LMFDB - Embedded newform 48.4.j.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.954009 + 2.66268i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.17974 + 5.08044i) q^{4} +(-8.83384 + 8.83384i) q^{5} +(3.62464 - 7.67216i) q^{6} +29.4760i q^{7} +(-19.4231 - 11.6079i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(0.954009 + 2.66268i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.17974 + 5.08044i) q^{4} +(-8.83384 + 8.83384i) q^{5} +(3.62464 - 7.67216i) q^{6} +29.4760i q^{7} +(-19.4231 - 11.6079i) q^{8} +9.00000i q^{9} +(-31.9493 - 15.0941i) q^{10} +(44.6891 - 44.6891i) q^{11} +(23.8864 + 2.33196i) q^{12} +(6.83195 + 6.83195i) q^{13} +(-78.4851 + 28.1203i) q^{14} +37.4788 q^{15} +(12.3783 - 62.7916i) q^{16} -56.8078 q^{17} +(-23.9641 + 8.58608i) q^{18} +(91.0660 + 91.0660i) q^{19} +(9.71099 - 99.4706i) q^{20} +(62.5280 - 62.5280i) q^{21} +(161.626 + 76.3590i) q^{22} +96.8367i q^{23} +(16.5786 + 65.8267i) q^{24} -31.0735i q^{25} +(-11.6736 + 24.7090i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-149.751 - 182.154i) q^{28} +(-59.2957 - 59.2957i) q^{29} +(35.7551 + 99.7941i) q^{30} +103.074 q^{31} +(179.003 - 26.9444i) q^{32} -189.600 q^{33} +(-54.1952 - 151.261i) q^{34} +(-260.386 - 260.386i) q^{35} +(-45.7240 - 55.6176i) q^{36} +(-79.5300 + 79.5300i) q^{37} +(-155.602 + 329.357i) q^{38} -28.9855i q^{39} +(274.123 - 69.0385i) q^{40} +105.830i q^{41} +(226.144 + 106.840i) q^{42} +(39.9965 - 39.9965i) q^{43} +(-49.1265 + 503.207i) q^{44} +(-79.5046 - 79.5046i) q^{45} +(-257.845 + 92.3831i) q^{46} +9.34353 q^{47} +(-159.459 + 106.943i) q^{48} -525.834 q^{49} +(82.7387 - 29.6444i) q^{50} +(120.508 + 120.508i) q^{51} +(-76.9289 - 7.51033i) q^{52} +(245.782 - 245.782i) q^{53} +(69.0494 + 32.6218i) q^{54} +789.552i q^{55} +(342.154 - 572.515i) q^{56} -386.360i q^{57} +(101.317 - 214.454i) q^{58} +(345.255 - 345.255i) q^{59} +(-231.609 + 190.409i) q^{60} +(370.197 + 370.197i) q^{61} +(98.3331 + 274.452i) q^{62} -265.284 q^{63} +(242.514 + 450.922i) q^{64} -120.705 q^{65} +(-180.880 - 504.843i) q^{66} +(-595.125 - 595.125i) q^{67} +(351.057 - 288.609i) q^{68} +(205.422 - 205.422i) q^{69} +(444.915 - 941.736i) q^{70} -493.871i q^{71} +(104.471 - 174.808i) q^{72} -33.2892i q^{73} +(-287.635 - 135.891i) q^{74} +(-65.9168 + 65.9168i) q^{75} +(-1025.42 - 100.108i) q^{76} +(1317.25 + 1317.25i) q^{77} +(77.1791 - 27.6524i) q^{78} +552.982 q^{79} +(445.343 + 664.038i) q^{80} -81.0000 q^{81} +(-281.792 + 100.963i) q^{82} +(-18.5187 - 18.5187i) q^{83} +(-68.7367 + 704.076i) q^{84} +(501.831 - 501.831i) q^{85} +(144.655 + 68.3409i) q^{86} +251.570i q^{87} +(-1386.75 + 349.255i) q^{88} +934.120i q^{89} +(135.847 - 287.543i) q^{90} +(-201.378 + 201.378i) q^{91} +(-491.973 - 598.425i) q^{92} +(-218.652 - 218.652i) q^{93} +(8.91381 + 24.8788i) q^{94} -1608.93 q^{95} +(-436.880 - 322.565i) q^{96} +1426.12 q^{97} +(-501.650 - 1400.13i) q^{98} +(402.202 + 402.202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.954009	+	2.66268i	0.337293	+	0.941400i
$2$	0.954009	+	2.66268i	0.337293	+	0.941400i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	−6.17974	+	5.08044i	−0.772467	+	0.635055i
$5$	−8.83384	+	8.83384i	−0.790123	+	0.790123i	−0.981514	−	0.191391i	$-0.938700\pi$
$5$	−8.83384	+	8.83384i	−0.790123	+	0.790123i	0.191391	+	0.981514i	$0.438700\pi$
$6$	3.62464	−	7.67216i	0.246626	−	0.522024i
$7$			29.4760i			1.59155i	0.605590	+	0.795777i	$0.292937\pi$
$7$			29.4760i			1.59155i	−0.605590	+	0.795777i	$0.707063\pi$
$8$	−19.4231	−	11.6079i	−0.858388	−	0.513001i
$9$			9.00000i			0.333333i
$10$	−31.9493	−	15.0941i	−1.01032	−	0.477318i
$11$	44.6891	−	44.6891i	1.22493	−	1.22493i	0.259076	−	0.965857i	$-0.416582\pi$
$11$	44.6891	−	44.6891i	1.22493	−	1.22493i	0.965857	−	0.259076i	$-0.0834179\pi$
$12$	23.8864	+	2.33196i	0.574618	+	0.0560981i
$13$	6.83195	+	6.83195i	0.145757	+	0.145757i	0.776220	−	0.630463i	$-0.217135\pi$
$13$	6.83195	+	6.83195i	0.145757	+	0.145757i	−0.630463	+	0.776220i	$0.717135\pi$
$14$	−78.4851	+	28.1203i	−1.49829	+	0.536820i
$15$	37.4788			0.645132
$16$	12.3783	−	62.7916i	0.193410	−	0.981118i
$17$	−56.8078			−0.810466			−0.405233	−	0.914213i	$-0.632810\pi$
$17$	−56.8078			−0.810466			−0.405233	+	0.914213i	$0.632810\pi$
$18$	−23.9641	+	8.58608i	−0.313800	+	0.112431i
$19$	91.0660	+	91.0660i	1.09958	+	1.09958i	0.994460	+	0.105118i	$0.0335220\pi$
$19$	91.0660	+	91.0660i	1.09958	+	1.09958i	0.105118	+	0.994460i	$0.466478\pi$
$20$	9.71099	−	99.4706i	0.108572	−	1.11212i
$21$	62.5280	−	62.5280i	0.649749	−	0.649749i
$22$	161.626	+	76.3590i	1.56631	+	0.739990i
$23$			96.8367i			0.877907i	0.898510	+	0.438953i	$0.144651\pi$
$23$			96.8367i			0.877907i	−0.898510	+	0.438953i	$0.855349\pi$
$24$	16.5786	+	65.8267i	0.141004	+	0.559867i
$25$		−	31.0735i		−	0.248588i
$26$	−11.6736	+	24.7090i	−0.0880528	+	0.186378i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	−149.751	−	182.154i	−1.01072	−	1.22942i
$29$	−59.2957	−	59.2957i	−0.379688	−	0.379688i	0.491302	−	0.870989i	$-0.336521\pi$
$29$	−59.2957	−	59.2957i	−0.379688	−	0.379688i	−0.870989	+	0.491302i	$0.836521\pi$
$30$	35.7551	+	99.7941i	0.217599	+	0.607328i
$31$	103.074			0.597180			0.298590	−	0.954382i	$-0.403484\pi$
$31$	103.074			0.597180			0.298590	+	0.954382i	$0.403484\pi$
$32$	179.003	−	26.9444i	0.988860	−	0.148848i
$33$	−189.600			−1.00015
$34$	−54.1952	−	151.261i	−0.273365	−	0.762973i
$35$	−260.386	−	260.386i	−1.25752	−	1.25752i
$36$	−45.7240	−	55.6176i	−0.211685	−	0.257489i
$37$	−79.5300	+	79.5300i	−0.353369	+	0.353369i	−0.861361	−	0.507993i	$-0.830388\pi$
$37$	−79.5300	+	79.5300i	−0.353369	+	0.353369i	0.507993	+	0.861361i	$0.330388\pi$
$38$	−155.602	+	329.357i	−0.664262	+	1.40602i
$39$		−	28.9855i		−	0.119010i
$40$	274.123	−	69.0385i	1.08357	−	0.272899i
$41$			105.830i			0.403120i	0.979476	+	0.201560i	$0.0646011\pi$
$41$			105.830i			0.403120i	−0.979476	+	0.201560i	$0.935399\pi$
$42$	226.144	+	106.840i	0.830829	+	0.392518i
$43$	39.9965	−	39.9965i	0.141847	−	0.141847i	−0.632618	−	0.774464i	$-0.718019\pi$
$43$	39.9965	−	39.9965i	0.141847	−	0.141847i	0.774464	+	0.632618i	$0.218019\pi$
$44$	−49.1265	+	503.207i	−0.168320	+	1.72412i
$45$	−79.5046	−	79.5046i	−0.263374	−	0.263374i
$46$	−257.845	+	92.3831i	−0.826461	+	0.296112i
$47$	9.34353			0.0289977			0.0144989	−	0.999895i	$-0.495385\pi$
$47$	9.34353			0.0289977			0.0144989	+	0.999895i	$0.495385\pi$
$48$	−159.459	+	106.943i	−0.479499	+	0.321580i
$49$	−525.834			−1.53304
$50$	82.7387	−	29.6444i	0.234020	−	0.0838469i
$51$	120.508	+	120.508i	0.330871	+	0.330871i
$52$	−76.9289	−	7.51033i	−0.205156	−	0.0200287i
$53$	245.782	−	245.782i	0.636995	−	0.636995i	−0.312818	−	0.949813i	$-0.601273\pi$
$53$	245.782	−	245.782i	0.636995	−	0.636995i	0.949813	+	0.312818i	$0.101273\pi$
$54$	69.0494	+	32.6218i	0.174008	+	0.0822085i
$55$			789.552i			1.93569i
$56$	342.154	−	572.515i	0.816468	−	1.36617i
$57$		−	386.360i		−	0.897801i
$58$	101.317	−	214.454i	0.229372	−	0.485504i
$59$	345.255	−	345.255i	0.761836	−	0.761836i	−0.214818	−	0.976654i	$-0.568916\pi$
$59$	345.255	−	345.255i	0.761836	−	0.761836i	0.976654	+	0.214818i	$0.0689158\pi$
$60$	−231.609	+	190.409i	−0.498343	+	0.409695i
$61$	370.197	+	370.197i	0.777031	+	0.777031i	0.979325	−	0.202294i	$-0.0648395\pi$
$61$	370.197	+	370.197i	0.777031	+	0.777031i	−0.202294	+	0.979325i	$0.564840\pi$
$62$	98.3331	+	274.452i	0.201425	+	0.562185i
$63$	−265.284			−0.530518
$64$	242.514	+	450.922i	0.473661	+	0.880707i
$65$	−120.705			−0.230332
$66$	−180.880	−	504.843i	−0.337345	−	0.941544i
$67$	−595.125	−	595.125i	−1.08517	−	1.08517i	−0.996018	−	0.0891470i	$-0.971586\pi$
$67$	−595.125	−	595.125i	−1.08517	−	1.08517i	−0.0891470	−	0.996018i	$-0.528414\pi$
$68$	351.057	−	288.609i	0.626058	−	0.514691i
$69$	205.422	−	205.422i	0.358404	−	0.358404i
$70$	444.915	−	941.736i	0.759678	−	1.60799i
$71$		−	493.871i		−	0.825517i	−0.910840	−	0.412759i	$-0.864565\pi$
$71$		−	493.871i		−	0.825517i	0.910840	−	0.412759i	$-0.135435\pi$
$72$	104.471	−	174.808i	0.171000	−	0.286129i
$73$		−	33.2892i		−	0.0533726i	−0.999644	−	0.0266863i	$-0.991504\pi$
$73$		−	33.2892i		−	0.0533726i	0.999644	−	0.0266863i	$-0.00849553\pi$
$74$	−287.635	−	135.891i	−0.451850	−	0.213473i
$75$	−65.9168	+	65.9168i	−0.101486	+	0.101486i
$76$	−1025.42	−	100.108i	−1.54768	−	0.151095i
$77$	1317.25	+	1317.25i	1.94955	+	1.94955i
$78$	77.1791	−	27.6524i	0.112036	−	0.0401413i
$79$	552.982			0.787536			0.393768	−	0.919210i	$-0.371171\pi$
$79$	552.982			0.787536			0.393768	+	0.919210i	$0.371171\pi$
