LMFDB - Embedded newform 546.2.ch.a.401.33

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			401.33
Character	$\chi$	$=$	546.401
Dual form			546.2.ch.a.305.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.958098 + 1.44293i) q^{3} -1.00000i q^{4} +(-0.421014 - 1.57124i) q^{5} +(1.69778 + 0.342829i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16410 + 2.76494i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.958098 + 1.44293i) q^{3} -1.00000i q^{4} +(-0.421014 - 1.57124i) q^{5} +(1.69778 + 0.342829i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16410 + 2.76494i) q^{9} +(-1.40874 - 0.813336i) q^{10} +(4.90284 - 1.31371i) q^{11} +(1.44293 - 0.958098i) q^{12} +(3.58027 - 0.426188i) q^{13} +(-2.60408 - 0.467704i) q^{14} +(1.86382 - 2.11290i) q^{15} -1.00000 q^{16} +0.853434 q^{17} +(1.13196 + 2.77825i) q^{18} +(1.44975 - 5.41052i) q^{19} +(-1.57124 + 0.421014i) q^{20} +(1.68682 - 4.26083i) q^{21} +(2.53789 - 4.39576i) q^{22} -2.49659 q^{23} +(0.342829 - 1.69778i) q^{24} +(2.03857 - 1.17697i) q^{25} +(2.23028 - 2.83300i) q^{26} +(-5.10493 + 0.969366i) q^{27} +(-2.17208 + 1.51065i) q^{28} +(-4.98976 + 2.88084i) q^{29} +(-0.176122 - 2.81197i) q^{30} +(-1.47908 + 5.51999i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.59299 + 5.81579i) q^{33} +(0.603469 - 0.603469i) q^{34} +(-2.77687 + 3.28807i) q^{35} +(2.76494 + 1.16410i) q^{36} +(3.88598 - 3.88598i) q^{37} +(-2.80069 - 4.85094i) q^{38} +(4.04521 + 4.75776i) q^{39} +(-0.813336 + 1.40874i) q^{40} +(-2.07420 - 0.555780i) q^{41} +(-1.82010 - 4.20562i) q^{42} +(11.2486 + 6.49440i) q^{43} +(-1.31371 - 4.90284i) q^{44} +(4.83449 + 0.665007i) q^{45} +(-1.76535 + 1.76535i) q^{46} +(-7.23248 + 1.93794i) q^{47} +(-0.958098 - 1.44293i) q^{48} +(-2.43588 + 6.56251i) q^{49} +(0.609244 - 2.27373i) q^{50} +(0.817673 + 1.23145i) q^{51} +(-0.426188 - 3.58027i) q^{52} +(-9.96523 + 5.75343i) q^{53} +(-2.92429 + 4.29518i) q^{54} +(-4.12832 - 7.15047i) q^{55} +(-0.467704 + 2.60408i) q^{56} +(9.19601 - 3.09193i) q^{57} +(-1.49123 + 5.56536i) q^{58} +(0.583751 + 0.583751i) q^{59} +(-2.11290 - 1.86382i) q^{60} +(-2.92693 - 5.06959i) q^{61} +(2.85736 + 4.94909i) q^{62} +(7.76421 - 1.64833i) q^{63} +1.00000i q^{64} +(-2.17699 - 5.44606i) q^{65} +(8.77433 - 0.549563i) q^{66} +(11.8441 - 3.17363i) q^{67} -0.853434i q^{68} +(-2.39197 - 3.60240i) q^{69} +(0.361477 + 4.28856i) q^{70} +(3.90925 + 14.5895i) q^{71} +(2.77825 - 1.13196i) q^{72} +(-10.5632 - 2.83040i) q^{73} -5.49560i q^{74} +(3.65143 + 1.81386i) q^{75} +(-5.41052 - 1.44975i) q^{76} +(-10.2600 - 8.66481i) q^{77} +(6.22464 + 0.503847i) q^{78} +(-6.03981 + 10.4613i) q^{79} +(0.421014 + 1.57124i) q^{80} +(-6.28975 - 6.43732i) q^{81} +(-1.85968 + 1.07368i) q^{82} +(-3.18424 + 3.18424i) q^{83} +(-4.26083 - 1.68682i) q^{84} +(-0.359308 - 1.34095i) q^{85} +(12.5462 - 3.36175i) q^{86} +(-8.93753 - 4.43976i) q^{87} +(-4.39576 - 2.53789i) q^{88} +(5.02101 + 5.02101i) q^{89} +(3.88873 - 2.94827i) q^{90} +(-6.33425 - 7.13283i) q^{91} +2.49659i q^{92} +(-9.38207 + 3.15449i) q^{93} +(-3.74381 + 6.48447i) q^{94} -9.11162 q^{95} +(-1.69778 - 0.342829i) q^{96} +(-14.9348 + 4.00176i) q^{97} +(2.91796 + 6.36282i) q^{98} +(-2.07506 + 15.0853i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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
$3$	0.958098	+	1.44293i	0.553158	+	0.833076i
$3$	0.958098	+	1.44293i	0.553158	+	0.833076i
$4$		−	1.00000i		−	0.500000i
$5$	−0.421014	−	1.57124i	−0.188283	−	0.702682i	−0.993904	−	0.110250i	$-0.964835\pi$
$5$	−0.421014	−	1.57124i	−0.188283	−	0.702682i	0.805621	−	0.592432i	$-0.201832\pi$
$6$	1.69778	+	0.342829i	0.693117	+	0.139959i
$7$	−1.51065	−	2.17208i	−0.570971	−	0.820970i
$7$	−1.51065	−	2.17208i	−0.570971	−	0.820970i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.16410	+	2.76494i	−0.388033	+	0.921646i
$10$	−1.40874	−	0.813336i	−0.445482	−	0.257199i
$11$	4.90284	−	1.31371i	1.47826	−	0.396099i	0.572506	−	0.819901i	$-0.305971\pi$
$11$	4.90284	−	1.31371i	1.47826	−	0.396099i	0.905755	+	0.423802i	$0.139305\pi$
$12$	1.44293	−	0.958098i	0.416538	−	0.276579i
$13$	3.58027	−	0.426188i	0.992989	−	0.118203i
$13$	3.58027	−	0.426188i	0.992989	−	0.118203i
$14$	−2.60408	−	0.467704i	−0.695971	−	0.124999i
$15$	1.86382	−	2.11290i	0.481238	−	0.545548i
$16$	−1.00000			−0.250000
$17$	0.853434			0.206988			0.103494	−	0.994630i	$-0.466998\pi$
$17$	0.853434			0.206988			0.103494	+	0.994630i	$0.466998\pi$
$18$	1.13196	+	2.77825i	0.266806	+	0.654839i
$19$	1.44975	−	5.41052i	0.332594	−	1.24126i	−0.573859	−	0.818954i	$-0.694554\pi$
$19$	1.44975	−	5.41052i	0.332594	−	1.24126i	0.906454	−	0.422305i	$-0.138779\pi$
$20$	−1.57124	+	0.421014i	−0.351341	+	0.0941415i
$21$	1.68682	−	4.26083i	0.368093	−	0.929789i
$22$	2.53789	−	4.39576i	0.541081	−	0.937180i
$23$	−2.49659			−0.520575			−0.260287	−	0.965531i	$-0.583817\pi$
$23$	−2.49659			−0.520575			−0.260287	+	0.965531i	$0.583817\pi$
$24$	0.342829	−	1.69778i	0.0699796	−	0.346559i
$25$	2.03857	−	1.17697i	0.407714	−	0.235394i
$26$	2.23028	−	2.83300i	0.437393	−	0.555596i
$27$	−5.10493	+	0.969366i	−0.982445	+	0.186555i
$28$	−2.17208	+	1.51065i	−0.410485	+	0.285486i
$29$	−4.98976	+	2.88084i	−0.926576	+	0.534959i	−0.885727	−	0.464207i	$-0.846340\pi$
$29$	−4.98976	+	2.88084i	−0.926576	+	0.534959i	−0.0408488	+	0.999165i	$0.513006\pi$
$30$	−0.176122	−	2.81197i	−0.0321554	−	0.513393i
$31$	−1.47908	+	5.51999i	−0.265650	+	0.991420i	0.696201	+	0.717847i	$0.254872\pi$
$31$	−1.47908	+	5.51999i	−0.265650	+	0.991420i	−0.961851	+	0.273573i	$0.911794\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	6.59299	+	5.81579i	1.14769	+	1.01240i
$34$	0.603469	−	0.603469i	0.103494	−	0.103494i
$35$	−2.77687	+	3.28807i	−0.469376	+	0.555786i
$36$	2.76494	+	1.16410i	0.460823	+	0.194016i
$37$	3.88598	−	3.88598i	0.638851	−	0.638851i	−0.311421	−	0.950272i	$-0.600805\pi$
$37$	3.88598	−	3.88598i	0.638851	−	0.638851i	0.950272	+	0.311421i	$0.100805\pi$
$38$	−2.80069	−	4.85094i	−0.454332	−	0.786927i
$39$	4.04521	+	4.75776i	0.647752	+	0.761851i
$40$	−0.813336	+	1.40874i	−0.128600	+	0.222741i
$41$	−2.07420	−	0.555780i	−0.323935	−	0.0867982i	0.0931868	−	0.995649i	$-0.470295\pi$
$41$	−2.07420	−	0.555780i	−0.323935	−	0.0867982i	−0.417122	+	0.908850i	$0.636961\pi$
$42$	−1.82010	−	4.20562i	−0.280848	−	0.648941i
$43$	11.2486	+	6.49440i	1.71540	+	0.990386i	0.926865	+	0.375395i	$0.122493\pi$
$43$	11.2486	+	6.49440i	1.71540	+	0.990386i	0.788534	+	0.614991i	$0.210841\pi$
$44$	−1.31371	−	4.90284i	−0.198049	−	0.739130i
$45$	4.83449	+	0.665007i	0.720684	+	0.0991334i
$46$	−1.76535	+	1.76535i	−0.260287	+	0.260287i
$47$	−7.23248	+	1.93794i	−1.05497	+	0.282677i	−0.744303	−	0.667843i	$-0.767218\pi$
$47$	−7.23248	+	1.93794i	−1.05497	+	0.282677i	−0.310664	+	0.950520i	$0.600551\pi$
$48$	−0.958098	−	1.44293i	−0.138289	−	0.208269i
$49$	−2.43588	+	6.56251i	−0.347983	+	0.937501i
$50$	0.609244	−	2.27373i	0.0861601	−	0.321554i
$51$	0.817673	+	1.23145i	0.114497	+	0.172437i
$52$	−0.426188	−	3.58027i	−0.0591016	−	0.496495i
$53$	−9.96523	+	5.75343i	−1.36883	+	0.790294i	−0.990779	−	0.135490i	$-0.956739\pi$
$53$	−9.96523	+	5.75343i	−1.36883	+	0.790294i	−0.378051	+	0.925785i	$0.623406\pi$
$54$	−2.92429	+	4.29518i	−0.397945	+	0.584500i
$55$	−4.12832	−	7.15047i	−0.556663	−	0.964169i
$56$	−0.467704	+	2.60408i	−0.0624996	+	0.347985i
$57$	9.19601	−	3.09193i	1.21804	−	0.409536i
$58$	−1.49123	+	5.56536i	−0.195809	+	0.730767i
$59$	0.583751	+	0.583751i	0.0759979	+	0.0759979i	0.744084	−	0.668086i	$-0.232886\pi$
$59$	0.583751	+	0.583751i	0.0759979	+	0.0759979i	−0.668086	+	0.744084i	$0.732886\pi$
$60$	−2.11290	−	1.86382i	−0.272774	−	0.240619i
$61$	−2.92693	−	5.06959i	−0.374755	−	0.649095i	0.615535	−	0.788109i	$-0.288940\pi$
$61$	−2.92693	−	5.06959i	−0.374755	−	0.649095i	−0.990290	+	0.139014i	$0.955607\pi$
$62$	2.85736	+	4.94909i	0.362885	+	0.628535i
$63$	7.76421	−	1.64833i	0.978199	−	0.207670i
$64$			1.00000i			0.125000i
$65$	−2.17699	−	5.44606i	−0.270022	−	0.675500i
$66$	8.77433	−	0.549563i	1.08005	−	0.0676465i
$67$	11.8441	−	3.17363i	1.44699	−	0.387720i	0.552015	−	0.833834i	$-0.313859\pi$
$67$	11.8441	−	3.17363i	1.44699	−	0.387720i	0.894976	+	0.446114i	$0.147192\pi$
$68$		−	0.853434i		−	0.103494i
$69$	−2.39197	−	3.60240i	−0.287960	−	0.433678i
$70$	0.361477	+	4.28856i	0.0432048	+	0.512581i
$71$	3.90925	+	14.5895i	0.463942	+	1.73146i	0.660373	+	0.750938i	$0.270398\pi$
$71$	3.90925	+	14.5895i	0.463942	+	1.73146i	−0.196431	+	0.980518i	$0.562935\pi$
$72$	2.77825	−	1.13196i	0.327420	−	0.133403i
$73$	−10.5632	−	2.83040i	−1.23633	−	0.331273i	−0.419288	−	0.907853i	$-0.637720\pi$
$73$	−10.5632	−	2.83040i	−1.23633	−	0.331273i	−0.817040	+	0.576580i	$0.804387\pi$
$74$		−	5.49560i		−	0.638851i
$75$	3.65143	+	1.81386i	0.421631	+	0.209447i
$76$	−5.41052	−	1.44975i	−0.620630	−	0.166297i
$77$	−10.2600	−	8.66481i	−1.16923	−	0.987447i
$78$	6.22464	+	0.503847i	0.704802	+	0.0570494i
$79$	−6.03981	+	10.4613i	−0.679532	+	1.17698i	0.295590	+	0.955315i	$0.404484\pi$
$79$	−6.03981	+	10.4613i	−0.679532	+	1.17698i	−0.975122	+	0.221669i	$0.928850\pi$
$80$	0.421014	+	1.57124i	0.0470708	+	0.175670i
