LMFDB - Embedded newform 471.2.e.c.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26155 q^{2} +(-0.500000 - 0.866025i) q^{3} +3.11460 q^{4} +(1.51133 + 2.61769i) q^{5} +(1.13077 + 1.95856i) q^{6} +4.51481 q^{7} -2.52072 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.26155 q^{2} +(-0.500000 - 0.866025i) q^{3} +3.11460 q^{4} +(1.51133 + 2.61769i) q^{5} +(1.13077 + 1.95856i) q^{6} +4.51481 q^{7} -2.52072 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.41793 - 5.92004i) q^{10} +(2.39139 + 4.14200i) q^{11} +(-1.55730 - 2.69732i) q^{12} +(-0.539175 + 0.933878i) q^{13} -10.2105 q^{14} +(1.51133 - 2.61769i) q^{15} -0.528471 q^{16} +(0.551745 + 0.955651i) q^{17} +(1.13077 - 1.95856i) q^{18} +(-0.576715 - 0.998900i) q^{19} +(4.70717 + 8.15306i) q^{20} +(-2.25741 - 3.90994i) q^{21} +(-5.40823 - 9.36733i) q^{22} -9.14913 q^{23} +(1.26036 + 2.18301i) q^{24} +(-2.06821 + 3.58224i) q^{25} +(1.21937 - 2.11201i) q^{26} +1.00000 q^{27} +14.0618 q^{28} +0.0486737 q^{29} +(-3.41793 + 5.92004i) q^{30} +(-3.69473 + 6.39947i) q^{31} +6.23660 q^{32} +(2.39139 - 4.14200i) q^{33} +(-1.24780 - 2.16125i) q^{34} +(6.82335 + 11.8184i) q^{35} +(-1.55730 + 2.69732i) q^{36} +(4.96729 - 8.60359i) q^{37} +(1.30427 + 2.25906i) q^{38} +1.07835 q^{39} +(-3.80963 - 6.59847i) q^{40} +2.73743 q^{41} +(5.10523 + 8.84252i) q^{42} +(-2.25754 + 3.91017i) q^{43} +(7.44821 + 12.9007i) q^{44} -3.02265 q^{45} +20.6912 q^{46} +(0.536882 - 0.929906i) q^{47} +(0.264235 + 0.457669i) q^{48} +13.3835 q^{49} +(4.67735 - 8.10141i) q^{50} +(0.551745 - 0.955651i) q^{51} +(-1.67931 + 2.90866i) q^{52} +(-0.443671 + 0.768460i) q^{53} -2.26155 q^{54} +(-7.22832 + 12.5198i) q^{55} -11.3806 q^{56} +(-0.576715 + 0.998900i) q^{57} -0.110078 q^{58} -7.89393 q^{59} +(4.70717 - 8.15306i) q^{60} +(-0.325984 - 0.564621i) q^{61} +(8.35582 - 14.4727i) q^{62} +(-2.25741 + 3.90994i) q^{63} -13.0474 q^{64} -3.25947 q^{65} +(-5.40823 + 9.36733i) q^{66} +7.64073 q^{67} +(1.71847 + 2.97647i) q^{68} +(4.57456 + 7.92338i) q^{69} +(-15.4313 - 26.7278i) q^{70} +(1.13512 - 1.96609i) q^{71} +(1.26036 - 2.18301i) q^{72} +(6.26191 + 10.8459i) q^{73} +(-11.2338 + 19.4574i) q^{74} +4.13642 q^{75} +(-1.79624 - 3.11117i) q^{76} +(10.7967 + 18.7004i) q^{77} -2.43874 q^{78} -4.49612 q^{79} +(-0.798692 - 1.38337i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.19084 q^{82} +(6.07345 - 10.5195i) q^{83} +(-7.03091 - 12.1779i) q^{84} +(-1.66773 + 2.88860i) q^{85} +(5.10553 - 8.84304i) q^{86} +(-0.0243369 - 0.0421527i) q^{87} +(-6.02801 - 10.4408i) q^{88} +(-7.58759 - 13.1421i) q^{89} +6.83587 q^{90} +(-2.43427 + 4.21628i) q^{91} -28.4959 q^{92} +7.38947 q^{93} +(-1.21418 + 2.10303i) q^{94} +(1.74321 - 3.01933i) q^{95} +(-3.11830 - 5.40105i) q^{96} +(2.88364 - 4.99460i) q^{97} -30.2675 q^{98} -4.78277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.26155			−1.59916			−0.799578	−	0.600562i	$-0.794943\pi$
$2$	−2.26155			−1.59916			−0.799578	+	0.600562i	$0.794943\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	3.11460			1.55730
$5$	1.51133	+	2.61769i	0.675885	+	1.17067i	0.976209	+	0.216830i	$0.0695719\pi$
$5$	1.51133	+	2.61769i	0.675885	+	1.17067i	−0.300324	+	0.953837i	$0.597095\pi$
$6$	1.13077	+	1.95856i	0.461637	+	0.799578i
$7$	4.51481			1.70644			0.853219	−	0.521553i	$-0.174647\pi$
$7$	4.51481			1.70644			0.853219	+	0.521553i	$0.174647\pi$
$8$	−2.52072			−0.891209
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.41793	−	5.92004i	−1.08085	−	1.87208i
$11$	2.39139	+	4.14200i	0.721030	+	1.24886i	0.960587	+	0.277978i	$0.0896643\pi$
$11$	2.39139	+	4.14200i	0.721030	+	1.24886i	−0.239558	+	0.970882i	$0.577002\pi$
$12$	−1.55730	−	2.69732i	−0.449554	−	0.778650i
$13$	−0.539175	+	0.933878i	−0.149540	+	0.259011i	−0.931058	−	0.364872i	$-0.881113\pi$
$13$	−0.539175	+	0.933878i	−0.149540	+	0.259011i	0.781517	+	0.623883i	$0.214446\pi$
$14$	−10.2105			−2.72886
$15$	1.51133	−	2.61769i	0.390223	−	0.675885i
$16$	−0.528471			−0.132118
$17$	0.551745	+	0.955651i	0.133818	+	0.231779i	0.925145	−	0.379613i	$-0.123943\pi$
$17$	0.551745	+	0.955651i	0.133818	+	0.231779i	−0.791327	+	0.611393i	$0.790610\pi$
$18$	1.13077	−	1.95856i	0.266526	−	0.461637i
$19$	−0.576715	−	0.998900i	−0.132308	−	0.229163i	0.792258	−	0.610186i	$-0.208905\pi$
$19$	−0.576715	−	0.998900i	−0.132308	−	0.229163i	−0.924566	+	0.381023i	$0.875572\pi$
$20$	4.70717	+	8.15306i	1.05256	+	1.82308i
$21$	−2.25741	−	3.90994i	−0.492606	−	0.853219i
$22$	−5.40823	−	9.36733i	−1.15304	−	1.99712i
$23$	−9.14913			−1.90772			−0.953862	−	0.300244i	$-0.902932\pi$
$23$	−9.14913			−1.90772			−0.953862	+	0.300244i	$0.902932\pi$
$24$	1.26036	+	2.18301i	0.257270	+	0.445604i
$25$	−2.06821	+	3.58224i	−0.413642	+	0.716449i
$26$	1.21937	−	2.11201i	0.239138	−	0.414199i
$27$	1.00000			0.192450
$28$	14.0618			2.65744
$29$	0.0486737			0.00903849			0.00451924	−	0.999990i	$-0.498561\pi$
$29$	0.0486737			0.00903849			0.00451924	+	0.999990i	$0.498561\pi$
$30$	−3.41793	+	5.92004i	−0.624027	+	1.08085i
$31$	−3.69473	+	6.39947i	−0.663594	+	1.14938i	0.316071	+	0.948736i	$0.397636\pi$
$31$	−3.69473	+	6.39947i	−0.663594	+	1.14938i	−0.979664	+	0.200643i	$0.935697\pi$
$32$	6.23660			1.10249
$33$	2.39139	−	4.14200i	0.416287	−	0.721030i
$34$	−1.24780	−	2.16125i	−0.213996	−	0.370651i
$35$	6.82335	+	11.8184i	1.15336	+	1.99767i
$36$	−1.55730	+	2.69732i	−0.259550	+	0.449554i
$37$	4.96729	−	8.60359i	0.816617	−	1.41442i	−0.0915441	−	0.995801i	$-0.529180\pi$
$37$	4.96729	−	8.60359i	0.816617	−	1.41442i	0.908161	−	0.418621i	$-0.137486\pi$
$38$	1.30427	+	2.25906i	0.211580	+	0.366468i
$39$	1.07835			0.172674
$40$	−3.80963	−	6.59847i	−0.602355	−	1.04331i
$41$	2.73743			0.427515			0.213758	−	0.976887i	$-0.431430\pi$
$41$	2.73743			0.427515			0.213758	+	0.976887i	$0.431430\pi$
$42$	5.10523	+	8.84252i	0.787754	+	1.36443i
$43$	−2.25754	+	3.91017i	−0.344271	+	0.596296i	−0.985221	−	0.171287i	$-0.945207\pi$
$43$	−2.25754	+	3.91017i	−0.344271	+	0.596296i	0.640950	+	0.767583i	$0.278541\pi$
$44$	7.44821	+	12.9007i	1.12286	+	1.94485i
$45$	−3.02265			−0.450590
$46$	20.6912			3.05075
$47$	0.536882	−	0.929906i	0.0783122	−	0.135641i	−0.824210	−	0.566285i	$-0.808380\pi$
$47$	0.536882	−	0.929906i	0.0783122	−	0.135641i	0.902522	+	0.430644i	$0.141714\pi$
$48$	0.264235	+	0.457669i	0.0381391	+	0.0660589i
$49$	13.3835			1.91193
$50$	4.67735	−	8.10141i	0.661478	−	1.14571i
$51$	0.551745	−	0.955651i	0.0772598	−	0.133818i
$52$	−1.67931	+	2.90866i	−0.232879	+	0.403358i
$53$	−0.443671	+	0.768460i	−0.0609428	+	0.105556i	−0.894887	−	0.446293i	$-0.852744\pi$
$53$	−0.443671	+	0.768460i	−0.0609428	+	0.105556i	0.833944	+	0.551849i	$0.186077\pi$
$54$	−2.26155			−0.307758
$55$	−7.22832	+	12.5198i	−0.974667	+	1.68817i
$56$	−11.3806			−1.52079
$57$	−0.576715	+	0.998900i	−0.0763878	+	0.132308i
$58$	−0.110078			−0.0144539
$59$	−7.89393			−1.02770			−0.513851	−	0.857879i	$-0.671782\pi$
$59$	−7.89393			−1.02770			−0.513851	+	0.857879i	$0.671782\pi$
$60$	4.70717	−	8.15306i	0.607693	−	1.05256i
$61$	−0.325984	−	0.564621i	−0.0417380	−	0.0722923i	0.844402	−	0.535710i	$-0.179956\pi$
$61$	−0.325984	−	0.564621i	−0.0417380	−	0.0722923i	−0.886140	+	0.463418i	$0.846623\pi$
$62$	8.35582	−	14.4727i	1.06119	−	1.83804i
$63$	−2.25741	+	3.90994i	−0.284406	+	0.492606i
$64$	−13.0474			−1.63093
$65$	−3.25947			−0.404288
$66$	−5.40823	+	9.36733i	−0.665707	+	1.15304i
$67$	7.64073			0.933464			0.466732	−	0.884399i	$-0.345431\pi$
$67$	7.64073			0.933464			0.466732	+	0.884399i	$0.345431\pi$
$68$	1.71847	+	2.97647i	0.208394	+	0.360950i
$69$	4.57456	+	7.92338i	0.550713	+	0.953862i
$70$	−15.4313	−	26.7278i	−1.84440	−	3.19459i
$71$	1.13512	−	1.96609i	0.134714	−	0.233331i	−0.790774	−	0.612108i	$-0.790322\pi$
$71$	1.13512	−	1.96609i	0.134714	−	0.233331i	0.925488	+	0.378777i	$0.123655\pi$
$72$	1.26036	−	2.18301i	0.148535	−	0.257270i
$73$	6.26191	+	10.8459i	0.732901	+	1.26942i	0.955638	+	0.294543i	$0.0951674\pi$
$73$	6.26191	+	10.8459i	0.732901	+	1.26942i	−0.222737	+	0.974878i	$0.571499\pi$
$74$	−11.2338	+	19.4574i	−1.30590	+	2.26188i
$75$	4.13642			0.477632
$76$	−1.79624	−	3.11117i	−0.206043	−	0.356876i
$77$	10.7967	+	18.7004i	1.23039	+	2.13110i
$78$	−2.43874			−0.276133