$80$	445.343	+	664.038i	0.622386	+	0.928021i
$81$	−81.0000			−0.111111
$82$	−281.792	+	100.963i	−0.379497	+	0.135970i
$83$	−18.5187	−	18.5187i	−0.0244903	−	0.0244903i	0.694756	−	0.719246i	$-0.255513\pi$
$83$	−18.5187	−	18.5187i	−0.0244903	−	0.0244903i	−0.719246	+	0.694756i	$0.755513\pi$
$84$	−68.7367	+	704.076i	−0.0892832	+	0.914536i
$85$	501.831	−	501.831i	0.640368	−	0.640368i
$86$	144.655	+	68.3409i	0.181378	+	0.0856906i
$87$			251.570i			0.310014i
$88$	−1386.75	+	349.255i	−1.67986	+	0.423077i
$89$			934.120i			1.11254i	0.831000	+	0.556272i	$0.187769\pi$
$89$			934.120i			1.11254i	−0.831000	+	0.556272i	$0.812231\pi$
$90$	135.847	−	287.543i	0.159106	−	0.336775i
$91$	−201.378	+	201.378i	−0.231980	+	0.231980i
$92$	−491.973	−	598.425i	−0.557519	−	0.678154i
$93$	−218.652	−	218.652i	−0.243798	−	0.243798i
$94$	8.91381	+	24.8788i	0.00978074	+	0.0272985i
$95$	−1608.93			−1.73760
$96$	−436.880	−	322.565i	−0.464467	−	0.342934i
$97$	1426.12			1.49279			0.746395	−	0.665503i	$-0.231783\pi$
$97$	1426.12			1.49279			0.746395	+	0.665503i	$0.231783\pi$
$98$	−501.650	−	1400.13i	−0.517085	−	1.44321i
$99$	402.202	+	402.202i	0.408311	+	0.408311i
$100$	157.867	+	192.026i	0.157867	+	0.192026i
$101$	60.4465	−	60.4465i	0.0595510	−	0.0595510i	−0.676704	−	0.736255i	$-0.736592\pi$
$101$	60.4465	−	60.4465i	0.0595510	−	0.0595510i	0.736255	+	0.676704i	$0.236592\pi$
$102$	−205.908	+	435.839i	−0.199882	+	0.423083i
$103$			1207.46i			1.15510i	0.816356	+	0.577548i	$0.195991\pi$
$103$			1207.46i			1.15510i	−0.816356	+	0.577548i	$0.804009\pi$
$104$	−53.3933	−	212.002i	−0.0503427	−	0.199890i
$105$			1104.72i			1.02676i
$106$	888.917	+	419.961i	0.814521	+	0.384813i
$107$	−423.474	+	423.474i	−0.382605	+	0.382605i	−0.872040	−	0.489435i	$-0.837203\pi$
$107$	−423.474	+	423.474i	−0.382605	+	0.382605i	0.489435	+	0.872040i	$0.337203\pi$
$108$	−20.9876	+	214.978i	−0.0186994	+	0.191539i
$109$	−1278.26	−	1278.26i	−1.12325	−	1.12325i	−0.991249	−	0.132005i	$-0.957858\pi$
$109$	−1278.26	−	1278.26i	−1.12325	−	1.12325i	−0.132005	−	0.991249i	$-0.542142\pi$
$110$	−2102.33	+	753.240i	−1.82226	+	0.652896i
$111$	337.417			0.288525
$112$	1850.84	+	364.861i	1.56150	+	0.307823i
$113$	303.164			0.252383			0.126191	−	0.992006i	$-0.459725\pi$
$113$	303.164			0.252383			0.126191	+	0.992006i	$0.459725\pi$
$114$	1028.75	−	368.591i	0.845190	−	0.302822i
$115$	−855.440	−	855.440i	−0.693654	−	0.693654i
$116$	667.680	+	65.1835i	0.534419	+	0.0521736i
$117$	−61.4875	+	61.4875i	−0.0485857	+	0.0485857i
$118$	1248.68	+	589.927i	0.974155	+	0.460230i
$119$		−	1674.47i		−	1.28990i
$120$	−727.955	−	435.049i	−0.553774	−	0.330953i
$121$		−	2663.23i		−	2.00092i
$122$	−632.546	+	1338.89i	−0.469410	+	0.993584i
$123$	224.500	−	224.500i	0.164573	−	0.164573i
$124$	−636.968	+	523.659i	−0.461302	+	0.379242i
$125$	−829.732	−	829.732i	−0.593708	−	0.593708i
$126$	−253.083	−	706.366i	−0.178940	−	0.499429i
$127$	568.985			0.397553			0.198777	−	0.980045i	$-0.436303\pi$
$127$	568.985			0.397553			0.198777	+	0.980045i	$0.436303\pi$
$128$	−969.301	+	1075.92i	−0.669335	+	0.742961i
$129$	−169.691			−0.115817
$130$	−115.153	−	321.398i	−0.0776893	−	0.216834i
$131$	8.27279	+	8.27279i	0.00551753	+	0.00551753i	0.709860	−	0.704343i	$-0.248758\pi$
$131$	8.27279	+	8.27279i	0.00551753	+	0.00551753i	−0.704343	+	0.709860i	$0.748758\pi$
$132$	1171.68	−	963.250i	0.772585	−	0.635152i
$133$	−2684.26	+	2684.26i	−1.75004	+	1.75004i
$134$	1016.87	−	2152.38i	0.655556	−	1.38759i
$135$			337.309i			0.215044i
$136$	1103.38	+	659.418i	0.695695	+	0.415770i
$137$			1697.47i			1.05857i	0.848443	+	0.529287i	$0.177541\pi$
$137$			1697.47i			1.05857i	−0.848443	+	0.529287i	$0.822459\pi$
$138$	742.946	+	350.998i	0.458288	+	0.216514i
$139$	1037.90	−	1037.90i	0.633337	−	0.633337i	−0.315566	−	0.948904i	$-0.602194\pi$
$139$	1037.90	−	1037.90i	0.633337	−	0.633337i	0.948904	+	0.315566i	$0.102194\pi$
$140$	2931.99	+	286.241i	1.76999	+	0.172799i
$141$	−19.8206	−	19.8206i	−0.0118383	−	0.0118383i
$142$	1315.02	−	471.157i	0.777142	−	0.278441i
$143$	610.627			0.357085
$144$	565.124	+	111.404i	0.327039	+	0.0644701i
$145$	1047.62			0.600000
$146$	88.6384	−	31.7581i	0.0502450	−	0.0180022i
$147$	1115.46	+	1115.46i	0.625862	+	0.625862i
$148$	87.4269	−	895.522i	0.0485571	−	0.497374i
$149$	870.791	−	870.791i	0.478778	−	0.478778i	−0.425963	−	0.904741i	$-0.640064\pi$
$149$	870.791	−	870.791i	0.478778	−	0.478778i	0.904741	+	0.425963i	$0.140064\pi$
$150$	−238.401	−	112.630i	−0.129769	−	0.0613081i
$151$		−	3199.78i		−	1.72447i	−0.506510	−	0.862234i	$-0.669065\pi$
$151$		−	3199.78i		−	1.72447i	0.506510	−	0.862234i	$-0.330935\pi$
$152$	−711.702	−	2825.87i	−0.379781	−	1.50795i
$153$		−	511.271i		−	0.270155i
$154$	−2250.76	+	4764.10i	−1.17773	+	2.49287i
$155$	−910.536	+	910.536i	−0.471845	+	0.471845i
$156$	147.259	+	179.123i	0.0755780	+	0.0919314i
$157$	231.811	+	231.811i	0.117838	+	0.117838i	0.763567	−	0.645729i	$-0.223446\pi$
$157$	231.811	+	231.811i	0.117838	+	0.117838i	−0.645729	+	0.763567i	$0.723446\pi$
$158$	527.550	+	1472.42i	0.265630	+	0.741387i
$159$	−1042.76			−0.520104
$160$	−1343.26	+	1819.30i	−0.663713	+	0.898929i
$161$	−2854.36			−1.39724
$162$	−77.2747	−	215.677i	−0.0374770	−	0.104600i
$163$	1250.64	+	1250.64i	0.600968	+	0.600968i	0.940569	−	0.339601i	$-0.110292\pi$
$163$	1250.64	+	1250.64i	0.600968	+	0.600968i	−0.339601	+	0.940569i	$0.610292\pi$
$164$	−537.665	−	654.003i	−0.256003	−	0.311397i
$165$	1674.89	−	1674.89i	0.790244	−	0.790244i
$166$	31.6424	−	66.9765i	0.0147947	−	0.0313156i
$167$			348.392i			0.161433i	0.996737	+	0.0807166i	$0.0257209\pi$
$167$			348.392i			0.161433i	−0.996737	+	0.0807166i	$0.974279\pi$
$168$	−1940.31	+	488.671i	−0.891059	+	0.224415i
$169$		−	2103.65i		−	0.957510i
$170$	1814.97	+	857.465i	0.818834	+	0.386850i
$171$	−819.594	+	819.594i	−0.366526	+	0.366526i
$172$	−43.9679	+	450.368i	−0.0194914	+	0.199652i
$173$	−1439.03	−	1439.03i	−0.632412	−	0.632412i	0.316260	−	0.948673i	$-0.397573\pi$
$173$	−1439.03	−	1439.03i	−0.632412	−	0.632412i	−0.948673	+	0.316260i	$0.897573\pi$
$174$	−669.852	+	240.000i	−0.291847	+	0.104565i
$175$	915.921			0.395641
$176$	−2252.92	−	3359.27i	−0.964889	−	1.43872i
$177$	−1464.79			−0.622037
$178$	−2487.26	+	891.158i	−1.04735	+	0.375254i
$179$	3211.36	+	3211.36i	1.34094	+	1.34094i	0.895126	+	0.445813i	$0.147085\pi$
$179$	3211.36	+	3211.36i	1.34094	+	1.34094i	0.445813	+	0.895126i	$0.352915\pi$
$180$	895.235	+	87.3989i	0.370705	+	0.0361907i
$181$	−1964.36	+	1964.36i	−0.806683	+	0.806683i	−0.984130	−	0.177447i	$-0.943216\pi$
$181$	−1964.36	+	1964.36i	−0.806683	+	0.806683i	0.177447	+	0.984130i	$0.443216\pi$
$182$	−728.323	−	344.090i	−0.296631	−	0.140141i
$183$		−	1570.61i		−	0.634443i
$184$	1124.07	−	1880.87i	0.450367	−	0.753585i
$185$		−	1405.11i		−	0.558410i
$186$	373.605	−	790.797i	0.147280	−	0.311742i
$187$	−2538.69	+	2538.69i	−0.992767	+	0.992767i
$188$	−57.7405	+	47.4692i	−0.0223998	+	0.0184152i
$189$	562.752	+	562.752i	0.216583	+	0.216583i
$190$	−1534.93	−	4284.05i	−0.586081	−	1.63578i
$191$	2190.94			0.830004			0.415002	−	0.909820i	$-0.363781\pi$
$191$	2190.94			0.830004			0.415002	+	0.909820i	$0.363781\pi$
$192$	442.100	−	1471.00i	0.166176	−	0.552919i
$193$	1787.78			0.666773			0.333386	−	0.942790i	$-0.391809\pi$
$193$	1787.78			0.666773			0.333386	+	0.942790i	$0.391809\pi$
$194$	1360.53	+	3797.30i	0.503508	+	1.40531i
$195$	256.053	+	256.053i	0.0940326	+	0.0940326i
$196$	3249.51	−	2671.47i	1.18423	−	0.973567i
$197$	−3015.39	+	3015.39i	−1.09055	+	1.09055i	−0.0950772	+	0.995470i	$0.530310\pi$
$197$	−3015.39	+	3015.39i	−1.09055	+	1.09055i	−0.995470	+	0.0950772i	$0.969690\pi$
$198$	−687.231	+	1454.64i	−0.246663	+	0.522104i
$199$			2621.42i			0.933807i	0.884308	+	0.466904i	$0.154631\pi$
$199$			2621.42i			0.933807i	−0.884308	+	0.466904i	$0.845369\pi$
$200$	−360.697	+	603.543i	−0.127526	+	0.213385i
$201$			2524.90i			0.886034i
$202$	218.616	+	103.283i	0.0761474	+	0.0359752i
$203$	1747.80	−	1747.80i	0.604293	−	0.604293i
$204$	−1356.94	−	132.473i	−0.465709	−	0.0454657i
$205$	−934.888	−	934.888i	−0.318514	−	0.318514i
$206$	−3215.09	+	1151.93i	−1.08741	+	0.389606i
$207$	−871.530			−0.292636
$208$	513.556	−	344.421i	0.171196	−	0.114814i
$209$	8139.31			2.69382
$210$	−2941.53	+	1053.92i	−0.966594	+	0.346320i
$211$	−2937.62	−	2937.62i	−0.958456	−	0.958456i	0.0407149	−	0.999171i	$-0.487036\pi$
$211$	−2937.62	−	2937.62i	−0.958456	−	0.958456i	−0.999171	+	0.0407149i	$0.987036\pi$
$212$	−270.187	+	2767.55i	−0.0875307	+	0.896585i
$213$	−1047.66	+	1047.66i	−0.337016	+	0.337016i
