LMFDB - Embedded newform 32.3.h.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,3,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	32.19
Dual form			32.3.h.a.27.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82416 - 0.820030i) q^{2} +(-0.374985 - 0.155324i) q^{3} +(2.65510 - 2.99173i) q^{4} +(-7.60625 + 3.15061i) q^{5} +(-0.811401 + 0.0241638i) q^{6} +(6.84161 + 6.84161i) q^{7} +(2.39002 - 7.63465i) q^{8} +(-6.24747 - 6.24747i) q^{9} +O(q^{10})$	\(q+(1.82416 - 0.820030i) q^{2} +(-0.374985 - 0.155324i) q^{3} +(2.65510 - 2.99173i) q^{4} +(-7.60625 + 3.15061i) q^{5} +(-0.811401 + 0.0241638i) q^{6} +(6.84161 + 6.84161i) q^{7} +(2.39002 - 7.63465i) q^{8} +(-6.24747 - 6.24747i) q^{9} +(-11.2914 + 11.9846i) q^{10} +(-2.23818 + 0.927086i) q^{11} +(-1.46031 + 0.709452i) q^{12} +(1.40964 + 0.583890i) q^{13} +(18.0905 + 6.86984i) q^{14} +3.34159 q^{15} +(-1.90088 - 15.8867i) q^{16} +2.67812i q^{17} +(-16.5195 - 6.27326i) q^{18} +(5.38908 - 13.0104i) q^{19} +(-10.7696 + 31.1210i) q^{20} +(-1.50283 - 3.62816i) q^{21} +(-3.32256 + 3.52653i) q^{22} +(18.8388 - 18.8388i) q^{23} +(-2.08206 + 2.49165i) q^{24} +(30.2510 - 30.2510i) q^{25} +(3.05020 - 0.0908360i) q^{26} +(2.77024 + 6.68795i) q^{27} +(38.6334 - 2.30307i) q^{28} +(-10.0298 + 24.2140i) q^{29} +(6.09559 - 2.74021i) q^{30} +47.5858i q^{31} +(-16.4951 - 27.4210i) q^{32} +0.983283 q^{33} +(2.19614 + 4.88532i) q^{34} +(-73.5942 - 30.4837i) q^{35} +(-35.2784 + 2.10307i) q^{36} +(-28.2682 + 11.7091i) q^{37} +(-0.838382 - 28.1522i) q^{38} +(-0.437900 - 0.437900i) q^{39} +(5.87475 + 65.6010i) q^{40} +(6.93962 + 6.93962i) q^{41} +(-5.71661 - 5.38597i) q^{42} +(8.48982 - 3.51660i) q^{43} +(-3.16902 + 9.15755i) q^{44} +(67.2032 + 27.8365i) q^{45} +(18.9165 - 49.8132i) q^{46} -67.0112 q^{47} +(-1.75478 + 6.25251i) q^{48} +44.6152i q^{49} +(30.3759 - 79.9893i) q^{50} +(0.415976 - 1.00426i) q^{51} +(5.48956 - 2.66696i) q^{52} +(-10.5006 - 25.3507i) q^{53} +(10.5377 + 9.92819i) q^{54} +(14.1033 - 14.1033i) q^{55} +(68.5848 - 35.8817i) q^{56} +(-4.04165 + 4.04165i) q^{57} +(1.56034 + 52.3950i) q^{58} +(27.9364 + 67.4445i) q^{59} +(8.87226 - 9.99714i) q^{60} +(31.5752 - 76.2294i) q^{61} +(39.0218 + 86.8040i) q^{62} -85.4855i q^{63} +(-52.5757 - 36.4938i) q^{64} -12.5616 q^{65} +(1.79366 - 0.806322i) q^{66} +(90.1903 + 37.3580i) q^{67} +(8.01222 + 7.11069i) q^{68} +(-9.99035 + 4.13814i) q^{69} +(-159.245 + 4.74236i) q^{70} +(1.98379 + 1.98379i) q^{71} +(-62.6288 + 32.7657i) q^{72} +(-55.5273 - 55.5273i) q^{73} +(-41.9639 + 44.5400i) q^{74} +(-16.0424 + 6.64496i) q^{75} +(-24.6150 - 50.6666i) q^{76} +(-21.6555 - 8.97002i) q^{77} +(-1.15789 - 0.439707i) q^{78} +10.9856 q^{79} +(64.5113 + 114.849i) q^{80} +76.5792i q^{81} +(18.3496 + 6.96826i) q^{82} +(34.1779 - 82.5128i) q^{83} +(-14.8447 - 5.13707i) q^{84} +(-8.43772 - 20.3705i) q^{85} +(12.6031 - 13.3767i) q^{86} +(7.52203 - 7.52203i) q^{87} +(1.72868 + 19.3035i) q^{88} +(-16.1705 + 16.1705i) q^{89} +(145.416 - 4.33053i) q^{90} +(5.64942 + 13.6389i) q^{91} +(-6.34164 - 106.379i) q^{92} +(7.39121 - 17.8440i) q^{93} +(-122.239 + 54.9512i) q^{94} +115.939i q^{95} +(1.92626 + 12.8445i) q^{96} -62.6434 q^{97} +(36.5858 + 81.3851i) q^{98} +(19.7749 + 8.19105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

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 $

$2$	1.82416	−	0.820030i	0.912079	−	0.410015i
$2$	1.82416	−	0.820030i	0.912079	−	0.410015i
$3$	−0.374985	−	0.155324i	−0.124995	−	0.0517746i	0.319309	−	0.947651i	$-0.396549\pi$
$3$	−0.374985	−	0.155324i	−0.124995	−	0.0517746i	−0.444304	+	0.895876i	$0.646549\pi$
$4$	2.65510	−	2.99173i	0.663775	−	0.747932i
$5$	−7.60625	+	3.15061i	−1.52125	+	0.630122i	−0.977842	−	0.209346i	$-0.932866\pi$
$5$	−7.60625	+	3.15061i	−1.52125	+	0.630122i	−0.543408	+	0.839469i	$0.682866\pi$
$6$	−0.811401	+	0.0241638i	−0.135234	+	0.00402730i
$7$	6.84161	+	6.84161i	0.977372	+	0.977372i	0.999750	−	0.0223772i	$-0.00712349\pi$
$7$	6.84161	+	6.84161i	0.977372	+	0.977372i	−0.0223772	+	0.999750i	$0.507123\pi$
$8$	2.39002	−	7.63465i	0.298752	−	0.954331i
$9$	−6.24747	−	6.24747i	−0.694164	−	0.694164i
$10$	−11.2914	+	11.9846i	−1.12914	+	1.19846i
$11$	−2.23818	+	0.927086i	−0.203471	+	0.0842806i	−0.482092	−	0.876121i	$-0.660123\pi$
$11$	−2.23818	+	0.927086i	−0.203471	+	0.0842806i	0.278621	+	0.960401i	$0.410123\pi$
$12$	−1.46031	+	0.709452i	−0.121692	+	0.0591210i
$13$	1.40964	+	0.583890i	0.108433	+	0.0449146i	0.436241	−	0.899830i	$-0.356310\pi$
$13$	1.40964	+	0.583890i	0.108433	+	0.0449146i	−0.327807	+	0.944745i	$0.606310\pi$
$14$	18.0905	+	6.86984i	1.29218	+	0.490703i
$15$	3.34159			0.222773
$16$	−1.90088	−	15.8867i	−0.118805	−	0.992918i
$17$			2.67812i			0.157537i	0.996893	+	0.0787683i	$0.0250987\pi$
$17$			2.67812i			0.157537i	−0.996893	+	0.0787683i	$0.974901\pi$
$18$	−16.5195	−	6.27326i	−0.917749	−	0.348514i
$19$	5.38908	−	13.0104i	0.283636	−	0.684757i	−0.716279	−	0.697814i	$-0.754156\pi$
$19$	5.38908	−	13.0104i	0.283636	−	0.684757i	0.999915	+	0.0130566i	$0.00415616\pi$
$20$	−10.7696	+	31.1210i	−0.538479	+	1.55605i
$21$	−1.50283	−	3.62816i	−0.0715635	−	0.172770i
$22$	−3.32256	+	3.52653i	−0.151026	+	0.160297i
$23$	18.8388	−	18.8388i	0.819076	−	0.819076i	−0.166898	−	0.985974i	$-0.553375\pi$
$23$	18.8388	−	18.8388i	0.819076	−	0.819076i	0.985974	+	0.166898i	$0.0533750\pi$
$24$	−2.08206	+	2.49165i	−0.0867525	+	0.103819i
$25$	30.2510	−	30.2510i	1.21004	−	1.21004i
$26$	3.05020	−	0.0908360i	0.117316	−	0.00349369i
$27$	2.77024	+	6.68795i	0.102601	+	0.247702i
$28$	38.6334	−	2.30307i	1.37976	−	0.0822525i
$29$	−10.0298	+	24.2140i	−0.345855	+	0.834967i	0.651245	+	0.758867i	$0.274247\pi$
$29$	−10.0298	+	24.2140i	−0.345855	+	0.834967i	−0.997100	+	0.0761000i	$0.975753\pi$
$30$	6.09559	−	2.74021i	0.203186	−	0.0913402i
$31$			47.5858i			1.53503i	0.641033	+	0.767513i	$0.278506\pi$
$31$			47.5858i			1.53503i	−0.641033	+	0.767513i	$0.721494\pi$
$32$	−16.4951	−	27.4210i	−0.515470	−	0.856907i
$33$	0.983283			0.0297965
$34$	2.19614	+	4.88532i	0.0645924	+	0.143686i
$35$	−73.5942	−	30.4837i	−2.10269	−	0.870963i
$36$	−35.2784	+	2.10307i	−0.979956	+	0.0584186i
$37$	−28.2682	+	11.7091i	−0.764006	+	0.316462i	−0.730442	−	0.682975i	$-0.760686\pi$
$37$	−28.2682	+	11.7091i	−0.764006	+	0.316462i	−0.0335642	+	0.999437i	$0.510686\pi$
$38$	−0.838382	−	28.1522i	−0.0220627	−	0.740848i
$39$	−0.437900	−	0.437900i	−0.0112282	−	0.0112282i
$40$	5.87475	+	65.6010i	0.146869	+	1.64003i
$41$	6.93962	+	6.93962i	0.169259	+	0.169259i	0.786654	−	0.617395i	$-0.211812\pi$
$41$	6.93962	+	6.93962i	0.169259	+	0.169259i	−0.617395	+	0.786654i	$0.711812\pi$
$42$	−5.71661	−	5.38597i	−0.136110	−	0.128237i
$43$	8.48982	−	3.51660i	0.197438	−	0.0817814i	−0.281774	−	0.959481i	$-0.590923\pi$
$43$	8.48982	−	3.51660i	0.197438	−	0.0817814i	0.479211	+	0.877700i	$0.340923\pi$
$44$	−3.16902	+	9.15755i	−0.0720231	+	0.208126i
$45$	67.2032	+	27.8365i	1.49340	+	0.618588i
$46$	18.9165	−	49.8132i	0.411228	−	1.08290i
$47$	−67.0112			−1.42577			−0.712885	−	0.701281i	$-0.752612\pi$
$47$	−67.0112			−1.42577			−0.712885	+	0.701281i	$0.752612\pi$
$48$	−1.75478	+	6.25251i	−0.0365579	+	0.130261i
$49$			44.6152i			0.910513i
$50$	30.3759	−	79.9893i	0.607517	−	1.59979i
$51$	0.415976	−	1.00426i	0.00815639	−	0.0196913i
$52$	5.48956	−	2.66696i	0.105569	−	0.0512877i
$53$	−10.5006	−	25.3507i	−0.198124	−	0.478315i	0.793326	−	0.608797i	$-0.208347\pi$
$53$	−10.5006	−	25.3507i	−0.198124	−	0.478315i	−0.991451	+	0.130482i	$0.958347\pi$
$54$	10.5377	+	9.92819i	0.195142	+	0.183855i
$55$	14.1033	−	14.1033i	0.256424	−	0.256424i
$56$	68.5848	−	35.8817i	1.22473	−	0.640745i
$57$	−4.04165	+	4.04165i	−0.0709061	+	0.0709061i
$58$	1.56034	+	52.3950i	0.0269024	+	0.903361i
$59$	27.9364	+	67.4445i	0.473499	+	1.14313i	0.962606	+	0.270904i	$0.0873227\pi$
$59$	27.9364	+	67.4445i	0.473499	+	1.14313i	−0.489107	+	0.872224i	$0.662677\pi$
$60$	8.87226	−	9.99714i	0.147871	−	0.166619i
$61$	31.5752	−	76.2294i	0.517627	−	1.24966i	−0.421730	−	0.906721i	$-0.638577\pi$
$61$	31.5752	−	76.2294i	0.517627	−	1.24966i	0.939357	−	0.342941i	$-0.111423\pi$
$62$	39.0218	+	86.8040i	0.629384	+	1.40006i
$63$		−	85.4855i		−	1.35691i
$64$	−52.5757	−	36.4938i	−0.821495	−	0.570216i
$65$	−12.5616			−0.193256
$66$	1.79366	−	0.806322i	0.0271767	−	0.0122170i
$67$	90.1903	+	37.3580i	1.34612	+	0.557583i	0.935211	−	0.354092i	$-0.115210\pi$
$67$	90.1903	+	37.3580i	1.34612	+	0.557583i	0.410913	+	0.911674i	$0.365210\pi$
$68$	8.01222	+	7.11069i	0.117827	+	0.104569i
$69$	−9.99035	+	4.13814i	−0.144788	+	0.0599730i
$70$	−159.245	+	4.74236i	−2.27493	+	0.0677481i
$71$	1.98379	+	1.98379i	0.0279407	+	0.0279407i	0.720939	−	0.692998i	$-0.243711\pi$
$71$	1.98379	+	1.98379i	0.0279407	+	0.0279407i	−0.692998	+	0.720939i	$0.743711\pi$
$72$	−62.6288	+	32.7657i	−0.869844	+	0.455079i
$73$	−55.5273	−	55.5273i	−0.760648	−	0.760648i	0.215792	−	0.976439i	$-0.430767\pi$
$73$	−55.5273	−	55.5273i	−0.760648	−	0.760648i	−0.976439	+	0.215792i	$0.930767\pi$
$74$	−41.9639	+	44.5400i	−0.567080	+	0.601892i
