LMFDB - Embedded newform 425.2.k.b.86.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.12
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.557913 - 0.405348i) q^{2} +(-0.826041 + 2.54229i) q^{3} +(-0.471074 + 1.44982i) q^{4} +(0.0377362 + 2.23575i) q^{5} +(0.569653 + 1.75321i) q^{6} -0.350888 q^{7} +(0.751069 + 2.31155i) q^{8} +(-3.35386 - 2.43672i) q^{9} +(0.927309 + 1.23206i) q^{10} +(3.16834 - 2.30194i) q^{11} +(-3.29673 - 2.39521i) q^{12} +(0.350534 + 0.254678i) q^{13} +(-0.195765 + 0.142231i) q^{14} +(-5.71510 - 1.75088i) q^{15} +(-1.11056 - 0.806869i) q^{16} +(0.309017 + 0.951057i) q^{17} -2.85888 q^{18} +(-0.288547 - 0.888056i) q^{19} +(-3.25920 - 0.998492i) q^{20} +(0.289847 - 0.892059i) q^{21} +(0.834576 - 2.56856i) q^{22} +(0.736170 - 0.534859i) q^{23} -6.49706 q^{24} +(-4.99715 + 0.168737i) q^{25} +0.298801 q^{26} +(2.47747 - 1.79999i) q^{27} +(0.165294 - 0.508722i) q^{28} +(1.44524 - 4.44799i) q^{29} +(-3.89825 + 1.33976i) q^{30} +(1.20579 + 3.71105i) q^{31} -5.80768 q^{32} +(3.23501 + 9.95635i) q^{33} +(0.557913 + 0.405348i) q^{34} +(-0.0132412 - 0.784497i) q^{35} +(5.11271 - 3.71460i) q^{36} +(0.499438 + 0.362863i) q^{37} +(-0.520956 - 0.378496i) q^{38} +(-0.937022 + 0.680786i) q^{39} +(-5.13971 + 1.76643i) q^{40} +(4.19913 + 3.05085i) q^{41} +(-0.199884 - 0.615180i) q^{42} +10.0492 q^{43} +(1.84486 + 5.67789i) q^{44} +(5.32133 - 7.59034i) q^{45} +(0.193915 - 0.596810i) q^{46} +(-2.08789 + 6.42586i) q^{47} +(2.96866 - 2.15686i) q^{48} -6.87688 q^{49} +(-2.71958 + 2.11972i) q^{50} -2.67312 q^{51} +(-0.534364 + 0.388238i) q^{52} +(1.01429 - 3.12168i) q^{53} +(0.652592 - 2.00847i) q^{54} +(5.26611 + 6.99675i) q^{55} +(-0.263541 - 0.811095i) q^{56} +2.49605 q^{57} +(-0.996664 - 3.06741i) q^{58} +(-2.11959 - 1.53997i) q^{59} +(5.23069 - 7.46105i) q^{60} +(5.50439 - 3.99918i) q^{61} +(2.17700 + 1.58168i) q^{62} +(1.17683 + 0.855015i) q^{63} +(-1.01906 + 0.740392i) q^{64} +(-0.556169 + 0.793318i) q^{65} +(5.84064 + 4.24347i) q^{66} +(4.75809 + 14.6439i) q^{67} -1.52443 q^{68} +(0.751661 + 2.31338i) q^{69} +(-0.325381 - 0.432314i) q^{70} +(-1.79469 + 5.52348i) q^{71} +(3.11363 - 9.58276i) q^{72} +(-1.40554 + 1.02118i) q^{73} +0.425729 q^{74} +(3.69887 - 12.8436i) q^{75} +1.42344 q^{76} +(-1.11173 + 0.807721i) q^{77} +(-0.246822 + 0.759639i) q^{78} +(4.69587 - 14.4524i) q^{79} +(1.76205 - 2.51338i) q^{80} +(-1.31358 - 4.04278i) q^{81} +3.57941 q^{82} +(3.76605 + 11.5907i) q^{83} +(1.15678 + 0.840451i) q^{84} +(-2.11466 + 0.726774i) q^{85} +(5.60657 - 4.07341i) q^{86} +(10.1143 + 7.34844i) q^{87} +(7.70069 + 5.59488i) q^{88} +(-1.80115 + 1.30861i) q^{89} +(-0.107883 - 6.39174i) q^{90} +(-0.122998 - 0.0893634i) q^{91} +(0.428657 + 1.31927i) q^{92} -10.4306 q^{93} +(1.43985 + 4.43140i) q^{94} +(1.97458 - 0.678630i) q^{95} +(4.79738 - 14.7648i) q^{96} +(2.35892 - 7.26002i) q^{97} +(-3.83670 + 2.78753i) q^{98} -16.2353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.557913	−	0.405348i	0.394504	−	0.286624i	−0.372795	−	0.927914i	$-0.621600\pi$
$2$	0.557913	−	0.405348i	0.394504	−	0.286624i	0.767299	+	0.641290i	$0.221600\pi$
$3$	−0.826041	+	2.54229i	−0.476915	+	1.46779i	0.366443	+	0.930441i	$0.380576\pi$
$3$	−0.826041	+	2.54229i	−0.476915	+	1.46779i	−0.843358	+	0.537353i	$0.819424\pi$
$4$	−0.471074	+	1.44982i	−0.235537	+	0.724908i
$5$	0.0377362	+	2.23575i	0.0168761	+	0.999858i
$5$	0.0377362	+	2.23575i	0.0168761	+	0.999858i
$6$	0.569653	+	1.75321i	0.232560	+	0.715746i
$7$	−0.350888			−0.132623			−0.0663115	−	0.997799i	$-0.521123\pi$
$7$	−0.350888			−0.132623			−0.0663115	+	0.997799i	$0.521123\pi$
$8$	0.751069	+	2.31155i	0.265543	+	0.817257i
$9$	−3.35386	−	2.43672i	−1.11795	−	0.812240i
$10$	0.927309	+	1.23206i	0.293241	+	0.389611i
$11$	3.16834	−	2.30194i	0.955291	−	0.694060i	0.00323893	−	0.999995i	$-0.498969\pi$
$11$	3.16834	−	2.30194i	0.955291	−	0.694060i	0.952052	+	0.305935i	$0.0989690\pi$
$12$	−3.29673	−	2.39521i	−0.951684	−	0.691439i
$13$	0.350534	+	0.254678i	0.0972207	+	0.0706350i	0.635334	−	0.772238i	$-0.280863\pi$
$13$	0.350534	+	0.254678i	0.0972207	+	0.0706350i	−0.538113	+	0.842873i	$0.680863\pi$
$14$	−0.195765	+	0.142231i	−0.0523204	+	0.0380130i
$15$	−5.71510	−	1.75088i	−1.47563	−	0.452076i
$16$	−1.11056	−	0.806869i	−0.277640	−	0.201717i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−2.85888			−0.673844
$19$	−0.288547	−	0.888056i	−0.0661972	−	0.203734i	0.912487	−	0.409106i	$-0.134159\pi$
$19$	−0.288547	−	0.888056i	−0.0661972	−	0.203734i	−0.978684	+	0.205372i	$0.934159\pi$
$20$	−3.25920	−	0.998492i	−0.728779	−	0.223270i
$21$	0.289847	−	0.892059i	0.0632499	−	0.194663i
$22$	0.834576	−	2.56856i	0.177932	−	0.547619i
$23$	0.736170	−	0.534859i	0.153502	−	0.111526i	−0.508383	−	0.861131i	$-0.669757\pi$
$23$	0.736170	−	0.534859i	0.153502	−	0.111526i	0.661885	+	0.749605i	$0.269757\pi$
$24$	−6.49706			−1.32621
$25$	−4.99715	+	0.168737i	−0.999430	+	0.0337475i
$26$	0.298801			0.0585997
$27$	2.47747	−	1.79999i	0.476789	−	0.346407i
$28$	0.165294	−	0.508722i	0.0312376	−	0.0961395i
$29$	1.44524	−	4.44799i	0.268374	−	0.825970i	−0.722523	−	0.691347i	$-0.757018\pi$
$29$	1.44524	−	4.44799i	0.268374	−	0.825970i	0.990897	−	0.134623i	$-0.0429824\pi$
$30$	−3.89825	+	1.33976i	−0.711719	+	0.244606i
$31$	1.20579	+	3.71105i	0.216567	+	0.666525i	0.999039	+	0.0438387i	$0.0139588\pi$
$31$	1.20579	+	3.71105i	0.216567	+	0.666525i	−0.782472	+	0.622686i	$0.786041\pi$
$32$	−5.80768			−1.02666
$33$	3.23501	+	9.95635i	0.563144	+	1.73318i
$34$	0.557913	+	0.405348i	0.0956813	+	0.0695166i
$35$	−0.0132412	−	0.784497i	−0.00223816	−	0.132604i
$36$	5.11271	−	3.71460i	0.852118	−	0.619100i
$37$	0.499438	+	0.362863i	0.0821071	+	0.0596543i	0.628082	−	0.778148i	$-0.283840\pi$
$37$	0.499438	+	0.362863i	0.0821071	+	0.0596543i	−0.545974	+	0.837802i	$0.683840\pi$
$38$	−0.520956	−	0.378496i	−0.0845102	−	0.0614002i
$39$	−0.937022	+	0.680786i	−0.150044	+	0.109013i
$40$	−5.13971	+	1.76643i	−0.812660	+	0.279297i
$41$	4.19913	+	3.05085i	0.655794	+	0.476462i	0.865240	−	0.501358i	$-0.167166\pi$
$41$	4.19913	+	3.05085i	0.655794	+	0.476462i	−0.209446	+	0.977820i	$0.567166\pi$
$42$	−0.199884	−	0.615180i	−0.0308428	−	0.0949244i
$43$	10.0492			1.53248			0.766242	−	0.642552i	$-0.222124\pi$
$43$	10.0492			1.53248			0.766242	+	0.642552i	$0.222124\pi$
$44$	1.84486	+	5.67789i	0.278123	+	0.855975i
$45$	5.32133	−	7.59034i	0.793257	−	1.13150i
$46$	0.193915	−	0.596810i	0.0285913	−	0.0879948i
$47$	−2.08789	+	6.42586i	−0.304550	+	0.937309i	0.675295	+	0.737548i	$0.264016\pi$
$47$	−2.08789	+	6.42586i	−0.304550	+	0.937309i	−0.979845	+	0.199761i	$0.935984\pi$
$48$	2.96866	−	2.15686i	0.428490	−	0.311316i
$49$	−6.87688			−0.982411
$50$	−2.71958	+	2.11972i	−0.384607	+	0.299774i
$51$	−2.67312			−0.374312
$52$	−0.534364	+	0.388238i	−0.0741029	+	0.0538389i
$53$	1.01429	−	3.12168i	0.139324	−	0.428795i	−0.856913	−	0.515460i	$-0.827621\pi$
$53$	1.01429	−	3.12168i	0.139324	−	0.428795i	0.996238	+	0.0866649i	$0.0276209\pi$
$54$	0.652592	−	2.00847i	0.0888065	−	0.273318i
$55$	5.26611	+	6.99675i	0.710083	+	0.943442i
$56$	−0.263541	−	0.811095i	−0.0352171	−	0.108387i
$57$	2.49605			0.330610
$58$	−0.996664	−	3.06741i	−0.130868	−	0.402771i
$59$	−2.11959	−	1.53997i	−0.275948	−	0.200488i	0.441200	−	0.897409i	$-0.354553\pi$
$59$	−2.11959	−	1.53997i	−0.275948	−	0.200488i	−0.717148	+	0.696921i	$0.754553\pi$
$60$	5.23069	−	7.46105i	0.675279	−	0.963217i
$61$	5.50439	−	3.99918i	0.704765	−	0.512042i	−0.176715	−	0.984262i	$-0.556547\pi$
$61$	5.50439	−	3.99918i	0.704765	−	0.512042i	0.881481	+	0.472220i	$0.156547\pi$
$62$	2.17700	+	1.58168i	0.276479	+	0.200874i
$63$	1.17683	+	0.855015i	0.148266	+	0.107722i
$64$	−1.01906	+	0.740392i	−0.127383	+	0.0925490i
$65$	−0.556169	+	0.793318i	−0.0689842	+	0.0983989i
$66$	5.84064	+	4.24347i	0.718933	+	0.522335i
$67$	4.75809	+	14.6439i	0.581293	+	1.78904i	0.613674	+	0.789560i	$0.289691\pi$
$67$	4.75809	+	14.6439i	0.581293	+	1.78904i	−0.0323810	+	0.999476i	$0.510309\pi$
$68$	−1.52443			−0.184864
$69$	0.751661	+	2.31338i	0.0904894	+	0.278498i
$70$	−0.325381	−	0.432314i	−0.0388905	−	0.0516714i
$71$	−1.79469	+	5.52348i	−0.212990	+	0.655517i	0.786300	+	0.617845i	$0.211994\pi$
$71$	−1.79469	+	5.52348i	−0.212990	+	0.655517i	−0.999290	+	0.0376716i	$0.988006\pi$
$72$	3.11363	−	9.58276i	0.366945	−	1.12934i
$73$	−1.40554	+	1.02118i	−0.164506	+	0.119521i	−0.666992	−	0.745064i	$-0.732419\pi$
$73$	−1.40554	+	1.02118i	−0.164506	+	0.119521i	0.502486	+	0.864585i	$0.332419\pi$
$74$	0.425729			0.0494900
$75$	3.69887	−	12.8436i	0.427109	−	1.48305i
$76$	1.42344			0.163280
$77$	−1.11173	+	0.807721i	−0.126694	+	0.0920483i
$78$	−0.246822	+	0.759639i	−0.0279471	+	0.0860122i
$79$	4.69587	−	14.4524i	0.528327	−	1.62602i	−0.229315	−	0.973352i	$-0.573649\pi$
$79$	4.69587	−	14.4524i	0.528327	−	1.62602i	0.757642	−	0.652671i	$-0.226351\pi$
