LMFDB - Embedded newform 350.3.p.e.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,3,Mod(93,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

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

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

chi := DirichletCharacter("350.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (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:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.3
Root			$0.303047 - 1.13099i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.e.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(1.13099 - 0.303047i) q^{3} +(1.73205 + 1.00000i) q^{4} +1.65588 q^{6} +(4.97940 + 4.91991i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.60693 + 3.81451i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(1.13099 - 0.303047i) q^{3} +(1.73205 + 1.00000i) q^{4} +1.65588 q^{6} +(4.97940 + 4.91991i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.60693 + 3.81451i) q^{9} +(-6.06635 + 10.5072i) q^{11} +(2.26198 + 0.606095i) q^{12} +(8.70195 + 8.70195i) q^{13} +(5.00118 + 8.54331i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.44959 + 5.40994i) q^{17} +(-10.4214 + 2.79242i) q^{18} +(26.9104 - 15.5367i) q^{19} +(7.12261 + 4.05537i) q^{21} +(-12.1327 + 12.1327i) q^{22} +(8.07902 - 30.1513i) q^{23} +(2.86807 + 1.65588i) q^{24} +(8.70195 + 15.0722i) q^{26} +(-13.7679 + 13.7679i) q^{27} +(3.70467 + 13.5009i) q^{28} -25.2388i q^{29} +(-13.4239 + 23.2509i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-3.67678 + 13.7219i) q^{33} +7.92070i q^{34} -15.2581 q^{36} +(55.5832 + 14.8935i) q^{37} +(42.4472 - 11.3737i) q^{38} +(12.4789 + 7.20470i) q^{39} -45.8087 q^{41} +(8.24530 + 8.14679i) q^{42} +(-18.2199 - 18.2199i) q^{43} +(-21.0144 + 12.1327i) q^{44} +(22.0723 - 38.2303i) q^{46} +(-5.40994 - 1.44959i) q^{47} +(3.31176 + 3.31176i) q^{48} +(0.588922 + 48.9965i) q^{49} +(3.27894 + 5.67928i) q^{51} +(6.37027 + 23.7742i) q^{52} +(32.0345 - 8.58361i) q^{53} +(-23.8466 + 13.7679i) q^{54} +(0.118982 + 19.7986i) q^{56} +(25.7270 - 25.7270i) q^{57} +(9.23806 - 34.4769i) q^{58} +(-51.0186 - 29.4556i) q^{59} +(-37.7986 - 65.4691i) q^{61} +(-26.8478 + 26.8478i) q^{62} +(-51.6657 - 13.5115i) q^{63} +8.00000i q^{64} +(-10.0452 + 17.3987i) q^{66} +(-14.5178 - 54.1813i) q^{67} +(-2.89918 + 10.8199i) q^{68} -36.5491i q^{69} +22.2886 q^{71} +(-20.8429 - 5.58484i) q^{72} +(-3.21840 + 0.862368i) q^{73} +(70.4767 + 40.6897i) q^{74} +62.1470 q^{76} +(-81.9014 + 22.4738i) q^{77} +(14.4094 + 14.4094i) q^{78} +(37.4851 - 21.6420i) q^{79} +(22.9317 - 39.7188i) q^{81} +(-62.5758 - 16.7671i) q^{82} +(35.1320 + 35.1320i) q^{83} +(8.28136 + 14.1467i) q^{84} +(-18.2199 - 31.5578i) q^{86} +(-7.64857 - 28.5448i) q^{87} +(-33.1471 + 8.88175i) q^{88} +(-11.8780 + 6.85780i) q^{89} +(0.517689 + 86.1433i) q^{91} +(44.1446 - 44.1446i) q^{92} +(-8.13615 + 30.3645i) q^{93} +(-6.85953 - 3.96035i) q^{94} +(3.31176 + 5.73614i) q^{96} +(58.3777 - 58.3777i) q^{97} +(-17.1295 + 67.1460i) q^{98} -92.5606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	1.13099	−	0.303047i	0.376996	−	0.101016i	−0.0653449	−	0.997863i	$-0.520815\pi$
$3$	1.13099	−	0.303047i	0.376996	−	0.101016i	0.442341	+	0.896847i	$0.354148\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.65588			0.275980
$7$	4.97940	+	4.91991i	0.711343	+	0.702845i
$7$	4.97940	+	4.91991i	0.711343	+	0.702845i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−6.60693	+	3.81451i	−0.734104	+	0.423835i
$10$		0			0
$11$	−6.06635	+	10.5072i	−0.551486	+	0.955202i	0.446682	+	0.894693i	$0.352606\pi$
$11$	−6.06635	+	10.5072i	−0.551486	+	0.955202i	−0.998168	+	0.0605088i	$0.980728\pi$
$12$	2.26198	+	0.606095i	0.188498	+	0.0505079i
$13$	8.70195	+	8.70195i	0.669380	+	0.669380i	0.957573	−	0.288192i	$-0.0930542\pi$
$13$	8.70195	+	8.70195i	0.669380	+	0.669380i	−0.288192	+	0.957573i	$0.593054\pi$
$14$	5.00118	+	8.54331i	0.357227	+	0.610237i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	1.44959	+	5.40994i	0.0852699	+	0.318232i	0.995365	−	0.0961674i	$-0.0306584\pi$
$17$	1.44959	+	5.40994i	0.0852699	+	0.318232i	−0.910095	+	0.414399i	$0.863992\pi$
$18$	−10.4214	+	2.79242i	−0.578969	+	0.155134i
$19$	26.9104	−	15.5367i	1.41634	−	0.817723i	0.420363	−	0.907356i	$-0.361903\pi$
$19$	26.9104	−	15.5367i	1.41634	−	0.817723i	0.995975	+	0.0896326i	$0.0285693\pi$
$20$		0			0
$21$	7.12261	+	4.05537i	0.339172	+	0.193113i
$22$	−12.1327	+	12.1327i	−0.551486	+	0.551486i
$23$	8.07902	−	30.1513i	0.351262	−	1.31093i	−0.533862	−	0.845571i	$-0.679260\pi$
$23$	8.07902	−	30.1513i	0.351262	−	1.31093i	0.885124	−	0.465355i	$-0.154073\pi$
$24$	2.86807	+	1.65588i	0.119503	+	0.0689951i
$25$		0			0
$26$	8.70195	+	15.0722i	0.334690	+	0.579700i
$27$	−13.7679	+	13.7679i	−0.509920	+	0.509920i
$28$	3.70467	+	13.5009i	0.132310	+	0.482177i
$29$		−	25.2388i		−	0.870305i	−0.900357	−	0.435153i	$-0.856694\pi$
$29$		−	25.2388i		−	0.870305i	0.900357	−	0.435153i	$-0.143306\pi$
$30$		0			0
$31$	−13.4239	+	23.2509i	−0.433029	+	0.750028i	−0.997132	−	0.0756762i	$-0.975888\pi$
$31$	−13.4239	+	23.2509i	−0.433029	+	0.750028i	0.564104	+	0.825704i	$0.309222\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−3.67678	+	13.7219i	−0.111418	+	0.415816i
$34$			7.92070i			0.232962i
$35$		0			0
$36$	−15.2581			−0.423835
$37$	55.5832	+	14.8935i	1.50225	+	0.402526i	0.913852	−	0.406047i	$-0.133093\pi$
$37$	55.5832	+	14.8935i	1.50225	+	0.402526i	0.588396	+	0.808573i	$0.299760\pi$
$38$	42.4472	−	11.3737i	1.11703	−	0.299307i
$39$	12.4789	+	7.20470i	0.319972	+	0.184736i
$40$		0			0
$41$	−45.8087			−1.11728			−0.558642	−	0.829409i	$-0.688678\pi$
$41$	−45.8087			−1.11728			−0.558642	+	0.829409i	$0.688678\pi$
$42$	8.24530	+	8.14679i	0.196317	+	0.193971i
$43$	−18.2199	−	18.2199i	−0.423719	−	0.423719i	0.462763	−	0.886482i	$-0.346858\pi$
$43$	−18.2199	−	18.2199i	−0.423719	−	0.423719i	−0.886482	+	0.462763i	$0.846858\pi$
$44$	−21.0144	+	12.1327i	−0.477601	+	0.275743i
$45$		0			0
$46$	22.0723	−	38.2303i	0.479832	−	0.831094i
$47$	−5.40994	−	1.44959i	−0.115105	−	0.0308423i	0.200807	−	0.979631i	$-0.435644\pi$
$47$	−5.40994	−	1.44959i	−0.115105	−	0.0308423i	−0.315912	+	0.948789i	$0.602310\pi$
$48$	3.31176	+	3.31176i	0.0689951	+	0.0689951i
$49$	0.588922	+	48.9965i	0.0120188	+	0.999928i
$50$		0			0
$51$	3.27894	+	5.67928i	0.0642929	+	0.111358i
$52$	6.37027	+	23.7742i	0.122505	+	0.457195i
$53$	32.0345	−	8.58361i	0.604424	−	0.161955i	0.0563871	−	0.998409i	$-0.482042\pi$
$53$	32.0345	−	8.58361i	0.604424	−	0.161955i	0.548037	+	0.836454i	$0.315375\pi$
$54$	−23.8466	+	13.7679i	−0.441604	+	0.254960i
$55$		0			0
$56$	0.118982	+	19.7986i	0.00212468	+	0.353547i
$57$	25.7270	−	25.7270i	0.451351	−	0.451351i
$58$	9.23806	−	34.4769i	0.159277	−	0.594429i
$59$	−51.0186	−	29.4556i	−0.864722	−	0.499248i	0.000868446	−	1.00000i	$-0.499724\pi$
$59$	−51.0186	−	29.4556i	−0.864722	−	0.499248i	−0.865591	+	0.500752i	$0.833057\pi$
$60$		0			0
$61$	−37.7986	−	65.4691i	−0.619649	−	1.07326i	−0.989550	−	0.144193i	$-0.953941\pi$
$61$	−37.7986	−	65.4691i	−0.619649	−	1.07326i	0.369900	−	0.929072i	$-0.379392\pi$
$62$	−26.8478	+	26.8478i	−0.433029	+	0.433029i
$63$	−51.6657	−	13.5115i	−0.820090	−	0.214469i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−10.0452	+	17.3987i	−0.152199	+	0.263617i
$67$	−14.5178	−	54.1813i	−0.216684	−	0.808676i	−0.985567	−	0.169286i	$-0.945854\pi$
$67$	−14.5178	−	54.1813i	−0.216684	−	0.808676i	0.768883	−	0.639390i	$-0.220813\pi$
$68$	−2.89918	+	10.8199i	−0.0426350	+	0.159116i
$69$		−	36.5491i		−	0.529697i
$70$		0			0
$71$	22.2886			0.313924			0.156962	−	0.987605i	$-0.449830\pi$
$71$	22.2886			0.313924			0.156962	+	0.987605i	$0.449830\pi$
$72$	−20.8429	−	5.58484i	−0.289485	−	0.0775672i
$73$	−3.21840	+	0.862368i	−0.0440877	+	0.0118133i	−0.280795	−	0.959768i	$-0.590598\pi$
$73$	−3.21840	+	0.862368i	−0.0440877	+	0.0118133i	0.236708	+	0.971581i	$0.423932\pi$
$74$	70.4767	+	40.6897i	0.952387	+	0.549861i
$75$		0			0
$76$	62.1470			0.817723
$77$	−81.9014	+	22.4738i	−1.06365	+	0.291867i
$78$	14.4094	+	14.4094i	0.184736	+	0.184736i
