LMFDB - Embedded newform 403.2.k.d.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	403.157
Dual form			403.2.k.d.326.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607778 + 0.441577i) q^{2} +(0.0305971 - 0.0222301i) q^{3} +(-0.443630 - 1.36535i) q^{4} +2.26489 q^{5} +0.0284125 q^{6} +(1.52318 + 4.68785i) q^{7} +(0.797580 - 2.45470i) q^{8} +(-0.926609 + 2.85181i) q^{9} +O(q^{10})$	\(q+(0.607778 + 0.441577i) q^{2} +(0.0305971 - 0.0222301i) q^{3} +(-0.443630 - 1.36535i) q^{4} +2.26489 q^{5} +0.0284125 q^{6} +(1.52318 + 4.68785i) q^{7} +(0.797580 - 2.45470i) q^{8} +(-0.926609 + 2.85181i) q^{9} +(1.37655 + 1.00012i) q^{10} +(-0.967284 - 2.97699i) q^{11} +(-0.0439256 - 0.0319138i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.14429 + 3.52177i) q^{14} +(0.0692989 - 0.0503486i) q^{15} +(-0.754184 + 0.547947i) q^{16} +(1.95555 - 6.01855i) q^{17} +(-1.82247 + 1.32410i) q^{18} +(6.42241 + 4.66616i) q^{19} +(-1.00477 - 3.09237i) q^{20} +(0.150816 + 0.109574i) q^{21} +(0.726677 - 2.23648i) q^{22} +(-0.716339 + 2.20466i) q^{23} +(-0.0301645 - 0.0928369i) q^{24} +0.129718 q^{25} +0.751255 q^{26} +(0.0701055 + 0.215763i) q^{27} +(5.72484 - 4.15934i) q^{28} +(-1.68106 - 1.22136i) q^{29} +0.0643512 q^{30} +(5.18732 - 2.02280i) q^{31} -5.86239 q^{32} +(-0.0957749 - 0.0695845i) q^{33} +(3.84619 - 2.79442i) q^{34} +(3.44982 + 10.6175i) q^{35} +4.30479 q^{36} -3.51693 q^{37} +(1.84294 + 5.67198i) q^{38} +(0.0116870 - 0.0359690i) q^{39} +(1.80643 - 5.55962i) q^{40} +(-3.57000 - 2.59375i) q^{41} +(0.0432772 + 0.133194i) q^{42} +(-6.60141 - 4.79620i) q^{43} +(-3.63553 + 2.64137i) q^{44} +(-2.09867 + 6.45903i) q^{45} +(-1.40890 + 1.02363i) q^{46} +(4.28081 - 3.11019i) q^{47} +(-0.0108949 + 0.0335311i) q^{48} +(-13.9928 + 10.1663i) q^{49} +(0.0788395 + 0.0572802i) q^{50} +(-0.0739588 - 0.227622i) q^{51} +(-1.16144 - 0.843834i) q^{52} +(-2.96680 + 9.13087i) q^{53} +(-0.0526671 + 0.162093i) q^{54} +(-2.19079 - 6.74256i) q^{55} +12.7221 q^{56} +0.300236 q^{57} +(-0.482386 - 1.48463i) q^{58} +(5.27694 - 3.83392i) q^{59} +(-0.0994866 - 0.0722813i) q^{60} -10.5383 q^{61} +(4.04596 + 1.06119i) q^{62} -14.7802 q^{63} +(-2.05466 - 1.49280i) q^{64} +(1.83233 - 1.33127i) q^{65} +(-0.0274830 - 0.0845839i) q^{66} -8.70583 q^{67} -9.08497 q^{68} +(0.0270920 + 0.0833805i) q^{69} +(-2.59170 + 7.97642i) q^{70} +(1.27915 - 3.93683i) q^{71} +(6.26129 + 4.54909i) q^{72} +(4.29337 + 13.2136i) q^{73} +(-2.13751 - 1.55299i) q^{74} +(0.00396898 - 0.00288363i) q^{75} +(3.52177 - 10.8389i) q^{76} +(12.4824 - 9.06897i) q^{77} +(0.0229862 - 0.0167005i) q^{78} +(2.40280 - 7.39504i) q^{79} +(-1.70814 + 1.24104i) q^{80} +(-7.27074 - 5.28250i) q^{81} +(-1.02442 - 3.15285i) q^{82} +(-13.0164 - 9.45697i) q^{83} +(0.0827009 - 0.254527i) q^{84} +(4.42909 - 13.6313i) q^{85} +(-1.89430 - 5.83006i) q^{86} -0.0785863 q^{87} -8.07912 q^{88} +(0.889244 + 2.73681i) q^{89} +(-4.12768 + 2.99894i) q^{90} +(3.98772 + 2.89725i) q^{91} +3.32793 q^{92} +(0.113750 - 0.177206i) q^{93} +3.97517 q^{94} +(14.5460 + 10.5683i) q^{95} +(-0.179372 + 0.130321i) q^{96} +(-2.93705 - 9.03930i) q^{97} -12.9937 q^{98} +9.38612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.607778	+	0.441577i	0.429764	+	0.312242i	0.781555	−	0.623837i	$-0.214427\pi$
$2$	0.607778	+	0.441577i	0.429764	+	0.312242i	−0.351790	+	0.936079i	$0.614427\pi$
$3$	0.0305971	−	0.0222301i	0.0176652	−	0.0128345i	−0.578918	−	0.815386i	$-0.696525\pi$
$3$	0.0305971	−	0.0222301i	0.0176652	−	0.0128345i	0.596583	+	0.802552i	$0.296525\pi$
$4$	−0.443630	−	1.36535i	−0.221815	−	0.682676i
$5$	2.26489			1.01289			0.506444	−	0.862273i	$-0.330960\pi$
$5$	2.26489			1.01289			0.506444	+	0.862273i	$0.330960\pi$
$6$	0.0284125			0.0115994
$7$	1.52318	+	4.68785i	0.575706	+	1.77184i	0.633762	+	0.773528i	$0.281510\pi$
$7$	1.52318	+	4.68785i	0.575706	+	1.77184i	−0.0580563	+	0.998313i	$0.518490\pi$
$8$	0.797580	−	2.45470i	0.281987	−	0.867867i
$9$	−0.926609	+	2.85181i	−0.308870	+	0.950603i
$10$	1.37655	+	1.00012i	0.435303	+	0.316266i
$11$	−0.967284	−	2.97699i	−0.291647	−	0.897598i	−0.984327	−	0.176353i	$-0.943570\pi$
$11$	−0.967284	−	2.97699i	−0.291647	−	0.897598i	0.692680	−	0.721245i	$-0.256430\pi$
$12$	−0.0439256	−	0.0319138i	−0.0126802	−	0.00921273i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−1.14429	+	3.52177i	−0.305825	+	0.941233i
$15$	0.0692989	−	0.0503486i	0.0178929	−	0.0130000i
$16$	−0.754184	+	0.547947i	−0.188546	+	0.136987i
$17$	1.95555	−	6.01855i	0.474289	−	1.45971i	−0.372624	−	0.927982i	$-0.621542\pi$
$17$	1.95555	−	6.01855i	0.474289	−	1.45971i	0.846914	−	0.531730i	$-0.178458\pi$
$18$	−1.82247	+	1.32410i	−0.429559	+	0.312093i
$19$	6.42241	+	4.66616i	1.47340	+	1.07049i	0.979610	+	0.200910i	$0.0643898\pi$
$19$	6.42241	+	4.66616i	1.47340	+	1.07049i	0.493793	+	0.869580i	$0.335610\pi$
$20$	−1.00477	−	3.09237i	−0.224674	−	0.691475i
$21$	0.150816	+	0.109574i	0.0329107	+	0.0239110i
$22$	0.726677	−	2.23648i	0.154928	−	0.476820i
$23$	−0.716339	+	2.20466i	−0.149367	+	0.459704i	−0.997547	−	0.0700044i	$-0.977699\pi$
$23$	−0.716339	+	2.20466i	−0.149367	+	0.459704i	0.848180	+	0.529708i	$0.177699\pi$
$24$	−0.0301645	−	0.0928369i	−0.00615731	−	0.0189502i
$25$	0.129718			0.0259435
$26$	0.751255			0.147333
$27$	0.0701055	+	0.215763i	0.0134918	+	0.0415235i
$28$	5.72484	−	4.15934i	1.08189	−	0.786041i
$29$	−1.68106	−	1.22136i	−0.312165	−	0.226801i	0.420660	−	0.907218i	$-0.361798\pi$
$29$	−1.68106	−	1.22136i	−0.312165	−	0.226801i	−0.732825	+	0.680417i	$0.761798\pi$
$30$	0.0643512			0.0117489
$31$	5.18732	−	2.02280i	0.931670	−	0.363305i
$31$	5.18732	−	2.02280i	0.931670	−	0.363305i
$32$	−5.86239			−1.03633
$33$	−0.0957749	−	0.0695845i	−0.0166723	−	0.0121131i
$34$	3.84619	−	2.79442i	0.659616	−	0.479239i
$35$	3.44982	+	10.6175i	0.583126	+	1.79468i
$36$	4.30479			0.717466
$37$	−3.51693			−0.578179			−0.289090	−	0.957302i	$-0.593353\pi$
$37$	−3.51693			−0.578179			−0.289090	+	0.957302i	$0.593353\pi$
$38$	1.84294	+	5.67198i	0.298964	+	0.920116i
$39$	0.0116870	−	0.0359690i	0.00187142	−	0.00575965i
$40$	1.80643	−	5.55962i	0.285622	−	0.879053i
$41$	−3.57000	−	2.59375i	−0.557540	−	0.405076i	0.273018	−	0.962009i	$-0.411978\pi$
$41$	−3.57000	−	2.59375i	−0.557540	−	0.405076i	−0.830558	+	0.556933i	$0.811978\pi$
$42$	0.0432772	+	0.133194i	0.00667782	+	0.0205522i
$43$	−6.60141	−	4.79620i	−1.00671	−	0.731414i	−0.0431898	−	0.999067i	$-0.513752\pi$
$43$	−6.60141	−	4.79620i	−1.00671	−	0.731414i	−0.963515	+	0.267653i	$0.913752\pi$
$44$	−3.63553	+	2.64137i	−0.548077	+	0.398201i
$45$	−2.09867	+	6.45903i	−0.312851	+	0.962855i
$46$	−1.40890	+	1.02363i	−0.207731	+	0.150926i
$47$	4.28081	−	3.11019i	0.624420	−	0.453668i	−0.230043	−	0.973181i	$-0.573887\pi$
$47$	4.28081	−	3.11019i	0.624420	−	0.453668i	0.854463	+	0.519513i	$0.173887\pi$
$48$	−0.0108949	+	0.0335311i	−0.00157255	+	0.00483980i
$49$	−13.9928	+	10.1663i	−1.99897	+	1.45233i
$50$	0.0788395	+	0.0572802i	0.0111496	+	0.00810065i
$51$	−0.0739588	−	0.227622i	−0.0103563	−	0.0318734i
$52$	−1.16144	−	0.843834i	−0.161062	−	0.117019i
$53$	−2.96680	+	9.13087i	−0.407521	+	1.25422i	0.511251	+	0.859432i	$0.329182\pi$
$53$	−2.96680	+	9.13087i	−0.407521	+	1.25422i	−0.918772	+	0.394789i	$0.870818\pi$
$54$	−0.0526671	+	0.162093i	−0.00716709	+	0.0220580i
$55$	−2.19079	−	6.74256i	−0.295406	−	0.909167i
$56$	12.7221			1.70007
$57$	0.300236			0.0397672
$58$	−0.482386	−	1.48463i	−0.0633404	−	0.194942i
$59$	5.27694	−	3.83392i	0.686999	−	0.499134i	−0.188674	−	0.982040i	$-0.560419\pi$
$59$	5.27694	−	3.83392i	0.686999	−	0.499134i	0.875672	+	0.482906i	$0.160419\pi$
$60$	−0.0994866	−	0.0722813i	−0.0128437	−	0.00933147i
$61$	−10.5383			−1.34929			−0.674645	−	0.738142i	$-0.735703\pi$
$61$	−10.5383			−1.34929			−0.674645	+	0.738142i	$0.735703\pi$
$62$	4.04596	+	1.06119i	0.513838	+	0.134771i
$63$	−14.7802			−1.86214
$64$	−2.05466	−	1.49280i	−0.256833	−	0.186600i
$65$	1.83233	−	1.33127i	0.227273	−	0.165123i
$66$	−0.0274830	−	0.0845839i	−0.00338292	−	0.0104116i
$67$	−8.70583			−1.06359			−0.531793	−	0.846874i	$-0.678482\pi$
$67$	−8.70583			−1.06359			−0.531793	+	0.846874i	$0.678482\pi$
$68$	−9.08497			−1.10171
$69$	0.0270920	+	0.0833805i	0.00326149	+	0.0100378i
$70$	−2.59170	+	7.97642i	−0.309767	+	0.953365i
$71$	1.27915	−	3.93683i	0.151808	−	0.467216i	−0.846016	−	0.533158i	$-0.821005\pi$
$71$	1.27915	−	3.93683i	0.151808	−	0.467216i	0.997823	+	0.0659421i	$0.0210053\pi$
$72$	6.26129	+	4.54909i	0.737900	+	0.536116i
$73$	4.29337	+	13.2136i	0.502501	+	1.54654i	0.804932	+	0.593367i	$0.202202\pi$
$73$	4.29337	+	13.2136i	0.502501	+	1.54654i	−0.302431	+	0.953171i	$0.597798\pi$
$74$	−2.13751	−	1.55299i	−0.248481	−	0.180532i
$75$	0.00396898	−	0.00288363i	0.000458298	−	0.000332973i
$76$	3.52177	−	10.8389i	0.403975	−	1.24331i
$77$	12.4824	−	9.06897i	1.42250	−	1.03350i
$78$	0.0229862	−	0.0167005i	0.00260268	−	0.00189095i
