LMFDB - Embedded newform 210.3.p.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(19,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("210.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.p (of order $6$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	210.19
Dual form			210.3.p.a.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.86586 - 3.17098i) q^{5} -2.44949i q^{6} +(6.18245 + 3.28288i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.86586 - 3.17098i) q^{5} -2.44949i q^{6} +(6.18245 + 3.28288i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.49248 + 6.61722i) q^{10} +(-1.46312 - 2.53420i) q^{11} +(-1.73205 + 3.00000i) q^{12} +16.5305 q^{13} +(-5.25058 - 8.39235i) q^{14} +(1.40853 - 8.54494i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(10.2165 + 17.6956i) q^{17} +(3.67423 - 2.12132i) q^{18} +(5.28456 + 3.05104i) q^{19} +(1.62643 - 9.86685i) q^{20} +(0.429835 + 12.1167i) q^{21} +4.13833i q^{22} +(12.3238 + 7.11514i) q^{23} +(4.24264 - 2.44949i) q^{24} +(4.88979 + 24.5171i) q^{25} +(-20.2456 - 11.6888i) q^{26} -5.19615 q^{27} +(0.496330 + 13.9912i) q^{28} +34.1877 q^{29} +(-7.76728 + 9.46939i) q^{30} +(-4.16673 + 2.40566i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.53420 - 4.38936i) q^{33} -28.8967i q^{34} +(-13.4906 - 32.2956i) q^{35} -6.00000 q^{36} +(38.4155 + 22.1792i) q^{37} +(-4.31482 - 7.47349i) q^{38} +(14.3158 + 24.7957i) q^{39} +(-8.96888 + 10.9343i) q^{40} -39.2889i q^{41} +(8.04139 - 15.1438i) q^{42} -50.0809i q^{43} +(2.92624 - 5.06840i) q^{44} +(14.0372 - 5.28734i) q^{45} +(-10.0623 - 17.4285i) q^{46} +(-2.08202 + 3.60617i) q^{47} -6.92820 q^{48} +(27.4454 + 40.5925i) q^{49} +(11.3475 - 33.4848i) q^{50} +(-17.6956 + 30.6496i) q^{51} +(16.5305 + 28.6316i) q^{52} +(-51.1793 + 29.5484i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-2.37967 + 14.4364i) q^{55} +(9.28539 - 17.4866i) q^{56} +10.5691i q^{57} +(-41.8712 - 24.1743i) q^{58} +(31.2419 - 18.0375i) q^{59} +(16.2088 - 6.10529i) q^{60} +(-47.8841 - 27.6459i) q^{61} +6.80425 q^{62} +(-17.8029 + 11.1382i) q^{63} -8.00000 q^{64} +(-63.9046 - 52.4178i) q^{65} +(-6.20750 + 3.58390i) q^{66} +(-60.0714 + 34.6822i) q^{67} +(-20.4331 + 35.3911i) q^{68} +24.6476i q^{69} +(-6.31394 + 49.0931i) q^{70} -110.218 q^{71} +(7.34847 + 4.24264i) q^{72} +(-47.6606 - 82.5505i) q^{73} +(-31.3661 - 54.3277i) q^{74} +(-32.5410 + 28.5672i) q^{75} +12.2042i q^{76} +(-0.726191 - 20.4708i) q^{77} -40.4912i q^{78} +(-64.7217 + 112.101i) q^{79} +(18.7163 - 7.04979i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.7814 + 48.1189i) q^{82} +5.92917 q^{83} +(-20.5570 + 12.8612i) q^{84} +(16.6165 - 100.805i) q^{85} +(-35.4125 + 61.3363i) q^{86} +(29.6074 + 51.2815i) q^{87} +(-7.16780 + 4.13833i) q^{88} +(-85.9402 - 49.6176i) q^{89} +(-20.9307 - 3.45018i) q^{90} +(102.199 + 54.2676i) q^{91} +28.4606i q^{92} +(-7.21699 - 4.16673i) q^{93} +(5.09990 - 2.94443i) q^{94} +(-10.7546 - 28.5521i) q^{95} +(8.48528 + 4.89898i) q^{96} +116.887 q^{97} +(-4.91033 - 69.1223i) q^{98} +8.77872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−3.86586	−	3.17098i	−0.773173	−	0.634196i
$5$	−3.86586	−	3.17098i	−0.773173	−	0.634196i
$6$		−	2.44949i		−	0.408248i
$7$	6.18245	+	3.28288i	0.883207	+	0.468983i
$7$	6.18245	+	3.28288i	0.883207	+	0.468983i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	2.49248	+	6.61722i	0.249248	+	0.661722i
$11$	−1.46312	−	2.53420i	−0.133011	−	0.230382i	0.791825	−	0.610748i	$-0.209131\pi$
$11$	−1.46312	−	2.53420i	−0.133011	−	0.230382i	−0.924836	+	0.380366i	$0.875798\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	16.5305			1.27158			0.635788	−	0.771864i	$-0.280675\pi$
$13$	16.5305			1.27158			0.635788	+	0.771864i	$0.280675\pi$
$14$	−5.25058	−	8.39235i	−0.375041	−	0.599453i
$15$	1.40853	−	8.54494i	0.0939021	−	0.569663i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	10.2165	+	17.6956i	0.600973	+	1.04092i	0.992674	+	0.120823i	$0.0385534\pi$
$17$	10.2165	+	17.6956i	0.600973	+	1.04092i	−0.391701	+	0.920093i	$0.628113\pi$
$18$	3.67423	−	2.12132i	0.204124	−	0.117851i
$19$	5.28456	+	3.05104i	0.278134	+	0.160581i	0.632579	−	0.774496i	$-0.281997\pi$
$19$	5.28456	+	3.05104i	0.278134	+	0.160581i	−0.354444	+	0.935077i	$0.615330\pi$
$20$	1.62643	−	9.86685i	0.0813216	−	0.493342i
$21$	0.429835	+	12.1167i	0.0204683	+	0.576987i
$22$			4.13833i			0.188106i
$23$	12.3238	+	7.11514i	0.535817	+	0.309354i	0.743382	−	0.668867i	$-0.233221\pi$
$23$	12.3238	+	7.11514i	0.535817	+	0.309354i	−0.207565	+	0.978221i	$0.566554\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	4.88979	+	24.5171i	0.195592	+	0.980685i
$26$	−20.2456	−	11.6888i	−0.778678	−	0.449570i
$27$	−5.19615			−0.192450
$28$	0.496330	+	13.9912i	0.0177261	+	0.499686i
$29$	34.1877			1.17889			0.589443	−	0.807810i	$-0.299347\pi$
$29$	34.1877			1.17889			0.589443	+	0.807810i	$0.299347\pi$
$30$	−7.76728	+	9.46939i	−0.258909	+	0.315646i
$31$	−4.16673	+	2.40566i	−0.134411	+	0.0776021i	−0.565698	−	0.824613i	$-0.691393\pi$
$31$	−4.16673	+	2.40566i	−0.134411	+	0.0776021i	0.431287	+	0.902215i	$0.358060\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	2.53420	−	4.38936i	0.0767939	−	0.133011i
$34$		−	28.8967i		−	0.849904i
$35$	−13.4906	−	32.2956i	−0.385444	−	0.922731i
$36$	−6.00000			−0.166667
$37$	38.4155	+	22.1792i	1.03826	+	0.599437i	0.919339	−	0.393467i	$-0.128724\pi$
$37$	38.4155	+	22.1792i	1.03826	+	0.599437i	0.118917	+	0.992904i	$0.462058\pi$
$38$	−4.31482	−	7.47349i	−0.113548	−	0.196671i
$39$	14.3158	+	24.7957i	0.367072	+	0.635788i
$40$	−8.96888	+	10.9343i	−0.224222	+	0.273358i
$41$		−	39.2889i		−	0.958266i	−0.877742	−	0.479133i	$-0.840951\pi$
$41$		−	39.2889i		−	0.958266i	0.877742	−	0.479133i	$-0.159049\pi$
$42$	8.04139	−	15.1438i	0.191462	−	0.360568i
$43$		−	50.0809i		−	1.16467i	−0.812948	−	0.582336i	$-0.802139\pi$
$43$		−	50.0809i		−	1.16467i	0.812948	−	0.582336i	$-0.197861\pi$
$44$	2.92624	−	5.06840i	0.0665055	−	0.115191i
$45$	14.0372	−	5.28734i	0.311939	−	0.117496i
$46$	−10.0623	−	17.4285i	−0.218746	−	0.378880i
$47$	−2.08202	+	3.60617i	−0.0442984	+	0.0767271i	−0.887324	−	0.461146i	$-0.847439\pi$
$47$	−2.08202	+	3.60617i	−0.0442984	+	0.0767271i	0.843026	+	0.537873i	$0.180772\pi$
$48$	−6.92820			−0.144338
$49$	27.4454	+	40.5925i	0.560110	+	0.828419i
$50$	11.3475	−	33.4848i	0.226950	−	0.669697i
$51$	−17.6956	+	30.6496i	−0.346972	+	0.600973i
$52$	16.5305	+	28.6316i	0.317894	+	0.550608i
$53$	−51.1793	+	29.5484i	−0.965646	+	0.557516i	−0.897906	−	0.440187i	$-0.854912\pi$
$53$	−51.1793	+	29.5484i	−0.965646	+	0.557516i	−0.0677402	+	0.997703i	$0.521579\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$	−2.37967	+	14.4364i	−0.0432667	+	0.262480i
$56$	9.28539	−	17.4866i	0.165811	−	0.312261i
$57$			10.5691i			0.185423i
$58$	−41.8712	−	24.1743i	−0.721917	−	0.416799i
$59$	31.2419	−	18.0375i	0.529523	−	0.305720i	−0.211299	−	0.977421i	$-0.567769\pi$
$59$	31.2419	−	18.0375i	0.529523	−	0.305720i	0.740822	+	0.671701i	$0.234436\pi$
$60$	16.2088	−	6.10529i	0.270147	−	0.101755i
$61$	−47.8841	−	27.6459i	−0.784986	−	0.453212i	0.0532085	−	0.998583i	$-0.483055\pi$
$61$	−47.8841	−	27.6459i	−0.784986	−	0.453212i	−0.838194	+	0.545372i	$0.816389\pi$
$62$	6.80425			0.109746
$63$	−17.8029	+	11.1382i	−0.282585	+	0.176796i
$64$	−8.00000			−0.125000
$65$	−63.9046	−	52.4178i	−0.983147	−	0.806427i
$66$	−6.20750	+	3.58390i	−0.0940530	+	0.0543015i
$67$	−60.0714	+	34.6822i	−0.896588	+	0.517645i	−0.876092	−	0.482145i	$-0.839858\pi$
$67$	−60.0714	+	34.6822i	−0.896588	+	0.517645i	−0.0204963	+	0.999790i	$0.506525\pi$
$68$	−20.4331	+	35.3911i	−0.300487	+	0.520458i
$69$			24.6476i			0.357211i
$70$	−6.31394	+	49.0931i	−0.0901992	+	0.701330i
$71$	−110.218			−1.55237			−0.776183	−	0.630507i	$-0.782847\pi$
$71$	−110.218			−1.55237			−0.776183	+	0.630507i	$0.782847\pi$
$72$	7.34847	+	4.24264i	0.102062	+	0.0589256i
$73$	−47.6606	−	82.5505i	−0.652884	−	1.13083i	−0.982420	−	0.186686i	$-0.940225\pi$
$73$	−47.6606	−	82.5505i	−0.652884	−	1.13083i	0.329535	−	0.944143i	$-0.393108\pi$
$74$	−31.3661	−	54.3277i	−0.423866	−	0.734158i
$75$	−32.5410	+	28.5672i	−0.433880	+	0.380895i
$76$			12.2042i			0.160581i
$77$	−0.726191	−	20.4708i	−0.00943106	−	0.265855i
$78$		−	40.4912i		−	0.519118i
$79$	−64.7217	+	112.101i	−0.819263	+	1.41900i	0.0869638	+	0.996211i	$0.472284\pi$
$79$	−64.7217	+	112.101i	−0.819263	+	1.41900i	−0.906226	+	0.422793i	$0.861050\pi$
$80$	18.7163	−	7.04979i	0.233954	−	0.0881223i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−27.7814	+	48.1189i	−0.338798	+	0.586815i
$83$	5.92917			0.0714358			0.0357179	−	0.999362i	$-0.488628\pi$
$83$	5.92917			0.0714358			0.0357179	+	0.999362i	$0.488628\pi$
