LMFDB - Embedded newform 19.5.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,5,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("19.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	19.d (of order $6$, 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:	$1.96402929859$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.1
Root			$6.00126i$ of defining polynomial
Character	$\chi$	$=$	19.8
Dual form			19.5.d.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.19724 - 3.00063i) q^{2} +(-1.61920 - 0.934844i) q^{3} +(10.0076 + 17.3336i) q^{4} +(-20.3151 + 35.1867i) q^{5} +(5.61024 + 9.71722i) q^{6} -11.8590 q^{7} -24.0959i q^{8} +(-38.7521 - 67.1207i) q^{9} +O(q^{10})$	\(q+(-5.19724 - 3.00063i) q^{2} +(-1.61920 - 0.934844i) q^{3} +(10.0076 + 17.3336i) q^{4} +(-20.3151 + 35.1867i) q^{5} +(5.61024 + 9.71722i) q^{6} -11.8590 q^{7} -24.0959i q^{8} +(-38.7521 - 67.1207i) q^{9} +(211.165 - 121.916i) q^{10} -91.6624 q^{11} -37.4220i q^{12} +(-81.2188 + 46.8917i) q^{13} +(61.6343 + 35.5846i) q^{14} +(65.7881 - 37.9828i) q^{15} +(87.8183 - 152.106i) q^{16} +(-205.675 + 356.240i) q^{17} +465.123i q^{18} +(333.054 - 139.270i) q^{19} -813.217 q^{20} +(19.2021 + 11.0863i) q^{21} +(476.392 + 275.045i) q^{22} +(-168.437 - 291.742i) q^{23} +(-22.5259 + 39.0159i) q^{24} +(-512.903 - 888.373i) q^{25} +562.819 q^{26} +296.353i q^{27} +(-118.680 - 205.560i) q^{28} +(932.048 - 538.118i) q^{29} -455.889 q^{30} +1784.95i q^{31} +(-1246.71 + 719.787i) q^{32} +(148.419 + 85.6900i) q^{33} +(2137.89 - 1234.31i) q^{34} +(240.917 - 417.280i) q^{35} +(775.629 - 1343.43i) q^{36} -240.886i q^{37} +(-2148.86 - 275.552i) q^{38} +175.346 q^{39} +(847.854 + 489.508i) q^{40} +(-1872.91 - 1081.32i) q^{41} +(-66.5320 - 115.237i) q^{42} +(-1140.06 + 1974.64i) q^{43} +(-917.318 - 1588.84i) q^{44} +3149.01 q^{45} +2021.67i q^{46} +(818.120 + 1417.03i) q^{47} +(-284.390 + 164.193i) q^{48} -2260.36 q^{49} +6156.12i q^{50} +(666.057 - 384.548i) q^{51} +(-1625.61 - 938.544i) q^{52} +(108.818 - 62.8260i) q^{53} +(889.247 - 1540.22i) q^{54} +(1862.13 - 3225.30i) q^{55} +285.754i q^{56} +(-669.475 - 85.8478i) q^{57} -6458.78 q^{58} +(3426.06 + 1978.03i) q^{59} +(1316.76 + 760.231i) q^{60} +(-1093.26 - 1893.58i) q^{61} +(5355.99 - 9276.84i) q^{62} +(459.563 + 795.986i) q^{63} +5829.08 q^{64} -3810.43i q^{65} +(-514.248 - 890.704i) q^{66} +(1585.36 - 915.311i) q^{67} -8233.23 q^{68} +629.849i q^{69} +(-2504.21 + 1445.81i) q^{70} +(994.638 + 574.254i) q^{71} +(-1617.33 + 933.766i) q^{72} +(-2476.02 + 4288.59i) q^{73} +(-722.811 + 1251.95i) q^{74} +1917.93i q^{75} +(5747.11 + 4379.27i) q^{76} +1087.03 q^{77} +(-911.314 - 526.148i) q^{78} +(103.935 + 60.0068i) q^{79} +(3568.07 + 6180.07i) q^{80} +(-2861.88 + 4956.92i) q^{81} +(6489.30 + 11239.8i) q^{82} -10396.8 q^{83} +443.789i q^{84} +(-8356.60 - 14474.1i) q^{85} +(11850.4 - 6841.81i) q^{86} -2012.23 q^{87} +2208.68i q^{88} +(-661.303 + 381.804i) q^{89} +(-16366.2 - 9449.00i) q^{90} +(963.177 - 556.091i) q^{91} +(3371.29 - 5839.25i) q^{92} +(1668.65 - 2890.19i) q^{93} -9819.51i q^{94} +(-1865.56 + 14548.3i) q^{95} +2691.55 q^{96} +(3751.56 + 2165.96i) q^{97} +(11747.7 + 6782.51i) q^{98} +(3552.11 + 6152.44i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.19724	−	3.00063i	−1.29931	−	0.750158i	−0.319026	−	0.947746i	$-0.603356\pi$
$2$	−5.19724	−	3.00063i	−1.29931	−	0.750158i	−0.980285	+	0.197588i	$0.936689\pi$
$3$	−1.61920	−	0.934844i	−0.179911	−	0.103872i	0.407340	−	0.913277i	$-0.366456\pi$
$3$	−1.61920	−	0.934844i	−0.179911	−	0.103872i	−0.587251	+	0.809405i	$0.699790\pi$
$4$	10.0076	+	17.3336i	0.625473	+	1.08335i
$5$	−20.3151	+	35.1867i	−0.812602	+	1.40747i	0.0984350	+	0.995143i	$0.468616\pi$
$5$	−20.3151	+	35.1867i	−0.812602	+	1.40747i	−0.911037	+	0.412325i	$0.864717\pi$
$6$	5.61024	+	9.71722i	0.155840	+	0.269923i
$7$	−11.8590			−0.242021			−0.121011	−	0.992651i	$-0.538613\pi$
$7$	−11.8590			−0.242021			−0.121011	+	0.992651i	$0.538613\pi$
$8$		−	24.0959i		−	0.376498i
$9$	−38.7521	−	67.1207i	−0.478421	−	0.828650i
$10$	211.165	−	121.916i	2.11165	−	1.21916i
$11$	−91.6624			−0.757541			−0.378770	−	0.925491i	$-0.623653\pi$
$11$	−91.6624			−0.757541			−0.378770	+	0.925491i	$0.623653\pi$
$12$		−	37.4220i		−	0.259875i
$13$	−81.2188	+	46.8917i	−0.480585	+	0.277466i	−0.720660	−	0.693288i	$-0.756161\pi$
$13$	−81.2188	+	46.8917i	−0.480585	+	0.277466i	0.240075	+	0.970754i	$0.422828\pi$
$14$	61.6343	+	35.5846i	0.314461	+	0.181554i
$15$	65.7881	−	37.9828i	0.292392	−	0.168812i
$16$	87.8183	−	152.106i	0.343040	−	0.594163i
$17$	−205.675	+	356.240i	−0.711678	+	1.23266i	0.252548	+	0.967584i	$0.418731\pi$
$17$	−205.675	+	356.240i	−0.711678	+	1.23266i	−0.964227	+	0.265079i	$0.914602\pi$
$18$			465.123i			1.43557i
$19$	333.054	−	139.270i	0.922587	−	0.385789i
$19$	333.054	−	139.270i	0.922587	−	0.385789i
$20$	−813.217			−2.03304
$21$	19.2021	+	11.0863i	0.0435422	+	0.0251391i
$22$	476.392	+	275.045i	0.984281	+	0.568275i
$23$	−168.437	−	291.742i	−0.318407	−	0.551496i	0.661749	−	0.749725i	$-0.269814\pi$
$23$	−168.437	−	291.742i	−0.318407	−	0.551496i	−0.980156	+	0.198229i	$0.936481\pi$
$24$	−22.5259	+	39.0159i	−0.0391074	+	0.0677360i
$25$	−512.903	−	888.373i	−0.820644	−	1.42140i
$26$	562.819			0.832572
$27$			296.353i			0.406520i
$28$	−118.680	−	205.560i	−0.151378	−	0.262194i
$29$	932.048	−	538.118i	1.10826	−	0.639855i	0.169883	−	0.985464i	$-0.445661\pi$
$29$	932.048	−	538.118i	1.10826	−	0.639855i	0.938379	+	0.345609i	$0.112328\pi$
$30$	−455.889			−0.506544
$31$			1784.95i			1.85739i	0.370842	+	0.928696i	$0.379069\pi$
$31$			1784.95i			1.85739i	−0.370842	+	0.928696i	$0.620931\pi$
$32$	−1246.71	+	719.787i	−1.21749	+	0.702917i
$33$	148.419	+	85.6900i	0.136290	+	0.0786869i
$34$	2137.89	−	1234.31i	1.84938	−	1.06774i
$35$	240.917	−	417.280i	0.196667	−	0.340637i
$36$	775.629	−	1343.43i	0.598479	−	1.03660i
$37$		−	240.886i		−	0.175958i	−0.996122	−	0.0879790i	$-0.971959\pi$
$37$		−	240.886i		−	0.175958i	0.996122	−	0.0879790i	$-0.0280408\pi$
$38$	−2148.86	−	275.552i	−1.48813	−	0.190825i
$39$	175.346			0.115283
$40$	847.854	+	489.508i	0.529908	+	0.305943i
$41$	−1872.91	−	1081.32i	−1.11416	−	0.643262i	−0.174258	−	0.984700i	$-0.555753\pi$
$41$	−1872.91	−	1081.32i	−1.11416	−	0.643262i	−0.939904	+	0.341439i	$0.889086\pi$
$42$	−66.5320	−	115.237i	−0.0377166	−	0.0653270i
$43$	−1140.06	+	1974.64i	−0.616583	+	1.06795i	0.373522	+	0.927621i	$0.378150\pi$
$43$	−1140.06	+	1974.64i	−0.616583	+	1.06795i	−0.990105	+	0.140331i	$0.955183\pi$
$44$	−917.318	−	1588.84i	−0.473821	−	0.820682i
$45$	3149.01			1.55506
$46$			2021.67i			0.955420i
$47$	818.120	+	1417.03i	0.370358	+	0.641479i	0.989621	−	0.143705i	$-0.0459018\pi$
$47$	818.120	+	1417.03i	0.370358	+	0.641479i	−0.619263	+	0.785184i	$0.712568\pi$
$48$	−284.390	+	164.193i	−0.123433	+	0.0712642i
$49$	−2260.36			−0.941426
$50$			6156.12i			2.46245i
$51$	666.057	−	384.548i	0.256077	−	0.147846i
$52$	−1625.61	−	938.544i	−0.601186	−	0.347095i
$53$	108.818	−	62.8260i	0.0387390	−	0.0223660i	−0.480505	−	0.876992i	$-0.659547\pi$
$53$	108.818	−	62.8260i	0.0387390	−	0.0223660i	0.519244	+	0.854626i	$0.326213\pi$
$54$	889.247	−	1540.22i	0.304954	−	0.528197i
$55$	1862.13	−	3225.30i	0.615579	−	1.06621i
$56$			285.754i			0.0911204i
$57$	−669.475	−	85.8478i	−0.206056	−	0.0264228i
$58$	−6458.78			−1.91997
$59$	3426.06	+	1978.03i	0.984216	+	0.568237i	0.903540	−	0.428503i	$-0.140959\pi$
$59$	3426.06	+	1978.03i	0.984216	+	0.568237i	0.0806758	+	0.996740i	$0.474292\pi$
$60$	1316.76	+	760.231i	0.365766	+	0.211175i
$61$	−1093.26	−	1893.58i	−0.293807	−	0.508889i	0.680899	−	0.732377i	$-0.261589\pi$
$61$	−1093.26	−	1893.58i	−0.293807	−	0.508889i	−0.974707	+	0.223488i	$0.928256\pi$
$62$	5355.99	−	9276.84i	1.39334	−	2.41333i
$63$	459.563	+	795.986i	0.115788	+	0.200551i
$64$	5829.08			1.42311
$65$		−	3810.43i		−	0.901877i
$66$	−514.248	−	890.704i	−0.118055	−	0.204477i
$67$	1585.36	−	915.311i	0.353166	−	0.203901i	−0.312913	−	0.949782i	$-0.601305\pi$
$67$	1585.36	−	915.311i	0.353166	−	0.203901i	0.666079	+	0.745881i	$0.267971\pi$
$68$	−8233.23			−1.78054
$69$			629.849i			0.132293i
$70$	−2504.21	+	1445.81i	−0.511063	+	0.295062i
$71$	994.638	+	574.254i	0.197310	+	0.113917i	0.595400	−	0.803429i	$-0.296994\pi$
$71$	994.638	+	574.254i	0.197310	+	0.113917i	−0.398090	+	0.917346i	$0.630327\pi$
$72$	−1617.33	+	933.766i	−0.311985	+	0.180125i
