LMFDB - Embedded newform 105.4.m.a.13.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.m (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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.18
Character	$\chi$	$=$	105.13
Dual form			105.4.m.a.97.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79945 - 1.79945i) q^{2} +(2.12132 - 2.12132i) q^{3} +1.52398i q^{4} +(11.1587 + 0.695951i) q^{5} -7.63441i q^{6} +(13.3607 + 12.8255i) q^{7} +(17.1379 + 17.1379i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(1.79945 - 1.79945i) q^{2} +(2.12132 - 2.12132i) q^{3} +1.52398i q^{4} +(11.1587 + 0.695951i) q^{5} -7.63441i q^{6} +(13.3607 + 12.8255i) q^{7} +(17.1379 + 17.1379i) q^{8} -9.00000i q^{9} +(21.3317 - 18.8271i) q^{10} -62.0501 q^{11} +(3.23285 + 3.23285i) q^{12} +(54.1331 - 54.1331i) q^{13} +(47.1206 - 0.963085i) q^{14} +(25.1474 - 22.1948i) q^{15} +49.4856 q^{16} +(-9.49779 - 9.49779i) q^{17} +(-16.1950 - 16.1950i) q^{18} -102.840 q^{19} +(-1.06062 + 17.0056i) q^{20} +(55.5492 - 1.13536i) q^{21} +(-111.656 + 111.656i) q^{22} +(-67.3079 - 67.3079i) q^{23} +72.7099 q^{24} +(124.031 + 15.5318i) q^{25} -194.819i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-19.5457 + 20.3614i) q^{28} -41.5785i q^{29} +(5.31317 - 85.1897i) q^{30} +35.7192i q^{31} +(-48.0564 + 48.0564i) q^{32} +(-131.628 + 131.628i) q^{33} -34.1816 q^{34} +(140.161 + 152.413i) q^{35} +13.7158 q^{36} +(-127.066 + 127.066i) q^{37} +(-185.054 + 185.054i) q^{38} -229.667i q^{39} +(179.309 + 203.163i) q^{40} +76.2138i q^{41} +(97.9148 - 102.001i) q^{42} +(161.871 + 161.871i) q^{43} -94.5631i q^{44} +(6.26356 - 100.428i) q^{45} -242.234 q^{46} +(33.7996 + 33.7996i) q^{47} +(104.975 - 104.975i) q^{48} +(14.0151 + 342.714i) q^{49} +(251.136 - 195.239i) q^{50} -40.2957 q^{51} +(82.4978 + 82.4978i) q^{52} +(-502.866 - 502.866i) q^{53} -68.7097 q^{54} +(-692.396 - 43.1838i) q^{55} +(9.17240 + 448.775i) q^{56} +(-218.156 + 218.156i) q^{57} +(-74.8183 - 74.8183i) q^{58} -137.315 q^{59} +(33.8244 + 38.3242i) q^{60} -254.079i q^{61} +(64.2748 + 64.2748i) q^{62} +(115.429 - 120.246i) q^{63} +568.835i q^{64} +(641.727 - 566.379i) q^{65} +473.716i q^{66} +(-522.692 + 522.692i) q^{67} +(14.4745 - 14.4745i) q^{68} -285.563 q^{69} +(526.472 + 22.0469i) q^{70} +386.808 q^{71} +(154.241 - 154.241i) q^{72} +(142.499 - 142.499i) q^{73} +457.297i q^{74} +(296.058 - 230.162i) q^{75} -156.726i q^{76} +(-829.031 - 795.821i) q^{77} +(-413.274 - 413.274i) q^{78} -160.688i q^{79} +(552.193 + 34.4396i) q^{80} -81.0000 q^{81} +(137.143 + 137.143i) q^{82} +(227.086 - 227.086i) q^{83} +(1.73026 + 84.6559i) q^{84} +(-99.3726 - 112.593i) q^{85} +582.556 q^{86} +(-88.2013 - 88.2013i) q^{87} +(-1063.41 - 1063.41i) q^{88} +486.783 q^{89} +(-169.444 - 191.986i) q^{90} +(1417.54 - 28.9727i) q^{91} +(102.576 - 102.576i) q^{92} +(75.7718 + 75.7718i) q^{93} +121.641 q^{94} +(-1147.55 - 71.5713i) q^{95} +203.886i q^{96} +(769.449 + 769.449i) q^{97} +(641.914 + 591.475i) q^{98} +558.451i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) $ 48 * q + 4 * q^7 - 168 * q^8	$ 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) $ 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.79945	−	1.79945i	0.636201	−	0.636201i	−0.313415	−	0.949616i	$-0.601473\pi$
$2$	1.79945	−	1.79945i	0.636201	−	0.636201i	0.949616	+	0.313415i	$0.101473\pi$
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$			1.52398i			0.190498i
$5$	11.1587	+	0.695951i	0.998061	+	0.0622477i
$5$	11.1587	+	0.695951i	0.998061	+	0.0622477i
$6$		−	7.63441i		−	0.519456i
$7$	13.3607	+	12.8255i	0.721408	+	0.692510i
$7$	13.3607	+	12.8255i	0.721408	+	0.692510i
$8$	17.1379	+	17.1379i	0.757395	+	0.757395i
$9$		−	9.00000i		−	0.333333i
$10$	21.3317	−	18.8271i	0.674569	−	0.595365i
$11$	−62.0501			−1.70080			−0.850400	−	0.526136i	$-0.823640\pi$
$11$	−62.0501			−1.70080			−0.850400	+	0.526136i	$0.823640\pi$
$12$	3.23285	+	3.23285i	0.0777703	+	0.0777703i
$13$	54.1331	−	54.1331i	1.15491	−	1.15491i	0.169354	−	0.985555i	$-0.445832\pi$
$13$	54.1331	−	54.1331i	1.15491	−	1.15491i	0.985555	−	0.169354i	$-0.0541683\pi$
$14$	47.1206	−	0.963085i	0.899536	−	0.0183854i
$15$	25.1474	−	22.1948i	0.432869	−	0.382044i
$16$	49.4856			0.773213
$17$	−9.49779	−	9.49779i	−0.135503	−	0.135503i	0.636102	−	0.771605i	$-0.280546\pi$
$17$	−9.49779	−	9.49779i	−0.135503	−	0.135503i	−0.771605	+	0.636102i	$0.780546\pi$
$18$	−16.1950	−	16.1950i	−0.212067	−	0.212067i
$19$	−102.840			−1.24174			−0.620869	−	0.783914i	$-0.713220\pi$
$19$	−102.840			−1.24174			−0.620869	+	0.783914i	$0.713220\pi$
$20$	−1.06062	+	17.0056i	−0.0118580	+	0.190128i
$21$	55.5492	−	1.13536i	0.577230	−	0.0117979i
$22$	−111.656	+	111.656i	−1.08205	+	1.08205i
$23$	−67.3079	−	67.3079i	−0.610203	−	0.610203i	0.332796	−	0.942999i	$-0.392008\pi$
$23$	−67.3079	−	67.3079i	−0.610203	−	0.610203i	−0.942999	+	0.332796i	$0.892008\pi$
$24$	72.7099			0.618411
$25$	124.031	+	15.5318i	0.992250	+	0.124254i
$26$		−	194.819i		−	1.46951i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	−19.5457	+	20.3614i	−0.131921	+	0.137427i
$29$		−	41.5785i		−	0.266239i	−0.991100	−	0.133120i	$-0.957501\pi$
$29$		−	41.5785i		−	0.266239i	0.991100	−	0.133120i	$-0.0424994\pi$
$30$	5.31317	−	85.1897i	0.0323349	−	0.518448i
$31$			35.7192i			0.206947i	0.994632	+	0.103473i	$0.0329957\pi$
$31$			35.7192i			0.206947i	−0.994632	+	0.103473i	$0.967004\pi$
$32$	−48.0564	+	48.0564i	−0.265477	+	0.265477i
$33$	−131.628	+	131.628i	−0.694349	+	0.694349i
$34$	−34.1816			−0.172414
$35$	140.161	+	152.413i	0.676902	+	0.736073i
$36$	13.7158			0.0634992
$37$	−127.066	+	127.066i	−0.564582	+	0.564582i	−0.930605	−	0.366024i	$-0.880719\pi$
$37$	−127.066	+	127.066i	−0.564582	+	0.564582i	0.366024	+	0.930605i	$0.380719\pi$
$38$	−185.054	+	185.054i	−0.789994	+	0.789994i
$39$		−	229.667i		−	0.942980i
$40$	179.309	+	203.163i	0.708780	+	0.803073i
$41$			76.2138i			0.290307i	0.989409	+	0.145154i	$0.0463676\pi$
$41$			76.2138i			0.290307i	−0.989409	+	0.145154i	$0.953632\pi$
$42$	97.9148	−	102.001i	0.359728	−	0.374740i
$43$	161.871	+	161.871i	0.574071	+	0.574071i	0.933264	−	0.359192i	$-0.116948\pi$
$43$	161.871	+	161.871i	0.574071	+	0.574071i	−0.359192	+	0.933264i	$0.616948\pi$
$44$		−	94.5631i		−	0.323998i
$45$	6.26356	−	100.428i	0.0207492	−	0.332687i
$46$	−242.234			−0.776423
$47$	33.7996	+	33.7996i	0.104898	+	0.104898i	0.757608	−	0.652710i	$-0.226368\pi$
$47$	33.7996	+	33.7996i	0.104898	+	0.104898i	−0.652710	+	0.757608i	$0.726368\pi$
$48$	104.975	−	104.975i	0.315663	−	0.315663i
$49$	14.0151	+	342.714i	0.0408604	+	0.999165i
$50$	251.136	−	195.239i	0.710321	−	0.552220i
$51$	−40.2957			−0.110638
$52$	82.4978	+	82.4978i	0.220007	+	0.220007i
$53$	−502.866	−	502.866i	−1.30328	−	1.30328i	−0.926165	−	0.377118i	$-0.876915\pi$
$53$	−502.866	−	502.866i	−1.30328	−	1.30328i	−0.377118	−	0.926165i	$-0.623085\pi$
$54$	−68.7097			−0.173152
$55$	−692.396	−	43.1838i	−1.69750	−	0.105871i
$56$	9.17240	+	448.775i	0.0218877	+	1.07090i
$57$	−218.156	+	218.156i	−0.506937	+	0.506937i
$58$	−74.8183	−	74.8183i	−0.169382	−	0.169382i
$59$	−137.315			−0.302998			−0.151499	−	0.988457i	$-0.548410\pi$
$59$	−137.315			−0.302998			−0.151499	+	0.988457i	$0.548410\pi$
$60$	33.8244	+	38.3242i	0.0727785	+	0.0824605i
$61$		−	254.079i		−	0.533304i	−0.963793	−	0.266652i	$-0.914083\pi$
$61$		−	254.079i		−	0.533304i	0.963793	−	0.266652i	$-0.0859174\pi$
$62$	64.2748	+	64.2748i	0.131660	+	0.131660i
$63$	115.429	−	120.246i	0.230837	−	0.240469i
$64$			568.835i			1.11101i
$65$	641.727	−	566.379i	1.22456	−	1.08078i
$66$			473.716i			0.883491i
$67$	−522.692	+	522.692i	−0.953090	+	0.953090i	−0.998948	−	0.0458581i	$-0.985398\pi$
$67$	−522.692	+	522.692i	−0.953090	+	0.953090i	0.0458581	+	0.998948i	$0.485398\pi$
$68$	14.4745	−	14.4745i	0.0258130	−	0.0258130i
$69$	−285.563			−0.498229
$70$	526.472	+	22.0469i	0.898936	+	0.0376443i
$71$	386.808			0.646559			0.323279	−	0.946304i	$-0.395215\pi$
$71$	386.808			0.646559			0.323279	+	0.946304i	$0.395215\pi$
$72$	154.241	−	154.241i	0.252465	−	0.252465i
$73$	142.499	−	142.499i	0.228469	−	0.228469i	−0.583584	−	0.812053i	$-0.698350\pi$
$73$	142.499	−	142.499i	0.228469	−	0.228469i	0.812053	+	0.583584i	$0.198350\pi$
$74$			457.297i			0.718374i
$75$	296.058	−	230.162i	0.455811	−	0.354358i
