LMFDB - Embedded newform 980.2.k.k.687.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("980.687");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$980 = 2^{2} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	980.k (of order $4$ , degree $2$ , 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			687.10
Character	$\chi$	$=$	980.687
Dual form			980.2.k.k.883.10

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0374590 + 1.41372i) q^{2} +(1.81487 + 1.81487i) q^{3} +(-1.99719 + 0.105913i) q^{4} +(0.00568855 + 2.23606i) q^{5} +(-2.49773 + 2.63369i) q^{6} +(-0.224544 - 2.81950i) q^{8} +3.58748i q^{9} +(-3.16094 + 0.0918026i) q^{10} -1.84352i q^{11} +(-3.81686 - 3.43242i) q^{12} +(-2.94578 + 2.94578i) q^{13} +(-4.04783 + 4.06848i) q^{15} +(3.97756 - 0.423057i) q^{16} +(2.17370 + 2.17370i) q^{17} +(-5.07169 + 0.134384i) q^{18} -5.32748 q^{19} +(-0.248189 - 4.46524i) q^{20} +(2.60621 - 0.0690563i) q^{22} +(-1.78934 - 1.78934i) q^{23} +(4.70950 - 5.52453i) q^{24} +(-4.99994 + 0.0254399i) q^{25} +(-4.27484 - 4.05415i) q^{26} +(-1.06621 + 1.06621i) q^{27} +6.35796i q^{29} +(-5.90330 - 5.57008i) q^{30} +4.36858i q^{31} +(0.747079 + 5.60731i) q^{32} +(3.34574 - 3.34574i) q^{33} +(-2.99158 + 3.15443i) q^{34} +(-0.379961 - 7.16490i) q^{36} +(-2.83192 - 2.83192i) q^{37} +(-0.199562 - 7.53156i) q^{38} -10.6924 q^{39} +(6.30330 - 0.518133i) q^{40} +10.6462 q^{41} +(-1.02386 - 1.02386i) q^{43} +(0.195252 + 3.68186i) q^{44} +(-8.02183 + 0.0204076i) q^{45} +(2.46260 - 2.59665i) q^{46} +(0.575006 - 0.575006i) q^{47} +(7.98654 + 6.45096i) q^{48} +(-0.223257 - 7.06754i) q^{50} +7.88996i q^{51} +(5.57129 - 6.19528i) q^{52} +(1.91155 - 1.91155i) q^{53} +(-1.54725 - 1.46737i) q^{54} +(4.12221 - 0.0104869i) q^{55} +(-9.66867 - 9.66867i) q^{57} +(-8.98836 + 0.238163i) q^{58} +4.22891 q^{59} +(7.65339 - 8.55425i) q^{60} +12.0120 q^{61} +(-6.17593 + 0.163643i) q^{62} +(-7.89916 + 1.26620i) q^{64} +(-6.60369 - 6.57018i) q^{65} +(4.85525 + 4.60460i) q^{66} +(2.33920 - 2.33920i) q^{67} +(-4.57153 - 4.11108i) q^{68} -6.49484i q^{69} +10.5316i q^{71} +(10.1149 - 0.805548i) q^{72} +(-1.44730 + 1.44730i) q^{73} +(3.89745 - 4.10962i) q^{74} +(-9.12039 - 9.02805i) q^{75} +(10.6400 - 0.564249i) q^{76} +(-0.400526 - 15.1160i) q^{78} +7.91595 q^{79} +(0.968608 + 8.89167i) q^{80} +6.89241 q^{81} +(0.398798 + 15.0508i) q^{82} +(-0.227439 - 0.227439i) q^{83} +(-4.84817 + 4.87290i) q^{85} +(1.40910 - 1.48580i) q^{86} +(-11.5389 + 11.5389i) q^{87} +(-5.19779 + 0.413950i) q^{88} +4.33857i q^{89} +(-0.329341 - 11.3398i) q^{90} +(3.76318 + 3.38415i) q^{92} +(-7.92838 + 7.92838i) q^{93} +(0.834434 + 0.791356i) q^{94} +(-0.0303056 - 11.9126i) q^{95} +(-8.82066 + 11.5324i) q^{96} +(0.196142 + 0.196142i) q^{97} +6.61358 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$36 q - 2 q^{2} + 8 q^{5} - 8 q^{6} - 2 q^{8} - 2 q^{10} - 10 q^{12} + 28 q^{16} - 4 q^{17} + 20 q^{18} - 28 q^{20} - 8 q^{22} + 16 q^{25} + 4 q^{26} + 32 q^{30} + 38 q^{32} + 64 q^{33} + 8 q^{36} + 4 q^{37}+ \cdots - 12 q^{97}+O(q^{100})$ 36 * q - 2 * q^2 + 8 * q^5 - 8 * q^6 - 2 * q^8 - 2 * q^10 - 10 * q^12 + 28 * q^16 - 4 * q^17 + 20 * q^18 - 28 * q^20 - 8 * q^22 + 16 * q^25 + 4 * q^26 + 32 * q^30 + 38 * q^32 + 64 * q^33 + 8 * q^36 + 4 * q^37 - 12 * q^38 - 2 * q^40 - 20 * q^41 + 12 * q^45 + 28 * q^46 + 6 * q^48 - 14 * q^50 - 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 + 20 * q^61 + 28 * q^62 - 4 * q^65 - 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 56 * q^76 + 32 * q^78 - 52 * q^80 + 52 * q^81 + 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 - 16 * q^90 + 22 * q^92 - 12 * q^93 + 48 * q^96 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$ .

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.0374590	+	1.41372i	0.0264875	+	0.999649i
$2$	0.0374590	+	1.41372i	0.0264875	+	0.999649i
$3$	1.81487	+	1.81487i	1.04781	+	1.04781i	0.998798	+	0.0490159i	$0.0156085\pi$
$3$	1.81487	+	1.81487i	1.04781	+	1.04781i	0.0490159	+	0.998798i	$0.484391\pi$
$4$	−1.99719	+	0.105913i	−0.998597	+	0.0529565i
$5$	0.00568855	+	2.23606i	0.00254399	+	0.999997i
$5$	0.00568855	+	2.23606i	0.00254399	+	0.999997i
$6$	−2.49773	+	2.63369i	−1.01969	+	1.07520i
$7$		0			0
$7$		0			0
$8$	−0.224544	−	2.81950i	−0.0793882	−	0.996844i
$9$			3.58748i			1.19583i
$10$	−3.16094	+	0.0918026i	−0.999579	+	0.0290305i
$11$		−	1.84352i		−	0.555841i	−0.960604	−	0.277920i	$-0.910355\pi$
$11$		−	1.84352i		−	0.555841i	0.960604	−	0.277920i	$-0.0896451\pi$
$12$	−3.81686	−	3.43242i	−1.10183	−	0.990855i
$13$	−2.94578	+	2.94578i	−0.817012	+	0.817012i	−0.985674	−	0.168662i	$-0.946055\pi$
$13$	−2.94578	+	2.94578i	−0.817012	+	0.817012i	0.168662	+	0.985674i	$0.446055\pi$
$14$		0			0
$15$	−4.04783	+	4.06848i	−1.04514	+	1.05048i
$16$	3.97756	−	0.423057i	0.994391	−	0.105764i
$17$	2.17370	+	2.17370i	0.527200	+	0.527200i	0.919737	−	0.392536i	$-0.128402\pi$
$17$	2.17370	+	2.17370i	0.527200	+	0.527200i	−0.392536	+	0.919737i	$0.628402\pi$
$18$	−5.07169	+	0.134384i	−1.19541	+	0.0316745i
$19$	−5.32748			−1.22221			−0.611104	−	0.791550i	$-0.709274\pi$
$19$	−5.32748			−1.22221			−0.611104	+	0.791550i	$0.709274\pi$
$20$	−0.248189	−	4.46524i	−0.0554967	−	0.998459i
$21$		0			0
$22$	2.60621	−	0.0690563i	0.555646	−	0.0147228i
$23$	−1.78934	−	1.78934i	−0.373104	−	0.373104i	0.495503	−	0.868606i	$-0.334984\pi$
$23$	−1.78934	−	1.78934i	−0.373104	−	0.373104i	−0.868606	+	0.495503i	$0.834984\pi$
$24$	4.70950	−	5.52453i	0.961323	−	1.12769i
$25$	−4.99994	+	0.0254399i	−0.999987	+	0.00508797i
$26$	−4.27484	−	4.05415i	−0.838365	−	0.795084i
$27$	−1.06621	+	1.06621i	−0.205191	+	0.205191i
$28$		0			0
$29$			6.35796i			1.18064i	0.807168	+	0.590322i	$0.200999\pi$
$29$			6.35796i			1.18064i	−0.807168	+	0.590322i	$0.799001\pi$
$30$	−5.90330	−	5.57008i	−1.07779	−	1.01695i
$31$			4.36858i			0.784619i	0.919833	+	0.392310i	$0.128324\pi$
$31$			4.36858i			0.784619i	−0.919833	+	0.392310i	$0.871676\pi$
$32$	0.747079	+	5.60731i	0.132066	+	0.991241i
$33$	3.34574	−	3.34574i	0.582418	−	0.582418i
$34$	−2.99158	+	3.15443i	−0.513051	+	0.540980i
$35$		0			0
$36$	−0.379961	−	7.16490i	−0.0633268	−	1.19415i
$37$	−2.83192	−	2.83192i	−0.465565	−	0.465565i	0.434909	−	0.900474i	$-0.356780\pi$
$37$	−2.83192	−	2.83192i	−0.465565	−	0.465565i	−0.900474	+	0.434909i	$0.856780\pi$
$38$	−0.199562	−	7.53156i	−0.0323733	−	1.22178i
$39$	−10.6924			−1.71215
$40$	6.30330	−	0.518133i	0.996639	−	0.0819240i
$41$	10.6462			1.66266			0.831331	−	0.555777i	$-0.187579\pi$
$41$	10.6462			1.66266			0.831331	+	0.555777i	$0.187579\pi$
$42$		0			0
$43$	−1.02386	−	1.02386i	−0.156137	−	0.156137i	0.624715	−	0.780853i	$-0.285215\pi$
$43$	−1.02386	−	1.02386i	−0.156137	−	0.156137i	−0.780853	+	0.624715i	$0.785215\pi$
$44$	0.195252	+	3.68186i	0.0294354	+	0.555061i
$45$	−8.02183	+	0.0204076i	−1.19582	+	0.00304218i
$46$	2.46260	−	2.59665i	0.363090	−	0.382855i
$47$	0.575006	−	0.575006i	0.0838732	−	0.0838732i	−0.663926	−	0.747799i	$-0.731111\pi$
$47$	0.575006	−	0.575006i	0.0838732	−	0.0838732i	0.747799	+	0.663926i	$0.231111\pi$
$48$	7.98654	+	6.45096i	1.15276	+	0.931116i
$49$		0			0
$50$	−0.223257	−	7.06754i	−0.0315734	−	0.999501i
$51$			7.88996i			1.10482i
$52$	5.57129	−	6.19528i	0.772599	−	0.859131i
$53$	1.91155	−	1.91155i	0.262571	−	0.262571i	−0.563527	−	0.826098i	$-0.690556\pi$
$53$	1.91155	−	1.91155i	0.262571	−	0.262571i	0.826098	+	0.563527i	$0.190556\pi$
$54$	−1.54725	−	1.46737i	−0.210554	−	0.199684i
$55$	4.12221	−	0.0104869i	0.555839	−	0.00141406i
$56$		0			0
$57$	−9.66867	−	9.66867i	−1.28065	−	1.28065i
$58$	−8.98836	+	0.238163i	−1.18023	+	0.0312723i
$59$	4.22891			0.550558			0.275279	−	0.961364i	$-0.411230\pi$
$59$	4.22891			0.550558			0.275279	+	0.961364i	$0.411230\pi$
$60$	7.65339	−	8.55425i	0.988049	−	1.10435i
$61$	12.0120			1.53798			0.768988	−	0.639263i	$-0.220760\pi$
$61$	12.0120			1.53798			0.768988	+	0.639263i	$0.220760\pi$
$62$	−6.17593	+	0.163643i	−0.784344	+	0.0207826i
$63$		0			0
$64$	−7.89916	+	1.26620i	−0.987395	+	0.158275i
$65$	−6.60369	−	6.57018i	−0.819087	−	0.814930i
