LMFDB - Embedded newform 153.4.r.a.25.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(25,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([16, 15]))

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

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

chi := DirichletCharacter("153.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.r (of order $24$, degree $8$, 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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			25.16
Character	$\chi$	$=$	153.25
Dual form			153.4.r.a.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.644442 - 2.40509i) q^{2} +(-4.50009 + 2.59792i) q^{3} +(1.55905 - 0.900121i) q^{4} +(-0.693294 - 5.26609i) q^{5} +(9.14828 + 9.14891i) q^{6} +(-4.07107 + 30.9228i) q^{7} +(-17.2548 - 17.2548i) q^{8} +(13.5016 - 23.3818i) q^{9} +(-12.2186 + 5.06113i) q^{10} +(51.3852 + 6.76499i) q^{11} +(-4.67745 + 8.10093i) q^{12} +(-25.8403 + 14.9189i) q^{13} +(76.9957 - 10.1367i) q^{14} +(16.8008 + 21.8968i) q^{15} +(-23.1786 + 40.1465i) q^{16} +(37.6485 + 59.1235i) q^{17} +(-64.9362 - 17.4044i) q^{18} +(75.5553 - 75.5553i) q^{19} +(-5.82100 - 7.58608i) q^{20} +(-62.0149 - 149.732i) q^{21} +(-16.8444 - 127.946i) q^{22} +(77.0129 - 100.365i) q^{23} +(122.475 + 32.8215i) q^{24} +(93.4896 - 25.0505i) q^{25} +(52.5338 + 52.5338i) q^{26} +(-0.0145624 + 140.296i) q^{27} +(21.4873 + 51.8748i) q^{28} +(124.078 - 95.2081i) q^{29} +(41.8366 - 54.5186i) q^{30} +(70.8943 - 9.33342i) q^{31} +(-77.0704 - 20.6510i) q^{32} +(-248.813 + 103.052i) q^{33} +(117.935 - 128.650i) q^{34} +165.665 q^{35} +(0.00336349 - 48.6065i) q^{36} +(-16.3655 + 39.5099i) q^{37} +(-230.408 - 133.026i) q^{38} +(77.5254 - 134.267i) q^{39} +(-78.9026 + 102.828i) q^{40} +(127.240 + 97.6344i) q^{41} +(-320.153 + 245.645i) q^{42} +(-102.396 + 27.4370i) q^{43} +(86.2017 - 35.7059i) q^{44} +(-132.491 - 54.8904i) q^{45} +(-291.017 - 120.543i) q^{46} +(395.994 + 228.627i) q^{47} +(0.00833421 - 240.879i) q^{48} +(-608.335 - 163.003i) q^{49} +(-120.497 - 208.707i) q^{50} +(-323.020 - 168.253i) q^{51} +(-26.8576 + 46.5187i) q^{52} +(-162.677 + 162.677i) q^{53} +(337.434 - 90.3776i) q^{54} -275.290i q^{55} +(603.811 - 463.321i) q^{56} +(-143.719 + 536.292i) q^{57} +(-308.945 - 237.062i) q^{58} +(-116.184 + 433.606i) q^{59} +(45.9031 + 19.0155i) q^{60} +(-102.755 + 780.499i) q^{61} +(-68.1350 - 164.492i) q^{62} +(668.064 + 512.697i) q^{63} +569.527i q^{64} +(96.4791 + 125.734i) q^{65} +(408.194 + 532.007i) q^{66} +(171.476 + 297.005i) q^{67} +(111.914 + 58.2886i) q^{68} +(-85.8242 + 651.725i) q^{69} +(-106.761 - 398.439i) q^{70} +(224.611 - 542.258i) q^{71} +(-636.414 + 170.479i) q^{72} +(-384.912 - 159.436i) q^{73} +(105.572 + 13.8988i) q^{74} +(-355.633 + 355.608i) q^{75} +(49.7860 - 185.804i) q^{76} +(-418.385 + 1561.44i) q^{77} +(-372.885 - 99.9281i) q^{78} +(959.705 + 126.348i) q^{79} +(227.485 + 94.2273i) q^{80} +(-364.413 - 631.383i) q^{81} +(152.821 - 368.942i) q^{82} +(-332.230 - 1239.90i) q^{83} +(-231.461 - 177.619i) q^{84} +(285.249 - 239.251i) q^{85} +(131.977 + 228.590i) q^{86} +(-311.017 + 750.789i) q^{87} +(-769.912 - 1003.37i) q^{88} +315.006i q^{89} +(-46.6334 + 354.027i) q^{90} +(-356.136 - 859.789i) q^{91} +(29.7266 - 225.796i) q^{92} +(-294.783 + 226.179i) q^{93} +(294.674 - 1099.74i) q^{94} +(-450.263 - 345.499i) q^{95} +(400.473 - 107.292i) q^{96} +(406.495 - 311.915i) q^{97} +1568.14i q^{98} +(851.961 - 1110.14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 80 q^{8} + 52 q^{9} - 16 q^{10} + 96 q^{11} - 212 q^{12} - 4 q^{14} - 256 q^{15} + 2936 q^{16} - 16 q^{17} - 240 q^{18} - 16 q^{19} - 516 q^{20}+ \cdots - 18916 q^{99}+O(q^{100}) $ 416 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 80 * q^8 + 52 * q^9 - 16 * q^10 + 96 * q^11 - 212 * q^12 - 4 * q^14 - 256 * q^15 + 2936 * q^16 - 16 * q^17 - 240 * q^18 - 16 * q^19 - 516 * q^20 - 4 * q^22 - 172 * q^23 + 1216 * q^24 - 4 * q^25 - 80 * q^26 + 544 * q^27 - 528 * q^28 - 4 * q^29 - 4 * q^31 + 316 * q^32 - 512 * q^33 - 796 * q^34 - 4512 * q^35 + 328 * q^36 - 16 * q^37 + 1148 * q^39 + 252 * q^40 + 956 * q^41 + 3648 * q^42 - 688 * q^43 - 1040 * q^44 - 1240 * q^45 + 128 * q^46 + 528 * q^48 - 4 * q^49 - 5288 * q^50 - 352 * q^51 - 1032 * q^52 - 1424 * q^53 + 1708 * q^54 + 284 * q^56 + 4372 * q^57 - 4 * q^58 + 56 * q^59 - 3248 * q^60 - 4 * q^61 + 5168 * q^62 + 1008 * q^63 - 2284 * q^65 - 7516 * q^66 - 8 * q^67 + 252 * q^68 + 6224 * q^69 - 36 * q^70 + 624 * q^71 - 16 * q^73 - 3644 * q^74 - 508 * q^75 + 188 * q^76 + 1772 * q^77 - 10080 * q^78 - 4 * q^79 + 472 * q^80 + 3296 * q^82 + 4364 * q^83 + 8632 * q^84 + 3308 * q^85 + 1312 * q^86 + 4376 * q^87 - 1380 * q^88 - 15160 * q^90 - 4776 * q^91 - 1748 * q^92 - 1720 * q^93 - 68 * q^94 + 4436 * q^95 - 2196 * q^96 + 104 * q^97 - 18916 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.644442	−	2.40509i	−0.227845	−	0.850327i	−0.981245	−	0.192765i	$-0.938254\pi$
$2$	−0.644442	−	2.40509i	−0.227845	−	0.850327i	0.753400	−	0.657562i	$-0.228412\pi$
$3$	−4.50009	+	2.59792i	−0.866043	+	0.499970i
$3$	−4.50009	+	2.59792i	−0.866043	+	0.499970i
$4$	1.55905	−	0.900121i	0.194882	−	0.112515i
$5$	−0.693294	−	5.26609i	−0.0620101	−	0.471014i	−0.994073	−	0.108717i	$-0.965326\pi$
$5$	−0.693294	−	5.26609i	−0.0620101	−	0.471014i	0.932063	−	0.362297i	$-0.118007\pi$
$6$	9.14828	+	9.14891i	0.622461	+	0.622504i
$7$	−4.07107	+	30.9228i	−0.219817	+	1.66968i	0.424890	+	0.905245i	$0.360313\pi$
$7$	−4.07107	+	30.9228i	−0.219817	+	1.66968i	−0.644707	+	0.764430i	$0.723020\pi$
$8$	−17.2548	−	17.2548i	−0.762560	−	0.762560i
$9$	13.5016	−	23.3818i	0.500060	−	0.865991i
$10$	−12.2186	+	5.06113i	−0.386387	+	0.160047i
$11$	51.3852	+	6.76499i	1.40848	+	0.185429i	0.796113	−	0.605148i	$-0.206886\pi$
$11$	51.3852	+	6.76499i	1.40848	+	0.185429i	0.612362	+	0.790577i	$0.290219\pi$
$12$	−4.67745	+	8.10093i	−0.112522	+	0.194878i
$13$	−25.8403	+	14.9189i	−0.551292	+	0.318289i	−0.749643	−	0.661842i	$-0.769775\pi$
$13$	−25.8403	+	14.9189i	−0.551292	+	0.318289i	0.198351	+	0.980131i	$0.436441\pi$
$14$	76.9957	−	10.1367i	1.46985	−	0.193510i
$15$	16.8008	+	21.8968i	0.289196	+	0.376915i
$16$	−23.1786	+	40.1465i	−0.362166	+	0.627289i
$17$	37.6485	+	59.1235i	0.537124	+	0.843504i
$17$	37.6485	+	59.1235i	0.537124	+	0.843504i
$18$	−64.9362	−	17.4044i	−0.850312	−	0.227903i
$19$	75.5553	−	75.5553i	0.912293	−	0.912293i	−0.0841590	−	0.996452i	$-0.526820\pi$
$19$	75.5553	−	75.5553i	0.912293	−	0.912293i	0.996452	+	0.0841590i	$0.0268204\pi$
$20$	−5.82100	−	7.58608i	−0.0650808	−	0.0848150i
$21$	−62.0149	−	149.732i	−0.644417	−	1.55591i
$22$	−16.8444	−	127.946i	−0.163238	−	1.23991i
$23$	77.0129	−	100.365i	0.698187	−	0.909894i	−0.300855	−	0.953670i	$-0.597272\pi$
$23$	77.0129	−	100.365i	0.698187	−	0.909894i	0.999041	+	0.0437755i	$0.0139386\pi$
$24$	122.475	+	32.8215i	1.04167	+	0.279152i
$25$	93.4896	−	25.0505i	0.747917	−	0.200404i
$26$	52.5338	+	52.5338i	0.396258	+	0.396258i
$27$	−0.0145624	+	140.296i	−0.000103797	+	1.00000i
$28$	21.4873	+	51.8748i	0.145025	+	0.350122i
$29$	124.078	−	95.2081i	0.794505	−	0.609645i	−0.129695	−	0.991554i	$-0.541400\pi$
$29$	124.078	−	95.2081i	0.794505	−	0.609645i	0.924200	+	0.381909i	$0.124733\pi$
$30$	41.8366	−	54.5186i	0.254609	−	0.331789i
$31$	70.8943	−	9.33342i	0.410742	−	0.0540752i	0.0776758	−	0.996979i	$-0.475250\pi$
$31$	70.8943	−	9.33342i	0.410742	−	0.0540752i	0.333066	+	0.942903i	$0.391917\pi$
$32$	−77.0704	−	20.6510i	−0.425758	−	0.114082i
$33$	−248.813	+	103.052i	−1.31251	+	0.543606i
$34$	117.935	−	128.650i	0.594873	−	0.648919i
$35$	165.665			0.800071
$36$	0.00336349	−	48.6065i	1.55717e−5	−	0.225030i
$37$	−16.3655	+	39.5099i	−0.0727157	+	0.175551i	−0.956058	−	0.293177i	$-0.905288\pi$
$37$	−16.3655	+	39.5099i	−0.0727157	+	0.175551i	0.883343	+	0.468728i	$0.155288\pi$
$38$	−230.408	−	133.026i	−0.983609	−	0.567887i
$39$	77.5254	−	134.267i	0.318308	−	0.551281i
$40$	−78.9026	+	102.828i	−0.311890	+	0.406463i
$41$	127.240	+	97.6344i	0.484671	+	0.371901i	0.822002	−	0.569485i	$-0.192857\pi$
$41$	127.240	+	97.6344i	0.484671	+	0.371901i	−0.337331	+	0.941386i	$0.609524\pi$
$42$	−320.153	+	245.645i	−1.17621	+	0.902471i
$43$	−102.396	+	27.4370i	−0.363146	+	0.0973046i	−0.435778	−	0.900054i	$-0.643527\pi$
$43$	−102.396	+	27.4370i	−0.363146	+	0.0973046i	0.0726323	+	0.997359i	$0.476860\pi$
$44$	86.2017	−	35.7059i	0.295350	−	0.122338i
$45$	−132.491	−	54.8904i	−0.438902	−	0.181835i
$46$	−291.017	−	120.543i	−0.932786	−	0.386373i
$47$	395.994	+	228.627i	1.22897	+	0.709547i	0.966815	−	0.255478i	$-0.0822328\pi$
$47$	395.994	+	228.627i	1.22897	+	0.709547i	0.262157	+	0.965025i	$0.415566\pi$
$48$	0.00833421	−	240.879i	2.50612e−5	−	0.724331i
$49$	−608.335	−	163.003i	−1.77357	−	0.475227i
$50$	−120.497	−	208.707i	−0.340818	−	0.590314i
$51$	−323.020	−	168.253i	−0.886899	−	0.461964i
$52$	−26.8576	+	46.5187i	−0.0716246	+	0.124057i
$53$	−162.677	+	162.677i	−0.421611	+	0.421611i	−0.885758	−	0.464147i	$-0.846361\pi$
$53$	−162.677	+	162.677i	−0.421611	+	0.421611i	0.464147	+	0.885758i	$0.346361\pi$
$54$	337.434	−	90.3776i	0.850351	−	0.227756i
$55$		−	275.290i		−	0.674910i
$56$	603.811	−	463.321i	1.44085	−	1.10560i
$57$	−143.719	+	536.292i	−0.333966	+	1.24620i
$58$	−308.945	−	237.062i	−0.699421	−	0.536685i
$59$	−116.184	+	433.606i	−0.256371	+	0.956791i	0.710951	+	0.703242i	$0.248265\pi$
$59$	−116.184	+	433.606i	−0.256371	+	0.956791i	−0.967322	+	0.253550i	$0.918402\pi$
$60$	45.9031	+	19.0155i	0.0987677	+	0.0409149i
$61$	−102.755	+	780.499i	−0.215678	+	1.63824i	0.450735	+	0.892658i	$0.351162\pi$
