LMFDB - Embedded newform 475.2.n.a.39.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.8
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396268 - 0.545416i) q^{2} +(2.29043 + 0.744207i) q^{3} +(0.477583 - 1.46985i) q^{4} +(-1.89679 - 1.18414i) q^{5} +(-0.501723 - 1.54414i) q^{6} -2.02861i q^{7} +(-2.27328 + 0.738634i) q^{8} +(2.26518 + 1.64575i) q^{9} +O(q^{10})$	\(q+(-0.396268 - 0.545416i) q^{2} +(2.29043 + 0.744207i) q^{3} +(0.477583 - 1.46985i) q^{4} +(-1.89679 - 1.18414i) q^{5} +(-0.501723 - 1.54414i) q^{6} -2.02861i q^{7} +(-2.27328 + 0.738634i) q^{8} +(2.26518 + 1.64575i) q^{9} +(0.105787 + 1.50378i) q^{10} +(4.02237 - 2.92242i) q^{11} +(2.18774 - 3.01117i) q^{12} +(-2.73694 + 3.76708i) q^{13} +(-1.10644 + 0.803873i) q^{14} +(-3.46322 - 4.12380i) q^{15} +(-1.19697 - 0.869647i) q^{16} +(3.04964 - 0.990889i) q^{17} -1.88763i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.64639 + 2.22247i) q^{20} +(1.50970 - 4.64639i) q^{21} +(-3.18787 - 1.03580i) q^{22} +(-4.09410 - 5.63505i) q^{23} -5.75650 q^{24} +(2.19561 + 4.49213i) q^{25} +3.13919 q^{26} +(-0.283223 - 0.389822i) q^{27} +(-2.98175 - 0.968829i) q^{28} +(1.53204 - 4.71515i) q^{29} +(-0.876824 + 3.52303i) q^{30} +(1.88728 + 5.80846i) q^{31} +5.77800i q^{32} +(11.3878 - 3.70014i) q^{33} +(-1.74892 - 1.27067i) q^{34} +(-2.40216 + 3.84784i) q^{35} +(3.50083 - 2.54350i) q^{36} +(-0.290477 + 0.399807i) q^{37} +(-0.396268 + 0.545416i) q^{38} +(-9.07227 + 6.59139i) q^{39} +(5.18658 + 1.29086i) q^{40} +(8.39444 + 6.09892i) q^{41} +(-3.13246 + 1.01780i) q^{42} +0.846649i q^{43} +(-2.37451 - 7.30798i) q^{44} +(-2.34777 - 5.80395i) q^{45} +(-1.45109 + 4.46598i) q^{46} +(5.21713 + 1.69515i) q^{47} +(-2.09437 - 2.88266i) q^{48} +2.88475 q^{49} +(1.58003 - 2.97761i) q^{50} +7.72243 q^{51} +(4.22992 + 5.82199i) q^{52} +(3.79590 + 1.23336i) q^{53} +(-0.100383 + 0.308948i) q^{54} +(-11.0901 + 0.780160i) q^{55} +(1.49840 + 4.61160i) q^{56} -2.40830i q^{57} +(-3.17882 + 1.03286i) q^{58} +(3.56346 + 2.58901i) q^{59} +(-7.71535 + 3.12096i) q^{60} +(-2.78555 + 2.02382i) q^{61} +(2.42016 - 3.33106i) q^{62} +(3.33859 - 4.59517i) q^{63} +(0.757483 - 0.550344i) q^{64} +(9.65216 - 3.90442i) q^{65} +(-6.53076 - 4.74487i) q^{66} +(-11.8116 + 3.83782i) q^{67} -4.95575i q^{68} +(-5.18363 - 15.9536i) q^{69} +(3.05057 - 0.214599i) q^{70} +(3.84879 - 11.8453i) q^{71} +(-6.36502 - 2.06812i) q^{72} +(3.57401 + 4.91920i) q^{73} +0.333168 q^{74} +(1.68583 + 11.9229i) q^{75} -1.54549 q^{76} +(-5.92845 - 8.15981i) q^{77} +(7.19010 + 2.33621i) q^{78} +(-2.55505 + 7.86363i) q^{79} +(1.24061 + 3.06692i) q^{80} +(-2.95426 - 9.09229i) q^{81} -6.99528i q^{82} +(0.467160 - 0.151789i) q^{83} +(-6.10849 - 4.43808i) q^{84} +(-6.95788 - 1.73170i) q^{85} +(0.461776 - 0.335500i) q^{86} +(7.01809 - 9.65957i) q^{87} +(-6.98538 + 9.61455i) q^{88} +(-14.0339 + 10.1962i) q^{89} +(-2.23522 + 3.58043i) q^{90} +(7.64192 + 5.55218i) q^{91} +(-10.2380 + 3.32652i) q^{92} +14.7084i q^{93} +(-1.14282 - 3.51724i) q^{94} +(-0.540046 + 2.16987i) q^{95} +(-4.30003 + 13.2341i) q^{96} +(7.21523 + 2.34437i) q^{97} +(-1.14314 - 1.57339i) q^{98} +13.9210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.396268	−	0.545416i	−0.280204	−	0.385668i	0.645597	−	0.763678i	$-0.276608\pi$
$2$	−0.396268	−	0.545416i	−0.280204	−	0.385668i	−0.925801	+	0.378010i	$0.876608\pi$
$3$	2.29043	+	0.744207i	1.32238	+	0.429668i	0.883312	−	0.468785i	$-0.155308\pi$
$3$	2.29043	+	0.744207i	1.32238	+	0.429668i	0.439069	+	0.898453i	$0.355308\pi$
$4$	0.477583	−	1.46985i	0.238792	−	0.734925i
$5$	−1.89679	−	1.18414i	−0.848270	−	0.529564i
$5$	−1.89679	−	1.18414i	−0.848270	−	0.529564i
$6$	−0.501723	−	1.54414i	−0.204828	−	0.630394i
$7$		−	2.02861i		−	0.766742i	−0.923595	−	0.383371i	$-0.874763\pi$
$7$		−	2.02861i		−	0.766742i	0.923595	−	0.383371i	$-0.125237\pi$
$8$	−2.27328	+	0.738634i	−0.803727	+	0.261147i
$9$	2.26518	+	1.64575i	0.755062	+	0.548584i
$10$	0.105787	+	1.50378i	0.0334526	+	0.475536i
$11$	4.02237	−	2.92242i	1.21279	−	0.881143i	0.217308	−	0.976103i	$-0.430272\pi$
$11$	4.02237	−	2.92242i	1.21279	−	0.881143i	0.995481	+	0.0949599i	$0.0302723\pi$
$12$	2.18774	−	3.01117i	0.631548	−	0.869251i
$13$	−2.73694	+	3.76708i	−0.759091	+	1.04480i	0.238198	+	0.971217i	$0.423443\pi$
$13$	−2.73694	+	3.76708i	−0.759091	+	1.04480i	−0.997289	+	0.0735830i	$0.976557\pi$
$14$	−1.10644	+	0.803873i	−0.295707	+	0.214844i
$15$	−3.46322	−	4.12380i	−0.894199	−	1.06476i
$16$	−1.19697	−	0.869647i	−0.299242	−	0.217412i
$17$	3.04964	−	0.990889i	0.739647	−	0.240326i	0.0851266	−	0.996370i	$-0.472871\pi$
$17$	3.04964	−	0.990889i	0.739647	−	0.240326i	0.654521	+	0.756044i	$0.272871\pi$
$18$		−	1.88763i		−	0.444918i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−2.64639	+	2.22247i	−0.591750	+	0.496959i
$21$	1.50970	−	4.64639i	0.329444	−	1.01392i
$22$	−3.18787	−	1.03580i	−0.679657	−	0.220834i
$23$	−4.09410	−	5.63505i	−0.853680	−	1.17499i	−0.983040	−	0.183392i	$-0.941292\pi$
$23$	−4.09410	−	5.63505i	−0.853680	−	1.17499i	0.129360	−	0.991598i	$-0.458708\pi$
$24$	−5.75650			−1.17504
$25$	2.19561	+	4.49213i	0.439123	+	0.898427i
$26$	3.13919			0.615646
$27$	−0.283223	−	0.389822i	−0.0545062	−	0.0750213i
$28$	−2.98175	−	0.968829i	−0.563498	−	0.183092i
$29$	1.53204	−	4.71515i	0.284494	−	0.875581i	−0.702056	−	0.712121i	$-0.747735\pi$
$29$	1.53204	−	4.71515i	0.284494	−	0.875581i	0.986550	−	0.163460i	$-0.0522654\pi$
$30$	−0.876824	+	3.52303i	−0.160085	+	0.643214i
$31$	1.88728	+	5.80846i	0.338966	+	1.04323i	0.964735	+	0.263222i	$0.0847851\pi$
$31$	1.88728	+	5.80846i	0.338966	+	1.04323i	−0.625769	+	0.780008i	$0.715215\pi$
$32$			5.77800i			1.02142i
$33$	11.3878	−	3.70014i	1.98237	−	0.644111i
$34$	−1.74892	−	1.27067i	−0.299938	−	0.217918i
$35$	−2.40216	+	3.84784i	−0.406039	+	0.650404i
$36$	3.50083	−	2.54350i	0.583471	−	0.423917i
$37$	−0.290477	+	0.399807i	−0.0477541	+	0.0657279i	−0.832226	−	0.554436i	$-0.812934\pi$
$37$	−0.290477	+	0.399807i	−0.0477541	+	0.0657279i	0.784472	+	0.620164i	$0.212934\pi$
$38$	−0.396268	+	0.545416i	−0.0642832	+	0.0884782i
$39$	−9.07227	+	6.59139i	−1.45273	+	1.05547i
$40$	5.18658	+	1.29086i	0.820071	+	0.204102i
$41$	8.39444	+	6.09892i	1.31099	+	0.952491i	0.999998	+	0.00207965i	$0.000661974\pi$
$41$	8.39444	+	6.09892i	1.31099	+	0.952491i	0.310994	+	0.950412i	$0.399338\pi$
$42$	−3.13246	+	1.01780i	−0.483350	+	0.157050i
$43$			0.846649i			0.129113i	0.997914	+	0.0645564i	$0.0205632\pi$
$43$			0.846649i			0.129113i	−0.997914	+	0.0645564i	$0.979437\pi$
$44$	−2.37451	−	7.30798i	−0.357970	−	1.10172i
$45$	−2.34777	−	5.80395i	−0.349985	−	0.865201i
$46$	−1.45109	+	4.46598i	−0.213951	+	0.658473i
$47$	5.21713	+	1.69515i	0.760997	+	0.247263i	0.663707	−	0.747993i	$-0.268982\pi$
$47$	5.21713	+	1.69515i	0.760997	+	0.247263i	0.0972907	+	0.995256i	$0.468982\pi$
$48$	−2.09437	−	2.88266i	−0.302297	−	0.416076i
$49$	2.88475			0.412107
$50$	1.58003	−	2.97761i	0.223450	−	0.421098i
$51$	7.72243			1.08136
$52$	4.22992	+	5.82199i	0.586585	+	0.807365i
$53$	3.79590	+	1.23336i	0.521407	+	0.169416i	0.557884	−	0.829919i	$-0.311613\pi$
$53$	3.79590	+	1.23336i	0.521407	+	0.169416i	−0.0364765	+	0.999335i	$0.511613\pi$
$54$	−0.100383	+	0.308948i	−0.0136605	+	0.0420426i
$55$	−11.0901	+	0.780160i	−1.49539	+	0.105197i
$56$	1.49840	+	4.61160i	0.200232	+	0.616251i
$57$		−	2.40830i		−	0.318988i
$58$	−3.17882	+	1.03286i	−0.417400	+	0.135621i
$59$	3.56346	+	2.58901i	0.463923	+	0.337060i	0.795068	−	0.606520i	$-0.207435\pi$
$59$	3.56346	+	2.58901i	0.463923	+	0.337060i	−0.331145	+	0.943580i	$0.607435\pi$
$60$	−7.71535	+	3.12096i	−0.996047	+	0.402914i
$61$	−2.78555	+	2.02382i	−0.356653	+	0.259123i	−0.751655	−	0.659557i	$-0.770744\pi$
$61$	−2.78555	+	2.02382i	−0.356653	+	0.259123i	0.395002	+	0.918680i	$0.370744\pi$
$62$	2.42016	−	3.33106i	0.307360	−	0.423045i
$63$	3.33859	−	4.59517i	0.420622	−	0.578937i
$64$	0.757483	−	0.550344i	0.0946854	−	0.0687930i
$65$	9.65216	−	3.90442i	1.19720	−	0.484284i
$66$	−6.53076	−	4.74487i	−0.803880	−	0.584053i
$67$	−11.8116	+	3.83782i	−1.44301	+	0.468864i	−0.922836	−	0.385193i	$-0.874135\pi$
$67$	−11.8116	+	3.83782i	−1.44301	+	0.468864i	−0.520179	+	0.854057i	$0.674135\pi$
$68$		−	4.95575i		−	0.600973i
$69$	−5.18363	−	15.9536i	−0.624035	−	1.92058i
$70$	3.05057	−	0.214599i	0.364613	−	0.0256495i
$71$	3.84879	−	11.8453i	0.456767	−	1.40578i	−0.412281	−	0.911057i	$-0.635268\pi$
$71$	3.84879	−	11.8453i	0.456767	−	1.40578i	0.869048	−	0.494728i	$-0.164732\pi$
$72$	−6.36502	−	2.06812i	−0.750124	−	0.243730i
$73$	3.57401	+	4.91920i	0.418306	+	0.575749i	0.965220	−	0.261440i	$-0.0841973\pi$
$73$	3.57401	+	4.91920i	0.418306	+	0.575749i	−0.546913	+	0.837189i	$0.684197\pi$
$74$	0.333168			0.0387300
$75$	1.68583	+	11.9229i	0.194663	+	1.37674i
$76$	−1.54549			−0.177280
$77$	−5.92845	−	8.15981i	−0.675609	−	0.929896i
$78$	7.19010	+	2.33621i	0.814119	+	0.264523i
