LMFDB - Embedded newform 153.4.r.a.25.2

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			25.2
Character	$\chi$	$=$	153.25
Dual form			153.4.r.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33497 - 4.98219i) q^{2} +(0.502950 - 5.17175i) q^{3} +(-16.1118 + 9.30216i) q^{4} +(0.892751 + 6.78112i) q^{5} +(-26.4381 + 4.39836i) q^{6} +(-2.46465 + 18.7209i) q^{7} +(38.6762 + 38.6762i) q^{8} +(-26.4941 - 5.20227i) q^{9} +(32.5930 - 13.5005i) q^{10} +(47.8996 + 6.30610i) q^{11} +(40.0051 + 88.0049i) q^{12} +(-24.5504 + 14.1742i) q^{13} +(96.5613 - 12.7125i) q^{14} +(35.5193 - 1.20652i) q^{15} +(66.6431 - 115.429i) q^{16} +(-60.1200 + 36.0359i) q^{17} +(9.45020 + 138.943i) q^{18} +(-32.9497 + 32.9497i) q^{19} +(-77.4629 - 100.952i) q^{20} +(95.5804 + 22.1623i) q^{21} +(-32.5265 - 247.063i) q^{22} +(-68.5469 + 89.3320i) q^{23} +(219.476 - 180.572i) q^{24} +(75.5542 - 20.2447i) q^{25} +(103.393 + 103.393i) q^{26} +(-40.2301 + 134.404i) q^{27} +(-134.435 - 324.555i) q^{28} +(-90.6468 + 69.5558i) q^{29} +(-53.4284 - 175.353i) q^{30} +(-265.627 + 34.9705i) q^{31} +(-241.395 - 64.6817i) q^{32} +(56.7047 - 244.553i) q^{33} +(259.796 + 251.422i) q^{34} -129.149 q^{35} +(475.260 - 162.634i) q^{36} +(153.908 - 371.568i) q^{37} +(208.148 + 120.174i) q^{38} +(60.9578 + 134.098i) q^{39} +(-227.740 + 296.796i) q^{40} +(120.198 + 92.2308i) q^{41} +(-17.1806 - 505.785i) q^{42} +(88.0942 - 23.6048i) q^{43} +(-830.409 + 343.967i) q^{44} +(11.6246 - 184.304i) q^{45} +(536.577 + 222.257i) q^{46} +(182.591 + 105.419i) q^{47} +(-563.454 - 402.717i) q^{48} +(-13.0855 - 3.50624i) q^{49} +(-201.726 - 349.399i) q^{50} +(156.132 + 329.050i) q^{51} +(263.701 - 456.744i) q^{52} +(-232.225 + 232.225i) q^{53} +(723.334 + 21.0074i) q^{54} +330.442i q^{55} +(-819.378 + 628.731i) q^{56} +(153.836 + 186.980i) q^{57} +(467.551 + 358.764i) q^{58} +(-50.3039 + 187.737i) q^{59} +(-561.057 + 349.845i) q^{60} +(-102.529 + 778.785i) q^{61} +(528.835 + 1276.72i) q^{62} +(162.690 - 483.172i) q^{63} +222.734i q^{64} +(-118.034 - 153.825i) q^{65} +(-1294.11 + 43.9585i) q^{66} +(68.0891 + 117.934i) q^{67} +(633.430 - 1139.85i) q^{68} +(427.528 + 399.437i) q^{69} +(172.410 + 643.444i) q^{70} +(314.729 - 759.822i) q^{71} +(-823.487 - 1225.90i) q^{72} +(-491.076 - 203.410i) q^{73} +(-2056.68 - 270.767i) q^{74} +(-66.7005 - 400.930i) q^{75} +(224.376 - 837.382i) q^{76} +(-236.112 + 881.181i) q^{77} +(586.722 - 482.719i) q^{78} +(-1141.30 - 150.255i) q^{79} +(842.235 + 348.865i) q^{80} +(674.873 + 275.659i) q^{81} +(299.051 - 721.972i) q^{82} +(122.093 + 455.657i) q^{83} +(-1746.13 + 532.029i) q^{84} +(-298.036 - 375.509i) q^{85} +(-235.207 - 407.390i) q^{86} +(314.134 + 503.786i) q^{87} +(1608.68 + 2096.47i) q^{88} +954.110i q^{89} +(-933.754 + 188.125i) q^{90} +(-204.845 - 494.540i) q^{91} +(273.434 - 2076.94i) q^{92} +(47.2615 + 1391.35i) q^{93} +(281.463 - 1050.43i) q^{94} +(-252.851 - 194.020i) q^{95} +(-455.928 + 1215.91i) q^{96} +(-191.345 + 146.824i) q^{97} +69.8749i q^{98} +(-1236.25 - 416.261i) 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 $

$2$	−1.33497	−	4.98219i	−0.471984	−	1.76147i	−0.632628	−	0.774456i	$-0.718024\pi$
$2$	−1.33497	−	4.98219i	−0.471984	−	1.76147i	0.160644	−	0.987012i	$-0.448643\pi$
$3$	0.502950	−	5.17175i	0.0967928	−	0.995305i
$3$	0.502950	−	5.17175i	0.0967928	−	0.995305i
$4$	−16.1118	+	9.30216i	−2.01398	+	1.16277i
$5$	0.892751	+	6.78112i	0.0798501	+	0.606521i	0.983851	+	0.178991i	$0.0572832\pi$
$5$	0.892751	+	6.78112i	0.0798501	+	0.606521i	−0.904001	+	0.427531i	$0.859384\pi$
$6$	−26.4381	+	4.39836i	−1.79888	+	0.299270i
$7$	−2.46465	+	18.7209i	−0.133079	+	1.01083i	0.786406	+	0.617710i	$0.211939\pi$
$7$	−2.46465	+	18.7209i	−0.133079	+	1.01083i	−0.919485	+	0.393125i	$0.871394\pi$
$8$	38.6762	+	38.6762i	1.70926	+	1.70926i
$9$	−26.4941	−	5.20227i	−0.981262	−	0.192677i
$10$	32.5930	−	13.5005i	1.03068	−	0.426922i
$11$	47.8996	+	6.30610i	1.31293	+	0.172851i	0.754281	−	0.656552i	$-0.227986\pi$
$11$	47.8996	+	6.30610i	1.31293	+	0.172851i	0.558652	+	0.829402i	$0.311319\pi$
$12$	40.0051	+	88.0049i	0.962372	+	2.11707i
$13$	−24.5504	+	14.1742i	−0.523774	+	0.302401i	−0.738477	−	0.674278i	$-0.764455\pi$
$13$	−24.5504	+	14.1742i	−0.523774	+	0.302401i	0.214704	+	0.976679i	$0.431121\pi$
$14$	96.5613	−	12.7125i	1.84336	−	0.242683i
$15$	35.5193	−	1.20652i	0.611402	−	0.0207682i
$16$	66.6431	−	115.429i	1.04130	−	1.80358i
$17$	−60.1200	+	36.0359i	−0.857720	+	0.514118i
$17$	−60.1200	+	36.0359i	−0.857720	+	0.514118i
$18$	9.45020	+	138.943i	0.123746	+	1.81940i
$19$	−32.9497	+	32.9497i	−0.397851	+	0.397851i	−0.877474	−	0.479623i	$-0.840773\pi$
$19$	−32.9497	+	32.9497i	−0.397851	+	0.397851i	0.479623	+	0.877474i	$0.340773\pi$
$20$	−77.4629	−	100.952i	−0.866061	−	1.12867i
$21$	95.5804	+	22.1623i	0.993207	+	0.230295i
$22$	−32.5265	−	247.063i	−0.315212	−	2.39427i
$23$	−68.5469	+	89.3320i	−0.621435	+	0.809870i	−0.992947	−	0.118558i	$-0.962173\pi$
$23$	−68.5469	+	89.3320i	−0.621435	+	0.809870i	0.371512	+	0.928428i	$0.378840\pi$
$24$	219.476	−	180.572i	1.86668	−	1.53579i
$25$	75.5542	−	20.2447i	0.604434	−	0.161957i
$26$	103.393	+	103.393i	0.779882	+	0.779882i
$27$	−40.2301	+	134.404i	−0.286751	+	0.958005i
$28$	−134.435	−	324.555i	−0.907350	−	2.19054i
$29$	−90.6468	+	69.5558i	−0.580438	+	0.445385i	−0.856786	−	0.515672i	$-0.827542\pi$
$29$	−90.6468	+	69.5558i	−0.580438	+	0.445385i	0.276348	+	0.961058i	$0.410876\pi$
$30$	−53.4284	−	175.353i	−0.325155	−	1.06716i
$31$	−265.627	+	34.9705i	−1.53897	+	0.202609i	−0.851792	−	0.523880i	$-0.824484\pi$
$31$	−265.627	+	34.9705i	−1.53897	+	0.202609i	−0.687178	+	0.726489i	$0.741151\pi$
$32$	−241.395	−	64.6817i	−1.33353	−	0.357319i
$33$	56.7047	−	244.553i	0.299122	−	1.29004i
$34$	259.796	+	251.422i	1.31043	+	1.26819i
$35$	−129.149			−0.623719
$36$	475.260	−	162.634i	2.20028	−	0.752936i
$37$	153.908	−	371.568i	0.683848	−	1.65096i	−0.0729734	−	0.997334i	$-0.523249\pi$
$37$	153.908	−	371.568i	0.683848	−	1.65096i	0.756822	−	0.653622i	$-0.226751\pi$
$38$	208.148	+	120.174i	0.888582	+	0.513023i
$39$	60.9578	+	134.098i	0.250283	+	0.550585i
$40$	−227.740	+	296.796i	−0.900220	+	1.17319i
$41$	120.198	+	92.2308i	0.457846	+	0.351318i	0.811791	−	0.583949i	$-0.198493\pi$
$41$	120.198	+	92.2308i	0.457846	+	0.351318i	−0.353944	+	0.935267i	$0.615160\pi$
$42$	−17.1806	−	505.785i	−0.0631196	−	1.85820i
$43$	88.0942	−	23.6048i	0.312424	−	0.0837138i	−0.0991999	−	0.995068i	$-0.531628\pi$
$43$	88.0942	−	23.6048i	0.312424	−	0.0837138i	0.411624	+	0.911354i	$0.364962\pi$
$44$	−830.409	+	343.967i	−2.84520	+	1.17852i
$45$	11.6246	−	184.304i	0.0385087	−	0.610542i
$46$	536.577	+	222.257i	1.71987	+	0.712393i
$47$	182.591	+	105.419i	0.566673	+	0.327169i	0.755819	−	0.654780i	$-0.227239\pi$
$47$	182.591	+	105.419i	0.566673	+	0.327169i	−0.189146	+	0.981949i	$0.560572\pi$
$48$	−563.454	−	402.717i	−1.69432	−	1.21098i
$49$	−13.0855	−	3.50624i	−0.0381500	−	0.0102223i
$50$	−201.726	−	349.399i	−0.570566	−	0.988249i
$51$	156.132	+	329.050i	0.428683	+	0.903455i
$52$	263.701	−	456.744i	0.703245	−	1.21806i
$53$	−232.225	+	232.225i	−0.601860	+	0.601860i	−0.940806	−	0.338946i	$-0.889930\pi$
$53$	−232.225	+	232.225i	−0.601860	+	0.601860i	0.338946	+	0.940806i	$0.389930\pi$
$54$	723.334	+	21.0074i	1.82284	+	0.0529398i
$55$			330.442i			0.810124i
$56$	−819.378	+	628.731i	−1.95525	+	1.50032i
$57$	153.836	+	186.980i	0.357474	+	0.434492i
$58$	467.551	+	358.764i	1.05849	+	0.812208i
$59$	−50.3039	+	187.737i	−0.111000	+	0.414258i	−0.998957	−	0.0456695i	$-0.985458\pi$
$59$	−50.3039	+	187.737i	−0.111000	+	0.414258i	0.887957	+	0.459927i	$0.152125\pi$
$60$	−561.057	+	349.845i	−1.20720	+	0.752747i
$61$	−102.529	+	778.785i	−0.215205	+	1.63464i	0.453601	+	0.891205i	$0.350139\pi$
$61$	−102.529	+	778.785i	−0.215205	+	1.63464i	−0.668805	+	0.743437i	$0.733194\pi$
$62$	528.835	+	1276.72i	1.08326	+	2.61522i
$63$	162.690	−	483.172i	0.325349	−	0.966252i
$64$			222.734i			0.435028i
$65$	−118.034	−	153.825i	−0.225236	−	0.293533i
$66$	−1294.11	+	43.9585i	−2.41354	+	0.0819835i
$67$	68.0891	+	117.934i	0.124155	+	0.215043i	0.921402	−	0.388610i	$-0.127045\pi$
$67$	68.0891	+	117.934i	0.124155	+	0.215043i	−0.797247	+	0.603653i	$0.793711\pi$
$68$	633.430	−	1139.85i	1.12963	−	2.03275i
$69$	427.528	+	399.437i	0.745917	+	0.696907i
$70$	172.410	+	643.444i	0.294385	+	1.09866i
$71$	314.729	−	759.822i	0.526076	−	1.27006i	−0.407999	−	0.912983i	$-0.633773\pi$
$71$	314.729	−	759.822i	0.526076	−	1.27006i	0.934075	−	0.357078i	$-0.116227\pi$
$72$	−823.487	−	1225.90i	−1.34790	−	2.00657i
$73$	−491.076	−	203.410i	−0.787344	−	0.326129i	−0.0474689	−	0.998873i	$-0.515116\pi$
$73$	−491.076	−	203.410i	−0.787344	−	0.326129i	−0.739875	+	0.672744i	$0.765116\pi$
$74$	−2056.68	−	270.767i	−3.23087	−	0.425352i
$75$	−66.7005	−	400.930i	−0.102692	−	0.617272i
$76$	224.376	−	837.382i	0.338654	−	1.26387i
$77$	−236.112	+	881.181i	−0.349447	+	1.30415i
$78$	586.722	−	482.719i	0.851708	−	0.700734i
$79$	−1141.30	−	150.255i	−1.62540	−	0.213988i	−0.737938	−	0.674868i	$-0.764201\pi$