$80$	1.76205	−	2.51338i	0.197003	−	0.281004i
$81$	−1.31358	−	4.04278i	−0.145953	−	0.449197i
$82$	3.57941			0.395279
$83$	3.76605	+	11.5907i	0.413378	+	1.27225i	0.913694	+	0.406403i	$0.133217\pi$
$83$	3.76605	+	11.5907i	0.413378	+	1.27225i	−0.500316	+	0.865843i	$0.666783\pi$
$84$	1.15678	+	0.840451i	0.126215	+	0.0917007i
$85$	−2.11466	+	0.726774i	−0.229367	+	0.0788297i
$86$	5.60657	−	4.07341i	0.604572	−	0.439247i
$87$	10.1143	+	7.34844i	1.08436	+	0.787835i
$88$	7.70069	+	5.59488i	0.820896	+	0.596416i
$89$	−1.80115	+	1.30861i	−0.190922	+	0.138713i	−0.679140	−	0.734009i	$-0.737647\pi$
$89$	−1.80115	+	1.30861i	−0.190922	+	0.138713i	0.488218	+	0.872722i	$0.337647\pi$
$90$	−0.107883	−	6.39174i	−0.0113719	−	0.673748i
$91$	−0.122998	−	0.0893634i	−0.0128937	−	0.00936783i
$92$	0.428657	+	1.31927i	0.0446905	+	0.137543i
$93$	−10.4306			−1.08161
$94$	1.43985	+	4.43140i	0.148509	+	0.457064i
$95$	1.97458	−	0.678630i	0.202588	−	0.0696260i
$96$	4.79738	−	14.7648i	0.489631	−	1.50693i
$97$	2.35892	−	7.26002i	0.239512	−	0.737143i	−0.756978	−	0.653440i	$-0.773325\pi$
$97$	2.35892	−	7.26002i	0.239512	−	0.737143i	0.996491	−	0.0837032i	$-0.0266748\pi$
$98$	−3.83670	+	2.78753i	−0.387565	+	0.281583i
$99$	−16.2353			−1.63171
$100$	2.10939	−	7.32444i	0.210939	−	0.732444i
$101$	−8.04711			−0.800717			−0.400359	−	0.916359i	$-0.631114\pi$
$101$	−8.04711			−0.800717			−0.400359	+	0.916359i	$0.631114\pi$
$102$	−1.49137	+	1.08354i	−0.147668	+	0.107287i
$103$	−3.38606	+	10.4212i	−0.333638	+	1.02683i	0.633751	+	0.773537i	$0.281514\pi$
$103$	−3.38606	+	10.4212i	−0.333638	+	1.02683i	−0.967389	+	0.253295i	$0.918486\pi$
$104$	−0.325426	+	1.00156i	−0.0319107	+	0.0982110i
$105$	2.00536	+	0.614363i	0.195703	+	0.0599557i
$106$	−0.699477	−	2.15277i	−0.0679392	−	0.209095i
$107$	−7.21212			−0.697222			−0.348611	−	0.937268i	$-0.613347\pi$
$107$	−7.21212			−0.697222			−0.348611	+	0.937268i	$0.613347\pi$
$108$	1.44258	+	4.43980i	0.138812	+	0.427220i
$109$	3.32643	+	2.41679i	0.318614	+	0.231487i	0.735584	−	0.677434i	$-0.236908\pi$
$109$	3.32643	+	2.41679i	0.318614	+	0.231487i	−0.416970	+	0.908920i	$0.636908\pi$
$110$	5.77415	+	1.76898i	0.550544	+	0.168665i
$111$	−1.33506	+	0.969978i	−0.126718	+	0.0920663i
$112$	0.389681	+	0.283120i	0.0368214	+	0.0267523i
$113$	−15.5662	−	11.3095i	−1.46434	−	1.06391i	−0.982205	−	0.187811i	$-0.939861\pi$
$113$	−15.5662	−	11.3095i	−1.46434	−	1.06391i	−0.482137	−	0.876096i	$-0.660139\pi$
$114$	1.39258	−	1.01177i	0.130427	−	0.0947608i
$115$	1.22359	+	1.62571i	0.114100	+	0.151598i
$116$	5.76795	+	4.19066i	0.535540	+	0.389093i
$117$	−0.555063	−	1.70831i	−0.0513156	−	0.157933i
$118$	−1.80677			−0.166327
$119$	−0.108430	−	0.333714i	−0.00993978	−	0.0305915i
$120$	−0.245174	−	14.5258i	−0.0223812	−	1.32602i
$121$	1.34030	−	4.12502i	0.121846	−	0.375002i
$122$	1.44992	−	4.46239i	0.131269	−	0.404005i
$123$	−11.2248	+	8.15530i	−1.01211	+	0.735338i
$124$	−5.94836			−0.534179
$125$	−0.565828	−	11.1660i	−0.0506092	−	0.998719i
$126$	1.00315			0.0893673
$127$	12.0405	−	8.74791i	1.06842	−	0.776251i	0.0927911	−	0.995686i	$-0.470421\pi$
$127$	12.0405	−	8.74791i	1.06842	−	0.776251i	0.975627	+	0.219434i	$0.0704211\pi$
$128$	3.32091	−	10.2207i	0.293530	−	0.903392i
$129$	−8.30103	+	25.5479i	−0.730865	+	2.24937i
$130$	0.0112756	+	0.668044i	0.000988936	+	0.0585913i
$131$	−2.30182	−	7.08427i	−0.201111	−	0.618956i	−0.999851	−	0.0172791i	$-0.994500\pi$
$131$	−2.30182	−	7.08427i	−0.201111	−	0.618956i	0.798740	−	0.601677i	$-0.205500\pi$
$132$	−15.9588			−1.38903
$133$	0.101248	+	0.311608i	0.00877927	+	0.0270198i
$134$	8.59046	+	6.24134i	0.742103	+	0.539169i
$135$	4.11781	+	5.47107i	0.354404	+	0.470875i
$136$	−1.96632	+	1.42862i	−0.168611	+	0.122503i
$137$	16.5283	+	12.0085i	1.41211	+	1.02596i	0.993011	+	0.118019i	$0.0376543\pi$
$137$	16.5283	+	12.0085i	1.41211	+	1.02596i	0.419100	+	0.907940i	$0.362346\pi$
$138$	1.35708	+	0.985979i	0.115523	+	0.0839321i
$139$	7.08313	−	5.14619i	0.600783	−	0.436494i	−0.245374	−	0.969429i	$-0.578911\pi$
$139$	7.08313	−	5.14619i	0.600783	−	0.436494i	0.846157	+	0.532934i	$0.178911\pi$
$140$	1.14361	+	0.350358i	0.0966529	+	0.0296107i
$141$	−14.6117	−	10.6161i	−1.23053	−	0.894033i
$142$	1.23765	+	3.80910i	0.103861	+	0.319652i
$143$	1.69687			0.141899
$144$	1.75854	+	5.41224i	0.146545	+	0.451020i
$145$	9.99912	+	3.06334i	0.830382	+	0.254397i
$146$	−0.370235	+	1.13946i	−0.0306408	+	0.0943028i
$147$	5.68058	−	17.4830i	0.468527	−	1.44198i
$148$	−0.761357	+	0.553158i	−0.0625831	+	0.0454693i
$149$	−13.2974			−1.08936			−0.544682	−	0.838643i	$-0.683350\pi$
$149$	−13.2974			−1.08936			−0.544682	+	0.838643i	$0.683350\pi$
$150$	−3.14248	−	8.66495i	−0.256582	−	0.707490i
$151$	9.38998			0.764145			0.382073	−	0.924132i	$-0.375210\pi$
$151$	9.38998			0.764145			0.382073	+	0.924132i	$0.375210\pi$
$152$	1.83607	−	1.33398i	0.148925	−	0.108200i
$153$	1.28106	−	3.94270i	0.103568	−	0.318748i
$154$	−0.292842	+	0.901276i	−0.0235979	+	0.0726269i
$155$	−8.25149	+	2.83590i	−0.662775	+	0.227785i
$156$	−0.545608	−	1.67921i	−0.0436836	−	0.134444i
$157$	0.791912			0.0632015			0.0316007	−	0.999501i	$-0.489940\pi$
$157$	0.791912			0.0632015			0.0316007	+	0.999501i	$0.489940\pi$
$158$	−3.23836	−	9.96665i	−0.257630	−	0.792904i
$159$	7.09837	+	5.15727i	0.562937	+	0.408998i
$160$	−0.219160	−	12.9845i	−0.0173261	−	1.02652i
$161$	−0.258313	+	0.187675i	−0.0203579	+	0.0147909i
$162$	−2.37159	−	1.72306i	−0.186330	−	0.135377i
$163$	−4.53516	−	3.29498i	−0.355221	−	0.258083i	0.395835	−	0.918322i	$-0.370455\pi$
$163$	−4.53516	−	3.29498i	−0.355221	−	0.258083i	−0.751056	+	0.660239i	$0.770455\pi$
$164$	−6.40127	+	4.65079i	−0.499855	+	0.363166i
$165$	−22.1378	+	7.60839i	−1.72343	+	0.592313i
$166$	6.79940	+	4.94005i	0.527736	+	0.383422i
$167$	7.15769	+	22.0291i	0.553879	+	1.70466i	0.698886	+	0.715233i	$0.253680\pi$
$167$	7.15769	+	22.0291i	0.553879	+	1.70466i	−0.145007	+	0.989431i	$0.546320\pi$
$168$	2.27974			0.175885
$169$	−3.95921	−	12.1852i	−0.304554	−	0.937322i
$170$	−0.885202	+	1.26265i	−0.0678919	+	0.0968409i
$171$	−1.19620	+	3.68152i	−0.0914756	+	0.281533i
$172$	−4.73390	+	14.5694i	−0.360956	+	1.11091i
$173$	2.33551	−	1.69685i	0.177565	−	0.129009i	−0.495452	−	0.868635i	$-0.664998\pi$
$173$	2.33551	−	1.69685i	0.177565	−	0.129009i	0.673018	+	0.739626i	$0.264998\pi$
$174$	8.62155			0.653598
$175$	1.75344	−	0.0592078i	0.132547	−	0.00447569i
$176$	−5.37599			−0.405231
$177$	5.66594	−	4.11654i	0.425878	−	0.309418i
$178$	−0.474443	+	1.46019i	−0.0355610	+	0.109446i
$179$	−4.46453	+	13.7404i	−0.333694	+	1.02701i	0.633667	+	0.773606i	$0.281549\pi$
$179$	−4.46453	+	13.7404i	−0.333694	+	1.02701i	−0.967362	+	0.253400i	$0.918451\pi$
$180$	8.49785	+	11.2906i	0.633392	+	0.841548i
$181$	−6.32074	−	19.4532i	−0.469817	−	1.44595i	−0.852822	−	0.522201i	$-0.825111\pi$
$181$	−6.32074	−	19.4532i	−0.469817	−	1.44595i	0.383005	−	0.923746i	$-0.374889\pi$
$182$	−0.104846			−0.00777167
$183$	5.62022	+	17.2973i	0.415459	+	1.27865i
$184$	1.78927	+	1.29998i	0.131907	+	0.0958358i
$185$	−0.792424	+	1.13031i	−0.0582602	+	0.0831022i
$186$	−5.81938	+	4.22803i	−0.426698	+	0.310014i
$187$	3.16834	+	2.30194i	0.231692	+	0.168334i
$188$	−8.33277	−	6.05411i	−0.607729	−	0.441541i
$189$	−0.869312	+	0.631592i	−0.0632332	+	0.0459416i
$190$	0.826564	−	1.17901i	0.0599653	−	0.0855343i
$191$	8.06930	+	5.86269i	0.583874	+	0.424209i	0.840119	−	0.542403i	$-0.182485\pi$
$191$	8.06930	+	5.86269i	0.583874	+	0.424209i	−0.256245	+	0.966612i	$0.582485\pi$
$192$	−1.04051	−	3.20235i	−0.0750921	−	0.231110i
$193$	24.2845			1.74804			0.874018	−	0.485894i	$-0.161506\pi$
$193$	24.2845			1.74804			0.874018	+	0.485894i	$0.161506\pi$
$194$	−1.62676	−	5.00664i	−0.116794	−	0.359456i
$195$	−1.55743	−	2.06926i	−0.111530	−	0.148182i
$196$	3.23952	−	9.97020i	0.231394	−	0.712157i
$197$	−1.46844	+	4.51939i	−0.104622	+	0.321993i	−0.989642	−	0.143561i	$-0.954145\pi$
$197$	−1.46844	+	4.51939i	−0.104622	+	0.321993i	0.885020	+	0.465554i	$0.154145\pi$
$198$	−9.05791	+	6.58096i	−0.643718	+	0.467688i
$199$	26.0506			1.84668			0.923340	−	0.383983i	$-0.125448\pi$
$199$	26.0506			1.84668			0.923340	+	0.383983i	$0.125448\pi$
$200$	−4.14325	−	11.4244i	−0.292972	−	0.807830i
$201$	−41.1594			−2.90316
$202$	−4.48959	+	3.26188i	−0.315886	+	0.229505i
$203$	−0.507116	+	1.56074i	−0.0355926	+	0.109543i
$204$	1.25924	−	3.87554i	0.0881643	−	0.271342i
$205$	−6.66247	+	9.50334i	−0.465327	+	0.663742i
$206$	2.33509	+	7.18666i	0.162693	+	0.500719i
$207$	−3.77231			−0.262194
$208$	−0.183797	−	0.565670i	−0.0127441	−	0.0392222i
$209$	−2.95846	−	2.14945i	−0.204641	−	0.148681i
$210$	1.36785	−	0.470106i	0.0943904	−	0.0324404i
$211$	−12.4756	+	9.06403i	−0.858854	+	0.623994i	−0.927573	−	0.373642i	$-0.878109\pi$
$211$	−12.4756	+	9.06403i	−0.858854	+	0.623994i	0.0687193	+	0.997636i	$0.478109\pi$