$81$	−6.28975	−	6.43732i	−0.698861	−	0.715257i
$82$	−1.85968	+	1.07368i	−0.205367	+	0.118569i
$83$	−3.18424	+	3.18424i	−0.349516	+	0.349516i	−0.859929	−	0.510413i	$-0.829492\pi$
$83$	−3.18424	+	3.18424i	−0.349516	+	0.349516i	0.510413	+	0.859929i	$0.329492\pi$
$84$	−4.26083	−	1.68682i	−0.464894	−	0.184047i
$85$	−0.359308	−	1.34095i	−0.0389724	−	0.145447i
$86$	12.5462	−	3.36175i	1.35289	−	0.362506i
$87$	−8.93753	−	4.43976i	−0.958204	−	0.475992i
$88$	−4.39576	−	2.53789i	−0.468590	−	0.270541i
$89$	5.02101	+	5.02101i	0.532226	+	0.532226i	0.921234	−	0.389008i	$-0.127182\pi$
$89$	5.02101	+	5.02101i	0.532226	+	0.532226i	−0.389008	+	0.921234i	$0.627182\pi$
$90$	3.88873	−	2.94827i	0.409909	−	0.310775i
$91$	−6.33425	−	7.13283i	−0.664010	−	0.747724i
$92$			2.49659i			0.260287i
$93$	−9.38207	+	3.15449i	−0.972875	+	0.327105i
$94$	−3.74381	+	6.48447i	−0.386144	+	0.668822i
$95$	−9.11162			−0.934832
$96$	−1.69778	−	0.342829i	−0.173279	−	0.0349898i
$97$	−14.9348	+	4.00176i	−1.51640	+	0.406317i	−0.918554	−	0.395296i	$-0.870642\pi$
$97$	−14.9348	+	4.00176i	−1.51640	+	0.406317i	−0.597843	+	0.801613i	$0.703975\pi$
$98$	2.91796	+	6.36282i	0.294759	+	0.642742i
$99$	−2.07506	+	15.0853i	−0.208551	+	1.51613i
$100$	−1.17697	−	2.03857i	−0.117697	−	0.203857i
$101$	1.06029	−	1.83647i	0.105502	−	0.182736i	−0.808441	−	0.588577i	$-0.799688\pi$
$101$	1.06029	−	1.83647i	0.105502	−	0.182736i	0.913943	+	0.405842i	$0.133022\pi$
$102$	1.44895	+	0.292582i	0.143467	+	0.0289699i
$103$	2.43480	+	1.40573i	0.239908	+	0.138511i	0.615135	−	0.788422i	$-0.289102\pi$
$103$	2.43480	+	1.40573i	0.239908	+	0.138511i	−0.375226	+	0.926933i	$0.622435\pi$
$104$	−2.83300	−	2.23028i	−0.277798	−	0.218697i
$105$	−7.40498	−	0.856533i	−0.722652	−	0.0835891i
$106$	−2.97819	+	11.1148i	−0.289268	+	1.07956i
$107$		−	12.1409i		−	1.17370i	−0.809694	−	0.586852i	$-0.800367\pi$
$107$		−	12.1409i		−	1.17370i	0.809694	−	0.586852i	$-0.199633\pi$
$108$	0.969366	+	5.10493i	0.0932773	+	0.491222i
$109$	1.87488	−	6.99713i	0.179581	−	0.670204i	−0.816145	−	0.577847i	$-0.803893\pi$
$109$	1.87488	−	6.99713i	0.179581	−	0.670204i	0.995726	−	0.0923571i	$-0.0294401\pi$
$110$	−7.97531	−	2.13698i	−0.760416	−	0.203753i
$111$	9.33034	+	1.88405i	0.885597	+	0.178826i
$112$	1.51065	+	2.17208i	0.142743	+	0.205242i
$113$	9.65602	+	5.57491i	0.908362	+	0.524443i	0.879904	−	0.475152i	$-0.157607\pi$
$113$	9.65602	+	5.57491i	0.908362	+	0.524443i	0.0284582	+	0.999595i	$0.490940\pi$
$114$	4.31624	−	8.68888i	0.404253	−	0.813788i
$115$	1.05110	+	3.92275i	0.0980154	+	0.365798i
$116$	2.88084	+	4.98976i	0.267479	+	0.463288i
$117$	−2.98941	+	10.3954i	−0.276371	+	0.961051i
$118$	0.825548			0.0759979
$119$	−1.28924	−	1.85373i	−0.118184	−	0.169931i
$120$	−2.81197	+	0.176122i	−0.256696	+	0.0160777i
$121$	12.7857	−	7.38182i	1.16234	−	0.671075i
$122$	−5.65440	−	1.51509i	−0.511925	−	0.137170i
$123$	−1.18533	−	3.52542i	−0.106878	−	0.317876i
$124$	5.51999	+	1.47908i	0.495710	+	0.132825i
$125$	−8.45873	−	8.45873i	−0.756571	−	0.756571i
$126$	4.32458	−	6.65567i	0.385264	−	0.592935i
$127$	6.85083	−	3.95533i	0.607913	−	0.350979i	−0.164235	−	0.986421i	$-0.552516\pi$
$127$	6.85083	−	3.95533i	0.607913	−	0.350979i	0.772148	+	0.635442i	$0.219182\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	1.40631	+	22.4532i	0.123819	+	1.97690i
$130$	−5.39031	−	2.31158i	−0.472761	−	0.202739i
$131$	6.60251	+	3.81196i	0.576864	+	0.333053i	0.759886	−	0.650056i	$-0.225255\pi$
$131$	6.60251	+	3.81196i	0.576864	+	0.333053i	−0.183022	+	0.983109i	$0.558588\pi$
$132$	5.81579	−	6.59299i	0.506200	−	0.573846i
$133$	−13.9422	+	5.02443i	−1.20894	+	0.435674i
$134$	6.13098	−	10.6192i	0.529636	−	0.917356i
$135$	3.67236	+	7.61298i	0.316066	+	0.655221i
$136$	−0.603469	−	0.603469i	−0.0517471	−	0.0517471i
$137$	5.11722	+	5.11722i	0.437194	+	0.437194i	0.891067	−	0.453873i	$-0.149958\pi$
$137$	5.11722	+	5.11722i	0.437194	+	0.437194i	−0.453873	+	0.891067i	$0.649958\pi$
$138$	−4.23867	−	0.855902i	−0.360819	−	0.0728592i
$139$	2.22956	−	3.86172i	0.189109	−	0.327547i	−0.755844	−	0.654751i	$-0.772773\pi$
$139$	2.22956	−	3.86172i	0.189109	−	0.327547i	0.944953	+	0.327205i	$0.106107\pi$
$140$	3.28807	+	2.77687i	0.277893	+	0.234688i
$141$	−9.72573	−	8.57924i	−0.819055	−	0.722502i
$142$	13.0806	+	7.55208i	1.09770	+	0.633757i
$143$	16.9936	−	6.79298i	1.42108	−	0.568057i
$144$	1.16410	−	2.76494i	0.0970082	−	0.230411i
$145$	6.62726	+	6.62726i	0.550364	+	0.550364i
$146$	−9.47070	+	5.46791i	−0.783801	+	0.452527i
$147$	−11.8031	+	2.77271i	−0.973499	+	0.228689i
$148$	−3.88598	−	3.88598i	−0.319425	−	0.319425i
$149$	11.8620	+	3.17841i	0.971772	+	0.260386i	0.709576	−	0.704629i	$-0.248887\pi$
$149$	11.8620	+	3.17841i	0.971772	+	0.260386i	0.262196	+	0.965015i	$0.415553\pi$
$150$	3.86455	−	1.29936i	0.315539	−	0.106092i
$151$	−0.0546937	−	0.0146551i	−0.00445091	−	0.00119262i	0.256593	−	0.966520i	$-0.417400\pi$
$151$	−0.0546937	−	0.0146551i	−0.00445091	−	0.00119262i	−0.261044	+	0.965327i	$0.584067\pi$
$152$	−4.85094	+	2.80069i	−0.393463	+	0.227166i
$153$	−0.993481	+	2.35969i	−0.0803182	+	0.190770i
$154$	−13.3818	+	1.12794i	−1.07834	+	0.0908917i
$155$	9.29597			0.746671
$156$	4.75776	−	4.04521i	0.380926	−	0.323876i
$157$	−2.03262	−	3.52061i	−0.162221	−	0.280975i	0.773444	−	0.633865i	$-0.218532\pi$
$157$	−2.03262	−	3.52061i	−0.162221	−	0.280975i	−0.935665	+	0.352890i	$0.885199\pi$
$158$	3.12644	+	11.6680i	0.248726	+	0.928258i
$159$	−17.8495	−	8.86679i	−1.41555	−	0.703183i
$160$	1.40874	+	0.813336i	0.111371	+	0.0642999i
$161$	3.77147	+	5.42279i	0.297233	+	0.427376i
$162$	−8.99940	−	0.104345i	−0.707059	−	0.00819809i
$163$	9.83491	+	2.63526i	0.770330	+	0.206409i	0.622517	−	0.782606i	$-0.286110\pi$
$163$	9.83491	+	2.63526i	0.770330	+	0.206409i	0.147813	+	0.989015i	$0.452777\pi$
$164$	−0.555780	+	2.07420i	−0.0433991	+	0.161968i
$165$	6.36229	−	12.8077i	0.495304	−	0.997080i
$166$			4.50320i			0.349516i
$167$	−2.89910	+	10.8196i	−0.224339	+	0.837245i	0.758329	+	0.651872i	$0.226016\pi$
$167$	−2.89910	+	10.8196i	−0.224339	+	0.837245i	−0.982668	+	0.185373i	$0.940651\pi$
$168$	−4.20562	+	1.82010i	−0.324471	+	0.140424i
$169$	12.6367	−	3.05174i	0.972056	−	0.234749i
$170$	−1.20227	−	0.694129i	−0.0922096	−	0.0532373i
$171$	13.2721	+	10.3068i	1.01494	+	0.788183i
$172$	6.49440	−	11.2486i	0.495193	−	0.857699i
$173$	−5.97152	−	10.3430i	−0.454007	−	0.786362i	0.544624	−	0.838680i	$-0.316672\pi$
$173$	−5.97152	−	10.3430i	−0.454007	−	0.786362i	−0.998630	+	0.0523180i	$0.983339\pi$
$174$	−9.45917	+	3.18041i	−0.717098	+	0.241106i
$175$	−5.63604	−	2.64996i	−0.426044	−	0.200318i
$176$	−4.90284	+	1.31371i	−0.369565	+	0.0990247i
$177$	−0.283022	+	1.40160i	−0.0212732	+	0.105351i
$178$	7.10078			0.532226
$179$	−8.54897	+	14.8072i	−0.638980	+	1.10675i	0.346677	+	0.937985i	$0.387310\pi$
$179$	−8.54897	+	14.8072i	−0.638980	+	1.10675i	−0.985657	+	0.168761i	$0.946023\pi$
$180$	0.665007	−	4.83449i	0.0495667	−	0.360342i
$181$			10.3755i			0.771203i	0.922665	+	0.385602i	$0.126006\pi$
$181$			10.3755i			0.771203i	−0.922665	+	0.385602i	$0.873994\pi$
$182$	−9.52266	−	0.564681i	−0.705867	−	0.0418569i
$183$	4.51079	−	9.08053i	0.333447	−	0.671252i
$184$	1.76535	+	1.76535i	0.130144	+	0.130144i
$185$	−7.74187	−	4.46977i	−0.569194	−	0.328624i
$186$	−4.40357	+	8.86468i	−0.322885	+	0.649990i
$187$	4.18425	−	1.12117i	0.305983	−	0.0819878i
$188$	1.93794	+	7.23248i	0.141339	+	0.527483i
$189$	9.81730	+	9.62396i	0.714104	+	0.700040i
$190$	−6.44289	+	6.44289i	−0.467416	+	0.467416i
$191$	−9.07557	+	5.23979i	−0.656685	+	0.379138i	−0.791013	−	0.611799i	$-0.790446\pi$
$191$	−9.07557	+	5.23979i	−0.656685	+	0.379138i	0.134327	+	0.990937i	$0.457113\pi$
$192$	−1.44293	+	0.958098i	−0.104135	+	0.0691447i
$193$	0.790055	+	2.94853i	0.0568694	+	0.212240i	0.988514	−	0.151133i	$-0.0482920\pi$
$193$	0.790055	+	2.94853i	0.0568694	+	0.212240i	−0.931644	+	0.363372i	$0.881625\pi$
$194$	−7.73081	+	13.3902i	−0.555040	+	0.961357i
$195$	5.77251	−	8.35910i	0.413378	−	0.598607i
$196$	6.56251	+	2.43588i	0.468750	+	0.173992i
$197$	−21.4008	−	5.73433i	−1.52474	−	0.408554i	−0.603444	−	0.797405i	$-0.706205\pi$
$197$	−21.4008	−	5.73433i	−1.52474	−	0.408554i	−0.921301	+	0.388851i	$0.872872\pi$
$198$	9.19965	+	12.1342i	0.653790	+	0.862341i
$199$			4.95816i			0.351475i	0.984437	+	0.175737i	$0.0562310\pi$
$199$			4.95816i			0.351475i	−0.984437	+	0.175737i	$0.943769\pi$
$200$	−2.27373	−	0.609244i	−0.160777	−	0.0430801i
$201$	15.9272	+	14.0496i	1.12342	+	0.990984i
$202$	−0.548845	−	2.04832i	−0.0386166	−	0.144119i
$203$	13.7952	+	6.48624i	0.968233	+	0.455245i
$204$	1.23145	−	0.817673i	0.0862185	−	0.0572486i
$205$			3.49306i			0.243966i
$206$	2.71567	−	0.727662i	0.189210	−	0.0506986i
$207$	2.90627	−	6.90291i	0.202000	−	0.479785i
$208$	−3.58027	+	0.426188i	−0.248247	+	0.0295508i
$209$		−	28.4315i		−	1.96664i
$210$	−5.84177	+	4.63045i	−0.403120	+	0.319531i
$211$	−2.66289	−	4.61226i	−0.183321	−	0.317521i	0.759689	−	0.650287i	$-0.225351\pi$
$211$	−2.66289	−	4.61226i	−0.183321	−	0.317521i	−0.943009	+	0.332766i	$0.892018\pi$
$212$	5.75343	+	9.96523i	0.395147	+	0.684415i