$79$	−2.55505	+	7.86363i	−0.287465	+	0.884728i	0.698183	+	0.715919i	$0.253992\pi$
$79$	−2.55505	+	7.86363i	−0.287465	+	0.884728i	−0.985649	+	0.168809i	$0.946008\pi$
$80$	1.24061	+	3.06692i	0.138704	+	0.342892i
$81$	−2.95426	−	9.09229i	−0.328252	−	1.01025i
$82$		−	6.99528i		−	0.772499i
$83$	0.467160	−	0.151789i	0.0512775	−	0.0166611i	−0.283266	−	0.959041i	$-0.591418\pi$
$83$	0.467160	−	0.151789i	0.0512775	−	0.0166611i	0.334543	+	0.942380i	$0.391418\pi$
$84$	−6.10849	−	4.43808i	−0.666491	−	0.484234i
$85$	−6.95788	−	1.73170i	−0.754688	−	0.187830i
$86$	0.461776	−	0.335500i	0.0497946	−	0.0361779i
$87$	7.01809	−	9.65957i	0.752418	−	1.03561i
$88$	−6.98538	+	9.61455i	−0.744644	+	1.02491i
$89$	−14.0339	+	10.1962i	−1.48759	+	1.08080i	−0.512577	+	0.858641i	$0.671309\pi$
$89$	−14.0339	+	10.1962i	−1.48759	+	1.08080i	−0.975011	+	0.222155i	$0.928691\pi$
$90$	−2.23522	+	3.58043i	−0.235613	+	0.377411i
$91$	7.64192	+	5.55218i	0.801091	+	0.582027i
$92$	−10.2380	+	3.32652i	−1.06738	+	0.346813i
$93$			14.7084i			1.52519i
$94$	−1.14282	−	3.51724i	−0.117873	−	0.362776i
$95$	−0.540046	+	2.16987i	−0.0554076	+	0.222624i
$96$	−4.30003	+	13.2341i	−0.438870	+	1.35070i
$97$	7.21523	+	2.34437i	0.732595	+	0.238035i	0.651476	−	0.758670i	$-0.274150\pi$
$97$	7.21523	+	2.34437i	0.732595	+	0.238035i	0.0811199	+	0.996704i	$0.474150\pi$
$98$	−1.14314	−	1.57339i	−0.115474	−	0.158936i
$99$	13.9210			1.39911
$100$	7.65136	−	1.08186i	0.765136	−	0.108186i
$101$	15.4259			1.53493			0.767466	−	0.641090i	$-0.221517\pi$
$101$	15.4259			1.53493			0.767466	+	0.641090i	$0.221517\pi$
$102$	−3.06015	−	4.21194i	−0.303000	−	0.417044i
$103$	3.83124	+	1.24485i	0.377504	+	0.122658i	0.491622	−	0.870809i	$-0.336404\pi$
$103$	3.83124	+	1.24485i	0.377504	+	0.122658i	−0.114118	+	0.993467i	$0.536404\pi$
$104$	3.43935	−	10.5852i	0.337256	−	1.03797i
$105$	−8.36557	+	7.02551i	−0.816396	+	0.685620i
$106$	−0.831499	−	2.55909i	−0.0807623	−	0.248561i
$107$			16.0209i			1.54880i	0.632697	+	0.774399i	$0.281948\pi$
$107$			16.0209i			1.54880i	−0.632697	+	0.774399i	$0.718052\pi$
$108$	−0.708243	+	0.230122i	−0.0681507	+	0.0221435i
$109$	−0.359352	−	0.261085i	−0.0344197	−	0.0250074i	0.570442	−	0.821338i	$-0.306772\pi$
$109$	−0.359352	−	0.261085i	−0.0344197	−	0.0250074i	−0.604862	+	0.796330i	$0.706772\pi$
$110$	4.82018	+	5.73959i	0.459586	+	0.547249i
$111$	−0.962857	+	0.699556i	−0.0913903	+	0.0663990i
$112$	−1.76417	+	2.42818i	−0.166699	+	0.229441i
$113$	−1.29217	+	1.77852i	−0.121557	+	0.167309i	−0.865459	−	0.500980i	$-0.832973\pi$
$113$	−1.29217	+	1.77852i	−0.121557	+	0.167309i	0.743902	+	0.668289i	$0.232973\pi$
$114$	−1.31353	+	0.954334i	−0.123023	+	0.0893816i
$115$	1.09295	+	15.5365i	0.101918	+	1.44879i
$116$	−6.19889	−	4.50375i	−0.575552	−	0.418163i
$117$	−12.3994	+	4.02880i	−1.14632	+	0.372462i
$118$		−	2.96951i		−	0.273366i
$119$	−2.01013	−	6.18653i	−0.184268	−	0.567118i
$120$	10.9189	+	6.81651i	0.996751	+	0.622259i
$121$	4.23971	−	13.0485i	0.385428	−	1.18623i
$122$	2.20765	+	0.717308i	0.199871	+	0.0649420i
$123$	14.6880	+	20.2164i	1.32438	+	1.82285i
$124$	9.43890			0.847638
$125$	1.15471	−	11.1206i	0.103280	−	0.994652i
$126$	−3.82926			−0.341137
$127$	3.39869	+	4.67790i	0.301585	+	0.415096i	0.932734	−	0.360566i	$-0.117416\pi$
$127$	3.39869	+	4.67790i	0.301585	+	0.415096i	−0.631149	+	0.775662i	$0.717416\pi$
$128$	10.3901	+	3.37594i	0.918362	+	0.298394i
$129$	−0.630082	+	1.93919i	−0.0554756	+	0.170736i
$130$	−5.95438	−	3.71725i	−0.522234	−	0.326024i
$131$	−6.64362	−	20.4470i	−0.580456	−	1.78646i	−0.616801	−	0.787119i	$-0.711572\pi$
$131$	−6.64362	−	20.4470i	−0.580456	−	1.78646i	0.0363452	−	0.999339i	$-0.488428\pi$
$132$		−	18.5056i		−	1.61070i
$133$	−1.92932	+	0.626874i	−0.167293	+	0.0543569i
$134$	6.77376	+	4.92143i	0.585164	+	0.425147i
$135$	0.0756082	+	1.07479i	0.00650732	+	0.0925029i
$136$	−6.20080	+	4.50514i	−0.531714	+	0.386313i
$137$	−4.51663	+	6.21661i	−0.385882	+	0.531121i	−0.957131	−	0.289656i	$-0.906459\pi$
$137$	−4.51663	+	6.21661i	−0.385882	+	0.531121i	0.571249	+	0.820777i	$0.306459\pi$
$138$	−6.64723	+	9.14912i	−0.565850	+	0.778825i
$139$	16.7429	−	12.1644i	1.42011	−	1.03177i	0.428359	−	0.903608i	$-0.359092\pi$
$139$	16.7429	−	12.1644i	1.42011	−	1.03177i	0.991753	−	0.128164i	$-0.0409083\pi$
$140$	4.50852	+	5.36848i	0.381039	+	0.453719i
$141$	10.6880	+	7.76525i	0.900088	+	0.653952i
$142$	−7.98580	+	2.59474i	−0.670153	+	0.217746i
$143$			23.1511i			1.93599i
$144$	−1.28013	−	3.93982i	−0.106677	−	0.328319i
$145$	−8.48937	+	7.12948i	−0.705004	+	0.592071i
$146$	1.26675	−	3.89865i	0.104837	−	0.322654i
$147$	6.60733	+	2.14685i	0.544963	+	0.177069i
$148$	0.448930	+	0.617899i	0.0369018	+	0.0507910i
$149$	−8.62061			−0.706228			−0.353114	−	0.935580i	$-0.614877\pi$
$149$	−8.62061			−0.706228			−0.353114	+	0.935580i	$0.614877\pi$
$150$	5.83492	−	5.64415i	0.476419	−	0.460843i
$151$	−4.40335			−0.358340			−0.179170	−	0.983818i	$-0.557341\pi$
$151$	−4.40335			−0.358340			−0.179170	+	0.983818i	$0.557341\pi$
$152$	1.40497	+	1.93377i	0.113958	+	0.156849i
$153$	8.53877	+	2.77441i	0.690318	+	0.224298i
$154$	−2.10124	+	6.46694i	−0.169323	+	0.521121i
$155$	3.29826	−	13.2522i	0.264923	−	1.06444i
$156$	5.35559	+	16.4828i	0.428790	+	1.31968i
$157$			12.2774i			0.979845i	0.871766	+	0.489922i	$0.162975\pi$
$157$			12.2774i			0.979845i	−0.871766	+	0.489922i	$0.837025\pi$
$158$	5.30144	−	1.72254i	0.421760	−	0.137038i
$159$	7.77638	+	5.64987i	0.616707	+	0.448064i
$160$	6.84197	−	10.9596i	0.540906	−	0.866436i
$161$	−11.4313	+	8.30533i	−0.900913	+	0.654552i
$162$	−3.78840	+	5.21429i	−0.297645	+	0.409673i
$163$	−7.99128	+	10.9991i	−0.625926	+	0.861513i	−0.997768	−	0.0667833i	$-0.978726\pi$
$163$	−7.99128	+	10.9991i	−0.625926	+	0.861513i	0.371842	+	0.928296i	$0.378726\pi$
$164$	12.9736	−	9.42584i	1.01306	−	0.736034i
$165$	−25.9818	−	6.46645i	−2.02268	−	0.503413i
$166$	−0.267909	−	0.194647i	−0.0207938	−	0.0151076i
$167$	−24.1041	+	7.83188i	−1.86523	+	0.606049i	−0.872054	+	0.489410i	$0.837212\pi$
$167$	−24.1041	+	7.83188i	−1.86523	+	0.606049i	−0.993174	+	0.116639i	$0.962788\pi$
$168$			11.6777i			0.900952i
$169$	−2.68280	−	8.25682i	−0.206370	−	0.635140i
$170$	1.81269	+	4.48116i	0.139027	+	0.343689i
$171$	0.865224	−	2.66288i	0.0661653	−	0.203636i
$172$	1.24445	+	0.404346i	0.0948883	+	0.0308311i
$173$	−3.42021	−	4.70751i	−0.260034	−	0.357906i	0.658960	−	0.752178i	$-0.270997\pi$
$173$	−3.42021	−	4.70751i	−0.260034	−	0.357906i	−0.918994	+	0.394272i	$0.870997\pi$
$174$	−8.04953			−0.610234
$175$	9.11278	−	4.45404i	0.688861	−	0.336694i
$176$	−7.35611			−0.554488
$177$	6.23511	+	8.58190i	0.468660	+	0.645055i
$178$	11.1224	+	3.61388i	0.833656	+	0.270871i
$179$	2.59483	−	7.98606i	0.193947	−	0.596906i	−0.806041	−	0.591860i	$-0.798394\pi$
$179$	2.59483	−	7.98606i	0.193947	−	0.596906i	0.999987	−	0.00504610i	$-0.00160623\pi$
$180$	−9.65219	+	0.679005i	−0.719432	+	0.0506100i
$181$	0.496698	+	1.52868i	0.0369192	+	0.113626i	0.967818	−	0.251652i	$-0.0809739\pi$
$181$	0.496698	+	1.52868i	0.0369192	+	0.113626i	−0.930898	+	0.365278i	$0.880974\pi$
$182$		−	6.36818i		−	0.472041i
$183$	−7.88624	+	2.56240i	−0.582968	+	0.189418i
$184$	13.4693	+	9.78602i	0.992970	+	0.721435i
$185$	1.02440	−	0.414384i	0.0753155	−	0.0304661i
$186$	8.02221	−	5.82847i	0.588217	−	0.427364i
$187$	9.37099	−	12.8981i	0.685275	−	0.943200i
$188$	4.98323	−	6.85883i	0.363440	−	0.500232i
$189$	−0.790797	+	0.574547i	−0.0575220	+	0.0417922i
$190$	1.39749	−	0.565302i	0.101384	−	0.0410113i
$191$	−3.42727	−	2.49006i	−0.247988	−	0.180174i	0.456846	−	0.889546i	$-0.348979\pi$
$191$	−3.42727	−	2.49006i	−0.247988	−	0.180174i	−0.704835	+	0.709371i	$0.748979\pi$
$192$	2.14453	−	0.696801i	0.154768	−	0.0502873i
$193$		−	9.40008i		−	0.676632i	−0.941032	−	0.338316i	$-0.890143\pi$
$193$		−	9.40008i		−	0.676632i	0.941032	−	0.338316i	$-0.109857\pi$
$194$	−1.58051	−	4.86430i	−0.113474	−	0.349237i
$195$	25.0133	−	1.75962i	1.79124	−	0.126009i
$196$	1.37771	−	4.24015i	0.0984078	−	0.302868i
$197$	6.27780	+	2.03978i	0.447275	+	0.145328i	0.523990	−	0.851725i	$-0.324443\pi$
$197$	6.27780	+	2.03978i	0.447275	+	0.145328i	−0.0767146	+	0.997053i	$0.524443\pi$
$198$	−5.51645	−	7.59274i	−0.392037	−	0.539592i
$199$	−18.9142			−1.34079			−0.670397	−	0.742003i	$-0.733876\pi$
$199$	−18.9142			−1.34079			−0.670397	+	0.742003i	$0.733876\pi$
$200$	−8.30930	−	8.59014i	−0.587556	−	0.607414i
$201$	−29.9098			−2.10967
$202$	−6.11278	−	8.41352i	−0.430094	−	0.591973i
$203$	−9.56519	−	3.10792i	−0.671345	−	0.218133i
$204$	3.68810	−	11.3508i	0.258219	−	0.794716i
$205$	−8.70050	−	21.5086i	−0.607669	−	1.50222i
$206$	−0.839240	−	2.58292i	−0.0584726	−	0.179960i
$207$		−	19.5023i		−	1.35550i
$208$	6.55206	−	2.12889i	0.454303	−	0.147612i
$209$	−4.02237	−	2.92242i	−0.278233	−	0.202148i
$210$	7.14684	+	1.77873i	0.493179	+	0.122744i
