LMFDB - Embedded newform 546.2.ch.a.401.1

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			401.1
Character	$\chi$	$=$	546.401
Dual form			546.2.ch.a.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.72866 - 0.108271i) q^{3} -1.00000i q^{4} +(0.421014 + 1.57124i) q^{5} +(1.29891 - 1.14579i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97655 + 0.374330i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.72866 - 0.108271i) q^{3} -1.00000i q^{4} +(0.421014 + 1.57124i) q^{5} +(1.29891 - 1.14579i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97655 + 0.374330i) q^{9} +(-1.40874 - 0.813336i) q^{10} +(-4.90284 + 1.31371i) q^{11} +(-0.108271 + 1.72866i) q^{12} +(3.58027 - 0.426188i) q^{13} +(2.60408 + 0.467704i) q^{14} +(-0.557670 - 2.76174i) q^{15} -1.00000 q^{16} -0.853434 q^{17} +(-2.36943 + 1.84005i) q^{18} +(1.44975 - 5.41052i) q^{19} +(1.57124 - 0.421014i) q^{20} +(2.37623 + 3.91836i) q^{21} +(2.53789 - 4.39576i) q^{22} +2.49659 q^{23} +(-1.14579 - 1.29891i) 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} +(2.34718 + 1.55851i) q^{30} +(-1.47908 + 5.51999i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.61759 - 1.74013i) q^{33} +(0.603469 - 0.603469i) q^{34} +(2.77687 - 3.28807i) q^{35} +(0.374330 - 2.97655i) q^{36} +(3.88598 - 3.88598i) q^{37} +(2.80069 + 4.85094i) q^{38} +(-6.23523 + 0.349094i) q^{39} +(-0.813336 + 1.40874i) q^{40} +(2.07420 + 0.555780i) q^{41} +(-4.45095 - 1.09045i) q^{42} +(11.2486 + 6.49440i) q^{43} +(1.31371 + 4.90284i) q^{44} +(0.665007 + 4.83449i) q^{45} +(-1.76535 + 1.76535i) q^{46} +(7.23248 - 1.93794i) q^{47} +(1.72866 + 0.108271i) q^{48} +(-2.43588 + 6.56251i) q^{49} +(-0.609244 + 2.27373i) q^{50} +(1.47530 + 0.0924026i) q^{51} +(-0.426188 - 3.58027i) q^{52} +(9.96523 - 5.75343i) q^{53} +(4.29518 - 2.92429i) q^{54} +(-4.12832 - 7.15047i) q^{55} +(0.467704 - 2.60408i) q^{56} +(-3.09193 + 9.19601i) q^{57} +(-1.49123 + 5.56536i) q^{58} +(-0.583751 - 0.583751i) q^{59} +(-2.76174 + 0.557670i) q^{60} +(-2.92693 - 5.06959i) q^{61} +(-2.85736 - 4.94909i) q^{62} +(-3.68345 - 7.03080i) q^{63} +1.00000i q^{64} +(2.17699 + 5.44606i) q^{65} +(-4.86310 + 7.32401i) q^{66} +(11.8441 - 3.17363i) q^{67} +0.853434i q^{68} +(-4.31576 - 0.270309i) q^{69} +(0.361477 + 4.28856i) q^{70} +(-3.90925 - 14.5895i) q^{71} +(1.84005 + 2.36943i) 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} +(4.16213 - 4.65582i) q^{78} +(-6.03981 + 10.4613i) q^{79} +(-0.421014 - 1.57124i) q^{80} +(8.71975 + 2.22843i) q^{81} +(-1.85968 + 1.07368i) q^{82} +(3.18424 - 3.18424i) q^{83} +(3.91836 - 2.37623i) 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} +(3.15449 - 9.38207i) q^{93} +(-3.74381 + 6.48447i) q^{94} +9.11162 q^{95} +(-1.29891 + 1.14579i) q^{96} +(-14.9348 + 4.00176i) q^{97} +(-2.91796 - 6.36282i) q^{98} +(-15.0853 + 2.07506i) 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
$3$	−1.72866	−	0.108271i	−0.998044	−	0.0625105i
$3$	−1.72866	−	0.108271i	−0.998044	−	0.0625105i
$4$		−	1.00000i		−	0.500000i
$5$	0.421014	+	1.57124i	0.188283	+	0.702682i	0.993904	+	0.110250i	$0.0351653\pi$
$5$	0.421014	+	1.57124i	0.188283	+	0.702682i	−0.805621	+	0.592432i	$0.798168\pi$
$6$	1.29891	−	1.14579i	0.530277	−	0.467767i
$7$	−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
$9$	2.97655	+	0.374330i	0.992185	+	0.124777i
$10$	−1.40874	−	0.813336i	−0.445482	−	0.257199i
$11$	−4.90284	+	1.31371i	−1.47826	+	0.396099i	−0.905755	−	0.423802i	$-0.860695\pi$
$11$	−4.90284	+	1.31371i	−1.47826	+	0.396099i	−0.572506	+	0.819901i	$0.694029\pi$
$12$	−0.108271	+	1.72866i	−0.0312553	+	0.499022i
$13$	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
$15$	−0.557670	−	2.76174i	−0.143990	−	0.713077i
$16$	−1.00000			−0.250000
$17$	−0.853434			−0.206988			−0.103494	−	0.994630i	$-0.533002\pi$
$17$	−0.853434			−0.206988			−0.103494	+	0.994630i	$0.533002\pi$
$18$	−2.36943	+	1.84005i	−0.558481	+	0.433704i
$19$	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
$21$	2.37623	+	3.91836i	0.518536	+	0.855056i
$22$	2.53789	−	4.39576i	0.541081	−	0.937180i
$23$	2.49659			0.520575			0.260287	−	0.965531i	$-0.416183\pi$
$23$	2.49659			0.520575			0.260287	+	0.965531i	$0.416183\pi$
$24$	−1.14579	−	1.29891i	−0.233883	−	0.265139i
$25$	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	0.0408488	−	0.999165i	$-0.486994\pi$
$29$	4.98976	−	2.88084i	0.926576	−	0.534959i	0.885727	+	0.464207i	$0.153660\pi$
$30$	2.34718	+	1.55851i	0.428534	+	0.284544i
$31$	−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
$33$	8.61759	−	1.74013i	1.50013	−	0.302917i
$34$	0.603469	−	0.603469i	0.103494	−	0.103494i
$35$	2.77687	−	3.28807i	0.469376	−	0.555786i
$36$	0.374330	−	2.97655i	0.0623883	−	0.496092i
$37$	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
$39$	−6.23523	+	0.349094i	−0.998436	+	0.0558998i
$40$	−0.813336	+	1.40874i	−0.128600	+	0.222741i
$41$	2.07420	+	0.555780i	0.323935	+	0.0867982i	0.417122	−	0.908850i	$-0.363039\pi$
$41$	2.07420	+	0.555780i	0.323935	+	0.0867982i	−0.0931868	+	0.995649i	$0.529705\pi$
$42$	−4.45095	−	1.09045i	−0.686796	−	0.168260i
$43$	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
$45$	0.665007	+	4.83449i	0.0991334	+	0.720684i
$46$	−1.76535	+	1.76535i	−0.260287	+	0.260287i
$47$	7.23248	−	1.93794i	1.05497	−	0.282677i	0.310664	−	0.950520i	$-0.399449\pi$
$47$	7.23248	−	1.93794i	1.05497	−	0.282677i	0.744303	+	0.667843i	$0.232782\pi$
$48$	1.72866	+	0.108271i	0.249511	+	0.0156276i
$49$	−2.43588	+	6.56251i	−0.347983	+	0.937501i
$50$	−0.609244	+	2.27373i	−0.0861601	+	0.321554i
$51$	1.47530	+	0.0924026i	0.206583	+	0.0129389i
$52$	−0.426188	−	3.58027i	−0.0591016	−	0.496495i
$53$	9.96523	−	5.75343i	1.36883	−	0.790294i	0.378051	−	0.925785i	$-0.376594\pi$
$53$	9.96523	−	5.75343i	1.36883	−	0.790294i	0.990779	+	0.135490i	$0.0432609\pi$
$54$	4.29518	−	2.92429i	0.584500	−	0.397945i
$55$	−4.12832	−	7.15047i	−0.556663	−	0.964169i
$56$	0.467704	−	2.60408i	0.0624996	−	0.347985i
$57$	−3.09193	+	9.19601i	−0.409536	+	1.21804i
$58$	−1.49123	+	5.56536i	−0.195809	+	0.730767i
$59$	−0.583751	−	0.583751i	−0.0759979	−	0.0759979i	0.668086	−	0.744084i	$-0.267114\pi$
$59$	−0.583751	−	0.583751i	−0.0759979	−	0.0759979i	−0.744084	+	0.668086i	$0.767114\pi$
$60$	−2.76174	+	0.557670i	−0.356539	+	0.0719949i
$61$	−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
$63$	−3.68345	−	7.03080i	−0.464071	−	0.885798i
$64$			1.00000i			0.125000i
$65$	2.17699	+	5.44606i	0.270022	+	0.675500i
$66$	−4.86310	+	7.32401i	−0.598606	+	0.901524i
$67$	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
$69$	−4.31576	−	0.270309i	−0.519556	−	0.0325414i
$70$	0.361477	+	4.28856i	0.0432048	+	0.512581i
$71$	−3.90925	−	14.5895i	−0.463942	−	1.73146i	−0.660373	−	0.750938i	$-0.729602\pi$
