LMFDB - Embedded newform 350.3.p.e.207.2

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			207.2
Root			$-1.13099 - 0.303047i$ of defining polynomial
Character	$\chi$	$=$	350.207
Dual form			350.3.p.e.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(-0.303047 - 1.13099i) q^{3} +(-1.73205 - 1.00000i) q^{4} +1.65588 q^{6} +(-4.91991 + 4.97940i) q^{7} +(2.00000 - 2.00000i) q^{8} +(6.60693 - 3.81451i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(-0.303047 - 1.13099i) q^{3} +(-1.73205 - 1.00000i) q^{4} +1.65588 q^{6} +(-4.91991 + 4.97940i) q^{7} +(2.00000 - 2.00000i) q^{8} +(6.60693 - 3.81451i) q^{9} +(-6.06635 + 10.5072i) q^{11} +(-0.606095 + 2.26198i) q^{12} +(8.70195 - 8.70195i) q^{13} +(-5.00118 - 8.54331i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-5.40994 + 1.44959i) q^{17} +(2.79242 + 10.4214i) q^{18} +(-26.9104 + 15.5367i) q^{19} +(7.12261 + 4.05537i) q^{21} +(-12.1327 - 12.1327i) q^{22} +(-30.1513 - 8.07902i) q^{23} +(-2.86807 - 1.65588i) q^{24} +(8.70195 + 15.0722i) q^{26} +(-13.7679 - 13.7679i) q^{27} +(13.5009 - 3.70467i) q^{28} +25.2388i q^{29} +(-13.4239 + 23.2509i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(13.7219 + 3.67678i) q^{33} -7.92070i q^{34} -15.2581 q^{36} +(-14.8935 + 55.5832i) q^{37} +(-11.3737 - 42.4472i) q^{38} +(-12.4789 - 7.20470i) q^{39} -45.8087 q^{41} +(-8.14679 + 8.24530i) q^{42} +(-18.2199 + 18.2199i) q^{43} +(21.0144 - 12.1327i) q^{44} +(22.0723 - 38.2303i) q^{46} +(1.44959 - 5.40994i) q^{47} +(3.31176 - 3.31176i) q^{48} +(-0.588922 - 48.9965i) q^{49} +(3.27894 + 5.67928i) q^{51} +(-23.7742 + 6.37027i) q^{52} +(-8.58361 - 32.0345i) q^{53} +(23.8466 - 13.7679i) q^{54} +(0.118982 + 19.7986i) q^{56} +(25.7270 + 25.7270i) q^{57} +(-34.4769 - 9.23806i) q^{58} +(51.0186 + 29.4556i) q^{59} +(-37.7986 - 65.4691i) q^{61} +(-26.8478 - 26.8478i) q^{62} +(-13.5115 + 51.6657i) q^{63} -8.00000i q^{64} +(-10.0452 + 17.3987i) q^{66} +(54.1813 - 14.5178i) q^{67} +(10.8199 + 2.89918i) q^{68} +36.5491i q^{69} +22.2886 q^{71} +(5.58484 - 20.8429i) q^{72} +(0.862368 + 3.21840i) q^{73} +(-70.4767 - 40.6897i) q^{74} +62.1470 q^{76} +(-22.4738 - 81.9014i) q^{77} +(14.4094 - 14.4094i) q^{78} +(-37.4851 + 21.6420i) q^{79} +(22.9317 - 39.7188i) q^{81} +(16.7671 - 62.5758i) q^{82} +(35.1320 - 35.1320i) q^{83} +(-8.28136 - 14.1467i) q^{84} +(-18.2199 - 31.5578i) q^{86} +(28.5448 - 7.64857i) q^{87} +(8.88175 + 33.1471i) q^{88} +(11.8780 - 6.85780i) q^{89} +(0.517689 + 86.1433i) q^{91} +(44.1446 + 44.1446i) q^{92} +(30.3645 + 8.13615i) q^{93} +(6.85953 + 3.96035i) q^{94} +(3.31176 + 5.73614i) q^{96} +(58.3777 + 58.3777i) q^{97} +(67.1460 + 17.1295i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$3$	−0.303047	−	1.13099i	−0.101016	−	0.376996i	0.896847	−	0.442341i	$-0.145852\pi$
$3$	−0.303047	−	1.13099i	−0.101016	−	0.376996i	−0.997863	+	0.0653449i	$0.979185\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.65588			0.275980
$7$	−4.91991	+	4.97940i	−0.702845	+	0.711343i
$7$	−4.91991	+	4.97940i	−0.702845	+	0.711343i
$8$	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	$0.980728\pi$
$12$	−0.606095	+	2.26198i	−0.0505079	+	0.188498i
$13$	8.70195	−	8.70195i	0.669380	−	0.669380i	−0.288192	−	0.957573i	$-0.593054\pi$
$13$	8.70195	−	8.70195i	0.669380	−	0.669380i	0.957573	+	0.288192i	$0.0930542\pi$
$14$	−5.00118	−	8.54331i	−0.357227	−	0.610237i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−5.40994	+	1.44959i	−0.318232	+	0.0852699i	−0.414399	−	0.910095i	$-0.636008\pi$
$17$	−5.40994	+	1.44959i	−0.318232	+	0.0852699i	0.0961674	+	0.995365i	$0.469342\pi$
$18$	2.79242	+	10.4214i	0.155134	+	0.578969i
$19$	−26.9104	+	15.5367i	−1.41634	+	0.817723i	−0.995975	−	0.0896326i	$-0.971431\pi$
$19$	−26.9104	+	15.5367i	−1.41634	+	0.817723i	−0.420363	+	0.907356i	$0.638097\pi$
$20$		0			0
$21$	7.12261	+	4.05537i	0.339172	+	0.193113i
$22$	−12.1327	−	12.1327i	−0.551486	−	0.551486i
$23$	−30.1513	−	8.07902i	−1.31093	−	0.351262i	−0.465355	−	0.885124i	$-0.654073\pi$
$23$	−30.1513	−	8.07902i	−1.31093	−	0.351262i	−0.845571	+	0.533862i	$0.820740\pi$
$24$	−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
$28$	13.5009	−	3.70467i	0.482177	−	0.132310i
$29$			25.2388i			0.870305i	0.900357	+	0.435153i	$0.143306\pi$
$29$			25.2388i			0.870305i	−0.900357	+	0.435153i	$0.856694\pi$
$30$		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	$0.309222\pi$
$32$	−5.46410	+	1.46410i	−0.170753	+	0.0457532i
$33$	13.7219	+	3.67678i	0.415816	+	0.111418i
$34$		−	7.92070i		−	0.232962i
$35$		0			0
$36$	−15.2581			−0.423835
$37$	−14.8935	+	55.5832i	−0.402526	+	1.50225i	0.406047	+	0.913852i	$0.366907\pi$
$37$	−14.8935	+	55.5832i	−0.402526	+	1.50225i	−0.808573	+	0.588396i	$0.799760\pi$
$38$	−11.3737	−	42.4472i	−0.299307	−	1.11703i
$39$	−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	$0.688678\pi$
$42$	−8.14679	+	8.24530i	−0.193971	+	0.196317i
$43$	−18.2199	+	18.2199i	−0.423719	+	0.423719i	−0.886482	−	0.462763i	$-0.846858\pi$
$43$	−18.2199	+	18.2199i	−0.423719	+	0.423719i	0.462763	+	0.886482i	$0.346858\pi$
$44$	21.0144	−	12.1327i	0.477601	−	0.275743i
$45$		0			0
$46$	22.0723	−	38.2303i	0.479832	−	0.831094i
$47$	1.44959	−	5.40994i	0.0308423	−	0.115105i	−0.948789	−	0.315912i	$-0.897690\pi$
$47$	1.44959	−	5.40994i	0.0308423	−	0.115105i	0.979631	+	0.200807i	$0.0643563\pi$
$48$	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
$52$	−23.7742	+	6.37027i	−0.457195	+	0.122505i
$53$	−8.58361	−	32.0345i	−0.161955	−	0.604424i	−0.998409	−	0.0563871i	$-0.982042\pi$
$53$	−8.58361	−	32.0345i	−0.161955	−	0.604424i	0.836454	−	0.548037i	$-0.184625\pi$
$54$	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
$58$	−34.4769	−	9.23806i	−0.594429	−	0.159277i
$59$	51.0186	+	29.4556i	0.864722	+	0.499248i	0.865591	−	0.500752i	$-0.166943\pi$
$59$	51.0186	+	29.4556i	0.864722	+	0.499248i	−0.000868446		1.00000i	$0.500276\pi$
$60$		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
$63$	−13.5115	+	51.6657i	−0.214469	+	0.820090i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−10.0452	+	17.3987i	−0.152199	+	0.263617i
$67$	54.1813	−	14.5178i	0.808676	−	0.216684i	0.169286	−	0.985567i	$-0.445854\pi$
$67$	54.1813	−	14.5178i	0.808676	−	0.216684i	0.639390	+	0.768883i	$0.279187\pi$
$68$	10.8199	+	2.89918i	0.159116	+	0.0426350i
