LMFDB - Embedded newform 445.2.o.b.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [445,2,Mod(16,445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(445, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("445.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 445 = 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	445.o (of order $11$, degree $10$, 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:	$3.55334288995$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	445.91
Dual form			445.2.o.b.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00203 + 0.587849i) q^{2} +(1.98305 + 1.27443i) q^{3} +(1.98005 - 1.27250i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-4.71930 - 1.38571i) q^{6} +(0.642378 - 0.741344i) q^{7} +(-0.483284 + 0.557740i) q^{8} +(1.06207 + 2.32561i) q^{9} +(0.866784 - 1.89799i) q^{10} +(-0.302339 - 0.348917i) q^{11} +5.54825 q^{12} +(4.53111 + 2.91197i) q^{13} +(-0.850262 + 1.86181i) q^{14} +(-2.26177 + 0.664116i) q^{15} +(-1.31583 + 2.88128i) q^{16} +(-1.60243 - 0.470516i) q^{17} +(-3.49341 - 4.03161i) q^{18} +(3.28300 + 7.18877i) q^{19} +(-0.334965 + 2.32973i) q^{20} +(2.21866 - 0.651456i) q^{21} +(0.810402 + 0.520814i) q^{22} +(0.913420 + 2.00011i) q^{23} +(-1.66918 + 0.490115i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(-10.7832 - 3.16624i) q^{26} +(0.148730 - 1.03444i) q^{27} +(0.328580 - 2.28533i) q^{28} +(-1.70834 + 1.97153i) q^{29} +(4.13773 - 2.65916i) q^{30} +(0.521089 - 1.14103i) q^{31} +(1.15064 - 8.00288i) q^{32} +(-0.154882 - 1.07723i) q^{33} +3.48471 q^{34} +(0.139602 + 0.970954i) q^{35} +(5.06231 + 3.25335i) q^{36} -1.28451 q^{37} +(-10.7986 - 12.4622i) q^{38} +(5.27433 + 11.5492i) q^{39} +(-0.105028 - 0.730484i) q^{40} +(-1.19083 + 0.765303i) q^{41} +(-4.05886 + 2.60847i) q^{42} +(-3.66997 - 4.23537i) q^{43} +(-1.04264 - 0.306148i) q^{44} +(-2.45309 - 0.720293i) q^{45} +(-3.00446 - 3.46733i) q^{46} +(2.38380 - 1.53197i) q^{47} +(-6.28135 + 4.03678i) q^{48} +(0.859263 + 5.97630i) q^{49} +(0.866784 + 1.89799i) q^{50} +(-2.57806 - 2.97524i) q^{51} +12.6773 q^{52} +(-1.51575 - 0.974112i) q^{53} +(0.310333 + 2.15841i) q^{54} +0.461684 q^{55} +(0.103026 + 0.716560i) q^{56} +(-2.65122 + 18.4396i) q^{57} +(2.26118 - 4.95130i) q^{58} +(-5.81674 + 3.73819i) q^{59} +(-3.63333 + 4.19309i) q^{60} +(-1.50404 + 10.4608i) q^{61} +(-0.372485 + 2.59069i) q^{62} +(2.40633 + 0.706563i) q^{63} +(1.49930 + 10.4279i) q^{64} +(-5.16797 + 1.51745i) q^{65} +(0.943327 + 2.06560i) q^{66} +(2.16334 + 1.39029i) q^{67} +(-3.77163 + 1.10745i) q^{68} +(-0.737641 + 5.13041i) q^{69} +(-0.850262 - 1.86181i) q^{70} +(2.53441 + 2.92486i) q^{71} +(-1.81037 - 0.531573i) q^{72} +(3.12139 - 6.83488i) q^{73} +(2.57162 - 0.755096i) q^{74} +(0.979239 - 2.14424i) q^{75} +(15.6482 + 10.0565i) q^{76} -0.452883 q^{77} +(-17.3485 - 20.0213i) q^{78} +(6.05248 - 13.2531i) q^{79} +(-1.31583 - 2.88128i) q^{80} +(6.63602 - 7.65837i) q^{81} +(1.93420 - 2.23219i) q^{82} +(-10.7850 - 3.16677i) q^{83} +(3.56408 - 4.11316i) q^{84} +(1.40496 - 0.902914i) q^{85} +(9.83714 + 6.32195i) q^{86} +(-5.90029 + 1.73248i) q^{87} +0.340721 q^{88} +(9.30401 - 1.56055i) q^{89} +5.33459 q^{90} +(5.06946 - 1.48853i) q^{91} +(4.35376 + 2.79799i) q^{92} +(2.48750 - 1.59862i) q^{93} +(-3.87187 + 4.46837i) q^{94} +(-7.58282 - 2.22652i) q^{95} +(12.4809 - 14.4037i) q^{96} +(9.04805 - 10.4420i) q^{97} +(-5.23344 - 11.4596i) q^{98} +(0.490342 - 1.07370i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 2 q^{3} - 22 q^{4} - 16 q^{5} - 6 q^{6} - 2 q^{7} - 6 q^{8} - 32 q^{9} - 2 q^{10} - q^{11} - 16 q^{12} - 8 q^{13} + 27 q^{14} - 2 q^{15} - 34 q^{16} + 19 q^{17} + 53 q^{18} - 14 q^{19}+ \cdots + 50 q^{99}+O(q^{100}) $ 160 * q - 2 * q^2 - 2 * q^3 - 22 * q^4 - 16 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 - 32 * q^9 - 2 * q^10 - q^11 - 16 * q^12 - 8 * q^13 + 27 * q^14 - 2 * q^15 - 34 * q^16 + 19 * q^17 + 53 * q^18 - 14 * q^19 - 22 * q^20 - 26 * q^21 + 34 * q^22 + 33 * q^23 + 50 * q^24 - 16 * q^25 - 35 * q^26 + 7 * q^27 + 49 * q^28 - 17 * q^29 - 6 * q^30 + 20 * q^31 + 11 * q^32 - 20 * q^33 + 2 * q^34 - 2 * q^35 - 102 * q^36 + 130 * q^37 - 19 * q^38 + 3 * q^39 - 6 * q^40 - 52 * q^41 - 92 * q^42 - 26 * q^43 + 14 * q^44 + q^45 + 102 * q^46 - 4 * q^47 + 3 * q^48 - 68 * q^49 - 2 * q^50 + 46 * q^51 - 66 * q^52 - 2 * q^53 - 79 * q^54 + 32 * q^55 + 199 * q^56 - 86 * q^57 - 74 * q^58 - 47 * q^59 - 16 * q^60 - 24 * q^61 + 41 * q^62 + 94 * q^63 + 70 * q^64 + 25 * q^65 - 130 * q^66 + 21 * q^67 - 57 * q^68 + 64 * q^69 + 27 * q^70 - 26 * q^71 - 66 * q^72 + 12 * q^73 - 70 * q^74 - 2 * q^75 - 137 * q^76 - 100 * q^77 - 170 * q^78 - 59 * q^79 - 34 * q^80 - 84 * q^81 + 359 * q^82 - 39 * q^83 + 202 * q^84 - 14 * q^85 - 108 * q^86 + 133 * q^87 + 48 * q^88 + 42 * q^90 + 22 * q^91 + 57 * q^92 + 69 * q^93 - 74 * q^94 - 3 * q^95 - 116 * q^96 - 37 * q^97 + 3 * q^98 + 50 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/445\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

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 $

$2$	−2.00203	+	0.587849i	−1.41565	+	0.415672i	−0.898028	−	0.439938i	$-0.855000\pi$
$2$	−2.00203	+	0.587849i	−1.41565	+	0.415672i	−0.517621	+	0.855610i	$0.673182\pi$
$3$	1.98305	+	1.27443i	1.14491	+	0.735792i	0.968620	−	0.248546i	$-0.0799526\pi$
$3$	1.98305	+	1.27443i	1.14491	+	0.735792i	0.176294	+	0.984338i	$0.443589\pi$
$4$	1.98005	−	1.27250i	0.990026	−	0.636251i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−4.71930	−	1.38571i	−1.92665	−	0.565714i
$7$	0.642378	−	0.741344i	0.242796	−	0.280202i	−0.621252	−	0.783611i	$-0.713376\pi$
$7$	0.642378	−	0.741344i	0.242796	−	0.280202i	0.864048	+	0.503409i	$0.167921\pi$
$8$	−0.483284	+	0.557740i	−0.170867	+	0.197191i
$9$	1.06207	+	2.32561i	0.354024	+	0.775205i
$10$	0.866784	−	1.89799i	0.274101	−	0.600198i
$11$	−0.302339	−	0.348917i	−0.0911585	−	0.105203i	0.708338	−	0.705874i	$-0.249445\pi$
$11$	−0.302339	−	0.348917i	−0.0911585	−	0.105203i	−0.799496	+	0.600671i	$0.794900\pi$
$12$	5.54825			1.60164
$13$	4.53111	+	2.91197i	1.25671	+	0.807635i	0.987830	−	0.155540i	$-0.0497116\pi$
$13$	4.53111	+	2.91197i	1.25671	+	0.807635i	0.268876	+	0.963175i	$0.413348\pi$
$14$	−0.850262	+	1.86181i	−0.227242	+	0.497591i
$15$	−2.26177	+	0.664116i	−0.583987	+	0.171474i
$16$	−1.31583	+	2.88128i	−0.328959	+	0.720319i
$17$	−1.60243	−	0.470516i	−0.388647	−	0.114117i	0.0815708	−	0.996668i	$-0.474006\pi$
$17$	−1.60243	−	0.470516i	−0.388647	−	0.114117i	−0.470217	+	0.882551i	$0.655825\pi$
$18$	−3.49341	−	4.03161i	−0.823405	−	0.950260i
$19$	3.28300	+	7.18877i	0.753172	+	1.64922i	0.760580	+	0.649244i	$0.224915\pi$
$19$	3.28300	+	7.18877i	0.753172	+	1.64922i	−0.00740805	+	0.999973i	$0.502358\pi$
$20$	−0.334965	+	2.32973i	−0.0749005	+	0.520945i
$21$	2.21866	−	0.651456i	0.484151	−	0.142159i
$22$	0.810402	+	0.520814i	0.172778	+	0.111038i
$23$	0.913420	+	2.00011i	0.190461	+	0.417052i	0.980639	−	0.195826i	$-0.0627389\pi$
$23$	0.913420	+	2.00011i	0.190461	+	0.417052i	−0.790177	+	0.612878i	$0.790012\pi$
$24$	−1.66918	+	0.490115i	−0.340719	+	0.100044i
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−10.7832	−	3.16624i	−2.11477	−	0.620951i
$27$	0.148730	−	1.03444i	0.0286231	−	0.199078i
$28$	0.328580	−	2.28533i	0.0620958	−	0.431886i
$29$	−1.70834	+	1.97153i	−0.317230	+	0.366103i	−0.891861	−	0.452310i	$-0.850600\pi$
$29$	−1.70834	+	1.97153i	−0.317230	+	0.366103i	0.574631	+	0.818413i	$0.305146\pi$
$30$	4.13773	−	2.65916i	0.755443	−	0.485494i
$31$	0.521089	−	1.14103i	0.0935904	−	0.204934i	−0.857047	−	0.515238i	$-0.827703\pi$
$31$	0.521089	−	1.14103i	0.0935904	−	0.204934i	0.950637	+	0.310304i	$0.100431\pi$
$32$	1.15064	−	8.00288i	0.203406	−	1.41472i
$33$	−0.154882	−	1.07723i	−0.0269615	−	0.187522i
$34$	3.48471			0.597623
$35$	0.139602	+	0.970954i	0.0235971	+	0.164121i
$36$	5.06231	+	3.25335i	0.843718	+	0.542225i
$37$	−1.28451			−0.211172			−0.105586	−	0.994410i	$-0.533672\pi$
$37$	−1.28451			−0.211172			−0.105586	+	0.994410i	$0.533672\pi$
$38$	−10.7986	−	12.4622i	−1.75176	−	2.02164i
$39$	5.27433	+	11.5492i	0.844568	+	1.84935i
$40$	−0.105028	−	0.730484i	−0.0166063	−	0.115500i
$41$	−1.19083	+	0.765303i	−0.185977	+	0.119520i	−0.630316	−	0.776338i	$-0.717075\pi$
$41$	−1.19083	+	0.765303i	−0.185977	+	0.119520i	0.444339	+	0.895859i	$0.353438\pi$
$42$	−4.05886	+	2.60847i	−0.626296	+	0.402496i
$43$	−3.66997	−	4.23537i	−0.559665	−	0.645887i	0.403443	−	0.915005i	$-0.367813\pi$
$43$	−3.66997	−	4.23537i	−0.559665	−	0.645887i	−0.963107	+	0.269118i	$0.913268\pi$
$44$	−1.04264	−	0.306148i	−0.157185	−	0.0461535i
$45$	−2.45309	−	0.720293i	−0.365685	−	0.107375i
$46$	−3.00446	−	3.46733i	−0.442983	−	0.511230i
$47$	2.38380	−	1.53197i	0.347713	−	0.223461i	−0.355113	−	0.934823i	$-0.615558\pi$
$47$	2.38380	−	1.53197i	0.347713	−	0.223461i	0.702826	+	0.711362i	$0.251921\pi$
$48$	−6.28135	+	4.03678i	−0.906634	+	0.582658i
$49$	0.859263	+	5.97630i	0.122752	+	0.853758i
$50$	0.866784	+	1.89799i	0.122582	+	0.268417i
$51$	−2.57806	−	2.97524i	−0.361001	−	0.416617i
$52$	12.6773			1.75803
$53$	−1.51575	−	0.974112i	−0.208204	−	0.133805i	0.432383	−	0.901690i	$-0.357673\pi$
$53$	−1.51575	−	0.974112i	−0.208204	−	0.133805i	−0.640587	+	0.767885i	$0.721309\pi$
$54$	0.310333	+	2.15841i	0.0422310	+	0.293723i
$55$	0.461684			0.0622534
$56$	0.103026	+	0.716560i	0.0137674	+	0.0957543i
$57$	−2.65122	+	18.4396i	−0.351163	+	2.44239i
$58$	2.26118	−	4.95130i	0.296908	−	0.650137i
