LMFDB - Embedded newform 552.2.j.d.323.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(323,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.323"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [42,0,2,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.39
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29483 - 0.568707i) q^{2} +(-1.25835 + 1.19019i) q^{3} +(1.35315 - 1.47275i) q^{4} +0.156681 q^{5} +(-0.952479 + 2.25672i) q^{6} -3.17007i q^{7} +(0.914523 - 2.67650i) q^{8} +(0.166904 - 2.99535i) q^{9} +(0.202875 - 0.0891057i) q^{10} +3.38771i q^{11} +(0.0501168 + 3.46374i) q^{12} -3.13303i q^{13} +(-1.80284 - 4.10469i) q^{14} +(-0.197160 + 0.186480i) q^{15} +(-0.337995 - 3.98569i) q^{16} -3.67452i q^{17} +(-1.48737 - 3.97338i) q^{18} +5.24729 q^{19} +(0.212013 - 0.230753i) q^{20} +(3.77298 + 3.98907i) q^{21} +(1.92661 + 4.38649i) q^{22} +1.00000 q^{23} +(2.03474 + 4.45644i) q^{24} -4.97545 q^{25} +(-1.78178 - 4.05673i) q^{26} +(3.35501 + 3.96786i) q^{27} +(-4.66873 - 4.28957i) q^{28} +6.81728 q^{29} +(-0.149236 + 0.353586i) q^{30} +2.63390i q^{31} +(-2.70433 - 4.96856i) q^{32} +(-4.03201 - 4.26293i) q^{33} +(-2.08972 - 4.75786i) q^{34} -0.496691i q^{35} +(-4.18557 - 4.29896i) q^{36} -3.68893i q^{37} +(6.79432 - 2.98417i) q^{38} +(3.72890 + 3.94246i) q^{39} +(0.143289 - 0.419357i) q^{40} +3.21361i q^{41} +(7.15396 + 3.01943i) q^{42} -9.14455 q^{43} +(4.98925 + 4.58406i) q^{44} +(0.0261508 - 0.469316i) q^{45} +(1.29483 - 0.568707i) q^{46} +11.1268 q^{47} +(5.16904 + 4.61313i) q^{48} -3.04935 q^{49} +(-6.44234 + 2.82957i) q^{50} +(4.37337 + 4.62384i) q^{51} +(-4.61418 - 4.23945i) q^{52} +1.24333 q^{53} +(6.60070 + 3.22967i) q^{54} +0.530790i q^{55} +(-8.48469 - 2.89910i) q^{56} +(-6.60294 + 6.24526i) q^{57} +(8.82719 - 3.87703i) q^{58} +9.90197i q^{59} +(0.00785237 + 0.542703i) q^{60} -0.598751i q^{61} +(1.49791 + 3.41043i) q^{62} +(-9.49548 - 0.529099i) q^{63} +(-6.32729 - 4.89544i) q^{64} -0.490888i q^{65} +(-7.64511 - 3.22672i) q^{66} -6.22235 q^{67} +(-5.41165 - 4.97216i) q^{68} +(-1.25835 + 1.19019i) q^{69} +(-0.282471 - 0.643128i) q^{70} -11.9654 q^{71} +(-7.86442 - 3.18604i) q^{72} -8.73037 q^{73} +(-2.09792 - 4.77653i) q^{74} +(6.26087 - 5.92172i) q^{75} +(7.10034 - 7.72795i) q^{76} +10.7393 q^{77} +(7.07038 + 2.98415i) q^{78} +12.5424i q^{79} +(-0.0529574 - 0.624484i) q^{80} +(-8.94429 - 0.999875i) q^{81} +(1.82760 + 4.16106i) q^{82} +8.47249i q^{83} +(10.9803 - 0.158874i) q^{84} -0.575728i q^{85} +(-11.8406 + 5.20057i) q^{86} +(-8.57855 + 8.11385i) q^{87} +(9.06720 + 3.09814i) q^{88} -4.22264i q^{89} +(-0.233042 - 0.622554i) q^{90} -9.93194 q^{91} +(1.35315 - 1.47275i) q^{92} +(-3.13483 - 3.31437i) q^{93} +(14.4073 - 6.32790i) q^{94} +0.822152 q^{95} +(9.31653 + 3.03353i) q^{96} +9.28707 q^{97} +(-3.94837 + 1.73419i) q^{98} +(10.1474 + 0.565423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24}+ \cdots + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.29483	−	0.568707i	0.915580	−	0.402136i
$2$	1.29483	−	0.568707i	0.915580	−	0.402136i
$3$	−1.25835	+	1.19019i	−0.726510	+	0.687155i
$3$	−1.25835	+	1.19019i	−0.726510	+	0.687155i
$4$	1.35315	−	1.47275i	0.676573	−	0.736376i
$5$	0.156681			0.0700700			0.0350350	−	0.999386i	$-0.488846\pi$
$5$	0.156681			0.0700700			0.0350350	+	0.999386i	$0.488846\pi$
$6$	−0.952479	+	2.25672i	−0.388848	+	0.921302i
$7$		−	3.17007i		−	1.19817i	−0.800684	−	0.599087i	$-0.795530\pi$
$7$		−	3.17007i		−	1.19817i	0.800684	−	0.599087i	$-0.204470\pi$
$8$	0.914523	−	2.67650i	0.323333	−	0.946285i
$9$	0.166904	−	2.99535i	0.0556348	−	0.998451i
$10$	0.202875	−	0.0891057i	0.0641547	−	0.0281777i
$11$			3.38771i			1.02143i	0.859749	+	0.510716i	$0.170620\pi$
$11$			3.38771i			1.02143i	−0.859749	+	0.510716i	$0.829380\pi$
$12$	0.0501168	+	3.46374i	0.0144675	+	0.999895i
$13$		−	3.13303i		−	0.868947i	−0.900685	−	0.434474i	$-0.856934\pi$
$13$		−	3.13303i		−	0.868947i	0.900685	−	0.434474i	$-0.143066\pi$
$14$	−1.80284	−	4.10469i	−0.481829	−	1.09702i
$15$	−0.197160	+	0.186480i	−0.0509066	+	0.0481490i
$16$	−0.337995	−	3.98569i	−0.0844986	−	0.996424i
$17$		−	3.67452i		−	0.891202i	−0.895232	−	0.445601i	$-0.852990\pi$
$17$		−	3.67452i		−	0.891202i	0.895232	−	0.445601i	$-0.147010\pi$
$18$	−1.48737	−	3.97338i	−0.350575	−	0.936535i
$19$	5.24729			1.20381			0.601905	−	0.798568i	$-0.294409\pi$
$19$	5.24729			1.20381			0.601905	+	0.798568i	$0.294409\pi$
$20$	0.212013	−	0.230753i	0.0474075	−	0.0515979i
$21$	3.77298	+	3.98907i	0.823332	+	0.870486i
$22$	1.92661	+	4.38649i	0.410755	+	0.935203i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.03474	+	4.45644i	0.415340	+	0.909666i
$25$	−4.97545			−0.995090
$26$	−1.78178	−	4.05673i	−0.349435	−	0.795590i
$27$	3.35501	+	3.96786i	0.645672	+	0.763615i
$28$	−4.66873	−	4.28957i	−0.882306	−	0.810652i
$29$	6.81728			1.26594			0.632969	−	0.774177i	$-0.281836\pi$
$29$	6.81728			1.26594			0.632969	+	0.774177i	$0.281836\pi$
$30$	−0.149236	+	0.353586i	−0.0272466	+	0.0645556i
$31$			2.63390i			0.473062i	0.971624	+	0.236531i	$0.0760104\pi$
$31$			2.63390i			0.473062i	−0.971624	+	0.236531i	$0.923990\pi$
$32$	−2.70433	−	4.96856i	−0.478063	−	0.878325i
$33$	−4.03201	−	4.26293i	−0.701883	−	0.742081i
$34$	−2.08972	−	4.75786i	−0.358385	−	0.815966i
$35$		−	0.496691i		−	0.0839561i
$36$	−4.18557	−	4.29896i	−0.697594	−	0.716493i
$37$		−	3.68893i		−	0.606457i	−0.952918	−	0.303228i	$-0.901935\pi$
$37$		−	3.68893i		−	0.606457i	0.952918	−	0.303228i	$-0.0980645\pi$
$38$	6.79432	−	2.98417i	1.10218	−	0.484096i
$39$	3.72890	+	3.94246i	0.597102	+	0.631299i
$40$	0.143289	−	0.419357i	0.0226559	−	0.0663062i
$41$			3.21361i			0.501881i	0.968002	+	0.250941i	$0.0807399\pi$
$41$			3.21361i			0.501881i	−0.968002	+	0.250941i	$0.919260\pi$
$42$	7.15396	+	3.01943i	1.10388	+	0.465908i
$43$	−9.14455			−1.39453			−0.697265	−	0.716813i	$-0.745600\pi$
$43$	−9.14455			−1.39453			−0.697265	+	0.716813i	$0.745600\pi$
$44$	4.98925	+	4.58406i	0.752158	+	0.691073i
$45$	0.0261508	−	0.469316i	0.00389833	−	0.0699615i
$46$	1.29483	−	0.568707i	0.190912	−	0.0838512i
$47$	11.1268			1.62301			0.811507	−	0.584343i	$-0.198648\pi$
$47$	11.1268			1.62301			0.811507	+	0.584343i	$0.198648\pi$
$48$	5.16904	+	4.61313i	0.746087	+	0.665848i
$49$	−3.04935			−0.435621
$50$	−6.44234	+	2.82957i	−0.911084	+	0.400162i
$51$	4.37337	+	4.62384i	0.612394	+	0.647467i
$52$	−4.61418	−	4.23945i	−0.639872	−	0.587906i
$53$	1.24333			0.170784			0.0853922	−	0.996347i	$-0.472786\pi$
$53$	1.24333			0.170784			0.0853922	+	0.996347i	$0.472786\pi$
$54$	6.60070	+	3.22967i	0.898241	+	0.439502i
$55$			0.530790i			0.0715718i
$56$	−8.48469	−	2.89910i	−1.13381	−	0.387409i
$57$	−6.60294	+	6.24526i	−0.874581	+	0.827205i
$58$	8.82719	−	3.87703i	1.15907	−	0.509080i
$59$			9.90197i			1.28913i	0.764551	+	0.644563i	$0.222961\pi$
$59$			9.90197i			1.28913i	−0.764551	+	0.644563i	$0.777039\pi$
$60$	0.00785237	+	0.542703i	0.00101374	+	0.0700627i
$61$		−	0.598751i		−	0.0766623i	−0.999265	−	0.0383311i	$-0.987796\pi$
$61$		−	0.598751i		−	0.0766623i	0.999265	−	0.0383311i	$-0.0122042\pi$
$62$	1.49791	+	3.41043i	0.190235	+	0.433126i
$63$	−9.49548	−	0.529099i	−1.19632	−	0.0666602i
$64$	−6.32729	−	4.89544i	−0.790912	−	0.611930i
$65$		−	0.490888i		−	0.0608871i
$66$	−7.64511	−	3.22672i	−0.941047	−	0.397182i
$67$	−6.22235			−0.760181			−0.380090	−	0.924949i	$-0.624107\pi$
$67$	−6.22235			−0.760181			−0.380090	+	0.924949i	$0.624107\pi$
$68$	−5.41165	−	4.97216i	−0.656259	−	0.602963i
$69$	−1.25835	+	1.19019i	−0.151488	+	0.143282i
$70$	−0.282471	−	0.643128i	−0.0337618	−	0.0768685i
$71$	−11.9654			−1.42003			−0.710015	−	0.704187i	$-0.751312\pi$
$71$	−11.9654			−1.42003			−0.710015	+	0.704187i	$0.751312\pi$
$72$	−7.86442	−	3.18604i	−0.926831	−	0.375478i
$73$	−8.73037			−1.02181			−0.510906	−	0.859637i	$-0.670690\pi$
$73$	−8.73037			−1.02181			−0.510906	+	0.859637i	$0.670690\pi$
$74$	−2.09792	−	4.77653i	−0.243878	−	0.555260i
$75$	6.26087	−	5.92172i	0.722943	−	0.683782i
$76$	7.10034	−	7.72795i	0.814465	−	0.886457i
$77$	10.7393			1.22385
$78$	7.07038	+	2.98415i	0.800563	+	0.337888i
$79$			12.5424i			1.41113i	0.708648	+	0.705563i	$0.249306\pi$
