LMFDB - Embedded newform 48.4.j.a.37.9

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			37.9
Character	$\chi$	$=$	48.37
Dual form			48.4.j.a.13.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94824 + 2.05046i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-0.408732 + 7.98955i) q^{4} +(2.24191 + 2.24191i) q^{5} +(-8.48251 - 0.216833i) q^{6} +9.00196i q^{7} +(-17.1785 + 14.7275i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(1.94824 + 2.05046i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-0.408732 + 7.98955i) q^{4} +(2.24191 + 2.24191i) q^{5} +(-8.48251 - 0.216833i) q^{6} +9.00196i q^{7} +(-17.1785 + 14.7275i) q^{8} -9.00000i q^{9} +(-0.229160 + 8.96471i) q^{10} +(11.0476 + 11.0476i) q^{11} +(-16.0813 - 17.8154i) q^{12} +(54.5799 - 54.5799i) q^{13} +(-18.4581 + 17.5380i) q^{14} -9.51162 q^{15} +(-63.6659 - 6.53116i) q^{16} +44.0029 q^{17} +(18.4541 - 17.5341i) q^{18} +(49.9906 - 49.9906i) q^{19} +(-18.8282 + 16.9955i) q^{20} +(-19.0960 - 19.0960i) q^{21} +(-1.12925 + 44.1761i) q^{22} +117.070i q^{23} +(5.19947 - 67.6828i) q^{24} -114.948i q^{25} +(218.248 + 5.57895i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-71.9216 - 3.67938i) q^{28} +(40.6415 - 40.6415i) q^{29} +(-18.5309 - 19.5031i) q^{30} -196.655 q^{31} +(-110.644 - 143.268i) q^{32} -46.8712 q^{33} +(85.7281 + 90.2259i) q^{34} +(-20.1816 + 20.1816i) q^{35} +(71.9060 + 3.67858i) q^{36} +(-248.601 - 248.601i) q^{37} +(199.897 + 5.10985i) q^{38} +231.563i q^{39} +(-71.5304 - 5.49504i) q^{40} +457.402i q^{41} +(1.95192 - 76.3592i) q^{42} +(204.721 + 204.721i) q^{43} +(-92.7813 + 83.7502i) q^{44} +(20.1772 - 20.1772i) q^{45} +(-240.048 + 228.081i) q^{46} -390.477 q^{47} +(148.910 - 121.201i) q^{48} +261.965 q^{49} +(235.695 - 223.946i) q^{50} +(-93.3442 + 93.3442i) q^{51} +(413.760 + 458.377i) q^{52} +(-138.315 - 138.315i) q^{53} +(-1.95150 + 76.3426i) q^{54} +49.5357i q^{55} +(-132.576 - 154.640i) q^{56} +212.092i q^{57} +(162.513 + 4.15422i) q^{58} +(-263.209 - 263.209i) q^{59} +(3.88770 - 75.9936i) q^{60} +(29.1443 - 29.1443i) q^{61} +(-383.132 - 403.233i) q^{62} +81.0176 q^{63} +(78.2033 - 505.992i) q^{64} +244.726 q^{65} +(-91.3163 - 96.1073i) q^{66} +(508.985 - 508.985i) q^{67} +(-17.9854 + 351.563i) q^{68} +(-248.344 - 248.344i) q^{69} +(-80.6999 - 2.06289i) q^{70} -788.707i q^{71} +(132.547 + 154.607i) q^{72} -92.2717i q^{73} +(25.4111 - 994.081i) q^{74} +(243.841 + 243.841i) q^{75} +(378.969 + 419.835i) q^{76} +(-99.4504 + 99.4504i) q^{77} +(-474.809 + 451.140i) q^{78} -174.554 q^{79} +(-128.091 - 157.375i) q^{80} -81.0000 q^{81} +(-937.882 + 891.128i) q^{82} +(914.838 - 914.838i) q^{83} +(160.374 - 144.764i) q^{84} +(98.6505 + 98.6505i) q^{85} +(-20.9258 + 818.615i) q^{86} +172.427i q^{87} +(-352.486 - 27.0784i) q^{88} +1454.97i q^{89} +(80.6824 + 2.06244i) q^{90} +(491.326 + 491.326i) q^{91} +(-935.340 - 47.8504i) q^{92} +(417.169 - 417.169i) q^{93} +(-760.742 - 800.655i) q^{94} +224.149 q^{95} +(538.630 + 69.2056i) q^{96} -229.203 q^{97} +(510.370 + 537.147i) q^{98} +(99.4288 - 99.4288i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.94824	+	2.05046i	0.688806	+	0.724945i
$2$	1.94824	+	2.05046i	0.688806	+	0.724945i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$	−0.408732	+	7.98955i	−0.0510914	+	0.998694i
$5$	2.24191	+	2.24191i	0.200523	+	0.200523i	0.800224	−	0.599701i	$-0.204714\pi$
$5$	2.24191	+	2.24191i	0.200523	+	0.200523i	−0.599701	+	0.800224i	$0.704714\pi$
$6$	−8.48251	−	0.216833i	−0.577162	−	0.0147536i
$7$			9.00196i			0.486060i	0.970019	+	0.243030i	$0.0781413\pi$
$7$			9.00196i			0.486060i	−0.970019	+	0.243030i	$0.921859\pi$
$8$	−17.1785	+	14.7275i	−0.759191	+	0.650868i
$9$		−	9.00000i		−	0.333333i
$10$	−0.229160	+	8.96471i	−0.00724666	+	0.283489i
$11$	11.0476	+	11.0476i	0.302817	+	0.302817i	0.842115	−	0.539298i	$-0.181310\pi$
$11$	11.0476	+	11.0476i	0.302817	+	0.302817i	−0.539298	+	0.842115i	$0.681310\pi$
$12$	−16.0813	−	17.8154i	−0.386857	−	0.428573i
$13$	54.5799	−	54.5799i	1.16444	−	1.16444i	0.180949	−	0.983493i	$-0.442083\pi$
$13$	54.5799	−	54.5799i	1.16444	−	1.16444i	0.983493	−	0.180949i	$-0.0579168\pi$
$14$	−18.4581	+	17.5380i	−0.352367	+	0.334801i
$15$	−9.51162			−0.163726
$16$	−63.6659	−	6.53116i	−0.994779	−	0.102049i
$17$	44.0029			0.627780			0.313890	−	0.949459i	$-0.398368\pi$
$17$	44.0029			0.627780			0.313890	+	0.949459i	$0.398368\pi$
$18$	18.4541	−	17.5341i	0.241648	−	0.229602i
$19$	49.9906	−	49.9906i	0.603612	−	0.603612i	−0.337657	−	0.941269i	$-0.609635\pi$
$19$	49.9906	−	49.9906i	0.603612	−	0.603612i	0.941269	+	0.337657i	$0.109635\pi$
$20$	−18.8282	+	16.9955i	−0.210506	+	0.190016i
$21$	−19.0960	−	19.0960i	−0.198433	−	0.198433i
$22$	−1.12925	+	44.1761i	−0.0109435	+	0.428108i
$23$			117.070i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$23$			117.070i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$24$	5.19947	−	67.6828i	0.0442224	−	0.575654i
$25$		−	114.948i		−	0.919581i
$26$	218.248	+	5.57895i	1.64623	+	0.0420816i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	−71.9216	−	3.67938i	−0.485425	−	0.0248335i
$29$	40.6415	−	40.6415i	0.260239	−	0.260239i	−0.564912	−	0.825151i	$-0.691090\pi$
$29$	40.6415	−	40.6415i	0.260239	−	0.260239i	0.825151	+	0.564912i	$0.191090\pi$
$30$	−18.5309	−	19.5031i	−0.112775	−	0.118692i
$31$	−196.655			−1.13937			−0.569683	−	0.821865i	$-0.692934\pi$
$31$	−196.655			−1.13937			−0.569683	+	0.821865i	$0.692934\pi$
$32$	−110.644	−	143.268i	−0.611230	−	0.791453i
$33$	−46.8712			−0.247249
$34$	85.7281	+	90.2259i	0.432419	+	0.455106i
$35$	−20.1816	+	20.1816i	−0.0974660	+	0.0974660i
$36$	71.9060	+	3.67858i	0.332898	+	0.0170305i
$37$	−248.601	−	248.601i	−1.10459	−	1.10459i	−0.993849	−	0.110741i	$-0.964678\pi$
$37$	−248.601	−	248.601i	−1.10459	−	1.10459i	−0.110741	−	0.993849i	$-0.535322\pi$
$38$	199.897	+	5.10985i	0.853357	+	0.0218139i
$39$			231.563i			0.950762i
$40$	−71.5304	−	5.49504i	−0.282749	−	0.0217211i
$41$			457.402i			1.74230i	0.491021	+	0.871148i	$0.336624\pi$
$41$			457.402i			1.74230i	−0.491021	+	0.871148i	$0.663376\pi$
$42$	1.95192	−	76.3592i	0.00717116	−	0.280535i
$43$	204.721	+	204.721i	0.726037	+	0.726037i	0.969828	−	0.243791i	$-0.0783910\pi$
$43$	204.721	+	204.721i	0.726037	+	0.726037i	−0.243791	+	0.969828i	$0.578391\pi$
$44$	−92.7813	+	83.7502i	−0.317893	+	0.286950i
$45$	20.1772	−	20.1772i	0.0668408	−	0.0668408i
$46$	−240.048	+	228.081i	−0.769415	+	0.731059i
$47$	−390.477			−1.21185			−0.605924	−	0.795522i	$-0.707197\pi$
$47$	−390.477			−1.21185			−0.605924	+	0.795522i	$0.707197\pi$
$48$	148.910	−	121.201i	0.447778	−	0.364455i
$49$	261.965			0.763746
$50$	235.695	−	223.946i	0.666646	−	0.633414i
$51$	−93.3442	+	93.3442i	−0.256290	+	0.256290i
$52$	413.760	+	458.377i	1.10343	+	1.22241i
$53$	−138.315	−	138.315i	−0.358473	−	0.358473i	0.504777	−	0.863250i	$-0.331575\pi$
$53$	−138.315	−	138.315i	−0.358473	−	0.358473i	−0.863250	+	0.504777i	$0.831575\pi$
$54$	−1.95150	+	76.3426i	−0.00491788	+	0.192387i
$55$			49.5357i			0.121443i
$56$	−132.576	−	154.640i	−0.316361	−	0.369012i
$57$			212.092i			0.492847i
$58$	162.513	+	4.15422i	0.367914	+	0.00940477i
$59$	−263.209	−	263.209i	−0.580796	−	0.580796i	0.354326	−	0.935122i	$-0.384710\pi$
$59$	−263.209	−	263.209i	−0.580796	−	0.580796i	−0.935122	+	0.354326i	$0.884710\pi$
$60$	3.88770	−	75.9936i	0.00836500	−	0.163512i
$61$	29.1443	−	29.1443i	0.0611729	−	0.0611729i	−0.675858	−	0.737031i	$-0.736227\pi$
$61$	29.1443	−	29.1443i	0.0611729	−	0.0611729i	0.737031	+	0.675858i	$0.236227\pi$
$62$	−383.132	−	403.233i	−0.784802	−	0.825978i
$63$	81.0176			0.162020
$64$	78.2033	−	505.992i	0.152741	−	0.988266i
$65$	244.726			0.466993
$66$	−91.3163	−	96.1073i	−0.170307	−	0.179242i
$67$	508.985	−	508.985i	0.928095	−	0.928095i	−0.0694876	−	0.997583i	$-0.522136\pi$
$67$	508.985	−	508.985i	0.928095	−	0.928095i	0.997583	+	0.0694876i	$0.0221364\pi$
$68$	−17.9854	+	351.563i	−0.0320742	+	0.626960i
$69$	−248.344	−	248.344i	−0.433291	−	0.433291i
$70$	−80.6999	−	2.06289i	−0.137793	−	0.00352231i
$71$		−	788.707i		−	1.31834i	−0.751993	−	0.659171i	$-0.770907\pi$
$71$		−	788.707i		−	1.31834i	0.751993	−	0.659171i	$-0.229093\pi$
$72$	132.547	+	154.607i	0.216956	+	0.253064i
$73$		−	92.2717i		−	0.147940i	−0.997260	−	0.0739698i	$-0.976433\pi$
$73$		−	92.2717i		−	0.147940i	0.997260	−	0.0739698i	$-0.0235668\pi$
$74$	25.4111	−	994.081i	0.0399187	−	1.56162i
$75$	243.841	+	243.841i	0.375418	+	0.375418i
$76$	378.969	+	419.835i	0.571984	+	0.633663i
$77$	−99.4504	+	99.4504i	−0.147187	+	0.147187i
$78$	−474.809	+	451.140i	−0.689251	+	0.654891i
