LMFDB - Embedded newform 32.3.h.a.3.4

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			3.4
Character	$\chi$	$=$	32.3
Dual form			32.3.h.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.658450 + 1.88850i) q^{2} +(-1.31872 + 3.18367i) q^{3} +(-3.13289 - 2.48697i) q^{4} +(-0.659338 - 1.59178i) q^{5} +(-5.14406 - 4.58669i) q^{6} +(9.54718 + 9.54718i) q^{7} +(6.75950 - 4.27892i) q^{8} +(-2.03276 - 2.03276i) q^{9} +O(q^{10})$	\(q+(-0.658450 + 1.88850i) q^{2} +(-1.31872 + 3.18367i) q^{3} +(-3.13289 - 2.48697i) q^{4} +(-0.659338 - 1.59178i) q^{5} +(-5.14406 - 4.58669i) q^{6} +(9.54718 + 9.54718i) q^{7} +(6.75950 - 4.27892i) q^{8} +(-2.03276 - 2.03276i) q^{9} +(3.44023 - 0.197052i) q^{10} +(-3.96481 - 9.57189i) q^{11} +(12.0491 - 6.69446i) q^{12} +(1.91784 - 4.63007i) q^{13} +(-24.3162 + 11.7435i) q^{14} +5.93719 q^{15} +(3.62996 + 15.5828i) q^{16} -15.3143i q^{17} +(5.17735 - 2.50041i) q^{18} +(0.827335 + 0.342693i) q^{19} +(-1.89308 + 6.62663i) q^{20} +(-42.9851 + 17.8050i) q^{21} +(20.6872 - 1.18494i) q^{22} +(-12.9230 + 12.9230i) q^{23} +(4.70879 + 27.1627i) q^{24} +(15.5786 - 15.5786i) q^{25} +(7.48110 + 6.67051i) q^{26} +(-19.5007 + 8.07746i) q^{27} +(-6.16668 - 53.6538i) q^{28} +(23.7905 + 9.85436i) q^{29} +(-3.90934 + 11.2124i) q^{30} -25.1562i q^{31} +(-31.8183 - 3.40530i) q^{32} +35.7022 q^{33} +(28.9211 + 10.0837i) q^{34} +(8.90221 - 21.4918i) q^{35} +(1.31300 + 11.4238i) q^{36} +(13.6161 + 32.8721i) q^{37} +(-1.19194 + 1.33678i) q^{38} +(12.2115 + 12.2115i) q^{39} +(-11.2679 - 7.93840i) q^{40} +(-32.9116 - 32.9116i) q^{41} +(-5.32127 - 92.9012i) q^{42} +(-17.9473 - 43.3286i) q^{43} +(-11.3837 + 39.8480i) q^{44} +(-1.89544 + 4.57600i) q^{45} +(-15.8960 - 32.9143i) q^{46} +20.1127 q^{47} +(-54.3973 - 8.99273i) q^{48} +133.297i q^{49} +(19.1625 + 39.6780i) q^{50} +(48.7557 + 20.1953i) q^{51} +(-17.5232 + 9.73588i) q^{52} +(35.0503 - 14.5183i) q^{53} +(-2.41406 - 42.1458i) q^{54} +(-12.6222 + 12.6222i) q^{55} +(105.386 + 23.6825i) q^{56} +(-2.18204 + 2.18204i) q^{57} +(-34.2749 + 38.4399i) q^{58} +(-60.6706 + 25.1306i) q^{59} +(-18.6005 - 14.7656i) q^{60} +(-27.9825 - 11.5907i) q^{61} +(47.5076 + 16.5641i) q^{62} -38.8143i q^{63} +(27.3817 - 57.8467i) q^{64} -8.63457 q^{65} +(-23.5081 + 67.4237i) q^{66} +(1.13412 - 2.73801i) q^{67} +(-38.0862 + 47.9780i) q^{68} +(-24.1008 - 58.1845i) q^{69} +(34.7257 + 30.9632i) q^{70} +(-45.6144 - 45.6144i) q^{71} +(-22.4385 - 5.04243i) q^{72} +(-29.1727 - 29.1727i) q^{73} +(-71.0445 + 4.06934i) q^{74} +(29.0534 + 70.1410i) q^{75} +(-1.73968 - 3.13118i) q^{76} +(53.5318 - 129.237i) q^{77} +(-31.1022 + 15.0208i) q^{78} +3.27983 q^{79} +(22.4110 - 16.0524i) q^{80} -98.6086i q^{81} +(83.8242 - 40.4830i) q^{82} +(56.7834 + 23.5205i) q^{83} +(178.948 + 51.1215i) q^{84} +(-24.3770 + 10.0973i) q^{85} +(93.6436 - 5.36380i) q^{86} +(-62.7460 + 62.7460i) q^{87} +(-67.7575 - 47.7361i) q^{88} +(-44.5059 + 44.5059i) q^{89} +(-7.39373 - 6.59261i) q^{90} +(62.5140 - 25.8942i) q^{91} +(72.6256 - 8.34720i) q^{92} +(80.0891 + 33.1740i) q^{93} +(-13.2432 + 37.9829i) q^{94} -1.54289i q^{95} +(52.8007 - 96.8083i) q^{96} -106.417 q^{97} +(-251.732 - 87.7695i) q^{98} +(-11.3979 + 27.5169i) 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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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 $

$2$	−0.658450	+	1.88850i	−0.329225	+	0.944251i
$2$	−0.658450	+	1.88850i	−0.329225	+	0.944251i
$3$	−1.31872	+	3.18367i	−0.439573	+	1.06122i	0.536524	+	0.843885i	$0.319737\pi$
$3$	−1.31872	+	3.18367i	−0.439573	+	1.06122i	−0.976097	+	0.217337i	$0.930263\pi$
$4$	−3.13289	−	2.48697i	−0.783222	−	0.621742i
$5$	−0.659338	−	1.59178i	−0.131868	−	0.318356i	0.844130	−	0.536139i	$-0.180118\pi$
$5$	−0.659338	−	1.59178i	−0.131868	−	0.318356i	−0.975997	+	0.217782i	$0.930118\pi$
$6$	−5.14406	−	4.58669i	−0.857343	−	0.764448i
$7$	9.54718	+	9.54718i	1.36388	+	1.36388i	0.868907	+	0.494975i	$0.164823\pi$
$7$	9.54718	+	9.54718i	1.36388	+	1.36388i	0.494975	+	0.868907i	$0.335177\pi$
$8$	6.75950	−	4.27892i	0.844937	−	0.534865i
$9$	−2.03276	−	2.03276i	−0.225863	−	0.225863i
$10$	3.44023	−	0.197052i	0.344023	−	0.0197052i
$11$	−3.96481	−	9.57189i	−0.360437	−	0.870172i	−0.995236	−	0.0974947i	$-0.968917\pi$
$11$	−3.96481	−	9.57189i	−0.360437	−	0.870172i	0.634799	−	0.772677i	$-0.281083\pi$
$12$	12.0491	−	6.69446i	1.00409	−	0.557872i
$13$	1.91784	−	4.63007i	0.147526	−	0.356159i	−0.832792	−	0.553587i	$-0.813259\pi$
$13$	1.91784	−	4.63007i	0.147526	−	0.356159i	0.980317	+	0.197428i	$0.0632587\pi$
$14$	−24.3162	+	11.7435i	−1.73687	+	0.838824i
$15$	5.93719			0.395813
$16$	3.62996	+	15.5828i	0.226873	+	0.973924i
$17$		−	15.3143i		−	0.900842i	−0.892816	−	0.450421i	$-0.851274\pi$
$17$		−	15.3143i		−	0.900842i	0.892816	−	0.450421i	$-0.148726\pi$
$18$	5.17735	−	2.50041i	0.287631	−	0.138912i
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	0.404349	−	0.914605i	$-0.367498\pi$
$19$	0.827335	+	0.342693i	0.0435439	+	0.0180365i	−0.360805	+	0.932641i	$0.617498\pi$
$20$	−1.89308	+	6.62663i	−0.0946542	+	0.331331i
$21$	−42.9851	+	17.8050i	−2.04691	+	0.847857i
$22$	20.6872	−	1.18494i	0.940326	−	0.0538608i
$23$	−12.9230	+	12.9230i	−0.561871	+	0.561871i	−0.929839	−	0.367968i	$-0.880054\pi$
$23$	−12.9230	+	12.9230i	−0.561871	+	0.561871i	0.367968	+	0.929839i	$0.380054\pi$
$24$	4.70879	+	27.1627i	0.196199	+	1.13178i
$25$	15.5786	−	15.5786i	0.623145	−	0.623145i
$26$	7.48110	+	6.67051i	0.287735	+	0.256558i
$27$	−19.5007	+	8.07746i	−0.722249	+	0.299165i
$28$	−6.16668	−	53.6538i	−0.220239	−	1.91621i
$29$	23.7905	+	9.85436i	0.820363	+	0.339805i	0.753080	−	0.657929i	$-0.228567\pi$
$29$	23.7905	+	9.85436i	0.820363	+	0.339805i	0.0672825	+	0.997734i	$0.478567\pi$
$30$	−3.90934	+	11.2124i	−0.130311	+	0.373747i
$31$		−	25.1562i		−	0.811491i	−0.913986	−	0.405746i	$-0.867012\pi$
$31$		−	25.1562i		−	0.811491i	0.913986	−	0.405746i	$-0.132988\pi$
$32$	−31.8183	−	3.40530i	−0.994322	−	0.106416i
$33$	35.7022			1.08188
$34$	28.9211	+	10.0837i	0.850621	+	0.296580i
$35$	8.90221	−	21.4918i	0.254349	−	0.614053i
$36$	1.31300	+	11.4238i	0.0364721	+	0.317329i
$37$	13.6161	+	32.8721i	0.368001	+	0.888434i	0.994078	+	0.108672i	$0.0346599\pi$
$37$	13.6161	+	32.8721i	0.368001	+	0.888434i	−0.626076	+	0.779762i	$0.715340\pi$
$38$	−1.19194	+	1.33678i	−0.0313667	+	0.0351784i
$39$	12.2115	+	12.2115i	0.313116	+	0.313116i
$40$	−11.2679	−	7.93840i	−0.281698	−	0.198460i
$41$	−32.9116	−	32.9116i	−0.802721	−	0.802721i	0.180799	−	0.983520i	$-0.442132\pi$
$41$	−32.9116	−	32.9116i	−0.802721	−	0.802721i	−0.983520	+	0.180799i	$0.942132\pi$
$42$	−5.32127	−	92.9012i	−0.126697	−	2.21193i
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	−0.983104	−	0.183048i	$-0.941404\pi$
$43$	−17.9473	−	43.3286i	−0.417379	−	1.00764i	0.565725	−	0.824594i	$-0.308596\pi$
$44$	−11.3837	+	39.8480i	−0.258721	+	0.905637i
$45$	−1.89544	+	4.57600i	−0.0421209	+	0.101689i
$46$	−15.8960	−	32.9143i	−0.345565	−	0.715529i
$47$	20.1127			0.427930			0.213965	−	0.976841i	$-0.431362\pi$
$47$	20.1127			0.427930			0.213965	+	0.976841i	$0.431362\pi$
$48$	−54.3973	−	8.99273i	−1.13328	−	0.187348i
$49$			133.297i			2.72035i
$50$	19.1625	+	39.6780i	0.383251	+	0.793561i
$51$	48.7557	+	20.1953i	0.955994	+	0.395986i
$52$	−17.5232	+	9.73588i	−0.336985	+	0.187228i
$53$	35.0503	−	14.5183i	0.661327	−	0.273931i	−0.0266698	−	0.999644i	$-0.508490\pi$
$53$	35.0503	−	14.5183i	0.661327	−	0.273931i	0.687997	+	0.725714i	$0.258490\pi$
$54$	−2.41406	−	42.1458i	−0.0447048	−	0.780477i
$55$	−12.6222	+	12.6222i	−0.229495	+	0.229495i
$56$	105.386	+	23.6825i	1.88189	+	0.422902i
$57$	−2.18204	+	2.18204i	−0.0382815	+	0.0382815i
$58$	−34.2749	+	38.4399i	−0.590946	+	0.662756i
$59$	−60.6706	+	25.1306i	−1.02832	+	0.425942i	−0.832104	−	0.554619i	$-0.812864\pi$
$59$	−60.6706	+	25.1306i	−1.02832	+	0.425942i	−0.196212	+	0.980562i	$0.562864\pi$
$60$	−18.6005	−	14.7656i	−0.310009	−	0.246093i
$61$	−27.9825	−	11.5907i	−0.458730	−	0.190012i	0.141338	−	0.989961i	$-0.454860\pi$
$61$	−27.9825	−	11.5907i	−0.458730	−	0.190012i	−0.600067	+	0.799949i	$0.704860\pi$
$62$	47.5076	+	16.5641i	0.766252	+	0.267163i
$63$		−	38.8143i		−	0.616100i
$64$	27.3817	−	57.8467i	0.427839	−	0.903855i
$65$	−8.63457			−0.132839
$66$	−23.5081	+	67.4237i	−0.356184	+	1.02157i
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	−0.915190	−	0.403023i	$-0.867960\pi$
$67$	1.13412	−	2.73801i	0.0169272	−	0.0408659i	0.932117	+	0.362157i	$0.117960\pi$
$68$	−38.0862	+	47.9780i	−0.560092	+	0.705559i
$69$	−24.1008	−	58.1845i	−0.349287	−	0.843253i
$70$	34.7257	+	30.9632i	0.496082	+	0.442331i
$71$	−45.6144	−	45.6144i	−0.642456	−	0.642456i	0.308702	−	0.951159i	$-0.400105\pi$
$71$	−45.6144	−	45.6144i	−0.642456	−	0.642456i	−0.951159	+	0.308702i	$0.900105\pi$
$72$	−22.4385	−	5.04243i	−0.311646	−	0.0700338i
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	0.478475	−	0.878101i	$-0.341190\pi$
$73$	−29.1727	−	29.1727i	−0.399626	−	0.399626i	−0.878101	+	0.478475i	$0.841190\pi$