$211$	7.16820	−	5.20800i	0.493479	−	0.358534i	−0.313041	−	0.949739i	$-0.601348\pi$
$211$	7.16820	−	5.20800i	0.493479	−	0.358534i	0.806521	+	0.591206i	$0.201348\pi$
$212$	3.62572	−	4.99038i	0.249016	−	0.342740i
$213$	17.6308	−	24.2667i	1.20804	−	1.66273i
$214$	8.73806	−	6.34857i	0.597321	−	0.433979i
$215$	1.00255	−	1.60591i	0.0683736	−	0.109522i
$216$	0.931781	+	0.676979i	0.0633997	+	0.0460626i
$217$	11.7831	−	3.82856i	0.799888	−	0.259899i
$218$			0.299456i			0.0202817i
$219$	4.52513	+	13.9269i	0.305780	+	0.941093i
$220$	−4.14975	+	16.6734i	−0.279776	+	1.12412i
$221$	−4.61394	+	14.2003i	−0.310367	+	0.955212i
$222$	0.763099	+	0.247946i	0.0512159	+	0.0166410i
$223$	−10.2738	−	14.1407i	−0.687988	−	0.946934i	0.312007	−	0.950080i	$-0.398999\pi$
$223$	−10.2738	−	14.1407i	−0.687988	−	0.946934i	−0.999995	+	0.00314572i	$0.998999\pi$
$224$	11.7213			0.783162
$225$	−2.41947	+	13.7890i	−0.161298	+	0.919264i
$226$	1.48208			0.0985865
$227$	−9.47420	−	13.0401i	−0.628825	−	0.865503i	0.369133	−	0.929376i	$-0.379655\pi$
$227$	−9.47420	−	13.0401i	−0.628825	−	0.865503i	−0.997958	+	0.0638735i	$0.979655\pi$
$228$	−3.53985	−	1.15017i	−0.234432	−	0.0761716i
$229$	2.08909	−	6.42957i	0.138051	−	0.424878i	−0.858001	−	0.513648i	$-0.828294\pi$
$229$	2.08909	−	6.42957i	0.138051	−	0.424878i	0.996052	+	0.0887703i	$0.0282937\pi$
$230$	8.04076	−	6.75273i	0.530192	−	0.445262i
$231$	−7.50612	−	23.1015i	−0.493867	−	1.51997i
$232$			11.8505i			0.778023i
$233$	13.3641	−	4.34227i	0.875513	−	0.284471i	0.163420	−	0.986557i	$-0.447747\pi$
$233$	13.3641	−	4.34227i	0.875513	−	0.284471i	0.712093	+	0.702085i	$0.247747\pi$
$234$	7.11085	+	5.16633i	0.464851	+	0.337734i
$235$	−7.88850	−	9.39317i	−0.514589	−	0.612743i
$236$	5.50731	−	4.00129i	0.358495	−	0.260462i
$237$	−11.7043	+	16.1096i	−0.760278	+	1.04643i
$238$	−2.57769	+	3.54788i	−0.167087	+	0.229975i
$239$	−4.19432	+	3.04735i	−0.271308	+	0.197117i	−0.715117	−	0.699005i	$-0.753627\pi$
$239$	−4.19432	+	3.04735i	−0.271308	+	0.197117i	0.443809	+	0.896121i	$0.353627\pi$
$240$	0.559107	+	7.94783i	0.0360902	+	0.513030i
$241$	19.0605	+	13.8483i	1.22780	+	0.892045i	0.996723	−	0.0808911i	$-0.0257766\pi$
$241$	19.0605	+	13.8483i	1.22780	+	0.892045i	0.231072	+	0.972937i	$0.425777\pi$
$242$	−8.79692	+	2.85829i	−0.565487	+	0.183738i
$243$		−	21.5783i		−	1.38425i
$244$	1.64438	+	5.06088i	0.105271	+	0.323990i
$245$	−5.47176	−	3.41596i	−0.349578	−	0.218237i
$246$	5.20593	−	16.0222i	0.331918	−	1.02154i
$247$	4.42847	+	1.43890i	0.281777	+	0.0915548i
$248$	−8.58065	−	11.8103i	−0.544872	−	0.749952i
$249$	1.18296			0.0749671
$250$	−6.52291	+	3.77692i	−0.412545	+	0.238874i
$251$	−25.5290			−1.61137			−0.805687	−	0.592342i	$-0.798204\pi$
$251$	−25.5290			−1.61137			−0.805687	+	0.592342i	$0.798204\pi$
$252$	−5.15976	−	7.10180i	−0.325034	−	0.447372i
$253$	−32.9360	−	10.7016i	−2.07067	−	0.672801i
$254$	1.20461	−	3.70740i	0.0755838	−	0.232623i
$255$	−14.6478	−	9.14445i	−0.917282	−	0.572648i
$256$	−2.85463	−	8.78565i	−0.178414	−	0.549103i
$257$		−	17.3965i		−	1.08516i	−0.840003	−	0.542582i	$-0.817447\pi$
$257$		−	17.3965i		−	1.08516i	0.840003	−	0.542582i	$-0.182553\pi$
$258$	1.30735	−	0.424783i	0.0813920	−	0.0264459i
$259$	0.811052	+	0.589264i	0.0503963	+	0.0366151i
$260$	−1.12921	−	16.0519i	−0.0700305	−	0.995498i
$261$	11.2303	−	8.15932i	0.695140	−	0.505049i
$262$	−8.51945	+	11.7260i	−0.526333	+	0.724436i
$263$	9.21810	−	12.6876i	0.568412	−	0.782353i	−0.423953	−	0.905684i	$-0.639358\pi$
$263$	9.21810	−	12.6876i	0.568412	−	0.782353i	0.992366	+	0.123332i	$0.0393579\pi$
$264$	−23.1547	+	16.8229i	−1.42508	+	1.03538i
$265$	−5.73955	−	6.83432i	−0.352578	−	0.419829i
$266$	1.10644	+	0.803873i	0.0678399	+	0.0492886i
$267$	−39.7317	+	12.9096i	−2.43154	+	0.790056i
$268$			19.1941i			1.17247i
$269$	1.40539	+	4.32533i	0.0856879	+	0.263720i	0.984715	−	0.174172i	$-0.0557250\pi$
$269$	1.40539	+	4.32533i	0.0856879	+	0.263720i	−0.899027	+	0.437893i	$0.855725\pi$
$270$	0.556245	−	0.467142i	0.0338520	−	0.0284293i
$271$	−5.87013	+	18.0664i	−0.356585	+	1.09746i	0.598500	+	0.801123i	$0.295764\pi$
$271$	−5.87013	+	18.0664i	−0.356585	+	1.09746i	−0.955085	+	0.296332i	$0.904236\pi$
$272$	−4.51204	−	1.46605i	−0.273583	−	0.0888925i
$273$	13.3713	+	18.4041i	0.809270	+	1.11386i
$274$	5.18044			0.312962
$275$	21.9595	+	11.6525i	1.32421	+	0.702673i
$276$	−25.9250			−1.56050
$277$	0.549720	+	0.756624i	0.0330295	+	0.0454612i	0.825212	−	0.564823i	$-0.191055\pi$
$277$	0.549720	+	0.756624i	0.0330295	+	0.0454612i	−0.792183	+	0.610284i	$0.791055\pi$
$278$	−13.2693	−	4.31147i	−0.795842	−	0.258585i
$279$	−5.28424	+	16.2632i	−0.316359	+	0.973654i
$280$	2.61864	−	10.5215i	0.156494	−	0.628783i
$281$	4.11260	+	12.6573i	0.245337	+	0.755071i	0.995581	+	0.0939091i	$0.0299363\pi$
$281$	4.11260	+	12.6573i	0.245337	+	0.755071i	−0.750243	+	0.661162i	$0.770064\pi$
$282$		−	8.90651i		−	0.530375i
$283$	20.7866	−	6.75398i	1.23564	−	0.401482i	0.382883	−	0.923797i	$-0.374931\pi$
$283$	20.7866	−	6.75398i	1.23564	−	0.401482i	0.852753	+	0.522314i	$0.174931\pi$
$284$	−15.5728	−	11.3143i	−0.924074	−	0.671379i
$285$	−2.85177	+	4.56804i	−0.168924	+	0.270587i
$286$	12.6270	−	9.17404i	0.746649	−	0.542472i
$287$	12.3723	−	17.0290i	0.730315	−	1.00519i
$288$	−9.50916	+	13.0882i	−0.560333	+	0.771232i
$289$	−5.43483	+	3.94863i	−0.319696	+	0.232272i
$290$	7.25261	+	1.80506i	0.425888	+	0.105997i
$291$	14.7813	+	10.7392i	0.866495	+	0.629545i
$292$	8.93738	−	2.90393i	0.523021	−	0.169940i
$293$			8.30495i			0.485180i	0.970129	+	0.242590i	$0.0779970\pi$
$293$			8.30495i			0.485180i	−0.970129	+	0.242590i	$0.922003\pi$
$294$	−1.44735	−	4.45447i	−0.0844109	−	0.259790i
$295$	−3.69338	−	9.13045i	−0.215037	−	0.531595i
$296$	0.365025	−	1.12343i	0.0212166	−	0.0652981i
$297$	−2.27845	−	0.740313i	−0.132209	−	0.0429573i
$298$	3.41607	+	4.70182i	0.197888	+	0.272369i
$299$	32.4330			1.87565
$300$	18.3300	+	3.21627i	1.05829	+	0.185691i
$301$	1.71752			0.0989962
$302$	1.74491	+	2.40166i	0.100408	+	0.138200i
$303$	35.3319	+	11.4800i	2.02977	+	0.659511i
$304$	−0.457201	+	1.40712i	−0.0262222	+	0.0807038i
$305$	7.68008	−	0.540272i	0.439760	−	0.0309359i
$306$	−1.87043	−	5.75659i	−0.106925	−	0.329083i
$307$			12.8271i			0.732079i	0.930599	+	0.366040i	$0.119287\pi$
$307$			12.8271i			0.732079i	−0.930599	+	0.366040i	$0.880713\pi$
$308$	−14.8250	+	4.81694i	−0.844734	+	0.274471i
$309$	7.84878	+	5.70247i	0.446501	+	0.324402i
$310$	−8.53498	+	3.45251i	−0.484754	+	0.196089i
$311$	25.1209	−	18.2514i	1.42447	−	1.03494i	0.433461	−	0.901172i	$-0.357292\pi$
$311$	25.1209	−	18.2514i	1.42447	−	1.03494i	0.991013	−	0.133769i	$-0.0427079\pi$
$312$	15.7552	−	21.6852i	0.891963	−	1.22768i
$313$	4.85640	−	6.68426i	0.274500	−	0.377817i	−0.649402	−	0.760445i	$-0.724981\pi$
$313$	4.85640	−	6.68426i	0.274500	−	0.377817i	0.923902	+	0.382628i	$0.124981\pi$
$314$	6.69631	−	4.86515i	0.377894	−	0.274556i
$315$	−11.7739	+	4.76271i	−0.663386	+	0.268348i
$316$	10.3381	+	7.51108i	0.581564	+	0.422531i
$317$	7.75066	−	2.51834i	0.435320	−	0.141444i	−0.0831552	−	0.996537i	$-0.526500\pi$
$317$	7.75066	−	2.51834i	0.435320	−	0.141444i	0.518476	+	0.855092i	$0.326500\pi$
$318$		−	6.48023i		−	0.363393i
$319$	−7.61720	−	23.4433i	−0.426482	−	1.31258i
$320$	−2.08847	+	0.146918i	−0.116749	+	0.00821297i
$321$	−11.9229	+	36.6948i	−0.665469	+	2.04810i
$322$	9.05973	+	2.94368i	0.504879	+	0.164045i
$323$	−1.88478	−	2.59418i	−0.104872	−	0.144344i
$324$	−14.7752			−0.820846
$325$	−22.9315	−	4.02366i	−1.27201	−	0.223193i
$326$	9.16576			0.507644
$327$	−0.628771	−	0.865429i	−0.0347711	−	0.0478583i
$328$	−23.5878	−	7.66415i	−1.30242	−	0.423182i
$329$	3.43879	−	10.5835i	0.189587	−	0.583488i
$330$	6.76886	+	16.7334i	0.372614	+	0.921141i
$331$	−3.41999	−	10.5256i	−0.187980	−	0.578542i	0.812007	−	0.583647i	$-0.198375\pi$
$331$	−3.41999	−	10.5256i	−0.187980	−	0.578542i	−0.999987	+	0.00510542i	$0.998375\pi$
$332$		−	0.759148i		−	0.0416636i
$333$	−1.31597	+	0.427584i	−0.0721146	+	0.0234315i
$334$	13.8233	+	10.0432i	0.756378	+	0.549541i
$335$	26.9486	+	6.70707i	1.47236	+	0.366446i
$336$	−5.84778	+	4.24866i	−0.319023	+	0.231784i
$337$	1.42152	−	1.95656i	0.0774353	−	0.106580i	−0.768542	−	0.639799i	$-0.779018\pi$
$337$	1.42152	−	1.95656i	0.0774353	−	0.106580i	0.845978	+	0.533218i	$0.179018\pi$
$338$	−3.44030	+	4.73516i	−0.187127	+	0.257559i
$339$	−4.28322	+	3.11194i	−0.232632	+	0.169017i
$340$	−5.86832	+	9.40002i	−0.318254	+	0.509787i
$341$	24.5661	+	17.8483i	1.33033	+	0.966541i
$342$	−1.79524	+	0.583309i	−0.0970755	+	0.0315418i
$343$		−	20.0523i		−	1.08272i
$344$	−0.625364	−	1.92467i	−0.0337174	−	0.103771i
$345$	−9.05904	+	36.3987i	−0.487722	+	1.95964i
$346$	−1.21223	+	3.73088i	−0.0651701	+	0.200573i
$347$	9.16133	+	2.97670i	0.491806	+	0.159798i	0.544412	−	0.838818i	$-0.316753\pi$
$347$	9.16133	+	2.97670i	0.491806	+	0.159798i	−0.0526060	+	0.998615i	$0.516753\pi$
