LMFDB - Embedded newform 103.4.c.a.46.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,4,Mod(46,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("103.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	103.c (of order $3$, 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:	$6.07719673059$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.23
Character	$\chi$	$=$	103.46
Dual form			103.4.c.a.56.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.46067 + 4.26201i) q^{2} -9.26768 q^{3} +(-8.10981 + 14.0466i) q^{4} +(-6.00715 + 10.4047i) q^{5} +(-22.8047 - 39.4989i) q^{6} +(15.4448 - 26.7511i) q^{7} -40.4516 q^{8} +58.8899 q^{9} +O(q^{10})$	\(q+(2.46067 + 4.26201i) q^{2} -9.26768 q^{3} +(-8.10981 + 14.0466i) q^{4} +(-6.00715 + 10.4047i) q^{5} +(-22.8047 - 39.4989i) q^{6} +(15.4448 - 26.7511i) q^{7} -40.4516 q^{8} +58.8899 q^{9} -59.1265 q^{10} +(-15.0523 + 26.0713i) q^{11} +(75.1591 - 130.179i) q^{12} -51.5593 q^{13} +152.018 q^{14} +(55.6724 - 96.4274i) q^{15} +(-34.6596 - 60.0321i) q^{16} +(-7.56962 + 13.1110i) q^{17} +(144.909 + 250.989i) q^{18} +(-69.3640 - 120.142i) q^{19} +(-97.4337 - 168.760i) q^{20} +(-143.137 + 247.921i) q^{21} -148.155 q^{22} -153.520 q^{23} +374.892 q^{24} +(-9.67174 - 16.7520i) q^{25} +(-126.871 - 219.746i) q^{26} -295.545 q^{27} +(250.509 + 433.893i) q^{28} +(10.2429 + 17.7413i) q^{29} +547.966 q^{30} +57.8733 q^{31} +(8.76528 - 15.1819i) q^{32} +(139.500 - 241.621i) q^{33} -74.5054 q^{34} +(185.558 + 321.396i) q^{35} +(-477.586 + 827.203i) q^{36} -132.701 q^{37} +(341.364 - 591.260i) q^{38} +477.835 q^{39} +(242.999 - 420.886i) q^{40} +(59.0303 + 102.243i) q^{41} -1408.86 q^{42} +(139.691 + 241.951i) q^{43} +(-244.142 - 422.867i) q^{44} +(-353.760 + 612.731i) q^{45} +(-377.762 - 654.304i) q^{46} +(-27.8375 + 48.2160i) q^{47} +(321.214 + 556.358i) q^{48} +(-305.583 - 529.285i) q^{49} +(47.5980 - 82.4421i) q^{50} +(70.1528 - 121.508i) q^{51} +(418.136 - 724.233i) q^{52} +(-263.604 + 456.575i) q^{53} +(-727.240 - 1259.62i) q^{54} +(-180.843 - 313.229i) q^{55} +(-624.766 + 1082.13i) q^{56} +(642.844 + 1113.44i) q^{57} +(-50.4090 + 87.3109i) q^{58} +(258.987 + 448.579i) q^{59} +(902.984 + 1564.01i) q^{60} -494.137 q^{61} +(142.407 + 246.657i) q^{62} +(909.541 - 1575.37i) q^{63} -468.279 q^{64} +(309.725 - 536.459i) q^{65} +1373.05 q^{66} +(299.688 - 519.074i) q^{67} +(-122.776 - 212.655i) q^{68} +1422.77 q^{69} +(-913.196 + 1581.70i) q^{70} +(-120.141 + 208.091i) q^{71} -2382.19 q^{72} -674.492 q^{73} +(-326.534 - 565.574i) q^{74} +(89.6346 + 155.252i) q^{75} +2250.12 q^{76} +(464.958 + 805.331i) q^{77} +(1175.80 + 2036.54i) q^{78} +521.492 q^{79} +832.821 q^{80} +1148.99 q^{81} +(-290.508 + 503.175i) q^{82} +(-581.897 - 1007.88i) q^{83} +(-2321.63 - 4021.19i) q^{84} +(-90.9437 - 157.519i) q^{85} +(-687.466 + 1190.73i) q^{86} +(-94.9282 - 164.421i) q^{87} +(608.888 - 1054.63i) q^{88} -23.0448 q^{89} -3481.95 q^{90} +(-796.323 + 1379.27i) q^{91} +(1245.02 - 2156.43i) q^{92} -536.351 q^{93} -273.996 q^{94} +1666.72 q^{95} +(-81.2338 + 140.701i) q^{96} +(-356.071 - 616.733i) q^{97} +(1503.88 - 2604.79i) q^{98} +(-886.427 + 1535.34i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} + 4 q^{3} - 97 q^{4} - 3 q^{5} - 17 q^{6} + 13 q^{7} - 30 q^{8} + 534 q^{9}+O(q^{10}) $ 50 * q - q^2 + 4 * q^3 - 97 * q^4 - 3 * q^5 - 17 * q^6 + 13 * q^7 - 30 * q^8 + 534 * q^9	\( 50 q - q^{2} + 4 q^{3} - 97 q^{4} - 3 q^{5} - 17 q^{6} + 13 q^{7} - 30 q^{8} + 534 q^{9} - 56 q^{10} - 17 q^{11} - 186 q^{12} - 16 q^{13} + 274 q^{14} + 70 q^{15} - 289 q^{16} - 41 q^{17} + 48 q^{18} + 133 q^{19} + 117 q^{20} - 416 q^{21} + 88 q^{22} - 184 q^{23} + 1002 q^{24} - 934 q^{25} - 522 q^{26} - 380 q^{27} + 578 q^{28} - 51 q^{29} + 1076 q^{30} - 216 q^{31} - 471 q^{32} - 182 q^{33} - 58 q^{34} - 27 q^{35} - 1486 q^{36} + 276 q^{37} + 1800 q^{38} + 220 q^{39} + 7 q^{40} - 133 q^{41} - 372 q^{42} + 549 q^{43} - 117 q^{44} - 251 q^{45} + 506 q^{46} + 767 q^{47} - 2082 q^{48} - 440 q^{49} - 1106 q^{50} - 456 q^{51} + 2053 q^{52} - 75 q^{53} - 2473 q^{54} + 201 q^{55} - 1278 q^{56} + 1176 q^{57} - 294 q^{58} + 871 q^{59} + 762 q^{60} - 2732 q^{61} - 603 q^{62} + 1165 q^{63} + 3518 q^{64} - 1392 q^{65} + 7624 q^{66} + 2635 q^{67} + 3025 q^{68} - 2468 q^{69} - 4724 q^{70} - 397 q^{71} - 6040 q^{72} + 3240 q^{73} - 1039 q^{74} - 3356 q^{75} - 2990 q^{76} - 319 q^{77} - 2654 q^{78} - 2340 q^{79} + 5284 q^{80} + 538 q^{81} - 687 q^{82} + 1243 q^{83} - 4271 q^{84} + 1397 q^{85} - 829 q^{86} - 1850 q^{87} + 991 q^{88} + 4068 q^{89} + 7258 q^{90} - 4778 q^{91} + 891 q^{92} - 3704 q^{93} + 5564 q^{94} - 3910 q^{95} - 3443 q^{96} + 2197 q^{97} + 994 q^{98} - 6033 q^{99}+O(q^{100}) \) 50 * q - q^2 + 4 * q^3 - 97 * q^4 - 3 * q^5 - 17 * q^6 + 13 * q^7 - 30 * q^8 + 534 * q^9 - 56 * q^10 - 17 * q^11 - 186 * q^12 - 16 * q^13 + 274 * q^14 + 70 * q^15 - 289 * q^16 - 41 * q^17 + 48 * q^18 + 133 * q^19 + 117 * q^20 - 416 * q^21 + 88 * q^22 - 184 * q^23 + 1002 * q^24 - 934 * q^25 - 522 * q^26 - 380 * q^27 + 578 * q^28 - 51 * q^29 + 1076 * q^30 - 216 * q^31 - 471 * q^32 - 182 * q^33 - 58 * q^34 - 27 * q^35 - 1486 * q^36 + 276 * q^37 + 1800 * q^38 + 220 * q^39 + 7 * q^40 - 133 * q^41 - 372 * q^42 + 549 * q^43 - 117 * q^44 - 251 * q^45 + 506 * q^46 + 767 * q^47 - 2082 * q^48 - 440 * q^49 - 1106 * q^50 - 456 * q^51 + 2053 * q^52 - 75 * q^53 - 2473 * q^54 + 201 * q^55 - 1278 * q^56 + 1176 * q^57 - 294 * q^58 + 871 * q^59 + 762 * q^60 - 2732 * q^61 - 603 * q^62 + 1165 * q^63 + 3518 * q^64 - 1392 * q^65 + 7624 * q^66 + 2635 * q^67 + 3025 * q^68 - 2468 * q^69 - 4724 * q^70 - 397 * q^71 - 6040 * q^72 + 3240 * q^73 - 1039 * q^74 - 3356 * q^75 - 2990 * q^76 - 319 * q^77 - 2654 * q^78 - 2340 * q^79 + 5284 * q^80 + 538 * q^81 - 687 * q^82 + 1243 * q^83 - 4271 * q^84 + 1397 * q^85 - 829 * q^86 - 1850 * q^87 + 991 * q^88 + 4068 * q^89 + 7258 * q^90 - 4778 * q^91 + 891 * q^92 - 3704 * q^93 + 5564 * q^94 - 3910 * q^95 - 3443 * q^96 + 2197 * q^97 + 994 * q^98 - 6033 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/103\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.46067	+	4.26201i	0.869979	+	1.50685i	0.862017	+	0.506879i	$0.169201\pi$
$2$	2.46067	+	4.26201i	0.869979	+	1.50685i	0.00796170	+	0.999968i	$0.497466\pi$
$3$	−9.26768			−1.78357			−0.891783	−	0.452464i	$-0.850545\pi$
$3$	−9.26768			−1.78357			−0.891783	+	0.452464i	$0.850545\pi$
$4$	−8.10981	+	14.0466i	−1.01373	+	1.75583i
$5$	−6.00715	+	10.4047i	−0.537296	+	0.930624i	0.461752	+	0.887009i	$0.347221\pi$
$5$	−6.00715	+	10.4047i	−0.537296	+	0.930624i	−0.999048	+	0.0436151i	$0.986112\pi$
$6$	−22.8047	−	39.4989i	−1.55166	−	2.68756i
$7$	15.4448	−	26.7511i	0.833940	−	1.44443i	−0.0609508	−	0.998141i	$-0.519413\pi$
$7$	15.4448	−	26.7511i	0.833940	−	1.44443i	0.894891	−	0.446285i	$-0.147253\pi$
$8$	−40.4516			−1.78772
$9$	58.8899			2.18111
$10$	−59.1265			−1.86974
$11$	−15.0523	+	26.0713i	−0.412585	+	0.714618i	−0.995172	−	0.0981507i	$-0.968707\pi$
$11$	−15.0523	+	26.0713i	−0.412585	+	0.714618i	0.582587	+	0.812768i	$0.302041\pi$
$12$	75.1591	−	130.179i	1.80805	−	3.13163i
$13$	−51.5593			−1.10000			−0.549999	−	0.835165i	$-0.685372\pi$
$13$	−51.5593			−1.10000			−0.549999	+	0.835165i	$0.685372\pi$
$14$	152.018			2.90204
$15$	55.6724	−	96.4274i	0.958303	−	1.65983i
$16$	−34.6596	−	60.0321i	−0.541556	−	0.938002i
$17$	−7.56962	+	13.1110i	−0.107994	+	0.187052i	−0.914958	−	0.403550i	$-0.867776\pi$
$17$	−7.56962	+	13.1110i	−0.107994	+	0.187052i	0.806963	+	0.590602i	$0.201109\pi$
$18$	144.909	+	250.989i	1.89752	+	3.28660i
$19$	−69.3640	−	120.142i	−0.837537	−	1.45066i	−0.891948	−	0.452138i	$-0.850662\pi$
$19$	−69.3640	−	120.142i	−0.837537	−	1.45066i	0.0544113	−	0.998519i	$-0.482672\pi$
$20$	−97.4337	−	168.760i	−1.08934	−	1.88680i
$21$	−143.137	+	247.921i	−1.48739	+	2.57623i
$22$	−148.155			−1.43576
$23$	−153.520			−1.39179			−0.695894	−	0.718144i	$-0.744992\pi$
$23$	−153.520			−1.39179			−0.695894	+	0.718144i	$0.744992\pi$
$24$	374.892			3.18852
$25$	−9.67174	−	16.7520i	−0.0773740	−	0.134016i
$26$	−126.871	−	219.746i	−0.956976	−	1.65753i
$27$	−295.545			−2.10658
$28$	250.509	+	433.893i	1.69077	+	2.92851i
$29$	10.2429	+	17.7413i	0.0655885	+	0.113603i	0.896955	−	0.442122i	$-0.145774\pi$
$29$	10.2429	+	17.7413i	0.0655885	+	0.113603i	−0.831366	+	0.555725i	$0.812441\pi$
$30$	547.966			3.33481
$31$	57.8733			0.335302			0.167651	−	0.985846i	$-0.446382\pi$
$31$	57.8733			0.335302			0.167651	+	0.985846i	$0.446382\pi$
$32$	8.76528	−	15.1819i	0.0484218	−	0.0838690i
$33$	139.500	−	241.621i	0.735872	−	1.27457i
$34$	−74.5054			−0.375811
$35$	185.558	+	321.396i	0.896145	+	1.55217i
$36$	−477.586	+	827.203i	−2.21105	+	3.82964i
$37$	−132.701			−0.589620			−0.294810	−	0.955556i	$-0.595256\pi$
$37$	−132.701			−0.589620			−0.294810	+	0.955556i	$0.595256\pi$
$38$	341.364	−	591.260i	1.45728	−	2.52408i
$39$	477.835			1.96192
$40$	242.999	−	420.886i	0.960537	−	1.66370i