$71$	−3.90925	−	14.5895i	−0.463942	−	1.73146i	0.196431	−	0.980518i	$-0.437065\pi$
$72$	1.84005	+	2.36943i	0.216852	+	0.279240i
$73$	−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
$78$	4.16213	−	4.65582i	0.471268	−	0.527168i
$79$	−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
$81$	8.71975	+	2.22843i	0.968862	+	0.247603i
$82$	−1.85968	+	1.07368i	−0.205367	+	0.118569i
$83$	3.18424	−	3.18424i	0.349516	−	0.349516i	−0.510413	−	0.859929i	$-0.670508\pi$
$83$	3.18424	−	3.18424i	0.349516	−	0.349516i	0.859929	+	0.510413i	$0.170508\pi$
$84$	3.91836	−	2.37623i	0.427528	−	0.259268i
$85$	−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	0.389008	−	0.921234i	$-0.372818\pi$
$89$	−5.02101	−	5.02101i	−0.532226	−	0.532226i	−0.921234	+	0.389008i	$0.872818\pi$
$90$	−3.88873	−	2.94827i	−0.409909	−	0.310775i
$91$	−6.33425	−	7.13283i	−0.664010	−	0.747724i
$92$		−	2.49659i		−	0.260287i
$93$	3.15449	−	9.38207i	0.327105	−	0.972875i
$94$	−3.74381	+	6.48447i	−0.386144	+	0.668822i
$95$	9.11162			0.934832
$96$	−1.29891	+	1.14579i	−0.132569	+	0.116942i
$97$	−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
$99$	−15.0853	+	2.07506i	−1.51613	+	0.208551i
$100$	−1.17697	−	2.03857i	−0.117697	−	0.203857i
$101$	−1.06029	+	1.83647i	−0.105502	+	0.182736i	−0.913943	−	0.405842i	$-0.866978\pi$
$101$	−1.06029	+	1.83647i	−0.105502	+	0.182736i	0.808441	+	0.588577i	$0.200312\pi$
$102$	−1.10853	+	0.977857i	−0.109761	+	0.0968222i
$103$	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
$105$	−5.15628	+	5.38332i	−0.503201	+	0.525358i
$106$	−2.97819	+	11.1148i	−0.289268	+	1.07956i
$107$			12.1409i			1.17370i	0.809694	+	0.586852i	$0.199633\pi$
$107$			12.1409i			1.17370i	−0.809694	+	0.586852i	$0.800367\pi$
$108$	−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
$111$	−7.13829	+	6.29681i	−0.677536	+	0.597667i
$112$	1.51065	+	2.17208i	0.142743	+	0.205242i
$113$	−9.65602	−	5.57491i	−0.908362	−	0.524443i	−0.0284582	−	0.999595i	$-0.509060\pi$
$113$	−9.65602	−	5.57491i	−0.908362	−	0.524443i	−0.879904	+	0.475152i	$0.842393\pi$
$114$	−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
$117$	10.8164	+	0.0716318i	0.999978	+	0.00662237i
$118$	0.825548			0.0759979
$119$	1.28924	+	1.85373i	0.118184	+	0.169931i
$120$	1.55851	−	2.34718i	0.142272	−	0.214267i
$121$	12.7857	−	7.38182i	1.16234	−	0.671075i
$122$	5.65440	+	1.51509i	0.511925	+	0.137170i
$123$	−3.52542	−	1.18533i	−0.317876	−	0.106878i
$124$	5.51999	+	1.47908i	0.495710	+	0.132825i
$125$	8.45873	+	8.45873i	0.756571	+	0.756571i
$126$	7.57612	+	2.36693i	0.674935	+	0.210863i
$127$	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
$129$	−18.7419	−	12.4445i	−1.65013	−	1.09568i
$130$	−5.39031	−	2.31158i	−0.472761	−	0.202739i
$131$	−6.60251	−	3.81196i	−0.576864	−	0.333053i	0.183022	−	0.983109i	$-0.441412\pi$
$131$	−6.60251	−	3.81196i	−0.576864	−	0.333053i	−0.759886	+	0.650056i	$0.774745\pi$
$132$	−1.74013	−	8.61759i	−0.151459	−	0.750065i
$133$	−13.9422	+	5.02443i	−1.20894	+	0.435674i
$134$	−6.13098	+	10.6192i	−0.529636	+	0.917356i
$135$	−0.626135	−	8.42921i	−0.0538892	−	0.725471i
$136$	−0.603469	−	0.603469i	−0.0517471	−	0.0517471i
$137$	−5.11722	−	5.11722i	−0.437194	−	0.437194i	0.453873	−	0.891067i	$-0.350042\pi$
$137$	−5.11722	−	5.11722i	−0.437194	−	0.437194i	−0.891067	+	0.453873i	$0.850042\pi$
$138$	3.24284	−	2.86057i	0.276049	−	0.243508i
$139$	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
$141$	−12.7124	+	2.56697i	−1.07057	+	0.216178i
$142$	13.0806	+	7.55208i	1.09770	+	0.633757i
$143$	−16.9936	+	6.79298i	−1.42108	+	0.568057i
$144$	−2.97655	−	0.374330i	−0.248046	−	0.0311941i
$145$	6.62726	+	6.62726i	0.550364	+	0.550364i
$146$	9.47070	−	5.46791i	0.783801	−	0.452527i
$147$	4.92135	−	11.0806i	0.405906	−	0.913915i
$148$	−3.88598	−	3.88598i	−0.319425	−	0.319425i
$149$	−11.8620	−	3.17841i	−0.971772	−	0.260386i	−0.262196	−	0.965015i	$-0.584447\pi$
$149$	−11.8620	−	3.17841i	−0.971772	−	0.260386i	−0.709576	+	0.704629i	$0.751113\pi$
$150$	1.29936	−	3.86455i	0.106092	−	0.315539i
$151$	−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
$153$	−2.54029	−	0.319466i	−0.205371	−	0.0258273i
$154$	−13.3818	+	1.12794i	−1.07834	+	0.0908917i
$155$	−9.29597			−0.746671
$156$	0.349094	+	6.23523i	0.0279499	+	0.499218i
$157$	−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
$162$	−7.74153	+	4.59006i	−0.608232	+	0.360629i
$163$	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	$-0.773984\pi$
$167$	2.89910	−	10.8196i	0.224339	−	0.837245i	0.982668	−	0.185373i	$-0.0593493\pi$
$168$	−1.09045	+	4.45095i	−0.0841301	+	0.343398i
$169$	12.6367	−	3.05174i	0.972056	−	0.234749i
$170$	1.20227	+	0.694129i	0.0922096	+	0.0532373i
$171$	6.34057	−	15.5620i	0.484875	−	1.19006i
$172$	6.49440	−	11.2486i	0.495193	−	0.857699i
$173$	5.97152	+	10.3430i	0.454007	+	0.786362i	0.998630	−	0.0523180i	$-0.0166609\pi$
$173$	5.97152	+	10.3430i	0.454007	+	0.786362i	−0.544624	+	0.838680i	$0.683328\pi$
$174$	3.18041	−	9.45917i	0.241106	−	0.717098i
$175$	−5.63604	−	2.64996i	−0.426044	−	0.200318i
$176$	4.90284	−	1.31371i	0.369565	−	0.0990247i
$177$	0.945905	+	1.07231i	0.0710986	+	0.0805999i
$178$	7.10078			0.532226
$179$	8.54897	−	14.8072i	0.638980	−	1.10675i	−0.346677	−	0.937985i	$-0.612690\pi$
$179$	8.54897	−	14.8072i	0.638980	−	1.10675i	0.985657	−	0.168761i	$-0.0539766\pi$
$180$	4.83449	−	0.665007i	0.360342	−	0.0495667i
$181$			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
$189$	5.60622	+	12.5527i	0.407792	+	0.913075i
$190$	−6.44289	+	6.44289i	−0.467416	+	0.467416i
$191$	9.07557	−	5.23979i	0.656685	−	0.379138i	−0.134327	−	0.990937i	$-0.542887\pi$
$191$	9.07557	−	5.23979i	0.656685	−	0.379138i	0.791013	+	0.611799i	$0.209554\pi$
$192$	0.108271	−	1.72866i	0.00781382	−	0.124756i
$193$	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
$195$	−3.17363	−	9.65010i	−0.227268	−	0.691058i
$196$	6.56251	+	2.43588i	0.468750	+	0.173992i
$197$	21.4008	+	5.73433i	1.52474	+	0.408554i	0.921301	−	0.388851i	$-0.127128\pi$
$197$	21.4008	+	5.73433i	1.52474	+	0.408554i	0.603444	+	0.797405i	$0.293795\pi$
$198$	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
$201$	−20.8181	+	4.20375i	−1.46840	+	0.296510i
$202$	−0.548845	−	2.04832i	−0.0386166	−	0.144119i
$203$	−13.7952	−	6.48624i	−0.968233	−	0.455245i
$204$	0.0924026	−	1.47530i	0.00646947	−	0.103292i
$205$			3.49306i			0.243966i
$206$	−2.71567	+	0.727662i	−0.189210	+	0.0506986i
$207$	7.43123	+	0.934547i	0.516506	+	0.0649555i
$208$	−3.58027	+	0.426188i	−0.248247	+	0.0295508i
$209$			28.4315i			1.96664i
$210$	−0.160544	−	7.45262i	−0.0110786	−	0.514280i
$211$	−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
$213$	5.17814	+	25.6436i	0.354801	+	1.75707i
$214$	−8.58491	−	8.58491i	−0.586852	−	0.586852i
$215$	−5.46846	+	20.4086i	−0.372946	+	1.39185i
