LMFDB - Embedded newform 32.3.h.a.27.7

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			27.7
Character	$\chi$	$=$	32.27
Dual form			32.3.h.a.19.7

$q$-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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

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

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	−0.444304	−	0.895876i	$-0.646549\pi$
$3$	−0.374985	+	0.155324i	−0.124995	+	0.0517746i	0.319309	+	0.947651i	$0.396549\pi$
$4$	2.65510	+	2.99173i	0.663775	+	0.747932i
$5$	−7.60625	−	3.15061i	−1.52125	−	0.630122i	−0.543408	−	0.839469i	$-0.682866\pi$
$5$	−7.60625	−	3.15061i	−1.52125	−	0.630122i	−0.977842	+	0.209346i	$0.932866\pi$
$6$	−0.811401	−	0.0241638i	−0.135234	−	0.00402730i
$7$	6.84161	−	6.84161i	0.977372	−	0.977372i	−0.0223772	−	0.999750i	$-0.507123\pi$
$7$	6.84161	−	6.84161i	0.977372	−	0.977372i	0.999750	+	0.0223772i	$0.00712349\pi$
$8$	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	0.278621	−	0.960401i	$-0.410123\pi$
$11$	−2.23818	−	0.927086i	−0.203471	−	0.0842806i	−0.482092	+	0.876121i	$0.660123\pi$
$12$	−1.46031	−	0.709452i	−0.121692	−	0.0591210i
$13$	1.40964	−	0.583890i	0.108433	−	0.0449146i	−0.327807	−	0.944745i	$-0.606310\pi$
$13$	1.40964	−	0.583890i	0.108433	−	0.0449146i	0.436241	+	0.899830i	$0.356310\pi$
$14$	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	$-0.974901\pi$
$17$		−	2.67812i		−	0.157537i	0.996893	−	0.0787683i	$-0.0250987\pi$
$18$	−16.5195	+	6.27326i	−0.917749	+	0.348514i
$19$	5.38908	+	13.0104i	0.283636	+	0.684757i	0.999915	−	0.0130566i	$-0.00415616\pi$
$19$	5.38908	+	13.0104i	0.283636	+	0.684757i	−0.716279	+	0.697814i	$0.754156\pi$
$20$	−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	0.985974	−	0.166898i	$-0.0533750\pi$
$23$	18.8388	+	18.8388i	0.819076	+	0.819076i	−0.166898	+	0.985974i	$0.553375\pi$
$24$	−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	−0.997100	−	0.0761000i	$-0.975753\pi$
$29$	−10.0298	−	24.2140i	−0.345855	−	0.834967i	0.651245	−	0.758867i	$-0.274247\pi$
$30$	6.09559	+	2.74021i	0.203186	+	0.0913402i
$31$		−	47.5858i		−	1.53503i	−0.641033	−	0.767513i	$-0.721494\pi$
$31$		−	47.5858i		−	1.53503i	0.641033	−	0.767513i	$-0.278506\pi$
$32$	−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	−0.0335642	−	0.999437i	$-0.510686\pi$
$37$	−28.2682	−	11.7091i	−0.764006	−	0.316462i	−0.730442	+	0.682975i	$0.760686\pi$
$38$	−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	−0.617395	−	0.786654i	$-0.711812\pi$
$41$	6.93962	−	6.93962i	0.169259	−	0.169259i	0.786654	+	0.617395i	$0.211812\pi$
$42$	−5.71661	+	5.38597i	−0.136110	+	0.128237i
$43$	8.48982	+	3.51660i	0.197438	+	0.0817814i	0.479211	−	0.877700i	$-0.340923\pi$
$43$	8.48982	+	3.51660i	0.197438	+	0.0817814i	−0.281774	+	0.959481i	$0.590923\pi$
$44$	−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	−0.991451	−	0.130482i	$-0.958347\pi$
$53$	−10.5006	+	25.3507i	−0.198124	+	0.478315i	0.793326	+	0.608797i	$0.208347\pi$
$54$	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	−0.489107	−	0.872224i	$-0.662677\pi$
$59$	27.9364	−	67.4445i	0.473499	−	1.14313i	0.962606	−	0.270904i	$-0.0873227\pi$
$60$	8.87226	+	9.99714i	0.147871	+	0.166619i
$61$	31.5752	+	76.2294i	0.517627	+	1.24966i	0.939357	+	0.342941i	$0.111423\pi$
$61$	31.5752	+	76.2294i	0.517627	+	1.24966i	−0.421730	+	0.906721i	$0.638577\pi$
$62$	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	0.410913	−	0.911674i	$-0.365210\pi$
$67$	90.1903	−	37.3580i	1.34612	−	0.557583i	0.935211	+	0.354092i	$0.115210\pi$
