0.642114	+	1.15252i
$131$		−	17.1154i		−	1.49538i	−0.664049	−	0.747689i	$-0.731163\pi$
$131$		−	17.1154i		−	1.49538i	0.664049	−	0.747689i	$-0.268837\pi$
$132$	7.66491	−	2.94592i	0.667144	−	0.256409i
$133$	−0.903313	−	1.56458i	−0.0783272	−	0.135667i
$134$	−2.57362	+	4.45764i	−0.222327	+	0.385081i
$135$	−19.3281	−	9.81796i	−1.66350	−	0.844996i
$136$	0.0268067	+	0.100044i	0.00229866	+	0.00857870i
$137$	2.07438	+	7.74168i	0.177226	+	0.661416i	0.996162	+	0.0875311i	$0.0278977\pi$
$137$	2.07438	+	7.74168i	0.177226	+	0.661416i	−0.818936	+	0.573885i	$0.805436\pi$
$138$	1.99326	−	12.6188i	0.169678	−	1.07418i
$139$	−10.9960	+	19.0456i	−0.932666	+	1.61542i	−0.153922	+	0.988083i	$0.549190\pi$
$139$	−10.9960	+	19.0456i	−0.932666	+	1.61542i	−0.778744	+	0.627341i	$0.784143\pi$
$140$	2.08604	+	3.61312i	0.176302	+	0.305365i
$141$	−0.923321	−	2.40236i	−0.0777576	−	0.202315i
$142$			13.9031i			1.16672i
$143$	−4.67613	+	16.4416i	−0.391038	+	1.37492i
$144$	0.924690	−	2.85394i	0.0770575	−	0.237828i
$145$	−27.2805	−	7.30978i	−2.26552	−	0.607044i
$146$	−3.77221	+	2.17788i	−0.312190	+	0.180243i
$147$	0.181761	+	1.72249i	0.0149914	+	0.142068i
$148$	−4.75364	+	4.75364i	−0.390747	+	0.390747i
$149$	−1.75740	+	0.470895i	−0.143972	+	0.0385772i	−0.330085	−	0.943951i	$-0.607078\pi$
$149$	−1.75740	+	0.470895i	−0.143972	+	0.0385772i	0.186113	+	0.982528i	$0.440411\pi$
$150$	13.5161	−	16.7051i	1.10358	−	1.36396i
$151$	−1.45928	−	1.45928i	−0.118754	−	0.118754i	0.645232	−	0.763987i	$-0.276761\pi$
$151$	−1.45928	−	1.45928i	−0.118754	−	0.118754i	−0.763987	+	0.645232i	$0.776761\pi$
$152$	−1.56458	−	0.903313i	−0.126904	−	0.0732683i
$153$	0.303876	−	0.0648537i	0.0245669	−	0.00524311i
$154$	−1.22704	+	4.57939i	−0.0988779	+	0.369017i
$155$	−33.0106			−2.65147
$156$	3.59514	+	5.10636i	0.287842	+	0.408836i
$157$	−10.0860			−0.804954			−0.402477	−	0.915430i	$-0.631851\pi$
$157$	−10.0860			−0.804954			−0.402477	+	0.915430i	$0.631851\pi$
$158$	0.281471	−	1.05047i	0.0223927	−	0.0835706i
$159$	−11.1258	−	4.94803i	−0.882337	−	0.392404i
$160$	3.61312	+	2.08604i	0.285643	+	0.164916i
$161$	5.21546	+	5.21546i	0.411036	+	0.411036i
$162$	−8.40755	−	3.21140i	−0.660559	−	0.252312i
$163$	0.222679	−	0.0596666i	0.0174415	−	0.00467345i	−0.250088	−	0.968223i	$-0.580459\pi$
$163$	0.222679	−	0.0596666i	0.0174415	−	0.00467345i	0.267529	+	0.963550i	$0.413793\pi$
$164$	1.66673	−	1.66673i	0.130149	−	0.130149i
$165$	34.0700	−	3.59515i	2.65234	−	0.279882i
$166$	10.7677	−	6.21674i	0.835737	−	0.482513i
$167$	3.37163	+	0.903426i	0.260905	+	0.0699092i	0.386900	−	0.922122i	$-0.373546\pi$
$167$	3.37163	+	0.903426i	0.260905	+	0.0699092i	−0.125996	+	0.992031i	$0.540212\pi$
$168$	1.01865	+	1.40084i	0.0785908	+	0.108077i
$169$	−12.9939	−	0.397541i	−0.999532	−	0.0305801i
$170$			0.432115i			0.0331417i
$171$	−2.94811	+	4.54793i	−0.225448	+	0.347789i
$172$	0.738312	+	1.27879i	0.0562957	+	0.0975071i
$173$	11.7841	−	20.4106i	0.895925	−	1.55179i	0.0632700	−	0.997996i	$-0.479847\pi$
$173$	11.7841	−	20.4106i	0.895925	−	1.55179i	0.832655	−	0.553792i	$-0.186820\pi$
$174$	−11.5815	−	1.82942i	−0.877991	−	0.138688i
$175$	3.21097	+	11.9835i	0.242726	+	0.905867i
$176$	1.22704	+	4.57939i	0.0924918	+	0.345184i
$177$	−17.0095	−	2.68682i	−1.27851	−	0.201954i
$178$	−5.17889	+	8.97011i	−0.388174	+	0.672338i
$179$	−10.5732	−	18.3133i	−0.790276	−	1.36880i	−0.925796	−	0.378024i	$-0.876604\pi$
$179$	−10.5732	−	18.3133i	−0.790276	−	1.36880i	0.135519	−	0.990775i	$-0.456730\pi$
$180$	6.80814	−	10.5026i	0.507449	−	0.782820i
$181$		−	0.0482642i		−	0.00358745i	−0.999998	−	0.00179373i	$-0.999429\pi$
$181$		−	0.0482642i		−	0.00358745i	0.999998	−	0.00179373i	$-0.000570961\pi$
$182$	−3.60513	−	0.0551355i	−0.267230	−	0.00408691i
$183$	8.25220	+	11.3483i	0.610020	+	0.838891i
$184$	7.12445	+	1.90899i	0.525221	+	0.140733i
$185$	−24.2898	+	14.0237i	−1.78582	+	1.03105i
$186$	−13.6288	+	1.43814i	−0.999311	+	0.105450i
$187$	−0.347213	+	0.347213i	−0.0253907	+	0.0253907i
$188$	1.43529	−	0.384584i	0.104679	−	0.0280487i
$189$	4.35434	−	2.83543i	0.316732	−	0.206247i
$190$	−5.32973	−	5.32973i	−0.386659	−	0.386659i
$191$	−4.60045	−	2.65607i	−0.332877	−	0.192187i	0.324241	−	0.945975i	$-0.394891\pi$
$191$	−4.60045	−	2.65607i	−0.332877	−	0.192187i	−0.657118	+	0.753788i	$0.728225\pi$
$192$	1.58260	+	0.703834i	0.114214	+	0.0507948i
$193$	−0.698913	+	2.60838i	−0.0503089	+	0.187755i	−0.986507	−	0.163716i	$-0.947652\pi$
$193$	−0.698913	+	2.60838i	−0.0503089	+	0.187755i	0.936199	+	0.351471i	$0.114319\pi$
$194$	−1.62645			−0.116773
$195$	8.97421	+	24.4603i	0.642656	+	1.75164i
$196$	−1.00000			−0.0714286
$197$	−1.51048	+	5.63719i	−0.107617	+	0.401633i	−0.998629	−	0.0523474i	$-0.983330\pi$
$197$	−1.51048	+	5.63719i	−0.107617	+	0.401633i	0.891012	+	0.453980i	$0.149996\pi$
$198$	13.9095	−	2.96859i	0.988507	−	0.210969i
$199$	−9.34223	−	5.39374i	−0.662253	−	0.382352i	0.130882	−	0.991398i	$-0.458219\pi$
$199$	−9.34223	−	5.39374i	−0.662253	−	0.382352i	−0.793135	+	0.609046i	$0.791552\pi$
$200$	8.77253	+	8.77253i	0.620311	+	0.620311i
$201$	−5.60770	+	6.93079i	−0.395537	+	0.488860i
$202$	6.88945	−	1.84602i	0.484740	−	0.129886i
$203$	4.78675	−	4.78675i	0.335964	−	0.335964i
$204$	0.0188256	+	0.178404i	0.00131806	+	0.0124907i
$205$	8.51652	−	4.91701i	0.594819	−	0.343419i
$206$	−13.3847	−	3.58643i	−0.932559	−	0.249878i
$207$	6.82030	−	21.0500i	0.474044	−	1.46307i
$208$	−3.14970	+	1.75482i	−0.218393	+	0.121675i
$209$		−	8.56508i		−	0.592459i
$210$	2.59245	+	6.74521i	0.178896	+	0.465464i
$211$	−7.35043	−	12.7313i	−0.506025	−	0.876460i	−0.999976	−	0.00697061i	$-0.997781\pi$
$211$	−7.35043	−	12.7313i	−0.506025	−	0.876460i	0.493951	−	0.869490i	$-0.335552\pi$
$212$	3.51506	−	6.08825i	0.241415	−	0.418143i
$213$	−3.75724	+	23.7860i	−0.257442	+	1.62979i
$214$	1.05505	+	3.93751i	0.0721220	+	0.269163i
$215$	1.59448	+	5.95067i	0.108742	+	0.405832i
$216$	2.35326	−	4.63273i	0.160119	−	0.315217i
$217$	3.95613	−	6.85222i	0.268560	−	0.465159i
$218$	1.30788	+	2.26531i	0.0885806	+	0.153426i
$219$	−7.04220	+	2.70659i	−0.475867	+	0.182894i
$220$			19.7795i			1.33353i
$221$	−0.320514	−	0.191643i	−0.0215601	−	0.0128913i
$222$	−9.41736	+	6.84807i	−0.632052	+	0.459612i
$223$	12.1400	+	3.25289i	0.812951	+	0.217830i	0.641262	−	0.767322i	$-0.278411\pi$
$223$	12.1400	+	3.25289i	0.812951	+	0.217830i	0.171689	+	0.985151i	$0.445078\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	27.6382	−	24.9270i	1.84255	−	1.66180i
$226$	4.93595	−	4.93595i	0.328335	−	0.328335i
$227$	−3.63497	+	0.973988i	−0.241262	+	0.0646459i	−0.377424	−	0.926041i	$-0.623190\pi$
$227$	−3.63497	+	0.973988i	−0.241262	+	0.0646459i	0.136162	+	0.990687i	$0.456523\pi$
$228$	−2.43263	−	1.96824i	−0.161105	−	0.130350i
$229$	−0.978773	−	0.978773i	−0.0646792	−	0.0646792i	0.674027	−	0.738706i	$-0.264563\pi$
$229$	−0.978773	−	0.978773i	−0.0646792	−	0.0646792i	−0.738706	+	0.674027i	$0.764563\pi$
$230$	26.6496	+	15.3861i	1.75722	+	1.01453i
$231$	−3.33683	+	7.50299i	−0.219547	+	0.493660i
$232$	1.75207	−	6.53883i	0.115029	−	0.429295i
$233$	0.0898158			0.00588403			0.00294201	−	0.999996i	$-0.499064\pi$
$233$	0.0898158			0.00588403			0.00294201	+	0.999996i	$0.499064\pi$
$234$	4.77074	+	9.70773i	0.311873	+	0.634614i
$235$	6.19937			0.404402
$236$	2.57322	−	9.60340i	0.167503	−	0.625128i
$237$	0.765435	−	1.72111i	0.0497203	−	0.111798i
$238$	−0.0896970	−	0.0517866i	−0.00581419	−	0.00335683i
$239$	19.6388	+	19.6388i	1.27033	+	1.27033i	0.945915	+	0.324415i	$0.105167\pi$