$75$	−16.0424	+	6.64496i	−0.213898	+	0.0885995i
$76$	−24.6150	−	50.6666i	−0.323882	−	0.666665i
$77$	−21.6555	−	8.97002i	−0.281241	−	0.116494i
$78$	−1.15789	−	0.439707i	−0.0148447	−	0.00563727i
$79$	10.9856			0.139058			0.0695292	−	0.997580i	$-0.477850\pi$
$79$	10.9856			0.139058			0.0695292	+	0.997580i	$0.477850\pi$
$80$	64.5113	+	114.849i	0.806391	+	1.43561i
$81$			76.5792i			0.945422i
$82$	18.3496	+	6.96826i	0.223776	+	0.0849788i
$83$	34.1779	−	82.5128i	0.411782	−	0.994130i	−0.572877	−	0.819641i	$-0.694173\pi$
$83$	34.1779	−	82.5128i	0.411782	−	0.994130i	0.984659	−	0.174489i	$-0.0558272\pi$
$84$	−14.8447	−	5.13707i	−0.176722	−	0.0611555i
$85$	−8.43772	−	20.3705i	−0.0992674	−	0.239653i
$86$	12.6031	−	13.3767i	0.146547	−	0.155543i
$87$	7.52203	−	7.52203i	0.0864602	−	0.0864602i
$88$	1.72868	+	19.3035i	0.0196441	+	0.219358i
$89$	−16.1705	+	16.1705i	−0.181691	+	0.181691i	−0.792093	−	0.610401i	$-0.791008\pi$
$89$	−16.1705	+	16.1705i	−0.181691	+	0.181691i	0.610401	+	0.792093i	$0.291008\pi$
$90$	145.416	−	4.33053i	1.61573	−	0.0481170i
$91$	5.64942	+	13.6389i	0.0620816	+	0.149878i
$92$	−6.34164	−	106.379i	−0.0689308	−	1.15630i
$93$	7.39121	−	17.8440i	0.0794754	−	0.191870i
$94$	−122.239	+	54.9512i	−1.30042	+	0.584587i
$95$			115.939i			1.22041i
$96$	1.92626	+	12.8445i	0.0200652	+	0.133797i
$97$	−62.6434			−0.645808			−0.322904	−	0.946432i	$-0.604659\pi$
$97$	−62.6434			−0.645808			−0.322904	+	0.946432i	$0.604659\pi$
$98$	36.5858	+	81.3851i	0.373324	+	0.830460i
$99$	19.7749	+	8.19105i	0.199747	+	0.0827379i
$100$	−10.1833	−	170.822i	−0.101833	−	1.70822i
$101$	39.7340	−	16.4584i	0.393406	−	0.162954i	−0.177206	−	0.984174i	$-0.556706\pi$
$101$	39.7340	−	16.4584i	0.393406	−	0.162954i	0.570612	+	0.821220i	$0.306706\pi$
$102$	−0.0647136	−	2.17303i	−0.000634447	−	0.0213042i
$103$	−36.3254	−	36.3254i	−0.352674	−	0.352674i	0.508430	−	0.861104i	$-0.330226\pi$
$103$	−36.3254	−	36.3254i	−0.352674	−	0.352674i	−0.861104	+	0.508430i	$0.830226\pi$
$104$	7.82684	−	9.36656i	0.0752581	−	0.0900631i
$105$	22.8619	+	22.8619i	0.217732	+	0.217732i
$106$	−39.9431	−	37.6328i	−0.376821	−	0.355027i
$107$	111.798	−	46.3084i	1.04484	−	0.432789i	0.206796	−	0.978384i	$-0.433696\pi$
$107$	111.798	−	46.3084i	1.04484	−	0.432789i	0.838049	+	0.545596i	$0.183696\pi$
$108$	27.3638	+	9.46938i	0.253368	+	0.0876794i
$109$	−55.7631	−	23.0978i	−0.511588	−	0.211907i	0.111929	−	0.993716i	$-0.464297\pi$
$109$	−55.7631	−	23.0978i	−0.511588	−	0.211907i	−0.623517	+	0.781809i	$0.714297\pi$
$110$	14.1615	−	37.2918i	0.128741	−	0.339016i
$111$	12.4189			0.111882
$112$	95.6854	−	121.695i	0.854334	−	1.08657i
$113$		−	80.7753i		−	0.714825i	−0.933947	−	0.357413i	$-0.883659\pi$
$113$		−	80.7753i		−	0.714825i	0.933947	−	0.357413i	$-0.116341\pi$
$114$	−4.05833	+	10.6869i	−0.0355994	+	0.0937445i
$115$	−83.9387	+	202.646i	−0.729901	+	1.76214i
$116$	45.8118	+	94.2971i	0.394929	+	0.812906i
$117$	−5.15882	−	12.4545i	−0.0440925	−	0.106449i
$118$	106.267	+	100.121i	0.900568	+	0.848481i
$119$	−18.3227	+	18.3227i	−0.153972	+	0.153972i
$120$	7.98646	−	25.5119i	0.0665538	−	0.212599i
$121$	−81.4099	+	81.4099i	−0.672809	+	0.672809i
$122$	−4.91217	−	164.947i	−0.0402637	−	1.35203i
$123$	−1.52436	−	3.68014i	−0.0123932	−	0.0299198i
$124$	142.364	+	126.345i	1.14810	+	1.01891i
$125$	−56.0222	+	135.250i	−0.448178	+	1.08200i
$126$	−70.1007	−	155.939i	−0.556355	−	1.23761i
$127$		−	143.036i		−	1.12627i	−0.826365	−	0.563135i	$-0.809595\pi$
$127$		−	143.036i		−	1.12627i	0.826365	−	0.563135i	$-0.190405\pi$
$128$	−125.832	−	23.4569i	−0.983065	−	0.183257i
$129$	−3.72976			−0.0289129
$130$	−22.9144	+	10.3009i	−0.176265	+	0.0792379i
$131$	−56.1430	−	23.2552i	−0.428573	−	0.177521i	0.157961	−	0.987445i	$-0.449508\pi$
$131$	−56.1430	−	23.2552i	−0.428573	−	0.177521i	−0.586534	+	0.809925i	$0.699508\pi$
$132$	2.61072	−	2.94172i	0.0197782	−	0.0222857i
$133$	125.882	−	52.1420i	0.946481	−	0.392045i
$134$	195.156	−	5.81181i	1.45639	−	0.0433717i
$135$	−42.1423	−	42.1423i	−0.312165	−	0.312165i
$136$	20.4465	+	6.40075i	0.150342	+	0.0470644i
$137$	168.165	+	168.165i	1.22748	+	1.22748i	0.964915	+	0.262563i	$0.0845679\pi$
$137$	168.165	+	168.165i	1.22748	+	1.22748i	0.262563	+	0.964915i	$0.415432\pi$
$138$	−14.8306	+	15.7410i	−0.107468	+	0.114065i
$139$	−97.5768	+	40.4176i	−0.701991	+	0.290774i	−0.704986	−	0.709221i	$-0.749047\pi$
$139$	−97.5768	+	40.4176i	−0.701991	+	0.290774i	0.00299484	+	0.999996i	$0.499047\pi$
$140$	−286.599	+	139.237i	−2.04714	+	0.994547i
$141$	25.1282	+	10.4084i	0.178214	+	0.0738187i
$142$	5.24551	+	1.99198i	0.0369402	+	0.0140280i
$143$	−3.69634			−0.0258485
$144$	−87.3759	+	111.127i	−0.606777	+	0.771717i
$145$		−	215.778i		−	1.48812i
$146$	−146.825	−	55.7565i	−1.00565	−	0.381894i
$147$	6.92979	−	16.7300i	0.0471415	−	0.113810i
$148$	−40.0246	+	115.660i	−0.270437	+	0.781484i
$149$	44.3735	+	107.127i	0.297809	+	0.718974i	0.999976	+	0.00696156i	$0.00221595\pi$
$149$	44.3735	+	107.127i	0.297809	+	0.718974i	−0.702167	+	0.712012i	$0.747784\pi$
$150$	−23.8147	+	25.2767i	−0.158765	+	0.168511i
$151$	−128.078	+	128.078i	−0.848200	+	0.848200i	−0.989908	−	0.141708i	$-0.954741\pi$
$151$	−128.078	+	128.078i	−0.848200	+	0.848200i	0.141708	+	0.989908i	$0.454741\pi$
$152$	−86.4498	−	72.2388i	−0.568748	−	0.475255i
$153$	16.7315	−	16.7315i	0.109356	−	0.109356i
$154$	−46.8588	+	1.39547i	−0.304278	+	0.00906149i
$155$	−149.924	−	361.950i	−0.967254	−	2.33516i
$156$	−2.47274	+	0.147409i	−0.0158509	+	0.000944929i
$157$	20.1590	−	48.6682i	0.128401	−	0.309988i	−0.846585	−	0.532254i	$-0.821345\pi$
$157$	20.1590	−	48.6682i	0.128401	−	0.309988i	0.974986	+	0.222265i	$0.0713452\pi$
$158$	20.0395	−	9.00854i	0.126832	−	0.0570161i
$159$			11.1371i			0.0700447i
$160$	211.859	+	156.602i	1.32412	+	0.978761i
$161$	257.775			1.60109
$162$	62.7972	+	139.692i	0.387637	+	0.862299i
$163$	68.6749	+	28.4461i	0.421319	+	0.174516i	0.583262	−	0.812284i	$-0.301776\pi$
$163$	68.6749	+	28.4461i	0.421319	+	0.174516i	−0.161943	+	0.986800i	$0.551776\pi$
$164$	39.1868	−	2.33606i	0.238944	−	0.0142443i
$165$	−7.47910	+	3.09794i	−0.0453279	+	0.0187754i
$166$	−5.31707	−	178.543i	−0.0320306	−	1.07556i
$167$	131.350	+	131.350i	0.786527	+	0.786527i	0.980923	−	0.194396i	$-0.0622748\pi$
$167$	131.350	+	131.350i	0.786527	+	0.786527i	−0.194396	+	0.980923i	$0.562275\pi$
$168$	−31.2915	+	2.80224i	−0.186259	+	0.0166800i
$169$	−117.855	−	117.855i	−0.697366	−	0.697366i
$170$	−32.0961	−	30.2398i	−0.188801	−	0.177881i
$171$	−114.950	+	47.6139i	−0.672223	+	0.278444i
$172$	12.0206	−	34.7362i	0.0698873	−	0.201954i
$173$	−206.045	−	85.3465i	−1.19101	−	0.493333i	−0.302926	−	0.953014i	$-0.597964\pi$
$173$	−206.045	−	85.3465i	−1.19101	−	0.493333i	−0.888084	+	0.459681i	$0.847964\pi$
$174$	7.55308	−	19.8897i	0.0434085	−	0.114308i
$175$	413.931			2.36532
$176$	18.9828	+	33.7950i	0.107857	+	0.192017i
$177$		−	29.6299i		−	0.167400i
$178$	−16.2373	+	42.7579i	−0.0912207	+	0.240213i
$179$	80.2014	−	193.623i	0.448053	−	1.08169i	−0.524998	−	0.851104i	$-0.675934\pi$
$179$	80.2014	−	193.623i	0.448053	−	1.08169i	0.973051	−	0.230591i	$-0.0740661\pi$
$180$	261.710	−	127.145i	1.45395	−	0.706361i
$181$	93.4345	+	225.571i	0.516213	+	1.24625i	0.940213	+	0.340586i	$0.110626\pi$
$181$	93.4345	+	225.571i	0.516213	+	1.24625i	−0.424000	+	0.905662i	$0.639374\pi$
$182$	21.4898	+	20.2468i	0.118076	+	0.111246i
$183$	−23.6805	+	23.6805i	−0.129401	+	0.129401i
$184$	−98.8023	−	188.852i	−0.536969	−	1.02637i
$185$	178.124	−	178.124i	0.962835	−	0.962835i
$186$	−1.14985	−	38.6112i	−0.00618201	−	0.207587i
$187$	−2.48285	−	5.99413i	−0.0132773	−	0.0320542i
$188$	−177.922	+	200.479i	−0.946391	+	1.06638i
$189$	−26.8034	+	64.7092i	−0.141817	+	0.342377i
$190$	95.0736	+	211.491i	0.500388	+	1.11311i
$191$		−	20.1639i		−	0.105570i	−0.998606	−	0.0527851i	$-0.983190\pi$
$191$		−	20.1639i		−	0.105570i	0.998606	−	0.0527851i	$-0.0168098\pi$
$192$	14.0467	+	21.8509i	0.0731599	+	0.113807i
$193$	115.896			0.600497			0.300248	−	0.953861i	$-0.402930\pi$
$193$	115.896			0.600497			0.300248	+	0.953861i	$0.402930\pi$
$194$	−114.271	+	51.3694i	−0.589028	+	0.264791i
$195$	4.71043	+	1.95112i	0.0241560	+	0.0100058i
$196$	133.476	+	118.458i	0.681002	+	0.604376i
$197$	−177.705	+	73.6077i	−0.902055	+	0.373643i	−0.785010	−	0.619483i	$-0.787342\pi$
$197$	−177.705	+	73.6077i	−0.902055	+	0.373643i	−0.117045	+	0.993127i	$0.537342\pi$
$198$	42.7895	−	1.27428i	0.216109	−	0.00643578i
$199$	−22.1763	−	22.1763i	−0.111439	−	0.111439i	0.649189	−	0.760627i	$-0.275109\pi$
$199$	−22.1763	−	22.1763i	−0.111439	−	0.111439i	−0.760627	+	0.649189i	$0.775109\pi$
$200$	−158.655	−	303.256i	−0.793277	−	1.51628i
$201$	−28.0174	−	28.0174i	−0.139390	−	0.139390i
$202$	58.9847	−	62.6057i	0.292003	−	0.309929i
$203$	−234.283	+	97.0431i	−1.15410	+	0.478045i
$204$	−1.90000	−	3.91089i	−0.00931373	−	0.0191710i
$205$	−74.6485	−	30.9204i	−0.364139	−	0.150831i
$206$	−96.0512	−	36.4753i	−0.466268	−	0.177065i
$207$	−235.389			−1.13715
$208$	6.59653	−	23.5043i	0.0317141	−	0.113002i
$209$			34.1158i			0.163233i