$59$	−5.81674	+	3.73819i	−0.757275	+	0.486671i	−0.861421	−	0.507891i	$-0.830425\pi$
$59$	−5.81674	+	3.73819i	−0.757275	+	0.486671i	0.104147	+	0.994562i	$0.466789\pi$
$60$	−3.63333	+	4.19309i	−0.469061	+	0.541326i
$61$	−1.50404	+	10.4608i	−0.192572	+	1.33937i	0.632595	+	0.774483i	$0.281990\pi$
$61$	−1.50404	+	10.4608i	−0.192572	+	1.33937i	−0.825168	+	0.564888i	$0.808919\pi$
$62$	−0.372485	+	2.59069i	−0.0473057	+	0.329018i
$63$	2.40633	+	0.706563i	0.303169	+	0.0890185i
$64$	1.49930	+	10.4279i	0.187413	+	1.30348i
$65$	−5.16797	+	1.51745i	−0.641008	+	0.188217i
$66$	0.943327	+	2.06560i	0.116116	+	0.254258i
$67$	2.16334	+	1.39029i	0.264294	+	0.169851i	0.666076	−	0.745884i	$-0.267973\pi$
$67$	2.16334	+	1.39029i	0.264294	+	0.169851i	−0.401782	+	0.915735i	$0.631609\pi$
$68$	−3.77163	+	1.10745i	−0.457377	+	0.134298i
$69$	−0.737641	+	5.13041i	−0.0888015	+	0.617628i
$70$	−0.850262	−	1.86181i	−0.101626	−	0.222529i
$71$	2.53441	+	2.92486i	0.300779	+	0.347118i	0.885940	−	0.463799i	$-0.153514\pi$
$71$	2.53441	+	2.92486i	0.300779	+	0.347118i	−0.585161	+	0.810917i	$0.698969\pi$
$72$	−1.81037	−	0.531573i	−0.213354	−	0.0626465i
$73$	3.12139	−	6.83488i	0.365331	−	0.799962i	−0.634308	−	0.773080i	$-0.718715\pi$
$73$	3.12139	−	6.83488i	0.365331	−	0.799962i	0.999639	−	0.0268820i	$-0.00855783\pi$
$74$	2.57162	−	0.755096i	0.298945	−	0.0877781i
$75$	0.979239	−	2.14424i	0.113073	−	0.247595i
$76$	15.6482	+	10.0565i	1.79498	+	1.15356i
$77$	−0.452883			−0.0516108
$78$	−17.3485	−	20.0213i	−1.96433	−	2.26696i
$79$	6.05248	−	13.2531i	0.680957	−	1.49109i	−0.180669	−	0.983544i	$-0.557826\pi$
$79$	6.05248	−	13.2531i	0.680957	−	1.49109i	0.861626	−	0.507544i	$-0.169446\pi$
$80$	−1.31583	−	2.88128i	−0.147115	−	0.322136i
$81$	6.63602	−	7.65837i	0.737335	−	0.850930i
$82$	1.93420	−	2.23219i	0.213597	−	0.246504i
$83$	−10.7850	−	3.16677i	−1.18381	−	0.347598i	−0.370168	−	0.928965i	$-0.620700\pi$
$83$	−10.7850	−	3.16677i	−1.18381	−	0.347598i	−0.813641	+	0.581367i	$0.802518\pi$
$84$	3.56408	−	4.11316i	0.388872	−	0.448783i
$85$	1.40496	−	0.902914i	0.152390	−	0.0979348i
$86$	9.83714	+	6.32195i	1.06077	+	0.681713i
$87$	−5.90029	+	1.73248i	−0.632577	+	0.185741i
$88$	0.340721			0.0363210
$89$	9.30401	−	1.56055i	0.986224	−	0.165418i
$89$	9.30401	−	1.56055i	0.986224	−	0.165418i
$90$	5.33459			0.562315
$91$	5.06946	−	1.48853i	0.531424	−	0.156040i
$92$	4.35376	+	2.79799i	0.453911	+	0.291711i
$93$	2.48750	−	1.59862i	0.257942	−	0.165769i
$94$	−3.87187	+	4.46837i	−0.399352	+	0.460877i
$95$	−7.58282	−	2.22652i	−0.777981	−	0.228436i
$96$	12.4809	−	14.4037i	1.27382	−	1.47007i
$97$	9.04805	−	10.4420i	0.918690	−	1.06023i	−0.0792994	−	0.996851i	$-0.525268\pi$
$97$	9.04805	−	10.4420i	0.918690	−	1.06023i	0.997990	−	0.0633745i	$-0.0201862\pi$
$98$	−5.23344	−	11.4596i	−0.528657	−	1.15760i
$99$	0.490342	−	1.07370i	0.0492812	−	0.107911i
$100$	−1.54134	−	1.77880i	−0.154134	−	0.177880i
$101$	−16.0315			−1.59520			−0.797598	−	0.603190i	$-0.793896\pi$
$101$	−16.0315			−1.59520			−0.797598	+	0.603190i	$0.793896\pi$
$102$	6.91035	+	4.44101i	0.684227	+	0.439726i
$103$	−0.803642	+	1.75973i	−0.0791852	+	0.173391i	−0.945084	−	0.326828i	$-0.894020\pi$
$103$	−0.803642	+	1.75973i	−0.0791852	+	0.173391i	0.865899	+	0.500220i	$0.166747\pi$
$104$	−3.81394	+	1.11987i	−0.373988	+	0.109813i
$105$	−0.960573	+	2.10336i	−0.0937424	+	0.205267i
$106$	3.60720	+	1.05917i	0.350363	+	0.102876i
$107$	7.60167	+	8.77279i	0.734881	+	0.848098i	0.993012	−	0.118012i	$-0.0376521\pi$
$107$	7.60167	+	8.77279i	0.734881	+	0.848098i	−0.258131	+	0.966110i	$0.583107\pi$
$108$	−1.02183	−	2.23751i	−0.0983261	−	0.215304i
$109$	1.24941	−	8.68982i	0.119672	−	0.832334i	−0.838246	−	0.545292i	$-0.816419\pi$
$109$	1.24941	−	8.68982i	0.119672	−	0.832334i	0.957918	−	0.287042i	$-0.0926720\pi$
$110$	−0.924305	+	0.271400i	−0.0881290	+	0.0258770i
$111$	−2.54724	−	1.63701i	−0.241773	−	0.155378i
$112$	1.29075	+	2.82635i	0.121965	+	0.267065i
$113$	12.8929	−	3.78571i	1.21287	−	0.356129i	0.388107	−	0.921614i	$-0.373129\pi$
$113$	12.8929	−	3.78571i	1.21287	−	0.356129i	0.824759	+	0.565485i	$0.191311\pi$
$114$	−5.53190	−	38.4752i	−0.518110	−	3.60354i
$115$	−2.10974	−	0.619477i	−0.196735	−	0.0577665i
$116$	−0.873825	+	6.07758i	−0.0811326	+	0.564290i
$117$	−1.95975	+	13.6304i	−0.181179	+	1.26013i
$118$	9.44779	−	10.9033i	0.869740	−	1.00373i
$119$	−1.37818	+	0.885703i	−0.126338	+	0.0811923i
$120$	0.722675	−	1.58244i	0.0659709	−	0.144456i
$121$	1.53513	−	10.6771i	0.139557	−	0.970641i
$122$	−3.13825	−	21.8270i	−0.284124	−	1.97613i
$123$	−3.33681			−0.300870
$124$	−0.420175	−	2.92238i	−0.0377328	−	0.262437i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−5.23290			−0.466184
$127$	−10.3684	−	11.9658i	−0.920045	−	1.06179i	−0.997897	−	0.0648241i	$-0.979351\pi$
$127$	−10.3684	−	11.9658i	−0.920045	−	1.06179i	0.0778512	−	0.996965i	$-0.475194\pi$
$128$	−2.41424	−	5.28646i	−0.213391	−	0.467261i
$129$	−1.88005	−	13.0761i	−0.165529	−	1.15128i
$130$	9.45440	−	6.07597i	0.829206	−	0.532898i
$131$	−2.89965	+	1.86349i	−0.253343	+	0.162814i	−0.661148	−	0.750255i	$-0.729931\pi$
$131$	−2.89965	+	1.86349i	−0.253343	+	0.162814i	0.407805	+	0.913069i	$0.366294\pi$
$132$	−1.67745	−	1.93588i	−0.146003	−	0.168497i
$133$	7.43827	+	2.18407i	0.644980	+	0.189383i
$134$	−5.14835	−	1.51169i	−0.444749	−	0.130590i
$135$	0.684381	+	0.789818i	0.0589021	+	0.0679767i
$136$	1.03686	−	0.666347i	0.0889097	−	0.0571388i
$137$	18.0174	−	11.5791i	1.53933	−	0.989267i	0.551421	−	0.834227i	$-0.314086\pi$
$137$	18.0174	−	11.5791i	1.53933	−	0.989267i	0.987908	−	0.155039i	$-0.0495504\pi$
$138$	−1.53912	−	10.7048i	−0.131019	−	0.911257i
$139$	2.59156	+	5.67474i	0.219814	+	0.481325i	0.987125	−	0.159950i	$-0.0511332\pi$
$139$	2.59156	+	5.67474i	0.219814	+	0.481325i	−0.767311	+	0.641275i	$0.778406\pi$
$140$	1.51196	+	1.74489i	0.127784	+	0.147470i
$141$	6.67958			0.562522
$142$	−6.79334	−	4.36582i	−0.570085	−	0.366371i
$143$	−0.353894	−	2.46139i	−0.0295941	−	0.205831i
$144$	−8.09825			−0.674854
$145$	−0.371257	−	2.58215i	−0.0308312	−	0.214436i
$146$	−2.23123	+	15.5185i	−0.184658	+	1.28432i
$147$	−5.91241	+	12.9464i	−0.487648	+	1.06780i
$148$	−2.54339	+	1.63454i	−0.209065	+	0.134358i
$149$	−0.0398143	+	0.0459482i	−0.00326172	+	0.00376422i	−0.757378	−	0.652977i	$-0.773520\pi$
$149$	−0.0398143	+	0.0459482i	−0.00326172	+	0.00376422i	0.754116	+	0.656741i	$0.228065\pi$
$150$	−0.699980	+	4.86847i	−0.0571531	+	0.397509i
$151$	0.925790	−	6.43901i	0.0753397	−	0.523999i	−0.916847	−	0.399238i	$-0.869275\pi$
$151$	0.925790	−	6.43901i	0.0753397	−	0.523999i	0.992187	−	0.124761i	$-0.0398164\pi$
$152$	−5.59609	−	1.64316i	−0.453903	−	0.133278i
$153$	−0.607659	−	4.22636i	−0.0491263	−	0.341681i
$154$	0.906686	−	0.266227i	0.0730628	−	0.0214532i
$155$	0.521089	+	1.14103i	0.0418549	+	0.0916495i
$156$	25.1398	+	16.1564i	2.01279	+	1.29354i
$157$	−21.6996	+	6.37157i	−1.73181	+	0.508507i	−0.987268	−	0.159065i	$-0.949152\pi$
$157$	−21.6996	+	6.37157i	−1.73181	+	0.508507i	−0.744546	+	0.667571i	$0.767334\pi$
$158$	−4.32643	+	30.0910i	−0.344193	+	2.39391i
$159$	−1.76437	−	3.86343i	−0.139923	−	0.306390i
$160$	5.29467	+	6.11037i	0.418580	+	0.483067i
$161$	2.06953	+	0.607669i	0.163102	+	0.0478910i
$162$	−8.78354	+	19.2333i	−0.690100	+	1.51111i
$163$	20.8462	−	6.12101i	1.63280	−	0.479434i	0.668385	−	0.743815i	$-0.266986\pi$
$163$	20.8462	−	6.12101i	1.63280	−	0.479434i	0.964418	+	0.264381i	$0.0851676\pi$
$164$	−1.38406	+	3.03068i	−0.108077	+	0.236656i
$165$	0.915542	+	0.588383i	0.0712749	+	0.0458056i
$166$	23.4535			1.82035
$167$	1.24848	+	1.44083i	0.0966106	+	0.111495i	0.801996	−	0.597329i	$-0.203771\pi$
$167$	1.24848	+	1.44083i	0.0966106	+	0.111495i	−0.705385	+	0.708824i	$0.749226\pi$
$168$	−0.708899	+	1.55227i	−0.0546927	+	0.119760i
$169$	6.65103	+	14.5637i	0.511618	+	1.12029i
$170$	−2.28200	+	2.63357i	−0.175021	+	0.201985i
$171$	−13.2315	+	15.2700i	−1.01184	+	1.16773i
$172$	−12.6562	−	3.71621i	−0.965029	−	0.283358i
$173$	−1.03608	+	1.19570i	−0.0787719	+	0.0909077i	−0.793767	−	0.608221i	$-0.791883\pi$
$173$	−1.03608	+	1.19570i	−0.0787719	+	0.0909077i	0.714995	+	0.699129i	$0.246429\pi$
$174$	10.7941	−	6.93696i	0.818300	−	0.525889i
$175$	−0.825218	−	0.530335i	−0.0623806	−	0.0400896i
$176$	1.40316	−	0.412003i	0.105767	−	0.0310559i
$177$	−16.2989			−1.22510
$178$	−17.7095	+	8.59363i	−1.32739	+	0.644120i
$179$	1.14787			0.0857957			0.0428979	−	0.999079i	$-0.486341\pi$
$179$	1.14787			0.0857957			0.0428979	+	0.999079i	$0.486341\pi$
$180$	−5.77382	+	1.69535i	−0.430355	+	0.126364i
$181$	−4.63266	−	2.97723i	−0.344343	−	0.221296i	0.357026	−	0.934095i	$-0.383791\pi$
$181$	−4.63266	−	2.97723i	−0.344343	−	0.221296i	−0.701369	+	0.712799i	$0.747427\pi$
$182$	−9.27418	+	5.96015i	−0.687448	+	0.441796i
$183$	−16.3142	+	18.8275i	−1.20598	+	1.39177i
$184$	−1.55698	−	0.457171i	−0.114782	−	0.0337031i
$185$	0.841173	−	0.970765i	0.0618443	−	0.0713721i
$186$	−4.04031	+	4.66276i	−0.296250	+	0.341890i
$187$	0.320306	+	0.701371i	0.0234231	+	0.0512894i
$188$	2.77060	−	6.06677i	0.202067	−	0.442465i
$189$	−0.671335	−	0.774762i	−0.0488324	−	0.0563556i
$190$	16.4899			1.19630
$191$	6.33443	+	4.07089i	0.458343	+	0.294559i	0.749365	−	0.662157i	$-0.230359\pi$
$191$	6.33443	+	4.07089i	0.458343	+	0.294559i	−0.291022	+	0.956716i	$0.593995\pi$
$192$	−10.3164	+	22.5897i	−0.744520	+	1.63027i
$193$	−0.0857105	+	0.0251669i	−0.00616958	+	0.00181155i	−0.284816	−	0.958582i	$-0.591932\pi$
$193$	−0.0857105	+	0.0251669i	−0.00616958	+	0.00181155i	0.278646	+	0.960394i	$0.410114\pi$