$79$	2.40280	−	7.39504i	0.270336	−	0.832007i	−0.720080	−	0.693891i	$-0.755895\pi$
$79$	2.40280	−	7.39504i	0.270336	−	0.832007i	0.990416	−	0.138117i	$-0.0441049\pi$
$80$	−1.70814	+	1.24104i	−0.190976	+	0.138752i
$81$	−7.27074	−	5.28250i	−0.807860	−	0.586945i
$82$	−1.02442	−	3.15285i	−0.113129	−	0.348175i
$83$	−13.0164	−	9.45697i	−1.42874	−	1.03804i	−0.990250	−	0.139298i	$-0.955515\pi$
$83$	−13.0164	−	9.45697i	−1.42874	−	1.03804i	−0.438485	−	0.898739i	$-0.644485\pi$
$84$	0.0827009	−	0.254527i	0.00902341	−	0.0277712i
$85$	4.42909	−	13.6313i	0.480402	−	1.47853i
$86$	−1.89430	−	5.83006i	−0.204268	−	0.628671i
$87$	−0.0785863			−0.00842534
$88$	−8.07912			−0.861237
$89$	0.889244	+	2.73681i	0.0942597	+	0.290102i	0.987060	−	0.160351i	$-0.0512626\pi$
$89$	0.889244	+	2.73681i	0.0942597	+	0.290102i	−0.892800	+	0.450453i	$0.851263\pi$
$90$	−4.12768	+	2.99894i	−0.435096	+	0.316116i
$91$	3.98772	+	2.89725i	0.418027	+	0.303714i
$92$	3.32793			0.346961
$93$	0.113750	−	0.177206i	0.0117953	−	0.0183754i
$94$	3.97517			0.410007
$95$	14.5460	+	10.5683i	1.49239	+	1.08429i
$96$	−0.179372	+	0.130321i	−0.0183071	+	0.0133009i
$97$	−2.93705	−	9.03930i	−0.298212	−	0.917801i	−0.982124	−	0.188237i	$-0.939723\pi$
$97$	−2.93705	−	9.03930i	−0.298212	−	0.917801i	0.683912	−	0.729565i	$-0.260277\pi$
$98$	−12.9937			−1.31256
$99$	9.38612			0.943340
$100$	−0.0575465	−	0.177110i	−0.00575465	−	0.0177110i
$101$	1.20730	−	3.71569i	0.120131	−	0.369725i	−0.872852	−	0.487986i	$-0.837732\pi$
$101$	1.20730	−	3.71569i	0.120131	−	0.369725i	0.992983	+	0.118261i	$0.0377318\pi$
$102$	0.0555620	−	0.171002i	0.00550145	−	0.0169317i
$103$	5.96758	+	4.33570i	0.588003	+	0.427209i	0.841600	−	0.540101i	$-0.181614\pi$
$103$	5.96758	+	4.33570i	0.588003	+	0.427209i	−0.253597	+	0.967310i	$0.581614\pi$
$104$	−0.797580	−	2.45470i	−0.0782092	−	0.240703i
$105$	0.341581	+	0.248173i	0.0333349	+	0.0242192i
$106$	−5.83513	+	4.23947i	−0.566758	+	0.411774i
$107$	−5.31908	+	16.3704i	−0.514214	+	1.58259i	0.270492	+	0.962722i	$0.412814\pi$
$107$	−5.31908	+	16.3704i	−0.514214	+	1.58259i	−0.784707	+	0.619867i	$0.787186\pi$
$108$	0.263491	−	0.191437i	0.0253544	−	0.0184211i
$109$	−0.598078	+	0.434529i	−0.0572855	+	0.0416203i	−0.616059	−	0.787700i	$-0.711272\pi$
$109$	−0.598078	+	0.434529i	−0.0572855	+	0.0416203i	0.558774	+	0.829320i	$0.311272\pi$
$110$	1.64584	−	5.06538i	0.156925	−	0.482965i
$111$	−0.107608	+	0.0781815i	−0.0102137	+	0.00742066i
$112$	−3.71745	−	2.70088i	−0.351266	−	0.255210i
$113$	−1.97686	−	6.08416i	−0.185968	−	0.572349i	0.813996	−	0.580870i	$-0.197288\pi$
$113$	−1.97686	−	6.08416i	−0.185968	−	0.572349i	−0.999964	+	0.00852088i	$0.997288\pi$
$114$	0.182477	+	0.132577i	0.0170905	+	0.0124170i
$115$	−1.62243	+	4.99332i	−0.151292	+	0.465629i
$116$	−0.921819	+	2.83707i	−0.0855887	+	0.263415i
$117$	0.926609	+	2.85181i	0.0856650	+	0.263650i
$118$	4.90018			0.451098
$119$	31.1927			2.85943
$120$	−0.0683193	−	0.210265i	−0.00623667	−	0.0191945i
$121$	0.972328	−	0.706438i	0.0883935	−	0.0642216i
$122$	−6.40495	−	4.65347i	−0.579877	−	0.421305i
$123$	−0.166891			−0.0150480
$124$	−5.06308	−	6.18514i	−0.454678	−	0.555442i
$125$	−11.0306			−0.986611
$126$	−8.98311	−	6.52661i	−0.800279	−	0.581437i
$127$	3.59873	−	2.61463i	0.319336	−	0.232011i	−0.416556	−	0.909110i	$-0.636763\pi$
$127$	3.59873	−	2.61463i	0.319336	−	0.232011i	0.735892	+	0.677099i	$0.236763\pi$
$128$	3.03356	+	9.33634i	0.268131	+	0.825224i
$129$	−0.308604			−0.0271710
$130$	1.70151			0.149232
$131$	0.309367	+	0.952135i	0.0270296	+	0.0831884i	0.963661	−	0.267127i	$-0.0860744\pi$
$131$	0.309367	+	0.952135i	0.0270296	+	0.0831884i	−0.936632	+	0.350316i	$0.886074\pi$
$132$	−0.0525187	+	0.161636i	−0.00457117	+	0.0140686i
$133$	−12.0918	+	37.2147i	−1.04849	+	3.22692i
$134$	−5.29122	−	3.84429i	−0.457091	−	0.332096i
$135$	0.158781	+	0.488678i	0.0136657	+	0.0420587i
$136$	−13.2140	−	9.60055i	−1.13309	−	0.823241i
$137$	5.08034	−	3.69109i	0.434043	−	0.315351i	−0.349220	−	0.937041i	$-0.613554\pi$
$137$	5.08034	−	3.69109i	0.434043	−	0.315351i	0.783264	+	0.621690i	$0.213554\pi$
$138$	−0.0203530	+	0.0626400i	−0.00173256	+	0.00533227i
$139$	−1.64321	+	1.19386i	−0.139375	+	0.101262i	−0.655288	−	0.755379i	$-0.727453\pi$
$139$	−1.64321	+	1.19386i	−0.139375	+	0.101262i	0.515913	+	0.856641i	$0.327453\pi$
$140$	12.9661	−	9.42044i	1.09584	−	0.796172i
$141$	0.0618404	−	0.190325i	0.00520790	−	0.0160283i
$142$	2.51585	−	1.82787i	0.211126	−	0.153392i
$143$	−2.53238	−	1.83988i	−0.211769	−	0.153859i
$144$	−0.863806	−	2.65852i	−0.0719839	−	0.221544i
$145$	−3.80741	−	2.76624i	−0.316188	−	0.229724i
$146$	−3.22542	+	9.92681i	−0.266937	+	0.821548i
$147$	−0.202139	+	0.622120i	−0.0166722	+	0.0513116i
$148$	1.56021	+	4.80184i	0.128249	+	0.394709i
$149$	−8.18293			−0.670372			−0.335186	−	0.942152i	$-0.608799\pi$
$149$	−8.18293			−0.670372			−0.335186	+	0.942152i	$0.608799\pi$
$150$	0.00368560			0.000300928
$151$	−0.507356	−	1.56148i	−0.0412880	−	0.127072i	0.928288	−	0.371862i	$-0.121281\pi$
$151$	−0.507356	−	1.56148i	−0.0412880	−	0.127072i	−0.969576	+	0.244791i	$0.921281\pi$
$152$	16.5764	−	12.0435i	1.34452	−	0.976854i
$153$	15.3517	+	11.1537i	1.24111	+	0.901722i
$154$	11.5912			0.934042
$155$	11.7487	−	4.58141i	0.943678	−	0.367987i
$156$	−0.0542951			−0.00434708
$157$	4.01059	+	2.91386i	0.320080	+	0.232551i	0.736209	−	0.676754i	$-0.236614\pi$
$157$	4.01059	+	2.91386i	0.320080	+	0.232551i	−0.416130	+	0.909305i	$0.636614\pi$
$158$	4.72585	−	3.43353i	0.375968	−	0.273157i
$159$	0.112204	+	0.345330i	0.00889839	+	0.0273864i
$160$	−13.2776			−1.04969
$161$	−11.4262			−0.900514
$162$	−2.08637	−	6.42118i	−0.163921	−	0.504496i
$163$	−4.35670	+	13.4086i	−0.341243	+	1.05024i	0.622321	+	0.782762i	$0.286190\pi$
$163$	−4.35670	+	13.4086i	−0.341243	+	1.05024i	−0.963564	+	0.267477i	$0.913810\pi$
$164$	−1.95763	+	6.02497i	−0.152865	+	0.470471i
$165$	−0.216919	−	0.157601i	−0.0168871	−	0.0122692i
$166$	−3.73511	−	11.4955i	−0.289900	−	0.892222i
$167$	6.05733	+	4.40091i	0.468730	+	0.340552i	0.796946	−	0.604050i	$-0.206447\pi$
$167$	6.05733	+	4.40091i	0.468730	+	0.340552i	−0.328216	+	0.944603i	$0.606447\pi$
$168$	0.389260	−	0.282814i	0.0300320	−	0.0218195i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	8.71119	−	6.32905i	0.668118	−	0.485416i
$171$	−19.2580	+	13.9918i	−1.47270	+	1.06998i
$172$	−3.61992	+	11.1410i	−0.276017	+	0.849492i
$173$	2.01959	−	1.46732i	0.153547	−	0.111558i	−0.508359	−	0.861145i	$-0.669748\pi$
$173$	2.01959	−	1.46732i	0.153547	−	0.111558i	0.661906	+	0.749587i	$0.269748\pi$
$174$	−0.0477631	−	0.0347019i	−0.00362091	−	0.00263074i
$175$	0.197582	+	0.608096i	0.0149358	+	0.0459678i
$176$	2.36075	+	1.71518i	0.177948	+	0.129287i
$177$	0.0762305	−	0.234613i	0.00572983	−	0.0176346i
$178$	−0.668050	+	2.05605i	−0.0500724	+	0.154107i
$179$	−3.13887	−	9.66043i	−0.234610	−	0.722055i	−0.997173	−	0.0751410i	$-0.976059\pi$
$179$	−3.13887	−	9.66043i	−0.234610	−	0.722055i	0.762563	−	0.646914i	$-0.223941\pi$
$180$	9.74987			0.726713
$181$	−3.87280			−0.287863			−0.143931	−	0.989588i	$-0.545974\pi$
$181$	−3.87280			−0.287863			−0.143931	+	0.989588i	$0.545974\pi$
$182$	1.14429	+	3.52177i	0.0848207	+	0.261051i
$183$	−0.322441	+	0.234267i	−0.0238355	+	0.0173175i
$184$	4.84045	+	3.51679i	0.356843	+	0.259261i
$185$	−7.96544			−0.585631
$186$	0.147385	−	0.0574727i	0.0108068	−	0.00421410i
$187$	−19.8088			−1.44856
$188$	−6.14559	−	4.46503i	−0.448213	−	0.325646i
$189$	−0.904680	+	0.657288i	−0.0658058	+	0.0478107i
$190$	4.17404	+	12.8464i	0.302817	+	0.931975i
$191$	9.36160			0.677381			0.338691	−	0.940898i	$-0.390016\pi$
$191$	9.36160			0.677381			0.338691	+	0.940898i	$0.390016\pi$
$192$	−0.0960517			−0.00693193
$193$	−5.12915	−	15.7859i	−0.369204	−	1.13629i	−0.947306	−	0.320330i	$-0.896206\pi$
$193$	−5.12915	−	15.7859i	−0.369204	−	1.13629i	0.578102	−	0.815965i	$-0.303794\pi$
$194$	2.20647	−	6.79082i	0.158415	−	0.487552i
$195$	0.0264698	−	0.0814658i	0.00189554	−	0.00583388i
$196$	20.0882	+	14.5950i	1.43487	+	1.04250i
$197$	4.92959	+	15.1717i	0.351219	+	1.08094i	0.958170	+	0.286201i	$0.0923925\pi$
$197$	4.92959	+	15.1717i	0.351219	+	1.08094i	−0.606951	+	0.794739i	$0.707608\pi$
$198$	5.70468	+	4.14469i	0.405414	+	0.294550i
$199$	20.9748	−	15.2391i	1.48687	−	1.08027i	0.511604	−	0.859222i	$-0.329052\pi$
$199$	20.9748	−	15.2391i	1.48687	−	1.08027i	0.975263	−	0.221050i	$-0.0709483\pi$
$200$	0.103460	−	0.318418i	0.00731574	−	0.0225155i
$201$	−0.266373	+	0.193531i	−0.0187885	+	0.0136506i
$202$	2.37453	−	1.72520i	0.167072	−	0.121385i
$203$	3.16501	−	9.74089i	0.222140	−	0.683677i
$204$	−0.277974	+	0.201960i	−0.0194620	+	0.0141400i
$205$	−8.08564	−	5.87456i	−0.564726	−	0.410297i
$206$	1.71242	+	5.27029i	0.119310	+	0.367198i
$207$	−5.62351	−	4.08572i	−0.390861	−	0.283977i
$208$	−0.288073	+	0.886597i	−0.0199743	+	0.0614744i
$209$	7.67882	−	23.6330i	0.531155	−	1.63473i