$66$	4.85525	+	4.60460i	0.597640	+	0.566787i
$67$	2.33920	−	2.33920i	0.285779	−	0.285779i	−0.549629	−	0.835409i	$-0.685231\pi$
$67$	2.33920	−	2.33920i	0.285779	−	0.285779i	0.835409	+	0.549629i	$0.185231\pi$
$68$	−4.57153	−	4.11108i	−0.554379	−	0.498542i
$69$		−	6.49484i		−	0.781886i
$70$		0			0
$71$			10.5316i			1.24988i	0.780675	+	0.624938i	$0.214876\pi$
$71$			10.5316i			1.24988i	−0.780675	+	0.624938i	$0.785124\pi$
$72$	10.1149	−	0.805548i	1.19205	−	0.0949347i
$73$	−1.44730	+	1.44730i	−0.169393	+	0.169393i	−0.786713	−	0.617319i	$-0.788219\pi$
$73$	−1.44730	+	1.44730i	−0.169393	+	0.169393i	0.617319	+	0.786713i	$0.288219\pi$
$74$	3.89745	−	4.10962i	0.453070	−	0.477733i
$75$	−9.12039	−	9.02805i	−1.05313	−	1.04247i
$76$	10.6400	−	0.564249i	1.22049	−	0.0647238i
$77$		0			0
$78$	−0.400526	−	15.1160i	−0.0453507	−	1.71155i
$79$	7.91595			0.890613			0.445307	−	0.895378i	$-0.353095\pi$
$79$	7.91595			0.890613			0.445307	+	0.895378i	$0.353095\pi$
$80$	0.968608	+	8.89167i	0.108294	+	0.994119i
$81$	6.89241			0.765823
$82$	0.398798	+	15.0508i	0.0440398	+	1.66208i
$83$	−0.227439	−	0.227439i	−0.0249647	−	0.0249647i	0.694514	−	0.719479i	$-0.255619\pi$
$83$	−0.227439	−	0.227439i	−0.0249647	−	0.0249647i	−0.719479	+	0.694514i	$0.755619\pi$
$84$		0			0
$85$	−4.84817	+	4.87290i	−0.525858	+	0.528540i
$86$	1.40910	−	1.48580i	0.151947	−	0.160218i
$87$	−11.5389	+	11.5389i	−1.23710	+	1.23710i
$88$	−5.19779	+	0.413950i	−0.554086	+	0.0441272i
$89$			4.33857i			0.459888i	0.973204	+	0.229944i	$0.0738543\pi$
$89$			4.33857i			0.459888i	−0.973204	+	0.229944i	$0.926146\pi$
$90$	−0.329341	−	11.3398i	−0.0347155	−	1.19532i
$91$		0			0
$92$	3.76318	+	3.38415i	0.392338	+	0.352822i
$93$	−7.92838	+	7.92838i	−0.822135	+	0.822135i
$94$	0.834434	+	0.791356i	0.0860653	+	0.0816222i
$95$	−0.0303056	−	11.9126i	−0.00310929	−	1.22220i
$96$	−8.82066	+	11.5324i	−0.900255	+	1.17702i
$97$	0.196142	+	0.196142i	0.0199152	+	0.0199152i	0.716994	−	0.697079i	$-0.245517\pi$
$97$	0.196142	+	0.196142i	0.0199152	+	0.0199152i	−0.697079	+	0.716994i	$0.745517\pi$
$98$		0			0
$99$	6.61358			0.664690
$100$	9.98314	−	0.580366i	0.998314	−	0.0580366i
$101$	−7.34897			−0.731250			−0.365625	−	0.930762i	$-0.619145\pi$
$101$	−7.34897			−0.731250			−0.365625	+	0.930762i	$0.619145\pi$
$102$	−11.1542	+	0.295550i	−1.10443	+	0.0292638i
$103$	9.64495	+	9.64495i	0.950345	+	0.950345i	0.998824	−	0.0484790i	$-0.0154374\pi$
$103$	9.64495	+	9.64495i	0.950345	+	0.950345i	−0.0484790	+	0.998824i	$0.515437\pi$
$104$	8.96707	+	7.64416i	0.879294	+	0.749572i
$105$		0			0
$106$	2.77399	+	2.63078i	0.269434	+	0.255524i
$107$	−3.30237	+	3.30237i	−0.319252	+	0.319252i	−0.848480	−	0.529228i	$-0.822482\pi$
$107$	−3.30237	+	3.30237i	−0.319252	+	0.319252i	0.529228	+	0.848480i	$0.322482\pi$
$108$	2.01649	−	2.24234i	0.194037	−	0.215770i
$109$			10.1310i			0.970377i	0.874410	+	0.485188i	$0.161249\pi$
$109$			10.1310i			0.970377i	−0.874410	+	0.485188i	$0.838751\pi$
$110$	0.169240	+	5.82725i	0.0161364	+	0.555607i
$111$		−	10.2791i		−	0.975651i
$112$		0			0
$113$	−7.70435	+	7.70435i	−0.724764	+	0.724764i	−0.969572	−	0.244807i	$-0.921275\pi$
$113$	−7.70435	+	7.70435i	−0.724764	+	0.724764i	0.244807	+	0.969572i	$0.421275\pi$
$114$	13.3066	−	14.0310i	1.24628	−	1.31412i
$115$	3.99090	−	4.01126i	0.372153	−	0.374052i
$116$	−0.673391	−	12.6981i	−0.0625227	−	1.17899i
$117$	−10.5679	−	10.5679i	−0.977005	−	0.977005i
$118$	0.158411	+	5.97849i	0.0145829	+	0.550365i
$119$		0			0
$120$	12.3800	+	10.4993i	1.13013	+	0.958451i
$121$	7.60145			0.691041
$122$	0.449957	+	16.9815i	0.0407372	+	1.53744i
$123$	19.3215	+	19.3215i	1.74216	+	1.74216i
$124$	−0.462689	−	8.72489i	−0.0415507	−	0.783518i
$125$	−0.0853274	−	11.1800i	−0.00763192	−	0.999971i
$126$		0			0
$127$	9.01446	−	9.01446i	0.799904	−	0.799904i	−0.183176	−	0.983080i	$-0.558638\pi$
$127$	9.01446	−	9.01446i	0.799904	−	0.799904i	0.983080	+	0.183176i	$0.0586380\pi$
$128$	−2.08595	−	11.1197i	−0.184373	−	0.982856i
$129$		−	3.71634i		−	0.327206i
$130$	9.04101	−	9.58187i	0.792949	−	0.840385i
$131$		−	18.7512i		−	1.63830i	−0.573577	−	0.819152i	$-0.694445\pi$
$131$		−	18.7512i		−	1.63830i	0.573577	−	0.819152i	$-0.305555\pi$
$132$	−6.32772	+	7.03644i	−0.550758	+	0.612443i
$133$		0			0
$134$	3.39460	+	3.21935i	0.293248	+	0.278109i
$135$	−2.39017	−	2.37804i	−0.205713	−	0.204669i
$136$	5.64066	−	6.61685i	0.483683	−	0.567390i
$137$	−12.7603	−	12.7603i	−1.09019	−	1.09019i	−0.995508	−	0.0946771i	$-0.969818\pi$
$137$	−12.7603	−	12.7603i	−1.09019	−	1.09019i	−0.0946771	−	0.995508i	$-0.530182\pi$
$138$	9.18186	−	0.243290i	0.781612	−	0.0207102i
$139$	2.38747			0.202503			0.101251	−	0.994861i	$-0.467715\pi$
$139$	2.38747			0.202503			0.101251	+	0.994861i	$0.467715\pi$
$140$		0			0
$141$	2.08712			0.175767
$142$	−14.8888	+	0.394505i	−1.24944	+	0.0331061i
$143$	5.43058	+	5.43058i	0.454128	+	0.454128i
$144$	1.51771	+	14.2695i	0.126476	+	1.18912i
$145$	−14.2168	+	0.0361676i	−1.18064	+	0.00300355i
$146$	−2.10028	−	1.99185i	−0.173821	−	0.164847i
$147$		0			0
$148$	5.95583	+	5.35596i	0.489566	+	0.440257i
$149$		−	11.0191i		−	0.902723i	−0.892341	−	0.451362i	$-0.850938\pi$
$149$		−	11.0191i		−	0.902723i	0.892341	−	0.451362i	$-0.149062\pi$
$150$	12.4215	−	13.2318i	1.01421	−	1.08037i
$151$			16.5496i			1.34678i	0.739285	+	0.673392i	$0.235163\pi$
$151$			16.5496i			1.34678i	−0.739285	+	0.673392i	$0.764837\pi$
$152$	1.19625	+	15.0208i	0.0970290	+	1.21835i
$153$	−7.79813	+	7.79813i	−0.630441	+	0.630441i
$154$		0			0
$155$	−9.76840	+	0.0248508i	−0.784617	+	0.00199607i
$156$	21.3548	−	1.13246i	1.70975	−	0.0906695i
$157$	−4.01049	−	4.01049i	−0.320072	−	0.320072i	0.528722	−	0.848795i	$-0.322671\pi$
$157$	−4.01049	−	4.01049i	−0.320072	−	0.320072i	−0.848795	+	0.528722i	$0.822671\pi$
$158$	0.296524	+	11.1909i	0.0235901	+	0.890301i
$159$	6.93840			0.550251
$160$	−12.5340	+	1.70241i	−0.990902	+	0.134587i
$161$		0			0
$162$	0.258183	+	9.74392i	0.0202848	+	0.765555i
$163$	2.09960	+	2.09960i	0.164454	+	0.164454i	0.784536	−	0.620083i	$-0.212901\pi$
$163$	2.09960	+	2.09960i	0.164454	+	0.164454i	−0.620083	+	0.784536i	$0.712901\pi$
$164$	−21.2626	+	1.12757i	−1.66033	+	0.0880487i
$165$	7.50030	+	7.46223i	0.583897	+	0.580934i
$166$	0.313015	−	0.330054i	0.0242947	−	0.0256172i
$167$	−11.1720	+	11.1720i	−0.864517	+	0.864517i	−0.991859	−	0.127342i	$-0.959355\pi$
$167$	−11.1720	+	11.1720i	−0.864517	+	0.864517i	0.127342	+	0.991859i	$0.459355\pi$
$168$		0			0
$169$		−	4.35520i		−	0.335016i
$170$	−7.07051	−	6.67140i	−0.542283	−	0.511673i
$171$		−	19.1123i		−	1.46155i
$172$	2.15329	+	1.93641i	0.164187	+	0.147650i
$173$	−4.90852	+	4.90852i	−0.373188	+	0.373188i	−0.868637	−	0.495449i	$-0.835003\pi$
$173$	−4.90852	+	4.90852i	−0.373188	+	0.373188i	0.495449	+	0.868637i	$0.335003\pi$
$174$	−16.7449	−	15.8805i	−1.26943	−	1.20389i
$175$		0			0
$176$	−0.779913	−	7.33270i	−0.0587881	−	0.552723i
$177$	7.67492	+	7.67492i	0.576882	+	0.576882i
$178$	−6.13352	+	0.162519i	−0.459726	+	0.0121813i
$179$	−10.1763			−0.760613			−0.380307	−	0.924860i	$-0.624182\pi$
$179$	−10.1763			−0.760613			−0.380307	+	0.924860i	$0.624182\pi$
$180$	16.0190	−	0.890374i	1.19399	−	0.0663645i
$181$	−10.8055			−0.803166			−0.401583	−	0.915823i	$-0.631540\pi$
$181$	−10.8055			−0.803166			−0.401583	+	0.915823i	$0.631540\pi$
$182$		0			0
$183$	21.8002	+	21.8002i	1.61151	+	1.61151i
$184$	−4.64327	+	5.44684i	−0.342306	+	0.401546i
$185$	6.31624	−	6.34846i	0.464379	−	0.466748i
$186$	−11.5055	−	10.9115i	−0.843623	−	0.800070i
$187$	4.00726	−	4.00726i	0.293040	−	0.293040i
$188$	−1.08750	+	1.20930i	−0.0793139	+	0.0881971i
$189$		0			0
$190$	16.8399	−	0.489077i	1.22169	−	0.0354814i
$191$			13.8265i			1.00045i	0.865896	+	0.500225i	$0.166749\pi$
$191$			13.8265i			1.00045i	−0.865896	+	0.500225i	$0.833251\pi$
$192$	−16.6339	−	12.0379i	−1.20045	−	0.868763i
$193$	4.87713	−	4.87713i	0.351063	−	0.351063i	−0.509442	−	0.860505i	$-0.670148\pi$
$193$	4.87713	−	4.87713i	0.351063	−	0.351063i	0.860505	+	0.509442i	$0.170148\pi$
$194$	−0.269941	+	0.284636i	−0.0193807	+	0.0204357i
$195$	−0.0608241	−	23.9088i	−0.00435571	−	1.71215i
