LMFDB - Embedded newform 153.4.r.a.49.16

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			49.16
Character	$\chi$	$=$	153.49
Dual form			153.4.r.a.25.16

$q$-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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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	0.753400	+	0.657562i	$0.228412\pi$
$2$	−0.644442	+	2.40509i	−0.227845	+	0.850327i	−0.981245	+	0.192765i	$0.938254\pi$
$3$	−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	0.932063	+	0.362297i	$0.118007\pi$
$5$	−0.693294	+	5.26609i	−0.0620101	+	0.471014i	−0.994073	+	0.108717i	$0.965326\pi$
$6$	9.14828	−	9.14891i	0.622461	−	0.622504i
$7$	−4.07107	−	30.9228i	−0.219817	−	1.66968i	−0.644707	−	0.764430i	$-0.723020\pi$
$7$	−4.07107	−	30.9228i	−0.219817	−	1.66968i	0.424890	−	0.905245i	$-0.360313\pi$
$8$	−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	0.612362	−	0.790577i	$-0.290219\pi$
$11$	51.3852	−	6.76499i	1.40848	−	0.185429i	0.796113	+	0.605148i	$0.206886\pi$
$12$	−4.67745	−	8.10093i	−0.112522	−	0.194878i
$13$	−25.8403	−	14.9189i	−0.551292	−	0.318289i	0.198351	−	0.980131i	$-0.436441\pi$
$13$	−25.8403	−	14.9189i	−0.551292	−	0.318289i	−0.749643	+	0.661842i	$0.769775\pi$
$14$	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	0.996452	−	0.0841590i	$-0.0268204\pi$
$19$	75.5553	+	75.5553i	0.912293	+	0.912293i	−0.0841590	+	0.996452i	$0.526820\pi$
$20$	−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	0.999041	−	0.0437755i	$-0.0139386\pi$
$23$	77.0129	+	100.365i	0.698187	+	0.909894i	−0.300855	+	0.953670i	$0.597272\pi$
$24$	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	0.924200	−	0.381909i	$-0.124733\pi$
$29$	124.078	+	95.2081i	0.794505	+	0.609645i	−0.129695	+	0.991554i	$0.541400\pi$
$30$	41.8366	+	54.5186i	0.254609	+	0.331789i
$31$	70.8943	+	9.33342i	0.410742	+	0.0540752i	0.333066	−	0.942903i	$-0.391917\pi$
$31$	70.8943	+	9.33342i	0.410742	+	0.0540752i	0.0776758	+	0.996979i	$0.475250\pi$
$32$	−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	0.883343	−	0.468728i	$-0.155288\pi$
$37$	−16.3655	−	39.5099i	−0.0727157	−	0.175551i	−0.956058	+	0.293177i	$0.905288\pi$
$38$	−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	−0.337331	−	0.941386i	$-0.609524\pi$
$41$	127.240	−	97.6344i	0.484671	−	0.371901i	0.822002	+	0.569485i	$0.192857\pi$
$42$	−320.153	−	245.645i	−1.17621	−	0.902471i
$43$	−102.396	−	27.4370i	−0.363146	−	0.0973046i	0.0726323	−	0.997359i	$-0.476860\pi$
$43$	−102.396	−	27.4370i	−0.363146	−	0.0973046i	−0.435778	+	0.900054i	$0.643527\pi$
$44$	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	0.262157	−	0.965025i	$-0.415566\pi$
$47$	395.994	−	228.627i	1.22897	−	0.709547i	0.966815	+	0.255478i	$0.0822328\pi$
$48$	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	0.464147	−	0.885758i	$-0.346361\pi$
$53$	−162.677	−	162.677i	−0.421611	−	0.421611i	−0.885758	+	0.464147i	$0.846361\pi$
$54$	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	−0.967322	−	0.253550i	$-0.918402\pi$
$59$	−116.184	−	433.606i	−0.256371	−	0.956791i	0.710951	−	0.703242i	$-0.248265\pi$
$60$	45.9031	−	19.0155i	0.0987677	−	0.0409149i
$61$	−102.755	−	780.499i	−0.215678	−	1.63824i	−0.666414	−	0.745582i	$-0.732171\pi$
$61$	−102.755	−	780.499i	−0.215678	−	1.63824i	0.450735	−	0.892658i	$-0.351162\pi$
$62$	−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	−0.666266	−	0.745714i	$-0.732109\pi$
$67$	171.476	−	297.005i	0.312674	−	0.541567i	0.978940	+	0.204147i	$0.0654420\pi$
$68$	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	0.992808	+	0.119721i	$0.0381999\pi$
$71$	224.611	+	542.258i	0.375442	+	0.906397i	−0.617366	+	0.786676i	$0.711800\pi$
$72$	−636.414	−	170.479i	−1.04170	−	0.279044i
$73$	−384.912	+	159.436i	−0.617131	+	0.255624i	−0.669274	−	0.743015i	$-0.733395\pi$
