LMFDB - Embedded newform 32.3.h.a.19.5

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			19.5
Character	$\chi$	$=$	32.19
Dual form			32.3.h.a.27.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.345994 - 1.96984i) q^{2} +(-3.70255 - 1.53365i) q^{3} +(-3.76058 - 1.36311i) q^{4} +(7.20074 - 2.98264i) q^{5} +(-4.30210 + 6.76281i) q^{6} +(4.26150 + 4.26150i) q^{7} +(-3.98625 + 6.93612i) q^{8} +(4.99283 + 4.99283i) q^{9} +O(q^{10})$	\(q+(0.345994 - 1.96984i) q^{2} +(-3.70255 - 1.53365i) q^{3} +(-3.76058 - 1.36311i) q^{4} +(7.20074 - 2.98264i) q^{5} +(-4.30210 + 6.76281i) q^{6} +(4.26150 + 4.26150i) q^{7} +(-3.98625 + 6.93612i) q^{8} +(4.99283 + 4.99283i) q^{9} +(-3.38393 - 15.2163i) q^{10} +(6.19818 - 2.56737i) q^{11} +(11.8332 + 10.8144i) q^{12} +(-8.05345 - 3.33585i) q^{13} +(9.86895 - 6.92004i) q^{14} -31.2354 q^{15} +(12.2839 + 10.2522i) q^{16} +24.5802i q^{17} +(11.5626 - 8.10762i) q^{18} +(4.96459 - 11.9856i) q^{19} +(-31.1446 + 1.40106i) q^{20} +(-9.24278 - 22.3140i) q^{21} +(-2.91279 - 13.0978i) q^{22} +(-9.72199 + 9.72199i) q^{23} +(25.3968 - 19.5678i) q^{24} +(25.2768 - 25.2768i) q^{25} +(-9.35754 + 14.7099i) q^{26} +(2.97384 + 7.17949i) q^{27} +(-10.2168 - 21.8346i) q^{28} +(-5.86371 + 14.1563i) q^{29} +(-10.8073 + 61.5289i) q^{30} -17.5320i q^{31} +(24.4453 - 20.6501i) q^{32} -26.8865 q^{33} +(48.4192 + 8.50460i) q^{34} +(43.3965 + 17.9754i) q^{35} +(-11.9702 - 25.5817i) q^{36} +(-36.0346 + 14.9260i) q^{37} +(-21.8920 - 13.9264i) q^{38} +(24.7023 + 24.7023i) q^{39} +(-8.01597 + 61.8348i) q^{40} +(10.9784 + 10.9784i) q^{41} +(-47.1531 + 10.4863i) q^{42} +(-22.4024 + 9.27937i) q^{43} +(-26.8084 + 1.20599i) q^{44} +(50.8439 + 21.0603i) q^{45} +(15.7871 + 22.5146i) q^{46} +27.0104 q^{47} +(-29.7584 - 56.7982i) q^{48} -12.6792i q^{49} +(-41.0458 - 58.5371i) q^{50} +(37.6973 - 91.0093i) q^{51} +(25.7385 + 23.5224i) q^{52} +(-34.0172 - 82.1247i) q^{53} +(15.1714 - 3.37395i) q^{54} +(36.9740 - 36.9740i) q^{55} +(-46.5457 + 12.5709i) q^{56} +(-36.7633 + 36.7633i) q^{57} +(25.8568 + 16.4486i) q^{58} +(27.8391 + 67.2095i) q^{59} +(117.463 + 42.5773i) q^{60} +(-6.37082 + 15.3805i) q^{61} +(-34.5354 - 6.06598i) q^{62} +42.5539i q^{63} +(-32.2196 - 55.2983i) q^{64} -67.9404 q^{65} +(-9.30258 + 52.9623i) q^{66} +(-99.2165 - 41.0968i) q^{67} +(33.5055 - 92.4357i) q^{68} +(50.9062 - 21.0860i) q^{69} +(50.4237 - 79.2650i) q^{70} +(-2.55754 - 2.55754i) q^{71} +(-54.5336 + 14.7282i) q^{72} +(30.7498 + 30.7498i) q^{73} +(16.9342 + 76.1469i) q^{74} +(-132.354 + 54.8230i) q^{75} +(-35.0074 + 38.3054i) q^{76} +(37.3544 + 15.4727i) q^{77} +(57.2065 - 40.1128i) q^{78} -90.6600 q^{79} +(119.031 + 37.1847i) q^{80} -94.6916i q^{81} +(25.4241 - 17.8272i) q^{82} +(-39.3191 + 94.9247i) q^{83} +(4.34169 + 96.5126i) q^{84} +(73.3140 + 176.996i) q^{85} +(10.5278 + 47.3398i) q^{86} +(43.4214 - 43.4214i) q^{87} +(-6.89991 + 53.2256i) q^{88} +(109.290 - 109.290i) q^{89} +(59.0771 - 92.8680i) q^{90} +(-20.1040 - 48.5355i) q^{91} +(49.8124 - 23.3081i) q^{92} +(-26.8879 + 64.9132i) q^{93} +(9.34545 - 53.2063i) q^{94} -101.113i q^{95} +(-122.180 + 38.9677i) q^{96} +63.7161 q^{97} +(-24.9761 - 4.38694i) q^{98} +(43.7650 + 18.1280i) 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 $

$2$	0.345994	−	1.96984i	0.172997	−	0.984922i
$2$	0.345994	−	1.96984i	0.172997	−	0.984922i
$3$	−3.70255	−	1.53365i	−1.23418	−	0.511215i	−0.332291	−	0.943177i	$-0.607822\pi$
$3$	−3.70255	−	1.53365i	−1.23418	−	0.511215i	−0.901892	+	0.431962i	$0.857822\pi$
$4$	−3.76058	−	1.36311i	−0.940144	−	0.340777i
$5$	7.20074	−	2.98264i	1.44015	−	0.596529i	0.480314	−	0.877097i	$-0.340523\pi$
$5$	7.20074	−	2.98264i	1.44015	−	0.596529i	0.959834	+	0.280568i	$0.0905227\pi$
$6$	−4.30210	+	6.76281i	−0.717017	+	1.12714i
$7$	4.26150	+	4.26150i	0.608786	+	0.608786i	0.942629	−	0.333843i	$-0.108346\pi$
$7$	4.26150	+	4.26150i	0.608786	+	0.608786i	−0.333843	+	0.942629i	$0.608346\pi$
$8$	−3.98625	+	6.93612i	−0.498281	+	0.867015i
$9$	4.99283	+	4.99283i	0.554759	+	0.554759i
$10$	−3.38393	−	15.2163i	−0.338393	−	1.52163i
$11$	6.19818	−	2.56737i	0.563471	−	0.233397i	−0.0827202	−	0.996573i	$-0.526361\pi$
$11$	6.19818	−	2.56737i	0.563471	−	0.233397i	0.646191	+	0.763175i	$0.276361\pi$
$12$	11.8332	+	10.8144i	0.986099	+	0.901197i
$13$	−8.05345	−	3.33585i	−0.619496	−	0.256604i	0.0507868	−	0.998710i	$-0.483827\pi$
$13$	−8.05345	−	3.33585i	−0.619496	−	0.256604i	−0.670283	+	0.742106i	$0.733827\pi$
$14$	9.86895	−	6.92004i	0.704925	−	0.494288i
$15$	−31.2354			−2.08236
$16$	12.2839	+	10.2522i	0.767742	+	0.640760i
$17$			24.5802i			1.44589i	0.690904	+	0.722947i	$0.257213\pi$
$17$			24.5802i			1.44589i	−0.690904	+	0.722947i	$0.742787\pi$
$18$	11.5626	−	8.10762i	0.642367	−	0.450423i
$19$	4.96459	−	11.9856i	0.261294	−	0.630820i	−0.737725	−	0.675101i	$-0.764100\pi$
$19$	4.96459	−	11.9856i	0.261294	−	0.630820i	0.999019	+	0.0442815i	$0.0140998\pi$
$20$	−31.1446	+	1.40106i	−1.55723	+	0.0700532i
$21$	−9.24278	−	22.3140i	−0.440132	−	1.06257i
$22$	−2.91279	−	13.0978i	−0.132399	−	0.595353i
$23$	−9.72199	+	9.72199i	−0.422695	+	0.422695i	−0.886131	−	0.463435i	$-0.846617\pi$
$23$	−9.72199	+	9.72199i	−0.422695	+	0.422695i	0.463435	+	0.886131i	$0.346617\pi$
$24$	25.3968	−	19.5678i	1.05820	−	0.815326i
$25$	25.2768	−	25.2768i	1.01107	−	1.01107i
$26$	−9.35754	+	14.7099i	−0.359906	+	0.565764i
$27$	2.97384	+	7.17949i	0.110142	+	0.265907i
$28$	−10.2168	−	21.8346i	−0.364886	−	0.779807i
$29$	−5.86371	+	14.1563i	−0.202197	+	0.488147i	−0.992155	−	0.125014i	$-0.960102\pi$
$29$	−5.86371	+	14.1563i	−0.202197	+	0.488147i	0.789958	+	0.613161i	$0.210102\pi$
$30$	−10.8073	+	61.5289i	−0.360242	+	2.05096i
$31$		−	17.5320i		−	0.565550i	−0.959186	−	0.282775i	$-0.908745\pi$
$31$		−	17.5320i		−	0.565550i	0.959186	−	0.282775i	$-0.0912549\pi$
$32$	24.4453	−	20.6501i	0.763915	−	0.645316i
$33$	−26.8865			−0.814743
$34$	48.4192	+	8.50460i	1.42409	+	0.250135i
$35$	43.3965	+	17.9754i	1.23990	+	0.513583i
$36$	−11.9702	−	25.5817i	−0.332504	−	0.710603i
$37$	−36.0346	+	14.9260i	−0.973909	+	0.403406i	−0.812166	−	0.583427i	$-0.801712\pi$
$37$	−36.0346	+	14.9260i	−0.973909	+	0.403406i	−0.161743	+	0.986833i	$0.551712\pi$
$38$	−21.8920	−	13.9264i	−0.576106	−	0.366485i
$39$	24.7023	+	24.7023i	0.633391	+	0.633391i
$40$	−8.01597	+	61.8348i	−0.200399	+	1.54587i
$41$	10.9784	+	10.9784i	0.267765	+	0.267765i	0.828199	−	0.560434i	$-0.189366\pi$
$41$	10.9784	+	10.9784i	0.267765	+	0.267765i	−0.560434	+	0.828199i	$0.689366\pi$
$42$	−47.1531	+	10.4863i	−1.12269	+	0.249674i
$43$	−22.4024	+	9.27937i	−0.520985	+	0.215799i	−0.627650	−	0.778496i	$-0.715983\pi$
$43$	−22.4024	+	9.27937i	−0.520985	+	0.215799i	0.106664	+	0.994295i	$0.465983\pi$
$44$	−26.8084	+	1.20599i	−0.609281	+	0.0274090i
$45$	50.8439	+	21.0603i	1.12987	+	0.468006i
$46$	15.7871	+	22.5146i	0.343197	+	0.489447i
$47$	27.0104			0.574690			0.287345	−	0.957827i	$-0.407227\pi$
$47$	27.0104			0.574690			0.287345	+	0.957827i	$0.407227\pi$
$48$	−29.7584	−	56.7982i	−0.619967	−	1.18330i
$49$		−	12.6792i		−	0.258760i
$50$	−41.0458	−	58.5371i	−0.820916	−	1.17074i
$51$	37.6973	−	91.0093i	0.739163	−	1.78450i
$52$	25.7385	+	23.5224i	0.494971	+	0.452354i
$53$	−34.0172	−	82.1247i	−0.641833	−	1.54952i	−0.824204	−	0.566293i	$-0.808377\pi$
$53$	−34.0172	−	82.1247i	−0.641833	−	1.54952i	0.182371	−	0.983230i	$-0.441623\pi$
$54$	15.1714	−	3.37395i	0.280952	−	0.0624805i
$55$	36.9740	−	36.9740i	0.672254	−	0.672254i
$56$	−46.5457	+	12.5709i	−0.831173	+	0.224480i
$57$	−36.7633	+	36.7633i	−0.644970	+	0.644970i
$58$	25.8568	+	16.4486i	0.445807	+	0.283596i
$59$	27.8391	+	67.2095i	0.471849	+	1.13914i	0.963345	+	0.268264i	$0.0864499\pi$
$59$	27.8391	+	67.2095i	0.471849	+	1.13914i	−0.491497	+	0.870879i	$0.663550\pi$
$60$	117.463	+	42.5773i	1.95772	+	0.709621i
$61$	−6.37082	+	15.3805i	−0.104440	+	0.252140i	−0.967457	−	0.253034i	$-0.918572\pi$
$61$	−6.37082	+	15.3805i	−0.104440	+	0.252140i	0.863018	+	0.505174i	$0.168572\pi$
$62$	−34.5354	−	6.06598i	−0.557022	−	0.0978384i
$63$			42.5539i			0.675459i
$64$	−32.2196	−	55.2983i	−0.503431	−	0.864035i
$65$	−67.9404			−1.04524
$66$	−9.30258	+	52.9623i	−0.140948	+	0.802458i
$67$	−99.2165	−	41.0968i	−1.48084	−	0.613386i	−0.511542	−	0.859258i	$-0.670925\pi$
$67$	−99.2165	−	41.0968i	−1.48084	−	0.613386i	−0.969302	+	0.245873i	$0.920925\pi$
$68$	33.5055	−	92.4357i	0.492728	−	1.35935i
$69$	50.9062	−	21.0860i	0.737771	−	0.305595i
$70$	50.4237	−	79.2650i	0.720339	−	1.13236i
$71$	−2.55754	−	2.55754i	−0.0360217	−	0.0360217i	0.688867	−	0.724888i	$-0.258109\pi$
$71$	−2.55754	−	2.55754i	−0.0360217	−	0.0360217i	−0.724888	+	0.688867i	$0.758109\pi$
$72$	−54.5336	+	14.7282i	−0.757411	+	0.204559i
$73$	30.7498	+	30.7498i	0.421230	+	0.421230i	0.885627	−	0.464397i	$-0.153729\pi$
$73$	30.7498	+	30.7498i	0.421230	+	0.421230i	−0.464397	+	0.885627i	$0.653729\pi$
$74$	16.9342	+	76.1469i	0.228840	+	1.02901i
$75$	−132.354	+	54.8230i	−1.76473	+	0.730973i
$76$	−35.0074	+	38.3054i	−0.460623	+	0.504019i