$79$	37.4851	−	21.6420i	0.474495	−	0.273950i	−0.243625	−	0.969870i	$-0.578337\pi$
$79$	37.4851	−	21.6420i	0.474495	−	0.273950i	0.718119	+	0.695920i	$0.245003\pi$
$80$		0			0
$81$	22.9317	−	39.7188i	0.283107	−	0.490356i
$82$	−62.5758	−	16.7671i	−0.763120	−	0.204477i
$83$	35.1320	+	35.1320i	0.423277	+	0.423277i	0.886331	−	0.463053i	$-0.153246\pi$
$83$	35.1320	+	35.1320i	0.423277	+	0.423277i	−0.463053	+	0.886331i	$0.653246\pi$
$84$	8.28136	+	14.1467i	0.0985876	+	0.168413i
$85$		0			0
$86$	−18.2199	−	31.5578i	−0.211860	−	0.366951i
$87$	−7.64857	−	28.5448i	−0.0879146	−	0.328102i
$88$	−33.1471	+	8.88175i	−0.376672	+	0.100929i
$89$	−11.8780	+	6.85780i	−0.133461	+	0.0770539i	−0.565244	−	0.824924i	$-0.691218\pi$
$89$	−11.8780	+	6.85780i	−0.133461	+	0.0770539i	0.431783	+	0.901978i	$0.357885\pi$
$90$		0			0
$91$	0.517689	+	86.1433i	0.00568889	+	0.946630i
$92$	44.1446	−	44.1446i	0.479832	−	0.479832i
$93$	−8.13615	+	30.3645i	−0.0874855	+	0.326500i
$94$	−6.85953	−	3.96035i	−0.0729737	−	0.0421314i
$95$		0			0
$96$	3.31176	+	5.73614i	0.0344975	+	0.0597515i
$97$	58.3777	−	58.3777i	0.601832	−	0.601832i	−0.338967	−	0.940798i	$-0.610077\pi$
$97$	58.3777	−	58.3777i	0.601832	−	0.601832i	0.940798	+	0.338967i	$0.110077\pi$
$98$	−17.1295	+	67.1460i	−0.174790	+	0.685163i
$99$		−	92.5606i		−	0.934956i
$100$		0			0
$101$	4.64552	−	8.04628i	0.0459953	−	0.0796661i	−0.842111	−	0.539304i	$-0.818687\pi$
$101$	4.64552	−	8.04628i	0.0459953	−	0.0796661i	0.888106	+	0.459638i	$0.152021\pi$
$102$	2.40035	+	8.95822i	0.0235328	+	0.0878257i
$103$	−11.7833	+	43.9758i	−0.114401	+	0.426950i	−0.999241	−	0.0389443i	$-0.987601\pi$
$103$	−11.7833	+	43.9758i	−0.114401	+	0.426950i	0.884841	+	0.465894i	$0.154267\pi$
$104$			34.8078i			0.334690i
$105$		0			0
$106$	46.9017			0.442469
$107$	66.6460	+	17.8577i	0.622860	+	0.166895i	0.556428	−	0.830896i	$-0.312172\pi$
$107$	66.6460	+	17.8577i	0.622860	+	0.166895i	0.0664323	+	0.997791i	$0.478838\pi$
$108$	−37.6145	+	10.0788i	−0.348282	+	0.0933219i
$109$	−145.704	−	84.1220i	−1.33673	−	0.771761i	−0.350409	−	0.936597i	$-0.613957\pi$
$109$	−145.704	−	84.1220i	−1.33673	−	0.771761i	−0.986321	+	0.164836i	$0.947291\pi$
$110$		0			0
$111$	67.3774			0.607003
$112$	−7.08427	+	27.0890i	−0.0632524	+	0.241866i
$113$	−133.637	−	133.637i	−1.18263	−	1.18263i	−0.979060	−	0.203573i	$-0.934745\pi$
$113$	−133.637	−	133.637i	−1.18263	−	1.18263i	−0.203573	−	0.979060i	$-0.565255\pi$
$114$	44.5605	−	25.7270i	0.390881	−	0.225675i
$115$		0			0
$116$	25.2388	−	43.7150i	0.217576	−	0.376853i
$117$	−90.6869	−	24.2995i	−0.775101	−	0.207688i
$118$	−58.9112	−	58.9112i	−0.499248	−	0.499248i
$119$	−19.3983	+	34.0701i	−0.163011	+	0.286304i
$120$		0			0
$121$	−13.1011	−	22.6918i	−0.108274	−	0.187535i
$122$	−27.6705	−	103.268i	−0.226807	−	0.846457i
$123$	−51.8091	+	13.8822i	−0.421212	+	0.112863i
$124$	−46.5017	+	26.8478i	−0.375014	+	0.216514i
$125$		0			0
$126$	−65.6310	−	37.3680i	−0.520881	−	0.296572i
$127$	91.8825	−	91.8825i	0.723484	−	0.723484i	−0.245829	−	0.969313i	$-0.579060\pi$
$127$	91.8825	−	91.8825i	0.723484	−	0.723484i	0.969313	+	0.245829i	$0.0790601\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−26.1280	−	15.0850i	−0.202543	−	0.116938i
$130$		0			0
$131$	−52.4303	−	90.8119i	−0.400231	−	0.693221i	0.593522	−	0.804817i	$-0.297737\pi$
$131$	−52.4303	−	90.8119i	−0.400231	−	0.693221i	−0.993754	+	0.111597i	$0.964403\pi$
$132$	−20.0903	+	20.0903i	−0.152199	+	0.152199i
$133$	210.437	+	55.0332i	1.58224	+	0.413784i
$134$		−	79.3269i		−	0.591992i
$135$		0			0
$136$	−7.92070	+	13.7191i	−0.0582404	+	0.100875i
$137$	7.90696	+	29.5092i	0.0577150	+	0.215395i	0.988761	−	0.149508i	$-0.0477688\pi$
$137$	7.90696	+	29.5092i	0.0577150	+	0.215395i	−0.931046	+	0.364903i	$0.881102\pi$
$138$	13.3779	−	49.9270i	0.0969413	−	0.361790i
$139$			254.693i			1.83232i	0.400809	+	0.916162i	$0.368729\pi$
$139$			254.693i			1.83232i	−0.400809	+	0.916162i	$0.631271\pi$
$140$		0			0
$141$	−6.55787			−0.0465097
$142$	30.4468	+	8.15819i	0.214414	+	0.0574520i
$143$	−144.222	+	38.6442i	−1.00855	+	0.270239i
$144$	−26.4277	−	15.2581i	−0.183526	−	0.105959i
$145$		0			0
$146$	−4.71207			−0.0322744
$147$	15.5143	+	55.2359i	0.105540	+	0.375755i
$148$	81.3794	+	81.3794i	0.549861	+	0.549861i
$149$	231.769	−	133.812i	1.55550	−	0.898067i	0.557819	−	0.829962i	$-0.311638\pi$
$149$	231.769	−	133.812i	1.55550	−	0.898067i	0.997678	−	0.0681047i	$-0.0216952\pi$
$150$		0			0
$151$	−14.9718	+	25.9319i	−0.0991509	+	0.171734i	−0.911333	−	0.411669i	$-0.864946\pi$
$151$	−14.9718	+	25.9319i	−0.0991509	+	0.171734i	0.812183	+	0.583403i	$0.198279\pi$
$152$	84.8943	+	22.7474i	0.558515	+	0.149654i
$153$	−30.2136	−	30.2136i	−0.197475	−	0.197475i
$154$	−120.105	+	0.721788i	−0.779905	+	0.00468693i
$155$		0			0
$156$	14.4094	+	24.9578i	0.0923679	+	0.159986i
$157$	−59.7786	−	223.097i	−0.380755	−	1.42100i	−0.844751	−	0.535160i	$-0.820251\pi$
$157$	−59.7786	−	223.097i	−0.380755	−	1.42100i	0.463995	−	0.885838i	$-0.346415\pi$
$158$	59.1271	−	15.8431i	0.374222	−	0.100272i
$159$	33.6294	−	19.4159i	0.211506	−	0.122113i
$160$		0			0
$161$	188.570	−	110.387i	1.17125	−	0.685636i
$162$	45.8633	−	45.8633i	0.283107	−	0.283107i
$163$	−46.4442	+	173.332i	−0.284934	+	1.06339i	0.663954	+	0.747773i	$0.268877\pi$
$163$	−46.4442	+	173.332i	−0.284934	+	1.06339i	−0.948888	+	0.315614i	$0.897790\pi$
$164$	−79.3429	−	45.8087i	−0.483798	−	0.279321i
$165$		0			0
$166$	35.1320	+	60.8505i	0.211639	+	0.366569i
$167$	−76.3559	+	76.3559i	−0.457221	+	0.457221i	−0.897742	−	0.440521i	$-0.854794\pi$
$167$	−76.3559	+	76.3559i	−0.457221	+	0.457221i	0.440521	+	0.897742i	$0.354794\pi$
$168$	6.13449	+	22.3560i	0.0365148	+	0.133071i
$169$		−	17.5523i		−	0.103860i
$170$		0			0
$171$	−118.530	+	205.300i	−0.693159	+	1.20059i
$172$	−13.3379	−	49.7777i	−0.0775460	−	0.289405i
$173$	5.54111	−	20.6797i	0.0320296	−	0.119536i	−0.948060	−	0.318091i	$-0.896958\pi$
$173$	5.54111	−	20.6797i	0.0320296	−	0.119536i	0.980090	+	0.198555i	$0.0636249\pi$
$174$		−	41.7925i		−	0.240187i
$175$		0			0
$176$	−48.5308			−0.275743
$177$	−66.6279	−	17.8529i	−0.376429	−	0.100864i
$178$	−18.7358	+	5.02025i	−0.105258	+	0.0282037i
$179$	142.223	+	82.1127i	0.794544	+	0.458730i	0.841560	−	0.540164i	$-0.181638\pi$
$179$	142.223	+	82.1127i	0.794544	+	0.458730i	−0.0470161	+	0.998894i	$0.514971\pi$
$180$		0			0
$181$	266.876			1.47446			0.737228	−	0.675644i	$-0.236135\pi$
$181$	266.876			1.47446			0.737228	+	0.675644i	$0.236135\pi$
$182$	−30.8235	+	117.863i	−0.169360	+	0.647601i
$183$	−62.5900	−	62.5900i	−0.342022	−	0.342022i
$184$	76.4606	−	44.1446i	0.415547	−	0.239916i
$185$		0			0
$186$	−22.2284	+	38.5007i	−0.119507	+	0.206993i
$187$	−65.6371	−	17.5874i	−0.351001	−	0.0940503i
$188$	−7.92070	−	7.92070i	−0.0421314	−	0.0421314i
$189$	−136.292	+	0.819066i	−0.721123	+	0.00433368i
$190$		0			0
$191$	−96.3019	−	166.800i	−0.504198	−	0.873297i	−0.999988	−	0.00485444i	$-0.998455\pi$
$191$	−96.3019	−	166.800i	−0.504198	−	0.873297i	0.495790	−	0.868442i	$-0.334879\pi$
$192$	2.42438	+	9.04791i	0.0126270	+	0.0471245i
$193$	148.955	−	39.9124i	0.771787	−	0.206800i	0.148626	−	0.988893i	$-0.452515\pi$
$193$	148.955	−	39.9124i	0.771787	−	0.206800i	0.623161	+	0.782094i	$0.285848\pi$
$194$	101.113	−	58.3777i	0.521201	−	0.300916i
$195$		0			0
$196$	−47.9764	+	85.4533i	−0.244778	+	0.435986i
$197$	−137.941	+	137.941i	−0.700210	+	0.700210i	−0.964455	−	0.264246i	$-0.914877\pi$
$197$	−137.941	+	137.941i	−0.700210	+	0.700210i	0.264246	+	0.964455i	$0.414877\pi$
$198$	33.8795	−	126.440i	0.171109	−	0.638587i
$199$	−53.0439	−	30.6249i	−0.266552	−	0.153894i	0.360767	−	0.932656i	$-0.382515\pi$
$199$	−53.0439	−	30.6249i	−0.266552	−	0.153894i	−0.627320	+	0.778762i	$0.715848\pi$
$200$		0			0
$201$	−32.8390	−	56.8788i	−0.163378	−	0.282979i
$202$	9.29104	−	9.29104i	0.0459953	−	0.0459953i
$203$	124.173	−	125.674i	0.611689	−	0.619086i
$204$			13.1157i			0.0642929i
$205$		0			0
$206$	−32.1925	+	55.7591i	−0.156274	+	0.270675i
$207$	61.6351	+	230.025i	0.297754	+	1.11123i
$208$	−12.7405	+	47.5483i	−0.0612526	+	0.228598i
$209$			377.005i			1.80385i
$210$		0			0
