LMFDB - Embedded newform 35.3.g.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.g (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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 70 x^{8} - 248 x^{7} + 464 x^{6} + 432 x^{5} + 1129 x^{4} + \cdots + 100 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 70x^8 - 248x^7 + 464x^6 + 432x^5 + 1129x^4 - 2708x^3 + 3528x^2 + 840*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.4
Root			$-0.109772 + 0.109772i$ of defining polynomial
Character	$\chi$	$=$	35.8
Dual form			35.3.g.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.109772 - 0.109772i) q^{2} +(1.67281 + 1.67281i) q^{3} +3.97590i q^{4} +(-0.861142 - 4.92529i) q^{5} +0.367256 q^{6} +(1.87083 - 1.87083i) q^{7} +(0.875529 + 0.875529i) q^{8} -3.40339i q^{9} +O(q^{10})$	\(q+(0.109772 - 0.109772i) q^{2} +(1.67281 + 1.67281i) q^{3} +3.97590i q^{4} +(-0.861142 - 4.92529i) q^{5} +0.367256 q^{6} +(1.87083 - 1.87083i) q^{7} +(0.875529 + 0.875529i) q^{8} -3.40339i q^{9} +(-0.635186 - 0.446128i) q^{10} -17.1643 q^{11} +(-6.65094 + 6.65094i) q^{12} +(1.79113 + 1.79113i) q^{13} -0.410728i q^{14} +(6.79856 - 9.67962i) q^{15} -15.7114 q^{16} +(14.9720 - 14.9720i) q^{17} +(-0.373596 - 0.373596i) q^{18} +20.4041i q^{19} +(19.5824 - 3.42382i) q^{20} +6.25910 q^{21} +(-1.88416 + 1.88416i) q^{22} +(16.8342 + 16.8342i) q^{23} +2.92919i q^{24} +(-23.5169 + 8.48274i) q^{25} +0.393231 q^{26} +(20.7486 - 20.7486i) q^{27} +(7.43823 + 7.43823i) q^{28} +2.55919i q^{29} +(-0.316259 - 1.80884i) q^{30} +14.2925 q^{31} +(-5.22678 + 5.22678i) q^{32} +(-28.7127 - 28.7127i) q^{33} -3.28700i q^{34} +(-10.8254 - 7.60332i) q^{35} +13.5315 q^{36} +(-35.9154 + 35.9154i) q^{37} +(2.23979 + 2.23979i) q^{38} +5.99245i q^{39} +(3.55827 - 5.06618i) q^{40} -23.4716 q^{41} +(0.687072 - 0.687072i) q^{42} +(7.15327 + 7.15327i) q^{43} -68.2437i q^{44} +(-16.7626 + 2.93080i) q^{45} +3.69585 q^{46} +(-6.36936 + 6.36936i) q^{47} +(-26.2822 - 26.2822i) q^{48} -7.00000i q^{49} +(-1.65032 + 3.51265i) q^{50} +50.0906 q^{51} +(-7.12134 + 7.12134i) q^{52} +(-10.9292 - 10.9292i) q^{53} -4.55521i q^{54} +(14.7809 + 84.5392i) q^{55} +3.27593 q^{56} +(-34.1322 + 34.1322i) q^{57} +(0.280927 + 0.280927i) q^{58} +19.4341i q^{59} +(38.4852 + 27.0304i) q^{60} +73.9951 q^{61} +(1.56891 - 1.56891i) q^{62} +(-6.36715 - 6.36715i) q^{63} -61.6980i q^{64} +(7.27940 - 10.3642i) q^{65} -6.30370 q^{66} +(86.3083 - 86.3083i) q^{67} +(59.5270 + 59.5270i) q^{68} +56.3211i q^{69} +(-2.02295 + 0.353696i) q^{70} +22.2693 q^{71} +(2.97976 - 2.97976i) q^{72} +(-73.4511 - 73.4511i) q^{73} +7.88500i q^{74} +(-53.5294 - 25.1493i) q^{75} -81.1246 q^{76} +(-32.1115 + 32.1115i) q^{77} +(0.657802 + 0.657802i) q^{78} +55.0137i q^{79} +(13.5297 + 77.3830i) q^{80} +38.7865 q^{81} +(-2.57652 + 2.57652i) q^{82} +(-52.8192 - 52.8192i) q^{83} +24.8855i q^{84} +(-86.6341 - 60.8482i) q^{85} +1.57046 q^{86} +(-4.28104 + 4.28104i) q^{87} +(-15.0279 - 15.0279i) q^{88} -129.153i q^{89} +(-1.51835 + 2.16178i) q^{90} +6.70179 q^{91} +(-66.9313 + 66.9313i) q^{92} +(23.9086 + 23.9086i) q^{93} +1.39835i q^{94} +(100.496 - 17.5708i) q^{95} -17.4869 q^{96} +(94.8483 - 94.8483i) q^{97} +(-0.768403 - 0.768403i) q^{98} +58.4168i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.109772	−	0.109772i	0.0548859	−	0.0548859i	−0.679131	−	0.734017i	$-0.737643\pi$
$2$	0.109772	−	0.109772i	0.0548859	−	0.0548859i	0.734017	+	0.679131i	$0.237643\pi$
$3$	1.67281	+	1.67281i	0.557605	+	0.557605i	0.928625	−	0.371020i	$-0.120992\pi$
$3$	1.67281	+	1.67281i	0.557605	+	0.557605i	−0.371020	+	0.928625i	$0.620992\pi$
$4$			3.97590i			0.993975i
$5$	−0.861142	−	4.92529i	−0.172228	−	0.985057i
$5$	−0.861142	−	4.92529i	−0.172228	−	0.985057i
$6$	0.367256			0.0612093
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	0.875529	+	0.875529i	0.109441	+	0.109441i
$9$		−	3.40339i		−	0.378154i
$10$	−0.635186	−	0.446128i	−0.0635186	−	0.0446128i
$11$	−17.1643			−1.56039			−0.780197	−	0.625534i	$-0.784881\pi$
$11$	−17.1643			−1.56039			−0.780197	+	0.625534i	$0.784881\pi$
$12$	−6.65094	+	6.65094i	−0.554245	+	0.554245i
$13$	1.79113	+	1.79113i	0.137779	+	0.137779i	0.772633	−	0.634853i	$-0.218940\pi$
$13$	1.79113	+	1.79113i	0.137779	+	0.137779i	−0.634853	+	0.772633i	$0.718940\pi$
$14$		−	0.410728i		−	0.0293377i
$15$	6.79856	−	9.67962i	0.453237	−	0.645308i
$16$	−15.7114			−0.981962
$17$	14.9720	−	14.9720i	0.880703	−	0.880703i	−0.112903	−	0.993606i	$-0.536015\pi$
$17$	14.9720	−	14.9720i	0.880703	−	0.880703i	0.993606	+	0.112903i	$0.0360149\pi$
$18$	−0.373596	−	0.373596i	−0.0207553	−	0.0207553i
$19$			20.4041i			1.07390i	0.843614	+	0.536950i	$0.180424\pi$
$19$			20.4041i			1.07390i	−0.843614	+	0.536950i	$0.819576\pi$
$20$	19.5824	−	3.42382i	0.979122	−	0.171191i
$21$	6.25910			0.298052
$22$	−1.88416	+	1.88416i	−0.0856436	+	0.0856436i
$23$	16.8342	+	16.8342i	0.731924	+	0.731924i	0.971001	−	0.239077i	$-0.0768448\pi$
$23$	16.8342	+	16.8342i	0.731924	+	0.731924i	−0.239077	+	0.971001i	$0.576845\pi$
$24$			2.92919i			0.122050i
$25$	−23.5169	+	8.48274i	−0.940675	+	0.339310i
$26$	0.393231			0.0151243
$27$	20.7486	−	20.7486i	0.768465	−	0.768465i
$28$	7.43823	+	7.43823i	0.265651	+	0.265651i
$29$			2.55919i			0.0882478i	0.999026	+	0.0441239i	$0.0140496\pi$
$29$			2.55919i			0.0882478i	−0.999026	+	0.0441239i	$0.985950\pi$
$30$	−0.316259	−	1.80884i	−0.0105420	−	0.0602946i
$31$	14.2925			0.461047			0.230524	−	0.973067i	$-0.425956\pi$
$31$	14.2925			0.461047			0.230524	+	0.973067i	$0.425956\pi$
$32$	−5.22678	+	5.22678i	−0.163337	+	0.163337i
$33$	−28.7127	−	28.7127i	−0.870083	−	0.870083i
$34$		−	3.28700i		−	0.0966764i
$35$	−10.8254	−	7.60332i	−0.309298	−	0.217238i
$36$	13.5315			0.375876
$37$	−35.9154	+	35.9154i	−0.970686	+	0.970686i	−0.999582	−	0.0288960i	$-0.990801\pi$
$37$	−35.9154	+	35.9154i	−0.970686	+	0.970686i	0.0288960	+	0.999582i	$0.490801\pi$
$38$	2.23979	+	2.23979i	0.0589419	+	0.0589419i
$39$			5.99245i			0.153652i
$40$	3.55827	−	5.06618i	0.0889569	−	0.126655i
$41$	−23.4716			−0.572477			−0.286239	−	0.958158i	$-0.592405\pi$
$41$	−23.4716			−0.572477			−0.286239	+	0.958158i	$0.592405\pi$
$42$	0.687072	−	0.687072i	0.0163589	−	0.0163589i
$43$	7.15327	+	7.15327i	0.166355	+	0.166355i	0.785375	−	0.619020i	$-0.212470\pi$
$43$	7.15327	+	7.15327i	0.166355	+	0.166355i	−0.619020	+	0.785375i	$0.712470\pi$
$44$		−	68.2437i		−	1.55099i
$45$	−16.7626	+	2.93080i	−0.372503	+	0.0651289i
$46$	3.69585			0.0803446
$47$	−6.36936	+	6.36936i	−0.135518	+	0.135518i	−0.771612	−	0.636094i	$-0.780549\pi$
$47$	−6.36936	+	6.36936i	−0.135518	+	0.135518i	0.636094	+	0.771612i	$0.280549\pi$
$48$	−26.2822	−	26.2822i	−0.547546	−	0.547546i
$49$		−	7.00000i		−	0.142857i
$50$	−1.65032	+	3.51265i	−0.0330065	+	0.0702531i
$51$	50.0906			0.982169
$52$	−7.12134	+	7.12134i	−0.136949	+	0.136949i
$53$	−10.9292	−	10.9292i	−0.206212	−	0.206212i	0.596443	−	0.802655i	$-0.296580\pi$
$53$	−10.9292	−	10.9292i	−0.206212	−	0.206212i	−0.802655	+	0.596443i	$0.796580\pi$
$54$		−	4.55521i		−	0.0843558i
$55$	14.7809	+	84.5392i	0.268744	+	1.53708i
$56$	3.27593			0.0584987
$57$	−34.1322	+	34.1322i	−0.598811	+	0.598811i
$58$	0.280927	+	0.280927i	0.00484356	+	0.00484356i
$59$			19.4341i			0.329391i	0.986344	+	0.164695i	$0.0526641\pi$
$59$			19.4341i			0.329391i	−0.986344	+	0.164695i	$0.947336\pi$
$60$	38.4852	+	27.0304i	0.641420	+	0.450506i
$61$	73.9951			1.21303			0.606517	−	0.795070i	$-0.292566\pi$
$61$	73.9951			1.21303			0.606517	+	0.795070i	$0.292566\pi$
$62$	1.56891	−	1.56891i	0.0253050	−	0.0253050i
$63$	−6.36715	−	6.36715i	−0.101066	−	0.101066i
$64$		−	61.6980i		−	0.964032i
$65$	7.27940	−	10.3642i	0.111991	−	0.159450i
$66$	−6.30370			−0.0955105
$67$	86.3083	−	86.3083i	1.28818	−	1.28818i	0.352294	−	0.935890i	$-0.385402\pi$
$67$	86.3083	−	86.3083i	1.28818	−	1.28818i	0.935890	−	0.352294i	$-0.114598\pi$
$68$	59.5270	+	59.5270i	0.875397	+	0.875397i
$69$			56.3211i			0.816248i
$70$	−2.02295	+	0.353696i	−0.0288994	+	0.00505279i
$71$	22.2693			0.313652			0.156826	−	0.987626i	$-0.449874\pi$
$71$	22.2693			0.313652			0.156826	+	0.987626i	$0.449874\pi$
$72$	2.97976	−	2.97976i	0.0413856	−	0.0413856i
$73$	−73.4511	−	73.4511i	−1.00618	−	1.00618i	−0.999981	−	0.00619848i	$-0.998027\pi$
$73$	−73.4511	−	73.4511i	−1.00618	−	1.00618i	−0.00619848	−	0.999981i	$-0.501973\pi$