$76$		−	156.726i		−	0.236548i
$77$	−829.031	−	795.821i	−1.22697	−	1.17782i
$78$	−413.274	−	413.274i	−0.599924	−	0.599924i
$79$		−	160.688i		−	0.228846i	−0.993432	−	0.114423i	$-0.963498\pi$
$79$		−	160.688i		−	0.228846i	0.993432	−	0.114423i	$-0.0365019\pi$
$80$	552.193	+	34.4396i	0.771714	+	0.0481308i
$81$	−81.0000			−0.111111
$82$	137.143	+	137.143i	0.184694	+	0.184694i
$83$	227.086	−	227.086i	0.300312	−	0.300312i	−0.540824	−	0.841136i	$-0.681887\pi$
$83$	227.086	−	227.086i	0.300312	−	0.300312i	0.841136	+	0.540824i	$0.181887\pi$
$84$	1.73026	+	84.6559i	0.00224746	+	0.109961i
$85$	−99.3726	−	112.593i	−0.126806	−	0.143675i
$86$	582.556			0.730449
$87$	−88.2013	−	88.2013i	−0.108692	−	0.108692i
$88$	−1063.41	−	1063.41i	−1.28818	−	1.28818i
$89$	486.783			0.579763			0.289881	−	0.957063i	$-0.406384\pi$
$89$	486.783			0.579763			0.289881	+	0.957063i	$0.406384\pi$
$90$	−169.444	−	191.986i	−0.198455	−	0.224856i
$91$	1417.54	−	28.9727i	1.63295	−	0.0333754i
$92$	102.576	−	102.576i	0.116242	−	0.116242i
$93$	75.7718	+	75.7718i	0.0844857	+	0.0844857i
$94$	121.641			0.133472
$95$	−1147.55	−	71.5713i	−1.23933	−	0.0772954i
$96$			203.886i			0.216761i
$97$	769.449	+	769.449i	0.805420	+	0.805420i	0.983937	−	0.178517i	$-0.0571300\pi$
$97$	769.449	+	769.449i	0.805420	+	0.805420i	−0.178517	+	0.983937i	$0.557130\pi$
$98$	641.914	+	591.475i	0.661665	+	0.609674i
$99$			558.451i			0.566934i
$100$	−23.6701	+	189.021i	−0.0236701	+	0.189021i
$101$		−	1644.69i		−	1.62032i	−0.586209	−	0.810160i	$-0.699380\pi$
$101$		−	1644.69i		−	1.62032i	0.586209	−	0.810160i	$-0.300620\pi$
$102$	−72.5100	+	72.5100i	−0.0703879	+	0.0703879i
$103$	958.482	−	958.482i	0.916913	−	0.916913i	−0.0798906	−	0.996804i	$-0.525457\pi$
$103$	958.482	−	958.482i	0.916913	−	0.916913i	0.996804	+	0.0798906i	$0.0254571\pi$
$104$	1855.46			1.74945
$105$	620.644	+	25.9905i	0.576845	+	0.0241563i
$106$	−1809.76			−1.65830
$107$	−448.717	+	448.717i	−0.405412	+	0.405412i	−0.880135	−	0.474723i	$-0.842548\pi$
$107$	−448.717	+	448.717i	−0.405412	+	0.405412i	0.474723	+	0.880135i	$0.342548\pi$
$108$	29.0957	−	29.0957i	0.0259234	−	0.0259234i
$109$			504.676i			0.443479i	0.975106	+	0.221740i	$0.0711735\pi$
$109$			504.676i			0.443479i	−0.975106	+	0.221740i	$0.928826\pi$
$110$	−1323.64	+	1168.22i	−1.14731	+	1.01260i
$111$			539.095i			0.460979i
$112$	661.161	+	634.676i	0.557803	+	0.535458i
$113$	−1102.46	−	1102.46i	−0.917794	−	0.917794i	0.0790746	−	0.996869i	$-0.474803\pi$
$113$	−1102.46	−	1102.46i	−0.917794	−	0.917794i	−0.996869	+	0.0790746i	$0.974803\pi$
$114$			785.119i			0.645028i
$115$	−704.223	−	797.909i	−0.571036	−	0.647004i
$116$	63.3648			0.0507179
$117$	−487.198	−	487.198i	−0.384970	−	0.384970i
$118$	−247.091	+	247.091i	−0.192767	+	0.192767i
$119$	−5.08333	−	248.710i	−0.00391587	−	0.191590i
$120$	811.345	+	50.6026i	0.617211	+	0.0384947i
$121$	2519.21			1.89272
$122$	−457.202	−	457.202i	−0.339288	−	0.339288i
$123$	161.674	+	161.674i	0.118517	+	0.118517i
$124$	−54.4353			−0.0394229
$125$	1373.21	+	259.633i	0.982592	+	0.185778i
$126$	−8.66777	−	424.085i	−0.00612846	−	0.299845i
$127$	1669.01	−	1669.01i	1.16615	−	1.16615i	0.183042	−	0.983105i	$-0.441406\pi$
$127$	1669.01	−	1669.01i	1.16615	−	1.16615i	0.983105	−	0.183042i	$-0.0585943\pi$
$128$	639.137	+	639.137i	0.441346	+	0.441346i
$129$	686.760			0.468727
$130$	135.585	−	2173.92i	0.0914736	−	1.46666i
$131$			2225.02i			1.48398i	0.670413	+	0.741988i	$0.266117\pi$
$131$			2225.02i			1.48398i	−0.670413	+	0.741988i	$0.733883\pi$
$132$	−200.599	−	200.599i	−0.132272	−	0.132272i
$133$	−1374.01	−	1318.97i	−0.895800	−	0.859916i
$134$			1881.11i			1.21271i
$135$	−199.753	−	226.327i	−0.127348	−	0.144290i
$136$		−	325.544i		−	0.205259i
$137$	−1373.95	+	1373.95i	−0.856822	+	0.856822i	−0.990962	−	0.134140i	$-0.957173\pi$
$137$	−1373.95	+	1373.95i	−0.856822	+	0.856822i	0.134140	+	0.990962i	$0.457173\pi$
$138$	−513.856	+	513.856i	−0.316973	+	0.316973i
$139$	−2811.44			−1.71556			−0.857781	−	0.514015i	$-0.828158\pi$
$139$	−2811.44			−1.71556			−0.857781	+	0.514015i	$0.828158\pi$
$140$	−232.275	+	213.603i	−0.140220	+	0.128948i
$141$	143.400			0.0856485
$142$	696.041	−	696.041i	0.411341	−	0.411341i
$143$	−3358.97	+	3358.97i	−1.96427	+	1.96427i
$144$		−	445.371i		−	0.257738i
$145$	28.9366	−	463.960i	0.0165728	−	0.265723i
$146$		−	512.838i		−	0.290704i
$147$	756.736	+	697.275i	0.424589	+	0.391226i
$148$	−193.646	−	193.646i	−0.107551	−	0.107551i
$149$			2499.57i			1.37432i	0.726508	+	0.687158i	$0.241142\pi$
$149$			2499.57i			1.37432i	−0.726508	+	0.687158i	$0.758858\pi$
$150$	118.576	−	946.906i	0.0645445	−	0.515430i
$151$	−1299.60			−0.700397			−0.350198	−	0.936676i	$-0.613886\pi$
$151$	−1299.60			−0.700397			−0.350198	+	0.936676i	$0.613886\pi$
$152$	−1762.45	−	1762.45i	−0.940486	−	0.940486i
$153$	−85.4801	+	85.4801i	−0.0451677	+	0.0451677i
$154$	−2923.84	+	59.7595i	−1.52993	+	0.0312699i
$155$	−24.8588	+	398.578i	−0.0128820	+	0.206546i
$156$	350.009			0.179635
$157$	1859.42	+	1859.42i	0.945211	+	0.945211i	0.998575	−	0.0533641i	$-0.0169944\pi$
$157$	1859.42	+	1859.42i	0.945211	+	0.945211i	−0.0533641	+	0.998575i	$0.516994\pi$
$158$	−289.150	−	289.150i	−0.145592	−	0.145592i
$159$	−2133.48			−1.06413
$160$	−569.690	+	502.800i	−0.281487	+	0.248436i
$161$	−36.0240	−	1762.53i	−0.0176341	−	0.862777i
$162$	−145.755	+	145.755i	−0.0706890	+	0.0706890i
$163$	1857.37	+	1857.37i	0.892517	+	0.892517i	0.994760	−	0.102243i	$-0.0326018\pi$
$163$	1857.37	+	1857.37i	0.892517	+	0.892517i	−0.102243	+	0.994760i	$0.532602\pi$
$164$	−116.148			−0.0553028
$165$	−1560.40	+	1377.19i	−0.736224	+	0.649781i
$166$		−	817.258i		−	0.382118i
$167$	−118.460	−	118.460i	−0.0548904	−	0.0548904i	0.679129	−	0.734019i	$-0.262358\pi$
$167$	−118.460	−	118.460i	−0.0548904	−	0.0548904i	−0.734019	+	0.679129i	$0.762358\pi$
$168$	971.454	+	932.539i	0.446127	+	0.428255i
$169$		−	3663.79i		−	1.66763i
$170$	−381.420	−	23.7887i	−0.172080	−	0.0107324i
$171$			925.556i			0.413913i
$172$	−246.688	+	246.688i	−0.109359	+	0.109359i
$173$	1263.05	−	1263.05i	0.555075	−	0.555075i	−0.372826	−	0.927901i	$-0.621611\pi$
$173$	1263.05	−	1263.05i	0.555075	−	0.555075i	0.927901	+	0.372826i	$0.121611\pi$
$174$	−317.427			−0.138299
$175$	1457.94	+	1798.27i	0.629771	+	0.776781i
$176$	−3070.59			−1.31508
$177$	−291.289	+	291.289i	−0.123698	+	0.123698i
$178$	875.940	−	875.940i	0.368845	−	0.368845i
$179$		−	3252.59i		−	1.35816i	−0.734065	−	0.679079i	$-0.762379\pi$
$179$		−	3252.59i		−	1.35816i	0.734065	−	0.679079i	$-0.237621\pi$
$180$	153.050	+	9.54554i	0.0633760	+	0.00395268i
$181$			2075.14i			0.852176i	0.904682	+	0.426088i	$0.140109\pi$
$181$			2075.14i			0.852176i	−0.904682	+	0.426088i	$0.859891\pi$
$182$	2498.65	−	2602.92i	1.01765	−	1.06012i
$183$	−538.984	−	538.984i	−0.217720	−	0.217720i
$184$		−	2307.03i		−	0.924330i
$185$	−1506.32	+	1329.45i	−0.598631	+	0.528343i
$186$	272.695			0.107500
$187$	589.339	+	589.339i	0.230464	+	0.230464i
$188$	−51.5100	+	51.5100i	−0.0199827	+	0.0199827i
$189$	−10.2182	−	499.943i	−0.00393262	−	0.192410i
$190$	−2193.75	+	1936.17i	−0.837638	+	0.739287i
$191$	1650.05			0.625095			0.312547	−	0.949902i	$-0.398818\pi$
$191$	1650.05			0.625095			0.312547	+	0.949902i	$0.398818\pi$
$192$	1206.68	+	1206.68i	0.453566	+	0.453566i
$193$	1808.56	+	1808.56i	0.674524	+	0.674524i	0.958756	−	0.284231i	$-0.0917384\pi$
$193$	1808.56	+	1808.56i	0.674524	+	0.674524i	−0.284231	+	0.958756i	$0.591738\pi$
$194$	2769.17			1.02482
$195$	159.837	−	2562.78i	0.0586984	−	0.941151i
$196$	−522.289	+	21.3588i	−0.190338	+	0.00778381i
$197$	−918.396	+	918.396i	−0.332147	+	0.332147i	−0.853401	−	0.521254i	$-0.825464\pi$
$197$	−918.396	+	918.396i	−0.332147	+	0.332147i	0.521254	+	0.853401i	$0.325464\pi$
$198$	1004.90	+	1004.90i	0.360683	+	0.360683i
$199$	2921.92			1.04085			0.520425	−	0.853907i	$-0.325773\pi$
$199$	2921.92			1.04085			0.520425	+	0.853907i	$0.325773\pi$
$200$	1859.45	+	2391.82i	0.657416	+	0.845635i
$201$			2217.60i			0.778195i
$202$	−2959.52	−	2959.52i	−1.03085	−	1.03085i
$203$	533.264	−	555.517i	0.184373	−	0.192067i
$204$		−	61.4099i		−	0.0210762i
$205$	−53.0410	+	850.443i	−0.0180710	+	0.289744i
$206$		−	3449.48i		−	1.16668i
$207$	−605.771	+	605.771i	−0.203401	+	0.203401i
$208$	2678.81	−	2678.81i	0.892991	−	0.892991i
$209$	6381.21			2.11195