$210$	60.4510	+	22.9562i	0.287862	+	0.109315i
$211$	−116.936	+	282.308i	−0.554197	+	1.33795i	0.360103	+	0.932913i	$0.382742\pi$
$211$	−116.936	+	282.308i	−0.554197	+	1.33795i	−0.914300	+	0.405038i	$0.867258\pi$
$212$	−103.722	−	35.8937i	−0.489257	−	0.169310i
$213$	−0.435761	−	1.05202i	−0.00204583	−	0.00493906i
$214$	165.963	−	176.152i	0.775530	−	0.823139i
$215$	−53.4962	+	53.4962i	−0.248820	+	0.248820i
$216$	57.6811	−	5.16550i	0.267042	−	0.0239143i
$217$	−325.563	+	325.563i	−1.50029	+	1.50029i
$218$	−120.662	+	3.59334i	−0.553493	+	0.0164832i
$219$	12.1972	+	29.4466i	0.0556949	+	0.134459i
$220$	−4.74755	−	79.6389i	−0.0215798	−	0.361995i
$221$	−1.56373	+	3.77518i	−0.00707570	+	0.0170822i
$222$	22.6539	−	10.1838i	0.102045	−	0.0458731i
$223$			12.1409i			0.0544434i	0.999629	+	0.0272217i	$0.00866601\pi$
$223$			12.1409i			0.0544434i	−0.999629	+	0.0272217i	$0.991334\pi$
$224$	74.7512	−	300.457i	0.333711	−	1.34132i
$225$	−377.985			−1.67993
$226$	−66.2381	−	147.347i	−0.293089	−	0.651977i
$227$	215.118	+	89.1048i	0.947656	+	0.392532i	0.802350	−	0.596854i	$-0.203583\pi$
$227$	215.118	+	89.1048i	0.947656	+	0.392532i	0.145307	+	0.989387i	$0.453583\pi$
$228$	1.36053	+	22.8225i	0.00596723	+	0.100099i
$229$	85.4872	−	35.4100i	0.373307	−	0.154629i	−0.188139	−	0.982142i	$-0.560245\pi$
$229$	85.4872	−	35.4100i	0.373307	−	0.154629i	0.561445	+	0.827514i	$0.310245\pi$
$230$	13.0584	+	438.490i	0.0567755	+	1.90648i
$231$	6.72724	+	6.72724i	0.0291222	+	0.0291222i
$232$	160.894	+	134.446i	0.693510	+	0.579508i
$233$	33.1162	+	33.1162i	0.142129	+	0.142129i	0.774591	−	0.632462i	$-0.217956\pi$
$233$	33.1162	+	33.1162i	0.142129	+	0.142129i	−0.632462	+	0.774591i	$0.717956\pi$
$234$	−19.6236	−	18.4886i	−0.0838614	−	0.0790110i
$235$	509.704	−	211.126i	2.16895	−	0.898410i
$236$	275.950	+	95.4938i	1.16928	+	0.404635i
$237$	−4.11944	−	1.70633i	−0.0173816	−	0.00719970i
$238$	−18.3983	+	48.4486i	−0.0773037	+	0.203565i
$239$	332.992			1.39327			0.696636	−	0.717425i	$-0.254679\pi$
$239$	332.992			1.39327			0.696636	+	0.717425i	$0.254679\pi$
$240$	−6.35195	−	53.0868i	−0.0264665	−	0.221195i
$241$		−	218.867i		−	0.908160i	−0.890961	−	0.454080i	$-0.849968\pi$
$241$		−	218.867i		−	0.908160i	0.890961	−	0.454080i	$-0.150032\pi$
$242$	−81.7459	+	215.263i	−0.337793	+	0.889517i
$243$	36.8267	−	88.9076i	0.151550	−	0.365875i
$244$	−144.222	−	296.861i	−0.591074	−	1.21664i
$245$	−140.565	−	339.354i	−0.573735	−	1.38512i
$246$	−5.79850	−	5.46313i	−0.0235711	−	0.0222078i
$247$	15.1933	−	15.1933i	0.0615112	−	0.0615112i
$248$	363.301	+	113.731i	1.46492	+	0.458592i
$249$	−25.6324	+	25.6324i	−0.102941	+	0.102941i
$250$	8.71540	+	292.657i	0.0348616	+	1.17063i
$251$	92.6681	+	223.721i	0.369196	+	0.891318i	0.993883	+	0.110442i	$0.0352267\pi$
$251$	92.6681	+	223.721i	0.369196	+	0.891318i	−0.624687	+	0.780875i	$0.714773\pi$
$252$	−255.749	−	226.973i	−1.01488	−	0.900685i
$253$	−24.6995	+	59.6298i	−0.0976263	+	0.235691i
$254$	−117.294	−	260.921i	−0.461788	−	1.02725i
$255$			8.94919i			0.0350949i
$256$	−248.773	+	60.3972i	−0.971771	+	0.235927i
$257$	−138.514			−0.538966			−0.269483	−	0.963005i	$-0.586853\pi$
$257$	−138.514			−0.538966			−0.269483	+	0.963005i	$0.586853\pi$
$258$	−6.80368	+	3.05852i	−0.0263708	+	0.0118547i
$259$	−273.509	−	113.291i	−1.05602	−	0.437418i
$260$	−33.3524	+	37.5810i	−0.128279	+	0.144542i
$261$	213.937	−	88.6158i	0.819684	−	0.339524i
$262$	−121.484	+	3.61782i	−0.463678	+	0.0138085i
$263$	91.6940	+	91.6940i	0.348647	+	0.348647i	0.859605	−	0.510959i	$-0.170710\pi$
$263$	91.6940	+	91.6940i	0.348647	+	0.348647i	−0.510959	+	0.859605i	$0.670710\pi$
$264$	2.35006	−	7.50702i	0.00890175	−	0.0284357i
$265$	159.740	+	159.740i	0.602793	+	0.602793i
$266$	186.870	−	198.342i	0.702521	−	0.745648i
$267$	8.57537	−	3.55204i	0.0321175	−	0.0133035i
$268$	351.230	−	170.636i	1.31056	−	0.636700i
$269$	179.504	+	74.3530i	0.667301	+	0.276405i	0.690507	−	0.723325i	$-0.257387\pi$
$269$	179.504	+	74.3530i	0.667301	+	0.276405i	−0.0232059	+	0.999731i	$0.507387\pi$
$270$	−111.432	−	42.3162i	−0.412711	−	0.156727i
$271$	−454.375			−1.67666			−0.838331	−	0.545161i	$-0.816468\pi$
$271$	−454.375			−1.67666			−0.838331	+	0.545161i	$0.816468\pi$
$272$	42.5465	−	5.09078i	0.156421	−	0.0187161i
$273$		−	5.99188i		−	0.0219483i
$274$	444.659	+	168.859i	1.62284	+	0.616272i
$275$	−39.6620	+	95.7526i	−0.144226	+	0.348191i
$276$	−14.1452	+	40.8756i	−0.0512507	+	0.148100i
$277$	−12.5345	−	30.2610i	−0.0452510	−	0.109246i	0.899638	−	0.436637i	$-0.143830\pi$
$277$	−12.5345	−	30.2610i	−0.0452510	−	0.109246i	−0.944889	+	0.327391i	$0.893830\pi$
$278$	−144.852	+	153.744i	−0.521049	+	0.553036i
$279$	297.291	−	297.291i	1.06556	−	1.06556i
$280$	−408.624	+	489.009i	−1.45937	+	1.74646i
$281$	312.777	−	312.777i	1.11308	−	1.11308i	0.120353	−	0.992731i	$-0.461597\pi$
$281$	312.777	−	312.777i	1.11308	−	1.11308i	0.992731	−	0.120353i	$-0.0384027\pi$
$282$	54.3730	−	1.61924i	0.192812	−	0.00574200i
$283$	−74.2838	−	179.337i	−0.262487	−	0.633700i	0.736604	−	0.676324i	$-0.236428\pi$
$283$	−74.2838	−	179.337i	−0.262487	−	0.633700i	−0.999091	+	0.0426244i	$0.986428\pi$
$284$	11.2021	−	0.667798i	0.0394441	−	0.00235140i
$285$	18.0081	−	43.4754i	0.0631864	−	0.152545i
$286$	−6.74271	+	3.03111i	−0.0235759	+	0.0105983i
$287$			94.9562i			0.330858i
$288$	−68.2598	+	274.365i	−0.237013	+	0.952655i
$289$	281.828			0.975182
$290$	−176.944	−	393.613i	−0.610153	−	1.35729i
$291$	23.4903	+	9.73000i	0.0807227	+	0.0334364i
$292$	−313.553	+	18.6920i	−1.07381	+	0.0640137i
$293$	−156.211	+	64.7046i	−0.533143	+	0.220835i	−0.632979	−	0.774169i	$-0.718168\pi$
$293$	−156.211	+	64.7046i	−0.533143	+	0.220835i	0.0998364	+	0.995004i	$0.468168\pi$
$294$	−1.07807	−	36.2008i	−0.00366691	−	0.123132i
$295$	−424.983	−	424.983i	−1.44062	−	1.44062i
$296$	21.8332	+	243.803i	0.0737609	+	0.823658i
$297$	−12.4006	−	12.4006i	−0.0417529	−	0.0417529i
$298$	168.792	+	159.029i	0.566415	+	0.533655i
$299$	37.5555	−	15.5560i	0.125604	−	0.0520268i
$300$	−22.7142	+	65.6374i	−0.0757139	+	0.218791i
$301$	82.1432	+	34.0248i	0.272901	+	0.113039i
$302$	−128.607	+	338.663i	−0.425851	+	1.12140i
$303$	−17.4560			−0.0576106
$304$	−216.936	−	60.8835i	−0.713605	−	0.200275i
$305$			679.301i			2.22722i
$306$	16.8006	−	44.2412i	0.0549038	−	0.144579i
$307$	111.488	−	269.157i	0.363155	−	0.876733i	−0.631681	−	0.775229i	$-0.717635\pi$
$307$	111.488	−	269.157i	0.363155	−	0.876733i	0.994835	−	0.101504i	$-0.0323654\pi$
$308$	−84.3335	+	40.9712i	−0.273810	+	0.133023i
$309$	7.97928	+	19.2637i	0.0258229	+	0.0623420i
$310$	−570.295	−	537.311i	−1.83966	−	1.73326i
$311$	−74.0508	+	74.0508i	−0.238105	+	0.238105i	−0.816065	−	0.577960i	$-0.803849\pi$
$311$	−74.0508	+	74.0508i	−0.238105	+	0.238105i	0.577960	+	0.816065i	$0.303849\pi$
$312$	−4.38980	+	2.29662i	−0.0140699	+	0.00736097i
$313$	−119.709	+	119.709i	−0.382458	+	0.382458i	−0.871987	−	0.489529i	$-0.837169\pi$
$313$	−119.709	+	119.709i	−0.382458	+	0.382458i	0.489529	+	0.871987i	$0.337169\pi$
$314$	−3.13615	−	105.309i	−0.00998773	−	0.335380i
$315$	269.332	+	650.224i	0.855021	+	2.06420i
$316$	29.1679	−	32.8660i	0.0923036	−	0.104006i
$317$	154.558	−	373.135i	0.487563	−	1.17708i	−0.468379	−	0.883528i	$-0.655162\pi$
$317$	154.558	−	373.135i	0.487563	−	1.17708i	0.955942	−	0.293554i	$-0.0948382\pi$
$318$	9.13276	+	20.3158i	0.0287194	+	0.0638863i
$319$		−	63.4940i		−	0.199041i
$320$	514.881	+	111.936i	1.60900	+	0.349799i
$321$	−49.1155			−0.153008
$322$	470.222	−	211.383i	1.46032	−	0.656469i
$323$	34.8434	+	14.4326i	0.107874	+	0.0446830i
$324$	229.104	+	203.325i	0.707111	+	0.627548i
$325$	60.3061	−	24.9796i	0.185557	−	0.0768604i
$326$	148.601	−	4.42537i	0.455830	−	0.0135748i
$327$	17.3227	+	17.3227i	0.0529745	+	0.0529745i
$328$	69.5673	−	36.3957i	0.212095	−	0.110963i
$329$	−458.464	−	458.464i	−1.39351	−	1.39351i
$330$	−11.1026	+	11.7842i	−0.0336444	+	0.0357098i
$331$	−376.019	+	155.752i	−1.13601	+	0.470551i	−0.869820	−	0.493370i	$-0.835765\pi$
$331$	−376.019	+	155.752i	−1.13601	+	0.470551i	−0.266190	+	0.963921i	$0.585765\pi$
$332$	−156.110	−	321.331i	−0.470211	−	0.967864i
$333$	249.757	+	103.453i	0.750021	+	0.310669i
$334$	347.314	+	131.892i	1.03986	+	0.394887i
$335$	−803.711			−2.39914
$336$	−54.7828	+	30.7717i	−0.163044	+	0.0915825i
$337$			584.284i			1.73378i	0.498499	+	0.866890i	$0.333885\pi$
$337$			584.284i			1.73378i	−0.498499	+	0.866890i	$0.666115\pi$
$338$	−311.630	−	118.341i	−0.921984	−	0.350122i
$339$	−12.5463	+	30.2895i	−0.0370098	+	0.0893495i
$340$	−83.3459	−	28.8423i	−0.245135	−	0.0848302i
$341$	−44.1162	−	106.506i	−0.129373	−	0.312334i
$342$	−170.642	+	181.118i	−0.498954	+	0.529585i
$343$	29.9994	−	29.9994i	0.0874617	−	0.0874617i
$344$	−6.55719	−	73.2215i	−0.0190616	−	0.212853i
$345$	62.9514	−	62.9514i	0.182468	−	0.182468i
$346$	−445.845	+	13.2774i	−1.28857	+	0.0383740i
$347$	−15.0226	−	36.2679i	−0.0432929	−	0.104518i	0.900754	−	0.434330i	$-0.143015\pi$
$347$	−15.0226	−	36.2679i	−0.0432929	−	0.104518i	−0.944047	+	0.329812i	$0.893015\pi$
$348$	−2.53212	−	42.4756i	−0.00727621	−	0.122056i