$74$	−71.0445	+	4.06934i	−0.960060	+	0.0549911i
$75$	29.0534	+	70.1410i	0.387378	+	0.935213i
$76$	−1.73968	−	3.13118i	−0.0228905	−	0.0411997i
$77$	53.5318	−	129.237i	0.695219	−	1.67841i
$78$	−31.1022	+	15.0208i	−0.398746	+	0.192575i
$79$	3.27983			0.0415169			0.0207584	−	0.999785i	$-0.493392\pi$
$79$	3.27983			0.0415169			0.0207584	+	0.999785i	$0.493392\pi$
$80$	22.4110	−	16.0524i	0.280138	−	0.200655i
$81$		−	98.6086i		−	1.21739i
$82$	83.8242	−	40.4830i	1.02225	−	0.493695i
$83$	56.7834	+	23.5205i	0.684138	+	0.283379i	0.697555	−	0.716531i	$-0.254271\pi$
$83$	56.7834	+	23.5205i	0.684138	+	0.283379i	−0.0134176	+	0.999910i	$0.504271\pi$
$84$	178.948	+	51.1215i	2.13033	+	0.608590i
$85$	−24.3770	+	10.0973i	−0.286789	+	0.118792i
$86$	93.6436	−	5.36380i	1.08888	−	0.0623697i
$87$	−62.7460	+	62.7460i	−0.721218	+	0.721218i
$88$	−67.7575	−	47.7361i	−0.769971	−	0.542456i
$89$	−44.5059	+	44.5059i	−0.500066	+	0.500066i	−0.911458	−	0.411392i	$-0.865043\pi$
$89$	−44.5059	+	44.5059i	−0.500066	+	0.500066i	0.411392	+	0.911458i	$0.365043\pi$
$90$	−7.39373	−	6.59261i	−0.0821525	−	0.0732512i
$91$	62.5140	−	25.8942i	0.686967	−	0.284551i
$92$	72.6256	−	8.34720i	0.789408	−	0.0907305i
$93$	80.0891	+	33.1740i	0.861173	+	0.356709i
$94$	−13.2432	+	37.9829i	−0.140885	+	0.404074i
$95$		−	1.54289i		−	0.0162409i
$96$	52.8007	−	96.8083i	0.550008	−	1.00842i
$97$	−106.417			−1.09708			−0.548542	−	0.836123i	$-0.684817\pi$
$97$	−106.417			−1.09708			−0.548542	+	0.836123i	$0.684817\pi$
$98$	−251.732	−	87.7695i	−2.56869	−	0.895607i
$99$	−11.3979	+	27.5169i	−0.115130	+	0.277949i
$100$	−87.5496	+	10.0625i	−0.875496	+	0.100625i
$101$	3.62243	+	8.74531i	0.0358656	+	0.0865872i	0.940797	−	0.338969i	$-0.110078\pi$
$101$	3.62243	+	8.74531i	0.0358656	+	0.0865872i	−0.904932	+	0.425557i	$0.860078\pi$
$102$	−70.2420	+	78.7777i	−0.688647	+	0.772330i
$103$	26.0911	+	26.0911i	0.253312	+	0.253312i	0.822327	−	0.569015i	$-0.192675\pi$
$103$	26.0911	+	26.0911i	0.253312	+	0.253312i	−0.569015	+	0.822327i	$0.692675\pi$
$104$	−6.84808	−	39.5032i	−0.0658469	−	0.379839i
$105$	56.6834	+	56.6834i	0.539842	+	0.539842i
$106$	4.33900	+	75.7523i	0.0409340	+	0.714644i
$107$	32.1753	+	77.6781i	0.300704	+	0.725963i	0.999939	+	0.0110713i	$0.00352416\pi$
$107$	32.1753	+	77.6781i	0.300704	+	0.725963i	−0.699235	+	0.714892i	$0.746476\pi$
$108$	81.1820	+	23.1919i	0.751685	+	0.214740i
$109$	−36.0541	+	87.0422i	−0.330771	+	0.798553i	0.667760	+	0.744377i	$0.267253\pi$
$109$	−36.0541	+	87.0422i	−0.330771	+	0.798553i	−0.998531	+	0.0541760i	$0.982747\pi$
$110$	−15.5260	−	32.1482i	−0.141145	−	0.292256i
$111$	−122.609			−1.10459
$112$	−114.116	+	183.428i	−1.01889	+	1.63775i
$113$		−	6.32445i		−	0.0559686i	−0.999608	−	0.0279843i	$-0.991091\pi$
$113$		−	6.32445i		−	0.0559686i	0.999608	−	0.0279843i	$-0.00890884\pi$
$114$	−2.68403	−	5.55756i	−0.0235441	−	0.0487506i
$115$	29.0913	+	12.0500i	0.252968	+	0.104783i
$116$	−50.0255	−	90.0389i	−0.431255	−	0.776197i
$117$	−13.3104	+	5.51333i	−0.113764	+	0.0471225i
$118$	−7.51063	−	131.124i	−0.0636494	−	1.11122i
$119$	146.208	−	146.208i	1.22864	−	1.22864i
$120$	40.1324	−	25.4048i	0.334437	−	0.211706i
$121$	9.65850	−	9.65850i	0.0798223	−	0.0798223i
$122$	40.3142	−	45.2131i	0.330444	−	0.370599i
$123$	148.181	−	61.3784i	1.20472	−	0.499011i
$124$	−62.5628	+	78.8116i	−0.504539	+	0.635577i
$125$	−74.8639	−	31.0096i	−0.598911	−	0.248077i
$126$	73.3010	+	25.5573i	0.581754	+	0.202836i
$127$			34.6015i			0.272453i	0.990678	+	0.136226i	$0.0434975\pi$
$127$			34.6015i			0.272453i	−0.990678	+	0.136226i	$0.956503\pi$
$128$	91.2142	+	89.7996i	0.712611	+	0.701559i
$129$	161.611			1.25280
$130$	5.68543	−	16.3064i	0.0437341	−	0.125434i
$131$	−68.0051	+	164.179i	−0.519123	+	1.25327i	0.419320	+	0.907838i	$0.362268\pi$
$131$	−68.0051	+	164.179i	−0.519123	+	1.25327i	−0.938443	+	0.345434i	$0.887732\pi$
$132$	−111.851	−	88.7903i	−0.847356	−	0.672654i
$133$	4.62696	+	11.1705i	0.0347892	+	0.0839885i
$134$	4.42398	+	3.94464i	0.0330148	+	0.0294376i
$135$	25.7151	+	25.7151i	0.190482	+	0.190482i
$136$	−65.5287	−	103.517i	−0.481829	−	0.761155i
$137$	71.5748	+	71.5748i	0.522444	+	0.522444i	0.918309	−	0.395865i	$-0.129555\pi$
$137$	71.5748	+	71.5748i	0.522444	+	0.522444i	−0.395865	+	0.918309i	$0.629555\pi$
$138$	125.751	−	7.20286i	0.911237	−	0.0521946i
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	−0.924056	−	0.382258i	$-0.875147\pi$
$139$	−75.1916	−	181.529i	−0.540947	−	1.30596i	0.383109	−	0.923703i	$-0.374853\pi$
$140$	−81.3392	+	45.1920i	−0.580994	+	0.322800i
$141$	−26.5230	+	64.0322i	−0.188107	+	0.454129i
$142$	116.178	−	56.1081i	0.818153	−	0.395128i
$143$	−51.9224			−0.363094
$144$	24.2973	−	39.0550i	0.168731	−	0.271215i
$145$		−	44.3667i		−	0.305977i
$146$	74.3015	−	35.8840i	0.508915	−	0.245781i
$147$	−424.374	−	175.781i	−2.88690	−	1.19579i
$148$	39.0943	−	136.847i	0.264150	−	0.924643i
$149$	211.685	−	87.6826i	1.42070	−	0.588474i	0.465665	−	0.884961i	$-0.345815\pi$
$149$	211.685	−	87.6826i	1.42070	−	0.588474i	0.955037	+	0.296487i	$0.0958152\pi$
$150$	−151.592	+	8.68299i	−1.01061	+	0.0578866i
$151$	10.5820	−	10.5820i	0.0700794	−	0.0700794i	−0.671198	−	0.741278i	$-0.734220\pi$
$151$	10.5820	−	10.5820i	0.0700794	−	0.0700794i	0.741278	+	0.671198i	$0.234220\pi$
$152$	7.05873	−	1.22366i	0.0464390	−	0.00805043i
$153$	−31.1304	+	31.1304i	−0.203467	+	0.203467i
$154$	208.817	+	186.191i	1.35595	+	1.20903i
$155$	−40.0432	+	16.5864i	−0.258343	+	0.107009i
$156$	−7.88763	−	68.6270i	−0.0505617	−	0.439917i
$157$	26.9641	+	11.1689i	0.171746	+	0.0711394i	0.466900	−	0.884310i	$-0.345371\pi$
$157$	26.9641	+	11.1689i	0.171746	+	0.0711394i	−0.295154	+	0.955450i	$0.595371\pi$
$158$	−2.15961	+	6.19398i	−0.0136684	+	0.0392024i
$159$			130.734i			0.822228i
$160$	15.5585	+	52.8930i	0.0972407	+	0.330581i
$161$	−246.757			−1.53265
$162$	186.223	+	64.9288i	1.14952	+	0.400795i
$163$	111.743	−	269.771i	0.685540	−	1.65504i	−0.0680396	−	0.997683i	$-0.521674\pi$
$163$	111.743	−	269.771i	0.685540	−	1.65504i	0.753579	−	0.657357i	$-0.228326\pi$
$164$	21.2581	+	184.958i	0.129623	+	1.12779i
$165$	−23.5398	−	56.8301i	−0.142665	−	0.344425i
$166$	−81.8075	+	91.7486i	−0.492816	+	0.552703i
$167$	−10.3664	−	10.3664i	−0.0620741	−	0.0620741i	0.675388	−	0.737462i	$-0.263976\pi$
$167$	−10.3664	−	10.3664i	−0.0620741	−	0.0620741i	−0.737462	+	0.675388i	$0.763976\pi$
$168$	−214.371	+	304.283i	−1.27602	+	1.81121i
$169$	101.742	+	101.742i	0.602021	+	0.602021i
$170$	−3.01772	−	52.6847i	−0.0177513	−	0.309910i
$171$	−0.985162	−	2.37839i	−0.00576118	−	0.0139087i
$172$	−51.5301	+	180.378i	−0.299594	+	1.04871i
$173$	−88.6518	+	214.024i	−0.512438	+	1.23714i	0.430022	+	0.902818i	$0.358506\pi$
$173$	−88.6518	+	214.024i	−0.512438	+	1.23714i	−0.942461	+	0.334317i	$0.891494\pi$
$174$	−77.1809	−	159.811i	−0.443568	−	0.918455i
$175$	297.464			1.69979
$176$	134.765	−	96.5284i	0.765709	−	0.548457i
$177$		−	226.295i		−	1.27850i
$178$	−54.7446	−	113.354i	−0.307554	−	0.636822i
$179$	2.58312	+	1.06996i	0.0144308	+	0.00597744i	0.389887	−	0.920863i	$-0.372514\pi$
$179$	2.58312	+	1.06996i	0.0144308	+	0.00597744i	−0.375456	+	0.926840i	$0.622514\pi$
$180$	17.3186	−	9.62218i	0.0962142	−	0.0534565i
$181$	−184.394	+	76.3786i	−1.01875	+	0.421981i	−0.828640	−	0.559781i	$-0.810885\pi$
$181$	−184.394	+	76.3786i	−1.01875	+	0.421981i	−0.190112	+	0.981762i	$0.560885\pi$
$182$	7.73883	+	135.108i	0.0425210	+	0.742351i
$183$	73.8021	−	73.8021i	0.403290	−	0.403290i
$184$	−32.0566	+	142.650i	−0.174221	+	0.775271i
$185$	43.3476	−	43.3476i	0.234311	−	0.234311i
$186$	−115.384	+	129.405i	−0.620343	+	0.695726i
$187$	−146.587	+	60.7183i	−0.783887	+	0.324697i
$188$	−63.0109	−	50.0197i	−0.335164	−	0.266062i
$189$	−263.294	−	109.060i	−1.39309	−	0.577036i
$190$	2.91375	+	1.01591i	0.0153355	+	0.00534692i
$191$			185.771i			0.972625i	0.873785	+	0.486313i	$0.161658\pi$
$191$			185.771i			0.972625i	−0.873785	+	0.486313i	$0.838342\pi$
$192$	148.056	+	163.458i	0.771125	+	0.851342i
$193$	208.055			1.07800			0.539002	−	0.842305i	$-0.318802\pi$
$193$	208.055			1.07800			0.539002	+	0.842305i	$0.318802\pi$
$194$	70.0704	−	200.969i	0.361188	−	1.03592i
$195$	11.3866	−	27.4896i	0.0583926	−	0.140972i
$196$	331.506	−	417.605i	1.69136	−	2.13064i
$197$	123.852	+	299.006i	0.628691	+	1.51780i	0.841250	+	0.540647i	$0.181820\pi$
$197$	123.852	+	299.006i	0.628691	+	1.51780i	−0.212558	+	0.977148i	$0.568180\pi$
$198$	−44.4608	−	39.6434i	−0.224550	−	0.200219i
$199$	−253.762	−	253.762i	−1.27519	−	1.27519i	−0.943329	−	0.331858i	$-0.892324\pi$
$199$	−253.762	−	253.762i	−1.27519	−	1.27519i	−0.331858	−	0.943329i	$-0.607676\pi$
$200$	38.6440	−	171.963i	0.193220	−	0.859817i
$201$	7.22134	+	7.22134i	0.0359270	+	0.0359270i
$202$	−18.9007	+	1.08261i	−0.0935680	+	0.00535946i
$203$	133.051	+	321.214i	0.655424	+	1.58233i
$204$	−102.521	−	184.523i	−0.502554	−	0.904526i
$205$	−30.6882	+	74.0879i	−0.149699	+	0.361404i
$206$	−66.4529	+	32.0935i	−0.322587	+	0.155794i
$207$	52.5389			0.253811
$208$	79.1111	+	13.0783i	0.380342	+	0.0628764i
$209$		−	9.27787i		−	0.0443917i