$74$			7.88500i			0.106554i
$75$	−53.5294	−	25.1493i	−0.713725	−	0.335324i
$76$	−81.1246			−1.06743
$77$	−32.1115	+	32.1115i	−0.417033	+	0.417033i
$78$	0.657802	+	0.657802i	0.00843335	+	0.00843335i
$79$			55.0137i			0.696376i	0.937425	+	0.348188i	$0.113203\pi$
$79$			55.0137i			0.696376i	−0.937425	+	0.348188i	$0.886797\pi$
$80$	13.5297	+	77.3830i	0.169122	+	0.967288i
$81$	38.7865			0.478846
$82$	−2.57652	+	2.57652i	−0.0314209	+	0.0314209i
$83$	−52.8192	−	52.8192i	−0.636376	−	0.636376i	0.313284	−	0.949660i	$-0.398571\pi$
$83$	−52.8192	−	52.8192i	−0.636376	−	0.636376i	−0.949660	+	0.313284i	$0.898571\pi$
$84$			24.8855i			0.296257i
$85$	−86.6341	−	60.8482i	−1.01923	−	0.715861i
$86$	1.57046			0.0182611
$87$	−4.28104	+	4.28104i	−0.0492074	+	0.0492074i
$88$	−15.0279	−	15.0279i	−0.170771	−	0.170771i
$89$		−	129.153i		−	1.45115i	−0.688142	−	0.725576i	$-0.741573\pi$
$89$		−	129.153i		−	1.45115i	0.688142	−	0.725576i	$-0.258427\pi$
$90$	−1.51835	+	2.16178i	−0.0168705	+	0.0240198i
$91$	6.70179			0.0736460
$92$	−66.9313	+	66.9313i	−0.727514	+	0.727514i
$93$	23.9086	+	23.9086i	0.257082	+	0.257082i
$94$			1.39835i			0.0148761i
$95$	100.496	−	17.5708i	1.05785	−	0.184956i
$96$	−17.4869			−0.182155
$97$	94.8483	−	94.8483i	0.977818	−	0.977818i	−0.0219413	−	0.999759i	$-0.506985\pi$
$97$	94.8483	−	94.8483i	0.977818	−	0.977818i	0.999759	+	0.0219413i	$0.00698468\pi$
$98$	−0.768403	−	0.768403i	−0.00784084	−	0.00784084i
$99$			58.4168i			0.590069i
$100$	−33.7265	−	93.5007i	−0.337265	−	0.935007i
$101$	−115.042			−1.13903			−0.569513	−	0.821983i	$-0.692868\pi$
$101$	−115.042			−1.13903			−0.569513	+	0.821983i	$0.692868\pi$
$102$	5.49853	−	5.49853i	0.0539072	−	0.0539072i
$103$	64.6116	+	64.6116i	0.627297	+	0.627297i	0.947387	−	0.320090i	$-0.103713\pi$
$103$	64.6116	+	64.6116i	0.627297	+	0.627297i	−0.320090	+	0.947387i	$0.603713\pi$
$104$			3.13637i			0.0301574i
$105$	−5.38997	−	30.8278i	−0.0513331	−	0.293598i
$106$	−2.39944			−0.0226362
$107$	−59.9095	+	59.9095i	−0.559902	+	0.559902i	−0.929279	−	0.369378i	$-0.879571\pi$
$107$	−59.9095	+	59.9095i	−0.559902	+	0.559902i	0.369378	+	0.929279i	$0.379571\pi$
$108$	82.4942	+	82.4942i	0.763835	+	0.763835i
$109$			18.5915i			0.170565i	0.996357	+	0.0852823i	$0.0271792\pi$
$109$			18.5915i			0.170565i	−0.996357	+	0.0852823i	$0.972821\pi$
$110$	10.9025	+	7.65749i	0.0991141	+	0.0696136i
$111$	−120.160			−1.08252
$112$	−29.3933	+	29.3933i	−0.262440	+	0.262440i
$113$	129.454	+	129.454i	1.14561	+	1.14561i	0.987407	+	0.158199i	$0.0505688\pi$
$113$	129.454	+	129.454i	1.14561	+	1.14561i	0.158199	+	0.987407i	$0.449431\pi$
$114$			7.49352i			0.0657326i
$115$	68.4168	−	97.4101i	0.594928	−	0.847045i
$116$	−10.1751			−0.0877161
$117$	6.09590	−	6.09590i	0.0521017	−	0.0521017i
$118$	2.13331	+	2.13331i	0.0180789	+	0.0180789i
$119$		−	56.0199i		−	0.470756i
$120$	14.4271	−	2.52245i	0.120226	−	0.0210204i
$121$	173.614			1.43483
$122$	8.12258	−	8.12258i	0.0665785	−	0.0665785i
$123$	−39.2636	−	39.2636i	−0.319216	−	0.319216i
$124$			56.8254i			0.458269i
$125$	62.0313	+	108.522i	0.496250	+	0.868180i
$126$	−1.39787			−0.0110942
$127$	79.9057	−	79.9057i	0.629179	−	0.629179i	−0.318683	−	0.947861i	$-0.603240\pi$
$127$	79.9057	−	79.9057i	0.629179	−	0.629179i	0.947861	+	0.318683i	$0.103240\pi$
$128$	−27.6798	−	27.6798i	−0.216249	−	0.216249i
$129$			23.9322i			0.185521i
$130$	−0.338627	−	1.93677i	−0.00260483	−	0.0148983i
$131$	−115.044			−0.878198			−0.439099	−	0.898439i	$-0.644702\pi$
$131$	−115.044			−0.878198			−0.439099	+	0.898439i	$0.644702\pi$
$132$	114.159	−	114.159i	0.864841	−	0.864841i
$133$	38.1726	+	38.1726i	0.287012	+	0.287012i
$134$		−	18.9484i		−	0.141406i
$135$	−120.060	−	84.3251i	−0.889334	−	0.624630i
$136$	26.2168			0.192770
$137$	−57.4672	+	57.4672i	−0.419468	+	0.419468i	−0.885020	−	0.465552i	$-0.845856\pi$
$137$	−57.4672	+	57.4672i	−0.419468	+	0.419468i	0.465552	+	0.885020i	$0.345856\pi$
$138$	6.18247	+	6.18247i	0.0448005	+	0.0448005i
$139$			177.795i			1.27910i	0.768748	+	0.639551i	$0.220880\pi$
$139$			177.795i			1.27910i	−0.768748	+	0.639551i	$0.779120\pi$
$140$	30.2300	−	43.0408i	0.215929	−	0.307434i
$141$	−21.3095			−0.151131
$142$	2.44454	−	2.44454i	0.0172151	−	0.0172151i
$143$	−30.7435	−	30.7435i	−0.214990	−	0.214990i
$144$			53.4719i			0.371333i
$145$	12.6047	−	2.20382i	0.0869292	−	0.0151988i
$146$	−16.1257			−0.110450
$147$	11.7097	−	11.7097i	0.0796578	−	0.0796578i
$148$	−142.796	−	142.796i	−0.964838	−	0.964838i
$149$			52.9630i			0.355456i	0.984080	+	0.177728i	$0.0568748\pi$
$149$			52.9630i			0.355456i	−0.984080	+	0.177728i	$0.943125\pi$
$150$	−8.63670	+	3.11533i	−0.0575780	+	0.0207689i
$151$	−293.336			−1.94262			−0.971311	−	0.237812i	$-0.923570\pi$
$151$	−293.336			−1.94262			−0.971311	+	0.237812i	$0.923570\pi$
$152$	−17.8644	+	17.8644i	−0.117529	+	0.117529i
$153$	−50.9553	−	50.9553i	−0.333041	−	0.333041i
$154$			7.04988i			0.0457784i
$155$	−12.3078	−	70.3945i	−0.0794054	−	0.454158i
$156$	−23.8254			−0.152727
$157$	9.08116	−	9.08116i	0.0578418	−	0.0578418i	−0.677594	−	0.735436i	$-0.736977\pi$
$157$	9.08116	−	9.08116i	0.0578418	−	0.0578418i	0.735436	+	0.677594i	$0.236977\pi$
$158$	6.03895	+	6.03895i	0.0382212	+	0.0382212i
$159$		−	36.5651i		−	0.229969i
$160$	30.2444	+	21.2424i	0.189027	+	0.132765i
$161$	62.9880			0.391230
$162$	4.25766	−	4.25766i	0.0262819	−	0.0262819i
$163$	67.7002	+	67.7002i	0.415339	+	0.415339i	0.883594	−	0.468255i	$-0.155117\pi$
$163$	67.7002	+	67.7002i	0.415339	+	0.415339i	−0.468255	+	0.883594i	$0.655117\pi$
$164$		−	93.3206i		−	0.569028i
$165$	−116.693	+	166.144i	−0.707228	+	1.00693i
$166$	−11.5961			−0.0698561
$167$	78.2923	−	78.2923i	0.468816	−	0.468816i	−0.432715	−	0.901531i	$-0.642444\pi$
$167$	78.2923	−	78.2923i	0.468816	−	0.468816i	0.901531	+	0.432715i	$0.142444\pi$
$168$	5.48002	+	5.48002i	0.0326192	+	0.0326192i
$169$		−	162.584i		−	0.962034i
$170$	−16.1894	+	2.83057i	−0.0952317	+	0.0166504i
$171$	69.4430			0.406099
$172$	−28.4407	+	28.4407i	−0.165353	+	0.165353i
$173$	−76.1690	−	76.1690i	−0.440283	−	0.440283i	0.451824	−	0.892107i	$-0.350774\pi$
$173$	−76.1690	−	76.1690i	−0.440283	−	0.440283i	−0.892107	+	0.451824i	$0.850774\pi$
$174$			0.939876i			0.00540159i
$175$	−28.1263	+	59.8658i	−0.160722	+	0.342090i
$176$	269.675			1.53225
$177$	−32.5096	+	32.5096i	−0.183670	+	0.183670i
$178$	−14.1773	−	14.1773i	−0.0796478	−	0.0796478i
$179$		−	31.7250i		−	0.177235i	−0.996066	−	0.0886174i	$-0.971755\pi$
$179$		−	31.7250i		−	0.177235i	0.996066	−	0.0886174i	$-0.0282449\pi$
$180$	−11.6526	−	66.6466i	−0.0647365	−	0.370259i
$181$	215.588			1.19109			0.595546	−	0.803321i	$-0.296936\pi$
$181$	215.588			1.19109			0.595546	+	0.803321i	$0.296936\pi$
$182$	0.735667	−	0.735667i	0.00404213	−	0.00404213i
$183$	123.780	+	123.780i	0.676394	+	0.676394i
$184$			29.4777i			0.160205i
$185$	207.822	+	145.965i	1.12336	+	0.789002i
$186$	5.24899			0.0282204
$187$	−256.984	+	256.984i	−1.37424	+	1.37424i
$188$	−25.3239	−	25.3239i	−0.134702	−	0.134702i
$189$		−	77.6340i		−	0.410762i
$190$	9.10284	−	12.9604i	0.0479097	−	0.0682126i
$191$	−116.720			−0.611099			−0.305549	−	0.952176i	$-0.598840\pi$
$191$	−116.720			−0.611099			−0.305549	+	0.952176i	$0.598840\pi$
$192$	103.209	−	103.209i	0.537549	−	0.537549i
$193$	4.07763	+	4.07763i	0.0211276	+	0.0211276i	0.717592	−	0.696464i	$-0.245244\pi$
$193$	4.07763	+	4.07763i	0.0211276	+	0.0211276i	−0.696464	+	0.717592i	$0.745244\pi$
$194$		−	20.8233i		−	0.107337i
$195$	29.5145	−	5.16035i	0.151356	−	0.0264633i
$196$	27.8313			0.141996
$197$	−193.847	+	193.847i	−0.983997	+	0.983997i	−0.999874	−	0.0158768i	$-0.994946\pi$
$197$	−193.847	+	193.847i	−0.983997	+	0.983997i	0.0158768	+	0.999874i	$0.494946\pi$
$198$	6.41252	+	6.41252i	0.0323865	+	0.0323865i
$199$		−	38.8368i		−	0.195160i	−0.995228	−	0.0975800i	$-0.968890\pi$
$199$		−	38.8368i		−	0.195160i	0.995228	−	0.0975800i	$-0.0311102\pi$
$200$	−28.0166	−	13.1628i	−0.140083	−	0.0658141i
$201$	288.755			1.43659
$202$	−12.6283	+	12.6283i	−0.0625164	+	0.0625164i
$203$	4.78780	+	4.78780i	0.0235852	+	0.0235852i
$204$			199.155i			0.976251i
$205$	20.2124	+	115.604i	0.0985969	+	0.563923i
$206$	14.1851			0.0688595
$207$	57.2934	−	57.2934i	0.276780	−	0.276780i
$208$	−28.1411	−	28.1411i	−0.135294	−	0.135294i
$209$		−	350.222i		−	1.67571i