$349$	82.9090	−	200.160i	0.237562	−	0.573525i	−0.759468	−	0.650545i	$-0.774541\pi$
$349$	82.9090	−	200.160i	0.237562	−	0.573525i	0.997030	+	0.0770202i	$0.0245406\pi$
$350$	755.075	−	339.436i	2.15736	−	0.969817i
$351$			11.0451i			0.0314675i
$352$	62.3406	+	46.0810i	0.177104	+	0.130912i
$353$	−213.926			−0.606022			−0.303011	−	0.952987i	$-0.597992\pi$
$353$	−213.926			−0.606022			−0.303011	+	0.952987i	$0.597992\pi$
$354$	−24.2974	−	54.0495i	−0.0686367	−	0.152682i
$355$	−21.3394	−	8.83905i	−0.0601109	−	0.0248987i
$356$	5.44344	+	91.3123i	0.0152906	+	0.256495i
$357$	9.71666	−	4.02477i	0.0272175	−	0.0112739i
$358$	−12.4770	−	418.967i	−0.0348519	−	1.17030i
$359$	235.583	+	235.583i	0.656219	+	0.656219i	0.954483	−	0.298264i	$-0.0964077\pi$
$359$	235.583	+	235.583i	0.656219	+	0.656219i	−0.298264	+	0.954483i	$0.596408\pi$
$360$	373.138	−	446.543i	1.03650	−	1.24040i
$361$	115.037	+	115.037i	0.318663	+	0.318663i
$362$	355.414	+	334.858i	0.981807	+	0.925021i
$363$	43.1724	−	17.8826i	0.118932	−	0.0492633i
$364$	55.8037	+	19.3112i	0.153307	+	0.0530526i
$365$	597.299	+	247.410i	1.63644	+	0.677834i
$366$	−23.7782	+	62.6156i	−0.0649678	+	0.171081i
$367$	266.252			0.725482			0.362741	−	0.931890i	$-0.381841\pi$
$367$	266.252			0.725482			0.362741	+	0.931890i	$0.381841\pi$
$368$	−335.095	−	263.475i	−0.910585	−	0.715965i
$369$		−	86.7101i		−	0.234987i
$370$	178.860	−	470.994i	0.483404	−	1.27296i
$371$	101.598	−	245.280i	0.273850	−	0.661133i
$372$	−33.7599	−	69.4900i	−0.0907523	−	0.186801i
$373$	133.648	+	322.655i	0.358306	+	0.865028i	0.995539	+	0.0943560i	$0.0300792\pi$
$373$	133.648	+	322.655i	0.358306	+	0.865028i	−0.637232	+	0.770672i	$0.719921\pi$
$374$	−9.44448	−	8.89823i	−0.0252526	−	0.0237921i
$375$	42.0150	−	42.0150i	0.112040	−	0.112040i
$376$	−160.158	+	511.607i	−0.425952	+	1.36066i
$377$	−28.2767	+	28.2767i	−0.0750045	+	0.0750045i
$378$	4.16982	+	140.019i	0.0110313	+	0.370422i
$379$	1.26349	+	3.05034i	0.00333376	+	0.00804840i	0.925538	−	0.378656i	$-0.123614\pi$
$379$	1.26349	+	3.05034i	0.00333376	+	0.00804840i	−0.922204	+	0.386704i	$0.873614\pi$
$380$	346.859	+	307.830i	0.912786	+	0.810080i
$381$	−22.2169	+	53.6364i	−0.0583122	+	0.140778i
$382$	−16.5350	−	36.7822i	−0.0432854	−	0.0962884i
$383$		−	310.584i		−	0.810923i	−0.914112	−	0.405462i	$-0.867111\pi$
$383$		−	310.584i		−	0.810923i	0.914112	−	0.405462i	$-0.132889\pi$
$384$	43.5418	+	28.3407i	0.113390	+	0.0738040i
$385$	192.978			0.501243
$386$	211.412	−	95.0381i	0.547700	−	0.246213i
$387$	−75.0098	−	31.0701i	−0.193824	−	0.0802844i
$388$	−166.324	+	187.412i	−0.428671	+	0.483020i
$389$	−677.246	+	280.524i	−1.74099	+	0.721142i	−0.742296	+	0.670072i	$0.766263\pi$
$389$	−677.246	+	280.524i	−1.74099	+	0.721142i	−0.998695	+	0.0510705i	$0.983737\pi$
$390$	10.1925	−	0.303537i	0.0261347	−	0.000778300i
$391$	50.4525	+	50.4525i	0.129035	+	0.129035i
$392$	340.621	+	106.631i	0.868931	+	0.272018i
$393$	17.4407	+	17.4407i	0.0443783	+	0.0443783i
$394$	−263.801	+	279.995i	−0.669545	+	0.710648i
$395$	−83.5594	+	34.6114i	−0.211543	+	0.0876239i
$396$	77.0099	−	37.4132i	0.194469	−	0.0944777i
$397$	−467.679	−	193.719i	−1.17803	−	0.487957i	−0.294192	−	0.955746i	$-0.595051\pi$
$397$	−467.679	−	193.719i	−1.17803	−	0.487957i	−0.883840	+	0.467789i	$0.845051\pi$
$398$	−58.6383	−	22.2678i	−0.147332	−	0.0559493i
$399$	−55.3027			−0.138603
$400$	−538.092	−	423.085i	−1.34523	−	1.05771i
$401$		−	447.783i		−	1.11667i	−0.829617	−	0.558333i	$-0.811441\pi$
$401$		−	447.783i		−	1.11667i	0.829617	−	0.558333i	$-0.188559\pi$
$402$	−74.0833	−	28.1330i	−0.184287	−	0.0699827i
$403$	−27.7849	+	67.0786i	−0.0689451	+	0.166448i
$404$	56.2588	−	162.572i	0.139255	−	0.402406i
$405$	−241.271	−	582.480i	−0.595732	−	1.43822i
$406$	−347.790	+	369.141i	−0.856627	+	0.909214i
$407$	52.4142	−	52.4142i	0.128782	−	0.128782i
$408$	−6.67294	−	5.57602i	−0.0163553	−	0.0136667i
$409$	266.640	−	266.640i	0.651931	−	0.651931i	−0.301527	−	0.953458i	$-0.597496\pi$
$409$	266.640	−	266.640i	0.651931	−	0.651931i	0.953458	+	0.301527i	$0.0974962\pi$
$410$	−161.526	+	4.81030i	−0.393966	+	0.0117324i
$411$	−36.9392	−	89.1791i	−0.0898763	−	0.216981i
$412$	−205.123	+	12.2281i	−0.497872	+	0.0296799i
$413$	−270.299	+	652.559i	−0.654477	+	1.58005i
$414$	−429.387	+	193.026i	−1.03717	+	0.466247i
$415$			735.294i			1.77179i
$416$	−7.24114	−	48.2850i	−0.0174066	−	0.116070i
$417$	42.8676			0.102800
$418$	27.9760	+	62.2326i	0.0669282	+	0.148882i
$419$	−565.518	−	234.245i	−1.34969	−	0.559058i	−0.413481	−	0.910513i	$-0.635687\pi$
$419$	−565.518	−	234.245i	−1.34969	−	0.559058i	−0.936205	+	0.351455i	$0.885687\pi$
$420$	129.097	−	7.69592i	0.307374	−	0.0183236i
$421$	−184.538	+	76.4382i	−0.438333	+	0.181564i	−0.590926	−	0.806726i	$-0.701238\pi$
$421$	−184.538	+	76.4382i	−0.438333	+	0.181564i	0.152593	+	0.988289i	$0.451238\pi$
$422$	18.1917	+	610.864i	0.0431084	+	1.44755i
$423$	418.651	+	418.651i	0.989718	+	0.989718i
$424$	−218.640	+	19.5798i	−0.515660	+	0.0461788i
$425$	81.0159	+	81.0159i	0.190626	+	0.190626i
$426$	−1.65759	−	1.56171i	−0.00389105	−	0.00366600i
$427$	737.557	−	305.506i	1.72730	−	0.715471i
$428$	158.294	−	457.424i	0.369845	−	1.06875i
$429$	1.38607	+	0.574129i	0.00323093	+	0.00133830i
$430$	−53.7170	+	141.454i	−0.124923	+	0.328963i
$431$	329.019			0.763385			0.381692	−	0.924289i	$-0.375341\pi$
$431$	329.019			0.763385			0.381692	+	0.924289i	$0.375341\pi$
$432$	100.983	−	56.7229i	0.233758	−	0.131303i
$433$		−	403.449i		−	0.931753i	−0.884850	−	0.465877i	$-0.845739\pi$
$433$		−	403.449i		−	0.931753i	0.884850	−	0.465877i	$-0.154261\pi$
$434$	−326.907	+	860.851i	−0.753242	+	1.98353i
$435$	−33.5155	+	80.9135i	−0.0770470	+	0.186008i
$436$	−217.159	+	105.501i	−0.498071	+	0.241975i
$437$	−143.576	−	346.623i	−0.328549	−	0.793188i
$438$	46.3967	+	43.7132i	0.105928	+	0.0998018i
$439$	432.214	−	432.214i	0.984542	−	0.984542i	−0.0153402	−	0.999882i	$-0.504883\pi$
$439$	432.214	−	432.214i	0.984542	−	0.984542i	0.999882	+	0.0153402i	$0.00488314\pi$
$440$	−73.9666	−	141.381i	−0.168106	−	0.321320i
$441$	278.732	−	278.732i	0.632045	−	0.632045i
$442$	0.243270	+	8.16882i	0.000550385	+	0.0184815i
$443$	138.144	+	333.509i	0.311838	+	0.752843i	0.999637	+	0.0269419i	$0.00857692\pi$
$443$	138.144	+	333.509i	0.311838	+	0.752843i	−0.687799	+	0.725901i	$0.741423\pi$
$444$	32.9733	−	37.1538i	0.0742642	−	0.0836798i
$445$	72.0501	−	173.944i	0.161910	−	0.390886i
$446$	9.95589	+	22.1469i	0.0223226	+	0.0496567i
$447$		−	47.0633i		−	0.105287i
$448$	−110.025	−	609.378i	−0.245592	−	1.36022i
$449$	−320.009			−0.712715			−0.356358	−	0.934350i	$-0.615981\pi$
$449$	−320.009			−0.712715			−0.356358	+	0.934350i	$0.615981\pi$
$450$	−689.504	+	309.959i	−1.53223	+	0.688797i
$451$	−21.9658	−	9.09852i	−0.0487046	−	0.0201741i
$452$	−241.658	−	214.466i	−0.534641	−	0.474483i
$453$	67.9210	−	28.1338i	0.149936	−	0.0621055i
$454$	465.478	−	13.8621i	1.02528	−	0.0305332i
$455$	−85.9419	−	85.9419i	−0.188883	−	0.188883i
$456$	21.1969	+	40.5161i	0.0464845	+	0.0888512i
$457$	−148.390	−	148.390i	−0.324705	−	0.324705i	0.525864	−	0.850569i	$-0.323742\pi$
$457$	−148.390	−	148.390i	−0.324705	−	0.324705i	−0.850569	+	0.525864i	$0.823742\pi$
$458$	126.905	−	134.695i	0.277085	−	0.294095i
$459$	−17.9112	+	7.41904i	−0.0390221	+	0.0161635i
$460$	383.396	+	789.167i	0.833469	+	1.71558i
$461$	−224.303	−	92.9092i	−0.486557	−	0.201538i	0.125899	−	0.992043i	$-0.459818\pi$
$461$	−224.303	−	92.9092i	−0.486557	−	0.201538i	−0.612456	+	0.790505i	$0.709818\pi$
$462$	17.7881	+	6.75500i	0.0385023	+	0.0146212i
$463$	675.592			1.45916			0.729581	−	0.683894i	$-0.239715\pi$
$463$	675.592			1.45916			0.729581	+	0.683894i	$0.239715\pi$
$464$	403.746	+	113.312i	0.870143	+	0.244207i
$465$			159.012i			0.341962i
$466$	87.5654	+	33.2529i	0.187909	+	0.0713581i
$467$	190.920	−	460.923i	0.408823	−	0.986987i	−0.576625	−	0.817009i	$-0.695631\pi$
$467$	190.920	−	460.923i	0.408823	−	0.986987i	0.985448	−	0.169977i	$-0.0543695\pi$
$468$	−50.9577	−	17.6342i	−0.108884	−	0.0376798i
$469$	361.458	+	872.636i	0.770698	+	1.86063i
$470$	756.651	−	803.100i	1.60989	−	1.70872i
$471$	−15.1187	+	15.1187i	−0.0320991	+	0.0320991i
$472$	581.684	−	52.0914i	1.23238	−	0.110363i
$473$	−15.7416	+	15.7416i	−0.0332803	+	0.0332803i
$474$	−8.91375	+	0.265454i	−0.0188054	+	0.000560030i
$475$	−230.552	−	556.603i	−0.485373	−	1.17179i
$476$	6.16791	+	103.465i	0.0129578	+	0.217363i
$477$	−92.7755	+	223.980i	−0.194498	+	0.469559i
$478$	607.430	−	273.063i	1.27077	−	0.571262i
$479$			775.709i			1.61943i	0.586821	+	0.809717i	$0.300379\pi$
$479$			775.709i			1.61943i	−0.586821	+	0.809717i	$0.699621\pi$
$480$	−55.1197	−	91.6299i	−0.114833	−	0.190896i
$481$	−46.6847			−0.0970576
$482$	−179.477	−	399.247i	−0.372359	−	0.828314i
$483$	−96.6616	−	40.0385i	−0.200127	−	0.0828955i
$484$	27.4048	+	459.708i	0.0566215	+	0.949810i
$485$	476.481	−	197.365i	0.982435	−	0.406938i
$486$	−5.72915	−	192.380i	−0.0117884	−	0.395845i
$487$	−422.101	−	422.101i	−0.866738	−	0.866738i	0.125372	−	0.992110i	$-0.459988\pi$