$73$	−384.912	+	159.436i	−0.617131	+	0.255624i	0.0521430	+	0.998640i	$0.483395\pi$
$74$	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	0.588823	−	0.808262i	$-0.299592\pi$
$79$	959.705	−	126.348i	1.36678	−	0.179939i	0.777953	+	0.628323i	$0.216258\pi$
$80$	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	0.291047	+	0.956709i	$0.405996\pi$
$83$	−332.230	+	1239.90i	−0.439361	+	1.63972i	−0.730409	+	0.683010i	$0.760670\pi$
$84$	−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	$-0.939933\pi$
$89$		−	315.006i		−	0.375175i	0.982248	−	0.187588i	$-0.0600668\pi$
$90$	−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	0.799213	−	0.601047i	$-0.205250\pi$
$97$	406.495	+	311.915i	0.425498	+	0.326496i	−0.373715	+	0.927543i	$0.621916\pi$
$98$		−	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	0.982687	−	0.185276i	$-0.0593178\pi$
$101$	335.866	+	581.736i	0.330890	+	0.573118i	−0.651797	+	0.758394i	$0.725984\pi$
$102$	−196.497	−	885.321i	−0.190746	−	0.859410i
$103$	16.6649	−	28.8644i	0.0159421	−	0.0276126i	−0.857944	−	0.513743i	$-0.828259\pi$
$103$	16.6649	−	28.8644i	0.0159421	−	0.0276126i	0.873886	+	0.486130i	$0.161592\pi$
$104$	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	−0.481660	−	0.876358i	$-0.659966\pi$
$107$	−224.204	+	92.8685i	−0.202567	+	0.0839060i	0.279093	+	0.960264i	$0.409966\pi$
$108$	126.261	−	218.742i	0.112495	−	0.194894i
$109$	−1733.88	−	718.199i	−1.52363	−	0.631110i	−0.545318	−	0.838229i	$-0.683591\pi$
$109$	−1733.88	−	718.199i	−1.52363	−	0.631110i	−0.978316	+	0.207120i	$0.933591\pi$
$110$	−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	0.860891	−	0.508789i	$-0.169907\pi$
$113$	176.125	+	229.531i	0.146624	+	0.191084i	−0.714267	+	0.699873i	$0.753240\pi$
$114$	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	−0.871482	−	0.490427i	$-0.836841\pi$
$127$	−545.373	+	545.373i	−0.381056	+	0.381056i	0.490427	+	0.871482i	$0.336841\pi$
$128$	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	−0.997291	−	0.0735562i	$-0.976565\pi$
$131$	−22.4067	+	170.195i	−0.0149441	+	0.113512i	0.982347	+	0.187068i	$0.0598985\pi$
$132$	−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	1.00000		0.000341224i	$0.000108615\pi$
$137$	802.246	+	1389.53i	0.500295	+	0.866537i	−0.499704	+	0.866196i	$0.666558\pi$
$138$	1622.77	+	213.584i	1.00101	+	0.131750i
$139$	−2760.22	−	363.390i	−1.68431	−	0.221744i	−0.773274	−	0.634072i	$-0.781382\pi$
$139$	−2760.22	−	363.390i	−1.68431	−	0.221744i	−0.911035	+	0.412328i	$0.864716\pi$
$140$	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	0.719007	−	0.695003i	$-0.244597\pi$
$149$	866.865	+	500.485i	0.476620	+	0.275177i	−0.242387	+	0.970180i	$0.577930\pi$
$150$	1084.45	−	626.160i	0.590302	−	0.340838i
$151$	516.322	−	1926.94i	0.278263	−	1.03849i	−0.675361	−	0.737488i	$-0.736012\pi$
$151$	516.322	−	1926.94i	0.278263	−	1.03849i	0.953623	−	0.301003i	$-0.0973213\pi$
$152$	−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	0.995853	−	0.0909719i	$-0.0289973\pi$
$157$	2783.59	+	1607.10i	1.41500	+	0.816948i	0.419143	+	0.907920i	$0.362331\pi$
$158$	−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	0.988013	−	0.154374i	$-0.0493360\pi$
$163$	3282.82	+	1359.79i	1.57748	+	0.653415i	0.589472	+	0.807789i	$0.299336\pi$
$164$	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	0.000319904	−	1.00000i	$-0.499898\pi$
$167$	−557.204	−	73.3573i	−0.258190	−	0.0339914i	−0.258510	+	0.966009i	$0.583232\pi$
$168$	−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	−0.515772	−	0.856726i	$-0.672495\pi$
$173$	1013.15	−	1320.37i	0.445253	−	0.580265i	0.961025	+	0.276461i	$0.0891616\pi$
$174$	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	−0.109763	+	0.993958i	$0.535009\pi$
$179$	−2643.25	+	2643.25i	−1.10372	+	1.10372i	−0.993958	+	0.109763i	$0.964991\pi$