$69$			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	$0.449830\pi$
$72$	5.58484	−	20.8429i	0.0775672	−	0.289485i
$73$	0.862368	+	3.21840i	0.0118133	+	0.0440877i	0.971581	−	0.236708i	$-0.0760684\pi$
$73$	0.862368	+	3.21840i	0.0118133	+	0.0440877i	−0.959768	+	0.280795i	$0.909402\pi$
$74$	−70.4767	−	40.6897i	−0.952387	−	0.549861i
$75$		0			0
$76$	62.1470			0.817723
$77$	−22.4738	−	81.9014i	−0.291867	−	1.06365i
$78$	14.4094	−	14.4094i	0.184736	−	0.184736i
$79$	−37.4851	+	21.6420i	−0.474495	+	0.273950i	−0.718119	−	0.695920i	$-0.754997\pi$
$79$	−37.4851	+	21.6420i	−0.474495	+	0.273950i	0.243625	+	0.969870i	$0.421663\pi$
$80$		0			0
$81$	22.9317	−	39.7188i	0.283107	−	0.490356i
$82$	16.7671	−	62.5758i	0.204477	−	0.763120i
$83$	35.1320	−	35.1320i	0.423277	−	0.423277i	−0.463053	−	0.886331i	$-0.653246\pi$
$83$	35.1320	−	35.1320i	0.423277	−	0.423277i	0.886331	+	0.463053i	$0.153246\pi$
$84$	−8.28136	−	14.1467i	−0.0985876	−	0.168413i
$85$		0			0
$86$	−18.2199	−	31.5578i	−0.211860	−	0.366951i
$87$	28.5448	−	7.64857i	0.328102	−	0.0879146i
$88$	8.88175	+	33.1471i	0.100929	+	0.376672i
$89$	11.8780	−	6.85780i	0.133461	−	0.0770539i	−0.431783	−	0.901978i	$-0.642115\pi$
$89$	11.8780	−	6.85780i	0.133461	−	0.0770539i	0.565244	+	0.824924i	$0.308782\pi$
$90$		0			0
$91$	0.517689	+	86.1433i	0.00568889	+	0.946630i
$92$	44.1446	+	44.1446i	0.479832	+	0.479832i
$93$	30.3645	+	8.13615i	0.326500	+	0.0874855i
$94$	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	0.940798	−	0.338967i	$-0.110077\pi$
$97$	58.3777	+	58.3777i	0.601832	+	0.601832i	−0.338967	+	0.940798i	$0.610077\pi$
$98$	67.1460	+	17.1295i	0.685163	+	0.174790i
$99$			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	$0.152021\pi$
$102$	−8.95822	+	2.40035i	−0.0878257	+	0.0235328i
$103$	43.9758	+	11.7833i	0.426950	+	0.114401i	0.465894	−	0.884841i	$-0.345733\pi$
$103$	43.9758	+	11.7833i	0.426950	+	0.114401i	−0.0389443	+	0.999241i	$0.512399\pi$
$104$		−	34.8078i		−	0.334690i
$105$		0			0
$106$	46.9017			0.442469
$107$	−17.8577	+	66.6460i	−0.166895	+	0.622860i	0.830896	+	0.556428i	$0.187828\pi$
$107$	−17.8577	+	66.6460i	−0.166895	+	0.622860i	−0.997791	+	0.0664323i	$0.978838\pi$
$108$	10.0788	+	37.6145i	0.0933219	+	0.348282i
$109$	145.704	+	84.1220i	1.33673	+	0.771761i	0.986321	−	0.164836i	$-0.0527094\pi$
$109$	145.704	+	84.1220i	1.33673	+	0.771761i	0.350409	+	0.936597i	$0.386043\pi$
$110$		0			0
$111$	67.3774			0.607003
$112$	−27.0890	−	7.08427i	−0.241866	−	0.0632524i
$113$	−133.637	+	133.637i	−1.18263	+	1.18263i	−0.203573	+	0.979060i	$0.565255\pi$
$113$	−133.637	+	133.637i	−1.18263	+	1.18263i	−0.979060	+	0.203573i	$0.934745\pi$
$114$	−44.5605	+	25.7270i	−0.390881	+	0.225675i
$115$		0			0
$116$	25.2388	−	43.7150i	0.217576	−	0.376853i
$117$	24.2995	−	90.6869i	0.207688	−	0.775101i
$118$	−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
$122$	103.268	−	27.6705i	0.846457	−	0.226807i
$123$	13.8822	+	51.8091i	0.112863	+	0.421212i
$124$	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	0.969313	−	0.245829i	$-0.0790601\pi$
$127$	91.8825	+	91.8825i	0.723484	+	0.723484i	−0.245829	+	0.969313i	$0.579060\pi$
$128$	10.9282	+	2.92820i	0.0853766	+	0.0228766i
$129$	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
$133$	55.0332	−	210.437i	0.413784	−	1.58224i
$134$			79.3269i			0.591992i
$135$		0			0
$136$	−7.92070	+	13.7191i	−0.0582404	+	0.100875i
$137$	−29.5092	+	7.90696i	−0.215395	+	0.0577150i	−0.364903	−	0.931046i	$-0.618898\pi$
$137$	−29.5092	+	7.90696i	−0.215395	+	0.0577150i	0.149508	+	0.988761i	$0.452231\pi$
$138$	−49.9270	−	13.3779i	−0.361790	−	0.0969413i
$139$		−	254.693i		−	1.83232i	−0.400809	−	0.916162i	$-0.631271\pi$
$139$		−	254.693i		−	1.83232i	0.400809	−	0.916162i	$-0.368729\pi$
$140$		0			0
$141$	−6.55787			−0.0465097
$142$	−8.15819	+	30.4468i	−0.0574520	+	0.214414i
$143$	38.6442	+	144.222i	0.270239	+	1.00855i
$144$	26.4277	+	15.2581i	0.183526	+	0.105959i
$145$		0			0
$146$	−4.71207			−0.0322744
$147$	−55.2359	+	15.5143i	−0.375755	+	0.105540i
$148$	81.3794	−	81.3794i	0.549861	−	0.549861i
$149$	−231.769	+	133.812i	−1.55550	+	0.898067i	−0.557819	+	0.829962i	$0.688362\pi$
$149$	−231.769	+	133.812i	−1.55550	+	0.898067i	−0.997678	+	0.0681047i	$0.978305\pi$
$150$		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	$0.198279\pi$
$152$	−22.7474	+	84.8943i	−0.149654	+	0.558515i
$153$	−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
$157$	223.097	−	59.7786i	1.42100	−	0.380755i	0.535160	−	0.844751i	$-0.320251\pi$
$157$	223.097	−	59.7786i	1.42100	−	0.380755i	0.885838	+	0.463995i	$0.153585\pi$
$158$	−15.8431	−	59.1271i	−0.100272	−	0.374222i
$159$	−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
$163$	173.332	+	46.4442i	1.06339	+	0.284934i	0.747773	−	0.663954i	$-0.231123\pi$
$163$	173.332	+	46.4442i	1.06339	+	0.284934i	0.315614	+	0.948888i	$0.397790\pi$
$164$	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	0.440521	−	0.897742i	$-0.354794\pi$
$167$	−76.3559	−	76.3559i	−0.457221	−	0.457221i	−0.897742	+	0.440521i	$0.854794\pi$
$168$	22.3560	−	6.13449i	0.133071	−	0.0365148i
$169$			17.5523i			0.103860i
$170$		0			0
$171$	−118.530	+	205.300i	−0.693159	+	1.20059i
$172$	49.7777	−	13.3379i	0.289405	−	0.0775460i
$173$	−20.6797	−	5.54111i	−0.119536	−	0.0320296i	0.198555	−	0.980090i	$-0.436375\pi$
$173$	−20.6797	−	5.54111i	−0.119536	−	0.0320296i	−0.318091	+	0.948060i	$0.603042\pi$
$174$			41.7925i			0.240187i
$175$		0			0
$176$	−48.5308			−0.275743
$177$	17.8529	−	66.6279i	0.100864	−	0.376429i
$178$	5.02025	+	18.7358i	0.0282037	+	0.105258i
$179$	−142.223	−	82.1127i	−0.794544	−	0.458730i	0.0470161	−	0.998894i	$-0.485029\pi$
$179$	−142.223	−	82.1127i	−0.794544	−	0.458730i	−0.841560	+	0.540164i	$0.818362\pi$
$180$		0			0
$181$	266.876			1.47446			0.737228	−	0.675644i	$-0.236135\pi$
$181$	266.876			1.47446			0.737228	+	0.675644i	$0.236135\pi$
$182$	−117.863	−	30.8235i	−0.647601	−	0.169360i
$183$	−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
$187$	17.5874	−	65.6371i	0.0940503	−	0.351001i
$188$	−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	$-0.334879\pi$
$192$	−9.04791	+	2.42438i	−0.0471245	+	0.0126270i
$193$	−39.9124	−	148.955i	−0.206800	−	0.771787i	−0.988893	−	0.148626i	$-0.952515\pi$
$193$	−39.9124	−	148.955i	−0.206800	−	0.771787i	0.782094	−	0.623161i	$-0.214152\pi$