$210$	1163.59	−	1070.05i	0.382357	−	0.351621i
$211$	1482.97			0.483849			0.241924	−	0.970295i	$-0.422221\pi$
$211$	1482.97			0.483849			0.241924	+	0.970295i	$0.422221\pi$
$212$	766.358	−	766.358i	0.248272	−	0.248272i
$213$	820.544	−	820.544i	0.263956	−	0.263956i
$214$			1614.88i			0.515846i
$215$	1693.61	+	1918.91i	0.537223	+	0.608693i
$216$		−	654.390i		−	0.206137i
$217$	−458.115	+	477.232i	−0.143313	+	0.149293i
$218$	908.139	+	908.139i	0.282142	+	0.282142i
$219$		−	604.570i		−	0.186544i
$220$	65.8113	−	1055.20i	0.0201682	−	0.323370i
$221$	−1028.29			−0.312988
$222$	970.073	+	970.073i	0.293275	+	0.293275i
$223$	−1259.66	+	1259.66i	−0.378264	+	0.378264i	−0.870476	−	0.492211i	$-0.836189\pi$
$223$	−1259.66	+	1259.66i	−0.378264	+	0.378264i	0.492211	+	0.870476i	$0.336189\pi$
$224$	−1258.41	+	25.7203i	−0.375362	+	0.00767193i
$225$	139.786	−	1116.28i	0.0414180	−	0.330750i
$226$	−3967.64			−1.16780
$227$	−19.4717	−	19.4717i	−0.00569331	−	0.00569331i	0.704254	−	0.709948i	$-0.251281\pi$
$227$	−19.4717	−	19.4717i	−0.00569331	−	0.00569331i	−0.709948	+	0.704254i	$0.751281\pi$
$228$	−332.465	−	332.465i	−0.0965703	−	0.0965703i
$229$	1693.57			0.488709			0.244355	−	0.969686i	$-0.421424\pi$
$229$	1693.57			0.488709			0.244355	+	0.969686i	$0.421424\pi$
$230$	−2703.01	−	168.583i	−0.774918	−	0.0483306i
$231$	−3446.83	+	70.4489i	−0.981753	+	0.0200658i
$232$	712.568	−	712.568i	0.201648	−	0.201648i
$233$	2361.35	+	2361.35i	0.663938	+	0.663938i	0.956306	−	0.292368i	$-0.0944433\pi$
$233$	2361.35	+	2361.35i	0.663938	+	0.663938i	−0.292368	+	0.956306i	$0.594443\pi$
$234$	−1753.37			−0.489836
$235$	353.636	+	400.681i	0.0981645	+	0.111224i
$236$		−	209.265i		−	0.0577203i
$237$	−340.871	−	340.871i	−0.0934259	−	0.0934259i
$238$	−456.689	−	438.394i	−0.124381	−	0.119399i
$239$		−	5706.02i		−	1.54432i	−0.635429	−	0.772159i	$-0.719177\pi$
$239$		−	5706.02i		−	1.54432i	0.635429	−	0.772159i	$-0.280823\pi$
$240$	1244.44	−	1098.32i	0.334700	−	0.295401i
$241$		−	3411.89i		−	0.911946i	−0.889994	−	0.455973i	$-0.849291\pi$
$241$		−	3411.89i		−	0.911946i	0.889994	−	0.455973i	$-0.150709\pi$
$242$	4533.19	−	4533.19i	1.20415	−	1.20415i
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	387.212			0.101593
$245$	−82.1218	+	3833.98i	−0.0214146	+	0.999771i
$246$	581.847			0.150802
$247$	−5567.03	+	5567.03i	−1.43410	+	1.43410i
$248$	−612.152	+	612.152i	−0.156741	+	0.156741i
$249$		−	963.444i		−	0.245204i
$250$	2938.22	−	2003.83i	0.743318	−	0.506933i
$251$			769.958i			0.193623i	0.995303	+	0.0968113i	$0.0308643\pi$
$251$			769.958i			0.193623i	−0.995303	+	0.0968113i	$0.969136\pi$
$252$	183.253	+	175.912i	0.0458088	+	0.0439738i
$253$	4176.46	+	4176.46i	1.03783	+	1.03783i
$254$		−	6006.59i		−	1.48381i
$255$	−449.646	−	28.0438i	−0.110423	−	0.00688696i
$256$	−2250.49			−0.549437
$257$	−3933.12	−	3933.12i	−0.954634	−	0.954634i	0.0443805	−	0.999015i	$-0.485869\pi$
$257$	−3933.12	−	3933.12i	−0.954634	−	0.954634i	−0.999015	+	0.0443805i	$0.985869\pi$
$258$	1235.79	−	1235.79i	0.298205	−	0.298205i
$259$	−3327.37	+	68.0072i	−0.798272	+	0.0163157i
$260$	863.150	+	977.979i	0.205886	+	0.233276i
$261$	−374.207			−0.0887464
$262$	4003.80	+	4003.80i	0.944106	+	0.944106i
$263$	3157.53	+	3157.53i	0.740310	+	0.740310i	0.972638	−	0.232327i	$-0.0746341\pi$
$263$	3157.53	+	3157.53i	0.740310	+	0.740310i	−0.232327	+	0.972638i	$0.574634\pi$
$264$	−4511.66			−1.05179
$265$	−5261.34	−	5961.28i	−1.21963	−	1.38188i
$266$	−4845.86	+	99.0433i	−1.11699	+	0.0228298i
$267$	1032.62	−	1032.62i	0.236687	−	0.236687i
$268$	−796.573	−	796.573i	−0.181561	−	0.181561i
$269$	3846.35			0.871807			0.435903	−	0.899994i	$-0.356429\pi$
$269$	3846.35			0.871807			0.435903	+	0.899994i	$0.356429\pi$
$270$	−766.708	−	47.8186i	−0.172816	−	0.0107783i
$271$		−	502.190i		−	0.112568i	−0.998415	−	0.0562839i	$-0.982075\pi$
$271$		−	502.190i		−	0.112568i	0.998415	−	0.0562839i	$-0.0179252\pi$
$272$	−470.004	−	470.004i	−0.104773	−	0.104773i
$273$	2945.59	−	3068.51i	0.653023	−	0.680274i
$274$			4944.71i			1.09022i
$275$	−7696.15	−	963.747i	−1.68762	−	0.211331i
$276$		−	435.193i		−	0.0949114i
$277$	2537.12	−	2537.12i	0.550328	−	0.550328i	−0.376208	−	0.926535i	$-0.622772\pi$
$277$	2537.12	−	2537.12i	0.550328	−	0.550328i	0.926535	+	0.376208i	$0.122772\pi$
$278$	−5059.04	+	5059.04i	−1.09144	+	1.09144i
$279$	321.473			0.0689823
$280$	−209.974	+	5014.11i	−0.0448155	+	1.07018i
$281$	5125.15			1.08804			0.544022	−	0.839071i	$-0.316901\pi$
$281$	5125.15			1.08804			0.544022	+	0.839071i	$0.316901\pi$
$282$	258.040	−	258.040i	0.0544896	−	0.0544896i
$283$	−6480.20	+	6480.20i	−1.36116	+	1.36116i	−0.488714	+	0.872444i	$0.662534\pi$
$283$	−6480.20	+	6480.20i	−1.36116	+	1.36116i	−0.872444	+	0.488714i	$0.837466\pi$
$284$			589.488i			0.123168i
$285$	−2586.15	+	2282.50i	−0.537510	+	0.474399i
$286$			12088.6i			2.49934i
$287$	−977.477	+	1018.27i	−0.201040	+	0.209430i
$288$	432.508	+	432.508i	0.0884922	+	0.0884922i
$289$		−	4732.58i		−	0.963278i
$290$	−782.802	−	886.942i	−0.158509	−	0.179597i
$291$	3264.50			0.657622
$292$	217.165	+	217.165i	0.0435227	+	0.0435227i
$293$	4316.68	−	4316.68i	0.860692	−	0.860692i	−0.130726	−	0.991419i	$-0.541731\pi$
$293$	4316.68	−	4316.68i	0.860692	−	0.860692i	0.991419	+	0.130726i	$0.0417309\pi$
$294$	2616.41	−	106.997i	0.519022	−	0.0212252i
$295$	−1532.25	−	95.5644i	−0.302410	−	0.0188609i
$296$	−4355.29			−0.855223
$297$	1184.65	+	1184.65i	0.231450	+	0.231450i
$298$	4497.85	+	4497.85i	0.874341	+	0.874341i
$299$	−7287.18			−1.40946
$300$	350.763	+	451.187i	0.0675043	+	0.0868309i
$301$	86.6351	+	4238.77i	0.0165899	+	0.811690i
$302$	−2338.56	+	2338.56i	−0.445593	+	0.445593i
$303$	−3488.91	−	3488.91i	−0.661493	−	0.661493i
$304$	−5089.08			−0.960128
$305$	176.827	−	2835.18i	0.0331969	−	0.532269i
$306$			307.634i			0.0574715i
$307$	−85.2914	−	85.2914i	−0.0158561	−	0.0158561i	0.699134	−	0.714990i	$-0.253569\pi$
$307$	−85.2914	−	85.2914i	−0.0158561	−	0.0158561i	−0.714990	+	0.699134i	$0.753569\pi$
$308$	1212.82	−	1263.43i	0.224372	−	0.233735i
$309$		−	4066.49i		−	0.748656i
$310$	672.488	+	761.952i	0.123209	+	0.139600i
$311$		−	4499.38i		−	0.820374i	−0.912001	−	0.410187i	$-0.865463\pi$
$311$		−	4499.38i		−	0.820374i	0.912001	−	0.410187i	$-0.134537\pi$
$312$	3936.02	−	3936.02i	0.714208	−	0.714208i
$313$	6558.45	−	6558.45i	1.18436	−	1.18436i	0.205760	−	0.978602i	$-0.434033\pi$
$313$	6558.45	−	6558.45i	1.18436	−	1.18436i	0.978602	−	0.205760i	$-0.0659667\pi$
$314$	6691.87			1.20269
$315$	1371.72	−	1261.45i	0.245358	−	0.225634i
$316$	244.885			0.0435945
$317$	579.920	−	579.920i	0.102749	−	0.102749i	−0.653863	−	0.756613i	$-0.726853\pi$
$317$	579.920	−	579.920i	0.102749	−	0.102749i	0.756613	+	0.653863i	$0.226853\pi$
$318$	−3839.09	+	3839.09i	−0.676998	+	0.676998i
$319$			2579.95i			0.452820i
$320$	−395.881	+	6347.44i	−0.0691576	+	1.10885i
$321$			1903.74i			0.331017i
$322$	−3236.41	−	3106.76i	−0.560118	−	0.537681i
$323$	976.749	+	976.749i	0.168259	+	0.168259i
$324$		−	123.442i		−	0.0211664i
$325$	7554.98	−	5873.42i	1.28946	−	1.00246i
$326$	6684.47			1.13564
$327$	1070.58	+	1070.58i	0.181050	+	0.181050i
$328$	−1306.14	+	1306.14i	−0.219877	+	0.219877i
$329$	18.0900	+	885.082i	0.00303140	+	0.148317i
$330$	−329.683	+	5286.03i	−0.0549953	+	0.881777i
$331$	375.939			0.0624274			0.0312137	−	0.999513i	$-0.490063\pi$
$331$	375.939			0.0624274			0.0312137	+	0.999513i	$0.490063\pi$
$332$	346.074	+	346.074i	0.0572087	+	0.0572087i
$333$	1143.59	+	1143.59i	0.188194	+	0.188194i
$334$	−426.324			−0.0698426
$335$	−6196.31	+	5468.78i	−1.01057	+	0.891914i
$336$	2748.89	−	56.1838i	0.446322	−	0.00912225i
$337$	1123.21	−	1123.21i	0.181558	−	0.181558i	−0.610476	−	0.792034i	$-0.709022\pi$
$337$	1123.21	−	1123.21i	0.181558	−	0.181558i	0.792034	+	0.610476i	$0.209022\pi$
$338$	−6592.79	−	6592.79i	−1.06095	−	1.06095i
$339$	−4677.34			−0.749376
$340$	171.589	−	151.442i	0.0273698	−	0.0241562i
$341$		−	2216.38i		−	0.351975i
$342$	1665.49	+	1665.49i	0.263331	+	0.263331i
$343$	−4208.21	+	4758.63i	−0.662454	+	0.749102i
$344$			5548.25i			0.869598i
$345$	−3186.50	−	198.738i	−0.497263	−	0.0310136i
$346$		−	4545.58i		−	0.706278i
$347$	−5017.42	+	5017.42i	−0.776222	+	0.776222i	−0.979186	−	0.202964i	$-0.934943\pi$
$347$	−5017.42	+	5017.42i	−0.776222	+	0.776222i	0.202964	+	0.979186i	$0.434943\pi$