$180$	−255.969	−	33.6809i	−0.105993	−	0.0139468i
$181$	42.1025	−	101.644i	0.0172898	−	0.0417412i	−0.914999	−	0.403456i	$-0.867809\pi$
$181$	42.1025	−	101.644i	0.0172898	−	0.0417412i	0.932289	+	0.361715i	$0.117809\pi$
$182$	−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	−0.486138	−	0.873882i	$-0.661595\pi$
$191$	72.8484	−	42.0590i	0.0275975	−	0.0159334i	0.513735	+	0.857949i	$0.328261\pi$
$192$	−1479.59	+	2562.92i	−0.556146	+	0.963349i
$193$	−1083.27	−	1411.75i	−0.404019	−	0.526527i	0.546390	−	0.837531i	$-0.316002\pi$
$193$	−1083.27	−	1411.75i	−0.404019	−	0.526527i	−0.950409	+	0.311004i	$0.899335\pi$
$194$	−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	−0.109368	−	0.994001i	$-0.534883\pi$
$197$	−2459.68	−	1018.83i	−0.889569	−	0.368471i	−0.780200	+	0.625530i	$0.784883\pi$
$198$	−3219.02	+	1333.62i	−1.15538	+	0.478669i
$199$	4627.95	−	1916.96i	1.64858	−	0.682862i	0.651454	−	0.758688i	$-0.274159\pi$
$199$	4627.95	−	1916.96i	1.64858	−	0.682862i	0.997121	+	0.0758257i	$0.0241593\pi$
$200$	−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	−0.973993	−	0.226578i	$-0.927246\pi$
$211$	−3087.09	+	2368.81i	−1.00722	+	0.772870i	−0.0332306	+	0.999448i	$0.510580\pi$
$212$	−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	−0.914912	−	0.403652i	$-0.867740\pi$
$223$	263.915	−	984.942i	0.0792512	−	0.295770i	0.994164	+	0.107883i	$0.0344072\pi$
$224$	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	−0.483757	−	0.875202i	$-0.660728\pi$
$227$	−2477.90	+	326.222i	−0.724511	+	0.0953837i	−0.240754	+	0.970586i	$0.577395\pi$
$228$	258.662	−	965.474i	0.0751330	−	0.280439i
$229$	−1316.60	−	4913.63i	−0.379928	−	1.41791i	−0.846009	−	0.533169i	$-0.821001\pi$
$229$	−1316.60	−	4913.63i	−0.379928	−	1.41791i	0.466080	−	0.884742i	$-0.345666\pi$
$230$	−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	−0.536898	−	0.843647i	$-0.680404\pi$
$233$	−1138.09	+	471.411i	−0.319994	+	0.132546i	0.216904	+	0.976193i	$0.430404\pi$
$234$	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	0.362599	+	0.931945i	$0.381889\pi$
$239$	−2312.20	+	4004.84i	−0.625789	+	1.08390i	−0.988388	+	0.151953i	$0.951444\pi$
$240$	−1268.50	−	166.956i	−0.341172	−	0.0449041i
$241$	−1066.92	+	1390.43i	−0.285170	+	0.371641i	−0.913870	−	0.406007i	$-0.866921\pi$
$241$	−1066.92	+	1390.43i	−0.285170	+	0.371641i	0.628700	+	0.777648i	$0.283588\pi$
$242$			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	$-0.987008\pi$
$251$		−	324.516i		−	0.0816067i	0.999167	−	0.0408034i	$-0.0129917\pi$
$252$	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	−0.915825	−	0.401578i	$-0.868462\pi$
$257$	−6213.67	+	1664.95i	−1.50816	+	0.404111i	−0.592339	+	0.805689i	$0.701795\pi$
$258$	−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	−0.137697	−	0.990474i	$-0.543970\pi$
$263$	−3208.17	−	859.627i	−0.752184	−	0.201547i	−0.614487	+	0.788927i	$0.710637\pi$
$264$	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	0.998441	−	0.0558155i	$-0.0177759\pi$
$269$	1116.08	+	2694.46i	0.252969	+	0.610721i	−0.745472	+	0.666537i	$0.767776\pi$
$270$	−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	0.989130	+	0.147046i	$0.0469765\pi$
$277$	6395.13	+	4907.16i	1.38717	+	1.06441i	0.398041	+	0.917368i	$0.369690\pi$
$278$	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	0.153391	−	0.988166i	$-0.450981\pi$
$281$	−979.067	−	262.340i	−0.207851	−	0.0556936i	−0.361242	+	0.932472i	$0.617647\pi$
$282$	1530.97	−	5714.46i	0.323291	−	1.20671i
$283$	5539.74	+	7219.53i	1.16362	+	1.51645i	0.815264	+	0.579089i	$0.196592\pi$
$283$	5539.74	+	7219.53i	1.16362	+	1.51645i	0.348352	+	0.937364i	$0.386742\pi$
$284$	−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	−0.362974	−	0.931799i	$-0.618239\pi$