$84$	−20.5570	+	12.8612i	−0.244726	+	0.153110i
$85$	16.6165	−	100.805i	0.195488	−	1.18594i
$86$	−35.4125	+	61.3363i	−0.411774	+	0.713213i
$87$	29.6074	+	51.2815i	0.340315	+	0.589443i
$88$	−7.16780	+	4.13833i	−0.0814523	+	0.0470265i
$89$	−85.9402	−	49.6176i	−0.965620	−	0.557501i	−0.0677217	−	0.997704i	$-0.521573\pi$
$89$	−85.9402	−	49.6176i	−0.965620	−	0.557501i	−0.897898	+	0.440203i	$0.854906\pi$
$90$	−20.9307	−	3.45018i	−0.232564	−	0.0383354i
$91$	102.199	+	54.2676i	1.12306	+	0.596347i
$92$			28.4606i			0.309354i
$93$	−7.21699	−	4.16673i	−0.0776021	−	0.0448036i
$94$	5.09990	−	2.94443i	0.0542542	−	0.0313237i
$95$	−10.7546	−	28.5521i	−0.113206	−	0.300549i
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$	116.887			1.20502			0.602510	−	0.798111i	$-0.294167\pi$
$97$	116.887			1.20502			0.602510	+	0.798111i	$0.294167\pi$
$98$	−4.91033	−	69.1223i	−0.0501054	−	0.705329i
$99$	8.77872			0.0886740
$100$	−37.5751	+	32.9865i	−0.375751	+	0.329865i
$101$	156.925	−	90.6005i	1.55371	−	0.897035i	0.555876	−	0.831265i	$-0.312383\pi$
$101$	156.925	−	90.6005i	1.55371	−	0.897035i	0.997835	−	0.0657697i	$-0.0209503\pi$
$102$	43.3451	−	25.0253i	0.424952	−	0.245346i
$103$	26.5376	−	45.9644i	0.257646	−	0.446256i	−0.707965	−	0.706248i	$-0.750386\pi$
$103$	26.5376	−	45.9644i	0.257646	−	0.446256i	0.965611	+	0.259992i	$0.0837198\pi$
$104$		−	46.7552i		−	0.449570i
$105$	36.7602	−	48.2046i	0.350097	−	0.459092i
$106$	83.5754			0.788447
$107$	111.838	+	64.5698i	1.04522	+	0.603456i	0.921307	−	0.388837i	$-0.127123\pi$
$107$	111.838	+	64.5698i	1.04522	+	0.603456i	0.123911	+	0.992293i	$0.460456\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	−77.7390	−	134.648i	−0.713202	−	1.23530i	−0.963649	−	0.267172i	$-0.913911\pi$
$109$	−77.7390	−	134.648i	−0.713202	−	1.23530i	0.250447	−	0.968130i	$-0.419423\pi$
$110$	13.1226	−	15.9982i	0.119296	−	0.145438i
$111$			76.8309i			0.692170i
$112$	−23.7371	+	14.8509i	−0.211939	+	0.132597i
$113$			152.414i			1.34880i	0.738367	+	0.674399i	$0.235597\pi$
$113$			152.414i			1.34880i	−0.738367	+	0.674399i	$0.764403\pi$
$114$	7.47349	−	12.9445i	0.0655569	−	0.113548i
$115$	−25.0801	−	66.5846i	−0.218088	−	0.578997i
$116$	34.1877	+	59.2148i	0.294721	+	0.510472i
$117$	−24.7957	+	42.9474i	−0.211929	+	0.367072i
$118$	−51.0178			−0.432354
$119$	5.07078	+	142.942i	0.0426116	+	1.20119i
$120$	−24.1687	−	3.98393i	−0.201406	−	0.0331994i
$121$	56.2186	−	97.3734i	0.464616	−	0.804739i
$122$	39.0972	+	67.7184i	0.320469	+	0.555069i
$123$	58.9333	−	34.0252i	0.479133	−	0.276627i
$124$	−8.33347	−	4.81133i	−0.0672054	−	0.0388010i
$125$	58.8400	−	110.285i	0.470720	−	0.882283i
$126$	29.6798	−	1.05288i	0.235554	−	0.00835616i
$127$		−	24.4687i		−	0.192667i	−0.995349	−	0.0963334i	$-0.969288\pi$
$127$		−	24.4687i		−	0.192667i	0.995349	−	0.0963334i	$-0.0307115\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	75.1213	−	43.3713i	0.582336	−	0.336212i
$130$	41.2018	+	109.386i	0.316937	+	0.841429i
$131$	−39.0803	−	22.5630i	−0.298323	−	0.172237i	0.343366	−	0.939202i	$-0.388433\pi$
$131$	−39.0803	−	22.5630i	−0.298323	−	0.172237i	−0.641689	+	0.766965i	$0.721766\pi$
$132$	10.1368			0.0767939
$133$	22.6553	+	36.2115i	0.170341	+	0.272267i
$134$	98.0962			0.732061
$135$	20.0876	+	16.4769i	0.148797	+	0.122051i
$136$	50.0506	−	28.8967i	0.368019	−	0.212476i
$137$	−100.073	+	57.7774i	−0.730463	+	0.421733i	−0.818591	−	0.574376i	$-0.805245\pi$
$137$	−100.073	+	57.7774i	−0.730463	+	0.421733i	0.0881288	+	0.996109i	$0.471911\pi$
$138$	17.4285	−	30.1870i	0.126293	−	0.218746i
$139$			15.0170i			0.108036i	0.998540	+	0.0540180i	$0.0172028\pi$
$139$			15.0170i			0.108036i	−0.998540	+	0.0540180i	$0.982797\pi$
$140$	42.4470	−	55.6619i	0.303193	−	0.397585i
$141$	−7.21234			−0.0511514
$142$	134.989	+	77.9359i	0.950627	+	0.548845i
$143$	−24.1861	−	41.8915i	−0.169133	−	0.292948i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	−132.165	−	108.408i	−0.911482	−	0.747644i
$146$			134.804i			0.923318i
$147$	−37.1204	+	76.3222i	−0.252520	+	0.519199i
$148$			88.7167i			0.599437i
$149$	−64.7241	+	112.105i	−0.434390	+	0.752385i	−0.997246	−	0.0741697i	$-0.976369\pi$
$149$	−64.7241	+	112.105i	−0.434390	+	0.752385i	0.562856	+	0.826555i	$0.309703\pi$
$150$	60.0545	−	11.9775i	0.400363	−	0.0798500i
$151$	−89.4166	−	154.874i	−0.592163	−	1.02566i	−0.993941	−	0.109919i	$-0.964941\pi$
$151$	−89.4166	−	154.874i	−0.592163	−	1.02566i	0.401778	−	0.915737i	$-0.368392\pi$
$152$	8.62964	−	14.9470i	0.0567740	−	0.0983354i
$153$	−61.2993			−0.400649
$154$	−13.5857	+	25.5850i	−0.0882185	+	0.166136i
$155$	23.7363	+	3.91265i	0.153138	+	0.0252429i
$156$	−28.6316	+	49.5914i	−0.183536	+	0.317894i
$157$	12.4518	+	21.5672i	0.0793111	+	0.137371i	0.902953	−	0.429740i	$-0.141395\pi$
$157$	12.4518	+	21.5672i	0.0793111	+	0.137371i	−0.823642	+	0.567110i	$0.808061\pi$
$158$	158.535	−	91.5304i	1.00339	−	0.579306i
$159$	−88.6451	−	51.1793i	−0.557516	−	0.321882i
$160$	−27.9077	−	4.60025i	−0.174423	−	0.0287515i
$161$	52.8330	+	84.4466i	0.328155	+	0.524513i
$162$			12.7279i			0.0785674i
$163$	42.7858	+	24.7024i	0.262490	+	0.151548i	0.625470	−	0.780248i	$-0.284907\pi$
$163$	42.7858	+	24.7024i	0.262490	+	0.151548i	−0.362980	+	0.931797i	$0.618241\pi$
$164$	68.0504	−	39.2889i	0.414941	−	0.239566i
$165$	−23.7154	+	8.93278i	−0.143730	+	0.0541381i
$166$	−7.26172	−	4.19256i	−0.0437453	−	0.0252564i
$167$	213.641			1.27929			0.639644	−	0.768671i	$-0.279082\pi$
$167$	213.641			1.27929			0.639644	+	0.768671i	$0.279082\pi$
$168$	34.2713	−	1.21576i	0.203996	−	0.00723664i
$169$	104.257			0.616903
$170$	−91.6309	+	111.711i	−0.539006	+	0.657123i
$171$	−15.8537	+	9.15312i	−0.0927115	+	0.0535270i
$172$	86.7427	−	50.0809i	0.504318	−	0.291168i
$173$	−15.7905	+	27.3499i	−0.0912743	+	0.158092i	−0.908048	−	0.418867i	$-0.862427\pi$
$173$	−15.7905	+	27.3499i	−0.0912743	+	0.158092i	0.816773	+	0.576959i	$0.195761\pi$
$174$		−	83.7424i		−	0.481278i
$175$	−50.2560	+	167.629i	−0.287177	+	0.957878i
$176$	11.7050			0.0665055
$177$	54.1125	+	31.2419i	0.305720	+	0.176508i
$178$	70.1698	+	121.538i	0.394213	+	0.682796i
$179$	44.1032	+	76.3890i	0.246387	+	0.426754i	0.962521	−	0.271209i	$-0.0874233\pi$
$179$	44.1032	+	76.3890i	0.246387	+	0.426754i	−0.716134	+	0.697963i	$0.754090\pi$
$180$	23.1952	+	19.0259i	0.128862	+	0.105699i
$181$		−	311.172i		−	1.71918i	−0.510982	−	0.859591i	$-0.670718\pi$
$181$		−	311.172i		−	1.71918i	0.510982	−	0.859591i	$-0.329282\pi$
$182$	−86.7945	−	138.729i	−0.476893	−	0.762250i
$183$		−	95.7683i		−	0.523324i
$184$	20.1247	−	34.8569i	0.109373	−	0.189440i
$185$	−78.1792	−	207.556i	−0.422590	−	1.12193i
$186$	5.89265	+	10.2064i	0.0316809	+	0.0548730i
$187$	29.8961	−	51.7815i	0.159872	−	0.276906i
$188$	−8.32810			−0.0442984
$189$	−32.1250	−	17.0584i	−0.169973	−	0.0902559i
$190$	−7.01777	+	42.5737i	−0.0369356	+	0.224072i
$191$	−151.707	+	262.764i	−0.794276	+	1.37573i	0.129021	+	0.991642i	$0.458816\pi$
$191$	−151.707	+	262.764i	−0.794276	+	1.37573i	−0.923298	+	0.384085i	$0.874517\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	199.729	−	115.314i	1.03487	−	0.597481i	0.116492	−	0.993192i	$-0.462835\pi$
$193$	199.729	−	115.314i	1.03487	−	0.597481i	0.918375	+	0.395711i	$0.129502\pi$
$194$	−143.157	−	82.6516i	−0.737922	−	0.426039i
$195$	23.2837	−	141.252i	0.119404	−	0.724369i
$196$	−42.8629	+	88.1293i	−0.218688	+	0.449639i
$197$			213.281i			1.08264i	0.840815	+	0.541322i	$0.182076\pi$
$197$			213.281i			1.08264i	−0.840815	+	0.541322i	$0.817924\pi$
$198$	−10.7517	−	6.20750i	−0.0543015	−	0.0313510i
$199$	−314.734	+	181.712i	−1.58158	+	0.913126i	−0.586951	+	0.809622i	$0.699672\pi$
$199$	−314.734	+	181.712i	−1.58158	+	0.913126i	−0.994629	+	0.103504i	$0.966995\pi$
$200$	69.3449	−	13.8304i	0.346725	−	0.0691521i
$201$	−104.047	−	60.0714i	−0.517645	−	0.298863i
$202$	−256.257			−1.26860
$203$	211.364	+	112.234i	1.04120	+	0.552878i
$204$	−70.7823			−0.346972
$205$	−124.584	+	151.885i	−0.607728	+	0.740905i
$206$	−65.0035	+	37.5298i	−0.315551	+	0.182183i
$207$	−36.9714	+	21.3454i	−0.178606	+	0.103118i
$208$	−33.0610	+	57.2633i	−0.158947	+	0.275304i
$209$		−	17.8562i		−	0.0854362i
$210$	−79.1077	+	33.0450i	−0.376703	+	0.157357i
$211$	186.025			0.881637			0.440819	−	0.897596i	$-0.354688\pi$
$211$	186.025			0.881637			0.440819	+	0.897596i	$0.354688\pi$
$212$	−102.359	−	59.0967i	−0.482823	−	0.278758i
$213$	−95.4516	−	165.327i	−0.448130	−	0.776183i
$214$	−91.3155	−	158.163i	−0.426708	−	0.739080i
$215$	−158.805	+	193.606i	−0.738630	+	0.900492i
$216$			14.6969i			0.0680414i
$217$	−33.6581	+	1.19400i	−0.155107	+	0.00550232i
$218$			219.879i			1.00862i
$219$	82.5505	−	142.982i	0.376943	−	0.652884i