$68$	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	−0.692998	−	0.720939i	$-0.743711\pi$
$71$	1.98379	−	1.98379i	0.0279407	−	0.0279407i	0.720939	+	0.692998i	$0.243711\pi$
$72$	−62.6288	−	32.7657i	−0.869844	−	0.455079i
$73$	−55.5273	+	55.5273i	−0.760648	+	0.760648i	−0.976439	−	0.215792i	$-0.930767\pi$
$73$	−55.5273	+	55.5273i	−0.760648	+	0.760648i	0.215792	+	0.976439i	$0.430767\pi$
$74$	−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	0.984659	+	0.174489i	$0.0558272\pi$
$83$	34.1779	+	82.5128i	0.411782	+	0.994130i	−0.572877	+	0.819641i	$0.694173\pi$
$84$	−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	0.610401	−	0.792093i	$-0.291008\pi$
$89$	−16.1705	−	16.1705i	−0.181691	−	0.181691i	−0.792093	+	0.610401i	$0.791008\pi$
$90$	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	0.570612	−	0.821220i	$-0.306706\pi$
$101$	39.7340	+	16.4584i	0.393406	+	0.162954i	−0.177206	+	0.984174i	$0.556706\pi$
$102$	−0.0647136	+	2.17303i	−0.000634447	+	0.0213042i
$103$	−36.3254	+	36.3254i	−0.352674	+	0.352674i	−0.861104	−	0.508430i	$-0.830226\pi$
$103$	−36.3254	+	36.3254i	−0.352674	+	0.352674i	0.508430	+	0.861104i	$0.330226\pi$
$104$	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	0.838049	−	0.545596i	$-0.183696\pi$
$107$	111.798	+	46.3084i	1.04484	+	0.432789i	0.206796	+	0.978384i	$0.433696\pi$
$108$	27.3638	−	9.46938i	0.253368	−	0.0876794i
$109$	−55.7631	+	23.0978i	−0.511588	+	0.211907i	−0.623517	−	0.781809i	$-0.714297\pi$
$109$	−55.7631	+	23.0978i	−0.511588	+	0.211907i	0.111929	+	0.993716i	$0.464297\pi$
$110$	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	$0.116341\pi$
$113$			80.7753i			0.714825i	−0.933947	+	0.357413i	$0.883659\pi$
$114$	−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	$0.190405\pi$
$127$			143.036i			1.12627i	−0.826365	+	0.563135i	$0.809595\pi$
$128$	−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	−0.586534	−	0.809925i	$-0.699508\pi$
$131$	−56.1430	+	23.2552i	−0.428573	+	0.177521i	0.157961	+	0.987445i	$0.449508\pi$
$132$	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	0.262563	−	0.964915i	$-0.415432\pi$
$137$	168.165	−	168.165i	1.22748	−	1.22748i	0.964915	−	0.262563i	$-0.0845679\pi$
$138$	−14.8306	−	15.7410i	−0.107468	−	0.114065i
$139$	−97.5768	−	40.4176i	−0.701991	−	0.290774i	0.00299484	−	0.999996i	$-0.499047\pi$
$139$	−97.5768	−	40.4176i	−0.701991	−	0.290774i	−0.704986	+	0.709221i	$0.749047\pi$
$140$	−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	−0.702167	−	0.712012i	$-0.747784\pi$
$149$	44.3735	−	107.127i	0.297809	−	0.718974i	0.999976	−	0.00696156i	$-0.00221595\pi$
$150$	−23.8147	−	25.2767i	−0.158765	−	0.168511i
$151$	−128.078	−	128.078i	−0.848200	−	0.848200i	0.141708	−	0.989908i	$-0.454741\pi$
$151$	−128.078	−	128.078i	−0.848200	−	0.848200i	−0.989908	+	0.141708i	$0.954741\pi$
$152$	−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	0.974986	−	0.222265i	$-0.0713452\pi$
$157$	20.1590	+	48.6682i	0.128401	+	0.309988i	−0.846585	+	0.532254i	$0.821345\pi$
$158$	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	−0.161943	−	0.986800i	$-0.551776\pi$
$163$	68.6749	−	28.4461i	0.421319	−	0.174516i	0.583262	+	0.812284i	$0.301776\pi$
$164$	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	−0.194396	−	0.980923i	$-0.562275\pi$
$167$	131.350	−	131.350i	0.786527	−	0.786527i	0.980923	+	0.194396i	$0.0622748\pi$
$168$	−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	−0.888084	−	0.459681i	$-0.847964\pi$