$211$	−147.425			−0.698695			−0.349348	−	0.936993i	$-0.613597\pi$
$211$	−147.425			−0.698695			−0.349348	+	0.936993i	$0.613597\pi$
$212$	64.0690	+	17.1672i	0.302212	+	0.0809775i
$213$	25.2081	−	6.75450i	0.118348	−	0.0317113i
$214$	84.5037	+	48.7883i	0.394877	+	0.227983i
$215$		0			0
$216$	−55.0714			−0.254960
$217$	−181.235	+	49.7311i	−0.835185	+	0.229175i
$218$	−168.244	−	168.244i	−0.771761	−	0.771761i
$219$	−3.37864	+	1.95066i	−0.0154276	+	0.00890711i
$220$		0			0
$221$	−34.4628	+	59.6912i	−0.155940	+	0.270096i
$222$	92.0392	+	24.6618i	0.414591	+	0.111089i
$223$	168.214	+	168.214i	0.754322	+	0.754322i	0.975283	−	0.220961i	$-0.0709192\pi$
$223$	168.214	+	168.214i	0.754322	+	0.754322i	−0.220961	+	0.975283i	$0.570919\pi$
$224$	−19.5925	+	34.4112i	−0.0874667	+	0.153622i
$225$		0			0
$226$	−133.637	−	231.467i	−0.591316	−	1.02419i
$227$	91.5345	+	341.611i	0.403236	+	1.50490i	0.807287	+	0.590159i	$0.200935\pi$
$227$	91.5345	+	341.611i	0.403236	+	1.50490i	−0.404051	+	0.914736i	$0.632398\pi$
$228$	70.2875	−	18.8335i	0.308278	−	0.0826030i
$229$	−168.586	+	97.3332i	−0.736184	+	0.425036i	−0.820680	−	0.571388i	$-0.806405\pi$
$229$	−168.586	+	97.3332i	−0.736184	+	0.425036i	0.0844964	+	0.996424i	$0.473072\pi$
$230$		0			0
$231$	−85.8189	+	50.2376i	−0.371510	+	0.217479i
$232$	50.4777	−	50.4777i	0.217576	−	0.217576i
$233$	80.1559	−	299.146i	0.344017	−	1.28389i	−0.549740	−	0.835336i	$-0.685273\pi$
$233$	80.1559	−	299.146i	0.344017	−	1.28389i	0.893757	−	0.448552i	$-0.148060\pi$
$234$	−114.986	−	66.3874i	−0.491395	−	0.283707i
$235$		0			0
$236$	−58.9112	−	102.037i	−0.249624	−	0.432361i
$237$	35.8366	−	35.8366i	0.151209	−	0.151209i
$238$	−38.9692	+	39.4404i	−0.163736	+	0.165716i
$239$			17.4917i			0.0731870i	0.999330	+	0.0365935i	$0.0116507\pi$
$239$			17.4917i			0.0731870i	−0.999330	+	0.0365935i	$0.988349\pi$
$240$		0			0
$241$	−48.6715	+	84.3015i	−0.201956	+	0.349799i	−0.949159	−	0.314798i	$-0.898063\pi$
$241$	−48.6715	+	84.3015i	−0.201956	+	0.349799i	0.747202	+	0.664597i	$0.231397\pi$
$242$	−9.59067	−	35.7929i	−0.0396309	−	0.147904i
$243$	59.2532	−	221.136i	0.243840	−	0.910025i
$244$		−	151.194i		−	0.619649i
$245$		0			0
$246$	−75.8537			−0.308348
$247$	369.373	+	98.9732i	1.49544	+	0.400701i
$248$	−73.3495	+	19.6539i	−0.295764	+	0.0792498i
$249$	50.3806	+	29.0872i	0.202332	+	0.116816i
$250$		0			0
$251$	22.0051			0.0876697			0.0438348	−	0.999039i	$-0.486042\pi$
$251$	22.0051			0.0876697			0.0438348	+	0.999039i	$0.486042\pi$
$252$	−75.9760	−	75.0683i	−0.301492	−	0.297890i
$253$	267.796	+	267.796i	1.05848	+	1.05848i
$254$	159.145	−	91.8825i	0.626556	−	0.361742i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	255.042	+	68.3382i	0.992380	+	0.265908i	0.718250	−	0.695785i	$-0.244943\pi$
$257$	255.042	+	68.3382i	0.992380	+	0.265908i	0.274130	+	0.961693i	$0.411610\pi$
$258$	−30.1700	−	30.1700i	−0.116938	−	0.116938i
$259$	203.497	+	347.625i	0.785701	+	1.34218i
$260$		0			0
$261$	96.2739	+	166.751i	0.368866	+	0.638894i
$262$	−38.3816	−	143.242i	−0.146495	−	0.546726i
$263$	−250.567	+	67.1391i	−0.952724	+	0.255282i	−0.701518	−	0.712652i	$-0.747494\pi$
$263$	−250.567	+	67.1391i	−0.952724	+	0.255282i	−0.251207	+	0.967934i	$0.580827\pi$
$264$	−34.7974	+	20.0903i	−0.131808	+	0.0760996i
$265$		0			0
$266$	267.319	+	152.202i	1.00496	+	0.572189i
$267$	−11.3557	+	11.3557i	−0.0425307	+	0.0425307i
$268$	29.0357	−	108.363i	0.108342	−	0.404338i
$269$	−332.165	−	191.775i	−1.23481	−	0.712920i	−0.266784	−	0.963756i	$-0.585961\pi$
$269$	−332.165	−	191.775i	−1.23481	−	0.712920i	−0.968029	+	0.250837i	$0.919294\pi$
$270$		0			0
$271$	208.466	+	361.074i	0.769247	+	1.33237i	0.937972	+	0.346712i	$0.112702\pi$
$271$	208.466	+	361.074i	0.769247	+	1.33237i	−0.168725	+	0.985663i	$0.553965\pi$
$272$	−15.8414	+	15.8414i	−0.0582404	+	0.0582404i
$273$	26.6910	+	97.2702i	0.0977693	+	0.356301i
$274$			43.2044i			0.157680i
$275$		0			0
$276$	36.5491	−	63.3049i	0.132424	−	0.229366i
$277$	99.3094	+	370.628i	0.358518	+	1.33801i	0.876000	+	0.482312i	$0.160203\pi$
$277$	99.3094	+	370.628i	0.358518	+	1.33801i	−0.517482	+	0.855694i	$0.673130\pi$
$278$	−93.2241	+	347.917i	−0.335338	+	1.25150i
$279$		−	204.822i		−	0.734131i
$280$		0			0
$281$	41.8655			0.148988			0.0744938	−	0.997221i	$-0.476266\pi$
$281$	41.8655			0.148988			0.0744938	+	0.997221i	$0.476266\pi$
$282$	−8.95822	−	2.40035i	−0.0317667	−	0.00851187i
$283$	−87.6264	+	23.4794i	−0.309634	+	0.0829662i	−0.410290	−	0.911955i	$-0.634573\pi$
$283$	−87.6264	+	23.4794i	−0.309634	+	0.0829662i	0.100656	+	0.994921i	$0.467906\pi$
$284$	38.6050	+	22.2886i	0.135933	+	0.0784809i
$285$		0			0
$286$	−211.156			−0.738308
$287$	−228.100	−	225.375i	−0.794773	−	0.785277i
$288$	−30.5161	−	30.5161i	−0.105959	−	0.105959i
$289$	223.115	−	128.816i	0.772025	−	0.445729i
$290$		0			0
$291$	48.3333	−	83.7157i	0.166094	−	0.287683i
$292$	−6.43680	−	1.72474i	−0.0220438	−	0.00590663i
$293$	238.524	+	238.524i	0.814077	+	0.814077i	0.985242	−	0.171166i	$-0.0547533\pi$
$293$	238.524	+	238.524i	0.814077	+	0.814077i	−0.171166	+	0.985242i	$0.554753\pi$
$294$	0.975185	+	81.1323i	0.00331696	+	0.275960i
$295$		0			0
$296$	81.3794	+	140.953i	0.274931	+	0.476194i
$297$	−61.1413	−	228.182i	−0.205863	−	0.768291i
$298$	365.581	−	97.9572i	1.22678	−	0.328715i
$299$	332.678	−	192.072i	1.11264	−	0.642381i
$300$		0			0
$301$	−1.08392	−	180.365i	−0.00360108	−	0.599218i
$302$	−29.9436	+	29.9436i	−0.0991509	+	0.0991509i
$303$	2.81563	−	10.5081i	0.00929249	−	0.0346801i
$304$	107.642	+	62.1470i	0.354085	+	0.204431i
$305$		0			0
$306$	−30.2136	−	52.3315i	−0.0987373	−	0.171018i
$307$	−318.085	+	318.085i	−1.03611	+	1.03611i	−0.0367853	+	0.999323i	$0.511712\pi$
$307$	−318.085	+	318.085i	−1.03611	+	1.03611i	−0.999323	+	0.0367853i	$0.988288\pi$
$308$	−164.331	−	42.9756i	−0.533543	−	0.139531i
$309$			53.3070i			0.172515i
$310$		0			0
$311$	−139.353	+	241.366i	−0.448079	+	0.776096i	−0.998261	−	0.0589489i	$-0.981225\pi$
$311$	−139.353	+	241.366i	−0.448079	+	0.776096i	0.550182	+	0.835045i	$0.314558\pi$
$312$	10.5484	+	39.3672i	0.0338090	+	0.126177i
$313$	77.7362	−	290.116i	0.248359	−	0.926887i	−0.723307	−	0.690527i	$-0.757379\pi$
$313$	77.7362	−	290.116i	0.248359	−	0.926887i	0.971666	−	0.236360i	$-0.0759545\pi$
$314$		−	326.636i		−	1.04024i
$315$		0			0
$316$	86.5681			0.273950
$317$	−53.4088	−	14.3109i	−0.168482	−	0.0451446i	0.173592	−	0.984818i	$-0.444463\pi$
$317$	−53.4088	−	14.3109i	−0.168482	−	0.0451446i	−0.342074	+	0.939673i	$0.611129\pi$
$318$	53.0453	−	14.2134i	0.166809	−	0.0446964i
$319$	265.190	+	153.108i	0.831317	+	0.479961i
$320$		0			0
$321$	80.7876			0.251675
$322$	297.997	−	81.7705i	0.925456	−	0.253946i
$323$	123.062	+	123.062i	0.380997	+	0.380997i
$324$	79.4376	−	45.8633i	0.245178	−	0.141553i
$325$		0			0
$326$	−126.888	+	219.776i	−0.389227	+	0.674161i
$327$	−190.282	−	50.9859i	−0.581902	−	0.155920i
$328$	−91.6173	−	91.6173i	−0.279321	−	0.279321i
$329$	−19.8064	−	33.8345i	−0.0602019	−	0.102840i
$330$		0			0
$331$	102.565	+	177.647i	0.309863	+	0.536698i	0.978332	−	0.207041i	$-0.0663835\pi$
$331$	102.565	+	177.647i	0.309863	+	0.536698i	−0.668469	+	0.743740i	$0.733050\pi$
$332$	25.7184	+	95.9825i	0.0774651	+	0.289104i
$333$	−424.046	+	113.623i	−1.27341	+	0.341209i
$334$	−132.252	+	76.3559i	−0.395965	+	0.228611i
$335$		0			0
$336$	0.197021	+	32.7842i	0.000586371	+	0.0975720i
$337$	399.822	−	399.822i	1.18641	−	1.18641i	0.208363	−	0.978052i	$-0.433187\pi$
$337$	399.822	−	399.822i	1.18641	−	1.18641i	0.978052	−	0.208363i	$-0.0668134\pi$
$338$	6.42458	−	23.9769i	0.0190076	−	0.0709374i
$339$	−191.641	−	110.644i	−0.565312	−	0.326383i
$340$		0			0
$341$	−162.868	−	282.096i	−0.477619	−	0.827260i
$342$	−237.060	+	237.060i	−0.693159	+	0.693159i
$343$	−238.126	+	246.871i	−0.694244	+	0.719739i
$344$		−	72.8797i		−	0.211860i
$345$		0			0
$346$	15.1386	−	26.2208i	0.0437532	−	0.0757828i
$347$	−123.027	−	459.142i	−0.354544	−	1.32318i	−0.881058	−	0.473009i	$-0.843168\pi$
$347$	−123.027	−	459.142i	−0.354544	−	1.32318i	0.526514	−	0.850167i	$-0.323499\pi$
$348$	15.2971	−	57.0897i	0.0439573	−	0.164051i
$349$			282.718i			0.810080i	0.914299	+	0.405040i	$0.132742\pi$
