LMFDB - Embedded newform 26.5.f.b.15.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,5,Mod(7,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.7"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 494x^{6} + 90747x^{4} - 7343258x^{2} + 221087161 $ x^8 - 494x^6 + 90747x^4 - 7343258*x^2 + 221087161
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			15.2
Root			$10.0615 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.15
Dual form			26.5.f.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+(2.73205 + 0.732051i) q^{2} +(3.73170 + 6.46350i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-3.43687 + 3.43687i) q^{5} +(5.46359 + 20.3904i) q^{6} +(5.09773 - 1.36593i) q^{7} +(16.0000 + 16.0000i) q^{8} +(12.6488 - 21.9084i) q^{9} +(-11.9057 + 6.87373i) q^{10} +(18.2390 - 68.0690i) q^{11} +59.7072i q^{12} +(-147.694 - 82.1426i) q^{13} +14.9272 q^{14} +(-35.0395 - 9.38881i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-163.821 - 94.5819i) q^{17} +(50.5953 - 50.5953i) q^{18} +(-51.3183 - 191.523i) q^{19} +(-37.5588 + 10.0638i) q^{20} +(27.8519 + 27.8519i) q^{21} +(99.6599 - 172.616i) q^{22} +(-27.6437 + 15.9601i) q^{23} +(-43.7087 + 163.123i) q^{24} +601.376i q^{25} +(-343.376 - 332.538i) q^{26} +793.342 q^{27} +(40.7818 + 10.9275i) q^{28} +(724.108 + 1254.19i) q^{29} +(-88.8567 - 51.3014i) q^{30} +(-23.2321 + 23.2321i) q^{31} +(46.8513 + 174.851i) q^{32} +(508.026 - 136.125i) q^{33} +(-378.328 - 378.328i) q^{34} +(-12.8257 + 22.2147i) q^{35} +(175.267 - 101.191i) q^{36} +(-203.328 + 758.831i) q^{37} -560.817i q^{38} +(-20.2222 - 1261.15i) q^{39} -109.980 q^{40} +(-439.297 - 117.709i) q^{41} +(55.7038 + 96.4818i) q^{42} +(-2519.78 - 1454.80i) q^{43} +(398.640 - 398.640i) q^{44} +(31.8239 + 118.769i) q^{45} +(-87.2077 + 23.3672i) q^{46} +(-1379.78 - 1379.78i) q^{47} +(-238.829 + 413.664i) q^{48} +(-2055.21 + 1186.57i) q^{49} +(-440.238 + 1642.99i) q^{50} -1411.81i q^{51} +(-694.685 - 1159.88i) q^{52} +3454.55 q^{53} +(2167.45 + 580.767i) q^{54} +(171.259 + 296.629i) q^{55} +(103.419 + 59.7087i) q^{56} +(1046.40 - 1046.40i) q^{57} +(1060.17 + 3956.60i) q^{58} +(6208.82 - 1663.65i) q^{59} +(-205.206 - 205.206i) q^{60} +(-3107.03 + 5381.54i) q^{61} +(-80.4783 + 46.4642i) q^{62} +(34.5548 - 128.960i) q^{63} +512.000i q^{64} +(789.919 - 225.292i) q^{65} +1487.60 q^{66} +(-2782.68 - 745.618i) q^{67} +(-756.655 - 1310.57i) q^{68} +(-206.316 - 119.117i) q^{69} +(-51.3027 + 51.3027i) q^{70} +(791.269 + 2953.06i) q^{71} +(552.915 - 148.153i) q^{72} +(-4761.10 - 4761.10i) q^{73} +(-1111.01 + 1924.32i) q^{74} +(-3886.99 + 2244.15i) q^{75} +(410.547 - 1532.18i) q^{76} -371.910i q^{77} +(867.980 - 3460.34i) q^{78} +2823.19 q^{79} +(-300.470 - 80.5107i) q^{80} +(1935.96 + 3353.18i) q^{81} +(-1114.01 - 643.175i) q^{82} +(7467.92 - 7467.92i) q^{83} +(81.5560 + 304.371i) q^{84} +(888.095 - 237.964i) q^{85} +(-5819.18 - 5819.18i) q^{86} +(-5404.31 + 9360.54i) q^{87} +(1380.93 - 797.279i) q^{88} +(979.775 - 3656.57i) q^{89} +347.778i q^{90} +(-865.106 - 217.000i) q^{91} -255.362 q^{92} +(-236.856 - 63.4653i) q^{93} +(-2759.57 - 4779.71i) q^{94} +(834.612 + 481.863i) q^{95} +(-955.315 + 955.315i) q^{96} +(63.2272 + 235.967i) q^{97} +(-6483.56 + 1737.26i) q^{98} +(-1260.58 - 1260.58i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21}+ \cdots - 55296 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	2.73205	+	0.732051i	0.683013	+	0.183013i
$2$	2.73205	+	0.732051i	0.683013	+	0.183013i
$3$	3.73170	+	6.46350i	0.414633	+	0.718166i	0.995390	−	0.0959112i	$-0.0305765\pi$
$3$	3.73170	+	6.46350i	0.414633	+	0.718166i	−0.580756	+	0.814077i	$0.697243\pi$
$4$	6.92820	+	4.00000i	0.433013	+	0.250000i
$5$	−3.43687	+	3.43687i	−0.137475	+	0.137475i	−0.772495	−	0.635021i	$-0.780992\pi$
$5$	−3.43687	+	3.43687i	−0.137475	+	0.137475i	0.635021	+	0.772495i	$0.280992\pi$
$6$	5.46359	+	20.3904i	0.151766	+	0.566400i
$7$	5.09773	−	1.36593i	0.104035	−	0.0278762i	−0.206426	−	0.978462i	$-0.566183\pi$
$7$	5.09773	−	1.36593i	0.104035	−	0.0278762i	0.310461	+	0.950586i	$0.399517\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	12.6488	−	21.9084i	0.156158	−	0.270474i
$10$	−11.9057	+	6.87373i	−0.119057	+	0.0687373i
$11$	18.2390	−	68.0690i	0.150736	−	0.562554i	−0.848697	−	0.528879i	$-0.822612\pi$
$11$	18.2390	−	68.0690i	0.150736	−	0.562554i	0.999433	−	0.0336744i	$-0.0107209\pi$
$12$			59.7072i			0.414633i
$13$	−147.694	−	82.1426i	−0.873930	−	0.486051i
$13$	−147.694	−	82.1426i	−0.873930	−	0.486051i
$14$	14.9272			0.0761591
$15$	−35.0395	−	9.38881i	−0.155731	−	0.0417281i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−163.821	−	94.5819i	−0.566854	−	0.327273i	0.189038	−	0.981970i	$-0.439463\pi$
$17$	−163.821	−	94.5819i	−0.566854	−	0.327273i	−0.755892	+	0.654697i	$0.772796\pi$
$18$	50.5953	−	50.5953i	0.156158	−	0.156158i
$19$	−51.3183	−	191.523i	−0.142156	−	0.530533i	−0.999866	−	0.0163988i	$-0.994780\pi$
$19$	−51.3183	−	191.523i	−0.142156	−	0.530533i	0.857710	−	0.514135i	$-0.171887\pi$
$20$	−37.5588	+	10.0638i	−0.0938969	+	0.0251596i
$21$	27.8519	+	27.8519i	0.0631562	+	0.0631562i
$22$	99.6599	−	172.616i	0.205909	−	0.356645i
$23$	−27.6437	+	15.9601i	−0.0522566	+	0.0301703i	−0.525901	−	0.850546i	$-0.676272\pi$
$23$	−27.6437	+	15.9601i	−0.0522566	+	0.0301703i	0.473644	+	0.880716i	$0.342938\pi$
$24$	−43.7087	+	163.123i	−0.0758832	+	0.283200i
$25$			601.376i			0.962201i
$26$	−343.376	−	332.538i	−0.507952	−	0.491919i
$27$	793.342			1.08826
$28$	40.7818	+	10.9275i	0.0520176	+	0.0139381i
$29$	724.108	+	1254.19i	0.861009	+	1.49131i	0.870956	+	0.491360i	$0.163500\pi$
$29$	724.108	+	1254.19i	0.861009	+	1.49131i	−0.00994752	+	0.999951i	$0.503166\pi$
$30$	−88.8567	−	51.3014i	−0.0987296	−	0.0570016i
$31$	−23.2321	+	23.2321i	−0.0241749	+	0.0241749i	−0.719091	−	0.694916i	$-0.755442\pi$
$31$	−23.2321	+	23.2321i	−0.0241749	+	0.0241749i	0.694916	+	0.719091i	$0.255442\pi$
$32$	46.8513	+	174.851i	0.0457532	+	0.170753i
$33$	508.026	−	136.125i	0.466507	−	0.125000i
$34$	−378.328	−	378.328i	−0.327273	−	0.327273i
$35$	−12.8257	+	22.2147i	−0.0104699	+	0.0181345i
$36$	175.267	−	101.191i	0.135237	−	0.0780791i
$37$	−203.328	+	758.831i	−0.148523	+	0.554296i	0.851050	+	0.525084i	$0.175966\pi$
$37$	−203.328	+	758.831i	−0.148523	+	0.554296i	−0.999573	+	0.0292114i	$0.990700\pi$
$38$		−	560.817i		−	0.388377i
$39$	−20.2222	−	1261.15i	−0.0132953	−	0.829160i
$40$	−109.980			−0.0687373
$41$	−439.297	−	117.709i	−0.261331	−	0.0700233i	0.125775	−	0.992059i	$-0.459858\pi$
$41$	−439.297	−	117.709i	−0.261331	−	0.0700233i	−0.387105	+	0.922036i	$0.626525\pi$
$42$	55.7038	+	96.4818i	0.0315781	+	0.0546949i
$43$	−2519.78	−	1454.80i	−1.36278	−	0.786801i	−0.372787	−	0.927917i	$-0.621598\pi$
$43$	−2519.78	−	1454.80i	−1.36278	−	0.786801i	−0.989993	+	0.141116i	$0.954931\pi$
$44$	398.640	−	398.640i	0.205909	−	0.205909i
$45$	31.8239	+	118.769i	0.0157155	+	0.0586511i
$46$	−87.2077	+	23.3672i	−0.0412135	+	0.0110431i
$47$	−1379.78	−	1379.78i	−0.624619	−	0.624619i	0.322090	−	0.946709i	$-0.395615\pi$
$47$	−1379.78	−	1379.78i	−0.624619	−	0.624619i	−0.946709	+	0.322090i	$0.895615\pi$
$48$	−238.829	+	413.664i	−0.103658	+	0.179542i
$49$	−2055.21	+	1186.57i	−0.855979	+	0.494200i
$50$	−440.238	+	1642.99i	−0.176095	+	0.657196i
$51$		−	1411.81i		−	0.542794i
$52$	−694.685	−	1159.88i	−0.256910	−	0.428949i
$53$	3454.55			1.22982			0.614908	−	0.788599i	$-0.289193\pi$
$53$	3454.55			1.22982			0.614908	+	0.788599i	$0.289193\pi$
$54$	2167.45	+	580.767i	0.743296	+	0.199166i
$55$	171.259	+	296.629i	0.0566145	+	0.0980592i
$56$	103.419	+	59.7087i	0.0329778	+	0.0190398i
$57$	1046.40	−	1046.40i	0.322069	−	0.322069i
$58$	1060.17	+	3956.60i	0.315151	+	1.17616i
$59$	6208.82	−	1663.65i	1.78363	−	0.477922i	0.792393	−	0.610011i	$-0.208835\pi$
$59$	6208.82	−	1663.65i	1.78363	−	0.477922i	0.991238	+	0.132089i	$0.0421685\pi$
$60$	−205.206	−	205.206i	−0.0570016	−	0.0570016i
$61$	−3107.03	+	5381.54i	−0.834999	+	1.44626i	0.0590314	+	0.998256i	$0.481199\pi$
$61$	−3107.03	+	5381.54i	−0.834999	+	1.44626i	−0.894031	+	0.448005i	$0.852135\pi$
$62$	−80.4783	+	46.4642i	−0.0209361	+	0.0120875i
$63$	34.5548	−	128.960i	0.00870618	−	0.0324919i
$64$			512.000i			0.125000i
$65$	789.919	−	225.292i	0.186963	−	0.0533236i
$66$	1487.60			0.341507
$67$	−2782.68	−	745.618i	−0.619889	−	0.166099i	−0.0648119	−	0.997898i	$-0.520645\pi$
$67$	−2782.68	−	745.618i	−0.619889	−	0.166099i	−0.555077	+	0.831799i	$0.687311\pi$
$68$	−756.655	−	1310.57i	−0.163637	−	0.283427i
$69$	−206.316	−	119.117i	−0.0433346	−	0.0250193i
$70$	−51.3027	+	51.3027i	−0.0104699	+	0.0104699i
$71$	791.269	+	2953.06i	0.156967	+	0.585808i	0.998929	+	0.0462711i	$0.0147338\pi$
$71$	791.269	+	2953.06i	0.156967	+	0.585808i	−0.841962	+	0.539536i	$0.818600\pi$
$72$	552.915	−	148.153i	0.106658	−	0.0285789i
$73$	−4761.10	−	4761.10i	−0.893431	−	0.893431i	0.101413	−	0.994844i	$-0.467664\pi$
$73$	−4761.10	−	4761.10i	−0.893431	−	0.893431i	−0.994844	+	0.101413i	$0.967664\pi$
$74$	−1111.01	+	1924.32i	−0.202886	+	0.351409i
$75$	−3886.99	+	2244.15i	−0.691021	+	0.398961i
$76$	410.547	−	1532.18i	0.0710780	−	0.265267i
$77$		−	371.910i		−	0.0627273i
$78$	867.980	−	3460.34i	0.142666	−	0.568760i