$194$	−11.9761	+	26.2241i	−0.859837	+	1.88278i
$195$	−12.1822	−	3.57702i	−0.872387	−	0.256156i
$196$	9.30624	+	10.7400i	0.664732	+	0.767141i
$197$	−9.23331	−	20.2181i	−0.657846	−	1.44048i	−0.884516	−	0.466510i	$-0.845511\pi$
$197$	−9.23331	−	20.2181i	−0.657846	−	1.44048i	0.226670	−	0.973972i	$-0.427216\pi$
$198$	−0.350506	+	2.43782i	−0.0249094	+	0.173249i
$199$	−18.5257	+	5.43965i	−1.31326	+	0.385607i	−0.862054	−	0.506816i	$-0.830822\pi$
$199$	−18.5257	+	5.43965i	−1.31326	+	0.385607i	−0.451201	+	0.892422i	$0.649004\pi$
$200$	0.620842	+	0.398991i	0.0439001	+	0.0282129i
$201$	2.51818	+	5.51404i	0.177618	+	0.388930i
$202$	32.0956	−	9.42411i	2.25824	−	0.663078i
$203$	0.364180	+	2.53293i	0.0255604	+	0.177777i
$204$	−8.89070	−	2.61054i	−0.622473	−	0.182775i
$205$	0.201453	−	1.40114i	0.0140701	−	0.0978598i
$206$	0.574460	−	3.99545i	0.0400245	−	0.278376i
$207$	−3.68137	+	4.24852i	−0.255873	+	0.295293i
$208$	−14.3524	+	9.22372i	−0.995159	+	0.639550i
$209$	1.51571	−	3.31894i	0.104844	−	0.229576i
$210$	0.686637	−	4.77567i	0.0473825	−	0.329552i
$211$	−0.985153	−	6.85189i	−0.0678207	−	0.471704i	−0.995222	−	0.0976360i	$-0.968872\pi$
$211$	−0.985153	−	6.85189i	−0.0678207	−	0.471704i	0.927401	−	0.374068i	$-0.122037\pi$
$212$	−4.24082			−0.291261
$213$	1.29833	+	9.03008i	0.0889600	+	0.618731i
$214$	−20.3758	−	13.0948i	−1.39286	−	0.895139i
$215$	5.60419			0.382203
$216$	0.505070	+	0.582882i	0.0343657	+	0.0396601i
$217$	−0.511156	−	1.11928i	−0.0346996	−	0.0759814i
$218$	2.60695	+	18.1317i	0.176565	+	1.22804i
$219$	14.9004	−	9.57593i	1.00688	−	0.647081i
$220$	0.914158	−	0.587494i	0.0616325	−	0.0396088i
$221$	−5.89067	−	6.79820i	−0.396249	−	0.457296i
$222$	6.06197	+	1.77995i	0.406853	+	0.119463i
$223$	25.3356	+	7.43921i	1.69660	+	0.498166i	0.979946	−	0.199265i	$-0.0638553\pi$
$223$	25.3356	+	7.43921i	1.69660	+	0.498166i	0.716652	+	0.697431i	$0.245674\pi$
$224$	−5.19374	−	5.99389i	−0.347021	−	0.400484i
$225$	2.15079	−	1.38223i	0.143386	−	0.0921488i
$226$	−23.5866	+	15.1582i	−1.56896	+	1.00831i
$227$	−1.16630	−	8.11179i	−0.0774100	−	0.538399i	−0.991217	−	0.132249i	$-0.957780\pi$
$227$	−1.16630	−	8.11179i	−0.0774100	−	0.538399i	0.913807	−	0.406150i	$-0.133129\pi$
$228$	18.2149	+	39.8851i	1.20631	+	2.64146i
$229$	8.69587	+	10.0356i	0.574639	+	0.663169i	0.966443	−	0.256880i	$-0.0826944\pi$
$229$	8.69587	+	10.0356i	0.574639	+	0.663169i	−0.391804	+	0.920049i	$0.628149\pi$
$230$	4.58793			0.302519
$231$	−0.898090	−	0.577167i	−0.0590900	−	0.0379748i
$232$	−0.273986	−	1.90562i	−0.0179881	−	0.125110i
$233$	−7.15251			−0.468576			−0.234288	−	0.972167i	$-0.575276\pi$
$233$	−7.15251			−0.468576			−0.234288	+	0.972167i	$0.575276\pi$
$234$	−4.08911	−	28.4404i	−0.267314	−	1.85921i
$235$	−0.403267	+	2.80478i	−0.0263062	+	0.182964i
$236$	−6.76059	+	14.8036i	−0.440077	+	0.963634i
$237$	28.8925	−	18.5681i	1.87677	−	1.20612i
$238$	2.23850	−	2.58337i	0.145100	−	0.167455i
$239$	1.64000	−	11.4064i	0.106083	−	0.737822i	−0.865464	−	0.500972i	$-0.832976\pi$
$239$	1.64000	−	11.4064i	0.106083	−	0.737822i	0.971546	−	0.236850i	$-0.0761149\pi$
$240$	1.06262	−	7.39065i	0.0685915	−	0.477064i
$241$	−21.1708	−	6.21630i	−1.36373	−	0.400427i	−0.483654	−	0.875259i	$-0.660691\pi$
$241$	−21.1708	−	6.21630i	−1.36373	−	0.400427i	−0.880076	+	0.474832i	$0.842509\pi$
$242$	3.20312	+	22.2782i	0.205905	+	1.43210i
$243$	19.9114	−	5.84651i	1.27732	−	0.375054i
$244$	10.3333	+	22.6269i	0.661524	+	1.44854i
$245$	−5.07929	−	3.26426i	−0.324504	−	0.208546i
$246$	6.68039	−	1.96154i	0.425926	−	0.125063i
$247$	−6.05783	+	42.1331i	−0.385451	+	2.68087i
$248$	0.384562	+	0.842073i	0.0244197	+	0.0534717i
$249$	−17.3514	−	20.0246i	−1.09960	−	1.26901i
$250$	−2.00203	−	0.587849i	−0.126620	−	0.0371788i
$251$	3.30974	−	7.24732i	0.208909	−	0.457447i	−0.775952	−	0.630792i	$-0.782730\pi$
$251$	3.30974	−	7.24732i	0.208909	−	0.457447i	0.984861	+	0.173345i	$0.0554575\pi$
$252$	5.66376	−	1.66303i	0.356784	−	0.104761i
$253$	0.421711	−	0.923418i	0.0265127	−	0.0580548i
$254$	27.7919	+	17.8608i	1.74382	+	1.12068i
$255$	3.93681			0.246533
$256$	−5.85701	−	6.75935i	−0.366063	−	0.422459i
$257$	11.9330	−	26.1295i	0.744357	−	1.62991i	−0.0318946	−	0.999491i	$-0.510154\pi$
$257$	11.9330	−	26.1295i	0.744357	−	1.62991i	0.776252	−	0.630423i	$-0.217119\pi$
$258$	11.4507	+	25.0735i	0.712887	+	1.56101i
$259$	−0.825139	+	0.952261i	−0.0512716	+	0.0591706i
$260$	−8.30189	+	9.58089i	−0.514861	+	0.594181i
$261$	−6.39939	−	1.87903i	−0.396112	−	0.116309i
$262$	4.70973	−	5.43532i	0.290968	−	0.335795i
$263$	−8.91090	+	5.72669i	−0.549470	+	0.353123i	−0.785732	−	0.618567i	$-0.787714\pi$
$263$	−8.91090	+	5.72669i	−0.549470	+	0.353123i	0.236263	+	0.971689i	$0.424077\pi$
$264$	0.675666	+	0.434224i	0.0415844	+	0.0267247i
$265$	1.72879	−	0.507618i	0.106199	−	0.0311827i
$266$	−16.1756			−0.991787
$267$	20.4391	+	8.76265i	1.25085	+	0.536266i
$268$	6.05267			0.369725
$269$	−23.5592	+	6.91759i	−1.43643	+	0.421773i	−0.905029	−	0.425349i	$-0.860151\pi$
$269$	−23.5592	+	6.91759i	−1.43643	+	0.421773i	−0.531398	+	0.847122i	$0.678333\pi$
$270$	−1.83444	−	1.17893i	−0.111641	−	0.0717471i
$271$	7.47419	−	4.80337i	0.454025	−	0.291784i	−0.293572	−	0.955937i	$-0.594844\pi$
$271$	7.47419	−	4.80337i	0.454025	−	0.291784i	0.747597	+	0.664153i	$0.231208\pi$
$272$	3.46422	−	3.99793i	0.210049	−	0.242410i
$273$	11.9500	+	3.50884i	0.723248	+	0.212365i
$274$	−29.2646	+	33.7731i	−1.76794	+	2.04031i
$275$	−0.302339	+	0.348917i	−0.0182317	+	0.0210405i
$276$	5.06788	+	11.0971i	0.305051	+	0.667968i
$277$	3.32025	−	7.27034i	0.199495	−	0.436832i	−0.783273	−	0.621678i	$-0.786451\pi$
$277$	3.32025	−	7.27034i	0.199495	−	0.436832i	0.982768	+	0.184846i	$0.0591785\pi$
$278$	−8.52428	−	9.83754i	−0.511252	−	0.590017i
$279$	3.20702			0.191999
$280$	−0.609007	−	0.391385i	−0.0363951	−	0.0233897i
$281$	−0.978431	+	2.14247i	−0.0583683	+	0.127809i	−0.936569	−	0.350484i	$-0.886017\pi$
$281$	−0.978431	+	2.14247i	−0.0583683	+	0.127809i	0.878200	+	0.478293i	$0.158744\pi$
$282$	−13.3727	+	3.92659i	−0.796334	+	0.233825i
$283$	−8.22669	+	18.0139i	−0.489026	+	1.07082i	0.490856	+	0.871241i	$0.336684\pi$
$283$	−8.22669	+	18.0139i	−0.489026	+	1.07082i	−0.979882	+	0.199577i	$0.936043\pi$
$284$	8.74016	+	2.56634i	0.518633	+	0.152284i
$285$	−12.1996	−	14.0791i	−0.722640	−	0.833971i
$286$	2.15543	+	4.71973i	0.127453	+	0.279084i
$287$	−0.197613	+	1.37443i	−0.0116647	+	0.0811301i
$288$	19.8337	−	5.82370i	1.16871	−	0.343165i
$289$	−11.9549	−	7.68295i	−0.703230	−	0.451938i
$290$	2.26118	+	4.95130i	0.132781	+	0.290750i
$291$	31.2503	−	9.17593i	1.83193	−	0.537902i
$292$	−2.51689	−	17.5054i	−0.147290	−	1.02443i
$293$	14.2361	+	4.18009i	0.831680	+	0.244203i	0.669738	−	0.742597i	$-0.266406\pi$
$293$	14.2361	+	4.18009i	0.831680	+	0.244203i	0.161942	+	0.986800i	$0.448224\pi$
$294$	4.22631	−	29.3946i	0.246484	−	1.71433i
$295$	0.984017	−	6.84399i	0.0572917	−	0.398473i
$296$	0.620782	−	0.716421i	0.0360822	−	0.0416411i
$297$	−0.405901	+	0.260857i	−0.0235528	+	0.0151365i
$298$	0.0526989	−	0.115394i	0.00305276	−	0.00668462i
$299$	−1.68545	+	11.7226i	−0.0974722	+	0.677934i
$300$	−0.789599	−	5.49178i	−0.0455875	−	0.317068i
$301$	−5.49737			−0.316863
$302$	1.93171	+	13.4353i	0.111157	+	0.773116i
$303$	−31.7913	−	20.4310i	−1.82636	−	1.17373i
$304$	−25.0327			−1.43572
$305$	−6.92082	−	7.98706i	−0.396285	−	0.457338i
$306$	3.70101	+	8.10409i	0.211573	+	0.463280i
$307$	−1.83871	−	12.7885i	−0.104941	−	0.729878i	−0.972560	−	0.232650i	$-0.925260\pi$
$307$	−1.83871	−	12.7885i	−0.104941	−	0.729878i	0.867620	−	0.497228i	$-0.165649\pi$
$308$	−0.896732	+	0.576295i	−0.0510961	+	0.0328374i
$309$	−3.83631	+	2.46545i	−0.218240	+	0.140254i
$310$	−1.71399	−	1.97805i	−0.0973480	−	0.112346i
$311$	12.0501	+	3.53823i	0.683299	+	0.200635i	0.604917	−	0.796289i	$-0.293206\pi$
$311$	12.0501	+	3.53823i	0.683299	+	0.200635i	0.0783823	+	0.996923i	$0.475025\pi$
$312$	−8.99043	−	2.63983i	−0.508983	−	0.149451i
$313$	−6.05072	−	6.98291i	−0.342007	−	0.394697i	0.558524	−	0.829488i	$-0.311368\pi$
$313$	−6.05072	−	6.98291i	−0.342007	−	0.394697i	−0.900531	+	0.434791i	$0.856822\pi$
$314$	39.6977	−	25.5121i	2.24027	−	1.43973i
$315$	−2.10980	+	1.35588i	−0.118874	+	0.0763954i
$316$	−4.88035	−	33.9436i	−0.274541	−	1.90947i
$317$	2.42298	+	5.30559i	0.136088	+	0.297992i	0.965391	−	0.260808i	$-0.0839891\pi$
$317$	2.42298	+	5.30559i	0.136088	+	0.297992i	−0.829302	+	0.558800i	$0.811262\pi$
$318$	5.80343	+	6.69751i	0.325440	+	0.375578i
$319$	1.20440			0.0674332
$320$	−8.86268	−	5.69570i	−0.495439	−	0.318399i
$321$	3.89419	+	27.0847i	0.217352	+	1.51172i
$322$	−4.50048			−0.250802
$323$	−1.87835	−	13.0642i	−0.104514	−	0.726912i
$324$	3.39436	−	23.6083i	0.188576	−	1.31157i
$325$	2.23749	−	4.89941i	0.124113	−	0.271770i
$326$	−38.1366	+	24.5089i	−2.11219	+	1.35742i
$327$	13.5522	−	15.6401i	0.749438	−	0.864898i
$328$	0.148672	−	1.03403i	0.00820903	−	0.0570950i
$329$	0.395580	−	2.75132i	0.0218090	−	0.151685i
$330$	−2.17882	−	0.639760i	−0.119940	−	0.0352176i
$331$	−2.60204	−	18.0976i	−0.143021	−	0.994734i	−0.927298	−	0.374323i	$-0.877875\pi$
$331$	−2.60204	−	18.0976i	−0.143021	−	0.994734i	0.784277	−	0.620411i	$-0.213034\pi$
$332$	−25.3846	+	7.45359i	−1.39316	+	0.409069i
$333$	−1.36424	−	2.98727i	−0.0747599	−	0.163701i
$334$	−3.34649	−	2.15066i	−0.183112	−	0.117679i
$335$	−2.46740	+	0.724493i	−0.134808	+	0.0395833i
$336$	−1.04236	+	7.24977i	−0.0568654	+	0.395507i
$337$	−5.18960	−	11.3636i	−0.282695	−	0.619017i	0.714009	−	0.700137i	$-0.246878\pi$