$61$	−102.755	+	780.499i	−0.215678	+	1.63824i	−0.666414	+	0.745582i	$0.732171\pi$
$62$	−68.1350	−	164.492i	−0.139567	−	0.336944i
$63$	668.064	+	512.697i	1.33600	+	1.02530i
$64$			569.527i			1.11236i
$65$	96.4791	+	125.734i	0.184104	+	0.239929i
$66$	408.194	+	532.007i	0.761291	+	0.992205i
$67$	171.476	+	297.005i	0.312674	+	0.541567i	0.978940	−	0.204147i	$-0.0654420\pi$
$67$	171.476	+	297.005i	0.312674	+	0.541567i	−0.666266	+	0.745714i	$0.732109\pi$
$68$	111.914	+	58.2886i	0.199583	+	0.103949i
$69$	−85.8242	+	651.725i	−0.149739	+	1.13708i
$70$	−106.761	−	398.439i	−0.182292	−	0.680322i
$71$	224.611	−	542.258i	0.375442	−	0.906397i	−0.617366	−	0.786676i	$-0.711800\pi$
$71$	224.611	−	542.258i	0.375442	−	0.906397i	0.992808	−	0.119721i	$-0.0381999\pi$
$72$	−636.414	+	170.479i	−1.04170	+	0.279044i
$73$	−384.912	−	159.436i	−0.617131	−	0.255624i	0.0521430	−	0.998640i	$-0.483395\pi$
$73$	−384.912	−	159.436i	−0.617131	−	0.255624i	−0.669274	+	0.743015i	$0.733395\pi$
$74$	105.572	+	13.8988i	0.165844	+	0.0218338i
$75$	−355.633	+	355.608i	−0.547532	+	0.547494i
$76$	49.7860	−	185.804i	0.0751427	−	0.280436i
$77$	−418.385	+	1561.44i	−0.619213	+	2.31094i
$78$	−372.885	−	99.9281i	−0.541294	−	0.145059i
$79$	959.705	+	126.348i	1.36678	+	0.179939i	0.777953	−	0.628323i	$-0.216258\pi$
$79$	959.705	+	126.348i	1.36678	+	0.179939i	0.588823	+	0.808262i	$0.299592\pi$
$80$	227.485	+	94.2273i	0.317920	+	0.131687i
$81$	−364.413	−	631.383i	−0.499880	−	0.866095i
$82$	152.821	−	368.942i	0.205808	−	0.496864i
$83$	−332.230	−	1239.90i	−0.439361	−	1.63972i	−0.730409	−	0.683010i	$-0.760670\pi$
$83$	−332.230	−	1239.90i	−0.439361	−	1.63972i	0.291047	−	0.956709i	$-0.405996\pi$
$84$	−231.461	−	177.619i	−0.300649	−	0.230712i
$85$	285.249	−	239.251i	0.363995	−	0.305298i
$86$	131.977	+	228.590i	0.165481	+	0.286622i
$87$	−311.017	+	750.789i	−0.383271	+	0.925207i
$88$	−769.912	−	1003.37i	−0.932646	−	1.21545i
$89$			315.006i			0.375175i	0.982248	+	0.187588i	$0.0600668\pi$
$89$			315.006i			0.375175i	−0.982248	+	0.187588i	$0.939933\pi$
$90$	−46.6334	+	354.027i	−0.0546177	+	0.414641i
$91$	−356.136	−	859.789i	−0.410255	−	0.990444i
$92$	29.7266	−	225.796i	0.0336870	−	0.255878i
$93$	−294.783	+	226.179i	−0.328684	+	0.252190i
$94$	294.674	−	1099.74i	0.323333	−	1.20670i
$95$	−450.263	−	345.499i	−0.486274	−	0.373131i
$96$	400.473	−	107.292i	0.425762	−	0.114067i
$97$	406.495	−	311.915i	0.425498	−	0.326496i	−0.373715	−	0.927543i	$-0.621916\pi$
$97$	406.495	−	311.915i	0.425498	−	0.326496i	0.799213	+	0.601047i	$0.205250\pi$
$98$			1568.14i			1.61639i
$99$	851.961	−	1110.14i	0.864902	−	1.12700i
$100$	123.207	−	123.207i	0.123207	−	0.123207i
$101$	335.866	−	581.736i	0.330890	−	0.573118i	−0.651797	−	0.758394i	$-0.725984\pi$
$101$	335.866	−	581.736i	0.330890	−	0.573118i	0.982687	+	0.185276i	$0.0593178\pi$
$102$	−196.497	+	885.321i	−0.190746	+	0.859410i
$103$	16.6649	+	28.8644i	0.0159421	+	0.0276126i	0.873886	−	0.486130i	$-0.161592\pi$
$103$	16.6649	+	28.8644i	0.0159421	+	0.0276126i	−0.857944	+	0.513743i	$0.828259\pi$
$104$	703.289	+	188.446i	0.663108	+	0.177679i
$105$	−745.507	+	430.384i	−0.692896	+	0.400011i
$106$	496.088	+	286.417i	0.454569	+	0.262446i
$107$	−224.204	−	92.8685i	−0.202567	−	0.0839060i	0.279093	−	0.960264i	$-0.409966\pi$
$107$	−224.204	−	92.8685i	−0.202567	−	0.0839060i	−0.481660	+	0.876358i	$0.659966\pi$
$108$	126.261	+	218.742i	0.112495	+	0.194894i
$109$	−1733.88	+	718.199i	−1.52363	+	0.631110i	−0.978316	−	0.207120i	$-0.933591\pi$
$109$	−1733.88	+	718.199i	−1.52363	+	0.631110i	−0.545318	+	0.838229i	$0.683591\pi$
$110$	−662.096	+	177.408i	−0.573894	+	0.153775i
$111$	−28.9972	−	220.315i	−0.0247954	−	0.188390i
$112$	−1147.08	−	880.187i	−0.967759	−	0.742588i
$113$	176.125	−	229.531i	0.146624	−	0.191084i	−0.714267	−	0.699873i	$-0.753240\pi$
$113$	176.125	−	229.531i	0.146624	−	0.191084i	0.860891	+	0.508789i	$0.169907\pi$
$114$	1382.45	+	0.0478316i	1.13577	+	3.92968e-5i
$115$	−581.925	−	335.974i	−0.471867	−	0.272433i
$116$	107.745	−	260.120i	0.0862403	−	0.208203i
$117$	−0.0557475	+	805.619i	−4.40501e−5	+	0.636577i
$118$	1117.74			0.871999
$119$	−1981.54	+	923.502i	−1.52645	+	0.711406i
$120$	87.9302	−	667.717i	0.0668907	−	0.507950i
$121$	1309.03	+	350.753i	0.983493	+	0.263526i
$122$	1943.39	−	255.852i	1.44218	−	0.189867i
$123$	−826.236	−	108.805i	−0.605685	−	0.0797612i
$124$	102.127	−	78.3648i	0.0739619	−	0.0567529i
$125$	−450.814	−	1088.36i	−0.322576	−	0.778767i
$126$	802.553	−	1937.16i	0.567438	−	1.36965i
$127$	−545.373	−	545.373i	−0.381056	−	0.381056i	0.490427	−	0.871482i	$-0.336841\pi$
$127$	−545.373	−	545.373i	−0.381056	−	0.381056i	−0.871482	+	0.490427i	$0.836841\pi$
$128$	753.200	−	201.819i	0.520110	−	0.139363i
$129$	389.513	−	389.486i	0.265850	−	0.265832i
$130$	240.226	−	313.069i	0.162071	−	0.211215i
$131$	−22.4067	−	170.195i	−0.0149441	−	0.113512i	0.982347	−	0.187068i	$-0.0598985\pi$
$131$	−22.4067	−	170.195i	−0.0149441	−	0.113512i	−0.997291	+	0.0735562i	$0.976565\pi$
$132$	−295.154	+	384.625i	−0.194620	+	0.253616i
$133$	2028.79	+	2643.97i	1.32270	+	1.72377i
$134$	603.818	−	603.818i	0.389268	−	0.389268i
$135$	738.823	−	97.1898i	0.471020	−	0.0619612i
$136$	370.547	−	1669.78i	0.233633	−	1.05281i
$137$	802.246	−	1389.53i	0.500295	−	0.866537i	−0.499704	−	0.866196i	$-0.666558\pi$
$137$	802.246	−	1389.53i	0.500295	−	0.866537i	1.00000		0.000341224i	$-0.000108615\pi$
$138$	1622.77	−	213.584i	1.00101	−	0.131750i
$139$	−2760.22	+	363.390i	−1.68431	+	0.221744i	−0.911035	−	0.412328i	$-0.864716\pi$
$139$	−2760.22	+	363.390i	−1.68431	+	0.221744i	−0.773274	+	0.634072i	$0.781382\pi$
$140$	258.281	−	149.118i	0.155919	−	0.0900201i
$141$	−2375.97	−	0.0822064i	−1.41909	−	4.90995e-5i
$142$	−1448.93	−	190.755i	−0.856277	−	0.112731i
$143$	−1428.73	+	591.801i	−0.835501	+	0.346076i
$144$	625.747	+	1084.00i	0.362122	+	0.627314i
$145$	−587.397	−	587.397i	−0.336419	−	0.336419i
$146$	−135.404	+	1028.50i	−0.0767542	+	0.583006i
$147$	3161.03	−	846.878i	1.77359	−	0.475165i
$148$	10.0489	+	76.3291i	0.00558119	+	0.0423933i
$149$	866.865	−	500.485i	0.476620	−	0.275177i	−0.242387	−	0.970180i	$-0.577930\pi$
$149$	866.865	−	500.485i	0.476620	−	0.275177i	0.719007	+	0.695003i	$0.244597\pi$
$150$	1084.45	+	626.160i	0.590302	+	0.340838i
$151$	516.322	+	1926.94i	0.278263	+	1.03849i	0.953623	+	0.301003i	$0.0973213\pi$
$151$	516.322	+	1926.94i	0.278263	+	1.03849i	−0.675361	+	0.737488i	$0.736012\pi$
$152$	−2607.38			−1.39136
$153$	1890.73	−	82.0247i	0.999060	−	0.0433419i
$154$	4025.02			2.10614
$155$	−98.3013	−	366.865i	−0.0509403	−	0.190112i
$156$	0.00965704	−	279.112i	4.95630e−6	−	0.143249i
$157$	2783.59	−	1607.10i	1.41500	−	0.816948i	0.419143	−	0.907920i	$-0.362331\pi$
$157$	2783.59	−	1607.10i	1.41500	−	0.816948i	0.995853	+	0.0909719i	$0.0289973\pi$
$158$	−314.597	−	2389.60i	−0.158405	−	1.20321i
$159$	309.439	−	1154.68i	0.154340	−	0.575926i
$160$	−55.3174	+	420.177i	−0.0273327	+	0.207612i
$161$	2790.05	+	2790.05i	1.36576	+	1.36576i
$162$	−1283.69	+	1283.33i	−0.622569	+	0.622397i
$163$	3282.82	−	1359.79i	1.57748	−	0.653415i	0.589472	−	0.807789i	$-0.299336\pi$
$163$	3282.82	−	1359.79i	1.57748	−	0.653415i	0.988013	+	0.154374i	$0.0493360\pi$
$164$	286.256	+	37.6864i	0.136298	+	0.0179440i
$165$	715.180	+	1238.83i	0.337435	+	0.584501i
$166$	−2767.97	+	1598.09i	−1.29419	+	0.747202i
$167$	−557.204	+	73.3573i	−0.258190	+	0.0339914i	−0.258510	−	0.966009i	$-0.583232\pi$
$167$	−557.204	+	73.3573i	−0.258190	+	0.0339914i	0.000319904		1.00000i	$0.499898\pi$
$168$	−1513.54	+	3653.64i	−0.695070	+	1.67788i
$169$	−653.354	+	1131.64i	−0.297385	+	0.515085i
$170$	−759.245	−	531.865i	−0.342538	−	0.239954i
$171$	−746.496	−	2786.73i	−0.333836	−	1.24624i
$172$	−134.945	+	134.945i	−0.0598223	+	0.0598223i
$173$	1013.15	+	1320.37i	0.445253	+	0.580265i	0.961025	−	0.276461i	$-0.0891616\pi$
$173$	1013.15	+	1320.37i	0.445253	+	0.580265i	−0.515772	+	0.856726i	$0.672495\pi$
$174$	2006.15	+	264.185i	0.874055	+	0.115102i
$175$	394.029	+	2992.95i	0.170204	+	1.29283i
$176$	−1462.63	+	1906.13i	−0.626419	+	0.816365i
$177$	−603.634	−	2253.10i	−0.256338	−	0.956800i
$178$	757.618	−	203.003i	0.319022	−	0.0854816i
$179$	−2643.25	−	2643.25i	−1.10372	−	1.10372i	−0.993958	−	0.109763i	$-0.964991\pi$
$179$	−2643.25	−	2643.25i	−1.10372	−	1.10372i	−0.109763	−	0.993958i	$-0.535009\pi$
$180$	−255.969	+	33.6809i	−0.105993	+	0.0139468i
$181$	42.1025	+	101.644i	0.0172898	+	0.0417412i	0.932289	−	0.361715i	$-0.117809\pi$
$181$	42.1025	+	101.644i	0.0172898	+	0.0417412i	−0.914999	+	0.403456i	$0.867809\pi$
$182$	−1838.36	+	1410.62i	−0.748727	+	0.574519i
$183$	−1565.27	−	3779.26i	−0.632284	−	1.52662i
$184$	−3060.62	+	402.938i	−1.22626	+	0.161440i
$185$	219.409	+	58.7905i	0.0871961	+	0.0233641i
$186$	733.952	+	563.221i	0.289333	+	0.222029i
$187$	1534.61	+	3292.77i	0.600115	+	1.28765i
$188$	823.169			0.319339
$189$	−4338.29	−	571.605i	−1.66965	−	0.219990i
$190$	−540.788	+	1305.58i	−0.206489	+	0.498508i
$191$	72.8484	+	42.0590i	0.0275975	+	0.0159334i	0.513735	−	0.857949i	$-0.328261\pi$
$191$	72.8484	+	42.0590i	0.0275975	+	0.0159334i	−0.486138	+	0.873882i	$0.661595\pi$
$192$	−1479.59	−	2562.92i	−0.556146	−	0.963349i
$193$	−1083.27	+	1411.75i	−0.404019	+	0.526527i	−0.950409	−	0.311004i	$-0.899335\pi$
$193$	−1083.27	+	1411.75i	−0.404019	+	0.526527i	0.546390	+	0.837531i	$0.316002\pi$
$194$	−1012.14	−	776.646i	−0.374576	−	0.287422i
$195$	−760.812	−	315.169i	−0.279399	−	0.115742i
$196$	−1095.15	+	293.444i	−0.399107	+	0.106940i