$220$	−27.3842	+	10.3147i	−0.124474	+	0.0468849i
$221$	168.884	+	292.516i	0.764182	+	1.32360i
$222$	54.3277	−	94.0983i	0.244719	−	0.423866i
$223$	−396.614			−1.77854			−0.889270	−	0.457383i	$-0.848787\pi$
$223$	−396.614			−1.77854			−0.889270	+	0.457383i	$0.848787\pi$
$224$	39.5731	−	1.40383i	0.176666	−	0.00626712i
$225$	−71.0321	−	24.0716i	−0.315698	−	0.106985i
$226$	107.773	−	186.668i	0.476872	−	0.825966i
$227$	−181.905	−	315.069i	−0.801344	−	1.38797i	−0.918732	−	0.394883i	$-0.870785\pi$
$227$	−181.905	−	315.069i	−0.801344	−	1.38797i	0.117387	−	0.993086i	$-0.462548\pi$
$228$	−18.3062	+	10.5691i	−0.0802905	+	0.0463557i
$229$	332.768	+	192.124i	1.45314	+	0.838969i	0.998658	−	0.0517889i	$-0.0164923\pi$
$229$	332.768	+	192.124i	1.45314	+	0.838969i	0.454478	+	0.890758i	$0.349826\pi$
$230$	−16.3657	+	99.2835i	−0.0711552	+	0.431667i
$231$	30.0773	−	18.8175i	0.130205	−	0.0814612i
$232$		−	96.6974i		−	0.416799i
$233$	−266.628	−	153.938i	−1.14433	−	0.660677i	−0.196828	−	0.980438i	$-0.563064\pi$
$233$	−266.628	−	153.938i	−1.14433	−	0.660677i	−0.947498	+	0.319761i	$0.896397\pi$
$234$	60.7369	−	35.0664i	0.259559	−	0.149857i
$235$	19.4839	−	7.33891i	0.0829103	−	0.0312294i
$236$	62.4838	+	36.0750i	0.264762	+	0.152860i
$237$	−224.203			−0.946003
$238$	94.8646	−	178.653i	0.398591	−	0.750641i
$239$	227.991			0.953938			0.476969	−	0.878920i	$-0.341735\pi$
$239$	227.991			0.953938			0.476969	+	0.878920i	$0.341735\pi$
$240$	26.7835	+	21.9692i	0.111598	+	0.0915383i
$241$	302.624	−	174.720i	1.25570	−	0.724979i	0.283465	−	0.958983i	$-0.408516\pi$
$241$	302.624	−	174.720i	1.25570	−	0.724979i	0.972236	+	0.234003i	$0.0751826\pi$
$242$	−137.707	+	79.5050i	−0.569036	+	0.328533i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		−	110.584i		−	0.453212i
$245$	22.6179	−	243.954i	0.0923181	−	0.995730i
$246$	−96.2377			−0.391210
$247$	87.3562	+	50.4351i	0.353669	+	0.204191i
$248$	6.80425	+	11.7853i	0.0274365	+	0.0475214i
$249$	5.13481	+	8.89375i	0.0206217	+	0.0357179i
$250$	−150.048	+	93.4652i	−0.600190	+	0.373861i
$251$			145.610i			0.580119i	0.957009	+	0.290060i	$0.0936752\pi$
$251$			145.610i			0.580119i	−0.957009	+	0.290060i	$0.906325\pi$
$252$	−37.0947	−	19.6973i	−0.147201	−	0.0781639i
$253$		−	41.6413i		−	0.164590i
$254$	−17.3020	+	29.9679i	−0.0681180	+	0.117984i
$255$	165.598	−	62.3750i	0.649404	−	0.244608i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	223.674	−	387.414i	0.870325	−	1.50745i	0.00866487	−	0.999962i	$-0.497242\pi$
$257$	223.674	−	387.414i	0.870325	−	1.50745i	0.861660	−	0.507485i	$-0.169425\pi$
$258$	−122.673			−0.475475
$259$	164.690	+	263.235i	0.635869	+	1.01635i
$260$	26.8857	−	163.104i	0.103407	−	0.627322i
$261$	−51.2815	+	88.8222i	−0.196481	+	0.340315i
$262$	31.9089	+	55.2679i	0.121790	+	0.210946i
$263$	−274.819	+	158.667i	−1.04494	+	0.603295i	−0.921228	−	0.389023i	$-0.872813\pi$
$263$	−274.819	+	158.667i	−1.04494	+	0.603295i	−0.123710	+	0.992318i	$0.539479\pi$
$264$	−12.4150	−	7.16780i	−0.0470265	−	0.0271508i
$265$	291.549	+	48.0584i	1.10019	+	0.181352i
$266$	−2.14158	−	60.3695i	−0.00805104	−	0.226953i
$267$		−	171.880i		−	0.643746i
$268$	−120.143	−	69.3645i	−0.448294	−	0.258823i
$269$	−194.920	+	112.537i	−0.724609	+	0.418353i	−0.816447	−	0.577421i	$-0.804059\pi$
$269$	−194.920	+	112.537i	−0.724609	+	0.418353i	0.0918377	+	0.995774i	$0.470726\pi$
$270$	−12.9513	−	34.3841i	−0.0479677	−	0.127348i
$271$	−262.563	−	151.591i	−0.968866	−	0.559375i	−0.0699759	−	0.997549i	$-0.522292\pi$
$271$	−262.563	−	151.591i	−0.968866	−	0.559375i	−0.898890	+	0.438173i	$0.855626\pi$
$272$	−81.7323			−0.300487
$273$	7.10537	+	200.295i	0.0260270	+	0.733683i
$274$	163.419			0.596420
$275$	54.9770	−	48.2632i	0.199916	−	0.175503i
$276$	−42.6909	+	24.6476i	−0.154677	+	0.0893028i
$277$	−290.770	+	167.876i	−1.04971	+	0.606051i	−0.922568	−	0.385833i	$-0.873914\pi$
$277$	−290.770	+	167.876i	−1.04971	+	0.606051i	−0.127143	+	0.991884i	$0.540581\pi$
$278$	10.6186	−	18.3920i	0.0381965	−	0.0661582i
$279$		−	14.4340i		−	0.0517347i
$280$	−91.3457	+	38.1570i	−0.326235	+	0.136275i
$281$	−214.696			−0.764043			−0.382022	−	0.924153i	$-0.624772\pi$
$281$	−214.696			−0.764043			−0.382022	+	0.924153i	$0.624772\pi$
$282$	8.83328	+	5.09990i	0.0313237	+	0.0180847i
$283$	41.0520	+	71.1042i	0.145060	+	0.251252i	0.929395	−	0.369086i	$-0.120329\pi$
$283$	41.0520	+	71.1042i	0.145060	+	0.251252i	−0.784335	+	0.620337i	$0.786996\pi$
$284$	−110.218	−	190.903i	−0.388092	−	0.672195i
$285$	33.5144	−	40.8587i	0.117594	−	0.143364i
$286$			68.4086i			0.239191i
$287$	128.981	−	242.902i	0.449410	−	0.846347i
$288$			16.9706i			0.0589256i
$289$	−64.2555	+	111.294i	−0.222337	+	0.385099i
$290$	85.2120	+	226.227i	0.293834	+	0.780094i
$291$	101.227	+	175.331i	0.347860	+	0.602510i
$292$	95.3211	−	165.101i	0.326442	−	0.565414i
$293$	274.931			0.938330			0.469165	−	0.883111i	$-0.344555\pi$
$293$	274.931			0.938330			0.469165	+	0.883111i	$0.344555\pi$
$294$	99.4309	−	67.2271i	0.338200	−	0.228664i
$295$	−177.973	−	29.3368i	−0.603299	−	0.0994467i
$296$	62.7322	−	108.655i	0.211933	−	0.367079i
$297$	7.60260	+	13.1681i	0.0255980	+	0.0443370i
$298$	158.541	−	91.5337i	0.532017	−	0.307160i
$299$	203.718	+	117.617i	0.681331	+	0.393367i
$300$	−82.0208	−	27.7955i	−0.273403	−	0.0926518i
$301$	164.410	−	309.623i	0.546212	−	1.02865i
$302$			252.908i			0.837445i
$303$	271.802	+	156.925i	0.897035	+	0.517903i
$304$	−21.1382	+	12.2042i	−0.0695336	+	0.0401453i
$305$	97.4489	+	258.715i	0.319505	+	0.848245i
$306$	75.0759	+	43.3451i	0.245346	+	0.141651i
$307$	−483.445			−1.57474			−0.787370	−	0.616480i	$-0.788558\pi$
$307$	−483.445			−1.57474			−0.787370	+	0.616480i	$0.788558\pi$
$308$	34.7303	−	21.7286i	0.112761	−	0.0705475i
$309$	91.9288			0.297504
$310$	−26.3043	−	21.5761i	−0.0848525	−	0.0696004i
$311$	−173.042	+	99.9057i	−0.556404	+	0.321240i	−0.751701	−	0.659504i	$-0.770766\pi$
$311$	−173.042	+	99.9057i	−0.556404	+	0.321240i	0.195297	+	0.980744i	$0.437433\pi$
$312$	70.1329	−	40.4912i	0.224785	−	0.129780i
$313$	89.7918	−	155.524i	0.286875	−	0.496882i	−0.686187	−	0.727425i	$-0.740717\pi$
$313$	89.7918	−	155.524i	0.286875	−	0.496882i	0.973062	+	0.230543i	$0.0740503\pi$
$314$		−	35.2191i		−	0.112163i
$315$	104.142	+	13.3939i	0.330610	+	0.0425203i
$316$	−258.887			−0.819263
$317$	−327.771	−	189.239i	−1.03398	−	0.596968i	−0.115857	−	0.993266i	$-0.536962\pi$
$317$	−327.771	−	189.239i	−1.03398	−	0.596968i	−0.918122	+	0.396298i	$0.870295\pi$
$318$	72.3784	+	125.363i	0.227605	+	0.394223i
$319$	−50.0207	−	86.6384i	−0.156805	−	0.271594i
$320$	30.9269	+	25.3678i	0.0966466	+	0.0792745i
$321$			223.676i			0.696811i
$322$	−4.99424	−	140.784i	−0.0155101	−	0.437218i
$323$			124.684i			0.386019i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$	80.8306	+	405.280i	0.248710	+	1.24702i
$326$	−34.9345	−	60.5083i	−0.107161	−	0.185608i
$327$	134.648	−	233.217i	0.411768	−	0.713202i
$328$	−111.126			−0.338798
$329$	−24.7107	+	15.4599i	−0.0751084	+	0.0469907i
$330$	35.3618	+	5.82897i	0.107157	+	0.0176635i
$331$	71.3591	−	123.598i	0.215586	−	0.373407i	−0.737867	−	0.674946i	$-0.764167\pi$
$331$	71.3591	−	123.598i	0.215586	−	0.373407i	0.953454	+	0.301539i	$0.0975004\pi$
$332$	5.92917	+	10.2696i	0.0178589	+	0.0309326i
$333$	−115.246	+	66.5375i	−0.346085	+	0.199812i
$334$	−261.656	−	151.067i	−0.783401	−	0.452297i
$335$	342.204	+	56.4083i	1.02151	+	0.168383i
$336$	−42.8333	−	22.7445i	−0.127480	−	0.0676919i
$337$		−	31.9862i		−	0.0949147i	−0.998873	−	0.0474573i	$-0.984888\pi$
$337$		−	31.9862i		−	0.0949147i	0.998873	−	0.0474573i	$-0.0151118\pi$
$338$	−127.688	−	73.7206i	−0.377775	−	0.218108i
$339$	−228.621	+	131.994i	−0.674399	+	0.389364i
$340$	191.216	−	72.0244i	0.562400	−	0.211837i
$341$	12.1929	+	7.03956i	0.0357562	+	0.0206439i
$342$	25.8889			0.0756986
$343$	36.4192	+	341.061i	0.106178	+	0.994347i
$344$	−141.650			−0.411774
$345$	78.1569	−	95.2842i	0.226542	−	0.276186i
$346$	38.6786	−	22.3311i	0.111788	−	0.0645407i
$347$	−34.0370	+	19.6513i	−0.0980893	+	0.0566319i	−0.548242	−	0.836320i	$-0.684703\pi$
$347$	−34.0370	+	19.6513i	−0.0980893	+	0.0566319i	0.450153	+	0.892951i	$0.351369\pi$
$348$	−59.2148	+	102.563i	−0.170157	+	0.294721i
$349$			231.465i			0.663222i	0.943416	+	0.331611i	$0.107592\pi$
$349$			231.465i			0.663222i	−0.943416	+	0.331611i	$0.892408\pi$
$350$	180.082	−	169.766i	0.514520	−	0.485045i
$351$	−85.8949			−0.244715
$352$	−14.3356	−	8.27666i	−0.0407261	−	0.0235132i
$353$	−20.0281	−	34.6897i	−0.0567369	−	0.0982711i	0.836262	−	0.548330i	$-0.184736\pi$
$353$	−20.0281	−	34.6897i	−0.0567369	−	0.0982711i	−0.892999	+	0.450059i	$0.851403\pi$
$354$	−44.1827	−	76.5267i	−0.124810	−	0.216177i
$355$	426.088	+	349.499i	1.20025	+	0.984504i