$77$	37.3544	+	15.4727i	0.485122	+	0.200944i
$78$	57.2065	−	40.1128i	0.733416	−	0.514267i
$79$	−90.6600			−1.14759			−0.573797	−	0.818997i	$-0.694530\pi$
$79$	−90.6600			−1.14759			−0.573797	+	0.818997i	$0.694530\pi$
$80$	119.031	+	37.1847i	1.48789	+	0.464809i
$81$		−	94.6916i		−	1.16903i
$82$	25.4241	−	17.8272i	0.310051	−	0.217405i
$83$	−39.3191	+	94.9247i	−0.473724	+	1.14367i	0.488781	+	0.872407i	$0.337442\pi$
$83$	−39.3191	+	94.9247i	−0.473724	+	1.14367i	−0.962505	+	0.271264i	$0.912558\pi$
$84$	4.34169	+	96.5126i	0.0516868	+	1.14896i
$85$	73.3140	+	176.996i	0.862517	+	2.08230i
$86$	10.5278	+	47.3398i	0.122417	+	0.550463i
$87$	43.4214	−	43.4214i	0.499096	−	0.499096i
$88$	−6.89991	+	53.2256i	−0.0784081	+	0.604836i
$89$	109.290	−	109.290i	1.22798	−	1.22798i	0.263248	−	0.964728i	$-0.415206\pi$
$89$	109.290	−	109.290i	1.22798	−	1.22798i	0.964728	−	0.263248i	$-0.0847937\pi$
$90$	59.0771	−	92.8680i	0.656413	−	1.03187i
$91$	−20.1040	−	48.5355i	−0.220924	−	0.533357i
$92$	49.8124	−	23.3081i	0.541439	−	0.253349i
$93$	−26.8879	+	64.9132i	−0.289118	+	0.697992i
$94$	9.34545	−	53.2063i	0.0994196	−	0.566025i
$95$		−	101.113i		−	1.06434i
$96$	−122.180	+	38.9677i	−1.27271	+	0.405913i
$97$	63.7161			0.656867			0.328433	−	0.944527i	$-0.393479\pi$
$97$	63.7161			0.656867			0.328433	+	0.944527i	$0.393479\pi$
$98$	−24.9761	−	4.38694i	−0.254859	−	0.0447647i
$99$	43.7650	+	18.1280i	0.442070	+	0.183112i
$100$	−129.511	+	60.6004i	−1.29511	+	0.606004i
$101$	−14.4312	+	5.97761i	−0.142883	+	0.0591842i	−0.452979	−	0.891521i	$-0.649639\pi$
$101$	−14.4312	+	5.97761i	−0.142883	+	0.0591842i	0.310096	+	0.950705i	$0.399639\pi$
$102$	−166.231	−	105.747i	−1.62972	−	1.03673i
$103$	−9.69681	−	9.69681i	−0.0941438	−	0.0941438i	0.658466	−	0.752610i	$-0.271205\pi$
$103$	−9.69681	−	9.69681i	−0.0941438	−	0.0941438i	−0.752610	+	0.658466i	$0.771205\pi$
$104$	55.2409	−	42.5622i	0.531163	−	0.409252i
$105$	−133.110	−	133.110i	−1.26771	−	1.26771i
$106$	−173.543	+	38.5939i	−1.63719	+	0.364093i
$107$	138.127	−	57.2140i	1.29091	−	0.534710i	0.371650	−	0.928373i	$-0.378792\pi$
$107$	138.127	−	57.2140i	1.29091	−	0.534710i	0.919255	+	0.393662i	$0.128792\pi$
$108$	−1.39693	−	31.0527i	−0.0129345	−	0.287525i
$109$	−32.0941	−	13.2938i	−0.294442	−	0.121962i	0.230573	−	0.973055i	$-0.425940\pi$
$109$	−32.0941	−	13.2938i	−0.294442	−	0.121962i	−0.525014	+	0.851093i	$0.675940\pi$
$110$	−60.0402	−	85.6257i	−0.545820	−	0.778416i
$111$	156.311			1.40821
$112$	8.65814	+	96.0372i	0.0773048	+	0.857475i
$113$			125.923i			1.11436i	0.830392	+	0.557180i	$0.188117\pi$
$113$			125.923i			1.11436i	−0.830392	+	0.557180i	$0.811883\pi$
$114$	59.6981	+	85.1378i	0.523667	+	0.746823i
$115$	−41.0083	+	99.0028i	−0.356594	+	0.860894i
$116$	41.3475	−	45.2428i	0.356444	−	0.390024i
$117$	−23.5542	−	56.8648i	−0.201318	−	0.486024i
$118$	142.024	−	31.5846i	1.20360	−	0.267666i
$119$	−104.748	+	104.748i	−0.880239	+	0.880239i
$120$	124.512	−	216.653i	1.03760	−	1.80544i
$121$	−53.7338	+	53.7338i	−0.444081	+	0.444081i
$122$	28.0930	+	17.8711i	0.230270	+	0.146484i
$123$	−23.8110	−	57.4849i	−0.193586	−	0.467357i
$124$	−23.8981	+	65.9306i	−0.192727	+	0.531698i
$125$	32.0540	−	77.3852i	0.256432	−	0.619081i
$126$	83.8246	+	14.7234i	0.665275	+	0.116852i
$127$		−	79.4160i		−	0.625322i	−0.949865	−	0.312661i	$-0.898780\pi$
$127$		−	79.4160i		−	0.625322i	0.949865	−	0.312661i	$-0.101220\pi$
$128$	−120.077	+	44.3347i	−0.938100	+	0.346365i
$129$	97.1771			0.753311
$130$	−23.5070	+	133.832i	−0.180823	+	1.02948i
$131$	53.2656	+	22.0633i	0.406608	+	0.168422i	0.576607	−	0.817022i	$-0.304376\pi$
$131$	53.2656	+	22.0633i	0.406608	+	0.168422i	−0.169999	+	0.985444i	$0.554376\pi$
$132$	101.109	+	36.6493i	0.765976	+	0.277646i
$133$	72.2331	−	29.9199i	0.543106	−	0.224962i
$134$	−115.283	+	181.222i	−0.860319	+	1.35240i
$135$	42.8277	+	42.8277i	0.317242	+	0.317242i
$136$	−170.491	−	97.9828i	−1.25361	−	0.720462i
$137$	50.7359	+	50.7359i	0.370335	+	0.370335i	0.867599	−	0.497264i	$-0.165662\pi$
$137$	50.7359	+	50.7359i	0.370335	+	0.370335i	−0.497264	+	0.867599i	$0.665662\pi$
$138$	−23.9230	−	107.573i	−0.173355	−	0.779515i
$139$	133.213	−	55.1786i	0.958366	−	0.396968i	0.151997	−	0.988381i	$-0.451430\pi$
$139$	133.213	−	55.1786i	0.958366	−	0.396968i	0.806369	+	0.591413i	$0.201430\pi$
$140$	−138.693	−	126.752i	−0.990667	−	0.905372i
$141$	−100.007	−	41.4244i	−0.709272	−	0.293790i
$142$	−5.92286	+	4.15307i	−0.0417102	+	0.0292469i
$143$	−58.4811			−0.408959
$144$	10.1440	+	112.519i	0.0704444	+	0.781379i
$145$			119.425i			0.823620i
$146$	71.2116	−	49.9331i	0.487751	−	0.342007i
$147$	−19.4455	+	46.9455i	−0.132282	+	0.319357i
$148$	155.857	−	7.01134i	1.05309	−	0.0473739i
$149$	5.00779	+	12.0899i	0.0336093	+	0.0811401i	0.939793	−	0.341744i	$-0.111018\pi$
$149$	5.00779	+	12.0899i	0.0336093	+	0.0811401i	−0.906184	+	0.422884i	$0.861018\pi$
$150$	62.1989	+	279.686i	0.414659	+	1.86457i
$151$	−17.6867	+	17.6867i	−0.117130	+	0.117130i	−0.763243	−	0.646112i	$-0.776394\pi$
$151$	−17.6867	+	17.6867i	−0.117130	+	0.117130i	0.646112	+	0.763243i	$0.276394\pi$
$152$	63.3434	+	82.2125i	0.416733	+	0.540872i
$153$	−122.725	+	122.725i	−0.802123	+	0.802123i
$154$	43.4032	−	68.2289i	0.281839	−	0.443045i
$155$	−52.2918	−	126.244i	−0.337367	−	0.814475i
$156$	−59.2229	−	126.567i	−0.379634	−	0.811325i
$157$	73.8536	−	178.298i	0.470405	−	1.13566i	−0.493580	−	0.869701i	$-0.664312\pi$
$157$	73.8536	−	178.298i	0.470405	−	1.13566i	0.963985	−	0.265958i	$-0.0856882\pi$
$158$	−31.3678	+	178.586i	−0.198531	+	1.13029i
$159$			356.241i			2.24051i
$160$	114.432	−	221.608i	0.715202	−	1.38505i
$161$	−82.8605			−0.514662
$162$	−186.528	−	32.7627i	−1.15141	−	0.202239i
$163$	−132.246	−	54.7779i	−0.811322	−	0.336061i	−0.0618408	−	0.998086i	$-0.519697\pi$
$163$	−132.246	−	54.7779i	−0.811322	−	0.336061i	−0.749481	+	0.662025i	$0.769697\pi$
$164$	−26.3203	−	56.2497i	−0.160490	−	0.342986i
$165$	−193.603	+	80.1929i	−1.17335	+	0.486018i
$166$	173.383	+	110.296i	1.04447	+	0.664433i
$167$	−109.750	−	109.750i	−0.657187	−	0.657187i	0.297526	−	0.954714i	$-0.403838\pi$
$167$	−109.750	−	109.750i	−0.657187	−	0.657187i	−0.954714	+	0.297526i	$0.903838\pi$
$168$	191.617	+	24.8403i	1.14058	+	0.147859i
$169$	−65.7709	−	65.7709i	−0.389177	−	0.389177i
$170$	374.020	−	83.1777i	2.20012	−	0.489281i
$171$	84.6294	−	35.0546i	0.494909	−	0.204998i
$172$	96.8946	−	4.35888i	0.563341	−	0.0253423i
$173$	−287.188	−	118.957i	−1.66005	−	0.687613i	−0.661964	−	0.749535i	$-0.730277\pi$
$173$	−287.188	−	118.957i	−1.66005	−	0.687613i	−0.998081	+	0.0619221i	$0.980277\pi$
$174$	−70.5098	−	100.557i	−0.405229	−	0.577913i
$175$	215.434			1.23105
$176$	102.459	+	32.0075i	0.582152	+	0.181861i
$177$		−	291.542i		−	1.64713i
$178$	−177.470	−	253.098i	−0.997025	−	1.42190i
$179$	48.9443	−	118.162i	0.273432	−	0.660122i	−0.726194	−	0.687490i	$-0.758712\pi$
$179$	48.9443	−	118.162i	0.273432	−	0.660122i	0.999625	+	0.0273677i	$0.00871248\pi$
$180$	−162.495	−	148.505i	−0.902751	−	0.825025i
$181$	38.9220	+	93.9660i	0.215039	+	0.519149i	0.994184	−	0.107694i	$-0.0343466\pi$
$181$	38.9220	+	93.9660i	0.215039	+	0.519149i	−0.779145	+	0.626843i	$0.784347\pi$
$182$	−102.563	+	22.8089i	−0.563534	+	0.125323i
$183$	47.1765	−	47.1765i	0.257795	−	0.257795i
$184$	−28.6786	−	106.187i	−0.155862	−	0.577104i
$185$	−214.957	+	214.957i	−1.16193	+	1.16193i
$186$	118.566	+	75.4247i	0.637451	+	0.405509i
$187$	63.1065	+	152.353i	0.337468	+	0.814719i
$188$	−101.575	−	36.8182i	−0.540291	−	0.195841i
$189$	−17.9224	+	43.2684i	−0.0948273	+	0.228933i
$190$	−199.176	−	34.9844i	−1.04830	−	0.184128i
$191$		−	66.5635i		−	0.348500i	−0.984701	−	0.174250i	$-0.944250\pi$
$191$		−	66.5635i		−	0.348500i	0.984701	−	0.174250i	$-0.0557500\pi$
$192$	34.4867	+	254.158i	0.179618	+	1.32374i
$193$	275.880			1.42943			0.714714	−	0.699417i	$-0.246557\pi$
$193$	275.880			1.42943			0.714714	+	0.699417i	$0.246557\pi$
$194$	22.0454	−	125.511i	0.113636	−	0.646962i
$195$	251.553	+	104.197i	1.29001	+	0.534341i
$196$	−17.2832	+	47.6813i	−0.0881796	+	0.243272i
$197$	167.300	−	69.2980i	0.849240	−	0.351767i	0.0847497	−	0.996402i	$-0.472991\pi$
$197$	167.300	−	69.2980i	0.849240	−	0.351767i	0.764490	+	0.644636i	$0.222991\pi$
$198$	50.8518	−	79.9380i	0.256827	−	0.403727i
$199$	−233.526	−	233.526i	−1.17350	−	1.17350i	−0.981370	−	0.192125i	$-0.938462\pi$
$199$	−233.526	−	233.526i	−1.17350	−	1.17350i	−0.192125	−	0.981370i	$-0.561538\pi$
$200$	74.5634	+	276.083i	0.372817	+	1.38041i
$201$	304.326	+	304.326i	1.51406	+	1.51406i
$202$	6.78184	+	30.4955i	0.0335735	+	0.150968i
$203$	−85.3151	+	35.3387i	−0.420271	+	0.174082i
$204$	−265.819	+	290.862i	−1.30304	+	1.42579i
$205$	111.797	+	46.3078i	0.545351	+	0.225892i
$206$	−22.4562	+	15.7462i	−0.109011	+	0.0764377i
$207$	−97.0806			−0.468988
$208$	−64.7278	−	123.542i	−0.311192	−	0.593953i
$209$		−	87.0348i		−	0.416434i
$210$	−308.261	+	216.150i	−1.46791	+	1.02929i