$348$	134.417	−	134.417i	0.0207055	−	0.0207055i
$349$	1143.12			0.175329			0.0876646	−	0.996150i	$-0.472060\pi$
$349$	1143.12			0.175329			0.0876646	+	0.996150i	$0.472060\pi$
$350$	5859.38	+	612.412i	0.894849	+	0.0935280i
$351$	−2067.01			−0.314327
$352$	2981.90	−	2981.90i	0.451523	−	0.451523i
$353$	−6363.59	+	6363.59i	−0.959490	+	0.959490i	−0.999211	−	0.0397210i	$-0.987353\pi$
$353$	−6363.59	+	6363.59i	−0.959490	+	0.959490i	0.0397210	+	0.999211i	$0.487353\pi$
$354$			1048.32i			0.157394i
$355$	4316.26	+	269.199i	0.645305	+	0.0402468i
$356$			741.847i			0.110443i
$357$	−538.378	−	516.811i	−0.0798151	−	0.0766178i
$358$	−5852.87	−	5852.87i	−0.864061	−	0.864061i
$359$			4520.35i			0.664554i	0.943182	+	0.332277i	$0.107817\pi$
$359$			4520.35i			0.664554i	−0.943182	+	0.332277i	$0.892183\pi$
$360$	1828.47	−	1613.78i	0.267691	−	0.236260i
$361$	3716.98			0.541913
$362$	3734.10	+	3734.10i	0.542155	+	0.542155i
$363$	5344.06	−	5344.06i	0.772701	−	0.772701i
$364$	44.1538	+	2160.30i	0.00635793	+	0.311073i
$365$	1689.27	−	1490.92i	0.242247	−	0.213804i
$366$	−1939.74			−0.277028
$367$	−3003.27	−	3003.27i	−0.427164	−	0.427164i	0.460497	−	0.887661i	$-0.347671\pi$
$367$	−3003.27	−	3003.27i	−0.427164	−	0.427164i	−0.887661	+	0.460497i	$0.847671\pi$
$368$	−3330.78	−	3330.78i	−0.471817	−	0.471817i
$369$	685.924			0.0967690
$370$	−318.256	+	5102.82i	−0.0447172	+	0.716981i
$371$	−269.140	−	13168.1i	−0.0376632	−	1.84274i
$372$	−115.475	+	115.475i	−0.0160943	+	0.0160943i
$373$	−5569.94	−	5569.94i	−0.773192	−	0.773192i	0.205471	−	0.978663i	$-0.434127\pi$
$373$	−5569.94	−	5569.94i	−0.773192	−	0.773192i	−0.978663	+	0.205471i	$0.934127\pi$
$374$	2120.97			0.293242
$375$	3463.79	−	2362.26i	0.476985	−	0.325298i
$376$			1158.51i			0.158898i
$377$	−2250.77	−	2250.77i	−0.307482	−	0.307482i
$378$	−918.007	−	881.233i	−0.124913	−	0.119909i
$379$			8752.18i			1.18620i	0.805129	+	0.593099i	$0.202096\pi$
$379$			8752.18i			1.18620i	−0.805129	+	0.593099i	$0.797904\pi$
$380$	109.073	−	1748.85i	0.0147246	−	0.236089i
$381$		−	7081.01i		−	0.952155i
$382$	2969.17	−	2969.17i	0.397686	−	0.397686i
$383$	−477.949	+	477.949i	−0.0637652	+	0.0637652i	−0.738270	−	0.674505i	$-0.764357\pi$
$383$	−477.949	+	477.949i	−0.0637652	+	0.0637652i	0.674505	+	0.738270i	$0.264357\pi$
$384$	2711.63			0.360358
$385$	−8697.02	−	9457.26i	−1.15128	−	1.25191i
$386$	6508.83			0.858266
$387$	1456.84	−	1456.84i	0.191357	−	0.191357i
$388$	−1172.63	+	1172.63i	−0.153430	+	0.153430i
$389$			8577.62i			1.11800i	0.829167	+	0.559001i	$0.188815\pi$
$389$			8577.62i			1.11800i	−0.829167	+	0.559001i	$0.811185\pi$
$390$	−4323.97	−	4899.21i	−0.561417	−	0.636105i
$391$			1278.55i			0.165369i
$392$	−5633.20	+	6113.58i	−0.725815	+	0.787710i
$393$	4719.98	+	4719.98i	0.605831	+	0.605831i
$394$			3305.21i			0.422625i
$395$	111.831	−	1793.06i	0.0142451	−	0.228402i
$396$	−851.068			−0.107999
$397$	−6375.27	−	6375.27i	−0.805959	−	0.805959i	0.178061	−	0.984020i	$-0.443018\pi$
$397$	−6375.27	−	6375.27i	−0.805959	−	0.805959i	−0.984020	+	0.178061i	$0.943018\pi$
$398$	5257.84	−	5257.84i	0.662190	−	0.662190i
$399$	−5712.65	+	116.759i	−0.716768	+	0.0146498i
$400$	6137.77	+	768.599i	0.767221	+	0.0960749i
$401$	−7593.28			−0.945611			−0.472806	−	0.881167i	$-0.656759\pi$
$401$	−7593.28			−0.945611			−0.472806	+	0.881167i	$0.656759\pi$
$402$	3990.45	+	3990.45i	0.495088	+	0.495088i
$403$	1933.59	+	1933.59i	0.239005	+	0.239005i
$404$	2506.47			0.308667
$405$	−903.851	−	56.3720i	−0.110896	−	0.00691642i
$406$	−40.0436	−	1959.20i	−0.00489491	−	0.239492i
$407$	7884.46	−	7884.46i	0.960241	−	0.960241i
$408$	−690.584	−	690.584i	−0.0837966	−	0.0837966i
$409$	6312.73			0.763189			0.381594	−	0.924330i	$-0.375375\pi$
$409$	6312.73			0.763189			0.381594	+	0.924330i	$0.375375\pi$
$410$	1434.88	+	1625.77i	0.172839	+	0.195832i
$411$			5829.18i			0.699592i
$412$	1460.71	+	1460.71i	0.174670	+	0.174670i
$413$	−1834.62	−	1761.13i	−0.218585	−	0.209829i
$414$			2180.11i			0.258808i
$415$	2692.01	−	2375.93i	0.318424	−	0.281036i
$416$			5202.89i			0.613203i
$417$	−5963.96	+	5963.96i	−0.700375	+	0.700375i
$418$	11482.6	−	11482.6i	1.34362	−	1.34362i
$419$	−3382.86			−0.394423			−0.197212	−	0.980361i	$-0.563189\pi$
$419$	−3382.86			−0.394423			−0.197212	+	0.980361i	$0.563189\pi$
$420$	−39.6089	+	945.850i	−0.00460171	+	0.109887i
$421$	3674.34			0.425359			0.212680	−	0.977122i	$-0.431781\pi$
$421$	3674.34			0.425359			0.212680	+	0.977122i	$0.431781\pi$
$422$	2668.53	−	2668.53i	0.307825	−	0.307825i
$423$	304.197	−	304.197i	0.0349658	−	0.0349658i
$424$		−	17236.1i		−	1.97420i
$425$	−1030.51	−	1325.54i	−0.117616	−	0.151290i
$426$		−	2953.05i		−	0.335859i
$427$	3258.68	−	3394.67i	0.369318	−	0.384730i
$428$	−683.835	−	683.835i	−0.0772300	−	0.0772300i
$429$			14250.9i			1.60382i
$430$	6500.54	+	405.430i	0.729032	+	0.0454688i
$431$	9193.93			1.02751			0.513754	−	0.857938i	$-0.328254\pi$
$431$	9193.93			1.02751			0.513754	+	0.857938i	$0.328254\pi$
$432$	−944.774	−	944.774i	−0.105221	−	0.105221i
$433$	−1958.19	+	1958.19i	−0.217332	+	0.217332i	−0.807373	−	0.590041i	$-0.799111\pi$
$433$	−1958.19	+	1958.19i	−0.217332	+	0.217332i	0.590041	+	0.807373i	$0.299111\pi$
$434$	34.4006	+	1683.11i	0.00380480	+	0.186156i
$435$	−922.825	−	1045.59i	−0.101715	−	0.115247i
$436$	−769.117			−0.0844817
$437$	6921.92	+	6921.92i	0.757712	+	0.757712i
$438$	−1087.89	−	1087.89i	−0.118679	−	0.118679i
$439$	15635.8			1.69990			0.849951	−	0.526862i	$-0.176631\pi$
$439$	15635.8			1.69990			0.849951	+	0.526862i	$0.176631\pi$
$440$	−11126.1	−	12606.3i	−1.20549	−	1.36587i
$441$	3084.42	−	126.136i	0.333055	−	0.0136201i
$442$	−1850.35	+	1850.35i	−0.199123	+	0.199123i
$443$	8137.55	+	8137.55i	0.872747	+	0.872747i	0.992771	−	0.120024i	$-0.0382973\pi$
$443$	8137.55	+	8137.55i	0.872747	+	0.872747i	−0.120024	+	0.992771i	$0.538297\pi$
$444$	−821.571			−0.0878153
$445$	5431.84	+	338.777i	0.578638	+	0.0360889i
$446$			4533.38i			0.481304i
$447$	5302.40	+	5302.40i	0.561062	+	0.561062i
$448$	−7295.57	+	7600.02i	−0.769382	+	0.801489i
$449$		−	4389.43i		−	0.461359i	−0.973030	−	0.230679i	$-0.925905\pi$
$449$		−	4389.43i		−	0.461359i	0.973030	−	0.230679i	$-0.0740949\pi$
$450$	−1757.15	−	2260.23i	−0.184073	−	0.236774i
$451$		−	4729.07i		−	0.493754i
$452$	1680.13	−	1680.13i	0.174838	−	0.174838i
$453$	−2756.87	+	2756.87i	−0.285936	+	0.285936i
$454$	−70.0765			−0.00724417
$455$	15838.0	+	663.240i	1.63186	+	0.0683366i
$456$	−7477.46			−0.767904
$457$	−10227.5	+	10227.5i	−1.04687	+	1.04687i	−0.0480255	+	0.998846i	$0.515293\pi$
$457$	−10227.5	+	10227.5i	−1.04687	+	1.04687i	−0.998846	+	0.0480255i	$0.984707\pi$
$458$	3047.50	−	3047.50i	0.310917	−	0.310917i
$459$			362.662i			0.0368793i
$460$	1216.00	−	1073.22i	0.123253	−	0.108781i
$461$			2468.69i			0.249411i	0.992194	+	0.124705i	$0.0397986\pi$
$461$			2468.69i			0.249411i	−0.992194	+	0.124705i	$0.960201\pi$
$462$	−6075.62	+	6329.16i	−0.611826	+	0.637358i
$463$	−12605.6	−	12605.6i	−1.26529	−	1.26529i	−0.948492	−	0.316800i	$-0.897392\pi$
$463$	−12605.6	−	12605.6i	−1.26529	−	1.26529i	−0.316800	−	0.948492i	$-0.602608\pi$
$464$		−	2057.54i		−	0.205860i
$465$	792.778	+	898.245i	0.0790628	+	0.0895809i
$466$	8498.26			0.844795
$467$	1399.35	+	1399.35i	0.138660	+	0.138660i	0.773030	−	0.634370i	$-0.218740\pi$
$467$	1399.35	+	1399.35i	0.138660	+	0.138660i	−0.634370	+	0.773030i	$0.718740\pi$
$468$	742.480	−	742.480i	0.0733358	−	0.0733358i
$469$	−13687.3	+	279.751i	−1.34759	+	0.0275431i
$470$	1357.35	+	84.6564i	0.133213	+	0.00830831i
$471$	7888.86			0.771762
$472$	−2353.29	−	2353.29i	−0.229489	−	0.229489i
$473$	−10044.1	−	10044.1i	−0.976381	−	0.976381i
$474$	−1226.76			−0.118875
$475$	−12755.3	−	1597.28i	−1.23211	−	0.154291i
$476$	379.030	−	7.74689i	0.0364975	−	0.000745963i
$477$	−4525.80	+	4525.80i	−0.434428	+	0.434428i
$478$	−10267.7	−	10267.7i	−0.982496	−	0.982496i
$479$	−425.593			−0.0405968			−0.0202984	−	0.999794i	$-0.506462\pi$
$479$	−425.593			−0.0405968			−0.0202984	+	0.999794i	$0.506462\pi$
$480$	−141.895	+	2275.09i	−0.0134929	+	0.216340i
$481$			13757.0i			1.30408i
$482$	−6139.51	−	6139.51i	−0.580180	−	0.580180i
$483$	−3815.32	−	3662.48i	−0.359426	−	0.345028i
$484$			3839.23i			0.360559i
$485$	8050.52	+	9121.52i	0.753722	+	0.853993i
$486$			618.387i			0.0577173i