$356$		−	198.470i		−	0.557501i
$357$	−210.021	+	131.397i	−0.588294	+	0.368060i
$358$		−	124.743i		−	0.348443i
$359$	285.927	−	495.241i	0.796455	−	1.37950i	−0.125456	−	0.992099i	$-0.540039\pi$
$359$	285.927	−	495.241i	0.796455	−	1.37950i	0.921911	−	0.387402i	$-0.126627\pi$
$360$	−14.9549	−	39.7033i	−0.0415413	−	0.110287i
$361$	−161.882	−	280.388i	−0.448427	−	0.776699i
$362$	−220.032	+	381.106i	−0.607823	+	1.05278i
$363$	194.747			0.536493
$364$	8.20458	+	231.281i	0.0225401	+	0.635388i
$365$	−77.5167	+	470.259i	−0.212374	+	1.28838i
$366$	−67.7184	+	117.292i	−0.185023	+	0.320469i
$367$	−162.515	−	281.484i	−0.442820	−	0.766987i	0.555077	−	0.831799i	$-0.312689\pi$
$367$	−162.515	−	281.484i	−0.442820	−	0.766987i	−0.997897	+	0.0648119i	$0.979355\pi$
$368$	−49.2952	+	28.4606i	−0.133954	+	0.0773385i
$369$	102.076	+	58.9333i	0.276627	+	0.159711i
$370$	−51.0148	+	309.485i	−0.137878	+	0.836445i
$371$	−413.417	+	14.6657i	−1.11433	+	0.0395303i
$372$		−	16.6669i		−	0.0448036i
$373$	211.287	+	121.987i	0.566454	+	0.327042i	0.755732	−	0.654881i	$-0.227281\pi$
$373$	211.287	+	121.987i	0.566454	+	0.327042i	−0.189278	+	0.981924i	$0.560615\pi$
$374$	−73.2301	+	42.2794i	−0.195802	+	0.113047i
$375$	216.385	−	7.24984i	0.577026	−	0.0193329i
$376$	10.1998	+	5.88885i	0.0271271	+	0.0156618i
$377$	565.139			1.49904
$378$	27.2828	+	43.6079i	0.0721767	+	0.115365i
$379$	−36.9951			−0.0976124			−0.0488062	−	0.998808i	$-0.515542\pi$
$379$	−36.9951			−0.0976124			−0.0488062	+	0.998808i	$0.515542\pi$
$380$	38.6991	−	47.1796i	0.101840	−	0.124157i
$381$	36.7030	−	21.1905i	0.0963334	−	0.0556181i
$382$	371.604	−	214.546i	0.972786	−	0.561638i
$383$	46.4626	−	80.4756i	0.121312	−	0.210119i	−0.798973	−	0.601367i	$-0.794623\pi$
$383$	46.4626	−	80.4756i	0.121312	−	0.210119i	0.920285	+	0.391248i	$0.127956\pi$
$384$			19.5959i			0.0510310i
$385$	−62.1052	+	81.4401i	−0.161312	+	0.211533i
$386$	−326.157			−0.844965
$387$	130.114	+	75.1213i	0.336212	+	0.194112i
$388$	116.887	+	202.454i	0.301255	+	0.521789i
$389$	−113.148	−	195.978i	−0.290869	−	0.503799i	0.683147	−	0.730281i	$-0.260611\pi$
$389$	−113.148	−	195.978i	−0.290869	−	0.503799i	−0.974015	+	0.226482i	$0.927278\pi$
$390$	−128.397	+	156.534i	−0.329223	+	0.401368i
$391$			290.769i			0.743654i
$392$	114.813	−	77.6272i	0.292890	−	0.198029i
$393$		−	78.1606i		−	0.198882i
$394$	150.812	−	261.215i	0.382772	−	0.662981i
$395$	605.676	−	228.137i	1.53336	−	0.577563i
$396$	8.77872	+	15.2052i	0.0221685	+	0.0383970i
$397$	72.0276	−	124.755i	0.181430	−	0.314245i	−0.760938	−	0.648825i	$-0.775261\pi$
$397$	72.0276	−	124.755i	0.181430	−	0.314245i	0.942368	+	0.334579i	$0.108594\pi$
$398$	513.959			1.29135
$399$	−34.6971	+	65.3430i	−0.0869603	+	0.163767i
$400$	−94.7094	−	32.0955i	−0.236774	−	0.0802388i
$401$	169.001	−	292.718i	0.421448	−	0.729970i	−0.574633	−	0.818411i	$-0.694855\pi$
$401$	169.001	−	292.718i	0.421448	−	0.729970i	0.996081	+	0.0884411i	$0.0281885\pi$
$402$	84.9538	+	147.144i	0.211328	+	0.366031i
$403$	−68.8781	+	39.7668i	−0.170913	+	0.0986769i
$404$	313.850	+	181.201i	0.776855	+	0.448518i
$405$	−7.31895	+	44.4008i	−0.0180715	+	0.109632i
$406$	−179.505	−	286.915i	−0.442131	−	0.706687i
$407$		−	129.803i		−	0.318927i
$408$	86.6902	+	50.0506i	0.212476	+	0.122673i
$409$	−496.881	+	286.874i	−1.21487	+	0.701404i	−0.963816	−	0.266569i	$-0.914110\pi$
$409$	−496.881	+	286.874i	−1.21487	+	0.701404i	−0.251052	+	0.967974i	$0.580777\pi$
$410$	259.983	−	97.9266i	0.634105	−	0.238845i
$411$	−173.332	−	100.073i	−0.421733	−	0.243488i
$412$	106.150			0.257646
$413$	252.366	−	8.95256i	0.611056	−	0.0216769i
$414$	60.3740			0.145831
$415$	−22.9214	−	18.8013i	−0.0552322	−	0.0453043i
$416$	80.9825	−	46.7552i	0.194669	−	0.112392i
$417$	−22.5255	+	13.0051i	−0.0540180	+	0.0311873i
$418$	−12.6262	+	21.8692i	−0.0302062	+	0.0523187i
$419$		−	453.356i		−	1.08200i	−0.841024	−	0.540998i	$-0.818047\pi$
$419$		−	453.356i		−	1.08200i	0.841024	−	0.540998i	$-0.181953\pi$
$420$	120.253	+	15.4659i	0.286317	+	0.0368237i
$421$	89.9901			0.213753			0.106877	−	0.994272i	$-0.465915\pi$
$421$	89.9901			0.213753			0.106877	+	0.994272i	$0.465915\pi$
$422$	−227.834	−	131.540i	−0.539890	−	0.311706i
$423$	−6.24607	−	10.8185i	−0.0147661	−	0.0255757i
$424$	83.5754	+	144.757i	0.197112	+	0.341408i
$425$	−383.888	+	337.008i	−0.903266	+	0.792960i
$426$			269.978i			0.633751i
$427$	−205.283	−	328.117i	−0.480756	−	0.768425i
$428$			258.279i			0.603456i
$429$	41.8915	−	72.5583i	0.0976493	−	0.169133i
$430$	331.396	−	124.825i	0.770689	−	0.290292i
$431$	−122.293	−	211.818i	−0.283743	−	0.491458i	0.688560	−	0.725179i	$-0.258243\pi$
$431$	−122.293	−	211.818i	−0.283743	−	0.491458i	−0.972304	+	0.233721i	$0.924910\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	108.943			0.251600			0.125800	−	0.992056i	$-0.459850\pi$
$433$	108.943			0.251600			0.125800	+	0.992056i	$0.459850\pi$
$434$	42.0669	+	22.3375i	0.0969284	+	0.0514690i
$435$	48.1544	−	292.132i	0.110700	−	0.671567i
$436$	155.478	−	269.296i	0.356601	−	0.617651i
$437$	43.4172	+	75.2007i	0.0993528	+	0.172084i
$438$	−202.207	+	116.744i	−0.461659	+	0.266539i
$439$	329.897	+	190.466i	0.751473	+	0.433863i	0.826226	−	0.563339i	$-0.190483\pi$
$439$	329.897	+	190.466i	0.751473	+	0.433863i	−0.0747527	+	0.997202i	$0.523817\pi$
$440$	40.8323	+	6.73072i	0.0928006	+	0.0152971i
$441$	−146.630	+	10.4164i	−0.332495	+	0.0236199i
$442$		−	477.677i		−	1.08072i
$443$	−43.6255	−	25.1872i	−0.0984775	−	0.0568560i	0.449952	−	0.893053i	$-0.351441\pi$
$443$	−43.6255	−	25.1872i	−0.0984775	−	0.0568560i	−0.548430	+	0.836197i	$0.684774\pi$
$444$	−133.075	+	76.8309i	−0.299719	+	0.173043i
$445$	174.897	+	464.329i	0.393026	+	1.04344i
$446$	485.751	+	280.449i	1.08913	+	0.628809i
$447$	−224.211			−0.501590
$448$	−49.4596	−	26.2631i	−0.110401	−	0.0586229i
$449$	240.479			0.535588			0.267794	−	0.963476i	$-0.413705\pi$
$449$	240.479			0.535588			0.267794	+	0.963476i	$0.413705\pi$
$450$	69.9749	+	79.7089i	0.155500	+	0.177131i
$451$	−99.5659	+	57.4844i	−0.220767	+	0.127460i
$452$	−263.989	+	152.414i	−0.584046	+	0.337199i
$453$	154.874	−	268.250i	0.341885	−	0.592163i
$454$			514.505i			1.13327i
$455$	−223.005	−	533.861i	−0.490122	−	1.17332i
$456$	29.8940			0.0655569
$457$	592.842	+	342.278i	1.29725	+	0.748967i	0.979928	−	0.199352i	$-0.0638837\pi$
$457$	592.842	+	342.278i	1.29725	+	0.748967i	0.317320	+	0.948318i	$0.397217\pi$
$458$	−271.704	−	470.605i	−0.593241	−	1.02752i
$459$	−53.0867	−	91.9489i	−0.115657	−	0.200324i
$460$	90.2479	−	110.025i	0.196191	−	0.239184i
$461$		−	506.777i		−	1.09930i	−0.835395	−	0.549649i	$-0.814761\pi$
$461$		−	506.777i		−	1.09930i	0.835395	−	0.549649i	$-0.185239\pi$
$462$	−50.1431	+	1.77880i	−0.108535	+	0.00385021i
$463$		−	166.656i		−	0.359948i	−0.983671	−	0.179974i	$-0.942399\pi$
$463$		−	166.656i		−	0.359948i	0.983671	−	0.179974i	$-0.0576013\pi$
$464$	−68.3754	+	118.430i	−0.147361	+	0.255236i
$465$	14.6873	+	38.9929i	0.0315856	+	0.0838558i
$466$	217.701	+	377.069i	0.467169	+	0.809160i
$467$	45.8091	−	79.3438i	0.0980924	−	0.169901i	−0.812803	−	0.582539i	$-0.802059\pi$
$467$	45.8091	−	79.3438i	0.0980924	−	0.169901i	0.910895	+	0.412638i	$0.135393\pi$
$468$	−99.1829			−0.211929
$469$	−485.246	+	17.2138i	−1.03464	+	0.0367033i
$470$	−29.0522	−	4.78891i	−0.0618132	−	0.0101892i
$471$	−21.5672	+	37.3555i	−0.0457903	+	0.0793111i
$472$	−51.0178	−	88.3654i	−0.108088	−	0.187215i
$473$	−126.915	+	73.2744i	−0.268319	+	0.154914i
$474$	274.591	+	158.535i	0.579306	+	0.334463i
$475$	−48.9624	+	144.481i	−0.103079	+	0.304171i
$476$	−242.511	+	151.725i	−0.509478	+	0.318749i
$477$		−	177.290i		−	0.371677i
$478$	−279.231	−	161.214i	−0.584166	−	0.337268i
$479$	−654.243	+	377.728i	−1.36585	+	0.788575i	−0.990395	−	0.138264i	$-0.955848\pi$
$479$	−654.243	+	377.728i	−1.36585	+	0.788575i	−0.375457	+	0.926840i	$0.622514\pi$
$480$	−17.2684	−	45.8454i	−0.0359758	−	0.0955113i
$481$	635.026	+	366.632i	1.32022	+	0.762229i
$482$	−494.183			−1.02528
$483$	−80.9151	+	152.382i	−0.167526	+	0.315492i
$484$	224.874			0.464616
$485$	−451.869	−	370.646i	−0.931689	−	0.764219i
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	−686.217	+	396.187i	−1.40907	+	0.813526i	−0.995299	−	0.0968547i	$-0.969122\pi$
$487$	−686.217	+	396.187i	−1.40907	+	0.813526i	−0.413771	+	0.910381i	$0.635788\pi$
$488$	−78.1945	+	135.437i	−0.160235	+	0.277534i
$489$			85.5716i			0.174993i
$490$	−200.203	+	282.788i	−0.408577	+	0.577118i
$491$	221.144			0.450395			0.225198	−	0.974313i	$-0.427697\pi$
$491$	221.144			0.450395			0.225198	+	0.974313i	$0.427697\pi$
$492$	117.867	+	68.0504i	0.239566	+	0.138314i
$493$	349.280	+	604.971i	0.708479	+	1.22712i