$79$	−4.49612			−0.505853			−0.252926	−	0.967486i	$-0.581393\pi$
$79$	−4.49612			−0.505853			−0.252926	+	0.967486i	$0.581393\pi$
$80$	−0.798692	−	1.38337i	−0.0892964	−	0.154666i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.19084			−0.683664
$83$	6.07345	−	10.5195i	0.666648	−	1.15467i	−0.312188	−	0.950020i	$-0.601062\pi$
$83$	6.07345	−	10.5195i	0.666648	−	1.15467i	0.978836	−	0.204648i	$-0.0656048\pi$
$84$	−7.03091	−	12.1779i	−0.767136	−	1.32872i
$85$	−1.66773	+	2.88860i	−0.180891	+	0.313312i
$86$	5.10553	−	8.84304i	0.550544	−	0.953570i
$87$	−0.0243369	−	0.0421527i	−0.00260919	−	0.00451924i
$88$	−6.02801	−	10.4408i	−0.642588	−	1.11300i
$89$	−7.58759	−	13.1421i	−0.804283	−	1.39306i	−0.916774	−	0.399406i	$-0.869216\pi$
$89$	−7.58759	−	13.1421i	−0.804283	−	1.39306i	0.112491	−	0.993653i	$-0.464117\pi$
$90$	6.83587			0.720564
$91$	−2.43427	+	4.21628i	−0.255181	+	0.441987i
$92$	−28.4959			−2.97090
$93$	7.38947			0.766252
$94$	−1.21418	+	2.10303i	−0.125233	+	0.216911i
$95$	1.74321	−	3.01933i	0.178849	−	0.309776i
$96$	−3.11830	−	5.40105i	−0.318260	−	0.551243i
$97$	2.88364	−	4.99460i	0.292789	−	0.507125i	−0.681679	−	0.731651i	$-0.738750\pi$
$97$	2.88364	−	4.99460i	0.292789	−	0.507125i	0.974468	+	0.224526i	$0.0720834\pi$
$98$	−30.2675			−3.05748
$99$	−4.78277			−0.480687
$100$	−6.44164	+	11.1572i	−0.644164	+	1.11572i
$101$	−16.6507			−1.65680			−0.828401	−	0.560136i	$-0.810749\pi$
$101$	−16.6507			−1.65680			−0.828401	+	0.560136i	$0.810749\pi$
$102$	−1.24780	+	2.16125i	−0.123550	+	0.213996i
$103$	12.6049			1.24199			0.620997	−	0.783813i	$-0.286728\pi$
$103$	12.6049			1.24199			0.620997	+	0.783813i	$0.286728\pi$
$104$	1.35911	−	2.35404i	0.133272	−	0.230833i
$105$	6.82335	−	11.8184i	0.665891	−	1.15336i
$106$	1.00338	−	1.73791i	0.0974571	−	0.168801i
$107$	8.97333	−	15.5423i	0.867485	−	1.50253i	0.00292607	−	0.999996i	$-0.499069\pi$
$107$	8.97333	−	15.5423i	0.867485	−	1.50253i	0.864559	−	0.502532i	$-0.167598\pi$
$108$	3.11460			0.299702
$109$	−2.16159	−	3.74399i	−0.207043	−	0.358609i	0.743739	−	0.668470i	$-0.233051\pi$
$109$	−2.16159	−	3.74399i	−0.207043	−	0.358609i	−0.950782	+	0.309861i	$0.899717\pi$
$110$	16.3472	−	28.3142i	1.55864	−	2.69965i
$111$	−9.93457			−0.942948
$112$	−2.38595			−0.225451
$113$	4.34042	+	7.51784i	0.408313	+	0.707218i	0.994701	−	0.102812i	$-0.0327840\pi$
$113$	4.34042	+	7.51784i	0.408313	+	0.707218i	−0.586388	+	0.810030i	$0.699451\pi$
$114$	1.30427	−	2.25906i	0.122156	−	0.211580i
$115$	−13.8273	−	23.9496i	−1.28940	−	2.23331i
$116$	0.151599			0.0140756
$117$	−0.539175	−	0.933878i	−0.0498467	−	0.0863371i
$118$	17.8525			1.64346
$119$	2.49103	+	4.31458i	0.228352	+	0.395517i
$120$	−3.80963	+	6.59847i	−0.347770	+	0.602355i
$121$	−5.93745	+	10.2840i	−0.539768	+	0.934906i
$122$	0.737229	+	1.27692i	0.0667456	+	0.115607i
$123$	−1.36872	−	2.37069i	−0.123413	−	0.213758i
$124$	−11.5076	+	19.9318i	−1.03341	+	1.78993i
$125$	2.61031			0.233473
$126$	5.10523	−	8.84252i	0.454810	−	0.787754i
$127$	3.98590	−	6.90377i	0.353691	−	0.612611i	−0.633202	−	0.773987i	$-0.718260\pi$
$127$	3.98590	−	6.90377i	0.353691	−	0.612611i	0.986893	+	0.161376i	$0.0515931\pi$
$128$	17.0342			1.50562
$129$	4.51508			0.397530
$130$	7.37146			0.646520
$131$	0.967011	−	1.67491i	0.0844882	−	0.146338i	−0.820685	−	0.571381i	$-0.806408\pi$
$131$	0.967011	−	1.67491i	0.0844882	−	0.146338i	0.905173	+	0.425043i	$0.139741\pi$
$132$	7.44821	−	12.9007i	0.648283	−	1.12286i
$133$	−2.60376	−	4.50985i	−0.225775	−	0.391053i
$134$	−17.2799			−1.49275
$135$	1.51133	+	2.61769i	0.130074	+	0.225295i
$136$	−1.39079	−	2.40893i	−0.119260	−	0.206564i
$137$	9.63969	+	16.6964i	0.823574	+	1.42647i	0.903004	+	0.429632i	$0.141357\pi$
$137$	9.63969	+	16.6964i	0.823574	+	1.42647i	−0.0794296	+	0.996840i	$0.525310\pi$
$138$	−10.3456	−	17.9191i	−0.880675	−	1.52537i
$139$	−9.84270	+	17.0481i	−0.834847	+	1.44600i	0.0593073	+	0.998240i	$0.481111\pi$
$139$	−9.84270	+	17.0481i	−0.834847	+	1.44600i	−0.894155	+	0.447758i	$0.852223\pi$
$140$	21.2520	+	36.8095i	1.79612	+	3.11097i
$141$	−1.07376			−0.0904272
$142$	−2.56713	+	4.44640i	−0.215429	+	0.373133i
$143$	−5.15750			−0.431292
$144$	0.264235	−	0.457669i	0.0220196	−	0.0381391i
$145$	0.0735618	+	0.127413i	0.00610898	+	0.0105811i
$146$	−14.1616	−	24.5286i	−1.17202	−	2.03000i
$147$	−6.69176	−	11.5905i	−0.551927	−	0.955966i
$148$	15.4711	−	26.7967i	1.27172	−	2.20268i
$149$	20.3413			1.66642			0.833212	−	0.552954i	$-0.186499\pi$
$149$	20.3413			1.66642			0.833212	+	0.552954i	$0.186499\pi$
$150$	−9.35471			−0.763809
$151$	−0.405873	−	0.702993i	−0.0330295	−	0.0572088i	0.849038	−	0.528332i	$-0.177182\pi$
$151$	−0.405873	−	0.702993i	−0.0330295	−	0.0572088i	−0.882068	+	0.471123i	$0.843849\pi$
$152$	1.45374	+	2.51795i	0.117914	+	0.204232i
$153$	−1.10349			−0.0892119
$154$	−24.4172	−	42.2917i	−1.96759	−	3.40797i
$155$	−22.3358			−1.79405
$156$	3.35863			0.268905
$157$	−1.12287	−	12.4795i	−0.0896148	−	0.995977i
$157$	−1.12287	−	12.4795i	−0.0896148	−	0.995977i
$158$	10.1682			0.808938
$159$	0.887341			0.0703707
$160$	9.42553	+	16.3255i	0.745154	+	1.29064i
$161$	−41.3066			−3.25541
$162$	1.13077	+	1.95856i	0.0888420	+	0.153879i
$163$	−4.98924	−	8.64162i	−0.390787	−	0.676864i	0.601766	−	0.798672i	$-0.294464\pi$
$163$	−4.98924	−	8.64162i	−0.390787	−	0.676864i	−0.992554	+	0.121809i	$0.961131\pi$
$164$	8.52601			0.665769
$165$	14.4566			1.12545
$166$	−13.7354	+	23.7904i	−1.06607	+	1.84649i
$167$	−1.96954	−	3.41134i	−0.152408	−	0.263978i	0.779704	−	0.626148i	$-0.215369\pi$
$167$	−1.96954	−	3.41134i	−0.152408	−	0.263978i	−0.932112	+	0.362170i	$0.882036\pi$
$168$	5.69029	+	9.85586i	0.439015	+	0.760396i
$169$	5.91858	+	10.2513i	0.455275	+	0.788560i
$170$	3.77166	−	6.53270i	0.289273	−	0.501035i
$171$	1.15343			0.0882050
$172$	−7.03133	+	12.1786i	−0.536134	+	0.928611i
$173$	22.1940			1.68738			0.843689	−	0.536833i	$-0.180379\pi$
$173$	22.1940			1.68738			0.843689	+	0.536833i	$0.180379\pi$
$174$	0.0550390	+	0.0953303i	0.00417250	+	0.00722697i
$175$	−9.33757	+	16.1732i	−0.705854	+	1.22258i
$176$	−1.26378	−	2.18893i	−0.0952608	−	0.164997i
$177$	3.94697	+	6.83635i	0.296672	+	0.513851i
$178$	17.1597	+	29.7215i	1.28617	+	2.22772i
$179$	−0.968712	−	1.67786i	−0.0724049	−	0.125409i	0.827550	−	0.561392i	$-0.189734\pi$
$179$	−0.968712	−	1.67786i	−0.0724049	−	0.125409i	−0.899955	+	0.435983i	$0.856401\pi$
$180$	−9.41435			−0.701704
$181$	8.38162	+	14.5174i	0.623001	+	1.07907i	0.988924	+	0.148424i	$0.0474201\pi$
$181$	8.38162	+	14.5174i	0.623001	+	1.07907i	−0.365923	+	0.930645i	$0.619247\pi$
$182$	5.50522	−	9.53533i	0.408074	−	0.706806i
$183$	−0.325984	+	0.564621i	−0.0240974	+	0.0417380i
$184$	23.0624			1.70018
$185$	30.0287			2.20776
$186$	−16.7116			−1.22536
$187$	−2.63887	+	4.57066i	−0.192973	+	0.334240i
$188$	1.67217	−	2.89628i	0.121956	−	0.211233i
$189$	4.51481			0.328404
$190$	−3.94235	+	6.82835i	−0.286008	+	0.495381i
$191$	−7.85578	−	13.6066i	−0.568425	−	0.984540i	−0.996722	−	0.0809024i	$-0.974220\pi$
$191$	−7.85578	−	13.6066i	−0.568425	−	0.984540i	0.428297	−	0.903638i	$-0.359114\pi$
$192$	6.52371	+	11.2994i	0.470809	+	0.815464i
$193$	−7.81035	+	13.5279i	−0.562201	+	0.973761i	0.435103	+	0.900381i	$0.356712\pi$
$193$	−7.81035	+	13.5279i	−0.562201	+	0.973761i	−0.997304	+	0.0733802i	$0.976621\pi$
$194$	−6.52148	+	11.2955i	−0.468215	+	0.810972i
$195$	1.62974	+	2.82279i	0.116708	+	0.202144i
$196$	41.6843			2.97745
$197$	−0.536127	−	0.928599i	−0.0381975	−	0.0661600i	0.846295	−	0.532715i	$-0.178828\pi$
$197$	−0.536127	−	0.928599i	−0.0381975	−	0.0661600i	−0.884492	+	0.466555i	$0.845495\pi$
$198$	10.8165			0.768693
$199$	8.78009	+	15.2076i	0.622404	+	1.07804i	0.989037	+	0.147670i	$0.0471772\pi$
$199$	8.78009	+	15.2076i	0.622404	+	1.07804i	−0.366633	+	0.930366i	$0.619489\pi$
$200$	5.21337	−	9.02983i	0.368641	−	0.638505i
$201$	−3.82037	−	6.61707i	−0.269468	−	0.466732i
$202$	37.6562			2.64948
$203$	0.219753			0.0154236
$204$	1.71847	−	2.97647i	0.120317	−	0.208394i
$205$	4.13715	+	7.16576i	0.288951	+	0.500478i
$206$	−28.5065			−1.98614
$207$	4.57456	−	7.92338i	0.317954	−	0.550713i
$208$	0.284938	−	0.493527i	0.0197569	−	0.0342200i
$209$	2.75830	−	4.77751i	0.190795	−	0.330467i
$210$	−15.4313	+	26.7278i	−1.06486	+	1.84440i