$79$	−174.554			−0.248593			−0.124297	−	0.992245i	$-0.539667\pi$
$79$	−174.554			−0.248593			−0.124297	+	0.992245i	$0.539667\pi$
$80$	−128.091	−	157.375i	−0.179012	−	0.219939i
$81$	−81.0000			−0.111111
$82$	−937.882	+	891.128i	−1.26307	+	1.20010i
$83$	914.838	−	914.838i	1.20984	−	1.20984i	0.238759	−	0.971079i	$-0.423259\pi$
$83$	914.838	−	914.838i	1.20984	−	1.20984i	0.971079	−	0.238759i	$-0.0767405\pi$
$84$	160.374	−	144.764i	0.208312	−	0.188036i
$85$	98.6505	+	98.6505i	0.125884	+	0.125884i
$86$	−20.9258	+	818.615i	−0.0262382	+	1.02644i
$87$			172.427i			0.212485i
$88$	−352.486	−	27.0784i	−0.426990	−	0.0328019i
$89$			1454.97i			1.73289i	0.499277	+	0.866443i	$0.333599\pi$
$89$			1454.97i			1.73289i	−0.499277	+	0.866443i	$0.666401\pi$
$90$	80.6824	+	2.06244i	0.0944964	+	0.00241555i
$91$	491.326	+	491.326i	0.565988	+	0.565988i
$92$	−935.340	−	47.8504i	−1.05996	−	0.0542255i
$93$	417.169	−	417.169i	0.465144	−	0.465144i
$94$	−760.742	−	800.655i	−0.834729	−	0.878524i
$95$	224.149			0.242075
$96$	538.630	+	69.2056i	0.572643	+	0.0735756i
$97$	−229.203			−0.239918			−0.119959	−	0.992779i	$-0.538276\pi$
$97$	−229.203			−0.239918			−0.119959	+	0.992779i	$0.538276\pi$
$98$	510.370	+	537.147i	0.526073	+	0.553674i
$99$	99.4288	−	99.4288i	0.100939	−	0.100939i
$100$	918.380	+	46.9827i	0.918380	+	0.0469827i
$101$	700.059	+	700.059i	0.689688	+	0.689688i	0.962163	−	0.272475i	$-0.0878421\pi$
$101$	700.059	+	700.059i	0.689688	+	0.689688i	−0.272475	+	0.962163i	$0.587842\pi$
$102$	−373.255	−	9.54129i	−0.362331	−	0.00926205i
$103$		−	35.5591i		−	0.0340169i	−0.999855	−	0.0170085i	$-0.994586\pi$
$103$		−	35.5591i		−	0.0340169i	0.999855	−	0.0170085i	$-0.00541422\pi$
$104$	−133.778	+	1741.43i	−0.126135	+	1.64193i
$105$		−	85.6232i		−	0.0795806i
$106$	14.1381	−	553.080i	0.0129548	−	0.506792i
$107$	−946.695	−	946.695i	−0.855331	−	0.855331i	0.135453	−	0.990784i	$-0.456751\pi$
$107$	−946.695	−	946.695i	−0.855331	−	0.855331i	−0.990784	+	0.135453i	$0.956751\pi$
$108$	−160.339	+	144.732i	−0.142858	+	0.128952i
$109$	−1362.69	+	1362.69i	−1.19745	+	1.19745i	−0.222527	+	0.974927i	$0.571430\pi$
$109$	−1362.69	+	1362.69i	−1.19745	+	1.19745i	−0.974927	+	0.222527i	$0.928570\pi$
$110$	−101.571	+	96.5073i	−0.0880398	+	0.0836510i
$111$	1054.73			0.901894
$112$	58.7932	−	573.117i	0.0496021	−	0.483522i
$113$	−93.4714			−0.0778146			−0.0389073	−	0.999243i	$-0.512388\pi$
$113$	−93.4714			−0.0778146			−0.0389073	+	0.999243i	$0.512388\pi$
$114$	−434.885	+	413.206i	−0.357287	+	0.339476i
$115$	−262.461	+	262.461i	−0.212823	+	0.212823i
$116$	308.096	+	341.319i	0.246603	+	0.273195i
$117$	−491.219	−	491.219i	−0.388147	−	0.388147i
$118$	26.9043	−	1052.49i	0.0209893	−	0.821101i
$119$			396.112i			0.305139i
$120$	163.396	−	140.082i	0.124299	−	0.106564i
$121$		−	1086.90i		−	0.816603i
$122$	116.539	+	2.97902i	0.0864833	+	0.00221072i
$123$	−970.295	−	970.295i	−0.711289	−	0.711289i
$124$	80.3792	−	1571.19i	0.0582118	−	1.13788i
$125$	537.941	−	537.941i	0.384919	−	0.384919i
$126$	157.842	+	166.123i	0.111600	+	0.117456i
$127$	−2074.24			−1.44928			−0.724640	−	0.689127i	$-0.757994\pi$
$127$	−2074.24			−1.44928			−0.724640	+	0.689127i	$0.757994\pi$
$128$	1189.87	−	825.441i	0.821648	−	0.569995i
$129$	−868.556			−0.592807
$130$	476.785	+	501.800i	0.321668	+	0.338545i
$131$	−1180.76	+	1180.76i	−0.787510	+	0.787510i	−0.981085	−	0.193575i	$-0.937992\pi$
$131$	−1180.76	+	1180.76i	−0.787510	+	0.787510i	0.193575	+	0.981085i	$0.437992\pi$
$132$	19.1577	−	374.480i	0.0126323	−	0.246926i
$133$	450.013	+	450.013i	0.293391	+	0.293391i
$134$	2035.27	+	52.0265i	1.31210	+	0.0335403i
$135$			85.6046i			0.0545753i
$136$	−755.904	+	648.051i	−0.476605	+	0.408602i
$137$		−	1095.24i		−	0.683012i	−0.939880	−	0.341506i	$-0.889063\pi$
$137$		−	1095.24i		−	0.683012i	0.939880	−	0.341506i	$-0.110937\pi$
$138$	25.3848	−	993.051i	0.0156587	−	0.612566i
$139$	1577.81	+	1577.81i	0.962790	+	0.962790i	0.999332	−	0.0365418i	$-0.0116342\pi$
$139$	1577.81	+	1577.81i	0.962790	+	0.962790i	−0.0365418	+	0.999332i	$0.511634\pi$
$140$	−152.993	−	169.491i	−0.0923590	−	0.102318i
$141$	828.326	−	828.326i	0.494735	−	0.494735i
$142$	1617.21	−	1536.59i	0.955726	−	0.908082i
$143$	1205.96			0.705226
$144$	−58.7805	+	572.993i	−0.0340165	+	0.331593i
$145$	182.229			0.104368
$146$	189.199	−	179.767i	0.107248	−	0.101902i
$147$	−555.711	+	555.711i	−0.311798	+	0.311798i
$148$	2087.83	−	1884.60i	1.15958	−	1.04671i
$149$	576.268	+	576.268i	0.316844	+	0.316844i	0.847554	−	0.530710i	$-0.178075\pi$
$149$	576.268	+	576.268i	0.316844	+	0.316844i	−0.530710	+	0.847554i	$0.678075\pi$
$150$	−24.9245	+	975.045i	−0.0135672	+	0.530747i
$151$			352.096i			0.189756i	0.995489	+	0.0948779i	$0.0302461\pi$
$151$			352.096i			0.189756i	−0.995489	+	0.0948779i	$0.969754\pi$
$152$	−122.530	+	1595.00i	−0.0653846	+	0.851128i
$153$		−	396.026i		−	0.209260i
$154$	−397.672	−	10.1654i	−0.208086	−	0.00531919i
$155$	−440.884	−	440.884i	−0.228469	−	0.228469i
$156$	−1850.08	−	94.6470i	−0.949520	−	0.0485758i
$157$	−748.006	+	748.006i	−0.380238	+	0.380238i	−0.871188	−	0.490950i	$-0.836650\pi$
$157$	−748.006	+	748.006i	−0.380238	+	0.380238i	0.490950	+	0.871188i	$0.336650\pi$
$158$	−340.073	−	357.915i	−0.171233	−	0.180216i
$159$	586.822			0.292692
$160$	73.1396	−	569.250i	0.0361387	−	0.281270i
$161$	−1053.86			−0.515876
$162$	−157.807	−	166.087i	−0.0765340	−	0.0805495i
$163$	−1909.06	+	1909.06i	−0.917355	+	0.917355i	−0.996836	−	0.0794815i	$-0.974674\pi$
$163$	−1909.06	+	1909.06i	−0.917355	+	0.917355i	0.0794815	+	0.996836i	$0.474674\pi$
$164$	−3654.43	−	186.954i	−1.74002	−	0.0890164i
$165$	−105.081	−	105.081i	−0.0495791	−	0.0495791i
$166$	3658.16	+	93.5113i	1.71041	+	0.0437222i
$167$		−	471.378i		−	0.218421i	−0.994019	−	0.109211i	$-0.965168\pi$
$167$		−	471.378i		−	0.218421i	0.994019	−	0.109211i	$-0.0348323\pi$
$168$	609.278	+	46.8054i	0.279802	+	0.0214947i
$169$		−	3760.93i		−	1.71185i
$170$	−10.0837	+	394.473i	−0.00454931	+	0.177969i
$171$	−449.915	−	449.915i	−0.201204	−	0.201204i
$172$	−1719.30	+	1551.95i	−0.762183	+	0.687995i
$173$	406.351	−	406.351i	0.178580	−	0.178580i	−0.612157	−	0.790736i	$-0.709698\pi$
$173$	406.351	−	406.351i	0.178580	−	0.178580i	0.790736	+	0.612157i	$0.209698\pi$
$174$	−353.555	+	335.930i	−0.154040	+	0.146361i
$175$	1034.75			0.446972
$176$	−631.204	−	775.512i	−0.270334	−	0.332139i
$177$	1116.70			0.474218
$178$	−2983.36	+	2834.63i	−1.25625	+	1.19362i
$179$	−2017.10	+	2017.10i	−0.842262	+	0.842262i	−0.989153	−	0.146890i	$-0.953074\pi$
$179$	−2017.10	+	2017.10i	−0.842262	+	0.842262i	0.146890	+	0.989153i	$0.453074\pi$
$180$	152.960	+	169.454i	0.0633386	+	0.0701685i
$181$	2278.23	+	2278.23i	0.935578	+	0.935578i	0.998047	−	0.0624686i	$-0.0198973\pi$
$181$	2278.23	+	2278.23i	0.935578	+	0.935578i	−0.0624686	+	0.998047i	$0.519897\pi$
$182$	−50.2215	+	1964.66i	−0.0204542	+	0.800167i
$183$			123.649i			0.0499475i
$184$	−1724.15	−	2011.10i	−0.690794	−	0.805761i
$185$		−	1114.68i		−	0.442990i
$186$	1668.13	+	42.6414i	0.657598	+	0.0168098i
$187$	486.128	+	486.128i	0.190103	+	0.190103i
$188$	159.600	−	3119.73i	0.0619151	−	1.21027i
$189$	−171.864	+	171.864i	−0.0661444	+	0.0661444i
$190$	436.695	+	459.607i	0.166743	+	0.175491i
$191$	3432.87			1.30049			0.650245	−	0.759725i	$-0.274666\pi$
$191$	3432.87			1.30049			0.650245	+	0.759725i	$0.274666\pi$
$192$	907.478	+	1239.27i	0.341102	+	0.465814i
$193$	331.880			0.123779			0.0618893	−	0.998083i	$-0.480287\pi$
$193$	331.880			0.123779			0.0618893	+	0.998083i	$0.480287\pi$
$194$	−446.542	−	469.970i	−0.165257	−	0.173927i
$195$	−519.143	+	519.143i	−0.190649	+	0.190649i
$196$	−107.073	+	2092.98i	−0.0390209	+	0.762748i
$197$	−2602.11	−	2602.11i	−0.941080	−	0.941080i	0.0572783	−	0.998358i	$-0.481758\pi$
$197$	−2602.11	−	2602.11i	−0.941080	−	0.941080i	−0.998358	+	0.0572783i	$0.981758\pi$
$198$	397.585	+	10.1632i	0.142703	+	0.00364783i
$199$		−	1727.40i		−	0.615339i	−0.951493	−	0.307669i	$-0.900451\pi$
$199$		−	1727.40i		−	0.615339i	0.951493	−	0.307669i	$-0.0995490\pi$
$200$	1692.89	+	1974.63i	0.598526	+	0.698138i
$201$			2159.44i			0.757787i
$202$	−71.5575	+	2799.32i	−0.0249246	+	0.975048i
$203$	365.853	+	365.853i	0.126492	+	0.126492i
$204$	−707.625	−	783.931i	−0.242861	−	0.269050i
$205$	−1025.45	+	1025.45i	−0.349370	+	0.349370i
$206$	72.9123	−	69.2776i	0.0246604	−	0.0234311i
$207$	1053.63			0.353781
$208$	−3831.35	+	3118.41i	−1.27719	+	1.03953i
$209$	1104.56			0.365568
$210$	175.566	−	166.814i	0.0576916	−	0.0548156i
$211$	2406.47	−	2406.47i	0.785156	−	0.785156i	−0.195540	−	0.980696i	$-0.562646\pi$
$211$	2406.47	−	2406.47i	0.785156	−	0.785156i	0.980696	+	0.195540i	$0.0626458\pi$