$194$	−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	0.264246	−	0.964455i	$-0.414877\pi$
$197$	−137.941	−	137.941i	−0.700210	−	0.700210i	−0.964455	+	0.264246i	$0.914877\pi$
$198$	−126.440	−	33.8795i	−0.638587	−	0.171109i
$199$	53.0439	+	30.6249i	0.266552	+	0.153894i	0.627320	−	0.778762i	$-0.284152\pi$
$199$	53.0439	+	30.6249i	0.266552	+	0.153894i	−0.360767	+	0.932656i	$0.617485\pi$
$200$		0			0
$201$	−32.8390	−	56.8788i	−0.163378	−	0.282979i
$202$	9.29104	+	9.29104i	0.0459953	+	0.0459953i
$203$	−125.674	−	124.173i	−0.619086	−	0.611689i
$204$		−	13.1157i		−	0.0642929i
$205$		0			0
$206$	−32.1925	+	55.7591i	−0.156274	+	0.270675i
$207$	−230.025	+	61.6351i	−1.11123	+	0.297754i
$208$	47.5483	+	12.7405i	0.228598	+	0.0612526i
$209$		−	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	$0.613597\pi$
$212$	−17.1672	+	64.0690i	−0.0809775	+	0.302212i
$213$	−6.75450	−	25.2081i	−0.0317113	−	0.118348i
$214$	−84.5037	−	48.7883i	−0.394877	−	0.227983i
$215$		0			0
$216$	−55.0714			−0.254960
$217$	−49.7311	−	181.235i	−0.229175	−	0.835185i
$218$	−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
$222$	−24.6618	+	92.0392i	−0.111089	+	0.414591i
$223$	168.214	−	168.214i	0.754322	−	0.754322i	−0.220961	−	0.975283i	$-0.570919\pi$
$223$	168.214	−	168.214i	0.754322	−	0.754322i	0.975283	+	0.220961i	$0.0709192\pi$
$224$	19.5925	−	34.4112i	0.0874667	−	0.153622i
$225$		0			0
$226$	−133.637	−	231.467i	−0.591316	−	1.02419i
$227$	−341.611	+	91.5345i	−1.50490	+	0.403236i	−0.914736	−	0.404051i	$-0.867602\pi$
$227$	−341.611	+	91.5345i	−1.50490	+	0.403236i	−0.590159	+	0.807287i	$0.700935\pi$
$228$	−18.8335	−	70.2875i	−0.0826030	−	0.308278i
$229$	168.586	−	97.3332i	0.736184	−	0.425036i	−0.0844964	−	0.996424i	$-0.526928\pi$
$229$	168.586	−	97.3332i	0.736184	−	0.425036i	0.820680	+	0.571388i	$0.193595\pi$
$230$		0			0
$231$	−85.8189	+	50.2376i	−0.371510	+	0.217479i
$232$	50.4777	+	50.4777i	0.217576	+	0.217576i
$233$	−299.146	−	80.1559i	−1.28389	−	0.344017i	−0.448552	−	0.893757i	$-0.648060\pi$
$233$	−299.146	−	80.1559i	−1.28389	−	0.344017i	−0.835336	+	0.549740i	$0.814727\pi$
$234$	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
$238$	39.4404	+	38.9692i	0.165716	+	0.163736i
$239$		−	17.4917i		−	0.0731870i	−0.999330	−	0.0365935i	$-0.988349\pi$
$239$		−	17.4917i		−	0.0731870i	0.999330	−	0.0365935i	$-0.0116507\pi$
$240$		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	$0.231397\pi$
$242$	35.7929	−	9.59067i	0.147904	−	0.0396309i
$243$	−221.136	−	59.2532i	−0.910025	−	0.243840i
$244$			151.194i			0.619649i
$245$		0			0
$246$	−75.8537			−0.308348
$247$	−98.9732	+	369.373i	−0.400701	+	1.49544i
$248$	19.6539	+	73.3495i	0.0792498	+	0.295764i
$249$	−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	$0.486042\pi$
$252$	75.0683	−	75.9760i	0.297890	−	0.301492i
$253$	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
$257$	−68.3382	+	255.042i	−0.265908	+	0.992380i	0.695785	+	0.718250i	$0.255057\pi$
$257$	−68.3382	+	255.042i	−0.265908	+	0.992380i	−0.961693	+	0.274130i	$0.911610\pi$
$258$	−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
$262$	143.242	−	38.3816i	0.546726	−	0.146495i
$263$	67.1391	+	250.567i	0.255282	+	0.952724i	0.967934	+	0.251207i	$0.0808273\pi$
$263$	67.1391	+	250.567i	0.255282	+	0.952724i	−0.712652	+	0.701518i	$0.752506\pi$
$264$	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
$268$	−108.363	−	29.0357i	−0.404338	−	0.108342i
$269$	332.165	+	191.775i	1.23481	+	0.712920i	0.968029	−	0.250837i	$-0.0807057\pi$
$269$	332.165	+	191.775i	1.23481	+	0.712920i	0.266784	+	0.963756i	$0.414039\pi$
$270$		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
$273$	97.2702	−	26.6910i	0.356301	−	0.0977693i
$274$		−	43.2044i		−	0.157680i
$275$		0			0
$276$	36.5491	−	63.3049i	0.132424	−	0.229366i
$277$	−370.628	+	99.3094i	−1.33801	+	0.358518i	−0.855694	−	0.517482i	$-0.826870\pi$
$277$	−370.628	+	99.3094i	−1.33801	+	0.358518i	−0.482312	+	0.876000i	$0.660203\pi$
$278$	347.917	+	93.2241i	1.25150	+	0.335338i
$279$			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	$0.476266\pi$
$282$	2.40035	−	8.95822i	0.00851187	−	0.0317667i
$283$	23.4794	+	87.6264i	0.0829662	+	0.309634i	0.994921	−	0.100656i	$-0.0320941\pi$
$283$	23.4794	+	87.6264i	0.0829662	+	0.309634i	−0.911955	+	0.410290i	$0.865427\pi$
$284$	−38.6050	−	22.2886i	−0.135933	−	0.0784809i
$285$		0			0
$286$	−211.156			−0.738308
$287$	225.375	−	228.100i	0.785277	−	0.794773i
$288$	−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
$292$	1.72474	−	6.43680i	0.00590663	−	0.0220438i
$293$	238.524	−	238.524i	0.814077	−	0.814077i	−0.171166	−	0.985242i	$-0.554753\pi$
$293$	238.524	−	238.524i	0.814077	−	0.814077i	0.985242	+	0.171166i	$0.0547533\pi$
$294$	−0.975185	−	81.1323i	−0.00331696	−	0.275960i
$295$		0			0
$296$	81.3794	+	140.953i	0.274931	+	0.476194i
$297$	228.182	−	61.1413i	0.768291	−	0.205863i
$298$	−97.9572	−	365.581i	−0.328715	−	1.22678i
$299$	−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
$303$	−10.5081	−	2.81563i	−0.0346801	−	0.00929249i
$304$	−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	−0.999323	−	0.0367853i	$-0.988288\pi$
$307$	−318.085	−	318.085i	−1.03611	−	1.03611i	−0.0367853	−	0.999323i	$-0.511712\pi$
$308$	−42.9756	+	164.331i	−0.139531	+	0.533543i
$309$		−	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	$0.314558\pi$
$312$	−39.3672	+	10.5484i	−0.126177	+	0.0338090i
$313$	−290.116	−	77.7362i	−0.926887	−	0.248359i	−0.236360	−	0.971666i	$-0.575955\pi$
$313$	−290.116	−	77.7362i	−0.926887	−	0.248359i	−0.690527	+	0.723307i	$0.742621\pi$
$314$			326.636i			1.04024i
$315$		0			0
$316$	86.5681			0.273950
$317$	14.3109	−	53.4088i	0.0451446	−	0.168482i	−0.939673	−	0.342074i	$-0.888871\pi$
$317$	14.3109	−	53.4088i	0.0451446	−	0.168482i	0.984818	+	0.173592i	$0.0555373\pi$
$318$	−14.2134	−	53.0453i	−0.0446964	−	0.166809i
$319$	−265.190	−	153.108i	−0.831317	−	0.479961i
$320$		0			0
$321$	80.7876			0.251675
$322$	81.7705	+	297.997i	0.253946	+	0.925456i
$323$	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
$327$	50.9859	−	190.282i	0.155920	−	0.581902i
$328$	−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	$0.733050\pi$
$332$	−95.9825	+	25.7184i	−0.289104	+	0.0774651i
$333$	113.623	+	424.046i	0.341209	+	1.27341i