$173$	−206.045	+	85.3465i	−1.19101	+	0.493333i	−0.302926	+	0.953014i	$0.597964\pi$
$174$	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	0.973051	+	0.230591i	$0.0740661\pi$
$179$	80.2014	+	193.623i	0.448053	+	1.08169i	−0.524998	+	0.851104i	$0.675934\pi$
$180$	261.710	+	127.145i	1.45395	+	0.706361i
$181$	93.4345	−	225.571i	0.516213	−	1.24625i	−0.424000	−	0.905662i	$-0.639374\pi$
$181$	93.4345	−	225.571i	0.516213	−	1.24625i	0.940213	−	0.340586i	$-0.110626\pi$
$182$	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	$0.0168098\pi$
$191$			20.1639i			0.105570i	−0.998606	+	0.0527851i	$0.983190\pi$
$192$	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	−0.117045	−	0.993127i	$-0.537342\pi$
$197$	−177.705	−	73.6077i	−0.902055	−	0.373643i	−0.785010	+	0.619483i	$0.787342\pi$
$198$	42.7895	+	1.27428i	0.216109	+	0.00643578i
$199$	−22.1763	+	22.1763i	−0.111439	+	0.111439i	−0.760627	−	0.649189i	$-0.775109\pi$
$199$	−22.1763	+	22.1763i	−0.111439	+	0.111439i	0.649189	+	0.760627i	$0.275109\pi$
$200$	−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	−0.914300	−	0.405038i	$-0.867258\pi$
$211$	−116.936	−	282.308i	−0.554197	−	1.33795i	0.360103	−	0.932913i	$-0.382742\pi$
$212$	−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	$-0.991334\pi$
$223$		−	12.1409i		−	0.0544434i	0.999629	−	0.0272217i	$-0.00866601\pi$
$224$	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	0.145307	−	0.989387i	$-0.453583\pi$
$227$	215.118	−	89.1048i	0.947656	−	0.392532i	0.802350	+	0.596854i	$0.203583\pi$
$228$	1.36053	−	22.8225i	0.00596723	−	0.100099i
$229$	85.4872	+	35.4100i	0.373307	+	0.154629i	0.561445	−	0.827514i	$-0.310245\pi$
$229$	85.4872	+	35.4100i	0.373307	+	0.154629i	−0.188139	+	0.982142i	$0.560245\pi$
$230$	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	−0.632462	−	0.774591i	$-0.717956\pi$
$233$	33.1162	−	33.1162i	0.142129	−	0.142129i	0.774591	+	0.632462i	$0.217956\pi$
$234$	−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	$0.150032\pi$
$241$			218.867i			0.908160i	−0.890961	+	0.454080i	$0.849968\pi$
$242$	−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	−0.624687	−	0.780875i	$-0.714773\pi$
$251$	92.6681	−	223.721i	0.369196	−	0.891318i	0.993883	−	0.110442i	$-0.0352267\pi$
$252$	−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	−0.510959	−	0.859605i	$-0.670710\pi$
$263$	91.6940	−	91.6940i	0.348647	−	0.348647i	0.859605	+	0.510959i	$0.170710\pi$
$264$	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	−0.0232059	−	0.999731i	$-0.507387\pi$
$269$	179.504	−	74.3530i	0.667301	−	0.276405i	0.690507	+	0.723325i	$0.257387\pi$
$270$	−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	−0.944889	−	0.327391i	$-0.893830\pi$
$277$	−12.5345	+	30.2610i	−0.0452510	+	0.109246i	0.899638	+	0.436637i	$0.143830\pi$
$278$	−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	0.992731	+	0.120353i	$0.0384027\pi$
$281$	312.777	+	312.777i	1.11308	+	1.11308i	0.120353	+	0.992731i	$0.461597\pi$
$282$	54.3730	+	1.61924i	0.192812	+	0.00574200i
$283$	−74.2838	+	179.337i	−0.262487	+	0.633700i	−0.999091	−	0.0426244i	$-0.986428\pi$
$283$	−74.2838	+	179.337i	−0.262487	+	0.633700i	0.736604	+	0.676324i	$0.236428\pi$
$284$	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	0.0998364	−	0.995004i	$-0.468168\pi$
$293$	−156.211	−	64.7046i	−0.533143	−	0.220835i	−0.632979	+	0.774169i	$0.718168\pi$
$294$	−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	0.994835	+	0.101504i	$0.0323654\pi$
$307$	111.488	+	269.157i	0.363155	+	0.876733i	−0.631681	+	0.775229i	$0.717635\pi$