$79$			12.5424i			1.41113i	−0.708648	+	0.705563i	$0.750694\pi$
$80$	−0.0529574	−	0.624484i	−0.00592082	−	0.0698194i
$81$	−8.94429	−	0.999875i	−0.993810	−	0.111097i
$82$	1.82760	+	4.16106i	0.201825	+	0.459512i
$83$			8.47249i			0.929977i	0.885317	+	0.464988i	$0.153941\pi$
$83$			8.47249i			0.929977i	−0.885317	+	0.464988i	$0.846059\pi$
$84$	10.9803	−	0.158874i	1.19805	−	0.0173346i
$85$		−	0.575728i		−	0.0624465i
$86$	−11.8406	+	5.20057i	−1.27680	+	0.560791i
$87$	−8.57855	+	8.11385i	−0.919717	+	0.869896i
$88$	9.06720	+	3.09814i	0.966566	+	0.330263i
$89$		−	4.22264i		−	0.447599i	−0.974635	−	0.223799i	$-0.928154\pi$
$89$		−	4.22264i		−	0.447599i	0.974635	−	0.223799i	$-0.0718460\pi$
$90$	−0.233042	−	0.622554i	−0.0245648	−	0.0656230i
$91$	−9.93194			−1.04115
$92$	1.35315	−	1.47275i	0.141075	−	0.153545i
$93$	−3.13483	−	3.31437i	−0.325067	−	0.343684i
$94$	14.4073	−	6.32790i	1.48600	−	0.652673i
$95$	0.822152			0.0843510
$96$	9.31653	+	3.03353i	0.950864	+	0.309609i
$97$	9.28707			0.942959			0.471479	−	0.881877i	$-0.343720\pi$
$97$	9.28707			0.942959			0.471479	+	0.881877i	$0.343720\pi$
$98$	−3.94837	+	1.73419i	−0.398846	+	0.175179i
$99$	10.1474	+	0.565423i	1.01985	+	0.0568272i
$100$	−6.73251	+	7.32760i	−0.673251	+	0.732760i
$101$	4.13544			0.411492			0.205746	−	0.978605i	$-0.434038\pi$
$101$	4.13544			0.411492			0.205746	+	0.978605i	$0.434038\pi$
$102$	8.29236	+	3.49990i	0.821066	+	0.346542i
$103$			9.03244i			0.889993i	0.895532	+	0.444996i	$0.146795\pi$
$103$			9.03244i			0.889993i	−0.895532	+	0.444996i	$0.853205\pi$
$104$	−8.38556	−	2.86523i	−0.822272	−	0.280959i
$105$	0.591155	+	0.625012i	0.0576909	+	0.0609950i
$106$	1.60989	−	0.707090i	0.156367	−	0.0686786i
$107$			13.8812i			1.34194i	0.741483	+	0.670972i	$0.234123\pi$
$107$			13.8812i			1.34194i	−0.741483	+	0.670972i	$0.765877\pi$
$108$	10.3835	+	0.427996i	0.999152	+	0.0411839i
$109$			15.4440i			1.47926i	0.673011	+	0.739632i	$0.265000\pi$
$109$			15.4440i			1.47926i	−0.673011	+	0.739632i	$0.735000\pi$
$110$	0.301864	+	0.687281i	0.0287816	+	0.0655297i
$111$	4.39053	+	4.64198i	0.416730	+	0.440597i
$112$	−12.6349	+	1.07147i	−1.19389	+	0.101244i
$113$		−	0.682535i		−	0.0642075i	−0.999485	−	0.0321037i	$-0.989779\pi$
$113$		−	0.682535i		−	0.0642075i	0.999485	−	0.0321037i	$-0.0102207\pi$
$114$	−4.99793	+	11.8417i	−0.468099	+	1.10907i
$115$	0.156681			0.0146106
$116$	9.22478	−	10.0402i	0.856499	−	0.932206i
$117$	−9.38454	−	0.522917i	−0.867601	−	0.0483437i
$118$	5.63132	+	12.8213i	0.518405	+	1.18030i
$119$	−11.6485			−1.06781
$120$	0.318806	+	0.698240i	0.0291029	+	0.0637403i
$121$	−0.476561			−0.0433237
$122$	−0.340514	−	0.775279i	−0.0308287	−	0.0701904i
$123$	−3.82480	−	4.04385i	−0.344870	−	0.364622i
$124$	3.87907	+	3.56404i	0.348351	+	0.320061i
$125$	−1.56297			−0.139796
$126$	−12.5959	+	4.71505i	−1.12213	+	0.420050i
$127$		−	20.6314i		−	1.83074i	−0.402612	−	0.915371i	$-0.631898\pi$
$127$		−	20.6314i		−	1.83074i	0.402612	−	0.915371i	$-0.368102\pi$
$128$	−10.9768	−	2.74037i	−0.970222	−	0.242217i
$129$	11.5071	−	10.8837i	1.01314	−	0.958259i
$130$	−0.279171	−	0.635614i	−0.0244849	−	0.0557470i
$131$		−	7.14222i		−	0.624019i	−0.950079	−	0.312010i	$-0.898998\pi$
$131$		−	7.14222i		−	0.624019i	0.950079	−	0.312010i	$-0.101002\pi$
$132$	−11.7341	+	0.169781i	−1.02133	+	0.0147776i
$133$		−	16.6343i		−	1.44237i
$134$	−8.05686	+	3.53869i	−0.696006	+	0.305696i
$135$	0.525667	+	0.621689i	0.0452422	+	0.0535065i
$136$	−9.83484	−	3.36043i	−0.843331	−	0.288155i
$137$			4.82633i			0.412341i	0.978516	+	0.206171i	$0.0661002\pi$
$137$			4.82633i			0.412341i	−0.978516	+	0.206171i	$0.933900\pi$
$138$	−0.952479	+	2.25672i	−0.0810804	+	0.192105i
$139$	21.9008			1.85760			0.928800	−	0.370583i	$-0.120842\pi$
$139$	21.9008			1.85760			0.928800	+	0.370583i	$0.120842\pi$
$140$	−0.731502	−	0.672095i	−0.0618232	−	0.0568024i
$141$	−14.0015	+	13.2430i	−1.17914	+	1.11526i
$142$	−15.4931	+	6.80479i	−1.30015	+	0.571046i
$143$	10.6138			0.887571
$144$	−11.9950	+	0.347183i	−0.999581	+	0.0289319i
$145$	1.06814			0.0887043
$146$	−11.3043	+	4.96502i	−0.935550	+	0.410908i
$147$	3.83716	−	3.62930i	0.316483	−	0.299340i
$148$	−5.43288	−	4.99166i	−0.446580	−	0.410312i
$149$	−3.01335			−0.246864			−0.123432	−	0.992353i	$-0.539390\pi$
$149$	−3.01335			−0.246864			−0.123432	+	0.992353i	$0.539390\pi$
$150$	4.73901	−	11.2282i	0.386939	−	0.916778i
$151$		−	12.5857i		−	1.02421i	−0.858924	−	0.512103i	$-0.828867\pi$
$151$		−	12.5857i		−	1.02421i	0.858924	−	0.512103i	$-0.171133\pi$
$152$	4.79877	−	14.0444i	0.389231	−	1.13915i
$153$	−11.0065	−	0.613293i	−0.889821	−	0.0495818i
$154$	13.9055	−	6.10750i	1.12054	−	0.492156i
$155$			0.412682i			0.0331474i
$156$	10.8520	−	0.157018i	0.868856	−	0.0125715i
$157$			8.69475i			0.693917i	0.937881	+	0.346958i	$0.112785\pi$
$157$			8.69475i			0.693917i	−0.937881	+	0.346958i	$0.887215\pi$
$158$	7.13292	+	16.2402i	0.567465	+	1.29200i
$159$	−1.56455	+	1.47980i	−0.124077	+	0.117355i
$160$	−0.423719	−	0.778480i	−0.0334979	−	0.0615443i
$161$		−	3.17007i		−	0.249837i
$162$	−12.1499	+	3.79201i	−0.954588	+	0.297929i
$163$	13.3602			1.04645			0.523226	−	0.852194i	$-0.324728\pi$
$163$	13.3602			1.04645			0.523226	+	0.852194i	$0.324728\pi$
$164$	4.73285	+	4.34848i	0.369573	+	0.339559i
$165$	−0.631740	−	0.667922i	−0.0491809	−	0.0519976i
$166$	4.81836	+	10.9704i	0.373977	+	0.851468i
$167$	11.9623			0.925672			0.462836	−	0.886444i	$-0.346832\pi$
$167$	11.9623			0.925672			0.462836	+	0.886444i	$0.346832\pi$
$168$	14.1272	−	6.45028i	1.08994	−	0.497650i
$169$	3.18410			0.244931
$170$	−0.327420	−	0.745468i	−0.0251120	−	0.0571748i
$171$	0.875795	−	15.7175i	0.0669737	−	1.20195i
$172$	−12.3739	+	13.4676i	−0.943501	+	1.02690i
$173$	1.64010			0.124695			0.0623473	−	0.998055i	$-0.480141\pi$
$173$	1.64010			0.124695			0.0623473	+	0.998055i	$0.480141\pi$
$174$	−6.49332	+	15.3847i	−0.492257	+	1.16631i
$175$			15.7725i			1.19229i
$176$	13.5024	−	1.14503i	1.01778	−	0.0863096i
$177$	−11.7852	−	12.4602i	−0.885830	−	0.936564i
$178$	−2.40144	−	5.46758i	−0.179996	−	0.409812i
$179$		−	1.54232i		−	0.115278i	−0.998337	−	0.0576391i	$-0.981643\pi$
$179$		−	1.54232i		−	0.115278i	0.998337	−	0.0576391i	$-0.0183573\pi$
$180$	−0.655800	−	0.673566i	−0.0488804	−	0.0502047i
$181$			4.96408i			0.368978i	0.982835	+	0.184489i	$0.0590629\pi$
$181$			4.96408i			0.368978i	−0.982835	+	0.184489i	$0.940937\pi$
$182$	−12.8601	+	5.64836i	−0.953256	+	0.418684i
$183$	0.712627	+	0.753441i	0.0526789	+	0.0556959i
$184$	0.914523	−	2.67650i	0.0674196	−	0.197314i
$185$		−	0.577987i		−	0.0424944i
$186$	−5.94396	−	2.50873i	−0.435833	−	0.183949i
$187$	12.4482			0.910302
$188$	15.0562	−	16.3870i	1.09809	−	1.19515i
$189$	12.5784	−	10.6356i	0.914944	−	0.773627i
$190$	1.06454	−	0.467563i	0.0772301	−	0.0339206i
$191$	11.1627			0.807708			0.403854	−	0.914823i	$-0.367670\pi$
$191$	11.1627			0.807708			0.403854	+	0.914823i	$0.367670\pi$
$192$	13.7885	−	1.37048i	0.995097	−	0.0989055i
$193$	18.7063			1.34651			0.673253	−	0.739412i	$-0.264896\pi$
$193$	18.7063			1.34651			0.673253	+	0.739412i	$0.264896\pi$
$194$	12.0251	−	5.28162i	0.863354	−	0.379198i
$195$	0.584249	+	0.617710i	0.0418389	+	0.0442351i
$196$	−4.12621	+	4.49093i	−0.294729	+	0.320781i
$197$	−19.4982			−1.38919			−0.694596	−	0.719400i	$-0.744417\pi$
$197$	−19.4982			−1.38919			−0.694596	+	0.719400i	$0.744417\pi$
$198$	13.4606	−	5.03876i	0.956607	−	0.358089i
$199$		−	18.9995i		−	1.34684i	−0.739262	−	0.673418i	$-0.764825\pi$
$199$		−	18.9995i		−	1.34684i	0.739262	−	0.673418i	$-0.235175\pi$
$200$	−4.55017	+	13.3168i	−0.321745	+	0.941639i
$201$	7.82991	−	7.40577i	0.552279	−	0.522363i
$202$	5.35468	−	2.35185i	0.376754	−	0.165476i
$203$		−	21.6113i		−	1.51681i
$204$	12.7276	−	0.184155i	0.891108	−	0.0128934i
$205$			0.503512i			0.0351668i
$206$	5.13681	+	11.6954i	0.357898	+	0.814859i
$207$	0.166904	−	2.99535i	0.0116007	−	0.208191i
$208$	−12.4873	+	1.05895i	−0.865839	+	0.0734249i
$209$			17.7763i			1.22961i
$210$	1.12089	+	0.473088i	0.0773489	+	0.0326462i
$211$	−20.3679			−1.40218			−0.701091	−	0.713072i	$-0.747303\pi$
$211$	−20.3679			−1.40218			−0.701091	+	0.713072i	$0.747303\pi$
