LMFDB - Embedded newform 625.2.d.n.126.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.4
Root			$-1.80544i$ of defining polynomial
Character	$\chi$	$=$	625.126
Dual form			625.2.d.n.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764617 + 2.35325i) q^{2} +(-1.71249 + 1.24419i) q^{3} +(-3.33511 + 2.42310i) q^{4} +(-4.23730 - 3.07858i) q^{6} -0.973070 q^{7} +(-4.24866 - 3.08683i) q^{8} +(0.457541 - 1.40817i) q^{9} +O(q^{10})$	\(q+(0.764617 + 2.35325i) q^{2} +(-1.71249 + 1.24419i) q^{3} +(-3.33511 + 2.42310i) q^{4} +(-4.23730 - 3.07858i) q^{6} -0.973070 q^{7} +(-4.24866 - 3.08683i) q^{8} +(0.457541 - 1.40817i) q^{9} +(-1.66321 - 5.11883i) q^{11} +(2.69653 - 8.29906i) q^{12} +(-0.617014 + 1.89897i) q^{13} +(-0.744026 - 2.28988i) q^{14} +(1.46769 - 4.51708i) q^{16} +(1.65283 + 1.20085i) q^{17} +3.66361 q^{18} +(-5.01937 - 3.64678i) q^{19} +(1.66637 - 1.21069i) q^{21} +(10.7742 - 7.82789i) q^{22} +(0.598915 + 1.84327i) q^{23} +11.1164 q^{24} -4.94054 q^{26} +(-0.993836 - 3.05871i) q^{27} +(3.24530 - 2.35785i) q^{28} +(-3.89794 + 2.83202i) q^{29} +(5.37199 + 3.90298i) q^{31} +1.24877 q^{32} +(9.21704 + 6.69657i) q^{33} +(-1.56212 + 4.80771i) q^{34} +(1.88618 + 5.80506i) q^{36} +(-0.302501 + 0.931002i) q^{37} +(4.74390 - 14.6002i) q^{38} +(-1.30607 - 4.01966i) q^{39} +(0.844603 - 2.59942i) q^{41} +(4.12319 + 2.99567i) q^{42} +3.99413 q^{43} +(17.9504 + 13.0417i) q^{44} +(-3.87974 + 2.81879i) q^{46} +(-5.83576 + 4.23993i) q^{47} +(3.10673 + 9.56153i) q^{48} -6.05313 q^{49} -4.32454 q^{51} +(-2.54359 - 7.82838i) q^{52} +(-10.7393 + 7.80259i) q^{53} +(6.43801 - 4.67749i) q^{54} +(4.13424 + 3.00370i) q^{56} +13.1329 q^{57} +(-9.64488 - 7.00741i) q^{58} +(2.02105 - 6.22014i) q^{59} +(0.842602 + 2.59326i) q^{61} +(-5.07717 + 15.6259i) q^{62} +(-0.445219 + 1.37024i) q^{63} +(-1.98054 - 6.09548i) q^{64} +(-8.71120 + 26.8103i) q^{66} +(-7.74195 - 5.62485i) q^{67} -8.42215 q^{68} +(-3.31902 - 2.41141i) q^{69} +(4.59943 - 3.34168i) q^{71} +(-6.29070 + 4.57046i) q^{72} +(-2.89018 - 8.89505i) q^{73} -2.42218 q^{74} +25.5767 q^{76} +(1.61842 + 4.98098i) q^{77} +(8.46061 - 6.14700i) q^{78} +(2.57405 - 1.87016i) q^{79} +(9.10114 + 6.61236i) q^{81} +6.76289 q^{82} +(-4.94623 - 3.59365i) q^{83} +(-2.62391 + 8.07556i) q^{84} +(3.05398 + 9.39919i) q^{86} +(3.15159 - 9.69959i) q^{87} +(-8.73455 + 26.8822i) q^{88} +(-0.929346 - 2.86023i) q^{89} +(0.600398 - 1.84784i) q^{91} +(-6.46388 - 4.69629i) q^{92} -14.0555 q^{93} +(-14.4397 - 10.4911i) q^{94} +(-2.13851 + 1.55372i) q^{96} +(-4.81791 + 3.50042i) q^{97} +(-4.62833 - 14.2445i) q^{98} -7.96914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.764617	+	2.35325i	0.540666	+	1.66400i	0.731077	+	0.682295i	$0.239018\pi$
$2$	0.764617	+	2.35325i	0.540666	+	1.66400i	−0.190411	+	0.981704i	$0.560982\pi$
$3$	−1.71249	+	1.24419i	−0.988705	+	0.718336i	−0.959637	−	0.281241i	$-0.909254\pi$
$3$	−1.71249	+	1.24419i	−0.988705	+	0.718336i	−0.0290678	+	0.999577i	$0.509254\pi$
$4$	−3.33511	+	2.42310i	−1.66756	+	1.21155i
$5$		0			0
$5$		0			0
$6$	−4.23730	−	3.07858i	−1.72987	−	1.25682i
$7$	−0.973070			−0.367786			−0.183893	−	0.982946i	$-0.558870\pi$
$7$	−0.973070			−0.367786			−0.183893	+	0.982946i	$0.558870\pi$
$8$	−4.24866	−	3.08683i	−1.50213	−	1.09136i
$9$	0.457541	−	1.40817i	0.152514	−	0.469389i
$10$		0			0
$11$	−1.66321	−	5.11883i	−0.501476	−	1.54338i	−0.806615	−	0.591077i	$-0.798703\pi$
$11$	−1.66321	−	5.11883i	−0.501476	−	1.54338i	0.305139	−	0.952308i	$-0.401297\pi$
$12$	2.69653	−	8.29906i	0.778420	−	2.39573i
$13$	−0.617014	+	1.89897i	−0.171129	+	0.526681i	−0.999436	−	0.0335943i	$-0.989305\pi$
$13$	−0.617014	+	1.89897i	−0.171129	+	0.526681i	0.828307	+	0.560275i	$0.189305\pi$
$14$	−0.744026	−	2.28988i	−0.198849	−	0.611995i
$15$		0			0
$16$	1.46769	−	4.51708i	0.366922	−	1.12927i
$17$	1.65283	+	1.20085i	0.400870	+	0.291249i	0.769895	−	0.638170i	$-0.220308\pi$
$17$	1.65283	+	1.20085i	0.400870	+	0.291249i	−0.369025	+	0.929419i	$0.620308\pi$
$18$	3.66361			0.863521
$19$	−5.01937	−	3.64678i	−1.15152	−	0.836630i	−0.162839	−	0.986653i	$-0.552065\pi$
$19$	−5.01937	−	3.64678i	−1.15152	−	0.836630i	−0.988682	+	0.150023i	$0.952065\pi$
$20$		0			0
$21$	1.66637	−	1.21069i	0.363632	−	0.264194i
$22$	10.7742	−	7.82789i	2.29706	−	1.66891i
$23$	0.598915	+	1.84327i	0.124882	+	0.384349i	0.993880	−	0.110468i	$-0.0352351\pi$
$23$	0.598915	+	1.84327i	0.124882	+	0.384349i	−0.868997	+	0.494817i	$0.835235\pi$
$24$	11.1164			2.26912
$25$		0			0
$26$	−4.94054			−0.968920
$27$	−0.993836	−	3.05871i	−0.191264	−	0.588650i
$28$	3.24530	−	2.35785i	0.613304	−	0.445591i
$29$	−3.89794	+	2.83202i	−0.723829	+	0.525893i	−0.887605	−	0.460605i	$-0.847632\pi$
$29$	−3.89794	+	2.83202i	−0.723829	+	0.525893i	0.163776	+	0.986498i	$0.447632\pi$
$30$		0			0
$31$	5.37199	+	3.90298i	0.964837	+	0.700995i	0.954269	−	0.298949i	$-0.0966360\pi$
$31$	5.37199	+	3.90298i	0.964837	+	0.700995i	0.0105683	+	0.999944i	$0.496636\pi$
$32$	1.24877			0.220754
$33$	9.21704	+	6.69657i	1.60448	+	1.16572i
$34$	−1.56212	+	4.80771i	−0.267901	+	0.824515i
$35$		0			0
$36$	1.88618	+	5.80506i	0.314363	+	0.967509i
$37$	−0.302501	+	0.931002i	−0.0497308	+	0.153056i	−0.972838	−	0.231487i	$-0.925641\pi$
$37$	−0.302501	+	0.931002i	−0.0497308	+	0.153056i	0.923107	+	0.384543i	$0.125641\pi$
$38$	4.74390	−	14.6002i	0.769562	−	2.36847i
$39$	−1.30607	−	4.01966i	−0.209138	−	0.643660i
$40$		0			0
$41$	0.844603	−	2.59942i	0.131905	−	0.405961i	−0.863191	−	0.504878i	$-0.831538\pi$
$41$	0.844603	−	2.59942i	0.131905	−	0.405961i	0.995096	+	0.0989163i	$0.0315376\pi$
$42$	4.12319	+	2.99567i	0.636222	+	0.462242i
$43$	3.99413			0.609100			0.304550	−	0.952496i	$-0.401494\pi$
$43$	3.99413			0.609100			0.304550	+	0.952496i	$0.401494\pi$
$44$	17.9504	+	13.0417i	2.70613	+	1.96612i
$45$		0			0
$46$	−3.87974	+	2.81879i	−0.572036	+	0.415609i
$47$	−5.83576	+	4.23993i	−0.851233	+	0.618457i	−0.925486	−	0.378783i	$-0.876343\pi$
$47$	−5.83576	+	4.23993i	−0.851233	+	0.618457i	0.0742528	+	0.997239i	$0.476343\pi$
$48$	3.10673	+	9.56153i	0.448418	+	1.38009i
$49$	−6.05313			−0.864734
$50$		0			0
$51$	−4.32454			−0.605557
$52$	−2.54359	−	7.82838i	−0.352733	−	1.08560i
$53$	−10.7393	+	7.80259i	−1.47516	+	1.07177i	−0.496085	+	0.868274i	$0.665230\pi$
$53$	−10.7393	+	7.80259i	−1.47516	+	1.07177i	−0.979076	+	0.203494i	$0.934770\pi$
$54$	6.43801	−	4.67749i	0.876102	−	0.636526i
$55$		0			0
$56$	4.13424	+	3.00370i	0.552461	+	0.401387i
$57$	13.1329			1.73950
$58$	−9.64488	−	7.00741i	−1.26643	−	0.920118i
$59$	2.02105	−	6.22014i	0.263118	−	0.809793i	−0.729003	−	0.684510i	$-0.760016\pi$
$59$	2.02105	−	6.22014i	0.263118	−	0.809793i	0.992121	−	0.125283i	$-0.0399839\pi$
$60$		0			0
$61$	0.842602	+	2.59326i	0.107884	+	0.332033i	0.990397	−	0.138256i	$-0.0441496\pi$
$61$	0.842602	+	2.59326i	0.107884	+	0.332033i	−0.882512	+	0.470289i	$0.844150\pi$
$62$	−5.07717	+	15.6259i	−0.644801	+	1.98449i
$63$	−0.445219	+	1.37024i	−0.0560923	+	0.172634i
$64$	−1.98054	−	6.09548i	−0.247568	−	0.761935i
$65$		0			0
$66$	−8.71120	+	26.8103i	−1.07227	+	3.30012i
$67$	−7.74195	−	5.62485i	−0.945829	−	0.687185i	0.00398757	−	0.999992i	$-0.498731\pi$
$67$	−7.74195	−	5.62485i	−0.945829	−	0.687185i	−0.949817	+	0.312807i	$0.898731\pi$
$68$	−8.42215			−1.02134
$69$	−3.31902	−	2.41141i	−0.399563	−	0.290300i
$70$		0			0
$71$	4.59943	−	3.34168i	0.545852	−	0.396584i	−0.280402	−	0.959883i	$-0.590468\pi$
$71$	4.59943	−	3.34168i	0.545852	−	0.396584i	0.826254	+	0.563298i	$0.190468\pi$
$72$	−6.29070	+	4.57046i	−0.741366	+	0.538634i
$73$	−2.89018	−	8.89505i	−0.338269	−	1.04109i	−0.965089	−	0.261922i	$-0.915644\pi$
$73$	−2.89018	−	8.89505i	−0.338269	−	1.04109i	0.626820	−	0.779164i	$-0.284356\pi$
$74$	−2.42218			−0.281572
$75$		0			0
$76$	25.5767			2.93385
$77$	1.61842	+	4.98098i	0.184436	+	0.567635i
$78$	8.46061	−	6.14700i	0.957976	−	0.696010i
$79$	2.57405	−	1.87016i	0.289604	−	0.210409i	−0.433492	−	0.901158i	$-0.642719\pi$