$308$	−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	0.577960	−	0.816065i	$-0.303849\pi$
$311$	−74.0508	−	74.0508i	−0.238105	−	0.238105i	−0.816065	+	0.577960i	$0.803849\pi$
$312$	−4.38980	−	2.29662i	−0.0140699	−	0.00736097i
$313$	−119.709	−	119.709i	−0.382458	−	0.382458i	0.489529	−	0.871987i	$-0.337169\pi$
$313$	−119.709	−	119.709i	−0.382458	−	0.382458i	−0.871987	+	0.489529i	$0.837169\pi$
$314$	−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	0.955942	+	0.293554i	$0.0948382\pi$
$317$	154.558	+	373.135i	0.487563	+	1.17708i	−0.468379	+	0.883528i	$0.655162\pi$
$318$	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	−0.266190	−	0.963921i	$-0.585765\pi$
$331$	−376.019	−	155.752i	−1.13601	−	0.470551i	−0.869820	+	0.493370i	$0.835765\pi$
$332$	−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	$-0.666115\pi$
$337$		−	584.284i		−	1.73378i	0.498499	−	0.866890i	$-0.333885\pi$
$338$	−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	−0.944047	−	0.329812i	$-0.893015\pi$
$347$	−15.0226	+	36.2679i	−0.0432929	+	0.104518i	0.900754	+	0.434330i	$0.143015\pi$
$348$	−2.53212	+	42.4756i	−0.00727621	+	0.122056i
$349$	82.9090	+	200.160i	0.237562	+	0.573525i	0.997030	−	0.0770202i	$-0.0245406\pi$
$349$	82.9090	+	200.160i	0.237562	+	0.573525i	−0.759468	+	0.650545i	$0.774541\pi$
$350$	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	−0.298264	−	0.954483i	$-0.596408\pi$
$359$	235.583	−	235.583i	0.656219	−	0.656219i	0.954483	+	0.298264i	$0.0964077\pi$
$360$	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	−0.637232	−	0.770672i	$-0.719921\pi$
$373$	133.648	−	322.655i	0.358306	−	0.865028i	0.995539	−	0.0943560i	$-0.0300792\pi$
$374$	−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	−0.922204	−	0.386704i	$-0.873614\pi$
$379$	1.26349	−	3.05034i	0.00333376	−	0.00804840i	0.925538	+	0.378656i	$0.123614\pi$
$380$	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	$0.132889\pi$
$383$			310.584i			0.810923i	−0.914112	+	0.405462i	$0.867111\pi$
$384$	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	−0.998695	−	0.0510705i	$-0.983737\pi$
$389$	−677.246	−	280.524i	−1.74099	−	0.721142i	−0.742296	−	0.670072i	$-0.766263\pi$
$390$	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	−0.883840	−	0.467789i	$-0.845051\pi$
$397$	−467.679	+	193.719i	−1.17803	+	0.487957i	−0.294192	+	0.955746i	$0.595051\pi$
$398$	−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	$0.188559\pi$
$401$			447.783i			1.11667i	−0.829617	+	0.558333i	$0.811441\pi$
$402$	−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	0.953458	−	0.301527i	$-0.0974962\pi$
$409$	266.640	+	266.640i	0.651931	+	0.651931i	−0.301527	+	0.953458i	$0.597496\pi$
$410$	−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	−0.936205	−	0.351455i	$-0.885687\pi$
$419$	−565.518	+	234.245i	−1.34969	+	0.559058i	−0.413481	+	0.910513i	$0.635687\pi$
$420$	129.097	+	7.69592i	0.307374	+	0.0183236i
$421$	−184.538	−	76.4382i	−0.438333	−	0.181564i	0.152593	−	0.988289i	$-0.451238\pi$
$421$	−184.538	−	76.4382i	−0.438333	−	0.181564i	−0.590926	+	0.806726i	$0.701238\pi$
$422$	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	$0.154261\pi$
$433$			403.449i			0.931753i	−0.884850	+	0.465877i	$0.845739\pi$
$434$	−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	0.999882	−	0.0153402i	$-0.00488314\pi$
$439$	432.214	+	432.214i	0.984542	+	0.984542i	−0.0153402	+	0.999882i	$0.504883\pi$
$440$	−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	−0.687799	−	0.725901i	$-0.741423\pi$