$41$	59.0303	+	102.243i	0.224853	+	0.389457i	0.956275	−	0.292468i	$-0.0944764\pi$
$41$	59.0303	+	102.243i	0.224853	+	0.389457i	−0.731422	+	0.681925i	$0.761143\pi$
$42$	−1408.86			−5.17598
$43$	139.691	+	241.951i	0.495410	+	0.858076i	0.999986	−	0.00529171i	$-0.00168441\pi$
$43$	139.691	+	241.951i	0.495410	+	0.858076i	−0.504576	+	0.863367i	$0.668351\pi$
$44$	−244.142	−	422.867i	−0.836496	−	1.44885i
$45$	−353.760	+	612.731i	−1.17190	+	2.02979i
$46$	−377.762	−	654.304i	−1.21083	−	2.09721i
$47$	−27.8375	+	48.2160i	−0.0863940	+	0.149639i	−0.905984	−	0.423311i	$-0.860868\pi$
$47$	−27.8375	+	48.2160i	−0.0863940	+	0.149639i	0.819590	+	0.572950i	$0.194201\pi$
$48$	321.214	+	556.358i	0.965900	+	1.67299i
$49$	−305.583	−	529.285i	−0.890911	−	1.54310i
$50$	47.5980	−	82.4421i	0.134627	−	0.233181i
$51$	70.1528	−	121.508i	0.192615	−	0.333619i
$52$	418.136	−	724.233i	1.11510	−	1.93141i
$53$	−263.604	+	456.575i	−0.683184	+	1.18331i	0.290820	+	0.956778i	$0.406072\pi$
$53$	−263.604	+	456.575i	−0.683184	+	1.18331i	−0.974004	+	0.226531i	$0.927261\pi$
$54$	−727.240	−	1259.62i	−1.83268	−	3.17430i
$55$	−180.843	−	313.229i	−0.443360	−	0.767922i
$56$	−624.766	+	1082.13i	−1.49085	+	2.58224i
$57$	642.844	+	1113.44i	1.49380	+	2.58734i
$58$	−50.4090	+	87.3109i	−0.114121	+	0.197664i
$59$	258.987	+	448.579i	0.571479	+	0.989831i	0.996414	+	0.0846069i	$0.0269635\pi$
$59$	258.987	+	448.579i	0.571479	+	0.989831i	−0.424935	+	0.905224i	$0.639703\pi$
$60$	902.984	+	1564.01i	1.94291	+	3.36522i
$61$	−494.137			−1.03718			−0.518588	−	0.855024i	$-0.673542\pi$
$61$	−494.137			−1.03718			−0.518588	+	0.855024i	$0.673542\pi$
$62$	142.407	+	246.657i	0.291705	+	0.505249i
$63$	909.541	−	1575.37i	1.81891	−	3.15045i
$64$	−468.279			−0.914607
$65$	309.725	−	536.459i	0.591025	−	1.02369i
$66$	1373.05			2.56077
$67$	299.688	−	519.074i	0.546458	−	0.946492i	−0.452056	−	0.891990i	$-0.649309\pi$
$67$	299.688	−	519.074i	0.546458	−	0.946492i	0.998514	−	0.0545028i	$-0.0173574\pi$
$68$	−122.776	−	212.655i	−0.218953	−	0.379238i
$69$	1422.77			2.48235
$70$	−913.196	+	1581.70i	−1.55925	+	2.70071i
$71$	−120.141	+	208.091i	−0.200819	+	0.347829i	−0.948793	−	0.315900i	$-0.897694\pi$
$71$	−120.141	+	208.091i	−0.200819	+	0.347829i	0.747974	+	0.663729i	$0.231027\pi$
$72$	−2382.19			−3.89922
$73$	−674.492			−1.08141			−0.540707	−	0.841211i	$-0.681843\pi$
$73$	−674.492			−1.08141			−0.540707	+	0.841211i	$0.681843\pi$
$74$	−326.534	−	565.574i	−0.512957	−	0.888467i
$75$	89.6346	+	155.252i	0.138002	+	0.239026i
$76$	2250.12			3.39613
$77$	464.958	+	805.331i	0.688142	+	1.19190i
$78$	1175.80	+	2036.54i	1.70683	+	2.95631i
$79$	521.492			0.742689			0.371345	−	0.928495i	$-0.378897\pi$
$79$	521.492			0.742689			0.371345	+	0.928495i	$0.378897\pi$
$80$	832.821			1.16390
$81$	1148.99			1.57612
$82$	−290.508	+	503.175i	−0.391235	+	0.677639i
$83$	−581.897	−	1007.88i	−0.769536	−	1.33288i	−0.937815	−	0.347136i	$-0.887154\pi$
$83$	−581.897	−	1007.88i	−0.769536	−	1.33288i	0.168278	−	0.985740i	$-0.446179\pi$
$84$	−2321.63	−	4021.19i	−3.01561	−	5.22318i
$85$	−90.9437	−	157.519i	−0.116050	−	0.201004i
$86$	−687.466	+	1190.73i	−0.861993	+	1.49302i
$87$	−94.9282	−	164.421i	−0.116981	−	0.202618i
$88$	608.888	−	1054.63i	0.737588	−	1.27754i
$89$	−23.0448			−0.0274466			−0.0137233	−	0.999906i	$-0.504368\pi$
$89$	−23.0448			−0.0274466			−0.0137233	+	0.999906i	$0.504368\pi$
$90$	−3481.95			−4.07811
$91$	−796.323	+	1379.27i	−0.917333	+	1.58887i
$92$	1245.02	−	2156.43i	1.41089	−	2.44374i
$93$	−536.351			−0.598033
$94$	−273.996			−0.300644
$95$	1666.72			1.80002
$96$	−81.2338	+	140.701i	−0.0863635	+	0.149586i
$97$	−356.071	−	616.733i	−0.372717	−	0.645564i	0.617266	−	0.786755i	$-0.288240\pi$
$97$	−356.071	−	616.733i	−0.372717	−	0.645564i	−0.989982	+	0.141190i	$0.954907\pi$
$98$	1503.88	−	2604.79i	1.55015	−	2.68494i
$99$	−886.427	+	1535.34i	−0.899891	+	1.55866i
$100$	313.744			0.313744
$101$	607.766	+	1052.68i	0.598762	+	1.03709i	0.993004	+	0.118080i	$0.0376740\pi$
$101$	607.766	+	1052.68i	0.598762	+	1.03709i	−0.394242	+	0.919007i	$0.628993\pi$
$102$	690.492			0.670284
$103$	379.906	+	973.857i	0.363430	+	0.931621i
$103$	379.906	+	973.857i	0.363430	+	0.931621i
$104$	2085.66			1.96649
$105$	−1719.69	−	2978.60i	−1.59833	−	2.76840i
$106$	−2594.57			−2.37742
$107$	127.198	−	220.313i	0.114922	−	0.199051i	−0.802827	−	0.596213i	$-0.796672\pi$
$107$	127.198	−	220.313i	0.114922	−	0.199051i	0.917749	+	0.397162i	$0.130005\pi$
$108$	2396.82	−	4151.41i	2.13550	−	3.69879i
$109$	652.353	+	1129.91i	0.573249	+	0.992896i	0.996230	+	0.0867570i	$0.0276504\pi$
$109$	652.353	+	1129.91i	0.573249	+	0.992896i	−0.422981	+	0.906139i	$0.639016\pi$
$110$	889.989	−	1541.51i	0.771428	−	1.33615i
$111$	1229.83			1.05163
$112$	−2141.24			−1.80650
$113$	−1186.82			−0.988023			−0.494011	−	0.869455i	$-0.664470\pi$
$113$	−1186.82			−0.988023			−0.494011	+	0.869455i	$0.664470\pi$
$114$	−3163.65	+	5479.61i	−2.59915	+	4.50186i
$115$	922.218	−	1597.33i	0.747802	−	1.29523i
$116$	−332.273			−0.265955
$117$	−3036.32			−2.39922
$118$	−1274.56	+	2207.61i	−0.994349	+	1.72226i
$119$	233.822	+	404.992i	0.180121	+	0.311980i
$120$	−2252.03	+	3900.64i	−1.71318	+	2.96732i
$121$	212.358	+	367.815i	0.159548	+	0.276345i
$122$	−1215.91	−	2106.01i	−0.902321	−	1.56287i
$123$	−547.074	−	947.559i	−0.401040	−	0.694622i
$124$	−469.342	+	812.924i	−0.339904	+	0.588731i
$125$	−1269.39			−0.908301
$126$	8952.33			6.32966
$127$	842.876			0.588922			0.294461	−	0.955663i	$-0.404860\pi$
$127$	842.876			0.588922			0.294461	+	0.955663i	$0.404860\pi$
$128$	−1222.40	−	2117.26i	−0.844111	−	1.46204i
$129$	−1294.61	−	2242.33i	−0.883597	−	1.53043i
$130$	3048.52			2.05672
$131$	665.719	+	1153.06i	0.444001	+	0.769032i	0.997982	−	0.0634971i	$-0.0202254\pi$
$131$	665.719	+	1153.06i	0.444001	+	0.769032i	−0.553981	+	0.832529i	$0.686892\pi$
$132$	2262.63	+	3918.99i	1.49195	+	2.58413i
$133$	−4285.25			−2.79382
$134$	2949.73			1.90163
$135$	1775.38	−	3075.06i	1.13186	−	1.96044i
$136$	306.203	−	530.359i	0.193064	−	0.334397i
$137$	1862.89			1.16174			0.580868	−	0.813998i	$-0.302713\pi$
$137$	1862.89			1.16174			0.580868	+	0.813998i	$0.302713\pi$
$138$	3500.98	+	6063.88i	2.15959	+	3.74052i
$139$	−218.931	+	379.199i	−0.133593	+	0.231390i	−0.925059	−	0.379823i	$-0.875985\pi$
$139$	−218.931	+	379.199i	−0.133593	+	0.231390i	0.791466	+	0.611213i	$0.209318\pi$
$140$	−6019.37			−3.63378
$141$	257.989	−	446.850i	0.154089	−	0.266891i
$142$	−1182.51			−0.698833
$143$	776.085	−	1344.22i	0.453843	−	0.786079i
$144$	−2041.10	−	3535.28i	−1.18119	−	2.04588i
$145$	−246.123			−0.140962
$146$	−1659.70	−	2874.69i	−0.940808	−	1.62953i
$147$	2832.04	+	4905.24i	1.58900	+	2.75223i
$148$	1076.18	−	1864.00i	0.597713	−	1.03527i
$149$	−166.003	−	287.526i	−0.0912720	−	0.158088i	0.816775	−	0.576957i	$-0.195760\pi$
$149$	−166.003	−	287.526i	−0.0912720	−	0.158088i	−0.908047	+	0.418869i	$0.862427\pi$
$150$	−441.123	+	764.047i	−0.240117	+	0.415895i
$151$	761.985	+	1319.80i	0.410659	+	0.711282i	0.994962	−	0.100254i	$-0.0319655\pi$
$151$	761.985	+	1319.80i	0.410659	+	0.711282i	−0.584303	+	0.811535i	$0.698632\pi$
$152$	2805.88	+	4859.93i	1.49728	+	2.59337i
$153$	−445.774	+	772.103i	−0.235547	+	0.407980i
$154$	−2288.22	+	3963.31i	−1.19734	+	2.07385i
$155$	−347.654	+	602.154i	−0.180156	+	0.312040i
$156$	−3875.15	+	6711.96i	−1.98885	+	3.44479i
$157$	534.223	+	925.301i	0.271564	+	0.470363i	0.969263	−	0.246028i	$-0.0791257\pi$
$157$	534.223	+	925.301i	0.271564	+	0.470363i	−0.697698	+	0.716392i	$0.745792\pi$
$158$	1283.22	+	2222.60i	0.646124	+	1.11912i
$159$	2442.99	−	4231.39i	1.21850	−	2.11051i
$160$	105.309	+	182.400i	0.0520337	+	0.0901250i
$161$	−2371.08	+	4106.84i	−1.16067	+	2.01034i
$162$	2827.29	+	4897.01i	1.37119	+	2.37497i
$163$	695.431	+	1204.52i	0.334174	+	0.578807i	0.983326	−	0.181852i	$-0.0582093\pi$
$163$	695.431	+	1204.52i	0.334174	+	0.578807i	−0.649152	+	0.760659i	$0.724876\pi$
$164$	−1914.90			−0.911758
$165$	1675.99	+	2902.90i	0.790762	+	1.36964i
$166$	2863.72	−	4960.10i	1.33896	−	2.31915i
$167$	−2675.23			−1.23962			−0.619808	−	0.784754i	$-0.712789\pi$
$167$	−2675.23			−1.23962			−0.619808	+	0.784754i	$0.712789\pi$
$168$	5790.13	−	10028.8i	2.65904	−	4.60559i
$169$	461.365			0.209998
$170$	447.565	−	775.206i	0.201922	−	0.349739i
$171$	−4084.84	−	7075.15i	−1.82676	−	3.16404i
$172$	−4531.46			−2.00884
$173$	2034.84	−	3524.44i	0.894252	−	1.54889i	0.0595250	−	0.998227i	$-0.481041\pi$
$173$	2034.84	−	3524.44i	0.894252	−	1.54889i	0.834727	−	0.550664i	$-0.185625\pi$
$174$	467.174	−	809.170i	0.203543	−	0.352546i
$175$	−597.512			−0.258101
$176$	2086.82			0.893750
$177$	−2400.21	−	4157.29i	−1.01927	−	1.76543i
$178$	−56.7058	−	98.2172i	−0.0238780	−	0.0413578i
$179$	−1221.04			−0.509860			−0.254930	−	0.966960i	$-0.582052\pi$
$179$	−1221.04			−0.509860			−0.254930	+	0.966960i	$0.582052\pi$
$180$	−5737.86	−	9938.27i	−2.37597	−	4.11530i