$210$	−144.370	+	69.7236i	−0.687476	+	0.332017i
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	0.612182	−	0.790717i	$-0.290292\pi$
$211$	102.533	+	42.4705i	0.485938	+	0.201282i	−0.126244	+	0.991999i	$0.540292\pi$
$212$	−145.915	−	41.6849i	−0.688280	−	0.196627i
$213$	205.374	−	85.0685i	0.964195	−	0.399383i
$214$	−167.881	+	9.61603i	−0.784491	+	0.0449347i
$215$	−57.1364	+	57.1364i	−0.265751	+	0.265751i
$216$	−97.2523	+	138.042i	−0.450242	+	0.639082i
$217$	240.171	−	240.171i	1.10678	−	1.10678i
$218$	−140.640	−	125.401i	−0.645136	−	0.575235i
$219$	131.347	−	54.4056i	0.599757	−	0.248428i
$220$	70.9351	−	8.15291i	0.322432	−	0.0370587i
$221$	−70.9063	−	29.3704i	−0.320843	−	0.132898i
$222$	80.7322	−	231.548i	0.363659	−	1.04301i
$223$			187.153i			0.839252i	0.907697	+	0.419626i	$0.137839\pi$
$223$			187.153i			0.839252i	−0.907697	+	0.419626i	$0.862161\pi$
$224$	−271.264	−	336.286i	−1.21100	−	1.50128i
$225$	−63.3353			−0.281490
$226$	11.9437	+	4.16433i	0.0528484	+	0.0184263i
$227$	−2.72348	+	6.57507i	−0.0119977	+	0.0289650i	−0.929765	−	0.368154i	$-0.879990\pi$
$227$	−2.72348	+	6.57507i	−0.0119977	+	0.0289650i	0.917767	+	0.397119i	$0.129990\pi$
$228$	12.2628	−	1.40942i	0.0537841	−	0.00618166i
$229$	−124.655	−	300.944i	−0.544345	−	1.31416i	−0.921631	−	0.388068i	$-0.873143\pi$
$229$	−124.655	−	300.944i	−0.544345	−	1.31416i	0.377286	−	0.926097i	$-0.376857\pi$
$230$	−41.9116	+	47.0047i	−0.182225	+	0.204368i
$231$	340.855	+	340.855i	1.47556	+	1.47556i
$232$	202.978	−	35.1872i	0.874905	−	0.151669i
$233$	−208.047	−	208.047i	−0.892904	−	0.892904i	0.101891	−	0.994796i	$-0.467511\pi$
$233$	−208.047	−	208.047i	−0.892904	−	0.892904i	−0.994796	+	0.101891i	$0.967511\pi$
$234$	−1.64773	−	28.7669i	−0.00704160	−	0.122935i
$235$	−13.2611	−	32.0151i	−0.0564301	−	0.136234i
$236$	252.573	+	72.1547i	1.07023	+	0.305740i
$237$	−4.32518	+	10.4419i	−0.0182497	+	0.0440587i
$238$	179.844	+	372.386i	0.755647	+	1.56465i
$239$	−277.832			−1.16248			−0.581239	−	0.813733i	$-0.697432\pi$
$239$	−277.832			−1.16248			−0.581239	+	0.813733i	$0.697432\pi$
$240$	21.5518	+	92.5180i	0.0897990	+	0.385491i
$241$			63.2696i			0.262529i	0.991347	+	0.131265i	$0.0419038\pi$
$241$			63.2696i			0.262529i	−0.991347	+	0.131265i	$0.958096\pi$
$242$	11.8805	+	24.5997i	0.0490928	+	0.101652i
$243$	138.431	+	57.3398i	0.569673	+	0.235966i
$244$	58.8402	+	105.904i	0.241148	+	0.434033i
$245$	212.180	−	87.8879i	0.866041	−	0.358726i
$246$	18.3438	+	320.254i	0.0745682	+	1.30185i
$247$	3.17339	−	3.17339i	0.0128477	−	0.0128477i
$248$	−107.641	−	170.043i	−0.434038	−	0.685659i
$249$	−149.763	+	149.763i	−0.601457	+	0.601457i
$250$	107.856	−	120.962i	0.431424	−	0.483850i
$251$	161.948	−	67.0812i	0.645212	−	0.267256i	−0.0359886	−	0.999352i	$-0.511458\pi$
$251$	161.948	−	67.0812i	0.645212	−	0.267256i	0.681201	+	0.732097i	$0.261458\pi$
$252$	−96.5300	+	121.601i	−0.383056	+	0.482543i
$253$	174.935	+	72.4605i	0.691443	+	0.286405i
$254$	−65.3451	−	22.7834i	−0.257264	−	0.0896983i
$255$		−	90.9239i		−	0.356564i
$256$	−229.647	+	113.130i	−0.897058	+	0.441913i
$257$	−82.9690			−0.322836			−0.161418	−	0.986886i	$-0.551607\pi$
$257$	−82.9690			−0.322836			−0.161418	+	0.986886i	$0.551607\pi$
$258$	−106.413	+	305.204i	−0.412454	+	1.18296i
$259$	−183.840	+	443.830i	−0.709809	+	1.71363i
$260$	27.0511	+	21.4739i	0.104043	+	0.0825919i
$261$	−28.3289	−	68.3921i	−0.108540	−	0.262039i
$262$	−265.274	−	236.531i	−1.01250	−	0.902791i
$263$	−148.394	−	148.394i	−0.564235	−	0.564235i	0.366272	−	0.930508i	$-0.380634\pi$
$263$	−148.394	−	148.394i	−0.564235	−	0.564235i	−0.930508	+	0.366272i	$0.880634\pi$
$264$	241.329	−	152.767i	0.914125	−	0.578662i
$265$	−46.2200	−	46.2200i	−0.174415	−	0.174415i
$266$	−24.1421	+	1.38283i	−0.0907597	+	0.00519861i
$267$	−83.0012	−	200.383i	−0.310866	−	0.750497i
$268$	−10.3624	+	5.75736i	−0.0386658	+	0.0214827i
$269$	78.7117	−	190.027i	0.292609	−	0.706420i	−0.707391	−	0.706822i	$-0.750128\pi$
$269$	78.7117	−	190.027i	0.292609	−	0.706420i	1.00000		0.000402393i	$0.000128086\pi$
$270$	−65.4952	+	31.6310i	−0.242575	+	0.117152i
$271$	−29.7996			−0.109962			−0.0549809	−	0.998487i	$-0.517510\pi$
$271$	−29.7996			−0.109962			−0.0549809	+	0.998487i	$0.517510\pi$
$272$	238.640	−	55.5903i	0.877352	−	0.204376i
$273$			233.171i			0.854106i
$274$	−182.298	+	88.0408i	−0.665320	+	0.321317i
$275$	−210.883	−	87.3507i	−0.766848	−	0.317639i
$276$	−69.1980	+	242.223i	−0.250717	+	0.877621i
$277$	−368.831	+	152.775i	−1.33152	+	0.551534i	−0.931089	−	0.364793i	$-0.881140\pi$
$277$	−368.831	+	152.775i	−1.33152	+	0.551534i	−0.400431	+	0.916327i	$0.631140\pi$
$278$	392.327	−	22.4721i	1.41125	−	0.0808347i
$279$	−51.1367	+	51.1367i	−0.183286	+	0.183286i
$280$	−31.7874	−	183.366i	−0.113526	−	0.654878i
$281$	−280.258	+	280.258i	−0.997358	+	0.997358i	−0.999997	−	0.00263807i	$-0.999160\pi$
$281$	−280.258	+	280.258i	−0.997358	+	0.997358i	0.00263807	+	0.999997i	$0.499160\pi$
$282$	−103.461	−	92.2509i	−0.366883	−	0.327131i
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	−0.672288	−	0.740289i	$-0.734688\pi$
$283$	−176.650	+	73.1708i	−0.624204	+	0.258554i	0.0480840	+	0.998843i	$0.484688\pi$
$284$	29.4631	+	256.346i	0.103743	+	0.902628i
$285$	4.91204	+	2.03463i	0.0172352	+	0.00713907i
$286$	34.1883	−	98.0556i	0.119540	−	0.342852i
$287$		−	628.425i		−	2.18963i
$288$	57.7569	+	71.6013i	0.200545	+	0.248615i
$289$	54.4719			0.188484
$290$	83.7866	+	29.2132i	0.288919	+	0.100735i
$291$	140.334	−	338.797i	0.482249	−	1.16425i
$292$	18.8432	+	163.946i	0.0645313	+	0.561461i
$293$	11.3590	+	27.4231i	0.0387679	+	0.0935940i	0.942078	−	0.335395i	$-0.108870\pi$
$293$	11.3590	+	27.4231i	0.0387679	+	0.0935940i	−0.903310	+	0.428989i	$0.858870\pi$
$294$	611.393	−	685.688i	2.07957	−	2.33227i
$295$	80.0049	+	80.0049i	0.271203	+	0.271203i
$296$	232.695	+	163.937i	0.786130	+	0.553840i
$297$	154.633	+	154.633i	0.520651	+	0.520651i
$298$	26.2052	+	457.502i	0.0879368	+	1.53524i
$299$	35.0503	+	84.6188i	0.117225	+	0.283006i
$300$	83.4177	−	291.999i	0.278059	−	0.973329i
$301$	242.320	−	585.012i	0.805049	−	1.94356i
$302$	13.0164	+	26.9518i	0.0431007	+	0.0892444i
$303$	−32.6191			−0.107654
$304$	−2.33693	+	14.1362i	−0.00768726	+	0.0465005i
$305$			52.1843i			0.171096i
$306$	−38.2920	−	79.2876i	−0.125137	−	0.259110i
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.975734	−	0.218957i	$-0.0702655\pi$
$307$	463.833	+	192.126i	1.51086	+	0.625817i	0.535122	+	0.844775i	$0.320266\pi$
$308$	−489.118	+	271.754i	−1.58805	+	0.882317i
$309$	−117.472	+	48.6586i	−0.380169	+	0.157471i
$310$	−4.95709	−	86.5431i	−0.0159906	−	0.279171i
$311$	230.516	−	230.516i	0.741210	−	0.741210i	−0.231601	−	0.972811i	$-0.574396\pi$
$311$	230.516	−	230.516i	0.741210	−	0.741210i	0.972811	+	0.231601i	$0.0743963\pi$
$312$	134.796	+	30.2916i	0.432038	+	0.0970886i
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	−0.702461	−	0.711722i	$-0.747915\pi$
$313$	2.89884	−	2.89884i	0.00926146	−	0.00926146i	0.711722	+	0.702461i	$0.247915\pi$
$314$	−38.8469	+	43.5676i	−0.123716	+	0.138750i
$315$	−61.7839	+	25.5917i	−0.196139	+	0.0812436i
$316$	−10.2753	−	8.15685i	−0.0325169	−	0.0258128i
$317$	510.087	+	211.285i	1.60911	+	0.666514i	0.992666	−	0.120887i	$-0.0385738\pi$
$317$	510.087	+	211.285i	1.60911	+	0.666514i	0.616441	+	0.787401i	$0.288574\pi$
$318$	−246.892	−	86.0820i	−0.776390	−	0.270698i
$319$		−	266.791i		−	0.836335i
$320$	−110.133	−	5.44514i	−0.344166	−	0.0170161i
$321$	−289.731			−0.902590
$322$	162.477	−	466.001i	0.504587	−	1.44721i
$323$	5.24811	−	12.6701i	0.0162480	−	0.0392262i
$324$	−245.237	+	308.930i	−0.756903	+	0.953486i
$325$	−42.2528	−	102.007i	−0.130009	−	0.313869i
$326$	435.887	+	388.658i	1.33708	+	1.19220i
$327$	−229.568	−	229.568i	−0.702044	−	0.702044i
$328$	−363.292	−	81.6397i	−1.10760	−	0.248902i
$329$	192.020	+	192.020i	0.583647	+	0.583647i
$330$	122.824	−	7.03520i	0.372193	−	0.0213188i
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	0.712051	−	0.702128i	$-0.247766\pi$
$331$	−95.3030	−	230.082i	−0.287924	−	0.695111i	−0.999975	+	0.00701670i	$0.997766\pi$
$332$	−119.401	−	214.906i	−0.359643	−	0.647306i
$333$	39.1429	−	94.4994i	0.117546	−	0.283782i
$334$	26.4027	−	12.7512i	0.0790499	−	0.0381772i
$335$	−5.10609			−0.0152421
$336$	−433.486	−	605.196i	−1.29014	−	1.80118i
$337$			203.997i			0.605334i	0.953096	+	0.302667i	$0.0978769\pi$
$337$			203.997i			0.605334i	−0.953096	+	0.302667i	$0.902123\pi$
$338$	−259.131	+	125.148i	−0.766660	+	0.370259i
$339$	20.1349	+	8.34017i	0.0593951	+	0.0246023i
$340$	101.482	+	28.9913i	0.298477	+	0.0852684i
$341$	−240.793	+	99.7396i	−0.706137	+	0.292491i
$342$	5.14028	−	0.294429i	0.0150301	−	0.000860904i
$343$	−804.800	+	804.800i	−2.34636	+	2.34636i
$344$	−306.714	−	216.085i	−0.891612	−	0.628153i
$345$	−76.7264	+	76.7264i	−0.222395	+	0.222395i
$346$	−345.813	−	308.344i	−0.999459	−	0.891167i
$347$	−120.709	+	49.9993i	−0.347865	+	0.144090i	−0.549773	−	0.835314i	$-0.685286\pi$
$347$	−120.709	+	49.9993i	−0.347865	+	0.144090i	0.201908	+	0.979404i	$0.435286\pi$