$210$	−3.97569	−	2.79236i	−0.0189319	−	0.0132970i
$211$	−13.5037			−0.0639984			−0.0319992	−	0.999488i	$-0.510187\pi$
$211$	−13.5037			−0.0639984			−0.0319992	+	0.999488i	$0.510187\pi$
$212$	43.4535	−	43.4535i	0.204969	−	0.204969i
$213$	37.2524	+	37.2524i	0.174894	+	0.174894i
$214$			13.1527i			0.0614614i
$215$	29.0719	−	41.3919i	0.135218	−	0.192520i
$216$	36.3319			0.168203
$217$	26.7387	−	26.7387i	0.123220	−	0.123220i
$218$	2.04083	+	2.04083i	0.00936159	+	0.00936159i
$219$		−	245.740i		−	1.12210i
$220$	−336.119	+	58.7675i	−1.52782	+	0.267125i
$221$	53.6334			0.242685
$222$	−13.1901	+	13.1901i	−0.0594150	+	0.0594150i
$223$	−37.5360	−	37.5360i	−0.168323	−	0.168323i	0.617919	−	0.786242i	$-0.287976\pi$
$223$	−37.5360	−	37.5360i	−0.168323	−	0.168323i	−0.786242	+	0.617919i	$0.787976\pi$
$224$			19.5568i			0.0873073i
$225$	28.8700	+	80.0370i	0.128311	+	0.355720i
$226$	28.4207			0.125755
$227$	15.1231	−	15.1231i	0.0666215	−	0.0666215i	−0.673011	−	0.739632i	$-0.734999\pi$
$227$	15.1231	−	15.1231i	0.0666215	−	0.0666215i	0.739632	+	0.673011i	$0.234999\pi$
$228$	−135.706	−	135.706i	−0.595204	−	0.595204i
$229$			237.801i			1.03843i	0.854643	+	0.519216i	$0.173776\pi$
$229$			237.801i			1.03843i	−0.854643	+	0.519216i	$0.826224\pi$
$230$	−3.18265	−	18.2031i	−0.0138376	−	0.0791440i
$231$	−107.433			−0.465079
$232$	−2.24064	+	2.24064i	−0.00965794	+	0.00965794i
$233$	−129.648	−	129.648i	−0.556428	−	0.556428i	0.371860	−	0.928289i	$-0.378720\pi$
$233$	−129.648	−	129.648i	−0.556428	−	0.556428i	−0.928289	+	0.371860i	$0.878720\pi$
$234$		−	1.33832i		−	0.00571930i
$235$	36.8558	+	25.8860i	0.156833	+	0.110153i
$236$	−77.2678			−0.327406
$237$	−92.0277	+	92.0277i	−0.388303	+	0.388303i
$238$	−6.14941	−	6.14941i	−0.0258378	−	0.0258378i
$239$		−	106.131i		−	0.444063i	−0.975039	−	0.222032i	$-0.928731\pi$
$239$		−	106.131i		−	0.444063i	0.975039	−	0.222032i	$-0.0712688\pi$
$240$	−106.815	+	152.080i	−0.445061	+	0.633667i
$241$	14.5269			0.0602774			0.0301387	−	0.999546i	$-0.490405\pi$
$241$	14.5269			0.0602774			0.0301387	+	0.999546i	$0.490405\pi$
$242$	19.0579	−	19.0579i	0.0787518	−	0.0787518i
$243$	−121.854	−	121.854i	−0.501459	−	0.501459i
$244$			294.197i			1.20573i
$245$	−34.4770	+	6.02799i	−0.140722	+	0.0246041i
$246$	−8.62007			−0.0350409
$247$	−36.5463	+	36.5463i	−0.147961	+	0.147961i
$248$	12.5135	+	12.5135i	0.0504575	+	0.0504575i
$249$		−	176.713i		−	0.709692i
$250$	18.7220	+	5.10342i	0.0748880	+	0.0204137i
$251$	−229.619			−0.914815			−0.457408	−	0.889257i	$-0.651222\pi$
$251$	−229.619			−0.914815			−0.457408	+	0.889257i	$0.651222\pi$
$252$	25.3152	−	25.3152i	0.100457	−	0.100457i
$253$	−288.948	−	288.948i	−1.14209	−	1.14209i
$254$		−	17.5428i		−	0.0690661i
$255$	−43.1351	−	246.710i	−0.169157	−	0.967492i
$256$	240.715			0.940294
$257$	273.704	−	273.704i	1.06500	−	1.06500i	0.0672617	−	0.997735i	$-0.478574\pi$
$257$	273.704	−	273.704i	1.06500	−	1.06500i	0.997735	−	0.0672617i	$-0.0214263\pi$
$258$	2.62708	+	2.62708i	0.0101825	+	0.0101825i
$259$			134.383i			0.518854i
$260$	41.2071	+	28.9422i	0.158489	+	0.111316i
$261$	8.70990			0.0333713
$262$	−12.6286	+	12.6286i	−0.0482007	+	0.0482007i
$263$	287.060	+	287.060i	1.09148	+	1.09148i	0.995371	+	0.0961109i	$0.0306403\pi$
$263$	287.060	+	287.060i	1.09148	+	1.09148i	0.0961109	+	0.995371i	$0.469360\pi$
$264$		−	50.2776i		−	0.190446i
$265$	−44.4179	+	63.2411i	−0.167615	+	0.238646i
$266$	8.38054			0.0315058
$267$	216.048	−	216.048i	0.809169	−	0.809169i
$268$	343.153	+	343.153i	1.28042	+	1.28042i
$269$			340.500i			1.26580i	0.774234	+	0.632899i	$0.218135\pi$
$269$			340.500i			1.26580i	−0.774234	+	0.632899i	$0.781865\pi$
$270$	−22.4357	+	3.92269i	−0.0830953	+	0.0145285i
$271$	6.78802			0.0250481			0.0125240	−	0.999922i	$-0.496013\pi$
$271$	6.78802			0.0250481			0.0125240	+	0.999922i	$0.496013\pi$
$272$	−235.230	+	235.230i	−0.864817	+	0.864817i
$273$	11.2108	+	11.2108i	0.0410654	+	0.0410654i
$274$			12.6165i			0.0460458i
$275$	403.651	−	145.601i	1.46782	−	0.529457i
$276$	−223.927			−0.811330
$277$	114.582	−	114.582i	0.413655	−	0.413655i	−0.469355	−	0.883010i	$-0.655514\pi$
$277$	114.582	−	114.582i	0.413655	−	0.413655i	0.883010	+	0.469355i	$0.155514\pi$
$278$	19.5169	+	19.5169i	0.0702047	+	0.0702047i
$279$		−	48.6428i		−	0.174347i
$280$	−2.82104	−	16.1349i	−0.0100751	−	0.0576246i
$281$	−394.087			−1.40245			−0.701223	−	0.712942i	$-0.747362\pi$
$281$	−394.087			−1.40245			−0.701223	+	0.712942i	$0.747362\pi$
$282$	−2.33918	+	2.33918i	−0.00829498	+	0.00829498i
$283$	29.8072	+	29.8072i	0.105326	+	0.105326i	0.757806	−	0.652480i	$-0.226271\pi$
$283$	29.8072	+	29.8072i	0.105326	+	0.105326i	−0.652480	+	0.757806i	$0.726271\pi$
$284$			88.5404i			0.311762i
$285$	197.504	+	138.718i	0.692996	+	0.486731i
$286$	−6.74954			−0.0235998
$287$	−43.9113	+	43.9113i	−0.153001	+	0.153001i
$288$	17.7888	+	17.7888i	0.0617665	+	0.0617665i
$289$		−	159.319i		−	0.551276i
$290$	1.14173	−	1.62556i	0.00393699	−	0.00560538i
$291$	317.327			1.09047
$292$	292.034	−	292.034i	1.00012	−	1.00012i
$293$	251.344	+	251.344i	0.857831	+	0.857831i	0.991082	−	0.133251i	$-0.0425417\pi$
$293$	251.344	+	251.344i	0.857831	+	0.857831i	−0.133251	+	0.991082i	$0.542542\pi$
$294$		−	2.57079i		−	0.00874418i
$295$	95.7182	−	16.7355i	0.324469	−	0.0567304i
$296$	−62.8899			−0.212466
$297$	−356.135	+	356.135i	−1.19911	+	1.19911i
$298$	5.81384	+	5.81384i	0.0195095	+	0.0195095i
$299$			60.3045i			0.201687i
$300$	99.9911	−	212.828i	0.333304	−	0.709425i
$301$	26.7651			0.0889206
$302$	−32.2000	+	32.2000i	−0.106623	+	0.106623i
$303$	−192.443	−	192.443i	−0.635126	−	0.635126i
$304$		−	320.576i		−	1.05453i
$305$	−63.7203	−	364.447i	−0.208919	−	1.19491i
$306$	−11.1869			−0.0365586
$307$	−247.579	+	247.579i	−0.806446	+	0.806446i	−0.984094	−	0.177648i	$-0.943151\pi$
$307$	−247.579	+	247.579i	−0.806446	+	0.806446i	0.177648	+	0.984094i	$0.443151\pi$
$308$	−127.672	−	127.672i	−0.414520	−	0.414520i
$309$			216.166i			0.699567i
$310$	−9.07838	−	6.37627i	−0.0292851	−	0.0205686i
$311$	147.915			0.475610			0.237805	−	0.971313i	$-0.423572\pi$
$311$	147.915			0.475610			0.237805	+	0.971313i	$0.423572\pi$
$312$	−5.24656	+	5.24656i	−0.0168159	+	0.0168159i
$313$	118.730	+	118.730i	0.379328	+	0.379328i	0.870860	−	0.491531i	$-0.163563\pi$
$313$	118.730	+	118.730i	0.379328	+	0.379328i	−0.491531	+	0.870860i	$0.663563\pi$
$314$		−	1.99371i		−	0.00634940i
$315$	−25.8770	+	36.8431i	−0.0821493	+	0.116962i
$316$	−218.729			−0.692180
$317$	148.838	−	148.838i	0.469520	−	0.469520i	−0.432239	−	0.901759i	$-0.642276\pi$
$317$	148.838	−	148.838i	0.469520	−	0.469520i	0.901759	+	0.432239i	$0.142276\pi$
$318$	−4.01382	−	4.01382i	−0.0126221	−	0.0126221i
$319$		−	43.9267i		−	0.137701i
$320$	−303.880	+	53.1308i	−0.949626	+	0.166034i
$321$	−200.435			−0.624408
$322$	6.91430	−	6.91430i	0.0214730	−	0.0214730i
$323$	305.489	+	305.489i	0.945787	+	0.945787i
$324$			154.211i			0.475961i
$325$	−57.3154	−	26.9280i	−0.176355	−	0.0828555i
$326$	14.8632			0.0455925
$327$	−31.1002	+	31.1002i	−0.0951076	+	0.0951076i
$328$	−20.5500	−	20.5500i	−0.0626526	−	0.0626526i
$329$			23.8320i			0.0724376i
$330$	5.42838	+	31.0475i	0.0164496	+	0.0940833i
$331$	−479.920			−1.44991			−0.724955	−	0.688796i	$-0.758139\pi$
$331$	−479.920			−1.44991			−0.724955	+	0.688796i	$0.758139\pi$
$332$	210.004	−	210.004i	0.632542	−	0.632542i
$333$	122.234	+	122.234i	0.367069	+	0.367069i
$334$		−	17.1886i		−	0.0514628i
$335$	−499.417	−	350.769i	−1.49080	−	1.04707i
$336$	−98.3391			−0.292676
$337$	54.9580	−	54.9580i	0.163080	−	0.163080i	−0.620850	−	0.783930i	$-0.713212\pi$
$337$	54.9580	−	54.9580i	0.163080	−	0.163080i	0.783930	+	0.620850i	$0.213212\pi$
$338$	−17.8471	−	17.8471i	−0.0528021	−	0.0528021i
$339$			433.103i			1.27759i
$340$	241.926	−	344.449i	0.711548	−	1.01308i
$341$	−245.320			−0.719415
$342$	7.62288	−	7.62288i	0.0222891	−	0.0222891i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			12.5258i			0.0364122i
$345$	277.398	−	48.5005i	0.804051	−	0.140581i
$346$	−16.7224			−0.0483307
$347$	−150.539	+	150.539i	−0.433830	+	0.433830i	−0.889929	−	0.456099i	$-0.849246\pi$
$347$	−150.539	+	150.539i	−0.433830	+	0.433830i	0.456099	+	0.889929i	$0.349246\pi$
$348$	−17.0210	−	17.0210i	−0.0489109	−	0.0489109i
$349$		−	545.358i		−	1.56263i	−0.624137	−	0.781315i	$-0.714549\pi$