$73$	−2476.02	+	4288.59i	−0.464632	+	0.804765i	−0.999185	−	0.0403694i	$-0.987147\pi$
$73$	−2476.02	+	4288.59i	−0.464632	+	0.804765i	0.534553	+	0.845135i	$0.320480\pi$
$74$	−722.811	+	1251.95i	−0.131996	+	0.228624i
$75$			1917.93i			0.340966i
$76$	5747.11	+	4379.27i	0.994998	+	0.758184i
$77$	1087.03			0.183341
$78$	−911.314	−	526.148i	−0.149789	−	0.0864805i
$79$	103.935	+	60.0068i	0.0166535	+	0.00961493i	0.508304	−	0.861178i	$-0.330273\pi$
$79$	103.935	+	60.0068i	0.0166535	+	0.00961493i	−0.491650	+	0.870793i	$0.663606\pi$
$80$	3568.07	+	6180.07i	0.557510	+	0.965636i
$81$	−2861.88	+	4956.92i	−0.436196	+	0.755513i
$82$	6489.30	+	11239.8i	0.965095	+	1.67159i
$83$	−10396.8			−1.50919			−0.754595	−	0.656191i	$-0.772167\pi$
$83$	−10396.8			−1.50919			−0.754595	+	0.656191i	$0.772167\pi$
$84$			443.789i			0.0628953i
$85$	−8356.60	−	14474.1i	−1.15662	−	2.00333i
$86$	11850.4	−	6841.81i	1.60227	−	0.925068i
$87$	−2012.23			−0.265851
$88$			2208.68i			0.285212i
$89$	−661.303	+	381.804i	−0.0834873	+	0.0482014i	−0.541162	−	0.840918i	$-0.682016\pi$
$89$	−661.303	+	381.804i	−0.0834873	+	0.0482014i	0.457675	+	0.889119i	$0.348682\pi$
$90$	−16366.2	−	9449.00i	−2.02051	−	1.16654i
$91$	963.177	−	556.091i	0.116312	−	0.0671526i
$92$	3371.29	−	5839.25i	0.398309	−	0.689892i
$93$	1668.65	−	2890.19i	0.192930	−	0.334165i
$94$		−	9819.51i		−	1.11131i
$95$	−1865.56	+	14548.3i	−0.206710	+	1.61200i
$96$	2691.55			0.292052
$97$	3751.56	+	2165.96i	0.398720	+	0.230201i	0.685932	−	0.727666i	$-0.259395\pi$
$97$	3751.56	+	2165.96i	0.398720	+	0.230201i	−0.287211	+	0.957867i	$0.592728\pi$
$98$	11747.7	+	6782.51i	1.22320	+	0.706218i
$99$	3552.11	+	6152.44i	0.362424	+	0.627736i
$100$	10265.8	−	17780.9i	1.02658	−	1.77809i
$101$	600.107	+	1039.42i	0.0588283	+	0.101894i	0.893940	−	0.448187i	$-0.147930\pi$
$101$	600.107	+	1039.42i	0.0588283	+	0.101894i	−0.835111	+	0.550081i	$0.814597\pi$
$102$	−4615.55			−0.443632
$103$			6516.50i			0.614242i	0.951670	+	0.307121i	$0.0993657\pi$
$103$			6516.50i			0.614242i	−0.951670	+	0.307121i	$0.900634\pi$
$104$	1129.90	+	1957.04i	0.104465	+	0.180939i
$105$	−780.184	+	450.439i	−0.0707650	+	0.0408562i
$106$	−754.070			−0.0671120
$107$		−	10674.7i		−	0.932366i	−0.884688	−	0.466183i	$-0.845629\pi$
$107$		−	10674.7i		−	0.932366i	0.884688	−	0.466183i	$-0.154371\pi$
$108$	−5136.88	+	2965.78i	−0.440404	+	0.254268i
$109$	−4010.62	−	2315.53i	−0.337566	−	0.194894i	0.321629	−	0.946866i	$-0.395770\pi$
$109$	−4010.62	−	2315.53i	−0.337566	−	0.194894i	−0.659195	+	0.751972i	$0.729103\pi$
$110$	−19355.9	+	11175.1i	−1.59966	+	0.923562i
$111$	−225.191	+	390.043i	−0.0182770	+	0.0316567i
$112$	−1041.44	+	1803.83i	−0.0830230	+	0.143800i
$113$		−	16437.6i		−	1.28731i	−0.765317	−	0.643654i	$-0.777418\pi$
$113$		−	16437.6i		−	1.28731i	0.765317	−	0.643654i	$-0.222582\pi$
$114$	3221.83	+	2455.02i	0.247909	+	0.188906i
$115$	13687.2			1.03495
$116$	18655.1	+	10770.5i	1.38638	+	0.800424i
$117$	6294.81	+	3634.31i	0.459844	+	0.265491i
$118$	−11870.7	−	20560.7i	−0.852535	−	1.47663i
$119$	2439.11	−	4224.66i	0.172241	−	0.298331i
$120$	−915.228	−	1585.22i	−0.0635575	−	0.110085i
$121$	−6239.00			−0.426132
$122$			13121.8i			0.881607i
$123$	2021.74	+	3501.75i	0.133633	+	0.231459i
$124$	−30939.7	+	17863.0i	−2.01221	+	1.16175i
$125$	16284.8			1.04222
$126$		−	5515.91i		−	0.347437i
$127$	1438.48	−	830.505i	0.0891857	−	0.0514914i	−0.454744	−	0.890622i	$-0.650269\pi$
$127$	1438.48	−	830.505i	0.0891857	−	0.0514914i	0.543930	+	0.839131i	$0.316936\pi$
$128$	−10347.8	−	5974.31i	−0.631580	−	0.364643i
$129$	3691.97	−	2131.56i	0.221860	−	0.128091i
$130$	−11433.7	+	19803.7i	−0.676550	+	1.17182i
$131$	7285.48	−	12618.8i	0.424537	−	0.735320i	−0.571840	−	0.820365i	$-0.693770\pi$
$131$	7285.48	−	12618.8i	0.424537	−	0.735320i	0.996377	+	0.0850455i	$0.0271036\pi$
$132$			3430.19i			0.196866i
$133$	−3949.70	+	1651.61i	−0.223286	+	0.0933692i
$134$	−10986.0			−0.611831
$135$	−10427.7	−	6020.43i	−0.572165	−	0.330339i
$136$	8583.90	+	4955.92i	0.464095	+	0.267945i
$137$	6406.68	+	11096.7i	0.341344	+	0.591225i	0.984683	−	0.174357i	$-0.0557846\pi$
$137$	6406.68	+	11096.7i	0.341344	+	0.591225i	−0.643339	+	0.765582i	$0.722451\pi$
$138$	1889.94	−	3273.48i	0.0992410	−	0.171890i
$139$	7078.90	+	12261.0i	0.366383	+	0.634595i	0.988997	−	0.147935i	$-0.0472625\pi$
$139$	7078.90	+	12261.0i	0.366383	+	0.634595i	−0.622614	+	0.782529i	$0.713929\pi$
$140$	9643.97			0.492039
$141$		−	3059.26i		−	0.153878i
$142$	−3446.25	−	5969.08i	−0.170911	−	0.296027i
$143$	7444.71	−	4298.21i	0.364062	−	0.210192i
$144$	−13612.6			−0.656471
$145$			43727.6i			2.07979i
$146$	25737.0	−	14859.2i	1.20740	−	0.697094i
$147$	3659.97	+	2113.09i	0.169373	+	0.0977873i
$148$	4175.43	−	2410.69i	0.190624	−	0.110057i
$149$	2826.57	−	4895.77i	0.127317	−	0.220520i	−0.795319	−	0.606191i	$-0.792697\pi$
$149$	2826.57	−	4895.77i	0.127317	−	0.220520i	0.922636	+	0.385671i	$0.126030\pi$
$150$	5755.01	−	9967.98i	0.255778	−	0.443021i
$151$		−	26081.3i		−	1.14387i	−0.820301	−	0.571933i	$-0.806194\pi$
$151$		−	26081.3i		−	1.14387i	0.820301	−	0.571933i	$-0.193806\pi$
$152$	−3355.83	−	8025.22i	−0.145249	−	0.347352i
$153$	31881.4			1.36193
$154$	−5649.55	−	3261.77i	−0.238217	−	0.137535i
$155$	−62806.6	−	36261.4i	−2.61422	−	1.50932i
$156$	1754.78	+	3039.37i	0.0721065	+	0.124892i
$157$	−14250.9	+	24683.3i	−0.578153	+	1.00139i	0.417538	+	0.908659i	$0.362893\pi$
$157$	−14250.9	+	24683.3i	−0.578153	+	1.00139i	−0.995691	+	0.0927312i	$0.970440\pi$
$158$	−360.116	−	623.740i	−0.0144254	−	0.0249856i
$159$	−234.930			−0.00929274
$160$		−	58490.1i		−	2.28477i
$161$	1997.50	+	3459.77i	0.0770611	+	0.133474i
$162$	29747.8	−	17174.9i	1.13351	−	0.654431i
$163$	7801.50			0.293632			0.146816	−	0.989164i	$-0.453098\pi$
$163$	7801.50			0.293632			0.146816	+	0.989164i	$0.453098\pi$
$164$		−	43285.6i		−	1.60937i
$165$	−6030.30	+	3481.59i	−0.221499	+	0.127882i
$166$	54034.8	+	31197.0i	1.96091	+	1.13213i
$167$	12136.4	−	7006.98i	0.435170	−	0.251245i	−0.266377	−	0.963869i	$-0.585827\pi$
$167$	12136.4	−	7006.98i	0.435170	−	0.251245i	0.701547	+	0.712624i	$0.252493\pi$
$168$	267.135	−	462.691i	0.00946481	−	0.0163935i
$169$	−9882.83	+	17117.6i	−0.346025	+	0.599334i
$170$			100300.i			3.47060i
$171$	−22254.4	−	16957.8i	−0.761070	−	0.579932i
$172$	−45637.0			−1.54262
$173$	−39394.7	−	22744.6i	−1.31627	−	0.759951i	−0.333146	−	0.942875i	$-0.608110\pi$
$173$	−39394.7	−	22744.6i	−1.31627	−	0.759951i	−0.983127	+	0.182925i	$0.941444\pi$
$174$	10458.0	+	6037.95i	0.345423	+	0.199430i
$175$	6082.53	+	10535.3i	0.198613	+	0.344008i
$176$	−8049.64	+	13942.4i	−0.259867	+	0.450103i
$177$	−3698.31	−	6405.65i	−0.118047	−	0.204464i
$178$	4582.61			0.144635
$179$			60369.5i			1.88413i	0.335427	+	0.942066i	$0.391119\pi$
$179$			60369.5i			1.88413i	−0.335427	+	0.942066i	$0.608881\pi$
$180$	31513.9	+	54583.7i	0.972651	+	1.68468i
$181$	−9362.15	+	5405.24i	−0.285771	+	0.164990i	−0.636033	−	0.771662i	$-0.719426\pi$
$181$	−9362.15	+	5405.24i	−0.285771	+	0.164990i	0.350262	+	0.936652i	$0.386093\pi$
$182$	−6674.49			−0.201500
$183$			4088.10i			0.122073i
$184$	−7029.76	+	4058.63i	−0.207637	+	0.119879i
$185$	8476.00	+	4893.62i	0.247655	+	0.142984i
$186$	−17344.8	+	10014.0i	−0.501352	+	0.289456i
$187$	18852.7	−	32653.8i	0.539125	−	0.933792i
$188$	−16374.8	+	28362.0i	−0.463297	+	0.802455i
$189$		−	3514.47i		−	0.0983866i
$190$	53349.9	−	70013.4i	1.47784	−	1.93943i
$191$	−44650.7			−1.22394			−0.611972	−	0.790880i	$-0.709623\pi$
$191$	−44650.7			−1.22394			−0.611972	+	0.790880i	$0.709623\pi$
$192$	−9438.42	−	5449.28i	−0.256034	−	0.147821i
$193$	22957.5	+	13254.5i	0.616324	+	0.355835i	0.775437	−	0.631425i	$-0.217530\pi$
$193$	22957.5	+	13254.5i	0.616324	+	0.355835i	−0.159112	+	0.987260i	$0.550863\pi$
$194$	−12998.5	−	22514.1i	−0.345375	−	0.598206i
$195$	−3562.16	+	6169.84i	−0.0936793	+	0.162257i
$196$	−22620.7	−	39180.3i	−0.588836	−	1.01989i
$197$	39532.1			1.01863			0.509316	−	0.860580i	$-0.329899\pi$
$197$	39532.1			1.01863			0.509316	+	0.860580i	$0.329899\pi$
$198$		−	42634.3i		−	1.08750i
$199$	−14619.7	−	25322.0i	−0.369175	−	0.639429i	0.620262	−	0.784395i	$-0.287026\pi$
$199$	−14619.7	−	25322.0i	−0.369175	−	0.639429i	−0.989437	+	0.144966i	$0.953693\pi$
$200$	−21406.1	+	12358.8i	−0.535153	+	0.308971i
$201$	−3422.69			−0.0847179
$202$		−	7202.80i		−	0.176522i
$203$	−11053.2	+	6381.56i	−0.268223	+	0.154858i
$204$	13331.2	+	7696.78i	0.320339	+	0.184948i
$205$	76096.4	−	43934.2i	1.81074	−	1.04543i