$211$	−19.3167			−1.32981			−0.664907	−	0.746926i	$-0.731529\pi$
$211$	−19.3167			−1.32981			−0.664907	+	0.746926i	$0.731529\pi$
$212$	−1.38186	+	2.39345i	−0.0949063	+	0.164382i
$213$	−2.27024			−0.155554
$214$	−20.2936	+	35.1496i	−1.38724	+	2.40278i
$215$	−13.6475			−0.930752
$216$	−2.52072			−0.171513
$217$	−16.6810	+	28.8924i	−1.13238	+	1.96134i
$218$	4.88854	+	8.46721i	0.331094	+	0.573472i
$219$	6.26191	−	10.8459i	0.423140	−	0.732901i
$220$	−22.5133	+	38.9942i	−1.51785	+	2.62899i
$221$	−1.18995			−0.0800446
$222$	22.4675			1.50792
$223$	−0.944131	+	1.63528i	−0.0632237	+	0.109507i	−0.895905	−	0.444246i	$-0.853471\pi$
$223$	−0.944131	+	1.63528i	−0.0632237	+	0.109507i	0.832681	+	0.553753i	$0.186805\pi$
$224$	28.1571			1.88132
$225$	−2.06821	−	3.58224i	−0.137881	−	0.238816i
$226$	−9.81608	−	17.0019i	−0.652956	−	1.13095i
$227$	−12.1450	−	21.0357i	−0.806089	−	1.39619i	−0.915553	−	0.402197i	$-0.868247\pi$
$227$	−12.1450	−	21.0357i	−0.806089	−	1.39619i	0.109464	−	0.993991i	$-0.465086\pi$
$228$	−1.79624	+	3.11117i	−0.118959	+	0.206043i
$229$	12.2688	−	21.2502i	0.810746	−	1.40425i	−0.101596	−	0.994826i	$-0.532395\pi$
$229$	12.2688	−	21.2502i	0.810746	−	1.40425i	0.912342	−	0.409428i	$-0.134272\pi$
$230$	31.2711	+	54.1632i	2.06196	+	3.57141i
$231$	10.7967	−	18.7004i	0.710368	−	1.23039i
$232$	−0.122693			−0.00805518
$233$	−11.6253	−	20.1357i	−0.761601	−	1.31913i	−0.942025	−	0.335543i	$-0.891080\pi$
$233$	−11.6253	−	20.1357i	−0.761601	−	1.31913i	0.180424	−	0.983589i	$-0.442253\pi$
$234$	1.21937	+	2.11201i	0.0797127	+	0.138066i
$235$	3.24561			0.211720
$236$	−24.5864			−1.60044
$237$	2.24806	+	3.89375i	0.146027	+	0.252926i
$238$	−5.63357	−	9.75764i	−0.365170	−	0.632494i
$239$	18.6524			1.20652			0.603261	−	0.797544i	$-0.293868\pi$
$239$	18.6524			1.20652			0.603261	+	0.797544i	$0.293868\pi$
$240$	−0.798692	+	1.38337i	−0.0515553	+	0.0892964i
$241$	7.22260	+	12.5099i	0.465249	+	0.805835i	0.999213	−	0.0396727i	$-0.0126315\pi$
$241$	7.22260	+	12.5099i	0.465249	+	0.805835i	−0.533964	+	0.845507i	$0.679298\pi$
$242$	13.4278	−	23.2577i	0.863173	−	1.49506i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.01531	−	1.75857i	−0.0649986	−	0.112581i
$245$	20.2269	+	35.0339i	1.29225	+	2.23824i
$246$	3.09542	+	5.36142i	0.197357	+	0.341832i
$247$	1.24380			0.0791412
$248$	9.31339	−	16.1313i	0.591401	−	1.02434i
$249$	−12.1469			−0.769779
$250$	−5.90334			−0.373360
$251$	−0.460982	+	0.798445i	−0.0290970	+	0.0503974i	−0.880207	−	0.474590i	$-0.842596\pi$
$251$	−0.460982	+	0.798445i	−0.0290970	+	0.0503974i	0.851110	+	0.524987i	$0.175930\pi$
$252$	−7.03091	+	12.1779i	−0.442906	+	0.767136i
$253$	−21.8791	−	37.8957i	−1.37553	−	2.38248i
$254$	−9.01429	+	15.6132i	−0.565607	+	0.979660i
$255$	3.33547			0.208875
$256$	−12.4288			−0.776798
$257$	3.05611	−	5.29334i	0.190635	−	0.330189i	−0.754826	−	0.655925i	$-0.772279\pi$
$257$	3.05611	−	5.29334i	0.190635	−	0.330189i	0.945461	+	0.325736i	$0.105612\pi$
$258$	−10.2111			−0.635713
$259$	22.4264	−	38.8436i	1.39351	−	2.41362i
$260$	−10.1520			−0.629598
$261$	−0.0243369	+	0.0421527i	−0.00150641	+	0.00260919i
$262$	−2.18694	+	3.78790i	−0.135110	+	0.234017i
$263$	−11.1516	+	19.3151i	−0.687635	+	1.19102i	0.284966	+	0.958538i	$0.408018\pi$
$263$	−11.1516	+	19.3151i	−0.687635	+	1.19102i	−0.972601	+	0.232481i	$0.925316\pi$
$264$	−6.02801	+	10.4408i	−0.370998	+	0.642588i
$265$	−2.68212			−0.164761
$266$	5.88853	+	10.1992i	0.361049	+	0.625355i
$267$	−7.58759	+	13.1421i	−0.464353	+	0.804283i
$268$	23.7978			1.45368
$269$	5.73833			0.349872			0.174936	−	0.984580i	$-0.444028\pi$
$269$	5.73833			0.349872			0.174936	+	0.984580i	$0.444028\pi$
$270$	−3.41793	−	5.92004i	−0.208009	−	0.360282i
$271$	9.28125	−	16.0756i	0.563796	−	0.976522i	−0.433365	−	0.901218i	$-0.642674\pi$
$271$	9.28125	−	16.0756i	0.563796	−	0.976522i	0.997161	−	0.0753040i	$-0.0239927\pi$
$272$	−0.291581	−	0.505034i	−0.0176797	−	0.0306222i
$273$	4.86855			0.294658
$274$	−21.8006	−	37.7598i	−1.31702	−	2.28115i
$275$	−19.7835			−1.19299
$276$	14.2479	+	24.6781i	0.857625	+	1.48545i
$277$	5.24905	−	9.09162i	0.315385	−	0.546262i	−0.664134	−	0.747613i	$-0.731200\pi$
$277$	5.24905	−	9.09162i	0.315385	−	0.546262i	0.979519	+	0.201351i	$0.0645331\pi$
$278$	22.2597	−	38.5550i	1.33505	−	2.31238i
$279$	−3.69473	−	6.39947i	−0.221198	−	0.383126i
$280$	−17.1997	−	29.7908i	−1.02788	−	1.78034i
$281$	−1.09352	+	1.89403i	−0.0652337	+	0.112988i	−0.896798	−	0.442441i	$-0.854113\pi$
$281$	−1.09352	+	1.89403i	−0.0652337	+	0.112988i	0.831564	+	0.555429i	$0.187446\pi$
$282$	2.42837			0.144607
$283$	7.12033	−	12.3328i	0.423260	−	0.733107i	−0.572996	−	0.819558i	$-0.694219\pi$
$283$	7.12033	−	12.3328i	0.423260	−	0.733107i	0.996256	+	0.0864505i	$0.0275524\pi$
$284$	3.53544	−	6.12357i	0.209790	−	0.363367i
$285$	−3.48642			−0.206518
$286$	11.6639			0.689703
$287$	12.3590			0.729529
$288$	−3.11830	+	5.40105i	−0.183748	+	0.318260i
$289$	7.89115	−	13.6679i	0.464186	−	0.803993i
$290$	−0.166364	−	0.288150i	−0.00976921	−	0.0169208i
$291$	−5.76727			−0.338083
$292$	19.5033	+	33.7808i	1.14135	+	1.97687i
$293$	1.98843	+	3.44406i	0.116165	+	0.201204i	0.918245	−	0.396013i	$-0.129606\pi$
$293$	1.98843	+	3.44406i	0.116165	+	0.201204i	−0.802080	+	0.597217i	$0.796273\pi$
$294$	15.1337	+	26.2124i	0.882618	+	1.52874i
$295$	−11.9303	−	20.6639i	−0.694609	−	1.20310i
$296$	−12.5211	+	21.6872i	−0.727776	+	1.26055i
$297$	2.39139	+	4.14200i	0.138762	+	0.240343i
$298$	−46.0028			−2.66487
$299$	4.93298	−	8.54417i	0.285282	−	0.494122i
$300$	12.8833			0.743817
$301$	−10.1924	+	17.6537i	−0.587478	+	1.01754i
$302$	0.917902	+	1.58985i	0.0528193	+	0.0914857i
$303$	8.32533	+	14.4199i	0.478277	+	0.828401i
$304$	0.304777	+	0.527890i	0.0174802	+	0.0302766i
$305$	0.985336	−	1.70665i	0.0564202	−	0.0977226i
$306$	2.49560			0.142664
$307$	−13.7181			−0.782932			−0.391466	−	0.920193i	$-0.628032\pi$
$307$	−13.7181			−0.782932			−0.391466	+	0.920193i	$0.628032\pi$
$308$	33.6272	+	58.2441i	1.91609	+	3.31877i
$309$	−6.30243	−	10.9161i	−0.358533	−	0.620997i
$310$	50.5134			2.86897
$311$	0.431124	+	0.746729i	0.0244468	+	0.0423431i	0.877990	−	0.478679i	$-0.158884\pi$
$311$	0.431124	+	0.746729i	0.0244468	+	0.0423431i	−0.853543	+	0.521022i	$0.825551\pi$
$312$	−2.71822			−0.153889
$313$	−27.2730			−1.54156			−0.770782	−	0.637100i	$-0.780134\pi$
$313$	−27.2730			−1.54156			−0.770782	+	0.637100i	$0.780134\pi$
$314$	2.53942	+	28.2231i	0.143308	+	1.59272i
$315$	−13.6467			−0.768904
$316$	−14.0036			−0.787764
$317$	−7.31866	−	12.6763i	−0.411057	−	0.711972i	0.583949	−	0.811791i	$-0.301507\pi$
$317$	−7.31866	−	12.6763i	−0.411057	−	0.711972i	−0.995006	+	0.0998190i	$0.968174\pi$
$318$	−2.00676			−0.112534
$319$	0.116398	+	0.201607i	0.00651702	+	0.0112878i
$320$	−19.7189	−	34.1542i	−1.10232	−	1.90928i
$321$	−17.9467			−1.00169
$322$	93.4168			5.20592
$323$	0.636400	−	1.10228i	0.0354102	−	0.0613323i
$324$	−1.55730	−	2.69732i	−0.0865166	−	0.149851i
$325$	−2.23025	−	3.86291i	−0.123712	−	0.214276i
$326$	11.2834	+	19.5434i	0.624930	+	1.08241i
$327$	−2.16159	+	3.74399i	−0.119536	+	0.207043i
$328$	−6.90030			−0.381005
$329$	2.42392	−	4.19835i	0.133635	−	0.231463i
$330$	−32.6944			−1.79977
$331$	−6.27084	−	10.8614i	−0.344676	−	0.596997i	0.640619	−	0.767859i	$-0.278678\pi$
$331$	−6.27084	−	10.8614i	−0.344676	−	0.596997i	−0.985295	+	0.170862i	$0.945345\pi$
$332$	18.9164	−	32.7641i	1.03817	−	1.79816i
$333$	4.96729	+	8.60359i	0.272206	+	0.471474i
$334$	4.45421	+	7.71491i	0.243723	+	0.422141i
$335$	11.5476	+	20.0011i	0.630915	+	1.09278i
$336$	1.19297	+	2.06629i	0.0650820	+	0.112725i
$337$	5.00410			0.272591			0.136295	−	0.990668i	$-0.456480\pi$
$337$	5.00410			0.272591			0.136295	+	0.990668i	$0.456480\pi$
$338$	−13.3852	−	23.1838i	−0.728056	−	1.26103i
$339$	4.34042	−	7.51784i	0.235739	−	0.408313i
$340$	−5.19432	+	8.99683i	−0.281702	+	0.487921i
$341$	−35.3421			−1.91388
$342$	−2.60854			−0.141054
$343$	28.8204			1.55616
$344$	5.69062	−	9.85644i	0.306818	−	0.531424i
$345$	−13.8273	+	23.9496i	−0.744437	+	1.28940i
$346$	−50.1928			−2.69838
$347$	−6.33274	+	10.9686i	−0.339959	+	0.588827i	−0.984425	−	0.175807i	$-0.943747\pi$
$347$	−6.33274	+	10.9686i	−0.339959	+	0.588827i	0.644465	+	0.764633i	$0.277080\pi$