$216$	−2.92429	−	4.29518i	−0.198973	−	0.292250i
$217$	14.2242	−	5.12609i	0.965605	−	0.347982i
$218$	3.62198	+	6.27346i	0.245312	+	0.424892i
$219$	17.9538	+	6.03650i	1.21320	+	0.407909i
$220$	−7.15047	+	4.12832i	−0.482084	+	0.278331i
$221$	−3.05553	+	0.363723i	−0.205537	+	0.0244667i
$222$	0.595017	−	9.50005i	0.0399349	−	0.637601i
$223$	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
$225$	6.50849	−	2.74022i	0.433899	−	0.182681i
$226$	10.7699	−	2.88578i	0.716403	−	0.191959i
$227$	−2.85759	+	2.85759i	−0.189665	+	0.189665i	−0.795551	−	0.605886i	$-0.792819\pi$
$227$	−2.85759	+	2.85759i	−0.189665	+	0.189665i	0.605886	+	0.795551i	$0.292819\pi$
$228$	9.19601	+	3.09193i	0.609020	+	0.204768i
$229$	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
$231$	−16.7979	−	16.0894i	−1.10522	−	1.05860i
$232$	5.56536	+	1.49123i	0.365384	+	0.0979043i
$233$	−6.28957	+	10.8939i	−0.412044	+	0.713681i	−0.995113	−	0.0987417i	$-0.968518\pi$
$233$	−6.28957	+	10.8939i	−0.412044	+	0.713681i	0.583069	+	0.812422i	$0.301852\pi$
$234$	−7.69901	+	7.59771i	−0.503300	+	0.496678i
$235$	6.08995	+	10.5481i	0.397264	+	0.688082i
$236$	−0.583751	+	0.583751i	−0.0379989	+	0.0379989i
$237$	11.5735	−	17.4301i	0.751777	−	1.13220i
$238$	−2.22241	−	0.399155i	−0.144058	−	0.0258734i
$239$	−14.2838	+	14.2838i	−0.923944	+	0.923944i	−0.997305	−	0.0733617i	$-0.976627\pi$
$239$	−14.2838	+	14.2838i	−0.923944	+	0.923944i	0.0733617	+	0.997305i	$0.476627\pi$
$240$	0.557670	+	2.76174i	0.0359975	+	0.178269i
$241$	−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
$243$	−14.8322	−	4.79630i	−0.951489	−	0.307683i
$244$	−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
$249$	−5.84925	+	5.15972i	−0.370681	+	0.326984i
$250$	−11.9624			−0.756571
$251$	−0.773364	+	1.33951i	−0.0488143	+	0.0845489i	−0.889400	−	0.457129i	$-0.848878\pi$
$251$	−0.773364	+	1.33951i	−0.0488143	+	0.0845489i	0.840586	+	0.541678i	$0.182211\pi$
$252$	−7.03080	+	3.68345i	−0.442899	+	0.232036i
$253$	−12.2404	+	3.27979i	−0.769545	+	0.206199i
$254$	−2.04743	+	7.64111i	−0.128467	+	0.479446i
$255$	0.475935	+	2.35696i	0.0298042	+	0.147599i
$256$	1.00000			0.0625000
$257$	6.88973			0.429770			0.214885	−	0.976639i	$-0.431062\pi$
$257$	6.88973			0.429770			0.214885	+	0.976639i	$0.431062\pi$
$258$	22.0522	−	4.45293i	1.37291	−	0.277227i
$259$	−14.3110	−	2.57032i	−0.889243	−	0.159712i
$260$	5.44606	−	2.17699i	0.337750	−	0.135011i
$261$	15.9307	−	6.70716i	0.986085	−	0.415163i
$262$	7.36415	−	1.97322i	0.454959	−	0.121906i
$263$	4.57214	+	2.63972i	0.281930	+	0.162772i	0.634297	−	0.773090i	$-0.281290\pi$
$263$	4.57214	+	2.63972i	0.281930	+	0.162772i	−0.352367	+	0.935862i	$0.614623\pi$
$264$	7.32401	+	4.86310i	0.450762	+	0.299303i
$265$	13.2355	+	13.2355i	0.813053	+	0.813053i
$266$	6.30578	−	13.4114i	0.386632	−	0.822306i
$267$	8.13600	+	9.22327i	0.497915	+	0.564455i
$268$	−3.17363	−	11.8441i	−0.193860	−	0.723496i
$269$		−	19.0496i		−	1.16147i	−0.814091	−	0.580737i	$-0.802764\pi$
$269$		−	19.0496i		−	1.16147i	0.814091	−	0.580737i	$-0.197236\pi$
$270$	6.40310	+	5.51761i	0.389680	+	0.335791i
$271$	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
$273$	10.1775	+	13.0161i	0.615971	+	0.787769i
$274$	7.23685			0.437194
$275$	−8.44858	+	8.44858i	−0.509468	+	0.509468i
$276$	−0.270309	+	4.31576i	−0.0162707	+	0.259778i
$277$		−	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
$279$	−6.46885	+	15.8769i	−0.387280	+	0.950525i
$280$	4.28856	−	0.361477i	0.256291	−	0.0216024i
$281$	18.3020	+	18.3020i	1.09180	+	1.09180i	0.995336	+	0.0964690i	$0.0307548\pi$
$281$	18.3020	+	18.3020i	1.09180	+	1.09180i	0.0964690	+	0.995336i	$0.469245\pi$
$282$	7.17387	−	10.8041i	0.427198	−	0.643376i
$283$	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
$285$	−15.7509	−	0.986528i	−0.933004	−	0.0584369i
$286$	7.21294	−	16.8197i	0.426510	−	0.994567i
$287$	−1.92619	−	5.34492i	−0.113699	−	0.315501i
$288$	2.36943	−	1.84005i	0.139620	−	0.108426i
$289$	−16.2716			−0.957156
$290$	−9.37237			−0.550364
$291$	26.2505	−	5.30069i	1.53883	−	0.310732i
$292$	−2.83040	+	10.5632i	−0.165637	+	0.618164i
$293$	−12.2954	+	3.29454i	−0.718304	+	0.192469i	−0.599415	−	0.800439i	$-0.704600\pi$
$293$	−12.2954	+	3.29454i	−0.718304	+	0.192469i	−0.118889	+	0.992908i	$0.537933\pi$
$294$	4.35526	+	11.3151i	0.254004	+	0.659910i
$295$	0.671448	−	1.16298i	0.0390932	−	0.0677114i
$296$	5.49560			0.319425
$297$	26.3021	−	1.95376i	1.52620	−	0.113369i
$298$	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
$303$	2.03172	−	3.05984i	0.116719	−	0.175783i
$304$	−1.44975	+	5.41052i	−0.0831486	+	0.310315i
$305$	6.73329	−	6.73329i	0.385547	−	0.385547i
$306$	2.02216	−	1.57036i	0.115599	−	0.0897717i
$307$	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
$309$	−4.05676	−	2.69366i	−0.230781	−	0.153237i
$310$	6.57325	−	6.57325i	0.373335	−	0.373335i
$311$	6.66105	+	11.5373i	0.377714	+	0.654219i	0.990729	−	0.135852i	$-0.0433770\pi$
$311$	6.66105	+	11.5373i	0.377714	+	0.654219i	−0.613016	+	0.790071i	$0.710044\pi$
$312$	−4.65582	−	4.16213i	−0.263584	−	0.235634i
$313$	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
$315$	9.49633	−	8.74767i	0.535057	−	0.492875i
$316$	10.4613	+	6.03981i	0.588492	+	0.339766i
$317$	−1.41750	−	5.29018i	−0.0796148	−	0.297126i	0.914625	−	0.404303i	$-0.132486\pi$
$317$	−1.41750	−	5.29018i	−0.0796148	−	0.297126i	−0.994240	+	0.107176i	$0.965819\pi$
$318$	6.35171	−	18.8912i	0.356186	−	1.05937i
$319$	−20.6794	+	20.6794i	−1.15782	+	1.15782i
$320$	−1.57124	+	0.421014i	−0.0878352	+	0.0235354i
$321$	1.31451	−	20.9875i	0.0733689	−	1.17141i
$322$	6.50132	+	1.16766i	0.362305	+	0.0650714i
$323$	−1.23726	+	4.61753i	−0.0688431	+	0.256926i
$324$	2.22843	−	8.71975i	0.123801	−	0.484431i
$325$	6.79703	−	5.08269i	0.377031	−	0.281937i
$326$	−8.81774	+	5.09093i	−0.488370	+	0.281960i
$327$	−3.99862	+	11.8927i	−0.221124	+	0.657667i
$328$	1.07368	+	1.85968i	0.0592843	+	0.102683i
$329$	−15.1351	−	12.7820i	−0.834425	−	0.704695i
$330$	−13.5552	−	4.55761i	−0.746192	−	0.250888i
$331$	−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
$333$	13.0215	−	10.1122i	0.713572	−	0.554145i
$334$	5.60063	+	9.70058i	0.306453	+	0.530792i
$335$	9.97309	+	17.2739i	0.544888	+	0.943774i
$336$	−2.37623	−	3.91836i	−0.129634	−	0.213764i
$337$		−	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
$339$	16.0884	+	10.6826i	0.873802	+	0.580200i
$340$	−1.34095	+	0.359308i	−0.0727234	+	0.0194862i
$341$		−	29.0067i		−	1.57080i
$342$	6.52056	+	15.4875i	0.352592	+	0.837467i
$343$	17.9341	−	4.62270i	0.968348	−	0.249602i
$344$	3.36175	+	12.5462i	0.181253	+	0.676446i
$345$	−1.39227	−	6.89492i	−0.0749574	−	0.371210i
$346$	−11.5361	−	3.09109i	−0.620184	−	0.166178i
$347$		−	22.8686i		−	1.22765i	−0.789443	−	0.613824i	$-0.789630\pi$
$347$		−	22.8686i		−	1.22765i	0.789443	−	0.613824i	$-0.210370\pi$