$334$	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	0.978052	+	0.208363i	$0.0668134\pi$
$337$	399.822	+	399.822i	1.18641	+	1.18641i	0.208363	+	0.978052i	$0.433187\pi$
$338$	−23.9769	−	6.42458i	−0.0709374	−	0.0190076i
$339$	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
$343$	246.871	+	238.126i	0.719739	+	0.694244i
$344$			72.8797i			0.211860i
$345$		0			0
$346$	15.1386	−	26.2208i	0.0437532	−	0.0757828i
$347$	459.142	−	123.027i	1.32318	−	0.354544i	0.473009	−	0.881058i	$-0.343168\pi$
$347$	459.142	−	123.027i	1.32318	−	0.354544i	0.850167	+	0.526514i	$0.176501\pi$
$348$	−57.0897	−	15.2971i	−0.164051	−	0.0439573i
$349$		−	282.718i		−	0.810080i	−0.914299	−	0.405040i	$-0.867258\pi$
$349$		−	282.718i		−	0.810080i	0.914299	−	0.405040i	$-0.132742\pi$
$350$		0			0
$351$	−239.614			−0.682662
$352$	17.7635	−	66.2943i	0.0504645	−	0.188336i
$353$	72.0991	+	269.078i	0.204247	+	0.762259i	0.989678	+	0.143310i	$0.0457747\pi$
$353$	72.0991	+	269.078i	0.204247	+	0.762259i	−0.785431	+	0.618949i	$0.787559\pi$
$354$	84.4808	+	48.7750i	0.238646	+	0.137783i
$355$		0			0
$356$	−27.4312			−0.0770539
$357$	−44.4115	−	11.6144i	−0.124402	−	0.0325334i
$358$	164.225	−	164.225i	0.458730	−	0.458730i
$359$	582.216	−	336.143i	1.62177	−	0.936330i	0.635326	−	0.772244i	$-0.280866\pi$
$359$	582.216	−	336.143i	1.62177	−	0.936330i	0.986446	−	0.164086i	$-0.0524675\pi$
$360$		0			0
$361$	302.281	−	523.565i	0.837343	−	1.45032i
$362$	−97.6835	+	364.560i	−0.269844	+	1.00707i
$363$	−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
$367$	111.422	−	29.8554i	0.303602	−	0.0813499i	−0.103802	−	0.994598i	$-0.533101\pi$
$367$	111.422	−	29.8554i	0.303602	−	0.0813499i	0.407404	+	0.913248i	$0.366434\pi$
$368$	−32.3161	−	120.605i	−0.0878154	−	0.327732i
$369$	−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
$373$	−27.9301	−	7.48386i	−0.0748797	−	0.0200640i	0.221185	−	0.975232i	$-0.429008\pi$
$373$	−27.9301	−	7.48386i	−0.0748797	−	0.0200640i	−0.296064	+	0.955168i	$0.595674\pi$
$374$	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
$378$	−48.7676	+	186.479i	−0.129015	+	0.493330i
$379$			203.578i			0.537145i	0.963259	+	0.268573i	$0.0865519\pi$
$379$			203.578i			0.537145i	−0.963259	+	0.268573i	$0.913448\pi$
$380$		0			0
$381$	76.0733	−	131.763i	0.199667	−	0.345834i
$382$	263.102	−	70.4978i	0.688748	−	0.184549i
$383$	−248.929	−	66.7003i	−0.649945	−	0.174152i	−0.0812409	−	0.996694i	$-0.525888\pi$
$383$	−248.929	−	66.7003i	−0.649945	−	0.174152i	−0.568704	+	0.822542i	$0.692555\pi$
$384$		−	13.2471i		−	0.0344975i
$385$		0			0
$386$	218.085			0.564988
$387$	−50.8776	+	189.878i	−0.131467	+	0.490641i
$388$	−42.7354	−	159.491i	−0.110143	−	0.411059i
$389$	272.609	+	157.391i	0.700793	+	0.404603i	0.807643	−	0.589672i	$-0.200743\pi$
$389$	272.609	+	157.391i	0.700793	+	0.404603i	−0.106850	+	0.994275i	$0.534076\pi$
$390$		0			0
$391$	174.828			0.447130
$392$	−99.1708	−	96.8151i	−0.252987	−	0.246977i
$393$	−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
$397$	5.61021	−	20.9376i	0.0141315	−	0.0527395i	−0.958500	−	0.285092i	$-0.907976\pi$
$397$	5.61021	−	20.9376i	0.0141315	−	0.0527395i	0.972632	+	0.232353i	$0.0746424\pi$
$398$	−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	$-0.425327\pi$
$402$	89.7178	−	24.0398i	0.223179	−	0.0598005i
$403$	85.5138	+	319.142i	0.212193	+	0.791915i
$404$	−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
$408$	17.9164	+	4.80069i	0.0439128	+	0.0117664i
$409$	320.292	+	184.921i	0.783109	+	0.452128i	0.837531	−	0.546390i	$-0.183998\pi$
$409$	320.292	+	184.921i	0.783109	+	0.452128i	−0.0544217	+	0.998518i	$0.517332\pi$
$410$		0			0
$411$	17.8853	+	30.9783i	0.0435167	+	0.0753731i
$412$	−64.3851	−	64.3851i	−0.156274	−	0.156274i
$413$	−397.679	+	109.123i	−0.962902	+	0.264221i
$414$		−	336.780i		−	0.813479i
$415$		0			0
$416$	−34.8078	+	60.2889i	−0.0836726	+	0.144925i
$417$	−288.055	+	77.1840i	−0.690779	+	0.185094i
$418$	514.998	+	137.993i	1.23205	+	0.330128i
$419$		−	29.9924i		−	0.0715809i	−0.999359	−	0.0357904i	$-0.988605\pi$
$419$		−	29.9924i		−	0.0715809i	0.999359	−	0.0357904i	$-0.0113949\pi$
$420$		0			0
$421$	−59.1882			−0.140590			−0.0702948	−	0.997526i	$-0.522394\pi$
$421$	−59.1882			−0.140590			−0.0702948	+	0.997526i	$0.522394\pi$
$422$	53.9612	−	201.386i	0.127870	−	0.477218i
$423$	−11.0590	−	41.2726i	−0.0261441	−	0.0975711i
$424$	−81.2362	−	46.9017i	−0.191595	−	0.110617i
$425$		0			0
$426$	36.9073			0.0866368
$427$	511.963	+	133.888i	1.19898	+	0.313555i
$428$	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	$0.879806\pi$
$432$	20.1575	−	75.2289i	0.0466610	−	0.174141i
$433$	202.377	−	202.377i	0.467382	−	0.467382i	−0.433683	−	0.901065i	$-0.642786\pi$
$433$	202.377	−	202.377i	0.467382	−	0.467382i	0.901065	+	0.433683i	$0.142786\pi$
$434$	265.775	−	1.59721i	0.612384	−	0.00368020i
$435$		0			0
$436$	−168.244	−	291.407i	−0.385881	−	0.668365i
$437$	936.906	−	251.043i	2.14395	−	0.574470i
$438$	1.42798	+	5.32929i	0.00326023	+	0.0121673i
$439$	−137.892	+	79.6122i	−0.314106	+	0.181349i	−0.648762	−	0.760991i	$-0.724713\pi$
$439$	−137.892	+	79.6122i	−0.314106	+	0.181349i	0.334657	+	0.942340i	$0.391380\pi$
$440$		0			0
$441$	−190.789	−	321.470i	−0.432627	−	0.728957i
$442$	−68.9255	−	68.9255i	−0.155940	−	0.155940i
$443$	−144.806	−	38.8006i	−0.326875	−	0.0875859i	0.0916496	−	0.995791i	$-0.470786\pi$
$443$	−144.806	−	38.8006i	−0.326875	−	0.0875859i	−0.418525	+	0.908205i	$0.637453\pi$
$444$	−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
$448$	39.8352	+	39.3593i	0.0889179	+	0.0878556i
$449$			634.911i			1.41406i	0.707185	+	0.707028i	$0.249965\pi$
$449$			634.911i			1.41406i	−0.707185	+	0.707028i	$0.750035\pi$
$450$		0			0
$451$	277.891	−	481.322i	0.616167	−	1.06723i
$452$	365.104	−	97.8294i	0.807753	−	0.216437i
$453$	33.8658	+	9.07433i	0.0747590	+	0.0200316i
$454$		−	500.154i		−	1.10166i
$455$		0			0
$456$	102.908			0.225675
$457$	51.8803	−	193.620i	0.113524	−	0.423676i	−0.885649	−	0.464356i	$-0.846286\pi$
$457$	51.8803	−	193.620i	0.113524	−	0.423676i	0.999172	+	0.0406802i	$0.0129525\pi$
$458$	71.2529	+	265.919i	0.155574	+	0.580610i
$459$	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	$0.645226\pi$
$462$	−37.2139	−	135.619i	−0.0805497	−	0.293548i