$181$	−1097.01	−	1900.08i	−0.450499	−	0.780287i	0.547918	−	0.836532i	$-0.315421\pi$
$181$	−1097.01	−	1900.08i	−0.450499	−	0.780287i	−0.998417	+	0.0562448i	$0.982087\pi$
$182$	−7837.95			−3.19224
$183$	4579.50			1.84987
$184$	6210.13			2.48813
$185$	797.156	−	1380.71i	0.316800	−	0.548714i
$186$	−1319.78	−	2285.93i	−0.520276	−	0.901144i
$187$	−227.880	−	394.700i	−0.0891136	−	0.154349i
$188$	−451.514	−	782.045i	−0.175160	−	0.303386i
$189$	−4564.63	+	7906.17i	−1.75676	+	3.04280i
$190$	4101.25	+	7103.58i	1.56598	+	2.71236i
$191$	350.334	−	606.796i	0.132719	−	0.229876i	−0.792005	−	0.610515i	$-0.790963\pi$
$191$	350.334	−	606.796i	0.132719	−	0.229876i	0.924724	+	0.380639i	$0.124296\pi$
$192$	4339.86			1.63126
$193$	−280.630			−0.104664			−0.0523322	−	0.998630i	$-0.516665\pi$
$193$	−280.630			−0.104664			−0.0523322	+	0.998630i	$0.516665\pi$
$194$	1752.35	−	3035.15i	0.648511	−	1.12325i
$195$	−2870.43	+	4971.73i	−1.05413	+	1.82581i
$196$	9912.87			3.61256
$197$	−1246.06			−0.450650			−0.225325	−	0.974284i	$-0.572344\pi$
$197$	−1246.06			−0.450650			−0.225325	+	0.974284i	$0.572344\pi$
$198$	−8724.82			−3.13155
$199$	−3.31820	+	5.74729i	−0.00118201	+	0.00204731i	−0.866616	−	0.498976i	$-0.833710\pi$
$199$	−3.31820	+	5.74729i	−0.00118201	+	0.00204731i	0.865434	+	0.501023i	$0.167043\pi$
$200$	391.237	+	677.643i	0.138323	+	0.239583i
$201$	−2777.41	+	4810.61i	−0.974643	+	1.68813i
$202$	−2991.03	+	5180.61i	−1.04182	+	1.80449i
$203$	632.800			0.218787
$204$	1137.85	+	1970.82i	0.390518	+	0.676396i
$205$	−1418.42			−0.483251
$206$	−3215.76	+	4015.51i	−1.08764	+	1.35812i
$207$	−9040.78			−3.03564
$208$	1787.02	+	3095.22i	0.595711	+	1.03180i
$209$	4176.35			1.38222
$210$	8463.21	−	14658.7i	2.78103	−	4.81689i
$211$	−610.197	+	1056.89i	−0.199089	+	0.344832i	−0.948233	−	0.317575i	$-0.897132\pi$
$211$	−610.197	+	1056.89i	−0.199089	+	0.344832i	0.749144	+	0.662407i	$0.230465\pi$
$212$	−4275.55	−	7405.47i	−1.38512	−	2.39910i
$213$	1113.43	−	1928.52i	0.358174	−	0.620376i
$214$	1251.97			0.399919
$215$	−3356.57			−1.06473
$216$	11955.3			3.76599
$217$	893.841	−	1548.18i	0.279622	−	0.484319i
$218$	−3210.45	+	5560.67i	−0.997428	+	1.72760i
$219$	6250.97			1.92877
$220$	5866.40			1.79778
$221$	390.285	−	675.993i	0.118794	−	0.205757i
$222$	3026.21	+	5241.55i	0.914892	+	1.58464i
$223$	46.5874	−	80.6917i	0.0139898	−	0.0242310i	−0.858946	−	0.512067i	$-0.828880\pi$
$223$	46.5874	−	80.6917i	0.0139898	−	0.0242310i	0.872936	+	0.487836i	$0.162213\pi$
$224$	−270.756	−	468.963i	−0.0807618	−	0.139883i
$225$	−569.568	−	986.520i	−0.168761	−	0.292302i
$226$	−2920.37	−	5058.23i	−0.859559	−	1.48880i
$227$	−1758.82	+	3046.37i	−0.514261	+	0.890727i	0.485602	+	0.874180i	$0.338600\pi$
$227$	−1758.82	+	3046.37i	−0.514261	+	0.890727i	−0.999863	+	0.0165464i	$0.994733\pi$
$228$	−20853.4			−6.05723
$229$	2355.87			0.679828			0.339914	−	0.940457i	$-0.389602\pi$
$229$	2355.87			0.679828			0.339914	+	0.940457i	$0.389602\pi$
$230$	9077.10			2.60229
$231$	−4309.08	−	7463.55i	−1.22735	−	2.12583i
$232$	−414.343	−	717.663i	−0.117254	−	0.203090i
$233$	3040.37			0.854855			0.427427	−	0.904050i	$-0.359420\pi$
$233$	3040.37			0.854855			0.427427	+	0.904050i	$0.359420\pi$
$234$	−7471.39	−	12940.8i	−2.08727	−	3.61525i
$235$	−334.448	−	579.282i	−0.0928383	−	0.160801i
$236$	−8401.35			−2.31729
$237$	−4833.02			−1.32463
$238$	−1150.72	+	1993.11i	−0.313404	+	0.542831i
$239$	1562.44	−	2706.23i	0.422871	−	0.732433i	−0.573348	−	0.819312i	$-0.694356\pi$
$239$	1562.44	−	2706.23i	0.422871	−	0.732433i	0.996219	+	0.0868784i	$0.0276892\pi$
$240$	−7718.32			−2.07590
$241$	3487.86	+	6041.15i	0.932252	+	1.61471i	0.779463	+	0.626448i	$0.215492\pi$
$241$	3487.86	+	6041.15i	0.932252	+	1.61471i	0.152789	+	0.988259i	$0.451175\pi$
$242$	−1045.09	+	1810.14i	−0.277606	+	0.480828i
$243$	−2668.76			−0.704532
$244$	4007.35	−	6940.94i	1.05141	−	1.82110i
$245$	7342.72			1.91473
$246$	2692.34	−	4663.27i	0.697793	−	1.20861i
$247$	3576.36	+	6194.44i	0.921290	+	1.59572i
$248$	−2341.07			−0.599427
$249$	5392.84	+	9340.67i	1.37252	+	2.37727i
$250$	−3123.55	−	5410.15i	−0.790203	−	1.36867i
$251$	820.612	−	1421.34i	0.206361	−	0.357428i	−0.744205	−	0.667952i	$-0.767171\pi$
$251$	820.612	−	1421.34i	0.206361	−	0.357428i	0.950565	+	0.310524i	$0.100505\pi$
$252$	14752.4	+	25551.9i	3.68776	+	6.38738i
$253$	2310.83	−	4002.47i	0.574231	−	0.994597i
$254$	2074.04	+	3592.34i	0.512350	+	0.887416i
$255$	842.837	+	1459.84i	0.206982	+	0.358504i
$256$	4142.75	−	7175.45i	1.01141	−	1.75182i
$257$	1298.19	−	2248.53i	0.315093	−	0.545757i	−0.664364	−	0.747409i	$-0.731298\pi$
$257$	1298.19	−	2248.53i	0.315093	−	0.545757i	0.979457	+	0.201652i	$0.0646309\pi$
$258$	6371.22	−	11035.3i	1.53742	−	2.66289i
$259$	−2049.54	+	3549.91i	−0.491708	+	0.851663i
$260$	5023.62	+	8701.16i	1.19828	+	2.07547i
$261$	603.205	+	1044.78i	0.143055	+	0.247779i
$262$	−3276.23	+	5674.60i	−0.772543	+	1.33808i
$263$	−2510.07	−	4347.58i	−0.588509	−	1.01933i	−0.994428	−	0.105418i	$-0.966382\pi$
$263$	−2510.07	−	4347.58i	−0.588509	−	1.01933i	0.405919	−	0.913909i	$-0.366951\pi$
$264$	−5642.98	+	9773.93i	−1.31554	+	2.27858i
$265$	−3167.01	−	5485.43i	−0.734144	−	1.27157i
$266$	−10544.6	−	18263.8i	−2.43057	−	4.20986i
$267$	213.572			0.0489528
$268$	4860.82	+	8419.18i	1.10792	+	1.91897i
$269$	2076.68	−	3596.91i	0.470696	−	0.815270i	−0.528742	−	0.848783i	$-0.677336\pi$
$269$	2076.68	−	3596.91i	0.470696	−	0.815270i	0.999438	+	0.0335127i	$0.0106694\pi$
$270$	17474.6			3.93877
$271$	−2308.68	+	3998.75i	−0.517500	+	0.896336i	0.482294	+	0.876010i	$0.339804\pi$
$271$	−2308.68	+	3998.75i	−0.517500	+	0.896336i	−0.999793	+	0.0203262i	$0.993530\pi$
$272$	1049.44			0.233940
$273$	7380.06	−	12782.6i	1.63612	−	2.83385i
$274$	4583.97	+	7939.67i	1.01069	+	1.75056i
$275$	582.327			0.127693
$276$	−11538.4	+	19985.1i	−2.51642	+	4.35857i
$277$	−236.908	+	410.338i	−0.0513879	+	0.0890065i	−0.890575	−	0.454836i	$-0.849698\pi$
$277$	−236.908	+	410.338i	−0.0513879	+	0.0890065i	0.839187	+	0.543843i	$0.183031\pi$
$278$	−2154.86			−0.464893
$279$	3408.15			0.731329
$280$	−7506.12	−	13001.0i	−1.60206	−	2.77485i
$281$	−334.698	−	579.714i	−0.0710549	−	0.123071i	0.828309	−	0.560272i	$-0.189303\pi$
$281$	−334.698	−	579.714i	−0.0710549	−	0.123071i	−0.899364	+	0.437201i	$0.855970\pi$
$282$	2539.31			0.536218
$283$	−3069.67	−	5316.82i	−0.644780	−	1.11679i	−0.984352	−	0.176212i	$-0.943615\pi$
$283$	−3069.67	−	5316.82i	−0.644780	−	1.11679i	0.339572	−	0.940580i	$-0.389718\pi$
$284$	−1948.65	−	3375.16i	−0.407151	−	0.705206i
$285$	−15446.6			−3.21046
$286$	7638.76			1.57933
$287$	3646.84			0.750056
$288$	516.187	−	894.061i	0.105613	−	0.182927i
$289$	2341.90	+	4056.29i	0.476674	+	0.825624i
$290$	−605.629	−	1048.98i	−0.122634	−	0.212408i
$291$	3299.95	+	5715.68i	0.664765	+	1.15141i
$292$	5470.00	−	9474.32i	1.09626	−	1.89878i
$293$	3549.61	+	6148.11i	0.707749	+	1.22586i	0.965690	+	0.259697i	$0.0836225\pi$
$293$	3549.61	+	6148.11i	0.707749	+	1.22586i	−0.257941	+	0.966161i	$0.583044\pi$
$294$	−13937.4	+	24140.4i	−2.76479	+	4.78876i
$295$	−6223.10			−1.22821
$296$	5367.97			1.05408
$297$	4448.63	−	7705.25i	0.869143	−	1.50540i
$298$	816.960	−	1415.02i	0.158809	−	0.275066i
$299$	7915.39			1.53097
$300$	−2907.68			−0.559583
$301$	8629.97			1.65257
$302$	−3749.99	+	6495.17i	−0.714529	+	1.23760i
$303$	−5632.58	−	9755.92i	−1.06793	−	1.84971i
$304$	−4808.25	+	8328.14i	−0.907145	+	1.57122i
$305$	2968.35	−	5141.34i	0.557270	−	0.965220i
$306$	−4387.62			−0.819684
$307$	−4722.49	−	8179.60i	−0.877938	−	1.52063i	−0.853600	−	0.520930i	$-0.825585\pi$
$307$	−4722.49	−	8179.60i	−0.877938	−	1.52063i	−0.0243386	−	0.999704i	$-0.507748\pi$
$308$	−15082.9			−2.79035
$309$	−3520.85	−	9025.40i	−0.648201	−	1.66161i
$310$	−3421.85			−0.626929
$311$	−1669.09	−	2890.95i	−0.304327	−	0.527109i	0.672785	−	0.739838i	$-0.265098\pi$
$311$	−1669.09	−	2890.95i	−0.304327	−	0.527109i	−0.977111	+	0.212729i	$0.931765\pi$
$312$	−19329.2			−3.50737
$313$	−4608.02	+	7981.33i	−0.832143	+	1.44131i	0.0641918	+	0.997938i	$0.479553\pi$
$313$	−4608.02	+	7981.33i	−0.832143	+	1.44131i	−0.896335	+	0.443377i	$0.853780\pi$
$314$	−2629.09	+	4553.72i	−0.472511	+	0.818412i
$315$	10927.5	+	18927.0i	1.95459	+	3.38545i
$316$	−4229.20	+	7325.19i	−0.752883	+	1.30403i
$317$	−4526.03			−0.801915			−0.400957	−	0.916097i	$-0.631322\pi$
$317$	−4526.03			−0.801915			−0.400957	+	0.916097i	$0.631322\pi$
$318$	24045.6			4.24029
$319$	−616.718			−0.108243
$320$	2813.02	−	4872.30i	0.491415	−	0.851155i
$321$	−1178.83	+	2041.79i	−0.204971	+	0.355020i
$322$	−23337.8			−4.03903
$323$	2100.24			0.361797
$324$	−9318.10	+	16139.4i	−1.59775	+	2.76739i
$325$	498.669	+	863.719i	0.0851113	+	0.147417i
$326$	−3422.46	+	5927.87i	−0.581449	+	1.00710i
$327$	−6045.80	−	10471.6i	−1.02243	−	1.77089i
$328$	−2387.87	−	4135.91i	−0.401975	−	0.696242i
$329$	859.889	+	1489.37i	0.144095	+	0.249580i
$330$	−8248.13	+	14286.2i	−1.37589	+	2.38312i
$331$	−3111.08			−0.516618			−0.258309	−	0.966062i	$-0.583165\pi$