$348$	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
$351$	−18.6902	−	1.29494i	−0.997608	−	0.0691186i
$352$	−2.53789	+	4.39576i	−0.135270	+	0.234295i
$353$	2.42180	+	9.03830i	0.128900	+	0.481060i	0.999949	−	0.0101361i	$-0.00322649\pi$
$353$	2.42180	+	9.03830i	0.128900	+	0.481060i	−0.871049	+	0.491196i	$0.836560\pi$
$354$	−1.42710	−	0.0893833i	−0.0758492	−	0.00475067i
$355$	21.2778	−	12.2848i	1.12931	−	0.652007i
$356$	−5.02101	+	5.02101i	−0.266113	+	0.266113i
$357$	−2.02795	−	3.34406i	−0.107331	−	0.176987i
$358$	4.42527	+	16.5153i	0.233883	+	0.872863i
$359$	−35.6238	+	9.54536i	−1.88015	+	0.503785i	−0.880599	+	0.473863i	$0.842859\pi$
$359$	−35.6238	+	9.54536i	−1.88015	+	0.503785i	−0.999552	+	0.0299221i	$0.990474\pi$
$360$	−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
$366$	−9.61051	−	3.23129i	−0.502349	−	0.168902i
$367$	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
$369$	5.96592	+	2.43074i	0.310573	+	0.126539i
$370$	−8.63494	+	2.31372i	−0.448909	+	0.120285i
$371$	−27.5509	−	12.9539i	−1.43037	−	0.672533i
$372$	−9.38207	−	3.15449i	−0.486438	−	0.163552i
$373$	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
$375$	−13.7065	−	15.5381i	−0.707798	−	0.802386i
$376$	6.48447	+	3.74381i	0.334411	+	0.193072i
$377$	16.6369	−	12.4408i	0.856846	−	0.640733i
$378$	−12.8403	−	4.91191i	−0.660433	−	0.252641i
$379$	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	−0.327969	−	0.944688i	$-0.606364\pi$
$383$	−21.2210	−	5.68615i	−1.08434	−	0.290549i	−0.756374	+	0.654140i	$0.773031\pi$
$384$	1.14579	+	1.29891i	0.0584709	+	0.0662847i
$385$	−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	0.892451	−	0.451145i	$-0.148984\pi$
$389$	1.09507	+	1.89671i	0.0555220	+	0.0961669i	−0.836929	+	0.547312i	$0.815651\pi$
$390$	9.06775	+	4.57956i	0.459163	+	0.231895i
$391$	−2.13067			−0.107753
$392$	−6.36282	+	2.91796i	−0.321371	+	0.147379i
$393$	11.0008	+	7.30446i	0.554917	+	0.368461i
$394$	−19.1874	+	11.0779i	−0.966649	+	0.558095i
$395$	−18.9800	−	5.08569i	−0.954989	−	0.255889i
$396$	2.07506	+	15.0853i	0.104275	+	0.758066i
$397$	−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
$399$	24.6453	−	7.17602i	1.23381	−	0.359250i
$400$	−2.03857	+	1.17697i	−0.101929	+	0.0588484i
$401$	17.3470	+	17.3470i	0.866269	+	0.866269i	0.992057	−	0.125788i	$-0.0401459\pi$
$401$	17.3470	+	17.3470i	0.866269	+	0.866269i	−0.125788	+	0.992057i	$0.540146\pi$
$402$	11.7481	−	17.6932i	0.585944	−	0.882454i
$403$	−2.94295	+	20.3935i	−0.146599	+	1.01587i
$404$	1.83647	+	1.06029i	0.0913678	+	0.0527512i
$405$	0.169735	+	14.6391i	0.00843418	+	0.727421i
$406$	14.3411	−	5.16822i	0.711739	−	0.256494i
$407$	−13.9473	+	24.1574i	−0.691340	+	1.19744i
$408$	0.977857	+	1.10853i	0.0484111	+	0.0548806i
$409$	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
$411$	8.29191	+	9.40001i	0.409010	+	0.463668i
$412$	1.40573	−	2.43480i	0.0692556	−	0.119954i
$413$	−0.386112	+	2.14980i	−0.0189994	+	0.105785i
$414$	−5.91550	+	4.59385i	−0.290731	+	0.225775i
$415$	6.34383	+	3.66261i	0.311407	+	0.179791i
$416$	2.23028	−	2.83300i	0.109348	−	0.138899i
$417$	−4.27228	+	6.43421i	−0.209214	+	0.315085i
$418$	−20.1041	−	20.1041i	−0.983322	−	0.983322i
$419$	17.5508	−	10.1330i	0.857413	−	0.495028i	−0.00573204	−	0.999984i	$-0.501825\pi$
$419$	17.5508	−	10.1330i	0.857413	−	0.495028i	0.863145	+	0.504956i	$0.168491\pi$
$420$	5.38332	+	5.15628i	0.262679	+	0.251600i
$421$	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
$423$	22.2533	−	3.06104i	1.08199	−	0.148833i
$424$	11.1148	+	2.97819i	0.539781	+	0.144634i
$425$	−1.73979	+	1.00447i	−0.0843920	+	0.0487237i
$426$	−21.7943	−	14.4713i	−1.05594	−	0.701135i
$427$	−6.59001	+	14.0159i	−0.318913	+	0.678277i
$428$	12.1409			0.586852
$429$	30.1117	−	9.90285i	1.45381	−	0.478114i
$430$	−10.5643	−	18.2978i	−0.509453	−	0.882399i
$431$	−1.47412	−	5.50147i	−0.0710056	−	0.264997i	0.921292	−	0.388871i	$-0.127135\pi$
$431$	−1.47412	−	5.50147i	−0.0710056	−	0.264997i	−0.992298	+	0.123874i	$0.960468\pi$
$432$	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
$435$	−10.7388	−	12.1739i	−0.514884	−	0.583692i
$436$	−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
$441$	−9.70708	+	18.6218i	−0.462242	+	0.886754i
$442$	1.90339	−	2.41778i	0.0905352	−	0.115002i
$443$	16.1647	+	9.33267i	0.768007	+	0.443409i	0.832163	−	0.554531i	$-0.187102\pi$
$443$	16.1647	+	9.33267i	0.768007	+	0.443409i	−0.0641565	+	0.997940i	$0.520436\pi$
$444$	6.29681	+	7.13829i	0.298833	+	0.338768i
$445$	5.77532	−	10.0031i	0.273776	−	0.474195i
$446$	5.26656	+	9.12194i	0.249379	+	0.431936i
$447$	20.1613	+	6.77872i	0.953595	+	0.320622i
$448$	2.17208	−	1.51065i	0.102621	−	0.0713714i
$449$	13.6899	−	3.66820i	0.646066	−	0.173113i	0.0791167	−	0.996865i	$-0.474790\pi$
$449$	13.6899	−	3.66820i	0.646066	−	0.173113i	0.566950	+	0.823752i	$0.308123\pi$
$450$	−2.66457	+	6.53982i	−0.125609	+	0.308290i
$451$	−10.8996			−0.513242
$452$	−5.57491	+	9.65602i	−0.262222	+	0.454181i
$453$	0.0929602	+	0.0312555i	0.00436765	+	0.00146851i
$454$		−	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	$0.0181095\pi$
$461$	3.48234	+	12.9963i	0.162189	+	0.605297i	−0.836193	+	0.548435i	$0.815224\pi$
$462$	23.2548	−	0.500953i	1.08191	−	0.0233064i
$463$	−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
$465$	16.0696	+	1.00649i	0.745210	+	0.0466748i
$466$	−3.25572	−	12.1505i	−0.150818	−	0.562862i
$467$	−5.68598	+	9.84841i	−0.263116	+	0.455730i	−0.967068	−	0.254517i	$-0.918083\pi$
$467$	−5.68598	+	9.84841i	−0.263116	+	0.455730i	0.703952	+	0.710247i	$0.251417\pi$
$468$	0.0716318	−	10.8164i	0.00331118	−	0.499989i
$469$	−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
$474$	4.14124	+	20.5086i	0.190214	+	0.941990i
$475$	−3.41261	−	12.7360i	−0.156581	−	0.584369i
$476$	1.85373	−	1.28924i	0.0849656	−	0.0590922i
$477$	31.8157	−	13.3951i	1.45674	−	0.613320i
$478$		−	20.2004i		−	0.923944i
$479$	4.45283	−	1.19313i	0.203455	−	0.0545156i	−0.155652	−	0.987812i	$-0.549748\pi$
$479$	4.45283	−	1.19313i	0.203455	−	0.0545156i	0.359107	+	0.933296i	$0.383081\pi$
$480$	−2.34718	−	1.55851i	−0.107133	−	0.0711359i
$481$	12.2567	−	15.5690i	0.558858	−	0.709886i
$482$		−	23.6500i		−	1.07723i
$483$	5.93246	+	9.78253i	0.269936	+	0.445120i
$484$	−7.38182	−	12.7857i	−0.335537	−	0.581168i
$485$	−12.5755	−	21.7814i	−0.571024	−	0.989042i
$486$	13.8795	−	7.09649i	0.629586	−	0.321903i
$487$	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
$489$	−16.7159	−	5.62031i	−0.755921	−	0.254159i
$490$	8.76905	−	7.26367i	0.396145	−	0.328139i
$491$	−13.9676	−	24.1925i	−0.630347	−	1.09179i	−0.987481	−	0.157739i	$-0.949579\pi$
$491$	−13.9676	−	24.1925i	−0.630347	−	1.09179i	0.357134	−	0.934053i	$-0.383754\pi$
$492$	−1.18533	+	3.52542i	−0.0534389	+	0.158938i