$212$	4.04805	+	2.94108i	0.278021	+	0.201994i
$213$	−12.5598	−	9.12524i	−0.860585	−	0.625251i
$214$	−4.02374	+	2.92342i	−0.275057	+	0.199841i
$215$	0.379218	+	22.4674i	0.0258624	+	1.53227i
$216$	6.02151	+	4.37488i	0.409712	+	0.297673i
$217$	−0.423098	−	1.30216i	−0.0287218	−	0.0883966i
$218$	2.83550			0.192044
$219$	−1.43512	−	4.41683i	−0.0969762	−	0.298462i
$220$	−12.6247	+	4.33891i	−0.851159	+	0.292529i
$221$	−0.133892	+	0.412078i	−0.00900656	+	0.0277194i
$222$	−0.351670	+	1.08233i	−0.0236025	+	0.0726411i
$223$	12.4394	−	9.03777i	0.833005	−	0.605214i	−0.0874029	−	0.996173i	$-0.527857\pi$
$223$	12.4394	−	9.03777i	0.833005	−	0.605214i	0.920408	+	0.390960i	$0.127857\pi$
$224$	2.03784			0.136159
$225$	17.1709	+	11.6107i	1.14473	+	0.774049i
$226$	−13.2688			−0.882630
$227$	11.2013	−	8.13825i	0.743459	−	0.540155i	−0.150333	−	0.988635i	$-0.548035\pi$
$227$	11.2013	−	8.13825i	0.743459	−	0.540155i	0.893793	+	0.448481i	$0.148035\pi$
$228$	−1.17582	+	3.61881i	−0.0778708	+	0.239662i
$229$	−4.56562	+	14.0515i	−0.301705	+	0.928552i	0.679182	+	0.733970i	$0.262335\pi$
$229$	−4.56562	+	14.0515i	−0.301705	+	0.928552i	−0.980886	+	0.194581i	$0.937665\pi$
$230$	1.34164	+	0.411025i	0.0884648	+	0.0271022i
$231$	−1.13513	−	3.49356i	−0.0746858	−	0.229859i
$232$	11.3672			0.746295
$233$	−4.71319	−	14.5057i	−0.308771	−	0.950300i	−0.978243	−	0.207462i	$-0.933480\pi$
$233$	−4.71319	−	14.5057i	−0.308771	−	0.950300i	0.669472	−	0.742837i	$-0.266520\pi$
$234$	−1.00214	−	0.728094i	−0.0655116	−	0.0475970i
$235$	−14.4454	−	4.42551i	−0.942315	−	0.288689i
$236$	3.23116	−	2.34758i	0.210331	−	0.152814i
$237$	32.8633	+	23.8766i	2.13470	+	1.55095i
$238$	−0.195765	−	0.142231i	−0.0126895	−	0.00921950i
$239$	11.1744	−	8.11864i	0.722809	−	0.525151i	−0.164472	−	0.986382i	$-0.552592\pi$
$239$	11.1744	−	8.11864i	0.722809	−	0.525151i	0.887280	+	0.461231i	$0.152592\pi$
$240$	4.93422	+	6.55580i	0.318503	+	0.423175i
$241$	23.8749	+	17.3462i	1.53792	+	1.11736i	0.951623	+	0.307269i	$0.0994153\pi$
$241$	23.8749	+	17.3462i	1.53792	+	1.11736i	0.586298	+	0.810095i	$0.300585\pi$
$242$	−0.924297	−	2.84469i	−0.0594161	−	0.182864i
$243$	20.5499			1.31828
$244$	3.20509	+	9.86426i	0.205185	+	0.631494i
$245$	−0.259507	−	15.3750i	−0.0165793	−	0.982271i
$246$	−2.95674	+	9.09990i	−0.188515	+	0.580188i
$247$	0.125023	−	0.384781i	0.00795501	−	0.0244830i
$248$	−7.67266	+	5.57452i	−0.487215	+	0.353982i
$249$	−32.5779			−2.06454
$250$	−4.84180	−	6.00031i	−0.306222	−	0.379493i
$251$	7.29590			0.460513			0.230257	−	0.973130i	$-0.426043\pi$
$251$	7.29590			0.460513			0.230257	+	0.973130i	$0.426043\pi$
$252$	−1.79399	+	1.30341i	−0.113010	+	0.0821069i
$253$	1.10123	−	3.38923i	0.0692337	−	0.213079i
$254$	3.17159	−	9.76115i	0.199003	−	0.612469i
$255$	−0.100874	−	5.97644i	−0.00631695	−	0.374259i
$256$	−3.06866	−	9.44435i	−0.191791	−	0.590272i
$257$	−12.4438			−0.776225			−0.388112	−	0.921612i	$-0.626873\pi$
$257$	−12.4438			−0.776225			−0.388112	+	0.921612i	$0.626873\pi$
$258$	5.72454	+	17.6183i	0.356395	+	1.09687i
$259$	−0.175247	−	0.127324i	−0.0108893	−	0.00791154i
$260$	−0.888168	−	1.18005i	−0.0550818	−	0.0731838i
$261$	−15.6856	+	11.3963i	−0.970915	+	0.705411i
$262$	−4.15581	−	3.01937i	−0.256747	−	0.186537i
$263$	−24.9418	−	18.1213i	−1.53798	−	1.11741i	−0.951586	−	0.307382i	$-0.900547\pi$
$263$	−24.9418	−	18.1213i	−1.53798	−	1.11741i	−0.586394	−	0.810026i	$-0.699453\pi$
$264$	−20.5849	+	14.9558i	−1.26691	+	0.920466i
$265$	7.01757	+	2.14991i	0.431086	+	0.132068i
$266$	0.182797	+	0.132810i	0.0112080	+	0.00814308i
$267$	−1.83905	−	5.66002i	−0.112548	−	0.346388i
$268$	−23.4723			−1.43380
$269$	−7.60269	−	23.3987i	−0.463544	−	1.42664i	−0.860804	−	0.508936i	$-0.830039\pi$
$269$	−7.60269	−	23.3987i	−0.463544	−	1.42664i	0.397260	−	0.917706i	$-0.369961\pi$
$270$	4.51507	+	1.38324i	0.274778	+	0.0841813i
$271$	−0.711670	+	2.19029i	−0.0432309	+	0.133051i	−0.970342	−	0.241735i	$-0.922284\pi$
$271$	−0.711670	+	2.19029i	−0.0432309	+	0.133051i	0.927112	+	0.374786i	$0.122284\pi$
$272$	0.424196	−	1.30554i	0.0257207	−	0.0791600i
$273$	0.328789	−	0.238879i	0.0198992	−	0.0144576i
$274$	14.0890			0.851148
$275$	−15.4443	+	12.0377i	−0.931324	+	0.725903i
$276$	−3.70806			−0.223199
$277$	−6.65576	+	4.83569i	−0.399906	+	0.290549i	−0.769503	−	0.638644i	$-0.779496\pi$
$277$	−6.65576	+	4.83569i	−0.399906	+	0.290549i	0.369597	+	0.929192i	$0.379496\pi$
$278$	1.86577	−	5.74226i	0.111902	−	0.344398i
$279$	4.99874	−	15.3845i	0.299267	−	0.921048i
$280$	1.80346	−	0.619819i	0.107777	−	0.0370413i
$281$	−2.22248	−	6.84010i	−0.132582	−	0.408046i	0.862624	−	0.505846i	$-0.168820\pi$
$281$	−2.22248	−	6.84010i	−0.132582	−	0.408046i	−0.995206	+	0.0977996i	$0.968820\pi$
$282$	−12.4553			−0.741701
$283$	3.30281	+	10.1650i	0.196332	+	0.604247i	0.999958	+	0.00911315i	$0.00290085\pi$
$283$	3.30281	+	10.1650i	0.196332	+	0.604247i	−0.803627	+	0.595134i	$0.797099\pi$
$284$	−7.16260	−	5.20393i	−0.425022	−	0.308797i
$285$	0.0941914	+	5.58054i	0.00557942	+	0.330563i
$286$	0.946704	−	0.687821i	0.0559798	−	0.0406717i
$287$	−1.47342	−	1.07050i	−0.0869734	−	0.0631899i
$288$	19.4781	+	14.1517i	1.14776	+	0.833896i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	6.82036	−	2.34404i	0.400505	−	0.137647i
$291$	16.5085	+	11.9941i	0.967747	+	0.703109i
$292$	−0.818416	−	2.51883i	−0.0478942	−	0.147403i
$293$	−21.5346			−1.25807			−0.629033	−	0.777379i	$-0.716549\pi$
$293$	−21.5346			−1.25807			−0.629033	+	0.777379i	$0.716549\pi$
$294$	−3.91744	−	12.0566i	−0.228470	−	0.703157i
$295$	3.36301	−	4.79699i	0.195802	−	0.279292i
$296$	−0.463665	+	1.42701i	−0.0269500	+	0.0829434i
$297$	3.70602	−	11.4059i	0.215045	−	0.661840i
$298$	−7.41878	+	5.39006i	−0.429758	+	0.312238i
$299$	0.394270			0.0228012
$300$	16.8784	+	11.4130i	0.974476	+	0.658928i
$301$	−3.52613			−0.203243
$302$	5.23879	−	3.80621i	0.301459	−	0.219022i
$303$	6.64724	−	20.4581i	0.381874	−	1.17529i
$304$	−0.396096	+	1.21906i	−0.0227177	+	0.0699178i
$305$	9.14887	+	12.1555i	0.523863	+	0.696024i
$306$	−0.883442	−	2.71896i	−0.0505030	−	0.155432i
$307$	−15.7604			−0.899495			−0.449748	−	0.893156i	$-0.648486\pi$
$307$	−15.7604			−0.899495			−0.449748	+	0.893156i	$0.648486\pi$
$308$	−0.647338	−	1.99230i	−0.0368855	−	0.113522i
$309$	−23.6968	−	17.2167i	−1.34806	−	0.979424i
$310$	−3.45409	+	4.92690i	−0.196179	+	0.279829i
$311$	7.26166	−	5.27591i	0.411771	−	0.299169i	−0.362547	−	0.931965i	$-0.618093\pi$
$311$	7.26166	−	5.27591i	0.411771	−	0.299169i	0.774318	+	0.632796i	$0.218093\pi$
$312$	−2.27744	−	1.65466i	−0.128935	−	0.0936766i
$313$	−2.38739	−	1.73454i	−0.134943	−	0.0980419i	0.518266	−	0.855220i	$-0.326578\pi$
$313$	−2.38739	−	1.73454i	−0.134943	−	0.0980419i	−0.653209	+	0.757178i	$0.726578\pi$
$314$	0.441818	−	0.321000i	0.0249332	−	0.0181151i
$315$	−1.86719	+	2.66335i	−0.105204	+	0.150063i
$316$	18.7412	+	13.6163i	1.05428	+	0.765976i
$317$	−7.70591	−	23.7164i	−0.432807	−	1.33204i	−0.895317	−	0.445429i	$-0.853051\pi$
$317$	−7.70591	−	23.7164i	−0.432807	−	1.33204i	0.462510	−	0.886614i	$-0.346949\pi$
$318$	6.05076			0.339310
$319$	−5.65997	−	17.4196i	−0.316897	−	0.975310i
$320$	−1.69379	−	2.25043i	−0.0946856	−	0.125803i
$321$	5.95751	−	18.3353i	0.332516	−	1.02338i
$322$	−0.0680425	+	0.209413i	−0.00379186	+	0.0116701i
$323$	0.755426	−	0.548849i	0.0420330	−	0.0305388i
$324$	6.48007			0.360004
$325$	−1.79465	−	1.21352i	−0.0995491	−	0.0673138i
$326$	−3.86584			−0.214109
$327$	−8.89196	+	6.46039i	−0.491726	+	0.357260i
$328$	−3.89836	+	11.9979i	−0.215251	+	0.662474i
$329$	0.732615	−	2.25476i	0.0403903	−	0.124309i
$330$	−9.26694	+	13.2183i	−0.510128	+	0.727646i
$331$	−6.15695	−	18.9492i	−0.338417	−	1.04154i	−0.965014	−	0.262197i	$-0.915553\pi$
$331$	−6.15695	−	18.9492i	−0.338417	−	1.04154i	0.626598	−	0.779343i	$-0.284447\pi$
$332$	−18.5785			−1.01963
$333$	−0.790849	−	2.43398i	−0.0433382	−	0.133381i
$334$	12.9228	+	9.38898i	0.707105	+	0.513742i
$335$	−32.5605	+	11.1905i	−1.77897	+	0.611402i
$336$	−1.04167	+	0.756815i	−0.0568276	+	0.0412877i
$337$	4.09123	+	2.97245i	0.222864	+	0.161920i	0.693615	−	0.720346i	$-0.256017\pi$
$337$	4.09123	+	2.97245i	0.222864	+	0.161920i	−0.470751	+	0.882266i	$0.656017\pi$
$338$	−7.14813	−	5.19342i	−0.388807	−	0.282485i
$339$	41.6103	−	30.2317i	2.25996	−	1.64196i
$340$	−0.0575260	−	3.40823i	−0.00311979	−	0.184837i
$341$	12.3630	+	8.98223i	0.669493	+	0.486415i
$342$	0.824921	+	2.53885i	0.0446066	+	0.137285i
$343$	4.86922			0.262913
$344$	7.54762	+	23.2292i	0.406940	+	1.25243i
$345$	−5.14376	+	1.76782i	−0.276931	+	0.0951765i
$346$	0.615199	−	1.89339i	0.0330733	−	0.101789i
$347$	0.269667	−	0.829950i	0.0144765	−	0.0445540i	−0.943557	−	0.331209i	$-0.892543\pi$
$347$	0.269667	−	0.829950i	0.0144765	−	0.0445540i	0.958034	+	0.286655i	$0.0925434\pi$
$348$	−15.4184	+	11.2022i	−0.826515	+	0.600498i