$213$	−17.3062	+	19.6189i	−1.18580	+	1.34427i
$214$	−8.58491	−	8.58491i	−0.586852	−	0.586852i
$215$	5.46846	−	20.4086i	0.372946	−	1.39185i
$216$	4.29518	+	2.92429i	0.292250	+	0.198973i
$217$	14.2242	−	5.12609i	0.965605	−	0.347982i
$218$	−3.62198	−	6.27346i	−0.245312	−	0.424892i
$219$	−6.03650	−	17.9538i	−0.407909	−	1.21320i
$220$	−7.15047	+	4.12832i	−0.482084	+	0.278331i
$221$	3.05553	−	0.363723i	0.205537	−	0.0244667i
$222$	7.92977	−	5.26532i	0.532212	−	0.353385i
$223$	2.72617	−	10.1742i	0.182558	−	0.681315i	−0.812582	−	0.582846i	$-0.801939\pi$
$223$	2.72617	−	10.1742i	0.182558	−	0.681315i	0.995140	−	0.0984687i	$-0.0313944\pi$
$224$	2.60408	+	0.467704i	0.173993	+	0.0312498i
$225$	0.881149	+	7.00662i	0.0587433	+	0.467108i
$226$	10.7699	−	2.88578i	0.716403	−	0.191959i
$227$	2.85759	−	2.85759i	0.189665	−	0.189665i	−0.605886	−	0.795551i	$-0.707181\pi$
$227$	2.85759	−	2.85759i	0.189665	−	0.189665i	0.795551	+	0.605886i	$0.207181\pi$
$228$	−3.09193	−	9.19601i	−0.204768	−	0.609020i
$229$	1.58519	+	5.91603i	0.104753	+	0.390942i	0.998317	−	0.0579930i	$-0.0184701\pi$
$229$	1.58519	+	5.91603i	0.104753	+	0.390942i	−0.893564	+	0.448935i	$0.851803\pi$
$230$	3.51704	+	2.03056i	0.231907	+	0.133891i
$231$	2.67268	−	23.1061i	0.175850	−	1.52027i
$232$	5.56536	+	1.49123i	0.365384	+	0.0979043i
$233$	6.28957	−	10.8939i	0.412044	−	0.713681i	−0.583069	−	0.812422i	$-0.698148\pi$
$233$	6.28957	−	10.8939i	0.412044	−	0.713681i	0.995113	+	0.0987417i	$0.0314818\pi$
$234$	5.23680	+	9.46446i	0.342340	+	0.618711i
$235$	6.08995	+	10.5481i	0.397264	+	0.688082i
$236$	0.583751	−	0.583751i	0.0379989	−	0.0379989i
$237$	−20.8816	+	1.30788i	−1.35641	+	0.0849558i
$238$	−2.22241	−	0.399155i	−0.144058	−	0.0258734i
$239$	14.2838	−	14.2838i	0.923944	−	0.923944i	−0.0733617	−	0.997305i	$-0.523373\pi$
$239$	14.2838	−	14.2838i	0.923944	−	0.923944i	0.997305	+	0.0733617i	$0.0233727\pi$
$240$	−1.86382	+	2.11290i	−0.120309	+	0.136387i
$241$	−16.7231	+	16.7231i	−1.07723	+	1.07723i	−0.0804706	+	0.996757i	$0.525642\pi$
$241$	−16.7231	+	16.7231i	−1.07723	+	1.07723i	−0.996757	+	0.0804706i	$0.974358\pi$
$242$	3.82111	−	14.2606i	0.245630	−	0.916705i
$243$	3.26241	−	15.2433i	0.209284	−	0.977855i
$244$	−5.06959	+	2.92693i	−0.324548	+	0.187378i
$245$	11.3368	+	1.06446i	0.724284	+	0.0680060i
$246$	−3.33100	−	1.65469i	−0.212377	−	0.105499i
$247$	2.88459	−	19.9890i	0.183542	−	1.27187i
$248$	4.94909	−	2.85736i	0.314268	−	0.181442i
$249$	−7.64546	−	1.54383i	−0.484511	−	0.0978360i
$250$	−11.9624			−0.756571
$251$	0.773364	−	1.33951i	0.0488143	−	0.0845489i	−0.840586	−	0.541678i	$-0.817789\pi$
$251$	0.773364	−	1.33951i	0.0488143	−	0.0845489i	0.889400	+	0.457129i	$0.151122\pi$
$252$	−1.64833	−	7.76421i	−0.103835	−	0.489099i
$253$	−12.2404	+	3.27979i	−0.769545	+	0.206199i
$254$	2.04743	−	7.64111i	0.128467	−	0.479446i
$255$	1.59065	−	1.80322i	0.0996105	−	0.112922i
$256$	1.00000			0.0625000
$257$	−6.88973			−0.429770			−0.214885	−	0.976639i	$-0.568938\pi$
$257$	−6.88973			−0.429770			−0.214885	+	0.976639i	$0.568938\pi$
$258$	16.8713	+	14.8824i	1.05036	+	0.926540i
$259$	−14.3110	−	2.57032i	−0.889243	−	0.159712i
$260$	−5.44606	+	2.17699i	−0.337750	+	0.135011i
$261$	−2.15677	−	17.1500i	−0.133501	−	1.06156i
$262$	7.36415	−	1.97322i	0.454959	−	0.121906i
$263$	−4.57214	−	2.63972i	−0.281930	−	0.162772i	0.352367	−	0.935862i	$-0.385377\pi$
$263$	−4.57214	−	2.63972i	−0.281930	−	0.162772i	−0.634297	+	0.773090i	$0.718710\pi$
$264$	−0.549563	−	8.77433i	−0.0338233	−	0.540023i
$265$	13.2355	+	13.2355i	0.813053	+	0.813053i
$266$	−6.30578	+	13.4114i	−0.386632	+	0.822306i
$267$	−2.43435	+	12.0556i	−0.148980	+	0.737790i
$268$	−3.17363	−	11.8441i	−0.193860	−	0.723496i
$269$			19.0496i			1.16147i	0.814091	+	0.580737i	$0.197236\pi$
$269$			19.0496i			1.16147i	−0.814091	+	0.580737i	$0.802764\pi$
$270$	7.97994	+	2.78644i	0.485644	+	0.169577i
$271$	0.181696	−	0.181696i	0.0110372	−	0.0110372i	−0.701567	−	0.712604i	$-0.747516\pi$
$271$	0.181696	−	0.181696i	0.0110372	−	0.0110372i	0.712604	+	0.701567i	$0.247516\pi$
$272$	−0.853434			−0.0517471
$273$	4.22335	−	15.9738i	0.255609	−	0.966780i
$274$	7.23685			0.437194
$275$	8.44858	−	8.44858i	0.509468	−	0.509468i
$276$	−3.60240	+	2.39197i	−0.216839	+	0.143980i
$277$		−	1.40523i		−	0.0844322i	−0.999109	−	0.0422161i	$-0.986558\pi$
$277$		−	1.40523i		−	0.0844322i	0.999109	−	0.0422161i	$-0.0134418\pi$
$278$	−1.15411	−	4.30719i	−0.0692187	−	0.258328i
$279$	−13.5406	−	10.5154i	−0.810657	−	0.629539i
$280$	4.28856	−	0.361477i	0.256291	−	0.0216024i
$281$	−18.3020	−	18.3020i	−1.09180	−	1.09180i	−0.995336	−	0.0964690i	$-0.969245\pi$
$281$	−18.3020	−	18.3020i	−1.09180	−	1.09180i	−0.0964690	−	0.995336i	$-0.530755\pi$
$282$	−12.9436	+	0.810695i	−0.770778	+	0.0482762i
$283$	20.8092	+	12.0142i	1.23698	+	0.714169i	0.968475	−	0.249110i	$-0.0801381\pi$
$283$	20.8092	+	12.0142i	1.23698	+	0.714169i	0.268502	+	0.963279i	$0.413471\pi$
$284$	14.5895	−	3.90925i	0.865728	−	0.231971i
$285$	−8.72982	−	13.1474i	−0.517110	−	0.778787i
$286$	7.21294	−	16.8197i	0.426510	−	0.994567i
$287$	1.92619	+	5.34492i	0.113699	+	0.315501i
$288$	−1.13196	−	2.77825i	−0.0667016	−	0.163710i
$289$	−16.2716			−0.957156
$290$	9.37237			0.550364
$291$	−20.0832	−	17.7158i	−1.17730	−	1.03852i
$292$	−2.83040	+	10.5632i	−0.165637	+	0.618164i
$293$	12.2954	−	3.29454i	0.718304	−	0.192469i	0.118889	−	0.992908i	$-0.462067\pi$
$293$	12.2954	−	3.29454i	0.718304	−	0.192469i	0.599415	+	0.800439i	$0.295400\pi$
$294$	−6.38542	+	10.3066i	−0.372405	+	0.601094i
$295$	0.671448	−	1.16298i	0.0390932	−	0.0677114i
$296$	−5.49560			−0.319425
$297$	−23.7552	+	11.4590i	−1.37842	+	0.664921i
$298$	10.6352	−	6.14022i	0.616079	−	0.355693i
$299$	−8.93847	+	1.06402i	−0.516925	+	0.0615336i
$300$	1.81386	−	3.65143i	0.104724	−	0.210816i
$301$	−2.88635	−	34.2437i	−0.166367	−	1.97377i
$302$	−0.0490370	+	0.0283115i	−0.00282176	+	0.00162915i
$303$	3.66576	−	0.229598i	0.210592	−	0.0131900i
$304$	−1.44975	+	5.41052i	−0.0831486	+	0.310315i
$305$	−6.73329	+	6.73329i	−0.385547	+	0.385547i
$306$	0.966057	+	2.37105i	0.0552258	+	0.135544i
$307$	6.70956	−	6.70956i	0.382935	−	0.382935i	−0.489223	−	0.872158i	$-0.662720\pi$
$307$	6.70956	−	6.70956i	0.382935	−	0.382935i	0.872158	+	0.489223i	$0.162720\pi$
$308$	−8.66481	+	10.2600i	−0.493723	+	0.584615i
$309$	0.304402	+	4.86008i	0.0173168	+	0.276481i
$310$	6.57325	−	6.57325i	0.373335	−	0.373335i
$311$	−6.66105	−	11.5373i	−0.377714	−	0.654219i	0.613016	−	0.790071i	$-0.289956\pi$
$311$	−6.66105	−	11.5373i	−0.377714	−	0.654219i	−0.990729	+	0.135852i	$0.956623\pi$
$312$	0.503847	−	6.22464i	0.0285247	−	0.352401i
$313$	12.9713	−	22.4670i	0.733183	−	1.26991i	−0.222333	−	0.974971i	$-0.571367\pi$
$313$	12.9713	−	22.4670i	0.733183	−	1.26991i	0.955516	−	0.294939i	$-0.0952994\pi$
$314$	−3.92673	−	1.05216i	−0.221598	−	0.0593770i
$315$	−5.85877	−	11.5055i	−0.330104	−	0.648262i
$316$	10.4613	+	6.03981i	0.588492	+	0.339766i
$317$	1.41750	+	5.29018i	0.0796148	+	0.297126i	0.994240	−	0.107176i	$-0.0341809\pi$
$317$	1.41750	+	5.29018i	0.0796148	+	0.297126i	−0.914625	+	0.404303i	$0.867514\pi$
$318$	−18.8912	+	6.35171i	−1.05937	+	0.356186i
$319$	−20.6794	+	20.6794i	−1.15782	+	1.15782i
$320$	1.57124	−	0.421014i	0.0878352	−	0.0235354i
$321$	17.5185	−	11.6322i	0.977785	−	0.649244i
$322$	6.50132	+	1.16766i	0.362305	+	0.0650714i
$323$	1.23726	−	4.61753i	0.0688431	−	0.256926i
$324$	−6.43732	+	6.28975i	−0.357629	+	0.349431i
$325$	6.79703	−	5.08269i	0.377031	−	0.281937i
$326$	8.81774	−	5.09093i	0.488370	−	0.281960i
$327$	11.8927	−	3.99862i	0.657667	−	0.221124i
$328$	1.07368	+	1.85968i	0.0592843	+	0.102683i
$329$	15.1351	+	12.7820i	0.834425	+	0.704695i
$330$	−4.55761	−	13.5552i	−0.250888	−	0.746192i
$331$	−0.627222	+	2.34082i	−0.0344752	+	0.128663i	−0.981019	−	0.193913i	$-0.937882\pi$
$331$	−0.627222	+	2.34082i	−0.0344752	+	0.128663i	0.946544	+	0.322576i	$0.104549\pi$
$332$	3.18424	+	3.18424i	0.174758	+	0.174758i
$333$	6.22082	+	15.2681i	0.340899	+	0.836689i
$334$	5.60063	+	9.70058i	0.306453	+	0.530792i
$335$	−9.97309	−	17.2739i	−0.544888	−	0.943774i
$336$	−1.68682	+	4.26083i	−0.0920233	+	0.232447i
$337$		−	7.56541i		−	0.412114i	−0.978540	−	0.206057i	$-0.933937\pi$
$337$		−	7.56541i		−	0.412114i	0.978540	−	0.206057i	$-0.0660633\pi$
$338$	6.77761	−	11.0934i	0.368653	−	0.603403i
$339$	1.20721	+	19.2743i	0.0655664	+	1.04683i
$340$	−1.34095	+	0.359308i	−0.0727234	+	0.0194862i
$341$			29.0067i			1.57080i
$342$	16.6728	−	2.09676i	0.901563	−	0.113380i
$343$	17.9341	−	4.62270i	0.968348	−	0.249602i
$344$	−3.36175	−	12.5462i	−0.181253	−	0.676446i
$345$	−4.65320	+	5.27504i	−0.250520	+	0.283999i
$346$	−11.5361	−	3.09109i	−0.620184	−	0.166178i
$347$			22.8686i			1.22765i	0.789443	+	0.613824i	$0.210370\pi$
$347$			22.8686i			1.22765i	−0.789443	+	0.613824i	$0.789630\pi$
$348$	−4.43976	+	8.93753i	−0.237996	+	0.479102i
$349$	−14.5245	−	3.89183i	−0.777480	−	0.208325i	−0.151806	−	0.988410i	$-0.548509\pi$
$349$	−14.5245	−	3.89183i	−0.777480	−	0.208325i	−0.625673	+	0.780085i	$0.715176\pi$
$350$	−5.85908	+	2.11148i	−0.313181	+	0.112863i
$351$	−17.8639	+	5.64626i	−0.953506	+	0.301375i