$487$	−3756.26	+	3756.26i	−0.349512	+	0.349512i	−0.859928	−	0.510416i	$-0.829492\pi$
$487$	−3756.26	+	3756.26i	−0.349512	+	0.349512i	0.510416	+	0.859928i	$0.329492\pi$
$488$	4354.39	−	4354.39i	0.403922	−	0.403922i
$489$	7880.14			0.728737
$490$	6751.27	+	7046.81i	0.622431	+	0.649679i
$491$	−13487.0			−1.23963			−0.619815	−	0.784748i	$-0.712792\pi$
$491$	−13487.0			−1.23963			−0.619815	+	0.784748i	$0.712792\pi$
$492$	−246.388	+	246.388i	−0.0225773	+	0.0225773i
$493$	−394.904	+	394.904i	−0.0360762	+	0.0360762i
$494$			20035.1i			1.82474i
$495$	−388.654	+	6231.56i	−0.0352903	+	0.565834i
$496$			1767.59i			0.160014i
$497$	5168.02	+	4960.99i	0.466433	+	0.447748i
$498$	−1733.67	−	1733.67i	−0.155999	−	0.155999i
$499$		−	1278.25i		−	0.114674i	−0.998355	−	0.0573371i	$-0.981739\pi$
$499$		−	1278.25i		−	0.114674i	0.998355	−	0.0573371i	$-0.0182610\pi$
$500$	−395.676	+	2092.75i	−0.0353903	+	0.187181i
$501$	−502.582			−0.0448178
$502$	1385.50	+	1385.50i	0.123183	+	0.123183i
$503$	−3272.20	+	3272.20i	−0.290060	+	0.290060i	−0.837104	−	0.547044i	$-0.815753\pi$
$503$	−3272.20	+	3272.20i	−0.290060	+	0.290060i	0.547044	+	0.837104i	$0.315753\pi$
$504$	4038.98	−	82.5516i	0.356965	−	0.00729592i
$505$	1144.62	−	18352.5i	0.100861	−	1.61718i
$506$	15030.7			1.32054
$507$	−7772.07	−	7772.07i	−0.680808	−	0.680808i
$508$	2543.54	+	2543.54i	0.222148	+	0.222148i
$509$	−15453.9			−1.34574			−0.672870	−	0.739761i	$-0.734939\pi$
$509$	−15453.9			−1.34574			−0.672870	+	0.739761i	$0.734939\pi$
$510$	−859.578	+	758.651i	−0.0746329	+	0.0658699i
$511$	3731.49	−	76.2669i	0.323036	−	0.00660245i
$512$	−9162.74	+	9162.74i	−0.790898	+	0.790898i
$513$	1963.40	+	1963.40i	0.168979	+	0.168979i
$514$	−14154.9			−1.21468
$515$	11362.4	−	10028.3i	0.972211	−	0.858059i
$516$			1046.61i			0.0892914i
$517$	−2097.27	−	2097.27i	−0.178410	−	0.178410i
$518$	−5865.04	+	6109.80i	−0.497481	+	0.518241i
$519$		−	5358.67i		−	0.453217i
$520$	20704.4	+	1291.31i	1.74605	+	0.108899i
$521$			2591.61i			0.217928i	0.994046	+	0.108964i	$0.0347533\pi$
$521$			2591.61i			0.217928i	−0.994046	+	0.108964i	$0.965247\pi$
$522$	−673.365	+	673.365i	−0.0564605	+	0.0564605i
$523$	−6598.62	+	6598.62i	−0.551697	+	0.551697i	−0.926930	−	0.375233i	$-0.877563\pi$
$523$	−6598.62	+	6598.62i	−0.551697	+	0.551697i	0.375233	+	0.926930i	$0.377563\pi$
$524$	−3390.89			−0.282694
$525$	6907.47	+	721.957i	0.574222	+	0.0600167i
$526$	11363.6			0.941972
$527$	339.253	−	339.253i	0.0280420	−	0.0280420i
$528$	−6513.70	+	6513.70i	−0.536880	+	0.536880i
$529$		−	3106.29i		−	0.255304i
$530$	−20194.5	−	1259.51i	−1.65508	−	0.103225i
$531$			1235.83i			0.100999i
$532$	2010.08	−	2093.96i	0.163812	−	0.170648i
$533$	4125.69	+	4125.69i	0.335278	+	0.335278i
$534$		−	3716.30i		−	0.301161i
$535$	−5319.36	+	4694.79i	−0.429862	+	0.379390i
$536$	−17915.7			−1.44373
$537$	−6899.79	−	6899.79i	−0.554466	−	0.554466i
$538$	6921.30	−	6921.30i	0.554644	−	0.554644i
$539$	−869.640	−	21265.4i	−0.0694954	−	1.69938i
$540$	344.918	−	304.419i	0.0274868	−	0.0242595i
$541$	−13740.0			−1.09192			−0.545960	−	0.837811i	$-0.683835\pi$
$541$	−13740.0			−1.09192			−0.545960	+	0.837811i	$0.683835\pi$
$542$	−903.664	−	903.664i	−0.0716157	−	0.0716157i
$543$	4402.03	+	4402.03i	0.347899	+	0.347899i
$544$	912.859			0.0719458
$545$	−351.230	+	5631.51i	−0.0276056	+	0.442619i
$546$	−221.189	−	10822.1i	−0.0173370	−	0.848244i
$547$	−3772.02	+	3772.02i	−0.294844	+	0.294844i	−0.838990	−	0.544146i	$-0.816854\pi$
$547$	−3772.02	+	3772.02i	−0.294844	+	0.294844i	0.544146	+	0.838990i	$0.316854\pi$
$548$	−2093.88	−	2093.88i	−0.163222	−	0.163222i
$549$	−2286.71			−0.177768
$550$	−15583.0	+	12114.6i	−1.20811	+	0.939216i
$551$			4275.92i			0.330599i
$552$	−4893.96	−	4893.96i	−0.377356	−	0.377356i
$553$	2060.90	−	2146.90i	0.158478	−	0.165091i
$554$		−	9130.83i		−	0.700238i
$555$	−375.184	+	6015.58i	−0.0286949	+	0.460085i
$556$		−	4284.58i		−	0.326810i
$557$	−4109.18	+	4109.18i	−0.312588	+	0.312588i	−0.845911	−	0.533324i	$-0.820943\pi$
$557$	−4109.18	+	4109.18i	−0.312588	+	0.312588i	0.533324	+	0.845911i	$0.320943\pi$
$558$	578.473	−	578.473i	0.0438866	−	0.0438866i
$559$	17525.1			1.32600
$560$	6935.97	+	7542.27i	0.523390	+	0.569141i
$561$	2500.35			0.188173
$562$	9222.43	−	9222.43i	0.692215	−	0.692215i
$563$	6189.75	−	6189.75i	0.463351	−	0.463351i	−0.436401	−	0.899752i	$-0.643747\pi$
$563$	6189.75	−	6189.75i	0.463351	−	0.463351i	0.899752	+	0.436401i	$0.143747\pi$
$564$			218.538i			0.0163158i
$565$	−11534.7	−	13069.2i	−0.858884	−	0.973145i
$566$			23321.5i			1.73194i
$567$	−1082.21	−	1038.86i	−0.0801565	−	0.0769455i
$568$	6629.08	+	6629.08i	0.489701	+	0.489701i
$569$			14461.0i			1.06544i	0.846291	+	0.532721i	$0.178831\pi$
$569$			14461.0i			1.06544i	−0.846291	+	0.532721i	$0.821169\pi$
$570$	−546.404	+	8760.88i	−0.0401515	+	0.643777i
$571$	−20831.5			−1.52674			−0.763370	−	0.645961i	$-0.776457\pi$
$571$	−20831.5			−1.52674			−0.763370	+	0.645961i	$0.776457\pi$
$572$	−5119.00	−	5119.00i	−0.374189	−	0.374189i
$573$	3500.28	−	3500.28i	0.255194	−	0.255194i
$574$	73.4003	+	3591.24i	0.00533741	+	0.261142i
$575$	−7302.88	−	9393.70i	−0.529654	−	0.681295i
$576$	5119.52			0.370335
$577$	8997.29	+	8997.29i	0.649155	+	0.649155i	0.952789	−	0.303634i	$-0.0982000\pi$
$577$	8997.29	+	8997.29i	0.649155	+	0.649155i	−0.303634	+	0.952789i	$0.598200\pi$
$578$	−8516.03	−	8516.03i	−0.612838	−	0.612838i
$579$	7673.08			0.550747
$580$	707.066	+	44.0988i	0.0506195	+	0.00315707i
$581$	5946.50	−	121.539i	0.424617	−	0.00867864i
$582$	5874.29	−	5874.29i	0.418380	−	0.418380i
$583$	31202.9	+	31202.9i	2.21662	+	2.21662i
$584$	4884.25			0.346082
$585$	−5097.41	−	5775.54i	−0.360260	−	0.408187i
$586$		−	15535.3i		−	1.09515i
$587$	−9790.20	−	9790.20i	−0.688390	−	0.688390i	0.273486	−	0.961876i	$-0.411823\pi$
$587$	−9790.20	−	9790.20i	−0.688390	−	0.688390i	−0.961876	+	0.273486i	$0.911823\pi$
$588$	−1062.63	+	1153.25i	−0.0745276	+	0.0808831i
$589$		−	3673.35i		−	0.256974i
$590$	−2929.16	+	2585.24i	−0.204393	+	0.180394i
$591$			3896.43i			0.271197i
$592$	−6287.94	+	6287.94i	−0.436542	+	0.436542i
$593$	3963.46	−	3963.46i	0.274468	−	0.274468i	−0.556428	−	0.830896i	$-0.687828\pi$
$593$	3963.46	−	3963.46i	0.274468	−	0.274468i	0.830896	+	0.556428i	$0.187828\pi$
$594$	4263.44			0.294497
$595$	116.367	−	2778.81i	0.00801779	−	0.191463i
$596$	−3809.30			−0.261804
$597$	6198.33	−	6198.33i	0.424926	−	0.424926i
$598$	−13112.9	+	13112.9i	−0.896699	+	0.896699i
$599$		−	1891.10i		−	0.128995i	−0.997918	−	0.0644977i	$-0.979455\pi$
$599$		−	1891.10i		−	0.128995i	0.997918	−	0.0644977i	$-0.0205445\pi$
$600$	9018.31	+	1129.31i	0.613618	+	0.0768400i
$601$			14830.7i			1.00659i	0.864116	+	0.503293i	$0.167878\pi$
$601$			14830.7i			1.00659i	−0.864116	+	0.503293i	$0.832122\pi$
$602$	7783.34	+	7471.55i	0.526952	+	0.505843i
$603$	4704.23	+	4704.23i	0.317697	+	0.317697i
$604$		−	1980.56i		−	0.133424i
$605$	28111.1	+	1753.25i	1.88905	+	0.117818i
$606$	−12556.2			−0.841684
$607$	7057.17	+	7057.17i	0.471897	+	0.471897i	0.902528	−	0.430631i	$-0.141709\pi$
$607$	7057.17	+	7057.17i	0.471897	+	0.471897i	−0.430631	+	0.902528i	$0.641709\pi$
$608$	4942.10	−	4942.10i	0.329652	−	0.329652i
$609$	−47.2064	−	2309.65i	−0.00314105	−	0.153681i
$610$	−4783.57	−	5419.95i	−0.317510	−	0.359750i
$611$	3659.36			0.242294
$612$	−130.270	−	130.270i	−0.00860434	−	0.00860434i
$613$	−17261.2	−	17261.2i	−1.13731	−	1.13731i	−0.988930	−	0.148384i	$-0.952593\pi$
$613$	−17261.2	−	17261.2i	−1.13731	−	1.13731i	−0.148384	−	0.988930i	$-0.547407\pi$
$614$	−306.955			−0.0201754
$615$	1691.55	+	1916.58i	0.110910	+	0.125665i
$616$	−569.149	−	27846.6i	−0.0372267	−	1.82138i
$617$	−16901.0	+	16901.0i	−1.10277	+	1.10277i	−0.108697	+	0.994075i	$0.534668\pi$
$617$	−16901.0	+	16901.0i	−1.10277	+	1.10277i	−0.994075	+	0.108697i	$0.965332\pi$
$618$	−7317.44	−	7317.44i	−0.476296	−	0.476296i
$619$	−1285.90			−0.0834968			−0.0417484	−	0.999128i	$-0.513293\pi$
$619$	−1285.90			−0.0834968			−0.0417484	+	0.999128i	$0.513293\pi$
$620$	−607.425	−	37.8843i	−0.0393464	−	0.00245398i
$621$			2570.07i			0.166076i
$622$	−8096.40	−	8096.40i	−0.521923	−	0.521923i
$623$	6503.75	+	6243.21i	0.418246	+	0.401491i
$624$		−	11365.2i		−	0.729124i
$625$	15142.5	+	3852.85i	0.969122	+	0.246582i
$626$		−	23603.2i		−	1.50698i