$79$	2823.19			0.452362			0.226181	−	0.974085i	$-0.427376\pi$
$79$	2823.19			0.452362			0.226181	+	0.974085i	$0.427376\pi$
$80$	−300.470	−	80.5107i	−0.0469485	−	0.0125798i
$81$	1935.96	+	3353.18i	0.295071	+	0.511078i
$82$	−1114.01	−	643.175i	−0.165677	−	0.0956536i
$83$	7467.92	−	7467.92i	1.08404	−	1.08404i	0.0879069	−	0.996129i	$-0.471982\pi$
$83$	7467.92	−	7467.92i	1.08404	−	1.08404i	0.996129	−	0.0879069i	$-0.0280178\pi$
$84$	81.5560	+	304.371i	0.0115584	+	0.0431365i
$85$	888.095	−	237.964i	0.122920	−	0.0329363i
$86$	−5819.18	−	5819.18i	−0.786801	−	0.786801i
$87$	−5404.31	+	9360.54i	−0.714006	+	1.23669i
$88$	1380.93	−	797.279i	0.178322	−	0.102954i
$89$	979.775	−	3656.57i	0.123693	−	0.461630i	−0.876096	−	0.482136i	$-0.839861\pi$
$89$	979.775	−	3656.57i	0.123693	−	0.461630i	0.999790	+	0.0205061i	$0.00652775\pi$
$90$			347.778i			0.0429356i
$91$	−865.106	−	217.000i	−0.104469	−	0.0262046i
$92$	−255.362			−0.0301703
$93$	−236.856	−	63.4653i	−0.0273853	−	0.00733788i
$94$	−2759.57	−	4779.71i	−0.312309	−	0.540936i
$95$	834.612	+	481.863i	0.0924777	+	0.0533920i
$96$	−955.315	+	955.315i	−0.103658	+	0.103658i
$97$	63.2272	+	235.967i	0.00671986	+	0.0250789i	0.969204	−	0.246258i	$-0.0792010\pi$
$97$	63.2272	+	235.967i	0.00671986	+	0.0250789i	−0.962484	+	0.271337i	$0.912534\pi$
$98$	−6483.56	+	1737.26i	−0.675089	+	0.180890i
$99$	−1260.58	−	1260.58i	−0.128618	−	0.128618i
$100$	−2405.50	+	4166.45i	−0.240550	+	0.416645i
$101$	−5249.00	+	3030.51i	−0.514558	+	0.297080i	−0.734705	−	0.678387i	$-0.762680\pi$
$101$	−5249.00	+	3030.51i	−0.514558	+	0.297080i	0.220147	+	0.975467i	$0.429346\pi$
$102$	1033.51	−	3857.13i	0.0993381	−	0.370735i
$103$			3519.81i			0.331776i	0.986145	+	0.165888i	$0.0530490\pi$
$103$			3519.81i			0.331776i	−0.986145	+	0.165888i	$0.946951\pi$
$104$	−1048.83	−	3677.39i	−0.0969698	−	0.339995i
$105$	−191.446			−0.0173648
$106$	9438.01	+	2528.91i	0.839980	+	0.225072i
$107$	7552.66	+	13081.6i	0.659678	+	1.14260i	0.980699	+	0.195524i	$0.0626408\pi$
$107$	7552.66	+	13081.6i	0.659678	+	1.14260i	−0.321021	+	0.947072i	$0.604026\pi$
$108$	5496.43	+	3173.37i	0.471231	+	0.272065i
$109$	14901.1	−	14901.1i	1.25419	−	1.25419i	0.300371	−	0.953822i	$-0.402889\pi$
$109$	14901.1	−	14901.1i	1.25419	−	1.25419i	0.953822	−	0.300371i	$-0.0971106\pi$
$110$	250.740	+	935.776i	0.0207224	+	0.0773369i
$111$	−5663.46	+	1517.52i	−0.459659	+	0.123165i
$112$	238.835	+	238.835i	0.0190398	+	0.0190398i
$113$	−87.2072	+	151.047i	−0.00682960	+	0.0118292i	−0.869420	−	0.494074i	$-0.835507\pi$
$113$	−87.2072	+	151.047i	−0.00682960	+	0.0118292i	0.862590	+	0.505903i	$0.168841\pi$
$114$	3624.84	−	2092.80i	0.278920	−	0.161034i
$115$	40.1550	−	149.861i	0.00303630	−	0.0113316i
$116$			11585.7i			0.861009i
$117$	−3667.77	+	2196.74i	−0.267936	+	0.160475i
$118$	18180.7			1.30571
$119$	−964.306	−	258.385i	−0.0680959	−	0.0182462i
$120$	−410.411	−	710.853i	−0.0285008	−	0.0493648i
$121$	8378.75	+	4837.47i	0.572280	+	0.330406i
$122$	−12428.1	+	12428.1i	−0.834999	+	0.834999i
$123$	−878.511	−	3278.65i	−0.0580680	−	0.216713i
$124$	−253.885	+	68.0283i	−0.0165118	+	0.00442432i
$125$	−4214.89	−	4214.89i	−0.269753	−	0.269753i
$126$	188.811	−	327.031i	0.0118929	−	0.0205990i
$127$	−14442.5	+	8338.36i	−0.895435	+	0.516980i	−0.875716	−	0.482826i	$-0.839610\pi$
$127$	−14442.5	+	8338.36i	−0.895435	+	0.516980i	−0.0197186	+	0.999806i	$0.506277\pi$
$128$	−374.810	+	1398.81i	−0.0228766	+	0.0853766i
$129$		−	21715.5i		−	1.30494i
$130$	2323.02	−	37.2490i	0.137457	−	0.00220408i
$131$	−5665.11			−0.330115			−0.165058	−	0.986284i	$-0.552781\pi$
$131$	−5665.11			−0.330115			−0.165058	+	0.986284i	$0.552781\pi$
$132$	4064.21	+	1089.00i	0.233254	+	0.0625001i
$133$	−523.213	−	906.232i	−0.0295785	−	0.0512314i
$134$	−7056.60	−	4074.13i	−0.392994	−	0.226895i
$135$	−2726.61	+	2726.61i	−0.149608	+	0.149608i
$136$	−1107.82	−	4134.44i	−0.0598951	−	0.223532i
$137$	−7131.49	+	1910.88i	−0.379961	+	0.101810i	−0.443744	−	0.896153i	$-0.646350\pi$
$137$	−7131.49	+	1910.88i	−0.379961	+	0.101810i	0.0637830	+	0.997964i	$0.479683\pi$
$138$	−476.467	−	476.467i	−0.0250193	−	0.0250193i
$139$	14181.5	−	24563.2i	0.733997	−	1.27132i	−0.221166	−	0.975236i	$-0.570986\pi$
$139$	14181.5	−	24563.2i	0.733997	−	1.27132i	0.955162	−	0.296083i	$-0.0956805\pi$
$140$	−177.718	+	102.605i	−0.00906724	+	0.00523497i
$141$	3769.28	−	14067.2i	0.189592	−	0.707568i
$142$			8647.15i			0.428841i
$143$	−8285.17	+	8555.20i	−0.405162	+	0.418367i
$144$	1619.05			0.0780791
$145$	−6799.16	−	1821.83i	−0.323384	−	0.0866506i
$146$	−9522.19	−	16492.9i	−0.446716	−	0.773734i
$147$	−15338.8	−	8855.88i	−0.709835	−	0.409824i
$148$	−4444.02	+	4444.02i	−0.202886	+	0.202886i
$149$	−3090.39	−	11533.5i	−0.139200	−	0.519503i	−0.999945	−	0.0104661i	$-0.996668\pi$
$149$	−3090.39	−	11533.5i	−0.139200	−	0.519503i	0.860745	−	0.509036i	$-0.169998\pi$
$150$	−12262.3	+	3285.67i	−0.544991	+	0.146030i
$151$	18671.2	+	18671.2i	0.818878	+	0.818878i	0.985946	−	0.167067i	$-0.0534296\pi$
$151$	18671.2	+	18671.2i	0.818878	+	0.818878i	−0.167067	+	0.985946i	$0.553430\pi$
$152$	2243.27	−	3885.45i	0.0970944	−	0.168172i
$153$	−4144.28	+	2392.70i	−0.177038	+	0.102213i
$154$	272.257	−	1016.08i	0.0114799	−	0.0428436i
$155$		−	159.691i		−	0.00664687i
$156$	4904.51	−	8818.41i	0.201533	−	0.362361i
$157$	−21956.7			−0.890774			−0.445387	−	0.895338i	$-0.646934\pi$
$157$	−21956.7			−0.890774			−0.445387	+	0.895338i	$0.646934\pi$
$158$	7713.10	+	2066.72i	0.308969	+	0.0827880i
$159$	12891.4	+	22328.5i	0.509923	+	0.883212i
$160$	−761.962	−	439.919i	−0.0297641	−	0.0171843i
$161$	−119.120	+	119.120i	−0.00459549	+	0.00459549i
$162$	2834.44	+	10578.3i	0.108003	+	0.403074i
$163$	35516.2	−	9516.52i	1.33675	−	0.358181i	0.481523	−	0.876433i	$-0.340084\pi$
$163$	35516.2	−	9516.52i	1.33675	−	0.358181i	0.855228	+	0.518252i	$0.173417\pi$
$164$	−2572.70	−	2572.70i	−0.0956536	−	0.0956536i
$165$	−1278.17	+	2213.86i	−0.0469485	+	0.0813173i
$166$	25869.6	−	14935.8i	0.938802	−	0.542018i
$167$	−12061.7	+	45014.7i	−0.432488	+	1.61407i	0.314518	+	0.949251i	$0.398157\pi$
$167$	−12061.7	+	45014.7i	−0.432488	+	1.61407i	−0.747007	+	0.664817i	$0.768510\pi$
$168$			891.260i			0.0315781i
$169$	15066.2	+	24264.0i	0.527509	+	0.849550i
$170$	2600.52			0.0899835
$171$	−4845.07	−	1298.23i	−0.165694	−	0.0443977i
$172$	−11638.4	−	20158.2i	−0.393401	−	0.681390i
$173$	16565.0	+	9563.81i	0.553477	+	0.319550i	0.750523	−	0.660844i	$-0.229802\pi$
$173$	16565.0	+	9563.81i	0.553477	+	0.319550i	−0.197046	+	0.980394i	$0.563135\pi$
$174$	−21617.2	+	21617.2i	−0.714006	+	0.714006i
$175$	821.438	+	3065.65i	0.0268225	+	0.100103i
$176$	4356.42	−	1167.30i	0.140638	−	0.0376840i
$177$	33922.4	+	33922.4i	1.08278	+	1.08278i
$178$	5353.59	−	9272.69i	0.168968	−	0.292662i
$179$	43323.9	−	25013.1i	1.35214	−	0.780658i	0.363590	−	0.931559i	$-0.381551\pi$
$179$	43323.9	−	25013.1i	1.35214	−	0.780658i	0.988549	+	0.150901i	$0.0482176\pi$
$180$	−254.591	+	950.148i	−0.00785776	+	0.0293256i
$181$		−	11146.2i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$181$		−	11146.2i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$182$	−2204.66	−	1226.16i	−0.0665577	−	0.0370172i
$183$	−46378.1			−1.38487
$184$	−697.661	−	186.938i	−0.0206067	−	0.00552156i
$185$	−1909.19	−	3306.81i	−0.0557835	−	0.0966198i
$186$	−600.642	−	346.781i	−0.0173616	−	0.0100237i
$187$	−9426.03	+	9426.03i	−0.269554	+	0.269554i
$188$	−4040.29	−	15078.6i	−0.114313	−	0.426623i
$189$	4044.24	−	1083.65i	0.113217	−	0.0303365i
$190$	1927.45	+	1927.45i	0.0533920	+	0.0533920i
$191$	21050.9	−	36461.2i	0.577037	−	0.999457i	−0.418780	−	0.908088i	$-0.637542\pi$
$191$	21050.9	−	36461.2i	0.577037	−	0.999457i	0.995817	−	0.0913696i	$-0.0291245\pi$
$192$	−3309.31	+	1910.63i	−0.0897708	+	0.0518292i
$193$	−3524.96	+	13155.3i	−0.0946322	+	0.353172i	−0.996963	−	0.0778710i	$-0.975188\pi$
$193$	−3524.96	+	13155.3i	−0.0946322	+	0.353172i	0.902331	+	0.431043i	$0.141854\pi$
$194$			690.960i			0.0183590i
$195$	4403.91	+	4264.91i	0.115816	+	0.112161i
$196$	−18985.2			−0.494200
$197$	−48863.5	−	13092.9i	−1.25908	−	0.337368i	−0.433240	−	0.901279i	$-0.642630\pi$
$197$	−48863.5	−	13092.9i	−1.25908	−	0.337368i	−0.825836	+	0.563910i	$0.809296\pi$
$198$	−2521.16	−	4366.78i	−0.0643088	−	0.111386i
$199$	−23206.2	−	13398.1i	−0.586000	−	0.338327i	0.177514	−	0.984118i	$-0.443194\pi$
$199$	−23206.2	−	13398.1i	−0.586000	−	0.338327i	−0.763514	+	0.645791i	$0.776528\pi$
$200$	−9622.01	+	9622.01i	−0.240550	+	0.240550i
$201$	−5564.84	−	20768.3i	−0.137740	−	0.514054i
$202$	−16559.0	+	4436.98i	−0.405819	+	0.108739i
$203$	5404.45	+	5404.45i	0.131147	+	0.131147i
$204$	5647.22	−	9781.28i	0.135698	−	0.235036i
$205$	1914.35	−	1105.25i	0.0455528	−	0.0262999i
$206$	−2576.68	+	9616.29i	−0.0607192	+	0.226607i
$207$			807.506i			0.0188454i
$208$	−173.409	−	10814.6i	−0.00400816	−	0.249968i
$209$	−13972.7			−0.319882
$210$	−523.041	−	140.148i	−0.0118603	−	0.00317797i
$211$	−28024.1	−	48539.2i	−0.629458	−	1.09025i	−0.987661	−	0.156609i	$-0.949944\pi$
$211$	−28024.1	−	48539.2i	−0.629458	−	1.09025i	0.358203	−	0.933644i	$-0.383390\pi$
$212$	23933.8	+	13818.2i	0.532526	+	0.307454i
$213$	−16134.3	+	16134.3i	−0.355624	+	0.355624i