$352$	−2.53789	+	4.39576i	−0.135270	+	0.234295i
$353$	−2.42180	−	9.03830i	−0.128900	−	0.481060i	0.871049	−	0.491196i	$-0.163440\pi$
$353$	−2.42180	−	9.03830i	−0.128900	−	0.481060i	−0.999949	+	0.0101361i	$0.996774\pi$
$354$	0.790956	+	1.19121i	0.0420388	+	0.0633120i
$355$	21.2778	−	12.2848i	1.12931	−	0.652007i
$356$	5.02101	−	5.02101i	0.266113	−	0.266113i
$357$	1.43959	−	3.63634i	0.0761910	−	0.192455i
$358$	4.42527	+	16.5153i	0.233883	+	0.872863i
$359$	35.6238	−	9.54536i	1.88015	−	0.503785i	0.880599	−	0.473863i	$-0.157141\pi$
$359$	35.6238	−	9.54536i	1.88015	−	0.503785i	0.999552	−	0.0299221i	$-0.00952593\pi$
$360$	−2.94827	−	3.88873i	−0.155388	−	0.204954i
$361$	−10.7175	−	6.18776i	−0.564080	−	0.325672i
$362$	7.33657	+	7.33657i	0.385602	+	0.385602i
$363$	22.9014	+	11.3764i	1.20201	+	0.597104i
$364$	−7.13283	+	6.33425i	−0.373862	+	0.332005i
$365$			17.7890i			0.931118i
$366$	−3.23129	−	9.61051i	−0.168902	−	0.502349i
$367$	16.8558	−	29.1952i	0.879868	−	1.52398i	0.0283834	−	0.999597i	$-0.490964\pi$
$367$	16.8558	−	29.1952i	0.879868	−	1.52398i	0.851485	−	0.524379i	$-0.175703\pi$
$368$	2.49659			0.130144
$369$	3.95127	−	5.08805i	0.205695	−	0.264873i
$370$	−8.63494	+	2.31372i	−0.448909	+	0.120285i
$371$	27.5509	+	12.9539i	1.43037	+	0.672533i
$372$	3.15449	+	9.38207i	0.163552	+	0.486438i
$373$	10.0898	+	17.4761i	0.522432	+	0.904878i	0.999659	+	0.0260985i	$0.00830836\pi$
$373$	10.0898	+	17.4761i	0.522432	+	0.904878i	−0.477228	+	0.878780i	$0.658358\pi$
$374$	2.16593	−	3.75150i	0.111997	−	0.193985i
$375$	4.10107	−	20.3096i	0.211778	−	1.04879i
$376$	6.48447	+	3.74381i	0.334411	+	0.193072i
$377$	−16.6369	+	12.4408i	−0.856846	+	0.640733i
$378$	13.7470	−	0.136712i	0.707072	−	0.00703170i
$379$	2.45073	−	9.14625i	0.125886	−	0.469811i	−0.873984	−	0.485954i	$-0.838472\pi$
$379$	2.45073	−	9.14625i	0.125886	−	0.469811i	0.999870	+	0.0161431i	$0.00513874\pi$
$380$			9.11162i			0.467416i
$381$	12.2710	+	6.09569i	0.628664	+	0.312291i
$382$	−2.71231	+	10.1225i	−0.138774	+	0.517912i
$383$	21.2210	+	5.68615i	1.08434	+	0.290549i	0.756374	−	0.654140i	$-0.226969\pi$
$383$	21.2210	+	5.68615i	1.08434	+	0.290549i	0.327969	+	0.944688i	$0.393636\pi$
$384$	−0.342829	+	1.69778i	−0.0174949	+	0.0866396i
$385$	−9.29495	+	19.7689i	−0.473715	+	1.00752i
$386$	2.64358	+	1.52627i	0.134555	+	0.0776851i
$387$	−31.0511	+	23.5416i	−1.57842	+	1.19669i
$388$	4.00176	+	14.9348i	0.203159	+	0.758199i
$389$	−1.09507	−	1.89671i	−0.0555220	−	0.0961669i	0.836929	−	0.547312i	$-0.184349\pi$
$389$	−1.09507	−	1.89671i	−0.0555220	−	0.0961669i	−0.892451	+	0.451145i	$0.851016\pi$
$390$	−1.82899	−	9.99256i	−0.0926146	−	0.505993i
$391$	−2.13067			−0.107753
$392$	6.36282	−	2.91796i	0.321371	−	0.147379i
$393$	0.825453	+	13.1792i	0.0416386	+	0.664803i
$394$	−19.1874	+	11.0779i	−0.966649	+	0.558095i
$395$	18.9800	+	5.08569i	0.954989	+	0.255889i
$396$	15.0853	+	2.07506i	0.758066	+	0.104275i
$397$	−10.1722	−	2.72562i	−0.510526	−	0.136795i	−0.00564529	−	0.999984i	$-0.501797\pi$
$397$	−10.1722	−	2.72562i	−0.510526	−	0.136795i	−0.504881	+	0.863189i	$0.668464\pi$
$398$	3.50595	+	3.50595i	0.175737	+	0.175737i
$399$	−20.6079	−	15.3037i	−1.03168	−	0.766142i
$400$	−2.03857	+	1.17697i	−0.101929	+	0.0588484i
$401$	−17.3470	−	17.3470i	−0.866269	−	0.866269i	0.125788	−	0.992057i	$-0.459854\pi$
$401$	−17.3470	−	17.3470i	−0.866269	−	0.866269i	−0.992057	+	0.125788i	$0.959854\pi$
$402$	21.1968	−	1.32762i	1.05720	−	0.0662156i
$403$	−2.94295	+	20.3935i	−0.146599	+	1.01587i
$404$	−1.83647	−	1.06029i	−0.0913678	−	0.0527512i
$405$	−7.46653	+	12.5929i	−0.371015	+	0.625748i
$406$	14.3411	−	5.16822i	0.711739	−	0.256494i
$407$	13.9473	−	24.1574i	0.691340	−	1.19744i
$408$	0.292582	−	1.44895i	0.0144850	−	0.0717335i
$409$	3.30511	+	3.30511i	0.163427	+	0.163427i	0.784083	−	0.620656i	$-0.213134\pi$
$409$	3.30511	+	3.30511i	0.163427	+	0.163427i	−0.620656	+	0.784083i	$0.713134\pi$
$410$	2.46997	+	2.46997i	0.121983	+	0.121983i
$411$	−2.48100	+	12.2866i	−0.122379	+	0.606053i
$412$	1.40573	−	2.43480i	0.0692556	−	0.119954i
$413$	0.386112	−	2.14980i	0.0189994	−	0.105785i
$414$	−2.82605	−	6.93614i	−0.138893	−	0.340893i
$415$	6.34383	+	3.66261i	0.311407	+	0.179791i
$416$	−2.23028	+	2.83300i	−0.109348	+	0.138899i
$417$	7.70833	−	0.482796i	0.377479	−	0.0236426i
$418$	−20.1041	−	20.1041i	−0.983322	−	0.983322i
$419$	−17.5508	+	10.1330i	−0.857413	+	0.495028i	−0.863145	−	0.504956i	$-0.831509\pi$
$419$	−17.5508	+	10.1330i	−0.857413	+	0.495028i	0.00573204	+	0.999984i	$0.498175\pi$
$420$	−0.856533	+	7.40498i	−0.0417945	+	0.361326i
$421$	6.81033	+	6.81033i	0.331915	+	0.331915i	0.853313	−	0.521398i	$-0.174589\pi$
$421$	6.81033	+	6.81033i	0.331915	+	0.331915i	−0.521398	+	0.853313i	$0.674589\pi$
$422$	−5.14430	−	1.37841i	−0.250421	−	0.0671001i
$423$	3.06104	−	22.2533i	0.148833	−	1.08199i
$424$	11.1148	+	2.97819i	0.539781	+	0.144634i
$425$	1.73979	−	1.00447i	0.0843920	−	0.0487237i
$426$	1.63535	+	26.1100i	0.0792329	+	1.26503i
$427$	−6.59001	+	14.0159i	−0.318913	+	0.678277i
$428$	−12.1409			−0.586852
$429$	26.0833	+	18.0123i	1.25932	+	0.869641i
$430$	−10.5643	−	18.2978i	−0.509453	−	0.882399i
$431$	1.47412	+	5.50147i	0.0710056	+	0.264997i	0.992298	−	0.123874i	$-0.0395319\pi$
$431$	1.47412	+	5.50147i	0.0710056	+	0.264997i	−0.921292	+	0.388871i	$0.872865\pi$
$432$	5.10493	−	0.969366i	0.245611	−	0.0466386i
$433$	−29.1233	−	16.8144i	−1.39958	−	0.808047i	−0.405230	−	0.914215i	$-0.632808\pi$
$433$	−29.1233	−	16.8144i	−1.39958	−	0.808047i	−0.994348	+	0.106168i	$0.966142\pi$
$434$	6.43337	−	13.6828i	0.308812	−	0.656793i
$435$	−3.21312	+	15.9123i	−0.154057	+	0.762934i
$436$	−6.99713	−	1.87488i	−0.335102	−	0.0897903i
$437$	−3.61942	+	13.5078i	−0.173140	+	0.646168i
$438$	−16.9637	−	8.42677i	−0.810555	−	0.402647i
$439$			1.40144i			0.0668871i	0.999441	+	0.0334436i	$0.0106474\pi$
$439$			1.40144i			0.0668871i	−0.999441	+	0.0334436i	$0.989353\pi$
$440$	−2.13698	+	7.97531i	−0.101876	+	0.380208i
$441$	−15.3093	−	14.3745i	−0.729015	−	0.684498i
$442$	1.90339	−	2.41778i	0.0905352	−	0.115002i
$443$	−16.1647	−	9.33267i	−0.768007	−	0.443409i	0.0641565	−	0.997940i	$-0.479564\pi$
$443$	−16.1647	−	9.33267i	−0.768007	−	0.443409i	−0.832163	+	0.554531i	$0.812898\pi$
$444$	1.88405	−	9.33034i	0.0894131	−	0.442799i
$445$	5.77532	−	10.0031i	0.273776	−	0.474195i
$446$	−5.26656	−	9.12194i	−0.249379	−	0.431936i
$447$	6.77872	+	20.1613i	0.320622	+	0.953595i
$448$	2.17208	−	1.51065i	0.102621	−	0.0713714i
$449$	−13.6899	+	3.66820i	−0.646066	+	0.173113i	−0.566950	−	0.823752i	$-0.691877\pi$
$449$	−13.6899	+	3.66820i	−0.646066	+	0.173113i	−0.0791167	+	0.996865i	$0.525210\pi$
$450$	5.57750	+	4.33137i	0.262926	+	0.204183i
$451$	−10.8996			−0.513242
$452$	5.57491	−	9.65602i	0.262222	−	0.454181i
$453$	−0.0312555	−	0.0929602i	−0.00146851	−	0.00436765i
$454$		−	4.04124i		−	0.189665i
$455$	−8.54061	+	12.9557i	−0.400390	+	0.607371i
$456$	−8.68888	−	4.31624i	−0.406894	−	0.202126i
$457$	−1.40299	−	1.40299i	−0.0656291	−	0.0656291i	0.673530	−	0.739159i	$-0.264777\pi$
$457$	−1.40299	−	1.40299i	−0.0656291	−	0.0656291i	−0.739159	+	0.673530i	$0.764777\pi$
$458$	5.30417	+	3.06236i	0.247847	+	0.143095i
$459$	−4.35672	+	0.827290i	−0.203354	+	0.0386146i
$460$	3.92275	−	1.05110i	0.182899	−	0.0490077i
$461$	−3.48234	−	12.9963i	−0.162189	−	0.605297i	−0.998382	−	0.0568621i	$-0.981890\pi$
$461$	−3.48234	−	12.9963i	−0.162189	−	0.605297i	0.836193	−	0.548435i	$-0.184776\pi$
$462$	−14.4486	−	18.2284i	−0.672211	−	0.848061i
$463$	−25.6449	+	25.6449i	−1.19182	+	1.19182i	−0.215266	+	0.976555i	$0.569062\pi$
$463$	−25.6449	+	25.6449i	−1.19182	+	1.19182i	−0.976555	+	0.215266i	$0.930938\pi$
$464$	4.98976	−	2.88084i	0.231644	−	0.133740i
$465$	8.90645	+	13.4134i	0.413027	+	0.622034i
$466$	−3.25572	−	12.1505i	−0.150818	−	0.562862i
$467$	5.68598	−	9.84841i	0.263116	−	0.455730i	−0.703952	−	0.710247i	$-0.748583\pi$
$467$	5.68598	−	9.84841i	0.263116	−	0.455730i	0.967068	+	0.254517i	$0.0819165\pi$
$468$	10.3954	+	2.98941i	0.480526	+	0.138185i
$469$	−24.7857	−	20.9322i	−1.14450	−	0.966559i
$470$	11.7649	+	3.15239i	0.542673	+	0.145409i
$471$	3.13254	−	6.30602i	0.144340	−	0.290566i
$472$		−	0.825548i		−	0.0379989i
$473$	63.6819	+	17.0635i	2.92810	+	0.784581i
$474$	−13.8407	+	15.6903i	−0.635725	+	0.720681i
$475$	−3.41261	−	12.7360i	−0.156581	−	0.584369i
$476$	−1.85373	+	1.28924i	−0.0849656	+	0.0590922i
$477$	−4.30736	−	34.2508i	−0.197220	−	1.56824i
$478$		−	20.2004i		−	0.923944i
$479$	−4.45283	+	1.19313i	−0.203455	+	0.0545156i	−0.359107	−	0.933296i	$-0.616919\pi$
$479$	−4.45283	+	1.19313i	−0.203455	+	0.0545156i	0.155652	+	0.987812i	$0.450252\pi$
$480$	0.176122	+	2.81197i	0.00803884	+	0.128348i
$481$	12.2567	−	15.5690i	0.558858	−	0.709886i
$482$			23.6500i			1.07723i
$483$	−4.21128	+	10.6375i	−0.191620	+	0.484024i
$484$	−7.38182	−	12.7857i	−0.335537	−	0.581168i
$485$	12.5755	+	21.7814i	0.571024	+	0.989042i
$486$	−8.47174	−	13.0855i	−0.384286	−	0.593569i
$487$	6.55708	+	6.55708i	0.297130	+	0.297130i	0.839889	−	0.542759i	$-0.182620\pi$
$487$	6.55708	+	6.55708i	0.297130	+	0.297130i	−0.542759	+	0.839889i	$0.682620\pi$