$197$	−2459.68	+	1018.83i	−0.889569	+	0.368471i	−0.780200	−	0.625530i	$-0.784883\pi$
$197$	−2459.68	+	1018.83i	−0.889569	+	0.368471i	−0.109368	+	0.994001i	$0.534883\pi$
$198$	−3219.02	−	1333.62i	−1.15538	−	0.478669i
$199$	4627.95	+	1916.96i	1.64858	+	0.682862i	0.997121	−	0.0758257i	$-0.0241593\pi$
$199$	4627.95	+	1916.96i	1.64858	+	0.682862i	0.651454	+	0.758688i	$0.274159\pi$
$200$	−2045.38	−	1180.90i	−0.723152	−	0.417512i
$201$	−1543.25	−	891.070i	−0.541556	−	0.312693i
$202$	−1615.57	−	432.892i	−0.562729	−	0.150783i
$203$	2438.98	+	4224.43i	0.843264	+	1.46058i
$204$	−655.054	+	28.4407i	−0.224818	+	0.00976101i
$205$	425.938	−	737.745i	0.145116	−	0.251348i
$206$	58.6820	−	58.6820i	0.0198474	−	0.0198474i
$207$	−1306.91	−	3155.79i	−0.438825	−	1.05962i
$208$		−	1383.19i		−	0.461093i
$209$	4393.56	−	3371.30i	1.45411	−	1.11578i
$210$	1515.55	+	1515.65i	0.498013	+	0.498048i
$211$	−3087.09	−	2368.81i	−1.00722	−	0.772870i	−0.0332306	−	0.999448i	$-0.510580\pi$
$211$	−3087.09	−	2368.81i	−1.00722	−	0.772870i	−0.973993	+	0.226578i	$0.927246\pi$
$212$	−107.193	+	400.051i	−0.0347267	+	0.129602i
$213$	397.975	+	3023.73i	0.128023	+	0.972688i
$214$	−78.8704	+	599.080i	−0.0251938	+	0.191366i
$215$	215.476	+	520.206i	0.0683505	+	0.165013i
$216$	2421.03	−	2420.53i	0.762639	−	0.762481i
$217$			2230.25i			0.697692i
$218$	2844.72	+	3707.31i	0.883801	+	1.15179i
$219$	2146.34	−	282.496i	0.662266	−	0.0871657i
$220$	−247.794	−	429.192i	−0.0759375	−	0.131528i
$221$	−1854.90	−	966.093i	−0.564590	−	0.294056i
$222$	−511.189	+	211.721i	−0.154544	+	0.0640080i
$223$	263.915	+	984.942i	0.0792512	+	0.295770i	0.994164	−	0.107883i	$-0.0344072\pi$
$223$	263.915	+	984.942i	0.0792512	+	0.295770i	−0.914912	+	0.403652i	$0.867740\pi$
$224$	952.345	−	2299.16i	0.284068	−	0.685801i
$225$	676.537	−	2524.17i	0.200456	−	0.747903i
$226$	−665.546	−	275.678i	−0.195891	−	0.0811408i
$227$	−2477.90	−	326.222i	−0.724511	−	0.0953837i	−0.240754	−	0.970586i	$-0.577395\pi$
$227$	−2477.90	−	326.222i	−0.724511	−	0.0953837i	−0.483757	+	0.875202i	$0.660728\pi$
$228$	258.662	+	965.474i	0.0751330	+	0.280439i
$229$	−1316.60	+	4913.63i	−0.379928	+	1.41791i	0.466080	+	0.884742i	$0.345666\pi$
$229$	−1316.60	+	4913.63i	−0.379928	+	1.41791i	−0.846009	+	0.533169i	$0.821001\pi$
$230$	−433.032	+	1616.10i	−0.124145	+	0.463314i
$231$	−2173.71	−	8113.53i	−0.619134	−	2.31096i
$232$	−3783.73	−	498.137i	−1.07075	−	0.140967i
$233$	−1138.09	−	471.411i	−0.319994	−	0.132546i	0.216904	−	0.976193i	$-0.430404\pi$
$233$	−1138.09	−	471.411i	−0.319994	−	0.132546i	−0.536898	+	0.843647i	$0.680404\pi$
$234$	1937.62	−	519.041i	0.541309	−	0.145003i
$235$	929.433	−	2243.85i	0.257998	−	0.622862i
$236$	209.160	+	780.596i	0.0576913	+	0.215307i
$237$	−4647.00	+	1924.66i	−1.27365	+	0.527512i
$238$	3498.09	+	4170.63i	0.952720	+	1.13589i
$239$	−2312.20	−	4004.84i	−0.625789	−	1.08390i	−0.988388	−	0.151953i	$-0.951444\pi$
$239$	−2312.20	−	4004.84i	−0.625789	−	1.08390i	0.362599	−	0.931945i	$-0.381889\pi$
$240$	−1268.50	+	166.956i	−0.341172	+	0.0449041i
$241$	−1066.92	−	1390.43i	−0.285170	−	0.371641i	0.628700	−	0.777648i	$-0.283588\pi$
$241$	−1066.92	−	1390.43i	−0.285170	−	0.371641i	−0.913870	+	0.406007i	$0.866921\pi$
$242$		−	3374.37i		−	0.896334i
$243$	3280.17	+	1894.57i	0.865939	+	0.500150i
$244$	542.343	+	1309.33i	0.142295	+	0.343530i
$245$	−436.633	+	3316.56i	−0.113859	+	0.864845i
$246$	270.775	+	2057.29i	0.0701788	+	0.533204i
$247$	−825.168	+	3079.57i	−0.212567	+	0.793313i
$248$	−1384.31	−	1062.22i	−0.354451	−	0.271980i
$249$	4716.23	+	4716.55i	1.20032	+	1.20040i
$250$	−2327.08	+	1785.63i	−0.588710	+	0.451733i
$251$			324.516i			0.0816067i	0.999167	+	0.0408034i	$0.0129917\pi$
$251$			324.516i			0.0816067i	−0.999167	+	0.0408034i	$0.987008\pi$
$252$	1503.04	+	197.984i	0.375724	+	0.0494914i
$253$	4636.29	−	4636.29i	1.15210	−	1.15210i
$254$	−960.210	+	1663.13i	−0.237201	+	0.410843i
$255$	−662.090	+	1817.70i	−0.162595	+	0.446388i
$256$	1307.32	+	2264.35i	0.319170	+	0.552819i
$257$	−6213.67	−	1664.95i	−1.50816	−	0.404111i	−0.592339	−	0.805689i	$-0.701795\pi$
$257$	−6213.67	−	1664.95i	−1.50816	−	0.404111i	−0.915825	+	0.401578i	$0.868462\pi$
$258$	−1187.77	−	685.812i	−0.286617	−	0.165491i
$259$	−1155.13	−	666.916i	−0.277129	−	0.160001i
$260$	263.592	+	109.183i	0.0628742	+	0.0260433i
$261$	−550.884	−	4186.62i	−0.130647	−	0.992893i
$262$	−394.895	+	163.571i	−0.0931173	+	0.0385704i
$263$	−3208.17	+	859.627i	−0.752184	+	0.201547i	−0.614487	−	0.788927i	$-0.710637\pi$
$263$	−3208.17	+	859.627i	−0.752184	+	0.201547i	−0.137697	+	0.990474i	$0.543970\pi$
$264$	6071.35	+	2515.08i	1.41540	+	0.586335i
$265$	969.455	+	743.889i	0.224729	+	0.172440i
$266$	5051.55	−	6583.31i	1.16440	−	1.51748i
$267$	−818.361	−	1417.56i	−0.187576	−	0.324918i
$268$	534.682	+	308.699i	0.121869	+	0.0703611i
$269$	1116.08	−	2694.46i	0.252969	−	0.610721i	−0.745472	−	0.666537i	$-0.767776\pi$
$269$	1116.08	−	2694.46i	0.252969	−	0.610721i	0.998441	+	0.0558155i	$0.0177759\pi$
$270$	−709.878	−	1714.30i	−0.160007	−	0.386404i
$271$	1347.45			0.302036			0.151018	−	0.988531i	$-0.451745\pi$
$271$	1347.45			0.302036			0.151018	+	0.988531i	$0.451745\pi$
$272$	−3246.24	+	141.056i	−0.723648	+	0.0314439i
$273$	3836.31	+	2943.91i	0.850491	+	0.652651i
$274$	−3858.94	−	1034.00i	−0.850830	−	0.227979i
$275$	4973.45	−	654.768i	1.09058	−	0.143578i
$276$	452.827	+	1093.33i	0.0987571	+	0.238444i
$277$	6395.13	−	4907.16i	1.38717	−	1.06441i	0.398041	−	0.917368i	$-0.369690\pi$
$277$	6395.13	−	4907.16i	1.38717	−	1.06441i	0.989130	−	0.147046i	$-0.0469765\pi$
$278$	2652.79	+	6404.40i	0.572315	+	1.38169i
$279$	738.957	−	1783.65i	0.158567	−	0.382740i
$280$	−2858.51	−	2858.51i	−0.610102	−	0.610102i
$281$	−979.067	+	262.340i	−0.207851	+	0.0556936i	−0.361242	−	0.932472i	$-0.617647\pi$
$281$	−979.067	+	262.340i	−0.207851	+	0.0556936i	0.153391	+	0.988166i	$0.450981\pi$
$282$	1530.97	+	5714.46i	0.323291	+	1.20671i
$283$	5539.74	−	7219.53i	1.16362	−	1.51645i	0.348352	−	0.937364i	$-0.386742\pi$
$283$	5539.74	−	7219.53i	1.16362	−	1.51645i	0.815264	−	0.579089i	$-0.196592\pi$
$284$	−137.917	−	1047.59i	−0.0288165	−	0.218883i
$285$	2923.81	+	385.029i	0.607689	+	0.0800251i
$286$	2344.07	+	3054.85i	0.484642	+	0.631598i
$287$	−3537.13	+	3537.13i	−0.727493	+	0.727493i
$288$	−1523.43	+	1523.22i	−0.311698	+	0.311655i
$289$	−2078.18	+	4451.82i	−0.422996	+	0.906131i
$290$	−1034.20	+	1791.29i	−0.209415	+	0.362717i
$291$	−1018.93	+	2459.68i	−0.205261	+	0.495496i
$292$	−743.611	+	97.8983i	−0.149029	+	0.0196201i
$293$	−6777.86	+	3913.20i	−1.35142	+	0.780244i	−0.988449	−	0.151555i	$-0.951572\pi$
$293$	−6777.86	+	3913.20i	−1.35142	+	0.780244i	−0.362974	+	0.931799i	$0.618239\pi$
$294$	−4073.92	−	7056.79i	−0.808148	−	1.39987i
$295$	2363.96	+	311.221i	0.466560	+	0.0614237i
$296$	964.118	−	399.351i	0.189318	−	0.0784183i
$297$	−949.851	+	7209.05i	−0.185576	+	1.40846i
$298$	−1762.35	−	1762.35i	−0.342585	−	0.342585i
$299$	−492.697	+	3742.41i	−0.0952957	+	0.723842i
$300$	−234.361	+	874.525i	−0.0451027	+	0.168302i
$301$	−431.567	−	3278.07i	−0.0826415	−	0.627724i
$302$	4301.72	−	2483.60i	0.819656	−	0.473229i
$303$	−0.120765	+	3490.42i	−2.28970e−5	+	0.661780i
$304$	1282.02	+	4784.55i	0.241871	+	0.902673i
$305$	4181.42			0.785008
$306$	−1415.74	−	4494.51i	−0.264485	−	0.839653i
$307$	−8585.35			−1.59606			−0.798032	−	0.602615i	$-0.794126\pi$
$307$	−8585.35			−1.59606			−0.798032	+	0.602615i	$0.794126\pi$
$308$	753.195	+	2810.96i	0.139342	+	0.520030i
$309$	−149.981	−	86.5985i	−0.0276120	−	0.0159431i
$310$	−818.995	+	472.847i	−0.150051	+	0.0866319i
$311$	81.6608	+	620.275i	0.0148893	+	0.113095i	0.997276	−	0.0737662i	$-0.0235018\pi$
$311$	81.6608	+	620.275i	0.0148893	+	0.113095i	−0.982386	+	0.186861i	$0.940169\pi$
$312$	−3654.43	+	979.067i	−0.663114	+	0.177656i
$313$	−101.433	+	770.458i	−0.0183173	+	0.139134i	−0.998160	−	0.0606376i	$-0.980687\pi$
$313$	−101.433	+	770.458i	−0.0183173	+	0.139134i	0.979843	+	0.199771i	$0.0640199\pi$
$314$	−5659.09	−	5659.09i	−1.01707	−	1.01707i
$315$	2236.74	−	3873.54i	0.400083	−	0.692854i
$316$	1609.96	−	666.868i	0.286606	−	0.118716i
$317$	5732.00	+	754.633i	1.01559	+	0.133705i	0.619900	−	0.784680i	$-0.287173\pi$
$317$	5732.00	+	754.633i	1.01559	+	0.133705i	0.395688	+	0.918385i	$0.370506\pi$
$318$	−2976.53	−	0.102985i	−0.524891	−	1.81608e-5i
$319$	7019.84	−	4052.91i	1.23209	−	0.711345i
$320$	2999.18	−	394.850i	0.523936	−	0.0689775i
$321$	1250.21	−	164.549i	0.217382	−	0.0286112i
$322$	4912.29	−	8508.34i	0.850159	−	1.47252i
$323$	7311.64	+	1622.55i	1.25954	+	0.279508i
$324$	−1136.46	−	656.345i	−0.194866	−	0.112542i
$325$	−2042.07	+	2042.07i	−0.348535	+	0.348535i
$326$	−5385.99	−	7019.16i	−0.915038	−	1.19250i
$327$	5936.81	−	7736.45i	1.00400	−	1.30834i
$328$	−510.832	−	3880.15i	−0.0859938	−	0.653187i
$329$	−8681.92	+	11314.5i	−1.45486	+	1.89601i
$330$	2518.60	−	2518.42i	0.420134	−	0.420105i
$331$	4652.75	−	1246.70i	0.772623	−	0.207024i	0.149093	−	0.988823i	$-0.452365\pi$
$331$	4652.75	−	1246.70i	0.772623	−	0.207024i	0.623530	+	0.781799i	$0.285698\pi$
$332$	−1634.02	−	1634.02i	−0.270117	−	0.270117i
$333$	702.850	+	916.103i	0.115663	+	0.150757i
$334$	535.516	+	1292.85i	0.0877310	+	0.211801i
$335$	1445.18	−	1108.92i	0.235697	−	0.180856i
$336$	7448.63	+	980.892i	1.20939	+	0.159262i
$337$	−2868.88	+	377.695i	−0.463732	+	0.0610515i	−0.358772	−	0.933425i	$-0.616805\pi$
$337$	−2868.88	+	377.695i	−0.463732	+	0.0610515i	−0.104959	+	0.994477i	$0.533471\pi$
$338$	3142.75	+	842.097i	0.505749	+	0.135515i
$339$	−196.277	+	1490.47i	−0.0314463	+	0.238794i