$212$	1161.61	−	1048.54i	0.376320	−	0.339690i
$213$	1673.10	+	1673.10i	0.538211	+	0.538211i
$214$	96.7676	−	3785.54i	0.0309107	−	1.20923i
$215$			917.931i			0.291174i
$216$	−609.145	−	46.7952i	−0.191885	−	0.0147408i
$217$		−	1770.28i		−	0.553800i
$218$	−5449.00	−	139.289i	−1.69290	−	0.0432746i
$219$	195.738	+	195.738i	0.0603961	+	0.0603961i
$220$	−395.768	−	20.2468i	−0.121285	−	0.00620472i
$221$	2401.67	−	2401.67i	0.731013	−	0.731013i
$222$	2054.86	+	2162.67i	0.621230	+	0.653824i
$223$	−1772.23			−0.532184			−0.266092	−	0.963948i	$-0.585732\pi$
$223$	−1772.23			−0.532184			−0.266092	+	0.963948i	$0.585732\pi$
$224$	1289.69	−	996.017i	0.384694	−	0.297094i
$225$	−1034.53			−0.306527
$226$	−182.105	−	191.659i	−0.0535992	−	0.0564113i
$227$	−410.406	+	410.406i	−0.119998	+	0.119998i	−0.764556	−	0.644558i	$-0.777042\pi$
$227$	−410.406	+	410.406i	−0.119998	+	0.119998i	0.644558	+	0.764556i	$0.277042\pi$
$228$	−1694.52	−	86.6887i	−0.492203	−	0.0251803i
$229$	207.155	+	207.155i	0.0597780	+	0.0597780i	0.736364	−	0.676586i	$-0.236541\pi$
$229$	207.155	+	207.155i	0.0597780	+	0.0597780i	−0.676586	+	0.736364i	$0.736541\pi$
$230$	−1049.50	−	26.8278i	−0.300879	−	0.00769119i
$231$		−	421.932i		−	0.120178i
$232$	−99.6146	+	1296.71i	−0.0281897	+	0.366953i
$233$		−	2283.00i		−	0.641908i	−0.947095	−	0.320954i	$-0.895997\pi$
$233$		−	2283.00i		−	0.641908i	0.947095	−	0.320954i	$-0.104003\pi$
$234$	50.2106	−	1964.23i	0.0140272	−	0.548744i
$235$	−875.414	−	875.414i	−0.243003	−	0.243003i
$236$	2210.51	−	1995.34i	0.609711	−	0.550364i
$237$	370.285	−	370.285i	0.101488	−	0.101488i
$238$	−812.210	+	771.720i	−0.221209	+	0.210182i
$239$	1097.58			0.297058			0.148529	−	0.988908i	$-0.452546\pi$
$239$	1097.58			0.297058			0.148529	+	0.988908i	$0.452546\pi$
$240$	605.566	+	62.1219i	0.162871	+	0.0167081i
$241$	3892.54			1.04042			0.520209	−	0.854039i	$-0.325854\pi$
$241$	3892.54			1.04042			0.520209	+	0.854039i	$0.325854\pi$
$242$	2228.64	−	2117.54i	0.591993	−	0.562482i
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$	220.938	+	244.762i	0.0579676	+	0.0642184i
$245$	587.302	+	587.302i	0.153148	+	0.153148i
$246$	99.1800	−	3879.91i	0.0257052	−	1.00559i
$247$		−	5456.96i		−	1.40574i
$248$	3378.25	−	2896.24i	0.864996	−	0.741577i
$249$			3881.33i			0.987828i
$250$	2151.06	+	54.9863i	0.544180	+	0.0139106i
$251$	−984.886	−	984.886i	−0.247671	−	0.247671i	0.572343	−	0.820014i	$-0.306035\pi$
$251$	−984.886	−	984.886i	−0.247671	−	0.247671i	−0.820014	+	0.572343i	$0.806035\pi$
$252$	−33.1144	+	647.294i	−0.00827783	+	0.161808i
$253$	−1293.35	+	1293.35i	−0.321393	+	0.321393i
$254$	−4041.11	−	4253.13i	−0.998274	−	1.05065i
$255$	−418.539			−0.102784
$256$	4010.69	+	831.624i	0.979172	+	0.203033i
$257$	−6204.15			−1.50585			−0.752927	−	0.658104i	$-0.771359\pi$
$257$	−6204.15			−1.50585			−0.752927	+	0.658104i	$0.771359\pi$
$258$	−1692.15	−	1780.94i	−0.408329	−	0.429753i
$259$	2237.90	−	2237.90i	0.536897	−	0.536897i
$260$	−100.027	+	1955.25i	−0.0238594	+	0.466383i
$261$	−365.774	−	365.774i	−0.0867465	−	0.0867465i
$262$	−4721.51	−	120.693i	−1.11334	−	0.0284598i
$263$			5905.73i			1.38465i	0.721586	+	0.692325i	$0.243413\pi$
$263$			5905.73i			1.38465i	−0.721586	+	0.692325i	$0.756587\pi$
$264$	805.178	−	690.294i	0.187709	−	0.160927i
$265$		−	620.181i		−	0.143764i
$266$	−45.9986	+	1799.46i	−0.0106028	+	0.414783i
$267$	−3086.46	−	3086.46i	−0.707447	−	0.707447i
$268$	3858.52	+	4274.60i	0.879465	+	0.974301i
$269$	−3932.01	+	3932.01i	−0.891222	+	0.891222i	−0.994638	−	0.103416i	$-0.967023\pi$
$269$	−3932.01	+	3932.01i	−0.891222	+	0.891222i	0.103416	+	0.994638i	$0.467023\pi$
$270$	−175.528	+	166.778i	−0.0395641	+	0.0375918i
$271$	−3555.50			−0.796978			−0.398489	−	0.917173i	$-0.630465\pi$
$271$	−3555.50			−0.796978			−0.398489	+	0.917173i	$0.630465\pi$
$272$	−2801.48	−	287.390i	−0.624503	−	0.0640646i
$273$	−2084.52			−0.462127
$274$	2245.74	−	2133.79i	0.495146	−	0.470463i
$275$	1269.90	−	1269.90i	0.278465	−	0.278465i
$276$	2085.66	−	1882.65i	0.454863	−	0.410588i
$277$	2068.37	+	2068.37i	0.448651	+	0.448651i	0.894906	−	0.446255i	$-0.147243\pi$
$277$	2068.37	+	2068.37i	0.448651	+	0.448651i	−0.446255	+	0.894906i	$0.647243\pi$
$278$	−161.278	+	6309.17i	−0.0347942	+	1.36115i
$279$			1769.90i			0.379789i
$280$	49.4661	−	643.913i	0.0105577	−	0.137433i
$281$			8952.86i			1.90065i	0.311259	+	0.950325i	$0.399249\pi$
$281$			8952.86i			1.90065i	−0.311259	+	0.950325i	$0.600751\pi$
$282$	3312.22	+	84.6684i	0.699433	+	0.0178792i
$283$	−9.56186	−	9.56186i	−0.00200846	−	0.00200846i	0.706102	−	0.708110i	$-0.250452\pi$
$283$	−9.56186	−	9.56186i	−0.00200846	−	0.00200846i	−0.708110	+	0.706102i	$0.750452\pi$
$284$	6301.41	+	322.369i	1.31662	+	0.0673560i
$285$	−475.491	+	475.491i	−0.0988269	+	0.0988269i
$286$	2349.49	+	2472.76i	0.485764	+	0.511250i
$287$	−4117.51			−0.846860
$288$	−1289.41	+	995.800i	−0.263818	+	0.203743i
$289$	−2976.75			−0.605892
$290$	355.026	+	373.653i	0.0718891	+	0.0756609i
$291$	486.213	−	486.213i	0.0979461	−	0.0979461i
$292$	737.210	+	37.7144i	0.147746	+	0.00755845i
$293$	−1846.37	−	1846.37i	−0.368143	−	0.368143i	0.498656	−	0.866800i	$-0.333827\pi$
$293$	−1846.37	−	1846.37i	−0.368143	−	0.368143i	−0.866800	+	0.498656i	$0.833827\pi$
$294$	−2222.12	−	56.8027i	−0.440805	−	0.0112680i
$295$		−	1180.18i		−	0.232925i
$296$	7931.88	+	609.336i	1.55754	+	0.119652i
$297$			421.841i			0.0824164i
$298$	−58.9040	+	2304.32i	−0.0114504	+	0.447939i
$299$	6389.69	+	6389.69i	1.23587	+	1.23587i
$300$	−2047.84	+	1848.51i	−0.394108	+	0.355747i
$301$	−1842.89	+	1842.89i	−0.352898	+	0.352898i
$302$	−721.956	+	685.966i	−0.137563	+	0.130705i
$303$	−2970.10			−0.563128
$304$	−3509.19	+	2856.20i	−0.662059	+	0.538862i
$305$	130.678			0.0245331
$306$	812.033	−	771.553i	0.151702	−	0.144140i
$307$	3022.83	−	3022.83i	0.561961	−	0.561961i	−0.367903	−	0.929864i	$-0.619924\pi$
$307$	3022.83	−	3022.83i	0.561961	−	0.561961i	0.929864	+	0.367903i	$0.119924\pi$
$308$	−753.916	−	835.213i	−0.139475	−	0.154515i
$309$	75.4322	+	75.4322i	0.0138873	+	0.0138873i
$310$	45.0655	−	1762.96i	0.00825660	−	0.322998i
$311$			123.709i			0.0225560i	0.999936	+	0.0112780i	$0.00358997\pi$
$311$			123.709i			0.0225560i	−0.999936	+	0.0112780i	$0.996410\pi$
$312$	−3410.33	−	3977.91i	−0.618821	−	0.721810i
$313$			8413.05i			1.51928i	0.650345	+	0.759639i	$0.274624\pi$
$313$			8413.05i			1.51928i	−0.650345	+	0.759639i	$0.725376\pi$
$314$	−2991.05	−	76.4584i	−0.537562	−	0.0137414i
$315$	181.634	+	181.634i	0.0324887	+	0.0324887i
$316$	71.3457	−	1394.61i	0.0127010	−	0.248269i
$317$	3201.27	−	3201.27i	0.567196	−	0.567196i	−0.364146	−	0.931342i	$-0.618639\pi$
$317$	3201.27	−	3201.27i	0.567196	−	0.567196i	0.931342	+	0.364146i	$0.118639\pi$
$318$	1143.27	+	1203.25i	0.201608	+	0.212186i
$319$	897.986			0.157610
$320$	1309.71	−	959.065i	0.228798	−	0.167542i
$321$	4016.49			0.698375
$322$	−2053.18	−	2160.90i	−0.355338	−	0.373982i
$323$	2199.73	−	2199.73i	0.378935	−	0.378935i
$324$	33.1073	−	647.154i	0.00567683	−	0.110966i
$325$	−6273.83	−	6273.83i	−1.07080	−	1.07080i
$326$	−7633.73	−	195.137i	−1.29691	−	0.0331522i
$327$		−	5781.42i		−	0.977716i
$328$	−6736.37	−	7857.48i	−1.13401	−	1.32273i
$329$		−	3515.05i		−	0.589031i
$330$	10.7410	−	420.187i	0.00179173	−	0.0700925i
$331$	−3154.15	−	3154.15i	−0.523770	−	0.523770i	0.394938	−	0.918708i	$-0.370766\pi$
$331$	−3154.15	−	3154.15i	−0.523770	−	0.523770i	−0.918708	+	0.394938i	$0.870766\pi$
$332$	6935.22	+	7683.07i	1.14645	+	1.27007i
$333$	−2237.41	+	2237.41i	−0.368197	+	0.368197i
$334$	966.540	−	918.357i	0.158343	−	0.150450i
$335$	2282.20			0.372208
$336$	1091.05	+	1340.48i	0.177147	+	0.217647i
$337$	1697.70			0.274421			0.137210	−	0.990542i	$-0.456186\pi$
$337$	1697.70			0.274421			0.137210	+	0.990542i	$0.456186\pi$
$338$	7711.61	−	7327.18i	1.24099	−	1.17913i
$339$	198.283	−	198.283i	0.0317677	−	0.0317677i
$340$	−828.495	+	747.852i	−0.132151	+	0.119288i
$341$	−2172.58	−	2172.58i	−0.345020	−	0.345020i
$342$	45.9886	−	1799.07i	0.00727129	−	0.284452i
$343$			5445.87i			0.857286i
$344$	−6531.82	−	501.781i	−1.02376	−	0.0786460i
$345$		−	1113.53i		−	0.173769i
$346$	1624.87	+	41.5357i	0.252467	+	0.00645368i
$347$	−823.789	−	823.789i	−0.127445	−	0.127445i	0.640507	−	0.767952i	$-0.278724\pi$
$347$	−823.789	−	823.789i	−0.127445	−	0.127445i	−0.767952	+	0.640507i	$0.778724\pi$
$348$	−1377.62	−	70.4765i	−0.212207	−	0.0108561i
$349$	8381.74	−	8381.74i	1.28557	−	1.28557i	0.348120	−	0.937450i	$-0.386820\pi$
$349$	8381.74	−	8381.74i	1.28557	−	1.28557i	0.937450	−	0.348120i	$-0.113180\pi$
