LMFDB - Embedded newform 39.3.l.b.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(7,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("39.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	39.l (of order $12$, 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:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} + \cdots + 5184 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 178x^8 - 620x^7 + 1088x^6 + 640x^5 + 7921x^4 - 22128x^3 + 28800x^2 - 17280*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.2
Root			$0.689992 - 0.689992i$ of defining polynomial
Character	$\chi$	$=$	39.28
Dual form			39.3.l.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.942546 - 0.252555i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-2.63949 - 1.52391i) q^{4} +(6.89545 - 6.89545i) q^{5} +(0.437437 + 1.63254i) q^{6} +(-5.17460 + 1.38653i) q^{7} +(4.86294 + 4.86294i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-8.24076 + 4.75781i) q^{10} +(0.0813836 - 0.303728i) q^{11} +5.27898i q^{12} +(12.0477 + 4.88406i) q^{13} +5.22747 q^{14} +(-16.3148 - 4.37154i) q^{15} +(2.74026 + 4.74626i) q^{16} +(3.97936 + 2.29749i) q^{17} +(2.06998 - 2.06998i) q^{18} +(1.10893 + 4.13857i) q^{19} +(-28.7086 + 7.69243i) q^{20} +(6.56113 + 6.56113i) q^{21} +(-0.153416 + 0.265724i) q^{22} +(23.2175 - 13.4046i) q^{23} +(3.08298 - 11.5058i) q^{24} -70.0946i q^{25} +(-10.1220 - 7.64615i) q^{26} +5.19615 q^{27} +(15.7713 + 4.22589i) q^{28} +(7.34569 + 12.7231i) q^{29} +(14.2734 + 8.24076i) q^{30} +(-33.3193 + 33.3193i) q^{31} +(-8.50397 - 31.7372i) q^{32} +(-0.526072 + 0.140961i) q^{33} +(-3.17049 - 3.17049i) q^{34} +(-26.1204 + 45.2419i) q^{35} +(7.91848 - 4.57173i) q^{36} +(-6.45378 + 24.0858i) q^{37} -4.18086i q^{38} +(-3.10748 - 22.3012i) q^{39} +67.0644 q^{40} +(-33.5135 - 8.97992i) q^{41} +(-4.52712 - 7.84121i) q^{42} +(32.3017 + 18.6494i) q^{43} +(-0.677665 + 0.677665i) q^{44} +(7.57173 + 28.2581i) q^{45} +(-25.2690 + 6.77081i) q^{46} +(15.4956 + 15.4956i) q^{47} +(4.74626 - 8.22077i) q^{48} +(-17.5813 + 10.1505i) q^{49} +(-17.7027 + 66.0674i) q^{50} -7.95873i q^{51} +(-24.3568 - 31.2510i) q^{52} +10.8673 q^{53} +(-4.89761 - 1.31231i) q^{54} +(-1.53316 - 2.65552i) q^{55} +(-31.9064 - 18.4211i) q^{56} +(5.24749 - 5.24749i) q^{57} +(-3.71038 - 13.8473i) q^{58} +(-36.6456 + 9.81916i) q^{59} +(36.4010 + 36.4010i) q^{60} +(14.9287 - 25.8573i) q^{61} +(39.8199 - 22.9900i) q^{62} +(4.15959 - 15.5238i) q^{63} +10.1395i q^{64} +(116.752 - 49.3962i) q^{65} +0.531447 q^{66} +(-86.6166 - 23.2088i) q^{67} +(-7.00233 - 12.1284i) q^{68} +(-40.2139 - 23.2175i) q^{69} +(36.0458 - 36.0458i) q^{70} +(-10.0790 - 37.6154i) q^{71} +(-19.9287 + 5.33988i) q^{72} +(74.0873 + 74.0873i) q^{73} +(12.1660 - 21.0721i) q^{74} +(-105.142 + 60.7037i) q^{75} +(3.37981 - 12.6136i) q^{76} +1.68451i q^{77} +(-2.70333 + 21.8047i) q^{78} -61.9843 q^{79} +(51.6230 + 13.8323i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(29.3201 + 16.9280i) q^{82} +(63.4852 - 63.4852i) q^{83} +(-7.31946 - 27.3166i) q^{84} +(43.2817 - 11.5973i) q^{85} +(-25.7358 - 25.7358i) q^{86} +(12.7231 - 22.0371i) q^{87} +(1.87277 - 1.08125i) q^{88} +(-16.7879 + 62.6535i) q^{89} -28.5468i q^{90} +(-69.1136 - 8.56865i) q^{91} -81.7100 q^{92} +(78.8343 + 21.1236i) q^{93} +(-10.6918 - 18.5188i) q^{94} +(36.1838 + 20.8908i) q^{95} +(-40.2412 + 40.2412i) q^{96} +(-6.66892 - 24.8887i) q^{97} +(19.1347 - 5.12713i) q^{98} +(0.667032 + 0.667032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9 + 30 * q^10 + 22 * q^11 + 2 * q^13 + 92 * q^14 + 52 * q^16 - 6 * q^17 + 12 * q^18 + 4 * q^19 - 208 * q^20 + 54 * q^21 - 98 * q^22 - 18 * q^23 - 54 * q^24 - 44 * q^26 - 78 * q^28 + 128 * q^29 + 6 * q^30 - 66 * q^31 + 358 * q^32 - 6 * q^33 + 336 * q^34 + 14 * q^35 + 36 * q^36 - 36 * q^37 - 18 * q^39 - 12 * q^40 - 326 * q^41 - 6 * q^42 + 60 * q^43 - 236 * q^44 - 24 * q^45 - 138 * q^46 + 40 * q^47 - 144 * q^48 + 78 * q^49 - 40 * q^50 - 392 * q^52 + 80 * q^53 - 18 * q^54 + 166 * q^55 - 102 * q^56 + 250 * q^58 - 164 * q^59 + 396 * q^60 - 98 * q^61 + 228 * q^62 + 66 * q^63 + 514 * q^65 + 60 * q^66 - 230 * q^67 + 78 * q^68 - 54 * q^69 - 92 * q^70 + 70 * q^71 - 18 * q^72 + 106 * q^73 - 16 * q^74 - 150 * q^75 + 534 * q^76 - 456 * q^78 + 16 * q^79 + 124 * q^80 - 54 * q^81 - 156 * q^82 - 176 * q^83 - 30 * q^84 + 90 * q^85 - 612 * q^86 + 48 * q^87 - 318 * q^88 - 476 * q^89 + 106 * q^91 + 228 * q^92 + 66 * q^93 - 374 * q^94 - 234 * q^95 + 384 * q^96 - 306 * q^97 - 350 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.942546	−	0.252555i	−0.471273	−	0.126277i	0.0153630	−	0.999882i	$-0.495110\pi$
$2$	−0.942546	−	0.252555i	−0.471273	−	0.126277i	−0.486636	+	0.873605i	$0.661776\pi$
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$4$	−2.63949	−	1.52391i	−0.659873	−	0.380978i
$5$	6.89545	−	6.89545i	1.37909	−	1.37909i	0.532934	−	0.846157i	$-0.321089\pi$
$5$	6.89545	−	6.89545i	1.37909	−	1.37909i	0.846157	−	0.532934i	$-0.178911\pi$
$6$	0.437437	+	1.63254i	0.0729062	+	0.272090i
$7$	−5.17460	+	1.38653i	−0.739228	+	0.198076i	−0.608735	−	0.793374i	$-0.708323\pi$
$7$	−5.17460	+	1.38653i	−0.739228	+	0.198076i	−0.130493	+	0.991449i	$0.541656\pi$
$8$	4.86294	+	4.86294i	0.607867	+	0.607867i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−8.24076	+	4.75781i	−0.824076	+	0.475781i
$11$	0.0813836	−	0.303728i	0.00739851	−	0.0276116i	−0.962128	−	0.272598i	$-0.912117\pi$
$11$	0.0813836	−	0.303728i	0.00739851	−	0.0276116i	0.969526	+	0.244987i	$0.0787836\pi$
$12$			5.27898i			0.439915i
$13$	12.0477	+	4.88406i	0.926742	+	0.375697i
$13$	12.0477	+	4.88406i	0.926742	+	0.375697i
$14$	5.22747			0.373391
$15$	−16.3148	−	4.37154i	−1.08765	−	0.291436i
$16$	2.74026	+	4.74626i	0.171266	+	0.296641i
$17$	3.97936	+	2.29749i	0.234080	+	0.135146i	0.612453	−	0.790507i	$-0.290183\pi$
$17$	3.97936	+	2.29749i	0.234080	+	0.135146i	−0.378373	+	0.925653i	$0.623516\pi$
$18$	2.06998	−	2.06998i	0.114999	−	0.114999i
$19$	1.10893	+	4.13857i	0.0583645	+	0.217819i	0.988949	−	0.148259i	$-0.0473669\pi$
$19$	1.10893	+	4.13857i	0.0583645	+	0.217819i	−0.930584	+	0.366078i	$0.880700\pi$
$20$	−28.7086	+	7.69243i	−1.43543	+	0.384622i
$21$	6.56113	+	6.56113i	0.312435	+	0.312435i
$22$	−0.153416	+	0.265724i	−0.00697344	+	0.0120783i
$23$	23.2175	−	13.4046i	1.00946	−	0.582811i	0.0984248	−	0.995144i	$-0.468620\pi$
$23$	23.2175	−	13.4046i	1.00946	−	0.582811i	0.911033	+	0.412334i	$0.135286\pi$
$24$	3.08298	−	11.5058i	0.128458	−	0.479410i
$25$		−	70.0946i		−	2.80378i
$26$	−10.1220	−	7.64615i	−0.389307	−	0.294083i
$27$	5.19615			0.192450
$28$	15.7713	+	4.22589i	0.563259	+	0.150925i
$29$	7.34569	+	12.7231i	0.253300	+	0.438728i	0.964432	−	0.264330i	$-0.0851508\pi$
$29$	7.34569	+	12.7231i	0.253300	+	0.438728i	−0.711133	+	0.703058i	$0.751817\pi$
$30$	14.2734	+	8.24076i	0.475781	+	0.274692i
$31$	−33.3193	+	33.3193i	−1.07482	+	1.07482i	−0.0778512	+	0.996965i	$0.524806\pi$
$31$	−33.3193	+	33.3193i	−1.07482	+	1.07482i	−0.996965	+	0.0778512i	$0.975194\pi$
$32$	−8.50397	−	31.7372i	−0.265749	−	0.991789i
$33$	−0.526072	+	0.140961i	−0.0159416	+	0.00427153i
$34$	−3.17049	−	3.17049i	−0.0932498	−	0.0932498i
$35$	−26.1204	+	45.2419i	−0.746299	+	1.29263i
$36$	7.91848	−	4.57173i	0.219958	−	0.126993i
$37$	−6.45378	+	24.0858i	−0.174427	+	0.650969i	0.822222	+	0.569167i	$0.192734\pi$
$37$	−6.45378	+	24.0858i	−0.174427	+	0.650969i	−0.996649	+	0.0818020i	$0.973932\pi$
$38$		−	4.18086i		−	0.110023i
$39$	−3.10748	−	22.3012i	−0.0796789	−	0.571826i
$40$	67.0644			1.67661
$41$	−33.5135	−	8.97992i	−0.817403	−	0.219023i	−0.174192	−	0.984712i	$-0.555731\pi$
$41$	−33.5135	−	8.97992i	−0.817403	−	0.219023i	−0.643211	+	0.765689i	$0.722398\pi$
$42$	−4.52712	−	7.84121i	−0.107789	−	0.186695i
$43$	32.3017	+	18.6494i	0.751201	+	0.433706i	0.826128	−	0.563483i	$-0.190539\pi$
$43$	32.3017	+	18.6494i	0.751201	+	0.433706i	−0.0749265	+	0.997189i	$0.523872\pi$
$44$	−0.677665	+	0.677665i	−0.0154015	+	0.0154015i
$45$	7.57173	+	28.2581i	0.168261	+	0.627958i
$46$	−25.2690	+	6.77081i	−0.549326	+	0.147191i
$47$	15.4956	+	15.4956i	0.329693	+	0.329693i	0.852470	−	0.522777i	$-0.175104\pi$
$47$	15.4956	+	15.4956i	0.329693	+	0.329693i	−0.522777	+	0.852470i	$0.675104\pi$
$48$	4.74626	−	8.22077i	0.0988805	−	0.171266i
$49$	−17.5813	+	10.1505i	−0.358801	+	0.207154i
$50$	−17.7027	+	66.0674i	−0.354054	+	1.32135i
$51$		−	7.95873i		−	0.156053i
$52$	−24.3568	−	31.2510i	−0.468400	−	0.600981i
$53$	10.8673			0.205043			0.102522	−	0.994731i	$-0.467309\pi$
$53$	10.8673			0.205043			0.102522	+	0.994731i	$0.467309\pi$
$54$	−4.89761	−	1.31231i	−0.0906966	−	0.0243021i
$55$	−1.53316	−	2.65552i	−0.0278757	−	0.0482821i
$56$	−31.9064	−	18.4211i	−0.569756	−	0.328949i
$57$	5.24749	−	5.24749i	0.0920613	−	0.0920613i
$58$	−3.71038	−	13.8473i	−0.0639720	−	0.238747i
$59$	−36.6456	+	9.81916i	−0.621112	+	0.166426i	−0.555633	−	0.831428i	$-0.687524\pi$
$59$	−36.6456	+	9.81916i	−0.621112	+	0.166426i	−0.0654786	+	0.997854i	$0.520857\pi$
$60$	36.4010	+	36.4010i	0.606683	+	0.606683i
$61$	14.9287	−	25.8573i	0.244733	−	0.423890i	−0.717324	−	0.696740i	$-0.754633\pi$
$61$	14.9287	−	25.8573i	0.244733	−	0.423890i	0.962056	+	0.272851i	$0.0879664\pi$