$487$	−422.101	−	422.101i	−0.866738	−	0.866738i	−0.992110	+	0.125372i	$0.959988\pi$
$488$	−506.519	−	423.255i	−1.03795	−	0.867326i
$489$	−21.3337	−	21.3337i	−0.0436272	−	0.0436272i
$490$	−534.693	−	503.768i	−1.09121	−	1.02810i
$491$	−277.565	+	114.971i	−0.565306	+	0.234157i	−0.646987	−	0.762501i	$-0.723971\pi$
$491$	−277.565	+	114.971i	−0.565306	+	0.234157i	0.0816809	+	0.996659i	$0.473971\pi$
$492$	−15.0573	−	5.21066i	−0.0306043	−	0.0105908i
$493$	−64.8482	−	26.8610i	−0.131538	−	0.0544848i
$494$	15.2560	−	40.1739i	0.0308826	−	0.0813236i
$495$	−176.220			−0.356000
$496$	755.981	−	90.4548i	1.52415	−	0.182368i
$497$			27.1446i			0.0546170i
$498$	−25.7382	+	67.7768i	−0.0516831	+	0.136098i
$499$	−328.498	+	793.063i	−0.658312	+	1.58930i	0.142099	+	0.989852i	$0.454615\pi$
$499$	−328.498	+	793.063i	−0.658312	+	1.58930i	−0.800410	+	0.599452i	$0.795385\pi$
$500$	255.885	+	526.705i	0.511771	+	1.05341i
$501$	−28.8525	−	69.6560i	−0.0575897	−	0.139034i
$502$	352.499	+	332.111i	0.702189	+	0.661576i
$503$	−115.459	+	115.459i	−0.229540	+	0.229540i	−0.812501	−	0.582960i	$-0.801894\pi$
$503$	−115.459	+	115.459i	−0.229540	+	0.229540i	0.582960	+	0.812501i	$0.301894\pi$
$504$	−652.652	−	204.312i	−1.29494	−	0.405380i
$505$	−250.373	+	250.373i	−0.495788	+	0.495788i
$506$	3.84250	+	129.028i	0.00759388	+	0.254997i
$507$	25.8881	+	62.4995i	0.0510614	+	0.123273i
$508$	−427.926	−	379.776i	−0.842374	−	0.747590i
$509$	−97.7110	+	235.895i	−0.191967	+	0.463449i	−0.990331	−	0.138727i	$-0.955699\pi$
$509$	−97.7110	+	235.895i	−0.191967	+	0.463449i	0.798364	+	0.602175i	$0.205699\pi$
$510$	7.33861	+	16.3247i	0.0143894	+	0.0320093i
$511$		−	759.792i		−	1.48687i
$512$	−404.274	+	314.176i	−0.789598	+	0.613624i
$513$	101.942			0.198717
$514$	−252.672	+	113.586i	−0.491579	+	0.220984i
$515$	390.747	+	161.853i	0.758733	+	0.314277i
$516$	−9.90290	+	11.1584i	−0.0191917	+	0.0216249i
$517$	149.983	−	62.1252i	0.290103	−	0.120165i
$518$	−591.826	+	17.6248i	−1.14252	+	0.0340246i
$519$	64.0073	+	64.0073i	0.123328	+	0.123328i
$520$	−30.0225	+	95.9037i	−0.0577356	+	0.184430i
$521$	229.899	+	229.899i	0.441264	+	0.441264i	0.892437	−	0.451173i	$-0.148994\pi$
$521$	229.899	+	229.899i	0.441264	+	0.441264i	−0.451173	+	0.892437i	$0.648994\pi$
$522$	317.588	−	337.084i	0.608406	−	0.645755i
$523$	−900.921	+	373.174i	−1.72260	+	0.713525i	−0.722856	+	0.690999i	$0.757171\pi$
$523$	−900.921	+	373.174i	−1.72260	+	0.713525i	−0.999746	+	0.0225265i	$0.992829\pi$
$524$	−218.639	+	106.220i	−0.417249	+	0.202709i
$525$	−155.218	−	64.2933i	−0.295653	−	0.122463i
$526$	242.456	+	92.0725i	0.460943	+	0.175043i
$527$	−127.441			−0.241823
$528$	−1.86910	−	15.6211i	−0.00353996	−	0.0295854i
$529$		−	180.797i		−	0.341772i
$530$	422.383	+	160.400i	0.796950	+	0.302641i
$531$	246.826	−	595.890i	0.464832	−	1.12220i
$532$	178.235	−	515.047i	0.335027	−	0.968133i
$533$	5.73035	+	13.8343i	0.0107511	+	0.0259555i
$534$	12.7301	−	13.5115i	0.0238391	−	0.0253025i
$535$	−704.466	+	704.466i	−1.31676	+	1.31676i
$536$	500.772	−	599.285i	0.934276	−	1.11807i
$537$	−60.1486	+	60.1486i	−0.112009	+	0.112009i
$538$	388.415	−	11.5671i	0.721962	−	0.0215002i
$539$	−41.3621	−	99.8569i	−0.0767386	−	0.185263i
$540$	−237.970	+	14.1862i	−0.440686	+	0.0262708i
$541$	86.3781	−	208.535i	0.159664	−	0.385462i	−0.823721	−	0.566995i	$-0.808106\pi$
$541$	86.3781	−	208.535i	0.159664	−	0.385462i	0.983385	+	0.181533i	$0.0581058\pi$
$542$	−828.852	+	372.602i	−1.52925	+	0.687457i
$543$		−	99.0983i		−	0.182501i
$544$	73.4369	−	44.1758i	0.134994	−	0.0812055i
$545$	496.920			0.911780
$546$	−4.91352	−	10.9301i	−0.00899912	−	0.0200185i
$547$	497.491	+	206.067i	0.909489	+	0.376723i	0.787861	−	0.615853i	$-0.211188\pi$
$547$	497.491	+	206.067i	0.909489	+	0.376723i	0.121628	+	0.992576i	$0.461188\pi$
$548$	949.596	−	56.6087i	1.73284	−	0.103301i
$549$	−673.507	+	278.976i	−1.22679	+	0.508152i
$550$	6.17024	+	207.192i	0.0112186	+	0.376713i
$551$	260.983	+	260.983i	0.473653	+	0.473653i
$552$	7.71614	+	86.1630i	0.0139785	+	0.156092i
$553$	75.1593	+	75.1593i	0.135912	+	0.135912i
$554$	−47.6799	−	44.9222i	−0.0860648	−	0.0810869i
$555$	−94.4609	+	39.1270i	−0.170200	+	0.0704991i
$556$	−138.158	+	399.236i	−0.248485	+	0.718050i
$557$	−527.914	−	218.669i	−0.947782	−	0.392584i	−0.145385	−	0.989375i	$-0.546442\pi$
$557$	−527.914	−	218.669i	−0.947782	−	0.392584i	−0.802397	+	0.596791i	$0.796442\pi$
$558$	298.518	−	786.093i	0.534979	−	1.40877i
$559$	14.0209			0.0250820
$560$	−344.392	+	1227.11i	−0.614985	+	2.19127i
$561$			2.63335i			0.00469404i
$562$	314.068	−	827.040i	0.558839	−	1.47160i
$563$	−303.900	+	733.680i	−0.539788	+	1.30316i	0.385084	+	0.922882i	$0.374173\pi$
$563$	−303.900	+	733.680i	−0.539788	+	1.30316i	−0.924871	+	0.380281i	$0.875827\pi$
$564$	97.8571	−	47.5413i	0.173505	−	0.0842930i
$565$	254.491	+	614.397i	0.450427	+	1.08743i
$566$	−282.567	−	266.224i	−0.499235	−	0.470360i
$567$	−523.925	+	523.925i	−0.924029	+	0.924029i
$568$	19.8868	−	10.4042i	0.0350120	−	0.0183173i
$569$	−143.631	+	143.631i	−0.252426	+	0.252426i	−0.821965	−	0.569538i	$-0.807122\pi$
$569$	−143.631	+	143.631i	−0.252426	+	0.252426i	0.569538	+	0.821965i	$0.307122\pi$
$570$	−2.80153	−	94.0732i	−0.00491496	−	0.165041i
$571$	−371.018	−	895.717i	−0.649769	−	1.56868i	−0.813109	−	0.582112i	$-0.802227\pi$
$571$	−371.018	−	895.717i	−0.649769	−	1.56868i	0.163339	−	0.986570i	$-0.447773\pi$
$572$	−9.81416	+	11.0584i	−0.0171576	+	0.0193329i
$573$	−3.13194	+	7.56116i	−0.00546586	+	0.0131957i
$574$	77.8670	+	173.215i	0.135657	+	0.301769i
$575$		−	1139.78i		−	1.98223i
$576$	100.471	+	556.459i	0.174428	+	0.966075i
$577$	706.702			1.22479			0.612393	−	0.790553i	$-0.290207\pi$
$577$	706.702			1.22479			0.612393	+	0.790553i	$0.290207\pi$
$578$	514.098	−	231.107i	0.889443	−	0.399839i
$579$	−43.4592	−	18.0014i	−0.0750590	−	0.0310905i
$580$	−645.549	−	572.912i	−1.11302	−	0.987780i
$581$	798.352	−	330.688i	1.37410	−	0.569171i
$582$	50.8289	−	1.51370i	0.0873349	−	0.00260086i
$583$	47.0045	+	47.0045i	0.0806253	+	0.0806253i
$584$	−556.642	+	291.220i	−0.953155	+	0.498665i
$585$	78.4786	+	78.4786i	0.134151	+	0.134151i
$586$	−231.893	+	246.129i	−0.395722	+	0.420015i
$587$	293.599	−	121.613i	0.500169	−	0.207177i	−0.118312	−	0.992976i	$-0.537748\pi$
$587$	293.599	−	121.613i	0.500169	−	0.207177i	0.618481	+	0.785800i	$0.287748\pi$
$588$	−31.6523	−	65.1519i	−0.0538305	−	0.110803i
$589$	619.110	+	256.444i	1.05112	+	0.435389i
$590$	−1123.74	−	426.737i	−1.90464	−	0.723283i
$591$	78.0696			0.132097
$592$	239.753	+	426.831i	0.404988	+	0.720998i
$593$		−	674.627i		−	1.13765i	−0.822458	−	0.568825i	$-0.807398\pi$
$593$		−	674.627i		−	1.13765i	0.822458	−	0.568825i	$-0.192602\pi$
$594$	−32.7895	−	12.4518i	−0.0552013	−	0.0209626i
$595$	81.6391	−	197.094i	0.137209	−	0.331251i
$596$	438.311	+	151.680i	0.735422	+	0.254496i
$597$	4.87127	+	11.7603i	0.00815958	+	0.0196990i
$598$	55.7508	−	59.1733i	0.0932288	−	0.0989520i
$599$	379.725	−	379.725i	0.633932	−	0.633932i	−0.315120	−	0.949052i	$-0.602045\pi$
$599$	379.725	−	379.725i	0.633932	−	0.633932i	0.949052	+	0.315120i	$0.102045\pi$
$600$	12.3905	+	138.359i	0.0206508	+	0.230599i
$601$	−548.542	+	548.542i	−0.912715	+	0.912715i	−0.996485	−	0.0837700i	$-0.973304\pi$
$601$	−548.542	+	548.542i	−0.912715	+	0.912715i	0.0837700	+	0.996485i	$0.473304\pi$
$602$	177.743	−	5.29326i	0.295255	−	0.00879278i
$603$	−330.068	−	796.855i	−0.547377	−	1.32148i
$604$	43.1146	+	723.236i	0.0713818	+	1.19741i
$605$	362.733	−	875.715i	0.599559	−	1.44746i
$606$	−31.8425	+	14.3145i	−0.0525454	+	0.0236212i
$607$		−	1.05067i		−	0.00173092i	−1.00000		0.000865460i	$-0.999725\pi$
$607$		−	1.05067i		−	0.00173092i	1.00000		0.000865460i	$-0.000275484\pi$
$608$	−445.652	+	66.8330i	−0.732980	+	0.109923i
$609$	102.926			0.169008
$610$	557.047	+	1239.15i	0.913192	+	2.03140i
$611$	−94.4614	−	39.1272i	−0.154601	−	0.0640379i
$612$	−5.63228	−	94.4799i	−0.00920307	−	0.154379i
$613$	625.826	−	259.226i	1.02092	−	0.422881i	0.191495	−	0.981494i	$-0.438666\pi$
$613$	625.826	−	259.226i	1.02092	−	0.422881i	0.829428	+	0.558613i	$0.188666\pi$
$614$	−17.3443	−	582.408i	−0.0282481	−	0.948548i
$615$	23.1894	+	23.1894i	0.0377063	+	0.0377063i
$616$	−120.240	+	143.894i	−0.195195	+	0.233594i
$617$	180.644	+	180.644i	0.292779	+	0.292779i	0.838177	−	0.545398i	$-0.183622\pi$
$617$	180.644	+	180.644i	0.292779	+	0.292779i	−0.545398	+	0.838177i	$0.683622\pi$
$618$	30.3523	+	28.5967i	0.0491137	+	0.0462730i
$619$	555.651	−	230.158i	0.897658	−	0.371822i	0.114339	−	0.993442i	$-0.463525\pi$
$619$	555.651	−	230.158i	0.897658	−	0.371822i	0.783319	+	0.621620i	$0.213525\pi$
$620$	−1480.92	−	512.480i	−2.38858	−	0.826580i
$621$	178.181	+	73.8048i	0.286925	+	0.118848i
$622$	−74.3564	+	195.804i	−0.119544	+	0.314798i
$623$	−221.265			−0.355160
$624$	−6.12438	+	7.78917i	−0.00981471	+	0.0124826i
$625$		−	135.712i		−	0.217139i
$626$	−120.203	+	316.534i	−0.192018	+	0.505645i
$627$	5.29899	−	12.7929i	0.00845135	−	0.0204034i
$628$	−92.0778	−	189.529i	−0.146621	−	0.301798i
$629$	−31.3584	−	75.7058i	−0.0498543	−	0.120359i