$348$	−0.0757996	−	0.131289i	−0.00406328	−	0.00703781i
$349$	−3.65821	−	6.33621i	−0.195820	−	0.339170i	0.751349	−	0.659905i	$-0.229403\pi$
$349$	−3.65821	−	6.33621i	−0.195820	−	0.339170i	−0.947169	+	0.320735i	$0.896070\pi$
$350$	21.1174	−	36.5764i	1.12877	−	1.95509i
$351$	−0.539175	+	0.933878i	−0.0287790	+	0.0498467i
$352$	14.9141	+	25.8320i	0.794925	+	1.37685i
$353$	31.0024			1.65009			0.825045	−	0.565067i	$-0.191150\pi$
$353$	31.0024			1.65009			0.825045	+	0.565067i	$0.191150\pi$
$354$	−8.92625	−	15.4607i	−0.474425	−	0.821728i
$355$	6.86214			0.364205
$356$	−23.6323	−	40.9323i	−1.25251	−	2.16941i
$357$	2.49103	−	4.31458i	0.131839	−	0.228352i
$358$	2.19079	+	3.79456i	0.115787	+	0.200549i
$359$	−14.6695			−0.774229			−0.387114	−	0.922032i	$-0.626528\pi$
$359$	−14.6695			−0.774229			−0.387114	+	0.922032i	$0.626528\pi$
$360$	7.61925			0.401570
$361$	8.83480	−	15.3023i	0.464989	−	0.805385i
$362$	−18.9554	−	32.8318i	−0.996276	−	1.72560i
$363$	11.8749			0.623270
$364$	−7.58178	+	13.1320i	−0.397393	+	0.688306i
$365$	−18.9276	+	32.7835i	−0.990714	+	1.71597i
$366$	0.737229	−	1.27692i	0.0385356	−	0.0667456i
$367$	7.25271	−	12.5621i	0.378589	−	0.655735i	−0.612269	−	0.790650i	$-0.709743\pi$
$367$	7.25271	−	12.5621i	0.378589	−	0.655735i	0.990857	+	0.134915i	$0.0430762\pi$
$368$	4.83505			0.252044
$369$	−1.36872	+	2.37069i	−0.0712526	+	0.123413i
$370$	−67.9115			−3.53055
$371$	−2.00309	+	3.46945i	−0.103995	+	0.180125i
$372$	23.0152			1.19328
$373$	−27.1015			−1.40326			−0.701631	−	0.712541i	$-0.747544\pi$
$373$	−27.1015			−1.40326			−0.701631	+	0.712541i	$0.747544\pi$
$374$	5.96793	−	10.3368i	0.308594	−	0.534501i
$375$	−1.30515	−	2.26059i	−0.0673979	−	0.116737i
$376$	−1.35333	+	2.34403i	−0.0697925	+	0.120884i
$377$	−0.0262437	+	0.0454553i	−0.00135162	+	0.00234107i
$378$	−10.2105			−0.525170
$379$	11.9944			0.616113			0.308056	−	0.951368i	$-0.400321\pi$
$379$	11.9944			0.616113			0.308056	+	0.951368i	$0.400321\pi$
$380$	5.42940	−	9.40399i	0.278522	−	0.482415i
$381$	−7.97179			−0.408407
$382$	17.7662	+	30.7720i	0.908999	+	1.57443i
$383$	8.03780	+	13.9219i	0.410712	+	0.711375i	0.994968	−	0.100195i	$-0.0319467\pi$
$383$	8.03780	+	13.9219i	0.410712	+	0.711375i	−0.584255	+	0.811570i	$0.698613\pi$
$384$	−8.51709	−	14.7520i	−0.434636	−	0.752812i
$385$	−32.6345	+	56.5246i	−1.66321	+	2.88076i
$386$	17.6635	−	30.5940i	0.899047	−	1.55720i
$387$	−2.25754	−	3.91017i	−0.114757	−	0.198765i
$388$	8.98137	−	15.5562i	0.455960	−	0.789746i
$389$	−4.80131			−0.243436			−0.121718	−	0.992565i	$-0.538840\pi$
$389$	−4.80131			−0.243436			−0.121718	+	0.992565i	$0.538840\pi$
$390$	−3.68573	−	6.38387i	−0.186634	−	0.323260i
$391$	−5.04799	−	8.74337i	−0.255288	−	0.442171i
$392$	−33.7361			−1.70393
$393$	−1.93402			−0.0975585
$394$	1.21248	+	2.10007i	0.0610837	+	0.105800i
$395$	−6.79510	−	11.7695i	−0.341898	−	0.592186i
$396$	−14.8964			−0.748573
$397$	3.05023	−	5.28316i	0.153087	−	0.265154i	−0.779274	−	0.626683i	$-0.784412\pi$
$397$	3.05023	−	5.28316i	0.153087	−	0.265154i	0.932361	+	0.361529i	$0.117745\pi$
$398$	−19.8566	−	34.3926i	−0.995321	−	1.72395i
$399$	−2.60376	+	4.50985i	−0.130351	+	0.225775i
$400$	1.09299	−	1.89311i	0.0546494	−	0.0946556i
$401$	12.0293	+	20.8354i	0.600716	+	1.04047i	0.992713	+	0.120504i	$0.0384509\pi$
$401$	12.0293	+	20.8354i	0.600716	+	1.04047i	−0.391997	+	0.919966i	$0.628216\pi$
$402$	8.63994	+	14.9648i	0.430921	+	0.746377i
$403$	−3.98422	−	6.90086i	−0.198468	−	0.343757i
$404$	−51.8601			−2.58014
$405$	1.51133	−	2.61769i	0.0750984	−	0.130074i
$406$	−0.496981			−0.0246648
$407$	47.5148			2.35522
$408$	−1.39079	+	2.40893i	−0.0688546	+	0.119260i
$409$	−2.54532	+	4.40862i	−0.125858	+	0.217992i	−0.922068	−	0.387028i	$-0.873502\pi$
$409$	−2.54532	+	4.40862i	−0.125858	+	0.217992i	0.796210	+	0.605020i	$0.206835\pi$
$410$	−9.35637	−	16.2057i	−0.462078	−	0.800343i
$411$	9.63969	−	16.6964i	0.475491	−	0.823574i
$412$	39.2591			1.93416
$413$	−35.6396			−1.75371
$414$	−10.3456	+	17.9191i	−0.508458	+	0.880675i
$415$	36.7158			1.80231
$416$	−3.36262	+	5.82423i	−0.164866	+	0.285556i
$417$	19.6854			0.963999
$418$	−6.23802	+	10.8046i	−0.305112	+	0.528469i
$419$	−15.7010	+	27.1950i	−0.767046	+	1.32856i	0.172111	+	0.985077i	$0.444941\pi$
$419$	−15.7010	+	27.1950i	−0.767046	+	1.32856i	−0.939158	+	0.343486i	$0.888392\pi$
$420$	21.2520	−	36.8095i	1.03699	−	1.79612i
$421$	15.5375	−	26.9118i	0.757252	−	1.31160i	−0.186995	−	0.982361i	$-0.559875\pi$
$421$	15.5375	−	26.9118i	0.757252	−	1.31160i	0.944247	−	0.329238i	$-0.106792\pi$
$422$	43.6856			2.12658
$423$	0.536882	+	0.929906i	0.0261041	+	0.0452136i
$424$	1.11837	−	1.93707i	0.0543128	−	0.0940725i
$425$	−4.56450			−0.221411
$426$	5.13426			0.248756
$427$	−1.47176	−	2.54916i	−0.0712233	−	0.123362i
$428$	27.9483	−	48.4079i	1.35093	−	2.33989i
$429$	2.57875	+	4.46653i	0.124503	+	0.215646i
$430$	30.8645			1.48842
$431$	−12.2088	−	21.1462i	−0.588076	−	1.01858i	−0.994484	−	0.104885i	$-0.966552\pi$
$431$	−12.2088	−	21.1462i	−0.588076	−	1.01858i	0.406409	−	0.913691i	$-0.366781\pi$
$432$	−0.528471			−0.0254261
$433$	−10.8380	−	18.7719i	−0.520839	−	0.902119i	−0.999706	−	0.0242323i	$-0.992286\pi$
$433$	−10.8380	−	18.7719i	−0.520839	−	0.902119i	0.478867	−	0.877887i	$-0.341047\pi$
$434$	37.7249	−	65.3415i	1.81086	−	3.13649i
$435$	0.0735618	−	0.127413i	0.00352702	−	0.00610898i
$436$	−6.73249	−	11.6610i	−0.322428	−	0.558461i
$437$	5.27644	+	9.13907i	0.252406	+	0.437181i
$438$	−14.1616	+	24.5286i	−0.676668	+	1.17202i
$439$	−33.2914			−1.58891			−0.794457	−	0.607321i	$-0.792244\pi$
$439$	−33.2914			−1.58891			−0.794457	+	0.607321i	$0.792244\pi$
$440$	18.2206	−	31.5590i	0.868632	−	1.50451i
$441$	−6.69176	+	11.5905i	−0.318655	+	0.551927i
$442$	2.69113			0.128004
$443$	−27.0709			−1.28618			−0.643088	−	0.765792i	$-0.722347\pi$
$443$	−27.0709			−1.28618			−0.643088	+	0.765792i	$0.722347\pi$
$444$	−30.9422			−1.46845
$445$	22.9346	−	39.7239i	1.08721	−	1.88310i
$446$	2.13520	−	3.69827i	0.101105	−	0.175118i
$447$	−10.1706	−	17.6161i	−0.481055	−	0.833212i
$448$	−58.9067			−2.78308
$449$	1.83667	+	3.18120i	0.0866777	+	0.150130i	0.906105	−	0.423053i	$-0.139042\pi$
$449$	1.83667	+	3.18120i	0.0866777	+	0.150130i	−0.819427	+	0.573183i	$0.805708\pi$
$450$	4.67735	+	8.10141i	0.220493	+	0.381904i
$451$	6.54626	+	11.3385i	0.308251	+	0.533907i
$452$	13.5187	+	23.4150i	0.635865	+	1.10135i
$453$	−0.405873	+	0.702993i	−0.0190696	+	0.0330295i
$454$	27.4664	+	47.5732i	1.28906	+	2.23272i
$455$	−14.7159			−0.689893
$456$	1.45374	−	2.51795i	0.0680775	−	0.117914i
$457$	5.23017			0.244657			0.122329	−	0.992490i	$-0.460964\pi$
$457$	5.23017			0.244657			0.122329	+	0.992490i	$0.460964\pi$
$458$	−27.7465	+	48.0584i	−1.29651	+	2.24562i
$459$	0.551745	+	0.955651i	0.0257533	+	0.0446060i
$460$	−43.0665	−	74.5934i	−2.00799	−	3.47794i
$461$	−6.95242	−	12.0420i	−0.323807	−	0.560850i	0.657463	−	0.753486i	$-0.271629\pi$
$461$	−6.95242	−	12.0420i	−0.323807	−	0.560850i	−0.981270	+	0.192637i	$0.938296\pi$
$462$	−24.4172	+	42.2917i	−1.13599	+	1.96759i
$463$	−20.2916			−0.943030			−0.471515	−	0.881858i	$-0.656293\pi$
$463$	−20.2916			−0.943030			−0.471515	+	0.881858i	$0.656293\pi$
$464$	−0.0257227			−0.00119414
$465$	11.1679	+	19.3434i	0.517899	+	0.897027i
$466$	26.2913	+	45.5378i	1.21792	+	2.10950i
$467$	−26.1428			−1.20975			−0.604873	−	0.796322i	$-0.706776\pi$
$467$	−26.1428			−1.20975			−0.604873	+	0.796322i	$0.706776\pi$
$468$	−1.67931	−	2.90866i	−0.0776263	−	0.134453i
$469$	34.4965			1.59290
$470$	−7.34010			−0.338574
$471$	−10.2462	+	7.21221i	−0.472119	+	0.332321i
$472$	19.8984			0.915897
$473$	−21.5946			−0.992920
$474$	−5.08409	−	8.80591i	−0.233520	−	0.404469i
$475$	4.77107			0.218912
$476$	7.75855	+	13.4382i	0.355612	+	0.615939i
$477$	−0.443671	−	0.768460i	−0.0203143	−	0.0351854i
$478$	−42.1832			−1.92942
$479$	−2.36518			−0.108068			−0.0540339	−	0.998539i	$-0.517208\pi$
$479$	−2.36518			−0.108068			−0.0540339	+	0.998539i	$0.517208\pi$
$480$	9.42553	−	16.3255i	0.430215	−	0.745154i
$481$	5.35647	+	9.27768i	0.244234	+	0.423026i
$482$	−16.3343	−	28.2918i	−0.744005	−	1.28866i
$483$	20.6533	+	35.7725i	0.939757	+	1.62771i
$484$	−18.4928	+	32.0304i	−0.840581	+	1.45593i