$62$	39.8199	−	22.9900i	0.642257	−	0.370807i
$63$	4.15959	−	15.5238i	0.0660252	−	0.246409i
$64$			10.1395i			0.158429i
$65$	116.752	−	49.3962i	1.79618	−	0.759941i
$66$	0.531447			0.00805223
$67$	−86.6166	−	23.2088i	−1.29278	−	0.346401i	−0.454067	−	0.890967i	$-0.650027\pi$
$67$	−86.6166	−	23.2088i	−1.29278	−	0.346401i	−0.838717	+	0.544567i	$0.816694\pi$
$68$	−7.00233	−	12.1284i	−0.102975	−	0.178359i
$69$	−40.2139	−	23.2175i	−0.582811	−	0.336486i
$70$	36.0458	−	36.0458i	0.514940	−	0.514940i
$71$	−10.0790	−	37.6154i	−0.141958	−	0.529794i	−0.999872	−	0.0160009i	$-0.994907\pi$
$71$	−10.0790	−	37.6154i	−0.141958	−	0.529794i	0.857914	−	0.513793i	$-0.171760\pi$
$72$	−19.9287	+	5.33988i	−0.276787	+	0.0741650i
$73$	74.0873	+	74.0873i	1.01490	+	1.01490i	0.999887	+	0.0150077i	$0.00477727\pi$
$73$	74.0873	+	74.0873i	1.01490	+	1.01490i	0.0150077	+	0.999887i	$0.495223\pi$
$74$	12.1660	−	21.0721i	0.164405	−	0.284758i
$75$	−105.142	+	60.7037i	−1.40189	+	0.809382i
$76$	3.37981	−	12.6136i	0.0444712	−	0.165969i
$77$			1.68451i			0.0218767i
$78$	−2.70333	+	21.8047i	−0.0346581	+	0.279548i
$79$	−61.9843			−0.784612			−0.392306	−	0.919835i	$-0.628323\pi$
$79$	−61.9843			−0.784612			−0.392306	+	0.919835i	$0.628323\pi$
$80$	51.6230	+	13.8323i	0.645287	+	0.172904i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	29.3201	+	16.9280i	0.357563	+	0.206439i
$83$	63.4852	−	63.4852i	0.764882	−	0.764882i	−0.212318	−	0.977201i	$-0.568101\pi$
$83$	63.4852	−	63.4852i	0.764882	−	0.764882i	0.977201	+	0.212318i	$0.0681013\pi$
$84$	−7.31946	−	27.3166i	−0.0871365	−	0.325198i
$85$	43.2817	−	11.5973i	0.509197	−	0.136439i
$86$	−25.7358	−	25.7358i	−0.299254	−	0.299254i
$87$	12.7231	−	22.0371i	0.146243	−	0.253300i
$88$	1.87277	−	1.08125i	0.0212815	−	0.0122869i
$89$	−16.7879	+	62.6535i	−0.188629	+	0.703972i	0.805196	+	0.593009i	$0.202060\pi$
$89$	−16.7879	+	62.6535i	−0.188629	+	0.703972i	−0.993825	+	0.110963i	$0.964607\pi$
$90$		−	28.5468i		−	0.317187i
$91$	−69.1136	−	8.56865i	−0.759491	−	0.0941609i
$92$	−81.7100			−0.888152
$93$	78.8343	+	21.1236i	0.847681	+	0.227135i
$94$	−10.6918	−	18.5188i	−0.113743	−	0.197008i
$95$	36.1838	+	20.8908i	0.380883	+	0.219903i
$96$	−40.2412	+	40.2412i	−0.419179	+	0.419179i
$97$	−6.66892	−	24.8887i	−0.0687517	−	0.256585i	0.922992	−	0.384818i	$-0.125736\pi$
$97$	−6.66892	−	24.8887i	−0.0687517	−	0.256585i	−0.991744	+	0.128234i	$0.959069\pi$
$98$	19.1347	−	5.12713i	0.195252	−	0.0523177i
$99$	0.667032	+	0.667032i	0.00673770	+	0.00673770i
$100$	−106.818	+	185.014i	−1.06818	+	1.85014i
$101$	−29.2083	+	16.8634i	−0.289191	+	0.166964i	−0.637577	−	0.770387i	$-0.720063\pi$
$101$	−29.2083	+	16.8634i	−0.289191	+	0.166964i	0.348386	+	0.937351i	$0.386730\pi$
$102$	−2.01001	+	7.50147i	−0.0197060	+	0.0735438i
$103$			57.8138i			0.561299i	0.959810	+	0.280650i	$0.0905499\pi$
$103$			57.8138i			0.561299i	−0.959810	+	0.280650i	$0.909450\pi$
$104$	34.8361	+	82.3379i	0.334962	+	0.791711i
$105$	90.4839			0.861751
$106$	−10.2429	−	2.74458i	−0.0966313	−	0.0258923i
$107$	93.3606	+	161.705i	0.872529	+	1.51126i	0.859372	+	0.511351i	$0.170855\pi$
$107$	93.3606	+	161.705i	0.872529	+	1.51126i	0.0131573	+	0.999913i	$0.495812\pi$
$108$	−13.7152	−	7.91848i	−0.126993	−	0.0733192i
$109$	−76.2177	+	76.2177i	−0.699245	+	0.699245i	−0.964248	−	0.265002i	$-0.914627\pi$
$109$	−76.2177	+	76.2177i	−0.699245	+	0.699245i	0.265002	+	0.964248i	$0.414627\pi$
$110$	0.774415	+	2.89016i	0.00704013	+	0.0262741i
$111$	41.7179	−	11.1783i	0.375837	−	0.100705i
$112$	−20.7606	−	20.7606i	−0.185362	−	0.185362i
$113$	52.2233	−	90.4534i	0.462153	−	0.800472i	−0.536915	−	0.843636i	$-0.680410\pi$
$113$	52.2233	−	90.4534i	0.462153	−	0.800472i	0.999068	+	0.0431640i	$0.0137438\pi$
$114$	−6.27128	+	3.62073i	−0.0550113	+	0.0317608i
$115$	67.6643	−	252.526i	0.588385	−	2.19588i
$116$		−	44.7767i		−	0.386006i
$117$	−30.7606	+	23.9746i	−0.262912	+	0.204911i
$118$	37.0200			0.313729
$119$	−23.7771	−	6.37106i	−0.199808	−	0.0535384i
$120$	−58.0794	−	100.597i	−0.483995	−	0.838304i
$121$	104.703	+	60.4506i	0.865318	+	0.499591i
$122$	−20.6014	+	20.6014i	−0.168864	+	0.168864i
$123$	15.5537	+	58.0471i	0.126453	+	0.471928i
$124$	138.722	−	37.1704i	1.11872	−	0.299761i
$125$	−310.948	−	310.948i	−2.48758	−	2.48758i
$126$	−7.84121	+	13.5814i	−0.0622318	+	0.107789i
$127$	55.4089	−	31.9903i	0.436290	−	0.251892i	−0.265732	−	0.964047i	$-0.585614\pi$
$127$	55.4089	−	31.9903i	0.436290	−	0.251892i	0.702023	+	0.712154i	$0.252280\pi$
$128$	−31.4551	+	117.392i	−0.245743	+	0.917125i
$129$		−	64.6033i		−	0.500801i
$130$	−122.519	+	17.0720i	−0.942456	+	0.131323i
$131$	−84.2275			−0.642958			−0.321479	−	0.946917i	$-0.604180\pi$
$131$	−84.2275			−0.642958			−0.321479	+	0.946917i	$0.604180\pi$
$132$	1.60337	+	0.429623i	0.0121468	+	0.00325472i
$133$	−11.4765	−	19.8779i	−0.0862894	−	0.149458i
$134$	75.7786	+	43.7508i	0.565512	+	0.326499i
$135$	35.8298	−	35.8298i	0.265406	−	0.265406i
$136$	8.17887	+	30.5239i	0.0601387	+	0.224441i
$137$	−122.118	+	32.7214i	−0.891372	+	0.238842i	−0.675307	−	0.737537i	$-0.735989\pi$
$137$	−122.118	+	32.7214i	−0.891372	+	0.238842i	−0.216065	+	0.976379i	$0.569322\pi$
$138$	32.0398	+	32.0398i	0.232172	+	0.232172i
$139$	88.6393	−	153.528i	0.637693	−	1.10452i	−0.348245	−	0.937404i	$-0.613222\pi$
$139$	88.6393	−	153.528i	0.637693	−	1.10452i	0.985938	−	0.167113i	$-0.0534444\pi$
$140$	137.889	−	79.6105i	0.984924	−	0.568646i
$141$	9.82381	−	36.6629i	0.0696724	−	0.260021i
$142$			37.9997i			0.267604i
$143$	2.46391	−	3.26172i	0.0172301	−	0.0228093i
$144$	−16.4415			−0.114177
$145$	138.384	+	37.0798i	0.954369	+	0.255722i
$146$	−51.1197	−	88.5418i	−0.350135	−	0.606451i
$147$	30.4516	+	17.5813i	0.207154	+	0.119600i
$148$	53.7394	−	53.7394i	0.363104	−	0.363104i
$149$	−0.101905	−	0.380316i	−0.000683929	−	0.00255246i	0.965583	−	0.260095i	$-0.0837539\pi$
$149$	−0.101905	−	0.380316i	−0.000683929	−	0.00255246i	−0.966267	+	0.257543i	$0.917087\pi$
$150$	114.432	−	30.6620i	0.762880	−	0.204413i
$151$	28.4273	+	28.4273i	0.188260	+	0.188260i	0.794944	−	0.606683i	$-0.207500\pi$
$151$	28.4273	+	28.4273i	0.188260	+	0.188260i	−0.606683	+	0.794944i	$0.707500\pi$
$152$	−14.7330	+	25.5182i	−0.0969274	+	0.167883i
$153$	−11.9381	+	6.89246i	−0.0780267	+	0.0450488i
$154$	0.425430	−	1.58773i	0.00276254	−	0.0103099i
$155$			459.503i			2.96454i
$156$	−25.7829	+	63.5994i	−0.165275	+	0.407688i
$157$	−122.557			−0.780617			−0.390308	−	0.920684i	$-0.627632\pi$
$157$	−122.557			−0.780617			−0.390308	+	0.920684i	$0.627632\pi$
$158$	58.4231	+	15.6544i	0.369767	+	0.0990786i
$159$	−9.41135	−	16.3009i	−0.0591909	−	0.102522i
$160$	−277.481	−	160.204i	−1.73426	−	1.00127i
$161$	−101.555	+	101.555i	−0.630779	+	0.630779i
$162$	2.27299	+	8.48292i	0.0140308	+	0.0523637i
$163$	1.84022	−	0.493087i	0.0112897	−	0.00302507i	−0.253170	−	0.967422i	$-0.581473\pi$
$163$	1.84022	−	0.493087i	0.0112897	−	0.00302507i	0.264459	+	0.964397i	$0.414806\pi$
$164$	74.7741	+	74.7741i	0.455940	+	0.455940i
$165$	−2.65552	+	4.59949i	−0.0160940	+	0.0278757i
$166$	−75.8713	+	43.8043i	−0.457056	+	0.263881i
$167$	34.2280	−	127.741i	0.204958	−	0.764914i	−0.784504	−	0.620123i	$-0.787083\pi$
$167$	34.2280	−	127.741i	0.204958	−	0.764914i	0.989462	−	0.144790i	$-0.0462508\pi$
$168$			63.8127i			0.379838i
$169$	121.292	+	117.683i	0.717703	+	0.696349i
$170$	−43.7240			−0.257200
$171$	−12.4157	−	3.32678i	−0.0726064	−	0.0194548i
$172$	−56.8400	−	98.4497i	−0.330465	−	0.572382i
$173$	−251.676	−	145.305i	−1.45478	−	0.839915i	−0.456029	−	0.889965i	$-0.650729\pi$
$173$	−251.676	−	145.305i	−1.45478	−	0.839915i	−0.998747	+	0.0500494i	$0.984062\pi$
$174$	−17.5577	+	17.5577i	−0.100906	+	0.100906i
$175$	97.1882	+	362.711i	0.555361	+	2.07264i
$176$	1.66458	−	0.446024i	0.00945786	−	0.00253423i
$177$	46.4647	+	46.4647i	0.262513	+	0.262513i
$178$	31.6468	−	54.8139i	0.177791	−	0.307943i
$179$	163.408	−	94.3436i	0.912893	−	0.527059i	0.0315322	−	0.999503i	$-0.489961\pi$
$179$	163.408	−	94.3436i	0.912893	−	0.527059i	0.881361	+	0.472444i	$0.156628\pi$
$180$	23.0773	−	86.1257i	0.128207	−	0.478476i
$181$		−	41.0627i		−	0.226865i	−0.993546	−	0.113433i	$-0.963815\pi$
$181$		−	41.0627i		−	0.226865i	0.993546	−	0.113433i	$-0.0361846\pi$
$182$	62.9788	+	25.5313i	0.346037	+	0.140282i
$183$	−51.7145			−0.282593
$184$	178.091	+	47.7194i	0.967888	+	0.259345i
$185$	121.581	+	210.585i	0.657195	+	1.13830i
$186$	−68.9701	−	39.8199i	−0.370807	−	0.214086i
$187$	1.02167	−	1.02167i	0.00546345	−	0.00546345i
$188$	−17.2866	−	64.5144i	−0.0919498	−	0.343161i
$189$	−26.8880	+	7.20462i	−0.142265	+	0.0381197i
$190$	−28.8289	−	28.8289i	−0.151731	−	0.151731i
$191$	76.6779	−	132.810i	0.401455	−	0.695341i	−0.592447	−	0.805610i	$-0.701838\pi$
$191$	76.6779	−	132.810i	0.401455	−	0.695341i	0.993902	+	0.110269i	$0.0351712\pi$
$192$	15.2092	−	8.78105i	0.0792147	−	0.0457346i
$193$	−50.0546	+	186.806i	−0.259350	+	0.967908i	0.706268	+	0.707944i	$0.250377\pi$
$193$	−50.0546	+	186.806i	−0.259350	+	0.967908i	−0.965618	+	0.259964i	$0.916289\pi$
$194$			25.1430i			0.129603i
$195$	−175.204	−	132.349i	−0.898484	−	0.678715i
$196$	61.8741			0.315684
$197$	−125.139	−	33.5308i	−0.635222	−	0.170207i	−0.0731837	−	0.997318i	$-0.523316\pi$
$197$	−125.139	−	33.5308i	−0.635222	−	0.170207i	−0.562038	+	0.827111i	$0.689983\pi$