$206$	19553.6	−	33867.8i	0.460778	−	0.798092i
$207$	−13054.6	+	22611.2i	−0.304665	+	0.527695i
$208$			16471.8i			0.380728i
$209$	−30528.5	+	12765.8i	−0.698897	+	0.292251i
$210$	5406.41			0.122594
$211$	35236.3	+	20343.7i	0.791453	+	0.456946i	0.840474	−	0.541852i	$-0.182277\pi$
$211$	35236.3	+	20343.7i	0.791453	+	0.456946i	−0.0490206	+	0.998798i	$0.515610\pi$
$212$	2178.00	+	1257.47i	0.0484603	+	0.0279786i
$213$	−1073.68	−	1859.66i	−0.0236654	−	0.0409897i
$214$	−32030.7	+	55478.8i	−0.699422	+	1.21143i
$215$	−46320.8	−	80230.0i	−1.00207	−	1.73564i
$216$	7140.89			0.153054
$217$		−	21167.8i		−	0.449528i
$218$	13896.1	+	24068.8i	0.292402	+	0.506455i
$219$	8018.33	−	4629.39i	0.167184	−	0.0965240i
$220$	74541.4			1.54011
$221$		−	38577.8i		−	0.789866i
$222$	2340.75	−	1351.43i	0.0474951	−	0.0274213i
$223$	39975.0	+	23079.6i	0.803857	+	0.464107i	0.844818	−	0.535054i	$-0.179709\pi$
$223$	39975.0	+	23079.6i	0.803857	+	0.464107i	−0.0409612	+	0.999161i	$0.513042\pi$
$224$	14784.8	−	8535.98i	0.294658	−	0.170121i
$225$	−39752.1	+	68852.7i	−0.785227	+	1.36005i
$226$	−49323.3	+	85430.4i	−0.965684	+	1.67261i
$227$		−	30216.1i		−	0.586391i	−0.956053	−	0.293195i	$-0.905281\pi$
$227$		−	30216.1i		−	0.586391i	0.956053	−	0.293195i	$-0.0947187\pi$
$228$	−5211.77	−	12463.6i	−0.100257	−	0.239758i
$229$	91714.5			1.74891			0.874454	−	0.485109i	$-0.161220\pi$
$229$	91714.5			1.74891			0.874454	+	0.485109i	$0.161220\pi$
$230$	−71135.9	−	41070.3i	−1.34472	−	0.776377i
$231$	−1760.11	−	1016.20i	−0.0329850	−	0.0190439i
$232$	−12966.4	−	22458.5i	−0.240904	−	0.417258i
$233$	−43758.2	+	75791.4i	−0.806023	+	1.39607i	0.109576	+	0.993978i	$0.465051\pi$
$233$	−43758.2	+	75791.4i	−0.806023	+	1.39607i	−0.915599	+	0.402094i	$0.868283\pi$
$234$	−21810.4	−	37776.8i	−0.398320	−	0.689911i
$235$	−66480.6			−1.20381
$236$			79181.2i			1.42167i
$237$	−112.194	−	194.325i	−0.00199743	−	0.00345966i
$238$	−25353.3	+	14637.7i	−0.447590	+	0.258416i
$239$	81006.2			1.41815			0.709075	−	0.705133i	$-0.249113\pi$
$239$	81006.2			1.41815			0.709075	+	0.705133i	$0.249113\pi$
$240$		−	13342.3i		−	0.231638i
$241$	−65043.0	+	37552.6i	−1.11987	+	0.646556i	−0.941367	−	0.337384i	$-0.890458\pi$
$241$	−65043.0	+	37552.6i	−1.11987	+	0.646556i	−0.178501	+	0.983940i	$0.557125\pi$
$242$	32425.6	+	18720.9i	0.553679	+	0.319666i
$243$	30056.5	−	17353.1i	0.509010	−	0.293877i
$244$	21881.7	−	37900.2i	0.367537	−	0.636593i
$245$	45919.4	−	79534.7i	0.765004	−	1.32503i
$246$		−	24265.9i		−	0.400984i
$247$	−20519.6	+	26928.8i	−0.336338	+	0.441391i
$248$	43010.0			0.699304
$249$	16834.5	+	9719.39i	0.271520	+	0.156762i
$250$	−84635.8	−	48864.5i	−1.35417	−	0.781832i
$251$	3360.52	+	5820.58i	0.0533407	+	0.0923888i	0.891463	−	0.453094i	$-0.149680\pi$
$251$	3360.52	+	5820.58i	0.0533407	+	0.0923888i	−0.838122	+	0.545483i	$0.816346\pi$
$252$	−9198.21	+	15931.8i	−0.144845	+	0.250878i
$253$	15439.3	+	26741.7i	0.241206	+	0.417781i
$254$	−9968.15			−0.154507
$255$			31248.4i			0.480561i
$256$	−10779.2	−	18670.2i	−0.164478	−	0.284884i
$257$	−16532.2	+	9544.89i	−0.250303	+	0.144512i	−0.619903	−	0.784679i	$-0.712828\pi$
$257$	−16532.2	+	9544.89i	−0.250303	+	0.144512i	0.369600	+	0.929191i	$0.379495\pi$
$258$	−25584.1			−0.384353
$259$			2856.68i			0.0425855i
$260$	66048.5	−	38133.1i	0.977049	−	0.564100i
$261$	−72237.7	−	41706.5i	−1.06043	−	0.612241i
$262$	−75728.8	+	43722.1i	−1.10321	+	0.636939i
$263$	−7465.22	+	12930.1i	−0.107927	+	0.186935i	−0.914930	−	0.403612i	$-0.867755\pi$
$263$	−7465.22	+	12930.1i	−0.107927	+	0.186935i	0.807003	+	0.590547i	$0.201088\pi$
$264$	2064.77	−	3576.29i	0.0296254	−	0.0513127i
$265$			5105.25i			0.0726985i
$266$	25483.4	+	3267.78i	0.360159	+	0.0461837i
$267$	1427.71			0.0200270
$268$	31731.3	+	18320.1i	0.441792	+	0.255069i
$269$	32089.2	+	18526.7i	0.443459	+	0.256031i	0.705064	−	0.709144i	$-0.250918\pi$
$269$	32089.2	+	18526.7i	0.443459	+	0.256031i	−0.261605	+	0.965175i	$0.584252\pi$
$270$	36130.2	+	62579.3i	0.495613	+	0.858427i
$271$	8928.33	−	15464.3i	0.121571	−	0.210568i	−0.798816	−	0.601575i	$-0.794540\pi$
$271$	8928.33	−	15464.3i	0.121571	−	0.210568i	0.920388	+	0.391007i	$0.127873\pi$
$272$	36124.1	+	62568.7i	0.488269	+	0.845706i
$273$	−2079.43			−0.0279010
$274$		−	76896.4i		−	1.02425i
$275$	47013.9	+	81430.4i	0.621671	+	1.07677i
$276$	−10917.6	+	6303.26i	−0.143320	+	0.0827460i
$277$	−5464.50			−0.0712182			−0.0356091	−	0.999366i	$-0.511337\pi$
$277$	−5464.50			−0.0712182			−0.0356091	+	0.999366i	$0.511337\pi$
$278$		−	84964.6i		−	1.09938i
$279$	119807.	−	69170.8i	1.53913	−	0.888616i
$280$	−10054.7	−	5805.10i	−0.128249	−	0.0740446i
$281$	−111901.	+	64606.0i	−1.41717	+	0.818201i	−0.996049	−	0.0888050i	$-0.971695\pi$
$281$	−111901.	+	64606.0i	−1.41717	+	0.818201i	−0.421117	+	0.907006i	$0.638362\pi$
$282$	−9179.70	+	15899.7i	−0.115433	+	0.199936i
$283$	48789.9	−	84506.6i	0.609196	−	1.05516i	−0.382177	−	0.924089i	$-0.624826\pi$
$283$	48789.9	−	84506.6i	0.609196	−	1.05516i	0.991373	−	0.131069i	$-0.0418410\pi$
$284$			22987.6i			0.285007i
$285$	16621.1	−	21812.6i	0.204631	−	0.268546i
$286$	−51589.3			−0.630707
$287$	22210.9	+	12823.4i	0.269651	+	0.155683i
$288$	96625.2	+	55786.6i	1.16495	+	0.672581i
$289$	−42843.9	−	74207.9i	−0.512972	−	0.888494i
$290$	131210.	−	227263.i	1.56017	−	2.70229i
$291$	−4049.68	−	7014.25i	−0.0478227	−	0.0828314i
$292$	−99115.8			−1.16246
$293$		−	90636.0i		−	1.05576i	−0.849319	−	0.527881i	$-0.822987\pi$
$293$		−	90636.0i		−	1.05576i	0.849319	−	0.527881i	$-0.177013\pi$
$294$	−12681.2	−	21964.5i	−0.146712	−	0.254112i
$295$	−139201.	+	80367.7i	−1.59955	+	0.923502i
$296$	−5804.36			−0.0662478
$297$		−	27164.5i		−	0.307956i
$298$	−29380.8	+	16963.0i	−0.330850	+	0.191016i
$299$	27360.5	+	15796.6i	0.306043	+	0.176694i
$300$	−33244.7	+	19193.9i	−0.369386	+	0.213265i
$301$	13520.0	−	23417.4i	0.149226	−	0.258467i
$302$	−78260.3	+	135551.i	−0.858079	+	1.48624i
$303$		−	2244.03i		−	0.0244423i
$304$	8064.46	−	62889.9i	0.0872626	−	0.680508i
$305$	88838.3			0.954993
$306$	−165695.	−	95664.3i	−1.76957	−	1.02166i
$307$	−34359.3	−	19837.4i	−0.364559	−	0.210478i	0.306520	−	0.951864i	$-0.400835\pi$
$307$	−34359.3	−	19837.4i	−0.364559	−	0.210478i	−0.671079	+	0.741386i	$0.734169\pi$
$308$	10878.5	+	18842.1i	0.114675	+	0.198622i
$309$	6091.90	−	10551.5i	0.0638023	−	0.110509i
$310$	217614.	+	376919.i	2.26446	+	3.92215i
$311$	36804.0			0.380517			0.190258	−	0.981734i	$-0.439067\pi$
$311$	36804.0			0.380517			0.190258	+	0.981734i	$0.439067\pi$
$312$		−	4225.10i		−	0.0434038i
$313$	−6969.24	−	12071.1i	−0.0711372	−	0.123213i	0.828263	−	0.560340i	$-0.189329\pi$
$313$	−6969.24	−	12071.1i	−0.0711372	−	0.123213i	−0.899400	+	0.437127i	$0.855996\pi$
$314$	148131.	−	85523.3i	1.50240	−	0.867412i
$315$	−37344.2			−0.376359
$316$			2402.09i			0.0240555i
$317$	46616.2	−	26913.9i	0.463894	−	0.267829i	−0.249786	−	0.968301i	$-0.580360\pi$
$317$	46616.2	−	26913.9i	0.463894	−	0.267829i	0.713680	+	0.700472i	$0.247027\pi$
$318$	1220.99	+	704.937i	0.0120742	+	0.00697102i
$319$	−85433.8	+	49325.2i	−0.839553	+	0.484716i
$320$	−118418.	+	205106.i	−1.15643	+	2.00299i
$321$	−9979.14	+	17284.4i	−0.0968463	+	0.167743i
$322$		−	23975.1i		−	0.231232i
$323$	−18887.4	+	147291.i	−0.181037	+	1.41180i
$324$	−114562.			−1.09131
$325$	83314.7	+	48101.8i	0.788778	+	0.455401i
$326$	−40546.3	−	23409.4i	−0.381519	−	0.220270i
$327$	4329.32	+	7498.60i	0.0404878	+	0.0701269i
$328$	−26055.4	+	45129.3i	−0.242186	+	0.419479i
$329$	−9702.12	−	16804.6i	−0.0896344	−	0.155251i
$330$	41787.9			0.383727
$331$			81529.0i			0.744142i	0.928204	+	0.372071i	$0.121352\pi$
$331$			81529.0i			0.744142i	−0.928204	+	0.372071i	$0.878648\pi$
$332$	−104047.	−	180214.i	−0.943958	−	1.63498i
$333$	−16168.5	+	9334.86i	−0.145808	+	0.0841821i
$334$	−84101.5			−0.753895
$335$			74378.3i			0.662761i
$336$	3372.59	−	1947.17i	0.0298735	−	0.0172474i
$337$	−142785.	−	82436.8i	−1.25725	−	0.725874i	−0.284711	−	0.958613i	$-0.591898\pi$
$337$	−142785.	−	82436.8i	−1.25725	−	0.725874i	−0.972539	+	0.232739i	$0.925231\pi$
$338$	102727.	−	59309.5i	0.899189	−	0.519147i
$339$	−15366.6	+	26615.8i	−0.133715	+	0.231601i
$340$	167258.	−	289700.i	1.44687	−	2.50606i
$341$		−	163613.i		−	1.40705i
$342$	64777.7	+	154911.i	0.553826	+	1.32443i
$343$	55279.3			0.469866
$344$	47580.7	+	27470.7i	0.402082	+	0.232142i
$345$	−22162.3	−	12795.4i	−0.186199	−	0.107502i
$346$	136496.	+	236418.i	1.14017	+	1.97482i