$214$	−1531.57	−	723.578i	−0.489235	−	0.231134i
$215$			706.645i			0.224153i
$216$	−592.440	+	149.208i	−0.186622	+	0.0470013i
$217$			3038.20i			0.950444i
$218$	2184.12	−	4623.05i	0.678565	−	1.43630i
$219$	−70.6170	+	70.6170i	−0.0217893	+	0.0217893i
$220$	−4011.27	−	4879.22i	−1.22927	−	1.49526i
$221$	−388.108	−	388.108i	−0.118131	−	0.118131i
$222$	321.899	+	898.434i	0.0973173	+	0.271617i
$223$	5441.22			1.63395			0.816976	−	0.576672i	$-0.195649\pi$
$223$	5441.22			1.63395			0.816976	+	0.576672i	$0.195649\pi$
$224$	794.211	+	5276.28i	0.236899	+	1.57382i
$225$	279.661			0.0828626
$226$	289.221	+	807.229i	0.0851270	+	0.237593i
$227$	1720.83	+	1720.83i	0.503152	+	0.503152i	0.912416	−	0.409264i	$-0.134214\pi$
$227$	1720.83	+	1720.83i	0.503152	+	0.503152i	−0.409264	+	0.912416i	$0.634214\pi$
$228$	1962.88	+	2387.60i	0.570153	+	0.693522i
$229$	1204.81	−	1204.81i	0.347667	−	0.347667i	−0.511573	−	0.859240i	$-0.670937\pi$
$229$	1204.81	−	1204.81i	0.347667	−	0.347667i	0.859240	+	0.511573i	$0.170937\pi$
$230$	1461.67	−	3093.86i	0.419041	−	0.886970i
$231$		−	5588.64i		−	1.59180i
$232$	463.410	+	1840.00i	0.131139	+	0.520699i
$233$		−	3192.24i		−	0.897556i	−0.893643	−	0.448778i	$-0.851859\pi$
$233$		−	3192.24i		−	0.897556i	0.893643	−	0.448778i	$-0.148141\pi$
$234$	−222.381	−	105.062i	−0.0621262	−	0.0293509i
$235$	−82.5393	+	82.5393i	−0.0229118	+	0.0229118i
$236$	−379.537	+	3887.63i	−0.104685	+	1.07230i
$237$	−1173.05	−	1173.05i	−0.321510	−	0.321510i
$238$	4458.57	−	1597.46i	1.21431	−	0.435074i
$239$	−4294.20			−1.16221			−0.581106	−	0.813828i	$-0.697380\pi$
$239$	−4294.20			−1.16221			−0.581106	+	0.813828i	$0.697380\pi$
$240$	463.922	−	2353.35i	0.124775	−	0.632951i
$241$	1498.49			0.400524			0.200262	−	0.979742i	$-0.435821\pi$
$241$	1498.49			0.400524			0.200262	+	0.979742i	$0.435821\pi$
$242$	7091.32	−	2540.74i	1.88367	−	0.674896i
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	−4168.49	−	406.956i	−1.09369	−	0.106773i
$245$	4645.13	−	4645.13i	1.21129	−	1.21129i
$246$	811.947	+	383.597i	0.210438	+	0.0994197i
$247$			1244.32i			0.320542i
$248$	−2002.01	−	1196.47i	−0.512612	−	0.306353i
$249$			78.5683i			0.0199962i
$250$	1417.74	−	3000.88i	0.358663	−	0.759170i
$251$	−1300.19	+	1300.19i	−0.326961	+	0.326961i	−0.851430	−	0.524469i	$-0.824264\pi$
$251$	−1300.19	+	1300.19i	−0.326961	+	0.326961i	0.524469	+	0.851430i	$0.324264\pi$
$252$	1639.38	−	1347.76i	0.409808	−	0.336908i
$253$	4327.54	+	4327.54i	1.07538	+	1.07538i
$254$	542.817	+	1515.03i	0.134092	+	0.374256i
$255$	−2129.09			−0.522858
$256$	−3789.56	−	1554.50i	−0.925185	−	0.379516i
$257$	−7244.09			−1.75826			−0.879132	−	0.476579i	$-0.841877\pi$
$257$	−7244.09			−1.75826			−0.879132	+	0.476579i	$0.841877\pi$
$258$	−161.886	−	451.832i	−0.0390644	−	0.109030i
$259$	−2344.22	−	2344.22i	−0.562406	−	0.562406i
$260$	745.923	−	613.233i	0.177924	−	0.146273i
$261$	533.662	−	533.662i	0.126563	−	0.126563i
$262$	−14.1355	+	29.9201i	−0.00333318	+	0.00705523i
$263$		−	2406.78i		−	0.564290i	−0.959372	−	0.282145i	$-0.908954\pi$
$263$		−	2406.78i		−	0.564290i	0.959372	−	0.282145i	$-0.0910459\pi$
$264$	3682.61	+	2200.85i	0.858520	+	0.513079i
$265$			4342.40i			1.00661i
$266$	−9708.14	−	4586.52i	−2.23776	−	1.05721i
$267$	1981.57	−	1981.57i	0.454195	−	0.454195i
$268$	6701.21	+	654.218i	1.52739	+	0.149115i
$269$	−3147.36	−	3147.36i	−0.713374	−	0.713374i	0.253865	−	0.967240i	$-0.418298\pi$
$269$	−3147.36	−	3147.36i	−0.713374	−	0.713374i	−0.967240	+	0.253865i	$0.918298\pi$
$270$	−898.147	+	321.796i	−0.202443	+	0.0725329i
$271$	−5929.91			−1.32921			−0.664606	−	0.747194i	$-0.731401\pi$
$271$	−5929.91			−1.32921			−0.664606	+	0.747194i	$0.731401\pi$
$272$	−703.182	+	3567.05i	−0.156752	+	0.795163i
$273$	854.376			0.189411
$274$	−4519.82	+	1619.40i	−0.996542	+	0.357050i
$275$	−1388.64	−	1388.64i	−0.304503	−	0.304503i
$276$	−225.819	+	2313.08i	−0.0492489	+	0.504461i
$277$	−1916.09	+	1916.09i	−0.415620	+	0.415620i	−0.883691	−	0.468071i	$-0.844949\pi$
$277$	−1916.09	+	1916.09i	−0.415620	+	0.415620i	0.468071	+	0.883691i	$0.344949\pi$
$278$	3753.78	+	1773.44i	0.809844	+	0.382603i
$279$			927.663i			0.199060i
$280$	2034.98	+	8080.04i	0.434333	+	1.72455i
$281$			525.861i			0.111638i	0.998441	+	0.0558189i	$0.0177769\pi$
$281$			525.861i			0.111638i	−0.998441	+	0.0558189i	$0.982223\pi$
$282$	33.8669	−	71.6850i	0.00715158	−	0.0151375i
$283$	−34.2270	+	34.2270i	−0.00718934	+	0.00718934i	−0.710692	−	0.703503i	$-0.751618\pi$
$283$	−34.2270	+	34.2270i	−0.00718934	+	0.00718934i	0.703503	+	0.710692i	$0.251618\pi$
$284$	2509.08	+	3051.99i	0.524249	+	0.637685i
$285$	3413.05	+	3413.05i	0.709373	+	0.709373i
$286$	582.543	+	1625.90i	0.120442	+	0.336160i
$287$	−3119.45			−0.641587
$288$	242.499	+	1611.03i	0.0496160	+	0.329620i
$289$	−1685.87			−0.343145
$290$	999.437	+	2789.47i	0.202376	+	0.564839i
$291$	−3025.26	−	3025.26i	−0.609429	−	0.609429i
$292$	169.124	+	205.718i	0.0338946	+	0.0412286i
$293$	843.259	−	843.259i	0.168136	−	0.168136i	−0.618024	−	0.786159i	$-0.712066\pi$
$293$	843.259	−	843.259i	0.168136	−	0.168136i	0.786159	+	0.618024i	$0.212066\pi$
$294$	−1905.96	+	4034.28i	−0.378088	+	0.800286i
$295$			6099.85i			1.20389i
$296$	2467.89	−	621.545i	0.484606	−	0.122049i
$297$		−	1706.40i		−	0.333384i
$298$	3149.38	+	1487.90i	0.612210	+	0.289233i
$299$	−661.584	+	661.584i	−0.127961	+	0.127961i
$300$	72.4620	−	742.235i	0.0139453	−	0.142843i
$301$	1178.94	+	1178.94i	0.225757	+	0.225757i
$302$	8520.00	−	3052.62i	1.62341	−	0.581651i
$303$	−256.453			−0.0486232
$304$	6845.41	−	4590.94i	1.29149	−	0.866146i
$305$	−6540.53			−1.22790
$306$	1361.35	−	487.757i	0.254324	−	0.0911215i
$307$	−2462.54	−	2462.54i	−0.457799	−	0.457799i	0.440133	−	0.897932i	$-0.354931\pi$
$307$	−2462.54	−	2462.54i	−0.457799	−	0.457799i	−0.897932	+	0.440133i	$0.854931\pi$
$308$	−14832.5	−	1448.05i	−2.74403	−	0.267891i
$309$	2561.42	−	2561.42i	0.471566	−	0.471566i
$310$	−3293.13	−	1555.81i	−0.603345	−	0.285045i
$311$			8502.54i			1.55027i	0.631794	+	0.775136i	$0.282319\pi$
$311$			8502.54i			1.55027i	−0.631794	+	0.775136i	$0.717681\pi$
$312$	−336.460	+	562.989i	−0.0610523	+	0.102157i
$313$		−	7987.66i		−	1.44246i	−0.692697	−	0.721229i	$-0.743578\pi$
$313$		−	7987.66i		−	1.44246i	0.692697	−	0.721229i	$-0.256422\pi$
$314$	−396.088	+	838.387i	−0.0711865	+	0.150678i
$315$	2343.48	−	2343.48i	0.419174	−	0.419174i
$316$	−3417.28	+	2809.39i	−0.608346	+	0.500129i
$317$	3124.20	+	3124.20i	0.553542	+	0.553542i	0.927461	−	0.373919i	$-0.121986\pi$
$317$	3124.20	+	3124.20i	0.553542	+	0.553542i	−0.373919	+	0.927461i	$0.621986\pi$
$318$	−994.806	−	2776.55i	−0.175428	−	0.489626i
$319$	−5299.74			−0.930183
$320$	−6125.71	−	1841.04i	−1.07012	−	0.321617i
$321$	1796.65			0.312396
$322$	−2723.08	−	7600.24i	−0.471278	−	1.31536i
$323$	−5173.26	−	5173.26i	−0.891171	−	0.891171i
$324$	500.559	−	411.516i	0.0858297	−	0.0705617i
$325$	212.292	−	212.292i	0.0362334	−	0.0362334i
$326$	−2136.94	+	4523.18i	−0.363049	+	0.768453i
$327$			5423.18i			0.917133i
$328$	1228.47	−	2055.55i	0.206801	−	0.346033i
$329$			275.410i			0.0461515i
$330$	6057.57	+	2861.84i	1.01048	+	0.477392i
$331$	5026.78	−	5026.78i	0.834734	−	0.834734i	−0.153426	−	0.988160i	$-0.549031\pi$
$331$	5026.78	−	5026.78i	0.834734	−	0.834734i	0.988160	+	0.153426i	$0.0490306\pi$
$332$	208.524	+	20.3575i	0.0344706	+	0.00336526i
$333$	−715.770	−	715.770i	−0.117790	−	0.117790i
$334$	−927.656	+	332.369i	−0.151973	+	0.0544503i
$335$	10514.5			1.71483
$336$	−3152.24	−	4700.22i	−0.511812	−	0.763149i
$337$	9230.68			1.49207			0.746034	−	0.665908i	$-0.231956\pi$
$337$	9230.68			1.49207			0.746034	+	0.665908i	$0.231956\pi$
$338$	5601.35	−	2006.90i	0.901399	−	0.322961i
$339$	−643.108	−	643.108i	−0.103035	−	0.103035i
$340$	−551.661	+	5650.71i	−0.0879941	+	0.901332i
$341$	4606.26	−	4606.26i	0.731505	−	0.731505i
$342$	−2964.22	−	1400.42i	−0.468674	−	0.221421i
$343$		−	5389.21i		−	0.848367i
$344$	−1241.13	+	312.582i	−0.194527	+	0.0489921i
$345$			3629.32i			0.566366i
$346$	2458.83	−	5204.52i	0.382045	−	0.808661i
$347$	1606.79	−	1606.79i	0.248579	−	0.248579i	−0.571809	−	0.820387i	$-0.693758\pi$
$347$	1606.79	−	1606.79i	0.248579	−	0.248579i	0.820387	+	0.571809i	$0.193758\pi$
$348$	−1278.09	−	1554.64i	−0.196876	−	0.239475i
$349$	3732.76	+	3732.76i	0.572521	+	0.572521i	0.932832	−	0.360311i	$-0.117329\pi$
$349$	3732.76	+	3732.76i	0.572521	+	0.572521i	−0.360311	+	0.932832i	$0.617329\pi$
$350$	873.797	+	2438.81i	0.133447	+	0.372456i
$351$	260.870			0.0396700
$352$	6795.35	−	9203.59i	1.02896	−	1.39362i