$331$	−3111.08			−0.516618			−0.258309	+	0.966062i	$0.583165\pi$
$332$	18876.3			3.12040
$333$	−7814.76			−1.28602
$334$	−6582.87	−	11401.9i	−1.07844	−	1.86791i
$335$	3600.54	+	6236.31i	0.587219	+	1.01709i
$336$	19844.3			3.22201
$337$	−5618.43	−	9731.41i	−0.908176	−	1.57301i	−0.816596	−	0.577210i	$-0.804141\pi$
$337$	−5618.43	−	9731.41i	−0.908176	−	1.57301i	−0.0915808	−	0.995798i	$-0.529192\pi$
$338$	1135.27	+	1966.34i	0.182694	+	0.316434i
$339$	10999.1			1.76220
$340$	2950.15			0.470571
$341$	−871.125	+	1508.83i	−0.138340	+	0.239613i
$342$	20102.9	−	34819.2i	3.17848	−	5.50529i
$343$	−8283.51			−1.30399
$344$	−5650.71	−	9787.32i	−0.885657	−	1.53400i
$345$	−8546.82	+	14803.5i	−1.33375	+	2.31013i
$346$	20028.2			3.11192
$347$	3896.54	−	6749.01i	0.602817	−	1.04411i	−0.389575	−	0.920995i	$-0.627378\pi$
$347$	3896.54	−	6749.01i	0.602817	−	1.04411i	0.992392	−	0.123115i	$-0.0392884\pi$
$348$	3079.40			0.474348
$349$	−4244.36	+	7351.45i	−0.650989	+	1.12755i	0.331894	+	0.943317i	$0.392312\pi$
$349$	−4244.36	+	7351.45i	−0.650989	+	1.12755i	−0.982883	+	0.184230i	$0.941021\pi$
$350$	−1470.28	−	2546.60i	−0.224542	−	0.388919i
$351$	15238.1			2.31724
$352$	263.875	+	457.045i	0.0399562	+	0.0692062i
$353$	5597.13	+	9694.51i	0.843924	+	1.46172i	0.886553	+	0.462628i	$0.153093\pi$
$353$	5597.13	+	9694.51i	0.843924	+	1.46172i	−0.0426292	+	0.999091i	$0.513573\pi$
$354$	11812.3	−	20459.4i	1.77349	−	3.07177i
$355$	−1443.41	−	2500.07i	−0.215799	−	0.373774i
$356$	186.889	−	323.702i	0.0278233	−	0.0481914i
$357$	−2166.99	−	3753.34i	−0.321259	−	0.556436i
$358$	−3004.58	−	5204.09i	−0.443567	−	0.768281i
$359$	−3403.45	+	5894.95i	−0.500354	+	0.866639i	0.499646	+	0.866230i	$0.333464\pi$
$359$	−3403.45	+	5894.95i	−0.500354	+	0.866639i	−1.00000		0.000409182i	$0.999870\pi$
$360$	14310.2	−	24785.9i	2.09503	−	3.62870i
$361$	−6193.24	+	10727.0i	−0.902936	+	1.56393i
$362$	5398.78	−	9350.96i	0.783849	−	1.35767i
$363$	−1968.07	−	3408.79i	−0.284564	−	0.492879i
$364$	−12916.1	−	22371.3i	−1.85985	−	3.22135i
$365$	4051.77	−	7017.88i	0.581040	−	1.00639i
$366$	11268.6	+	19517.9i	1.60935	+	2.78747i
$367$	511.600	−	886.116i	0.0727664	−	0.126035i	−0.827346	−	0.561692i	$-0.810151\pi$
$367$	511.600	−	886.116i	0.0727664	−	0.126035i	0.900113	+	0.435657i	$0.143484\pi$
$368$	5320.94	+	9216.13i	0.753731	+	1.30550i
$369$	3476.29	+	6021.10i	0.490429	+	0.849448i
$370$	7846.16			1.10244
$371$	8142.60	+	14103.4i	1.13947	+	1.97362i
$372$	4349.71	−	7533.91i	0.606242	−	1.05004i
$373$	7373.86			1.02360			0.511802	−	0.859104i	$-0.328978\pi$
$373$	7373.86			1.02360			0.511802	+	0.859104i	$0.328978\pi$
$374$	1121.48	−	1942.45i	0.155054	−	0.268561i
$375$	11764.3			1.62001
$376$	1126.07	−	1950.41i	0.154449	−	0.267513i
$377$	−528.119	−	914.729i	−0.0721472	−	0.124963i
$378$	−44928.2			−6.11338
$379$	4674.80	−	8096.98i	0.633584	−	1.09740i	−0.353230	−	0.935537i	$-0.614917\pi$
$379$	4674.80	−	8096.98i	0.633584	−	1.09740i	0.986813	−	0.161862i	$-0.0517500\pi$
$380$	−13516.8	+	23411.8i	−1.82473	+	3.16052i
$381$	−7811.51			−1.05038
$382$	3448.23			0.461850
$383$	−1810.78	−	3136.36i	−0.241584	−	0.418435i	0.719582	−	0.694408i	$-0.244334\pi$
$383$	−1810.78	−	3136.36i	−0.241584	−	0.418435i	−0.961166	+	0.275972i	$0.911000\pi$
$384$	11328.8	+	19622.1i	1.50553	+	2.60765i
$385$	−11172.3			−1.47894
$386$	−690.539	−	1196.05i	−0.0910557	−	0.157713i
$387$	8226.37	+	14248.5i	1.08054	+	1.87155i
$388$	11550.7			1.51133
$389$	−4690.78			−0.611393			−0.305696	−	0.952129i	$-0.598889\pi$
$389$	−4690.78			−0.611393			−0.305696	+	0.952129i	$0.598889\pi$
$390$	−28252.7			−3.66829
$391$	1162.09	−	2012.80i	0.150305	−	0.260336i
$392$	12361.3	+	21410.4i	1.59270	+	2.75864i
$393$	−6169.67	−	10686.2i	−0.791905	−	1.37162i
$394$	−3066.15	−	5310.72i	−0.392056	−	0.679061i
$395$	−3132.68	+	5425.96i	−0.399044	+	0.691164i
$396$	−14377.5	−	24902.6i	−1.82449	−	3.16010i
$397$	2569.71	−	4450.86i	0.324861	−	0.562676i	−0.656623	−	0.754219i	$-0.728016\pi$
$397$	2569.71	−	4450.86i	0.324861	−	0.562676i	0.981484	+	0.191543i	$0.0613491\pi$
$398$	−32.6600			−0.00411331
$399$	39714.3			4.98296
$400$	−670.437	+	1161.23i	−0.0838046	+	0.145154i
$401$	−1949.82	+	3377.18i	−0.242816	+	0.420569i	−0.961515	−	0.274752i	$-0.911404\pi$
$401$	−1949.82	+	3377.18i	−0.242816	+	0.420569i	0.718699	+	0.695321i	$0.244738\pi$
$402$	−27337.2			−3.39168
$403$	−2983.91			−0.368832
$404$	−19715.5			−2.42792
$405$	−6902.17	+	11954.9i	−0.846843	+	1.46678i
$406$	1557.11	+	2697.00i	0.190340	+	0.329679i
$407$	1997.45	−	3459.69i	0.243268	−	0.421353i
$408$	−2837.79	+	4915.20i	−0.344342	+	0.596418i
$409$	5919.80			0.715685			0.357843	−	0.933782i	$-0.383512\pi$
$409$	5919.80			0.715685			0.357843	+	0.933782i	$0.383512\pi$
$410$	−3490.25	−	6045.30i	−0.420418	−	0.728185i
$411$	−17264.7			−2.07203
$412$	−16760.4	−	2561.40i	−2.00418	−	0.306289i
$413$	16000.0			1.90632
$414$	−22246.4	−	38531.9i	−2.64094	−	4.57425i
$415$	13982.2			1.65387
$416$	−451.932	+	782.769i	−0.0532639	+	0.0922558i
$417$	2028.98	−	3514.29i	0.238272	−	0.412699i
$418$	10276.6	+	17799.6i	1.20250	+	2.08279i
$419$	−1458.72	+	2526.58i	−0.170079	+	0.294586i	−0.938447	−	0.345422i	$-0.887736\pi$
$419$	−1458.72	+	2526.58i	−0.170079	+	0.294586i	0.768368	+	0.640008i	$0.221069\pi$
$420$	55785.6			6.48109
$421$	16397.7			1.89828			0.949138	−	0.314859i	$-0.101957\pi$
$421$	16397.7			1.89828			0.949138	+	0.314859i	$0.101957\pi$
$422$	−6005.98			−0.692812
$423$	−1639.35	+	2839.43i	−0.188435	+	0.326378i
$424$	10663.2	−	18469.2i	1.22134	−	2.11543i
$425$	292.846			0.0334238
$426$	10959.2			1.24642
$427$	−7631.83	+	13218.7i	−0.864942	+	1.49812i
$428$	2063.10	+	3573.39i	0.232999	+	0.403566i
$429$	−7192.51	+	12457.8i	−0.809458	+	1.40202i
$430$	−8259.43	−	14305.7i	−0.926291	−	1.60438i
$431$	−8601.07	−	14897.5i	−0.961251	−	1.66493i	−0.719368	−	0.694629i	$-0.755568\pi$
$431$	−8601.07	−	14897.5i	−0.961251	−	1.66493i	−0.241883	−	0.970305i	$-0.577765\pi$
$432$	10243.5	+	17742.2i	1.14083	+	1.97598i
$433$	−3713.36	+	6431.72i	−0.412130	+	0.713831i	−0.995122	−	0.0986470i	$-0.968549\pi$
$433$	−3713.36	+	6431.72i	−0.412130	+	0.713831i	0.582992	+	0.812478i	$0.301882\pi$
$434$	8797.80			0.973059
$435$	2280.99			0.251414
$436$	−21161.8			−2.32447
$437$	10648.8	+	18444.2i	1.16567	+	2.01901i
$438$	15381.6	+	26641.7i	1.67799	+	2.90637i
$439$	−5918.67			−0.643469			−0.321735	−	0.946830i	$-0.604266\pi$
$439$	−5918.67			−0.643469			−0.321735	+	0.946830i	$0.604266\pi$
$440$	7315.37	+	12670.6i	0.792606	+	1.37283i
$441$	−17995.7	−	31169.5i	−1.94317	−	3.36567i
$442$	3841.45			0.413392
$443$	−7800.38			−0.836586			−0.418293	−	0.908312i	$-0.637371\pi$
$443$	−7800.38			−0.836586			−0.418293	+	0.908312i	$0.637371\pi$
$444$	−9973.70	+	17275.0i	−1.06606	+	1.84647i
$445$	138.434	−	239.774i	0.0147469	−	0.0255425i
$446$	458.545			0.0486832
$447$	1538.47	+	2664.70i	0.162790	+	0.281960i
$448$	−7232.47	+	12527.0i	−0.762727	+	1.32108i
$449$	−7763.83			−0.816031			−0.408015	−	0.912975i	$-0.633779\pi$
$449$	−7763.83			−0.816031			−0.408015	+	0.912975i	$0.633779\pi$
$450$	2803.04	−	4855.01i	0.293637	−	0.508594i
$451$	−3554.16			−0.371084
$452$	9624.88	−	16670.8i	1.00158	−	1.73480i
$453$	−7061.83	−	12231.5i	−0.732437	−	1.26862i
$454$	−17311.6			−1.78959
$455$	−9567.26	−	16571.0i	−0.985759	−	1.70738i
$456$	−26004.0	−	45040.3i	−2.67051	−	4.62545i
$457$	−3066.67	+	5311.63i	−0.313901	+	0.543693i	−0.979203	−	0.202882i	$-0.934969\pi$
$457$	−3066.67	+	5311.63i	−0.313901	+	0.543693i	0.665302	+	0.746574i	$0.268303\pi$
$458$	5797.03	+	10040.8i	0.591436	+	1.02440i
$459$	2237.17	−	3874.88i	0.227499	−	0.394039i
$460$	14958.0	+	25908.1i	1.51613	+	2.62602i
$461$	8095.95	+	14022.6i	0.817930	+	1.41670i	0.907205	+	0.420690i	$0.138212\pi$
$461$	8095.95	+	14022.6i	0.817930	+	1.41670i	−0.0892744	+	0.996007i	$0.528455\pi$
$462$	21206.5	−	36730.7i	2.13553	−	3.69885i
$463$	−2521.45	+	4367.28i	−0.253093	+	0.438369i	−0.964376	−	0.264536i	$-0.914781\pi$
$463$	−2521.45	+	4367.28i	−0.253093	+	0.438369i	0.711283	+	0.702906i	$0.248114\pi$
$464$	710.031	−	1229.81i	0.0710396	−	0.123044i
$465$	3221.94	−	5580.57i	0.321321	−	0.556544i
$466$	7481.35	+	12958.1i	0.743706	+	1.28814i
$467$	1586.13	+	2747.26i	0.157168	+	0.272223i	0.933846	−	0.357674i	$-0.116430\pi$
$467$	1586.13	+	2747.26i	0.157168	+	0.272223i	−0.776678	+	0.629898i	$0.783097\pi$
$468$	24624.0	−	42650.0i	2.43215	−	4.21260i
$469$	−9257.22	−	16034.0i	−0.911426	−	1.57864i
$470$	1645.94	−	2850.84i	0.161535	−	0.279786i
$471$	−4951.01	−	8575.39i	−0.484353	−	0.838924i
$472$	−10476.4	−	18145.7i	−1.02165	−	1.76954i
$473$	−8410.66			−0.817595
$474$	−11892.5	−	20598.4i	−1.15240	−	1.99602i
$475$	−1341.74	+	2323.97i	−0.129607	+	0.224486i
$476$	−7585.02			−0.730376
$477$	−15523.6	+	26887.6i	−1.49010	+	2.58092i
$478$	15378.6			1.47155
$479$	−8972.41	+	15540.7i	−0.855866	+	1.48240i	0.0199726	+	0.999801i	$0.493642\pi$
$479$	−8972.41	+	15540.7i	−0.855866	+	1.48240i	−0.875839	+	0.482604i	$0.839691\pi$