$349$		−	545.358i		−	1.56263i	0.624137	−	0.781315i	$-0.285451\pi$
$350$	3.48410	+	9.65905i	0.00995458	+	0.0275973i
$351$	74.3266			0.211757
$352$	89.7142	−	89.7142i	0.254870	−	0.254870i
$353$	−378.330	−	378.330i	−1.07176	−	1.07176i	−0.997218	−	0.0745367i	$-0.976252\pi$
$353$	−378.330	−	378.330i	−1.07176	−	1.07176i	−0.0745367	−	0.997218i	$-0.523748\pi$
$354$			7.13726i			0.0201618i
$355$	−19.1770	−	109.683i	−0.0540198	−	0.308965i
$356$	513.498			1.44241
$357$	93.7109	−	93.7109i	0.262496	−	0.262496i
$358$	−3.48251	−	3.48251i	−0.00972769	−	0.00972769i
$359$			447.039i			1.24523i	0.782527	+	0.622617i	$0.213930\pi$
$359$			447.039i			1.24523i	−0.782527	+	0.622617i	$0.786070\pi$
$360$	−17.2422	−	12.1102i	−0.0478949	−	0.0336394i
$361$	−55.3268			−0.153260
$362$	23.6655	−	23.6655i	0.0653742	−	0.0653742i
$363$	290.424	+	290.424i	0.800067	+	0.800067i
$364$			26.6456i			0.0732023i
$365$	−298.516	+	425.019i	−0.817851	+	1.16444i
$366$	27.1751			0.0742490
$367$	21.2826	−	21.2826i	0.0579908	−	0.0579908i	−0.677517	−	0.735507i	$-0.736944\pi$
$367$	21.2826	−	21.2826i	0.0579908	−	0.0579908i	0.735507	+	0.677517i	$0.236944\pi$
$368$	−264.489	−	264.489i	−0.718721	−	0.718721i
$369$			79.8828i			0.216485i
$370$	38.8359	−	6.79010i	0.104962	−	0.0183516i
$371$	−40.8934			−0.110225
$372$	−95.0583	+	95.0583i	−0.255533	+	0.255533i
$373$	−361.227	−	361.227i	−0.968436	−	0.968436i	0.0310806	−	0.999517i	$-0.490105\pi$
$373$	−361.227	−	361.227i	−0.968436	−	0.968436i	−0.999517	+	0.0310806i	$0.990105\pi$
$374$			56.4191i			0.150853i
$375$	−77.7711	+	285.305i	−0.207389	+	0.760812i
$376$	−11.1531			−0.0296626
$377$	−4.58383	+	4.58383i	−0.0121587	+	0.0121587i
$378$	−8.52202	−	8.52202i	−0.0225450	−	0.0225450i
$379$		−	226.019i		−	0.596355i	−0.954510	−	0.298178i	$-0.903621\pi$
$379$		−	226.019i		−	0.596355i	0.954510	−	0.298178i	$-0.0963787\pi$
$380$	69.8598	+	399.562i	0.183842	+	1.05148i
$381$	267.335			0.701666
$382$	−12.8125	+	12.8125i	−0.0335407	+	0.0335407i
$383$	284.092	+	284.092i	0.741755	+	0.741755i	0.972916	−	0.231161i	$-0.0742523\pi$
$383$	284.092	+	284.092i	0.741755	+	0.741755i	−0.231161	+	0.972916i	$0.574252\pi$
$384$		−	92.6064i		−	0.241163i
$385$	185.811	+	130.506i	0.482626	+	0.338976i
$386$	0.895219			0.00231922
$387$	24.3454	−	24.3454i	0.0629079	−	0.0629079i
$388$	377.108	+	377.108i	0.971927	+	0.971927i
$389$			322.147i			0.828141i	0.910245	+	0.414071i	$0.135893\pi$
$389$			322.147i			0.828141i	−0.910245	+	0.414071i	$0.864107\pi$
$390$	2.67340	−	3.80632i	0.00685487	−	0.00975980i
$391$	504.083			1.28921
$392$	6.12870	−	6.12870i	0.0156344	−	0.0156344i
$393$	−192.447	−	192.447i	−0.489687	−	0.489687i
$394$			42.5580i			0.108015i
$395$	270.958	−	47.3746i	0.685970	−	0.119936i
$396$	−232.259			−0.586514
$397$	39.3179	−	39.3179i	0.0990375	−	0.0990375i	−0.655852	−	0.754890i	$-0.727690\pi$
$397$	39.3179	−	39.3179i	0.0990375	−	0.0990375i	0.754890	+	0.655852i	$0.227690\pi$
$398$	−4.26319	−	4.26319i	−0.0107115	−	0.0107115i
$399$			127.711i			0.320078i
$400$	369.483	−	133.276i	0.923706	−	0.333189i
$401$	241.621			0.602546			0.301273	−	0.953538i	$-0.402588\pi$
$401$	241.621			0.602546			0.301273	+	0.953538i	$0.402588\pi$
$402$	31.6972	−	31.6972i	0.0788487	−	0.0788487i
$403$	25.5996	+	25.5996i	0.0635226	+	0.0635226i
$404$		−	457.394i		−	1.13216i
$405$	−33.4007	−	191.035i	−0.0824708	−	0.471690i
$406$	1.05113			0.00258899
$407$	616.464	−	616.464i	1.51465	−	1.51465i
$408$	43.8558	+	43.8558i	0.107490	+	0.107490i
$409$		−	488.035i		−	1.19324i	−0.802524	−	0.596619i	$-0.796510\pi$
$409$		−	488.035i		−	1.19324i	0.802524	−	0.596619i	$-0.203490\pi$
$410$	14.9088	+	10.4713i	0.0363630	+	0.0255398i
$411$	−192.264			−0.467795
$412$	−256.889	+	256.889i	−0.623517	+	0.623517i
$413$	36.3578	+	36.3578i	0.0880334	+	0.0880334i
$414$		−	12.5784i		−	0.0303826i
$415$	−214.665	+	305.634i	−0.517264	+	0.736468i
$416$	−18.7237			−0.0450088
$417$	−297.418	+	297.418i	−0.713234	+	0.713234i
$418$	−38.4445	−	38.4445i	−0.0919726	−	0.0919726i
$419$			110.880i			0.264629i	0.991208	+	0.132315i	$0.0422409\pi$
$419$			110.880i			0.264629i	−0.991208	+	0.132315i	$0.957759\pi$
$420$	122.568	−	21.4300i	0.291830	−	0.0510238i
$421$	−23.0291			−0.0547008			−0.0273504	−	0.999626i	$-0.508707\pi$
$421$	−23.0291			−0.0547008			−0.0273504	+	0.999626i	$0.508707\pi$
$422$	−1.48232	+	1.48232i	−0.00351261	+	0.00351261i
$423$	21.6774	+	21.6774i	0.0512468	+	0.0512468i
$424$		−	19.1377i		−	0.0451361i
$425$	−225.090	+	479.097i	−0.529624	+	1.12729i
$426$	8.17852			0.0191984
$427$	138.432	−	138.432i	0.324197	−	0.324197i
$428$	−238.194	−	238.194i	−0.556528	−	0.556528i
$429$		−	102.856i		−	0.239758i
$430$	−1.35239	−	7.73494i	−0.00314508	−	0.0179882i
$431$	−17.3083			−0.0401585			−0.0200793	−	0.999798i	$-0.506392\pi$
$431$	−17.3083			−0.0401585			−0.0200793	+	0.999798i	$0.506392\pi$
$432$	−325.989	+	325.989i	−0.754603	+	0.754603i
$433$	133.398	+	133.398i	0.308079	+	0.308079i	0.844164	−	0.536085i	$-0.180097\pi$
$433$	133.398	+	133.398i	0.308079	+	0.308079i	−0.536085	+	0.844164i	$0.680097\pi$
$434$		−	5.87032i		−	0.0135261i
$435$	24.7720	+	17.3988i	0.0569470	+	0.0399972i
$436$	−73.9181			−0.169537
$437$	−343.487	+	343.487i	−0.786012	+	0.786012i
$438$	−26.9753	−	26.9753i	−0.0615875	−	0.0615875i
$439$			74.5347i			0.169783i	0.996390	+	0.0848915i	$0.0270544\pi$
$439$			74.5347i			0.169783i	−0.996390	+	0.0848915i	$0.972946\pi$
$440$	−61.0754	+	86.9576i	−0.138808	+	0.197631i
$441$	−23.8237			−0.0540220
$442$	5.88743	−	5.88743i	0.0133200	−	0.0133200i
$443$	−358.923	−	358.923i	−0.810211	−	0.810211i	0.174455	−	0.984665i	$-0.444184\pi$
$443$	−358.923	−	358.923i	−0.810211	−	0.810211i	−0.984665	+	0.174455i	$0.944184\pi$
$444$		−	477.742i		−	1.07600i
$445$	−636.113	+	111.219i	−1.42947	+	0.249930i
$446$	−8.24079			−0.0184771
$447$	−88.5972	+	88.5972i	−0.198204	+	0.198204i
$448$	−115.426	−	115.426i	−0.257648	−	0.257648i
$449$			6.21583i			0.0138437i	0.999976	+	0.00692186i	$0.00220332\pi$
$449$			6.21583i			0.0138437i	−0.999976	+	0.00692186i	$0.997797\pi$
$450$	11.9549	+	5.61669i	0.0265665	+	0.0124815i
$451$	402.874			0.893290
$452$	−514.694	+	514.694i	−1.13870	+	1.13870i
$453$	−490.697	−	490.697i	−1.08322	−	1.08322i
$454$		−	3.32018i		−	0.00731316i
$455$	−5.77119	−	33.0082i	−0.0126839	−	0.0725455i
$456$	−59.7675			−0.131069
$457$	228.493	−	228.493i	0.499986	−	0.499986i	−0.411448	−	0.911433i	$-0.634977\pi$
$457$	228.493	−	228.493i	0.499986	−	0.499986i	0.911433	+	0.411448i	$0.134977\pi$
$458$	26.1038	+	26.1038i	0.0569953	+	0.0569953i
$459$		−	621.293i		−	1.35358i
$460$	387.293	+	272.018i	0.841941	+	0.591344i
$461$	698.161			1.51445			0.757224	−	0.653155i	$-0.226555\pi$
$461$	698.161			1.51445			0.757224	+	0.653155i	$0.226555\pi$
$462$	−11.7931	+	11.7931i	−0.0255263	+	0.0255263i
$463$	38.8495	+	38.8495i	0.0839082	+	0.0839082i	0.747815	−	0.663907i	$-0.231103\pi$
$463$	38.8495	+	38.8495i	0.0839082	+	0.0839082i	−0.663907	+	0.747815i	$0.731103\pi$
$464$		−	40.2084i		−	0.0866560i
$465$	97.1681	−	138.346i	0.208964	−	0.297517i
$466$	−28.4633			−0.0610801
$467$	191.314	−	191.314i	0.409666	−	0.409666i	−0.471956	−	0.881622i	$-0.656452\pi$
$467$	191.314	−	191.314i	0.409666	−	0.409666i	0.881622	+	0.471956i	$0.156452\pi$
$468$	24.2367	+	24.2367i	0.0517878	+	0.0517878i
$469$		−	322.936i		−	0.688563i
$470$	6.88728	−	1.20418i	0.0146538	−	0.00256209i
$471$	30.3822			0.0645057
$472$	−17.0151	+	17.0151i	−0.0360489	+	0.0360489i
$473$	−122.781	−	122.781i	−0.259580	−	0.259580i
$474$			20.2041i			0.0426247i
$475$	−173.083	−	479.840i	−0.364384	−	1.01019i
$476$	222.730			0.467919
$477$	−37.1963	+	37.1963i	−0.0779797	+	0.0779797i
$478$	−11.6502	−	11.6502i	−0.0243728	−	0.0243728i
$479$			162.010i			0.338225i	0.985597	+	0.169113i	$0.0540902\pi$
$479$			162.010i			0.338225i	−0.985597	+	0.169113i	$0.945910\pi$
$480$	15.0587	+	86.1278i	0.0313723	+	0.179433i
$481$	−128.658			−0.267480
$482$	1.59464	−	1.59464i	0.00330838	−	0.00330838i
$483$	105.367	+	105.367i	0.218151	+	0.218151i
$484$			690.273i			1.42618i
$485$	−548.833	−	385.477i	−1.13161	−	0.794798i
$486$	−26.7524			−0.0550460
$487$	−264.461	+	264.461i	−0.543042	+	0.543042i	−0.924419	−	0.381378i	$-0.875450\pi$
$487$	−264.461	+	264.461i	−0.543042	+	0.543042i	0.381378	+	0.924419i	$0.375450\pi$
$488$	64.7849	+	64.7849i	0.132756	+	0.132756i