$353$	−3894.03			−0.587134			−0.293567	−	0.955939i	$-0.594842\pi$
$353$	−3894.03			−0.587134			−0.293567	+	0.955939i	$0.594842\pi$
$354$	−1397.42	−	3900.27i	−0.209809	−	0.585585i
$355$	4362.78	+	4362.78i	0.652260	+	0.652260i
$356$	−4745.74	−	5772.61i	−0.706527	−	0.859404i
$357$	−3552.08	+	3552.08i	−0.526600	+	0.526600i
$358$	−5487.16	+	11614.5i	−0.810070	+	1.71465i
$359$		−	1726.81i		−	0.253864i	−0.991911	−	0.126932i	$-0.959487\pi$
$359$		−	1726.81i		−	0.253864i	0.991911	−	0.126932i	$-0.0405131\pi$
$360$	621.347	+	2467.11i	0.0909662	+	0.361188i
$361$			9727.04i			1.41814i
$362$	−7104.47	−	3356.44i	−1.03150	−	0.487323i
$363$	−5649.55	+	5649.55i	−0.816872	+	0.816872i
$364$	221.374	−	2267.56i	0.0318768	−	0.326517i
$365$	294.071	+	294.071i	0.0421709	+	0.0421709i
$366$	4182.04	−	1498.38i	0.597265	−	0.213993i
$367$	9392.98			1.33599			0.667997	−	0.744164i	$-0.267152\pi$
$367$	9392.98			1.33599			0.667997	+	0.744164i	$0.267152\pi$
$368$	6080.53	+	1198.67i	0.861330	+	0.169796i
$369$	−952.473			−0.134373
$370$	3741.36	−	1340.49i	0.525687	−	0.188348i
$371$	7244.66	+	7244.66i	1.01381	+	1.01381i
$372$	2462.06	+	240.363i	0.343150	+	0.0335007i
$373$	3948.87	−	3948.87i	0.548163	−	0.548163i	−0.377746	−	0.925909i	$-0.623301\pi$
$373$	3948.87	−	3948.87i	0.548163	−	0.548163i	0.925909	+	0.377746i	$0.123301\pi$
$374$	−9181.65	−	4337.79i	−1.26944	−	0.599737i
$375$			3520.25i			0.484760i
$376$	−181.480	−	108.459i	−0.0248913	−	0.0148759i
$377$		−	810.211i		−	0.110684i
$378$	−961.559	+	2035.30i	−0.130839	+	0.276943i
$379$	5388.81	−	5388.81i	0.730355	−	0.730355i	−0.240335	−	0.970690i	$-0.577257\pi$
$379$	5388.81	−	5388.81i	0.730355	−	0.730355i	0.970690	+	0.240335i	$0.0772572\pi$
$380$	9942.73	−	8174.05i	1.34224	−	1.10347i
$381$	−1207.00	−	1207.00i	−0.162300	−	0.162300i
$382$	2090.18	+	5833.77i	0.279955	+	0.781366i
$383$	2060.06			0.274841			0.137421	−	0.990513i	$-0.456119\pi$
$383$	2060.06			0.274841			0.137421	+	0.990513i	$0.456119\pi$
$384$	4338.57	−	226.178i	0.576567	−	0.0300575i
$385$	−23272.8			−3.08076
$386$	1705.56	+	4760.29i	0.224898	+	0.627700i
$387$	359.968	+	359.968i	0.0472822	+	0.0472822i
$388$	−8813.05	+	7245.32i	−1.15313	+	0.948004i
$389$	−1680.58	+	1680.58i	−0.219045	+	0.219045i	−0.808096	−	0.589051i	$-0.799502\pi$
$389$	−1680.58	+	1680.58i	−0.219045	+	0.219045i	0.589051	+	0.808096i	$0.299502\pi$
$390$	−437.511	+	926.065i	−0.0568057	+	0.120239i
$391$		−	5501.08i		−	0.711514i
$392$	10213.3	+	6103.81i	1.31595	+	0.786452i
$393$		−	35.0985i		−	0.00450505i
$394$	−10905.7	−	5152.32i	−1.39447	−	0.658807i
$395$	−4884.96	+	4884.96i	−0.622250	+	0.622250i
$396$	−4528.86	−	442.138i	−0.574707	−	0.0561068i
$397$	−8476.68	−	8476.68i	−1.07162	−	1.07162i	−0.997229	−	0.0743892i	$-0.976299\pi$
$397$	−8476.68	−	8476.68i	−1.07162	−	1.07162i	−0.0743892	−	0.997229i	$-0.523701\pi$
$398$	−6980.01	+	2500.86i	−0.879086	+	0.314967i
$399$	11388.4			1.42890
$400$	−1951.15	−	384.635i	−0.243894	−	0.0480794i
$401$	1952.75			0.243182			0.121591	−	0.992580i	$-0.461200\pi$
$401$	1952.75			0.243182			0.121591	+	0.992580i	$0.461200\pi$
$402$	−6723.01	+	2408.78i	−0.834112	+	0.298853i
$403$	704.194	+	704.194i	0.0870432	+	0.0870432i
$404$	−66.4485	+	680.638i	−0.00818301	+	0.0838193i
$405$	715.541	−	715.541i	0.0877914	−	0.0877914i
$406$	6321.25	+	2986.42i	0.772705	+	0.365058i
$407$			7108.24i			0.865706i
$408$	−941.795	−	3739.47i	−0.114279	−	0.453753i
$409$		−	11615.1i		−	1.40423i	−0.712064	−	0.702115i	$-0.752239\pi$
$409$		−	11615.1i		−	1.40423i	0.712064	−	0.702115i	$-0.247761\pi$
$410$	1597.42	−	3381.20i	0.192417	−	0.407282i
$411$	3600.88	−	3600.88i	0.432161	−	0.432161i
$412$	−6134.45	−	7461.81i	−0.733550	−	0.892274i
$413$	10176.7	+	10176.7i	1.21250	+	1.21250i
$414$	−831.448	−	2320.61i	−0.0987039	−	0.275487i
$415$	327.183			0.0387007
$416$	1407.02	+	1038.86i	0.165829	+	0.122438i
$417$	−4403.46			−0.517118
$418$	7764.97	+	21672.4i	0.908606	+	2.53596i
$419$	646.755	+	646.755i	0.0754082	+	0.0754082i	0.743805	−	0.668397i	$-0.233019\pi$
$419$	646.755	+	646.755i	0.0754082	+	0.0754082i	−0.668397	+	0.743805i	$0.733019\pi$
$420$	−5612.49	−	6826.91i	−0.652051	−	0.793140i
$421$	626.853	−	626.853i	0.0725676	−	0.0725676i	−0.669891	−	0.742459i	$-0.733659\pi$
$421$	626.853	−	626.853i	0.0725676	−	0.0725676i	0.742459	+	0.669891i	$0.233659\pi$
$422$	5019.43	−	10624.5i	0.579010	−	1.22557i
$423$			84.0918i			0.00966591i
$424$	−7626.85	+	1920.84i	−0.873568	+	0.220010i
$425$			1765.22i			0.201472i
$426$	−3789.06	−	1790.11i	−0.430940	−	0.203594i
$427$	−10911.9	+	10911.9i	−1.23669	+	1.23669i
$428$	465.523	−	4768.39i	0.0525745	−	0.538525i
$429$	−1295.34	−	1295.34i	−0.145779	−	0.145779i
$430$	−1881.57	+	674.146i	−0.211017	+	0.0756051i
$431$	−6954.33			−0.777212			−0.388606	−	0.921404i	$-0.627043\pi$
$431$	−6954.33			−0.777212			−0.388606	+	0.921404i	$0.627043\pi$
$432$	−962.485	−	1435.13i	−0.107193	−	0.159833i
$433$	−2824.33			−0.313461			−0.156731	−	0.987641i	$-0.550095\pi$
$433$	−2824.33			−0.313461			−0.156731	+	0.987641i	$0.550095\pi$
$434$	−8089.75	+	2898.47i	−0.894747	+	0.320578i
$435$	−2222.33	−	2222.33i	−0.244949	−	0.244949i
$436$	14393.4	+	1405.18i	1.58100	+	0.154348i
$437$	−8818.53	+	8818.53i	−0.965327	+	0.965327i
$438$	−255.400	−	120.661i	−0.0278618	−	0.0131631i
$439$			3531.90i			0.383983i	0.981397	+	0.191991i	$0.0614945\pi$
$439$			3531.90i			0.383983i	−0.981397	+	0.191991i	$0.938505\pi$
$440$	9165.02	−	15335.6i	0.993012	−	1.66158i
$441$		−	4732.50i		−	0.511014i
$442$	663.150	−	1403.67i	0.0713638	−	0.151053i
$443$	12495.4	−	12495.4i	1.34012	−	1.34012i	0.444185	−	0.895935i	$-0.353493\pi$
$443$	12495.4	−	12495.4i	1.34012	−	1.34012i	0.895935	−	0.444185i	$-0.146507\pi$
$444$	−2085.15	+	1714.23i	−0.222876	+	0.183229i
$445$	−8251.87	−	8251.87i	−0.879047	−	0.879047i
$446$	5190.97	+	14488.2i	0.551121	+	1.53820i
$447$	−3694.45			−0.390921
$448$	−13291.4	+	7148.35i	−1.40169	+	0.753857i
$449$	10350.1			1.08787			0.543934	−	0.839128i	$-0.316934\pi$
$449$	10350.1			1.08787			0.543934	+	0.839128i	$0.316934\pi$
$450$	266.799	+	744.648i	0.0279490	+	0.0780068i
$451$	4729.46	+	4729.46i	0.493795	+	0.493795i
$452$	−1873.47	+	1540.21i	−0.194957	+	0.160277i
$453$	−6787.77	+	6787.77i	−0.704011	+	0.704011i
$454$	−2940.33	+	6223.71i	−0.303958	+	0.643377i
$455$		−	3557.89i		−	0.366586i
$456$	−4484.82	+	7504.32i	−0.460573	+	0.770662i
$457$			6249.81i			0.639724i	0.947464	+	0.319862i	$0.103637\pi$
$457$			6249.81i			0.639724i	−0.947464	+	0.319862i	$0.896363\pi$
$458$	4357.41	+	2058.62i	0.444559	+	0.210028i
$459$	−1084.57	+	1084.57i	−0.110290	+	0.110290i
$460$	9632.41	+	940.381i	0.976333	+	0.0953163i
$461$	−4923.21	−	4923.21i	−0.497390	−	0.497390i	0.413235	−	0.910625i	$-0.364399\pi$
$461$	−4923.21	−	4923.21i	−0.497390	−	0.497390i	−0.910625	+	0.413235i	$0.864399\pi$
$462$	14880.8	−	5331.61i	1.49852	−	0.536902i
$463$	−17231.2			−1.72959			−0.864794	−	0.502126i	$-0.832551\pi$
$463$	−17231.2			−1.72959			−0.864794	+	0.502126i	$0.832551\pi$
$464$	−4457.25	+	2989.29i	−0.445954	+	0.299083i
$465$	3863.08			0.385260
$466$	8499.91	−	3045.42i	0.844959	−	0.302739i
$467$	−12708.0	−	12708.0i	−1.25922	−	1.25922i	−0.951468	−	0.307748i	$-0.900425\pi$
$467$	−12708.0	−	12708.0i	−1.25922	−	1.25922i	−0.307748	−	0.951468i	$-0.599575\pi$
$468$	67.5929	−	692.360i	0.00667625	−	0.0683854i
$469$	17541.9	−	17541.9i	1.72710	−	1.72710i
$470$	−298.519	−	141.033i	−0.0292971	−	0.0138412i
$471$		−	983.489i		−	0.0962139i
$472$	−10713.6	+	2698.25i	−1.04477	+	0.263129i
$473$		−	3574.81i		−	0.347505i
$474$	2004.36	−	4242.57i	0.194227	−	0.411113i
$475$	2829.74	−	2829.74i	0.273342	−	0.273342i
$476$	8507.03	+	10347.8i	0.819158	+	0.996405i
$477$	2212.04	+	2212.04i	0.212332	+	0.212332i
$478$	−4096.71	−	11434.1i	−0.392006	−	1.09411i
$479$	5951.57			0.567712			0.283856	−	0.958867i	$-0.408386\pi$
$479$	5951.57			0.567712			0.283856	+	0.958867i	$0.408386\pi$
$480$	6708.81	−	1009.84i	0.637946	−	0.0960266i
$481$	−1086.69			−0.103012
$482$	1429.57	+	3990.00i	0.135094	+	0.377053i
$483$	6055.01	+	6055.01i	0.570419	+	0.570419i
$484$	13530.4	+	16458.0i	1.27069	+	1.54564i
$485$	−12598.1	+	12598.1i	−1.17949	+	1.17949i
$486$	−293.596	+	621.445i	−0.0274028	+	0.0580027i
$487$		−	5466.49i		−	0.508645i	−0.967119	−	0.254323i	$-0.918148\pi$
$487$		−	5466.49i		−	0.508645i	0.967119	−	0.254323i	$-0.0818525\pi$
$488$	−2893.18	−	11487.6i	−0.268377	−	1.06561i
$489$		−	5306.02i		−	0.490688i
$490$	16800.0	+	7937.01i	1.54887	+	0.731750i
$491$	4502.14	−	4502.14i	0.413806	−	0.413806i	−0.469256	−	0.883062i	$-0.655478\pi$