$480$	−975.968	−	1690.43i	−0.0928055	−	0.160744i
$481$	6841.98			0.648581
$482$	−17164.9	+	29730.6i	−1.62208	+	2.80952i
$483$	21974.4	−	38060.8i	2.07013	−	3.58557i
$484$	−6888.73			−0.646951
$485$	8555.89			0.801037
$486$	−6566.95	−	11374.3i	−0.612928	−	1.06162i
$487$	−6437.17	−	11149.5i	−0.598965	−	1.03744i	−0.992974	−	0.118331i	$-0.962246\pi$
$487$	−6437.17	−	11149.5i	−0.598965	−	1.03744i	0.394009	−	0.919106i	$-0.371088\pi$
$488$	19988.6			1.85418
$489$	−6445.04	−	11163.1i	−0.596022	−	1.03234i
$490$	18068.0	+	31294.8i	1.66578	+	2.88521i
$491$	−2901.68			−0.266703			−0.133351	−	0.991069i	$-0.542574\pi$
$491$	−2901.68			−0.266703			−0.133351	+	0.991069i	$0.542574\pi$
$492$	17746.7			1.62618
$493$	−310.141			−0.0283327
$494$	−17600.5	+	30485.0i	−1.60300	+	2.77649i
$495$	−10649.8	−	18446.0i	−0.967016	−	1.67492i
$496$	−2005.86	−	3474.26i	−0.181585	−	0.314514i
$497$	3711.11	+	6427.84i	0.334942	+	0.580137i
$498$	−26540.0	+	45968.6i	−2.38812	+	4.13635i
$499$	2434.20	+	4216.15i	0.218376	+	0.378238i	0.954312	−	0.298813i	$-0.0965907\pi$
$499$	2434.20	+	4216.15i	0.218376	+	0.378238i	−0.735936	+	0.677052i	$0.763257\pi$
$500$	10294.5	−	17830.6i	0.920769	−	1.59482i
$501$	24793.2			2.21094
$502$	8077.03			0.718118
$503$	4820.56	−	8349.45i	0.427312	−	0.740126i	−0.569321	−	0.822115i	$-0.692794\pi$
$503$	4820.56	−	8349.45i	0.427312	−	0.740126i	0.996633	+	0.0819888i	$0.0261272\pi$
$504$	−36792.4	+	63726.3i	−3.25171	+	5.63213i
$505$	−14603.8			−1.28685
$506$	22744.7			1.99827
$507$	−4275.78			−0.374545
$508$	−6835.56	+	11839.5i	−0.597006	+	1.03405i
$509$	−4475.13	−	7751.16i	−0.389699	−	0.674978i	0.602710	−	0.797960i	$-0.294088\pi$
$509$	−4475.13	−	7751.16i	−0.389699	−	0.674978i	−0.992409	+	0.122982i	$0.960754\pi$
$510$	−4147.89	+	7184.36i	−0.360141	+	0.623782i
$511$	−10417.4	+	18043.4i	−0.901835	+	1.56202i
$512$	21217.3			1.83141
$513$	20500.2	+	35507.4i	1.76434	+	3.05593i
$514$	12777.7			1.09650
$515$	−12414.8	−	1897.30i	−1.06226	−	0.162340i
$516$	41996.1			3.58290
$517$	−838.036	−	1451.52i	−0.0712897	−	0.123477i
$518$	−20173.0			−1.71110
$519$	−18858.2	+	32663.4i	−1.59496	+	2.76255i
$520$	−12528.9	+	21700.6i	−1.05659	+	1.83007i
$521$	−9853.61	−	17067.0i	−0.828589	−	1.43516i	−0.899145	−	0.437650i	$-0.855811\pi$
$521$	−9853.61	−	17067.0i	−0.828589	−	1.43516i	0.0705569	−	0.997508i	$-0.477522\pi$
$522$	−2968.58	+	5141.73i	−0.248910	+	0.431125i
$523$	−23379.1			−1.95468			−0.977340	−	0.211674i	$-0.932108\pi$
$523$	−23379.1			−1.95468			−0.977340	+	0.211674i	$0.932108\pi$
$524$	−21595.4			−1.80038
$525$	5537.55			0.460340
$526$	12352.9	−	21395.9i	1.02398	−	1.77359i
$527$	−438.079	+	758.775i	−0.0362107	+	0.0627187i
$528$	−19340.0			−1.59406
$529$	11401.4			0.937076
$530$	15586.0	−	26995.7i	1.27738	−	2.21249i
$531$	15251.7	+	26416.8i	1.24646	+	2.15893i
$532$	34752.6	−	60193.2i	2.83217	−	4.90546i
$533$	−3043.56	−	5271.60i	−0.247338	−	0.428402i
$534$	525.531	+	910.246i	0.0425879	+	0.0737644i
$535$	1528.19	+	2646.90i	0.123494	+	0.213898i
$536$	−12122.8	+	20997.4i	−0.976915	+	1.69207i
$537$	11316.2			0.909369
$538$	20440.1			1.63798
$539$	18398.9			1.47031
$540$	28796.1	+	49876.3i	2.29479	+	3.97469i
$541$	−5256.36	−	9104.29i	−0.417724	−	0.723519i	0.577986	−	0.816047i	$-0.303839\pi$
$541$	−5256.36	−	9104.29i	−0.417724	−	0.723519i	−0.995710	+	0.0925275i	$0.970505\pi$
$542$	−22723.6			−1.80086
$543$	10166.8	+	17609.4i	0.803495	+	1.39169i
$544$	132.700	+	229.843i	0.0104586	+	0.0181148i
$545$	−15675.1			−1.23202
$546$	72639.7			5.69357
$547$	5574.94	−	9656.08i	0.435772	−	0.754779i	−0.561587	−	0.827418i	$-0.689809\pi$
$547$	5574.94	−	9656.08i	0.435772	−	0.754779i	0.997358	+	0.0726392i	$0.0231422\pi$
$548$	−15107.7	+	26167.3i	−1.17768	+	2.03981i
$549$	−29099.6			−2.26219
$550$	1432.92	+	2481.88i	0.111090	+	0.192414i
$551$	1420.98	−	2461.21i	0.109865	−	0.190293i
$552$	−57553.5			−4.43775
$553$	8054.33	−	13950.5i	0.619358	−	1.07276i
$554$	−2331.82			−0.178826
$555$	−7387.79	+	12796.0i	−0.565034	+	0.978668i
$556$	−3550.97	−	6150.46i	−0.270854	−	0.469132i
$557$	4161.85			0.316594			0.158297	−	0.987392i	$-0.449400\pi$
$557$	4161.85			0.316594			0.158297	+	0.987392i	$0.449400\pi$
$558$	8386.35	+	14525.6i	0.636241	+	1.10200i
$559$	−7202.36	−	12474.9i	−0.544951	−	0.943882i
$560$	12862.7	−	22278.9i	0.970625	−	1.68117i
$561$	2111.92	+	3657.95i	0.158940	+	0.275292i
$562$	1647.17	−	2852.97i	0.123633	−	0.214138i
$563$	7263.87	+	12581.4i	0.543758	+	0.941816i	0.998684	+	0.0512866i	$0.0163322\pi$
$563$	7263.87	+	12581.4i	0.543758	+	0.941816i	−0.454926	+	0.890529i	$0.650334\pi$
$564$	4184.49	+	7247.74i	0.312409	+	0.541108i
$565$	7129.40	−	12348.5i	0.530861	−	0.919478i
$566$	15106.9	−	26165.9i	1.12189	−	1.94317i
$567$	17745.9	−	30736.8i	1.31439	−	2.27659i
$568$	4859.91	−	8417.60i	0.359009	−	0.621822i
$569$	−680.632	−	1178.89i	−0.0501469	−	0.0868570i	0.839862	−	0.542799i	$-0.182636\pi$
$569$	−680.632	−	1178.89i	−0.0501469	−	0.0868570i	−0.890009	+	0.455942i	$0.849302\pi$
$570$	−38009.1	−	65833.7i	−2.79303	−	4.83767i
$571$	8589.89	−	14878.1i	0.629555	−	1.09042i	−0.358086	−	0.933688i	$-0.616571\pi$
$571$	8589.89	−	14878.1i	0.629555	−	1.09042i	0.987641	−	0.156732i	$-0.0500960\pi$
$572$	12587.8	+	21802.7i	0.920145	+	1.59374i
$573$	−3246.78	+	5623.59i	−0.236713	+	0.409998i
$574$	8973.67	+	15542.9i	0.652533	+	1.13022i
$575$	1484.81	+	2571.76i	0.107688	+	0.186521i
$576$	−27576.9			−1.99486
$577$	−349.122	−	604.696i	−0.0251891	−	0.0436288i	0.853156	−	0.521656i	$-0.174685\pi$
$577$	−349.122	−	604.696i	−0.0251891	−	0.0436288i	−0.878345	+	0.478027i	$0.841352\pi$
$578$	−11525.3	+	19962.4i	−0.829393	+	1.43655i
$579$	2600.79			0.186676
$580$	1996.01	−	3457.20i	0.142897	−	0.247504i
$581$	−35949.1			−2.56699
$582$	−16240.2	+	28128.8i	−1.15666	+	2.00340i
$583$	−7935.67	−	13745.0i	−0.563742	−	0.976431i
$584$	27284.3			1.93327
$585$	18239.7	−	31592.0i	1.28909	−	2.23277i
$586$	−17468.9	+	30256.9i	−1.23145	+	2.13294i
$587$	3112.86			0.218878			0.109439	−	0.993993i	$-0.465095\pi$
$587$	3112.86			0.218878			0.109439	+	0.993993i	$0.465095\pi$
$588$	−91869.3			−6.44324
$589$	−4014.33	−	6953.02i	−0.280828	−	0.486408i
$590$	−15313.0	−	26522.9i	−1.06852	−	1.85073i
$591$	11548.1			0.803765
$592$	4599.36	+	7966.33i	0.319312	+	0.553065i
$593$	2960.75	+	5128.17i	0.205031	+	0.355125i	0.950143	−	0.311815i	$-0.100937\pi$
$593$	2960.75	+	5128.17i	0.205031	+	0.355125i	−0.745111	+	0.666940i	$0.767604\pi$
$594$	43786.5			3.02455
$595$	−5618.42			−0.387114
$596$	5385.02			0.370099
$597$	30.7520	−	53.2640i	0.00210820	−	0.00365151i
$598$	19477.2	+	33735.5i	1.33191	+	2.30693i
$599$	6130.69	+	10618.7i	0.418186	+	0.724319i	0.995757	−	0.0920213i	$-0.0293328\pi$
$599$	6130.69	+	10618.7i	0.418186	+	0.724319i	−0.577571	+	0.816340i	$0.695999\pi$
$600$	−3625.86	−	6280.18i	−0.246709	−	0.427312i
$601$	10588.0	−	18338.9i	0.718624	−	1.24469i	−0.242921	−	0.970046i	$-0.578106\pi$
$601$	10588.0	−	18338.9i	0.718624	−	1.24469i	0.961545	−	0.274647i	$-0.0885611\pi$
$602$	21235.5	+	36781.0i	1.43770	+	2.49017i
$603$	17648.6	−	30568.2i	1.19188	−	2.06440i
$604$	−24718.2			−1.66518
$605$	−5102.67			−0.342897
$606$	27719.9	−	48012.2i	1.85816	−	3.21842i
$607$	1168.52	−	2023.93i	0.0781362	−	0.135336i	−0.824310	−	0.566139i	$-0.808436\pi$
$607$	1168.52	−	2023.93i	0.0781362	−	0.135336i	0.902446	+	0.430803i	$0.141770\pi$
$608$	−2431.98			−0.162220
$609$	−5864.58			−0.390222
$610$	29216.6			1.93925
$611$	1435.28	−	2485.98i	0.0950333	−	0.164603i
$612$	−7230.29	−	12523.2i	−0.477561	−	0.827159i
$613$	−5391.56	+	9338.46i	−0.355242	+	0.615296i	−0.987159	−	0.159739i	$-0.948935\pi$
$613$	−5391.56	+	9338.46i	−0.355242	+	0.615296i	0.631918	+	0.775035i	$0.282268\pi$
$614$	23241.0	−	40254.6i	1.52758	−	2.64584i
$615$	13145.4			0.861910
$616$	−18808.3	−	32576.9i	−1.23021	−	2.13078i
$617$	−18834.1			−1.22890			−0.614450	−	0.788956i	$-0.710622\pi$
$617$	−18834.1			−1.22890			−0.614450	+	0.788956i	$0.710622\pi$
$618$	29802.7	−	37214.4i	1.93987	−	2.42230i
$619$	11828.4			0.768052			0.384026	−	0.923322i	$-0.374537\pi$
$619$	11828.4			0.768052			0.384026	+	0.923322i	$0.374537\pi$
$620$	−5638.81	−	9766.71i	−0.365258	−	0.632646i
$621$	45372.1			2.93192
$622$	8214.18	−	14227.4i	0.529515	−	0.917147i
$623$	−355.922	+	616.476i	−0.0228888	+	0.0396446i
$624$	−16561.6	−	28685.5i	−1.06249	−	1.84028i
$625$	8834.38	−	15301.6i	0.565400	−	0.979302i
$626$	−45355.3			−2.89579
$627$	−38705.0			−2.46528
$628$	−17329.8			−1.10117
$629$	1004.50	−	1739.84i	0.0636756	−	0.110289i
$630$	−53778.0	+	93146.2i	−3.40090	+	5.89053i
$631$	−13489.6			−0.851051			−0.425525	−	0.904946i	$-0.639911\pi$
$631$	−13489.6			−0.851051			−0.425525	+	0.904946i	$0.639911\pi$
$632$	−21095.2			−1.32772
$633$	5655.11	−	9794.94i	0.355088	−	0.615030i
$634$	−11137.1	−	19290.0i	−0.697649	−	1.20836i
$635$	−5063.28	+	8769.87i	−0.316426	+	0.548065i
$636$	39624.4	+	68631.5i	2.47046	+	4.27896i