$630$	1024.51	+	965.251i	1.62620	+	1.53214i
$631$	−267.583	+	267.583i	−0.424062	+	0.424062i	−0.886600	−	0.462537i	$-0.846939\pi$
$631$	−267.583	+	267.583i	−0.424062	+	0.424062i	0.462537	+	0.886600i	$0.346939\pi$
$632$	26.2558	−	83.8713i	0.0415440	−	0.132708i
$633$	87.6981	−	87.6981i	0.138544	−	0.138544i
$634$	−24.0446	−	807.399i	−0.0379252	−	1.27350i
$635$	450.652	+	1087.97i	0.709688	+	1.71334i
$636$	33.3192	+	29.5701i	0.0523887	+	0.0464939i
$637$	−26.0503	+	62.8911i	−0.0408954	+	0.0987301i
$638$	−52.0670	−	115.823i	−0.0816097	−	0.181541i
$639$		−	24.7874i		−	0.0387908i
$640$	1031.02	−	218.030i	1.61096	−	0.340672i
$641$	−834.869			−1.30245			−0.651224	−	0.758886i	$-0.725744\pi$
$641$	−834.869			−1.30245			−0.651224	+	0.758886i	$0.725744\pi$
$642$	−89.5943	+	40.2762i	−0.139555	+	0.0627354i
$643$	1006.71	+	416.995i	1.56565	+	0.648514i	0.986060	−	0.166393i	$-0.0532119\pi$
$643$	1006.71	+	416.995i	1.56565	+	0.648514i	0.579592	+	0.814907i	$0.303212\pi$
$644$	684.418	−	771.192i	1.06276	−	1.19750i
$645$	28.3695	−	11.7510i	0.0439837	−	0.0182187i
$646$	75.3951	−	2.24529i	0.116711	−	0.00347568i
$647$	−857.194	−	857.194i	−1.32488	−	1.32488i	−0.909776	−	0.415099i	$-0.863747\pi$
$647$	−857.194	−	857.194i	−1.32488	−	1.32488i	−0.415099	−	0.909776i	$-0.636253\pi$
$648$	584.655	+	183.025i	0.902245	+	0.282447i
$649$	−125.054	−	125.054i	−0.192687	−	0.192687i
$650$	89.5239	−	95.0196i	0.137729	−	0.146184i
$651$	172.649	−	71.5136i	0.265206	−	0.109852i
$652$	267.442	−	129.930i	0.410187	−	0.199278i
$653$	−105.248	−	43.5953i	−0.161177	−	0.0667616i	0.300636	−	0.953739i	$-0.402801\pi$
$653$	−105.248	−	43.5953i	−0.161177	−	0.0667616i	−0.461813	+	0.886977i	$0.652801\pi$
$654$	45.8044	+	17.3942i	0.0700373	+	0.0265966i
$655$	500.306			0.763826
$656$	97.0561	−	123.439i	0.147951	−	0.188169i
$657$			693.811i			1.05603i
$658$	−1212.27	−	460.357i	−1.84235	−	0.699630i
$659$	−222.875	+	538.067i	−0.338201	+	0.816490i	0.659687	+	0.751540i	$0.270689\pi$
$659$	−222.875	+	538.067i	−0.338201	+	0.816490i	−0.997889	+	0.0649499i	$0.979311\pi$
$660$	−10.5896	+	30.6008i	−0.0160448	+	0.0463648i
$661$	−396.971	−	958.372i	−0.600561	−	1.44988i	−0.873005	−	0.487711i	$-0.837832\pi$
$661$	−396.971	−	958.372i	−0.600561	−	1.44988i	0.272445	−	0.962171i	$-0.412168\pi$
$662$	−558.197	+	592.464i	−0.843197	+	0.894960i
$663$	1.17275	−	1.17275i	0.00176885	−	0.00176885i
$664$	−548.270	−	458.143i	−0.825708	−	0.689974i
$665$	−793.210	+	793.210i	−1.19280	+	1.19280i
$666$	540.431	−	16.0942i	0.811458	−	0.0241655i
$667$	267.214	+	645.111i	0.400620	+	0.967183i
$668$	741.711	−	44.2160i	1.11035	−	0.0661916i
$669$	1.88577	−	4.55265i	0.00281879	−	0.00680515i
$670$	−1466.09	+	659.067i	−2.18820	+	0.983682i
$671$			199.888i			0.297896i
$672$	−74.6986	+	101.056i	−0.111159	+	0.150381i
$673$	−908.805			−1.35038			−0.675190	−	0.737644i	$-0.735938\pi$
$673$	−908.805			−1.35038			−0.675190	+	0.737644i	$0.735938\pi$
$674$	479.131	+	1065.83i	0.710876	+	1.58134i
$675$	286.120	+	118.515i	0.423881	+	0.175577i
$676$	−665.507	+	39.6732i	−0.984477	+	0.0586881i
$677$	963.142	−	398.947i	1.42266	−	0.589286i	0.467134	−	0.884186i	$-0.345287\pi$
$677$	963.142	−	398.947i	1.42266	−	0.589286i	0.955528	+	0.294900i	$0.0952865\pi$
$678$	1.95184	+	65.5412i	0.00287881	+	0.0966684i
$679$	−428.581	−	428.581i	−0.631195	−	0.631195i
$680$	−175.688	+	15.7333i	−0.258364	+	0.0231372i
$681$	−66.8259	−	66.8259i	−0.0981290	−	0.0981290i
$682$	−167.813	−	158.107i	−0.246060	−	0.231828i
$683$	248.963	−	103.124i	0.364515	−	0.150987i	−0.192906	−	0.981217i	$-0.561791\pi$
$683$	248.963	−	103.124i	0.364515	−	0.150987i	0.557420	+	0.830230i	$0.311791\pi$
$684$	−162.756	+	470.320i	−0.237948	+	0.687602i
$685$	−1808.92	−	749.280i	−2.64076	−	1.09384i
$686$	30.1232	−	79.3239i	0.0439113	−	0.115633i
$687$	−37.5564			−0.0546673
$688$	−72.0052	−	128.190i	−0.104659	−	0.186323i
$689$		−	41.8664i		−	0.0607640i
$690$	63.2113	−	166.455i	0.0916105	−	0.241240i
$691$	−222.756	+	537.780i	−0.322367	+	0.778263i	0.676748	+	0.736214i	$0.263388\pi$
$691$	−222.756	+	537.780i	−0.322367	+	0.778263i	−0.999116	+	0.0420488i	$0.986612\pi$
$692$	−802.403	+	389.826i	−1.15954	+	0.563333i
$693$	79.2524	+	191.332i	0.114361	+	0.276093i
$694$	−57.1444	−	53.8393i	−0.0823407	−	0.0775782i
$695$	614.853	−	614.853i	0.884681	−	0.884681i
$696$	−39.4503	−	75.4058i	−0.0566815	−	0.108342i
$697$	−18.5851	+	18.5851i	−0.0266645	+	0.0266645i
$698$	−12.8982	−	433.111i	−0.0184788	−	0.620504i
$699$	−7.27433	−	17.5618i	−0.0104068	−	0.0251242i
$700$	1099.03	−	1238.37i	1.57004	−	1.76910i
$701$	−236.347	+	570.592i	−0.337157	+	0.813969i	0.660829	+	0.750536i	$0.270205\pi$
$701$	−236.347	+	570.592i	−0.337157	+	0.813969i	−0.997986	+	0.0634324i	$0.979795\pi$
$702$	9.05730	+	20.1480i	0.0129021	+	0.0287008i
$703$			430.882i			0.612919i
$704$	151.507	+	32.9378i	0.215209	+	0.0467866i
$705$	−223.924			−0.317623
$706$	−390.234	+	175.426i	−0.552740	+	0.248478i
$707$	384.446	+	159.243i	0.543771	+	0.225237i
$708$	−88.6445	−	78.6703i	−0.125204	−	0.111116i
$709$	−599.630	+	248.375i	−0.845740	+	0.350317i	−0.763114	−	0.646264i	$-0.776331\pi$
$709$	−599.630	+	248.375i	−0.845740	+	0.350317i	−0.0826257	+	0.996581i	$0.526331\pi$
$710$	−46.1746	+	1.37509i	−0.0650347	+	0.00193675i
$711$	−68.6324	−	68.6324i	−0.0965293	−	0.0965293i
$712$	84.8085	+	162.104i	0.119113	+	0.227674i
$713$	896.458	+	896.458i	1.25730	+	1.25730i
$714$	14.4243	−	15.3098i	0.0202021	−	0.0214423i
$715$	28.1153	−	11.6457i	0.0393221	−	0.0162877i
$716$	−366.326	−	754.031i	−0.511628	−	1.05312i
$717$	−124.867	−	51.7216i	−0.174152	−	0.0721361i
$718$	622.925	+	236.555i	0.867583	+	0.329464i
$719$	96.4410			0.134132			0.0670661	−	0.997749i	$-0.478636\pi$
$719$	96.4410			0.134132			0.0670661	+	0.997749i	$0.478636\pi$
$720$	314.484	−	1120.55i	0.436784	−	1.55632i
$721$		−	497.048i		−	0.689388i
$722$	304.181	+	115.512i	0.421303	+	0.159989i
$723$	−33.9952	+	82.0716i	−0.0470196	+	0.113515i
$724$	922.925	+	319.383i	1.27476	+	0.441137i
$725$	429.088	+	1035.91i	0.591846	+	1.42884i
$726$	64.0890	−	68.0233i	0.0882768	−	0.0936960i
$727$	−708.402	+	708.402i	−0.974418	+	0.974418i	−0.999681	−	0.0252626i	$-0.991958\pi$
$727$	−708.402	+	708.402i	−0.974418	+	0.974418i	0.0252626	+	0.999681i	$0.491958\pi$
$728$	117.631	−	10.5341i	0.161580	−	0.0144700i
$729$	459.728	−	459.728i	0.630628	−	0.630628i
$730$	1292.45	−	38.4896i	1.77048	−	0.0527255i
$731$	9.41788	+	22.7368i	0.0128836	+	0.0311037i
$732$	7.97149	+	133.720i	0.0108900	+	0.182677i
$733$	−149.531	+	361.000i	−0.203999	+	0.492497i	−0.992457	−	0.122591i	$-0.960880\pi$
$733$	−149.531	+	361.000i	−0.203999	+	0.492497i	0.788458	+	0.615088i	$0.210880\pi$
$734$	485.686	−	218.335i	0.661697	−	0.297459i
$735$			149.086i			0.202838i
$736$	−827.324	−	205.832i	−1.12408	−	0.279663i
$737$	−236.497			−0.320891
$738$	−71.1049	−	158.173i	−0.0963481	−	0.214326i
$739$	−971.442	−	402.384i	−1.31454	−	0.544499i	−0.388331	−	0.921520i	$-0.626948\pi$
$739$	−971.442	−	402.384i	−1.31454	−	0.544499i	−0.926205	+	0.377021i	$0.876948\pi$
$740$	−59.9615	−	1005.84i	−0.0810291	−	1.35924i
$741$	−8.05712	+	3.33737i	−0.0108733	+	0.00450387i
$742$	−15.8057	−	530.744i	−0.0213015	−	0.715288i
$743$	117.181	+	117.181i	0.157714	+	0.157714i	0.781553	−	0.623839i	$-0.214428\pi$
$743$	117.181	+	117.181i	0.157714	+	0.157714i	−0.623839	+	0.781553i	$0.714428\pi$
$744$	−118.567	−	99.0766i	−0.159365	−	0.133167i
$745$	−675.032	−	675.032i	−0.906083	−	0.906083i
$746$	508.383	+	478.979i	0.681478	+	0.642063i
$747$	−729.022	+	301.971i	−0.975933	+	0.404245i
$748$	−24.5250	−	8.48701i	−0.0327875	−	0.0113463i
$749$	1081.70	+	448.056i	1.44420	+	0.598206i
$750$	42.1884	−	111.095i	0.0562512	−	0.148127i
$751$	604.910			0.805473			0.402736	−	0.915316i	$-0.368059\pi$
$751$	604.910			0.805473			0.402736	+	0.915316i	$0.368059\pi$
$752$	127.380	+	1064.59i	0.169388	+	1.41567i
$753$		−	98.2854i		−	0.130525i
$754$	−28.3934	+	74.7689i	−0.0376570	+	0.0991629i
$755$	570.670	−	1377.72i	0.755855	−	1.82479i
$756$	122.427	+	251.998i	0.161940	+	0.333331i
$757$	−459.899	−	1110.29i	−0.607528	−	1.46670i	−0.865680	−	0.500598i	$-0.833113\pi$
$757$	−459.899	−	1110.29i	−0.607528	−	1.46670i	0.258152	−	0.966104i	$-0.416887\pi$
$758$	4.80619	+	4.52820i	0.00634061	+	0.00597388i
$759$	18.5238	−	18.5238i	0.0244056	−	0.0244056i
$760$	885.155	+	277.096i	1.16468	+	0.364601i
$761$	202.753	−	202.753i	0.266430	−	0.266430i	−0.561230	−	0.827660i	$-0.689672\pi$
$761$	202.753	−	202.753i	0.266430	−	0.266430i	0.827660	+	0.561230i	$0.189672\pi$
$762$	3.45630	+	116.060i	0.00453582	+	0.152310i
$763$	−223.483	−	539.535i	−0.292900	−	0.707124i
$764$	−60.3250	−	53.5372i	−0.0789594	−	0.0700749i
$765$	−74.5495	+	179.978i	−0.0974503	+	0.235266i
$766$	−254.688	−	566.553i	−0.332491	−	0.739626i
$767$			111.384i			0.145220i
$768$	102.667	+	15.9924i	0.133681	+	0.0208234i
$769$	954.072			1.24067			0.620333	−	0.784338i	$-0.286997\pi$
$769$	954.072			1.24067			0.620333	+	0.784338i	$0.286997\pi$
$770$	352.023	−	158.248i	0.457173	−	0.205517i
$771$	51.9407	+	21.5146i	0.0673680	+	0.0279047i