$443$	138.144	−	333.509i	0.311838	−	0.752843i	0.999637	−	0.0269419i	$-0.00857692\pi$
$444$	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	−0.850569	−	0.525864i	$-0.823742\pi$
$457$	−148.390	+	148.390i	−0.324705	+	0.324705i	0.525864	+	0.850569i	$0.323742\pi$
$458$	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	−0.612456	−	0.790505i	$-0.709818\pi$
$461$	−224.303	+	92.9092i	−0.486557	+	0.201538i	0.125899	+	0.992043i	$0.459818\pi$
$462$	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	0.985448	+	0.169977i	$0.0543695\pi$
$467$	190.920	+	460.923i	0.408823	+	0.986987i	−0.576625	+	0.817009i	$0.695631\pi$
$468$	−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	$-0.699621\pi$
$479$		−	775.709i		−	1.61943i	0.586821	−	0.809717i	$-0.300379\pi$
$480$	−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	−0.992110	−	0.125372i	$-0.959988\pi$
$487$	−422.101	+	422.101i	−0.866738	+	0.866738i	0.125372	+	0.992110i	$0.459988\pi$
$488$	−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	0.0816809	−	0.996659i	$-0.473971\pi$
$491$	−277.565	−	114.971i	−0.565306	−	0.234157i	−0.646987	+	0.762501i	$0.723971\pi$
$492$	−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	−0.800410	−	0.599452i	$-0.795385\pi$
$499$	−328.498	−	793.063i	−0.658312	−	1.58930i	0.142099	−	0.989852i	$-0.454615\pi$
$500$	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	0.582960	−	0.812501i	$-0.301894\pi$
$503$	−115.459	−	115.459i	−0.229540	−	0.229540i	−0.812501	+	0.582960i	$0.801894\pi$
$504$	−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	0.798364	−	0.602175i	$-0.205699\pi$
$509$	−97.7110	−	235.895i	−0.191967	−	0.463449i	−0.990331	+	0.138727i	$0.955699\pi$
$510$	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	−0.451173	−	0.892437i	$-0.648994\pi$
$521$	229.899	−	229.899i	0.441264	−	0.441264i	0.892437	+	0.451173i	$0.148994\pi$
$522$	317.588	+	337.084i	0.608406	+	0.645755i
$523$	−900.921	−	373.174i	−1.72260	−	0.713525i	−0.999746	−	0.0225265i	$-0.992829\pi$
$523$	−900.921	−	373.174i	−1.72260	−	0.713525i	−0.722856	−	0.690999i	$-0.757171\pi$
$524$	−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	0.983385	−	0.181533i	$-0.0581058\pi$
$541$	86.3781	+	208.535i	0.159664	+	0.385462i	−0.823721	+	0.566995i	$0.808106\pi$
$542$	−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	0.121628	−	0.992576i	$-0.461188\pi$
$547$	497.491	−	206.067i	0.909489	−	0.376723i	0.787861	+	0.615853i	$0.211188\pi$
$548$	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	−0.802397	−	0.596791i	$-0.796442\pi$
$557$	−527.914	+	218.669i	−0.947782	+	0.392584i	−0.145385	+	0.989375i	$0.546442\pi$
$558$	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	−0.924871	−	0.380281i	$-0.875827\pi$
$563$	−303.900	−	733.680i	−0.539788	−	1.30316i	0.385084	−	0.922882i	$-0.374173\pi$
$564$	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	0.569538	−	0.821965i	$-0.307122\pi$
$569$	−143.631	−	143.631i	−0.252426	−	0.252426i	−0.821965	+	0.569538i	$0.807122\pi$
$570$	−2.80153	+	94.0732i	−0.00491496	+	0.165041i
$571$	−371.018	+	895.717i	−0.649769	+	1.56868i	0.163339	+	0.986570i	$0.447773\pi$
$571$	−371.018	+	895.717i	−0.649769	+	1.56868i	−0.813109	+	0.582112i	$0.802227\pi$
$572$	−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	0.618481	−	0.785800i	$-0.287748\pi$
$587$	293.599	+	121.613i	0.500169	+	0.207177i	−0.118312	+	0.992976i	$0.537748\pi$
$588$	−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	$0.192602\pi$
$593$			674.627i			1.13765i	−0.822458	+	0.568825i	$0.807398\pi$