$485$	17.4325			0.791567
$486$	1.13077	−	1.95856i	0.0512929	−	0.0888420i
$487$	2.52761			0.114537			0.0572684	−	0.998359i	$-0.481761\pi$
$487$	2.52761			0.114537			0.0572684	+	0.998359i	$0.481761\pi$
$488$	0.821715	+	1.42325i	0.0371973	+	0.0644276i
$489$	−4.98924	+	8.64162i	−0.225621	+	0.390787i
$490$	−45.7440	−	79.2309i	−2.06650	−	3.57929i
$491$	−4.36772	−	7.56511i	−0.197112	−	0.341409i	0.750479	−	0.660895i	$-0.229823\pi$
$491$	−4.36772	−	7.56511i	−0.197112	−	0.341409i	−0.947591	+	0.319486i	$0.896490\pi$
$492$	−4.26300	−	7.38374i	−0.192191	−	0.332885i
$493$	0.0268555	+	0.0465151i	0.00120951	+	0.00209493i
$494$	−2.81292			−0.126559
$495$	−7.22832	−	12.5198i	−0.324889	−	0.562724i
$496$	1.95256	−	3.38193i	0.0876725	−	0.151853i
$497$	5.12485	−	8.87650i	0.229881	−	0.398166i
$498$	27.4708			1.23100
$499$	4.78365			0.214146			0.107073	−	0.994251i	$-0.465852\pi$
$499$	4.78365			0.214146			0.107073	+	0.994251i	$0.465852\pi$
$500$	8.13006			0.363587
$501$	−1.96954	+	3.41134i	−0.0879925	+	0.152408i
$502$	1.04253	−	1.80572i	0.0465306	−	0.0805933i
$503$	−20.1941			−0.900412			−0.450206	−	0.892925i	$-0.648649\pi$
$503$	−20.1941			−0.900412			−0.450206	+	0.892925i	$0.648649\pi$
$504$	5.69029	−	9.85586i	0.253465	−	0.439015i
$505$	−25.1646	−	43.5863i	−1.11981	−	1.93956i
$506$	49.4806	+	85.7029i	2.19968	+	3.80996i
$507$	5.91858	−	10.2513i	0.262853	−	0.455275i
$508$	12.4145	−	21.5025i	0.550803	−	0.954019i
$509$	10.8815	+	18.8473i	0.482314	+	0.835392i	0.999794	−	0.0203033i	$-0.00646318\pi$
$509$	10.8815	+	18.8473i	0.482314	+	0.835392i	−0.517480	+	0.855695i	$0.673130\pi$
$510$	−7.54332			−0.334024
$511$	28.2713	+	48.9674i	1.25065	+	2.16619i
$512$	−5.96012			−0.263402
$513$	−0.576715	−	0.998900i	−0.0254626	−	0.0441025i
$514$	−6.91154	+	11.9711i	−0.304855	+	0.528024i
$515$	19.0501	+	32.9957i	0.839446	+	1.45396i
$516$	14.0627			0.619074
$517$	5.13556			0.225862
$518$	−50.7183	+	87.8467i	−2.22843	+	3.85976i
$519$	−11.0970	−	19.2206i	−0.487104	−	0.843689i
$520$	8.21622			0.360305
$521$	5.83702	−	10.1100i	0.255725	−	0.442928i	−0.709367	−	0.704839i	$-0.751019\pi$
$521$	5.83702	−	10.1100i	0.255725	−	0.442928i	0.965092	+	0.261911i	$0.0843526\pi$
$522$	0.0550390	−	0.0953303i	0.00240899	−	0.00417250i
$523$	−7.75860	+	13.4383i	−0.339260	+	0.587616i	−0.984294	−	0.176538i	$-0.943510\pi$
$523$	−7.75860	+	13.4383i	−0.339260	+	0.587616i	0.645034	+	0.764154i	$0.276843\pi$
$524$	3.01185	−	5.21668i	0.131573	−	0.227892i
$525$	18.6751			0.815050
$526$	25.2198	−	43.6820i	1.09964	−	1.90462i
$527$	−8.15421			−0.355203
$528$	−1.26378	+	2.18893i	−0.0549989	+	0.0952608i
$529$	60.7065			2.63941
$530$	6.06575			0.263479
$531$	3.94697	−	6.83635i	0.171284	−	0.296672i
$532$	−8.10967	−	14.0464i	−0.351599	−	0.608987i
$533$	−1.47596	+	2.55643i	−0.0639307	+	0.110731i
$534$	17.1597	−	29.7215i	0.742573	−	1.28617i
$535$	54.2465			2.34528
$536$	−19.2601			−0.831911
$537$	−0.968712	+	1.67786i	−0.0418030	+	0.0724049i
$538$	−12.9775			−0.559500
$539$	32.0052	+	55.4346i	1.37856	+	2.38774i
$540$	4.70717	+	8.15306i	0.202564	+	0.350852i
$541$	14.5610	+	25.2204i	0.626028	+	1.08431i	0.988341	+	0.152255i	$0.0486536\pi$
$541$	14.5610	+	25.2204i	0.626028	+	1.08431i	−0.362314	+	0.932056i	$0.618013\pi$
$542$	−20.9900	+	36.3557i	−0.901597	+	1.56161i
$543$	8.38162	−	14.5174i	0.359690	−	0.623001i
$544$	3.44101	+	5.96001i	0.147532	+	0.255533i
$545$	6.53374	−	11.3168i	0.279875	−	0.484757i
$546$	−11.0104			−0.471204
$547$	−18.2432	−	31.5982i	−0.780025	−	1.35104i	−0.931927	−	0.362647i	$-0.881873\pi$
$547$	−18.2432	−	31.5982i	−0.780025	−	1.35104i	0.151902	−	0.988396i	$-0.451460\pi$
$548$	30.0238	+	52.0027i	1.28255	+	2.22145i
$549$	0.651968			0.0278253
$550$	44.7414			1.90778
$551$	−0.0280709	−	0.0486202i	−0.00119586	−	0.00207129i
$552$	−11.5312	−	19.9726i	−0.490800	−	0.850091i
$553$	−20.2991			−0.863207
$554$	−11.8710	+	20.5611i	−0.504349	+	0.873559i
$555$	−15.0144	−	26.0057i	−0.637325	−	1.10388i
$556$	−30.6561	+	53.0979i	−1.30011	+	2.25185i
$557$	−2.71896	+	4.70937i	−0.115206	+	0.199542i	−0.917862	−	0.396900i	$-0.870086\pi$
$557$	−2.71896	+	4.70937i	−0.115206	+	0.199542i	0.802656	+	0.596442i	$0.203419\pi$
$558$	8.35582	+	14.4727i	0.353730	+	0.612678i
$559$	−2.43442	−	4.21653i	−0.102965	−	0.178340i
$560$	−3.60594	−	6.24567i	−0.152379	−	0.263928i
$561$	5.27774			0.222826
$562$	2.47304	−	4.28343i	0.104319	−	0.180686i
$563$	16.5891			0.699148			0.349574	−	0.936909i	$-0.386326\pi$
$563$	16.5891			0.699148			0.349574	+	0.936909i	$0.386326\pi$
$564$	−3.34434			−0.140822
$565$	−13.1196	+	22.7238i	−0.551945	+	0.955997i
$566$	−16.1030	+	27.8912i	−0.676858	+	1.17235i
$567$	−2.25741	−	3.90994i	−0.0948021	−	0.164202i
$568$	−2.86132	+	4.95595i	−0.120058	+	0.207947i
$569$	−14.3332			−0.600880			−0.300440	−	0.953801i	$-0.597134\pi$
$569$	−14.3332			−0.600880			−0.300440	+	0.953801i	$0.597134\pi$
$570$	7.88470			0.330254
$571$	3.52533	−	6.10606i	0.147531	−	0.255531i	−0.782784	−	0.622294i	$-0.786201\pi$
$571$	3.52533	−	6.10606i	0.147531	−	0.255531i	0.930314	+	0.366763i	$0.119534\pi$
$572$	−16.0635			−0.671650
$573$	−7.85578	+	13.6066i	−0.328180	+	0.568425i
$574$	−27.9505			−1.16663
$575$	18.9223	−	32.7744i	0.789115	−	1.36679i
$576$	6.52371	−	11.2994i	0.271821	−	0.470809i
$577$	−4.39243	+	7.60791i	−0.182859	+	0.316722i	−0.942853	−	0.333209i	$-0.891869\pi$
$577$	−4.39243	+	7.60791i	−0.182859	+	0.316722i	0.759994	+	0.649930i	$0.225202\pi$
$578$	−17.8462	+	30.9106i	−0.742305	+	1.28571i
$579$	15.6207			0.649174
$580$	0.229116	+	0.396840i	0.00951351	+	0.0164779i
$581$	27.4205	−	47.4937i	1.13759	−	1.97037i
$582$	13.0430			0.540648
$583$	−4.24395			−0.175766
$584$	−15.7845	−	27.3396i	−0.653168	−	1.13132i
$585$	1.62974	−	2.82279i	0.0673813	−	0.116708i
$586$	−4.49693	−	7.78891i	−0.185767	−	0.321757i
$587$	24.1551			0.996989			0.498494	−	0.866893i	$-0.333886\pi$
$587$	24.1551			0.996989			0.498494	+	0.866893i	$0.333886\pi$
$588$	−20.8422	−	36.0997i	−0.859516	−	1.48873i
$589$	8.52324			0.351194
$590$	26.9809	+	46.7324i	1.11079	+	1.92394i
$591$	−0.536127	+	0.928599i	−0.0220533	+	0.0381975i
$592$	−2.62507	+	4.54675i	−0.107890	+	0.186870i
$593$	−3.98100	−	6.89529i	−0.163480	−	0.283156i	0.772634	−	0.634851i	$-0.218939\pi$
$593$	−3.98100	−	6.89529i	−0.163480	−	0.283156i	−0.936114	+	0.351695i	$0.885605\pi$
$594$	−5.40823	−	9.36733i	−0.221902	−	0.384346i
$595$	−7.52950	+	13.0415i	−0.308679	+	0.534648i
$596$	63.3550			2.59512
$597$	8.78009	−	15.2076i	0.359345	−	0.622404i
$598$	−11.1562	+	19.3230i	−0.456210	+	0.790178i
$599$	34.8715			1.42481			0.712406	−	0.701768i	$-0.247606\pi$
$599$	34.8715			1.42481			0.712406	+	0.701768i	$0.247606\pi$
$600$	−10.4267			−0.425670
$601$	−37.1341			−1.51473			−0.757366	−	0.652991i	$-0.773514\pi$
$601$	−37.1341			−1.51473			−0.757366	+	0.652991i	$0.773514\pi$
$602$	23.0505	−	39.9247i	0.939469	−	1.62721i
$603$	−3.82037	+	6.61707i	−0.155577	+	0.269468i
$604$	−1.26413	−	2.18954i	−0.0514368	−	0.0890912i
$605$	−35.8937			−1.45929
$606$	−18.8281	−	32.6113i	−0.764840	−	1.32474i
$607$	−6.37616	−	11.0438i	−0.258800	−	0.448256i	0.707120	−	0.707093i	$-0.249994\pi$
$607$	−6.37616	−	11.0438i	−0.258800	−	0.448256i	−0.965921	+	0.258838i	$0.916661\pi$
$608$	−3.59674	−	6.22974i	−0.145867	−	0.252649i
$609$	−0.109876	−	0.190311i	−0.00445241	−	0.00771181i
$610$	−2.22839	+	3.85968i	−0.0902247	+	0.156274i
$611$	0.578946	+	1.00276i	0.0234216	+	0.0405675i
$612$	−3.43693			−0.138930
$613$	10.8337	−	18.7646i	0.437570	−	0.757893i	−0.559932	−	0.828539i	$-0.689173\pi$
$613$	10.8337	−	18.7646i	0.437570	−	0.757893i	0.997501	+	0.0706457i	$0.0225060\pi$
$614$	31.0241			1.25203
$615$	4.13715	−	7.16576i	0.166826	−	0.288951i
$616$	−27.2153	−	47.1383i	−1.09654	−	1.89926i
$617$	5.95462	+	10.3137i	0.239724	+	0.415214i	0.960635	−	0.277813i	$-0.0896097\pi$
$617$	5.95462	+	10.3137i	0.239724	+	0.415214i	−0.720911	+	0.693028i	$0.756276\pi$
$618$	14.2533	+	24.6874i	0.573350	+	0.993071i
$619$	−9.65688	+	16.7262i	−0.388143	+	0.672283i	−0.992200	−	0.124658i	$-0.960217\pi$
$619$	−9.65688	+	16.7262i	−0.388143	+	0.672283i	0.604057	+	0.796941i	$0.293550\pi$
$620$	−69.5670			−2.79388
$621$	−9.14913			−0.367142
$622$	−0.975008	−	1.68876i	−0.0390943	−	0.0677132i