$79$	2.57405	−	1.87016i	0.289604	−	0.210409i	0.723095	+	0.690748i	$0.242719\pi$
$80$		0			0
$81$	9.10114	+	6.61236i	1.01124	+	0.734707i
$82$	6.76289			0.746836
$83$	−4.94623	−	3.59365i	−0.542919	−	0.394454i	0.282249	−	0.959341i	$-0.408920\pi$
$83$	−4.94623	−	3.59365i	−0.542919	−	0.394454i	−0.825168	+	0.564887i	$0.808920\pi$
$84$	−2.62391	+	8.07556i	−0.286292	+	0.881116i
$85$		0			0
$86$	3.05398	+	9.39919i	0.329319	+	1.01354i
$87$	3.15159	−	9.69959i	0.337886	−	1.03991i
$88$	−8.73455	+	26.8822i	−0.931106	+	2.86565i
$89$	−0.929346	−	2.86023i	−0.0985105	−	0.303184i	0.889642	−	0.456658i	$-0.150954\pi$
$89$	−0.929346	−	2.86023i	−0.0985105	−	0.303184i	−0.988153	+	0.153474i	$0.950954\pi$
$90$		0			0
$91$	0.600398	−	1.84784i	0.0629388	−	0.193706i
$92$	−6.46388	−	4.69629i	−0.673906	−	0.489622i
$93$	−14.0555			−1.45749
$94$	−14.4397	−	10.4911i	−1.48934	−	1.08207i
$95$		0			0
$96$	−2.13851	+	1.55372i	−0.218261	+	0.158576i
$97$	−4.81791	+	3.50042i	−0.489185	+	0.355413i	−0.804871	−	0.593450i	$-0.797765\pi$
$97$	−4.81791	+	3.50042i	−0.489185	+	0.355413i	0.315686	+	0.948864i	$0.397765\pi$
$98$	−4.62833	−	14.2445i	−0.467532	−	1.43892i
$99$	−7.96914			−0.800929
$100$		0			0
$101$	−7.77373			−0.773515			−0.386758	−	0.922181i	$-0.626405\pi$
$101$	−7.77373			−0.773515			−0.386758	+	0.922181i	$0.626405\pi$
$102$	−3.30662	−	10.1767i	−0.327404	−	1.00765i
$103$	−4.00509	+	2.90987i	−0.394633	+	0.286718i	−0.767351	−	0.641227i	$-0.778426\pi$
$103$	−4.00509	+	2.90987i	−0.394633	+	0.286718i	0.372718	+	0.927945i	$0.378426\pi$
$104$	8.48329	−	6.16347i	0.831855	−	0.604378i
$105$		0			0
$106$	−26.5729	−	19.3064i	−2.58099	−	1.87520i
$107$	1.16798			0.112913			0.0564567	−	0.998405i	$-0.482020\pi$
$107$	1.16798			0.112913			0.0564567	+	0.998405i	$0.482020\pi$
$108$	10.7261	+	7.79298i	1.03212	+	0.749880i
$109$	−5.46588	+	16.8222i	−0.523536	+	1.61128i	0.243657	+	0.969862i	$0.421653\pi$
$109$	−5.46588	+	16.8222i	−0.523536	+	1.61128i	−0.767193	+	0.641417i	$0.778347\pi$
$110$		0			0
$111$	−0.640319	−	1.97070i	−0.0607764	−	0.187050i
$112$	−1.42816	+	4.39543i	−0.134949	+	0.415329i
$113$	1.55634	−	4.78993i	0.146408	−	0.450598i	−0.850781	−	0.525520i	$-0.823871\pi$
$113$	1.55634	−	4.78993i	0.146408	−	0.450598i	0.997189	+	0.0749218i	$0.0238707\pi$
$114$	10.0417	+	30.9050i	0.940487	+	2.89452i
$115$		0			0
$116$	6.13780	−	18.8902i	0.569880	−	1.75391i
$117$	2.39176	+	1.73772i	0.221118	+	0.160652i
$118$	16.1829			1.48975
$119$	−1.60832	−	1.16851i	−0.147434	−	0.107117i
$120$		0			0
$121$	−14.5369	+	10.5617i	−1.32154	+	0.960156i
$122$	−5.45833	+	3.96571i	−0.494174	+	0.359038i
$123$	1.78781	+	5.50233i	0.161202	+	0.496128i
$124$	−27.3735			−2.45821
$125$		0			0
$126$	−3.56495			−0.317591
$127$	2.40866	+	7.41308i	0.213734	+	0.657804i	0.999241	+	0.0389522i	$0.0124020\pi$
$127$	2.40866	+	7.41308i	0.213734	+	0.657804i	−0.785507	+	0.618852i	$0.787598\pi$
$128$	14.8504	−	10.7894i	1.31260	−	0.953661i
$129$	−6.83990	+	4.96948i	−0.602220	+	0.437538i
$130$		0			0
$131$	7.92040	+	5.75451i	0.692008	+	0.502774i	0.877320	−	0.479906i	$-0.159329\pi$
$131$	7.92040	+	5.75451i	0.692008	+	0.502774i	−0.185311	+	0.982680i	$0.559329\pi$
$132$	−46.9663			−4.08789
$133$	4.88420	+	3.54858i	0.423513	+	0.307701i
$134$	7.31706	−	22.5196i	0.632098	−	1.94540i
$135$		0			0
$136$	−3.31548	−	10.2040i	−0.284300	−	0.874986i
$137$	−1.12274	+	3.45544i	−0.0959222	+	0.295218i	−0.987493	−	0.157663i	$-0.949604\pi$
$137$	−1.12274	+	3.45544i	−0.0959222	+	0.295218i	0.891571	+	0.452881i	$0.149604\pi$
$138$	3.13687	−	9.65430i	0.267028	−	0.821829i
$139$	−0.575015	−	1.76971i	−0.0487721	−	0.150105i	0.923704	−	0.383106i	$-0.125146\pi$
$139$	−0.575015	−	1.76971i	−0.0487721	−	0.150105i	−0.972477	+	0.233001i	$0.925146\pi$
$140$		0			0
$141$	4.71837	−	14.5216i	0.397358	−	1.22294i
$142$	11.3806	+	8.26850i	0.955039	+	0.693877i
$143$	10.7467			0.898688
$144$	−5.68927	−	4.13349i	−0.474106	−	0.344458i
$145$		0			0
$146$	18.7224	−	13.6026i	1.54948	−	1.12576i
$147$	10.3659	−	7.53128i	0.854966	−	0.621169i
$148$	−1.24704	−	3.83799i	−0.102506	−	0.315480i
$149$	16.8530			1.38066			0.690328	−	0.723497i	$-0.257466\pi$
$149$	16.8530			1.38066			0.690328	+	0.723497i	$0.257466\pi$
$150$		0			0
$151$	−14.3201			−1.16536			−0.582678	−	0.812703i	$-0.697995\pi$
$151$	−14.3201			−1.16536			−0.582678	+	0.812703i	$0.697995\pi$
$152$	10.0686	+	30.9879i	0.816669	+	2.51345i
$153$	2.44723	−	1.77802i	0.197847	−	0.143744i
$154$	−10.4840	+	7.61708i	−0.844826	+	0.613802i
$155$		0			0
$156$	14.0959	+	10.2413i	1.12858	+	0.819958i
$157$	−21.6869			−1.73080			−0.865400	−	0.501081i	$-0.832936\pi$
$157$	−21.6869			−1.73080			−0.865400	+	0.501081i	$0.832936\pi$
$158$	6.36912	+	4.62744i	0.506700	+	0.368139i
$159$	8.68304	−	26.7237i	0.688610	−	2.11932i
$160$		0			0
$161$	−0.582786	−	1.79363i	−0.0459300	−	0.141358i
$162$	−8.60166	+	26.4732i	−0.675810	+	2.07993i
$163$	−6.09412	+	18.7558i	−0.477329	+	1.46907i	0.365463	+	0.930826i	$0.380911\pi$
$163$	−6.09412	+	18.7558i	−0.477329	+	1.46907i	−0.842791	+	0.538240i	$0.819089\pi$
$164$	3.48181	+	10.7159i	0.271884	+	0.836773i
$165$		0			0
$166$	4.67477	−	14.3875i	0.362833	−	1.11668i
$167$	−4.91839	−	3.57342i	−0.380597	−	0.276520i	0.380995	−	0.924577i	$-0.375582\pi$
$167$	−4.91839	−	3.57342i	−0.380597	−	0.276520i	−0.761591	+	0.648057i	$0.775582\pi$
$168$	−10.8170			−0.834552
$169$	7.29182	+	5.29782i	0.560909	+	0.407525i
$170$		0			0
$171$	−7.43184	+	5.39955i	−0.568327	+	0.412914i
$172$	−13.3209	+	9.67819i	−1.01571	+	0.737955i
$173$	4.64480	+	14.2952i	0.353137	+	1.08684i	0.957082	+	0.289818i	$0.0935949\pi$
$173$	4.64480	+	14.2952i	0.353137	+	1.08684i	−0.603944	+	0.797027i	$0.706405\pi$
$174$	25.2353			1.91308
$175$		0			0
$176$	−25.5632			−1.92690
$177$	4.27805	+	13.1665i	0.321558	+	0.989654i
$178$	6.02025	−	4.37397i	0.451237	−	0.327843i
$179$	16.1939	−	11.7655i	1.21039	−	0.879397i	0.215120	−	0.976588i	$-0.430986\pi$
$179$	16.1939	−	11.7655i	1.21039	−	0.879397i	0.995266	+	0.0971905i	$0.0309856\pi$
$180$		0			0
$181$	−16.4225	−	11.9316i	−1.22067	−	0.886871i	−0.224517	−	0.974470i	$-0.572080\pi$
$181$	−16.4225	−	11.9316i	−1.22067	−	0.886871i	−0.996156	+	0.0875995i	$0.972080\pi$
$182$	4.80749			0.356355
$183$	−4.66947	−	3.39257i	−0.345177	−	0.250786i
$184$	3.14528	−	9.68018i	0.231873	−	0.713632i
$185$		0			0
$186$	−10.7471	−	33.0762i	−0.788015	−	2.42526i
$187$	3.39795	−	10.4578i	0.248483	−	0.764751i
$188$	9.18914	−	28.2813i	0.670187	−	2.06262i
$189$	0.967072	+	2.97634i	0.0703441	+	0.216497i
$190$		0			0
$191$	−2.92850	+	9.01298i	−0.211898	+	0.652156i	0.787461	+	0.616365i	$0.211395\pi$
$191$	−2.92850	+	9.01298i	−0.211898	+	0.652156i	−0.999359	+	0.0357917i	$0.988605\pi$
$192$	10.9756	+	7.97425i	0.792097	+	0.575492i
$193$	2.72478			0.196134			0.0980671	−	0.995180i	$-0.468734\pi$
$193$	2.72478			0.196134			0.0980671	+	0.995180i	$0.468734\pi$
$194$	−11.9212	−	8.66127i	−0.855893	−	0.621843i
$195$		0			0
$196$	20.1879	−	14.6674i	1.44199	−	1.04767i
$197$	−0.631062	+	0.458494i	−0.0449613	+	0.0326663i	−0.610039	−	0.792371i	$-0.708846\pi$
$197$	−0.631062	+	0.458494i	−0.0449613	+	0.0326663i	0.565078	+	0.825038i	$0.308846\pi$
$198$	−6.09334	−	18.7534i	−0.433035	−	1.33274i
$199$	−7.42526			−0.526363			−0.263181	−	0.964746i	$-0.584772\pi$
$199$	−7.42526			−0.526363			−0.263181	+	0.964746i	$0.584772\pi$
$200$		0			0
$201$	20.2564			1.42878
$202$	−5.94393	−	18.2935i	−0.418214	−	1.28713i
$203$	3.79297	−	2.75575i	0.266214	−	0.193416i
$204$	14.4228	−	10.4788i	1.00980	−	0.733662i
$205$		0			0
$206$	−9.91001	−	7.20004i	−0.690463	−	0.501651i
$207$	2.86966			0.199455
$208$	7.67223	+	5.57420i	0.531974	+	0.386501i
$209$	−10.3190	+	31.7586i	−0.713781	+	2.19679i
$210$		0			0
$211$	−0.921266	−	2.83536i	−0.0634226	−	0.195195i	0.914324	−	0.404983i	$-0.132723\pi$
$211$	−0.921266	−	2.83536i	−0.0634226	−	0.195195i	−0.977747	+	0.209788i	$0.932723\pi$
$212$	16.9104	−	52.0450i	1.16141	−	3.57446i
$213$	−3.71876	+	11.4452i	−0.254805	+	0.784210i