$348$	−10.8464	−	14.9288i	−0.581428	−	0.800267i
$349$	−10.5603			−0.565278			−0.282639	−	0.959226i	$-0.591210\pi$
$349$	−10.5603			−0.565278			−0.282639	+	0.959226i	$0.591210\pi$
$350$	−6.04041	−	3.20526i	−0.322874	−	0.171329i
$351$	2.24366			0.119757
$352$	16.8858	+	23.2412i	0.900014	+	1.23876i
$353$	5.17757	+	1.68229i	0.275574	+	0.0895394i	0.443544	−	0.896253i	$-0.353721\pi$
$353$	5.17757	+	1.68229i	0.275574	+	0.0895394i	−0.167970	+	0.985792i	$0.553721\pi$
$354$	2.20993	−	6.80147i	0.117456	−	0.361494i
$355$	−21.3269	+	17.9106i	−1.13192	+	0.950597i
$356$	8.28456	+	25.4973i	0.439081	+	1.35135i
$357$		−	15.6658i		−	0.829121i
$358$	−5.38398	+	1.74936i	−0.284552	+	0.0924566i
$359$	7.04399	+	5.11776i	0.371767	+	0.270105i	0.757943	−	0.652320i	$-0.226204\pi$
$359$	7.04399	+	5.11776i	0.371767	+	0.270105i	−0.386176	+	0.922425i	$0.626204\pi$
$360$	9.62414	+	11.4599i	0.507237	+	0.603988i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	0.636941	−	0.876673i	0.0334769	−	0.0460769i
$363$	19.4215	−	26.7314i	1.01937	−	1.40304i
$364$	11.8105	−	8.58086i	0.619040	−	0.449759i
$365$	−0.954107	−	13.5628i	−0.0499402	−	0.709911i
$366$	4.52264	+	3.28589i	0.236402	+	0.171756i
$367$	−34.1422	+	11.0935i	−1.78221	+	0.579074i	−0.999084	−	0.0427926i	$-0.986375\pi$
$367$	−34.1422	+	11.0935i	−1.78221	+	0.579074i	−0.783123	+	0.621867i	$0.786375\pi$
$368$			10.3054i			0.537206i
$369$	8.97765	+	27.6304i	0.467358	+	1.43838i
$370$	−0.631950	−	0.394518i	−0.0328535	−	0.0205100i
$371$	2.50201	−	7.70040i	0.129898	−	0.399785i
$372$	21.6192	+	7.02449i	1.12090	+	0.364203i
$373$	−15.5851	−	21.4510i	−0.806964	−	1.11069i	−0.991785	−	0.127919i	$-0.959170\pi$
$373$	−15.5851	−	21.4510i	−0.806964	−	1.11069i	0.184820	−	0.982772i	$-0.440830\pi$
$374$	−10.7482			−0.555778
$375$	10.9208	−	24.6115i	0.563946	−	1.27093i
$376$	−13.1121			−0.676206
$377$	13.5692	+	18.6764i	0.698850	+	0.961885i
$378$	0.626735	+	0.203639i	0.0322358	+	0.0104740i
$379$	0.291312	−	0.896566i	0.0149637	−	0.0460535i	−0.943296	−	0.331953i	$-0.892292\pi$
$379$	0.291312	−	0.896566i	0.0149637	−	0.0460535i	0.958260	+	0.285900i	$0.0922924\pi$
$380$	2.93147	+	1.83008i	0.150381	+	0.0938813i
$381$	4.30315	+	13.2437i	0.220457	+	0.678497i
$382$			2.85602i			0.146127i
$383$	−15.9898	+	5.19540i	−0.817040	+	0.265472i	−0.687577	−	0.726112i	$-0.741325\pi$
$383$	−15.9898	+	5.19540i	−0.817040	+	0.265472i	−0.129463	+	0.991584i	$0.541325\pi$
$384$	21.2854	+	15.4647i	1.08621	+	0.789181i
$385$	1.58264	+	22.4975i	0.0806588	+	1.14658i
$386$	−5.12696	+	3.72495i	−0.260955	+	0.189595i
$387$	−1.39338	+	1.91782i	−0.0708293	+	0.0974881i
$388$	6.89175	−	9.48568i	0.349875	−	0.481562i
$389$	−24.9252	+	18.1092i	−1.26376	+	0.918172i	−0.998936	−	0.0461255i	$-0.985313\pi$
$389$	−24.9252	+	18.1092i	−1.26376	+	0.918172i	−0.264820	+	0.964298i	$0.585313\pi$
$390$	−10.8717	−	12.9454i	−0.550510	−	0.655515i
$391$	−18.0693	−	13.1281i	−0.913802	−	0.663916i
$392$	−6.55785	+	2.13078i	−0.331222	+	0.107620i
$393$		−	51.7766i		−	2.61178i
$394$	−1.37516	−	4.23232i	−0.0692797	−	0.213221i
$395$	14.1580	−	11.8901i	0.712369	−	0.598256i
$396$	6.64843	−	20.4618i	0.334096	−	1.02824i
$397$	19.0163	+	6.17878i	0.954403	+	0.310104i	0.744503	−	0.667619i	$-0.232686\pi$
$397$	19.0163	+	6.17878i	0.954403	+	0.310104i	0.209900	+	0.977723i	$0.432686\pi$
$398$	7.49510	+	10.3161i	0.375696	+	0.517101i
$399$	−4.88550			−0.244581
$400$	1.27849	−	7.28634i	0.0639247	−	0.364317i
$401$	−6.65513			−0.332341			−0.166171	−	0.986097i	$-0.553140\pi$
$401$	−6.65513			−0.332341			−0.166171	+	0.986097i	$0.553140\pi$
$402$	11.8523	+	16.3133i	0.591138	+	0.813632i
$403$	−27.0463	−	8.78788i	−1.34727	−	0.437755i
$404$	7.36714	−	22.6737i	0.366529	−	1.12806i
$405$	−5.16295	+	20.7444i	−0.256549	+	1.03080i
$406$	2.09527	+	6.44858i	0.103987	+	0.320038i
$407$			2.45707i			0.121792i
$408$	−17.5553	+	5.70405i	−0.869115	+	0.282393i
$409$	2.74947	+	1.99761i	0.135953	+	0.0987754i	0.653683	−	0.756768i	$-0.273223\pi$
$409$	2.74947	+	1.99761i	0.135953	+	0.0987754i	−0.517730	+	0.855544i	$0.673223\pi$
$410$	−8.28340	+	13.2686i	−0.409088	+	0.655288i
$411$	−14.9715	+	10.8774i	−0.738489	+	0.536544i
$412$	3.65948	−	5.03684i	0.180289	−	0.248147i
$413$	5.25208	−	7.22887i	0.258438	−	0.355709i
$414$	−10.6369	+	7.72815i	−0.522774	+	0.379818i
$415$	−1.06584	−	0.265271i	−0.0523202	−	0.0130217i
$416$	−21.7662	−	15.8141i	−1.06717	−	0.775348i
$417$	47.4013	−	15.4016i	2.32125	−	0.754220i
$418$			3.35193i			0.163948i
$419$	−1.07052	−	3.29473i	−0.0522984	−	0.160958i	0.921496	−	0.388388i	$-0.126968\pi$
$419$	−1.07052	−	3.29473i	−0.0522984	−	0.160958i	−0.973795	+	0.227430i	$0.926968\pi$
$420$	6.33120	+	15.6514i	0.308931	+	0.763711i
$421$	4.82217	−	14.8411i	0.235018	−	0.723311i	−0.762101	−	0.647458i	$-0.775832\pi$
$421$	4.82217	−	14.8411i	0.235018	−	0.723311i	0.997119	−	0.0758531i	$-0.0241680\pi$
$422$	−5.68106	−	1.84589i	−0.276550	−	0.0898565i
$423$	9.02798	+	12.4259i	0.438955	+	0.604170i
$424$	−9.54017			−0.463311
$425$	11.1471	+	11.5238i	0.540711	+	0.558986i
$426$	−20.2220			−0.979757
$427$	4.10553	+	5.65078i	0.198681	+	0.273460i
$428$	23.5483	+	7.65131i	1.13825	+	0.369840i
$429$	−17.2292	+	53.0260i	−0.831833	+	2.56012i
$430$	−1.27317	+	0.0895641i	−0.0613978	+	0.00431916i
$431$	−4.88565	−	15.0365i	−0.235334	−	0.724282i	−0.997077	−	0.0764034i	$-0.975656\pi$
$431$	−4.88565	−	15.0365i	−0.235334	−	0.724282i	0.761743	−	0.647879i	$-0.224344\pi$
$432$			0.712908i			0.0342998i
$433$	−19.0562	+	6.19175i	−0.915784	+	0.297556i	−0.728736	−	0.684794i	$-0.759892\pi$
$433$	−19.0562	+	6.19175i	−0.915784	+	0.297556i	−0.187048	+	0.982351i	$0.559892\pi$
$434$	−6.75742	−	4.90955i	−0.324366	−	0.235666i
$435$	−24.7501	+	10.0118i	−1.18668	+	0.480027i
$436$	−0.555376	+	0.403504i	−0.0265977	+	0.0193244i
$437$	−4.09410	+	5.63505i	−0.195848	+	0.269561i
$438$	5.80280	−	7.98687i	0.277268	−	0.381627i
$439$	8.02926	−	5.83360i	0.383215	−	0.278422i	−0.379454	−	0.925211i	$-0.623888\pi$
$439$	8.02926	−	5.83360i	0.383215	−	0.278422i	0.762670	+	0.646788i	$0.223888\pi$
$440$	24.6348	−	9.96509i	1.17442	−	0.475067i
$441$	6.53450	+	4.74759i	0.311166	+	0.226076i
$442$	9.57341	−	3.11059i	0.455361	−	0.147956i
$443$		−	1.13958i		−	0.0541429i	−0.999634	−	0.0270714i	$-0.991382\pi$
$443$		−	1.13958i		−	0.0541429i	0.999634	−	0.0270714i	$-0.00861816\pi$
$444$	0.568399	+	1.74935i	0.0269750	+	0.0830206i
$445$	38.6931	−	2.72195i	1.83423	−	0.129033i
$446$	−3.64139	+	11.2071i	−0.172425	+	0.530669i
$447$	−19.7449	−	6.41551i	−0.933902	−	0.303443i
$448$	−1.11643	−	1.53664i	−0.0527464	−	0.0725992i
$449$	−28.1942			−1.33057			−0.665283	−	0.746591i	$-0.731689\pi$
$449$	−28.1942			−1.33057			−0.665283	+	0.746591i	$0.731689\pi$
$450$	8.47948	−	4.14451i	0.399727	−	0.195374i
$451$	51.5892			2.42924
$452$	1.99704	+	2.74869i	0.0939329	+	0.129287i
$453$	−10.0856	−	3.27700i	−0.473862	−	0.153967i
$454$	−3.35797	+	10.3348i	−0.157597	+	0.485035i
$455$	−7.92054	−	19.5804i	−0.371321	−	0.917945i
$456$	1.77886	+	5.47475i	0.0833025	+	0.256379i
$457$		−	3.40431i		−	0.159247i	−0.996825	−	0.0796233i	$-0.974628\pi$
$457$		−	3.40431i		−	0.159247i	0.996825	−	0.0796233i	$-0.0253718\pi$
$458$	−4.33463	+	1.40841i	−0.202544	+	0.0658106i
$459$	−1.25000	−	0.908177i	−0.0583449	−	0.0423901i
$460$	23.3583	+	5.81350i	1.08909	+	0.271056i
$461$	−14.3561	+	10.4303i	−0.668628	+	0.485787i	−0.869566	−	0.493817i	$-0.835601\pi$
$461$	−14.3561	+	10.4303i	−0.668628	+	0.485787i	0.200937	+	0.979604i	$0.435601\pi$
$462$	−9.62548	+	13.2483i	−0.447818	+	0.616369i
$463$	−20.2295	+	27.8436i	−0.940147	+	1.29400i	0.0156211	+	0.999878i	$0.495027\pi$
$463$	−20.2295	+	27.8436i	−0.940147	+	1.29400i	−0.955768	+	0.294123i	$0.904973\pi$
$464$	−5.93432	+	4.31154i	−0.275494	+	0.200158i
$465$	17.4168	−	27.8987i	0.807687	−	1.29377i
$466$	−7.66412	−	5.56831i	−0.355034	−	0.257947i
$467$	2.12267	−	0.689698i	0.0982255	−	0.0319154i	−0.259492	−	0.965745i	$-0.583555\pi$
$467$	2.12267	−	0.689698i	0.0982255	−	0.0319154i	0.357717	+	0.933830i	$0.383555\pi$
$468$			20.1493i			0.931402i
$469$	7.78542	+	23.9611i	0.359497	+	1.10642i
$470$	−1.99723	+	8.02473i	−0.0921251	+	0.370153i
$471$	−9.13694	+	28.1206i	−0.421008	+	1.29573i
$472$	−10.0131	−	3.25345i	−0.460890	−	0.149752i
$473$	2.47427	+	3.40553i	0.113767	+	0.156587i
$474$	13.4245			0.616608
$475$	3.59379	−	3.47630i	0.164894	−	0.159504i
$476$	−10.0533			−0.460791
$477$	6.56861	+	9.04092i	0.300756	+	0.413955i
$478$	3.32415	+	1.08008i	0.152043	+	0.0494018i
$479$	2.57135	−	7.91379i	0.117488	−	0.361590i	−0.874970	−	0.484177i	$-0.839119\pi$
$479$	2.57135	−	7.91379i	0.117488	−	0.361590i	0.992458	+	0.122587i	$0.0391190\pi$
$480$	23.8273	−	20.0105i	1.08756	−	0.913349i
$481$	−0.711086	−	2.18850i	−0.0324227	−	0.0997870i
$482$		−	15.8835i		−	0.723476i
$483$	−32.3635	+	10.5155i	−1.47259	+	0.478474i
$484$	−17.1545	−	12.4635i	−0.779750	−	0.566522i