$196$		0			0
$197$	−7.85372	−	7.85372i	−0.559554	−	0.559554i	0.369626	−	0.929181i	$-0.379486\pi$
$197$	−7.85372	−	7.85372i	−0.559554	−	0.559554i	−0.929181	+	0.369626i	$0.879486\pi$
$198$	0.247738	+	9.34974i	0.0176060	+	0.664457i
$199$	17.2759			1.22465			0.612327	−	0.790605i	$-0.290234\pi$
$199$	17.2759			1.22465			0.612327	+	0.790605i	$0.290234\pi$
$200$	1.19443	+	14.0916i	0.0844591	+	0.996427i
$201$	8.49068			0.598887
$202$	−0.275285	−	10.3894i	−0.0193690	−	0.730994i
$203$		0			0
$204$	−0.835649	−	15.7578i	−0.0585071	−	1.10327i
$205$	0.0605616	+	23.8056i	0.00422980	+	1.66266i
$206$	−13.2739	+	13.9965i	−0.924839	+	0.975184i
$207$	6.41924	−	6.41924i	0.446168	−	0.446168i
$208$	−10.4708	+	12.9633i	−0.726018	+	0.898840i
$209$			9.82130i			0.679353i
$210$		0			0
$211$		−	18.6740i		−	1.28557i	−0.766045	−	0.642787i	$-0.777778\pi$
$211$		−	18.6740i		−	1.28557i	0.766045	−	0.642787i	$-0.222222\pi$
$212$	−3.61527	+	4.02019i	−0.248298	+	0.276107i
$213$	−19.1135	+	19.1135i	−1.30964	+	1.30964i
$214$	−4.79232	−	4.54491i	−0.327596	−	0.310684i
$215$	2.28359	−	2.29524i	0.155740	−	0.156534i
$216$	3.24558	+	2.76676i	0.220834	+	0.188254i
$217$		0			0
$218$	−14.3224	+	0.379499i	−0.970036	+	0.0257029i
$219$	−5.25330			−0.354985
$220$	−8.23175	+	0.457540i	−0.554984	+	0.0308473i
$221$	−12.8065			−0.861458
$222$	14.5318	−	0.385046i	0.975308	−	0.0258426i
$223$	11.0752	+	11.0752i	0.741650	+	0.741650i	0.972895	−	0.231245i	$-0.0742800\pi$
$223$	11.0752	+	11.0752i	0.741650	+	0.741650i	−0.231245	+	0.972895i	$0.574280\pi$
$224$		0			0
$225$	−0.0912651	−	17.9372i	−0.00608434	−	1.19581i
$226$	−11.1804	−	10.6032i	−0.743707	−	0.705313i
$227$	−1.85642	+	1.85642i	−0.123215	+	0.123215i	−0.766025	−	0.642811i	$-0.777768\pi$
$227$	−1.85642	+	1.85642i	−0.123215	+	0.123215i	0.642811	+	0.766025i	$0.277768\pi$
$228$	20.3343	+	18.2862i	1.34667	+	1.21103i
$229$			2.03277i			0.134329i	0.997742	+	0.0671646i	$0.0213953\pi$
$229$			2.03277i			0.134329i	−0.997742	+	0.0671646i	$0.978605\pi$
$230$	5.82028	+	5.49175i	0.383778	+	0.362115i
$231$		0			0
$232$	17.9263	−	1.42764i	1.17692	−	0.0937293i
$233$	9.85147	−	9.85147i	0.645391	−	0.645391i	−0.306485	−	0.951876i	$-0.599153\pi$
$233$	9.85147	−	9.85147i	0.645391	−	0.645391i	0.951876	+	0.306485i	$0.0991528\pi$
$234$	14.5442	−	15.3359i	0.950784	−	1.00254i
$235$	1.28902	+	1.28248i	0.0840863	+	0.0836595i
$236$	−8.44596	+	0.447897i	−0.549785	+	0.0291556i
$237$	14.3664	+	14.3664i	0.933197	+	0.933197i
$238$		0			0
$239$	−9.72902			−0.629318			−0.314659	−	0.949205i	$-0.601890\pi$
$239$	−9.72902			−0.629318			−0.314659	+	0.949205i	$0.601890\pi$
$240$	−14.3793	+	17.8951i	−0.928180	+	1.15512i
$241$	15.9461			1.02718			0.513588	−	0.858037i	$-0.328316\pi$
$241$	15.9461			1.02718			0.513588	+	0.858037i	$0.328316\pi$
$242$	0.284743	+	10.7463i	0.0183040	+	0.690799i
$243$	15.7074	+	15.7074i	1.00763	+	1.00763i
$244$	−23.9903	+	1.27222i	−1.53582	+	0.0814458i
$245$		0			0
$246$	−26.5914	+	28.0389i	−1.69540	+	1.78770i
$247$	15.6936	−	15.6936i	0.998558	−	0.998558i
$248$	12.3172	−	0.980937i	0.782143	−	0.0622896i
$249$		−	0.825543i		−	0.0523167i
$250$	15.8022	−	0.539421i	0.999418	−	0.0341160i
$251$		−	5.62289i		−	0.354913i	−0.984129	−	0.177457i	$-0.943213\pi$
$251$		−	5.62289i		−	0.354913i	0.984129	−	0.177457i	$-0.0567870\pi$
$252$		0			0
$253$	−3.29868	+	3.29868i	−0.207386	+	0.207386i
$254$	13.0816	+	12.4062i	0.820810	+	0.778435i
$255$	−17.6424	+	0.0448824i	−1.10481	+	0.00281065i
$256$	15.6420	−	3.36548i	0.977628	−	0.210342i
$257$	3.62397	+	3.62397i	0.226057	+	0.226057i	0.811043	−	0.584986i	$-0.198900\pi$
$257$	3.62397	+	3.62397i	0.226057	+	0.226057i	−0.584986	+	0.811043i	$0.698900\pi$
$258$	5.25386	−	0.139211i	0.327091	−	0.00866687i
$259$		0			0
$260$	13.8847	+	12.4225i	0.861094	+	0.770411i
$261$	−22.8091			−1.41185
$262$	26.5090	−	0.702403i	1.63773	−	0.0433946i
$263$	−5.57985	−	5.57985i	−0.344069	−	0.344069i	0.513826	−	0.857894i	$-0.328228\pi$
$263$	−5.57985	−	5.57985i	−0.344069	−	0.344069i	−0.857894	+	0.513826i	$0.828228\pi$
$264$	−10.1846	−	8.68204i	−0.626817	−	0.534342i
$265$	4.28521	+	4.26346i	0.263238	+	0.261902i
$266$		0			0
$267$	−7.87393	+	7.87393i	−0.481877	+	0.481877i
$268$	−4.42409	+	4.91959i	−0.270244	+	0.300512i
$269$			4.59516i			0.280172i	0.990139	+	0.140086i	$0.0447379\pi$
$269$			4.59516i			0.280172i	−0.990139	+	0.140086i	$0.955262\pi$
$270$	3.27234	−	3.46810i	0.199148	−	0.211062i
$271$			28.6627i			1.74114i	0.492049	+	0.870568i	$0.336248\pi$
$271$			28.6627i			1.74114i	−0.492049	+	0.870568i	$0.663752\pi$
$272$	9.56565	+	7.72644i	0.580002	+	0.468485i
$273$		0			0
$274$	17.5615	−	18.5174i	1.06093	−	1.11868i
$275$	0.0468988	+	9.21746i	0.00282810	+	0.555834i
$276$	0.687887	+	12.9714i	0.0414059	+	0.780789i
$277$	3.80033	+	3.80033i	0.228339	+	0.228339i	0.811999	−	0.583659i	$-0.198380\pi$
$277$	3.80033	+	3.80033i	0.228339	+	0.228339i	−0.583659	+	0.811999i	$0.698380\pi$
$278$	0.0894324	+	3.37521i	0.00536380	+	0.202432i
$279$	−15.6722			−0.938270
$280$		0			0
$281$	24.2851			1.44873			0.724365	−	0.689417i	$-0.242133\pi$
$281$	24.2851			1.44873			0.724365	+	0.689417i	$0.242133\pi$
$282$	0.0781814	+	2.95059i	0.00465563	+	0.175705i
$283$	−7.20136	−	7.20136i	−0.428076	−	0.428076i	0.459896	−	0.887973i	$-0.347887\pi$
$283$	−7.20136	−	7.20136i	−0.428076	−	0.428076i	−0.887973	+	0.459896i	$0.847887\pi$
$284$	−1.11544	−	21.0337i	−0.0661890	−	1.24812i
$285$	21.5647	−	21.6747i	1.27738	−	1.28390i
$286$	−7.47389	+	7.88074i	−0.441940	+	0.465998i
$287$		0			0
$288$	−20.1161	+	2.68013i	−1.18535	+	0.157928i
$289$		−	7.55003i		−	0.444119i
$290$	−0.583678	−	20.0972i	−0.0342747	−	1.18015i
$291$			0.711942i			0.0417348i
$292$	2.73724	−	3.04382i	0.160185	−	0.178126i
$293$	19.5889	−	19.5889i	1.14440	−	1.14440i	0.156762	−	0.987636i	$-0.449894\pi$
$293$	19.5889	−	19.5889i	1.14440	−	1.14440i	0.987636	−	0.156762i	$-0.0501056\pi$
$294$		0			0
$295$	0.0240564	+	9.45611i	0.00140062	+	0.550556i
$296$	−7.34871	+	8.62049i	−0.427135	+	0.501056i
$297$	1.96557	+	1.96557i	0.114054	+	0.114054i
$298$	15.5780	−	0.412766i	0.902406	−	0.0239109i
$299$	10.5420			0.609660
$300$	19.1714	+	17.0648i	1.10686	+	0.985236i
$301$		0			0
$302$	−23.3964	+	0.619930i	−1.34631	+	0.0356730i
$303$	−13.3374	−	13.3374i	−0.766214	−	0.766214i
$304$	−21.1904	+	2.25383i	−1.21535	+	0.129266i
$305$	0.0683307	+	26.8595i	0.00391261	+	1.53797i
$306$	−11.3165	−	10.7322i	−0.646919	−	0.613521i
$307$	−20.7290	+	20.7290i	−1.18307	+	1.18307i	−0.204121	+	0.978946i	$0.565433\pi$
$307$	−20.7290	+	20.7290i	−1.18307	+	1.18307i	−0.978946	+	0.204121i	$0.934567\pi$
$308$		0			0
$309$			35.0086i			1.99157i
$310$	−0.401047	−	13.8088i	−0.0227779	−	0.784289i
$311$			4.34312i			0.246276i	0.992390	+	0.123138i	$0.0392957\pi$
$311$			4.34312i			0.246276i	−0.992390	+	0.123138i	$0.960704\pi$
$312$	2.40091	+	30.1472i	0.135925	+	1.70675i
$313$	−5.54957	+	5.54957i	−0.313680	+	0.313680i	−0.846334	−	0.532653i	$-0.821195\pi$
$313$	−5.54957	+	5.54957i	−0.313680	+	0.313680i	0.532653	+	0.846334i	$0.321195\pi$
$314$	5.51948	−	5.81993i	0.311482	−	0.328438i
$315$		0			0
$316$	−15.8097	+	0.838401i	−0.889364	+	0.0471637i
$317$	−1.71502	−	1.71502i	−0.0963251	−	0.0963251i	0.657302	−	0.753627i	$-0.271698\pi$
$317$	−1.71502	−	1.71502i	−0.0963251	−	0.0963251i	−0.753627	+	0.657302i	$0.771698\pi$
$318$	0.259906	+	9.80894i	0.0145748	+	0.550058i
$319$	11.7210			0.656250
$320$	−2.87624	−	17.6558i	−0.160787	−	0.986989i
$321$	−11.9867			−0.669034
$322$		0			0
$323$	−11.5804	−	11.5804i	−0.644349	−	0.644349i
$324$	−13.7655	+	0.729995i	−0.764749	+	0.0405553i
$325$	14.6538	−	14.8036i	0.812844	−	0.821158i
$326$	−2.88960	+	3.04689i	−0.160040	+	0.168752i
$327$	−18.3865	+	18.3865i	−1.01677	+	1.01677i
$328$	−2.39055	−	30.0171i	−0.131996	−	1.65741i
$329$		0			0
$330$	−10.2685	+	10.8828i	−0.565264	+	0.599080i
$331$		−	12.8330i		−	0.705368i	−0.935743	−	0.352684i	$-0.885269\pi$
$331$		−	12.8330i		−	0.705368i	0.935743	−	0.352684i	$-0.114731\pi$
$332$	0.478328	+	0.430151i	0.0262517	+	0.0236076i
$333$	10.1595	−	10.1595i	0.556736	−	0.556736i