$488$	−1.51509	+	5.65440i	−0.0685850	+	0.255963i
$489$	5.62031	+	16.7159i	0.254159	+	0.755921i
$490$	8.76905	−	7.26367i	0.396145	−	0.328139i
$491$	13.9676	+	24.1925i	0.630347	+	1.09179i	0.987481	+	0.157739i	$0.0504206\pi$
$491$	13.9676	+	24.1925i	0.630347	+	1.09179i	−0.357134	+	0.934053i	$0.616246\pi$
$492$	−3.52542	+	1.18533i	−0.158938	+	0.0534389i
$493$	−4.25844	+	2.45861i	−0.191790	+	0.110730i
$494$	−12.0947	−	16.1741i	−0.544164	−	0.727706i
$495$	24.5764	−	3.09071i	1.10463	−	0.138917i
$496$	1.47908	−	5.51999i	0.0664126	−	0.247855i
$497$	25.7841	−	30.5308i	1.15658	−	1.36949i
$498$	−6.49781	+	4.31450i	−0.291174	+	0.193338i
$499$	−4.88887	+	1.30997i	−0.218856	+	0.0586423i	−0.366581	−	0.930386i	$-0.619472\pi$
$499$	−4.88887	+	1.30997i	−0.218856	+	0.0586423i	0.147725	+	0.989029i	$0.452805\pi$
$500$	−8.45873	+	8.45873i	−0.378286	+	0.378286i
$501$	−18.3895	+	6.18302i	−0.821584	+	0.276237i
$502$	−0.400323	−	1.49403i	−0.0178673	−	0.0666816i
$503$	−19.2261	−	11.1002i	−0.857248	−	0.494932i	0.00584193	−	0.999983i	$-0.498140\pi$
$503$	−19.2261	−	11.1002i	−0.857248	−	0.494932i	−0.863090	+	0.505051i	$0.831474\pi$
$504$	−6.65567	−	4.32458i	−0.296467	−	0.192632i
$505$	−3.33194	−	0.892791i	−0.148269	−	0.0397287i
$506$	−6.33608	+	10.9744i	−0.281673	+	0.487872i
$507$	16.5107	+	15.3101i	0.733264	+	0.679944i
$508$	−3.95533	−	6.85083i	−0.175489	−	0.303957i
$509$	18.3639	−	18.3639i	0.813966	−	0.813966i	−0.171260	−	0.985226i	$-0.554784\pi$
$509$	18.3639	−	18.3639i	0.813966	−	0.813966i	0.985226	+	0.171260i	$0.0547838\pi$
$510$	−0.150309	−	2.39983i	−0.00665578	−	0.106266i
$511$	9.80941	+	27.2199i	0.433943	+	1.20414i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.15607	+	29.0257i	−0.0951930	+	1.28152i
$514$	−4.87178	+	4.87178i	−0.214885	+	0.214885i
$515$	1.18367	−	4.41751i	0.0521586	−	0.194659i
$516$	22.4532	−	1.40631i	0.988449	−	0.0619096i
$517$	−32.9138	+	19.0028i	−1.44755	+	0.835742i
$518$	−11.9369	+	8.30192i	−0.524477	+	0.364766i
$519$	9.20291	−	18.5261i	0.403963	−	0.813205i
$520$	−2.31158	+	5.39031i	−0.101369	+	0.236381i
$521$	−24.5520	+	14.1751i	−1.07564	+	0.621021i	−0.929717	−	0.368275i	$-0.879949\pi$
$521$	−24.5520	+	14.1751i	−1.07564	+	0.621021i	−0.145923	+	0.989296i	$0.546615\pi$
$522$	−13.6519	−	10.6018i	−0.597528	−	0.464028i
$523$	−42.0930			−1.84060			−0.920299	−	0.391216i	$-0.872054\pi$
$523$	−42.0930			−1.84060			−0.920299	+	0.391216i	$0.872054\pi$
$524$	3.81196	−	6.60251i	0.166526	−	0.288432i
$525$	−1.57617	−	10.6713i	−0.0687897	−	0.465735i
$526$	−5.09956	+	1.36642i	−0.222351	+	0.0595788i
$527$	−1.26230	+	4.71095i	−0.0549865	+	0.205212i
$528$	−6.59299	−	5.81579i	−0.286923	−	0.253100i
$529$	−16.7671			−0.729002
$530$	18.7179			0.813053
$531$	−2.29358	+	0.934491i	−0.0995328	+	0.0405534i
$532$	5.02443	+	13.9422i	0.217837	+	0.604469i
$533$	−7.66307	−	1.10585i	−0.331924	−	0.0478995i
$534$	6.80324	+	10.2459i	0.294405	+	0.443385i
$535$	−19.0763	+	5.11148i	−0.824741	+	0.220989i
$536$	−10.6192	−	6.13098i	−0.458678	−	0.264818i
$537$	−29.5566	+	1.85122i	−1.27546	+	0.0798859i
$538$	13.4701	+	13.4701i	0.580737	+	0.580737i
$539$	−3.32150	+	35.3749i	−0.143067	+	1.52371i
$540$	7.61298	−	3.67236i	0.327611	−	0.158033i
$541$	−0.184580	−	0.688861i	−0.00793570	−	0.0296164i	0.961844	−	0.273597i	$-0.0882134\pi$
$541$	−0.184580	−	0.688861i	−0.00793570	−	0.0296164i	−0.969780	+	0.243980i	$0.921547\pi$
$542$		−	0.256957i		−	0.0110372i
$543$	−14.9711	+	9.94072i	−0.642471	+	0.426597i
$544$	−0.603469	+	0.603469i	−0.0258735	+	0.0258735i
$545$	−11.7836			−0.504752
$546$	−8.30885	−	14.2816i	−0.355586	−	0.611195i
$547$	3.36783			0.143998			0.0719990	−	0.997405i	$-0.477062\pi$
$547$	3.36783			0.143998			0.0719990	+	0.997405i	$0.477062\pi$
$548$	5.11722	−	5.11722i	0.218597	−	0.218597i
$549$	17.4243	−	2.19127i	0.743653	−	0.0935213i
$550$		−	11.9481i		−	0.509468i
$551$	8.35297	+	31.1737i	0.355849	+	1.32804i
$552$	−0.855902	+	4.23867i	−0.0364296	+	0.180410i
$553$	31.8467	−	2.68432i	1.35426	−	0.114149i
$554$	−0.993649	−	0.993649i	−0.0422161	−	0.0422161i
$555$	−0.967897	−	15.4535i	−0.0410849	−	0.655963i
$556$	−3.86172	−	2.22956i	−0.163773	−	0.0945546i
$557$	−1.53348	+	0.410894i	−0.0649756	+	0.0174102i	−0.291160	−	0.956674i	$-0.594041\pi$
$557$	−1.53348	+	0.410894i	−0.0649756	+	0.0174102i	0.226185	+	0.974084i	$0.427375\pi$
$558$	−17.0102	+	2.13919i	−0.720098	+	0.0905591i
$559$	43.0410	+	18.4577i	1.82044	+	0.780677i
$560$	2.77687	−	3.28807i	0.117344	−	0.138947i
$561$	5.62668	+	4.96340i	0.237559	+	0.209555i
$562$	−25.8829			−1.09180
$563$	9.72303			0.409777			0.204889	−	0.978785i	$-0.434317\pi$
$563$	9.72303			0.409777			0.204889	+	0.978785i	$0.434317\pi$
$564$	−8.57924	+	9.72573i	−0.361251	+	0.409527i
$565$	4.69422	−	17.5191i	0.197487	−	0.737033i
$566$	23.2096	−	6.21900i	0.975573	−	0.261404i
$567$	−4.48078	+	23.3864i	−0.188175	+	0.982136i
$568$	7.55208	−	13.0806i	0.316878	−	0.548849i
$569$	22.2382			0.932275			0.466138	−	0.884712i	$-0.345645\pi$
$569$	22.2382			0.932275			0.466138	+	0.884712i	$0.345645\pi$
$570$	−15.4696	−	3.12373i	−0.647948	−	0.130838i
$571$	−0.631338	+	0.364503i	−0.0264207	+	0.0152540i	−0.513152	−	0.858298i	$-0.671522\pi$
$571$	−0.631338	+	0.364503i	−0.0264207	+	0.0152540i	0.486731	+	0.873552i	$0.338189\pi$
$572$	−6.79298	−	16.9936i	−0.284029	−	0.710539i
$573$	−16.2559	−	8.07520i	−0.679101	−	0.337346i
$574$	5.14145	+	2.41741i	0.214600	+	0.100901i
$575$	−5.08947	+	2.93841i	−0.212246	+	0.122540i
$576$	−2.76494	−	1.16410i	−0.115206	−	0.0485041i
$577$	10.9682	−	40.9337i	0.456610	−	1.70409i	−0.226700	−	0.973965i	$-0.572794\pi$
$577$	10.9682	−	40.9337i	0.456610	−	1.70409i	0.683310	−	0.730128i	$-0.260540\pi$
$578$	−11.5058	+	11.5058i	−0.478578	+	0.478578i
$579$	−3.49757	+	3.96497i	−0.145354	+	0.164779i
$580$	6.62726	−	6.62726i	0.275182	−	0.275182i
$581$	11.7267	+	2.10617i	0.486506	+	0.0873785i
$582$	−26.7279	+	1.67405i	−1.10791	+	0.0693917i
$583$	−41.2996	+	41.2996i	−1.71045	+	1.71045i
$584$	5.46791	+	9.47070i	0.226264	+	0.391900i
$585$	17.5922	+	0.320505i	0.727349	+	0.0132512i
$586$	6.36456	−	11.0237i	0.262918	−	0.455387i
$587$	−26.7015	−	7.15465i	−1.10209	−	0.295304i	−0.338474	−	0.940976i	$-0.609911\pi$
$587$	−26.7015	−	7.15465i	−1.10209	−	0.295304i	−0.763615	+	0.645672i	$0.776578\pi$
$588$	2.77271	+	11.8031i	0.114345	+	0.486750i
$589$	27.7218	+	16.0052i	1.14226	+	0.659482i
$590$	−0.347567	−	1.29714i	−0.0143091	−	0.0534023i
$591$	−12.2298	−	36.3739i	−0.503068	−	1.49622i
$592$	−3.88598	+	3.88598i	−0.159713	+	0.159713i
$593$	−23.9716	+	6.42316i	−0.984394	+	0.263768i	−0.714894	−	0.699233i	$-0.753525\pi$
$593$	−23.9716	+	6.42316i	−0.984394	+	0.263768i	−0.269500	+	0.963000i	$0.586858\pi$
$594$	−8.69468	+	24.9002i	−0.356747	+	1.02167i
$595$	−2.36988	+	2.80616i	−0.0971554	+	0.115041i
$596$	3.17841	−	11.8620i	0.130193	−	0.485886i
$597$	−7.15429	+	4.75041i	−0.292806	+	0.194421i
$598$	−5.56808	+	7.07282i	−0.227696	+	0.289229i
$599$	−13.1943	+	7.61771i	−0.539103	+	0.311251i	−0.744715	−	0.667382i	$-0.767415\pi$
$599$	−13.1943	+	7.61771i	−0.539103	+	0.311251i	0.205612	+	0.978634i	$0.434081\pi$
$600$	−1.29936	−	3.86455i	−0.0530461	−	0.157770i
$601$	4.51090	+	7.81311i	0.184004	+	0.318703i	0.943240	−	0.332111i	$-0.107761\pi$
$601$	4.51090	+	7.81311i	0.184004	+	0.318703i	−0.759237	+	0.650815i	$0.774428\pi$
$602$	−26.2549	−	22.1730i	−1.07007	−	0.903703i
$603$	−5.01286	+	36.4427i	−0.204140	+	1.48406i
$604$	−0.0146551	+	0.0546937i	−0.000596308	+	0.00222545i
$605$	−16.9816	−	16.9816i	−0.690400	−	0.690400i
$606$	2.42973	−	2.75443i	0.0987011	−	0.111891i
$607$	18.2375	+	31.5882i	0.740237	+	1.28213i	0.952387	+	0.304890i	$0.0986198\pi$
$607$	18.2375	+	31.5882i	0.740237	+	1.28213i	−0.212151	+	0.977237i	$0.568047\pi$
$608$	2.80069	+	4.85094i	0.113583	+	0.196732i
$609$	3.85796	+	26.1200i	0.156332	+	1.05843i
$610$			9.52232i			0.385547i
$611$	−25.0683	+	10.0207i	−1.01416	+	0.405396i
$612$	2.35969	+	0.993481i	0.0953849	+	0.0401591i
$613$	4.92172	−	1.31877i	0.198786	−	0.0532646i	−0.158052	−	0.987431i	$-0.550521\pi$
$613$	4.92172	−	1.31877i	0.198786	−	0.0532646i	0.356838	+	0.934166i	$0.383855\pi$
$614$		−	9.48876i		−	0.382935i
$615$	−5.04025	+	3.34670i	−0.203242	+	0.134952i
$616$	1.12794	+	13.3818i	0.0454459	+	0.539169i
$617$	0.366038	+	1.36607i	0.0147361	+	0.0549960i	0.972902	−	0.231216i	$-0.0742705\pi$
$617$	0.366038	+	1.36607i	0.0147361	+	0.0549960i	−0.958166	+	0.286212i	$0.907604\pi$
$618$	3.65184	+	3.22135i	0.146899	+	0.129582i
$619$	0.0928089	+	0.0248681i	0.00373031	+	0.000999532i	0.260684	−	0.965424i	$-0.416052\pi$
$619$	0.0928089	+	0.0248681i	0.00373031	+	0.000999532i	−0.256953	+	0.966424i	$0.582719\pi$
$620$		−	9.29597i		−	0.373335i
$621$	12.7449	−	2.42011i	0.511436	−	0.0971155i
$622$	−12.8682	−	3.44801i	−0.515966	−	0.138253i
$623$	3.32106	−	18.4910i	0.133056	−	0.740827i
$624$	−4.04521	−	4.75776i	−0.161938	−	0.190463i
$625$	−3.84464	+	6.65912i	−0.153786	+	0.266365i
$626$	−6.71445	−	25.0587i	−0.268364	−	1.00155i
$627$	41.0246	−	27.2401i	1.63837	−	1.08787i
$628$	−3.52061	+	2.03262i	−0.140487	+	0.0811105i
$629$	3.31643	−	3.31643i	0.132235	−	0.132235i
$630$	−12.2784	−	3.99285i	−0.489183	−	0.159079i