$463$	−288.227	+	288.227i	−0.622520	+	0.622520i	−0.946175	−	0.323655i	$-0.895088\pi$
$463$	−288.227	+	288.227i	−0.622520	+	0.622520i	0.323655	+	0.946175i	$0.395088\pi$
$464$	−87.4299	+	50.4777i	−0.188427	+	0.108788i
$465$		0			0
$466$	218.990	−	379.302i	0.469936	−	0.813952i
$467$	−21.9936	+	82.0814i	−0.0470956	+	0.175763i	−0.985468	−	0.169864i	$-0.945667\pi$
$467$	−21.9936	+	82.0814i	−0.0470956	+	0.175763i	0.938372	+	0.345627i	$0.112334\pi$
$468$	−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
$472$	160.948	−	43.1260i	0.340993	−	0.0913687i
$473$	−80.9123	−	301.969i	−0.171062	−	0.638412i
$474$	−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
$478$	23.8941	+	6.40240i	0.0499876	+	0.0133942i
$479$	21.9122	+	12.6510i	0.0457458	+	0.0264114i	0.522698	−	0.852518i	$-0.324925\pi$
$479$	21.9122	+	12.6510i	0.0457458	+	0.0264114i	−0.476953	+	0.878929i	$0.658259\pi$
$480$		0			0
$481$	354.080	+	613.284i	0.736132	+	1.27502i
$482$	−97.3430	−	97.3430i	−0.201956	−	0.201956i
$483$	−181.993	−	179.818i	−0.376796	−	0.372295i
$484$			52.4044i			0.108274i
$485$		0			0
$486$	161.883	−	280.389i	0.333092	−	0.576933i
$487$	−213.967	+	57.3322i	−0.439357	+	0.117725i	−0.471715	−	0.881751i	$-0.656365\pi$
$487$	−213.967	+	57.3322i	−0.439357	+	0.117725i	0.0323584	+	0.999476i	$0.489698\pi$
$488$	−206.535	−	55.3410i	−0.423228	−	0.113404i
$489$		−	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	$0.629312\pi$
$492$	27.7644	−	103.618i	0.0564317	−	0.210606i
$493$	−36.5859	−	136.541i	−0.0742108	−	0.276959i
$494$	−468.346	−	270.400i	−0.948069	−	0.547368i
$495$		0			0
$496$	−107.391			−0.216514
$497$	−109.658	+	110.984i	−0.220640	+	0.223308i
$498$	58.1745	−	58.1745i	0.116816	−	0.116816i
$499$	−73.8171	+	42.6183i	−0.147930	+	0.0854075i	−0.572138	−	0.820157i	$-0.693886\pi$
$499$	−73.8171	+	42.6183i	−0.147930	+	0.0854075i	0.424208	+	0.905565i	$0.360553\pi$
$500$		0			0
$501$	−63.2182	+	109.497i	−0.126184	+	0.218557i
$502$	−8.05442	+	30.0595i	−0.0160447	+	0.0598795i
$503$	25.3086	−	25.3086i	0.0503154	−	0.0503154i	−0.681501	−	0.731817i	$-0.738673\pi$
$503$	25.3086	−	25.3086i	0.0503154	−	0.0503154i	0.731817	+	0.681501i	$0.238673\pi$
$504$	76.3083	+	130.354i	0.151405	+	0.258640i
$505$		0			0
$506$	267.796	+	463.837i	0.529242	+	0.916673i
$507$	19.8514	−	5.31917i	0.0391547	−	0.0104915i
$508$	−67.2627	−	251.028i	−0.132407	−	0.494149i
$509$	487.485	−	281.450i	0.957731	−	0.552946i	0.0622572	−	0.998060i	$-0.480170\pi$
$509$	487.485	−	281.450i	0.957731	−	0.552946i	0.895474	+	0.445114i	$0.146837\pi$
$510$		0			0
$511$	−20.2685	−	11.5402i	−0.0396644	−	0.0225835i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	584.406	+	156.591i	1.13919	+	0.305246i
$514$	−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
$518$	549.349	−	150.742i	1.06052	−	0.291007i
$519$			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	$0.110617\pi$
$522$	−263.025	+	70.4774i	−0.503880	+	0.135014i
$523$	333.855	+	89.4563i	0.638347	+	0.171044i	0.563454	−	0.826147i	$-0.309472\pi$
$523$	333.855	+	89.4563i	0.638347	+	0.171044i	0.0748922	+	0.997192i	$0.476139\pi$
$524$			209.721i			0.400231i
$525$		0			0
$526$	−366.855			−0.697443
$527$	38.9182	−	145.245i	0.0738487	−	0.275607i
$528$	14.7071	+	54.8877i	0.0278544	+	0.103954i
$529$	385.703	+	222.686i	0.729118	+	0.420956i
$530$		0			0
$531$	449.435			0.846394
$532$	−305.758	+	309.455i	−0.574732	+	0.581682i
$533$	−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
$537$	−49.7681	+	185.737i	−0.0926779	+	0.345879i
$538$	−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	$0.619385\pi$
$542$	−569.540	+	152.608i	−1.05081	+	0.281564i
$543$	−80.8762	−	301.834i	−0.148943	−	0.555864i
$544$	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	0.909054	−	0.416678i	$-0.136806\pi$
$547$	269.330	+	269.330i	0.492377	+	0.492377i	−0.416678	+	0.909054i	$0.636806\pi$
$548$	59.0183	+	15.8139i	0.107698	+	0.0288575i
$549$	−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
$553$	76.6589	−	293.130i	0.138624	−	0.530073i
$554$		−	542.637i		−	0.979489i
$555$		0			0
$556$	−254.693	+	441.141i	−0.458081	+	0.793419i
$557$	31.9552	−	8.56238i	0.0573703	−	0.0153723i	−0.230020	−	0.973186i	$-0.573879\pi$
$557$	31.9552	−	8.56238i	0.0573703	−	0.0153723i	0.287390	+	0.957814i	$0.407212\pi$
$558$	−279.793	−	74.9702i	−0.501421	−	0.134355i
$559$			317.097i			0.567258i
$560$		0			0
$561$	−79.5646			−0.141826
$562$	−15.3238	+	57.1893i	−0.0272666	+	0.101760i
$563$	33.5416	+	125.179i	0.0595766	+	0.222343i	0.989295	−	0.145928i	$-0.0466167\pi$
$563$	33.5416	+	125.179i	0.0595766	+	0.222343i	−0.929719	+	0.368271i	$0.879950\pi$
$564$	11.3586	+	6.55787i	0.0201393	+	0.0116274i
$565$		0			0
$566$	−128.294			−0.226668
$567$	84.9542	+	309.599i	0.149831	+	0.546030i
$568$	44.5772	−	44.5772i	0.0784809	−	0.0784809i
$569$	−781.667	+	451.296i	−1.37376	+	0.793139i	−0.991399	−	0.130876i	$-0.958221\pi$
$569$	−781.667	+	451.296i	−1.37376	+	0.793139i	−0.382358	+	0.924014i	$0.624888\pi$
$570$		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	$0.229108\pi$
$572$	77.2885	−	288.445i	0.135120	−	0.504274i
$573$	−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
$577$	−971.962	+	260.437i	−1.68451	+	0.451363i	−0.968964	−	0.247202i	$-0.920489\pi$
$577$	−971.962	+	260.437i	−1.68451	+	0.451363i	−0.715546	+	0.698565i	$0.753822\pi$
$578$	−94.2996	−	351.931i	−0.163148	−	0.608877i
$579$	−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
$583$	388.665	+	104.142i	0.666663	+	0.178632i
$584$	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	0.997538	−	0.0701276i	$-0.0223407\pi$
$587$	544.390	+	544.390i	0.927410	+	0.927410i	−0.0701276	+	0.997538i	$0.522341\pi$
$588$	111.186	+	28.3644i	0.189091	+	0.0482387i
$589$		−	834.254i		−	1.41639i
$590$		0			0
$591$	−114.207	+	197.813i	−0.193244	+	0.334708i
$592$	−222.333	+	59.5739i	−0.375562	+	0.100632i
$593$	−577.944	−	154.860i	−0.974610	−	0.261146i	−0.263837	−	0.964567i	$-0.584988\pi$
$593$	−577.944	−	154.860i	−0.974610	−	0.261146i	−0.710773	+	0.703421i	$0.751655\pi$
$594$			334.082i			0.562428i
$595$		0			0
$596$	535.248			0.898067
$597$	18.5616	−	69.2729i	0.0310915	−	0.116035i
$598$	−140.606	−	524.750i	−0.235128	−	0.877508i
$599$	350.560	+	202.396i	0.585243	+	0.337890i	0.763214	−	0.646146i	$-0.223620\pi$
$599$	350.560	+	202.396i	0.585243	+	0.337890i	−0.177972	+	0.984036i	$0.556953\pi$