$623$	−34.2565	−	59.3341i	−1.37246	−	2.37717i
$624$	−0.569876			−0.0228133
$625$	14.2861	+	24.7442i	0.571443	+	0.989768i
$626$	61.6793			2.46520
$627$	−5.51659			−0.220312
$628$	−3.49729	−	38.8688i	−0.139557	−	1.55103i
$629$	10.9627			0.437112
$630$	30.8627			1.22960
$631$	12.7889	+	22.1511i	0.509120	+	0.881822i	0.999944	+	0.0105630i	$0.00336238\pi$
$631$	12.7889	+	22.1511i	0.509120	+	0.881822i	−0.490824	+	0.871259i	$0.663304\pi$
$632$	11.3335			0.450821
$633$	9.65833	+	16.7287i	0.383884	+	0.664907i
$634$	16.5515	+	28.6680i	0.657344	+	1.13855i
$635$	24.0959			0.956218
$636$	2.76371			0.109588
$637$	−7.21606	+	12.4986i	−0.285911	+	0.495212i
$638$	−0.263239	−	0.455943i	−0.0104217	−	0.0180510i
$639$	1.13512	+	1.96609i	0.0449047	+	0.0777771i
$640$	25.7442	+	44.5903i	1.01763	+	1.76258i
$641$	6.20868	−	10.7537i	0.245228	−	0.424747i	−0.716968	−	0.697106i	$-0.754471\pi$
$641$	6.20868	−	10.7537i	0.245228	−	0.424747i	0.962196	+	0.272359i	$0.0878039\pi$
$642$	40.5872			1.60185
$643$	10.3889	−	17.9941i	0.409697	−	0.709616i	−0.585158	−	0.810919i	$-0.698968\pi$
$643$	10.3889	−	17.9941i	0.409697	−	0.709616i	0.994856	+	0.101303i	$0.0323010\pi$
$644$	−128.653			−5.06966
$645$	6.82375	+	11.8191i	0.268685	+	0.465376i
$646$	−1.43925	+	2.49285i	−0.0566265	+	0.0980799i
$647$	14.8842	+	25.7803i	0.585160	+	1.01353i	0.994855	+	0.101304i	$0.0323015\pi$
$647$	14.8842	+	25.7803i	0.585160	+	1.01353i	−0.409696	+	0.912222i	$0.634365\pi$
$648$	1.26036	+	2.18301i	0.0495116	+	0.0857566i
$649$	−18.8774	−	32.6967i	−0.741004	−	1.28346i
$650$	5.04382	+	8.73616i	0.197835	+	0.342660i
$651$	33.3621			1.30756
$652$	−15.5395	−	26.9152i	−0.608573	−	1.05408i
$653$	0.774510	−	1.34149i	0.0303089	−	0.0524966i	−0.850473	−	0.526019i	$-0.823684\pi$
$653$	0.774510	−	1.34149i	0.0303089	−	0.0524966i	0.880782	+	0.473522i	$0.157018\pi$
$654$	4.88854	−	8.46721i	0.191157	−	0.331094i
$655$	5.84587			0.228417
$656$	−1.44665			−0.0564824
$657$	−12.5238			−0.488601
$658$	−5.48181	+	9.49477i	−0.213703	+	0.370145i
$659$	−23.9893	+	41.5506i	−0.934490	+	1.61858i	−0.158948	+	0.987287i	$0.550810\pi$
$659$	−23.9893	+	41.5506i	−0.934490	+	1.61858i	−0.775542	+	0.631296i	$0.782523\pi$
$660$	45.0267			1.75266
$661$	−22.4251	+	38.8414i	−0.872236	+	1.51076i	−0.0125580	+	0.999921i	$0.503997\pi$
$661$	−22.4251	+	38.8414i	−0.872236	+	1.51076i	−0.859678	+	0.510836i	$0.829336\pi$
$662$	14.1818	+	24.5636i	0.551191	+	0.954691i
$663$	0.594974	+	1.03053i	0.0231069	+	0.0400223i
$664$	−15.3095	+	26.5168i	−0.594122	+	1.02905i
$665$	7.87026	−	13.6317i	0.305196	−	0.528614i
$666$	−11.2338	−	19.4574i	−0.435299	−	0.753960i
$667$	−0.445322			−0.0172429
$668$	−6.13433	−	10.6250i	−0.237344	−	0.411092i
$669$	1.88826			0.0730044
$670$	−26.1155	−	45.2334i	−1.00893	−	1.74752i
$671$	1.55911	−	2.70045i	0.0601887	−	0.104250i
$672$	−14.0785	−	24.3847i	−0.543091	−	0.940662i
$673$	26.7396			1.03074			0.515368	−	0.856969i	$-0.327655\pi$
$673$	26.7396			1.03074			0.515368	+	0.856969i	$0.327655\pi$
$674$	−11.3170			−0.435915
$675$	−2.06821	+	3.58224i	−0.0796054	+	0.137881i
$676$	18.4340	+	31.9286i	0.709000	+	1.22802i
$677$	11.0281			0.423844			0.211922	−	0.977287i	$-0.432028\pi$
$677$	11.0281			0.423844			0.211922	+	0.977287i	$0.432028\pi$
$678$	−9.81608	+	17.0019i	−0.376984	+	0.652956i
$679$	13.0191	−	22.5497i	0.499626	−	0.865378i
$680$	4.20389	−	7.28135i	0.161212	−	0.279227i
$681$	−12.1450	+	21.0357i	−0.465396	+	0.806089i
$682$	79.9279			3.06060
$683$	−13.8735	+	24.0296i	−0.530856	+	0.919469i	0.468496	+	0.883466i	$0.344796\pi$
$683$	−13.8735	+	24.0296i	−0.530856	+	0.919469i	−0.999352	+	0.0360033i	$0.988537\pi$
$684$	3.59247			0.137362
$685$	−29.1374	+	50.4675i	−1.11328	+	1.92826i
$686$	−65.1787			−2.48853
$687$	−24.5376			−0.936169
$688$	1.19304	−	2.06641i	0.0454844	−	0.0787812i
$689$	−0.478432	−	0.828669i	−0.0182268	−	0.0315698i
$690$	31.2711	−	54.1632i	1.19047	−	2.06196i
$691$	−3.77566	+	6.53964i	−0.143633	+	0.248780i	−0.928862	−	0.370426i	$-0.879212\pi$
$691$	−3.77566	+	6.53964i	−0.143633	+	0.248780i	0.785229	+	0.619205i	$0.212545\pi$
$692$	69.1254			2.62775
$693$	−21.5933			−0.820262
$694$	14.3218	−	24.8061i	0.543648	−	0.941626i
$695$	−59.5021			−2.25704
$696$	0.0613464	+	0.106255i	0.00232533	+	0.00402759i
$697$	1.51037	+	2.61603i	0.0572092	+	0.0990892i
$698$	8.27322	+	14.3296i	0.313146	+	0.542385i
$699$	−11.6253	+	20.1357i	−0.439711	+	0.761601i
$700$	−29.0828	+	50.3729i	−1.09923	+	1.90392i
$701$	−21.6015	−	37.4148i	−0.815876	−	1.41314i	−0.908698	−	0.417455i	$-0.862922\pi$
$701$	−21.6015	−	37.4148i	−0.815876	−	1.41314i	0.0928220	−	0.995683i	$-0.470411\pi$
$702$	1.21937	−	2.11201i	0.0460221	−	0.0797127i
$703$	−11.4588			−0.432178
$704$	−31.2014	−	54.0425i	−1.17595	−	2.03680i
$705$	−1.62281	−	2.81078i	−0.0611184	−	0.105860i
$706$	−70.1134			−2.63875
$707$	−75.1746			−2.82723
$708$	12.2932	+	21.2925i	0.462007	+	0.800220i
$709$	−3.95117	−	6.84363i	−0.148389	−	0.257018i	0.782243	−	0.622974i	$-0.214076\pi$
$709$	−3.95117	−	6.84363i	−0.148389	−	0.257018i	−0.930632	+	0.365955i	$0.880742\pi$
$710$	−15.5191			−0.582420
$711$	2.24806	−	3.89375i	0.0843088	−	0.146027i
$712$	19.1262	+	33.1275i	0.716784	+	1.24151i
$713$	33.8036	−	58.5495i	1.26595	−	2.19270i
$714$	−5.63357	+	9.75764i	−0.210831	+	0.365170i
$715$	−7.79466	−	13.5007i	−0.291504	−	0.504899i
$716$	−3.01715	−	5.22586i	−0.112756	−	0.195299i
$717$	−9.32618	−	16.1534i	−0.348293	−	0.603261i
$718$	33.1759			1.23811
$719$	7.27806	−	12.6060i	0.271426	−	0.470124i	−0.697801	−	0.716291i	$-0.745838\pi$
$719$	7.27806	−	12.6060i	0.271426	−	0.470124i	0.969227	+	0.246168i	$0.0791715\pi$
$720$	1.59738			0.0595310
$721$	56.9086			2.11939
$722$	−19.9803	+	34.6069i	−0.743591	+	1.28794i
$723$	7.22260	−	12.5099i	0.268612	−	0.465249i
$724$	26.1054	+	45.2159i	0.970199	+	1.68043i
$725$	−0.100667	+	0.174361i	−0.00373869	+	0.00647561i
$726$	−26.8557			−0.996707
$727$	12.7048			0.471195			0.235598	−	0.971851i	$-0.424295\pi$
$727$	12.7048			0.471195			0.235598	+	0.971851i	$0.424295\pi$
$728$	6.13612	−	10.6281i	0.227420	−	0.393902i
$729$	1.00000			0.0370370
$730$	42.8056	−	74.1414i	1.58431	−	2.74410i
$731$	−4.98234			−0.184279
$732$	−1.01531	+	1.75857i	−0.0375269	+	0.0649986i
$733$	−8.76849	+	15.1875i	−0.323871	+	0.560962i	−0.981283	−	0.192570i	$-0.938318\pi$
$733$	−8.76849	+	15.1875i	−0.323871	+	0.560962i	0.657412	+	0.753531i	$0.271651\pi$
$734$	−16.4024	+	28.4097i	−0.605422	+	1.04862i
$735$	20.2269	−	35.0339i	0.746079	−	1.29225i
$736$	−57.0594			−2.10324
$737$	18.2719	+	31.6479i	0.673055	+	1.16577i
$738$	3.09542	−	5.36142i	0.113944	−	0.197357i
$739$	−34.1504			−1.25624			−0.628121	−	0.778116i	$-0.716176\pi$
$739$	−34.1504			−1.25624			−0.628121	+	0.778116i	$0.716176\pi$
$740$	93.5275			3.43814
$741$	−0.621901	−	1.07716i	−0.0228461	−	0.0395706i
$742$	4.53008	−	7.84633i	0.166305	−	0.288048i
$743$	2.98042	+	5.16225i	0.109341	+	0.189384i	0.915504	−	0.402310i	$-0.131793\pi$
$743$	2.98042	+	5.16225i	0.109341	+	0.189384i	−0.806162	+	0.591694i	$0.798459\pi$
$744$	−18.6268			−0.682891
$745$	30.7423	+	53.2473i	1.12631	+	1.95083i
$746$	61.2913			2.24403
$747$	6.07345	+	10.5195i	0.222216	+	0.384889i
$748$	−8.21902	+	14.2358i	−0.300517	+	0.520511i
$749$	40.5129	−	70.1704i	1.48031	−	2.56397i
$750$	2.95167	+	5.11244i	0.107780	+	0.186680i
$751$	0.522221	+	0.904514i	0.0190561	+	0.0330062i	0.875396	−	0.483406i	$-0.160601\pi$
$751$	0.522221	+	0.904514i	0.0190561	+	0.0330062i	−0.856340	+	0.516412i	$0.827267\pi$
$752$	−0.283726	+	0.491428i	−0.0103464	+	0.0179205i
$753$	0.921965			0.0335983
$754$	0.0593513	−	0.102799i	0.00216145	−	0.00374373i
$755$	1.22681	−	2.12490i	0.0446483	−	0.0773331i
$756$	14.0618			0.511424
$757$	−14.8339			−0.539148			−0.269574	−	0.962980i	$-0.586883\pi$
$757$	−14.8339			−0.539148			−0.269574	+	0.962980i	$0.586883\pi$
$758$	−27.1260			−0.985260
$759$	−21.8791	+	37.8957i	−0.794161	+	1.37553i
$760$	−4.39414	+	7.61087i	−0.159392	+	0.276075i
$761$	8.31158	+	14.3961i	0.301294	+	0.521857i	0.976429	−	0.215837i	$-0.0692480\pi$
$761$	8.31158	+	14.3961i	0.301294	+	0.521857i	−0.675135	+	0.737694i	$0.735915\pi$
$762$	18.0286			0.653107
$763$	−9.75918	−	16.9034i	−0.353306	−	0.611944i
$764$	−24.4676	−	42.3792i	−0.885207	−	1.53322i