$334$	−16.2126	−	15.3756i	−0.887112	−	0.841314i
$335$	5.24391	+	5.21729i	0.286505	+	0.285051i
$336$		0			0
$337$	25.1079	+	25.1079i	1.36771	+	1.36771i	0.863691	+	0.504022i	$0.168147\pi$
$337$	25.1079	+	25.1079i	1.36771	+	1.36771i	0.504022	+	0.863691i	$0.331853\pi$
$338$	6.15703	−	0.163142i	0.334898	−	0.00887374i
$339$	−27.9647			−1.51884
$340$	9.16663	−	10.2456i	0.497130	−	0.555646i
$341$	8.05354			0.436123
$342$	27.0193	−	0.715927i	1.46104	−	0.0387129i
$343$		0			0
$344$	−2.65688	+	3.11668i	−0.143249	+	0.168040i
$345$	14.5229	−	0.0369462i	0.781884	−	0.00198912i
$346$	−7.12312	−	6.75539i	−0.382941	−	0.363172i
$347$	−3.00692	+	3.00692i	−0.161420	+	0.161420i	−0.783195	−	0.621776i	$-0.786412\pi$
$347$	−3.00692	+	3.00692i	−0.161420	+	0.161420i	0.621776	+	0.783195i	$0.286412\pi$
$348$	21.8232	−	24.2675i	1.16985	−	1.30087i
$349$		−	4.09263i		−	0.219074i	−0.993983	−	0.109537i	$-0.965063\pi$
$349$		−	4.09263i		−	0.219074i	0.993983	−	0.109537i	$-0.0349368\pi$
$350$		0			0
$351$		−	6.28161i		−	0.335288i
$352$	10.3372	−	1.37725i	0.550972	−	0.0734078i
$353$	14.1289	−	14.1289i	0.752003	−	0.752003i	−0.222849	−	0.974853i	$-0.571536\pi$
$353$	14.1289	−	14.1289i	0.752003	−	0.752003i	0.974853	+	0.222849i	$0.0715358\pi$
$354$	−10.5627	+	11.1377i	−0.561400	+	0.591960i
$355$	−23.5494	+	0.0599097i	−1.24987	+	0.00317968i
$356$	−0.459511	−	8.66497i	−0.0243540	−	0.459242i
$357$		0			0
$358$	−0.381195	−	14.3864i	−0.0201468	−	0.760346i
$359$	−9.71793			−0.512893			−0.256446	−	0.966558i	$-0.582552\pi$
$359$	−9.71793			−0.512893			−0.256446	+	0.966558i	$0.582552\pi$
$360$	1.85879	+	22.6130i	0.0979670	+	1.19181i
$361$	9.38208			0.493794
$362$	−0.404763	−	15.2759i	−0.0212739	−	0.802885i
$363$	13.7956	+	13.7956i	0.724082	+	0.724082i
$364$		0			0
$365$	−3.24447	−	3.22801i	−0.169824	−	0.168962i
$366$	−30.0026	+	31.6359i	−1.56826	+	1.65363i
$367$	10.7427	−	10.7427i	0.560763	−	0.560763i	−0.368761	−	0.929524i	$-0.620218\pi$
$367$	10.7427	−	10.7427i	0.560763	−	0.560763i	0.929524	+	0.368761i	$0.120218\pi$
$368$	−7.87422	−	6.36023i	−0.410472	−	0.331550i
$369$			38.1932i			1.98826i
$370$	9.21152	+	8.69157i	0.478884	+	0.451853i
$371$		0			0
$372$	14.9948	−	16.6742i	0.777444	−	0.864519i
$373$	22.8232	−	22.8232i	1.18174	−	1.18174i	0.202449	−	0.979293i	$-0.435110\pi$
$373$	22.8232	−	22.8232i	1.18174	−	1.18174i	0.979293	−	0.202449i	$-0.0648900\pi$
$374$	5.81523	+	5.51502i	0.300699	+	0.285175i
$375$	20.1354	−	20.4451i	1.03979	−	1.05578i
$376$	−1.75034	−	1.49211i	−0.0902670	−	0.0769499i
$377$	−18.7291	−	18.7291i	−0.964600	−	0.964600i
$378$		0			0
$379$	29.2598			1.50297			0.751487	−	0.659747i	$-0.229337\pi$
$379$	29.2598			1.50297			0.751487	+	0.659747i	$0.229337\pi$
$380$	1.32222	+	23.7885i	0.0678286	+	1.22032i
$381$	32.7201			1.67630
$382$	−19.5467	+	0.517927i	−1.00010	+	0.0264994i
$383$	7.98331	+	7.98331i	0.407928	+	0.407928i	0.881016	−	0.473087i	$-0.156861\pi$
$383$	7.98331	+	7.98331i	0.407928	+	0.407928i	−0.473087	+	0.881016i	$0.656861\pi$
$384$	16.3951	−	23.9666i	0.836661	−	1.22304i
$385$		0			0
$386$	7.07757	+	6.71218i	0.360239	+	0.341641i
$387$	3.67309	−	3.67309i	0.186713	−	0.186713i
$388$	−0.412507	−	0.370959i	−0.0209418	−	0.0188326i
$389$		−	38.6309i		−	1.95867i	−0.202255	−	0.979333i	$-0.564827\pi$
$389$		−	38.6309i		−	1.95867i	0.202255	−	0.979333i	$-0.435173\pi$
$390$	33.7980	−	0.981589i	1.71143	−	0.0497047i
$391$		−	7.77900i		−	0.393401i
$392$		0			0
$393$	34.0310	−	34.0310i	1.71664	−	1.71664i
$394$	10.8087	−	11.3971i	0.544537	−	0.574179i
$395$	0.0450302	+	17.7005i	0.00226572	+	0.890611i
$396$	−13.2086	+	0.700464i	−0.663757	+	0.0351996i
$397$	−6.06780	−	6.06780i	−0.304534	−	0.304534i	0.538251	−	0.842785i	$-0.319085\pi$
$397$	−6.06780	−	6.06780i	−0.304534	−	0.304534i	−0.842785	+	0.538251i	$0.819085\pi$
$398$	0.647137	+	24.4232i	0.0324381	+	1.22422i
$399$		0			0
$400$	−19.8768	+	2.21645i	−0.993840	+	0.110822i
$401$	−2.32659			−0.116184			−0.0580922	−	0.998311i	$-0.518502\pi$
$401$	−2.32659			−0.116184			−0.0580922	+	0.998311i	$0.518502\pi$
$402$	0.318053	+	12.0034i	0.0158630	+	0.598677i
$403$	−12.8689	−	12.8689i	−0.641043	−	0.641043i
$404$	14.6773	−	0.778351i	0.730224	−	0.0387244i
$405$	0.0392078	+	15.4118i	0.00194825	+	0.765821i
$406$		0			0
$407$	−5.22069	+	5.22069i	−0.258780	+	0.258780i
$408$	22.2458	−	1.77164i	1.10133	−	0.0877094i
$409$			0.187986i			0.00929531i	0.999989	+	0.00464765i	$0.00147940\pi$
$409$			0.187986i			0.00929531i	−0.999989	+	0.00464765i	$0.998521\pi$
$410$	−33.6522	+	0.977352i	−1.66196	+	0.0482680i
$411$		−	46.3165i		−	2.28462i
$412$	−20.2844	−	18.2413i	−0.999339	−	0.898685i
$413$		0			0
$414$	9.31545	+	8.83453i	0.457829	+	0.434193i
$415$	0.507273	−	0.509861i	0.0249011	−	0.0250281i
$416$	−18.7186	−	14.3171i	−0.917755	−	0.701956i
$417$	4.33295	+	4.33295i	0.212185	+	0.212185i
$418$	−13.8845	+	0.367896i	−0.679115	+	0.0179944i
$419$	−13.0861			−0.639297			−0.319648	−	0.947536i	$-0.603565\pi$
$419$	−13.0861			−0.639297			−0.319648	+	0.947536i	$0.603565\pi$
$420$		0			0
$421$	3.33535			0.162555			0.0812776	−	0.996692i	$-0.474100\pi$
$421$	3.33535			0.162555			0.0812776	+	0.996692i	$0.474100\pi$
$422$	26.3998	−	0.699511i	1.28512	−	0.0340517i
$423$	2.06282	+	2.06282i	0.100298	+	0.100298i
$424$	−5.81883	−	4.96038i	−0.282587	−	0.240897i
$425$	−10.9237	−	10.8131i	−0.529876	−	0.524511i
$426$	−27.7371	−	26.3051i	−1.34387	−	1.27449i
$427$		0			0
$428$	6.24571	−	6.94524i	0.301898	−	0.335711i
$429$			19.7116i			0.951684i
$430$	3.33036	+	3.14238i	0.160604	+	0.151539i
$431$			2.41077i			0.116122i	0.998313	+	0.0580612i	$0.0184919\pi$
$431$			2.41077i			0.116122i	−0.998313	+	0.0580612i	$0.981508\pi$
$432$	−3.78984	+	4.69197i	−0.182339	+	0.225742i
$433$	0.313016	−	0.313016i	0.0150426	−	0.0150426i	−0.699545	−	0.714588i	$-0.746614\pi$
$433$	0.313016	−	0.313016i	0.0150426	−	0.0150426i	0.714588	+	0.699545i	$0.246614\pi$
$434$		0			0
$435$	−25.8672	−	25.7360i	−1.24024	−	1.23394i
$436$	−1.07301	−	20.2336i	−0.0513877	−	0.969015i
$437$	9.53269	+	9.53269i	0.456010	+	0.456010i
$438$	−0.196783	−	7.42668i	−0.00940267	−	0.354860i
$439$	−22.4600			−1.07196			−0.535978	−	0.844232i	$-0.680057\pi$
$439$	−22.4600			−1.07196			−0.535978	+	0.844232i	$0.680057\pi$
$440$	−0.955185	−	11.6202i	−0.0455367	−	0.553972i
$441$		0			0
$442$	−0.479719	−	18.1048i	−0.0228179	−	0.861155i
$443$	−12.3349	−	12.3349i	−0.586050	−	0.586050i	0.350509	−	0.936559i	$-0.386008\pi$
$443$	−12.3349	−	12.3349i	−0.586050	−	0.586050i	−0.936559	+	0.350509i	$0.886008\pi$
$444$	1.08869	+	20.5294i	0.0516670	+	0.974282i
$445$	−9.70131	+	0.0246802i	−0.459886	+	0.00116995i
$446$	−15.2423	+	16.0721i	−0.721745	+	0.761034i
$447$	19.9983	−	19.9983i	0.945886	−	0.945886i
$448$		0			0
$449$		−	24.3525i		−	1.14927i	−0.818411	−	0.574633i	$-0.805145\pi$
$449$		−	24.3525i		−	1.14927i	0.818411	−	0.574633i	$-0.194855\pi$
$450$	25.3547	−	0.800933i	1.19523	−	0.0377563i
$451$		−	19.6265i		−	0.924176i
$452$	14.5711	−	16.2031i	0.685366	−	0.762128i
$453$	−30.0353	+	30.0353i	−1.41118	+	1.41118i
$454$	−2.69399	−	2.55491i	−0.126435	−	0.119908i
$455$		0			0
$456$	−25.0898	+	29.4319i	−1.17494	+	1.37827i
$457$	−9.85909	−	9.85909i	−0.461189	−	0.461189i	0.437856	−	0.899045i	$-0.355738\pi$
$457$	−9.85909	−	9.85909i	−0.461189	−	0.461189i	−0.899045	+	0.437856i	$0.855738\pi$
$458$	−2.87376	+	0.0761456i	−0.134282	+	0.00355805i
$459$	−4.63523			−0.216354
$460$	−7.54576	+	8.43395i	−0.351823	+	0.393235i
$461$	−15.8798			−0.739597			−0.369799	−	0.929112i	$-0.620573\pi$
$461$	−15.8798			−0.739597			−0.369799	+	0.929112i	$0.620573\pi$
$462$		0			0
$463$	−21.2388	−	21.2388i	−0.987052	−	0.987052i	0.0128649	−	0.999917i	$-0.495905\pi$
$463$	−21.2388	−	21.2388i	−0.987052	−	0.987052i	−0.999917	+	0.0128649i	$0.995905\pi$
$464$	2.68978	+	25.2892i	0.124870	+	1.17402i
$465$	−17.7734	−	17.6832i	−0.824224	−	0.820041i
$466$	14.2962	+	13.5582i	0.662259	+	0.628070i
$467$	−16.7414	+	16.7414i	−0.774700	+	0.774700i	−0.978924	−	0.204224i	$-0.934533\pi$
$467$	−16.7414	+	16.7414i	−0.774700	+	0.774700i	0.204224	+	0.978924i	$0.434533\pi$
$468$	22.2255	+	19.9869i	1.02737	+	0.923896i