$627$	13536.6	−	13536.6i	0.862199	−	0.862199i
$628$	−2833.72	+	2833.72i	−0.180060	+	0.180060i
$629$	2413.69			0.153005
$630$	198.422	−	4738.25i	0.0125481	−	0.299645i
$631$	−4516.31			−0.284931			−0.142465	−	0.989800i	$-0.545503\pi$
$631$	−4516.31			−0.284931			−0.142465	+	0.989800i	$0.545503\pi$
$632$	2753.85	−	2753.85i	0.173327	−	0.173327i
$633$	3145.86	−	3145.86i	0.197530	−	0.197530i
$634$		−	2087.07i		−	0.130738i
$635$	19785.5	−	17462.4i	1.23648	−	1.09130i
$636$		−	3251.38i		−	0.202713i
$637$	19310.8	+	17793.5i	1.20114	+	1.10676i
$638$	4642.48	+	4642.48i	0.288084	+	0.288084i
$639$		−	3481.27i		−	0.215520i
$640$	6687.11	+	7576.72i	0.413017	+	0.467963i
$641$	5084.85			0.313322			0.156661	−	0.987652i	$-0.449927\pi$
$641$	5084.85			0.313322			0.156661	+	0.987652i	$0.449927\pi$
$642$	3425.68	+	3425.68i	0.210593	+	0.210593i
$643$	19380.8	−	19380.8i	1.18865	−	1.18865i	0.211211	−	0.977441i	$-0.432259\pi$
$643$	19380.8	−	19380.8i	1.18865	−	1.18865i	0.977441	−	0.211211i	$-0.0677406\pi$
$644$	2686.07	−	54.8998i	0.164357	−	0.00335925i
$645$	7663.31	+	477.951i	0.467818	+	0.0291772i
$646$	3515.22			0.214093
$647$	14961.1	+	14961.1i	0.909093	+	0.909093i	0.996199	−	0.0871059i	$-0.0277618\pi$
$647$	14961.1	+	14961.1i	0.909093	+	0.909093i	−0.0871059	+	0.996199i	$0.527762\pi$
$648$	−1388.17	−	1388.17i	−0.0841550	−	0.0841550i
$649$	8520.40			0.515339
$650$	3025.89	−	24163.7i	0.182592	−	1.45812i
$651$	40.5540	+	1984.17i	0.00244153	+	0.119456i
$652$	−2830.59	+	2830.59i	−0.170022	+	0.170022i
$653$	−5764.15	−	5764.15i	−0.345434	−	0.345434i	0.512971	−	0.858406i	$-0.328545\pi$
$653$	−5764.15	−	5764.15i	−0.345434	−	0.345434i	−0.858406	+	0.512971i	$0.828545\pi$
$654$	3852.91			0.230368
$655$	−1548.50	+	24828.2i	−0.0923741	+	1.48110i
$656$			3771.49i			0.224469i
$657$	−1282.49	−	1282.49i	−0.0761562	−	0.0761562i
$658$	1625.21	+	1560.11i	0.0962877	+	0.0924305i
$659$		−	3931.08i		−	0.232372i	−0.993227	−	0.116186i	$-0.962933\pi$
$659$		−	3931.08i		−	0.232372i	0.993227	−	0.116186i	$-0.0370669\pi$
$660$	−2098.81	−	2378.02i	−0.123782	−	0.140249i
$661$		−	26964.4i		−	1.58668i	−0.608781	−	0.793339i	$-0.708341\pi$
$661$		−	26964.4i		−	1.58668i	0.608781	−	0.793339i	$-0.291659\pi$
$662$	676.482	−	676.482i	0.0397163	−	0.0397163i
$663$	−2181.33	+	2181.33i	−0.127777	+	0.127777i
$664$	7783.55			0.454910
$665$	−14414.1	−	15674.1i	−0.840535	−	0.914010i
$666$	4115.67			0.239458
$667$	−2798.56	+	2798.56i	−0.162460	+	0.162460i
$668$	180.530	−	180.530i	0.0104565	−	0.0104565i
$669$			5344.28i			0.308852i
$670$	−1309.16	+	20990.7i	−0.0754886	+	1.21036i
$671$			15765.6i			0.907043i
$672$	−2614.93	+	2724.05i	−0.150109	+	0.156373i
$673$	−4845.68	−	4845.68i	−0.277544	−	0.277544i	0.554584	−	0.832128i	$-0.312878\pi$
$673$	−4845.68	−	4845.68i	−0.277544	−	0.277544i	−0.832128	+	0.554584i	$0.812878\pi$
$674$		−	4042.31i		−	0.231015i
$675$	−2071.46	−	2664.52i	−0.118119	−	0.151937i
$676$	5583.54			0.317680
$677$	6985.78	+	6985.78i	0.396581	+	0.396581i	0.877025	−	0.480444i	$-0.159525\pi$
$677$	6985.78	+	6985.78i	0.396581	+	0.396581i	−0.480444	+	0.877025i	$0.659525\pi$
$678$	−8416.63	+	8416.63i	−0.476753	+	0.476753i
$679$	411.818	+	20148.9i	0.0232756	+	1.13880i
$680$	226.563	−	3632.64i	0.0127769	−	0.204861i
$681$	−82.6113			−0.00464857
$682$	−3988.26	−	3988.26i	−0.223927	−	0.223927i
$683$	−1819.76	−	1819.76i	−0.101949	−	0.101949i	0.654293	−	0.756241i	$-0.272966\pi$
$683$	−1819.76	−	1819.76i	−0.101949	−	0.101949i	−0.756241	+	0.654293i	$0.772966\pi$
$684$	−1410.53			−0.0788493
$685$	−16287.7	+	14375.3i	−0.908496	+	0.801825i
$686$	990.463	+	16135.4i	0.0551254	+	0.898033i
$687$	3592.61	−	3592.61i	0.199515	−	0.199515i
$688$	8010.28	+	8010.28i	0.443879	+	0.443879i
$689$	−54443.4			−3.01035
$690$	−6091.56	+	5376.33i	−0.336090	+	0.296628i
$691$		−	17700.6i		−	0.974477i	−0.873269	−	0.487238i	$-0.838004\pi$
$691$		−	17700.6i		−	0.974477i	0.873269	−	0.487238i	$-0.161996\pi$
$692$	1924.86	+	1924.86i	0.105740	+	0.105740i
$693$	−7162.39	+	7461.28i	−0.392607	+	0.408991i
$694$			18057.2i			0.987666i
$695$	−31371.9	−	1956.62i	−1.71224	−	0.106790i
$696$		−	3023.17i		−	0.164645i
$697$	723.863	−	723.863i	0.0393375	−	0.0393375i
$698$	2056.99	−	2056.99i	0.111544	−	0.111544i
$699$	10018.4			0.542103
$700$	−2740.53	+	2221.87i	−0.147975	+	0.119970i
$701$	−3805.23			−0.205024			−0.102512	−	0.994732i	$-0.532688\pi$
$701$	−3805.23			−0.205024			−0.102512	+	0.994732i	$0.532688\pi$
$702$	−3719.47	+	3719.47i	−0.199975	+	0.199975i
$703$	13067.4	−	13067.4i	0.701062	−	0.701062i
$704$		−	35296.3i		−	1.88960i
$705$	1600.15	+	99.7992i	0.0854824	+	0.00533142i
$706$			22901.9i			1.22086i
$707$	21093.9	−	21974.1i	1.12209	−	1.16891i
$708$	−443.918	−	443.918i	−0.0235642	−	0.0235642i
$709$		−	2373.32i		−	0.125715i	−0.998023	−	0.0628576i	$-0.979979\pi$
$709$		−	2373.32i		−	0.125715i	0.998023	−	0.0628576i	$-0.0200214\pi$
$710$	8251.29	−	7282.47i	0.436148	−	0.384938i
$711$	−1446.19			−0.0762819
$712$	8342.43	+	8342.43i	0.439109	+	0.439109i
$713$	2404.18	−	2404.18i	0.126280	−	0.126280i
$714$	−1898.76	+	38.8082i	−0.0995227	+	0.00203412i
$715$	−39819.2	+	35143.9i	−2.08273	+	1.83819i
$716$	4956.89			0.258726
$717$	−12104.3	−	12104.3i	−0.630465	−	0.630465i
$718$	8134.13	+	8134.13i	0.422790	+	0.422790i
$719$	9413.24			0.488254			0.244127	−	0.969743i	$-0.421499\pi$
$719$	9413.24			0.488254			0.244127	+	0.969743i	$0.421499\pi$
$720$	309.956	−	4969.74i	0.0160436	−	0.257238i
$721$	25098.9	−	512.991i	1.29644	−	0.0264976i
$722$	6688.51	−	6688.51i	0.344765	−	0.344765i
$723$	−7237.70	−	7237.70i	−0.372300	−	0.372300i
$724$	−3162.47			−0.162337
$725$	645.787	−	5157.04i	0.0330813	−	0.264176i
$726$		−	19232.7i		−	0.983186i
$727$	−15012.1	−	15012.1i	−0.765841	−	0.765841i	0.211531	−	0.977371i	$-0.432155\pi$
$727$	−15012.1	−	15012.1i	−0.765841	−	0.765841i	−0.977371	+	0.211531i	$0.932155\pi$
$728$	24790.1	+	23797.1i	1.26207	+	1.21151i
$729$			729.000i			0.0370370i
$730$	356.910	−	5722.58i	0.0180956	−	0.290140i
$731$		−	3074.83i		−	0.155577i
$732$	821.400	−	821.400i	0.0414752	−	0.0414752i
$733$	−22789.8	+	22789.8i	−1.14838	+	1.14838i	−0.161507	+	0.986872i	$0.551635\pi$
$733$	−22789.8	+	22789.8i	−1.14838	+	1.14838i	−0.986872	+	0.161507i	$0.948365\pi$
$734$	−10808.4			−0.543524
$735$	7958.89	+	8307.30i	0.399412	+	0.416897i
$736$	6469.15			0.323989
$737$	32433.1	−	32433.1i	1.62102	−	1.62102i
$738$	1234.28	−	1234.28i	0.0615645	−	0.0615645i
$739$		−	11456.8i		−	0.570290i	−0.958484	−	0.285145i	$-0.907958\pi$
$739$		−	11456.8i		−	0.570290i	0.958484	−	0.285145i	$-0.0920418\pi$
$740$	−2026.06	−	2295.60i	−0.100648	−	0.114038i
$741$			23618.9i			1.17093i
$742$	−24179.6	−	23211.0i	−1.19631	−	1.14839i
$743$	7937.13	+	7937.13i	0.391904	+	0.391904i	0.875366	−	0.483461i	$-0.160621\pi$
$743$	7937.13	+	7937.13i	0.391904	+	0.391904i	−0.483461	+	0.875366i	$0.660621\pi$
$744$			2597.14i			0.127978i
$745$	−1739.58	+	27891.9i	−0.0855481	+	1.37165i
$746$	−20045.6			−0.983811
$747$	−2043.77	−	2043.77i	−0.100104	−	0.100104i
$748$	−898.141	+	898.141i	−0.0439028	+	0.0439028i
$749$	−11750.2	+	240.158i	−0.573219	+	0.0117159i
$750$	1982.15	−	10483.7i	0.0965037	−	0.510413i
$751$	−27597.4			−1.34094			−0.670468	−	0.741939i	$-0.733907\pi$
$751$	−27597.4			−1.34094			−0.670468	+	0.741939i	$0.733907\pi$
$752$	1672.60	+	1672.60i	0.0811081	+	0.0811081i
$753$	1633.33	+	1633.33i	0.0790461	+	0.0790461i
$754$	−8100.30			−0.391241
$755$	−14501.8	−	904.458i	−0.699039	−	0.0435981i
$756$	761.903	−	15.5723i	0.0366536	−	0.000749154i
$757$	26068.8	−	26068.8i	1.25163	−	1.25163i	0.296645	−	0.954988i	$-0.404132\pi$
$757$	26068.8	−	26068.8i	1.25163	−	1.25163i	0.954988	−	0.296645i	$-0.0958680\pi$
$758$	15749.1	+	15749.1i	0.754660	+	0.754660i
$759$	17719.2			0.847388
$760$	−18440.0	−	20893.2i	−0.880119	−	0.997206i
$761$			23360.7i			1.11278i	0.830922	+	0.556388i	$0.187813\pi$
$761$			23360.7i			1.11278i	−0.830922	+	0.556388i	$0.812187\pi$
$762$	−12741.9	−	12741.9i	−0.605761	−	0.605761i
$763$	−6472.71	+	6742.82i	−0.307114	+	0.319930i
$764$			2514.64i			0.119079i
$765$	−1013.33	+	894.354i	−0.0478917	+	0.0422685i
$766$			1720.09i			0.0811349i
$767$	−7433.28	+	7433.28i	−0.349935	+	0.349935i
$768$	−4774.02	+	4774.02i	−0.224307	+	0.224307i
$769$	6822.54			0.319931			0.159966	−	0.987123i	$-0.448862\pi$