$293$	−6777.86	−	3913.20i	−1.35142	−	0.780244i	−0.988449	+	0.151555i	$0.951572\pi$
$294$	−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	−0.982386	−	0.186861i	$-0.940169\pi$
$311$	81.6608	−	620.275i	0.0148893	−	0.113095i	0.997276	+	0.0737662i	$0.0235018\pi$
$312$	−3654.43	−	979.067i	−0.663114	−	0.177656i
$313$	−101.433	−	770.458i	−0.0183173	−	0.139134i	0.979843	−	0.199771i	$-0.0640199\pi$
$313$	−101.433	−	770.458i	−0.0183173	−	0.139134i	−0.998160	+	0.0606376i	$0.980687\pi$
$314$	−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	0.395688	−	0.918385i	$-0.370506\pi$
$317$	5732.00	−	754.633i	1.01559	−	0.133705i	0.619900	+	0.784680i	$0.287173\pi$
$318$	−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	0.623530	−	0.781799i	$-0.285698\pi$
$331$	4652.75	+	1246.70i	0.772623	+	0.207024i	0.149093	+	0.988823i	$0.452365\pi$
$332$	−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	−0.104959	−	0.994477i	$-0.533471\pi$
$337$	−2868.88	−	377.695i	−0.463732	−	0.0610515i	−0.358772	+	0.933425i	$0.616805\pi$
$338$	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	−0.838764	−	0.544495i	$-0.816721\pi$
$347$	−3425.29	+	2628.31i	−0.529911	+	0.406615i	0.308854	+	0.951110i	$0.400055\pi$
$348$	190.908	−	1450.47i	0.0294072	−	0.223430i
$349$	−6025.45	−	1614.51i	−0.924168	−	0.247630i	−0.234802	−	0.972043i	$-0.575444\pi$
$349$	−6025.45	−	1614.51i	−0.924168	−	0.247630i	−0.689366	+	0.724413i	$0.742111\pi$
$350$	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	−0.237671	−	0.971346i	$-0.576384\pi$
$353$	3214.68	−	1856.00i	0.484704	−	0.279844i	0.722375	+	0.691502i	$0.243051\pi$
$354$	−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	0.953449	−	0.301554i	$-0.0975052\pi$
$359$	4434.24	+	4434.24i	0.651896	+	0.651896i	−0.301554	+	0.953449i	$0.597505\pi$
$360$	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	−0.912636	−	0.408774i	$-0.865957\pi$
$367$	−962.474	−	7310.72i	−0.136896	−	1.03983i	0.775740	−	0.631053i	$-0.217377\pi$
$368$	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	−0.968251	−	0.249981i	$-0.919575\pi$
$373$	−1928.00	+	3339.39i	−0.267635	+	0.463558i	0.700616	+	0.713539i	$0.252909\pi$
$374$	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	−0.793636	−	0.608392i	$-0.791815\pi$
$379$	−6822.19	+	2825.84i	−0.924623	+	0.382992i	−0.130987	+	0.991384i	$0.541815\pi$
$380$	−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	0.951458	+	0.307780i	$0.0995860\pi$
$383$	2108.93	+	7870.63i	0.281361	+	1.05005i	−0.670097	+	0.742274i	$0.733747\pi$
$384$	−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	0.658132	+	0.752903i	$0.271347\pi$
$389$	−2211.75	+	8254.38i	−0.288279	+	1.07587i	−0.946410	+	0.322967i	$0.895320\pi$
$390$	−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	−0.526076	−	0.850438i	$-0.676337\pi$
$397$	3537.95	−	8541.37i	0.447266	−	1.07980i	0.973342	−	0.229358i	$-0.0736628\pi$
$398$	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	−0.903722	−	0.428121i	$-0.859176\pi$
$401$	−5814.45	+	4461.58i	−0.724089	+	0.555613i	0.179633	+	0.983734i	$0.442509\pi$
$402$	−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	−0.886831	−	0.462093i	$-0.847099\pi$
$409$	−357.588	+	619.361i	−0.0432313	+	0.0748788i	0.843600	+	0.536972i	$0.180432\pi$
$410$	−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	0.697336	−	0.716745i	$-0.254369\pi$
$419$	−1504.96	−	1961.30i	−0.175470	−	0.228678i	−0.872806	+	0.488067i	$0.837702\pi$
$420$	−774.889	−	1342.04i	−0.0900255	−	0.155916i
$421$	−11465.7	+	6619.72i	−1.32732	+	0.766331i	−0.984885	−	0.173209i	$-0.944586\pi$
$421$	−11465.7	+	6619.72i	−1.32732	+	0.766331i	−0.342439	+	0.939540i	$0.611253\pi$
$422$	−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	−0.266086	−	0.963949i	$-0.585731\pi$
$431$	5401.60	−	13040.6i	0.603680	−	1.45741i	0.869767	−	0.493464i	$-0.164269\pi$