$350$	2015.95	+	2121.72i	0.307877	+	0.324030i
$351$	2084.07			0.316921
$352$	360.416	−	2805.14i	0.0545746	−	0.424757i
$353$	9390.45			1.41587			0.707937	−	0.706276i	$-0.249626\pi$
$353$	9390.45			1.41587			0.707937	+	0.706276i	$0.249626\pi$
$354$	2175.60	+	2289.75i	0.326644	+	0.343782i
$355$	1768.21	−	1768.21i	0.264357	−	0.264357i
$356$	−11624.6	−	594.693i	−1.73062	−	0.0885356i
$357$	−840.280	−	840.280i	−0.124572	−	0.124572i
$358$	−8065.76	−	206.180i	−1.19075	−	0.0304384i
$359$			449.651i			0.0661049i	0.999454	+	0.0330524i	$0.0105228\pi$
$359$			449.651i			0.0661049i	−0.999454	+	0.0330524i	$0.989477\pi$
$360$	−49.4554	+	643.773i	−0.00724036	+	0.0942495i
$361$			1860.89i			0.271306i
$362$	−232.872	+	9109.95i	−0.0338108	+	1.32268i
$363$	2305.66	+	2305.66i	0.333377	+	0.333377i
$364$	−4126.29	+	3724.65i	−0.594166	+	0.536332i
$365$	206.865	−	206.865i	0.0296652	−	0.0296652i
$366$	−253.536	+	240.898i	−0.0362092	+	0.0344041i
$367$	−4578.45			−0.651207			−0.325603	−	0.945506i	$-0.605567\pi$
$367$	−4578.45			−0.651207			−0.325603	+	0.945506i	$0.605567\pi$
$368$	764.606	−	7453.39i	0.108309	−	1.05580i
$369$	4116.61			0.580765
$370$	2285.61	−	2171.67i	0.321144	−	0.305135i
$371$	1245.11	−	1245.11i	0.174239	−	0.174239i
$372$	3162.48	+	3503.50i	0.440772	+	0.488302i
$373$	−1494.93	−	1494.93i	−0.207520	−	0.207520i	0.595693	−	0.803212i	$-0.296878\pi$
$373$	−1494.93	−	1494.93i	−0.207520	−	0.207520i	−0.803212	+	0.595693i	$0.796878\pi$
$374$	−49.6902	+	1943.88i	−0.00687010	+	0.268758i
$375$			2282.29i			0.314285i
$376$	6707.81	−	5750.73i	0.920024	−	0.788754i
$377$		−	4436.42i		−	0.606067i
$378$	−687.233	−	17.5673i	−0.0935117	−	0.00239039i
$379$	5939.03	+	5939.03i	0.804927	+	0.804927i	0.983861	−	0.178934i	$-0.0572649\pi$
$379$	5939.03	+	5939.03i	0.804927	+	0.804927i	−0.178934	+	0.983861i	$0.557265\pi$
$380$	−91.6166	+	1790.85i	−0.0123680	+	0.241759i
$381$	4400.12	−	4400.12i	0.591666	−	0.591666i
$382$	6688.05	+	7038.94i	0.895786	+	0.942784i
$383$	−4497.11			−0.599978			−0.299989	−	0.953943i	$-0.596983\pi$
$383$	−4497.11			−0.599978			−0.299989	+	0.953943i	$0.596983\pi$
$384$	−773.077	+	4275.13i	−0.102737	+	0.568136i
$385$	−445.918			−0.0590288
$386$	646.582	+	680.506i	0.0852595	+	0.0897327i
$387$	1842.49	−	1842.49i	0.242012	−	0.242012i
$388$	93.6825	−	1831.23i	0.0122578	−	0.239605i
$389$	−3539.12	−	3539.12i	−0.461287	−	0.461287i	0.437790	−	0.899077i	$-0.355761\pi$
$389$	−3539.12	−	3539.12i	−0.461287	−	0.461287i	−0.899077	+	0.437790i	$0.855761\pi$
$390$	−2075.89	−	53.0649i	−0.269531	−	0.00688986i
$391$			5151.43i			0.666289i
$392$	−4500.17	+	3858.08i	−0.579829	+	0.497098i
$393$		−	5009.56i		−	0.642999i
$394$	265.978	−	10405.0i	0.0340096	−	1.33045i
$395$	−391.334	−	391.334i	−0.0498485	−	0.0498485i
$396$	753.752	+	835.031i	0.0956501	+	0.105964i
$397$	604.283	−	604.283i	0.0763932	−	0.0763932i	−0.667878	−	0.744271i	$-0.732797\pi$
$397$	604.283	−	604.283i	0.0763932	−	0.0763932i	0.744271	+	0.667878i	$0.232797\pi$
$398$	3541.96	−	3365.39i	0.446087	−	0.423849i
$399$	−1909.24			−0.239553
$400$	−750.742	+	7318.24i	−0.0938428	+	0.914781i
$401$	4518.24			0.562668			0.281334	−	0.959610i	$-0.409223\pi$
$401$	4518.24			0.562668			0.281334	+	0.959610i	$0.409223\pi$
$402$	−4427.83	+	4207.10i	−0.549354	+	0.521968i
$403$	−10733.4	+	10733.4i	−1.32672	+	1.32672i
$404$	−5879.30	+	5307.02i	−0.724025	+	0.653550i
$405$	−181.595	−	181.595i	−0.0222803	−	0.0222803i
$406$	−37.3961	+	1462.93i	−0.00457128	+	0.178828i
$407$		−	5492.92i		−	0.668978i
$408$	228.792	−	2978.24i	0.0277619	−	0.361384i
$409$			9999.05i			1.20885i	0.796660	+	0.604427i	$0.206598\pi$
$409$			9999.05i			1.20885i	−0.796660	+	0.604427i	$0.793402\pi$
$410$	−4100.47	−	104.818i	−0.493922	−	0.0126258i
$411$	2323.35	+	2323.35i	0.278838	+	0.278838i
$412$	284.101	+	14.5341i	0.0339725	+	0.00173797i
$413$	2369.40	−	2369.40i	0.282302	−	0.282302i
$414$	2052.73	+	2160.43i	0.243686	+	0.256472i
$415$	4101.97			0.485199
$416$	−13858.5	−	1780.60i	−1.63334	−	0.209859i
$417$	−6694.07			−0.786115
$418$	2151.94	+	2264.84i	0.251806	+	0.265017i
$419$	2613.92	−	2613.92i	0.304769	−	0.304769i	−0.538107	−	0.842876i	$-0.680860\pi$
$419$	2613.92	−	2613.92i	0.304769	−	0.304769i	0.842876	+	0.538107i	$0.180860\pi$
$420$	684.091	+	34.9969i	0.0794767	+	0.00406589i
$421$	−1245.36	−	1245.36i	−0.144168	−	0.144168i	0.631339	−	0.775507i	$-0.282506\pi$
$421$	−1245.36	−	1245.36i	−0.144168	−	0.144168i	−0.775507	+	0.631339i	$0.782506\pi$
$422$	9622.72	+	245.980i	1.11002	+	0.0283747i
$423$			3514.29i			0.403949i
$424$	4413.09	+	339.018i	0.505468	+	0.0388306i
$425$		−	5058.03i		−	0.577295i
$426$	−171.018	+	6690.21i	−0.0194504	+	0.760897i
$427$	262.356	+	262.356i	0.0297337	+	0.0297337i
$428$	7950.61	−	7176.72i	0.897914	−	0.810514i
$429$	−2558.22	+	2558.22i	−0.287907	+	0.287907i
$430$	−1882.18	+	1788.35i	−0.211085	+	0.200562i
$431$	−15126.6			−1.69054			−0.845269	−	0.534341i	$-0.820560\pi$
$431$	−15126.6			−1.69054			−0.845269	+	0.534341i	$0.820560\pi$
$432$	−1090.81	−	1340.19i	−0.121485	−	0.149259i
$433$	8672.65			0.962543			0.481271	−	0.876572i	$-0.340175\pi$
$433$	8672.65			0.962543			0.481271	+	0.876572i	$0.340175\pi$
$434$	3629.88	−	3448.93i	0.401475	−	0.381461i
$435$	−386.567	+	386.567i	−0.0426079	+	0.0426079i
$436$	−10330.3	−	11444.3i	−1.13471	−	1.25707i
$437$	5852.41	+	5852.41i	0.640638	+	0.640638i
$438$	−20.0076	+	782.696i	−0.00218265	+	0.0853851i
$439$			11290.4i			1.22748i	0.789508	+	0.613740i	$0.210336\pi$
$439$			11290.4i			1.22748i	−0.789508	+	0.613740i	$0.789664\pi$
$440$	−729.535	−	850.949i	−0.0790437	−	0.0921987i
$441$		−	2357.68i		−	0.254582i
$442$	9603.55	+	245.490i	1.03347	+	0.0264180i
$443$	−3150.02	−	3150.02i	−0.337838	−	0.337838i	0.517715	−	0.855553i	$-0.326783\pi$
$443$	−3150.02	−	3150.02i	−0.337838	−	0.337838i	−0.855553	+	0.517715i	$0.826783\pi$
$444$	−431.100	+	8426.79i	−0.0460791	+	0.900716i
$445$	−3261.92	+	3261.92i	−0.347483	+	0.347483i
$446$	−3452.72	−	3633.87i	−0.366572	−	0.385804i
$447$	−2444.90			−0.258702
$448$	4554.92	+	703.983i	0.480357	+	0.0742412i
$449$	−11125.0			−1.16931			−0.584656	−	0.811281i	$-0.698770\pi$
$449$	−11125.0			−1.16931			−0.584656	+	0.811281i	$0.698770\pi$
$450$	−2015.51	−	2121.26i	−0.211138	−	0.222215i
$451$	−5053.21	+	5053.21i	−0.527597	+	0.527597i
$452$	38.2047	−	746.794i	0.00397566	−	0.0777130i
$453$	−746.908	−	746.908i	−0.0774675	−	0.0774675i
$454$	−1641.09	−	41.9502i	−0.169648	−	0.00433661i
$455$			2203.02i			0.226987i
$456$	−3123.58	−	3643.43i	−0.320778	−	0.374165i
$457$		−	7940.94i		−	0.812826i	−0.913690	−	0.406413i	$-0.866779\pi$
$457$		−	7940.94i		−	0.812826i	0.913690	−	0.406413i	$-0.133221\pi$
$458$	−21.1746	+	828.348i	−0.00216031	+	0.0845113i
$459$	840.098	+	840.098i	0.0854301	+	0.0854301i
$460$	−1989.67	−	2204.22i	−0.201672	−	0.223418i
$461$	−2550.31	+	2550.31i	−0.257657	+	0.257657i	−0.824101	−	0.566443i	$-0.808319\pi$
$461$	−2550.31	+	2550.31i	−0.257657	+	0.257657i	0.566443	+	0.824101i	$0.308319\pi$
$462$	865.153	−	822.025i	0.0871225	−	0.0827794i
$463$	15821.1			1.58805			0.794027	−	0.607883i	$-0.207981\pi$
$463$	15821.1			1.58805			0.794027	+	0.607883i	$0.207981\pi$
$464$	−2852.91	+	2322.04i	−0.285438	+	0.232323i
$465$	1870.51			0.186544
$466$	4681.19	−	4447.83i	0.465348	−	0.442150i
$467$	−3890.78	+	3890.78i	−0.385533	+	0.385533i	−0.873091	−	0.487558i	$-0.837888\pi$
$467$	−3890.78	+	3890.78i	−0.385533	+	0.385533i	0.487558	+	0.873091i	$0.337888\pi$
$468$	4125.40	−	3723.84i	0.407471	−	0.367809i
$469$	4581.86	+	4581.86i	0.451110	+	0.451110i
$470$	89.4815	−	3500.51i	0.00878186	−	0.343546i
$471$		−	3173.52i		−	0.310463i
$472$	8397.96	+	645.141i	0.818956	+	0.0629131i
$473$			4523.36i			0.439713i
$474$	1480.66	+	37.8491i	0.143478	+	0.00366766i
$475$	−5746.30	−	5746.30i	−0.555070	−	0.555070i
$476$	−3164.76	−	161.903i	−0.304740	−	0.0155900i
$477$	−1244.84	+	1244.84i	−0.119491	+	0.119491i
$478$	2138.36	+	2250.55i	0.204615	+	0.215351i
$479$	14574.8			1.39027			0.695136	−	0.718878i	$-0.255344\pi$
$479$	14574.8			1.39027			0.695136	+	0.718878i	$0.255344\pi$
$480$	1052.41	+	1362.71i	0.100074	+	0.129581i
$481$	−27137.3			−2.57246
$482$	7583.60	+	7981.48i	0.716646	+	0.754246i
$483$	2235.58	−	2235.58i	0.210605	−	0.210605i
$484$	8683.84	+	444.250i	0.815537	+	0.0417214i
$485$	−513.852	−	513.852i	−0.0481089	−	0.0481089i
$486$	687.083	+	17.5635i	0.0641291	+	0.00163929i
$487$			343.996i			0.0320081i	0.999872	+	0.0160040i	$0.00509446\pi$
$487$			343.996i			0.0320081i	−0.999872	+	0.0160040i	$0.994906\pi$
$488$	−71.4343	+	929.878i	−0.00662639	+	0.0862574i
$489$		−	8099.44i		−	0.749017i