$631$	−2.23294	−	8.33346i	−0.0888921	−	0.331750i	0.907131	−	0.420849i	$-0.138268\pi$
$631$	−2.23294	−	8.33346i	−0.0888921	−	0.331750i	−0.996023	+	0.0890992i	$0.971601\pi$
$632$	11.6680	−	3.12644i	0.464129	−	0.124363i
$633$	4.10386	−	8.26135i	0.163114	−	0.328359i
$634$	4.74305	+	2.73840i	0.188371	+	0.108756i
$635$	−9.09909	−	9.09909i	−0.361086	−	0.361086i
$636$	−8.86679	+	17.8495i	−0.351591	+	0.707777i
$637$	−5.92427	+	24.5337i	−0.234728	+	0.972061i
$638$			29.2451i			1.15782i
$639$	−44.8898	−	6.17480i	−1.77581	−	0.244271i
$640$	0.813336	−	1.40874i	0.0321499	−	0.0556853i
$641$	−38.6190			−1.52536			−0.762680	−	0.646776i	$-0.776117\pi$
$641$	−38.6190			−1.52536			−0.762680	+	0.646776i	$0.776117\pi$
$642$	4.16225	−	20.6126i	0.164271	−	0.813515i
$643$	−11.1923	+	2.99896i	−0.441380	+	0.118268i	−0.472663	−	0.881243i	$-0.656707\pi$
$643$	−11.1923	+	2.99896i	−0.441380	+	0.118268i	0.0312830	+	0.999511i	$0.490041\pi$
$644$	5.42279	−	3.77147i	0.213688	−	0.148617i
$645$	34.6875	−	11.6628i	1.36582	−	0.459222i
$646$	−2.39021	−	4.13996i	−0.0940414	−	0.162885i
$647$	22.8744	−	39.6196i	0.899285	−	1.55761i	0.0708753	−	0.997485i	$-0.477421\pi$
$647$	22.8744	−	39.6196i	0.899285	−	1.55761i	0.828410	−	0.560122i	$-0.189246\pi$
$648$	−0.104345	+	8.99940i	−0.00409904	+	0.353530i
$649$	3.62891	+	2.09515i	0.142447	+	0.0822420i
$650$	1.21222	−	8.40023i	0.0475474	−	0.329484i
$651$	21.0248	+	15.6133i	0.824027	+	0.611934i
$652$	2.63526	−	9.83491i	0.103205	−	0.385165i
$653$			14.7980i			0.579090i	0.957164	+	0.289545i	$0.0935040\pi$
$653$			14.7980i			0.579090i	−0.957164	+	0.289545i	$0.906496\pi$
$654$	5.58195	−	11.2369i	0.218272	−	0.439396i
$655$	3.20978	−	11.9791i	0.125416	−	0.468060i
$656$	2.07420	+	0.555780i	0.0809838	+	0.0216996i
$657$	20.1225	−	25.9117i	0.785052	−	1.01091i
$658$	19.7404	−	1.66389i	0.769560	−	0.0648652i
$659$	−32.1017	−	18.5340i	−1.25051	−	0.721980i	−0.279296	−	0.960205i	$-0.590101\pi$
$659$	−32.1017	−	18.5340i	−1.25051	−	0.721980i	−0.971210	+	0.238225i	$0.923435\pi$
$660$	−12.8077	−	6.36229i	−0.498540	−	0.247652i
$661$	−2.45433	−	9.15969i	−0.0954625	−	0.356271i	0.901627	−	0.432515i	$-0.142374\pi$
$661$	−2.45433	−	9.15969i	−0.0954625	−	0.356271i	−0.997089	+	0.0762443i	$0.975707\pi$
$662$	1.21170	+	2.09872i	0.0470940	+	0.0815692i
$663$	3.45232	+	4.06043i	0.134077	+	0.157694i
$664$	4.50320			0.174758
$665$	13.7645	+	19.7912i	0.533763	+	0.767469i
$666$	15.1950	+	6.39742i	0.588794	+	0.247895i
$667$	12.4574	−	7.19227i	0.482352	−	0.278486i
$668$	10.8196	+	2.89910i	0.418622	+	0.112170i
$669$	17.2926	−	5.81421i	0.668571	−	0.224790i
$670$	−19.2665	−	5.16245i	−0.744331	−	0.199443i
$671$	−21.0102	−	21.0102i	−0.811092	−	0.811092i
$672$	1.82010	+	4.20562i	0.0702119	+	0.162235i
$673$	−5.16640	+	2.98282i	−0.199150	+	0.114979i	−0.596259	−	0.802792i	$-0.703347\pi$
$673$	−5.16640	+	2.98282i	−0.199150	+	0.114979i	0.397109	+	0.917772i	$0.370014\pi$
$674$	−5.34955	−	5.34955i	−0.206057	−	0.206057i
$675$	−9.26585	+	7.98447i	−0.356643	+	0.307322i
$676$	−3.05174	−	12.6367i	−0.117375	−	0.486028i
$677$	6.02868	+	3.48066i	0.231701	+	0.133773i	0.611357	−	0.791355i	$-0.290624\pi$
$677$	6.02868	+	3.48066i	0.231701	+	0.133773i	−0.379655	+	0.925128i	$0.623957\pi$
$678$	14.4826	+	12.7753i	0.556201	+	0.490634i
$679$	31.2534	+	26.3943i	1.19939	+	1.01292i
$680$	−0.694129	+	1.20227i	−0.0266186	+	0.0461048i
$681$	6.86115	+	1.38545i	0.262920	+	0.0530907i
$682$	20.5108	+	20.5108i	0.785401	+	0.785401i
$683$	−23.6186	−	23.6186i	−0.903741	−	0.903741i	0.0920164	−	0.995757i	$-0.470669\pi$
$683$	−23.6186	−	23.6186i	−0.903741	−	0.903741i	−0.995757	+	0.0920164i	$0.970669\pi$
$684$	10.3068	−	13.2721i	0.394092	−	0.507472i
$685$	5.88599	−	10.1948i	0.224892	−	0.389524i
$686$	9.41255	−	15.9500i	0.359373	−	0.608975i
$687$	−7.01765	+	7.95546i	−0.267740	+	0.303520i
$688$	−11.2486	−	6.49440i	−0.428850	−	0.247597i
$689$	−33.2262	+	24.8459i	−1.26582	+	0.946554i
$690$	0.439704	+	7.02033i	0.0167393	+	0.267259i
$691$	14.9779	+	14.9779i	0.569785	+	0.569785i	0.932068	−	0.362283i	$-0.118003\pi$
$691$	14.9779	+	14.9779i	0.569785	+	0.569785i	−0.362283	+	0.932068i	$0.618003\pi$
$692$	−10.3430	+	5.97152i	−0.393181	+	0.227003i
$693$	35.9012	−	18.2814i	1.36378	−	0.694454i
$694$	16.1705	+	16.1705i	0.613824	+	0.613824i
$695$	−7.00638	−	1.87735i	−0.265767	−	0.0712121i
$696$	3.18041	+	9.45917i	0.120553	+	0.358549i
$697$	−1.77019	−	0.474322i	−0.0670508	−	0.0179662i
$698$	−13.0223	+	7.51845i	−0.492902	+	0.284577i
$699$	21.7451	−	1.36196i	0.822476	−	0.0515142i
$700$	−2.64996	+	5.63604i	−0.100159	+	0.213022i
$701$	33.5732			1.26804			0.634021	−	0.773315i	$-0.281403\pi$
$701$	33.5732			1.26804			0.634021	+	0.773315i	$0.281403\pi$
$702$	−8.63920	+	16.6242i	−0.326065	+	0.627440i
$703$	−15.3915	−	26.6589i	−0.580501	−	1.00546i
$704$	1.31371	+	4.90284i	0.0495124	+	0.184783i
$705$	−9.38541	+	18.8935i	−0.353475	+	0.711570i
$706$	−8.10352	−	4.67857i	−0.304980	−	0.176080i
$707$	−5.59069	+	0.471232i	−0.210259	+	0.0177225i
$708$	1.40160	+	0.283022i	0.0526754	+	0.0106366i
$709$	1.54637	+	0.414349i	0.0580752	+	0.0155612i	0.287740	−	0.957709i	$-0.407096\pi$
$709$	1.54637	+	0.414349i	0.0580752	+	0.0155612i	−0.229664	+	0.973270i	$0.573763\pi$
$710$	6.35906	−	23.7323i	0.238651	−	0.890659i
$711$	−21.8938	−	28.8776i	−0.821081	−	1.08300i
$712$		−	7.10078i		−	0.266113i
$713$	3.69265	−	13.7811i	0.138291	−	0.516108i
$714$	−1.55334	−	3.58922i	−0.0581322	−	0.134323i
$715$	−17.8280	−	23.8412i	−0.666728	−	0.891610i
$716$	14.8072	+	8.54897i	0.553373	+	0.319490i
$717$	34.2959	+	6.92527i	1.28080	+	0.258629i
$718$	18.4402	−	31.9394i	0.688183	−	1.19197i
$719$	24.5283	+	42.4842i	0.914750	+	1.58439i	0.807267	+	0.590186i	$0.200946\pi$
$719$	24.5283	+	42.4842i	0.914750	+	1.58439i	0.107482	+	0.994207i	$0.465721\pi$
$720$	−4.83449	−	0.665007i	−0.180171	−	0.0247833i
$721$	−0.624762	−	7.41217i	−0.0232673	−	0.276043i
$722$	−11.9538	+	3.20302i	−0.444876	+	0.119204i
$723$	−40.1526	−	8.10790i	−1.49329	−	0.301536i
$724$	10.3755			0.385602
$725$	−6.78132	+	11.7456i	−0.251852	+	0.436220i
$726$	24.2380	−	8.14943i	0.899558	−	0.302454i
$727$		−	8.58214i		−	0.318294i	−0.987255	−	0.159147i	$-0.949126\pi$
$727$		−	8.58214i		−	0.318294i	0.987255	−	0.159147i	$-0.0508744\pi$
$728$	−0.564681	+	9.52266i	−0.0209285	+	0.352933i
$729$	25.1207	−	9.89709i	0.930395	−	0.366559i
$730$	12.5787	+	12.5787i	0.465559	+	0.465559i
$731$	9.59996	+	5.54254i	0.355067	+	0.204998i
$732$	−9.08053	−	4.51079i	−0.335626	−	0.166724i
$733$	−43.0122	+	11.5251i	−1.58869	+	0.425689i	−0.941603	−	0.336726i	$-0.890681\pi$
$733$	−43.0122	+	11.5251i	−1.58869	+	0.425689i	−0.647089	+	0.762414i	$0.724014\pi$
$734$	−8.72523	−	32.5630i	−0.322054	−	1.20192i
$735$	9.32585	+	17.3781i	0.343989	+	0.641002i
$736$	1.76535	−	1.76535i	0.0650718	−	0.0650718i
$737$	53.9006	−	31.1196i	1.98546	−	1.14630i
$738$	−0.803824	−	6.39176i	−0.0295892	−	0.235284i
$739$	13.0641	+	48.7560i	0.480572	+	1.79352i	0.599222	+	0.800583i	$0.295477\pi$
$739$	13.0641	+	48.7560i	0.480572	+	1.79352i	−0.118650	+	0.992936i	$0.537857\pi$
$740$	−4.46977	+	7.74187i	−0.164312	+	0.284597i
$741$	31.6065	−	14.9892i	1.16109	−	0.550641i
$742$	28.6412	−	10.3216i	1.05145	−	0.378919i
$743$	−29.5583	−	7.92014i	−1.08439	−	0.290562i	−0.327997	−	0.944679i	$-0.606374\pi$
$743$	−29.5583	−	7.92014i	−1.08439	−	0.290562i	−0.756393	+	0.654117i	$0.773040\pi$
$744$	8.86468	+	4.40357i	0.324995	+	0.161443i
$745$		−	19.9762i		−	0.731873i
$746$	19.4921	+	5.22288i	0.713655	+	0.191223i
$747$	−5.09746	−	12.5110i	−0.186506	−	0.457754i
$748$	−1.12117	−	4.18425i	−0.0409939	−	0.152991i
$749$	−26.3710	+	18.3406i	−0.963576	+	0.670152i
$750$	−11.4612	−	17.2610i	−0.418503	−	0.630282i
$751$			31.1811i			1.13782i	0.822401	+	0.568908i	$0.192634\pi$
$751$			31.1811i			1.13782i	−0.822401	+	0.568908i	$0.807366\pi$
$752$	7.23248	−	1.93794i	0.263742	−	0.0706693i
$753$	2.67377	−	0.167467i	0.0974377	−	0.00610282i
$754$	−2.96714	+	20.5611i	−0.108057	+	0.748789i
$755$			0.0921071i			0.00335212i
$756$	9.62396	−	9.81730i	0.350020	−	0.357052i
$757$	−5.92020	−	10.2541i	−0.215173	−	0.372691i	0.738153	−	0.674633i	$-0.235698\pi$
$757$	−5.92020	−	10.2541i	−0.215173	−	0.372691i	−0.953326	+	0.301942i	$0.902365\pi$
$758$	−4.73445	−	8.20030i	−0.171963	−	0.297848i
$759$	−16.4600	−	14.5196i	−0.597459	−	0.527029i
$760$	6.44289	+	6.44289i	0.233708	+	0.233708i
$761$	−5.21146	+	19.4494i	−0.188915	+	0.705042i	0.804843	+	0.593488i	$0.202249\pi$
$761$	−5.21146	+	19.4494i	−0.188915	+	0.705042i	−0.993758	+	0.111554i	$0.964417\pi$
$762$	12.9872	−	4.36663i	0.470478	−	0.158186i
$763$	−18.0306	+	6.49782i	−0.652752	+	0.235237i
$764$	5.23979	+	9.07557i	0.189569	+	0.328343i
$765$	4.12592	+	0.567540i	0.149173	+	0.0205194i
$766$	19.0262	−	10.9848i	0.687446	−	0.396897i
$767$	2.33878	+	1.84120i	0.0844483	+	0.0664819i
$768$	0.958098	+	1.44293i	0.0345724	+	0.0520673i
$769$	−9.69031	+	36.1647i	−0.349442	+	1.30413i	0.537895	+	0.843012i	$0.319220\pi$
$769$	−9.69031	+	36.1647i	−0.349442	+	1.30413i	−0.887337	+	0.461122i	$0.847447\pi$
$770$	7.40620	+	20.5512i	0.266901	+	0.740615i
$771$	−6.60104	−	9.94141i	−0.237731	−	0.358031i