$769$	6822.54			0.319931			0.159966	+	0.987123i	$0.448862\pi$
$770$	−32667.7	−	1368.01i	−1.52891	−	0.0640255i
$771$	−16686.8			−0.779456
$772$	−2756.21	+	2756.21i	−0.128495	+	0.128495i
$773$	−23358.4	+	23358.4i	−1.08686	+	1.08686i	−0.0910115	+	0.995850i	$0.529010\pi$
$773$	−23358.4	+	23358.4i	−1.08686	+	1.08686i	−0.995850	+	0.0910115i	$0.970990\pi$
$774$		−	5243.00i		−	0.243483i
$775$	−554.782	+	4430.30i	−0.0257140	+	0.205343i
$776$			26373.5i			1.22004i
$777$	−6914.15	+	7202.68i	−0.319232	+	0.332554i
$778$	15435.0	+	15435.0i	0.711274	+	0.711274i
$779$		−	7837.79i		−	0.360485i
$780$	3905.63	+	243.589i	0.179287	+	0.0111819i
$781$	−24001.5			−1.09967
$782$	2300.69	+	2300.69i	0.105208	+	0.105208i
$783$	−793.812	+	793.812i	−0.0362306	+	0.0362306i
$784$	693.547	+	16959.4i	0.0315938	+	0.772567i
$785$	19454.6	+	22042.7i	0.884541	+	1.00222i
$786$	16986.7			0.770860
$787$	−2995.86	−	2995.86i	−0.135694	−	0.135694i	0.635997	−	0.771691i	$-0.280589\pi$
$787$	−2995.86	−	2995.86i	−0.135694	−	0.135694i	−0.771691	+	0.635997i	$0.780589\pi$
$788$	−1399.62	−	1399.62i	−0.0632732	−	0.0632732i
$789$	13396.3			0.604461
$790$	−3025.29	−	3427.75i	−0.136247	−	0.154372i
$791$	−590.050	−	28869.2i	−0.0265231	−	1.29769i
$792$	−9570.67	+	9570.67i	−0.429393	+	0.429393i
$793$	−13754.1	−	13754.1i	−0.615917	−	0.615917i
$794$	−22943.9			−1.02550
$795$	−23806.8	−	1484.80i	−1.06206	−	0.0662395i
$796$			4452.95i			0.198280i
$797$	17451.4	+	17451.4i	0.775610	+	0.775610i	0.979081	−	0.203471i	$-0.0652221\pi$
$797$	17451.4	+	17451.4i	0.775610	+	0.775610i	−0.203471	+	0.979081i	$0.565222\pi$
$798$	−10069.5	+	10489.7i	−0.446688	+	0.465328i
$799$		−	642.044i		−	0.0284279i
$800$	−6706.90	+	5214.10i	−0.296406	+	0.230433i
$801$		−	4381.05i		−	0.193254i
$802$	−13663.7	+	13663.7i	−0.601598	+	0.601598i
$803$	−8842.05	+	8842.05i	−0.388579	+	0.388579i
$804$	−3379.57			−0.148244
$805$	824.658	−	19692.6i	0.0361061	−	0.862202i
$806$	6958.79			0.304110
$807$	8159.34	−	8159.34i	0.355914	−	0.355914i
$808$	28186.5	−	28186.5i	1.22722	−	1.22722i
$809$			29624.4i			1.28744i	0.765261	+	0.643721i	$0.222610\pi$
$809$			29624.4i			1.28744i	−0.765261	+	0.643721i	$0.777390\pi$
$810$	−1727.87	+	1524.99i	−0.0749521	+	0.0661516i
$811$		−	29120.7i		−	1.26087i	−0.776241	−	0.630436i	$-0.782876\pi$
$811$		−	29120.7i		−	1.26087i	0.776241	−	0.630436i	$-0.217124\pi$
$812$	846.597	+	812.683i	0.0365883	+	0.0351226i
$813$	−1065.31	−	1065.31i	−0.0459556	−	0.0459556i
$814$		−	28375.3i		−	1.22181i
$815$	19433.1	+	22018.4i	0.835229	+	0.946343i
$816$	−1994.06			−0.0855466
$817$	−16646.7	−	16646.7i	−0.712846	−	0.712846i
$818$	11359.4	−	11359.4i	0.485541	−	0.485541i
$819$	−260.754	−	12757.8i	−0.0111251	−	0.544316i
$820$	−1296.06	−	80.8335i	−0.0551955	−	0.00344247i
$821$	14162.2			0.602027			0.301014	−	0.953620i	$-0.402675\pi$
$821$	14162.2			0.602027			0.301014	+	0.953620i	$0.402675\pi$
$822$	10489.3	+	10489.3i	0.445081	+	0.445081i
$823$	10535.8	+	10535.8i	0.446238	+	0.446238i	0.894102	−	0.447864i	$-0.147815\pi$
$823$	10535.8	+	10535.8i	0.446238	+	0.446238i	−0.447864	+	0.894102i	$0.647815\pi$
$824$	32852.7			1.38893
$825$	−18370.4	+	14281.6i	−0.775244	+	0.602692i
$826$	−6470.35	+	132.246i	−0.272557	+	0.00557073i
$827$	6845.35	−	6845.35i	0.287831	−	0.287831i	−0.548391	−	0.836222i	$-0.684759\pi$
$827$	6845.35	−	6845.35i	0.287831	−	0.287831i	0.836222	+	0.548391i	$0.184759\pi$
$828$	−923.184	−	923.184i	−0.0387474	−	0.0387474i
$829$	−17028.9			−0.713435			−0.356718	−	0.934212i	$-0.616104\pi$
$829$	−17028.9			−0.713435			−0.356718	+	0.934212i	$0.616104\pi$
$830$	568.771	−	9119.50i	0.0237860	−	0.381377i
$831$		−	10764.1i		−	0.449341i
$832$	30792.8	+	30792.8i	1.28311	+	1.28311i
$833$	3121.91	−	3388.14i	0.129853	−	0.140927i
$834$			21463.7i			0.891159i
$835$	−1239.41	−	1404.29i	−0.0513671	−	0.0582007i
$836$			9724.83i			0.402321i
$837$	681.946	−	681.946i	0.0281619	−	0.0281619i
$838$	−6087.27	+	6087.27i	−0.250932	+	0.250932i
$839$	4215.81			0.173475			0.0867377	−	0.996231i	$-0.472356\pi$
$839$	4215.81			0.173475			0.0867377	+	0.996231i	$0.472356\pi$
$840$	10191.1	+	11082.0i	0.418604	+	0.455195i
$841$	22660.2			0.929117
$842$	6611.78	−	6611.78i	0.270614	−	0.270614i
$843$	10872.1	−	10872.1i	0.444192	−	0.444192i
$844$			2260.02i			0.0921719i
$845$	2549.82	−	40883.0i	0.103806	−	1.66440i
$846$		−	1094.77i		−	0.0444906i
$847$	33658.4	+	32310.1i	1.36543	+	1.31073i
$848$	−24884.7	−	24884.7i	−1.00772	−	1.00772i
$849$			27493.1i			1.11138i
$850$	−4239.58	−	530.900i	−0.171078	−	0.0214232i
$851$	17105.1			0.689019
$852$	1250.49	+	1250.49i	0.0502831	+	0.0502831i
$853$	12012.2	−	12012.2i	0.482170	−	0.482170i	−0.423654	−	0.905824i	$-0.639253\pi$
$853$	12012.2	−	12012.2i	0.482170	−	0.482170i	0.905824	+	0.423654i	$0.139253\pi$
$854$	−244.700	−	11972.4i	−0.00980499	−	0.479726i
$855$	−644.142	+	10328.0i	−0.0257651	+	0.413110i
$856$	−15380.1			−0.614114
$857$	−28726.8	−	28726.8i	−1.14503	−	1.14503i	−0.987517	−	0.157513i	$-0.949652\pi$
$857$	−28726.8	−	28726.8i	−1.14503	−	1.14503i	−0.157513	−	0.987517i	$-0.550348\pi$
$858$	25643.7	+	25643.7i	1.02035	+	1.02035i
$859$	−33888.5			−1.34606			−0.673028	−	0.739617i	$-0.735006\pi$
$859$	−33888.5			−1.34606			−0.673028	+	0.739617i	$0.735006\pi$
$860$	−2924.39	+	2581.02i	−0.115954	+	0.102340i
$861$	86.5297	+	4233.61i	0.00342500	+	0.167574i
$862$	16544.0	−	16544.0i	0.653701	−	0.653701i
$863$	−15974.0	−	15974.0i	−0.630083	−	0.630083i	0.318005	−	0.948089i	$-0.396987\pi$
$863$	−15974.0	−	15974.0i	−0.630083	−	0.630083i	−0.948089	+	0.318005i	$0.896987\pi$
$864$	1834.97			0.0722536
$865$	14973.0	−	13214.9i	0.588550	−	0.519446i
$866$			7047.32i			0.276533i
$867$	−10039.3	−	10039.3i	−0.393257	−	0.393257i
$868$	−727.293	−	698.158i	−0.0284400	−	0.0273007i
$869$			9970.70i			0.389221i
$870$	−3542.06	−	220.914i	−0.138031	−	0.00860883i
$871$			56589.9i			2.20147i
$872$	−8649.09	+	8649.09i	−0.335889	+	0.335889i
$873$	6925.04	−	6925.04i	0.268473	−	0.268473i
$874$	24911.3			0.964114
$875$	15017.1	+	21081.0i	0.580197	+	0.814476i
$876$	921.354			0.0355361
$877$	−11718.2	+	11718.2i	−0.451190	+	0.451190i	−0.895750	−	0.444559i	$-0.853360\pi$
$877$	−11718.2	+	11718.2i	−0.451190	+	0.451190i	0.444559	+	0.895750i	$0.353360\pi$
$878$	28135.8	−	28135.8i	1.08148	−	1.08148i
$879$		−	18314.1i		−	0.702752i
$880$	−34263.7	−	2136.98i	−1.31253	−	0.0818608i
$881$		−	23746.3i		−	0.908097i	−0.890977	−	0.454049i	$-0.849979\pi$
$881$		−	23746.3i		−	0.908097i	0.890977	−	0.454049i	$-0.150021\pi$
$882$	5323.28	−	5777.23i	0.203225	−	0.220555i
$883$	8322.79	+	8322.79i	0.317196	+	0.317196i	0.847689	−	0.530493i	$-0.177993\pi$
$883$	8322.79	+	8322.79i	0.317196	+	0.317196i	−0.530493	+	0.847689i	$0.677993\pi$
$884$		−	1567.09i		−	0.0596234i
$885$	−3453.11	+	3047.67i	−0.131158	+	0.115758i
$886$	29286.2			1.11048
$887$	2736.05	+	2736.05i	0.103571	+	0.103571i	0.756993	−	0.653422i	$-0.226667\pi$
$887$	2736.05	+	2736.05i	0.103571	+	0.103571i	−0.653422	+	0.756993i	$0.726667\pi$
$888$	−9238.96	+	9238.96i	−0.349143	+	0.349143i
$889$	43704.9	−	893.273i	1.64884	−	0.0337001i
$890$	10383.9	−	9164.70i	0.391090	−	0.345170i
$891$	5026.06			0.188978
$892$	−1919.69	−	1919.69i	−0.0720584	−	0.0720584i
$893$	−3475.94	−	3475.94i	−0.130255	−	0.130255i
$894$	19082.8			0.713896
$895$	2263.65	−	36294.6i	0.0845422	−	1.35552i
$896$	342.074	+	16736.5i	0.0127543	+	0.624027i
$897$	−15458.4	+	15458.4i	−0.575409	+	0.575409i
$898$	−7898.55	−	7898.55i	−0.293517	−	0.293517i
$899$	1485.15			0.0550974
$900$	1701.19	+	213.031i	0.0630071	+	0.00789003i
$901$			9552.24i			0.353198i
$902$	−8509.71	−	8509.71i	−0.314127	−	0.314127i
$903$	9175.57	+	8808.01i	0.338144	+	0.324598i
$904$		−	37787.7i		−	1.39027i
$905$	−1444.19	+	23155.8i	−0.0530460	+	0.850523i
$906$			9921.67i			0.363825i
$907$	37071.6	−	37071.6i	1.35716	−	1.35716i	0.479757	−	0.877402i	$-0.340725\pi$
$907$	37071.6	−	37071.6i	1.35716	−	1.35716i	0.877402	−	0.479757i	$-0.159275\pi$
$908$	29.6745	−	29.6745i	0.00108456	−	0.00108456i
$909$	−14802.2			−0.540107
$910$	29693.1	−	27306.1i	1.08167	−	0.994714i
$911$	−14037.3			−0.510514			−0.255257	−	0.966873i	$-0.582160\pi$
$911$	−14037.3			−0.510514			−0.255257	+	0.966873i	$0.582160\pi$
$912$	−10795.6	+	10795.6i	−0.391971	+	0.391971i
$913$	−14090.7	+	14090.7i	−0.510771	+	0.510771i
$914$			36807.5i			1.33204i