$340$	229.364	−	629.763i	0.0365853	−	0.100452i
$341$	3706.06			0.588547
$342$	−6221.27	+	3591.28i	−0.983648	+	0.567819i
$343$	3423.11	−	8264.12i	0.538865	−	1.30093i
$344$	2240.24	+	1293.40i	0.351121	+	0.202720i
$345$	3491.55	+	0.120805i	0.544866	+	1.88519e-5i
$346$	2522.69	−	3287.63i	0.391967	−	0.510821i
$347$	−3425.29	−	2628.31i	−0.529911	−	0.406615i	0.308854	−	0.951110i	$-0.400055\pi$
$347$	−3425.29	−	2628.31i	−0.529911	−	0.406615i	−0.838764	+	0.544495i	$0.816721\pi$
$348$	190.908	+	1450.47i	0.0294072	+	0.223430i
$349$	−6025.45	+	1614.51i	−0.924168	+	0.247630i	−0.689366	−	0.724413i	$-0.742111\pi$
$349$	−6025.45	+	1614.51i	−0.924168	+	0.247630i	−0.234802	+	0.972043i	$0.575444\pi$
$350$	6944.37	−	2876.45i	1.06055	−	0.439294i
$351$	−2092.68	−	3625.50i	−0.318231	−	0.551325i
$352$	−3820.58	−	1582.54i	−0.578516	−	0.239629i
$353$	3214.68	+	1856.00i	0.484704	+	0.279844i	0.722375	−	0.691502i	$-0.243051\pi$
$353$	3214.68	+	1856.00i	0.484704	+	0.279844i	−0.237671	+	0.971346i	$0.576384\pi$
$354$	−5029.91	+	2903.79i	−0.755188	+	0.435973i
$355$	−3011.30	−	806.876i	−0.450207	−	0.120633i
$356$	283.544	+	491.112i	0.0422129	+	0.0731148i
$357$	6517.90	−	9303.71i	0.966286	−	1.37928i
$358$	−4653.84	+	8060.68i	−0.687047	+	1.19000i
$359$	4434.24	−	4434.24i	0.651896	−	0.651896i	−0.301554	−	0.953449i	$-0.597505\pi$
$359$	4434.24	−	4434.24i	0.651896	−	0.651896i	0.953449	+	0.301554i	$0.0975052\pi$
$360$	1338.98	+	3233.22i	0.196029	+	0.473350i
$361$		−	4558.21i		−	0.664558i
$362$	217.331	−	166.764i	0.0315543	−	0.0242125i
$363$	−6801.98	+	1822.33i	−0.983502	+	0.263492i
$364$	−1329.15	−	1019.89i	−0.191391	−	0.146860i
$365$	−572.747	+	2137.52i	−0.0821341	+	0.306529i
$366$	−8080.74	+	6200.13i	−1.15406	+	0.885480i
$367$	−962.474	+	7310.72i	−0.136896	+	1.03983i	0.775740	+	0.631053i	$0.217377\pi$
$367$	−962.474	+	7310.72i	−0.136896	+	1.03983i	−0.912636	+	0.408774i	$0.865957\pi$
$368$	2244.26	+	5418.12i	0.317908	+	0.767497i
$369$	4000.81	−	1656.86i	0.564427	−	0.233748i
$370$		−	565.586i		−	0.0794686i
$371$	−4368.16	−	5692.70i	−0.611276	−	0.796631i
$372$	−255.995	+	617.966i	−0.0356794	+	0.0861292i
$373$	−1928.00	−	3339.39i	−0.267635	−	0.463558i	0.700616	−	0.713539i	$-0.252909\pi$
$373$	−1928.00	−	3339.39i	−0.267635	−	0.463558i	−0.968251	+	0.249981i	$0.919575\pi$
$374$	6930.43	−	5812.86i	0.958193	−	0.803679i
$375$	4856.17	+	3726.54i	0.668725	+	0.513167i
$376$	−2887.88	−	10777.7i	−0.396093	−	1.47824i
$377$	−1785.80	+	4311.30i	−0.243961	+	0.588974i
$378$	1421.02	+	10802.3i	0.193357	+	1.46987i
$379$	−6822.19	−	2825.84i	−0.924623	−	0.382992i	−0.130987	−	0.991384i	$-0.541815\pi$
$379$	−6822.19	−	2825.84i	−0.924623	−	0.382992i	−0.793636	+	0.608392i	$0.791815\pi$
$380$	−1012.98	−	133.361i	−0.136749	−	0.0180033i
$381$	3871.07	+	1037.39i	0.520527	+	0.139494i
$382$	54.2092	−	202.312i	0.00726069	−	0.0270973i
$383$	2108.93	−	7870.63i	0.281361	−	1.05005i	−0.670097	−	0.742274i	$-0.733747\pi$
$383$	2108.93	−	7870.63i	0.281361	−	1.05005i	0.951458	−	0.307780i	$-0.0995860\pi$
$384$	−2865.16	+	2864.96i	−0.380760	+	0.380734i
$385$	8512.73	+	1120.72i	1.12688	+	0.148357i
$386$	4093.48	+	1695.58i	0.539774	+	0.223582i
$387$	−740.989	+	2764.64i	−0.0973297	+	0.363139i
$388$	352.987	−	852.186i	0.0461861	−	0.111503i
$389$	−2211.75	−	8254.38i	−0.288279	−	1.07587i	−0.946410	−	0.322967i	$-0.895320\pi$
$389$	−2211.75	−	8254.38i	−0.288279	−	1.07587i	0.658132	−	0.752903i	$-0.271347\pi$
$390$	−267.712	+	2032.93i	−0.0347592	+	0.263952i
$391$	8833.36	+	774.675i	1.14251	+	0.100197i
$392$	7684.10	+	13309.2i	0.990065	+	1.71484i
$393$	542.986	+	707.684i	0.0696947	+	0.0908345i
$394$	4035.51	+	5259.17i	0.516005	+	0.672470i
$395$		−	5141.49i		−	0.654928i
$396$	328.996	−	2497.63i	0.0417491	−	0.316947i
$397$	3537.95	+	8541.37i	0.447266	+	1.07980i	0.973342	+	0.229358i	$0.0736628\pi$
$397$	3537.95	+	8541.37i	0.447266	+	1.07980i	−0.526076	+	0.850438i	$0.676337\pi$
$398$	1628.01	−	12366.0i	0.205038	−	1.55742i
$399$	−15998.6	−	6627.48i	−2.00735	−	0.831551i
$400$	−1161.27	+	4333.92i	−0.145159	+	0.541740i
$401$	−5814.45	−	4461.58i	−0.724089	−	0.555613i	0.179633	−	0.983734i	$-0.442509\pi$
$401$	−5814.45	−	4461.58i	−0.724089	−	0.555613i	−0.903722	+	0.428121i	$0.859176\pi$
$402$	−1148.56	+	4285.91i	−0.142500	+	0.531745i
$403$	−1692.68	+	1298.84i	−0.209227	+	0.160546i
$404$		−	1209.28i		−	0.148920i
$405$	−3072.28	+	2356.77i	−0.376945	+	0.289157i
$406$	8588.35	−	8588.35i	1.04983	−	1.04983i
$407$	−1108.23	+	1919.51i	−0.134971	+	0.233776i
$408$	2670.46	+	8476.81i	0.324038	+	1.02859i
$409$	−357.588	−	619.361i	−0.0432313	−	0.0748788i	0.843600	−	0.536972i	$-0.180432\pi$
$409$	−357.588	−	619.361i	−0.0432313	−	0.0748788i	−0.886831	+	0.462093i	$0.847099\pi$
$410$	−2048.84	−	548.984i	−0.246792	−	0.0661278i
$411$	−0.288459	+	8337.18i	−3.46196e−5	+	1.00059i
$412$	51.9630	+	30.0008i	0.00621367	+	0.00358746i
$413$	−12935.3	−	5357.99i	−1.54118	−	0.638376i
$414$	−6747.72	+	5176.96i	−0.801044	+	0.614575i
$415$	−6299.09	+	2609.17i	−0.745085	+	0.308624i
$416$	2299.61	−	616.178i	0.271028	−	0.0726217i
$417$	11477.2	−	8806.13i	1.34782	−	1.03414i
$418$	−10939.7	−	8394.29i	−1.28009	−	0.982245i
$419$	−1504.96	+	1961.30i	−0.175470	+	0.228678i	−0.872806	−	0.488067i	$-0.837702\pi$
$419$	−1504.96	+	1961.30i	−0.175470	+	0.228678i	0.697336	+	0.716745i	$0.254369\pi$
$420$	−774.889	+	1342.04i	−0.0900255	+	0.155916i
$421$	−11465.7	−	6619.72i	−1.32732	−	0.766331i	−0.342439	−	0.939540i	$-0.611253\pi$
$421$	−11465.7	−	6619.72i	−1.32732	−	0.766331i	−0.984885	+	0.173209i	$0.944586\pi$
$422$	−3707.75	+	8951.29i	−0.427702	+	1.03256i
$423$	10692.3	−	6172.20i	1.22902	−	0.709462i
$424$	5613.90			0.643008
$425$	5000.82	+	4584.32i	0.570765	+	0.523229i
$426$	7015.87	−	2905.78i	0.797934	−	0.330483i
$427$	−23716.9	−	6354.93i	−2.68792	−	0.720226i
$428$	−433.140	+	57.0240i	−0.0489173	+	0.00644009i
$429$	4891.98	−	6374.89i	0.550552	−	0.717442i
$430$	1112.28	−	853.482i	0.124742	−	0.0957176i
$431$	5401.60	+	13040.6i	0.603680	+	1.45741i	0.869767	+	0.493464i	$0.164269\pi$
$431$	5401.60	+	13040.6i	0.603680	+	1.45741i	−0.266086	+	0.963949i	$0.585731\pi$
$432$	−5632.06	−	3252.45i	−0.627252	−	0.362231i
$433$	340.460	+	340.460i	0.0377863	+	0.0377863i	0.725747	−	0.687961i	$-0.241494\pi$
$433$	340.460	+	340.460i	0.0377863	+	0.0377863i	−0.687961	+	0.725747i	$0.741494\pi$
$434$	5363.95	−	1437.27i	0.593267	−	0.158965i
$435$	4169.35	+	1117.33i	0.459552	+	0.123154i
$436$	−2056.76	+	2680.42i	−0.225919	+	0.294424i
$437$	−1764.39	−	13401.8i	−0.193140	−	1.46704i
$438$	−2062.62	−	4980.09i	−0.225013	−	0.543283i
$439$	826.134	+	1076.64i	0.0898160	+	0.117051i	0.836100	−	0.548577i	$-0.184830\pi$
$439$	826.134	+	1076.64i	0.0898160	+	0.117051i	−0.746284	+	0.665628i	$0.768164\pi$
$440$	−4750.06	+	4750.06i	−0.514659	+	0.514659i
$441$	−12024.8	+	12023.1i	−1.29843	+	1.29825i
$442$	−1128.16	+	5083.80i	−0.121406	+	0.547085i
$443$	−7752.69	+	13428.0i	−0.831470	+	1.44015i	0.0654025	+	0.997859i	$0.479167\pi$
$443$	−7752.69	+	13428.0i	−0.831470	+	1.44015i	−0.896872	+	0.442289i	$0.854166\pi$
$444$	−243.518	−	317.382i	−0.0260289	−	0.0339240i
$445$	1658.85	−	218.392i	0.176713	−	0.0232647i
$446$	2198.80	−	1269.48i	0.233444	−	0.134779i
$447$	−2600.75	+	4504.27i	−0.275193	+	0.476610i
$448$	−17611.4	−	2318.58i	−1.85728	−	0.244515i
$449$	5311.96	−	2200.29i	0.558323	−	0.231265i	−0.0856342	−	0.996327i	$-0.527292\pi$
$449$	5311.96	−	2200.29i	0.558323	−	0.231265i	0.643957	+	0.765062i	$0.277292\pi$
$450$	−6506.85	−	0.450263i	−0.681635	−	4.71680e-5i
$451$	5877.74	+	5877.74i	0.613685	+	0.613685i
$452$	67.9835	−	516.386i	0.00707450	−	0.0537362i
$453$	−7329.53	−	7330.03i	−0.760201	−	0.760254i
$454$	812.270	+	6169.80i	0.0839685	+	0.637804i
$455$	−4280.82	+	2471.53i	−0.441073	+	0.254653i
$456$	11733.4	−	6773.76i	1.20497	−	0.695637i
$457$	648.921	+	2421.80i	0.0664228	+	0.247893i	0.991152	−	0.132733i	$-0.0423752\pi$
$457$	648.921	+	2421.80i	0.0664228	+	0.247893i	−0.924729	+	0.380626i	$0.875709\pi$
$458$	12666.2			1.29225
$459$	−8295.35	+	5281.08i	−0.843559	+	0.537036i
$460$	−1209.67			−0.122611
$461$	−291.703	−	1088.65i	−0.0294707	−	0.109986i	0.949624	−	0.313392i	$-0.101465\pi$
$461$	−291.703	−	1088.65i	−0.0294707	−	0.109986i	−0.979094	+	0.203406i	$0.934799\pi$
$462$	−18112.9	+	10456.7i	−1.82400	+	1.05301i
$463$	1423.92	−	822.099i	0.142927	−	0.0825188i	−0.426831	−	0.904331i	$-0.640370\pi$
$463$	1423.92	−	822.099i	0.142927	−	0.0825188i	0.569758	+	0.821812i	$0.307037\pi$
$464$	946.328	+	7188.07i	0.0946814	+	0.719177i
$465$	1395.45	+	1395.55i	0.139167	+	0.139176i
$466$	−400.355	+	3041.00i	−0.0397985	+	0.302299i
$467$	8876.11	+	8876.11i	0.879524	+	0.879524i	0.993485	−	0.113962i	$-0.0363541\pi$
$467$	8876.11	+	8876.11i	0.879524	+	0.879524i	−0.113962	+	0.993485i	$0.536354\pi$
$468$	725.068	+	1256.06i	0.0716160	+	0.124062i
$469$	−9882.34	+	4093.40i	−0.972972	+	0.403018i
$470$	−5995.62	−	789.338i	−0.588420	−	0.0774670i
$471$	−8351.26	+	14463.7i	−0.816997	+	1.41497i
$472$	9486.51	−	5477.04i	0.925110	−	0.534112i
$473$	−5447.26	+	717.145i	−0.529525	+	0.0697133i
$474$	7623.71	+	9936.12i	0.738752	+	0.962829i
$475$	5170.94	−	8956.33i	0.499493	−	0.865147i
$476$	−2258.06	+	3223.41i	−0.217433	+	0.310388i
$477$	1607.27	+	6000.07i	0.154281	+	0.575942i
$478$	−8141.92	+	8141.92i	−0.779086	+	0.779086i
$479$	8198.26	+	10684.2i	0.782021	+	1.01915i	0.999075	+	0.0429902i	$0.0136884\pi$
$479$	8198.26	+	10684.2i	0.782021	+	1.01915i	−0.217054	+	0.976160i	$0.569645\pi$
$480$	−842.654	−	2034.55i	−0.0801286	−	0.193466i
$481$	−166.554	−	1265.10i	−0.0157884	−	0.119925i