$432$	−5632.06	+	3252.45i	−0.627252	+	0.362231i
$433$	340.460	−	340.460i	0.0377863	−	0.0377863i	−0.687961	−	0.725747i	$-0.741494\pi$
$433$	340.460	−	340.460i	0.0377863	−	0.0377863i	0.725747	+	0.687961i	$0.241494\pi$
$434$	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	−0.746284	−	0.665628i	$-0.768164\pi$
$439$	826.134	−	1076.64i	0.0898160	−	0.117051i	0.836100	+	0.548577i	$0.184830\pi$
$440$	−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	−0.896872	−	0.442289i	$-0.854166\pi$
$443$	−7752.69	−	13428.0i	−0.831470	−	1.44015i	0.0654025	−	0.997859i	$-0.479167\pi$
$444$	−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	0.643957	−	0.765062i	$-0.277292\pi$
$449$	5311.96	+	2200.29i	0.558323	+	0.231265i	−0.0856342	+	0.996327i	$0.527292\pi$
$450$	−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	−0.924729	−	0.380626i	$-0.875709\pi$
$457$	648.921	−	2421.80i	0.0664228	−	0.247893i	0.991152	+	0.132733i	$0.0423752\pi$
$458$	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	−0.979094	−	0.203406i	$-0.934799\pi$
$461$	−291.703	+	1088.65i	−0.0294707	+	0.109986i	0.949624	+	0.313392i	$0.101465\pi$
$462$	−18112.9	−	10456.7i	−1.82400	−	1.05301i
$463$	1423.92	+	822.099i	0.142927	+	0.0825188i	0.569758	−	0.821812i	$-0.307037\pi$
$463$	1423.92	+	822.099i	0.142927	+	0.0825188i	−0.426831	+	0.904331i	$0.640370\pi$
$464$	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	−0.113962	−	0.993485i	$-0.536354\pi$
$467$	8876.11	−	8876.11i	0.879524	−	0.879524i	0.993485	+	0.113962i	$0.0363541\pi$
$468$	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	−0.217054	−	0.976160i	$-0.569645\pi$
$479$	8198.26	−	10684.2i	0.782021	−	1.01915i	0.999075	−	0.0429902i	$-0.0136884\pi$
$480$	−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	−0.782219	−	0.623003i	$-0.785912\pi$
$487$	2272.20	−	5485.57i	0.211423	−	0.510421i	0.993642	+	0.112583i	$0.0359123\pi$
$488$	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	0.334252	−	0.942484i	$-0.391516\pi$
$491$	11913.0	−	3192.09i	1.09496	−	0.293395i	0.760713	+	0.649089i	$0.224850\pi$
$492$	−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	0.917276	−	0.398251i	$-0.130383\pi$
$499$	3290.39	+	4288.12i	0.295186	+	0.384694i	−0.622090	+	0.782946i	$0.713716\pi$
$500$	−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	0.478574	−	0.878047i	$-0.341154\pi$
$503$	2212.27	+	916.350i	0.196103	+	0.0812287i	−0.282470	+	0.959276i	$0.591154\pi$
$504$	−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	−0.822287	−	0.569073i	$-0.807302\pi$
$509$	938.066	−	1624.78i	0.0816877	−	0.141487i	0.903975	+	0.427585i	$0.140636\pi$
$510$	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	0.601511	+	0.798865i	$0.294566\pi$
$521$	−4622.49	+	11159.7i	−0.388704	+	0.938415i	−0.990215	+	0.139550i	$0.955434\pi$
$522$	−9714.17	−	4022.95i	−0.814517	−	0.337318i
$523$			16484.1i			1.37820i	0.724666	+	0.689100i	$0.241994\pi$
$523$			16484.1i			1.37820i	−0.724666	+	0.689100i	$0.758006\pi$
$524$	−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	0.898795	−	0.438369i	$-0.144444\pi$
$541$	−587.927	−	1419.38i	−0.0467227	−	0.112798i	−0.945518	+	0.325570i	$0.894444\pi$
$542$	−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	−0.999999	−	0.00170881i	$-0.999456\pi$
$547$	−9460.99	+	12329.8i	−0.739529	+	0.963773i	0.260469	+	0.965482i	$0.416123\pi$
$548$			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	$-0.842313\pi$
$557$		−	12498.2i		−	0.950747i	0.879784	−	0.475374i	$-0.157687\pi$
$558$	−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	−0.326761	−	0.945107i	$-0.605957\pi$
$563$	−1832.69	+	491.067i	−0.137191	+	0.0367602i	0.189570	+	0.981867i	$0.439291\pi$
$564$	−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	0.300039	−	0.953927i	$-0.403000\pi$