$239$	19.6388	+	19.6388i	1.27033	+	1.27033i	0.324415	+	0.945915i	$0.394833\pi$
$240$	5.61773	+	4.54530i	0.362623	+	0.293398i
$241$	−1.34686	+	0.360891i	−0.0867592	+	0.0232471i	−0.301938	−	0.953328i	$-0.597633\pi$
$241$	−1.34686	+	0.360891i	−0.0867592	+	0.0232471i	0.215178	+	0.976575i	$0.430967\pi$
$242$	−8.11505	+	8.11505i	−0.521655	+	0.521655i
$243$	−13.5161	−	7.76629i	−0.867058	−	0.498207i
$244$	−7.01575	+	4.05054i	−0.449137	+	0.259309i
$245$	−4.02992	−	1.07981i	−0.257462	−	0.0689867i
$246$	3.30192	−	2.40107i	0.210523	−	0.153087i
$247$	6.31697	−	1.58950i	0.401939	−	0.101138i
$248$		−	7.91227i		−	0.502429i
$249$	20.1019	−	7.72593i	1.27390	−	0.489611i
$250$	15.4497	+	26.7596i	0.977123	+	1.69243i
$251$	−10.2710	+	17.7899i	−0.648299	+	1.12289i	0.335230	+	0.942136i	$0.391186\pi$
$251$	−10.2710	+	17.7899i	−0.648299	+	1.12289i	−0.983529	+	0.180751i	$0.942147\pi$
$252$	1.36418	+	2.67189i	0.0859354	+	0.168313i
$253$	9.05039	+	33.7765i	0.568993	+	2.12351i
$254$	−0.712470	−	2.65897i	−0.0447043	−	0.166839i
$255$	−0.116777	+	0.739279i	−0.00731285	+	0.0462955i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.6045	+	21.8317i	0.786250	+	1.36182i	0.928250	+	0.371958i	$0.121313\pi$
$257$	12.6045	+	21.8317i	0.786250	+	1.36182i	−0.142000	+	0.989867i	$0.545353\pi$
$258$	0.917545	+	2.38733i	0.0571238	+	0.148629i
$259$		−	6.72267i		−	0.417726i
$260$	−14.5879	+	3.67067i	−0.904704	+	0.227646i
$261$	−19.3197	−	6.25968i	−1.19586	−	0.387464i
$262$	16.5322	+	4.42979i	1.02136	+	0.273673i
$263$	5.89399	−	3.40289i	0.363439	−	0.209831i	−0.307149	−	0.951661i	$-0.599375\pi$
$263$	5.89399	−	3.40289i	0.363439	−	0.209831i	0.670588	+	0.741830i	$0.266042\pi$
$264$	0.861717	+	8.16619i	0.0530350	+	0.502594i
$265$	20.7396	−	20.7396i	1.27402	−	1.27402i
$266$	1.74507	−	0.467589i	0.106997	−	0.0286697i
$267$	−11.2844	+	13.9468i	−0.690592	+	0.853532i
$268$	−3.63965	−	3.63965i	−0.222327	−	0.222327i
$269$	−9.97693	−	5.76018i	−0.608304	−	0.351205i	0.163997	−	0.986461i	$-0.447561\pi$
$269$	−9.97693	−	5.76018i	−0.608304	−	0.351205i	−0.772301	+	0.635256i	$0.780894\pi$
$270$	14.4859	−	16.1284i	0.881584	−	0.981546i
$271$	1.87135	−	6.98396i	0.113676	−	0.424246i	−0.885508	−	0.464624i	$-0.846190\pi$
$271$	1.87135	−	6.98396i	0.113676	−	0.424246i	0.999184	+	0.0403781i	$0.0128563\pi$
$272$	−0.103573			−0.00628005
$273$	−6.15289	−	1.06859i	−0.372390	−	0.0646743i
$274$	−8.01477			−0.484190
$275$	−15.2230	+	56.8129i	−0.917979	+	3.42595i
$276$	11.6729	+	5.19132i	0.702625	+	0.312481i
$277$	22.4542	+	12.9640i	1.34914	+	0.778929i	0.988128	−	0.153631i	$-0.0490968\pi$
$277$	22.4542	+	12.9640i	1.34914	+	0.778929i	0.361016	+	0.932560i	$0.382430\pi$
$278$	−15.5506	−	15.5506i	−0.932666	−	0.932666i
$279$	−23.7053	−	1.22267i	−1.41920	−	0.0731996i
$280$	−4.02992	+	1.07981i	−0.240834	+	0.0645312i
$281$	−16.6785	+	16.6785i	−0.994954	+	0.994954i	−0.999987	−	0.00503350i	$-0.998398\pi$
$281$	−16.6785	+	16.6785i	−0.994954	+	0.994954i	0.00503350	+	0.999987i	$0.498398\pi$
$282$	2.55948	−	0.270082i	0.152415	−	0.0160832i
$283$	7.88176	−	4.55053i	0.468522	−	0.270501i	−0.247099	−	0.968990i	$-0.579477\pi$
$283$	7.88176	−	4.55053i	0.468522	−	0.270501i	0.715621	+	0.698489i	$0.246144\pi$
$284$	−13.4294	−	3.59839i	−0.796887	−	0.213525i
$285$	−7.67798	−	10.5586i	−0.454804	−	0.625440i
$286$	−14.6711	−	8.77221i	−0.867521	−	0.518711i
$287$			2.35711i			0.139136i
$288$	2.51736	+	1.63183i	0.148337	+	0.0961568i
$289$	8.49464	+	14.7131i	0.499684	+	0.865479i
$290$	14.1214	−	24.4590i	0.829238	−	1.43628i
$291$	−2.78260	−	0.439541i	−0.163119	−	0.0257663i
$292$	−1.12736	−	4.20735i	−0.0659735	−	0.246216i
$293$	−5.91373	−	22.0704i	−0.345484	−	1.28936i	−0.892046	−	0.451945i	$-0.850730\pi$
$293$	−5.91373	−	22.0704i	−0.345484	−	1.28936i	0.546562	−	0.837419i	$-0.315936\pi$
$294$	−1.71084	−	0.270245i	−0.0997781	−	0.0157610i
$295$	20.7398	−	35.9223i	1.20752	−	2.09148i
$296$	−3.36133	−	5.82200i	−0.195374	−	0.338397i
$297$	24.5992	−	1.31981i	1.42739	−	0.0765830i
$298$		−	1.81940i		−	0.105395i
$299$	−23.2315	+	12.9431i	−1.34351	+	0.748520i
$300$	12.6376	+	17.3791i	0.729635	+	1.00338i
$301$	−1.42631	−	0.382178i	−0.0822111	−	0.0220284i
$302$	1.78724	−	1.03187i	0.102844	−	0.0593772i
$303$	12.2856	−	1.29641i	0.705790	−	0.0744768i
$304$	1.27748	−	1.27748i	0.0732683	−	0.0732683i
$305$	−32.6467	+	8.74766i	−1.86934	+	0.500889i
$306$	−0.0160051	+	0.310307i	−0.000914948	+	0.0177391i
$307$	−3.72310	−	3.72310i	−0.212489	−	0.212489i	0.592835	−	0.805324i	$-0.298009\pi$
$307$	−3.72310	−	3.72310i	−0.212489	−	0.212489i	−0.805324	+	0.592835i	$0.798009\pi$
$308$	−4.10576	−	2.37046i	−0.233948	−	0.135070i
$309$	−21.9299	−	9.75295i	−1.24755	−	0.554826i
$310$	8.54377	−	31.8858i	0.485253	−	1.81099i
$311$	−4.86351			−0.275784			−0.137892	−	0.990447i	$-0.544033\pi$
$311$	−4.86351			−0.275784			−0.137892	+	0.990447i	$0.544033\pi$
$312$	−5.86286	+	2.15102i	−0.331919	+	0.121777i
$313$	−5.85878			−0.331158			−0.165579	−	0.986197i	$-0.552949\pi$
$313$	−5.85878			−0.331158			−0.165579	+	0.986197i	$0.552949\pi$
$314$	2.61046	−	9.74237i	0.147317	−	0.549794i
$315$	2.61240	+	12.2406i	0.147192	+	0.689678i
$316$	0.941822	+	0.543761i	0.0529816	+	0.0305890i
$317$	16.7473	+	16.7473i	0.940621	+	0.940621i	0.998333	−	0.0577120i	$-0.0183805\pi$
$317$	16.7473	+	16.7473i	0.940621	+	0.940621i	−0.0577120	+	0.998333i	$0.518381\pi$
$318$	7.65901	−	9.46609i	0.429496	−	0.530832i
$319$	31.0001	−	8.30645i	1.73567	−	0.465072i
$320$	−2.95010	+	2.95010i	−0.164916	+	0.164916i
$321$	0.740934	+	7.02157i	0.0413549	+	0.391906i
$322$	−6.38760	+	3.68789i	−0.355967	+	0.205518i
$323$	0.180742	+	0.0484297i	0.0100568	+	0.00269470i
$324$	5.27801	−	7.28990i	0.293223	−	0.404994i
$325$	−44.7260	−	0.684023i	−2.48095	−	0.0379428i
$326$			0.230534i			0.0127681i
$327$	1.62538	+	4.22902i	0.0898836	+	0.233865i
$328$	1.17855	+	2.04131i	0.0650747	+	0.112713i
$329$	−0.742959	+	1.28684i	−0.0409607	+	0.0709460i
$330$	−5.34531	+	33.8396i	−0.294250	+	1.86281i
$331$	−3.62641	−	13.5340i	−0.199326	−	0.743893i	−0.991105	−	0.133086i	$-0.957511\pi$
$331$	−3.62641	−	13.5340i	−0.199326	−	0.743893i	0.791779	−	0.610808i	$-0.209155\pi$
$332$	3.21802	+	12.0098i	0.176612	+	0.659125i
$333$	−17.9622	+	9.17095i	−0.984325	+	0.502565i
$334$	−1.74528	+	3.02292i	−0.0954977	+	0.165407i
$335$	−10.7373	−	18.5976i	−0.586643	−	1.01610i
$336$	−1.61675	+	0.621380i	−0.0882010	+	0.0338991i
$337$			8.57510i			0.467115i	0.972343	+	0.233558i	$0.0750368\pi$
$337$			8.57510i			0.467115i	−0.972343	+	0.233558i	$0.924963\pi$
$338$	3.74707	−	12.4483i	0.203814	−	0.677097i
$339$	9.77853	−	7.11070i	0.531097	−	0.386200i
$340$	−0.417391	−	0.111840i	−0.0226362	−	0.00606536i
$341$	32.4859	−	18.7557i	1.75921	−	1.01568i
$342$	−3.62994	−	4.02475i	−0.196285	−	0.217634i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−1.42631	+	0.382178i	−0.0769014	+	0.0206057i
$345$	41.4351	+	33.5251i	2.23079	+	1.80493i
$346$	16.6652	+	16.6652i	0.895925	+	0.895925i
$347$	−11.3329	−	6.54304i	−0.608380	−	0.351249i	0.163951	−	0.986469i	$-0.447576\pi$
$347$	−11.3329	−	6.54304i	−0.608380	−	0.351249i	−0.772331	+	0.635220i	$0.780909\pi$
$348$	4.76460	−	10.7134i	0.255409	−	0.574298i
$349$	−7.59982	+	28.3629i	−0.406809	+	1.51823i	0.393886	+	0.919159i	$0.371131\pi$
$349$	−7.59982	+	28.3629i	−0.406809	+	1.51823i	−0.800695	+	0.599072i	$0.795536\pi$
$350$	−12.4062			−0.663141
$351$	5.53850	+	17.8976i	0.295623	+	0.955305i
$352$	−4.74093			−0.252692
$353$	−4.31522	+	16.1046i	−0.229676	+	0.857162i	0.750801	+	0.660528i	$0.229668\pi$
$353$	−4.31522	+	16.1046i	−0.229676	+	0.857162i	−0.980477	+	0.196634i	$0.936999\pi$