$210$	0.0980181	+	0.301669i	0.00676389	+	0.0208171i
$211$	1.36864			0.0942209			0.0471104	−	0.998890i	$-0.484999\pi$
$211$	1.36864			0.0942209			0.0471104	+	0.998890i	$0.484999\pi$
$212$	13.7830			0.946620
$213$	−0.0483776	−	0.148891i	−0.00331478	−	0.0102018i
$214$	−10.4616	+	7.60081i	−0.715142	+	0.519581i
$215$	−14.9514	−	10.8629i	−1.01968	−	0.740841i
$216$	0.585547			0.0398414
$217$	17.3838	+	21.2363i	1.18009	+	1.44161i
$218$	−0.555377			−0.0376149
$219$	0.425104	+	0.308856i	0.0287259	+	0.0208706i
$220$	−8.23406	+	5.98240i	−0.555141	+	0.403333i
$221$	−1.95555	−	6.01855i	−0.131544	−	0.404851i
$222$	−0.0999247			−0.00670651
$223$	9.64867			0.646122			0.323061	−	0.946378i	$-0.395288\pi$
$223$	9.64867			0.646122			0.323061	+	0.946378i	$0.395288\pi$
$224$	−8.92944	−	27.4820i	−0.596623	−	1.83622i
$225$	−0.120197	+	0.369930i	−0.00801316	+	0.0246620i
$226$	1.48513	−	4.57076i	0.0987893	−	0.304042i
$227$	22.2801	+	16.1875i	1.47879	+	1.07440i	0.977945	+	0.208860i	$0.0669754\pi$
$227$	22.2801	+	16.1875i	1.47879	+	1.07440i	0.500840	+	0.865540i	$0.333025\pi$
$228$	−0.133194	−	0.409928i	−0.00882096	−	0.0271481i
$229$	15.4283	+	11.2093i	1.01953	+	0.740734i	0.966187	−	0.257842i	$-0.0830114\pi$
$229$	15.4283	+	11.2093i	1.01953	+	0.740734i	0.0533460	+	0.998576i	$0.483011\pi$
$230$	−3.19101	+	2.31840i	−0.210409	+	0.152871i
$231$	0.180320	−	0.554968i	0.0118642	−	0.0365142i
$232$	−4.33885	+	3.15236i	−0.284859	+	0.206963i
$233$	0.126551	−	0.0919444i	0.00829060	−	0.00602348i	−0.583632	−	0.812018i	$-0.698369\pi$
$233$	0.126551	−	0.0919444i	0.00829060	−	0.00602348i	0.591923	+	0.805995i	$0.298369\pi$
$234$	−0.696120	+	2.14244i	−0.0455068	+	0.140055i
$235$	9.69555	−	7.04423i	0.632468	−	0.459515i
$236$	−7.57565	−	5.50403i	−0.493133	−	0.358282i
$237$	−0.0908738	−	0.279681i	−0.00590289	−	0.0181672i
$238$	18.9582	+	13.7740i	1.22888	+	0.892834i
$239$	−0.386452	+	1.18938i	−0.0249975	+	0.0769344i	−0.962777	−	0.270297i	$-0.912878\pi$
$239$	−0.386452	+	1.18938i	−0.0249975	+	0.0769344i	0.937780	+	0.347231i	$0.112878\pi$
$240$	−0.0246758	+	0.0759443i	−0.00159282	+	0.00490218i
$241$	4.46025	+	13.7272i	0.287310	+	0.884249i	0.985697	+	0.168528i	$0.0539014\pi$
$241$	4.46025	+	13.7272i	0.287310	+	0.884249i	−0.698387	+	0.715720i	$0.746099\pi$
$242$	0.902907			0.0580410
$243$	−1.02049			−0.0654646
$244$	4.67510	+	14.3885i	0.299293	+	0.921128i
$245$	−31.6920	+	23.0256i	−2.02473	+	1.47105i
$246$	−0.101433	−	0.0736951i	−0.00646710	−	0.00469863i
$247$	7.93854			0.505117
$248$	−0.828052	−	14.3467i	−0.0525814	−	0.911014i
$249$	−0.608492			−0.0385616
$250$	−6.70419	−	4.87088i	−0.424010	−	0.308061i
$251$	−0.0900355	+	0.0654146i	−0.00568299	+	0.00412894i	−0.590623	−	0.806948i	$-0.701118\pi$
$251$	−0.0900355	+	0.0654146i	−0.00568299	+	0.00412894i	0.584940	+	0.811076i	$0.301118\pi$
$252$	6.55695	+	20.1802i	0.413049	+	1.27123i
$253$	7.25617			0.456192
$254$	3.34179			0.209683
$255$	−0.167508	−	0.515538i	−0.0104898	−	0.0322842i
$256$	−3.84860	+	11.8448i	−0.240538	+	0.740298i
$257$	5.15613	−	15.8689i	0.321631	−	0.989877i	−0.651308	−	0.758813i	$-0.725779\pi$
$257$	5.15613	−	15.8689i	0.321631	−	0.989877i	0.972939	−	0.231064i	$-0.0742206\pi$
$258$	−0.187563	−	0.136272i	−0.0116771	−	0.00848394i
$259$	−5.35689	−	16.4868i	−0.332861	−	1.02444i
$260$	−2.63053	−	1.91119i	−0.163138	−	0.118527i
$261$	5.04077	−	3.66233i	0.312016	−	0.226693i
$262$	−0.232414	+	0.715296i	−0.0143586	+	0.0441912i
$263$	20.5320	−	14.9174i	1.26606	−	0.919845i	0.267020	−	0.963691i	$-0.413961\pi$
$263$	20.5320	−	14.9174i	1.26606	−	0.919845i	0.999038	+	0.0438454i	$0.0139609\pi$
$264$	−0.247197	+	0.179599i	−0.0152139	+	0.0110536i
$265$	−6.71947	+	20.6804i	−0.412773	+	1.27039i
$266$	−23.7823	+	17.2788i	−1.45818	+	1.05943i
$267$	0.0880478	+	0.0639705i	0.00538844	+	0.00391493i
$268$	3.86217	+	11.8865i	0.235919	+	0.726085i
$269$	−1.01999	−	0.741067i	−0.0621899	−	0.0451836i	0.556256	−	0.831011i	$-0.312237\pi$
$269$	−1.01999	−	0.741067i	−0.0621899	−	0.0451836i	−0.618446	+	0.785827i	$0.712237\pi$
$270$	−0.119285	+	0.367122i	−0.00725946	+	0.0223423i
$271$	−6.28334	+	19.3381i	−0.381686	+	1.17471i	0.557170	+	0.830398i	$0.311887\pi$
$271$	−6.28334	+	19.3381i	−0.381686	+	1.17471i	−0.938856	+	0.344310i	$0.888113\pi$
$272$	1.82300	+	5.61063i	0.110536	+	0.340194i
$273$	0.186419			0.0112826
$274$	4.71762			0.285002
$275$	−0.125474	−	0.386168i	−0.00756635	−	0.0232868i
$276$	0.101825	−	0.0739801i	0.00612914	−	0.00445308i
$277$	−3.51642	−	2.55483i	−0.211281	−	0.153505i	0.477112	−	0.878842i	$-0.341684\pi$
$277$	−3.51642	−	2.55483i	−0.211281	−	0.153505i	−0.688393	+	0.725338i	$0.741684\pi$
$278$	−1.52589			−0.0915165
$279$	0.962011	+	16.6676i	0.0575941	+	0.997863i
$280$	28.8142			1.72198
$281$	−1.86472	−	1.35480i	−0.111240	−	0.0808204i	0.530775	−	0.847513i	$-0.321901\pi$
$281$	−1.86472	−	1.35480i	−0.111240	−	0.0808204i	−0.642014	+	0.766693i	$0.721901\pi$
$282$	0.121628	−	0.0883683i	0.00724287	−	0.00526225i
$283$	−6.73238	−	20.7201i	−0.400199	−	1.23168i	−0.924838	−	0.380360i	$-0.875800\pi$
$283$	−6.73238	−	20.7201i	−0.400199	−	1.23168i	0.524640	−	0.851324i	$-0.324200\pi$
$284$	−5.94262			−0.352630
$285$	0.680001			0.0402798
$286$	−0.726677	−	2.23648i	−0.0429693	−	0.132246i
$287$	6.72140	−	20.6863i	0.396752	−	1.22108i
$288$	5.43214	−	16.7184i	0.320092	−	0.985142i
$289$	−18.6455	−	13.5467i	−1.09679	−	0.796867i
$290$	−1.09255	−	3.36252i	−0.0641568	−	0.197454i
$291$	−0.290809	−	0.211285i	−0.0170475	−	0.0123858i
$292$	16.1366	−	11.7239i	0.944322	−	0.686090i
$293$	6.87281	−	21.1523i	0.401514	−	1.23573i	−0.522257	−	0.852788i	$-0.674910\pi$
$293$	6.87281	−	21.1523i	0.401514	−	1.23573i	0.923771	−	0.382945i	$-0.125090\pi$
$294$	−0.397570	+	0.288851i	−0.0231867	+	0.0168461i
$295$	11.9517	−	8.68340i	0.695853	−	0.505567i
$296$	−2.80503	+	8.63300i	−0.163039	+	0.501783i
$297$	0.574512	−	0.417407i	0.0333366	−	0.0242204i
$298$	−4.97341	−	3.61339i	−0.288102	−	0.209318i
$299$	0.716339	+	2.20466i	0.0414269	+	0.127499i
$300$	−0.00569792	−	0.00413978i	−0.000328970	−	0.000239010i
$301$	12.4288	−	38.2519i	0.716383	−	2.20480i
$302$	0.381154	−	1.17307i	0.0219329	−	0.0675027i
$303$	−0.0456602	−	0.140528i	−0.00262311	−	0.00807310i
$304$	−7.40049			−0.424447
$305$	−23.8681			−1.36668
$306$	4.40524	+	13.5579i	0.251831	+	0.775055i
$307$	−2.19783	+	1.59682i	−0.125437	+	0.0911353i	−0.648735	−	0.761015i	$-0.724702\pi$
$307$	−2.19783	+	1.59682i	−0.125437	+	0.0911353i	0.523298	+	0.852150i	$0.324702\pi$
$308$	−17.9199	−	13.0196i	−1.02108	−	0.741858i
$309$	0.278973			0.0158702
$310$	9.16365	+	2.40347i	0.520460	+	0.136508i
$311$	19.1878			1.08804			0.544019	−	0.839073i	$-0.316902\pi$
$311$	19.1878			1.08804			0.544019	+	0.839073i	$0.316902\pi$
$312$	−0.0789718	−	0.0573763i	−0.00447090	−	0.00324830i
$313$	−0.0754387	+	0.0548094i	−0.00426405	+	0.00309801i	−0.589915	−	0.807465i	$-0.700839\pi$
$313$	−0.0754387	+	0.0548094i	−0.00426405	+	0.00309801i	0.585651	+	0.810563i	$0.300839\pi$
$314$	1.15085	+	3.54196i	0.0649464	+	0.199885i
$315$	−33.4756			−1.88614
$316$	−11.1628			−0.627956
$317$	3.87934	+	11.9394i	0.217886	+	0.670583i	0.998936	+	0.0461151i	$0.0146841\pi$
$317$	3.87934	+	11.9394i	0.217886	+	0.670583i	−0.781051	+	0.624468i	$0.785316\pi$
$318$	−0.0842942	+	0.259431i	−0.00472698	+	0.0145482i
$319$	−2.00992	+	6.18590i	−0.112534	+	0.346344i
$320$	−4.65358	−	3.38102i	−0.260143	−	0.189005i
$321$	0.201168	+	0.619131i	0.0112281	+	0.0345565i
$322$	−6.94462	−	5.04556i	−0.387009	−	0.281178i
$323$	40.6428	−	29.5287i	2.26143	−	1.64302i
$324$	−3.98696	+	12.2706i	−0.221498	+	0.681699i
$325$	0.104944	−	0.0762460i	0.00582123	−	0.00422937i
$326$	−8.56881	+	6.22561i	−0.474583	+	0.344804i
$327$	−0.00863982	+	0.0265906i	−0.000477783	+	0.00147046i
$328$	−9.21425	+	6.69454i	−0.508772	+	0.369644i
$329$	21.1005	+	15.3304i	1.16331	+	0.845194i
$330$	−0.0622459	−	0.191573i	−0.00342652	−	0.0105457i
$331$	−4.68803	−	3.40605i	−0.257677	−	0.187213i	0.451445	−	0.892299i	$-0.350909\pi$
$331$	−4.68803	−	3.40605i	−0.257677	−	0.187213i	−0.709122	+	0.705085i	$0.750909\pi$
$332$	−7.13762	+	21.9673i	−0.391728	+	1.20561i
$333$	3.25882	−	10.0296i	0.178582	−	0.549619i
$334$	1.73817	+	5.34955i	0.0951087	+	0.292714i
$335$	−19.7177			−1.07730
$336$	−0.173784			−0.00948069
$337$	8.00749	+	24.6445i	0.436196	+	1.34247i	0.891856	+	0.452319i	$0.149403\pi$
$337$	8.00749	+	24.6445i	0.436196	+	1.34247i	−0.455661	+	0.890153i	$0.650597\pi$
$338$	0.607778	−	0.441577i	0.0330588	−	0.0240186i
$339$	−0.195737	−	0.142212i	−0.0106310	−	0.00772387i
$340$	−20.5764			−1.11591
$341$	−11.0395	−	13.4860i	−0.597821	−	0.730308i
$342$	−17.8831			−0.967006
$343$	−41.0576	−	29.8301i	−2.21690	−	1.61068i
$344$	−17.0384	+	12.3791i	−0.918649	+	0.667437i
$345$	0.0613603	+	0.188847i	0.00330353	+	0.0101672i
$346$	1.87540			0.100822
$347$	8.78886			0.471811			0.235905	−	0.971776i	$-0.424194\pi$
$347$	8.78886			0.471811			0.235905	+	0.971776i	$0.424194\pi$