$772$	307.715	−	346.729i	0.398595	−	0.449131i
$773$	244.204	−	101.153i	0.315918	−	0.130857i	−0.219090	−	0.975705i	$-0.570309\pi$
$773$	244.204	−	101.153i	0.315918	−	0.130857i	0.535007	+	0.844847i	$0.320309\pi$
$774$	−162.308	+	4.83358i	−0.209700	+	0.00624494i
$775$	1439.52	+	1439.52i	1.85744	+	1.85744i
$776$	−149.719	+	478.260i	−0.192936	+	0.616314i
$777$	84.9649	+	84.9649i	0.109350	+	0.109350i
$778$	−1005.36	+	1067.08i	−1.29224	+	1.37157i
$779$	127.685	−	52.8890i	0.163909	−	0.0678934i
$780$	18.3439	−	8.91189i	0.0235178	−	0.0114255i
$781$	−6.27923	−	2.60094i	−0.00803999	−	0.00333027i
$782$	133.406	+	50.6607i	0.170596	+	0.0647835i
$783$	−189.727			−0.242308
$784$	708.787	−	84.8079i	0.904065	−	0.108173i
$785$			433.696i			0.552479i
$786$	46.1164	+	17.5127i	0.0586723	+	0.0222807i
$787$	−19.8368	+	47.8903i	−0.0252056	+	0.0608518i	−0.935981	−	0.352050i	$-0.885485\pi$
$787$	−19.8368	+	47.8903i	−0.0252056	+	0.0608518i	0.910776	+	0.412902i	$0.135485\pi$
$788$	−251.610	+	727.080i	−0.319302	+	0.922691i
$789$	−20.1416	−	48.6261i	−0.0255280	−	0.0616301i
$790$	−124.043	+	131.658i	−0.157016	+	0.166656i
$791$	552.633	−	552.633i	0.698650	−	0.698650i
$792$	109.798	−	131.398i	0.138634	−	0.165907i
$793$	89.0192	−	89.0192i	0.112256	−	0.112256i
$794$	−1011.98	+	30.1369i	−1.27453	+	0.0379558i
$795$	−35.0887	−	84.7116i	−0.0441367	−	0.106556i
$796$	−125.226	+	7.46515i	−0.157319	+	0.00937832i
$797$	187.462	−	452.574i	0.235210	−	0.567847i	−0.761566	−	0.648088i	$-0.775569\pi$
$797$	187.462	−	452.574i	0.235210	−	0.567847i	0.996775	+	0.0802411i	$0.0255690\pi$
$798$	−100.881	+	45.3499i	−0.126417	+	0.0568294i
$799$		−	179.464i		−	0.224611i
$800$	−1328.51	−	330.522i	−1.66063	−	0.413152i
$801$	202.050			0.252247
$802$	−367.195	−	816.826i	−0.457849	−	1.01849i
$803$	175.759	+	72.8017i	0.218878	+	0.0906622i
$804$	−158.209	+	9.43142i	−0.196778	+	0.0117306i
$805$	−1960.70	+	812.148i	−2.43565	+	1.00888i
$806$	4.32251	+	145.146i	0.00536291	+	0.180082i
$807$	−55.7625	−	55.7625i	−0.0690985	−	0.0690985i
$808$	−30.6889	−	342.691i	−0.0379813	−	0.424122i
$809$	−772.357	−	772.357i	−0.954706	−	0.954706i	0.0443114	−	0.999018i	$-0.485891\pi$
$809$	−772.357	−	772.357i	−0.954706	−	0.954706i	−0.999018	+	0.0443114i	$0.985891\pi$
$810$	−917.768	−	864.686i	−1.13305	−	1.06751i
$811$	518.106	−	214.607i	0.638849	−	0.264620i	−0.0396587	−	0.999213i	$-0.512627\pi$
$811$	518.106	−	214.607i	0.638849	−	0.264620i	0.678508	+	0.734593i	$0.262627\pi$
$812$	−331.718	+	958.570i	−0.408520	+	1.18050i
$813$	170.384	+	70.5753i	0.209574	+	0.0868085i
$814$	52.6305	−	138.593i	0.0646566	−	0.170262i
$815$	−611.981			−0.750897
$816$	−16.7450	−	4.69952i	−0.0205208	−	0.00575921i
$817$		−	129.407i		−	0.158393i
$818$	267.740	−	705.046i	0.327311	−	0.861914i
$819$	49.9141	−	120.503i	0.0609452	−	0.147135i
$820$	−290.705	+	141.231i	−0.354518	+	0.172233i
$821$	328.590	+	793.287i	0.400232	+	0.966245i	0.987609	+	0.156932i	$0.0501604\pi$
$821$	328.590	+	793.287i	0.400232	+	0.966245i	−0.587378	+	0.809313i	$0.699840\pi$
$822$	−140.512	−	132.385i	−0.170940	−	0.161053i
$823$	−370.318	+	370.318i	−0.449961	+	0.449961i	−0.895341	−	0.445381i	$-0.853068\pi$
$823$	−370.318	+	370.318i	−0.449961	+	0.449961i	0.445381	+	0.895341i	$0.353068\pi$
$824$	−364.150	+	190.513i	−0.441930	+	0.231206i
$825$	29.7453	−	29.7453i	0.0360549	−	0.0360549i
$826$	42.0505	+	1412.02i	0.0509086	+	1.70947i
$827$	−55.6405	−	134.328i	−0.0672799	−	0.162428i	0.886663	−	0.462416i	$-0.153017\pi$
$827$	−55.6405	−	134.328i	−0.0672799	−	0.162428i	−0.953943	+	0.299988i	$0.903017\pi$
$828$	−624.982	+	704.221i	−0.754809	+	0.850508i
$829$	492.586	−	1189.21i	0.594193	−	1.43451i	−0.285226	−	0.958460i	$-0.592069\pi$
$829$	492.586	−	1189.21i	0.594193	−	1.43451i	0.879419	−	0.476048i	$-0.157931\pi$
$830$	602.963	+	1341.29i	0.726462	+	1.61601i
$831$			13.2943i			0.0159980i
$832$	−52.8041	−	82.1414i	−0.0634665	−	0.0987277i
$833$	−119.485			−0.143439
$834$	78.1973	−	35.1527i	0.0937617	−	0.0421496i
$835$	−1412.91	−	585.248i	−1.69211	−	0.700896i
$836$	102.065	+	90.5809i	0.122088	+	0.108350i
$837$	−318.252	+	131.824i	−0.380229	+	0.157496i
$838$	−1223.68	+	36.4417i	−1.46024	+	0.0434865i
$839$	−215.217	−	215.217i	−0.256516	−	0.256516i	0.567119	−	0.823636i	$-0.308058\pi$
$839$	−215.217	−	215.217i	−0.256516	−	0.256516i	−0.823636	+	0.567119i	$0.808058\pi$
$840$	229.182	−	119.902i	0.272836	−	0.142740i
$841$	108.953	+	108.953i	0.129552	+	0.129552i
$842$	−273.945	+	290.762i	−0.325351	+	0.345323i
$843$	−165.868	+	68.7048i	−0.196759	+	0.0815004i
$844$	534.112	+	1099.39i	0.632834	+	1.30260i
$845$	1267.75	+	525.119i	1.50029	+	0.621442i
$846$	1106.99	+	420.379i	1.30850	+	0.496902i
$847$	−1113.95			−1.31517
$848$	−382.778	+	215.008i	−0.451389	+	0.253547i
$849$			78.7867i			0.0927994i
$850$	214.221	+	81.3503i	0.252025	+	0.0957062i
$851$	−311.954	+	753.123i	−0.366573	+	0.884986i
$852$	−4.30435	−	1.48954i	−0.00505205	−	0.00174829i
$853$	−68.6449	−	165.723i	−0.0804747	−	0.194283i	0.878521	−	0.477704i	$-0.158531\pi$
$853$	−68.6449	−	165.723i	−0.0804747	−	0.194283i	−0.958996	+	0.283421i	$0.908531\pi$
$854$	1094.90	−	1162.11i	1.28208	−	1.36078i
$855$	724.327	−	724.327i	0.847166	−	0.847166i
$856$	−86.3484	−	964.219i	−0.100874	−	1.12642i
$857$	713.771	−	713.771i	0.832871	−	0.832871i	−0.155037	−	0.987909i	$-0.549550\pi$
$857$	713.771	−	713.771i	0.832871	−	0.832871i	0.987909	+	0.155037i	$0.0495497\pi$
$858$	2.99922	−	0.0893175i	0.00349559	−	0.000104100i
$859$	343.845	+	830.116i	0.400285	+	0.966375i	0.987596	+	0.157013i	$0.0501866\pi$
$859$	343.845	+	830.116i	0.400285	+	0.966375i	−0.587311	+	0.809361i	$0.699813\pi$
$860$	18.0083	+	302.084i	0.0209399	+	0.351261i
$861$	14.7490	−	35.6071i	0.0171300	−	0.0413556i
$862$	600.182	−	269.805i	0.696267	−	0.312999i
$863$		−	1574.26i		−	1.82417i	−0.410002	−	0.912085i	$-0.634472\pi$
$863$		−	1574.26i		−	1.82417i	0.410002	−	0.912085i	$-0.365528\pi$
$864$	137.695	−	186.281i	0.159370	−	0.215603i
$865$	1836.12			2.12268
$866$	−330.840	−	735.955i	−0.382033	−	0.849832i
$867$	−105.681	−	43.7745i	−0.121893	−	0.0504897i
$868$	109.594	+	1838.40i	0.126260	+	2.11797i
$869$	−24.5878	+	10.1846i	−0.0282944	+	0.0117199i
$870$	5.21401	+	175.083i	0.00599312	+	0.201244i
$871$	105.322	+	105.322i	0.120921	+	0.120921i
$872$	−309.618	+	370.527i	−0.355067	+	0.424917i
$873$	391.363	+	391.363i	0.448296	+	0.448296i
$874$	−546.147	−	514.559i	−0.624882	−	0.588740i
$875$	−1308.61	+	542.043i	−1.49555	+	0.619477i
$876$	120.481	+	41.6930i	0.137535	+	0.0475948i
$877$	1227.56	+	508.470i	1.39972	+	0.579784i	0.949679	−	0.313224i	$-0.101409\pi$
$877$	1227.56	+	508.470i	1.39972	+	0.579784i	0.450042	+	0.893007i	$0.351409\pi$
$878$	433.998	−	1142.85i	0.494303	−	1.30166i
$879$	68.6268			0.0780738
$880$	−250.863	−	197.246i	−0.285072	−	0.224143i
$881$			1187.59i			1.34800i	0.738732	+	0.674000i	$0.235425\pi$
$881$			1187.59i			1.34800i	−0.738732	+	0.674000i	$0.764575\pi$
$882$	279.882	−	737.020i	0.317327	−	0.835623i
$883$	544.271	−	1313.99i	0.616389	−	1.48809i	−0.239480	−	0.970901i	$-0.576977\pi$
$883$	544.271	−	1313.99i	0.616389	−	1.48809i	0.855869	−	0.517193i	$-0.173023\pi$
$884$	7.14244	+	14.7017i	0.00807969	+	0.0166309i
$885$	93.3522	+	225.372i	0.105483	+	0.254658i
$886$	525.484	+	495.091i	0.593097	+	0.558794i
$887$	−95.1081	+	95.1081i	−0.107224	+	0.107224i	−0.758684	−	0.651459i	$-0.774157\pi$
$887$	−95.1081	+	95.1081i	−0.107224	+	0.107224i	0.651459	+	0.758684i	$0.274157\pi$
$888$	29.6812	−	94.8135i	0.0334248	−	0.106772i
$889$	978.598	−	978.598i	1.10079	−	1.10079i
$890$	−11.2089	−	376.385i	−0.0125942	−	0.422904i
$891$	−70.9955	−	171.398i	−0.0796807	−	0.192366i
$892$	36.3222	+	32.2353i	0.0407200	+	0.0361382i
$893$	−361.129	+	871.842i	−0.404400	+	0.976307i
$894$	−38.5933	−	85.8508i	−0.0431693	−	0.0960300i
$895$			1725.43i			1.92786i
$896$	−700.412	−	1021.38i	−0.781710	−	1.13993i
$897$	−16.4990			−0.0183935
$898$	−583.747	+	262.417i	−0.650052	+	0.292224i
$899$	−1152.25	−	477.276i	−1.28170	−	0.530896i
$900$	−1003.59	+	1130.83i	−1.11510	+	1.25647i
$901$	67.8922	−	28.1219i	0.0753521	−	0.0312119i
$902$	−47.5301	+	1.41546i	−0.0526941	+	0.00156925i
$903$	−25.5176	−	25.5176i	−0.0282587	−	0.0282587i
$904$	−616.691	−	193.054i	−0.682180	−	0.213555i
$905$	−1421.37	−	1421.37i	−1.57058	−	1.57058i
$906$	100.828	−	107.018i	0.111289	−	0.118121i
$907$	103.742	−	42.9713i	0.114379	−	0.0473774i	−0.324760	−	0.945796i	$-0.605284\pi$
$907$	103.742	−	42.9713i	0.114379	−	0.0473774i	0.439139	+	0.898419i	$0.355284\pi$
$908$	837.737	−	406.992i	0.922618	−	0.448230i
$909$	−351.060	−	145.414i	−0.386205	−	0.159971i
$910$	−227.246	−	86.2966i	−0.249721	−	0.0948314i
$911$	134.755			0.147920			0.0739598	−	0.997261i	$-0.476436\pi$
$911$	134.755			0.147920			0.0739598	+	0.997261i	$0.476436\pi$
$912$	71.8910	+	56.5257i	0.0788279	+	0.0619799i
$913$			216.365i			0.236982i
$914$	−392.372	−	149.003i	−0.429291	−	0.163023i
$915$	105.512	−	254.728i	0.115313	−	0.278391i
$916$	121.040	−	349.772i	0.132140	−	0.381847i
$917$	−225.005	−	543.211i	−0.245371	−	0.592379i
$918$	−26.5889	+	28.2212i	−0.0289640	+	0.0307420i