$79$	−1141.30	−	150.255i	−1.62540	−	0.213988i	−0.887462	+	0.460880i	$0.847534\pi$
$80$	842.235	+	348.865i	1.17706	+	0.487554i
$81$	674.873	+	275.659i	0.925751	+	0.378133i
$82$	299.051	−	721.972i	0.402739	−	0.972298i
$83$	122.093	+	455.657i	0.161463	+	0.602589i	0.998465	+	0.0553885i	$0.0176397\pi$
$83$	122.093	+	455.657i	0.161463	+	0.602589i	−0.837002	+	0.547200i	$0.815694\pi$
$84$	−1746.13	+	532.029i	−2.26808	+	0.691062i
$85$	−298.036	−	375.509i	−0.380312	−	0.479173i
$86$	−235.207	−	407.390i	−0.294919	−	0.510814i
$87$	314.134	+	503.786i	0.387112	+	0.620822i
$88$	1608.68	+	2096.47i	1.94870	+	2.53960i
$89$			954.110i			1.13635i	0.822907	+	0.568176i	$0.192351\pi$
$89$			954.110i			1.13635i	−0.822907	+	0.568176i	$0.807649\pi$
$90$	−933.754	+	188.125i	−1.09363	+	0.220334i
$91$	−204.845	−	494.540i	−0.235974	−	0.569691i
$92$	273.434	−	2076.94i	0.309863	−	2.35365i
$93$	47.2615	+	1391.35i	0.0526967	+	1.55135i
$94$	281.463	−	1050.43i	0.308837	−	1.15260i
$95$	−252.851	−	194.020i	−0.273074	−	0.209537i
$96$	−455.928	+	1215.91i	−0.484718	+	1.29269i
$97$	−191.345	+	146.824i	−0.200290	+	0.153688i	−0.704037	−	0.710163i	$-0.748621\pi$
$97$	−191.345	+	146.824i	−0.200290	+	0.153688i	0.503747	+	0.863851i	$0.331954\pi$
$98$			69.8749i			0.0720248i
$99$	−1236.25	−	416.261i	−1.25503	−	0.422583i
$100$	−1029.00	+	1029.00i	−1.02900	+	1.02900i
$101$	521.996	−	904.123i	0.514263	−	0.890729i	−0.485600	−	0.874181i	$-0.661399\pi$
$101$	521.996	−	904.123i	0.514263	−	0.890729i	0.999863	−	0.0165482i	$-0.00526771\pi$
$102$	1430.96	−	1217.15i	1.38908	−	1.18153i
$103$	192.620	+	333.628i	0.184266	+	0.319158i	0.943329	−	0.331859i	$-0.107676\pi$
$103$	192.620	+	333.628i	0.184266	+	0.319158i	−0.759063	+	0.651017i	$0.774342\pi$
$104$	−1497.72	−	401.313i	−1.41215	−	0.378385i
$105$	−64.9555	+	667.927i	−0.0603715	+	0.620790i
$106$	1467.00	+	846.975i	1.34423	+	0.776090i
$107$	1950.23	+	807.810i	1.76201	+	0.729850i	0.996230	+	0.0867533i	$0.0276492\pi$
$107$	1950.23	+	807.810i	1.76201	+	0.729850i	0.765785	+	0.643097i	$0.222351\pi$
$108$	−602.072	−	2539.73i	−0.536430	−	2.26283i
$109$	−1157.93	+	479.630i	−1.01752	+	0.421470i	−0.828192	−	0.560445i	$-0.810630\pi$
$109$	−1157.93	+	479.630i	−1.01752	+	0.421470i	−0.189326	+	0.981914i	$0.560630\pi$
$110$	1646.32	−	441.131i	1.42701	−	0.382366i
$111$	−1844.25	−	982.856i	−1.57701	−	0.840438i
$112$	1996.69	+	1532.11i	1.68455	+	1.29260i
$113$	344.714	−	449.240i	0.286973	−	0.373990i	−0.627514	−	0.778605i	$-0.715928\pi$
$113$	344.714	−	449.240i	0.286973	−	0.373990i	0.914487	+	0.404615i	$0.132594\pi$
$114$	726.201	−	1016.05i	0.596622	−	0.834753i
$115$	−666.966	−	385.073i	−0.540825	−	0.312246i
$116$	813.466	−	1963.88i	0.651107	−	1.57191i
$117$	724.178	−	247.814i	0.572225	−	0.195816i
$118$	1002.49			0.782093
$119$	−526.451	−	1214.32i	−0.405543	−	0.935431i
$120$	1420.42	+	1327.09i	1.08055	+	1.00955i
$121$	968.953	+	259.630i	0.727989	+	0.195064i
$122$	4016.92	−	528.838i	2.98094	−	0.392449i
$123$	537.448	−	575.245i	0.393985	−	0.421692i
$124$	3954.44	−	3034.35i	2.86386	−	2.19752i
$125$	531.909	+	1284.14i	0.380603	+	0.918858i
$126$	−2624.44	−	165.531i	−1.85558	−	0.117037i
$127$	−626.771	−	626.771i	−0.437929	−	0.437929i	0.453386	−	0.891314i	$-0.350216\pi$
$127$	−626.771	−	626.771i	−0.437929	−	0.437929i	−0.891314	+	0.453386i	$0.850216\pi$
$128$	−821.459	+	220.109i	−0.567245	+	0.151993i
$129$	−77.7711	−	467.474i	−0.0530803	−	0.319060i
$130$	−608.813	+	793.421i	−0.410742	+	0.535289i
$131$	60.7006	+	461.067i	0.0404843	+	0.307509i	0.999692	+	0.0248072i	$0.00789720\pi$
$131$	60.7006	+	461.067i	0.0404843	+	0.307509i	−0.959208	+	0.282701i	$0.908769\pi$
$132$	1361.26	+	4467.67i	0.897593	+	2.94592i
$133$	−535.638	−	698.057i	−0.349216	−	0.455107i
$134$	496.671	−	496.671i	0.320193	−	0.320193i
$135$	−947.327	−	152.815i	−0.603948	−	0.0974239i
$136$	−3718.95	−	931.479i	−2.34483	−	0.587307i
$137$	273.756	−	474.159i	0.170719	−	0.295694i	−0.767952	−	0.640507i	$-0.778724\pi$
$137$	273.756	−	474.159i	0.170719	−	0.295694i	0.938672	+	0.344813i	$0.112058\pi$
$138$	1419.33	−	2663.26i	0.875519	−	1.64284i
$139$	−1439.38	+	189.498i	−0.878319	+	0.115633i	−0.556183	−	0.831060i	$-0.687734\pi$
$139$	−1439.38	+	189.498i	−0.878319	+	0.115633i	−0.322137	+	0.946693i	$0.604401\pi$
$140$	2080.83	−	1201.36i	1.25616	−	0.725242i
$141$	637.035	−	891.295i	0.380482	−	0.532345i
$142$	−4205.73	−	553.695i	−2.48547	−	0.327218i
$143$	−1265.34	+	524.120i	−0.739950	+	0.306497i
$144$	−2366.14	+	2711.50i	−1.36930	+	1.56915i
$145$	−552.591	−	552.591i	−0.316484	−	0.316484i
$146$	−357.855	+	2718.18i	−0.202851	+	1.54081i
$147$	−24.7147	+	65.9113i	−0.0138669	+	0.0369815i
$148$	976.639	+	7418.31i	0.542427	+	4.12014i
$149$	−2355.90	+	1360.18i	−1.29532	+	0.747855i	−0.979592	−	0.200994i	$-0.935583\pi$
$149$	−2355.90	+	1360.18i	−1.29532	+	0.747855i	−0.315730	+	0.948849i	$0.602249\pi$
$150$	−1908.46	+	867.545i	−1.03884	+	0.472232i
$151$	−918.892	−	3429.35i	−0.495221	−	1.84819i	−0.528788	−	0.848754i	$-0.677353\pi$
$151$	−918.892	−	3429.35i	−0.495221	−	1.84819i	0.0335667	−	0.999436i	$-0.489313\pi$
$152$	−2548.74			−1.36007
$153$	1780.29	−	641.979i	0.940706	−	0.339222i
$154$	4705.41			2.46216
$155$	−474.278	−	1770.03i	−0.245774	−	0.917240i
$156$	−2229.54	−	1593.52i	−1.14427	−	0.817843i
$157$	2091.62	−	1207.60i	1.06325	−	0.613866i	0.136918	−	0.990582i	$-0.456280\pi$
$157$	2091.62	−	1207.60i	1.06325	−	0.613866i	0.926329	+	0.376716i	$0.122947\pi$
$158$	775.008	+	5886.77i	0.390230	+	2.96409i
$159$	1084.21	+	1317.81i	0.540779	+	0.657290i
$160$	223.108	−	1694.67i	0.110239	−	0.837349i
$161$	−1503.43	−	1503.43i	−0.735945	−	0.735945i
$162$	472.446	−	3730.34i	0.229129	−	1.80915i
$163$	704.750	−	291.917i	0.338652	−	0.140274i	−0.206875	−	0.978367i	$-0.566329\pi$
$163$	704.750	−	291.917i	0.338652	−	0.140274i	0.545527	+	0.838093i	$0.316329\pi$
$164$	−2794.55	−	367.909i	−1.33059	−	0.175176i
$165$	1708.97	+	166.196i	0.806320	+	0.0784142i
$166$	2107.18	−	1216.58i	0.985233	−	0.568825i
$167$	−2409.14	+	317.169i	−1.11631	+	0.146966i	−0.666034	−	0.745922i	$-0.732009\pi$
$167$	−2409.14	+	317.169i	−1.11631	+	0.146966i	−0.450280	+	0.892887i	$0.648676\pi$
$168$	2839.53	+	4553.84i	1.30402	+	2.09129i
$169$	−696.685	+	1206.69i	−0.317107	+	0.549246i
$170$	−1472.99	+	1986.17i	−0.664547	+	0.896070i
$171$	1044.38	−	701.558i	0.467053	−	0.313740i
$172$	−1199.78	+	1199.78i	−0.531875	+	0.531875i
$173$	−1080.81	−	1408.54i	−0.474985	−	0.619013i	0.492997	−	0.870031i	$-0.335901\pi$
$173$	−1080.81	−	1408.54i	−0.474985	−	0.619013i	−0.967982	+	0.251018i	$0.919235\pi$
$174$	2090.60	−	2237.62i	0.910848	−	0.974904i
$175$	192.784	+	1464.34i	0.0832748	+	0.632535i
$176$	3920.09	−	5108.75i	1.67891	−	2.18799i
$177$	945.627	+	354.581i	0.401569	+	0.150576i
$178$	4753.55	−	1273.71i	2.00165	−	0.536341i
$179$	720.042	+	720.042i	0.300662	+	0.300662i	0.841273	−	0.540611i	$-0.181807\pi$
$179$	720.042	+	720.042i	0.300662	+	0.300662i	−0.540611	+	0.841273i	$0.681807\pi$
$180$	1527.13	+	3077.60i	0.632364	+	1.27439i
$181$	1238.21	+	2989.30i	0.508483	+	1.22759i	0.944757	+	0.327773i	$0.106298\pi$
$181$	1238.21	+	2989.30i	0.508483	+	1.22759i	−0.436273	+	0.899814i	$0.643702\pi$
$182$	−2190.43	+	1680.78i	−0.892118	+	0.684546i
$183$	3976.12	+	921.945i	1.60614	+	0.372416i
$184$	−6106.16	+	803.891i	−2.44648	+	0.322085i
$185$	2657.05	+	711.953i	1.05595	+	0.282940i
$186$	6868.86	−	2092.88i	2.70779	−	0.825038i
$187$	−3106.97	+	1346.98i	−1.21499	+	0.526744i
$188$	−3922.50			−1.52169
$189$	−2417.02	−	1084.40i	−0.930224	−	0.417348i
$190$	−629.092	+	1518.76i	−0.240206	+	0.579909i
$191$	1801.78	+	1040.26i	0.682576	+	0.394086i	0.800825	−	0.598898i	$-0.204395\pi$
$191$	1801.78	+	1040.26i	0.682576	+	0.394086i	−0.118249	+	0.992984i	$0.537728\pi$
$192$	1151.93	+	112.024i	0.432985	+	0.0421076i
$193$	1970.08	−	2567.46i	0.734764	−	0.957563i	−0.265214	−	0.964190i	$-0.585443\pi$
$193$	1970.08	−	2567.46i	0.734764	−	0.957563i	0.999978	+	0.00662616i	$0.00210919\pi$
$194$	986.946	+	757.310i	0.365251	+	0.280267i
$195$	−854.911	+	533.077i	−0.313956	+	0.195766i
$196$	243.446	−	65.2312i	0.0887195	−	0.0237723i
$197$	−3445.01	+	1426.97i	−1.24592	+	0.516078i	−0.905561	−	0.424217i	$-0.860549\pi$
$197$	−3445.01	+	1426.97i	−1.24592	+	0.516078i	−0.340361	+	0.940295i	$0.610549\pi$
$198$	−423.529	+	6714.92i	−0.152015	+	2.41014i
$199$	−4268.06	−	1767.89i	−1.52037	−	0.629760i	−0.542708	−	0.839922i	$-0.682601\pi$
$199$	−4268.06	−	1767.89i	−1.52037	−	0.629760i	−0.977667	+	0.210162i	$0.932601\pi$
$200$	3705.14	+	2139.16i	1.30996	+	0.756308i
$201$	644.170	−	292.825i	0.226051	−	0.102758i
$202$	−5201.36	−	1393.70i	−1.81172	−	0.485448i
$203$	−1078.73	−	1868.42i	−0.372967	−	0.645998i
$204$	−5576.44	−	3849.23i	−1.91387	−	1.32108i
$205$	−518.121	+	897.413i	−0.176523	+	0.305746i
$206$	1405.05	−	1405.05i	0.475217	−	0.475217i
$207$	2280.82	−	2010.17i	0.765834	−	0.674959i
$208$			3778.45i			1.25956i
$209$	−1786.06	+	1370.49i	−0.591121	+	0.453583i
$210$	3414.45	−	568.044i	1.12200	−	0.186661i
$211$	−1075.13	−	824.979i	−0.350783	−	0.269166i	0.418307	−	0.908306i	$-0.362624\pi$