$211$	32.7097	−	78.9682i	0.155022	−	0.374257i	−0.827219	−	0.561880i	$-0.810078\pi$
$211$	32.7097	−	78.9682i	0.155022	−	0.374257i	0.982241	+	0.187623i	$0.0600783\pi$
$212$	15.9792	+	355.205i	0.0753735	+	1.67550i
$213$	5.54706	+	13.3918i	0.0260425	+	0.0628722i
$214$	−64.9117	−	291.884i	−0.303325	−	1.36394i
$215$	−133.637	+	133.637i	−0.621566	+	0.621566i
$216$	−61.6523	−	7.99232i	−0.285427	−	0.0370015i
$217$	74.7128	−	74.7128i	0.344298	−	0.344298i
$218$	−37.2912	+	58.6209i	−0.171060	+	0.268903i
$219$	−66.6933	−	161.012i	−0.304536	−	0.735214i
$220$	−189.443	+	88.6438i	−0.861104	+	0.402927i
$221$	81.9957	−	197.955i	0.371021	−	0.895725i
$222$	54.0828	−	307.909i	0.243616	−	1.38698i
$223$			373.446i			1.67465i	0.546708	+	0.837323i	$0.315881\pi$
$223$			373.446i			1.67465i	−0.546708	+	0.837323i	$0.684119\pi$
$224$	192.174	+	16.1731i	0.857920	+	0.0722015i
$225$	252.406			1.12180
$226$	248.048	+	43.5685i	1.09756	+	0.192781i
$227$	7.71962	+	3.19757i	0.0340071	+	0.0140862i	0.399622	−	0.916680i	$-0.369141\pi$
$227$	7.71962	+	3.19757i	0.0340071	+	0.0140862i	−0.365615	+	0.930766i	$0.619141\pi$
$228$	188.363	−	88.1387i	0.826155	−	0.386573i
$229$	−165.203	+	68.4293i	−0.721410	+	0.298818i	−0.713017	−	0.701147i	$-0.752672\pi$
$229$	−165.203	+	68.4293i	−0.721410	+	0.298818i	−0.00839310	+	0.999965i	$0.502672\pi$
$230$	180.831	+	115.034i	0.786224	+	0.500149i
$231$	−114.577	−	114.577i	−0.496004	−	0.496004i
$232$	−74.8153	−	97.1018i	−0.322480	−	0.418542i
$233$	14.0197	+	14.0197i	0.0601703	+	0.0601703i	0.736552	−	0.676381i	$-0.236453\pi$
$233$	14.0197	+	14.0197i	0.0601703	+	0.0601703i	−0.676381	+	0.736552i	$0.736453\pi$
$234$	−120.165	+	26.7232i	−0.513524	+	0.114202i
$235$	194.495	−	80.5625i	0.827638	−	0.342819i
$236$	−13.0771	−	290.694i	−0.0554114	−	1.23175i
$237$	335.673	+	139.040i	1.41634	+	0.586668i
$238$	170.096	+	242.581i	0.714688	+	1.01925i
$239$	−230.951			−0.966321			−0.483161	−	0.875532i	$-0.660511\pi$
$239$	−230.951			−0.966321			−0.483161	+	0.875532i	$0.660511\pi$
$240$	−383.692	−	320.230i	−1.59871	−	1.33429i
$241$			111.407i			0.462269i	0.972922	+	0.231135i	$0.0742438\pi$
$241$			111.407i			0.462269i	−0.972922	+	0.231135i	$0.925756\pi$
$242$	87.2557	+	124.439i	0.360561	+	0.514210i
$243$	−118.459	+	285.985i	−0.487485	+	1.17689i
$244$	44.9233	−	49.1555i	0.184112	−	0.201457i
$245$	−37.8177	−	91.3000i	−0.154358	−	0.372653i
$246$	−121.475	+	27.0146i	−0.493800	+	0.109815i
$247$	−79.9641	+	79.9641i	−0.323741	+	0.323741i
$248$	121.604	+	69.8871i	0.490340	+	0.281803i
$249$	291.162	−	291.162i	1.16932	−	1.16932i
$250$	−141.346	−	89.9162i	−0.565385	−	0.359665i
$251$	93.4234	+	225.544i	0.372205	+	0.898581i	0.993376	+	0.114907i	$0.0366570\pi$
$251$	93.4234	+	225.544i	0.372205	+	0.898581i	−0.621172	+	0.783675i	$0.713343\pi$
$252$	58.0056	−	160.027i	0.230181	−	0.635029i
$253$	−35.2987	+	85.2186i	−0.139521	+	0.336833i
$254$	−156.437	−	27.4775i	−0.615894	−	0.108179i
$255$		−	767.772i		−	3.01087i
$256$	45.7867	+	251.872i	0.178854	+	0.983876i
$257$	−278.684			−1.08437			−0.542187	−	0.840258i	$-0.682403\pi$
$257$	−278.684			−1.08437			−0.542187	+	0.840258i	$0.682403\pi$
$258$	33.6227	−	191.424i	0.130321	−	0.741953i
$259$	−217.169	−	89.9543i	−0.838490	−	0.347314i
$260$	255.495	+	92.6102i	0.982674	+	0.356193i
$261$	−99.9564	+	41.4033i	−0.382975	+	0.158633i
$262$	61.8909	−	97.2912i	0.236225	−	0.371340i
$263$	271.210	+	271.210i	1.03122	+	1.03122i	0.999497	+	0.0317197i	$0.0100984\pi$
$263$	271.210	+	271.210i	1.03122	+	1.03122i	0.0317197	+	0.999497i	$0.489902\pi$
$264$	107.176	−	186.488i	0.405971	−	0.706395i
$265$	−489.898	−	489.898i	−1.84867	−	1.84867i
$266$	−33.9454	−	152.640i	−0.127614	−	0.573835i
$267$	−572.263	+	237.039i	−2.14331	+	0.887787i
$268$	317.092	+	289.791i	1.18318	+	1.08131i
$269$	54.9518	+	22.7618i	0.204282	+	0.0846163i	0.482478	−	0.875908i	$-0.339737\pi$
$269$	54.9518	+	22.7618i	0.204282	+	0.0846163i	−0.278197	+	0.960524i	$0.589737\pi$
$270$	99.1821	−	69.5458i	0.367341	−	0.257577i
$271$	443.976			1.63829			0.819143	−	0.573589i	$-0.194449\pi$
$271$	443.976			1.63829			0.819143	+	0.573589i	$0.194449\pi$
$272$	−252.000	+	301.940i	−0.926470	+	1.11007i
$273$			210.537i			0.771199i
$274$	117.496	−	82.3875i	0.428818	−	0.300684i
$275$	91.7754	−	221.565i	0.333729	−	0.805693i
$276$	−220.179	+	9.90494i	−0.797751	+	0.0358875i
$277$	23.1329	+	55.8478i	0.0835124	+	0.201617i	0.960119	−	0.279590i	$-0.0901986\pi$
$277$	23.1329	+	55.8478i	0.0835124	+	0.201617i	−0.876607	+	0.481207i	$0.840199\pi$
$278$	−62.6023	−	281.500i	−0.225188	−	1.01259i
$279$	87.5345	−	87.5345i	0.313744	−	0.313744i
$280$	−297.669	+	229.349i	−1.06310	+	0.819103i
$281$	−159.772	+	159.772i	−0.568582	+	0.568582i	−0.931731	−	0.363149i	$-0.881702\pi$
$281$	−159.772	+	159.772i	−0.568582	+	0.568582i	0.363149	+	0.931731i	$0.381702\pi$
$282$	−116.202	+	182.666i	−0.412062	+	0.647753i
$283$	−185.468	−	447.761i	−0.655366	−	1.58219i	−0.804883	−	0.593434i	$-0.797772\pi$
$283$	−185.468	−	447.761i	−0.655366	−	1.58219i	0.149517	−	0.988759i	$-0.452228\pi$
$284$	6.13162	+	13.1040i	0.0215902	+	0.0461410i
$285$	−155.071	+	374.375i	−0.544109	+	1.31359i
$286$	−20.2341	+	115.199i	−0.0707487	+	0.402793i
$287$			93.5687i			0.326023i
$288$	225.154	+	18.9487i	0.781784	+	0.0657940i
$289$	−315.186			−1.09061
$290$	235.249	+	41.3203i	0.811202	+	0.142484i
$291$	−235.912	−	97.7178i	−0.810693	−	0.335800i
$292$	−73.7216	−	157.552i	−0.252471	−	0.539563i
$293$	476.574	−	197.403i	1.62653	−	0.673732i	0.631696	−	0.775216i	$-0.282359\pi$
$293$	476.574	−	197.403i	1.62653	−	0.673732i	0.994837	+	0.101485i	$0.0323592\pi$
$294$	85.7474	+	54.5474i	0.291658	+	0.185535i
$295$	400.924	+	400.924i	1.35906	+	1.35906i
$296$	40.1143	−	309.439i	0.135521	−	1.04540i
$297$	36.8648	+	36.8648i	0.124124	+	0.124124i
$298$	25.5479	−	5.68155i	0.0857310	−	0.0190656i
$299$	110.727	−	45.8645i	0.370323	−	0.153393i
$300$	572.458	−	25.7525i	1.90819	−	0.0858416i
$301$	−135.012	−	55.9237i	−0.448544	−	0.185793i
$302$	28.7206	+	40.9595i	0.0951012	+	0.135628i
$303$	62.5998			0.206600
$304$	183.862	−	96.3315i	0.604810	−	0.316880i
$305$			129.753i			0.425420i
$306$	199.287	+	284.211i	0.651264	+	0.928794i
$307$	−196.212	+	473.698i	−0.639127	+	1.54299i	0.188716	+	0.982032i	$0.439567\pi$
$307$	−196.212	+	473.698i	−0.639127	+	1.54299i	−0.827844	+	0.560959i	$0.810433\pi$
$308$	−119.383	−	109.104i	−0.387608	−	0.354235i
$309$	21.0314	+	50.7744i	0.0680629	+	0.164318i
$310$	−266.773	+	59.3272i	−0.860558	+	0.191378i
$311$	386.346	−	386.346i	1.24227	−	1.24227i	0.283215	−	0.959057i	$-0.408599\pi$
$311$	386.346	−	386.346i	1.24227	−	1.24227i	0.959057	−	0.283215i	$-0.0914008\pi$
$312$	−269.807	+	72.8685i	−0.864767	+	0.233553i
$313$	127.090	−	127.090i	0.406038	−	0.406038i	−0.474316	−	0.880354i	$-0.657305\pi$
$313$	127.090	−	127.090i	0.406038	−	0.406038i	0.880354	+	0.474316i	$0.157305\pi$
$314$	−325.667	−	207.170i	−1.03716	−	0.659778i
$315$	126.923	+	306.420i	0.402931	+	0.972761i
$316$	340.934	+	123.579i	1.07890	+	0.391074i
$317$	−24.4377	+	58.9979i	−0.0770906	+	0.186113i	−0.957726	−	0.287681i	$-0.907116\pi$
$317$	−24.4377	+	58.9979i	−0.0770906	+	0.186113i	0.880636	+	0.473794i	$0.157116\pi$
$318$	701.739	+	123.257i	2.20673	+	0.387602i
$319$			102.797i			0.322249i
$320$	−396.940	−	302.089i	−1.24044	−	0.944027i
$321$	−599.167			−1.86657
$322$	−28.6693	+	163.222i	−0.0890349	+	0.506902i
$323$	294.608	+	122.031i	0.912099	+	0.377804i
$324$	−129.075	+	356.095i	−0.398380	+	1.09906i
$325$	−287.885	+	119.246i	−0.885801	+	0.366911i
$326$	−153.660	+	241.550i	−0.471350	+	0.740952i
$327$	98.4421	+	98.4421i	0.301046	+	0.301046i
$328$	−119.910	+	32.3848i	−0.365579	+	0.0987341i
$329$	115.105	+	115.105i	0.349863	+	0.349863i
$330$	90.9821	+	409.114i	0.275703	+	1.23974i
$331$	53.7512	−	22.2645i	0.162390	−	0.0672643i	−0.300007	−	0.953937i	$-0.596989\pi$
$331$	53.7512	−	22.2645i	0.162390	−	0.0672643i	0.462398	+	0.886673i	$0.346989\pi$
$332$	277.255	−	303.375i	0.835106	−	0.913781i
$333$	−254.438	−	105.392i	−0.764078	−	0.316492i
$334$	−254.164	+	178.218i	−0.760970	+	0.533587i
$335$	−837.010			−2.49854
$336$	115.230	−	368.861i	0.342946	−	1.09780i
$337$		−	368.803i		−	1.09437i	−0.837012	−	0.547185i	$-0.815700\pi$
$337$		−	368.803i		−	1.09437i	0.837012	−	0.547185i	$-0.184300\pi$
$338$	−152.315	+	106.802i	−0.450636	+	0.315983i
$339$	193.121	−	466.235i	0.569678	−	1.37532i
$340$	−34.4384	−	765.540i	−0.101289	−	2.25159i
$341$	−45.0113	−	108.667i	−0.131998	−	0.318671i
$342$	−39.7709	−	178.835i	−0.116289	−	0.522911i
$343$	262.846	−	262.846i	0.766315	−	0.766315i
$344$	24.9387	−	192.376i	0.0724961	−	0.559231i
$345$	303.670	−	303.670i	0.880204	−	0.880204i
$346$	−333.692	+	524.557i	−0.964429	+	1.51606i
$347$	166.265	+	401.400i	0.479151	+	1.15677i	0.960008	+	0.279973i	$0.0903255\pi$
$347$	166.265	+	401.400i	0.479151	+	1.15677i	−0.480857	+	0.876799i	$0.659675\pi$
$348$	−222.477	+	104.101i	−0.639303	+	0.299142i
$349$	−24.6685	+	59.5550i	−0.0706833	+	0.170645i	−0.955273	−	0.295726i	$-0.904439\pi$