$198$	−0.460247	−	0.797171i	−0.00232448	−	0.00402612i
$199$	−154.129	−	88.9864i	−0.774518	−	0.447168i	0.0599662	−	0.998200i	$-0.480901\pi$
$199$	−154.129	−	88.9864i	−0.774518	−	0.447168i	−0.834484	+	0.551032i	$0.814234\pi$
$200$	340.866	−	340.866i	1.70433	−	1.70433i
$201$	40.1989	+	150.024i	0.199994	+	0.746390i
$202$	31.7891	−	8.51786i	0.157372	−	0.0421676i
$203$	−55.6520	−	55.6520i	−0.274148	−	0.274148i
$204$	−12.1284	+	21.0070i	−0.0594529	+	0.102975i
$205$	−293.012	+	169.170i	−1.42933	+	0.825221i
$206$	14.6011	−	54.4922i	0.0708793	−	0.264525i
$207$			80.4279i			0.388540i
$208$	9.83260	+	70.5649i	0.0472721	+	0.339254i
$209$	1.34725			0.00644615
$210$	−85.2853	−	22.8521i	−0.406120	−	0.108820i
$211$	−99.4899	−	172.322i	−0.471516	−	0.816690i	0.527953	−	0.849274i	$-0.322960\pi$
$211$	−99.4899	−	172.322i	−0.471516	−	0.816690i	−0.999469	+	0.0325837i	$0.989626\pi$
$212$	−28.6841	−	16.5608i	−0.135302	−	0.0781169i
$213$	−47.6944	+	47.6944i	−0.223917	+	0.223917i
$214$	−47.1573	−	175.993i	−0.220361	−	0.822399i
$215$	351.330	−	94.1387i	1.63410	−	0.437854i
$216$	25.2686	+	25.2686i	0.116984	+	0.116984i
$217$	126.216	−	218.612i	0.581640	−	1.00743i
$218$	91.0879	−	52.5896i	0.417834	−	0.241237i
$219$	46.9695	−	175.293i	0.214473	−	0.800422i
$220$			9.34562i			0.0424801i
$221$	36.7209	+	47.1148i	0.166158	+	0.213189i
$222$	−42.1442			−0.189839
$223$	−104.323	−	27.9532i	−0.467815	−	0.125351i	0.0172080	−	0.999852i	$-0.494522\pi$
$223$	−104.323	−	27.9532i	−0.467815	−	0.125351i	−0.485023	+	0.874501i	$0.661189\pi$
$224$	88.0092	+	152.436i	0.392898	+	0.680520i
$225$	182.111	+	105.142i	0.809382	+	0.467297i
$226$	−72.0673	+	72.0673i	−0.318882	+	0.318882i
$227$	−19.5749	−	73.0545i	−0.0862330	−	0.321826i	0.909312	−	0.416115i	$-0.136609\pi$
$227$	−19.5749	−	73.0545i	−0.0862330	−	0.321826i	−0.995545	+	0.0942894i	$0.969942\pi$
$228$	−21.8474	+	5.85400i	−0.0958220	+	0.0256754i
$229$	−166.985	−	166.985i	−0.729194	−	0.729194i	0.241265	−	0.970459i	$-0.422438\pi$
$229$	−166.985	−	166.985i	−0.729194	−	0.729194i	−0.970459	+	0.241265i	$0.922438\pi$
$230$	−127.553	+	220.929i	−0.554580	+	0.960561i
$231$	2.52676	−	1.45883i	0.0109384	−	0.00631527i
$232$	−26.1501	+	97.5934i	−0.112716	+	0.420661i
$233$		−	250.124i		−	1.07349i	−0.843743	−	0.536747i	$-0.819653\pi$
$233$		−	250.124i		−	1.07349i	0.843743	−	0.536747i	$-0.180347\pi$
$234$	35.0482	−	14.8285i	0.149779	−	0.0633694i
$235$	213.698			0.909354
$236$	111.689	+	29.9270i	0.473260	+	0.126810i
$237$	53.6800	+	92.9765i	0.226498	+	0.392306i
$238$	20.8020	+	12.0100i	0.0874034	+	0.0504624i
$239$	−200.613	+	200.613i	−0.839385	+	0.839385i	−0.988778	−	0.149393i	$-0.952268\pi$
$239$	−200.613	+	200.613i	−0.839385	+	0.839385i	0.149393	+	0.988778i	$0.452268\pi$
$240$	−23.9583	−	89.4136i	−0.0998262	−	0.372557i
$241$	74.0273	−	19.8355i	0.307167	−	0.0823052i	−0.101943	−	0.994790i	$-0.532506\pi$
$241$	74.0273	−	19.8355i	0.307167	−	0.0823052i	0.409110	+	0.912485i	$0.365839\pi$
$242$	−83.4208	−	83.4208i	−0.344714	−	0.344714i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$	−78.8083	+	45.5000i	−0.322985	+	0.186475i
$245$	−51.2381	+	191.223i	−0.209135	+	0.780503i
$246$		−	58.6403i		−	0.238375i
$247$	−6.85308	+	55.2761i	−0.0277452	+	0.223790i
$248$	−324.060			−1.30669
$249$	−150.208	−	40.2480i	−0.603244	−	0.161639i
$250$	214.551	+	371.614i	0.858205	+	1.48645i
$251$	401.597	+	231.862i	1.59999	+	0.923754i	0.991487	+	0.130202i	$0.0415627\pi$
$251$	401.597	+	231.862i	1.59999	+	0.923754i	0.608502	+	0.793552i	$0.291771\pi$
$252$	−34.6361	+	34.6361i	−0.137445	+	0.137445i
$253$	−2.18184	−	8.14272i	−0.00862386	−	0.0321847i
$254$	−60.3048	+	16.1586i	−0.237420	+	0.0636166i
$255$	−54.8790	−	54.8790i	−0.215212	−	0.215212i
$256$	79.5747	−	137.827i	0.310839	−	0.538389i
$257$	225.803	−	130.368i	0.878612	−	0.507267i	0.00841152	−	0.999965i	$-0.497322\pi$
$257$	225.803	−	130.368i	0.878612	−	0.507267i	0.870201	+	0.492698i	$0.163989\pi$
$258$	−16.3159	+	60.8916i	−0.0632398	+	0.236014i
$259$		−	133.583i		−	0.515764i
$260$	−383.441	−	47.5387i	−1.47477	−	0.182841i
$261$	−44.0742			−0.168866
$262$	79.3884	+	21.2720i	0.303009	+	0.0811910i
$263$	−203.056	−	351.704i	−0.772078	−	1.33728i	−0.936422	−	0.350875i	$-0.885884\pi$
$263$	−203.056	−	351.704i	−0.772078	−	1.33728i	0.164344	−	0.986403i	$-0.447449\pi$
$264$	−3.24374	−	1.87277i	−0.0122869	−	0.00709384i
$265$	74.9349	−	74.9349i	0.282773	−	0.282773i
$266$	5.79688	+	21.6342i	0.0217928	+	0.0813317i
$267$	108.519	−	29.0776i	0.406438	−	0.108905i
$268$	193.256	+	193.256i	0.721103	+	0.721103i
$269$	−188.681	+	326.805i	−0.701417	+	1.21489i	0.266552	+	0.963821i	$0.414116\pi$
$269$	−188.681	+	326.805i	−0.701417	+	1.21489i	−0.967969	+	0.251069i	$0.919218\pi$
$270$	−42.8203	+	24.7223i	−0.158594	+	0.0915640i
$271$	9.57586	−	35.7376i	0.0353353	−	0.131873i	−0.946005	−	0.324152i	$-0.894921\pi$
$271$	9.57586	−	35.7376i	0.0353353	−	0.131873i	0.981340	+	0.192279i	$0.0615878\pi$
$272$			25.1828i			0.0925839i
$273$	47.0012	+	111.091i	0.172166	+	0.406927i
$274$	123.366			0.450240
$275$	−21.2897	−	5.70455i	−0.0774170	−	0.0207438i
$276$	70.7629	+	122.565i	0.256387	+	0.444076i
$277$	287.203	+	165.817i	1.03683	+	0.598616i	0.918935	−	0.394410i	$-0.129051\pi$
$277$	287.203	+	165.817i	1.03683	+	0.598616i	0.117898	+	0.993026i	$0.462384\pi$
$278$	−122.321	+	122.321i	−0.440003	+	0.440003i
$279$	−36.5871	−	136.545i	−0.131137	−	0.489409i
$280$	−347.031	+	92.9867i	−1.23940	+	0.332095i
$281$	167.285	+	167.285i	0.595321	+	0.595321i	0.939064	−	0.343743i	$-0.111695\pi$
$281$	167.285	+	167.285i	0.595321	+	0.595321i	−0.343743	+	0.939064i	$0.611695\pi$
$282$	−18.5188	+	32.0755i	−0.0656694	+	0.113743i
$283$	57.6310	−	33.2733i	0.203643	−	0.117574i	−0.394710	−	0.918806i	$-0.629155\pi$
$283$	57.6310	−	33.2733i	0.203643	−	0.117574i	0.598354	+	0.801232i	$0.295822\pi$
$284$	−30.7190	+	114.645i	−0.108166	+	0.403680i
$285$		−	72.3677i		−	0.253922i
$286$	−3.14611	+	2.45205i	−0.0110004	+	0.00857362i
$287$	185.870			0.647631
$288$	95.2117	+	25.5119i	0.330596	+	0.0885830i
$289$	−133.943	−	231.996i	−0.463471	−	0.802755i
$290$	−121.068	−	69.8988i	−0.417477	−	0.241030i
$291$	−31.5576	+	31.5576i	−0.108446	+	0.108446i
$292$	−82.6504	−	308.455i	−0.283049	−	1.05635i
$293$	−268.304	+	71.8917i	−0.915712	+	0.245364i	−0.685752	−	0.727836i	$-0.740526\pi$
$293$	−268.304	+	71.8917i	−0.915712	+	0.245364i	−0.229960	+	0.973200i	$0.573860\pi$
$294$	−24.2618	−	24.2618i	−0.0825233	−	0.0825233i
$295$	−184.980	+	320.396i	−0.627052	+	1.08609i
$296$	−148.512	+	85.7437i	−0.501731	+	0.289675i
$297$	0.422882	−	1.57822i	0.00142384	−	0.00531386i
$298$			0.384203i			0.00128927i
$299$	345.186	−	48.0986i	1.15447	−	0.160865i
$300$	370.028			1.23343
$301$	−193.006	−	51.7158i	−0.641216	−	0.171813i
$302$	−19.6146	−	33.9735i	−0.0649491	−	0.112495i
$303$	50.5902	+	29.2083i	0.166964	+	0.0963970i
$304$	−16.6040	+	16.6040i	−0.0546184	+	0.0546184i
$305$	−75.3574	−	281.238i	−0.247073	−	0.922091i
$306$	12.9929	−	3.48144i	0.0424605	−	0.0113773i
$307$	123.072	+	123.072i	0.400886	+	0.400886i	0.878545	−	0.477659i	$-0.158515\pi$
$307$	123.072	+	123.072i	0.400886	+	0.400886i	−0.477659	+	0.878545i	$0.658515\pi$
$308$	2.56704	−	4.44625i	0.00833455	−	0.0144359i
$309$	86.7207	−	50.0682i	0.280650	−	0.162033i
$310$	116.050	−	433.103i	0.374354	−	1.39711i
$311$		−	300.718i		−	0.966939i	−0.875361	−	0.483469i	$-0.839376\pi$
$311$		−	300.718i		−	0.966939i	0.875361	−	0.483469i	$-0.160624\pi$
$312$	93.3379	−	123.561i	0.299160	−	0.396028i
$313$	−361.233			−1.15410			−0.577050	−	0.816709i	$-0.695796\pi$
$313$	−361.233			−1.15410			−0.577050	+	0.816709i	$0.695796\pi$
$314$	115.515	+	30.9523i	0.367884	+	0.0985741i
$315$	−78.3613	−	135.726i	−0.248766	−	0.430876i
$316$	163.607	+	94.4586i	0.517744	+	0.298920i
$317$	108.893	−	108.893i	0.343512	−	0.343512i	−0.514174	−	0.857686i	$-0.671902\pi$
$317$	108.893	−	108.893i	0.343512	−	0.343512i	0.857686	+	0.514174i	$0.171902\pi$
$318$	4.75376	+	17.7413i	0.0149489	+	0.0557901i
$319$	4.46218	−	1.19564i	0.0139880	−	0.00374808i
$320$	69.9163	+	69.9163i	0.218488	+	0.218488i
$321$	161.705	−	280.082i	0.503755	−	0.872529i
$322$	121.369	−	70.0724i	0.376922	−	0.217616i
$323$	−5.09548	+	19.0166i	−0.0157755	+	0.0588749i
$324$			27.4304i			0.0846617i
$325$	342.346	−	844.475i	1.05337	−	2.59838i
$326$	−1.85903			−0.00570254
$327$	180.333	+	48.3201i	0.551477	+	0.147768i
$328$	−119.305	−	206.643i	−0.363736	−	0.630010i
$329$	−101.668	−	58.6983i	−0.309023	−	0.178414i
$330$	3.66457	−	3.66457i	0.0111048	−	0.0111048i
$331$	131.451	+	490.584i	0.397134	+	1.48213i	0.818114	+	0.575056i	$0.195020\pi$
$331$	131.451	+	490.584i	0.397134	+	1.48213i	−0.420980	+	0.907070i	$0.638314\pi$
$332$	−264.315	+	70.8229i	−0.796128	+	0.213322i
$333$	−52.8962	−	52.8962i	−0.158847	−	0.158847i
$334$	−64.5229	+	111.757i	−0.193182	+	0.334602i
$335$	−757.296	+	437.225i	−2.26059	+	1.30515i
$336$	−13.1617	+	49.1200i	−0.0391716	+	0.146190i
$337$			458.553i			1.36069i	0.732891	+	0.680346i	$0.238171\pi$
$337$			458.553i			1.36069i	−0.732891	+	0.680346i	$0.761829\pi$
$338$	−84.6018	−	141.554i	−0.250301	−	0.418800i
$339$	−180.907			−0.533648
$340$	−131.915	−	35.3465i	−0.387985	−	0.103960i