$490$	−60.0318	+	2348.44i	−0.00553461	+	0.216514i
$491$	−4602.72	−	4602.72i	−0.423051	−	0.423051i	0.463202	−	0.886253i	$-0.346700\pi$
$491$	−4602.72	−	4602.72i	−0.423051	−	0.423051i	−0.886253	+	0.463202i	$0.846700\pi$
$492$	8148.82	−	7355.64i	0.746701	−	0.674020i
$493$	1788.34	−	1788.34i	0.163373	−	0.163373i
$494$	11189.2	−	10631.5i	1.01909	−	0.968283i
$495$	445.821			0.0404811
$496$	12520.2	+	1284.39i	1.13342	+	0.116272i
$497$	7099.90			0.640793
$498$	−7958.49	+	7561.76i	−0.716122	+	0.680422i
$499$	−887.498	+	887.498i	−0.0796189	+	0.0796189i	−0.745795	−	0.666176i	$-0.767930\pi$
$499$	−887.498	+	887.498i	−0.0796189	+	0.0796189i	0.666176	+	0.745795i	$0.267930\pi$
$500$	4078.04	+	4517.78i	0.364751	+	0.404083i
$501$	999.944	+	999.944i	0.0891701	+	0.0891701i
$502$	100.671	−	3938.26i	0.00895057	−	0.350146i
$503$		−	22299.9i		−	1.97674i	−0.152060	−	0.988371i	$-0.548591\pi$
$503$		−	22299.9i		−	1.97674i	0.152060	−	0.988371i	$-0.451409\pi$
$504$	−1391.76	+	1193.18i	−0.123004	+	0.105454i
$505$			3138.94i			0.276596i
$506$	−5171.72	−	132.202i	−0.454369	−	0.0116148i
$507$	7978.13	+	7978.13i	0.698858	+	0.698858i
$508$	847.805	−	16572.2i	0.0740458	−	1.44739i
$509$	−9078.73	+	9078.73i	−0.790585	+	0.790585i	−0.981589	−	0.191005i	$-0.938825\pi$
$509$	−9078.73	+	9078.73i	−0.790585	+	0.790585i	0.191005	+	0.981589i	$0.438825\pi$
$510$	−815.413	−	858.194i	−0.0707982	−	0.0745127i
$511$	830.626			0.0719075
$512$	6108.57	+	9843.94i	0.527272	+	0.849697i
$513$	1908.83			0.164282
$514$	−12087.2	−	12721.3i	−1.03724	−	1.09166i
$515$	79.7203	−	79.7203i	0.00682116	−	0.00682116i
$516$	355.006	−	6939.37i	0.0302874	−	0.592033i
$517$	−4313.85	−	4313.85i	−0.366969	−	0.366969i
$518$	8948.67	+	228.750i	0.759039	+	0.0194029i
$519$			1724.00i			0.145810i
$520$	−4204.04	+	3604.20i	−0.354537	+	0.303951i
$521$			4706.81i			0.395795i	0.980223	+	0.197897i	$0.0634113\pi$
$521$			4706.81i			0.395795i	−0.980223	+	0.197897i	$0.936589\pi$
$522$	37.3880	−	1462.62i	0.00313492	−	0.122638i
$523$	−14410.4	−	14410.4i	−1.20482	−	1.20482i	−0.972683	−	0.232137i	$-0.925428\pi$
$523$	−14410.4	−	14410.4i	−1.20482	−	1.20482i	−0.232137	−	0.972683i	$-0.574572\pi$
$524$	−8951.16	−	9916.39i	−0.746247	−	0.826717i
$525$	−2195.04	+	2195.04i	−0.182475	+	0.182475i
$526$	−12109.4	+	11505.8i	−1.00380	+	0.953756i
$527$	−8653.40			−0.715271
$528$	2984.10	+	306.123i	0.245958	+	0.0252316i
$529$	−1538.47			−0.126446
$530$	1271.65	−	1208.26i	0.104221	−	0.0990254i
$531$	−2368.88	+	2368.88i	−0.193599	+	0.193599i
$532$	−3779.34	+	3411.47i	−0.307998	+	0.278018i
$533$	24964.9	+	24964.9i	2.02880	+	2.02880i
$534$	315.487	−	12341.8i	0.0255664	−	1.00016i
$535$		−	4244.81i		−	0.343026i
$536$	−1247.55	+	16239.7i	−0.100533	+	1.30867i
$537$		−	8557.82i		−	0.687704i
$538$	−15722.9	−	401.915i	−1.25997	−	0.0322078i
$539$	2894.09	+	2894.09i	0.231275	+	0.231275i
$540$	−683.942	−	34.9893i	−0.0545040	−	0.00278833i
$541$	17034.4	−	17034.4i	1.35373	−	1.35373i	0.472274	−	0.881452i	$-0.343433\pi$
$541$	17034.4	−	17034.4i	1.35373	−	1.35373i	0.881452	−	0.472274i	$-0.156567\pi$
$542$	−6926.96	−	7290.38i	−0.548963	−	0.577765i
$543$	−9665.72			−0.763896
$544$	−4868.67	−	6304.22i	−0.383718	−	0.496858i
$545$	−6110.07			−0.480233
$546$	−4061.14	−	4274.21i	−0.318316	−	0.335017i
$547$	2119.84	−	2119.84i	0.165699	−	0.165699i	−0.619387	−	0.785086i	$-0.712619\pi$
$547$	2119.84	−	2119.84i	0.165699	−	0.165699i	0.785086	+	0.619387i	$0.212619\pi$
$548$	8750.47	+	447.659i	0.682120	+	0.0348961i
$549$	−262.299	−	262.299i	−0.0203910	−	0.0203910i
$550$	5077.95	+	129.805i	0.393681	+	0.0100634i
$551$		−	4063.39i		−	0.314167i
$552$	7923.65	+	608.704i	0.610966	+	0.0469351i
$553$		−	1571.33i		−	0.120831i
$554$	−211.421	+	8270.78i	−0.0162137	+	0.634281i
$555$	2364.60	+	2364.60i	0.180850	+	0.180850i
$556$	−13250.9	+	11961.1i	−1.01072	+	0.912343i
$557$	−12828.0	+	12828.0i	−0.975837	+	0.975837i	−0.999715	−	0.0238775i	$-0.992399\pi$
$557$	−12828.0	+	12828.0i	−0.975837	+	0.975837i	0.0238775	+	0.999715i	$0.492399\pi$
$558$	−3629.10	+	3448.18i	−0.275326	+	0.261601i
$559$	22347.3			1.69086
$560$	1416.69	−	1153.07i	0.106903	−	0.0870108i
$561$	−2062.47			−0.155218
$562$	−18357.4	+	17442.3i	−1.37787	+	1.30918i
$563$	9385.78	−	9385.78i	0.702600	−	0.702600i	−0.262368	−	0.964968i	$-0.584504\pi$
$563$	9385.78	−	9385.78i	0.702600	−	0.702600i	0.964968	+	0.262368i	$0.0845035\pi$
$564$	6279.39	+	6956.52i	0.468812	+	0.519366i
$565$	−209.554	−	209.554i	−0.0156036	−	0.0156036i
$566$	0.977378	−	38.2350i	7.25835e−5	−	0.00283946i
$567$		−	729.158i		−	0.0540067i
$568$	11615.7	+	13548.8i	0.858067	+	1.00087i
$569$		−	323.243i		−	0.0238156i	−0.999929	−	0.0119078i	$-0.996210\pi$
$569$		−	323.243i		−	0.0238156i	0.999929	−	0.0119078i	$-0.00379046\pi$
$570$	−1901.34	−	48.6029i	−0.139717	−	0.00357150i
$571$	−4407.72	−	4407.72i	−0.323043	−	0.323043i	0.526890	−	0.849933i	$-0.323358\pi$
$571$	−4407.72	−	4407.72i	−0.323043	−	0.323043i	−0.849933	+	0.526890i	$0.823358\pi$
$572$	−492.913	+	9635.07i	−0.0360310	+	0.704305i
$573$	−7282.21	+	7282.21i	−0.530923	+	0.530923i
$574$	−8021.89	−	8442.77i	−0.583323	−	0.613927i
$575$	13457.0			0.975990
$576$	−4553.93	−	703.830i	−0.329422	−	0.0509136i
$577$	6162.62			0.444633			0.222317	−	0.974975i	$-0.428638\pi$
$577$	6162.62			0.444633			0.222317	+	0.974975i	$0.428638\pi$
$578$	−5799.42	−	6103.69i	−0.417342	−	0.439239i
$579$	−704.024	+	704.024i	−0.0505324	+	0.0505324i
$580$	−74.4829	+	1455.93i	−0.00533230	+	0.104231i
$581$	8235.33	+	8235.33i	0.588054	+	0.588054i
$582$	1944.22	+	49.6989i	0.138471	+	0.00353966i
$583$		−	3056.12i		−	0.217104i
$584$	1358.93	+	1585.09i	0.0962892	+	0.112314i
$585$		−	2202.54i		−	0.155664i
$586$	188.729	−	7383.06i	0.0133043	−	0.520463i
$587$	3717.84	+	3717.84i	0.261417	+	0.261417i	0.825630	−	0.564213i	$-0.190820\pi$
$587$	3717.84	+	3717.84i	0.261417	+	0.261417i	−0.564213	+	0.825630i	$0.690820\pi$
$588$	−4212.75	−	4667.02i	−0.295460	−	0.327321i
$589$	−9830.91	+	9830.91i	−0.687735	+	0.687735i
$590$	2419.91	−	2299.28i	0.168858	−	0.160440i
$591$	11039.8			0.768389
$592$	14203.8	+	17451.1i	0.986101	+	1.21155i
$593$	25817.8			1.78788			0.893938	−	0.448190i	$-0.147931\pi$
$593$	25817.8			1.78788			0.893938	+	0.448190i	$0.147931\pi$
$594$	−864.965	+	821.846i	−0.0597474	+	0.0567690i
$595$	−888.047	+	888.047i	−0.0611872	+	0.0611872i
$596$	−4839.66	+	4368.59i	−0.332618	+	0.300242i
$597$	3664.38	+	3664.38i	0.251211	+	0.251211i
$598$	−653.130	+	25550.4i	−0.0446630	+	1.74721i
$599$			6912.23i			0.471496i	0.971814	+	0.235748i	$0.0757540\pi$
$599$			6912.23i			0.471496i	−0.971814	+	0.235748i	$0.924246\pi$
$600$	−7779.98	−	597.667i	−0.529361	−	0.0406661i
$601$		−	417.273i		−	0.0283210i	−0.999900	−	0.0141605i	$-0.995492\pi$
$601$		−	417.273i		−	0.0283210i	0.999900	−	0.0141605i	$-0.00450757\pi$
$602$	−7369.14	−	188.373i	−0.498910	−	0.0127533i
$603$	−4580.86	−	4580.86i	−0.309365	−	0.309365i
$604$	−2813.09	−	143.913i	−0.189508	−	0.00969490i
$605$	2436.73	−	2436.73i	0.163747	−	0.163747i
$606$	−5786.47	−	6090.06i	−0.387886	−	0.408237i
$607$	19837.0			1.32646			0.663229	−	0.748417i	$-0.269186\pi$
$607$	19837.0			1.32646			0.663229	+	0.748417i	$0.269186\pi$
$608$	−12693.2	−	1630.88i	−0.846676	−	0.108785i
$609$	−1552.18			−0.103280
$610$	254.592	+	267.949i	0.0168986	+	0.0177852i
$611$	−21312.2	+	21312.2i	−1.41113	+	1.41113i
$612$	3164.07	+	161.868i	0.208987	+	0.0106914i
$613$	107.526	+	107.526i	0.00708475	+	0.00708475i	0.710640	−	0.703556i	$-0.248405\pi$
$613$	107.526	+	107.526i	0.00708475	+	0.00708475i	−0.703556	+	0.710640i	$0.748405\pi$
$614$	12087.4	+	308.982i	0.794473	+	0.0203086i
$615$		−	4350.63i		−	0.285259i
$616$	243.758	−	3173.06i	0.0159437	−	0.207543i
$617$		−	6836.40i		−	0.446067i	−0.974811	−	0.223033i	$-0.928404\pi$
$617$		−	6836.40i		−	0.446067i	0.974811	−	0.223033i	$-0.0715959\pi$
$618$	−7.71040	+	301.630i	−0.000501873	+	0.0196333i
$619$	2430.46	+	2430.46i	0.157817	+	0.157817i	0.781598	−	0.623782i	$-0.214405\pi$
$619$	2430.46	+	2430.46i	0.157817	+	0.157817i	−0.623782	+	0.781598i	$0.714405\pi$
$620$	3702.67	−	3342.26i	0.239843	−	0.216497i
$621$	−2235.09	+	2235.09i	−0.144430	+	0.144430i
$622$	−253.660	+	241.015i	−0.0163518	+	0.0155367i
$623$	−13097.6			−0.842286
$624$	1512.37	−	14742.6i	0.0970247	−	0.945799i
$625$	−11956.4			−0.765211
$626$	−17250.6	+	16390.6i	−1.10139	+	1.04649i
$627$	−2343.12	+	2343.12i	−0.149243	+	0.149243i
$628$	−5670.50	−	6281.97i	−0.360315	−	0.399168i
$629$	−10939.2	−	10939.2i	−0.693440	−	0.693440i
$630$	−18.5660	+	726.299i	−0.00117410	+	0.0459309i
$631$		−	23225.1i		−	1.46525i	−0.680630	−	0.732627i	$-0.738294\pi$