$494$	−71.3261	−	123.540i	−0.144385	−	0.250082i
$495$	−33.9373	−	27.8371i	−0.0685603	−	0.0562367i
$496$		−	19.2453i		−	0.0388010i
$497$	−681.418	−	361.833i	−1.37106	−	0.728034i
$498$		−	14.5234i		−	0.0291635i
$499$	465.567	−	806.385i	0.932999	−	1.61600i	0.154836	−	0.987940i	$-0.450515\pi$
$499$	465.567	−	806.385i	0.932999	−	1.61600i	0.778164	−	0.628062i	$-0.216151\pi$
$500$	249.860	−	8.37139i	0.499720	−	0.0167428i
$501$	185.019	+	320.462i	0.369299	+	0.639644i
$502$	102.962	−	178.335i	0.205103	−	0.355249i
$503$	137.667			0.273691			0.136846	−	0.990592i	$-0.456304\pi$
$503$	137.667			0.273691			0.136846	+	0.990592i	$0.456304\pi$
$504$	31.5035	+	50.3541i	0.0625068	+	0.0999089i
$505$	−893.942	−	147.356i	−1.77018	−	0.291793i
$506$	−29.4448	+	50.9999i	−0.0581913	+	0.100790i
$507$	90.2889	+	156.385i	0.178085	+	0.308452i
$508$	42.3810	−	24.4687i	0.0834272	−	0.0481667i
$509$	−329.747	−	190.380i	−0.647833	−	0.374027i	0.139792	−	0.990181i	$-0.455356\pi$
$509$	−329.747	−	190.380i	−0.647833	−	0.374027i	−0.787625	+	0.616154i	$0.788690\pi$
$510$	−246.921	−	40.7020i	−0.484159	−	0.0798078i
$511$	−23.6554	−	666.828i	−0.0462923	−	1.30495i
$512$			22.6274i			0.0441942i
$513$	−27.4594	−	15.8537i	−0.0535270	−	0.0309038i
$514$	−547.886	+	316.322i	−1.06593	+	0.615413i
$515$	−248.343	+	93.5420i	−0.482219	+	0.181635i
$516$	150.243	+	86.7427i	0.291168	+	0.168106i
$517$	12.1850			0.0235687
$518$	−15.5679	−	438.849i	−0.0300540	−	0.847199i
$519$	−54.6998			−0.105395
$520$	−148.260	+	180.749i	−0.285115	+	0.347595i
$521$	−72.5702	+	41.8984i	−0.139290	+	0.0804193i	−0.568026	−	0.823011i	$-0.692293\pi$
$521$	−72.5702	+	41.8984i	−0.139290	+	0.0804193i	0.428735	+	0.903430i	$0.358959\pi$
$522$	125.614	−	72.5230i	0.240639	−	0.138933i
$523$	−271.114	+	469.583i	−0.518382	+	0.897864i	0.481390	+	0.876507i	$0.340132\pi$
$523$	−271.114	+	469.583i	−0.518382	+	0.897864i	−0.999772	+	0.0213573i	$0.993201\pi$
$524$		−	90.2521i		−	0.172237i
$525$	−294.966	+	69.7866i	−0.561840	+	0.132927i
$526$	448.777			0.853189
$527$	−85.1392	−	49.1551i	−0.161554	−	0.0932735i
$528$	10.1368	+	17.5574i	0.0191985	+	0.0332527i
$529$	−163.249	−	282.756i	−0.308600	−	0.534511i
$530$	−323.091	−	265.016i	−0.609606	−	0.500030i
$531$			108.225i			0.203814i
$532$	−40.0648	+	75.4516i	−0.0753098	+	0.141826i
$533$		−	649.464i		−	1.21851i
$534$	−121.538	+	210.510i	−0.227599	+	0.394213i
$535$	−227.602	−	604.255i	−0.425424	−	1.12945i
$536$	98.0962	+	169.908i	0.183015	+	0.316992i
$537$	−76.3890	+	132.310i	−0.142251	+	0.246387i
$538$	318.303			0.591641
$539$	62.7136	−	128.944i	0.116352	−	0.239228i
$540$	−8.45119	+	51.2697i	−0.0156504	+	0.0949438i
$541$	−349.573	+	605.479i	−0.646161	+	1.11918i	0.337871	+	0.941192i	$0.390293\pi$
$541$	−349.573	+	605.479i	−0.646161	+	1.11918i	−0.984032	+	0.177991i	$0.943040\pi$
$542$	214.382	+	371.320i	0.395538	+	0.685092i
$543$	466.758	−	269.483i	0.859591	−	0.496285i
$544$	100.101	+	57.7935i	0.184010	+	0.106238i
$545$	−126.437	+	767.039i	−0.231995	+	1.40741i
$546$	132.928	−	250.335i	0.243458	−	0.458489i
$547$			77.0407i			0.140842i	0.997517	+	0.0704211i	$0.0224343\pi$
$547$			77.0407i			0.140842i	−0.997517	+	0.0704211i	$0.977566\pi$
$548$	−200.147	−	115.555i	−0.365231	−	0.210866i
$549$	143.652	−	82.9378i	0.261662	−	0.151071i
$550$	−101.460	+	20.2356i	−0.184473	+	0.0367920i
$551$	180.667	+	104.308i	0.327889	+	0.189307i
$552$	69.7139			0.126293
$553$	−768.154	+	480.587i	−1.38907	+	0.869054i
$554$	474.825			0.857086
$555$	243.629	−	297.018i	0.438972	−	0.535167i
$556$	−26.0102	+	15.0170i	−0.0467809	+	0.0270090i
$557$	227.814	−	131.528i	0.409001	−	0.236137i	−0.281359	−	0.959602i	$-0.590785\pi$
$557$	227.814	−	131.528i	0.409001	−	0.236137i	0.690360	+	0.723466i	$0.257452\pi$
$558$	−10.2064	+	17.6780i	−0.0182910	+	0.0316809i
$559$		−	827.861i		−	1.48097i
$560$	138.856	+	17.8585i	0.247958	+	0.0318902i
$561$	103.563			0.184604
$562$	262.948	+	151.813i	0.467879	+	0.270130i
$563$	−420.872	−	728.972i	−0.747553	−	1.29480i	−0.948992	−	0.315299i	$-0.897895\pi$
$563$	−420.872	−	728.972i	−0.747553	−	1.29480i	0.201439	−	0.979501i	$-0.435438\pi$
$564$	−7.21234	−	12.4921i	−0.0127878	−	0.0221492i
$565$	483.302	−	589.212i	0.855401	−	1.04285i
$566$		−	116.113i		−	0.205146i
$567$	−2.23349	−	62.9604i	−0.00393913	−	0.111041i
$568$			311.744i			0.548845i
$569$	163.209	−	282.686i	0.286835	−	0.496812i	−0.686218	−	0.727396i	$-0.740730\pi$
$569$	163.209	−	282.686i	0.286835	−	0.496812i	0.973052	+	0.230584i	$0.0740637\pi$
$570$	−69.9381	+	26.3432i	−0.122698	+	0.0462162i
$571$	268.537	+	465.120i	0.470293	+	0.814571i	0.999423	−	0.0339697i	$-0.0108150\pi$
$571$	268.537	+	465.120i	0.470293	+	0.814571i	−0.529130	+	0.848541i	$0.677482\pi$
$572$	48.3722	−	83.7831i	0.0845667	−	0.146474i
$573$	−525.528			−0.917151
$574$	−329.726	+	206.289i	−0.574435	+	0.359389i
$575$	−114.182	+	336.936i	−0.198578	+	0.585975i
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−174.434	−	302.128i	−0.302311	−	0.523619i	0.674348	−	0.738414i	$-0.264425\pi$
$577$	−174.434	−	302.128i	−0.302311	−	0.523619i	−0.976659	+	0.214795i	$0.931092\pi$
$578$	157.393	−	90.8709i	0.272306	−	0.157216i
$579$	345.941	+	199.729i	0.597481	+	0.344956i
$580$	55.6040	−	337.325i	0.0958689	−	0.581594i
$581$	36.6568	+	19.4648i	0.0630926	+	0.0335022i
$582$		−	286.314i		−	0.491948i
$583$	149.763	+	86.4656i	0.256883	+	0.148312i
$584$	−233.488	+	134.804i	−0.399808	+	0.230829i
$585$	232.042	−	87.4022i	0.396653	−	0.149406i
$586$	−336.720	−	194.405i	−0.574607	−	0.331750i
$587$	937.962			1.59789			0.798946	−	0.601403i	$-0.205391\pi$
$587$	937.962			1.59789			0.798946	+	0.601403i	$0.205391\pi$
$588$	−169.314	+	12.0278i	−0.287949	+	0.0204555i
$589$	−29.3591			−0.0498457
$590$	197.228	+	161.776i	0.334284	+	0.274197i
$591$	−319.921	+	184.707i	−0.541322	+	0.312532i
$592$	−153.662	+	88.7167i	−0.259564	+	0.149859i
$593$	−254.325	+	440.503i	−0.428878	+	0.742839i	−0.996774	−	0.0802619i	$-0.974424\pi$
$593$	−254.325	+	440.503i	−0.428878	+	0.742839i	0.567896	+	0.823100i	$0.307758\pi$
$594$		−	21.5034i		−	0.0362010i
$595$	433.662	−	568.672i	0.728844	−	0.955752i
$596$	−258.896			−0.434390
$597$	−545.136	−	314.734i	−0.913126	−	0.527193i
$598$	−166.335	−	288.101i	−0.278152	−	0.481774i
$599$	−447.411	−	774.939i	−0.746930	−	1.29372i	−0.949288	−	0.314409i	$-0.898194\pi$
$599$	−447.411	−	774.939i	−0.746930	−	1.29372i	0.202357	−	0.979312i	$-0.435140\pi$
$600$	80.8001	+	92.0399i	0.134667	+	0.153400i
$601$		−	89.5680i		−	0.149032i	−0.997220	−	0.0745158i	$-0.976259\pi$
$601$		−	89.5680i		−	0.149032i	0.997220	−	0.0745158i	$-0.0237411\pi$
$602$	−420.296	+	262.953i	−0.698166	+	0.436800i
$603$		−	208.093i		−	0.345097i
$604$	178.833	−	309.748i	0.296081	−	0.512828i
$605$	−526.102	+	198.164i	−0.869590	+	0.327544i
$606$	−221.925	−	384.386i	−0.366213	−	0.634300i
$607$	−472.644	+	818.644i	−0.778656	+	1.34867i	0.154061	+	0.988061i	$0.450765\pi$
$607$	−472.644	+	818.644i	−0.778656	+	1.34867i	−0.932717	+	0.360610i	$0.882568\pi$
$608$	34.5186			0.0567740
$609$	14.6951	+	414.243i	0.0241298	+	0.680202i
$610$	63.5890	−	385.766i	0.104244	−	0.632404i
$611$	−34.4169	+	59.6117i	−0.0563287	+	0.0975642i
$612$	−61.2993	−	106.173i	−0.100162	−	0.173486i
$613$	836.589	−	483.005i	1.36474	−	0.787936i	0.374494	−	0.927229i	$-0.377817\pi$
$613$	836.589	−	483.005i	1.36474	−	0.787936i	0.990251	+	0.139294i	$0.0444832\pi$
$614$	592.097	+	341.848i	0.964328	+	0.556755i
$615$	−335.721	−	55.3397i	−0.545888	−	0.0899832i
$616$	−57.9002	+	2.05398i	−0.0939938	+	0.00333438i
$617$			898.224i			1.45579i	0.685687	+	0.727896i	$0.259502\pi$
$617$			898.224i			1.45579i	−0.685687	+	0.727896i	$0.740498\pi$
$618$	−112.589	−	65.0035i	−0.182183	−	0.105184i
$619$	−20.5293	+	11.8526i	−0.0331653	+	0.0191480i	−0.516491	−	0.856293i	$-0.672762\pi$
$619$	−20.5293	+	11.8526i	−0.0331653	+	0.0191480i	0.483326	+	0.875441i	$0.339429\pi$
$620$	16.9594	+	45.0252i	0.0273539	+	0.0726213i
$621$	−64.0363	−	36.9714i	−0.103118	−	0.0595352i
$622$	282.576			0.454302
$623$	−368.432	−	588.890i	−0.591384	−	0.945248i
$624$	−114.527			−0.183536
$625$	−577.180	+	239.767i	−0.923488	+	0.383628i
$626$	−219.944	+	126.985i	−0.351349	+	0.202851i
$627$	26.7842	−	15.4639i	0.0427181	−	0.0246633i
$628$	−24.9037	+	43.1344i	−0.0396555	+	0.0686854i
$629$			906.378i			1.44098i
$630$	−118.077	−	90.0438i	−0.187423	−	0.142927i
$631$	−1082.18			−1.71502			−0.857511	−	0.514465i	$-0.827991\pi$
$631$	−1082.18			−1.71502			−0.857511	+	0.514465i	$0.827991\pi$
$632$	317.070	+	183.061i	0.501694	+	0.289653i
$633$	161.103	+	279.038i	0.254507	+	0.440819i
$634$	267.624	+	463.539i	0.422120	+	0.731134i
$635$	−77.5897	+	94.5926i	−0.122188	+	0.148965i
$636$		−	204.717i		−	0.321882i