$349$			282.718i			0.810080i	−0.914299	+	0.405040i	$0.867258\pi$
$350$		0			0
$351$	−239.614			−0.682662
$352$	−66.2943	−	17.7635i	−0.188336	−	0.0504645i
$353$	−269.078	+	72.0991i	−0.762259	+	0.204247i	−0.618949	−	0.785431i	$-0.712441\pi$
$353$	−269.078	+	72.0991i	−0.762259	+	0.204247i	−0.143310	+	0.989678i	$0.545775\pi$
$354$	−84.4808	−	48.7750i	−0.238646	−	0.137783i
$355$		0			0
$356$	−27.4312			−0.0770539
$357$	−11.6144	+	44.4115i	−0.0325334	+	0.124402i
$358$	164.225	+	164.225i	0.458730	+	0.458730i
$359$	−582.216	+	336.143i	−1.62177	+	0.936330i	−0.635326	+	0.772244i	$0.719134\pi$
$359$	−582.216	+	336.143i	−1.62177	+	0.936330i	−0.986446	+	0.164086i	$0.947533\pi$
$360$		0			0
$361$	302.281	−	523.565i	0.837343	−	1.45032i
$362$	364.560	+	97.6835i	1.00707	+	0.269844i
$363$	−21.6939	−	21.6939i	−0.0597627	−	0.0597627i
$364$	−85.2467	+	149.722i	−0.234194	+	0.411325i
$365$		0			0
$366$	−62.5900	−	108.409i	−0.171011	−	0.296200i
$367$	−29.8554	−	111.422i	−0.0813499	−	0.303602i	0.913248	−	0.407404i	$-0.133566\pi$
$367$	−29.8554	−	111.422i	−0.0813499	−	0.303602i	−0.994598	+	0.103802i	$0.966899\pi$
$368$	120.605	−	32.3161i	0.327732	−	0.0878154i
$369$	302.655	−	174.738i	0.820203	−	0.473544i
$370$		0			0
$371$	201.743	+	114.866i	0.543782	+	0.309611i
$372$	−44.4568	+	44.4568i	−0.119507	+	0.119507i
$373$	7.48386	−	27.9301i	0.0200640	−	0.0748797i	−0.955168	−	0.296064i	$-0.904326\pi$
$373$	7.48386	−	27.9301i	0.0200640	−	0.0748797i	0.975232	+	0.221185i	$0.0709924\pi$
$374$	−83.2245	−	48.0497i	−0.222525	−	0.128475i
$375$		0			0
$376$	−7.92070	−	13.7191i	−0.0210657	−	0.0364868i
$377$	219.627	−	219.627i	0.582565	−	0.582565i
$378$	−186.479	−	48.7676i	−0.493330	−	0.129015i
$379$		−	203.578i		−	0.537145i	−0.963259	−	0.268573i	$-0.913448\pi$
$379$		−	203.578i		−	0.537145i	0.963259	−	0.268573i	$-0.0865519\pi$
$380$		0			0
$381$	76.0733	−	131.763i	0.199667	−	0.345834i
$382$	−70.4978	−	263.102i	−0.184549	−	0.688748i
$383$	66.7003	−	248.929i	0.174152	−	0.649945i	−0.822542	−	0.568704i	$-0.807445\pi$
$383$	66.7003	−	248.929i	0.174152	−	0.649945i	0.996694	−	0.0812409i	$-0.0258883\pi$
$384$			13.2471i			0.0344975i
$385$		0			0
$386$	218.085			0.564988
$387$	189.878	+	50.8776i	0.490641	+	0.131467i
$388$	159.491	−	42.7354i	0.411059	−	0.110143i
$389$	−272.609	−	157.391i	−0.700793	−	0.404603i	0.106850	−	0.994275i	$-0.465924\pi$
$389$	−272.609	−	157.391i	−0.700793	−	0.404603i	−0.807643	+	0.589672i	$0.799257\pi$
$390$		0			0
$391$	174.828			0.447130
$392$	−96.8151	+	99.1708i	−0.246977	+	0.252987i
$393$	−86.8183	−	86.8183i	−0.220912	−	0.220912i
$394$	−238.921	+	137.941i	−0.606399	+	0.350105i
$395$		0			0
$396$	92.5606	−	160.320i	0.233739	−	0.404848i
$397$	−20.9376	−	5.61021i	−0.0527395	−	0.0141315i	0.232353	−	0.972632i	$-0.425358\pi$
$397$	−20.9376	−	5.61021i	−0.0527395	−	0.0141315i	−0.285092	+	0.958500i	$0.592024\pi$
$398$	−61.2499	−	61.2499i	−0.153894	−	0.153894i
$399$	254.680	−	1.53053i	0.638295	−	0.00383591i
$400$		0			0
$401$	−291.159	−	504.302i	−0.726082	−	1.25761i	−0.958527	−	0.285001i	$-0.908006\pi$
$401$	−291.159	−	504.302i	−0.726082	−	1.25761i	0.232445	−	0.972609i	$-0.425327\pi$
$402$	−24.0398	−	89.7178i	−0.0598005	−	0.223179i
$403$	−319.142	+	85.5138i	−0.791915	+	0.212193i
$404$	16.0926	−	9.29104i	0.0398331	−	0.0229976i
$405$		0			0
$406$	215.623	−	126.224i	0.531092	−	0.310897i
$407$	−493.676	+	493.676i	−1.21296	+	1.21296i
$408$	−4.80069	+	17.9164i	−0.0117664	+	0.0439128i
$409$	−320.292	−	184.921i	−0.783109	−	0.452128i	0.0544217	−	0.998518i	$-0.482668\pi$
$409$	−320.292	−	184.921i	−0.783109	−	0.452128i	−0.837531	+	0.546390i	$0.816002\pi$
$410$		0			0
$411$	17.8853	+	30.9783i	0.0435167	+	0.0753731i
$412$	−64.3851	+	64.3851i	−0.156274	+	0.156274i
$413$	−109.123	−	397.679i	−0.264221	−	0.962902i
$414$			336.780i			0.813479i
$415$		0			0
$416$	−34.8078	+	60.2889i	−0.0836726	+	0.144925i
$417$	77.1840	+	288.055i	0.185094	+	0.690779i
$418$	−137.993	+	514.998i	−0.330128	+	1.23205i
$419$			29.9924i			0.0715809i	0.999359	+	0.0357904i	$0.0113949\pi$
$419$			29.9924i			0.0715809i	−0.999359	+	0.0357904i	$0.988605\pi$
$420$		0			0
$421$	−59.1882			−0.140590			−0.0702948	−	0.997526i	$-0.522394\pi$
$421$	−59.1882			−0.140590			−0.0702948	+	0.997526i	$0.522394\pi$
$422$	−201.386	−	53.9612i	−0.477218	−	0.127870i
$423$	41.2726	−	11.0590i	0.0975711	−	0.0261441i
$424$	81.2362	+	46.9017i	0.191595	+	0.110617i
$425$		0			0
$426$	36.9073			0.0866368
$427$	133.888	−	511.963i	0.313555	−	1.19898i
$428$	97.5765	+	97.5765i	0.227983	+	0.227983i
$429$	−151.403	+	87.4124i	−0.352920	+	0.203758i
$430$		0			0
$431$	−337.935	+	585.320i	−0.784072	+	1.35805i	0.145481	+	0.989361i	$0.453527\pi$
$431$	−337.935	+	585.320i	−0.784072	+	1.35805i	−0.929552	+	0.368691i	$0.879806\pi$
$432$	−75.2289	−	20.1575i	−0.174141	−	0.0466610i
$433$	202.377	+	202.377i	0.467382	+	0.467382i	0.901065	−	0.433683i	$-0.142786\pi$
$433$	202.377	+	202.377i	0.467382	+	0.467382i	−0.433683	+	0.901065i	$0.642786\pi$
$434$	−265.775	+	1.59721i	−0.612384	+	0.00368020i
$435$		0			0
$436$	−168.244	−	291.407i	−0.385881	−	0.668365i
$437$	−251.043	−	936.906i	−0.574470	−	2.14395i
$438$	−5.32929	+	1.42798i	−0.0121673	+	0.00326023i
$439$	137.892	−	79.6122i	0.314106	−	0.181349i	−0.334657	−	0.942340i	$-0.608620\pi$
$439$	137.892	−	79.6122i	0.314106	−	0.181349i	0.648762	+	0.760991i	$0.275287\pi$
$440$		0			0
$441$	−190.789	−	321.470i	−0.432627	−	0.728957i
$442$	−68.9255	+	68.9255i	−0.155940	+	0.155940i
$443$	38.8006	−	144.806i	0.0875859	−	0.326875i	−0.908205	−	0.418525i	$-0.862547\pi$
$443$	38.8006	−	144.806i	0.0875859	−	0.326875i	0.995791	+	0.0916496i	$0.0292140\pi$
$444$	116.701	+	67.3774i	0.262840	+	0.151751i
$445$		0			0
$446$	168.214	+	291.355i	0.377161	+	0.653262i
$447$	221.577	−	221.577i	0.495698	−	0.495698i
$448$	−39.3593	+	39.8352i	−0.0878556	+	0.0889179i
$449$		−	634.911i		−	1.41406i	−0.707185	−	0.707028i	$-0.750035\pi$
$449$		−	634.911i		−	1.41406i	0.707185	−	0.707028i	$-0.249965\pi$
$450$		0			0
$451$	277.891	−	481.322i	0.616167	−	1.06723i
$452$	−97.8294	−	365.104i	−0.216437	−	0.807753i
$453$	−9.07433	+	33.8658i	−0.0200316	+	0.0747590i
$454$			500.154i			1.10166i
$455$		0			0
$456$	102.908			0.225675
$457$	−193.620	−	51.8803i	−0.423676	−	0.113524i	0.0406802	−	0.999172i	$-0.487048\pi$
$457$	−193.620	−	51.8803i	−0.423676	−	0.113524i	−0.464356	+	0.885649i	$0.653714\pi$
$458$	−265.919	+	71.2529i	−0.580610	+	0.155574i
$459$	−94.4410	−	54.5255i	−0.205754	−	0.118792i
$460$		0			0
$461$	−406.211			−0.881151			−0.440576	−	0.897715i	$-0.645226\pi$
$461$	−406.211			−0.881151			−0.440576	+	0.897715i	$0.645226\pi$
$462$	−135.619	+	37.2139i	−0.293548	+	0.0805497i
$463$	−288.227	−	288.227i	−0.622520	−	0.622520i	0.323655	−	0.946175i	$-0.395088\pi$
$463$	−288.227	−	288.227i	−0.622520	−	0.622520i	−0.946175	+	0.323655i	$0.895088\pi$
$464$	87.4299	−	50.4777i	0.188427	−	0.108788i
$465$		0			0
$466$	218.990	−	379.302i	0.469936	−	0.813952i
$467$	82.0814	+	21.9936i	0.175763	+	0.0470956i	0.345627	−	0.938372i	$-0.387666\pi$
$467$	82.0814	+	21.9936i	0.175763	+	0.0470956i	−0.169864	+	0.985468i	$0.554333\pi$
$468$	−132.775	−	132.775i	−0.283707	−	0.283707i
$469$	194.277	−	341.217i	0.414237	−	0.727542i
$470$		0			0
$471$	−135.218	−	234.204i	−0.287086	−	0.497248i
$472$	−43.1260	−	160.948i	−0.0913687	−	0.340993i
$473$	301.969	−	80.9123i	0.638412	−	0.171062i
$474$	62.0708	−	35.8366i	0.130951	−	0.0756047i
$475$		0			0
$476$	−67.6690	+	39.6128i	−0.142162	+	0.0832202i
$477$	−178.907	+	178.907i	−0.375068	+	0.375068i
$478$	−6.40240	+	23.8941i	−0.0133942	+	0.0499876i
$479$	−21.9122	−	12.6510i	−0.0457458	−	0.0264114i	0.476953	−	0.878929i	$-0.341741\pi$
$479$	−21.9122	−	12.6510i	−0.0457458	−	0.0264114i	−0.522698	+	0.852518i	$0.675075\pi$
$480$		0			0
$481$	354.080	+	613.284i	0.736132	+	1.27502i
$482$	−97.3430	+	97.3430i	−0.201956	+	0.201956i
$483$	179.818	−	181.993i	0.372295	−	0.376796i
$484$		−	52.4044i		−	0.108274i
$485$		0			0
$486$	161.883	−	280.389i	0.333092	−	0.576933i
$487$	57.3322	+	213.967i	0.117725	+	0.439357i	0.999476	−	0.0323584i	$-0.0103018\pi$