$493$	−4.25844	+	2.45861i	−0.191790	+	0.110730i
$494$	12.0947	+	16.1741i	0.544164	+	0.727706i
$495$	−9.61155	−	22.8291i	−0.432007	−	1.02609i
$496$	1.47908	−	5.51999i	0.0664126	−	0.247855i
$497$	−25.7841	+	30.5308i	−1.15658	+	1.36949i
$498$	0.487568	−	7.78452i	0.0218484	−	0.348833i
$499$	−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
$501$	−6.18302	+	18.3895i	−0.276237	+	0.821584i
$502$	−0.400323	−	1.49403i	−0.0178673	−	0.0666816i
$503$	19.2261	+	11.1002i	0.857248	+	0.494932i	0.863090	−	0.505051i	$-0.168526\pi$
$503$	19.2261	+	11.1002i	0.857248	+	0.494932i	−0.00584193	+	0.999983i	$0.501860\pi$
$504$	2.36693	−	7.57612i	0.105432	−	0.337467i
$505$	−3.33194	−	0.892791i	−0.148269	−	0.0397287i
$506$	6.33608	−	10.9744i	0.281673	−	0.487872i
$507$	−22.1751	+	3.90723i	−0.984829	+	0.173526i
$508$	−3.95533	−	6.85083i	−0.175489	−	0.303957i
$509$	−18.3639	+	18.3639i	−0.813966	+	0.813966i	−0.985226	−	0.171260i	$-0.945216\pi$
$509$	−18.3639	+	18.3639i	−0.813966	+	0.813966i	0.171260	+	0.985226i	$0.445216\pi$
$510$	−2.00316	−	1.33009i	−0.0887014	−	0.0588972i
$511$	9.80941	+	27.2199i	0.433943	+	1.20414i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−12.6456	+	26.2150i	−0.558318	+	1.15742i
$514$	−4.87178	+	4.87178i	−0.214885	+	0.214885i
$515$	−1.18367	+	4.41751i	−0.0521586	+	0.194659i
$516$	−12.4445	+	18.7419i	−0.547840	+	0.825067i
$517$	−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	0.145923	−	0.989296i	$-0.453385\pi$
$521$	24.5520	−	14.1751i	1.07564	−	0.621021i	0.929717	+	0.368275i	$0.120051\pi$
$522$	−6.52202	+	16.0074i	−0.285461	+	0.700624i
$523$	−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
$525$	9.45590	+	5.19110i	0.412689	+	0.226558i
$526$	−5.09956	+	1.36642i	−0.222351	+	0.0595788i
$527$	1.26230	−	4.71095i	0.0549865	−	0.205212i
$528$	−8.61759	+	1.74013i	−0.375033	+	0.0757293i
$529$	−16.7671			−0.729002
$530$	−18.7179			−0.813053
$531$	−1.51905	−	1.95608i	−0.0659212	−	0.0848867i
$532$	5.02443	+	13.9422i	0.217837	+	0.604469i
$533$	7.66307	+	1.10585i	0.331924	+	0.0478995i
$534$	−12.2749	−	0.768811i	−0.531185	−	0.0332697i
$535$	−19.0763	+	5.11148i	−0.824741	+	0.220989i
$536$	10.6192	+	6.13098i	0.458678	+	0.264818i
$537$	−16.3815	+	24.6711i	−0.706913	+	1.06464i
$538$	13.4701	+	13.4701i	0.580737	+	0.580737i
$539$	3.32150	−	35.3749i	0.143067	−	1.52371i
$540$	−8.42921	+	0.626135i	−0.362736	+	0.0269446i
$541$	−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
$543$	1.12337	−	17.9357i	0.0482083	−	0.769695i
$544$	−0.603469	+	0.603469i	−0.0258735	+	0.0258735i
$545$	11.7836			0.504752
$546$	−16.4003	−	2.00718i	−0.701870	−	0.0858992i
$547$	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
$549$	−6.81447	−	16.1856i	−0.290835	−	0.690783i
$550$		−	11.9481i		−	0.509468i
$551$	−8.35297	−	31.1737i	−0.355849	−	1.32804i
$552$	−2.86057	−	3.24284i	−0.121754	−	0.138024i
$553$	31.8467	−	2.68432i	1.35426	−	0.114149i
$554$	0.993649	+	0.993649i	0.0422161	+	0.0422161i
$555$	−12.8991	−	8.56496i	−0.547538	−	0.363562i
$556$	−3.86172	−	2.22956i	−0.163773	−	0.0945546i
$557$	1.53348	−	0.410894i	0.0649756	−	0.0174102i	−0.226185	−	0.974084i	$-0.572625\pi$
$557$	1.53348	−	0.410894i	0.0649756	−	0.0174102i	0.291160	+	0.956674i	$0.405959\pi$
$558$	−6.65249	−	15.8008i	−0.281623	−	0.668903i
$559$	43.0410	+	18.4577i	1.82044	+	0.780677i
$560$	−2.77687	+	3.28807i	−0.117344	+	0.138947i
$561$	−7.35455	+	1.48508i	−0.310509	+	0.0627003i
$562$	−25.8829			−1.09180
$563$	−9.72303			−0.409777			−0.204889	−	0.978785i	$-0.565683\pi$
$563$	−9.72303			−0.409777			−0.204889	+	0.978785i	$0.565683\pi$
$564$	2.56697	+	12.7124i	0.108089	+	0.535287i
$565$	4.69422	−	17.5191i	0.197487	−	0.737033i
$566$	−23.2096	+	6.21900i	−0.975573	+	0.261404i
$567$	−8.33216	−	22.3064i	−0.349918	−	0.936780i
$568$	7.55208	−	13.0806i	0.316878	−	0.548849i
$569$	−22.2382			−0.932275			−0.466138	−	0.884712i	$-0.654355\pi$
$569$	−22.2382			−0.932275			−0.466138	+	0.884712i	$0.654355\pi$
$570$	11.8352	−	10.4400i	0.495720	−	0.437284i
$571$	−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
$576$	−0.374330	+	2.97655i	−0.0155971	+	0.124023i
$577$	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
$579$	−1.04650	−	5.18255i	−0.0434910	−	0.215379i
$580$	6.62726	−	6.62726i	0.275182	−	0.275182i
$581$	−11.7267	−	2.10617i	−0.486506	−	0.0873785i
$582$	−14.8137	+	22.3101i	−0.614049	+	0.924781i
$583$	−41.2996	+	41.2996i	−1.71045	+	1.71045i
$584$	−5.46791	−	9.47070i	−0.226264	−	0.391900i
$585$	4.44131	+	17.0254i	0.183626	+	0.703913i
$586$	6.36456	−	11.0237i	0.262918	−	0.455387i
$587$	26.7015	+	7.15465i	1.10209	+	0.295304i	0.763615	−	0.645672i	$-0.223422\pi$
$587$	26.7015	+	7.15465i	1.10209	+	0.295304i	0.338474	+	0.940976i	$0.390089\pi$
$588$	−11.0806	−	4.92135i	−0.456957	−	0.202953i
$589$	27.7218	+	16.0052i	1.14226	+	0.659482i
$590$	0.347567	+	1.29714i	0.0143091	+	0.0534023i
$591$	−36.3739	−	12.2298i	−1.49622	−	0.503068i
$592$	−3.88598	+	3.88598i	−0.159713	+	0.159713i
$593$	23.9716	−	6.42316i	0.984394	−	0.263768i	0.269500	−	0.963000i	$-0.413142\pi$
$593$	23.9716	−	6.42316i	0.984394	−	0.263768i	0.714894	+	0.699233i	$0.246475\pi$
$594$	−17.2169	+	19.9799i	−0.706417	+	0.819786i
$595$	−2.36988	+	2.80616i	−0.0971554	+	0.115041i
$596$	−3.17841	+	11.8620i	−0.130193	+	0.485886i
$597$	0.536828	−	8.57100i	0.0219709	−	0.350788i
$598$	−5.56808	+	7.07282i	−0.227696	+	0.289229i
$599$	13.1943	−	7.61771i	0.539103	−	0.311251i	−0.205612	−	0.978634i	$-0.565919\pi$
$599$	13.1943	−	7.61771i	0.539103	−	0.311251i	0.744715	+	0.667382i	$0.232585\pi$
$600$	−3.86455	−	1.29936i	−0.157770	−	0.0530461i
$601$	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
$603$	36.4427	−	5.01286i	1.48406	−	0.204140i
$604$	−0.0146551	+	0.0546937i	−0.000596308	+	0.00222545i
$605$	16.9816	+	16.9816i	0.690400	+	0.690400i
$606$	0.726994	+	3.60027i	0.0295321	+	0.146251i
$607$	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
$609$	23.1450	+	12.7061i	0.937882	+	0.514879i
$610$			9.52232i			0.385547i
$611$	25.0683	−	10.0207i	1.01416	−	0.405396i
$612$	−0.319466	+	2.54029i	−0.0129136	+	0.102685i
$613$	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
$615$	0.378199	−	6.03833i	0.0152505	−	0.243489i
$616$	1.12794	+	13.3818i	0.0454459	+	0.539169i
$617$	−0.366038	−	1.36607i	−0.0147361	−	0.0549960i	0.958166	−	0.286212i	$-0.0923962\pi$
$617$	−0.366038	−	1.36607i	−0.0147361	−	0.0549960i	−0.972902	+	0.231216i	$0.925730\pi$
$618$	4.77327	−	0.963853i	0.192009	−	0.0387718i
$619$	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
$624$	6.23523	−	0.349094i	0.249609	−	0.0139749i
$625$	−3.84464	+	6.65912i	−0.153786	+	0.266365i
$626$	6.71445	+	25.0587i	0.268364	+	1.00155i
$627$	3.07831	−	49.1484i	0.122936	−	1.96280i
$628$	−3.52061	+	2.03262i	−0.140487	+	0.0811105i