$482$	−2656.55	+	3462.08i	−0.251042	+	0.327165i
$483$	−19803.8	−	5307.14i	−1.86564	−	0.499966i
$484$	2356.57	−	631.441i	0.221316	−	0.0593014i
$485$	−1924.39	−	1924.39i	−0.180169	−	0.180169i
$486$	2442.72	−	9110.04i	0.227992	−	0.850288i
$487$	2272.20	+	5485.57i	0.211423	+	0.510421i	0.993642	−	0.112583i	$-0.0359123\pi$
$487$	2272.20	+	5485.57i	0.211423	+	0.510421i	−0.782219	+	0.623003i	$0.785912\pi$
$488$	15240.3	−	11694.3i	1.41372	−	1.08479i
$489$	−11240.3	+	14647.7i	−1.03948	+	1.35458i
$490$	8258.00	−	1087.19i	0.761343	−	0.100233i
$491$	11913.0	+	3192.09i	1.09496	+	0.293395i	0.760713	−	0.649089i	$-0.224850\pi$
$491$	11913.0	+	3192.09i	1.09496	+	0.293395i	0.334252	+	0.942484i	$0.391516\pi$
$492$	−1386.09	+	574.079i	−0.127011	+	0.0526047i
$493$	10300.4	+	3751.46i	0.940985	+	0.342713i
$494$	7938.41			0.723008
$495$	−6436.75	−	3716.85i	−0.584466	−	0.337495i
$496$	−1268.53	+	3062.50i	−0.114836	+	0.277238i
$497$	15853.7	+	9153.16i	1.43086	+	0.826107i
$498$	8304.40	−	14382.5i	0.747247	−	1.29417i
$499$	3290.39	−	4288.12i	0.295186	−	0.384694i	−0.622090	−	0.782946i	$-0.713716\pi$
$499$	3290.39	−	4288.12i	0.295186	−	0.384694i	0.917276	+	0.398251i	$0.130383\pi$
$500$	−1682.50	−	1291.03i	−0.150487	−	0.115473i
$501$	2316.89	−	1777.69i	0.206609	−	0.158525i
$502$	780.491	−	209.132i	0.0693924	−	0.0185936i
$503$	2212.27	−	916.350i	0.196103	−	0.0812287i	−0.282470	−	0.959276i	$-0.591154\pi$
$503$	2212.27	−	916.350i	0.196103	−	0.0812287i	0.478574	+	0.878047i	$0.341154\pi$
$504$	−2680.82	−	20373.7i	−0.236931	−	1.80063i
$505$	−3296.33	−	1365.39i	−0.290465	−	0.120315i
$506$	−14138.5	−	8162.88i	−1.24216	−	0.717162i
$507$	0.234923	−	6789.86i	2.05785e−5	−	0.594769i
$508$	−1341.17	−	359.365i	−0.117135	−	0.0313863i
$509$	938.066	+	1624.78i	0.0816877	+	0.141487i	0.903975	−	0.427585i	$-0.140636\pi$
$509$	938.066	+	1624.78i	0.0816877	+	0.141487i	−0.822287	+	0.569073i	$0.807302\pi$
$510$	4798.41	+	420.983i	0.416622	+	0.0365518i
$511$	6497.21	−	11253.5i	0.562465	−	0.974218i
$512$	9014.51	−	9014.51i	0.778103	−	0.778103i
$513$	10599.0	+	10601.2i	0.912199	+	0.912388i
$514$			16017.4i			1.37451i
$515$	140.449	−	107.770i	0.0120173	−	0.00922123i
$516$	256.687	−	957.838i	0.0218993	−	0.0817180i
$517$	18801.6	+	14427.0i	1.59941	+	1.22727i
$518$	−859.577	+	3207.99i	−0.0729106	+	0.272106i
$519$	−7989.50	−	3309.68i	−0.675723	−	0.279921i
$520$	504.787	−	3834.24i	0.0425699	−	0.323351i
$521$	−4622.49	−	11159.7i	−0.388704	−	0.938415i	−0.990215	−	0.139550i	$-0.955434\pi$
$521$	−4622.49	−	11159.7i	−0.388704	−	0.938415i	0.601511	−	0.798865i	$-0.294566\pi$
$522$	−9714.17	+	4022.95i	−0.814517	+	0.337318i
$523$		−	16484.1i		−	1.37820i	−0.724666	−	0.689100i	$-0.758006\pi$
$523$		−	16484.1i		−	1.37820i	0.724666	−	0.689100i	$-0.241994\pi$
$524$	−188.130	−	245.175i	−0.0156841	−	0.0204400i
$525$	−9548.60	−	12444.9i	−0.793781	−	1.03455i
$526$	4134.96	+	7161.96i	0.342762	+	0.593681i
$527$	3220.89	+	3840.13i	0.266232	+	0.317417i
$528$	1629.97	−	12377.6i	0.134348	−	1.02020i
$529$	−993.124	−	3706.39i	−0.0816244	−	0.304626i
$530$	1164.36	−	2811.02i	0.0954276	−	0.230383i
$531$	8569.79	+	8570.98i	0.700371	+	0.700468i
$532$	5542.89	+	2295.94i	0.451720	+	0.187108i
$533$	−4744.50	−	624.625i	−0.385567	−	0.0507608i
$534$	−2881.96	+	2881.76i	−0.233548	+	0.233532i
$535$	−333.615	+	1245.07i	−0.0269597	+	0.100615i
$536$	2165.98	−	8083.54i	0.174545	−	0.651410i
$537$	18761.8	+	5027.92i	1.50770	+	0.404042i
$538$	−7199.66	−	947.854i	−0.576951	−	0.0759570i
$539$	−30156.7	−	12491.3i	−2.40991	−	0.998217i
$540$	1064.38	−	816.554i	0.0848217	−	0.0650720i
$541$	−587.927	+	1419.38i	−0.0467227	+	0.112798i	−0.945518	−	0.325570i	$-0.894444\pi$
$541$	−587.927	+	1419.38i	−0.0467227	+	0.112798i	0.898795	+	0.438369i	$0.144444\pi$
$542$	−868.353	−	3240.74i	−0.0688173	−	0.256830i
$543$	−453.529	−	348.030i	−0.0358431	−	0.0275053i
$544$	−1680.63	−	5334.15i	−0.132457	−	0.420404i
$545$	4984.19	+	8632.88i	0.391742	+	0.678517i
$546$	4608.10	−	11123.8i	0.361188	−	0.871899i
$547$	−9460.99	−	12329.8i	−0.739529	−	0.963773i	0.260469	−	0.965482i	$-0.416123\pi$
$547$	−9460.99	−	12329.8i	−0.739529	−	0.963773i	−0.999999	+	0.00170881i	$0.999456\pi$
$548$		−	2888.47i		−	0.225163i
$549$	16862.1	+	12940.6i	1.31085	+	1.00599i
$550$	−4779.87	−	11539.6i	−0.370572	−	0.894640i
$551$	2181.24	−	16568.2i	0.168646	−	1.28100i
$552$	12726.2	−	9764.49i	0.981277	−	0.752907i
$553$	−7814.05	+	29162.4i	−0.600881	+	2.24252i
$554$	−15923.4	−	12218.5i	−1.22116	−	0.937029i
$555$	−1140.09	+	305.445i	−0.0871969	+	0.0233611i
$556$	−3976.24	+	3051.08i	−0.303292	+	0.232724i
$557$			12498.2i			0.950747i	0.879784	+	0.475374i	$0.157687\pi$
$557$			12498.2i			0.950747i	−0.879784	+	0.475374i	$0.842313\pi$
$558$	−4766.05	−	627.798i	−0.361583	−	0.0476287i
$559$	2236.61	−	2236.61i	0.169228	−	0.169228i
$560$	−3839.88	+	6650.87i	−0.289758	+	0.501876i
$561$	−15460.2	−	10831.0i	−1.16351	−	0.815122i
$562$	1261.90	+	2185.68i	0.0947156	+	0.164052i
$563$	−1832.69	−	491.067i	−0.137191	−	0.0367602i	0.189570	−	0.981867i	$-0.439291\pi$
$563$	−1832.69	−	491.067i	−0.137191	−	0.0367602i	−0.326761	+	0.945107i	$0.605957\pi$
$564$	−3704.33	+	2138.53i	−0.276561	+	0.159660i
$565$	−1330.84	−	768.361i	−0.0990953	−	0.0572127i
$566$	−20933.6	−	8671.00i	−1.55461	−	0.643939i
$567$	21007.7	−	8698.26i	1.55598	−	0.644255i
$568$	−13232.1	+	5480.93i	−0.977479	+	0.404885i
$569$	1125.40	−	301.551i	0.0829164	−	0.0222174i	−0.217122	−	0.976144i	$-0.569667\pi$
$569$	1125.40	−	301.551i	0.0829164	−	0.0222174i	0.300039	+	0.953927i	$0.403000\pi$
$570$	−958.192	−	7280.14i	−0.0704110	−	0.534968i
$571$	6140.61	+	4711.85i	0.450046	+	0.345333i	0.808784	−	0.588106i	$-0.200126\pi$
$571$	6140.61	+	4711.85i	0.450046	+	0.345333i	−0.358738	+	0.933438i	$0.616793\pi$
$572$	−1694.78	+	2208.68i	−0.123885	+	0.161450i
$573$	−437.090	−	0.0151230i	−0.0318669	−	1.10257e-6i
$574$	10786.6	+	6227.64i	0.784362	+	0.452852i
$575$	4685.71	−	11312.3i	0.339839	−	0.820445i
$576$	13316.5	+	7689.54i	0.963292	+	0.556246i
$577$	−10696.6			−0.771759			−0.385879	−	0.922549i	$-0.626102\pi$
$577$	−10696.6			−0.771759			−0.385879	+	0.922549i	$0.626102\pi$
$578$	12046.3	+	2129.27i	0.866886	+	0.153228i
$579$	1207.21	−	9167.24i	0.0866495	−	0.657992i
$580$	−1444.51	−	387.056i	−0.103414	−	0.0277097i
$581$	39693.7	−	5225.78i	2.83438	−	0.373153i
$582$	6572.40	+	865.505i	0.468101	+	0.0616432i
$583$	−9459.70	+	7258.68i	−0.672008	+	0.515650i
$584$	3890.54	+	9392.60i	0.275671	+	0.665529i
$585$	4242.51	−	558.238i	0.299839	−	0.0394535i
$586$	13779.5	+	13779.5i	0.971377	+	0.971377i
$587$	10113.7	−	2709.97i	0.711140	−	0.190549i	0.114925	−	0.993374i	$-0.463337\pi$
$587$	10113.7	−	2709.97i	0.711140	−	0.190549i	0.596215	+	0.802825i	$0.296671\pi$
$588$	4165.93	−	4165.64i	0.292177	−	0.292156i
$589$	4651.25	−	6061.63i	0.325385	−	0.424050i
$590$	−774.919	−	5886.10i	−0.0540728	−	0.410723i
$591$	8421.94	−	10974.9i	0.586180	−	0.763870i
$592$	−1206.86	−	1572.80i	−0.0837862	−	0.109192i
$593$	−9151.87	+	9151.87i	−0.633765	+	0.633765i	−0.949010	−	0.315246i	$-0.897913\pi$
$593$	−9151.87	+	9151.87i	−0.633765	+	0.633765i	0.315246	+	0.949010i	$0.397913\pi$
$594$	17950.5	−	2361.34i	1.23993	−	0.163109i
$595$	6237.04	+	9794.69i	0.429737	+	0.674863i
$596$	900.993	−	1560.57i	0.0619230	−	0.107254i
$597$	−25806.3	+	3396.55i	−1.76915	+	0.232850i
$598$	9318.33	−	1226.78i	0.637216	−	0.0838910i
$599$	−11645.0	+	6723.23i	−0.794326	+	0.458604i	−0.841483	−	0.540283i	$-0.818317\pi$
$599$	−11645.0	+	6723.23i	−0.794326	+	0.458604i	0.0471575	+	0.998887i	$0.484984\pi$
$600$	12272.3	+	0.424611i	0.835024	+	2.88911e-5i
$601$	−12202.8	−	1606.52i	−0.828221	−	0.109037i	−0.295515	−	0.955338i	$-0.595491\pi$
$601$	−12202.8	−	1606.52i	−0.828221	−	0.109037i	−0.532705	+	0.846301i	$0.678825\pi$
$602$	−7605.94	+	3150.48i	−0.514942	+	0.213296i
$603$	9259.71	+	0.640756i	0.625348	+	4.32730e-5i
$604$	2539.45	+	2539.45i	0.171074	+	0.171074i
$605$	939.558	−	7136.65i	0.0631379	−	0.479580i
$606$	8394.84	−	2249.08i	0.562735	−	0.150763i
$607$	2856.48	+	21697.2i	0.191007	+	1.45084i	0.771320	+	0.636448i	$0.219597\pi$
$607$	2856.48	+	21697.2i	0.191007	+	1.45084i	−0.580313	+	0.814393i	$0.697070\pi$
$608$	−7383.37	+	4262.79i	−0.492492	+	0.284340i
$609$	−21950.3	−	12674.0i	−1.46055	−	0.843314i
$610$	−2694.68	−	10056.7i	−0.178860	−	0.667514i
$611$	−13643.5			−0.903363
$612$	2873.92	−	1829.76i	0.189822	−	0.120856i
$613$	−25406.1			−1.67397			−0.836984	−	0.547228i	$-0.815683\pi$
$613$	−25406.1			−1.67397			−0.836984	+	0.547228i	$0.815683\pi$
$614$	5532.76	+	20648.5i	0.363655	+	1.35718i
$615$	−0.153152	+	4426.47i	−1.00418e−5	+	0.290232i
$616$	34161.4	−	19723.1i	2.23442	−	1.29004i
$617$	−76.2399	−	579.099i	−0.00497456	−	0.0377855i	0.988778	−	0.149395i	$-0.0477327\pi$
$617$	−76.2399	−	579.099i	−0.00497456	−	0.0377855i	−0.993752	+	0.111610i	$0.964399\pi$
$618$	−111.623	+	416.525i	−0.00726560	+	0.0271118i
$619$	2175.63	−	16525.5i	0.141269	−	1.07305i	−0.763095	−	0.646287i	$-0.776321\pi$
$619$	2175.63	−	16525.5i	0.141269	−	1.07305i	0.904364	−	0.426761i	$-0.140346\pi$
$620$	−483.480	−	483.480i	−0.0313178	−	0.0313178i
$621$	14079.7	+	10806.1i	0.909822	+	0.698281i
$622$	1439.19	−	596.133i	0.0927754	−	0.0384288i
$623$	−9740.88	−	1282.41i	−0.626421	−	0.0824699i
$624$	3593.43	+	6224.50i	0.230533	+	0.399326i
$625$	5058.70	−	2920.64i	0.323757	−	0.186921i
$626$	1918.39	−	252.560i	0.122483	−	0.0161252i
$627$	−11013.0	+	26585.2i	−0.701465	+	1.69332i
$628$	2893.18	−	5011.13i	0.183838	−	0.318417i
$629$	−2952.10	+	519.901i	−0.187135	+	0.0329568i
$630$	−10757.7	−	2883.30i	−0.680310	−	0.182339i