$348$	0.0348632	+	0.107298i	0.00186887	+	0.00575178i
$349$	−2.00456	+	6.16940i	−0.107302	+	0.330241i	−0.990264	−	0.139204i	$-0.955546\pi$
$349$	−2.00456	+	6.16940i	−0.107302	+	0.330241i	0.882962	+	0.469444i	$0.155546\pi$
$350$	−0.148435	+	0.456836i	−0.00793418	+	0.0244189i
$351$	0.183539	+	0.133349i	0.00979657	+	0.00711762i
$352$	5.67059	+	17.4523i	0.302244	+	0.930210i
$353$	−25.7496	−	18.7082i	−1.37052	−	0.995738i	−0.997697	−	0.0678332i	$-0.978391\pi$
$353$	−25.7496	−	18.7082i	−1.37052	−	0.995738i	−0.372818	−	0.927904i	$-0.621609\pi$
$354$	0.149931	−	0.108931i	0.00796874	−	0.00578963i
$355$	2.89714	−	8.91647i	0.153764	−	0.473237i
$356$	3.34222	−	2.42826i	0.177137	−	0.128698i
$357$	0.954405	−	0.693416i	0.0505125	−	0.0366995i
$358$	2.35809	−	7.25745i	0.124629	−	0.383568i
$359$	5.69669	−	4.13889i	0.300660	−	0.218442i	−0.427218	−	0.904148i	$-0.640506\pi$
$359$	5.69669	−	4.13889i	0.300660	−	0.218442i	0.727878	+	0.685706i	$0.240506\pi$
$360$	14.1811	+	10.3032i	0.747411	+	0.543026i
$361$	13.6030	+	41.8659i	0.715950	+	2.20347i
$362$	−2.35380	−	1.71014i	−0.123713	−	0.0898828i
$363$	0.0140462	−	0.0432298i	0.000737236	−	0.00226898i
$364$	2.18669	−	6.72995i	0.114614	−	0.352745i
$365$	9.72400	+	29.9274i	0.508977	+	1.56647i
$366$	−0.299419			−0.0156509
$367$	−12.7882			−0.667536			−0.333768	−	0.942655i	$-0.608320\pi$
$367$	−12.7882			−0.667536			−0.333768	+	0.942655i	$0.608320\pi$
$368$	−0.667787	−	2.05524i	−0.0348108	−	0.107137i
$369$	10.7049	−	7.77755i	0.557274	−	0.404883i
$370$	−4.84122	−	3.51735i	−0.251683	−	0.182859i
$371$	−47.3231			−2.45689
$372$	−0.292411	−	0.0766947i	−0.0151608	−	0.00397644i
$373$	−0.852604			−0.0441462			−0.0220731	−	0.999756i	$-0.507027\pi$
$373$	−0.852604			−0.0441462			−0.0220731	+	0.999756i	$0.507027\pi$
$374$	−12.0393	−	8.74709i	−0.622539	−	0.452301i
$375$	−0.337505	+	0.245212i	−0.0174287	+	0.0126627i
$376$	−4.22029	−	12.9887i	−0.217645	−	0.669842i
$377$	−2.07790			−0.107017
$378$	−0.840088			−0.0432095
$379$	−2.86262	−	8.81022i	−0.147043	−	0.452551i	0.850225	−	0.526419i	$-0.176466\pi$
$379$	−2.86262	−	8.81022i	−0.147043	−	0.452551i	−0.997268	+	0.0738681i	$0.976466\pi$
$380$	7.97641	−	24.5489i	0.409181	−	1.25933i
$381$	0.0519872	−	0.160000i	0.00266339	−	0.00819706i
$382$	5.68978	+	4.13386i	0.291114	+	0.211507i
$383$	10.7719	+	33.1524i	0.550417	+	1.69401i	0.707750	+	0.706463i	$0.249710\pi$
$383$	10.7719	+	33.1524i	0.550417	+	1.69401i	−0.157333	+	0.987546i	$0.550290\pi$
$384$	0.300365	+	0.218228i	0.0153280	+	0.0111364i
$385$	28.2712	−	20.5402i	1.44083	−	1.04683i
$386$	3.85330	−	11.8592i	0.196128	−	0.603620i
$387$	19.7948	−	14.3817i	1.00623	−	0.731065i
$388$	−11.0389	+	8.02020i	−0.560413	+	0.407164i
$389$	−3.45401	+	10.6304i	−0.175125	+	0.538980i	−0.999639	−	0.0268615i	$-0.991449\pi$
$389$	−3.45401	+	10.6304i	−0.175125	+	0.538980i	0.824514	+	0.565842i	$0.191449\pi$
$390$	0.0520612	−	0.0378247i	0.00263622	−	0.00191533i
$391$	11.8680	+	8.62264i	0.600193	+	0.436066i
$392$	13.7950	+	42.4565i	0.696751	+	2.14438i
$393$	0.0306318	+	0.0222553i	0.00154517	+	0.00112263i
$394$	−3.70338	+	11.3978i	−0.186574	+	0.574215i
$395$	5.44206	−	16.7489i	0.273820	−	0.842731i
$396$	−4.16396	−	12.8153i	−0.209247	−	0.643995i
$397$	−25.4907			−1.27934			−0.639671	−	0.768649i	$-0.720929\pi$
$397$	−25.4907			−1.27934			−0.639671	+	0.768649i	$0.720929\pi$
$398$	19.4773			0.976308
$399$	0.457312	+	1.40746i	0.0228942	+	0.0704612i
$400$	−0.0978309	+	0.0710783i	−0.00489155	+	0.00355392i
$401$	−13.7414	−	9.98374i	−0.686215	−	0.498564i	0.189199	−	0.981939i	$-0.439411\pi$
$401$	−13.7414	−	9.98374i	−0.686215	−	0.498564i	−0.875414	+	0.483374i	$0.839411\pi$
$402$	−0.247355			−0.0123369
$403$	3.00766	−	4.68551i	0.149822	−	0.233402i
$404$	−5.60882			−0.279049
$405$	−16.4674	−	11.9643i	−0.818272	−	0.594510i
$406$	6.22497	−	4.52271i	0.308940	−	0.224458i
$407$	3.40187	+	10.4699i	0.168624	+	0.518972i
$408$	−0.617731			−0.0305823
$409$	−21.8069			−1.07828			−0.539141	−	0.842215i	$-0.681251\pi$
$409$	−21.8069			−1.07828			−0.539141	+	0.842215i	$0.681251\pi$
$410$	−2.32021	−	7.14086i	−0.114587	−	0.352662i
$411$	0.0733905	−	0.225873i	0.00362009	−	0.0111415i
$412$	3.27236	−	10.0713i	0.161218	−	0.496177i
$413$	26.0105	+	18.8978i	1.27989	+	0.929898i
$414$	−1.61369	−	4.96643i	−0.0793085	−	0.244087i
$415$	−29.4807	−	21.4190i	−1.44715	−	1.05142i
$416$	−4.74277	+	3.44582i	−0.232533	+	0.168945i
$417$	−0.0237377	+	0.0730572i	−0.00116244	+	0.00357762i
$418$	15.1028	−	10.9728i	0.738702	−	0.536698i
$419$	−1.47404	+	1.07095i	−0.0720116	+	0.0523195i	−0.623209	−	0.782056i	$-0.714171\pi$
$419$	−1.47404	+	1.07095i	−0.0720116	+	0.0523195i	0.551197	+	0.834375i	$0.314171\pi$
$420$	0.187308	−	0.576475i	0.00913970	−	0.0281291i
$421$	−7.64530	+	5.55464i	−0.372609	+	0.270716i	−0.758292	−	0.651915i	$-0.773966\pi$
$421$	−7.64530	+	5.55464i	−0.372609	+	0.270716i	0.385683	+	0.922631i	$0.373966\pi$
$422$	0.831828	+	0.604358i	0.0404928	+	0.0294197i
$423$	4.90303	+	15.0900i	0.238393	+	0.733700i
$424$	20.0473	+	14.5652i	0.973582	+	0.707349i
$425$	0.253668	−	0.780711i	0.0123047	−	0.0378701i
$426$	0.0363439	−	0.111855i	0.00176087	−	0.00541940i
$427$	−16.0517	−	49.4020i	−0.776795	−	2.39073i
$428$	24.7111			1.19446
$429$	−0.118384			−0.00571564
$430$	−4.29038	−	13.2044i	−0.206900	−	0.636774i
$431$	14.0495	−	10.2075i	0.676740	−	0.491680i	−0.195535	−	0.980697i	$-0.562644\pi$
$431$	14.0495	−	10.2075i	0.676740	−	0.491680i	0.872274	+	0.489017i	$0.162644\pi$
$432$	−0.171099	−	0.124311i	−0.00823200	−	0.00598090i
$433$	−13.3029			−0.639297			−0.319649	−	0.947536i	$-0.603565\pi$
$433$	−13.3029			−0.639297			−0.319649	+	0.947536i	$0.603565\pi$
$434$	1.18801	+	20.5832i	0.0570264	+	0.988027i
$435$	−0.177989			−0.00853393
$436$	0.858610	+	0.623817i	0.0411200	+	0.0298754i
$437$	−14.8879	+	10.8167i	−0.712186	+	0.517433i
$438$	0.121985	+	0.375432i	0.00582869	+	0.0179389i
$439$	8.39670			0.400753			0.200376	−	0.979719i	$-0.435784\pi$
$439$	8.39670			0.400753			0.200376	+	0.979719i	$0.435784\pi$
$440$	−18.2983			−0.872337
$441$	−16.0266	−	49.3249i	−0.763173	−	2.34881i
$442$	1.46911	−	4.52147i	0.0698786	−	0.215064i
$443$	−9.07942	+	27.9436i	−0.431376	+	1.32764i	0.465378	+	0.885112i	$0.345918\pi$
$443$	−9.07942	+	27.9436i	−0.431376	+	1.32764i	−0.896755	+	0.442528i	$0.854082\pi$
$444$	0.154483	+	0.112239i	0.00733145	+	0.00532661i
$445$	2.01404	+	6.19857i	0.0954746	+	0.293841i
$446$	5.86425	+	4.26063i	0.277680	+	0.201747i
$447$	−0.250374	+	0.181907i	−0.0118423	+	0.00860391i
$448$	3.86841	−	11.9057i	0.182765	−	0.562494i
$449$	15.3905	−	11.1818i	0.726321	−	0.527703i	−0.162076	−	0.986778i	$-0.551819\pi$
$449$	15.3905	−	11.1818i	0.726321	−	0.527703i	0.888398	+	0.459075i	$0.151819\pi$
$450$	−0.236406	+	0.171759i	−0.0111443	+	0.00809679i
$451$	−4.26839	+	13.1368i	−0.200991	+	0.618586i
$452$	−7.43002	+	5.39823i	−0.349479	+	0.253911i
$453$	−0.0502354	−	0.0364982i	−0.00236027	−	0.00171483i
$454$	6.39338	+	19.6768i	0.300056	+	0.923477i
$455$	9.03175	+	6.56195i	0.423415	+	0.307629i
$456$	0.239462	−	0.736989i	0.0112138	−	0.0345127i
$457$	2.98443	−	9.18512i	0.139606	−	0.429662i	−0.856672	−	0.515861i	$-0.827472\pi$
$457$	2.98443	−	9.18512i	0.139606	−	0.429662i	0.996278	+	0.0861992i	$0.0274721\pi$
$458$	4.42722	+	13.6256i	0.206871	+	0.636682i
$459$	1.43567			0.0670114
$460$	7.53739			0.351433
$461$	−4.42966	−	13.6331i	−0.206310	−	0.634956i	−0.999657	−	0.0261870i	$-0.991663\pi$
$461$	−4.42966	−	13.6331i	−0.206310	−	0.634956i	0.793347	−	0.608769i	$-0.208337\pi$
$462$	0.354655	−	0.257672i	0.0165001	−	0.0119880i
$463$	−20.7280	−	15.0598i	−0.963312	−	0.699887i	−0.00939473	−	0.999956i	$-0.502990\pi$
$463$	−20.7280	−	15.0598i	−0.963312	−	0.699887i	−0.953918	+	0.300068i	$0.902990\pi$
$464$	1.93707			0.0899261
$465$	0.257631	−	0.401352i	0.0119473	−	0.0186123i
$466$	0.117515			0.00544379
$467$	28.1867	+	20.4788i	1.30432	+	0.947647i	0.999988	−	0.00491733i	$-0.00156524\pi$
$467$	28.1867	+	20.4788i	1.30432	+	0.947647i	0.304337	+	0.952565i	$0.401565\pi$
$468$	3.48265	−	2.53029i	0.160986	−	0.116963i
$469$	−13.2605	−	40.8117i	−0.612313	−	1.88451i
$470$	9.00331			0.415292
$471$	0.187488			0.00863897
$472$	−5.20234	−	16.0112i	−0.239457	−	0.736973i
$473$	−7.89283	+	24.2916i	−0.362913	+	1.11693i
$474$	0.0682695	−	0.210112i	0.00313572	−	0.00965075i
$475$	0.833099	+	0.605282i	0.0382252	+	0.0277722i
$476$	−13.8380	−	42.5890i	−0.634264	−	1.95206i
$477$	−23.2904	−	16.9215i	−1.06640	−	0.774782i
$478$	−0.760078	+	0.552229i	−0.0347652	+	0.0252584i
$479$	−4.13231	+	12.7179i	−0.188810	+	0.581098i	−0.999993	−	0.00369461i	$-0.998824\pi$
$479$	−4.13231	+	12.7179i	−0.188810	+	0.581098i	0.811183	+	0.584792i	$0.198824\pi$
$480$	−0.406257	+	0.295163i	−0.0185430	+	0.0134723i
$481$	−2.84525	+	2.06720i	−0.129732	+	0.0942561i
$482$	−3.35078	+	10.3127i	−0.152624	+	0.469728i