$485$	−10.9097	−	12.9906i	−0.495384	−	0.589874i
$486$	−11.7692	+	8.55080i	−0.533860	+	0.387872i
$487$	2.62031	−	3.60655i	0.118738	−	0.163429i	−0.745511	−	0.666494i	$-0.767794\pi$
$487$	2.62031	−	3.60655i	0.118738	−	0.163429i	0.864249	+	0.503065i	$0.167794\pi$
$488$	4.83747	−	6.65821i	0.218982	−	0.301403i
$489$	−26.4891	+	19.2454i	−1.19788	+	0.870309i
$490$	0.305168	+	4.33802i	0.0137861	+	0.195972i
$491$	−6.94851	−	5.04839i	−0.313582	−	0.227831i	0.419850	−	0.907594i	$-0.362083\pi$
$491$	−6.94851	−	5.04839i	−0.313582	−	0.227831i	−0.733432	+	0.679763i	$0.762083\pi$
$492$	36.7298	−	11.9342i	1.65591	−	0.538037i
$493$		−	15.8976i		−	0.715992i
$494$	−0.970063	−	2.98555i	−0.0436452	−	0.134326i
$495$	−26.4052	−	16.4844i	−1.18682	−	0.740920i
$496$	2.79229	−	8.59380i	0.125378	−	0.385873i
$497$	−24.0296	−	7.80768i	−1.07787	−	0.350222i
$498$	−0.468770	−	0.645206i	−0.0210061	−	0.0289124i
$499$	37.5085			1.67911			0.839557	−	0.543272i	$-0.182815\pi$
$499$	37.5085			1.67911			0.839557	+	0.543272i	$0.182815\pi$
$500$	−15.7941	−	7.00824i	−0.706333	−	0.313418i
$501$	−61.0373			−2.72694
$502$	10.1163	+	13.9239i	0.451513	+	0.621455i
$503$	31.5174	+	10.2406i	1.40529	+	0.456606i	0.910898	−	0.412632i	$-0.135391\pi$
$503$	31.5174	+	10.2406i	1.40529	+	0.456606i	0.494392	+	0.869239i	$0.335391\pi$
$504$	−4.19540	+	12.9121i	−0.186878	+	0.575151i
$505$	−29.2596	−	18.2664i	−1.30204	−	0.812845i
$506$	7.21468	+	22.2045i	0.320732	+	0.987111i
$507$		−	20.9083i		−	0.928568i
$508$	8.49897	−	2.76148i	0.377081	−	0.122521i
$509$	−19.2278	−	13.9699i	−0.852259	−	0.619203i	0.0735086	−	0.997295i	$-0.476580\pi$
$509$	−19.2278	−	13.9699i	−0.852259	−	0.619203i	−0.925768	+	0.378092i	$0.876580\pi$
$510$	0.816929	+	11.6128i	0.0361742	+	0.514224i
$511$	9.97913	−	7.25026i	0.441451	−	0.320733i
$512$	9.18220	−	12.6382i	0.405800	−	0.558536i
$513$	−0.283223	+	0.389822i	−0.0125046	+	0.0172111i
$514$	−9.48834	+	6.89368i	−0.418513	+	0.304067i
$515$	−5.79298	−	6.89795i	−0.255269	−	0.303960i
$516$	2.54941	+	1.85225i	0.112231	+	0.0815409i
$517$	25.9392	−	8.42815i	1.14080	−	0.370670i
$518$		−	0.675867i		−	0.0296959i
$519$	−4.33039	−	13.3276i	−0.190083	−	0.585016i
$520$	−19.0581	+	16.0053i	−0.835755	+	0.701878i
$521$	−11.0543	+	34.0215i	−0.484296	+	1.49051i	0.348701	+	0.937234i	$0.386623\pi$
$521$	−11.0543	+	34.0215i	−0.484296	+	1.49051i	−0.832997	+	0.553277i	$0.813377\pi$
$522$	−8.90045	−	2.89193i	−0.389562	−	0.126576i
$523$	−24.8708	−	34.2317i	−1.08752	−	1.49685i	−0.850960	−	0.525231i	$-0.823979\pi$
$523$	−24.8708	−	34.2317i	−1.08752	−	1.49685i	−0.236563	−	0.971616i	$-0.576021\pi$
$524$	−33.2269			−1.45152
$525$	24.1869	−	3.41989i	1.05560	−	0.149256i
$526$	−10.5729			−0.460999
$527$	11.5111	+	15.8436i	0.501430	+	0.690160i
$528$	−16.8487	−	5.47447i	−0.733245	−	0.238246i
$529$	−7.88472	+	24.2667i	−0.342814	+	1.05507i
$530$	−1.45315	+	5.83867i	−0.0631208	+	0.253616i
$531$	3.81104	+	11.7292i	0.165385	+	0.509002i
$532$			3.13520i			0.135928i
$533$	−45.9502	+	14.9301i	−1.99033	+	0.646696i
$534$	22.7855	+	16.5547i	0.986027	+	0.716391i
$535$	18.9710	−	30.3883i	0.820189	−	1.31380i
$536$	24.0163	−	17.4489i	1.03735	−	0.753677i
$537$	11.8866	−	16.3604i	0.512943	−	0.706005i
$538$	1.80220	−	2.48051i	0.0776982	−	0.106942i
$539$	11.6035	−	8.43046i	0.499799	−	0.363126i
$540$	1.61588	+	0.402167i	0.0695366	+	0.0173065i
$541$	10.6474	+	7.73582i	0.457769	+	0.332589i	0.792656	−	0.609670i	$-0.208698\pi$
$541$	10.6474	+	7.73582i	0.457769	+	0.332589i	−0.334886	+	0.942259i	$0.608698\pi$
$542$	12.1799	−	3.95747i	0.523169	−	0.169988i
$543$			3.87098i			0.166120i
$544$	5.72536	+	17.6208i	0.245473	+	0.755487i
$545$	0.372454	+	0.920746i	0.0159542	+	0.0394404i
$546$	4.73924	−	14.5859i	0.202821	−	0.624219i
$547$	−19.8789	−	6.45904i	−0.849959	−	0.276169i	−0.148530	−	0.988908i	$-0.547454\pi$
$547$	−19.8789	−	6.45904i	−0.849959	−	0.276169i	−0.701429	+	0.712739i	$0.747454\pi$
$548$	6.98042	+	9.60773i	0.298189	+	0.410422i
$549$	−9.64048			−0.411446
$550$	−2.34638	−	16.5946i	−0.100050	−	0.707595i
$551$	−4.95780			−0.211209
$552$	23.5677	+	32.4382i	1.00311	+	1.38066i
$553$	15.9522	+	5.18319i	0.678358	+	0.220412i
$554$	0.194839	−	0.599652i	0.00827791	−	0.0254768i
$555$	2.65471	−	0.186751i	0.112686	−	0.00792715i
$556$	−9.88375	−	30.4191i	−0.419164	−	1.29006i
$557$			30.9468i			1.31126i	0.755084	+	0.655628i	$0.227596\pi$
$557$			30.9468i			1.31126i	−0.755084	+	0.655628i	$0.772404\pi$
$558$	10.9642	−	3.56249i	0.464152	−	0.150812i
$559$	−3.18939	−	2.31723i	−0.134897	−	0.0980084i
$560$	6.22157	−	2.51670i	0.262909	−	0.106350i
$561$	31.0624	−	22.5682i	1.31146	−	0.952830i
$562$	5.27380	−	7.25876i	0.222462	−	0.306193i
$563$	10.2579	−	14.1188i	0.432320	−	0.595037i	−0.536164	−	0.844114i	$-0.680127\pi$
$563$	10.2579	−	14.1188i	0.432320	−	0.595037i	0.968484	+	0.249077i	$0.0801271\pi$
$564$	16.5181	−	12.0011i	0.695539	−	0.505339i
$565$	4.55700	−	1.84336i	0.191714	−	0.0775509i
$566$	−11.9208	−	8.66097i	−0.501069	−	0.364048i
$567$	−18.4447	+	5.99304i	−0.774604	+	0.251684i
$568$			29.7707i			1.24915i
$569$	13.2176	+	40.6797i	0.554112	+	1.70538i	0.698278	+	0.715827i	$0.253950\pi$
$569$	13.2176	+	40.6797i	0.554112	+	1.70538i	−0.144167	+	0.989553i	$0.546050\pi$
$570$	3.62155	−	0.254766i	0.151690	−	0.0106710i
$571$	−1.14957	+	3.53800i	−0.0481078	+	0.148061i	−0.972225	−	0.234049i	$-0.924802\pi$
$571$	−1.14957	+	3.53800i	−0.0481078	+	0.148061i	0.924117	+	0.382110i	$0.124802\pi$
$572$	34.0286	+	11.0566i	1.42281	+	0.462298i
$573$	−5.99681	−	8.25390i	−0.250520	−	0.344812i
$574$	−14.1907			−0.592307
$575$	16.3243	−	30.7637i	0.680772	−	1.28293i
$576$	2.62157			0.109232
$577$	2.32734	+	3.20331i	0.0968885	+	0.133356i	0.854709	−	0.519108i	$-0.173736\pi$
$577$	2.32734	+	3.20331i	0.0968885	+	0.133356i	−0.757820	+	0.652463i	$0.773736\pi$
$578$	4.30730	+	1.39953i	0.179160	+	0.0582126i
$579$	6.99560	−	21.5302i	0.290727	−	0.894766i
$580$	6.42489	+	15.8830i	0.266779	+	0.659507i
$581$	−0.307921	−	0.947684i	−0.0127747	−	0.0393166i
$582$		−	12.3176i		−	0.510580i
$583$	18.8729	−	6.13219i	0.781637	−	0.253969i
$584$	−11.7582	−	8.54285i	−0.486559	−	0.353506i
$585$	28.2896	+	7.04083i	1.16963	+	0.291103i
$586$	4.52965	−	3.29099i	0.187118	−	0.135949i
$587$	24.5138	−	33.7404i	1.01179	−	1.39262i	0.0939951	−	0.995573i	$-0.470036\pi$
$587$	24.5138	−	33.7404i	1.01179	−	1.39262i	0.917800	−	0.397043i	$-0.129964\pi$
$588$	6.31110	−	8.68648i	0.260265	−	0.358225i
$589$	4.94097	−	3.58982i	0.203589	−	0.147916i
$590$	−3.51633	+	5.63254i	−0.144765	+	0.231888i
$591$	12.8609	+	9.34396i	0.529025	+	0.384359i
$592$	0.695382	−	0.225943i	0.0285800	−	0.00928622i
$593$			44.2788i			1.81831i	0.416457	+	0.909155i	$0.363272\pi$
$593$			44.2788i			1.81831i	−0.416457	+	0.909155i	$0.636728\pi$
$594$	0.499098	+	1.53607i	0.0204783	+	0.0630256i
$595$	−3.51295	+	14.1148i	−0.144017	+	0.578651i
$596$	−4.11706	+	12.6710i	−0.168641	+	0.519025i
$597$	−43.3217	−	14.0761i	−1.77304	−	0.576096i
$598$	−12.8522	−	17.6895i	−0.525564	−	0.723377i
$599$	−8.03009			−0.328101			−0.164050	−	0.986452i	$-0.552456\pi$
$599$	−8.03009			−0.328101			−0.164050	+	0.986452i	$0.552456\pi$
$600$	−12.6390	−	25.8590i	−0.515987	−	1.05569i
$601$	26.0958			1.06447			0.532235	−	0.846597i	$-0.321352\pi$
$601$	26.0958			1.06447			0.532235	+	0.846597i	$0.321352\pi$
$602$	−0.680598	−	0.936763i	−0.0277391	−	0.0381796i
$603$	−33.0715	−	10.7456i	−1.34678	−	0.437594i
$604$	−2.10297	+	6.47227i	−0.0855686	+	0.263353i
$605$	−23.4931	+	19.7298i	−0.955130	+	0.802130i
$606$	−7.73951	−	23.8198i	−0.314396	−	0.967612i
$607$		−	4.84324i		−	0.196581i	−0.995158	−	0.0982905i	$-0.968663\pi$
$607$		−	4.84324i		−	0.196581i	0.995158	−	0.0982905i	$-0.0313374\pi$
$608$	5.49520	−	1.78550i	0.222860	−	0.0724116i
$609$	−19.5955	−	14.2369i	−0.794049	−	0.576910i
$610$	−3.33805	−	3.97475i	−0.135154	−	0.160933i
$611$	−20.6648	+	15.0138i	−0.836007	+	0.607394i
$612$	8.15595	−	11.2257i	0.329685	−	0.453772i
$613$	−11.5694	+	15.9239i	−0.467284	+	0.643161i	−0.975999	−	0.217774i	$-0.930121\pi$
$613$	−11.5694	+	15.9239i	−0.467284	+	0.643161i	0.508715	+	0.860935i	$0.330121\pi$
$614$	6.99609	−	5.08296i	0.282339	−	0.205131i
$615$	−3.92108	−	55.7389i	−0.158113	−	2.24761i
$616$	19.5041	+	14.1706i	0.785844	+	0.570949i
$617$	−34.3454	+	11.1595i	−1.38270	+	0.449265i	−0.903554	−	0.428473i	$-0.859052\pi$
$617$	−34.3454	+	11.1595i	−1.38270	+	0.449265i	−0.479141	+	0.877738i	$0.659052\pi$
$618$		−	6.54056i		−	0.263100i
$619$	11.7333	+	36.1112i	0.471599	+	1.45143i	0.850490	+	0.525992i	$0.176306\pi$
$619$	11.7333	+	36.1112i	0.471599	+	1.45143i	−0.378890	+	0.925442i	$0.623694\pi$
$620$	−17.9036	−	11.1770i	−0.719026	−	0.448879i
$621$	−1.03713	+	3.19195i	−0.0416185	+	0.128088i
$622$	−19.9092	−	6.46889i	−0.798286	−	0.259379i
$623$	20.6841	+	28.4692i	0.828692	+	1.14060i
$624$	16.5914			0.664187
$625$	−15.3586	+	19.7260i	−0.614342	+	0.789040i