$211$	−1075.13	−	824.979i	−0.350783	−	0.269166i	−0.769090	+	0.639140i	$0.779290\pi$
$212$	1581.37	−	5901.77i	0.512308	−	1.91196i
$213$	−3771.32	−	2009.85i	−1.21318	−	0.646539i
$214$	1421.16	−	10794.8i	0.453966	−	3.44821i
$215$	238.713	+	576.304i	0.0757213	+	0.182808i
$216$	−6754.20	+	3642.31i	−2.12762	+	1.14735i
$217$		−	5058.97i		−	1.58261i
$218$	3935.41	+	5128.72i	1.22266	+	1.59340i
$219$	−1298.98	+	2437.42i	−0.400807	+	0.752080i
$220$	−3073.83	−	5324.02i	−0.941988	−	1.63157i
$221$	965.190	−	1736.85i	0.293781	−	0.528656i
$222$	−2434.75	+	10500.5i	−0.736080	+	3.17453i
$223$	−479.661	−	1790.12i	−0.144038	−	0.537558i	−0.999796	−	0.0201817i	$-0.993576\pi$
$223$	−479.661	−	1790.12i	−0.144038	−	0.537558i	0.855758	−	0.517376i	$-0.173091\pi$
$224$	1805.86	−	4359.72i	0.538656	−	1.30043i
$225$	−2107.06	+	143.311i	−0.624313	+	0.0424625i
$226$	−2698.38	−	1117.71i	−0.794219	−	0.328976i
$227$	3402.09	+	447.893i	0.994733	+	0.130959i	0.610280	−	0.792185i	$-0.291057\pi$
$227$	3402.09	+	447.893i	0.994733	+	0.130959i	0.384453	+	0.923145i	$0.374390\pi$
$228$	−4217.89	−	1581.58i	−1.22516	−	0.459397i
$229$	−1016.65	+	3794.20i	−0.293372	+	1.09488i	0.649129	+	0.760678i	$0.275134\pi$
$229$	−1016.65	+	3794.20i	−0.293372	+	1.09488i	−0.942501	+	0.334202i	$0.891533\pi$
$230$	−1028.12	+	3837.01i	−0.294750	+	1.10002i
$231$	4438.50	+	1664.30i	1.26421	+	0.474039i
$232$	−6196.03	−	815.723i	−1.75340	−	0.230840i
$233$	5635.50	+	2334.30i	1.58452	+	0.656331i	0.989122	−	0.147096i	$-0.0469928\pi$
$233$	5635.50	+	2334.30i	1.58452	+	0.656331i	0.595402	+	0.803428i	$0.296993\pi$
$234$	−2201.41	−	3277.17i	−0.615004	−	0.915534i
$235$	−551.850	+	1332.28i	−0.153186	+	0.369824i
$236$	−935.869	−	3492.71i	−0.258135	−	0.963374i
$237$	−1351.10	+	5826.97i	−0.370310	+	1.59706i
$238$	−5347.15	+	4243.96i	−1.45632	+	1.15586i
$239$	387.257	+	670.749i	0.104810	+	0.181536i	0.913661	−	0.406478i	$-0.133243\pi$
$239$	387.257	+	670.749i	0.104810	+	0.181536i	−0.808851	+	0.588014i	$0.799910\pi$
$240$	2227.85	−	4180.37i	0.599196	−	1.12434i
$241$	2211.60	+	2882.21i	0.591127	+	0.770371i	0.989135	−	0.147011i	$-0.0469651\pi$
$241$	2211.60	+	2882.21i	0.591127	+	0.770371i	−0.398008	+	0.917382i	$0.630298\pi$
$242$		−	5174.10i		−	1.37440i
$243$	1765.07	−	3351.63i	0.465963	−	0.884804i
$244$	−5592.46	−	13501.4i	−1.46730	−	3.54237i
$245$	12.0942	−	91.8642i	0.00315374	−	0.0239551i
$246$	−3583.45	−	1909.73i	−0.928751	−	0.494960i
$247$	341.893	−	1275.96i	0.0880734	−	0.328695i
$248$	−11626.0	−	8920.93i	−2.97682	−	2.28419i
$249$	2417.95	−	402.262i	0.615388	−	0.102379i
$250$	5687.75	−	4364.37i	1.43890	−	1.10411i
$251$		−	7509.83i		−	1.88851i	−0.329212	−	0.944256i	$-0.606783\pi$
$251$		−	7509.83i		−	1.88851i	0.329212	−	0.944256i	$-0.393217\pi$
$252$	1873.31	+	9298.14i	0.468283	+	2.32432i
$253$	−3846.70	+	3846.70i	−0.955890	+	0.955890i
$254$	−2285.97	+	3959.41i	−0.564702	+	0.978093i
$255$	−2091.94	+	1352.51i	−0.513735	+	0.332146i
$256$	3084.19	+	5341.97i	0.752976	+	1.30419i
$257$	−460.373	−	123.357i	−0.111741	−	0.0299408i	0.202515	−	0.979279i	$-0.435088\pi$
$257$	−460.373	−	123.357i	−0.111741	−	0.0299408i	−0.314256	+	0.949338i	$0.601755\pi$
$258$	−2225.22	+	1011.53i	−0.536962	+	0.244091i
$259$	6576.76	+	3797.09i	1.57784	+	0.910964i
$260$	3332.65	+	1380.43i	0.794932	+	0.329272i
$261$	2763.45	−	1371.25i	0.655377	−	0.325203i
$262$	2216.09	−	917.934i	0.522559	−	0.216451i
$263$	4453.22	−	1193.24i	1.04410	−	0.279765i	0.304286	−	0.952581i	$-0.401582\pi$
$263$	4453.22	−	1193.24i	1.04410	−	0.279765i	0.739810	+	0.672816i	$0.234916\pi$
$264$	11651.5	−	7265.27i	2.71629	−	1.69374i
$265$	−1782.07	−	1367.43i	−0.413100	−	0.316983i
$266$	−2762.79	+	3600.54i	−0.636833	+	0.829936i
$267$	4934.42	+	479.870i	1.13102	+	0.109991i
$268$	−2194.08	−	1266.75i	−0.500092	−	0.288728i
$269$	26.7540	−	64.5899i	0.00606402	−	0.0146398i	−0.920819	−	0.389991i	$-0.872478\pi$
$269$	26.7540	−	64.5899i	0.00606402	−	0.0146398i	0.926883	+	0.375352i	$0.122478\pi$
$270$	503.303	+	4923.76i	0.113445	+	1.10982i
$271$	−645.128			−0.144608			−0.0723039	−	0.997383i	$-0.523035\pi$
$271$	−645.128			−0.144608			−0.0723039	+	0.997383i	$0.523035\pi$
$272$	153.021	+	9341.16i	0.0341111	+	2.08232i
$273$	−2660.67	+	810.681i	−0.589857	+	0.179724i
$274$	−2727.80	−	730.913i	−0.601433	−	0.161153i
$275$	3746.68	−	493.259i	0.821575	−	0.108162i
$276$	−10603.9	−	2458.73i	−2.31260	−	0.536225i
$277$	−3789.81	+	2908.03i	−0.822050	+	0.630781i	−0.931716	−	0.363188i	$-0.881688\pi$
$277$	−3789.81	+	2908.03i	−0.822050	+	0.630781i	0.109666	+	0.993968i	$0.465022\pi$
$278$	2865.64	+	6918.27i	0.618237	+	1.49256i
$279$	7219.48	+	455.353i	1.54917	+	0.0977108i
$280$	−4995.00	−	4995.00i	−1.06610	−	1.06610i
$281$	2244.55	−	601.425i	0.476508	−	0.127680i	−0.0125684	−	0.999921i	$-0.504001\pi$
$281$	2244.55	−	601.425i	0.476508	−	0.127680i	0.489076	+	0.872241i	$0.337334\pi$
$282$	−5291.02	−	1983.97i	−1.11729	−	0.418950i
$283$	3274.75	−	4267.74i	0.687858	−	0.896434i	−0.310678	−	0.950515i	$-0.600556\pi$
$283$	3274.75	−	4267.74i	0.687858	−	0.896434i	0.998537	+	0.0540809i	$0.0172229\pi$
$284$	1997.14	+	15169.8i	0.417283	+	3.16958i
$285$	−1130.59	+	1210.10i	−0.234985	+	0.251510i
$286$	4300.45	+	5604.46i	0.889130	+	1.15874i
$287$	−2022.89	+	2022.89i	−0.416054	+	0.416054i
$288$	6059.06	+	2969.49i	1.23970	+	0.607565i
$289$	2315.82	−	4332.96i	0.471366	−	0.881938i
$290$	−2015.42	+	3490.80i	−0.408101	+	0.706852i
$291$	663.102	+	1063.44i	0.133580	+	0.214226i
$292$	9804.29	−	1290.76i	1.96491	−	0.258685i
$293$	6279.71	−	3625.59i	1.25210	−	0.722899i	0.280573	−	0.959833i	$-0.409476\pi$
$293$	6279.71	−	3625.59i	1.25210	−	0.722899i	0.971526	+	0.236933i	$0.0761423\pi$
$294$	361.376	+	35.1436i	0.0716867	+	0.00697149i
$295$	−1317.97	−	173.514i	−0.260120	−	0.0342454i
$296$	20323.4	−	8418.24i	3.99080	−	1.65304i
$297$	−2774.57	+	6184.22i	−0.542077	+	1.20823i
$298$	9921.74	+	9921.74i	1.92869	+	1.92869i
$299$	416.645	−	3164.73i	0.0805860	−	0.612111i
$300$	4804.18	+	5839.25i	0.924565	+	1.12376i
$301$	224.781	+	1707.38i	0.0430438	+	0.326950i
$302$	−15859.0	+	9156.18i	−3.02179	+	1.74463i
$303$	−4413.37	−	3154.36i	−0.836770	−	0.598064i
$304$	1607.49	+	5999.23i	0.303276	+	1.13184i
$305$	−5372.56			−1.00863
$306$	−5575.10	−	8012.72i	−1.04153	−	1.49692i
$307$	3535.81			0.657326			0.328663	−	0.944447i	$-0.393402\pi$
$307$	3535.81			0.657326			0.328663	+	0.944447i	$0.393402\pi$
$308$	−4392.70	−	16393.8i	−0.812653	−	3.03286i
$309$	1822.32	−	828.385i	0.335495	−	0.152509i
$310$	−8185.47	+	4725.88i	−1.49969	+	0.865845i
$311$	−141.230	−	1072.75i	−0.0257505	−	0.195594i	0.973734	−	0.227687i	$-0.0731162\pi$
$311$	−141.230	−	1072.75i	−0.0257505	−	0.195594i	−0.999485	+	0.0320925i	$0.989783\pi$
$312$	−2828.77	+	7544.00i	−0.513294	+	1.36889i
$313$	−950.370	+	7218.78i	−0.171623	+	1.30361i	0.661259	+	0.750158i	$0.270023\pi$
$313$	−950.370	+	7218.78i	−0.171623	+	1.30361i	−0.832882	+	0.553451i	$0.813311\pi$
$314$	−8808.75	−	8808.75i	−1.58314	−	1.58314i
$315$	3421.68	+	671.868i	0.612032	+	0.120176i
$316$	19786.2	−	8195.70i	3.52234	−	1.45900i
$317$	6661.63	+	877.021i	1.18030	+	0.155389i	0.695033	−	0.718978i	$-0.255390\pi$
$317$	6661.63	+	877.021i	1.18030	+	0.155389i	0.485265	+	0.874367i	$0.338723\pi$
$318$	5118.18	−	7161.00i	0.902557	−	1.26280i
$319$	−4780.57	+	2760.06i	−0.839061	+	0.484432i
$320$	−1510.39	+	198.846i	−0.263854	+	0.0347370i
$321$	5158.66	−	9679.81i	0.896974	−	1.68310i
$322$	−5483.34	+	9497.42i	−0.948989	+	1.64370i
$323$	793.561	−	3168.31i	0.136702	−	0.545787i
$324$	−13437.6	+	1836.41i	−2.30412	+	0.314886i
$325$	−1567.93	+	1567.93i	−0.267610	+	0.267610i
$326$	−2395.20	−	3121.49i	−0.406927	−	0.530317i
$327$	1898.15	+	6229.75i	0.321002	+	1.05354i
$328$	1081.65	+	8215.93i	0.182085	+	1.38308i
$329$	−2423.56	+	3158.45i	−0.406126	+	0.529273i
$330$	−1453.40	−	8736.25i	−0.242446	−	1.45732i
$331$	−1451.41	+	388.904i	−0.241017	+	0.0645804i	−0.377306	−	0.926089i	$-0.623149\pi$
$331$	−1451.41	+	388.904i	−0.241017	+	0.0645804i	0.136288	+	0.990669i	$0.456483\pi$
$332$	−6205.74	−	6205.74i	−1.02586	−	1.02586i
$333$	−6010.66	+	9043.67i	−0.989135	+	1.48826i
$334$	4796.32	+	11579.3i	0.785758	+	1.89699i
$335$	−738.936	+	567.005i	−0.120515	+	0.0924741i
$336$	8927.95	−	9555.81i	1.44958	−	1.55152i
$337$	9478.61	−	1247.88i	1.53215	−	0.201711i	0.683216	−	0.730217i	$-0.260581\pi$
$337$	9478.61	−	1247.88i	1.53215	−	0.201711i	0.848930	+	0.528506i	$0.177248\pi$
$338$	6942.03	+	1860.11i	1.11715	+	0.299339i
$339$	−2149.98	−	2008.72i	−0.344457	−	0.321825i
$340$	8294.95	+	3277.76i	1.32311	+	0.522828i
$341$	−12944.0			−2.05558
$342$	−4889.52	−	4266.76i	−0.773084	−	0.674619i
$343$	−2380.63	+	5747.34i	−0.374757	+	0.904745i
$344$	4320.10	+	2494.21i	0.677105	+	0.390927i
$345$	−2326.95	+	3255.71i	−0.363128	+	0.508063i
$346$	−5574.75	+	7265.16i	−0.866186	+	1.12884i
$347$	1758.27	+	1349.17i	0.272015	+	0.208724i	0.735757	−	0.677246i	$-0.236827\pi$
$347$	1758.27	+	1349.17i	0.272015	+	0.208724i	−0.463742	+	0.885970i	$0.653493\pi$
$348$	−9747.58	−	5194.78i	−1.50151	−	0.800200i
$349$	5714.85	−	1531.29i	0.876530	−	0.234866i	0.207621	−	0.978209i	$-0.433428\pi$