$214$	11057.9	+	41268.5i	0.241459	+	0.901137i
$215$	13660.1	−	3660.21i	0.295513	−	0.0791825i
$216$	12693.5	+	12693.5i	0.272065	+	0.272065i
$217$	−86.6974	+	150.164i	−0.00184114	+	0.00318895i
$218$	51618.8	−	29802.1i	1.08616	−	0.627097i
$219$	13006.3	−	48540.3i	0.271186	−	1.01208i
$220$			2740.14i			0.0566145i
$221$	16426.2	+	27425.9i	0.336319	+	0.561534i
$222$	−16583.8			−0.336494
$223$	−57100.1	−	15299.9i	−1.14823	−	0.307666i	−0.365972	−	0.930626i	$-0.619263\pi$
$223$	−57100.1	−	15299.9i	−1.14823	−	0.307666i	−0.782254	+	0.622960i	$0.785930\pi$
$224$	477.670	+	827.348i	0.00951988	+	0.0164889i
$225$	13175.2	+	7606.69i	0.260250	+	0.150256i
$226$	−348.829	+	348.829i	−0.00682960	+	0.00682960i
$227$	−15065.2	−	56224.2i	−0.292364	−	1.09112i	−0.943288	−	0.331975i	$-0.892285\pi$
$227$	−15065.2	−	56224.2i	−0.292364	−	1.09112i	0.650924	−	0.759143i	$-0.274382\pi$
$228$	11435.3	−	3064.07i	0.219977	−	0.0589426i
$229$	41844.5	+	41844.5i	0.797936	+	0.797936i	0.982770	−	0.184834i	$-0.0591748\pi$
$229$	41844.5	+	41844.5i	0.797936	+	0.797936i	−0.184834	+	0.982770i	$0.559175\pi$
$230$	219.411	−	380.031i	0.00414766	−	0.00718395i
$231$	2403.84	−	1387.86i	0.0450487	−	0.0260089i
$232$	−8481.35	+	31652.8i	−0.157576	+	0.588080i
$233$			10344.7i			0.190548i	0.995451	+	0.0952742i	$0.0303728\pi$
$233$			10344.7i			0.190548i	−0.995451	+	0.0952742i	$0.969627\pi$
$234$	−11628.7	+	3316.60i	−0.212372	+	0.0605706i
$235$	9484.26			0.171739
$236$	49670.5	+	13309.2i	0.891815	+	0.238961i
$237$	10535.3	+	18247.7i	0.187564	+	0.324871i
$238$	−2445.38	−	1411.84i	−0.0431711	−	0.0249248i
$239$	−10334.1	+	10334.1i	−0.180916	+	0.180916i	−0.791755	−	0.610839i	$-0.790832\pi$
$239$	−10334.1	+	10334.1i	−0.180916	+	0.180916i	0.610839	+	0.791755i	$0.290832\pi$
$240$	−600.884	−	2242.53i	−0.0104320	−	0.0389328i
$241$	−52730.0	+	14129.0i	−0.907870	+	0.243263i	−0.682393	−	0.730985i	$-0.739061\pi$
$241$	−52730.0	+	14129.0i	−0.907870	+	0.243263i	−0.225477	+	0.974249i	$0.572394\pi$
$242$	19349.9	+	19349.9i	0.330406	+	0.330406i
$243$	17681.5	−	30625.3i	0.299438	−	0.518641i
$244$	−43052.3	+	24856.3i	−0.723131	+	0.417500i
$245$	2985.37	−	11141.6i	0.0497355	−	0.185615i
$246$		−	9600.55i		−	0.158645i
$247$	−8152.75	+	32502.2i	−0.133632	+	0.532744i
$248$	−743.427			−0.0120875
$249$	76136.9	+	20400.8i	1.22800	+	0.329040i
$250$	−8429.78	−	14600.8i	−0.134876	−	0.233613i
$251$	5881.31	+	3395.58i	0.0933527	+	0.0538972i	0.545950	−	0.837818i	$-0.316169\pi$
$251$	5881.31	+	3395.58i	0.0933527	+	0.0538972i	−0.452597	+	0.891715i	$0.649502\pi$
$252$	755.245	−	755.245i	0.0118929	−	0.0118929i
$253$	582.194	+	2172.78i	0.00909550	+	0.0339449i
$254$	−45561.7	+	12208.2i	−0.706207	+	0.189228i
$255$	4852.19	+	4852.19i	0.0746204	+	0.0746204i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−22631.9	+	13066.5i	−0.342653	+	0.197831i	−0.661445	−	0.749994i	$-0.730056\pi$
$257$	−22631.9	+	13066.5i	−0.342653	+	0.197831i	0.318791	+	0.947825i	$0.396723\pi$
$258$	15896.8	−	59327.7i	0.238820	−	0.891288i
$259$			4146.04i			0.0618065i
$260$	6373.88	+	1598.80i	0.0942882	+	0.0236510i
$261$	36636.5			0.537814
$262$	−15477.4	−	4147.15i	−0.225473	−	0.0604153i
$263$	25951.3	+	44948.9i	0.375186	+	0.649842i	0.990355	−	0.138554i	$-0.0442454\pi$
$263$	25951.3	+	44948.9i	0.375186	+	0.649842i	−0.615169	+	0.788396i	$0.710912\pi$
$264$	10306.4	+	5950.42i	0.147877	+	0.0853767i
$265$	−11872.8	+	11872.8i	−0.169068	+	0.169068i
$266$	−766.038	−	2858.89i	−0.0108265	−	0.0404049i
$267$	27290.5	−	7312.46i	0.382814	−	0.102575i
$268$	−16296.5	−	16296.5i	−0.226895	−	0.226895i
$269$	−1923.19	+	3331.07i	−0.0265778	+	0.0460340i	−0.879008	−	0.476806i	$-0.841794\pi$
$269$	−1923.19	+	3331.07i	−0.0265778	+	0.0460340i	0.852431	+	0.522840i	$0.175128\pi$
$270$	−9445.25	+	5453.22i	−0.129565	+	0.0748041i
$271$	2327.53	−	8686.45i	0.0316925	−	0.118278i	−0.948267	−	0.317472i	$-0.897166\pi$
$271$	2327.53	−	8686.45i	0.0316925	−	0.118278i	0.979960	+	0.199195i	$0.0638326\pi$
$272$		−	12106.5i		−	0.163637i
$273$	−1825.74	−	6401.39i	−0.0244970	−	0.0858913i
$274$	−20882.5			−0.278151
$275$	40935.1	+	10968.5i	0.541290	+	0.145038i
$276$	−952.934	−	1650.53i	−0.0125096	−	0.0216673i
$277$	62797.5	+	36256.1i	0.818432	+	0.472522i	0.849875	−	0.526984i	$-0.176677\pi$
$277$	62797.5	+	36256.1i	0.818432	+	0.472522i	−0.0314435	+	0.999506i	$0.510010\pi$
$278$	56726.2	−	56726.2i	0.733997	−	0.733997i
$279$	215.119	+	802.836i	0.00276357	+	0.0103138i
$280$	−560.647	+	150.225i	−0.00715110	+	0.00191613i
$281$	−69961.4	−	69961.4i	−0.886025	−	0.886025i	0.108114	−	0.994139i	$-0.465519\pi$
$281$	−69961.4	−	69961.4i	−0.886025	−	0.886025i	−0.994139	+	0.108114i	$0.965519\pi$
$282$	20595.8	−	35672.9i	0.258988	−	0.448580i
$283$	−24318.4	+	14040.3i	−0.303643	+	0.175308i	−0.644078	−	0.764960i	$-0.722759\pi$
$283$	−24318.4	+	14040.3i	−0.303643	+	0.175308i	0.340435	+	0.940268i	$0.389426\pi$
$284$	−6330.15	+	23624.4i	−0.0784833	+	0.292904i
$285$			7192.68i			0.0885525i
$286$	−28898.3	+	17308.1i	−0.353298	+	0.211600i
$287$	−2400.20			−0.0291396
$288$	4423.32	+	1185.23i	0.0533290	+	0.0142895i
$289$	−23869.0	−	41342.3i	−0.285785	−	0.494993i
$290$	−17242.0	−	9954.65i	−0.205017	−	0.118367i
$291$	−1289.23	+	1289.23i	−0.0152245	+	0.0152245i
$292$	−13941.5	−	52030.2i	−0.163509	−	0.610225i
$293$	−155749.	+	41732.9i	−1.81422	+	0.486120i	−0.996045	−	0.0888459i	$-0.971682\pi$
$293$	−155749.	+	41732.9i	−1.81422	+	0.486120i	−0.818178	+	0.574965i	$0.805015\pi$
$294$	−35423.5	−	35423.5i	−0.409824	−	0.409824i
$295$	−15621.1	+	27056.6i	−0.179502	+	0.310906i
$296$	−15394.5	+	8888.04i	−0.175705	+	0.101443i
$297$	14469.8	−	54002.0i	0.164040	−	0.612205i
$298$		−	33772.4i		−	0.380302i
$299$	5393.82	−	86.4884i	0.0603329	−	0.000967421i
$300$	−35906.5			−0.398961
$301$	−14832.3	−	3974.30i	−0.163710	−	0.0438660i
$302$	37342.5	+	64679.1i	0.409439	+	0.709170i
$303$	−39175.4	−	22617.9i	−0.426706	−	0.246359i
$304$	8973.07	−	8973.07i	0.0970944	−	0.0970944i
$305$	−7817.17	−	29174.1i	−0.0840330	−	0.313616i
$306$	−13074.0	+	3503.15i	−0.139625	+	0.0374125i
$307$	−64876.9	−	64876.9i	−0.688357	−	0.688357i	0.273512	−	0.961869i	$-0.411815\pi$
$307$	−64876.9	−	64876.9i	−0.688357	−	0.688357i	−0.961869	+	0.273512i	$0.911815\pi$
$308$	1487.64	−	2576.67i	0.0156818	−	0.0271617i
$309$	−22750.3	+	13134.9i	−0.238270	+	0.137565i
$310$	116.902	−	436.284i	0.00121646	−	0.00453990i
$311$			105337.i			1.08908i	0.838735	+	0.544539i	$0.183295\pi$
$311$			105337.i			1.08908i	−0.838735	+	0.544539i	$0.816705\pi$
$312$	19854.9	−	20502.0i	0.203966	−	0.210614i
$313$	96656.3			0.986601			0.493301	−	0.869859i	$-0.335790\pi$
$313$	96656.3			0.986601			0.493301	+	0.869859i	$0.335790\pi$
$314$	−59986.8	−	16073.4i	−0.608410	−	0.163023i
$315$	324.459	+	561.980i	0.00326994	+	0.00566369i
$316$	19559.6	+	11292.8i	0.195878	+	0.113090i
$317$	89641.5	−	89641.5i	0.892052	−	0.892052i	−0.102664	−	0.994716i	$-0.532737\pi$
$317$	89641.5	−	89641.5i	0.892052	−	0.892052i	0.994716	+	0.102664i	$0.0327365\pi$
$318$	18874.3	+	70439.7i	0.186645	+	0.696567i
$319$	98578.7	−	26414.1i	0.968727	−	0.259570i
$320$	−1759.68	−	1759.68i	−0.0171843	−	0.0171843i
$321$	−56368.5	+	97633.1i	−0.547049	+	0.947517i
$322$	−412.643	+	238.239i	−0.00397981	+	0.00229775i
$323$	−9707.57	+	36229.1i	−0.0930477	+	0.347259i
$324$			30975.4i			0.295071i
$325$	49398.6	−	88819.8i	0.467679	−	0.840897i
$326$	103999.			0.978570
$327$	151919.	+	40706.7i	1.42075	+	0.380689i
$328$	−5145.40	−	8912.09i	−0.0478268	−	0.0828385i
$329$	−8918.45	−	5149.07i	−0.0823943	−	0.0475704i
$330$	−5112.70	+	5112.70i	−0.0469485	+	0.0469485i
$331$	46400.7	+	173170.i	0.423514	+	1.58058i	0.767146	+	0.641473i	$0.221676\pi$
$331$	46400.7	+	173170.i	0.423514	+	1.58058i	−0.343632	+	0.939105i	$0.611657\pi$
$332$	81611.0	−	21867.6i	0.740410	−	0.198392i
$333$	14052.9	+	14052.9i	0.126729	+	0.126729i
$334$	−65906.2	+	114153.i	−0.590790	+	1.02328i
$335$	12126.3	−	7001.12i	0.108053	−	0.0623847i
$336$	−652.448	+	2434.97i	−0.00577919	+	0.0215682i
$337$		−	120658.i		−	1.06242i	−0.847240	−	0.531211i	$-0.821737\pi$
$337$		−	120658.i		−	1.06242i	0.847240	−	0.531211i	$-0.178263\pi$
$338$	23399.1	+	77319.7i	0.204817	+	0.676794i
$339$	−1301.73			−0.0113271
$340$	7104.76	+	1903.72i	0.0614599	+	0.0164681i
$341$	1157.65	+	2005.12i	0.00995566	+	0.0172437i
$342$	−12286.6	−	7093.67i	−0.105046	−	0.0606483i
$343$	−17816.1	+	17816.1i	−0.151435	+	0.151435i
$344$	−17039.8	−	63593.2i	−0.143995	−	0.537395i
$345$	1118.47	−	299.693i	0.00939693	−	0.00251790i
$346$	38255.3	+	38255.3i	0.319550	+	0.319550i
$347$	−38514.1	+	66708.5i	−0.319861	+	0.554016i	−0.980459	−	0.196724i	$-0.936970\pi$
$347$	−38514.1	+	66708.5i	−0.319861	+	0.554016i	0.660598	+	0.750740i	$0.270303\pi$
$348$	−74884.3	+	43234.5i	−0.618347	+	0.357003i
$349$	−5313.20	+	19829.1i	−0.0436220	+	0.162799i	−0.984301	−	0.176499i	$-0.943523\pi$
$349$	−5313.20	+	19829.1i	−0.0436220	+	0.162799i	0.940679	+	0.339298i	$0.110190\pi$
$350$			8976.85i			0.0732804i
$351$	−117172.	−	65167.2i	−0.951064	−	0.528950i
$352$	12756.5			0.102954
$353$	−78298.7	−	20980.1i	−0.628355	−	0.168367i	−0.0694319	−	0.997587i	$-0.522119\pi$
$353$	−78298.7	−	20980.1i	−0.628355	−	0.168367i	−0.558923	+	0.829219i	$0.688785\pi$