$354$	6.99764	−	15.7345i	0.371920	−	0.836278i
$355$	−50.2337	−	29.0024i	−2.66613	−	1.53929i
$356$	−7.32406	−	7.32406i	−0.388174	−	0.388174i
$357$	−0.139462	−	0.112839i	−0.00738111	−	0.00597205i
$358$	20.4258	−	5.47308i	1.07954	−	0.289261i
$359$	4.13027	−	4.13027i	0.217987	−	0.217987i	−0.589662	−	0.807650i	$-0.700739\pi$
$359$	4.13027	−	4.13027i	0.217987	−	0.217987i	0.807650	+	0.589662i	$0.200739\pi$
$360$	8.38269	+	9.29444i	0.441806	+	0.489860i
$361$	13.6279	−	7.86805i	0.717256	−	0.414108i
$362$	0.0466197	+	0.0124917i	0.00245027	+	0.000656549i
$363$	−16.0766	+	11.6905i	−0.843802	+	0.613591i
$364$	0.986333	−	3.46802i	0.0516979	−	0.181774i
$365$		−	18.1726i		−	0.951197i
$366$	−13.0974	+	5.03386i	−0.684614	+	0.263124i
$367$	9.22631	+	15.9804i	0.481610	+	0.834172i	0.999777	−	0.0211067i	$-0.00671897\pi$
$367$	9.22631	+	15.9804i	0.481610	+	0.834172i	−0.518168	+	0.855279i	$0.673386\pi$
$368$	−3.68789	+	6.38760i	−0.192244	+	0.332977i
$369$	6.29793	−	3.21552i	0.327857	−	0.167393i
$370$	−7.25922	−	27.0918i	−0.377389	−	1.40844i
$371$	1.81953	+	6.79057i	0.0944651	+	0.352549i
$372$	2.13825	−	13.5366i	0.110863	−	0.701841i
$373$	−11.6021	+	20.0954i	−0.600733	+	1.04050i	0.391977	+	0.919975i	$0.371791\pi$
$373$	−11.6021	+	20.0954i	−0.600733	+	1.04050i	−0.992710	+	0.120525i	$0.961542\pi$
$374$	−0.245517	−	0.425247i	−0.0126954	−	0.0219890i
$375$	19.2002	+	49.9566i	0.991496	+	2.57975i
$376$			1.48592i			0.0766304i
$377$	11.8792	+	21.3219i	0.611810	+	1.09813i
$378$	1.61183	+	4.93984i	0.0829037	+	0.254078i
$379$	7.11452	+	1.90633i	0.365448	+	0.0979216i	0.436870	−	0.899525i	$-0.356087\pi$
$379$	7.11452	+	1.90633i	0.365448	+	0.0979216i	−0.0714217	+	0.997446i	$0.522754\pi$
$380$	6.52756	−	3.76869i	0.334857	−	0.193330i
$381$	−0.500347	−	4.74162i	−0.0256336	−	0.242920i
$382$	3.75625	−	3.75625i	0.192187	−	0.192187i
$383$	4.01147	−	1.07487i	0.204977	−	0.0549233i	−0.154870	−	0.987935i	$-0.549496\pi$
$383$	4.01147	−	1.07487i	0.204977	−	0.0549233i	0.359846	+	0.933012i	$0.382829\pi$
$384$	−1.08946	+	1.34651i	−0.0555962	+	0.0687137i
$385$	−13.9862	−	13.9862i	−0.712804	−	0.712804i
$386$	−2.33861	−	1.35020i	−0.119032	−	0.0687232i
$387$	0.924607	+	4.33230i	0.0470004	+	0.220223i
$388$	0.420957	−	1.57103i	0.0213709	−	0.0797572i
$389$	−0.214733			−0.0108874			−0.00544369	−	0.999985i	$-0.501733\pi$
$389$	−0.214733			−0.0108874			−0.00544369	+	0.999985i	$0.501733\pi$
$390$	−25.9495	+	2.33763i	−1.31401	+	0.118370i
$391$	−0.763932			−0.0386337
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$	27.0868	+	12.0464i	1.36635	+	0.607660i
$394$	−5.05416	−	2.91802i	−0.254625	−	0.147008i
$395$	3.20830	+	3.20830i	0.161427	+	0.161427i
$396$	−0.732611	+	14.2039i	−0.0368151	+	0.713773i
$397$	31.1696	−	8.35188i	1.56436	−	0.419169i	0.630319	−	0.776336i	$-0.282924\pi$
$397$	31.1696	−	8.35188i	1.56436	−	0.419169i	0.934040	+	0.357167i	$0.116257\pi$
$398$	7.62790	−	7.62790i	0.382352	−	0.382352i
$399$	3.11189	−	0.328375i	0.155789	−	0.0164393i
$400$	−10.7441	+	6.20311i	−0.537205	+	0.310156i
$401$	−29.0147	−	7.77448i	−1.44893	−	0.388239i	−0.553277	−	0.832998i	$-0.686623\pi$
$401$	−29.0147	−	7.77448i	−1.44893	−	0.388239i	−0.895650	+	0.444759i	$0.853289\pi$
$402$	−5.24325	−	7.21044i	−0.261510	−	0.359624i
$403$	19.8616	+	20.4785i	0.989375	+	1.02011i
$404$			7.13248i			0.354854i
$405$	29.1417	−	23.6784i	1.44806	−	1.17659i
$406$	3.38474	+	5.86255i	0.167982	+	0.290953i
$407$	15.9358	−	27.6017i	0.789910	−	1.36817i
$408$	−0.177197	−	0.0279901i	−0.00877256	−	0.00138572i
$409$	2.65086	+	9.89314i	0.131077	+	0.489184i	0.999983	−	0.00579155i	$-0.00184352\pi$
$409$	2.65086	+	9.89314i	0.131077	+	0.489184i	−0.868907	+	0.494976i	$0.835177\pi$
$410$	2.54523	+	9.49894i	0.125700	+	0.469119i
$411$	−13.7120	−	2.16595i	−0.676362	−	0.106838i
$412$	6.92845	−	12.0004i	0.341340	−	0.591218i
$413$	4.97109	+	8.61018i	0.244611	+	0.423679i
$414$	18.5675	+	12.0360i	0.912542	+	0.591539i
$415$			51.8735i			2.54637i
$416$	−0.879819	−	3.49656i	−0.0431367	−	0.171433i
$417$	−22.4022	−	30.8071i	−1.09704	−	1.50863i
$418$	8.27324	+	2.21681i	0.404657	+	0.108428i
$419$	−13.6818	+	7.89918i	−0.668399	+	0.385900i	−0.795470	−	0.605993i	$-0.792776\pi$
$419$	−13.6818	+	7.89918i	−0.668399	+	0.385900i	0.127071	+	0.991894i	$0.459442\pi$
$420$	−7.18635	+	0.758322i	−0.350658	+	0.0370023i
$421$	−12.5693	+	12.5693i	−0.612592	+	0.612592i	−0.943621	−	0.331028i	$-0.892604\pi$
$421$	−12.5693	+	12.5693i	−0.612592	+	0.612592i	0.331028	+	0.943621i	$0.392604\pi$
$422$	14.1999	−	3.80486i	0.691242	−	0.185218i
$423$	4.45184	+	0.229617i	0.216456	+	0.0111644i
$424$	4.97104	+	4.97104i	0.241415	+	0.241415i
$425$	−1.11280	−	0.642476i	−0.0539788	−	0.0311647i
$426$	−22.0031	−	9.78549i	−1.06605	−	0.474108i
$427$	2.09672	−	7.82505i	0.101467	−	0.378681i
$428$	−4.07641			−0.197041
$429$	−22.7293	−	18.9726i	−1.09738	−	0.916007i
$430$	−6.16059			−0.297090
$431$	4.06934	−	15.1870i	0.196013	−	0.731531i	−0.795989	−	0.605311i	$-0.793049\pi$
$431$	4.06934	−	15.1870i	0.196013	−	0.731531i	0.992002	−	0.126220i	$-0.0402846\pi$
$432$	3.86581	+	3.47211i	0.185994	+	0.167052i
$433$	−30.7795	−	17.7705i	−1.47917	−	0.853998i	−0.479446	−	0.877571i	$-0.659162\pi$
$433$	−30.7795	−	17.7705i	−1.47917	−	0.853998i	−0.999722	+	0.0235735i	$0.992496\pi$
$434$	5.59482	+	5.59482i	0.268560	+	0.268560i
$435$	30.7694	−	38.0292i	1.47528	−	1.82336i
$436$	−2.52662	+	0.677007i	−0.121003	+	0.0324227i
$437$	9.42238	−	9.42238i	0.450733	−	0.450733i
$438$	−0.791710	−	7.50275i	−0.0378294	−	0.358495i
$439$	1.08192	−	0.624646i	0.0516372	−	0.0298127i	−0.473959	−	0.880547i	$-0.657176\pi$
$439$	1.08192	−	0.624646i	0.0516372	−	0.0298127i	0.525596	+	0.850734i	$0.323842\pi$
$440$	−19.1055	−	5.11932i	−0.910821	−	0.244054i
$441$	−2.85394	−	0.924690i	−0.135902	−	0.0440328i
$442$	0.268068	−	0.259992i	0.0127507	−	0.0123666i
$443$		−	25.6877i		−	1.22046i	−0.792225	−	0.610229i	$-0.791077\pi$
$443$		−	25.6877i		−	1.22046i	0.792225	−	0.610229i	$-0.208923\pi$
$444$	−4.17733	−	10.8689i	−0.198247	−	0.515814i
$445$	−21.6067	−	37.4240i	−1.02426	−	1.77407i
$446$	−6.28410	+	10.8844i	−0.297561	+	0.515390i
$447$	0.491682	−	3.11270i	0.0232558	−	0.147225i
$448$	−0.258819	−	0.965926i	−0.0122281	−	0.0456357i
$449$	−3.97995	−	14.8534i	−0.187825	−	0.700974i	−0.994008	−	0.109307i	$-0.965137\pi$
$449$	−3.97995	−	14.8534i	−0.187825	−	0.700974i	0.806183	−	0.591667i	$-0.201530\pi$
$450$	16.9244	+	33.1481i	0.797822	+	1.56262i
$451$	−5.58744	+	9.67773i	−0.263102	+	0.455706i
$452$	3.49024	+	6.04528i	0.164167	+	0.284346i
$453$	3.33654	−	1.28236i	0.156764	−	0.0602507i
$454$		−	3.76320i		−	0.176616i
$455$	7.71965	−	12.9108i	0.361903	−	0.605266i
$456$	2.53079	−	1.84033i	0.118515	−	0.0861811i
$457$	−29.3164	−	7.85531i	−1.37136	−	0.367456i	−0.503387	−	0.864061i	$-0.667913\pi$
$457$	−29.3164	−	7.85531i	−1.37136	−	0.367456i	−0.867977	+	0.496605i	$0.834580\pi$
$458$	1.19875	−	0.692097i	0.0560138	−	0.0323396i
$459$	−0.111241	+	0.526560i	−0.00519228	+	0.0245777i
$460$	−21.7593	+	21.7593i	−1.01453	+	1.01453i
$461$	10.5705	−	2.83234i	0.492315	−	0.131915i	−0.00411612	−	0.999992i	$-0.501310\pi$
$461$	10.5705	−	2.83234i	0.492315	−	0.131915i	0.496431	+	0.868076i	$0.334644\pi$
$462$	−6.38369	−	5.16504i	−0.296996	−	0.240300i
$463$	−18.0493	−	18.0493i	−0.838821	−	0.838821i	0.149883	−	0.988704i	$-0.452110\pi$
$463$	−18.0493	−	18.0493i	−0.838821	−	0.838821i	−0.988704	+	0.149883i	$0.952110\pi$
$464$	5.86255	+	3.38474i	0.272162	+	0.157133i
$465$	23.2340	−	52.2425i	1.07745	−	2.42269i