$489$			226.500i			0.463190i
$490$	−3.12290	+	4.44631i	−0.00637326	+	0.00907409i
$491$	455.352			0.927396			0.463698	−	0.885993i	$-0.346522\pi$
$491$	455.352			0.927396			0.463698	+	0.885993i	$0.346522\pi$
$492$	156.108	−	156.108i	0.317293	−	0.317293i
$493$	38.3160	+	38.3160i	0.0777202	+	0.0777202i
$494$			8.02351i			0.0162419i
$495$	287.720	−	50.3052i	0.581252	−	0.101627i
$496$	−224.554			−0.452731
$497$	41.6620	−	41.6620i	0.0838270	−	0.0838270i
$498$	−19.3981	−	19.3981i	−0.0389521	−	0.0389521i
$499$			495.456i			0.992897i	0.868066	+	0.496449i	$0.165363\pi$
$499$			495.456i			0.992897i	−0.868066	+	0.496449i	$0.834637\pi$
$500$	−431.474	+	246.630i	−0.862949	+	0.493260i
$501$	261.937			0.522828
$502$	−25.2056	+	25.2056i	−0.0502104	+	0.0502104i
$503$	−8.67254	−	8.67254i	−0.0172416	−	0.0172416i	0.698433	−	0.715675i	$-0.253881\pi$
$503$	−8.67254	−	8.67254i	−0.0172416	−	0.0172416i	−0.715675	+	0.698433i	$0.753881\pi$
$504$		−	11.1493i		−	0.0221215i
$505$	99.0671	+	566.612i	0.196173	+	1.12200i
$506$	−63.4368			−0.125369
$507$	271.972	−	271.972i	0.536435	−	0.536435i
$508$	317.697	+	317.697i	0.625388	+	0.625388i
$509$			391.691i			0.769531i	0.923014	+	0.384766i	$0.125718\pi$
$509$			391.691i			0.769531i	−0.923014	+	0.384766i	$0.874282\pi$
$510$	−31.8169	−	22.3468i	−0.0623860	−	0.0438173i
$511$	−274.829			−0.537825
$512$	137.143	−	137.143i	0.267858	−	0.267858i
$513$	423.355	+	423.355i	0.825254	+	0.825254i
$514$		−	60.0900i		−	0.116907i
$515$	262.591	−	373.870i	0.509885	−	0.725961i
$516$	−95.1520			−0.184403
$517$	109.326	−	109.326i	0.211462	−	0.211462i
$518$	14.7515	+	14.7515i	0.0284778	+	0.0284778i
$519$		−	254.833i		−	0.491008i
$520$	15.4475	−	2.70086i	0.0297067	−	0.00519396i
$521$	164.416			0.315578			0.157789	−	0.987473i	$-0.449563\pi$
$521$	164.416			0.315578			0.157789	+	0.987473i	$0.449563\pi$
$522$	0.956101	−	0.956101i	0.00183161	−	0.00183161i
$523$	−519.275	−	519.275i	−0.992878	−	0.992878i	0.00709689	−	0.999975i	$-0.497741\pi$
$523$	−519.275	−	519.275i	−0.992878	−	0.992878i	−0.999975	+	0.00709689i	$0.997741\pi$
$524$		−	457.403i		−	0.872907i
$525$	−147.194	+	53.0943i	−0.280370	+	0.101132i
$526$	63.0221			0.119814
$527$	213.986	−	213.986i	0.406046	−	0.406046i
$528$	451.117	+	451.117i	0.854388	+	0.854388i
$529$			37.7834i			0.0714242i
$530$	2.06626	+	11.8179i	0.00389860	+	0.0222980i
$531$	66.1416			0.124560
$532$	−151.770	+	151.770i	−0.285282	+	0.285282i
$533$	−42.0406	−	42.0406i	−0.0788754	−	0.0788754i
$534$		−	47.4320i		−	0.0888240i
$535$	346.662	+	243.481i	0.647966	+	0.455104i
$536$	151.131			0.281960
$537$	53.0701	−	53.0701i	0.0988270	−	0.0988270i
$538$	37.3773	+	37.3773i	0.0694745	+	0.0694745i
$539$			120.150i			0.222913i
$540$	335.268	−	477.347i	0.620867	−	0.883975i
$541$	53.2006			0.0983375			0.0491688	−	0.998790i	$-0.484343\pi$
$541$	53.2006			0.0983375			0.0491688	+	0.998790i	$0.484343\pi$
$542$	0.745133	−	0.745133i	0.00137478	−	0.00137478i
$543$	360.638	+	360.638i	0.664159	+	0.664159i
$544$			156.510i			0.287703i
$545$	91.5686	−	16.0100i	0.168016	−	0.0293761i
$546$	2.46127			0.00450782
$547$	−347.403	+	347.403i	−0.635107	+	0.635107i	−0.949344	−	0.314238i	$-0.898251\pi$
$547$	−347.403	+	347.403i	−0.635107	+	0.635107i	0.314238	+	0.949344i	$0.398251\pi$
$548$	−228.484	−	228.484i	−0.416941	−	0.416941i
$549$		−	251.834i		−	0.458714i
$550$	28.3267	−	60.2924i	0.0515031	−	0.109622i
$551$	−52.2179			−0.0947693
$552$	−49.3108	+	49.3108i	−0.0893311	+	0.0893311i
$553$	102.921	+	102.921i	0.186114	+	0.186114i
$554$		−	25.1558i		−	0.0454076i
$555$	103.474	+	591.820i	0.186440	+	1.06634i
$556$	−706.896			−1.27140
$557$	648.564	−	648.564i	1.16439	−	1.16439i	0.180884	−	0.983504i	$-0.442104\pi$
$557$	648.564	−	648.564i	1.16439	−	1.16439i	0.983504	−	0.180884i	$-0.0578958\pi$
$558$	−5.33960	−	5.33960i	−0.00956918	−	0.00956918i
$559$			25.6249i			0.0458405i
$560$	170.082	+	119.459i	0.303718	+	0.213319i
$561$	−859.771			−1.53257
$562$	−43.2597	+	43.2597i	−0.0769745	+	0.0769745i
$563$	−445.012	−	445.012i	−0.790430	−	0.790430i	0.191134	−	0.981564i	$-0.438783\pi$
$563$	−445.012	−	445.012i	−0.790430	−	0.790430i	−0.981564	+	0.191134i	$0.938783\pi$
$564$		−	84.7245i		−	0.150221i
$565$	526.118	−	749.073i	0.931182	−	1.32579i
$566$	6.54399			0.0115618
$567$	72.5629	−	72.5629i	0.127977	−	0.127977i
$568$	19.4974	+	19.4974i	0.0343264	+	0.0343264i
$569$			717.103i			1.26029i	0.776479	+	0.630143i	$0.217004\pi$
$569$			717.103i			1.26029i	−0.776479	+	0.630143i	$0.782996\pi$
$570$	36.9077	−	6.45298i	0.0647504	−	0.0113210i
$571$	−722.535			−1.26538			−0.632692	−	0.774403i	$-0.718050\pi$
$571$	−722.535			−1.26538			−0.632692	+	0.774403i	$0.718050\pi$
$572$	122.233	−	122.233i	0.213694	−	0.213694i
$573$	−195.251	−	195.251i	−0.340752	−	0.340752i
$574$			9.64044i			0.0167952i
$575$	−538.689	−	253.088i	−0.936851	−	0.440153i
$576$	−209.982			−0.364552
$577$	−416.867	+	416.867i	−0.722473	+	0.722473i	−0.969108	−	0.246635i	$-0.920675\pi$
$577$	−416.867	+	416.867i	−0.722473	+	0.722473i	0.246635	+	0.969108i	$0.420675\pi$
$578$	−17.4887	−	17.4887i	−0.0302573	−	0.0302573i
$579$			13.6422i			0.0235617i
$580$	8.76218	+	50.1151i	0.0151072	+	0.0864054i
$581$	−197.631			−0.340157
$582$	34.8336	−	34.8336i	0.0598515	−	0.0598515i
$583$	187.593	+	187.593i	0.321771	+	0.321771i
$584$		−	128.617i		−	0.220235i
$585$	−35.2735	−	24.7746i	−0.0602965	−	0.0423497i
$586$	55.1811			0.0941656
$587$	−231.729	+	231.729i	−0.394768	+	0.394768i	−0.876383	−	0.481615i	$-0.840050\pi$
$587$	−231.729	+	231.729i	−0.394768	+	0.394768i	0.481615	+	0.876383i	$0.340050\pi$
$588$	46.5566	+	46.5566i	0.0791779	+	0.0791779i
$589$			291.625i			0.495118i
$590$	8.67008	−	12.3442i	0.0146950	−	0.0209225i
$591$	−648.541			−1.09736
$592$	564.281	−	564.281i	0.953177	−	0.953177i
$593$	744.025	+	744.025i	1.25468	+	1.25468i	0.953598	+	0.301081i	$0.0973476\pi$
$593$	744.025	+	744.025i	1.25468	+	1.25468i	0.301081	+	0.953598i	$0.402652\pi$
$594$			78.1872i			0.131628i
$595$	−275.914	+	48.2411i	−0.463721	+	0.0810775i
$596$	−210.576			−0.353315
$597$	64.9668	−	64.9668i	0.108822	−	0.108822i
$598$	6.61974	+	6.61974i	0.0110698	+	0.0110698i
$599$		−	108.257i		−	0.180729i	−0.995909	−	0.0903644i	$-0.971197\pi$
$599$		−	108.257i		−	0.180729i	0.995909	−	0.0903644i	$-0.0288032\pi$
$600$	−24.8476	−	68.8855i	−0.0414127	−	0.114809i
$601$	−643.706			−1.07106			−0.535529	−	0.844517i	$-0.679888\pi$
$601$	−643.706			−1.07106			−0.535529	+	0.844517i	$0.679888\pi$
$602$	2.93805	−	2.93805i	0.00488049	−	0.00488049i
$603$	−293.740	−	293.740i	−0.487132	−	0.487132i
$604$		−	1166.27i		−	1.93092i
$605$	−149.506	−	855.099i	−0.247118	−	1.41339i
$606$	−42.2497			−0.0697189
$607$	−604.070	+	604.070i	−0.995172	+	0.995172i	−0.999988	−	0.00481613i	$-0.998467\pi$
$607$	−604.070	+	604.070i	−0.995172	+	0.995172i	0.00481613	+	0.999988i	$0.498467\pi$
$608$	−106.648	−	106.648i	−0.175407	−	0.175407i
$609$			16.0182i			0.0263025i
$610$	−47.0007	−	33.0113i	−0.0770503	−	0.0541169i
$611$	−22.8167			−0.0373432
$612$	202.593	−	202.593i	0.331035	−	0.331035i
$613$	274.581	+	274.581i	0.447929	+	0.447929i	0.894666	−	0.446736i	$-0.147414\pi$
$613$	274.581	+	274.581i	0.447929	+	0.447929i	−0.446736	+	0.894666i	$0.647414\pi$
$614$			54.3544i			0.0885251i
$615$	−159.573	+	227.196i	−0.259468	+	0.369424i
$616$	−56.2291			−0.0912810
$617$	44.3007	−	44.3007i	0.0718001	−	0.0718001i	−0.670295	−	0.742095i	$-0.733832\pi$
$617$	44.3007	−	44.3007i	0.0718001	−	0.0718001i	0.742095	+	0.670295i	$0.233832\pi$
$618$	23.7290	+	23.7290i	0.0383964	+	0.0383964i
$619$			1046.44i			1.69054i	0.534342	+	0.845269i	$0.320560\pi$
$619$			1046.44i			1.69054i	−0.534342	+	0.845269i	$0.679440\pi$
$620$	279.881	−	48.9347i	0.451421	−	0.0789270i
$621$	698.573			1.12492
$622$	16.2369	−	16.2369i	0.0261043	−	0.0261043i
$623$	−241.622	−	241.622i	−0.387837	−	0.387837i
$624$		−	94.1496i		−	0.150881i
$625$	481.086	−	398.975i	0.769738	−	0.638360i
$626$	26.0664			0.0416396
$627$	585.857	−	585.857i	0.934381	−	0.934381i
$628$	36.1058	+	36.1058i	0.0574933	+	0.0574933i
$629$			1075.45i			1.70977i
$630$	1.20376	+	6.88490i	0.00191073	+	0.0109284i
$631$	744.083			1.17921			0.589607	−	0.807691i	$-0.299283\pi$
$631$	744.083			1.17921			0.589607	+	0.807691i	$0.299283\pi$
$632$	−48.1661	+	48.1661i	−0.0762122	+	0.0762122i