$214$	0.893061	+	2.74856i	0.0610484	+	0.187888i
$215$		0			0
$216$	−5.21926	+	16.0632i	−0.355126	+	1.09296i
$217$	−5.22732	−	3.79787i	−0.354854	−	0.257816i
$218$	−43.7662			−2.96422
$219$	16.0166	+	11.6367i	1.08230	+	0.786336i
$220$		0			0
$221$	−3.30020	+	2.39774i	−0.221996	+	0.161289i
$222$	4.14795	−	3.01366i	0.278392	−	0.202264i
$223$	7.68589	+	23.6547i	0.514685	+	1.58404i	0.783854	+	0.620945i	$0.213251\pi$
$223$	7.68589	+	23.6547i	0.514685	+	1.58404i	−0.269169	+	0.963093i	$0.586749\pi$
$224$	−1.21514			−0.0811903
$225$		0			0
$226$	12.4619			0.828953
$227$	−5.42615	−	16.7000i	−0.360146	−	1.10842i	−0.952965	−	0.303080i	$-0.901985\pi$
$227$	−5.42615	−	16.7000i	−0.360146	−	1.10842i	0.592819	−	0.805336i	$-0.298015\pi$
$228$	−43.7997	+	31.8224i	−2.90071	+	2.10749i
$229$	−5.67808	+	4.12537i	−0.375218	+	0.272612i	−0.759371	−	0.650657i	$-0.774493\pi$
$229$	−5.67808	+	4.12537i	−0.375218	+	0.272612i	0.384153	+	0.923269i	$0.374493\pi$
$230$		0			0
$231$	−8.96883	−	6.51623i	−0.590105	−	0.428737i
$232$	25.3030			1.66122
$233$	7.03138	+	5.10860i	0.460641	+	0.334675i	0.793783	−	0.608202i	$-0.208109\pi$
$233$	7.03138	+	5.10860i	0.460641	+	0.334675i	−0.333142	+	0.942877i	$0.608109\pi$
$234$	−2.26050	+	6.95710i	−0.147773	+	0.454800i
$235$		0			0
$236$	8.33161	+	25.6421i	0.542342	+	1.66916i
$237$	−2.08119	+	6.40525i	−0.135188	+	0.416066i
$238$	1.52005	−	4.67824i	0.0985303	−	0.303245i
$239$	6.59536	+	20.2984i	0.426618	+	1.31300i	0.901436	+	0.432912i	$0.142514\pi$
$239$	6.59536	+	20.2984i	0.426618	+	1.31300i	−0.474818	+	0.880084i	$0.657486\pi$
$240$		0			0
$241$	−6.60978	+	20.3428i	−0.425774	+	1.31040i	0.476478	+	0.879186i	$0.341913\pi$
$241$	−6.60978	+	20.3428i	−0.425774	+	1.31040i	−0.902252	+	0.431210i	$0.858087\pi$
$242$	−35.9696	−	26.1334i	−2.31221	−	1.67992i
$243$	−14.1643			−0.908639
$244$	−9.09391	−	6.60711i	−0.582178	−	0.422977i
$245$		0			0
$246$	−11.5814	+	8.41435i	−0.738400	+	0.536479i
$247$	10.0222	−	7.28153i	0.637695	−	0.463313i
$248$	−10.7759	−	33.1648i	−0.684271	−	2.10597i
$249$	12.9415			0.820137
$250$		0			0
$251$	14.9016			0.940580			0.470290	−	0.882512i	$-0.344149\pi$
$251$	14.9016			0.940580			0.470290	+	0.882512i	$0.344149\pi$
$252$	−1.83538	−	5.64873i	−0.115618	−	0.355836i
$253$	8.43927	−	6.13149i	0.530572	−	0.385483i
$254$	−15.6031	+	11.3363i	−0.979027	+	0.711305i
$255$		0			0
$256$	26.3749	+	19.1625i	1.64843	+	1.19765i
$257$	19.0689			1.18948			0.594741	−	0.803917i	$-0.297254\pi$
$257$	19.0689			1.18948			0.594741	+	0.803917i	$0.297254\pi$
$258$	−16.9243	−	12.2962i	−1.05366	−	0.765531i
$259$	0.294355	−	0.905930i	0.0182903	−	0.0562918i
$260$		0			0
$261$	2.20448	+	6.78471i	0.136454	+	0.419963i
$262$	−7.48572	+	23.0387i	−0.462469	+	1.42333i
$263$	−2.09619	+	6.45141i	−0.129257	+	0.397811i	−0.994653	−	0.103278i	$-0.967067\pi$
$263$	−2.09619	+	6.45141i	−0.129257	+	0.397811i	0.865396	+	0.501089i	$0.167067\pi$
$264$	−18.4889	−	56.9029i	−1.13791	−	3.50213i
$265$		0			0
$266$	−4.61615	+	14.2070i	−0.283034	+	0.871089i
$267$	5.15018	+	3.74183i	0.315186	+	0.228996i
$268$	39.4498			2.40978
$269$	−0.400191	−	0.290755i	−0.0244000	−	0.0177277i	0.575518	−	0.817789i	$-0.304800\pi$
$269$	−0.400191	−	0.290755i	−0.0244000	−	0.0177277i	−0.599918	+	0.800061i	$0.704800\pi$
$270$		0			0
$271$	−7.94948	+	5.77563i	−0.482896	+	0.350845i	−0.802446	−	0.596725i	$-0.796468\pi$
$271$	−7.94948	+	5.77563i	−0.482896	+	0.350845i	0.319550	+	0.947570i	$0.396468\pi$
$272$	7.85017	−	5.70348i	0.475986	−	0.345824i
$273$	1.27089	+	3.91141i	0.0769179	+	0.236729i
$274$	−8.98998			−0.543104
$275$		0			0
$276$	16.9124			1.01801
$277$	7.76865	+	23.9095i	0.466773	+	1.43658i	0.856739	+	0.515751i	$0.172487\pi$
$277$	7.76865	+	23.9095i	0.466773	+	1.43658i	−0.389966	+	0.920829i	$0.627513\pi$
$278$	3.72491	−	2.70631i	0.223405	−	0.162314i
$279$	7.95394	−	5.77888i	0.476190	−	0.345972i
$280$		0			0
$281$	6.28647	+	4.56738i	0.375019	+	0.272467i	0.759289	−	0.650753i	$-0.225547\pi$
$281$	6.28647	+	4.56738i	0.375019	+	0.272467i	−0.384270	+	0.923221i	$0.625547\pi$
$282$	37.7808			2.24981
$283$	−23.4305	−	17.0233i	−1.39280	−	1.01193i	−0.995552	−	0.0942184i	$-0.969965\pi$
$283$	−23.4305	−	17.0233i	−1.39280	−	1.01193i	−0.397249	−	0.917711i	$-0.630035\pi$
$284$	−7.24238	+	22.2897i	−0.429756	+	1.32265i
$285$		0			0
$286$	8.21715	+	25.2898i	0.485890	+	1.49542i
$287$	−0.821858	+	2.52942i	−0.0485127	+	0.149307i
$288$	0.571365	−	1.75848i	0.0336680	−	0.103619i
$289$	−3.96349	−	12.1984i	−0.233146	−	0.717551i
$290$		0			0
$291$	3.89541	−	11.9888i	0.228353	−	0.702798i
$292$	31.1927	+	22.6628i	1.82541	+	1.32624i
$293$	−0.154329			−0.00901602			−0.00450801	−	0.999990i	$-0.501435\pi$
$293$	−0.154329			−0.00901602			−0.00450801	+	0.999990i	$0.501435\pi$
$294$	25.6489	+	18.6350i	1.49588	+	1.08682i
$295$		0			0
$296$	4.15907	−	3.02174i	0.241741	−	0.175635i
$297$	−14.0041	+	10.1746i	−0.812598	+	0.590387i
$298$	12.8861	+	39.6594i	0.746473	+	2.29741i
$299$	−3.86987			−0.223800
$300$		0			0
$301$	−3.88657			−0.224018
$302$	−10.9494	−	33.6988i	−0.630068	−	1.93915i
$303$	13.3124	−	9.67204i	0.764778	−	0.555644i
$304$	−23.8397	+	17.3205i	−1.36730	+	0.993401i
$305$		0			0
$306$	6.05532	+	4.39945i	0.346159	+	0.251500i
$307$	−14.4875			−0.826845			−0.413423	−	0.910539i	$-0.635667\pi$
$307$	−14.4875			−0.826845			−0.413423	+	0.910539i	$0.635667\pi$
$308$	−17.4670	−	12.6905i	−0.995275	−	0.723110i
$309$	3.23822	−	9.96622i	0.184216	−	0.566959i
$310$		0			0
$311$	5.72870	+	17.6311i	0.324845	+	0.999770i	0.971511	+	0.236996i	$0.0761629\pi$
$311$	5.72870	+	17.6311i	0.324845	+	0.999770i	−0.646666	+	0.762774i	$0.723837\pi$
$312$	−6.85897	+	21.1097i	−0.388313	+	1.19510i
$313$	2.11894	−	6.52142i	0.119769	−	0.368612i	−0.873142	−	0.487465i	$-0.837922\pi$
$313$	2.11894	−	6.52142i	0.119769	−	0.368612i	0.992912	+	0.118853i	$0.0379216\pi$
$314$	−16.5822	−	51.0346i	−0.935785	−	2.88005i
$315$		0			0
$316$	−4.05317	+	12.4744i	−0.228009	+	0.701739i
$317$	22.0708	+	16.0354i	1.23962	+	0.900636i	0.997573	−	0.0696285i	$-0.0221814\pi$
$317$	22.0708	+	16.0354i	1.23962	+	0.900636i	0.242046	+	0.970265i	$0.422181\pi$
$318$	69.5266			3.89886
$319$	20.9797	+	15.2426i	1.17464	+	0.853424i
$320$		0			0
$321$	−2.00016	+	1.45320i	−0.111638	+	0.0811098i
$322$	3.77526	−	2.74288i	0.210387	−	0.152855i
$323$	−3.91691	−	12.0550i	−0.217943	−	0.670759i
$324$	−46.3757			−2.57643
$325$		0			0
$326$	−48.7967			−2.70260
$327$	−11.5699	−	35.6085i	−0.639817	−	1.96915i
$328$	−11.6124	+	8.43690i	−0.641188	+	0.465850i
$329$	5.67860	−	4.12575i	0.313071	−	0.227460i
$330$		0			0
$331$	10.5519	+	7.66641i	0.579985	+	0.421384i	0.838719	−	0.544565i	$-0.183305\pi$
$331$	10.5519	+	7.66641i	0.579985	+	0.421384i	−0.258734	+	0.965949i	$0.583305\pi$
$332$	25.2040			1.38325
$333$	1.17260	+	0.851943i	0.0642580	+	0.0466862i
$334$	4.64847	−	14.3065i	0.254353	−	0.782818i
$335$		0			0
$336$	−3.02306	−	9.30404i	−0.164922	−	0.507577i
$337$	−6.07241	+	18.6890i	−0.330785	+	1.01805i	0.637976	+	0.770056i	$0.279772\pi$
$337$	−6.07241	+	18.6890i	−0.330785	+	1.01805i	−0.968761	+	0.247996i	$0.920228\pi$
$338$	−6.89164	+	21.2103i	−0.374856	+	1.15369i
$339$	3.29439	+	10.1391i	0.178927	+	0.550679i
$340$		0			0
$341$	11.0439	−	33.9897i	0.598063	−	1.84065i
$342$	−18.3890	−	13.3604i	−0.994363	−	0.722447i
$343$	12.7016			0.685823
$344$	−16.9697	−	12.3292i	−0.914945	−	0.664746i
$345$		0			0
$346$	−30.0887	+	21.8607i	−1.61758	+	1.17524i
$347$	−3.55112	+	2.58004i	−0.190634	+	0.138504i	−0.679008	−	0.734130i	$-0.737590\pi$
$347$	−3.55112	+	2.58004i	−0.190634	+	0.138504i	0.488374	+	0.872634i	$0.337590\pi$
$348$	12.9922	+	39.9858i	0.696454	+	2.14347i
$349$	27.1955			1.45574			0.727872	−	0.685713i	$-0.240510\pi$
$349$	27.1955			1.45574			0.727872	+	0.685713i	$0.240510\pi$
$350$		0			0
$351$	6.42163			0.342761
$352$	−2.07697	−	6.39226i	−0.110703	−	0.340709i
$353$	12.8890	−	9.36443i	0.686014	−	0.498418i	−0.189334	−	0.981913i	$-0.560633\pi$