$349$	34.9709			1.87195			0.935976	−	0.352064i	$-0.114520\pi$
$349$	34.9709			1.87195			0.935976	+	0.352064i	$0.114520\pi$
$350$	0.954267	−	0.743785i	0.0510077	−	0.0397570i
$351$	1.32685			0.0708222
$352$	−18.4007	+	13.3689i	−0.980762	+	0.712565i
$353$	10.0059	−	30.7950i	0.532561	−	1.63905i	−0.216299	−	0.976327i	$-0.569399\pi$
$353$	10.0059	−	30.7950i	0.532561	−	1.63905i	0.748860	−	0.662728i	$-0.230601\pi$
$354$	1.49247	−	4.59335i	0.0793239	−	0.244134i
$355$	−12.4168	−	3.80404i	−0.659018	−	0.201897i
$356$	−1.04877	−	3.22779i	−0.0555848	−	0.171073i
$357$	0.937966			0.0496424
$358$	3.07882	+	9.47564i	0.162721	+	0.500803i
$359$	−5.21088	−	3.78593i	−0.275020	−	0.199814i	0.441722	−	0.897152i	$-0.354368\pi$
$359$	−5.21088	−	3.78593i	−0.275020	−	0.199814i	−0.716742	+	0.697338i	$0.754368\pi$
$360$	21.5421	+	6.59967i	1.13537	+	0.347833i
$361$	14.6659	−	10.6554i	0.771892	−	0.560812i
$362$	−11.4117	−	8.29112i	−0.599788	−	0.435772i
$363$	9.37987	+	6.81488i	0.492316	+	0.357688i
$364$	0.187502	−	0.136228i	0.00982775	−	0.00714028i
$365$	−2.33615	−	3.10390i	−0.122280	−	0.162466i
$366$	10.1470	+	7.37223i	0.530392	+	0.385352i
$367$	−5.00839	−	15.4142i	−0.261436	−	0.804617i	−0.992493	−	0.122301i	$-0.960973\pi$
$367$	−5.00839	−	15.4142i	−0.261436	−	0.804617i	0.731057	−	0.682316i	$-0.239027\pi$
$368$	−1.24912			−0.0651150
$369$	−6.64923	−	20.4642i	−0.346145	−	1.06532i
$370$	0.0160654	+	0.951823i	0.000835200	+	0.0494829i
$371$	−0.355903	+	1.09536i	−0.0184776	+	0.0568682i
$372$	4.91359	−	15.1225i	0.254758	−	0.784064i
$373$	10.2482	−	7.44573i	0.530630	−	0.385525i	−0.289963	−	0.957038i	$-0.593643\pi$
$373$	10.2482	−	7.44573i	0.530630	−	0.385525i	0.820593	+	0.571513i	$0.193643\pi$
$374$	2.70075			0.139652
$375$	28.8547	+	7.78508i	1.49005	+	0.402020i
$376$	−16.4219			−0.846893
$377$	1.63941	−	1.19110i	0.0844339	−	0.0613448i
$378$	−0.228986	+	0.704748i	−0.0117778	+	0.0362483i
$379$	1.58014	−	4.86316i	0.0811662	−	0.249804i	−0.902236	−	0.431242i	$-0.858075\pi$
$379$	1.58014	−	4.86316i	0.0811662	−	0.249804i	0.983402	+	0.181439i	$0.0580754\pi$
$380$	0.0537154	+	3.18246i	0.00275554	+	0.163257i
$381$	12.2938	+	37.8365i	0.629832	+	1.93842i
$382$	6.87840			0.351929
$383$	−0.928466	−	2.85752i	−0.0474424	−	0.146013i	0.924529	−	0.381111i	$-0.124459\pi$
$383$	−0.928466	−	2.85752i	−0.0474424	−	0.146013i	−0.971971	+	0.235099i	$0.924459\pi$
$384$	23.2408	+	16.8855i	1.18600	+	0.861682i
$385$	−1.84781	−	2.45507i	−0.0941733	−	0.125122i
$386$	13.5486	−	9.84366i	0.689608	−	0.501029i
$387$	−33.7035	−	24.4870i	−1.71324	−	1.24475i
$388$	9.41446	+	6.84000i	0.477947	+	0.347249i
$389$	−12.6179	+	9.16742i	−0.639751	+	0.464807i	−0.859765	−	0.510690i	$-0.829390\pi$
$389$	−12.6179	+	9.16742i	−0.639751	+	0.464807i	0.220013	+	0.975497i	$0.429390\pi$
$390$	−1.70768	−	0.523166i	−0.0864716	−	0.0264915i
$391$	0.736170	+	0.534859i	0.0372297	+	0.0270490i
$392$	−5.16501	−	15.8963i	−0.260872	−	0.802883i
$393$	19.9117			1.00441
$394$	1.01266	+	3.11665i	0.0510172	+	0.157015i
$395$	32.4892	+	9.95341i	1.63471	+	0.500811i
$396$	7.64804	−	23.5382i	0.384328	−	1.18284i
$397$	−2.87168	+	8.83812i	−0.144125	+	0.443572i	−0.996897	−	0.0787109i	$-0.974920\pi$
$397$	−2.87168	+	8.83812i	−0.144125	+	0.443572i	0.852772	+	0.522283i	$0.174920\pi$
$398$	14.5340	−	10.5596i	0.728523	−	0.529303i
$399$	−0.875833			−0.0438465
$400$	5.68578	+	3.84465i	0.284289	+	0.192233i
$401$	26.4304			1.31987			0.659937	−	0.751321i	$-0.270583\pi$
$401$	26.4304			1.31987			0.659937	+	0.751321i	$0.270583\pi$
$402$	−22.9634	+	16.6839i	−1.14531	+	0.832116i
$403$	−0.522452	+	1.60794i	−0.0260252	+	0.0800973i
$404$	3.79078	−	11.6668i	0.188598	−	0.580446i
$405$	8.98907	−	3.08939i	0.446670	−	0.153513i
$406$	0.349717	+	1.07632i	0.0173562	+	0.0534168i
$407$	2.41768			0.119840
$408$	−2.00770	−	6.17907i	−0.0993960	−	0.305909i
$409$	20.1713	+	14.6553i	0.997405	+	0.724657i	0.961530	−	0.274699i	$-0.0885783\pi$
$409$	20.1713	+	14.6553i	0.997405	+	0.724657i	0.0358746	+	0.999356i	$0.488578\pi$
$410$	0.135073	+	8.00266i	0.00667079	+	0.395223i
$411$	−44.1823	+	32.1003i	−2.17935	+	1.58339i
$412$	−13.5138	−	9.81832i	−0.665775	−	0.483714i
$413$	0.743739	+	0.540358i	0.0365970	+	0.0265893i
$414$	−2.10462	+	1.52910i	−0.103437	+	0.0751511i
$415$	−25.7718	+	8.85734i	−1.26509	+	0.434790i
$416$	−2.03579	−	1.47909i	−0.0998128	−	0.0725183i
$417$	7.23217	+	22.2583i	0.354161	+	1.09000i
$418$	−2.52184			−0.123347
$419$	7.94870	+	24.4636i	0.388319	+	1.19512i	0.934043	+	0.357159i	$0.116255\pi$
$419$	7.94870	+	24.4636i	0.388319	+	1.19512i	−0.545724	+	0.837965i	$0.683745\pi$
$420$	−1.83538	+	2.61799i	−0.0895576	+	0.127745i
$421$	7.84191	−	24.1349i	0.382191	−	1.17626i	−0.556306	−	0.830977i	$-0.687782\pi$
$421$	7.84191	−	24.1349i	0.382191	−	1.17626i	0.938497	−	0.345286i	$-0.112218\pi$
$422$	−3.28620	+	10.1139i	−0.159970	+	0.492336i
$423$	22.6605	−	16.4638i	1.10179	−	0.800499i
$424$	7.97773			0.387433
$425$	−1.70468	−	4.70043i	−0.0826893	−	0.228004i
$426$	−10.7062			−0.518716
$427$	−1.93142	+	1.40326i	−0.0934681	+	0.0679086i
$428$	3.39744	−	10.4562i	0.164221	−	0.505421i
$429$	−1.40168	+	4.31393i	−0.0676738	+	0.208278i
$430$	9.31869	+	12.3812i	0.449387	+	0.597073i
$431$	11.7805	+	36.2567i	0.567448	+	1.74643i	0.660564	+	0.750770i	$0.270317\pi$
$431$	11.7805	+	36.2567i	0.567448	+	1.74643i	−0.0931159	+	0.995655i	$0.529683\pi$
$432$	−4.20373			−0.202252
$433$	3.90310	+	12.0125i	0.187571	+	0.577285i	0.999983	−	0.00579899i	$-0.00184589\pi$
$433$	3.90310	+	12.0125i	0.187571	+	0.577285i	−0.812412	+	0.583084i	$0.801846\pi$
$434$	−0.763881	−	0.554992i	−0.0366675	−	0.0266405i
$435$	−16.0476	+	22.8902i	−0.769423	+	1.09750i
$436$	−5.07089	+	3.68422i	−0.242852	+	0.176442i
$437$	−0.687405	−	0.499429i	−0.0328830	−	0.0238909i
$438$	−2.59102	−	1.88249i	−0.123804	−	0.0899488i
$439$	21.3559	−	15.5159i	1.01926	−	0.740535i	0.0531283	−	0.998588i	$-0.483081\pi$
$439$	21.3559	−	15.5159i	1.01926	−	0.740535i	0.966131	+	0.258053i	$0.0830808\pi$
$440$	−12.2182	+	17.4279i	−0.582478	+	0.830845i
$441$	23.0641	+	16.7570i	1.09829	+	0.797953i
$442$	0.0923346	+	0.284177i	0.00439191	+	0.0135169i
$443$	−20.8555			−0.990873			−0.495437	−	0.868644i	$-0.664992\pi$
$443$	−20.8555			−0.990873			−0.495437	+	0.868644i	$0.664992\pi$
$444$	−0.777378	−	2.39252i	−0.0368927	−	0.113544i
$445$	−2.99370	−	3.97754i	−0.141915	−	0.188554i
$446$	3.27668	−	10.0846i	0.155155	−	0.477519i
$447$	10.9842	−	33.8058i	0.519534	−	1.59896i
$448$	0.357576	−	0.259794i	0.0168939	−	0.0122741i
$449$	3.10738			0.146646			0.0733232	−	0.997308i	$-0.476640\pi$
$449$	3.10738			0.146646			0.0733232	+	0.997308i	$0.476640\pi$
$450$	14.2863	−	0.482400i	0.673461	−	0.0227405i
$451$	20.3272			0.957168
$452$	23.7295	−	17.2405i	1.11614	−	0.810924i
$453$	−7.75650	+	23.8721i	−0.364432	+	1.12161i
$454$	2.95056	−	9.08088i	0.138476	−	0.426187i
$455$	0.195153	−	0.278365i	0.00914890	−	0.0130500i
$456$	1.87471	+	5.76975i	0.0877911	+	0.270193i
$457$	−10.2837			−0.481052			−0.240526	−	0.970643i	$-0.577320\pi$
$457$	−10.2837			−0.481052			−0.240526	+	0.970643i	$0.577320\pi$
$458$	3.14854	+	9.69020i	0.147121	+	0.452793i
$459$	2.47747	+	1.79999i	0.115638	+	0.0840161i
$460$	−2.93338	+	1.00815i	−0.136770	+	0.0470054i
$461$	−10.4950	+	7.62503i	−0.488799	+	0.355133i	−0.804722	−	0.593652i	$-0.797686\pi$
$461$	−10.4950	+	7.62503i	−0.488799	+	0.355133i	0.315923	+	0.948785i	$0.397686\pi$
$462$	−2.04941	−	1.48898i	−0.0953471	−	0.0692737i
$463$	−5.38846	−	3.91495i	−0.250423	−	0.181943i	0.455491	−	0.890240i	$-0.349464\pi$
$463$	−5.38846	−	3.91495i	−0.250423	−	0.181943i	−0.705914	+	0.708297i	$0.749464\pi$
$464$	−5.19396	+	3.77364i	−0.241124	+	0.175187i
$465$	−0.393612	−	23.3203i	−0.0182533	−	1.08145i
$466$	−8.50940	−	6.18244i	−0.394190	−	0.286396i
$467$	−1.18556	−	3.64877i	−0.0548610	−	0.168845i	0.919872	−	0.392220i	$-0.128293\pi$
$467$	−1.18556	−	3.64877i	−0.0548610	−	0.168845i	−0.974733	+	0.223375i	$0.928293\pi$
$468$	2.73821			0.126574
$469$	−1.66955	−	5.13836i	−0.0770928	−	0.237267i
$470$	−9.85316	+	3.38636i	−0.454492	+	0.156201i
$471$	−0.654152	+	2.01327i	−0.0301417	+	0.0927667i
$472$	1.96777	−	6.05618i	0.0905740	−	0.278758i
$473$	31.8392	−	23.1326i	1.46397	−	1.06364i
$474$	28.0132			1.28669
$475$	1.59176	+	4.38906i	0.0730350	+	0.201384i
$476$	0.534902			0.0245172
$477$	−11.0085	+	7.99811i	−0.504042	+	0.366208i
$478$	2.94345	−	9.05900i	0.134630	−	0.414349i
$479$	11.9012	−	36.6282i	0.543781	−	1.67359i	−0.180090	−	0.983650i	$-0.557639\pi$
$479$	11.9012	−	36.6282i	0.543781	−	1.67359i	0.723871	−	0.689936i	$-0.242361\pi$
$480$	33.1915	+	10.1686i	1.51498	+	0.464130i
$481$	0.0826570	+	0.254392i	0.00376883	+	0.0115993i
$482$	20.3514			0.926980
$483$	−0.263749	−	0.811735i	−0.0120010	−	0.0369352i
$484$	5.34914	+	3.88638i	0.243143	+	0.176654i
$485$	16.3206	+	4.99999i	0.741080	+	0.227038i