$483$	−0.349609	+	0.254006i	−0.0159078	+	0.0115577i
$484$	−1.39589	−	1.01417i	−0.0634495	−	0.0460988i
$485$	−6.65208	−	20.4730i	−0.302055	−	0.929631i
$486$	−0.620233	−	0.450626i	−0.0281343	−	0.0204408i
$487$	−5.71201	+	17.5798i	−0.258836	+	0.796615i	0.734214	+	0.678918i	$0.237551\pi$
$487$	−5.71201	+	17.5798i	−0.258836	+	0.796615i	−0.993050	+	0.117696i	$0.962449\pi$
$488$	−8.40514	+	25.8684i	−0.380483	+	1.17101i
$489$	0.164771	+	0.507112i	0.00745119	+	0.0229324i
$490$	−29.4293			−1.32948
$491$	−19.0472			−0.859587			−0.429793	−	0.902927i	$-0.641414\pi$
$491$	−19.0472			−0.859587			−0.429793	+	0.902927i	$0.641414\pi$
$492$	0.0740377	+	0.227864i	0.00333788	+	0.0102729i
$493$	−10.6382	+	7.72910i	−0.479120	+	0.348101i
$494$	4.82487	+	3.50547i	0.217081	+	0.157719i
$495$	21.2585			0.955498
$496$	−2.80381	+	4.36794i	−0.125895	+	0.196126i
$497$	20.4036			0.915228
$498$	−0.369829	−	0.268696i	−0.0165724	−	0.0120406i
$499$	2.54870	−	1.85174i	0.114095	−	0.0828951i	−0.529274	−	0.848451i	$-0.677536\pi$
$499$	2.54870	−	1.85174i	0.114095	−	0.0828951i	0.643370	+	0.765556i	$0.277536\pi$
$500$	4.89352	+	15.0607i	0.218845	+	0.673535i
$501$	0.283169			0.0126511
$502$	−0.0836072			−0.00373157
$503$	3.14072	+	9.66615i	0.140038	+	0.430992i	0.996340	−	0.0854837i	$-0.0272436\pi$
$503$	3.14072	+	9.66615i	0.140038	+	0.430992i	−0.856302	+	0.516476i	$0.827244\pi$
$504$	−11.7884	+	36.2811i	−0.525099	+	1.61609i
$505$	2.73440	−	8.41562i	0.121679	−	0.374490i
$506$	4.41015	+	3.20416i	0.196055	+	0.142442i
$507$	−0.0116870	−	0.0359690i	−0.000519040	−	0.00159744i
$508$	−5.16640	−	3.75361i	−0.229222	−	0.166539i
$509$	−19.0405	+	13.8337i	−0.843955	+	0.613169i	−0.923473	−	0.383665i	$-0.874662\pi$
$509$	−19.0405	+	13.8337i	−0.843955	+	0.613169i	0.0795180	+	0.996833i	$0.474662\pi$
$510$	0.125842	−	0.387301i	0.00557236	−	0.0171500i
$511$	−55.4040	+	40.2533i	−2.45093	+	1.78070i
$512$	8.31446	−	6.04081i	0.367450	−	0.266968i
$513$	−0.556535	+	1.71284i	−0.0245716	+	0.0756237i
$514$	10.1411	−	7.36797i	0.447306	−	0.324987i
$515$	13.5159	+	9.81988i	0.595582	+	0.432715i
$516$	0.136906	+	0.421352i	0.00602694	+	0.0185490i
$517$	−13.3998	−	9.73550i	−0.589321	−	0.428167i
$518$	4.02440	−	12.3858i	0.176822	−	0.544201i
$519$	0.0291750	−	0.0897915i	0.00128064	−	0.00394141i
$520$	−1.80643	−	5.55962i	−0.0792172	−	0.243805i
$521$	−28.3717			−1.24299			−0.621494	−	0.783419i	$-0.713474\pi$
$521$	−28.3717			−1.24299			−0.621494	+	0.783419i	$0.713474\pi$
$522$	4.68087			0.204876
$523$	10.4260	+	32.0879i	0.455897	+	1.40311i	0.870078	+	0.492913i	$0.164068\pi$
$523$	10.4260	+	32.0879i	0.455897	+	1.40311i	−0.414181	+	0.910195i	$0.635932\pi$
$524$	1.16275	−	0.844791i	0.0507952	−	0.0369048i
$525$	0.0195635	+	0.0142137i	0.000853820	+	0.000620336i
$526$	19.0661			0.831321
$527$	−2.03026	−	35.1758i	−0.0884394	−	1.53228i
$528$	0.110361			0.00480282
$529$	14.2600	+	10.3605i	0.620000	+	0.450456i
$530$	−13.2159	+	9.60193i	−0.574063	+	0.417081i
$531$	6.04395	+	18.6014i	0.262285	+	0.807230i
$532$	56.1754			2.43551
$533$	−4.41276			−0.191138
$534$	0.0252657	+	0.0777597i	0.00109335	+	0.00336499i
$535$	−12.0471	+	37.0772i	−0.520842	+	1.60299i
$536$	−6.94360	+	21.3702i	−0.299918	+	0.923052i
$537$	−0.310792	−	0.225804i	−0.0134117	−	0.00974415i
$538$	−0.292690	−	0.900809i	−0.0126188	−	0.0388366i
$539$	43.8001	+	31.8226i	1.88660	+	1.37070i
$540$	0.596777	−	0.433584i	0.0256812	−	0.0186585i
$541$	11.7257	−	36.0881i	0.504128	−	1.55155i	−0.298103	−	0.954534i	$-0.596354\pi$
$541$	11.7257	−	36.0881i	0.504128	−	1.55155i	0.802231	−	0.597013i	$-0.203646\pi$
$542$	−12.3581	+	8.97872i	−0.530828	+	0.385669i
$543$	−0.118496	+	0.0860925i	−0.00508516	+	0.00369458i
$544$	−11.4642	+	35.2831i	−0.491522	+	1.51275i
$545$	−1.35458	+	0.984160i	−0.0580238	+	0.0421568i
$546$	0.113301	+	0.0823182i	0.00484885	+	0.00352289i
$547$	12.4779	+	38.4031i	0.533518	+	1.64200i	0.746830	+	0.665015i	$0.231575\pi$
$547$	12.4779	+	38.4031i	0.533518	+	1.64200i	−0.213312	+	0.976984i	$0.568425\pi$
$548$	−7.29342	−	5.29898i	−0.311560	−	0.226361i
$549$	9.76488	−	30.0532i	0.416755	−	1.28264i
$550$	0.0942628	−	0.290111i	0.00401938	−	0.0123704i
$551$	−5.09739	−	15.6882i	−0.217156	−	0.668338i
$552$	0.226282			0.00963121
$553$	38.3267			1.62982
$554$	−1.00905	−	3.10554i	−0.0428704	−	0.131942i
$555$	−0.243719	+	0.177072i	−0.0103453	+	0.00751630i
$556$	2.35901	+	1.71392i	0.100044	+	0.0726865i
$557$	−10.1991			−0.432149			−0.216075	−	0.976377i	$-0.569325\pi$
$557$	−10.1991			−0.432149			−0.216075	+	0.976377i	$0.569325\pi$
$558$	−6.77533	+	10.5550i	−0.286823	+	0.446829i
$559$	−8.15979			−0.345122
$560$	−8.41960	−	6.11720i	−0.355793	−	0.258499i
$561$	−0.606090	+	0.440350i	−0.0255891	+	0.0185916i
$562$	−0.535088	−	1.64683i	−0.0225713	−	0.0694675i
$563$	10.5848			0.446095			0.223048	−	0.974808i	$-0.428399\pi$
$563$	10.5848			0.446095			0.223048	+	0.974808i	$0.428399\pi$
$564$	−0.287295			−0.0120973
$565$	−4.47737	−	13.7799i	−0.188365	−	0.579726i
$566$	5.05774	−	15.5661i	0.212593	−	0.654293i
$567$	13.6890	−	42.1303i	0.574883	−	1.76931i
$568$	−8.64350	−	6.27987i	−0.362673	−	0.263498i
$569$	5.86373	+	18.0467i	0.245820	+	0.756558i	0.995500	+	0.0947571i	$0.0302074\pi$
$569$	5.86373	+	18.0467i	0.245820	+	0.756558i	−0.749680	+	0.661801i	$0.769793\pi$
$570$	0.413290	+	0.300272i	0.0173108	+	0.0125770i
$571$	8.47851	−	6.16000i	0.354815	−	0.257788i	−0.396071	−	0.918220i	$-0.629627\pi$
$571$	8.47851	−	6.16000i	0.354815	−	0.257788i	0.750886	+	0.660432i	$0.229627\pi$
$572$	−1.38865	+	4.27382i	−0.0580623	+	0.178697i
$573$	0.286437	−	0.208109i	0.0119661	−	0.00869388i
$574$	13.2197	−	9.60470i	0.551781	−	0.400892i
$575$	−0.0929217	+	0.285983i	−0.00387510	+	0.0119263i
$576$	6.16105	−	4.47626i	0.256710	−	0.186511i
$577$	20.6663	+	15.0150i	0.860351	+	0.625081i	0.927980	−	0.372629i	$-0.121544\pi$
$577$	20.6663	+	15.0150i	0.860351	+	0.625081i	−0.0676295	+	0.997711i	$0.521544\pi$
$578$	−5.35040	−	16.4668i	−0.222547	−	0.684930i
$579$	−0.507859	−	0.368981i	−0.0211059	−	0.0153343i
$580$	−2.08782	+	6.42564i	−0.0866918	+	0.266810i
$581$	24.5066	−	75.4235i	1.01670	−	3.12910i
$582$	−0.0834488	−	0.256829i	−0.00345907	−	0.0106459i
$583$	30.0523			1.24464
$584$	35.8598			1.48389
$585$	2.09867	+	6.45903i	0.0867691	+	0.267048i
$586$	13.5175	−	9.82106i	0.558404	−	0.405704i
$587$	19.3137	+	14.0322i	0.797163	+	0.579173i	0.910080	−	0.414432i	$-0.136020\pi$
$587$	19.3137	+	14.0322i	0.797163	+	0.579173i	−0.112918	+	0.993604i	$0.536020\pi$
$588$	0.939088			0.0387273
$589$	42.7538	+	11.2136i	1.76164	+	0.462049i
$590$	11.0984			0.456912
$591$	0.488099	+	0.354625i	0.0200777	+	0.0145873i
$592$	2.65241	−	1.92709i	0.109013	−	0.0792029i
$593$	7.13570	+	21.9614i	0.293028	+	0.901848i	0.983877	+	0.178848i	$0.0572372\pi$
$593$	7.13570	+	21.9614i	0.293028	+	0.901848i	−0.690848	+	0.723000i	$0.742763\pi$
$594$	0.533493			0.0218895
$595$	70.6480			2.89628
$596$	3.63019	+	11.1726i	0.148698	+	0.457647i
$597$	0.303002	−	0.932544i	0.0124010	−	0.0381665i
$598$	−0.538153	+	1.65627i	−0.0220067	+	0.0677297i
$599$	−14.3470	−	10.4237i	−0.586203	−	0.425901i	0.254752	−	0.967006i	$-0.418006\pi$
$599$	−14.3470	−	10.4237i	−0.586203	−	0.425901i	−0.840955	+	0.541105i	$0.818006\pi$
$600$	−0.00391287	−	0.0120426i	−0.000159742	−	0.000491636i
$601$	23.9870	+	17.4275i	0.978449	+	0.710884i	0.957361	−	0.288893i	$-0.0932872\pi$
$601$	23.9870	+	17.4275i	0.978449	+	0.710884i	0.0210872	+	0.999778i	$0.493287\pi$
$602$	24.4451	−	17.7604i	0.996307	−	0.723860i
$603$	8.06690	−	24.8274i	0.328510	−	1.01105i
$604$	−1.90689	+	1.38544i	−0.0775904	+	0.0563727i
$605$	2.20221	−	1.60000i	0.0895328	−	0.0650494i
$606$	0.0343025	−	0.105572i	0.00139344	−	0.00428857i
$607$	−24.0547	+	17.4768i	−0.976352	+	0.709361i	−0.956890	−	0.290449i	$-0.906195\pi$
$607$	−24.0547	+	17.4768i	−0.976352	+	0.709361i	−0.0194615	+	0.999811i	$0.506195\pi$
$608$	−37.6507	−	27.3548i	−1.52694	−	1.10938i
$609$	−0.119701	−	0.368401i	−0.00485052	−	0.0149284i
$610$	−14.5065	−	10.5396i	−0.587350	−	0.426735i
$611$	1.63512	−	5.03239i	0.0661500	−	0.203589i
$612$	8.41822	−	25.9086i	0.340286	−	1.04729i
$613$	−7.33065	−	22.5614i	−0.296082	−	0.911247i	−0.982856	−	0.184376i	$-0.940974\pi$
$613$	−7.33065	−	22.5614i	−0.296082	−	0.911247i	0.686774	−	0.726871i	$-0.259026\pi$
$614$	−2.04091			−0.0823646
$615$	−0.377989			−0.0152420
$616$	−12.3059	−	37.8737i	−0.495819	−	1.52597i
$617$	23.1535	−	16.8220i	0.932127	−	0.677230i	−0.0143860	−	0.999897i	$-0.504579\pi$
$617$	23.1535	−	16.8220i	0.932127	−	0.677230i	0.946513	+	0.322667i	$0.104579\pi$
$618$	0.169554	+	0.123188i	0.00682046	+	0.00495535i
$619$	16.2468			0.653015			0.326507	−	0.945195i	$-0.394128\pi$
$619$	16.2468			0.653015			0.326507	+	0.945195i	$0.394128\pi$
$620$	−11.4673	−	14.0087i	−0.460538	−	0.562601i
$621$	−0.525903			−0.0211038
$622$	11.6619	+	8.47287i	0.467600	+	0.339731i
$623$	−11.4753	+	8.33729i	−0.459748	+	0.334026i