$469$		0			0
$470$	−1.76477	+	1.87035i	−0.0814029	+	0.0862727i
$471$		−	14.5570i		−	0.670752i
$472$	−0.949577	−	11.9234i	−0.0437078	−	0.548820i
$473$	−1.88750	+	1.88750i	−0.0867875	+	0.0867875i
$474$	−19.7719	+	20.8482i	−0.908152	+	0.957588i
$475$	26.6371	−	0.135530i	1.22219	−	0.00621856i
$476$		0			0
$477$	6.85764	+	6.85764i	0.313990	+	0.313990i
$478$	−0.364440	−	13.7541i	−0.0166691	−	0.629097i
$479$	23.4635			1.07208			0.536038	−	0.844194i	$-0.319920\pi$
$479$	23.4635			1.07208			0.536038	+	0.844194i	$0.319920\pi$
$480$	−25.8372	−	19.6579i	−1.17930	−	0.897258i
$481$	16.6844			0.760744
$482$	0.597324	+	22.5432i	0.0272073	+	1.02682i
$483$		0			0
$484$	−15.1816	+	0.805092i	−0.690071	+	0.0365951i
$485$	−0.437469	+	0.439700i	−0.0198644	+	0.0199658i
$486$	−21.6175	+	22.7942i	−0.980588	+	1.03397i
$487$	−5.81519	+	5.81519i	−0.263511	+	0.263511i	−0.826479	−	0.562968i	$-0.809660\pi$
$487$	−5.81519	+	5.81519i	−0.263511	+	0.263511i	0.562968	+	0.826479i	$0.309660\pi$
$488$	−2.69722	−	33.8678i	−0.122097	−	1.53312i
$489$			7.62100i			0.344633i
$490$		0			0
$491$		−	25.5075i		−	1.15114i	−0.817753	−	0.575569i	$-0.804781\pi$
$491$		−	25.5075i		−	1.15114i	0.817753	−	0.575569i	$-0.195219\pi$
$492$	−40.6352	−	36.5424i	−1.83198	−	1.64746i
$493$	−13.8203	+	13.8203i	−0.622436	+	0.622436i
$494$	22.7741	+	21.5984i	1.02466	+	0.971759i
$495$	0.0376217	+	14.7884i	0.00169097	+	0.664688i
$496$	1.84816	+	17.3763i	0.0829847	+	0.780219i
$497$		0			0
$498$	1.16708	−	0.0309240i	0.0522983	−	0.00138574i
$499$	24.4561			1.09480			0.547402	−	0.836870i	$-0.315617\pi$
$499$	24.4561			1.09480			0.547402	+	0.836870i	$0.315617\pi$
$500$	1.35452	+	22.3196i	0.0605761	+	0.998164i
$501$	−40.5515			−1.81171
$502$	7.94917	−	0.210628i	0.354789	−	0.00940078i
$503$	18.7502	+	18.7502i	0.836032	+	0.836032i	0.988334	−	0.152302i	$-0.0486687\pi$
$503$	18.7502	+	18.7502i	0.836032	+	0.836032i	−0.152302	+	0.988334i	$0.548669\pi$
$504$		0			0
$505$	−0.0418050	−	16.4327i	−0.00186030	−	0.731248i
$506$	−4.78697	−	4.53984i	−0.212807	−	0.201820i
$507$	7.90412	−	7.90412i	0.351034	−	0.351034i
$508$	−17.0489	+	18.9584i	−0.756421	+	0.841141i
$509$		−	19.1037i		−	0.846756i	−0.905953	−	0.423378i	$-0.860844\pi$
$509$		−	19.1037i		−	0.846756i	0.905953	−	0.423378i	$-0.139156\pi$
$510$	−0.724319	−	24.9397i	−0.0320734	−	1.10435i
$511$		0			0
$512$	5.34377	+	21.9874i	0.236163	+	0.971713i
$513$	5.68019	−	5.68019i	0.250787	−	0.250787i
$514$	−4.98752	+	5.25902i	−0.219990	+	0.231965i
$515$	−21.5118	+	21.6216i	−0.947924	+	0.952760i
$516$	0.393609	+	7.42226i	0.0173277	+	0.326747i
$517$	−1.06003	−	1.06003i	−0.0466201	−	0.0466201i
$518$		0			0
$519$	−17.8166			−0.782062
$520$	−17.0418	+	20.0944i	−0.747332	+	0.881198i
$521$	10.4003			0.455646			0.227823	−	0.973703i	$-0.426839\pi$
$521$	10.4003			0.455646			0.227823	+	0.973703i	$0.426839\pi$
$522$	−0.854406	−	32.2456i	−0.0373964	−	1.41135i
$523$	2.98601	+	2.98601i	0.130569	+	0.130569i	0.769371	−	0.638802i	$-0.220570\pi$
$523$	2.98601	+	2.98601i	0.130569	+	0.130569i	−0.638802	+	0.769371i	$0.720570\pi$
$524$	1.98600	+	37.4499i	0.0867588	+	1.63600i
$525$		0			0
$526$	7.67932	−	8.09735i	0.334834	−	0.353061i
$527$	−9.49599	+	9.49599i	−0.413652	+	0.413652i
$528$	11.8924	−	14.7233i	0.517552	−	0.640750i
$529$		−	16.5965i		−	0.721587i
$530$	−5.86681	+	6.21778i	−0.254838	+	0.270083i
$531$			15.1712i			0.658372i
$532$		0			0
$533$	−31.3614	+	31.3614i	−1.35841	+	1.35841i
$534$	−11.4265	−	10.8366i	−0.494471	−	0.468944i
$535$	−7.40309	−	7.36551i	−0.320063	−	0.318439i
$536$	−7.12064	−	6.07013i	−0.307565	−	0.262190i
$537$	−18.4686	−	18.4686i	−0.796981	−	0.796981i
$538$	−6.49626	+	0.172130i	−0.280074	+	0.00742106i
$539$		0			0
$540$	5.02549	+	4.49625i	0.216263	+	0.193488i
$541$	−0.383853			−0.0165031			−0.00825157	−	0.999966i	$-0.502627\pi$
$541$	−0.383853			−0.0165031			−0.00825157	+	0.999966i	$0.502627\pi$
$542$	−40.5210	+	1.07368i	−1.74052	+	0.0461184i
$543$	−19.6105	−	19.6105i	−0.841569	−	0.841569i
$544$	−10.5647	+	13.8125i	−0.452957	+	0.592208i
$545$	−22.6536	+	0.0576308i	−0.970374	+	0.00246863i
$546$		0			0
$547$	0.879876	−	0.879876i	0.0376208	−	0.0376208i	−0.688046	−	0.725667i	$-0.741531\pi$
$547$	0.879876	−	0.879876i	0.0376208	−	0.0376208i	0.725667	+	0.688046i	$0.241531\pi$
$548$	26.8363	+	24.1333i	1.14639	+	1.03092i
$549$			43.0928i			1.83916i
$550$	−13.0291	+	0.411579i	−0.555564	+	0.0175498i
$551$		−	33.8719i		−	1.44299i
$552$	−18.3122	+	1.45838i	−0.779419	+	0.0620726i
$553$		0			0
$554$	−5.23023	+	5.51494i	−0.222211	+	0.234308i
$555$	22.9847	−	0.0584732i	0.975648	−	0.00248205i
$556$	−4.76825	+	0.252864i	−0.202219	+	0.0107238i
$557$	27.4948	+	27.4948i	1.16499	+	1.16499i	0.983368	+	0.181623i	$0.0581352\pi$
$557$	27.4948	+	27.4948i	1.16499	+	1.16499i	0.181623	+	0.983368i	$0.441865\pi$
$558$	−0.587065	−	22.1561i	−0.0248524	−	0.937941i
$559$	6.03213			0.255132
$560$		0			0
$561$	14.5453			0.614102
$562$	0.909698	+	34.3323i	0.0383733	+	1.44822i
$563$	6.69099	+	6.69099i	0.281992	+	0.281992i	0.833903	−	0.551911i	$-0.186101\pi$
$563$	6.69099	+	6.69099i	0.281992	+	0.281992i	−0.551911	+	0.833903i	$0.686101\pi$
$564$	−4.16838	+	0.221053i	−0.175520	+	0.00930800i
$565$	−17.2712	−	17.1836i	−0.726606	−	0.722918i
$566$	9.91093	−	10.4504i	0.416587	−	0.439265i
$567$		0			0
$568$	29.6940	−	2.36481i	1.24593	−	0.0992254i
$569$		−	36.2606i		−	1.52012i	−0.649850	−	0.760062i	$-0.725168\pi$
$569$		−	36.2606i		−	1.52012i	0.649850	−	0.760062i	$-0.274832\pi$
$570$	31.4498	+	29.6745i	1.31729	+	1.24293i
$571$		−	47.6335i		−	1.99340i	−0.0811838	−	0.996699i	$-0.525870\pi$
$571$		−	47.6335i		−	1.99340i	0.0811838	−	0.996699i	$-0.474130\pi$
$572$	−11.4211	−	10.2708i	−0.477540	−	0.429442i
$573$	−25.0932	+	25.0932i	−1.04828	+	1.04828i
$574$		0			0
$575$	8.99212	+	8.90108i	0.374997	+	0.371201i
$576$	−4.54248	−	28.3381i	−0.189270	−	1.18075i
$577$	−32.2110	−	32.2110i	−1.34096	−	1.34096i	−0.895102	−	0.445861i	$-0.852898\pi$
$577$	−32.2110	−	32.2110i	−1.34096	−	1.34096i	−0.445861	−	0.895102i	$-0.647102\pi$
$578$	10.6736	−	0.282817i	0.443964	−	0.0117636i
$579$	17.7027			0.735698
$580$	28.3899	−	1.57798i	1.17882	−	0.0655219i
$581$		0			0
$582$	−1.00648	+	0.0266686i	−0.0417201	+	0.00110545i
$583$	−3.52396	−	3.52396i	−0.145948	−	0.145948i
$584$	4.40563	+	3.75567i	0.182306	+	0.155411i
$585$	23.5704	−	23.6906i	0.974517	−	0.979488i
$586$	28.4270	+	26.9595i	1.17431	+	1.11368i
$587$	15.9943	−	15.9943i	0.660155	−	0.660155i	−0.295261	−	0.955417i	$-0.595407\pi$
$587$	15.9943	−	15.9943i	0.660155	−	0.660155i	0.955417	+	0.295261i	$0.0954067\pi$
$588$		0			0
$589$		−	23.2735i		−	0.958968i
$590$	−13.3674	+	0.388225i	−0.550326	+	0.0159830i
$591$		−	28.5069i		−	1.17262i
$592$	−12.4622	−	10.0661i	−0.512194	−	0.413713i
$593$	−4.71970	+	4.71970i	−0.193815	+	0.193815i	−0.797342	−	0.603527i	$-0.793761\pi$
$593$	−4.71970	+	4.71970i	−0.193815	+	0.193815i	0.603527	+	0.797342i	$0.293761\pi$
$594$	−2.70513	+	2.85238i	−0.110993	+	0.117035i
$595$		0			0
$596$	1.16707	+	22.0074i	0.0478050	+	0.901457i
$597$	31.3534	+	31.3534i	1.28321	+	1.28321i
$598$	0.394893	+	14.9034i	0.0161484	+	0.609446i
$599$	−33.9895			−1.38877			−0.694387	−	0.719602i	$-0.744324\pi$
$599$	−33.9895			−1.38877			−0.694387	+	0.719602i	$0.744324\pi$
$600$	−23.4067	+	27.7421i	−0.955573	+	1.13257i
$601$	32.7782			1.33705			0.668526	−	0.743689i	$-0.266926\pi$
$601$	32.7782			1.33705			0.668526	+	0.743689i	$0.266926\pi$
$602$		0			0
$603$	8.39185	+	8.39185i	0.341743	+	0.341743i
$604$	−1.75281	−	33.0527i	−0.0713209	−	1.34489i
$605$	0.0432412	+	16.9973i	0.00175800	+	0.691039i
$606$	18.3557	−	19.3549i	0.745650	−	0.786240i
$607$	14.8465	−	14.8465i	0.602600	−	0.602600i	−0.338402	−	0.941002i	$-0.609886\pi$
$607$	14.8465	−	14.8465i	0.602600	−	0.602600i	0.941002	+	0.338402i	$0.109886\pi$
$608$	−3.98005	−	29.8728i	−0.161412	−	1.21150i
$609$		0			0
$610$	−37.9692	+	1.10273i	−1.53733	+	0.0446483i
$611$			3.38768i			0.137051i
$612$	14.7484	−	16.4003i	0.596171	−	0.662942i
$613$	−20.7100	+	20.7100i	−0.836470	+	0.836470i	−0.988392	−	0.151922i	$-0.951454\pi$