$354$	67844.9	+	117511.i	0.541390	+	0.937715i
$355$	−12868.7	−	7429.77i	−0.102113	−	0.0589548i
$356$	21414.4	−	21414.4i	0.168968	−	0.168968i
$357$	−1928.43	−	7197.00i	−0.0151310	−	0.0564697i
$358$	136674.	−	36621.7i	1.06640	−	0.285741i
$359$	−120449.	−	120449.i	−0.934579	−	0.934579i	0.0634085	−	0.997988i	$-0.479803\pi$
$359$	−120449.	−	120449.i	−0.934579	−	0.934579i	−0.997988	+	0.0634085i	$0.979803\pi$
$360$	−1391.11	+	2409.48i	−0.0107339	+	0.0185917i
$361$	78814.0	−	45503.3i	0.604768	−	0.349163i
$362$	8159.61	−	30452.1i	0.0622662	−	0.232380i
$363$			72208.0i			0.547990i
$364$	−5125.63	−	4963.85i	−0.0386852	−	0.0374641i
$365$	32726.5			0.245648
$366$	−126707.	−	33951.1i	−0.945887	−	0.253450i
$367$	−70453.2	−	122029.i	−0.523081	−	0.906002i	−0.999639	−	0.0268596i	$-0.991449\pi$
$367$	−70453.2	−	122029.i	−0.523081	−	0.906002i	0.476559	−	0.879143i	$-0.341884\pi$
$368$	−1769.20	−	1021.45i	−0.0130641	−	0.00754259i
$369$	−8135.40	+	8135.40i	−0.0597484	+	0.0597484i
$370$	−2795.25	−	10432.0i	−0.0204182	−	0.0762016i
$371$	17610.4	−	4718.68i	0.127944	−	0.0342825i
$372$	−1387.12	−	1387.12i	−0.0100237	−	0.0100237i
$373$	−64078.4	+	110987.i	−0.460568	+	0.797728i	−0.998989	−	0.0449481i	$-0.985688\pi$
$373$	−64078.4	+	110987.i	−0.460568	+	0.797728i	0.538421	+	0.842676i	$0.319021\pi$
$374$	−32652.7	+	18852.1i	−0.233440	+	0.134777i
$375$	11514.2	−	42971.6i	0.0818789	−	0.305576i
$376$		−	44153.1i		−	0.312309i
$377$	−3923.97	−	244717.i	−0.0276085	−	1.72180i
$378$	11842.4			0.0828809
$379$	−26864.0	−	7198.19i	−0.187022	−	0.0501124i	0.164092	−	0.986445i	$-0.447530\pi$
$379$	−26864.0	−	7198.19i	−0.187022	−	0.0501124i	−0.351114	+	0.936333i	$0.614197\pi$
$380$	3854.91	+	6676.89i	0.0266960	+	0.0462389i
$381$	−107790.	−	62232.6i	−0.742554	−	0.428714i
$382$	84203.5	−	84203.5i	0.577037	−	0.577037i
$383$	49162.3	+	183476.i	0.335147	+	1.25078i	0.903710	+	0.428145i	$0.140833\pi$
$383$	49162.3	+	183476.i	0.335147	+	1.25078i	−0.568563	+	0.822639i	$0.692501\pi$
$384$	−10439.9	+	2797.36i	−0.0708000	+	0.0189708i
$385$	1278.21	+	1278.21i	0.00862342	+	0.00862342i
$386$	−19260.7	+	33360.5i	−0.129270	+	0.223902i
$387$	−63744.5	+	36802.9i	−0.425619	+	0.245731i
$388$	−505.818	+	1887.74i	−0.00335993	+	0.0125394i
$389$		−	101373.i		−	0.669919i	−0.942232	−	0.334960i	$-0.891277\pi$
$389$		−	101373.i		−	0.669919i	0.942232	−	0.334960i	$-0.108723\pi$
$390$	8909.59	+	14875.8i	0.0585772	+	0.0978031i
$391$	6038.15			0.0394958
$392$	−51868.5	−	13898.1i	−0.337545	−	0.0904448i
$393$	−21140.5	−	36616.4i	−0.136877	−	0.237078i
$394$	−123913.	−	71541.1i	−0.798222	−	0.460854i
$395$	−9702.93	+	9702.93i	−0.0621883	+	0.0621883i
$396$	−3691.23	−	13775.9i	−0.0235386	−	0.0878474i
$397$	240238.	−	64371.5i	1.52426	−	0.408425i	0.603120	−	0.797650i	$-0.293924\pi$
$397$	240238.	−	64371.5i	1.52426	−	0.408425i	0.921143	+	0.389225i	$0.127257\pi$
$398$	−53592.4	−	53592.4i	−0.338327	−	0.338327i
$399$	3904.95	−	6763.58i	0.0245284	−	0.0424845i
$400$	−33331.6	+	19244.0i	−0.208323	+	0.120275i
$401$	−61846.7	+	230815.i	−0.384616	+	1.43541i	0.454155	+	0.890923i	$0.349941\pi$
$401$	−61846.7	+	230815.i	−0.384616	+	1.43541i	−0.838771	+	0.544484i	$0.816725\pi$
$402$		−	60813.8i		−	0.376313i
$403$	5339.59	−	1522.90i	0.0328774	−	0.00937695i
$404$	−48488.2			−0.297080
$405$	−18178.1	−	4870.80i	−0.110825	−	0.0296955i
$406$	10808.9	+	18721.6i	0.0655736	+	0.113577i
$407$	47944.4	+	27680.7i	0.289433	+	0.167104i
$408$	22588.9	−	22588.9i	0.135698	−	0.135698i
$409$	62668.4	+	233882.i	0.374629	+	1.39814i	0.853886	+	0.520461i	$0.174240\pi$
$409$	62668.4	+	233882.i	0.374629	+	1.39814i	−0.479256	+	0.877675i	$0.659094\pi$
$410$	6039.22	−	1618.20i	0.0359263	−	0.00962643i
$411$	−38963.6	−	38963.6i	−0.230661	−	0.230661i
$412$	−14079.2	+	24385.9i	−0.0829439	+	0.143663i
$413$	29378.4	−	16961.6i	0.172238	−	0.0994415i
$414$	−591.136	+	2206.15i	−0.00344895	+	0.0128716i
$415$			51332.5i			0.298055i
$416$	7443.08	−	29673.0i	0.0430097	−	0.171465i
$417$	211685.			1.21736
$418$	−38174.2	−	10228.8i	−0.218483	−	0.0585424i
$419$	92089.0	+	159503.i	0.524541	+	0.908532i	0.999592	+	0.0285734i	$0.00909645\pi$
$419$	92089.0	+	159503.i	0.524541	+	0.908532i	−0.475051	+	0.879959i	$0.657570\pi$
$420$	−1326.38	−	765.786i	−0.00751916	−	0.00434119i
$421$	−68545.5	+	68545.5i	−0.386736	+	0.386736i	−0.873522	−	0.486785i	$-0.838169\pi$
$421$	−68545.5	+	68545.5i	−0.386736	+	0.386736i	0.486785	+	0.873522i	$0.338169\pi$
$422$	−41030.1	−	153127.i	−0.230398	−	0.859856i
$423$	−47681.5	+	12776.2i	−0.266483	+	0.0714038i
$424$	55272.8	+	55272.8i	0.307454	+	0.307454i
$425$	56879.3	−	98517.8i	0.314903	−	0.545427i
$426$	−55890.8	+	32268.6i	−0.307979	+	0.177812i
$427$	−8487.99	+	31677.6i	−0.0465532	+	0.173739i
$428$			120842.i			0.659678i
$429$	−86214.2	−	21625.7i	−0.468451	−	0.117505i
$430$	39999.5			0.216330
$431$	306100.	+	82019.2i	1.64782	+	0.441531i	0.959000	−	0.283406i	$-0.0914644\pi$
$431$	306100.	+	82019.2i	1.64782	+	0.441531i	0.688815	+	0.724937i	$0.258131\pi$
$432$	25386.9	+	43971.5i	0.136033	+	0.235615i
$433$	22761.4	+	13141.3i	0.121402	+	0.0700912i	0.559471	−	0.828850i	$-0.311004\pi$
$433$	22761.4	+	13141.3i	0.121402	+	0.0700912i	−0.438070	+	0.898941i	$0.644338\pi$
$434$	−346.790	+	346.790i	−0.00184114	+	0.00184114i
$435$	−13597.0	−	50744.8i	−0.0718564	−	0.268172i
$436$	162842.	−	43633.4i	0.856630	−	0.229533i
$437$	4475.35	+	4475.35i	0.0234350	+	0.0234350i
$438$	71067.9	−	123093.i	0.370447	−	0.641632i
$439$	117967.	−	68108.5i	0.612115	−	0.353405i	−0.161678	−	0.986844i	$-0.551691\pi$
$439$	117967.	−	68108.5i	0.612115	−	0.353405i	0.773793	+	0.633439i	$0.218357\pi$
$440$	−2005.92	+	7486.21i	−0.0103612	+	0.0386684i
$441$			60035.0i			0.308693i
$442$	24800.0	+	86953.7i	0.126942	+	0.445085i
$443$	−25715.8			−0.131036			−0.0655182	−	0.997851i	$-0.520870\pi$
$443$	−25715.8			−0.131036			−0.0655182	+	0.997851i	$0.520870\pi$
$444$	−45307.7	−	12140.2i	−0.229830	−	0.0615826i
$445$	9199.79	+	15934.5i	0.0464577	+	0.0804671i
$446$	−144800.	−	83600.4i	−0.727946	−	0.420280i
$447$	63014.2	−	63014.2i	0.315372	−	0.315372i
$448$	699.357	+	2610.04i	0.00348452	+	0.0130044i
$449$	−302622.	+	81087.4i	−1.50110	+	0.402217i	−0.913467	−	0.406914i	$-0.866605\pi$
$449$	−302622.	+	81087.4i	−1.50110	+	0.402217i	−0.587629	+	0.809131i	$0.699938\pi$
$450$	30426.8	+	30426.8i	0.150256	+	0.150256i
$451$	−16024.7	+	27755.6i	−0.0787837	+	0.136457i
$452$	−1208.38	+	697.658i	−0.00591461	+	0.00341480i
$453$	−51006.0	+	190357.i	−0.248556	+	0.927625i
$454$		−	164636.i		−	0.798754i
$455$	3719.05	−	2227.45i	0.0179643	−	0.0107593i
$456$	33484.8			0.161034
$457$	15703.0	+	4207.60i	0.0751883	+	0.0201466i	0.296217	−	0.955121i	$-0.404275\pi$
$457$	15703.0	+	4207.60i	0.0751883	+	0.0201466i	−0.221029	+	0.975267i	$0.570941\pi$
$458$	83689.1	+	144954.i	0.398968	+	0.691033i
$459$	−129966.	−	75035.8i	−0.616885	−	0.356158i
$460$	877.644	−	877.644i	0.00414766	−	0.00414766i
$461$	−45390.3	−	169399.i	−0.213580	−	0.797093i	−0.986661	−	0.162786i	$-0.947952\pi$
$461$	−45390.3	−	169399.i	−0.213580	−	0.797093i	0.773081	−	0.634307i	$-0.218715\pi$
$462$	7583.40	−	2031.97i	0.0355288	−	0.00951990i
$463$	−179992.	−	179992.i	−0.839635	−	0.839635i	0.149175	−	0.988811i	$-0.452338\pi$
$463$	−179992.	−	179992.i	−0.839635	−	0.839635i	−0.988811	+	0.149175i	$0.952338\pi$
$464$	−46342.9	+	80268.3i	−0.215252	+	0.372828i
$465$	1032.16	−	595.920i	0.00477356	−	0.00275602i
$466$	−7572.83	+	28262.2i	−0.0348728	+	0.130147i
$467$			262581.i			1.20401i	0.798493	+	0.602004i	$0.205631\pi$
$467$			262581.i			1.20401i	−0.798493	+	0.602004i	$0.794369\pi$
$468$	−34198.0	+	548.355i	−0.156138	+	0.00250363i
$469$	−15203.8			−0.0691205
$470$	25911.5	+	6942.96i	0.117300	+	0.0314303i
$471$	−81935.8	−	141917.i	−0.369345	−	0.639724i
$472$	125959.	+	72722.7i	0.565388	+	0.326427i
$473$	−144985.	+	144985.i	−0.648038	+	0.648038i
$474$	15424.8	+	57566.0i	0.0686533	+	0.256218i
$475$	115177.	−	30861.6i	0.510480	−	0.136783i
$476$	−5647.37	−	5647.37i	−0.0249248	−	0.0249248i
$477$	43696.0	−	75683.7i	0.192046	−	0.332633i
$478$	−35798.3	+	20668.1i	−0.156677	+	0.0904578i
$479$	100039.	−	373351.i	0.436013	−	1.62722i	−0.302619	−	0.953112i	$-0.597861\pi$
$479$	100039.	−	373351.i	0.436013	−	1.62722i	0.738631	−	0.674110i	$-0.235472\pi$
$480$		−	6566.58i		−	0.0285008i
$481$	92362.8	−	95373.0i	0.399215	−	0.412226i
$482$	−154404.			−0.664607
$483$	−1214.45	−	325.411i	−0.00520577	−	0.00139488i
$484$	38699.8	+	67030.0i	0.165203	+	0.286140i
$485$	−1028.29	−	593.684i	−0.00437152	−	0.00252390i
$486$	70726.0	−	70726.0i	0.299438	−	0.299438i
$487$	−58542.2	−	218482.i	−0.246838	−	0.921210i	−0.972451	−	0.233108i	$-0.925111\pi$
$487$	−58542.2	−	218482.i	−0.246838	−	0.921210i	0.725613	−	0.688103i	$-0.241556\pi$
$488$	−135817.	+	36392.1i	−0.570315	+	0.152816i
$489$	194046.	+	194046.i	0.811496	+	0.811496i
$490$	16312.4	−	28253.9i	0.0679399	−	0.117675i
$491$	2440.54	−	1409.05i	0.0101233	−	0.00584470i	−0.494930	−	0.868933i	$-0.664806\pi$
$491$	2440.54	−	1409.05i	0.0101233	−	0.00584470i	0.505053	+	0.863088i	$0.331473\pi$
$492$	7028.09	−	26229.2i	0.0290340	−	0.108356i
$493$		−	273950.i		−	1.12714i
$494$	−46067.0	+	82829.4i	−0.188771	+	0.339415i