$624$	0.0108949	+	0.0335311i	0.000436146	+	0.00134232i
$625$	−25.6318			−1.02527
$626$	−0.0700526			−0.00279986
$627$	−0.290413	−	0.893801i	−0.0115980	−	0.0356950i
$628$	2.19923	−	6.76854i	0.0877589	−	0.270094i
$629$	−6.87751	+	21.1668i	−0.274224	+	0.843975i
$630$	−20.3457	−	14.7820i	−0.810594	−	0.588931i
$631$	9.01889	+	27.7573i	0.359036	+	1.10500i	0.953632	+	0.300975i	$0.0973122\pi$
$631$	9.01889	+	27.7573i	0.359036	+	1.10500i	−0.594595	+	0.804025i	$0.702688\pi$
$632$	−16.2362	−	11.7963i	−0.645841	−	0.469231i
$633$	0.0418763	−	0.0304249i	0.00166443	−	0.00120928i
$634$	−2.91438	+	8.96953i	−0.115745	+	0.356225i
$635$	8.15073	−	5.92185i	0.323452	−	0.235001i
$636$	0.421719	−	0.306397i	0.0167223	−	0.0121494i
$637$	−5.34476	+	16.4495i	−0.211767	+	0.651752i
$638$	−3.95314	+	2.87212i	−0.156506	+	0.113708i
$639$	10.0418	+	7.29580i	0.397248	+	0.288617i
$640$	6.87067	+	21.1458i	0.271587	+	0.835860i
$641$	21.2756	+	15.4576i	0.840336	+	0.610540i	0.922464	−	0.386082i	$-0.126172\pi$
$641$	21.2756	+	15.4576i	0.840336	+	0.610540i	−0.0821287	+	0.996622i	$0.526172\pi$
$642$	−0.151128	+	0.465125i	−0.00596456	+	0.0183570i
$643$	3.57656	−	11.0075i	0.141046	−	0.434094i	−0.855436	−	0.517909i	$-0.826711\pi$
$643$	3.57656	−	11.0075i	0.141046	−	0.434094i	0.996481	+	0.0838152i	$0.0267106\pi$
$644$	5.06902	+	15.6008i	0.199747	+	0.614759i
$645$	−0.698953			−0.0275212
$646$	37.7410			1.48490
$647$	−7.03082	−	21.6386i	−0.276410	−	0.850703i	−0.988843	−	0.148962i	$-0.952407\pi$
$647$	−7.03082	−	21.6386i	−0.276410	−	0.850703i	0.712433	−	0.701740i	$-0.247593\pi$
$648$	−18.7660	+	13.6343i	−0.737196	+	0.535605i
$649$	−16.5179	−	12.0009i	−0.648382	−	0.471077i
$650$	0.0974510			0.00382234
$651$	1.00398	+	0.263327i	0.0393490	+	0.0103206i
$652$	20.2401			0.792665
$653$	13.0903	+	9.51069i	0.512265	+	0.372182i	0.813682	−	0.581310i	$-0.197460\pi$
$653$	13.0903	+	9.51069i	0.512265	+	0.372182i	−0.301417	+	0.953492i	$0.597460\pi$
$654$	−0.0169929	+	0.0123461i	−0.000664475	+	0.000482769i
$655$	0.700683	+	2.15648i	0.0273779	+	0.0842606i
$656$	4.11367			0.160612
$657$	−41.6610			−1.62535
$658$	6.05488	+	18.6350i	0.236044	+	0.726468i
$659$	−1.80413	+	5.55254i	−0.0702789	+	0.216296i	−0.980027	−	0.198864i	$-0.936275\pi$
$659$	−1.80413	+	5.55254i	−0.0702789	+	0.216296i	0.909748	+	0.415161i	$0.136275\pi$
$660$	−0.118949	+	0.366088i	−0.00463009	+	0.0142499i
$661$	−11.6512	−	8.46512i	−0.453181	−	0.329255i	0.337670	−	0.941265i	$-0.390361\pi$
$661$	−11.6512	−	8.46512i	−0.453181	−	0.329255i	−0.790850	+	0.612010i	$0.790361\pi$
$662$	−1.34525	−	4.14025i	−0.0522845	−	0.160915i
$663$	−0.193627	−	0.140678i	−0.00751984	−	0.00546348i
$664$	−33.5956	+	24.4087i	−1.30376	+	0.947240i
$665$	−27.3865	+	84.2871i	−1.06200	+	3.26851i
$666$	6.40948	−	4.65676i	0.248362	−	0.180446i
$667$	3.89689	−	2.83126i	0.150888	−	0.109627i
$668$	3.32157	−	10.2228i	0.128516	−	0.395530i
$669$	0.295221	−	0.214490i	0.0114139	−	0.00829268i
$670$	−11.9840	−	8.70689i	−0.462983	−	0.336377i
$671$	10.1935	+	31.3724i	0.393517	+	1.21112i
$672$	−0.884141	−	0.642366i	−0.0341065	−	0.0247798i
$673$	−3.16878	+	9.75251i	−0.122148	+	0.375932i	−0.993371	−	0.114956i	$-0.963327\pi$
$673$	−3.16878	+	9.75251i	−0.122148	+	0.375932i	0.871223	+	0.490887i	$0.163327\pi$
$674$	−6.01567	+	18.5143i	−0.231715	+	0.713145i
$675$	0.00909391	+	0.0279882i	0.000350025	+	0.00107727i
$676$	−1.43562			−0.0552160
$677$	36.1922			1.39098			0.695490	−	0.718536i	$-0.255187\pi$
$677$	36.1922			1.39098			0.695490	+	0.718536i	$0.255187\pi$
$678$	−0.0561676	−	0.172866i	−0.00215711	−	0.00663889i
$679$	37.9012	−	27.5369i	1.45452	−	1.05677i
$680$	−29.9283	−	21.7442i	−1.14770	−	0.833851i
$681$	1.04156			0.0399125
$682$	−0.754441	−	13.0713i	−0.0288890	−	0.500525i
$683$	−26.2449			−1.00423			−0.502117	−	0.864800i	$-0.667445\pi$
$683$	−26.2449			−1.00423			−0.502117	+	0.864800i	$0.667445\pi$
$684$	27.6472	+	20.0868i	1.05712	+	0.768039i
$685$	11.5064	−	8.35990i	0.439637	−	0.319415i
$686$	−11.7817	−	36.2602i	−0.449826	−	1.38442i
$687$	0.721246			0.0275173
$688$	7.60674			0.290004
$689$	2.96680	+	9.13087i	0.113026	+	0.347858i
$690$	−0.0460972	+	0.141873i	−0.00175489	+	0.00540100i
$691$	−0.146717	+	0.451549i	−0.00558138	+	0.0171777i	−0.953808	−	0.300416i	$-0.902875\pi$
$691$	−0.146717	+	0.451549i	−0.00558138	+	0.0171777i	0.948227	+	0.317593i	$0.102875\pi$
$692$	−2.89936	−	2.10651i	−0.110217	−	0.0800775i
$693$	14.2967	+	44.0007i	0.543087	+	1.67145i
$694$	5.34168	+	3.88095i	0.202767	+	0.147319i
$695$	−3.72168	+	2.70396i	−0.141171	+	0.102567i
$696$	−0.0626789	+	0.192906i	−0.00237584	+	0.00731208i
$697$	−22.5919	+	16.4140i	−0.855730	+	0.621724i
$698$	−3.94259	+	2.86446i	−0.149229	+	0.108421i
$699$	0.00182815	−	0.00562646i	6.91468e−5	−	0.000212812i
$700$	0.742612	−	0.539539i	0.0280681	−	0.0203927i
$701$	−2.35629	−	1.71194i	−0.0889957	−	0.0646592i	0.542398	−	0.840122i	$-0.317517\pi$
$701$	−2.35629	−	1.71194i	−0.0889957	−	0.0646592i	−0.631393	+	0.775463i	$0.717517\pi$
$702$	0.0526671	+	0.162093i	0.00198779	+	0.00611780i
$703$	−22.5871	−	16.4105i	−0.851890	−	0.618935i
$704$	−2.45661	+	7.56068i	−0.0925871	+	0.284954i
$705$	0.140062	−	0.431065i	0.00527503	−	0.0162349i
$706$	−7.38896	−	22.7409i	−0.278087	−	0.855865i
$707$	19.2575			0.724254
$708$	−0.354148			−0.0133097
$709$	−10.7455	−	33.0713i	−0.403557	−	1.24202i	−0.922094	−	0.386965i	$-0.873523\pi$
$709$	−10.7455	−	33.0713i	−0.403557	−	1.24202i	0.518538	−	0.855055i	$-0.326477\pi$
$710$	5.69813	−	4.13993i	0.213847	−	0.155369i
$711$	18.8628	+	13.7046i	0.707410	+	0.513964i
$712$	7.42730			0.278350
$713$	0.743707	+	12.8853i	0.0278520	+	0.482558i
$714$	0.886263			0.0331676
$715$	−5.73556	−	4.16713i	−0.214498	−	0.155842i
$716$	−11.7974	+	8.57131i	−0.440889	+	0.320325i
$717$	0.0146156	+	0.0449823i	0.000545831	+	0.00167989i
$718$	5.28997			0.197420
$719$	−47.4195			−1.76845			−0.884224	−	0.467063i	$-0.845312\pi$
$719$	−47.4195			−1.76845			−0.884224	+	0.467063i	$0.845312\pi$
$720$	−1.95642	−	6.02126i	−0.0729116	−	0.224399i
$721$	−11.2354	+	34.5792i	−0.418430	+	1.28779i
$722$	−10.2194	+	31.4520i	−0.380325	+	1.17052i
$723$	0.441628	+	0.320861i	0.0164243	+	0.0119330i
$724$	1.71809	+	5.28773i	0.0638522	+	0.196517i
$725$	−0.218063	−	0.158432i	−0.00809864	−	0.00588401i
$726$	0.0276263	−	0.0200717i	0.00102531	−	0.000744930i
$727$	−0.331449	+	1.02009i	−0.0122928	+	0.0378332i	−0.957015	−	0.290039i	$-0.906332\pi$
$727$	−0.331449	+	1.02009i	−0.0122928	+	0.0378332i	0.944722	+	0.327872i	$0.106332\pi$
$728$	10.2924	−	7.47788i	0.381462	−	0.277149i
$729$	21.7810	−	15.8248i	0.806704	−	0.586104i
$730$	−7.30520	+	22.4831i	−0.270378	+	0.832137i
$731$	−41.7755	+	30.3517i	−1.54512	+	1.12260i
$732$	0.462901	+	0.336317i	0.0171093	+	0.0124306i
$733$	−4.45927	−	13.7242i	−0.164707	−	0.506915i	0.834308	−	0.551299i	$-0.185868\pi$
$733$	−4.45927	−	13.7242i	−0.164707	−	0.506915i	−0.999015	+	0.0443836i	$0.985868\pi$
$734$	−7.77236	−	5.64695i	−0.286883	−	0.208433i
$735$	−0.457822	+	1.40903i	−0.0168870	+	0.0519730i
$736$	4.19945	−	12.9246i	0.154794	−	0.476407i
$737$	8.42102	+	25.9172i	0.310192	+	0.954673i
$738$	9.94058			0.365918
$739$	−16.0154			−0.589137			−0.294569	−	0.955630i	$-0.595176\pi$
$739$	−16.0154			−0.589137			−0.294569	+	0.955630i	$0.595176\pi$
$740$	3.53371	+	10.8756i	0.129902	+	0.399796i
$741$	0.242896	−	0.176474i	0.00892301	−	0.00648294i
$742$	−28.7619	−	20.8968i	−1.05588	−	0.767145i
$743$	−16.2297			−0.595411			−0.297705	−	0.954658i	$-0.596221\pi$
$743$	−16.2297			−0.595411			−0.297705	+	0.954658i	$0.596221\pi$
$744$	−0.344263	−	0.420558i	−0.0126213	−	0.0154184i
$745$	−18.5334			−0.679012
$746$	−0.518194	−	0.376490i	−0.0189724	−	0.0137843i
$747$	39.0306	−	28.3574i	1.42805	−	1.03754i
$748$	8.78775	+	27.0459i	0.321312	+	0.988897i
$749$	−84.8440			−3.10013
$750$	−0.313408			−0.0114441
$751$	−10.4486	−	32.1573i	−0.381273	−	1.17344i	−0.939148	−	0.343513i	$-0.888383\pi$
$751$	−10.4486	−	32.1573i	−0.381273	−	1.17344i	0.557875	−	0.829925i	$-0.311617\pi$
$752$	−1.52430	+	4.69131i	−0.0555855	+	0.171074i
$753$	−0.00130065	+	0.00400299i	−4.73984e−5	+	0.000145877i
$754$	−1.26290	−	0.917553i	−0.0459922	−	0.0334153i
$755$	−1.14910	−	3.53658i	−0.0418202	−	0.128709i
$756$	1.29877	+	0.943613i	0.0472359	+	0.0343189i
$757$	12.4496	−	9.04516i	0.452488	−	0.328752i	−0.338089	−	0.941114i	$-0.609781\pi$
$757$	12.4496	−	9.04516i	0.452488	−	0.328752i	0.790577	+	0.612362i	$0.209781\pi$
$758$	2.15055	−	6.61873i	0.0781117	−	0.240403i
$759$	0.222018	−	0.161305i	0.00805873	−	0.00585501i
$760$	37.5437	−	27.2771i	1.36185	−	0.989444i
$761$	1.24947	−	3.84549i	0.0452934	−	0.139399i	−0.925852	−	0.377885i	$-0.876651\pi$
$761$	1.24947	−	3.84549i	0.0452934	−	0.139399i	0.971146	+	0.238487i	$0.0766513\pi$
$762$	0.102249	−	0.0742883i	0.00370409	−	0.00269118i
$763$	−2.94798	−	2.14184i	−0.106724	−	0.0775397i
$764$	−4.15308	−	12.7819i	−0.150253	−	0.462432i