$629$	−3.31643	+	3.31643i	−0.132235	+	0.132235i
$630$	−0.529380	+	12.9005i	−0.0210910	+	0.513966i
$631$	−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
$639$	−6.17480	−	44.8898i	−0.244271	−	1.77581i
$640$	0.813336	−	1.40874i	0.0321499	−	0.0556853i
$641$	38.6190			1.52536			0.762680	−	0.646776i	$-0.223883\pi$
$641$	38.6190			1.52536			0.762680	+	0.646776i	$0.223883\pi$
$642$	13.9109	+	15.7699i	0.549020	+	0.622389i
$643$	−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
$645$	11.6628	−	34.6875i	0.459222	−	1.36582i
$646$	−2.39021	−	4.13996i	−0.0940414	−	0.162885i
$647$	−22.8744	+	39.6196i	−0.899285	+	1.55761i	−0.0708753	+	0.997485i	$0.522579\pi$
$647$	−22.8744	+	39.6196i	−0.899285	+	1.55761i	−0.828410	+	0.560122i	$0.810754\pi$
$648$	4.59006	+	7.74153i	0.180315	+	0.304116i
$649$	3.62891	+	2.09515i	0.142447	+	0.0822420i
$650$	−1.21222	+	8.40023i	−0.0475474	+	0.329484i
$651$	−25.1439	+	7.32121i	−0.985469	+	0.286941i
$652$	2.63526	−	9.83491i	0.103205	−	0.385165i
$653$		−	14.7980i		−	0.579090i	−0.957164	−	0.289545i	$-0.906496\pi$
$653$		−	14.7980i		−	0.579090i	0.957164	−	0.289545i	$-0.0935040\pi$
$654$	−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
$657$	−30.3824	−	12.3790i	−1.18533	−	0.482949i
$658$	19.7404	−	1.66389i	0.769560	−	0.0648652i
$659$	32.1017	+	18.5340i	1.25051	+	0.721980i	0.971210	−	0.238225i	$-0.0765655\pi$
$659$	32.1017	+	18.5340i	1.25051	+	0.721980i	0.279296	+	0.960205i	$0.409899\pi$
$660$	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
$663$	5.32136	−	0.297929i	0.206665	−	0.0115706i
$664$	4.50320			0.174758
$665$	−13.7645	−	19.7912i	−0.533763	−	0.767469i
$666$	−2.05717	+	16.3580i	−0.0797136	+	0.633858i
$667$	12.4574	−	7.19227i	0.482352	−	0.278486i
$668$	−10.8196	−	2.89910i	−0.418622	−	0.112170i
$669$	−5.81421	+	17.2926i	−0.224790	+	0.668571i
$670$	−19.2665	−	5.16245i	−0.744331	−	0.199443i
$671$	21.0102	+	21.0102i	0.811092	+	0.811092i
$672$	4.45095	+	1.09045i	0.171699	+	0.0420651i
$673$	−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
$675$	−11.5477	+	4.03223i	−0.444470	+	0.155200i
$676$	−3.05174	−	12.6367i	−0.117375	−	0.486028i
$677$	−6.02868	−	3.48066i	−0.231701	−	0.133773i	0.379655	−	0.925128i	$-0.376043\pi$
$677$	−6.02868	−	3.48066i	−0.231701	−	0.133773i	−0.611357	+	0.791355i	$0.709376\pi$
$678$	−18.9300	+	3.82248i	−0.727001	+	0.146801i
$679$	31.2534	+	26.3943i	1.19939	+	1.01292i
$680$	0.694129	−	1.20227i	0.0266186	−	0.0461048i
$681$	5.24920	−	4.63041i	0.201150	−	0.177438i
$682$	20.5108	+	20.5108i	0.785401	+	0.785401i
$683$	23.6186	+	23.6186i	0.903741	+	0.903741i	0.995757	−	0.0920164i	$-0.0293312\pi$
$683$	23.6186	+	23.6186i	0.903741	+	0.903741i	−0.0920164	+	0.995757i	$0.529331\pi$
$684$	−15.5620	−	6.34057i	−0.595029	−	0.242438i
$685$	5.88599	−	10.1948i	0.224892	−	0.389524i
$686$	−9.41255	+	15.9500i	−0.359373	+	0.608975i
$687$	−2.09973	−	10.3985i	−0.0801098	−	0.396726i
$688$	−11.2486	−	6.49440i	−0.428850	−	0.247597i
$689$	33.2262	−	24.8459i	1.26582	−	0.946554i
$690$	5.85993	+	3.89096i	0.223084	+	0.148126i
$691$	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
$693$	27.2958	+	29.6319i	1.03688	+	1.12562i
$694$	16.1705	+	16.1705i	0.613824	+	0.613824i
$695$	7.00638	+	1.87735i	0.265767	+	0.0712121i
$696$	−9.45917	−	3.18041i	−0.358549	−	0.120553i
$697$	−1.77019	−	0.474322i	−0.0670508	−	0.0179662i
$698$	13.0223	−	7.51845i	0.492902	−	0.284577i
$699$	12.0521	−	18.1508i	0.455850	−	0.686528i
$700$	−2.64996	+	5.63604i	−0.100159	+	0.213022i
$701$	−33.5732			−1.26804			−0.634021	−	0.773315i	$-0.718597\pi$
$701$	−33.5732			−1.26804			−0.634021	+	0.773315i	$0.718597\pi$
$702$	14.1316	−	12.3003i	0.533364	−	0.464245i
$703$	−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
$708$	1.07231	−	0.945905i	0.0403000	−	0.0355493i
$709$	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
$714$	3.79859	+	0.930628i	0.142159	+	0.0348279i
$715$	−17.8280	−	23.8412i	−0.666728	−	0.891610i
$716$	−14.8072	−	8.54897i	−0.553373	−	0.319490i
$717$	26.2385	−	23.1454i	0.979893	−	0.864381i
$718$	18.4402	−	31.9394i	0.688183	−	1.19197i
$719$	−24.5283	−	42.4842i	−0.914750	−	1.58439i	−0.807267	−	0.590186i	$-0.799054\pi$
$719$	−24.5283	−	42.4842i	−0.914750	−	1.58439i	−0.107482	−	0.994207i	$-0.534279\pi$
$720$	−0.665007	−	4.83449i	−0.0247833	−	0.180171i
$721$	−0.624762	−	7.41217i	−0.0232673	−	0.276043i
$722$	11.9538	−	3.20302i	0.444876	−	0.119204i
$723$	30.7192	−	27.0979i	1.14246	−	1.00778i
$724$	10.3755			0.385602
$725$	6.78132	−	11.7456i	0.251852	−	0.436220i
$726$	8.14943	−	24.2380i	0.302454	−	0.899558i
$727$		−	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
$735$	19.4823	+	3.06755i	0.718617	+	0.113148i
$736$	1.76535	−	1.76535i	0.0650718	−	0.0650718i
$737$	−53.9006	+	31.1196i	−1.98546	+	1.14630i
$738$	−5.93734	+	2.49975i	−0.218556	+	0.0920170i
$739$	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
$741$	−7.15072	+	34.2420i	−0.262688	+	1.25791i
$742$	28.6412	−	10.3216i	1.05145	−	0.378919i
$743$	29.5583	+	7.92014i	1.08439	+	0.290562i	0.756393	−	0.654117i	$-0.226960\pi$
$743$	29.5583	+	7.92014i	1.08439	+	0.290562i	0.327997	+	0.944679i	$0.393626\pi$
$744$	8.86468	−	4.40357i	0.324995	−	0.161443i
$745$		−	19.9762i		−	0.731873i
$746$	−19.4921	−	5.22288i	−0.713655	−	0.191223i
$747$	10.6700	−	8.28612i	0.390396	−	0.303173i
$748$	−1.12117	−	4.18425i	−0.0409939	−	0.152991i
$749$	26.3710	−	18.3406i	0.963576	−	0.670152i
$750$	20.6790	+	1.29519i	0.755092	+	0.0472937i
$751$			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
$753$	1.48192	−	2.23182i	0.0540041	−	0.0813321i
$754$	−2.96714	+	20.5611i	−0.108057	+	0.748789i
$755$		−	0.0921071i		−	0.00335212i
$756$	12.5527	−	5.60622i	0.456537	−	0.203896i
$757$	−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
$759$	21.5146	−	4.34438i	0.780930	−	0.157691i
$760$	6.44289	+	6.44289i	0.233708	+	0.233708i
$761$	5.21146	−	19.4494i	0.188915	−	0.705042i	−0.804843	−	0.593488i	$-0.797751\pi$
$761$	5.21146	−	19.4494i	0.188915	−	0.705042i	0.993758	−	0.111554i	$-0.0355828\pi$
$762$	4.36663	−	12.9872i	0.158186	−	0.470478i
$763$	−18.0306	+	6.49782i	−0.652752	+	0.235237i
$764$	−5.23979	−	9.07557i	−0.189569	−	0.328343i
$765$	−0.567540	−	4.12592i	−0.0205194	−	0.149173i
$766$	19.0262	−	10.9848i	0.687446	−	0.396897i
$767$	−2.33878	−	1.84120i	−0.0844483	−	0.0664819i
$768$	−1.72866	−	0.108271i	−0.0623778	−	0.00390691i
$769$	−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
$771$	−11.9100	−	0.745961i	−0.428929	−	0.0268651i
$772$	2.94853	−	0.790055i	0.106120	−	0.0284347i
$773$	4.54294	−	4.54294i	0.163398	−	0.163398i	−0.620672	−	0.784070i	$-0.713140\pi$
$773$	4.54294	−	4.54294i	0.163398	−	0.163398i	0.784070	+	0.620672i	$0.213140\pi$
$774$	−38.6029	+	5.31000i	−1.38755	+	0.190864i
$775$	3.48166	+	12.9937i	0.125065	+	0.466748i