$212$	1.68241	−	1.83112i	0.115548	−	0.125762i
$213$	15.0567	−	14.2411i	1.03167	−	0.975781i
$214$	7.89432	+	17.9737i	0.539645	+	1.22866i
$215$	−1.43278			−0.0977148
$216$	13.6882	−	5.35098i	0.931365	−	0.364088i
$217$	8.34964			0.566810
$218$	8.78309	+	19.9972i	0.594866	+	1.35438i
$219$	10.9859	−	10.3908i	0.742357	−	0.702144i
$220$	0.781722	+	0.718237i	0.0527037	+	0.0484235i
$221$	−11.5124			−0.774407
$222$	8.32489	+	3.51363i	0.558730	+	0.235820i
$223$		−	18.6142i		−	1.24650i	−0.782024	−	0.623248i	$-0.785813\pi$
$223$		−	18.6142i		−	1.24650i	0.782024	−	0.623248i	$-0.214187\pi$
$224$	−15.7507	+	8.57293i	−1.05239	+	0.572803i
$225$	−0.830425	+	14.9032i	−0.0553616	+	0.993549i
$226$	−0.388162	−	0.883763i	−0.0258202	−	0.0587871i
$227$			20.5103i			1.36131i	0.732603	+	0.680657i	$0.238305\pi$
$227$			20.5103i			1.36131i	−0.732603	+	0.680657i	$0.761695\pi$
$228$	0.262977	+	18.1752i	0.0174161	+	1.20368i
$229$		−	20.8719i		−	1.37925i	−0.724166	−	0.689626i	$-0.757775\pi$
$229$		−	20.8719i		−	1.37925i	0.724166	−	0.689626i	$-0.242225\pi$
$230$	0.202875	−	0.0891057i	0.0133772	−	0.00587546i
$231$	−13.5138	+	12.7818i	−0.889142	+	0.840978i
$232$	6.23457	−	18.2465i	0.409319	−	1.19794i
$233$			0.629101i			0.0412137i	0.999788	+	0.0206069i	$0.00655984\pi$
$233$			0.629101i			0.0412137i	−0.999788	+	0.0206069i	$0.993440\pi$
$234$	−12.4487	+	4.65997i	−0.813799	+	0.304631i
$235$	1.74336			0.113725
$236$	14.5831	+	13.3988i	0.949282	+	0.872188i
$237$	−14.9278	−	15.7827i	−0.969662	−	1.02520i
$238$	−15.0828	+	6.62457i	−0.977670	+	0.429407i
$239$	−14.6090			−0.944980			−0.472490	−	0.881336i	$-0.656645\pi$
$239$	−14.6090			−0.944980			−0.472490	+	0.881336i	$0.656645\pi$
$240$	0.809892	+	0.722792i	0.0522783	+	0.0466560i
$241$	−18.4840			−1.19066			−0.595330	−	0.803481i	$-0.702979\pi$
$241$	−18.4840			−1.19066			−0.595330	+	0.803481i	$0.702979\pi$
$242$	−0.617064	+	0.271024i	−0.0396663	+	0.0174221i
$243$	12.4451	−	9.38719i	0.798354	−	0.602188i
$244$	−0.881812	−	0.810198i	−0.0564522	−	0.0518676i
$245$	−0.477776			−0.0305240
$246$	−7.25221	−	3.06089i	−0.462384	−	0.195156i
$247$		−	16.4399i		−	1.04605i
$248$	7.04962	+	2.40876i	0.447651	+	0.152956i
$249$	−10.0839	−	10.6614i	−0.639038	−	0.675638i
$250$	−2.02377	+	0.888869i	−0.127994	+	0.0562170i
$251$			17.1737i			1.08399i	0.840381	+	0.541996i	$0.182331\pi$
$251$			17.1737i			1.08399i	−0.840381	+	0.541996i	$0.817669\pi$
$252$	−13.6280	+	13.2685i	−0.858483	+	0.835839i
$253$			3.38771i			0.212983i
$254$	−11.7332	−	26.7141i	−0.736208	−	1.67619i
$255$	0.685225	+	0.724469i	0.0429105	+	0.0453680i
$256$	−15.7715	+	2.69429i	−0.985720	+	0.168393i
$257$			5.99822i			0.374159i	0.982345	+	0.187079i	$0.0599022\pi$
$257$			5.99822i			0.374159i	−0.982345	+	0.187079i	$0.940098\pi$
$258$	8.70999	−	20.6367i	0.542261	−	1.28478i
$259$	−11.6942			−0.726641
$260$	−0.722956	−	0.664243i	−0.0448358	−	0.0411946i
$261$	1.13783	−	20.4202i	0.0704302	−	1.26398i
$262$	−4.06183	−	9.24793i	−0.250941	−	0.571339i
$263$	−25.9591			−1.60070			−0.800352	−	0.599531i	$-0.795354\pi$
$263$	−25.9591			−1.60070			−0.800352	+	0.599531i	$0.795354\pi$
$264$	−15.0971	+	6.89312i	−0.929162	+	0.424242i
$265$	0.194806			0.0119669
$266$	−9.46002	−	21.5385i	−0.580031	−	1.32061i
$267$	5.02573	+	5.31357i	0.307570	+	0.325185i
$268$	−8.41974	+	9.16398i	−0.514318	+	0.559779i
$269$	10.5130			0.640988			0.320494	−	0.947251i	$-0.396151\pi$
$269$	10.5130			0.640988			0.320494	+	0.947251i	$0.396151\pi$
$270$	1.03421	+	0.506029i	0.0629398	+	0.0307959i
$271$			5.20394i			0.316117i	0.987430	+	0.158058i	$0.0505234\pi$
$271$			5.20394i			0.316117i	−0.987430	+	0.158058i	$0.949477\pi$
$272$	−14.6455	+	1.24197i	−0.888014	+	0.0753053i
$273$	12.4979	−	11.8209i	0.756406	−	0.715432i
$274$	2.74477	+	6.24926i	0.165817	+	0.377531i
$275$		−	16.8554i		−	1.01642i
$276$	0.0501168	+	3.46374i	0.00301668	+	0.208493i
$277$		−	2.97385i		−	0.178681i	−0.996001	−	0.0893407i	$-0.971524\pi$
$277$		−	2.97385i		−	0.178681i	0.996001	−	0.0893407i	$-0.0284760\pi$
$278$	28.3577	−	12.4551i	1.70078	−	0.747008i
$279$	7.88945	+	0.439609i	0.472329	+	0.0263187i
$280$	−1.32939	−	0.454235i	−0.0794464	−	0.0271458i
$281$			25.9535i			1.54825i	0.633030	+	0.774127i	$0.281811\pi$
$281$			25.9535i			1.54825i	−0.633030	+	0.774127i	$0.718189\pi$
$282$	−10.5981	+	25.1101i	−0.631106	+	1.49529i
$283$	−18.9612			−1.12713			−0.563563	−	0.826073i	$-0.690570\pi$
$283$	−18.9612			−1.12713			−0.563563	+	0.826073i	$0.690570\pi$
$284$	−16.1909	+	17.6220i	−0.960754	+	1.04568i
$285$	−1.03456	+	0.978515i	−0.0612819	+	0.0579622i
$286$	13.7430	−	6.03614i	0.812642	−	0.356924i
$287$	10.1874			0.601341
$288$	−15.3340	+	7.27116i	−0.903562	+	0.428457i
$289$	3.49792			0.205760
$290$	1.38306	−	0.607459i	0.0812158	−	0.0356712i
$291$	−11.6864	+	11.0534i	−0.685070	+	0.647959i
$292$	−11.8135	+	12.8577i	−0.691330	+	0.752438i
$293$	24.8220			1.45011			0.725057	−	0.688688i	$-0.241813\pi$
$293$	24.8220			1.45011			0.725057	+	0.688688i	$0.241813\pi$
$294$	2.90444	−	6.88153i	0.169391	−	0.401339i
$295$			1.55145i			0.0903291i
$296$	−9.87343	−	3.37362i	−0.573881	−	0.196087i
$297$	−13.4419	+	11.3658i	−0.779981	+	0.659510i
$298$	−3.90177	+	1.71371i	−0.226023	+	0.0992728i
$299$		−	3.13303i		−	0.181188i
$300$	−0.249354	−	17.2337i	−0.0143965	−	0.994986i
$301$			28.9889i			1.67089i
$302$	−7.15754	−	16.2962i	−0.411870	−	0.937742i
$303$	−5.20385	+	4.92196i	−0.298953	+	0.282759i
$304$	−1.77355	−	20.9141i	−0.101720	−	1.19950i
$305$		−	0.0938131i		−	0.00537173i
$306$	−14.6003	+	5.46535i	−0.834641	+	0.312433i
$307$	−20.1823			−1.15187			−0.575933	−	0.817497i	$-0.695361\pi$
$307$	−20.1823			−1.15187			−0.575933	+	0.817497i	$0.695361\pi$
$308$	14.5318	−	15.8163i	0.828026	−	0.901216i
$309$	−10.7503	−	11.3660i	−0.611563	−	0.646589i
$310$	0.234695	+	0.534351i	0.0133298	+	0.0303491i
$311$	26.9576			1.52862			0.764312	−	0.644846i	$-0.223079\pi$
$311$	26.9576			1.52862			0.764312	+	0.644846i	$0.223079\pi$
$312$	13.9622	−	6.37492i	0.790452	−	0.360909i
$313$	27.5544			1.55746			0.778732	−	0.627356i	$-0.215863\pi$
$313$	27.5544			1.55746			0.778732	+	0.627356i	$0.215863\pi$
$314$	4.94476	+	11.2582i	0.279049	+	0.635336i
$315$	−1.48776	−	0.0828999i	−0.0838260	−	0.00467088i
$316$	18.4718	+	16.9716i	1.03912	+	0.954729i
$317$	10.8555			0.609704			0.304852	−	0.952400i	$-0.401393\pi$
$317$	10.8555			0.609704			0.304852	+	0.952400i	$0.401393\pi$
$318$	−1.18425	+	2.80585i	−0.0664092	+	0.157344i
$319$			23.0950i			1.29307i
$320$	−0.991369	−	0.767024i	−0.0554192	−	0.0428780i
$321$	−16.5212	−	17.4674i	−0.922124	−	0.974936i
$322$	−1.80284	−	4.10469i	−0.100468	−	0.228745i
$323$		−	19.2813i		−	1.07284i
$324$	−13.5755	+	11.8197i	−0.754194	+	0.656652i
$325$			15.5883i			0.864681i
$326$	17.2991	−	7.59803i	0.958110	−	0.420816i
$327$	−18.3812	−	19.4340i	−1.01648	−	1.07470i
$328$	8.60122	+	2.93892i	0.474923	+	0.162275i
$329$		−	35.2728i		−	1.94465i
$330$	−1.19784	−	0.505567i	−0.0659392	−	0.0278305i
$331$	5.50051			0.302335			0.151168	−	0.988508i	$-0.451697\pi$
$331$	5.50051			0.302335			0.151168	+	0.988508i	$0.451697\pi$
$332$	12.4779	+	11.4645i	0.684812	+	0.629197i
$333$	−11.0497	−	0.615699i	−0.605518	−	0.0337401i
$334$	15.4891	−	6.80305i	0.847527	−	0.372246i
$335$	−0.974926			−0.0532659
$336$	14.6240	−	16.3862i	0.797802	−	0.893942i
$337$	25.3175			1.37913			0.689565	−	0.724223i	$-0.257802\pi$
$337$	25.3175			1.37913			0.689565	+	0.724223i	$0.257802\pi$
$338$	4.12286	−	1.81082i	0.224254	−	0.0984956i
$339$	0.812345	+	0.858870i	0.0441205	+	0.0466474i
$340$	−0.847905	−	0.779044i	−0.0459841	−	0.0422496i
$341$	−8.92287			−0.483200
$342$	−7.80463	−	20.8495i	−0.422026	−	1.12741i
$343$		−	12.5238i		−	0.676224i
$344$	−8.36290	+	24.4754i	−0.450898	+	1.31962i
$345$	−0.197160	+	0.186480i	−0.0106148	+	0.0100398i
$346$	2.12365	−	0.932737i	0.114168	−	0.0501443i
$347$		−	3.32681i		−	0.178593i	−0.996005	−	0.0892963i	$-0.971538\pi$
$347$		−	3.32681i		−	0.178593i	0.996005	−	0.0892963i	$-0.0284618\pi$
$348$	0.341661	+	23.6133i	0.0183149	+	1.26581i
$349$			20.6654i			1.10620i	0.833116	+	0.553098i	$0.186554\pi$
$349$			20.6654i			1.10620i	−0.833116	+	0.553098i	$0.813446\pi$