$466$	−0.0232460	+	0.0867554i	−0.00107685	+	0.00401887i
$467$	−2.47419			−0.114492			−0.0572458	−	0.998360i	$-0.518232\pi$
$467$	−2.47419			−0.114492			−0.0572458	+	0.998360i	$0.518232\pi$
$468$	−10.6117	+	2.09564i	−0.490526	+	0.0968708i
$469$	5.14724			0.237677
$470$	−1.60451	+	5.98813i	−0.0740107	+	0.276212i
$471$	7.09890	−	15.9622i	0.327100	−	0.735497i
$472$	8.61018	+	4.97109i	0.396315	+	0.228813i
$473$	−4.95015	−	4.95015i	−0.227608	−	0.227608i
$474$	1.46436	+	1.18481i	0.0672601	+	0.0544201i
$475$	21.6497	−	5.80102i	0.993356	−	0.266169i
$476$	0.0732373	−	0.0732373i	0.00335683	−	0.00335683i
$477$	15.6615	−	14.1251i	0.717090	−	0.646746i
$478$	−24.0525	+	13.8867i	−1.10014	+	0.635165i
$479$	8.31474	+	2.22793i	0.379910	+	0.101797i	0.443720	−	0.896165i	$-0.353658\pi$
$479$	8.31474	+	2.22793i	0.379910	+	0.101797i	−0.0638099	+	0.997962i	$0.520325\pi$
$480$	−5.84440	+	4.24990i	−0.266759	+	0.193981i
$481$	23.3143	+	6.63079i	1.06304	+	0.302338i
$482$		−	1.39438i		−	0.0635121i
$483$	−11.9248	+	4.58316i	−0.542597	+	0.208541i
$484$	−5.73820	−	9.93886i	−0.260827	−	0.451766i
$485$	3.39285	−	5.87658i	0.154061	−	0.266842i
$486$	10.9999	−	11.0455i	0.498965	−	0.501033i
$487$	−8.42687	−	31.4495i	−0.381858	−	1.42511i	−0.843061	−	0.537818i	$-0.819249\pi$
$487$	−8.42687	−	31.4495i	−0.381858	−	1.42511i	0.461203	−	0.887295i	$-0.347418\pi$
$488$	−2.09672	−	7.82505i	−0.0949138	−	0.354223i
$489$	−0.0623005	+	0.394406i	−0.00281733	+	0.0178357i
$490$	2.08604	−	3.61312i	0.0942376	−	0.163224i
$491$	−1.00976	−	1.74895i	−0.0455696	−	0.0789289i	0.842341	−	0.538945i	$-0.181177\pi$
$491$	−1.00976	−	1.74895i	−0.0455696	−	0.0789289i	−0.887911	+	0.460016i	$0.847844\pi$
$492$	1.46466	+	3.81086i	0.0660320	+	0.171807i
$493$			0.701138i			0.0315777i
$494$	−0.0996092	+	6.51312i	−0.00448163	+	0.293039i
$495$	−18.2899	+	56.4495i	−0.822071	+	2.53722i
$496$	7.64266	+	2.04785i	0.343166	+	0.0919510i
$497$	12.0405	−	6.95156i	0.540088	−	0.311820i
$498$	2.25993	+	21.4165i	0.101270	+	0.959698i
$499$	10.4669	−	10.4669i	0.468564	−	0.468564i	−0.432885	−	0.901449i	$-0.642504\pi$
$499$	10.4669	−	10.4669i	0.468564	−	0.468564i	0.901449	+	0.432885i	$0.142504\pi$
$500$	−29.8465	+	7.99734i	−1.33477	+	0.357652i
$501$	−3.80283	+	4.70008i	−0.169898	+	0.209984i
$502$	−14.5254	−	14.5254i	−0.648299	−	0.648299i
$503$	20.9311	+	12.0846i	0.933272	+	0.538825i	0.887845	−	0.460143i	$-0.152202\pi$
$503$	20.9311	+	12.0846i	0.933272	+	0.538825i	0.0454272	+	0.998968i	$0.485535\pi$
$504$	−2.93393	+	0.626163i	−0.130687	+	0.0278915i
$505$	−7.70175	+	28.7433i	−0.342723	+	1.27906i
$506$	−34.9680			−1.55452
$507$	9.77471	−	20.2844i	0.434110	−	0.900860i
$508$	2.75277			0.122135
$509$	−6.72082	+	25.0824i	−0.297895	+	1.11176i	0.640996	+	0.767545i	$0.278522\pi$
$509$	−6.72082	+	25.0824i	−0.297895	+	1.11176i	−0.938891	+	0.344215i	$0.888145\pi$
$510$	−0.683865	−	0.304137i	−0.0302821	−	0.0134674i
$511$	3.77221	+	2.17788i	0.166873	+	0.0963439i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.12257	−	7.86667i	−0.226167	−	0.347322i
$514$	−24.3501	+	6.52459i	−1.07404	+	0.287787i
$515$	40.8793	−	40.8793i	1.80136	−	1.80136i
$516$	−2.54346	+	0.268393i	−0.111970	+	0.0118153i
$517$	−6.10083	+	3.52232i	−0.268314	+	0.154911i
$518$	6.49360	+	1.73995i	0.285312	+	0.0764492i
$519$	24.0077	+	33.0151i	1.05382	+	1.44920i
$520$	0.230029	−	15.0409i	0.0100875	−	0.659586i
$521$		−	9.17765i		−	0.402080i	−0.979583	−	0.201040i	$-0.935568\pi$
$521$		−	9.17765i		−	0.402080i	0.979583	−	0.201040i	$-0.0644321\pi$
$522$	11.0467	−	17.0413i	0.483500	−	0.745876i
$523$	−3.98644	−	6.90471i	−0.174315	−	0.301922i	0.765609	−	0.643306i	$-0.222438\pi$
$523$	−3.98644	−	6.90471i	−0.174315	−	0.301922i	−0.939924	+	0.341384i	$0.889104\pi$
$524$	−8.55770	+	14.8224i	−0.373845	+	0.647518i
$525$	−21.2250	−	3.35272i	−0.926337	−	0.146325i
$526$	1.76147	+	6.57389i	0.0768036	+	0.286635i
$527$	0.212102	+	0.791575i	0.00923930	+	0.0344816i
$528$	−8.11096	−	1.28121i	−0.352984	−	0.0557575i
$529$	−15.7010	+	27.1949i	−0.682652	+	1.18239i
$530$	14.6651	+	25.4007i	0.637010	+	1.10333i
$531$	16.2240	−	25.0281i	0.704061	−	1.08613i
$532$			1.80663i			0.0783272i
$533$	−8.17449	−	2.32489i	−0.354076	−	0.100702i
$534$	−10.5510	−	14.5096i	−0.456586	−	0.627891i
$535$	−16.4276	−	4.40176i	−0.710227	−	0.190305i
$536$	4.45764	−	2.57362i	0.192541	−	0.111163i
$537$	36.4243	−	3.84359i	1.57183	−	0.165863i
$538$	8.14613	−	8.14613i	0.351205	−	0.351205i
$539$	4.57939	−	1.22704i	0.197248	−	0.0528525i
$540$	11.8296	+	18.1667i	0.509067	+	0.781769i
$541$	−5.50181	−	5.50181i	−0.236541	−	0.236541i	0.578875	−	0.815416i	$-0.303492\pi$
$541$	−5.50181	−	5.50181i	−0.236541	−	0.236541i	−0.815416	+	0.578875i	$0.803492\pi$
$542$	6.26165	+	3.61517i	0.268961	+	0.155285i
$543$	0.0763829	+	0.0339700i	0.00327790	+	0.00145779i
$544$	0.0268067	−	0.100044i	0.00114933	−	0.00428935i
$545$	−10.9131			−0.467467
$546$	2.62467	−	5.66667i	0.112325	−	0.242511i
$547$	29.0628			1.24263			0.621317	−	0.783559i	$-0.286598\pi$
$547$	29.0628			1.24263			0.621317	+	0.783559i	$0.286598\pi$
$548$	2.07438	−	7.74168i	0.0886130	−	0.330708i
$549$	−23.7680	+	5.07260i	−1.01439	+	0.216493i
$550$	−50.9370	−	29.4085i	−2.17196	−	1.25398i
$551$	−8.64787	−	8.64787i	−0.368412	−	0.368412i
$552$	−8.03559	+	9.93153i	−0.342017	+	0.422714i
$553$	−1.05047	+	0.281471i	−0.0446704	+	0.0119694i
$554$	−18.3338	+	18.3338i	−0.778929	+	0.778929i
$555$	−5.09795	−	48.3114i	−0.216396	−	2.05071i
$556$	19.0456	−	10.9960i	0.807712	−	0.466333i
$557$	16.1034	+	4.31489i	0.682323	+	0.182828i	0.583299	−	0.812257i	$-0.301761\pi$
$557$	16.1034	+	4.31489i	0.682323	+	0.182828i	0.0990234	+	0.995085i	$0.468428\pi$
$558$	7.31639	−	22.5811i	0.309728	−	0.955934i
$559$	2.73222	−	4.56951i	0.115560	−	0.193270i
$560$		−	4.17208i		−	0.176302i
$561$	−0.305118	−	0.793879i	−0.0128821	−	0.0335176i
$562$	−11.7935	−	20.4269i	−0.497477	−	0.861655i
$563$	−12.6418	+	21.8962i	−0.532787	+	0.922815i	0.466480	+	0.884532i	$0.345522\pi$
$563$	−12.6418	+	21.8962i	−0.532787	+	0.922815i	−0.999267	+	0.0382828i	$0.987811\pi$
$564$	−0.401561	+	2.54217i	−0.0169088	+	0.107044i
$565$	7.53762	+	28.1308i	0.317110	+	1.18347i
$566$	2.35553	+	8.79096i	0.0990103	+	0.369511i
$567$	1.42262	+	8.88685i	0.0597444	+	0.373213i
$568$	6.95156	−	12.0405i	0.291681	−	0.505206i
$569$	5.38383	+	9.32507i	0.225702	+	0.390927i	0.956530	−	0.291635i	$-0.0941991\pi$
$569$	5.38383	+	9.32507i	0.225702	+	0.390927i	−0.730828	+	0.682562i	$0.760866\pi$
$570$	12.1861	−	4.68358i	0.510418	−	0.196174i
$571$		−	9.68481i		−	0.405297i	−0.979252	−	0.202648i	$-0.935045\pi$
$571$		−	9.68481i		−	0.405297i	0.979252	−	0.202648i	$-0.0649549\pi$
$572$	12.2705	−	11.9008i	0.513054	−	0.497597i
$573$	7.44145	−	5.41123i	0.310871	−	0.226057i
$574$	−2.27679	−	0.610064i	−0.0950314	−	0.0254636i
$575$	−79.2461	+	45.7527i	−3.30479	+	1.90802i
$576$	−2.22777	+	2.00924i	−0.0928239	+	0.0837182i
$577$	27.1300	−	27.1300i	1.12944	−	1.12944i	0.139168	−	0.990269i	$-0.455557\pi$
$577$	27.1300	−	27.1300i	1.12944	−	1.12944i	0.990269	−	0.139168i	$-0.0444428\pi$
$578$	−16.4104	+	4.39715i	−0.682582	+	0.182897i
$579$	−3.63610	−	2.94196i	−0.151111	−	0.122264i
$580$	19.9707	+	19.9707i	0.829238	+	0.829238i
$581$	−10.7677	−	6.21674i	−0.446720	−	0.257914i
$582$	1.14475	−	2.57402i	0.0474516	−	0.106697i
$583$	−8.62625	+	32.1936i	−0.357263	+	1.33332i
$584$	4.35577			0.180243
$585$	−45.0272	−	3.01342i	−1.86165	−	0.124590i
$586$	22.8489			0.943880
$587$	7.86521	−	29.3534i	0.324632	−	1.21154i	−0.590050	−	0.807367i	$-0.700892\pi$