$915$	−5639.23	−	6389.44i	−0.203745	−	0.230851i
$916$			2580.97i			0.0930979i
$917$	−28536.9	+	29727.7i	−1.02767	+	1.07055i
$918$	652.590	+	652.590i	0.0234626	+	0.0234626i
$919$		−	39118.1i		−	1.40412i	−0.712117	−	0.702061i	$-0.752263\pi$
$919$		−	39118.1i		−	1.40412i	0.712117	−	0.702061i	$-0.247737\pi$
$920$	1605.58	−	25743.4i	0.0575375	−	0.922537i
$921$	−361.861			−0.0129465
$922$	4442.28	+	4442.28i	0.158675	+	0.158675i
$923$	20939.1	−	20939.1i	0.746717	−	0.746717i
$924$	−107.363	−	5252.90i	−0.00382248	−	0.187021i
$925$	−17733.7	+	13786.6i	−0.630358	+	0.490055i
$926$	−45366.1			−1.60996
$927$	−8626.34	−	8626.34i	−0.305638	−	0.305638i
$928$	1998.11	+	1998.11i	0.0706803	+	0.0706803i
$929$	15594.9			0.550754			0.275377	−	0.961336i	$-0.411197\pi$
$929$	15594.9			0.550754			0.275377	+	0.961336i	$0.411197\pi$
$930$	3042.91	+	189.782i	0.107291	+	0.00669162i
$931$	−1441.31	−	35244.5i	−0.0507379	−	1.24070i
$932$	−3598.66	+	3598.66i	−0.126478	+	0.126478i
$933$	−9544.63	−	9544.63i	−0.334916	−	0.334916i
$934$	5036.12			0.176431
$935$	6166.08	+	6986.38i	0.215671	+	0.244363i
$936$		−	16699.1i		−	0.583149i
$937$	−28365.5	−	28365.5i	−0.988964	−	0.988964i	0.0109762	−	0.999940i	$-0.496506\pi$
$937$	−28365.5	−	28365.5i	−0.988964	−	0.988964i	−0.999940	+	0.0109762i	$0.996506\pi$
$938$	−24126.2	+	25132.9i	−0.839815	+	0.874861i
$939$		−	27825.1i		−	0.967028i
$940$	−610.631	+	538.934i	−0.0211878	+	0.0187001i
$941$			1224.05i			0.0424049i	0.999775	+	0.0212024i	$0.00674945\pi$
$941$			1224.05i			0.0424049i	−0.999775	+	0.0212024i	$0.993251\pi$
$942$	14195.6	−	14195.6i	0.490995	−	0.490995i
$943$	5129.79	−	5129.79i	0.177146	−	0.177146i
$944$	−6795.11			−0.234282
$945$	233.914	−	5585.80i	0.00805209	−	0.192282i
$946$	−36147.6			−1.24235
$947$	−29004.0	+	29004.0i	−0.995252	+	0.995252i	−0.999989	−	0.00473644i	$-0.998492\pi$
$947$	−29004.0	+	29004.0i	−0.995252	+	0.995252i	0.00473644	+	0.999989i	$0.498492\pi$
$948$	519.480	−	519.480i	0.0177974	−	0.0177974i
$949$		−	15427.8i		−	0.527721i
$950$	−25826.8	+	20078.3i	−0.882032	+	0.685712i
$951$		−	2460.39i		−	0.0838945i
$952$	4175.26	−	4349.49i	0.142144	−	0.148075i
$953$	−9741.18	−	9741.18i	−0.331110	−	0.331110i	0.521898	−	0.853008i	$-0.325224\pi$
$953$	−9741.18	−	9741.18i	−0.331110	−	0.331110i	−0.853008	+	0.521898i	$0.825224\pi$
$954$			16287.9i			0.552766i
$955$	18412.3	+	1148.35i	0.623883	+	0.0389107i
$956$	8695.87			0.294189
$957$	5472.90	+	5472.90i	0.184863	+	0.184863i
$958$	−765.832	+	765.832i	−0.0258277	+	0.0258277i
$959$	−35978.5	+	735.355i	−1.21148	+	0.0247611i
$960$	12625.2	+	14304.7i	0.424453	+	0.480920i
$961$	28515.1			0.957173
$962$	24754.9	+	24754.9i	0.829657	+	0.829657i
$963$	4038.45	+	4038.45i	0.135137	+	0.135137i
$964$	5199.65			0.173723
$965$	18922.5	+	21439.8i	0.631229	+	0.715204i
$966$	−13455.9	+	275.022i	−0.448175	+	0.00916013i
$967$	8939.68	−	8939.68i	0.297291	−	0.297291i	−0.542661	−	0.839952i	$-0.682583\pi$
$967$	8939.68	−	8939.68i	0.297291	−	0.297291i	0.839952	+	0.542661i	$0.182583\pi$
$968$	43174.0	+	43174.0i	1.43354	+	1.43354i
$969$	4144.00			0.137383
$970$	30900.2	+	1927.20i	1.02283	+	0.0637925i
$971$		−	39194.8i		−	1.29539i	−0.761901	−	0.647693i	$-0.775734\pi$
$971$		−	39194.8i		−	1.29539i	0.761901	−	0.647693i	$-0.224266\pi$
$972$	−261.861	−	261.861i	−0.00864114	−	0.00864114i
$973$	−37562.7	−	36058.0i	−1.23762	−	1.18804i
$974$			13518.4i			0.444719i
$975$	3567.14	−	28485.9i	0.117169	−	0.935672i
$976$		−	12573.3i		−	0.412357i
$977$	2989.55	−	2989.55i	0.0978959	−	0.0978959i	−0.656463	−	0.754359i	$-0.727948\pi$
$977$	2989.55	−	2989.55i	0.0978959	−	0.0978959i	0.754359	+	0.656463i	$0.227948\pi$
$978$	14179.9	−	14179.9i	0.463623	−	0.463623i
$979$	−30204.9			−0.986061
$980$	−5842.91	−	125.152i	−0.190454	−	0.00407942i
$981$	4542.09			0.147826
$982$	−24269.1	+	24269.1i	−0.788654	+	0.788654i
$983$	1887.35	−	1887.35i	0.0612383	−	0.0612383i	−0.675824	−	0.737063i	$-0.736212\pi$
$983$	1887.35	−	1887.35i	0.0612383	−	0.0612383i	0.737063	+	0.675824i	$0.236212\pi$
$984$			5541.50i			0.179529i
$985$	−10887.2	+	9608.91i	−0.352179	+	0.310828i
$986$			1421.22i			0.0459035i
$987$	1915.92	+	1839.17i	0.0617875	+	0.0593124i
$988$	−8484.04	−	8484.04i	−0.273192	−	0.273192i
$989$		−	21790.4i		−	0.700600i
$990$	10514.0	+	11912.7i	0.337532	+	0.382436i
$991$	35981.4			1.15337			0.576683	−	0.816968i	$-0.304347\pi$
$991$	35981.4			1.15337			0.576683	+	0.816968i	$0.304347\pi$
$992$	−1716.54	−	1716.54i	−0.0549396	−	0.0549396i
$993$	797.486	−	797.486i	0.0254859	−	0.0254859i
$994$	18226.6	−	372.529i	0.581603	−	0.0118872i
$995$	32604.7	+	2033.51i	1.03883	+	0.0647906i
$996$	1468.27			0.0467107
$997$	−20290.3	−	20290.3i	−0.644532	−	0.644532i	0.307134	−	0.951666i	$-0.400630\pi$
$997$	−20290.3	−	20290.3i	−0.644532	−	0.644532i	−0.951666	+	0.307134i	$0.900630\pi$
$998$	−2300.15	−	2300.15i	−0.0729558	−	0.0729558i
$999$	4851.86			0.153660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.m.a.13.18	yes	48
5.2	odd	4	inner	105.4.m.a.97.17	yes	48
7.6	odd	2	inner	105.4.m.a.13.17	✓	48
35.27	even	4	inner	105.4.m.a.97.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.m.a.13.17	✓	48	7.6	odd	2	inner
105.4.m.a.13.18	yes	48	1.1	even	1	trivial
105.4.m.a.97.17	yes	48	5.2	odd	4	inner
105.4.m.a.97.18	yes	48	35.27	even	4	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79945 - 1.79945i) q^{2} +(2.12132 - 2.12132i) q^{3} +1.52398i q^{4} +(11.1587 + 0.695951i) q^{5} -7.63441i q^{6} +(13.3607 + 12.8255i) q^{7} +(17.1379 + 17.1379i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(1.79945 - 1.79945i) q^{2} +(2.12132 - 2.12132i) q^{3} +1.52398i q^{4} +(11.1587 + 0.695951i) q^{5} -7.63441i q^{6} +(13.3607 + 12.8255i) q^{7} +(17.1379 + 17.1379i) q^{8} -9.00000i q^{9} +(21.3317 - 18.8271i) q^{10} -62.0501 q^{11} +(3.23285 + 3.23285i) q^{12} +(54.1331 - 54.1331i) q^{13} +(47.1206 - 0.963085i) q^{14} +(25.1474 - 22.1948i) q^{15} +49.4856 q^{16} +(-9.49779 - 9.49779i) q^{17} +(-16.1950 - 16.1950i) q^{18} -102.840 q^{19} +(-1.06062 + 17.0056i) q^{20} +(55.5492 - 1.13536i) q^{21} +(-111.656 + 111.656i) q^{22} +(-67.3079 - 67.3079i) q^{23} +72.7099 q^{24} +(124.031 + 15.5318i) q^{25} -194.819i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-19.5457 + 20.3614i) q^{28} -41.5785i q^{29} +(5.31317 - 85.1897i) q^{30} +35.7192i q^{31} +(-48.0564 + 48.0564i) q^{32} +(-131.628 + 131.628i) q^{33} -34.1816 q^{34} +(140.161 + 152.413i) q^{35} +13.7158 q^{36} +(-127.066 + 127.066i) q^{37} +(-185.054 + 185.054i) q^{38} -229.667i q^{39} +(179.309 + 203.163i) q^{40} +76.2138i q^{41} +(97.9148 - 102.001i) q^{42} +(161.871 + 161.871i) q^{43} -94.5631i q^{44} +(6.26356 - 100.428i) q^{45} -242.234 q^{46} +(33.7996 + 33.7996i) q^{47} +(104.975 - 104.975i) q^{48} +(14.0151 + 342.714i) q^{49} +(251.136 - 195.239i) q^{50} -40.2957 q^{51} +(82.4978 + 82.4978i) q^{52} +(-502.866 - 502.866i) q^{53} -68.7097 q^{54} +(-692.396 - 43.1838i) q^{55} +(9.17240 + 448.775i) q^{56} +(-218.156 + 218.156i) q^{57} +(-74.8183 - 74.8183i) q^{58} -137.315 q^{59} +(33.8244 + 38.3242i) q^{60} -254.079i q^{61} +(64.2748 + 64.2748i) q^{62} +(115.429 - 120.246i) q^{63} +568.835i q^{64} +(641.727 - 566.379i) q^{65} +473.716i q^{66} +(-522.692 + 522.692i) q^{67} +(14.4745 - 14.4745i) q^{68} -285.563 q^{69} +(526.472 + 22.0469i) q^{70} +386.808 q^{71} +(154.241 - 154.241i) q^{72} +(142.499 - 142.499i) q^{73} +457.297i q^{74} +(296.058 - 230.162i) q^{75} -156.726i q^{76} +(-829.031 - 795.821i) q^{77} +(-413.274 - 413.274i) q^{78} -160.688i q^{79} +(552.193 + 34.4396i) q^{80} -81.0000 q^{81} +(137.143 + 137.143i) q^{82} +(227.086 - 227.086i) q^{83} +(1.73026 + 84.6559i) q^{84} +(-99.3726 - 112.593i) q^{85} +582.556 q^{86} +(-88.2013 - 88.2013i) q^{87} +(-1063.41 - 1063.41i) q^{88} +486.783 q^{89} +(-169.444 - 191.986i) q^{90} +(1417.54 - 28.9727i) q^{91} +(102.576 - 102.576i) q^{92} +(75.7718 + 75.7718i) q^{93} +121.641 q^{94} +(-1147.55 - 71.5713i) q^{95} +203.886i q^{96} +(769.449 + 769.449i) q^{97} +(641.914 + 591.475i) q^{98} +558.451i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \) 48 * q + 4 * q^7 - 168 * q^8	\( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) \) 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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