$919$	847.025	−	847.025i	0.921681	−	0.921681i	−0.0754671	−	0.997148i	$-0.524045\pi$
$919$	847.025	−	847.025i	0.921681	−	0.921681i	0.997148	+	0.0754671i	$0.0240448\pi$
$920$	1346.51	+	1125.17i	1.46360	+	1.22301i
$921$	−83.6129	+	83.6129i	−0.0907849	+	0.0907849i
$922$	−485.352	+	14.4539i	−0.526412	+	0.0156767i
$923$	1.63811	+	3.95474i	0.00177476	+	0.00428465i
$924$	37.9876	−	2.26457i	0.0411121	−	0.00245083i
$925$	−500.931	+	1209.35i	−0.541547	+	1.30741i
$926$	1232.39	−	554.006i	1.33087	−	0.598278i
$927$			453.884i			0.489627i
$928$	829.416	−	124.385i	0.893767	−	0.134035i
$929$	−1150.33			−1.23824			−0.619121	−	0.785295i	$-0.712511\pi$
$929$	−1150.33			−1.23824			−0.619121	+	0.785295i	$0.712511\pi$
$930$	130.395	+	290.064i	0.140210	+	0.311896i
$931$	580.461	+	240.435i	0.623481	+	0.258254i
$932$	187.001	−	11.1478i	0.200645	−	0.0119612i
$933$	39.2698	−	16.2661i	0.0420898	−	0.0174342i
$934$	−29.7016	−	997.356i	−0.0318004	−	1.06783i
$935$	37.7704	+	37.7704i	0.0403961	+	0.0403961i
$936$	−107.415	+	9.61934i	−0.114760	+	0.0102771i
$937$	1191.07	+	1191.07i	1.27115	+	1.27115i	0.945484	+	0.325670i	$0.105590\pi$
$937$	1191.07	+	1191.07i	1.27115	+	1.27115i	0.325670	+	0.945484i	$0.394410\pi$
$938$	1374.94	+	1295.42i	1.46582	+	1.38104i
$939$	63.4828	−	26.2954i	0.0676068	−	0.0280037i
$940$	721.683	−	2085.46i	0.767748	−	2.21857i
$941$	−741.098	−	306.973i	−0.787564	−	0.326220i	−0.0476005	−	0.998866i	$-0.515157\pi$
$941$	−741.098	−	306.973i	−0.787564	−	0.326220i	−0.739964	+	0.672647i	$0.765157\pi$
$942$	−15.1811	+	39.9766i	−0.0161158	+	0.0424380i
$943$	261.467			0.277272
$944$	1018.37	−	572.021i	1.07878	−	0.605955i
$945$		−	576.642i		−	0.610203i
$946$	−15.8066	+	41.6237i	−0.0167088	+	0.0439997i
$947$	−75.9383	+	183.331i	−0.0801883	+	0.193592i	−0.958889	−	0.283781i	$-0.908411\pi$
$947$	−75.9383	+	183.331i	−0.0801883	+	0.193592i	0.878701	+	0.477373i	$0.158411\pi$
$948$	−16.0424	+	7.79377i	−0.0169224	+	0.00822128i
$949$	−45.8514	−	110.695i	−0.0483155	−	0.116644i
$950$	−876.995	−	826.271i	−0.923152	−	0.869759i
$951$	−115.913	+	115.913i	−0.121886	+	0.121886i
$952$	96.0956	+	183.678i	0.100941	+	0.192940i
$953$	−240.916	+	240.916i	−0.252798	+	0.252798i	−0.822117	−	0.569319i	$-0.807207\pi$
$953$	−240.916	+	240.916i	−0.252798	+	0.252798i	0.569319	+	0.822117i	$0.307207\pi$
$954$	14.4331	+	484.653i	0.0151291	+	0.508022i
$955$	63.5287	+	153.372i	0.0665222	+	0.160599i
$956$	884.127	−	996.221i	0.924819	−	1.04207i
$957$	−9.86212	+	23.8093i	−0.0103052	+	0.0248791i
$958$	636.105	+	1415.02i	0.663992	+	1.47705i
$959$			2301.03i			2.39941i
$960$	−175.686	−	121.948i	−0.183007	−	0.127029i
$961$	−1303.41			−1.35631
$962$	−85.1603	+	38.2829i	−0.0885242	+	0.0397951i
$963$	−987.767	−	409.147i	−1.02572	−	0.424867i
$964$	−654.789	−	581.113i	−0.679242	−	0.602814i
$965$	−881.533	+	365.143i	−0.913506	+	0.378386i
$966$	−209.159	+	6.22881i	−0.216520	+	0.00644805i
$967$	474.501	+	474.501i	0.490694	+	0.490694i	0.908525	−	0.417831i	$-0.137209\pi$
$967$	474.501	+	474.501i	0.490694	+	0.490694i	−0.417831	+	0.908525i	$0.637209\pi$
$968$	426.965	+	816.107i	0.441080	+	0.843086i
$969$	−10.8240	−	10.8240i	−0.0111703	−	0.0111703i
$970$	707.331	−	750.753i	0.729208	−	0.773973i
$971$	486.579	−	201.548i	0.501111	−	0.207567i	−0.117786	−	0.993039i	$-0.537580\pi$
$971$	486.579	−	201.548i	0.501111	−	0.207567i	0.618897	+	0.785472i	$0.287580\pi$
$972$	−168.209	−	346.234i	−0.173054	−	0.356208i
$973$	−944.103	−	391.060i	−0.970301	−	0.401912i
$974$	−1116.11	−	423.843i	−1.14591	−	0.435158i
$975$	−26.4938			−0.0271731
$976$	−1271.05	−	356.723i	−1.30231	−	0.365495i
$977$			137.589i			0.140828i	0.997518	+	0.0704140i	$0.0224320\pi$
$977$			137.589i			0.140828i	−0.997518	+	0.0704140i	$0.977568\pi$
$978$	−56.4103	−	21.4218i	−0.0576793	−	0.0219036i
$979$	21.2012	−	51.1841i	0.0216559	−	0.0522821i
$980$	−1388.47	−	480.487i	−1.41681	−	0.490293i
$981$	204.075	+	492.681i	0.208028	+	0.502224i
$982$	−412.043	+	437.338i	−0.419596	+	0.445354i
$983$	−602.812	+	602.812i	−0.613237	+	0.613237i	−0.943788	−	0.330551i	$-0.892765\pi$
$983$	−602.812	+	602.812i	−0.613237	+	0.613237i	0.330551	+	0.943788i	$0.392765\pi$
$984$	−31.7398	+	2.84239i	−0.0322559	+	0.00288860i
$985$	1119.76	−	1119.76i	1.13681	−	1.13681i
$986$	−140.320	+	4.17878i	−0.142313	+	0.00423811i
$987$	100.707	+	243.128i	0.102033	+	0.246330i
$988$	−5.11447	−	85.7938i	−0.00517659	−	0.0868359i
$989$	93.6893	−	226.186i	0.0947313	−	0.228702i
$990$	−321.453	+	144.506i	−0.324700	+	0.145965i
$991$		−	82.2289i		−	0.0829757i	−0.999139	−	0.0414879i	$-0.986790\pi$
$991$		−	82.2289i		−	0.0829757i	0.999139	−	0.0414879i	$-0.0132098\pi$
$992$	1304.85	−	784.931i	1.31538	−	0.791261i
$993$	165.193			0.166358
$994$	22.2594	+	49.5161i	0.0223938	+	0.0498150i
$995$	238.547	+	98.8096i	0.239746	+	0.0993061i
$996$	8.62856	+	144.742i	0.00866321	+	0.145323i
$997$	1201.68	−	497.750i	1.20529	−	0.499248i	0.312586	−	0.949889i	$-0.398805\pi$
$997$	1201.68	−	497.750i	1.20529	−	0.499248i	0.892705	+	0.450641i	$0.148805\pi$
$998$	51.1045	+	1716.05i	0.0512069	+	1.71949i
$999$	−156.620	−	156.620i	−0.156776	−	0.156776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.19.7	✓	28
3.2	odd	2		288.3.u.a.19.1		28
4.3	odd	2		128.3.h.a.111.4		28
8.3	odd	2		256.3.h.a.223.4		28
8.5	even	2		256.3.h.b.223.4		28
32.5	even	8		128.3.h.a.15.4		28
32.11	odd	8		256.3.h.b.31.4		28
32.21	even	8		256.3.h.a.31.4		28
32.27	odd	8	inner	32.3.h.a.27.7	yes	28
96.59	even	8		288.3.u.a.91.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.7	✓	28	1.1	even	1	trivial
32.3.h.a.27.7	yes	28	32.27	odd	8	inner
128.3.h.a.15.4		28	32.5	even	8
128.3.h.a.111.4		28	4.3	odd	2
256.3.h.a.31.4		28	32.21	even	8
256.3.h.a.223.4		28	8.3	odd	2
256.3.h.b.31.4		28	32.11	odd	8
256.3.h.b.223.4		28	8.5	even	2
288.3.u.a.19.1		28	3.2	odd	2
288.3.u.a.91.1		28	96.59	even	8

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82416 - 0.820030i) q^{2} +(-0.374985 - 0.155324i) q^{3} +(2.65510 - 2.99173i) q^{4} +(-7.60625 + 3.15061i) q^{5} +(-0.811401 + 0.0241638i) q^{6} +(6.84161 + 6.84161i) q^{7} +(2.39002 - 7.63465i) q^{8} +(-6.24747 - 6.24747i) q^{9} +O(q^{10})\)	\(q+(1.82416 - 0.820030i) q^{2} +(-0.374985 - 0.155324i) q^{3} +(2.65510 - 2.99173i) q^{4} +(-7.60625 + 3.15061i) q^{5} +(-0.811401 + 0.0241638i) q^{6} +(6.84161 + 6.84161i) q^{7} +(2.39002 - 7.63465i) q^{8} +(-6.24747 - 6.24747i) q^{9} +(-11.2914 + 11.9846i) q^{10} +(-2.23818 + 0.927086i) q^{11} +(-1.46031 + 0.709452i) q^{12} +(1.40964 + 0.583890i) q^{13} +(18.0905 + 6.86984i) q^{14} +3.34159 q^{15} +(-1.90088 - 15.8867i) q^{16} +2.67812i q^{17} +(-16.5195 - 6.27326i) q^{18} +(5.38908 - 13.0104i) q^{19} +(-10.7696 + 31.1210i) q^{20} +(-1.50283 - 3.62816i) q^{21} +(-3.32256 + 3.52653i) q^{22} +(18.8388 - 18.8388i) q^{23} +(-2.08206 + 2.49165i) q^{24} +(30.2510 - 30.2510i) q^{25} +(3.05020 - 0.0908360i) q^{26} +(2.77024 + 6.68795i) q^{27} +(38.6334 - 2.30307i) q^{28} +(-10.0298 + 24.2140i) q^{29} +(6.09559 - 2.74021i) q^{30} +47.5858i q^{31} +(-16.4951 - 27.4210i) q^{32} +0.983283 q^{33} +(2.19614 + 4.88532i) q^{34} +(-73.5942 - 30.4837i) q^{35} +(-35.2784 + 2.10307i) q^{36} +(-28.2682 + 11.7091i) q^{37} +(-0.838382 - 28.1522i) q^{38} +(-0.437900 - 0.437900i) q^{39} +(5.87475 + 65.6010i) q^{40} +(6.93962 + 6.93962i) q^{41} +(-5.71661 - 5.38597i) q^{42} +(8.48982 - 3.51660i) q^{43} +(-3.16902 + 9.15755i) q^{44} +(67.2032 + 27.8365i) q^{45} +(18.9165 - 49.8132i) q^{46} -67.0112 q^{47} +(-1.75478 + 6.25251i) q^{48} +44.6152i q^{49} +(30.3759 - 79.9893i) q^{50} +(0.415976 - 1.00426i) q^{51} +(5.48956 - 2.66696i) q^{52} +(-10.5006 - 25.3507i) q^{53} +(10.5377 + 9.92819i) q^{54} +(14.1033 - 14.1033i) q^{55} +(68.5848 - 35.8817i) q^{56} +(-4.04165 + 4.04165i) q^{57} +(1.56034 + 52.3950i) q^{58} +(27.9364 + 67.4445i) q^{59} +(8.87226 - 9.99714i) q^{60} +(31.5752 - 76.2294i) q^{61} +(39.0218 + 86.8040i) q^{62} -85.4855i q^{63} +(-52.5757 - 36.4938i) q^{64} -12.5616 q^{65} +(1.79366 - 0.806322i) q^{66} +(90.1903 + 37.3580i) q^{67} +(8.01222 + 7.11069i) q^{68} +(-9.99035 + 4.13814i) q^{69} +(-159.245 + 4.74236i) q^{70} +(1.98379 + 1.98379i) q^{71} +(-62.6288 + 32.7657i) q^{72} +(-55.5273 - 55.5273i) q^{73} +(-41.9639 + 44.5400i) q^{74} +(-16.0424 + 6.64496i) q^{75} +(-24.6150 - 50.6666i) q^{76} +(-21.6555 - 8.97002i) q^{77} +(-1.15789 - 0.439707i) q^{78} +10.9856 q^{79} +(64.5113 + 114.849i) q^{80} +76.5792i q^{81} +(18.3496 + 6.96826i) q^{82} +(34.1779 - 82.5128i) q^{83} +(-14.8447 - 5.13707i) q^{84} +(-8.43772 - 20.3705i) q^{85} +(12.6031 - 13.3767i) q^{86} +(7.52203 - 7.52203i) q^{87} +(1.72868 + 19.3035i) q^{88} +(-16.1705 + 16.1705i) q^{89} +(145.416 - 4.33053i) q^{90} +(5.64942 + 13.6389i) q^{91} +(-6.34164 - 106.379i) q^{92} +(7.39121 - 17.8440i) q^{93} +(-122.239 + 54.9512i) q^{94} +115.939i q^{95} +(1.92626 + 12.8445i) q^{96} -62.6434 q^{97} +(36.5858 + 81.3851i) q^{98} +(19.7749 + 8.19105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

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