$487$	57.3322	+	213.967i	0.117725	+	0.439357i	−0.881751	+	0.471715i	$0.843635\pi$
$488$	55.3410	−	206.535i	0.113404	−	0.423228i
$489$			210.111i			0.429676i
$490$		0			0
$491$	−388.049			−0.790325			−0.395162	−	0.918611i	$-0.629312\pi$
$491$	−388.049			−0.790325			−0.395162	+	0.918611i	$0.629312\pi$
$492$	−103.618	−	27.7644i	−0.210606	−	0.0564317i
$493$	136.541	−	36.5859i	0.276959	−	0.0742108i
$494$	468.346	+	270.400i	0.948069	+	0.547368i
$495$		0			0
$496$	−107.391			−0.216514
$497$	110.984	+	109.658i	0.223308	+	0.220640i
$498$	58.1745	+	58.1745i	0.116816	+	0.116816i
$499$	73.8171	−	42.6183i	0.147930	−	0.0854075i	−0.424208	−	0.905565i	$-0.639447\pi$
$499$	73.8171	−	42.6183i	0.147930	−	0.0854075i	0.572138	+	0.820157i	$0.306114\pi$
$500$		0			0
$501$	−63.2182	+	109.497i	−0.126184	+	0.218557i
$502$	30.0595	+	8.05442i	0.0598795	+	0.0160447i
$503$	25.3086	+	25.3086i	0.0503154	+	0.0503154i	0.731817	−	0.681501i	$-0.238673\pi$
$503$	25.3086	+	25.3086i	0.0503154	+	0.0503154i	−0.681501	+	0.731817i	$0.738673\pi$
$504$	−76.3083	−	130.354i	−0.151405	−	0.258640i
$505$		0			0
$506$	267.796	+	463.837i	0.529242	+	0.916673i
$507$	−5.31917	−	19.8514i	−0.0104915	−	0.0391547i
$508$	251.028	−	67.2627i	0.494149	−	0.132407i
$509$	−487.485	+	281.450i	−0.957731	+	0.552946i	−0.895474	−	0.445114i	$-0.853163\pi$
$509$	−487.485	+	281.450i	−0.957731	+	0.552946i	−0.0622572	+	0.998060i	$0.519830\pi$
$510$		0			0
$511$	−20.2685	−	11.5402i	−0.0396644	−	0.0225835i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−156.591	+	584.406i	−0.305246	+	1.13919i
$514$	323.380	+	186.704i	0.629144	+	0.363236i
$515$		0			0
$516$	−30.1700	−	52.2560i	−0.0584690	−	0.101271i
$517$	48.0497	−	48.0497i	0.0929395	−	0.0929395i
$518$	150.742	+	549.349i	0.291007	+	1.06052i
$519$		−	25.0677i		−	0.0483001i
$520$		0			0
$521$	91.2668	−	158.079i	0.175176	−	0.303414i	−0.765046	−	0.643976i	$-0.777284\pi$
$521$	91.2668	−	158.079i	0.175176	−	0.303414i	0.940222	+	0.340561i	$0.110617\pi$
$522$	70.4774	+	263.025i	0.135014	+	0.503880i
$523$	−89.4563	+	333.855i	−0.171044	+	0.638347i	0.826147	+	0.563454i	$0.190528\pi$
$523$	−89.4563	+	333.855i	−0.171044	+	0.638347i	−0.997192	+	0.0748922i	$0.976139\pi$
$524$		−	209.721i		−	0.400231i
$525$		0			0
$526$	−366.855			−0.697443
$527$	−145.245	−	38.9182i	−0.275607	−	0.0738487i
$528$	−54.8877	+	14.7071i	−0.103954	+	0.0278544i
$529$	−385.703	−	222.686i	−0.729118	−	0.420956i
$530$		0			0
$531$	449.435			0.846394
$532$	309.455	+	305.758i	0.581682	+	0.574732i
$533$	−398.625	−	398.625i	−0.747888	−	0.747888i
$534$	−19.6686	+	11.3557i	−0.0368327	+	0.0212654i
$535$		0			0
$536$	79.3269	−	137.398i	0.147998	−	0.256340i
$537$	185.737	+	49.7681i	0.345879	+	0.0926779i
$538$	−383.551	−	383.551i	−0.712920	−	0.712920i
$539$	−518.389	−	291.042i	−0.961761	−	0.539966i
$540$		0			0
$541$	336.860	+	583.458i	0.622661	+	1.07848i	0.988988	+	0.147995i	$0.0472818\pi$
$541$	336.860	+	583.458i	0.622661	+	1.07848i	−0.366327	+	0.930486i	$0.619385\pi$
$542$	152.608	+	569.540i	0.281564	+	1.05081i
$543$	301.834	−	80.8762i	0.555864	−	0.148943i
$544$	−27.4381	+	15.8414i	−0.0504377	+	0.0291202i
$545$		0			0
$546$	0.857232	+	142.643i	0.00157002	+	0.261251i
$547$	269.330	−	269.330i	0.492377	−	0.492377i	−0.416678	−	0.909054i	$-0.636806\pi$
$547$	269.330	−	269.330i	0.492377	−	0.492377i	0.909054	+	0.416678i	$0.136806\pi$
$548$	−15.8139	+	59.0183i	−0.0288575	+	0.107698i
$549$	499.466	+	288.367i	0.909774	+	0.525258i
$550$		0			0
$551$	−392.129	−	679.188i	−0.711669	−	1.23265i
$552$	73.0982	−	73.0982i	0.132424	−	0.132424i
$553$	293.130	+	76.6589i	0.530073	+	0.138624i
$554$			542.637i			0.979489i
$555$		0			0
$556$	−254.693	+	441.141i	−0.458081	+	0.793419i
$557$	−8.56238	−	31.9552i	−0.0153723	−	0.0573703i	0.957814	−	0.287390i	$-0.0927876\pi$
$557$	−8.56238	−	31.9552i	−0.0153723	−	0.0573703i	−0.973186	+	0.230020i	$0.926121\pi$
$558$	74.9702	−	279.793i	0.134355	−	0.501421i
$559$		−	317.097i		−	0.567258i
$560$		0			0
$561$	−79.5646			−0.141826
$562$	57.1893	+	15.3238i	0.101760	+	0.0272666i
$563$	−125.179	+	33.5416i	−0.222343	+	0.0595766i	−0.368271	−	0.929719i	$-0.620050\pi$
$563$	−125.179	+	33.5416i	−0.222343	+	0.0595766i	0.145928	+	0.989295i	$0.453383\pi$
$564$	−11.3586	−	6.55787i	−0.0201393	−	0.0116274i
$565$		0			0
$566$	−128.294			−0.226668
$567$	309.599	−	84.9542i	0.546030	−	0.149831i
$568$	44.5772	+	44.5772i	0.0784809	+	0.0784809i
$569$	781.667	−	451.296i	1.37376	−	0.793139i	0.382358	−	0.924014i	$-0.375112\pi$
$569$	781.667	−	451.296i	1.37376	−	0.793139i	0.991399	+	0.130876i	$0.0417789\pi$
$570$		0			0
$571$	−111.294	+	192.767i	−0.194911	+	0.337595i	−0.946871	−	0.321613i	$-0.895775\pi$
$571$	−111.294	+	192.767i	−0.194911	+	0.337595i	0.751961	+	0.659208i	$0.229108\pi$
$572$	−288.445	−	77.2885i	−0.504274	−	0.135120i
$573$	−159.464	−	159.464i	−0.278298	−	0.278298i
$574$	−229.097	−	391.358i	−0.399124	−	0.681808i
$575$		0			0
$576$	−30.5161	−	52.8555i	−0.0529794	−	0.0917629i
$577$	260.437	+	971.962i	0.451363	+	1.68451i	0.698565	+	0.715546i	$0.253822\pi$
$577$	260.437	+	971.962i	0.451363	+	1.68451i	−0.247202	+	0.968964i	$0.579511\pi$
$578$	351.931	−	94.2996i	0.608877	−	0.163148i
$579$	156.371	−	90.2808i	0.270071	−	0.155925i
$580$		0			0
$581$	2.09005	+	347.783i	0.00359732	+	0.598594i
$582$	96.6665	−	96.6665i	0.166094	−	0.166094i
$583$	−104.142	+	388.665i	−0.178632	+	0.666663i
$584$	−8.16154	−	4.71207i	−0.0139752	−	0.00806861i
$585$		0			0
$586$	238.524	+	413.137i	0.407038	+	0.705011i
$587$	544.390	−	544.390i	0.927410	−	0.927410i	−0.0701276	−	0.997538i	$-0.522341\pi$
$587$	544.390	−	544.390i	0.927410	−	0.927410i	0.997538	+	0.0701276i	$0.0223407\pi$
$588$	−28.3644	+	111.186i	−0.0482387	+	0.189091i
$589$			834.254i			1.41639i
$590$		0			0
$591$	−114.207	+	197.813i	−0.193244	+	0.334708i
$592$	59.5739	+	222.333i	0.100632	+	0.375562i
$593$	154.860	−	577.944i	0.261146	−	0.974610i	−0.703421	−	0.710773i	$-0.748345\pi$
$593$	154.860	−	577.944i	0.261146	−	0.974610i	0.964567	−	0.263837i	$-0.0849881\pi$
$594$		−	334.082i		−	0.562428i
$595$		0			0
$596$	535.248			0.898067
$597$	−69.2729	−	18.5616i	−0.116035	−	0.0310915i
$598$	524.750	−	140.606i	0.877508	−	0.235128i
$599$	−350.560	−	202.396i	−0.585243	−	0.337890i	0.177972	−	0.984036i	$-0.443047\pi$
$599$	−350.560	−	202.396i	−0.585243	−	0.337890i	−0.763214	+	0.646146i	$0.776380\pi$
$600$		0			0
$601$	−808.864			−1.34586			−0.672932	−	0.739705i	$-0.734965\pi$
$601$	−808.864			−1.34586			−0.672932	+	0.739705i	$0.734965\pi$
$602$	64.5374	−	246.780i	0.107205	−	0.409933i
$603$	302.594	+	302.594i	0.501814	+	0.501814i
$604$	−51.8638	+	29.9436i	−0.0858672	+	0.0495755i
$605$		0			0
$606$	7.69243	−	13.3237i	0.0126938	−	0.0219863i
$607$	386.611	+	103.592i	0.636920	+	0.170662i	0.562808	−	0.826588i	$-0.309721\pi$
$607$	386.611	+	103.592i	0.636920	+	0.170662i	0.0741122	+	0.997250i	$0.476388\pi$
$608$	124.294	+	124.294i	0.204431	+	0.204431i
$609$	102.353	−	179.767i	0.168067	−	0.295183i
$610$		0			0
$611$	−34.4628	−	59.6912i	−0.0564038	−	0.0976943i
$612$	−22.1179	−	82.5451i	−0.0361404	−	0.134878i
$613$	−176.754	+	47.3611i	−0.288343	+	0.0772613i	−0.400091	−	0.916475i	$-0.631022\pi$
$613$	−176.754	+	47.3611i	−0.288343	+	0.0772613i	0.111748	+	0.993737i	$0.464355\pi$
$614$	−550.940	+	318.085i	−0.897296	+	0.518054i
$615$		0			0
$616$	−208.750	−	118.855i	−0.338880	−	0.192947i
$617$	−290.152	+	290.152i	−0.470263	+	0.470263i	−0.902000	−	0.431737i	$-0.857901\pi$
$617$	−290.152	+	290.152i	−0.470263	+	0.470263i	0.431737	+	0.902000i	$0.357901\pi$
$618$	−19.5117	+	72.8187i	−0.0315724	+	0.117830i
$619$	982.654	+	567.335i	1.58749	+	0.916535i	0.993720	+	0.111898i	$0.0356930\pi$
$619$	982.654	+	567.335i	1.58749	+	0.916535i	0.593766	+	0.804638i	$0.297640\pi$
$620$		0			0
$621$	303.888	+	526.349i	0.489353	+	0.847584i
$622$	−278.705	+	278.705i	−0.448079	+	0.448079i
$623$	−92.8854	−	24.2912i	−0.149094	−	0.0389907i
$624$			57.6376i			0.0923679i
$625$		0			0
$626$	212.379	−	367.852i	0.339264	−	0.587623i
$627$	114.250	+	426.388i	0.182218	+	0.680045i
$628$	119.557	−	446.193i	0.190378	−	0.710499i
$629$			322.291i			0.512386i