$633$	−22.5891	−	22.5891i	−0.0356858	−	0.0356858i
$634$		−	32.6764i		−	0.0515400i
$635$	−462.368	−	324.748i	−0.728139	−	0.511414i
$636$	145.379			0.228584
$637$	12.5379	−	12.5379i	0.0196827	−	0.0196827i
$638$	−4.82192	−	4.82192i	−0.00755786	−	0.00755786i
$639$		−	75.7910i		−	0.118609i
$640$	−112.495	+	160.167i	−0.175773	+	0.250261i
$641$	591.040			0.922060			0.461030	−	0.887385i	$-0.347480\pi$
$641$	591.040			0.922060			0.461030	+	0.887385i	$0.347480\pi$
$642$	−22.0021	+	22.0021i	−0.0342712	+	0.0342712i
$643$	−1.13741	−	1.13741i	−0.00176891	−	0.00176891i	0.706222	−	0.707991i	$-0.250398\pi$
$643$	−1.13741	−	1.13741i	−0.00176891	−	0.00176891i	−0.707991	+	0.706222i	$0.750398\pi$
$644$			250.434i			0.388872i
$645$	117.873	−	20.6090i	0.182749	−	0.0319520i
$646$	67.0682			0.103821
$647$	8.43740	−	8.43740i	0.0130408	−	0.0130408i	−0.700556	−	0.713597i	$-0.747065\pi$
$647$	8.43740	−	8.43740i	0.0130408	−	0.0130408i	0.713597	+	0.700556i	$0.247065\pi$
$648$	33.9587	+	33.9587i	0.0524054	+	0.0524054i
$649$		−	333.572i		−	0.513979i
$650$	−9.24755	+	3.33567i	−0.0142270	+	0.00513180i
$651$	89.4579			0.137416
$652$	−269.169	+	269.169i	−0.412836	+	0.412836i
$653$	388.275	+	388.275i	0.594602	+	0.594602i	0.938871	−	0.344269i	$-0.111873\pi$
$653$	388.275	+	388.275i	0.594602	+	0.594602i	−0.344269	+	0.938871i	$0.611873\pi$
$654$			6.82785i			0.0104401i
$655$	99.0692	+	566.624i	0.151251	+	0.865075i
$656$	368.771			0.562151
$657$	−249.982	+	249.982i	−0.380491	+	0.380491i
$658$	2.61608	+	2.61608i	0.00397580	+	0.00397580i
$659$		−	91.5844i		−	0.138975i	−0.997583	−	0.0694874i	$-0.977864\pi$
$659$		−	91.5844i		−	0.138975i	0.997583	−	0.0694874i	$-0.0221364\pi$
$660$	−660.572	−	463.958i	−1.00087	−	0.702967i
$661$	406.403			0.614830			0.307415	−	0.951575i	$-0.400536\pi$
$661$	406.403			0.614830			0.307415	+	0.951575i	$0.400536\pi$
$662$	−52.6817	+	52.6817i	−0.0795796	+	0.0795796i
$663$	89.7186	+	89.7186i	0.135322	+	0.135322i
$664$		−	92.4894i		−	0.139291i
$665$	155.139	−	220.883i	0.233291	−	0.332154i
$666$	26.8357			0.0402938
$667$	−43.0820	+	43.0820i	−0.0645907	+	0.0645907i
$668$	311.282	+	311.282i	0.465992	+	0.465992i
$669$		−	125.581i		−	0.187715i
$670$	−93.3264	+	16.3173i	−0.139293	+	0.0243542i
$671$	−1270.08			−1.89281
$672$	−32.7149	+	32.7149i	−0.0486829	+	0.0486829i
$673$	858.587	+	858.587i	1.27576	+	1.27576i	0.943018	+	0.332742i	$0.107974\pi$
$673$	858.587	+	858.587i	1.27576	+	1.27576i	0.332742	+	0.943018i	$0.392026\pi$
$674$		−	12.0657i		−	0.0179016i
$675$	−311.936	+	663.946i	−0.462128	+	0.983623i
$676$	646.417			0.956238
$677$	701.144	−	701.144i	1.03566	−	1.03566i	0.0363228	−	0.999340i	$-0.488436\pi$
$677$	701.144	−	701.144i	1.03566	−	1.03566i	0.999340	−	0.0363228i	$-0.0115644\pi$
$678$	47.5425	+	47.5425i	0.0701217	+	0.0701217i
$679$		−	354.890i		−	0.522666i
$680$	−22.5764	−	129.125i	−0.0332005	−	0.189890i
$681$	50.5962			0.0742969
$682$	−26.9293	+	26.9293i	−0.0394857	+	0.0394857i
$683$	−696.825	−	696.825i	−1.02024	−	1.02024i	−0.999791	−	0.0204510i	$-0.993490\pi$
$683$	−696.825	−	696.825i	−1.02024	−	1.02024i	−0.0204510	−	0.999791i	$-0.506510\pi$
$684$			276.098i			0.403653i
$685$	332.530	+	233.555i	0.485445	+	0.340956i
$686$	−2.87510			−0.00419111
$687$	−397.797	+	397.797i	−0.579035	+	0.579035i
$688$	−112.388	−	112.388i	−0.163354	−	0.163354i
$689$		−	39.1512i		−	0.0568233i
$690$	25.1264	−	35.7744i	0.0364151	−	0.0518470i
$691$	58.3671			0.0844676			0.0422338	−	0.999108i	$-0.486553\pi$
$691$	58.3671			0.0844676			0.0422338	+	0.999108i	$0.486553\pi$
$692$	302.841	−	302.841i	0.437631	−	0.437631i
$693$	109.288	+	109.288i	0.157703	+	0.157703i
$694$			33.0499i			0.0476223i
$695$	875.692	−	153.107i	1.25999	−	0.220298i
$696$	−7.49636			−0.0107706
$697$	−351.415	+	351.415i	−0.504183	+	0.504183i
$698$	−59.8649	−	59.8649i	−0.0857663	−	0.0857663i
$699$		−	433.753i		−	0.620534i
$700$	−238.020	−	111.827i	−0.340029	−	0.159753i
$701$	−352.650			−0.503067			−0.251534	−	0.967849i	$-0.580935\pi$
$701$	−352.650			−0.503067			−0.251534	+	0.967849i	$0.580935\pi$
$702$	8.15897	−	8.15897i	0.0116225	−	0.0116225i
$703$	−732.821	−	732.821i	−1.04242	−	1.04242i
$704$			1059.01i			1.50427i
$705$	18.3505	+	104.955i	0.0260291	+	0.148873i
$706$	−83.0598			−0.117648
$707$	−215.223	+	215.223i	−0.304417	+	0.304417i
$708$	−129.255	−	129.255i	−0.182563	−	0.182563i
$709$		−	490.835i		−	0.692291i	−0.938181	−	0.346146i	$-0.887490\pi$
$709$		−	490.835i		−	0.692291i	0.938181	−	0.346146i	$-0.112510\pi$
$710$	−14.1451	−	9.93496i	−0.0199227	−	0.0139929i
$711$	187.233			0.263337
$712$	113.077	−	113.077i	0.158816	−	0.158816i
$713$	240.603	+	240.603i	0.337451	+	0.337451i
$714$		−	20.5736i		−	0.0288146i
$715$	−124.946	+	177.895i	−0.174750	+	0.248804i
$716$	126.136			0.176167
$717$	177.538	−	177.538i	0.247612	−	0.247612i
$718$	49.0723	+	49.0723i	0.0683458	+	0.0683458i
$719$		−	935.903i		−	1.30167i	−0.759218	−	0.650837i	$-0.774418\pi$
$719$		−	935.903i		−	1.30167i	0.759218	−	0.650837i	$-0.225582\pi$
$720$	263.364	−	46.0469i	0.365784	−	0.0639540i
$721$	241.754			0.335304
$722$	−6.07332	+	6.07332i	−0.00841180	+	0.00841180i
$723$	24.3007	+	24.3007i	0.0336110	+	0.0336110i
$724$			857.156i			1.18392i
$725$	−21.7089	−	60.1841i	−0.0299433	−	0.0830125i
$726$	63.7608			0.0878248
$727$	674.369	−	674.369i	0.927606	−	0.927606i	−0.0699452	−	0.997551i	$-0.522282\pi$
$727$	674.369	−	674.369i	0.927606	−	0.927606i	0.997551	+	0.0699452i	$0.0222824\pi$
$728$	5.86761	+	5.86761i	0.00805990	+	0.00805990i
$729$		−	756.758i		−	1.03808i
$730$	13.8865	+	79.4237i	0.0190226	+	0.108800i
$731$	214.197			0.293019
$732$	−492.137	+	492.137i	−0.672319	+	0.672319i
$733$	−891.123	−	891.123i	−1.21572	−	1.21572i	−0.969116	−	0.246604i	$-0.920685\pi$
$733$	−891.123	−	891.123i	−1.21572	−	1.21572i	−0.246604	−	0.969116i	$-0.579315\pi$
$734$		−	4.67246i		−	0.00636575i
$735$	−67.7573	−	47.5899i	−0.0921868	−	0.0647482i
$736$	−175.978			−0.239100
$737$	−1481.42	+	1481.42i	−2.01007	+	2.01007i
$738$	8.76888	+	8.76888i	0.0118820	+	0.0118820i
$739$		−	419.418i		−	0.567549i	−0.958891	−	0.283774i	$-0.908413\pi$
$739$		−	419.418i		−	0.567549i	0.958891	−	0.283774i	$-0.0915867\pi$
$740$	−580.344	+	826.279i	−0.784248	+	1.11659i
$741$	−122.270			−0.165007
$742$	−4.48894	+	4.48894i	−0.00604978	+	0.00604978i
$743$	−156.843	−	156.843i	−0.211094	−	0.211094i	0.593638	−	0.804732i	$-0.297691\pi$
$743$	−156.843	−	156.843i	−0.211094	−	0.211094i	−0.804732	+	0.593638i	$0.797691\pi$
$744$			41.8654i			0.0562707i
$745$	260.858	−	45.6087i	0.350145	−	0.0612197i
$746$	−79.3050			−0.106307
$747$	−179.764	+	179.764i	−0.240648	+	0.240648i
$748$	−1021.74	−	1021.74i	−1.36596	−	1.36596i
$749$			224.161i			0.299280i
$750$	22.7813	+	39.8555i	0.0303751	+	0.0531406i
$751$	129.344			0.172230			0.0861148	−	0.996285i	$-0.472555\pi$
$751$	129.344			0.172230			0.0861148	+	0.996285i	$0.472555\pi$
$752$	100.071	−	100.071i	0.133074	−	0.133074i
$753$	−384.109	−	384.109i	−0.510105	−	0.510105i
$754$			1.00635i			0.00133468i
$755$	252.604	+	1444.76i	0.334575	+	1.91359i
$756$	308.665			0.408287
$757$	287.782	−	287.782i	0.380161	−	0.380161i	−0.490999	−	0.871160i	$-0.663368\pi$
$757$	287.782	−	287.782i	0.380161	−	0.380161i	0.871160	+	0.490999i	$0.163368\pi$
$758$	−24.8105	−	24.8105i	−0.0327315	−	0.0327315i
$759$		−	966.714i		−	1.27367i
$760$	103.371	+	72.6033i	0.136014	+	0.0955307i
$761$	−1012.93			−1.33105			−0.665526	−	0.746374i	$-0.731793\pi$
$761$	−1012.93			−1.33105			−0.665526	+	0.746374i	$0.731793\pi$
$762$	29.3458	−	29.3458i	0.0385116	−	0.0385116i
$763$	34.7816	+	34.7816i	0.0455853	+	0.0455853i
$764$		−	464.067i		−	0.607417i
$765$	−207.090	+	294.849i	−0.270706	+	0.385424i
$766$	62.3706			0.0814238
$767$	−34.8089	+	34.8089i	−0.0453831	+	0.0453831i
$768$	402.672	+	402.672i	0.524312	+	0.524312i
$769$		−	941.987i		−	1.22495i	−0.790490	−	0.612475i	$-0.790174\pi$
$769$		−	941.987i		−	1.22495i	0.790490	−	0.612475i	$-0.209826\pi$
$770$	34.7227	−	6.07095i	0.0450944	−	0.00788435i
$771$	915.713			1.18769
$772$	−16.2123	+	16.2123i	−0.0210003	+	0.0210003i
$773$	282.778	+	282.778i	0.365818	+	0.365818i	0.865950	−	0.500131i	$-0.166715\pi$
$773$	282.778	+	282.778i	0.365818	+	0.365818i	−0.500131	+	0.865950i	$0.666715\pi$
$774$		−	5.34487i		−	0.00690551i
$775$	−336.114	+	121.239i	−0.433695	+	0.156438i
$776$	166.085			0.214027