$353$	12.8890	−	9.36443i	0.686014	−	0.498418i	0.875347	+	0.483495i	$0.160633\pi$
$354$	−27.7130	+	20.1346i	−1.47293	+	1.07014i
$355$		0			0
$356$	10.0301	+	7.28730i	0.531595	+	0.386226i
$357$	4.20808			0.222715
$358$	40.0693	+	29.1121i	2.11773	+	1.53862i
$359$	−1.54974	+	4.76962i	−0.0817923	+	0.251731i	−0.983587	−	0.180433i	$-0.942250\pi$
$359$	−1.54974	+	4.76962i	−0.0817923	+	0.251731i	0.901795	+	0.432164i	$0.142250\pi$
$360$		0			0
$361$	6.02369	+	18.5390i	0.317036	+	0.975738i
$362$	15.5212	−	47.7693i	0.815776	−	2.51070i
$363$	11.7535	−	36.1736i	0.616899	−	1.89862i
$364$	2.47510	+	7.61756i	0.129730	+	0.399269i
$365$		0			0
$366$	4.41321	−	13.5824i	0.230682	−	0.709966i
$367$	−22.9493	−	16.6736i	−1.19794	−	0.870357i	−0.203862	−	0.979000i	$-0.565349\pi$
$367$	−22.9493	−	16.6736i	−1.19794	−	0.870357i	−0.994081	+	0.108643i	$0.965349\pi$
$368$	9.20522			0.479855
$369$	−3.27397	−	2.37868i	−0.170436	−	0.123829i
$370$		0			0
$371$	10.4501	−	7.59246i	0.542544	−	0.394181i
$372$	46.8767	−	34.0579i	2.43045	−	1.76582i
$373$	−10.1116	−	31.1203i	−0.523558	−	1.61135i	−0.767149	−	0.641469i	$-0.778325\pi$
$373$	−10.1116	−	31.1203i	−0.523558	−	1.61135i	0.243590	−	0.969878i	$-0.421675\pi$
$374$	27.2080			1.40689
$375$		0			0
$376$	37.8821			1.95362
$377$	−2.97285	−	9.14948i	−0.153109	−	0.471222i
$378$	−6.26464	+	4.55152i	−0.322218	+	0.234105i
$379$	−3.62830	+	2.63612i	−0.186373	+	0.135408i	−0.677060	−	0.735928i	$-0.736746\pi$
$379$	−3.62830	+	2.63612i	−0.186373	+	0.135408i	0.490686	+	0.871336i	$0.336746\pi$
$380$		0			0
$381$	−13.3481	−	9.69797i	−0.683844	−	0.496842i
$382$	−23.4490			−1.19975
$383$	−13.1740	−	9.57144i	−0.673158	−	0.489078i	0.197923	−	0.980218i	$-0.436580\pi$
$383$	−13.1740	−	9.57144i	−0.673158	−	0.489078i	−0.871081	+	0.491140i	$0.836580\pi$
$384$	−12.0069	+	36.9535i	−0.612726	+	1.88578i
$385$		0			0
$386$	2.08342	+	6.41210i	0.106043	+	0.326367i
$387$	1.82748	−	5.62440i	0.0928960	−	0.285904i
$388$	7.58641	−	23.3486i	0.385141	−	1.18534i
$389$	6.64075	+	20.4381i	0.336699	+	1.03625i	0.965879	+	0.258994i	$0.0833910\pi$
$389$	6.64075	+	20.4381i	0.336699	+	1.03625i	−0.629180	+	0.777260i	$0.716609\pi$
$390$		0			0
$391$	−1.22359	+	3.76582i	−0.0618796	+	0.190446i
$392$	25.7177	+	18.6850i	1.29894	+	0.943735i
$393$	−20.7233			−1.04535
$394$	−1.56147	−	1.13448i	−0.0786658	−	0.0571540i
$395$		0			0
$396$	26.5780	−	19.3100i	1.33559	−	0.970366i
$397$	16.8980	−	12.2771i	0.848084	−	0.616169i	−0.0765330	−	0.997067i	$-0.524385\pi$
$397$	16.8980	−	12.2771i	0.848084	−	0.616169i	0.924617	+	0.380898i	$0.124385\pi$
$398$	−5.67748	−	17.4735i	−0.284586	−	0.875867i
$399$	−12.7792			−0.639762
$400$		0			0
$401$	−0.633423			−0.0316316			−0.0158158	−	0.999875i	$-0.505035\pi$
$401$	−0.633423			−0.0316316			−0.0158158	+	0.999875i	$0.505035\pi$
$402$	15.4884	+	47.6684i	0.772491	+	2.37748i
$403$	−10.7262	+	7.79307i	−0.534312	+	0.388201i
$404$	25.9263	−	18.8365i	1.28988	−	0.937153i
$405$		0			0
$406$	9.38514	+	6.81870i	0.465777	+	0.338407i
$407$	5.26876			0.261163
$408$	18.3735	+	13.3491i	0.909623	+	0.660880i
$409$	−1.32822	+	4.08785i	−0.0656765	+	0.202131i	−0.978510	−	0.206202i	$-0.933890\pi$
$409$	−1.32822	+	4.08785i	−0.0656765	+	0.202131i	0.912833	+	0.408333i	$0.133890\pi$
$410$		0			0
$411$	−2.37656	−	7.31430i	−0.117227	−	0.360788i
$412$	6.30652	−	19.4095i	0.310700	−	0.956236i
$413$	−1.96662	+	6.05263i	−0.0967710	+	0.297831i
$414$	2.19419	+	6.75303i	0.107839	+	0.331893i
$415$		0			0
$416$	−0.770512	+	2.37139i	−0.0377774	+	0.116267i
$417$	3.18657	+	2.31518i	0.156047	+	0.113375i
$418$	−82.6261			−4.04137
$419$	−27.2003	−	19.7622i	−1.32882	−	0.965447i	−0.999777	−	0.0211337i	$-0.993272\pi$
$419$	−27.2003	−	19.7622i	−1.32882	−	0.965447i	−0.329047	−	0.944313i	$-0.606728\pi$
$420$		0			0
$421$	17.2942	−	12.5650i	0.842867	−	0.612379i	−0.0803031	−	0.996770i	$-0.525589\pi$
$421$	17.2942	−	12.5650i	0.842867	−	0.612379i	0.923170	+	0.384392i	$0.125589\pi$
$422$	5.96791	−	4.33594i	0.290513	−	0.211070i
$423$	3.30042	+	10.1577i	0.160472	+	0.493882i
$424$	69.7130			3.38556
$425$		0			0
$426$	−29.7768			−1.44269
$427$	−0.819911	−	2.52343i	−0.0396783	−	0.122117i
$428$	−3.89536	+	2.83014i	−0.188289	+	0.136800i
$429$	−18.4037	+	13.3710i	−0.888537	+	0.645560i
$430$		0			0
$431$	−21.1077	−	15.3356i	−1.01672	−	0.738690i	−0.0511120	−	0.998693i	$-0.516277\pi$
$431$	−21.1077	−	15.3356i	−1.01672	−	0.738690i	−0.965608	+	0.260003i	$0.916277\pi$
$432$	−15.2751			−0.734923
$433$	−9.52016	−	6.91680i	−0.457510	−	0.332400i	0.335044	−	0.942203i	$-0.391249\pi$
$433$	−9.52016	−	6.91680i	−0.457510	−	0.332400i	−0.792554	+	0.609802i	$0.791249\pi$
$434$	4.94044	−	15.2051i	0.237149	−	0.729868i
$435$		0			0
$436$	−22.5327	−	69.3484i	−1.07912	−	3.32119i
$437$	3.71584	−	11.4362i	0.177753	−	0.547066i
$438$	−15.1376	+	46.5886i	−0.723300	+	2.22609i
$439$	1.52213	+	4.68464i	0.0726473	+	0.223586i	0.980787	−	0.195082i	$-0.0624973\pi$
$439$	1.52213	+	4.68464i	0.0726473	+	0.223586i	−0.908140	+	0.418667i	$0.862497\pi$
$440$		0			0
$441$	−2.76956	+	8.52382i	−0.131884	+	0.405896i
$442$	−8.16587	−	5.93285i	−0.388411	−	0.282197i
$443$	9.35961			0.444689			0.222344	−	0.974968i	$-0.428629\pi$
$443$	9.35961			0.444689			0.222344	+	0.974968i	$0.428629\pi$
$444$	6.91074	+	5.02094i	0.327969	+	0.238283i
$445$		0			0
$446$	−49.7887	+	36.1736i	−2.35756	+	1.71287i
$447$	−28.8606	+	20.9685i	−1.36506	+	0.991775i
$448$	1.92720	+	5.93133i	0.0910519	+	0.280229i
$449$	7.41602			0.349983			0.174992	−	0.984570i	$-0.444010\pi$
$449$	7.41602			0.349983			0.174992	+	0.984570i	$0.444010\pi$
$450$		0			0
$451$	−14.7107			−0.692702
$452$	6.41590	+	19.7461i	0.301779	+	0.928779i
$453$	24.5230	−	17.8170i	1.15219	−	0.837117i
$454$	35.1503	−	25.5382i	1.64968	−	1.19857i
$455$		0			0
$456$	−55.7972	−	40.5391i	−2.61295	−	1.89842i
$457$	8.79714			0.411513			0.205756	−	0.978603i	$-0.434035\pi$
$457$	8.79714			0.411513			0.205756	+	0.978603i	$0.434035\pi$
$458$	−14.0496	−	10.2076i	−0.656493	−	0.476970i
$459$	2.03042	−	6.24898i	0.0947717	−	0.291677i
$460$		0			0
$461$	−13.0259	−	40.0895i	−0.606675	−	1.86715i	−0.484836	−	0.874605i	$-0.661121\pi$
$461$	−13.0259	−	40.0895i	−0.606675	−	1.86715i	−0.121840	−	0.992550i	$-0.538879\pi$
$462$	8.47661	−	26.0883i	0.394367	−	1.21374i
$463$	7.12485	−	21.9280i	0.331120	−	1.01908i	−0.637482	−	0.770465i	$-0.720024\pi$
$463$	7.12485	−	21.9280i	0.331120	−	1.01908i	0.968602	−	0.248617i	$-0.0799761\pi$
$464$	7.07149	+	21.7638i	0.328286	+	1.01036i
$465$		0			0
$466$	−6.64549	+	20.4527i	−0.307846	+	0.947454i
$467$	−3.54321	−	2.57429i	−0.163960	−	0.119124i	0.502780	−	0.864415i	$-0.332311\pi$
$467$	−3.54321	−	2.57429i	−0.163960	−	0.119124i	−0.666740	+	0.745291i	$0.732311\pi$
$468$	−12.1875			−0.563365
$469$	7.53345	+	5.47338i	0.347863	+	0.252737i
$470$		0			0
$471$	37.1385	−	26.9827i	1.71125	−	1.24330i
$472$	−27.7872	+	20.1886i	−1.27901	+	0.929256i
$473$	−6.64307	−	20.4453i	−0.305449	−	0.940075i
$474$	−16.6645			−0.765424
$475$		0			0
$476$	8.19534			0.375633
$477$	6.07365	+	18.6928i	0.278093	+	0.855883i
$478$	−42.7243	+	31.0410i	−1.95417	+	1.41978i
$479$	−11.4810	+	8.34144i	−0.524581	+	0.381130i	−0.818327	−	0.574753i	$-0.805098\pi$
$479$	−11.4810	+	8.34144i	−0.524581	+	0.381130i	0.293746	+	0.955883i	$0.405098\pi$
$480$		0			0
$481$	−1.58130	−	1.14888i	−0.0721011	−	0.0523846i
$482$	−52.9257			−2.41070
$483$	3.22964	+	2.34647i	0.146954	+	0.106768i
$484$	22.8903	−	70.4490i	1.04047	−	3.20223i
$485$		0			0
$486$	−10.8303	−	33.3321i	−0.491270	−	1.51198i
$487$	6.81980	−	20.9892i	0.309035	−	0.951111i	−0.669106	−	0.743167i	$-0.733323\pi$
$487$	6.81980	−	20.9892i	0.309035	−	0.951111i	0.978141	−	0.207944i	$-0.0666773\pi$
$488$	4.42504	−	13.6189i	0.200312	−	0.616497i
$489$	−12.8997	−	39.7013i	−0.583346	−	1.79536i
$490$		0			0
$491$	−2.45886	+	7.56759i	−0.110967	+	0.341521i	−0.991084	−	0.133235i	$-0.957464\pi$
$491$	−2.45886	+	7.56759i	−0.110967	+	0.341521i	0.880118	+	0.474756i	$0.157464\pi$
$492$	−19.2952	−	14.0188i	−0.869897	−	0.632017i