$341$	7.40835	+	12.8316i	0.0217254	+	0.0376294i
$342$	10.8622	+	6.27128i	0.0317608	+	0.0183371i
$343$	262.517	−	262.517i	0.765356	−	0.765356i
$344$	66.3902	+	247.772i	0.192995	+	0.720267i
$345$	−437.389	+	117.198i	−1.26779	+	0.339704i
$346$	200.519	+	200.519i	0.579535	+	0.579535i
$347$	141.666	−	245.373i	0.408260	−	0.707127i	−0.586435	−	0.809996i	$-0.699469\pi$
$347$	141.666	−	245.373i	0.408260	−	0.707127i	0.994695	+	0.102869i	$0.0328023\pi$
$348$	−67.1651	+	38.7778i	−0.193003	+	0.111430i
$349$	−91.8619	+	342.833i	−0.263214	+	0.982330i	0.700120	+	0.714025i	$0.253130\pi$
$349$	−91.8619	+	342.833i	−0.263214	+	0.982330i	−0.963334	+	0.268304i	$0.913537\pi$
$350$		−	366.417i		−	1.04691i
$351$	62.6014	+	25.3783i	0.178352	+	0.0723030i
$352$	−10.3316			−0.0293510
$353$	−12.6618	−	3.39272i	−0.0358692	−	0.00961112i	0.240840	−	0.970565i	$-0.422577\pi$
$353$	−12.6618	−	3.39272i	−0.0358692	−	0.00961112i	−0.276709	+	0.960954i	$0.589244\pi$
$354$	−32.0603	−	55.5301i	−0.0905658	−	0.156865i
$355$	−328.874	−	189.876i	−0.926407	−	0.534861i
$356$	139.790	−	139.790i	0.392668	−	0.392668i
$357$	11.0350	+	41.1832i	0.0309104	+	0.115359i
$358$	−177.846	+	47.6538i	−0.496778	+	0.133111i
$359$	290.563	+	290.563i	0.809369	+	0.809369i	0.984538	−	0.175170i	$-0.0560474\pi$
$359$	290.563	+	290.563i	0.809369	+	0.809369i	−0.175170	+	0.984538i	$0.556047\pi$
$360$	−100.597	+	174.238i	−0.279435	+	0.483995i
$361$	296.737	−	171.321i	0.821987	−	0.474574i
$362$	−10.3706	+	38.7035i	−0.0286480	+	0.106916i
$363$		−	209.407i		−	0.576878i
$364$	169.367	+	127.940i	0.465294	+	0.351483i
$365$	1021.73			2.79926
$366$	48.7433	+	13.0607i	0.133179	+	0.0356851i
$367$	198.828	+	344.380i	0.541766	+	0.938366i	0.998803	+	0.0489181i	$0.0155773\pi$
$367$	198.828	+	344.380i	0.541766	+	0.938366i	−0.457037	+	0.889448i	$0.651089\pi$
$368$	127.244	+	73.4643i	0.345772	+	0.199631i
$369$	73.6008	−	73.6008i	0.199460	−	0.199460i
$370$	−61.4117	−	229.192i	−0.165978	−	0.619437i
$371$	−56.2338	+	15.0678i	−0.151574	+	0.0406140i
$372$	−175.892	−	175.892i	−0.472828	−	0.472828i
$373$	−289.584	+	501.575i	−0.776365	+	1.34470i	0.157659	+	0.987494i	$0.449605\pi$
$373$	−289.584	+	501.575i	−0.776365	+	1.34470i	−0.934024	+	0.357210i	$0.883728\pi$
$374$	−1.22099	+	0.704941i	−0.00326469	+	0.00188487i
$375$	−197.133	+	735.710i	−0.525688	+	1.96189i
$376$			150.708i			0.400820i
$377$	26.3578	+	189.160i	0.0699147	+	0.501752i
$378$	27.1627			0.0718591
$379$	−566.316	−	151.744i	−1.49424	−	0.400380i	−0.583072	−	0.812420i	$-0.698150\pi$
$379$	−566.316	−	151.744i	−1.49424	−	0.400380i	−0.911166	+	0.412040i	$0.864816\pi$
$380$	−63.6713	−	110.282i	−0.167556	−	0.290216i
$381$	−95.9710	−	55.4089i	−0.251892	−	0.145430i
$382$	−105.814	+	105.814i	−0.277001	+	0.277001i
$383$	−16.7397	−	62.4733i	−0.0437067	−	0.163116i	0.940623	−	0.339453i	$-0.110242\pi$
$383$	−16.7397	−	62.4733i	−0.0437067	−	0.163116i	−0.984330	+	0.176337i	$0.943575\pi$
$384$	203.329	−	54.4818i	0.529502	−	0.141880i
$385$	11.6155	+	11.6155i	0.0301700	+	0.0301700i
$386$	94.3575	−	163.432i	0.244450	−	0.423399i
$387$	−96.9050	+	55.9481i	−0.250400	+	0.144569i
$388$	−20.3257	+	75.8564i	−0.0523858	+	0.195506i
$389$			262.126i			0.673847i	0.941532	+	0.336923i	$0.109386\pi$
$389$			262.126i			0.673847i	−0.941532	+	0.336923i	$0.890614\pi$
$390$	131.713	+	168.994i	0.337725	+	0.433318i
$391$	123.188			0.315059
$392$	−134.858	−	36.1351i	−0.344026	−	0.0921814i
$393$	72.9432	+	126.341i	0.185606	+	0.321479i
$394$	109.481	+	63.2087i	0.277870	+	0.160428i
$395$	−427.410	+	427.410i	−1.08205	+	1.08205i
$396$	−0.744128	−	2.77712i	−0.00187911	−	0.00701294i
$397$	−363.818	+	97.4848i	−0.916418	+	0.245554i	−0.686054	−	0.727551i	$-0.740659\pi$
$397$	−363.818	+	97.4848i	−0.916418	+	0.245554i	−0.230365	+	0.973104i	$0.573992\pi$
$398$	122.800	+	122.800i	0.308542	+	0.308542i
$399$	−19.8779	+	34.4295i	−0.0498192	+	0.0862894i
$400$	332.687	−	192.077i	0.831718	−	0.480193i
$401$	110.749	−	413.319i	0.276181	−	1.03072i	−0.678865	−	0.734263i	$-0.737528\pi$
$401$	110.749	−	413.319i	0.276181	−	1.03072i	0.955046	−	0.296458i	$-0.0958055\pi$
$402$		−	151.557i		−	0.377008i
$403$	−564.153	+	238.686i	−1.39988	+	0.592272i
$404$	102.793			0.254439
$405$	−84.7743	−	22.7152i	−0.209319	−	0.0560869i
$406$	38.3994	+	66.5097i	0.0945798	+	0.163817i
$407$	6.79031	+	3.92039i	0.0166838	+	0.00963240i
$408$	38.7028	−	38.7028i	0.0948598	−	0.0948598i
$409$	−138.605	−	517.279i	−0.338886	−	1.26474i	−0.899594	−	0.436727i	$-0.856137\pi$
$409$	−138.605	−	517.279i	−0.338886	−	1.26474i	0.560708	−	0.828014i	$-0.310529\pi$
$410$	318.902	−	85.4495i	0.777809	−	0.208413i
$411$	154.839	+	154.839i	0.376738	+	0.376738i
$412$	88.1031	−	152.599i	0.213843	−	0.370386i
$413$	176.012	−	101.620i	0.426178	−	0.246054i
$414$	20.3124	−	75.8070i	0.0490638	−	0.183109i
$415$		−	875.519i		−	2.10968i
$416$	52.5539	−	423.893i	0.126331	−	1.01897i
$417$	−307.056			−0.736344
$418$	−1.26984	−	0.340253i	−0.00303790	−	0.000814002i
$419$	−42.8617	−	74.2387i	−0.102295	−	0.177181i	0.810335	−	0.585967i	$-0.199285\pi$
$419$	−42.8617	−	74.2387i	−0.102295	−	0.177181i	−0.912630	+	0.408787i	$0.865952\pi$
$420$	−238.831	−	137.889i	−0.568646	−	0.328308i
$421$	337.386	−	337.386i	0.801391	−	0.801391i	−0.181922	−	0.983313i	$-0.558232\pi$
$421$	337.386	−	337.386i	0.801391	−	0.801391i	0.983313	+	0.181922i	$0.0582318\pi$
$422$	50.2533	+	187.548i	0.119084	+	0.444426i
$423$	−63.5021	+	17.0153i	−0.150123	+	0.0402254i
$424$	52.8470	+	52.8470i	0.124639	+	0.124639i
$425$	161.041	−	278.932i	0.378921	−	0.656310i
$426$	56.9996	−	32.9087i	0.133802	−	0.0772506i
$427$	−41.3981	+	154.500i	−0.0969512	+	0.361827i
$428$		−	569.093i		−	1.32966i
$429$	−7.02639	−	0.871125i	−0.0163785	−	0.00203060i
$430$	−354.920			−0.825396
$431$	−73.1773	−	19.6078i	−0.169785	−	0.0454937i	0.172925	−	0.984935i	$-0.444678\pi$
$431$	−73.1773	−	19.6078i	−0.169785	−	0.0454937i	−0.342710	+	0.939441i	$0.611345\pi$
$432$	14.2388	+	24.6623i	0.0329602	+	0.0570887i
$433$	511.717	+	295.440i	1.18179	+	0.682309i	0.956429	−	0.291965i	$-0.0943092\pi$
$433$	511.717	+	295.440i	1.18179	+	0.682309i	0.225365	+	0.974274i	$0.427642\pi$
$434$	−174.176	+	174.176i	−0.401327	+	0.401327i
$435$	−64.2240	−	239.687i	−0.147641	−	0.551005i
$436$	317.325	−	85.0270i	0.727810	−	0.195016i
$437$	81.2225	+	81.2225i	0.185864	+	0.185864i
$438$	−88.5418	+	153.359i	−0.202150	+	0.350135i
$439$	49.6419	−	28.6608i	0.113079	−	0.0652865i	−0.442394	−	0.896821i	$-0.645871\pi$
$439$	49.6419	−	28.6608i	0.113079	−	0.0652865i	0.555473	+	0.831535i	$0.312537\pi$
$440$	5.45794	−	20.3693i	0.0124044	−	0.0462939i
$441$		−	60.9032i		−	0.138103i
$442$	−22.7121	−	53.6819i	−0.0513849	−	0.121452i
$443$	−90.2289			−0.203677			−0.101838	−	0.994801i	$-0.532472\pi$
$443$	−90.2289			−0.203677			−0.101838	+	0.994801i	$0.532472\pi$
$444$	−127.149	−	34.0694i	−0.286371	−	0.0767329i
$445$	316.264	+	547.785i	0.710705	+	1.23098i
$446$	91.2694	+	52.6944i	0.204640	+	0.118149i
$447$	−0.482222	+	0.482222i	−0.00107880	+	0.00107880i
$448$	−14.0587	−	52.4677i	−0.0313810	−	0.117115i
$449$	213.236	−	57.1363i	0.474913	−	0.127252i	−0.0134202	−	0.999910i	$-0.504272\pi$
$449$	213.236	−	57.1363i	0.474913	−	0.127252i	0.488333	+	0.872658i	$0.337605\pi$
$450$	−145.094	−	145.094i	−0.322431	−	0.322431i
$451$	−5.45490	+	9.44817i	−0.0120951	+	0.0209494i
$452$	−275.686	+	159.167i	−0.609924	+	0.352140i
$453$	18.0222	−	67.2597i	0.0397841	−	0.148476i
$454$			73.8010i			0.162557i
$455$	−535.655	+	417.485i	−1.17726	+	0.917550i
$456$	51.0365			0.111922
$457$	244.381	+	65.4817i	0.534751	+	0.143286i	0.516081	−	0.856540i	$-0.327390\pi$
$457$	244.381	+	65.4817i	0.534751	+	0.143286i	0.0186697	+	0.999826i	$0.494057\pi$
$458$	115.219	+	199.565i	0.251569	+	0.435730i
$459$	20.6774	+	11.9381i	0.0450488	+	0.0260089i
$460$	−563.427	+	563.427i	−1.22484	+	1.22484i
$461$	5.06613	+	18.9071i	0.0109894	+	0.0410131i	0.971203	−	0.238254i	$-0.0765751\pi$
$461$	5.06613	+	18.9071i	0.0109894	+	0.0410131i	−0.960213	+	0.279267i	$0.909908\pi$
$462$	−2.75003	+	0.736867i	−0.00595244	+	0.00159495i
$463$	−474.372	−	474.372i	−1.02456	−	1.02456i	−0.999691	−	0.0248701i	$-0.992083\pi$
$463$	−474.372	−	474.372i	−1.02456	−	1.02456i	−0.0248701	−	0.999691i	$-0.507917\pi$
$464$	−40.2582	+	69.7292i	−0.0867633	+	0.150278i
$465$	689.255	−	397.942i	1.48227	−	0.855788i
$466$	−63.1700	+	235.754i	−0.135558	+	0.505909i
$467$		−	115.781i		−	0.247926i	−0.992287	−	0.123963i	$-0.960440\pi$
$467$		−	115.781i		−	0.247926i	0.992287	−	0.123963i	$-0.0395604\pi$
$468$	117.728	−	16.4043i	0.251555	−	0.0350520i
$469$	480.386			1.02428
$470$	−201.420	−	53.9704i	−0.428554	−	0.114831i
$471$	106.137	+	183.835i	0.225345	+	0.390308i
$472$	−225.955	−	130.455i	−0.478719	−	0.276388i
$473$	8.29315	−	8.29315i	0.0175331	−	0.0175331i
$474$	−27.1143	−	101.192i	−0.0572031	−	0.213485i
$475$	290.091	−	77.7297i	0.610718	−	0.163641i
$476$	53.0506	+	53.0506i	0.111451	+	0.111451i
$477$	−16.3009	+	28.2340i	−0.0341739	+	0.0591909i
$478$	239.753	−	138.421i	0.501575	−	0.289585i
$479$	244.866	−	913.851i	0.511202	−	1.90783i	0.103752	−	0.994603i	$-0.466915\pi$
$479$	244.866	−	913.851i	0.511202	−	1.90783i	0.407450	−	0.913227i	$-0.366418\pi$
$480$			554.963i			1.15617i