$594$	−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	0.949052	−	0.315120i	$-0.102045\pi$
$599$	379.725	+	379.725i	0.633932	+	0.633932i	−0.315120	+	0.949052i	$0.602045\pi$
$600$	12.3905	−	138.359i	0.0206508	−	0.230599i
$601$	−548.542	−	548.542i	−0.912715	−	0.912715i	0.0837700	−	0.996485i	$-0.473304\pi$
$601$	−548.542	−	548.542i	−0.912715	−	0.912715i	−0.996485	+	0.0837700i	$0.973304\pi$
$602$	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	$0.000275484\pi$
$607$			1.05067i			0.00173092i	−1.00000		0.000865460i	$0.999725\pi$
$608$	−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	0.829428	−	0.558613i	$-0.188666\pi$
$613$	625.826	+	259.226i	1.02092	+	0.422881i	0.191495	+	0.981494i	$0.438666\pi$
$614$	−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	−0.545398	−	0.838177i	$-0.683622\pi$
$617$	180.644	−	180.644i	0.292779	−	0.292779i	0.838177	+	0.545398i	$0.183622\pi$
$618$	30.3523	−	28.5967i	0.0491137	−	0.0462730i
$619$	555.651	+	230.158i	0.897658	+	0.371822i	0.783319	−	0.621620i	$-0.213525\pi$
$619$	555.651	+	230.158i	0.897658	+	0.371822i	0.114339	+	0.993442i	$0.463525\pi$
$620$	−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	0.462537	−	0.886600i	$-0.346939\pi$
$631$	−267.583	−	267.583i	−0.424062	−	0.424062i	−0.886600	+	0.462537i	$0.846939\pi$
$632$	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	0.579592	−	0.814907i	$-0.303212\pi$
$643$	1006.71	−	416.995i	1.56565	−	0.648514i	0.986060	+	0.166393i	$0.0532119\pi$
$644$	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	−0.415099	+	0.909776i	$0.636253\pi$
$647$	−857.194	+	857.194i	−1.32488	+	1.32488i	−0.909776	+	0.415099i	$0.863747\pi$
$648$	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	−0.461813	−	0.886977i	$-0.652801\pi$
$653$	−105.248	+	43.5953i	−0.161177	+	0.0667616i	0.300636	+	0.953739i	$0.402801\pi$
$654$	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	−0.997889	−	0.0649499i	$-0.979311\pi$
$659$	−222.875	−	538.067i	−0.338201	−	0.816490i	0.659687	−	0.751540i	$-0.270689\pi$
$660$	−10.5896	−	30.6008i	−0.0160448	−	0.0463648i
$661$	−396.971	+	958.372i	−0.600561	+	1.44988i	0.272445	+	0.962171i	$0.412168\pi$
$661$	−396.971	+	958.372i	−0.600561	+	1.44988i	−0.873005	+	0.487711i	$0.837832\pi$
$662$	−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	0.955528	−	0.294900i	$-0.0952865\pi$
$677$	963.142	+	398.947i	1.42266	+	0.589286i	0.467134	+	0.884186i	$0.345287\pi$
$678$	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	0.557420	−	0.830230i	$-0.311791\pi$
$683$	248.963	+	103.124i	0.364515	+	0.150987i	−0.192906	+	0.981217i	$0.561791\pi$
$684$	−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	−0.999116	−	0.0420488i	$-0.986612\pi$
$691$	−222.756	−	537.780i	−0.322367	−	0.778263i	0.676748	−	0.736214i	$-0.263388\pi$
$692$	−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	−0.997986	−	0.0634324i	$-0.979795\pi$
$701$	−236.347	−	570.592i	−0.337157	−	0.813969i	0.660829	−	0.750536i	$-0.270205\pi$
$702$	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	−0.0826257	−	0.996581i	$-0.526331\pi$
$709$	−599.630	−	248.375i	−0.845740	−	0.350317i	−0.763114	+	0.646264i	$0.776331\pi$
$710$	−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	0.0252626	−	0.999681i	$-0.491958\pi$
$727$	−708.402	−	708.402i	−0.974418	−	0.974418i	−0.999681	+	0.0252626i	$0.991958\pi$
$728$	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	0.788458	−	0.615088i	$-0.210880\pi$
$733$	−149.531	−	361.000i	−0.203999	−	0.492497i	−0.992457	+	0.122591i	$0.960880\pi$