$337$	−5.18960	−	11.3636i	−0.282695	−	0.619017i	−0.996704	+	0.0811200i	$0.974150\pi$
$338$	−21.8768	−	25.2472i	−1.18994	−	1.37327i
$339$	30.3919	+	8.92388i	1.65066	+	0.484679i
$340$	1.63294	−	3.57563i	0.0885584	−	0.193916i
$341$	−0.555669	+	0.163159i	−0.0300912	+	0.00883557i
$342$	17.5135	−	38.3491i	0.947019	−	2.07368i
$343$	10.7590	+	6.91438i	0.580931	+	0.373342i
$344$	4.13587			0.222991
$345$	−3.39425	−	3.91717i	−0.182740	−	0.210893i
$346$	1.37138	−	3.00290i	0.0737257	−	0.161437i
$347$	7.26552	+	15.9093i	0.390034	+	0.854055i	0.998184	+	0.0602332i	$0.0191844\pi$
$347$	7.26552	+	15.9093i	0.390034	+	0.854055i	−0.608151	+	0.793822i	$0.708088\pi$
$348$	−9.47829	+	10.9385i	−0.508089	+	0.586366i
$349$	−18.8944	+	21.8053i	−1.01140	+	1.16721i	−0.0255308	+	0.999674i	$0.508128\pi$
$349$	−18.8944	+	21.8053i	−1.01140	+	1.16721i	−0.985865	+	0.167539i	$0.946418\pi$
$350$	1.96387	+	0.576644i	0.104973	+	0.0308229i
$351$	3.68618	−	4.25407i	0.196753	−	0.227066i
$352$	−3.14023	+	2.01810i	−0.167375	+	0.107565i
$353$	13.5740	+	8.72347i	0.722470	+	0.464304i	0.849495	−	0.527596i	$-0.176906\pi$
$353$	13.5740	+	8.72347i	0.722470	+	0.464304i	−0.127025	+	0.991900i	$0.540543\pi$
$354$	32.6310	−	9.58132i	1.73432	−	0.509241i
$355$	−3.87015			−0.205406
$356$	16.4366	−	14.9293i	0.871139	−	0.791254i
$357$	−3.86177			−0.204386
$358$	−2.29807	+	0.674774i	−0.121457	+	0.0356629i
$359$	−12.9214	−	8.30406i	−0.681964	−	0.438271i	0.153257	−	0.988186i	$-0.451024\pi$
$359$	−12.9214	−	8.30406i	−0.681964	−	0.438271i	−0.835221	+	0.549915i	$0.814660\pi$
$360$	1.58728	−	1.02008i	0.0836569	−	0.0537630i
$361$	−28.4580	+	32.8422i	−1.49779	+	1.72854i
$362$	11.0249	+	3.23720i	0.579455	+	0.170143i
$363$	16.6514	−	19.2167i	0.873971	−	1.00862i
$364$	8.14364	−	9.39826i	0.426842	−	0.492602i
$365$	3.12139	+	6.83488i	0.163381	+	0.357754i
$366$	21.5937	−	47.2836i	1.12872	−	2.47155i
$367$	−3.10585	−	3.58435i	−0.162124	−	0.187101i	0.668875	−	0.743375i	$-0.266776\pi$
$367$	−3.10585	−	3.58435i	−0.162124	−	0.187101i	−0.830999	+	0.556274i	$0.812231\pi$
$368$	−6.96478			−0.363064
$369$	−3.04455	−	1.95661i	−0.158493	−	0.101857i
$370$	−1.11339	+	2.43798i	−0.0578824	+	0.126745i
$371$	−1.69583	+	0.497942i	−0.0880433	+	0.0258519i
$372$	2.89114	−	6.33070i	0.149898	−	0.328232i
$373$	−33.4889	−	9.83324i	−1.73399	−	0.509146i	−0.746307	−	0.665602i	$-0.768175\pi$
$373$	−33.4889	−	9.83324i	−1.73399	−	0.509146i	−0.987685	+	0.156457i	$0.949993\pi$
$374$	−1.05356	−	1.21588i	−0.0544784	−	0.0628714i
$375$	0.979239	+	2.14424i	0.0505677	+	0.110728i
$376$	−0.297609	+	2.06992i	−0.0153480	+	0.106748i
$377$	−13.4817	+	3.95858i	−0.694343	+	0.203877i
$378$	1.79948	+	1.15645i	0.0925551	+	0.0594815i
$379$	6.23387	+	13.6503i	0.320212	+	0.701167i	0.999464	−	0.0327381i	$-0.0104227\pi$
$379$	6.23387	+	13.6503i	0.320212	+	0.701167i	−0.679252	+	0.733906i	$0.737695\pi$
$380$	−17.8476	+	5.24053i	−0.915563	+	0.268834i
$381$	−5.31152	−	36.9425i	−0.272118	−	1.89262i
$382$	−15.0748	−	4.42636i	−0.771293	−	0.226472i
$383$	−4.00572	+	27.8604i	−0.204683	+	1.42360i	0.585471	+	0.810693i	$0.300910\pi$
$383$	−4.00572	+	27.8604i	−0.204683	+	1.42360i	−0.790154	+	0.612908i	$0.790000\pi$
$384$	1.94965	−	13.5601i	0.0994925	−	0.691986i
$385$	0.296575	−	0.342266i	0.0151149	−	0.0174435i
$386$	0.156801	−	0.100770i	0.00798095	−	0.00512904i
$387$	5.95206	−	13.0332i	0.302560	−	0.662514i
$388$	4.62813	−	32.1894i	0.234958	−	1.63417i
$389$	−3.31931	−	23.0863i	−0.168296	−	1.17052i	−0.882406	−	0.470489i	$-0.844078\pi$
$389$	−3.31931	−	23.0863i	−0.168296	−	1.17052i	0.714110	−	0.700033i	$-0.246832\pi$
$390$	26.4919			1.34147
$391$	−0.522608	−	3.63482i	−0.0264294	−	0.183821i
$392$	−3.74849	−	2.40901i	−0.189327	−	0.121673i
$393$	−8.12503			−0.409853
$394$	30.3706	+	35.0495i	1.53005	+	1.76577i
$395$	6.05248	+	13.2531i	0.304533	+	0.666835i
$396$	−0.395382	−	2.74994i	−0.0198687	−	0.138190i
$397$	10.3847	−	6.67384i	0.521193	−	0.334950i	−0.253451	−	0.967348i	$-0.581566\pi$
$397$	10.3847	−	6.67384i	0.521193	−	0.334950i	0.774644	+	0.632398i	$0.217929\pi$
$398$	33.8914	−	21.7807i	1.69882	−	1.09177i
$399$	11.9670	+	13.8107i	0.599100	+	0.691399i
$400$	3.03921	+	0.892393i	0.151961	+	0.0446197i
$401$	−11.8286	−	3.47320i	−0.590693	−	0.173443i	−0.0272931	−	0.999627i	$-0.508689\pi$
$401$	−11.8286	−	3.47320i	−0.590693	−	0.173443i	−0.563400	+	0.826184i	$0.690507\pi$
$402$	−8.28289	−	9.55896i	−0.413113	−	0.476758i
$403$	5.68375	−	3.65273i	0.283128	−	0.181955i
$404$	−31.7432	+	20.4001i	−1.57928	+	1.01494i
$405$	1.44214	+	10.0303i	0.0716607	+	0.498411i
$406$	−2.21808	−	4.85692i	−0.110081	−	0.241045i
$407$	0.388356	+	0.448187i	0.0192501	+	0.0222158i
$408$	2.90535			0.143836
$409$	10.1617	+	6.53050i	0.502462	+	0.322913i	0.767200	−	0.641408i	$-0.221649\pi$
$409$	10.1617	+	6.53050i	0.502462	+	0.322913i	−0.264738	+	0.964320i	$0.585286\pi$
$410$	0.420343	+	2.92355i	0.0207592	+	0.144384i
$411$	50.4861			2.49029
$412$	0.648008	+	4.50699i	0.0319250	+	0.222044i
$413$	−0.965260	+	6.71353i	−0.0474973	+	0.330351i
$414$	4.87272	−	10.6698i	0.239481	−	0.524390i
$415$	9.45597	−	6.07698i	0.464175	−	0.298307i
$416$	28.5178	−	32.9113i	1.39820	−	1.61361i
$417$	−2.09284	+	14.5560i	−0.102487	+	0.712813i
$418$	−1.08346	+	7.53562i	−0.0529937	+	0.368579i
$419$	9.64554	+	2.83219i	0.471215	+	0.138361i	0.508714	−	0.860935i	$-0.330121\pi$
$419$	9.64554	+	2.83219i	0.471215	+	0.138361i	−0.0374990	+	0.999297i	$0.511939\pi$
$420$	0.774548	+	5.38710i	0.0377941	+	0.262863i
$421$	−22.3600	+	6.56549i	−1.08976	+	0.319982i	−0.776777	−	0.629776i	$-0.783147\pi$
$421$	−22.3600	+	6.56549i	−1.08976	+	0.319982i	−0.312983	+	0.949759i	$0.601328\pi$
$422$	6.00018	+	13.1386i	0.292084	+	0.639576i
$423$	6.09455	+	3.91673i	0.296327	+	0.190438i
$424$	1.27584	−	0.374620i	0.0619602	−	0.0181932i
$425$	−0.237677	+	1.65308i	−0.0115290	+	0.0801863i
$426$	−7.90762	−	17.3153i	−0.383125	−	0.838927i
$427$	6.78890	+	7.83481i	0.328538	+	0.379153i
$428$	26.2151	+	7.69744i	1.26715	+	0.372070i
$429$	2.43507	−	5.33206i	0.117566	−	0.257434i
$430$	−11.2198	+	3.29442i	−0.541065	+	0.158871i
$431$	2.56996	−	5.62742i	0.123791	−	0.271063i	−0.837583	−	0.546310i	$-0.816032\pi$
$431$	2.56996	−	5.62742i	0.123791	−	0.271063i	0.961374	+	0.275246i	$0.0887594\pi$
$432$	2.78481	+	1.78969i	0.133984	+	0.0861063i
$433$	−6.35331			−0.305321			−0.152660	−	0.988279i	$-0.548784\pi$
$433$	−6.35331			−0.305321			−0.152660	+	0.988279i	$0.548784\pi$
$434$	1.68132	+	1.94034i	0.0807058	+	0.0931394i
$435$	2.55454	−	5.59367i	0.122481	−	0.268196i
$436$	−8.58392	−	18.7962i	−0.411095	−	0.900173i
$437$	−11.3796	+	13.1327i	−0.544359	+	0.628223i
$438$	−24.2019	+	27.9305i	−1.15641	+	1.33457i
$439$	−19.7478	−	5.79849i	−0.942512	−	0.276747i	−0.225846	−	0.974163i	$-0.572515\pi$
$439$	−19.7478	−	5.79849i	−0.942512	−	0.276747i	−0.716666	+	0.697416i	$0.754333\pi$
$440$	−0.223125	+	0.257500i	−0.0106371	+	0.0122758i
$441$	−12.9860	+	8.34558i	−0.618380	+	0.397409i
$442$	15.7896	+	10.1474i	0.751035	+	0.482661i
$443$	15.6402	−	4.59239i	0.743090	−	0.218191i	0.111793	−	0.993732i	$-0.464341\pi$
$443$	15.6402	−	4.59239i	0.743090	−	0.218191i	0.631298	+	0.775541i	$0.282523\pi$
$444$	−7.12677			−0.338221
$445$	−4.91345	+	8.05345i	−0.232920	+	0.381770i
$446$	−55.0958			−2.60886
$447$	−0.137511	+	0.0403770i	−0.00650407	+	0.00190977i
$448$	8.69374	+	5.58713i	0.410741	+	0.263967i
$449$	22.0087	−	14.1441i	1.03865	−	0.667503i	0.0940009	−	0.995572i	$-0.470034\pi$
$449$	22.0087	−	14.1441i	1.03865	−	0.667503i	0.944654	+	0.328069i	$0.106398\pi$
$450$	−3.49341	+	4.03161i	−0.164681	+	0.190052i
$451$	0.627063	+	0.184122i	0.0295272	+	0.00866998i
$452$	20.7114	−	23.9022i	0.974180	−	1.12426i
$453$	10.0419	−	11.5890i	0.471812	−	0.544500i
$454$	7.10348	+	15.5544i	0.333383	+	0.730006i
$455$	−2.19484	+	4.80602i	−0.102895	+	0.225310i
$456$	−9.00323	−	10.3903i	−0.421615	−	0.486569i
$457$	11.0335			0.516123			0.258062	−	0.966128i	$-0.416916\pi$
$457$	11.0335			0.516123			0.258062	+	0.966128i	$0.416916\pi$
$458$	−23.3088	−	14.9796i	−1.08915	−	0.699953i
$459$	−0.725051	+	1.58764i	−0.0338425	+	0.0741047i
$460$	−4.96569	+	1.45806i	−0.231526	+	0.0679823i
$461$	−16.3266	+	35.7503i	−0.760406	+	1.66506i	−0.0136981	+	0.999906i	$0.504360\pi$
$461$	−16.3266	+	35.7503i	−0.760406	+	1.66506i	−0.746708	+	0.665152i	$0.768367\pi$
$462$	2.13729	+	0.627565i	0.0994358	+	0.0291970i
$463$	−4.83623	−	5.58131i	−0.224759	−	0.259386i	0.632159	−	0.774839i	$-0.282169\pi$
$463$	−4.83623	−	5.58131i	−0.224759	−	0.259386i	−0.856918	+	0.515453i	$0.827624\pi$
$464$	−3.43262	−	7.51639i	−0.159355	−	0.348940i
$465$	−0.420811	+	2.92680i	−0.0195146	+	0.135727i
$466$	14.3195	−	4.20459i	0.663339	−	0.194774i
$467$	−9.58372	−	6.15908i	−0.443481	−	0.285008i	0.299781	−	0.954008i	$-0.403086\pi$
$467$	−9.58372	−	6.15908i	−0.443481	−	0.285008i	−0.743263	+	0.669000i	$0.766723\pi$
$468$	13.4642	+	29.4826i	0.622385	+	1.36283i
$469$	2.42036	−	0.710683i	0.111762	−	0.0328163i
$470$	−0.841437	−	5.85232i	−0.0388126	−	0.269947i
$471$	−51.1514	−	15.0194i	−2.35693	−	0.692058i
$472$	0.726201	−	5.05084i	0.0334261	−	0.232484i
$473$	−0.368220	+	2.56103i	−0.0169308	+	0.117756i
$474$	−46.9284	+	54.1582i	−2.15549	+	2.48757i
$475$	6.64838	−	4.27265i	0.305048	−	0.196043i
$476$	−1.60181	+	3.50747i	−0.0734188	+	0.160765i
$477$	0.655575	−	4.55962i	0.0300167	−	0.208771i
$478$	3.42194	+	23.8001i	0.156516	+	1.08859i
$479$	26.2108			1.19760			0.598802	−	0.800897i	$-0.295644\pi$
$479$	26.2108			1.19760			0.598802	+	0.800897i	$0.295644\pi$