$491$	4502.14	−	4502.14i	0.413806	−	0.413806i	0.883062	+	0.469256i	$0.155478\pi$
$492$	−246.792	+	2527.91i	−0.0226143	+	0.231640i
$493$	3368.46	+	3368.46i	0.307724	+	0.307724i
$494$	−3313.22	+	1187.09i	−0.301759	+	0.108117i
$495$	−7105.97			−0.645231
$496$	1275.87	−	6472.15i	0.115501	−	0.585904i
$497$	14557.3			1.31385
$498$	−209.202	+	74.9548i	−0.0188245	+	0.00674459i
$499$	4481.53	+	4481.53i	0.402045	+	0.402045i	0.878953	−	0.476908i	$-0.158242\pi$
$499$	4481.53	+	4481.53i	0.402045	+	0.402045i	−0.476908	+	0.878953i	$0.658242\pi$
$500$	9342.93	+	912.120i	0.835657	+	0.0815825i
$501$	739.050	−	739.050i	0.0659049	−	0.0659049i
$502$	−4702.38	−	2221.59i	−0.418082	−	0.197519i
$503$		−	7122.95i		−	0.631405i	−0.948858	−	0.315702i	$-0.897760\pi$
$503$		−	7122.95i		−	0.631405i	0.948858	−	0.315702i	$-0.102240\pi$
$504$	5152.64	+	3079.38i	0.455390	+	0.272156i
$505$			1067.95i			0.0941052i
$506$	−7394.35	+	15651.4i	−0.649642	+	1.37508i
$507$	−4462.51	+	4462.51i	−0.390902	+	0.390902i
$508$	−3516.18	+	2890.69i	−0.307097	+	0.252468i
$509$	−9365.42	−	9365.42i	−0.815550	−	0.815550i	0.169910	−	0.985460i	$-0.445652\pi$
$509$	−9365.42	−	9365.42i	−0.815550	−	0.815550i	−0.985460	+	0.169910i	$0.945652\pi$
$510$	−2031.17	−	5669.09i	−0.176356	−	0.492218i
$511$	981.231			0.0849454
$512$	523.864	−	11573.4i	0.0452182	−	0.998977i
$513$	3477.24			0.299267
$514$	−6910.92	−	19288.7i	−0.593050	−	1.65523i
$515$	−10666.5	−	10666.5i	−0.912668	−	0.912668i
$516$	1048.64	−	862.104i	0.0894651	−	0.0735504i
$517$	417.554	−	417.554i	0.0355203	−	0.0355203i
$518$	4005.51	−	8478.33i	0.339753	−	0.719144i
$519$			6105.28i			0.516363i
$520$	2344.46	+	1401.13i	0.197714	+	0.118160i
$521$			19173.3i			1.61228i	0.591727	+	0.806138i	$0.298446\pi$
$521$			19173.3i			1.61228i	−0.591727	+	0.806138i	$0.701554\pi$
$522$	1930.09	+	911.852i	0.161835	+	0.0764573i
$523$	4919.87	−	4919.87i	0.411340	−	0.411340i	−0.470865	−	0.882205i	$-0.656058\pi$
$523$	4919.87	−	4919.87i	0.411340	−	0.411340i	0.882205	+	0.470865i	$0.156058\pi$
$524$	−93.1531	−	9.09424i	−0.00776605	−	0.000758175i
$525$	−1942.96	−	1942.96i	−0.161520	−	0.161520i
$526$	6408.48	−	2296.09i	0.531222	−	0.190331i
$527$	−5855.39			−0.483994
$528$	−2346.91	+	11905.3i	−0.193440	+	0.981268i
$529$	2789.65			0.229280
$530$	−11562.4	+	4142.68i	−0.947621	+	0.339522i
$531$	3107.29	+	3107.29i	0.253945	+	0.253945i
$532$	2950.79	−	30225.2i	0.240476	−	2.46322i
$533$	−723.027	+	723.027i	−0.0587576	+	0.0587576i
$534$	7166.71	+	3385.85i	0.580775	+	0.274382i
$535$		−	7481.80i		−	0.604610i
$536$	4651.04	+	18467.3i	0.374803	+	1.48818i
$537$		−	13624.6i		−	1.09487i
$538$	5377.80	−	11383.0i	0.430954	−	0.912187i
$539$	−23499.0	+	23499.0i	−1.87787	+	1.87787i
$540$	−1713.68	−	2084.48i	−0.136565	−	0.166114i
$541$	94.7412	+	94.7412i	0.00752910	+	0.00752910i	0.710861	−	0.703332i	$-0.248305\pi$
$541$	94.7412	+	94.7412i	0.00752910	+	0.00752910i	−0.703332	+	0.710861i	$0.748305\pi$
$542$	−5657.19	−	15789.5i	−0.448334	−	1.25132i
$543$	8334.07			0.658654
$544$	−10168.8	+	1530.65i	−0.801438	+	0.120636i
$545$	22583.8			1.77502
$546$	815.082	+	2274.93i	0.0638870	+	0.178311i
$547$	12381.4	+	12381.4i	0.967804	+	0.967804i	0.999498	−	0.0316935i	$-0.0100900\pi$
$547$	12381.4	+	12381.4i	0.967804	+	0.967804i	−0.0316935	+	0.999498i	$0.510090\pi$
$548$	−8623.90	−	10489.9i	−0.672253	−	0.817714i
$549$	−3331.78	+	3331.78i	−0.259010	+	0.259010i
$550$	2372.74	−	5022.29i	0.183952	−	0.389366i
$551$		−	10799.7i		−	0.834992i
$552$	−6374.44	+	1605.42i	−0.491511	+	0.123788i
$553$			16299.7i			1.25341i
$554$	−6929.91	−	3273.97i	−0.531451	−	0.251079i
$555$	−2980.69	+	2980.69i	−0.227970	+	0.227970i
$556$	−1140.96	+	11687.0i	−0.0870281	+	0.891436i
$557$	435.529	+	435.529i	0.0331310	+	0.0331310i	0.723478	−	0.690347i	$-0.242542\pi$
$557$	435.529	+	435.529i	0.0331310	+	0.0331310i	−0.690347	+	0.723478i	$0.742542\pi$
$558$	−2470.07	+	884.998i	−0.187395	+	0.0671415i
$559$	546.508			0.0413503
$560$	−19573.2	+	13126.9i	−1.47700	+	0.990560i
$561$	10770.7			0.810591
$562$	−1400.20	+	501.676i	−0.105096	+	0.0376546i
$563$	2065.88	+	2065.88i	0.154647	+	0.154647i	0.780190	−	0.625543i	$-0.215122\pi$
$563$	2065.88	+	2065.88i	0.154647	+	0.154647i	−0.625543	+	0.780190i	$0.715122\pi$
$564$	223.184	+	21.7887i	0.0166626	+	0.00162672i
$565$	−2678.10	+	2678.10i	−0.199413	+	0.199413i
$566$	−123.788	−	58.4827i	−0.00919296	−	0.00434313i
$567$		−	2387.56i		−	0.176839i
$568$	−5732.79	+	9592.51i	−0.423491	+	0.708614i
$569$		−	21002.5i		−	1.54740i	−0.633551	−	0.773701i	$-0.718404\pi$
$569$		−	21002.5i		−	1.54740i	0.633551	−	0.773701i	$-0.281596\pi$
$570$	−5831.78	+	12343.9i	−0.428537	+	0.907070i
$571$	−16443.6	+	16443.6i	−1.20515	+	1.20515i	−0.232576	+	0.972578i	$0.574715\pi$
$571$	−16443.6	+	16443.6i	−1.20515	+	1.20515i	−0.972578	+	0.232576i	$0.925285\pi$
$572$	−3773.51	+	3102.25i	−0.275836	+	0.226769i
$573$	−4647.68	−	4647.68i	−0.338848	−	0.338848i
$574$	−2975.99	−	8306.11i	−0.216403	−	0.603990i
$575$	3009.05			0.218237
$576$	−4058.30	+	2182.63i	−0.293569	+	0.157887i
$577$	5584.08			0.402891			0.201446	−	0.979500i	$-0.435436\pi$
$577$	5584.08			0.402891			0.201446	+	0.979500i	$0.435436\pi$
$578$	−1608.33	−	4488.93i	−0.115740	−	0.323036i
$579$	−3792.45	−	3792.45i	−0.272209	−	0.272209i
$580$	−6474.00	+	5322.36i	−0.463480	+	0.381033i
$581$	545.858	−	545.858i	0.0389776	−	0.0389776i
$582$	5169.17	−	10941.4i	0.368160	−	0.779272i
$583$		−	21967.5i		−	1.56055i
$584$	−386.416	+	646.579i	−0.0273802	+	0.0458144i
$585$		−	1086.34i		−	0.0767773i
$586$	3049.81	+	1440.85i	0.214994	+	0.101572i
$587$	4071.35	−	4071.35i	0.286274	−	0.286274i	−0.549331	−	0.835605i	$-0.685117\pi$
$587$	4071.35	−	4071.35i	0.286274	−	0.286274i	0.835605	+	0.549331i	$0.185117\pi$
$588$	−12560.3	−	1226.22i	−0.880915	−	0.0860009i
$589$	9386.51	+	9386.51i	0.656646	+	0.656646i
$590$	−16242.0	+	5819.31i	−1.13334	+	0.406063i
$591$	12793.2			0.890428
$592$	4009.37	+	5978.25i	0.278351	+	0.415042i
$593$	−9274.19			−0.642235			−0.321118	−	0.947039i	$-0.604058\pi$
$593$	−9274.19			−0.642235			−0.321118	+	0.947039i	$0.604058\pi$
$594$	4543.59	−	1627.92i	0.313848	−	0.112448i
$595$	14792.0	+	14792.0i	1.01918	+	1.01918i
$596$	−957.256	+	9805.25i	−0.0657898	+	0.673891i
$597$	5560.87	−	5560.87i	0.381225	−	0.381225i
$598$	−2392.74	−	1130.43i	−0.163623	−	0.0773022i
$599$		−	6941.05i		−	0.473462i	−0.971575	−	0.236731i	$-0.923924\pi$
$599$		−	6941.05i		−	0.473462i	0.971575	−	0.236731i	$-0.0760760\pi$
$600$	2045.46	−	515.155i	0.139176	−	0.0350519i
$601$			23911.9i			1.62294i	0.584397	+	0.811468i	$0.301331\pi$
$601$			23911.9i			1.62294i	−0.584397	+	0.811468i	$0.698669\pi$
$602$	−2014.42	+	4263.85i	−0.136381	+	0.288673i
$603$	5356.12	−	5356.12i	0.361722	−	0.361722i
$604$	16256.3	+	19773.8i	1.09513	+	1.33209i
$605$	23526.5	+	23526.5i	1.58097	+	1.58097i
$606$	−244.658	−	682.852i	−0.0164003	−	0.0457739i
$607$	−8100.05			−0.541633			−0.270816	−	0.962631i	$-0.587294\pi$
$607$	−8100.05			−0.541633			−0.270816	+	0.962631i	$0.587294\pi$
$608$	18754.8	+	13847.4i	1.25100	+	0.923659i
$609$	−7415.29			−0.493403
$610$	−6239.72	−	17415.3i	−0.414162	−	1.15594i
$611$	63.8345	+	63.8345i	0.00422663	+	0.00422663i
$612$	2597.48	+	3159.52i	0.171564	+	0.208686i
$613$	−17040.5	+	17040.5i	−1.12277	+	1.12277i	−0.131447	+	0.991323i	$0.541962\pi$
$613$	−17040.5	+	17040.5i	−1.12277	+	1.12277i	−0.991323	+	0.131447i	$0.958038\pi$
$614$	4207.67	−	8906.23i	0.276560	−	0.585384i
$615$			3966.39i			0.260066i
$616$	−10294.7	−	40875.7i	−0.673350	−	2.67359i
$617$			21789.9i			1.42176i	0.703311	+	0.710882i	$0.251704\pi$
$617$			21789.9i			1.42176i	−0.703311	+	0.710882i	$0.748296\pi$
$618$	9263.85	+	4376.62i	0.602988	+	0.284876i
$619$	−2910.91	+	2910.91i	−0.189013	+	0.189013i	−0.795269	−	0.606256i	$-0.792671\pi$
$619$	−2910.91	+	2910.91i	−0.189013	+	0.189013i	0.606256	+	0.795269i	$0.292671\pi$
$620$	1000.95	−	10252.8i	0.0648371	−	0.664133i
$621$	1848.80	+	1848.80i	0.119468	+	0.119468i
$622$	−22639.5	+	8111.49i	−1.45943	+	0.522896i
$623$	−27534.1			−1.77068
$624$	−1820.04	−	358.790i	−0.116763	−	0.0230178i
$625$	18543.6			1.18679
$626$	21268.6	−	7620.29i	1.35793	−	0.486531i
$627$	−17266.1	−	17266.1i	−1.09975	−	1.09975i
$628$	−2610.23	−	254.828i	−0.165859	−	0.0161923i
$629$	4517.93	−	4517.93i	0.286394	−	0.286394i
$630$	8475.62	+	4004.23i	0.535995	+	0.253226i
$631$			1496.32i			0.0944020i	0.998885	+	0.0472010i	$0.0150301\pi$
$631$			1496.32i			0.0944020i	−0.998885	+	0.0472010i	$0.984970\pi$
$632$	−10740.6	−	6418.95i	−0.676012	−	0.404007i