$734$	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	−0.926205	−	0.377021i	$-0.876948\pi$
$739$	−971.442	+	402.384i	−1.31454	+	0.544499i	−0.388331	+	0.921520i	$0.626948\pi$
$740$	−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	−0.623839	−	0.781553i	$-0.714428\pi$
$743$	117.181	−	117.181i	0.157714	−	0.157714i	0.781553	+	0.623839i	$0.214428\pi$
$744$	−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	0.258152	+	0.966104i	$0.416887\pi$
$757$	−459.899	+	1110.29i	−0.607528	+	1.46670i	−0.865680	+	0.500598i	$0.833113\pi$
$758$	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	0.827660	−	0.561230i	$-0.189672\pi$
$761$	202.753	+	202.753i	0.266430	+	0.266430i	−0.561230	+	0.827660i	$0.689672\pi$
$762$	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	0.535007	−	0.844847i	$-0.320309\pi$
$773$	244.204	+	101.153i	0.315918	+	0.130857i	−0.219090	+	0.975705i	$0.570309\pi$
$774$	−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	0.910776	−	0.412902i	$-0.135485\pi$
$787$	−19.8368	−	47.8903i	−0.0252056	−	0.0608518i	−0.935981	+	0.352050i	$0.885485\pi$
$788$	−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	0.996775	−	0.0802411i	$-0.0255690\pi$
$797$	187.462	+	452.574i	0.235210	+	0.567847i	−0.761566	+	0.648088i	$0.775569\pi$
$798$	−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	−0.999018	−	0.0443114i	$-0.985891\pi$
$809$	−772.357	+	772.357i	−0.954706	+	0.954706i	0.0443114	+	0.999018i	$0.485891\pi$
$810$	−917.768	+	864.686i	−1.13305	+	1.06751i
$811$	518.106	+	214.607i	0.638849	+	0.264620i	0.678508	−	0.734593i	$-0.262627\pi$
$811$	518.106	+	214.607i	0.638849	+	0.264620i	−0.0396587	+	0.999213i	$0.512627\pi$
$812$	−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	−0.587378	−	0.809313i	$-0.699840\pi$
$821$	328.590	−	793.287i	0.400232	−	0.966245i	0.987609	−	0.156932i	$-0.0501604\pi$
$822$	−140.512	+	132.385i	−0.170940	+	0.161053i
$823$	−370.318	−	370.318i	−0.449961	−	0.449961i	0.445381	−	0.895341i	$-0.353068\pi$
$823$	−370.318	−	370.318i	−0.449961	−	0.449961i	−0.895341	+	0.445381i	$0.853068\pi$
$824$	−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	−0.953943	−	0.299988i	$-0.903017\pi$
$827$	−55.6405	+	134.328i	−0.0672799	+	0.162428i	0.886663	+	0.462416i	$0.153017\pi$
$828$	−624.982	−	704.221i	−0.754809	−	0.850508i
$829$	492.586	+	1189.21i	0.594193	+	1.43451i	0.879419	+	0.476048i	$0.157931\pi$
$829$	492.586	+	1189.21i	0.594193	+	1.43451i	−0.285226	+	0.958460i	$0.592069\pi$
$830$	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	−0.823636	−	0.567119i	$-0.808058\pi$
$839$	−215.217	+	215.217i	−0.256516	+	0.256516i	0.567119	+	0.823636i	$0.308058\pi$
$840$	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	−0.958996	−	0.283421i	$-0.908531\pi$
$853$	−68.6449	+	165.723i	−0.0804747	+	0.194283i	0.878521	+	0.477704i	$0.158531\pi$
$854$	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	0.987909	−	0.155037i	$-0.0495497\pi$
$857$	713.771	+	713.771i	0.832871	+	0.832871i	−0.155037	+	0.987909i	$0.549550\pi$
$858$	2.99922	+	0.0893175i	0.00349559	+	0.000104100i
$859$	343.845	−	830.116i	0.400285	−	0.966375i	−0.587311	−	0.809361i	$-0.699813\pi$
$859$	343.845	−	830.116i	0.400285	−	0.966375i	0.987596	−	0.157013i	$-0.0501866\pi$
$860$	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	$0.365528\pi$
$863$			1574.26i			1.82417i	−0.410002	+	0.912085i	$0.634472\pi$
$864$	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	0.450042	−	0.893007i	$-0.351409\pi$