$350$	8.96994	+	20.4227i	0.479464	+	1.09164i
$351$	12.4314	−	10.5114i	0.663541	−	0.561055i
$352$	16.8320	−	9.16150i	0.897150	−	0.488309i
$353$		−	28.0934i		−	1.49526i	−0.664116	−	0.747630i	$-0.731192\pi$
$353$		−	28.0934i		−	1.49526i	0.664116	−	0.747630i	$-0.268808\pi$
$354$	−22.3460	−	9.43142i	−1.18767	−	0.501274i
$355$	−1.87475			−0.0995015
$356$	−6.21890	−	5.71384i	−0.329601	−	0.302833i
$357$	14.6579	−	13.8639i	0.775778	−	0.733755i
$358$	−0.877126	−	1.99703i	−0.0463575	−	0.105546i
$359$	−26.2038			−1.38299			−0.691493	−	0.722383i	$-0.743047\pi$
$359$	−26.2038			−1.38299			−0.691493	+	0.722383i	$0.743047\pi$
$360$	−1.23221	−	0.499193i	−0.0649431	−	0.0263098i
$361$	8.53402			0.449159
$362$	2.82311	+	6.42762i	0.148379	+	0.337828i
$363$	0.599682	−	0.567198i	0.0314752	−	0.0297701i
$364$	−13.4394	+	14.6273i	−0.704414	+	0.766678i
$365$	−1.36788			−0.0715984
$366$	1.35121	+	0.570298i	0.0706291	+	0.0298100i
$367$			18.4607i			0.963639i	0.876271	+	0.481819i	$0.160024\pi$
$367$			18.4607i			0.963639i	−0.876271	+	0.481819i	$0.839976\pi$
$368$	−0.337995	−	3.98569i	−0.0176192	−	0.207769i
$369$	9.62589	+	0.536365i	0.501104	+	0.0279221i
$370$	−0.328705	−	0.748392i	−0.0170886	−	0.0389071i
$371$		−	3.94144i		−	0.204629i
$372$	−9.12313	+	0.132003i	−0.473012	+	0.00684401i
$373$		−	2.70030i		−	0.139816i	−0.997553	−	0.0699082i	$-0.977729\pi$
$373$		−	2.70030i		−	0.139816i	0.997553	−	0.0699082i	$-0.0222706\pi$
$374$	16.1182	−	7.07937i	0.833454	−	0.366065i
$375$	1.96676	−	1.86022i	0.101563	−	0.0960616i
$376$	10.1757	−	29.7809i	0.524774	−	1.53583i
$377$		−	21.3588i		−	1.10003i
$378$	10.2383	−	20.9247i	0.526600	−	1.07625i
$379$	−21.6100			−1.11003			−0.555015	−	0.831840i	$-0.687288\pi$
$379$	−21.6100			−1.11003			−0.555015	+	0.831840i	$0.687288\pi$
$380$	1.11249	−	1.21083i	0.0570696	−	0.0621140i
$381$	24.5553	+	25.9616i	1.25800	+	1.33005i
$382$	14.4538	−	6.34833i	0.739521	−	0.324809i
$383$	15.1956			0.776457			0.388229	−	0.921563i	$-0.373087\pi$
$383$	15.1956			0.776457			0.388229	+	0.921563i	$0.373087\pi$
$384$	17.0743	−	9.61612i	0.871317	−	0.490721i
$385$	1.68264			0.0857554
$386$	24.2213	−	10.6384i	1.23283	−	0.541479i
$387$	−1.52627	+	27.3912i	−0.0775844	+	1.39237i
$388$	12.5668	−	13.6775i	0.637980	−	0.694372i
$389$	−29.0818			−1.47450			−0.737252	−	0.675617i	$-0.763877\pi$
$389$	−29.0818			−1.47450			−0.737252	+	0.675617i	$0.763877\pi$
$390$	1.10780	+	0.467560i	0.0560954	+	0.0236758i
$391$		−	3.67452i		−	0.185828i
$392$	−2.78870	+	8.16158i	−0.140851	+	0.412222i
$393$	8.50059	+	8.98744i	0.428798	+	0.453356i
$394$	−25.2468	+	11.0888i	−1.27192	+	0.558644i
$395$			1.96515i			0.0988776i
$396$	14.5636	−	14.1795i	0.731849	−	0.712545i
$397$			6.31520i			0.316951i	0.987363	+	0.158476i	$0.0506579\pi$
$397$			6.31520i			0.316951i	−0.987363	+	0.158476i	$0.949342\pi$
$398$	−10.8051	−	24.6010i	−0.541612	−	1.23314i
$399$	19.7979	+	20.9318i	0.991135	+	1.04790i
$400$	1.68168	+	19.8306i	0.0840838	+	0.991531i
$401$			23.9318i			1.19510i	0.801833	+	0.597548i	$0.203858\pi$
$401$			23.9318i			1.19510i	−0.801833	+	0.597548i	$0.796142\pi$
$402$	5.92666	−	14.0421i	0.295595	−	0.700356i
$403$	8.25208			0.411066
$404$	5.59586	−	6.09048i	0.278404	−	0.303013i
$405$	−1.40140	−	0.156662i	−0.0696362	−	0.00778459i
$406$	−12.2905	−	27.9828i	−0.609966	−	1.38876i
$407$	12.4970			0.619455
$408$	16.3753	−	7.47670i	0.810696	−	0.370152i
$409$	12.5587			0.620988			0.310494	−	0.950575i	$-0.399506\pi$
$409$	12.5587			0.620988			0.310494	+	0.950575i	$0.399506\pi$
$410$	0.286351	+	0.651960i	0.0141419	+	0.0321980i
$411$	−5.74424	−	6.07323i	−0.283343	−	0.299570i
$412$	13.3025	+	12.2222i	0.655369	+	0.602145i
$413$	31.3899			1.54460
$414$	−1.48737	−	3.97338i	−0.0731000	−	0.195281i
$415$			1.32748i			0.0651635i
$416$	−15.5667	+	8.47277i	−0.763218	+	0.415412i
$417$	−27.5589	+	26.0660i	−1.34957	+	1.27646i
$418$	10.1095	+	23.0172i	0.494471	+	1.12581i
$419$		−	2.96910i		−	0.145050i	−0.997367	−	0.0725249i	$-0.976894\pi$
$419$		−	2.96910i		−	0.145050i	0.997367	−	0.0725249i	$-0.0231057\pi$
$420$	1.72041	−	0.0248926i	0.0839473	−	0.00121463i
$421$		−	20.4350i		−	0.995942i	−0.867194	−	0.497971i	$-0.834079\pi$
$421$		−	20.4350i		−	0.995942i	0.867194	−	0.497971i	$-0.165921\pi$
$422$	−26.3728	+	11.5833i	−1.28381	+	0.563868i
$423$	1.85712	−	33.3288i	0.0902960	−	1.62050i
$424$	1.13705	−	3.32777i	0.0552202	−	0.161611i
$425$			18.2824i			0.886826i
$426$	11.3968	−	27.0025i	0.552176	−	1.30828i
$427$	−1.89808			−0.0918547
$428$	20.4435	+	18.7833i	0.988175	+	0.907923i
$429$	−13.3559	+	12.6324i	−0.644829	+	0.609899i
$430$	−1.85520	+	0.814831i	−0.0894657	+	0.0392947i
$431$	−11.2843			−0.543545			−0.271773	−	0.962361i	$-0.587610\pi$
$431$	−11.2843			−0.543545			−0.271773	+	0.962361i	$0.587610\pi$
$432$	14.6807	−	14.7132i	0.706326	−	0.707887i
$433$	−1.53424			−0.0737311			−0.0368655	−	0.999320i	$-0.511737\pi$
$433$	−1.53424			−0.0737311			−0.0368655	+	0.999320i	$0.511737\pi$
$434$	10.8113	−	4.74849i	0.518960	−	0.227935i
$435$	−1.34410	+	1.27129i	−0.0644446	+	0.0609536i
$436$	22.7451	+	20.8979i	1.08929	+	1.00083i
$437$	5.24729			0.251012
$438$	8.31549	−	19.7020i	0.397330	−	0.941397i
$439$		−	11.5991i		−	0.553597i	−0.960928	−	0.276798i	$-0.910727\pi$
$439$		−	11.5991i		−	0.553597i	0.960928	−	0.276798i	$-0.0892734\pi$
$440$	1.42066	+	0.485420i	0.0677273	+	0.0231415i
$441$	−0.508950	+	9.13388i	−0.0242357	+	0.434947i
$442$	−14.9065	+	6.54717i	−0.709031	+	0.311417i
$443$			19.7938i			0.940430i	0.882552	+	0.470215i	$0.155824\pi$
$443$			19.7938i			0.940430i	−0.882552	+	0.470215i	$0.844176\pi$
$444$	12.7775	−	0.184878i	0.606394	−	0.00877391i
$445$		−	0.661608i		−	0.0313632i
$446$	−10.5860	−	24.1021i	−0.501262	−	1.14127i
$447$	3.79186	−	3.58646i	0.179349	−	0.169634i
$448$	−15.5189	+	20.0580i	−0.733199	+	0.947650i
$449$		−	12.3624i		−	0.583419i	−0.956507	−	0.291709i	$-0.905776\pi$
$449$		−	12.3624i		−	0.583419i	0.956507	−	0.291709i	$-0.0942240\pi$
$450$	7.40031	+	19.7694i	0.348854	+	0.931936i
$451$	−10.8868			−0.512638
$452$	−1.00520	−	0.923569i	−0.0472808	−	0.0434410i
$453$	14.9793	+	15.8372i	0.703789	+	0.744096i
$454$	11.6643	+	26.5572i	0.547434	+	1.24639i
$455$	−1.55615			−0.0729534
$456$	10.6769	+	23.3842i	0.499991	+	1.09507i
$457$	10.8345			0.506816			0.253408	−	0.967359i	$-0.418448\pi$
$457$	10.8345			0.506816			0.253408	+	0.967359i	$0.418448\pi$
$458$	−11.8700	−	27.0254i	−0.554647	−	1.26282i
$459$	14.5800	−	12.3280i	0.680535	−	0.575424i
$460$	0.212013	−	0.230753i	0.00988514	−	0.0107589i
$461$	−34.2633			−1.59580			−0.797901	−	0.602788i	$-0.794056\pi$
$461$	−34.2633			−1.59580			−0.797901	+	0.602788i	$0.794056\pi$
$462$	−10.2289	+	24.2355i	−0.475893	+	1.12754i
$463$			26.9297i			1.25153i	0.780012	+	0.625764i	$0.215213\pi$
$463$			26.9297i			1.25153i	−0.780012	+	0.625764i	$0.784787\pi$
$464$	−2.30420	−	27.1716i	−0.106970	−	1.26141i
$465$	−0.491169	−	0.519300i	−0.0227774	−	0.0240820i
$466$	0.357774	+	0.814575i	0.0165735	+	0.0377345i
$467$		−	33.3521i		−	1.54335i	−0.636017	−	0.771675i	$-0.719419\pi$
$467$		−	33.3521i		−	1.54335i	0.636017	−	0.771675i	$-0.280581\pi$
$468$	−13.4688	+	13.1135i	−0.622595	+	0.606173i
$469$			19.7253i			0.910829i
$470$	2.25735	−	0.991463i	0.104124	−	0.0457328i
$471$	−10.3484	−	10.9411i	−0.476829	−	0.504138i
$472$	26.5026	+	9.05558i	1.21988	+	0.416817i
$473$		−	30.9791i		−	1.42442i
$474$	−28.3046	−	11.9463i	−1.30007	−	0.548713i
$475$	−26.1076			−1.19790
$476$	−15.7621	+	17.1553i	−0.722454	+	0.786313i
$477$	0.207517	−	3.72421i	0.00950156	−	0.170520i
$478$	−18.9161	+	8.30825i	−0.865204	+	0.380011i
$479$	12.6737			0.579074			0.289537	−	0.957167i	$-0.406499\pi$
$479$	12.6737			0.579074			0.289537	+	0.957167i	$0.406499\pi$
$480$	1.45973	+	0.475298i	0.0666270	+	0.0216943i
$481$	−11.5576			−0.526979
$482$	−23.9336	+	10.5120i	−1.09014	+	0.478808i
$483$	3.77298	+	3.98907i	0.171677	+	0.181509i
$484$	−0.644857	+	0.701856i	−0.0293117	+	0.0319026i
$485$	1.45511			0.0660731
$486$	10.7757	−	19.2324i	0.488795	−	0.872399i
$487$		−	22.4756i		−	1.01847i	−0.860628	−	0.509234i	$-0.829929\pi$
$487$		−	22.4756i		−	1.01847i	0.860628	−	0.509234i	$-0.170071\pi$