$348$	352.624	−	40.5287i	1.01329	−	0.116462i
$349$	279.116	+	115.614i	0.799759	+	0.331271i	0.744860	−	0.667221i	$-0.232516\pi$
$349$	279.116	+	115.614i	0.799759	+	0.331271i	0.0548993	+	0.998492i	$0.482516\pi$
$350$	−195.865	+	561.761i	−0.559614	+	1.60503i
$351$			105.781i			0.301370i
$352$	93.5583	+	318.063i	0.265791	+	0.903587i
$353$	608.156			1.72282			0.861410	−	0.507910i	$-0.169582\pi$
$353$	608.156			1.72282			0.861410	+	0.507910i	$0.169582\pi$
$354$	427.359	+	149.004i	1.20723	+	0.420916i
$355$	−42.5329	+	102.683i	−0.119811	+	0.289249i
$356$	250.117	−	28.7471i	0.702575	−	0.0807503i
$357$	272.671	+	658.287i	0.763785	+	1.84394i
$358$	−3.72148	+	4.17371i	−0.0103952	+	0.0116584i
$359$	196.029	+	196.029i	0.546041	+	0.546041i	0.925293	−	0.379252i	$-0.123819\pi$
$359$	196.029	+	196.029i	0.546041	+	0.546041i	−0.379252	+	0.925293i	$0.623819\pi$
$360$	6.76810	+	39.0419i	0.0188003	+	0.108450i
$361$	−254.699	−	254.699i	−0.705536	−	0.705536i
$362$	−22.8268	−	398.521i	−0.0630574	−	1.10089i
$363$	18.0126	+	43.4863i	0.0496215	+	0.119797i
$364$	−260.247	−	74.3470i	−0.714965	−	0.204250i
$365$	−27.2019	+	65.6713i	−0.0745259	+	0.179921i
$366$	90.7805	+	187.970i	0.248034	+	0.513581i
$367$	−33.0375			−0.0900203			−0.0450102	−	0.998987i	$-0.514332\pi$
$367$	−33.0375			−0.0900203			−0.0450102	+	0.998987i	$0.514332\pi$
$368$	−248.287	−	154.467i	−0.674693	−	0.419747i
$369$			133.803i			0.362609i
$370$	53.3198	+	110.404i	0.144108	+	0.298390i
$371$	473.241	+	196.023i	1.27558	+	0.528363i
$372$	−168.407	−	303.109i	−0.452708	−	0.814810i
$373$	115.583	−	47.8760i	0.309874	−	0.128354i	−0.222327	−	0.974972i	$-0.571365\pi$
$373$	115.583	−	47.8760i	0.309874	−	0.128354i	0.532201	+	0.846618i	$0.321365\pi$
$374$	−18.1465	−	316.810i	−0.0485200	−	0.847085i
$375$	197.449	−	197.449i	0.526530	−	0.526530i
$376$	135.952	−	86.0608i	0.361574	−	0.228885i
$377$	91.2527	−	91.2527i	0.242050	−	0.242050i
$378$	379.326	−	425.421i	1.00351	−	1.12545i
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	−0.154415	−	0.988006i	$-0.549349\pi$
$379$	164.874	−	68.2930i	0.435024	−	0.180193i	0.589438	+	0.807813i	$0.299349\pi$
$380$	−3.83712	+	4.83369i	−0.0100977	+	0.0127202i
$381$	−110.160	−	45.6297i	−0.289133	−	0.119763i
$382$	−350.830	−	122.321i	−0.918403	−	0.320213i
$383$		−	307.309i		−	0.802373i	−0.915996	−	0.401186i	$-0.868598\pi$
$383$		−	307.309i		−	0.802373i	0.915996	−	0.401186i	$-0.131402\pi$
$384$	−406.178	+	171.976i	−1.05776	+	0.447853i
$385$	−241.013			−0.626008
$386$	−136.994	+	392.912i	−0.354906	+	1.01791i
$387$	−51.5942	+	124.559i	−0.133318	+	0.321859i
$388$	333.393	+	264.656i	0.859261	+	0.682104i
$389$	−204.874	−	494.611i	−0.526669	−	1.27149i	−0.933693	−	0.358075i	$-0.883433\pi$
$389$	−204.874	−	494.611i	−0.526669	−	1.27149i	0.407024	−	0.913418i	$-0.366567\pi$
$390$	44.4167	+	39.6041i	0.113889	+	0.101549i
$391$	197.907	+	197.907i	0.506157	+	0.506157i
$392$	570.368	+	901.022i	1.45502	+	2.29853i
$393$	−433.011	−	433.011i	−1.10181	−	1.10181i
$394$	−646.224	+	37.0149i	−1.64016	+	0.0939465i
$395$	−2.16252	−	5.22078i	−0.00547473	−	0.0132172i
$396$	104.142	−	57.8612i	0.262985	−	0.146114i
$397$	−224.796	+	542.706i	−0.566237	+	1.36702i	0.338467	+	0.940978i	$0.390092\pi$
$397$	−224.796	+	542.706i	−0.566237	+	1.36702i	−0.904705	+	0.426040i	$0.859908\pi$
$398$	646.321	−	312.141i	1.62392	−	0.784274i
$399$	−41.6647			−0.104423
$400$	299.308	+	186.209i	0.748271	+	0.465522i
$401$		−	125.790i		−	0.313691i	−0.987623	−	0.156846i	$-0.949868\pi$
$401$		−	125.790i		−	0.313691i	0.987623	−	0.156846i	$-0.0501325\pi$
$402$	−18.3924	+	8.88263i	−0.0457522	+	0.0220961i
$403$	−116.475	−	48.2456i	−0.289020	−	0.119716i
$404$	10.4007	−	36.4069i	0.0257442	−	0.0901162i
$405$	−156.963	+	65.0164i	−0.387564	+	0.160534i
$406$	−694.220	+	39.7641i	−1.70990	+	0.0979412i
$407$	260.663	−	260.663i	0.640449	−	0.640449i
$408$	415.978	−	72.1118i	1.01955	−	0.176745i
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.232717	−	0.972544i	$-0.425238\pi$
$409$	492.952	−	492.952i	1.20526	−	1.20526i	0.972544	−	0.232717i	$-0.0747617\pi$
$410$	−119.708	−	106.738i	−0.291972	−	0.260336i
$411$	−322.257	+	133.483i	−0.784081	+	0.324777i
$412$	−16.8527	−	146.628i	−0.0409046	−	0.355894i
$413$	−819.159	−	339.307i	−1.98344	−	0.821567i
$414$	−34.5943	+	99.2199i	−0.0835610	+	0.239662i
$415$		−	105.895i		−	0.255168i
$416$	−76.7891	+	140.790i	−0.184589	+	0.338438i
$417$	677.084			1.62370
$418$	17.5213	+	6.10902i	0.0419170	+	0.0146149i
$419$	203.456	−	491.187i	0.485576	−	1.17228i	−0.471349	−	0.881947i	$-0.656233\pi$
$419$	203.456	−	491.187i	0.485576	−	1.17228i	0.956925	−	0.290336i	$-0.0937672\pi$
$420$	−36.6128	−	318.552i	−0.0871732	−	0.758458i
$421$	−0.995616	−	2.40363i	−0.00236488	−	0.00570934i	0.922693	−	0.385536i	$-0.125984\pi$
$421$	−0.995616	−	2.40363i	−0.00236488	−	0.00570934i	−0.925058	+	0.379827i	$0.875984\pi$
$422$	−147.718	+	165.669i	−0.350044	+	0.392580i
$423$	−40.8844	−	40.8844i	−0.0966535	−	0.0966535i
$424$	174.800	−	248.114i	0.412264	−	0.585175i
$425$	−238.576	−	238.576i	−0.561355	−	0.561355i
$426$	25.4239	+	443.862i	0.0596805	+	1.04193i
$427$	−156.495	−	377.813i	−0.366499	−	0.884807i
$428$	92.3814	−	323.376i	0.215844	−	0.755551i
$429$	68.4710	−	165.304i	0.159606	−	0.385323i
$430$	−70.2808	−	145.524i	−0.163444	−	0.338427i
$431$	404.244			0.937920			0.468960	−	0.883219i	$-0.344629\pi$
$431$	404.244			0.937920			0.468960	+	0.883219i	$0.344629\pi$
$432$	−196.656	−	274.555i	−0.455223	−	0.635544i
$433$			446.431i			1.03102i	0.856884	+	0.515509i	$0.172397\pi$
$433$			446.431i			1.03102i	−0.856884	+	0.515509i	$0.827603\pi$
$434$	295.423	+	611.704i	0.680698	+	1.40946i
$435$	141.249	+	58.5072i	0.324710	+	0.134499i
$436$	329.425	−	183.028i	0.755561	−	0.419789i
$437$	−15.1203	+	6.26304i	−0.0346003	+	0.0143319i
$438$	16.2599	+	283.872i	0.0371230	+	0.648110i
$439$	−203.077	+	203.077i	−0.462590	+	0.462590i	−0.899503	−	0.436914i	$-0.856072\pi$
$439$	−203.077	+	203.077i	−0.462590	+	0.462590i	0.436914	+	0.899503i	$0.356072\pi$
$440$	−31.3104	+	139.329i	−0.0711600	+	0.316658i
$441$	270.962	−	270.962i	0.614426	−	0.614426i
$442$	102.154	−	114.568i	0.231118	−	0.259203i
$443$	−440.203	+	182.338i	−0.993685	+	0.411598i	−0.819478	−	0.573111i	$-0.805736\pi$
$443$	−440.203	+	182.338i	−0.993685	+	0.411598i	−0.174207	+	0.984709i	$0.555736\pi$
$444$	384.122	+	304.926i	0.865139	+	0.686770i
$445$	100.188	+	41.4993i	0.225142	+	0.0932568i
$446$	−353.439	−	123.231i	−0.792465	−	0.276303i
$447$			789.562i			1.76636i
$448$	813.691	−	290.855i	1.81627	−	0.649230i
$449$	−636.256			−1.41705			−0.708526	−	0.705685i	$-0.750639\pi$
$449$	−636.256			−1.41705			−0.708526	+	0.705685i	$0.750639\pi$
$450$	41.7032	−	119.609i	0.0926737	−	0.265798i
$451$	−184.538	+	445.514i	−0.409175	+	0.987836i
$452$	−15.7287	+	19.8138i	−0.0347980	+	0.0438358i
$453$	19.7349	+	47.6442i	0.0435648	+	0.105175i
$454$	−10.6238	−	9.47266i	−0.0234003	−	0.0208649i
$455$	−82.4357	−	82.4357i	−0.181177	−	0.181177i
$456$	−5.41273	+	24.0863i	−0.0118700	+	0.0528209i
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	0.194685	−	0.980866i	$-0.437632\pi$
$457$	−359.285	−	359.285i	−0.786181	−	0.786181i	−0.980866	+	0.194685i	$0.937632\pi$
$458$	650.412	−	37.2549i	1.42011	−	0.0813425i
$459$	123.701	+	298.640i	0.269501	+	0.650632i
$460$	−61.1717	−	110.100i	−0.132982	−	0.239349i
$461$	68.2156	−	164.687i	0.147973	−	0.357239i	−0.832462	−	0.554083i	$-0.813069\pi$
$461$	68.2156	−	164.687i	0.147973	−	0.357239i	0.980435	+	0.196844i	$0.0630692\pi$
$462$	−868.142	+	419.270i	−1.87910	+	0.907511i
$463$	662.155			1.43014			0.715070	−	0.699053i	$-0.246395\pi$
$463$	662.155			1.43014			0.715070	+	0.699053i	$0.246395\pi$
$464$	−67.1997	+	406.494i	−0.144827	+	0.876064i
$465$		−	149.357i		−	0.321198i
$466$	529.885	−	255.908i	1.13709	−	0.549160i
$467$	−854.762	−	354.054i	−1.83033	−	0.758146i	−0.967607	−	0.252461i	$-0.918760\pi$
$467$	−854.762	−	354.054i	−1.83033	−	0.758146i	−0.862718	−	0.505685i	$-0.831240\pi$
$468$	55.4113	+	15.8298i	0.118400	+	0.0338244i
$469$	36.9680	−	15.3126i	0.0788229	−	0.0326495i
$470$	69.1923	−	3.96326i	0.147218	−	0.00843246i
$471$	−71.1160	+	71.1160i	−0.150989	+	0.150989i
$472$	−302.571	+	429.475i	−0.641041	+	0.909905i
$473$	−343.579	+	343.579i	−0.726383	+	0.726383i
$474$	−16.8717	−	15.0436i	−0.0355942	−	0.0317375i
$475$	18.2274	−	7.55005i	0.0383735	−	0.0158948i
$476$	−821.670	+	94.4385i	−1.72620	+	0.198400i
$477$	−100.761	−	41.7367i	−0.211240	−	0.0874984i
$478$	182.939	−	524.687i	0.382717	−	1.09767i
$479$			926.802i			1.93487i	0.253122	+	0.967434i	$0.418542\pi$
$479$			926.802i			1.93487i	−0.253122	+	0.967434i	$0.581458\pi$
$480$	−188.911	−	20.2179i	−0.393565	−	0.0421206i
$481$	178.313			0.370714
$482$	−119.485	−	41.6599i	−0.247894	−	0.0864312i
$483$	325.403	−	785.592i	0.673712	−	1.62648i
$484$	−54.2794	+	6.23859i	−0.112147	+	0.0128896i
$485$	70.1649	+	169.393i	0.144670	+	0.349264i
$486$	−199.436	+	223.671i	−0.410362	+	0.460229i
$487$	586.001	+	586.001i	1.20329	+	1.20329i	0.973161	+	0.230127i	$0.0739141\pi$