$631$	12828.2	−	12828.2i	0.809320	−	0.809320i	−0.175211	−	0.984531i	$-0.556061\pi$
$631$	12828.2	−	12828.2i	0.809320	−	0.809320i	0.984531	+	0.175211i	$0.0560607\pi$
$632$	−14379.4	−	18739.6i	−0.905034	−	1.17946i
$633$	20046.2	+	2639.83i	1.25871	+	0.165757i
$634$	−1878.98	−	14272.3i	−0.117703	−	0.894046i
$635$	−2493.88	+	3250.09i	−0.155853	+	0.203112i
$636$	−556.921	−	2078.75i	−0.0347223	−	0.129603i
$637$	18151.3	−	4863.64i	1.12901	−	0.302519i
$638$	−14271.5	−	14271.5i	−0.885601	−	0.885601i
$639$	−9646.33	−	12573.1i	−0.597188	−	0.778382i
$640$	−1584.99	−	3826.50i	−0.0978941	−	0.236337i
$641$	−23096.0	+	17722.2i	−1.42315	+	1.09202i	−0.442385	+	0.896825i	$0.645868\pi$
$641$	−23096.0	+	17722.2i	−1.42315	+	1.09202i	−0.980764	+	0.195196i	$0.937466\pi$
$642$	−1201.44	−	2900.81i	−0.0738582	−	0.178327i
$643$	15729.8	−	2070.86i	0.964730	−	0.127009i	0.368329	−	0.929696i	$-0.379930\pi$
$643$	15729.8	−	2070.86i	0.964730	−	0.127009i	0.596401	+	0.802686i	$0.296597\pi$
$644$	6861.22	+	1838.46i	0.419829	+	0.112493i
$645$	−2321.12	−	1781.18i	−0.141696	−	0.108735i
$646$	−809.544	−	18630.8i	−0.0493051	−	1.13470i
$647$	−10938.9			−0.664687			−0.332343	−	0.943158i	$-0.607839\pi$
$647$	−10938.9			−0.664687			−0.332343	+	0.943158i	$0.607839\pi$
$648$	−4606.51	+	17182.2i	−0.279261	+	1.04164i
$649$	−8903.50	+	21495.0i	−0.538510	+	1.30008i
$650$	6227.36	+	3595.37i	0.375780	+	0.216957i
$651$	−5794.01	−	10036.3i	−0.348825	−	0.604231i
$652$	3894.12	−	5074.91i	0.233904	−	0.304830i
$653$	2273.32	+	1744.38i	0.136236	+	0.104537i	0.674631	−	0.738155i	$-0.264303\pi$
$653$	2273.32	+	1744.38i	0.136236	+	0.104537i	−0.538395	+	0.842692i	$0.680969\pi$
$654$	−22432.8	−	9292.87i	−1.34127	−	0.555627i
$655$	−880.731	+	235.991i	−0.0525389	+	0.0140778i
$656$	−6868.92	+	2845.20i	−0.408820	+	0.169339i
$657$	−8924.83	+	6847.28i	−0.529971	+	0.406603i
$658$	32807.4	+	13589.3i	1.94371	+	0.805113i
$659$	1560.44	+	900.918i	0.0922397	+	0.0532546i	0.545410	−	0.838169i	$-0.316374\pi$
$659$	1560.44	+	900.918i	0.0922397	+	0.0532546i	−0.453171	+	0.891424i	$0.649707\pi$
$660$	2230.10	+	1287.65i	0.131525	+	0.0759421i
$661$	−8743.01	−	2342.68i	−0.514469	−	0.137851i	−0.00776186	−	0.999970i	$-0.502471\pi$
$661$	−8743.01	−	2342.68i	−0.514469	−	0.137851i	−0.506707	+	0.862118i	$0.669137\pi$
$662$	−5996.85	−	10386.9i	−0.352076	−	0.609813i
$663$	10857.1	−	471.384i	0.635978	−	0.0276124i
$664$	−15661.6	+	27126.7i	−0.915345	+	1.58542i
$665$	12516.9	−	12516.9i	0.729899	−	0.729899i
$666$	1750.36	−	2280.79i	0.101840	−	0.132701i
$667$		−	19785.3i		−	1.14856i
$668$	−802.681	+	615.919i	−0.0464920	+	0.0356746i
$669$	−3746.44	−	3746.70i	−0.216511	−	0.216526i
$670$	−3598.39	−	2761.14i	−0.207489	−	0.159212i
$671$	−10560.1	+	39411.0i	−0.607555	+	2.26743i
$672$	1687.41	+	12820.6i	0.0968648	+	0.735958i
$673$	−1615.47	+	12270.7i	−0.0925288	+	0.702826i	0.880813	+	0.473465i	$0.156997\pi$
$673$	−1615.47	+	12270.7i	−0.0925288	+	0.702826i	−0.973341	+	0.229361i	$0.926336\pi$
$674$	2757.21	+	6656.50i	0.157573	+	0.380414i
$675$	3513.12	+	13116.6i	0.200326	+	0.747938i
$676$			2352.39i			0.133841i
$677$	−9711.37	−	12656.1i	−0.551312	−	0.718484i	0.431701	−	0.902017i	$-0.357913\pi$
$677$	−9711.37	−	12656.1i	−0.551312	−	0.718484i	−0.983014	+	0.183532i	$0.941247\pi$
$678$	3711.20	−	488.459i	0.210218	−	0.0276684i
$679$	7990.41	+	13839.8i	0.451611	+	0.782213i
$680$	−9050.11	−	793.684i	−0.510376	−	0.0447594i
$681$	11998.3	−	4969.36i	0.675146	−	0.279627i
$682$	−2388.34	−	8913.41i	−0.134097	−	0.500458i
$683$	1965.30	−	4744.66i	0.110103	−	0.265811i	−0.859219	−	0.511609i	$-0.829050\pi$
$683$	1965.30	−	4744.66i	0.110103	−	0.265811i	0.969321	+	0.245797i	$0.0790498\pi$
$684$	−3672.23	−	3672.73i	−0.205279	−	0.205308i
$685$	−7873.59	−	3261.35i	−0.439174	−	0.181912i
$686$	−22081.9	−	2907.14i	−1.22900	−	0.161801i
$687$	−6840.39	−	25532.2i	−0.379879	−	1.41792i
$688$	1271.90	−	4746.80i	0.0704807	−	0.263038i
$689$	1776.66	−	6630.57i	0.0982368	−	0.366625i
$690$	−2249.81	−	8397.56i	−0.124129	−	0.463318i
$691$	26296.6	+	3462.01i	1.44771	+	0.190595i	0.813050	−	0.582194i	$-0.197805\pi$
$691$	26296.6	+	3462.01i	1.44771	+	0.190595i	0.634663	+	0.772789i	$0.281139\pi$
$692$	2768.06	+	1146.57i	0.152060	+	0.0629854i
$693$	30860.2	+	30864.5i	1.69161	+	1.69184i
$694$	−4113.93	+	9931.91i	−0.225018	+	0.543242i
$695$	3827.29	+	14283.7i	0.208889	+	0.779583i
$696$	18321.2	−	7588.16i	0.997793	−	0.413259i
$697$	−982.109	+	11198.6i	−0.0533716	+	0.608578i
$698$	7766.10	+	13451.3i	0.421133	+	0.729424i
$699$	6346.18	−	835.267i	0.343397	−	0.0451970i
$700$	3308.32	+	4311.49i	0.178633	+	0.232799i
$701$			3421.18i			0.184331i	0.995744	+	0.0921656i	$0.0293789\pi$
$701$			3421.18i			0.184331i	−0.995744	+	0.0921656i	$0.970621\pi$
$702$	−7371.05	+	7369.52i	−0.396300	+	0.396217i
$703$	1748.68	+	4221.69i	0.0938161	+	0.226492i
$704$	−3852.85	+	29265.3i	−0.206264	+	1.56673i
$705$	1646.81	+	12512.1i	0.0879751	+	0.668416i
$706$	2392.17	−	8927.69i	0.127522	−	0.475918i
$707$	16621.6	+	12754.2i	0.884186	+	0.678460i
$708$	−2969.16	−	2969.37i	−0.157610	−	0.157621i
$709$	−20525.1	+	15749.5i	−1.08722	+	0.834251i	−0.987001	−	0.160714i	$-0.948620\pi$
$709$	−20525.1	+	15749.5i	−1.08722	+	0.834251i	−0.100217	+	0.994966i	$0.531954\pi$
$710$			7762.44i			0.410308i
$711$	15911.8	−	20733.7i	0.839296	−	1.09363i
$712$	5435.36	−	5435.36i	0.286094	−	0.286094i
$713$	4523.03	−	7834.11i	0.237572	−	0.411486i
$714$	−26576.7	−	9680.44i	−1.39301	−	0.507397i
$715$	4107.01	+	7113.55i	0.214816	+	0.372072i
$716$	−6500.22	−	1741.73i	−0.339280	−	0.0909099i
$717$	20809.3	+	12015.2i	1.08388	+	0.625826i
$718$	−13522.4	−	7807.14i	−0.702855	−	0.405794i
$719$	−5334.37	−	2209.57i	−0.276688	−	0.114608i	0.240025	−	0.970767i	$-0.422844\pi$
$719$	−5334.37	−	2209.57i	−0.276688	−	0.114608i	−0.516712	+	0.856159i	$0.672844\pi$
$720$	5274.61	−	4046.77i	0.273018	−	0.209464i
$721$	−960.414	+	397.816i	−0.0496084	+	0.0205485i
$722$	−10962.9	+	2937.50i	−0.565092	+	0.151416i
$723$	8413.45	+	3485.30i	0.432779	+	0.179281i
$724$	157.132	+	120.572i	0.00806599	+	0.00618925i
$725$	9214.96	−	12009.2i	0.472049	−	0.615186i
$726$	8766.35	+	15185.0i	0.448140	+	0.776264i
$727$	18021.0	+	10404.4i	0.919342	+	0.530782i	0.883425	−	0.468573i	$-0.155232\pi$
$727$	18021.0	+	10404.4i	0.919342	+	0.530782i	0.0359166	+	0.999355i	$0.488565\pi$
$728$	−8690.41	+	20980.5i	−0.442429	+	1.06812i
$729$	−19683.0	−	4.08609i	−1.00000	−	0.000207595i
$730$	5510.03			0.279363
$731$	−5477.23	−	5021.06i	−0.277131	−	0.254050i
$732$	−5842.13	−	4483.15i	−0.294988	−	0.226369i
$733$	−6359.95	−	1704.14i	−0.320478	−	0.0858718i	0.0949940	−	0.995478i	$-0.469717\pi$
$733$	−6359.95	−	1704.14i	−0.320478	−	0.0858718i	−0.415472	+	0.909606i	$0.636383\pi$
$734$	18203.2	−	2396.49i	0.915384	−	0.120513i
$735$	−6651.26	−	16059.1i	−0.333790	−	0.805919i
$736$	−8008.05	+	6144.79i	−0.401061	+	0.307745i
$737$	6802.10	+	16421.7i	0.339971	+	0.820763i
$738$	−6563.19	−	8554.54i	−0.327364	−	0.426690i
$739$	6808.00	+	6808.00i	0.338885	+	0.338885i	0.855948	−	0.517062i	$-0.172974\pi$
$739$	6808.00	+	6808.00i	0.338885	+	0.338885i	−0.517062	+	0.855948i	$0.672974\pi$
$740$	394.989	−	105.837i	0.0196218	−	0.00525763i
$741$	−4287.14	−	16002.1i	−0.212540	−	0.793320i
$742$	−10876.4	+	14174.4i	−0.538121	+	0.701293i
$743$	−3374.73	−	25633.6i	−0.166631	−	1.26569i	−0.846514	−	0.532366i	$-0.821303\pi$
$743$	−3374.73	−	25633.6i	−0.166631	−	1.26569i	0.679883	−	0.733320i	$-0.262030\pi$
$744$	8989.09	+	1183.75i	0.442952	+	0.0583313i
$745$	−3236.59	−	4218.01i	−0.159167	−	0.207431i
$746$	−6789.05	+	6789.05i	−0.333197	+	0.333197i
$747$	−33476.7	−	8972.53i	−1.63969	−	0.439475i
$748$	5356.42	+	3752.27i	0.261832	+	0.183418i
$749$	3784.51	−	6554.96i	0.184623	−	0.319777i
$750$	5833.14	−	14081.1i	0.283995	−	0.685557i
$751$	−24748.0	+	3258.13i	−1.20249	+	0.158310i	−0.705029	−	0.709179i	$-0.749066\pi$
$751$	−24748.0	+	3258.13i	−1.20249	+	0.158310i	−0.497456	+	0.867489i	$0.665733\pi$
$752$	−18357.2	+	10598.5i	−0.890183	+	0.513947i
$753$	−843.068	−	1460.35i	−0.0408009	−	0.0706749i
$754$	11519.9	+	1516.62i	0.556406	+	0.0732523i
$755$	9789.48	−	4054.93i	0.471888	−	0.195462i
$756$	−7278.15	+	3013.82i	−0.350137	+	0.144989i
$757$	−14139.6	−	14139.6i	−0.678881	−	0.678881i	0.280866	−	0.959747i	$-0.409378\pi$
$757$	−14139.6	−	14139.6i	−0.678881	−	0.678881i	−0.959747	+	0.280866i	$0.909378\pi$
$758$	−2399.90	+	18229.1i	−0.114998	+	0.873495i
$759$	−8819.01	+	32908.5i	−0.421752	+	1.57378i
$760$	1807.68	+	13730.7i	0.0862783	+	0.655348i
$761$	−10421.0	+	6016.55i	−0.496399	+	0.286596i	−0.727225	−	0.686399i	$-0.759190\pi$
$761$	−10421.0	+	6016.55i	−0.496399	+	0.286596i	0.230826	+	0.972995i	$0.425857\pi$
$762$	0.345258	−	9978.79i	1.64139e−5	−	0.474401i
$763$	−15150.0	−	56540.4i	−0.718828	−	2.68270i
$764$	151.433			0.00717101
$765$	−1742.78	−	9899.88i	−0.0823665	−	0.467884i
$766$	−20288.7			−0.956996
$767$	−3466.68	−	12937.8i	−0.163200	−	0.609072i
$768$	−11765.7	−	6793.45i	−0.552808	−	0.319189i
$769$	−24904.7	+	14378.8i	−1.16786	+	0.674267i	−0.953176	−	0.302416i	$-0.902207\pi$
$769$	−24904.7	+	14378.8i	−1.16786	+	0.674267i	−0.214688	+	0.976683i	$0.568874\pi$
$770$	−2790.52	−	21196.1i	−0.130602	−	0.992019i
$771$	32287.5	−	8650.20i	1.50818	−	0.404059i
$772$	−418.137	+	3176.07i	−0.0194936	+	0.148069i
$773$	−4354.72	−	4354.72i	−0.202624	−	0.202624i	0.598499	−	0.801123i	$-0.295764\pi$
$773$	−4354.72	−	4354.72i	−0.202624	−	0.202624i	−0.801123	+	0.598499i	$0.795764\pi$
$774$	7126.74	+	0.493158i	0.330963	+	2.29021e-5i
$775$	6394.08	−	2648.51i	0.296364	−	0.122758i