$626$	−5.57014			−0.222628
$627$	−7.03808	−	9.68708i	−0.281074	−	0.386865i
$628$	18.0460	+	5.86349i	0.720113	+	0.233979i
$629$	−0.489686	+	1.50710i	−0.0195251	+	0.0600920i
$630$	7.26329	+	4.53439i	0.289377	+	0.180654i
$631$	10.4314	+	32.1045i	0.415267	+	1.27806i	0.912012	+	0.410164i	$0.134529\pi$
$631$	10.4314	+	32.1045i	0.415267	+	1.27806i	−0.496744	+	0.867897i	$0.665471\pi$
$632$		−	19.7635i		−	0.786150i
$633$	20.2941	−	6.59396i	0.806618	−	0.262086i
$634$	−4.44489	−	3.22940i	−0.176529	−	0.128256i
$635$	−0.907304	−	12.8975i	−0.0360052	−	0.511822i
$636$	12.0183	−	8.73183i	0.476558	−	0.346240i
$637$	−7.89540	+	10.8671i	−0.312827	+	0.430570i
$638$	−9.76793	+	13.4444i	−0.386716	+	0.532269i
$639$	28.2127	−	20.4978i	1.11608	−	0.810879i
$640$	−15.7102	−	18.7068i	−0.621000	−	0.739450i
$641$	−32.0008	−	23.2499i	−1.26396	−	0.918317i	−0.265011	−	0.964245i	$-0.585376\pi$
$641$	−32.0008	−	23.2499i	−1.26396	−	0.918317i	−0.998945	+	0.0459280i	$0.985376\pi$
$642$	24.7386	−	8.03805i	0.976354	−	0.317237i
$643$		−	20.7542i		−	0.818465i	−0.912430	−	0.409232i	$-0.865797\pi$
$643$		−	20.7542i		−	0.818465i	0.912430	−	0.409232i	$-0.134203\pi$
$644$	6.74819	+	20.7688i	0.265916	+	0.818406i
$645$	3.49141	−	2.93213i	0.137474	−	0.115453i
$646$	−0.668030	+	2.05598i	−0.0262833	+	0.0808916i
$647$	29.4658	+	9.57401i	1.15842	+	0.376393i	0.824308	−	0.566141i	$-0.191564\pi$
$647$	29.4658	+	9.57401i	1.15842	+	0.376393i	0.334110	+	0.942534i	$0.391564\pi$
$648$	13.4318	+	18.4872i	0.527649	+	0.726247i
$649$	21.8997			0.859640
$650$	6.89245	+	14.1017i	0.270344	+	0.553113i
$651$	29.8376			1.16943
$652$	12.3505	+	16.9990i	0.483682	+	0.665731i
$653$	0.352560	+	0.114554i	0.0137967	+	0.00448283i	0.315907	−	0.948790i	$-0.397691\pi$
$653$	0.352560	+	0.114554i	0.0137967	+	0.00448283i	−0.302110	+	0.953273i	$0.597691\pi$
$654$	−0.222857	+	0.685884i	−0.00871441	+	0.0268202i
$655$	−11.6106	+	46.6505i	−0.453662	+	1.82279i
$656$	−4.74396	−	14.6004i	−0.185221	−	0.570050i
$657$			17.0248i			0.664202i
$658$	−7.13511	+	2.31834i	−0.278156	+	0.0903782i
$659$	11.9418	+	8.67619i	0.465185	+	0.337976i	0.795562	−	0.605873i	$-0.207176\pi$
$659$	11.9418	+	8.67619i	0.465185	+	0.337976i	−0.330377	+	0.943849i	$0.607176\pi$
$660$	−21.9132	+	35.1011i	−0.852970	+	1.36631i
$661$	−38.8062	+	28.1944i	−1.50939	+	1.09663i	−0.542938	+	0.839773i	$0.682688\pi$
$661$	−38.8062	+	28.1944i	−1.50939	+	1.09663i	−0.966448	+	0.256861i	$0.917312\pi$
$662$	−4.38563	+	6.03630i	−0.170452	+	0.234607i
$663$	−21.1358	+	29.0910i	−0.820848	+	1.12980i
$664$	−0.949870	+	0.690121i	−0.0368621	+	0.0267819i
$665$	4.40182	+	1.09554i	0.170695	+	0.0424833i
$666$	0.754688	+	0.548313i	0.0292435	+	0.0212467i
$667$	−32.8425	+	10.6712i	−1.27167	+	0.413189i
$668$			39.1697i			1.51552i
$669$	−13.0079	−	40.0343i	−0.502915	−	1.54781i
$670$	−7.02073	−	17.3560i	−0.271234	−	0.670521i
$671$	−5.29004	+	16.2811i	−0.204220	+	0.628524i
$672$	26.8468	+	8.72306i	1.03564	+	0.336500i
$673$	−23.8072	−	32.7678i	−0.917699	−	1.26310i	−0.964468	−	0.264199i	$-0.914892\pi$
$673$	−23.8072	−	32.7678i	−0.917699	−	1.26310i	0.0467686	−	0.998906i	$-0.485108\pi$
$674$	−1.63044			−0.0628023
$675$	1.12929	−	2.12817i	0.0434663	−	0.0819134i
$676$	−13.4176			−0.516060
$677$	16.3873	+	22.5551i	0.629814	+	0.866864i	0.998021	−	0.0628796i	$-0.0200284\pi$
$677$	16.3873	+	22.5551i	0.629814	+	0.866864i	−0.368208	+	0.929744i	$0.620028\pi$
$678$	3.39460	+	1.10297i	0.130369	+	0.0423594i
$679$	4.75581	−	14.6369i	0.182511	−	0.561711i
$680$	17.0963	−	1.20268i	0.655614	−	0.0461206i
$681$	−11.9955	−	36.9183i	−0.459667	−	1.41471i
$682$		−	20.4715i		−	0.783893i
$683$	14.5402	−	4.72440i	0.556365	−	0.180774i	−0.0173198	−	0.999850i	$-0.505513\pi$
$683$	14.5402	−	4.72440i	0.556365	−	0.180774i	0.573685	+	0.819076i	$0.305513\pi$
$684$	−3.50083	−	2.54350i	−0.133857	−	0.0972531i
$685$	15.9285	−	6.44327i	0.608595	−	0.246185i
$686$	−10.9368	+	7.94608i	−0.417571	+	0.303383i
$687$	9.56985	−	13.1718i	0.365113	−	0.502534i
$688$	0.736286	−	1.01341i	0.0280706	−	0.0386359i
$689$	−15.0353	+	10.9238i	−0.572801	+	0.416164i
$690$	23.4422	−	9.48269i	0.892431	−	0.361000i
$691$	−4.01146	−	2.91449i	−0.152603	−	0.110873i	0.508864	−	0.860847i	$-0.330066\pi$
$691$	−4.01146	−	2.91449i	−0.152603	−	0.110873i	−0.661467	+	0.749975i	$0.730066\pi$
$692$	−8.55278	+	2.77897i	−0.325128	+	0.105640i
$693$		−	28.2402i		−	1.07276i
$694$	−2.00681	−	6.17631i	−0.0761773	−	0.234450i
$695$	−46.1621	+	3.24737i	−1.75103	+	0.123180i
$696$	−8.81921	+	27.1427i	−0.334291	+	1.02884i
$697$	31.6434	+	10.2816i	1.19858	+	0.389442i
$698$	4.18470	+	5.75974i	0.158393	+	0.218009i
$699$	33.8412			1.27999
$700$	−2.19466	−	15.5216i	−0.0829504	−	0.586661i
$701$	−7.54835			−0.285097			−0.142549	−	0.989788i	$-0.545530\pi$
$701$	−7.54835			−0.285097			−0.142549	+	0.989788i	$0.545530\pi$
$702$	−0.889089	−	1.22373i	−0.0335565	−	0.0461866i
$703$	0.470002	+	0.152713i	0.0177264	+	0.00575967i
$704$	1.43854	−	4.42737i	0.0542170	−	0.166863i
$705$	−11.0776	−	27.3851i	−0.417207	−	1.03138i
$706$	−1.13415	−	3.49057i	−0.0426845	−	0.131369i
$707$		−	31.2930i		−	1.17690i
$708$	15.5919	−	5.06611i	0.585979	−	0.190396i
$709$	−17.3917	−	12.6358i	−0.653161	−	0.474549i	0.211186	−	0.977446i	$-0.432267\pi$
$709$	−17.3917	−	12.6358i	−0.653161	−	0.474549i	−0.864346	+	0.502897i	$0.832267\pi$
$710$	18.2199	+	4.53464i	0.683781	+	0.170182i
$711$	−18.7293	+	13.6076i	−0.702402	+	0.510325i
$712$	24.3717	−	33.5448i	0.913368	−	1.25714i
$713$	25.0042	−	34.4154i	0.936416	−	1.28887i
$714$	−8.54437	+	6.20785i	−0.319765	+	0.232323i
$715$	27.4142	−	43.9127i	1.02523	−	1.64224i
$716$	−10.4991	−	7.62802i	−0.392369	−	0.285073i
$717$	−11.8747	+	3.85831i	−0.443467	+	0.144091i
$718$		−	5.86991i		−	0.219063i
$719$	9.29241	+	28.5991i	0.346548	+	1.06657i	0.960750	+	0.277417i	$0.0894783\pi$
$719$	9.29241	+	28.5991i	0.346548	+	1.06657i	−0.614201	+	0.789149i	$0.710522\pi$
$720$	−2.23718	+	8.98886i	−0.0833748	+	0.334995i
$721$	2.52530	−	7.77209i	0.0940472	−	0.289448i
$722$	0.641175	+	0.208331i	0.0238621	+	0.00775326i
$723$	33.3508	+	45.9035i	1.24033	+	1.70717i
$724$	2.48414			0.0923224
$725$	24.5449	−	3.47050i	0.911573	−	0.128891i
$726$	−22.2759			−0.826736
$727$	−7.76678	−	10.6901i	−0.288054	−	0.396472i	0.640327	−	0.768103i	$-0.278799\pi$
$727$	−7.76678	−	10.6901i	−0.288054	−	0.396472i	−0.928381	+	0.371630i	$0.878799\pi$
$728$	−21.4733	−	6.97709i	−0.795853	−	0.258588i
$729$	7.19593	−	22.1468i	0.266516	−	0.820252i
$730$	−7.01931	+	5.89490i	−0.259796	+	0.218180i
$731$	0.838936	+	2.58198i	0.0310292	+	0.0954979i
$732$			12.8154i			0.473669i
$733$	10.5459	−	3.42657i	0.389521	−	0.126563i	−0.107707	−	0.994183i	$-0.534351\pi$
$733$	10.5459	−	3.42657i	0.389521	−	0.126563i	0.497229	+	0.867620i	$0.334351\pi$
$734$	19.5800	+	14.2257i	0.722712	+	0.525081i
$735$	−9.99053	−	11.8961i	−0.368506	−	0.438796i
$736$	32.5593	−	23.6557i	1.20015	−	0.871962i
$737$	−36.2948	+	49.9555i	−1.33694	+	1.84014i
$738$	11.5125	−	15.8456i	0.423781	−	0.583284i
$739$	19.6046	−	14.2436i	0.721166	−	0.523958i	−0.165590	−	0.986195i	$-0.552953\pi$
$739$	19.6046	−	14.2436i	0.721166	−	0.523958i	0.886757	+	0.462237i	$0.152953\pi$
$740$	−0.119845	−	1.70362i	−0.00440559	−	0.0626263i
$741$	9.07227	+	6.59139i	0.333278	+	0.242141i
$742$	−5.19139	+	1.68679i	−0.190582	+	0.0619238i
$743$		−	25.3492i		−	0.929973i	−0.885318	−	0.464987i	$-0.846059\pi$
$743$		−	25.3492i		−	0.929973i	0.885318	−	0.464987i	$-0.153941\pi$
$744$	−10.8641	−	33.4364i	−0.398298	−	1.22584i
$745$	16.3515	+	10.2080i	0.599071	+	0.373993i
$746$	−5.52387	+	17.0007i	−0.202243	+	0.622440i
$747$	1.30801	+	0.424999i	0.0478577	+	0.0155499i
$748$	−14.4828	−	19.9339i	−0.529544	−	0.728854i
$749$	32.5001			1.18753
$750$	−17.7511	+	3.79640i	−0.648178	+	0.138625i
$751$	37.5685			1.37089			0.685446	−	0.728123i	$-0.259607\pi$
$751$	37.5685			1.37089			0.685446	+	0.728123i	$0.259607\pi$
$752$	−4.77055	−	6.56610i	−0.173964	−	0.239441i
$753$	−58.4724	−	18.9988i	−2.13085	−	0.692355i
$754$	4.80938	−	14.8017i	0.175147	−	0.539048i
$755$	8.35223	+	5.21419i	0.303969	+	0.189764i
$756$	0.466827	+	1.43675i	0.0169784	+	0.0522540i
$757$			9.52318i			0.346126i	0.984911	+	0.173063i	$0.0553664\pi$
$757$			9.52318i			0.346126i	−0.984911	+	0.173063i	$0.944634\pi$
$758$	−0.604439	+	0.196394i	−0.0219542	+	0.00713336i
$759$	−67.4735	−	49.0224i	−2.44913	−	1.77940i
$760$	−0.375065	−	5.33163i	−0.0136050	−	0.193399i
$761$	19.1088	−	13.8833i	0.692692	−	0.503271i	−0.184852	−	0.982766i	$-0.559180\pi$
$761$	19.1088	−	13.8833i	0.692692	−	0.503271i	0.877544	+	0.479496i	$0.159180\pi$
$762$	5.51815	−	7.59508i	0.199901	−	0.275141i
$763$	−0.529638	+	0.728985i	−0.0191742	+	0.0263910i
$764$	−5.29682	+	3.84836i	−0.191632	+	0.139229i
$765$	−12.9109	−	15.3736i	−0.466796	−	0.555833i
$766$	9.16990	+	6.66232i	0.331322	+	0.240719i
$767$	−19.5060	+	6.33788i	−0.704321	+	0.228848i