$347$	54981.4	−	95230.5i	0.456622	−	0.790892i	−0.542158	−	0.840276i	$-0.682393\pi$
$347$	54981.4	−	95230.5i	0.456622	−	0.790892i	0.998780	+	0.0493845i	$0.0157260\pi$
$348$	−20137.5	−	34879.1i	−0.166283	−	0.288010i
$349$	−101514.			−0.833439			−0.416719	−	0.909035i	$-0.636820\pi$
$349$	−101514.			−0.833439			−0.416719	+	0.909035i	$0.636820\pi$
$350$		−	73005.7i		−	0.595965i
$351$	−13896.5	−	24069.5i	−0.112796	−	0.195368i
$352$	114276.	−	65977.4i	0.922297	−	0.532488i
$353$	−53392.2			−0.428478			−0.214239	−	0.976781i	$-0.568727\pi$
$353$	−53392.2			−0.428478			−0.214239	+	0.976781i	$0.568727\pi$
$354$			44389.0i			0.354217i
$355$	−40412.2	+	23332.0i	−0.320668	+	0.185138i
$356$	−13236.1	−	7641.85i	−0.104438	−	0.0602974i
$357$	−7898.79	+	4560.37i	−0.0619761	+	0.0357819i
$358$	181146.	−	313755.i	1.41340	−	2.44807i
$359$	−75410.4	+	130615.i	−0.585116	+	1.01345i	0.409744	+	0.912200i	$0.365618\pi$
$359$	−75410.4	+	130615.i	−0.585116	+	1.01345i	−0.994861	+	0.101251i	$0.967715\pi$
$360$		−	75878.0i		−	0.585478i
$361$	91528.8	−	92768.8i	0.702333	−	0.711848i
$362$	64876.5			0.495074
$363$	10102.2	+	5832.49i	0.0766658	+	0.0442630i
$364$	19278.1	+	11130.2i	0.145500	+	0.0840042i
$365$	−100601.	−	174246.i	−0.755121	−	1.30791i
$366$	12266.9	−	21246.8i	0.0915738	−	0.158611i
$367$	−89546.0	−	155098.i	−0.664835	−	1.15153i	−0.979330	−	0.202269i	$-0.935168\pi$
$367$	−89546.0	−	155098.i	−0.664835	−	1.15153i	0.314495	−	0.949259i	$-0.398165\pi$
$368$	−59167.4			−0.436905
$369$			167614.i			1.23100i
$370$	−29367.9	−	50866.7i	−0.214521	−	0.371561i
$371$	−1290.47	+	745.055i	−0.00937565	+	0.00541303i
$372$	66796.6			0.482690
$373$			82507.2i			0.593027i	0.955029	+	0.296513i	$0.0958239\pi$
$373$			82507.2i			0.593027i	−0.955029	+	0.296513i	$0.904176\pi$
$374$	−195964.	+	113140.i	−1.40098	+	0.808858i
$375$	−26368.2	−	15223.7i	−0.187507	−	0.108257i
$376$	34144.4	−	19713.3i	0.241515	−	0.139439i
$377$	−50466.6	+	87410.7i	−0.355076	+	0.615009i
$378$	−10545.6	+	18265.5i	−0.0738054	+	0.127835i
$379$			54526.8i			0.379605i	0.981822	+	0.189802i	$0.0607848\pi$
$379$			54526.8i			0.379605i	−0.981822	+	0.189802i	$0.939215\pi$
$380$	−270845.	+	113257.i	−1.87566	+	0.784326i
$381$	−3105.57			−0.0213940
$382$	232061.	+	133980.i	1.59028	+	0.918151i
$383$	224354.	+	129531.i	1.52945	+	0.883029i	0.999385	+	0.0350730i	$0.0111664\pi$
$383$	224354.	+	129531.i	1.52945	+	0.883029i	0.530066	+	0.847956i	$0.322167\pi$
$384$	11170.1	+	19347.2i	0.0757520	+	0.131206i
$385$	−22083.0	+	38248.9i	−0.148983	+	0.258046i
$386$	−79543.7	−	137774.i	−0.533865	−	0.924681i
$387$	176719.			1.17995
$388$			86704.1i			0.575939i
$389$	92669.8	+	160509.i	0.612406	+	1.06072i	0.990834	+	0.135087i	$0.0431313\pi$
$389$	92669.8	+	160509.i	0.612406	+	1.06072i	−0.378428	+	0.925631i	$0.623535\pi$
$390$	37026.8	−	21377.4i	0.243437	−	0.140549i
$391$	138573.			0.906412
$392$			54465.4i			0.354445i
$393$	−23593.2	+	13621.6i	−0.152758	+	0.0881946i
$394$	−205458.	−	118621.i	−1.32352	−	0.764134i
$395$	−4222.88	+	2438.08i	−0.0270654	+	0.0156262i
$396$	−71096.0	+	123142.i	−0.453372	+	0.785264i
$397$	3617.94	−	6266.45i	0.0229551	−	0.0397595i	−0.854320	−	0.519748i	$-0.826026\pi$
$397$	3617.94	−	6266.45i	0.0229551	−	0.0397595i	0.877275	+	0.479989i	$0.159359\pi$
$398$			175473.i			1.10776i
$399$	7939.33	+	1018.07i	0.0498699	+	0.00639489i
$400$	−180169.			−1.12606
$401$	164211.	+	94807.1i	1.02120	+	0.589593i	0.914453	−	0.404693i	$-0.132622\pi$
$401$	164211.	+	94807.1i	1.02120	+	0.589593i	0.106752	+	0.994286i	$0.465955\pi$
$402$	17788.6	+	10270.2i	0.110075	+	0.0635518i
$403$	−83699.5	−	144972.i	−0.515363	−	0.892634i
$404$	−12011.2	+	20804.1i	−0.0735910	+	0.127463i
$405$	−116278.	−	201400.i	−0.708907	−	1.22786i
$406$	76594.9			0.464673
$407$			22080.2i			0.133295i
$408$	−9266.01	−	16049.2i	−0.0556638	−	0.0964125i
$409$	−97628.5	+	56365.8i	−0.583620	+	0.336953i	−0.762571	−	0.646905i	$-0.776063\pi$
$409$	−97628.5	+	56365.8i	−0.583620	+	0.336953i	0.178951	+	0.983858i	$0.442730\pi$
$410$	−527322.			−3.13695
$411$		−	23957.0i		−	0.141824i
$412$	−112954.	+	65214.3i	−0.665440	+	0.384192i
$413$	−40629.7	−	23457.6i	−0.238201	−	0.137525i
$414$	135696.	−	78344.0i	0.791709	−	0.457094i
$415$	211212.	−	365830.i	1.22637	−	2.12414i
$416$	67504.1	−	116921.i	0.390071	−	0.675623i
$417$		−	26470.6i		−	0.152227i
$418$	196970.	+	25257.7i	1.12732	+	0.144558i
$419$	−102250.			−0.582421			−0.291210	−	0.956659i	$-0.594058\pi$
$419$	−102250.			−0.582421			−0.291210	+	0.956659i	$0.594058\pi$
$420$	−15615.5	−	9015.60i	−0.0885231	−	0.0511089i
$421$	56613.0	+	32685.5i	0.319412	+	0.184413i	0.651131	−	0.758966i	$-0.274295\pi$
$421$	56613.0	+	32685.5i	0.319412	+	0.184413i	−0.331718	+	0.943378i	$0.607628\pi$
$422$	−122088.	−	211462.i	−0.685563	−	1.18743i
$423$	63407.8	−	109826.i	0.354374	−	0.613794i
$424$	−1513.84	−	2622.06i	−0.00842073	−	0.0145851i
$425$	421965.			2.33614
$426$			12886.8i			0.0710112i
$427$	12965.0	+	22456.0i	0.0711076	+	0.123162i
$428$	185030.	−	106827.i	1.01008	−	0.583170i
$429$	−16072.6			−0.0873317
$430$			555966.i			3.00685i
$431$	−273912.	+	158143.i	−1.47454	+	0.851327i	−0.999589	−	0.0286839i	$-0.990868\pi$
$431$	−273912.	+	158143.i	−1.47454	+	0.851327i	−0.474953	+	0.880011i	$0.657535\pi$
$432$	45077.1	+	26025.3i	0.241539	+	0.139453i
$433$	130589.	−	75395.7i	0.696516	−	0.402134i	−0.109532	−	0.993983i	$-0.534935\pi$
$433$	130589.	−	75395.7i	0.696516	−	0.402134i	0.806049	+	0.591849i	$0.201602\pi$
$434$	−63516.8	+	110014.i	−0.337217	+	0.584077i
$435$	40878.5	−	70803.6i	0.216031	−	0.374177i
$436$		−	92691.4i		−	0.487603i
$437$	−96729.5	−	73707.4i	−0.506519	−	0.385965i
$438$	−55564.3			−0.289633
$439$	89522.7	+	51686.0i	0.464520	+	0.268191i	0.713943	−	0.700204i	$-0.246908\pi$
$439$	89522.7	+	51686.0i	0.464520	+	0.268191i	−0.249423	+	0.968395i	$0.580241\pi$
$440$	−77716.3	−	44869.5i	−0.401427	−	0.231764i
$441$	87593.9	+	151717.i	0.450398	+	0.780113i
$442$	−115758.	+	200498.i	−0.592524	+	1.02628i
$443$	41965.4	+	72686.2i	0.213837	+	0.370377i	0.952912	−	0.303246i	$-0.0980704\pi$
$443$	41965.4	+	72686.2i	0.213837	+	0.370377i	−0.739075	+	0.673623i	$0.764737\pi$
$444$	−9014.46			−0.0457271
$445$		−	31025.4i		−	0.156674i
$446$	−138507.	−	239900.i	−0.696307	−	1.20604i
$447$	−9153.55	+	5284.81i	−0.0458115	+	0.0264493i
$448$	−69127.2			−0.344424
$449$		−	46324.3i		−	0.229782i	−0.993378	−	0.114891i	$-0.963348\pi$
$449$		−	46324.3i		−	0.229782i	0.993378	−	0.114891i	$-0.0366519\pi$
$450$	413203.	−	238563.i	2.04051	−	1.17809i
$451$	171675.	+	99116.6i	0.844023	+	0.487297i
$452$	284924.	−	164501.i	1.39461	−	0.805176i
$453$	−24381.9	+	42230.7i	−0.118815	+	0.205794i
$454$	−90667.5	+	157041.i	−0.439886	+	0.761904i
$455$			45188.0i			0.218273i
$456$	−2068.58	+	16131.6i	−0.00994814	+	0.0775795i
$457$	−281437.			−1.34756			−0.673780	−	0.738932i	$-0.735331\pi$
$457$	−281437.			−1.34756			−0.673780	+	0.738932i	$0.735331\pi$
$458$	−476662.	−	275201.i	−2.27237	−	1.31196i
$459$	−105573.	−	60952.5i	−0.501103	−	0.289312i
$460$	136976.	+	237249.i	0.647334	+	1.12122i
$461$	18731.8	−	32444.4i	0.0881410	−	0.152665i	−0.818584	−	0.574386i	$-0.805241\pi$
$461$	18731.8	−	32444.4i	0.0881410	−	0.152665i	0.906725	+	0.421722i	$0.138574\pi$
$462$	6098.49	+	10562.9i	0.0285718	+	0.0494879i
$463$	−352568.			−1.64468			−0.822339	−	0.568998i	$-0.807331\pi$
$463$	−352568.			−1.64468			−0.822339	+	0.568998i	$0.807331\pi$
$464$		−	189027.i		−	0.877984i
$465$	67797.5	+	117429.i	0.313551	+	0.543086i
$466$	454844.	−	262604.i	2.09455	−	1.20929i
$467$	87566.9			0.401519			0.200760	−	0.979641i	$-0.435659\pi$
$467$	87566.9			0.401519			0.200760	+	0.979641i	$0.435659\pi$
$468$			145482.i			0.664230i
$469$	−18800.9	+	10854.7i	−0.0854738	+	0.0493483i
$470$	345516.	+	199484.i	1.56413	+	0.903050i
$471$	46150.0	−	26644.7i	0.208032	−	0.120107i
$472$	47662.4	−	82553.8i	0.213940	−	0.370555i
$473$	104501.	−	181001.i	0.467086	−	0.809017i
$474$			1346.61i			0.00599356i
$475$	−294548.	−	224444.i	−1.30548	−	0.994767i
$476$	97638.1			0.430929
$477$	−8433.84	−	4869.28i	−0.0370671	−	0.0214007i
$478$	−421009.	−	243070.i	−1.84262	−	1.06384i
$479$	60264.1	+	104380.i	0.262656	+	0.454934i	0.966947	−	0.254978i	$-0.0820682\pi$
$479$	60264.1	+	104380.i	0.262656	+	0.454934i	−0.704291	+	0.709912i	$0.748735\pi$
$480$	−54679.1	+	94706.9i	−0.237322	+	0.411054i
$481$	11295.6	+	19564.5i	0.0488223	+	0.0845627i
$482$	450726.			1.94008
$483$		−	7469.41i		−	0.0320178i