$765$	34.7699	+	25.2618i	1.25711	+	0.913344i
$766$	−8.09242	+	24.9059i	−0.292391	+	0.899887i
$767$	2.01561	−	6.20341i	0.0727795	−	0.223992i
$768$	0.145554	+	0.447970i	0.00525224	+	0.0161647i
$769$	−34.7502			−1.25312			−0.626561	−	0.779372i	$-0.715538\pi$
$769$	−34.7502			−1.25312			−0.626561	+	0.779372i	$0.715538\pi$
$770$	26.2527			0.946081
$771$	−0.195005	−	0.600164i	−0.00702294	−	0.0216144i
$772$	−19.2779	+	14.0062i	−0.693826	+	0.504094i
$773$	−32.5566	−	23.6537i	−1.17098	−	0.850766i	−0.179853	−	0.983693i	$-0.557562\pi$
$773$	−32.5566	−	23.6537i	−1.17098	−	0.850766i	−0.991126	+	0.132927i	$0.957562\pi$
$774$	18.3815			0.660709
$775$	0.672886	−	0.262392i	0.0241708	−	0.00942540i
$776$	−24.5313			−0.880622
$777$	−0.530409	−	0.385364i	−0.0190283	−	0.0138249i
$778$	−6.79339	+	4.93569i	−0.243555	+	0.176953i
$779$	−10.8251	−	33.3163i	−0.387850	−	1.19368i
$780$	−0.122972			−0.00440311
$781$	−12.9572			−0.463646
$782$	3.40558	+	10.4813i	0.121783	+	0.374811i
$783$	0.145672	−	0.448333i	0.00520591	−	0.0160221i
$784$	4.98251	−	15.3346i	0.177947	−	0.547664i
$785$	9.08353	+	6.59957i	0.324205	+	0.235549i
$786$	0.00878991	+	0.0270525i	0.000313526	+	0.000964932i
$787$	34.8721	+	25.3361i	1.24306	+	0.903133i	0.997798	−	0.0663243i	$-0.0211272\pi$
$787$	34.8721	+	25.3361i	1.24306	+	0.903133i	0.245258	+	0.969458i	$0.421127\pi$
$788$	18.5278	−	13.4612i	0.660026	−	0.479537i
$789$	0.296605	−	0.912856i	0.0105594	−	0.0324986i
$790$	10.7035	−	7.77656i	0.380814	−	0.276677i
$791$	25.5105	−	18.5345i	0.907050	−	0.659010i
$792$	7.48618	−	23.0401i	0.266010	−	0.818694i
$793$	−8.52566	+	6.19425i	−0.302755	+	0.219964i
$794$	−15.4927	−	11.2561i	−0.549815	−	0.399464i
$795$	0.254131	+	0.782133i	0.00901308	+	0.0277394i
$796$	−30.1118	−	21.8775i	−1.06728	−	0.775427i
$797$	−13.8049	+	42.4872i	−0.488996	+	1.50498i	0.337112	+	0.941464i	$0.390550\pi$
$797$	−13.8049	+	42.4872i	−0.488996	+	1.50498i	−0.826109	+	0.563511i	$0.809450\pi$
$798$	−0.343558	+	1.05736i	−0.0121618	+	0.0374302i
$799$	−10.3475	−	31.8464i	−0.366069	−	1.12664i
$800$	−0.760454			−0.0268861
$801$	−8.62885			−0.304885
$802$	−3.94316	−	12.1358i	−0.139238	−	0.428530i
$803$	35.1840	−	25.5627i	1.24162	−	0.902087i
$804$	0.382409	+	0.277836i	0.0134865	+	0.00979854i
$805$	−25.8792			−0.912121
$806$	3.89700	−	1.51964i	0.137266	−	0.0535269i
$807$	−0.0476827			−0.00167851
$808$	−8.15799	−	5.92712i	−0.286997	−	0.208515i
$809$	−3.32413	+	2.41512i	−0.116870	+	0.0849112i	−0.644685	−	0.764448i	$-0.723011\pi$
$809$	−3.32413	+	2.41512i	−0.116870	+	0.0849112i	0.527815	+	0.849359i	$0.323011\pi$
$810$	−4.72539	−	14.5433i	−0.166033	−	0.510998i
$811$	25.7376			0.903771			0.451886	−	0.892076i	$-0.350752\pi$
$811$	25.7376			0.903771			0.451886	+	0.892076i	$0.350752\pi$
$812$	−14.7038			−0.516003
$813$	0.237636	+	0.731369i	0.00833427	+	0.0256502i
$814$	−2.55567	+	7.86555i	−0.0895762	+	0.275687i
$815$	−9.86744	+	30.3689i	−0.345641	+	1.06377i
$816$	0.180503	+	0.131143i	0.00631888	+	0.00459093i
$817$	−20.0171	−	61.6064i	−0.700311	−	2.15533i
$818$	−13.2538	−	9.62943i	−0.463407	−	0.336685i
$819$	−11.9575	+	8.68761i	−0.417828	+	0.303570i
$820$	−4.43381	+	13.6459i	−0.154835	+	0.476534i
$821$	34.5536	−	25.1046i	1.20593	−	0.876158i	0.211073	−	0.977470i	$-0.432304\pi$
$821$	34.5536	−	25.1046i	1.20593	−	0.876158i	0.994855	+	0.101312i	$0.0323041\pi$
$822$	0.144345	−	0.104873i	0.00503462	−	0.00365787i
$823$	9.82543	−	30.2396i	0.342493	−	1.05409i	−0.620419	−	0.784270i	$-0.713037\pi$
$823$	9.82543	−	30.2396i	0.342493	−	1.05409i	0.962912	−	0.269815i	$-0.0869625\pi$
$824$	15.4025	−	11.1905i	0.536570	−	0.389841i
$825$	−0.0124237	−	0.00902633i	−0.000432537	−	0.000314256i
$826$	7.46383	+	22.9713i	0.259700	+	0.799274i
$827$	34.4057	+	24.9972i	1.19640	+	0.869238i	0.993926	−	0.110049i	$-0.0351007\pi$
$827$	34.4057	+	24.9972i	1.19640	+	0.869238i	0.202477	+	0.979287i	$0.435101\pi$
$828$	−3.08369	+	9.49062i	−0.107166	+	0.329822i
$829$	2.06283	−	6.34875i	0.0716452	−	0.220501i	−0.908822	−	0.417184i	$-0.863017\pi$
$829$	2.06283	−	6.34875i	0.0716452	−	0.220501i	0.980467	+	0.196683i	$0.0630170\pi$
$830$	−8.45960	−	26.0360i	−0.293637	−	0.903722i
$831$	−0.164386			−0.00570249
$832$	−2.53970			−0.0880483
$833$	33.8231	+	104.097i	1.17190	+	3.60674i
$834$	−0.0466876	+	0.0339205i	−0.00161666	+	0.00117457i
$835$	13.7192	+	9.96756i	0.474771	+	0.344942i
$836$	−35.6739			−1.23381
$837$	0.800104	+	0.977421i	0.0276556	+	0.0337846i
$838$	−1.36880			−0.0472843
$839$	−40.9053	−	29.7194i	−1.41221	−	1.02603i	−0.992997	−	0.118140i	$-0.962307\pi$
$839$	−40.9053	−	29.7194i	−1.41221	−	1.02603i	−0.419210	−	0.907889i	$-0.637693\pi$
$840$	0.881629	−	0.640541i	0.0304191	−	0.0221008i
$841$	−7.62726	−	23.4743i	−0.263009	−	0.809458i
$842$	−7.09945			−0.244663
$843$	−0.0871722			−0.00300237
$844$	−0.607168	−	1.86867i	−0.0208996	−	0.0643223i
$845$	0.699889	−	2.15404i	0.0240769	−	0.0741011i
$846$	−3.68343	+	11.3364i	−0.126639	+	0.389754i
$847$	4.79270	+	3.48210i	0.164679	+	0.119646i
$848$	−2.76572	−	8.51200i	−0.0949751	−	0.292303i
$849$	−0.666601	−	0.484314i	−0.0228777	−	0.0166216i
$850$	0.498918	−	0.362485i	0.0171128	−	0.0124331i
$851$	2.51931	−	7.75364i	0.0863608	−	0.265791i
$852$	−0.181827	+	0.132105i	−0.00622929	+	0.00452584i
$853$	−4.65945	+	3.38529i	−0.159537	+	0.115910i	−0.664689	−	0.747120i	$-0.731436\pi$
$853$	−4.65945	+	3.38529i	−0.159537	+	0.115910i	0.505153	+	0.863030i	$0.331436\pi$
$854$	12.0589	−	37.1135i	0.412647	−	1.27000i
$855$	−43.6173	+	31.6898i	−1.49168	+	1.08377i
$856$	35.9421	+	26.1135i	1.22848	+	0.892540i
$857$	−4.67358	−	14.3838i	−0.159646	−	0.491341i	0.838956	−	0.544200i	$-0.183167\pi$
$857$	−4.67358	−	14.3838i	−0.159646	−	0.491341i	−0.998602	+	0.0528586i	$0.983167\pi$
$858$	−0.0719514	−	0.0522757i	−0.00245638	−	0.00178466i
$859$	0.748098	−	2.30241i	0.0255248	−	0.0785572i	−0.937483	−	0.348032i	$-0.886850\pi$
$859$	0.748098	−	2.30241i	0.0255248	−	0.0785572i	0.963007	+	0.269475i	$0.0868501\pi$
$860$	−8.19872	+	25.2331i	−0.279574	+	0.860441i
$861$	−0.254204	−	0.782359i	−0.00866324	−	0.0266627i
$862$	13.0464			0.444362
$863$	0.454762			0.0154803			0.00774014	−	0.999970i	$-0.497536\pi$
$863$	0.454762			0.0154803			0.00774014	+	0.999970i	$0.497536\pi$
$864$	−0.410986	−	1.26488i	−0.0139820	−	0.0430322i
$865$	4.57416	−	3.32332i	0.155526	−	0.112996i
$866$	−8.08522	−	5.87426i	−0.274747	−	0.199615i
$867$	−0.871642			−0.0296025
$868$	21.2831	−	33.1560i	0.722395	−	1.12539i
$869$	−24.3392			−0.825651
$870$	−0.108178	−	0.0785959i	−0.00366758	−	0.00266465i
$871$	−7.04317	+	5.11716i	−0.238649	+	0.173388i
$872$	0.589623	+	1.81467i	0.0199672	+	0.0614526i
$873$	28.4998			0.964573
$874$	−13.8250			−0.467636
$875$	−16.8016	−	51.7100i	−0.567998	−	1.74812i
$876$	0.233109	−	0.717435i	0.00787601	−	0.0242399i
$877$	−10.8523	+	33.3999i	−0.366456	+	1.12784i	0.582608	+	0.812753i	$0.302032\pi$
$877$	−10.8523	+	33.3999i	−0.366456	+	1.12784i	−0.949064	+	0.315082i	$0.897968\pi$
$878$	5.10333	+	3.70779i	0.172229	+	0.125132i
$879$	−0.259930	−	0.799983i	−0.00876723	−	0.0269828i
$880$	5.34682	+	3.88470i	0.180241	+	0.130953i
$881$	−29.3634	+	21.3338i	−0.989278	+	0.718752i	−0.959763	−	0.280812i	$-0.909396\pi$
$881$	−29.3634	+	21.3338i	−0.989278	+	0.718752i	−0.0295151	+	0.999564i	$0.509396\pi$
$882$	12.0401	−	37.0556i	0.405411	−	1.24773i
$883$	−39.4235	+	28.6428i	−1.32671	+	0.963908i	−0.326883	+	0.945065i	$0.605998\pi$
$883$	−39.4235	+	28.6428i	−1.32671	+	0.963908i	−0.999822	+	0.0188433i	$0.994002\pi$
$884$	−7.34990	+	5.34001i	−0.247204	+	0.179604i
$885$	0.172653	−	0.531373i	0.00580368	−	0.0178619i
$886$	−17.8575	+	12.9742i	−0.599935	+	0.435878i
$887$	19.1606	+	13.9210i	0.643351	+	0.467422i	0.861000	−	0.508605i	$-0.169839\pi$
$887$	19.1606	+	13.9210i	0.643351	+	0.467422i	−0.217649	+	0.976027i	$0.569839\pi$
$888$	0.106086	+	0.326500i	0.00356003	+	0.0109566i
$889$	17.7385	+	12.8878i	0.594930	+	0.432242i
$890$	−1.51306	+	4.65671i	−0.0507178	+	0.156093i
$891$	−8.69311	+	26.7546i	−0.291230	+	0.896314i
$892$	−4.28043	−	13.1738i	−0.143320	−	0.441092i
$893$	42.0057			1.40567
$894$	−0.232498			−0.00777589
$895$	−7.10918	−	21.8798i	−0.237634	−	0.731361i
$896$	−39.1467	+	28.4418i	−1.30780	+	0.950172i
$897$	0.0709277	+	0.0515320i	0.00236821	+	0.00172060i
$898$	14.2916			0.476918
$899$	−11.1907	−	2.93515i	−0.373232	−	0.0978927i
$900$	0.558407			0.0186136
$901$	49.1529	+	35.7116i	1.63752	+	1.18973i
$902$	−8.39512	+	6.09941i	−0.279527	+	0.203088i
$903$	−0.470057	−	1.44669i	−0.0156425	−	0.0481428i
$904$	−16.5115			−0.549164
$905$	−8.77145			−0.291573
$906$	−0.0144153	−	0.0443656i	−0.000478915	−	0.00147395i
$907$	−3.23721	+	9.96310i	−0.107490	+	0.330819i	−0.990307	−	0.138898i	$-0.955644\pi$
$907$	−3.23721	+	9.96310i	−0.107490	+	0.330819i	0.882817	+	0.469717i	$0.155644\pi$
$908$	12.2175	−	37.6015i	0.405451	−	1.24785i
$909$	9.47774	+	6.88598i	0.314357	+	0.228394i
$910$	2.59170	+	7.97642i	0.0859139	+	0.264416i