$349$	5714.85	−	1531.29i	0.876530	−	0.234866i	0.668909	+	0.743344i	$0.266761\pi$
$350$	7038.25	−	2915.34i	1.07489	−	0.445233i
$351$	−917.408	−	3869.91i	−0.139509	−	0.588492i
$352$	−11154.8	−	4620.49i	−1.68908	−	0.699638i
$353$	−1249.49	−	721.391i	−0.188395	−	0.108770i	0.402836	−	0.915272i	$-0.368025\pi$
$353$	−1249.49	−	721.391i	−0.188395	−	0.108770i	−0.591231	+	0.806502i	$0.701358\pi$
$354$	504.204	−	5184.65i	0.0757009	−	0.778420i
$355$	5433.41	+	1455.88i	0.812326	+	0.217662i
$356$	−8875.28	−	15372.4i	−1.32132	−	2.28859i
$357$	−6544.93	+	2111.93i	−0.970292	+	0.313096i
$358$	2626.15	−	4548.62i	0.387699	−	0.671514i
$359$	−2120.29	+	2120.29i	−0.311713	+	0.311713i	−0.845573	−	0.533860i	$-0.820741\pi$
$359$	−2120.29	+	2120.29i	−0.311713	+	0.311713i	0.533860	+	0.845573i	$0.320741\pi$
$360$	7577.77	−	6678.58i	1.10940	−	0.977756i
$361$			4687.64i			0.683429i
$362$	13240.3	−	10159.6i	1.92236	−	1.47508i
$363$	1830.08	−	4880.61i	0.264612	−	0.705690i
$364$	7900.73	+	6062.44i	1.13767	+	0.872962i
$365$	940.941	−	3511.64i	0.134935	−	0.503583i
$366$	−714.708	−	21040.5i	−0.102072	−	3.00493i
$367$	1470.53	−	11169.8i	0.209158	−	1.58871i	−0.488685	−	0.872460i	$-0.662523\pi$
$367$	1470.53	−	11169.8i	0.209158	−	1.58871i	0.697843	−	0.716251i	$-0.254143\pi$
$368$	5743.36	+	13865.7i	0.813568	+	1.96413i
$369$	−2704.71	−	3068.87i	−0.381577	−	0.432951i
$370$		−	14188.3i		−	1.99356i
$371$	−3775.11	−	4919.83i	−0.528286	−	0.688476i
$372$	−13704.0	−	21977.5i	−1.91000	−	3.06312i
$373$	799.897	+	1385.46i	0.111038	+	0.192323i	0.916189	−	0.400747i	$-0.131249\pi$
$373$	799.897	+	1385.46i	0.111038	+	0.192323i	−0.805151	+	0.593070i	$0.797916\pi$
$374$	10858.6	+	13681.3i	1.50130	+	1.89156i
$375$	6908.79	−	2105.04i	0.951383	−	0.289877i
$376$	2984.72	+	11139.1i	0.409376	+	1.52781i
$377$	1239.52	−	2992.47i	0.169333	−	0.408806i
$378$	−2176.05	+	13489.7i	−0.296095	+	1.83554i
$379$	−868.033	−	359.551i	−0.117646	−	0.0487306i	0.323084	−	0.946370i	$-0.395280\pi$
$379$	−868.033	−	359.551i	−0.117646	−	0.0487306i	−0.440730	+	0.897640i	$0.645280\pi$
$380$	5878.70	+	773.945i	0.793608	+	0.104480i
$381$	−3556.74	+	2926.27i	−0.478261	+	0.393484i
$382$	2777.43	−	10365.5i	0.372004	−	1.38834i
$383$	−393.521	+	1468.64i	−0.0525012	+	0.195937i	−0.987195	−	0.159516i	$-0.949007\pi$
$383$	−393.521	+	1468.64i	−0.0525012	+	0.195937i	0.934694	+	0.355453i	$0.115673\pi$
$384$	725.198	+	4359.09i	0.0963740	+	0.579294i
$385$	−6186.18	−	814.426i	−0.818901	−	0.107810i
$386$	−15421.6	−	6387.82i	−2.03352	−	0.842310i
$387$	−2456.77	+	167.097i	−0.322700	+	0.0219484i
$388$	1717.13	−	4145.53i	0.224676	−	0.542416i
$389$	−1942.74	−	7250.39i	−0.253215	−	0.945011i	−0.969075	−	0.246767i	$-0.920632\pi$
$389$	−1942.74	−	7250.39i	−0.253215	−	0.945011i	0.715860	−	0.698244i	$-0.246035\pi$
$390$	3797.17	+	3547.68i	0.493019	+	0.460625i
$391$	901.872	−	7840.79i	0.116649	−	1.01413i
$392$	−370.488	−	641.704i	−0.0477359	−	0.0826810i
$393$	2415.06	−	82.0350i	0.309983	−	0.0105296i
$394$	11708.4	+	15258.7i	1.49711	+	1.95107i
$395$		−	7873.45i		−	1.00293i
$396$	23790.3	−	4793.07i	3.01896	−	0.608235i
$397$	−2895.32	−	6989.91i	−0.366025	−	0.883662i	−0.994393	−	0.105746i	$-0.966277\pi$
$397$	−2895.32	−	6989.91i	−0.366025	−	0.883662i	0.628369	−	0.777916i	$-0.283723\pi$
$398$	−3110.20	+	23624.3i	−0.391709	+	2.97533i
$399$	−3879.58	+	2419.10i	−0.486772	+	0.303525i
$400$	2698.34	−	10070.3i	0.337292	−	1.25879i
$401$	8395.96	+	6442.45i	1.04557	+	0.802296i	0.980684	−	0.195597i	$-0.0626644\pi$
$401$	8395.96	+	6442.45i	1.04557	+	0.802296i	0.0648878	+	0.997893i	$0.479331\pi$
$402$	−2318.86	−	2818.46i	−0.287697	−	0.349681i
$403$	6025.58	−	4623.59i	0.744803	−	0.571507i
$404$			19422.8i			2.39188i
$405$	−1266.78	+	4822.49i	−0.155424	+	0.591682i
$406$	−7868.75	+	7868.75i	−0.961870	+	0.961870i
$407$	9715.28	−	16827.4i	1.18322	−	2.04939i
$408$	−6687.83	+	18765.0i	−0.811512	+	2.27698i
$409$	−1565.25	−	2711.09i	−0.189233	−	0.327762i	0.755762	−	0.654847i	$-0.227267\pi$
$409$	−1565.25	−	2711.09i	−0.189233	−	0.327762i	−0.944995	+	0.327085i	$0.893934\pi$
$410$	5162.75	+	1383.36i	0.621879	+	0.166632i
$411$	−2314.55	−	1654.28i	−0.277781	−	0.198539i
$412$	−6206.92	−	3583.57i	−0.742216	−	0.428518i
$413$	−3390.62	−	1404.44i	−0.403974	−	0.167332i
$414$	−13059.9	−	8679.93i	−1.55038	−	1.03042i
$415$	−2980.87	+	1234.71i	−0.352590	+	0.146048i
$416$	6843.16	−	1833.62i	0.806523	−	0.216107i
$417$	256.100	+	7539.41i	0.0300750	+	0.885388i
$418$	9212.38	+	7068.91i	1.07797	+	0.827157i
$419$	−3512.33	+	4577.36i	−0.409520	+	0.533696i	−0.951889	−	0.306444i	$-0.900861\pi$
$419$	−3512.33	+	4577.36i	−0.409520	+	0.533696i	0.542369	+	0.840140i	$0.317527\pi$
$420$	−5166.61	−	11365.7i	−0.600250	−	1.32046i
$421$	−7530.74	−	4347.88i	−0.871796	−	0.503331i	−0.00385102	−	0.999993i	$-0.501226\pi$
$421$	−7530.74	−	4347.88i	−0.871796	−	0.503331i	−0.867944	+	0.496661i	$0.834559\pi$
$422$	−2674.93	+	6457.84i	−0.308562	+	0.744936i
$423$	−4289.16	−	3742.87i	−0.493017	−	0.430223i
$424$	−17963.2			−2.05748
$425$	−3812.78	+	3939.78i	−0.435169	+	0.449664i
$426$	−4978.84	+	21472.5i	−0.566258	+	2.44213i
$427$	−14326.9	−	3838.87i	−1.62371	−	0.435073i
$428$	−38936.1	+	5126.03i	−4.39731	+	0.578916i
$429$	2074.22	+	6807.62i	0.233436	+	0.766142i
$430$	2552.58	−	1958.66i	0.286270	−	0.219663i
$431$	1868.50	+	4510.96i	0.208823	+	0.504142i	0.993238	−	0.116093i	$-0.0370371\pi$
$431$	1868.50	+	4510.96i	0.208823	+	0.504142i	−0.784416	+	0.620235i	$0.787037\pi$
$432$	12833.1	+	13600.9i	1.42925	+	1.51475i
$433$	4547.38	+	4547.38i	0.504696	+	0.504696i	0.912893	−	0.408198i	$-0.133843\pi$
$433$	4547.38	+	4547.38i	0.504696	+	0.504696i	−0.408198	+	0.912893i	$0.633843\pi$
$434$	−25204.8	+	6753.59i	−2.78771	+	0.746965i
$435$	−3135.79	+	2579.94i	−0.345631	+	0.284364i
$436$	14194.7	−	18498.9i	1.55918	−	2.03197i
$437$	−684.864	−	5202.06i	−0.0749691	−	0.569447i
$438$	13877.8	+	3217.85i	1.51394	+	0.351038i
$439$	5612.26	+	7314.04i	0.610156	+	0.795171i	0.991617	−	0.129214i	$-0.0412454\pi$
$439$	5612.26	+	7314.04i	0.610156	+	0.795171i	−0.381460	+	0.924385i	$0.624579\pi$
$440$	−12780.3	+	12780.3i	−1.38472	+	1.38472i
$441$	328.447	+	160.969i	0.0354656	+	0.0173814i
$442$	−9941.80	−	2490.11i	−1.06987	−	0.267969i
$443$	6018.32	−	10424.0i	0.645460	−	1.11797i	−0.338735	−	0.940882i	$-0.609999\pi$
$443$	6018.32	−	10424.0i	0.645460	−	1.11797i	0.984195	−	0.177088i	$-0.0566677\pi$
$444$	38856.9	−	1319.90i	4.15330	−	0.141080i
$445$	−6469.93	+	851.782i	−0.689222	+	0.0907379i
$446$	−8278.38	+	4779.52i	−0.878907	+	0.507437i
$447$	5849.62	+	12868.3i	0.618965	+	1.36163i
$448$	−4169.79	−	548.963i	−0.439741	−	0.0578930i
$449$	2465.64	−	1021.30i	0.259155	−	0.107346i	−0.249323	−	0.968420i	$-0.580208\pi$
$449$	2465.64	−	1021.30i	0.259155	−	0.107346i	0.508478	+	0.861075i	$0.330208\pi$
$450$	3526.87	+	10306.4i	0.369462	+	1.07967i
$451$	5175.79	+	5175.79i	0.540396	+	0.540396i
$452$	−1375.06	+	10444.7i	−0.143092	+	1.08689i
$453$	−18197.9	+	3027.49i	−1.88745	+	0.314004i
$454$	−2310.21	−	17547.8i	−0.238818	−	1.81400i
$455$	3170.66	−	1830.58i	0.326688	−	0.188613i
$456$	−1281.89	+	13181.4i	−0.131645	+	1.35368i
$457$	−1235.78	−	4611.98i	−0.126493	−	0.472078i	0.873396	−	0.487011i	$-0.161913\pi$
$457$	−1235.78	−	4611.98i	−0.126493	−	0.472078i	−0.999888	+	0.0149337i	$0.995246\pi$
$458$	20260.6			2.06707
$459$	−2424.76	−	9530.12i	−0.246575	−	0.969124i
$460$	14328.1			1.45228
$461$	215.536	+	804.393i	0.0217756	+	0.0812675i	0.975959	−	0.217956i	$-0.0699390\pi$
$461$	215.536	+	804.393i	0.0217756	+	0.0812675i	−0.954183	+	0.299224i	$0.903272\pi$
$462$	2366.59	−	24335.2i	0.238319	−	2.45060i
$463$	−5203.18	+	3004.06i	−0.522272	+	0.301534i	−0.737864	−	0.674950i	$-0.764165\pi$
$463$	−5203.18	+	3004.06i	−0.522272	+	0.301534i	0.215591	+	0.976484i	$0.430832\pi$
$464$	1987.78	+	15098.7i	0.198880	+	1.51065i
$465$	−9392.70	+	1562.61i	−0.936722	+	0.155837i
$466$	4106.68	−	31193.4i	0.408237	−	3.10087i
$467$	−6710.82	−	6710.82i	−0.664968	−	0.664968i	0.291579	−	0.956547i	$-0.405819\pi$
$467$	−6710.82	−	6710.82i	−0.664968	−	0.664968i	−0.956547	+	0.291579i	$0.905819\pi$
$468$	−9362.62	+	10729.2i	−0.924759	+	1.05973i
$469$	−2375.64	+	984.023i	−0.233896	+	0.0968827i
$470$	7374.39	+	970.857i	0.723734	+	0.0952814i
$471$	−5193.43	−	11424.7i	−0.508069	−	1.11767i
$472$	−9206.51	+	5315.38i	−0.897805	+	0.518348i
$473$	4368.53	−	575.128i	0.424662	−	0.0559078i
$474$	30834.7	−	1047.40i	2.98795	−	0.101495i
$475$	−1822.43	+	3156.54i	−0.176040	+	0.304910i
$476$	19777.9	+	14667.7i	1.90445	+	1.41238i
$477$	7360.70	−	4944.50i	0.706547	−	0.474619i
$478$	2824.82	−	2824.82i	0.270302	−	0.270302i
$479$	575.388	+	749.861i	0.0548855	+	0.0715282i	0.819990	−	0.572378i	$-0.193979\pi$
$479$	575.388	+	749.861i	0.0548855	+	0.0715282i	−0.765104	+	0.643907i	$0.777313\pi$
$480$	−8652.23	−	2006.20i	−0.822747	−	0.190771i
$481$	1488.16	+	11303.7i	0.141069	+	1.07152i
$482$	11407.3	−	14866.3i	1.07798	−	1.40485i
$483$	−8531.54	+	7019.23i	−0.803723	+	0.661255i
$484$	−18026.7	+	4830.25i	−1.69297	+	0.453629i