$487$	586.001	+	586.001i	1.20329	+	1.20329i	0.230127	+	0.973161i	$0.426086\pi$
$488$	−238.744	+	41.3874i	−0.489229	+	0.0848102i
$489$	711.505	+	711.505i	1.45502	+	1.45502i
$490$	26.2665	+	458.572i	0.0536051	+	0.935862i
$491$	−17.1543	−	41.4142i	−0.0349375	−	0.0843466i	0.905448	−	0.424458i	$-0.139535\pi$
$491$	−17.1543	−	41.4142i	−0.0349375	−	0.0843466i	−0.940385	+	0.340111i	$0.889535\pi$
$492$	−616.879	−	176.229i	−1.25382	−	0.358189i
$493$	150.913	−	364.335i	0.306111	−	0.739017i
$494$	3.90344	+	8.08247i	0.00790169	+	0.0163613i
$495$	51.3160			0.103669
$496$	392.004	−	91.3161i	0.790331	−	0.184105i
$497$		−	870.977i		−	1.75247i
$498$	−184.216	−	381.439i	−0.369912	−	0.765941i
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	0.234456	−	0.972127i	$-0.424669\pi$
$499$	−143.291	−	59.3531i	−0.287156	−	0.118944i	−0.521612	+	0.853183i	$0.674669\pi$
$500$	157.420	+	283.334i	0.314840	+	0.566668i
$501$	46.6734	−	19.3328i	0.0931605	−	0.0385884i
$502$	20.0481	+	350.009i	0.0399365	+	0.697230i
$503$	74.0929	−	74.0929i	0.147302	−	0.147302i	−0.629610	−	0.776912i	$-0.716785\pi$
$503$	74.0929	−	74.0929i	0.147302	−	0.147302i	0.776912	+	0.629610i	$0.216785\pi$
$504$	−166.083	−	262.365i	−0.329531	−	0.520566i
$505$	11.5322	−	11.5322i	0.0228361	−	0.0228361i
$506$	−252.028	+	282.654i	−0.498079	+	0.558605i
$507$	−458.080	+	189.743i	−0.903511	+	0.374246i
$508$	86.0529	−	108.403i	0.169396	−	0.213391i
$509$	467.540	+	193.661i	0.918546	+	0.380474i	0.791322	−	0.611400i	$-0.209393\pi$
$509$	467.540	+	193.661i	0.918546	+	0.380474i	0.127224	+	0.991874i	$0.459393\pi$
$510$	171.710	+	59.8689i	0.336686	+	0.117390i
$511$		−	557.034i		−	1.09009i
$512$	−62.4351	−	508.179i	−0.121944	−	0.992537i
$513$	−18.9017			−0.0368455
$514$	54.6309	−	156.687i	0.106286	−	0.304839i
$515$	24.3285	−	58.7343i	0.0472399	−	0.114047i
$516$	−506.310	−	401.923i	−0.981221	−	0.778920i
$517$	−79.7431	−	192.517i	−0.154242	−	0.372373i
$518$	−717.125	−	639.423i	−1.38441	−	1.23441i
$519$	−564.476	−	564.476i	−1.08762	−	1.08762i
$520$	−58.3653	+	36.9466i	−0.112241	+	0.0710512i
$521$	694.307	+	694.307i	1.33264	+	1.33264i	0.902998	+	0.429644i	$0.141361\pi$
$521$	694.307	+	694.307i	1.33264	+	1.33264i	0.429644	+	0.902998i	$0.358639\pi$
$522$	147.812	−	8.46649i	0.283164	−	0.0162193i
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	0.975142	−	0.221581i	$-0.0711216\pi$
$523$	67.4311	+	162.793i	0.128931	+	0.311268i	−0.846211	+	0.532848i	$0.821122\pi$
$524$	621.360	−	345.227i	1.18580	−	0.658830i
$525$	−392.271	+	947.026i	−0.747183	+	1.80386i
$526$	377.952	−	182.532i	0.718540	−	0.347020i
$527$	−385.250			−0.731025
$528$	129.598	+	556.340i	0.245450	+	1.05367i
$529$			194.991i			0.368602i
$530$	117.720	−	56.8531i	0.222114	−	0.107270i
$531$	174.414	+	72.2445i	0.328463	+	0.136054i
$532$	13.2849	−	46.5029i	0.0249716	−	0.0874115i
$533$	−215.502	+	89.2638i	−0.404319	+	0.167474i
$534$	433.076	−	24.8061i	0.811003	−	0.0464533i
$535$	102.432	−	102.432i	0.191462	−	0.191462i
$536$	−4.04964	−	23.3604i	−0.00755530	−	0.0435829i
$537$	−6.81281	+	6.81281i	−0.0126868	+	0.0126868i
$538$	307.039	+	273.771i	0.570704	+	0.508867i
$539$	1275.91	−	528.498i	2.36717	−	0.980515i
$540$	−16.6098	−	144.515i	−0.0307590	−	0.267621i
$541$	125.547	+	52.0035i	0.232066	+	0.0961247i	0.495686	−	0.868502i	$-0.334917\pi$
$541$	125.547	+	52.0035i	0.232066	+	0.0961247i	−0.263620	+	0.964626i	$0.584917\pi$
$542$	19.6216	−	56.2767i	0.0362022	−	0.103832i
$543$		−	687.772i		−	1.26661i
$544$	−52.1498	+	487.275i	−0.0958636	+	0.895727i
$545$	162.324			0.297842
$546$	−440.344	−	153.531i	−0.806491	−	0.281193i
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	0.433956	+	0.900934i	$0.357117\pi$
$547$	−278.945	+	673.432i	−0.509954	+	1.23114i	−0.943910	+	0.330204i	$0.892883\pi$
$548$	−46.2314	−	402.240i	−0.0843638	−	0.734015i
$549$	33.3206	+	80.4431i	0.0606933	+	0.146527i
$550$	303.818	−	340.737i	0.552396	−	0.619523i
$551$	16.3057	+	16.3057i	0.0295929	+	0.0295929i
$552$	−411.876	−	290.173i	−0.746152	−	0.525675i
$553$	31.3132	+	31.3132i	0.0566241	+	0.0566241i
$554$	−45.6589	−	797.133i	−0.0824167	−	1.43887i
$555$	80.8410	+	195.168i	0.145660	+	0.351653i
$556$	−215.889	+	755.708i	−0.388290	+	1.35919i
$557$	−228.207	+	550.942i	−0.409708	+	0.989123i	0.575506	+	0.817797i	$0.304805\pi$
$557$	−228.207	+	550.942i	−0.409708	+	0.989123i	−0.985214	+	0.171326i	$0.945195\pi$
$558$	−62.9008	−	130.243i	−0.112725	−	0.233410i
$559$	−235.035			−0.420455
$560$	367.218	+	60.7068i	0.655746	+	0.108405i
$561$		−	546.754i		−	0.974607i
$562$	−344.732	−	713.803i	−0.613402	−	1.27011i
$563$	−236.899	−	98.1268i	−0.420780	−	0.174293i	0.162239	−	0.986752i	$-0.448129\pi$
$563$	−236.899	−	98.1268i	−0.420780	−	0.174293i	−0.583019	+	0.812459i	$0.698129\pi$
$564$	242.340	−	134.644i	0.429681	−	0.238730i
$565$	−10.0671	+	4.16995i	−0.0178180	+	0.00738044i
$566$	−21.8681	−	381.783i	−0.0386362	−	0.674528i
$567$	941.434	−	941.434i	1.66038	−	1.66038i
$568$	−503.511	−	113.150i	−0.886463	−	0.199208i
$569$	−289.568	+	289.568i	−0.508907	+	0.508907i	−0.914191	−	0.405284i	$-0.867173\pi$
$569$	−289.568	+	289.568i	−0.508907	+	0.508907i	0.405284	+	0.914191i	$0.367173\pi$
$570$	−7.07675	+	7.93670i	−0.0124153	+	0.0139240i
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.453464	−	0.891275i	$-0.350188\pi$
$571$	801.877	−	332.148i	1.40434	−	0.581695i	0.950874	+	0.309579i	$0.100188\pi$
$572$	162.667	+	129.129i	0.284383	+	0.225751i
$573$	−591.435	−	244.980i	−1.03217	−	0.427540i
$574$	1186.78	+	413.786i	2.06756	+	0.720882i
$575$			402.646i			0.700254i
$576$	−173.249	+	61.9283i	−0.300780	+	0.107514i
$577$	−107.872			−0.186953			−0.0934767	−	0.995621i	$-0.529798\pi$
$577$	−107.872			−0.186953			−0.0934767	+	0.995621i	$0.529798\pi$
$578$	−35.8670	+	102.870i	−0.0620537	+	0.177976i
$579$	−274.365	+	662.377i	−0.473861	+	1.14400i
$580$	−110.339	+	138.996i	−0.190239	+	0.239648i
$581$	317.567	+	766.676i	0.546588	+	1.31958i
$582$	547.416	+	488.103i	0.940578	+	0.838665i
$583$	−277.936	−	277.936i	−0.476734	−	0.476734i
$584$	−322.021	−	72.3652i	−0.551405	−	0.123913i
$585$	17.5520	+	17.5520i	0.0300035	+	0.0300035i
$586$	−59.2679	+	3.39479i	−0.101140	+	0.00579316i
$587$	−292.393	−	705.899i	−0.498114	−	1.20255i	−0.950498	−	0.310730i	$-0.899426\pi$
$587$	−292.393	−	705.899i	−0.498114	−	1.20255i	0.452384	−	0.891823i	$-0.350574\pi$
$588$	892.352	+	1606.11i	1.51761	+	2.73148i
$589$	8.62087	−	20.8126i	0.0146365	−	0.0353355i
$590$	−203.769	+	98.4102i	−0.345371	+	0.166797i
$591$	−1115.26			−1.88707
$592$	−462.813	+	331.500i	−0.781778	+	0.559967i
$593$			247.178i			0.416826i	0.978041	+	0.208413i	$0.0668298\pi$
$593$			247.178i			0.416826i	−0.978041	+	0.208413i	$0.933170\pi$
$594$	−393.844	+	190.207i	−0.663036	+	0.320214i
$595$	−329.133	−	136.331i	−0.553164	−	0.229128i
$596$	−881.248	−	251.753i	−1.47860	−	0.422405i
$597$	1142.54	−	473.254i	1.91380	−	0.792720i
$598$	−182.882	+	10.4753i	−0.305822	+	0.0175171i
$599$	−633.115	+	633.115i	−1.05695	+	1.05695i	−0.0586768	+	0.998277i	$0.518688\pi$
$599$	−633.115	+	633.115i	−1.05695	+	1.05695i	−0.998277	+	0.0586768i	$0.981312\pi$
$600$	496.514	+	349.801i	0.827523	+	0.583002i
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	−0.818760	−	0.574136i	$-0.805338\pi$
$601$	−147.019	+	147.019i	−0.244624	+	0.244624i	0.574136	+	0.818760i	$0.305338\pi$
$602$	945.241	+	842.823i	1.57017	+	1.40004i
$603$	−7.87114	+	3.26033i	−0.0130533	+	0.00540685i
$604$	−59.4692	+	6.83508i	−0.0984590	+	0.0113164i
$605$	−21.7424	−	9.00601i	−0.0359379	−	0.0148860i
$606$	21.4781	−	61.6013i	0.0354424	−	0.101652i
$607$		−	52.6594i		−	0.0867536i	−0.999059	−	0.0433768i	$-0.986188\pi$
$607$		−	52.6594i		−	0.0867536i	0.999059	−	0.0433768i	$-0.0138116\pi$
$608$	−25.1574	−	13.7212i	−0.0413773	−	0.0225678i
$609$	−1198.09			−1.96731
$610$	−98.5501	−	34.3607i	−0.161558	−	0.0563291i
$611$	38.5729	−	93.1233i	0.0631308	−	0.152411i
$612$	174.948	−	20.1076i	0.285863	−	0.0328556i
$613$	−336.988	−	813.562i	−0.549737	−	1.32718i	−0.917675	−	0.397331i	$-0.869936\pi$
$613$	−336.988	−	813.562i	−0.549737	−	1.32718i	0.367939	−	0.929850i	$-0.380064\pi$
$614$	−668.241	+	749.445i	−1.08834	+	1.22059i
$615$	−195.402	−	195.402i	−0.317727	−	0.317727i
$616$	−191.148	−	1102.64i	−0.310305	−	1.79000i
$617$	−150.269	−	150.269i	−0.243547	−	0.243547i	0.574769	−	0.818316i	$-0.305092\pi$
$617$	−150.269	−	150.269i	−0.243547	−	0.243547i	−0.818316	+	0.574769i	$0.805092\pi$
$618$	−14.5423	−	253.886i	−0.0235312	−	0.410819i
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	0.927347	−	0.374202i	$-0.122083\pi$
$619$	4.34083	+	10.4797i	0.00701265	+	0.0169300i	−0.920334	+	0.391132i	$0.872083\pi$
$620$	166.701	+	47.6228i	0.268872	+	0.0768110i
$621$	147.623	−	356.394i	0.237718	−	0.573903i
$622$	283.547	+	587.114i	0.455864	+	0.943914i
$623$	−849.811			−1.36406
$624$	−145.962	+	234.617i	−0.233914	+	0.375989i
$625$		−	411.175i		−	0.657880i
$626$	3.56572	+	7.38320i	0.00569604	+	0.0117942i
$627$	29.5377	+	12.2349i	0.0471095	+	0.0195134i
$628$	−56.6987	−	102.050i	−0.0902845	−	0.162499i