$631$		−	23225.1i		−	1.46525i	0.680630	−	0.732627i	$-0.261706\pi$
$632$	2998.58	−	2570.74i	0.188730	−	0.161801i
$633$			10209.8i			0.641077i
$634$	12800.9	+	327.222i	0.801874	+	0.0204978i
$635$	−4650.25	−	4650.25i	−0.290613	−	0.290613i
$636$	−239.853	+	4688.44i	−0.0149541	+	0.292310i
$637$	14298.0	−	14298.0i	0.889337	−	0.889337i
$638$	1749.49	+	1841.28i	0.108563	+	0.114259i
$639$	−7098.36			−0.439447
$640$	4518.15	+	817.023i	0.279056	+	0.0504620i
$641$	−19028.9			−1.17254			−0.586270	−	0.810116i	$-0.699404\pi$
$641$	−19028.9			−1.17254			−0.586270	+	0.810116i	$0.699404\pi$
$642$	7825.07	+	8235.62i	0.481045	+	0.506284i
$643$	6412.59	−	6412.59i	0.393293	−	0.393293i	−0.482566	−	0.875860i	$-0.660295\pi$
$643$	6412.59	−	6412.59i	0.393293	−	0.393293i	0.875860	+	0.482566i	$0.160295\pi$
$644$	430.747	−	8419.89i	0.0263568	−	0.515202i
$645$	−1947.22	−	1947.22i	−0.118871	−	0.118871i
$646$	8796.04	+	224.848i	0.535721	+	0.0136943i
$647$		−	6947.77i		−	0.422172i	−0.977468	−	0.211086i	$-0.932300\pi$
$647$		−	6947.77i		−	0.422172i	0.977468	−	0.211086i	$-0.0677000\pi$
$648$	1391.46	−	1192.92i	0.0843545	−	0.0723187i
$649$		−	5815.69i		−	0.351750i
$650$	641.287	−	25087.1i	0.0386975	−	1.51384i
$651$	3755.34	+	3755.34i	0.226088	+	0.226088i
$652$	−14472.2	−	16032.8i	−0.869288	−	0.963026i
$653$	−4068.22	+	4068.22i	−0.243801	+	0.243801i	−0.818420	−	0.574620i	$-0.805150\pi$
$653$	−4068.22	+	4068.22i	−0.243801	+	0.243801i	0.574620	+	0.818420i	$0.305150\pi$
$654$	11854.5	−	11263.6i	0.708791	−	0.673457i
$655$	−5294.33			−0.315827
$656$	2987.36	−	29120.9i	0.177800	−	1.73320i
$657$	−830.446			−0.0493132
$658$	7207.46	−	6848.16i	0.427015	−	0.405728i
$659$	15581.5	−	15581.5i	0.921044	−	0.921044i	−0.0760589	−	0.997103i	$-0.524234\pi$
$659$	15581.5	−	15581.5i	0.921044	−	0.921044i	0.997103	+	0.0760589i	$0.0242337\pi$
$660$	882.500	−	796.600i	0.0520474	−	0.0469812i
$661$	−6272.08	−	6272.08i	−0.369070	−	0.369070i	0.498068	−	0.867138i	$-0.334043\pi$
$661$	−6272.08	−	6272.08i	−0.369070	−	0.369070i	−0.867138	+	0.498068i	$0.834043\pi$
$662$	322.405	−	12612.5i	0.0189285	−	0.740480i
$663$			10189.4i			0.596870i
$664$	−2242.32	+	29188.8i	−0.131052	+	1.70594i
$665$			2017.78i			0.117663i
$666$	−8946.73	−	228.700i	−0.520539	−	0.0133062i
$667$	4757.92	+	4757.92i	0.276203	+	0.276203i
$668$	3766.10	+	192.667i	0.218136	+	0.0111595i
$669$	3759.46	−	3759.46i	0.217263	−	0.217263i
$670$	4446.26	+	4679.54i	0.256379	+	0.269830i
$671$	643.952			0.0370484
$672$	−622.985	+	4848.73i	−0.0357622	+	0.278339i
$673$	22285.5			1.27644			0.638219	−	0.769855i	$-0.279672\pi$
$673$	22285.5			1.27644			0.638219	+	0.769855i	$0.279672\pi$
$674$	3307.53	+	3481.07i	0.189023	+	0.198940i
$675$	2194.57	−	2194.57i	0.125139	−	0.125139i
$676$	30048.1	+	1537.21i	1.70961	+	0.0874607i
$677$	−6022.13	−	6022.13i	−0.341875	−	0.341875i	0.515197	−	0.857072i	$-0.327719\pi$
$677$	−6022.13	−	6022.13i	−0.341875	−	0.341875i	−0.857072	+	0.515197i	$0.827719\pi$
$678$	792.872	+	20.2677i	0.0449116	+	0.00114805i
$679$		−	2063.28i		−	0.116614i
$680$	−3147.54	−	241.798i	−0.177504	−	0.0136361i
$681$		−	1741.21i		−	0.0979782i
$682$	222.073	−	8687.47i	0.0124686	−	0.487772i
$683$	−2638.61	−	2638.61i	−0.147824	−	0.147824i	0.629321	−	0.777145i	$-0.283333\pi$
$683$	−2638.61	−	2638.61i	−0.147824	−	0.147824i	−0.777145	+	0.629321i	$0.783333\pi$
$684$	3778.51	−	3410.73i	0.211221	−	0.190661i
$685$	2455.43	−	2455.43i	0.136959	−	0.136959i
$686$	−11166.5	+	10609.8i	−0.621486	+	0.590504i
$687$	−878.883			−0.0488086
$688$	−11696.7	−	14370.8i	−0.648155	−	0.796339i
$689$	−15098.5			−0.834841
$690$	2283.24	−	2169.42i	0.125973	−	0.119693i
$691$	−21023.6	+	21023.6i	−1.15742	+	1.15742i	−0.172391	+	0.985029i	$0.555149\pi$
$691$	−21023.6	+	21023.6i	−1.15742	+	1.15742i	−0.985029	+	0.172391i	$0.944851\pi$
$692$	3080.47	+	3412.65i	0.169223	+	0.187470i
$693$	895.054	+	895.054i	0.0490624	+	0.0490624i
$694$	84.2046	−	3294.08i	0.00460571	−	0.180175i
$695$			7074.60i			0.386122i
$696$	−2539.42	−	2962.05i	−0.138299	−	0.161316i
$697$			20127.0i			1.09378i
$698$	33516.0	+	856.750i	1.81748	+	0.0464591i
$699$	4842.98	+	4842.98i	0.262058	+	0.262058i
$700$	−422.937	+	8267.22i	−0.0228364	+	0.446388i
$701$	3987.03	−	3987.03i	0.214819	−	0.214819i	−0.591492	−	0.806311i	$-0.701461\pi$
$701$	3987.03	−	3987.03i	0.214819	−	0.214819i	0.806311	+	0.591492i	$0.201461\pi$
$702$	4060.26	+	4273.28i	0.218297	+	0.229750i
$703$	−24855.5			−1.33349
$704$	6453.99	−	4726.06i	0.345517	−	0.253012i
$705$	3714.07			0.198411
$706$	18294.8	+	19254.7i	0.975263	+	1.02643i
$707$	−6301.90	+	6301.90i	−0.335230	+	0.335230i
$708$	−456.432	+	8921.96i	−0.0242285	+	0.473598i
$709$	−4544.18	−	4544.18i	−0.240706	−	0.240706i	0.576436	−	0.817142i	$-0.304443\pi$
$709$	−4544.18	−	4544.18i	−0.240706	−	0.240706i	−0.817142	+	0.576436i	$0.804443\pi$
$710$	7070.53	+	180.740i	0.373736	+	0.00955358i
$711$			1570.99i			0.0828644i
$712$	−21428.1	−	24994.3i	−1.12788	−	1.31559i
$713$		−	23022.5i		−	1.20926i
$714$	85.8903	−	3360.02i	0.00450191	−	0.176114i
$715$	2703.65	+	2703.65i	0.141414	+	0.141414i
$716$	−15291.3	−	16940.2i	−0.798130	−	0.884195i
$717$	−2328.33	+	2328.33i	−0.121273	+	0.121273i
$718$	−921.988	+	876.027i	−0.0479224	+	0.0455335i
$719$	4463.67			0.231526			0.115763	−	0.993277i	$-0.463069\pi$
$719$	4463.67			0.231526			0.115763	+	0.993277i	$0.463069\pi$
$720$	−1416.38	+	1152.82i	−0.0733130	+	0.0596708i
$721$	320.101			0.0165343
$722$	−3815.66	+	3625.45i	−0.196682	+	0.186877i
$723$	−8257.33	+	8257.33i	−0.424749	+	0.424749i
$724$	−19133.2	+	17270.9i	−0.982156	+	0.886556i
$725$	−4671.65	−	4671.65i	−0.239311	−	0.239311i
$726$	−235.676	+	9219.63i	−0.0120479	+	0.471312i
$727$			37422.0i			1.90909i	0.298071	+	0.954544i	$0.403657\pi$
$727$			37422.0i			1.90909i	−0.298071	+	0.954544i	$0.596343\pi$
$728$	−15676.2	−	1204.27i	−0.798077	−	0.0613091i
$729$			729.000i			0.0370370i
$730$	827.190	+	21.1450i	0.0419393	+	0.00107207i
$731$	9008.29	+	9008.29i	0.455792	+	0.455792i
$732$	−987.899	−	50.5392i	−0.0498822	−	0.00255189i
$733$	−10663.4	+	10663.4i	−0.537330	+	0.537330i	−0.922744	−	0.385414i	$-0.874059\pi$
$733$	−10663.4	+	10663.4i	−0.537330	+	0.537330i	0.385414	+	0.922744i	$0.374059\pi$
$734$	−8919.91	−	9387.90i	−0.448555	−	0.472089i
$735$	−2491.71			−0.125045
$736$	16772.5	−	12953.2i	0.840002	−	0.648724i
$737$	11246.2			0.562087
$738$	8020.15	+	8440.93i	0.400035	+	0.421023i
$739$	6100.64	−	6100.64i	0.303675	−	0.303675i	−0.538775	−	0.842450i	$-0.681113\pi$
$739$	6100.64	−	6100.64i	0.303675	−	0.303675i	0.842450	+	0.538775i	$0.181113\pi$
$740$	8905.83	+	455.607i	0.442412	+	0.0226330i
$741$	11576.0	+	11576.0i	0.573891	+	0.573891i
$742$	4978.81	+	127.270i	0.246331	+	0.00629682i
$743$			33779.2i			1.66789i	0.551850	+	0.833944i	$0.313922\pi$
$743$			33779.2i			1.66789i	−0.551850	+	0.833944i	$0.686078\pi$
$744$	−1022.50	+	13310.2i	−0.0503855	+	0.655881i
$745$			2583.88i			0.127069i
$746$	152.807	−	5977.79i	0.00749953	−	0.293381i
$747$	−8233.54	−	8233.54i	−0.403279	−	0.403279i
$748$	−4082.64	+	3685.25i	−0.199567	+	0.180142i
$749$	8522.10	−	8522.10i	0.415742	−	0.415742i
$750$	−4679.73	+	4446.45i	−0.227840	+	0.216482i
$751$	−15649.1			−0.760380			−0.380190	−	0.924908i	$-0.624141\pi$
$751$	−15649.1			−0.760380			−0.380190	+	0.924908i	$0.624141\pi$
$752$	24860.0	+	2550.27i	1.20552	+	0.123668i
$753$	4178.52			0.202223
$754$	9096.68	−	8643.20i	0.439365	−	0.417463i
$755$	−789.367	+	789.367i	−0.0380503	+	0.0380503i
$756$	−1302.87	−	1443.36i	−0.0626786	−	0.0694374i
$757$	8157.94	+	8157.94i	0.391685	+	0.391685i	0.875288	−	0.483603i	$-0.160672\pi$
$757$	8157.94	+	8157.94i	0.391685	+	0.391685i	−0.483603	+	0.875288i	$0.660672\pi$
$758$	−607.065	+	23748.4i	−0.0290892	+	1.13797i
$759$		−	5487.23i		−	0.262416i
$760$	−3850.54	+	3301.14i	−0.183781	+	0.157559i
$761$		−	2725.67i		−	0.129836i	−0.997891	−	0.0649182i	$-0.979321\pi$
$761$		−	2725.67i		−	0.129836i	0.997891	−	0.0649182i	$-0.0206786\pi$
$762$	17594.7	+	449.764i	0.836469	+	0.0213822i
$763$	−12266.9	−	12266.9i	−0.582034	−	0.582034i
$764$	−1403.12	+	27427.1i	−0.0664439	+	1.29879i
$765$	887.854	−	887.854i	0.0419614	−	0.0419614i
$766$	−8761.45	−	9221.12i	−0.413269	−	0.434951i
$767$	−28731.9			−1.35260
$768$	−10272.1	+	6743.81i	−0.482633	+	0.316857i
$769$	−15821.2			−0.741907			−0.370953	−	0.928652i	$-0.620969\pi$
$769$	−15821.2			−0.741907			−0.370953	+	0.928652i	$0.620969\pi$
$770$	−868.754	−	914.334i	−0.0406594	−	0.0427926i
$771$	13161.0	−	13161.0i	0.614762	−	0.614762i
$772$	−135.650	+	2651.57i	−0.00632403	+	0.123617i
$773$	−27225.7	−	27225.7i	−1.26680	−	1.26680i	−0.947730	−	0.319073i	$-0.896628\pi$