$488$	−1.60256	−	0.547572i	−0.0725444	−	0.0247874i
$489$	−16.8118	+	15.9012i	−0.760258	+	0.719075i
$490$	−0.618636	+	0.271714i	−0.0279471	+	0.0122748i
$491$			3.49545i			0.157747i	0.996885	+	0.0788736i	$0.0251324\pi$
$491$			3.49545i			0.157747i	−0.996885	+	0.0788736i	$0.974868\pi$
$492$	−11.1311	+	0.161056i	−0.501829	+	0.00726096i
$493$		−	25.0502i		−	1.12821i
$494$	−9.34949	−	21.2868i	−0.420654	−	0.957740i
$495$	1.58990	+	0.0885912i	0.0714609	+	0.00398188i
$496$	10.4979	−	0.890242i	0.471370	−	0.0399731i
$497$			37.9311i			1.70144i
$498$	−19.1200	−	8.06987i	−0.856789	−	0.361620i
$499$	20.7414			0.928512			0.464256	−	0.885701i	$-0.346322\pi$
$499$	20.7414			0.928512			0.464256	+	0.885701i	$0.346322\pi$
$500$	−2.11492	+	2.30186i	−0.0945821	+	0.102942i
$501$	−15.0528	+	14.2374i	−0.672511	+	0.636081i
$502$	9.76678	+	22.2369i	0.435913	+	0.992481i
$503$	−13.1051			−0.584329			−0.292165	−	0.956368i	$-0.594375\pi$
$503$	−13.1051			−0.584329			−0.292165	+	0.956368i	$0.594375\pi$
$504$	−10.1000	+	24.9308i	−0.449889	+	1.11051i
$505$	0.647947			0.0288332
$506$	1.92661	+	4.38649i	0.0856483	+	0.195003i
$507$	−4.00672	+	3.78968i	−0.177945	+	0.168306i
$508$	−30.3849	−	27.9173i	−1.34811	−	1.23863i
$509$	−21.8298			−0.967590			−0.483795	−	0.875181i	$-0.660742\pi$
$509$	−21.8298			−0.967590			−0.483795	+	0.875181i	$0.660742\pi$
$510$	1.29926	+	0.548369i	0.0575321	+	0.0242822i
$511$			27.6759i			1.22431i
$512$	−18.8891	+	12.4580i	−0.834788	+	0.550571i
$513$	17.6047	+	20.8205i	0.777266	+	0.919247i
$514$	3.41123	+	7.76665i	0.150463	+	0.342572i
$515$			1.41521i			0.0623618i
$516$	−0.458296	−	31.6743i	−0.0201754	−	1.39438i
$517$			37.6944i			1.65780i
$518$	−15.1419	+	6.65056i	−0.665298	+	0.292209i
$519$	−2.06383	+	1.95203i	−0.0905920	+	0.0856846i
$520$	−1.31386	−	0.448928i	−0.0576166	−	0.0196868i
$521$			14.9878i			0.656629i	0.944568	+	0.328315i	$0.106481\pi$
$521$			14.9878i			0.656629i	−0.944568	+	0.328315i	$0.893519\pi$
$522$	−10.1398	−	27.0877i	−0.443807	−	1.18559i
$523$	−8.55595			−0.374126			−0.187063	−	0.982348i	$-0.559897\pi$
$523$	−8.55595			−0.374126			−0.187063	+	0.982348i	$0.559897\pi$
$524$	−10.5187	−	9.66447i	−0.459513	−	0.422194i
$525$	−18.7723	−	19.8474i	−0.819289	−	0.866212i
$526$	−33.6124	+	14.7631i	−1.46557	+	0.643701i
$527$	9.67830			0.421593
$528$	−15.6279	+	17.5112i	−0.680119	+	0.762077i
$529$	1.00000			0.0434783
$530$	0.252240	−	0.110788i	0.0109566	−	0.00481231i
$531$	29.6599	+	1.65268i	1.28713	+	0.0717203i
$532$	−24.4981	−	22.5086i	−1.06213	−	0.975871i
$533$	10.0683			0.436108
$534$	9.52931	+	4.02198i	0.412374	+	0.174048i
$535$			2.17492i			0.0940300i
$536$	−5.69048	+	16.6541i	−0.245792	+	0.719348i
$537$	1.83565	+	1.94078i	0.0792140	+	0.0837508i
$538$	13.6125	−	5.97880i	0.586876	−	0.257765i
$539$		−	10.3303i		−	0.444958i
$540$	1.62690	+	0.0670589i	0.0700106	+	0.00288576i
$541$		−	1.58937i		−	0.0683323i	−0.999416	−	0.0341661i	$-0.989122\pi$
$541$		−	1.58937i		−	0.0683323i	0.999416	−	0.0341661i	$-0.0108775\pi$
$542$	2.95951	+	6.73819i	0.127122	+	0.289430i
$543$	−5.90819	−	6.24657i	−0.253545	−	0.268066i
$544$	−18.2571	+	9.93713i	−0.782765	+	0.426051i
$545$			2.41978i			0.103652i
$546$	9.45997	−	22.4136i	0.404849	−	0.959213i
$547$	13.1282			0.561320			0.280660	−	0.959807i	$-0.409447\pi$
$547$	13.1282			0.561320			0.280660	+	0.959807i	$0.409447\pi$
$548$	7.10799	+	6.53073i	0.303638	+	0.278979i
$549$	−1.79347	−	0.0999342i	−0.0765435	−	0.00426509i
$550$	−9.58576	−	21.8248i	−0.408738	−	0.930611i
$551$	35.7722			1.52395
$552$	2.03474	+	4.45644i	0.0866045	+	0.189678i
$553$	39.7602			1.69077
$554$	−1.69125	−	3.85062i	−0.0718543	−	0.163597i
$555$	0.687913	+	0.727312i	0.0292003	+	0.0308727i
$556$	29.6349	−	32.2544i	1.25680	−	1.36789i
$557$	−29.5816			−1.25341			−0.626706	−	0.779255i	$-0.715597\pi$
$557$	−29.5816			−1.25341			−0.626706	+	0.779255i	$0.715597\pi$
$558$	10.4655	−	3.91757i	0.443039	−	0.165844i
$559$			28.6502i			1.21177i
$560$	−1.97966	+	0.167879i	−0.0836558	+	0.00709417i
$561$	−15.6642	+	14.8157i	−0.661344	+	0.625519i
$562$	14.7599	+	33.6052i	0.622609	+	1.41755i
$563$			30.9529i			1.30451i	0.758001	+	0.652254i	$0.226176\pi$
$563$			30.9529i			1.30451i	−0.758001	+	0.652254i	$0.773824\pi$
$564$	0.557641	+	38.5404i	0.0234809	+	1.62284i
$565$		−	0.106940i		−	0.00449902i
$566$	−24.5514	+	10.7834i	−1.03197	+	0.453258i
$567$	−3.16968	+	28.3540i	−0.133114	+	1.19076i
$568$	−10.9426	+	32.0253i	−0.459142	+	1.34375i
$569$			6.91099i			0.289724i	0.989452	+	0.144862i	$0.0462738\pi$
$569$			6.91099i			0.289724i	−0.989452	+	0.144862i	$0.953726\pi$
$570$	−0.783083	+	1.85537i	−0.0327997	+	0.0777127i
$571$	−41.1665			−1.72277			−0.861383	−	0.507956i	$-0.830401\pi$
$571$	−41.1665			−1.72277			−0.861383	+	0.507956i	$0.830401\pi$
$572$	14.3620	−	15.6315i	0.600506	−	0.653586i
$573$	−14.0467	+	13.2858i	−0.586808	+	0.555021i
$574$	13.1909	−	5.79362i	0.550576	−	0.241821i
$575$	−4.97545			−0.207491
$576$	−15.7196	+	18.1354i	−0.654985	+	0.755642i
$577$	−14.3761			−0.598487			−0.299243	−	0.954177i	$-0.596734\pi$
$577$	−14.3761			−0.598487			−0.299243	+	0.954177i	$0.596734\pi$
$578$	4.52919	−	1.98929i	0.188389	−	0.0827435i
$579$	−23.5391	+	22.2640i	−0.978251	+	0.925259i
$580$	1.44535	−	1.57311i	0.0600149	−	0.0653197i
$581$	26.8584			1.11427
$582$	−8.84574	+	20.9583i	−0.366668	+	0.868750i
$583$			4.21204i			0.174445i
$584$	−7.98412	+	23.3668i	−0.330385	+	0.966926i
$585$	−1.47038	−	0.0819313i	−0.0607928	−	0.00338744i
$586$	32.1401	−	14.1164i	1.32770	−	0.583144i
$587$		−	39.1480i		−	1.61581i	−0.589312	−	0.807906i	$-0.700601\pi$
$587$		−	39.1480i		−	1.61581i	0.589312	−	0.807906i	$-0.299399\pi$
$588$	−0.152824	−	10.5621i	−0.00630234	−	0.435576i
$589$			13.8208i			0.569476i
$590$	0.882322	+	2.00886i	0.0363246	+	0.0827035i
$591$	24.5357	−	23.2066i	1.00926	−	0.954590i
$592$	−14.7030	+	1.24684i	−0.604288	+	0.0512448i
$593$			5.67397i			0.233002i	0.993191	+	0.116501i	$0.0371678\pi$
$593$			5.67397i			0.233002i	−0.993191	+	0.116501i	$0.962832\pi$
$594$	−10.9412	+	22.3612i	−0.448922	+	0.917493i
$595$	−1.82510			−0.0748218
$596$	−4.07751	+	4.43792i	−0.167021	+	0.181784i
$597$	22.6129	+	23.9080i	0.925486	+	0.978490i
$598$	−1.78178	−	4.05673i	−0.0728623	−	0.165892i
$599$	−14.8700			−0.607570			−0.303785	−	0.952741i	$-0.598250\pi$
$599$	−14.8700			−0.607570			−0.303785	+	0.952741i	$0.598250\pi$
$600$	−10.1238	−	22.1728i	−0.413301	−	0.905200i
$601$	7.39318			0.301574			0.150787	−	0.988566i	$-0.451819\pi$
$601$	7.39318			0.301574			0.150787	+	0.988566i	$0.451819\pi$
$602$	16.4862	+	37.5355i	0.671926	+	1.52983i
$603$	−1.03854	+	18.6381i	−0.0422925	+	0.759004i
$604$	−18.5355	−	17.0302i	−0.754200	−	0.692950i
$605$	−0.0746682			−0.00303570
$606$	−3.93892	+	9.33254i	−0.160008	+	0.379108i
$607$		−	15.8401i		−	0.642929i	−0.946922	−	0.321465i	$-0.895825\pi$
$607$		−	15.8401i		−	0.642929i	0.946922	−	0.321465i	$-0.104175\pi$
$608$	−14.1904	−	26.0715i	−0.575498	−	1.05734i
$609$	25.7215	+	27.1946i	1.04229	+	1.10198i
$610$	−0.0533522	−	0.121472i	−0.00216017	−	0.00491824i
$611$		−	34.8607i		−	1.41031i
$612$	−15.7966	+	15.3799i	−0.638540	+	0.621697i
$613$		−	38.9904i		−	1.57481i	−0.616438	−	0.787403i	$-0.711425\pi$
$613$		−	38.9904i		−	1.57481i	0.616438	−	0.787403i	$-0.288575\pi$
$614$	−26.1326	+	11.4778i	−1.05462	+	0.463207i
$615$	−0.599274	−	0.633596i	−0.0241651	−	0.0255491i
$616$	9.82132	−	28.7437i	0.395712	−	1.15811i
$617$			20.5392i			0.826877i	0.910532	+	0.413439i	$0.135672\pi$
$617$			20.5392i			0.826877i	−0.910532	+	0.413439i	$0.864328\pi$
$618$	−20.3837	−	8.60321i	−0.819952	−	0.346072i
$619$	−9.41085			−0.378254			−0.189127	−	0.981953i	$-0.560566\pi$
$619$	−9.41085			−0.378254			−0.189127	+	0.981953i	$0.560566\pi$
$620$	0.607778	+	0.558419i	0.0244090	+	0.0224266i
$621$	3.35501	+	3.96786i	0.134632	+	0.159225i
$622$	34.9054	−	15.3310i	1.39958	−	0.614715i
$623$	−13.3861			−0.536301
$624$	14.4531	−	16.1948i	0.578587	−	0.648310i
$625$	24.6324			0.985295
$626$	35.6781	−	15.6703i	1.42598	−	0.626313i
$627$	−21.1571	−	22.3688i	−0.844933	−	0.893325i
$628$	12.8052	+	11.7653i	0.510983	+	0.469485i
$629$	−13.5551			−0.540475