$587$	7.86521	−	29.3534i	0.324632	−	1.21154i	0.914681	−	0.404176i	$-0.132442\pi$
$588$	0.703834	−	1.58260i	0.0290256	−	0.0652653i
$589$	−12.3794	−	7.14725i	−0.510084	−	0.294497i
$590$	29.3304	+	29.3304i	1.20752	+	1.20752i
$591$	−7.85828	−	6.35812i	−0.323246	−	0.261538i
$592$	6.49360	−	1.73995i	0.266885	−	0.0715117i
$593$	1.17442	−	1.17442i	0.0482276	−	0.0482276i	−0.682582	−	0.730809i	$-0.739143\pi$
$593$	1.17442	−	1.17442i	0.0482276	−	0.0482276i	0.730809	+	0.682582i	$0.239143\pi$
$594$	−5.09191	+	24.1026i	−0.208924	+	0.988942i
$595$	0.374223	−	0.216058i	0.0153416	−	0.00885750i
$596$	1.75740	+	0.470895i	0.0719860	+	0.0192886i
$597$	15.1115	−	10.9887i	0.618472	−	0.449738i
$598$	−6.48935	−	25.7898i	−0.265369	−	1.05462i
$599$		−	44.1349i		−	1.80330i	−0.432463	−	0.901651i	$-0.642356\pi$
$599$		−	44.1349i		−	1.80330i	0.432463	−	0.901651i	$-0.357644\pi$
$600$	−20.0578	+	7.70899i	−0.818856	+	0.314718i
$601$	17.3512	+	30.0531i	0.707770	+	1.22589i	0.965683	+	0.259725i	$0.0836319\pi$
$601$	17.3512	+	30.0531i	0.707770	+	1.22589i	−0.257913	+	0.966168i	$0.583035\pi$
$602$	0.738312	−	1.27879i	0.0300913	−	0.0521197i
$603$	−7.02177	−	13.7529i	−0.285949	−	0.560060i
$604$	0.534133	+	1.99341i	0.0217336	+	0.0811108i
$605$	−12.3924	−	46.2490i	−0.503822	−	1.88029i
$606$	−1.92752	+	12.2025i	−0.0783000	+	0.495694i
$607$	12.3413	−	21.3757i	0.500917	−	0.867614i	−0.499082	−	0.866555i	$-0.666329\pi$
$607$	12.3413	−	21.3757i	0.500917	−	0.867614i	0.999999	−	0.00105972i	$-0.000337318\pi$
$608$	0.903313	+	1.56458i	0.0366342	+	0.0634522i
$609$	4.20643	+	10.9446i	0.170453	+	0.443497i
$610$		−	33.7983i		−	1.36846i
$611$	−3.72999	−	3.84585i	−0.150899	−	0.155586i
$612$	−0.295591	−	0.0957731i	−0.0119486	−	0.00387140i
$613$	3.13456	+	0.839904i	0.126604	+	0.0339234i	0.321565	−	0.946888i	$-0.395791\pi$
$613$	3.13456	+	0.839904i	0.126604	+	0.0339234i	−0.194961	+	0.980811i	$0.562458\pi$
$614$	4.55985	−	2.63263i	0.184021	−	0.106244i
$615$	1.78745	+	16.9390i	0.0720768	+	0.683046i
$616$	3.35234	−	3.35234i	0.135070	−	0.135070i
$617$	−8.99503	+	2.41021i	−0.362126	+	0.0970314i	−0.435294	−	0.900288i	$-0.643356\pi$
$617$	−8.99503	+	2.41021i	−0.362126	+	0.0970314i	0.0731681	+	0.997320i	$0.476689\pi$
$618$	15.0965	−	18.6584i	0.607271	−	0.750551i
$619$	−11.5999	−	11.5999i	−0.466238	−	0.466238i	0.434455	−	0.900693i	$-0.356941\pi$
$619$	−11.5999	−	11.5999i	−0.466238	−	0.466238i	−0.900693	+	0.434455i	$0.856941\pi$
$620$	28.5880	+	16.5053i	1.14812	+	0.662869i
$621$	28.5133	+	25.6095i	1.14420	+	1.02767i
$622$	1.25877	−	4.69779i	0.0504721	−	0.188364i
$623$	10.3578			0.414976
$624$	−0.560303	−	6.21981i	−0.0224301	−	0.248992i
$625$	−66.8833			−2.67533
$626$	1.51636	−	5.65914i	0.0606061	−	0.226185i
$627$	13.5551	+	6.02840i	0.541338	+	0.240751i
$628$	8.73477	+	5.04302i	0.348555	+	0.201238i
$629$	0.492350	+	0.492350i	0.0196313	+	0.0196313i
$630$	−12.4996	−	0.644706i	−0.497997	−	0.0256857i
$631$	−1.53963	+	0.412542i	−0.0612916	+	0.0164230i	−0.289335	−	0.957228i	$-0.593434\pi$
$631$	−1.53963	+	0.412542i	−0.0612916	+	0.0164230i	0.228043	+	0.973651i	$0.426767\pi$
$632$	−0.768994	+	0.768994i	−0.0305890	+	0.0305890i
$633$	25.3221	−	2.67205i	1.00646	−	0.106204i
$634$	−20.5112	+	11.8421i	−0.814602	+	0.470311i
$635$	11.0934	+	2.97248i	0.440230	+	0.117959i
$636$	7.16125	+	9.84804i	0.283962	+	0.390500i
$637$	1.75482	+	3.14970i	0.0695283	+	0.124796i
$638$			32.0937i			1.27060i
$639$	−34.9992	−	22.6876i	−1.38455	−	0.897507i
$640$	−2.08604	−	3.61312i	−0.0824579	−	0.142821i
$641$	−6.04688	+	10.4735i	−0.238837	+	0.413678i	−0.960381	−	0.278691i	$-0.910100\pi$
$641$	−6.04688	+	10.4735i	−0.238837	+	0.413678i	0.721544	+	0.692369i	$0.243433\pi$
$642$	−6.97408	−	1.10163i	−0.275245	−	0.0434778i
$643$	2.84467	+	10.6164i	0.112183	+	0.418672i	0.999061	−	0.0433320i	$-0.0137973\pi$
$643$	2.84467	+	10.6164i	0.112183	+	0.418672i	−0.886878	+	0.462004i	$0.847131\pi$
$644$	−1.90899	−	7.12445i	−0.0752247	−	0.280743i
$645$	−10.5398	−	1.66487i	−0.415003	−	0.0655540i
$646$	−0.0935590	+	0.162049i	−0.00368103	+	0.00637573i
$647$	23.8019	+	41.2261i	0.935750	+	1.62077i	0.773291	+	0.634051i	$0.218609\pi$
$647$	23.8019	+	41.2261i	0.935750	+	1.62077i	0.162459	+	0.986715i	$0.448057\pi$
$648$	5.67545	+	6.98493i	0.222953	+	0.274394i
$649$			47.1351i			1.85022i
$650$	12.2367	−	43.0250i	0.479962	−	1.68758i
$651$	8.05986	+	11.0838i	0.315891	+	0.434408i
$652$	−0.222679	−	0.0596666i	−0.00872077	−	0.00233672i
$653$	−30.5459	+	17.6357i	−1.19535	+	0.690137i	−0.959515	−	0.281656i	$-0.909116\pi$
$653$	−30.5459	+	17.6357i	−1.19535	+	0.690137i	−0.235837	+	0.971793i	$0.575783\pi$
$654$	−4.50560	+	0.475442i	−0.176183	+	0.0185913i
$655$	−50.4922	+	50.4922i	−1.97289	+	1.97289i
$656$	−2.27679	+	0.610064i	−0.0888937	+	0.0238190i
$657$	0.673092	−	13.0500i	0.0262598	−	0.509127i
$658$	−1.05070	−	1.05070i	−0.0409607	−	0.0409607i
$659$	−32.4044	−	18.7087i	−1.26229	−	0.728786i	−0.288777	−	0.957396i	$-0.593249\pi$
$659$	−32.4044	−	18.7087i	−1.26229	−	0.728786i	−0.973518	+	0.228610i	$0.926582\pi$
$660$	−31.3030	−	13.9215i	−1.21847	−	0.541893i
$661$	−4.89241	+	18.2587i	−0.190293	+	0.710182i	0.803143	+	0.595787i	$0.203160\pi$
$661$	−4.89241	+	18.2587i	−0.190293	+	0.710182i	−0.993435	+	0.114395i	$0.963507\pi$
$662$	14.0114			0.544568
$663$	0.528882	−	0.372360i	0.0205401	−	0.0144613i
$664$	−12.4335			−0.482513
$665$	−1.95082	+	7.28055i	−0.0756495	+	0.282328i
$666$	−4.20948	−	19.7238i	−0.163114	−	0.764282i
$667$	43.2408	+	24.9651i	1.67429	+	0.966653i
$668$	−2.46820	−	2.46820i	−0.0954977	−	0.0954977i
$669$	−13.6925	+	16.9232i	−0.529384	+	0.654288i
$670$	20.7429	−	5.55805i	0.801370	−	0.214726i
$671$	27.1576	−	27.1576i	1.04841	−	1.04841i
$672$	−0.181761	−	1.72249i	−0.00701159	−	0.0664464i
$673$	−19.6321	+	11.3346i	−0.756762	+	0.436916i	−0.828132	−	0.560533i	$-0.810596\pi$
$673$	−19.6321	+	11.3346i	−0.756762	+	0.436916i	0.0713703	+	0.997450i	$0.477263\pi$
$674$	−8.28291	−	2.21940i	−0.319046	−	0.0854881i
$675$	19.9967	+	61.2847i	0.769675	+	2.35885i
$676$	11.0543	+	6.84124i	0.425165	+	0.263125i
$677$			1.65211i			0.0634957i	0.999496	+	0.0317478i	$0.0101073\pi$
$677$			1.65211i			0.0634957i	−0.999496	+	0.0317478i	$0.989893\pi$
$678$	4.33754	+	11.2857i	0.166582	+	0.433425i
$679$	0.813227	+	1.40855i	0.0312088	+	0.0540552i
$680$	0.216058	−	0.374223i	0.00828543	−	0.0143508i
$681$	1.01699	−	6.43823i	0.0389710	−	0.246714i
$682$	9.70869	+	36.2333i	0.371765	+	1.38745i
$683$	−5.29155	−	19.7483i	−0.202475	−	0.755648i	−0.990204	−	0.139626i	$-0.955410\pi$
$683$	−5.29155	−	19.7483i	−0.202475	−	0.755648i	0.787729	−	0.616022i	$-0.211257\pi$
$684$	4.82711	−	2.46457i	0.184569	−	0.0942351i
$685$	16.7191	−	28.9584i	0.638805	−	1.10644i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	2.23790	−	0.860111i	0.0853812	−	0.0328153i
$688$		−	1.47662i		−	0.0562957i
$689$	−25.3445	−	0.387609i	−0.965547	−	0.0147667i
$690$	−43.1070	+	31.3463i	−1.64105	+	1.19333i
$691$	−14.9359	−	4.00205i	−0.568187	−	0.152245i	−0.0367220	−	0.999326i	$-0.511692\pi$
$691$	−14.9359	−	4.00205i	−0.568187	−	0.152245i	−0.531465	+	0.847080i	$0.678358\pi$
$692$	−20.4106	+	11.7841i	−0.775894	+	0.447963i
$693$	−9.52564	−	10.5617i	−0.361849	−	0.401206i
$694$	9.25325	−	9.25325i	0.351249	−	0.351249i
$695$	88.6257	−	23.7472i	3.36176	−	0.900782i
$696$	9.11517	+	7.37507i	0.345509	+	0.279551i
$697$	−0.172628	−	0.172628i	−0.00653876	−	0.00653876i
$698$	−25.4295	−	14.6817i	−0.962520	−	0.555711i
$699$	−0.0632154	+	0.142142i	−0.00239103	+	0.00537632i
$700$	3.21097	−	11.9835i	0.121363	−	0.452933i