$776$	−12396.0	−	1631.96i	−0.573441	−	0.0754949i
$777$	6930.80	+	0.239800i	0.320001	+	1.10718e-5i
$778$	−18427.2	+	10638.9i	−0.849159	+	0.490262i
$779$	16990.4	−	2236.83i	0.781445	−	0.102879i
$780$	−1469.84	+	193.456i	−0.0674726	+	0.00888056i
$781$	15210.0	−	26344.6i	0.696873	−	1.20702i
$782$	−3829.42	−	21744.2i	−0.175115	−	0.994338i
$783$	13355.5	+	17409.0i	0.609562	+	0.794568i
$784$	20644.3	−	20644.3i	0.940431	−	0.940431i
$785$	−10393.0	−	13544.4i	−0.472538	−	0.615824i
$786$	1352.12	−	1761.99i	0.0613595	−	0.0799595i
$787$	2850.40	+	21650.9i	0.129105	+	0.980652i	0.926262	+	0.376880i	$0.123003\pi$
$787$	2850.40	+	21650.9i	0.129105	+	0.980652i	−0.797157	+	0.603772i	$0.793664\pi$
$788$	−2917.70	+	3802.43i	−0.131902	+	0.171898i
$789$	12203.8	−	12203.0i	0.550656	−	0.550618i
$790$	−12365.8	+	3313.39i	−0.556903	+	0.149222i
$791$	6380.73	+	6380.73i	0.286818	+	0.286818i
$792$	−33855.6	+	4454.79i	−1.51895	+	0.199866i
$793$	−8988.96	−	21701.3i	−0.402531	−	0.971797i
$794$	18262.7	−	14013.5i	0.816273	−	0.626348i
$795$	−6295.20	−	829.000i	−0.280840	−	0.0369831i
$796$	8940.72	−	1177.07i	0.398110	−	0.0524121i
$797$	−34279.1	−	9185.05i	−1.52350	−	0.408220i	−0.602605	−	0.798040i	$-0.705871\pi$
$797$	−34279.1	−	9185.05i	−1.52350	−	0.408220i	−0.920891	+	0.389820i	$0.872537\pi$
$798$	−5629.52	+	42749.0i	−0.249728	+	1.89637i
$799$	1391.33	+	32020.0i	0.0616043	+	1.41776i
$800$	−7722.60			−0.341294
$801$	7365.40	+	4253.09i	0.324898	+	0.187610i
$802$	−6983.43	+	16859.5i	−0.307473	+	0.742306i
$803$	−18700.2	−	10796.6i	−0.821814	−	0.474475i
$804$	−3208.09	−	0.110997i	−0.140722	−	4.86886e-6i
$805$	12758.3	−	16627.0i	0.558599	−	0.727980i
$806$	4214.67	+	3234.03i	0.184188	+	0.141332i
$807$	1977.52	+	15024.8i	0.0862604	+	0.655388i
$808$	−15833.0	+	4242.44i	−0.689361	+	0.184714i
$809$	13831.5	−	5729.20i	0.601100	−	0.248984i	−0.0613180	−	0.998118i	$-0.519530\pi$
$809$	13831.5	−	5729.20i	0.601100	−	0.248984i	0.662418	+	0.749135i	$0.269530\pi$
$810$	7648.13	+	5870.30i	0.331763	+	0.254644i
$811$	19997.3	+	8283.16i	0.865846	+	0.358645i	0.770991	−	0.636846i	$-0.219761\pi$
$811$	19997.3	+	8283.16i	0.865846	+	0.358645i	0.0948547	+	0.995491i	$0.469761\pi$
$812$	7604.99	+	4390.74i	0.328674	+	0.189760i
$813$	−6063.65	+	3500.57i	−0.261576	+	0.151009i
$814$	5330.79	+	1428.38i	0.229538	+	0.0615046i
$815$	−9436.72	−	16344.9i	−0.405588	−	0.702498i
$816$	14241.9	−	9068.24i	0.610989	−	0.389034i
$817$	−5663.56	+	9809.58i	−0.242525	+	0.420066i
$818$	−1259.17	+	1259.17i	−0.0538215	+	0.0538215i
$819$	−24911.8	−	3281.45i	−1.06287	−	0.140004i
$820$		−	1533.58i		−	0.0653109i
$821$	27578.0	−	21161.3i	1.17232	−	0.899555i	0.175929	−	0.984403i	$-0.443707\pi$
$821$	27578.0	−	21161.3i	1.17232	−	0.899555i	0.996394	+	0.0848478i	$0.0270404\pi$
$822$	20051.9	−	5372.13i	0.850838	−	0.227950i
$823$	6696.46	+	5138.37i	0.283626	+	0.217634i	0.740770	−	0.671759i	$-0.234461\pi$
$823$	6696.46	+	5138.37i	0.283626	+	0.217634i	−0.457144	+	0.889393i	$0.651128\pi$
$824$	210.500	−	785.598i	0.00889943	−	0.0332131i
$825$	−20680.0	+	15867.1i	−0.872707	+	0.669604i
$826$	−4550.37	+	34563.5i	−0.191680	+	1.45595i
$827$	−8936.16	−	21573.8i	−0.375745	−	0.907128i	−0.992753	−	0.120171i	$-0.961656\pi$
$827$	−8936.16	−	21573.8i	−0.375745	−	0.907128i	0.617008	−	0.786956i	$-0.288344\pi$
$828$	−4878.14	−	3743.66i	−0.204743	−	0.157127i
$829$		−	143.572i		−	0.00601502i	−0.999995	−	0.00300751i	$-0.999043\pi$
$829$		−	143.572i		−	0.00601502i	0.999995	−	0.00300751i	$-0.000957322\pi$
$830$	10334.7	+	13468.4i	0.432195	+	0.563248i
$831$	−16030.3	+	38696.7i	−0.669174	+	1.61537i
$832$	−8496.71	−	14716.7i	−0.354051	−	0.613234i
$833$	−13265.6	−	42103.7i	−0.551771	−	1.75127i
$834$	−28575.9	−	21928.6i	−1.18645	−	0.910463i
$835$	772.613	+	2883.43i	0.0320208	+	0.119503i
$836$	3815.22	−	9210.77i	0.157838	−	0.381054i
$837$	1308.41	+	9946.34i	0.0540326	+	0.410748i
$838$	5686.97	+	2355.62i	0.234431	+	0.0971044i
$839$	−4986.17	−	656.441i	−0.205175	−	0.0270118i	0.0272382	−	0.999629i	$-0.491329\pi$
$839$	−4986.17	−	656.441i	−0.205175	−	0.0270118i	−0.232413	+	0.972617i	$0.574662\pi$
$840$	20289.7	+	5437.37i	0.833408	+	0.223342i
$841$	18.3360	−	68.4308i	0.000751814	−	0.00280581i
$842$	−8532.04	+	31842.0i	−0.349209	+	1.30326i
$843$	3724.35	−	3724.09i	0.152163	−	0.152153i
$844$	−6945.16	−	914.348i	−0.283249	−	0.0372905i
$845$	6412.30	+	2656.06i	0.261053	+	0.108132i
$846$	−21735.2	−	21738.2i	−0.883301	−	0.883423i
$847$	−16175.4	+	39050.9i	−0.656192	+	1.58419i
$848$	−2760.29	−	10301.5i	−0.111779	−	0.417165i
$849$	−6173.56	+	46880.3i	−0.249560	+	1.89509i
$850$	7802.97	−	14981.7i	0.314870	−	0.604552i
$851$	2705.06	+	4685.30i	0.108964	+	0.188731i
$852$	3342.19	+	4355.94i	0.134391	+	0.175155i
$853$	−6440.21	−	8393.04i	−0.258509	−	0.336896i	0.646010	−	0.763329i	$-0.276437\pi$
$853$	−6440.21	−	8393.04i	−0.258509	−	0.336896i	−0.904519	+	0.426433i	$0.859770\pi$
$854$			61136.6i			2.44971i
$855$	−14157.7	+	5863.15i	−0.566294	+	0.234521i
$856$	2266.17	+	5471.02i	0.0904861	+	0.218453i
$857$	−3976.49	+	30204.4i	−0.158500	+	1.20392i	0.708535	+	0.705676i	$0.249357\pi$
$857$	−3976.49	+	30204.4i	−0.158500	+	1.20392i	−0.867034	+	0.498249i	$0.833977\pi$
$858$	−18484.8	−	7657.40i	−0.735501	−	0.304684i
$859$	11470.4	−	42808.1i	0.455606	−	1.70034i	−0.230695	−	0.973026i	$-0.574100\pi$
$859$	11470.4	−	42808.1i	0.455606	−	1.70034i	0.686301	−	0.727318i	$-0.259233\pi$
$860$	804.187	+	617.075i	0.0318867	+	0.0244675i
$861$	6728.23	−	25106.6i	0.266315	−	0.993764i
$862$	27882.8	−	21395.3i	1.10173	−	0.845389i
$863$		−	14082.6i		−	0.555476i	−0.960657	−	0.277738i	$-0.910415\pi$
$863$		−	14082.6i		−	0.555476i	0.960657	−	0.277738i	$-0.0895848\pi$
$864$	2898.37	−	10812.4i	0.114126	−	0.425746i
$865$	6250.77	−	6250.77i	0.245702	−	0.245702i
$866$	599.430	−	1038.24i	0.0235213	−	0.0407401i
$867$	−2213.48	−	25432.6i	−0.0867057	−	0.996234i
$868$	2007.49	+	3477.08i	0.0785009	+	0.135968i
$869$	48459.9	+	12984.8i	1.89170	+	0.506881i
$870$	0.371862	−	10747.7i	1.44911e−5	−	0.418830i
$871$	−8861.98	−	5116.46i	−0.344749	−	0.199041i
$872$	42310.1	+	17525.4i	1.64312	+	0.680603i
$873$	−1804.77	−	13715.9i	−0.0699681	−	0.531745i
$874$	−31095.6	+	12880.2i	−1.20346	+	0.498489i
$875$	35490.5	−	9509.64i	1.37120	−	0.367411i
$876$	3091.98	−	2372.39i	0.119256	−	0.0915020i
$877$	7828.22	+	6006.81i	0.301414	+	0.231283i	0.748384	−	0.663266i	$-0.230830\pi$
$877$	7828.22	+	6006.81i	0.301414	+	0.231283i	−0.446970	+	0.894549i	$0.647497\pi$
$878$	2057.02	−	2680.76i	0.0790672	−	0.103042i
$879$	20334.8	−	35218.1i	0.780291	−	1.35140i
$880$	11051.9	+	6380.83i	0.423364	+	0.244429i
$881$	11378.4	−	27470.0i	0.435130	−	1.05050i	−0.542480	−	0.840069i	$-0.682514\pi$
$881$	11378.4	−	27470.0i	0.435130	−	1.05050i	0.977609	−	0.210427i	$-0.0674856\pi$
$882$	36666.0	+	21172.5i	1.39978	+	0.808294i
$883$	7129.01			0.271699			0.135849	−	0.990729i	$-0.456624\pi$
$883$	7129.01			0.271699			0.135849	+	0.990729i	$0.456624\pi$
$884$	−3761.50	+	163.444i	−0.143114	+	0.00621859i
$885$	−11446.6	+	4740.86i	−0.434771	+	0.180070i
$886$	37291.8	+	9992.31i	1.41404	+	0.378892i
$887$	21692.8	−	2855.91i	0.821165	−	0.108108i	0.291775	−	0.956487i	$-0.405754\pi$
$887$	21692.8	−	2855.91i	0.821165	−	0.108108i	0.529390	+	0.848379i	$0.322421\pi$
$888$	−3301.14	+	4301.82i	−0.124751	+	0.162567i
$889$	19084.7	−	14644.2i	0.720001	−	0.552477i
$890$	−1594.29	−	3848.95i	−0.0600456	−	0.144963i
$891$	−14454.1	−	34909.0i	−0.543470	−	1.31257i
$892$	1298.02	+	1298.02i	0.0487232	+	0.0487232i
$893$	47193.5	−	12645.5i	1.76850	−	0.473868i
$894$	12509.2	+	3352.30i	0.467976	+	0.125411i
$895$	−12087.1	+	15752.2i	−0.451426	+	0.588310i
$896$	3174.50	+	24112.7i	0.118362	+	0.899050i
$897$	−7505.29	−	18121.1i	−0.279369	−	0.674523i
$898$	−8715.13	−	11357.8i	−0.323862	−	0.422065i
$899$	7907.79	−	7907.79i	0.293370	−	0.293370i
$900$	−1217.30	−	4544.29i	−0.0450853	−	0.168307i
$901$	−15742.6	−	3493.49i	−0.582088	−	0.129173i
$902$	10348.6	−	17924.4i	0.382009	−	0.661658i
$903$	10458.3	+	13630.5i	0.385414	+	0.502318i
$904$	−6999.51	+	921.503i	−0.257522	+	0.0339035i
$905$	506.079	−	292.185i	0.0185886	−	0.0107321i
$906$	−12905.9	+	22351.9i	−0.473257	+	0.819640i
$907$	−18824.4	−	2478.28i	−0.689146	−	0.0907278i	−0.222183	−	0.975005i	$-0.571318\pi$
$907$	−18824.4	−	2478.28i	−0.689146	−	0.0907278i	−0.466962	+	0.884277i	$0.654652\pi$
$908$	−4156.82	+	1721.81i	−0.151926	+	0.0629299i
$909$	−9067.28	−	15707.5i	−0.330850	−	0.573141i
$910$	8703.00	+	8703.00i	0.317035	+	0.317035i
$911$	−4108.71	+	31208.8i	−0.149427	+	1.13501i	0.738245	+	0.674532i	$0.235655\pi$
$911$	−4108.71	+	31208.8i	−0.149427	+	1.13501i	−0.887672	+	0.460476i	$0.847679\pi$
$912$	−18199.1	−	18200.3i	−0.660780	−	0.660825i
$913$	−8683.81	−	65960.1i	−0.314778	−	2.39097i
$914$	5406.46	−	3121.42i	0.195656	−	0.112962i
$915$	−18816.8	+	10863.0i	−0.679850	+	0.392480i
$916$	2370.20	+	8845.72i	0.0854953	+	0.319073i
$917$	5354.14			0.192813
$918$	18047.3	+	16547.7i	0.648857	+	0.594941i
$919$	−8471.26			−0.304071			−0.152035	−	0.988375i	$-0.548583\pi$
$919$	−8471.26			−0.304071			−0.152035	+	0.988375i	$0.548583\pi$
$920$	4243.82	+	15838.1i	0.152081	+	0.567574i
$921$	38634.8	−	22304.1i	1.38226	−	0.797984i
$922$	−2430.32	+	1403.14i	−0.0868094	+	0.0501194i
$923$	2285.89	+	17363.0i	0.0815177	+	0.619188i
$924$	−10692.1	−	10692.8i	−0.380676	−	0.380702i
$925$	−540.267	+	4103.73i	−0.0192042	+	0.145870i
$926$	−2894.85	−	2894.85i	−0.102733	−	0.102733i
$927$	899.904	+	0.0622718i	0.0318843	+	2.20634e-6i
$928$	−11528.9	+	4775.41i	−0.407816	+	0.168923i