$349$	−24.6685	+	59.5550i	−0.0706833	+	0.170645i	0.884590	+	0.466370i	$0.154439\pi$
$350$	74.5390	−	424.372i	0.212969	−	1.21249i
$351$		−	67.7399i		−	0.192991i
$352$	98.4999	−	190.753i	0.279829	−	0.541913i
$353$	245.534			0.695563			0.347782	−	0.937576i	$-0.386935\pi$
$353$	245.534			0.695563			0.347782	+	0.937576i	$0.386935\pi$
$354$	−574.292	−	100.872i	−1.62229	−	0.284948i
$355$	−26.0444	−	10.7880i	−0.0733646	−	0.0303886i
$356$	−559.967	+	262.019i	−1.57294	+	0.736008i
$357$	548.483	−	227.189i	1.53637	−	0.636384i
$358$	−215.826	−	137.296i	−0.602866	−	0.383508i
$359$	61.7019	+	61.7019i	0.171872	+	0.171872i	0.787801	−	0.615930i	$-0.211219\pi$
$359$	61.7019	+	61.7019i	0.171872	+	0.171872i	−0.615930	+	0.787801i	$0.711219\pi$
$360$	−348.753	+	268.708i	−0.968759	+	0.746412i
$361$	136.259	+	136.259i	0.377448	+	0.377448i
$362$	198.565	−	44.1586i	0.548523	−	0.121985i
$363$	281.361	−	116.543i	0.775099	−	0.321056i
$364$	9.44365	+	209.925i	0.0259441	+	0.576718i
$365$	313.137	+	129.706i	0.857910	+	0.355358i
$366$	−76.6076	−	109.253i	−0.209310	−	0.298506i
$367$	123.349			0.336102			0.168051	−	0.985778i	$-0.446253\pi$
$367$	123.349			0.336102			0.168051	+	0.985778i	$0.446253\pi$
$368$	−219.095	+	19.7523i	−0.595367	+	0.0536747i
$369$			109.626i			0.297090i
$370$	349.058	+	497.806i	0.943400	+	1.34542i
$371$	205.010	−	494.939i	0.552588	−	1.33407i
$372$	189.598	−	207.460i	0.509672	−	0.557688i
$373$	−11.5942	−	27.9909i	−0.0310836	−	0.0750425i	0.907575	−	0.419889i	$-0.137931\pi$
$373$	−11.5942	−	27.9909i	−0.0310836	−	0.0750425i	−0.938659	+	0.344846i	$0.887931\pi$
$374$	321.945	−	71.5969i	0.860816	−	0.191436i
$375$	−237.363	+	237.363i	−0.632968	+	0.632968i
$376$	−107.670	+	187.348i	−0.286357	+	0.498265i
$377$	94.4462	−	94.4462i	0.250520	−	0.250520i
$378$	79.0310	+	50.2749i	0.209077	+	0.133002i
$379$	205.083	+	495.114i	0.541115	+	1.30637i	0.923937	+	0.382546i	$0.124953\pi$
$379$	205.083	+	495.114i	0.541115	+	1.30637i	−0.382821	+	0.923823i	$0.625047\pi$
$380$	−137.828	+	380.242i	−0.362704	+	1.00064i
$381$	−121.796	+	294.041i	−0.319674	+	0.771762i
$382$	−131.120	−	23.0306i	−0.343245	−	0.0602894i
$383$		−	605.809i		−	1.58175i	−0.611979	−	0.790874i	$-0.709626\pi$
$383$		−	605.809i		−	1.58175i	0.611979	−	0.790874i	$-0.290374\pi$
$384$	512.584	+	20.0037i	1.33485	+	0.0520930i
$385$	315.129			0.818517
$386$	95.4528	−	543.440i	0.247287	−	1.40788i
$387$	−158.182	−	65.5210i	−0.408738	−	0.169305i
$388$	−239.609	−	86.8519i	−0.617549	−	0.223845i
$389$	−426.567	+	176.690i	−1.09657	+	0.454215i	−0.856294	−	0.516489i	$-0.827239\pi$
$389$	−426.567	+	176.690i	−1.09657	+	0.454215i	−0.240279	+	0.970704i	$0.577239\pi$
$390$	292.287	−	459.468i	0.749453	−	1.17812i
$391$	−238.968	−	238.968i	−0.611172	−	0.611172i
$392$	87.9448	+	50.5427i	0.224349	+	0.128935i
$393$	−163.381	−	163.381i	−0.415728	−	0.415728i
$394$	−78.6214	−	353.532i	−0.199547	−	0.897290i
$395$	−652.819	+	270.407i	−1.65271	+	0.684573i
$396$	−139.871	−	127.828i	−0.353209	−	0.322799i
$397$	294.458	+	121.969i	0.741708	+	0.307226i	0.721353	−	0.692567i	$-0.243520\pi$
$397$	294.458	+	121.969i	0.741708	+	0.307226i	0.0203548	+	0.999793i	$0.493520\pi$
$398$	−540.808	+	379.211i	−1.35881	+	0.952791i
$399$	−313.333			−0.785296
$400$	569.639	−	51.3552i	1.42410	−	0.128388i
$401$		−	48.4544i		−	0.120834i	−0.998173	−	0.0604169i	$-0.980757\pi$
$401$		−	48.4544i		−	0.120834i	0.998173	−	0.0604169i	$-0.0192430\pi$
$402$	704.770	−	494.180i	1.75316	−	1.22930i
$403$	−58.4842	+	141.193i	−0.145122	+	0.350356i
$404$	62.4178	−	2.80791i	0.154500	−	0.00695028i
$405$	−282.431	−	681.850i	−0.697362	−	1.68358i
$406$	40.0932	+	180.284i	0.0987516	+	0.444050i
$407$	−185.029	+	185.029i	−0.454616	+	0.454616i
$408$	480.981	+	624.259i	1.17888	+	1.53005i
$409$	−242.037	+	242.037i	−0.591778	+	0.591778i	−0.938111	−	0.346334i	$-0.887427\pi$
$409$	−242.037	+	242.037i	−0.591778	+	0.591778i	0.346334	+	0.938111i	$0.387427\pi$
$410$	129.900	−	204.201i	0.316830	−	0.498050i
$411$	−110.041	−	265.663i	−0.267740	−	0.646382i
$412$	23.2478	+	49.6834i	0.0564266	+	0.120591i
$413$	−167.777	+	405.049i	−0.406239	+	0.980749i
$414$	−33.5893	+	191.234i	−0.0811336	+	0.461917i
$415$			800.803i			1.92965i
$416$	−265.755	+	84.7589i	−0.638833	+	0.203747i
$417$	−577.851			−1.38573
$418$	−171.445	−	30.1135i	−0.410155	−	0.0720419i
$419$	163.261	+	67.6248i	0.389644	+	0.161396i	0.568900	−	0.822407i	$-0.307369\pi$
$419$	163.261	+	67.6248i	0.389644	+	0.161396i	−0.179256	+	0.983802i	$0.557369\pi$
$420$	319.126	+	682.012i	0.759824	+	1.62384i
$421$	−624.400	+	258.635i	−1.48314	+	0.614335i	−0.969810	−	0.243860i	$-0.921586\pi$
$421$	−624.400	+	258.635i	−1.48314	+	0.614335i	−0.513325	+	0.858195i	$0.671586\pi$
$422$	−144.238	−	91.7555i	−0.341795	−	0.217430i
$423$	134.859	+	134.859i	0.318814	+	0.318814i
$424$	705.228	+	91.4225i	1.66327	+	0.215619i
$425$	621.309	+	621.309i	1.46190	+	1.46190i
$426$	28.2990	−	6.29337i	0.0664296	−	0.0147732i
$427$	−92.6933	+	38.3948i	−0.217080	+	0.0899176i
$428$	−597.426	+	26.8757i	−1.39585	+	0.0627936i
$429$	216.529	+	89.6893i	0.504730	+	0.209066i
$430$	217.006	+	309.481i	0.504665	+	0.719723i
$431$	606.510			1.40722			0.703608	−	0.710588i	$-0.251571\pi$
$431$	606.510			1.40722			0.703608	+	0.710588i	$0.251571\pi$
$432$	−37.0750	+	118.680i	−0.0858217	+	0.274723i
$433$		−	3.82972i		−	0.00884462i	−0.999990	−	0.00442231i	$-0.998592\pi$
$433$		−	3.82972i		−	0.00884462i	0.999990	−	0.00442231i	$-0.00140767\pi$
$434$	−121.322	−	173.023i	−0.279545	−	0.398670i
$435$	183.156	−	442.177i	0.421047	−	1.01650i
$436$	102.572	+	93.7403i	0.235256	+	0.215001i
$437$	68.2580	+	164.789i	0.156197	+	0.377092i
$438$	−340.244	+	75.6663i	−0.776813	+	0.172754i
$439$	−36.3389	+	36.3389i	−0.0827765	+	0.0827765i	−0.747283	−	0.664506i	$-0.768642\pi$
$439$	−36.3389	+	36.3389i	−0.0827765	+	0.0827765i	0.664506	+	0.747283i	$0.268642\pi$
$440$	109.068	+	403.843i	0.247883	+	0.917826i
$441$	63.3054	−	63.3054i	0.143550	−	0.143550i
$442$	−361.571	−	230.010i	−0.818034	−	0.520385i
$443$	−208.435	−	503.207i	−0.470508	−	1.13591i	−0.963939	−	0.266122i	$-0.914258\pi$
$443$	−208.435	−	503.207i	−0.470508	−	1.13591i	0.493431	−	0.869785i	$-0.335742\pi$
$444$	−587.820	−	213.069i	−1.32392	−	0.479886i
$445$	460.995	−	1112.94i	1.03594	−	2.50099i
$446$	735.631	+	129.210i	1.64940	+	0.289709i
$447$		−	52.4435i		−	0.117323i
$448$	98.3497	−	372.957i	0.219530	−	0.832494i
$449$	431.670			0.961402			0.480701	−	0.876884i	$-0.340382\pi$
$449$	431.670			0.961402			0.480701	+	0.876884i	$0.340382\pi$
$450$	87.3310	−	497.201i	0.194069	−	1.10489i
$451$	96.2316	+	39.8604i	0.213374	+	0.0883823i
$452$	171.646	−	473.542i	0.379749	−	1.04766i
$453$	92.6110	−	38.3607i	0.204439	−	0.0846815i
$454$	8.96966	−	14.1001i	0.0197570	−	0.0310575i
$455$	−289.528	−	289.528i	−0.636325	−	0.636325i
$456$	−108.447	−	401.542i	−0.237822	−	0.880575i
$457$	−187.054	−	187.054i	−0.409309	−	0.409309i	0.472189	−	0.881497i	$-0.343464\pi$
$457$	−187.054	−	187.054i	−0.409309	−	0.409309i	−0.881497	+	0.472189i	$0.843464\pi$
$458$	77.6358	+	349.100i	0.169510	+	0.762227i
$459$	−176.473	+	73.0976i	−0.384473	+	0.159254i
$460$	289.166	−	316.409i	0.628623	−	0.687845i
$461$	253.784	+	105.121i	0.550508	+	0.228028i	0.640558	−	0.767909i	$-0.278703\pi$
$461$	253.784	+	105.121i	0.550508	+	0.228028i	−0.0900508	+	0.995937i	$0.528703\pi$
$462$	−265.342	+	186.056i	−0.574332	+	0.402718i
$463$	−765.246			−1.65280			−0.826400	−	0.563084i	$-0.809615\pi$
$463$	−765.246			−1.65280			−0.826400	+	0.563084i	$0.809615\pi$
$464$	−217.161	+	113.778i	−0.468020	+	0.245211i
$465$			547.620i			1.17768i
$466$	32.4673	−	22.7659i	0.0696723	−	0.0488538i
$467$	−110.687	+	267.223i	−0.237018	+	0.572211i	−0.996972	−	0.0777657i	$-0.975221\pi$
$467$	−110.687	+	267.223i	−0.237018	+	0.572211i	0.759954	+	0.649977i	$0.225221\pi$
$468$	11.0643	+	245.951i	0.0236417	+	0.525537i
$469$	−247.677	−	597.945i	−0.528096	−	1.27494i
$470$	−91.4014	−	410.999i	−0.194471	−	0.874466i
$471$	−546.893	+	546.893i	−1.16113	+	1.16113i
$472$	−577.147	−	74.8186i	−1.22277	−	0.158514i
$473$	−115.030	+	115.030i	−0.243193	+	0.243193i
$474$	390.029	−	613.117i	0.822845	−	1.29349i
$475$	−177.468	−	428.447i	−0.373618	−	0.901993i
$476$	536.698	−	251.131i	1.12752	−	0.527586i
$477$	240.193	−	579.877i	0.503549	−	1.21568i
$478$	−79.9076	+	454.937i	−0.167171	+	0.951751i
$479$			158.059i			0.329977i	0.986296	+	0.164988i	$0.0527586\pi$
$479$			158.059i			0.329977i	−0.986296	+	0.164988i	$0.947241\pi$
$480$	−763.559	+	645.015i	−1.59075	+	1.34378i
$481$	339.994			0.706848
$482$	219.454	+	38.5461i	0.455299	+	0.0799712i
$483$	306.795	+	127.079i	0.635186	+	0.263103i
$484$	275.315	−	128.825i	0.568833	−	0.266168i
$485$	458.803	−	190.042i	0.945985	−	0.391840i
$486$	522.360	+	332.295i	1.07481	+	0.683734i
$487$	−675.116	−	675.116i	−1.38628	−	1.38628i	−0.832996	−	0.553280i	$-0.813376\pi$
$487$	−675.116	−	675.116i	−1.38628	−	1.38628i	−0.553280	−	0.832996i	$-0.686624\pi$
$488$	−81.2855	−	105.499i	−0.166569	−	0.216187i