$701$	−4.16688			−0.157381			−0.0786904	−	0.996899i	$-0.525074\pi$
$701$	−4.16688			−0.157381			−0.0786904	+	0.996899i	$0.525074\pi$
$702$	−18.7212	+	0.717536i	−0.706588	+	0.0270816i
$703$	−12.1453			−0.458070
$704$	1.22704	−	4.57939i	0.0462459	−	0.172592i
$705$	−4.36332	+	9.81111i	−0.164332	+	0.369508i
$706$	−14.4390	−	8.33636i	−0.543419	−	0.313743i
$707$	−5.04343	−	5.04343i	−0.189678	−	0.189678i
$708$	13.3872	+	10.8316i	0.503122	+	0.407076i
$709$	21.7146	−	5.81842i	0.815510	−	0.218515i	0.173127	−	0.984899i	$-0.444613\pi$
$709$	21.7146	−	5.81842i	0.815510	−	0.218515i	0.642382	+	0.766384i	$0.277946\pi$
$710$	41.0157	−	41.0157i	1.53929	−	1.53929i
$711$	2.18509	+	2.42275i	0.0819472	+	0.0908603i
$712$	8.97011	−	5.17889i	0.336169	−	0.194087i
$713$	56.3705	+	15.1044i	2.11109	+	0.565666i
$714$	0.145089	−	0.105505i	0.00542983	−	0.00394843i
$715$	62.2996	−	34.7094i	2.32987	−	1.29806i
$716$			21.1464i			0.790276i
$717$	−44.9028	+	17.2579i	−1.67693	+	0.644508i
$718$	2.92054	+	5.05853i	0.108994	+	0.188783i
$719$	7.39375	−	12.8064i	0.275741	−	0.477597i	−0.694581	−	0.719414i	$-0.744410\pi$
$719$	7.39375	−	12.8064i	0.275741	−	0.477597i	0.970322	+	0.241818i	$0.0777436\pi$
$720$	−11.1473	+	5.69148i	−0.415437	+	0.212109i
$721$	3.58643	+	13.3847i	0.133566	+	0.498474i
$722$	4.07280	+	15.1999i	0.151574	+	0.565682i
$723$	0.376823	−	2.38555i	0.0140142	−	0.0887197i
$724$	−0.0241321	+	0.0417980i	−0.000896863	+	0.00155341i
$725$	41.9919	+	72.7321i	1.55954	+	2.70120i
$726$	−7.13122	−	18.5545i	−0.264664	−	0.688622i
$727$		−	20.2185i		−	0.749863i	−0.927053	−	0.374932i	$-0.877666\pi$
$727$		−	20.2185i		−	0.749863i	0.927053	−	0.374932i	$-0.122334\pi$
$728$	3.09457	+	1.85031i	0.114692	+	0.0685772i
$729$	21.8040	−	15.9244i	0.807555	−	0.589792i
$730$	17.5534	+	4.70341i	0.649680	+	0.174081i
$731$	0.132449	−	0.0764693i	0.00489879	−	0.00282832i
$732$	−1.47246	−	13.9540i	−0.0544238	−	0.515755i
$733$	16.2291	−	16.2291i	0.599436	−	0.599436i	−0.340727	−	0.940162i	$-0.610673\pi$
$733$	16.2291	−	16.2291i	0.599436	−	0.599436i	0.940162	+	0.340727i	$0.110673\pi$
$734$	−17.8239	+	4.77589i	−0.657891	+	0.176281i
$735$	4.54530	−	5.61773i	0.167656	−	0.207213i
$736$	−5.21546	−	5.21546i	−0.192244	−	0.192244i
$737$	21.1333	+	12.2013i	0.778457	+	0.449442i
$738$	1.47593	+	6.91558i	0.0543298	+	0.254566i
$739$	4.48225	−	16.7280i	0.164882	−	0.615348i	−0.833173	−	0.553012i	$-0.813478\pi$
$739$	4.48225	−	16.7280i	0.164882	−	0.615348i	0.998055	−	0.0623361i	$-0.0198551\pi$
$740$	28.0475			1.03105
$741$	−1.93055	+	11.1160i	−0.0709206	+	0.408356i
$742$	−7.03011			−0.258083
$743$	3.73884	−	13.9536i	0.137165	−	0.511906i	−0.862815	−	0.505520i	$-0.831301\pi$
$743$	3.73884	−	13.9536i	0.137165	−	0.511906i	0.999980	−	0.00638596i	$-0.00203273\pi$
$744$	12.5219	+	5.56892i	0.459077	+	0.204167i
$745$	6.57371	+	3.79533i	0.240842	+	0.139050i
$746$	−16.4078	−	16.4078i	−0.600733	−	0.600733i
$747$	−1.92133	+	37.2510i	−0.0702979	+	1.36294i
$748$	0.474302	−	0.127089i	0.0173422	−	0.00464682i
$749$	2.88246	−	2.88246i	0.105323	−	0.105323i
$750$	−53.2237	+	5.61630i	−1.94346	+	0.205078i
$751$	−44.2861	+	25.5686i	−1.61602	+	0.933012i	−0.628089	+	0.778142i	$0.716162\pi$
$751$	−44.2861	+	25.5686i	−1.61602	+	0.933012i	−0.987935	+	0.154870i	$0.950504\pi$
$752$	−1.43529	−	0.384584i	−0.0523395	−	0.0140243i
$753$	−20.9252	−	28.7760i	−0.762555	−	1.04865i
$754$	−23.6699	+	5.95593i	−0.862007	+	0.216902i
$755$			8.61005i			0.313352i
$756$	−5.18869	+	0.278386i	−0.188711	+	0.0101248i
$757$	−7.71798	−	13.3679i	−0.280515	−	0.485866i	0.690997	−	0.722858i	$-0.257172\pi$
$757$	−7.71798	−	13.3679i	−0.280515	−	0.485866i	−0.971512	+	0.236992i	$0.923838\pi$
$758$	−3.68275	+	6.37870i	−0.133763	+	0.231685i
$759$	−59.8246	−	9.44992i	−2.17150	−	0.343010i
$760$	1.95082	+	7.28055i	0.0707636	+	0.264093i
$761$	−5.49712	−	20.5155i	−0.199270	−	0.743687i	−0.991120	−	0.132971i	$-0.957548\pi$
$761$	−5.49712	−	20.5155i	−0.199270	−	0.743687i	0.791849	−	0.610716i	$-0.209118\pi$
$762$	4.70955	+	0.743922i	0.170609	+	0.0269495i
$763$	1.30788	−	2.26531i	0.0473483	−	0.0820097i
$764$	2.65607	+	4.60045i	0.0960933	+	0.166438i
$765$	−1.08779	−	0.705141i	−0.0393292	−	0.0254944i
$766$			4.15298i			0.150053i
$767$	−34.7634	+	8.74732i	−1.25523	+	0.315847i
$768$	−1.01865	−	1.40084i	−0.0367575	−	0.0505484i
$769$	49.4224	+	13.2427i	1.78222	+	0.477544i	0.990985	−	0.133970i	$-0.0427726\pi$
$769$	49.4224	+	13.2427i	1.78222	+	0.477544i	0.791233	+	0.611514i	$0.209439\pi$
$770$	17.1296	−	9.88976i	0.617307	−	0.356402i
$771$	−43.4223	+	4.58204i	−1.56382	+	0.165018i
$772$	1.90947	−	1.90947i	0.0687232	−	0.0687232i
$773$	−44.3877	+	11.8936i	−1.59651	+	0.427784i	−0.943987	−	0.329982i	$-0.892957\pi$
$773$	−44.3877	+	11.8936i	−1.59651	+	0.427784i	−0.652526	+	0.757766i	$0.726291\pi$
$774$	−4.42399	−	0.228181i	−0.159017	−	0.00820180i
$775$	69.4106	+	69.4106i	2.49330	+	2.49330i
$776$	1.40855	+	0.813227i	0.0505640	+	0.0291931i
$777$	10.6393	+	4.73164i	0.381682	+	0.169747i
$778$	0.0555769	−	0.207416i	0.00199253	−	0.00743622i
$779$	4.25841			0.152573
$780$	4.45826	−	25.6703i	0.159631	−	0.919146i
$781$	65.9137			2.35858
$782$	0.197720	−	0.737902i	0.00707046	−	0.0263873i
$783$	23.5044	−	26.1695i	0.839979	−	0.935223i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	29.7549	+	29.7549i	1.06200	+	1.06200i
$786$	−18.6465	+	23.0460i	−0.665099	+	0.822024i
$787$	−9.58699	+	2.56883i	−0.341739	+	0.0915688i	−0.425607	−	0.904908i	$-0.639939\pi$
$787$	−9.58699	+	2.56883i	−0.341739	+	0.0915688i	0.0838676	+	0.996477i	$0.473273\pi$
$788$	4.12671	−	4.12671i	0.147008	−	0.147008i
$789$	1.23703	+	11.7229i	0.0440394	+	0.417346i
$790$	−3.92935	+	2.26861i	−0.139800	+	0.0807136i
$791$	−6.74263	−	1.80668i	−0.239740	−	0.0642383i
$792$	−13.5303	−	4.38389i	−0.480778	−	0.155775i
$793$	25.0693	+	14.9895i	0.890238	+	0.532294i
$794$			32.2692i			1.14519i
$795$	18.2252	+	47.4196i	0.646381	+	1.68180i
$796$	5.39374	+	9.34223i	0.191176	+	0.331126i
$797$	−10.4982	+	18.1835i	−0.371866	+	0.644091i	−0.989853	−	0.142098i	$-0.954615\pi$
$797$	−10.4982	+	18.1835i	−0.371866	+	0.644091i	0.617987	+	0.786189i	$0.287949\pi$
$798$	−0.488231	+	3.09084i	−0.0172832	+	0.109415i
$799$	−0.0398326	−	0.148657i	−0.00140918	−	0.00525912i
$800$	−3.21097	−	11.9835i	−0.113525	−	0.423680i
$801$	−14.1299	−	27.6749i	−0.499256	−	0.977844i
$802$	15.0191	−	26.0139i	0.530344	−	0.918583i
$803$	10.3252	+	17.8838i	0.364368	+	0.631104i
$804$	8.32181	−	3.19839i	0.293487	−	0.112799i
$805$		−	30.7723i		−	1.08458i
$806$	−24.9213	+	13.8846i	−0.877815	+	0.489063i
$807$	16.1382	−	11.7353i	0.568090	−	0.413101i
$808$	−6.88945	−	1.84602i	−0.242370	−	0.0649429i
$809$	−49.1581	+	28.3815i	−1.72831	+	0.997839i	−0.831300	+	0.555825i	$0.812403\pi$
$809$	−49.1581	+	28.3815i	−1.72831	+	0.997839i	−0.897008	+	0.442014i	$0.854264\pi$
$810$	15.3292	+	34.2771i	0.538612	+	1.20438i
$811$	22.1090	−	22.1090i	0.776352	−	0.776352i	−0.202856	−	0.979209i	$-0.565022\pi$
$811$	22.1090	−	22.1090i	0.776352	−	0.776352i	0.979209	+	0.202856i	$0.0650224\pi$
$812$	−6.53883	+	1.75207i	−0.229468	+	0.0614857i
$813$	9.73569	+	7.87714i	0.341446	+	0.276263i
$814$	22.5367	+	22.5367i	0.789910	+	0.789910i
$815$	−0.832948	−	0.480902i	−0.0291769	−	0.0168453i
$816$	0.0728983	−	0.163915i	0.00255195	−	0.00573817i
$817$	−0.690453	+	2.57681i	−0.0241559	+	0.0901510i
$818$	−10.2421			−0.358108
$819$	6.02177	−	8.98545i	0.210418	−	0.313977i
$820$	−9.83403			−0.343419
$821$	10.9071	−	40.7058i	0.380660	−	1.42064i	−0.464236	−	0.885711i	$-0.653671\pi$