$765$	−1.66773	−	2.88860i	−0.0602970	−	0.104437i
$766$	−18.1779	−	31.4850i	−0.656793	−	1.13760i
$767$	4.25621	−	7.37197i	0.153683	−	0.266186i
$768$	6.21438	+	10.7636i	0.224242	+	0.388399i
$769$	7.54874			0.272215			0.136107	−	0.990694i	$-0.456541\pi$
$769$	7.54874			0.272215			0.136107	+	0.990694i	$0.456541\pi$
$770$	73.8045	−	127.833i	2.65973	−	4.60679i
$771$	−6.11222			−0.220126
$772$	−24.3261	+	42.1340i	−0.875516	+	1.51644i
$773$	1.04580	+	1.81138i	0.0376148	+	0.0651507i	0.884220	−	0.467071i	$-0.154691\pi$
$773$	1.04580	+	1.81138i	0.0376148	+	0.0651507i	−0.846605	+	0.532221i	$0.821357\pi$
$774$	5.10553	+	8.84304i	0.183515	+	0.317857i
$775$	−15.2830	−	26.4709i	−0.548980	−	0.950862i
$776$	−7.26884	+	12.5900i	−0.260936	+	0.451954i
$777$	−44.8527			−1.60908
$778$	10.8584			0.389293
$779$	−1.57872	−	2.73442i	−0.0565635	−	0.0979709i
$780$	5.07598	+	8.79185i	0.181749	+	0.314799i
$781$	10.8580			0.388531
$782$	11.4163	+	19.7735i	0.408245	+	0.707101i
$783$	0.0486737			0.00173946
$784$	−7.07280			−0.252600
$785$	30.9706	−	21.8000i	1.10539	−	0.778075i
$786$	4.37388			0.156011
$787$	−2.25119			−0.0802461			−0.0401230	−	0.999195i	$-0.512775\pi$
$787$	−2.25119			−0.0802461			−0.0401230	+	0.999195i	$0.512775\pi$
$788$	−1.66982	−	2.89221i	−0.0594849	−	0.103031i
$789$	22.3031			0.794012
$790$	15.3674	+	26.6172i	0.546749	+	0.946997i
$791$	19.5962	+	33.9416i	0.696761	+	1.20682i
$792$	12.0560			0.428392
$793$	0.703050			0.0249660
$794$	−6.89825	+	11.9481i	−0.244810	+	0.424023i
$795$	1.34106	+	2.32279i	0.0475625	+	0.0823807i
$796$	27.3465	+	47.3654i	0.969269	+	1.67882i
$797$	−20.7800	−	35.9920i	−0.736064	−	1.27490i	−0.954255	−	0.298995i	$-0.903349\pi$
$797$	−20.7800	−	35.9920i	−0.736064	−	1.27490i	0.218190	−	0.975906i	$-0.429985\pi$
$798$	5.88853	−	10.1992i	0.208452	−	0.361049i
$799$	1.18489			0.0419183
$800$	−12.8986	+	22.3410i	−0.456034	+	0.789874i
$801$	15.1752			0.536189
$802$	−27.2049	−	47.1202i	−0.960638	−	1.66387i
$803$	−29.9493	+	51.8737i	−1.05689	+	1.83058i
$804$	−11.8989	−	20.6095i	−0.419642	−	0.726842i
$805$	−62.4277	−	108.128i	−2.20029	−	3.81101i
$806$	9.01049	+	15.6066i	0.317381	+	0.549720i
$807$	−2.86916	−	4.96954i	−0.100999	−	0.174936i
$808$	41.9716			1.47656
$809$	9.79987	+	16.9739i	0.344545	+	0.596770i	0.985271	−	0.171000i	$-0.0546998\pi$
$809$	9.79987	+	16.9739i	0.344545	+	0.596770i	−0.640726	+	0.767770i	$0.721366\pi$
$810$	−3.41793	+	5.92004i	−0.120094	+	0.208009i
$811$	12.3574	−	21.4036i	0.433926	−	0.751582i	−0.563281	−	0.826265i	$-0.690461\pi$
$811$	12.3574	−	21.4036i	0.433926	−	0.751582i	0.997207	+	0.0746832i	$0.0237946\pi$
$812$	0.684442			0.0240192
$813$	−18.5625			−0.651015
$814$	−107.457			−3.76637
$815$	15.0807	−	26.1206i	0.528255	−	0.914964i
$816$	−0.291581	+	0.505034i	−0.0102074	+	0.0176797i
$817$	5.20783			0.182199
$818$	5.75636	−	9.97031i	0.201266	−	0.348604i
$819$	−2.43427	−	4.21628i	−0.0850604	−	0.147329i
$820$	12.8856	+	22.3185i	0.449984	+	0.779395i
$821$	2.79218	−	4.83619i	0.0974477	−	0.168784i	−0.813180	−	0.582012i	$-0.802265\pi$
$821$	2.79218	−	4.83619i	0.0974477	−	0.168784i	0.910628	+	0.413228i	$0.135599\pi$
$822$	−21.8006	+	37.7598i	−0.760384	+	1.31702i
$823$	−21.8342	−	37.8179i	−0.761092	−	1.31825i	−0.942288	−	0.334803i	$-0.891330\pi$
$823$	−21.8342	−	37.8179i	−0.761092	−	1.31825i	0.181197	−	0.983447i	$-0.442003\pi$
$824$	−31.7733			−1.10688
$825$	9.89177	+	17.1330i	0.344387	+	0.596496i
$826$	80.6007			2.80446
$827$	18.7270	+	32.4361i	0.651202	+	1.12792i	0.982832	+	0.184505i	$0.0590683\pi$
$827$	18.7270	+	32.4361i	0.651202	+	1.12792i	−0.331629	+	0.943410i	$0.607598\pi$
$828$	14.2479	−	24.6781i	0.495150	−	0.857625i
$829$	4.03373	+	6.98663i	0.140097	+	0.242656i	0.927533	−	0.373741i	$-0.121925\pi$
$829$	4.03373	+	6.98663i	0.140097	+	0.242656i	−0.787436	+	0.616397i	$0.788592\pi$
$830$	−83.0346			−2.88217
$831$	−10.4981			−0.364175
$832$	7.03485	−	12.1847i	0.243889	−	0.422429i
$833$	7.38429	+	12.7900i	0.255851	+	0.443146i
$834$	−44.5195			−1.54158
$835$	5.95323	−	10.3113i	0.206020	−	0.356837i
$836$	8.59099	−	14.8800i	0.297126	−	0.514637i
$837$	−3.69473	+	6.39947i	−0.127709	+	0.221198i
$838$	35.5087	−	61.5028i	1.22663	−	2.12458i
$839$	−9.25955			−0.319675			−0.159838	−	0.987143i	$-0.551097\pi$
$839$	−9.25955			−0.319675			−0.159838	+	0.987143i	$0.551097\pi$
$840$	−17.1997	+	29.7908i	−0.593448	+	1.02788i
$841$	−28.9976			−0.999918
$842$	−35.1388	+	60.8622i	−1.21096	+	2.09745i
$843$	2.18703			0.0753254
$844$	−60.1637			−2.07092
$845$	−17.8898	+	30.9860i	−0.615428	+	1.06595i
$846$	−1.21418	−	2.10303i	−0.0417445	−	0.0723036i
$847$	−26.8065	+	46.4302i	−0.921081	+	1.59536i
$848$	0.234467	−	0.406109i	0.00805163	−	0.0139458i
$849$	−14.2407			−0.488738
$850$	10.3228			0.354070
$851$	−45.4463	+	78.7154i	−1.55788	+	2.69833i
$852$	−7.07089			−0.242245
$853$	15.3985	+	26.6709i	0.527233	+	0.913194i	0.999496	+	0.0317367i	$0.0101038\pi$
$853$	15.3985	+	26.6709i	0.527233	+	0.913194i	−0.472263	+	0.881458i	$0.656563\pi$
$854$	3.32845	+	5.76504i	0.113897	+	0.197276i
$855$	1.74321	+	3.01933i	0.0596165	+	0.103259i
$856$	−22.6192	+	39.1777i	−0.773110	+	1.33907i
$857$	25.8543	−	44.7809i	0.883165	−	1.52969i	0.0353634	−	0.999375i	$-0.488741\pi$
$857$	25.8543	−	44.7809i	0.883165	−	1.52969i	0.847802	−	0.530313i	$-0.177926\pi$
$858$	−5.83197	−	10.1013i	−0.199100	−	0.344851i
$859$	−12.4662	+	21.5920i	−0.425340	+	0.736711i	−0.996452	−	0.0841612i	$-0.973179\pi$
$859$	−12.4662	+	21.5920i	−0.425340	+	0.736711i	0.571112	+	0.820872i	$0.306512\pi$
$860$	−42.5065			−1.44946
$861$	−6.17950	−	10.7032i	−0.210597	−	0.364764i
$862$	27.6107	+	47.8231i	0.940424	+	1.62886i
$863$	34.4484			1.17264			0.586318	−	0.810081i	$-0.300577\pi$
$863$	34.4484			1.17264			0.586318	+	0.810081i	$0.300577\pi$
$864$	6.23660			0.212173
$865$	33.5423	+	58.0970i	1.14047	+	1.97536i
$866$	24.5106	+	42.4535i	0.832903	+	1.44263i
$867$	−15.7823			−0.535995
$868$	−51.9547	+	89.9882i	−1.76346	+	3.05440i
$869$	−10.7520	−	18.6229i	−0.364735	−	0.631740i
$870$	−0.166364	+	0.288150i	−0.00564026	+	0.00976921i
$871$	−4.11969	+	7.13551i	−0.139590	+	0.241778i
$872$	5.44877	+	9.43754i	0.184518	+	0.319595i
$873$	2.88364	+	4.99460i	0.0975963	+	0.169042i
$874$	−11.9329	−	20.6684i	−0.403637	−	0.699120i
$875$	11.7850			0.398407
$876$	19.5033	−	33.7808i	0.658956	−	1.14135i
$877$	14.7951			0.499596			0.249798	−	0.968298i	$-0.419636\pi$
$877$	14.7951			0.499596			0.249798	+	0.968298i	$0.419636\pi$
$878$	75.2902			2.54092
$879$	1.98843	−	3.44406i	0.0670681	−	0.116165i
$880$	3.81996	−	6.61636i	0.128771	−	0.223038i
$881$	6.36052	+	11.0167i	0.214291	+	0.371164i	0.953053	−	0.302803i	$-0.0979225\pi$
$881$	6.36052	+	11.0167i	0.214291	+	0.371164i	−0.738762	+	0.673967i	$0.764589\pi$
$882$	15.1337	−	26.2124i	0.509579	−	0.882618i
$883$	36.6160			1.23222			0.616112	−	0.787658i	$-0.288707\pi$
$883$	36.6160			1.23222			0.616112	+	0.787658i	$0.288707\pi$
$884$	−3.70621			−0.124653
$885$	−11.9303	+	20.6639i	−0.401033	+	0.694609i
$886$	61.2221			2.05680
$887$	12.2368	−	21.1947i	0.410870	−	0.711648i	−0.584115	−	0.811671i	$-0.698558\pi$
$887$	12.2368	−	21.1947i	0.410870	−	0.711648i	0.994985	+	0.100023i	$0.0318915\pi$
$888$	25.0423			0.840364
$889$	17.9956	−	31.1692i	0.603552	−	1.04538i
$890$	−51.8678	+	89.8376i	−1.73861	+	3.01136i
$891$	2.39139	−	4.14200i	0.0801144	−	0.138762i
$892$	−2.94059	+	5.09325i	−0.0984582	+	0.170535i
$893$	−1.23851			−0.0414452
$894$	23.0014	+	39.8396i	0.769282	+	1.33244i
$895$	2.92808	−	5.07158i	0.0978749	−	0.169524i
$896$	76.9061			2.56925
$897$	−9.86596			−0.329415
$898$	−4.15371	−	7.19444i	−0.138611	−	0.240082i
$899$	−0.179837	+	0.311486i	−0.00599788	+	0.0103886i
$900$	−6.44164	−	11.1572i	−0.214721	−	0.371908i
$901$	−0.979173			−0.0326210
$902$	−14.8047	−	25.6425i	−0.492942	−	0.853800i
$903$	20.3847			0.678361
$904$	−10.9410	−	18.9504i	−0.363892	−	0.630279i
$905$	−25.3347	+	43.8810i	−0.842154	+	1.45865i
$906$	0.917902	−	1.58985i	0.0304952	−	0.0528193i
$907$	−23.3212	−	40.3935i	−0.774367	−	1.34124i	−0.935150	−	0.354253i	$-0.884735\pi$
$907$	−23.3212	−	40.3935i	−0.774367	−	1.34124i	0.160783	−	0.986990i	$-0.448598\pi$
$908$	−37.8267	−	65.5177i	−1.25532	−	2.17428i
$909$	8.32533	−	14.4199i	0.276134	−	0.478277i
$910$	33.2807			1.10325