$481$	−195.390	+	258.657i	−0.406216	+	0.537749i
$482$	−74.7837			−0.155153
$483$	240.283	+	64.3835i	0.497480	+	0.133299i
$484$	−184.243	−	319.118i	−0.380667	−	0.659334i
$485$	−217.604	−	125.634i	−0.448669	−	0.259039i
$486$	10.7559	−	10.7559i	0.0221315	−	0.0221315i
$487$	50.5017	+	188.475i	0.103700	+	0.387012i	0.998194	−	0.0600663i	$-0.0191312\pi$
$487$	50.5017	+	188.475i	0.103700	+	0.387012i	−0.894495	+	0.447078i	$0.852465\pi$
$488$	198.340	−	53.1450i	0.406434	−	0.108904i
$489$	−2.33331	−	2.33331i	−0.00477160	−	0.00477160i
$490$	96.5886	−	167.296i	0.197120	−	0.341421i
$491$	−650.368	+	375.490i	−1.32458	+	0.764746i	−0.984455	−	0.175634i	$-0.943802\pi$
$491$	−650.368	+	375.490i	−1.32458	+	0.764746i	−0.340124	+	0.940381i	$0.610469\pi$
$492$	47.4049	−	176.917i	0.0963514	−	0.359588i
$493$			67.5065i			0.136930i
$494$	20.4196	−	50.3695i	0.0413352	−	0.101963i
$495$	9.19898			0.0185838
$496$	−249.446	−	66.8388i	−0.502915	−	0.134756i
$497$	104.310	+	180.670i	0.209879	+	0.363520i
$498$	131.413	+	75.8713i	0.263881	+	0.152352i
$499$	−142.732	+	142.732i	−0.286037	+	0.286037i	−0.835511	−	0.549474i	$-0.814828\pi$
$499$	−142.732	+	142.732i	−0.286037	+	0.286037i	0.549474	+	0.835511i	$0.314828\pi$
$500$	346.887	+	1294.60i	0.693774	+	2.58920i
$501$	−221.253	+	59.2846i	−0.441623	+	0.118333i
$502$	−319.966	−	319.966i	−0.637383	−	0.637383i
$503$	−51.3612	+	88.9602i	−0.102110	+	0.176859i	−0.912554	−	0.408957i	$-0.865893\pi$
$503$	−51.3612	+	88.9602i	−0.102110	+	0.176859i	0.810444	+	0.585816i	$0.199226\pi$
$504$	95.7191	−	55.2634i	0.189919	−	0.109650i
$505$	−85.1235	+	317.685i	−0.168561	+	0.629080i
$506$			8.22593i			0.0162568i
$507$	71.4827	−	283.854i	0.140992	−	0.559870i
$508$	−195.002			−0.383862
$509$	−491.180	−	131.611i	−0.964989	−	0.258568i	−0.258278	−	0.966071i	$-0.583155\pi$
$509$	−491.180	−	131.611i	−0.964989	−	0.258568i	−0.706711	+	0.707502i	$0.749822\pi$
$510$	37.8661	+	65.5860i	0.0742472	+	0.128600i
$511$	−486.096	−	280.648i	−0.951265	−	0.549213i
$512$	233.936	−	233.936i	0.456906	−	0.456906i
$513$	5.76215	+	21.5046i	0.0112323	+	0.0419193i
$514$	−245.755	+	65.8499i	−0.478123	+	0.128113i
$515$	398.653	+	398.653i	0.774083	+	0.774083i
$516$	−98.4497	+	170.520i	−0.190794	+	0.330465i
$517$	5.96752	−	3.44535i	0.0115426	−	0.00666412i
$518$	−33.7370	+	125.908i	−0.0651293	+	0.243066i
$519$			503.353i			0.969851i
$520$	807.968	+	327.547i	1.55378	+	0.629897i
$521$	−671.421			−1.28872			−0.644358	−	0.764724i	$-0.722875\pi$
$521$	−671.421			−1.28872			−0.644358	+	0.764724i	$0.722875\pi$
$522$	41.5419	+	11.1311i	0.0795822	+	0.0213240i
$523$	−0.627885	−	1.08753i	−0.00120055	−	0.00207941i	0.865425	−	0.501039i	$-0.167049\pi$
$523$	−0.627885	−	1.08753i	−0.00120055	−	0.00207941i	−0.866625	+	0.498960i	$0.833715\pi$
$524$	222.318	+	128.355i	0.424271	+	0.244953i
$525$	459.899	−	459.899i	0.875999	−	0.875999i
$526$	102.566	+	382.780i	0.194992	+	0.727719i
$527$	−209.140	+	56.0390i	−0.396851	+	0.106336i
$528$	−2.11061	−	2.11061i	−0.00399736	−	0.00399736i
$529$	94.8689	−	164.318i	0.179336	−	0.310620i
$530$	−89.5547	+	51.7044i	−0.168971	+	0.0975556i
$531$	29.4575	−	109.937i	0.0554755	−	0.207037i
$532$			69.9566i			0.131497i
$533$	−359.901	−	271.869i	−0.675236	−	0.510074i
$534$	−109.628			−0.205296
$535$	1758.80	+	471.268i	3.28747	+	0.880874i
$536$	−308.348	−	534.074i	−0.575276	−	0.996407i
$537$	−283.031	−	163.408i	−0.527059	−	0.304298i
$538$	260.377	−	260.377i	0.483972	−	0.483972i
$539$	1.65217	+	6.16600i	0.00306526	+	0.0114397i
$540$	−149.174	+	39.9711i	−0.276248	+	0.0740205i
$541$	−422.938	−	422.938i	−0.781770	−	0.781770i	0.198359	−	0.980129i	$-0.436439\pi$
$541$	−422.938	−	422.938i	−0.781770	−	0.781770i	−0.980129	+	0.198359i	$0.936439\pi$
$542$	−18.0514	+	31.2659i	−0.0333051	+	0.0576862i
$543$	−61.5940	+	35.5613i	−0.113433	+	0.0654904i
$544$	39.0755	−	145.832i	0.0718300	−	0.268073i
$545$			1051.11i			1.92865i
$546$	−16.2442	−	116.579i	−0.0297514	−	0.213514i
$547$	476.094			0.870372			0.435186	−	0.900341i	$-0.356683\pi$
$547$	476.094			0.870372			0.435186	+	0.900341i	$0.356683\pi$
$548$	372.194	+	99.7290i	0.679186	+	0.181987i
$549$	44.7861	+	77.5718i	0.0815776	+	0.141297i
$550$	18.6258	+	10.7536i	0.0338651	+	0.0195520i
$551$	−44.5096	+	44.5096i	−0.0807797	+	0.0807797i
$552$	−82.6525	−	308.463i	−0.149733	−	0.558810i
$553$	320.744	−	85.9431i	0.580007	−	0.155412i
$554$	−228.824	−	228.824i	−0.413040	−	0.413040i
$555$	210.585	−	364.743i	0.379432	−	0.657195i
$556$	−467.925	+	270.157i	−0.841592	+	0.485894i
$557$	94.4432	−	352.467i	0.169557	−	0.632795i	−0.827858	−	0.560938i	$-0.810441\pi$
$557$	94.4432	−	352.467i	0.169557	−	0.632795i	0.997415	−	0.0718572i	$-0.0228926\pi$
$558$			137.940i			0.247205i
$559$	298.074	+	382.444i	0.533228	+	0.684158i
$560$	−286.307			−0.511262
$561$	−2.41729	−	0.647710i	−0.00430889	−	0.00115456i
$562$	−115.425	−	199.923i	−0.205383	−	0.355735i
$563$	−575.667	−	332.362i	−1.02250	−	0.590341i	−0.107673	−	0.994186i	$-0.534340\pi$
$563$	−575.667	−	332.362i	−1.02250	−	0.590341i	−0.914827	+	0.403846i	$0.867673\pi$
$564$	−81.8009	+	81.8009i	−0.145037	+	0.145037i
$565$	−263.614	−	983.820i	−0.466573	−	1.74127i
$566$	−62.7233	+	16.8066i	−0.110818	+	0.0296937i
$567$	34.0926	+	34.0926i	0.0601281	+	0.0601281i
$568$	133.908	−	231.935i	0.235753	−	0.408336i
$569$	342.108	−	197.516i	0.601244	−	0.347129i	−0.168287	−	0.985738i	$-0.553823\pi$
$569$	342.108	−	197.516i	0.601244	−	0.347129i	0.769531	+	0.638610i	$0.220490\pi$
$570$	−18.2768	+	68.2099i	−0.0320645	+	0.119666i
$571$			106.069i			0.185760i	0.995677	+	0.0928800i	$0.0296073\pi$
$571$			106.069i			0.185760i	−0.995677	+	0.0928800i	$0.970393\pi$
$572$	−11.4740	+	4.85452i	−0.0200595	+	0.00848692i
$573$	−265.620			−0.463561
$574$	−175.191	−	46.9423i	−0.305211	−	0.0817810i
$575$	−939.593	−	1627.42i	−1.63407	−	2.83030i
$576$	−26.3431	−	15.2092i	−0.0457346	−	0.0264049i
$577$	49.3185	−	49.3185i	0.0854740	−	0.0854740i	−0.663077	−	0.748551i	$-0.730750\pi$
$577$	49.3185	−	49.3185i	0.0854740	−	0.0854740i	0.748551	+	0.663077i	$0.230750\pi$
$578$	67.6559	+	252.495i	0.117052	+	0.436843i
$579$	323.558	−	86.6971i	0.558822	−	0.149736i
$580$	−308.756	−	308.756i	−0.532338	−	0.532338i
$581$	−240.486	+	416.535i	−0.413918	+	0.716927i
$582$	37.7146	−	21.7745i	0.0648017	−	0.0374133i
$583$	0.884419	−	3.30070i	0.00151701	−	0.00566157i
$584$			720.565i			1.23384i
$585$	−46.7927	+	377.425i	−0.0799876	+	0.645170i
$586$	271.045			0.462534
$587$	544.114	+	145.795i	0.926940	+	0.248373i	0.690550	−	0.723285i	$-0.257369\pi$
$587$	544.114	+	145.795i	0.926940	+	0.248373i	0.236391	+	0.971658i	$0.424035\pi$
$588$	−53.5845	−	92.8111i	−0.0911302	−	0.157842i
$589$	−174.843	−	100.946i	−0.296847	−	0.171385i
$590$	255.270	−	255.270i	0.432661	−	0.432661i
$591$	58.0771	+	216.747i	0.0982692	+	0.366745i
$592$	−132.003	+	35.3700i	−0.222978	+	0.0597467i
$593$	418.464	+	418.464i	0.705672	+	0.705672i	0.965622	−	0.259950i	$-0.0837060\pi$
$593$	418.464	+	418.464i	0.705672	+	0.705672i	−0.259950	+	0.965622i	$0.583706\pi$
$594$	−0.797171	+	1.38074i	−0.00134204	+	0.00232448i
$595$	−207.886	+	120.023i	−0.349387	+	0.201719i
$596$	−0.310590	+	1.15914i	−0.000521124	+	0.00194486i
$597$			308.258i			0.516345i
$598$	−337.501	−	41.8431i	−0.564383	−	0.0699717i
$599$	673.651			1.12463			0.562313	−	0.826924i	$-0.309912\pi$
$599$	673.651			1.12463			0.562313	+	0.826924i	$0.309912\pi$
$600$	−806.497	−	216.100i	−1.34416	−	0.360167i
$601$	−21.0004	−	36.3737i	−0.0349424	−	0.0605220i	0.848025	−	0.529956i	$-0.177791\pi$
$601$	−21.0004	−	36.3737i	−0.0349424	−	0.0605220i	−0.882968	+	0.469434i	$0.844458\pi$
$602$	168.856	+	97.4890i	0.280492	+	0.161942i
$603$	190.223	−	190.223i	0.315461	−	0.315461i
$604$	−31.7130	−	118.354i	−0.0525049	−	0.195951i
$605$	1138.81	−	305.144i	1.88233	−	0.504370i
$606$	−40.3070	−	40.3070i	−0.0665131	−	0.0665131i
$607$	336.816	−	583.383i	0.554887	−	0.961092i	−0.443026	−	0.896509i	$-0.646095\pi$
$607$	336.816	−	583.383i	0.554887	−	0.961092i	0.997912	−	0.0645829i	$-0.0205717\pi$
$608$	121.916	−	70.3885i	0.200520	−	0.115771i
$609$	−35.2819	+	131.674i	−0.0579342	+	0.216213i
$610$			284.111i			0.465756i
$611$	111.004	+	262.367i	0.181676	+	0.429406i
$612$	42.0140			0.0686503
$613$	341.800	+	91.5849i	0.557585	+	0.149404i	0.526597	−	0.850115i	$-0.323468\pi$
$613$	341.800	+	91.5849i	0.557585	+	0.149404i	0.0309884	+	0.999520i	$0.490135\pi$
$614$	−84.9187	−	147.084i	−0.138304	−	0.239550i
$615$	507.511	+	293.012i	0.825221	+	0.476442i
$616$	−8.19167	+	8.19167i	−0.0132982	+	0.0132982i
$617$	−13.1564	−	49.1005i	−0.0213232	−	0.0795794i	0.954444	−	0.298389i	$-0.0964493\pi$
$617$	−13.1564	−	49.1005i	−0.0213232	−	0.0795794i	−0.975768	+	0.218810i	$0.929783\pi$
$618$	−94.3833	+	25.2899i	−0.152724	+	0.0409222i
$619$	−143.390	−	143.390i	−0.231647	−	0.231647i	0.581733	−	0.813380i	$-0.302375\pi$
$619$	−143.390	−	143.390i	−0.231647	−	0.231647i	−0.813380	+	0.581733i	$0.802375\pi$
$620$	700.242	−	1212.86i	1.12942	−	1.95622i
$621$	120.642	−	69.6526i	0.194270	−	0.112162i
$622$	−75.9477	+	283.441i	−0.122102	+	0.455692i
$623$		−	347.483i		−	0.557758i
$624$	97.3321	−	75.8599i	0.155981	−	0.121570i
$625$	−2535.88			−4.05742
$626$	340.479	+	91.2310i	0.543896	+	0.145736i
$627$	−1.16675	−	2.02087i	−0.00186084	−	0.00322308i