$485$	−1166.46	−	1166.46i	−0.109208	−	0.109208i
$486$	−19054.8	−	4319.55i	−1.77848	−	0.403166i
$487$	−925.318	−	2233.92i	−0.0860989	−	0.207861i	0.874966	−	0.484185i	$-0.160884\pi$
$487$	−925.318	−	2233.92i	−0.0860989	−	0.207861i	−0.961065	+	0.276324i	$0.910884\pi$
$488$	−34085.9	+	26155.0i	−3.16188	+	2.42619i
$489$	−1155.27	−	3791.61i	−0.106836	−	0.350639i
$490$	−473.830	+	62.3809i	−0.0436846	+	0.00575119i
$491$	−17256.4	−	4623.85i	−1.58609	−	0.424993i	−0.645289	−	0.763939i	$-0.723263\pi$
$491$	−17256.4	−	4623.85i	−1.58609	−	0.424993i	−0.940806	+	0.338946i	$0.889930\pi$
$492$	−3308.25	+	14267.7i	−0.303145	+	1.30739i
$493$	2943.18	−	7448.23i	0.268872	−	0.680429i
$494$	−6813.50			−0.620554
$495$	1719.05	−	8754.76i	0.156092	−	0.794944i
$496$	−13665.6	+	32991.7i	−1.23711	+	2.98664i
$497$	13448.9	+	7764.70i	1.21381	+	0.700794i
$498$	−5232.05	−	11509.7i	−0.470790	−	1.03567i
$499$	−2852.17	+	3717.02i	−0.255873	+	0.333460i	−0.903572	−	0.428436i	$-0.859065\pi$
$499$	−2852.17	+	3717.02i	−0.255873	+	0.333460i	0.647699	+	0.761896i	$0.275731\pi$
$500$	−20515.3	−	15742.0i	−1.83495	−	1.40800i
$501$	428.643	+	12619.0i	0.0382243	+	1.12530i
$502$	−37415.4	+	10025.4i	−3.32655	+	0.891348i
$503$	−11973.0	+	4959.39i	−1.06133	+	0.439619i	−0.843925	−	0.536462i	$-0.819761\pi$
$503$	−11973.0	+	4959.39i	−1.06133	+	0.439619i	−0.217409	+	0.976081i	$0.569761\pi$
$504$	24979.5	−	12395.0i	2.20769	−	1.09547i
$505$	6596.98	+	2732.56i	0.581310	+	0.240787i
$506$	24300.2	+	14029.7i	2.13493	+	1.23260i
$507$	5890.33	+	4209.99i	0.515974	+	0.368782i
$508$	15928.8	+	4268.10i	1.39119	+	0.372768i
$509$	5147.39	+	8915.54i	0.448240	+	0.776374i	0.998272	−	0.0587695i	$-0.0187177\pi$
$509$	5147.39	+	8915.54i	0.448240	+	0.776374i	−0.550032	+	0.835144i	$0.685384\pi$
$510$	9531.12	+	8616.87i	0.827540	+	0.748160i
$511$	5018.36	−	8692.06i	0.434441	−	0.752474i
$512$	17686.6	−	17686.6i	1.52665	−	1.52665i
$513$	−3103.01	−	5754.15i	−0.267059	−	0.495228i
$514$			2458.34i			0.210959i
$515$	−2090.41	+	1604.03i	−0.178863	+	0.137246i
$516$	5601.55	+	6808.41i	0.477896	+	0.580860i
$517$	8081.24	+	6200.96i	0.687452	+	0.527501i
$518$	10138.0	−	37835.6i	0.859921	−	3.20927i
$519$	−7828.21	+	4881.26i	−0.662082	+	0.412839i
$520$	1384.26	−	10514.5i	0.116738	−	0.886714i
$521$	3734.03	+	9014.74i	0.313994	+	0.758048i	0.999549	+	0.0300276i	$0.00955951\pi$
$521$	3734.03	+	9014.74i	0.313994	+	0.758048i	−0.685555	+	0.728021i	$0.740440\pi$
$522$	−10520.9	−	11937.5i	−0.882163	−	1.00094i
$523$			20429.7i			1.70809i	0.520201	+	0.854044i	$0.325857\pi$
$523$			20429.7i			1.70809i	−0.520201	+	0.854044i	$0.674143\pi$
$524$	−5266.92	−	6863.98i	−0.439096	−	0.572241i
$525$	7670.17	−	260.541i	0.637626	−	0.0216590i
$526$	−11889.8	−	20593.8i	−0.985593	−	1.70710i
$527$	14709.3	−	11674.6i	1.21584	−	0.964994i
$528$	−24449.6	−	22843.2i	−2.01521	−	1.88281i
$529$	−132.486	−	494.445i	−0.0108890	−	0.0406382i
$530$	−4433.77	+	10704.1i	−0.363378	+	0.877273i
$531$	2309.41	−	4712.21i	0.188738	−	0.385109i
$532$	15123.6	+	6264.38i	1.23250	+	0.510517i
$533$	−4258.19	−	560.602i	−0.346047	−	0.0455579i
$534$	−4196.52	−	25224.8i	−0.340077	−	2.04417i
$535$	−3736.79	+	13945.9i	−0.301973	+	1.12698i
$536$	−1927.80	+	7194.66i	−0.155352	+	0.579780i
$537$	4086.03	−	3361.74i	0.328352	−	0.270148i
$538$	−357.515	−	47.0677i	−0.0286497	−	0.00377181i
$539$	−604.677	−	250.465i	−0.0483215	−	0.0200154i
$540$	16684.7	−	6350.06i	1.32962	−	0.506043i
$541$	200.614	−	484.324i	0.0159428	−	0.0384893i	−0.915708	−	0.401845i	$-0.868369\pi$
$541$	200.614	−	484.324i	0.0159428	−	0.0384893i	0.931650	+	0.363356i	$0.118369\pi$
$542$	861.228	+	3214.15i	0.0682526	+	0.254722i
$543$	16082.7	−	4900.25i	1.27104	−	0.387274i
$544$	16843.5	−	4810.25i	1.32750	−	0.379113i
$545$	−4286.17	−	7423.86i	−0.336879	−	0.583492i
$546$	7590.88	+	12173.7i	0.594981	+	0.954188i
$547$	7796.58	+	10160.7i	0.609429	+	0.794224i	0.991527	−	0.129898i	$-0.0414650\pi$
$547$	7796.58	+	10160.7i	0.609429	+	0.794224i	−0.382098	+	0.924122i	$0.624798\pi$
$548$			10186.1i			0.794029i
$549$	6767.86	−	20099.8i	0.526130	−	1.56255i
$550$	−7459.22	−	18008.2i	−0.578295	−	1.39613i
$551$	694.944	−	5278.62i	0.0537307	−	0.408125i
$552$	1086.43	+	31983.9i	0.0837712	+	2.46617i
$553$	5625.84	−	20995.9i	0.432613	−	1.61453i
$554$	19547.6	+	14999.4i	1.49910	+	1.15030i
$555$	5018.41	−	13383.5i	0.383819	−	1.02360i
$556$	21428.2	−	16442.5i	1.63446	−	1.25417i
$557$		−	10352.9i		−	0.787551i	−0.919207	−	0.393776i	$-0.871169\pi$
$557$		−	10352.9i		−	0.787551i	0.919207	−	0.393776i	$-0.128831\pi$
$558$	−7369.15	−	36576.7i	−0.559070	−	2.77493i
$559$	−1828.17	+	1828.17i	−0.138324	+	0.138324i
$560$	−8606.90	+	14907.6i	−0.649478	+	1.12493i
$561$	5403.62	+	16745.9i	0.406668	+	1.26027i
$562$	−5992.83	−	10379.9i	−0.449808	−	0.779090i
$563$	869.022	+	232.854i	0.0650532	+	0.0174309i	0.291199	−	0.956663i	$-0.405946\pi$
$563$	869.022	+	232.854i	0.0650532	+	0.0174309i	−0.226146	+	0.974093i	$0.572613\pi$
$564$	−1972.82	+	20286.2i	−0.147289	+	1.51454i
$565$	3354.09	+	1936.49i	0.249748	+	0.144192i
$566$	−25634.4	−	10618.1i	−1.90370	−	0.788538i
$567$	−6823.91	+	11954.8i	−0.505427	+	0.885460i
$568$	41559.6	−	17214.5i	3.07007	−	1.27166i
$569$	−15146.0	+	4058.36i	−1.11591	+	0.299007i	−0.769227	−	0.638975i	$-0.779359\pi$
$569$	−15146.0	+	4058.36i	−1.11591	+	0.299007i	−0.346683	+	0.937982i	$0.612692\pi$
$570$	7538.27	+	4017.37i	0.553936	+	0.295209i
$571$	17843.4	+	13691.7i	1.30775	+	1.00347i	0.998624	+	0.0524487i	$0.0167026\pi$
$571$	17843.4	+	13691.7i	1.30775	+	1.00347i	0.309124	+	0.951022i	$0.399964\pi$
$572$	15511.4	−	20214.9i	1.13386	−	1.47767i
$573$	6286.16	−	8795.15i	0.458304	−	0.641227i
$574$	12778.9	+	7377.91i	0.929236	+	0.536495i
$575$	−3370.51	+	8137.12i	−0.244452	+	0.590159i
$576$	1158.72	−	5901.14i	0.0838197	−	0.426877i
$577$	5038.14			0.363502			0.181751	−	0.983345i	$-0.441824\pi$
$577$	5038.14			0.363502			0.181751	+	0.983345i	$0.441824\pi$
$578$	−24679.2	−	5753.47i	−1.77598	−	0.414036i
$579$	−12287.4	−	11480.1i	−0.881947	−	0.824000i
$580$	14043.5	+	3762.95i	1.00539	+	0.269393i
$581$	−8831.23	+	1162.65i	−0.630605	+	0.0830207i
$582$	4413.01	−	4723.35i	0.314304	−	0.336408i
$583$	−12587.9	+	9659.06i	−0.894234	+	0.686170i
$584$	−11125.8	−	26860.1i	−0.788339	−	1.90322i
$585$	2326.97	+	4689.50i	0.164459	+	0.331431i
$586$	−26446.6	−	26446.6i	−1.86434	−	1.86434i
$587$	−23136.9	+	6199.50i	−1.62685	+	0.435913i	−0.953003	−	0.302960i	$-0.902025\pi$
$587$	−23136.9	+	6199.50i	−1.62685	+	0.435913i	−0.673845	+	0.738873i	$0.735359\pi$
$588$	−214.918	−	1291.85i	−0.0150733	−	0.0906039i
$589$	7600.06	−	9904.60i	0.531673	−	0.692889i
$590$	894.976	+	6798.02i	0.0624501	+	0.474356i
$591$	5647.27	+	18534.4i	0.393058	+	1.29002i
$592$	−32632.9	−	42528.0i	−2.26554	−	2.95252i
$593$	−3253.45	+	3253.45i	−0.225301	+	0.225301i	−0.810726	−	0.585425i	$-0.800927\pi$
$593$	−3253.45	+	3253.45i	−0.225301	+	0.225301i	0.585425	+	0.810726i	$0.300927\pi$
$594$	34514.9	+	5567.66i	2.38411	+	0.384586i
$595$	7764.43	−	4654.01i	0.534976	−	0.320665i
$596$	25305.3	−	43830.0i	1.73917	−	3.01233i
$597$	−11289.7	+	21184.2i	−0.773964	+	1.45228i
$598$	−16323.5	+	2149.03i	−1.11625	+	0.146957i
$599$	14171.2	−	8181.77i	0.966646	−	0.558094i	0.0684342	−	0.997656i	$-0.478200\pi$
$599$	14171.2	−	8181.77i	0.966646	−	0.558094i	0.898212	+	0.439562i	$0.144866\pi$
$600$	12926.7	−	18086.2i	0.879552	−	1.23061i
$601$	−14971.6	−	1971.05i	−1.01615	−	0.133778i	−0.395990	−	0.918255i	$-0.629598\pi$
$601$	−14971.6	−	1971.05i	−1.01615	−	0.133778i	−0.620159	+	0.784476i	$0.712932\pi$
$602$	8206.42	−	3399.21i	0.555596	−	0.230135i
$603$	−1190.43	−	3478.76i	−0.0803951	−	0.234936i
$604$	46705.4	+	46705.4i	3.14639	+	3.14639i
$605$	−895.549	+	6802.37i	−0.0601806	+	0.457117i
$606$	−9823.90	+	26199.2i	−0.658529	+	1.75622i
$607$	1069.76	+	8125.63i	0.0715324	+	0.543343i	0.989264	+	0.146141i	$0.0466854\pi$
$607$	1069.76	+	8125.63i	0.0715324	+	0.543343i	−0.917731	+	0.397202i	$0.869981\pi$
$608$	10085.1	−	5822.66i	0.672708	−	0.388388i
$609$	−10205.6	+	4639.22i	−0.679065	+	0.308688i
$610$	7172.23	+	26767.1i	0.476057	+	1.77667i
$611$	−5976.91			−0.395745
$612$	−22711.9	+	26904.0i	−1.50012	+	1.77701i
$613$	−21091.9			−1.38971			−0.694857	−	0.719148i	$-0.744532\pi$
$613$	−21091.9			−1.38971			−0.694857	+	0.719148i	$0.744532\pi$
$614$	−4720.21	−	17616.0i	−0.310248	−	1.15786i
$615$	4380.61	+	3130.95i	0.287225	+	0.205288i
$616$	−43212.7	+	24948.8i	−2.82644	+	1.63185i
$617$	3947.59	+	29984.9i	0.257575	+	1.95648i	0.290066	+	0.957007i	$0.406323\pi$
$617$	3947.59	+	29984.9i	0.257575	+	1.95648i	−0.0324907	+	0.999472i	$0.510344\pi$
$618$	−6559.91	−	7973.26i	−0.426988	−	0.518983i
$619$	3458.72	−	26271.6i	0.224584	−	1.70589i	−0.393128	−	0.919484i	$-0.628607\pi$
$619$	3458.72	−	26271.6i	0.224584	−	1.70589i	0.617713	−	0.786404i	$-0.288059\pi$
$620$	24106.6	+	24106.6i	1.56152	+	1.56152i
$621$	−9248.97	−	12806.8i	−0.597663	−	0.827569i
$622$	−5156.08	+	2135.72i	−0.332379	+	0.137676i
$623$	−17861.8	−	2351.55i	−1.14866	−	0.151225i
$624$	19541.2	+	1900.37i	1.25364	+	0.121916i
$625$	234.447	−	135.358i	0.0150046	−	0.00866291i