$569$	1125.40	+	301.551i	0.0829164	+	0.0222174i	−0.217122	+	0.976144i	$0.569667\pi$
$570$	−958.192	+	7280.14i	−0.0704110	+	0.534968i
$571$	6140.61	−	4711.85i	0.450046	−	0.345333i	−0.358738	−	0.933438i	$-0.616793\pi$
$571$	6140.61	−	4711.85i	0.450046	−	0.345333i	0.808784	+	0.588106i	$0.200126\pi$
$572$	−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	0.596215	−	0.802825i	$-0.296671\pi$
$587$	10113.7	+	2709.97i	0.711140	+	0.190549i	0.114925	+	0.993374i	$0.463337\pi$
$588$	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	0.315246	−	0.949010i	$-0.397913\pi$
$593$	−9151.87	−	9151.87i	−0.633765	−	0.633765i	−0.949010	+	0.315246i	$0.897913\pi$
$594$	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	0.0471575	−	0.998887i	$-0.484984\pi$
$599$	−11645.0	−	6723.23i	−0.794326	−	0.458604i	−0.841483	+	0.540283i	$0.818317\pi$
$600$	12272.3	−	0.424611i	0.835024	−	2.88911e-5i
$601$	−12202.8	+	1606.52i	−0.828221	+	0.109037i	−0.532705	−	0.846301i	$-0.678825\pi$
$601$	−12202.8	+	1606.52i	−0.828221	+	0.109037i	−0.295515	+	0.955338i	$0.595491\pi$
$602$	−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	−0.580313	−	0.814393i	$-0.697070\pi$
$607$	2856.48	−	21697.2i	0.191007	−	1.45084i	0.771320	−	0.636448i	$-0.219597\pi$
$608$	−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	−0.993752	−	0.111610i	$-0.964399\pi$
$617$	−76.2399	+	579.099i	−0.00497456	+	0.0377855i	0.988778	+	0.149395i	$0.0477327\pi$
$618$	−111.623	−	416.525i	−0.00726560	−	0.0271118i
$619$	2175.63	+	16525.5i	0.141269	+	1.07305i	0.904364	+	0.426761i	$0.140346\pi$
$619$	2175.63	+	16525.5i	0.141269	+	1.07305i	−0.763095	+	0.646287i	$0.776321\pi$
$620$	−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	0.984531	−	0.175211i	$-0.0560607\pi$
$631$	12828.2	+	12828.2i	0.809320	+	0.809320i	−0.175211	+	0.984531i	$0.556061\pi$
$632$	−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	−0.980764	−	0.195196i	$-0.937466\pi$
$641$	−23096.0	−	17722.2i	−1.42315	−	1.09202i	−0.442385	−	0.896825i	$-0.645868\pi$
$642$	−1201.44	+	2900.81i	−0.0738582	+	0.178327i
$643$	15729.8	+	2070.86i	0.964730	+	0.127009i	0.596401	−	0.802686i	$-0.296597\pi$
$643$	15729.8	+	2070.86i	0.964730	+	0.127009i	0.368329	+	0.929696i	$0.379930\pi$
$644$	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	−0.538395	−	0.842692i	$-0.680969\pi$
$653$	2273.32	−	1744.38i	0.136236	−	0.104537i	0.674631	+	0.738155i	$0.264303\pi$
$654$	−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	−0.453171	−	0.891424i	$-0.649707\pi$
$659$	1560.44	−	900.918i	0.0922397	−	0.0532546i	0.545410	+	0.838169i	$0.316374\pi$
$660$	2230.10	−	1287.65i	0.131525	−	0.0759421i
$661$	−8743.01	+	2342.68i	−0.514469	+	0.137851i	−0.506707	−	0.862118i	$-0.669137\pi$
$661$	−8743.01	+	2342.68i	−0.514469	+	0.137851i	−0.00776186	+	0.999970i	$0.502471\pi$
$662$	−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	−0.973341	−	0.229361i	$-0.926336\pi$
$673$	−1615.47	−	12270.7i	−0.0925288	−	0.702826i	0.880813	−	0.473465i	$-0.156997\pi$
$674$	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	−0.983014	−	0.183532i	$-0.941247\pi$
$677$	−9711.37	+	12656.1i	−0.551312	+	0.718484i	0.431701	+	0.902017i	$0.357913\pi$
$678$	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	0.969321	−	0.245797i	$-0.0790498\pi$
$683$	1965.30	+	4744.66i	0.110103	+	0.265811i	−0.859219	+	0.511609i	$0.829050\pi$
$684$	−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	0.634663	−	0.772789i	$-0.281139\pi$
$691$	26296.6	−	3462.01i	1.44771	−	0.190595i	0.813050	+	0.582194i	$0.197805\pi$
$692$	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	$-0.970621\pi$
$701$		−	3421.18i		−	0.184331i	0.995744	−	0.0921656i	$-0.0293789\pi$
$702$	−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	−0.100217	−	0.994966i	$-0.531954\pi$