$600$		0			0
$601$	−808.864			−1.34586			−0.672932	−	0.739705i	$-0.734965\pi$
$601$	−808.864			−1.34586			−0.672932	+	0.739705i	$0.734965\pi$
$602$	246.780	+	64.5374i	0.409933	+	0.107205i
$603$	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
$607$	−103.592	+	386.611i	−0.170662	+	0.636920i	0.826588	+	0.562808i	$0.190279\pi$
$607$	−103.592	+	386.611i	−0.170662	+	0.636920i	−0.997250	+	0.0741122i	$0.976388\pi$
$608$	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
$612$	82.5451	−	22.1179i	0.134878	−	0.0361404i
$613$	47.3611	+	176.754i	0.0772613	+	0.288343i	0.993737	−	0.111748i	$-0.0356451\pi$
$613$	47.3611	+	176.754i	0.0772613	+	0.288343i	−0.916475	+	0.400091i	$0.868978\pi$
$614$	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	0.431737	−	0.902000i	$-0.357901\pi$
$617$	−290.152	−	290.152i	−0.470263	−	0.470263i	−0.902000	+	0.431737i	$0.857901\pi$
$618$	72.8187	+	19.5117i	0.117830	+	0.0315724i
$619$	−982.654	−	567.335i	−1.58749	−	0.916535i	−0.993720	−	0.111898i	$-0.964307\pi$
$619$	−982.654	−	567.335i	−1.58749	−	0.916535i	−0.593766	−	0.804638i	$-0.702360\pi$
$620$		0			0
$621$	303.888	+	526.349i	0.489353	+	0.847584i
$622$	−278.705	−	278.705i	−0.448079	−	0.448079i
$623$	−24.2912	+	92.8854i	−0.0389907	+	0.149094i
$624$		−	57.6376i		−	0.0923679i
$625$		0			0
$626$	212.379	−	367.852i	0.339264	−	0.587623i
$627$	−426.388	+	114.250i	−0.680045	+	0.182218i
$628$	−446.193	−	119.557i	−0.710499	−	0.190378i
$629$		−	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	$0.353393\pi$
$632$	−31.6861	+	118.254i	−0.0501362	+	0.187111i
$633$	44.6767	+	166.736i	0.0705793	+	0.263405i
$634$	67.7197	+	39.0980i	0.106813	+	0.0616687i
$635$		0			0
$636$	77.6637			0.122113
$637$	−431.489	−	421.240i	−0.677377	−	0.661287i
$638$	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	$0.921631\pi$
$642$	−29.5703	+	110.358i	−0.0460597	+	0.171897i
$643$	−139.636	+	139.636i	−0.217163	+	0.217163i	−0.807302	−	0.590139i	$-0.799073\pi$
$643$	−139.636	+	139.636i	−0.217163	+	0.217163i	0.590139	+	0.807302i	$0.299073\pi$
$644$	−437.001	+	2.62621i	−0.678573	+	0.00407797i
$645$		0			0
$646$	123.062	+	213.149i	0.190498	+	0.329953i
$647$	−1212.14	+	324.791i	−1.87347	+	0.501996i	−0.873592	+	0.486658i	$0.838216\pi$
$647$	−1212.14	+	324.791i	−1.87347	+	0.501996i	−0.999882	+	0.0153378i	$0.995118\pi$
$648$	−33.5743	−	125.301i	−0.0518122	−	0.193366i
$649$	−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
$653$	601.936	+	161.288i	0.921802	+	0.246996i	0.688355	−	0.725374i	$-0.258333\pi$
$653$	601.936	+	161.288i	0.921802	+	0.246996i	0.233446	+	0.972370i	$0.425000\pi$
$654$	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
$658$	−53.4685	+	14.6718i	−0.0812591	+	0.0222975i
$659$		−	251.197i		−	0.381180i	−0.981670	−	0.190590i	$-0.938960\pi$
$659$		−	251.197i		−	0.381180i	0.981670	−	0.190590i	$-0.0610401\pi$
$660$		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	$0.173412\pi$
$662$	−280.212	+	75.0825i	−0.423281	+	0.113418i
$663$	77.9539	+	20.8877i	0.117578	+	0.0315048i
$664$		−	140.528i		−	0.211639i
$665$		0			0
$666$	−620.846			−0.932201
$667$	203.905	−	760.984i	0.305705	−	1.14091i
$668$	55.8964	+	208.608i	0.0836773	+	0.312288i
$669$	−241.225	−	139.271i	−0.360575	−	0.208178i
$670$		0			0
$671$	917.198			1.36691
$672$	−44.8562	−	11.7307i	−0.0667502	−	0.0174564i
$673$	−21.1507	+	21.1507i	−0.0314275	+	0.0314275i	−0.722646	−	0.691218i	$-0.757074\pi$
$673$	−21.1507	+	21.1507i	−0.0314275	+	0.0314275i	0.691218	+	0.722646i	$0.257074\pi$
$674$	−692.511	+	399.822i	−1.02746	+	0.593207i
$675$		0			0
$676$	17.5523	−	30.4014i	0.0259649	−	0.0449725i
$677$	151.880	−	566.824i	0.224343	−	0.837259i	−0.758324	−	0.651878i	$-0.773981\pi$
$677$	151.880	−	566.824i	0.224343	−	0.837259i	0.982667	−	0.185381i	$-0.0593520\pi$
$678$	−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
$682$	444.963	−	119.228i	0.652439	−	0.174821i
$683$	−2.99308	−	11.1703i	−0.00438226	−	0.0163548i	0.963700	−	0.266987i	$-0.0860281\pi$
$683$	−2.99308	−	11.1703i	−0.00438226	−	0.0163548i	−0.968082	+	0.250632i	$0.919361\pi$
$684$	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
$688$	−99.5555	−	26.6758i	−0.144703	−	0.0387730i
$689$	−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
$693$	−460.897	−	455.390i	−0.665075	−	0.657129i
$694$			672.230i			0.968632i
$695$		0			0
$696$	41.7925	−	72.3868i	0.0600468	−	0.104004i
$697$	247.822	−	66.4037i	0.355555	−	0.0952708i
$698$	386.200	+	103.482i	0.553295	+	0.148255i
$699$			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	$0.358886\pi$
$702$	87.7049	−	327.319i	0.124936	−	0.466266i
$703$	−462.792	−	1727.16i	−0.658310	−	2.45685i
$704$	84.0578	+	48.5308i	0.119400	+	0.0689357i
$705$		0			0
$706$	−393.957			−0.558013
$707$	17.2101	+	62.7189i	0.0243424	+	0.0887113i
$708$	−97.5500	+	97.5500i	−0.137783	+	0.137783i
$709$	1202.79	−	694.434i	1.69647	−	0.979455i	0.747402	−	0.664372i	$-0.231301\pi$
$709$	1202.79	−	694.434i	1.69647	−	0.979455i	0.949064	−	0.315083i	$-0.102032\pi$
$710$		0			0
$711$	−165.108	+	285.975i	−0.232219	+	0.402215i
$712$	10.0405	−	37.4717i	0.0141018	−	0.0526288i
$713$	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
$717$	−19.7829	+	5.30081i	−0.0275912	+	0.00739304i
$718$	246.073	+	918.359i	0.342721	+	1.27905i
$719$	380.588	−	219.733i	0.529330	−	0.305609i	−0.211414	−	0.977397i	$-0.567807\pi$
$719$	380.588	−	219.733i	0.529330	−	0.305609i	0.740743	+	0.671788i	$0.234473\pi$
$720$		0			0
$721$	−275.031	+	161.001i	−0.381458	+	0.223302i
$722$	604.561	+	604.561i	0.837343	+	0.837343i
$723$	110.094	+	29.4995i	0.152273	+	0.0408016i
$724$	−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	0.959824	−	0.280604i	$-0.0905347\pi$
$727$	493.793	+	493.793i	0.679220	+	0.679220i	−0.280604	+	0.959824i	$0.590535\pi$
$728$	173.322	+	171.251i	0.238080	+	0.235235i
$729$		−	144.711i		−	0.198506i
$730$		0			0
$731$	72.1573	−	124.980i	0.0987103	−	0.170971i
$732$	170.999	−	45.8191i	0.233605	−	0.0625944i
$733$	326.331	+	87.4401i	0.445199	+	0.119291i	0.474452	−	0.880281i	$-0.342646\pi$
$733$	326.331	+	87.4401i	0.445199	+	0.119291i	−0.0292530	+	0.999572i	$0.509313\pi$
$734$			163.133i			0.222252i
$735$		0			0
$736$	176.578			0.239916
$737$	−176.140	+	657.365i	−0.238996	+	0.891947i
$738$	−127.917	−	477.393i	−0.173329	−	0.646873i