$637$	453.685	+	671.014i	0.712221	+	1.05340i
$638$			141.480i			0.221755i
$639$	165.327	−	286.355i	0.258728	−	0.448130i
$640$	−19.9398	−	52.9377i	−0.0311559	−	0.0827152i
$641$	486.119	+	841.983i	0.758376	+	1.31355i	0.943678	+	0.330864i	$0.107340\pi$
$641$	486.119	+	841.983i	0.758376	+	1.31355i	−0.185302	+	0.982682i	$0.559326\pi$
$642$	158.163	−	273.947i	0.246360	−	0.426708i
$643$	−324.120			−0.504075			−0.252037	−	0.967718i	$-0.581101\pi$
$643$	−324.120			−0.504075			−0.252037	+	0.967718i	$0.581101\pi$
$644$	−93.4327	+	175.956i	−0.145082	+	0.273224i
$645$	−427.938	−	70.5405i	−0.663470	−	0.109365i
$646$	88.1651	−	152.706i	0.136478	−	0.236388i
$647$	403.924	+	699.616i	0.624303	+	1.08132i	0.988675	+	0.150071i	$0.0479501\pi$
$647$	403.924	+	699.616i	0.624303	+	1.08132i	−0.364373	+	0.931253i	$0.618717\pi$
$648$	−22.0454	+	12.7279i	−0.0340207	+	0.0196419i
$649$	−91.4213	−	52.7821i	−0.140865	−	0.0813283i
$650$	187.579	−	553.520i	0.288584	−	0.851570i
$651$	−30.9398	−	49.4532i	−0.0475266	−	0.0759649i
$652$			98.8096i			0.151548i
$653$	−220.618	−	127.374i	−0.337854	−	0.195060i	0.321469	−	0.946920i	$-0.395823\pi$
$653$	−220.618	−	127.374i	−0.337854	−	0.195060i	−0.659322	+	0.751860i	$0.729157\pi$
$654$	−329.819	+	190.421i	−0.504310	+	0.291164i
$655$	79.5322	+	211.148i	0.121423	+	0.322364i
$656$	136.101	+	78.5778i	0.207471	+	0.119783i
$657$	285.963			0.435256
$658$	41.1961	−	1.46141i	0.0626080	−	0.00222099i
$659$	1056.57			1.60329			0.801645	−	0.597801i	$-0.203959\pi$
$659$	1056.57			1.60329			0.801645	+	0.597801i	$0.203959\pi$
$660$	−39.1875	−	32.1436i	−0.0593750	−	0.0487024i
$661$	599.500	−	346.122i	0.906960	−	0.523633i	0.0275079	−	0.999622i	$-0.491243\pi$
$661$	599.500	−	346.122i	0.906960	−	0.523633i	0.879452	+	0.475988i	$0.157910\pi$
$662$	−174.793	+	100.917i	−0.264038	+	0.152443i
$663$	−292.516	+	506.653i	−0.441201	+	0.764182i
$664$		−	16.7702i		−	0.0252564i
$665$	27.2435	−	211.828i	0.0409677	−	0.318538i
$666$	188.197			0.282577
$667$	421.322	+	243.250i	0.631667	+	0.364693i
$668$	213.641	+	370.037i	0.319822	+	0.553948i
$669$	−343.478	−	594.921i	−0.513420	−	0.889270i
$670$	−379.226	−	311.061i	−0.566010	−	0.464270i
$671$			161.797i			0.241129i
$672$	36.3771	+	58.1439i	0.0541325	+	0.0865236i
$673$		−	288.340i		−	0.428441i	−0.976785	−	0.214220i	$-0.931279\pi$
$673$		−	288.340i		−	0.428441i	0.976785	−	0.214220i	$-0.0687210\pi$
$674$	−22.6177	+	39.1750i	−0.0335574	+	0.0581231i
$675$	−25.4081	−	127.395i	−0.0376416	−	0.188733i
$676$	104.257	+	180.578i	0.154226	+	0.267127i
$677$	283.078	−	490.305i	0.418135	−	0.724232i	−0.577617	−	0.816308i	$-0.696017\pi$
$677$	283.078	−	490.305i	0.418135	−	0.724232i	0.995752	+	0.0920765i	$0.0293504\pi$
$678$	373.337			0.550644
$679$	722.648	+	383.726i	1.06428	+	0.565135i
$680$	−285.120	−	46.9986i	−0.419294	−	0.0691156i
$681$	315.069	−	545.715i	0.462656	−	0.801344i
$682$	−9.95543	−	17.2433i	−0.0145974	−	0.0252835i
$683$	135.474	−	78.2158i	0.198351	−	0.114518i	−0.397535	−	0.917587i	$-0.630134\pi$
$683$	135.474	−	78.2158i	0.198351	−	0.114518i	0.595886	+	0.803069i	$0.296801\pi$
$684$	−31.7073	−	18.3062i	−0.0463557	−	0.0267635i
$685$	570.081	+	93.9710i	0.832235	+	0.137184i
$686$	196.562	−	443.465i	0.286534	−	0.646450i
$687$			665.537i			0.968758i
$688$	173.485	+	100.162i	0.252159	+	0.145584i
$689$	−846.018	+	488.448i	−1.22789	+	0.708924i
$690$	−163.098	+	61.4335i	−0.236374	+	0.0890340i
$691$	356.923	+	206.070i	0.516531	+	0.298219i	0.735514	−	0.677509i	$-0.236941\pi$
$691$	356.923	+	206.070i	0.516531	+	0.298219i	−0.218983	+	0.975729i	$0.570274\pi$
$692$	−63.1618			−0.0912743
$693$	54.2740	+	28.8195i	0.0783175	+	0.0415866i
$694$	55.5822			0.0800896
$695$	47.6186	−	58.0536i	0.0685159	−	0.0835304i
$696$	145.046	−	83.7424i	0.208400	−	0.120320i
$697$	695.239	−	401.397i	0.997474	−	0.575892i
$698$	163.670	−	283.485i	0.234485	−	0.406139i
$699$		−	533.256i		−	0.762884i
$700$	−340.597	+	80.5827i	−0.486567	+	0.115118i
$701$	−154.301			−0.220116			−0.110058	−	0.993925i	$-0.535104\pi$
$701$	−154.301			−0.220116			−0.110058	+	0.993925i	$0.535104\pi$
$702$	105.199	+	60.7369i	0.149857	+	0.0865197i
$703$	135.339	+	234.414i	0.192516	+	0.333448i
$704$	11.7050	+	20.2736i	0.0166264	+	0.0287977i
$705$	27.8819	+	22.8702i	0.0395488	+	0.0324400i
$706$			56.6481i			0.0802380i
$707$	1267.61	−	44.9678i	1.79294	−	0.0636037i
$708$			124.968i			0.176508i
$709$	135.798	−	235.209i	0.191534	−	0.331747i	−0.754225	−	0.656616i	$-0.771987\pi$
$709$	135.798	−	235.209i	0.191534	−	0.331747i	0.945759	+	0.324869i	$0.105320\pi$
$710$	−274.716	−	729.337i	−0.386924	−	1.02723i
$711$	−194.165	−	336.304i	−0.273088	−	0.473001i
$712$	−140.340	+	243.075i	−0.197106	+	0.341398i
$713$	−68.4666			−0.0960261
$714$	350.134	−	12.4208i	0.490384	−	0.0173961i
$715$	−39.3370	+	238.640i	−0.0550168	+	0.333763i
$716$	−88.2064	+	152.778i	−0.123193	+	0.213377i
$717$	197.446	+	341.987i	0.275378	+	0.476969i
$718$	−700.376	+	404.362i	−0.975455	+	0.563179i
$719$	298.373	+	172.266i	0.414983	+	0.239591i	0.692929	−	0.721006i	$-0.256320\pi$
$719$	298.373	+	172.266i	0.414983	+	0.239591i	−0.277945	+	0.960597i	$0.589653\pi$
$720$	−9.75859	+	59.2011i	−0.0135536	+	0.0822237i
$721$	314.963	−	197.053i	0.436842	−	0.273305i
$722$			457.872i			0.634172i
$723$	524.160	+	302.624i	0.724979	+	0.418567i
$724$	538.966	−	311.172i	0.744428	−	0.429796i
$725$	167.171	+	838.184i	0.230580	+	1.15612i
$726$	−238.515	−	137.707i	−0.328533	−	0.189679i
$727$	−85.5032			−0.117611			−0.0588055	−	0.998269i	$-0.518729\pi$
$727$	−85.5032			−0.117611			−0.0588055	+	0.998269i	$0.518729\pi$
$728$	153.492	−	289.062i	0.210841	−	0.397063i
$729$	27.0000			0.0370370
$730$	427.462	−	521.135i	0.585564	−	0.713884i
$731$	886.210	−	511.654i	1.21233	−	0.699936i
$732$	165.876	−	95.7683i	0.226606	−	0.130831i
$733$	487.228	−	843.904i	0.664704	−	1.15130i	−0.314661	−	0.949204i	$-0.601891\pi$
$733$	487.228	−	843.904i	0.664704	−	1.15130i	0.979365	−	0.202098i	$-0.0647758\pi$
$734$			459.662i			0.626242i
$735$	385.518	−	177.343i	0.524515	−	0.241283i
$736$	80.4987			0.109373
$737$	175.783	+	101.489i	0.238512	+	0.137705i
$738$	−83.3443	−	144.357i	−0.112933	−	0.195605i
$739$	−572.640	−	991.841i	−0.774884	−	1.34214i	−0.934859	−	0.355018i	$-0.884475\pi$
$739$	−572.640	−	991.841i	−0.774884	−	1.34214i	0.159975	−	0.987121i	$-0.448859\pi$
$740$	281.319	−	342.967i	0.380160	−	0.463468i
$741$			174.712i			0.235779i
$742$	516.701	+	274.368i	0.696362	+	0.369768i
$743$			0.488126i			0.000656966i	1.00000		0.000328483i	$0.000104559\pi$
$743$			0.488126i			0.000656966i	−1.00000		0.000328483i	$0.999895\pi$
$744$	−11.7853	+	20.4127i	−0.0158405	+	0.0274365i
$745$	605.698	−	228.146i	0.813018	−	0.306236i
$746$	−172.515	−	298.806i	−0.231254	−	0.400544i
$747$	−8.89375	+	15.4044i	−0.0119060	+	0.0206217i
$748$	119.584			0.159872
$749$	479.459	+	766.352i	0.640132	+	1.02317i
$750$	−270.143	−	144.128i	−0.360190	−	0.192171i
$751$	−617.798	+	1070.06i	−0.822634	+	1.42484i	0.0810800	+	0.996708i	$0.474163\pi$
$751$	−617.798	+	1070.06i	−0.822634	+	1.42484i	−0.903714	+	0.428136i	$0.859170\pi$
$752$	−8.32810	−	14.4247i	−0.0110746	−	0.0191818i
$753$	−218.415	+	126.102i	−0.290060	+	0.167466i
$754$	−692.151	−	399.613i	−0.917972	−	0.529991i
$755$	−145.430	+	882.260i	−0.192623	+	1.16856i
$756$	−2.57901	−	72.7004i	−0.00341139	−	0.0961646i
$757$			194.009i			0.256286i	0.991756	+	0.128143i	$0.0409017\pi$
$757$			194.009i			0.256286i	−0.991756	+	0.128143i	$0.959098\pi$
$758$	45.3096	+	26.1595i	0.0597751	+	0.0345112i
$759$	62.4619	−	36.0624i	0.0822950	−	0.0475130i
$760$	−80.7576	+	30.4186i	−0.106260	+	0.0400244i
$761$	170.663	+	98.5326i	0.224262	+	0.129478i	0.607922	−	0.793997i	$-0.292003\pi$
$761$	170.663	+	98.5326i	0.224262	+	0.129478i	−0.383660	+	0.923474i	$0.625337\pi$
$762$	−59.9358			−0.0786559
$763$	−38.5843	−	1087.66i	−0.0505691	−	1.42551i
$764$	−606.827			−0.794276
$765$	236.975	+	194.379i	0.309771	+	0.254090i
$766$	−113.810	+	65.7080i	−0.148577	+	0.0857807i
$767$	516.443	−	298.169i	0.673329	−	0.388747i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$		−	125.074i		−	0.162645i	−0.996688	−	0.0813225i	$-0.974086\pi$
$769$		−	125.074i		−	0.162645i	0.996688	−	0.0813225i	$-0.0259144\pi$
$770$	133.650	−	55.8284i	0.173571	−	0.0725044i
$771$	774.828			1.00497
$772$	399.459	+	230.628i	0.517434	+	0.298740i
$773$	615.323	+	1065.77i	0.796020	+	1.37875i	0.922189	+	0.386738i	$0.126398\pi$
$773$	615.323	+	1065.77i	0.796020	+	1.37875i	−0.126169	+	0.992009i	$0.540268\pi$
$774$	−106.238	−	184.009i	−0.137258	−	0.237738i
$775$	−79.3545	−	90.3932i	−0.102393	−	0.116636i
$776$		−	330.606i		−	0.426039i
$777$	−252.227	+	475.003i	−0.324616	+	0.611330i
$778$			320.031i			0.411350i