$637$	15755.6	+	27289.6i	0.980002	+	1.69741i
$638$	−1517.54	−	2628.46i	−0.0941693	−	0.163106i
$639$	−7075.11	+	12254.4i	−0.438008	+	0.758652i
$640$	29372.6			1.81415
$641$	−8735.30			−0.538258			−0.269129	−	0.963104i	$-0.586736\pi$
$641$	−8735.30			−0.538258			−0.269129	+	0.963104i	$0.586736\pi$
$642$	−11602.8			−0.713281
$643$	−6050.21	−	10479.3i	−0.371069	−	0.642710i	0.618662	−	0.785658i	$-0.287675\pi$
$643$	−6050.21	−	10479.3i	−0.371069	−	0.642710i	−0.989730	+	0.142948i	$0.954342\pi$
$644$	−38458.1	−	66611.3i	−2.35320	−	4.07586i
$645$	31107.7			1.89901
$646$	5168.00	+	8951.23i	0.314756	+	0.545173i
$647$	14147.7	+	24504.5i	0.859663	+	1.48898i	0.872250	+	0.489060i	$0.162660\pi$
$647$	14147.7	+	24504.5i	0.859663	+	1.48898i	−0.0125870	+	0.999921i	$0.504007\pi$
$648$	−46478.5			−2.81767
$649$	−15593.4			−0.943134
$650$	−2454.12	+	4250.66i	−0.148090	+	0.256499i
$651$	−8283.83	+	14348.0i	−0.498723	+	0.863814i
$652$	−22559.3			−1.35504
$653$	8793.67	+	15231.1i	0.526987	+	0.912769i	0.999505	+	0.0314479i	$0.0100118\pi$
$653$	8793.67	+	15231.1i	0.526987	+	0.912769i	−0.472518	+	0.881321i	$0.656655\pi$
$654$	29753.5	−	51534.5i	1.77898	−	3.08128i
$655$	−15996.3			−0.954240
$656$	4091.93	−	7087.42i	0.243541	−	0.421825i
$657$	−39720.7			−2.35868
$658$	−4231.81	+	7329.71i	−0.250719	+	0.434258i
$659$	−1490.20	−	2581.10i	−0.0880879	−	0.152573i	0.818615	−	0.574343i	$-0.194742\pi$
$659$	−1490.20	−	2581.10i	−0.0880879	−	0.152573i	−0.906703	+	0.421770i	$0.861409\pi$
$660$	−54367.9			−3.20647
$661$	10830.2	+	18758.4i	0.637285	+	1.10381i	0.986026	+	0.166591i	$0.0532758\pi$
$661$	10830.2	+	18758.4i	0.637285	+	1.10381i	−0.348741	+	0.937219i	$0.613391\pi$
$662$	−7655.36	−	13259.5i	−0.449447	−	0.778465i
$663$	−3617.03	+	6264.89i	−0.211876	+	0.366980i
$664$	23538.7	+	40770.1i	1.37572	+	2.38281i
$665$	25742.1	−	44586.7i	1.50111	−	2.60000i
$666$	−19229.6	−	33306.6i	−1.11881	−	1.93784i
$667$	−1572.50	−	2723.64i	−0.0912853	−	0.158111i
$668$	21695.6	−	37577.9i	1.25663	−	2.17655i
$669$	−431.757	+	747.825i	−0.0249517	+	0.0432176i
$670$	−17719.5	+	30691.0i	−1.02174	+	1.76970i
$671$	7437.88	−	12882.8i	0.427923	−	0.741184i
$672$	2509.28	+	4346.20i	0.144044	+	0.249491i
$673$	11130.1	+	19277.9i	0.637495	+	1.10417i	0.985981	+	0.166859i	$0.0533625\pi$
$673$	11130.1	+	19277.9i	0.637495	+	1.10417i	−0.348486	+	0.937314i	$0.613304\pi$
$674$	27650.2	−	47891.6i	1.58019	−	2.73697i
$675$	2858.44	+	4950.96i	0.162995	+	0.282315i
$676$	−3741.58	+	6480.61i	−0.212880	+	0.368719i
$677$	1164.53	+	2017.02i	0.0661098	+	0.114506i	0.897186	−	0.441653i	$-0.145608\pi$
$677$	1164.53	+	2017.02i	0.0661098	+	0.114506i	−0.831076	+	0.556159i	$0.812275\pi$
$678$	27065.1	+	46878.1i	1.53308	+	2.65537i
$679$	−21997.7			−1.24329
$680$	3678.82	+	6371.90i	0.207465	+	0.359340i
$681$	16300.2	−	28232.8i	0.917219	−	1.58867i
$682$	−8574.21			−0.481413
$683$	−8058.90	+	13958.4i	−0.451487	+	0.781998i	−0.998479	−	0.0551402i	$-0.982439\pi$
$683$	−8058.90	+	13958.4i	−0.451487	+	0.781998i	0.546992	+	0.837138i	$0.315773\pi$
$684$	132509.			7.40733
$685$	−11190.7	+	19382.8i	−0.624196	+	1.08114i
$686$	−20383.0	−	35304.4i	−1.13444	−	1.96491i
$687$	−21833.5			−1.21252
$688$	9683.24	−	16771.9i	0.536584	−	0.929391i
$689$	13591.2	−	23540.7i	0.751502	−	1.30164i
$690$	−84123.7			−4.64135
$691$	2965.21			0.163245			0.0816223	−	0.996663i	$-0.473990\pi$
$691$	2965.21			0.163245			0.0816223	+	0.996663i	$0.473990\pi$
$692$	33004.3	+	57165.0i	1.81305	+	3.14030i
$693$	27381.3	+	47425.9i	1.50091	+	2.59965i
$694$	38352.5			2.09775
$695$	−2630.30	−	4555.81i	−0.143558	−	0.248650i
$696$	3840.00	+	6651.07i	0.209130	+	0.362224i
$697$	−1787.35			−0.0971314
$698$	−41775.9			−2.26539
$699$	−28177.2			−1.52469
$700$	4845.71	−	8393.01i	0.261644	−	0.453180i
$701$	7646.58	+	13244.3i	0.411994	+	0.713594i	0.995108	−	0.0987965i	$-0.0314993\pi$
$701$	7646.58	+	13244.3i	0.411994	+	0.713594i	−0.583114	+	0.812390i	$0.698166\pi$
$702$	37496.0	+	64945.0i	2.01595	+	3.49172i
$703$	9204.69	+	15943.0i	0.493828	+	0.855336i
$704$	7048.66	−	12208.6i	0.377353	−	0.653595i
$705$	3099.56	+	5368.60i	0.165583	+	0.286799i
$706$	−27545.4	+	47710.0i	−1.46839	+	2.54333i
$707$	37547.3			1.99733
$708$	77861.0			4.13304
$709$	−2772.25	+	4801.68i	−0.146846	+	0.254345i	−0.930060	−	0.367407i	$-0.880246\pi$
$709$	−2772.25	+	4801.68i	−0.146846	+	0.254345i	0.783214	+	0.621752i	$0.213579\pi$
$710$	7103.54	−	12303.7i	0.375480	−	0.650351i
$711$	30710.6			1.61988
$712$	932.199			0.0490669
$713$	−8884.71			−0.466669
$714$	10664.5	−	18471.5i	0.558976	−	0.968175i
$715$	9324.13	+	16149.9i	0.487696	+	0.844714i
$716$	9902.41	−	17151.5i	0.516858	−	0.895225i
$717$	−14480.2	+	25080.5i	−0.754217	+	1.30634i
$718$	−33499.1			−1.74119
$719$	9873.25	+	17101.0i	0.512114	+	0.887008i	0.999901	+	0.0140450i	$0.00447081\pi$
$719$	9873.25	+	17101.0i	0.512114	+	0.887008i	−0.487787	+	0.872962i	$0.662196\pi$
$720$	49044.7			2.53860
$721$	31919.4	+	4878.08i	1.64874	+	0.251968i
$722$	−60958.1			−3.14214
$723$	−32324.3	−	55987.4i	−1.66273	−	2.87994i
$724$	35586.3			1.82673
$725$	198.134	−	343.178i	0.0101497	−	0.0175798i
$726$	9685.52	−	16775.8i	0.495129	−	0.857588i
$727$	354.242	+	613.565i	0.0180717	+	0.0313010i	0.874920	−	0.484268i	$-0.160914\pi$
$727$	354.242	+	613.565i	0.0180717	+	0.0313010i	−0.856848	+	0.515569i	$0.827581\pi$
$728$	32212.5	−	55793.7i	1.63994	−	2.84046i
$729$	−6289.52			−0.319541
$730$	39880.3			2.02197
$731$	−4229.62			−0.214006
$732$	−37138.9	+	64326.4i	−1.87526	+	3.24805i
$733$	−9774.59	+	16930.1i	−0.492541	+	0.853106i	−0.999963	−	0.00859135i	$-0.997265\pi$
$733$	−9774.59	+	16930.1i	−0.492541	+	0.853106i	0.507422	+	0.861698i	$0.330599\pi$
$734$	5035.51			0.253221
$735$	−68050.0			−3.41505
$736$	−1345.65	+	2330.73i	−0.0673929	+	0.116728i
$737$	9021.96	+	15626.5i	0.450920	+	0.781017i
$738$	−17108.0	+	29631.9i	−0.853325	+	1.47800i
$739$	11696.2	+	20258.4i	0.582207	+	1.00841i	0.995217	+	0.0976861i	$0.0311441\pi$
$739$	11696.2	+	20258.4i	0.582207	+	1.00841i	−0.413010	+	0.910727i	$0.635523\pi$
$740$	12929.6	+	22394.7i	0.642298	+	1.11249i
$741$	−33144.6	−	57408.1i	−1.64318	−	2.84607i
$742$	−40072.5	+	69407.7i	−1.98263	+	3.43401i
$743$	10111.3			0.499255			0.249628	−	0.968342i	$-0.419692\pi$
$743$	10111.3			0.499255			0.249628	+	0.968342i	$0.419692\pi$
$744$	21696.3			1.06912
$745$	3988.83			0.196160
$746$	18144.7	+	31427.5i	0.890513	+	1.54241i
$747$	−34267.9	−	59353.7i	−1.67844	−	2.90714i
$748$	7392.26			0.361347
$749$	−3929.08	−	6805.36i	−0.191676	−	0.331993i
$750$	28948.1	+	50139.5i	1.40938	+	2.44112i
$751$	6354.30			0.308751			0.154375	−	0.988012i	$-0.450663\pi$
$751$	6354.30			0.308751			0.154375	+	0.988012i	$0.450663\pi$
$752$	3859.34			0.187149
$753$	−7605.17	+	13172.5i	−0.368058	+	0.637496i
$754$	2599.05	−	4501.69i	0.125533	−	0.217430i
$755$	−18309.4			−0.882581
$756$	−74036.6	−	128235.i	−3.56175	−	6.16914i
$757$	16783.8	−	29070.3i	0.805833	−	1.39574i	−0.109893	−	0.993943i	$-0.535051\pi$
$757$	16783.8	−	29070.3i	0.805833	−	1.39574i	0.915727	−	0.401801i	$-0.131616\pi$
$758$	46012.6			2.20482
$759$	−21416.0	+	37093.6i	−1.02418	+	1.77393i
$760$	−67421.5			−3.21794
$761$	−5811.45	+	10065.7i	−0.276826	+	0.479477i	−0.970594	−	0.240721i	$-0.922616\pi$
$761$	−5811.45	+	10065.7i	−0.276826	+	0.479477i	0.693768	+	0.720199i	$0.255949\pi$
$762$	−19221.5	−	33292.7i	−0.913810	−	1.58277i
$763$	40301.8			1.91222
$764$	5682.28	+	9842.01i	0.269081	+	0.466062i
$765$	−5355.67	−	9276.29i	−0.253117	−	0.438412i
$766$	8911.48	−	15435.1i	0.420346	−	0.728060i
$767$	−13353.2	−	23128.4i	−0.628626	−	1.08881i
$768$	−38393.7	+	66499.8i	−1.80392	+	3.12448i
$769$	−2700.76	−	4677.85i	−0.126647	−	0.219360i	0.795728	−	0.605654i	$-0.207088\pi$
$769$	−2700.76	−	4677.85i	−0.126647	−	0.219360i	−0.922376	+	0.386294i	$0.873755\pi$
$770$	−27491.4	−	47616.4i	−1.28665	−	2.22854i
$771$	−12031.2	+	20838.7i	−0.561989	+	0.973394i
$772$	2275.86	−	3941.90i	0.106101	−	0.183772i
$773$	−1197.17	+	2073.56i	−0.0557042	+	0.0964825i	−0.892533	−	0.450982i	$-0.851074\pi$
$773$	−1197.17	+	2073.56i	−0.0557042	+	0.0964825i	0.836829	+	0.547465i	$0.184407\pi$
$774$	−40484.8	+	70121.7i	−1.88010	+	3.25643i
$775$	−559.736	−	969.491i	−0.0259436	−	0.0449357i
$776$	14403.6	+	24947.8i	0.666315	+	1.15409i
$777$	18994.5	−	32899.4i	0.876993	−	1.51900i
$778$	−11542.5	−	19992.1i	−0.531899	−	0.921276i
$779$	8189.16	−	14184.0i	0.376646	−	0.652369i
$780$	−46557.3	−	80639.6i	−2.13720	−	3.70174i
$781$	−3616.80	−	6264.48i	−0.165710	−	0.287018i
$782$	11438.1			0.523049
$783$	−3027.25	−	5243.35i	−0.138167	−	0.239313i
$784$	−21182.7	+	36689.5i	−0.964956	+	1.67135i
$785$	−12836.6			−0.583642
$786$	30363.1	−	52590.4i	1.37788	−	2.38656i
$787$	859.612			0.0389350			0.0194675	−	0.999810i	$-0.493803\pi$
$787$	859.612			0.0389350			0.0194675	+	0.999810i	$0.493803\pi$
$788$	10105.3	−	17502.9i	0.456836	−	0.791263i
$789$	23262.6	+	40291.9i	1.04964	+	1.81804i
$790$	−30834.0			−1.38864