$628$	323.488	+	186.766i	0.515108	+	0.297398i
$629$	−81.0189	+	81.0189i	−0.128806	+	0.128806i
$630$	39.5810	+	147.718i	0.0628270	+	0.234474i
$631$	−423.417	+	113.454i	−0.671025	+	0.179801i	−0.578217	−	0.815883i	$-0.696251\pi$
$631$	−423.417	+	113.454i	−0.671025	+	0.179801i	−0.0928086	+	0.995684i	$0.529584\pi$
$632$	−301.426	−	301.426i	−0.476940	−	0.476940i
$633$	−172.322	+	298.470i	−0.272230	+	0.471516i
$634$	−130.138	+	75.1354i	−0.205265	+	0.118510i
$635$	161.482	−	602.657i	0.254302	−	0.949067i
$636$			57.3682i			0.0902016i
$637$	−261.389	+	36.4222i	−0.410343	+	0.0571777i
$638$	−4.50778			−0.00706548
$639$	112.846	+	30.2370i	0.176598	+	0.0473193i
$640$	592.574	+	1026.37i	0.925897	+	1.60370i
$641$	274.753	+	158.629i	0.428632	+	0.247471i	0.698764	−	0.715353i	$-0.253734\pi$
$641$	274.753	+	158.629i	0.428632	+	0.247471i	−0.270132	+	0.962823i	$0.587067\pi$
$642$	−223.151	+	223.151i	−0.347587	+	0.347587i
$643$	246.809	+	921.104i	0.383840	+	1.43251i	0.839987	+	0.542606i	$0.182562\pi$
$643$	246.809	+	921.104i	0.383840	+	1.43251i	−0.456147	+	0.889904i	$0.650771\pi$
$644$	422.816	−	113.293i	0.656547	−	0.175921i
$645$	−445.469	−	445.469i	−0.690650	−	0.690650i
$646$	9.60546	−	16.6371i	0.0148691	−	0.0257541i
$647$	−654.981	+	378.153i	−1.01233	+	0.584472i	−0.911874	−	0.410469i	$-0.865365\pi$
$647$	−654.981	+	378.153i	−1.01233	+	0.584472i	−0.100460	+	0.994941i	$0.532032\pi$
$648$	16.0196	−	59.7861i	0.0247217	−	0.0922625i
$649$			11.9294i			0.0183812i
$650$	−535.953	+	709.496i	−0.824544	+	1.09153i
$651$	−437.224			−0.671620
$652$	−5.60868	−	1.50284i	−0.00860227	−	0.00230497i
$653$	483.378	+	837.235i	0.740242	+	1.28214i	0.952385	+	0.304898i	$0.0986223\pi$
$653$	483.378	+	837.235i	0.740242	+	1.28214i	−0.212143	+	0.977239i	$0.568044\pi$
$654$	−157.769	−	91.0879i	−0.241237	−	0.139278i
$655$	−580.787	+	580.787i	−0.886698	+	0.886698i
$656$	−49.2146	−	183.671i	−0.0750222	−	0.279987i
$657$	−303.616	+	81.3535i	−0.462124	+	0.123826i
$658$	81.0027	+	81.0027i	0.123104	+	0.123104i
$659$	−607.966	+	1053.03i	−0.922559	+	1.59792i	−0.127118	+	0.991888i	$0.540573\pi$
$659$	−607.966	+	1053.03i	−0.922559	+	1.59792i	−0.795441	+	0.606031i	$0.792761\pi$
$660$	14.0184	−	8.09355i	0.0212400	−	0.0122629i
$661$	28.8873	−	107.809i	0.0437025	−	0.163100i	−0.940626	−	0.339445i	$-0.889761\pi$
$661$	28.8873	−	107.809i	0.0437025	−	0.163100i	0.984328	+	0.176345i	$0.0564275\pi$
$662$		−	495.596i		−	0.748635i
$663$	38.8709	−	95.8840i	0.0586289	−	0.144621i
$664$	617.450			0.929894
$665$	−216.202	−	57.9313i	−0.325116	−	0.0871147i
$666$	36.4979	+	63.2163i	0.0548017	+	0.0949194i
$667$	341.098	+	196.933i	0.511391	+	0.295252i
$668$	−285.010	+	285.010i	−0.426661	+	0.426661i
$669$	48.4164	+	180.692i	0.0723713	+	0.270093i
$670$	824.210	−	220.846i	1.23016	−	0.329621i
$671$	−6.63862	−	6.63862i	−0.00989362	−	0.00989362i
$672$	152.436	−	264.028i	0.226840	−	0.392898i
$673$	789.813	−	455.998i	1.17357	−	0.677561i	0.219052	−	0.975713i	$-0.429704\pi$
$673$	789.813	−	455.998i	1.17357	−	0.677561i	0.954518	+	0.298152i	$0.0963703\pi$
$674$	115.810	−	432.208i	0.171825	−	0.641258i
$675$		−	364.222i		−	0.539588i
$676$	−140.810	−	495.461i	−0.208299	−	0.732931i
$677$	243.272			0.359338			0.179669	−	0.983727i	$-0.442497\pi$
$677$	243.272			0.359338			0.179669	+	0.983727i	$0.442497\pi$
$678$	170.513	+	45.6888i	0.251494	+	0.0673876i
$679$	69.0179	+	119.543i	0.101646	+	0.176057i
$680$	266.873	+	154.079i	0.392461	+	0.226587i
$681$	−92.6294	+	92.6294i	−0.136020	+	0.136020i
$682$	−3.74203	−	13.9654i	−0.00548684	−	0.0204772i
$683$	779.390	−	208.837i	1.14113	−	0.305764i	0.361723	−	0.932286i	$-0.382189\pi$
$683$	779.390	−	208.837i	1.14113	−	0.305764i	0.779404	+	0.626522i	$0.215522\pi$
$684$	27.7014	+	27.7014i	0.0404992	+	0.0404992i
$685$	−616.430	+	1067.69i	−0.899897	+	1.55867i
$686$	−313.735	+	181.135i	−0.457339	+	0.264045i
$687$	−105.865	+	395.092i	−0.154097	+	0.575097i
$688$			204.416i			0.297117i
$689$	130.925	+	53.0765i	0.190022	+	0.0770341i
$690$	441.858			0.640374
$691$	−505.499	−	135.448i	−0.731546	−	0.196017i	−0.126229	−	0.992001i	$-0.540287\pi$
$691$	−505.499	−	135.448i	−0.731546	−	0.196017i	−0.605318	+	0.795984i	$0.706954\pi$
$692$	442.865	+	767.065i	0.639978	+	1.10847i
$693$	−4.37648	−	2.52676i	−0.00631527	−	0.00364612i
$694$	−195.497	+	195.497i	−0.281696	+	0.281696i
$695$	−447.435	−	1669.85i	−0.643792	−	2.40266i
$696$	169.037	−	45.2933i	0.242869	−	0.0650765i
$697$	−112.731	−	112.731i	−0.161738	−	0.161738i
$698$	173.168	−	299.936i	0.248092	−	0.429708i
$699$	−375.186	+	216.614i	−0.536747	+	0.309891i
$700$	296.212	−	1105.48i	0.423160	−	1.57926i
$701$			485.809i			0.693023i	0.938046	+	0.346512i	$0.112634\pi$
$701$			485.809i			0.693023i	−0.938046	+	0.346512i	$0.887366\pi$
$702$	−52.5953	−	39.7305i	−0.0749221	−	0.0565962i
$703$	−106.838			−0.151974
$704$	3.07964	+	0.825187i	0.00437449	+	0.00117214i
$705$	−185.068	−	320.547i	−0.262508	−	0.454677i
$706$	11.0775	+	6.39560i	0.0156905	+	0.00905892i
$707$	127.759	−	127.759i	0.180706	−	0.180706i
$708$	−51.8352	−	193.451i	−0.0732135	−	0.273237i
$709$	910.021	−	243.839i	1.28353	−	0.343920i	0.448329	−	0.893869i	$-0.352019\pi$
$709$	910.021	−	243.839i	1.28353	−	0.343920i	0.835199	+	0.549948i	$0.185353\pi$
$710$	262.025	+	262.025i	0.369050	+	0.369050i
$711$	92.9765	−	161.040i	0.130769	−	0.226498i
$712$	−386.319	+	223.041i	−0.542583	+	0.313260i
$713$	−326.958	+	1220.23i	−0.458567	+	1.71140i
$714$		−	41.6040i		−	0.0582689i
$715$	−5.50130	−	39.4808i	−0.00769413	−	0.0552179i
$716$	−575.085			−0.803191
$717$	474.656	+	127.184i	0.662002	+	0.177383i
$718$	−200.486	−	347.252i	−0.279229	−	0.483639i
$719$	−982.025	−	566.972i	−1.36582	−	0.788557i	−0.375429	−	0.926851i	$-0.622505\pi$
$719$	−982.025	−	566.972i	−1.36582	−	0.788557i	−0.990391	+	0.138294i	$0.955838\pi$
$720$	−113.372	+	113.372i	−0.157461	+	0.157461i
$721$	−80.1606	−	299.163i	−0.111180	−	0.414928i
$722$	−322.956	+	86.5359i	−0.447308	+	0.119856i
$723$	−93.8628	−	93.8628i	−0.129824	−	0.129824i
$724$	−62.5758	+	108.385i	−0.0864307	+	0.149702i
$725$	891.821	−	514.893i	1.23010	−	0.710197i
$726$	−52.8867	+	197.376i	−0.0728466	+	0.271867i
$727$		−	96.4774i		−	0.132706i	−0.997796	−	0.0663531i	$-0.978864\pi$
$727$		−	96.4774i		−	0.132706i	0.997796	−	0.0663531i	$-0.0211364\pi$
$728$	−294.427	−	377.764i	−0.404432	−	0.518907i
$729$	27.0000			0.0370370
$730$	−963.029	−	258.043i	−1.31922	−	0.353484i
$731$	85.6933	+	148.425i	0.117228	+	0.203044i
$732$	136.500	+	78.8083i	0.186475	+	0.107662i
$733$	573.659	−	573.659i	0.782618	−	0.782618i	−0.197654	−	0.980272i	$-0.563332\pi$
$733$	573.659	−	573.659i	0.782618	−	0.782618i	0.980272	+	0.197654i	$0.0633323\pi$
$734$	−100.430	−	374.809i	−0.136825	−	0.510639i
$735$	331.208	−	88.7470i	0.450624	−	0.120744i
$736$	−622.867	−	622.867i	−0.846287	−	0.846287i
$737$	−14.0983	+	24.4190i	−0.0191294	+	0.0331330i
$738$	−87.9604	+	50.7840i	−0.119188	+	0.0688130i
$739$	−66.7623	+	249.160i	−0.0903415	+	0.337159i	−0.996272	−	0.0862673i	$-0.972506\pi$
$739$	−66.7623	+	249.160i	−0.0903415	+	0.337159i	0.905931	+	0.423426i	$0.139173\pi$
$740$		−	741.115i		−	1.00151i
$741$	88.8491	−	37.5909i	0.119904	−	0.0507299i
$742$	56.8084			0.0765612
$743$	849.884	+	227.726i	1.14385	+	0.306495i	0.780500	−	0.625156i	$-0.214965\pi$
$743$	849.884	+	227.726i	1.14385	+	0.306495i	0.363355	+	0.931651i	$0.381631\pi$
$744$	280.644	+	486.089i	0.377209	+	0.653346i
$745$	−3.32514	−	1.91977i	−0.00446327	−	0.00257687i
$746$	399.621	−	399.621i	0.535686	−	0.535686i
$747$	69.7116	+	260.167i	0.0933221	+	0.348283i
$748$	−4.25360	+	1.13975i	−0.00568664	+	0.00152373i
$749$	−707.313	−	707.313i	−0.944343	−	0.944343i
$750$	371.614	−	643.654i	0.495485	−	0.858205i
$751$	522.287	−	301.542i	0.695455	−	0.401521i	−0.110197	−	0.993910i	$-0.535148\pi$
$751$	522.287	−	301.542i	0.695455	−	0.401521i	0.805652	+	0.592389i	$0.201815\pi$
$752$	−31.0842	+	116.008i	−0.0413354	+	0.154266i
$753$		−	803.195i		−	1.06666i
$754$	22.9298	−	184.949i	0.0304109	−	0.245291i
$755$	392.038			0.519256
$756$	81.9498	+	21.9584i	0.108399	+	0.0290455i
$757$	−369.921	−	640.722i	−0.488667	−	0.846396i	0.511248	−	0.859433i	$-0.329183\pi$
$757$	−369.921	−	640.722i	−0.488667	−	0.846396i	−0.999915	+	0.0130371i	$0.995850\pi$
$758$	495.456	+	286.051i	0.653635	+	0.377377i
$759$	−10.3246	+	10.3246i	−0.0136028	+	0.0136028i
$760$	74.3694	+	277.550i	0.0978545	+	0.365198i
$761$	−798.767	+	214.029i	−1.04963	+	0.281247i	−0.742098	−	0.670292i	$-0.766169\pi$
$761$	−798.767	+	214.029i	−1.04963	+	0.281247i	−0.307530	+	0.951538i	$0.599502\pi$
$762$	76.4634	+	76.4634i	0.100346	+	0.100346i
$763$	288.718	−	500.074i	0.378398	−	0.655405i
$764$	−404.782	+	233.701i	−0.529819	+	0.305891i
$765$	−34.7919	+	129.845i	−0.0454796	+	0.169732i
$766$			63.1117i			0.0823912i
$767$	−489.451	−	60.6816i	−0.638137	−	0.0791156i
$768$	−275.655			−0.358926
$769$	−721.379	−	193.293i	−0.938074	−	0.251356i	−0.242780	−	0.970081i	$-0.578059\pi$
$769$	−721.379	−	193.293i	−0.938074	−	0.251356i	−0.695294	+	0.718725i	$0.744726\pi$
$770$	−8.01457	−	13.8816i	−0.0104085	−	0.0180281i
$771$	−391.103	−	225.803i	−0.507267	−	0.292871i
$772$	416.795	−	416.795i	0.539890	−	0.539890i