$777$	−224.798	+	224.798i	−0.289315	+	0.289315i
$778$	35.3626	+	35.3626i	0.0454533	+	0.0454533i
$779$		−	478.916i		−	0.614783i
$780$	20.5170	+	117.347i	0.0263039	+	0.150445i
$781$	−382.237			−0.489420
$782$	55.3341	−	55.3341i	0.0707597	−	0.0707597i
$783$	53.0994	+	53.0994i	0.0678154	+	0.0678154i
$784$			109.980i			0.140280i
$785$	−52.5475	−	36.9071i	−0.0669395	−	0.0470155i
$786$	−42.2505			−0.0537538
$787$	680.900	−	680.900i	0.865185	−	0.865185i	−0.126750	−	0.991935i	$-0.540455\pi$
$787$	680.900	−	680.900i	0.865185	−	0.865185i	0.991935	+	0.126750i	$0.0404546\pi$
$788$	−770.718	−	770.718i	−0.978069	−	0.978069i
$789$			960.395i			1.21723i
$790$	24.5432	−	34.9440i	0.0310673	−	0.0442329i
$791$	484.371			0.612352
$792$	−51.1456	+	51.1456i	−0.0645778	+	0.0645778i
$793$	132.535	+	132.535i	0.167131	+	0.167131i
$794$		−	8.63199i		−	0.0108715i
$795$	−180.094	+	31.4877i	−0.226533	+	0.0396072i
$796$	154.411			0.193984
$797$	1078.25	−	1078.25i	1.35289	−	1.35289i	0.470474	−	0.882414i	$-0.344083\pi$
$797$	1078.25	−	1078.25i	1.35289	−	1.35289i	0.882414	−	0.470474i	$-0.155917\pi$
$798$	14.0191	+	14.0191i	0.0175678	+	0.0175678i
$799$			190.724i			0.238703i
$800$	78.5801	−	167.255i	0.0982251	−	0.209069i
$801$	−439.556			−0.548759
$802$	26.5232	−	26.5232i	0.0330713	−	0.0330713i
$803$	1260.74	+	1260.74i	1.57004	+	1.57004i
$804$			1148.06i			1.42794i
$805$	−54.2416	−	310.234i	−0.0673809	−	0.385383i
$806$	5.62023			0.00697299
$807$	−569.593	+	569.593i	−0.705815	+	0.705815i
$808$	−100.722	−	100.722i	−0.124656	−	0.124656i
$809$			757.466i			0.936299i	0.883649	+	0.468149i	$0.155079\pi$
$809$			757.466i			0.936299i	−0.883649	+	0.468149i	$0.844921\pi$
$810$	−24.6367	−	17.3038i	−0.0304156	−	0.0213627i
$811$	1153.11			1.42183			0.710916	−	0.703277i	$-0.248281\pi$
$811$	1153.11			1.42183			0.710916	+	0.703277i	$0.248281\pi$
$812$	−19.0358	+	19.0358i	−0.0234431	+	0.0234431i
$813$	11.3551	+	11.3551i	0.0139669	+	0.0139669i
$814$		−	135.341i		−	0.166266i
$815$	275.143	−	391.742i	0.337599	−	0.480666i
$816$	−786.993			−0.964452
$817$	−145.956	+	145.956i	−0.178649	+	0.178649i
$818$	−53.5724	−	53.5724i	−0.0654920	−	0.0654920i
$819$		−	22.8088i		−	0.0278495i
$820$	−459.631	+	80.3623i	−0.560525	+	0.0980029i
$821$	1247.91			1.51998			0.759992	−	0.649932i	$-0.225203\pi$
$821$	1247.91			1.51998			0.759992	+	0.649932i	$0.225203\pi$
$822$	−21.1051	+	21.1051i	−0.0256754	+	0.0256754i
$823$	181.780	+	181.780i	0.220875	+	0.220875i	0.808867	−	0.587992i	$-0.200081\pi$
$823$	181.780	+	181.780i	0.220875	+	0.220875i	−0.587992	+	0.808867i	$0.700081\pi$
$824$			113.139i			0.137304i
$825$	918.796	+	431.671i	1.11369	+	0.523237i
$826$	7.98212			0.00966358
$827$	−503.573	+	503.573i	−0.608915	+	0.608915i	−0.942662	−	0.333748i	$-0.891687\pi$
$827$	−503.573	+	503.573i	−0.608915	+	0.608915i	0.333748	+	0.942662i	$0.391687\pi$
$828$	227.793	+	227.793i	0.275112	+	0.275112i
$829$			113.998i			0.137513i	0.997633	+	0.0687566i	$0.0219032\pi$
$829$			113.998i			0.137513i	−0.997633	+	0.0687566i	$0.978097\pi$
$830$	9.98590	+	57.1142i	0.0120312	+	0.0688123i
$831$	383.350			0.461311
$832$	110.509	−	110.509i	0.132823	−	0.132823i
$833$	−104.804	−	104.804i	−0.125815	−	0.125815i
$834$			65.2963i			0.0782929i
$835$	−453.033	−	318.191i	−0.542554	−	0.381067i
$836$	1392.45			1.66561
$837$	296.548	−	296.548i	0.354299	−	0.354299i
$838$	12.1715	+	12.1715i	0.0145244	+	0.0145244i
$839$		−	430.572i		−	0.513196i	−0.966518	−	0.256598i	$-0.917398\pi$
$839$		−	430.572i		−	0.513196i	0.966518	−	0.256598i	$-0.0826017\pi$
$840$	22.2716	−	31.7097i	0.0265138	−	0.0377497i
$841$	834.451			0.992212
$842$	−2.52794	+	2.52794i	−0.00300230	+	0.00300230i
$843$	−659.235	−	659.235i	−0.782011	−	0.782011i
$844$		−	53.6892i		−	0.0636128i
$845$	−800.771	+	140.008i	−0.947658	+	0.165690i
$846$	4.75913			0.00562545
$847$	324.802	−	324.802i	0.383474	−	0.383474i
$848$	171.713	+	171.713i	0.202492	+	0.202492i
$849$			99.7240i			0.117460i
$850$	27.8827	+	77.2999i	0.0328032	+	0.0909410i
$851$	−1209.22			−1.42094
$852$	−148.112	+	148.112i	−0.173840	+	0.173840i
$853$	49.8441	+	49.8441i	0.0584338	+	0.0584338i	0.735720	−	0.677286i	$-0.236844\pi$
$853$	49.8441	+	49.8441i	0.0584338	+	0.0584338i	−0.677286	+	0.735720i	$0.736844\pi$
$854$		−	30.3919i		−	0.0355877i
$855$	−59.8003	−	342.026i	−0.0699418	−	0.400031i
$856$	−104.905			−0.122552
$857$	−362.419	+	362.419i	−0.422893	+	0.422893i	−0.886199	−	0.463306i	$-0.846663\pi$
$857$	−362.419	+	362.419i	−0.422893	+	0.422893i	0.463306	+	0.886199i	$0.346663\pi$
$858$	−11.2907	−	11.2907i	−0.0131594	−	0.0131594i
$859$		−	780.281i		−	0.908360i	−0.890910	−	0.454180i	$-0.849932\pi$
$859$		−	780.281i		−	0.908360i	0.890910	−	0.454180i	$-0.150068\pi$
$860$	164.570	+	115.587i	0.191361	+	0.134404i
$861$	−146.911			−0.170628
$862$	−1.89997	+	1.89997i	−0.00220414	+	0.00220414i
$863$	−274.148	−	274.148i	−0.317669	−	0.317669i	0.530202	−	0.847871i	$-0.322116\pi$
$863$	−274.148	−	274.148i	−0.317669	−	0.317669i	−0.847871	+	0.530202i	$0.822116\pi$
$864$			216.896i			0.251038i
$865$	−309.562	+	440.747i	−0.357875	+	0.509534i
$866$	29.2868			0.0338184
$867$	266.511	−	266.511i	0.307394	−	0.307394i
$868$	106.311	+	106.311i	0.122478	+	0.122478i
$869$		−	944.273i		−	1.08662i
$870$	4.62916	−	0.809367i	0.00532087	−	0.000930307i
$871$	309.178			0.354969
$872$	−16.2774	+	16.2774i	−0.0186668	+	0.0186668i
$873$	−322.806	−	322.806i	−0.369766	−	0.369766i
$874$			75.4104i			0.0862820i
$875$	319.077	+	86.9770i	0.364659	+	0.0994023i
$876$	977.038			1.11534
$877$	−241.282	+	241.282i	−0.275122	+	0.275122i	−0.831158	−	0.556036i	$-0.812322\pi$
$877$	−241.282	+	241.282i	−0.275122	+	0.275122i	0.556036	+	0.831158i	$0.312322\pi$
$878$	8.18181	+	8.18181i	0.00931869	+	0.00931869i
$879$			840.905i			0.956661i
$880$	−232.229	−	1328.23i	−0.263896	−	1.50935i
$881$	−1662.32			−1.88685			−0.943426	−	0.331583i	$-0.892417\pi$
$881$	−1662.32			−1.88685			−0.943426	+	0.331583i	$0.892417\pi$
$882$	−2.61517	+	2.61517i	−0.00296505	+	0.00296505i
$883$	805.479	+	805.479i	0.912208	+	0.912208i	0.996446	−	0.0842380i	$-0.0268456\pi$
$883$	805.479	+	805.479i	0.912208	+	0.912208i	−0.0842380	+	0.996446i	$0.526846\pi$
$884$			213.241i			0.241223i
$885$	188.114	+	132.123i	0.212558	+	0.149292i
$886$	−78.7993			−0.0889383
$887$	−1107.55	+	1107.55i	−1.24865	+	1.24865i	−0.292333	+	0.956317i	$0.594431\pi$
$887$	−1107.55	+	1107.55i	−1.24865	+	1.24865i	−0.956317	+	0.292333i	$0.905569\pi$
$888$	−105.203	−	105.203i	−0.118472	−	0.118472i
$889$		−	298.980i		−	0.336310i
$890$	−57.6186	+	82.0359i	−0.0647400	+	0.0921752i
$891$	−665.744			−0.747188
$892$	149.239	−	149.239i	0.167309	−	0.167309i
$893$	−129.961	−	129.961i	−0.145533	−	0.145533i
$894$			19.4510i			0.0217572i
$895$	−156.255	+	27.3198i	−0.174586	+	0.0305249i
$896$	−103.568			−0.115590
$897$	−100.878	+	100.878i	−0.112462	+	0.112462i
$898$	0.682323	+	0.682323i	0.000759826	+	0.000759826i
$899$			36.5771i			0.0406864i
$900$	−318.219	+	114.784i	−0.353577	+	0.127538i
$901$	−327.263			−0.363222
$902$	44.2242	−	44.2242i	0.0490290	−	0.0490290i
$903$	44.7730	+	44.7730i	0.0495825	+	0.0495825i
$904$			226.681i			0.250753i
$905$	−185.652	−	1061.83i	−0.205140	−	1.17329i
$906$	−107.729			−0.118906
$907$	−82.6372	+	82.6372i	−0.0911104	+	0.0911104i	−0.751193	−	0.660083i	$-0.770521\pi$
$907$	−82.6372	+	82.6372i	−0.0911104	+	0.0911104i	0.660083	+	0.751193i	$0.270521\pi$
$908$	60.1279	+	60.1279i	0.0662201	+	0.0662201i
$909$			391.531i			0.430727i
$910$	−4.25688	−	2.98986i	−0.00467789	−	0.00328556i
$911$	−1244.79			−1.36640			−0.683198	−	0.730233i	$-0.739411\pi$
$911$	−1244.79			−1.36640			−0.683198	+	0.730233i	$0.739411\pi$
$912$	536.265	−	536.265i	0.588010	−	0.588010i
$913$	906.606	+	906.606i	0.992997	+	0.992997i
$914$		−	50.1643i		−	0.0548843i
$915$	503.060	−	716.244i	0.549792	−	0.782781i
$916$	−945.473			−1.03218
$917$	−215.227	+	215.227i	−0.234708	+	0.234708i
$918$	−68.2004	−	68.2004i	−0.0742924	−	0.0742924i
$919$			279.541i			0.304179i	0.988367	+	0.152090i	$0.0486003\pi$
$919$			279.541i			0.304179i	−0.988367	+	0.152090i	$0.951400\pi$
$920$	145.186	−	25.3845i	0.157811	−	0.0275919i
$921$	−828.307			−0.899357
$922$	76.6384	−	76.6384i	0.0831219	−	0.0831219i
$923$	39.8871	+	39.8871i	0.0432146	+	0.0432146i
$924$		−	427.144i		−	0.462277i
$925$	539.957	−	1149.28i	0.583737	−	1.24246i