$486$	11.4651	−	8.32987i	0.520067	−	0.377851i
$487$	−29.5027	−	21.4350i	−1.33690	−	0.971312i	−0.999552	−	0.0299303i	$-0.990471\pi$
$487$	−29.5027	−	21.4350i	−1.33690	−	0.971312i	−0.337344	−	0.941381i	$-0.609529\pi$
$488$	13.3785	+	9.72004i	0.605615	+	0.440005i
$489$	12.1230	−	8.80790i	0.548223	−	0.398307i
$490$	−6.37699	−	8.47271i	−0.288083	−	0.382758i
$491$	−0.447522	−	0.325144i	−0.0201964	−	0.0146735i	0.577641	−	0.816291i	$-0.303973\pi$
$491$	−0.447522	−	0.325144i	−0.0201964	−	0.0146735i	−0.597838	+	0.801617i	$0.703973\pi$
$492$	−6.53597	−	20.1156i	−0.294664	−	0.906883i
$493$	4.67689			0.210637
$494$	−0.0862181	−	0.265352i	−0.00387913	−	0.0119387i
$495$	−0.612660	−	36.2982i	−0.0275370	−	1.63148i
$496$	1.65523	−	5.09426i	0.0743219	−	0.228739i
$497$	0.629734	−	1.93812i	0.0282474	−	0.0869366i
$498$	−18.1756	+	13.2054i	−0.814470	+	0.591747i
$499$	−0.0171335			−0.000767002			−0.000383501	−	1.00000i	$-0.500122\pi$
$499$	−0.0171335			−0.000767002			−0.000383501		1.00000i	$0.500122\pi$
$500$	16.4552	+	4.43967i	0.735899	+	0.198548i
$501$	−61.9170			−2.76625
$502$	4.07048	−	2.95738i	0.181674	−	0.131994i
$503$	−1.38481	+	4.26200i	−0.0617455	+	0.190033i	−0.977171	−	0.212454i	$-0.931854\pi$
$503$	−1.38481	+	4.26200i	−0.0617455	+	0.190033i	0.915425	+	0.402487i	$0.131854\pi$
$504$	−1.09253	+	3.36247i	−0.0486653	+	0.149776i
$505$	−0.303667	−	17.9913i	−0.0135130	−	0.800603i
$506$	−0.759428	−	2.33728i	−0.0337607	−	0.103905i
$507$	34.2488			1.52104
$508$	7.01091	+	21.5774i	0.311059	+	0.957340i
$509$	−24.1945	−	17.5784i	−1.07240	−	0.779147i	−0.0960609	−	0.995375i	$-0.530624\pi$
$509$	−24.1945	−	17.5784i	−1.07240	−	0.779147i	−0.976343	+	0.216229i	$0.930624\pi$
$510$	−2.47881	−	3.29344i	−0.109764	−	0.145836i
$511$	0.493187	−	0.358321i	0.0218173	−	0.0158512i
$512$	11.8482	+	8.60824i	0.523622	+	0.380434i
$513$	−2.31335	−	1.68075i	−0.102137	−	0.0742069i
$514$	−6.94258	+	5.04408i	−0.306224	+	0.222485i
$515$	−23.4270	−	7.17712i	−1.03232	−	0.316262i
$516$	−33.1294	−	24.0699i	−1.45844	−	1.05962i
$517$	8.17678	+	25.1655i	0.359614	+	1.10678i
$518$	−0.149383			−0.00656351
$519$	2.38465	+	7.33921i	0.104675	+	0.322156i
$520$	−2.25152	−	0.689777i	−0.0987355	−	0.0302487i
$521$	−8.87454	+	27.3130i	−0.388801	+	1.19661i	0.544885	+	0.838511i	$0.316573\pi$
$521$	−8.87454	+	27.3130i	−0.388801	+	1.19661i	−0.933685	+	0.358095i	$0.883427\pi$
$522$	−4.13176	+	12.7163i	−0.180842	+	0.556576i
$523$	29.4724	−	21.4129i	1.28874	−	0.936322i	0.288958	−	0.957342i	$-0.406691\pi$
$523$	29.4724	−	21.4129i	1.28874	−	0.936322i	0.999779	+	0.0210195i	$0.00669121\pi$
$524$	11.3552			0.496055
$525$	−1.29789	+	4.50666i	−0.0566445	+	0.196687i
$526$	−21.2608			−0.927016
$527$	−3.15681	+	2.29356i	−0.137513	+	0.0999089i
$528$	4.44079	−	13.6673i	0.193261	−	0.594795i
$529$	−6.85152	+	21.0868i	−0.297892	+	0.916818i
$530$	4.78665	−	1.64509i	0.207919	−	0.0714582i
$531$	3.35633	+	10.3297i	0.145652	+	0.448271i
$532$	−0.499469			−0.0216547
$533$	0.694956	+	2.13885i	0.0301019	+	0.0926441i
$534$	−3.32031	−	2.41235i	−0.143684	−	0.104392i
$535$	−0.272158	−	16.1245i	−0.0117664	−	0.697123i
$536$	−30.2765	+	21.9971i	−1.30774	+	0.950131i
$537$	−31.2442	−	22.7003i	−1.34829	−	0.979589i
$538$	−13.7262	−	9.97270i	−0.591780	−	0.429954i
$539$	−21.7883	+	15.8301i	−0.938489	+	0.681852i
$540$	−9.87183	+	3.39278i	−0.424816	+	0.146002i
$541$	−22.8904	−	16.6308i	−0.984134	−	0.715015i	−0.0255051	−	0.999675i	$-0.508119\pi$
$541$	−22.8904	−	16.6308i	−0.984134	−	0.715015i	−0.958629	+	0.284660i	$0.908119\pi$
$542$	0.490781	+	1.51047i	0.0210808	+	0.0648802i
$543$	54.6770			2.34641
$544$	−1.79467	−	5.52343i	−0.0769459	−	0.236815i
$545$	−5.27781	+	7.52826i	−0.226077	+	0.322475i
$546$	0.0866067	−	0.266548i	0.00370642	−	0.0114072i
$547$	−8.30905	+	25.5726i	−0.355269	+	1.09341i	0.600584	+	0.799562i	$0.294935\pi$
$547$	−8.30905	+	25.5726i	−0.355269	+	1.09341i	−0.955853	+	0.293844i	$0.905065\pi$
$548$	−25.1962	+	18.3061i	−1.07633	+	0.781999i
$549$	−28.2058			−1.20379
$550$	−3.73709	+	12.9763i	−0.159350	+	0.553312i
$551$	−4.36708			−0.186044
$552$	−4.78294	+	3.47501i	−0.203575	+	0.147906i
$553$	−1.64772	+	5.07117i	−0.0700683	+	0.215648i
$554$	−1.75320	+	5.39579i	−0.0744863	+	0.229245i
$555$	−2.21901	−	2.94826i	−0.0941917	−	0.125147i
$556$	4.12435	+	12.6935i	0.174912	+	0.538323i
$557$	6.30564			0.267179			0.133589	−	0.991037i	$-0.457350\pi$
$557$	6.30564			0.267179			0.133589	+	0.991037i	$0.457350\pi$
$558$	−3.44722	−	10.6095i	−0.145933	−	0.449134i
$559$	3.52258	+	2.55930i	0.148989	+	0.108247i
$560$	−0.618281	+	0.881914i	−0.0261271	+	0.0372677i
$561$	−8.46938	+	6.15336i	−0.357577	+	0.259795i
$562$	−4.01257	−	2.91531i	−0.169260	−	0.122975i
$563$	−15.6677	−	11.3832i	−0.660314	−	0.479746i	0.206455	−	0.978456i	$-0.433807\pi$
$563$	−15.6677	−	11.3832i	−0.660314	−	0.479746i	−0.866769	+	0.498710i	$0.833807\pi$
$564$	22.2745	−	16.1834i	0.937927	−	0.681444i
$565$	24.6978	−	35.2288i	1.03904	−	1.48209i
$566$	5.96304	+	4.33240i	0.250645	+	0.182105i
$567$	0.460918	+	1.41856i	0.0193567	+	0.0595739i
$568$	−14.1158			−0.592284
$569$	11.2635	+	34.6654i	0.472189	+	1.45325i	0.849711	+	0.527248i	$0.176776\pi$
$569$	11.2635	+	34.6654i	0.472189	+	1.45325i	−0.377522	+	0.926001i	$0.623224\pi$
$570$	2.31461	+	3.07528i	0.0969484	+	0.128809i
$571$	8.36898	−	25.7571i	0.350231	−	1.07790i	−0.608492	−	0.793560i	$-0.708225\pi$
$571$	8.36898	−	25.7571i	0.350231	−	1.07790i	0.958723	−	0.284340i	$-0.0917746\pi$
$572$	−0.799348	+	2.46014i	−0.0334224	+	0.102864i
$573$	−21.5702	+	15.6717i	−0.901110	+	0.654694i
$574$	−1.25597			−0.0524231
$575$	−3.58850	+	2.79699i	−0.149651	+	0.116643i
$576$	5.22192			0.217580
$577$	−28.7008	+	20.8523i	−1.19483	+	0.868095i	−0.993766	−	0.111484i	$-0.964440\pi$
$577$	−28.7008	+	20.8523i	−1.19483	+	0.868095i	−0.201064	+	0.979578i	$0.564440\pi$
$578$	−0.213104	+	0.655866i	−0.00886395	+	0.0272804i
$579$	−20.0600	+	61.7383i	−0.833664	+	2.56576i
$580$	−9.15160	+	13.0538i	−0.380000	+	0.542030i
$581$	−1.32146	−	4.06704i	−0.0548234	−	0.168729i
$582$	14.0721			0.583308
$583$	−3.97227	−	12.2254i	−0.164515	−	0.506324i
$584$	−3.41618	−	2.48200i	−0.141363	−	0.102706i
$585$	3.79840	−	1.30545i	0.157045	−	0.0539736i
$586$	−12.0144	+	8.72900i	−0.496312	+	0.360592i
$587$	−2.75227	−	1.99964i	−0.113598	−	0.0825341i	0.529536	−	0.848288i	$-0.322366\pi$
$587$	−2.75227	−	1.99964i	−0.113598	−	0.0825341i	−0.643134	+	0.765754i	$0.722366\pi$
$588$	22.6712	+	16.4716i	0.934945	+	0.679277i
$589$	2.94770	−	2.14163i	0.121458	−	0.0882442i
$590$	−0.0681808	−	4.03950i	−0.00280696	−	0.166303i
$591$	−10.2766	−	7.46640i	−0.422723	−	0.307126i
$592$	−0.261873	−	0.805962i	−0.0107629	−	0.0331248i
$593$	−21.0415			−0.864072			−0.432036	−	0.901856i	$-0.642205\pi$
$593$	−21.0415			−0.864072			−0.432036	+	0.901856i	$0.642205\pi$
$594$	−2.55574	−	7.86575i	−0.104863	−	0.322736i
$595$	0.742009	−	0.255016i	0.0304194	−	0.0104546i
$596$	6.26404	−	19.2787i	0.256585	−	0.789688i
$597$	−21.5189	+	66.2283i	−0.880710	+	2.71055i
$598$	0.219968	−	0.159816i	0.00899518	−	0.00653538i
$599$	−36.3689			−1.48599			−0.742996	−	0.669296i	$-0.766596\pi$
$599$	−36.3689			−1.48599			−0.742996	+	0.669296i	$0.766596\pi$
$600$	32.4668	−	1.09630i	1.32545	−	0.0447561i
$601$	−2.75379			−0.112329			−0.0561647	−	0.998422i	$-0.517887\pi$
$601$	−2.75379			−0.112329			−0.0561647	+	0.998422i	$0.517887\pi$
$602$	−1.96727	+	1.42931i	−0.0801801	+	0.0582543i
$603$	19.7251	−	60.7076i	0.803268	−	2.47221i
$604$	−4.42337	+	13.6137i	−0.179984	+	0.553935i
$605$	9.27310	+	2.84092i	0.377005	+	0.115500i
$606$	−4.58406	−	14.1083i	−0.186215	−	0.573110i
$607$	−15.1572			−0.615210			−0.307605	−	0.951514i	$-0.599528\pi$
$607$	−15.1572			−0.615210			−0.307605	+	0.951514i	$0.599528\pi$
$608$	1.67579	+	5.15754i	0.0679622	+	0.209166i
$609$	−3.54897	−	2.57848i	−0.143811	−	0.104485i
$610$	10.0315	+	3.07326i	0.406163	+	0.124433i
$611$	−2.36840	+	1.72075i	−0.0958154	+	0.0696139i
$612$	5.11271	+	3.71460i	0.206669	+	0.150154i
$613$	−27.3259	−	19.8534i	−1.10368	−	0.801872i	−0.122026	−	0.992527i	$-0.538939\pi$
$613$	−27.3259	−	19.8534i	−1.10368	−	0.801872i	−0.981657	+	0.190655i	$0.938939\pi$
$614$	−8.79295	+	6.38846i	−0.354855	+	0.257817i
$615$	−18.6568	−	24.7881i	−0.752314	−	0.999553i
$616$	−2.70208	−	1.96317i	−0.108870	−	0.0790985i
$617$	−0.753430	−	2.31882i	−0.0303319	−	0.0933521i	0.934744	−	0.355321i	$-0.115628\pi$
$617$	−0.753430	−	2.31882i	−0.0303319	−	0.0933521i	−0.965076	+	0.261969i	$0.915628\pi$
$618$	−20.1995			−0.812542
$619$	−5.49511	−	16.9122i	−0.220867	−	0.679759i	−0.998685	−	0.0512690i	$-0.983673\pi$
$619$	−5.49511	−	16.9122i	−0.220867	−	0.679759i	0.777818	−	0.628490i	$-0.216327\pi$
$620$	−0.224469	−	13.2990i	−0.00901487	−	0.534103i
$621$	0.861100	−	2.65019i	0.0345547	−	0.106349i
$622$	1.91280	−	5.88700i	0.0766963	−	0.236047i