$630$		0			0
$631$	560.917			0.888933			0.444466	−	0.895796i	$-0.353393\pi$
$631$	560.917			0.888933			0.444466	+	0.895796i	$0.353393\pi$
$632$	118.254	+	31.6861i	0.187111	+	0.0501362i
$633$	−166.736	+	44.6767i	−0.263405	+	0.0705793i
$634$	−67.7197	−	39.0980i	−0.106813	−	0.0616687i
$635$		0			0
$636$	77.6637			0.122113
$637$	−421.240	+	431.489i	−0.661287	+	0.677377i
$638$	306.215	+	306.215i	0.479961	+	0.479961i
$639$	−147.259	+	85.0201i	−0.230453	+	0.133052i
$640$		0			0
$641$	−446.132	+	772.723i	−0.695994	+	1.20550i	0.273851	+	0.961772i	$0.411703\pi$
$641$	−446.132	+	772.723i	−0.695994	+	1.20550i	−0.969845	+	0.243724i	$0.921631\pi$
$642$	110.358	+	29.5703i	0.171897	+	0.0460597i
$643$	−139.636	−	139.636i	−0.217163	−	0.217163i	0.590139	−	0.807302i	$-0.299073\pi$
$643$	−139.636	−	139.636i	−0.217163	−	0.217163i	−0.807302	+	0.590139i	$0.799073\pi$
$644$	437.001	−	2.62621i	0.678573	−	0.00407797i
$645$		0			0
$646$	123.062	+	213.149i	0.190498	+	0.329953i
$647$	324.791	+	1212.14i	0.501996	+	1.87347i	0.486658	+	0.873592i	$0.338216\pi$
$647$	324.791	+	1212.14i	0.501996	+	1.87347i	0.0153378	+	0.999882i	$0.495118\pi$
$648$	125.301	−	33.5743i	0.193366	−	0.0518122i
$649$	618.993	−	357.376i	0.953765	−	0.550656i
$650$		0			0
$651$	−189.904	+	111.168i	−0.291711	+	0.170765i
$652$	−253.776	+	253.776i	−0.389227	+	0.389227i
$653$	−161.288	+	601.936i	−0.246996	+	0.921802i	0.725374	+	0.688355i	$0.241667\pi$
$653$	−161.288	+	601.936i	−0.246996	+	0.921802i	−0.972370	+	0.233446i	$0.925000\pi$
$654$	−241.268	−	139.296i	−0.368911	−	0.212991i
$655$		0			0
$656$	−91.6173	−	158.686i	−0.139661	−	0.241899i
$657$	17.9742	−	17.9742i	0.0273581	−	0.0273581i
$658$	−14.6718	−	53.4685i	−0.0222975	−	0.0812591i
$659$			251.197i			0.381180i	0.981670	+	0.190590i	$0.0610401\pi$
$659$			251.197i			0.381180i	−0.981670	+	0.190590i	$0.938960\pi$
$660$		0			0
$661$	−14.0072	+	24.2612i	−0.0211909	+	0.0367038i	−0.876426	−	0.481536i	$-0.840079\pi$
$661$	−14.0072	+	24.2612i	−0.0211909	+	0.0367038i	0.855235	+	0.518240i	$0.173412\pi$
$662$	75.0825	+	280.212i	0.113418	+	0.423281i
$663$	−20.8877	+	77.9539i	−0.0315048	+	0.117578i
$664$			140.528i			0.211639i
$665$		0			0
$666$	−620.846			−0.932201
$667$	−760.984	−	203.905i	−1.14091	−	0.305705i
$668$	−208.608	+	55.8964i	−0.312288	+	0.0836773i
$669$	241.225	+	139.271i	0.360575	+	0.208178i
$670$		0			0
$671$	917.198			1.36691
$672$	−11.7307	+	44.8562i	−0.0174564	+	0.0667502i
$673$	−21.1507	−	21.1507i	−0.0314275	−	0.0314275i	0.691218	−	0.722646i	$-0.257074\pi$
$673$	−21.1507	−	21.1507i	−0.0314275	−	0.0314275i	−0.722646	+	0.691218i	$0.757074\pi$
$674$	692.511	−	399.822i	1.02746	−	0.593207i
$675$		0			0
$676$	17.5523	−	30.4014i	0.0259649	−	0.0449725i
$677$	−566.824	−	151.880i	−0.837259	−	0.224343i	−0.185381	−	0.982667i	$-0.559352\pi$
$677$	−566.824	−	151.880i	−0.837259	−	0.224343i	−0.651878	+	0.758324i	$0.726019\pi$
$678$	−221.288	−	221.288i	−0.326383	−	0.326383i
$679$	577.899	−	3.47296i	0.851103	−	0.00511481i
$680$		0			0
$681$	207.049	+	358.619i	0.304036	+	0.526607i
$682$	−119.228	−	444.963i	−0.174821	−	0.652439i
$683$	11.1703	−	2.99308i	0.0163548	−	0.00438226i	−0.250632	−	0.968082i	$-0.580639\pi$
$683$	11.1703	−	2.99308i	0.0163548	−	0.00438226i	0.266987	+	0.963700i	$0.413972\pi$
$684$	−410.601	+	237.060i	−0.600294	+	0.346580i
$685$		0			0
$686$	−415.647	+	250.071i	−0.605899	+	0.364536i
$687$	−161.172	+	161.172i	−0.234603	+	0.234603i
$688$	26.6758	−	99.5555i	0.0387730	−	0.144703i
$689$	353.456	+	204.068i	0.512999	+	0.296180i
$690$		0			0
$691$	−383.714	−	664.611i	−0.555302	−	0.961811i	−0.997880	−	0.0650811i	$-0.979269\pi$
$691$	−383.714	−	664.611i	−0.555302	−	0.961811i	0.442578	−	0.896730i	$-0.354064\pi$
$692$	30.2772	−	30.2772i	0.0437532	−	0.0437532i
$693$	455.390	−	460.897i	0.657129	−	0.665075i
$694$		−	672.230i		−	0.968632i
$695$		0			0
$696$	41.7925	−	72.3868i	0.0600468	−	0.104004i
$697$	−66.4037	−	247.822i	−0.0952708	−	0.355555i
$698$	−103.482	+	386.200i	−0.148255	+	0.553295i
$699$		−	362.622i		−	0.518772i
$700$		0			0
$701$	601.377			0.857884			0.428942	−	0.903332i	$-0.358886\pi$
$701$	601.377			0.857884			0.428942	+	0.903332i	$0.358886\pi$
$702$	−327.319	−	87.7049i	−0.466266	−	0.124936i
$703$	1727.16	−	462.792i	2.45685	−	0.658310i
$704$	−84.0578	−	48.5308i	−0.119400	−	0.0689357i
$705$		0			0
$706$	−393.957			−0.558013
$707$	62.7189	−	17.2101i	0.0887113	−	0.0243424i
$708$	−97.5500	−	97.5500i	−0.137783	−	0.137783i
$709$	−1202.79	+	694.434i	−1.69647	+	0.979455i	−0.747402	+	0.664372i	$0.768699\pi$
$709$	−1202.79	+	694.434i	−1.69647	+	0.979455i	−0.949064	+	0.315083i	$0.897968\pi$
$710$		0			0
$711$	−165.108	+	285.975i	−0.232219	+	0.402215i
$712$	−37.4717	−	10.0405i	−0.0526288	−	0.0141018i
$713$	592.592	+	592.592i	0.831125	+	0.831125i
$714$	−32.1214	+	56.4161i	−0.0449879	+	0.0790141i
$715$		0			0
$716$	164.225	+	284.447i	0.229365	+	0.397272i
$717$	5.30081	+	19.7829i	0.00739304	+	0.0275912i
$718$	−918.359	+	246.073i	−1.27905	+	0.342721i
$719$	−380.588	+	219.733i	−0.529330	+	0.305609i	−0.740743	−	0.671788i	$-0.765527\pi$
$719$	−380.588	+	219.733i	−0.529330	+	0.305609i	0.211414	+	0.977397i	$0.432193\pi$
$720$		0			0
$721$	−275.031	+	161.001i	−0.381458	+	0.223302i
$722$	604.561	−	604.561i	0.837343	−	0.837343i
$723$	−29.4995	+	110.094i	−0.0408016	+	0.152273i
$724$	462.244	+	266.876i	0.638458	+	0.368614i
$725$		0			0
$726$	−21.6939	−	37.5749i	−0.0298814	−	0.0517561i
$727$	493.793	−	493.793i	0.679220	−	0.679220i	−0.280604	−	0.959824i	$-0.590535\pi$
$727$	493.793	−	493.793i	0.679220	−	0.679220i	0.959824	+	0.280604i	$0.0905347\pi$
$728$	−171.251	+	173.322i	−0.235235	+	0.238080i
$729$			144.711i			0.198506i
$730$		0			0
$731$	72.1573	−	124.980i	0.0987103	−	0.170971i
$732$	−45.8191	−	170.999i	−0.0625944	−	0.233605i
$733$	−87.4401	+	326.331i	−0.119291	+	0.445199i	−0.999572	−	0.0292530i	$-0.990687\pi$
$733$	−87.4401	+	326.331i	−0.119291	+	0.445199i	0.880281	+	0.474452i	$0.157354\pi$
$734$		−	163.133i		−	0.222252i
$735$		0			0
$736$	176.578			0.239916
$737$	657.365	+	176.140i	0.891947	+	0.238996i
$738$	477.393	−	127.917i	0.646873	−	0.173329i
$739$	−1077.39	−	622.034i	−1.45791	−	0.841724i	−0.459000	−	0.888436i	$-0.651792\pi$
$739$	−1077.39	−	622.034i	−1.45791	−	0.841724i	−0.998908	+	0.0467130i	$0.985125\pi$
$740$		0			0
$741$	447.750			0.604251
$742$	233.543	+	230.752i	0.314748	+	0.310987i
$743$	−286.451	−	286.451i	−0.385533	−	0.385533i	0.487558	−	0.873091i	$-0.337888\pi$
$743$	−286.451	−	286.451i	−0.385533	−	0.385533i	−0.873091	+	0.487558i	$0.837888\pi$
$744$	−77.0014	+	44.4568i	−0.103496	+	0.0597537i
$745$		0			0
$746$	20.4463	−	35.4140i	0.0274079	−	0.0474718i
$747$	−366.127	−	98.1033i	−0.490129	−	0.131330i
$748$	−96.0994	−	96.0994i	−0.128475	−	0.128475i
$749$	243.999	+	416.813i	0.325766	+	0.556493i
$750$		0			0
$751$	−201.068	−	348.259i	−0.267733	−	0.463728i	0.700543	−	0.713610i	$-0.252941\pi$
$751$	−201.068	−	348.259i	−0.267733	−	0.463728i	−0.968276	+	0.249883i	$0.919608\pi$
$752$	−5.79835	−	21.6398i	−0.00771058	−	0.0287763i
$753$	24.8875	−	6.66858i	0.0330511	−	0.00885602i
$754$	380.405	−	219.627i	0.504516	−	0.291283i
$755$		0			0
$756$	−236.884	−	134.874i	−0.313339	−	0.178404i
$757$	111.601	−	111.601i	0.147425	−	0.147425i	−0.629542	−	0.776967i	$-0.716757\pi$
$757$	111.601	−	111.601i	0.147425	−	0.147425i	0.776967	+	0.629542i	$0.216757\pi$
$758$	74.5147	−	278.093i	0.0983044	−	0.366877i
$759$	384.029	+	221.719i	0.505968	+	0.292121i
$760$		0			0
$761$	−689.909	−	1194.96i	−0.906582	−	1.57025i	−0.818779	−	0.574108i	$-0.805349\pi$
$761$	−689.909	−	1194.96i	−0.906582	−	1.57025i	−0.0878027	−	0.996138i	$-0.527984\pi$
$762$	152.147	−	152.147i	0.199667	−	0.199667i
$763$	−311.644	−	1135.73i	−0.408446	−	1.48850i
$764$		−	385.207i		−	0.504198i
$765$		0			0
$766$	182.229	−	315.629i	0.237896	−	0.412048i
$767$	−187.640	−	700.282i	−0.244642	−	0.913015i
$768$	−4.84876	+	18.0958i	−0.00631349	+	0.0235623i
$769$		−	967.610i		−	1.25827i	−0.777296	−	0.629136i	$-0.783409\pi$
$769$		−	967.610i		−	1.25827i	0.777296	−	0.629136i	$-0.216591\pi$
$770$		0			0
$771$	309.159			0.400984