$629$	503.413	−	208.520i	0.800338	−	0.331511i
$630$	−7.64845	−	133.530i	−0.0121404	−	0.211952i
$631$	356.485	−	356.485i	0.564952	−	0.564952i	−0.365758	−	0.930710i	$-0.619190\pi$
$631$	356.485	−	356.485i	0.564952	−	0.564952i	0.930710	+	0.365758i	$0.119190\pi$
$632$	22.1700	−	14.0341i	0.0350792	−	0.0222059i
$633$	−270.424	+	270.424i	−0.427210	+	0.427210i
$634$	−734.879	+	824.180i	−1.15912	+	1.29997i
$635$	55.0781	−	22.8141i	0.0867371	−	0.0359277i
$636$	325.132	−	409.576i	0.511214	−	0.643987i
$637$	617.175	+	255.642i	0.968878	+	0.401322i
$638$	503.835	+	175.669i	0.789711	+	0.275343i
$639$			185.447i			0.290214i
$640$	82.8004	−	204.401i	0.129376	−	0.319377i
$641$	741.748			1.15717			0.578587	−	0.815621i	$-0.303604\pi$
$641$	741.748			1.15717			0.578587	+	0.815621i	$0.303604\pi$
$642$	190.774	−	547.159i	0.297155	−	0.852272i
$643$	181.837	−	438.994i	0.282795	−	0.682729i	−0.717103	−	0.696967i	$-0.754532\pi$
$643$	181.837	−	438.994i	0.282795	−	0.682729i	0.999899	+	0.0142385i	$0.00453240\pi$
$644$	773.061	+	613.677i	1.20041	+	0.952915i
$645$	−106.556	−	257.250i	−0.165204	−	0.398837i
$646$	20.4718	+	18.2537i	0.0316901	+	0.0282565i
$647$	520.304	+	520.304i	0.804180	+	0.804180i	0.983746	−	0.179566i	$-0.0574694\pi$
$647$	520.304	+	520.304i	0.804180	+	0.804180i	−0.179566	+	0.983746i	$0.557469\pi$
$648$	−421.938	−	666.545i	−0.651139	−	1.02862i
$649$	481.095	+	481.095i	0.741286	+	0.741286i
$650$	220.463	−	12.6278i	0.339173	−	0.0194275i
$651$	447.907	+	1081.34i	0.688029	+	1.66105i
$652$	−1020.99	+	567.262i	−1.56594	+	0.870034i
$653$	161.753	−	390.507i	0.247708	−	0.598019i	−0.750301	−	0.661096i	$-0.770091\pi$
$653$	161.753	−	390.507i	0.247708	−	0.598019i	0.998009	+	0.0630771i	$0.0200914\pi$
$654$	584.700	−	282.381i	0.894037	−	0.431776i
$655$	306.175			0.467443
$656$	393.386	−	632.322i	0.599674	−	0.963905i
$657$			118.603i			0.180521i
$658$	−489.065	+	236.194i	−0.743260	+	0.358958i
$659$	70.1853	+	29.0717i	0.106503	+	0.0441149i	0.435299	−	0.900286i	$-0.356643\pi$
$659$	70.1853	+	29.0717i	0.106503	+	0.0441149i	−0.328796	+	0.944401i	$0.606643\pi$
$660$	−67.5873	+	236.585i	−0.102405	+	0.358462i
$661$	−81.1193	+	33.6007i	−0.122722	+	0.0508331i	−0.443199	−	0.896423i	$-0.646157\pi$
$661$	−81.1193	+	33.6007i	−0.122722	+	0.0508331i	0.320477	+	0.947256i	$0.396157\pi$
$662$	497.262	−	28.4826i	0.751152	−	0.0430251i
$663$	187.011	−	187.011i	0.282068	−	0.282068i
$664$	484.470	−	83.9852i	0.729623	−	0.126484i
$665$	14.7302	−	14.7302i	0.0221507	−	0.0221507i
$666$	152.689	+	136.145i	0.229262	+	0.204421i
$667$	−434.794	+	180.097i	−0.651865	+	0.270011i
$668$	6.69582	+	58.2575i	0.0100237	+	0.0872119i
$669$	−595.833	−	246.802i	−0.890633	−	0.368912i
$670$	3.36210	−	9.64286i	0.00501807	−	0.0143923i
$671$			313.801i			0.467661i
$672$	1428.34	−	420.148i	2.12551	−	0.625220i
$673$	−851.239			−1.26484			−0.632421	−	0.774625i	$-0.717939\pi$
$673$	−851.239			−1.26484			−0.632421	+	0.774625i	$0.717939\pi$
$674$	−385.250	−	134.322i	−0.571587	−	0.199291i
$675$	−177.959	+	429.630i	−0.263642	+	0.636489i
$676$	−65.7166	−	571.773i	−0.0972139	−	0.845818i
$677$	−380.410	−	918.390i	−0.561905	−	1.35656i	−0.908241	−	0.418448i	$-0.862574\pi$
$677$	−380.410	−	918.390i	−0.561905	−	1.35656i	0.346335	−	0.938111i	$-0.387426\pi$
$678$	−29.0083	+	32.5333i	−0.0427851	+	0.0479842i
$679$	−1015.98	−	1015.98i	−1.49629	−	1.49629i
$680$	−121.571	+	172.560i	−0.178781	+	0.253765i
$681$	−17.3413	−	17.3413i	−0.0254645	−	0.0254645i
$682$	−29.8086	−	520.411i	−0.0437076	−	0.763066i
$683$	425.467	+	1027.17i	0.622939	+	1.50391i	0.848236	+	0.529618i	$0.177665\pi$
$683$	425.467	+	1027.17i	0.622939	+	1.50391i	−0.225297	+	0.974290i	$0.572335\pi$
$684$	−2.82859	+	9.90130i	−0.00413536	+	0.0144756i
$685$	66.7395	−	161.123i	0.0974299	−	0.235217i
$686$	−989.946	−	2049.79i	−1.44307	−	2.98803i
$687$	1122.49			1.63390
$688$	610.033	−	436.950i	0.886675	−	0.635102i
$689$		−	190.129i		−	0.275950i
$690$	−94.3776	−	195.419i	−0.136779	−	0.283215i
$691$	260.940	+	108.085i	0.377627	+	0.156418i	0.563420	−	0.826171i	$-0.309485\pi$
$691$	260.940	+	108.085i	0.377627	+	0.156418i	−0.185793	+	0.982589i	$0.559485\pi$
$692$	810.008	−	450.040i	1.17053	−	0.650347i
$693$	−371.526	+	153.891i	−0.536113	+	0.222065i
$694$	−14.9430	−	260.881i	−0.0215317	−	0.375910i
$695$	−239.377	+	239.377i	−0.344428	+	0.344428i
$696$	−155.646	+	692.617i	−0.223630	+	0.995139i
$697$	−504.018	+	504.018i	−0.723124	+	0.723124i
$698$	−402.121	+	450.986i	−0.576104	+	0.646111i
$699$	936.707	−	387.997i	1.34007	−	0.555074i
$700$	−931.920	−	739.783i	−1.33131	−	1.05683i
$701$	−727.192	−	301.213i	−1.03736	−	0.429690i	−0.201999	−	0.979386i	$-0.564744\pi$
$701$	−727.192	−	301.213i	−1.03736	−	0.429690i	−0.835365	+	0.549695i	$0.814744\pi$
$702$	−199.768	−	69.6515i	−0.284569	−	0.0992187i
$703$			31.8623i			0.0453234i
$704$	−662.266	−	32.7433i	−0.940718	−	0.0465104i
$705$	119.413			0.169380
$706$	−400.440	+	1148.50i	−0.567196	+	1.62678i
$707$	−48.9091	+	118.077i	−0.0691783	+	0.167011i
$708$	−562.790	+	708.958i	−0.794901	+	1.00135i
$709$	259.577	+	626.675i	0.366118	+	0.883886i	0.994379	+	0.105883i	$0.0337670\pi$
$709$	259.577	+	626.675i	0.366118	+	0.883886i	−0.628261	+	0.778003i	$0.716233\pi$
$710$	−165.912	−	147.935i	−0.233679	−	0.208360i
$711$	−6.66713	−	6.66713i	−0.00937711	−	0.00937711i
$712$	−110.400	+	491.275i	−0.155057	+	0.689992i
$713$	325.095	+	325.095i	0.455953	+	0.455953i
$714$	−1422.72	+	81.4916i	−1.99260	+	0.114134i
$715$	34.2344	+	82.6491i	0.0478803	+	0.115593i
$716$	−5.43165	−	9.77621i	−0.00758611	−	0.0136539i
$717$	366.383	−	884.526i	0.510994	−	1.23365i
$718$	−499.276	+	241.126i	−0.695370	+	0.335830i
$719$	1034.71			1.43910			0.719549	−	0.694442i	$-0.244349\pi$
$719$	1034.71			1.43910			0.719549	+	0.694442i	$0.244349\pi$
$720$	−78.1872	−	12.9256i	−0.108593	−	0.0179522i
$721$			498.193i			0.690975i
$722$	648.705	−	313.293i	0.898484	−	0.433923i
$723$	−201.429	−	83.4348i	−0.278602	−	0.115401i
$724$	767.638	+	219.297i	1.06027	+	0.302897i
$725$	524.141	−	217.106i	0.722953	−	0.299457i
$726$	−93.9844	+	5.38332i	−0.129455	+	0.00741504i
$727$	227.066	−	227.066i	0.312332	−	0.312332i	−0.533480	−	0.845813i	$-0.679116\pi$
$727$	227.066	−	227.066i	0.312332	−	0.312332i	0.845813	+	0.533480i	$0.179116\pi$
$728$	311.765	−	442.524i	0.428248	−	0.607863i
$729$	262.439	−	262.439i	0.359999	−	0.359999i
$730$	−106.109	−	94.6122i	−0.145355	−	0.129606i
$731$	−663.548	+	274.850i	−0.907726	+	0.375992i
$732$	−414.757	+	47.6700i	−0.566608	+	0.0651230i
$733$	973.386	+	403.190i	1.32795	+	0.550054i	0.930070	−	0.367384i	$-0.119746\pi$
$733$	973.386	+	403.190i	1.32795	+	0.550054i	0.397879	+	0.917438i	$0.369746\pi$
$734$	21.7535	−	62.3913i	0.0296369	−	0.0850018i
$735$			791.410i			1.07675i
$736$	455.196	−	367.182i	0.618472	−	0.498889i
$737$	−30.7045			−0.0416615
$738$	−252.687	−	88.1025i	−0.342394	−	0.119380i
$739$	387.131	−	934.616i	0.523857	−	1.26470i	−0.411632	−	0.911350i	$-0.635041\pi$
$739$	387.131	−	934.616i	0.523857	−	1.26470i	0.935490	−	0.353354i	$-0.114959\pi$
$740$	−243.607	+	27.9989i	−0.329199	+	0.0378364i
$741$	5.91821	+	14.2878i	0.00798679	+	0.0192818i
$742$	−681.795	+	764.645i	−0.918861	+	1.03052i
$743$	528.819	+	528.819i	0.711735	+	0.711735i	0.966898	−	0.255163i	$-0.0821293\pi$
$743$	528.819	+	528.819i	0.711735	+	0.711735i	−0.255163	+	0.966898i	$0.582129\pi$
$744$	683.311	−	118.455i	0.918429	−	0.159214i
$745$	−279.143	−	279.143i	−0.374689	−	0.374689i
$746$	14.3084	+	249.803i	0.0191802	+	0.334856i
$747$	−67.6158	−	163.239i	−0.0905164	−	0.218526i
$748$	610.245	+	174.334i	0.815835	+	0.233066i
$749$	−434.423	+	1048.79i	−0.580004	+	1.40025i
$750$	242.873	+	502.893i	0.323830	+	0.670524i
$751$	−176.760			−0.235366			−0.117683	−	0.993051i	$-0.537547\pi$
$751$	−176.760			−0.235366			−0.117683	+	0.993051i	$0.537547\pi$
$752$	73.0084	+	313.412i	0.0970856	+	0.416772i
$753$			604.051i			0.802192i
$754$	112.246	+	232.416i	0.148867	+	0.308245i
$755$	−23.8213	−	9.86711i	−0.0315514	−	0.0130690i
$756$	553.641	+	996.476i	0.732330	+	1.31809i
$757$	−59.8575	+	24.7938i	−0.0790720	+	0.0327527i	−0.421869	−	0.906657i	$-0.638626\pi$
$757$	−59.8575	+	24.7938i	−0.0790720	+	0.0327527i	0.342797	+	0.939410i	$0.388626\pi$
$758$	20.4103	+	356.333i	0.0269265	+	0.470096i
$759$	−461.381	+	461.381i	−0.607879	+	0.607879i
$760$	−6.60189	−	10.4292i	−0.00868670	−	0.0137226i
$761$	713.497	−	713.497i	0.937579	−	0.937579i	−0.0605844	−	0.998163i	$-0.519296\pi$
$761$	713.497	−	713.497i	0.937579	−	0.937579i	0.998163	+	0.0605844i	$0.0192964\pi$
$762$	158.706	−	177.992i	0.208276	−	0.233585i
$763$	−1175.22	+	486.793i	−1.54026	+	0.637999i
$764$	462.008	−	582.001i	0.604722	−	0.761781i
$765$	70.0782	+	29.0273i	0.0916055	+	0.0379442i
$766$	580.354	+	202.348i	0.757642	+	0.264161i
$767$			329.106i			0.429082i
$768$	−57.3284	−	880.306i	−0.0746464	−	1.14623i
$769$	−147.511			−0.191821			−0.0959107	−	0.995390i	$-0.530576\pi$
$769$	−147.511			−0.191821			−0.0959107	+	0.995390i	$0.530576\pi$
$770$	158.695	−	455.154i	0.206098	−	0.591109i
$771$	109.413	−	264.146i	0.141910	−	0.342601i