$709$	−20525.1	−	15749.5i	−1.08722	−	0.834251i	−0.987001	+	0.160714i	$0.948620\pi$
$710$		−	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	−0.516712	−	0.856159i	$-0.672844\pi$
$719$	−5334.37	+	2209.57i	−0.276688	+	0.114608i	0.240025	+	0.970767i	$0.422844\pi$
$720$	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	0.0359166	−	0.999355i	$-0.488565\pi$
$727$	18021.0	−	10404.4i	0.919342	−	0.530782i	0.883425	+	0.468573i	$0.155232\pi$
$728$	−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	−0.415472	−	0.909606i	$-0.636383\pi$
$733$	−6359.95	+	1704.14i	−0.320478	+	0.0858718i	0.0949940	+	0.995478i	$0.469717\pi$
$734$	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	−0.517062	−	0.855948i	$-0.672974\pi$
$739$	6808.00	−	6808.00i	0.338885	−	0.338885i	0.855948	+	0.517062i	$0.172974\pi$
$740$	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	0.679883	+	0.733320i	$0.262030\pi$
$743$	−3374.73	+	25633.6i	−0.166631	+	1.26569i	−0.846514	+	0.532366i	$0.821303\pi$
$744$	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	−0.497456	−	0.867489i	$-0.665733\pi$
$751$	−24748.0	−	3258.13i	−1.20249	−	0.158310i	−0.705029	+	0.709179i	$0.749066\pi$
$752$	−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	−0.959747	−	0.280866i	$-0.909378\pi$
$757$	−14139.6	+	14139.6i	−0.678881	+	0.678881i	0.280866	+	0.959747i	$0.409378\pi$
$758$	−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	0.230826	−	0.972995i	$-0.425857\pi$
$761$	−10421.0	−	6016.55i	−0.496399	−	0.286596i	−0.727225	+	0.686399i	$0.759190\pi$
$762$	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	−0.214688	−	0.976683i	$-0.568874\pi$
$769$	−24904.7	−	14378.8i	−1.16786	−	0.674267i	−0.953176	+	0.302416i	$0.902207\pi$
$770$	−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	−0.801123	−	0.598499i	$-0.795764\pi$
$773$	−4354.72	+	4354.72i	−0.202624	+	0.202624i	0.598499	+	0.801123i	$0.295764\pi$
$774$	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	−0.797157	−	0.603772i	$-0.793664\pi$
$787$	2850.40	−	21650.9i	0.129105	−	0.980652i	0.926262	−	0.376880i	$-0.123003\pi$
$788$	−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	−0.920891	−	0.389820i	$-0.872537\pi$
$797$	−34279.1	+	9185.05i	−1.52350	+	0.408220i	−0.602605	+	0.798040i	$0.705871\pi$
$798$	−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	0.662418	−	0.749135i	$-0.269530\pi$
$809$	13831.5	+	5729.20i	0.601100	+	0.248984i	−0.0613180	+	0.998118i	$0.519530\pi$
$810$	7648.13	−	5870.30i	0.331763	−	0.254644i
$811$	19997.3	−	8283.16i	0.865846	−	0.358645i	0.0948547	−	0.995491i	$-0.469761\pi$
$811$	19997.3	−	8283.16i	0.865846	−	0.358645i	0.770991	+	0.636846i	$0.219761\pi$
$812$	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	0.996394	−	0.0848478i	$-0.0270404\pi$
$821$	27578.0	+	21161.3i	1.17232	+	0.899555i	0.175929	+	0.984403i	$0.443707\pi$
$822$	20051.9	+	5372.13i	0.850838	+	0.227950i
$823$	6696.46	−	5138.37i	0.283626	−	0.217634i	−0.457144	−	0.889393i	$-0.651128\pi$
$823$	6696.46	−	5138.37i	0.283626	−	0.217634i	0.740770	+	0.671759i	$0.234461\pi$
$824$	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	0.617008	+	0.786956i	$0.288344\pi$
$827$	−8936.16	+	21573.8i	−0.375745	+	0.907128i	−0.992753	+	0.120171i	$0.961656\pi$
$828$	−4878.14	+	3743.66i	−0.204743	+	0.157127i
$829$			143.572i			0.00601502i	0.999995	+	0.00300751i	$0.000957322\pi$
$829$			143.572i			0.00601502i	−0.999995	+	0.00300751i	$0.999043\pi$
$830$	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	−0.232413	−	0.972617i	$-0.574662\pi$
$839$	−4986.17	+	656.441i	−0.205175	+	0.0270118i	0.0272382	+	0.999629i	$0.491329\pi$
$840$	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	−0.904519	−	0.426433i	$-0.859770\pi$
$853$	−6440.21	+	8393.04i	−0.258509	+	0.336896i	0.646010	+	0.763329i	$0.276437\pi$