$633$			12463.3i			0.782576i
$634$	−5338.24	+	11299.3i	−0.334398	+	0.707810i
$635$	−5026.32	+	5026.32i	−0.314116	+	0.314116i
$636$	6444.01	−	5297.70i	0.401763	−	0.330295i
$637$	−3592.47	−	3592.47i	−0.223452	−	0.223452i
$638$	−5056.00	−	14111.5i	−0.313744	−	0.875674i
$639$	4444.84			0.275172
$640$	−941.875	−	18067.2i	−0.0581733	−	1.11589i
$641$	−7774.27			−0.479041			−0.239520	−	0.970891i	$-0.576990\pi$
$641$	−7774.27			−0.479041			−0.239520	+	0.970891i	$0.576990\pi$
$642$	1714.02	+	4783.90i	0.105369	+	0.294089i
$643$	7612.84	+	7612.84i	0.466907	+	0.466907i	0.900911	−	0.434004i	$-0.142900\pi$
$643$	7612.84	+	7612.84i	0.466907	+	0.466907i	−0.434004	+	0.900911i	$0.642900\pi$
$644$	17639.2	−	14501.4i	1.07932	−	0.887321i
$645$	1499.02	−	1499.02i	0.0915099	−	0.0915099i
$646$	8839.41	−	18710.1i	0.538362	−	1.13953i
$647$		−	5718.22i		−	0.347460i	−0.984793	−	0.173730i	$-0.944418\pi$
$647$		−	5718.22i		−	0.347460i	0.984793	−	0.173730i	$-0.0555820\pi$
$648$	1573.27	+	940.238i	0.0953765	+	0.0570001i
$649$		−	30858.2i		−	1.86640i
$650$	767.795	+	362.738i	0.0463314	+	0.0218889i
$651$	6444.99	−	6444.99i	0.388017	−	0.388017i
$652$	−14082.4	−	1374.82i	−0.845876	−	0.0825801i
$653$	−15558.6	−	15558.6i	−0.932394	−	0.932394i	0.0654608	−	0.997855i	$-0.479148\pi$
$653$	−15558.6	−	15558.6i	−0.932394	−	0.932394i	−0.997855	+	0.0654608i	$0.979148\pi$
$654$	−14440.2	+	5173.76i	−0.863389	+	0.309343i
$655$	−146.161			−0.00871906
$656$	6645.25	+	1309.99i	0.395508	+	0.0779675i
$657$	299.602			0.0177909
$658$	−733.328	+	262.743i	−0.0434470	+	0.0155666i
$659$	−993.665	−	993.665i	−0.0587370	−	0.0587370i	0.677128	−	0.735865i	$-0.263224\pi$
$659$	−993.665	−	993.665i	−0.0587370	−	0.0587370i	−0.735865	+	0.677128i	$0.763224\pi$
$660$	−1841.20	+	18859.6i	−0.108589	+	1.11229i
$661$	15752.5	−	15752.5i	0.926930	−	0.926930i	−0.0705764	−	0.997506i	$-0.522484\pi$
$661$	15752.5	−	15752.5i	0.926930	−	0.926930i	0.997506	+	0.0705764i	$0.0224839\pi$
$662$	18180.3	+	8589.12i	1.06737	+	0.504269i
$663$			1646.60i			0.0964537i
$664$	144.728	+	574.654i	0.00845865	+	0.0335857i
$665$		−	47424.7i		−	2.76549i
$666$	1223.02	−	2588.72i	0.0711575	−	0.150617i
$667$	5742.00	−	5742.00i	0.333330	−	0.333330i
$668$	−1769.98	−	2152.97i	−0.102519	−	0.124702i
$669$	−11542.6	−	11542.6i	−0.667058	−	0.667058i
$670$	10030.9	+	27996.7i	0.578399	+	1.61434i
$671$	33087.5			1.90362
$672$	9507.91	−	12877.5i	0.545797	−	0.739225i
$673$	−6956.60			−0.398451			−0.199225	−	0.979954i	$-0.563843\pi$
$673$	−6956.60			−0.398451			−0.199225	+	0.979954i	$0.563843\pi$
$674$	8806.15	+	24578.3i	0.503264	+	1.40463i
$675$	−593.251	−	593.251i	−0.0338285	−	0.0338285i
$676$	10687.5	+	13000.0i	0.608071	+	0.739645i
$677$	5062.86	−	5062.86i	0.287417	−	0.287417i	−0.548641	−	0.836058i	$-0.684855\pi$
$677$	5062.86	−	5062.86i	0.287417	−	0.287417i	0.836058	+	0.548641i	$0.184855\pi$
$678$	1098.86	−	2325.92i	0.0622441	−	0.131750i
$679$			42036.3i			2.37586i
$680$	−15572.3	+	3921.93i	−0.878193	+	0.221175i
$681$		−	7300.87i		−	0.410822i
$682$	16659.4	+	7870.59i	0.935370	+	0.441907i
$683$	21495.7	−	21495.7i	1.20426	−	1.20426i	0.231401	−	0.972858i	$-0.425669\pi$
$683$	21495.7	−	21495.7i	1.20426	−	1.20426i	0.972858	−	0.231401i	$-0.0743311\pi$
$684$	900.976	−	9228.77i	0.0503650	−	0.515893i
$685$	−14995.2	−	14995.2i	−0.836404	−	0.836404i
$686$	14349.7	−	5141.35i	0.798653	−	0.286148i
$687$	−5111.56			−0.283869
$688$	−2016.36	−	3006.53i	−0.111734	−	0.166603i
$689$	3358.34			0.185693
$690$	−9663.73	+	3462.41i	−0.533177	+	0.191031i
$691$	−8250.85	−	8250.85i	−0.454236	−	0.454236i	0.442522	−	0.896758i	$-0.354084\pi$
$691$	−8250.85	−	8250.85i	−0.454236	−	0.454236i	−0.896758	+	0.442522i	$0.854084\pi$
$692$	16203.7	+	1581.92i	0.890134	+	0.0869010i
$693$	−11855.3	+	11855.3i	−0.649849	+	0.649849i
$694$	5811.24	+	2745.47i	0.317856	+	0.150168i
$695$			18337.4i			1.00083i
$696$	2920.20	−	4886.28i	0.159037	−	0.266112i
$697$		−	6011.99i		−	0.326715i
$698$	−6378.06	+	13500.2i	−0.345864	+	0.732079i
$699$	−6771.76	+	6771.76i	−0.366426	+	0.366426i
$700$	−5660.15	+	4653.28i	−0.305619	+	0.251254i
$701$	8228.87	+	8228.87i	0.443367	+	0.443367i	0.893142	−	0.449775i	$-0.148496\pi$
$701$	8228.87	+	8228.87i	0.443367	+	0.443367i	−0.449775	+	0.893142i	$0.648496\pi$
$702$	248.872	+	694.612i	0.0133804	+	0.0373454i
$703$	−14485.0			−0.777113
$704$	30989.0	+	9313.55i	1.65901	+	0.498604i
$705$	350.184			0.0187074
$706$	−3714.94	−	10368.5i	−0.198036	−	0.552727i
$707$	1781.72	+	1781.72i	0.0947786	+	0.0947786i
$708$	9052.03	−	7441.79i	0.480503	−	0.395028i
$709$	−12890.7	+	12890.7i	−0.682819	+	0.682819i	−0.960634	−	0.277815i	$-0.910390\pi$
$709$	−12890.7	+	12890.7i	−0.682819	+	0.682819i	0.277815	+	0.960634i	$0.410390\pi$
$710$	−7454.56	+	15778.8i	−0.394035	+	0.834040i
$711$			4976.84i			0.262512i
$712$	10843.1	−	18143.5i	0.570736	−	0.954996i
$713$			9981.31i			0.524268i
$714$	−12846.8	−	6069.34i	−0.673359	−	0.318122i
$715$	−5394.18	+	5394.18i	−0.282141	+	0.282141i
$716$	−36160.4	−	3530.23i	−1.88740	−	0.184261i
$717$	9109.38	+	9109.38i	0.474471	+	0.474471i
$718$	4597.93	−	1647.39i	0.238988	−	0.0856267i
$719$	21571.4			1.11888			0.559441	−	0.828870i	$-0.311016\pi$
$719$	21571.4			1.11888			0.559441	+	0.828870i	$0.311016\pi$
$720$	−5976.34	+	4008.09i	−0.309340	+	0.207462i
$721$	−35591.2			−1.83840
$722$	−25900.0	+	9279.68i	−1.33504	+	0.478330i
$723$	−3178.78	−	3178.78i	−0.163513	−	0.163513i
$724$	2159.41	−	22119.0i	0.110848	−	1.13542i
$725$	−1842.52	+	1842.52i	−0.0943857	+	0.0943857i
$726$	−20432.7	−	9653.23i	−1.04453	−	0.493478i
$727$		−	22624.2i		−	1.15418i	−0.816682	−	0.577088i	$-0.804189\pi$
$727$		−	22624.2i		−	1.15418i	0.816682	−	0.577088i	$-0.195811\pi$
$728$	6248.97	−	1573.82i	0.318135	−	0.0801231i
$729$		−	729.000i		−	0.0370370i
$730$	−502.471	+	1063.56i	−0.0254757	+	0.0539237i
$731$	−2272.11	+	2272.11i	−0.114962	+	0.114962i
$732$	7979.41	+	9705.98i	0.402906	+	0.490087i
$733$	19225.0	+	19225.0i	0.968749	+	0.968749i	0.999526	−	0.0307771i	$-0.00979820\pi$
$733$	19225.0	+	19225.0i	0.968749	+	0.968749i	−0.0307771	+	0.999526i	$0.509798\pi$
$734$	8960.98	+	25010.5i	0.450621	+	1.25770i
$735$	−19707.6			−0.989016
$736$	2609.20	+	17334.0i	0.130675	+	0.868127i
$737$	−53191.2			−2.65851
$738$	−908.667	−	2536.13i	−0.0453232	−	0.126499i
$739$	−17944.0	−	17944.0i	−0.893207	−	0.893207i	0.101616	−	0.994824i	$-0.467599\pi$
$739$	−17944.0	−	17944.0i	−0.893207	−	0.893207i	−0.994824	+	0.101616i	$0.967599\pi$
$740$	7138.58	+	8683.21i	0.354621	+	0.431353i
$741$	2639.59	−	2639.59i	0.130861	−	0.130861i
$742$	−12378.8	+	26201.7i	−0.612451	+	1.29635i
$743$			3907.59i			0.192941i	0.995336	+	0.0964707i	$0.0307554\pi$
$743$			3907.59i			0.192941i	−0.995336	+	0.0964707i	$0.969245\pi$
$744$	1708.82	+	6784.99i	0.0842047	+	0.334341i
$745$			15384.9i			0.756587i
$746$	14281.8	+	6747.33i	0.700932	+	0.331149i
$747$	166.668	−	166.668i	0.00816343	−	0.00816343i
$748$	2790.77	−	28586.1i	0.136418	−	1.39734i
$749$	−12482.3	−	12482.3i	−0.608937	−	0.608937i
$750$	−9373.31	+	3358.35i	−0.456353	+	0.163506i
$751$	10642.3			0.517101			0.258550	−	0.965998i	$-0.416755\pi$
$751$	10642.3			0.517101			0.258550	+	0.965998i	$0.416755\pi$
$752$	115.657	−	586.695i	0.00560846	−	0.0284502i
$753$	5516.23			0.266962
$754$	2157.33	−	772.948i	0.104198	−	0.0373330i
$755$	28266.4	+	28266.4i	1.36254	+	1.36254i
$756$	−6336.69	−	618.630i	−0.304845	−	0.0297611i
$757$	11983.9	−	11983.9i	0.575377	−	0.575377i	−0.358249	−	0.933626i	$-0.616626\pi$
$757$	11983.9	−	11983.9i	0.575377	−	0.575377i	0.933626	+	0.358249i	$0.116626\pi$
$758$	19489.7	+	9207.71i	0.933900	+	0.441213i
$759$		−	18360.2i		−	0.878041i
$760$	31250.3	+	18676.2i	1.49154	+	0.891391i
$761$			37539.1i			1.78816i	0.447906	+	0.894080i	$0.352170\pi$
$761$			37539.1i			1.78816i	−0.447906	+	0.894080i	$0.647830\pi$
$762$	2062.37	−	4365.34i	0.0980468	−	0.207532i
$763$	37677.9	−	37677.9i	1.78772	−	1.78772i
$764$	−13539.4	+	11130.9i	−0.641151	+	0.527098i
$765$	4516.48	+	4516.48i	0.213456	+	0.213456i
$766$	1965.32	+	5485.29i	0.0927021	+	0.258736i
$767$	4717.53			0.222086
$768$	4741.28	+	11336.5i	0.222768	+	0.532642i
$769$	−9092.45			−0.426375			−0.213187	−	0.977011i	$-0.568384\pi$
$769$	−9092.45			−0.426375			−0.213187	+	0.977011i	$0.568384\pi$
$770$	−22202.5	−	61968.1i	−1.03912	−	2.90023i
$771$	15367.0	+	15367.0i	0.717808	+	0.717808i
$772$	−11048.0	+	9082.71i	−0.515060	+	0.423438i
$773$	3385.85	−	3385.85i	0.157543	−	0.157543i	−0.623934	−	0.781477i	$-0.714467\pi$
$773$	3385.85	−	3385.85i	0.157543	−	0.157543i	0.781477	+	0.623934i	$0.214467\pi$