$877$	1227.56	−	508.470i	1.39972	−	0.579784i	0.949679	+	0.313224i	$0.101409\pi$
$878$	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	$-0.764575\pi$
$881$		−	1187.59i		−	1.34800i	0.738732	−	0.674000i	$-0.235425\pi$
$882$	279.882	+	737.020i	0.317327	+	0.835623i
$883$	544.271	+	1313.99i	0.616389	+	1.48809i	0.855869	+	0.517193i	$0.173023\pi$
$883$	544.271	+	1313.99i	0.616389	+	1.48809i	−0.239480	+	0.970901i	$0.576977\pi$
$884$	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	0.651459	−	0.758684i	$-0.274157\pi$
$887$	−95.1081	−	95.1081i	−0.107224	−	0.107224i	−0.758684	+	0.651459i	$0.774157\pi$
$888$	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	0.439139	−	0.898419i	$-0.355284\pi$
$907$	103.742	+	42.9713i	0.114379	+	0.0473774i	−0.324760	+	0.945796i	$0.605284\pi$
$908$	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	0.997148	−	0.0754671i	$-0.0240448\pi$
$919$	847.025	+	847.025i	0.921681	+	0.921681i	−0.0754671	+	0.997148i	$0.524045\pi$
$920$	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	0.325670	−	0.945484i	$-0.394410\pi$
$937$	1191.07	−	1191.07i	1.27115	−	1.27115i	0.945484	−	0.325670i	$-0.105590\pi$
$938$	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	−0.739964	−	0.672647i	$-0.765157\pi$
$941$	−741.098	+	306.973i	−0.787564	+	0.326220i	−0.0476005	+	0.998866i	$0.515157\pi$
$942$	−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	0.878701	−	0.477373i	$-0.158411\pi$
$947$	−75.9383	−	183.331i	−0.0801883	−	0.193592i	−0.958889	+	0.283781i	$0.908411\pi$
$948$	−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	0.569319	−	0.822117i	$-0.307207\pi$
$953$	−240.916	−	240.916i	−0.252798	−	0.252798i	−0.822117	+	0.569319i	$0.807207\pi$
$954$	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	−0.417831	−	0.908525i	$-0.637209\pi$
$967$	474.501	−	474.501i	0.490694	−	0.490694i	0.908525	+	0.417831i	$0.137209\pi$
$968$	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	0.618897	−	0.785472i	$-0.287580\pi$
$971$	486.579	+	201.548i	0.501111	+	0.207567i	−0.117786	+	0.993039i	$0.537580\pi$
$972$	−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	$-0.977568\pi$
$977$		−	137.589i		−	0.140828i	0.997518	−	0.0704140i	$-0.0224320\pi$
$978$	−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	0.330551	−	0.943788i	$-0.392765\pi$
$983$	−602.812	−	602.812i	−0.613237	−	0.613237i	−0.943788	+	0.330551i	$0.892765\pi$
$984$	−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	$0.0132098\pi$
$991$			82.2289i			0.0829757i	−0.999139	+	0.0414879i	$0.986790\pi$
$992$	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	0.892705	−	0.450641i	$-0.148805\pi$
$997$	1201.68	+	497.750i	1.20529	+	0.499248i	0.312586	+	0.949889i	$0.398805\pi$
$998$	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.27.7	yes	28
3.2	odd	2		288.3.u.a.91.1		28
4.3	odd	2		128.3.h.a.15.4		28
8.3	odd	2		256.3.h.a.31.4		28
8.5	even	2		256.3.h.b.31.4		28
32.3	odd	8		256.3.h.b.223.4		28
32.13	even	8		128.3.h.a.111.4		28
32.19	odd	8	inner	32.3.h.a.19.7	✓	28
32.29	even	8		256.3.h.a.223.4		28
96.83	even	8		288.3.u.a.19.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.7	✓	28	32.19	odd	8	inner
32.3.h.a.27.7	yes	28	1.1	even	1	trivial
128.3.h.a.15.4		28	4.3	odd	2
128.3.h.a.111.4		28	32.13	even	8
256.3.h.a.31.4		28	8.3	odd	2
256.3.h.a.223.4		28	32.29	even	8
256.3.h.b.31.4		28	8.5	even	2
256.3.h.b.223.4		28	32.3	odd	8
288.3.u.a.19.1		28	96.83	even	8
288.3.u.a.91.1		28	3.2	odd	2

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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