$779$	119.872	−	207.624i	0.153879	−	0.266527i
$780$	267.939	−	100.923i	0.343512	−	0.129389i
$781$	161.262	+	279.315i	0.206482	+	0.357637i
$782$	205.604	−	356.117i	0.262921	−	0.455393i
$783$	−177.644			−0.226877
$784$	−195.507	+	13.8885i	−0.249372	+	0.0177149i
$785$	20.2521	−	122.860i	0.0257988	−	0.156510i
$786$	−55.2679	+	95.7268i	−0.0703154	+	0.121790i
$787$	−145.164	−	251.431i	−0.184452	−	0.319480i	0.758940	−	0.651161i	$-0.225718\pi$
$787$	−145.164	−	251.431i	−0.184452	−	0.319480i	−0.943392	+	0.331681i	$0.892384\pi$
$788$	−369.413	+	213.281i	−0.468799	+	0.270661i
$789$	−476.000	−	274.819i	−0.603295	−	0.348313i
$790$	−903.116	−	148.868i	−1.14319	−	0.188440i
$791$	−500.358	+	942.293i	−0.632563	+	1.19127i
$792$		−	24.8300i		−	0.0313510i
$793$	−791.548	−	457.000i	−0.998168	−	0.576293i
$794$	−176.431	+	101.862i	−0.222205	+	0.128290i
$795$	180.401	+	478.944i	0.226920	+	0.602445i
$796$	−629.469	−	363.424i	−0.790790	−	0.456563i
$797$	−651.529			−0.817477			−0.408739	−	0.912652i	$-0.634031\pi$
$797$	−651.529			−0.817477			−0.408739	+	0.912652i	$0.634031\pi$
$798$	88.6996	−	55.4939i	0.111152	−	0.0695412i
$799$	−85.0844			−0.106489
$800$	93.2999	+	106.279i	0.116625	+	0.132848i
$801$	257.820	−	148.853i	0.321873	−	0.185834i
$802$	−413.966	+	239.003i	−0.516167	+	0.298009i
$803$	−139.466	+	241.563i	−0.173682	+	0.300825i
$804$		−	240.286i		−	0.298863i
$805$	63.5330	−	493.991i	0.0789229	−	0.613654i
$806$	112.477			0.139550
$807$	−337.611	−	194.920i	−0.418353	−	0.241536i
$808$	−256.257	−	443.850i	−0.317150	−	0.549320i
$809$	−306.517	−	530.903i	−0.378884	−	0.656246i	0.612017	−	0.790845i	$-0.290359\pi$
$809$	−306.517	−	530.903i	−0.378884	−	0.656246i	−0.990900	+	0.134599i	$0.957025\pi$
$810$	40.3600	−	49.2044i	0.0498271	−	0.0607462i
$811$			480.831i			0.592886i	0.955051	+	0.296443i	$0.0958005\pi$
$811$			480.831i			0.592886i	−0.955051	+	0.296443i	$0.904200\pi$
$812$	16.9684	+	478.327i	0.0208970	+	0.589072i
$813$		−	525.126i		−	0.645911i
$814$	−91.7848	+	158.976i	−0.112758	+	0.195302i
$815$	−87.0733	−	231.169i	−0.106838	−	0.283643i
$816$	−70.7823	−	122.599i	−0.0867430	−	0.150243i
$817$	152.799	−	264.655i	0.187024	−	0.323935i
$818$	811.403			0.991936
$819$	−294.290	+	184.119i	−0.359328	+	0.224809i
$820$	−387.658	−	63.9007i	−0.472753	−	0.0779277i
$821$	98.0760	−	169.873i	0.119459	−	0.206909i	−0.800094	−	0.599874i	$-0.795217\pi$
$821$	98.0760	−	169.873i	0.119459	−	0.206909i	0.919554	+	0.392965i	$0.128551\pi$
$822$	141.525	+	245.129i	0.172172	+	0.298210i
$823$	135.831	−	78.4220i	0.165044	−	0.0952880i	−0.415203	−	0.909729i	$-0.636289\pi$
$823$	135.831	−	78.4220i	0.165044	−	0.0952880i	0.580247	+	0.814441i	$0.302956\pi$
$824$	−130.007	−	75.0595i	−0.157775	−	0.0910917i
$825$	120.006	+	40.6682i	0.145462	+	0.0492948i
$826$	−315.415	−	167.485i	−0.381858	−	0.202767i
$827$			584.462i			0.706726i	0.935486	+	0.353363i	$0.114962\pi$
$827$			584.462i			0.706726i	−0.935486	+	0.353363i	$0.885038\pi$
$828$	−73.9427	−	42.6909i	−0.0893028	−	0.0515590i
$829$	270.851	−	156.376i	0.326720	−	0.188632i	−0.327664	−	0.944794i	$-0.606261\pi$
$829$	270.851	−	156.376i	0.326720	−	0.188632i	0.654384	+	0.756162i	$0.272928\pi$
$830$	14.7783	+	39.2346i	0.0178052	+	0.0472706i
$831$	−503.628	−	290.770i	−0.606051	−	0.349904i
$832$	−132.244			−0.158947
$833$	−437.911	+	900.376i	−0.525703	+	1.08088i
$834$	36.7840			0.0441055
$835$	−825.907	−	677.451i	−0.989110	−	0.811319i
$836$	30.9278	−	17.8562i	0.0369949	−	0.0213590i
$837$	21.6510	−	12.5002i	0.0258674	−	0.0149345i
$838$	−320.571	+	555.246i	−0.382543	+	0.662584i
$839$			125.784i			0.149921i	0.997187	+	0.0749604i	$0.0238830\pi$
$839$			125.784i			0.149921i	−0.997187	+	0.0749604i	$0.976117\pi$
$840$	−136.343	−	103.974i	−0.162313	−	0.123778i
$841$	327.798			0.389771
$842$	−110.215	−	63.6326i	−0.130897	−	0.0755732i
$843$	−185.932	−	322.044i	−0.220560	−	0.382022i
$844$	186.025	+	322.205i	0.220409	+	0.381760i
$845$	−403.042	−	330.596i	−0.476973	−	0.391237i
$846$			17.6666i			0.0208825i
$847$	667.234	−	417.447i	0.787761	−	0.492854i
$848$		−	236.387i		−	0.278758i
$849$	−71.1042	+	123.156i	−0.0837506	+	0.145060i
$850$	708.465	−	141.299i	0.833489	−	0.166234i
$851$	315.616	+	546.663i	0.370877	+	0.642377i
$852$	190.903	−	330.654i	0.224065	−	0.388092i
$853$	−689.161			−0.807926			−0.403963	−	0.914775i	$-0.632367\pi$
$853$	−689.161			−0.807926			−0.403963	+	0.914775i	$0.632367\pi$
$854$	19.4051	+	547.017i	0.0227227	+	0.640535i
$855$	90.3124	+	14.8869i	0.105629	+	0.0174116i
$856$	182.631	−	316.326i	0.213354	−	0.369540i
$857$	224.503	+	388.851i	0.261964	+	0.453735i	0.966764	−	0.255671i	$-0.0822964\pi$
$857$	224.503	+	388.851i	0.261964	+	0.453735i	−0.704800	+	0.709406i	$0.748963\pi$
$858$	−102.613	+	59.2436i	−0.119595	+	0.0690484i
$859$	73.3584	+	42.3535i	0.0853998	+	0.0493056i	0.542092	−	0.840319i	$-0.317633\pi$
$859$	73.3584	+	42.3535i	0.0853998	+	0.0493056i	−0.456692	+	0.889625i	$0.650966\pi$
$860$	−494.141	−	81.4532i	−0.574582	−	0.0947130i
$861$	476.053	−	16.8877i	0.552907	−	0.0196141i
$862$			345.898i			0.401274i
$863$	985.213	+	568.813i	1.14161	+	0.659111i	0.946830	−	0.321735i	$-0.104266\pi$
$863$	985.213	+	568.813i	1.14161	+	0.659111i	0.194784	+	0.980846i	$0.437599\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$	147.770	−	55.6597i	0.170832	−	0.0643465i
$866$	−133.427	−	77.0343i	−0.154073	−	0.0889541i
$867$	−222.587			−0.256733
$868$	−35.7262	−	57.1036i	−0.0411592	−	0.0657875i
$869$	378.783			0.435884
$870$	−265.545	+	323.737i	−0.305224	+	0.372111i
$871$	−993.009	+	573.314i	−1.14008	+	0.658225i
$872$	−380.842	+	219.879i	−0.436745	+	0.252155i
$873$	−175.331	+	303.681i	−0.200837	+	0.347860i
$874$		−	122.802i		−	0.140506i
$875$	725.829	−	488.668i	0.829519	−	0.558478i
$876$	330.202			0.376943
$877$	−374.693	−	216.329i	−0.427244	−	0.246669i	0.270928	−	0.962600i	$-0.412670\pi$
$877$	−374.693	−	216.329i	−0.427244	−	0.246669i	−0.698172	+	0.715930i	$0.746003\pi$
$878$	−269.360	−	466.545i	−0.306788	−	0.531372i
$879$	238.097	+	412.396i	0.270873	+	0.469165i
$880$	−45.2498	−	37.1162i	−0.0514202	−	0.0421775i
$881$		−	821.955i		−	0.932979i	−0.884527	−	0.466490i	$-0.845519\pi$
$881$		−	821.955i		−	0.932979i	0.884527	−	0.466490i	$-0.154481\pi$
$882$	186.950	+	90.9260i	0.211962	+	0.103091i
$883$		−	1084.85i		−	1.22859i	−0.789076	−	0.614295i	$-0.789440\pi$
$883$		−	1084.85i		−	1.22859i	0.789076	−	0.614295i	$-0.210560\pi$
$884$	−337.769	+	585.032i	−0.382091	+	0.661801i
$885$	−110.124	−	292.366i	−0.124434	−	0.330358i
$886$	35.6201	+	61.6958i	0.0402033	+	0.0696341i
$887$	−346.129	+	599.513i	−0.390225	+	0.675889i	−0.992479	−	0.122415i	$-0.960936\pi$
$887$	−346.129	+	599.513i	−0.390225	+	0.675889i	0.602254	+	0.798304i	$0.294269\pi$
$888$	217.311			0.244719
$889$	80.3278	−	151.276i	0.0903575	−	0.170165i
$890$	114.127	−	692.355i	0.128232	−	0.777927i
$891$	−13.1681	+	22.8078i	−0.0147790	+	0.0255980i
$892$	−396.614	−	686.956i	−0.444635	−	0.770130i
$893$	−22.0051	+	12.7047i	−0.0246418	+	0.0142270i
$894$	274.601	+	158.541i	0.307160	+	0.177339i
$895$	71.7309	−	435.160i	0.0801463	−	0.486212i
$896$	42.0046	+	67.1388i	0.0468801	+	0.0749317i
$897$			407.436i			0.454221i
$898$	−294.525	−	170.044i	−0.327979	−	0.189359i
$899$	−142.451	+	82.2441i	−0.158455	+	0.0914840i
$900$	−29.3388	−	147.103i	−0.0325986	−	0.163448i
$901$	−1045.75	−	603.764i	−1.16065	−	0.670104i
$902$	162.590			0.180255
$903$	606.817	−	21.5265i	0.672001	−	0.0238389i
$904$	431.092			0.476872
$905$	−986.720	+	1202.95i	−1.09030	+	1.32922i
$906$	−379.363	+	219.025i	−0.418722	+	0.241750i
$907$	1.22539	−	0.707477i	0.00135103	−	0.000780019i	−0.499324	−	0.866415i	$-0.666418\pi$
$907$	1.22539	−	0.707477i	0.00135103	−	0.000780019i	0.500675	+	0.865635i	$0.333085\pi$
$908$	363.810	−	630.138i	0.400672	−	0.693984i
$909$			543.603i			0.598023i
$910$	−104.372	+	811.533i	−0.114695	+	0.891794i
$911$	−1493.48			−1.63939			−0.819693	−	0.572803i	$-0.805856\pi$
$911$	−1493.48			−1.63939			−0.819693	+	0.572803i	$0.805856\pi$
$912$	−36.6125	−	21.1382i	−0.0401453	−	0.0231779i
$913$	−8.67509	−	15.0257i	−0.00950174	−	0.0164575i
$914$	−484.054	−	838.406i	−0.529599	−	0.917293i
$915$	−303.679	+	370.227i	−0.331890	+	0.404620i
$916$			768.495i			0.838969i
$917$	−167.540	−	267.791i	−0.182705	−	0.292029i
$918$			150.152i			0.163564i
$919$	−682.102	+	1181.44i	−0.742222	+	1.28557i	0.209259	+	0.977860i	$0.432895\pi$
$919$	−682.102	+	1181.44i	−0.742222	+	1.28557i	−0.951481	+	0.307707i	$0.900438\pi$
$920$	−188.330	+	70.9373i	−0.204706	+	0.0771057i
$921$	−418.676	−	725.168i	−0.454589	−	0.787370i
$922$	−358.345	+	620.672i	−0.388661	+	0.673180i
$923$	−1821.96			−1.97395
$924$	62.6702	+	33.2779i	0.0678249	+	0.0360151i