$772$	2.94853	−	0.790055i	0.106120	−	0.0284347i
$773$	−4.54294	+	4.54294i	−0.163398	+	0.163398i	−0.784070	−	0.620672i	$-0.786860\pi$
$773$	−4.54294	+	4.54294i	−0.163398	+	0.163398i	0.620672	+	0.784070i	$0.286860\pi$
$774$	−5.31000	+	38.6029i	−0.190864	+	1.38755i
$775$	3.48166	+	12.9937i	0.125065	+	0.466748i
$776$	13.3902	+	7.73081i	0.480679	+	0.277520i
$777$	−10.0026	−	23.1124i	−0.358840	−	0.829153i
$778$	−2.11550	−	0.566847i	−0.0758445	−	0.0203225i
$779$	−6.01412	+	10.4168i	−0.215478	+	0.373219i
$780$	−8.35910	−	5.77251i	−0.299304	−	0.206689i
$781$	38.3328	+	66.3943i	1.37165	+	2.37578i
$782$	−1.50661	+	1.50661i	−0.0538764	+	0.0538764i
$783$	22.6798	−	19.5434i	0.810510	−	0.698424i
$784$	2.43588	−	6.56251i	0.0869958	−	0.234375i
$785$	−4.67597	+	4.67597i	−0.166893	+	0.166893i
$786$	9.90279	+	8.73542i	0.353221	+	0.311582i
$787$	26.5099	−	26.5099i	0.944975	−	0.944975i	−0.0535878	−	0.998563i	$-0.517066\pi$
$787$	26.5099	−	26.5099i	0.944975	−	0.944975i	0.998563	+	0.0535878i	$0.0170657\pi$
$788$	−5.73433	+	21.4008i	−0.204277	+	0.762372i
$789$	−0.571613	−	9.12639i	−0.0203500	−	0.324908i
$790$	17.0170	−	9.82479i	0.605439	−	0.349550i
$791$	−2.47770	−	29.3954i	−0.0880968	−	1.04518i
$792$	12.1342	−	9.19965i	0.431171	−	0.326895i
$793$	−12.6398	−	16.9031i	−0.448853	−	0.600247i
$794$	−9.12011	+	5.26550i	−0.323661	+	0.186866i
$795$	−6.41703	+	31.7789i	−0.227589	+	1.12708i
$796$	4.95816			0.175737
$797$	18.3966	−	31.8639i	0.651642	−	1.12868i	−0.331083	−	0.943602i	$-0.607414\pi$
$797$	18.3966	−	31.8639i	0.651642	−	1.12868i	0.982724	−	0.185075i	$-0.0592527\pi$
$798$	−25.3933	+	3.75062i	−0.898912	+	0.132771i
$799$	−6.17245	+	1.65390i	−0.218366	+	0.0585109i
$800$	−0.609244	+	2.27373i	−0.0215400	+	0.0803885i
$801$	−19.7277	+	8.03782i	−0.697045	+	0.284003i
$802$	−24.5324			−0.866269
$803$	−55.5079			−1.95883
$804$	14.0496	−	15.9272i	0.495492	−	0.561708i
$805$	6.93270	−	8.20897i	0.244345	−	0.289328i
$806$	12.3394	+	16.5013i	0.434636	+	0.581235i
$807$	−27.4872	+	18.2514i	−0.967597	+	0.642478i
$808$	−2.04832	+	0.548845i	−0.0720595	+	0.0193083i
$809$	4.19679	+	2.42302i	0.147551	+	0.0851888i	0.571958	−	0.820283i	$-0.306184\pi$
$809$	4.19679	+	2.42302i	0.147551	+	0.0851888i	−0.424407	+	0.905472i	$0.639517\pi$
$810$	3.62492	+	14.1842i	0.127367	+	0.498381i
$811$	8.37484	+	8.37484i	0.294080	+	0.294080i	0.838690	−	0.544609i	$-0.183322\pi$
$811$	8.37484	+	8.37484i	0.294080	+	0.294080i	−0.544609	+	0.838690i	$0.683322\pi$
$812$	6.48624	−	13.7952i	0.227622	−	0.484117i
$813$	0.436257	+	0.0880922i	0.0153002	+	0.00308953i
$814$	−7.21963	−	26.9440i	−0.253048	−	0.944388i
$815$		−	16.5625i		−	0.580160i
$816$	−0.817673	−	1.23145i	−0.0286243	−	0.0431093i
$817$	51.4457	−	51.4457i	1.79986	−	1.79986i
$818$	4.67413			0.163427
$819$	27.0955	−	9.21049i	0.946794	−	0.321841i
$820$	3.49306			0.121983
$821$	16.1934	−	16.1934i	0.565153	−	0.565153i	−0.365614	−	0.930767i	$-0.619141\pi$
$821$	16.1934	−	16.1934i	0.565153	−	0.565153i	0.930767	+	0.365614i	$0.119141\pi$
$822$	6.93360	+	10.4423i	0.241837	+	0.364216i
$823$		−	4.67226i		−	0.162865i	−0.996679	−	0.0814324i	$-0.974051\pi$
$823$		−	4.67226i		−	0.162865i	0.996679	−	0.0814324i	$-0.0259495\pi$
$824$	−0.727662	−	2.71567i	−0.0253493	−	0.0946049i
$825$	20.2853	+	4.09615i	0.706243	+	0.142610i
$826$	−1.24711	−	1.79316i	−0.0433926	−	0.0623920i
$827$	37.4338	+	37.4338i	1.30170	+	1.30170i	0.927245	+	0.374455i	$0.122170\pi$
$827$	37.4338	+	37.4338i	1.30170	+	1.30170i	0.374455	+	0.927245i	$0.377830\pi$
$828$	−6.90291	−	2.90627i	−0.239893	−	0.101000i
$829$	−5.18298	−	2.99240i	−0.180012	−	0.103930i	0.407286	−	0.913301i	$-0.366475\pi$
$829$	−5.18298	−	2.99240i	−0.180012	−	0.103930i	−0.587299	+	0.809370i	$0.699809\pi$
$830$	7.07563	−	1.89591i	0.245599	−	0.0658080i
$831$	2.02765	−	1.34635i	0.0703385	−	0.0467043i
$832$	0.426188	+	3.58027i	0.0147754	+	0.124124i
$833$	−2.07887	+	5.60067i	−0.0720284	+	0.194052i
$834$	5.10922	−	5.79200i	0.176918	−	0.200561i
$835$	18.2208			0.630556
$836$	−28.4315			−0.983322
$837$	2.19970	−	29.6130i	0.0760327	−	1.02357i
$838$	−5.24521	+	19.5754i	−0.181193	+	0.676220i
$839$	7.35666	−	1.97121i	0.253980	−	0.0680538i	−0.129583	−	0.991569i	$-0.541364\pi$
$839$	7.35666	−	1.97121i	0.253980	−	0.0680538i	0.383563	+	0.923515i	$0.374697\pi$
$840$	4.63045	+	5.84177i	0.159766	+	0.201560i
$841$	2.09849	−	3.63470i	0.0723618	−	0.125334i
$842$	9.63126			0.331915
$843$	8.87341	−	43.9436i	0.305616	−	1.51350i
$844$	−4.61226	+	2.66289i	−0.158760	+	0.0916604i
$845$	−10.1153	−	18.5706i	−0.347976	−	0.638847i
$846$	−13.5710	−	17.9000i	−0.466580	−	0.615413i
$847$	−35.3486	−	16.6202i	−1.21459	−	0.571078i
$848$	9.96523	−	5.75343i	0.342208	−	0.197574i
$849$	2.60159	+	41.5370i	0.0892862	+	1.42554i
$850$	0.519950	−	1.94048i	0.0178341	−	0.0665579i
$851$	−9.70169	+	9.70169i	−0.332569	+	0.332569i
$852$	19.6189	+	17.3062i	0.672134	+	0.592901i
$853$	19.9037	−	19.9037i	0.681490	−	0.681490i	−0.278846	−	0.960336i	$-0.589952\pi$
$853$	19.9037	−	19.9037i	0.681490	−	0.681490i	0.960336	+	0.278846i	$0.0899518\pi$
$854$	5.25090	+	14.5706i	0.179682	+	0.498595i
$855$	10.6068	−	25.1930i	0.362746	−	0.861584i
$856$	−8.58491	+	8.58491i	−0.293426	+	0.293426i
$857$	−24.4329	−	42.3191i	−0.834613	−	1.44559i	−0.894345	−	0.447378i	$-0.852358\pi$
$857$	−24.4329	−	42.3191i	−0.834613	−	1.44559i	0.0597321	−	0.998214i	$-0.480975\pi$
$858$	31.1803	−	5.70710i	1.06448	−	0.194837i
$859$	13.8247	−	23.9452i	0.471694	−	0.816999i	−0.527781	−	0.849380i	$-0.676976\pi$
$859$	13.8247	−	23.9452i	0.471694	−	0.816999i	0.999476	+	0.0323818i	$0.0103092\pi$
$860$	−20.4086	−	5.46846i	−0.695926	−	0.186473i
$861$	−5.86687	+	7.90030i	−0.199942	+	0.269242i
$862$	4.93248	+	2.84777i	0.168001	+	0.0969955i
$863$	−7.11305	−	26.5462i	−0.242131	−	0.903645i	−0.974804	−	0.223064i	$-0.928394\pi$
$863$	−7.11305	−	26.5462i	−0.242131	−	0.903645i	0.732673	−	0.680581i	$-0.238273\pi$
$864$	2.92429	−	4.29518i	0.0994863	−	0.146125i
$865$	−13.7373	+	13.7373i	−0.467081	+	0.467081i
$866$	−32.4829	+	8.70376i	−1.10381	+	0.295766i
$867$	−15.5898	−	23.4789i	−0.529458	−	0.797384i
$868$	−5.12609	−	14.2242i	−0.173991	−	0.482802i
$869$	−15.8691	+	59.2244i	−0.538323	+	2.00905i
$870$	8.97964	+	13.5237i	0.304438	+	0.458496i
$871$	41.0527	−	16.4103i	1.39102	−	0.556041i
$872$	−6.27346	+	3.62198i	−0.212446	+	0.122656i
$873$	6.32093	−	45.9522i	0.213931	−	1.55525i
$874$	6.99217	+	12.1108i	0.236514	+	0.409654i
$875$	−5.59489	+	31.1512i	−0.189142	+	1.05310i
$876$	−17.9538	+	6.03650i	−0.606601	+	0.203954i
$877$	8.63015	−	32.2082i	0.291420	−	1.08759i	−0.652600	−	0.757703i	$-0.726322\pi$
$877$	8.63015	−	32.2082i	0.291420	−	1.08759i	0.944019	−	0.329890i	$-0.107012\pi$
$878$	0.990968	+	0.990968i	0.0334436	+	0.0334436i
$879$	16.5340	+	14.5849i	0.557677	+	0.491937i
$880$	4.12832	+	7.15047i	0.139166	+	0.241042i
$881$	−9.75282	−	16.8924i	−0.328581	−	0.569118i	0.653650	−	0.756797i	$-0.273237\pi$
$881$	−9.75282	−	16.8924i	−0.328581	−	0.569118i	−0.982230	+	0.187679i	$0.939904\pi$
$882$	−20.9896	+	0.661035i	−0.706756	+	0.0222582i
$883$		−	4.92582i		−	0.165767i	−0.996559	−	0.0828835i	$-0.973587\pi$
$883$		−	4.92582i		−	0.165767i	0.996559	−	0.0828835i	$-0.0264129\pi$
$884$	−0.363723	−	3.05553i	−0.0122333	−	0.102769i
$885$	2.32142	−	0.145397i	0.0780335	−	0.00488748i
$886$	−18.0293	+	4.83095i	−0.605708	+	0.162299i
$887$		−	35.7457i		−	1.20022i	−0.799916	−	0.600112i	$-0.795123\pi$
$887$		−	35.7457i		−	1.20022i	0.799916	−	0.600112i	$-0.204877\pi$
$888$	−5.26532	−	7.92977i	−0.176693	−	0.266106i
$889$	−18.9405	−	8.90546i	−0.635244	−	0.298680i
$890$	−2.98953	−	11.1571i	−0.100209	−	0.373986i
$891$	−39.2944	−	23.2982i	−1.31641	−	0.780519i
$892$	−10.1742	−	2.72617i	−0.340658	−	0.0912789i
$893$			41.9410i			1.40350i
$894$	19.0494	+	9.46289i	0.637109	+	0.316486i
$895$	26.8650	+	7.19847i	0.897999	+	0.240618i
$896$	0.467704	−	2.60408i	0.0156249	−	0.0869963i
$897$	−10.0992	−	11.8782i	−0.337203	−	0.396600i
$898$	−7.08641	+	12.2740i	−0.236477	+	0.409590i
$899$	−8.52198	−	31.8045i	−0.284224	−	1.06074i
$900$	7.00662	−	0.881149i	0.233554	−	0.0293716i
$901$	−8.50467	+	4.91017i	−0.283332	+	0.163582i
$902$	−7.70717	+	7.70717i	−0.256621	+	0.256621i
$903$	46.6459	−	36.9736i	1.55228	−	1.23040i
$904$	−2.88578	−	10.7699i	−0.0959797	−	0.358201i
$905$	16.3024	−	4.36822i	0.541910	−	0.145204i
$906$	−0.0878338	−	0.0436318i	−0.00291808	−	0.00144957i
$907$	−31.7518	−	18.3319i	−1.05430	−	0.608701i	−0.130451	−	0.991455i	$-0.541643\pi$
$907$	−31.7518	−	18.3319i	−1.05430	−	0.608701i	−0.923851	+	0.382753i	$0.874976\pi$
$908$	−2.85759	−	2.85759i	−0.0948324	−	0.0948324i
$909$	3.84345	+	5.06946i	0.127479	+	0.168143i
$910$	3.12192	+	15.2002i	0.103491	+	0.503881i
$911$		−	30.8260i		−	1.02131i	−0.859786	−	0.510655i	$-0.829403\pi$
$911$		−	30.8260i		−	1.02131i	0.859786	−	0.510655i	$-0.170597\pi$
$912$	−9.19601	+	3.09193i	−0.304510	+	0.102384i
$913$	−11.4286	+	19.7950i	−0.378233	+	0.655119i
$914$	−1.98413			−0.0656291
$915$	−16.1668	−	3.26452i	−0.534459	−	0.107922i
$916$	5.91603	−	1.58519i	0.195471	−	0.0523763i
$917$	−1.69418	−	20.0997i	−0.0559468	−	0.663752i