$776$	−13.3902	−	7.73081i	−0.480679	−	0.277520i
$777$	24.4606	+	5.99269i	0.877520	+	0.214986i
$778$	−2.11550	−	0.566847i	−0.0758445	−	0.0203225i
$779$	6.01412	−	10.4168i	0.215478	−	0.373219i
$780$	−9.65010	+	3.17363i	−0.345529	+	0.113634i
$781$	38.3328	+	66.3943i	1.37165	+	2.37578i
$782$	1.50661	−	1.50661i	0.0538764	−	0.0538764i
$783$	−28.2650	+	9.86959i	−1.01011	+	0.352710i
$784$	2.43588	−	6.56251i	0.0869958	−	0.234375i
$785$	4.67597	−	4.67597i	0.166893	−	0.166893i
$786$	−12.9438	+	2.61370i	−0.461689	+	0.0932277i
$787$	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
$789$	−7.61788	−	5.05823i	−0.271204	−	0.180078i
$790$	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
$795$	−21.4468	−	24.3128i	−0.760639	−	0.862287i
$796$	4.95816			0.175737
$797$	−18.3966	+	31.8639i	−0.651642	+	1.12868i	0.331083	+	0.943602i	$0.392586\pi$
$797$	−18.3966	+	31.8639i	−0.651642	+	1.12868i	−0.982724	+	0.185075i	$0.940747\pi$
$798$	−12.3526	+	22.5011i	−0.437279	+	0.796529i
$799$	−6.17245	+	1.65390i	−0.218366	+	0.0585109i
$800$	0.609244	−	2.27373i	0.0215400	−	0.0803885i
$801$	−13.0658	−	16.8248i	−0.461657	−	0.594476i
$802$	−24.5324			−0.866269
$803$	55.5079			1.95883
$804$	4.20375	+	20.8181i	0.148255	+	0.734199i
$805$	6.93270	−	8.20897i	0.244345	−	0.289328i
$806$	−12.3394	−	16.5013i	−0.434636	−	0.581235i
$807$	−2.06253	+	32.9303i	−0.0726044	+	1.15920i
$808$	−2.04832	+	0.548845i	−0.0720595	+	0.0193083i
$809$	−4.19679	−	2.42302i	−0.147551	−	0.0851888i	0.424407	−	0.905472i	$-0.360483\pi$
$809$	−4.19679	−	2.42302i	−0.147551	−	0.0851888i	−0.571958	+	0.820283i	$0.693816\pi$
$810$	−10.4714	−	10.2314i	−0.367928	−	0.359493i
$811$	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
$813$	−0.333764	+	0.294419i	−0.0117056	+	0.0103257i
$814$	−7.21963	−	26.9440i	−0.253048	−	0.944388i
$815$			16.5625i			0.580160i
$816$	−1.47530	−	0.0924026i	−0.0516459	−	0.00323474i
$817$	51.4457	−	51.4457i	1.79986	−	1.79986i
$818$	−4.67413			−0.163427
$819$	−16.1842	−	23.6024i	−0.565522	−	0.824733i
$820$	3.49306			0.121983
$821$	−16.1934	+	16.1934i	−0.565153	+	0.565153i	−0.930767	−	0.365614i	$-0.880859\pi$
$821$	−16.1934	+	16.1934i	−0.565153	+	0.565153i	0.365614	+	0.930767i	$0.380859\pi$
$822$	−12.5101	−	0.783544i	−0.436339	−	0.0273292i
$823$		−	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
$825$	15.5195	−	13.6900i	0.540319	−	0.476625i
$826$	−1.24711	−	1.79316i	−0.0433926	−	0.0623920i
$827$	−37.4338	−	37.4338i	−1.30170	−	1.30170i	−0.927245	−	0.374455i	$-0.877830\pi$
$827$	−37.4338	−	37.4338i	−1.30170	−	1.30170i	−0.374455	−	0.927245i	$-0.622170\pi$
$828$	0.934547	−	7.43123i	0.0324778	−	0.258253i
$829$	−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
$831$	−0.152146	+	2.42917i	−0.00527790	+	0.0842671i
$832$	0.426188	+	3.58027i	0.0147754	+	0.124124i
$833$	2.07887	−	5.60067i	0.0720284	−	0.194052i
$834$	−1.52872	−	7.57063i	−0.0529352	−	0.262150i
$835$	18.2208			0.630556
$836$	28.4315			0.983322
$837$	12.9015	−	26.7454i	0.445941	−	0.924457i
$838$	−5.24521	+	19.5754i	−0.181193	+	0.676220i
$839$	−7.35666	+	1.97121i	−0.253980	+	0.0680538i	−0.383563	−	0.923515i	$-0.625303\pi$
$839$	−7.35666	+	1.97121i	−0.253980	+	0.0680538i	0.129583	+	0.991569i	$0.458636\pi$
$840$	−7.45262	+	0.160544i	−0.257140	+	0.00553929i
$841$	2.09849	−	3.63470i	0.0723618	−	0.125334i
$842$	−9.63126			−0.331915
$843$	−29.6564	−	33.6196i	−1.02142	−	1.15792i
$844$	−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
$849$	−34.6713	−	23.0215i	−1.18991	−	0.790097i
$850$	0.519950	−	1.94048i	0.0178341	−	0.0665579i
$851$	9.70169	−	9.70169i	0.332569	−	0.332569i
$852$	25.6436	−	5.17814i	0.878535	−	0.177400i
$853$	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
$855$	27.1212	+	3.41075i	0.927526	+	0.116645i
$856$	−8.58491	+	8.58491i	−0.293426	+	0.293426i
$857$	24.4329	+	42.3191i	0.834613	+	1.44559i	0.894345	+	0.447378i	$0.147642\pi$
$857$	24.4329	+	42.3191i	0.834613	+	1.44559i	−0.0597321	+	0.998214i	$0.519025\pi$
$858$	−14.2898	+	28.2946i	−0.487847	+	0.965961i
$859$	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
$861$	2.75102	+	9.44811i	0.0937547	+	0.321991i
$862$	4.93248	+	2.84777i	0.168001	+	0.0969955i
$863$	7.11305	+	26.5462i	0.242131	+	0.903645i	0.974804	+	0.223064i	$0.0716059\pi$
$863$	7.11305	+	26.5462i	0.242131	+	0.903645i	−0.732673	+	0.680581i	$0.761727\pi$
$864$	−4.29518	+	2.92429i	−0.146125	+	0.0994863i
$865$	−13.7373	+	13.7373i	−0.467081	+	0.467081i
$866$	32.4829	−	8.70376i	1.10381	−	0.295766i
$867$	28.1282	+	1.76175i	0.955284	+	0.0598323i
$868$	−5.12609	−	14.2242i	−0.173991	−	0.482802i
$869$	15.8691	−	59.2244i	0.538323	−	2.00905i
$870$	16.2017	+	1.01476i	0.549288	+	0.0344036i
$871$	41.0527	−	16.4103i	1.39102	−	0.556041i
$872$	6.27346	−	3.62198i	0.212446	−	0.122656i
$873$	−45.9522	+	6.32093i	−1.55525	+	0.213931i
$874$	6.99217	+	12.1108i	0.236514	+	0.409654i
$875$	5.59489	−	31.1512i	0.189142	−	1.05310i
$876$	6.03650	−	17.9538i	0.203954	−	0.606601i
$877$	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
$879$	21.6113	−	4.36391i	0.728931	−	0.147191i
$880$	4.12832	+	7.15047i	0.139166	+	0.241042i
$881$	9.75282	+	16.8924i	0.328581	+	0.569118i	0.982230	−	0.187679i	$-0.0600964\pi$
$881$	9.75282	+	16.8924i	0.328581	+	0.569118i	−0.653650	+	0.756797i	$0.726763\pi$
$882$	−6.30368	−	20.0316i	−0.212256	−	0.674498i
$883$		−	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
$885$	−1.28663	+	1.93771i	−0.0432494	+	0.0651353i
$886$	−18.0293	+	4.83095i	−0.605708	+	0.162299i
$887$			35.7457i			1.20022i	0.799916	+	0.600112i	$0.204877\pi$
$887$			35.7457i			1.20022i	−0.799916	+	0.600112i	$0.795123\pi$
$888$	−9.50005	−	0.595017i	−0.318801	−	0.0199675i
$889$	−18.9405	−	8.90546i	−0.635244	−	0.298680i
$890$	2.98953	+	11.1571i	0.100209	+	0.373986i
$891$	−45.6790	+	0.529632i	−1.53031	+	0.0177433i
$892$	−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
$897$	−15.5668	+	0.871543i	−0.519761	+	0.0291000i
$898$	−7.08641	+	12.2740i	−0.236477	+	0.409590i
$899$	8.52198	+	31.8045i	0.284224	+	1.06074i
$900$	−2.74022	−	6.50849i	−0.0913405	−	0.216950i
$901$	−8.50467	+	4.91017i	−0.283332	+	0.163582i
$902$	7.70717	−	7.70717i	0.256621	−	0.256621i
$903$	1.28192	+	59.5083i	0.0426597	+	1.98031i
$904$	−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	$0.170597\pi$
$911$			30.8260i			1.02131i	−0.859786	+	0.510655i	$0.829403\pi$
$912$	3.09193	−	9.19601i	0.102384	−	0.304510i
$913$	−11.4286	+	19.7950i	−0.378233	+	0.655119i
$914$	1.98413			0.0656291
$915$	−12.3686	+	10.9106i	−0.408894	+	0.360693i
$916$	5.91603	−	1.58519i	0.195471	−	0.0523763i
$917$	1.69418	+	20.0997i	0.0559468	+	0.663752i
$918$	−3.66565	+	2.49569i	−0.120985	+	0.0823699i
$919$	−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
$921$	−12.3250	+	10.8721i	−0.406124	+	0.358249i
$922$	−11.6521	−	6.72737i	−0.383743	−	0.221554i