$630$	−1.97354	+	0.738761i	−0.0786278	+	0.0294329i
$631$		−	19.9401i		−	0.793803i	−0.917861	−	0.396901i	$-0.870085\pi$
$631$		−	19.9401i		−	0.793803i	0.917861	−	0.396901i	$-0.129915\pi$
$632$	33.5696	+	11.4703i	1.33533	+	0.456263i
$633$	25.6300	−	24.2416i	1.01870	−	0.963517i
$634$	14.0559	−	6.17358i	0.558233	−	0.245184i
$635$		−	3.23256i		−	0.128280i
$636$	0.0623117	+	4.30657i	0.00247082	+	0.170767i
$637$			9.55371i			0.378532i
$638$	13.1343	+	29.9039i	0.519990	+	1.18391i
$639$	−1.99708	+	35.8406i	−0.0790031	+	1.41783i
$640$	−1.71986	−	0.429365i	−0.0679835	−	0.0169721i
$641$			13.5184i			0.533944i	0.963704	+	0.266972i	$0.0860231\pi$
$641$			13.5184i			0.533944i	−0.963704	+	0.266972i	$0.913977\pi$
$642$	−31.3259	−	13.2215i	−1.23634	−	0.521812i
$643$	−29.6496			−1.16927			−0.584634	−	0.811297i	$-0.698762\pi$
$643$	−29.6496			−1.16927			−0.584634	+	0.811297i	$0.698762\pi$
$644$	−4.66873	−	4.28957i	−0.183974	−	0.169033i
$645$	1.80294	−	1.70528i	0.0709908	−	0.0671452i
$646$	−10.9654	−	24.9659i	−0.431427	−	0.982268i
$647$	−30.4388			−1.19667			−0.598337	−	0.801244i	$-0.704172\pi$
$647$	−30.4388			−1.19667			−0.598337	+	0.801244i	$0.704172\pi$
$648$	−10.8559	+	23.0250i	−0.426461	+	0.904506i
$649$	−33.5450			−1.31676
$650$	8.86514	+	20.1841i	0.347720	+	0.791684i
$651$	−10.5068	+	9.93764i	−0.411794	+	0.389487i
$652$	18.0783	−	19.6763i	0.708001	−	0.770582i
$653$	−0.0649892			−0.00254322			−0.00127161	−	0.999999i	$-0.500405\pi$
$653$	−0.0649892			−0.00254322			−0.00127161	+	0.999999i	$0.500405\pi$
$654$	−34.8527	−	14.7101i	−1.36285	−	0.575209i
$655$		−	1.11905i		−	0.0437250i
$656$	12.8085	−	1.08618i	0.500086	−	0.0424083i
$657$	−1.45714	+	26.1505i	−0.0568483	+	1.02023i
$658$	−20.0599	−	45.6721i	−0.782015	−	1.78048i
$659$			28.7385i			1.11949i	0.828664	+	0.559746i	$0.189101\pi$
$659$			28.7385i			1.11949i	−0.828664	+	0.559746i	$0.810899\pi$
$660$	−1.83852	+	0.0266015i	−0.0715643	+	0.00103546i
$661$			38.9333i			1.51433i	0.653223	+	0.757166i	$0.273416\pi$
$661$			38.9333i			1.51433i	−0.653223	+	0.757166i	$0.726584\pi$
$662$	7.12220	−	3.12818i	0.276812	−	0.121580i
$663$	14.4866	−	13.7019i	0.562615	−	0.532138i
$664$	22.6766	+	7.74829i	0.880023	+	0.300692i
$665$		−	2.60628i		−	0.101067i
$666$	−14.6575	+	5.48679i	−0.567968	+	0.212609i
$667$	6.81728			0.263966
$668$	16.1868	−	17.6175i	0.626285	−	0.681643i
$669$	22.1544	+	23.4232i	0.856537	+	0.905593i
$670$	−1.26236	+	0.554447i	−0.0487692	+	0.0214201i
$671$	2.02839			0.0783053
$672$	9.61651	−	29.5341i	0.370965	−	1.13930i
$673$	−39.5327			−1.52387			−0.761937	−	0.647651i	$-0.775751\pi$
$673$	−39.5327			−1.52387			−0.761937	+	0.647651i	$0.775751\pi$
$674$	32.7817	−	14.3982i	1.26270	−	0.554599i
$675$	−16.6927	−	19.7419i	−0.642502	−	0.759866i
$676$	4.30855	−	4.68939i	0.165714	−	0.180361i
$677$	18.9301			0.727543			0.363772	−	0.931488i	$-0.381489\pi$
$677$	18.9301			0.727543			0.363772	+	0.931488i	$0.381489\pi$
$678$	1.54029	+	0.650100i	0.0591545	+	0.0249670i
$679$		−	29.4407i		−	1.12983i
$680$	−1.54094	−	0.526517i	−0.0590922	−	0.0201910i
$681$	−24.4111	−	25.8091i	−0.935434	−	0.989008i
$682$	−11.5536	+	5.07449i	−0.442408	+	0.194312i
$683$		−	7.59568i		−	0.290641i	−0.989385	−	0.145320i	$-0.953579\pi$
$683$		−	7.59568i		−	0.290641i	0.989385	−	0.145320i	$-0.0464213\pi$
$684$	−21.9629	−	22.5579i	−0.839771	−	0.862521i
$685$			0.756196i			0.0288928i
$686$	−7.12239	−	16.2162i	−0.271934	−	0.619137i
$687$	24.8415	+	26.2642i	0.947761	+	1.00204i
$688$	3.09081	+	36.4474i	0.117836	+	1.38954i
$689$		−	3.89539i		−	0.148403i
$690$	−0.149236	+	0.353586i	−0.00568131	+	0.0134608i
$691$	−12.9224			−0.491591			−0.245795	−	0.969322i	$-0.579049\pi$
$691$	−12.9224			−0.491591			−0.245795	+	0.969322i	$0.579049\pi$
$692$	2.21930	−	2.41546i	0.0843650	−	0.0918221i
$693$	1.79243	−	32.1679i	0.0680889	−	1.22196i
$694$	−1.89198	−	4.30764i	−0.0718185	−	0.163516i
$695$	3.43144			0.130162
$696$	13.8714	+	30.3808i	0.525795	+	1.15158i
$697$	11.8085			0.447277
$698$	11.7526	+	26.7581i	0.444842	+	1.01281i
$699$	−0.748748	−	0.791631i	−0.0283203	−	0.0299422i
$700$	23.2290	+	21.3425i	0.877974	+	0.806672i
$701$	17.9538			0.678107			0.339053	−	0.940767i	$-0.389893\pi$
$701$	17.9538			0.678107			0.339053	+	0.940767i	$0.389893\pi$
$702$	10.1187	−	20.6802i	0.381904	−	0.780524i
$703$		−	19.3569i		−	0.730059i
$704$	16.5843	−	21.4350i	0.625045	−	0.807863i
$705$	−2.19377	+	2.07493i	−0.0826221	+	0.0781464i
$706$	−15.9769	−	36.3760i	−0.601298	−	1.36903i
$707$		−	13.1096i		−	0.493039i
$708$	−34.2978	+	0.496255i	−1.28899	+	0.0186504i
$709$		−	15.9683i		−	0.599701i	−0.953986	−	0.299850i	$-0.903063\pi$
$709$		−	15.9683i		−	0.599701i	0.953986	−	0.299850i	$-0.0969367\pi$
$710$	−2.42748	+	1.06618i	−0.0911016	+	0.0400132i
$711$	37.5688	+	2.09337i	1.40894	+	0.0785077i
$712$	−11.3019	−	3.86170i	−0.423556	−	0.144723i
$713$			2.63390i			0.0986402i
$714$	11.0949	−	26.2874i	0.415218	−	0.983780i
$715$	1.66298			0.0621921
$716$	−2.27145	−	2.08698i	−0.0848880	−	0.0779941i
$717$	18.3833	−	17.3875i	0.686538	−	0.649348i
$718$	−33.9294	+	14.9023i	−1.26623	+	0.556149i
$719$	−7.62509			−0.284368			−0.142184	−	0.989840i	$-0.545412\pi$
$719$	−7.62509			−0.284368			−0.142184	+	0.989840i	$0.545412\pi$
$720$	−1.87939	+	0.0543971i	−0.0700407	+	0.00202726i
$721$	28.6335			1.06637
$722$	11.0501	−	4.85335i	0.411241	−	0.180623i
$723$	23.2594	−	21.9995i	0.865027	−	0.818169i
$724$	7.31086	+	6.71713i	0.271706	+	0.249640i
$725$	−33.9191			−1.25972
$726$	0.453915	−	1.07547i	0.0168464	−	0.0399143i
$727$			41.4515i			1.53735i	0.639640	+	0.768675i	$0.279084\pi$
$727$			41.4515i			1.53735i	−0.639640	+	0.768675i	$0.720916\pi$
$728$	−9.08299	+	26.5828i	−0.336638	+	0.985225i
$729$	−4.48782	+	26.6244i	−0.166216	+	0.986089i
$730$	−1.77117	+	0.777925i	−0.0655540	+	0.0287923i
$731$			33.6018i			1.24281i
$732$	2.07392	−	0.0300075i	0.0766542	−	0.00110911i
$733$		−	33.2881i		−	1.22952i	−0.788713	−	0.614762i	$-0.789252\pi$
$733$		−	33.2881i		−	1.22952i	0.788713	−	0.614762i	$-0.210748\pi$
$734$	10.4987	+	23.9033i	0.387514	+	0.882288i
$735$	0.601211	−	0.568643i	0.0221760	−	0.0209747i
$736$	−2.70433	−	4.96856i	−0.0996831	−	0.183143i
$737$		−	21.0795i		−	0.776473i
$738$	12.7689	−	4.77981i	0.470029	−	0.175947i
$739$	11.9136			0.438249			0.219124	−	0.975697i	$-0.429680\pi$
$739$	11.9136			0.438249			0.219124	+	0.975697i	$0.429680\pi$
$740$	−0.851231	−	0.782100i	−0.0312919	−	0.0287506i
$741$	19.5666	+	20.6872i	0.718797	+	0.759964i
$742$	−2.24152	−	5.10348i	−0.0822889	−	0.187355i
$743$	1.10266			0.0404526			0.0202263	−	0.999795i	$-0.493561\pi$
$743$	1.10266			0.0404526			0.0202263	+	0.999795i	$0.493561\pi$
$744$	−11.7378	+	5.35930i	−0.430328	+	0.196482i
$745$	−0.472136			−0.0172977
$746$	−1.53568	−	3.49642i	−0.0562253	−	0.128013i
$747$	25.3781	+	1.41410i	0.928536	+	0.0517391i
$748$	16.8442	−	18.3331i	0.615886	−	0.670324i
$749$	44.0043			1.60788
$750$	1.48869	−	3.52718i	0.0543594	−	0.128794i
$751$			3.29526i			0.120246i	0.998191	+	0.0601228i	$0.0191492\pi$
$751$			3.29526i			0.120246i	−0.998191	+	0.0601228i	$0.980851\pi$
$752$	−3.76080	−	44.3481i	−0.137142	−	1.61721i
$753$	−20.4399	−	21.6105i	−0.744871	−	0.787532i
$754$	−12.1469	−	27.6559i	−0.442363	−	1.00717i
$755$		−	1.97194i		−	0.0717661i
$756$	1.35678	−	32.9164i	0.0493455	−	1.19716i
$757$			2.70669i			0.0983762i	0.998790	+	0.0491881i	$0.0156634\pi$
$757$			2.70669i			0.0983762i	−0.998790	+	0.0491881i	$0.984337\pi$
$758$	−27.9812	+	12.2897i	−1.01632	+	0.446384i
$759$	−4.03201	−	4.26293i	−0.146353	−	0.154735i
$760$	0.751877	−	2.20049i	0.0272734	−	0.0798201i
$761$			37.3083i			1.35243i	0.736707	+	0.676213i	$0.236380\pi$
$761$			37.3083i			1.35243i	−0.736707	+	0.676213i	$0.763620\pi$
$762$	46.5593	+	19.6510i	1.68667	+	0.711880i
$763$	48.9585			1.77242
$764$	15.1048	−	16.4400i	0.546473	−	0.594777i
$765$	−1.72451	−	0.0960916i	−0.0623498	−	0.00347420i
$766$	19.6756	−	8.64182i	0.710908	−	0.312242i
$767$	31.0232			1.12018
$768$	16.6394	−	22.1614i	0.600424	−	0.799682i
$769$	2.15675			0.0777744			0.0388872	−	0.999244i	$-0.487619\pi$
$769$	2.15675			0.0777744			0.0388872	+	0.999244i	$0.487619\pi$