$480$	2.71235	+	18.8648i	0.123801	+	0.861058i
$481$	−5.82025	−	3.74045i	−0.265380	−	0.170550i
$482$	46.0388			2.09701
$483$	3.32955	+	3.84250i	0.151500	+	0.174840i
$484$	−10.5469	−	23.0946i	−0.479406	−	1.04975i
$485$	1.96633	+	13.6761i	0.0892864	+	0.621001i
$486$	−36.4263	+	23.4098i	−1.65233	+	1.06189i
$487$	−21.8366	+	14.0335i	−0.989510	+	0.635919i	−0.932012	−	0.362427i	$-0.881948\pi$
$487$	−21.8366	+	14.0335i	−0.989510	+	0.635919i	−0.0574972	+	0.998346i	$0.518312\pi$
$488$	−5.10754	−	5.89441i	−0.231207	−	0.266828i
$489$	49.1399	+	14.4288i	2.22218	+	0.652492i
$490$	12.0878	+	3.54929i	0.546070	+	0.160341i
$491$	28.5567	+	32.9562i	1.28874	+	1.48729i	0.779091	+	0.626911i	$0.215681\pi$
$491$	28.5567	+	32.9562i	1.28874	+	1.48729i	0.509654	+	0.860379i	$0.329773\pi$
$492$	−6.60705	+	4.24609i	−0.297869	+	0.191429i
$493$	3.66513	−	2.35543i	0.165069	−	0.106083i
$494$	−12.6400	−	87.9129i	−0.568699	−	3.95539i
$495$	0.490342	+	1.07370i	0.0220392	+	0.0482592i
$496$	2.60195	+	3.00280i	0.116831	+	0.134830i
$497$	3.79638			0.170291
$498$	46.5095	+	29.8898i	2.08414	+	1.33940i
$499$	3.47626	+	24.1779i	0.155619	+	1.08235i	0.906589	+	0.422016i	$0.138677\pi$
$499$	3.47626	+	24.1779i	0.155619	+	1.08235i	−0.750970	+	0.660337i	$0.770414\pi$
$500$	2.35369			0.105260
$501$	0.639575	+	4.44834i	0.0285741	+	0.198737i
$502$	−2.36587	+	16.4550i	−0.105594	+	0.734422i
$503$	−15.9844	+	35.0009i	−0.712709	+	1.56061i	0.111140	+	0.993805i	$0.464550\pi$
$503$	−15.9844	+	35.0009i	−0.712709	+	1.56061i	−0.823849	+	0.566810i	$0.808177\pi$
$504$	−1.55702	+	1.00064i	−0.0693552	+	0.0445719i
$505$	10.4984	−	12.1158i	0.467173	−	0.539147i
$506$	−0.301448	+	2.09661i	−0.0134010	+	0.0932059i
$507$	−5.37111	+	37.3569i	−0.238539	+	1.65908i
$508$	−35.7564	−	10.4990i	−1.58643	−	0.465819i
$509$	0.132134	+	0.919011i	0.00585673	+	0.0407344i	0.992540	−	0.121917i	$-0.0389043\pi$
$509$	0.132134	+	0.919011i	0.00585673	+	0.0407344i	−0.986684	+	0.162652i	$0.947995\pi$
$510$	−7.88161	+	2.31425i	−0.349004	+	0.102477i
$511$	−3.06189	−	6.70460i	−0.135450	−	0.296594i
$512$	25.4775	+	16.3734i	1.12596	+	0.723609i
$513$	7.92464	−	2.32688i	0.349881	−	0.102734i
$514$	−8.52991	+	59.3269i	−0.376238	+	2.61680i
$515$	−0.803642	−	1.75973i	−0.0354127	−	0.0775430i
$516$	−20.3619	−	23.4989i	−0.896383	−	1.03448i
$517$	−1.25525	−	0.368574i	−0.0552057	−	0.0162098i
$518$	1.09217	−	2.39151i	0.0479871	−	0.105077i
$519$	−3.57844	+	1.05073i	−0.157076	+	0.0461217i
$520$	1.65126	−	3.61575i	0.0724123	−	0.158561i
$521$	−35.9069	−	23.0759i	−1.57311	−	1.01098i	−0.978321	−	0.207092i	$-0.933600\pi$
$521$	−35.9069	−	23.0759i	−1.57311	−	1.01098i	−0.594787	−	0.803883i	$-0.702764\pi$
$522$	13.9164			0.609102
$523$	−12.8290	−	14.8055i	−0.560975	−	0.647399i	0.402430	−	0.915451i	$-0.368166\pi$
$523$	−12.8290	−	14.8055i	−0.560975	−	0.647399i	−0.963405	+	0.268052i	$0.913620\pi$
$524$	−3.37016	+	7.37961i	−0.147226	+	0.322380i
$525$	−0.960573	−	2.10336i	−0.0419229	−	0.0917982i
$526$	14.4735	−	16.7033i	0.631073	−	0.728297i
$527$	−1.37188	+	1.58324i	−0.0597601	+	0.0689668i
$528$	3.30760	+	0.971198i	0.143945	+	0.0422659i
$529$	11.8957	−	13.7284i	0.517204	−	0.596885i
$530$	−3.16268	+	2.03253i	−0.137378	+	0.0882876i
$531$	−14.8714	−	9.55726i	−0.645363	−	0.414750i
$532$	17.5074	−	5.14064i	0.759042	−	0.222875i
$533$	−7.62435			−0.330247
$534$	−46.0709	−	5.52796i	−1.99368	−	0.239218i
$535$	−11.6081			−0.501861
$536$	−1.82093	+	0.534673i	−0.0786521	+	0.0230943i
$537$	2.27628	+	1.46288i	0.0982288	+	0.0631278i
$538$	43.0997	−	27.6985i	1.85816	−	1.19417i
$539$	1.82545	−	2.10668i	0.0786276	−	0.0907411i
$540$	2.36015	+	0.693004i	0.101565	+	0.0298221i
$541$	25.2946	−	29.1916i	1.08750	−	1.25504i	0.122593	−	0.992457i	$-0.460879\pi$
$541$	25.2946	−	29.1916i	1.08750	−	1.25504i	0.964908	−	0.262587i	$-0.0845756\pi$
$542$	−12.1399	+	14.0102i	−0.521454	+	0.601789i
$543$	−5.39253	−	11.8080i	−0.231416	−	0.506729i
$544$	−5.60931	+	12.2827i	−0.240497	+	0.526615i
$545$	5.74914	+	6.63486i	0.246266	+	0.284206i
$546$	−25.9870			−1.11214
$547$	−22.3853	−	14.3862i	−0.957128	−	0.615109i	−0.0339265	−	0.999424i	$-0.510801\pi$
$547$	−22.3853	−	14.3862i	−0.957128	−	0.615109i	−0.923202	+	0.384315i	$0.874438\pi$
$548$	20.9410	−	45.8543i	0.894553	−	1.95880i
$549$	−25.9252	+	7.61234i	−1.10646	+	0.324887i
$550$	0.400180	−	0.876273i	0.0170637	−	0.0373644i
$551$	−19.7813	−	5.80832i	−0.842712	−	0.247443i
$552$	−2.50494	−	2.89086i	−0.106617	−	0.123043i
$553$	−5.93710	−	13.0004i	−0.252471	−	0.552835i
$554$	−2.37338	+	16.5072i	−0.100835	+	0.701326i
$555$	2.90526	−	0.853061i	0.123321	−	0.0362104i
$556$	12.3525	+	7.93850i	0.523865	+	0.336667i
$557$	−13.6910	−	29.9791i	−0.580106	−	1.27025i	−0.941239	−	0.337740i	$-0.890337\pi$
$557$	−13.6910	−	29.9791i	−0.580106	−	1.27025i	0.361134	−	0.932514i	$-0.382390\pi$
$558$	−6.42056	+	1.88525i	−0.271804	+	0.0798088i
$559$	−4.29577	−	29.8778i	−0.181692	−	1.26369i
$560$	−2.98128	−	0.875382i	−0.125982	−	0.0369917i
$561$	−0.258666	+	1.79906i	−0.0109209	+	0.0759564i
$562$	0.699403	−	4.86445i	0.0295025	−	0.205195i
$563$	−19.7744	+	22.8209i	−0.833393	+	0.961787i	−0.999705	−	0.0242864i	$-0.992269\pi$
$563$	−19.7744	+	22.8209i	−0.833393	+	0.961787i	0.166312	+	0.986073i	$0.446814\pi$
$564$	13.2259	−	8.49978i	0.556911	−	0.357905i
$565$	−5.58203	+	12.2229i	−0.234838	+	0.514223i
$566$	5.88061	−	40.9005i	0.247180	−	1.71918i
$567$	−1.41465	−	9.83914i	−0.0594099	−	0.413205i
$568$	−2.85615			−0.119842
$569$	−3.70961	−	25.8009i	−0.155515	−	1.08163i	−0.906772	−	0.421621i	$-0.861461\pi$
$569$	−3.70961	−	25.8009i	−0.155515	−	1.08163i	0.751257	−	0.660009i	$-0.229448\pi$
$570$	32.7003	+	21.0152i	1.36966	+	0.880229i
$571$	22.3331			0.934613			0.467307	−	0.884095i	$-0.345224\pi$
$571$	22.3331			0.934613			0.467307	+	0.884095i	$0.345224\pi$
$572$	−3.83285	−	4.42334i	−0.160259	−	0.184949i
$573$	7.37343	+	16.1456i	0.308029	+	0.674490i
$574$	−0.412330	−	2.86782i	−0.0172103	−	0.119700i
$575$	1.84976	−	1.18877i	0.0771403	−	0.0495750i
$576$	−22.6588	+	14.5619i	−0.944118	+	0.606748i
$577$	−17.3303	−	20.0003i	−0.721471	−	0.832622i	0.270012	−	0.962857i	$-0.412972\pi$
$577$	−17.3303	−	20.0003i	−0.721471	−	0.832622i	−0.991483	+	0.130235i	$0.958427\pi$
$578$	28.4505	+	8.35382i	1.18339	+	0.347473i
$579$	−0.202042	−	0.0593248i	−0.00839656	−	0.00246545i
$580$	−4.02090	−	4.64036i	−0.166959	−	0.192681i
$581$	−9.27572	+	5.96114i	−0.384822	+	0.247310i
$582$	−57.1700	+	36.7410i	−2.36977	+	1.52296i
$583$	0.118385	+	0.823382i	0.00490299	+	0.0341010i
$584$	2.30357	+	5.04411i	0.0953224	+	0.208727i
$585$	−9.01777	−	10.4071i	−0.372839	−	0.430279i
$586$	−30.9583			−1.27888
$587$	−27.2568	−	17.5169i	−1.12501	−	0.722999i	−0.160496	−	0.987037i	$-0.551309\pi$
$587$	−27.2568	−	17.5169i	−1.12501	−	0.722999i	−0.964512	+	0.264038i	$0.914946\pi$
$588$	4.76741	+	33.1581i	0.196605	+	1.36742i
$589$	9.91331			0.408471
$590$	2.05320	+	14.2803i	0.0845290	+	0.587912i
$591$	7.45645	−	51.8608i	0.306717	−	2.13327i
$592$	1.69020	−	3.70102i	0.0694667	−	0.152111i
$593$	8.47952	−	5.44946i	0.348212	−	0.223782i	−0.354829	−	0.934931i	$-0.615461\pi$
$593$	8.47952	−	5.44946i	0.348212	−	0.223782i	0.703042	+	0.711149i	$0.251825\pi$
$594$	0.659282	−	0.760852i	0.0270507	−	0.0312181i
$595$	0.233147	−	1.62157i	0.00955809	−	0.0664780i
$596$	−0.0203653	+	0.141644i	−0.000834194	+	0.00580194i
$597$	−43.6699	−	12.8226i	−1.78729	−	0.524796i
$598$	−3.51678	−	24.4597i	−0.143812	−	1.00023i
$599$	42.1573	−	12.3785i	1.72250	−	0.505772i	0.737066	−	0.675821i	$-0.236211\pi$
$599$	42.1573	−	12.3785i	1.72250	−	0.505772i	0.985436	+	0.170049i	$0.0543926\pi$
$600$	0.722675	+	1.58244i	0.0295031	+	0.0646027i
$601$	3.94166	+	2.53315i	0.160784	+	0.103330i	0.618558	−	0.785739i	$-0.287717\pi$
$601$	3.94166	+	2.53315i	0.160784	+	0.103330i	−0.457775	+	0.889068i	$0.651353\pi$
$602$	11.0059	−	3.23162i	0.448567	−	0.131711i
$603$	−0.935663	+	6.50768i	−0.0381031	+	0.265013i
$604$	−6.36054	−	13.9276i	−0.258807	−	0.566708i
$605$	7.06388	+	8.15216i	0.287188	+	0.331432i
$606$	75.6575	+	22.2150i	3.07338	+	0.902425i
$607$	−17.0973	+	37.4378i	−0.693957	+	1.51955i	0.153192	+	0.988196i	$0.451045\pi$
$607$	−17.0973	+	37.4378i	−0.693957	+	1.51955i	−0.847148	+	0.531356i	$0.821683\pi$
$608$	61.3084	−	18.0018i	2.48639	−	0.730069i
$609$	−2.50585	+	5.48705i	−0.101542	+	0.222346i
$610$	18.5509	+	11.9219i	0.751103	+	0.482705i
$611$	15.2623			0.617448
$612$	−6.58125	−	7.59517i	−0.266031	−	0.307016i
$613$	−1.65905	+	3.63281i	−0.0670084	+	0.146728i	−0.940173	−	0.340698i	$-0.889337\pi$
$613$	−1.65905	+	3.63281i	−0.0670084	+	0.146728i	0.873164	+	0.487426i	$0.162064\pi$
$614$	11.1989	+	24.5221i	0.451949	+	0.989631i
$615$	2.18514	−	2.52179i	0.0881135	−	0.101688i
$616$	0.218871	−	0.252591i	0.00881858	−	0.0101772i
$617$	−10.4950	−	3.08160i	−0.422512	−	0.124061i	0.0635631	−	0.997978i	$-0.479754\pi$
$617$	−10.4950	−	3.08160i	−0.422512	−	0.124061i	−0.486075	+	0.873917i	$0.661572\pi$
$618$	6.23110	−	7.19108i	0.250652	−	0.289267i
$619$	−18.8812	+	12.1342i	−0.758900	+	0.487715i	−0.861970	−	0.506959i	$-0.830770\pi$
$619$	−18.8812	+	12.1342i	−0.758900	+	0.487715i	0.103071	+	0.994674i	$0.467133\pi$
$620$	2.48374	+	1.59620i	0.0997495	+	0.0641051i
$621$	2.20485	−	0.647402i	0.0884775	−	0.0259793i
$622$	−26.2046			−1.05071
$623$	4.81979	−	7.89993i	0.193101	−	0.316504i
$624$	−40.2165			−1.60995
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	16.2186	+	10.4231i	0.648227	+	0.416590i
$627$	7.23548	−	4.64996i	0.288957	−	0.185701i
$628$	−34.8584	+	40.2288i	−1.39100	+	1.60530i