$489$	405.636	+	405.636i	0.829521	+	0.829521i
$490$	−192.931	+	42.9057i	−0.393738	+	0.0875627i
$491$	87.1226	−	36.0874i	0.177439	−	0.0734977i	−0.292195	−	0.956359i	$-0.594386\pi$
$491$	87.1226	−	36.0874i	0.177439	−	0.0734977i	0.469634	+	0.882861i	$0.344386\pi$
$492$	11.1850	+	248.633i	0.0227337	+	0.505352i
$493$	−347.963	−	144.131i	−0.705808	−	0.292355i
$494$	129.850	+	185.184i	0.262854	+	0.374866i
$495$	369.210			0.745878
$496$	179.741	−	215.361i	0.362381	−	0.434196i
$497$		−	21.7979i		−	0.0438590i
$498$	−472.803	−	674.283i	−0.949404	−	1.35398i
$499$	164.812	−	397.892i	0.330285	−	0.797378i	−0.668284	−	0.743906i	$-0.732971\pi$
$499$	164.812	−	397.892i	0.330285	−	0.797378i	0.998569	−	0.0534724i	$-0.0170289\pi$
$500$	−226.026	+	247.320i	−0.452052	+	0.494640i
$501$	238.038	+	574.674i	0.475125	+	1.14705i
$502$	476.610	−	105.993i	0.949423	−	0.211141i
$503$	−270.905	+	270.905i	−0.538578	+	0.538578i	−0.923111	−	0.384533i	$-0.874362\pi$
$503$	−270.905	+	270.905i	−0.538578	+	0.538578i	0.384533	+	0.923111i	$0.374362\pi$
$504$	−295.159	−	169.631i	−0.585633	−	0.336569i
$505$	−86.0864	+	86.0864i	−0.170468	+	0.170468i
$506$	155.654	+	99.0181i	0.307617	+	0.195688i
$507$	142.651	+	344.389i	0.281362	+	0.679269i
$508$	−108.253	+	298.650i	−0.213096	+	0.587893i
$509$	−194.137	+	468.689i	−0.381409	+	0.920803i	0.610285	+	0.792182i	$0.291055\pi$
$509$	−194.137	+	468.689i	−0.381409	+	0.920803i	−0.991694	+	0.128621i	$0.958945\pi$
$510$	−1512.39	−	265.645i	−2.96547	−	0.520872i
$511$			262.081i			0.512878i
$512$	511.991	−	3.04640i	0.999982	−	0.00595000i
$513$	100.814			0.196519
$514$	−96.4230	+	548.964i	−0.187593	+	1.06802i
$515$	−98.7463	−	40.9021i	−0.191740	−	0.0794215i
$516$	−365.442	−	132.463i	−0.708221	−	0.256711i
$517$	167.416	−	69.3458i	0.323821	−	0.134131i
$518$	−252.335	+	396.665i	−0.487133	+	0.765763i
$519$	880.889	+	880.889i	1.69728	+	1.69728i
$520$	270.828	−	471.243i	0.520822	−	0.906237i
$521$	−240.434	−	240.434i	−0.461486	−	0.461486i	0.437656	−	0.899142i	$-0.355809\pi$
$521$	−240.434	−	240.434i	−0.461486	−	0.461486i	−0.899142	+	0.437656i	$0.855809\pi$
$522$	46.9737	+	211.224i	0.0899880	+	0.404643i
$523$	846.467	−	350.618i	1.61848	−	0.670398i	0.624611	−	0.780936i	$-0.285257\pi$
$523$	846.467	−	350.618i	1.61848	−	0.670398i	0.993872	+	0.110538i	$0.0352574\pi$
$524$	−170.235	−	155.578i	−0.324875	−	0.296904i
$525$	−797.656	−	330.400i	−1.51935	−	0.629333i
$526$	628.078	−	440.404i	1.19407	−	0.837271i
$527$	430.941			0.817725
$528$	−330.270	−	275.645i	−0.625512	−	0.522054i
$529$			339.966i			0.642657i
$530$	−1134.52	+	795.521i	−2.14061	+	1.50098i
$531$	−196.570	+	474.561i	−0.370188	+	0.893713i
$532$	−312.422	+	14.0546i	−0.587260	+	0.0264183i
$533$	−51.7916	−	125.036i	−0.0971699	−	0.234589i
$534$	268.931	+	1209.28i	0.503615	+	2.26458i
$535$	823.967	−	823.967i	1.54012	−	1.54012i
$536$	680.555	−	524.356i	1.26969	−	0.978276i
$537$	−362.437	+	362.437i	−0.674929	+	0.674929i
$538$	63.8502	−	100.371i	0.118681	−	0.186563i
$539$	−32.5523	−	78.5883i	−0.0603939	−	0.145804i
$540$	−102.678	−	219.436i	−0.190145	−	0.406363i
$541$	−6.87337	+	16.5938i	−0.0127049	+	0.0306724i	−0.930105	−	0.367294i	$-0.880284\pi$
$541$	−6.87337	+	16.5938i	−0.0127049	+	0.0306724i	0.917400	+	0.397967i	$0.130284\pi$
$542$	153.613	−	874.563i	0.283419	−	1.61358i
$543$		−	407.606i		−	0.750656i
$544$	507.584	+	600.870i	0.933059	+	1.10454i
$545$	−270.752			−0.496793
$546$	414.726	+	72.8447i	0.759571	+	0.133415i
$547$	354.417	+	146.804i	0.647929	+	0.268381i	0.682349	−	0.731026i	$-0.260958\pi$
$547$	354.417	+	146.804i	0.647929	+	0.268381i	−0.0344200	+	0.999407i	$0.510958\pi$
$548$	−121.638	−	259.955i	−0.221967	−	0.474370i
$549$	−108.601	+	44.9839i	−0.197816	+	0.0819379i
$550$	−404.696	−	257.444i	−0.735811	−	0.468079i
$551$	140.560	+	140.560i	0.255100	+	0.255100i
$552$	−56.6696	+	437.146i	−0.102662	+	0.791931i
$553$	−386.348	−	386.348i	−0.698639	−	0.698639i
$554$	118.015	−	26.2452i	0.213024	−	0.0473741i
$555$	1125.56	−	466.221i	2.02803	−	0.840037i
$556$	−576.171	+	25.9195i	−1.03628	+	0.0466178i
$557$	−549.588	−	227.647i	−0.986692	−	0.408701i	−0.169792	−	0.985480i	$-0.554310\pi$
$557$	−549.588	−	227.647i	−0.986692	−	0.408701i	−0.816900	+	0.576779i	$0.804310\pi$
$558$	−142.143	−	202.716i	−0.254737	−	0.363290i
$559$	211.371			0.378123
$560$	348.790	+	665.715i	0.622839	+	1.18878i
$561$		−	660.876i		−	1.17803i
$562$	259.445	+	370.005i	0.461646	+	0.658372i
$563$	−150.445	+	363.205i	−0.267219	+	0.645125i	−0.999350	−	0.0360391i	$-0.988526\pi$
$563$	−150.445	+	363.205i	−0.267219	+	0.645125i	0.732131	+	0.681164i	$0.238526\pi$
$564$	319.619	+	292.101i	0.566701	+	0.517909i
$565$	375.583	+	906.737i	0.664748	+	1.60484i
$566$	−946.190	+	210.422i	−1.67171	+	0.371770i
$567$	403.528	−	403.528i	0.711690	−	0.711690i
$568$	27.9344	−	7.54442i	0.0491803	−	0.0132824i
$569$	510.987	−	510.987i	0.898045	−	0.898045i	−0.0972186	−	0.995263i	$-0.530995\pi$
$569$	510.987	−	510.987i	0.898045	−	0.898045i	0.995263	+	0.0972186i	$0.0309946\pi$
$570$	683.806	+	434.997i	1.19966	+	0.763153i
$571$	328.247	+	792.459i	0.574864	+	1.38784i	0.897371	+	0.441277i	$0.145474\pi$
$571$	328.247	+	792.459i	0.574864	+	1.38784i	−0.322507	+	0.946567i	$0.604526\pi$
$572$	219.923	+	79.7161i	0.384480	+	0.139364i
$573$	−102.085	+	246.454i	−0.178158	+	0.430112i
$574$	184.316	+	32.3742i	0.321108	+	0.0564011i
$575$			491.482i			0.854752i
$576$	115.228	−	436.962i	0.200048	−	0.758615i
$577$	305.039			0.528663			0.264332	−	0.964432i	$-0.414849\pi$
$577$	305.039			0.528663			0.264332	+	0.964432i	$0.414849\pi$
$578$	−109.052	+	620.867i	−0.188672	+	1.07416i
$579$	−1021.46	−	423.102i	−1.76418	−	0.730746i
$580$	162.789	−	449.106i	0.280671	−	0.774322i
$581$	−572.080	+	236.963i	−0.984647	+	0.407854i
$582$	−274.113	+	430.900i	−0.470985	+	0.740378i
$583$	−421.689	−	421.689i	−0.723309	−	0.723309i
$584$	−335.861	+	90.7080i	−0.575104	+	0.155322i
$585$	−339.215	−	339.215i	−0.579855	−	0.579855i
$586$	−223.962	−	1007.08i	−0.382188	−	1.71856i
$587$	−388.900	+	161.088i	−0.662521	+	0.274425i	−0.688499	−	0.725237i	$-0.741730\pi$
$587$	−388.900	+	161.088i	−0.662521	+	0.274425i	0.0259780	+	0.999663i	$0.491730\pi$
$588$	137.118	−	150.036i	0.233194	−	0.255163i
$589$	−210.132	−	87.0394i	−0.356760	−	0.147775i
$590$	928.475	−	651.040i	1.57369	−	1.10346i
$591$	−725.716			−1.22795
$592$	−595.668	−	186.083i	−1.00620	−	0.314330i
$593$		−	1039.64i		−	1.75319i	−0.481228	−	0.876595i	$-0.659809\pi$
$593$		−	1039.64i		−	1.75319i	0.481228	−	0.876595i	$-0.340191\pi$
$594$	85.3730	−	59.8630i	0.143726	−	0.100779i
$595$	−441.839	+	1066.69i	−0.742587	+	1.79276i
$596$	−2.35235	−	52.2911i	−0.00394690	−	0.0877367i
$597$	506.494	+	1222.79i	0.848399	+	2.04822i
$598$	−52.0351	−	233.983i	−0.0870152	−	0.391276i
$599$	22.4929	−	22.4929i	0.0375507	−	0.0375507i	−0.688082	−	0.725633i	$-0.741547\pi$
$599$	22.4929	−	22.4929i	0.0375507	−	0.0375507i	0.725633	+	0.688082i	$0.241547\pi$
$600$	147.339	−	1136.56i	0.245565	−	1.89427i
$601$	−640.653	+	640.653i	−1.06598	+	1.06598i	−0.0683147	+	0.997664i	$0.521762\pi$
$601$	−640.653	+	640.653i	−1.06598	+	1.06598i	−0.997664	+	0.0683147i	$0.978238\pi$
$602$	−156.874	+	246.603i	−0.260588	+	0.409639i
$603$	−290.182	−	700.561i	−0.481230	−	1.16179i
$604$	90.6211	−	42.4033i	0.150035	−	0.0702041i
$605$	−226.654	+	547.192i	−0.374636	+	0.904450i
$606$	21.6592	−	123.312i	0.0357412	−	0.203485i
$607$		−	860.149i		−	1.41705i	−0.705686	−	0.708524i	$-0.749361\pi$
$607$		−	860.149i		−	1.41705i	0.705686	−	0.708524i	$-0.250639\pi$
$608$	−126.143	−	395.510i	−0.207472	−	0.650511i
$609$	370.080			0.607685
$610$	255.593	+	44.8938i	0.419005	+	0.0735964i
$611$	−217.527	−	90.1026i	−0.356018	−	0.147467i
$612$	628.803	−	294.229i	1.02746	−	0.480766i
$613$	724.830	−	300.235i	1.18243	−	0.489779i	0.297148	−	0.954831i	$-0.403965\pi$
$613$	724.830	−	300.235i	1.18243	−	0.489779i	0.885283	+	0.465052i	$0.153965\pi$
$614$	865.223	+	550.404i	1.40916	+	0.896424i
$615$	−342.914	−	342.914i	−0.557584	−	0.557584i
$616$	−256.225	+	197.417i	−0.415949	+	0.320482i
$617$	−704.685	−	704.685i	−1.14212	−	1.14212i	−0.988063	−	0.154052i	$-0.950768\pi$
$617$	−704.685	−	704.685i	−1.14212	−	1.14212i	−0.154052	−	0.988063i	$-0.549232\pi$
$618$	107.294	−	23.8610i	0.173615	−	0.0386101i
$619$	−33.0442	+	13.6874i	−0.0533832	+	0.0221121i	−0.409215	−	0.912438i	$-0.634198\pi$
$619$	−33.0442	+	13.6874i	−0.0533832	+	0.0221121i	0.355832	+	0.934550i	$0.384198\pi$
$620$	24.5635	+	546.028i	0.0396186	+	0.880691i
$621$	−98.7106	−	40.8873i	−0.158954	−	0.0658410i
$622$	−627.369	−	894.716i	−1.00863	−	1.43845i
$623$	931.477			1.49515
$624$	50.1879	+	556.691i	0.0804293	+	0.892133i
$625$			240.835i			0.385335i
$626$	−206.375	−	294.320i	−0.329673	−	0.470159i
$627$	−133.481	+	322.250i	−0.212888	+	0.513956i
$628$	−520.772	+	569.834i	−0.829255	+	0.907379i
$629$	−366.885	−	885.738i	−0.583282	−	1.40817i
$630$	647.514	−	144.000i	1.02780	−	0.228571i