$770$	2.17873	−	0.956930i	0.0785159	−	0.0344854i
$771$	−7.13902	−	7.54788i	−0.257105	−	0.271830i
$772$	25.3123	−	27.5497i	0.911009	−	0.991535i
$773$	−54.7357			−1.96870			−0.984352	−	0.176211i	$-0.943616\pi$
$773$	−54.7357			−1.96870			−0.984352	+	0.176211i	$0.943616\pi$
$774$	13.6013	+	36.3348i	0.488888	+	1.30603i
$775$		−	13.1048i		−	0.470739i
$776$	8.49324	−	24.8568i	0.304890	−	0.892308i
$777$	14.7154	−	13.9183i	0.527912	−	0.499315i
$778$	−37.6558	+	16.5390i	−1.35003	+	0.592952i
$779$			16.8627i			0.604170i
$780$	1.70031	−	0.0246017i	0.0608808	−	0.000880884i
$781$		−	40.5352i		−	1.45046i
$782$	−2.08972	−	4.75786i	−0.0747283	−	0.170141i
$783$	22.8720	+	27.0500i	0.817380	+	0.966689i
$784$	1.03066	+	12.1538i	0.0368094	+	0.434063i
$785$			1.36230i			0.0486227i
$786$	16.1180	+	6.80282i	0.574910	+	0.242649i
$787$	−22.0076			−0.784485			−0.392243	−	0.919862i	$-0.628301\pi$
$787$	−22.0076			−0.784485			−0.392243	+	0.919862i	$0.628301\pi$
$788$	−26.3839	+	28.7160i	−0.939889	+	1.02297i
$789$	32.6657	−	30.8962i	1.16293	−	1.09993i
$790$	1.11760	+	2.54453i	0.0397623	+	0.0905303i
$791$	−2.16368			−0.0769317
$792$	10.7934	−	26.6424i	0.383526	−	0.946695i
$793$	−1.87591			−0.0666155
$794$	3.59150	+	8.17709i	0.127458	+	0.290194i
$795$	−0.245135	+	0.231856i	−0.00869405	+	0.00822310i
$796$	−27.9815	−	25.7090i	−0.991777	−	0.911232i
$797$	4.08475			0.144689			0.0723447	−	0.997380i	$-0.476952\pi$
$797$	4.08475			0.144689			0.0723447	+	0.997380i	$0.476952\pi$
$798$	37.5389	+	15.8438i	1.32886	+	0.560864i
$799$		−	40.8857i		−	1.44643i
$800$	13.4553	+	24.7208i	0.475716	+	0.874013i
$801$	−12.6483	−	0.704777i	−0.446905	−	0.0249021i
$802$	13.6102	+	30.9875i	0.480591	+	1.09421i
$803$		−	29.5759i		−	1.04371i
$804$	−0.311844	−	21.5526i	−0.0109979	−	0.760101i
$805$		−	0.496691i		−	0.0175061i
$806$	10.6850	−	4.69301i	0.376363	−	0.165304i
$807$	−13.2290	+	12.5124i	−0.465684	+	0.440458i
$808$	3.78196	−	11.0685i	0.133049	−	0.389389i
$809$		−	14.2082i		−	0.499534i	−0.968306	−	0.249767i	$-0.919646\pi$
$809$		−	14.2082i		−	0.499534i	0.968306	−	0.249767i	$-0.0803541\pi$
$810$	−1.90367	+	0.594137i	−0.0668880	+	0.0208759i
$811$	−15.6928			−0.551047			−0.275524	−	0.961294i	$-0.588851\pi$
$811$	−15.6928			−0.551047			−0.275524	+	0.961294i	$0.588851\pi$
$812$	−31.8280	−	29.2432i	−1.11694	−	1.02623i
$813$	−6.19366	−	6.54839i	−0.217221	−	0.229662i
$814$	16.1815	−	7.10714i	0.567160	−	0.249105i
$815$	2.09329			0.0733249
$816$	16.9510	−	18.9937i	0.593405	−	0.664914i
$817$	−47.9841			−1.67875
$818$	16.2613	−	7.14222i	0.568564	−	0.249722i
$819$	−1.65768	+	29.7497i	−0.0579242	+	1.03954i
$820$	0.741548	+	0.681325i	0.0258960	+	0.0237929i
$821$	−28.3906			−0.990838			−0.495419	−	0.868654i	$-0.664986\pi$
$821$	−28.3906			−0.990838			−0.495419	+	0.868654i	$0.664986\pi$
$822$	−10.8917	−	4.59698i	−0.379891	−	0.160338i
$823$		−	15.0615i		−	0.525012i	−0.964930	−	0.262506i	$-0.915451\pi$
$823$		−	15.0615i		−	0.525012i	0.964930	−	0.262506i	$-0.0845489\pi$
$824$	24.1753	+	8.26038i	0.842187	+	0.287764i
$825$	20.0611	+	21.2100i	0.698437	+	0.738438i
$826$	40.6445	−	17.8517i	1.41420	−	0.621139i
$827$		−	39.7845i		−	1.38344i	−0.722164	−	0.691721i	$-0.756853\pi$
$827$		−	39.7845i		−	1.38344i	0.722164	−	0.691721i	$-0.243147\pi$
$828$	−4.18557	−	4.29896i	−0.145458	−	0.149399i
$829$			2.50800i			0.0871064i	0.999051	+	0.0435532i	$0.0138678\pi$
$829$			2.50800i			0.0871064i	−0.999051	+	0.0435532i	$0.986132\pi$
$830$	0.754947	+	1.71886i	0.0262046	+	0.0596624i
$831$	3.53944	+	3.74215i	0.122782	+	0.129814i
$832$	−15.3376	+	19.8236i	−0.531735	+	0.687260i
$833$			11.2049i			0.388226i
$834$	−20.8600	+	49.4239i	−0.722324	+	1.71141i
$835$	1.87427			0.0648619
$836$	26.1800	+	24.0539i	0.905455	+	0.831921i
$837$	−10.4509	+	8.83674i	−0.361237	+	0.305443i
$838$	−1.68855	−	3.84446i	−0.0583298	−	0.132805i
$839$	−25.4051			−0.877080			−0.438540	−	0.898712i	$-0.644504\pi$
$839$	−25.4051			−0.877080			−0.438540	+	0.898712i	$0.644504\pi$
$840$	2.21347	−	1.01064i	0.0763720	−	0.0348703i
$841$	17.4753			0.602598
$842$	−11.6215	−	26.4598i	−0.400504	−	0.911864i
$843$	−30.8895	−	32.6586i	−1.06389	−	1.12482i
$844$	−27.5607	+	29.9968i	−0.948678	+	1.03253i
$845$	0.498889			0.0171623
$846$	−16.5496	−	44.2111i	−0.568989	−	1.52001i
$847$			1.51073i			0.0519094i
$848$	−0.420239	−	4.95553i	−0.0144311	−	0.170174i
$849$	23.8599	−	22.5674i	0.818868	−	0.774510i
$850$	10.3973	+	23.6725i	0.356625	+	0.811960i
$851$		−	3.68893i		−	0.126455i
$852$	−0.599667	−	41.4450i	−0.0205443	−	1.41988i
$853$			45.5424i			1.55934i	0.626190	+	0.779671i	$0.284614\pi$
$853$			45.5424i			1.55934i	−0.626190	+	0.779671i	$0.715386\pi$
$854$	−2.45769	+	1.07945i	−0.0841003	+	0.0369381i
$855$	0.137221	−	2.46263i	0.00469285	−	0.0842203i
$856$	37.1530	+	12.6947i	1.26986	+	0.433895i
$857$			13.1284i			0.448458i	0.974537	+	0.224229i	$0.0719863\pi$
$857$			13.1284i			0.448458i	−0.974537	+	0.224229i	$0.928014\pi$
$858$	−10.1094	+	23.9524i	−0.345130	+	0.817720i
$859$	22.9240			0.782158			0.391079	−	0.920357i	$-0.372102\pi$
$859$	22.9240			0.782158			0.391079	+	0.920357i	$0.372102\pi$
$860$	−1.93876	+	2.11013i	−0.0661111	+	0.0719548i
$861$	−12.8193	+	12.1249i	−0.436881	+	0.413215i
$862$	−14.6112	+	6.41745i	−0.497659	+	0.218579i
$863$	8.96510			0.305176			0.152588	−	0.988290i	$-0.451239\pi$
$863$	8.96510			0.305176			0.152588	+	0.988290i	$0.451239\pi$
$864$	10.6415	−	27.4000i	0.362030	−	0.932166i
$865$	0.256973			0.00873736
$866$	−1.98658	+	0.872535i	−0.0675067	+	0.0296500i
$867$	−4.40161	+	4.16318i	−0.149487	+	0.141389i
$868$	11.2983	−	12.2969i	0.383488	−	0.417385i
$869$	−42.4898			−1.44137
$870$	−1.01738	+	2.41049i	−0.0344925	+	0.0817234i
$871$			19.4948i			0.660557i
$872$	41.3358	+	14.1239i	1.39981	+	0.478295i
$873$	1.55005	−	27.8181i	0.0524613	−	0.941498i
$874$	6.79432	−	2.98417i	0.229821	−	0.100941i
$875$			4.95471i			0.167500i
$876$	−0.437538	−	30.2397i	−0.0147831	−	1.02171i
$877$		−	5.11155i		−	0.172605i	−0.996269	−	0.0863024i	$-0.972495\pi$
$877$		−	5.11155i		−	0.172605i	0.996269	−	0.0863024i	$-0.0275051\pi$
$878$	−6.59651	−	15.0189i	−0.222621	−	0.506862i
$879$	−31.2348	+	29.5428i	−1.05352	+	0.996454i
$880$	2.11557	−	0.179404i	0.0713158	−	0.00604772i
$881$		−	25.9825i		−	0.875372i	−0.899128	−	0.437686i	$-0.855798\pi$
$881$		−	25.9825i		−	0.875372i	0.899128	−	0.437686i	$-0.144202\pi$
$882$	4.53550	+	12.1162i	0.152718	+	0.407974i
$883$	17.0676			0.574372			0.287186	−	0.957875i	$-0.407280\pi$
$883$	17.0676			0.574372			0.287186	+	0.957875i	$0.407280\pi$
$884$	−15.5779	+	16.9549i	−0.523943	+	0.570255i
$885$	−1.84652	−	1.95228i	−0.0620701	−	0.0656250i
$886$	11.2568	+	25.6295i	0.378181	+	0.861039i
$887$	−55.7714			−1.87262			−0.936311	−	0.351172i	$-0.885783\pi$
$887$	−55.7714			−1.87262			−0.936311	+	0.351172i	$0.885783\pi$
$888$	16.4395	−	7.50604i	0.551673	−	0.251886i
$889$	−65.4030			−2.19355
$890$	−0.376261	−	0.856667i	−0.0126123	−	0.0287156i
$891$	3.38729	−	30.3006i	0.113478	−	1.01511i
$892$	−27.4140	−	25.1877i	−0.917890	−	0.843346i
$893$	58.3856			1.95380
$894$	2.87016	−	6.80029i	0.0959924	−	0.227436i
$895$		−	0.241652i		−	0.00807754i
$896$	−8.68716	+	34.7973i	−0.290218	+	1.16250i
$897$	3.72890	+	3.94246i	0.124504	+	0.131635i
$898$	−7.03059	−	16.0072i	−0.234614	−	0.534166i
$899$			17.9560i			0.598866i
$900$	20.8251	+	21.3893i	0.694169	+	0.712975i
$901$		−	4.56864i		−	0.152203i
$902$	−14.0965	+	6.19137i	−0.469361	+	0.206150i
$903$	−34.5022	−	36.4782i	−1.14816	−	1.21392i
$904$	−1.82680	−	0.624194i	−0.0607586	−	0.0207604i
$905$			0.777779i			0.0258543i
$906$	28.4023	+	11.9876i	0.943603	+	0.398260i
$907$	34.1626			1.13435			0.567176	−	0.823597i	$-0.308036\pi$
$907$	34.1626			1.13435			0.567176	+	0.823597i	$0.308036\pi$
$908$	30.2065	+	27.7534i	1.00244	+	0.921028i
$909$	0.690224	−	12.3871i	0.0228933	−	0.410855i
$910$	−2.01494	+	0.884992i	−0.0667946	+	0.0293372i
$911$	47.1143			1.56097			0.780483	−	0.625176i	$-0.214973\pi$
$911$	47.1143			1.56097			0.780483	+	0.625176i	$0.214973\pi$
$912$	27.1234	+	24.2064i	0.898147	+	0.801555i
$913$	−28.7023			−0.949908
$914$	14.0288	−	6.16165i	0.464031	−	0.203809i
$915$	0.111655	+	0.118050i	0.00369121	+	0.00390261i