$774$	−615.068	+	1301.89i	−0.0285635	+	0.0604595i
$775$		−	3202.86i		−	0.148452i
$776$	−27699.7	−	16554.2i	−1.28139	−	0.765802i
$777$			9945.70i			0.459202i
$778$	−6078.12	−	2871.55i	−0.280091	−	0.132327i
$779$	−9637.55	+	9637.55i	−0.443262	+	0.443262i
$780$	−2883.21	−	281.478i	−0.132353	−	0.0129212i
$781$	−22070.6	−	22070.6i	−1.01120	−	1.01120i
$782$	14647.6	−	5248.08i	0.669819	−	0.239989i
$783$	−2264.13			−0.103338
$784$	−6508.90	+	33017.9i	−0.296506	+	1.50410i
$785$	−4095.55			−0.186212
$786$	93.4560	−	33.4843i	0.00424105	−	0.00151952i
$787$	−18257.3	−	18257.3i	−0.826941	−	0.826941i	0.160151	−	0.987092i	$-0.448802\pi$
$787$	−18257.3	−	18257.3i	−0.826941	−	0.826941i	−0.987092	+	0.160151i	$0.948802\pi$
$788$	3314.80	−	33953.8i	0.149854	−	1.53497i
$789$	−5105.55	+	5105.55i	−0.230370	+	0.230370i
$790$	−17667.4	−	8346.79i	−0.795667	−	0.375906i
$791$			8936.06i			0.401681i
$792$	−3143.30	−	12480.7i	−0.141026	−	0.559953i
$793$			5058.34i			0.226516i
$794$	14483.9	−	30657.5i	0.647372	−	1.37027i
$795$	9211.61	−	9211.61i	0.410946	−	0.410946i
$796$	−13318.0	−	16199.7i	−0.593019	−	0.721335i
$797$	−24835.5	−	24835.5i	−1.10379	−	1.10379i	−0.993949	−	0.109839i	$-0.964967\pi$
$797$	−24835.5	−	24835.5i	−1.10379	−	1.10379i	−0.109839	−	0.993949i	$-0.535033\pi$
$798$	10864.6	+	30323.5i	0.481958	+	1.34517i
$799$	−530.786			−0.0235017
$800$	−837.254	−	5562.24i	−0.0370018	−	0.245819i
$801$	−8407.08			−0.370848
$802$	1862.94	+	5199.56i	0.0820234	+	0.228931i
$803$	−1487.66	−	1487.66i	−0.0653779	−	0.0653779i
$804$	−12827.6	−	15603.2i	−0.562680	−	0.684432i
$805$	25214.9	−	25214.9i	1.10399	−	1.10399i
$806$	−1203.24	+	2546.85i	−0.0525834	+	0.111301i
$807$			13353.1i			0.582468i
$808$	−1875.71	+	472.404i	−0.0816676	+	0.0205682i
$809$		−	26358.7i		−	1.14552i	−0.819725	−	0.572758i	$-0.805874\pi$
$809$		−	26358.7i		−	1.14552i	0.819725	−	0.572758i	$-0.194126\pi$
$810$	2587.89	+	1222.62i	0.112258	+	0.0530354i
$811$	−13692.8	+	13692.8i	−0.592871	+	0.592871i	−0.938406	−	0.345535i	$-0.887698\pi$
$811$	−13692.8	+	13692.8i	−0.592871	+	0.592871i	0.345535	+	0.938406i	$0.387698\pi$
$812$	−1921.35	+	19680.5i	−0.0830370	+	0.850556i
$813$	12579.2	+	12579.2i	0.542649	+	0.542649i
$814$	−18927.0	+	6781.32i	−0.814976	+	0.291997i
$815$	−22095.9			−0.949677
$816$	9058.53	−	6075.19i	0.388618	−	0.260630i
$817$	7284.64			0.311943
$818$	30927.3	−	11080.9i	1.32194	−	0.473637i
$819$	−1812.41	−	1812.41i	−0.0773267	−	0.0773267i
$820$	10527.0	+	1027.72i	0.448316	+	0.0437676i
$821$	−340.140	+	340.140i	−0.0144592	+	0.0144592i	−0.714299	−	0.699840i	$-0.753255\pi$
$821$	−340.140	+	340.140i	−0.0144592	+	0.0144592i	0.699840	+	0.714299i	$0.253255\pi$
$822$	13023.3	+	6152.72i	0.552601	+	0.261072i
$823$			32082.0i			1.35882i	0.733760	+	0.679409i	$0.237764\pi$
$823$			32082.0i			1.35882i	−0.733760	+	0.679409i	$0.762236\pi$
$824$	14016.1	−	23452.7i	0.592565	−	0.991522i
$825$			5891.52i			0.248626i
$826$	−17388.7	+	36806.1i	−0.732482	+	1.55042i
$827$	−9570.26	+	9570.26i	−0.402407	+	0.402407i	−0.879080	−	0.476674i	$-0.841842\pi$
$827$	−9570.26	+	9570.26i	−0.402407	+	0.402407i	0.476674	+	0.879080i	$0.341842\pi$
$828$	5385.83	−	4427.76i	0.226051	−	0.185840i
$829$	21904.2	+	21904.2i	0.917691	+	0.917691i	0.996861	−	0.0791705i	$-0.0252272\pi$
$829$	21904.2	+	21904.2i	0.917691	+	0.917691i	−0.0791705	+	0.996861i	$0.525227\pi$
$830$	312.135	+	871.183i	0.0130535	+	0.0364328i
$831$	8129.29			0.339353
$832$	−1423.83	+	4737.52i	−0.0593299	+	0.197409i
$833$	29871.5			1.24248
$834$	−4200.93	−	11725.0i	−0.174420	−	0.486815i
$835$	−3077.64	−	3077.64i	−0.127552	−	0.127552i
$836$	−50298.8	+	41351.3i	−2.08088	+	1.71072i
$837$	1967.87	−	1967.87i	0.0812659	−	0.0812659i
$838$	−1105.09	+	2339.11i	−0.0455546	+	0.0964239i
$839$			47615.1i			1.95931i	0.200700	+	0.979653i	$0.435678\pi$
$839$			47615.1i			1.95931i	−0.200700	+	0.979653i	$0.564322\pi$
$840$	12823.5	−	21457.2i	0.526730	−	0.881361i
$841$		−	17357.0i		−	0.711675i
$842$	2267.13	+	1071.09i	0.0927916	+	0.0438386i
$843$	1115.52	−	1115.52i	0.0455759	−	0.0455759i
$844$	33078.1	+	3229.31i	1.34905	+	0.131703i
$845$	18583.3	+	18583.3i	0.756550	+	0.756550i
$846$	−223.910	+	80.2243i	−0.00909949	+	0.00326025i
$847$	78501.2			3.18457
$848$	−12390.7	−	18475.4i	−0.501766	−	0.748169i
$849$	145.213			0.00587007
$850$	−4700.21	+	1684.03i	−0.189666	+	0.0679551i
$851$	−7701.42	−	7701.42i	−0.310225	−	0.310225i
$852$	1151.69	−	11796.8i	0.0463100	−	0.474357i
$853$	−21487.2	+	21487.2i	−0.862495	+	0.862495i	−0.991627	−	0.129132i	$-0.958781\pi$
$853$	−21487.2	+	21487.2i	−0.862495	+	0.862495i	0.129132	+	0.991627i	$0.458781\pi$
$854$	−39465.1	−	18644.9i	−1.58134	−	0.747091i
$855$		−	14480.3i		−	0.579201i
$856$	13140.8	−	3309.55i	0.524701	−	0.132147i
$857$		−	2056.71i		−	0.0819788i	−0.999160	−	0.0409894i	$-0.986949\pi$
$857$		−	2056.71i		−	0.0819788i	0.999160	−	0.0409894i	$-0.0130510\pi$
$858$	2213.30	−	4684.82i	0.0880663	−	0.186407i
$859$	16324.5	−	16324.5i	0.648410	−	0.648410i	−0.304198	−	0.952609i	$-0.598389\pi$
$859$	16324.5	−	16324.5i	0.648410	−	0.648410i	0.952609	+	0.304198i	$0.0983885\pi$
$860$	−3590.07	−	4366.88i	−0.142349	−	0.173150i
$861$	6617.36	+	6617.36i	0.261927	+	0.261927i
$862$	−6634.49	−	18517.2i	−0.262148	−	0.731667i
$863$	7623.05			0.300686			0.150343	−	0.988634i	$-0.451962\pi$
$863$	7623.05			0.300686			0.150343	+	0.988634i	$0.451962\pi$
$864$	2903.08	−	3931.92i	0.114311	−	0.154822i
$865$	25424.3			0.999367
$866$	−2694.44	−	7520.29i	−0.105728	−	0.295092i
$867$	3576.27	+	3576.27i	0.140088	+	0.140088i
$868$	−15435.4	−	18775.3i	−0.603584	−	0.734186i
$869$	24712.3	−	24712.3i	0.964679	−	0.964679i
$870$	3797.24	−	8037.49i	0.147975	−	0.313214i
$871$		−	8131.73i		−	0.316341i
$872$	9989.87	+	39665.5i	0.387958	+	1.54042i
$873$			12835.1i			0.497597i
$874$	−31893.9	−	15068.0i	−1.23436	−	0.583160i
$875$	24457.2	−	24457.2i	0.944918	−	0.944918i
$876$	77.6289	−	795.160i	0.00299411	−	0.0306689i
$877$	16409.6	+	16409.6i	0.631829	+	0.631829i	0.948527	−	0.316697i	$-0.102574\pi$
$877$	16409.6	+	16409.6i	0.631829	+	0.631829i	−0.316697	+	0.948527i	$0.602574\pi$
$878$	−9404.32	+	3369.46i	−0.361481	+	0.129515i
$879$	−3577.64			−0.137282
$880$	49577.2	+	9773.28i	1.89914	+	0.374383i
$881$	9804.39			0.374935			0.187468	−	0.982271i	$-0.439972\pi$
$881$	9804.39			0.374935			0.187468	+	0.982271i	$0.439972\pi$
$882$	12601.1	−	4514.85i	0.481069	−	0.172362i
$883$	−22496.3	−	22496.3i	−0.857372	−	0.857372i	0.133656	−	0.991028i	$-0.457328\pi$
$883$	−22496.3	−	22496.3i	−0.857372	−	0.857372i	−0.991028	+	0.133656i	$0.957328\pi$
$884$	4370.17	+	426.645i	0.166272	+	0.0162326i
$885$	12939.7	−	12939.7i	0.491485	−	0.491485i
$886$	45191.9	+	21350.5i	1.71360	+	0.809576i
$887$			48295.5i			1.82819i	0.405500	+	0.914095i	$0.367097\pi$
$887$			48295.5i			1.82819i	−0.405500	+	0.914095i	$0.632903\pi$
$888$	−6553.69	−	3916.70i	−0.247666	−	0.148013i
$889$			16771.4i			0.632727i
$890$	14099.7	−	29844.4i	0.531038	−	1.12403i
$891$	−3619.81	+	3619.81i	−0.136104	+	0.136104i
$892$	−33625.3	+	27643.8i	−1.26217	+	1.03765i
$893$	850.878	+	850.878i	0.0318853	+	0.0318853i
$894$	−3524.54	−	9837.14i	−0.131855	−	0.368013i
$895$	−56737.2			−2.11901
$896$	−31713.9	−	28571.1i	−1.18246	−	1.06528i
$897$	2806.86			0.104480
$898$	9874.11	+	27559.1i	0.366930	+	1.02412i
$899$	−6111.83	−	6111.83i	−0.226742	−	0.226742i
$900$	−1728.23	+	1420.80i	−0.0640086	+	0.0526223i
$901$	−13962.3	+	13962.3i	−0.516263	+	0.516263i
$902$	−8081.09	+	17105.0i	−0.298305	+	0.631412i
$903$		−	5001.80i		−	0.184330i
$904$	−5888.39	−	3519.09i	−0.216643	−	0.129473i
$905$		−	34705.7i		−	1.27476i
$906$	−24549.2	−	11598.1i	−0.900214	−	0.425298i
$907$	−2318.33	+	2318.33i	−0.0848721	+	0.0848721i	−0.748268	−	0.663396i	$-0.769114\pi$
$907$	−2318.33	+	2318.33i	−0.0848721	+	0.0848721i	0.663396	+	0.748268i	$0.269114\pi$
$908$	−19376.9	−	1891.70i	−0.708198	−	0.0691391i
$909$	544.019	+	544.019i	0.0198503	+	0.0198503i
$910$	9473.52	−	3394.26i	0.345104	−	0.123647i
$911$	−26365.2			−0.958856			−0.479428	−	0.877581i	$-0.659156\pi$
$911$	−26365.2			−0.958856			−0.479428	+	0.877581i	$0.659156\pi$
$912$	−24260.2	−	4782.47i	−0.880849	−	0.173644i
$913$	−1655.17			−0.0599979
$914$	−16641.3	+	5962.38i	−0.602236	+	0.215774i
$915$	13874.6	+	13874.6i	0.501288	+	0.501288i
$916$	−1324.44	+	13566.3i	−0.0477736	+	0.489349i
$917$	−243.849	+	243.849i	−0.00878145	+	0.00878145i
$918$	−3922.55	−	1853.17i	−0.141028	−	0.0666272i
$919$		−	16124.3i		−	0.578771i	−0.957213	−	0.289385i	$-0.906549\pi$