$495$	8664.89			0.0353633
$496$	−2031.08	−	544.226i	−0.00825589	−	0.00221216i
$497$	8067.35	+	13973.1i	0.0326601	+	0.0565690i
$498$	193076.	+	111472.i	0.778518	+	0.449477i
$499$	−136722.	+	136722.i	−0.549081	+	0.549081i	−0.926175	−	0.377094i	$-0.876923\pi$
$499$	−136722.	+	136722.i	−0.549081	+	0.549081i	0.377094	+	0.926175i	$0.376923\pi$
$500$	−12342.1	−	46061.2i	−0.0493682	−	0.184245i
$501$	−335963.	+	90021.0i	−1.33849	+	0.358648i
$502$	13582.3	+	13582.3i	0.0538972	+	0.0538972i
$503$	222174.	−	384816.i	0.878126	−	1.52096i	0.0247304	−	0.999694i	$-0.492127\pi$
$503$	222174.	−	384816.i	0.878126	−	1.52096i	0.853395	−	0.521264i	$-0.174539\pi$
$504$	2616.24	−	1510.49i	0.0102995	−	0.00594643i
$505$	7624.65	−	28455.6i	0.0298977	−	0.111580i
$506$			6362.33i			0.0248494i
$507$	−100608.	+	187926.i	−0.391395	+	0.731091i
$508$	−133414.			−0.516980
$509$	−33001.0	−	8842.59i	−0.127377	−	0.0341306i	0.194567	−	0.980889i	$-0.437670\pi$
$509$	−33001.0	−	8842.59i	−0.127377	−	0.0341306i	−0.321944	+	0.946759i	$0.604336\pi$
$510$	9704.38	+	16808.5i	0.0373102	+	0.0646231i
$511$	−30774.1	−	17767.4i	−0.117854	−	0.0680429i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−40713.0	−	151943.i	−0.154703	−	0.577359i
$514$	−71396.9	+	19130.7i	−0.270242	+	0.0724111i
$515$	−12097.1	−	12097.1i	−0.0456107	−	0.0456107i
$516$	86861.8	−	150449.i	0.326234	−	0.565054i
$517$	−119086.	+	68754.5i	−0.445534	+	0.257229i
$518$	−3035.12	+	11327.2i	−0.0113114	+	0.0422147i
$519$			142757.i			0.529985i
$520$	16243.4	+	9034.02i	0.0600716	+	0.0334098i
$521$	86231.1			0.317679			0.158839	−	0.987304i	$-0.449225\pi$
$521$	86231.1			0.317679			0.158839	+	0.987304i	$0.449225\pi$
$522$	100093.	+	26819.7i	0.367334	+	0.0984269i
$523$	−185608.	−	321482.i	−0.678567	−	1.17531i	−0.975413	−	0.220387i	$-0.929268\pi$
$523$	−185608.	−	321482.i	−0.678567	−	1.17531i	0.296846	−	0.954926i	$-0.404065\pi$
$524$	−39249.0	−	22660.4i	−0.142944	−	0.0825288i
$525$	−16749.5	+	16749.5i	−0.0607690	+	0.0607690i
$526$	37995.3	+	141800.i	0.137328	+	0.512514i
$527$	6003.23	−	1608.56i	0.0216154	−	0.00579184i
$528$	23801.7	+	23801.7i	0.0853767	+	0.0853767i
$529$	−139411.	+	241467.i	−0.498180	+	0.862872i
$530$	−41128.7	+	23745.7i	−0.146418	+	0.0845342i
$531$	42086.3	−	157068.i	0.149263	−	0.557057i
$532$		−	8371.42i		−	0.0295785i
$533$	55212.6	+	53469.9i	0.194350	+	0.188215i
$534$	79912.0			0.280240
$535$	−70917.1	−	19002.2i	−0.247767	−	0.0663890i
$536$	−32593.0	−	56452.8i	−0.113448	−	0.196497i
$537$	323344.	+	186682.i	1.12128	+	0.647374i
$538$	−7692.78	+	7692.78i	−0.0265778	+	0.0265778i
$539$	43283.9	+	161538.i	0.148987	+	0.556028i
$540$	−29796.9	+	7984.07i	−0.102184	+	0.0273802i
$541$	373080.	+	373080.i	1.27470	+	1.27470i	0.943595	+	0.331102i	$0.107420\pi$
$541$	373080.	+	373080.i	1.27470	+	1.27470i	0.331102	+	0.943595i	$0.392580\pi$
$542$	12717.8	−	22028.0i	0.0432927	−	0.0749852i
$543$	72043.6	−	41594.4i	0.244341	−	0.141070i
$544$	8862.56	−	33075.5i	0.0299476	−	0.111766i
$545$			102426.i			0.344840i
$546$	−301.861	−	18825.5i	−0.00101256	−	0.0631481i
$547$	−557281.			−1.86251			−0.931256	−	0.364365i	$-0.881286\pi$
$547$	−557281.			−1.86251			−0.931256	+	0.364365i	$0.881286\pi$
$548$	−57051.9	−	15287.0i	−0.189981	−	0.0509052i
$549$	78600.6	+	136140.i	0.260784	+	0.451691i
$550$	103807.	+	59933.1i	0.343164	+	0.198126i
$551$	203046.	−	203046.i	0.668793	−	0.668793i
$552$	−1395.19	−	5206.93i	−0.00457884	−	0.0170885i
$553$	14391.9	−	3856.29i	0.0470616	−	0.0126101i
$554$	145025.	+	145025.i	0.472522	+	0.472522i
$555$	14249.0	−	24680.1i	0.0462594	−	0.0801236i
$556$	196505.	−	113452.i	0.635660	−	0.366998i
$557$	−4275.64	+	15956.9i	−0.0137813	+	0.0514326i	−0.972474	−	0.233011i	$-0.925142\pi$
$557$	−4275.64	+	15956.9i	−0.0137813	+	0.0514326i	0.958693	+	0.284444i	$0.0918089\pi$
$558$			2350.87i			0.00755022i
$559$	252656.	+	421846.i	0.808549	+	1.34999i
$560$	−1641.69			−0.00523497
$561$	−96100.2	−	25750.0i	−0.305351	−	0.0818184i
$562$	−139923.	−	242353.i	−0.443012	−	0.767320i
$563$	315315.	+	182047.i	0.994781	+	0.574337i	0.906700	−	0.421776i	$-0.138593\pi$
$563$	315315.	+	182047.i	0.994781	+	0.574337i	0.0880812	+	0.996113i	$0.471926\pi$
$564$	82383.0	−	82383.0i	0.258988	−	0.258988i
$565$	−219.410	−	818.849i	−0.000687321	−	0.00256512i
$566$	−76717.4	+	20556.4i	−0.239475	+	0.0641673i
$567$	14449.2	+	14449.2i	0.0449447	+	0.0449447i
$568$	−34588.6	+	59909.2i	−0.107210	+	0.185694i
$569$	355519.	−	205259.i	1.09809	−	0.633983i	0.162372	−	0.986730i	$-0.448086\pi$
$569$	355519.	−	205259.i	1.09809	−	0.633983i	0.935719	+	0.352747i	$0.114752\pi$
$570$	−5265.41	+	19650.8i	−0.0162062	+	0.0604825i
$571$			60654.5i			0.186033i	0.995665	+	0.0930166i	$0.0296510\pi$
$571$			60654.5i			0.186033i	−0.995665	+	0.0930166i	$0.970349\pi$
$572$	−91622.1	+	26131.5i	−0.280032	+	0.0798678i
$573$	314222.			0.957035
$574$	−6557.46	−	1757.07i	−0.0199027	−	0.00533291i
$575$	−9598.03	−	16624.3i	−0.0290299	−	0.0502813i
$576$	11217.1	+	6476.19i	0.0338092	+	0.0195198i
$577$	−387868.	+	387868.i	−1.16502	+	1.16502i	−0.181656	+	0.983362i	$0.558146\pi$
$577$	−387868.	+	387868.i	−1.16502	+	1.16502i	−0.983362	+	0.181656i	$0.941854\pi$
$578$	−34946.7	−	130423.i	−0.104604	−	0.390389i
$579$	−98183.4	+	26308.2i	−0.292874	+	0.0784754i
$580$	−39818.6	−	39818.6i	−0.118367	−	0.118367i
$581$	27868.7	−	48270.1i	0.0825592	−	0.142997i
$582$	−4466.01	+	2578.45i	−0.0131848	+	0.00761226i
$583$	63007.7	−	235148.i	0.185377	−	0.691837i
$584$		−	152355.i		−	0.446716i
$585$	5055.75	−	20155.5i	0.0147732	−	0.0588955i
$586$	−456065.			−1.32810
$587$	220593.	+	59107.7i	0.640199	+	0.171541i	0.564294	−	0.825574i	$-0.309149\pi$
$587$	220593.	+	59107.7i	0.640199	+	0.171541i	0.0759056	+	0.997115i	$0.475815\pi$
$588$	−70847.0	−	122711.i	−0.204912	−	0.354918i
$589$	5641.70	+	3257.24i	0.0162622	+	0.00938899i
$590$	−62484.6	+	62484.6i	−0.179502	+	0.179502i
$591$	−97717.8	−	364688.i	−0.279768	−	1.04411i
$592$	−48565.2	+	13013.0i	−0.138574	+	0.0371308i
$593$	178959.	+	178959.i	0.508914	+	0.508914i	0.914193	−	0.405279i	$-0.132826\pi$
$593$	178959.	+	178959.i	0.508914	+	0.508914i	−0.405279	+	0.914193i	$0.632826\pi$
$594$	79064.4	−	136944.i	0.224083	−	0.388122i
$595$	4202.22	−	2426.16i	0.0118699	−	0.00685306i
$596$	24723.1	−	92267.8i	0.0696001	−	0.259751i
$597$		−	199991.i		−	0.561127i
$598$	14799.5	+	3712.26i	0.0413852	+	0.0103809i
$599$	−423552.			−1.18046			−0.590232	−	0.807233i	$-0.700964\pi$
$599$	−423552.			−1.18046			−0.590232	+	0.807233i	$0.700964\pi$
$600$	−98098.3	−	26285.4i	−0.272495	−	0.0730149i
$601$	−191347.	−	331423.i	−0.529753	−	0.917559i	−0.999398	−	0.0347033i	$-0.988951\pi$
$601$	−191347.	−	331423.i	−0.529753	−	0.917559i	0.469645	−	0.882855i	$-0.344382\pi$
$602$	−37613.2	−	21716.0i	−0.103788	−	0.0599221i
$603$	−51532.9	+	51532.9i	−0.141726	+	0.141726i
$604$	54673.2	+	204043.i	0.149865	+	0.559304i
$605$	−45422.4	+	12170.9i	−0.124096	+	0.0332515i
$606$	−90471.8	−	90471.8i	−0.246359	−	0.246359i
$607$	−181211.	+	313867.i	−0.491821	+	0.851860i	−0.999956	−	0.00941830i	$-0.997002\pi$
$607$	−181211.	+	313867.i	−0.491821	+	0.851860i	0.508134	+	0.861278i	$0.330335\pi$
$608$	31083.6	−	17946.1i	0.0840862	−	0.0485472i
$609$	−14763.8	+	55099.4i	−0.0398075	+	0.148564i
$610$		−	85427.7i		−	0.229583i
$611$	90447.0	+	317125.i	0.242277	+	0.849470i
$612$	−38283.2			−0.102213
$613$	−679467.	−	182063.i	−1.80820	−	0.484507i	−0.812995	−	0.582271i	$-0.802164\pi$
$613$	−679467.	−	182063.i	−1.80820	−	0.484507i	−0.995210	+	0.0977638i	$0.968831\pi$
$614$	−129754.	−	224740.i	−0.344178	−	0.596134i
$615$	14287.6	+	8248.95i	0.0377754	+	0.0218096i
$616$	5950.57	−	5950.57i	0.0156818	−	0.0156818i
$617$	−83717.8	−	312439.i	−0.219911	−	0.820720i	−0.984380	−	0.176059i	$-0.943665\pi$
$617$	−83717.8	−	312439.i	−0.219911	−	0.820720i	0.764469	−	0.644661i	$-0.223001\pi$
$618$	−71770.3	+	19230.8i	−0.187918	+	0.0503524i
$619$	−213459.	−	213459.i	−0.557100	−	0.557100i	0.371380	−	0.928481i	$-0.378885\pi$
$619$	−213459.	−	213459.i	−0.557100	−	0.557100i	−0.928481	+	0.371380i	$0.878885\pi$
$620$	638.765	−	1106.37i	0.00166172	−	0.00287818i
$621$	−21930.9	+	12661.8i	−0.0568688	+	0.0328332i
$622$	−77111.9	+	287785.i	−0.199315	+	0.743855i
$623$		−	19978.5i		−	0.0514739i
$624$	69253.1	−	41477.7i	0.177857	−	0.106524i
$625$	−346888.			−0.888033
$626$	264070.	+	70757.4i	0.673861	+	0.180561i
$627$	−52142.1	−	90312.8i	−0.132634	−	0.229728i
$628$	−152120.	−	87826.7i	−0.385716	−	0.222693i
$629$	105081.	−	105081.i	0.265597	−	0.265597i
$630$	475.041	+	1772.88i	0.00119688	+	0.00446681i
$631$	503606.	−	134941.i	1.26483	−	0.338910i	0.436782	−	0.899568i	$-0.356118\pi$
$631$	503606.	−	134941.i	1.26483	−	0.338910i	0.828048	+	0.560657i	$0.189452\pi$
$632$	45171.1	+	45171.1i	0.113090	+	0.113090i
$633$	209155.	−	362267.i	0.521989	−	0.904111i
$634$	310527.	−	179283.i	0.772540	−	0.446026i
$635$	20979.0	−	78294.7i	0.0520280	−	0.194171i
$636$			206262.i			0.509923i
$637$	401010.	−	6430.08i	0.988273	−	0.0158467i
$638$	288658.			0.709158
$639$	74705.3	+	20017.2i	0.182957	+	0.0490233i
$640$	−3519.35	−	6095.69i	−0.00859217	−	0.0148821i
$641$	−311385.	−	179778.i	−0.757847	−	0.437543i	0.0706749	−	0.997499i	$-0.477485\pi$