$631$	−718.112	+	718.112i	−1.13805	+	1.13805i	−0.149255	+	0.988799i	$0.547688\pi$
$631$	−718.112	+	718.112i	−1.13805	+	1.13805i	−0.988799	+	0.149255i	$0.952312\pi$
$632$	361.393	−	628.829i	0.571825	−	0.994982i
$633$	−242.218	+	242.218i	−0.382651	+	0.382651i
$634$	107.761	+	68.5514i	0.169971	+	0.108125i
$635$	−236.870	−	571.854i	−0.373023	−	0.900557i
$636$	485.595	−	1339.67i	0.763515	−	2.10640i
$637$	−42.2960	+	102.112i	−0.0663988	+	0.160301i
$638$	202.495	+	35.5673i	0.317390	+	0.0557481i
$639$		−	25.5388i		−	0.0399668i
$640$	−732.407	+	677.389i	−1.14439	+	1.05842i
$641$	−338.159			−0.527549			−0.263774	−	0.964584i	$-0.584967\pi$
$641$	−338.159			−0.527549			−0.263774	+	0.964584i	$0.584967\pi$
$642$	−207.308	+	1180.27i	−0.322910	+	1.83842i
$643$	332.477	+	137.716i	0.517071	+	0.214178i	0.625930	−	0.779879i	$-0.284720\pi$
$643$	332.477	+	137.716i	0.517071	+	0.214178i	−0.108859	+	0.994057i	$0.534720\pi$
$644$	311.603	+	112.948i	0.483856	+	0.175385i
$645$	699.747	−	289.845i	1.08488	−	0.449372i
$646$	342.314	−	538.110i	0.529898	−	0.832987i
$647$	−31.2745	−	31.2745i	−0.0483377	−	0.0483377i	0.682525	−	0.730862i	$-0.260882\pi$
$647$	−31.2745	−	31.2745i	−0.0483377	−	0.0483377i	−0.730862	+	0.682525i	$0.760882\pi$
$648$	656.793	+	377.465i	1.01357	+	0.582507i
$649$	345.103	+	345.103i	0.531746	+	0.531746i
$650$	135.289	+	608.348i	0.208138	+	0.935919i
$651$	−391.211	+	162.045i	−0.600938	+	0.248917i
$652$	422.651	+	386.262i	0.648238	+	0.592426i
$653$	355.409	+	147.215i	0.544271	+	0.225445i	0.637841	−	0.770168i	$-0.279828\pi$
$653$	355.409	+	147.215i	0.544271	+	0.225445i	−0.0935696	+	0.995613i	$0.529828\pi$
$654$	227.976	−	159.855i	0.348587	−	0.244427i
$655$	449.359			0.686044
$656$	22.3049	+	247.409i	0.0340014	+	0.377148i
$657$			307.057i			0.467363i
$658$	266.564	−	186.913i	0.405113	−	0.284062i
$659$	−116.271	+	280.702i	−0.176435	+	0.425952i	−0.987214	−	0.159401i	$-0.949044\pi$
$659$	−116.271	+	280.702i	−0.176435	+	0.425952i	0.810779	+	0.585352i	$0.199044\pi$
$660$	837.370	−	37.6697i	1.26874	−	0.0570753i
$661$	179.920	+	434.366i	0.272194	+	0.657134i	0.999577	−	0.0290979i	$-0.00926347\pi$
$661$	179.920	+	434.366i	0.272194	+	0.657134i	−0.727383	+	0.686232i	$0.759263\pi$
$662$	−25.2600	−	113.585i	−0.0381571	−	0.171579i
$663$	−607.186	+	607.186i	−0.915817	+	0.915817i
$664$	−501.673	−	651.116i	−0.755532	−	0.980596i
$665$	430.892	−	430.892i	0.647957	−	0.647957i
$666$	−295.639	+	464.739i	−0.443903	+	0.697806i
$667$	−80.6200	−	194.634i	−0.120870	−	0.291805i
$668$	263.123	+	562.326i	0.393896	+	0.841805i
$669$	572.734	−	1382.70i	0.856105	−	2.06682i
$670$	−289.600	+	1648.78i	−0.432240	+	2.46086i
$671$			111.688i			0.166449i
$672$	−686.730	−	354.609i	−1.02192	−	0.527692i
$673$	1168.06			1.73561			0.867803	−	0.496908i	$-0.165531\pi$
$673$	1168.06			1.73561			0.867803	+	0.496908i	$0.165531\pi$
$674$	−726.484	−	127.604i	−1.07787	−	0.189323i
$675$	256.644	+	106.305i	0.380213	+	0.157490i
$676$	157.684	+	336.990i	0.233260	+	0.498505i
$677$	−604.882	+	250.550i	−0.893474	+	0.370089i	−0.781707	−	0.623645i	$-0.785651\pi$
$677$	−604.882	+	250.550i	−0.893474	+	0.370089i	−0.111767	+	0.993734i	$0.535651\pi$
$678$	−851.591	−	541.732i	−1.25603	−	0.799015i
$679$	271.526	+	271.526i	0.399891	+	0.399891i
$680$	−1519.91	−	197.034i	−2.23516	−	0.289756i
$681$	−23.6783	−	23.6783i	−0.0347699	−	0.0347699i
$682$	−229.630	+	51.0671i	−0.336701	+	0.0748785i
$683$	−369.863	+	153.202i	−0.541527	+	0.224308i	−0.636644	−	0.771158i	$-0.719678\pi$
$683$	−369.863	+	153.202i	−0.541527	+	0.224308i	0.0951163	+	0.995466i	$0.469678\pi$
$684$	−366.039	+	16.4665i	−0.535144	+	0.0240739i
$685$	516.663	+	214.009i	0.754253	+	0.312422i
$686$	−426.823	−	608.709i	−0.622191	−	0.887331i
$687$	716.618			1.04311
$688$	−370.321	−	115.686i	−0.538258	−	0.168148i
$689$			774.863i			1.12462i
$690$	−493.115	−	703.252i	−0.714660	−	1.01921i
$691$	74.8080	−	180.602i	0.108260	−	0.261364i	−0.860460	−	0.509518i	$-0.829824\pi$
$691$	74.8080	−	180.602i	0.108260	−	0.261364i	0.968721	+	0.248154i	$0.0798239\pi$
$692$	917.840	+	838.816i	1.32636	+	1.21216i
$693$	109.252	+	263.757i	0.157650	+	0.380602i
$694$	848.222	−	188.635i	1.22222	−	0.271808i
$695$	794.653	−	794.653i	1.14339	−	1.14339i
$696$	128.087	+	474.264i	0.184034	+	0.681414i
$697$	−269.851	+	269.851i	−0.387160	+	0.387160i
$698$	108.779	+	69.1987i	0.155844	+	0.0991386i
$699$	−30.4073	−	73.4097i	−0.0435011	−	0.105021i
$700$	−810.157	−	293.661i	−1.15737	−	0.419515i
$701$	250.206	−	604.050i	0.356927	−	0.861698i	−0.638802	−	0.769371i	$-0.720570\pi$
$701$	250.206	−	604.050i	0.356927	−	0.861698i	0.995729	−	0.0923265i	$-0.0294303\pi$
$702$	−133.437	−	23.4376i	−0.190081	−	0.0333869i
$703$			505.998i			0.719769i
$704$	−341.674	−	260.029i	−0.485333	−	0.369359i
$705$	−843.681			−1.19671
$706$	84.9533	−	483.663i	0.120330	−	0.685076i
$707$	−86.9722	−	36.0251i	−0.123016	−	0.0509548i
$708$	−397.403	+	1096.36i	−0.561304	+	1.54854i
$709$	−771.157	+	319.424i	−1.08767	+	0.450527i	−0.853193	−	0.521595i	$-0.825337\pi$
$709$	−771.157	+	319.424i	−1.08767	+	0.450527i	−0.234476	+	0.972122i	$0.575337\pi$
$710$	−30.2618	+	47.5709i	−0.0426223	+	0.0670013i
$711$	−452.650	−	452.650i	−0.636639	−	0.636639i
$712$	322.391	+	1193.70i	0.452796	+	1.67655i
$713$	170.446	+	170.446i	0.239055	+	0.239055i
$714$	−257.755	−	1159.03i	−0.361002	−	1.62330i
$715$	−421.107	+	174.428i	−0.588961	+	0.243956i
$716$	−345.126	+	377.640i	−0.482020	+	0.527431i
$717$	855.106	+	354.197i	1.19262	+	0.493998i
$718$	142.892	−	100.195i	0.199013	−	0.139547i
$719$	263.077			0.365893			0.182947	−	0.983123i	$-0.441436\pi$
$719$	263.077			0.365893			0.182947	+	0.983123i	$0.441436\pi$
$720$	408.647	+	779.961i	0.567566	+	1.08328i
$721$		−	82.6459i		−	0.114627i
$722$	315.553	−	221.264i	0.437054	−	0.306459i
$723$	170.859	−	412.489i	0.236319	−	0.570525i
$724$	−18.2832	−	406.421i	−0.0252530	−	0.561355i
$725$	209.609	+	506.041i	0.289116	+	0.697988i
$726$	−132.223	−	594.560i	−0.182126	−	0.818954i
$727$	320.334	−	320.334i	0.440625	−	0.440625i	−0.451597	−	0.892222i	$-0.649146\pi$
$727$	320.334	−	320.334i	0.440625	−	0.440625i	0.892222	+	0.451597i	$0.149146\pi$
$728$	416.788	+	54.0304i	0.572511	+	0.0742176i
$729$	274.585	−	274.585i	0.376660	−	0.376660i
$730$	363.844	−	571.954i	0.498416	−	0.783499i
$731$	−228.089	−	550.655i	−0.312023	−	0.753289i
$732$	−241.718	+	113.104i	−0.330215	+	0.154514i
$733$	119.193	−	287.758i	0.162610	−	0.392575i	−0.821482	−	0.570234i	$-0.806852\pi$
$733$	119.193	−	287.758i	0.162610	−	0.392575i	0.984092	+	0.177659i	$0.0568524\pi$
$734$	42.6782	−	242.979i	0.0581446	−	0.331034i
$735$			396.041i			0.538832i
$736$	−36.8966	+	438.417i	−0.0501313	+	0.595676i
$737$	−720.473			−0.977576
$738$	215.947	+	37.9301i	0.292611	+	0.0513958i
$739$	−760.509	−	315.013i	−1.02911	−	0.426269i	−0.196716	−	0.980461i	$-0.563028\pi$
$739$	−760.509	−	315.013i	−1.02911	−	0.426269i	−0.832389	+	0.554191i	$0.813028\pi$
$740$	1101.37	−	515.352i	1.48834	−	0.696422i
$741$	418.708	−	173.434i	0.565058	−	0.234054i
$742$	−904.020	−	575.084i	−1.21836	−	0.775046i
$743$	89.2306	+	89.2306i	0.120095	+	0.120095i	0.764600	−	0.644505i	$-0.222937\pi$
$743$	89.2306	+	89.2306i	0.120095	+	0.120095i	−0.644505	+	0.764600i	$0.722937\pi$
$744$	−343.064	−	445.258i	−0.461108	−	0.598466i
$745$	72.1196	+	72.1196i	0.0968049	+	0.0968049i
$746$	−59.1492	+	13.1541i	−0.0792885	+	0.0176328i
$747$	−670.257	+	277.629i	−0.897265	+	0.371659i
$748$	−29.6436	−	658.954i	−0.0396304	−	0.880955i
$749$	832.445	+	344.810i	1.11141	+	0.460361i
$750$	385.442	+	549.694i	0.513922	+	0.732926i
$751$	−418.271			−0.556953			−0.278476	−	0.960443i	$-0.589829\pi$
$751$	−418.271			−0.556953			−0.278476	+	0.960443i	$0.589829\pi$
$752$	331.792	+	276.915i	0.441213	+	0.368238i
$753$		−	978.366i		−	1.29929i
$754$	−153.367	−	218.722i	−0.203404	−	0.290082i
$755$	−74.6042	+	180.110i	−0.0988135	+	0.238557i
$756$	126.378	−	138.284i	0.167167	−	0.182915i
$757$	−212.675	−	513.443i	−0.280944	−	0.678260i	0.718914	−	0.695099i	$-0.244640\pi$
$757$	−212.675	−	513.443i	−0.280944	−	0.678260i	−0.999858	+	0.0168395i	$0.994640\pi$
$758$	1046.25	−	232.675i	1.38028	−	0.306959i
$759$	261.390	−	261.390i	0.344388	−	0.344388i
$760$	701.330	+	403.060i	0.922802	+	0.530343i
$761$	60.9342	−	60.9342i	0.0800712	−	0.0800712i	−0.665937	−	0.746008i	$-0.731968\pi$
$761$	60.9342	−	60.9342i	0.0800712	−	0.0800712i	0.746008	+	0.665937i	$0.231968\pi$
$762$	537.075	+	341.656i	0.704823	+	0.448367i
$763$	−80.1175	−	193.421i	−0.105003	−	0.253500i
$764$	−90.7333	+	250.317i	−0.118761	+	0.327640i
$765$	−517.665	+	1249.75i	−0.676686	+	1.63367i
$766$	−1193.35	−	209.607i	−1.55790	−	0.273638i
$767$		−	634.135i		−	0.826773i
$768$	216.755	−	1002.79i	0.282233	−	1.30572i
$769$	387.688			0.504146			0.252073	−	0.967708i	$-0.418888\pi$
$769$	387.688			0.504146			0.252073	+	0.967708i	$0.418888\pi$
$770$	109.033	−	620.755i	0.141601	−	0.806176i
$771$	1031.84	+	427.402i	1.33831	+	0.554348i
$772$	−1037.47	−	376.054i	−1.34387	−	0.487117i