$772$	297.910	+	79.8247i	0.385894	+	0.103400i
$773$	−976.271	+	261.591i	−1.26296	+	0.338410i	−0.827331	−	0.561715i	$-0.810142\pi$
$773$	−976.271	+	261.591i	−1.26296	+	0.338410i	−0.435632	+	0.900125i	$0.643475\pi$
$774$	240.756	+	139.000i	0.311054	+	0.179587i
$775$		0			0
$776$	233.511			0.300916
$777$	335.499	+	331.491i	0.431788	+	0.426629i
$778$	−314.781	−	314.781i	−0.404603	−	0.404603i
$779$	−1232.73	+	711.717i	−1.58245	+	0.913629i
$780$		0			0
$781$	−135.210	+	234.191i	−0.173125	+	0.299860i
$782$	238.819	+	63.9915i	0.305396	+	0.0818305i
$783$	347.485	+	347.485i	0.443786	+	0.443786i
$784$	−168.551	+	100.033i	−0.214988	+	0.127593i
$785$		0			0
$786$	−86.8183	−	150.374i	−0.110456	−	0.191315i
$787$	152.395	+	568.747i	0.193641	+	0.722677i	0.992615	+	0.121311i	$0.0387098\pi$
$787$	152.395	+	568.747i	0.193641	+	0.722677i	−0.798974	+	0.601366i	$0.794623\pi$
$788$	−376.863	+	100.980i	−0.478252	+	0.128147i
$789$	−263.041	+	151.867i	−0.333386	+	0.192480i
$790$		0			0
$791$	−7.95025	−	1322.92i	−0.0100509	−	1.67246i
$792$	185.121	−	185.121i	0.233739	−	0.233739i
$793$	240.787	−	898.630i	0.303641	−	1.13320i
$794$	−26.5478	−	15.3274i	−0.0334355	−	0.0193040i
$795$		0			0
$796$	−61.2499	−	106.088i	−0.0769471	−	0.133276i
$797$	−331.594	+	331.594i	−0.416052	+	0.416052i	−0.883841	−	0.467788i	$-0.845051\pi$
$797$	−331.594	+	331.594i	−0.416052	+	0.416052i	0.467788	+	0.883841i	$0.345051\pi$
$798$	348.459	+	91.1285i	0.436666	+	0.114196i
$799$		−	31.3687i		−	0.0392600i
$800$		0			0
$801$	52.3183	−	90.6180i	0.0653162	−	0.113131i
$802$	−213.143	−	795.461i	−0.265764	−	0.991846i
$803$	10.4628	−	39.0479i	0.0130297	−	0.0486275i
$804$		−	131.356i		−	0.163378i
$805$		0			0
$806$	−467.256			−0.579722
$807$	−433.791	−	116.234i	−0.537536	−	0.144032i
$808$	25.3836	−	6.80151i	0.0314153	−	0.00841772i
$809$	523.515	+	302.251i	0.647114	+	0.373611i	0.787350	−	0.616507i	$-0.211453\pi$
$809$	523.515	+	302.251i	0.647114	+	0.373611i	−0.140236	+	0.990118i	$0.544786\pi$
$810$		0			0
$811$	−1186.18			−1.46262			−0.731309	−	0.682046i	$-0.761090\pi$
$811$	−1186.18			−1.46262			−0.731309	+	0.682046i	$0.761090\pi$
$812$	340.748	−	93.5015i	0.419641	−	0.115150i
$813$	345.195	+	345.195i	0.424594	+	0.424594i
$814$	−855.072	+	493.676i	−1.05046	+	0.606481i
$815$		0			0
$816$	−13.1157	+	22.7171i	−0.0160732	+	0.0278396i
$817$	−773.384	−	207.228i	−0.946614	−	0.253645i
$818$	−369.841	−	369.841i	−0.452128	−	0.452128i
$819$	−332.015	−	567.168i	−0.405391	−	0.692513i
$820$		0			0
$821$	528.493	+	915.376i	0.643718	+	1.11495i	0.984596	+	0.174845i	$0.0559424\pi$
$821$	528.493	+	915.376i	0.643718	+	1.11495i	−0.340878	+	0.940108i	$0.610724\pi$
$822$	13.0930	+	48.8637i	0.0159282	+	0.0594449i
$823$	−563.580	+	151.011i	−0.684788	+	0.183488i	−0.584407	−	0.811461i	$-0.698673\pi$
$823$	−563.580	+	151.011i	−0.684788	+	0.183488i	−0.100381	+	0.994949i	$0.532006\pi$
$824$	−111.518	+	64.3851i	−0.135338	+	0.0781372i
$825$		0			0
$826$	−3.50470	−	583.181i	−0.00424298	−	0.706030i
$827$	−429.765	+	429.765i	−0.519667	+	0.519667i	−0.917471	−	0.397803i	$-0.869773\pi$
$827$	−429.765	+	429.765i	−0.519667	+	0.519667i	0.397803	+	0.917471i	$0.369773\pi$
$828$	−123.270	+	460.050i	−0.148877	+	0.555616i
$829$	−187.412	−	108.202i	−0.226070	−	0.130522i	0.382688	−	0.923878i	$-0.374999\pi$
$829$	−187.412	−	108.202i	−0.226070	−	0.130522i	−0.608758	+	0.793356i	$0.708332\pi$
$830$		0			0
$831$	224.636	+	389.080i	0.270320	+	0.468207i
$832$	−69.6156	+	69.6156i	−0.0836726	+	0.0836726i
$833$	−264.214	+	74.2107i	−0.317184	+	0.0890885i
$834$			421.741i			0.505685i
$835$		0			0
$836$	−377.005	+	652.992i	−0.450963	+	0.781091i
$837$	−135.296	−	504.933i	−0.161644	−	0.603265i
$838$	−10.9780	+	40.9704i	−0.0131002	+	0.0488907i
$839$		−	44.2929i		−	0.0527925i	−0.999652	−	0.0263963i	$-0.991597\pi$
$839$		−	44.2929i		−	0.0527925i	0.999652	−	0.0263963i	$-0.00840316\pi$
$840$		0			0
$841$	204.001			0.242569
$842$	−80.8526	−	21.6644i	−0.0960245	−	0.0257297i
$843$	47.3494	−	12.6872i	0.0561677	−	0.0150501i
$844$	−255.347	−	147.425i	−0.302544	−	0.174674i
$845$		0			0
$846$	60.4272			0.0714270
$847$	46.4059	−	177.448i	0.0547885	−	0.209502i
$848$	93.8035	+	93.8035i	0.110617	+	0.110617i
$849$	−91.9891	+	53.1099i	−0.108350	+	0.0625559i
$850$		0			0
$851$	898.115	−	1555.58i	1.05536	−	1.82794i
$852$	50.4163	+	13.5090i	0.0591740	+	0.0158556i
$853$	−451.722	−	451.722i	−0.529568	−	0.529568i	0.390875	−	0.920444i	$-0.372172\pi$
$853$	−451.722	−	451.722i	−0.529568	−	0.529568i	−0.920444	+	0.390875i	$0.872172\pi$
$854$	370.286	−	650.348i	0.433590	−	0.761532i
$855$		0			0
$856$	97.5765	+	169.007i	0.113991	+	0.197439i
$857$	−30.9395	−	115.468i	−0.0361021	−	0.134735i	0.945523	−	0.325556i	$-0.105552\pi$
$857$	−30.9395	−	115.468i	−0.0361021	−	0.134735i	−0.981625	+	0.190821i	$0.938885\pi$
$858$	−238.815	+	63.9903i	−0.278339	+	0.0745808i
$859$	−528.189	+	304.950i	−0.614889	+	0.355006i	−0.774876	−	0.632113i	$-0.782188\pi$
$859$	−528.189	+	304.950i	−0.614889	+	0.355006i	0.159988	+	0.987119i	$0.448855\pi$
$860$		0			0
$861$	−326.277	−	185.771i	−0.378952	−	0.215762i
$862$	−675.870	+	675.870i	−0.784072	+	0.784072i
$863$	−51.4484	+	192.008i	−0.0596157	+	0.222489i	−0.989306	−	0.145852i	$-0.953408\pi$
$863$	−51.4484	+	192.008i	−0.0596157	+	0.222489i	0.929691	+	0.368341i	$0.120074\pi$
$864$	−95.3865	−	55.0714i	−0.110401	−	0.0637401i
$865$		0			0
$866$	202.377	+	350.527i	0.233691	+	0.404765i
$867$	213.303	−	213.303i	0.246025	−	0.246025i
$868$	−363.640	−	95.0985i	−0.418940	−	0.109560i
$869$			525.152i			0.604317i
$870$		0			0
$871$	345.149	−	597.816i	0.396268	−	0.686356i
$872$	−123.163	−	459.651i	−0.141242	−	0.527123i
$873$	−163.015	+	608.380i	−0.186729	+	0.696884i
$874$		−	1371.73i		−	1.56948i
$875$		0			0
$876$	−7.80263			−0.00890711
$877$	426.717	+	114.339i	0.486565	+	0.130375i	0.493758	−	0.869599i	$-0.335623\pi$
$877$	426.717	+	114.339i	0.486565	+	0.130375i	−0.00719299	+	0.999974i	$0.502290\pi$
$878$	217.505	−	58.2802i	0.247727	−	0.0663783i
$879$	342.053	+	197.484i	0.389138	+	0.224669i
$880$		0			0
$881$	−121.425			−0.137826			−0.0689131	−	0.997623i	$-0.521953\pi$
$881$	−121.425			−0.137826			−0.0689131	+	0.997623i	$0.521953\pi$
$882$	−142.956	−	508.969i	−0.162082	−	0.577063i
$883$	249.667	+	249.667i	0.282748	+	0.282748i	0.834204	−	0.551456i	$-0.185927\pi$
$883$	249.667	+	249.667i	0.282748	+	0.282748i	−0.551456	+	0.834204i	$0.685927\pi$
$884$	−119.382	+	68.9255i	−0.135048	+	0.0779700i
$885$		0			0
$886$	106.005	−	183.606i	0.119645	−	0.207231i
$887$	−1338.19	−	358.568i	−1.50867	−	0.404248i	−0.592679	−	0.805439i	$-0.701930\pi$
$887$	−1338.19	−	358.568i	−1.50867	−	0.404248i	−0.915995	+	0.401191i	$0.868597\pi$
$888$	134.755	+	134.755i	0.151751	+	0.151751i
$889$	909.574	−	5.46620i	1.02314	−	0.00614870i
$890$		0			0
$891$	278.223	+	481.896i	0.312259	+	0.540848i
$892$	123.141	+	459.569i	0.138051	+	0.515212i
$893$	−168.106	+	45.0438i	−0.188248	+	0.0504410i
$894$	383.782	−	221.577i	0.429287	−	0.247849i
$895$		0			0
$896$	−68.3465	+	40.0094i	−0.0762796	+	0.0446534i
$897$	318.048	−	318.048i	0.354569	−	0.354569i
$898$	232.394	−	867.305i	0.258790	−	0.965819i
$899$	586.825	+	338.804i	0.652753	+	0.376867i
$900$		0			0
$901$	92.8737	+	160.862i	0.103078	+	0.178537i
$902$	555.782	−	555.782i	0.616167	−	0.616167i
$903$	−55.8850	−	203.662i	−0.0618881	−	0.225539i
$904$		−	534.550i		−	0.591316i
$905$		0			0
$906$	−24.7915	+	42.9402i	−0.0273637	+	0.0473953i
$907$	−191.242	−	713.723i	−0.210851	−	0.786905i	−0.987586	−	0.157078i	$-0.949792\pi$
$907$	−191.242	−	713.723i	−0.210851	−	0.786905i	0.776735	−	0.629827i	$-0.216874\pi$
$908$	−183.069	+	683.223i	−0.201618	+	0.752448i
$909$			70.8816i			0.0779776i
$910$		0			0
$911$	619.393			0.679904			0.339952	−	0.940443i	$-0.389589\pi$
$911$	619.393			0.679904			0.339952	+	0.940443i	$0.389589\pi$
$912$	140.575	+	37.6670i	0.154139	+	0.0413015i
$913$	−582.263	+	156.017i	−0.637747	+	0.170884i
$914$	−245.500	−	141.740i	−0.268600	−	0.155076i
$915$		0			0
$916$	−389.333			−0.425036
$917$	185.715	−	710.141i	0.202525	−	0.774418i
$918$	−109.051	−	109.051i	−0.118792	−	0.118792i