$772$	−651.811	−	517.426i	−0.844315	−	0.670240i
$773$	104.027	+	251.144i	0.134576	+	0.324896i	0.976774	−	0.214273i	$-0.0687384\pi$
$773$	104.027	+	251.144i	0.134576	+	0.324896i	−0.842198	+	0.539169i	$0.818738\pi$
$774$	−201.259	−	179.452i	−0.260024	−	0.231850i
$775$	−391.899	−	391.899i	−0.505677	−	0.505677i
$776$	−719.327	+	455.351i	−0.926968	+	0.586792i
$777$	−1170.57	−	1170.57i	−1.50653	−	1.50653i
$778$	1068.97	−	61.2295i	1.37400	−	0.0787012i
$779$	−15.9503	−	38.5075i	−0.0204754	−	0.0494319i
$780$	−104.039	+	57.8037i	−0.133383	+	0.0741074i
$781$	−255.764	+	617.468i	−0.327482	+	0.790612i
$782$	−504.061	+	243.436i	−0.644579	+	0.311300i
$783$	−543.531			−0.694164
$784$	−2077.14	+	483.863i	−2.64942	+	0.617173i
$785$		−	50.2850i		−	0.0640573i
$786$	1102.86	−	532.627i	1.40313	−	0.677642i
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.913057	−	0.407832i	$-0.133715\pi$
$787$	999.730	+	414.102i	1.27031	+	0.526178i	0.357248	+	0.934010i	$0.383715\pi$
$788$	355.603	−	1244.77i	0.451273	−	1.57965i
$789$	668.127	−	276.747i	0.846802	−	0.350757i
$790$	11.2834	−	0.646298i	0.0142827	−	0.000818099i
$791$	60.3806	−	60.3806i	0.0763345	−	0.0763345i
$792$	40.6987	+	234.771i	0.0513873	+	0.296428i
$793$	−107.332	+	107.332i	−0.135349	+	0.135349i
$794$	−876.885	−	781.873i	−1.10439	−	0.984727i
$795$	208.100	−	86.1980i	0.261762	−	0.108425i
$796$	163.909	+	1426.11i	0.205916	+	1.79159i
$797$	−1138.14	−	471.431i	−1.42802	−	0.591507i	−0.471162	−	0.882047i	$-0.656165\pi$
$797$	−1138.14	−	471.431i	−1.42802	−	0.591507i	−0.956863	+	0.290540i	$0.906165\pi$
$798$	27.4341	−	78.6839i	0.0343786	−	0.0986014i
$799$		−	308.012i		−	0.385497i
$800$	−548.735	+	442.635i	−0.685919	+	0.553294i
$801$	180.940			0.225893
$802$	237.555	+	82.8265i	0.296203	+	0.103275i
$803$	−163.574	+	394.902i	−0.203703	+	0.491784i
$804$	−4.66438	−	40.5829i	−0.00580147	−	0.0504762i
$805$	162.696	+	392.783i	0.202107	+	0.487929i
$806$	167.805	−	188.196i	0.208195	−	0.233494i
$807$	501.184	+	501.184i	0.621046	+	0.621046i
$808$	61.9063	+	43.6138i	0.0766167	+	0.0539775i
$809$	−169.569	−	169.569i	−0.209603	−	0.209603i	0.594496	−	0.804099i	$-0.297352\pi$
$809$	−169.569	−	169.569i	−0.209603	−	0.209603i	−0.804099	+	0.594496i	$0.797352\pi$
$810$	−19.4310	−	339.236i	−0.0239889	−	0.418810i
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	−0.925048	−	0.379849i	$-0.875976\pi$
$811$	−437.562	−	1056.37i	−0.539534	−	1.30255i	0.385514	−	0.922702i	$-0.374024\pi$
$812$	382.015	−	1337.22i	0.470461	−	1.64682i
$813$	39.2973	−	94.8722i	0.0483362	−	0.116694i
$814$	320.629	+	663.896i	0.393893	+	0.815597i
$815$	−503.094			−0.617293
$816$	−137.717	+	833.058i	−0.168771	+	1.02090i
$817$		−	41.9977i		−	0.0514048i
$818$	606.357	+	1255.53i	0.741268	+	1.53487i
$819$	−179.713	−	74.4396i	−0.219430	−	0.0908908i
$820$	280.397	−	155.788i	0.341947	−	0.189986i
$821$	−930.724	+	385.518i	−1.13365	+	0.469572i	−0.869019	−	0.494779i	$-0.835249\pi$
$821$	−930.724	+	385.518i	−1.13365	+	0.469572i	−0.264627	+	0.964351i	$0.585249\pi$
$822$	−39.8933	−	696.476i	−0.0485320	−	0.847295i
$823$	−320.389	+	320.389i	−0.389294	+	0.389294i	−0.874435	−	0.485142i	$-0.838768\pi$
$823$	−320.389	+	320.389i	−0.389294	+	0.389294i	0.485142	+	0.874435i	$0.338768\pi$
$824$	288.005	+	64.7211i	0.349520	+	0.0785451i
$825$	556.191	−	556.191i	0.674171	−	0.674171i
$826$	1180.16	−	1323.57i	1.42876	−	1.60238i
$827$	14.6406	−	6.06433i	0.0177032	−	0.00733293i	−0.373814	−	0.927504i	$-0.621950\pi$
$827$	14.6406	−	6.06433i	0.0177032	−	0.00733293i	0.391517	+	0.920171i	$0.371950\pi$
$828$	−164.599	−	130.663i	−0.198791	−	0.157805i
$829$	−753.878	−	312.267i	−0.909383	−	0.376679i	−0.121562	−	0.992584i	$-0.538790\pi$
$829$	−753.878	−	312.267i	−0.909383	−	0.376679i	−0.787820	+	0.615905i	$0.788790\pi$
$830$	199.983	+	69.7264i	0.240943	+	0.0840078i
$831$		−	1375.70i		−	1.65548i
$832$	−215.321	−	237.720i	−0.258799	−	0.285721i
$833$	2041.35			2.45061
$834$	−445.826	+	1278.67i	−0.534563	+	1.53318i
$835$	−9.66607	+	23.3360i	−0.0115761	+	0.0279473i
$836$	−23.0738	+	29.0665i	−0.0276002	+	0.0347686i
$837$	203.199	+	490.565i	0.242770	+	0.586099i
$838$	793.642	+	707.649i	0.947066	+	0.844450i
$839$	−233.705	−	233.705i	−0.278552	−	0.278552i	0.553979	−	0.832531i	$-0.313109\pi$
$839$	−233.705	−	233.705i	−0.278552	−	0.278552i	−0.832531	+	0.553979i	$0.813109\pi$
$840$	625.695	+	140.608i	0.744875	+	0.167390i
$841$	−125.796	−	125.796i	−0.149579	−	0.149579i
$842$	5.19483	−	0.297554i	0.00616963	−	0.000353389i
$843$	−522.667	−	1261.83i	−0.620008	−	1.49683i
$844$	−215.601	−	388.052i	−0.255451	−	0.459777i
$845$	94.8684	−	229.033i	0.112270	−	0.271044i
$846$	104.131	−	50.2900i	0.123086	−	0.0594444i
$847$	184.423			0.217736
$848$	353.467	+	493.481i	0.416825	+	0.581935i
$849$		−	658.886i		−	0.776073i
$850$	607.642	−	293.461i	0.714872	−	0.345248i
$851$	−600.767	−	248.846i	−0.705954	−	0.292416i
$852$	−854.975	−	244.248i	−1.00349	−	0.286676i
$853$	−979.574	+	405.753i	−1.14839	+	0.475677i	−0.873992	−	0.485940i	$-0.838477\pi$
$853$	−979.574	+	405.753i	−1.14839	+	0.475677i	−0.274395	+	0.961617i	$0.588477\pi$
$854$	816.545	−	46.7707i	0.956141	−	0.0547667i
$855$	−3.13633	+	3.13633i	−0.00366822	+	0.00366822i
$856$	549.867	+	387.389i	0.642368	+	0.452558i
$857$	716.322	−	716.322i	0.835848	−	0.835848i	−0.152461	−	0.988309i	$-0.548720\pi$
$857$	716.322	−	716.322i	0.835848	−	0.835848i	0.988309	+	0.152461i	$0.0487198\pi$
$858$	267.092	+	238.152i	0.311296	+	0.277566i
$859$	398.325	−	164.992i	0.463708	−	0.192074i	−0.138583	−	0.990351i	$-0.544255\pi$
$859$	398.325	−	164.992i	0.463708	−	0.192074i	0.602291	+	0.798277i	$0.294255\pi$
$860$	321.098	−	36.9054i	0.373370	−	0.0429132i
$861$	2000.70	+	828.716i	2.32369	+	0.962504i
$862$	−266.174	+	763.415i	−0.308787	+	0.885633i
$863$		−	1279.79i		−	1.48295i	−0.670980	−	0.741475i	$-0.734126\pi$
$863$		−	1279.79i		−	1.48295i	0.670980	−	0.741475i	$-0.265874\pi$
$864$	647.986	−	190.605i	0.749984	−	0.220608i
$865$	399.132			0.461424
$866$	−843.086	−	293.952i	−0.973541	−	0.339437i
$867$	−71.8331	+	173.421i	−0.0828525	+	0.200024i
$868$	−1349.73	+	155.130i	−1.55498	+	0.178722i
$869$	−13.0039	−	31.3942i	−0.0149642	−	0.0361268i
$870$	−203.496	+	228.225i	−0.233904	+	0.262327i
$871$	−10.5021	−	10.5021i	−0.0120576	−	0.0120576i
$872$	128.739	+	742.634i	0.147637	+	0.851645i
$873$	216.321	+	216.321i	0.247790	+	0.247790i
$874$	−1.87180	−	32.6786i	−0.00214164	−	0.0373898i
$875$	−418.684	−	1010.79i	−0.478496	−	1.15519i
$876$	−546.800	−	156.209i	−0.624201	−	0.178321i
$877$	−351.648	+	848.954i	−0.400967	+	0.968021i	0.586464	+	0.809975i	$0.300519\pi$
$877$	−351.648	+	848.954i	−0.400967	+	0.968021i	−0.987432	+	0.158046i	$0.949481\pi$
$878$	−249.795	−	517.227i	−0.284505	−	0.589097i
$879$	−102.285			−0.116365
$880$	−242.508	−	150.871i	−0.275577	−	0.171445i
$881$			1327.06i			1.50632i	0.657839	+	0.753158i	$0.271471\pi$
$881$			1327.06i			1.50632i	−0.657839	+	0.753158i	$0.728529\pi$
$882$	333.297	+	690.127i	0.377888	+	0.782457i
$883$	412.717	+	170.953i	0.467403	+	0.193605i	0.603939	−	0.797030i	$-0.293597\pi$
$883$	412.717	+	170.953i	0.467403	+	0.193605i	−0.136536	+	0.990635i	$0.543597\pi$
$884$	149.098	+	268.356i	0.168663	+	0.303570i
$885$	−360.213	+	149.205i	−0.407020	+	0.168593i
$886$	−54.4942	−	951.384i	−0.0615058	−	1.07380i
$887$	−411.723	+	411.723i	−0.464174	+	0.464174i	−0.900021	−	0.435847i	$-0.856449\pi$
$887$	−411.723	+	411.723i	−0.464174	+	0.464174i	0.435847	+	0.900021i	$0.356449\pi$
$888$	−828.779	+	524.636i	−0.933309	+	0.590806i
$889$	−330.347	+	330.347i	−0.371594	+	0.371594i
$890$	−144.340	+	161.880i	−0.162180	+	0.181888i
$891$	−943.871	+	390.964i	−1.05934	+	0.438793i
$892$	465.444	−	586.329i	0.521798	−	0.657320i
$893$	16.6400	+	6.89250i	0.0186338	+	0.00771836i
$894$	−1491.09	−	519.887i	−1.66789	−	0.581529i
$895$		−	4.81723i		−	0.00538238i
$896$	13.5062	+	1728.17i	0.0150739	+	1.92876i
$897$	−315.620			−0.351861
$898$	418.943	−	1201.57i	0.466529	−	1.33805i
$899$	247.898	−	598.480i	0.275749	−	0.665717i
$900$	198.422	+	157.513i	0.220469	+	0.175015i
$901$	−222.338	−	536.772i	−0.246768	−	0.595751i
$902$	−719.845	−	641.849i	−0.798055	−	0.711584i
$903$	1542.93	+	1542.93i	1.70867	+	1.70867i
$904$	−27.0618	−	42.7501i	−0.0299356	−	0.0472899i
$905$	243.156	+	243.156i	0.268681	+	0.268681i
$906$	−102.971	+	5.89804i	−0.113654	+	0.00650997i
$907$	307.189	+	741.619i	0.338687	+	0.817662i	0.997842	+	0.0656553i	$0.0209138\pi$
$907$	307.189	+	741.619i	0.338687	+	0.817662i	−0.659156	+	0.752006i	$0.729086\pi$
$908$	24.8843	−	13.8257i	0.0274057	−	0.0152266i
$909$	10.4136	−	25.1407i	0.0114561	−	0.0276575i
$910$	209.960	−	101.400i	0.230725	−	0.111429i
$911$	708.126			0.777307			0.388653	−	0.921384i	$-0.372940\pi$
$911$	708.126			0.777307			0.388653	+	0.921384i	$0.372940\pi$
$912$	−41.9231	−	26.0816i	−0.0459683	−	0.0285982i
$913$		−	636.779i		−	0.697458i
$914$	915.082	−	441.939i	1.00118	−	0.483522i
$915$	−166.137	−	68.8164i	−0.181571	−	0.0752091i
$916$	−357.908	+	1252.84i	−0.390729	+	1.36772i
$917$	−2216.70	+	918.187i	−2.41734	+	1.00129i