$484$	−62437.2	−	108144.i	−0.266534	−	0.461651i
$485$	−152426.	+	88003.4i	−0.648002	+	0.374124i
$486$	−208281.			−0.881816
$487$			96168.4i			0.405485i	0.979232	+	0.202742i	$0.0649854\pi$
$487$			96168.4i			0.405485i	−0.979232	+	0.202742i	$0.935015\pi$
$488$	−45627.3	+	26343.0i	−0.191596	+	0.110618i
$489$	−12632.2	−	7293.18i	−0.0528275	−	0.0305000i
$490$	−477309.	+	275574.i	−1.98796	+	1.14775i
$491$	−160875.	+	278644.i	−0.667308	+	1.15581i	0.311346	+	0.950297i	$0.399220\pi$
$491$	−160875.	+	278644.i	−0.667308	+	1.15581i	−0.978654	+	0.205515i	$0.934113\pi$
$492$	−40465.3	+	70087.9i	−0.167168	+	0.289543i
$493$			442710.i			1.82148i
$494$	187449.	−	78383.8i	0.768120	−	0.321198i
$495$	−288645.			−1.17802
$496$	271502.	+	156752.i	1.10359	+	0.637160i
$497$	−11795.4	−	6810.10i	−0.0477531	−	0.0275703i
$498$	−58328.6	−	101028.i	−0.235192	−	0.407365i
$499$	163391.	−	283002.i	0.656187	−	1.13655i	−0.325407	−	0.945574i	$-0.605501\pi$
$499$	163391.	−	283002.i	0.656187	−	1.13655i	0.981595	−	0.190976i	$-0.0611652\pi$
$500$	162971.	+	282274.i	0.651883	+	1.12909i
$501$	−26201.7			−0.104389
$502$		−	40334.7i		−	0.160056i
$503$	41253.3	+	71452.8i	0.163051	+	0.282412i	0.935961	−	0.352103i	$-0.114533\pi$
$503$	41253.3	+	71452.8i	0.163051	+	0.282412i	−0.772911	+	0.634515i	$0.781200\pi$
$504$	19180.0	−	11073.6i	0.0755069	−	0.0435940i
$505$	−48764.8			−0.191216
$506$		−	185311.i		−	0.723770i
$507$	32004.5	−	18477.8i	0.124507	−	0.0718844i
$508$	28791.3	+	16622.7i	0.111567	+	0.0644130i
$509$	29416.1	−	16983.4i	0.113540	−	0.0655525i	−0.442154	−	0.896939i	$-0.645786\pi$
$509$	29416.1	−	16983.4i	0.113540	−	0.0655525i	0.555695	+	0.831386i	$0.312452\pi$
$510$	93765.0	−	162406.i	0.360496	−	0.624398i
$511$	29363.2	−	50858.6i	0.112451	−	0.194770i
$512$			320556.i			1.22282i
$513$	41273.1	+	98701.7i	0.156831	+	0.375050i
$514$	114563.			0.433628
$515$	−229294.	−	132383.i	−0.864526	−	0.499134i
$516$	73895.2	+	42663.4i	0.277534	+	0.160235i
$517$	−74990.9	−	129888.i	−0.280561	−	0.485946i
$518$	8571.84	−	14846.9i	0.0319459	−	0.0553319i
$519$	42525.2	+	73655.8i	0.157874	+	0.273447i
$520$	−91815.6			−0.339555
$521$			203766.i			0.750684i	0.926886	+	0.375342i	$0.122475\pi$
$521$			203766.i			0.750684i	−0.926886	+	0.375342i	$0.877525\pi$
$522$	250291.	+	433517.i	0.918554	+	1.59098i
$523$	−323927.	+	187020.i	−1.18425	+	0.683728i	−0.956994	−	0.290106i	$-0.906309\pi$
$523$	−323927.	+	187020.i	−1.18425	+	0.683728i	−0.227258	+	0.973835i	$0.572976\pi$
$524$	291640.			1.06215
$525$		−	22744.9i		−	0.0825210i
$526$	77597.1	−	44800.7i	0.280462	−	0.161925i
$527$	−635871.	−	367120.i	−2.28954	−	1.32187i
$528$	26067.9	−	15050.3i	0.0935057	−	0.0539855i
$529$	83178.4	−	144069.i	0.297235	−	0.514825i
$530$	15319.0	−	26533.2i	0.0545353	−	0.0944579i
$531$		−	306612.i		−	1.08743i
$532$	−68155.2	−	51934.0i	−0.240811	−	0.183497i
$533$	202820.			0.713932
$534$	−7420.14	−	4284.02i	−0.0260213	−	0.0150234i
$535$	375606.	+	216856.i	1.31228	+	0.757643i
$536$	−22055.2	−	38200.7i	−0.0767682	−	0.132966i
$537$	56436.0	−	97750.1i	0.195708	−	0.338976i
$538$	−111183.	−	192575.i	−0.384128	−	0.665329i
$539$	207190.			0.713168
$540$		−	241000.i		−	0.826473i
$541$	9995.51	+	17312.7i	0.0341516	+	0.0591522i	0.882596	−	0.470132i	$-0.155794\pi$
$541$	9995.51	+	17312.7i	0.0341516	+	0.0591522i	−0.848444	+	0.529284i	$0.822460\pi$
$542$	−92805.4	+	53581.2i	−0.315918	+	0.182395i
$543$	20212.2			0.0685510
$544$		−	592169.i		−	2.00100i
$545$	162952.	−	94080.3i	0.548613	−	0.316742i
$546$	10807.3	+	6239.60i	0.0362520	+	0.0209301i
$547$	104485.	−	60324.2i	0.349203	−	0.201612i	−0.315131	−	0.949048i	$-0.602049\pi$
$547$	104485.	−	60324.2i	0.349203	−	0.201612i	0.664334	+	0.747436i	$0.268715\pi$
$548$	−128231.	+	222102.i	−0.427003	+	0.739590i
$549$	−84732.1	+	146760.i	−0.281127	+	0.486927i
$550$		−	564285.i		−	1.86541i
$551$	235479.	−	309029.i	0.775618	−	1.01788i
$552$	15176.8			0.0498082
$553$	−1232.57	−	711.622i	−0.00403051	−	0.00232702i
$554$	28400.3	+	16396.9i	0.0925346	+	0.0534249i
$555$	−9149.54	−	15847.5i	−0.0297039	−	0.0514486i
$556$	−141685.	+	245406.i	−0.458326	+	0.793844i
$557$	43051.0	+	74566.5i	0.138763	+	0.240344i	0.927029	−	0.374991i	$-0.122354\pi$
$557$	43051.0	+	74566.5i	0.138763	+	0.240344i	−0.788266	+	0.615335i	$0.789021\pi$
$558$	−830224.			−2.66641
$559$		−	213838.i		−	0.684322i
$560$	−42313.8	−	73289.7i	−0.134929	−	0.233704i
$561$	−61052.4	+	35248.6i	−0.193989	+	0.111999i
$562$	775435.			2.45512
$563$		−	289759.i		−	0.914156i	−0.889427	−	0.457078i	$-0.848896\pi$
$563$		−	289759.i		−	0.914156i	0.889427	−	0.457078i	$-0.151104\pi$
$564$	53028.0	−	30615.7i	0.166704	−	0.0962468i
$565$	578386.	+	333931.i	1.81184	+	1.04607i
$566$	−507146.	+	292801.i	−1.58307	+	0.913986i
$567$	33939.1	−	58784.3i	0.105569	−	0.182850i
$568$	13837.1	−	23966.6i	0.0428894	−	0.0742866i
$569$		−	58768.3i		−	0.181518i	−0.995873	−	0.0907588i	$-0.971071\pi$
$569$		−	58768.3i		−	0.181518i	0.995873	−	0.0907588i	$-0.0289292\pi$
$570$	−151836.	+	63491.7i	−0.467331	+	0.195419i
$571$	589597.			1.80835			0.904177	−	0.427158i	$-0.140485\pi$
$571$	589597.			1.80835			0.904177	+	0.427158i	$0.140485\pi$
$572$	149007.	+	86029.2i	0.455422	+	0.262938i
$573$	72298.2	+	41741.4i	0.220201	+	0.127133i
$574$	−76956.8	−	133293.i	−0.233573	−	0.404561i
$575$	−172784.	+	299270.i	−0.522597	+	0.905164i
$576$	−225889.	−	391252.i	−0.680849	−	1.17926i
$577$	−475643.			−1.42866			−0.714332	−	0.699807i	$-0.753269\pi$
$577$	−475643.			−1.42866			−0.714332	+	0.699807i	$0.753269\pi$
$578$			514235.i			1.53924i
$579$	−24781.8	−	42923.3i	−0.0739222	−	0.128037i
$580$	−757957.	+	437607.i	−2.25314	+	1.30085i
$581$	123296.			0.365256
$582$			48606.3i			0.143498i
$583$	−9974.50	+	5758.78i	−0.0293463	+	0.0169431i
$584$	103337.	+	59661.8i	0.302992	+	0.174933i
$585$	−255759.	+	147662.i	−0.747341	+	0.431477i
$586$	−271965.	+	471058.i	−0.791987	+	1.37176i
$587$	−251162.	+	435025.i	−0.728915	+	1.26252i	0.228427	+	0.973561i	$0.426642\pi$
$587$	−251162.	+	435025.i	−0.728915	+	1.26252i	−0.957342	+	0.288957i	$0.906691\pi$
$588$			84587.4i			0.244653i
$589$	248590.	+	594486.i	0.716562	+	1.71361i
$590$	964616.			2.77109
$591$	−64010.2	−	36956.3i	−0.183263	−	0.105807i
$592$	−36640.2	−	21154.2i	−0.104548	−	0.0603607i
$593$	−134129.	−	232318.i	−0.381428	−	0.660653i	0.609838	−	0.792526i	$-0.291234\pi$
$593$	−134129.	−	232318.i	−0.381428	−	0.660653i	−0.991267	+	0.131873i	$0.957901\pi$
$594$	−81510.5	+	141180.i	−0.231015	+	0.400130i
$595$	99101.2	+	171648.i	0.279927	+	0.484848i
$596$	113148.			0.318534
$597$			54668.5i			0.153387i
$598$	−94799.6	−	164198.i	−0.265096	−	0.459161i
$599$	268692.	−	155130.i	0.748862	−	0.432356i	−0.0764205	−	0.997076i	$-0.524349\pi$
$599$	268692.	−	155130.i	0.748862	−	0.432356i	0.825283	+	0.564720i	$0.191016\pi$
$600$	46214.3			0.128373
$601$			32080.3i			0.0888157i	0.999013	+	0.0444079i	$0.0141401\pi$
$601$			32080.3i			0.0888157i	−0.999013	+	0.0444079i	$0.985860\pi$
$602$	−140534.	+	81137.2i	−0.387782	+	0.223886i
$603$	−122873.	−	70940.5i	−0.337925	−	0.195101i
$604$	452083.	−	261010.i	1.23921	−	0.715457i
$605$	126746.	−	219530.i	0.346276	−	0.599768i
$606$	−6733.49	+	11662.8i	−0.0183356	+	0.0317582i
$607$		−	602814.i		−	1.63608i	−0.575158	−	0.818042i	$-0.695059\pi$
$607$		−	602814.i		−	1.63608i	0.575158	−	0.818042i	$-0.304941\pi$
$608$	−314976.	+	413357.i	−0.852061	+	1.11820i
$609$	23863.1			0.0643415
$610$	−461714.	−	266571.i	−1.24083	−	0.716396i
$611$	−132894.	−	76726.1i	−0.355977	−	0.205523i
$612$	319055.	+	552620.i	0.851849	+	1.47545i
$613$	−45663.0	+	79090.6i	−0.121519	+	0.210477i	−0.920367	−	0.391056i	$-0.872110\pi$
$613$	−45663.0	+	79090.6i	−0.121519	+	0.210477i	0.798848	+	0.601533i	$0.205443\pi$
$614$	119049.	+	206199.i	0.315784	+	0.546953i
$615$	−164287.			−0.434362
$616$		−	26192.9i		−	0.0690274i
$617$	−277813.	−	481186.i	−0.729763	−	1.26399i	−0.956983	−	0.290143i	$-0.906297\pi$
$617$	−277813.	−	481186.i	−0.729763	−	1.26399i	0.227221	−	0.973843i	$-0.427036\pi$
$618$	−63322.2	+	36559.1i	−0.165798	+	0.0957235i
$619$	−10286.5			−0.0268464			−0.0134232	−	0.999910i	$-0.504273\pi$
$619$	−10286.5			−0.0268464			−0.0134232	+	0.999910i	$0.504273\pi$
$620$		−	1.45155e6i		−	3.77616i
$621$	86458.6	−	49916.9i	0.224195	−	0.129439i
$622$	−191279.	−	110435.i	−0.494410	−	0.285448i
$623$	7842.42	−	4527.82i	0.0202057	−	0.0116658i
$624$	15398.6	−	26671.1i	0.0395468	−	0.0684970i
$625$	−10261.5	+	17773.4i	−0.0262694	+	0.0455000i