$623$	0.632002	−	0.459176i	0.0253206	−	0.0183965i
$624$	1.58992			0.0636479
$625$	24.9431	−	1.68641i	0.997722	−	0.0674565i
$626$	−2.03505			−0.0813368
$627$	7.90834	−	5.74575i	0.315829	−	0.229463i
$628$	−0.373049	+	1.14813i	−0.0148863	+	0.0458152i
$629$	−0.190768	+	0.587125i	−0.00760644	+	0.0234102i
$630$	0.0378549	+	2.24278i	0.00150817	+	0.0893546i
$631$	9.00638	+	27.7188i	0.358538	+	1.10347i	0.953929	+	0.300032i	$0.0969973\pi$
$631$	9.00638	+	27.7188i	0.358538	+	1.10347i	−0.595391	+	0.803436i	$0.703003\pi$
$632$	36.9344			1.46917
$633$	−12.7381	−	39.2038i	−0.506294	−	1.55821i
$634$	−13.9126	−	10.1081i	−0.552540	−	0.401444i
$635$	20.0125	+	26.5893i	0.794172	+	1.05517i
$636$	−10.8209	+	7.86187i	−0.429078	+	0.311744i
$637$	−2.41058	−	1.75139i	−0.0955107	−	0.0693926i
$638$	−10.2188	−	7.42437i	−0.404565	−	0.293933i
$639$	19.4783	−	14.1518i	0.770550	−	0.559837i
$640$	22.9763	+	7.03903i	0.908217	+	0.278242i
$641$	21.7667	+	15.8144i	0.859733	+	0.624633i	0.927812	−	0.373047i	$-0.121687\pi$
$641$	21.7667	+	15.8144i	0.859733	+	0.624633i	−0.0680794	+	0.997680i	$0.521687\pi$
$642$	−4.10841	−	12.6444i	−0.162146	−	0.499034i
$643$	15.8739			0.626007			0.313004	−	0.949752i	$-0.398665\pi$
$643$	15.8739			0.626007			0.313004	+	0.949752i	$0.398665\pi$
$644$	−0.150410	−	0.462915i	−0.00592699	−	0.0182414i
$645$	−57.4320	−	17.5949i	−2.26138	−	0.692800i
$646$	0.198987	−	0.612420i	0.00782905	−	0.0240953i
$647$	8.73293	−	26.8772i	0.343327	−	1.05665i	−0.619146	−	0.785276i	$-0.712521\pi$
$647$	8.73293	−	26.8772i	0.343327	−	1.05665i	0.962473	−	0.271376i	$-0.0874788\pi$
$648$	8.35850	−	6.07281i	0.328353	−	0.238562i
$649$	−10.2605			−0.402761
$650$	−1.49315	+	0.0504189i	−0.0585663	+	0.00197759i
$651$	3.65998			0.143446
$652$	6.91351	−	5.02296i	0.270754	−	0.196714i
$653$	−3.81508	+	11.7416i	−0.149296	+	0.459485i	−0.997538	−	0.0701229i	$-0.977661\pi$
$653$	−3.81508	+	11.7416i	−0.149296	+	0.459485i	0.848243	+	0.529608i	$0.177661\pi$
$654$	−2.34224	+	7.20867i	−0.0915888	+	0.281881i
$655$	15.7518	−	5.41362i	0.615474	−	0.211528i
$656$	−2.20175	−	6.77630i	−0.0859640	−	0.264570i
$657$	7.20232			0.280989
$658$	−0.505225	−	1.55492i	−0.0196957	−	0.0606172i
$659$	28.7024	+	20.8535i	1.11809	+	0.812337i	0.983918	−	0.178622i	$-0.0571639\pi$
$659$	28.7024	+	20.8535i	1.11809	+	0.812337i	0.134168	+	0.990959i	$0.457164\pi$
$660$	−0.602224	−	35.6799i	−0.0234415	−	1.38884i
$661$	−21.8720	+	15.8909i	−0.850722	+	0.618086i	−0.925345	−	0.379126i	$-0.876225\pi$
$661$	−21.8720	+	15.8909i	−0.850722	+	0.618086i	0.0746227	+	0.997212i	$0.476225\pi$
$662$	−11.1160	−	8.07628i	−0.432037	−	0.313893i
$663$	−0.937022	−	0.680786i	−0.0363909	−	0.0264395i
$664$	−23.9640	+	17.4109i	−0.929983	+	0.675672i
$665$	−0.692856	+	0.238123i	−0.0268678	+	0.00923401i
$666$	−1.42783	−	1.03738i	−0.0553274	−	0.0401977i
$667$	−1.31510	−	4.04748i	−0.0509210	−	0.156719i
$668$	−35.3099			−1.36618
$669$	12.7012	+	39.0902i	0.491056	+	1.51131i
$670$	−13.6299	+	19.4417i	−0.526569	+	0.751097i
$671$	8.23396	−	25.3415i	0.317868	−	0.978298i
$672$	−1.68334	+	5.18079i	−0.0649363	+	0.199853i
$673$	−19.4193	+	14.1090i	−0.748560	+	0.543860i	−0.895380	−	0.445303i	$-0.853096\pi$
$673$	−19.4193	+	14.1090i	−0.748560	+	0.543860i	0.146820	+	0.989163i	$0.453096\pi$
$674$	3.48743			0.134331
$675$	−12.0766	+	9.41284i	−0.464827	+	0.362300i
$676$	19.5313			0.751206
$677$	2.40089	−	1.74435i	0.0922739	−	0.0670409i	−0.540692	−	0.841221i	$-0.681837\pi$
$677$	2.40089	−	1.74435i	0.0922739	−	0.0670409i	0.632966	+	0.774180i	$0.281837\pi$
$678$	10.9606	−	33.7333i	0.420940	−	1.29552i
$679$	−0.827717	+	2.54745i	−0.0317648	+	0.0977621i
$680$	−3.26823	−	4.34230i	−0.125331	−	0.166520i
$681$	11.4370	+	35.1996i	0.438269	+	1.34885i
$682$	10.5384			0.403536
$683$	4.00745	+	12.3337i	0.153341	+	0.471934i	0.997989	−	0.0633873i	$-0.0201904\pi$
$683$	4.00745	+	12.3337i	0.153341	+	0.471934i	−0.844648	+	0.535322i	$0.820190\pi$
$684$	−4.77403	−	3.46853i	−0.182539	−	0.132623i
$685$	−26.2244	+	37.4064i	−1.00198	+	1.42922i
$686$	2.71660	−	1.97373i	0.103720	−	0.0753573i
$687$	−31.9517	−	23.2143i	−1.21903	−	0.885680i
$688$	−11.1602	−	8.10836i	−0.425479	−	0.309128i
$689$	1.15057	−	0.835937i	0.0438332	−	0.0318467i
$690$	−2.15319	+	3.07131i	−0.0819706	+	0.116923i
$691$	18.9329	+	13.7556i	0.720243	+	0.523287i	0.886462	−	0.462802i	$-0.153156\pi$
$691$	18.9329	+	13.7556i	0.720243	+	0.523287i	−0.166219	+	0.986089i	$0.553156\pi$
$692$	1.35992	+	4.18540i	0.0516963	+	0.159105i
$693$	5.69678			0.216403
$694$	−0.185967	−	0.572349i	−0.00705923	−	0.0217261i
$695$	11.7729	+	15.6419i	0.446571	+	0.593331i
$696$	−9.38980	+	28.8988i	−0.355919	+	1.09541i
$697$	−1.60393	+	4.93638i	−0.0607530	+	0.186979i
$698$	19.5108	−	14.1754i	0.738493	−	0.536546i
$699$	40.7710			1.54210
$700$	−0.740158	+	2.57005i	−0.0279753	+	0.0971389i
$701$	−0.822500			−0.0310654			−0.0155327	−	0.999879i	$-0.504944\pi$
$701$	−0.822500			−0.0310654			−0.0155327	+	0.999879i	$0.504944\pi$
$702$	0.740270	−	0.537837i	0.0279397	−	0.0202994i
$703$	0.178131	−	0.548232i	0.00671835	−	0.0206770i
$704$	−1.52440	+	4.69163i	−0.0574531	+	0.176823i
$705$	23.1834	−	33.0688i	0.873139	−	1.24544i
$706$	−6.90027	−	21.2368i	−0.259695	−	0.799259i
$707$	2.82363			0.106194
$708$	3.29916	+	10.1538i	0.123990	+	0.381602i
$709$	−23.3997	−	17.0009i	−0.878794	−	0.638481i	0.0541385	−	0.998533i	$-0.482759\pi$
$709$	−23.3997	−	17.0009i	−0.878794	−	0.638481i	−0.932932	+	0.360053i	$0.882759\pi$
$710$	−8.46948	+	2.91082i	−0.317854	+	0.109241i
$711$	−50.9657	+	37.0288i	−1.91136	+	1.38869i
$712$	−4.37772	−	3.18060i	−0.164062	−	0.119198i
$713$	2.87256	+	2.08704i	0.107578	+	0.0781602i
$714$	0.523304	−	0.380202i	0.0195842	−	0.0142287i
$715$	0.0640332	+	3.79377i	0.00239471	+	0.141879i
$716$	−17.8179	−	12.9455i	−0.665887	−	0.483795i
$717$	11.4095	+	35.1148i	0.426095	+	1.31139i
$718$	−4.44184			−0.165768
$719$	14.2568	+	43.8780i	0.531690	+	1.63637i	0.750694	+	0.660650i	$0.229719\pi$
$719$	14.2568	+	43.8780i	0.531690	+	1.63637i	−0.219004	+	0.975724i	$0.570281\pi$
$720$	−12.0341	+	4.13590i	−0.448483	+	0.154136i
$721$	1.18813	−	3.65667i	0.0442481	−	0.136182i
$722$	3.86317	−	11.8896i	0.143772	−	0.442485i
$723$	−63.8207	+	46.3685i	−2.37352	+	1.72446i
$724$	31.1811			1.15884
$725$	−6.47153	+	22.4711i	−0.240347	+	0.834557i
$726$	7.99555			0.296743
$727$	−17.2889	+	12.5611i	−0.641209	+	0.465866i	−0.860265	−	0.509846i	$-0.829702\pi$
$727$	−17.2889	+	12.5611i	−0.641209	+	0.465866i	0.219056	+	0.975712i	$0.429702\pi$
$728$	0.114188	−	0.351435i	0.00423209	−	0.0130250i
$729$	−13.0344	+	40.1156i	−0.482754	+	1.48576i
$730$	−2.56153	−	0.784753i	−0.0948065	−	0.0290450i
$731$	3.10537	+	9.55733i	0.114856	+	0.353491i
$732$	−27.7254			−1.02476
$733$	−7.31873	−	22.5247i	−0.270323	−	0.831970i	−0.990419	−	0.138095i	$-0.955902\pi$
$733$	−7.31873	−	22.5247i	−0.270323	−	0.831970i	0.720096	−	0.693875i	$-0.244098\pi$
$734$	−9.04238	−	6.56967i	−0.333760	−	0.242491i
$735$	39.3021	+	12.0406i	1.44968	+	0.444125i
$736$	−4.27544	+	3.10629i	−0.157595	+	0.114499i
$737$	48.7845	+	35.4440i	1.79700	+	1.30560i
$738$	−12.0048	−	8.72201i	−0.441903	−	0.321062i
$739$	−28.8787	+	20.9816i	−1.06232	+	0.771821i	−0.974516	−	0.224317i	$-0.927985\pi$
$739$	−28.8787	+	20.9816i	−1.06232	+	0.771821i	−0.0878044	+	0.996138i	$0.527985\pi$
$740$	−1.26545	−	1.68133i	−0.0465190	−	0.0618069i
$741$	0.874951	+	0.635689i	0.0321421	+	0.0233526i
$742$	0.245438	+	0.755379i	0.00901030	+	0.0277309i
$743$	47.8493			1.75542			0.877711	−	0.479191i	$-0.159070\pi$
$743$	47.8493			1.75542			0.877711	+	0.479191i	$0.159070\pi$
$744$	−7.83412	−	24.1109i	−0.287213	−	0.883950i
$745$	−0.501792	−	29.7296i	−0.0183842	−	1.08921i
$746$	2.69948	−	8.30814i	0.0988349	−	0.304183i
$747$	15.6125	−	48.0504i	0.571232	−	1.75807i
$748$	−4.82990	+	3.50913i	−0.176599	+	0.128307i
$749$	2.53064			0.0924677
$750$	19.2541	−	7.35277i	0.703059	−	0.268485i
$751$	6.56368			0.239512			0.119756	−	0.992803i	$-0.461789\pi$
$751$	6.56368			0.239512			0.119756	+	0.992803i	$0.461789\pi$
$752$	7.50355	−	5.45165i	0.273626	−	0.198801i
$753$	−6.02671	+	18.5483i	−0.219626	+	0.675938i
$754$	0.431839	−	1.32906i	0.0157266	−	0.0484016i
$755$	0.354342	+	20.9936i	0.0128958	+	0.764037i
$756$	−0.506182	−	1.55787i	−0.0184097	−	0.0566591i
$757$	9.13812			0.332131			0.166065	−	0.986115i	$-0.446894\pi$
$757$	9.13812			0.332131			0.166065	+	0.986115i	$0.446894\pi$
$758$	−1.08969	−	3.35373i	−0.0395794	−	0.121813i
$759$	7.70677	+	5.59929i	0.279738	+	0.203241i
$760$	3.05174	+	4.05465i	0.110698	+	0.147078i
$761$	1.61115	−	1.17057i	0.0584042	−	0.0424332i	−0.558200	−	0.829706i	$-0.688508\pi$
$761$	1.61115	−	1.17057i	0.0584042	−	0.0424332i	0.616604	+	0.787273i	$0.288508\pi$
$762$	22.1958	+	16.1262i	0.804070	+	0.584191i
$763$	−1.16720	−	0.848022i	−0.0422556	−	0.0307005i
$764$	−12.3010	+	8.93723i	−0.445036	+	0.323338i