$739$	1077.39	+	622.034i	1.45791	+	0.841724i	0.998908	−	0.0467130i	$-0.0148746\pi$
$739$	1077.39	+	622.034i	1.45791	+	0.841724i	0.459000	+	0.888436i	$0.348208\pi$
$740$		0			0
$741$	447.750			0.604251
$742$	−230.752	+	233.543i	−0.310987	+	0.314748i
$743$	−286.451	+	286.451i	−0.385533	+	0.385533i	−0.873091	−	0.487558i	$-0.837888\pi$
$743$	−286.451	+	286.451i	−0.385533	+	0.385533i	0.487558	+	0.873091i	$0.337888\pi$
$744$	77.0014	−	44.4568i	0.103496	−	0.0597537i
$745$		0			0
$746$	20.4463	−	35.4140i	0.0274079	−	0.0474718i
$747$	98.1033	−	366.127i	0.131330	−	0.490129i
$748$	−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	$0.919608\pi$
$752$	21.6398	−	5.79835i	0.0287763	−	0.00771058i
$753$	−6.66858	−	24.8875i	−0.00885602	−	0.0330511i
$754$	−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	0.776967	−	0.629542i	$-0.216757\pi$
$757$	111.601	+	111.601i	0.147425	+	0.147425i	−0.629542	+	0.776967i	$0.716757\pi$
$758$	−278.093	−	74.5147i	−0.366877	−	0.0983044i
$759$	−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
$763$	−1135.73	+	311.644i	−1.48850	+	0.408446i
$764$			385.207i			0.504198i
$765$		0			0
$766$	182.229	−	315.629i	0.237896	−	0.412048i
$767$	700.282	−	187.640i	0.913015	−	0.244642i
$768$	18.0958	+	4.84876i	0.0235623	+	0.00631349i
$769$			967.610i			1.25827i	0.777296	+	0.629136i	$0.216591\pi$
$769$			967.610i			1.25827i	−0.777296	+	0.629136i	$0.783409\pi$
$770$		0			0
$771$	309.159			0.400984
$772$	−79.8247	+	297.910i	−0.103400	+	0.385894i
$773$	261.591	+	976.271i	0.338410	+	1.26296i	0.900125	+	0.435632i	$0.143475\pi$
$773$	261.591	+	976.271i	0.338410	+	1.26296i	−0.561715	+	0.827331i	$0.689858\pi$
$774$	−240.756	−	139.000i	−0.311054	−	0.179587i
$775$		0			0
$776$	233.511			0.300916
$777$	−331.491	+	335.499i	−0.426629	+	0.431788i
$778$	−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
$782$	−63.9915	+	238.819i	−0.0818305	+	0.305396i
$783$	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
$787$	−568.747	+	152.395i	−0.722677	+	0.193641i	−0.601366	−	0.798974i	$-0.705377\pi$
$787$	−568.747	+	152.395i	−0.722677	+	0.193641i	−0.121311	+	0.992615i	$0.538710\pi$
$788$	100.980	+	376.863i	0.128147	+	0.478252i
$789$	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
$793$	−898.630	−	240.787i	−1.13320	−	0.303641i
$794$	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	0.467788	−	0.883841i	$-0.345051\pi$
$797$	−331.594	−	331.594i	−0.416052	−	0.416052i	−0.883841	+	0.467788i	$0.845051\pi$
$798$	91.1285	−	348.459i	0.114196	−	0.436666i
$799$			31.3687i			0.0392600i
$800$		0			0
$801$	52.3183	−	90.6180i	0.0653162	−	0.113131i
$802$	795.461	−	213.143i	0.991846	−	0.265764i
$803$	−39.0479	−	10.4628i	−0.0486275	−	0.0130297i
$804$			131.356i			0.163378i
$805$		0			0
$806$	−467.256			−0.579722
$807$	116.234	−	433.791i	0.144032	−	0.537536i
$808$	−6.80151	−	25.3836i	−0.00841772	−	0.0314153i
$809$	−523.515	−	302.251i	−0.647114	−	0.373611i	0.140236	−	0.990118i	$-0.455214\pi$
$809$	−523.515	−	302.251i	−0.647114	−	0.373611i	−0.787350	+	0.616507i	$0.788547\pi$
$810$		0			0
$811$	−1186.18			−1.46262			−0.731309	−	0.682046i	$-0.761090\pi$
$811$	−1186.18			−1.46262			−0.731309	+	0.682046i	$0.761090\pi$
$812$	93.5015	+	340.748i	0.115150	+	0.419641i
$813$	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
$817$	207.228	−	773.384i	0.253645	−	0.946614i
$818$	−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	$0.610724\pi$
$822$	−48.8637	+	13.0930i	−0.0594449	+	0.0159282i
$823$	151.011	+	563.580i	0.183488	+	0.684788i	0.994949	+	0.100381i	$0.0320061\pi$
$823$	151.011	+	563.580i	0.183488	+	0.684788i	−0.811461	+	0.584407i	$0.801327\pi$
$824$	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	0.397803	−	0.917471i	$-0.369773\pi$
$827$	−429.765	−	429.765i	−0.519667	−	0.519667i	−0.917471	+	0.397803i	$0.869773\pi$
$828$	460.050	+	123.270i	0.555616	+	0.148877i
$829$	187.412	+	108.202i	0.226070	+	0.130522i	0.608758	−	0.793356i	$-0.291668\pi$
$829$	187.412	+	108.202i	0.226070	+	0.130522i	−0.382688	+	0.923878i	$0.625001\pi$
$830$		0			0
$831$	224.636	+	389.080i	0.270320	+	0.468207i
$832$	−69.6156	−	69.6156i	−0.0836726	−	0.0836726i
$833$	74.2107	+	264.214i	0.0890885	+	0.317184i
$834$		−	421.741i		−	0.505685i
$835$		0			0
$836$	−377.005	+	652.992i	−0.450963	+	0.781091i
$837$	504.933	−	135.296i	0.603265	−	0.161644i
$838$	40.9704	+	10.9780i	0.0488907	+	0.0131002i
$839$			44.2929i			0.0527925i	0.999652	+	0.0263963i	$0.00840316\pi$
$839$			44.2929i			0.0527925i	−0.999652	+	0.0263963i	$0.991597\pi$
$840$		0			0
$841$	204.001			0.242569
$842$	21.6644	−	80.8526i	0.0257297	−	0.0960245i
$843$	−12.6872	−	47.3494i	−0.0150501	−	0.0561677i
$844$	255.347	+	147.425i	0.302544	+	0.174674i
$845$		0			0
$846$	60.4272			0.0714270
$847$	177.448	+	46.4059i	0.209502	+	0.0547885i
$848$	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
$852$	−13.5090	+	50.4163i	−0.0158556	+	0.0591740i
$853$	−451.722	+	451.722i	−0.529568	+	0.529568i	−0.920444	−	0.390875i	$-0.872172\pi$
$853$	−451.722	+	451.722i	−0.529568	+	0.529568i	0.390875	+	0.920444i	$0.372172\pi$
$854$	−370.286	+	650.348i	−0.433590	+	0.761532i
$855$		0			0
$856$	97.5765	+	169.007i	0.113991	+	0.197439i
$857$	115.468	−	30.9395i	0.134735	−	0.0361021i	−0.190821	−	0.981625i	$-0.561115\pi$
$857$	115.468	−	30.9395i	0.134735	−	0.0361021i	0.325556	+	0.945523i	$0.394448\pi$
$858$	63.9903	+	238.815i	0.0745808	+	0.278339i
$859$	528.189	−	304.950i	0.614889	−	0.355006i	−0.159988	−	0.987119i	$-0.551145\pi$
$859$	528.189	−	304.950i	0.614889	−	0.355006i	0.774876	+	0.632113i	$0.217812\pi$
$860$		0			0
$861$	−326.277	−	185.771i	−0.378952	−	0.215762i
$862$	−675.870	−	675.870i	−0.784072	−	0.784072i
$863$	192.008	+	51.4484i	0.222489	+	0.0596157i	0.368341	−	0.929691i	$-0.379926\pi$
$863$	192.008	+	51.4484i	0.222489	+	0.0596157i	−0.145852	+	0.989306i	$0.546592\pi$
$864$	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
$868$	−95.0985	+	363.640i	−0.109560	+	0.418940i
$869$		−	525.152i		−	0.604317i
$870$		0			0
$871$	345.149	−	597.816i	0.396268	−	0.686356i
$872$	459.651	−	123.163i	0.527123	−	0.141242i
$873$	608.380	+	163.015i	0.696884	+	0.186729i
$874$			1371.73i			1.56948i
$875$		0			0
$876$	−7.80263			−0.00890711
$877$	−114.339	+	426.717i	−0.130375	+	0.486565i	−0.999974	−	0.00719299i	$-0.997710\pi$