$626$	37234.0	−	4901.95i	2.37727	−	0.312973i
$627$	6189.54	+	9926.34i	0.394237	+	0.632249i
$628$	−22466.6	+	38913.3i	−1.42757	+	2.47262i
$629$	4136.83	+	27884.9i	0.262235	+	1.76764i
$630$	−1220.48	−	17944.4i	−0.0771829	−	1.13480i
$631$	4675.74	−	4675.74i	0.294990	−	0.294990i	−0.544058	−	0.839048i	$-0.683113\pi$
$631$	4675.74	−	4675.74i	0.294990	−	0.294990i	0.839048	+	0.544058i	$0.183113\pi$
$632$	−38330.0	−	49952.6i	−2.41248	−	3.14400i
$633$	−4807.33	+	5145.41i	−0.301855	+	0.323083i
$634$	−4523.62	−	34360.3i	−0.283369	−	2.15240i
$635$	3690.66	−	4809.76i	0.230645	−	0.300582i
$636$	−29727.2	−	11146.8i	−1.85339	−	0.694966i
$637$	370.951	−	99.3962i	0.0230732	−	0.00618245i
$638$	20133.1	+	20133.1i	1.24934	+	1.24934i
$639$	−12291.2	+	18493.5i	−0.760930	+	1.14490i
$640$	−2225.94	−	5373.91i	−0.137482	−	0.331910i
$641$	12448.5	−	9552.06i	0.767060	−	0.588586i	−0.149369	−	0.988781i	$-0.547724\pi$
$641$	12448.5	−	9552.06i	0.767060	−	0.588586i	0.916430	+	0.400195i	$0.131058\pi$
$642$	−55113.3	−	12779.1i	−3.38808	−	0.785596i
$643$	6608.33	−	870.003i	0.405299	−	0.0533586i	0.0748789	−	0.997193i	$-0.476143\pi$
$643$	6608.33	−	870.003i	0.405299	−	0.0533586i	0.330420	+	0.943834i	$0.392810\pi$
$644$	38208.2	+	10237.9i	2.33791	+	0.626441i
$645$	3100.56	−	944.713i	0.189278	−	0.0576714i
$646$	−16844.5	+	275.935i	−1.02591	+	0.0168057i
$647$	15934.5			0.968240			0.484120	−	0.875002i	$-0.339140\pi$
$647$	15934.5			0.968240			0.484120	+	0.875002i	$0.339140\pi$
$648$	15440.1	+	36763.0i	0.936025	+	2.22868i
$649$	−3593.42	+	8675.28i	−0.217340	+	0.524706i
$650$	9904.89	+	5718.59i	0.597695	+	0.345079i
$651$	−26163.8	−	2544.41i	−1.57518	−	0.153185i
$652$	−8639.34	+	11259.0i	−0.518930	+	0.676283i
$653$	−1465.48	−	1124.51i	−0.0878236	−	0.0673895i	0.563916	−	0.825832i	$-0.309294\pi$
$653$	−1465.48	−	1124.51i	−0.0878236	−	0.0673895i	−0.651740	+	0.758442i	$0.725961\pi$
$654$	28503.8	−	17773.5i	1.70426	−	1.06269i
$655$	−3072.36	+	823.236i	−0.183278	+	0.0491092i
$656$	18656.5	−	7727.77i	1.11039	−	0.459937i
$657$	11952.4	+	7943.88i	0.709754	+	0.471721i
$658$	18971.4	+	7858.20i	1.12398	+	0.465569i
$659$	−5171.10	−	2985.54i	−0.305671	−	0.176479i	0.339316	−	0.940672i	$-0.389804\pi$
$659$	−5171.10	−	2985.54i	−0.305671	−	0.176479i	−0.644988	+	0.764193i	$0.723138\pi$
$660$	−29080.5	+	13219.4i	−1.71509	+	0.779641i
$661$	12198.1	+	3268.48i	0.717780	+	0.192328i	0.599181	−	0.800614i	$-0.295493\pi$
$661$	12198.1	+	3268.48i	0.717780	+	0.192328i	0.118599	+	0.992942i	$0.462160\pi$
$662$	3875.19	+	6712.02i	0.227513	+	0.394063i
$663$	−8497.11	−	5865.27i	−0.497738	−	0.343572i
$664$	−12901.0	+	22345.2i	−0.754000	+	1.30597i
$665$	4255.42	−	4255.42i	0.248147	−	0.248147i
$666$	53081.3	+	17873.2i	3.08838	+	1.03990i
$667$		−	12865.5i		−	0.746858i
$668$	35865.2	−	27520.3i	2.07734	−	1.59400i
$669$	−9499.31	+	1580.35i	−0.548975	+	0.0913301i
$670$	3811.38	+	2924.58i	0.219771	+	0.168636i
$671$	−9822.19	+	36656.9i	−0.565099	+	2.10898i
$672$	−21639.2	−	11532.2i	−1.24219	−	0.661999i
$673$	−2052.14	+	15587.5i	−0.117539	+	0.892800i	0.826493	+	0.562947i	$0.190333\pi$
$673$	−2052.14	+	15587.5i	−0.117539	+	0.892800i	−0.944032	+	0.329853i	$0.893001\pi$
$674$	−18870.9	−	45558.3i	−1.07846	−	2.60362i
$675$	−318.575	+	10969.3i	−0.0181659	+	0.625492i
$676$		−	25922.7i		−	1.47489i
$677$	15486.0	+	20181.8i	0.879138	+	1.14571i	0.988426	+	0.151705i	$0.0484762\pi$
$677$	15486.0	+	20181.8i	0.879138	+	1.14571i	−0.109288	+	0.994010i	$0.534857\pi$
$678$	−7137.65	+	13393.2i	−0.404306	+	0.758647i
$679$	−2277.08	−	3944.03i	−0.128699	−	0.222913i
$680$	2996.37	−	26050.2i	0.168979	−	1.46909i
$681$	4027.47	−	17369.5i	0.226627	−	0.977387i
$682$	17279.8	+	64489.2i	0.970203	+	3.62085i
$683$	1987.97	−	4799.39i	0.111373	−	0.268878i	−0.858359	−	0.513049i	$-0.828516\pi$
$683$	1987.97	−	4799.39i	0.111373	−	0.268878i	0.969732	+	0.244171i	$0.0785159\pi$
$684$	−10300.9	+	21018.4i	−0.575827	+	1.17494i
$685$	3459.72	+	1433.06i	0.192977	+	0.0799336i
$686$	31812.4	+	4188.18i	1.77056	+	0.233098i
$687$	19111.3	+	7166.17i	1.06134	+	0.397972i
$688$	3146.19	−	11741.8i	0.174342	−	0.650654i
$689$	2409.62	−	8992.83i	0.133236	−	0.497242i
$690$	19327.0	+	7247.03i	1.06633	+	0.399840i
$691$	−966.733	−	127.273i	−0.0532218	−	0.00700678i	0.103868	−	0.994591i	$-0.466878\pi$
$691$	−966.733	−	127.273i	−0.0532218	−	0.00700678i	−0.157090	+	0.987584i	$0.550211\pi$
$692$	30516.3	+	12640.3i	1.67638	+	0.694379i
$693$	10839.7	−	22117.8i	0.594179	−	1.21239i
$694$	4374.57	−	10561.2i	0.239275	−	0.577660i
$695$	−2570.01	−	9591.41i	−0.140268	−	0.523486i
$696$	−7335.01	+	31634.1i	−0.399473	+	1.72283i
$697$	−10549.9	−	1213.48i	−0.573323	−	0.0659453i
$698$	−15258.3	−	26428.2i	−0.827416	−	1.43313i
$699$	14906.8	−	27971.4i	0.806620	−	1.51356i
$700$	−16727.6	−	21799.9i	−0.903207	−	1.17708i
$701$			28286.1i			1.52404i	0.647555	+	0.762019i	$0.275792\pi$
$701$			28286.1i			1.52404i	−0.647555	+	0.762019i	$0.724208\pi$
$702$	−18055.9	+	9736.92i	−0.970763	+	0.523499i
$703$	7171.80	+	17314.3i	0.384765	+	0.928904i
$704$	−1404.58	+	10668.9i	−0.0751950	+	0.571162i
$705$	6612.69	+	3524.10i	0.353260	+	0.188263i
$706$	−1926.07	+	7188.21i	−0.102675	+	0.383190i
$707$	15639.5	+	12000.6i	0.831942	+	0.638372i
$708$	−18534.1	+	3083.43i	−0.983836	+	0.163675i
$709$	1376.89	−	1056.52i	0.0729338	−	0.0559640i	−0.571651	−	0.820497i	$-0.693697\pi$
$709$	1376.89	−	1056.52i	0.0729338	−	0.0559640i	0.644585	+	0.764533i	$0.277030\pi$
$710$		−	29013.8i		−	1.53362i
$711$	29456.1	+	9918.25i	1.55371	+	0.523155i
$712$	−36901.4	+	36901.4i	−1.94233	+	1.94233i
$713$	15083.9	−	26126.1i	0.792283	−	1.37227i
$714$	19259.3	+	29788.7i	1.00947	+	1.56136i
$715$	−4683.75	−	8112.49i	−0.244982	−	0.424322i
$716$	−18299.1	−	4903.24i	−0.955127	−	0.255926i
$717$	3663.72	−	1665.45i	0.190829	−	0.0867465i
$718$	13394.2	+	7733.17i	0.696196	+	0.401949i
$719$	−14837.3	−	6145.82i	−0.769594	−	0.318776i	−0.0368862	−	0.999319i	$-0.511744\pi$
$719$	−14837.3	−	6145.82i	−0.769594	−	0.318776i	−0.732708	+	0.680543i	$0.761744\pi$
$720$	−20499.4	−	13624.4i	−1.06106	−	0.705210i
$721$	−6720.56	+	2783.75i	−0.347138	+	0.143789i
$722$	23354.7	−	6257.87i	1.20384	−	0.322568i
$723$	16018.4	−	9988.23i	0.823971	−	0.513785i
$724$	−47756.8	−	36645.1i	−2.45148	−	1.88108i
$725$	−5440.61	+	7090.35i	−0.278702	+	0.363212i
$726$	−26759.2	−	2602.32i	−1.36794	−	0.133032i
$727$	20944.9	+	12092.5i	1.06850	+	0.616901i	0.927772	−	0.373147i	$-0.121721\pi$
$727$	20944.9	+	12092.5i	1.06850	+	0.616901i	0.140731	+	0.990048i	$0.455055\pi$
$728$	11204.3	−	27049.6i	0.570411	−	1.37709i
$729$	−16446.1	−	10814.2i	−0.835548	−	0.549418i
$730$	−18751.8			−0.950732
$731$	−4445.60	+	4593.68i	−0.224934	+	0.232426i
$732$	−72638.6	+	22132.3i	−3.66776	+	1.11753i
$733$	31672.1	+	8486.51i	1.59595	+	0.427635i	0.943818	−	0.330466i	$-0.107206\pi$
$733$	31672.1	+	8486.51i	1.59595	+	0.427635i	0.652137	+	0.758101i	$0.273873\pi$
$734$	−57613.0	+	7584.89i	−2.89718	+	0.381422i
$735$	−469.017	−	108.751i	−0.0235373	−	0.00545761i
$736$	22325.0	−	17130.6i	1.11809	−	0.857938i
$737$	2517.73	+	6078.35i	0.125837	+	0.303798i
$738$	−11679.0	+	17572.2i	−0.582532	+	0.876481i
$739$	−16484.8	−	16484.8i	−0.820574	−	0.820574i	0.165617	−	0.986190i	$-0.447039\pi$
$739$	−16484.8	−	16484.8i	−0.820574	−	0.820574i	−0.986190	+	0.165617i	$0.947039\pi$
$740$	−49432.5	+	13245.4i	−2.45564	+	0.657988i
$741$	−6427.01	−	2409.93i	−0.318626	−	0.119475i
$742$	−19471.8	+	25376.2i	−0.963386	+	1.25551i
$743$	−1838.20	−	13962.5i	−0.0907634	−	0.689416i	−0.974973	−	0.222325i	$-0.928635\pi$
$743$	−1838.20	−	13962.5i	−0.0907634	−	0.689416i	0.884209	−	0.467091i	$-0.154698\pi$
$744$	−51984.2	+	55640.0i	−2.56160	+	2.74175i
$745$	−11326.8	−	14761.3i	−0.557022	−	0.725925i
$746$	5834.79	−	5834.79i	0.286363	−	0.286363i
$747$	−864.290	−	12707.4i	−0.0423329	−	0.622408i
$748$	37529.0	−	50603.9i	1.83449	−	2.47361i
$749$	−19929.6	+	34519.1i	−0.972245	+	1.68398i
$750$	−19710.8	−	31610.7i	−0.959647	−	1.53901i
$751$	−19713.0	+	2595.27i	−0.957841	+	0.126102i	−0.593208	−	0.805049i	$-0.702139\pi$
$751$	−19713.0	+	2595.27i	−0.957841	+	0.126102i	−0.364633	+	0.931151i	$0.618805\pi$
$752$	24336.9	−	14050.9i	1.18015	−	0.681361i
$753$	−38839.0	−	3777.07i	−1.87964	−	0.182794i
$754$	−16563.7	−	2180.66i	−0.800021	−	0.105325i
$755$	22434.5	−	9292.67i	1.08142	−	0.447940i
$756$	49029.9	−	5011.79i	2.35873	−	0.241107i
$757$	6954.50	+	6954.50i	0.333904	+	0.333904i	0.854067	−	0.520163i	$-0.174129\pi$
$757$	6954.50	+	6954.50i	0.333904	+	0.333904i	−0.520163	+	0.854067i	$0.674129\pi$
$758$	−632.549	+	4804.69i	−0.0303103	+	0.230230i
$759$	17959.5	+	21828.9i	0.858878	+	1.04392i
$760$	−2275.39	−	17283.3i	−0.108601	−	0.824909i
$761$	4866.67	−	2809.77i	0.231822	−	0.133842i	−0.379590	−	0.925155i	$-0.623935\pi$
$761$	4866.67	−	2809.77i	0.231822	−	0.133842i	0.611412	+	0.791312i	$0.290602\pi$
$762$	19327.4	+	13813.9i	0.918842	+	0.656723i
$763$	−6125.21	−	22859.6i	−0.290626	−	1.08463i
$764$	−38706.5			−1.83292
$765$	5942.69	+	11499.2i	0.280861	+	0.543472i
$766$	7842.37			0.369917
$767$	−1426.03	−	5322.02i	−0.0671330	−	0.250544i