$641$	−311385.	−	179778.i	−0.757847	−	0.437543i	−0.828522	+	0.559956i	$0.810818\pi$
$642$	−225474.	+	225474.i	−0.547049	+	0.547049i
$643$	167611.	+	625531.i	0.405396	+	1.51296i	0.803324	+	0.595542i	$0.203063\pi$
$643$	167611.	+	625531.i	0.405396	+	1.51296i	−0.397928	+	0.917417i	$0.630271\pi$
$644$	−1301.76	+	348.807i	−0.00313878	+	0.000841033i
$645$	74633.1	+	74633.1i	0.179396	+	0.179396i
$646$	−53043.2	+	91873.4i	−0.127105	+	0.220153i
$647$	−222011.	+	128178.i	−0.530355	+	0.306201i	−0.741161	−	0.671327i	$-0.765725\pi$
$647$	−222011.	+	128178.i	−0.530355	+	0.306201i	0.210806	+	0.977528i	$0.432391\pi$
$648$	−22675.5	+	84626.3i	−0.0540017	+	0.201537i
$649$		−	452971.i		−	1.07543i
$650$	199980.	−	206498.i	0.473326	−	0.488752i
$651$	−1294.11			−0.00305359
$652$	284129.	+	76132.2i	0.668376	+	0.179091i
$653$	310662.	+	538082.i	0.728554	+	1.26189i	0.957494	+	0.288452i	$0.0931407\pi$
$653$	310662.	+	538082.i	0.728554	+	1.26189i	−0.228940	+	0.973441i	$0.573526\pi$
$654$	385252.	+	222425.i	0.900719	+	0.520031i
$655$	19470.2	−	19470.2i	0.0453825	−	0.0453825i
$656$	−7533.39	−	28115.0i	−0.0175058	−	0.0653326i
$657$	−164530.	+	44085.7i	−0.381167	+	0.102133i
$658$	−20596.3	−	20596.3i	−0.0475704	−	0.0475704i
$659$	223840.	−	387701.i	0.515426	−	0.892743i	−0.484414	−	0.874839i	$-0.660967\pi$
$659$	223840.	−	387701.i	0.515426	−	0.892743i	0.999840	−	0.0179045i	$-0.00569949\pi$
$660$	−17710.9	+	10225.4i	−0.0406586	+	0.0234743i
$661$	−94354.4	+	352135.i	−0.215953	+	0.805947i	0.769876	+	0.638194i	$0.220318\pi$
$661$	−94354.4	+	352135.i	−0.215953	+	0.805947i	−0.985829	+	0.167754i	$0.946349\pi$
$662$			507076.i			1.15706i
$663$	−115969.	+	208516.i	−0.263825	+	0.474364i
$664$	238973.			0.542018
$665$	4912.81	+	1316.38i	0.0111093	+	0.00297673i
$666$	28105.8	+	48680.7i	0.0633647	+	0.109751i
$667$	−40034.1	−	23113.7i	−0.0899867	−	0.0519539i
$668$	−263625.	+	263625.i	−0.590790	+	0.590790i
$669$	−114190.	−	426161.i	−0.255137	−	0.952185i
$670$	38254.8	−	10250.4i	0.0852191	−	0.0228344i
$671$	309647.	+	309647.i	0.687735	+	0.687735i
$672$	−3565.04	+	6174.83i	−0.00789452	+	0.0136737i
$673$	193480.	−	111706.i	0.427174	−	0.246629i	−0.270968	−	0.962588i	$-0.587344\pi$
$673$	193480.	−	111706.i	0.427174	−	0.246629i	0.698142	+	0.715959i	$0.254010\pi$
$674$	88327.9	−	329644.i	0.194437	−	0.725647i
$675$			477097.i			1.04713i
$676$	7325.59	+	228371.i	0.0160306	+	0.499743i
$677$	−220400.			−0.480878			−0.240439	−	0.970664i	$-0.577291\pi$
$677$	−220400.			−0.480878			−0.240439	+	0.970664i	$0.577291\pi$
$678$	−3556.38	−	952.929i	−0.00773657	−	0.00207301i
$679$	644.630	+	1116.53i	0.00139821	+	0.00242176i
$680$	18017.0	+	10402.1i	0.0389640	+	0.0224959i
$681$	307186.	−	307186.i	0.662380	−	0.662380i
$682$	1694.92	+	6325.54i	0.00364402	+	0.0135997i
$683$	67797.2	−	18166.2i	0.145335	−	0.0389424i	−0.185418	−	0.982660i	$-0.559364\pi$
$683$	67797.2	−	18166.2i	0.145335	−	0.0389424i	0.330753	+	0.943717i	$0.392697\pi$
$684$	−28374.7	−	28374.7i	−0.0606483	−	0.0606483i
$685$	17942.6	−	31077.4i	0.0382387	−	0.0662314i
$686$	−61716.9	+	35632.3i	−0.131146	+	0.0757173i
$687$	−114311.	+	426613.i	−0.242200	+	0.903901i
$688$		−	186214.i		−	0.393401i
$689$	−510217.	−	283766.i	−1.07477	−	0.597753i
$690$	3275.11			0.00687903
$691$	24288.6	+	6508.12i	0.0508683	+	0.0136301i	0.284163	−	0.958776i	$-0.408284\pi$
$691$	24288.6	+	6508.12i	0.0508683	+	0.0136301i	−0.233295	+	0.972406i	$0.574951\pi$
$692$	76510.5	+	132520.i	0.159775	+	0.276738i
$693$	−8147.96	−	4704.23i	−0.0169661	−	0.00979539i
$694$	−154057.	+	154057.i	−0.319861	+	0.319861i
$695$	35680.2	+	133160.i	0.0738683	+	0.275680i
$696$	−236238.	+	63299.7i	−0.487675	+	0.130672i
$697$	60832.7	+	60832.7i	0.125219	+	0.125219i
$698$	−29031.9	+	50284.7i	−0.0595887	+	0.103211i
$699$	−66862.8	+	38603.2i	−0.136845	+	0.0790077i
$700$	−6571.51	+	24525.2i	−0.0134112	+	0.0500514i
$701$		−	812545.i		−	1.65353i	−0.562550	−	0.826763i	$-0.690180\pi$
$701$		−	812545.i		−	1.65353i	0.562550	−	0.826763i	$-0.309820\pi$
$702$	−272414.	−	263816.i	−0.552784	−	0.535336i
$703$	155768.			0.315186
$704$	34851.3	+	9338.38i	0.0703192	+	0.0188420i
$705$	35392.4	+	61301.5i	0.0712085	+	0.123337i
$706$	−198558.	−	114637.i	−0.398361	−	0.229994i
$707$	−22618.5	+	22618.5i	−0.0452507	+	0.0452507i
$708$	99331.8	+	370711.i	0.198163	+	0.739553i
$709$	369541.	−	99018.2i	0.735140	−	0.196980i	0.128223	−	0.991745i	$-0.459073\pi$
$709$	369541.	−	99018.2i	0.735140	−	0.196980i	0.606917	+	0.794765i	$0.292406\pi$
$710$	−29719.1	−	29719.1i	−0.0589548	−	0.0589548i
$711$	35710.0	−	61851.6i	0.0706400	−	0.122352i
$712$	74181.5	−	42828.7i	0.146331	−	0.0844841i
$713$	271.435	−	1013.01i	0.000533933	−	0.00199266i
$714$		−	21074.3i		−	0.0413387i
$715$	−928.058	−	57878.1i	−0.00181536	−	0.113214i
$716$	400209.			0.780658
$717$	−105358.	−	28230.6i	−0.204941	−	0.0549138i
$718$	−240899.	−	417249.i	−0.467290	−	0.809369i
$719$	−447406.	−	258310.i	−0.865453	−	0.499670i	0.000381321	−	1.00000i	$-0.499879\pi$
$719$	−447406.	−	258310.i	−0.865453	−	0.499670i	−0.865835	+	0.500330i	$0.833212\pi$
$720$	−5564.45	+	5564.45i	−0.0107339	+	0.0107339i
$721$	4807.82	+	17943.0i	0.00924863	+	0.0345164i
$722$	248634.	−	66621.4i	0.476966	−	0.127803i
$723$	−288095.	−	288095.i	−0.551137	−	0.551137i
$724$	44584.9	−	77223.3i	0.0850571	−	0.147323i
$725$	−754241.	+	435461.i	−1.43494	+	0.828464i
$726$	−52859.9	+	197276.i	−0.100289	+	0.374284i
$727$			165150.i			0.312470i	0.987720	+	0.156235i	$0.0499358\pi$
$727$			165150.i			0.312470i	−0.987720	+	0.156235i	$0.950064\pi$
$728$	−10369.7	−	17313.7i	−0.0195660	−	0.0326684i
$729$	577554.			1.08677
$730$	89410.5	+	23957.5i	0.167781	+	0.0449568i
$731$	275195.	+	476651.i	0.514998	+	0.892003i
$732$	−321317.	−	185512.i	−0.599668	−	0.346219i
$733$	509526.	−	509526.i	0.948328	−	0.948328i	−0.0504015	−	0.998729i	$-0.516050\pi$
$733$	509526.	−	509526.i	0.948328	−	0.948328i	0.998729	+	0.0504015i	$0.0160501\pi$
$734$	−103151.	−	384964.i	−0.191461	−	0.714541i
$735$	83154.0	−	22281.0i	0.153925	−	0.0412440i
$736$	−4085.79	−	4085.79i	−0.00754259	−	0.00754259i
$737$	−101507.	+	175815.i	−0.186879	+	0.323684i
$738$	−28181.9	+	16270.8i	−0.0517436	+	0.0298742i
$739$	21068.9	−	78630.1i	0.0385791	−	0.143979i	−0.943950	−	0.330089i	$-0.892921\pi$
$739$	21068.9	−	78630.1i	0.0385791	−	0.143979i	0.982529	+	0.186110i	$0.0595880\pi$
$740$		−	30547.0i		−	0.0557835i
$741$	−240501.	+	68593.2i	−0.438007	+	0.124924i
$742$	51566.7			0.0936616
$743$	−28973.2	−	7763.35i	−0.0524831	−	0.0140628i	0.232482	−	0.972601i	$-0.425315\pi$
$743$	−28973.2	−	7763.35i	−0.0524831	−	0.0140628i	−0.284965	+	0.958538i	$0.591982\pi$
$744$	−2774.25	−	4805.14i	−0.00501186	−	0.00868080i
$745$	50260.3	+	29017.8i	0.0905549	+	0.0522819i
$746$	−256314.	+	256314.i	−0.460568	+	0.460568i
$747$	−69149.8	−	258071.i	−0.123922	−	0.462485i
$748$	−103010.	+	27601.3i	−0.184109	+	0.0493318i
$749$	56369.9	+	56369.9i	0.100481	+	0.100481i
$750$	62914.8	−	108972.i	0.111849	−	0.193727i
$751$	−57910.7	+	33434.7i	−0.102678	+	0.0592814i	−0.550460	−	0.834862i	$-0.685548\pi$
$751$	−57910.7	+	33434.7i	−0.102678	+	0.0592814i	0.447781	+	0.894143i	$0.352214\pi$
$752$	32322.3	−	120628.i	0.0571566	−	0.213311i
$753$			50685.1i			0.0893903i
$754$	168425.	−	671452.i	0.296254	−	1.18106i
$755$	−128341.			−0.225150
$756$	32353.9	+	8669.21i	0.0566087	+	0.0151683i
$757$	237324.	+	411057.i	0.414142	+	0.717316i	0.995338	−	0.0964482i	$-0.0307482\pi$
$757$	237324.	+	411057.i	0.414142	+	0.717316i	−0.581196	+	0.813764i	$0.697415\pi$
$758$	−68124.4	−	39331.7i	−0.118567	−	0.0684548i
$759$	−11871.2	+	11871.2i	−0.0206068	+	0.0206068i
$760$	5643.97	+	21063.6i	0.00977142	+	0.0364674i
$761$	−633879.	+	169847.i	−1.09455	+	0.293285i	−0.760545	−	0.649286i	$-0.775068\pi$
$761$	−633879.	+	169847.i	−1.09455	+	0.293285i	−0.334008	+	0.942570i	$0.608401\pi$
$762$	−248930.	−	248930.i	−0.428714	−	0.428714i
$763$	55607.8	−	96315.4i	0.0955182	−	0.165442i
$764$	291690.	−	168407.i	0.499729	−	0.288518i
$765$	6019.94	−	22466.7i	0.0102865	−	0.0383899i
$766$			537256.i			0.915638i
$767$	−1.05366e6	−	264297.i	−1.79106	−	0.449265i
$768$	−30570.1			−0.0518292
$769$	−50603.5	−	13559.2i	−0.0855713	−	0.0229287i	0.215779	−	0.976442i	$-0.430771\pi$
$769$	−50603.5	−	13559.2i	−0.0855713	−	0.0229287i	−0.301351	+	0.953513i	$0.597437\pi$
$770$	2556.41	+	4427.84i	0.00431171	+	0.00746810i
$771$	−168911.	−	97520.8i	−0.284151	−	0.164055i
$772$	−77042.9	+	77042.9i	−0.129270	+	0.129270i
$773$	66956.9	+	249886.i	0.112056	+	0.418200i	0.999050	−	0.0435821i	$-0.0138770\pi$
$773$	66956.9	+	249886.i	0.112056	+	0.418200i	−0.886994	+	0.461782i	$0.847210\pi$
$774$	−201095.	+	53883.2i	−0.335675	+	0.0899438i
$775$	−13971.2	−	13971.2i	−0.0232611	−	0.0232611i
$776$	−2763.84	+	4787.11i	−0.00458975	+	0.00794968i
$777$	−26797.9	+	15471.8i	−0.0443874	+	0.0256271i
$778$	74210.1	−	276956.i	0.122604	−	0.457563i
$779$			90175.9i			0.148599i
$780$	13451.6	+	47163.8i	0.0221097	+	0.0775211i
$781$	215444.			0.353209
$782$	16496.5	+	4420.24i	0.0269761	+	0.00722823i
$783$	574466.	+	995004.i	0.937002	+	1.62293i
$784$	−131533.	−	75940.7i	−0.213995	−	0.123550i
$785$	75462.2	−	75462.2i	0.122459	−	0.122459i
$786$	−30951.8	−	115514.i	−0.0501004	−	0.186977i