$626$			83648.4i			0.213456i
$627$	61365.7	+	7869.02i	0.156096	+	0.0200164i
$628$	−570467.			−1.44648
$629$	85813.3	+	49544.3i	0.216897	+	0.125225i
$630$	194087.	+	112056.i	0.489007	+	0.282328i
$631$	252071.	+	436600.i	0.633089	+	1.09654i	0.986917	+	0.161232i	$0.0515467\pi$
$631$	252071.	+	436600.i	0.633089	+	1.09654i	−0.353827	+	0.935311i	$0.615120\pi$
$632$	1445.91	−	2504.40i	0.00362000	−	0.00627002i
$633$	−38036.3	−	65880.8i	−0.0949273	−	0.164419i
$634$	−323035.			−0.803657
$635$			67487.0i			0.167368i
$636$	−2351.08	−	4072.18i	−0.00581236	−	0.0100673i
$637$	183584.	−	105992.i	0.452435	−	0.261213i
$638$	592027.			1.45445
$639$		−	89014.3i		−	0.218001i
$640$	420433.	−	242737.i	1.02645	−	0.592619i
$641$	250560.	+	144661.i	0.609812	+	0.352075i	0.772892	−	0.634538i	$-0.218810\pi$
$641$	250560.	+	144661.i	0.609812	+	0.352075i	−0.163080	+	0.986613i	$0.552143\pi$
$642$	103728.	−	59887.4i	0.251667	−	0.145300i
$643$	−102338.	+	177254.i	−0.247522	+	0.428720i	−0.962838	−	0.270081i	$-0.912950\pi$
$643$	−102338.	+	177254.i	−0.247522	+	0.428720i	0.715316	+	0.698801i	$0.246283\pi$
$644$	−39980.3	+	69247.8i	−0.0963993	+	0.166968i
$645$			173211.i			0.416347i
$646$	540129.	−	708835.i	1.29429	−	1.69856i
$647$	327109.			0.781420			0.390710	−	0.920514i	$-0.372230\pi$
$647$	327109.			0.781420			0.390710	+	0.920514i	$0.372230\pi$
$648$	119441.	+	68959.4i	0.284449	+	0.164227i
$649$	−314041.	−	181311.i	−0.745584	−	0.430463i
$650$	−288671.	−	499993.i	−0.683246	−	1.18342i
$651$	−19788.6	+	34274.9i	−0.0466932	+	0.0808749i
$652$	78074.0	+	135228.i	0.183659	+	0.318106i
$653$	−156357.			−0.366683			−0.183342	−	0.983049i	$-0.558691\pi$
$653$	−156357.			−0.366683			−0.183342	+	0.983049i	$0.558691\pi$
$654$		−	51962.8i		−	0.121489i
$655$	296010.	+	512704.i	0.689959	+	1.19504i
$656$	−328951.	+	189920.i	−0.764405	+	0.441329i
$657$	383804.			0.889159
$658$			116450.i			0.268960i
$659$	−330122.	+	190596.i	−0.760158	+	0.438877i	−0.829352	−	0.558726i	$-0.811290\pi$
$659$	−330122.	+	190596.i	−0.760158	+	0.438877i	0.0691945	+	0.997603i	$0.477957\pi$
$660$	−120697.	−	69684.6i	−0.277083	−	0.159974i
$661$	−708398.	+	408994.i	−1.62134	+	0.936081i	−0.634778	+	0.772694i	$0.718909\pi$
$661$	−708398.	+	408994.i	−1.62134	+	0.936081i	−0.986562	+	0.163387i	$0.947758\pi$
$662$	244638.	−	423726.i	0.558224	−	0.966872i
$663$	−36064.2	+	62465.1i	−0.0820445	+	0.142105i
$664$			250520.i			0.568207i
$665$	22123.7	−	172529.i	0.0500281	−	0.390139i
$666$	112042.			0.252599
$667$	−313983.	−	181278.i	−0.705756	−	0.407468i
$668$	242913.	+	140246.i	0.544374	+	0.314294i
$669$	−43151.6	−	74740.7i	−0.0964150	−	0.166996i
$670$	223182.	−	386562.i	0.497175	−	0.861132i
$671$	100211.	+	173570.i	0.222571	+	0.385504i
$672$	−31919.2			−0.0706828
$673$		−	664229.i		−	1.46652i	−0.679949	−	0.733259i	$-0.737998\pi$
$673$		−	664229.i		−	1.46652i	0.679949	−	0.733259i	$-0.262002\pi$
$674$	494725.	+	856888.i	1.08904	+	1.88627i
$675$	263272.	−	152000.i	0.577827	−	0.333609i
$676$	−395612.			−0.865718
$677$		−	127191.i		−	0.277510i	−0.990327	−	0.138755i	$-0.955690\pi$
$677$		−	127191.i		−	0.277510i	0.990327	−	0.138755i	$-0.0443101\pi$
$678$	159728.	−	92219.1i	0.347474	−	0.200614i
$679$	−44489.9	−	25686.3i	−0.0964988	−	0.0557136i
$680$	−348765.	+	201359.i	−0.754249	+	0.435466i
$681$	−28247.4	+	48925.9i	−0.0609093	+	0.105498i
$682$	−490943.	+	850337.i	−1.05551	+	1.82820i
$683$			787948.i			1.68910i	0.535474	+	0.844552i	$0.320133\pi$
$683$			787948.i			1.68910i	−0.535474	+	0.844552i	$0.679867\pi$
$684$	71227.0	−	555456.i	0.152241	−	1.18724i
$685$	−520608.			−1.10951
$686$	−287300.	−	165873.i	−0.610502	−	0.352474i
$687$	−148504.	−	85738.7i	−0.314647	−	0.181662i
$688$	200237.	+	346820.i	0.423025	+	0.732701i
$689$	−5892.03	+	10205.3i	−0.0124116	+	0.0214975i
$690$	76788.7	+	133002.i	0.161287	+	0.279357i
$691$	534905.			1.12026			0.560132	−	0.828403i	$-0.310750\pi$
$691$	534905.			1.12026			0.560132	+	0.828403i	$0.310750\pi$
$692$		−	910471.i		−	1.90131i
$693$	−42124.6	−	72962.0i	−0.0877142	−	0.151925i
$694$	−571503.	+	329957.i	−1.18659	+	0.685076i
$695$	−575232.			−1.19090
$696$			48486.3i			0.100092i
$697$	770420.	−	444802.i	1.58585	−	0.915591i
$698$	527591.	+	304605.i	1.08290	+	0.625210i
$699$	141706.	−	81814.1i	0.290024	−	0.167446i
$700$	−121743.	+	210864.i	−0.248454	+	0.430336i
$701$	217033.	−	375912.i	0.441661	−	0.764980i	−0.556152	−	0.831081i	$-0.687723\pi$
$701$	217033.	−	375912.i	0.441661	−	0.764980i	0.997813	+	0.0661010i	$0.0210560\pi$
$702$			166793.i			0.338458i
$703$	−33548.2	−	80228.2i	−0.0678827	−	0.162337i
$704$	−534307.			−1.07807
$705$	107645.	+	62149.0i	0.216579	+	0.125042i
$706$	277492.	+	160210.i	0.556726	+	0.321426i
$707$	−7116.70	−	12326.5i	−0.0142377	−	0.0246604i
$708$	74022.1	−	128210.i	0.147671	−	0.255773i
$709$	−77731.4	−	134635.i	−0.154634	−	0.267833i	0.778292	−	0.627903i	$-0.216086\pi$
$709$	−77731.4	−	134635.i	−0.154634	−	0.267833i	−0.932926	+	0.360069i	$0.882753\pi$
$710$	280043.			0.555531
$711$		−	9301.56i		−	0.0183999i
$712$	9199.88	+	15934.7i	0.0181477	+	0.0314328i
$713$	520745.	−	300652.i	1.02434	−	0.591406i
$714$	54735.9			0.107368
$715$			349273.i			0.683208i
$716$	−1.04642e6	+	604152.i	−2.04118	+	1.17847i
$717$	−131165.	−	75728.1i	−0.255141	−	0.147305i
$718$	783852.	−	452557.i	1.52050	−	0.877859i
$719$	−201992.	+	349860.i	−0.390730	+	0.676763i	−0.992546	−	0.121871i	$-0.961111\pi$
$719$	−201992.	+	349860.i	−0.390730	+	0.676763i	0.601816	+	0.798634i	$0.294444\pi$
$720$	276540.	−	478982.i	0.533450	−	0.923962i
$721$		−	77279.4i		−	0.148660i
$722$	−754062.	+	207498.i	−1.44655	+	0.398052i
$723$	140423.			0.268635
$724$	−187385.	−	108187.i	−0.357484	−	0.206394i
$725$	−956100.	−	552004.i	−1.81898	−	1.05019i
$726$	−35002.3	−	60625.8i	−0.0664085	−	0.115023i
$727$	−249536.	+	432209.i	−0.472133	+	0.817758i	−0.999492	−	0.0318847i	$-0.989849\pi$
$727$	−249536.	+	432209.i	−0.472133	+	0.817758i	0.527359	+	0.849643i	$0.323182\pi$
$728$	−13399.5	−	23208.6i	−0.0252828	−	0.0437911i
$729$	398735.			0.750289
$730$			1.20747e6i			2.26584i
$731$	−468964.	−	812270.i	−0.877617	−	1.52008i
$732$	−70861.5	+	40911.9i	−0.132248	+	0.0763532i
$733$	−759297.			−1.41320			−0.706601	−	0.707613i	$-0.749772\pi$
$733$	−759297.			−1.41320			−0.706601	+	0.707613i	$0.749772\pi$
$734$			1.07478e6i			1.99493i
$735$	−148705.	+	85854.9i	−0.275265	+	0.158924i
$736$	419984.	+	242478.i	0.775313	+	0.447627i
$737$	−145318.	+	83899.6i	−0.267538	+	0.154463i
$738$	502948.	−	871132.i	0.923444	−	1.59945i
$739$	159220.	−	275777.i	0.291547	−	0.504974i	−0.682629	−	0.730765i	$-0.739163\pi$
$739$	159220.	−	275777.i	0.291547	−	0.504974i	0.974176	+	0.225791i	$0.0724967\pi$
$740$			195893.i			0.357730i
$741$	58399.6	−	24420.4i	0.106359	−	0.0444750i
$742$	8942.54			0.0162425
$743$	−23527.3	−	13583.5i	−0.0426182	−	0.0246056i	0.478540	−	0.878066i	$-0.341166\pi$
$743$	−23527.3	−	13583.5i	−0.0426182	−	0.0246056i	−0.521158	+	0.853460i	$0.674500\pi$
$744$	−69641.6	−	40207.6i	−0.125812	−	0.0726377i
$745$	114844.	+	198915.i	0.206917	+	0.358390i
$746$	247574.	−	428810.i	0.444863	−	0.770526i
$747$	402899.	+	697841.i	0.722029	+	1.25059i
$748$	754677.			1.34883
$749$			126591.i			0.225652i
$750$	91361.4	+	158243.i	0.162420	+	0.281320i
$751$	303584.	−	175275.i	0.538269	−	0.310770i	−0.206108	−	0.978529i	$-0.566080\pi$
$751$	303584.	−	175275.i	0.538269	−	0.310770i	0.744377	+	0.667759i	$0.232746\pi$
$752$	287384.			0.508191
$753$		−	12566.2i		−	0.0221623i
$754$	524574.	−	302863.i	0.922708	−	0.532726i
$755$	917714.	+	529842.i	1.60995	+	0.929507i
$756$	60918.4	−	35171.2i	0.106587	−	0.0615381i
$757$	−300630.	+	520706.i	−0.524614	+	0.908659i	0.474975	+	0.879999i	$0.342457\pi$
$757$	−300630.	+	520706.i	−0.524614	+	0.908659i	−0.999589	+	0.0286594i	$0.990876\pi$
$758$	163615.	−	283389.i	0.284764	−	0.493225i
$759$		−	57733.5i		−	0.100218i
$760$	350555.	+	44952.2i	0.606916	+	0.0778258i
$761$	−222727.			−0.384595			−0.192298	−	0.981337i	$-0.561594\pi$
$761$	−222727.			−0.384595			−0.192298	+	0.981337i	$0.561594\pi$
$762$	16140.4	+	9318.66i	0.0277974	+	0.0160488i
$763$	47562.1	+	27460.0i	0.0816981	+	0.0471684i
$764$	−446845.	−	773958.i	−0.765543	−	1.32596i
$765$	−647672.	+	1.12180e6i	−1.10671	+	1.91687i
$766$	−777347.	−	1.34640e6i	−1.32482	−	2.29466i
$767$	−371014.			−0.630666
$768$			40307.6i			0.0683383i
$769$	−70557.9	−	122210.i	−0.119314	−	0.206659i	0.800182	−	0.599758i	$-0.204736\pi$