$613$	−20.7100	+	20.7100i	−0.836470	+	0.836470i	0.151922	+	0.988392i	$0.451454\pi$
$614$	−30.0814	−	28.5285i	−1.21399	−	1.15131i
$615$	−43.0941	+	43.3140i	−1.73772	+	1.74659i
$616$		0			0
$617$	−27.0214	−	27.0214i	−1.08784	−	1.08784i	−0.995751	−	0.0920892i	$-0.970646\pi$
$617$	−27.0214	−	27.0214i	−1.08784	−	1.08784i	−0.0920892	−	0.995751i	$-0.529354\pi$
$618$	−49.4923	+	1.31139i	−1.99087	+	0.0527518i
$619$	−12.8877			−0.518000			−0.259000	−	0.965877i	$-0.583393\pi$
$619$	−12.8877			−0.518000			−0.259000	+	0.965877i	$0.583393\pi$
$620$	19.5068	−	1.08423i	0.783410	−	0.0435438i
$621$	3.81562			0.153115
$622$	−6.13994	+	0.162689i	−0.246189	+	0.00652323i
$623$		0			0
$624$	−42.5297	+	4.52349i	−1.70255	+	0.181085i
$625$	24.9987	−	0.254395i	0.999948	−	0.0101758i
$626$	−8.05340	−	7.63764i	−0.321879	−	0.305262i
$627$	−17.8243	+	17.8243i	−0.711836	+	0.711836i
$628$	8.43450	+	7.58497i	0.336573	+	0.302673i
$629$		−	12.3115i		−	0.490892i
$630$		0			0
$631$		−	35.1539i		−	1.39945i	−0.714410	−	0.699727i	$-0.753305\pi$
$631$		−	35.1539i		−	1.39945i	0.714410	−	0.699727i	$-0.246695\pi$
$632$	−1.77748	−	22.3190i	−0.0707042	−	0.887802i
$633$	33.8909	−	33.8909i	1.34704	−	1.34704i
$634$	2.36031	−	2.48880i	0.0937399	−	0.0988427i
$635$	20.2081	+	20.1056i	0.801936	+	0.797866i
$636$	−13.8573	+	0.734867i	−0.549479	+	0.0291394i
$637$		0			0
$638$	0.439057	+	16.5702i	0.0173824	+	0.656020i
$639$	−37.7821			−1.49464
$640$	24.8526	−	4.72756i	0.982384	−	0.186873i
$641$	9.97368			0.393937			0.196968	−	0.980410i	$-0.436890\pi$
$641$	9.97368			0.393937			0.196968	+	0.980410i	$0.436890\pi$
$642$	−0.449011	−	16.9458i	−0.0177210	−	0.668799i
$643$	−25.3846	−	25.3846i	−1.00107	−	1.00107i	−0.999999	−	0.00107009i	$-0.999659\pi$
$643$	−25.3846	−	25.3846i	−1.00107	−	1.00107i	−0.00107009	−	0.999999i	$-0.500341\pi$
$644$		0			0
$645$	8.30997	−	0.0211406i	0.327205	−	0.000832410i
$646$	15.9376	−	16.8052i	0.627056	−	0.661190i
$647$	1.42612	−	1.42612i	0.0560667	−	0.0560667i	−0.678518	−	0.734584i	$-0.737377\pi$
$647$	1.42612	−	1.42612i	0.0560667	−	0.0560667i	0.734584	+	0.678518i	$0.237377\pi$
$648$	−1.54765	−	19.4331i	−0.0607974	−	0.763406i
$649$		−	7.79607i		−	0.306022i
$650$	21.4771	+	20.1617i	0.842400	+	0.790808i
$651$		0			0
$652$	−4.41569	−	3.97094i	−0.172932	−	0.155514i
$653$	−9.34898	+	9.34898i	−0.365854	+	0.365854i	−0.865963	−	0.500109i	$-0.833293\pi$
$653$	−9.34898	+	9.34898i	−0.365854	+	0.365854i	0.500109	+	0.865963i	$0.333293\pi$
$654$	−26.6820	−	25.3045i	−1.04335	−	0.989486i
$655$	41.9289	−	0.106667i	1.63830	−	0.00416784i
$656$	42.3461	−	4.50397i	1.65334	−	0.175850i
$657$	−5.19215	−	5.19215i	−0.202565	−	0.202565i
$658$		0			0
$659$	43.1794			1.68203			0.841015	−	0.541011i	$-0.181958\pi$
$659$	43.1794			1.68203			0.841015	+	0.541011i	$0.181958\pi$
$660$	−15.7699	−	14.1091i	−0.613842	−	0.549198i
$661$	−16.1804			−0.629346			−0.314673	−	0.949200i	$-0.601895\pi$
$661$	−16.1804			−0.629346			−0.314673	+	0.949200i	$0.601895\pi$
$662$	18.1423	−	0.480713i	0.705120	−	0.0186834i
$663$	−23.2421	−	23.2421i	−0.902647	−	0.902647i
$664$	−0.590194	+	0.692334i	−0.0229040	+	0.0268678i
$665$		0			0
$666$	14.7432	+	13.9821i	0.571287	+	0.541794i
$667$	11.3766	−	11.3766i	0.440503	−	0.440503i
$668$	21.1294	−	23.4959i	0.817522	−	0.909085i
$669$			40.2000i			1.55422i
$670$	−7.17935	+	7.60884i	−0.277362	+	0.293955i
$671$		−	22.1443i		−	0.854870i
$672$		0			0
$673$	−9.53669	+	9.53669i	−0.367612	+	0.367612i	−0.866606	−	0.498993i	$-0.833703\pi$
$673$	−9.53669	+	9.53669i	−0.367612	+	0.367612i	0.498993	+	0.866606i	$0.333703\pi$
$674$	−34.5549	+	36.4359i	−1.33101	+	1.40346i
$675$	5.30384	−	5.35808i	0.204145	−	0.206233i
$676$	0.461272	+	8.69819i	0.0177412	+	0.334546i
$677$	21.6625	+	21.6625i	0.832556	+	0.832556i	0.987866	−	0.155310i	$-0.0496375\pi$
$677$	21.6625	+	21.6625i	0.832556	+	0.832556i	−0.155310	+	0.987866i	$0.549638\pi$
$678$	−1.04753	−	39.5342i	−0.0402302	−	1.51830i
$679$		0			0
$680$	14.8278	+	12.5752i	0.568619	+	0.482238i
$681$	−6.73830			−0.258212
$682$	0.301678	+	11.3854i	0.0115518	+	0.435970i
$683$	14.7325	+	14.7325i	0.563725	+	0.563725i	0.930363	−	0.366639i	$-0.119491\pi$
$683$	14.7325	+	14.7325i	0.563725	+	0.563725i	−0.366639	+	0.930363i	$0.619491\pi$
$684$	2.02424	+	38.1709i	0.0773986	+	1.45950i
$685$	28.4602	−	28.6054i	1.08741	−	1.09296i
$686$		0			0
$687$	−3.68921	+	3.68921i	−0.140752	+	0.140752i
$688$	−4.50563	−	3.63932i	−0.171775	−	0.138748i
$689$			11.2620i			0.429047i
$690$	0.596243	+	20.5298i	0.0226986	+	0.781557i
$691$		−	5.85597i		−	0.222772i	−0.993777	−	0.111386i	$-0.964471\pi$
$691$		−	5.85597i		−	0.222772i	0.993777	−	0.111386i	$-0.0355289\pi$
$692$	9.28338	−	10.3231i	0.352901	−	0.392427i
$693$		0			0
$694$	−4.36357	−	4.13830i	−0.165639	−	0.157088i
$695$	0.0135813	+	5.33854i	0.000515166	+	0.202502i
$696$	35.1248	+	29.9428i	1.33140	+	1.13498i
$697$	23.1418	+	23.1418i	0.876556	+	0.876556i
$698$	5.78583	−	0.153306i	0.218997	−	0.00580272i
$699$	35.7582			1.35250
$700$		0			0
$701$	20.0349			0.756706			0.378353	−	0.925661i	$-0.376491\pi$
$701$	20.0349			0.756706			0.378353	+	0.925661i	$0.376491\pi$
$702$	8.88042	−	0.235303i	0.335170	−	0.00888094i
$703$	15.0870	+	15.0870i	0.569017	+	0.569017i
$704$	2.33426	+	14.5622i	0.0879759	+	0.548834i
$705$	0.0118727	+	4.66692i	0.000447150	+	0.175766i
$706$	20.5035	+	19.4450i	0.771658	+	0.731821i
$707$		0			0
$708$	−16.1412	−	14.5154i	−0.606622	−	0.545523i
$709$			49.4032i			1.85538i	0.373356	+	0.927688i	$0.378207\pi$
$709$			49.4032i			1.85538i	−0.373356	+	0.927688i	$0.621793\pi$
$710$	−0.966832	−	33.2899i	−0.0362846	−	1.24935i
$711$			28.3983i			1.06502i
$712$	12.2326	−	0.974200i	0.458436	−	0.0365097i
$713$	7.81688	−	7.81688i	0.292744	−	0.292744i
$714$		0			0
$715$	−12.1122	+	12.1740i	−0.452972	+	0.455282i
$716$	20.3241	−	1.07780i	0.759546	−	0.0402794i
$717$	−17.6569	−	17.6569i	−0.659408	−	0.659408i
$718$	−0.364024	−	13.7384i	−0.0135853	−	0.512713i
$719$	24.2954			0.906067			0.453033	−	0.891494i	$-0.350342\pi$
$719$	24.2954			0.906067			0.453033	+	0.891494i	$0.350342\pi$
$720$	−31.8987	+	3.47487i	−1.18880	+	0.129501i
$721$		0			0
$722$	0.351443	+	13.2636i	0.0130794	+	0.493620i
$723$	28.9400	+	28.9400i	1.07629	+	1.07629i
$724$	21.5807	−	1.14444i	0.802039	−	0.0425328i
$725$	−0.161746	−	31.7894i	−0.00600709	−	1.18063i
$726$	−18.9863	+	20.0199i	−0.704649	+	0.743008i
$727$	15.7313	−	15.7313i	0.583441	−	0.583441i	−0.352406	−	0.935847i	$-0.614636\pi$
$727$	15.7313	−	15.7313i	0.583441	−	0.583441i	0.935847	+	0.352406i	$0.114636\pi$
$728$		0			0
$729$			36.3365i			1.34580i
$730$	4.44196	−	4.70769i	0.164404	−	0.174239i
$731$		−	4.45114i		−	0.164631i
$732$	−45.8480	−	41.2302i	−1.69459	−	1.52391i
$733$	20.2499	−	20.2499i	0.747948	−	0.747948i	−0.226146	−	0.974094i	$-0.572613\pi$
$733$	20.2499	−	20.2499i	0.747948	−	0.747948i	0.974094	+	0.226146i	$0.0726125\pi$
$734$	15.5895	+	14.7847i	0.575420	+	0.545713i
$735$		0			0
$736$	8.69661	−	11.3702i	0.320561	−	0.419110i
$737$	−4.31236	−	4.31236i	−0.158848	−	0.158848i
$738$	−53.9944	+	1.43068i	−1.98756	+	0.0526641i
$739$	8.87027			0.326298			0.163149	−	0.986601i	$-0.447835\pi$
$739$	8.87027			0.326298			0.163149	+	0.986601i	$0.447835\pi$
$740$	−11.9424	+	13.3481i	−0.439010	+	0.490685i
$741$	56.9635			2.09261
$742$		0			0
$743$	−10.5849	−	10.5849i	−0.388323	−	0.388323i	0.485766	−	0.874089i	$-0.338541\pi$
$743$	−10.5849	−	10.5849i	−0.388323	−	0.388323i	−0.874089	+	0.485766i	$0.838541\pi$
$744$	24.1343	+	20.5738i	0.884808	+	0.754272i
$745$	24.6395	−	0.0626829i	0.902720	−	0.00229652i
$746$	33.1205	+	31.4107i	1.21263	+	1.15003i
$747$	0.815934	−	0.815934i	0.0298535	−	0.0298535i
$748$	−7.57884	+	8.42768i	−0.277110	+	0.308147i
$749$		0			0
$750$	29.6578	+	27.6999i	1.08295	+	1.01146i
$751$			30.2540i			1.10398i	0.833850	+	0.551992i	$0.186132\pi$
$751$			30.2540i			1.10398i	−0.833850	+	0.551992i	$0.813868\pi$
$752$	2.04386	−	2.53038i	0.0745320	−	0.0922735i
$753$	10.2048	−	10.2048i	0.371883	−	0.371883i
$754$	25.7761	−	27.1793i	0.938712	−	0.989811i
$755$	−37.0058	+	0.0941429i	−1.34678	+	0.00342621i
$756$		0			0