$929$	35737.8	+	4704.98i	1.26213	+	0.166163i	0.731737	−	0.681588i	$-0.238710\pi$
$929$	35737.8	+	4704.98i	1.26213	+	0.166163i	0.530395	+	0.847750i	$0.322044\pi$
$930$	2457.13	−	4255.54i	0.0866371	−	0.150048i
$931$	−58278.6	+	33647.2i	−2.05156	+	1.18447i
$932$	−2198.67	+	289.460i	−0.0772744	+	0.0101734i
$933$	−1978.91	−	2579.15i	−0.0694389	−	0.0905010i
$934$	15627.7	−	27068.0i	0.547488	−	0.948278i
$935$	16276.1	−	10364.2i	0.569289	−	0.362510i
$936$	13901.7	−	13899.8i	0.485462	−	0.485395i
$937$	−21768.1	+	21768.1i	−0.758947	+	0.758947i	−0.976131	−	0.217184i	$-0.930313\pi$
$937$	−21768.1	+	21768.1i	−0.758947	+	0.758947i	0.217184	+	0.976131i	$0.430313\pi$
$938$	16213.6	+	21129.9i	0.564384	+	0.735519i
$939$	−1545.13	−	3730.64i	−0.0536991	−	0.129654i
$940$	−570.698	−	4334.88i	−0.0198023	−	0.150413i
$941$	−21811.6	+	28425.4i	−0.755618	+	0.984741i	0.244269	+	0.969708i	$0.421452\pi$
$941$	−21811.6	+	28425.4i	−0.755618	+	0.984741i	−0.999887	+	0.0150331i	$0.995215\pi$
$942$	40168.3	+	10764.5i	1.38933	+	0.372323i
$943$	19598.2	−	5251.32i	0.676781	−	0.181343i
$944$	−14714.8	−	14714.8i	−0.507336	−	0.507336i
$945$	−2.41247	+	23242.1i	−8.30453e−5	+	0.800071i
$946$	5235.24	+	12639.0i	0.179928	+	0.434386i
$947$	−23379.2	+	17939.5i	−0.802241	+	0.615581i	−0.926340	−	0.376689i	$-0.877063\pi$
$947$	−23379.2	+	17939.5i	−0.802241	+	0.615581i	0.124099	+	0.992270i	$0.460396\pi$
$948$	−5512.50	+	7183.52i	−0.188858	+	0.246107i
$949$	12324.8	−	1622.60i	0.421582	−	0.0555023i
$950$	−24873.1	−	6664.74i	−0.849465	−	0.227613i
$951$	−27755.0	+	11495.4i	−0.946391	+	0.391970i
$952$	50125.8	+	18256.1i	1.70650	+	0.621517i
$953$	44785.0			1.52228			0.761138	−	0.648590i	$-0.224641\pi$
$953$	44785.0			1.52228			0.761138	+	0.648590i	$0.224641\pi$
$954$	13394.9	−	7732.32i	0.454587	−	0.262414i
$955$	170.982	−	412.786i	0.00579354	−	0.0139868i
$956$	−7209.68	−	4162.51i	−0.243910	−	0.140821i
$957$	−21060.8	+	36475.4i	−0.711388	+	1.23206i
$958$	20413.1	−	26602.9i	0.688432	−	0.897182i
$959$	39702.2	+	30464.6i	1.33686	+	1.02581i
$960$	−12470.8	+	9568.50i	−0.419264	+	0.321690i
$961$	−23837.0	+	6387.10i	−0.800141	+	0.214397i
$962$	−2935.35	+	1215.86i	−0.0983778	+	0.0407494i
$963$	−5198.55	+	3988.42i	−0.173957	+	0.133463i
$964$	−2914.94	−	1207.41i	−0.0973898	−	0.0403402i
$965$	8185.42	+	4725.85i	0.273055	+	0.157648i
$966$	−1.76629	+	51050.0i	−5.88296e−5	+	1.70032i
$967$	38628.0	+	10350.3i	1.28458	+	0.344203i	0.835601	−	0.549337i	$-0.185120\pi$
$967$	38628.0	+	10350.3i	1.28458	+	0.344203i	0.448983	+	0.893540i	$0.351786\pi$
$968$	−16534.8	−	28639.2i	−0.549018	−	0.950928i
$969$	−37118.3	+	11693.4i	−1.23056	+	0.387665i
$970$	−3388.18	+	5868.49i	−0.112152	+	0.194254i
$971$	10572.0	−	10572.0i	0.349405	−	0.349405i	−0.510483	−	0.859888i	$-0.670533\pi$
$971$	10572.0	−	10572.0i	0.349405	−	0.349405i	0.859888	+	0.510483i	$0.170533\pi$
$972$	6819.31	+	1.17971i	0.225030	+	3.89293e-5i
$973$		−	86833.3i		−	2.86099i
$974$	11729.0	−	8999.97i	0.385853	−	0.296076i
$975$	3884.37	−	14494.6i	0.127589	−	0.476103i
$976$	−28952.6	−	22216.1i	−0.949539	−	0.728607i
$977$	15409.3	−	57508.2i	0.504592	−	1.88316i	0.0368010	−	0.999323i	$-0.488283\pi$
$977$	15409.3	−	57508.2i	0.504592	−	1.88316i	0.467791	−	0.883839i	$-0.345050\pi$
$978$	42472.7	+	17594.5i	1.38868	+	0.575265i
$979$	−2131.01	+	16186.7i	−0.0695685	+	0.528425i
$980$	2304.57	+	5563.72i	0.0751191	+	0.181353i
$981$	−6617.51	+	50238.1i	−0.215373	+	1.63505i
$982$		−	30709.0i		−	0.997927i
$983$	11444.8	+	14915.2i	0.371346	+	0.483947i	0.941225	−	0.337782i	$-0.109677\pi$
$983$	11444.8	+	14915.2i	0.371346	+	0.483947i	−0.569879	+	0.821729i	$0.693010\pi$
$984$	12379.1	+	16133.9i	0.401048	+	0.522694i
$985$	7070.55	+	12246.6i	0.228717	+	0.396150i
$986$	2384.61	−	27190.9i	0.0770198	−	0.878231i
$987$	9675.25	−	73471.2i	0.312023	−	2.36942i
$988$	1485.50	+	5543.97i	0.0478341	+	0.178519i
$989$	−5132.10	+	12390.0i	−0.165006	+	0.398361i
$990$	−4791.26	+	17876.3i	−0.153814	+	0.573884i
$991$	37725.8	+	15626.5i	1.20928	+	0.500902i	0.893988	−	0.448091i	$-0.147896\pi$
$991$	37725.8	+	15626.5i	1.20928	+	0.500902i	0.315296	+	0.948993i	$0.397896\pi$
$992$	−5656.60	−	744.706i	−0.181046	−	0.0238351i
$993$	−17699.0	+	17697.7i	−0.565619	+	0.565580i
$994$	11797.4	−	44028.3i	0.376448	−	1.40492i
$995$	6886.35	−	25700.2i	0.219409	−	0.818846i
$996$	11598.3	+	3108.19i	0.368983	+	0.0988823i
$997$	18726.5	+	2465.39i	0.594860	+	0.0783147i	0.421944	−	0.906622i	$-0.361348\pi$
$997$	18726.5	+	2465.39i	0.594860	+	0.0783147i	0.172916	+	0.984937i	$0.444681\pi$
$998$	−12433.8	−	5150.24i	−0.394373	−	0.163355i
$999$	−5542.85	−	2296.60i	−0.175544	−	0.0727339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.r.a.25.16	✓	416
9.4	even	3	inner	153.4.r.a.76.37	yes	416
17.15	even	8	inner	153.4.r.a.151.37	yes	416
153.49	even	24	inner	153.4.r.a.49.16	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.r.a.25.16	✓	416	1.1	even	1	trivial
153.4.r.a.49.16	yes	416	153.49	even	24	inner
153.4.r.a.76.37	yes	416	9.4	even	3	inner
153.4.r.a.151.37	yes	416	17.15	even	8	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.r (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.644442 - 2.40509i) q^{2} +(-4.50009 + 2.59792i) q^{3} +(1.55905 - 0.900121i) q^{4} +(-0.693294 - 5.26609i) q^{5} +(9.14828 + 9.14891i) q^{6} +(-4.07107 + 30.9228i) q^{7} +(-17.2548 - 17.2548i) q^{8} +(13.5016 - 23.3818i) q^{9} +(-12.2186 + 5.06113i) q^{10} +(51.3852 + 6.76499i) q^{11} +(-4.67745 + 8.10093i) q^{12} +(-25.8403 + 14.9189i) q^{13} +(76.9957 - 10.1367i) q^{14} +(16.8008 + 21.8968i) q^{15} +(-23.1786 + 40.1465i) q^{16} +(37.6485 + 59.1235i) q^{17} +(-64.9362 - 17.4044i) q^{18} +(75.5553 - 75.5553i) q^{19} +(-5.82100 - 7.58608i) q^{20} +(-62.0149 - 149.732i) q^{21} +(-16.8444 - 127.946i) q^{22} +(77.0129 - 100.365i) q^{23} +(122.475 + 32.8215i) q^{24} +(93.4896 - 25.0505i) q^{25} +(52.5338 + 52.5338i) q^{26} +(-0.0145624 + 140.296i) q^{27} +(21.4873 + 51.8748i) q^{28} +(124.078 - 95.2081i) q^{29} +(41.8366 - 54.5186i) q^{30} +(70.8943 - 9.33342i) q^{31} +(-77.0704 - 20.6510i) q^{32} +(-248.813 + 103.052i) q^{33} +(117.935 - 128.650i) q^{34} +165.665 q^{35} +(0.00336349 - 48.6065i) q^{36} +(-16.3655 + 39.5099i) q^{37} +(-230.408 - 133.026i) q^{38} +(77.5254 - 134.267i) q^{39} +(-78.9026 + 102.828i) q^{40} +(127.240 + 97.6344i) q^{41} +(-320.153 + 245.645i) q^{42} +(-102.396 + 27.4370i) q^{43} +(86.2017 - 35.7059i) q^{44} +(-132.491 - 54.8904i) q^{45} +(-291.017 - 120.543i) q^{46} +(395.994 + 228.627i) q^{47} +(0.00833421 - 240.879i) q^{48} +(-608.335 - 163.003i) q^{49} +(-120.497 - 208.707i) q^{50} +(-323.020 - 168.253i) q^{51} +(-26.8576 + 46.5187i) q^{52} +(-162.677 + 162.677i) q^{53} +(337.434 - 90.3776i) q^{54} -275.290i q^{55} +(603.811 - 463.321i) q^{56} +(-143.719 + 536.292i) q^{57} +(-308.945 - 237.062i) q^{58} +(-116.184 + 433.606i) q^{59} +(45.9031 + 19.0155i) q^{60} +(-102.755 + 780.499i) q^{61} +(-68.1350 - 164.492i) q^{62} +(668.064 + 512.697i) q^{63} +569.527i q^{64} +(96.4791 + 125.734i) q^{65} +(408.194 + 532.007i) q^{66} +(171.476 + 297.005i) q^{67} +(111.914 + 58.2886i) q^{68} +(-85.8242 + 651.725i) q^{69} +(-106.761 - 398.439i) q^{70} +(224.611 - 542.258i) q^{71} +(-636.414 + 170.479i) q^{72} +(-384.912 - 159.436i) q^{73} +(105.572 + 13.8988i) q^{74} +(-355.633 + 355.608i) q^{75} +(49.7860 - 185.804i) q^{76} +(-418.385 + 1561.44i) q^{77} +(-372.885 - 99.9281i) q^{78} +(959.705 + 126.348i) q^{79} +(227.485 + 94.2273i) q^{80} +(-364.413 - 631.383i) q^{81} +(152.821 - 368.942i) q^{82} +(-332.230 - 1239.90i) q^{83} +(-231.461 - 177.619i) q^{84} +(285.249 - 239.251i) q^{85} +(131.977 + 228.590i) q^{86} +(-311.017 + 750.789i) q^{87} +(-769.912 - 1003.37i) q^{88} +315.006i q^{89} +(-46.6334 + 354.027i) q^{90} +(-356.136 - 859.789i) q^{91} +(29.7266 - 225.796i) q^{92} +(-294.783 + 226.179i) q^{93} +(294.674 - 1099.74i) q^{94} +(-450.263 - 345.499i) q^{95} +(400.473 - 107.292i) q^{96} +(406.495 - 311.915i) q^{97} +1568.14i q^{98} +(851.961 - 1110.14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 80 q^{8} + 52 q^{9} - 16 q^{10} + 96 q^{11} - 212 q^{12} - 4 q^{14} - 256 q^{15} + 2936 q^{16} - 16 q^{17} - 240 q^{18} - 16 q^{19} - 516 q^{20}+ \cdots - 18916 q^{99}+O(q^{100}) \) 416 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 80 * q^8 + 52 * q^9 - 16 * q^10 + 96 * q^11 - 212 * q^12 - 4 * q^14 - 256 * q^15 + 2936 * q^16 - 16 * q^17 - 240 * q^18 - 16 * q^19 - 516 * q^20 - 4 * q^22 - 172 * q^23 + 1216 * q^24 - 4 * q^25 - 80 * q^26 + 544 * q^27 - 528 * q^28 - 4 * q^29 - 4 * q^31 + 316 * q^32 - 512 * q^33 - 796 * q^34 - 4512 * q^35 + 328 * q^36 - 16 * q^37 + 1148 * q^39 + 252 * q^40 + 956 * q^41 + 3648 * q^42 - 688 * q^43 - 1040 * q^44 - 1240 * q^45 + 128 * q^46 + 528 * q^48 - 4 * q^49 - 5288 * q^50 - 352 * q^51 - 1032 * q^52 - 1424 * q^53 + 1708 * q^54 + 284 * q^56 + 4372 * q^57 - 4 * q^58 + 56 * q^59 - 3248 * q^60 - 4 * q^61 + 5168 * q^62 + 1008 * q^63 - 2284 * q^65 - 7516 * q^66 - 8 * q^67 + 252 * q^68 + 6224 * q^69 - 36 * q^70 + 624 * q^71 - 16 * q^73 - 3644 * q^74 - 508 * q^75 + 188 * q^76 + 1772 * q^77 - 10080 * q^78 - 4 * q^79 + 472 * q^80 + 3296 * q^82 + 4364 * q^83 + 8632 * q^84 + 3308 * q^85 + 1312 * q^86 + 4376 * q^87 - 1380 * q^88 - 15160 * q^90 - 4776 * q^91 - 1748 * q^92 - 1720 * q^93 - 68 * q^94 + 4436 * q^95 - 2196 * q^96 + 104 * q^97 - 18916 * q^99

Introduction

L-functions

Modular forms

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Database

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