$629$	2.05833	+	0.604381i	0.0820711	+	0.0240983i
$630$	3.42682	−	3.95476i	0.136528	−	0.157562i
$631$	9.15755	−	10.5684i	0.364556	−	0.420721i	−0.543605	−	0.839341i	$-0.682941\pi$
$631$	9.15755	−	10.5684i	0.364556	−	0.420721i	0.908161	+	0.418621i	$0.137486\pi$
$632$	4.46670	+	9.78071i	0.177676	+	0.389056i
$633$	6.77864	−	14.8431i	0.269427	−	0.589962i
$634$	−7.96978	−	9.19761i	−0.316520	−	0.365284i
$635$	15.8330			0.628312
$636$	−8.40975	−	5.40462i	−0.333468	−	0.214307i
$637$	−13.5094	+	29.5815i	−0.535262	+	1.17206i
$638$	−2.41124	+	0.708003i	−0.0954618	+	0.0280301i
$639$	−4.11038	+	9.00048i	−0.162604	+	0.356053i
$640$	5.57623	+	1.63733i	0.220420	+	0.0647211i
$641$	7.91206	+	9.13101i	0.312508	+	0.360653i	0.890175	−	0.455619i	$-0.150582\pi$
$641$	7.91206	+	9.13101i	0.312508	+	0.360653i	−0.577667	+	0.816273i	$0.696037\pi$
$642$	−23.7180	−	51.9351i	−0.936074	−	2.04972i
$643$	−4.73584	+	32.9385i	−0.186763	+	1.29897i	0.653557	+	0.756878i	$0.273276\pi$
$643$	−4.73584	+	32.9385i	−0.186763	+	1.29897i	−0.840320	+	0.542091i	$0.817633\pi$
$644$	4.87103	−	1.43026i	0.191946	−	0.0563603i
$645$	11.1134	+	7.14214i	0.437589	+	0.281222i
$646$	11.4403	+	25.0508i	0.450113	+	0.985609i
$647$	19.4009	−	5.69662i	0.762728	−	0.223957i	0.122841	−	0.992426i	$-0.460799\pi$
$647$	19.4009	−	5.69662i	0.762728	−	0.223957i	0.639887	+	0.768469i	$0.278981\pi$
$648$	1.06430	+	7.40235i	0.0418095	+	0.290792i
$649$	3.06294	+	0.899362i	0.120231	+	0.0353030i
$650$	−1.59940	+	11.1241i	−0.0627336	+	0.436322i
$651$	0.412789	−	2.87101i	0.0161785	−	0.112524i
$652$	33.4876	−	38.6468i	1.31148	−	1.51353i
$653$	−13.5541	+	8.71068i	−0.530412	+	0.340875i	−0.778279	−	0.627919i	$-0.783907\pi$
$653$	−13.5541	+	8.71068i	−0.530412	+	0.340875i	0.247866	+	0.968794i	$0.420271\pi$
$654$	−17.9379	+	39.2785i	−0.701428	+	1.53591i
$655$	0.490533	−	3.41173i	0.0191667	−	0.133307i
$656$	−0.638107	−	4.43813i	−0.0249139	−	0.173280i
$657$	19.2104			0.749471
$658$	0.825397	+	5.74077i	0.0321773	+	0.223798i
$659$	22.9517	+	14.7502i	0.894071	+	0.574584i	0.905026	−	0.425356i	$-0.139851\pi$
$659$	22.9517	+	14.7502i	0.894071	+	0.574584i	−0.0109555	+	0.999940i	$0.503487\pi$
$660$	2.56154			0.0997078
$661$	−15.3429	−	17.7067i	−0.596770	−	0.688709i	0.374354	−	0.927286i	$-0.377865\pi$
$661$	−15.3429	−	17.7067i	−0.596770	−	0.688709i	−0.971124	+	0.238577i	$0.923319\pi$
$662$	15.8480	+	34.7023i	0.615951	+	1.34874i
$663$	−3.01768	−	20.9884i	−0.117197	−	0.815122i
$664$	6.97846	−	4.48479i	0.270817	−	0.174043i
$665$	−6.52165	+	4.19121i	−0.252899	+	0.162528i
$666$	4.48731	+	5.17863i	0.173880	+	0.200668i
$667$	−5.50370	−	1.61603i	−0.213104	−	0.0625730i
$668$	4.30552	+	1.26421i	0.166586	+	0.0489139i
$669$	40.7610	+	47.0407i	1.57591	+	1.81870i
$670$	4.51391	−	2.90091i	0.174388	−	0.112072i
$671$	4.10469	−	2.63792i	0.158460	−	0.101836i
$672$	−2.66065	−	18.5052i	−0.102637	−	0.713855i
$673$	−3.51591	−	7.69877i	−0.135528	−	0.296766i	0.829684	−	0.558234i	$-0.188521\pi$
$673$	−3.51591	−	7.69877i	−0.135528	−	0.296766i	−0.965212	+	0.261468i	$0.915793\pi$
$674$	17.0698	+	19.6996i	0.657505	+	0.758802i
$675$	−1.04508			−0.0402251
$676$	31.7018	+	20.3735i	1.21930	+	0.783596i
$677$	−5.06071	−	35.1980i	−0.194499	−	1.35277i	−0.819918	−	0.572481i	$-0.805981\pi$
$677$	−5.06071	−	35.1980i	−0.194499	−	1.35277i	0.625419	−	0.780289i	$-0.284928\pi$
$678$	−66.0915			−2.53823
$679$	−1.92885	−	13.4154i	−0.0740224	−	0.514837i
$680$	−0.175405	+	1.21997i	−0.00672647	+	0.0467836i
$681$	8.02507	−	17.5725i	0.307521	−	0.673378i
$682$	1.01655	−	0.653300i	0.0389259	−	0.0250161i
$683$	5.89745	−	6.80602i	0.225660	−	0.260425i	−0.631618	−	0.775280i	$-0.717609\pi$
$683$	5.89745	−	6.80602i	0.225660	−	0.260425i	0.857277	+	0.514855i	$0.172154\pi$
$684$	−6.76800	+	47.0725i	−0.258781	+	1.79986i
$685$	−3.04800	+	21.1993i	−0.116458	+	0.809984i
$686$	−25.6044	−	7.51814i	−0.977582	−	0.287044i
$687$	4.45472	+	30.9833i	0.169958	+	1.18209i
$688$	17.0323	−	5.00114i	0.649351	−	0.190667i
$689$	−4.03144	−	8.82763i	−0.153586	−	0.336306i
$690$	9.09810	+	5.84699i	0.346359	+	0.222591i
$691$	46.3678	−	13.6148i	1.76391	−	0.517932i	0.771007	−	0.636827i	$-0.219753\pi$
$691$	46.3678	−	13.6148i	1.76391	−	0.517932i	0.992907	+	0.118895i	$0.0379352\pi$
$692$	−0.529963	+	3.68597i	−0.0201462	+	0.140120i
$693$	−0.480995	−	1.05323i	−0.0182715	−	0.0400090i
$694$	−23.8981	−	27.5798i	−0.907158	−	1.04692i
$695$	−5.98579	−	1.75759i	−0.227054	−	0.0666691i
$696$	1.88524	−	4.12811i	0.0714599	−	0.156475i
$697$	2.26832	−	0.666038i	0.0859187	−	0.0252280i
$698$	25.0090	−	54.7620i	0.946604	−	2.07277i
$699$	−14.1838	−	9.11536i	−0.536480	−	0.344774i
$700$	−2.30883			−0.0872654
$701$	−18.6813	−	21.5594i	−0.705585	−	0.814288i	0.283911	−	0.958851i	$-0.408368\pi$
$701$	−18.6813	−	21.5594i	−0.705585	−	0.814288i	−0.989496	+	0.144563i	$0.953823\pi$
$702$	−4.87908	+	10.6837i	−0.184149	+	0.403230i
$703$	−4.21704	−	9.23402i	−0.159049	−	0.348268i
$704$	3.18517	−	3.67588i	0.120045	−	0.138540i
$705$	−4.37419	+	5.04809i	−0.164742	+	0.190122i
$706$	−32.3036	−	9.48520i	−1.21576	−	0.356980i
$707$	−10.2983	+	11.8849i	−0.387307	+	0.446976i
$708$	−32.2727	+	20.7404i	−1.21288	+	0.779473i
$709$	27.1588	+	17.4539i	1.01997	+	0.655496i	0.939955	−	0.341298i	$-0.110866\pi$
$709$	27.1588	+	17.4539i	1.01997	+	0.655496i	0.0800161	+	0.996794i	$0.474503\pi$
$710$	7.74816	−	2.27506i	0.290783	−	0.0853817i
$711$	37.2497			1.39697
$712$	−3.62610	+	5.94341i	−0.135894	+	0.222739i
$713$	2.75815			0.103294
$714$	7.73137	−	2.27014i	0.289339	−	0.0849577i
$715$	2.09194	+	1.34441i	0.0782342	+	0.0502781i
$716$	2.27284	−	1.46067i	0.0849400	−	0.0545876i
$717$	17.7889	−	20.5295i	0.664339	−	0.766688i
$718$	30.7505	+	9.02916i	1.14760	+	0.336965i
$719$	−14.8118	+	17.0937i	−0.552387	+	0.637488i	−0.961438	−	0.275023i	$-0.911314\pi$
$719$	−14.8118	+	17.0937i	−0.552387	+	0.637488i	0.409051	+	0.912512i	$0.365860\pi$
$720$	5.30323	−	6.12025i	0.197640	−	0.228088i
$721$	0.788323	+	1.72619i	0.0293587	+	0.0642865i
$722$	37.6674	−	82.4801i	1.40184	−	3.06959i
$723$	−34.0605	−	39.3079i	−1.26672	−	1.46188i
$724$	−12.9614			−0.481708
$725$	2.19458	+	1.41037i	0.0815047	+	0.0523799i
$726$	−22.0400	+	48.2609i	−0.817982	+	1.79113i
$727$	33.0413	−	9.70181i	1.22543	−	0.359820i	0.395910	−	0.918290i	$-0.370429\pi$
$727$	33.0413	−	9.70181i	1.22543	−	0.359820i	0.829525	+	0.558469i	$0.188611\pi$
$728$	−1.61978	+	3.54682i	−0.0600330	+	0.131454i
$729$	17.7672	+	5.21692i	0.658044	+	0.193219i
$730$	−10.2670	−	11.8487i	−0.379998	−	0.438541i
$731$	3.88806	+	8.51366i	0.143805	+	0.314889i
$732$	−8.34479	+	58.0393i	−0.308432	+	2.14519i
$733$	−2.66854	+	0.783554i	−0.0985648	+	0.0289412i	−0.330643	−	0.943756i	$-0.607266\pi$
$733$	−2.66854	+	0.783554i	−0.0985648	+	0.0289412i	0.232078	+	0.972697i	$0.425447\pi$
$734$	8.32507	+	5.35020i	0.307284	+	0.197479i
$735$	−5.91241	−	12.9464i	−0.218083	−	0.477534i
$736$	17.0577	−	5.00858i	0.628754	−	0.184619i
$737$	−0.168963	−	1.17516i	−0.00622384	−	0.0432877i
$738$	7.24548	+	2.12746i	0.266710	+	0.0783131i
$739$	−1.58163	+	11.0005i	−0.0581813	+	0.404660i	0.939831	+	0.341640i	$0.110982\pi$
$739$	−1.58163	+	11.0005i	−0.0581813	+	0.404660i	−0.998012	+	0.0630201i	$0.979927\pi$
$740$	0.430265	−	2.99256i	0.0158169	−	0.110009i
$741$	−65.7087	+	75.8318i	−2.41387	+	2.78575i
$742$	3.10240	−	1.99379i	0.113893	−	0.0731943i
$743$	−20.6356	+	45.1858i	−0.757048	+	1.65770i	−0.00377903	+	0.999993i	$0.501203\pi$
$743$	−20.6356	+	45.1858i	−0.757048	+	1.65770i	−0.753269	+	0.657712i	$0.771524\pi$
$744$	−0.310557	+	2.15997i	−0.0113856	+	0.0791883i
$745$	−0.00865248	−	0.0601793i	−0.000317002	−	0.00220480i
$746$	72.8263			2.66636
$747$	−4.08979	−	28.4451i	−0.149638	−	1.04075i
$748$	1.52672	+	0.981162i	0.0558223	+	0.0358748i
$749$	11.3868			0.416064
$750$	−3.22095	−	3.71718i	−0.117613	−	0.135732i
$751$	17.1332	+	37.5165i	0.625200	+	1.36900i	0.911676	+	0.410910i	$0.134789\pi$
$751$	17.1332	+	37.5165i	0.625200	+	1.36900i	−0.286475	+	0.958088i	$0.592484\pi$
$752$	1.27736	+	8.88420i	0.0465804	+	0.323974i
$753$	15.7996	−	10.1538i	0.575769	−	0.370024i
$754$	24.6637	−	15.8504i	0.898199	−	0.577238i
$755$	4.26002	+	4.91632i	0.155038	+	0.178923i
$756$	−2.31516	−	0.679794i	−0.0842017	−	0.0247239i
$757$	−32.3472	−	9.49800i	−1.17568	−	0.345211i	−0.365172	−	0.930940i	$-0.618990\pi$
$757$	−32.3472	−	9.49800i	−1.17568	−	0.345211i	−0.810507	+	0.585729i	$0.800808\pi$
$758$	−20.5047	−	23.6637i	−0.744764	−	0.859504i
$759$	2.01310	−	1.29374i	0.0730711	−	0.0469599i
$760$	4.90647	−	3.15320i	0.177977	−	0.114379i
$761$	6.51273	+	45.2971i	0.236086	+	1.64202i	0.670937	+	0.741515i	$0.265892\pi$
$761$	6.51273	+	45.2971i	0.236086	+	1.64202i	−0.434850	+	0.900503i	$0.643199\pi$
$762$	32.3504	+	70.8375i	1.17193	+	2.56617i
$763$	−5.63955	−	6.50839i	−0.204165	−	0.235620i
$764$	17.7227			0.641185
$765$	3.59200	+	2.30844i	0.129869	+	0.0834618i
$766$	−8.35815	−	58.1322i	−0.301992	−	2.10040i
$767$	−37.2418			−1.34472
$768$	−3.00043	−	20.8685i	−0.108269	−	0.753026i
$769$	2.96982	−	20.6555i	0.107094	−	0.744858i	−0.863537	−	0.504286i	$-0.831756\pi$
$769$	2.96982	−	20.6555i	0.107094	−	0.744858i	0.970631	−	0.240572i	$-0.0773351\pi$
$770$	−0.392552	+	0.859569i	−0.0141466	+	0.0309767i
$771$	56.9638	−	36.6084i	2.05150	−	1.31842i
$772$	−0.137686	+	0.158899i	−0.00495544	+	0.00571888i
$773$	6.24502	−	43.4351i	0.224618	−	1.56225i	−0.495630	−	0.868534i	$-0.665063\pi$
$773$	6.24502	−	43.4351i	0.224618	−	1.56225i	0.720248	−	0.693717i	$-0.244028\pi$
$774$	−4.25465	+	29.5918i	−0.152930	+	1.06365i