$768$	29178.5	−	13263.9i	1.37095	−	0.623204i
$769$	15113.0	−	8725.52i	0.708700	−	0.409168i	−0.101880	−	0.994797i	$-0.532486\pi$
$769$	15113.0	−	8725.52i	0.708700	−	0.409168i	0.810580	+	0.585629i	$0.199152\pi$
$770$	4200.76	+	31907.9i	0.196604	+	1.49335i
$771$	−869.515	+	2318.90i	−0.0406159	+	0.108318i
$772$	−7858.66	+	59692.4i	−0.366372	+	2.78287i
$773$	6869.43	+	6869.43i	0.319633	+	0.319633i	0.848626	−	0.528993i	$-0.177430\pi$
$773$	6869.43	+	6869.43i	0.319633	+	0.319633i	−0.528993	+	0.848626i	$0.677430\pi$
$774$	4112.24	+	12017.0i	0.190971	+	0.558066i
$775$	−19361.3	+	8019.71i	−0.897391	+	0.371712i
$776$	−13079.1	−	1721.90i	−0.605042	−	0.0796553i
$777$	22945.4	−	32103.6i	1.05941	−	1.48225i
$778$	−33529.3	+	19358.1i	−1.54509	+	0.892061i
$779$	−6999.44	+	921.494i	−0.321927	+	0.0423825i
$780$	8815.40	−	16541.4i	0.404669	−	0.759328i
$781$	19866.9	−	34410.4i	0.910233	−	1.57657i
$782$	−40268.2	+	5973.95i	−1.84142	+	0.273181i
$783$	−5701.87	−	14981.6i	−0.260240	−	0.683777i
$784$	−1276.78	+	1276.78i	−0.0581623	+	0.0581623i
$785$	10056.2	+	13105.5i	0.457223	+	0.595865i
$786$	−3632.75	−	11922.7i	−0.164855	−	0.541056i
$787$	−2034.36	−	15452.5i	−0.0921438	−	0.699902i	−0.973702	−	0.227826i	$-0.926838\pi$
$787$	−2034.36	−	15452.5i	−0.0921438	−	0.699902i	0.881558	−	0.472076i	$-0.156495\pi$
$788$	42231.4	−	55037.1i	1.90918	−	2.48809i
$789$	−3931.38	−	23631.1i	−0.177390	−	1.06627i
$790$	−39227.0	+	10510.8i	−1.76663	+	0.473366i
$791$	7560.58	+	7560.58i	0.339852	+	0.339852i
$792$	−31714.0	−	63912.8i	−1.42287	−	2.86748i
$793$	−8521.51	−	20572.7i	−0.381599	−	0.921261i
$794$	−30959.9	+	23756.3i	−1.38378	+	1.06181i
$795$	−7968.29	+	8528.66i	−0.355479	+	0.380479i
$796$	85211.3	−	11218.3i	3.79426	−	0.499524i
$797$	3830.49	+	1026.38i	0.170242	+	0.0456162i	0.342933	−	0.939360i	$-0.388580\pi$
$797$	3830.49	+	1026.38i	0.170242	+	0.0456162i	−0.172691	+	0.984976i	$0.555246\pi$
$798$	17231.5	+	16099.4i	0.764399	+	0.714174i
$799$	−14776.2	+	242.054i	−0.654250	+	0.0107175i
$800$	−19547.9			−0.863903
$801$	4963.54	−	25278.3i	0.218949	−	1.11506i
$802$	20889.1	−	50430.7i	0.919725	−	2.22041i
$803$	−22239.6	−	12840.0i	−0.977358	−	0.564278i
$804$	−7654.84	+	10710.1i	−0.335778	+	0.469797i
$805$	8852.76	−	11537.1i	0.387601	−	0.505132i
$806$	−31079.6	−	23848.2i	−1.35823	−	1.04220i
$807$	−320.587	−	170.851i	−0.0139841	−	0.00745258i
$808$	55156.9	−	14779.3i	2.40150	−	0.643481i
$809$	−11792.3	+	4884.52i	−0.512477	+	0.212275i	−0.623909	−	0.781497i	$-0.714456\pi$
$809$	−11792.3	+	4884.52i	−0.512477	+	0.212275i	0.111432	+	0.993772i	$0.464456\pi$
$810$	25717.6	−	126.551i	1.11559	−	0.00548955i
$811$	7040.57	+	2916.30i	0.304843	+	0.126270i	0.529861	−	0.848084i	$-0.322244\pi$
$811$	7040.57	+	2916.30i	0.304843	+	0.126270i	−0.225018	+	0.974355i	$0.572244\pi$
$812$	34760.7	+	20069.1i	1.50229	+	0.867350i
$813$	−324.467	+	3336.44i	−0.0139970	+	0.143929i
$814$	−96806.7	−	25939.3i	−4.16839	−	1.11692i
$815$	2608.69	+	4518.38i	0.112121	+	0.194199i
$816$	48387.1	+	3906.75i	2.07584	+	0.167603i
$817$	−2124.91	+	3680.45i	−0.0909927	+	0.157604i
$818$	−11417.6	+	11417.6i	−0.488027	+	0.488027i
$819$	2854.46	+	14168.1i	0.121786	+	0.604483i
$820$		−	19278.6i		−	0.821022i
$821$	4004.08	−	3072.44i	0.170211	−	0.130608i	−0.520143	−	0.854079i	$-0.674121\pi$
$821$	4004.08	−	3072.44i	0.170211	−	0.130608i	0.690354	+	0.723472i	$0.257455\pi$
$822$	−5152.05	+	13739.9i	−0.218611	+	0.583010i
$823$	2165.72	+	1661.81i	0.0917281	+	0.0703854i	0.653607	−	0.756834i	$-0.273255\pi$
$823$	2165.72	+	1661.81i	0.0917281	+	0.0703854i	−0.561879	+	0.827219i	$0.689921\pi$
$824$	−5453.64	+	20353.3i	−0.230566	+	0.860485i
$825$	−666.624	−	19625.0i	−0.0281320	−	0.828187i
$826$	−2470.80	+	18767.6i	−0.104080	+	0.790566i
$827$	−1442.69	−	3482.97i	−0.0606618	−	0.146451i	0.890642	−	0.454705i	$-0.150255\pi$
$827$	−1442.69	−	3482.97i	−0.0606618	−	0.146451i	−0.951304	+	0.308254i	$0.900255\pi$
$828$	−18049.2	+	53604.0i	−0.757550	+	2.24984i
$829$		−	507.238i		−	0.0212510i	−0.999944	−	0.0106255i	$-0.996618\pi$
$829$		−	507.238i		−	0.0212510i	0.999944	−	0.0106255i	$-0.00338227\pi$
$830$	10131.0	+	13202.9i	0.423675	+	0.552144i
$831$	13133.5	+	21062.6i	0.548251	+	0.879245i
$832$	−3157.08	−	5468.22i	−0.131553	−	0.227856i
$833$	913.048	−	260.752i	0.0379775	−	0.0108458i
$834$	37220.9	−	11340.8i	1.54539	−	0.470865i
$835$	−4301.52	−	16053.5i	−0.178276	−	0.665333i
$836$	16028.1	−	38695.3i	0.663091	−	1.60084i
$837$	5986.01	−	37108.3i	0.247201	−	1.53244i
$838$	27494.1	+	11388.4i	1.13338	+	0.469460i
$839$	32697.2	+	4304.67i	1.34545	+	0.177132i	0.768606	−	0.639723i	$-0.220951\pi$
$839$	32697.2	+	4304.67i	1.34545	+	0.177132i	0.576844	+	0.816854i	$0.304284\pi$
$840$	−28345.1	+	23320.7i	−1.16429	+	0.957904i
$841$	−2933.49	+	10947.9i	−0.120279	+	0.448889i
$842$	−11608.6	+	43323.8i	−0.475129	+	1.77320i
$843$	−1981.53	−	11910.7i	−0.0809578	−	0.486629i
$844$	24996.5	+	3290.85i	1.01945	+	0.134213i
$845$	−8804.70	−	3647.03i	−0.358451	−	0.148475i
$846$	−12921.7	+	26366.0i	−0.525128	+	1.07149i
$847$	−7248.65	+	17499.8i	−0.294057	+	0.709917i
$848$	11329.4	+	42281.8i	0.458789	+	1.71222i
$849$	−20424.7	−	19082.7i	−0.825645	−	0.771397i
$850$	24718.7	+	13736.5i	0.997462	+	0.554303i
$851$	22643.0	+	39218.8i	0.912092	+	1.57979i
$852$	79458.8	−	2699.07i	3.19508	−	0.108531i
$853$	−5201.02	−	6778.10i	−0.208769	−	0.272072i	0.677219	−	0.735782i	$-0.263185\pi$
$853$	−5201.02	−	6778.10i	−0.208769	−	0.272072i	−0.885988	+	0.463709i	$0.846518\pi$
$854$			76503.9i			3.06547i
$855$	5689.72	+	6455.77i	0.227584	+	0.258226i
$856$	44184.4	+	106670.i	1.76424	+	4.25925i
$857$	−3316.10	+	25188.3i	−0.132177	+	1.00399i	0.788877	+	0.614551i	$0.210663\pi$
$857$	−3316.10	+	25188.3i	−0.132177	+	1.00399i	−0.921054	+	0.389435i	$0.872670\pi$
$858$	31147.8	−	19422.1i	1.23936	−	0.772798i
$859$	−1162.41	+	4338.16i	−0.0461709	+	0.172312i	−0.985161	−	0.171631i	$-0.945096\pi$
$859$	−1162.41	+	4338.16i	−0.0461709	+	0.172312i	0.938990	+	0.343944i	$0.111763\pi$
$860$	−9206.97	−	7064.76i	−0.365064	−	0.280124i
$861$	9444.48	+	11479.3i	0.373829	+	0.454371i
$862$	19980.0	−	15331.2i	0.789470	−	0.605781i
$863$		−	32488.8i		−	1.28150i	−0.767751	−	0.640748i	$-0.778624\pi$
$863$		−	32488.8i		−	1.28150i	0.767751	−	0.640748i	$-0.221376\pi$
$864$	18404.9	−	29842.4i	0.724706	−	1.17507i
$865$	8586.57	−	8586.57i	0.337517	−	0.337517i
$866$	16585.3	−	28726.5i	0.650797	−	1.12721i
$867$	−21244.3	−	14156.1i	−0.832172	−	0.554518i
$868$	47059.4	+	81509.3i	1.84021	+	3.18733i
$869$	−53720.4	−	14394.3i	−2.09705	−	0.561904i
$870$	17039.9	+	12178.9i	0.664031	+	0.474603i
$871$	−3343.23	−	1930.21i	−0.130059	−	0.0750893i
$872$	−63334.6	−	26234.0i	−2.45961	−	1.01880i
$873$	5833.33	−	2894.55i	0.226149	−	0.112217i
$874$	−25003.3	+	10356.7i	−0.967678	+	0.400825i
$875$	−25351.3	+	6792.86i	−0.979463	+	0.262446i
$876$	−1744.42	−	51354.6i	−0.0672814	−	1.98072i
$877$	9619.70	+	7381.45i	0.370392	+	0.284212i	0.777139	−	0.629329i	$-0.216670\pi$
$877$	9619.70	+	7381.45i	0.370392	+	0.284212i	−0.406747	+	0.913541i	$0.633337\pi$
$878$	28947.7	−	37725.4i	1.11269	−	1.45008i
$879$	−15592.3	−	34300.6i	−0.598311	−	1.31619i
$880$	38142.7	+	22021.7i	1.46113	+	0.843581i
$881$	−2126.52	+	5133.87i	−0.0813215	+	0.196328i	−0.959310	−	0.282353i	$-0.908885\pi$
$881$	−2126.52	+	5133.87i	−0.0813215	+	0.196328i	0.877989	+	0.478681i	$0.158885\pi$
$882$	363.508	−	1851.27i	0.0138775	−	0.0706753i
$883$	−21342.5			−0.813399			−0.406700	−	0.913562i	$-0.633320\pi$
$883$	−21342.5			−0.813399			−0.406700	+	0.913562i	$0.633320\pi$
$884$	605.489	+	36962.1i	0.0230371	+	1.40630i
$885$	−1560.25	+	6728.96i	−0.0592623	+	0.255584i
$886$	−59968.7	−	16068.6i	−2.27392	−	0.609294i
$887$	−13231.7	+	1741.98i	−0.500875	+	0.0659415i	−0.376731	−	0.926323i	$-0.622952\pi$
$887$	−13231.7	+	1741.98i	−0.500875	+	0.0659415i	−0.124144	+	0.992264i	$0.539619\pi$
$888$	−33315.4	−	109342.i	−1.25900	−	4.13206i
$889$	13278.5	−	10189.0i	0.500953	−	0.384394i
$890$	12880.9	+	31097.3i	0.485134	+	1.17122i
$891$	30587.8	+	17459.7i	1.15009	+	0.656480i
$892$	24380.2	+	24380.2i	0.915146	+	0.915146i
$893$	−9489.83	+	2542.79i	−0.355616	+	0.0952870i
$894$	56302.9	−	46322.7i	2.10632	−	1.73295i
$895$	−4239.87	+	5525.51i	−0.158350	+	0.206366i
$896$	−2096.03	−	15921.0i	−0.0781513	−	0.593618i
$897$	−16157.7	−	3746.49i	−0.601437	−	0.139456i
$898$	−8379.87	−	10920.9i	−0.311403	−	0.405828i
$899$	21645.9	−	21645.9i	0.803037	−	0.803037i
$900$	32615.4	−	21909.2i	1.20798	−	0.811452i
$901$	5592.92	−	22329.8i	0.206800	−	0.825655i
$902$	18877.2	−	32696.3i	0.696832	−	1.20695i
$903$	8943.21	−	303.785i	0.329581	−	0.0111953i
$904$	30707.1	−	4042.67i	1.12976	−	0.148736i
$905$	−19165.4	+	11065.2i	−0.703956	+	0.406429i
$906$	39377.3	+	86623.8i	1.44395	+	3.17647i
$907$	−41032.9	−	5402.08i	−1.50218	−	0.197765i	−0.665887	−	0.746052i	$-0.731947\pi$
$907$	−41032.9	−	5402.08i	−1.50218	−	0.197765i	−0.836290	+	0.548287i	$0.815280\pi$
$908$	−58980.2	+	24430.4i	−2.15565	+	0.892898i
$909$	−18533.3	+	21238.4i	−0.676249	+	0.774953i
$910$	−13353.0	−	13353.0i	−0.486427	−	0.486427i