$773$	19.2892	−	7.98984i	0.0249537	−	0.0103361i	−0.370172	−	0.928963i	$-0.620701\pi$
$773$	19.2892	−	7.98984i	0.0249537	−	0.0103361i	0.395125	+	0.918627i	$0.370701\pi$
$774$	−183.796	+	288.923i	−0.237463	+	0.373286i
$775$	−443.154	−	443.154i	−0.571812	−	0.571812i
$776$	−253.988	+	441.942i	−0.327304	+	0.569513i
$777$	666.120	+	666.120i	0.857297	+	0.857297i
$778$	200.462	+	901.404i	0.257663	+	1.15862i
$779$	186.085	−	77.0791i	0.238877	−	0.0989462i
$780$	−803.952	−	734.733i	−1.03071	−	0.941965i
$781$	−22.4183	−	9.28595i	−0.0287046	−	0.0118898i
$782$	−553.412	+	388.049i	−0.707688	+	0.496226i
$783$	−119.072			−0.152072
$784$	129.990	−	155.750i	0.165803	−	0.198661i
$785$		−	1504.16i		−	1.91613i
$786$	−378.364	+	265.307i	−0.481380	+	0.337540i
$787$	521.707	−	1259.51i	0.662906	−	1.60040i	−0.130321	−	0.991472i	$-0.541601\pi$
$787$	521.707	−	1259.51i	0.662906	−	1.60040i	0.793228	−	0.608925i	$-0.208399\pi$
$788$	−723.606	+	32.5520i	−0.918282	+	0.0413096i
$789$	−588.228	−	1420.11i	−0.745536	−	1.79988i
$790$	306.787	+	1379.51i	0.388338	+	1.74622i
$791$	−536.619	+	536.619i	−0.678406	+	0.678406i
$792$	−300.196	+	231.296i	−0.379036	+	0.292041i
$793$	102.614	−	102.614i	0.129400	−	0.129400i
$794$	342.140	−	537.836i	0.430907	−	0.677376i
$795$	1062.54	+	2565.20i	1.33653	+	3.22667i
$796$	559.870	+	1196.51i	0.703354	+	1.50316i
$797$	−397.554	+	959.781i	−0.498813	+	1.20424i	0.451310	+	0.892367i	$0.350957\pi$
$797$	−397.554	+	959.781i	−0.498813	+	1.20424i	−0.950123	+	0.311875i	$0.899043\pi$
$798$	−108.411	+	617.218i	−0.135854	+	0.773456i
$799$			663.921i			0.830940i
$800$	95.9300	−	1139.87i	0.119912	−	1.42484i
$801$	1091.33			1.36246
$802$	−95.4475	−	16.7649i	−0.119012	−	0.0209039i
$803$	269.539	+	111.647i	0.335665	+	0.139037i
$804$	−729.612	−	1559.27i	−0.907477	−	1.93939i
$805$	−596.657	+	247.143i	−0.741189	+	0.307010i
$806$	257.894	+	164.057i	0.319967	+	0.203544i
$807$	−168.553	−	168.553i	−0.208864	−	0.208864i
$808$	16.0650	−	123.925i	0.0198825	−	0.153372i
$809$	−349.674	−	349.674i	−0.432230	−	0.432230i	0.457157	−	0.889386i	$-0.348868\pi$
$809$	−349.674	−	349.674i	−0.432230	−	0.432230i	−0.889386	+	0.457157i	$0.848868\pi$
$810$	−1440.86	+	320.430i	−1.77884	+	0.395593i
$811$	179.312	−	74.2736i	0.221100	−	0.0915827i	−0.269384	−	0.963033i	$-0.586820\pi$
$811$	179.312	−	74.2736i	0.221100	−	0.0915827i	0.490484	+	0.871450i	$0.336820\pi$
$812$	369.004	−	16.5999i	0.454439	−	0.0204433i
$813$	−1643.84	−	680.901i	−2.02194	−	0.837517i
$814$	300.459	+	428.496i	0.369114	+	0.526408i
$815$	−1115.65			−1.36889
$816$	1396.11	−	731.468i	1.71092	−	0.896407i
$817$			314.574i			0.385035i
$818$	393.032	+	560.519i	0.480479	+	0.685231i
$819$	141.953	−	342.706i	0.173325	−	0.418444i
$820$	−357.299	−	326.536i	−0.435730	−	0.398214i
$821$	−41.2552	−	99.5988i	−0.0502499	−	0.121314i	0.896761	−	0.442515i	$-0.145914\pi$
$821$	−41.2552	−	99.5988i	−0.0502499	−	0.121314i	−0.947011	+	0.321201i	$0.895914\pi$
$822$	−561.389	+	124.846i	−0.682955	+	0.151881i
$823$	−818.928	+	818.928i	−0.995053	+	0.995053i	−0.999988	−	0.00493500i	$-0.998429\pi$
$823$	−818.928	+	818.928i	−0.995053	+	0.995053i	0.00493500	+	0.999988i	$0.498429\pi$
$824$	105.912	−	28.6043i	0.128534	−	0.0347140i
$825$	−679.606	+	679.606i	−0.823765	+	0.823765i
$826$	739.834	+	470.639i	0.895683	+	0.569781i
$827$	30.9529	+	74.7270i	0.0374280	+	0.0903591i	0.941488	−	0.337046i	$-0.109428\pi$
$827$	30.9529	+	74.7270i	0.0374280	+	0.0903591i	−0.904060	+	0.427405i	$0.859428\pi$
$828$	365.079	+	132.331i	0.440916	+	0.159821i
$829$	87.1070	−	210.295i	0.105075	−	0.253673i	−0.862594	−	0.505896i	$-0.831162\pi$
$829$	87.1070	−	210.295i	0.105075	−	0.253673i	0.967669	+	0.252223i	$0.0811618\pi$
$830$	1577.46	+	277.073i	1.90055	+	0.333823i
$831$		−	242.257i		−	0.291525i
$832$	75.0123	+	552.821i	0.0901591	+	0.664449i
$833$	311.658			0.374140
$834$	−199.933	+	1138.28i	−0.239728	+	1.36484i
$835$	−1117.63	−	462.937i	−1.33848	−	0.554416i
$836$	−118.638	+	327.301i	−0.141911	+	0.391508i
$837$	125.871	−	52.1375i	0.150384	−	0.0622909i
$838$	189.698	−	298.201i	0.226370	−	0.355848i
$839$	500.637	+	500.637i	0.596707	+	0.596707i	0.939435	−	0.342728i	$-0.111351\pi$
$839$	500.637	+	500.637i	0.596707	+	0.596707i	−0.342728	+	0.939435i	$0.611351\pi$
$840$	1453.87	−	392.657i	1.73080	−	0.467448i
$841$	428.660	+	428.660i	0.509703	+	0.509703i
$842$	293.432	+	1319.46i	0.348494	+	1.56705i
$843$	836.595	−	346.529i	0.992402	−	0.411067i
$844$	−230.650	+	252.379i	−0.273281	+	0.299027i
$845$	−669.771	−	277.428i	−0.792628	−	0.328317i
$846$	312.311	−	218.990i	0.369161	−	0.258853i
$847$	−457.973			−0.540701
$848$	424.093	−	1357.56i	0.500109	−	1.60089i
$849$			1942.30i			2.28775i
$850$	1438.85	−	1008.91i	1.69277	−	1.18696i
$851$	205.218	−	495.439i	0.241149	−	0.582184i
$852$	−2.60567	−	57.9221i	−0.00305830	−	0.0679837i
$853$	222.935	+	538.212i	0.261354	+	0.630964i	0.999023	−	0.0441988i	$-0.0140735\pi$
$853$	222.935	+	538.212i	0.261354	+	0.630964i	−0.737669	+	0.675162i	$0.764074\pi$
$854$	43.5605	+	195.876i	0.0510076	+	0.229363i
$855$	504.839	−	504.839i	0.590455	−	0.590455i
$856$	−153.765	+	1186.13i	−0.179632	+	1.38567i
$857$	−172.645	+	172.645i	−0.201453	+	0.201453i	−0.800622	−	0.599169i	$-0.795498\pi$
$857$	−172.645	+	172.645i	−0.201453	+	0.201453i	0.599169	+	0.800622i	$0.295498\pi$
$858$	251.592	−	395.497i	0.293230	−	0.460952i
$859$	66.9122	+	161.540i	0.0778954	+	0.188056i	0.958030	−	0.286668i	$-0.0925477\pi$
$859$	66.9122	+	161.540i	0.0778954	+	0.188056i	−0.880135	+	0.474724i	$0.842548\pi$
$860$	684.712	−	320.389i	0.796177	−	0.372546i
$861$	143.501	−	346.443i	0.166668	−	0.402372i
$862$	209.849	−	1194.73i	0.243444	−	1.38600i
$863$			325.900i			0.377636i	0.982012	+	0.188818i	$0.0604656\pi$
$863$			325.900i			0.377636i	−0.982012	+	0.188818i	$0.939534\pi$
$864$	220.954	+	114.095i	0.255734	+	0.132054i
$865$	−2422.77			−2.80089
$866$	−7.54396	−	1.32506i	−0.00871127	−	0.00153009i
$867$	1166.99	+	483.383i	1.34601	+	0.557535i
$868$	−382.805	+	179.121i	−0.441019	+	0.206361i
$869$	−561.927	+	232.758i	−0.646637	+	0.267846i
$870$	−807.648	−	513.778i	−0.928331	−	0.590550i
$871$	661.942	+	661.942i	0.759980	+	0.759980i
$872$	220.143	−	169.616i	0.252457	−	0.194514i
$873$	318.124	+	318.124i	0.364403	+	0.364403i
$874$	348.226	−	77.4415i	0.398428	−	0.0886058i
$875$	466.375	−	193.179i	0.533000	−	0.220776i
$876$	31.3285	+	696.408i	0.0357631	+	0.794986i
$877$	93.3817	+	38.6800i	0.106479	+	0.0441049i	0.435287	−	0.900292i	$-0.356647\pi$
$877$	93.3817	+	38.6800i	0.106479	+	0.0441049i	−0.328808	+	0.944397i	$0.606647\pi$
$878$	59.0089	+	84.1550i	0.0672083	+	0.0958485i
$879$	−2067.29			−2.35186
$880$	833.246	−	75.1204i	0.946870	−	0.0853641i
$881$			129.296i			0.146760i	0.997304	+	0.0733801i	$0.0233786\pi$
$881$			129.296i			0.146760i	−0.997304	+	0.0733801i	$0.976621\pi$
$882$	−102.798	−	146.605i	−0.116552	−	0.166219i
$883$	28.1493	−	67.9584i	0.0318792	−	0.0769631i	−0.907138	−	0.420833i	$-0.861738\pi$
$883$	28.1493	−	67.9584i	0.0318792	−	0.0769631i	0.939017	+	0.343870i	$0.111738\pi$
$884$	−578.186	+	632.657i	−0.654056	+	0.715675i
$885$	−869.565	−	2099.31i	−0.982559	−	2.37211i
$886$	−1063.36	+	236.478i	−1.20018	+	0.266905i
$887$	338.588	−	338.588i	0.381723	−	0.381723i	−0.490000	−	0.871723i	$-0.663003\pi$
$887$	338.588	−	338.588i	0.381723	−	0.381723i	0.871723	+	0.490000i	$0.163003\pi$
$888$	−623.096	+	1084.19i	−0.701684	+	1.22094i
$889$	338.431	−	338.431i	0.380687	−	0.380687i
$890$	−2032.82	−	1293.16i	−2.28407	−	1.45299i
$891$	−243.109	−	586.916i	−0.272849	−	0.658716i
$892$	509.048	−	1404.37i	0.570682	−	1.57441i
$893$	134.096	−	323.736i	0.150163	−	0.362526i
$894$	−103.306	−	18.1452i	−0.115554	−	0.0202966i
$895$		−	996.837i		−	1.11378i
$896$	−700.640	−	322.775i	−0.781964	−	0.360240i
$897$	−480.310			−0.535463
$898$	149.355	−	850.322i	0.166320	−	0.946907i
$899$	248.188	+	102.803i	0.276071	+	0.114352i
$900$	−949.192	−	344.057i	−1.05466	−	0.382286i
$901$	2018.64	−	836.148i	2.24045	−	0.928023i
$902$	111.814	−	175.770i	0.123963	−	0.194867i
$903$	414.120	+	414.120i	0.458605	+	0.458605i
$904$	−873.415	−	501.959i	−0.966167	−	0.555265i
$905$	560.535	+	560.535i	0.619375	+	0.619375i
$906$	−43.5218	−	195.702i	−0.0480373	−	0.216006i
$907$	1031.84	−	427.401i	1.13764	−	0.471225i	0.267268	−	0.963622i	$-0.413879\pi$
$907$	1031.84	−	427.401i	1.13764	−	0.471225i	0.870371	+	0.492397i	$0.163879\pi$
$908$	−24.6716	−	22.5474i	−0.0271713	−	0.0248319i
$909$	−101.898	−	42.2075i	−0.112099	−	0.0464329i
$910$	−670.500	+	470.150i	−0.736814	+	0.516649i
$911$	857.136			0.940873			0.470437	−	0.882434i	$-0.344096\pi$
$911$	857.136			0.940873			0.470437	+	0.882434i	$0.344096\pi$
$912$	−828.498	+	74.6924i	−0.908440	+	0.0818995i
$913$			689.307i			0.754992i
$914$	−433.187	+	303.748i	−0.473947	+	0.332328i
$915$	198.995	−	480.417i	0.217481	−	0.525046i
$916$	714.534	−	32.1439i	0.780059	−	0.0350916i
$917$	132.968	+	321.014i	0.145004	+	0.350070i
$918$	82.9322	+	372.916i	0.0903401	+	0.406227i