$916$	−30.7391	−	28.2427i	−1.01565	−	0.933164i
$917$	−22.6414			−0.747684
$918$	11.8675	−	24.2544i	0.391685	−	0.800514i
$919$		−	56.2370i		−	1.85509i	−0.373716	−	0.927543i	$-0.621916\pi$
$919$		−	56.2370i		−	1.85509i	0.373716	−	0.927543i	$-0.378084\pi$
$920$	0.143289	−	0.419357i	0.00472409	−	0.0138258i
$921$	25.3965	−	24.0207i	0.836842	−	0.791511i
$922$	−44.3650	+	19.4858i	−1.46108	+	0.641730i
$923$			37.4880i			1.23393i
$924$	0.538218	+	37.1980i	0.0177061	+	1.22373i
$925$			18.3541i			0.603479i
$926$	15.3151	+	34.8692i	0.503285	+	1.14587i
$927$	27.0553	+	1.50755i	0.888614	+	0.0495146i
$928$	−18.4362	−	33.8721i	−0.605198	−	1.11191i
$929$		−	39.2159i		−	1.28663i	−0.765601	−	0.643316i	$-0.777558\pi$
$929$		−	39.2159i		−	1.28663i	0.765601	−	0.643316i	$-0.222442\pi$
$930$	−0.931308	−	0.393071i	−0.0305388	−	0.0128893i
$931$	−16.0008			−0.524405
$932$	0.926509	+	0.851265i	0.0303488	+	0.0278841i
$933$	−33.9222	+	32.0846i	−1.11056	+	1.05040i
$934$	−18.9675	−	43.1851i	−0.620637	−	1.41306i
$935$	1.95040			0.0637849
$936$	−9.98197	+	24.6395i	−0.326271	+	0.805367i
$937$	−39.9576			−1.30536			−0.652679	−	0.757635i	$-0.726355\pi$
$937$	−39.9576			−1.30536			−0.652679	+	0.757635i	$0.726355\pi$
$938$	11.2179	+	25.5408i	0.366278	+	0.833937i
$939$	−34.6731	+	32.7949i	−1.13151	+	1.07022i
$940$	2.35903	−	2.56754i	0.0769429	−	0.0837440i
$941$	43.3232			1.41230			0.706148	−	0.708064i	$-0.250431\pi$
$941$	43.3232			1.41230			0.706148	+	0.708064i	$0.250431\pi$
$942$	−19.6216	−	8.28157i	−0.639307	−	0.269828i
$943$			3.21361i			0.104649i
$944$	39.4662	−	3.34681i	1.28452	−	0.108929i
$945$	1.97080	−	1.66640i	0.0641101	−	0.0542081i
$946$	−17.6180	−	40.1125i	−0.572810	−	1.30417i
$947$		−	45.8324i		−	1.48935i	−0.667425	−	0.744677i	$-0.732604\pi$
$947$		−	45.8324i		−	1.48935i	0.667425	−	0.744677i	$-0.267396\pi$
$948$	−43.4434	+	0.628583i	−1.41098	+	0.0204154i
$949$			27.3525i			0.887901i
$950$	−33.8048	+	14.8476i	−1.09677	+	0.481719i
$951$	−13.6600	+	12.9201i	−0.442956	+	0.418961i
$952$	−10.6528	+	31.1772i	−0.345260	+	1.01046i
$953$		−	38.1665i		−	1.23633i	−0.786047	−	0.618166i	$-0.787876\pi$
$953$		−	38.1665i		−	1.23633i	0.786047	−	0.618166i	$-0.212124\pi$
$954$	−1.84929	−	4.94022i	−0.0598728	−	0.159945i
$955$	1.74899			0.0565961
$956$	−19.7681	+	21.5155i	−0.639348	+	0.695860i
$957$	−27.4873	−	29.0616i	−0.888540	−	0.939428i
$958$	16.4102	−	7.20760i	0.530189	−	0.232867i
$959$	15.2998			0.494057
$960$	2.16039	−	0.214728i	0.0697264	−	0.00693031i
$961$	24.0626			0.776213
$962$	−14.9650	+	6.57286i	−0.482491	+	0.211917i
$963$	41.5790	+	2.31683i	1.33987	+	0.0746588i
$964$	−25.0116	+	27.2224i	−0.805568	+	0.876773i
$965$	2.93092			0.0943497
$966$	7.15396	+	3.01943i	0.230175	+	0.0971485i
$967$			53.3028i			1.71410i	0.515230	+	0.857052i	$0.327706\pi$
$967$			53.3028i			1.71410i	−0.515230	+	0.857052i	$0.672294\pi$
$968$	−0.435826	+	1.27552i	−0.0140080	+	0.0409966i
$969$	22.9483	+	24.2626i	0.737206	+	0.779428i
$970$	1.88411	−	0.827531i	0.0604952	−	0.0265704i
$971$		−	27.3322i		−	0.877133i	−0.898699	−	0.438566i	$-0.855486\pi$
$971$		−	27.3322i		−	0.877133i	0.898699	−	0.438566i	$-0.144514\pi$
$972$	3.01505	−	31.0308i	0.0967077	−	0.995313i
$973$		−	69.4270i		−	2.22573i
$974$	−12.7821	−	29.1020i	−0.409563	−	0.932490i
$975$	−18.5530	−	19.6155i	−0.594170	−	0.628200i
$976$	−2.38644	+	0.202375i	−0.0763881	+	0.00647786i
$977$		−	37.3455i		−	1.19479i	−0.801948	−	0.597394i	$-0.796203\pi$
$977$		−	37.3455i		−	1.19479i	0.801948	−	0.597394i	$-0.203797\pi$
$978$	−12.7253	+	30.1502i	−0.406911	+	0.964098i
$979$	14.3051			0.457192
$980$	−0.646500	+	0.703645i	−0.0206517	+	0.0224771i
$981$	46.2602	+	2.57767i	1.47697	+	0.0822986i
$982$	1.98788	+	4.52599i	0.0634359	+	0.144430i
$983$	−44.5643			−1.42138			−0.710689	−	0.703506i	$-0.751617\pi$
$983$	−44.5643			−1.42138			−0.710689	+	0.703506i	$0.751617\pi$
$984$	−14.3212	+	6.53887i	−0.456544	+	0.208452i
$985$	−3.05501			−0.0973406
$986$	−14.2462	−	32.4357i	−0.453692	−	1.03296i
$987$	41.9813	+	44.3856i	1.33628	+	1.41281i
$988$	−24.2119	−	22.2456i	−0.770284	−	0.707727i
$989$	−9.14455			−0.290780
$990$	2.10903	−	0.789479i	0.0670294	−	0.0250913i
$991$		−	27.2208i		−	0.864698i	−0.901706	−	0.432349i	$-0.857685\pi$
$991$		−	27.2208i		−	0.864698i	0.901706	−	0.432349i	$-0.142315\pi$
$992$	13.0867	−	7.12294i	0.415502	−	0.226153i
$993$	−6.92158	+	6.54664i	−0.219650	+	0.207751i
$994$	21.5717	+	49.1142i	0.684212	+	1.55781i
$995$		−	2.97686i		−	0.0943728i
$996$	−29.3465	+	0.424614i	−0.929879	+	0.0134544i
$997$		−	52.9741i		−	1.67771i	−0.544358	−	0.838853i	$-0.683227\pi$
$997$		−	52.9741i		−	1.67771i	0.544358	−	0.838853i	$-0.316773\pi$
$998$	26.8565	−	11.7958i	0.850127	−	0.373389i
$999$	14.6372	−	12.3764i	0.463100	−	0.391572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.39	yes	42
3.2	odd	2		552.2.j.c.323.4	yes	42
4.3	odd	2		2208.2.j.d.47.31		42
8.3	odd	2		552.2.j.c.323.3	✓	42
8.5	even	2		2208.2.j.c.47.31		42
12.11	even	2		2208.2.j.c.47.32		42
24.5	odd	2		2208.2.j.d.47.32		42
24.11	even	2	inner	552.2.j.d.323.40	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.3	✓	42	8.3	odd	2
552.2.j.c.323.4	yes	42	3.2	odd	2
552.2.j.d.323.39	yes	42	1.1	even	1	trivial
552.2.j.d.323.40	yes	42	24.11	even	2	inner
2208.2.j.c.47.31		42	8.5	even	2
2208.2.j.c.47.32		42	12.11	even	2
2208.2.j.d.47.31		42	4.3	odd	2
2208.2.j.d.47.32		42	24.5	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29483 - 0.568707i) q^{2} +(-1.25835 + 1.19019i) q^{3} +(1.35315 - 1.47275i) q^{4} +0.156681 q^{5} +(-0.952479 + 2.25672i) q^{6} -3.17007i q^{7} +(0.914523 - 2.67650i) q^{8} +(0.166904 - 2.99535i) q^{9} +(0.202875 - 0.0891057i) q^{10} +3.38771i q^{11} +(0.0501168 + 3.46374i) q^{12} -3.13303i q^{13} +(-1.80284 - 4.10469i) q^{14} +(-0.197160 + 0.186480i) q^{15} +(-0.337995 - 3.98569i) q^{16} -3.67452i q^{17} +(-1.48737 - 3.97338i) q^{18} +5.24729 q^{19} +(0.212013 - 0.230753i) q^{20} +(3.77298 + 3.98907i) q^{21} +(1.92661 + 4.38649i) q^{22} +1.00000 q^{23} +(2.03474 + 4.45644i) q^{24} -4.97545 q^{25} +(-1.78178 - 4.05673i) q^{26} +(3.35501 + 3.96786i) q^{27} +(-4.66873 - 4.28957i) q^{28} +6.81728 q^{29} +(-0.149236 + 0.353586i) q^{30} +2.63390i q^{31} +(-2.70433 - 4.96856i) q^{32} +(-4.03201 - 4.26293i) q^{33} +(-2.08972 - 4.75786i) q^{34} -0.496691i q^{35} +(-4.18557 - 4.29896i) q^{36} -3.68893i q^{37} +(6.79432 - 2.98417i) q^{38} +(3.72890 + 3.94246i) q^{39} +(0.143289 - 0.419357i) q^{40} +3.21361i q^{41} +(7.15396 + 3.01943i) q^{42} -9.14455 q^{43} +(4.98925 + 4.58406i) q^{44} +(0.0261508 - 0.469316i) q^{45} +(1.29483 - 0.568707i) q^{46} +11.1268 q^{47} +(5.16904 + 4.61313i) q^{48} -3.04935 q^{49} +(-6.44234 + 2.82957i) q^{50} +(4.37337 + 4.62384i) q^{51} +(-4.61418 - 4.23945i) q^{52} +1.24333 q^{53} +(6.60070 + 3.22967i) q^{54} +0.530790i q^{55} +(-8.48469 - 2.89910i) q^{56} +(-6.60294 + 6.24526i) q^{57} +(8.82719 - 3.87703i) q^{58} +9.90197i q^{59} +(0.00785237 + 0.542703i) q^{60} -0.598751i q^{61} +(1.49791 + 3.41043i) q^{62} +(-9.49548 - 0.529099i) q^{63} +(-6.32729 - 4.89544i) q^{64} -0.490888i q^{65} +(-7.64511 - 3.22672i) q^{66} -6.22235 q^{67} +(-5.41165 - 4.97216i) q^{68} +(-1.25835 + 1.19019i) q^{69} +(-0.282471 - 0.643128i) q^{70} -11.9654 q^{71} +(-7.86442 - 3.18604i) q^{72} -8.73037 q^{73} +(-2.09792 - 4.77653i) q^{74} +(6.26087 - 5.92172i) q^{75} +(7.10034 - 7.72795i) q^{76} +10.7393 q^{77} +(7.07038 + 2.98415i) q^{78} +12.5424i q^{79} +(-0.0529574 - 0.624484i) q^{80} +(-8.94429 - 0.999875i) q^{81} +(1.82760 + 4.16106i) q^{82} +8.47249i q^{83} +(10.9803 - 0.158874i) q^{84} -0.575728i q^{85} +(-11.8406 + 5.20057i) q^{86} +(-8.57855 + 8.11385i) q^{87} +(9.06720 + 3.09814i) q^{88} -4.22264i q^{89} +(-0.233042 - 0.622554i) q^{90} -9.93194 q^{91} +(1.35315 - 1.47275i) q^{92} +(-3.13483 - 3.31437i) q^{93} +(14.4073 - 6.32790i) q^{94} +0.822152 q^{95} +(9.31653 + 3.03353i) q^{96} +9.28707 q^{97} +(-3.94837 + 1.73419i) q^{98} +(10.1474 + 0.565423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24}+ \cdots + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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