$911$	1447.59	−	10995.5i	0.0526463	−	0.399888i	−0.944751	−	0.327789i	$-0.893697\pi$
$911$	1447.59	−	10995.5i	0.0526463	−	0.399888i	0.997397	−	0.0720998i	$-0.0229700\pi$
$912$	31835.0	−	5296.22i	1.15588	−	0.192298i
$913$	2974.78	+	22595.7i	0.107832	+	0.819068i
$914$	−21328.0	+	12313.7i	−0.771847	+	0.445626i
$915$	−2702.13	+	27785.6i	−0.0976281	+	1.00389i
$916$	−18914.1	−	70588.5i	−0.682250	−	2.54619i
$917$	−8781.20			−0.316228
$918$	−44243.8	+	24803.0i	−1.59070	+	0.891746i
$919$	−14449.7			−0.518662			−0.259331	−	0.965788i	$-0.583502\pi$
$919$	−14449.7			−0.518662			−0.259331	+	0.965788i	$0.583502\pi$
$920$	−10902.6	−	40688.9i	−0.390703	−	1.45812i
$921$	1778.34	−	18286.3i	0.0636245	−	0.654240i
$922$	3719.90	−	2147.69i	0.132872	−	0.0767139i
$923$	3043.14	+	23115.0i	0.108522	+	0.824310i
$924$	−86993.9	+	14472.7i	−3.09728	+	0.515278i
$925$	4106.15	−	31189.3i	0.145956	−	1.10865i
$926$	21912.9	+	21912.9i	0.777647	+	0.777647i
$927$	−3367.67	−	9841.22i	−0.119319	−	0.348682i
$928$	26380.7	−	10927.2i	0.933178	−	0.386535i
$929$	16852.3	+	2218.65i	0.595164	+	0.0783549i	0.422090	−	0.906554i	$-0.361297\pi$
$929$	16852.3	+	2218.65i	0.595164	+	0.0783549i	0.173074	+	0.984909i	$0.444630\pi$
$930$	20324.2	+	44710.1i	0.716621	+	1.57645i
$931$	546.691	−	315.632i	0.0192450	−	0.0111111i
$932$	−112512.	+	14812.5i	−3.95436	+	0.520601i
$933$	−5619.01	+	190.867i	−0.197168	+	0.00669745i
$934$	−24475.8	+	42393.3i	−0.857466	+	1.48517i
$935$	−11907.8	−	19866.2i	−0.416499	−	0.694859i
$936$	37593.0	+	18424.0i	1.31278	+	0.643383i
$937$	24489.6	−	24489.6i	0.853830	−	0.853830i	−0.136772	−	0.990603i	$-0.543673\pi$
$937$	24489.6	−	24489.6i	0.853830	−	0.853830i	0.990603	+	0.136772i	$0.0436729\pi$
$938$	8074.01	+	10522.2i	0.281051	+	0.366273i
$939$	36855.8	+	8545.77i	1.28088	+	0.296997i
$940$	−3501.81	−	26598.9i	−0.121507	−	0.922937i
$941$	11987.9	−	15623.0i	0.415298	−	0.541226i	−0.538125	−	0.842865i	$-0.680867\pi$
$941$	11987.9	−	15623.0i	0.415298	−	0.541226i	0.953422	+	0.301639i	$0.0975337\pi$
$942$	−49987.0	+	41126.3i	−1.72894	+	1.42247i
$943$	−16478.3	+	4415.36i	−0.569044	+	0.152475i
$944$	18317.9	+	18317.9i	0.631564	+	0.631564i
$945$	5195.67	−	17358.2i	0.178852	−	0.597526i
$946$	−8697.26	−	20997.0i	−0.298914	−	0.721641i
$947$	−33441.7	+	25660.7i	−1.14753	+	0.880530i	−0.994190	−	0.107644i	$-0.965669\pi$
$947$	−33441.7	+	25660.7i	−1.14753	+	0.880530i	−0.153340	+	0.988174i	$0.549003\pi$
$948$	−32434.7	−	106451.i	−1.11121	−	3.64702i
$949$	14939.3	−	1966.80i	0.511012	−	0.0672760i
$950$	18159.4	+	4865.79i	0.620177	+	0.166176i
$951$	7886.20	−	34011.2i	0.268904	−	1.15972i
$952$	26604.1	−	67326.3i	0.905717	−	2.29208i
$953$	45486.2			1.54611			0.773054	−	0.634340i	$-0.218728\pi$
$953$	45486.2			1.54611			0.773054	+	0.634340i	$0.218728\pi$
$954$	−34460.7	−	30071.6i	−1.16950	−	1.02055i
$955$	−5445.56	+	13146.8i	−0.184518	+	0.445465i
$956$	−12478.8	−	7204.66i	−0.422170	−	0.243740i
$957$	11870.0	+	26112.1i	0.400942	+	0.882011i
$958$	2967.82	−	3867.73i	0.100090	−	0.130439i
$959$	8201.97	+	6293.59i	0.276179	+	0.211919i
$960$	268.734	+	7911.36i	0.00903476	+	0.265977i
$961$	40559.0	−	10867.8i	1.36145	−	0.364800i
$962$	54330.3	−	22504.3i	1.82087	−	0.754230i
$963$	−47467.0	−	31547.8i	−1.58837	−	1.05567i
$964$	−62443.6	−	25865.0i	−2.08628	−	0.864166i
$965$	19169.0	+	11067.2i	0.639454	+	0.369189i
$966$	46360.5	+	33135.2i	1.54412	+	1.10363i
$967$	−12309.6	−	3298.34i	−0.409358	−	0.109687i	0.0482626	−	0.998835i	$-0.484632\pi$
$967$	−12309.6	−	3298.34i	−0.409358	−	0.109687i	−0.457621	+	0.889148i	$0.651298\pi$
$968$	27433.9	+	47517.0i	0.910909	+	1.57774i
$969$	−15986.6	−	5697.60i	−0.529993	−	0.188889i
$970$	−4254.31	+	7368.69i	−0.140822	+	0.243912i
$971$	−30648.7	+	30648.7i	−1.01294	+	1.01294i	−0.0130229	+	0.999915i	$0.504145\pi$
$971$	−30648.7	+	30648.7i	−1.01294	+	1.01294i	−0.999915	+	0.0130229i	$0.995855\pi$
$972$	2739.01	+	70419.8i	0.0903846	+	2.32378i
$973$		−	27413.5i		−	0.903224i
$974$	−9894.51	+	7592.32i	−0.325504	+	0.249768i
$975$	7320.38	+	8897.56i	0.240451	+	0.292256i
$976$	83061.8	+	63735.5i	2.72412	+	2.09029i
$977$	−5042.21	+	18817.8i	−0.165112	+	0.616207i	0.832914	+	0.553403i	$0.186671\pi$
$977$	−5042.21	+	18817.8i	−0.165112	+	0.616207i	−0.998026	+	0.0628042i	$0.979996\pi$
$978$	−17348.3	+	10817.5i	−0.567215	+	0.353685i
$979$	−6016.71	+	45701.4i	−0.196420	+	1.49195i
$980$	659.677	+	1592.60i	0.0215027	+	0.0519120i
$981$	33173.4	−	6683.49i	1.07966	−	0.217520i
$982$			92147.5i			2.99445i
$983$	25984.6	+	33863.8i	0.843114	+	1.09877i	0.993909	+	0.110202i	$0.0351499\pi$
$983$	25984.6	+	33863.8i	0.843114	+	1.09877i	−0.150795	+	0.988565i	$0.548183\pi$
$984$	43034.8	−	1461.81i	1.39421	−	0.0473586i
$985$	−12752.0	−	22087.1i	−0.412499	−	0.714470i
$986$	−41037.5	−	4720.27i	−1.32546	−	0.152458i
$987$	15115.8	+	14122.6i	0.487478	+	0.455449i
$988$	6360.69	+	23738.4i	0.204818	+	0.764392i
$989$	−3929.92	+	9487.67i	−0.126354	+	0.305046i
$990$	−45912.7	+	3122.75i	−1.47394	+	0.100250i
$991$	−4313.42	−	1786.68i	−0.138265	−	0.0572710i	0.312478	−	0.949925i	$-0.398841\pi$
$991$	−4313.42	−	1786.68i	−0.138265	−	0.0572710i	−0.450743	+	0.892654i	$0.648841\pi$
$992$	66383.1	+	8739.51i	2.12466	+	0.279717i
$993$	1281.33	+	7701.94i	0.0409484	+	0.246136i
$994$	20731.3	−	77370.4i	0.661527	−	2.46885i
$995$	8177.93	−	30520.5i	0.260561	−	0.972426i
$996$	−35215.7	+	28973.4i	−1.12033	+	0.921743i
$997$	−24330.2	−	3203.13i	−0.772863	−	0.101749i	−0.266228	−	0.963910i	$-0.585777\pi$
$997$	−24330.2	−	3203.13i	−0.772863	−	0.101749i	−0.506635	+	0.862161i	$0.669111\pi$
$998$	22326.4	+	9247.92i	0.708148	+	0.293324i
$999$	43748.6	+	35634.2i	1.38553	+	1.12854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.r.a.25.2	✓	416
9.4	even	3	inner	153.4.r.a.76.51	yes	416
17.15	even	8	inner	153.4.r.a.151.51	yes	416
153.49	even	24	inner	153.4.r.a.49.2	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.r.a.25.2	✓	416	1.1	even	1	trivial
153.4.r.a.49.2	yes	416	153.49	even	24	inner
153.4.r.a.76.51	yes	416	9.4	even	3	inner
153.4.r.a.151.51	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+(-1.33497 - 4.98219i) q^{2} +(0.502950 - 5.17175i) q^{3} +(-16.1118 + 9.30216i) q^{4} +(0.892751 + 6.78112i) q^{5} +(-26.4381 + 4.39836i) q^{6} +(-2.46465 + 18.7209i) q^{7} +(38.6762 + 38.6762i) q^{8} +(-26.4941 - 5.20227i) q^{9} +(32.5930 - 13.5005i) q^{10} +(47.8996 + 6.30610i) q^{11} +(40.0051 + 88.0049i) q^{12} +(-24.5504 + 14.1742i) q^{13} +(96.5613 - 12.7125i) q^{14} +(35.5193 - 1.20652i) q^{15} +(66.6431 - 115.429i) q^{16} +(-60.1200 + 36.0359i) q^{17} +(9.45020 + 138.943i) q^{18} +(-32.9497 + 32.9497i) q^{19} +(-77.4629 - 100.952i) q^{20} +(95.5804 + 22.1623i) q^{21} +(-32.5265 - 247.063i) q^{22} +(-68.5469 + 89.3320i) q^{23} +(219.476 - 180.572i) q^{24} +(75.5542 - 20.2447i) q^{25} +(103.393 + 103.393i) q^{26} +(-40.2301 + 134.404i) q^{27} +(-134.435 - 324.555i) q^{28} +(-90.6468 + 69.5558i) q^{29} +(-53.4284 - 175.353i) q^{30} +(-265.627 + 34.9705i) q^{31} +(-241.395 - 64.6817i) q^{32} +(56.7047 - 244.553i) q^{33} +(259.796 + 251.422i) q^{34} -129.149 q^{35} +(475.260 - 162.634i) q^{36} +(153.908 - 371.568i) q^{37} +(208.148 + 120.174i) q^{38} +(60.9578 + 134.098i) q^{39} +(-227.740 + 296.796i) q^{40} +(120.198 + 92.2308i) q^{41} +(-17.1806 - 505.785i) q^{42} +(88.0942 - 23.6048i) q^{43} +(-830.409 + 343.967i) q^{44} +(11.6246 - 184.304i) q^{45} +(536.577 + 222.257i) q^{46} +(182.591 + 105.419i) q^{47} +(-563.454 - 402.717i) q^{48} +(-13.0855 - 3.50624i) q^{49} +(-201.726 - 349.399i) q^{50} +(156.132 + 329.050i) q^{51} +(263.701 - 456.744i) q^{52} +(-232.225 + 232.225i) q^{53} +(723.334 + 21.0074i) q^{54} +330.442i q^{55} +(-819.378 + 628.731i) q^{56} +(153.836 + 186.980i) q^{57} +(467.551 + 358.764i) q^{58} +(-50.3039 + 187.737i) q^{59} +(-561.057 + 349.845i) q^{60} +(-102.529 + 778.785i) q^{61} +(528.835 + 1276.72i) q^{62} +(162.690 - 483.172i) q^{63} +222.734i q^{64} +(-118.034 - 153.825i) q^{65} +(-1294.11 + 43.9585i) q^{66} +(68.0891 + 117.934i) q^{67} +(633.430 - 1139.85i) q^{68} +(427.528 + 399.437i) q^{69} +(172.410 + 643.444i) q^{70} +(314.729 - 759.822i) q^{71} +(-823.487 - 1225.90i) q^{72} +(-491.076 - 203.410i) q^{73} +(-2056.68 - 270.767i) q^{74} +(-66.7005 - 400.930i) q^{75} +(224.376 - 837.382i) q^{76} +(-236.112 + 881.181i) q^{77} +(586.722 - 482.719i) q^{78} +(-1141.30 - 150.255i) q^{79} +(842.235 + 348.865i) q^{80} +(674.873 + 275.659i) q^{81} +(299.051 - 721.972i) q^{82} +(122.093 + 455.657i) q^{83} +(-1746.13 + 532.029i) q^{84} +(-298.036 - 375.509i) q^{85} +(-235.207 - 407.390i) q^{86} +(314.134 + 503.786i) q^{87} +(1608.68 + 2096.47i) q^{88} +954.110i q^{89} +(-933.754 + 188.125i) q^{90} +(-204.845 - 494.540i) q^{91} +(273.434 - 2076.94i) q^{92} +(47.2615 + 1391.35i) q^{93} +(281.463 - 1050.43i) q^{94} +(-252.851 - 194.020i) q^{95} +(-455.928 + 1215.91i) q^{96} +(-191.345 + 146.824i) q^{97} +69.8749i q^{98} +(-1236.25 - 416.261i) 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

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