$773$	−27225.7	−	27225.7i	−1.26680	−	1.26680i	−0.319073	−	0.947730i	$-0.603372\pi$
$774$	7367.54	+	188.332i	0.342146	+	0.00874606i
$775$			22605.1i			1.04774i
$776$	3937.37	−	3375.58i	0.182143	−	0.156155i
$777$			9494.60i			0.438375i
$778$	361.756	−	14151.9i	0.0166704	−	0.652145i
$779$	22865.8	+	22865.8i	1.05167	+	1.05167i
$780$	−3935.53	−	4359.91i	−0.180660	−	0.200141i
$781$	8713.35	−	8713.35i	0.399217	−	0.399217i
$782$	−10562.8	+	10036.2i	−0.483023	+	0.458944i
$783$	1551.85			0.0708282
$784$	−16678.2	−	1710.93i	−0.759759	−	0.0779398i
$785$	−3353.92			−0.152493
$786$	10271.9	−	9759.82i	0.466139	−	0.442902i
$787$	19647.0	−	19647.0i	0.889886	−	0.889886i	−0.104626	−	0.994512i	$-0.533365\pi$
$787$	19647.0	−	19647.0i	0.889886	−	0.889886i	0.994512	+	0.104626i	$0.0333645\pi$
$788$	21853.3	−	19726.1i	0.987932	−	0.891770i
$789$	−12527.9	−	12527.9i	−0.565281	−	0.565281i
$790$	40.0007	−	1564.83i	0.00180147	−	0.0704735i
$791$		−	841.425i		−	0.0378225i
$792$	−243.705	+	3172.37i	−0.0109340	+	0.142330i
$793$		−	3181.39i		−	0.142465i
$794$	2416.34	+	61.7675i	0.108001	+	0.00276077i
$795$	1315.60	+	1315.60i	0.0586913	+	0.0586913i
$796$	13801.2	+	706.044i	0.614535	+	0.0314385i
$797$	27755.3	−	27755.3i	1.23356	−	1.23356i	0.270969	−	0.962588i	$-0.412656\pi$
$797$	27755.3	−	27755.3i	1.23356	−	1.23356i	0.962588	−	0.270969i	$-0.0873440\pi$
$798$	−3719.66	−	3914.82i	−0.165006	−	0.173663i
$799$	−17182.1			−0.760774
$800$	−16468.4	+	12718.3i	−0.727805	+	0.562076i
$801$	13094.8			0.577628
$802$	8802.60	+	9264.44i	0.387569	+	0.407904i
$803$	1019.39	−	1019.39i	0.0447987	−	0.0447987i
$804$	−17253.0	−	882.631i	−0.756797	−	0.0387164i
$805$	−2362.66	−	2362.66i	−0.103445	−	0.103445i
$806$	−42919.7	−	1097.13i	−1.87566	−	0.0479464i
$807$		−	16682.1i		−	0.727680i
$808$	−22336.1	−	1715.88i	−0.972501	−	0.0747086i
$809$			11126.5i			0.483546i	0.970333	+	0.241773i	$0.0777289\pi$
$809$			11126.5i			0.483546i	−0.970333	+	0.241773i	$0.922271\pi$
$810$	18.5619	−	726.142i	0.000805185	−	0.0314988i
$811$	1035.64	+	1035.64i	0.0448412	+	0.0448412i	0.729172	−	0.684331i	$-0.239906\pi$
$811$	1035.64	+	1035.64i	0.0448412	+	0.0448412i	−0.684331	+	0.729172i	$0.739906\pi$
$812$	−3072.54	+	2773.47i	−0.132789	+	0.119864i
$813$	7542.35	−	7542.35i	0.325365	−	0.325365i
$814$	11263.0	−	10701.5i	0.484972	−	0.460796i
$815$	−8559.87			−0.367901
$816$	6552.48	−	5333.19i	0.281106	−	0.228798i
$817$	20468.2			0.876489
$818$	−20502.6	+	19480.5i	−0.876353	+	0.832667i
$819$	4421.93	−	4421.93i	0.188663	−	0.188663i
$820$	−7773.78	−	8612.05i	−0.331064	−	0.366763i
$821$	−5239.18	−	5239.18i	−0.222714	−	0.222714i	0.586926	−	0.809641i	$-0.300338\pi$
$821$	−5239.18	−	5239.18i	−0.222714	−	0.222714i	−0.809641	+	0.586926i	$0.800338\pi$
$822$	−237.485	+	9290.38i	−0.0100769	+	0.394208i
$823$		−	1911.58i		−	0.0809642i	−0.999180	−	0.0404821i	$-0.987111\pi$
$823$		−	1911.58i		−	0.0809642i	0.999180	−	0.0404821i	$-0.0128894\pi$
$824$	523.695	+	610.853i	0.0221405	+	0.0258253i
$825$			5387.73i			0.227366i
$826$	9474.50	+	242.191i	0.399104	+	0.0102021i
$827$	1350.33	+	1350.33i	0.0567782	+	0.0567782i	0.734926	−	0.678148i	$-0.237217\pi$
$827$	1350.33	+	1350.33i	0.0567782	+	0.0567782i	−0.678148	+	0.734926i	$0.737217\pi$
$828$	−430.653	+	8418.06i	−0.0180752	+	0.353319i
$829$	−7167.34	+	7167.34i	−0.300280	+	0.300280i	−0.841123	−	0.540843i	$-0.818105\pi$
$829$	−7167.34	+	7167.34i	−0.300280	+	0.300280i	0.540843	+	0.841123i	$0.318105\pi$
$830$	7991.62	+	8410.90i	0.334208	+	0.351743i
$831$	−8775.35			−0.366322
$832$	−23348.7	−	31885.3i	−0.972920	−	1.32864i
$833$	11527.2			0.479464
$834$	−13041.6	−	13725.9i	−0.541481	−	0.569890i
$835$	1056.79	−	1056.79i	0.0437984	−	0.0437984i
$836$	−451.467	+	8824.91i	−0.0186774	+	0.365091i
$837$	−3754.52	−	3754.52i	−0.155048	−	0.155048i
$838$	10452.3	+	267.185i	0.430868	+	0.0110140i
$839$			12213.6i			0.502575i	0.967913	+	0.251287i	$0.0808539\pi$
$839$			12213.6i			0.502575i	−0.967913	+	0.251287i	$0.919146\pi$
$840$	1261.01	+	1470.88i	0.0517965	+	0.0604169i
$841$			21085.5i			0.864551i
$842$	127.296	−	4979.80i	0.00521009	−	0.203818i
$843$	−18991.9	−	18991.9i	−0.775937	−	0.775937i
$844$	18243.0	+	20210.2i	0.744016	+	0.824246i
$845$	8431.66	−	8431.66i	0.343264	−	0.343264i
$846$	−7205.89	+	6846.68i	−0.292841	+	0.278243i
$847$	9784.22			0.396918
$848$	7902.60	+	9709.32i	0.320019	+	0.393183i
$849$	40.5676			0.00163990
$850$	10371.3	−	9854.24i	0.418507	−	0.397644i
$851$	29103.9	−	29103.9i	1.17235	−	1.17235i
$852$	−14051.2	+	12683.5i	−0.565006	+	0.510010i
$853$	15675.9	+	15675.9i	0.629228	+	0.629228i	0.947874	−	0.318646i	$-0.103228\pi$
$853$	15675.9	+	15675.9i	0.629228	+	0.629228i	−0.318646	+	0.947874i	$0.603228\pi$
$854$	−26.8170	+	1049.08i	−0.00107454	+	0.0420361i
$855$		−	2017.34i		−	0.0806918i
$856$	30205.2	+	2320.40i	1.20607	+	0.0926515i
$857$			6840.70i			0.272665i	0.990663	+	0.136333i	$0.0435316\pi$
$857$			6840.70i			0.272665i	−0.990663	+	0.136333i	$0.956468\pi$
$858$	−10229.6	−	261.492i	−0.407029	−	0.0104047i
$859$	20617.9	+	20617.9i	0.818944	+	0.818944i	0.985955	−	0.167011i	$-0.0534115\pi$
$859$	20617.9	+	20617.9i	0.818944	+	0.818944i	−0.167011	+	0.985955i	$0.553411\pi$
$860$	−7333.85	−	375.187i	−0.290793	−	0.0148765i
$861$	8734.56	−	8734.56i	0.345729	−	0.345729i
$862$	−29470.2	−	31016.4i	−1.16445	−	1.22555i
$863$	48111.2			1.89771			0.948856	−	0.315709i	$-0.102242\pi$
$863$	48111.2			1.89771			0.948856	+	0.315709i	$0.102242\pi$
$864$	622.850	−	4847.67i	0.0245252	−	0.190881i
$865$	1822.00			0.0716185
$866$	16896.4	+	17782.9i	0.663006	+	0.697791i
$867$	6314.64	−	6314.64i	0.247354	−	0.247354i
$868$	14143.8	+	723.570i	0.553077	+	0.0282944i
$869$	−1928.41	−	1928.41i	−0.0752783	−	0.0752783i
$870$	−1545.76	−	39.5134i	−0.0602370	−	0.00153980i
$871$		−	55560.6i		−	2.16142i
$872$	3340.04	−	43478.1i	0.129711	−	1.68848i
$873$			2062.83i			0.0799726i
$874$	−598.212	+	23402.0i	−0.0231520	+	0.905703i
$875$	4842.52	+	4842.52i	0.187094	+	0.187094i
$876$	−1643.86	+	1483.85i	−0.0634029	+	0.0572315i
$877$	−21370.7	+	21370.7i	−0.822847	+	0.822847i	−0.986515	−	0.163669i	$-0.947667\pi$
$877$	−21370.7	+	21370.7i	−0.822847	+	0.822847i	0.163669	+	0.986515i	$0.447667\pi$
$878$	−23150.5	+	21996.5i	−0.889855	+	0.845496i
$879$	7833.48			0.300588
$880$	323.525	−	3153.73i	0.0123932	−	0.120809i
$881$	15567.0			0.595306			0.297653	−	0.954674i	$-0.403796\pi$
$881$	15567.0			0.595306			0.297653	+	0.954674i	$0.403796\pi$
$882$	4834.32	−	4593.33i	0.184558	−	0.175358i
$883$	11192.2	−	11192.2i	0.426555	−	0.426555i	−0.460898	−	0.887453i	$-0.652473\pi$
$883$	11192.2	−	11192.2i	0.426555	−	0.426555i	0.887453	+	0.460898i	$0.152473\pi$
$884$	18206.6	+	20169.9i	0.692710	+	0.767407i
$885$	2503.55	+	2503.55i	0.0950913	+	0.0950913i
$886$	321.984	−	12596.0i	0.0122091	−	0.477619i
$887$		−	7466.96i		−	0.282656i	−0.989963	−	0.141328i	$-0.954863\pi$
$887$		−	7466.96i		−	0.282656i	0.989963	−	0.141328i	$-0.0451373\pi$
$888$	−18118.6	+	15533.5i	−0.684709	+	0.587014i
$889$		−	18672.2i		−	0.704437i
$890$	−13043.4	−	333.421i	−0.491254	−	0.0125576i
$891$	−894.859	−	894.859i	−0.0336464	−	0.0336464i
$892$	724.364	−	14159.3i	0.0271900	−	0.531489i
$893$	−19520.1	+	19520.1i	−0.731486	+	0.731486i
$894$	−4763.25	−	5013.16i	−0.178196	−	0.187545i
$895$	−9044.30			−0.337785
$896$	7430.59	+	10711.2i	0.277052	+	0.399370i
$897$	−27109.1			−1.00908
$898$	−21674.1	−	22811.3i	−0.805429	−	0.847687i
$899$	−7992.37	+	7992.37i	−0.296508	+	0.296508i
$900$	422.845	−	8265.42i	0.0156609	−	0.306127i
$901$	−6086.27	−	6086.27i	−0.225042	−	0.225042i
$902$	−20206.2	−	516.520i	−0.745892	−	0.0190668i
$903$		−	7818.70i		−	0.288140i
$904$	1605.70	−	1376.60i	0.0590761	−	0.0506470i
$905$			10215.2i			0.375209i
$906$	76.3461	−	2986.66i	0.00279959	−	0.109520i
$907$	18643.3	+	18643.3i	0.682516	+	0.682516i	0.960566	−	0.278050i	$-0.0896882\pi$
$907$	18643.3	+	18643.3i	0.682516	+	0.682516i	−0.278050	+	0.960566i	$0.589688\pi$
$908$	−3111.21	−	3446.71i	−0.113711	−	0.125972i
$909$	6300.54	−	6300.54i	0.229896	−	0.229896i
$910$	−4517.18	+	4292.00i	−0.164553	+	0.156350i
$911$	18129.2			0.659327			0.329663	−	0.944099i	$-0.393065\pi$
$911$	18129.2			0.659327			0.329663	+	0.944099i	$0.393065\pi$
$912$	1385.21	−	13503.0i	0.0502947	−	0.490274i
$913$	20213.6			0.732720
$914$	16282.5	−	15470.8i	0.589254	−	0.559880i
$915$	−277.210	+	277.210i	−0.0100156	+	0.0100156i
$916$	−1739.74	+	1570.40i	−0.0627541	+	0.0566458i
$917$	−10629.2	−	10629.2i	−0.382777	−	0.382777i
$918$	−85.8716	+	3359.29i	−0.00308735	+	0.120777i
$919$			17768.1i			0.637774i	0.947793	+	0.318887i	$0.103309\pi$