$775$	−1.20357	−	0.353400i	−0.0432336	−	0.0126945i
$776$	1.45114	+	10.0929i	0.0520930	+	0.362315i
$777$	−2.84988	+	0.836800i	−0.102239	+	0.0300200i
$778$	20.2166	+	44.2682i	0.724801	+	1.58709i
$779$	−9.41109	−	6.04814i	−0.337187	−	0.216697i
$780$	−28.6732	+	8.41921i	−1.02667	+	0.301456i
$781$	0.254286	−	1.76860i	0.00909907	−	0.0632855i
$782$	3.18300	+	6.96980i	0.113824	+	0.249240i
$783$	1.78535	+	2.06040i	0.0638030	+	0.0736326i
$784$	−18.3500	−	5.38806i	−0.655358	−	0.192431i
$785$	9.39489	−	20.5719i	0.335318	−	0.734244i
$786$	16.2666	−	4.77629i	0.580209	−	0.170365i
$787$	15.0843	−	33.0301i	0.537699	−	1.17740i	−0.424595	−	0.905383i	$-0.639583\pi$
$787$	15.0843	−	33.0301i	0.537699	−	1.17740i	0.962294	−	0.272013i	$-0.0876893\pi$
$788$	−44.0100	−	28.2835i	−1.56779	−	1.00756i
$789$	−24.9690			−0.888920
$790$	−19.9081	−	22.9751i	−0.708297	−	0.817418i
$791$	5.47563	−	11.9899i	0.194691	−	0.426314i
$792$	0.361870	+	0.792385i	0.0128585	+	0.0281562i
$793$	−37.2766	+	43.0195i	−1.32373	+	1.52767i
$794$	−16.8673	+	19.4659i	−0.598597	+	0.690817i
$795$	4.07520	+	1.19659i	0.144532	+	0.0424385i
$796$	−29.7600	+	34.3448i	−1.05481	+	1.21732i
$797$	−40.7109	+	26.1633i	−1.44205	+	0.926751i	−0.442502	+	0.896768i	$0.645909\pi$
$797$	−40.7109	+	26.1633i	−1.44205	+	0.926751i	−0.999550	+	0.0299833i	$0.990455\pi$
$798$	−32.0769	−	20.6146i	−1.13551	−	0.729749i
$799$	−4.54069	+	1.33327i	−0.160638	+	0.0471676i
$800$	−8.08518			−0.285854
$801$	13.5108	+	19.9801i	0.477380	+	0.705963i
$802$	25.7230			0.908309
$803$	−3.32852	+	0.977343i	−0.117461	+	0.0344897i
$804$	12.0027	+	7.71369i	0.423304	+	0.272041i
$805$	−1.81450	+	1.16611i	−0.0639527	+	0.0410999i
$806$	−9.23179	+	10.6541i	−0.325176	+	0.375273i
$807$	−55.5350	−	16.3065i	−1.95492	−	0.574017i
$808$	7.74778	−	8.94142i	0.272566	−	0.314558i
$809$	28.0780	−	32.4038i	0.987171	−	1.13926i	−0.00308416	−	0.999995i	$-0.500982\pi$
$809$	28.0780	−	32.4038i	0.987171	−	1.13926i	0.990256	−	0.139261i	$-0.0444728\pi$
$810$	−8.78354	−	19.2333i	−0.308622	−	0.675788i
$811$	−18.8687	+	41.3167i	−0.662570	+	1.45083i	0.217538	+	0.976052i	$0.430197\pi$
$811$	−18.8687	+	41.3167i	−0.662570	+	1.45083i	−0.880108	+	0.474774i	$0.842530\pi$
$812$	3.94425	+	4.55191i	0.138416	+	0.159741i
$813$	20.9433			0.734512
$814$	−1.04097	−	0.668989i	−0.0364859	−	0.0234480i
$815$	−9.02544	+	19.7629i	−0.316147	+	0.692266i
$816$	11.9648	−	3.51318i	0.418852	−	0.122986i
$817$	18.3986	−	40.2872i	0.643684	−	1.40947i
$818$	−24.1829	−	7.10074i	−0.845536	−	0.248272i
$819$	8.84588	+	10.2087i	0.309100	+	0.356720i
$820$	−1.38406	−	3.03068i	−0.0483336	−	0.105836i
$821$	−4.63120	+	32.2107i	−0.161630	+	1.12416i	0.733932	+	0.679223i	$0.237683\pi$
$821$	−4.63120	+	32.2107i	−0.161630	+	1.12416i	−0.895562	+	0.444937i	$0.853226\pi$
$822$	−101.075	+	29.6782i	−3.52538	+	1.03515i
$823$	−1.18312	−	0.760345i	−0.0412410	−	0.0265040i	0.519858	−	0.854253i	$-0.325985\pi$
$823$	−1.18312	−	0.760345i	−0.0412410	−	0.0265040i	−0.561099	+	0.827749i	$0.689621\pi$
$824$	−0.593084	−	1.29867i	−0.0206611	−	0.0452414i
$825$	−1.04422	+	0.306612i	−0.0363552	+	0.0106748i
$826$	−2.01406	−	14.0081i	−0.0700782	−	0.487405i
$827$	33.2486	+	9.76268i	1.15617	+	0.339482i	0.802943	−	0.596056i	$-0.203267\pi$
$827$	33.2486	+	9.76268i	1.15617	+	0.339482i	0.353226	+	0.935538i	$0.385085\pi$
$828$	−1.88304	+	13.0968i	−0.0654402	+	0.455147i
$829$	2.15923	−	15.0177i	0.0749930	−	0.521588i	−0.917351	−	0.398080i	$-0.869677\pi$
$829$	2.15923	−	15.0177i	0.0749930	−	0.521588i	0.992344	−	0.123508i	$-0.0394144\pi$
$830$	−15.3588	+	17.7250i	−0.533111	+	0.615243i
$831$	15.8498	−	10.1860i	0.549822	−	0.353349i
$832$	−23.5721	+	51.6158i	−0.817216	+	1.78945i
$833$	1.43504	−	9.98092i	0.0497212	−	0.345818i
$834$	−4.36682	−	30.3719i	−0.151211	−	1.05169i
$835$	−1.90649			−0.0659768
$836$	−1.22217	−	8.50041i	−0.0422698	−	0.293993i
$837$	−1.10282	−	0.708741i	−0.0381191	−	0.0244977i
$838$	−20.9756			−0.724589
$839$	32.8025	+	37.8561i	1.13247	+	1.30694i	0.945886	+	0.324499i	$0.105196\pi$
$839$	32.8025	+	37.8561i	1.13247	+	1.30694i	0.186582	+	0.982439i	$0.440259\pi$
$840$	−0.708899	−	1.55227i	−0.0244593	−	0.0535585i
$841$	3.15863	+	21.9688i	0.108918	+	0.757544i
$842$	40.9059	−	26.2886i	1.40971	−	0.905966i
$843$	−4.67070	+	3.00168i	−0.160867	+	0.103383i
$844$	−10.6697	−	12.3135i	−0.367266	−	0.423848i
$845$	−15.3620	−	4.51070i	−0.528470	−	0.155173i
$846$	−14.5039	−	4.25873i	−0.498655	−	0.146418i
$847$	−6.92923	−	7.99676i	−0.238091	−	0.274772i
$848$	4.80116	−	3.08552i	0.164872	−	0.105957i
$849$	−39.2714	+	25.2382i	−1.34779	+	0.866174i
$850$	−0.495926	−	3.44924i	−0.0170101	−	0.118308i
$851$	−1.17329	−	2.56915i	−0.0402200	−	0.0880695i
$852$	14.0615	+	16.2279i	0.481741	+	0.555958i
$853$	−6.89340			−0.236025			−0.118013	−	0.993012i	$-0.537652\pi$
$853$	−6.89340			−0.236025			−0.118013	+	0.993012i	$0.537652\pi$
$854$	−18.1973	−	11.6947i	−0.622698	−	0.400184i
$855$	−2.87548	−	19.9994i	−0.0983395	−	0.683966i
$856$	−8.56671			−0.292804
$857$	2.53043	+	17.5995i	0.0864378	+	0.601188i	0.986293	+	0.165000i	$0.0527626\pi$
$857$	2.53043	+	17.5995i	0.0864378	+	0.601188i	−0.899856	+	0.436188i	$0.856328\pi$
$858$	−1.74064	+	12.1064i	−0.0594244	+	0.413306i
$859$	−15.9796	+	34.9905i	−0.545218	+	1.19386i	0.413762	+	0.910385i	$0.364215\pi$
$859$	−15.9796	+	34.9905i	−0.545218	+	1.19386i	−0.958980	+	0.283475i	$0.908513\pi$
$860$	11.0966	−	7.13135i	0.378391	−	0.243177i
$861$	−2.14349	+	2.47372i	−0.0730500	+	0.0843042i
$862$	−1.83706	+	12.7770i	−0.0625705	+	0.435187i
$863$	−5.02425	+	34.9444i	−0.171027	+	1.18952i	0.705691	+	0.708519i	$0.250636\pi$
$863$	−5.02425	+	34.9444i	−0.171027	+	1.18952i	−0.876719	+	0.481003i	$0.840273\pi$
$864$	−8.10737	−	2.38054i	−0.275818	−	0.0809876i
$865$	−0.225162	−	1.56604i	−0.00765575	−	0.0532469i
$866$	12.7195	−	3.73479i	0.432227	−	0.126913i
$867$	−13.9158	−	30.4714i	−0.472605	−	1.03486i
$868$	−2.43640	−	1.56578i	−0.0826967	−	0.0531460i
$869$	−6.45413	+	1.89510i	−0.218941	+	0.0642869i
$870$	−1.82604	+	12.7004i	−0.0619085	+	0.430583i
$871$	5.75384	+	12.5991i	0.194961	+	0.426906i
$872$	4.24284	+	4.89650i	0.143681	+	0.165816i
$873$	33.8938	+	9.95211i	1.14713	+	0.336828i
$874$	15.0622	−	32.9816i	0.509486	−	1.11562i
$875$	0.941203	−	0.276362i	0.0318185	−	0.00934275i
$876$	17.3182	−	37.9217i	0.585129	−	1.28125i
$877$	19.0443	+	12.2390i	0.643081	+	0.413283i	0.821132	−	0.570738i	$-0.193343\pi$
$877$	19.0443	+	12.2390i	0.643081	+	0.413283i	−0.178051	+	0.984021i	$0.556979\pi$
$878$	42.9444			1.44930
$879$	22.9036	+	26.4322i	0.772520	+	0.891535i
$880$	−0.607500	+	1.33024i	−0.0204788	+	0.0448423i
$881$	13.4915	+	29.5423i	0.454541	+	0.995307i	0.988698	+	0.149921i	$0.0479020\pi$
$881$	13.4915	+	29.5423i	0.454541	+	0.995307i	−0.534157	+	0.845386i	$0.679371\pi$
$882$	21.0924	−	24.3419i	0.710218	−	0.819635i
$883$	26.5665	−	30.6593i	0.894033	−	1.03177i	−0.105270	−	0.994444i	$-0.533571\pi$
$883$	26.5665	−	30.6593i	0.894033	−	1.03177i	0.999303	−	0.0373255i	$-0.0118838\pi$
$884$	−20.3146	−	5.96489i	−0.683252	−	0.200621i
$885$	10.6735	−	12.3179i	0.358787	−	0.414062i
$886$	−28.6126	+	18.3882i	−0.961259	+	0.617764i
$887$	0.330090	+	0.212136i	0.0110833	+	0.00712282i	0.546171	−	0.837674i	$-0.316085\pi$
$887$	0.330090	+	0.212136i	0.0110833	+	0.00712282i	−0.535087	+	0.844797i	$0.679721\pi$
$888$	2.14407	−	0.629555i	0.0719502	−	0.0211265i
$889$	−15.5312			−0.520898
$890$	5.10266	−	19.0116i	0.171041	−	0.637271i
$891$	−4.67846			−0.156734
$892$	59.6322	−	17.5096i	1.99663	−	0.586265i
$893$	18.8390	+	12.1071i	0.630424	+	0.405149i
$894$	0.251566	−	0.161672i	0.00841364	−	0.00540712i
$895$	−0.751694	+	0.867501i	−0.0251264	+	0.0289974i
$896$	−5.46994	−	1.60612i	−0.182738	−	0.0536567i
$897$	−18.2819	+	21.0985i	−0.610416	+	0.704457i
$898$	−35.7475	+	41.2548i	−1.19291	+	1.37669i
$899$	1.35937	+	2.97660i	0.0453374	+	0.0992751i
$900$	2.49979	−	5.47378i	0.0833264	−	0.182459i
$901$	1.97055	+	2.27413i	0.0656484	+	0.0757623i
$902$	−1.36363			−0.0454041
$903$	−10.9016	−	7.00600i	−0.362781	−	0.233145i
$904$	−4.11952	+	9.02048i	−0.137013	+	0.300017i
$905$	5.28379	−	1.55146i	0.175639	−	0.0515723i
$906$	−13.2917	+	29.1047i	−0.441587	+	0.966940i
$907$	30.6554	+	9.00124i	1.01790	+	0.298881i	0.747780	−	0.663946i	$-0.231120\pi$
$907$	30.6554	+	9.00124i	1.01790	+	0.298881i	0.270116	+	0.962828i	$0.412938\pi$
$908$	−12.6316	−	14.5776i	−0.419195	−	0.483776i
$909$	−17.0266	−	37.2831i	−0.564738	−	1.23660i
$910$	1.56891	−	10.9120i	0.0520090	−	0.361730i
$911$	−3.84002	+	1.12753i	−0.127226	+	0.0373568i	−0.344726	−	0.938704i	$-0.612028\pi$
$911$	−3.84002	+	1.12753i	−0.127226	+	0.0373568i	0.217500	+	0.976060i	$0.430210\pi$
$912$	−49.6411	−	31.9024i	−1.64378	−	1.05639i
$913$	2.15579	+	4.72052i	0.0713462	+	0.156226i
$914$	−22.0893	+	6.48601i	−0.730650	+	0.214538i
$915$	−3.54540	−	24.6588i	−0.117207	−	0.815196i
$916$	29.9885	+	8.80543i	0.990849	+	0.290940i
$917$	−0.481183	+	3.34670i	−0.0158900	+	0.110518i
$918$	0.518281	−	3.60473i	0.0171058	−	0.118974i
$919$	10.1825	−	11.7512i	0.335890	−	0.387637i	−0.562529	−	0.826778i	$-0.690171\pi$
$919$	10.1825	−	11.7512i	0.335890	−	0.387637i	0.898418	+	0.439140i	$0.144717\pi$
$920$	1.36511	−	0.877305i	0.0450065	−	0.0289239i
$921$	12.6518	−	27.7035i	0.416890	−	0.912863i
$922$	11.6706	−	81.1708i	0.384351	−	2.67322i
$923$	2.96658	+	20.6330i	0.0976462	+	0.679144i
$924$	−2.51271			−0.0826621
$925$	0.182804	+	1.27143i	0.00601057	+	0.0418044i
$926$	12.9633	+	8.33098i	0.425999	+	0.273773i
$927$	−4.94598			−0.162447