$787$	1.06463e6	−	285266.i	1.71889	−	0.460575i	0.741313	−	0.671159i	$-0.234203\pi$
$787$	1.06463e6	−	285266.i	1.71889	−	0.460575i	0.977576	+	0.210585i	$0.0675367\pi$
$788$	−286164.	−	286164.i	−0.460854	−	0.460854i
$789$	−193685.	+	335472.i	−0.311130	+	0.538892i
$790$	−33611.9	+	19405.9i	−0.0538567	+	0.0310942i
$791$	−238.238	+	889.117i	−0.000380766	+	0.00142104i
$792$		−	40338.6i		−	0.0643088i
$793$	900945.	−	539602.i	1.43269	−	0.858080i
$794$	703464.			1.11584
$795$	−121046.	−	32434.1i	−0.191521	−	0.0513178i
$796$	−107185.	−	185649.i	−0.169164	−	0.293000i
$797$	582703.	+	336424.i	0.917341	+	0.529627i	0.882786	−	0.469776i	$-0.155665\pi$
$797$	582703.	+	336424.i	0.917341	+	0.529627i	0.0345553	+	0.999403i	$0.488999\pi$
$798$	15619.8	−	15619.8i	0.0245284	−	0.0245284i
$799$	95534.5	+	356540.i	0.149647	+	0.558489i
$800$	−105151.	+	28175.2i	−0.164299	+	0.0440238i
$801$	−67716.6	−	67716.6i	−0.105543	−	0.105543i
$802$	−337936.	+	585323.i	−0.525395	+	0.910012i
$803$	−410921.	+	237245.i	−0.637275	+	0.367931i
$804$	44518.8	−	166146.i	0.0688701	−	0.257027i
$805$		−	818.797i		−	0.00126353i
$806$	15702.9	−	251.791i	0.0241718	−	0.000387588i
$807$	−28707.1			−0.0440801
$808$	−132472.	−	35495.8i	−0.202909	−	0.0543694i
$809$	64317.5	+	111401.i	0.0982725	+	0.170213i	0.910970	−	0.412473i	$-0.135335\pi$
$809$	64317.5	+	111401.i	0.0982725	+	0.170213i	−0.812697	+	0.582686i	$0.802002\pi$
$810$	−46097.8	−	26614.6i	−0.0702603	−	0.0405648i
$811$	883275.	−	883275.i	1.34293	−	1.34293i	0.449807	−	0.893126i	$-0.351493\pi$
$811$	883275.	−	883275.i	1.34293	−	1.34293i	0.893126	−	0.449807i	$-0.148507\pi$
$812$	15825.3	+	59060.9i	0.0240016	+	0.0895752i
$813$	64830.5	−	17371.3i	0.0980840	−	0.0262815i
$814$	110723.	+	110723.i	0.167104	+	0.167104i
$815$	−89357.2	+	154771.i	−0.134529	+	0.233010i
$816$	78250.2	−	45177.8i	0.117518	−	0.0678492i
$817$	−149315.	+	557252.i	−0.223697	+	0.834849i
$818$			684853.i			1.02351i
$819$	−15696.7	+	16208.3i	−0.0234013	+	0.0241640i
$820$	17684.0			0.0262999
$821$	−280462.	−	75149.7i	−0.416091	−	0.111491i	0.0446989	−	0.999001i	$-0.485767\pi$
$821$	−280462.	−	75149.7i	−0.416091	−	0.111491i	−0.460790	+	0.887509i	$0.652434\pi$
$822$	−77927.1	−	134974.i	−0.115331	−	0.199759i
$823$	−314270.	−	181444.i	−0.463984	−	0.267881i	0.249734	−	0.968314i	$-0.419657\pi$
$823$	−314270.	−	181444.i	−0.463984	−	0.267881i	−0.713718	+	0.700433i	$0.752990\pi$
$824$	−56316.9	+	56316.9i	−0.0829439	+	0.0829439i
$825$	81862.4	+	305515.i	0.120275	+	0.448874i
$826$	92680.1	−	24833.6i	0.135840	−	0.0363981i
$827$	−471080.	−	471080.i	−0.688785	−	0.688785i	0.273178	−	0.961963i	$-0.411925\pi$
$827$	−471080.	−	471080.i	−0.688785	−	0.688785i	−0.961963	+	0.273178i	$0.911925\pi$
$828$	−3230.02	+	5594.57i	−0.00471135	+	0.00816029i
$829$	252126.	−	145565.i	0.366867	−	0.211811i	−0.305222	−	0.952281i	$-0.598731\pi$
$829$	252126.	−	145565.i	0.366867	−	0.211811i	0.672089	+	0.740471i	$0.265397\pi$
$830$	−37578.0	+	140243.i	−0.0545478	+	0.203575i
$831$			541188.i			0.783694i
$832$	42057.0	−	75619.5i	0.0607564	−	0.109241i
$833$	448914.			0.646953
$834$	578335.	+	154964.i	0.831471	+	0.222792i
$835$	−113255.	−	196164.i	−0.162437	−	0.281350i
$836$	−96806.0	−	55891.0i	−0.138513	−	0.0799704i
$837$	−18431.0	+	18431.0i	−0.0263086	+	0.0263086i
$838$	134828.	+	503184.i	0.191995	+	0.716537i
$839$	123372.	−	33057.5i	0.175264	−	0.0469619i	−0.170120	−	0.985423i	$-0.554415\pi$
$839$	123372.	−	33057.5i	0.175264	−	0.0469619i	0.345384	+	0.938462i	$0.387749\pi$
$840$	−3063.14	−	3063.14i	−0.00434119	−	0.00434119i
$841$	−695025.	+	1.20382e6i	−0.982672	+	1.70204i
$842$	−237449.	+	137091.i	−0.334923	+	0.193368i
$843$	191120.	−	713270.i	0.268937	−	1.00369i
$844$		−	448386.i		−	0.629458i
$845$	−135173.	−	31611.6i	−0.189311	−	0.0442725i
$846$	−139621.			−0.195079
$847$	49320.2	+	13215.3i	0.0687477	+	0.0184209i
$848$	110546.	+	191471.i	0.153727	+	0.266263i
$849$	−181498.	−	104788.i	−0.251801	−	0.145377i
$850$	227517.	−	227517.i	0.314903	−	0.314903i
$851$	−6490.28	−	24222.1i	−0.00896199	−	0.0334466i
$852$	−176319.	+	47244.5i	−0.242895	+	0.0650836i
$853$	−356068.	−	356068.i	−0.489368	−	0.489368i	0.418739	−	0.908107i	$-0.362472\pi$
$853$	−356068.	−	356068.i	−0.489368	−	0.489368i	−0.908107	+	0.418739i	$0.862472\pi$
$854$	−46379.2	+	80331.2i	−0.0635928	+	0.110146i
$855$	21113.7	−	12190.0i	0.0288823	−	0.0166752i
$856$	−88462.8	+	330148.i	−0.120729	+	0.450569i
$857$		−	386201.i		−	0.525838i	−0.964818	−	0.262919i	$-0.915315\pi$
$857$		−	386201.i		−	0.525838i	0.964818	−	0.262919i	$-0.0846852\pi$
$858$	−219711.	−	122196.i	−0.298453	−	0.165990i
$859$	−111552.			−0.151178			−0.0755891	−	0.997139i	$-0.524084\pi$
$859$	−111552.			−0.151178			−0.0755891	+	0.997139i	$0.524084\pi$
$860$	109281.	+	29281.7i	0.147756	+	0.0395912i
$861$	−8956.82	−	15513.7i	−0.0120822	−	0.0209270i
$862$	776238.	+	448161.i	1.04467	+	0.603142i
$863$	102726.	−	102726.i	0.137930	−	0.137930i	−0.634771	−	0.772701i	$-0.718905\pi$
$863$	102726.	−	102726.i	0.137930	−	0.137930i	0.772701	+	0.634771i	$0.218905\pi$
$864$	37169.1	+	138717.i	0.0497914	+	0.185824i
$865$	−89801.3	+	24062.2i	−0.120019	+	0.0321590i
$866$	52565.3	+	52565.3i	0.0700912	+	0.0700912i
$867$	178144.	−	308555.i	0.236992	−	0.410482i
$868$	−1201.31	+	693.579i	−0.00159447	+	0.000920569i
$869$	51492.3	−	192172.i	0.0681872	−	0.254478i
$870$		−	148591.i		−	0.196315i
$871$	349739.	+	338700.i	0.461008	+	0.446457i
$872$	476834.			0.627097
$873$	5969.41	+	1599.50i	0.00783255	+	0.00209872i
$874$	8950.70	+	15503.1i	0.0117175	+	0.0202953i
$875$	−27243.6	−	15729.1i	−0.0355835	−	0.0205441i
$876$	284272.	−	284272.i	0.370447	−	0.370447i
$877$	−116877.	−	436190.i	−0.151960	−	0.567122i	−0.999347	−	0.0361458i	$-0.988492\pi$
$877$	−116877.	−	436190.i	−0.151960	−	0.567122i	0.847387	−	0.530976i	$-0.178175\pi$
$878$	372152.	−	99717.7i	0.482760	−	0.129355i
$879$	−850950.	−	850950.i	−1.10135	−	1.10135i
$880$	−10960.6	+	18984.3i	−0.0141536	+	0.0245148i
$881$	−611025.	+	352776.i	−0.787240	+	0.454513i	−0.838990	−	0.544147i	$-0.816853\pi$
$881$	−611025.	+	352776.i	−0.787240	+	0.454513i	0.0517498	+	0.998660i	$0.483520\pi$
$882$	−43948.7	+	164019.i	−0.0564948	+	0.210842i
$883$		−	1.00938e6i		−	1.29459i	−0.762240	−	0.647294i	$-0.775900\pi$
$883$		−	1.00938e6i		−	1.29459i	0.762240	−	0.647294i	$-0.224100\pi$
$884$	4100.34	+	255717.i	0.00524705	+	0.327231i
$885$	−233174.			−0.297710
$886$	−70256.8	−	18825.3i	−0.0894996	−	0.0239813i
$887$	−453008.	−	784632.i	−0.575782	−	0.997284i	−0.995956	−	0.0898404i	$-0.971364\pi$
$887$	−453008.	−	784632.i	−0.575782	−	0.997284i	0.420174	−	0.907444i	$-0.361969\pi$
$888$	−114896.	−	66335.0i	−0.145706	−	0.0841235i
$889$	−62234.1	+	62234.1i	−0.0787454	+	0.0787454i
$890$	13469.4	+	50268.6i	0.0170047	+	0.0634624i
$891$	263558.	−	70620.1i	0.331987	−	0.0889555i
$892$	−334401.	−	334401.i	−0.420280	−	0.420280i
$893$	−193451.	+	335068.i	−0.242588	+	0.420175i
$894$	218288.	−	126028.i	0.273120	−	0.157686i
$895$	−62931.9	+	234865.i	−0.0785642	+	0.293205i
$896$			7642.72i			0.00951988i
$897$	20687.2	+	34540.2i	0.0257108	+	0.0429279i
$898$	−886140.			−1.09888
$899$	−45960.1	−	12315.0i	−0.0568671	−	0.0152375i
$900$	60853.5	+	105401.i	0.0751278	+	0.130125i
$901$	−565927.	−	326738.i	−0.697126	−	0.402486i
$902$	−64098.8	+	64098.8i	−0.0787837	+	0.0787837i
$903$	−29661.8	−	110699.i	−0.0363766	−	0.135759i
$904$	−3812.07	+	1021.44i	−0.00466471	+	0.00124990i
$905$	38308.1	+	38308.1i	0.0467728	+	0.0467728i
$906$	−278702.	+	482726.i	−0.339534	+	0.588091i
$907$	70608.3	−	40765.7i	0.0858305	−	0.0495542i	−0.456470	−	0.889739i	$-0.650887\pi$
$907$	70608.3	−	40765.7i	0.0858305	−	0.0495542i	0.542301	+	0.840184i	$0.317553\pi$
$908$	120522.	−	449794.i	0.146182	−	0.545559i
$909$			153330.i			0.185566i
$910$	11791.3	−	3362.98i	0.0142389	−	0.00406107i
$911$	65427.3			0.0788355			0.0394178	−	0.999223i	$-0.487450\pi$
$911$	65427.3			0.0788355			0.0394178	+	0.999223i	$0.487450\pi$
$912$	91482.2	+	24512.6i	0.109988	+	0.0294713i
$913$	−372126.	−	644542.i	−0.446425	−	0.773231i
$914$	39821.2	+	22990.8i	0.0476674	+	0.0275208i
$915$	159395.	−	159395.i	0.190385	−	0.190385i
$916$	122529.	+	457286.i	0.146032	+	0.545000i
$917$	−28879.2	+	7738.15i	−0.0343436	+	0.00920234i
$918$	−300143.	−	300143.i	−0.356158	−	0.356158i
$919$	−531453.	+	920503.i	−0.629265	+	1.08992i	0.358435	+	0.933555i	$0.383311\pi$
$919$	−531453.	+	920503.i	−0.629265	+	1.08992i	−0.987699	+	0.156364i	$0.950023\pi$
$920$	3040.25	−	1755.29i	0.00359198	−	0.00207383i
$921$	177230.	−	661433.i	0.208939	−	0.779770i
$922$		−	496035.i		−	0.583512i
$923$	125706.	−	501146.i	0.147554	−	0.588249i
$924$	22205.7			0.0260089
$925$	−456343.	−	122277.i	−0.533344	−	0.142909i
$926$	−359984.	−	623510.i	−0.419818	−	0.727146i
$927$	77113.3	+	44521.4i	0.0897367	+	0.0518095i
$928$	−185372.	+	185372.i	−0.215252	+	0.215252i
$929$	315932.	+	1.17908e6i	0.366069	+	1.36619i	0.865966	+	0.500103i	$0.166704\pi$
$929$	315932.	+	1.17908e6i	0.366069	+	1.36619i	−0.499897	+	0.866085i	$0.666629\pi$
$930$	3256.17	−	872.487i	0.00376479	−	0.00100877i
$931$	332725.	+	332725.i	0.383872	+	0.383872i
$932$	−41378.7	+	71670.0i	−0.0476371	+	0.0825099i
$933$	−680844.	+	393085.i	−0.782139	+	0.451568i