$919$	447.382	−	447.382i	0.486814	−	0.486814i	−0.420486	−	0.907299i	$-0.638140\pi$
$919$	447.382	−	447.382i	0.486814	−	0.486814i	0.907299	+	0.420486i	$0.138140\pi$
$920$	−523.226	−	679.088i	−0.568724	−	0.738140i
$921$	1452.97	−	1452.97i	1.57760	−	1.57760i
$922$	294.879	−	463.544i	0.319826	−	0.502759i
$923$	12.0655	+	29.1286i	0.0130720	+	0.0315586i
$924$	274.694	+	587.056i	0.297288	+	0.635342i
$925$	−533.558	+	1288.12i	−0.576820	+	1.39257i
$926$	−264.771	+	1507.42i	−0.285929	+	1.62788i
$927$		−	96.8291i		−	0.104454i
$928$	148.988	+	467.140i	0.160548	+	0.503384i
$929$	−357.338			−0.384648			−0.192324	−	0.981332i	$-0.561602\pi$
$929$	−357.338			−0.384648			−0.192324	+	0.981332i	$0.561602\pi$
$930$	1078.73	+	189.473i	1.15992	+	0.203735i
$931$	−151.968	−	62.9473i	−0.163231	−	0.0676125i
$932$	−33.6117	−	71.8324i	−0.0360641	−	0.0770734i
$933$	−2022.98	+	837.947i	−2.16826	+	0.898122i
$934$	488.090	+	310.494i	0.522580	+	0.332435i
$935$	908.827	+	908.827i	0.972007	+	0.972007i
$936$	488.314	+	63.3028i	0.521703	+	0.0676312i
$937$	−504.116	−	504.116i	−0.538011	−	0.538011i	0.384934	−	0.922944i	$-0.374224\pi$
$937$	−504.116	−	504.116i	−0.538011	−	0.538011i	−0.922944	+	0.384934i	$0.874224\pi$
$938$	−1263.55	+	281.000i	−1.34707	+	0.299573i
$939$	−665.468	+	275.646i	−0.708698	+	0.293552i
$940$	−841.229	+	37.8433i	−0.894924	+	0.0402589i
$941$	−503.223	−	208.442i	−0.534775	−	0.221511i	0.0989183	−	0.995096i	$-0.468462\pi$
$941$	−503.223	−	208.442i	−0.534775	−	0.221511i	−0.633693	+	0.773585i	$0.718462\pi$
$942$	888.073	+	1266.52i	0.942752	+	1.34450i
$943$	−213.463			−0.226366
$944$	−347.070	+	1111.00i	−0.367659	+	1.17691i
$945$			365.021i			0.386265i
$946$	186.792	+	266.392i	0.197455	+	0.281598i
$947$	−137.566	+	332.113i	−0.145265	+	0.350700i	−0.979719	−	0.200378i	$-0.935783\pi$
$947$	−137.566	+	332.113i	−0.145265	+	0.350700i	0.834454	+	0.551077i	$0.185783\pi$
$948$	−1072.80	−	980.431i	−1.13164	−	1.03421i
$949$	−145.065	−	350.219i	−0.152861	−	0.369040i
$950$	−905.376	+	201.345i	−0.953028	+	0.211942i
$951$	180.964	−	180.964i	0.190288	−	0.190288i
$952$	−308.995	−	1144.10i	−0.324574	−	1.20179i
$953$	129.115	−	129.115i	0.135483	−	0.135483i	−0.636113	−	0.771596i	$-0.719459\pi$
$953$	129.115	−	129.115i	0.135483	−	0.135483i	0.771596	+	0.636113i	$0.219459\pi$
$954$	−1059.16	−	673.777i	−1.11023	−	0.706265i
$955$	−198.535	−	479.306i	−0.207890	−	0.501891i
$956$	868.508	+	314.811i	0.908481	+	0.329300i
$957$	157.655	−	380.612i	0.164739	−	0.397714i
$958$	311.351	+	54.6874i	0.325001	+	0.0570850i
$959$			432.422i			0.450909i
$960$	1006.39	+	1727.26i	1.04833	+	1.79923i
$961$	653.628			0.680154
$962$	117.636	−	669.735i	0.122283	−	0.696190i
$963$	975.304	+	403.984i	1.01278	+	0.419506i
$964$	151.860	−	418.954i	0.157531	−	0.434600i
$965$	1986.54	−	822.851i	2.05859	−	0.852695i
$966$	356.475	−	560.370i	0.369021	−	0.580093i
$967$	657.007	+	657.007i	0.679428	+	0.679428i	0.959871	−	0.280443i	$-0.0904813\pi$
$967$	657.007	+	657.007i	0.679428	+	0.679428i	−0.280443	+	0.959871i	$0.590481\pi$
$968$	−158.508	−	586.901i	−0.163748	−	0.606303i
$969$	−903.648	−	903.648i	−0.932557	−	0.932557i
$970$	−215.611	−	969.524i	−0.222279	−	0.999509i
$971$	−654.912	+	271.274i	−0.674472	+	0.279376i	−0.693514	−	0.720443i	$-0.743938\pi$
$971$	−654.912	+	271.274i	−0.674472	+	0.279376i	0.0190418	+	0.999819i	$0.493938\pi$
$972$	835.302	−	913.996i	0.859364	−	0.940325i
$973$	802.830	+	332.543i	0.825108	+	0.341771i
$974$	−1563.46	+	1096.29i	−1.60519	+	1.12555i
$975$	1248.79			1.28081
$976$	−235.942	+	123.618i	−0.241744	+	0.126657i
$977$			1493.20i			1.52835i	0.645010	+	0.764174i	$0.276853\pi$
$977$			1493.20i			1.52835i	−0.645010	+	0.764174i	$0.723147\pi$
$978$	939.387	−	658.692i	0.960518	−	0.673509i
$979$	396.811	−	957.986i	0.405323	−	0.978536i
$980$	17.7644	+	394.890i	0.0181270	+	0.402949i
$981$	−93.8668	−	226.615i	−0.0956848	−	0.231004i
$982$	−40.9426	−	184.104i	−0.0416931	−	0.187479i
$983$	−856.189	+	856.189i	−0.870996	+	0.870996i	−0.992581	−	0.121585i	$-0.961202\pi$
$983$	−856.189	+	856.189i	−0.870996	+	0.870996i	0.121585	+	0.992581i	$0.461202\pi$
$984$	493.639	+	63.9930i	0.501666	+	0.0650336i
$985$	997.994	−	997.994i	1.01319	−	1.01319i
$986$	−404.309	+	635.565i	−0.410050	+	0.644590i
$987$	−249.651	−	602.711i	−0.252939	−	0.610650i
$988$	409.711	−	191.711i	0.414687	−	0.194040i
$989$	127.582	−	308.010i	0.129001	−	0.311435i
$990$	127.744	−	727.286i	0.129035	−	0.734632i
$991$		−	1223.32i		−	1.23443i	−0.786793	−	0.617217i	$-0.788260\pi$
$991$		−	1223.32i		−	1.23443i	0.786793	−	0.617217i	$-0.211740\pi$
$992$	−362.039	−	428.576i	−0.364958	−	0.432032i
$993$	−233.162			−0.234806
$994$	−42.9385	−	7.54196i	−0.0431977	−	0.00758748i
$995$	−2378.08	−	985.034i	−2.39003	−	0.989984i
$996$	−1491.82	+	698.050i	−1.49781	+	0.700854i
$997$	604.001	−	250.185i	0.605819	−	0.250938i	−0.0586209	−	0.998280i	$-0.518670\pi$
$997$	604.001	−	250.185i	0.605819	−	0.250938i	0.664440	+	0.747342i	$0.268670\pi$
$998$	−726.761	−	462.323i	−0.728217	−	0.463249i
$999$	−214.323	−	214.323i	−0.214537	−	0.214537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.19.5	✓	28
3.2	odd	2		288.3.u.a.19.3		28
4.3	odd	2		128.3.h.a.111.6		28
8.3	odd	2		256.3.h.a.223.2		28
8.5	even	2		256.3.h.b.223.6		28
32.5	even	8		128.3.h.a.15.6		28
32.11	odd	8		256.3.h.b.31.6		28
32.21	even	8		256.3.h.a.31.2		28
32.27	odd	8	inner	32.3.h.a.27.5	yes	28
96.59	even	8		288.3.u.a.91.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.5	✓	28	1.1	even	1	trivial
32.3.h.a.27.5	yes	28	32.27	odd	8	inner
128.3.h.a.15.6		28	32.5	even	8
128.3.h.a.111.6		28	4.3	odd	2
256.3.h.a.31.2		28	32.21	even	8
256.3.h.a.223.2		28	8.3	odd	2
256.3.h.b.31.6		28	32.11	odd	8
256.3.h.b.223.6		28	8.5	even	2
288.3.u.a.19.3		28	3.2	odd	2
288.3.u.a.91.3		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)

\(f(q)\)	\(=\)	\(q+(0.345994 - 1.96984i) q^{2} +(-3.70255 - 1.53365i) q^{3} +(-3.76058 - 1.36311i) q^{4} +(7.20074 - 2.98264i) q^{5} +(-4.30210 + 6.76281i) q^{6} +(4.26150 + 4.26150i) q^{7} +(-3.98625 + 6.93612i) q^{8} +(4.99283 + 4.99283i) q^{9} +O(q^{10})\)	\(q+(0.345994 - 1.96984i) q^{2} +(-3.70255 - 1.53365i) q^{3} +(-3.76058 - 1.36311i) q^{4} +(7.20074 - 2.98264i) q^{5} +(-4.30210 + 6.76281i) q^{6} +(4.26150 + 4.26150i) q^{7} +(-3.98625 + 6.93612i) q^{8} +(4.99283 + 4.99283i) q^{9} +(-3.38393 - 15.2163i) q^{10} +(6.19818 - 2.56737i) q^{11} +(11.8332 + 10.8144i) q^{12} +(-8.05345 - 3.33585i) q^{13} +(9.86895 - 6.92004i) q^{14} -31.2354 q^{15} +(12.2839 + 10.2522i) q^{16} +24.5802i q^{17} +(11.5626 - 8.10762i) q^{18} +(4.96459 - 11.9856i) q^{19} +(-31.1446 + 1.40106i) q^{20} +(-9.24278 - 22.3140i) q^{21} +(-2.91279 - 13.0978i) q^{22} +(-9.72199 + 9.72199i) q^{23} +(25.3968 - 19.5678i) q^{24} +(25.2768 - 25.2768i) q^{25} +(-9.35754 + 14.7099i) q^{26} +(2.97384 + 7.17949i) q^{27} +(-10.2168 - 21.8346i) q^{28} +(-5.86371 + 14.1563i) q^{29} +(-10.8073 + 61.5289i) q^{30} -17.5320i q^{31} +(24.4453 - 20.6501i) q^{32} -26.8865 q^{33} +(48.4192 + 8.50460i) q^{34} +(43.3965 + 17.9754i) q^{35} +(-11.9702 - 25.5817i) q^{36} +(-36.0346 + 14.9260i) q^{37} +(-21.8920 - 13.9264i) q^{38} +(24.7023 + 24.7023i) q^{39} +(-8.01597 + 61.8348i) q^{40} +(10.9784 + 10.9784i) q^{41} +(-47.1531 + 10.4863i) q^{42} +(-22.4024 + 9.27937i) q^{43} +(-26.8084 + 1.20599i) q^{44} +(50.8439 + 21.0603i) q^{45} +(15.7871 + 22.5146i) q^{46} +27.0104 q^{47} +(-29.7584 - 56.7982i) q^{48} -12.6792i q^{49} +(-41.0458 - 58.5371i) q^{50} +(37.6973 - 91.0093i) q^{51} +(25.7385 + 23.5224i) q^{52} +(-34.0172 - 82.1247i) q^{53} +(15.1714 - 3.37395i) q^{54} +(36.9740 - 36.9740i) q^{55} +(-46.5457 + 12.5709i) q^{56} +(-36.7633 + 36.7633i) q^{57} +(25.8568 + 16.4486i) q^{58} +(27.8391 + 67.2095i) q^{59} +(117.463 + 42.5773i) q^{60} +(-6.37082 + 15.3805i) q^{61} +(-34.5354 - 6.06598i) q^{62} +42.5539i q^{63} +(-32.2196 - 55.2983i) q^{64} -67.9404 q^{65} +(-9.30258 + 52.9623i) q^{66} +(-99.2165 - 41.0968i) q^{67} +(33.5055 - 92.4357i) q^{68} +(50.9062 - 21.0860i) q^{69} +(50.4237 - 79.2650i) q^{70} +(-2.55754 - 2.55754i) q^{71} +(-54.5336 + 14.7282i) q^{72} +(30.7498 + 30.7498i) q^{73} +(16.9342 + 76.1469i) q^{74} +(-132.354 + 54.8230i) q^{75} +(-35.0074 + 38.3054i) q^{76} +(37.3544 + 15.4727i) q^{77} +(57.2065 - 40.1128i) q^{78} -90.6600 q^{79} +(119.031 + 37.1847i) q^{80} -94.6916i q^{81} +(25.4241 - 17.8272i) q^{82} +(-39.3191 + 94.9247i) q^{83} +(4.34169 + 96.5126i) q^{84} +(73.3140 + 176.996i) q^{85} +(10.5278 + 47.3398i) q^{86} +(43.4214 - 43.4214i) q^{87} +(-6.89991 + 53.2256i) q^{88} +(109.290 - 109.290i) q^{89} +(59.0771 - 92.8680i) q^{90} +(-20.1040 - 48.5355i) q^{91} +(49.8124 - 23.3081i) q^{92} +(-26.8879 + 64.9132i) q^{93} +(9.34545 - 53.2063i) q^{94} -101.113i q^{95} +(-122.180 + 38.9677i) q^{96} +63.7161 q^{97} +(-24.9761 - 4.38694i) q^{98} +(43.7650 + 18.1280i) 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

Introduction

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