$791$	−18330.2	+	31748.8i	−0.823952	+	1.42713i
$792$	35857.4	−	62106.8i	1.60876	−	2.78645i
$793$	25477.4			1.14089
$794$	25292.8			1.13049
$795$	29350.9	+	50837.2i	1.30939	+	2.26794i
$796$	−53.8199	−	93.2189i	−0.00239648	−	0.00415082i
$797$	15500.2			0.688888			0.344444	−	0.938807i	$-0.388067\pi$
$797$	15500.2			0.688888			0.344444	+	0.938807i	$0.388067\pi$
$798$	97723.9	+	169263.i	4.33507	+	7.50857i
$799$	−421.439	−	729.954i	−0.0186601	−	0.0323203i
$800$	−339.102			−0.0149863
$801$	−1357.11			−0.0598639
$802$	−19191.4			−0.844978
$803$	10152.6	−	17584.9i	0.446175	−	0.772798i
$804$	−45048.5	−	78026.3i	−1.97604	−	3.42261i
$805$	−28486.9	−	49340.8i	−1.24724	−	2.16029i
$806$	−7342.42	−	12717.4i	−0.320876	−	0.555773i
$807$	−19246.0	+	33335.0i	−0.839518	+	1.45409i
$808$	−24585.1	−	42582.6i	−1.07042	−	1.85402i
$809$	−12856.9	+	22268.8i	−0.558746	+	0.967776i	0.438856	+	0.898557i	$0.355384\pi$
$809$	−12856.9	+	22268.8i	−0.558746	+	0.967776i	−0.997602	+	0.0692183i	$0.977949\pi$
$810$	−67935.9			−2.94694
$811$	−38497.5			−1.66687			−0.833434	−	0.552619i	$-0.813628\pi$
$811$	−38497.5			−1.66687			−0.833434	+	0.552619i	$0.813628\pi$
$812$	−5131.88	+	8888.68i	−0.221790	+	0.384152i
$813$	21396.1	−	37059.2i	0.922995	−	1.59867i
$814$	19660.3			0.846553
$815$	−16710.2			−0.718202
$816$	−9725.86			−0.417247
$817$	19379.0	−	33565.5i	0.829849	−	1.43734i
$818$	14566.7	+	25230.2i	0.622631	+	1.07843i
$819$	−46895.4	+	81225.1i	−2.00080	+	3.46549i
$820$	11503.1	−	19923.9i	0.489884	−	0.848504i
$821$	−8190.50			−0.348174			−0.174087	−	0.984730i	$-0.555697\pi$
$821$	−8190.50			−0.348174			−0.174087	+	0.984730i	$0.555697\pi$
$822$	−42482.8	−	73582.3i	−1.80262	−	3.12224i
$823$	6185.27			0.261975			0.130987	−	0.991384i	$-0.458185\pi$
$823$	6185.27			0.261975			0.130987	+	0.991384i	$0.458185\pi$
$824$	−15367.8	−	39394.1i	−0.649713	−	1.66548i
$825$	−5396.82			−0.227749
$826$	39370.8	+	68192.1i	1.65845	+	2.87253i
$827$	−24896.2			−1.04683			−0.523413	−	0.852079i	$-0.675342\pi$
$827$	−24896.2			−1.04683			−0.523413	+	0.852079i	$0.675342\pi$
$828$	73319.0	−	126992.i	3.07731	−	5.33005i
$829$	14155.6	−	24518.3i	0.593058	−	1.02721i	−0.400760	−	0.916183i	$-0.631254\pi$
$829$	14155.6	−	24518.3i	0.593058	−	1.02721i	0.993818	−	0.111024i	$-0.0354130\pi$
$830$	34405.5	+	59592.2i	1.43884	+	2.49214i
$831$	2195.59	−	3802.88i	0.0916537	−	0.158749i
$832$	24144.2			1.00607
$833$	9252.58			0.384853
$834$	19970.6			0.829167
$835$	16070.5	−	27835.0i	0.666040	−	1.15362i
$836$	−33869.4	+	58663.5i	−1.40119	+	2.42694i
$837$	−17104.2			−0.706341
$838$	−14357.7			−0.591861
$839$	10134.5	−	17553.5i	0.417024	−	0.722307i	−0.578615	−	0.815601i	$-0.696406\pi$
$839$	10134.5	−	17553.5i	0.417024	−	0.722307i	0.995639	+	0.0932944i	$0.0297398\pi$
$840$	69564.4	+	120489.i	2.85738	+	4.94913i
$841$	11984.7	−	20758.0i	0.491396	−	0.851123i
$842$	40349.3	+	69887.1i	1.65146	+	2.86041i
$843$	3101.88	+	5372.61i	0.126731	+	0.219505i
$844$	−9897.17	−	17142.4i	−0.403643	−	0.699130i
$845$	−2771.49	+	4800.36i	−0.112831	+	0.195429i
$846$	−16135.6			−0.655736
$847$	13119.3			0.532213
$848$	36545.5			1.47993
$849$	28448.7	+	49274.6i	1.15001	+	1.99187i
$850$	720.597	+	1248.11i	0.0290780	+	0.0503645i
$851$	20372.3			0.820626
$852$	18059.4	+	31279.9i	0.726181	+	1.25778i
$853$	16076.4	+	27845.1i	0.645304	+	1.11770i	0.984231	+	0.176886i	$0.0566025\pi$
$853$	16076.4	+	27845.1i	0.645304	+	1.11770i	−0.338928	+	0.940812i	$0.610064\pi$
$854$	−75117.7			−3.00992
$855$	98153.0			3.92604
$856$	−5145.34	+	8911.99i	−0.205449	+	0.355848i
$857$	9953.00	−	17239.1i	0.396719	−	0.687137i	−0.596600	−	0.802539i	$-0.703482\pi$
$857$	9953.00	−	17239.1i	0.396719	−	0.687137i	0.993319	+	0.115401i	$0.0368154\pi$
$858$	−70793.6			−2.81685
$859$	−12698.8	−	21995.0i	−0.504399	−	0.873644i	−0.999987	−	0.00508673i	$-0.998381\pi$
$859$	−12698.8	−	21995.0i	−0.504399	−	0.873644i	0.495588	−	0.868558i	$-0.334952\pi$
$860$	27221.2	−	47148.5i	1.07934	−	1.86948i
$861$	−33797.7			−1.33777
$862$	42328.8	−	73315.7i	1.67254	−	2.89692i
$863$	15020.2			0.592461			0.296230	−	0.955117i	$-0.404270\pi$
$863$	15020.2			0.592461			0.296230	+	0.955117i	$0.404270\pi$
$864$	−2590.54	+	4486.94i	−0.102004	+	0.176677i
$865$	24447.1	+	42343.7i	0.960956	+	1.66443i
$866$	−36549.4			−1.43418
$867$	−21704.0	−	37592.4i	−0.850180	−	1.47256i
$868$	14497.8	+	25110.9i	0.566919	+	0.981933i
$869$	−7849.64	+	13596.0i	−0.306422	+	0.530739i
$870$	5612.78	+	9721.61i	0.218725	+	0.378843i
$871$	−15451.7	+	26763.1i	−0.601103	+	1.04114i
$872$	−26388.7	−	45706.6i	−1.02481	−	1.77502i
$873$	−20969.0	−	36319.3i	−0.812935	−	1.40804i
$874$	−52406.2	+	90770.3i	−2.02822	+	3.51299i
$875$	−19605.4	+	33957.6i	−0.757469	+	1.31197i
$876$	−50694.2	+	87804.9i	−1.95525	+	3.38659i
$877$	20149.4	−	34899.8i	0.775823	−	1.34376i	−0.158508	−	0.987358i	$-0.550668\pi$
$877$	20149.4	−	34899.8i	0.775823	−	1.34376i	0.934331	−	0.356407i	$-0.115998\pi$
$878$	−14563.9	−	25225.4i	−0.559804	−	0.969610i
$879$	−32896.6	−	56978.7i	−1.26232	−	2.18640i
$880$	−12535.8	+	21712.7i	−0.480208	+	0.831745i
$881$	−17554.6	−	30405.4i	−0.671316	−	1.16275i	−0.977531	−	0.210791i	$-0.932396\pi$
$881$	−17554.6	−	30405.4i	−0.671316	−	1.16275i	0.306215	−	0.951962i	$-0.400937\pi$
$882$	88563.1	−	153396.i	3.38104	−	5.85613i
$883$	−11107.8	−	19239.2i	−0.423337	−	0.733241i	0.572927	−	0.819607i	$-0.305808\pi$
$883$	−11107.8	−	19239.2i	−0.423337	−	0.733241i	−0.996264	+	0.0863656i	$0.972475\pi$
$884$	6330.27	+	10964.3i	0.240848	+	0.417162i
$885$	57673.7			2.19060
$886$	−19194.2	−	33245.3i	−0.727812	−	1.26061i
$887$	−20839.2	+	36094.5i	−0.788851	+	1.36633i	0.137820	+	0.990457i	$0.455990\pi$
$887$	−20839.2	+	36094.5i	−0.788851	+	1.36633i	−0.926671	+	0.375873i	$0.877343\pi$
$888$	−49748.6			−1.88002
$889$	13018.0	−	22547.9i	0.491126	−	0.850655i
$890$	1362.56			0.0513181
$891$	−17294.9	+	29955.7i	−0.650283	+	1.12632i
$892$	755.629	+	1308.79i	0.0283636	+	0.0491272i
$893$	7723.69			0.289433
$894$	−7571.32	+	13113.9i	−0.283247	+	0.490598i
$895$	7334.98	−	12704.6i	0.273946	−	0.474488i
$896$	−75519.0			−2.81575
$897$	−73357.3			−2.73058
$898$	−19104.2	−	33089.5i	−0.709929	−	1.22963i
$899$	592.793	+	1026.75i	0.0219919	+	0.0380911i
$900$	18476.3			0.684309
$901$	−3990.76	−	6912.20i	−0.147560	−	0.255581i
$902$	−8745.62	−	15147.9i	−0.322835	−	0.559167i
$903$	−79979.8			−2.94747
$904$	48008.7			1.76631
$905$	26359.7			0.968205
$906$	34753.7	−	60195.2i	1.27441	−	2.20734i
$907$	−6932.12	−	12006.8i	−0.253779	−	0.439558i	0.710784	−	0.703410i	$-0.248340\pi$
$907$	−6932.12	−	12006.8i	−0.253779	−	0.439558i	−0.964563	+	0.263852i	$0.915007\pi$
$908$	−28527.5	−	49411.0i	−1.04264	−	1.80591i
$909$	35791.3	+	61992.3i	1.30596	+	2.26200i
$910$	47083.8	−	81551.5i	1.71518	−	2.97078i
$911$	226.682	+	392.625i	0.00824403	+	0.0142791i	0.870118	−	0.492843i	$-0.164042\pi$
$911$	226.682	+	392.625i	0.00824403	+	0.0142791i	−0.861874	+	0.507123i	$0.830709\pi$
$912$	44561.3	−	77182.5i	1.61795	−	2.80238i
$913$	35035.5			1.27000
$914$	−30184.3			−1.09235
$915$	−27509.7	+	47648.3i	−0.993928	+	1.72153i
$916$	−19105.7	+	33092.0i	−0.689159	+	1.19366i
$917$	41127.5			1.48108
$918$	22019.7			0.791676
$919$	6635.37			0.238173			0.119086	−	0.992884i	$-0.462003\pi$
$919$	6635.37			0.238173			0.119086	+	0.992884i	$0.462003\pi$
$920$	−37305.2	+	64614.5i	−1.33686	+	2.31552i
$921$	43766.6	+	75805.9i	1.56586	+	2.71215i
$922$	−39842.9	+	69010.0i	−1.42316	+	2.46499i
$923$	6194.41	−	10729.0i	0.220901	−	0.382611i
$924$	139783.			4.97677
$925$	1283.45	+	2223.00i	0.0456212	+	0.0790183i
$926$	−24817.9			−0.880741
$927$	22372.6	+	57350.3i	0.792680	+	2.03197i
$928$	359.129			0.0127036
$929$	19087.9	+	33061.3i	0.674117	+	1.16761i	0.976726	+	0.214490i	$0.0688091\pi$
$929$	19087.9	+	33061.3i	0.674117	+	1.16761i	−0.302609	+	0.953115i	$0.597858\pi$
$930$	31712.6			1.11817
$931$	−42392.9	+	73426.6i	−1.49234	+	2.58481i
$932$	−24656.8	+	42706.8i	−0.866589	+	1.50098i
$933$	15468.6	+	26792.4i	0.542786	+	0.940134i
$934$	−7805.91	+	13520.2i	−0.273466	+	0.473657i
$935$	5475.64			0.191522
$936$	122824.			4.28913
$937$	−30807.8			−1.07412			−0.537058	−	0.843545i	$-0.680464\pi$
$937$	−30807.8			−1.07412			−0.537058	+	0.843545i	$0.680464\pi$
$938$	45557.9	−	78908.7i	1.58584	−	2.74676i
$939$	42705.7	−	73968.4i	1.48418	−	2.57068i
$940$	10849.3			0.376451
$941$	−37655.3			−1.30449			−0.652246	−	0.758008i	$-0.726173\pi$
$941$	−37655.3			−1.30449			−0.652246	+	0.758008i	$0.726173\pi$
$942$	24365.6	−	42202.5i	0.842754	−	1.45969i
$943$	−9062.33	−	15696.4i	−0.312948	−	0.542042i
$944$	17952.8	−	31095.1i	0.618975	−	1.07210i
$945$	−54840.9	−	94987.2i	−1.88780	−	3.26977i
$946$	−20695.9	−	35846.3i	−0.711290	−	1.23199i
$947$	−206.012	−	356.824i	−0.00706917	−	0.0122442i	0.862469	−	0.506110i	$-0.168917\pi$
$947$	−206.012	−	356.824i	−0.00706917	−	0.0122442i	−0.869538	+	0.493865i	$0.835584\pi$
$948$	39194.9	−	67887.5i	1.34282	−	2.32583i
$949$	34776.3			1.18956
$950$	−13206.3			−0.451022