$919$		−	16124.3i		−	0.578771i	0.957213	−	0.289385i	$-0.0934509\pi$
$920$	6685.46	+	26545.2i	0.239580	+	0.951269i
$921$			10447.7i			0.373791i
$922$	8412.15	−	17805.7i	0.300477	−	0.636009i
$923$	3374.10	−	3374.10i	0.120325	−	0.120325i
$924$	28392.7	+	34536.3i	1.01088	+	1.22961i
$925$	2471.27	+	2471.27i	0.0878432	+	0.0878432i
$926$	−16438.7	−	45881.1i	−0.583378	−	1.62823i
$927$	−10867.2			−0.385032
$928$	−12211.8	−	9016.42i	−0.431974	−	0.318942i
$929$	−35451.9			−1.25203			−0.626017	−	0.779809i	$-0.715316\pi$
$929$	−35451.9			−1.25203			−0.626017	+	0.779809i	$0.715316\pi$
$930$	3685.41	+	10286.1i	0.129946	+	0.362684i
$931$	−47885.6	−	47885.6i	−1.68570	−	1.68570i
$932$	16218.0	+	19727.2i	0.569997	+	0.693332i
$933$	18036.6	−	18036.6i	0.632896	−	0.632896i
$934$	21713.7	−	45960.7i	0.760701	−	1.61015i
$935$		−	44852.8i		−	1.56881i
$936$	1908.02	−	480.540i	0.0666299	−	0.0167809i
$937$		−	8527.49i		−	0.297311i	−0.988889	−	0.148656i	$-0.952505\pi$
$937$		−	8527.49i		−	0.297311i	0.988889	−	0.148656i	$-0.0474946\pi$
$938$	63443.6	+	29973.3i	2.20843	+	1.04335i
$939$	−16944.4	+	16944.4i	−0.588881	+	0.588881i
$940$	90.7350	−	929.407i	0.00314835	−	0.0322488i
$941$	9106.05	+	9106.05i	0.315461	+	0.315461i	0.847021	−	0.531560i	$-0.178394\pi$
$941$	9106.05	+	9106.05i	0.315461	+	0.315461i	−0.531560	+	0.847021i	$0.678394\pi$
$942$	2618.72	−	938.257i	0.0905758	−	0.0324523i
$943$	−10248.3			−0.353902
$944$	−17405.4	−	25952.7i	−0.600104	−	0.894798i
$945$	−9942.52			−0.342254
$946$	9518.58	−	3410.40i	0.327141	−	0.117211i
$947$	21636.3	+	21636.3i	0.742436	+	0.742436i	0.973046	−	0.230611i	$-0.0740723\pi$
$947$	21636.3	+	21636.3i	0.742436	+	0.742436i	−0.230611	+	0.973046i	$0.574072\pi$
$948$	13208.8	+	1289.53i	0.452533	+	0.0441793i
$949$	227.430	−	227.430i	0.00777944	−	0.00777944i
$950$	10234.3	+	4835.09i	0.349520	+	0.165127i
$951$		−	13254.9i		−	0.451965i
$952$	−19437.0	+	32523.4i	−0.661720	+	1.10724i
$953$			16328.5i			0.555018i	0.960723	+	0.277509i	$0.0895089\pi$
$953$			16328.5i			0.555018i	−0.960723	+	0.277509i	$0.910491\pi$
$954$	−3779.65	+	8000.25i	−0.128271	+	0.271507i
$955$	−19354.4	+	19354.4i	−0.655805	+	0.655805i
$956$	26537.0	−	21816.4i	0.897771	−	0.738069i
$957$	11242.4	+	11242.4i	0.379746	+	0.379746i
$958$	5677.85	+	15847.1i	0.191485	+	0.534444i
$959$	−50034.6			−1.68478
$960$	9089.15	+	16900.0i	0.305574	+	0.568173i
$961$	−19166.8			−0.643376
$962$	−1036.71	−	2893.51i	−0.0347452	−	0.0969755i
$963$	−3811.27	−	3811.27i	−0.127535	−	0.127535i
$964$	−9260.27	+	7612.99i	−0.309391	+	0.254355i
$965$	−15793.0	+	15793.0i	−0.526832	+	0.526832i
$966$	−10346.0	+	21899.1i	−0.344594	+	0.729391i
$967$		−	17097.5i		−	0.568581i	−0.958738	−	0.284291i	$-0.908242\pi$
$967$		−	17097.5i		−	0.568581i	0.958738	−	0.284291i	$-0.0917580\pi$
$968$	−30914.4	+	51728.1i	−1.02647	+	1.71757i
$969$			21948.3i			0.727638i
$970$	−45563.5	−	21526.1i	−1.50820	−	0.712536i
$971$	−13762.3	+	13762.3i	−0.454843	+	0.454843i	−0.896958	−	0.442115i	$-0.854228\pi$
$971$	−13762.3	+	13762.3i	−0.454843	+	0.454843i	0.442115	+	0.896958i	$0.354228\pi$
$972$	−1934.80	−	188.888i	−0.0638465	−	0.00623313i
$973$	30593.3	+	30593.3i	1.00799	+	1.00799i
$974$	14555.5	−	5215.08i	0.478838	−	0.171562i
$975$	−900.680			−0.0295845
$976$	27827.7	−	18662.9i	0.912645	−	0.612074i
$977$	−10832.5			−0.354720			−0.177360	−	0.984146i	$-0.556756\pi$
$977$	−10832.5			−0.354720			−0.177360	+	0.984146i	$0.556756\pi$
$978$	14128.2	−	5061.99i	0.461934	−	0.165506i
$979$	41744.9	+	41744.9i	1.36279	+	1.36279i
$980$	−5106.37	+	52305.0i	−0.166446	+	1.70492i
$981$	11504.3	−	11504.3i	0.374418	−	0.374418i
$982$	16282.9	+	7692.69i	0.529131	+	0.249983i
$983$		−	37641.1i		−	1.22133i	−0.791890	−	0.610664i	$-0.790903\pi$
$983$		−	37641.1i		−	1.22133i	0.791890	−	0.610664i	$-0.209097\pi$
$984$	−6966.46	+	1754.52i	−0.225694	+	0.0568415i
$985$		−	53275.0i		−	1.72333i
$986$	−5755.60	+	12182.7i	−0.185898	+	0.393484i
$987$	584.232	−	584.232i	0.0188413	−	0.0188413i
$988$	−6321.68	−	7689.55i	−0.203562	−	0.247608i
$989$	3873.13	+	3873.13i	0.124528	+	0.124528i
$990$	−6779.16	−	18920.9i	−0.217632	−	0.607421i
$991$	−2392.58			−0.0766931			−0.0383466	−	0.999265i	$-0.512209\pi$
$991$	−2392.58			−0.0766931			−0.0383466	+	0.999265i	$0.512209\pi$
$992$	18450.5	−	2777.25i	0.590527	−	0.0888890i
$993$	−21326.8			−0.681558
$994$	13887.8	+	38761.5i	0.443154	+	1.23686i
$995$	−23157.2	−	23157.2i	−0.737822	−	0.737822i
$996$	−399.161	−	485.531i	−0.0126987	−	0.0154464i
$997$	15496.4	−	15496.4i	0.492252	−	0.492252i	−0.416763	−	0.909015i	$-0.636836\pi$
$997$	15496.4	−	15496.4i	0.492252	−	0.492252i	0.909015	+	0.416763i	$0.136836\pi$
$998$	−7657.46	+	16208.3i	−0.242878	+	0.514093i
$999$			3036.75i			0.0961748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.8	✓	24
3.2	odd	2		144.4.k.b.109.5		24
4.3	odd	2		192.4.j.a.145.8		24
8.3	odd	2		384.4.j.a.289.2		24
8.5	even	2		384.4.j.b.289.11		24
12.11	even	2		576.4.k.b.145.10		24
16.3	odd	4		384.4.j.a.97.2		24
16.5	even	4	inner	48.4.j.a.37.8	yes	24
16.11	odd	4		192.4.j.a.49.8		24
16.13	even	4		384.4.j.b.97.11		24
48.5	odd	4		144.4.k.b.37.5		24
48.11	even	4		576.4.k.b.433.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.8	✓	24	1.1	even	1	trivial
48.4.j.a.37.8	yes	24	16.5	even	4	inner
144.4.k.b.37.5		24	48.5	odd	4
144.4.k.b.109.5		24	3.2	odd	2
192.4.j.a.49.8		24	16.11	odd	4
192.4.j.a.145.8		24	4.3	odd	2
384.4.j.a.97.2		24	16.3	odd	4
384.4.j.a.289.2		24	8.3	odd	2
384.4.j.b.97.11		24	16.13	even	4
384.4.j.b.289.11		24	8.5	even	2
576.4.k.b.145.10		24	12.11	even	2
576.4.k.b.433.10		24	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.954009 + 2.66268i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.17974 + 5.08044i) q^{4} +(-8.83384 + 8.83384i) q^{5} +(3.62464 - 7.67216i) q^{6} +29.4760i q^{7} +(-19.4231 - 11.6079i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(0.954009 + 2.66268i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.17974 + 5.08044i) q^{4} +(-8.83384 + 8.83384i) q^{5} +(3.62464 - 7.67216i) q^{6} +29.4760i q^{7} +(-19.4231 - 11.6079i) q^{8} +9.00000i q^{9} +(-31.9493 - 15.0941i) q^{10} +(44.6891 - 44.6891i) q^{11} +(23.8864 + 2.33196i) q^{12} +(6.83195 + 6.83195i) q^{13} +(-78.4851 + 28.1203i) q^{14} +37.4788 q^{15} +(12.3783 - 62.7916i) q^{16} -56.8078 q^{17} +(-23.9641 + 8.58608i) q^{18} +(91.0660 + 91.0660i) q^{19} +(9.71099 - 99.4706i) q^{20} +(62.5280 - 62.5280i) q^{21} +(161.626 + 76.3590i) q^{22} +96.8367i q^{23} +(16.5786 + 65.8267i) q^{24} -31.0735i q^{25} +(-11.6736 + 24.7090i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-149.751 - 182.154i) q^{28} +(-59.2957 - 59.2957i) q^{29} +(35.7551 + 99.7941i) q^{30} +103.074 q^{31} +(179.003 - 26.9444i) q^{32} -189.600 q^{33} +(-54.1952 - 151.261i) q^{34} +(-260.386 - 260.386i) q^{35} +(-45.7240 - 55.6176i) q^{36} +(-79.5300 + 79.5300i) q^{37} +(-155.602 + 329.357i) q^{38} -28.9855i q^{39} +(274.123 - 69.0385i) q^{40} +105.830i q^{41} +(226.144 + 106.840i) q^{42} +(39.9965 - 39.9965i) q^{43} +(-49.1265 + 503.207i) q^{44} +(-79.5046 - 79.5046i) q^{45} +(-257.845 + 92.3831i) q^{46} +9.34353 q^{47} +(-159.459 + 106.943i) q^{48} -525.834 q^{49} +(82.7387 - 29.6444i) q^{50} +(120.508 + 120.508i) q^{51} +(-76.9289 - 7.51033i) q^{52} +(245.782 - 245.782i) q^{53} +(69.0494 + 32.6218i) q^{54} +789.552i q^{55} +(342.154 - 572.515i) q^{56} -386.360i q^{57} +(101.317 - 214.454i) q^{58} +(345.255 - 345.255i) q^{59} +(-231.609 + 190.409i) q^{60} +(370.197 + 370.197i) q^{61} +(98.3331 + 274.452i) q^{62} -265.284 q^{63} +(242.514 + 450.922i) q^{64} -120.705 q^{65} +(-180.880 - 504.843i) q^{66} +(-595.125 - 595.125i) q^{67} +(351.057 - 288.609i) q^{68} +(205.422 - 205.422i) q^{69} +(444.915 - 941.736i) q^{70} -493.871i q^{71} +(104.471 - 174.808i) q^{72} -33.2892i q^{73} +(-287.635 - 135.891i) q^{74} +(-65.9168 + 65.9168i) q^{75} +(-1025.42 - 100.108i) q^{76} +(1317.25 + 1317.25i) q^{77} +(77.1791 - 27.6524i) q^{78} +552.982 q^{79} +(445.343 + 664.038i) q^{80} -81.0000 q^{81} +(-281.792 + 100.963i) q^{82} +(-18.5187 - 18.5187i) q^{83} +(-68.7367 + 704.076i) q^{84} +(501.831 - 501.831i) q^{85} +(144.655 + 68.3409i) q^{86} +251.570i q^{87} +(-1386.75 + 349.255i) q^{88} +934.120i q^{89} +(135.847 - 287.543i) q^{90} +(-201.378 + 201.378i) q^{91} +(-491.973 - 598.425i) q^{92} +(-218.652 - 218.652i) q^{93} +(8.91381 + 24.8788i) q^{94} -1608.93 q^{95} +(-436.880 - 322.565i) q^{96} +1426.12 q^{97} +(-501.650 - 1400.13i) q^{98} +(402.202 + 402.202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more