$493$	−9.84345			−0.443327
$494$	24.7984	+	18.0171i	1.11573	+	0.810627i
$495$		0			0
$496$	25.5145	−	18.5373i	1.14563	−	0.832351i
$497$	−4.47556	+	3.25169i	−0.200757	+	0.145858i
$498$	9.89533	+	30.4547i	0.443420	+	1.36471i
$499$	−4.09384			−0.183266			−0.0916328	−	0.995793i	$-0.529209\pi$
$499$	−4.09384			−0.183266			−0.0916328	+	0.995793i	$0.529209\pi$
$500$		0			0
$501$	12.8687			0.574932
$502$	11.3940	+	35.0672i	0.508540	+	1.56512i
$503$	−21.8074	+	15.8440i	−0.972344	+	0.706449i	−0.955985	−	0.293417i	$-0.905208\pi$
$503$	−21.8074	+	15.8440i	−0.972344	+	0.706449i	−0.0163592	+	0.999866i	$0.505208\pi$
$504$	6.12129	−	4.44738i	0.272664	−	0.198102i
$505$		0			0
$506$	20.8817	+	15.1715i	0.928306	+	0.674454i
$507$	−19.0787			−0.847314
$508$	−25.9958	−	18.8870i	−1.15338	−	0.837977i
$509$	10.4706	−	32.2253i	0.464103	−	1.42836i	−0.396004	−	0.918249i	$-0.629603\pi$
$509$	10.4706	−	32.2253i	0.464103	−	1.42836i	0.860107	−	0.510114i	$-0.170397\pi$
$510$		0			0
$511$	2.81234	+	8.65550i	0.124411	+	0.382897i
$512$	−13.5827	+	41.8032i	−0.600276	+	1.84746i
$513$	−6.16604	+	18.9771i	−0.272237	+	0.837860i
$514$	14.5804	+	44.8738i	0.643113	+	1.97930i
$515$		0			0
$516$	10.7703	−	33.1475i	0.474136	−	1.45924i
$517$	31.4095	+	22.8204i	1.38139	+	1.00364i
$518$	2.35695			0.103558
$519$	−25.7402	−	18.7013i	−1.12987	−	0.820898i
$520$		0			0
$521$	21.5578	−	15.6627i	0.944464	−	0.686193i	−0.00502715	−	0.999987i	$-0.501600\pi$
$521$	21.5578	−	15.6627i	0.944464	−	0.686193i	0.949491	+	0.313794i	$0.101600\pi$
$522$	−14.2805	+	10.3754i	−0.625041	+	0.454119i
$523$	−0.559119	−	1.72079i	−0.0244486	−	0.0752449i	0.938088	−	0.346398i	$-0.112595\pi$
$523$	−0.559119	−	1.72079i	−0.0244486	−	0.0752449i	−0.962536	+	0.271153i	$0.912595\pi$
$524$	−40.3592			−1.76310
$525$		0			0
$526$	−16.7846			−0.731842
$527$	4.19208	+	12.9019i	0.182610	+	0.562016i
$528$	43.7767	−	31.8056i	1.90514	−	1.38416i
$529$	15.5684	−	11.3111i	0.676889	−	0.491788i
$530$		0			0
$531$	−7.83428	−	5.69193i	−0.339979	−	0.247009i
$532$	−24.8879			−1.07903
$533$	4.41510	+	3.20776i	0.191239	+	0.138943i
$534$	−4.86753	+	14.9807i	−0.210639	+	0.648280i
$535$		0			0
$536$	15.5299	+	47.7961i	0.670790	+	2.06448i
$537$	−13.0932	+	40.2966i	−0.565012	+	1.73893i
$538$	0.378228	−	1.16406i	0.0163066	−	0.0501864i
$539$	10.0676	+	30.9850i	0.433643	+	1.33462i
$540$		0			0
$541$	−10.3593	+	31.8826i	−0.445380	+	1.37074i	0.436686	+	0.899614i	$0.356152\pi$
$541$	−10.3593	+	31.8826i	−0.445380	+	1.37074i	−0.882066	+	0.471126i	$0.843848\pi$
$542$	−19.6698	−	14.2910i	−0.844891	−	0.613849i
$543$	42.9685			1.84396
$544$	2.06401	+	1.49959i	0.0884937	+	0.0642944i
$545$		0			0
$546$	−8.23277	+	5.98146i	−0.352330	+	0.255983i
$547$	22.2597	−	16.1727i	0.951758	−	0.691493i	0.000536037	−	1.00000i	$-0.499829\pi$
$547$	22.2597	−	16.1727i	0.951758	−	0.691493i	0.951222	+	0.308507i	$0.0998294\pi$
$548$	−4.62841	−	14.2448i	−0.197716	−	0.608507i
$549$	4.03727			0.172306
$550$		0			0
$551$	29.8929			1.27348
$552$	6.65778	+	20.4905i	0.283374	+	0.872135i
$553$	−2.50473	+	1.81980i	−0.106512	+	0.0773856i
$554$	−50.3249	+	36.5632i	−2.13810	+	1.55342i
$555$		0			0
$556$	6.20593	+	4.50887i	0.263190	+	0.191219i
$557$	2.16761			0.0918448			0.0459224	−	0.998945i	$-0.485377\pi$
$557$	2.16761			0.0918448			0.0459224	+	0.998945i	$0.485377\pi$
$558$	19.6809	+	14.2990i	0.833157	+	0.605324i
$559$	−2.46444	+	7.58476i	−0.104235	+	0.320801i
$560$		0			0
$561$	7.19261	+	22.1366i	0.303672	+	0.934607i
$562$	−5.94146	+	18.2859i	−0.250625	+	0.771345i
$563$	10.3470	−	31.8448i	0.436074	−	1.34210i	−0.455909	−	0.890027i	$-0.650686\pi$
$563$	10.3470	−	31.8448i	0.436074	−	1.34210i	0.891982	−	0.452070i	$-0.149314\pi$
$564$	19.4511	+	59.8644i	0.819040	+	2.52074i
$565$		0			0
$566$	22.1446	−	68.1542i	0.930809	−	2.86474i
$567$	−8.85604	−	6.43429i	−0.371919	−	0.270215i
$568$	−29.8566			−1.25275
$569$	−13.9412	−	10.1289i	−0.584446	−	0.424625i	0.255878	−	0.966709i	$-0.417635\pi$
$569$	−13.9412	−	10.1289i	−0.584446	−	0.424625i	−0.840324	+	0.542084i	$0.817635\pi$
$570$		0			0
$571$	−34.6201	+	25.1530i	−1.44881	+	1.05262i	−0.462697	+	0.886516i	$0.653118\pi$
$571$	−34.6201	+	25.1530i	−1.44881	+	1.05262i	−0.986109	+	0.166102i	$0.946882\pi$
$572$	−35.8416	+	26.0404i	−1.49861	+	1.08881i
$573$	−6.19889	−	19.0782i	−0.258963	−	0.797005i
$574$	−6.58076			−0.274676
$575$		0			0
$576$	−9.48962			−0.395401
$577$	−9.83865	−	30.2802i	−0.409588	−	1.26058i	−0.917003	−	0.398881i	$-0.869399\pi$
$577$	−9.83865	−	30.2802i	−0.409588	−	1.26058i	0.507414	−	0.861702i	$-0.330601\pi$
$578$	25.6752	−	18.6542i	1.06795	−	0.775911i
$579$	−4.66616	+	3.39016i	−0.193919	+	0.140890i
$580$		0			0
$581$	4.81303	+	3.49687i	0.199678	+	0.145075i
$582$	31.1912			1.29292
$583$	57.8018	+	41.9955i	2.39391	+	1.73928i
$584$	−15.1781	+	46.7135i	−0.628076	+	1.93302i
$585$		0			0
$586$	−0.118003	−	0.363176i	−0.00487466	−	0.0150027i
$587$	−7.66445	+	23.5888i	−0.316346	+	0.973612i	0.658851	+	0.752273i	$0.271043\pi$
$587$	−7.66445	+	23.5888i	−0.316346	+	0.973612i	−0.975197	+	0.221339i	$0.928957\pi$
$588$	−16.3224	+	50.2353i	−0.673126	+	2.07167i
$589$	−12.7307	−	39.1810i	−0.524558	−	1.61442i
$590$		0			0
$591$	0.510231	−	1.57033i	0.0209881	−	0.0645947i
$592$	3.76143	+	2.73284i	0.154594	+	0.112319i
$593$	17.8431			0.732728			0.366364	−	0.930472i	$-0.380603\pi$
$593$	17.8431			0.732728			0.366364	+	0.930472i	$0.380603\pi$
$594$	−34.6510	−	25.1754i	−1.42175	−	1.03296i
$595$		0			0
$596$	−56.2068	+	40.8366i	−2.30232	+	1.67273i
$597$	12.7157	−	9.23847i	0.520417	−	0.378105i
$598$	−2.95897	−	9.10676i	−0.121001	−	0.372403i
$599$	−28.1028			−1.14825			−0.574126	−	0.818767i	$-0.694658\pi$
$599$	−28.1028			−1.14825			−0.574126	+	0.818767i	$0.694658\pi$
$600$		0			0
$601$	−26.6296			−1.08624			−0.543121	−	0.839654i	$-0.682758\pi$
$601$	−26.6296			−1.08624			−0.543121	+	0.839654i	$0.682758\pi$
$602$	−2.97174	−	9.14607i	−0.121119	−	0.372766i
$603$	−11.4630	+	8.32834i	−0.466809	+	0.339156i
$604$	47.7592	−	34.6991i	1.94329	−	1.41189i
$605$		0			0
$606$	32.9396	+	23.9320i	1.33808	+	0.972173i
$607$	−19.2757			−0.782375			−0.391187	−	0.920311i	$-0.627936\pi$
$607$	−19.2757			−0.782375			−0.391187	+	0.920311i	$0.627936\pi$
$608$	−6.26806	−	4.55401i	−0.254203	−	0.184689i
$609$	−3.06672	+	9.43838i	−0.124270	+	0.382462i
$610$		0			0
$611$	−4.45077	−	13.6981i	−0.180059	−	0.554164i
$612$	−3.85348	+	11.8598i	−0.155768	+	0.479403i
$613$	−0.143903	+	0.442888i	−0.00581219	+	0.0178881i	−0.953921	−	0.300059i	$-0.902994\pi$
$613$	−0.143903	+	0.442888i	−0.00581219	+	0.0178881i	0.948108	+	0.317947i	$0.102994\pi$
$614$	−11.0774	−	34.0927i	−0.447047	−	1.37587i
$615$		0			0
$616$	8.49933	−	26.1582i	0.342448	−	1.05395i
$617$	35.8204	+	26.0251i	1.44208	+	1.04773i	0.987603	+	0.156970i	$0.0501726\pi$
$617$	35.8204	+	26.0251i	1.44208	+	1.04773i	0.454474	+	0.890760i	$0.349827\pi$
$618$	25.9290			1.04302
$619$	29.2556	+	21.2555i	1.17588	+	0.854329i	0.991701	−	0.128563i	$-0.0410365\pi$
$619$	29.2556	+	21.2555i	1.17588	+	0.854329i	0.184182	+	0.982892i	$0.441036\pi$
$620$		0			0
$621$	5.04282	−	3.66382i	0.202361	−	0.147024i
$622$	−37.1102	+	26.9621i	−1.48798	+	1.08108i
$623$	0.904319	+	2.78321i	0.0362308	+	0.111507i
$624$	−20.0740			−0.803603
$625$		0			0
$626$	16.9667			0.678126
$627$	−21.8428	−	67.2251i	−0.872316	−	2.68471i
$628$	72.3281	−	52.5495i	2.88621	−	2.09695i
$629$	−1.61798	+	1.17553i	−0.0645129	+	0.0468714i
$630$		0			0
$631$	0.161343	+	0.117222i	0.00642296	+	0.00466655i	0.590992	−	0.806677i	$-0.298736\pi$
$631$	0.161343	+	0.117222i	0.00642296	+	0.00466655i	−0.584569	+	0.811344i	$0.698736\pi$
$632$	−16.7091			−0.664654
$633$	5.10540	+	3.70929i	0.202922	+	0.147431i
$634$	−20.8595	+	64.1990i	−0.828438	+	2.54967i
$635$		0			0
$636$	35.7952	+	110.166i	1.41937	+	4.36838i
$637$	3.73487	−	11.4947i	0.147981	−	0.455439i
$638$	−19.8283	+	61.0252i	−0.785010	+	2.41601i
$639$	−2.60121	−	8.00571i	−0.102902	−	0.316701i
$640$		0			0