$951$	41945.8			1.43027
$952$	−9458.48	−	16382.6i	−0.322007	−	0.557733i
$953$	21280.1	+	36858.2i	0.723326	+	1.25284i	0.959659	+	0.281166i	$0.0907211\pi$
$953$	21280.1	+	36858.2i	0.723326	+	1.25284i	−0.236333	+	0.971672i	$0.575946\pi$
$954$	−152794.			−5.18541
$955$	4209.02	+	7290.24i	0.142618	+	0.247022i
$956$	25342.2	+	43894.0i	0.857350	+	1.48497i
$957$	5715.54			0.193059
$958$	−88312.6			−2.97834
$959$	28772.0	−	49834.6i	0.968818	−	1.67804i
$960$	−26070.2	+	45154.9i	−0.876471	+	1.51809i
$961$	−26441.7			−0.887573
$962$	16835.9	+	29160.6i	0.564252	+	0.977313i
$963$	7490.65	−	12974.2i	0.250657	−	0.434151i
$964$	−113143.			−3.78019
$965$	1685.79	−	2919.87i	0.0562357	−	0.0974031i
$966$	216288.			7.20387
$967$	−16231.2	+	28113.2i	−0.539771	+	0.934911i	0.459145	+	0.888361i	$0.348156\pi$
$967$	−16231.2	+	28113.2i	−0.539771	+	0.934911i	−0.998916	+	0.0465495i	$0.985177\pi$
$968$	−8590.21	−	14878.7i	−0.285227	−	0.494028i
$969$	−19464.3			−0.645288
$970$	21053.2	+	36465.3i	0.696885	+	1.20704i
$971$	−26915.8	−	46619.5i	−0.889566	−	1.54077i	−0.840389	−	0.541984i	$-0.817673\pi$
$971$	−26915.8	−	46619.5i	−0.889566	−	1.54077i	−0.0491774	−	0.998790i	$-0.515660\pi$
$972$	21643.2	−	37487.1i	0.714203	−	1.23704i
$973$	6762.67	+	11713.3i	0.222817	+	0.385931i
$974$	31679.5	−	54870.5i	1.04217	−	1.80510i
$975$	−4621.50	−	8004.68i	−0.151802	−	0.262928i
$976$	17126.6	+	29664.1i	0.561688	+	0.972872i
$977$	14319.6	−	24802.3i	0.468909	−	0.812175i	−0.530459	−	0.847711i	$-0.677980\pi$
$977$	14319.6	−	24802.3i	0.468909	−	0.812175i	0.999368	+	0.0355358i	$0.0113138\pi$
$978$	31718.2	−	54937.6i	1.03705	−	1.79623i
$979$	346.877	−	600.809i	0.0113240	−	0.0196138i
$980$	−59548.1	+	103140.i	−1.94101	+	3.36194i
$981$	38417.0	+	66540.2i	1.25032	+	2.16561i
$982$	−7140.09	−	12367.0i	−0.232026	−	0.401881i
$983$	−24467.3	+	42378.6i	−0.793882	+	1.37504i	0.129665	+	0.991558i	$0.458610\pi$
$983$	−24467.3	+	42378.6i	−0.793882	+	1.37504i	−0.923547	+	0.383486i	$0.874723\pi$
$984$	22130.0	+	38330.3i	0.716950	+	1.24179i
$985$	7485.27	−	12964.9i	0.242133	−	0.419386i
$986$	−763.154	−	1321.82i	−0.0246489	−	0.0426931i
$987$	−7969.17	−	13803.0i	−0.257003	−	0.445142i
$988$	−116015.			−3.73574
$989$	−21445.3	−	37144.4i	−0.689506	−	1.19426i
$990$	52411.3	−	90779.1i	1.68257	−	2.91429i
$991$	35255.3			1.13009			0.565046	−	0.825060i	$-0.308859\pi$
$991$	35255.3			1.13009			0.565046	+	0.825060i	$0.308859\pi$
$992$	507.276	−	878.628i	0.0162359	−	0.0281214i
$993$	28832.5			0.921423
$994$	−18263.7	+	31633.6i	−0.582785	+	1.00941i
$995$	−39.8659	−	69.0497i	−0.00127018	−	0.00220002i
$996$	−174939.			−5.56543
$997$	−9349.49	+	16193.8i	−0.296992	+	0.514406i	−0.975446	−	0.220237i	$-0.929317\pi$
$997$	−9349.49	+	16193.8i	−0.296992	+	0.514406i	0.678454	+	0.734643i	$0.262650\pi$
$998$	−11979.5	+	20749.1i	−0.379965	+	0.658119i
$999$	39219.2			1.24208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.4.c.a.46.23	✓	50
103.56	even	3	inner	103.4.c.a.56.23	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.4.c.a.46.23	✓	50	1.1	even	1	trivial
103.4.c.a.56.23	yes	50	103.56	even	3	inner

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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	103.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.46067 + 4.26201i) q^{2} -9.26768 q^{3} +(-8.10981 + 14.0466i) q^{4} +(-6.00715 + 10.4047i) q^{5} +(-22.8047 - 39.4989i) q^{6} +(15.4448 - 26.7511i) q^{7} -40.4516 q^{8} +58.8899 q^{9} +O(q^{10})\)	\(q+(2.46067 + 4.26201i) q^{2} -9.26768 q^{3} +(-8.10981 + 14.0466i) q^{4} +(-6.00715 + 10.4047i) q^{5} +(-22.8047 - 39.4989i) q^{6} +(15.4448 - 26.7511i) q^{7} -40.4516 q^{8} +58.8899 q^{9} -59.1265 q^{10} +(-15.0523 + 26.0713i) q^{11} +(75.1591 - 130.179i) q^{12} -51.5593 q^{13} +152.018 q^{14} +(55.6724 - 96.4274i) q^{15} +(-34.6596 - 60.0321i) q^{16} +(-7.56962 + 13.1110i) q^{17} +(144.909 + 250.989i) q^{18} +(-69.3640 - 120.142i) q^{19} +(-97.4337 - 168.760i) q^{20} +(-143.137 + 247.921i) q^{21} -148.155 q^{22} -153.520 q^{23} +374.892 q^{24} +(-9.67174 - 16.7520i) q^{25} +(-126.871 - 219.746i) q^{26} -295.545 q^{27} +(250.509 + 433.893i) q^{28} +(10.2429 + 17.7413i) q^{29} +547.966 q^{30} +57.8733 q^{31} +(8.76528 - 15.1819i) q^{32} +(139.500 - 241.621i) q^{33} -74.5054 q^{34} +(185.558 + 321.396i) q^{35} +(-477.586 + 827.203i) q^{36} -132.701 q^{37} +(341.364 - 591.260i) q^{38} +477.835 q^{39} +(242.999 - 420.886i) q^{40} +(59.0303 + 102.243i) q^{41} -1408.86 q^{42} +(139.691 + 241.951i) q^{43} +(-244.142 - 422.867i) q^{44} +(-353.760 + 612.731i) q^{45} +(-377.762 - 654.304i) q^{46} +(-27.8375 + 48.2160i) q^{47} +(321.214 + 556.358i) q^{48} +(-305.583 - 529.285i) q^{49} +(47.5980 - 82.4421i) q^{50} +(70.1528 - 121.508i) q^{51} +(418.136 - 724.233i) q^{52} +(-263.604 + 456.575i) q^{53} +(-727.240 - 1259.62i) q^{54} +(-180.843 - 313.229i) q^{55} +(-624.766 + 1082.13i) q^{56} +(642.844 + 1113.44i) q^{57} +(-50.4090 + 87.3109i) q^{58} +(258.987 + 448.579i) q^{59} +(902.984 + 1564.01i) q^{60} -494.137 q^{61} +(142.407 + 246.657i) q^{62} +(909.541 - 1575.37i) q^{63} -468.279 q^{64} +(309.725 - 536.459i) q^{65} +1373.05 q^{66} +(299.688 - 519.074i) q^{67} +(-122.776 - 212.655i) q^{68} +1422.77 q^{69} +(-913.196 + 1581.70i) q^{70} +(-120.141 + 208.091i) q^{71} -2382.19 q^{72} -674.492 q^{73} +(-326.534 - 565.574i) q^{74} +(89.6346 + 155.252i) q^{75} +2250.12 q^{76} +(464.958 + 805.331i) q^{77} +(1175.80 + 2036.54i) q^{78} +521.492 q^{79} +832.821 q^{80} +1148.99 q^{81} +(-290.508 + 503.175i) q^{82} +(-581.897 - 1007.88i) q^{83} +(-2321.63 - 4021.19i) q^{84} +(-90.9437 - 157.519i) q^{85} +(-687.466 + 1190.73i) q^{86} +(-94.9282 - 164.421i) q^{87} +(608.888 - 1054.63i) q^{88} -23.0448 q^{89} -3481.95 q^{90} +(-796.323 + 1379.27i) q^{91} +(1245.02 - 2156.43i) q^{92} -536.351 q^{93} -273.996 q^{94} +1666.72 q^{95} +(-81.2338 + 140.701i) q^{96} +(-356.071 - 616.733i) q^{97} +(1503.88 - 2604.79i) q^{98} +(-886.427 + 1535.34i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} + 4 q^{3} - 97 q^{4} - 3 q^{5} - 17 q^{6} + 13 q^{7} - 30 q^{8} + 534 q^{9}+O(q^{10}) \) 50 * q - q^2 + 4 * q^3 - 97 * q^4 - 3 * q^5 - 17 * q^6 + 13 * q^7 - 30 * q^8 + 534 * q^9	\( 50 q - q^{2} + 4 q^{3} - 97 q^{4} - 3 q^{5} - 17 q^{6} + 13 q^{7} - 30 q^{8} + 534 q^{9} - 56 q^{10} - 17 q^{11} - 186 q^{12} - 16 q^{13} + 274 q^{14} + 70 q^{15} - 289 q^{16} - 41 q^{17} + 48 q^{18} + 133 q^{19} + 117 q^{20} - 416 q^{21} + 88 q^{22} - 184 q^{23} + 1002 q^{24} - 934 q^{25} - 522 q^{26} - 380 q^{27} + 578 q^{28} - 51 q^{29} + 1076 q^{30} - 216 q^{31} - 471 q^{32} - 182 q^{33} - 58 q^{34} - 27 q^{35} - 1486 q^{36} + 276 q^{37} + 1800 q^{38} + 220 q^{39} + 7 q^{40} - 133 q^{41} - 372 q^{42} + 549 q^{43} - 117 q^{44} - 251 q^{45} + 506 q^{46} + 767 q^{47} - 2082 q^{48} - 440 q^{49} - 1106 q^{50} - 456 q^{51} + 2053 q^{52} - 75 q^{53} - 2473 q^{54} + 201 q^{55} - 1278 q^{56} + 1176 q^{57} - 294 q^{58} + 871 q^{59} + 762 q^{60} - 2732 q^{61} - 603 q^{62} + 1165 q^{63} + 3518 q^{64} - 1392 q^{65} + 7624 q^{66} + 2635 q^{67} + 3025 q^{68} - 2468 q^{69} - 4724 q^{70} - 397 q^{71} - 6040 q^{72} + 3240 q^{73} - 1039 q^{74} - 3356 q^{75} - 2990 q^{76} - 319 q^{77} - 2654 q^{78} - 2340 q^{79} + 5284 q^{80} + 538 q^{81} - 687 q^{82} + 1243 q^{83} - 4271 q^{84} + 1397 q^{85} - 829 q^{86} - 1850 q^{87} + 991 q^{88} + 4068 q^{89} + 7258 q^{90} - 4778 q^{91} + 891 q^{92} - 3704 q^{93} + 5564 q^{94} - 3910 q^{95} - 3443 q^{96} + 2197 q^{97} + 994 q^{98} - 6033 q^{99}+O(q^{100}) \) 50 * q - q^2 + 4 * q^3 - 97 * q^4 - 3 * q^5 - 17 * q^6 + 13 * q^7 - 30 * q^8 + 534 * q^9 - 56 * q^10 - 17 * q^11 - 186 * q^12 - 16 * q^13 + 274 * q^14 + 70 * q^15 - 289 * q^16 - 41 * q^17 + 48 * q^18 + 133 * q^19 + 117 * q^20 - 416 * q^21 + 88 * q^22 - 184 * q^23 + 1002 * q^24 - 934 * q^25 - 522 * q^26 - 380 * q^27 + 578 * q^28 - 51 * q^29 + 1076 * q^30 - 216 * q^31 - 471 * q^32 - 182 * q^33 - 58 * q^34 - 27 * q^35 - 1486 * q^36 + 276 * q^37 + 1800 * q^38 + 220 * q^39 + 7 * q^40 - 133 * q^41 - 372 * q^42 + 549 * q^43 - 117 * q^44 - 251 * q^45 + 506 * q^46 + 767 * q^47 - 2082 * q^48 - 440 * q^49 - 1106 * q^50 - 456 * q^51 + 2053 * q^52 - 75 * q^53 - 2473 * q^54 + 201 * q^55 - 1278 * q^56 + 1176 * q^57 - 294 * q^58 + 871 * q^59 + 762 * q^60 - 2732 * q^61 - 603 * q^62 + 1165 * q^63 + 3518 * q^64 - 1392 * q^65 + 7624 * q^66 + 2635 * q^67 + 3025 * q^68 - 2468 * q^69 - 4724 * q^70 - 397 * q^71 - 6040 * q^72 + 3240 * q^73 - 1039 * q^74 - 3356 * q^75 - 2990 * q^76 - 319 * q^77 - 2654 * q^78 - 2340 * q^79 + 5284 * q^80 + 538 * q^81 - 687 * q^82 + 1243 * q^83 - 4271 * q^84 + 1397 * q^85 - 829 * q^86 - 1850 * q^87 + 991 * q^88 + 4068 * q^89 + 7258 * q^90 - 4778 * q^91 + 891 * q^92 - 3704 * q^93 + 5564 * q^94 - 3910 * q^95 - 3443 * q^96 + 2197 * q^97 + 994 * q^98 - 6033 * q^99

Introduction

L-functions

Modular forms

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