$926$	8.52916			0.00921075
$927$	219.898	−	219.898i	0.237215	−	0.237215i
$928$	−13.3763	−	13.3763i	−0.0144141	−	0.0144141i
$929$		−	1295.36i		−	1.39436i	−0.716898	−	0.697178i	$-0.754439\pi$
$929$		−	1295.36i		−	1.39436i	0.716898	−	0.697178i	$-0.245561\pi$
$930$	−4.52012	−	25.8528i	−0.00486035	−	0.0277987i
$931$	142.829			0.153414
$932$	515.467	−	515.467i	0.553076	−	0.553076i
$933$	247.434	+	247.434i	0.265202	+	0.265202i
$934$		−	42.0018i		−	0.0449698i
$935$	1487.02	+	1044.42i	1.59039	+	1.11702i
$936$	10.6743			0.0114041
$937$	192.234	−	192.234i	0.205159	−	0.205159i	−0.597047	−	0.802206i	$-0.703659\pi$
$937$	192.234	−	192.234i	0.205159	−	0.205159i	0.802206	+	0.597047i	$0.203659\pi$
$938$	−35.4493	−	35.4493i	−0.0377924	−	0.0377924i
$939$			397.226i			0.423031i
$940$	−102.920	+	146.535i	−0.109490	+	0.155888i
$941$	−1570.22			−1.66867			−0.834334	−	0.551259i	$-0.814147\pi$
$941$	−1570.22			−1.66867			−0.834334	+	0.551259i	$0.814147\pi$
$942$	3.33511	−	3.33511i	0.00354045	−	0.00354045i
$943$	−395.126	−	395.126i	−0.419010	−	0.419010i
$944$		−	305.336i		−	0.323449i
$945$	−382.370	+	66.8539i	−0.404624	+	0.0707449i
$946$	−26.9558			−0.0284945
$947$	417.059	−	417.059i	0.440400	−	0.440400i	−0.451746	−	0.892147i	$-0.649199\pi$
$947$	417.059	−	417.059i	0.440400	−	0.440400i	0.892147	+	0.451746i	$0.149199\pi$
$948$	−365.893	−	365.893i	−0.385963	−	0.385963i
$949$		−	263.121i		−	0.277261i
$950$	−71.6725	−	33.6733i	−0.0754447	−	0.0354456i
$951$	497.956			0.523613
$952$	49.0471	−	49.0471i	0.0515200	−	0.0515200i
$953$	249.865	+	249.865i	0.262188	+	0.262188i	0.825942	−	0.563755i	$-0.190644\pi$
$953$	249.865	+	249.865i	0.262188	+	0.262188i	−0.563755	+	0.825942i	$0.690644\pi$
$954$			8.16622i			0.00855998i
$955$	100.512	+	574.879i	0.105249	+	0.601967i
$956$	421.967			0.441388
$957$	73.4813	−	73.4813i	0.0767829	−	0.0767829i
$958$	17.7841	+	17.7841i	0.0185638	+	0.0185638i
$959$			215.022i			0.224215i
$960$	−597.213	−	419.458i	−0.622097	−	0.436935i
$961$	−756.726			−0.787436
$962$	−14.1230	+	14.1230i	−0.0146809	+	0.0146809i
$963$	203.895	+	203.895i	0.211729	+	0.211729i
$964$			57.7573i			0.0599142i
$965$	16.5721	−	23.5949i	0.0171732	−	0.0244507i
$966$	23.1327			0.0239469
$967$	−974.337	+	974.337i	−1.00759	+	1.00759i	−0.00761690	+	0.999971i	$0.502425\pi$
$967$	−974.337	+	974.337i	−1.00759	+	1.00759i	−0.999971	+	0.00761690i	$0.997575\pi$
$968$	152.004	+	152.004i	0.157029	+	0.157029i
$969$			1022.05i			1.05475i
$970$	−102.561	+	17.9319i	−0.105733	+	0.0184865i
$971$	1218.99			1.25540			0.627699	−	0.778456i	$-0.283997\pi$
$971$	1218.99			1.25540			0.627699	+	0.778456i	$0.283997\pi$
$972$	484.481	−	484.481i	0.498437	−	0.498437i
$973$	332.625	+	332.625i	0.341855	+	0.341855i
$974$			58.0608i			0.0596107i
$975$	−50.8324	−	140.924i	−0.0521358	−	0.144537i
$976$	−1162.57			−1.19115
$977$	−110.024	+	110.024i	−0.112614	+	0.112614i	−0.761169	−	0.648554i	$-0.775374\pi$
$977$	−110.024	+	110.024i	−0.112614	+	0.112614i	0.648554	+	0.761169i	$0.275374\pi$
$978$	24.8633	+	24.8633i	0.0254226	+	0.0254226i
$979$			2216.82i			2.26437i
$980$	−23.9667	−	137.077i	−0.0244558	−	0.139875i
$981$	63.2742			0.0644997
$982$	49.9848	−	49.9848i	0.0509010	−	0.0509010i
$983$	224.125	+	224.125i	0.228001	+	0.228001i	0.811857	−	0.583856i	$-0.198457\pi$
$983$	224.125	+	224.125i	0.228001	+	0.228001i	−0.583856	+	0.811857i	$0.698457\pi$
$984$		−	68.7528i		−	0.0698707i
$985$	1121.68	+	787.824i	1.13877	+	0.799821i
$986$	8.41204			0.00853148
$987$	−39.8665	+	39.8665i	−0.0403915	+	0.0403915i
$988$	−145.305	−	145.305i	−0.147069	−	0.147069i
$989$			240.840i			0.243519i
$990$	26.0614	−	37.1056i	0.0263246	−	0.0374804i
$991$	719.396			0.725929			0.362964	−	0.931803i	$-0.381765\pi$
$991$	719.396			0.725929			0.362964	+	0.931803i	$0.381765\pi$
$992$	−74.7036	+	74.7036i	−0.0753060	+	0.0753060i
$993$	−802.817	−	802.817i	−0.808477	−	0.808477i
$994$		−	9.14663i		−	0.00920184i
$995$	−191.282	+	33.4440i	−0.192244	+	0.0336121i
$996$	702.595			0.705416
$997$	555.281	−	555.281i	0.556952	−	0.556952i	−0.371487	−	0.928438i	$-0.621152\pi$
$997$	555.281	−	555.281i	0.556952	−	0.556952i	0.928438	+	0.371487i	$0.121152\pi$
$998$	54.3871	+	54.3871i	0.0544961	+	0.0544961i
$999$			1490.39i			1.49188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.g.a.8.4	✓	12
3.2	odd	2		315.3.o.a.253.3		12
4.3	odd	2		560.3.bh.e.113.2		12
5.2	odd	4	inner	35.3.g.a.22.4	yes	12
5.3	odd	4		175.3.g.b.57.3		12
5.4	even	2		175.3.g.b.43.3		12
7.2	even	3		245.3.m.d.18.3		24
7.3	odd	6		245.3.m.c.128.4		24
7.4	even	3		245.3.m.d.128.4		24
7.5	odd	6		245.3.m.c.18.3		24
7.6	odd	2		245.3.g.a.148.4		12
15.2	even	4		315.3.o.a.127.3		12
20.7	even	4		560.3.bh.e.337.2		12
35.2	odd	12		245.3.m.d.67.4		24
35.12	even	12		245.3.m.c.67.4		24
35.17	even	12		245.3.m.c.177.3		24
35.27	even	4		245.3.g.a.197.4		12
35.32	odd	12		245.3.m.d.177.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.g.a.8.4	✓	12	1.1	even	1	trivial
35.3.g.a.22.4	yes	12	5.2	odd	4	inner
175.3.g.b.43.3		12	5.4	even	2
175.3.g.b.57.3		12	5.3	odd	4
245.3.g.a.148.4		12	7.6	odd	2
245.3.g.a.197.4		12	35.27	even	4
245.3.m.c.18.3		24	7.5	odd	6
245.3.m.c.67.4		24	35.12	even	12
245.3.m.c.128.4		24	7.3	odd	6
245.3.m.c.177.3		24	35.17	even	12
245.3.m.d.18.3		24	7.2	even	3
245.3.m.d.67.4		24	35.2	odd	12
245.3.m.d.128.4		24	7.4	even	3
245.3.m.d.177.3		24	35.32	odd	12
315.3.o.a.127.3		12	15.2	even	4
315.3.o.a.253.3		12	3.2	odd	2
560.3.bh.e.113.2		12	4.3	odd	2
560.3.bh.e.337.2		12	20.7	even	4

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.109772 - 0.109772i) q^{2} +(1.67281 + 1.67281i) q^{3} +3.97590i q^{4} +(-0.861142 - 4.92529i) q^{5} +0.367256 q^{6} +(1.87083 - 1.87083i) q^{7} +(0.875529 + 0.875529i) q^{8} -3.40339i q^{9} +O(q^{10})\)	\(q+(0.109772 - 0.109772i) q^{2} +(1.67281 + 1.67281i) q^{3} +3.97590i q^{4} +(-0.861142 - 4.92529i) q^{5} +0.367256 q^{6} +(1.87083 - 1.87083i) q^{7} +(0.875529 + 0.875529i) q^{8} -3.40339i q^{9} +(-0.635186 - 0.446128i) q^{10} -17.1643 q^{11} +(-6.65094 + 6.65094i) q^{12} +(1.79113 + 1.79113i) q^{13} -0.410728i q^{14} +(6.79856 - 9.67962i) q^{15} -15.7114 q^{16} +(14.9720 - 14.9720i) q^{17} +(-0.373596 - 0.373596i) q^{18} +20.4041i q^{19} +(19.5824 - 3.42382i) q^{20} +6.25910 q^{21} +(-1.88416 + 1.88416i) q^{22} +(16.8342 + 16.8342i) q^{23} +2.92919i q^{24} +(-23.5169 + 8.48274i) q^{25} +0.393231 q^{26} +(20.7486 - 20.7486i) q^{27} +(7.43823 + 7.43823i) q^{28} +2.55919i q^{29} +(-0.316259 - 1.80884i) q^{30} +14.2925 q^{31} +(-5.22678 + 5.22678i) q^{32} +(-28.7127 - 28.7127i) q^{33} -3.28700i q^{34} +(-10.8254 - 7.60332i) q^{35} +13.5315 q^{36} +(-35.9154 + 35.9154i) q^{37} +(2.23979 + 2.23979i) q^{38} +5.99245i q^{39} +(3.55827 - 5.06618i) q^{40} -23.4716 q^{41} +(0.687072 - 0.687072i) q^{42} +(7.15327 + 7.15327i) q^{43} -68.2437i q^{44} +(-16.7626 + 2.93080i) q^{45} +3.69585 q^{46} +(-6.36936 + 6.36936i) q^{47} +(-26.2822 - 26.2822i) q^{48} -7.00000i q^{49} +(-1.65032 + 3.51265i) q^{50} +50.0906 q^{51} +(-7.12134 + 7.12134i) q^{52} +(-10.9292 - 10.9292i) q^{53} -4.55521i q^{54} +(14.7809 + 84.5392i) q^{55} +3.27593 q^{56} +(-34.1322 + 34.1322i) q^{57} +(0.280927 + 0.280927i) q^{58} +19.4341i q^{59} +(38.4852 + 27.0304i) q^{60} +73.9951 q^{61} +(1.56891 - 1.56891i) q^{62} +(-6.36715 - 6.36715i) q^{63} -61.6980i q^{64} +(7.27940 - 10.3642i) q^{65} -6.30370 q^{66} +(86.3083 - 86.3083i) q^{67} +(59.5270 + 59.5270i) q^{68} +56.3211i q^{69} +(-2.02295 + 0.353696i) q^{70} +22.2693 q^{71} +(2.97976 - 2.97976i) q^{72} +(-73.4511 - 73.4511i) q^{73} +7.88500i q^{74} +(-53.5294 - 25.1493i) q^{75} -81.1246 q^{76} +(-32.1115 + 32.1115i) q^{77} +(0.657802 + 0.657802i) q^{78} +55.0137i q^{79} +(13.5297 + 77.3830i) q^{80} +38.7865 q^{81} +(-2.57652 + 2.57652i) q^{82} +(-52.8192 - 52.8192i) q^{83} +24.8855i q^{84} +(-86.6341 - 60.8482i) q^{85} +1.57046 q^{86} +(-4.28104 + 4.28104i) q^{87} +(-15.0279 - 15.0279i) q^{88} -129.153i q^{89} +(-1.51835 + 2.16178i) q^{90} +6.70179 q^{91} +(-66.9313 + 66.9313i) q^{92} +(23.9086 + 23.9086i) q^{93} +1.39835i q^{94} +(100.496 - 17.5708i) q^{95} -17.4869 q^{96} +(94.8483 - 94.8483i) q^{97} +(-0.768403 - 0.768403i) q^{98} +58.4168i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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