$773$	313.220	+	1168.95i	0.405201	+	1.51223i	0.803685	+	0.595055i	$0.202870\pi$
$773$	313.220	+	1168.95i	0.405201	+	1.51223i	−0.398484	+	0.917175i	$0.630464\pi$
$774$	105.467	−	28.2599i	0.136263	−	0.0365115i
$775$	2335.50	+	2335.50i	3.01355	+	3.01355i
$776$	88.6019	−	153.463i	0.114178	−	0.197762i
$777$	−200.374	+	115.686i	−0.257882	+	0.148888i
$778$	66.2012	−	247.066i	0.0850915	−	0.317566i
$779$		−	148.656i		−	0.190829i
$780$	260.762	+	616.331i	0.334310	+	0.790168i
$781$	−12.2451			−0.0156787
$782$	−116.110	−	31.1117i	−0.148479	−	0.0397847i
$783$	38.1693	+	66.1112i	0.0487476	+	0.0844332i
$784$	−96.3543	−	55.6302i	−0.122901	−	0.0709569i
$785$	−845.085	+	845.085i	−1.07654	+	1.07654i
$786$	−36.8443	−	137.505i	−0.0468757	−	0.174942i
$787$	−316.242	+	84.7369i	−0.401833	+	0.107671i	−0.454075	−	0.890964i	$-0.650030\pi$
$787$	−316.242	+	84.7369i	−0.401833	+	0.107671i	0.0522418	+	0.998634i	$0.483363\pi$
$788$	279.205	+	279.205i	0.354321	+	0.354321i
$789$	−351.704	+	609.169i	−0.445759	+	0.772078i
$790$	510.798	−	294.910i	0.646580	−	0.373303i
$791$	−144.818	+	540.469i	−0.183082	+	0.683273i
$792$			6.48748i			0.00819126i
$793$	306.144	−	238.607i	0.386058	−	0.300891i
$794$	367.536			0.462891
$795$	−177.298	−	47.5068i	−0.223016	−	0.0597570i
$796$	271.215	+	469.758i	0.340722	+	0.590148i
$797$	−1337.51	−	772.211i	−1.67818	−	0.968897i	−0.962821	−	0.270139i	$-0.912930\pi$
$797$	−1337.51	−	772.211i	−1.67818	−	0.968897i	−0.715358	−	0.698758i	$-0.753736\pi$
$798$	27.4311	−	27.4311i	0.0343748	−	0.0343748i
$799$	26.0617	+	97.2634i	0.0326178	+	0.121731i
$800$	−2224.61	+	596.082i	−2.78076	+	0.745102i
$801$	−137.597	−	137.597i	−0.171781	−	0.171781i
$802$	−208.771	+	361.602i	−0.260313	+	0.450876i
$803$	28.5319	−	16.4729i	0.0355316	−	0.0205142i
$804$	122.519	−	457.247i	0.152387	−	0.568716i
$805$			1400.54i			1.73980i
$806$	592.021	−	82.4930i	0.734518	−	0.102349i
$807$	653.611			0.809927
$808$	−224.044	−	60.0324i	−0.277282	−	0.0742975i
$809$	−424.887	−	735.925i	−0.525200	−	0.909673i	−0.999569	−	0.0293471i	$-0.990657\pi$
$809$	−424.887	−	735.925i	−0.525200	−	0.909673i	0.474369	−	0.880326i	$-0.342676\pi$
$810$	74.1669	+	42.8203i	0.0915640	+	0.0528645i
$811$	681.010	−	681.010i	0.839717	−	0.839717i	−0.149105	−	0.988821i	$-0.547639\pi$
$811$	681.010	−	681.010i	0.839717	−	0.839717i	0.988821	+	0.149105i	$0.0476391\pi$
$812$	62.0842	+	231.702i	0.0764584	+	0.285347i
$813$	−61.8993	+	16.5859i	−0.0761369	+	0.0204008i
$814$	−5.41007	−	5.41007i	−0.00664628	−	0.00664628i
$815$	9.28913	−	16.0892i	0.0113977	−	0.0197414i
$816$	37.7742	−	21.8090i	0.0462919	−	0.0267267i
$817$	−41.3615	+	154.363i	−0.0506261	+	0.188939i
$818$			522.565i			0.638832i
$819$	125.932	−	166.710i	0.153764	−	0.203553i
$820$	1031.20			1.25756
$821$	512.185	+	137.240i	0.623855	+	0.167161i	0.556880	−	0.830593i	$-0.311998\pi$
$821$	512.185	+	137.240i	0.623855	+	0.167161i	0.0669754	+	0.997755i	$0.478665\pi$
$822$	−106.838	−	185.049i	−0.129973	−	0.225120i
$823$	−115.461	−	66.6613i	−0.140293	−	0.0809980i	0.428211	−	0.903679i	$-0.359144\pi$
$823$	−115.461	−	66.6613i	−0.140293	−	0.0809980i	−0.568503	+	0.822681i	$0.692477\pi$
$824$	−281.145	+	281.145i	−0.341196	+	0.341196i
$825$	9.88057	+	36.8748i	0.0119764	+	0.0446967i
$826$	−191.564	+	51.3294i	−0.231917	+	0.0621421i
$827$	303.738	+	303.738i	0.367277	+	0.367277i	0.866483	−	0.499206i	$-0.166375\pi$
$827$	303.738	+	303.738i	0.367277	+	0.367277i	−0.499206	+	0.866483i	$0.666375\pi$
$828$	122.565	−	212.289i	0.148025	−	0.256387i
$829$	−68.0197	+	39.2712i	−0.0820503	+	0.0473718i	−0.540464	−	0.841367i	$-0.681751\pi$
$829$	−68.0197	+	39.2712i	−0.0820503	+	0.0473718i	0.458414	+	0.888739i	$0.348418\pi$
$830$	−221.116	+	825.217i	−0.266405	+	0.994238i
$831$		−	574.405i		−	0.691222i
$832$	−49.5219	+	122.157i	−0.0595215	+	0.146823i
$833$	−93.2829			−0.111984
$834$	289.414	+	77.5483i	0.347019	+	0.0929835i
$835$	−644.812	−	1116.85i	−0.772230	−	1.33754i
$836$	−3.55604	−	2.05308i	−0.00425364	−	0.00245584i
$837$	−173.132	+	173.132i	−0.206848	+	0.206848i
$838$	21.6498	+	80.7983i	0.0258351	+	0.0964181i
$839$	51.0874	−	13.6888i	0.0608908	−	0.0163157i	−0.228245	−	0.973604i	$-0.573299\pi$
$839$	51.0874	−	13.6888i	0.0608908	−	0.0163157i	0.289136	+	0.957288i	$0.406632\pi$
$840$	440.018	+	440.018i	0.523831	+	0.523831i
$841$	312.582	−	541.407i	0.371678	−	0.643766i
$842$	−403.210	+	232.793i	−0.478872	+	0.276477i
$843$	106.055	−	395.801i	0.125806	−	0.469515i
$844$			606.455i			0.718549i
$845$	1647.84	−	24.8844i	1.95011	−	0.0294490i
$846$	64.1509			0.0758285
$847$	−625.615	−	167.633i	−0.738624	−	0.197914i
$848$	29.7792	+	51.5790i	0.0351169	+	0.0608243i
$849$	−99.8199	−	57.6310i	−0.117574	−	0.0678811i
$850$	−222.234	+	222.234i	−0.261452	+	0.261452i
$851$	173.021	+	645.724i	0.203315	+	0.758783i
$852$	198.571	−	53.2069i	0.233065	−	0.0624495i
$853$	−7.55706	−	7.55706i	−0.00885939	−	0.00885939i	0.702663	−	0.711523i	$-0.251994\pi$
$853$	−7.55706	−	7.55706i	−0.00885939	−	0.00885939i	−0.711523	+	0.702663i	$0.751994\pi$
$854$	78.0393	−	135.168i	0.0913810	−	0.158276i
$855$	−108.552	+	62.6723i	−0.126961	+	0.0733009i
$856$	−332.356	+	1240.37i	−0.388267	+	1.44903i
$857$		−	1162.26i		−	1.35619i	−0.734974	−	0.678096i	$-0.762806\pi$
$857$		−	1162.26i		−	1.35619i	0.734974	−	0.678096i	$-0.237194\pi$
$858$	6.40269	+	2.59562i	0.00746234	+	0.00302520i
$859$	968.066			1.12697			0.563484	−	0.826127i	$-0.309461\pi$
$859$	968.066			1.12697			0.563484	+	0.826127i	$0.309461\pi$
$860$	−1070.79	−	286.918i	−1.24511	−	0.333626i
$861$	−160.968	−	278.805i	−0.186955	−	0.323815i
$862$	64.0209	+	36.9625i	0.0742702	+	0.0428799i
$863$	935.257	−	935.257i	1.08373	−	1.08373i	0.0875694	−	0.996158i	$-0.472090\pi$
$863$	935.257	−	935.257i	1.08373	−	1.08373i	0.996158	−	0.0875694i	$-0.0279099\pi$
$864$	−44.1879	−	164.912i	−0.0511434	−	0.190870i
$865$	−2737.37	+	733.476i	−3.16459	+	0.847949i
$866$	−407.702	−	407.702i	−0.470788	−	0.470788i
$867$	−231.996	+	401.829i	−0.267585	+	0.463471i
$868$	−666.291	+	384.683i	−0.767616	+	0.443184i
$869$	−5.04451	+	18.8264i	−0.00580496	+	0.0216644i
$870$			242.136i			0.278318i
$871$	−930.173	−	702.653i	−1.06794	−	0.806720i
$872$	−741.285			−0.850097
$873$	74.6662	+	20.0067i	0.0855283	+	0.0229172i
$874$	−56.0429	−	97.0691i	−0.0641223	−	0.111063i
$875$	2040.17	+	1177.89i	2.33162	+	1.34616i
$876$	−391.106	+	391.106i	−0.446468	+	0.446468i
$877$	42.4456	+	158.409i	0.0483986	+	0.180626i	0.985894	−	0.167372i	$-0.0535282\pi$
$877$	42.4456	+	158.409i	0.0483986	+	0.180626i	−0.937495	+	0.347998i	$0.886862\pi$
$878$	−54.0282	+	14.4768i	−0.0615355	+	0.0164884i
$879$	340.195	+	340.195i	0.387025	+	0.387025i
$880$	8.40252	−	14.5536i	0.00954832	−	0.0165382i
$881$	759.282	−	438.372i	0.861841	−	0.497584i	−0.00278713	−	0.999996i	$-0.500887\pi$
$881$	759.282	−	438.372i	0.861841	−	0.497584i	0.864628	+	0.502412i	$0.167554\pi$
$882$	−15.3814	+	57.4041i	−0.0174392	+	0.0650840i
$883$		−	1594.53i		−	1.80581i	−0.429839	−	0.902906i	$-0.641430\pi$
$883$		−	1594.53i		−	1.80581i	0.429839	−	0.902906i	$-0.358570\pi$
$884$	−25.1258	−	180.318i	−0.0284228	−	0.203980i
$885$	640.791			0.724058
$886$	85.0449	+	22.7877i	0.0959875	+	0.0257198i
$887$	540.875	+	936.823i	0.609780	+	1.05617i	0.991276	+	0.131800i	$0.0420755\pi$
$887$	540.875	+	936.823i	0.609780	+	1.05617i	−0.381496	+	0.924370i	$0.624591\pi$
$888$	257.231	+	148.512i	0.289675	+	0.167244i
$889$	−242.363	+	242.363i	−0.272624	+	0.272624i
$890$	−159.748	−	596.186i	−0.179492	−	0.669872i
$891$	−2.73355	+	0.732452i	−0.00306796	+	0.000822057i
$892$	232.761	+	232.761i	0.260943	+	0.260943i
$893$	−46.9461	+	81.3129i	−0.0525712	+	0.0910559i
$894$	0.576304	−	0.332729i	0.000644635	−	0.000372180i
$895$	476.230	−	1777.31i	0.532100	−	1.98582i
$896$		−	651.070i		−	0.726640i
$897$	−371.088	−	476.124i	−0.413699	−	0.530796i
$898$	−215.415			−0.239883
$899$	−668.679	−	179.172i	−0.743803	−	0.199301i
$900$	−320.454	−	555.042i	−0.356060	−	0.616713i
$901$	43.2449	+	24.9674i	0.0479965	+	0.0277108i
$902$	7.52768	−	7.52768i	0.00834554	−	0.00834554i
$903$	89.5744	+	334.296i	0.0991964	+	0.370206i
$904$	693.828	−	185.911i	0.767509	−	0.205653i
$905$	−283.146	−	283.146i	−0.312868	−	0.312868i
$906$	−33.9735	+	58.8438i	−0.0374984	+	0.0649491i
$907$	−77.6431	+	44.8272i	−0.0856043	+	0.0494236i	−0.542191	−	0.840255i	$-0.682405\pi$
$907$	−77.6431	+	44.8272i	−0.0856043	+	0.0494236i	0.456587	+	0.889679i	$0.349072\pi$
$908$	−59.6608	+	222.657i	−0.0657057	+	0.245217i
$909$		−	101.180i		−	0.111310i
$910$	610.317	−	258.217i	0.670678	−	0.283755i
$911$	378.748			0.415750			0.207875	−	0.978155i	$-0.433345\pi$
$911$	378.748			0.415750			0.207875	+	0.978155i	$0.433345\pi$
$912$	39.2855	+	10.5265i	0.0430762	+	0.0115422i
$913$	−14.1156	−	24.4489i	−0.0154606	−	0.0267786i
$914$	−213.803	−	123.439i	−0.233920	−	0.135054i
$915$	−356.595	+	356.595i	−0.389721	+	0.389721i
$916$	186.286	+	695.228i	0.203369	+	0.758982i
$917$	435.844	−	116.784i	0.475293	−	0.127354i
$918$	−16.4744	−	16.4744i	−0.0179459	−	0.0179459i
$919$	−576.994	+	999.383i	−0.627850	+	1.08747i	0.360132	+	0.932901i	$0.382732\pi$
$919$	−576.994	+	999.383i	−0.627850	+	1.08747i	−0.987982	+	0.154567i	$0.950602\pi$
$920$	1557.07	−	898.974i	1.69247	−	0.977145i
$921$	78.0245	−	291.192i	0.0847172	−	0.316169i