$765$	8.86322	+	2.71535i	0.320450	+	0.0981735i
$766$	−1.67629	−	1.21790i	−0.0605670	−	0.0440045i
$767$	−0.350792	−	1.07963i	−0.0126664	−	0.0389831i
$768$	26.5451			0.957865
$769$	7.66417	+	23.5879i	0.276377	+	0.850602i	0.988852	+	0.148904i	$0.0475744\pi$
$769$	7.66417	+	23.5879i	0.276377	+	0.850602i	−0.712475	+	0.701698i	$0.752426\pi$
$770$	−2.02608	−	0.620711i	−0.0730148	−	0.0223689i
$771$	10.2791	−	31.6359i	0.370193	−	1.13934i
$772$	−11.4398	+	35.2080i	−0.411727	+	1.26716i
$773$	28.5519	−	20.7442i	1.02694	−	0.746117i	0.0592473	−	0.998243i	$-0.481130\pi$
$773$	28.5519	−	20.7442i	1.02694	−	0.746117i	0.967694	+	0.252127i	$0.0811299\pi$
$774$	−28.7294			−1.03266
$775$	−6.65173	−	18.3412i	−0.238937	−	0.658837i
$776$	18.5536			0.666036
$777$	0.468456	−	0.340353i	0.0168058	−	0.0122101i
$778$	−3.32368	+	10.2293i	−0.119160	+	0.366736i
$779$	1.49768	−	4.60938i	0.0536599	−	0.165148i
$780$	3.73370	−	1.28321i	0.133688	−	0.0459463i
$781$	7.02851	+	21.6315i	0.251500	+	0.774037i
$782$	0.627523			0.0224402
$783$	−4.42578	−	13.6211i	−0.158164	−	0.486780i
$784$	7.63718	+	5.54874i	0.272756	+	0.198169i
$785$	0.0298837	+	1.77052i	0.00106660	+	0.0631925i
$786$	11.1090	−	8.07116i	0.396245	−	0.287889i
$787$	−38.9962	−	28.3324i	−1.39006	−	1.00994i	−0.995858	−	0.0909168i	$-0.971020\pi$
$787$	−38.9962	−	28.3324i	−1.39006	−	1.00994i	−0.394204	−	0.919023i	$-0.628980\pi$
$788$	−5.86053	−	4.25793i	−0.208773	−	0.151682i
$789$	66.6727	−	48.4405i	2.37361	−	1.72453i
$790$	22.1607	−	7.61627i	0.788443	−	0.270975i
$791$	5.46197	+	3.96836i	0.194205	+	0.141099i
$792$	−12.1939	−	37.5288i	−0.433290	−	1.33353i
$793$	2.94798			0.104686
$794$	1.98036	+	6.09493i	0.0702805	+	0.216301i
$795$	−11.2625	+	16.0648i	−0.399439	+	0.569759i
$796$	−12.2718	+	37.7686i	−0.434961	+	1.33867i
$797$	−10.2407	+	31.5177i	−0.362745	+	1.11641i	0.588636	+	0.808398i	$0.299665\pi$
$797$	−10.2407	+	31.5177i	−0.362745	+	1.11641i	−0.951381	+	0.308016i	$0.900335\pi$
$798$	−0.488639	+	0.355017i	−0.0172976	+	0.0125675i
$799$	−6.75655			−0.239030
$800$	29.0219	−	0.979972i	1.02608	−	0.0346472i
$801$	9.22953			0.326109
$802$	14.7459	−	10.7135i	0.520696	−	0.378308i
$803$	−2.10253	+	6.47093i	−0.0741967	+	0.228354i
$804$	19.3891	−	59.6735i	0.683801	−	2.10452i
$805$	−0.429343	−	0.570441i	−0.0151324	−	0.0201054i
$806$	0.360293	+	1.10887i	0.0126908	+	0.0390582i
$807$	65.7664			2.31509
$808$	−6.04393	−	18.6013i	−0.212625	−	0.654392i
$809$	−25.8310	−	18.7673i	−0.908170	−	0.659824i	0.0323813	−	0.999476i	$-0.489691\pi$
$809$	−25.8310	−	18.7673i	−0.908170	−	0.659824i	−0.940551	+	0.339651i	$0.889691\pi$
$810$	3.76284	−	5.36731i	0.132213	−	0.188588i
$811$	9.73020	−	7.06941i	0.341674	−	0.248240i	−0.403694	−	0.914894i	$-0.632274\pi$
$811$	9.73020	−	7.06941i	0.341674	−	0.248240i	0.745368	+	0.666654i	$0.232274\pi$
$812$	−2.02390	−	1.47045i	−0.0710250	−	0.0516027i
$813$	−4.98050	−	3.61855i	−0.174674	−	0.126908i
$814$	1.34886	−	0.980001i	0.0472774	−	0.0343490i
$815$	7.19562	−	10.2638i	0.252052	−	0.359526i
$816$	2.96866	+	2.15686i	0.103924	+	0.0755052i
$817$	−2.89966	−	8.92423i	−0.101446	−	0.312219i
$818$	17.1943			0.601185
$819$	0.194765	+	0.599424i	0.00680563	+	0.0209456i
$820$	−10.6396	−	14.1361i	−0.371550	−	0.493655i
$821$	4.77145	−	14.6850i	0.166525	−	0.512511i	−0.832621	−	0.553844i	$-0.813160\pi$
$821$	4.77145	−	14.6850i	0.166525	−	0.512511i	0.999145	+	0.0413329i	$0.0131604\pi$
$822$	−11.6381	+	35.8184i	−0.405925	+	1.24931i
$823$	−12.0878	+	8.78230i	−0.421354	+	0.306132i	−0.778182	−	0.628038i	$-0.783858\pi$
$823$	−12.0878	+	8.78230i	−0.421354	+	0.306132i	0.356828	+	0.934170i	$0.383858\pi$
$824$	−26.6323			−0.927782
$825$	−17.8459	−	49.2075i	−0.621313	−	1.71319i
$826$	0.633975			0.0220588
$827$	1.77153	−	1.28709i	0.0616022	−	0.0447566i	−0.556558	−	0.830809i	$-0.687878\pi$
$827$	1.77153	−	1.28709i	0.0616022	−	0.0447566i	0.618160	+	0.786052i	$0.287878\pi$
$828$	1.77704	−	5.46916i	0.0617563	−	0.190066i
$829$	5.56137	−	17.1161i	0.193154	−	0.594468i	−0.806839	−	0.590772i	$-0.798823\pi$
$829$	5.56137	−	17.1161i	0.193154	−	0.594468i	0.999993	−	0.00369641i	$-0.00117661\pi$
$830$	−10.7881	+	15.3882i	−0.374462	+	0.534131i
$831$	−6.79582	−	20.9154i	−0.235744	−	0.725546i
$832$	−0.545778			−0.0189214
$833$	−2.12507	−	6.54030i	−0.0736294	−	0.226608i
$834$	13.0573	+	9.48668i	0.452137	+	0.328497i
$835$	−48.9815	+	16.8341i	−1.69507	+	0.582568i
$836$	4.50996	−	3.27668i	0.155980	−	0.113326i
$837$	9.66716	+	7.02360i	0.334146	+	0.242771i
$838$	14.3509	+	10.4266i	0.495745	+	0.360180i
$839$	−15.0677	+	10.9473i	−0.520195	+	0.377944i	−0.816677	−	0.577095i	$-0.804186\pi$
$839$	−15.0677	+	10.9473i	−0.520195	+	0.377944i	0.296482	+	0.955038i	$0.404186\pi$
$840$	0.0860286	+	5.09692i	0.00296827	+	0.175860i
$841$	5.76562	+	4.18897i	0.198815	+	0.144447i
$842$	−5.40793	−	16.6439i	−0.186369	−	0.573586i
$843$	19.2254			0.662158
$844$	−7.26426	−	22.3571i	−0.250046	−	0.769563i
$845$	27.0936	−	9.31162i	0.932049	−	0.320329i
$846$	5.96903	−	18.3708i	0.205219	−	0.631600i
$847$	−0.470295	+	1.44742i	−0.0161595	+	0.0497339i
$848$	−3.64522	+	2.64841i	−0.125177	+	0.0909466i
$849$	−28.5707			−0.980543
$850$	−2.85637	−	1.93144i	−0.0979728	−	0.0662480i
$851$	0.561752			0.0192566
$852$	19.1465	−	13.9108i	0.655949	−	0.476575i
$853$	−7.17686	+	22.0881i	−0.245731	+	0.756282i	0.749784	+	0.661682i	$0.230157\pi$
$853$	−7.17686	+	22.0881i	−0.245731	+	0.756282i	−0.995515	+	0.0946000i	$0.969843\pi$
$854$	−0.508758	+	1.56580i	−0.0174093	+	0.0535804i
$855$	−8.27610	−	2.53547i	−0.283037	−	0.0867114i
$856$	−5.41680	−	16.6712i	−0.185142	−	0.569810i
$857$	21.5207			0.735134			0.367567	−	0.929997i	$-0.380191\pi$
$857$	21.5207			0.735134			0.367567	+	0.929997i	$0.380191\pi$
$858$	0.966625	+	2.97497i	0.0330000	+	0.101564i
$859$	5.98620	+	4.34923i	0.204247	+	0.148394i	0.685207	−	0.728349i	$-0.259712\pi$
$859$	5.98620	+	4.34923i	0.204247	+	0.148394i	−0.480960	+	0.876742i	$0.659712\pi$
$860$	−32.7523	−	10.0340i	−1.11684	−	0.342157i
$861$	3.93864	−	2.86159i	0.134229	−	0.0975228i
$862$	21.2691	+	15.4529i	0.724428	+	0.526328i
$863$	−29.0239	−	21.0871i	−0.987985	−	0.717813i	−0.0285063	−	0.999594i	$-0.509075\pi$
$863$	−29.0239	−	21.0871i	−0.987985	−	0.717813i	−0.959479	+	0.281780i	$0.909075\pi$
$864$	−14.3883	+	10.4537i	−0.489501	+	0.355643i
$865$	3.88186	+	5.15758i	0.131987	+	0.175363i
$866$	7.04684	+	5.11983i	0.239461	+	0.173979i
$867$	−0.826041	−	2.54229i	−0.0280538	−	0.0863408i
$868$	2.08721			0.0708444
$869$	−18.3904	−	56.5998i	−0.623851	−	1.92002i
$870$	0.325344	+	19.2756i	0.0110302	+	0.653505i
$871$	−2.06160	+	6.34496i	−0.0698548	+	0.214991i
$872$	−3.08816	+	9.50439i	−0.104578	+	0.321859i
$873$	−25.6021	+	18.6010i	−0.866500	+	0.629549i
$874$	−0.585954			−0.0198202
$875$	0.198542	+	3.91802i	0.00671194	+	0.132453i
$876$	7.07964			0.239199
$877$	4.43071	−	3.21910i	0.149615	−	0.108701i	−0.510460	−	0.859902i	$-0.670525\pi$
$877$	4.43071	−	3.21910i	0.149615	−	0.108701i	0.660074	+	0.751200i	$0.270525\pi$
$878$	5.62536	−	17.3131i	0.189847	−	0.584289i
$879$	17.7885	−	54.7473i	0.599990	−	1.84658i
$880$	−0.202869	−	12.0194i	−0.00683873	−	0.405173i
$881$	3.67046	+	11.2965i	0.123661	+	0.380589i	0.993655	−	0.112474i	$-0.0358774\pi$
$881$	3.67046	+	11.2965i	0.123661	+	0.380589i	−0.869994	+	0.493062i	$0.835877\pi$
$882$	19.6602			0.661992
$883$	11.5412	+	35.5201i	0.388391	+	1.19535i	0.933990	+	0.357299i	$0.116302\pi$
$883$	11.5412	+	35.5201i	0.388391	+	1.19535i	−0.545599	+	0.838046i	$0.683698\pi$
$884$	−0.534364	−	0.388238i	−0.0179726	−	0.0130579i
$885$	9.41737	+	12.5123i	0.316562	+	0.420595i
$886$	−11.6355	+	8.45372i	−0.390904	+	0.284008i
$887$	−43.0692	−	31.2916i	−1.44612	−	1.05067i	−0.986718	−	0.162441i	$-0.948063\pi$
$887$	−43.0692	−	31.2916i	−1.44612	−	1.05067i	−0.459404	−	0.888228i	$-0.651937\pi$
$888$	−3.24488	−	2.35754i	−0.108891	−	0.0791139i
$889$	−4.22485	+	3.06953i	−0.141697	+	0.102949i
$890$	−3.28251	−	1.00563i	−0.110030	−	0.0337089i
$891$	−13.4681	−	9.78513i	−0.451198	−	0.327814i
$892$	7.24321	+	22.2923i	0.242521	+	0.746402i
$893$	6.30898			0.211122
$894$	−7.57489	−	23.3131i	−0.253342	−	0.779708i
$895$	−30.8886	−	9.46305i	−1.03249	−	0.316315i
$896$	−1.16527	+	3.58632i	−0.0389288	+	0.119811i
$897$	−0.325683	+	1.00235i	−0.0108742	+	0.0334675i
$898$	1.73365	−	1.25957i	0.0578526	−	0.0420324i
$899$	18.2494			0.608651
$900$	−24.9222	+	19.4251i	−0.830739	+	0.647504i
$901$	3.28233			0.109350
$902$	11.3408	−	8.23956i	0.377607	−	0.274347i
$903$	2.91273	−	8.96445i	0.0969295	−	0.298318i
$904$	14.4512	−	44.4762i	0.480640	−	1.47926i
$905$	43.2540	−	14.8657i	1.43781	−	0.494152i
$906$	5.34903	+	16.4626i	0.177710	+	0.546934i
$907$	24.1586			0.802175			0.401087	−	0.916040i	$-0.368632\pi$
$907$	24.1586			0.802175			0.401087	+	0.916040i	$0.368632\pi$
$908$	6.52231	+	20.0736i	0.216450	+	0.666166i