$641$	−9.55104	+	29.3951i	−0.377244	+	1.16104i	0.564709	+	0.825290i	$0.308988\pi$
$641$	−9.55104	+	29.3951i	−0.377244	+	1.16104i	−0.941953	+	0.335746i	$0.891012\pi$
$642$	−4.94910	−	3.59573i	−0.195325	−	0.141912i
$643$	−22.2489			−0.877412			−0.438706	−	0.898631i	$-0.644563\pi$
$643$	−22.2489			−0.877412			−0.438706	+	0.898631i	$0.644563\pi$
$644$	6.28981	+	4.56981i	0.247853	+	0.180076i
$645$		0			0
$646$	25.3735	−	18.4349i	0.998308	−	0.725313i
$647$	28.3719	−	20.6134i	1.11541	−	0.810396i	0.131907	−	0.991262i	$-0.457890\pi$
$647$	28.3719	−	20.6134i	1.11541	−	0.810396i	0.983508	+	0.180866i	$0.0578900\pi$
$648$	−18.2564	−	56.1873i	−0.717178	−	2.20725i
$649$	−35.2012			−1.38177
$650$		0			0
$651$	13.6770			0.536044
$652$	−25.1226	−	77.3193i	−0.983875	−	3.02806i
$653$	3.23616	−	2.35121i	0.126641	−	0.0920099i	−0.522662	−	0.852540i	$-0.675061\pi$
$653$	3.23616	−	2.35121i	0.126641	−	0.0920099i	0.649303	+	0.760530i	$0.275061\pi$
$654$	74.9491	−	54.4537i	2.93074	−	2.12931i
$655$		0			0
$656$	−10.5022	−	7.63028i	−0.410041	−	0.297912i
$657$	−13.8481			−0.540265
$658$	14.0509	+	10.2086i	0.547760	+	0.397971i
$659$	3.10095	−	9.54375i	0.120796	−	0.371772i	−0.872316	−	0.488943i	$-0.837383\pi$
$659$	3.10095	−	9.54375i	0.120796	−	0.371772i	0.993112	+	0.117171i	$0.0373826\pi$
$660$		0			0
$661$	−15.0081	−	46.1902i	−0.583747	−	1.79659i	−0.604244	−	0.796800i	$-0.706525\pi$
$661$	−15.0081	−	46.1902i	−0.583747	−	1.79659i	0.0204964	−	0.999790i	$-0.493475\pi$
$662$	−9.97280	+	30.6931i	−0.387604	+	1.19292i
$663$	2.66830	−	8.21219i	0.103628	−	0.318935i
$664$	9.92186	+	30.5363i	0.385043	+	1.18504i
$665$		0			0
$666$	−1.10824	+	3.41083i	−0.0429436	+	0.132167i
$667$	−7.55471	−	5.48882i	−0.292520	−	0.212528i
$668$	25.0622			0.969684
$669$	−42.5931	−	30.9457i	−1.64674	−	1.19643i
$670$		0			0
$671$	11.8730	−	8.62627i	0.458354	−	0.333014i
$672$	2.08092	−	1.51188i	0.0802732	−	0.0583219i
$673$	1.56457	+	4.81526i	0.0603098	+	0.185615i	0.976672	−	0.214735i	$-0.0688887\pi$
$673$	1.56457	+	4.81526i	0.0603098	+	0.185615i	−0.916363	+	0.400349i	$0.868889\pi$
$674$	−48.6229			−1.87288
$675$		0			0
$676$	−37.1562			−1.42908
$677$	10.4037	+	32.0192i	0.399845	+	1.23060i	0.925124	+	0.379666i	$0.123961\pi$
$677$	10.4037	+	32.0192i	0.399845	+	1.23060i	−0.525278	+	0.850930i	$0.676039\pi$
$678$	−21.3408	+	15.5050i	−0.819590	+	0.595467i
$679$	4.68816	−	3.40615i	0.179915	−	0.130716i
$680$		0			0
$681$	30.0702	+	21.8473i	1.15229	+	0.837191i
$682$	88.4307			3.38619
$683$	−26.2545	−	19.0750i	−1.00460	−	0.729885i	−0.0415309	−	0.999137i	$-0.513223\pi$
$683$	−26.2545	−	19.0750i	−1.00460	−	0.729885i	−0.963070	+	0.269252i	$0.913223\pi$
$684$	11.7024	−	36.0162i	0.447451	−	1.37711i
$685$		0			0
$686$	9.71187	+	29.8901i	0.370801	+	1.14121i
$687$	4.59088	−	14.1293i	0.175153	−	0.539065i
$688$	5.86214	−	18.0418i	0.223492	−	0.687838i
$689$	−8.19059	−	25.2080i	−0.312037	−	0.960350i
$690$		0			0
$691$	−9.51188	+	29.2746i	−0.361849	+	1.11366i	0.590082	+	0.807343i	$0.299095\pi$
$691$	−9.51188	+	29.2746i	−0.361849	+	1.11366i	−0.951931	+	0.306313i	$0.900905\pi$
$692$	−50.1297	−	36.4213i	−1.90564	−	1.38453i
$693$	7.75453			0.294570
$694$	−8.78673	−	6.38393i	−0.333540	−	0.242331i
$695$		0			0
$696$	−43.3310	+	31.4818i	−1.64246	+	1.19332i
$697$	4.51750	−	3.28216i	0.171112	−	0.124320i
$698$	20.7942	+	63.9979i	0.787071	+	2.42236i
$699$	−18.3972			−0.695847
$700$		0			0
$701$	−13.1755			−0.497633			−0.248817	−	0.968551i	$-0.580042\pi$
$701$	−13.1755			−0.497633			−0.248817	+	0.968551i	$0.580042\pi$
$702$	4.91009	+	15.1117i	0.185319	+	0.570354i
$703$	4.91353	−	3.56989i	0.185317	−	0.134641i
$704$	−27.9076	+	20.2761i	−1.05181	+	0.764184i
$705$		0			0
$706$	31.8920	+	23.1709i	1.20027	+	0.872048i
$707$	7.56439			0.284488
$708$	−46.1715	−	33.5455i	−1.73523	−	1.26072i
$709$	−3.28508	+	10.1104i	−0.123374	+	0.379705i	−0.993601	−	0.112945i	$-0.963972\pi$
$709$	−3.28508	+	10.1104i	−0.123374	+	0.379705i	0.870228	+	0.492650i	$0.163972\pi$
$710$		0			0
$711$	−1.45576	−	4.48037i	−0.0545953	−	0.168027i
$712$	−4.88058	+	15.0209i	−0.182908	+	0.562932i
$713$	−3.97688	+	12.2396i	−0.148935	+	0.458376i
$714$	3.21757	+	9.90266i	0.120415	+	0.370598i
$715$		0			0
$716$	−25.4993	+	78.4787i	−0.952953	+	2.93289i
$717$	−36.5497	−	26.5549i	−1.36497	−	0.991710i
$718$	−12.4091			−0.463102
$719$	12.4155	+	9.02039i	0.463020	+	0.336404i	0.794715	−	0.606983i	$-0.207620\pi$
$719$	12.4155	+	9.02039i	0.463020	+	0.336404i	−0.331695	+	0.943387i	$0.607620\pi$
$720$		0			0
$721$	3.89723	−	2.83150i	0.145140	−	0.105451i
$722$	−39.0211	+	28.3505i	−1.45222	+	1.05510i
$723$	−13.9913	−	43.0607i	−0.520341	−	1.60144i
$724$	83.6823			3.11003
$725$		0			0
$726$	94.1124			3.49284
$727$	7.35942	+	22.6500i	0.272946	+	0.840041i	0.989756	+	0.142772i	$0.0456016\pi$
$727$	7.35942	+	22.6500i	0.272946	+	0.840041i	−0.716810	+	0.697269i	$0.754398\pi$
$728$	−8.25484	+	5.99749i	−0.305945	+	0.222282i
$729$	−3.04725	+	2.21396i	−0.112861	+	0.0819985i
$730$		0			0
$731$	6.60162	+	4.79636i	0.244170	+	0.177400i
$732$	23.7937			0.879442
$733$	3.31034	+	2.40510i	0.122270	+	0.0888344i	0.647240	−	0.762287i	$-0.275923\pi$
$733$	3.31034	+	2.40510i	0.122270	+	0.0888344i	−0.524970	+	0.851121i	$0.675923\pi$
$734$	21.6898	−	66.7544i	0.800585	−	2.46395i
$735$		0			0
$736$	0.747910	+	2.30183i	0.0275683	+	0.0848466i
$737$	−15.9162	+	48.9850i	−0.586280	+	1.80439i
$738$	3.09430	−	9.52326i	0.113903	−	0.350556i
$739$	0.759900	+	2.33873i	0.0279534	+	0.0860316i	0.964060	−	0.265685i	$-0.0855981\pi$
$739$	0.759900	+	2.33873i	0.0279534	+	0.0860316i	−0.936107	+	0.351717i	$0.885598\pi$
$740$		0			0
$741$	−8.10319	+	24.9391i	−0.297678	+	0.916159i
$742$	25.8573	+	18.7864i	0.949252	+	0.689672i
$743$	−11.1921			−0.410598			−0.205299	−	0.978699i	$-0.565817\pi$
$743$	−11.1921			−0.410598			−0.205299	+	0.978699i	$0.565817\pi$
$744$	59.7171	+	43.3870i	2.18934	+	1.59065i
$745$		0			0
$746$	65.5023	−	47.5902i	2.39821	−	1.74240i
$747$	−7.32355	+	5.32087i	−0.267955	+	0.194680i
$748$	14.0078	+	43.1115i	0.512175	+	1.57631i
$749$	−1.13653			−0.0415279
$750$		0			0
$751$	−10.3616			−0.378101			−0.189051	−	0.981967i	$-0.560541\pi$
$751$	−10.3616			−0.378101			−0.189051	+	0.981967i	$0.560541\pi$
$752$	10.5870	+	32.5835i	0.386069	+	1.18820i
$753$	−25.5188	+	18.5405i	−0.929956	+	0.675653i
$754$	19.2579	−	13.9917i	0.701332	−	0.509548i
$755$		0			0
$756$	−10.4373	−	7.58312i	−0.379600	−	0.275795i
$757$	−5.84722			−0.212521			−0.106260	−	0.994338i	$-0.533888\pi$
$757$	−5.84722			−0.212521			−0.106260	+	0.994338i	$0.533888\pi$
$758$	−8.97771	−	6.52269i	−0.326085	−	0.236915i
$759$	−6.82338	+	21.0002i	−0.247673	+	0.762259i
$760$		0			0
$761$	12.8839	+	39.6525i	0.467040	+	1.43740i	0.856398	+	0.516316i	$0.172697\pi$
$761$	12.8839	+	39.6525i	0.467040	+	1.43740i	−0.389358	+	0.921087i	$0.627303\pi$
$762$	12.6155	−	38.8267i	0.457013	−	1.40654i
$763$	5.31868	−	16.3692i	0.192549	−	0.592605i
$764$	−12.0725	−	37.1553i	−0.436768	−	1.34423i
$765$		0			0
$766$	12.4510	−	38.3201i	0.449871	−	1.38456i
$767$	10.5649	+	7.67583i	0.381475	+	0.277158i
$768$	−69.0084			−2.49013
$769$	14.0022	+	10.1732i	0.504931	+	0.366854i	0.810897	−	0.585189i	$-0.198979\pi$
$769$	14.0022	+	10.1732i	0.504931	+	0.366854i	−0.305966	+	0.952042i	$0.598979\pi$
$770$		0			0
$771$	−32.6552	+	23.7254i	−1.17605	+	0.854448i
$772$	−9.08746	+	6.60242i	−0.327065	+	0.237626i
$773$	5.52199	+	16.9949i	0.198612	+	0.611266i	0.999915	+	0.0130072i	$0.00414043\pi$
$773$	5.52199	+	16.9949i	0.198612	+	0.611266i	−0.801303	+	0.598259i	$0.795860\pi$
$774$	14.6329			0.525970
$775$		0			0
$776$	31.2748			1.12270
$777$	0.623075	+	1.91763i	0.0223527	+	0.0687945i
$778$	−43.0184	+	31.2547i	−1.54228	+	1.12053i
$779$	−13.7189	+	9.96736i	−0.491531	+	0.357118i
$780$		0			0
$781$	−24.7553	−	17.9858i	−0.885814	−	0.643581i
$782$	−9.79749			−0.350358
$783$	12.5362	+	9.10811i	0.448009	+	0.325497i
$784$	−8.88411	+	27.3425i	−0.317290	+	0.976517i
$785$		0			0