$919$			17768.1i			0.637774i	−0.947793	+	0.318887i	$0.896691\pi$
$920$	643.307	−	8374.09i	0.0230535	−	0.300093i
$921$			12824.8i			0.458839i
$922$	−10197.9	−	260.684i	−0.364263	−	0.00931145i
$923$	−43047.5	−	43047.5i	−1.53513	−	1.53513i
$924$	3371.05	+	172.457i	0.120021	+	0.00614007i
$925$	−28576.2	+	28576.2i	−1.01576	+	1.01576i
$926$	30823.3	+	32440.5i	1.09386	+	1.15125i
$927$	−320.032			−0.0113390
$928$	−10319.4	−	1325.88i	−0.365033	−	0.0469011i
$929$	−26554.6			−0.937813			−0.468907	−	0.883248i	$-0.655352\pi$
$929$	−26554.6			−0.937813			−0.468907	+	0.883248i	$0.655352\pi$
$930$	3644.20	+	3835.40i	0.128493	+	0.135234i
$931$	13095.8	−	13095.8i	0.461006	−	0.461006i
$932$	18240.2	+	933.135i	0.641069	+	0.0327960i
$933$	−262.427	−	262.427i	−0.00920843	−	0.00920843i
$934$	−15558.0	−	397.701i	−0.545047	−	0.0139327i
$935$			2179.71i			0.0762397i
$936$	15672.8	+	1204.00i	0.547310	+	0.0420450i
$937$			18517.6i			0.645617i	0.946464	+	0.322808i	$0.104627\pi$
$937$			18517.6i			0.645617i	−0.946464	+	0.322808i	$0.895373\pi$
$938$	−468.340	+	18321.4i	−0.0163026	+	0.637757i
$939$	−17846.8	−	17846.8i	−0.620243	−	0.620243i
$940$	7351.97	−	6636.35i	0.255101	−	0.230270i
$941$	18019.4	−	18019.4i	0.624247	−	0.624247i	−0.322368	−	0.946614i	$-0.604479\pi$
$941$	18019.4	−	18019.4i	0.624247	−	0.624247i	0.946614	+	0.322368i	$0.104479\pi$
$942$	6507.16	−	6182.78i	0.225069	−	0.213849i
$943$	−53548.2			−1.84917
$944$	15038.4	+	18476.5i	0.518494	+	0.637034i
$945$	−770.609			−0.0265269
$946$	−9274.95	+	8812.59i	−0.318768	+	0.302877i
$947$	−24841.6	+	24841.6i	−0.852422	+	0.852422i	−0.990431	−	0.138009i	$-0.955930\pi$
$947$	−24841.6	+	24841.6i	−0.852422	+	0.852422i	0.138009	+	0.990431i	$0.455930\pi$
$948$	2807.06	+	3109.76i	0.0961700	+	0.106540i
$949$	−5036.18	−	5036.18i	−0.172267	−	0.172267i
$950$	587.365	−	22977.7i	0.0200596	−	0.784731i
$951$			13581.8i			0.463114i
$952$	−5833.72	−	6804.62i	−0.198605	−	0.231658i
$953$			30149.1i			1.02479i	0.858750	+	0.512395i	$0.171242\pi$
$953$			30149.1i			1.02479i	−0.858750	+	0.512395i	$0.828758\pi$
$954$	−4977.72	−	127.243i	−0.168931	−	0.00431827i
$955$	7696.18	+	7696.18i	0.260778	+	0.260778i
$956$	−448.617	+	8769.20i	−0.0151771	+	0.296670i
$957$	−1904.92	+	1904.92i	−0.0643440	+	0.0643440i
$958$	28395.2	+	29885.0i	0.957629	+	1.00787i
$959$	9859.30			0.331985
$960$	−743.840	+	4812.81i	−0.0250076	+	0.161805i
$961$	8882.32			0.298154
$962$	−52869.9	−	55643.8i	−1.77193	−	1.86489i
$963$	−8520.25	+	8520.25i	−0.285110	+	0.285110i
$964$	−1591.00	+	31099.7i	−0.0531564	+	1.03906i
$965$	744.046	+	744.046i	0.0248204	+	0.0248204i
$966$	8939.40	+	228.513i	0.297744	+	0.00761105i
$967$		−	46556.4i		−	1.54824i	−0.633037	−	0.774122i	$-0.718192\pi$
$967$		−	46556.4i		−	1.54824i	0.633037	−	0.774122i	$-0.281808\pi$
$968$	16007.3	+	18671.3i	0.531501	+	0.619958i
$969$			9332.66i			0.309399i
$970$	52.5241	−	2054.74i	0.00173860	−	0.0680141i
$971$	40162.6	+	40162.6i	1.32737	+	1.32737i	0.907654	+	0.419719i	$0.137872\pi$
$971$	40162.6	+	40162.6i	1.32737	+	1.32737i	0.419719	+	0.907654i	$0.362128\pi$
$972$	1302.59	+	1443.05i	0.0429841	+	0.0476192i
$973$	−14203.3	+	14203.3i	−0.467974	+	0.467974i
$974$	−705.347	+	670.185i	−0.0232041	+	0.0220474i
$975$	26617.6			0.874303
$976$	−2045.84	+	1665.15i	−0.0670962	+	0.0546109i
$977$	−46837.9			−1.53376			−0.766878	−	0.641793i	$-0.778191\pi$
$977$	−46837.9			−1.53376			−0.766878	+	0.641793i	$0.778191\pi$
$978$	16607.5	−	15779.6i	0.542996	−	0.515928i
$979$	−16074.0	+	16074.0i	−0.524748	+	0.524748i
$980$	−4932.32	+	4452.23i	−0.160773	+	0.145124i
$981$	12264.2	+	12264.2i	0.399151	+	0.399151i
$982$	470.473	−	18404.9i	0.0152886	−	0.598089i
$983$		−	225.373i		−	0.00731258i	−0.999993	−	0.00365629i	$-0.998836\pi$
$983$		−	225.373i		−	0.00731258i	0.999993	−	0.00365629i	$-0.00116384\pi$
$984$	30958.2	+	2378.25i	1.00296	+	0.0770485i
$985$		−	11667.4i		−	0.377415i
$986$	7151.04	+	182.798i	0.230969	+	0.00590413i
$987$	7456.55	+	7456.55i	0.240471	+	0.240471i
$988$	43598.6	+	2230.43i	1.40390	+	0.0718213i
$989$	−23966.7	+	23966.7i	−0.770574	+	0.770574i
$990$	868.566	+	914.136i	0.0278837	+	0.0293466i
$991$	−36186.1			−1.15993			−0.579964	−	0.814642i	$-0.696934\pi$
$991$	−36186.1			−1.15993			−0.579964	+	0.814642i	$0.696934\pi$
$992$	21758.8	+	28174.5i	0.696415	+	0.901754i
$993$	13381.9			0.427656
$994$	13832.3	+	14558.0i	0.441382	+	0.464540i
$995$	3872.68	−	3872.68i	0.123389	−	0.123389i
$996$	−31010.1	−	1586.42i	−0.986538	−	0.0504696i
$997$	26031.5	+	26031.5i	0.826906	+	0.826906i	0.987088	−	0.160181i	$-0.0512079\pi$
$997$	26031.5	+	26031.5i	0.826906	+	0.826906i	−0.160181	+	0.987088i	$0.551208\pi$
$998$	−3548.83	−	90.7167i	−0.112561	−	0.00287734i
$999$		−	9492.54i		−	0.300631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.37.9	yes	24
3.2	odd	2		144.4.k.b.37.4		24
4.3	odd	2		192.4.j.a.49.10		24
8.3	odd	2		384.4.j.a.97.4		24
8.5	even	2		384.4.j.b.97.9		24
12.11	even	2		576.4.k.b.433.5		24
16.3	odd	4		192.4.j.a.145.10		24
16.5	even	4		384.4.j.b.289.9		24
16.11	odd	4		384.4.j.a.289.4		24
16.13	even	4	inner	48.4.j.a.13.9	✓	24
48.29	odd	4		144.4.k.b.109.4		24
48.35	even	4		576.4.k.b.145.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.9	✓	24	16.13	even	4	inner
48.4.j.a.37.9	yes	24	1.1	even	1	trivial
144.4.k.b.37.4		24	3.2	odd	2
144.4.k.b.109.4		24	48.29	odd	4
192.4.j.a.49.10		24	4.3	odd	2
192.4.j.a.145.10		24	16.3	odd	4
384.4.j.a.97.4		24	8.3	odd	2
384.4.j.a.289.4		24	16.11	odd	4
384.4.j.b.97.9		24	8.5	even	2
384.4.j.b.289.9		24	16.5	even	4
576.4.k.b.145.5		24	48.35	even	4
576.4.k.b.433.5		24	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.94824 + 2.05046i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-0.408732 + 7.98955i) q^{4} +(2.24191 + 2.24191i) q^{5} +(-8.48251 - 0.216833i) q^{6} +9.00196i q^{7} +(-17.1785 + 14.7275i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(1.94824 + 2.05046i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-0.408732 + 7.98955i) q^{4} +(2.24191 + 2.24191i) q^{5} +(-8.48251 - 0.216833i) q^{6} +9.00196i q^{7} +(-17.1785 + 14.7275i) q^{8} -9.00000i q^{9} +(-0.229160 + 8.96471i) q^{10} +(11.0476 + 11.0476i) q^{11} +(-16.0813 - 17.8154i) q^{12} +(54.5799 - 54.5799i) q^{13} +(-18.4581 + 17.5380i) q^{14} -9.51162 q^{15} +(-63.6659 - 6.53116i) q^{16} +44.0029 q^{17} +(18.4541 - 17.5341i) q^{18} +(49.9906 - 49.9906i) q^{19} +(-18.8282 + 16.9955i) q^{20} +(-19.0960 - 19.0960i) q^{21} +(-1.12925 + 44.1761i) q^{22} +117.070i q^{23} +(5.19947 - 67.6828i) q^{24} -114.948i q^{25} +(218.248 + 5.57895i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-71.9216 - 3.67938i) q^{28} +(40.6415 - 40.6415i) q^{29} +(-18.5309 - 19.5031i) q^{30} -196.655 q^{31} +(-110.644 - 143.268i) q^{32} -46.8712 q^{33} +(85.7281 + 90.2259i) q^{34} +(-20.1816 + 20.1816i) q^{35} +(71.9060 + 3.67858i) q^{36} +(-248.601 - 248.601i) q^{37} +(199.897 + 5.10985i) q^{38} +231.563i q^{39} +(-71.5304 - 5.49504i) q^{40} +457.402i q^{41} +(1.95192 - 76.3592i) q^{42} +(204.721 + 204.721i) q^{43} +(-92.7813 + 83.7502i) q^{44} +(20.1772 - 20.1772i) q^{45} +(-240.048 + 228.081i) q^{46} -390.477 q^{47} +(148.910 - 121.201i) q^{48} +261.965 q^{49} +(235.695 - 223.946i) q^{50} +(-93.3442 + 93.3442i) q^{51} +(413.760 + 458.377i) q^{52} +(-138.315 - 138.315i) q^{53} +(-1.95150 + 76.3426i) q^{54} +49.5357i q^{55} +(-132.576 - 154.640i) q^{56} +212.092i q^{57} +(162.513 + 4.15422i) q^{58} +(-263.209 - 263.209i) q^{59} +(3.88770 - 75.9936i) q^{60} +(29.1443 - 29.1443i) q^{61} +(-383.132 - 403.233i) q^{62} +81.0176 q^{63} +(78.2033 - 505.992i) q^{64} +244.726 q^{65} +(-91.3163 - 96.1073i) q^{66} +(508.985 - 508.985i) q^{67} +(-17.9854 + 351.563i) q^{68} +(-248.344 - 248.344i) q^{69} +(-80.6999 - 2.06289i) q^{70} -788.707i q^{71} +(132.547 + 154.607i) q^{72} -92.2717i q^{73} +(25.4111 - 994.081i) q^{74} +(243.841 + 243.841i) q^{75} +(378.969 + 419.835i) q^{76} +(-99.4504 + 99.4504i) q^{77} +(-474.809 + 451.140i) q^{78} -174.554 q^{79} +(-128.091 - 157.375i) q^{80} -81.0000 q^{81} +(-937.882 + 891.128i) q^{82} +(914.838 - 914.838i) q^{83} +(160.374 - 144.764i) q^{84} +(98.6505 + 98.6505i) q^{85} +(-20.9258 + 818.615i) q^{86} +172.427i q^{87} +(-352.486 - 27.0784i) q^{88} +1454.97i q^{89} +(80.6824 + 2.06244i) q^{90} +(491.326 + 491.326i) q^{91} +(-935.340 - 47.8504i) q^{92} +(417.169 - 417.169i) q^{93} +(-760.742 - 800.655i) q^{94} +224.149 q^{95} +(538.630 + 69.2056i) q^{96} -229.203 q^{97} +(510.370 + 537.147i) q^{98} +(99.4288 - 99.4288i) 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

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