$918$	−645.434	+	36.9697i	−0.703087	+	0.0402720i
$919$	628.260	−	628.260i	0.683635	−	0.683635i	−0.277183	−	0.960817i	$-0.589401\pi$
$919$	628.260	−	628.260i	0.683635	−	0.683635i	0.960817	+	0.277183i	$0.0894007\pi$
$920$	248.204	−	43.0273i	0.269787	−	0.0467688i
$921$	−1223.33	+	1223.33i	−1.32826	+	1.32826i
$922$	266.095	+	237.264i	0.288607	+	0.257336i
$923$	−298.679	+	123.717i	−0.323596	+	0.134038i
$924$	−220.164	−	1915.56i	−0.238273	−	2.07311i
$925$	724.221	+	299.982i	0.782941	+	0.324305i
$926$	−435.996	+	1250.48i	−0.470838	+	1.35041i
$927$		−	106.074i		−	0.114427i
$928$	−723.417	−	394.563i	−0.779544	−	0.425175i
$929$	−972.033			−1.04632			−0.523161	−	0.852234i	$-0.675247\pi$
$929$	−972.033			−1.04632			−0.523161	+	0.852234i	$0.675247\pi$
$930$	282.062	+	98.3443i	0.303292	+	0.105747i
$931$	−45.6801	+	110.281i	−0.0490656	+	0.118455i
$932$	134.381	+	1169.19i	0.144186	+	1.25450i
$933$	429.901	+	1037.87i	0.460773	+	1.11241i
$934$	1231.45	−	1381.09i	1.31847	−	1.47869i
$935$	193.301	+	193.301i	0.206739	+	0.206739i
$936$	−66.3802	+	94.2213i	−0.0709190	+	0.100664i
$937$	396.897	+	396.897i	0.423583	+	0.423583i	0.886435	−	0.462853i	$-0.153174\pi$
$937$	396.897	+	396.897i	0.423583	+	0.423583i	−0.462853	+	0.886435i	$0.653174\pi$
$938$	4.57639	+	79.8967i	0.00487888	+	0.0851777i
$939$	5.40618	+	13.0517i	0.00575738	+	0.0138996i
$940$	−38.0751	+	133.280i	−0.0405054	+	0.141787i
$941$	486.386	−	1174.24i	0.516882	−	1.24786i	−0.422928	−	0.906163i	$-0.638998\pi$
$941$	486.386	−	1174.24i	0.516882	−	1.24786i	0.939809	−	0.341699i	$-0.111002\pi$
$942$	−87.4764	−	181.129i	−0.0928625	−	0.192281i
$943$	850.634			0.902051
$944$	−611.837	−	854.195i	−0.648132	−	0.904867i
$945$			491.014i			0.519591i
$946$	−422.621	−	875.080i	−0.446745	−	0.925032i
$947$	−319.348	−	132.278i	−0.337221	−	0.139681i	0.207646	−	0.978204i	$-0.433420\pi$
$947$	−319.348	−	132.278i	−0.337221	−	0.139681i	−0.544867	+	0.838523i	$0.683420\pi$
$948$	39.5190	−	21.9567i	0.0416867	−	0.0231611i
$949$	−191.020	+	79.1232i	−0.201286	+	0.0833753i
$950$	2.25644	+	39.3939i	0.00237520	+	0.0414673i
$951$	−1345.32	+	1345.32i	−1.41464	+	1.41464i
$952$	362.682	−	1613.91i	0.380968	−	1.69528i
$953$	234.445	−	234.445i	0.246007	−	0.246007i	−0.573322	−	0.819330i	$-0.694346\pi$
$953$	234.445	−	234.445i	0.246007	−	0.246007i	0.819330	+	0.573322i	$0.194346\pi$
$954$	145.166	−	162.807i	0.152166	−	0.170657i
$955$	295.708	−	122.486i	0.309642	−	0.128258i
$956$	870.417	+	690.961i	0.910478	+	0.722762i
$957$	849.374	+	351.822i	0.887538	+	0.367630i
$958$	−1750.27	−	610.253i	−1.82700	−	0.637007i
$959$			1366.67i			1.42510i
$960$	162.570	−	343.447i	0.169344	−	0.357757i
$961$	328.164			0.341482
$962$	−117.410	+	336.745i	−0.122048	+	0.350047i
$963$	92.4964	−	223.306i	0.0960502	−	0.231886i
$964$	157.350	−	198.216i	0.163226	−	0.205619i
$965$	−137.178	−	331.178i	−0.142154	−	0.343189i
$966$	1269.33	+	1131.80i	1.31401	+	1.17163i
$967$	431.918	+	431.918i	0.446658	+	0.446658i	0.894242	−	0.447584i	$-0.147715\pi$
$967$	431.918	+	431.918i	0.446658	+	0.446658i	−0.447584	+	0.894242i	$0.647715\pi$
$968$	23.9587	−	106.615i	0.0247507	−	0.110139i
$969$	33.4165	+	33.4165i	0.0344855	+	0.0344855i
$970$	−366.099	+	20.9697i	−0.377422	+	0.0216183i
$971$	−391.385	−	944.887i	−0.403074	−	0.973107i	−0.986915	−	0.161239i	$-0.948451\pi$
$971$	−391.385	−	944.887i	−0.403074	−	0.973107i	0.583841	−	0.811868i	$-0.301549\pi$
$972$	−291.085	−	523.912i	−0.299470	−	0.539004i
$973$	1015.22	−	2450.95i	1.04339	−	2.51897i
$974$	−1492.52	+	720.812i	−1.53236	+	0.740054i
$975$	380.477			0.390233
$976$	79.0406	−	478.119i	0.0809842	−	0.489877i
$977$		−	1157.98i		−	1.18524i	−0.805481	−	0.592621i	$-0.798093\pi$
$977$		−	1157.98i		−	1.18524i	0.805481	−	0.592621i	$-0.201907\pi$
$978$	−1812.17	+	875.189i	−1.85293	+	0.894876i
$979$	602.463	+	249.548i	0.615386	+	0.254901i
$980$	−883.311	−	252.343i	−0.901337	−	0.257493i
$981$	250.226	−	103.647i	0.255072	−	0.105654i
$982$	89.5061	−	5.12681i	0.0911467	−	0.00522078i
$983$	396.529	−	396.529i	0.403386	−	0.403386i	−0.476038	−	0.879425i	$-0.657928\pi$
$983$	396.529	−	396.529i	0.403386	−	0.403386i	0.879425	+	0.476038i	$0.157928\pi$
$984$	738.993	−	1048.94i	0.751009	−	1.06600i
$985$	394.291	−	394.291i	0.400296	−	0.400296i
$986$	588.680	+	524.896i	0.597039	+	0.532349i
$987$	−864.547	+	358.107i	−0.875934	+	0.362824i
$988$	−17.8340	+	2.04975i	−0.0180506	+	0.00207464i
$989$	791.870	+	328.003i	0.800678	+	0.331652i
$990$	−33.7890	+	96.9104i	−0.0341303	+	0.0978893i
$991$		−	134.269i		−	0.135489i	−0.997703	−	0.0677444i	$-0.978420\pi$
$991$		−	134.269i		−	0.135489i	0.997703	−	0.0677444i	$-0.0215802\pi$
$992$	−85.6645	+	800.428i	−0.0863553	+	0.806883i
$993$	858.182			0.864232
$994$	1644.84	+	573.495i	1.65477	+	0.576957i
$995$	−236.619	+	571.249i	−0.237808	+	0.574120i
$996$	841.645	−	96.7343i	0.845025	−	0.0971228i
$997$	470.645	+	1136.24i	0.472061	+	1.13966i	0.963251	+	0.268603i	$0.0865620\pi$
$997$	470.645	+	1136.24i	0.472061	+	1.13966i	−0.491190	+	0.871052i	$0.663438\pi$
$998$	206.439	−	231.525i	0.206852	−	0.231989i
$999$	−531.046	−	531.046i	−0.531577	−	0.531577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.3.4	✓	28
3.2	odd	2		288.3.u.a.163.4		28
4.3	odd	2		128.3.h.a.47.6		28
8.3	odd	2		256.3.h.a.95.2		28
8.5	even	2		256.3.h.b.95.6		28
32.5	even	8		256.3.h.a.159.2		28
32.11	odd	8	inner	32.3.h.a.11.4	yes	28
32.21	even	8		128.3.h.a.79.6		28
32.27	odd	8		256.3.h.b.159.6		28
96.11	even	8		288.3.u.a.235.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.4	✓	28	1.1	even	1	trivial
32.3.h.a.11.4	yes	28	32.11	odd	8	inner
128.3.h.a.47.6		28	4.3	odd	2
128.3.h.a.79.6		28	32.21	even	8
256.3.h.a.95.2		28	8.3	odd	2
256.3.h.a.159.2		28	32.5	even	8
256.3.h.b.95.6		28	8.5	even	2
256.3.h.b.159.6		28	32.27	odd	8
288.3.u.a.163.4		28	3.2	odd	2
288.3.u.a.235.4		28	96.11	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)

\(f(q)\)	\(=\)	\(q+(-0.658450 + 1.88850i) q^{2} +(-1.31872 + 3.18367i) q^{3} +(-3.13289 - 2.48697i) q^{4} +(-0.659338 - 1.59178i) q^{5} +(-5.14406 - 4.58669i) q^{6} +(9.54718 + 9.54718i) q^{7} +(6.75950 - 4.27892i) q^{8} +(-2.03276 - 2.03276i) q^{9} +O(q^{10})\)	\(q+(-0.658450 + 1.88850i) q^{2} +(-1.31872 + 3.18367i) q^{3} +(-3.13289 - 2.48697i) q^{4} +(-0.659338 - 1.59178i) q^{5} +(-5.14406 - 4.58669i) q^{6} +(9.54718 + 9.54718i) q^{7} +(6.75950 - 4.27892i) q^{8} +(-2.03276 - 2.03276i) q^{9} +(3.44023 - 0.197052i) q^{10} +(-3.96481 - 9.57189i) q^{11} +(12.0491 - 6.69446i) q^{12} +(1.91784 - 4.63007i) q^{13} +(-24.3162 + 11.7435i) q^{14} +5.93719 q^{15} +(3.62996 + 15.5828i) q^{16} -15.3143i q^{17} +(5.17735 - 2.50041i) q^{18} +(0.827335 + 0.342693i) q^{19} +(-1.89308 + 6.62663i) q^{20} +(-42.9851 + 17.8050i) q^{21} +(20.6872 - 1.18494i) q^{22} +(-12.9230 + 12.9230i) q^{23} +(4.70879 + 27.1627i) q^{24} +(15.5786 - 15.5786i) q^{25} +(7.48110 + 6.67051i) q^{26} +(-19.5007 + 8.07746i) q^{27} +(-6.16668 - 53.6538i) q^{28} +(23.7905 + 9.85436i) q^{29} +(-3.90934 + 11.2124i) q^{30} -25.1562i q^{31} +(-31.8183 - 3.40530i) q^{32} +35.7022 q^{33} +(28.9211 + 10.0837i) q^{34} +(8.90221 - 21.4918i) q^{35} +(1.31300 + 11.4238i) q^{36} +(13.6161 + 32.8721i) q^{37} +(-1.19194 + 1.33678i) q^{38} +(12.2115 + 12.2115i) q^{39} +(-11.2679 - 7.93840i) q^{40} +(-32.9116 - 32.9116i) q^{41} +(-5.32127 - 92.9012i) q^{42} +(-17.9473 - 43.3286i) q^{43} +(-11.3837 + 39.8480i) q^{44} +(-1.89544 + 4.57600i) q^{45} +(-15.8960 - 32.9143i) q^{46} +20.1127 q^{47} +(-54.3973 - 8.99273i) q^{48} +133.297i q^{49} +(19.1625 + 39.6780i) q^{50} +(48.7557 + 20.1953i) q^{51} +(-17.5232 + 9.73588i) q^{52} +(35.0503 - 14.5183i) q^{53} +(-2.41406 - 42.1458i) q^{54} +(-12.6222 + 12.6222i) q^{55} +(105.386 + 23.6825i) q^{56} +(-2.18204 + 2.18204i) q^{57} +(-34.2749 + 38.4399i) q^{58} +(-60.6706 + 25.1306i) q^{59} +(-18.6005 - 14.7656i) q^{60} +(-27.9825 - 11.5907i) q^{61} +(47.5076 + 16.5641i) q^{62} -38.8143i q^{63} +(27.3817 - 57.8467i) q^{64} -8.63457 q^{65} +(-23.5081 + 67.4237i) q^{66} +(1.13412 - 2.73801i) q^{67} +(-38.0862 + 47.9780i) q^{68} +(-24.1008 - 58.1845i) q^{69} +(34.7257 + 30.9632i) q^{70} +(-45.6144 - 45.6144i) q^{71} +(-22.4385 - 5.04243i) q^{72} +(-29.1727 - 29.1727i) q^{73} +(-71.0445 + 4.06934i) q^{74} +(29.0534 + 70.1410i) q^{75} +(-1.73968 - 3.13118i) q^{76} +(53.5318 - 129.237i) q^{77} +(-31.1022 + 15.0208i) q^{78} +3.27983 q^{79} +(22.4110 - 16.0524i) q^{80} -98.6086i q^{81} +(83.8242 - 40.4830i) q^{82} +(56.7834 + 23.5205i) q^{83} +(178.948 + 51.1215i) q^{84} +(-24.3770 + 10.0973i) q^{85} +(93.6436 - 5.36380i) q^{86} +(-62.7460 + 62.7460i) q^{87} +(-67.7575 - 47.7361i) q^{88} +(-44.5059 + 44.5059i) q^{89} +(-7.39373 - 6.59261i) q^{90} +(62.5140 - 25.8942i) q^{91} +(72.6256 - 8.34720i) q^{92} +(80.0891 + 33.1740i) q^{93} +(-13.2432 + 37.9829i) q^{94} -1.54289i q^{95} +(52.8007 - 96.8083i) q^{96} -106.417 q^{97} +(-251.732 - 87.7695i) q^{98} +(-11.3979 + 27.5169i) 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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