$909$	26.9888	+	19.6085i	0.895164	+	0.650374i
$910$	−0.00395647	−	0.234408i	−0.000131156	−	0.00777056i
$911$	32.3620	−	23.5124i	1.07220	−	0.778999i	0.0958942	−	0.995392i	$-0.469429\pi$
$911$	32.3620	−	23.5124i	1.07220	−	0.778999i	0.976307	+	0.216392i	$0.0694289\pi$
$912$	−2.77201	−	2.01398i	−0.0917905	−	0.0666897i
$913$	38.6132	+	28.0541i	1.27791	+	0.928457i
$914$	−5.73742	+	4.16848i	−0.189777	+	0.137881i
$915$	−38.4602	+	13.2181i	−1.27146	+	0.436978i
$916$	−18.2214	−	13.2386i	−0.602052	−	0.437416i
$917$	0.807680	+	2.48578i	0.0266719	+	0.0820878i
$918$	2.11183			0.0697008
$919$	−11.2055	−	34.4868i	−0.369634	−	1.13762i	−0.947028	−	0.321151i	$-0.895930\pi$
$919$	−11.2055	−	34.4868i	−0.369634	−	1.13762i	0.577394	−	0.816466i	$-0.304070\pi$
$920$	−2.83891	+	4.04942i	−0.0935961	+	0.133505i
$921$	13.0188	−	40.0676i	0.428983	−	1.32027i
$922$	−2.76449	+	8.50821i	−0.0910435	+	0.280203i
$923$	−2.03581	+	1.47910i	−0.0670095	+	0.0486852i
$924$	5.59974			0.184218
$925$	−2.55700	−	1.72901i	−0.0840736	−	0.0568494i
$926$	−4.59321			−0.150942
$927$	36.7499	−	26.7004i	1.20703	−	0.876956i
$928$	−8.39348	+	25.8325i	−0.275529	+	0.847993i
$929$	−14.4025	+	44.3262i	−0.472530	+	1.45430i	0.376731	+	0.926323i	$0.377048\pi$
$929$	−14.4025	+	44.3262i	−0.472530	+	1.45430i	−0.849260	+	0.527974i	$0.822952\pi$
$930$	−9.67241	−	12.8511i	−0.317171	−	0.421405i
$931$	1.98430	+	6.10705i	0.0650329	+	0.200151i
$932$	23.2508			0.761606
$933$	7.41447	+	22.8194i	0.242739	+	0.747073i
$934$	−2.14046	−	1.55513i	−0.0700379	−	0.0508855i
$935$	−5.02699	+	7.17049i	−0.164400	+	0.234500i
$936$	3.53195	−	2.56611i	0.115445	−	0.0838760i
$937$	2.51603	+	1.82801i	0.0821953	+	0.0597184i	0.628124	−	0.778113i	$-0.283823\pi$
$937$	2.51603	+	1.82801i	0.0821953	+	0.0597184i	−0.545929	+	0.837832i	$0.683823\pi$
$938$	−3.01429	−	2.19001i	−0.0984200	−	0.0715063i
$939$	6.38179	−	4.63664i	0.208262	−	0.151311i
$940$	13.2210	−	18.8584i	0.431222	−	0.615094i
$941$	−21.4461	−	15.5815i	−0.699122	−	0.507942i	0.180524	−	0.983571i	$-0.442221\pi$
$941$	−21.4461	−	15.5815i	−0.699122	−	0.507942i	−0.879646	+	0.475628i	$0.842221\pi$
$942$	0.451115	+	1.38839i	0.0146981	+	0.0452362i
$943$	4.72305			0.153804
$944$	1.11138	+	3.42047i	0.0361722	+	0.111327i
$945$	−1.44489	−	1.91973i	−0.0470022	−	0.0624489i
$946$	8.38680	−	25.8119i	0.272678	−	0.839218i
$947$	−1.91408	+	5.89094i	−0.0621993	+	0.191430i	−0.977328	−	0.211733i	$-0.932089\pi$
$947$	−1.91408	+	5.89094i	−0.0621993	+	0.191430i	0.915128	+	0.403163i	$0.132089\pi$
$948$	−50.0976	+	36.3981i	−1.62710	+	1.18215i
$949$	−0.752763			−0.0244357
$950$	2.66716	+	1.80350i	0.0865341	+	0.0585132i
$951$	66.6593			2.16158
$952$	0.689959	−	0.501284i	0.0223617	−	0.0162467i
$953$	−3.43981	+	10.5866i	−0.111426	+	0.342935i	−0.991185	−	0.132486i	$-0.957704\pi$
$953$	−3.43981	+	10.5866i	−0.111426	+	0.342935i	0.879759	+	0.475421i	$0.157704\pi$
$954$	−2.89975	+	8.92450i	−0.0938828	+	0.288941i
$955$	−12.8030	+	18.2622i	−0.414295	+	0.590950i
$956$	6.50659	+	20.0252i	0.210438	+	0.647662i
$957$	48.9611			1.58269
$958$	−8.20731	−	25.2595i	−0.265166	−	0.816098i
$959$	−5.79959	−	4.21365i	−0.187278	−	0.136066i
$960$	7.12038	−	2.44716i	0.229809	−	0.0789816i
$961$	12.7615	−	9.27180i	0.411663	−	0.299090i
$962$	0.149233	+	0.108424i	0.00481145	+	0.00349573i
$963$	24.1884	+	17.5739i	0.779461	+	0.566311i
$964$	−36.3956	+	26.4429i	−1.17222	+	0.851670i
$965$	0.916404	+	54.2940i	0.0295001	+	1.74779i
$966$	−0.476184	−	0.345968i	−0.0153210	−	0.0111313i
$967$	−3.78347	−	11.6443i	−0.121668	−	0.374456i	0.871611	−	0.490198i	$-0.163075\pi$
$967$	−3.78347	−	11.6443i	−0.121668	−	0.374456i	−0.993279	+	0.115742i	$0.963075\pi$
$968$	10.5419			0.338828
$969$	0.771322	+	2.37388i	0.0247784	+	0.0762601i
$970$	11.1322	−	3.82595i	0.357434	−	0.122844i
$971$	−11.5332	+	35.4954i	−0.370116	+	1.13910i	0.576598	+	0.817028i	$0.304380\pi$
$971$	−11.5332	+	35.4954i	−0.370116	+	1.13910i	−0.946715	+	0.322073i	$0.895620\pi$
$972$	−9.68054	+	29.7936i	−0.310503	+	0.955631i
$973$	−2.48538	+	1.80573i	−0.0796777	+	0.0578892i
$974$	−25.1486			−0.805812
$975$	4.56757	−	3.56010i	0.146279	−	0.114015i
$976$	−9.33976			−0.298959
$977$	−10.4471	+	7.59026i	−0.334232	+	0.242834i	−0.742224	−	0.670152i	$-0.766229\pi$
$977$	−10.4471	+	7.59026i	−0.334232	+	0.242834i	0.407992	+	0.912985i	$0.366229\pi$
$978$	3.19334	−	9.82809i	0.102112	−	0.314268i
$979$	−2.69432	+	8.29227i	−0.0861109	+	0.265022i
$980$	22.4131	+	6.86651i	0.715961	+	0.219343i
$981$	−5.26732	−	16.2111i	−0.168173	−	0.517582i
$982$	−0.381475			−0.0121733
$983$	−1.78175	−	5.48367i	−0.0568290	−	0.174902i	0.918613	−	0.395159i	$-0.129310\pi$
$983$	−1.78175	−	5.48367i	−0.0568290	−	0.174902i	−0.975442	+	0.220257i	$0.929310\pi$
$984$	−27.2820	−	19.8215i	−0.869718	−	0.631887i
$985$	−10.1596	−	3.11251i	−0.323713	−	0.0991730i
$986$	2.60930	−	1.89577i	0.0830970	−	0.0603735i
$987$	5.12708	+	3.72504i	0.163197	+	0.118569i
$988$	0.498966	+	0.362520i	0.0158742	+	0.0115333i
$989$	7.39790	−	5.37489i	0.235240	−	0.170912i
$990$	−15.0552	−	20.0029i	−0.478485	−	0.635733i
$991$	−11.3829	−	8.27016i	−0.361590	−	0.262710i	0.392125	−	0.919912i	$-0.371740\pi$
$991$	−11.3829	−	8.27016i	−0.361590	−	0.262710i	−0.753715	+	0.657202i	$0.771740\pi$
$992$	−7.00287	−	21.5526i	−0.222341	−	0.684296i
$993$	53.2602			1.69016
$994$	−0.434276	−	1.33656i	−0.0137744	−	0.0423932i
$995$	0.983052	+	58.2427i	0.0311648	+	1.84642i
$996$	15.3466	−	47.2319i	0.486275	−	1.49660i
$997$	6.68408	−	20.5715i	0.211687	−	0.651505i	−0.787685	−	0.616078i	$-0.788721\pi$
$997$	6.68408	−	20.5715i	0.211687	−	0.651505i	0.999372	−	0.0354277i	$-0.0112793\pi$
$998$	−0.00955902	+	0.00694504i	−0.000302586	+	0.000219841i
$999$	1.89049			0.0598125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.12	✓	76
25.16	even	5	inner	425.2.k.b.341.12	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.12	✓	76	1.1	even	1	trivial
425.2.k.b.341.12	yes	76	25.16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.557913 - 0.405348i) q^{2} +(-0.826041 + 2.54229i) q^{3} +(-0.471074 + 1.44982i) q^{4} +(0.0377362 + 2.23575i) q^{5} +(0.569653 + 1.75321i) q^{6} -0.350888 q^{7} +(0.751069 + 2.31155i) q^{8} +(-3.35386 - 2.43672i) q^{9} +(0.927309 + 1.23206i) q^{10} +(3.16834 - 2.30194i) q^{11} +(-3.29673 - 2.39521i) q^{12} +(0.350534 + 0.254678i) q^{13} +(-0.195765 + 0.142231i) q^{14} +(-5.71510 - 1.75088i) q^{15} +(-1.11056 - 0.806869i) q^{16} +(0.309017 + 0.951057i) q^{17} -2.85888 q^{18} +(-0.288547 - 0.888056i) q^{19} +(-3.25920 - 0.998492i) q^{20} +(0.289847 - 0.892059i) q^{21} +(0.834576 - 2.56856i) q^{22} +(0.736170 - 0.534859i) q^{23} -6.49706 q^{24} +(-4.99715 + 0.168737i) q^{25} +0.298801 q^{26} +(2.47747 - 1.79999i) q^{27} +(0.165294 - 0.508722i) q^{28} +(1.44524 - 4.44799i) q^{29} +(-3.89825 + 1.33976i) q^{30} +(1.20579 + 3.71105i) q^{31} -5.80768 q^{32} +(3.23501 + 9.95635i) q^{33} +(0.557913 + 0.405348i) q^{34} +(-0.0132412 - 0.784497i) q^{35} +(5.11271 - 3.71460i) q^{36} +(0.499438 + 0.362863i) q^{37} +(-0.520956 - 0.378496i) q^{38} +(-0.937022 + 0.680786i) q^{39} +(-5.13971 + 1.76643i) q^{40} +(4.19913 + 3.05085i) q^{41} +(-0.199884 - 0.615180i) q^{42} +10.0492 q^{43} +(1.84486 + 5.67789i) q^{44} +(5.32133 - 7.59034i) q^{45} +(0.193915 - 0.596810i) q^{46} +(-2.08789 + 6.42586i) q^{47} +(2.96866 - 2.15686i) q^{48} -6.87688 q^{49} +(-2.71958 + 2.11972i) q^{50} -2.67312 q^{51} +(-0.534364 + 0.388238i) q^{52} +(1.01429 - 3.12168i) q^{53} +(0.652592 - 2.00847i) q^{54} +(5.26611 + 6.99675i) q^{55} +(-0.263541 - 0.811095i) q^{56} +2.49605 q^{57} +(-0.996664 - 3.06741i) q^{58} +(-2.11959 - 1.53997i) q^{59} +(5.23069 - 7.46105i) q^{60} +(5.50439 - 3.99918i) q^{61} +(2.17700 + 1.58168i) q^{62} +(1.17683 + 0.855015i) q^{63} +(-1.01906 + 0.740392i) q^{64} +(-0.556169 + 0.793318i) q^{65} +(5.84064 + 4.24347i) q^{66} +(4.75809 + 14.6439i) q^{67} -1.52443 q^{68} +(0.751661 + 2.31338i) q^{69} +(-0.325381 - 0.432314i) q^{70} +(-1.79469 + 5.52348i) q^{71} +(3.11363 - 9.58276i) q^{72} +(-1.40554 + 1.02118i) q^{73} +0.425729 q^{74} +(3.69887 - 12.8436i) q^{75} +1.42344 q^{76} +(-1.11173 + 0.807721i) q^{77} +(-0.246822 + 0.759639i) q^{78} +(4.69587 - 14.4524i) q^{79} +(1.76205 - 2.51338i) q^{80} +(-1.31358 - 4.04278i) q^{81} +3.57941 q^{82} +(3.76605 + 11.5907i) q^{83} +(1.15678 + 0.840451i) q^{84} +(-2.11466 + 0.726774i) q^{85} +(5.60657 - 4.07341i) q^{86} +(10.1143 + 7.34844i) q^{87} +(7.70069 + 5.59488i) q^{88} +(-1.80115 + 1.30861i) q^{89} +(-0.107883 - 6.39174i) q^{90} +(-0.122998 - 0.0893634i) q^{91} +(0.428657 + 1.31927i) q^{92} -10.4306 q^{93} +(1.43985 + 4.43140i) q^{94} +(1.97458 - 0.678630i) q^{95} +(4.79738 - 14.7648i) q^{96} +(2.35892 - 7.26002i) q^{97} +(-3.83670 + 2.78753i) q^{98} -16.2353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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