$757$	−18.0236	−	18.0236i	−0.655078	−	0.655078i	0.299133	−	0.954211i	$-0.403302\pi$
$757$	−18.0236	−	18.0236i	−0.655078	−	0.655078i	−0.954211	+	0.299133i	$0.903302\pi$
$758$	1.09604	+	41.3651i	0.0398101	+	1.50245i
$759$	−11.9733			−0.434604
$760$	−33.5807	+	2.76034i	−1.21810	+	0.100128i
$761$	−25.9242			−0.939750			−0.469875	−	0.882733i	$-0.655701\pi$
$761$	−25.9242			−0.939750			−0.469875	+	0.882733i	$0.655701\pi$
$762$	1.22566	+	46.2569i	0.0444010	+	1.67571i
$763$		0			0
$764$	−1.46440	−	27.6142i	−0.0529803	−	0.999046i
$765$	−17.4814	−	17.3927i	−0.632043	−	0.628835i
$766$	−10.9871	+	11.5852i	−0.396980	+	0.418590i
$767$	−12.4574	+	12.4574i	−0.449812	+	0.449812i
$768$	34.4961	+	22.2803i	1.24477	+	0.803973i
$769$			43.7662i			1.57825i	0.614232	+	0.789125i	$0.289466\pi$
$769$			43.7662i			1.57825i	−0.614232	+	0.789125i	$0.710534\pi$
$770$		0			0
$771$			13.1540i			0.473731i
$772$	−9.22401	+	10.2571i	−0.331979	+	0.369162i
$773$	−7.07081	+	7.07081i	−0.254319	+	0.254319i	−0.822739	−	0.568420i	$-0.807555\pi$
$773$	−7.07081	+	7.07081i	−0.254319	+	0.254319i	0.568420	+	0.822739i	$0.307555\pi$
$774$	5.33030	+	5.05512i	0.191594	+	0.181702i
$775$	−0.111136	−	21.8426i	−0.00399212	−	0.784609i
$776$	0.508979	−	0.597063i	0.0182713	−	0.0214333i
$777$		0			0
$778$	54.6132	−	1.44708i	1.95798	−	0.0518802i
$779$	−56.7176			−2.03212
$780$	2.65373	+	47.7441i	0.0950188	+	1.70951i
$781$	19.4152			0.694732
$782$	10.9973	−	0.291394i	0.393263	−	0.0104202i
$783$	−6.77890	−	6.77890i	−0.242258	−	0.242258i
$784$		0			0
$785$	8.94490	−	8.99052i	0.319257	−	0.320886i
$786$	49.3850	+	46.8355i	1.76150	+	1.67057i
$787$	10.2616	−	10.2616i	0.365788	−	0.365788i	−0.500151	−	0.865938i	$-0.666722\pi$
$787$	10.2616	−	10.2616i	0.365788	−	0.365788i	0.865938	+	0.500151i	$0.166722\pi$
$788$	16.5172	+	14.8536i	0.588401	+	0.529137i
$789$		−	20.2534i		−	0.721040i
$790$	−25.0219	+	0.726705i	−0.890238	+	0.0258550i
$791$		0			0
$792$	−1.48504	−	18.6470i	−0.0527686	−	0.662592i
$793$	−35.3846	+	35.3846i	−1.25654	+	1.25654i
$794$	8.35087	−	8.80545i	0.296361	−	0.312494i
$795$	0.0394694	+	15.5147i	0.00139984	+	0.550249i
$796$	−34.5033	+	1.82974i	−1.22294	+	0.0648533i
$797$	−16.4978	−	16.4978i	−0.584382	−	0.584382i	0.351723	−	0.936104i	$-0.385596\pi$
$797$	−16.4978	−	16.4978i	−0.584382	−	0.584382i	−0.936104	+	0.351723i	$0.885596\pi$
$798$		0			0
$799$	2.49978			0.0884360
$800$	−3.87800	−	28.0172i	−0.137108	−	0.990556i
$801$	−15.5646			−0.549947
$802$	−0.0871518	−	3.28914i	−0.00307744	−	0.116144i
$803$	2.66811	+	2.66811i	0.0941556	+	0.0941556i
$804$	−16.9575	+	0.899273i	−0.598046	+	0.0317149i
$805$		0			0
$806$	17.7109	−	18.6750i	0.623839	−	0.657798i
$807$	−8.33961	+	8.33961i	−0.293568	+	0.293568i
$808$	1.65017	+	20.7204i	0.0580527	+	0.728942i
$809$		−	10.6156i		−	0.373226i	−0.982433	−	0.186613i	$-0.940249\pi$
$809$		−	10.6156i		−	0.373226i	0.982433	−	0.186613i	$-0.0597511\pi$
$810$	−21.7865	+	0.632741i	−0.765500	+	0.0222323i
$811$			51.1988i			1.79783i	0.438122	+	0.898916i	$0.355644\pi$
$811$			51.1988i			1.79783i	−0.438122	+	0.898916i	$0.644356\pi$
$812$		0			0
$813$	−52.0190	+	52.0190i	−1.82439	+	1.82439i
$814$	−7.57614	−	7.18502i	−0.265544	−	0.251835i
$815$	−4.68290	+	4.70678i	−0.164035	+	0.164871i
$816$	3.33791	+	31.3828i	0.116850	+	1.09862i
$817$	5.45460	+	5.45460i	0.190832	+	0.190832i
$818$	−0.265759	+	0.00704177i	−0.00929205	+	0.000246210i
$819$		0			0
$820$	−2.64228	−	47.5380i	−0.0922723	−	1.66010i
$821$	−4.31325			−0.150534			−0.0752668	−	0.997163i	$-0.523981\pi$
$821$	−4.31325			−0.150534			−0.0752668	+	0.997163i	$0.523981\pi$
$822$	65.4784	−	1.73497i	2.28382	−	0.0605140i
$823$	−18.7346	−	18.7346i	−0.653048	−	0.653048i	0.300678	−	0.953726i	$-0.402787\pi$
$823$	−18.7346	−	18.7346i	−0.653048	−	0.653048i	−0.953726	+	0.300678i	$0.902787\pi$
$824$	25.0282	−	29.3597i	0.871899	−	1.02279i
$825$	−16.6433	+	16.8136i	−0.579447	+	0.585374i
$826$		0			0
$827$	−37.0665	+	37.0665i	−1.28893	+	1.28893i	−0.353490	+	0.935438i	$0.615005\pi$
$827$	−37.0665	+	37.0665i	−1.28893	+	1.28893i	−0.935438	+	0.353490i	$0.884995\pi$
$828$	−12.1406	+	13.5003i	−0.421914	+	0.469169i
$829$		−	10.5113i		−	0.365071i	−0.983199	−	0.182535i	$-0.941570\pi$
$829$		−	10.5113i		−	0.365071i	0.983199	−	0.182535i	$-0.0584304\pi$
$830$	0.739801	+	0.698042i	0.0256789	+	0.0242294i
$831$			13.7942i			0.478515i
$832$	19.5392	−	26.9991i	0.677400	−	0.936026i
$833$		0			0
$834$	−5.96326	+	6.28787i	−0.206491	+	0.217731i
$835$	−25.0449	−	24.9178i	−0.866713	−	0.862315i
$836$	−1.04020	−	19.6150i	−0.0359761	−	0.678400i
$837$	−4.65780	−	4.65780i	−0.160997	−	0.160997i
$838$	−0.490192	−	18.5000i	−0.0169334	−	0.639072i
$839$	−32.0936			−1.10799			−0.553996	−	0.832519i	$-0.686898\pi$
$839$	−32.0936			−1.10799			−0.553996	+	0.832519i	$0.686898\pi$
$840$		0			0
$841$	−11.4237			−0.393921
$842$	0.124939	+	4.71525i	0.00430568	+	0.162498i
$843$	44.0743	+	44.0743i	1.51800	+	1.51800i
$844$	1.97782	+	37.2957i	0.0680794	+	1.28377i
$845$	9.73850	−	0.0247748i	0.335015	−	0.000852278i
$846$	−2.83898	+	2.99352i	−0.0976061	+	0.102919i
$847$		0			0
$848$	6.79461	−	8.41199i	0.233328	−	0.288869i
$849$		−	26.1390i		−	0.897089i
$850$	14.8774	−	15.8480i	0.510292	−	0.543583i
$851$			10.1346i			0.347408i
$852$	36.1490	−	40.1978i	1.23845	−	1.37715i
$853$	−14.4800	+	14.4800i	−0.495785	+	0.495785i	−0.910123	−	0.414338i	$-0.864013\pi$
$853$	−14.4800	+	14.4800i	−0.495785	+	0.495785i	0.414338	+	0.910123i	$0.364013\pi$
$854$		0			0
$855$	42.7362	−	0.108721i	1.46155	−	0.00371818i
$856$	10.0526	+	8.56951i	0.343589	+	0.292900i
$857$	2.96368	+	2.96368i	0.101237	+	0.101237i	0.755911	−	0.654674i	$-0.227194\pi$
$857$	2.96368	+	2.96368i	0.101237	+	0.101237i	−0.654674	+	0.755911i	$0.727194\pi$
$858$	−27.8666	+	0.738376i	−0.951350	+	0.0252078i
$859$	35.5227			1.21202			0.606010	−	0.795457i	$-0.292769\pi$
$859$	35.5227			1.21202			0.606010	+	0.795457i	$0.292769\pi$
$860$	−4.31768	+	4.82590i	−0.147232	+	0.164562i
$861$		0			0
$862$	−3.40814	+	0.0903049i	−0.116082	+	0.00307580i
$863$	2.48046	+	2.48046i	0.0844359	+	0.0844359i	0.748063	−	0.663627i	$-0.230984\pi$
$863$	2.48046	+	2.48046i	0.0844359	+	0.0844359i	−0.663627	+	0.748063i	$0.730984\pi$
$864$	−6.77508	−	5.18200i	−0.230493	−	0.176295i
$865$	−11.0037	−	10.9478i	−0.374136	−	0.372237i
$866$	0.454241	+	0.430791i	0.0154357	+	0.0146389i
$867$	13.7023	−	13.7023i	0.465354	−	0.465354i
$868$		0			0
$869$		−	14.5932i		−	0.495039i
$870$	35.4144	−	37.5330i	1.20066	−	1.27249i
$871$			13.7815i			0.466970i
$872$	28.5644	−	2.27486i	0.967314	−	0.0770365i
$873$	−0.703655	+	0.703655i	−0.0238151	+	0.0238151i
$874$	−13.1194	+	13.8336i	−0.443772	+	0.467929i
$875$		0			0
$876$	10.4919	−	0.556392i	0.354487	−	0.0187987i
$877$	−15.7329	−	15.7329i	−0.531262	−	0.531262i	0.389686	−	0.920948i	$-0.372584\pi$
$877$	−15.7329	−	15.7329i	−0.531262	−	0.531262i	−0.920948	+	0.389686i	$0.872584\pi$
$878$	−0.841328	−	31.7520i	−0.0283934	−	1.07158i
$879$	71.1027			2.39823
$880$	16.3919	−	1.78564i	0.552572	−	0.0601941i
$881$	−35.9299			−1.21051			−0.605254	−	0.796032i	$-0.706929\pi$
$881$	−35.9299			−1.21051			−0.605254	+	0.796032i	$0.706929\pi$
$882$		0			0
$883$	39.0358	+	39.0358i	1.31366	+	1.31366i	0.918697	+	0.394964i	$0.129243\pi$
$883$	39.0358	+	39.0358i	1.31366	+	1.31366i	0.394964	+	0.918697i	$0.370757\pi$
$884$	25.5770	−	1.35637i	0.860249	−	0.0456198i
$885$	−17.1179	+	17.2052i	−0.575413	+	0.578348i
$886$	16.9760	−	17.9001i	0.570321	−	0.601367i
$887$	−20.7076	+	20.7076i	−0.695294	+	0.695294i	−0.963392	−	0.268098i	$-0.913605\pi$
$887$	−20.7076	+	20.7076i	−0.695294	+	0.695294i	0.268098	+	0.963392i	$0.413605\pi$
$888$	−28.9820	+	2.30811i	−0.972571	+	0.0774552i
$889$		0			0
$890$	−0.398292	−	13.7140i	−0.0133508	−	0.459694i
$891$		−	12.7063i		−	0.425676i
$892$	−23.2923	−	20.9463i	−0.779885	−	0.701334i
$893$	−3.06333	+	3.06333i	−0.102511	+	0.102511i
$894$	29.0210	+	27.5228i	0.970608	+	0.920500i
$895$	−0.0578884	−	22.7548i	−0.00193500	−	0.760611i
$896$		0			0
$897$	19.1323	+	19.1323i	0.638810	+	0.638810i
$898$	34.4276	−	0.912222i	1.14886	−	0.0304412i
$899$	−27.7752			−0.926356