$821$	10.9071	−	40.7058i	0.380660	−	1.42064i	0.844896	−	0.534930i	$-0.179662\pi$
$822$	5.64107	−	12.6842i	0.196755	−	0.442411i
$823$	−40.7349	−	23.5183i	−1.41993	−	0.819796i	−0.423637	−	0.905832i	$-0.639247\pi$
$823$	−40.7349	−	23.5183i	−1.41993	−	0.819796i	−0.996292	+	0.0860359i	$0.972580\pi$
$824$	9.79831	+	9.79831i	0.341340	+	0.341340i
$825$	−79.1975	−	64.0787i	−2.75730	−	2.23093i
$826$	−9.60340	+	2.57322i	−0.334145	+	0.0895339i
$827$	−19.5124	+	19.5124i	−0.678512	+	0.678512i	−0.959663	−	0.281152i	$-0.909284\pi$
$827$	−19.5124	+	19.5124i	−0.678512	+	0.678512i	0.281152	+	0.959663i	$0.409284\pi$
$828$	−16.4315	+	14.8197i	−0.571035	+	0.515019i
$829$	17.7218	−	10.2317i	0.615502	−	0.355360i	−0.159613	−	0.987180i	$-0.551025\pi$
$829$	17.7218	−	10.2317i	0.615502	−	0.355360i	0.775116	+	0.631819i	$0.217691\pi$
$830$	−50.1059	−	13.4258i	−1.73920	−	0.466018i
$831$	−36.3208	+	26.4116i	−1.25995	+	0.916207i
$832$	3.60513	+	0.0551355i	0.124985	+	0.00191148i
$833$			0.103573i			0.00358860i
$834$	35.5555	−	13.6654i	1.23119	−	0.473193i
$835$	−7.28146	−	12.6119i	−0.251985	−	0.436451i
$836$	−4.28254	+	7.41758i	−0.148115	+	0.256542i
$837$	18.6196	−	36.6554i	0.643587	−	1.26700i
$838$	−4.08892	−	15.2600i	−0.141249	−	0.527149i
$839$	11.4119	+	42.5898i	0.393983	+	1.47036i	0.823506	+	0.567308i	$0.192015\pi$
$839$	11.4119	+	42.5898i	0.393983	+	1.47036i	−0.429523	+	0.903056i	$0.641318\pi$
$840$	1.12748	−	7.13775i	0.0389018	−	0.246276i
$841$	8.41300	−	14.5717i	0.290103	−	0.502474i
$842$	−8.88787	−	15.3942i	−0.306296	−	0.530521i
$843$	−14.6564	−	38.1342i	−0.504795	−	1.31341i
$844$			14.7009i			0.506025i
$845$	37.1606	+	39.5062i	1.27836	+	1.35905i
$846$	−1.37401	+	4.24072i	−0.0472396	+	0.145799i
$847$	11.0854	+	2.97031i	0.380897	+	0.102061i
$848$	−6.08825	+	3.51506i	−0.209072	+	0.120707i
$849$	1.65422	+	15.6765i	0.0567727	+	0.538015i
$850$	0.908599	−	0.908599i	0.0311647	−	0.0311647i
$851$	47.8953	−	12.8335i	1.64183	−	0.439927i
$852$	15.1469	−	18.7207i	0.518923	−	0.641359i
$853$	−0.233348	−	0.233348i	−0.00798970	−	0.00798970i	0.703101	−	0.711090i	$-0.251798\pi$
$853$	−0.233348	−	0.233348i	−0.00798970	−	0.00798970i	−0.711090	+	0.703101i	$0.751798\pi$
$854$	7.01575	+	4.05054i	0.240074	+	0.138607i
$855$	22.1141	−	4.71963i	0.756287	−	0.161408i
$856$	1.05505	−	3.93751i	0.0360610	−	0.134581i
$857$	53.7061			1.83457			0.917283	−	0.398236i	$-0.130377\pi$
$857$	53.7061			1.83457			0.917283	+	0.398236i	$0.130377\pi$
$858$	24.2089	−	17.0443i	0.826479	−	0.581883i
$859$	29.5712			1.00896			0.504478	−	0.863424i	$-0.331685\pi$
$859$	29.5712			1.00896			0.504478	+	0.863424i	$0.331685\pi$
$860$	1.59448	−	5.95067i	0.0543712	−	0.202916i
$861$	−3.73035	−	1.65901i	−0.127130	−	0.0565390i
$862$	13.6163	+	7.86136i	0.463772	+	0.267759i
$863$	−19.1474	−	19.1474i	−0.651784	−	0.651784i	0.301638	−	0.953422i	$-0.402467\pi$
$863$	−19.1474	−	19.1474i	−0.651784	−	0.651784i	−0.953422	+	0.301638i	$0.902467\pi$
$864$	−4.35434	+	2.83543i	−0.148138	+	0.0964634i
$865$	−94.9775	+	25.4492i	−3.22933	+	0.865297i
$866$	25.1313	−	25.1313i	0.853998	−	0.853998i
$867$	−29.2638	+	3.08799i	−0.993851	+	0.104874i
$868$	−6.85222	+	3.95613i	−0.232580	+	0.134280i
$869$	−4.98018	−	1.33444i	−0.168941	−	0.0452677i
$870$	28.7697	+	39.5636i	0.975383	+	1.34133i
$871$	−5.07689	+	17.8507i	−0.172024	+	0.604848i
$872$		−	2.61575i		−	0.0885806i
$873$	2.65410	−	4.09437i	0.0898278	−	0.138574i
$874$	6.66263	+	11.5400i	0.225367	+	0.390347i
$875$	15.4497	−	26.7596i	0.522294	−	0.904640i
$876$	7.45201	+	1.17712i	0.251780	+	0.0397713i
$877$	−14.2485	−	53.1761i	−0.481137	−	1.79563i	−0.596858	−	0.802347i	$-0.703584\pi$
$877$	−14.2485	−	53.1761i	−0.481137	−	1.79563i	0.115721	−	0.993282i	$-0.463082\pi$
$878$	0.323341	+	1.20672i	0.0109122	+	0.0407249i
$879$	39.0908	+	6.17480i	1.31850	+	0.208271i
$880$	9.88976	−	17.1296i	0.333384	−	0.577438i
$881$	−9.11247	−	15.7833i	−0.307007	−	0.531752i	0.670699	−	0.741730i	$-0.265994\pi$
$881$	−9.11247	−	15.7833i	−0.307007	−	0.531752i	−0.977706	+	0.209978i	$0.932661\pi$
$882$	1.63183	−	2.51736i	0.0549467	−	0.0847640i
$883$			41.5949i			1.39978i	0.714250	+	0.699891i	$0.246768\pi$
$883$			41.5949i			1.39978i	−0.714250	+	0.699891i	$0.753232\pi$
$884$	0.181752	+	0.326225i	0.00611298	+	0.0109721i
$885$	42.2533	+	58.1060i	1.42033	+	1.95321i
$886$	24.8124	+	6.64846i	0.833589	+	0.223359i
$887$	−0.215828	+	0.124608i	−0.00724679	+	0.00418394i	−0.503619	−	0.863926i	$-0.667998\pi$
$887$	−0.215828	+	0.124608i	−0.00724679	+	0.00418394i	0.496372	+	0.868110i	$0.334665\pi$
$888$	11.5797	−	1.22192i	0.388590	−	0.0410050i
$889$	−1.94650	+	1.94650i	−0.0652837	+	0.0652837i
$890$	41.7410	−	11.1845i	1.39916	−	0.374904i
$891$	−15.2250	+	39.8596i	−0.510058	+	1.33535i
$892$	−8.88706	−	8.88706i	−0.297561	−	0.297561i
$893$	2.32484	+	1.34225i	0.0777979	+	0.0449166i
$894$	2.87938	+	1.28055i	0.0963007	+	0.0428281i
$895$	−22.8341	+	85.2180i	−0.763260	+	2.84853i
$896$	1.00000			0.0334077
$897$	−4.13266	−	45.8759i	−0.137986	−	1.53175i
$898$	15.3773			0.513148
$899$	13.8629	−	51.7369i	0.462353	−	1.72552i
$900$	−36.3989	+	7.76832i	−1.21330	+	0.258944i
$901$	−0.630580	−	0.364066i	−0.0210077	−	0.0121288i
$902$	−7.90183	−	7.90183i	−0.263102	−	0.263102i
$903$	1.60872	−	1.98828i	0.0535348	−	0.0661659i
$904$	−6.74263	+	1.80668i	−0.224257	+	0.0600894i
$905$	−0.142384	+	0.142384i	−0.00473302	+	0.00473302i
$906$	0.375107	+	3.55475i	0.0124621	+	0.118099i
$907$	−22.1610	+	12.7947i	−0.735844	+	0.424840i	−0.820556	−	0.571566i	$-0.806336\pi$
$907$	−22.1610	+	12.7947i	−0.735844	+	0.424840i	0.0847121	+	0.996405i	$0.473003\pi$
$908$	3.63497	+	0.973988i	0.120631	+	0.0323229i
$909$	−6.59534	+	20.3557i	−0.218754	+	0.675154i
$910$	10.4729	+	10.7982i	0.347172	+	0.357956i
$911$		−	31.6956i		−	1.05012i	−0.851064	−	0.525061i	$-0.824042\pi$
$911$		−	31.6956i		−	1.05012i	0.851064	−	0.525061i	$-0.175958\pi$
$912$	1.12260	+	2.92087i	0.0371731	+	0.0967195i
$913$	−29.4731	−	51.0490i	−0.975419	−	1.68947i
$914$	15.1753	−	26.2844i	0.501954	−	0.869410i
$915$	9.13382	−	57.8235i	0.301955	−	1.91159i
$916$	0.358256	+	1.33703i	0.0118371	+	0.0441767i
$917$	−4.42979	−	16.5322i	−0.146285	−	0.545941i
$918$	−0.479827	−	0.243734i	−0.0158366	−	0.00804443i
$919$	13.2743	−	22.9918i	0.437880	−	0.758430i	−0.559646	−	0.828732i	$-0.689063\pi$
$919$	13.2743	−	22.9918i	0.437880	−	0.758430i	0.997526	+	0.0703018i	$0.0223962\pi$
$920$	−15.3861	−	26.6496i	−0.507266	−	0.878611i
$921$	8.51262	−	3.27173i	0.280500	−	0.107807i
$922$			10.9433i			0.360400i
$923$	12.2322	+	48.6131i	0.402629	+	1.60012i
$924$	6.64127	−	4.82936i	0.218482	−	0.158874i
$925$	80.5610	+	21.5863i	2.64883	+	0.709752i
$926$	22.1058	−	12.7628i	0.726440	−	0.419411i
$927$	30.8700	−	27.8418i	1.01390	−	0.914444i
$928$	−4.78675	+	4.78675i	−0.157133	+	0.157133i
$929$	−10.6576	+	2.85570i	−0.349665	+	0.0936924i	−0.429377	−	0.903126i	$-0.641267\pi$
$929$	−10.6576	+	2.85570i	−0.349665	+	0.0936924i	0.0797117	+	0.996818i	$0.474600\pi$
$930$	44.4490	+	35.9636i	1.45754	+	1.17929i
$931$	−1.27748	−	1.27748i	−0.0418676	−	0.0418676i
$932$	−0.0777828	−	0.0449079i	−0.00254786	−	0.00147101i
$933$	3.42310	−	7.69699i	0.112067	−	0.251988i
$934$	0.640366	−	2.38988i	0.0209534	−	0.0781992i
$935$	2.04863			0.0669973
$936$	0.722284	−	10.7925i	0.0236086	−	0.352764i
$937$	−48.6487			−1.58928			−0.794642	−	0.607078i	$-0.792341\pi$
$937$	−48.6487			−1.58928			−0.794642	+	0.607078i	$0.792341\pi$
$938$	−1.33220	+	4.97185i	−0.0434980	+	0.162337i
$939$	4.12361	−	9.27209i	0.134569	−	0.302583i