$923$	−20.2140	−	50.5683i	−0.665353	−	1.66448i
$924$	−16.0894	+	16.7979i	−0.529302	+	0.552609i
$925$	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	0.0701494	−	0.997536i	$-0.477652\pi$
$929$	−11.2124	−	3.00436i	−0.367868	−	0.0985698i	−0.438017	+	0.898967i	$0.644319\pi$
$930$	−12.0746	+	10.6512i	−0.395943	+	0.349268i
$931$	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
$936$	7.59771	+	7.69901i	0.248339	+	0.251650i
$937$	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
$939$	−24.8556	+	37.4335i	−0.811132	+	1.22159i
$940$	10.5481	−	6.08995i	0.344041	−	0.198632i
$941$	3.59265	+	0.962648i	0.117117	+	0.0313814i	0.316902	−	0.948458i	$-0.397358\pi$
$941$	3.59265	+	0.962648i	0.117117	+	0.0313814i	−0.199784	+	0.979840i	$0.564024\pi$
$942$	−6.67407	−	2.24399i	−0.217453	−	0.0731131i
$943$	5.17842	+	1.38755i	0.168633	+	0.0451849i
$944$	0.583751	+	0.583751i	0.0189995	+	0.0189995i
$945$	−17.3631	+	14.0936i	−0.564821	+	0.458465i
$946$	57.0956	−	32.9642i	1.85634	−	1.07176i
$947$	−17.7392	−	17.7392i	−0.576446	−	0.576446i	0.357476	−	0.933922i	$-0.383637\pi$
$947$	−17.7392	−	17.7392i	−0.576446	−	0.576446i	−0.933922	+	0.357476i	$0.883637\pi$
$948$	−17.4301	−	11.5735i	−0.566102	−	0.375888i
$949$	−39.0254	−	5.63170i	−1.26682	−	0.182813i
$950$	11.4188	+	6.59266i	0.370475	+	0.213894i
$951$	1.87761	+	9.29842i	0.0608855	+	0.301522i
$952$	−0.399155	+	2.22241i	−0.0129367	+	0.0720289i
$953$	−7.75491	+	13.4319i	−0.251206	+	0.435102i	−0.963858	−	0.266416i	$-0.914161\pi$
$953$	−7.75491	+	13.4319i	−0.251206	+	0.435102i	0.712652	+	0.701518i	$0.247494\pi$
$954$	−13.0253	+	31.9689i	−0.421711	+	1.03503i
$955$	12.0539	+	12.0539i	0.390056	+	0.390056i
$956$	14.2838	+	14.2838i	0.461972	+	0.461972i
$957$	37.9867	−	33.5087i	1.22794	−	1.08318i
$958$	−2.30496	+	3.99230i	−0.0744697	+	0.128985i
$959$	−3.38470	+	18.8454i	−0.109298	+	0.608548i
$960$	2.76174	−	0.557670i	0.0891347	−	0.0179987i
$961$	−1.43588	−	0.829003i	−0.0463186	−	0.0267420i
$962$	2.34216	+	19.6758i	0.0755142	+	0.634372i
$963$	−4.54470	+	36.1380i	−0.146451	+	1.16453i
$964$	16.7231	+	16.7231i	0.538614	+	0.538614i
$965$	−4.30023	+	2.48274i	−0.138429	+	0.0799222i
$966$	−11.1122	−	2.72241i	−0.357528	−	0.0875920i
$967$	−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
$969$	2.63876	−	7.84819i	0.0847691	−	0.252120i
$970$	24.2940	+	6.50956i	0.780033	+	0.209009i
$971$	49.7321	−	28.7128i	1.59598	−	0.921439i	0.603727	−	0.797191i	$-0.293682\pi$
$971$	49.7321	−	28.7128i	1.59598	−	0.921439i	0.992251	−	0.124248i	$-0.0396518\pi$
$972$	−4.79630	+	14.8322i	−0.153841	+	0.475745i
$973$	−11.7561	+	0.990902i	−0.376882	+	0.0317669i
$974$	−9.27311			−0.297130
$975$	−12.3001	+	8.05033i	−0.393918	+	0.257817i
$976$	2.92693	+	5.06959i	0.0936888	+	0.162274i
$977$	2.12769	+	7.94066i	0.0680710	+	0.254044i	0.991573	−	0.129549i	$-0.0413530\pi$
$977$	2.12769	+	7.94066i	0.0680710	+	0.254044i	−0.923502	+	0.383594i	$0.874686\pi$
$978$	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
$981$	8.19990	−	20.1255i	0.261803	−	0.642558i
$982$	26.9832	+	7.23014i	0.861070	+	0.230723i
$983$	−12.4153	+	46.3345i	−0.395986	+	1.47784i	0.424108	+	0.905611i	$0.360588\pi$
$983$	−12.4153	+	46.3345i	−0.395986	+	1.47784i	−0.820094	+	0.572228i	$0.806079\pi$
$984$	−1.65469	−	3.33100i	−0.0527496	−	0.106188i
$985$			36.0401i			1.14833i
$986$	1.27267	−	4.74967i	0.0405301	−	0.151260i
$987$	24.7796	+	23.7345i	0.788742	+	0.755477i
$988$	−19.9890	−	2.88459i	−0.635935	−	0.0917709i
$989$	28.0832	+	16.2138i	0.892993	+	0.515570i
$990$	22.9390	+	9.34622i	0.729049	+	0.297042i
$991$	−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
$993$	1.33770	−	3.97858i	0.0424506	−	0.126257i
$994$	−3.35643	−	39.8207i	−0.106460	−	1.26303i
$995$	−7.79049	+	2.08746i	−0.246975	+	0.0661768i
$996$	5.15972	+	5.84925i	0.163492	+	0.185340i
$997$	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
$999$	−23.6046	+	16.0707i	−0.746816	+	0.508455i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.72866 - 0.108271i) q^{3} -1.00000i q^{4} +(0.421014 + 1.57124i) q^{5} +(1.29891 - 1.14579i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97655 + 0.374330i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.72866 - 0.108271i) q^{3} -1.00000i q^{4} +(0.421014 + 1.57124i) q^{5} +(1.29891 - 1.14579i) q^{6} +(-1.51065 - 2.17208i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97655 + 0.374330i) q^{9} +(-1.40874 - 0.813336i) q^{10} +(-4.90284 + 1.31371i) q^{11} +(-0.108271 + 1.72866i) q^{12} +(3.58027 - 0.426188i) q^{13} +(2.60408 + 0.467704i) q^{14} +(-0.557670 - 2.76174i) q^{15} -1.00000 q^{16} -0.853434 q^{17} +(-2.36943 + 1.84005i) q^{18} +(1.44975 - 5.41052i) q^{19} +(1.57124 - 0.421014i) q^{20} +(2.37623 + 3.91836i) q^{21} +(2.53789 - 4.39576i) q^{22} +2.49659 q^{23} +(-1.14579 - 1.29891i) 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} +(2.34718 + 1.55851i) q^{30} +(-1.47908 + 5.51999i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.61759 - 1.74013i) q^{33} +(0.603469 - 0.603469i) q^{34} +(2.77687 - 3.28807i) q^{35} +(0.374330 - 2.97655i) q^{36} +(3.88598 - 3.88598i) q^{37} +(2.80069 + 4.85094i) q^{38} +(-6.23523 + 0.349094i) q^{39} +(-0.813336 + 1.40874i) q^{40} +(2.07420 + 0.555780i) q^{41} +(-4.45095 - 1.09045i) q^{42} +(11.2486 + 6.49440i) q^{43} +(1.31371 + 4.90284i) q^{44} +(0.665007 + 4.83449i) q^{45} +(-1.76535 + 1.76535i) q^{46} +(7.23248 - 1.93794i) q^{47} +(1.72866 + 0.108271i) q^{48} +(-2.43588 + 6.56251i) q^{49} +(-0.609244 + 2.27373i) q^{50} +(1.47530 + 0.0924026i) q^{51} +(-0.426188 - 3.58027i) q^{52} +(9.96523 - 5.75343i) q^{53} +(4.29518 - 2.92429i) q^{54} +(-4.12832 - 7.15047i) q^{55} +(0.467704 - 2.60408i) q^{56} +(-3.09193 + 9.19601i) q^{57} +(-1.49123 + 5.56536i) q^{58} +(-0.583751 - 0.583751i) q^{59} +(-2.76174 + 0.557670i) q^{60} +(-2.92693 - 5.06959i) q^{61} +(-2.85736 - 4.94909i) q^{62} +(-3.68345 - 7.03080i) q^{63} +1.00000i q^{64} +(2.17699 + 5.44606i) q^{65} +(-4.86310 + 7.32401i) q^{66} +(11.8441 - 3.17363i) q^{67} +0.853434i q^{68} +(-4.31576 - 0.270309i) q^{69} +(0.361477 + 4.28856i) q^{70} +(-3.90925 - 14.5895i) q^{71} +(1.84005 + 2.36943i) 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} +(4.16213 - 4.65582i) q^{78} +(-6.03981 + 10.4613i) q^{79} +(-0.421014 - 1.57124i) q^{80} +(8.71975 + 2.22843i) q^{81} +(-1.85968 + 1.07368i) q^{82} +(3.18424 - 3.18424i) q^{83} +(3.91836 - 2.37623i) 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} +(3.15449 - 9.38207i) q^{93} +(-3.74381 + 6.48447i) q^{94} +9.11162 q^{95} +(-1.29891 + 1.14579i) q^{96} +(-14.9348 + 4.00176i) q^{97} +(-2.91796 - 6.36282i) q^{98} +(-15.0853 + 2.07506i) 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

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