$786$	−15.8454	−	48.7671i	−0.565187	−	1.73947i
$787$	3.06268	−	9.42596i	0.109173	−	0.335999i	−0.881514	−	0.472157i	$-0.843475\pi$
$787$	3.06268	−	9.42596i	0.109173	−	0.335999i	0.990687	+	0.136158i	$0.0434755\pi$
$788$	0.993687	−	3.05825i	0.0353986	−	0.108946i
$789$	−4.43711	−	13.6560i	−0.157965	−	0.486167i
$790$		0			0
$791$	−1.51443	+	4.66093i	−0.0538469	+	0.165724i
$792$	33.8582	+	24.5994i	1.20310	+	0.874101i
$793$	−5.44444			−0.193338
$794$	41.8115	+	30.3778i	1.48384	+	1.07807i
$795$		0			0
$796$	24.7641	−	17.9922i	0.877739	−	0.637715i
$797$	−32.1657	+	23.3697i	−1.13937	+	0.827799i	−0.987031	−	0.160530i	$-0.948680\pi$
$797$	−32.1657	+	23.3697i	−1.13937	+	0.827799i	−0.152336	+	0.988329i	$0.548680\pi$
$798$	−9.77123	−	30.0727i	−0.345898	−	1.06456i
$799$	−14.7370			−0.521359
$800$		0			0
$801$	−4.45290			−0.157335
$802$	−0.484326	−	1.49060i	−0.0171022	−	0.0526350i
$803$	−40.7252	+	29.5886i	−1.43716	+	1.04416i
$804$	−67.5573	+	49.0833i	−2.38256	+	1.73103i
$805$		0			0
$806$	−26.5405	−	19.2828i	−0.934850	−	0.679208i
$807$	1.04708			0.0368589
$808$	33.0279	+	23.9962i	1.16192	+	0.844183i
$809$	−1.56087	+	4.80388i	−0.0548774	+	0.168895i	−0.974739	−	0.223349i	$-0.928301\pi$
$809$	−1.56087	+	4.80388i	−0.0548774	+	0.168895i	0.919861	+	0.392244i	$0.128301\pi$
$810$		0			0
$811$	3.63846	+	11.1980i	0.127764	+	0.393216i	0.994394	−	0.105734i	$-0.0337192\pi$
$811$	3.63846	+	11.1980i	0.127764	+	0.393216i	−0.866631	+	0.498950i	$0.833719\pi$
$812$	−5.97250	+	18.3815i	−0.209594	+	0.645063i
$813$	6.42737	−	19.7814i	0.225418	−	0.693764i
$814$	4.02859	+	12.3987i	0.141202	+	0.434575i
$815$		0			0
$816$	−6.34707	+	19.5343i	−0.222192	+	0.683837i
$817$	−20.0480	−	14.5657i	−0.701391	−	0.509591i
$818$	−10.6353			−0.371855
$819$	−2.32735	−	1.69092i	−0.0813242	−	0.0590855i
$820$		0			0
$821$	−4.25059	+	3.08823i	−0.148347	+	0.107780i	−0.659483	−	0.751720i	$-0.729225\pi$
$821$	−4.25059	+	3.08823i	−0.148347	+	0.107780i	0.511136	+	0.859500i	$0.329225\pi$
$822$	15.3952	−	11.1853i	0.536970	−	0.390132i
$823$	−11.4349	−	35.1931i	−0.398597	−	1.22675i	−0.926125	−	0.377217i	$-0.876881\pi$
$823$	−11.4349	−	35.1931i	−0.398597	−	1.22675i	0.527528	−	0.849538i	$-0.323119\pi$
$824$	25.9985			0.905701
$825$		0			0
$826$	−15.7471			−0.547910
$827$	8.68793	+	26.7387i	0.302109	+	0.929795i	0.980740	+	0.195316i	$0.0625734\pi$
$827$	8.68793	+	26.7387i	0.302109	+	0.929795i	−0.678631	+	0.734479i	$0.737427\pi$
$828$	−9.57064	+	6.95347i	−0.332603	+	0.241650i
$829$	11.6929	−	8.49536i	0.406110	−	0.295056i	−0.365915	−	0.930648i	$-0.619244\pi$
$829$	11.6929	−	8.49536i	0.406110	−	0.295056i	0.772025	+	0.635592i	$0.219244\pi$
$830$		0			0
$831$	−43.0517	−	31.2789i	−1.49345	−	1.08505i
$832$	12.7972			0.443662
$833$	−10.0048	−	7.26891i	−0.346646	−	0.251853i
$834$	−3.01169	+	9.26903i	−0.104286	+	0.320960i
$835$		0			0
$836$	−42.5393	−	130.923i	−1.47125	−	4.52805i
$837$	6.59921	−	20.3103i	0.228102	−	0.702026i
$838$	25.7076	−	79.1197i	0.888053	−	2.73315i
$839$	5.05842	+	15.5682i	0.174636	+	0.537474i	0.999617	−	0.0276868i	$-0.00881410\pi$
$839$	5.05842	+	15.5682i	0.174636	+	0.537474i	−0.824981	+	0.565161i	$0.808814\pi$
$840$		0			0
$841$	−1.78790	+	5.50258i	−0.0616516	+	0.189744i
$842$	42.7919	+	31.0902i	1.47471	+	1.07144i
$843$	−16.4482			−0.566506
$844$	9.94290	+	7.22394i	0.342249	+	0.248658i
$845$		0			0
$846$	−21.3799	+	15.5334i	−0.735057	+	0.534051i
$847$	14.1455	−	10.2773i	0.486044	−	0.353132i
$848$	19.4829	+	59.9622i	0.669045	+	2.05911i
$849$	61.3048			2.10397
$850$		0			0
$851$	−1.89726			−0.0650373
$852$	−15.3303	−	47.1818i	−0.525208	−	1.61642i
$853$	37.8795	−	27.5211i	1.29697	−	0.942303i	0.297048	−	0.954863i	$-0.403998\pi$
$853$	37.8795	−	27.5211i	1.29697	−	0.942303i	0.999921	+	0.0125596i	$0.00399796\pi$
$854$	5.31134	−	3.85891i	0.181750	−	0.132049i
$855$		0			0
$856$	−4.96237	−	3.60537i	−0.169610	−	0.123229i
$857$	28.9569			0.989148			0.494574	−	0.869136i	$-0.335324\pi$
$857$	28.9569			0.989148			0.494574	+	0.869136i	$0.335324\pi$
$858$	−45.5372	−	33.0847i	−1.55461	−	1.12949i
$859$	7.57081	−	23.3006i	0.258313	−	0.795005i	−0.734846	−	0.678234i	$-0.762746\pi$
$859$	7.57081	−	23.3006i	0.258313	−	0.795005i	0.993159	−	0.116771i	$-0.0372543\pi$
$860$		0			0
$861$	−1.73967	−	5.35415i	−0.0592877	−	0.182469i
$862$	19.9492	−	61.3975i	0.679474	−	2.09121i
$863$	3.23530	−	9.95722i	0.110131	−	0.338948i	−0.880770	−	0.473545i	$-0.842974\pi$
$863$	3.23530	−	9.95722i	0.110131	−	0.338948i	0.990900	+	0.134597i	$0.0429741\pi$
$864$	−1.24108	−	3.81964i	−0.0422223	−	0.129947i
$865$		0			0
$866$	8.99769	−	27.6920i	0.305754	−	0.941013i
$867$	21.9646	+	15.9582i	0.745956	+	0.541968i
$868$	26.6363			0.904096
$869$	−13.8542	−	10.0657i	−0.469972	−	0.341455i
$870$		0			0
$871$	15.4583	−	11.2311i	0.523786	−	0.380553i
$872$	75.1500	−	54.5997i	2.54490	−	1.84898i
$873$	2.72478	+	8.38600i	0.0922197	+	0.283823i
$874$	29.7534			1.00642
$875$		0			0
$876$	−81.6139			−2.75748
$877$	12.3335	+	37.9587i	0.416473	+	1.28177i	0.910926	+	0.412569i	$0.135368\pi$
$877$	12.3335	+	37.9587i	0.416473	+	1.28177i	−0.494453	+	0.869204i	$0.664632\pi$
$878$	−9.86028	+	7.16391i	−0.332768	+	0.241770i
$879$	0.264287	−	0.192016i	0.00891419	−	0.00647654i
$880$		0			0
$881$	6.38286	+	4.63742i	0.215044	+	0.156239i	0.690093	−	0.723721i	$-0.257570\pi$
$881$	6.38286	+	4.63742i	0.215044	+	0.156239i	−0.475049	+	0.879959i	$0.657570\pi$
$882$	−22.1763			−0.746716
$883$	12.2407	+	8.89342i	0.411934	+	0.299288i	0.774384	−	0.632716i	$-0.218060\pi$
$883$	12.2407	+	8.89342i	0.411934	+	0.299288i	−0.362450	+	0.932003i	$0.618060\pi$
$884$	5.19659	−	15.9934i	0.174780	−	0.537918i
$885$		0			0
$886$	7.15652	+	22.0255i	0.240428	+	0.739961i
$887$	14.7366	−	45.3546i	0.494807	−	1.52286i	−0.322451	−	0.946586i	$-0.604507\pi$
$887$	14.7366	−	45.3546i	0.494807	−	1.52286i	0.817258	−	0.576272i	$-0.195493\pi$
$888$	−3.36272	+	10.3494i	−0.112845	+	0.347302i
$889$	−2.34379	−	7.21344i	−0.0786082	−	0.241931i
$890$		0			0
$891$	18.7105	−	57.5849i	0.626824	−	1.92917i
$892$	−82.9511	−	60.2675i	−2.77741	−	2.01790i
$893$	44.7539			1.49763
$894$	−71.4114	−	51.8834i	−2.38835	−	1.73524i
$895$		0			0
$896$	−14.4505	+	10.4989i	−0.482756	+	0.350743i
$897$	6.62709	−	4.81487i	0.221272	−	0.160764i
$898$	5.67041	+	17.4517i	0.189224	+	0.582372i
$899$	−31.9930			−1.06703
$900$		0			0
$901$	−27.1200			−0.903499
$902$	−11.2481	−	34.6180i	−0.374520	−	1.15265i
$903$	6.65570	−	4.83565i	0.221488	−	0.160920i
$904$	−21.3981	+	15.5466i	−0.711689	+	0.517072i
$905$		0			0
$906$	60.6786	+	44.0856i	2.01591	+	1.46465i
$907$	−38.9321			−1.29272			−0.646359	−	0.763033i	$-0.723709\pi$
$907$	−38.9321			−1.29272			−0.646359	+	0.763033i	$0.723709\pi$
$908$	58.5625	+	42.5482i	1.94347	+	1.41201i
$909$	−3.55680	+	10.9467i	−0.117972	+	0.363079i
$910$		0			0
$911$	11.6419	+	35.8301i	0.385713	+	1.18710i	0.935962	+	0.352102i	$0.114533\pi$
$911$	11.6419	+	35.8301i	0.385713	+	1.18710i	−0.550249	+	0.835001i	$0.685467\pi$
$912$	19.2750	−	59.3224i	0.638259	−	1.96436i
$913$	−10.1686	+	31.2959i	−0.336533	+	1.03574i
$914$	6.72644	+	20.7019i	0.222491	+	0.684757i
$915$		0			0
$916$	8.94085	−	27.5171i	0.295414	−	0.909191i
$917$	−7.70710	−	5.59954i	−0.254511	−	0.184913i
$918$	16.2579			0.536590
$919$	−11.7021	−	8.50210i	−0.386018	−	0.280459i	0.377804	−	0.925886i	$-0.376679\pi$
$919$	−11.7021	−	8.50210i	−0.386018	−	0.280459i	−0.763822	+	0.645427i	$0.776679\pi$
$920$		0			0
$921$	24.8097	−	18.0253i	0.817506	−	0.593953i
$922$	84.3808	−	61.3063i	2.77894	−	2.01901i
$923$	3.50785	+	10.7961i	0.115462	+	0.355357i
$924$	45.7015			1.50347
$925$		0			0
$926$	57.0499			1.87478
$927$	2.26508	+	6.97121i	0.0743951	+	0.228965i
$928$	−4.86765	+	3.53655i	−0.159788	+	0.116093i
$929$	33.0880	−	24.0398i	1.08558	−	0.788721i	0.106934	−	0.994266i	$-0.465897\pi$
$929$	33.0880	−	24.0398i	1.08558	−	0.788721i	0.978648	+	0.205545i	$0.0658966\pi$
$930$		0			0
$931$	30.3829	+	22.0745i	0.995760	+	0.723462i
$932$	−35.8291			−1.17362