$877$	−114.339	+	426.717i	−0.130375	+	0.486565i	0.869599	+	0.493758i	$0.164377\pi$
$878$	−58.2802	−	217.505i	−0.0663783	−	0.247727i
$879$	−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	$0.521953\pi$
$882$	508.969	−	142.956i	0.577063	−	0.162082i
$883$	249.667	−	249.667i	0.282748	−	0.282748i	−0.551456	−	0.834204i	$-0.685927\pi$
$883$	249.667	−	249.667i	0.282748	−	0.282748i	0.834204	+	0.551456i	$0.185927\pi$
$884$	119.382	−	68.9255i	0.135048	−	0.0779700i
$885$		0			0
$886$	106.005	−	183.606i	0.119645	−	0.207231i
$887$	358.568	−	1338.19i	0.404248	−	1.50867i	−0.401191	−	0.915995i	$-0.631403\pi$
$887$	358.568	−	1338.19i	0.404248	−	1.50867i	0.805439	−	0.592679i	$-0.201930\pi$
$888$	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
$892$	−459.569	+	123.141i	−0.515212	+	0.138051i
$893$	45.0438	+	168.106i	0.0504410	+	0.188248i
$894$	−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
$898$	−867.305	−	232.394i	−0.965819	−	0.258790i
$899$	−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
$903$	−203.662	+	55.8850i	−0.225539	+	0.0618881i
$904$			534.550i			0.591316i
$905$		0			0
$906$	−24.7915	+	42.9402i	−0.0273637	+	0.0473953i
$907$	713.723	−	191.242i	0.786905	−	0.210851i	0.157078	−	0.987586i	$-0.449792\pi$
$907$	713.723	−	191.242i	0.786905	−	0.210851i	0.629827	+	0.776735i	$0.283126\pi$
$908$	683.223	+	183.069i	0.752448	+	0.201618i
$909$		−	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	$0.389589\pi$
$912$	−37.6670	+	140.575i	−0.0413015	+	0.154139i
$913$	156.017	+	582.263i	0.170884	+	0.637747i
$914$	245.500	+	141.740i	0.268600	+	0.155076i
$915$		0			0
$916$	−389.333			−0.425036
$917$	710.141	+	185.715i	0.774418	+	0.202525i
$918$	−109.051	+	109.051i	−0.118792	+	0.118792i
$919$	−505.888	+	292.074i	−0.550476	+	0.317818i	−0.749314	−	0.662215i	$-0.769617\pi$
$919$	−505.888	+	292.074i	−0.550476	+	0.317818i	0.198838	+	0.980032i	$0.436283\pi$
$920$		0			0
$921$	−263.356	+	456.146i	−0.285946	+	0.495272i
$922$	148.683	−	554.894i	0.161262	−	0.601838i
$923$	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
$927$	335.493	−	89.8950i	0.361912	−	0.0969741i
$928$	−36.9522	−	137.908i	−0.0398192	−	0.148607i
$929$	−721.006	+	416.273i	−0.776110	+	0.448087i	−0.835050	−	0.550174i	$-0.814561\pi$
$929$	−721.006	+	416.273i	−0.776110	+	0.448087i	0.0589398	+	0.998262i	$0.481228\pi$
$930$		0			0
$931$	777.093	+	1309.37i	0.834687	+	1.40641i
$932$	437.980	+	437.980i	0.469936	+	0.469936i
$933$	315.212	+	84.4609i	0.337848	+	0.0905262i
$934$	−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	0.324586	−	0.945856i	$-0.394775\pi$
$937$	−582.131	−	582.131i	−0.621271	−	0.621271i	−0.945856	+	0.324586i	$0.894775\pi$
$938$	−395.001	−	390.281i	−0.421110	−	0.416078i
$939$			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	$0.0632561\pi$
$942$	369.422	−	98.9863i	0.392167	−	0.105081i
$943$	1381.19	+	370.089i	1.46468	+	0.392459i
$944$			235.645i			0.249624i
$945$		0			0
$946$	442.113			0.467350
$947$	242.706	−	905.793i	0.256290	−	0.956486i	−0.711079	−	0.703112i	$-0.751793\pi$
$947$	242.706	−	905.793i	0.256290	−	0.956486i	0.967368	−	0.253374i	$-0.0815403\pi$
$948$	−26.2342	−	97.9075i	−0.0276732	−	0.103278i
$949$	35.5106	+	20.5021i	0.0374190	+	0.0216039i
$950$		0			0
$951$	−64.7416			−0.0680774
$952$	−29.3436	−	106.937i	−0.0308231	−	0.112329i
$953$	−108.986	+	108.986i	−0.114361	+	0.114361i	−0.761971	−	0.647611i	$-0.775768\pi$
$953$	−108.986	+	108.986i	−0.114361	+	0.114361i	0.647611	+	0.761971i	$0.275768\pi$
$954$	309.877	−	178.907i	0.324818	−	0.187534i
$955$		0			0
$956$	−17.4917	+	30.2965i	−0.0182967	+	0.0316909i
$957$	−92.7977	+	346.326i	−0.0969673	+	0.361887i
$958$	−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
$962$	−967.364	+	259.204i	−1.00558	+	0.269443i
$963$	136.237	+	508.444i	0.141472	+	0.527979i
$964$	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	0.842346	−	0.538937i	$-0.181174\pi$
$967$	293.397	+	293.397i	0.303410	+	0.303410i	−0.538937	+	0.842346i	$0.681174\pi$
$968$	−71.5858	−	19.1813i	−0.0739522	−	0.0198154i
$969$	−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
$973$	1268.22	+	1253.07i	1.30341	+	1.28784i
$974$		−	313.269i		−	0.321631i
$975$		0			0
$976$	151.194	−	261.877i	0.154912	−	0.268316i
$977$	−753.293	+	201.844i	−0.771027	+	0.206596i	−0.622825	−	0.782361i	$-0.714015\pi$
$977$	−753.293	+	201.844i	−0.771027	+	0.206596i	−0.148202	+	0.988957i	$0.547349\pi$
$978$	287.018	+	76.9061i	0.293474	+	0.0786361i
$979$			166.407i			0.169977i
$980$		0			0
$981$	1283.54			1.30840
$982$	142.036	−	530.085i	0.144639	−	0.539802i
$983$	−472.090	−	1761.86i	−0.480254	−	1.79233i	−0.600541	−	0.799594i	$-0.705048\pi$
$983$	−472.090	−	1761.86i	−0.480254	−	1.79233i	0.120287	−	0.992739i	$-0.461618\pi$
$984$	131.383	+	75.8537i	0.133519	+	0.0770871i
$985$		0			0
$986$	199.909			0.202748
$987$	32.2642	−	32.6543i	0.0326891	−	0.0330844i
$988$	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	$0.0305951\pi$
$992$	39.3079	−	146.699i	0.0396249	−	0.147882i
$993$	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
$997$	−469.784	+	125.878i	−0.471197	+	0.126257i	−0.486601	−	0.873624i	$-0.661763\pi$
$997$	−469.784	+	125.878i	−0.471197	+	0.126257i	0.0154036	+	0.999881i	$0.495097\pi$
$998$	−31.1988	−	116.435i	−0.0312613	−	0.116669i
$999$	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.207.2		16
5.2	odd	4		70.3.l.c.53.2	yes	16
5.3	odd	4	inner	350.3.p.e.193.3		16
5.4	even	2		70.3.l.c.67.3	yes	16
7.2	even	3	inner	350.3.p.e.107.3		16
35.2	odd	12		70.3.l.c.23.3	✓	16
35.4	even	6		490.3.f.o.197.3		8
35.9	even	6		70.3.l.c.37.2	yes	16
35.17	even	12		490.3.f.p.393.2		8
35.23	odd	12	inner	350.3.p.e.93.2		16
35.24	odd	6		490.3.f.p.197.2		8
35.32	odd	12		490.3.f.o.393.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.3	✓	16	35.2	odd	12
70.3.l.c.37.2	yes	16	35.9	even	6
70.3.l.c.53.2	yes	16	5.2	odd	4
70.3.l.c.67.3	yes	16	5.4	even	2
350.3.p.e.93.2		16	35.23	odd	12	inner
350.3.p.e.107.3		16	7.2	even	3	inner
350.3.p.e.193.3		16	5.3	odd	4	inner
350.3.p.e.207.2		16	1.1	even	1	trivial
490.3.f.o.197.3		8	35.4	even	6
490.3.f.o.393.3		8	35.32	odd	12
490.3.f.p.197.2		8	35.24	odd	6
490.3.f.p.393.2		8	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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