$854$		−	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	−0.867034	−	0.498249i	$-0.833977\pi$
$857$	−3976.49	−	30204.4i	−0.158500	−	1.20392i	0.708535	−	0.705676i	$-0.249357\pi$
$858$	−18484.8	+	7657.40i	−0.735501	+	0.304684i
$859$	11470.4	+	42808.1i	0.455606	+	1.70034i	0.686301	+	0.727318i	$0.259233\pi$
$859$	11470.4	+	42808.1i	0.455606	+	1.70034i	−0.230695	+	0.973026i	$0.574100\pi$
$860$	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	$0.0895848\pi$
$863$			14082.6i			0.555476i	−0.960657	+	0.277738i	$0.910415\pi$
$864$	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	−0.446970	−	0.894549i	$-0.647497\pi$
$877$	7828.22	−	6006.81i	0.301414	−	0.231283i	0.748384	+	0.663266i	$0.230830\pi$
$878$	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	0.977609	+	0.210427i	$0.0674856\pi$
$881$	11378.4	+	27470.0i	0.435130	+	1.05050i	−0.542480	+	0.840069i	$0.682514\pi$
$882$	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	0.529390	−	0.848379i	$-0.322421\pi$
$887$	21692.8	+	2855.91i	0.821165	+	0.108108i	0.291775	+	0.956487i	$0.405754\pi$
$888$	−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	−0.466962	−	0.884277i	$-0.654652\pi$
$907$	−18824.4	+	2478.28i	−0.689146	+	0.0907278i	−0.222183	+	0.975005i	$0.571318\pi$
$908$	−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	−0.887672	−	0.460476i	$-0.847679\pi$
$911$	−4108.71	−	31208.8i	−0.149427	−	1.13501i	0.738245	−	0.674532i	$-0.235655\pi$
$912$	−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	0.530395	−	0.847750i	$-0.322044\pi$
$929$	35737.8	−	4704.98i	1.26213	−	0.166163i	0.731737	+	0.681588i	$0.238710\pi$
$930$	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	0.217184	−	0.976131i	$-0.430313\pi$
$937$	−21768.1	−	21768.1i	−0.758947	−	0.758947i	−0.976131	+	0.217184i	$0.930313\pi$
$938$	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	−0.999887	−	0.0150331i	$-0.995215\pi$
$941$	−21811.6	−	28425.4i	−0.755618	−	0.984741i	0.244269	−	0.969708i	$-0.421452\pi$
$942$	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	0.124099	−	0.992270i	$-0.460396\pi$
$947$	−23379.2	−	17939.5i	−0.802241	−	0.615581i	−0.926340	+	0.376689i	$0.877063\pi$
$948$	−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	0.448983	−	0.893540i	$-0.351786\pi$
$967$	38628.0	−	10350.3i	1.28458	−	0.344203i	0.835601	+	0.549337i	$0.185120\pi$
$968$	−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	0.859888	−	0.510483i	$-0.170533\pi$
$971$	10572.0	+	10572.0i	0.349405	+	0.349405i	−0.510483	+	0.859888i	$0.670533\pi$
$972$	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	0.467791	+	0.883839i	$0.345050\pi$
$977$	15409.3	+	57508.2i	0.504592	+	1.88316i	0.0368010	+	0.999323i	$0.488283\pi$
$978$	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	−0.569879	−	0.821729i	$-0.693010\pi$
$983$	11444.8	−	14915.2i	0.371346	−	0.483947i	0.941225	+	0.337782i	$0.109677\pi$
$984$	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	0.315296	−	0.948993i	$-0.397896\pi$
$991$	37725.8	−	15626.5i	1.20928	−	0.500902i	0.893988	+	0.448091i	$0.147896\pi$
$992$	−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	0.172916	−	0.984937i	$-0.444681\pi$
$997$	18726.5	−	2465.39i	0.594860	−	0.0783147i	0.421944	+	0.906622i	$0.361348\pi$
$998$	−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.49.16	yes	416
9.7	even	3	inner	153.4.r.a.151.37	yes	416
17.8	even	8	inner	153.4.r.a.76.37	yes	416
153.25	even	24	inner	153.4.r.a.25.16	✓	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.r.a.25.16	✓	416	153.25	even	24	inner
153.4.r.a.49.16	yes	416	1.1	even	1	trivial
153.4.r.a.76.37	yes	416	17.8	even	8	inner
153.4.r.a.151.37	yes	416	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
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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