$934$	−192222.	+	717384.i	−0.220349	+	0.822352i
$935$		−	64792.0i		−	0.0741136i
$936$	−93832.1	−	23536.5i	−0.107103	−	0.0268653i
$937$	671101.			0.764379			0.382189	−	0.924084i	$-0.375170\pi$
$937$	671101.			0.764379			0.382189	+	0.924084i	$0.375170\pi$
$938$	−41537.6	−	11130.0i	−0.0472102	−	0.0126499i
$939$	360693.	+	624738.i	0.409078	+	0.708544i
$940$	65708.9	+	37937.0i	0.0743650	+	0.0429346i
$941$	751728.	−	751728.i	0.848948	−	0.848948i	−0.141054	−	0.990002i	$-0.545049\pi$
$941$	751728.	−	751728.i	0.848948	−	0.848948i	0.990002	+	0.141054i	$0.0450490\pi$
$942$	−119962.	−	447705.i	−0.135190	−	0.504534i
$943$	14022.4	−	3757.30i	0.0157689	−	0.00422525i
$944$	290891.	+	290891.i	0.326427	+	0.326427i
$945$	−10175.1	+	17623.9i	−0.0113940	+	0.0197350i
$946$	−502242.	+	289970.i	−0.561217	+	0.324019i
$947$	77130.5	−	287855.i	0.0860054	−	0.320977i	−0.909497	−	0.415710i	$-0.863533\pi$
$947$	77130.5	−	287855.i	0.0860054	−	0.320977i	0.995503	+	0.0947333i	$0.0301998\pi$
$948$			168565.i			0.187564i
$949$	312098.	+	1.09428e6i	0.346544	+	1.21505i
$950$	337262.			0.373697
$951$	913912.	+	244882.i	1.01052	+	0.270767i
$952$	−11294.7	−	19563.0i	−0.0124624	−	0.0215855i
$953$	1.40495e6	+	811149.i	1.54695	+	0.893130i	0.998373	+	0.0570281i	$0.0181625\pi$
$953$	1.40495e6	+	811149.i	1.54695	+	0.893130i	0.548574	+	0.836102i	$0.315171\pi$
$954$	174784.	−	174784.i	0.192046	−	0.192046i
$955$	52963.2	+	197661.i	0.0580721	+	0.216728i
$956$	−112933.	+	30260.3i	−0.123568	+	0.0331098i
$957$	538593.	+	538593.i	0.588081	+	0.588081i
$958$	546624.	−	946781.i	0.595604	−	1.03162i
$959$	−33744.3	+	19482.3i	−0.0366913	+	0.0211837i
$960$	4807.07	−	17940.2i	0.00521601	−	0.0194664i
$961$			922442.i			0.998831i
$962$	322158.	−	192950.i	0.348111	−	0.208494i
$963$	382129.			0.412057
$964$	−421840.	−	113032.i	−0.453935	−	0.121632i
$965$	−33098.3	−	57327.9i	−0.0355427	−	0.0615618i
$966$	−3079.72	−	1778.08i	−0.00330033	−	0.00190544i
$967$	−1.08767e6	+	1.08767e6i	−1.16317	+	1.16317i	−0.179397	+	0.983777i	$0.557415\pi$
$967$	−1.08767e6	+	1.08767e6i	−1.16317	+	1.16317i	−0.983777	+	0.179397i	$0.942585\pi$
$968$	56660.4	+	211460.i	0.0604685	+	0.225672i
$969$	−270393.	+	72451.5i	−0.287970	+	0.0771614i
$970$	−2374.74	−	2374.74i	−0.00252390	−	0.00252390i
$971$	439185.	−	760691.i	0.465810	−	0.806807i	−0.533428	−	0.845846i	$-0.679096\pi$
$971$	439185.	−	760691.i	0.465810	−	0.806807i	0.999238	+	0.0390389i	$0.0124296\pi$
$972$	245002.	−	141452.i	0.259321	−	0.149719i
$973$	38742.0	−	144587.i	0.0409220	−	0.152723i
$974$		−	639761.i		−	0.674373i
$975$	758427.	−	12161.2i	0.797819	−	0.0127928i
$976$	−397700.			−0.417500
$977$	1.38543e6	+	371226.i	1.45143	+	0.388910i	0.896522	−	0.442999i	$-0.146086\pi$
$977$	1.38543e6	+	371226.i	1.45143	+	0.388910i	0.554911	+	0.831910i	$0.312752\pi$
$978$	388091.	+	672194.i	0.405748	+	0.702776i
$979$	−231029.	−	133385.i	−0.241047	−	0.139168i
$980$	65249.5	−	65249.5i	0.0679399	−	0.0679399i
$981$	−137978.	−	514940.i	−0.143374	−	0.535079i
$982$	7699.17	−	2062.99i	0.00798401	−	0.00213931i
$983$	470585.	+	470585.i	0.487002	+	0.487002i	0.907359	−	0.420357i	$-0.138095\pi$
$983$	470585.	+	470585.i	0.487002	+	0.487002i	−0.420357	+	0.907359i	$0.638095\pi$
$984$	38402.2	−	66514.5i	0.0396612	−	0.0686952i
$985$	212936.	−	122939.i	0.219471	−	0.126711i
$986$	200546.	−	748446.i	0.206281	−	0.769851i
$987$		−	76859.1i		−	0.0788971i
$988$	−186493.	+	192571.i	−0.191050	+	0.197277i
$989$	92874.8			0.0949523
$990$	23672.9	+	6343.14i	0.0241536	+	0.00647193i
$991$	−337605.	−	584749.i	−0.343765	−	0.595418i	0.641364	−	0.767237i	$-0.278369\pi$
$991$	−337605.	−	584749.i	−0.343765	−	0.595418i	−0.985129	+	0.171819i	$0.945036\pi$
$992$	−5150.61	−	2973.71i	−0.00523402	−	0.00302186i
$993$	−946128.	+	946128.i	−0.959514	+	0.959514i
$994$	11811.4	+	44080.8i	0.0119544	+	0.0446146i
$995$	125804.	−	33709.1i	0.127072	−	0.0340487i
$996$	445889.	+	445889.i	0.449477	+	0.449477i
$997$	−259558.	+	449568.i	−0.261123	+	0.452278i	−0.966541	−	0.256514i	$-0.917426\pi$
$997$	−259558.	+	449568.i	−0.261123	+	0.452278i	0.705418	+	0.708792i	$0.250759\pi$
$998$	−473618.	+	273443.i	−0.475518	+	0.274540i
$999$	−161309.	+	602012.i	−0.161632	+	0.603218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.b.15.2	yes	8
3.2	odd	2		234.5.bb.a.145.2		8
13.2	odd	12		338.5.d.g.99.2		8
13.3	even	3		338.5.d.f.239.2		8
13.7	odd	12	inner	26.5.f.b.7.2	✓	8
13.10	even	6		338.5.d.g.239.2		8
13.11	odd	12		338.5.d.f.99.2		8
39.20	even	12		234.5.bb.a.163.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.b.7.2	✓	8	13.7	odd	12	inner
26.5.f.b.15.2	yes	8	1.1	even	1	trivial
234.5.bb.a.145.2		8	3.2	odd	2
234.5.bb.a.163.2		8	39.20	even	12
338.5.d.f.99.2		8	13.11	odd	12
338.5.d.f.239.2		8	13.3	even	3
338.5.d.g.99.2		8	13.2	odd	12
338.5.d.g.239.2		8	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73205 + 0.732051i) q^{2} +(3.73170 + 6.46350i) q^{3} +(6.92820 + 4.00000i) q^{4} +(-3.43687 + 3.43687i) q^{5} +(5.46359 + 20.3904i) q^{6} +(5.09773 - 1.36593i) q^{7} +(16.0000 + 16.0000i) q^{8} +(12.6488 - 21.9084i) q^{9} +(-11.9057 + 6.87373i) q^{10} +(18.2390 - 68.0690i) q^{11} +59.7072i q^{12} +(-147.694 - 82.1426i) q^{13} +14.9272 q^{14} +(-35.0395 - 9.38881i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-163.821 - 94.5819i) q^{17} +(50.5953 - 50.5953i) q^{18} +(-51.3183 - 191.523i) q^{19} +(-37.5588 + 10.0638i) q^{20} +(27.8519 + 27.8519i) q^{21} +(99.6599 - 172.616i) q^{22} +(-27.6437 + 15.9601i) q^{23} +(-43.7087 + 163.123i) q^{24} +601.376i q^{25} +(-343.376 - 332.538i) q^{26} +793.342 q^{27} +(40.7818 + 10.9275i) q^{28} +(724.108 + 1254.19i) q^{29} +(-88.8567 - 51.3014i) q^{30} +(-23.2321 + 23.2321i) q^{31} +(46.8513 + 174.851i) q^{32} +(508.026 - 136.125i) q^{33} +(-378.328 - 378.328i) q^{34} +(-12.8257 + 22.2147i) q^{35} +(175.267 - 101.191i) q^{36} +(-203.328 + 758.831i) q^{37} -560.817i q^{38} +(-20.2222 - 1261.15i) q^{39} -109.980 q^{40} +(-439.297 - 117.709i) q^{41} +(55.7038 + 96.4818i) q^{42} +(-2519.78 - 1454.80i) q^{43} +(398.640 - 398.640i) q^{44} +(31.8239 + 118.769i) q^{45} +(-87.2077 + 23.3672i) q^{46} +(-1379.78 - 1379.78i) q^{47} +(-238.829 + 413.664i) q^{48} +(-2055.21 + 1186.57i) q^{49} +(-440.238 + 1642.99i) q^{50} -1411.81i q^{51} +(-694.685 - 1159.88i) q^{52} +3454.55 q^{53} +(2167.45 + 580.767i) q^{54} +(171.259 + 296.629i) q^{55} +(103.419 + 59.7087i) q^{56} +(1046.40 - 1046.40i) q^{57} +(1060.17 + 3956.60i) q^{58} +(6208.82 - 1663.65i) q^{59} +(-205.206 - 205.206i) q^{60} +(-3107.03 + 5381.54i) q^{61} +(-80.4783 + 46.4642i) q^{62} +(34.5548 - 128.960i) q^{63} +512.000i q^{64} +(789.919 - 225.292i) q^{65} +1487.60 q^{66} +(-2782.68 - 745.618i) q^{67} +(-756.655 - 1310.57i) q^{68} +(-206.316 - 119.117i) q^{69} +(-51.3027 + 51.3027i) q^{70} +(791.269 + 2953.06i) q^{71} +(552.915 - 148.153i) q^{72} +(-4761.10 - 4761.10i) q^{73} +(-1111.01 + 1924.32i) q^{74} +(-3886.99 + 2244.15i) q^{75} +(410.547 - 1532.18i) q^{76} -371.910i q^{77} +(867.980 - 3460.34i) q^{78} +2823.19 q^{79} +(-300.470 - 80.5107i) q^{80} +(1935.96 + 3353.18i) q^{81} +(-1114.01 - 643.175i) q^{82} +(7467.92 - 7467.92i) q^{83} +(81.5560 + 304.371i) q^{84} +(888.095 - 237.964i) q^{85} +(-5819.18 - 5819.18i) q^{86} +(-5404.31 + 9360.54i) q^{87} +(1380.93 - 797.279i) q^{88} +(979.775 - 3656.57i) q^{89} +347.778i q^{90} +(-865.106 - 217.000i) q^{91} -255.362 q^{92} +(-236.856 - 63.4653i) q^{93} +(-2759.57 - 4779.71i) q^{94} +(834.612 + 481.863i) q^{95} +(-955.315 + 955.315i) q^{96} +(63.2272 + 235.967i) q^{97} +(-6483.56 + 1737.26i) q^{98} +(-1260.58 - 1260.58i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 18 q^{5} - 36 q^{6} + 4 q^{7} + 128 q^{8} - 198 q^{9} + 348 q^{10} + 144 q^{11} - 318 q^{13} - 40 q^{14} - 924 q^{15} + 256 q^{16} - 390 q^{17} - 792 q^{18} + 2278 q^{19} + 624 q^{20} - 678 q^{21}+ \cdots - 55296 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 18 * q^5 - 36 * q^6 + 4 * q^7 + 128 * q^8 - 198 * q^9 + 348 * q^10 + 144 * q^11 - 318 * q^13 - 40 * q^14 - 924 * q^15 + 256 * q^16 - 390 * q^17 - 792 * q^18 + 2278 * q^19 + 624 * q^20 - 678 * q^21 - 756 * q^22 + 744 * q^23 + 288 * q^24 + 424 * q^26 - 1404 * q^27 + 32 * q^28 - 732 * q^29 - 2496 * q^30 + 368 * q^31 - 512 * q^32 + 7746 * q^33 - 312 * q^34 - 342 * q^35 + 1248 * q^36 - 280 * q^37 + 2808 * q^39 - 576 * q^40 + 744 * q^41 - 1356 * q^42 - 13014 * q^43 - 3024 * q^44 + 5766 * q^45 + 1884 * q^46 - 10896 * q^47 - 1842 * q^49 + 1508 * q^50 + 2624 * q^52 - 4728 * q^53 + 6372 * q^54 + 6630 * q^55 + 288 * q^56 + 18990 * q^57 + 8064 * q^58 + 3576 * q^59 - 4800 * q^60 - 13170 * q^61 + 4704 * q^62 - 6396 * q^63 + 6792 * q^65 + 4824 * q^66 + 3490 * q^67 - 624 * q^68 - 45354 * q^69 - 1368 * q^70 + 22710 * q^71 - 672 * q^72 - 7586 * q^73 - 10592 * q^74 - 7128 * q^75 - 18224 * q^76 - 6396 * q^78 + 37824 * q^79 + 4992 * q^80 + 17088 * q^81 + 4368 * q^82 + 21864 * q^83 + 9456 * q^84 + 6198 * q^85 - 2592 * q^86 - 39708 * q^87 - 1440 * q^88 + 17238 * q^89 + 12160 * q^91 + 3168 * q^92 - 258 * q^93 - 21792 * q^94 - 8280 * q^95 - 19450 * q^97 - 20548 * q^98 - 55296 * q^99

Introduction

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