$918$	−2.49569	+	3.66565i	−0.0823699	+	0.120985i
$919$	−12.4035	−	21.4835i	−0.409154	−	0.708676i	0.585641	−	0.810571i	$-0.300843\pi$
$919$	−12.4035	−	21.4835i	−0.409154	−	0.708676i	−0.994795	+	0.101895i	$0.967510\pi$
$920$	2.03056	−	3.51704i	0.0669457	−	0.115953i
$921$	16.1099	+	3.25302i	0.530838	+	0.107191i
$922$	−11.6521	−	6.72737i	−0.383743	−	0.221554i
$923$	20.2140	+	50.5683i	0.665353	+	1.66448i
$924$	−23.1061	−	2.67268i	−0.760136	−	0.0879249i
$925$	3.34816	−	12.4955i	0.110087	−	0.410850i
$926$			36.2674i			1.19182i
$927$	−6.72112	+	5.09567i	−0.220750	+	0.167364i
$928$	1.49123	−	5.56536i	0.0489521	−	0.182692i
$929$	11.2124	+	3.00436i	0.367868	+	0.0985698i	0.438017	−	0.898967i	$-0.355681\pi$
$929$	11.2124	+	3.00436i	0.367868	+	0.0985698i	−0.0701494	+	0.997536i	$0.522348\pi$
$930$	15.7825	+	3.18693i	0.517530	+	0.104503i
$931$	31.9752	+	22.6934i	1.04794	+	0.743745i
$932$	−10.8939	−	6.28957i	−0.356840	−	0.206022i
$933$	10.2656	−	20.6653i	0.336079	−	0.676551i
$934$	−2.94328	−	10.9845i	−0.0963071	−	0.359423i
$935$	−3.52325	−	6.10245i	−0.115223	−	0.199572i
$936$	9.46446	−	5.23680i	0.309355	−	0.171170i
$937$	32.6123			1.06540			0.532698	−	0.846305i	$-0.321178\pi$
$937$	32.6123			1.06540			0.532698	+	0.846305i	$0.321178\pi$
$938$	−32.3274	+	2.72484i	−1.05553	+	0.0889691i
$939$	44.8461	−	2.80885i	1.46350	−	0.0916633i
$940$	10.5481	−	6.08995i	0.344041	−	0.198632i
$941$	−3.59265	−	0.962648i	−0.117117	−	0.0313814i	0.199784	−	0.979840i	$-0.435976\pi$
$941$	−3.59265	−	0.962648i	−0.117117	−	0.0313814i	−0.316902	+	0.948458i	$0.602642\pi$
$942$	−2.24399	−	6.67407i	−0.0731131	−	0.217453i
$943$	5.17842	+	1.38755i	0.168633	+	0.0451849i
$944$	−0.583751	−	0.583751i	−0.0189995	−	0.0189995i
$945$	10.9884	−	19.4772i	0.357452	−	0.633593i
$946$	57.0956	−	32.9642i	1.85634	−	1.07176i
$947$	17.7392	+	17.7392i	0.576446	+	0.576446i	0.933922	−	0.357476i	$-0.116363\pi$
$947$	17.7392	+	17.7392i	0.576446	+	0.576446i	−0.357476	+	0.933922i	$0.616363\pi$
$948$	1.30788	+	20.8816i	0.0424779	+	0.678203i
$949$	−39.0254	−	5.63170i	−1.26682	−	0.182813i
$950$	−11.4188	−	6.59266i	−0.370475	−	0.213894i
$951$	−6.27527	+	7.11387i	−0.203489	+	0.230683i
$952$	−0.399155	+	2.22241i	−0.0129367	+	0.0720289i
$953$	7.75491	−	13.4319i	0.251206	−	0.435102i	−0.712652	−	0.701518i	$-0.752506\pi$
$953$	7.75491	−	13.4319i	0.251206	−	0.435102i	0.963858	+	0.266416i	$0.0858394\pi$
$954$	−27.2647	−	21.1732i	−0.882728	−	0.685508i
$955$	12.0539	+	12.0539i	0.390056	+	0.390056i
$956$	−14.2838	−	14.2838i	−0.461972	−	0.461972i
$957$	−49.6518	−	10.0261i	−1.60502	−	0.324097i
$958$	−2.30496	+	3.99230i	−0.0744697	+	0.128985i
$959$	3.38470	−	18.8454i	0.109298	−	0.608548i
$960$	2.11290	+	1.86382i	0.0681935	+	0.0601547i
$961$	−1.43588	−	0.829003i	−0.0463186	−	0.0267420i
$962$	−2.34216	−	19.6758i	−0.0755142	−	0.634372i
$963$	33.5688	+	14.1332i	1.08174	+	0.455436i
$964$	16.7231	+	16.7231i	0.538614	+	0.538614i
$965$	4.30023	−	2.48274i	0.138429	−	0.0799222i
$966$	4.54404	+	10.4997i	0.146202	+	0.337822i
$967$	−36.0785	−	36.0785i	−1.16021	−	1.16021i	−0.984430	−	0.175775i	$-0.943757\pi$
$967$	−36.0785	−	36.0785i	−1.16021	−	1.16021i	−0.175775	−	0.984430i	$-0.556243\pi$
$968$	−14.2606	−	3.82111i	−0.458353	−	0.122815i
$969$	7.84819	−	2.63876i	0.252120	−	0.0847691i
$970$	24.2940	+	6.50956i	0.780033	+	0.209009i
$971$	−49.7321	+	28.7128i	−1.59598	+	0.921439i	−0.603727	+	0.797191i	$0.706318\pi$
$971$	−49.7321	+	28.7128i	−1.59598	+	0.921439i	−0.992251	+	0.124248i	$0.960348\pi$
$972$	−15.2433	−	3.26241i	−0.488928	−	0.104642i
$973$	−11.7561	+	0.990902i	−0.376882	+	0.0317669i
$974$	9.27311			0.297130
$975$	13.8462	+	4.93794i	0.443433	+	0.158140i
$976$	2.92693	+	5.06959i	0.0936888	+	0.162274i
$977$	−2.12769	−	7.94066i	−0.0680710	−	0.254044i	0.923502	−	0.383594i	$-0.125314\pi$
$977$	−2.12769	−	7.94066i	−0.0680710	−	0.254044i	−0.991573	+	0.129549i	$0.958647\pi$
$978$	15.7941	+	7.84579i	0.505040	+	0.250881i
$979$	31.2133	+	18.0210i	0.997583	+	0.575955i
$980$	1.06446	−	11.3368i	0.0340030	−	0.362142i
$981$	17.1641	+	13.3293i	0.548007	+	0.425571i
$982$	26.9832	+	7.23014i	0.861070	+	0.230723i
$983$	12.4153	−	46.3345i	0.395986	−	1.47784i	−0.424108	−	0.905611i	$-0.639412\pi$
$983$	12.4153	−	46.3345i	0.395986	−	1.47784i	0.820094	−	0.572228i	$-0.193921\pi$
$984$	−1.65469	+	3.33100i	−0.0527496	+	0.106188i
$985$			36.0401i			1.14833i
$986$	−1.27267	+	4.74967i	−0.0405301	+	0.151260i
$987$	−3.94264	+	34.0853i	−0.125496	+	1.08495i
$988$	−19.9890	−	2.88459i	−0.635935	−	0.0917709i
$989$	−28.0832	−	16.2138i	−0.892993	−	0.515570i
$990$	15.1926	−	19.5636i	0.482854	−	0.621771i
$991$	−1.43711	+	2.48916i	−0.0456515	+	0.0790707i	−0.887948	−	0.459943i	$-0.847870\pi$
$991$	−1.43711	+	2.48916i	−0.0456515	+	0.0790707i	0.842297	+	0.539014i	$0.181203\pi$
$992$	−2.85736	−	4.94909i	−0.0907212	−	0.157134i
$993$	−3.97858	+	1.33770i	−0.126257	+	0.0424506i
$994$	−3.35643	−	39.8207i	−0.106460	−	1.26303i
$995$	7.79049	−	2.08746i	0.246975	−	0.0661768i
$996$	−1.54383	+	7.64546i	−0.0489180	+	0.242256i
$997$	15.3740			0.486899			0.243449	−	0.969914i	$-0.421721\pi$
$997$	15.3740			0.486899			0.243449	+	0.969914i	$0.421721\pi$
$998$	−2.53067	+	4.38324i	−0.0801069	+	0.138749i
$999$	−16.0707	+	23.6046i	−0.508455	+	0.746816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.401.33	yes	152
3.2	odd	2	inner	546.2.ch.a.401.1	yes	152
7.4	even	3		546.2.bw.a.11.32	yes	152
13.6	odd	12		546.2.bw.a.149.13	yes	152
21.11	odd	6		546.2.bw.a.11.13	✓	152
39.32	even	12		546.2.bw.a.149.32	yes	152
91.32	odd	12	inner	546.2.ch.a.305.1	yes	152
273.32	even	12	inner	546.2.ch.a.305.33	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.13	✓	152	21.11	odd	6
546.2.bw.a.11.32	yes	152	7.4	even	3
546.2.bw.a.149.13	yes	152	13.6	odd	12
546.2.bw.a.149.32	yes	152	39.32	even	12
546.2.ch.a.305.1	yes	152	91.32	odd	12	inner
546.2.ch.a.305.33	yes	152	273.32	even	12	inner
546.2.ch.a.401.1	yes	152	3.2	odd	2	inner
546.2.ch.a.401.33	yes	152	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.958098 + 1.44293i) q^{3} -1.00000i q^{4} +(-0.421014 - 1.57124i) q^{5} +(1.69778 + 0.342829i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16410 + 2.76494i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.958098 + 1.44293i) q^{3} -1.00000i q^{4} +(-0.421014 - 1.57124i) q^{5} +(1.69778 + 0.342829i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16410 + 2.76494i) q^{9} +(-1.40874 - 0.813336i) q^{10} +(4.90284 - 1.31371i) q^{11} +(1.44293 - 0.958098i) q^{12} +(3.58027 - 0.426188i) q^{13} +(-2.60408 - 0.467704i) q^{14} +(1.86382 - 2.11290i) q^{15} -1.00000 q^{16} +0.853434 q^{17} +(1.13196 + 2.77825i) q^{18} +(1.44975 - 5.41052i) q^{19} +(-1.57124 + 0.421014i) q^{20} +(1.68682 - 4.26083i) q^{21} +(2.53789 - 4.39576i) q^{22} -2.49659 q^{23} +(0.342829 - 1.69778i) q^{24} +(2.03857 - 1.17697i) q^{25} +(2.23028 - 2.83300i) q^{26} +(-5.10493 + 0.969366i) q^{27} +(-2.17208 + 1.51065i) q^{28} +(-4.98976 + 2.88084i) q^{29} +(-0.176122 - 2.81197i) q^{30} +(-1.47908 + 5.51999i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.59299 + 5.81579i) q^{33} +(0.603469 - 0.603469i) q^{34} +(-2.77687 + 3.28807i) q^{35} +(2.76494 + 1.16410i) q^{36} +(3.88598 - 3.88598i) q^{37} +(-2.80069 - 4.85094i) q^{38} +(4.04521 + 4.75776i) q^{39} +(-0.813336 + 1.40874i) q^{40} +(-2.07420 - 0.555780i) q^{41} +(-1.82010 - 4.20562i) q^{42} +(11.2486 + 6.49440i) q^{43} +(-1.31371 - 4.90284i) q^{44} +(4.83449 + 0.665007i) q^{45} +(-1.76535 + 1.76535i) q^{46} +(-7.23248 + 1.93794i) q^{47} +(-0.958098 - 1.44293i) q^{48} +(-2.43588 + 6.56251i) q^{49} +(0.609244 - 2.27373i) q^{50} +(0.817673 + 1.23145i) q^{51} +(-0.426188 - 3.58027i) q^{52} +(-9.96523 + 5.75343i) q^{53} +(-2.92429 + 4.29518i) q^{54} +(-4.12832 - 7.15047i) q^{55} +(-0.467704 + 2.60408i) q^{56} +(9.19601 - 3.09193i) q^{57} +(-1.49123 + 5.56536i) q^{58} +(0.583751 + 0.583751i) q^{59} +(-2.11290 - 1.86382i) q^{60} +(-2.92693 - 5.06959i) q^{61} +(2.85736 + 4.94909i) q^{62} +(7.76421 - 1.64833i) q^{63} +1.00000i q^{64} +(-2.17699 - 5.44606i) q^{65} +(8.77433 - 0.549563i) q^{66} +(11.8441 - 3.17363i) q^{67} -0.853434i q^{68} +(-2.39197 - 3.60240i) q^{69} +(0.361477 + 4.28856i) q^{70} +(3.90925 + 14.5895i) q^{71} +(2.77825 - 1.13196i) q^{72} +(-10.5632 - 2.83040i) q^{73} -5.49560i q^{74} +(3.65143 + 1.81386i) q^{75} +(-5.41052 - 1.44975i) q^{76} +(-10.2600 - 8.66481i) q^{77} +(6.22464 + 0.503847i) q^{78} +(-6.03981 + 10.4613i) q^{79} +(0.421014 + 1.57124i) q^{80} +(-6.28975 - 6.43732i) q^{81} +(-1.85968 + 1.07368i) q^{82} +(-3.18424 + 3.18424i) q^{83} +(-4.26083 - 1.68682i) q^{84} +(-0.359308 - 1.34095i) q^{85} +(12.5462 - 3.36175i) q^{86} +(-8.93753 - 4.43976i) q^{87} +(-4.39576 - 2.53789i) q^{88} +(5.02101 + 5.02101i) q^{89} +(3.88873 - 2.94827i) q^{90} +(-6.33425 - 7.13283i) q^{91} +2.49659i q^{92} +(-9.38207 + 3.15449i) q^{93} +(-3.74381 + 6.48447i) q^{94} -9.11162 q^{95} +(-1.69778 - 0.342829i) q^{96} +(-14.9348 + 4.00176i) q^{97} +(2.91796 + 6.36282i) q^{98} +(-2.07506 + 15.0853i) 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

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