$919$	505.888	−	292.074i	0.550476	−	0.317818i	−0.198838	−	0.980032i	$-0.563717\pi$
$919$	505.888	−	292.074i	0.550476	−	0.317818i	0.749314	+	0.662215i	$0.230383\pi$
$920$		0			0
$921$	−263.356	+	456.146i	−0.285946	+	0.495272i
$922$	−554.894	−	148.683i	−0.601838	−	0.161262i
$923$	193.954	+	193.954i	0.210134	+	0.210134i
$924$	−198.880	+	1.19520i	−0.215238	+	0.00129350i
$925$		0			0
$926$	−288.227	−	499.223i	−0.311260	−	0.539118i
$927$	−89.8950	−	335.493i	−0.0969741	−	0.361912i
$928$	137.908	−	36.9522i	0.148607	−	0.0398192i
$929$	721.006	−	416.273i	0.776110	−	0.448087i	−0.0589398	−	0.998262i	$-0.518772\pi$
$929$	721.006	−	416.273i	0.776110	−	0.448087i	0.835050	+	0.550174i	$0.185439\pi$
$930$		0			0
$931$	777.093	+	1309.37i	0.834687	+	1.40641i
$932$	437.980	−	437.980i	0.469936	−	0.469936i
$933$	−84.4609	+	315.212i	−0.0905262	+	0.337848i
$934$	104.075	+	60.0877i	0.111429	+	0.0643338i
$935$		0			0
$936$	−132.775	−	229.973i	−0.141853	−	0.245697i
$937$	−582.131	+	582.131i	−0.621271	+	0.621271i	−0.945856	−	0.324586i	$-0.894775\pi$
$937$	−582.131	+	582.131i	−0.621271	+	0.621271i	0.324586	+	0.945856i	$0.394775\pi$
$938$	390.281	−	395.001i	0.416078	−	0.421110i
$939$		−	351.675i		−	0.374521i
$940$		0			0
$941$	300.357	−	520.234i	0.319189	−	0.552852i	−0.661130	−	0.750271i	$-0.729923\pi$
$941$	300.357	−	520.234i	0.319189	−	0.552852i	0.980319	+	0.197420i	$0.0632561\pi$
$942$	−98.9863	−	369.422i	−0.105081	−	0.392167i
$943$	−370.089	+	1381.19i	−0.392459	+	1.46468i
$944$		−	235.645i		−	0.249624i
$945$		0			0
$946$	442.113			0.467350
$947$	−905.793	−	242.706i	−0.956486	−	0.256290i	−0.253374	−	0.967368i	$-0.581540\pi$
$947$	−905.793	−	242.706i	−0.956486	−	0.256290i	−0.703112	+	0.711079i	$0.748207\pi$
$948$	97.9075	−	26.2342i	0.103278	−	0.0276732i
$949$	−35.5106	−	20.5021i	−0.0374190	−	0.0216039i
$950$		0			0
$951$	−64.7416			−0.0680774
$952$	−106.937	+	29.3436i	−0.112329	+	0.0308231i
$953$	−108.986	−	108.986i	−0.114361	−	0.114361i	0.647611	−	0.761971i	$-0.275768\pi$
$953$	−108.986	−	108.986i	−0.114361	−	0.114361i	−0.761971	+	0.647611i	$0.775768\pi$
$954$	−309.877	+	178.907i	−0.324818	+	0.187534i
$955$		0			0
$956$	−17.4917	+	30.2965i	−0.0182967	+	0.0316909i
$957$	346.326	+	92.7977i	0.361887	+	0.0969673i
$958$	−25.3021	−	25.3021i	−0.0264114	−	0.0264114i
$959$	−105.811	+	185.840i	−0.110334	+	0.193785i
$960$		0			0
$961$	120.098	+	208.016i	0.124972	+	0.216458i
$962$	259.204	+	967.364i	0.269443	+	1.00558i
$963$	−508.444	+	136.237i	−0.527979	+	0.141472i
$964$	−168.603	+	97.3430i	−0.174899	+	0.100978i
$965$		0			0
$966$	312.250	−	182.789i	0.323241	−	0.189222i
$967$	293.397	−	293.397i	0.303410	−	0.303410i	−0.538937	−	0.842346i	$-0.681174\pi$
$967$	293.397	−	293.397i	0.303410	−	0.303410i	0.842346	+	0.538937i	$0.181174\pi$
$968$	19.1813	−	71.5858i	0.0198154	−	0.0739522i
$969$	176.475	+	101.888i	0.182121	+	0.105148i
$970$		0			0
$971$	634.715	+	1099.36i	0.653672	+	1.13219i	0.982225	+	0.187707i	$0.0601056\pi$
$971$	634.715	+	1099.36i	0.653672	+	1.13219i	−0.328553	+	0.944485i	$0.606561\pi$
$972$	323.766	−	323.766i	0.333092	−	0.333092i
$973$	−1253.07	+	1268.22i	−1.28784	+	1.30341i
$974$			313.269i			0.321631i
$975$		0			0
$976$	151.194	−	261.877i	0.154912	−	0.268316i
$977$	201.844	+	753.293i	0.206596	+	0.771027i	0.988957	+	0.148202i	$0.0473485\pi$
$977$	201.844	+	753.293i	0.206596	+	0.771027i	−0.782361	+	0.622825i	$0.785985\pi$
$978$	−76.9061	+	287.018i	−0.0786361	+	0.293474i
$979$		−	166.407i		−	0.169977i
$980$		0			0
$981$	1283.54			1.30840
$982$	−530.085	−	142.036i	−0.539802	−	0.144639i
$983$	1761.86	−	472.090i	1.79233	−	0.480254i	0.799594	−	0.600541i	$-0.205048\pi$
$983$	1761.86	−	472.090i	1.79233	−	0.480254i	0.992739	+	0.120287i	$0.0383816\pi$
$984$	−131.383	−	75.8537i	−0.133519	−	0.0770871i
$985$		0			0
$986$	199.909			0.202748
$987$	−32.6543	−	32.2642i	−0.0330844	−	0.0326891i
$988$	540.800	+	540.800i	0.547368	+	0.547368i
$989$	−696.553	+	402.155i	−0.704301	+	0.406628i
$990$		0			0
$991$	410.849	−	711.611i	0.414580	−	0.718074i	−0.580804	−	0.814043i	$-0.697262\pi$
$991$	410.849	−	711.611i	0.414580	−	0.718074i	0.995384	+	0.0959694i	$0.0305951\pi$
$992$	−146.699	−	39.3079i	−0.147882	−	0.0396249i
$993$	169.835	+	169.835i	0.171032	+	0.171032i
$994$	111.469	+	190.418i	0.112142	+	0.191568i
$995$		0			0
$996$	58.1745	+	100.761i	0.0584081	+	0.101166i
$997$	125.878	+	469.784i	0.126257	+	0.471197i	0.999881	−	0.0154036i	$-0.00490332\pi$
$997$	125.878	+	469.784i	0.126257	+	0.471197i	−0.873624	+	0.486601i	$0.838237\pi$
$998$	116.435	−	31.1988i	0.116669	−	0.0312613i
$999$	−970.312	+	560.210i	−0.971283	+	0.560771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.e.193.3		16
5.2	odd	4	inner	350.3.p.e.207.2		16
5.3	odd	4		70.3.l.c.67.3	yes	16
5.4	even	2		70.3.l.c.53.2	yes	16
7.2	even	3	inner	350.3.p.e.93.2		16
35.2	odd	12	inner	350.3.p.e.107.3		16
35.3	even	12		490.3.f.p.197.2		8
35.4	even	6		490.3.f.o.393.3		8
35.9	even	6		70.3.l.c.23.3	✓	16
35.18	odd	12		490.3.f.o.197.3		8
35.23	odd	12		70.3.l.c.37.2	yes	16
35.24	odd	6		490.3.f.p.393.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.3	✓	16	35.9	even	6
70.3.l.c.37.2	yes	16	35.23	odd	12
70.3.l.c.53.2	yes	16	5.4	even	2
70.3.l.c.67.3	yes	16	5.3	odd	4
350.3.p.e.93.2		16	7.2	even	3	inner
350.3.p.e.107.3		16	35.2	odd	12	inner
350.3.p.e.193.3		16	1.1	even	1	trivial
350.3.p.e.207.2		16	5.2	odd	4	inner
490.3.f.o.197.3		8	35.18	odd	12
490.3.f.o.393.3		8	35.4	even	6
490.3.f.p.197.2		8	35.3	even	12
490.3.f.p.393.2		8	35.24	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.13099 - 0.303047i) q^{3} +(1.73205 + 1.00000i) q^{4} +1.65588 q^{6} +(4.97940 + 4.91991i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.60693 + 3.81451i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.13099 - 0.303047i) q^{3} +(1.73205 + 1.00000i) q^{4} +1.65588 q^{6} +(4.97940 + 4.91991i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.60693 + 3.81451i) q^{9} +(-6.06635 + 10.5072i) q^{11} +(2.26198 + 0.606095i) q^{12} +(8.70195 + 8.70195i) q^{13} +(5.00118 + 8.54331i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.44959 + 5.40994i) q^{17} +(-10.4214 + 2.79242i) q^{18} +(26.9104 - 15.5367i) q^{19} +(7.12261 + 4.05537i) q^{21} +(-12.1327 + 12.1327i) q^{22} +(8.07902 - 30.1513i) q^{23} +(2.86807 + 1.65588i) q^{24} +(8.70195 + 15.0722i) q^{26} +(-13.7679 + 13.7679i) q^{27} +(3.70467 + 13.5009i) q^{28} -25.2388i q^{29} +(-13.4239 + 23.2509i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-3.67678 + 13.7219i) q^{33} +7.92070i q^{34} -15.2581 q^{36} +(55.5832 + 14.8935i) q^{37} +(42.4472 - 11.3737i) q^{38} +(12.4789 + 7.20470i) q^{39} -45.8087 q^{41} +(8.24530 + 8.14679i) q^{42} +(-18.2199 - 18.2199i) q^{43} +(-21.0144 + 12.1327i) q^{44} +(22.0723 - 38.2303i) q^{46} +(-5.40994 - 1.44959i) q^{47} +(3.31176 + 3.31176i) q^{48} +(0.588922 + 48.9965i) q^{49} +(3.27894 + 5.67928i) q^{51} +(6.37027 + 23.7742i) q^{52} +(32.0345 - 8.58361i) q^{53} +(-23.8466 + 13.7679i) q^{54} +(0.118982 + 19.7986i) q^{56} +(25.7270 - 25.7270i) q^{57} +(9.23806 - 34.4769i) q^{58} +(-51.0186 - 29.4556i) q^{59} +(-37.7986 - 65.4691i) q^{61} +(-26.8478 + 26.8478i) q^{62} +(-51.6657 - 13.5115i) q^{63} +8.00000i q^{64} +(-10.0452 + 17.3987i) q^{66} +(-14.5178 - 54.1813i) q^{67} +(-2.89918 + 10.8199i) q^{68} -36.5491i q^{69} +22.2886 q^{71} +(-20.8429 - 5.58484i) q^{72} +(-3.21840 + 0.862368i) q^{73} +(70.4767 + 40.6897i) q^{74} +62.1470 q^{76} +(-81.9014 + 22.4738i) q^{77} +(14.4094 + 14.4094i) q^{78} +(37.4851 - 21.6420i) q^{79} +(22.9317 - 39.7188i) q^{81} +(-62.5758 - 16.7671i) q^{82} +(35.1320 + 35.1320i) q^{83} +(8.28136 + 14.1467i) q^{84} +(-18.2199 - 31.5578i) q^{86} +(-7.64857 - 28.5448i) q^{87} +(-33.1471 + 8.88175i) q^{88} +(-11.8780 + 6.85780i) q^{89} +(0.517689 + 86.1433i) q^{91} +(44.1446 - 44.1446i) q^{92} +(-8.13615 + 30.3645i) q^{93} +(-6.85953 - 3.96035i) q^{94} +(3.31176 + 5.73614i) q^{96} +(58.3777 - 58.3777i) q^{97} +(-17.1295 + 67.1460i) q^{98} -92.5606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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