$933$	−31.7469	−	23.0655i	−1.03935	−	0.755130i
$934$	3.34875	−	10.3064i	0.109574	−	0.337236i
$935$		0			0
$936$	−4.79774	−	14.7659i	−0.156819	−	0.482639i
$937$	10.2768	−	31.6286i	0.335727	−	1.03326i	−0.630636	−	0.776079i	$-0.717206\pi$
$937$	10.2768	−	31.6286i	0.335727	−	1.03326i	0.966363	−	0.257183i	$-0.0827943\pi$
$938$	−7.12001	+	21.9131i	−0.232477	+	0.715489i
$939$	4.48526	+	13.8042i	0.146371	+	0.450484i
$940$		0			0
$941$	12.1004	−	37.2412i	0.394462	−	1.21403i	−0.534919	−	0.844904i	$-0.679658\pi$
$941$	12.1004	−	37.2412i	0.394462	−	1.21403i	0.929380	−	0.369124i	$-0.120342\pi$
$942$	91.8938	+	66.7647i	2.99406	+	2.17531i
$943$	5.29728			0.172503
$944$	−25.1306	−	18.2584i	−0.817931	−	0.594262i
$945$		0			0
$946$	43.0334	−	31.2656i	1.39914	−	1.01653i
$947$	23.1249	−	16.8012i	0.751459	−	0.545967i	−0.144820	−	0.989458i	$-0.546260\pi$
$947$	23.1249	−	16.8012i	0.751459	−	0.545967i	0.896279	+	0.443491i	$0.146260\pi$
$948$	−8.57955	−	26.4052i	−0.278651	−	0.857600i
$949$	18.6747			0.606208
$950$		0			0
$951$	−57.7471			−1.87258
$952$	3.22620	+	9.92921i	0.104562	+	0.321807i
$953$	35.0764	−	25.4845i	1.13624	−	0.825524i	0.149646	−	0.988740i	$-0.452187\pi$
$953$	35.0764	−	25.4845i	1.13624	−	0.825524i	0.986590	+	0.163216i	$0.0521867\pi$
$954$	−39.3447	+	28.5856i	−1.27383	+	0.925494i
$955$		0			0
$956$	−71.1814	−	51.7163i	−2.30217	−	1.67262i
$957$	−54.8923			−1.77442
$958$	−28.4081	−	20.6397i	−0.917823	−	0.666837i
$959$	1.09250	−	3.36238i	0.0352788	−	0.108577i
$960$		0			0
$961$	4.04549	+	12.4507i	0.130500	+	0.401637i
$962$	1.49452	−	4.59965i	0.0481852	−	0.148299i
$963$	0.534401	−	1.64472i	0.0172208	−	0.0530002i
$964$	−27.2483	−	83.8618i	−0.877610	−	2.70101i
$965$		0			0
$966$	−3.05240	+	9.39431i	−0.0982092	+	0.302257i
$967$	−26.0950	−	18.9591i	−0.839157	−	0.609683i	0.0829779	−	0.996551i	$-0.473557\pi$
$967$	−26.0950	−	18.9591i	−0.839157	−	0.609683i	−0.922135	+	0.386868i	$0.873557\pi$
$968$	94.3647			3.03300
$969$	21.7064	+	15.7707i	0.697312	+	0.506627i
$970$		0			0
$971$	−8.86509	+	6.44086i	−0.284494	+	0.206697i	−0.720875	−	0.693065i	$-0.756260\pi$
$971$	−8.86509	+	6.44086i	−0.284494	+	0.206697i	0.436381	+	0.899762i	$0.356260\pi$
$972$	47.2395	−	34.3215i	1.51521	−	1.10086i
$973$	0.559530	+	1.72206i	0.0179377	+	0.0552066i
$974$	54.6074			1.74973
$975$		0			0
$976$	12.9507			0.414540
$977$	−6.22779	−	19.1672i	−0.199245	−	0.613212i	−0.999901	−	0.0140880i	$-0.995516\pi$
$977$	−6.22779	−	19.1672i	−0.199245	−	0.613212i	0.800656	−	0.599124i	$-0.204484\pi$
$978$	83.5637	−	60.7126i	2.67207	−	1.94138i
$979$	−13.0953	+	9.51433i	−0.418529	+	0.304079i
$980$		0			0
$981$	21.1876	+	15.3937i	0.676469	+	0.491484i
$982$	−19.6885			−0.628286
$983$	12.9856	+	9.43460i	0.414177	+	0.300917i	0.775291	−	0.631605i	$-0.217603\pi$
$983$	12.9856	+	9.43460i	0.414177	+	0.300917i	−0.361114	+	0.932522i	$0.617603\pi$
$984$	9.38894	−	28.8962i	0.299308	−	0.921176i
$985$		0			0
$986$	−7.52647	−	23.1641i	−0.239692	−	0.737695i
$987$	−4.59130	+	14.1306i	−0.146143	+	0.449781i
$988$	−15.7812	+	48.5695i	−0.502066	+	1.54520i
$989$	2.39215	+	7.36227i	0.0760659	+	0.234107i
$990$		0			0
$991$	6.35242	−	19.5507i	0.201791	−	0.621050i	−0.798039	−	0.602606i	$-0.794129\pi$
$991$	6.35242	−	19.5507i	0.201791	−	0.621050i	0.999830	−	0.0184434i	$-0.00587106\pi$
$992$	6.70840	+	4.87394i	0.212992	+	0.154748i
$993$	−27.6085			−0.876129
$994$	−11.0741	−	8.04583i	−0.351250	−	0.255198i
$995$		0			0
$996$	−43.1615	+	31.3587i	−1.36762	+	0.993637i
$997$	−17.5796	+	12.7723i	−0.556752	+	0.404504i	−0.830269	−	0.557363i	$-0.811813\pi$
$997$	−17.5796	+	12.7723i	−0.556752	+	0.404504i	0.273517	+	0.961867i	$0.411813\pi$
$998$	−3.13022	−	9.63383i	−0.0990855	−	0.304954i
$999$	3.14830			0.0996079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.n.126.4		16
5.2	odd	4		625.2.e.k.499.1		32
5.3	odd	4		625.2.e.k.499.8		32
5.4	even	2		625.2.d.p.126.1		16
25.2	odd	20		625.2.b.d.624.15		16
25.3	odd	20		625.2.e.k.124.1		32
25.4	even	10		625.2.d.p.501.1		16
25.6	even	5		625.2.d.m.376.1		16
25.8	odd	20		625.2.e.j.249.1		32
25.9	even	10		625.2.d.q.251.4		16
25.11	even	5		625.2.a.g.1.7	yes	8
25.12	odd	20		625.2.e.j.374.1		32
25.13	odd	20		625.2.e.j.374.8		32
25.14	even	10		625.2.a.e.1.2	✓	8
25.16	even	5		625.2.d.m.251.1		16
25.17	odd	20		625.2.e.j.249.8		32
25.19	even	10		625.2.d.q.376.4		16
25.21	even	5	inner	625.2.d.n.501.4		16
25.22	odd	20		625.2.e.k.124.8		32
25.23	odd	20		625.2.b.d.624.2		16
75.11	odd	10		5625.2.a.s.1.2		8
75.14	odd	10		5625.2.a.be.1.7		8
100.11	odd	10		10000.2.a.be.1.3		8
100.39	odd	10		10000.2.a.bn.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.2	✓	8	25.14	even	10
625.2.a.g.1.7	yes	8	25.11	even	5
625.2.b.d.624.2		16	25.23	odd	20
625.2.b.d.624.15		16	25.2	odd	20
625.2.d.m.251.1		16	25.16	even	5
625.2.d.m.376.1		16	25.6	even	5
625.2.d.n.126.4		16	1.1	even	1	trivial
625.2.d.n.501.4		16	25.21	even	5	inner
625.2.d.p.126.1		16	5.4	even	2
625.2.d.p.501.1		16	25.4	even	10
625.2.d.q.251.4		16	25.9	even	10
625.2.d.q.376.4		16	25.19	even	10
625.2.e.j.249.1		32	25.8	odd	20
625.2.e.j.249.8		32	25.17	odd	20
625.2.e.j.374.1		32	25.12	odd	20
625.2.e.j.374.8		32	25.13	odd	20
625.2.e.k.124.1		32	25.3	odd	20
625.2.e.k.124.8		32	25.22	odd	20
625.2.e.k.499.1		32	5.2	odd	4
625.2.e.k.499.8		32	5.3	odd	4
5625.2.a.s.1.2		8	75.11	odd	10
5625.2.a.be.1.7		8	75.14	odd	10
10000.2.a.be.1.3		8	100.11	odd	10
10000.2.a.bn.1.6		8	100.39	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.764617 + 2.35325i) q^{2} +(-1.71249 + 1.24419i) q^{3} +(-3.33511 + 2.42310i) q^{4} +(-4.23730 - 3.07858i) q^{6} -0.973070 q^{7} +(-4.24866 - 3.08683i) q^{8} +(0.457541 - 1.40817i) q^{9} +O(q^{10})\)	\(q+(0.764617 + 2.35325i) q^{2} +(-1.71249 + 1.24419i) q^{3} +(-3.33511 + 2.42310i) q^{4} +(-4.23730 - 3.07858i) q^{6} -0.973070 q^{7} +(-4.24866 - 3.08683i) q^{8} +(0.457541 - 1.40817i) q^{9} +(-1.66321 - 5.11883i) q^{11} +(2.69653 - 8.29906i) q^{12} +(-0.617014 + 1.89897i) q^{13} +(-0.744026 - 2.28988i) q^{14} +(1.46769 - 4.51708i) q^{16} +(1.65283 + 1.20085i) q^{17} +3.66361 q^{18} +(-5.01937 - 3.64678i) q^{19} +(1.66637 - 1.21069i) q^{21} +(10.7742 - 7.82789i) q^{22} +(0.598915 + 1.84327i) q^{23} +11.1164 q^{24} -4.94054 q^{26} +(-0.993836 - 3.05871i) q^{27} +(3.24530 - 2.35785i) q^{28} +(-3.89794 + 2.83202i) q^{29} +(5.37199 + 3.90298i) q^{31} +1.24877 q^{32} +(9.21704 + 6.69657i) q^{33} +(-1.56212 + 4.80771i) q^{34} +(1.88618 + 5.80506i) q^{36} +(-0.302501 + 0.931002i) q^{37} +(4.74390 - 14.6002i) q^{38} +(-1.30607 - 4.01966i) q^{39} +(0.844603 - 2.59942i) q^{41} +(4.12319 + 2.99567i) q^{42} +3.99413 q^{43} +(17.9504 + 13.0417i) q^{44} +(-3.87974 + 2.81879i) q^{46} +(-5.83576 + 4.23993i) q^{47} +(3.10673 + 9.56153i) q^{48} -6.05313 q^{49} -4.32454 q^{51} +(-2.54359 - 7.82838i) q^{52} +(-10.7393 + 7.80259i) q^{53} +(6.43801 - 4.67749i) q^{54} +(4.13424 + 3.00370i) q^{56} +13.1329 q^{57} +(-9.64488 - 7.00741i) q^{58} +(2.02105 - 6.22014i) q^{59} +(0.842602 + 2.59326i) q^{61} +(-5.07717 + 15.6259i) q^{62} +(-0.445219 + 1.37024i) q^{63} +(-1.98054 - 6.09548i) q^{64} +(-8.71120 + 26.8103i) q^{66} +(-7.74195 - 5.62485i) q^{67} -8.42215 q^{68} +(-3.31902 - 2.41141i) q^{69} +(4.59943 - 3.34168i) q^{71} +(-6.29070 + 4.57046i) q^{72} +(-2.89018 - 8.89505i) q^{73} -2.42218 q^{74} +25.5767 q^{76} +(1.61842 + 4.98098i) q^{77} +(8.46061 - 6.14700i) q^{78} +(2.57405 - 1.87016i) q^{79} +(9.10114 + 6.61236i) q^{81} +6.76289 q^{82} +(-4.94623 - 3.59365i) q^{83} +(-2.62391 + 8.07556i) q^{84} +(3.05398 + 9.39919i) q^{86} +(3.15159 - 9.69959i) q^{87} +(-8.73455 + 26.8822i) q^{88} +(-0.929346 - 2.86023i) q^{89} +(0.600398 - 1.84784i) q^{91} +(-6.46388 - 4.69629i) q^{92} -14.0555 q^{93} +(-14.4397 - 10.4911i) q^{94} +(-2.13851 + 1.55372i) q^{96} +(-4.81791 + 3.50042i) q^{97} +(-4.62833 - 14.2445i) q^{98} -7.96914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

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