$911$	0.438992	+	0.318946i	0.0145445	+	0.0105672i	0.595034	−	0.803701i	$-0.297139\pi$
$911$	0.438992	+	0.318946i	0.0145445	+	0.0105672i	−0.580489	+	0.814268i	$0.697139\pi$
$912$	−0.226433	+	0.164513i	−0.00749795	+	0.00544758i
$913$	−15.5628	+	47.8973i	−0.515053	+	1.58517i
$914$	5.86980	−	4.26466i	0.194156	−	0.141062i
$915$	−0.730292	+	0.530589i	−0.0241427	+	0.0175407i
$916$	8.46023	−	26.0379i	0.279534	−	0.860316i
$917$	−3.99225	+	2.90054i	−0.131836	+	0.0957842i
$918$	0.872570	+	0.633960i	0.0287991	+	0.0209238i
$919$	5.74012	+	17.6663i	0.189349	+	0.582757i	0.999996	−	0.00277846i	$-0.000884414\pi$
$919$	5.74012	+	17.6663i	0.189349	+	0.582757i	−0.810647	+	0.585535i	$0.800884\pi$
$920$	10.9631	+	7.96514i	0.361442	+	0.262603i
$921$	−0.0317499	+	0.0977160i	−0.00104619	+	0.00321985i
$922$	3.32781	−	10.2419i	0.109595	−	0.337300i
$923$	−1.27915	−	3.93683i	−0.0421038	−	0.129582i
$924$	−0.837721			−0.0275590
$925$	−0.456207			−0.0150000
$926$	−5.94799	−	18.3060i	−0.195463	−	0.601573i
$927$	−17.8942	+	13.0009i	−0.587723	+	0.427006i
$928$	9.85501	+	7.16008i	0.323506	+	0.235041i
$929$	38.0342			1.24786			0.623930	−	0.781480i	$-0.285535\pi$
$929$	38.0342			1.24786			0.623930	+	0.781480i	$0.285535\pi$
$930$	0.333810	−	0.130169i	0.0109461	−	0.00426842i
$931$	−137.305			−4.49999
$932$	−0.181678	−	0.131997i	−0.00595106	−	0.00432370i
$933$	0.587089	−	0.426545i	0.0192204	−	0.0139645i
$934$	8.08828	+	24.8932i	0.264657	+	0.814530i
$935$	−44.8646			−1.46723
$936$	7.73938			0.252970
$937$	6.54503	+	20.1435i	0.213817	+	0.658061i	0.999235	+	0.0390957i	$0.0124477\pi$
$937$	6.54503	+	20.1435i	0.213817	+	0.658061i	−0.785419	+	0.618965i	$0.787552\pi$
$938$	9.96203	−	30.6600i	0.325272	−	1.00108i
$939$	−0.00108979	+	0.00335401i	−3.55638e−5	+	0.000109454i
$940$	−13.9191	−	10.1128i	−0.453990	−	0.329843i
$941$	−15.4515	−	47.5549i	−0.503706	−	1.55025i	−0.802936	−	0.596066i	$-0.796730\pi$
$941$	−15.4515	−	47.5549i	−0.503706	−	1.55025i	0.299230	−	0.954181i	$-0.403270\pi$
$942$	0.113951	+	0.0827901i	0.00371272	+	0.00269745i
$943$	8.27568	−	6.01263i	0.269493	−	0.195798i
$944$	−1.87900	+	5.78296i	−0.0611562	+	0.188219i
$945$	−2.04900	+	1.48868i	−0.0666539	+	0.0484269i
$946$	−15.5237	+	11.2786i	−0.504720	+	0.366700i
$947$	0.662232	−	2.03814i	0.0215196	−	0.0662306i	−0.939720	−	0.341945i	$-0.888914\pi$
$947$	0.662232	−	2.03814i	0.0215196	−	0.0662306i	0.961240	+	0.275714i	$0.0889144\pi$
$948$	−0.341548	+	0.248149i	−0.0110930	+	0.00805952i
$949$	11.2402	+	8.16647i	0.364872	+	0.265095i
$950$	0.239061	+	0.735755i	0.00775617	+	0.0238710i
$951$	0.384110	+	0.279072i	0.0124556	+	0.00904954i
$952$	24.8787	−	76.5687i	0.806323	−	2.48161i
$953$	−10.7053	+	32.9474i	−0.346778	+	1.06727i	0.613847	+	0.789425i	$0.289621\pi$
$953$	−10.7053	+	32.9474i	−0.346778	+	1.06727i	−0.960625	+	0.277848i	$0.910379\pi$
$954$	−6.68328	−	20.5690i	−0.216379	−	0.665947i
$955$	21.2030			0.686112
$956$	1.79536			0.0580661
$957$	0.0760153	+	0.233951i	0.00245723	+	0.00756257i
$958$	−8.12748	+	5.90496i	−0.262587	+	0.190781i
$959$	25.0415	+	18.1937i	0.808633	+	0.587506i
$960$	−0.217546			−0.00702128
$961$	22.8166	−	20.9858i	0.736019	−	0.676961i
$962$	−2.64211			−0.0851850
$963$	−41.7566	−	30.3380i	−1.34559	−	0.977628i
$964$	16.7638	−	12.1796i	0.539925	−	0.392279i
$965$	−11.6170	−	35.7533i	−0.373963	−	1.15094i
$966$	−0.324648			−0.0104454
$967$	−25.0415			−0.805280			−0.402640	−	0.915358i	$-0.631907\pi$
$967$	−25.0415			−0.805280			−0.402640	+	0.915358i	$0.631907\pi$
$968$	−0.958583	−	2.95022i	−0.0308100	−	0.0948235i
$969$	0.587125	−	1.80698i	0.0188612	−	0.0580487i
$970$	4.99741	−	15.3804i	0.160457	−	0.493836i
$971$	1.28212	+	0.931514i	0.0411452	+	0.0298937i	0.608168	−	0.793809i	$-0.291905\pi$
$971$	1.28212	+	0.931514i	0.0411452	+	0.0298937i	−0.567023	+	0.823702i	$0.691905\pi$
$972$	0.452721	+	1.39333i	0.0145210	+	0.0446911i
$973$	−8.09952	−	5.88465i	−0.259659	−	0.188653i
$974$	−11.2344	+	8.16230i	−0.359975	+	0.261537i
$975$	0.00151601	−	0.00466581i	4.85513e−5	−	0.000149426i
$976$	7.94782	−	5.77443i	0.254403	−	0.184835i
$977$	28.3097	−	20.5682i	0.905708	−	0.658035i	−0.0342177	−	0.999414i	$-0.510894\pi$
$977$	28.3097	−	20.5682i	0.905708	−	0.658035i	0.939926	+	0.341379i	$0.110894\pi$
$978$	−0.123785	+	0.380971i	−0.00395820	+	0.0121821i
$979$	7.28733	−	5.29455i	0.232904	−	0.169215i
$980$	45.4976	+	33.0559i	1.45337	+	1.05593i
$981$	−0.685009	−	2.10824i	−0.0218707	−	0.0673110i
$982$	−11.5765	−	8.41079i	−0.369420	−	0.268399i
$983$	−6.78982	+	20.8969i	−0.216562	+	0.666508i	0.782477	+	0.622679i	$0.213956\pi$
$983$	−6.78982	+	20.8969i	−0.216562	+	0.666508i	−0.999039	+	0.0438291i	$0.986044\pi$
$984$	−0.133109	+	0.409667i	−0.00424335	+	0.0130597i
$985$	11.1650	+	34.3622i	0.355746	+	1.09487i
$986$	−9.87866			−0.314601
$987$	0.986410			0.0313978
$988$	−3.52177	−	10.8389i	−0.112042	−	0.344831i
$989$	15.3029	−	11.1182i	0.486603	−	0.353537i
$990$	12.9205	+	9.38726i	0.410639	+	0.298347i
$991$	41.6110			1.32182			0.660909	−	0.750466i	$-0.270171\pi$
$991$	41.6110			1.32182			0.660909	+	0.750466i	$0.270171\pi$
$992$	−30.4101	+	11.8584i	−0.965521	+	0.376505i
$993$	−0.219157			−0.00695472
$994$	12.4009	+	9.00977i	0.393332	+	0.285773i
$995$	47.5056	−	34.5149i	1.50603	−	1.09419i
$996$	0.269945	+	0.830806i	0.00855354	+	0.0263251i
$997$	23.8159			0.754259			0.377129	−	0.926161i	$-0.376911\pi$
$997$	23.8159			0.754259			0.377129	+	0.926161i	$0.376911\pi$
$998$	2.36673			0.0749174
$999$	−0.246556	−	0.758821i	−0.00780068	−	0.0240080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.157.6	✓	48
31.16	even	5	inner	403.2.k.d.326.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.157.6	✓	48	1.1	even	1	trivial
403.2.k.d.326.6	yes	48	31.16	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.607778 + 0.441577i) q^{2} +(0.0305971 - 0.0222301i) q^{3} +(-0.443630 - 1.36535i) q^{4} +2.26489 q^{5} +0.0284125 q^{6} +(1.52318 + 4.68785i) q^{7} +(0.797580 - 2.45470i) q^{8} +(-0.926609 + 2.85181i) q^{9} +O(q^{10})\)	\(q+(0.607778 + 0.441577i) q^{2} +(0.0305971 - 0.0222301i) q^{3} +(-0.443630 - 1.36535i) q^{4} +2.26489 q^{5} +0.0284125 q^{6} +(1.52318 + 4.68785i) q^{7} +(0.797580 - 2.45470i) q^{8} +(-0.926609 + 2.85181i) q^{9} +(1.37655 + 1.00012i) q^{10} +(-0.967284 - 2.97699i) q^{11} +(-0.0439256 - 0.0319138i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.14429 + 3.52177i) q^{14} +(0.0692989 - 0.0503486i) q^{15} +(-0.754184 + 0.547947i) q^{16} +(1.95555 - 6.01855i) q^{17} +(-1.82247 + 1.32410i) q^{18} +(6.42241 + 4.66616i) q^{19} +(-1.00477 - 3.09237i) q^{20} +(0.150816 + 0.109574i) q^{21} +(0.726677 - 2.23648i) q^{22} +(-0.716339 + 2.20466i) q^{23} +(-0.0301645 - 0.0928369i) q^{24} +0.129718 q^{25} +0.751255 q^{26} +(0.0701055 + 0.215763i) q^{27} +(5.72484 - 4.15934i) q^{28} +(-1.68106 - 1.22136i) q^{29} +0.0643512 q^{30} +(5.18732 - 2.02280i) q^{31} -5.86239 q^{32} +(-0.0957749 - 0.0695845i) q^{33} +(3.84619 - 2.79442i) q^{34} +(3.44982 + 10.6175i) q^{35} +4.30479 q^{36} -3.51693 q^{37} +(1.84294 + 5.67198i) q^{38} +(0.0116870 - 0.0359690i) q^{39} +(1.80643 - 5.55962i) q^{40} +(-3.57000 - 2.59375i) q^{41} +(0.0432772 + 0.133194i) q^{42} +(-6.60141 - 4.79620i) q^{43} +(-3.63553 + 2.64137i) q^{44} +(-2.09867 + 6.45903i) q^{45} +(-1.40890 + 1.02363i) q^{46} +(4.28081 - 3.11019i) q^{47} +(-0.0108949 + 0.0335311i) q^{48} +(-13.9928 + 10.1663i) q^{49} +(0.0788395 + 0.0572802i) q^{50} +(-0.0739588 - 0.227622i) q^{51} +(-1.16144 - 0.843834i) q^{52} +(-2.96680 + 9.13087i) q^{53} +(-0.0526671 + 0.162093i) q^{54} +(-2.19079 - 6.74256i) q^{55} +12.7221 q^{56} +0.300236 q^{57} +(-0.482386 - 1.48463i) q^{58} +(5.27694 - 3.83392i) q^{59} +(-0.0994866 - 0.0722813i) q^{60} -10.5383 q^{61} +(4.04596 + 1.06119i) q^{62} -14.7802 q^{63} +(-2.05466 - 1.49280i) q^{64} +(1.83233 - 1.33127i) q^{65} +(-0.0274830 - 0.0845839i) q^{66} -8.70583 q^{67} -9.08497 q^{68} +(0.0270920 + 0.0833805i) q^{69} +(-2.59170 + 7.97642i) q^{70} +(1.27915 - 3.93683i) q^{71} +(6.26129 + 4.54909i) q^{72} +(4.29337 + 13.2136i) q^{73} +(-2.13751 - 1.55299i) q^{74} +(0.00396898 - 0.00288363i) q^{75} +(3.52177 - 10.8389i) q^{76} +(12.4824 - 9.06897i) q^{77} +(0.0229862 - 0.0167005i) q^{78} +(2.40280 - 7.39504i) q^{79} +(-1.70814 + 1.24104i) q^{80} +(-7.27074 - 5.28250i) q^{81} +(-1.02442 - 3.15285i) q^{82} +(-13.0164 - 9.45697i) q^{83} +(0.0827009 - 0.254527i) q^{84} +(4.42909 - 13.6313i) q^{85} +(-1.89430 - 5.83006i) q^{86} -0.0785863 q^{87} -8.07912 q^{88} +(0.889244 + 2.73681i) q^{89} +(-4.12768 + 2.99894i) q^{90} +(3.98772 + 2.89725i) q^{91} +3.32793 q^{92} +(0.113750 - 0.177206i) q^{93} +3.97517 q^{94} +(14.5460 + 10.5683i) q^{95} +(-0.179372 + 0.130321i) q^{96} +(-2.93705 - 9.03930i) q^{97} -12.9937 q^{98} +9.38612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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