$928$	13.8122	+	15.9401i	0.453408	+	0.523261i
$929$	−17.6300	−	38.6043i	−0.578421	−	1.26657i	−0.942191	−	0.335077i	$-0.891238\pi$
$929$	−17.6300	−	38.6043i	−0.578421	−	1.26657i	0.363769	−	0.931489i	$-0.381490\pi$
$930$	−0.878043	−	6.10692i	−0.0287922	−	0.200254i
$931$	−40.1413	+	25.7973i	−1.31558	+	0.845471i
$932$	−14.1623	+	9.10158i	−0.463903	+	0.298132i
$933$	19.3867	+	22.3735i	0.634694	+	0.732475i
$934$	22.8075	+	6.69689i	0.746284	+	0.219129i
$935$	−0.739817	−	0.217230i	−0.0241946	−	0.00710417i
$936$	−6.65508	−	7.68037i	−0.217528	−	0.251041i
$937$	−26.8639	+	17.2644i	−0.877604	+	0.564002i	−0.900070	−	0.435746i	$-0.856485\pi$
$937$	−26.8639	+	17.2644i	−0.877604	+	0.564002i	0.0224658	+	0.999748i	$0.492848\pi$
$938$	−4.42787	+	2.84562i	−0.144575	+	0.0929127i
$939$	−3.09967	−	21.5587i	−0.101154	−	0.703541i
$940$	2.77060	+	6.06677i	0.0903671	+	0.197876i
$941$	0.0339633	+	0.0391958i	0.00110717	+	0.00127775i	0.756303	−	0.654222i	$-0.227004\pi$
$941$	0.0339633	+	0.0391958i	0.00110717	+	0.00127775i	−0.755196	+	0.655499i	$0.772458\pi$
$942$	111.236			3.62426
$943$	−2.61842	−	1.68276i	−0.0852675	−	0.0547981i
$944$	−3.11689	−	21.6785i	−0.101446	−	0.705574i
$945$	1.02516			0.0333484
$946$	−0.768311	−	5.34372i	−0.0249799	−	0.173739i
$947$	−7.31054	+	50.8459i	−0.237561	+	1.65227i	0.426423	+	0.904524i	$0.359773\pi$
$947$	−7.31054	+	50.8459i	−0.237561	+	1.65227i	−0.663984	+	0.747747i	$0.731136\pi$
$948$	33.5807	−	73.5314i	1.09065	−	2.38819i
$949$	34.0463	−	21.8802i	1.10519	−	0.710263i
$950$	−10.7986	+	12.4622i	−0.350352	+	0.404328i
$951$	−1.95670	+	13.6092i	−0.0634505	+	0.441308i
$952$	0.172061	−	1.19671i	0.00557654	−	0.0387857i
$953$	34.1255	+	10.0202i	1.10543	+	0.324585i	0.783009	−	0.622010i	$-0.213684\pi$
$953$	34.1255	+	10.0202i	1.10543	+	0.324585i	0.322425	+	0.946595i	$0.395502\pi$
$954$	1.36789	+	9.51388i	0.0442871	+	0.308023i
$955$	−7.22474	+	2.12138i	−0.233787	+	0.0686461i
$956$	−11.2674	−	24.6723i	−0.364415	−	0.797958i
$957$	2.38838	+	1.53492i	0.0772053	+	0.0496168i
$958$	−52.4749	+	15.4080i	−1.69539	+	0.497811i
$959$	2.98990	−	20.7952i	0.0965489	−	0.671512i
$960$	−10.3164	−	22.5897i	−0.332960	−	0.729080i
$961$	19.2703	+	22.2391i	0.621622	+	0.717390i
$962$	13.8511	+	4.06706i	0.446578	+	0.131127i
$963$	−12.3286	+	26.9959i	−0.397284	+	0.869931i
$964$	−49.8295	+	14.6313i	−1.60490	+	0.471241i
$965$	0.0371086	−	0.0812565i	0.00119457	−	0.00261574i
$966$	−8.92467	−	5.73554i	−0.287147	−	0.184538i
$967$	−44.6744			−1.43663			−0.718316	−	0.695716i	$-0.755087\pi$
$967$	−44.6744			−1.43663			−0.718316	+	0.695716i	$0.755087\pi$
$968$	5.21312	+	6.01626i	0.167556	+	0.193370i
$969$	12.9245	−	28.3008i	0.415196	−	0.909153i
$970$	−11.9761	−	26.2241i	−0.384531	−	0.842005i
$971$	3.32623	−	3.83867i	0.106744	−	0.123189i	−0.699864	−	0.714277i	$-0.746756\pi$
$971$	3.32623	−	3.83867i	0.106744	−	0.123189i	0.806607	+	0.591088i	$0.201301\pi$
$972$	31.9859	−	36.9136i	1.02595	−	1.18401i
$973$	5.87169	+	1.72408i	0.188238	+	0.0552716i
$974$	35.4679	−	40.9321i	1.13646	−	1.31155i
$975$	10.6810	−	6.86426i	0.342066	−	0.219832i
$976$	−28.1614	−	18.0983i	−0.901426	−	0.579311i
$977$	41.0823	−	12.0628i	1.31434	−	0.385924i	0.451892	−	0.892073i	$-0.350749\pi$
$977$	41.0823	−	12.0628i	1.31434	−	0.385924i	0.862446	+	0.506148i	$0.168931\pi$
$978$	−106.862			−3.41706
$979$	−3.35747	−	2.77452i	−0.107305	−	0.0886740i
$980$	−14.2110			−0.453955
$981$	21.5361	−	6.32358i	0.687596	−	0.201896i
$982$	−76.5446	−	49.1922i	−2.44264	−	1.56979i
$983$	0.856343	−	0.550338i	0.0273131	−	0.0175531i	−0.526913	−	0.849919i	$-0.676651\pi$
$983$	0.856343	−	0.550338i	0.0273131	−	0.0175531i	0.554226	+	0.832366i	$0.313014\pi$
$984$	1.61263	−	1.86107i	0.0514087	−	0.0593288i
$985$	21.3264	+	6.26199i	0.679515	+	0.199524i
$986$	−5.95306	+	6.87019i	−0.189584	+	0.218792i
$987$	4.29081	−	4.95186i	0.136578	−	0.157620i
$988$	41.6197	+	91.1344i	1.32410	+	2.89937i
$989$	5.11898	−	11.2090i	0.162774	−	0.356425i
$990$	−1.61285	−	1.86133i	−0.0512598	−	0.0591570i
$991$	58.8955			1.87088			0.935439	−	0.353488i	$-0.115004\pi$
$991$	58.8955			1.87088			0.935439	+	0.353488i	$0.115004\pi$
$992$	−8.53191	−	5.48313i	−0.270889	−	0.174090i
$993$	17.9041	−	39.2046i	0.568170	−	1.24412i
$994$	−7.60046	+	2.23170i	−0.241072	+	0.0707851i
$995$	8.02077	−	17.5630i	0.254276	−	0.556786i
$996$	−59.8380	−	17.5700i	−1.89604	−	0.556728i
$997$	19.8877	+	22.9516i	0.629849	+	0.726884i	0.977546	−	0.210723i	$-0.0675818\pi$
$997$	19.8877	+	22.9516i	0.629849	+	0.726884i	−0.347697	+	0.937607i	$0.613036\pi$
$998$	−21.1725	−	46.3614i	−0.670205	−	1.46754i
$999$	−0.191045	+	1.32875i	−0.00604439	+	0.0420397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	445.2.o.b.91.3	✓	160
89.45	even	11	inner	445.2.o.b.401.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.o.b.91.3	✓	160	1.1	even	1	trivial
445.2.o.b.401.3	yes	160	89.45	even	11	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:	\( N \)	\(=\)	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	445.o (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00203 + 0.587849i) q^{2} +(1.98305 + 1.27443i) q^{3} +(1.98005 - 1.27250i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-4.71930 - 1.38571i) q^{6} +(0.642378 - 0.741344i) q^{7} +(-0.483284 + 0.557740i) q^{8} +(1.06207 + 2.32561i) q^{9} +(0.866784 - 1.89799i) q^{10} +(-0.302339 - 0.348917i) q^{11} +5.54825 q^{12} +(4.53111 + 2.91197i) q^{13} +(-0.850262 + 1.86181i) q^{14} +(-2.26177 + 0.664116i) q^{15} +(-1.31583 + 2.88128i) q^{16} +(-1.60243 - 0.470516i) q^{17} +(-3.49341 - 4.03161i) q^{18} +(3.28300 + 7.18877i) q^{19} +(-0.334965 + 2.32973i) q^{20} +(2.21866 - 0.651456i) q^{21} +(0.810402 + 0.520814i) q^{22} +(0.913420 + 2.00011i) q^{23} +(-1.66918 + 0.490115i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(-10.7832 - 3.16624i) q^{26} +(0.148730 - 1.03444i) q^{27} +(0.328580 - 2.28533i) q^{28} +(-1.70834 + 1.97153i) q^{29} +(4.13773 - 2.65916i) q^{30} +(0.521089 - 1.14103i) q^{31} +(1.15064 - 8.00288i) q^{32} +(-0.154882 - 1.07723i) q^{33} +3.48471 q^{34} +(0.139602 + 0.970954i) q^{35} +(5.06231 + 3.25335i) q^{36} -1.28451 q^{37} +(-10.7986 - 12.4622i) q^{38} +(5.27433 + 11.5492i) q^{39} +(-0.105028 - 0.730484i) q^{40} +(-1.19083 + 0.765303i) q^{41} +(-4.05886 + 2.60847i) q^{42} +(-3.66997 - 4.23537i) q^{43} +(-1.04264 - 0.306148i) q^{44} +(-2.45309 - 0.720293i) q^{45} +(-3.00446 - 3.46733i) q^{46} +(2.38380 - 1.53197i) q^{47} +(-6.28135 + 4.03678i) q^{48} +(0.859263 + 5.97630i) q^{49} +(0.866784 + 1.89799i) q^{50} +(-2.57806 - 2.97524i) q^{51} +12.6773 q^{52} +(-1.51575 - 0.974112i) q^{53} +(0.310333 + 2.15841i) q^{54} +0.461684 q^{55} +(0.103026 + 0.716560i) q^{56} +(-2.65122 + 18.4396i) q^{57} +(2.26118 - 4.95130i) q^{58} +(-5.81674 + 3.73819i) q^{59} +(-3.63333 + 4.19309i) q^{60} +(-1.50404 + 10.4608i) q^{61} +(-0.372485 + 2.59069i) q^{62} +(2.40633 + 0.706563i) q^{63} +(1.49930 + 10.4279i) q^{64} +(-5.16797 + 1.51745i) q^{65} +(0.943327 + 2.06560i) q^{66} +(2.16334 + 1.39029i) q^{67} +(-3.77163 + 1.10745i) q^{68} +(-0.737641 + 5.13041i) q^{69} +(-0.850262 - 1.86181i) q^{70} +(2.53441 + 2.92486i) q^{71} +(-1.81037 - 0.531573i) q^{72} +(3.12139 - 6.83488i) q^{73} +(2.57162 - 0.755096i) q^{74} +(0.979239 - 2.14424i) q^{75} +(15.6482 + 10.0565i) q^{76} -0.452883 q^{77} +(-17.3485 - 20.0213i) q^{78} +(6.05248 - 13.2531i) q^{79} +(-1.31583 - 2.88128i) q^{80} +(6.63602 - 7.65837i) q^{81} +(1.93420 - 2.23219i) q^{82} +(-10.7850 - 3.16677i) q^{83} +(3.56408 - 4.11316i) q^{84} +(1.40496 - 0.902914i) q^{85} +(9.83714 + 6.32195i) q^{86} +(-5.90029 + 1.73248i) q^{87} +0.340721 q^{88} +(9.30401 - 1.56055i) q^{89} +5.33459 q^{90} +(5.06946 - 1.48853i) q^{91} +(4.35376 + 2.79799i) q^{92} +(2.48750 - 1.59862i) q^{93} +(-3.87187 + 4.46837i) q^{94} +(-7.58282 - 2.22652i) q^{95} +(12.4809 - 14.4037i) q^{96} +(9.04805 - 10.4420i) q^{97} +(-5.23344 - 11.4596i) q^{98} +(0.490342 - 1.07370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 2 q^{3} - 22 q^{4} - 16 q^{5} - 6 q^{6} - 2 q^{7} - 6 q^{8} - 32 q^{9} - 2 q^{10} - q^{11} - 16 q^{12} - 8 q^{13} + 27 q^{14} - 2 q^{15} - 34 q^{16} + 19 q^{17} + 53 q^{18} - 14 q^{19}+ \cdots + 50 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 2 * q^3 - 22 * q^4 - 16 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 - 32 * q^9 - 2 * q^10 - q^11 - 16 * q^12 - 8 * q^13 + 27 * q^14 - 2 * q^15 - 34 * q^16 + 19 * q^17 + 53 * q^18 - 14 * q^19 - 22 * q^20 - 26 * q^21 + 34 * q^22 + 33 * q^23 + 50 * q^24 - 16 * q^25 - 35 * q^26 + 7 * q^27 + 49 * q^28 - 17 * q^29 - 6 * q^30 + 20 * q^31 + 11 * q^32 - 20 * q^33 + 2 * q^34 - 2 * q^35 - 102 * q^36 + 130 * q^37 - 19 * q^38 + 3 * q^39 - 6 * q^40 - 52 * q^41 - 92 * q^42 - 26 * q^43 + 14 * q^44 + q^45 + 102 * q^46 - 4 * q^47 + 3 * q^48 - 68 * q^49 - 2 * q^50 + 46 * q^51 - 66 * q^52 - 2 * q^53 - 79 * q^54 + 32 * q^55 + 199 * q^56 - 86 * q^57 - 74 * q^58 - 47 * q^59 - 16 * q^60 - 24 * q^61 + 41 * q^62 + 94 * q^63 + 70 * q^64 + 25 * q^65 - 130 * q^66 + 21 * q^67 - 57 * q^68 + 64 * q^69 + 27 * q^70 - 26 * q^71 - 66 * q^72 + 12 * q^73 - 70 * q^74 - 2 * q^75 - 137 * q^76 - 100 * q^77 - 170 * q^78 - 59 * q^79 - 34 * q^80 - 84 * q^81 + 359 * q^82 - 39 * q^83 + 202 * q^84 - 14 * q^85 - 108 * q^86 + 133 * q^87 + 48 * q^88 + 42 * q^90 + 22 * q^91 + 57 * q^92 + 69 * q^93 - 74 * q^94 - 3 * q^95 - 116 * q^96 - 37 * q^97 + 3 * q^98 + 50 * q^99

Introduction

L-functions

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