$900$	2.08205	+	35.8144i	0.0694018	+	1.19381i
$901$	8.31027			0.276855
$902$	27.7463	−	0.735189i	0.923851	−	0.0244791i
$903$		0			0
$904$	23.4524	+	19.9925i	0.780015	+	0.664939i
$905$	−0.0614676	−	24.1617i	−0.00204325	−	0.803164i
$906$	−43.5865	−	41.3363i	−1.44806	−	1.37331i
$907$	21.3587	−	21.3587i	0.709204	−	0.709204i	−0.257164	−	0.966368i	$-0.582788\pi$
$907$	21.3587	−	21.3587i	0.709204	−	0.709204i	0.966368	+	0.257164i	$0.0827879\pi$
$908$	3.51100	−	3.90424i	0.116517	−	0.129567i
$909$		−	26.3643i		−	0.874449i
$910$		0			0
$911$			31.4256i			1.04118i	0.853808	+	0.520588i	$0.174287\pi$
$911$			31.4256i			1.04118i	−0.853808	+	0.520588i	$0.825713\pi$
$912$	−42.5482	−	34.3674i	−1.40891	−	1.13802i
$913$	−0.419287	+	0.419287i	−0.0138764	+	0.0138764i
$914$	13.5687	−	14.3073i	0.448811	−	0.473243i
$915$	−48.6225	+	48.8705i	−1.60741	+	1.61561i
$916$	−0.215297	−	4.05984i	−0.00711360	−	0.134141i
$917$		0			0
$918$	−0.173631	−	6.55291i	−0.00573068	−	0.216278i
$919$	50.8371			1.67696			0.838480	−	0.544932i	$-0.183445\pi$
$919$	50.8371			1.67696			0.838480	+	0.544932i	$0.183445\pi$
$920$	−12.2059	−	10.3516i	−0.402416	−	0.341283i
$921$	−75.2407			−2.47927
$922$	−0.594843	−	22.4496i	−0.0195901	−	0.739338i
$923$	−31.0239	−	31.0239i	−1.02116	−	1.02116i
$924$		0			0
$925$	14.2315	+	14.0874i	0.467928	+	0.463190i
$926$	29.2301	−	30.8213i	0.960561	−	1.01285i
$927$	−34.6011	+	34.6011i	−1.13645	+	1.13645i
$928$	−35.6510	+	4.74990i	−1.17030	+	0.155923i
$929$			40.5422i			1.33015i	0.746779	+	0.665073i	$0.231599\pi$
$929$			40.5422i			1.33015i	−0.746779	+	0.665073i	$0.768401\pi$
$930$	24.3333	−	25.7890i	0.797922	−	0.845656i
$931$		0			0
$932$	−18.6319	+	20.7187i	−0.610308	+	0.678663i
$933$	−7.88218	+	7.88218i	−0.258051	+	0.258051i
$934$	−24.2948	−	23.0405i	−0.794949	−	0.753909i
$935$	8.98326	+	8.93767i	0.293784	+	0.292293i
$936$	−27.4233	+	32.1692i	−0.896359	+	1.05148i
$937$	7.47390	+	7.47390i	0.244162	+	0.244162i	0.818569	−	0.574408i	$-0.194768\pi$
$937$	7.47390	+	7.47390i	0.244162	+	0.244162i	−0.574408	+	0.818569i	$0.694768\pi$
$938$		0			0
$939$	−20.1435			−0.657357
$940$	−2.71025	−	2.42483i	−0.0883986	−	0.0790892i
$941$	−5.54597			−0.180794			−0.0903968	−	0.995906i	$-0.528814\pi$
$941$	−5.54597			−0.180794			−0.0903968	+	0.995906i	$0.528814\pi$
$942$	20.5795	−	0.545292i	0.670517	−	0.0177666i
$943$	−19.0498	−	19.0498i	−0.620346	−	0.620346i
$944$	16.8208	−	1.78907i	0.547470	−	0.0582294i
$945$		0			0
$946$	−2.73910	−	2.59769i	−0.0890559	−	0.0844583i
$947$	−15.2417	+	15.2417i	−0.495290	+	0.495290i	−0.909968	−	0.414678i	$-0.863894\pi$
$947$	−15.2417	+	15.2417i	−0.495290	+	0.495290i	0.414678	+	0.909968i	$0.363894\pi$
$948$	−30.2140	−	27.1709i	−0.981307	−	0.882469i
$949$		−	8.52682i		−	0.276792i
$950$	1.18940	+	37.6522i	0.0385892	+	1.22160i
$951$		−	6.22506i		−	0.201862i
$952$		0			0
$953$	32.3871	−	32.3871i	1.04912	−	1.04912i	0.0503899	−	0.998730i	$-0.483954\pi$
$953$	32.3871	−	32.3871i	1.04912	−	1.04912i	0.998730	−	0.0503899i	$-0.0160464\pi$
$954$	−9.43789	+	9.95165i	−0.305563	+	0.322197i
$955$	−30.9169	+	0.0786526i	−1.00045	+	0.00254514i
$956$	19.4307	−	1.03043i	0.628435	−	0.0333265i
$957$	21.2721	+	21.2721i	0.687628	+	0.687628i
$958$	0.878920	+	33.1708i	0.0283966	+	1.07170i
$959$		0			0
$960$	26.8229	−	37.2629i	0.865706	−	1.20266i
$961$	11.9155			0.384372
$962$	0.624982	+	23.5870i	0.0201502	+	0.760477i
$963$	−11.8472	−	11.8472i	−0.381771	−	0.381771i
$964$	−31.8474	+	1.68889i	−1.02573	+	0.0543956i
$965$	10.9333	+	10.8778i	0.351955	+	0.350169i
$966$		0			0
$967$	10.6422	−	10.6422i	0.342230	−	0.342230i	−0.514975	−	0.857205i	$-0.672199\pi$
$967$	10.6422	−	10.6422i	0.342230	−	0.342230i	0.857205	+	0.514975i	$0.172199\pi$
$968$	−1.70686	−	21.4323i	−0.0548605	−	0.688860i
$969$		−	42.0337i		−	1.35032i
$970$	−0.637999	−	0.601986i	−0.0204849	−	0.0193286i
$971$			11.6752i			0.374675i	0.982296	+	0.187337i	$0.0599858\pi$
$971$			11.6752i			0.374675i	−0.982296	+	0.187337i	$0.940014\pi$
$972$	−33.0344	−	29.7071i	−1.05958	−	0.952857i
$973$		0			0
$974$	−8.43886	−	8.00320i	−0.270399	−	0.256439i
$975$	53.4612	−	0.272013i	1.71213	−	0.00871138i
$976$	47.7784	−	5.08176i	1.52935	−	0.162663i
$977$	−21.7862	−	21.7862i	−0.697001	−	0.697001i	0.266761	−	0.963763i	$-0.414046\pi$
$977$	−21.7862	−	21.7862i	−0.697001	−	0.697001i	−0.963763	+	0.266761i	$0.914046\pi$
$978$	−10.7739	+	0.285475i	−0.344513	+	0.00912849i
$979$	7.99822			0.255624
$980$		0			0
$981$	−36.3449			−1.16040
$982$	36.0604	−	0.955486i	1.15073	−	0.0304908i
$983$	−33.0726	−	33.0726i	−1.05485	−	1.05485i	−0.998406	−	0.0564457i	$-0.982023\pi$
$983$	−33.0726	−	33.0726i	−1.05485	−	1.05485i	−0.0564457	−	0.998406i	$-0.517977\pi$
$984$	50.1384	−	58.8155i	1.59836	−	1.87497i
$985$	17.5167	−	17.6061i	0.558129	−	0.560976i
$986$	−20.0557	−	19.0203i	−0.638705	−	0.605731i
$987$		0			0
$988$	−29.6810	+	33.0053i	−0.944277	+	1.05004i
$989$			3.66408i			0.116511i
$990$	−20.9052	+	0.607144i	−0.664410	+	0.0192963i
$991$			50.1554i			1.59324i	0.604481	+	0.796620i	$0.293381\pi$
$991$			50.1554i			1.59324i	−0.604481	+	0.796620i	$0.706619\pi$
$992$	−24.4959	+	3.26367i	−0.777747	+	0.103622i
$993$	23.2903	−	23.2903i	0.739094	−	0.739094i
$994$		0			0
$995$	0.0982746	+	38.6299i	0.00311551	+	1.22465i
$996$	0.0874357	+	1.64877i	0.00277050	+	0.0522432i
$997$	20.5546	+	20.5546i	0.650972	+	0.650972i	0.953227	−	0.302255i	$-0.0977394\pi$
$997$	20.5546	+	20.5546i	0.650972	+	0.650972i	−0.302255	+	0.953227i	$0.597739\pi$
$998$	0.916101	+	34.5740i	0.0289987	+	1.09442i
$999$	6.03882			0.191060

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.k.687.10		36
4.3	odd	2	inner	980.2.k.k.687.18		36
5.3	odd	4	inner	980.2.k.k.883.18		36
7.2	even	3		140.2.w.b.67.16	yes	72
7.3	odd	6		980.2.x.m.667.2		72
7.4	even	3		140.2.w.b.107.2	yes	72
7.5	odd	6		980.2.x.m.67.16		72
7.6	odd	2		980.2.k.j.687.10		36
20.3	even	4	inner	980.2.k.k.883.10		36
28.3	even	6		980.2.x.m.667.5		72
28.11	odd	6		140.2.w.b.107.5	yes	72
28.19	even	6		980.2.x.m.67.7		72
28.23	odd	6		140.2.w.b.67.7	yes	72
28.27	even	2		980.2.k.j.687.18		36
35.2	odd	12		700.2.be.e.543.14		72
35.3	even	12		980.2.x.m.863.7		72
35.4	even	6		700.2.be.e.107.17		72
35.9	even	6		700.2.be.e.207.3		72
35.13	even	4		980.2.k.j.883.18		36
35.18	odd	12		140.2.w.b.23.7	✓	72
35.23	odd	12		140.2.w.b.123.5	yes	72
35.32	odd	12		700.2.be.e.443.12		72
35.33	even	12		980.2.x.m.263.5		72
140.3	odd	12		980.2.x.m.863.16		72
140.23	even	12		140.2.w.b.123.2	yes	72
140.39	odd	6		700.2.be.e.107.14		72
140.67	even	12		700.2.be.e.443.3		72
140.79	odd	6		700.2.be.e.207.12		72
140.83	odd	4		980.2.k.j.883.10		36
140.103	odd	12		980.2.x.m.263.2		72
140.107	even	12		700.2.be.e.543.17		72
140.123	even	12		140.2.w.b.23.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.7	✓	72	35.18	odd	12
140.2.w.b.23.16	yes	72	140.123	even	12
140.2.w.b.67.7	yes	72	28.23	odd	6
140.2.w.b.67.16	yes	72	7.2	even	3
140.2.w.b.107.2	yes	72	7.4	even	3
140.2.w.b.107.5	yes	72	28.11	odd	6
140.2.w.b.123.2	yes	72	140.23	even	12
140.2.w.b.123.5	yes	72	35.23	odd	12
700.2.be.e.107.14		72	140.39	odd	6
700.2.be.e.107.17		72	35.4	even	6
700.2.be.e.207.3		72	35.9	even	6
700.2.be.e.207.12		72	140.79	odd	6
700.2.be.e.443.3		72	140.67	even	12
700.2.be.e.443.12		72	35.32	odd	12
700.2.be.e.543.14		72	35.2	odd	12
700.2.be.e.543.17		72	140.107	even	12
980.2.k.j.687.10		36	7.6	odd	2
980.2.k.j.687.18		36	28.27	even	2
980.2.k.j.883.10		36	140.83	odd	4
980.2.k.j.883.18		36	35.13	even	4
980.2.k.k.687.10		36	1.1	even	1	trivial
980.2.k.k.687.18		36	4.3	odd	2	inner
980.2.k.k.883.10		36	20.3	even	4	inner
980.2.k.k.883.18		36	5.3	odd	4	inner
980.2.x.m.67.7		72	28.19	even	6
980.2.x.m.67.16		72	7.5	odd	6
980.2.x.m.263.2		72	140.103	odd	12
980.2.x.m.263.5		72	35.33	even	12
980.2.x.m.667.2		72	7.3	odd	6
980.2.x.m.667.5		72	28.3	even	6
980.2.x.m.863.7		72	35.3	even	12
980.2.x.m.863.16		72	140.3	odd	12

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	980.2.k.k.687.10

Level	$980$
Weight	$2$
Character	980.687
Analytic conductor	$7.825$
Analytic rank	$0$
Dimension	$36$
Inner twists	$4$