$769$	−70557.9	−	122210.i	−0.119314	−	0.206659i	−0.919496	+	0.393099i	$0.871403\pi$
$770$	229542.	−	132526.i	0.387151	−	0.223522i
$771$	35691.9			0.0600428
$772$			530581.i			0.890261i
$773$	604747.	−	349151.i	1.01208	−	0.584325i	0.100280	−	0.994959i	$-0.468026\pi$
$773$	604747.	−	349151.i	1.01208	−	0.584325i	0.911800	+	0.410635i	$0.134693\pi$
$774$	−918453.	−	530269.i	−1.53312	−	0.885145i
$775$	1.58571e6	−	915507.i	2.64009	−	1.52426i
$776$	52190.8	−	90397.1i	0.0866703	−	0.150117i
$777$	2670.55	−	4625.53i	0.00442343	−	0.00766160i
$778$		−	1.11227e6i		−	1.83760i
$779$	−774374.	−	99299.2i	−1.27607	−	0.163633i
$780$	−142594.			−0.234376
$781$	−91170.9	−	52637.5i	−0.149470	−	0.0862966i
$782$	−720199.	−	415807.i	−1.17771	−	0.679952i
$783$	159473.	+	276216.i	0.260114	+	0.450531i
$784$	−198501.	+	343814.i	−0.322947	+	0.559360i
$785$	−579015.	−	1.00288e6i	−0.939617	−	1.62746i
$786$	163493.			0.264639
$787$		−	648228.i		−	1.04659i	−0.852150	−	0.523297i	$-0.824702\pi$
$787$		−	648228.i		−	1.04659i	0.852150	−	0.523297i	$-0.175298\pi$
$788$	395620.	+	685234.i	0.637126	+	1.10354i
$789$	24175.3	−	13957.6i	0.0388345	−	0.0224211i
$790$	29263.1			0.0468885
$791$			194935.i			0.311556i
$792$	148248.	−	85591.2i	0.236341	−	0.136452i
$793$	177586.	+	102529.i	0.282399	+	0.163043i
$794$	−37606.6	+	21712.2i	−0.0596517	+	0.0344399i
$795$	4772.61	−	8266.40i	0.00755130	−	0.0130792i
$796$	292615.	−	506824.i	0.461817	−	0.799891i
$797$			590850.i			0.930166i	0.885267	+	0.465083i	$0.153976\pi$
$797$			590850.i			0.930166i	−0.885267	+	0.465083i	$0.846024\pi$
$798$	−38207.8	−	29114.2i	−0.0599993	−	0.0457192i
$799$	−673068.			−1.05430
$800$	1.27888e6	+	738362.i	1.99825	+	1.15369i
$801$	51253.8	+	29591.4i	0.0798843	+	0.0461212i
$802$	−568962.	−	985472.i	−0.884575	−	1.53213i
$803$	226958.	−	393103.i	0.351977	−	0.609642i
$804$	−34252.8	−	59327.6i	−0.0529888	−	0.0917792i
$805$	−162317.			−0.250480
$806$			1.00461e6i			1.54641i
$807$	−34639.1	−	59996.7i	−0.0531887	−	0.0921256i
$808$	25045.6	−	14460.1i	0.0383627	−	0.0221487i
$809$	25513.8			0.0389833			0.0194916	−	0.999810i	$-0.493795\pi$
$809$	25513.8			0.0389833			0.0194916	+	0.999810i	$0.493795\pi$
$810$			1.39563e6i			2.12717i
$811$	−866398.	+	500215.i	−1.31727	+	0.760528i	−0.983289	−	0.182050i	$-0.941727\pi$
$811$	−866398.	+	500215.i	−1.31727	+	0.760528i	−0.333984	+	0.942579i	$0.608393\pi$
$812$	−221231.	−	127728.i	−0.335532	−	0.193720i
$813$	−28913.4	+	16693.2i	−0.0437440	+	0.0252556i
$814$	66254.6	−	114756.i	0.0999925	−	0.173192i
$815$	−158488.	+	274509.i	−0.238606	+	0.413277i
$816$		−	135081.i		−	0.202869i
$817$	−104693.	+	816439.i	−0.156846	+	1.22315i
$818$	676532.			1.01107
$819$	−74650.3	−	43099.4i	−0.111292	−	0.0642545i
$820$	1.52308e6	+	879350.i	2.26514	+	1.30778i
$821$	416641.	+	721643.i	0.618124	+	1.07062i	0.989828	+	0.142270i	$0.0454403\pi$
$821$	416641.	+	721643.i	0.618124	+	1.07062i	−0.371704	+	0.928351i	$0.621226\pi$
$822$	−71886.1	+	124510.i	−0.106390	+	0.184273i
$823$	87934.5	+	152307.i	0.129825	+	0.224864i	0.923609	−	0.383336i	$-0.125225\pi$
$823$	87934.5	+	152307.i	0.129825	+	0.224864i	−0.793783	+	0.608200i	$0.791892\pi$
$824$	157021.			0.231261
$825$		−	175803.i		−	0.258296i
$826$	140775.	+	243830.i	0.206332	+	0.357377i
$827$	161180.	−	93057.1i	0.235667	−	0.136063i	−0.377517	−	0.926003i	$-0.623222\pi$
$827$	161180.	−	93057.1i	0.235667	−	0.136063i	0.613184	+	0.789940i	$0.289889\pi$
$828$	−522579.			−0.762239
$829$		−	162892.i		−	0.237023i	−0.992953	−	0.118511i	$-0.962188\pi$
$829$		−	162892.i		−	0.237023i	0.992953	−	0.118511i	$-0.0378122\pi$
$830$	−2.19544e6	+	1.26754e6i	−3.18688	+	1.83994i
$831$	8848.10	+	5108.45i	0.0128129	+	0.00739754i
$832$	−473431.	+	273335.i	−0.683927	+	0.394866i
$833$	464900.	−	805231.i	0.669992	−	1.16046i
$834$	−79428.6	+	137574.i	−0.114194	+	0.197791i
$835$			569389.i			0.816650i
$836$	−526794.	−	401415.i	−0.753751	−	0.574355i
$837$	−528977.			−0.755068
$838$	531420.	+	306816.i	0.756746	+	0.436907i
$839$	456896.	+	263789.i	0.649072	+	0.374742i	0.788101	−	0.615546i	$-0.211065\pi$
$839$	456896.	+	263789.i	0.649072	+	0.374742i	−0.139028	+	0.990288i	$0.544398\pi$
$840$	10853.7	+	18799.2i	0.0153823	+	0.0266428i
$841$	225502.	−	390581.i	0.318829	−	0.552228i
$842$	−196154.	−	339749.i	−0.276677	−	0.479219i
$843$	241586.			0.339951
$844$			814363.i			1.14323i
$845$	−401541.	−	695489.i	−0.562362	−	0.974040i
$846$	−659092.	+	380527.i	−0.920885	+	0.531673i
$847$	73988.6			0.103133
$848$		−	22069.1i		−	0.0306897i
$849$	−158001.	+	91221.8i	−0.219202	+	0.126556i
$850$	−2.19306e6	−	1.26616e6i	−3.03537	−	1.75247i
$851$	−70276.6	+	40574.2i	−0.0970402	+	0.0560262i
$852$	21489.8	−	37221.4i	0.0296041	−	0.0512759i
$853$	−81226.1	+	140688.i	−0.111634	+	0.193356i	−0.916429	−	0.400197i	$-0.868942\pi$
$853$	−81226.1	+	140688.i	−0.111634	+	0.193356i	0.804795	+	0.593553i	$0.202275\pi$
$854$		−	155612.i		−	0.213368i
$855$	1.04879e6	−	438562.i	1.43468	−	0.599927i
$856$	−257215.			−0.351034
$857$	784864.	+	453142.i	1.06864	+	0.616982i	0.927811	−	0.373051i	$-0.121689\pi$
$857$	784864.	+	453142.i	1.06864	+	0.616982i	0.140833	+	0.990033i	$0.455022\pi$
$858$	83533.3	+	48228.0i	0.113471	+	0.0655125i
$859$	−178058.	−	308405.i	−0.241310	−	0.417960i	0.719778	−	0.694204i	$-0.244244\pi$
$859$	−178058.	−	308405.i	−0.241310	−	0.417960i	−0.961088	+	0.276244i	$0.910910\pi$
$860$	927117.	−	1.60581e6i	1.25354	−	2.17119i
$861$	−23975.8	−	41527.4i	−0.0323420	−	0.0560181i
$862$	1.89812e6			2.55452
$863$			665333.i			0.893341i	0.894698	+	0.446671i	$0.147390\pi$
$863$			665333.i			0.893341i	−0.894698	+	0.446671i	$0.852610\pi$
$864$	−213311.	−	369466.i	−0.285750	−	0.494934i
$865$	1.60061e6	−	924114.i	2.13921	−	1.23507i
$866$	−904938.			−1.20665
$867$			160210.i			0.213133i
$868$	366915.	−	211838.i	0.486997	−	0.281168i
$869$	−9526.91	−	5500.36i	−0.0126157	−	0.00728370i
$870$	−424911.	+	245322.i	−0.561383	+	0.324115i
$871$	−85841.0	+	148681.i	−0.113151	+	0.195983i
$872$	−55794.7	+	96639.3i	−0.0733770	+	0.127093i
$873$		−	335743.i		−	0.440533i
$874$	281558.	+	673325.i	0.368591	+	0.881458i
$875$	−193121.			−0.252240
$876$	160488.	+	92657.8i	0.209139	+	0.120746i
$877$	358582.	+	207027.i	0.466218	+	0.269171i	0.714655	−	0.699477i	$-0.246584\pi$
$877$	358582.	+	207027.i	0.466218	+	0.269171i	−0.248437	+	0.968648i	$0.579917\pi$
$878$	−310181.	−	537249.i	−0.402371	−	0.696926i
$879$	−84730.5	+	146758.i	−0.109664	+	0.189943i
$880$	−327058.	−	566480.i	−0.422337	−	0.731509i
$881$	−621184.			−0.800329			−0.400164	−	0.916443i	$-0.631047\pi$
$881$	−621184.			−0.800329			−0.400164	+	0.916443i	$0.631047\pi$
$882$		−	1.05135e6i		−	1.35148i
$883$	82968.6	+	143706.i	0.106412	+	0.184312i	0.914314	−	0.405005i	$-0.132730\pi$
$883$	82968.6	+	143706.i	0.106412	+	0.184312i	−0.807902	+	0.589317i	$0.799397\pi$
$884$	668693.	−	386070.i	0.855701	−	0.494039i
$885$	300525.			0.383702
$886$		−	503690.i		−	0.641647i
$887$	702930.	−	405837.i	0.893438	−	0.515827i	0.0183728	−	0.999831i	$-0.494151\pi$
$887$	702930.	−	405837.i	0.893438	−	0.515827i	0.875066	+	0.484004i	$0.160818\pi$
$888$	9398.41	+	5426.17i	0.0119187	+	0.00688126i
$889$	−17058.9	+	9848.99i	−0.0215848	+	0.0124620i
$890$	−93095.9	+	161247.i	−0.117530	+	0.203569i
$891$	262327.	−	454363.i	0.330436	−	0.572332i
$892$			923881.i			1.16115i
$893$	469827.	+	358006.i	0.589163	+	0.448940i
$894$	63431.0			0.0793645
$895$	−2.12420e6	−	1.22641e6i	−2.65186	−	1.53105i
$896$	122715.	+	70849.6i	0.152856	+	0.0882513i
$897$	−29534.7	−	51155.6i	−0.0367069	−	0.0635782i
$898$	−139002.	+	240759.i	−0.172373	+	0.298558i
$899$	960516.	+	1.66366e6i	1.18846	+	2.05848i
$900$	−1.59129e6			−1.96455
$901$			51686.9i			0.0636694i
$902$	−594825.	−	1.03027e6i	−0.731099	−	1.26630i
$903$	−43783.2	+	25278.2i	−0.0536947	+	0.0310007i
$904$	−396079.			−0.484668
$905$		−	439231.i		−	0.536285i
$906$	253438.	−	146322.i	0.308755	−	0.178260i
$907$	−451267.	−	260539.i	−0.548553	−	0.316707i	0.199985	−	0.979799i	$-0.435911\pi$
$907$	−451267.	−	260539.i	−0.548553	−	0.316707i	−0.748538	+	0.663092i	$0.769244\pi$
$908$	523755.	−	302390.i	0.635267	−	0.366772i
$909$	46510.9	−	80559.2i	0.0562894	−	0.0974961i
$910$	135593.	−	234853.i	0.163739	−	0.283605i
$911$		−	1.18826e6i		−	1.43177i	−0.698219	−	0.715885i	$-0.746024\pi$
$911$		−	1.18826e6i		−	1.43177i	0.698219	−	0.715885i	$-0.253976\pi$
$912$	−71850.1	+	94292.1i	−0.0863849	+	0.113367i
$913$	952997.			1.14327