$768$		−	22.2474i		−	0.802782i
$769$	7.39116	+	22.7477i	0.266532	+	0.820302i	0.991336	+	0.131347i	$0.0419302\pi$
$769$	7.39116	+	22.7477i	0.266532	+	0.820302i	−0.724804	+	0.688955i	$0.758070\pi$
$770$	11.6434	−	9.77826i	0.419598	−	0.352384i
$771$	12.9466	−	39.8455i	0.466260	−	1.43500i
$772$	−13.8167	−	4.48932i	−0.497274	−	0.161574i
$773$	−4.08991	−	5.62928i	−0.147104	−	0.202471i	0.729106	−	0.684401i	$-0.239936\pi$
$773$	−4.08991	−	5.62928i	−0.147104	−	0.202471i	−0.876210	+	0.481930i	$0.839936\pi$
$774$	1.59816			0.0574447
$775$	−21.9486	+	21.2311i	−0.788418	+	0.762642i
$776$	−18.1339			−0.650969
$777$	1.41913	+	1.95326i	0.0509108	+	0.0700728i
$778$	19.7541	+	6.41850i	0.708219	+	0.230114i
$779$	3.20639	−	9.86826i	0.114881	−	0.353567i
$780$	9.35957	−	37.6062i	0.335126	−	1.34652i
$781$	−19.1359	−	58.8941i	−0.684735	−	2.10740i
$782$			15.0575i			0.538456i
$783$	−2.27198	+	0.738211i	−0.0811940	+	0.0263815i
$784$	−3.45295	−	2.50872i	−0.123320	−	0.0895970i
$785$	14.5382	−	23.2877i	0.518891	−	0.831173i
$786$	−28.2398	+	20.5174i	−1.00728	+	0.731832i
$787$	−31.5768	+	43.4618i	−1.12559	+	1.54924i	−0.329410	+	0.944187i	$0.606850\pi$
$787$	−31.5768	+	43.4618i	−1.12559	+	1.54924i	−0.796182	+	0.605057i	$0.793150\pi$
$788$	5.99635	−	8.25327i	0.213611	−	0.294010i
$789$	30.5556	−	22.2000i	1.08781	−	0.790340i
$790$	−12.0954	−	3.01036i	−0.430337	−	0.107104i
$791$	3.60792	+	2.62131i	0.128283	+	0.0932029i
$792$	−31.6463	+	10.2825i	−1.12450	+	0.365373i
$793$		−	16.0324i		−	0.569329i
$794$	−4.16556	−	12.8203i	−0.147830	−	0.454975i
$795$	−8.05990	−	19.9250i	−0.285855	−	0.706665i
$796$	−9.03312	+	27.8011i	−0.320170	+	0.985383i
$797$	29.3994	+	9.55245i	1.04138	+	0.338365i	0.779281	−	0.626675i	$-0.215585\pi$
$797$	29.3994	+	9.55245i	1.04138	+	0.338365i	0.262101	+	0.965041i	$0.415585\pi$
$798$	1.93597	+	2.66463i	0.0685326	+	0.0943270i
$799$	17.5901			0.622293
$800$	−25.9556	+	12.6863i	−0.917667	+	0.448527i
$801$	−48.5698			−1.71613
$802$	2.63722	+	3.62982i	0.0931233	+	0.128173i
$803$	28.7520	+	9.34208i	1.01463	+	0.329675i
$804$	−14.2844	+	43.9629i	−0.503772	+	1.55045i
$805$	31.5175	−	2.21717i	1.11084	−	0.0781448i
$806$	5.92454	+	18.2339i	0.208683	+	0.642260i
$807$			10.9528i			0.385556i
$808$	−35.0674	+	11.3941i	−1.23367	+	0.400842i
$809$	−21.0006	−	15.2578i	−0.738341	−	0.536436i	0.153850	−	0.988094i	$-0.450833\pi$
$809$	−21.0006	−	15.2578i	−0.738341	−	0.536436i	−0.892191	+	0.451658i	$0.850833\pi$
$810$	13.3603	−	5.40440i	0.469432	−	0.189891i
$811$	−17.8376	+	12.9598i	−0.626363	+	0.455079i	−0.855138	−	0.518400i	$-0.826528\pi$
$811$	−17.8376	+	12.9598i	−0.626363	+	0.455079i	0.228775	+	0.973479i	$0.426528\pi$
$812$	−9.13635	+	12.5751i	−0.320623	+	0.441300i
$813$	−26.8903	+	37.0113i	−0.943082	+	1.29804i
$814$	1.34012	−	0.973658i	0.0469714	−	0.0341267i
$815$	28.1822	−	11.4001i	0.987180	−	0.399327i
$816$	−9.24349	−	6.71579i	−0.323587	−	0.235100i
$817$	0.805211	−	0.261629i	0.0281708	−	0.00915324i
$818$		−	2.29120i		−	0.0801098i
$819$	8.17285	+	25.1534i	0.285582	+	0.878932i
$820$	−35.7696	+	2.51629i	−1.24913	+	0.0878727i
$821$	4.46011	−	13.7268i	0.155659	−	0.479069i	−0.842568	−	0.538590i	$-0.818957\pi$
$821$	4.46011	−	13.7268i	0.155659	−	0.479069i	0.998227	+	0.0595206i	$0.0189572\pi$
$822$	11.8654	+	3.85532i	0.413855	+	0.134470i
$823$	−5.55924	−	7.65163i	−0.193783	−	0.266719i	0.701058	−	0.713104i	$-0.252711\pi$
$823$	−5.55924	−	7.65163i	−0.193783	−	0.266719i	−0.894841	+	0.446385i	$0.852711\pi$
$824$	−9.62898			−0.335442
$825$	41.6248	+	43.0317i	1.44919	+	1.49817i
$826$	−6.02398			−0.209601
$827$	10.8689	+	14.9598i	0.377949	+	0.520202i	0.955040	−	0.296478i	$-0.0958122\pi$
$827$	10.8689	+	14.9598i	0.377949	+	0.520202i	−0.577091	+	0.816680i	$0.695812\pi$
$828$	−28.6655	−	9.31398i	−0.996195	−	0.323683i
$829$	6.32552	−	19.4679i	0.219694	−	0.676150i	−0.779093	−	0.626909i	$-0.784320\pi$
$829$	6.32552	−	19.4679i	0.219694	−	0.676150i	0.998787	−	0.0492408i	$-0.0156802\pi$
$830$	0.277677	+	0.686447i	0.00963830	+	0.0238269i
$831$	0.696011	+	2.14210i	0.0241444	+	0.0743087i
$832$			4.35976i			0.151147i
$833$	8.79746	−	2.85847i	0.304814	−	0.0990401i
$834$	−27.1839	−	19.7503i	−0.941302	−	0.683896i
$835$	54.9944	+	13.6872i	1.90316	+	0.473665i
$836$	−6.21654	+	4.51658i	−0.215003	+	0.156209i
$837$	1.72975	−	2.38079i	0.0597888	−	0.0822922i
$838$	−1.37279	+	1.88948i	−0.0474221	+	0.0652709i
$839$	−10.6649	+	7.74854i	−0.368195	+	0.267509i	−0.756462	−	0.654038i	$-0.773074\pi$
$839$	−10.6649	+	7.74854i	−0.368195	+	0.267509i	0.388267	+	0.921547i	$0.373074\pi$
$840$	13.8280	−	22.1501i	0.477112	−	0.764250i
$841$	3.57602	+	2.59813i	0.123311	+	0.0895907i
$842$	−10.0055	+	3.25097i	−0.344811	+	0.112036i
$843$			32.0513i			1.10391i
$844$	−4.23157	−	13.0234i	−0.145657	−	0.448285i
$845$	−4.68854	+	18.8383i	−0.161291	+	0.648056i
$846$	3.19981	−	9.84801i	0.110012	−	0.338582i
$847$	−26.4703	−	8.60071i	−0.909529	−	0.295524i
$848$	−3.47098	−	4.77739i	−0.119194	−	0.164056i
$849$	52.6367			1.80649
$850$	1.86805	−	10.6463i	0.0640735	−	0.365165i
$851$	3.44218			0.117996
$852$	−27.2482	−	37.5040i	−0.933509	−	1.28486i
$853$	24.4757	+	7.95263i	0.838032	+	0.272293i	0.696425	−	0.717630i	$-0.254773\pi$
$853$	24.4757	+	7.95263i	0.838032	+	0.272293i	0.141607	+	0.989923i	$0.454773\pi$
$854$	1.45514	−	4.47845i	0.0497937	−	0.153249i
$855$	−4.79438	+	4.02638i	−0.163964	+	0.137699i
$856$	−11.8336	−	36.4200i	−0.404464	−	1.24481i
$857$		−	32.1127i		−	1.09695i	−0.836168	−	0.548474i	$-0.815209\pi$
$857$		−	32.1127i		−	1.09695i	0.836168	−	0.548474i	$-0.184791\pi$
$858$	35.7486	−	11.6154i	1.22044	−	0.396544i
$859$	−4.11951	−	2.99300i	−0.140556	−	0.102120i	0.515285	−	0.857019i	$-0.327686\pi$
$859$	−4.11951	−	2.99300i	−0.140556	−	0.102120i	−0.655841	+	0.754899i	$0.727686\pi$
$860$	−1.88165	−	2.24056i	−0.0641638	−	0.0764025i
$861$	41.0111	−	29.7963i	1.39765	−	1.01545i
$862$	−6.26512	+	8.62320i	−0.213391	+	0.293707i
$863$	−28.0522	+	38.6106i	−0.954909	+	1.31432i	−0.00559711	+	0.999984i	$0.501782\pi$
$863$	−28.0522	+	38.6106i	−0.954909	+	1.31432i	−0.949312	+	0.314335i	$0.898218\pi$
$864$	2.25239	−	1.63646i	0.0766280	−	0.0556735i
$865$	0.913048	+	12.9792i	0.0310446	+	0.441305i
$866$	10.9285	+	7.93999i	0.371364	+	0.269812i
$867$	−15.3867	+	4.99944i	−0.522560	+	0.169790i
$868$		−	19.1478i		−	0.649920i
$869$	12.7035	+	39.0973i	0.430937	+	1.32629i
$870$	15.2683	+	9.53179i	0.517643	+	0.323158i
$871$	17.8703	−	54.9991i	0.605511	−	1.86357i
$872$	1.00976	+	0.328089i	0.0341946	+	0.0111105i
$873$	12.4856	+	17.1849i	0.422573	+	0.581621i
$874$	4.69581			0.158838
$875$	−22.5592	−	2.34245i	−0.762641	−	0.0791893i
$876$	22.6316			0.764651
$877$	−0.940056	−	1.29388i	−0.0317434	−	0.0436911i	0.792850	−	0.609416i	$-0.208596\pi$
$877$	−0.940056	−	1.29388i	−0.0317434	−	0.0436911i	−0.824594	+	0.565725i	$0.808596\pi$
$878$	−6.36348	−	2.06762i	−0.214757	−	0.0697788i
$879$	−6.18060	+	19.0219i	−0.208466	+	0.641593i
$880$	13.9530	+	8.71068i	0.470355	+	0.293637i
$881$	−11.8317	−	36.4142i	−0.398620	−	1.22683i	−0.926107	−	0.377262i	$-0.876866\pi$
$881$	−11.8317	−	36.4142i	−0.398620	−	1.22683i	0.527487	−	0.849563i	$-0.323134\pi$
$882$		−	5.44534i		−	0.183354i
$883$	−55.1805	+	17.9292i	−1.85697	+	0.603367i	−0.861564	+	0.507649i	$0.830515\pi$
$883$	−55.1805	+	17.9292i	−1.85697	+	0.603367i	−0.995409	+	0.0957179i	$0.969485\pi$
$884$	18.6687	+	13.5636i	0.627897	+	0.456194i
$885$	−1.66451	−	23.6613i	−0.0559518	−	0.795366i
$886$	−0.621543	+	0.451578i	−0.0208812	+	0.0151710i
$887$	−4.53353	+	6.23987i	−0.152221	+	0.209514i	−0.878317	−	0.478080i	$-0.841333\pi$
$887$	−4.53353	+	6.23987i	−0.152221	+	0.209514i	0.726095	+	0.687594i	$0.241333\pi$
$888$	1.67213	−	2.30149i	0.0561130	−	0.0772329i
$889$	9.48961	−	6.89461i	0.318271	−	0.231238i
$890$	−16.8174	−	20.0252i	−0.563722	−	0.671247i
$891$	−38.4546	−	27.9389i	−1.28828	−	0.935990i
$892$	−25.6914	+	8.34764i	−0.860212	+	0.279500i
$893$		−	5.48562i		−	0.183569i
$894$	4.32516	+	13.3115i	0.144655	+	0.445202i
$895$	−14.3785	+	12.0752i	−0.480619	+	0.403630i
$896$	6.84846	−	21.0774i	0.228791	−	0.704146i
$897$	74.2856	+	24.1369i	2.48032	+	0.805906i
$898$	11.1725	+	15.3776i	0.372830	+	0.513157i
$899$	30.2791			1.00987
$900$	19.1122	+	10.1416i	0.637074	+	0.338055i
$901$	12.7983			0.426372
$902$	−20.4431	−	28.1376i	−0.680682	−	0.936879i
$903$	3.93386	+	1.27819i	0.130911	+	0.0425355i
$904$	1.62379	−	4.99752i	0.0540065	−	0.166215i
$905$	0.868042	−	3.48774i	0.0288547	−	0.115936i
$906$	2.20926	+	6.79941i	0.0733978	+	0.225895i
$907$			14.5638i			0.483583i	0.970328	+	0.241791i	$0.0777350\pi$
$907$			14.5638i			0.483583i	−0.970328	+	0.241791i	$0.922265\pi$
$908$	−23.6917	+	7.69792i	−0.786238	+	0.255464i
$909$	34.9425	+	25.3872i	1.15897	+	0.842039i
$910$	−7.54084	+	12.0791i	−0.249976	+	0.400418i
$911$	−17.6955	+	12.8565i	−0.586279	+	0.425956i	−0.840982	−	0.541063i	$-0.818022\pi$