$925$	−355.926	+	1050.29i	−0.384785	+	1.13545i
$926$	−117.843	+	204.111i	−0.127261	+	0.220422i
$927$	79.6127	+	137.893i	0.0858821	+	0.148752i
$928$	167.485	−	96.6974i	0.180479	−	0.104200i
$929$	−289.555	−	167.174i	−0.311684	−	0.179951i	0.335996	−	0.941863i	$-0.390927\pi$
$929$	−289.555	−	167.174i	−0.311684	−	0.179951i	−0.647680	+	0.761913i	$0.724261\pi$
$930$	9.58400	−	58.1419i	0.0103054	−	0.0625182i
$931$	21.1872	+	298.250i	0.0227575	+	0.320355i
$932$		−	615.751i		−	0.660677i
$933$	−299.717	−	173.042i	−0.321240	−	0.185468i
$934$	−112.209	+	64.7839i	−0.120138	+	0.0693618i
$935$	−279.772	+	105.380i	−0.299222	+	0.112706i
$936$	121.474	+	70.1329i	0.129780	+	0.0749283i
$937$	−1080.69			−1.15335			−0.576675	−	0.816974i	$-0.695650\pi$
$937$	−1080.69			−1.15335			−0.576675	+	0.816974i	$0.695650\pi$
$938$	606.475	+	322.038i	0.646561	+	0.343324i
$939$	311.048			0.331255
$940$	32.1953	+	26.4082i	0.0342503	+	0.0280938i
$941$	1485.04	−	857.386i	1.57815	−	0.911143i	0.583028	−	0.812452i	$-0.301868\pi$
$941$	1485.04	−	857.386i	1.57815	−	0.911143i	0.995118	−	0.0986908i	$-0.0314655\pi$
$942$	52.8287	−	30.5007i	0.0560814	−	0.0323786i
$943$	279.546	−	484.188i	0.296443	−	0.513455i
$944$			144.300i			0.152860i
$945$	70.0990	+	167.813i	0.0741788	+	0.177580i
$946$	207.251			0.219082
$947$	−953.823	−	550.690i	−1.00720	−	0.581510i	−0.0968327	−	0.995301i	$-0.530871\pi$
$947$	−953.823	−	550.690i	−1.00720	−	0.581510i	−0.910372	+	0.413791i	$0.864205\pi$
$948$	−224.203	−	388.330i	−0.236501	−	0.409631i
$949$	−787.852	−	1364.60i	−0.830191	−	1.43793i
$950$	162.130	−	142.331i	0.170663	−	0.149822i
$951$		−	655.543i		−	0.689320i
$952$	404.300	−	14.3423i	0.424685	−	0.0150655i
$953$		−	15.8556i		−	0.0166375i	−0.999965	−	0.00831877i	$-0.997352\pi$
$953$		−	15.8556i		−	0.0166375i	0.999965	−	0.00831877i	$-0.00264798\pi$
$954$	−125.363	+	217.135i	−0.131408	+	0.227605i
$955$	1419.70	−	534.750i	1.48659	−	0.559948i
$956$	227.991	+	394.892i	0.238485	+	0.413067i
$957$	86.6384	−	150.062i	0.0905313	−	0.156805i
$958$	1068.37			1.11521
$959$	−808.375	+	28.6767i	−0.842935	+	0.0299027i
$960$	−11.2683	+	68.3595i	−0.0117378	+	0.0712079i
$961$	−468.926	+	812.203i	−0.487956	+	0.845164i
$962$	−518.496	−	898.062i	−0.538978	−	0.933537i
$963$	−335.515	+	193.709i	−0.348406	+	0.201152i
$964$	605.248	+	349.440i	0.627851	+	0.362490i
$965$	−1137.78	−	187.550i	−1.17905	−	0.194352i
$966$	206.851	−	129.414i	0.214131	−	0.133969i
$967$		−	480.848i		−	0.497257i	−0.968599	−	0.248629i	$-0.920020\pi$
$967$		−	480.848i		−	0.497257i	0.968599	−	0.248629i	$-0.0799798\pi$
$968$	−275.414	−	159.010i	−0.284518	−	0.164267i
$969$	−187.026	+	107.980i	−0.193010	+	0.111434i
$970$	291.338	+	773.467i	0.300349	+	0.797389i
$971$	−724.706	−	418.409i	−0.746350	−	0.430906i	0.0780234	−	0.996952i	$-0.475139\pi$
$971$	−724.706	−	418.409i	−0.746350	−	0.430906i	−0.824374	+	0.566046i	$0.808472\pi$
$972$	31.1769			0.0320750
$973$	−49.2990	+	92.8418i	−0.0506670	+	0.0954181i
$974$	1120.59			1.15050
$975$	−537.919	+	472.229i	−0.551711	+	0.484337i
$976$	191.537	−	110.584i	0.196246	−	0.113303i
$977$	598.545	−	345.570i	0.612635	−	0.353705i	−0.161361	−	0.986895i	$-0.551588\pi$
$977$	598.545	−	345.570i	0.612635	−	0.353705i	0.773996	+	0.633190i	$0.218255\pi$
$978$	60.5083	−	104.803i	0.0618694	−	0.107161i
$979$			290.386i			0.296615i
$980$	445.158	−	204.778i	0.454243	−	0.208957i
$981$	466.434			0.475468
$982$	−270.845	−	156.372i	−0.275809	−	0.159239i
$983$	−313.474	−	542.954i	−0.318896	−	0.552343i	0.661362	−	0.750067i	$-0.269979\pi$
$983$	−313.474	−	542.954i	−0.318896	−	0.552343i	−0.980258	+	0.197723i	$0.936645\pi$
$984$	−96.2377	−	166.689i	−0.0978026	−	0.169399i
$985$	676.309	−	824.515i	0.686608	−	0.837071i
$986$		−	987.913i		−	1.00194i
$987$	−44.5900	−	23.6773i	−0.0451773	−	0.0239891i
$988$			201.741i			0.204191i
$989$	356.333	−	617.186i	0.360296	−	0.624051i
$990$	21.8808	+	58.0907i	0.0221018	+	0.0586775i
$991$	18.7051	+	32.3982i	0.0188750	+	0.0326925i	0.875309	−	0.483565i	$-0.160658\pi$
$991$	18.7051	+	32.3982i	0.0188750	+	0.0326925i	−0.856434	+	0.516257i	$0.827325\pi$
$992$	−13.6085	+	23.5706i	−0.0137182	+	0.0237607i
$993$	247.195			0.248938
$994$	578.708	+	924.988i	0.582201	+	0.930571i
$995$	1792.93	+	295.542i	1.80193	+	0.297027i
$996$	−10.2696	+	17.7875i	−0.0103109	+	0.0178589i
$997$	409.793	+	709.782i	0.411026	+	0.711918i	0.995002	−	0.0998531i	$-0.0318373\pi$
$997$	409.793	+	709.782i	0.411026	+	0.711918i	−0.583976	+	0.811771i	$0.698504\pi$
$998$	−1140.40	+	658.411i	−1.14269	+	0.659730i
$999$	−199.613	−	115.246i	−0.199812	−	0.115362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.p.a.19.5	✓	32
3.2	odd	2		630.3.bc.b.19.13		32
5.2	odd	4		1050.3.p.h.901.6		16
5.3	odd	4		1050.3.p.g.901.3		16
5.4	even	2	inner	210.3.p.a.19.10	yes	32
7.2	even	3		1470.3.h.a.979.16		32
7.3	odd	6	inner	210.3.p.a.199.10	yes	32
7.5	odd	6		1470.3.h.a.979.14		32
15.14	odd	2		630.3.bc.b.19.2		32
21.17	even	6		630.3.bc.b.199.2		32
35.3	even	12		1050.3.p.g.451.3		16
35.9	even	6		1470.3.h.a.979.13		32
35.17	even	12		1050.3.p.h.451.6		16
35.19	odd	6		1470.3.h.a.979.15		32
35.24	odd	6	inner	210.3.p.a.199.5	yes	32
105.59	even	6		630.3.bc.b.199.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.p.a.19.5	✓	32	1.1	even	1	trivial
210.3.p.a.19.10	yes	32	5.4	even	2	inner
210.3.p.a.199.5	yes	32	35.24	odd	6	inner
210.3.p.a.199.10	yes	32	7.3	odd	6	inner
630.3.bc.b.19.2		32	15.14	odd	2
630.3.bc.b.19.13		32	3.2	odd	2
630.3.bc.b.199.2		32	21.17	even	6
630.3.bc.b.199.13		32	105.59	even	6
1050.3.p.g.451.3		16	35.3	even	12
1050.3.p.g.901.3		16	5.3	odd	4
1050.3.p.h.451.6		16	35.17	even	12
1050.3.p.h.901.6		16	5.2	odd	4
1470.3.h.a.979.13		32	35.9	even	6
1470.3.h.a.979.14		32	7.5	odd	6
1470.3.h.a.979.15		32	35.19	odd	6
1470.3.h.a.979.16		32	7.2	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.86586 - 3.17098i) q^{5} -2.44949i q^{6} +(6.18245 + 3.28288i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.86586 - 3.17098i) q^{5} -2.44949i q^{6} +(6.18245 + 3.28288i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.49248 + 6.61722i) q^{10} +(-1.46312 - 2.53420i) q^{11} +(-1.73205 + 3.00000i) q^{12} +16.5305 q^{13} +(-5.25058 - 8.39235i) q^{14} +(1.40853 - 8.54494i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(10.2165 + 17.6956i) q^{17} +(3.67423 - 2.12132i) q^{18} +(5.28456 + 3.05104i) q^{19} +(1.62643 - 9.86685i) q^{20} +(0.429835 + 12.1167i) q^{21} +4.13833i q^{22} +(12.3238 + 7.11514i) q^{23} +(4.24264 - 2.44949i) q^{24} +(4.88979 + 24.5171i) q^{25} +(-20.2456 - 11.6888i) q^{26} -5.19615 q^{27} +(0.496330 + 13.9912i) q^{28} +34.1877 q^{29} +(-7.76728 + 9.46939i) q^{30} +(-4.16673 + 2.40566i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.53420 - 4.38936i) q^{33} -28.8967i q^{34} +(-13.4906 - 32.2956i) q^{35} -6.00000 q^{36} +(38.4155 + 22.1792i) q^{37} +(-4.31482 - 7.47349i) q^{38} +(14.3158 + 24.7957i) q^{39} +(-8.96888 + 10.9343i) q^{40} -39.2889i q^{41} +(8.04139 - 15.1438i) q^{42} -50.0809i q^{43} +(2.92624 - 5.06840i) q^{44} +(14.0372 - 5.28734i) q^{45} +(-10.0623 - 17.4285i) q^{46} +(-2.08202 + 3.60617i) q^{47} -6.92820 q^{48} +(27.4454 + 40.5925i) q^{49} +(11.3475 - 33.4848i) q^{50} +(-17.6956 + 30.6496i) q^{51} +(16.5305 + 28.6316i) q^{52} +(-51.1793 + 29.5484i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-2.37967 + 14.4364i) q^{55} +(9.28539 - 17.4866i) q^{56} +10.5691i q^{57} +(-41.8712 - 24.1743i) q^{58} +(31.2419 - 18.0375i) q^{59} +(16.2088 - 6.10529i) q^{60} +(-47.8841 - 27.6459i) q^{61} +6.80425 q^{62} +(-17.8029 + 11.1382i) q^{63} -8.00000 q^{64} +(-63.9046 - 52.4178i) q^{65} +(-6.20750 + 3.58390i) q^{66} +(-60.0714 + 34.6822i) q^{67} +(-20.4331 + 35.3911i) q^{68} +24.6476i q^{69} +(-6.31394 + 49.0931i) q^{70} -110.218 q^{71} +(7.34847 + 4.24264i) q^{72} +(-47.6606 - 82.5505i) q^{73} +(-31.3661 - 54.3277i) q^{74} +(-32.5410 + 28.5672i) q^{75} +12.2042i q^{76} +(-0.726191 - 20.4708i) q^{77} -40.4912i q^{78} +(-64.7217 + 112.101i) q^{79} +(18.7163 - 7.04979i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.7814 + 48.1189i) q^{82} +5.92917 q^{83} +(-20.5570 + 12.8612i) q^{84} +(16.6165 - 100.805i) q^{85} +(-35.4125 + 61.3363i) q^{86} +(29.6074 + 51.2815i) q^{87} +(-7.16780 + 4.13833i) q^{88} +(-85.9402 - 49.6176i) q^{89} +(-20.9307 - 3.45018i) q^{90} +(102.199 + 54.2676i) q^{91} +28.4606i q^{92} +(-7.21699 - 4.16673i) q^{93} +(5.09990 - 2.94443i) q^{94} +(-10.7546 - 28.5521i) q^{95} +(8.48528 + 4.89898i) q^{96} +116.887 q^{97} +(-4.91033 - 69.1223i) q^{98} +8.77872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Introduction

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