$911$	5.39205	−	9.33930i	0.178646	−	0.309425i	−0.762771	−	0.646669i	$-0.776161\pi$
$911$	5.39205	−	9.33930i	0.178646	−	0.309425i	0.941417	+	0.337244i	$0.109495\pi$
$912$	0.304777	−	0.527890i	0.0100922	−	0.0174802i
$913$	58.0959			1.92269
$914$	−11.8283			−0.391245
$915$	−1.97067			−0.0651484
$916$	38.2124	−	66.1859i	1.26257	−	2.18684i
$917$	4.36587	−	7.56191i	0.144174	−	0.249716i
$918$	−1.24780	−	2.16125i	−0.0411835	−	0.0713319i
$919$	−16.4044			−0.541130			−0.270565	−	0.962702i	$-0.587210\pi$
$919$	−16.4044			−0.541130			−0.270565	+	0.962702i	$0.587210\pi$
$920$	34.8548	+	60.3702i	1.14913	+	1.99035i
$921$	6.85903	+	11.8802i	0.226013	+	0.391466i
$922$	15.7232	+	27.2335i	0.517817	+	0.896886i
$923$	1.22406	+	2.12013i	0.0402903	+	0.0697848i
$924$	33.6272	−	58.2441i	1.10626	−	1.91609i
$925$	20.5468	+	35.5881i	0.675574	+	1.17013i
$926$	45.8904			1.50805
$927$	−6.30243	+	10.9161i	−0.206999	+	0.358533i
$928$	0.303559			0.00996480
$929$	1.28350	−	2.22309i	0.0421102	−	0.0729371i	−0.844202	−	0.536025i	$-0.819925\pi$
$929$	1.28350	−	2.22309i	0.0421102	−	0.0729371i	0.886312	+	0.463088i	$0.153259\pi$
$930$	−25.2567	−	43.7459i	−0.828201	−	1.43449i
$931$	−7.71848	−	13.3688i	−0.252963	−	0.438145i
$932$	−36.2083	−	62.7145i	−1.18604	−	2.05428i
$933$	0.431124	−	0.746729i	0.0141144	−	0.0244468i
$934$	59.1232			1.93457
$935$	−15.9528			−0.521711
$936$	1.35911	+	2.35404i	0.0444238	+	0.0769444i
$937$	15.4862	+	26.8229i	0.505913	+	0.876267i	0.999977	+	0.00684099i	$0.00217757\pi$
$937$	15.4862	+	26.8229i	0.505913	+	0.876267i	−0.494064	+	0.869426i	$0.664489\pi$
$938$	−78.0154			−2.54729
$939$	13.6365	+	23.6191i	0.445011	+	0.770782i
$940$	10.1088			0.329712
$941$	39.8639			1.29953			0.649763	−	0.760137i	$-0.274868\pi$
$941$	39.8639			1.29953			0.649763	+	0.760137i	$0.274868\pi$
$942$	23.1722	−	16.3108i	0.754991	−	0.531433i
$943$	−25.0451			−0.815582
$944$	4.17171			0.135778
$945$	6.82335	+	11.8184i	0.221964	+	0.384452i
$946$	48.8372			1.58783
$947$	−22.2804	−	38.5908i	−0.724016	−	1.25403i	−0.959378	−	0.282124i	$-0.908961\pi$
$947$	−22.2804	−	38.5908i	−0.724016	−	1.25403i	0.235362	−	0.971908i	$-0.424372\pi$
$948$	7.00180	+	12.1275i	0.227408	+	0.393882i
$949$	−13.5051			−0.438393
$950$	−10.7900			−0.350074
$951$	−7.31866	+	12.6763i	−0.237324	+	0.411057i
$952$	−6.27918	−	10.8759i	−0.203509	−	0.352488i
$953$	−6.85285	−	11.8695i	−0.221986	−	0.384490i	0.733425	−	0.679770i	$-0.237920\pi$
$953$	−6.85285	−	11.8695i	−0.221986	−	0.384490i	−0.955411	+	0.295280i	$0.904587\pi$
$954$	1.00338	+	1.73791i	0.0324857	+	0.0562669i
$955$	23.7453	−	41.1280i	0.768380	−	1.33087i
$956$	58.0946			1.87892
$957$	0.116398	−	0.201607i	0.00376260	−	0.00651702i
$958$	5.34896			0.172817
$959$	43.5214	+	75.3813i	1.40538	+	2.43419i
$960$	−19.7189	+	34.1542i	−0.636425	+	1.10232i
$961$	−11.8021	−	20.4419i	−0.380714	−	0.659416i
$962$	−12.1139	−	20.9819i	−0.390568	−	0.676484i
$963$	8.97333	+	15.5423i	0.289162	+	0.500843i
$964$	22.4955	+	38.9634i	0.724532	+	1.25493i
$965$	−47.2159			−1.51993
$966$	−46.7084	−	80.9013i	−1.50282	−	2.60296i
$967$	10.1213	−	17.5305i	0.325477	−	0.563744i	−0.656131	−	0.754647i	$-0.727808\pi$
$967$	10.1213	−	17.5305i	0.325477	−	0.563744i	0.981609	+	0.190903i	$0.0611416\pi$
$968$	14.9666	−	25.9230i	0.481046	−	0.833196i
$969$	−1.27280			−0.0408882
$970$	−39.4243			−1.26584
$971$	5.20279			0.166965			0.0834827	−	0.996509i	$-0.473396\pi$
$971$	5.20279			0.166965			0.0834827	+	0.996509i	$0.473396\pi$
$972$	−1.55730	+	2.69732i	−0.0499504	+	0.0865166i
$973$	−44.4380	+	76.9688i	−1.42462	+	2.46751i
$974$	−5.71630			−0.183162
$975$	−2.23025	+	3.86291i	−0.0714252	+	0.123712i
$976$	0.172273	+	0.298386i	0.00551433	+	0.00955110i
$977$	17.1428	+	29.6922i	0.548448	+	0.949939i	0.998381	+	0.0568770i	$0.0181143\pi$
$977$	17.1428	+	29.6922i	0.548448	+	0.949939i	−0.449934	+	0.893062i	$0.648552\pi$
$978$	11.2834	−	19.5434i	0.360804	−	0.624930i
$979$	36.2897	−	62.8556i	1.15982	−	2.00887i
$980$	62.9985	+	109.117i	2.01241	+	3.48560i
$981$	4.32318			0.138029
$982$	9.87781	+	17.1089i	0.315214	+	0.545966i
$983$	−17.8173			−0.568282			−0.284141	−	0.958782i	$-0.591708\pi$
$983$	−17.8173			−0.568282			−0.284141	+	0.958782i	$0.591708\pi$
$984$	3.45015	+	5.97584i	0.109987	+	0.190503i
$985$	1.62052	−	2.80683i	0.0516342	−	0.0894331i
$986$	−0.0607350	−	0.105196i	−0.00193420	−	0.00335013i
$987$	−4.84784			−0.154308
$988$	3.87394			0.123247
$989$	20.6545	−	35.7747i	0.656775	−	1.13757i
$990$	16.3472	+	28.3142i	0.519548	+	0.899884i
$991$	−4.64642			−0.147599			−0.0737993	−	0.997273i	$-0.523512\pi$
$991$	−4.64642			−0.147599			−0.0737993	+	0.997273i	$0.523512\pi$
$992$	−23.0426	+	39.9109i	−0.731603	+	1.26717i
$993$	−6.27084	+	10.8614i	−0.198999	+	0.344676i
$994$	−11.5901	+	20.0746i	−0.367616	+	0.636729i
$995$	−26.5391	+	45.9671i	−0.841347	+	1.45726i
$996$	−37.8327			−1.19878
$997$	−1.61345	+	2.79457i	−0.0510984	+	0.0885050i	−0.890443	−	0.455094i	$-0.849606\pi$
$997$	−1.61345	+	2.79457i	−0.0510984	+	0.0885050i	0.839345	+	0.543599i	$0.182939\pi$
$998$	−10.8185			−0.342452
$999$	4.96729	−	8.60359i	0.157158	−	0.272206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.2	✓	28
157.144	even	3	inner	471.2.e.c.301.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.2	✓	28	1.1	even	1	trivial
471.2.e.c.301.2	yes	28	157.144	even	3	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.26155 q^{2} +(-0.500000 - 0.866025i) q^{3} +3.11460 q^{4} +(1.51133 + 2.61769i) q^{5} +(1.13077 + 1.95856i) q^{6} +4.51481 q^{7} -2.52072 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.26155 q^{2} +(-0.500000 - 0.866025i) q^{3} +3.11460 q^{4} +(1.51133 + 2.61769i) q^{5} +(1.13077 + 1.95856i) q^{6} +4.51481 q^{7} -2.52072 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.41793 - 5.92004i) q^{10} +(2.39139 + 4.14200i) q^{11} +(-1.55730 - 2.69732i) q^{12} +(-0.539175 + 0.933878i) q^{13} -10.2105 q^{14} +(1.51133 - 2.61769i) q^{15} -0.528471 q^{16} +(0.551745 + 0.955651i) q^{17} +(1.13077 - 1.95856i) q^{18} +(-0.576715 - 0.998900i) q^{19} +(4.70717 + 8.15306i) q^{20} +(-2.25741 - 3.90994i) q^{21} +(-5.40823 - 9.36733i) q^{22} -9.14913 q^{23} +(1.26036 + 2.18301i) q^{24} +(-2.06821 + 3.58224i) q^{25} +(1.21937 - 2.11201i) q^{26} +1.00000 q^{27} +14.0618 q^{28} +0.0486737 q^{29} +(-3.41793 + 5.92004i) q^{30} +(-3.69473 + 6.39947i) q^{31} +6.23660 q^{32} +(2.39139 - 4.14200i) q^{33} +(-1.24780 - 2.16125i) q^{34} +(6.82335 + 11.8184i) q^{35} +(-1.55730 + 2.69732i) q^{36} +(4.96729 - 8.60359i) q^{37} +(1.30427 + 2.25906i) q^{38} +1.07835 q^{39} +(-3.80963 - 6.59847i) q^{40} +2.73743 q^{41} +(5.10523 + 8.84252i) q^{42} +(-2.25754 + 3.91017i) q^{43} +(7.44821 + 12.9007i) q^{44} -3.02265 q^{45} +20.6912 q^{46} +(0.536882 - 0.929906i) q^{47} +(0.264235 + 0.457669i) q^{48} +13.3835 q^{49} +(4.67735 - 8.10141i) q^{50} +(0.551745 - 0.955651i) q^{51} +(-1.67931 + 2.90866i) q^{52} +(-0.443671 + 0.768460i) q^{53} -2.26155 q^{54} +(-7.22832 + 12.5198i) q^{55} -11.3806 q^{56} +(-0.576715 + 0.998900i) q^{57} -0.110078 q^{58} -7.89393 q^{59} +(4.70717 - 8.15306i) q^{60} +(-0.325984 - 0.564621i) q^{61} +(8.35582 - 14.4727i) q^{62} +(-2.25741 + 3.90994i) q^{63} -13.0474 q^{64} -3.25947 q^{65} +(-5.40823 + 9.36733i) q^{66} +7.64073 q^{67} +(1.71847 + 2.97647i) q^{68} +(4.57456 + 7.92338i) q^{69} +(-15.4313 - 26.7278i) q^{70} +(1.13512 - 1.96609i) q^{71} +(1.26036 - 2.18301i) q^{72} +(6.26191 + 10.8459i) q^{73} +(-11.2338 + 19.4574i) q^{74} +4.13642 q^{75} +(-1.79624 - 3.11117i) q^{76} +(10.7967 + 18.7004i) q^{77} -2.43874 q^{78} -4.49612 q^{79} +(-0.798692 - 1.38337i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.19084 q^{82} +(6.07345 - 10.5195i) q^{83} +(-7.03091 - 12.1779i) q^{84} +(-1.66773 + 2.88860i) q^{85} +(5.10553 - 8.84304i) q^{86} +(-0.0243369 - 0.0421527i) q^{87} +(-6.02801 - 10.4408i) q^{88} +(-7.58759 - 13.1421i) q^{89} +6.83587 q^{90} +(-2.43427 + 4.21628i) q^{91} -28.4959 q^{92} +7.38947 q^{93} +(-1.21418 + 2.10303i) q^{94} +(1.74321 - 3.01933i) q^{95} +(-3.11830 - 5.40105i) q^{96} +(2.88364 - 4.99460i) q^{97} -30.2675 q^{98} -4.78277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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