$914$	1.46270e6	+	844488.i	1.75090	+	1.01088i
$915$	−143847.	−	83049.9i	−0.171814	−	0.0991966i
$916$	917838.	+	1.58974e6i	1.09389	+	1.89468i
$917$	−86398.8	+	149647.i	−0.102747	+	0.177963i
$918$	365792.	+	633570.i	0.434059	+	0.751812i
$919$	−1.04891e6			−1.24196			−0.620982	−	0.783825i	$-0.713266\pi$
$919$	−1.04891e6			−1.24196			−0.620982	+	0.783825i	$0.713266\pi$
$920$		−	329805.i		−	0.389657i
$921$	37089.6	+	64241.2i	0.0437254	+	0.0757346i
$922$	−194708.	+	112414.i	−0.229045	+	0.132239i
$923$	−107711.			−0.126432
$924$		−	40678.8i		−	0.0476457i
$925$	−213997.	+	123551.i	−0.250106	+	0.144399i
$926$	1.83238e6	+	1.05793e6i	2.13695	+	1.23377i
$927$	437391.	−	252528.i	0.508992	−	0.293867i
$928$	−774661.	+	1.34175e6i	−0.899531	+	1.55803i
$929$	−219595.	+	380349.i	−0.254443	+	0.440708i	−0.964744	−	0.263190i	$-0.915226\pi$
$929$	−219595.	+	380349.i	−0.254443	+	0.440708i	0.710301	+	0.703898i	$0.248559\pi$
$930$		−	813741.i		−	0.940850i
$931$	−752823.	+	314801.i	−0.868547	+	0.363192i
$932$	−1.75165e6			−2.01658
$933$	−59592.8	−	34405.9i	−0.0684590	−	0.0395249i
$934$	−455107.	−	262756.i	−0.521698	−	0.301203i
$935$	765986.	+	1.32673e6i	0.876188	+	1.51760i
$936$	87571.8	−	151679.i	0.0999568	−	0.173130i
$937$	596424.	+	1.03304e6i	0.679322	+	1.17662i	0.975185	+	0.221391i	$0.0710595\pi$
$937$	596424.	+	1.03304e6i	0.679322	+	1.17662i	−0.295863	+	0.955230i	$0.595607\pi$
$938$	130284.			0.148076
$939$			26060.6i			0.0295565i
$940$	−665309.	−	1.15235e6i	−0.752953	−	1.30415i
$941$	51033.0	−	29463.9i	0.0576331	−	0.0332745i	−0.470907	−	0.882183i	$-0.656073\pi$
$941$	51033.0	−	29463.9i	0.0576331	−	0.0332745i	0.528540	+	0.848909i	$0.322740\pi$
$942$	−319804.			−0.360398
$943$			728539.i			0.819275i
$944$	601741.	−	347415.i	0.675252	−	0.389857i
$945$	123662.	+	71396.6i	0.138476	+	0.0799491i
$946$	−1.08623e6	+	627136.i	−1.21378	+	0.700777i
$947$	738050.	−	1.27834e6i	0.822973	−	1.42543i	−0.0804853	−	0.996756i	$-0.525647\pi$
$947$	738050.	−	1.27834e6i	0.822973	−	1.42543i	0.903458	−	0.428676i	$-0.141020\pi$
$948$	2245.57	−	3889.45i	0.00249868	−	0.00432784i
$949$		−	464420.i		−	0.515677i
$950$	857363.	+	2.05032e6i	0.949987	+	2.27182i
$951$	−100641.			−0.111279
$952$	−101797.	−	58772.4i	−0.112321	−	0.0648484i
$953$	−991668.	−	572540.i	−1.09189	−	0.630406i	−0.157814	−	0.987469i	$-0.550445\pi$
$953$	−991668.	−	572540.i	−1.09189	−	0.630406i	−0.934080	+	0.357063i	$0.883778\pi$
$954$	29221.8	+	50613.7i	0.0321078	+	0.0556123i
$955$	907081.	−	1.57111e6i	0.994579	−	1.72266i
$956$	810675.	+	1.40413e6i	0.887015	+	1.53635i
$957$	184445.			0.201393
$958$		−	723321.i		−	0.788134i
$959$	−75977.1	−	131596.i	−0.0826124	−	0.143089i
$960$	383484.	−	221405.i	0.416107	−	0.240239i
$961$	−2.26254e6			−2.44990
$962$		−	135575.i		−	0.146498i
$963$	−716490.	+	413666.i	−0.772605	+	0.446064i
$964$	−1.30185e6	−	751621.i	−1.40089	−	0.808807i
$965$	−932764.	+	538532.i	−1.00165	+	0.578304i
$966$	−22412.9	+	38820.3i	−0.0240184	+	0.0416011i
$967$	−649895.	+	1.12565e6i	−0.695008	+	1.20379i	0.275169	+	0.961396i	$0.411266\pi$
$967$	−649895.	+	1.12565e6i	−0.695008	+	1.20379i	−0.970178	+	0.242394i	$0.922067\pi$
$968$			150334.i			0.160438i
$969$	168277.	−	220837.i	0.179216	−	0.235193i
$970$	1.05626e6			1.12261
$971$	−1.29278e6	−	746385.i	−1.37115	−	0.791634i	−0.380078	−	0.924955i	$-0.624103\pi$
$971$	−1.29278e6	−	746385.i	−1.37115	−	0.791634i	−0.991073	+	0.133320i	$0.957436\pi$
$972$	601585.	+	347325.i	0.636743	+	0.367624i
$973$	−83948.9	−	145404.i	−0.0886726	−	0.153585i
$974$	288566.	−	499811.i	0.304177	−	0.526851i
$975$	−89935.3	−	155772.i	−0.0946065	−	0.163863i
$976$	−384032.			−0.403151
$977$		−	312170.i		−	0.327041i	−0.986540	−	0.163520i	$-0.947715\pi$
$977$		−	312170.i		−	0.327041i	0.986540	−	0.163520i	$-0.0522849\pi$
$978$	43768.3	+	75808.9i	0.0457596	+	0.0792579i
$979$	60616.6	−	34997.0i	0.0632450	−	0.0365145i
$980$	1.83817e6			1.91396
$981$			358927.i			0.372965i
$982$	1.67222e6	−	965455.i	1.73408	−	1.00117i
$983$	−1.11598e6	−	644313.i	−1.15492	−	0.666791i	−0.204836	−	0.978796i	$-0.565666\pi$
$983$	−1.11598e6	−	644313.i	−1.15492	−	0.666791i	−0.950080	+	0.312005i	$0.898999\pi$
$984$	84377.6	−	48715.4i	0.0871439	−	0.0503126i
$985$	−803096.	+	1.39100e6i	−0.827742	+	1.43369i
$986$	1.32841e6	−	2.30087e6i	1.36640	−	2.36667i
$987$			36279.9i			0.0372419i
$988$	−672125.	−	86187.6i	−0.688551	−	0.0882940i
$989$	768114.			0.785296
$990$	1.50016e6	+	866118.i	1.53062	+	0.883704i
$991$	409692.	+	236536.i	0.417167	+	0.240852i	0.693865	−	0.720105i	$-0.255907\pi$
$991$	409692.	+	236536.i	0.417167	+	0.240852i	−0.276697	+	0.960957i	$0.589240\pi$
$992$	−1.28479e6	−	2.22532e6i	−1.30559	−	2.26135i
$993$	76216.8	−	132011.i	0.0772952	−	0.133879i
$994$	40869.2	+	70787.6i	0.0413641	+	0.0716447i
$995$	1.18800e6			1.19997
$996$			389070.i			0.392201i
$997$	608127.	+	1.05331e6i	0.611792	+	1.05965i	0.990938	+	0.134318i	$0.0428844\pi$
$997$	608127.	+	1.05331e6i	0.611792	+	1.05965i	−0.379146	+	0.925337i	$0.623782\pi$
$998$	−1.69837e6	+	980554.i	−1.70518	+	0.984488i
$999$	71387.5			0.0715305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.5.d.a.8.1	✓	10
3.2	odd	2		171.5.p.a.46.5		10
4.3	odd	2		304.5.r.a.65.3		10
19.12	odd	6	inner	19.5.d.a.12.1	yes	10
57.50	even	6		171.5.p.a.145.5		10
76.31	even	6		304.5.r.a.145.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.1	✓	10	1.1	even	1	trivial
19.5.d.a.12.1	yes	10	19.12	odd	6	inner
171.5.p.a.46.5		10	3.2	odd	2
171.5.p.a.145.5		10	57.50	even	6
304.5.r.a.65.3		10	4.3	odd	2
304.5.r.a.145.3		10	76.31	even	6

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.19724 - 3.00063i) q^{2} +(-1.61920 - 0.934844i) q^{3} +(10.0076 + 17.3336i) q^{4} +(-20.3151 + 35.1867i) q^{5} +(5.61024 + 9.71722i) q^{6} -11.8590 q^{7} -24.0959i q^{8} +(-38.7521 - 67.1207i) q^{9} +O(q^{10})\)	\(q+(-5.19724 - 3.00063i) q^{2} +(-1.61920 - 0.934844i) q^{3} +(10.0076 + 17.3336i) q^{4} +(-20.3151 + 35.1867i) q^{5} +(5.61024 + 9.71722i) q^{6} -11.8590 q^{7} -24.0959i q^{8} +(-38.7521 - 67.1207i) q^{9} +(211.165 - 121.916i) q^{10} -91.6624 q^{11} -37.4220i q^{12} +(-81.2188 + 46.8917i) q^{13} +(61.6343 + 35.5846i) q^{14} +(65.7881 - 37.9828i) q^{15} +(87.8183 - 152.106i) q^{16} +(-205.675 + 356.240i) q^{17} +465.123i q^{18} +(333.054 - 139.270i) q^{19} -813.217 q^{20} +(19.2021 + 11.0863i) q^{21} +(476.392 + 275.045i) q^{22} +(-168.437 - 291.742i) q^{23} +(-22.5259 + 39.0159i) q^{24} +(-512.903 - 888.373i) q^{25} +562.819 q^{26} +296.353i q^{27} +(-118.680 - 205.560i) q^{28} +(932.048 - 538.118i) q^{29} -455.889 q^{30} +1784.95i q^{31} +(-1246.71 + 719.787i) q^{32} +(148.419 + 85.6900i) q^{33} +(2137.89 - 1234.31i) q^{34} +(240.917 - 417.280i) q^{35} +(775.629 - 1343.43i) q^{36} -240.886i q^{37} +(-2148.86 - 275.552i) q^{38} +175.346 q^{39} +(847.854 + 489.508i) q^{40} +(-1872.91 - 1081.32i) q^{41} +(-66.5320 - 115.237i) q^{42} +(-1140.06 + 1974.64i) q^{43} +(-917.318 - 1588.84i) q^{44} +3149.01 q^{45} +2021.67i q^{46} +(818.120 + 1417.03i) q^{47} +(-284.390 + 164.193i) q^{48} -2260.36 q^{49} +6156.12i q^{50} +(666.057 - 384.548i) q^{51} +(-1625.61 - 938.544i) q^{52} +(108.818 - 62.8260i) q^{53} +(889.247 - 1540.22i) q^{54} +(1862.13 - 3225.30i) q^{55} +285.754i q^{56} +(-669.475 - 85.8478i) q^{57} -6458.78 q^{58} +(3426.06 + 1978.03i) q^{59} +(1316.76 + 760.231i) q^{60} +(-1093.26 - 1893.58i) q^{61} +(5355.99 - 9276.84i) q^{62} +(459.563 + 795.986i) q^{63} +5829.08 q^{64} -3810.43i q^{65} +(-514.248 - 890.704i) q^{66} +(1585.36 - 915.311i) q^{67} -8233.23 q^{68} +629.849i q^{69} +(-2504.21 + 1445.81i) q^{70} +(994.638 + 574.254i) q^{71} +(-1617.33 + 933.766i) q^{72} +(-2476.02 + 4288.59i) q^{73} +(-722.811 + 1251.95i) q^{74} +1917.93i q^{75} +(5747.11 + 4379.27i) q^{76} +1087.03 q^{77} +(-911.314 - 526.148i) q^{78} +(103.935 + 60.0068i) q^{79} +(3568.07 + 6180.07i) q^{80} +(-2861.88 + 4956.92i) q^{81} +(6489.30 + 11239.8i) q^{82} -10396.8 q^{83} +443.789i q^{84} +(-8356.60 - 14474.1i) q^{85} +(11850.4 - 6841.81i) q^{86} -2012.23 q^{87} +2208.68i q^{88} +(-661.303 + 381.804i) q^{89} +(-16366.2 - 9449.00i) q^{90} +(963.177 - 556.091i) q^{91} +(3371.29 - 5839.25i) q^{92} +(1668.65 - 2890.19i) q^{93} -9819.51i q^{94} +(-1865.56 + 14548.3i) q^{95} +2691.55 q^{96} +(3751.56 + 2165.96i) q^{97} +(11747.7 + 6782.51i) q^{98} +(3552.11 + 6152.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Introduction

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