$922$		−	19.1003i		−	0.0207161i
$923$	62.2875	−	502.404i	0.0674838	−	0.544316i
$924$	−8.89250			−0.00962391
$925$	1688.29	+	452.375i	1.82518	+	0.489054i
$926$	327.313	+	566.922i	0.353469	+	0.612227i
$927$	−150.205	−	86.7207i	−0.162033	−	0.0935499i
$928$	341.329	−	341.329i	0.367811	−	0.367811i
$929$	−463.856	−	1731.13i	−0.499306	−	1.86344i	−0.504435	−	0.863450i	$-0.668299\pi$
$929$	−463.856	−	1731.13i	−0.499306	−	1.86344i	0.00512891	−	0.999987i	$-0.498367\pi$
$930$	−750.157	+	201.004i	−0.806620	+	0.216133i
$931$	−61.5050	−	61.5050i	−0.0660634	−	0.0660634i
$932$	−381.167	+	660.201i	−0.408977	+	0.708370i
$933$	−451.077	+	260.429i	−0.483469	+	0.279131i
$934$	−29.2411	+	109.129i	−0.0313074	+	0.116841i
$935$		−	14.0897i		−	0.0150692i
$936$	−266.174	−	33.0000i	−0.284374	−	0.0352565i
$937$	798.972			0.852692			0.426346	−	0.904560i	$-0.359801\pi$
$937$	798.972			0.852692			0.426346	+	0.904560i	$0.359801\pi$
$938$	−452.786	−	121.324i	−0.482714	−	0.129343i
$939$	312.837	+	541.850i	0.333160	+	0.577050i
$940$	−564.054	−	325.657i	−0.600058	−	0.346444i
$941$	−10.8954	+	10.8954i	−0.0115786	+	0.0115786i	−0.712872	−	0.701294i	$-0.752606\pi$
$941$	−10.8954	+	10.8954i	−0.0115786	+	0.0115786i	0.701294	+	0.712872i	$0.252606\pi$
$942$	−53.6109	−	200.079i	−0.0569118	−	0.212398i
$943$	−898.474	+	240.745i	−0.952783	+	0.255297i
$944$	−147.023	−	147.023i	−0.155744	−	0.155744i
$945$	−135.726	+	235.084i	−0.143625	+	0.248766i
$946$	−9.91116	+	5.72221i	−0.0104769	+	0.00604885i
$947$	341.173	−	1273.27i	0.360267	−	1.34453i	−0.513458	−	0.858115i	$-0.671636\pi$
$947$	341.173	−	1273.27i	0.360267	−	1.34453i	0.873725	−	0.486420i	$-0.161698\pi$
$948$		−	327.214i		−	0.345163i
$949$	530.731	+	1254.43i	0.559253	+	1.32184i
$950$	−293.055			−0.308479
$951$	−257.644	−	69.0355i	−0.270919	−	0.0725925i
$952$	−84.6447	−	146.609i	−0.0889125	−	0.154001i
$953$	−28.6812	−	16.5591i	−0.0300957	−	0.0173758i	0.484877	−	0.874583i	$-0.338864\pi$
$953$	−28.6812	−	16.5591i	−0.0300957	−	0.0173758i	−0.514972	+	0.857207i	$0.672198\pi$
$954$	22.4950	−	22.4950i	0.0235797	−	0.0235797i
$955$	−387.057	−	1444.52i	−0.405295	−	1.51258i
$956$	835.233	−	223.800i	0.873675	−	0.234101i
$957$	−5.65782	−	5.65782i	−0.00591204	−	0.00591204i
$958$	−461.594	+	799.505i	−0.481831	+	0.834556i
$959$	586.542	−	338.640i	0.611618	−	0.353118i
$960$	44.3252	−	165.424i	0.0461720	−	0.172316i
$961$		−	1259.35i		−	1.31046i
$962$	249.489	−	194.450i	0.259344	−	0.202131i
$963$	−560.164			−0.581686
$964$	−225.622	−	60.4552i	−0.234048	−	0.0627129i
$965$	942.965	+	1633.26i	0.977166	+	1.69250i
$966$	−210.217	−	121.369i	−0.217616	−	0.125641i
$967$	−977.248	+	977.248i	−1.01060	+	1.01060i	−0.0106547	+	0.999943i	$0.503392\pi$
$967$	−977.248	+	977.248i	−1.01060	+	1.01060i	−0.999943	+	0.0106547i	$0.996608\pi$
$968$	215.199	+	803.134i	0.222313	+	0.829684i
$969$	32.9377	−	8.82564i	0.0339915	−	0.00910798i
$970$	173.373	+	173.373i	0.178735	+	0.178735i
$971$	−736.766	+	1276.12i	−0.758770	+	1.31423i	0.184708	+	0.982793i	$0.440866\pi$
$971$	−736.766	+	1276.12i	−0.758770	+	1.31423i	−0.943478	+	0.331435i	$0.892467\pi$
$972$	41.1456	−	23.7554i	0.0423309	−	0.0244397i
$973$	−245.802	+	917.345i	−0.252623	+	0.942801i
$974$		−	190.401i		−	0.195483i
$975$	−1563.19	+	217.817i	−1.60328	+	0.223402i
$976$	163.634			0.167658
$977$	−371.388	−	99.5130i	−0.380131	−	0.101856i	0.0636938	−	0.997969i	$-0.479712\pi$
$977$	−371.388	−	99.5130i	−0.380131	−	0.101856i	−0.443824	+	0.896114i	$0.646379\pi$
$978$	1.60997	+	2.78854i	0.00164618	+	0.00285127i
$979$	17.6633	+	10.1979i	0.0180422	+	0.0104167i
$980$	426.650	−	426.650i	0.435357	−	0.435357i
$981$	−83.6929	−	312.346i	−0.0853139	−	0.318396i
$982$	707.834	−	189.664i	0.720809	−	0.193140i
$983$	−987.556	−	987.556i	−1.00464	−	1.00464i	−0.999989	−	0.00464599i	$-0.998521\pi$
$983$	−987.556	−	987.556i	−1.00464	−	1.00464i	−0.00464599	−	0.999989i	$-0.501479\pi$
$984$	−206.643	+	357.916i	−0.210003	+	0.363736i
$985$	−1094.10	+	631.678i	−1.11076	+	0.641297i
$986$	17.0491	−	63.6280i	0.0172912	−	0.0645315i
$987$			203.337i			0.206015i
$988$	102.324	−	135.457i	0.103567	−	0.137102i
$989$	999.953			1.01107
$990$	−8.67047	−	2.32324i	−0.00875805	−	0.00234671i
$991$	463.821	+	803.362i	0.468034	+	0.810658i	0.999333	−	0.0365264i	$-0.0116293\pi$
$991$	463.821	+	803.362i	0.468034	+	0.810658i	−0.531299	+	0.847184i	$0.678296\pi$
$992$	1340.81	+	774.116i	1.35162	+	0.780359i
$993$	622.035	−	622.035i	0.626420	−	0.626420i
$994$	−52.6877	−	196.633i	−0.0530058	−	0.197820i
$995$	−1676.39	+	449.188i	−1.68482	+	0.451445i
$996$	335.138	+	335.138i	0.336483	+	0.336483i
$997$	478.824	−	829.348i	0.480265	−	0.831844i	−0.519478	−	0.854484i	$-0.673874\pi$
$997$	478.824	−	829.348i	0.480265	−	0.831844i	0.999744	+	0.0226397i	$0.00720707\pi$
$998$	170.579	−	98.4841i	0.170921	−	0.0986814i
$999$	−33.5348	+	125.154i	−0.0335684	+	0.125279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.l.b.28.2	yes	12
3.2	odd	2		117.3.bd.d.28.2		12
13.7	odd	12	inner	39.3.l.b.7.2	✓	12
39.20	even	12		117.3.bd.d.46.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.b.7.2	✓	12	13.7	odd	12	inner
39.3.l.b.28.2	yes	12	1.1	even	1	trivial
117.3.bd.d.28.2		12	3.2	odd	2
117.3.bd.d.46.2		12	39.20	even	12

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	39.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.942546 - 0.252555i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-2.63949 - 1.52391i) q^{4} +(6.89545 - 6.89545i) q^{5} +(0.437437 + 1.63254i) q^{6} +(-5.17460 + 1.38653i) q^{7} +(4.86294 + 4.86294i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-8.24076 + 4.75781i) q^{10} +(0.0813836 - 0.303728i) q^{11} +5.27898i q^{12} +(12.0477 + 4.88406i) q^{13} +5.22747 q^{14} +(-16.3148 - 4.37154i) q^{15} +(2.74026 + 4.74626i) q^{16} +(3.97936 + 2.29749i) q^{17} +(2.06998 - 2.06998i) q^{18} +(1.10893 + 4.13857i) q^{19} +(-28.7086 + 7.69243i) q^{20} +(6.56113 + 6.56113i) q^{21} +(-0.153416 + 0.265724i) q^{22} +(23.2175 - 13.4046i) q^{23} +(3.08298 - 11.5058i) q^{24} -70.0946i q^{25} +(-10.1220 - 7.64615i) q^{26} +5.19615 q^{27} +(15.7713 + 4.22589i) q^{28} +(7.34569 + 12.7231i) q^{29} +(14.2734 + 8.24076i) q^{30} +(-33.3193 + 33.3193i) q^{31} +(-8.50397 - 31.7372i) q^{32} +(-0.526072 + 0.140961i) q^{33} +(-3.17049 - 3.17049i) q^{34} +(-26.1204 + 45.2419i) q^{35} +(7.91848 - 4.57173i) q^{36} +(-6.45378 + 24.0858i) q^{37} -4.18086i q^{38} +(-3.10748 - 22.3012i) q^{39} +67.0644 q^{40} +(-33.5135 - 8.97992i) q^{41} +(-4.52712 - 7.84121i) q^{42} +(32.3017 + 18.6494i) q^{43} +(-0.677665 + 0.677665i) q^{44} +(7.57173 + 28.2581i) q^{45} +(-25.2690 + 6.77081i) q^{46} +(15.4956 + 15.4956i) q^{47} +(4.74626 - 8.22077i) q^{48} +(-17.5813 + 10.1505i) q^{49} +(-17.7027 + 66.0674i) q^{50} -7.95873i q^{51} +(-24.3568 - 31.2510i) q^{52} +10.8673 q^{53} +(-4.89761 - 1.31231i) q^{54} +(-1.53316 - 2.65552i) q^{55} +(-31.9064 - 18.4211i) q^{56} +(5.24749 - 5.24749i) q^{57} +(-3.71038 - 13.8473i) q^{58} +(-36.6456 + 9.81916i) q^{59} +(36.4010 + 36.4010i) q^{60} +(14.9287 - 25.8573i) q^{61} +(39.8199 - 22.9900i) q^{62} +(4.15959 - 15.5238i) q^{63} +10.1395i q^{64} +(116.752 - 49.3962i) q^{65} +0.531447 q^{66} +(-86.6166 - 23.2088i) q^{67} +(-7.00233 - 12.1284i) q^{68} +(-40.2139 - 23.2175i) q^{69} +(36.0458 - 36.0458i) q^{70} +(-10.0790 - 37.6154i) q^{71} +(-19.9287 + 5.33988i) q^{72} +(74.0873 + 74.0873i) q^{73} +(12.1660 - 21.0721i) q^{74} +(-105.142 + 60.7037i) q^{75} +(3.37981 - 12.6136i) q^{76} +1.68451i q^{77} +(-2.70333 + 21.8047i) q^{78} -61.9843 q^{79} +(51.6230 + 13.8323i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(29.3201 + 16.9280i) q^{82} +(63.4852 - 63.4852i) q^{83} +(-7.31946 - 27.3166i) q^{84} +(43.2817 - 11.5973i) q^{85} +(-25.7358 - 25.7358i) q^{86} +(12.7231 - 22.0371i) q^{87} +(1.87277 - 1.08125i) q^{88} +(-16.7879 + 62.6535i) q^{89} -28.5468i q^{90} +(-69.1136 - 8.56865i) q^{91} -81.7100 q^{92} +(78.8343 + 21.1236i) q^{93} +(-10.6918 - 18.5188i) q^{94} +(36.1838 + 20.8908i) q^{95} +(-40.2412 + 40.2412i) q^{96} +(-6.66892 - 24.8887i) q^{97} +(19.1347 - 5.12713i) q^{98} +(0.667032 + 0.667032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9 + 30 * q^10 + 22 * q^11 + 2 * q^13 + 92 * q^14 + 52 * q^16 - 6 * q^17 + 12 * q^18 + 4 * q^19 - 208 * q^20 + 54 * q^21 - 98 * q^22 - 18 * q^23 - 54 * q^24 - 44 * q^26 - 78 * q^28 + 128 * q^29 + 6 * q^30 - 66 * q^31 + 358 * q^32 - 6 * q^33 + 336 * q^34 + 14 * q^35 + 36 * q^36 - 36 * q^37 - 18 * q^39 - 12 * q^40 - 326 * q^41 - 6 * q^42 + 60 * q^43 - 236 * q^44 - 24 * q^45 - 138 * q^46 + 40 * q^47 - 144 * q^48 + 78 * q^49 - 40 * q^50 - 392 * q^52 + 80 * q^53 - 18 * q^54 + 166 * q^55 - 102 * q^56 + 250 * q^58 - 164 * q^59 + 396 * q^60 - 98 * q^61 + 228 * q^62 + 66 * q^63 + 514 * q^65 + 60 * q^66 - 230 * q^67 + 78 * q^68 - 54 * q^69 - 92 * q^70 + 70 * q^71 - 18 * q^72 + 106 * q^73 - 16 * q^74 - 150 * q^75 + 534 * q^76 - 456 * q^78 + 16 * q^79 + 124 * q^80 - 54 * q^81 - 156 * q^82 - 176 * q^83 - 30 * q^84 + 90 * q^85 - 612 * q^86 + 48 * q^87 - 318 * q^88 - 476 * q^89 + 106 * q^91 + 228 * q^92 + 66 * q^93 - 374 * q^94 - 234 * q^95 + 384 * q^96 - 306 * q^97 - 350 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more