$911$	−17.6955	+	12.8565i	−0.586279	+	0.425956i	0.254704	+	0.967019i	$0.418022\pi$
$912$	−2.09437	+	2.88266i	−0.0693516	+	0.0954543i
$913$	1.43550	−	1.97579i	0.0475080	−	0.0653892i
$914$	−1.85676	+	1.34902i	−0.0614163	+	0.0446215i
$915$	17.9928	+	4.47811i	0.594823	+	0.148042i
$916$	−8.45279	−	6.14131i	−0.279288	−	0.202915i
$917$	−41.4788	+	13.4773i	−1.36975	+	0.445059i
$918$			1.04165i			0.0343796i
$919$	9.74797	+	30.0012i	0.321556	+	0.989647i	0.972971	+	0.230926i	$0.0741755\pi$
$919$	9.74797	+	30.0012i	0.321556	+	0.989647i	−0.651416	+	0.758721i	$0.725825\pi$
$920$	−13.9604	−	34.5116i	−0.460260	−	1.13781i
$921$	−9.54598	+	29.3795i	−0.314551	+	0.968088i
$922$	11.3777	+	3.69684i	0.374705	+	0.121749i
$923$	34.0885	+	46.9187i	1.12204	+	1.54435i
$924$	−37.5405			−1.23499
$925$	−2.43376	−	0.427039i	−0.0800216	−	0.0140410i
$926$	23.2027			0.762487
$927$	6.62976	+	9.12509i	0.217750	+	0.299707i
$928$	27.2441	+	8.85216i	0.894333	+	0.290586i
$929$	−13.2735	+	40.8517i	−0.435490	+	1.34030i	0.457093	+	0.889419i	$0.348891\pi$
$929$	−13.2735	+	40.8517i	−0.435490	+	1.34030i	−0.892583	+	0.450883i	$0.851109\pi$
$930$	−22.1182	+	1.55595i	−0.725283	+	0.0510216i
$931$	−0.891437	−	2.74356i	−0.0292157	−	0.0899166i
$932$		−	21.7171i		−	0.711366i
$933$	71.1204	−	23.1084i	2.32838	−	0.756536i
$934$	−1.21732	−	0.884435i	−0.0398319	−	0.0289396i
$935$	−33.0479	+	13.3683i	−1.08078	+	0.437191i
$936$	25.2115	−	18.3172i	0.824062	−	0.598716i
$937$	−26.2446	+	36.1226i	−0.857374	+	1.18007i	0.124815	+	0.992180i	$0.460166\pi$
$937$	−26.2446	+	36.1226i	−0.857374	+	1.18007i	−0.982189	+	0.187895i	$0.939834\pi$
$938$	9.98364	−	13.7413i	0.325978	−	0.448670i
$939$	16.0977	−	11.6957i	0.525329	−	0.381674i
$940$	−17.5740	+	7.10890i	−0.573200	+	0.231867i
$941$	20.2213	+	14.6916i	0.659196	+	0.478934i	0.866391	−	0.499366i	$-0.166434\pi$
$941$	20.2213	+	14.6916i	0.659196	+	0.478934i	−0.207195	+	0.978300i	$0.566434\pi$
$942$	18.9581	−	6.15986i	0.617689	−	0.200699i
$943$		−	72.2727i		−	2.35352i
$944$	−2.01382	−	6.19791i	−0.0655444	−	0.201725i
$945$	2.18032	−	0.153379i	0.0709258	−	0.00498943i
$946$	0.876962	−	2.69901i	0.0285125	−	0.0877524i
$947$	−36.2237	−	11.7698i	−1.17711	−	0.382467i	−0.345819	−	0.938301i	$-0.612399\pi$
$947$	−36.2237	−	11.7698i	−1.17711	−	0.382467i	−0.831293	+	0.555835i	$0.812399\pi$
$948$	18.0890	+	24.8973i	0.587502	+	0.808627i
$949$	−28.3129			−0.919075
$950$	−3.32014	−	0.582566i	−0.107719	−	0.0189009i
$951$	19.6265			0.636434
$952$	9.13917	+	12.5790i	0.296202	+	0.407687i
$953$	−34.3141	−	11.1493i	−1.11154	−	0.361162i	−0.305008	−	0.952350i	$-0.598659\pi$
$953$	−34.3141	−	11.1493i	−1.11154	−	0.361162i	−0.806534	+	0.591188i	$0.798659\pi$
$954$	2.32813	−	7.16526i	0.0753761	−	0.231984i
$955$	3.55222	+	8.78148i	0.114947	+	0.284162i
$956$	2.47601	+	7.62038i	0.0800800	+	0.246461i
$957$		−	59.3642i		−	1.91897i
$958$	−5.33526	+	1.73353i	−0.172374	+	0.0560078i
$959$	12.6111	+	9.16248i	0.407233	+	0.295872i
$960$	−4.89284	−	1.21775i	−0.157916	−	0.0393026i
$961$	−5.09682	+	3.70306i	−0.164414	+	0.119453i
$962$	−0.911862	+	1.25507i	−0.0293996	+	0.0404651i
$963$	−26.3664	+	36.2903i	−0.849647	+	1.16944i
$964$	29.4579	−	21.4024i	0.948774	−	0.689325i
$965$	−11.1310	+	17.8300i	−0.358320	+	0.573967i
$966$	18.5600	+	13.4846i	0.597158	+	0.433860i
$967$	40.5074	−	13.1617i	1.30263	−	0.423251i	0.426135	−	0.904659i	$-0.359875\pi$
$967$	40.5074	−	13.1617i	1.30263	−	0.423251i	0.876496	+	0.481409i	$0.159875\pi$
$968$			32.7945i			1.05405i
$969$	−2.38636	−	7.34446i	−0.0766610	−	0.235938i
$970$	−2.76214	+	11.0981i	−0.0886869	+	0.356339i
$971$	−4.99860	+	15.3841i	−0.160413	+	0.493700i	−0.998669	−	0.0515768i	$-0.983575\pi$
$971$	−4.99860	+	15.3841i	−0.160413	+	0.493700i	0.838256	+	0.545276i	$0.183575\pi$
$972$	−31.7169	−	10.3054i	−1.01732	−	0.330547i
$973$	−24.6768	−	33.9647i	−0.791103	−	1.08886i
$974$	−3.00542			−0.0962999
$975$	−49.5286	−	26.2817i	−1.58618	−	0.841688i
$976$	5.09421			0.163062
$977$	18.7921	+	25.8650i	0.601211	+	0.827496i	0.995818	−	0.0913538i	$-0.0291194\pi$
$977$	18.7921	+	25.8650i	0.601211	+	0.827496i	−0.394607	+	0.918850i	$0.629119\pi$
$978$	20.9935	+	6.82122i	0.671300	+	0.218118i
$979$	−26.6518	+	82.0258i	−0.851796	+	2.62156i
$980$	−7.63417	+	6.41127i	−0.243865	+	0.204801i
$981$	−0.384318	−	1.18281i	−0.0122703	−	0.0377642i
$982$			5.79035i			0.184777i
$983$	16.3092	−	5.29919i	0.520183	−	0.169018i	−0.0371452	−	0.999310i	$-0.511826\pi$
$983$	16.3092	−	5.29919i	0.520183	−	0.169018i	0.557328	+	0.830292i	$0.311826\pi$
$984$	−48.3226	−	35.1084i	−1.54047	−	1.11922i
$985$	−9.49228	−	11.3028i	−0.302449	−	0.360139i
$986$	−8.67082	+	6.29972i	−0.276135	+	0.200624i
$987$	15.7526	−	21.6817i	0.501412	−	0.690135i
$988$	4.22992	−	5.82199i	0.134572	−	0.185222i
$989$	4.77091	−	3.46627i	0.151706	−	0.110221i
$990$	1.47265	+	20.9341i	0.0468040	+	0.665329i
$991$	31.4521	+	22.8513i	0.999110	+	0.725896i	0.961897	−	0.273411i	$-0.0881520\pi$
$991$	31.4521	+	22.8513i	0.999110	+	0.725896i	0.0372130	+	0.999307i	$0.488152\pi$
$992$	−33.5613	+	10.9047i	−1.06557	+	0.346225i
$993$		−	26.6535i		−	0.845822i
$994$	5.26372	+	16.2001i	0.166955	+	0.513834i
$995$	35.8763	+	22.3971i	1.13735	+	0.710036i
$996$	0.564963	−	1.73878i	0.0179015	−	0.0550952i
$997$	−5.09999	−	1.65709i	−0.161518	−	0.0524805i	0.227142	−	0.973862i	$-0.427062\pi$
$997$	−5.09999	−	1.65709i	−0.161518	−	0.0524805i	−0.388660	+	0.921381i	$0.627062\pi$
$998$	−14.8634	−	20.4578i	−0.470494	−	0.647580i
$999$	0.238123			0.00753389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.8	✓	80
25.9	even	10	inner	475.2.n.a.134.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.8	✓	80	1.1	even	1	trivial
475.2.n.a.134.8	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396268 - 0.545416i) q^{2} +(2.29043 + 0.744207i) q^{3} +(0.477583 - 1.46985i) q^{4} +(-1.89679 - 1.18414i) q^{5} +(-0.501723 - 1.54414i) q^{6} -2.02861i q^{7} +(-2.27328 + 0.738634i) q^{8} +(2.26518 + 1.64575i) q^{9} +O(q^{10})\)	\(q+(-0.396268 - 0.545416i) q^{2} +(2.29043 + 0.744207i) q^{3} +(0.477583 - 1.46985i) q^{4} +(-1.89679 - 1.18414i) q^{5} +(-0.501723 - 1.54414i) q^{6} -2.02861i q^{7} +(-2.27328 + 0.738634i) q^{8} +(2.26518 + 1.64575i) q^{9} +(0.105787 + 1.50378i) q^{10} +(4.02237 - 2.92242i) q^{11} +(2.18774 - 3.01117i) q^{12} +(-2.73694 + 3.76708i) q^{13} +(-1.10644 + 0.803873i) q^{14} +(-3.46322 - 4.12380i) q^{15} +(-1.19697 - 0.869647i) q^{16} +(3.04964 - 0.990889i) q^{17} -1.88763i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.64639 + 2.22247i) q^{20} +(1.50970 - 4.64639i) q^{21} +(-3.18787 - 1.03580i) q^{22} +(-4.09410 - 5.63505i) q^{23} -5.75650 q^{24} +(2.19561 + 4.49213i) q^{25} +3.13919 q^{26} +(-0.283223 - 0.389822i) q^{27} +(-2.98175 - 0.968829i) q^{28} +(1.53204 - 4.71515i) q^{29} +(-0.876824 + 3.52303i) q^{30} +(1.88728 + 5.80846i) q^{31} +5.77800i q^{32} +(11.3878 - 3.70014i) q^{33} +(-1.74892 - 1.27067i) q^{34} +(-2.40216 + 3.84784i) q^{35} +(3.50083 - 2.54350i) q^{36} +(-0.290477 + 0.399807i) q^{37} +(-0.396268 + 0.545416i) q^{38} +(-9.07227 + 6.59139i) q^{39} +(5.18658 + 1.29086i) q^{40} +(8.39444 + 6.09892i) q^{41} +(-3.13246 + 1.01780i) q^{42} +0.846649i q^{43} +(-2.37451 - 7.30798i) q^{44} +(-2.34777 - 5.80395i) q^{45} +(-1.45109 + 4.46598i) q^{46} +(5.21713 + 1.69515i) q^{47} +(-2.09437 - 2.88266i) q^{48} +2.88475 q^{49} +(1.58003 - 2.97761i) q^{50} +7.72243 q^{51} +(4.22992 + 5.82199i) q^{52} +(3.79590 + 1.23336i) q^{53} +(-0.100383 + 0.308948i) q^{54} +(-11.0901 + 0.780160i) q^{55} +(1.49840 + 4.61160i) q^{56} -2.40830i q^{57} +(-3.17882 + 1.03286i) q^{58} +(3.56346 + 2.58901i) q^{59} +(-7.71535 + 3.12096i) q^{60} +(-2.78555 + 2.02382i) q^{61} +(2.42016 - 3.33106i) q^{62} +(3.33859 - 4.59517i) q^{63} +(0.757483 - 0.550344i) q^{64} +(9.65216 - 3.90442i) q^{65} +(-6.53076 - 4.74487i) q^{66} +(-11.8116 + 3.83782i) q^{67} -4.95575i q^{68} +(-5.18363 - 15.9536i) q^{69} +(3.05057 - 0.214599i) q^{70} +(3.84879 - 11.8453i) q^{71} +(-6.36502 - 2.06812i) q^{72} +(3.57401 + 4.91920i) q^{73} +0.333168 q^{74} +(1.68583 + 11.9229i) q^{75} -1.54549 q^{76} +(-5.92845 - 8.15981i) q^{77} +(7.19010 + 2.33621i) q^{78} +(-2.55505 + 7.86363i) q^{79} +(1.24061 + 3.06692i) q^{80} +(-2.95426 - 9.09229i) q^{81} -6.99528i q^{82} +(0.467160 - 0.151789i) q^{83} +(-6.10849 - 4.43808i) q^{84} +(-6.95788 - 1.73170i) q^{85} +(0.461776 - 0.335500i) q^{86} +(7.01809 - 9.65957i) q^{87} +(-6.98538 + 9.61455i) q^{88} +(-14.0339 + 10.1962i) q^{89} +(-2.23522 + 3.58043i) q^{90} +(7.64192 + 5.55218i) q^{91} +(-10.2380 + 3.32652i) q^{92} +14.7084i q^{93} +(-1.14282 - 3.51724i) q^{94} +(-0.540046 + 2.16987i) q^{95} +(-4.30003 + 13.2341i) q^{96} +(7.21523 + 2.34437i) q^{97} +(-1.14314 - 1.57339i) q^{98} +13.9210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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