$940$	−5.36881	−	3.09968i	−0.175111	−	0.101100i
$941$	−14.6217	−	14.6217i	−0.476655	−	0.476655i	0.427405	−	0.904060i	$-0.359428\pi$
$941$	−14.6217	−	14.6217i	−0.476655	−	0.476655i	−0.904060	+	0.427405i	$0.859428\pi$
$942$	13.5809	+	10.9883i	0.442490	+	0.358019i
$943$	−16.7931	+	4.49969i	−0.546858	+	0.146530i
$944$	−7.03018	+	7.03018i	−0.228813	+	0.228813i
$945$	−21.2106	−	4.48094i	−0.689981	−	0.145765i
$946$	6.06267	−	3.50028i	0.197114	−	0.113804i
$947$	2.53693	+	0.679769i	0.0824392	+	0.0220895i	0.299803	−	0.954001i	$-0.403079\pi$
$947$	2.53693	+	0.679769i	0.0824392	+	0.0220895i	−0.217364	+	0.976091i	$0.569746\pi$
$948$	−1.52344	+	1.10781i	−0.0494791	+	0.0359799i
$949$	−11.2736	+	10.9340i	−0.365956	+	0.354931i
$950$			22.4134i			0.727187i
$951$	−38.2915	+	14.7169i	−1.24169	+	0.477229i
$952$	0.0517866	+	0.0896970i	0.00167841	+	0.00290710i
$953$	−9.52546	+	16.4986i	−0.308560	+	0.534442i	−0.978048	−	0.208382i	$-0.933180\pi$
$953$	−9.52546	+	16.4986i	−0.308560	+	0.534442i	0.669488	+	0.742823i	$0.266514\pi$
$954$	9.59036	+	18.7837i	0.310499	+	0.608145i
$955$	5.73612	+	21.4075i	0.185616	+	0.692730i
$956$	−7.18831	−	26.8271i	−0.232486	−	0.867651i
$957$	−8.67314	+	54.9071i	−0.280363	+	1.77489i
$958$	−4.30402	+	7.45479i	−0.139057	+	0.240853i
$959$	4.00739	+	6.94100i	0.129405	+	0.224137i
$960$	−2.59245	−	6.74521i	−0.0836709	−	0.217701i
$961$		−	31.6040i		−	1.01948i
$962$	−12.4390	+	20.8037i	−0.401051	+	0.670739i
$963$	−11.6338	−	3.76942i	−0.374895	−	0.121468i
$964$	1.34686	+	0.360891i	0.0433796	+	0.0116235i
$965$	9.75686	−	5.63312i	0.314084	−	0.181337i
$966$	−1.34063	−	12.7047i	−0.0431340	−	0.408766i
$967$	−13.1662	+	13.1662i	−0.423395	+	0.423395i	−0.886371	−	0.462976i	$-0.846782\pi$
$967$	−13.1662	+	13.1662i	−0.423395	+	0.423395i	0.462976	+	0.886371i	$0.346782\pi$
$968$	11.0854	−	2.97031i	0.356297	−	0.0954695i
$969$	−0.203857	+	0.251956i	−0.00654884	+	0.00809398i
$970$	4.79821	+	4.79821i	0.154061	+	0.154061i
$971$	12.1094	+	6.99139i	0.388610	+	0.224364i	0.681558	−	0.731764i	$-0.261303\pi$
$971$	12.1094	+	6.99139i	0.388610	+	0.224364i	−0.292948	+	0.956129i	$0.594636\pi$
$972$	7.82214	+	13.4838i	0.250895	+	0.432495i
$973$	−5.69193	+	21.2426i	−0.182475	+	0.681006i
$974$	32.5589			1.04325
$975$	32.5622	−	70.3019i	1.04283	−	2.25146i
$976$	8.10109			0.259309
$977$	−1.90447	+	7.10757i	−0.0609294	+	0.227391i	−0.989676	−	0.143324i	$-0.954221\pi$
$977$	−1.90447	+	7.10757i	−0.0609294	+	0.227391i	0.928746	+	0.370716i	$0.120888\pi$
$978$	−0.364843	−	0.162258i	−0.0116664	−	0.00518842i
$979$	42.5266	+	24.5528i	1.35916	+	0.784710i
$980$	2.95010	+	2.95010i	0.0942376	+	0.0942376i
$981$	−7.83684	−	0.404209i	−0.250211	−	0.0129054i
$982$	1.95070	−	0.522688i	0.0622493	−	0.0166796i
$983$	−8.51885	+	8.51885i	−0.271709	+	0.271709i	−0.829788	−	0.558079i	$-0.811539\pi$
$983$	−8.51885	+	8.51885i	−0.271709	+	0.271709i	0.558079	+	0.829788i	$0.311539\pi$
$984$	−4.06009	+	0.428431i	−0.129431	+	0.0136579i
$985$	21.0864	−	12.1742i	0.671867	−	0.387903i
$986$	−0.677247	−	0.181468i	−0.0215679	−	0.00577911i
$987$	−1.51364	−	2.08153i	−0.0481796	−	0.0662558i
$988$	−6.26541	−	1.78193i	−0.199329	−	0.0566909i
$989$		−	10.8912i		−	0.346321i
$990$	−49.7922	−	32.2769i	−1.58250	−	1.02583i
$991$	7.13773	+	12.3629i	0.226737	+	0.392721i	0.956839	−	0.290618i	$-0.0938608\pi$
$991$	7.13773	+	12.3629i	0.226737	+	0.392721i	−0.730102	+	0.683338i	$0.760527\pi$
$992$	−3.95613	+	6.85222i	−0.125607	+	0.217558i
$993$	23.9712	+	3.78650i	0.760703	+	0.120161i
$994$	3.59839	+	13.4294i	0.114134	+	0.425954i
$995$	11.6485	+	43.4726i	0.369281	+	1.37817i
$996$	−21.2717	−	3.36008i	−0.674019	−	0.106468i
$997$	−17.4481	+	30.2210i	−0.552587	+	0.957109i	0.445500	+	0.895282i	$0.353026\pi$
$997$	−17.4481	+	30.2210i	−0.552587	+	0.957109i	−0.998087	+	0.0618267i	$0.980307\pi$
$998$	7.40123	+	12.8193i	0.234282	+	0.405788i
$999$	−1.87150	−	34.8818i	−0.0592115	−	1.10361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.197.3	✓	56
3.2	odd	2		546.2.bu.b.197.14	yes	56
13.7	odd	12		546.2.bu.b.449.14	yes	56
39.20	even	12	inner	546.2.bu.a.449.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.3	✓	56	1.1	even	1	trivial
546.2.bu.a.449.3	yes	56	39.20	even	12	inner
546.2.bu.b.197.14	yes	56	3.2	odd	2
546.2.bu.b.449.14	yes	56	13.7	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.703834 + 1.58260i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.95010 - 2.95010i) q^{5} +(-1.34651 - 1.08946i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.00924 - 2.22777i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.703834 + 1.58260i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.95010 - 2.95010i) q^{5} +(-1.34651 - 1.08946i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.00924 - 2.22777i) q^{9} +(3.61312 - 2.08604i) q^{10} +(4.57939 + 1.22704i) q^{11} +(1.40084 - 1.01865i) q^{12} +(-0.0551355 + 3.60513i) q^{13} +1.00000i q^{14} +(6.74521 - 2.59245i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0517866 + 0.0896970i) q^{17} +(2.67189 - 1.36418i) q^{18} +(-0.467589 - 1.74507i) q^{19} +(1.07981 + 4.02992i) q^{20} +(-0.270245 + 1.71084i) q^{21} +(-2.37046 + 4.10576i) q^{22} +(3.68789 + 6.38760i) q^{23} +(0.621380 + 1.61675i) q^{24} +12.4062i q^{25} +(-3.46802 - 0.986333i) q^{26} +(4.93984 - 1.61183i) q^{27} +(-0.965926 - 0.258819i) q^{28} +(5.86255 - 3.38474i) q^{29} +(0.758322 + 7.18635i) q^{30} +(5.59482 - 5.59482i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.16504 + 6.38369i) q^{33} +(-0.0732373 - 0.0732373i) q^{34} +(-3.61312 - 2.08604i) q^{35} +(0.626163 + 2.93393i) q^{36} +(1.73995 - 6.49360i) q^{37} +1.80663 q^{38} +(-5.66667 - 2.62467i) q^{39} -4.17208 q^{40} +(-0.610064 + 2.27679i) q^{41} +(-1.58260 - 0.703834i) q^{42} +(-1.27879 - 0.738312i) q^{43} +(-3.35234 - 3.35234i) q^{44} +(-0.644706 + 12.4996i) q^{45} +(-7.12445 + 1.90899i) q^{46} +(-1.05070 + 1.05070i) q^{47} +(-1.72249 + 0.181761i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-11.9835 - 3.21097i) q^{50} +(-0.105505 - 0.145089i) q^{51} +(1.85031 - 3.09457i) q^{52} +7.03011i q^{53} +(0.278386 + 5.18869i) q^{54} +(-9.88976 - 17.1296i) q^{55} +(0.500000 - 0.866025i) q^{56} +(3.09084 + 0.488231i) q^{57} +(1.75207 + 6.53883i) q^{58} +(2.57322 + 9.60340i) q^{59} +(-7.13775 - 1.12748i) q^{60} +(4.05054 - 7.01575i) q^{61} +(3.95613 + 6.85222i) q^{62} +(-2.51736 - 1.63183i) q^{63} -1.00000i q^{64} +(10.7982 - 10.4729i) q^{65} +(-4.82936 - 6.64127i) q^{66} +(4.97185 + 1.33220i) q^{67} +(0.0896970 - 0.0517866i) q^{68} +(-12.7047 + 1.34063i) q^{69} +(2.95010 - 2.95010i) q^{70} +(13.4294 - 3.59839i) q^{71} +(-2.99602 - 0.154529i) q^{72} +(3.07999 + 3.07999i) q^{73} +(5.82200 + 3.36133i) q^{74} +(-19.6341 - 8.73192i) q^{75} +(-0.467589 + 1.74507i) q^{76} +4.74093 q^{77} +(4.00188 - 4.79427i) q^{78} -1.08752 q^{79} +(1.07981 - 4.02992i) q^{80} +(-0.925943 + 8.95224i) q^{81} +(-2.04131 - 1.17855i) q^{82} +(-8.79180 - 8.79180i) q^{83} +(1.08946 - 1.34651i) q^{84} +(0.417391 - 0.111840i) q^{85} +(1.04413 - 1.04413i) q^{86} +(1.23043 + 11.6604i) q^{87} +(4.10576 - 2.37046i) q^{88} +(10.0049 + 2.68079i) q^{89} +(-11.9068 - 3.85788i) q^{90} +(0.879819 + 3.49656i) q^{91} -7.37577i q^{92} +(4.91653 + 12.7922i) q^{93} +(-0.742959 - 1.28684i) q^{94} +(-3.76869 + 6.52756i) q^{95} +(0.270245 - 1.71084i) q^{96} +(0.420957 + 1.57103i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-6.46749 - 12.6672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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